Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
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: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.60555 | 0.984806 | 0.492403 | − | 0.870367i | \(-0.336119\pi\) | ||||
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.60555 | −0.696363 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.60555 | 0.631939 | 0.315970 | − | 0.948769i | \(-0.397670\pi\) | ||||
0.315970 | + | 0.948769i | \(0.397670\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.60555 | −0.597754 | −0.298877 | − | 0.954292i | \(-0.596612\pi\) | ||||
−0.298877 | + | 0.954292i | \(0.596612\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.60555 | −0.568578 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.60555 | 1.79438 | 0.897191 | − | 0.441643i | \(-0.145604\pi\) | ||||
0.897191 | + | 0.441643i | \(0.145604\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.60555 | 0.492403 | ||||||||
\(29\) | −2.60555 | −0.483839 | −0.241919 | − | 0.970296i | \(-0.577777\pi\) | ||||
−0.241919 | + | 0.970296i | \(0.577777\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.60555 | −0.446848 | ||||||||
\(35\) | −2.60555 | −0.440419 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.21110 | 0.856700 | 0.428350 | − | 0.903613i | \(-0.359095\pi\) | ||||
0.428350 | + | 0.903613i | \(0.359095\pi\) | |||||||
\(38\) | 2.60555 | 0.422676 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 11.2111 | 1.75088 | 0.875440 | − | 0.483327i | \(-0.160572\pi\) | ||||
0.875440 | + | 0.483327i | \(0.160572\pi\) | |||||||
\(42\) | 2.60555 | 0.402045 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −8.60555 | −1.26882 | ||||||||
\(47\) | 5.21110 | 0.760117 | 0.380059 | − | 0.924962i | \(-0.375904\pi\) | ||||
0.380059 | + | 0.924962i | \(0.375904\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −0.211103 | −0.0301575 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −2.60555 | −0.364850 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.60555 | −0.348181 | ||||||||
\(57\) | 2.60555 | 0.345114 | ||||||||
\(58\) | 2.60555 | 0.342126 | ||||||||
\(59\) | 5.21110 | 0.678428 | 0.339214 | − | 0.940709i | \(-0.389839\pi\) | ||||
0.339214 | + | 0.940709i | \(0.389839\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 3.21110 | 0.411140 | 0.205570 | − | 0.978642i | \(-0.434095\pi\) | ||||
0.205570 | + | 0.978642i | \(0.434095\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 2.60555 | 0.328269 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2111 | −1.36965 | −0.684827 | − | 0.728706i | \(-0.740122\pi\) | ||||
−0.684827 | + | 0.728706i | \(0.740122\pi\) | |||||||
\(68\) | 2.60555 | 0.315970 | ||||||||
\(69\) | −8.60555 | −1.03599 | ||||||||
\(70\) | 2.60555 | 0.311423 | ||||||||
\(71\) | 5.21110 | 0.618444 | 0.309222 | − | 0.950990i | \(-0.399931\pi\) | ||||
0.309222 | + | 0.950990i | \(0.399931\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −8.60555 | −1.00720 | −0.503602 | − | 0.863936i | \(-0.667992\pi\) | ||||
−0.503602 | + | 0.863936i | \(0.667992\pi\) | |||||||
\(74\) | −5.21110 | −0.605778 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −2.60555 | −0.298877 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4222 | 1.62262 | 0.811312 | − | 0.584613i | \(-0.198754\pi\) | ||||
0.811312 | + | 0.584613i | \(0.198754\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.2111 | −1.23806 | ||||||||
\(83\) | −17.2111 | −1.88916 | −0.944582 | − | 0.328276i | \(-0.893533\pi\) | ||||
−0.944582 | + | 0.328276i | \(0.893533\pi\) | |||||||
\(84\) | −2.60555 | −0.284289 | ||||||||
\(85\) | −2.60555 | −0.282612 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 2.60555 | 0.279344 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.788897 | 0.0836230 | 0.0418115 | − | 0.999126i | \(-0.486687\pi\) | ||||
0.0418115 | + | 0.999126i | \(0.486687\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.60555 | 0.897191 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | −5.21110 | −0.537484 | ||||||||
\(95\) | 2.60555 | 0.267324 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −8.60555 | −0.873761 | −0.436881 | − | 0.899519i | \(-0.643917\pi\) | ||||
−0.436881 | + | 0.899519i | \(0.643917\pi\) | |||||||
\(98\) | 0.211103 | 0.0213246 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 14.6056 | 1.45331 | 0.726653 | − | 0.687004i | \(-0.241075\pi\) | ||||
0.726653 | + | 0.687004i | \(0.241075\pi\) | |||||||
\(102\) | 2.60555 | 0.257988 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.60555 | 0.254276 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −8.60555 | −0.824262 | −0.412131 | − | 0.911125i | \(-0.635215\pi\) | ||||
−0.412131 | + | 0.911125i | \(0.635215\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.21110 | −0.494616 | ||||||||
\(112\) | 2.60555 | 0.246201 | ||||||||
\(113\) | 7.81665 | 0.735329 | 0.367664 | − | 0.929959i | \(-0.380157\pi\) | ||||
0.367664 | + | 0.929959i | \(0.380157\pi\) | |||||||
\(114\) | −2.60555 | −0.244032 | ||||||||
\(115\) | −8.60555 | −0.802472 | ||||||||
\(116\) | −2.60555 | −0.241919 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.21110 | −0.479721 | ||||||||
\(119\) | 6.78890 | 0.622337 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | −3.21110 | −0.290720 | ||||||||
\(123\) | −11.2111 | −1.01087 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.60555 | −0.232121 | ||||||||
\(127\) | 13.2111 | 1.17230 | 0.586148 | − | 0.810204i | \(-0.300644\pi\) | ||||
0.586148 | + | 0.810204i | \(0.300644\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3944 | 1.34502 | 0.672510 | − | 0.740088i | \(-0.265216\pi\) | ||||
0.672510 | + | 0.740088i | \(0.265216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.78890 | −0.588672 | ||||||||
\(134\) | 11.2111 | 0.968492 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −2.60555 | −0.223424 | ||||||||
\(137\) | −11.2111 | −0.957829 | −0.478915 | − | 0.877862i | \(-0.658970\pi\) | ||||
−0.478915 | + | 0.877862i | \(0.658970\pi\) | |||||||
\(138\) | 8.60555 | 0.732553 | ||||||||
\(139\) | 2.78890 | 0.236551 | 0.118276 | − | 0.992981i | \(-0.462263\pi\) | ||||
0.118276 | + | 0.992981i | \(0.462263\pi\) | |||||||
\(140\) | −2.60555 | −0.220209 | ||||||||
\(141\) | −5.21110 | −0.438854 | ||||||||
