Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 7 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.64575 | −1.63043 | −0.815215 | − | 0.579159i | \(-0.803381\pi\) | ||||
−0.815215 | + | 0.579159i | \(0.803381\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.64575 | 1.15289 | ||||||||
\(11\) | 0.645751 | 0.194701 | 0.0973507 | − | 0.995250i | \(-0.468963\pi\) | ||||
0.0973507 | + | 0.995250i | \(0.468963\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.64575 | −0.941329 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.64575 | −1.61183 | −0.805916 | − | 0.592030i | \(-0.798327\pi\) | ||||
−0.805916 | + | 0.592030i | \(0.798327\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | −3.64575 | −0.815215 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.645751 | −0.137675 | ||||||||
\(23\) | −2.35425 | −0.490895 | −0.245447 | − | 0.969410i | \(-0.578935\pi\) | ||||
−0.245447 | + | 0.969410i | \(0.578935\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 8.29150 | 1.65830 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.29150 | 0.796912 | 0.398456 | − | 0.917187i | \(-0.369546\pi\) | ||||
0.398456 | + | 0.917187i | \(0.369546\pi\) | |||||||
\(30\) | 3.64575 | 0.665620 | ||||||||
\(31\) | 3.29150 | 0.591171 | 0.295586 | − | 0.955316i | \(-0.404485\pi\) | ||||
0.295586 | + | 0.955316i | \(0.404485\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.645751 | 0.112411 | ||||||||
\(34\) | 6.64575 | 1.13974 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.64575 | 0.928156 | 0.464078 | − | 0.885794i | \(-0.346386\pi\) | ||||
0.464078 | + | 0.885794i | \(0.346386\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 3.64575 | 0.576444 | ||||||||
\(41\) | −2.35425 | −0.367672 | −0.183836 | − | 0.982957i | \(-0.558852\pi\) | ||||
−0.183836 | + | 0.982957i | \(0.558852\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.29150 | −0.806947 | −0.403473 | − | 0.914991i | \(-0.632197\pi\) | ||||
−0.403473 | + | 0.914991i | \(0.632197\pi\) | |||||||
\(44\) | 0.645751 | 0.0973507 | ||||||||
\(45\) | −3.64575 | −0.543477 | ||||||||
\(46\) | 2.35425 | 0.347115 | ||||||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.29150 | −1.17260 | ||||||||
\(51\) | −6.64575 | −0.930591 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.35425 | −0.317447 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | −4.29150 | −0.563502 | ||||||||
\(59\) | −7.93725 | −1.03334 | −0.516671 | − | 0.856184i | \(-0.672829\pi\) | ||||
−0.516671 | + | 0.856184i | \(0.672829\pi\) | |||||||
\(60\) | −3.64575 | −0.470664 | ||||||||
\(61\) | −11.9373 | −1.52841 | −0.764204 | − | 0.644974i | \(-0.776868\pi\) | ||||
−0.764204 | + | 0.644974i | \(0.776868\pi\) | |||||||
\(62\) | −3.29150 | −0.418021 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.64575 | −0.452200 | ||||||||
\(66\) | −0.645751 | −0.0794865 | ||||||||
\(67\) | 7.58301 | 0.926412 | 0.463206 | − | 0.886251i | \(-0.346699\pi\) | ||||
0.463206 | + | 0.886251i | \(0.346699\pi\) | |||||||
\(68\) | −6.64575 | −0.805916 | ||||||||
\(69\) | −2.35425 | −0.283418 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2915 | 1.93345 | 0.966723 | − | 0.255826i | \(-0.0823474\pi\) | ||||
0.966723 | + | 0.255826i | \(0.0823474\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −13.6458 | −1.59711 | −0.798557 | − | 0.601919i | \(-0.794403\pi\) | ||||
−0.798557 | + | 0.601919i | \(0.794403\pi\) | |||||||
\(74\) | −5.64575 | −0.656305 | ||||||||
\(75\) | 8.29150 | 0.957420 | ||||||||
\(76\) | 5.00000 | 0.573539 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | −3.64575 | −0.407607 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.35425 | 0.259983 | ||||||||
\(83\) | −13.2915 | −1.45893 | −0.729466 | − | 0.684017i | \(-0.760231\pi\) | ||||
−0.729466 | + | 0.684017i | \(0.760231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.2288 | 2.62798 | ||||||||
\(86\) | 5.29150 | 0.570597 | ||||||||
\(87\) | 4.29150 | 0.460097 | ||||||||
\(88\) | −0.645751 | −0.0688373 | ||||||||
\(89\) | 16.9373 | 1.79535 | 0.897673 | − | 0.440663i | \(-0.145257\pi\) | ||||
0.897673 | + | 0.440663i | \(0.145257\pi\) | |||||||
\(90\) | 3.64575 | 0.384296 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.35425 | −0.245447 | ||||||||
\(93\) | 3.29150 | 0.341313 | ||||||||
\(94\) | −3.00000 | −0.309426 | ||||||||
\(95\) | −18.2288 | −1.87023 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 0.937254 | 0.0951637 | 0.0475819 | − | 0.998867i | \(-0.484849\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484849\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.645751 | 0.0649004 | ||||||||
\(100\) | 8.29150 | 0.829150 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 6.64575 | 0.658027 | ||||||||
\(103\) | −5.29150 | −0.521387 | −0.260694 | − | 0.965422i | \(-0.583951\pi\) | ||||
−0.260694 | + | 0.965422i | \(0.583951\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 2.35425 | 0.224469 | ||||||||
\(111\) | 5.64575 | 0.535871 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.2288 | 1.43260 | 0.716300 | − | 0.697792i | \(-0.245834\pi\) | ||||
0.716300 | + | 0.697792i | \(0.245834\pi\) | |||||||
\(114\) | −5.00000 | −0.468293 | ||||||||
\(115\) | 8.58301 | 0.800369 | ||||||||
\(116\) | 4.29150 | 0.398456 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 7.93725 | 0.730683 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.64575 | 0.332810 | ||||||||
\(121\) | −10.5830 | −0.962091 | ||||||||
\(122\) | 11.9373 | 1.08075 | ||||||||
\(123\) | −2.35425 | −0.212275 | ||||||||
\(124\) | 3.29150 | 0.295586 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2288 | −0.907655 | −0.453828 | − | 0.891089i | \(-0.649942\pi\) | ||||
−0.453828 | + | 0.891089i | \(0.649942\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.29150 | −0.465891 | ||||||||
\(130\) | 3.64575 | 0.319754 | ||||||||
\(131\) | 10.9373 | 0.955592 | 0.477796 | − | 0.878471i | \(-0.341436\pi\) | ||||
0.477796 | + | 0.878471i | \(0.341436\pi\) | |||||||
\(132\) | 0.645751 | 0.0562054 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.58301 | −0.655072 | ||||||||
\(135\) | −3.64575 | −0.313776 | ||||||||
\(136\) | 6.64575 | 0.569868 | ||||||||
\(137\) | −19.5203 | −1.66773 | −0.833864 | − | 0.551970i | \(-0.813876\pi\) | ||||
−0.833864 | + | 0.551970i | \(0.813876\pi\) | |||||||
\(138\) | 2.35425 | 0.200407 | ||||||||
\(139\) | −22.2288 | −1.88542 | −0.942709 | − | 0.333615i | \(-0.891731\pi\) | ||||
