Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(1,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, 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("1170.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.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: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60555 | −0.984806 | −0.492403 | − | 0.870367i | \(-0.663881\pi\) | ||||
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 2.60555 | 0.696363 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.60555 | −1.11701 | −0.558505 | − | 0.829501i | \(-0.688625\pi\) | ||||
−0.558505 | + | 0.829501i | \(0.688625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.60555 | 1.51542 | 0.757709 | − | 0.652593i | \(-0.226319\pi\) | ||||
0.757709 | + | 0.652593i | \(0.226319\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.60555 | −0.960324 | −0.480162 | − | 0.877180i | \(-0.659422\pi\) | ||||
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.60555 | −0.492403 | ||||||||
\(29\) | 4.60555 | 0.855229 | 0.427615 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427615 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.60555 | 0.789846 | ||||||||
\(35\) | 2.60555 | 0.440419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.2111 | 1.84309 | 0.921547 | − | 0.388267i | \(-0.126926\pi\) | ||||
0.921547 | + | 0.388267i | \(0.126926\pi\) | |||||||
\(38\) | −6.60555 | −1.07156 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.21110 | −0.501490 | −0.250745 | − | 0.968053i | \(-0.580676\pi\) | ||||
−0.250745 | + | 0.968053i | \(0.580676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.21110 | 0.794686 | 0.397343 | − | 0.917670i | \(-0.369932\pi\) | ||||
0.397343 | + | 0.917670i | \(0.369932\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.60555 | 0.679051 | ||||||||
\(47\) | 9.21110 | 1.34358 | 0.671789 | − | 0.740743i | \(-0.265526\pi\) | ||||
0.671789 | + | 0.740743i | \(0.265526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.211103 | −0.0301575 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.60555 | 0.348181 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.60555 | −0.604739 | ||||||||
\(59\) | 9.21110 | 1.19918 | 0.599592 | − | 0.800306i | \(-0.295330\pi\) | ||||
0.599592 | + | 0.800306i | \(0.295330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.21110 | −0.923287 | −0.461644 | − | 0.887066i | \(-0.652740\pi\) | ||||
−0.461644 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.21110 | −0.880976 | −0.440488 | − | 0.897758i | \(-0.645195\pi\) | ||||
−0.440488 | + | 0.897758i | \(0.645195\pi\) | |||||||
\(68\) | −4.60555 | −0.558505 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.60555 | −0.311423 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.60555 | 0.773121 | 0.386561 | − | 0.922264i | \(-0.373663\pi\) | ||||
0.386561 | + | 0.922264i | \(0.373663\pi\) | |||||||
\(74\) | −11.2111 | −1.30326 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.60555 | 0.757709 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.21110 | −0.136260 | −0.0681298 | − | 0.997676i | \(-0.521703\pi\) | ||||
−0.0681298 | + | 0.997676i | \(0.521703\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.21110 | 0.354607 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.60555 | 0.499542 | ||||||||
\(86\) | −5.21110 | −0.561928 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.21110 | −0.340376 | −0.170188 | − | 0.985412i | \(-0.554438\pi\) | ||||
−0.170188 | + | 0.985412i | \(0.554438\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.60555 | −0.273136 | ||||||||
\(92\) | −4.60555 | −0.480162 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.21110 | −0.950053 | ||||||||
\(95\) | −6.60555 | −0.677715 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.60555 | 0.670692 | 0.335346 | − | 0.942095i | \(-0.391147\pi\) | ||||
0.335346 | + | 0.942095i | \(0.391147\pi\) | |||||||
\(98\) | 0.211103 | 0.0213246 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.8167 | 1.37481 | 0.687404 | − | 0.726275i | \(-0.258750\pi\) | ||||
0.687404 | + | 0.726275i | \(0.258750\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.6056 | 1.78209 | 0.891044 | − | 0.453916i | \(-0.149974\pi\) | ||||
0.891044 | + | 0.453916i | \(0.149974\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.60555 | −0.246201 | ||||||||
\(113\) | −7.39445 | −0.695611 | −0.347806 | − | 0.937567i | \(-0.613073\pi\) | ||||
−0.347806 | + | 0.937567i | \(0.613073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.60555 | 0.429470 | ||||||||
\(116\) | 4.60555 | 0.427615 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.21110 | −0.847951 | ||||||||
\(119\) | 12.0000 | 1.10004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 7.21110 | 0.652863 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.21110 | −0.107468 | −0.0537340 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537340 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | 16.6056 | 1.45083 | 0.725417 | − | 0.688310i | \(-0.241647\pi\) | ||||
0.725417 | + | 0.688310i | \(0.241647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.2111 | −1.49239 | ||||||||
\(134\) | 7.21110 | 0.622944 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.60555 | 0.394923 | ||||||||
\(137\) | −21.6333 | −1.84826 | −0.924129 | − | 0.382080i | \(-0.875208\pi\) | ||||
−0.924129 | + | 0.382080i | \(0.875208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4222 | 1.22328 | 0.611638 | − | 0.791138i | \(-0.290511\pi\) | ||||
0.611638 | + | 0.791138i | \(0.290511\pi\) | |||||||