\(142\) | −5.21110 | −0.437306 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.60555 | 0.216379 | ||||||||
\(146\) | 8.60555 | 0.712200 | ||||||||
\(147\) | 0.211103 | 0.0174114 | ||||||||
\(148\) | 5.21110 | 0.428350 | ||||||||
\(149\) | −0.788897 | −0.0646290 | −0.0323145 | − | 0.999478i | \(-0.510288\pi\) | ||||
−0.0323145 | + | 0.999478i | \(0.510288\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 6.00000 | 0.488273 | 0.244137 | − | 0.969741i | \(-0.421495\pi\) | ||||
0.244137 | + | 0.969741i | \(0.421495\pi\) | |||||||
\(152\) | 2.60555 | 0.211338 | ||||||||
\(153\) | 2.60555 | 0.210646 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.42221 | −0.672165 | −0.336083 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336083 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(158\) | −14.4222 | −1.14737 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 22.4222 | 1.76712 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −4.42221 | −0.346374 | −0.173187 | − | 0.984889i | \(-0.555406\pi\) | ||||
−0.173187 | + | 0.984889i | \(0.555406\pi\) | |||||||
\(164\) | 11.2111 | 0.875440 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.2111 | 1.33584 | ||||||||
\(167\) | −5.21110 | −0.403247 | −0.201624 | − | 0.979463i | \(-0.564622\pi\) | ||||
−0.201624 | + | 0.979463i | \(0.564622\pi\) | |||||||
\(168\) | 2.60555 | 0.201023 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.60555 | 0.199837 | ||||||||
\(171\) | −2.60555 | −0.199251 | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | −16.4222 | −1.24856 | −0.624279 | − | 0.781202i | \(-0.714607\pi\) | ||||
−0.624279 | + | 0.781202i | \(0.714607\pi\) | |||||||
\(174\) | −2.60555 | −0.197526 | ||||||||
\(175\) | 2.60555 | 0.196961 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.21110 | −0.391690 | ||||||||
\(178\) | −0.788897 | −0.0591304 | ||||||||
\(179\) | −1.81665 | −0.135783 | −0.0678915 | − | 0.997693i | \(-0.521627\pi\) | ||||
−0.0678915 | + | 0.997693i | \(0.521627\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 20.4222 | 1.51797 | 0.758985 | − | 0.651108i | \(-0.225695\pi\) | ||||
0.758985 | + | 0.651108i | \(0.225695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.21110 | −0.237372 | ||||||||
\(184\) | −8.60555 | −0.634410 | ||||||||
\(185\) | −5.21110 | −0.383128 | ||||||||
\(186\) | −6.00000 | −0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.21110 | 0.380059 | ||||||||
\(189\) | −2.60555 | −0.189526 | ||||||||
\(190\) | −2.60555 | −0.189027 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −13.8167 | −0.994545 | −0.497272 | − | 0.867595i | \(-0.665665\pi\) | ||||
−0.497272 | + | 0.867595i | \(0.665665\pi\) | |||||||
\(194\) | 8.60555 | 0.617843 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.211103 | −0.0150788 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.42221 | 0.455258 | 0.227629 | − | 0.973748i | \(-0.426903\pi\) | ||||
0.227629 | + | 0.973748i | \(0.426903\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 11.2111 | 0.790770 | ||||||||
\(202\) | −14.6056 | −1.02764 | ||||||||
\(203\) | −6.78890 | −0.476487 | ||||||||
\(204\) | −2.60555 | −0.182425 | ||||||||
\(205\) | −11.2111 | −0.783017 | ||||||||
\(206\) | −4.00000 | −0.278693 | ||||||||
\(207\) | 8.60555 | 0.598127 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.60555 | −0.179800 | ||||||||
\(211\) | −2.78890 | −0.191996 | −0.0959978 | − | 0.995382i | \(-0.530604\pi\) | ||||
−0.0959978 | + | 0.995382i | \(0.530604\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | −5.21110 | −0.357059 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −15.6333 | −1.06126 | ||||||||
\(218\) | 8.60555 | 0.582841 | ||||||||
\(219\) | 8.60555 | 0.581509 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.21110 | 0.349746 | ||||||||
\(223\) | 19.8167 | 1.32702 | 0.663511 | − | 0.748167i | \(-0.269066\pi\) | ||||
0.663511 | + | 0.748167i | \(0.269066\pi\) | |||||||
\(224\) | −2.60555 | −0.174091 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −7.81665 | −0.519956 | ||||||||
\(227\) | −24.0000 | −1.59294 | −0.796468 | − | 0.604681i | \(-0.793301\pi\) | ||||
−0.796468 | + | 0.604681i | \(0.793301\pi\) | |||||||
\(228\) | 2.60555 | 0.172557 | ||||||||
\(229\) | 1.81665 | 0.120048 | 0.0600239 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600239 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(230\) | 8.60555 | 0.567433 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.60555 | 0.171063 | ||||||||
\(233\) | −19.8167 | −1.29823 | −0.649116 | − | 0.760689i | \(-0.724861\pi\) | ||||
−0.649116 | + | 0.760689i | \(0.724861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.21110 | −0.339935 | ||||||||
\(236\) | 5.21110 | 0.339214 | ||||||||
\(237\) | −14.4222 | −0.936823 | ||||||||
\(238\) | −6.78890 | −0.440059 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 22.4222 | 1.44434 | 0.722171 | − | 0.691715i | \(-0.243145\pi\) | ||||
0.722171 | + | 0.691715i | \(0.243145\pi\) | |||||||
\(242\) | 11.0000 | 0.707107 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.21110 | 0.205570 | ||||||||
\(245\) | 0.211103 | 0.0134868 | ||||||||
\(246\) | 11.2111 | 0.714794 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | 17.2111 | 1.09071 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 20.6056 | 1.30061 | 0.650305 | − | 0.759673i | \(-0.274641\pi\) | ||||
0.650305 | + | 0.759673i | \(0.274641\pi\) | |||||||
\(252\) | 2.60555 | 0.164134 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.2111 | −0.828938 | ||||||||
\(255\) | 2.60555 | 0.163166 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.3944 | 1.33455 | 0.667275 | − | 0.744812i | \(-0.267461\pi\) | ||||
0.667275 | + | 0.744812i | \(0.267461\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | 13.5778 | 0.843683 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.60555 | −0.161280 | ||||||||
\(262\) | −15.3944 | −0.951072 | ||||||||
\(263\) | 13.8167 | 0.851971 | 0.425986 | − | 0.904730i | \(-0.359927\pi\) | ||||
0.425986 | + | 0.904730i | \(0.359927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 6.78890 | 0.416254 | ||||||||
\(267\) | −0.788897 | −0.0482797 | ||||||||
\(268\) | −11.2111 | −0.684827 | ||||||||
\(269\) | 4.18335 | 0.255063 | 0.127532 | − | 0.991835i | \(-0.459295\pi\) | ||||