−0.942709 | + | 0.333615i | \(0.891731\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | −16.2915 | −1.36715 | ||||||||
\(143\) | 0.645751 | 0.0540004 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −15.6458 | −1.29931 | ||||||||
\(146\) | 13.6458 | 1.12933 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.64575 | 0.464078 | ||||||||
\(149\) | −7.06275 | −0.578603 | −0.289301 | − | 0.957238i | \(-0.593423\pi\) | ||||
−0.289301 | + | 0.957238i | \(0.593423\pi\) | |||||||
\(150\) | −8.29150 | −0.676998 | ||||||||
\(151\) | 6.06275 | 0.493379 | 0.246690 | − | 0.969095i | \(-0.420657\pi\) | ||||
0.246690 | + | 0.969095i | \(0.420657\pi\) | |||||||
\(152\) | −5.00000 | −0.405554 | ||||||||
\(153\) | −6.64575 | −0.537277 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | −0.963863 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 2.64575 | 0.211154 | 0.105577 | − | 0.994411i | \(-0.466331\pi\) | ||||
0.105577 | + | 0.994411i | \(0.466331\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | 3.64575 | 0.288222 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 2.41699 | 0.189314 | 0.0946568 | − | 0.995510i | \(-0.469825\pi\) | ||||
0.0946568 | + | 0.995510i | \(0.469825\pi\) | |||||||
\(164\) | −2.35425 | −0.183836 | ||||||||
\(165\) | −2.35425 | −0.183278 | ||||||||
\(166\) | 13.2915 | 1.03162 | ||||||||
\(167\) | −6.87451 | −0.531965 | −0.265983 | − | 0.963978i | \(-0.585696\pi\) | ||||
−0.265983 | + | 0.963978i | \(0.585696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −24.2288 | −1.85826 | ||||||||
\(171\) | 5.00000 | 0.382360 | ||||||||
\(172\) | −5.29150 | −0.403473 | ||||||||
\(173\) | −22.2915 | −1.69479 | −0.847396 | − | 0.530962i | \(-0.821831\pi\) | ||||
−0.847396 | + | 0.530962i | \(0.821831\pi\) | |||||||
\(174\) | −4.29150 | −0.325338 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.645751 | 0.0486753 | ||||||||
\(177\) | −7.93725 | −0.596601 | ||||||||
\(178\) | −16.9373 | −1.26950 | ||||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | −3.64575 | −0.271738 | ||||||||
\(181\) | 14.6458 | 1.08861 | 0.544305 | − | 0.838887i | \(-0.316793\pi\) | ||||
0.544305 | + | 0.838887i | \(0.316793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.9373 | −0.882427 | ||||||||
\(184\) | 2.35425 | 0.173558 | ||||||||
\(185\) | −20.5830 | −1.51329 | ||||||||
\(186\) | −3.29150 | −0.241345 | ||||||||
\(187\) | −4.29150 | −0.313826 | ||||||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.2288 | 1.32245 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 18.9373 | 1.36313 | 0.681567 | − | 0.731756i | \(-0.261299\pi\) | ||||
0.681567 | + | 0.731756i | \(0.261299\pi\) | |||||||
\(194\) | −0.937254 | −0.0672909 | ||||||||
\(195\) | −3.64575 | −0.261078 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.8118 | −1.91026 | −0.955129 | − | 0.296189i | \(-0.904284\pi\) | ||||
−0.955129 | + | 0.296189i | \(0.904284\pi\) | |||||||
\(198\) | −0.645751 | −0.0458915 | ||||||||
\(199\) | −22.2288 | −1.57575 | −0.787877 | − | 0.615832i | \(-0.788820\pi\) | ||||
−0.787877 | + | 0.615832i | \(0.788820\pi\) | |||||||
\(200\) | −8.29150 | −0.586298 | ||||||||
\(201\) | 7.58301 | 0.534864 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.64575 | −0.465296 | ||||||||
\(205\) | 8.58301 | 0.599463 | ||||||||
\(206\) | 5.29150 | 0.368676 | ||||||||
\(207\) | −2.35425 | −0.163632 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 3.22876 | 0.223338 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.35425 | −0.437445 | −0.218722 | − | 0.975787i | \(-0.570189\pi\) | ||||
−0.218722 | + | 0.975787i | \(0.570189\pi\) | |||||||
\(212\) | −3.00000 | −0.206041 | ||||||||
\(213\) | 16.2915 | 1.11628 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 19.2915 | 1.31567 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.00000 | 0.270914 | ||||||||
\(219\) | −13.6458 | −0.922094 | ||||||||
\(220\) | −2.35425 | −0.158723 | ||||||||
\(221\) | −6.64575 | −0.447042 | ||||||||
\(222\) | −5.64575 | −0.378918 | ||||||||
\(223\) | −20.5203 | −1.37414 | −0.687069 | − | 0.726592i | \(-0.741103\pi\) | ||||
−0.687069 | + | 0.726592i | \(0.741103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.29150 | 0.552767 | ||||||||
\(226\) | −15.2288 | −1.01300 | ||||||||
\(227\) | −4.70850 | −0.312514 | −0.156257 | − | 0.987716i | \(-0.549943\pi\) | ||||
−0.156257 | + | 0.987716i | \(0.549943\pi\) | |||||||
\(228\) | 5.00000 | 0.331133 | ||||||||
\(229\) | 26.4575 | 1.74836 | 0.874181 | − | 0.485601i | \(-0.161399\pi\) | ||||
0.874181 | + | 0.485601i | \(0.161399\pi\) | |||||||
\(230\) | −8.58301 | −0.565947 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.29150 | −0.281751 | ||||||||
\(233\) | 0.645751 | 0.0423046 | 0.0211523 | − | 0.999776i | \(-0.493267\pi\) | ||||
0.0211523 | + | 0.999776i | \(0.493267\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −10.9373 | −0.713468 | ||||||||
\(236\) | −7.93725 | −0.516671 | ||||||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | 0.194054 | 0.0970269 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970269 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(240\) | −3.64575 | −0.235332 | ||||||||
\(241\) | −13.8745 | −0.893736 | −0.446868 | − | 0.894600i | \(-0.647461\pi\) | ||||
−0.446868 | + | 0.894600i | \(0.647461\pi\) | |||||||
\(242\) | 10.5830 | 0.680301 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.9373 | −0.764204 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.35425 | 0.150101 | ||||||||
\(247\) | 5.00000 | 0.318142 | ||||||||
\(248\) | −3.29150 | −0.209011 | ||||||||
\(249\) | −13.2915 | −0.842315 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | −13.2915 | −0.838952 | −0.419476 | − | 0.907766i | \(-0.637786\pi\) | ||||
−0.419476 | + | 0.907766i | \(0.637786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.52026 | −0.0955779 | ||||||||
\(254\) | 10.2288 | 0.641809 | ||||||||
\(255\) | 24.2288 | 1.51726 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.8745 | −0.990225 | −0.495112 | − | 0.868829i | \(-0.664873\pi\) | ||||
−0.495112 | + | 0.868829i | \(0.664873\pi\) | |||||||
\(258\) | 5.29150 | 0.329435 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.64575 | −0.226100 | ||||||||
\(261\) | 4.29150 | 0.265637 | ||||||||
\(262\) | −10.9373 | −0.675706 | ||||||||
\(263\) | −3.64575 | −0.224807 | −0.112403 | − | 0.993663i | \(-0.535855\pi\) | ||||