\(140\) | 2.60555 | 0.220209 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.60555 | −0.382470 | ||||||||
\(146\) | −6.60555 | −0.546679 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.2111 | 0.921547 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.42221 | 0.685389 | 0.342695 | − | 0.939447i | \(-0.388660\pi\) | ||||
0.342695 | + | 0.939447i | \(0.388660\pi\) | |||||||
\(152\) | −6.60555 | −0.535781 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2111 | 0.894743 | 0.447372 | − | 0.894348i | \(-0.352360\pi\) | ||||
0.447372 | + | 0.894348i | \(0.352360\pi\) | |||||||
\(158\) | 1.21110 | 0.0963501 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | −3.21110 | −0.250745 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.4222 | 1.42555 | 0.712777 | − | 0.701391i | \(-0.247437\pi\) | ||||
0.712777 | + | 0.701391i | \(0.247437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −4.60555 | −0.353230 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.21110 | 0.397343 | ||||||||
\(173\) | −12.0000 | −0.912343 | −0.456172 | − | 0.889892i | \(-0.650780\pi\) | ||||
−0.456172 | + | 0.889892i | \(0.650780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.60555 | −0.196961 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.21110 | 0.240682 | ||||||||
\(179\) | −11.0278 | −0.824253 | −0.412127 | − | 0.911127i | \(-0.635214\pi\) | ||||
−0.412127 | + | 0.911127i | \(0.635214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.2111 | −1.42795 | −0.713975 | − | 0.700171i | \(-0.753107\pi\) | ||||
−0.713975 | + | 0.700171i | \(0.753107\pi\) | |||||||
\(182\) | 2.60555 | 0.193136 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.60555 | 0.339526 | ||||||||
\(185\) | −11.2111 | −0.824257 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.21110 | 0.671789 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.60555 | 0.479217 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.6056 | −1.05133 | −0.525665 | − | 0.850691i | \(-0.676184\pi\) | ||||
−0.525665 | + | 0.850691i | \(0.676184\pi\) | |||||||
\(194\) | −6.60555 | −0.474251 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.211103 | −0.0150788 | ||||||||
\(197\) | 24.4222 | 1.74001 | 0.870005 | − | 0.493043i | \(-0.164115\pi\) | ||||
0.870005 | + | 0.493043i | \(0.164115\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.21110 | 0.369405 | 0.184703 | − | 0.982794i | \(-0.440868\pi\) | ||||
0.184703 | + | 0.982794i | \(0.440868\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.8167 | −0.972136 | ||||||||
\(203\) | −12.0000 | −0.842235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.21110 | 0.224273 | ||||||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.2111 | −1.73560 | −0.867802 | − | 0.496910i | \(-0.834468\pi\) | ||||
−0.867802 | + | 0.496910i | \(0.834468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | −5.21110 | −0.355394 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.21110 | −0.353753 | ||||||||
\(218\) | −18.6056 | −1.26013 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.60555 | −0.309803 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3944 | −1.16482 | −0.582409 | − | 0.812896i | \(-0.697890\pi\) | ||||
−0.582409 | + | 0.812896i | \(0.697890\pi\) | |||||||
\(224\) | 2.60555 | 0.174091 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.39445 | 0.491871 | ||||||||
\(227\) | −6.42221 | −0.426257 | −0.213128 | − | 0.977024i | \(-0.568365\pi\) | ||||
−0.213128 | + | 0.977024i | \(0.568365\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.183346 | 0.0121159 | 0.00605793 | − | 0.999982i | \(-0.498072\pi\) | ||||
0.00605793 | + | 0.999982i | \(0.498072\pi\) | |||||||
\(230\) | −4.60555 | −0.303681 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.60555 | −0.302369 | ||||||||
\(233\) | 1.81665 | 0.119013 | 0.0595065 | − | 0.998228i | \(-0.481047\pi\) | ||||
0.0595065 | + | 0.998228i | \(0.481047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.21110 | −0.600866 | ||||||||
\(236\) | 9.21110 | 0.599592 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.0000 | −0.777844 | ||||||||
\(239\) | −18.4222 | −1.19163 | −0.595817 | − | 0.803120i | \(-0.703172\pi\) | ||||
−0.595817 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 11.0000 | 0.707107 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.21110 | −0.461644 | ||||||||
\(245\) | 0.211103 | 0.0134868 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.60555 | 0.420301 | ||||||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −4.60555 | −0.290700 | −0.145350 | − | 0.989380i | \(-0.546431\pi\) | ||||
−0.145350 | + | 0.989380i | \(0.546431\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.21110 | 0.0759913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.0278 | 0.687893 | 0.343946 | − | 0.938989i | \(-0.388236\pi\) | ||||
0.343946 | + | 0.938989i | \(0.388236\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.2111 | −1.81509 | ||||||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.6056 | −1.02589 | ||||||||
\(263\) | 11.0278 | 0.680001 | 0.340000 | − | 0.940425i | \(-0.389573\pi\) | ||||
0.340000 | + | 0.940425i | \(0.389573\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17.2111 | 1.05528 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.21110 | −0.440488 | ||||||||
\(269\) | −10.1833 | −0.620890 | −0.310445 | − | 0.950591i | \(-0.600478\pi\) | ||||
−0.310445 | + | 0.950591i | \(0.600478\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | −4.60555 | −0.279253 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.6333 | 1.30692 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.2111 | −1.87529 | −0.937647 | − | 0.347590i | \(-0.887000\pi\) | ||||