0.127532 | + | 0.991835i | \(0.459295\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 28.4222 | 1.72653 | 0.863263 | − | 0.504754i | \(-0.168417\pi\) | ||||
0.863263 | + | 0.504754i | \(0.168417\pi\) | |||||||
\(272\) | 2.60555 | 0.157985 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2111 | 0.677287 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.60555 | −0.517993 | ||||||||
\(277\) | −12.4222 | −0.746378 | −0.373189 | − | 0.927755i | \(-0.621736\pi\) | ||||
−0.373189 | + | 0.927755i | \(0.621736\pi\) | |||||||
\(278\) | −2.78890 | −0.167267 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 2.60555 | 0.155711 | ||||||||
\(281\) | 12.7889 | 0.762922 | 0.381461 | − | 0.924385i | \(-0.375421\pi\) | ||||
0.381461 | + | 0.924385i | \(0.375421\pi\) | |||||||
\(282\) | 5.21110 | 0.310317 | ||||||||
\(283\) | 18.4222 | 1.09509 | 0.547543 | − | 0.836777i | \(-0.315563\pi\) | ||||
0.547543 | + | 0.836777i | \(0.315563\pi\) | |||||||
\(284\) | 5.21110 | 0.309222 | ||||||||
\(285\) | −2.60555 | −0.154340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.2111 | 1.72428 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −10.2111 | −0.600653 | ||||||||
\(290\) | −2.60555 | −0.153003 | ||||||||
\(291\) | 8.60555 | 0.504466 | ||||||||
\(292\) | −8.60555 | −0.503602 | ||||||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | −0.211103 | −0.0123118 | ||||||||
\(295\) | −5.21110 | −0.303402 | ||||||||
\(296\) | −5.21110 | −0.302889 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.788897 | 0.0456996 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −20.8444 | −1.20145 | ||||||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | −14.6056 | −0.839067 | ||||||||
\(304\) | −2.60555 | −0.149439 | ||||||||
\(305\) | −3.21110 | −0.183867 | ||||||||
\(306\) | −2.60555 | −0.148949 | ||||||||
\(307\) | −23.2111 | −1.32473 | −0.662364 | − | 0.749182i | \(-0.730447\pi\) | ||||
−0.662364 | + | 0.749182i | \(0.730447\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | −6.00000 | −0.340777 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.4222 | 1.83261 | 0.916306 | − | 0.400480i | \(-0.131156\pi\) | ||||
0.916306 | + | 0.400480i | \(0.131156\pi\) | |||||||
\(314\) | 8.42221 | 0.475293 | ||||||||
\(315\) | −2.60555 | −0.146806 | ||||||||
\(316\) | 14.4222 | 0.811312 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 6.00000 | 0.336463 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.4222 | −1.24954 | ||||||||
\(323\) | −6.78890 | −0.377744 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.42221 | 0.244923 | ||||||||
\(327\) | 8.60555 | 0.475888 | ||||||||
\(328\) | −11.2111 | −0.619030 | ||||||||
\(329\) | 13.5778 | 0.748568 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.39445 | 0.516366 | 0.258183 | − | 0.966096i | \(-0.416876\pi\) | ||||
0.258183 | + | 0.966096i | \(0.416876\pi\) | |||||||
\(332\) | −17.2111 | −0.944582 | ||||||||
\(333\) | 5.21110 | 0.285567 | ||||||||
\(334\) | 5.21110 | 0.285139 | ||||||||
\(335\) | 11.2111 | 0.612528 | ||||||||
\(336\) | −2.60555 | −0.142144 | ||||||||
\(337\) | 29.6333 | 1.61423 | 0.807115 | − | 0.590395i | \(-0.201028\pi\) | ||||
0.807115 | + | 0.590395i | \(0.201028\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.81665 | −0.424542 | ||||||||
\(340\) | −2.60555 | −0.141306 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.60555 | 0.140892 | ||||||||
\(343\) | −18.7889 | −1.01451 | ||||||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 8.60555 | 0.463307 | ||||||||
\(346\) | 16.4222 | 0.882863 | ||||||||
\(347\) | 15.6333 | 0.839240 | 0.419620 | − | 0.907700i | \(-0.362163\pi\) | ||||
0.419620 | + | 0.907700i | \(0.362163\pi\) | |||||||
\(348\) | 2.60555 | 0.139672 | ||||||||
\(349\) | 13.8167 | 0.739589 | 0.369794 | − | 0.929114i | \(-0.379428\pi\) | ||||
0.369794 | + | 0.929114i | \(0.379428\pi\) | |||||||
\(350\) | −2.60555 | −0.139273 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.2111 | 1.23540 | 0.617701 | − | 0.786413i | \(-0.288064\pi\) | ||||
0.617701 | + | 0.786413i | \(0.288064\pi\) | |||||||
\(354\) | 5.21110 | 0.276967 | ||||||||
\(355\) | −5.21110 | −0.276577 | ||||||||
\(356\) | 0.788897 | 0.0418115 | ||||||||
\(357\) | −6.78890 | −0.359307 | ||||||||
\(358\) | 1.81665 | 0.0960131 | ||||||||
\(359\) | −27.6333 | −1.45843 | −0.729215 | − | 0.684285i | \(-0.760115\pi\) | ||||
−0.729215 | + | 0.684285i | \(0.760115\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −12.2111 | −0.642690 | ||||||||
\(362\) | −20.4222 | −1.07337 | ||||||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.60555 | 0.450435 | ||||||||
\(366\) | 3.21110 | 0.167847 | ||||||||
\(367\) | 23.6333 | 1.23365 | 0.616824 | − | 0.787101i | \(-0.288419\pi\) | ||||
0.616824 | + | 0.787101i | \(0.288419\pi\) | |||||||
\(368\) | 8.60555 | 0.448595 | ||||||||
\(369\) | 11.2111 | 0.583627 | ||||||||
\(370\) | 5.21110 | 0.270912 | ||||||||
\(371\) | 15.6333 | 0.811641 | ||||||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | 8.42221 | 0.436085 | 0.218043 | − | 0.975939i | \(-0.430033\pi\) | ||||
0.218043 | + | 0.975939i | \(0.430033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −5.21110 | −0.268742 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.60555 | 0.134015 | ||||||||
\(379\) | 1.02776 | 0.0527923 | 0.0263961 | − | 0.999652i | \(-0.491597\pi\) | ||||
0.0263961 | + | 0.999652i | \(0.491597\pi\) | |||||||
\(380\) | 2.60555 | 0.133662 | ||||||||
\(381\) | −13.2111 | −0.676825 | ||||||||
\(382\) | 12.0000 | 0.613973 | ||||||||
\(383\) | −15.6333 | −0.798825 | −0.399412 | − | 0.916771i | \(-0.630786\pi\) | ||||
−0.399412 | + | 0.916771i | \(0.630786\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8167 | 0.703249 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | −8.60555 | −0.436881 | ||||||||
\(389\) | 2.60555 | 0.132107 | 0.0660533 | − | 0.997816i | \(-0.478959\pi\) | ||||
0.0660533 | + | 0.997816i | \(0.478959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.4222 | 1.13394 | ||||||||
\(392\) | 0.211103 | 0.0106623 | ||||||||
\(393\) | −15.3944 | −0.776547 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | −14.4222 | −0.725660 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 39.6333 | 1.98914 | 0.994569 | − | 0.104076i | \(-0.0331885\pi\) | ||||
0.994569 | + | 0.104076i | \(0.0331885\pi\) | |||||||