−0.112403 | + | 0.993663i | \(0.535855\pi\) | |||||||
\(264\) | −0.645751 | −0.0397432 | ||||||||
\(265\) | 10.9373 | 0.671870 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9373 | 1.03654 | ||||||||
\(268\) | 7.58301 | 0.463206 | ||||||||
\(269\) | 6.87451 | 0.419146 | 0.209573 | − | 0.977793i | \(-0.432793\pi\) | ||||
0.209573 | + | 0.977793i | \(0.432793\pi\) | |||||||
\(270\) | 3.64575 | 0.221873 | ||||||||
\(271\) | −22.6458 | −1.37563 | −0.687816 | − | 0.725885i | \(-0.741430\pi\) | ||||
−0.687816 | + | 0.725885i | \(0.741430\pi\) | |||||||
\(272\) | −6.64575 | −0.402958 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.5203 | 1.17926 | ||||||||
\(275\) | 5.35425 | 0.322873 | ||||||||
\(276\) | −2.35425 | −0.141709 | ||||||||
\(277\) | 18.5203 | 1.11277 | 0.556387 | − | 0.830923i | \(-0.312187\pi\) | ||||
0.556387 | + | 0.830923i | \(0.312187\pi\) | |||||||
\(278\) | 22.2288 | 1.33319 | ||||||||
\(279\) | 3.29150 | 0.197057 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.58301 | −0.154089 | −0.0770446 | − | 0.997028i | \(-0.524548\pi\) | ||||
−0.0770446 | + | 0.997028i | \(0.524548\pi\) | |||||||
\(282\) | −3.00000 | −0.178647 | ||||||||
\(283\) | −11.0627 | −0.657612 | −0.328806 | − | 0.944397i | \(-0.606646\pi\) | ||||
−0.328806 | + | 0.944397i | \(0.606646\pi\) | |||||||
\(284\) | 16.2915 | 0.966723 | ||||||||
\(285\) | −18.2288 | −1.07978 | ||||||||
\(286\) | −0.645751 | −0.0381841 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 27.1660 | 1.59800 | ||||||||
\(290\) | 15.6458 | 0.918750 | ||||||||
\(291\) | 0.937254 | 0.0549428 | ||||||||
\(292\) | −13.6458 | −0.798557 | ||||||||
\(293\) | 7.52026 | 0.439338 | 0.219669 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219669 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.9373 | 1.68479 | ||||||||
\(296\) | −5.64575 | −0.328153 | ||||||||
\(297\) | 0.645751 | 0.0374703 | ||||||||
\(298\) | 7.06275 | 0.409134 | ||||||||
\(299\) | −2.35425 | −0.136150 | ||||||||
\(300\) | 8.29150 | 0.478710 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.06275 | −0.348872 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | 43.5203 | 2.49196 | ||||||||
\(306\) | 6.64575 | 0.379912 | ||||||||
\(307\) | −9.58301 | −0.546931 | −0.273465 | − | 0.961882i | \(-0.588170\pi\) | ||||
−0.273465 | + | 0.961882i | \(0.588170\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.29150 | −0.301023 | ||||||||
\(310\) | 12.0000 | 0.681554 | ||||||||
\(311\) | −1.06275 | −0.0602628 | −0.0301314 | − | 0.999546i | \(-0.509593\pi\) | ||||
−0.0301314 | + | 0.999546i | \(0.509593\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 13.1660 | 0.744187 | 0.372093 | − | 0.928195i | \(-0.378640\pi\) | ||||
0.372093 | + | 0.928195i | \(0.378640\pi\) | |||||||
\(314\) | −2.64575 | −0.149308 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −13.2915 | −0.746525 | −0.373263 | − | 0.927726i | \(-0.621761\pi\) | ||||
−0.373263 | + | 0.927726i | \(0.621761\pi\) | |||||||
\(318\) | 3.00000 | 0.168232 | ||||||||
\(319\) | 2.77124 | 0.155160 | ||||||||
\(320\) | −3.64575 | −0.203804 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.2288 | −1.84890 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 8.29150 | 0.459930 | ||||||||
\(326\) | −2.41699 | −0.133865 | ||||||||
\(327\) | −4.00000 | −0.221201 | ||||||||
\(328\) | 2.35425 | 0.129992 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.35425 | 0.129597 | ||||||||
\(331\) | 11.4170 | 0.627535 | 0.313767 | − | 0.949500i | \(-0.398409\pi\) | ||||
0.313767 | + | 0.949500i | \(0.398409\pi\) | |||||||
\(332\) | −13.2915 | −0.729466 | ||||||||
\(333\) | 5.64575 | 0.309385 | ||||||||
\(334\) | 6.87451 | 0.376156 | ||||||||
\(335\) | −27.6458 | −1.51045 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5830 | −0.848860 | −0.424430 | − | 0.905461i | \(-0.639526\pi\) | ||||
−0.424430 | + | 0.905461i | \(0.639526\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 15.2288 | 0.827113 | ||||||||
\(340\) | 24.2288 | 1.31399 | ||||||||
\(341\) | 2.12549 | 0.115102 | ||||||||
\(342\) | −5.00000 | −0.270369 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.29150 | 0.285299 | ||||||||
\(345\) | 8.58301 | 0.462093 | ||||||||
\(346\) | 22.2915 | 1.19840 | ||||||||
\(347\) | 0.228757 | 0.0122803 | 0.00614015 | − | 0.999981i | \(-0.498046\pi\) | ||||
0.00614015 | + | 0.999981i | \(0.498046\pi\) | |||||||
\(348\) | 4.29150 | 0.230049 | ||||||||
\(349\) | 18.9373 | 1.01369 | 0.506844 | − | 0.862038i | \(-0.330812\pi\) | ||||
0.506844 | + | 0.862038i | \(0.330812\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −0.645751 | −0.0344187 | ||||||||
\(353\) | −20.5830 | −1.09552 | −0.547761 | − | 0.836635i | \(-0.684520\pi\) | ||||
−0.547761 | + | 0.836635i | \(0.684520\pi\) | |||||||
\(354\) | 7.93725 | 0.421860 | ||||||||
\(355\) | −59.3948 | −3.15235 | ||||||||
\(356\) | 16.9373 | 0.897673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | 0.317110 | ||||||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | 3.64575 | 0.192148 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | −14.6458 | −0.769764 | ||||||||
\(363\) | −10.5830 | −0.555464 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 49.7490 | 2.60398 | ||||||||
\(366\) | 11.9373 | 0.623970 | ||||||||
\(367\) | −0.583005 | −0.0304326 | −0.0152163 | − | 0.999884i | \(-0.504844\pi\) | ||||
−0.0152163 | + | 0.999884i | \(0.504844\pi\) | |||||||
\(368\) | −2.35425 | −0.122724 | ||||||||
\(369\) | −2.35425 | −0.122557 | ||||||||
\(370\) | 20.5830 | 1.07006 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.29150 | 0.170656 | ||||||||
\(373\) | 14.6458 | 0.758328 | 0.379164 | − | 0.925329i | \(-0.376212\pi\) | ||||
0.379164 | + | 0.925329i | \(0.376212\pi\) | |||||||
\(374\) | 4.29150 | 0.221908 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | 4.29150 | 0.221024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.16601 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(380\) | −18.2288 | −0.935115 | ||||||||
\(381\) | −10.2288 | −0.524035 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.7490 | 1.31571 | 0.657857 | − | 0.753143i | \(-0.271463\pi\) | ||||
0.657857 | + | 0.753143i | \(0.271463\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.9373 | −0.963881 | ||||||||
\(387\) | −5.29150 | −0.268982 | ||||||||
\(388\) | 0.937254 | 0.0475819 | ||||||||
\(389\) | 7.70850 | 0.390836 | 0.195418 | − | 0.980720i | \(-0.437394\pi\) | ||||