−0.937647 | + | 0.347590i | \(0.887000\pi\) | |||||||
\(278\) | −14.4222 | −0.864986 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.60555 | −0.155711 | ||||||||
\(281\) | 3.21110 | 0.191558 | 0.0957792 | − | 0.995403i | \(-0.469466\pi\) | ||||
0.0957792 | + | 0.995403i | \(0.469466\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.21110 | −0.0719926 | −0.0359963 | − | 0.999352i | \(-0.511460\pi\) | ||||
−0.0359963 | + | 0.999352i | \(0.511460\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.36669 | 0.493870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.21110 | 0.247712 | ||||||||
\(290\) | 4.60555 | 0.270447 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.60555 | 0.386561 | ||||||||
\(293\) | −30.0000 | −1.75262 | −0.876309 | − | 0.481749i | \(-0.840002\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.21110 | −0.536291 | ||||||||
\(296\) | −11.2111 | −0.651632 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | −4.60555 | −0.266346 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.5778 | −0.782611 | ||||||||
\(302\) | −8.42221 | −0.484643 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.60555 | 0.378854 | ||||||||
\(305\) | 7.21110 | 0.412907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.78890 | 0.273317 | 0.136658 | − | 0.990618i | \(-0.456364\pi\) | ||||
0.136658 | + | 0.990618i | \(0.456364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.00000 | 0.113592 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2111 | 0.633689 | 0.316844 | − | 0.948478i | \(-0.397377\pi\) | ||||
0.316844 | + | 0.948478i | \(0.397377\pi\) | |||||||
\(314\) | −11.2111 | −0.632679 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.21110 | −0.0681298 | ||||||||
\(317\) | 12.4222 | 0.697701 | 0.348850 | − | 0.937178i | \(-0.386572\pi\) | ||||
0.348850 | + | 0.937178i | \(0.386572\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | −0.668734 | ||||||||
\(323\) | −30.4222 | −1.69274 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −2.00000 | −0.110770 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.21110 | 0.177303 | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.39445 | −0.296506 | −0.148253 | − | 0.988949i | \(-0.547365\pi\) | ||||
−0.148253 | + | 0.988949i | \(0.547365\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.4222 | −1.00802 | ||||||||
\(335\) | 7.21110 | 0.393985 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.8444 | 1.46231 | 0.731154 | − | 0.682212i | \(-0.238982\pi\) | ||||
0.731154 | + | 0.682212i | \(0.238982\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.60555 | 0.249771 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.7889 | 1.01451 | ||||||||
\(344\) | −5.21110 | −0.280964 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.0000 | 0.645124 | ||||||||
\(347\) | −14.7889 | −0.793910 | −0.396955 | − | 0.917838i | \(-0.629933\pi\) | ||||
−0.396955 | + | 0.917838i | \(0.629933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8167 | −0.632531 | −0.316265 | − | 0.948671i | \(-0.602429\pi\) | ||||
−0.316265 | + | 0.948671i | \(0.602429\pi\) | |||||||
\(350\) | 2.60555 | 0.139273 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.6333 | −1.15142 | −0.575712 | − | 0.817652i | \(-0.695275\pi\) | ||||
−0.575712 | + | 0.817652i | \(0.695275\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | −0.636894 | ||||||||
\(356\) | −3.21110 | −0.170188 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.0278 | 0.582835 | ||||||||
\(359\) | 30.4222 | 1.60562 | 0.802811 | − | 0.596233i | \(-0.203337\pi\) | ||||
0.802811 | + | 0.596233i | \(0.203337\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.6333 | 1.29649 | ||||||||
\(362\) | 19.2111 | 1.00971 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.60555 | −0.136568 | ||||||||
\(365\) | −6.60555 | −0.345750 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.78890 | −0.354378 | −0.177189 | − | 0.984177i | \(-0.556700\pi\) | ||||
−0.177189 | + | 0.984177i | \(0.556700\pi\) | |||||||
\(368\) | −4.60555 | −0.240081 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.2111 | 0.582837 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.788897 | −0.0408476 | −0.0204238 | − | 0.999791i | \(-0.506502\pi\) | ||||
−0.0204238 | + | 0.999791i | \(0.506502\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.21110 | −0.475026 | ||||||||
\(377\) | 4.60555 | 0.237198 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.6056 | −1.36664 | −0.683318 | − | 0.730121i | \(-0.739464\pi\) | ||||
−0.683318 | + | 0.730121i | \(0.739464\pi\) | |||||||
\(380\) | −6.60555 | −0.338858 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0000 | −0.613973 | ||||||||
\(383\) | −18.4222 | −0.941331 | −0.470665 | − | 0.882312i | \(-0.655986\pi\) | ||||
−0.470665 | + | 0.882312i | \(0.655986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.6056 | 0.743403 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.60555 | 0.335346 | ||||||||
\(389\) | 1.81665 | 0.0921080 | 0.0460540 | − | 0.998939i | \(-0.485335\pi\) | ||||
0.0460540 | + | 0.998939i | \(0.485335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.2111 | 1.07269 | ||||||||
\(392\) | 0.211103 | 0.0106623 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.4222 | −1.23037 | ||||||||
\(395\) | 1.21110 | 0.0609372 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.2111 | 1.76719 | 0.883597 | − | 0.468248i | \(-0.155114\pi\) | ||||