\(398\) | −6.42221 | −0.321916 | ||||||||
\(399\) | 6.78890 | 0.339870 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 23.2111 | 1.15911 | 0.579554 | − | 0.814934i | \(-0.303227\pi\) | ||||
0.579554 | + | 0.814934i | \(0.303227\pi\) | |||||||
\(402\) | −11.2111 | −0.559159 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.6056 | 0.726653 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 6.78890 | 0.336927 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.60555 | 0.128994 | ||||||||
\(409\) | 29.2111 | 1.44440 | 0.722198 | − | 0.691686i | \(-0.243132\pi\) | ||||
0.722198 | + | 0.691686i | \(0.243132\pi\) | |||||||
\(410\) | 11.2111 | 0.553677 | ||||||||
\(411\) | 11.2111 | 0.553003 | ||||||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | 13.5778 | 0.668120 | ||||||||
\(414\) | −8.60555 | −0.422940 | ||||||||
\(415\) | 17.2111 | 0.844860 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.78890 | −0.136573 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.8167 | 1.26123 | 0.630613 | − | 0.776097i | \(-0.282804\pi\) | ||||
0.630613 | + | 0.776097i | \(0.282804\pi\) | |||||||
\(420\) | 2.60555 | 0.127138 | ||||||||
\(421\) | −1.81665 | −0.0885383 | −0.0442691 | − | 0.999020i | \(-0.514096\pi\) | ||||
−0.0442691 | + | 0.999020i | \(0.514096\pi\) | |||||||
\(422\) | 2.78890 | 0.135761 | ||||||||
\(423\) | 5.21110 | 0.253372 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 2.60555 | 0.126388 | ||||||||
\(426\) | 5.21110 | 0.252479 | ||||||||
\(427\) | 8.36669 | 0.404893 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −4.78890 | −0.230140 | −0.115070 | − | 0.993357i | \(-0.536709\pi\) | ||||
−0.115070 | + | 0.993357i | \(0.536709\pi\) | |||||||
\(434\) | 15.6333 | 0.750423 | ||||||||
\(435\) | −2.60555 | −0.124927 | ||||||||
\(436\) | −8.60555 | −0.412131 | ||||||||
\(437\) | −22.4222 | −1.07260 | ||||||||
\(438\) | −8.60555 | −0.411189 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.211103 | −0.0100525 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.6333 | −1.31290 | −0.656449 | − | 0.754370i | \(-0.727942\pi\) | ||||
−0.656449 | + | 0.754370i | \(0.727942\pi\) | |||||||
\(444\) | −5.21110 | −0.247308 | ||||||||
\(445\) | −0.788897 | −0.0373973 | ||||||||
\(446\) | −19.8167 | −0.938346 | ||||||||
\(447\) | 0.788897 | 0.0373136 | ||||||||
\(448\) | 2.60555 | 0.123101 | ||||||||
\(449\) | −9.63331 | −0.454624 | −0.227312 | − | 0.973822i | \(-0.572994\pi\) | ||||
−0.227312 | + | 0.973822i | \(0.572994\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.81665 | 0.367664 | ||||||||
\(453\) | −6.00000 | −0.281905 | ||||||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.60555 | −0.122016 | ||||||||
\(457\) | 12.2389 | 0.572510 | 0.286255 | − | 0.958154i | \(-0.407590\pi\) | ||||
0.286255 | + | 0.958154i | \(0.407590\pi\) | |||||||
\(458\) | −1.81665 | −0.0848867 | ||||||||
\(459\) | −2.60555 | −0.121617 | ||||||||
\(460\) | −8.60555 | −0.401236 | ||||||||
\(461\) | −9.63331 | −0.448668 | −0.224334 | − | 0.974512i | \(-0.572021\pi\) | ||||
−0.224334 | + | 0.974512i | \(0.572021\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.6056 | −1.79415 | −0.897076 | − | 0.441876i | \(-0.854313\pi\) | ||||
−0.897076 | + | 0.441876i | \(0.854313\pi\) | |||||||
\(464\) | −2.60555 | −0.120960 | ||||||||
\(465\) | −6.00000 | −0.278243 | ||||||||
\(466\) | 19.8167 | 0.917989 | ||||||||
\(467\) | 1.57779 | 0.0730116 | 0.0365058 | − | 0.999333i | \(-0.488377\pi\) | ||||
0.0365058 | + | 0.999333i | \(0.488377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.2111 | −1.34884 | ||||||||
\(470\) | 5.21110 | 0.240370 | ||||||||
\(471\) | 8.42221 | 0.388075 | ||||||||
\(472\) | −5.21110 | −0.239860 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 14.4222 | 0.662434 | ||||||||
\(475\) | −2.60555 | −0.119551 | ||||||||
\(476\) | 6.78890 | 0.311169 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.4222 | 1.57279 | 0.786395 | − | 0.617724i | \(-0.211945\pi\) | ||||
0.786395 | + | 0.617724i | \(0.211945\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22.4222 | −1.02130 | ||||||||
\(483\) | −22.4222 | −1.02025 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 8.60555 | 0.390758 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 37.0278 | 1.67789 | 0.838944 | − | 0.544218i | \(-0.183174\pi\) | ||||
0.838944 | + | 0.544218i | \(0.183174\pi\) | |||||||
\(488\) | −3.21110 | −0.145360 | ||||||||
\(489\) | 4.42221 | 0.199979 | ||||||||
\(490\) | −0.211103 | −0.00953664 | ||||||||
\(491\) | 13.8167 | 0.623537 | 0.311768 | − | 0.950158i | \(-0.399079\pi\) | ||||
0.311768 | + | 0.950158i | \(0.399079\pi\) | |||||||
\(492\) | −11.2111 | −0.505436 | ||||||||
\(493\) | −6.78890 | −0.305757 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 13.5778 | 0.609047 | ||||||||
\(498\) | −17.2111 | −0.771248 | ||||||||
\(499\) | 13.0278 | 0.583202 | 0.291601 | − | 0.956540i | \(-0.405812\pi\) | ||||
0.291601 | + | 0.956540i | \(0.405812\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 5.21110 | 0.232815 | ||||||||
\(502\) | −20.6056 | −0.919671 | ||||||||
\(503\) | −41.4500 | −1.84816 | −0.924081 | − | 0.382196i | \(-0.875168\pi\) | ||||
−0.924081 | + | 0.382196i | \(0.875168\pi\) | |||||||
\(504\) | −2.60555 | −0.116060 | ||||||||
\(505\) | −14.6056 | −0.649939 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.2111 | 0.586148 | ||||||||
\(509\) | −9.63331 | −0.426989 | −0.213494 | − | 0.976944i | \(-0.568485\pi\) | ||||
−0.213494 | + | 0.976944i | \(0.568485\pi\) | |||||||
\(510\) | −2.60555 | −0.115376 | ||||||||
\(511\) | −22.4222 | −0.991900 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.60555 | 0.115038 | ||||||||
\(514\) | −21.3944 | −0.943669 | ||||||||
\(515\) | −4.00000 | −0.176261 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.5778 | −0.596574 | ||||||||
\(519\) | 16.4222 | 0.720855 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.6333 | −0.947772 | −0.473886 | − | 0.880586i | \(-0.657149\pi\) | ||||
−0.473886 | + | 0.880586i | \(0.657149\pi\) | |||||||
\(522\) | 2.60555 | 0.114042 | ||||||||
\(523\) | −24.8444 | −1.08637 | −0.543185 | − | 0.839613i | \(-0.682782\pi\) | ||||
−0.543185 | + | 0.839613i | \(0.682782\pi\) | |||||||
\(524\) | 15.3944 | 0.672510 | ||||||||
\(525\) | −2.60555 | −0.113716 | ||||||||