0.195418 | + | 0.980720i | \(0.437394\pi\) | |||||||
\(390\) | 3.64575 | 0.184610 | ||||||||
\(391\) | 15.6458 | 0.791240 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.9373 | 0.551711 | ||||||||
\(394\) | 26.8118 | 1.35076 | ||||||||
\(395\) | 36.4575 | 1.83438 | ||||||||
\(396\) | 0.645751 | 0.0324502 | ||||||||
\(397\) | −14.9373 | −0.749679 | −0.374840 | − | 0.927090i | \(-0.622302\pi\) | ||||
−0.374840 | + | 0.927090i | \(0.622302\pi\) | |||||||
\(398\) | 22.2288 | 1.11423 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.29150 | 0.414575 | ||||||||
\(401\) | −18.2288 | −0.910301 | −0.455150 | − | 0.890415i | \(-0.650414\pi\) | ||||
−0.455150 | + | 0.890415i | \(0.650414\pi\) | |||||||
\(402\) | −7.58301 | −0.378206 | ||||||||
\(403\) | 3.29150 | 0.163961 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.64575 | −0.181159 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.64575 | 0.180713 | ||||||||
\(408\) | 6.64575 | 0.329014 | ||||||||
\(409\) | −26.9373 | −1.33196 | −0.665981 | − | 0.745969i | \(-0.731987\pi\) | ||||
−0.665981 | + | 0.745969i | \(0.731987\pi\) | |||||||
\(410\) | −8.58301 | −0.423884 | ||||||||
\(411\) | −19.5203 | −0.962863 | ||||||||
\(412\) | −5.29150 | −0.260694 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.35425 | 0.115705 | ||||||||
\(415\) | 48.4575 | 2.37869 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −22.2288 | −1.08855 | ||||||||
\(418\) | −3.22876 | −0.157924 | ||||||||
\(419\) | 30.4575 | 1.48795 | 0.743973 | − | 0.668209i | \(-0.232939\pi\) | ||||
0.743973 | + | 0.668209i | \(0.232939\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.3542 | −1.18695 | −0.593477 | − | 0.804851i | \(-0.702245\pi\) | ||||
−0.593477 | + | 0.804851i | \(0.702245\pi\) | |||||||
\(422\) | 6.35425 | 0.309320 | ||||||||
\(423\) | 3.00000 | 0.145865 | ||||||||
\(424\) | 3.00000 | 0.145693 | ||||||||
\(425\) | −55.1033 | −2.67290 | ||||||||
\(426\) | −16.2915 | −0.789326 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0.645751 | 0.0311772 | ||||||||
\(430\) | −19.2915 | −0.930319 | ||||||||
\(431\) | 20.5830 | 0.991448 | 0.495724 | − | 0.868480i | \(-0.334903\pi\) | ||||
0.495724 | + | 0.868480i | \(0.334903\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −33.5830 | −1.61390 | −0.806948 | − | 0.590622i | \(-0.798882\pi\) | ||||
−0.806948 | + | 0.590622i | \(0.798882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.6458 | −0.750156 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | −11.7712 | −0.563095 | ||||||||
\(438\) | 13.6458 | 0.652019 | ||||||||
\(439\) | 23.6458 | 1.12855 | 0.564275 | − | 0.825587i | \(-0.309156\pi\) | ||||
0.564275 | + | 0.825587i | \(0.309156\pi\) | |||||||
\(440\) | 2.35425 | 0.112234 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.64575 | 0.316106 | ||||||||
\(443\) | 19.0627 | 0.905698 | 0.452849 | − | 0.891587i | \(-0.350408\pi\) | ||||
0.452849 | + | 0.891587i | \(0.350408\pi\) | |||||||
\(444\) | 5.64575 | 0.267935 | ||||||||
\(445\) | −61.7490 | −2.92718 | ||||||||
\(446\) | 20.5203 | 0.971662 | ||||||||
\(447\) | −7.06275 | −0.334056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | −8.29150 | −0.390865 | ||||||||
\(451\) | −1.52026 | −0.0715862 | ||||||||
\(452\) | 15.2288 | 0.716300 | ||||||||
\(453\) | 6.06275 | 0.284853 | ||||||||
\(454\) | 4.70850 | 0.220981 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.00000 | −0.234146 | ||||||||
\(457\) | 32.2288 | 1.50760 | 0.753799 | − | 0.657105i | \(-0.228219\pi\) | ||||
0.753799 | + | 0.657105i | \(0.228219\pi\) | |||||||
\(458\) | −26.4575 | −1.23628 | ||||||||
\(459\) | −6.64575 | −0.310197 | ||||||||
\(460\) | 8.58301 | 0.400185 | ||||||||
\(461\) | −36.4575 | −1.69800 | −0.848998 | − | 0.528396i | \(-0.822794\pi\) | ||||
−0.848998 | + | 0.528396i | \(0.822794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.1660 | 1.16956 | 0.584782 | − | 0.811191i | \(-0.301180\pi\) | ||||
0.584782 | + | 0.811191i | \(0.301180\pi\) | |||||||
\(464\) | 4.29150 | 0.199228 | ||||||||
\(465\) | −12.0000 | −0.556487 | ||||||||
\(466\) | −0.645751 | −0.0299139 | ||||||||
\(467\) | −37.5203 | −1.73623 | −0.868115 | − | 0.496363i | \(-0.834669\pi\) | ||||
−0.868115 | + | 0.496363i | \(0.834669\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.9373 | 0.504498 | ||||||||
\(471\) | 2.64575 | 0.121910 | ||||||||
\(472\) | 7.93725 | 0.365342 | ||||||||
\(473\) | −3.41699 | −0.157114 | ||||||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | 41.4575 | 1.90220 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00000 | −0.137361 | ||||||||
\(478\) | −3.00000 | −0.137217 | ||||||||
\(479\) | −34.7490 | −1.58772 | −0.793862 | − | 0.608099i | \(-0.791933\pi\) | ||||
−0.793862 | + | 0.608099i | \(0.791933\pi\) | |||||||
\(480\) | 3.64575 | 0.166405 | ||||||||
\(481\) | 5.64575 | 0.257424 | ||||||||
\(482\) | 13.8745 | 0.631967 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.5830 | −0.481046 | ||||||||
\(485\) | −3.41699 | −0.155158 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −23.9373 | −1.08470 | −0.542350 | − | 0.840152i | \(-0.682465\pi\) | ||||
−0.542350 | + | 0.840152i | \(0.682465\pi\) | |||||||
\(488\) | 11.9373 | 0.540374 | ||||||||
\(489\) | 2.41699 | 0.109300 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.1660 | 0.503915 | 0.251957 | − | 0.967738i | \(-0.418926\pi\) | ||||
0.251957 | + | 0.967738i | \(0.418926\pi\) | |||||||
\(492\) | −2.35425 | −0.106138 | ||||||||
\(493\) | −28.5203 | −1.28449 | ||||||||
\(494\) | −5.00000 | −0.224961 | ||||||||
\(495\) | −2.35425 | −0.105816 | ||||||||
\(496\) | 3.29150 | 0.147793 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.2915 | 0.595606 | ||||||||
\(499\) | −29.2915 | −1.31127 | −0.655634 | − | 0.755079i | \(-0.727599\pi\) | ||||
−0.655634 | + | 0.755079i | \(0.727599\pi\) | |||||||
\(500\) | −12.0000 | −0.536656 | ||||||||
\(501\) | −6.87451 | −0.307130 | ||||||||
\(502\) | 13.2915 | 0.593229 | ||||||||
\(503\) | 36.4575 | 1.62556 | 0.812780 | − | 0.582571i | \(-0.197953\pi\) | ||||
0.812780 | + | 0.582571i | \(0.197953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.52026 | 0.0675838 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −10.2288 | −0.453828 | ||||||||
\(509\) | 24.0000 | 1.06378 | 0.531891 | − | 0.846813i | \(-0.321482\pi\) | ||||
0.531891 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(510\) | −24.2288 | −1.07287 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.00000 | 0.220755 | ||||||||