0.883597 | + | 0.468248i | \(0.155114\pi\) | |||||||
\(398\) | −5.21110 | −0.261209 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −33.6333 | −1.67957 | −0.839784 | − | 0.542921i | \(-0.817318\pi\) | ||||
−0.839784 | + | 0.542921i | \(0.817318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | 0.0996271 | ||||||||
\(404\) | 13.8167 | 0.687404 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6333 | −0.674124 | −0.337062 | − | 0.941483i | \(-0.609433\pi\) | ||||
−0.337062 | + | 0.941483i | \(0.609433\pi\) | |||||||
\(410\) | −3.21110 | −0.158585 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | −24.0000 | −1.18096 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.4500 | 1.43872 | 0.719362 | − | 0.694635i | \(-0.244434\pi\) | ||||
0.719362 | + | 0.694635i | \(0.244434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.02776 | −0.439986 | −0.219993 | − | 0.975501i | \(-0.570603\pi\) | ||||
−0.219993 | + | 0.975501i | \(0.570603\pi\) | |||||||
\(422\) | 25.2111 | 1.22726 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.60555 | −0.223402 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.7889 | 0.909258 | ||||||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.21110 | 0.251302 | ||||||||
\(431\) | 24.0000 | 1.15604 | 0.578020 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578020 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.8444 | −1.09783 | −0.548916 | − | 0.835877i | \(-0.684959\pi\) | ||||
−0.548916 | + | 0.835877i | \(0.684959\pi\) | |||||||
\(434\) | 5.21110 | 0.250141 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.6056 | 0.891044 | ||||||||
\(437\) | −30.4222 | −1.45529 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.8444 | 1.56758 | 0.783789 | − | 0.621027i | \(-0.213284\pi\) | ||||
0.783789 | + | 0.621027i | \(0.213284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.60555 | 0.219064 | ||||||||
\(443\) | 39.6333 | 1.88304 | 0.941518 | − | 0.336964i | \(-0.109400\pi\) | ||||
0.941518 | + | 0.336964i | \(0.109400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.21110 | 0.152221 | ||||||||
\(446\) | 17.3944 | 0.823651 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.60555 | −0.123101 | ||||||||
\(449\) | 9.63331 | 0.454624 | 0.227312 | − | 0.973822i | \(-0.427006\pi\) | ||||
0.227312 | + | 0.973822i | \(0.427006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.39445 | −0.347806 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.42221 | 0.301409 | ||||||||
\(455\) | 2.60555 | 0.122150 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3944 | −0.813678 | −0.406839 | − | 0.913500i | \(-0.633369\pi\) | ||||
−0.406839 | + | 0.913500i | \(0.633369\pi\) | |||||||
\(458\) | −0.183346 | −0.00856720 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.60555 | 0.214735 | ||||||||
\(461\) | 3.21110 | 0.149556 | 0.0747780 | − | 0.997200i | \(-0.476175\pi\) | ||||
0.0747780 | + | 0.997200i | \(0.476175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1833 | 0.566208 | 0.283104 | − | 0.959089i | \(-0.408636\pi\) | ||||
0.283104 | + | 0.959089i | \(0.408636\pi\) | |||||||
\(464\) | 4.60555 | 0.213807 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.81665 | −0.0841549 | ||||||||
\(467\) | 5.57779 | 0.258110 | 0.129055 | − | 0.991637i | \(-0.458806\pi\) | ||||
0.129055 | + | 0.991637i | \(0.458806\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7889 | 0.867591 | ||||||||
\(470\) | 9.21110 | 0.424876 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.21110 | −0.423975 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.60555 | 0.303083 | ||||||||
\(476\) | 12.0000 | 0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.4222 | 0.842612 | ||||||||
\(479\) | −18.4222 | −0.841732 | −0.420866 | − | 0.907123i | \(-0.638274\pi\) | ||||
−0.420866 | + | 0.907123i | \(0.638274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2111 | 0.511182 | ||||||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | −6.60555 | −0.299943 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.97224 | 0.134685 | 0.0673426 | − | 0.997730i | \(-0.478548\pi\) | ||||
0.0673426 | + | 0.997730i | \(0.478548\pi\) | |||||||
\(488\) | 7.21110 | 0.326431 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.211103 | −0.00953664 | ||||||||
\(491\) | −32.2389 | −1.45492 | −0.727460 | − | 0.686150i | \(-0.759299\pi\) | ||||
−0.727460 | + | 0.686150i | \(0.759299\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.2111 | −0.955300 | ||||||||
\(494\) | −6.60555 | −0.297198 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −31.2666 | −1.40250 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.8167 | 1.24524 | 0.622622 | − | 0.782523i | \(-0.286067\pi\) | ||||
0.622622 | + | 0.782523i | \(0.286067\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.60555 | 0.205556 | ||||||||
\(503\) | −20.2389 | −0.902406 | −0.451203 | − | 0.892421i | \(-0.649005\pi\) | ||||
−0.451203 | + | 0.892421i | \(0.649005\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.8167 | −0.614833 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.21110 | −0.0537340 | ||||||||
\(509\) | −9.63331 | −0.426989 | −0.213494 | − | 0.976944i | \(-0.568485\pi\) | ||||
−0.213494 | + | 0.976944i | \(0.568485\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.2111 | −0.761374 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.0278 | −0.486413 | ||||||||
\(515\) | 4.00000 | 0.176261 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 29.2111 | 1.28346 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | 21.2111 | 0.929275 | 0.464638 | − | 0.885501i | \(-0.346185\pi\) | ||||