\(526\) | −13.8167 | −0.602435 | ||||||||
\(527\) | −15.6333 | −0.680998 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 51.0555 | 2.21980 | ||||||||
\(530\) | 6.00000 | 0.260623 | ||||||||
\(531\) | 5.21110 | 0.226143 | ||||||||
\(532\) | −6.78890 | −0.294336 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.788897 | 0.0341389 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.2111 | 0.484246 | ||||||||
\(537\) | 1.81665 | 0.0783944 | ||||||||
\(538\) | −4.18335 | −0.180357 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 43.0278 | 1.84991 | 0.924954 | − | 0.380079i | \(-0.124103\pi\) | ||||
0.924954 | + | 0.380079i | \(0.124103\pi\) | |||||||
\(542\) | −28.4222 | −1.22084 | ||||||||
\(543\) | −20.4222 | −0.876401 | ||||||||
\(544\) | −2.60555 | −0.111712 | ||||||||
\(545\) | 8.60555 | 0.368621 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.4222 | −0.616649 | −0.308324 | − | 0.951281i | \(-0.599768\pi\) | ||||
−0.308324 | + | 0.951281i | \(0.599768\pi\) | |||||||
\(548\) | −11.2111 | −0.478915 | ||||||||
\(549\) | 3.21110 | 0.137047 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.78890 | 0.289217 | ||||||||
\(552\) | 8.60555 | 0.366277 | ||||||||
\(553\) | 37.5778 | 1.59797 | ||||||||
\(554\) | 12.4222 | 0.527769 | ||||||||
\(555\) | 5.21110 | 0.221199 | ||||||||
\(556\) | 2.78890 | 0.118276 | ||||||||
\(557\) | 40.4222 | 1.71274 | 0.856372 | − | 0.516360i | \(-0.172713\pi\) | ||||
0.856372 | + | 0.516360i | \(0.172713\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.60555 | −0.110105 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.7889 | −0.539467 | ||||||||
\(563\) | 38.0555 | 1.60385 | 0.801924 | − | 0.597426i | \(-0.203810\pi\) | ||||
0.801924 | + | 0.597426i | \(0.203810\pi\) | |||||||
\(564\) | −5.21110 | −0.219427 | ||||||||
\(565\) | −7.81665 | −0.328849 | ||||||||
\(566\) | −18.4222 | −0.774343 | ||||||||
\(567\) | 2.60555 | 0.109423 | ||||||||
\(568\) | −5.21110 | −0.218653 | ||||||||
\(569\) | 9.63331 | 0.403849 | 0.201925 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201925 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(570\) | 2.60555 | 0.109135 | ||||||||
\(571\) | −42.0555 | −1.75997 | −0.879984 | − | 0.475003i | \(-0.842447\pi\) | ||||
−0.879984 | + | 0.475003i | \(0.842447\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | −29.2111 | −1.21925 | ||||||||
\(575\) | 8.60555 | 0.358876 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 44.6056 | 1.85695 | 0.928477 | − | 0.371391i | \(-0.121119\pi\) | ||||
0.928477 | + | 0.371391i | \(0.121119\pi\) | |||||||
\(578\) | 10.2111 | 0.424726 | ||||||||
\(579\) | 13.8167 | 0.574201 | ||||||||
\(580\) | 2.60555 | 0.108190 | ||||||||
\(581\) | −44.8444 | −1.86046 | ||||||||
\(582\) | −8.60555 | −0.356712 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.60555 | 0.356100 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | −22.4222 | −0.925463 | −0.462732 | − | 0.886498i | \(-0.653131\pi\) | ||||
−0.462732 | + | 0.886498i | \(0.653131\pi\) | |||||||
\(588\) | 0.211103 | 0.00870572 | ||||||||
\(589\) | 15.6333 | 0.644159 | ||||||||
\(590\) | 5.21110 | 0.214538 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | 5.21110 | 0.214175 | ||||||||
\(593\) | 4.42221 | 0.181598 | 0.0907991 | − | 0.995869i | \(-0.471058\pi\) | ||||
0.0907991 | + | 0.995869i | \(0.471058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.78890 | −0.278318 | ||||||||
\(596\) | −0.788897 | −0.0323145 | ||||||||
\(597\) | −6.42221 | −0.262843 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −41.6333 | −1.69826 | −0.849129 | − | 0.528185i | \(-0.822873\pi\) | ||||
−0.849129 | + | 0.528185i | \(0.822873\pi\) | |||||||
\(602\) | 20.8444 | 0.849555 | ||||||||
\(603\) | −11.2111 | −0.456551 | ||||||||
\(604\) | 6.00000 | 0.244137 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 14.6056 | 0.593310 | ||||||||
\(607\) | 2.78890 | 0.113198 | 0.0565989 | − | 0.998397i | \(-0.481974\pi\) | ||||
0.0565989 | + | 0.998397i | \(0.481974\pi\) | |||||||
\(608\) | 2.60555 | 0.105669 | ||||||||
\(609\) | 6.78890 | 0.275100 | ||||||||
\(610\) | 3.21110 | 0.130014 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.60555 | 0.105323 | ||||||||
\(613\) | 18.7889 | 0.758876 | 0.379438 | − | 0.925217i | \(-0.376117\pi\) | ||||
0.379438 | + | 0.925217i | \(0.376117\pi\) | |||||||
\(614\) | 23.2111 | 0.936724 | ||||||||
\(615\) | 11.2111 | 0.452075 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4222 | 0.661133 | 0.330567 | − | 0.943783i | \(-0.392760\pi\) | ||||
0.330567 | + | 0.943783i | \(0.392760\pi\) | |||||||
\(618\) | 4.00000 | 0.160904 | ||||||||
\(619\) | 4.18335 | 0.168143 | 0.0840714 | − | 0.996460i | \(-0.473208\pi\) | ||||
0.0840714 | + | 0.996460i | \(0.473208\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | −8.60555 | −0.345329 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 2.05551 | 0.0823524 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −32.4222 | −1.29585 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.42221 | −0.336083 | ||||||||
\(629\) | 13.5778 | 0.541382 | ||||||||
\(630\) | 2.60555 | 0.103808 | ||||||||
\(631\) | −11.2111 | −0.446307 | −0.223153 | − | 0.974783i | \(-0.571635\pi\) | ||||
−0.223153 | + | 0.974783i | \(0.571635\pi\) | |||||||
\(632\) | −14.4222 | −0.573685 | ||||||||
\(633\) | 2.78890 | 0.110849 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −13.2111 | −0.524267 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.21110 | 0.206148 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 28.4222 | 1.12261 | 0.561305 | − | 0.827609i | \(-0.310300\pi\) | ||||
0.561305 | + | 0.827609i | \(0.310300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.6333 | 1.32637 | 0.663184 | − | 0.748456i | \(-0.269205\pi\) | ||||
0.663184 | + | 0.748456i | \(0.269205\pi\) | |||||||
\(644\) | 22.4222 | 0.883559 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 6.78890 | 0.267106 | ||||||||
\(647\) | 27.3944 | 1.07699 | 0.538493 | − | 0.842630i | \(-0.318994\pi\) | ||||
0.538493 | + | 0.842630i | \(0.318994\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.6333 | 0.612718 | ||||||||
\(652\) | −4.42221 | −0.173187 | ||||||||
\(653\) | 24.7889 | 0.970065 | 0.485032 | − | 0.874496i | \(-0.338808\pi\) | ||||