\(514\) | 15.8745 | 0.700195 | ||||||||
\(515\) | 19.2915 | 0.850085 | ||||||||
\(516\) | −5.29150 | −0.232945 | ||||||||
\(517\) | 1.93725 | 0.0852003 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.2915 | −0.978488 | ||||||||
\(520\) | 3.64575 | 0.159877 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | −4.29150 | −0.187834 | ||||||||
\(523\) | −26.7085 | −1.16788 | −0.583941 | − | 0.811796i | \(-0.698490\pi\) | ||||
−0.583941 | + | 0.811796i | \(0.698490\pi\) | |||||||
\(524\) | 10.9373 | 0.477796 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.64575 | 0.158962 | ||||||||
\(527\) | −21.8745 | −0.952869 | ||||||||
\(528\) | 0.645751 | 0.0281027 | ||||||||
\(529\) | −17.4575 | −0.759022 | ||||||||
\(530\) | −10.9373 | −0.475084 | ||||||||
\(531\) | −7.93725 | −0.344447 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.35425 | −0.101974 | ||||||||
\(534\) | −16.9373 | −0.732947 | ||||||||
\(535\) | 43.7490 | 1.89143 | ||||||||
\(536\) | −7.58301 | −0.327536 | ||||||||
\(537\) | −6.00000 | −0.258919 | ||||||||
\(538\) | −6.87451 | −0.296381 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.64575 | −0.156888 | ||||||||
\(541\) | 41.6458 | 1.79049 | 0.895245 | − | 0.445574i | \(-0.147000\pi\) | ||||
0.895245 | + | 0.445574i | \(0.147000\pi\) | |||||||
\(542\) | 22.6458 | 0.972718 | ||||||||
\(543\) | 14.6458 | 0.628509 | ||||||||
\(544\) | 6.64575 | 0.284934 | ||||||||
\(545\) | 14.5830 | 0.624667 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.9373 | −0.895212 | −0.447606 | − | 0.894231i | \(-0.647723\pi\) | ||||
−0.447606 | + | 0.894231i | \(0.647723\pi\) | |||||||
\(548\) | −19.5203 | −0.833864 | ||||||||
\(549\) | −11.9373 | −0.509470 | ||||||||
\(550\) | −5.35425 | −0.228306 | ||||||||
\(551\) | 21.4575 | 0.914121 | ||||||||
\(552\) | 2.35425 | 0.100203 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.5203 | −0.786850 | ||||||||
\(555\) | −20.5830 | −0.873700 | ||||||||
\(556\) | −22.2288 | −0.942709 | ||||||||
\(557\) | 11.1660 | 0.473119 | 0.236560 | − | 0.971617i | \(-0.423980\pi\) | ||||
0.236560 | + | 0.971617i | \(0.423980\pi\) | |||||||
\(558\) | −3.29150 | −0.139340 | ||||||||
\(559\) | −5.29150 | −0.223807 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.29150 | −0.181187 | ||||||||
\(562\) | 2.58301 | 0.108958 | ||||||||
\(563\) | −27.0405 | −1.13962 | −0.569811 | − | 0.821776i | \(-0.692984\pi\) | ||||
−0.569811 | + | 0.821776i | \(0.692984\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | −55.5203 | −2.33575 | ||||||||
\(566\) | 11.0627 | 0.465002 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.2915 | −0.683576 | ||||||||
\(569\) | −33.2288 | −1.39302 | −0.696511 | − | 0.717546i | \(-0.745265\pi\) | ||||
−0.696511 | + | 0.717546i | \(0.745265\pi\) | |||||||
\(570\) | 18.2288 | 0.763519 | ||||||||
\(571\) | −16.0000 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | 0.645751 | 0.0270002 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.5203 | −0.814051 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −12.5830 | −0.523837 | −0.261919 | − | 0.965090i | \(-0.584355\pi\) | ||||
−0.261919 | + | 0.965090i | \(0.584355\pi\) | |||||||
\(578\) | −27.1660 | −1.12996 | ||||||||
\(579\) | 18.9373 | 0.787005 | ||||||||
\(580\) | −15.6458 | −0.649654 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.937254 | −0.0388504 | ||||||||
\(583\) | −1.93725 | −0.0802329 | ||||||||
\(584\) | 13.6458 | 0.564665 | ||||||||
\(585\) | −3.64575 | −0.150733 | ||||||||
\(586\) | −7.52026 | −0.310659 | ||||||||
\(587\) | 31.9373 | 1.31819 | 0.659096 | − | 0.752059i | \(-0.270939\pi\) | ||||
0.659096 | + | 0.752059i | \(0.270939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.4575 | 0.678120 | ||||||||
\(590\) | −28.9373 | −1.19133 | ||||||||
\(591\) | −26.8118 | −1.10289 | ||||||||
\(592\) | 5.64575 | 0.232039 | ||||||||
\(593\) | 43.5203 | 1.78716 | 0.893581 | − | 0.448901i | \(-0.148184\pi\) | ||||
0.893581 | + | 0.448901i | \(0.148184\pi\) | |||||||
\(594\) | −0.645751 | −0.0264955 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.06275 | −0.289301 | ||||||||
\(597\) | −22.2288 | −0.909762 | ||||||||
\(598\) | 2.35425 | 0.0962724 | ||||||||
\(599\) | −32.8118 | −1.34065 | −0.670326 | − | 0.742067i | \(-0.733846\pi\) | ||||
−0.670326 | + | 0.742067i | \(0.733846\pi\) | |||||||
\(600\) | −8.29150 | −0.338499 | ||||||||
\(601\) | 14.8745 | 0.606744 | 0.303372 | − | 0.952872i | \(-0.401888\pi\) | ||||
0.303372 | + | 0.952872i | \(0.401888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.58301 | 0.308804 | ||||||||
\(604\) | 6.06275 | 0.246690 | ||||||||
\(605\) | 38.5830 | 1.56862 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.8118 | 0.682368 | 0.341184 | − | 0.939996i | \(-0.389172\pi\) | ||||
0.341184 | + | 0.939996i | \(0.389172\pi\) | |||||||
\(608\) | −5.00000 | −0.202777 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −43.5203 | −1.76208 | ||||||||
\(611\) | 3.00000 | 0.121367 | ||||||||
\(612\) | −6.64575 | −0.268639 | ||||||||
\(613\) | 41.8745 | 1.69130 | 0.845648 | − | 0.533741i | \(-0.179214\pi\) | ||||
0.845648 | + | 0.533741i | \(0.179214\pi\) | |||||||
\(614\) | 9.58301 | 0.386739 | ||||||||
\(615\) | 8.58301 | 0.346100 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.7085 | −0.431108 | −0.215554 | − | 0.976492i | \(-0.569156\pi\) | ||||
−0.215554 | + | 0.976492i | \(0.569156\pi\) | |||||||
\(618\) | 5.29150 | 0.212855 | ||||||||
\(619\) | −41.7490 | −1.67803 | −0.839017 | − | 0.544105i | \(-0.816869\pi\) | ||||
−0.839017 | + | 0.544105i | \(0.816869\pi\) | |||||||
\(620\) | −12.0000 | −0.481932 | ||||||||
\(621\) | −2.35425 | −0.0944727 | ||||||||
\(622\) | 1.06275 | 0.0426122 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 2.29150 | 0.0916601 | ||||||||
\(626\) | −13.1660 | −0.526220 | ||||||||
\(627\) | 3.22876 | 0.128944 | ||||||||
\(628\) | 2.64575 | 0.105577 | ||||||||
\(629\) | −37.5203 | −1.49603 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.4575 | 0.575545 | 0.287772 | − | 0.957699i | \(-0.407085\pi\) | ||||
0.287772 | + | 0.957699i | \(0.407085\pi\) | |||||||
\(632\) | 10.0000 | 0.397779 | ||||||||
\(633\) | −6.35425 | −0.252559 | ||||||||
\(634\) | 13.2915 | 0.527873 | ||||||||
\(635\) | 37.2915 | 1.47987 | ||||||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.77124 | −0.109715 | ||||||||
\(639\) | 16.2915 | 0.644482 | ||||||||