0.464638 | + | 0.885501i | \(0.346185\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.4222 | 1.68009 | 0.840043 | − | 0.542520i | \(-0.182530\pi\) | ||||
0.840043 | + | 0.542520i | \(0.182530\pi\) | |||||||
\(524\) | 16.6056 | 0.725417 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.0278 | −0.480833 | ||||||||
\(527\) | −9.21110 | −0.401242 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.78890 | −0.0777781 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.2111 | −0.746196 | ||||||||
\(533\) | −3.21110 | −0.139088 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | −0.518805 | ||||||||
\(536\) | 7.21110 | 0.311472 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.1833 | 0.439035 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.02776 | −0.388134 | −0.194067 | − | 0.980988i | \(-0.562168\pi\) | ||||
−0.194067 | + | 0.980988i | \(0.562168\pi\) | |||||||
\(542\) | −2.00000 | −0.0859074 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.60555 | 0.197461 | ||||||||
\(545\) | −18.6056 | −0.796974 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | −21.6333 | −0.924129 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.4222 | 1.29603 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.15559 | 0.134189 | ||||||||
\(554\) | 31.2111 | 1.32603 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.4222 | 0.611638 | ||||||||
\(557\) | 18.8444 | 0.798463 | 0.399232 | − | 0.916850i | \(-0.369277\pi\) | ||||
0.399232 | + | 0.916850i | \(0.369277\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.21110 | 0.220406 | ||||||||
\(560\) | 2.60555 | 0.110105 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.21110 | −0.135452 | ||||||||
\(563\) | 15.6333 | 0.658865 | 0.329433 | − | 0.944179i | \(-0.393143\pi\) | ||||
0.329433 | + | 0.944179i | \(0.393143\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.39445 | 0.311087 | ||||||||
\(566\) | 1.21110 | 0.0509064 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 26.7889 | 1.12305 | 0.561525 | − | 0.827460i | \(-0.310215\pi\) | ||||
0.561525 | + | 0.827460i | \(0.310215\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.36669 | −0.349219 | ||||||||
\(575\) | −4.60555 | −0.192065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.8167 | 1.15802 | 0.579011 | − | 0.815320i | \(-0.303439\pi\) | ||||
0.579011 | + | 0.815320i | \(0.303439\pi\) | |||||||
\(578\) | −4.21110 | −0.175159 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.60555 | −0.191235 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −6.60555 | −0.273340 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0000 | 1.23929 | ||||||||
\(587\) | 6.42221 | 0.265073 | 0.132536 | − | 0.991178i | \(-0.457688\pi\) | ||||
0.132536 | + | 0.991178i | \(0.457688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.2111 | 0.544354 | ||||||||
\(590\) | 9.21110 | 0.379215 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.2111 | 0.460773 | ||||||||
\(593\) | −20.7889 | −0.853698 | −0.426849 | − | 0.904323i | \(-0.640376\pi\) | ||||
−0.426849 | + | 0.904323i | \(0.640376\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.60555 | 0.188335 | ||||||||
\(599\) | 36.8444 | 1.50542 | 0.752711 | − | 0.658351i | \(-0.228746\pi\) | ||||
0.752711 | + | 0.658351i | \(0.228746\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.6333 | 0.719278 | 0.359639 | − | 0.933092i | \(-0.382900\pi\) | ||||
0.359639 | + | 0.933092i | \(0.382900\pi\) | |||||||
\(602\) | 13.5778 | 0.553390 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.42221 | 0.342695 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.2111 | 1.67271 | 0.836354 | − | 0.548190i | \(-0.184683\pi\) | ||||
0.836354 | + | 0.548190i | \(0.184683\pi\) | |||||||
\(608\) | −6.60555 | −0.267890 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.21110 | −0.291969 | ||||||||
\(611\) | 9.21110 | 0.372641 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.63331 | 0.227527 | 0.113764 | − | 0.993508i | \(-0.463709\pi\) | ||||
0.113764 | + | 0.993508i | \(0.463709\pi\) | |||||||
\(614\) | −4.78890 | −0.193264 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8444 | 0.758647 | 0.379324 | − | 0.925264i | \(-0.376157\pi\) | ||||
0.379324 | + | 0.925264i | \(0.376157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.60555 | −0.104726 | −0.0523630 | − | 0.998628i | \(-0.516675\pi\) | ||||
−0.0523630 | + | 0.998628i | \(0.516675\pi\) | |||||||
\(620\) | −2.00000 | −0.0803219 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | 8.36669 | 0.335204 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.2111 | −0.448086 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.2111 | 0.447372 | ||||||||
\(629\) | −51.6333 | −2.05875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2111 | 0.924019 | 0.462010 | − | 0.886875i | \(-0.347129\pi\) | ||||
0.462010 | + | 0.886875i | \(0.347129\pi\) | |||||||
\(632\) | 1.21110 | 0.0481751 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.4222 | −0.493349 | ||||||||
\(635\) | 1.21110 | 0.0480611 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.211103 | −0.00836419 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −24.0000 | −0.947943 | −0.473972 | − | 0.880540i | \(-0.657180\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.0555 | 1.89512 | 0.947562 | − | 0.319571i | \(-0.103539\pi\) | ||||
0.947562 | + | 0.319571i | \(0.103539\pi\) | |||||||
\(644\) | 12.0000 | 0.472866 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 30.4222 | 1.19695 | ||||||||