0.485032 | + | 0.874496i | \(0.338808\pi\) | |||||||
\(654\) | −8.60555 | −0.336504 | ||||||||
\(655\) | −15.3944 | −0.601511 | ||||||||
\(656\) | 11.2111 | 0.437720 | ||||||||
\(657\) | −8.60555 | −0.335735 | ||||||||
\(658\) | −13.5778 | −0.529318 | ||||||||
\(659\) | 24.2389 | 0.944212 | 0.472106 | − | 0.881542i | \(-0.343494\pi\) | ||||
0.472106 | + | 0.881542i | \(0.343494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.238859 | −0.00929054 | −0.00464527 | − | 0.999989i | \(-0.501479\pi\) | ||||
−0.00464527 | + | 0.999989i | \(0.501479\pi\) | |||||||
\(662\) | −9.39445 | −0.365126 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.2111 | 0.667920 | ||||||||
\(665\) | 6.78890 | 0.263262 | ||||||||
\(666\) | −5.21110 | −0.201926 | ||||||||
\(667\) | −22.4222 | −0.868191 | ||||||||
\(668\) | −5.21110 | −0.201624 | ||||||||
\(669\) | −19.8167 | −0.766156 | ||||||||
\(670\) | −11.2111 | −0.433123 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.60555 | 0.100511 | ||||||||
\(673\) | −5.63331 | −0.217148 | −0.108574 | − | 0.994088i | \(-0.534628\pi\) | ||||
−0.108574 | + | 0.994088i | \(0.534628\pi\) | |||||||
\(674\) | −29.6333 | −1.14143 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.0555 | 1.69319 | 0.846595 | − | 0.532237i | \(-0.178648\pi\) | ||||
0.846595 | + | 0.532237i | \(0.178648\pi\) | |||||||
\(678\) | 7.81665 | 0.300197 | ||||||||
\(679\) | −22.4222 | −0.860485 | ||||||||
\(680\) | 2.60555 | 0.0999183 | ||||||||
\(681\) | 24.0000 | 0.919682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.21110 | −0.199397 | −0.0996986 | − | 0.995018i | \(-0.531788\pi\) | ||||
−0.0996986 | + | 0.995018i | \(0.531788\pi\) | |||||||
\(684\) | −2.60555 | −0.0996257 | ||||||||
\(685\) | 11.2111 | 0.428354 | ||||||||
\(686\) | 18.7889 | 0.717363 | ||||||||
\(687\) | −1.81665 | −0.0693097 | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.60555 | −0.327608 | ||||||||
\(691\) | 30.2389 | 1.15034 | 0.575170 | − | 0.818034i | \(-0.304936\pi\) | ||||
0.575170 | + | 0.818034i | \(0.304936\pi\) | |||||||
\(692\) | −16.4222 | −0.624279 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.6333 | −0.593432 | ||||||||
\(695\) | −2.78890 | −0.105789 | ||||||||
\(696\) | −2.60555 | −0.0987632 | ||||||||
\(697\) | 29.2111 | 1.10645 | ||||||||
\(698\) | −13.8167 | −0.522968 | ||||||||
\(699\) | 19.8167 | 0.749535 | ||||||||
\(700\) | 2.60555 | 0.0984806 | ||||||||
\(701\) | −10.9722 | −0.414416 | −0.207208 | − | 0.978297i | \(-0.566438\pi\) | ||||
−0.207208 | + | 0.978297i | \(0.566438\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.5778 | −0.512096 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.21110 | 0.196261 | ||||||||
\(706\) | −23.2111 | −0.873561 | ||||||||
\(707\) | 38.0555 | 1.43122 | ||||||||
\(708\) | −5.21110 | −0.195845 | ||||||||
\(709\) | −8.60555 | −0.323188 | −0.161594 | − | 0.986857i | \(-0.551664\pi\) | ||||
−0.161594 | + | 0.986857i | \(0.551664\pi\) | |||||||
\(710\) | 5.21110 | 0.195569 | ||||||||
\(711\) | 14.4222 | 0.540875 | ||||||||
\(712\) | −0.788897 | −0.0295652 | ||||||||
\(713\) | −51.6333 | −1.93368 | ||||||||
\(714\) | 6.78890 | 0.254068 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.81665 | −0.0678915 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.6333 | 1.03127 | ||||||||
\(719\) | 8.36669 | 0.312025 | 0.156012 | − | 0.987755i | \(-0.450136\pi\) | ||||
0.156012 | + | 0.987755i | \(0.450136\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 10.4222 | 0.388143 | ||||||||
\(722\) | 12.2111 | 0.454450 | ||||||||
\(723\) | −22.4222 | −0.833891 | ||||||||
\(724\) | 20.4222 | 0.758985 | ||||||||
\(725\) | −2.60555 | −0.0967677 | ||||||||
\(726\) | −11.0000 | −0.408248 | ||||||||
\(727\) | −14.4222 | −0.534890 | −0.267445 | − | 0.963573i | \(-0.586179\pi\) | ||||
−0.267445 | + | 0.963573i | \(0.586179\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.60555 | −0.318506 | ||||||||
\(731\) | −20.8444 | −0.770958 | ||||||||
\(732\) | −3.21110 | −0.118686 | ||||||||
\(733\) | −38.0555 | −1.40561 | −0.702806 | − | 0.711381i | \(-0.748070\pi\) | ||||
−0.702806 | + | 0.711381i | \(0.748070\pi\) | |||||||
\(734\) | −23.6333 | −0.872321 | ||||||||
\(735\) | −0.211103 | −0.00778663 | ||||||||
\(736\) | −8.60555 | −0.317205 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −11.2111 | −0.412686 | ||||||||
\(739\) | −30.2389 | −1.11235 | −0.556177 | − | 0.831064i | \(-0.687732\pi\) | ||||
−0.556177 | + | 0.831064i | \(0.687732\pi\) | |||||||
\(740\) | −5.21110 | −0.191564 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.6333 | −0.573917 | ||||||||
\(743\) | 20.8444 | 0.764707 | 0.382354 | − | 0.924016i | \(-0.375114\pi\) | ||||
0.382354 | + | 0.924016i | \(0.375114\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | 0.788897 | 0.0289030 | ||||||||
\(746\) | −8.42221 | −0.308359 | ||||||||
\(747\) | −17.2111 | −0.629721 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −18.4222 | −0.672236 | −0.336118 | − | 0.941820i | \(-0.609114\pi\) | ||||
−0.336118 | + | 0.941820i | \(0.609114\pi\) | |||||||
\(752\) | 5.21110 | 0.190029 | ||||||||
\(753\) | −20.6056 | −0.750908 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | −2.60555 | −0.0947630 | ||||||||
\(757\) | 27.2111 | 0.989004 | 0.494502 | − | 0.869176i | \(-0.335350\pi\) | ||||
0.494502 | + | 0.869176i | \(0.335350\pi\) | |||||||
\(758\) | −1.02776 | −0.0373298 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.60555 | −0.0945133 | ||||||||
\(761\) | −9.63331 | −0.349207 | −0.174604 | − | 0.984639i | \(-0.555864\pi\) | ||||
−0.174604 | + | 0.984639i | \(0.555864\pi\) | |||||||
\(762\) | 13.2111 | 0.478588 | ||||||||
\(763\) | −22.4222 | −0.811738 | ||||||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | −2.60555 | −0.0942039 | ||||||||
\(766\) | 15.6333 | 0.564854 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −44.8444 | −1.61713 | −0.808565 | − | 0.588406i | \(-0.799756\pi\) | ||||
−0.808565 | + | 0.588406i | \(0.799756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.3944 | −0.770502 | ||||||||
\(772\) | −13.8167 | −0.497272 | ||||||||
\(773\) | −30.0000 | −1.07903 | −0.539513 | − | 0.841978i | \(-0.681391\pi\) | ||||
−0.539513 | + | 0.841978i | \(0.681391\pi\) | |||||||
\(774\) | 8.00000 | 0.287554 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 8.60555 | 0.308921 | ||||||||