\(640\) | 3.64575 | 0.144111 | ||||||||
\(641\) | −21.4170 | −0.845920 | −0.422960 | − | 0.906148i | \(-0.639009\pi\) | ||||
−0.422960 | + | 0.906148i | \(0.639009\pi\) | |||||||
\(642\) | 12.0000 | 0.473602 | ||||||||
\(643\) | −10.8745 | −0.428849 | −0.214424 | − | 0.976741i | \(-0.568788\pi\) | ||||
−0.214424 | + | 0.976741i | \(0.568788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.2915 | 0.759602 | ||||||||
\(646\) | 33.2288 | 1.30737 | ||||||||
\(647\) | 25.7490 | 1.01230 | 0.506149 | − | 0.862446i | \(-0.331069\pi\) | ||||
0.506149 | + | 0.862446i | \(0.331069\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −5.12549 | −0.201193 | ||||||||
\(650\) | −8.29150 | −0.325219 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.41699 | 0.0946568 | ||||||||
\(653\) | 12.0000 | 0.469596 | 0.234798 | − | 0.972044i | \(-0.424557\pi\) | ||||
0.234798 | + | 0.972044i | \(0.424557\pi\) | |||||||
\(654\) | 4.00000 | 0.156412 | ||||||||
\(655\) | −39.8745 | −1.55803 | ||||||||
\(656\) | −2.35425 | −0.0919180 | ||||||||
\(657\) | −13.6458 | −0.532371 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9373 | −0.659782 | −0.329891 | − | 0.944019i | \(-0.607012\pi\) | ||||
−0.329891 | + | 0.944019i | \(0.607012\pi\) | |||||||
\(660\) | −2.35425 | −0.0916390 | ||||||||
\(661\) | 15.5203 | 0.603668 | 0.301834 | − | 0.953360i | \(-0.402401\pi\) | ||||
0.301834 | + | 0.953360i | \(0.402401\pi\) | |||||||
\(662\) | −11.4170 | −0.443734 | ||||||||
\(663\) | −6.64575 | −0.258100 | ||||||||
\(664\) | 13.2915 | 0.515810 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.64575 | −0.218768 | ||||||||
\(667\) | −10.1033 | −0.391200 | ||||||||
\(668\) | −6.87451 | −0.265983 | ||||||||
\(669\) | −20.5203 | −0.793359 | ||||||||
\(670\) | 27.6458 | 1.06805 | ||||||||
\(671\) | −7.70850 | −0.297583 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.58301 | −0.253756 | −0.126878 | − | 0.991918i | \(-0.540496\pi\) | ||||
−0.126878 | + | 0.991918i | \(0.540496\pi\) | |||||||
\(674\) | 15.5830 | 0.600235 | ||||||||
\(675\) | 8.29150 | 0.319140 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 20.1660 | 0.775043 | 0.387521 | − | 0.921861i | \(-0.373331\pi\) | ||||
0.387521 | + | 0.921861i | \(0.373331\pi\) | |||||||
\(678\) | −15.2288 | −0.584857 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −24.2288 | −0.929130 | ||||||||
\(681\) | −4.70850 | −0.180430 | ||||||||
\(682\) | −2.12549 | −0.0813893 | ||||||||
\(683\) | 19.2915 | 0.738169 | 0.369084 | − | 0.929396i | \(-0.379671\pi\) | ||||
0.369084 | + | 0.929396i | \(0.379671\pi\) | |||||||
\(684\) | 5.00000 | 0.191180 | ||||||||
\(685\) | 71.1660 | 2.71911 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.4575 | 1.00942 | ||||||||
\(688\) | −5.29150 | −0.201737 | ||||||||
\(689\) | −3.00000 | −0.114291 | ||||||||
\(690\) | −8.58301 | −0.326749 | ||||||||
\(691\) | −40.0405 | −1.52321 | −0.761607 | − | 0.648040i | \(-0.775589\pi\) | ||||
−0.761607 | + | 0.648040i | \(0.775589\pi\) | |||||||
\(692\) | −22.2915 | −0.847396 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.228757 | −0.00868348 | ||||||||
\(695\) | 81.0405 | 3.07404 | ||||||||
\(696\) | −4.29150 | −0.162669 | ||||||||
\(697\) | 15.6458 | 0.592625 | ||||||||
\(698\) | −18.9373 | −0.716786 | ||||||||
\(699\) | 0.645751 | 0.0244246 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 28.2288 | 1.06467 | ||||||||
\(704\) | 0.645751 | 0.0243377 | ||||||||
\(705\) | −10.9373 | −0.411921 | ||||||||
\(706\) | 20.5830 | 0.774652 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.93725 | −0.298300 | ||||||||
\(709\) | 6.47974 | 0.243352 | 0.121676 | − | 0.992570i | \(-0.461173\pi\) | ||||
0.121676 | + | 0.992570i | \(0.461173\pi\) | |||||||
\(710\) | 59.3948 | 2.22905 | ||||||||
\(711\) | −10.0000 | −0.375029 | ||||||||
\(712\) | −16.9373 | −0.634750 | ||||||||
\(713\) | −7.74902 | −0.290203 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.35425 | −0.0880439 | ||||||||
\(716\) | −6.00000 | −0.224231 | ||||||||
\(717\) | 3.00000 | 0.112037 | ||||||||
\(718\) | 6.00000 | 0.223918 | ||||||||
\(719\) | 44.5830 | 1.66267 | 0.831333 | − | 0.555775i | \(-0.187578\pi\) | ||||
0.831333 | + | 0.555775i | \(0.187578\pi\) | |||||||
\(720\) | −3.64575 | −0.135869 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.00000 | −0.223297 | ||||||||
\(723\) | −13.8745 | −0.515998 | ||||||||
\(724\) | 14.6458 | 0.544305 | ||||||||
\(725\) | 35.5830 | 1.32152 | ||||||||
\(726\) | 10.5830 | 0.392772 | ||||||||
\(727\) | −16.4575 | −0.610375 | −0.305188 | − | 0.952292i | \(-0.598719\pi\) | ||||
−0.305188 | + | 0.952292i | \(0.598719\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −49.7490 | −1.84129 | ||||||||
\(731\) | 35.1660 | 1.30066 | ||||||||
\(732\) | −11.9373 | −0.441214 | ||||||||
\(733\) | 14.2288 | 0.525551 | 0.262776 | − | 0.964857i | \(-0.415362\pi\) | ||||
0.262776 | + | 0.964857i | \(0.415362\pi\) | |||||||
\(734\) | 0.583005 | 0.0215191 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.35425 | 0.0867788 | ||||||||
\(737\) | 4.89674 | 0.180374 | ||||||||
\(738\) | 2.35425 | 0.0866611 | ||||||||
\(739\) | −17.2915 | −0.636078 | −0.318039 | − | 0.948078i | \(-0.603024\pi\) | ||||
−0.318039 | + | 0.948078i | \(0.603024\pi\) | |||||||
\(740\) | −20.5830 | −0.756646 | ||||||||
\(741\) | 5.00000 | 0.183680 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.4575 | −1.88779 | −0.943897 | − | 0.330241i | \(-0.892870\pi\) | ||||
−0.943897 | + | 0.330241i | \(0.892870\pi\) | |||||||
\(744\) | −3.29150 | −0.120672 | ||||||||
\(745\) | 25.7490 | 0.943371 | ||||||||
\(746\) | −14.6458 | −0.536219 | ||||||||
\(747\) | −13.2915 | −0.486311 | ||||||||
\(748\) | −4.29150 | −0.156913 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.0000 | 0.438178 | ||||||||
\(751\) | −33.1660 | −1.21024 | −0.605122 | − | 0.796132i | \(-0.706876\pi\) | ||||
−0.605122 | + | 0.796132i | \(0.706876\pi\) | |||||||
\(752\) | 3.00000 | 0.109399 | ||||||||
\(753\) | −13.2915 | −0.484369 | ||||||||
\(754\) | −4.29150 | −0.156287 | ||||||||
\(755\) | −22.1033 | −0.804420 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.6458 | 0.968456 | 0.484228 | − | 0.874942i | \(-0.339100\pi\) | ||||
0.484228 | + | 0.874942i | \(0.339100\pi\) | |||||||
\(758\) | 9.16601 | 0.332924 | ||||||||
\(759\) | −1.52026 | −0.0551819 | ||||||||
\(760\) | 18.2288 | 0.661226 | ||||||||