\(647\) | 35.0278 | 1.37708 | 0.688542 | − | 0.725197i | \(-0.258251\pi\) | ||||
0.688542 | + | 0.725197i | \(0.258251\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | 0.0783260 | ||||||||
\(653\) | 2.78890 | 0.109138 | 0.0545690 | − | 0.998510i | \(-0.482622\pi\) | ||||
0.0545690 | + | 0.998510i | \(0.482622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.6056 | −0.648833 | ||||||||
\(656\) | −3.21110 | −0.125372 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.0000 | 0.935617 | ||||||||
\(659\) | −13.8167 | −0.538220 | −0.269110 | − | 0.963109i | \(-0.586730\pi\) | ||||
−0.269110 | + | 0.963109i | \(0.586730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.0278 | −0.817885 | −0.408942 | − | 0.912560i | \(-0.634102\pi\) | ||||
−0.408942 | + | 0.912560i | \(0.634102\pi\) | |||||||
\(662\) | 5.39445 | 0.209661 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.2111 | 0.667418 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.2111 | −0.821297 | ||||||||
\(668\) | 18.4222 | 0.712777 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.21110 | −0.278589 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.2111 | −0.740534 | −0.370267 | − | 0.928925i | \(-0.620734\pi\) | ||||
−0.370267 | + | 0.928925i | \(0.620734\pi\) | |||||||
\(674\) | −26.8444 | −1.03401 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −9.21110 | −0.354011 | −0.177006 | − | 0.984210i | \(-0.556641\pi\) | ||||
−0.177006 | + | 0.984210i | \(0.556641\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.2111 | −0.660501 | ||||||||
\(680\) | −4.60555 | −0.176615 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.57779 | −0.213428 | −0.106714 | − | 0.994290i | \(-0.534033\pi\) | ||||
−0.106714 | + | 0.994290i | \(0.534033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.6333 | 0.826566 | ||||||||
\(686\) | −18.7889 | −0.717363 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.21110 | 0.198671 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.8167 | −0.906028 | −0.453014 | − | 0.891503i | \(-0.649651\pi\) | ||||
−0.453014 | + | 0.891503i | \(0.649651\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.7889 | 0.561379 | ||||||||
\(695\) | −14.4222 | −0.547065 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7889 | 0.560169 | ||||||||
\(698\) | 11.8167 | 0.447267 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.60555 | −0.0984806 | ||||||||
\(701\) | −16.6056 | −0.627183 | −0.313592 | − | 0.949558i | \(-0.601532\pi\) | ||||
−0.313592 | + | 0.949558i | \(0.601532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 74.0555 | 2.79306 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.6333 | 0.814180 | ||||||||
\(707\) | −36.0000 | −1.35392 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.4500 | 1.18113 | 0.590564 | − | 0.806991i | \(-0.298905\pi\) | ||||
0.590564 | + | 0.806991i | \(0.298905\pi\) | |||||||
\(710\) | 12.0000 | 0.450352 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.21110 | 0.120341 | ||||||||
\(713\) | −9.21110 | −0.344959 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.0278 | −0.412127 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.4222 | −1.13535 | ||||||||
\(719\) | −21.2111 | −0.791041 | −0.395520 | − | 0.918457i | \(-0.629436\pi\) | ||||
−0.395520 | + | 0.918457i | \(0.629436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4222 | 0.388143 | ||||||||
\(722\) | −24.6333 | −0.916757 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.2111 | −0.713975 | ||||||||
\(725\) | 4.60555 | 0.171046 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.6333 | −1.61827 | −0.809135 | − | 0.587623i | \(-0.800064\pi\) | ||||
−0.809135 | + | 0.587623i | \(0.800064\pi\) | |||||||
\(728\) | 2.60555 | 0.0965682 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.60555 | 0.244482 | ||||||||
\(731\) | −24.0000 | −0.887672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.6333 | 1.53776 | 0.768881 | − | 0.639392i | \(-0.220814\pi\) | ||||
0.768881 | + | 0.639392i | \(0.220814\pi\) | |||||||
\(734\) | 6.78890 | 0.250583 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.60555 | 0.169763 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.6056 | −0.978701 | −0.489351 | − | 0.872087i | \(-0.662766\pi\) | ||||
−0.489351 | + | 0.872087i | \(0.662766\pi\) | |||||||
\(740\) | −11.2111 | −0.412128 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.0555 | 1.68961 | 0.844806 | − | 0.535072i | \(-0.179716\pi\) | ||||
0.844806 | + | 0.535072i | \(0.179716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | −0.219823 | ||||||||
\(746\) | 0.788897 | 0.0288836 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.2666 | −1.14246 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.2666 | −1.28690 | −0.643449 | − | 0.765489i | \(-0.722497\pi\) | ||||
−0.643449 | + | 0.765489i | \(0.722497\pi\) | |||||||
\(752\) | 9.21110 | 0.335894 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.60555 | −0.167724 | ||||||||
\(755\) | −8.42221 | −0.306515 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.8444 | −1.26644 | −0.633221 | − | 0.773971i | \(-0.718268\pi\) | ||||
−0.633221 | + | 0.773971i | \(0.718268\pi\) | |||||||
\(758\) | 26.6056 | 0.966357 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.60555 | 0.239609 | ||||||||
\(761\) | 9.63331 | 0.349207 | 0.174604 | − | 0.984639i | \(-0.444136\pi\) | ||||
0.174604 | + | 0.984639i | \(0.444136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −48.4777 | −1.75501 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.4222 | 0.665621 | ||||||||