\(777\) | −13.5778 | −0.487101 | ||||||||
\(778\) | −2.60555 | −0.0934135 | ||||||||
\(779\) | −29.2111 | −1.04660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −22.4222 | −0.801816 | ||||||||
\(783\) | 2.60555 | 0.0931148 | ||||||||
\(784\) | −0.211103 | −0.00753938 | ||||||||
\(785\) | 8.42221 | 0.300601 | ||||||||
\(786\) | 15.3944 | 0.549102 | ||||||||
\(787\) | −37.2666 | −1.32841 | −0.664206 | − | 0.747550i | \(-0.731230\pi\) | ||||
−0.664206 | + | 0.747550i | \(0.731230\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | −13.8167 | −0.491886 | ||||||||
\(790\) | 14.4222 | 0.513119 | ||||||||
\(791\) | 20.3667 | 0.724156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −39.6333 | −1.40653 | ||||||||
\(795\) | 6.00000 | 0.212798 | ||||||||
\(796\) | 6.42221 | 0.227629 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | −6.78890 | −0.240324 | ||||||||
\(799\) | 13.5778 | 0.480348 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0.788897 | 0.0278743 | ||||||||
\(802\) | −23.2111 | −0.819613 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.2111 | 0.395385 | ||||||||
\(805\) | −22.4222 | −0.790279 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.18335 | −0.147261 | ||||||||
\(808\) | −14.6056 | −0.513822 | ||||||||
\(809\) | 50.8444 | 1.78759 | 0.893797 | − | 0.448471i | \(-0.148031\pi\) | ||||
0.893797 | + | 0.448471i | \(0.148031\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 18.2389 | 0.640453 | 0.320226 | − | 0.947341i | \(-0.396241\pi\) | ||||
0.320226 | + | 0.947341i | \(0.396241\pi\) | |||||||
\(812\) | −6.78890 | −0.238244 | ||||||||
\(813\) | −28.4222 | −0.996810 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.42221 | 0.154903 | ||||||||
\(816\) | −2.60555 | −0.0912125 | ||||||||
\(817\) | 20.8444 | 0.729254 | ||||||||
\(818\) | −29.2111 | −1.02134 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.2111 | −0.391509 | ||||||||
\(821\) | −11.2111 | −0.391270 | −0.195635 | − | 0.980677i | \(-0.562677\pi\) | ||||
−0.195635 | + | 0.980677i | \(0.562677\pi\) | |||||||
\(822\) | −11.2111 | −0.391032 | ||||||||
\(823\) | 4.00000 | 0.139431 | 0.0697156 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697156 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(824\) | −4.00000 | −0.139347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.5778 | −0.472432 | ||||||||
\(827\) | 15.6333 | 0.543623 | 0.271812 | − | 0.962350i | \(-0.412377\pi\) | ||||
0.271812 | + | 0.962350i | \(0.412377\pi\) | |||||||
\(828\) | 8.60555 | 0.299064 | ||||||||
\(829\) | 10.8444 | 0.376642 | 0.188321 | − | 0.982108i | \(-0.439695\pi\) | ||||
0.188321 | + | 0.982108i | \(0.439695\pi\) | |||||||
\(830\) | −17.2111 | −0.597406 | ||||||||
\(831\) | 12.4222 | 0.430922 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.550039 | −0.0190577 | ||||||||
\(834\) | 2.78890 | 0.0965716 | ||||||||
\(835\) | 5.21110 | 0.180338 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.00000 | 0.207390 | ||||||||
\(838\) | −25.8167 | −0.891822 | ||||||||
\(839\) | 10.4222 | 0.359814 | 0.179907 | − | 0.983684i | \(-0.442420\pi\) | ||||
0.179907 | + | 0.983684i | \(0.442420\pi\) | |||||||
\(840\) | −2.60555 | −0.0899001 | ||||||||
\(841\) | −22.2111 | −0.765900 | ||||||||
\(842\) | 1.81665 | 0.0626060 | ||||||||
\(843\) | −12.7889 | −0.440473 | ||||||||
\(844\) | −2.78890 | −0.0959978 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.21110 | −0.179161 | ||||||||
\(847\) | −28.6611 | −0.984806 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | −18.4222 | −0.632248 | ||||||||
\(850\) | −2.60555 | −0.0893697 | ||||||||
\(851\) | 44.8444 | 1.53725 | ||||||||
\(852\) | −5.21110 | −0.178529 | ||||||||
\(853\) | −29.2111 | −1.00017 | −0.500085 | − | 0.865977i | \(-0.666698\pi\) | ||||
−0.500085 | + | 0.865977i | \(0.666698\pi\) | |||||||
\(854\) | −8.36669 | −0.286302 | ||||||||
\(855\) | 2.60555 | 0.0891080 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.0278 | −0.445020 | −0.222510 | − | 0.974930i | \(-0.571425\pi\) | ||||
−0.222510 | + | 0.974930i | \(0.571425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7889 | 0.368112 | 0.184056 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184056 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | −29.2111 | −0.995512 | ||||||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | −8.36669 | −0.284806 | −0.142403 | − | 0.989809i | \(-0.545483\pi\) | ||||
−0.142403 | + | 0.989809i | \(0.545483\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 16.4222 | 0.558372 | ||||||||
\(866\) | 4.78890 | 0.162733 | ||||||||
\(867\) | 10.2111 | 0.346787 | ||||||||
\(868\) | −15.6333 | −0.530629 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2.60555 | 0.0883365 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.60555 | 0.291421 | ||||||||
\(873\) | −8.60555 | −0.291254 | ||||||||
\(874\) | 22.4222 | 0.758442 | ||||||||
\(875\) | −2.60555 | −0.0880837 | ||||||||
\(876\) | 8.60555 | 0.290755 | ||||||||
\(877\) | −32.8444 | −1.10908 | −0.554538 | − | 0.832158i | \(-0.687105\pi\) | ||||
−0.554538 | + | 0.832158i | \(0.687105\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | −18.0000 | −0.607125 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.7889 | −0.835159 | −0.417580 | − | 0.908640i | \(-0.637122\pi\) | ||||
−0.417580 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(882\) | 0.211103 | 0.00710819 | ||||||||
\(883\) | −38.4222 | −1.29301 | −0.646505 | − | 0.762910i | \(-0.723770\pi\) | ||||
−0.646505 | + | 0.762910i | \(0.723770\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.21110 | 0.175169 | ||||||||
\(886\) | 27.6333 | 0.928359 | ||||||||
\(887\) | 43.0278 | 1.44473 | 0.722365 | − | 0.691512i | \(-0.243055\pi\) | ||||
0.722365 | + | 0.691512i | \(0.243055\pi\) | |||||||
\(888\) | 5.21110 | 0.174873 | ||||||||
\(889\) | 34.4222 | 1.15448 | ||||||||
\(890\) | 0.788897 | 0.0264439 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.8167 | 0.663511 | ||||||||
\(893\) | −13.5778 | −0.454364 | ||||||||
\(894\) | −0.788897 | −0.0263847 | ||||||||
\(895\) | 1.81665 | 0.0607240 | ||||||||
\(896\) | −2.60555 | −0.0870454 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.63331 | 0.321468 | ||||||||