\(761\) | 7.29150 | 0.264317 | 0.132158 | − | 0.991229i | \(-0.457809\pi\) | ||||
0.132158 | + | 0.991229i | \(0.457809\pi\) | |||||||
\(762\) | 10.2288 | 0.370549 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 24.2288 | 0.875993 | ||||||||
\(766\) | −25.7490 | −0.930350 | ||||||||
\(767\) | −7.93725 | −0.286598 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 5.64575 | 0.203591 | 0.101795 | − | 0.994805i | \(-0.467541\pi\) | ||||
0.101795 | + | 0.994805i | \(0.467541\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.8745 | −0.571706 | ||||||||
\(772\) | 18.9373 | 0.681567 | ||||||||
\(773\) | 40.3320 | 1.45064 | 0.725321 | − | 0.688411i | \(-0.241691\pi\) | ||||
0.725321 | + | 0.688411i | \(0.241691\pi\) | |||||||
\(774\) | 5.29150 | 0.190199 | ||||||||
\(775\) | 27.2915 | 0.980340 | ||||||||
\(776\) | −0.937254 | −0.0336455 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.70850 | −0.276363 | ||||||||
\(779\) | −11.7712 | −0.421749 | ||||||||
\(780\) | −3.64575 | −0.130539 | ||||||||
\(781\) | 10.5203 | 0.376444 | ||||||||
\(782\) | −15.6458 | −0.559491 | ||||||||
\(783\) | 4.29150 | 0.153366 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.64575 | −0.344272 | ||||||||
\(786\) | −10.9373 | −0.390119 | ||||||||
\(787\) | 52.6235 | 1.87583 | 0.937913 | − | 0.346871i | \(-0.112756\pi\) | ||||
0.937913 | + | 0.346871i | \(0.112756\pi\) | |||||||
\(788\) | −26.8118 | −0.955129 | ||||||||
\(789\) | −3.64575 | −0.129792 | ||||||||
\(790\) | −36.4575 | −1.29710 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.645751 | −0.0229458 | ||||||||
\(793\) | −11.9373 | −0.423904 | ||||||||
\(794\) | 14.9373 | 0.530103 | ||||||||
\(795\) | 10.9373 | 0.387904 | ||||||||
\(796\) | −22.2288 | −0.787877 | ||||||||
\(797\) | −45.8745 | −1.62496 | −0.812479 | − | 0.582990i | \(-0.801883\pi\) | ||||
−0.812479 | + | 0.582990i | \(0.801883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.9373 | −0.705329 | ||||||||
\(800\) | −8.29150 | −0.293149 | ||||||||
\(801\) | 16.9373 | 0.598448 | ||||||||
\(802\) | 18.2288 | 0.643680 | ||||||||
\(803\) | −8.81176 | −0.310960 | ||||||||
\(804\) | 7.58301 | 0.267432 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.29150 | −0.115938 | ||||||||
\(807\) | 6.87451 | 0.241994 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.8118 | 0.837177 | 0.418588 | − | 0.908176i | \(-0.362525\pi\) | ||||
0.418588 | + | 0.908176i | \(0.362525\pi\) | |||||||
\(810\) | 3.64575 | 0.128099 | ||||||||
\(811\) | 38.0000 | 1.33436 | 0.667180 | − | 0.744896i | \(-0.267501\pi\) | ||||
0.667180 | + | 0.744896i | \(0.267501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.6458 | −0.794221 | ||||||||
\(814\) | −3.64575 | −0.127784 | ||||||||
\(815\) | −8.81176 | −0.308663 | ||||||||
\(816\) | −6.64575 | −0.232648 | ||||||||
\(817\) | −26.4575 | −0.925631 | ||||||||
\(818\) | 26.9373 | 0.941839 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.58301 | 0.299732 | ||||||||
\(821\) | −5.77124 | −0.201418 | −0.100709 | − | 0.994916i | \(-0.532111\pi\) | ||||
−0.100709 | + | 0.994916i | \(0.532111\pi\) | |||||||
\(822\) | 19.5203 | 0.680847 | ||||||||
\(823\) | 15.5203 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(824\) | 5.29150 | 0.184338 | ||||||||
\(825\) | 5.35425 | 0.186411 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.3542 | 1.22939 | 0.614694 | − | 0.788766i | \(-0.289280\pi\) | ||||
0.614694 | + | 0.788766i | \(0.289280\pi\) | |||||||
\(828\) | −2.35425 | −0.0818158 | ||||||||
\(829\) | 47.2288 | 1.64032 | 0.820161 | − | 0.572132i | \(-0.193884\pi\) | ||||
0.820161 | + | 0.572132i | \(0.193884\pi\) | |||||||
\(830\) | −48.4575 | −1.68198 | ||||||||
\(831\) | 18.5203 | 0.642461 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 22.2288 | 0.769719 | ||||||||
\(835\) | 25.0627 | 0.867332 | ||||||||
\(836\) | 3.22876 | 0.111669 | ||||||||
\(837\) | 3.29150 | 0.113771 | ||||||||
\(838\) | −30.4575 | −1.05214 | ||||||||
\(839\) | 21.0000 | 0.725001 | 0.362500 | − | 0.931984i | \(-0.381923\pi\) | ||||
0.362500 | + | 0.931984i | \(0.381923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5830 | −0.364931 | ||||||||
\(842\) | 24.3542 | 0.839303 | ||||||||
\(843\) | −2.58301 | −0.0889634 | ||||||||
\(844\) | −6.35425 | −0.218722 | ||||||||
\(845\) | −3.64575 | −0.125418 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | −11.0627 | −0.379672 | ||||||||
\(850\) | 55.1033 | 1.89003 | ||||||||
\(851\) | −13.2915 | −0.455627 | ||||||||
\(852\) | 16.2915 | 0.558138 | ||||||||
\(853\) | −20.1033 | −0.688323 | −0.344161 | − | 0.938911i | \(-0.611837\pi\) | ||||
−0.344161 | + | 0.938911i | \(0.611837\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.2288 | −0.623410 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | 13.9373 | 0.476088 | 0.238044 | − | 0.971254i | \(-0.423494\pi\) | ||||
0.238044 | + | 0.971254i | \(0.423494\pi\) | |||||||
\(858\) | −0.645751 | −0.0220456 | ||||||||
\(859\) | 44.4575 | 1.51687 | 0.758435 | − | 0.651748i | \(-0.225964\pi\) | ||||
0.758435 | + | 0.651748i | \(0.225964\pi\) | |||||||
\(860\) | 19.2915 | 0.657835 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.5830 | −0.701060 | ||||||||
\(863\) | 31.7490 | 1.08075 | 0.540375 | − | 0.841425i | \(-0.318283\pi\) | ||||
0.540375 | + | 0.841425i | \(0.318283\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 81.2693 | 2.76324 | ||||||||
\(866\) | 33.5830 | 1.14120 | ||||||||
\(867\) | 27.1660 | 0.922606 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.45751 | −0.219056 | ||||||||
\(870\) | 15.6458 | 0.530441 | ||||||||
\(871\) | 7.58301 | 0.256940 | ||||||||
\(872\) | 4.00000 | 0.135457 | ||||||||
\(873\) | 0.937254 | 0.0317212 | ||||||||
\(874\) | 11.7712 | 0.398168 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.6458 | −0.461047 | ||||||||
\(877\) | −54.8118 | −1.85086 | −0.925431 | − | 0.378917i | \(-0.876297\pi\) | ||||
−0.925431 | + | 0.378917i | \(0.876297\pi\) | |||||||
\(878\) | −23.6458 | −0.798005 | ||||||||
\(879\) | 7.52026 | 0.253652 | ||||||||
\(880\) | −2.35425 | −0.0793617 | ||||||||
\(881\) | −10.7085 | −0.360778 | −0.180389 | − | 0.983595i | \(-0.557736\pi\) | ||||
−0.180389 | + | 0.983595i | \(0.557736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.0627 | −0.978039 | −0.489020 | − | 0.872273i | \(-0.662645\pi\) | ||||
−0.489020 | + | 0.872273i | \(0.662645\pi\) | |||||||
\(884\) | −6.64575 | −0.223521 | ||||||||
\(885\) | 28.9373 | 0.972715 | ||||||||