\(767\) | 9.21110 | 0.332594 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.8444 | −1.25652 | −0.628261 | − | 0.778003i | \(-0.716233\pi\) | ||||
−0.628261 | + | 0.778003i | \(0.716233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.6056 | −0.525665 | ||||||||
\(773\) | 12.4222 | 0.446796 | 0.223398 | − | 0.974727i | \(-0.428285\pi\) | ||||
0.223398 | + | 0.974727i | \(0.428285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | −6.60555 | −0.237125 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.81665 | −0.0651302 | ||||||||
\(779\) | −21.2111 | −0.759967 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −21.2111 | −0.758507 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.211103 | −0.00753938 | ||||||||
\(785\) | −11.2111 | −0.400141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.0000 | 1.35455 | 0.677277 | − | 0.735728i | \(-0.263160\pi\) | ||||
0.677277 | + | 0.735728i | \(0.263160\pi\) | |||||||
\(788\) | 24.4222 | 0.870005 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.21110 | −0.0430891 | ||||||||
\(791\) | 19.2666 | 0.685042 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.21110 | −0.256074 | ||||||||
\(794\) | −35.2111 | −1.24960 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.21110 | 0.184703 | ||||||||
\(797\) | −42.4222 | −1.50267 | −0.751336 | − | 0.659920i | \(-0.770590\pi\) | ||||
−0.751336 | + | 0.659920i | \(0.770590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.4222 | −1.50079 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.6333 | 1.18763 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | −0.422944 | ||||||||
\(806\) | −2.00000 | −0.0704470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.8167 | −0.486068 | ||||||||
\(809\) | −6.42221 | −0.225793 | −0.112896 | − | 0.993607i | \(-0.536013\pi\) | ||||
−0.112896 | + | 0.993607i | \(0.536013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.0278 | 1.72160 | 0.860799 | − | 0.508946i | \(-0.169965\pi\) | ||||
0.860799 | + | 0.508946i | \(0.169965\pi\) | |||||||
\(812\) | −12.0000 | −0.421117 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | −0.0700569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.4222 | 1.20428 | ||||||||
\(818\) | 13.6333 | 0.476677 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.21110 | 0.112137 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0000 | 0.835067 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0.972244 | 0.0336862 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.4222 | −0.637527 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29.4500 | −1.01733 | ||||||||
\(839\) | 42.4222 | 1.46458 | 0.732289 | − | 0.680994i | \(-0.238452\pi\) | ||||
0.732289 | + | 0.680994i | \(0.238452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | 9.02776 | 0.311117 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.2111 | −0.867802 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.6611 | 0.984806 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.60555 | 0.157969 | ||||||||
\(851\) | −51.6333 | −1.76997 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0555 | 0.823645 | 0.411823 | − | 0.911264i | \(-0.364892\pi\) | ||||
0.411823 | + | 0.911264i | \(0.364892\pi\) | |||||||
\(854\) | −18.7889 | −0.642943 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | 29.4500 | 1.00599 | 0.502996 | − | 0.864289i | \(-0.332231\pi\) | ||||
0.502996 | + | 0.864289i | \(0.332231\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.36669 | 0.148990 | 0.0744948 | − | 0.997221i | \(-0.476266\pi\) | ||||
0.0744948 | + | 0.997221i | \(0.476266\pi\) | |||||||
\(860\) | −5.21110 | −0.177697 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.0000 | −0.817443 | ||||||||
\(863\) | 42.4222 | 1.44407 | 0.722034 | − | 0.691857i | \(-0.243207\pi\) | ||||
0.722034 | + | 0.691857i | \(0.243207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 22.8444 | 0.776285 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.21110 | −0.176876 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.21110 | −0.244339 | ||||||||
\(872\) | −18.6056 | −0.630063 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30.4222 | 1.02905 | ||||||||
\(875\) | 2.60555 | 0.0880837 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.0000 | 0.877958 | 0.438979 | − | 0.898497i | \(-0.355340\pi\) | ||||
0.438979 | + | 0.898497i | \(0.355340\pi\) | |||||||
\(878\) | −32.8444 | −1.10845 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.7889 | −0.902541 | −0.451270 | − | 0.892387i | \(-0.649029\pi\) | ||||
−0.451270 | + | 0.892387i | \(0.649029\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.4222 | 0.485346 | 0.242673 | − | 0.970108i | \(-0.421976\pi\) | ||||
0.242673 | + | 0.970108i | \(0.421976\pi\) | |||||||
\(884\) | −4.60555 | −0.154901 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.6333 | −1.33151 | ||||||||
\(887\) | −4.60555 | −0.154639 | −0.0773196 | − | 0.997006i | \(-0.524636\pi\) | ||||
−0.0773196 | + | 0.997006i | \(0.524636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.15559 | 0.105835 | ||||||||
\(890\) | −3.21110 | −0.107636 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17.3944 | −0.582409 | ||||||||
\(893\) | 60.8444 | 2.03608 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0278 | 0.368617 | ||||||||
\(896\) | 2.60555 | 0.0870454 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.63331 | −0.321468 | ||||||||
\(899\) | 9.21110 | 0.307207 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.39445 | 0.245936 | ||||||||
\(905\) | 19.2111 | 0.638599 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.3667 | −0.410629 | −0.205315 | − | 0.978696i | \(-0.565822\pi\) | ||||
−0.205315 | + | 0.978696i | \(0.565822\pi\) | |||||||
\(908\) | −6.42221 | −0.213128 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.60555 | −0.0863732 | ||||||||
\(911\) | −15.6333 | −0.517955 | −0.258977 | − | 0.965883i | \(-0.583385\pi\) | ||||
−0.258977 | + | 0.965883i | \(0.583385\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 17.3944 | 0.575357 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.183346 | 0.00605793 | ||||||||
\(917\) | −43.2666 | −1.42879 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.0000 | −1.71532 | −0.857661 | − | 0.514216i | \(-0.828083\pi\) | ||||
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | −4.60555 | −0.151841 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.21110 | −0.105752 | ||||||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.2111 | 0.368619 | ||||||||
\(926\) | −12.1833 | −0.400370 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.60555 | −0.151185 | ||||||||
\(929\) | 40.0555 | 1.31418 | 0.657089 | − | 0.753813i | \(-0.271787\pi\) | ||||
0.657089 | + | 0.753813i | \(0.271787\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.39445 | −0.0457012 | ||||||||
\(932\) | 1.81665 | 0.0595065 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.57779 | −0.182511 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.6333 | −0.445381 | −0.222690 | − | 0.974889i | \(-0.571484\pi\) | ||||
−0.222690 | + | 0.974889i | \(0.571484\pi\) | |||||||
\(938\) | −18.7889 | −0.613479 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.21110 | −0.300433 | ||||||||
\(941\) | −21.6333 | −0.705226 | −0.352613 | − | 0.935769i | \(-0.614707\pi\) | ||||
−0.352613 | + | 0.935769i | \(0.614707\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.7889 | 0.481593 | ||||||||
\(944\) | 9.21110 | 0.299796 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.4222 | −1.37854 | −0.689268 | − | 0.724506i | \(-0.742068\pi\) | ||||
−0.689268 | + | 0.724506i | \(0.742068\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.60555 | 0.214425 | ||||||||
\(950\) | −6.60555 | −0.214312 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.0000 | −0.388922 | ||||||||
\(953\) | −16.6056 | −0.537907 | −0.268953 | − | 0.963153i | \(-0.586678\pi\) | ||||
−0.268953 | + | 0.963153i | \(0.586678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0000 | −0.388311 | ||||||||
\(956\) | −18.4222 | −0.595817 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.4222 | 0.595194 | ||||||||
\(959\) | 56.3667 | 1.82018 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −11.2111 | −0.361460 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | 14.6056 | 0.470169 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.6056 | −0.855577 | −0.427788 | − | 0.903879i | \(-0.640707\pi\) | ||||
−0.427788 | + | 0.903879i | \(0.640707\pi\) | |||||||
\(968\) | 11.0000 | 0.353553 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.60555 | 0.212091 | ||||||||
\(971\) | 19.3944 | 0.622397 | 0.311199 | − | 0.950345i | \(-0.399270\pi\) | ||||
0.311199 | + | 0.950345i | \(0.399270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −37.5778 | −1.20469 | ||||||||
\(974\) | −2.97224 | −0.0952368 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.21110 | −0.230822 | ||||||||
\(977\) | −57.6333 | −1.84385 | −0.921926 | − | 0.387365i | \(-0.873385\pi\) | ||||
−0.921926 | + | 0.387365i | \(0.873385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.211103 | 0.00674342 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32.2389 | 1.02878 | ||||||||
\(983\) | −27.6333 | −0.881366 | −0.440683 | − | 0.897663i | \(-0.645264\pi\) | ||||
−0.440683 | + | 0.897663i | \(0.645264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.4222 | −0.778156 | ||||||||
\(986\) | 21.2111 | 0.675499 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.60555 | 0.210151 | ||||||||
\(989\) | −24.0000 | −0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.6333 | −1.00487 | −0.502433 | − | 0.864616i | \(-0.667561\pi\) | ||||
−0.502433 | + | 0.864616i | \(0.667561\pi\) | |||||||
\(992\) | −2.00000 | −0.0635001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 31.2666 | 0.991717 | ||||||||
\(995\) | −5.21110 | −0.165203 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.78890 | 0.151666 | 0.0758330 | − | 0.997121i | \(-0.475838\pi\) | ||||
0.0758330 | + | 0.997121i | \(0.475838\pi\) | |||||||
\(998\) | −27.8167 | −0.880521 | ||||||||
\(999\) | 0 | 0 |
(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 | 1170.2.a.p.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1170.2.a.q.1.1 | yes | 2 | ||
4.3 | odd | 2 | 9360.2.a.cf.1.2 | 2 | |||
5.2 | odd | 4 | 5850.2.e.bl.5149.1 | 4 | |||
5.3 | odd | 4 | 5850.2.e.bl.5149.4 | 4 | |||
5.4 | even | 2 | 5850.2.a.ck.1.2 | 2 | |||
12.11 | even | 2 | 9360.2.a.cn.1.2 | 2 | |||
15.2 | even | 4 | 5850.2.e.bj.5149.3 | 4 | |||
15.8 | even | 4 | 5850.2.e.bj.5149.2 | 4 | |||
15.14 | odd | 2 | 5850.2.a.ce.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1170.2.a.p.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1170.2.a.q.1.1 | yes | 2 | 3.2 | odd | 2 | ||
5850.2.a.ce.1.2 | 2 | 15.14 | odd | 2 | |||
5850.2.a.ck.1.2 | 2 | 5.4 | even | 2 | |||
5850.2.e.bj.5149.2 | 4 | 15.8 | even | 4 | |||
5850.2.e.bj.5149.3 | 4 | 15.2 | even | 4 | |||
5850.2.e.bl.5149.1 | 4 | 5.2 | odd | 4 | |||
5850.2.e.bl.5149.4 | 4 | 5.3 | odd | 4 | |||
9360.2.a.cf.1.2 | 2 | 4.3 | odd | 2 | |||
9360.2.a.cn.1.2 | 2 | 12.11 | even | 2 |