\(899\) | 15.6333 | 0.521400 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 15.6333 | 0.520821 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.8444 | 0.693659 | ||||||||
\(904\) | −7.81665 | −0.259978 | ||||||||
\(905\) | −20.4222 | −0.678857 | ||||||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | −50.4222 | −1.67424 | −0.837121 | − | 0.547018i | \(-0.815763\pi\) | ||||
−0.837121 | + | 0.547018i | \(0.815763\pi\) | |||||||
\(908\) | −24.0000 | −0.796468 | ||||||||
\(909\) | 14.6056 | 0.484436 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.6333 | 0.517955 | 0.258977 | − | 0.965883i | \(-0.416615\pi\) | ||||
0.258977 | + | 0.965883i | \(0.416615\pi\) | |||||||
\(912\) | 2.60555 | 0.0862784 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −12.2389 | −0.404825 | ||||||||
\(915\) | 3.21110 | 0.106156 | ||||||||
\(916\) | 1.81665 | 0.0600239 | ||||||||
\(917\) | 40.1110 | 1.32458 | ||||||||
\(918\) | 2.60555 | 0.0859960 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 8.60555 | 0.283717 | ||||||||
\(921\) | 23.2111 | 0.764832 | ||||||||
\(922\) | 9.63331 | 0.317256 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.21110 | 0.171340 | ||||||||
\(926\) | 38.6056 | 1.26866 | ||||||||
\(927\) | 4.00000 | 0.131377 | ||||||||
\(928\) | 2.60555 | 0.0855314 | ||||||||
\(929\) | −24.7889 | −0.813297 | −0.406649 | − | 0.913585i | \(-0.633303\pi\) | ||||
−0.406649 | + | 0.913585i | \(0.633303\pi\) | |||||||
\(930\) | 6.00000 | 0.196748 | ||||||||
\(931\) | 0.550039 | 0.0180268 | ||||||||
\(932\) | −19.8167 | −0.649116 | ||||||||
\(933\) | 12.0000 | 0.392862 | ||||||||
\(934\) | −1.57779 | −0.0516270 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.6333 | −1.75212 | −0.876062 | − | 0.482199i | \(-0.839838\pi\) | ||||
−0.876062 | + | 0.482199i | \(0.839838\pi\) | |||||||
\(938\) | 29.2111 | 0.953776 | ||||||||
\(939\) | −32.4222 | −1.05806 | ||||||||
\(940\) | −5.21110 | −0.169967 | ||||||||
\(941\) | 54.0000 | 1.76035 | 0.880175 | − | 0.474650i | \(-0.157425\pi\) | ||||
0.880175 | + | 0.474650i | \(0.157425\pi\) | |||||||
\(942\) | −8.42221 | −0.274410 | ||||||||
\(943\) | 96.4777 | 3.14175 | ||||||||
\(944\) | 5.21110 | 0.169607 | ||||||||
\(945\) | 2.60555 | 0.0847586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.6333 | 0.897962 | 0.448981 | − | 0.893541i | \(-0.351787\pi\) | ||||
0.448981 | + | 0.893541i | \(0.351787\pi\) | |||||||
\(948\) | −14.4222 | −0.468411 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.60555 | 0.0845352 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | −6.78890 | −0.220029 | ||||||||
\(953\) | −30.2389 | −0.979533 | −0.489766 | − | 0.871854i | \(-0.662918\pi\) | ||||
−0.489766 | + | 0.871854i | \(0.662918\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | 12.0000 | 0.388311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.4222 | −1.11213 | ||||||||
\(959\) | −29.2111 | −0.943276 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.4222 | 0.722171 | ||||||||
\(965\) | 13.8167 | 0.444774 | ||||||||
\(966\) | 22.4222 | 0.721423 | ||||||||
\(967\) | −42.2389 | −1.35831 | −0.679155 | − | 0.733995i | \(-0.737654\pi\) | ||||
−0.679155 | + | 0.733995i | \(0.737654\pi\) | |||||||
\(968\) | 11.0000 | 0.353553 | ||||||||
\(969\) | 6.78890 | 0.218091 | ||||||||
\(970\) | −8.60555 | −0.276308 | ||||||||
\(971\) | −16.9722 | −0.544665 | −0.272333 | − | 0.962203i | \(-0.587795\pi\) | ||||
−0.272333 | + | 0.962203i | \(0.587795\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 7.26662 | 0.232957 | ||||||||
\(974\) | −37.0278 | −1.18645 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.21110 | 0.102785 | ||||||||
\(977\) | 38.8444 | 1.24274 | 0.621371 | − | 0.783516i | \(-0.286576\pi\) | ||||
0.621371 | + | 0.783516i | \(0.286576\pi\) | |||||||
\(978\) | −4.42221 | −0.141407 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.211103 | 0.00674342 | ||||||||
\(981\) | −8.60555 | −0.274754 | ||||||||
\(982\) | −13.8167 | −0.440907 | ||||||||
\(983\) | −13.5778 | −0.433064 | −0.216532 | − | 0.976275i | \(-0.569475\pi\) | ||||
−0.216532 | + | 0.976275i | \(0.569475\pi\) | |||||||
\(984\) | 11.2111 | 0.357397 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 6.78890 | 0.216203 | ||||||||
\(987\) | −13.5778 | −0.432186 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −68.8444 | −2.18912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.42221 | 0.204008 | 0.102004 | − | 0.994784i | \(-0.467475\pi\) | ||||
0.102004 | + | 0.994784i | \(0.467475\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | −9.39445 | −0.298124 | ||||||||
\(994\) | −13.5778 | −0.430662 | ||||||||
\(995\) | −6.42221 | −0.203598 | ||||||||
\(996\) | 17.2111 | 0.545355 | ||||||||
\(997\) | 12.4222 | 0.393415 | 0.196708 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196708 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(998\) | −13.0278 | −0.412386 | ||||||||
\(999\) | −5.21110 | −0.164872 |
(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 | 5070.2.a.z.1.2 | 2 | ||
13.5 | odd | 4 | 390.2.b.c.181.4 | yes | 4 | ||
13.8 | odd | 4 | 390.2.b.c.181.1 | ✓ | 4 | ||
13.12 | even | 2 | 5070.2.a.bf.1.1 | 2 | |||
39.5 | even | 4 | 1170.2.b.d.181.2 | 4 | |||
39.8 | even | 4 | 1170.2.b.d.181.3 | 4 | |||
52.31 | even | 4 | 3120.2.g.q.961.3 | 4 | |||
52.47 | even | 4 | 3120.2.g.q.961.2 | 4 | |||
65.8 | even | 4 | 1950.2.f.m.649.1 | 4 | |||
65.18 | even | 4 | 1950.2.f.n.649.2 | 4 | |||
65.34 | odd | 4 | 1950.2.b.k.1351.4 | 4 | |||
65.44 | odd | 4 | 1950.2.b.k.1351.1 | 4 | |||
65.47 | even | 4 | 1950.2.f.n.649.4 | 4 | |||
65.57 | even | 4 | 1950.2.f.m.649.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.c.181.1 | ✓ | 4 | 13.8 | odd | 4 | ||
390.2.b.c.181.4 | yes | 4 | 13.5 | odd | 4 | ||
1170.2.b.d.181.2 | 4 | 39.5 | even | 4 | |||
1170.2.b.d.181.3 | 4 | 39.8 | even | 4 | |||
1950.2.b.k.1351.1 | 4 | 65.44 | odd | 4 | |||
1950.2.b.k.1351.4 | 4 | 65.34 | odd | 4 | |||
1950.2.f.m.649.1 | 4 | 65.8 | even | 4 | |||
1950.2.f.m.649.3 | 4 | 65.57 | even | 4 | |||
1950.2.f.n.649.2 | 4 | 65.18 | even | 4 | |||
1950.2.f.n.649.4 | 4 | 65.47 | even | 4 | |||
3120.2.g.q.961.2 | 4 | 52.47 | even | 4 | |||
3120.2.g.q.961.3 | 4 | 52.31 | even | 4 | |||
5070.2.a.z.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5070.2.a.bf.1.1 | 2 | 13.12 | even | 2 |