\(886\) | −19.0627 | −0.640425 | ||||||||
\(887\) | 20.5830 | 0.691110 | 0.345555 | − | 0.938399i | \(-0.387691\pi\) | ||||
0.345555 | + | 0.938399i | \(0.387691\pi\) | |||||||
\(888\) | −5.64575 | −0.189459 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 61.7490 | 2.06983 | ||||||||
\(891\) | 0.645751 | 0.0216335 | ||||||||
\(892\) | −20.5203 | −0.687069 | ||||||||
\(893\) | 15.0000 | 0.501956 | ||||||||
\(894\) | 7.06275 | 0.236214 | ||||||||
\(895\) | 21.8745 | 0.731184 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.35425 | −0.0786061 | ||||||||
\(898\) | −12.0000 | −0.400445 | ||||||||
\(899\) | 14.1255 | 0.471112 | ||||||||
\(900\) | 8.29150 | 0.276383 | ||||||||
\(901\) | 19.9373 | 0.664206 | ||||||||
\(902\) | 1.52026 | 0.0506191 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.2288 | −0.506501 | ||||||||
\(905\) | −53.3948 | −1.77490 | ||||||||
\(906\) | −6.06275 | −0.201421 | ||||||||
\(907\) | −3.77124 | −0.125222 | −0.0626110 | − | 0.998038i | \(-0.519943\pi\) | ||||
−0.0626110 | + | 0.998038i | \(0.519943\pi\) | |||||||
\(908\) | −4.70850 | −0.156257 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.7490 | −1.25068 | −0.625340 | − | 0.780352i | \(-0.715040\pi\) | ||||
−0.625340 | + | 0.780352i | \(0.715040\pi\) | |||||||
\(912\) | 5.00000 | 0.165567 | ||||||||
\(913\) | −8.58301 | −0.284056 | ||||||||
\(914\) | −32.2288 | −1.06603 | ||||||||
\(915\) | 43.5203 | 1.43874 | ||||||||
\(916\) | 26.4575 | 0.874181 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.64575 | 0.219342 | ||||||||
\(919\) | 47.8745 | 1.57923 | 0.789617 | − | 0.613600i | \(-0.210279\pi\) | ||||
0.789617 | + | 0.613600i | \(0.210279\pi\) | |||||||
\(920\) | −8.58301 | −0.282973 | ||||||||
\(921\) | −9.58301 | −0.315771 | ||||||||
\(922\) | 36.4575 | 1.20066 | ||||||||
\(923\) | 16.2915 | 0.536241 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.8118 | 1.53916 | ||||||||
\(926\) | −25.1660 | −0.827006 | ||||||||
\(927\) | −5.29150 | −0.173796 | ||||||||
\(928\) | −4.29150 | −0.140875 | ||||||||
\(929\) | −13.7490 | −0.451091 | −0.225545 | − | 0.974233i | \(-0.572416\pi\) | ||||
−0.225545 | + | 0.974233i | \(0.572416\pi\) | |||||||
\(930\) | 12.0000 | 0.393496 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.645751 | 0.0211523 | ||||||||
\(933\) | −1.06275 | −0.0347927 | ||||||||
\(934\) | 37.5203 | 1.22770 | ||||||||
\(935\) | 15.6458 | 0.511671 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −31.4575 | −1.02767 | −0.513836 | − | 0.857888i | \(-0.671776\pi\) | ||||
−0.513836 | + | 0.857888i | \(0.671776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.1660 | 0.429657 | ||||||||
\(940\) | −10.9373 | −0.356734 | ||||||||
\(941\) | −17.1660 | −0.559596 | −0.279798 | − | 0.960059i | \(-0.590267\pi\) | ||||
−0.279798 | + | 0.960059i | \(0.590267\pi\) | |||||||
\(942\) | −2.64575 | −0.0862032 | ||||||||
\(943\) | 5.54249 | 0.180488 | ||||||||
\(944\) | −7.93725 | −0.258336 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.41699 | 0.111096 | ||||||||
\(947\) | −10.5203 | −0.341862 | −0.170931 | − | 0.985283i | \(-0.554678\pi\) | ||||
−0.170931 | + | 0.985283i | \(0.554678\pi\) | |||||||
\(948\) | −10.0000 | −0.324785 | ||||||||
\(949\) | −13.6458 | −0.442960 | ||||||||
\(950\) | −41.4575 | −1.34506 | ||||||||
\(951\) | −13.2915 | −0.431007 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.1033 | −0.813174 | −0.406587 | − | 0.913612i | \(-0.633281\pi\) | ||||
−0.406587 | + | 0.913612i | \(0.633281\pi\) | |||||||
\(954\) | 3.00000 | 0.0971286 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | 0.0970269 | ||||||||
\(957\) | 2.77124 | 0.0895816 | ||||||||
\(958\) | 34.7490 | 1.12269 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.64575 | −0.117666 | ||||||||
\(961\) | −20.1660 | −0.650516 | ||||||||
\(962\) | −5.64575 | −0.182026 | ||||||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | −13.8745 | −0.446868 | ||||||||
\(965\) | −69.0405 | −2.22249 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.10326 | 0.292741 | 0.146371 | − | 0.989230i | \(-0.453241\pi\) | ||||
0.146371 | + | 0.989230i | \(0.453241\pi\) | |||||||
\(968\) | 10.5830 | 0.340151 | ||||||||
\(969\) | −33.2288 | −1.06746 | ||||||||
\(970\) | 3.41699 | 0.109713 | ||||||||
\(971\) | 16.9373 | 0.543542 | 0.271771 | − | 0.962362i | \(-0.412391\pi\) | ||||
0.271771 | + | 0.962362i | \(0.412391\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.9373 | 0.766999 | ||||||||
\(975\) | 8.29150 | 0.265541 | ||||||||
\(976\) | −11.9373 | −0.382102 | ||||||||
\(977\) | 20.1255 | 0.643872 | 0.321936 | − | 0.946762i | \(-0.395666\pi\) | ||||
0.321936 | + | 0.946762i | \(0.395666\pi\) | |||||||
\(978\) | −2.41699 | −0.0772870 | ||||||||
\(979\) | 10.9373 | 0.349556 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | −11.1660 | −0.356322 | ||||||||
\(983\) | −30.0405 | −0.958144 | −0.479072 | − | 0.877776i | \(-0.659027\pi\) | ||||
−0.479072 | + | 0.877776i | \(0.659027\pi\) | |||||||
\(984\) | 2.35425 | 0.0750507 | ||||||||
\(985\) | 97.7490 | 3.11454 | ||||||||
\(986\) | 28.5203 | 0.908270 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.00000 | 0.159071 | ||||||||
\(989\) | 12.4575 | 0.396126 | ||||||||
\(990\) | 2.35425 | 0.0748229 | ||||||||
\(991\) | 5.41699 | 0.172077 | 0.0860383 | − | 0.996292i | \(-0.472579\pi\) | ||||
0.0860383 | + | 0.996292i | \(0.472579\pi\) | |||||||
\(992\) | −3.29150 | −0.104505 | ||||||||
\(993\) | 11.4170 | 0.362307 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 81.0405 | 2.56916 | ||||||||
\(996\) | −13.2915 | −0.421157 | ||||||||
\(997\) | −1.22876 | −0.0389151 | −0.0194576 | − | 0.999811i | \(-0.506194\pi\) | ||||
−0.0194576 | + | 0.999811i | \(0.506194\pi\) | |||||||
\(998\) | 29.2915 | 0.927206 | ||||||||
\(999\) | 5.64575 | 0.178624 |
(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 | 3822.2.a.bk.1.1 | 2 | ||
7.2 | even | 3 | 546.2.i.j.235.2 | yes | 4 | ||
7.4 | even | 3 | 546.2.i.j.79.2 | ✓ | 4 | ||
7.6 | odd | 2 | 3822.2.a.bi.1.2 | 2 | |||
21.2 | odd | 6 | 1638.2.j.k.235.1 | 4 | |||
21.11 | odd | 6 | 1638.2.j.k.1171.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.i.j.79.2 | ✓ | 4 | 7.4 | even | 3 | ||
546.2.i.j.235.2 | yes | 4 | 7.2 | even | 3 | ||
1638.2.j.k.235.1 | 4 | 21.2 | odd | 6 | |||
1638.2.j.k.1171.1 | 4 | 21.11 | odd | 6 | |||
3822.2.a.bi.1.2 | 2 | 7.6 | odd | 2 | |||
3822.2.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial |