Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4114,2,Mod(1,4114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4114, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4114.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4114 = 2 \cdot 11^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4114.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: | \(32.8504553916\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4114.1 |
$q$-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 | ||||||||
\(3\) | −0.618034 | −0.356822 | −0.178411 | − | 0.983956i | \(-0.557096\pi\) | ||||
−0.178411 | + | 0.983956i | \(0.557096\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.618034 | 0.276393 | 0.138197 | − | 0.990405i | \(-0.455869\pi\) | ||||
0.138197 | + | 0.990405i | \(0.455869\pi\) | |||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | 3.85410 | 1.45671 | 0.728357 | − | 0.685198i | \(-0.240284\pi\) | ||||
0.728357 | + | 0.685198i | \(0.240284\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | 0.618034 | 0.195440 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | −2.23607 | −0.620174 | −0.310087 | − | 0.950708i | \(-0.600358\pi\) | ||||
−0.310087 | + | 0.950708i | \(0.600358\pi\) | |||||||
\(14\) | 3.85410 | 1.03005 | ||||||||
\(15\) | −0.381966 | −0.0986232 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.61803 | −0.617077 | ||||||||
\(19\) | −6.47214 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(20\) | 0.618034 | 0.138197 | ||||||||
\(21\) | −2.38197 | −0.519788 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.23607 | −1.30031 | −0.650155 | − | 0.759802i | \(-0.725296\pi\) | ||||
−0.650155 | + | 0.759802i | \(0.725296\pi\) | |||||||
\(24\) | −0.618034 | −0.126156 | ||||||||
\(25\) | −4.61803 | −0.923607 | ||||||||
\(26\) | −2.23607 | −0.438529 | ||||||||
\(27\) | 3.47214 | 0.668213 | ||||||||
\(28\) | 3.85410 | 0.728357 | ||||||||
\(29\) | −9.23607 | −1.71509 | −0.857547 | − | 0.514405i | \(-0.828013\pi\) | ||||
−0.857547 | + | 0.514405i | \(0.828013\pi\) | |||||||
\(30\) | −0.381966 | −0.0697371 | ||||||||
\(31\) | −7.47214 | −1.34204 | −0.671018 | − | 0.741441i | \(-0.734143\pi\) | ||||
−0.671018 | + | 0.741441i | \(0.734143\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 2.38197 | 0.402626 | ||||||||
\(36\) | −2.61803 | −0.436339 | ||||||||
\(37\) | 7.47214 | 1.22841 | 0.614206 | − | 0.789146i | \(-0.289476\pi\) | ||||
0.614206 | + | 0.789146i | \(0.289476\pi\) | |||||||
\(38\) | −6.47214 | −1.04992 | ||||||||
\(39\) | 1.38197 | 0.221292 | ||||||||
\(40\) | 0.618034 | 0.0977198 | ||||||||
\(41\) | −9.70820 | −1.51617 | −0.758083 | − | 0.652158i | \(-0.773864\pi\) | ||||
−0.758083 | + | 0.652158i | \(0.773864\pi\) | |||||||
\(42\) | −2.38197 | −0.367545 | ||||||||
\(43\) | −4.38197 | −0.668244 | −0.334122 | − | 0.942530i | \(-0.608440\pi\) | ||||
−0.334122 | + | 0.942530i | \(0.608440\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.61803 | −0.241202 | ||||||||
\(46\) | −6.23607 | −0.919458 | ||||||||
\(47\) | 6.32624 | 0.922777 | 0.461388 | − | 0.887198i | \(-0.347352\pi\) | ||||
0.461388 | + | 0.887198i | \(0.347352\pi\) | |||||||
\(48\) | −0.618034 | −0.0892055 | ||||||||
\(49\) | 7.85410 | 1.12201 | ||||||||
\(50\) | −4.61803 | −0.653089 | ||||||||
\(51\) | 0.618034 | 0.0865421 | ||||||||
\(52\) | −2.23607 | −0.310087 | ||||||||
\(53\) | −6.61803 | −0.909057 | −0.454528 | − | 0.890732i | \(-0.650192\pi\) | ||||
−0.454528 | + | 0.890732i | \(0.650192\pi\) | |||||||
\(54\) | 3.47214 | 0.472498 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.85410 | 0.515026 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | −9.23607 | −1.21276 | ||||||||
\(59\) | −7.76393 | −1.01078 | −0.505389 | − | 0.862892i | \(-0.668651\pi\) | ||||
−0.505389 | + | 0.862892i | \(0.668651\pi\) | |||||||
\(60\) | −0.381966 | −0.0493116 | ||||||||
\(61\) | 13.9443 | 1.78538 | 0.892691 | − | 0.450670i | \(-0.148815\pi\) | ||||
0.892691 | + | 0.450670i | \(0.148815\pi\) | |||||||
\(62\) | −7.47214 | −0.948962 | ||||||||
\(63\) | −10.0902 | −1.27124 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.38197 | −0.171412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0902 | 1.59922 | 0.799609 | − | 0.600520i | \(-0.205040\pi\) | ||||
0.799609 | + | 0.600520i | \(0.205040\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 3.85410 | 0.463979 | ||||||||
\(70\) | 2.38197 | 0.284699 | ||||||||
\(71\) | −15.5623 | −1.84691 | −0.923453 | − | 0.383712i | \(-0.874646\pi\) | ||||
−0.923453 | + | 0.383712i | \(0.874646\pi\) | |||||||
\(72\) | −2.61803 | −0.308538 | ||||||||
\(73\) | −7.61803 | −0.891623 | −0.445812 | − | 0.895127i | \(-0.647085\pi\) | ||||
−0.445812 | + | 0.895127i | \(0.647085\pi\) | |||||||
\(74\) | 7.47214 | 0.868618 | ||||||||
\(75\) | 2.85410 | 0.329563 | ||||||||
\(76\) | −6.47214 | −0.742405 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.38197 | 0.156477 | ||||||||
\(79\) | 10.2361 | 1.15165 | 0.575824 | − | 0.817574i | \(-0.304681\pi\) | ||||
0.575824 | + | 0.817574i | \(0.304681\pi\) | |||||||
\(80\) | 0.618034 | 0.0690983 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | −9.70820 | −1.07209 | ||||||||
\(83\) | −1.09017 | −0.119662 | −0.0598308 | − | 0.998209i | \(-0.519056\pi\) | ||||
−0.0598308 | + | 0.998209i | \(0.519056\pi\) | |||||||
\(84\) | −2.38197 | −0.259894 | ||||||||
\(85\) | −0.618034 | −0.0670352 | ||||||||
\(86\) | −4.38197 | −0.472520 | ||||||||
\(87\) | 5.70820 | 0.611984 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4164 | 1.52814 | 0.764068 | − | 0.645136i | \(-0.223199\pi\) | ||||
0.764068 | + | 0.645136i | \(0.223199\pi\) | |||||||
\(90\) | −1.61803 | −0.170556 | ||||||||
\(91\) | −8.61803 | −0.903415 | ||||||||
\(92\) | −6.23607 | −0.650155 | ||||||||
\(93\) | 4.61803 | 0.478868 | ||||||||
\(94\) | 6.32624 | 0.652502 | ||||||||
\(95\) | −4.00000 | −0.410391 | ||||||||
\(96\) | −0.618034 | −0.0630778 | ||||||||
\(97\) | 5.47214 | 0.555611 | 0.277806 | − | 0.960637i | \(-0.410393\pi\) | ||||
0.277806 | + | 0.960637i | \(0.410393\pi\) | |||||||
\(98\) | 7.85410 | 0.793384 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.61803 | −0.461803 | ||||||||
\(101\) | 13.4721 | 1.34053 | 0.670264 | − | 0.742123i | \(-0.266181\pi\) | ||||
0.670264 | + | 0.742123i | \(0.266181\pi\) | |||||||
\(102\) | 0.618034 | 0.0611945 | ||||||||
\(103\) | −11.4721 | −1.13038 | −0.565192 | − | 0.824960i | \(-0.691198\pi\) | ||||
−0.565192 | + | 0.824960i | \(0.691198\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | −1.47214 | −0.143666 | ||||||||
\(106\) | −6.61803 | −0.642800 | ||||||||
\(107\) | 2.70820 | 0.261812 | 0.130906 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130906 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(108\) | 3.47214 | 0.334106 | ||||||||
\(109\) | 14.3820 | 1.37754 | 0.688771 | − | 0.724979i | \(-0.258150\pi\) | ||||
0.688771 | + | 0.724979i | \(0.258150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.61803 | −0.438324 | ||||||||
\(112\) | 3.85410 | 0.364178 | ||||||||
\(113\) | −7.94427 | −0.747334 | −0.373667 | − | 0.927563i | \(-0.621900\pi\) | ||||
−0.373667 | + | 0.927563i | \(0.621900\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | −3.85410 | −0.359397 | ||||||||
\(116\) | −9.23607 | −0.857547 | ||||||||
\(117\) | 5.85410 | 0.541212 | ||||||||
\(118\) | −7.76393 | −0.714728 | ||||||||
\(119\) | −3.85410 | −0.353305 | ||||||||
\(120\) | −0.381966 | −0.0348686 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.9443 | 1.26246 | ||||||||
\(123\) | 6.00000 | 0.541002 | ||||||||
\(124\) | −7.47214 | −0.671018 | ||||||||
\(125\) | −5.94427 | −0.531672 | ||||||||
\(126\) | −10.0902 | −0.898904 | ||||||||
\(127\) | −8.32624 | −0.738834 | −0.369417 | − | 0.929264i | \(-0.620443\pi\) | ||||
−0.369417 | + | 0.929264i | \(0.620443\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.70820 | 0.238444 | ||||||||
\(130\) | −1.38197 | −0.121206 | ||||||||
\(131\) | 7.23607 | 0.632218 | 0.316109 | − | 0.948723i | \(-0.397623\pi\) | ||||
0.316109 | + | 0.948723i | \(0.397623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.9443 | −2.16294 | ||||||||
\(134\) | 13.0902 | 1.13082 | ||||||||
\(135\) | 2.14590 | 0.184689 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 7.18034 | 0.613458 | 0.306729 | − | 0.951797i | \(-0.400765\pi\) | ||||
0.306729 | + | 0.951797i | \(0.400765\pi\) | |||||||
\(138\) | 3.85410 | 0.328083 | ||||||||
\(139\) | −1.29180 | −0.109569 | −0.0547844 | − | 0.998498i | \(-0.517447\pi\) | ||||
−0.0547844 | + | 0.998498i | \(0.517447\pi\) | |||||||
\(140\) | 2.38197 | 0.201313 | ||||||||
\(141\) | −3.90983 | −0.329267 | ||||||||
\(142\) | −15.5623 | −1.30596 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.61803 | −0.218169 | ||||||||
\(145\) | −5.70820 | −0.474041 | ||||||||
\(146\) | −7.61803 | −0.630473 | ||||||||
\(147\) | −4.85410 | −0.400360 | ||||||||
\(148\) | 7.47214 | 0.614206 | ||||||||
\(149\) | 20.0344 | 1.64129 | 0.820643 | − | 0.571442i | \(-0.193616\pi\) | ||||
0.820643 | + | 0.571442i | \(0.193616\pi\) | |||||||
\(150\) | 2.85410 | 0.233036 | ||||||||
\(151\) | 14.8885 | 1.21161 | 0.605806 | − | 0.795612i | \(-0.292851\pi\) | ||||
0.605806 | + | 0.795612i | \(0.292851\pi\) | |||||||
\(152\) | −6.47214 | −0.524960 | ||||||||
\(153\) | 2.61803 | 0.211656 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.61803 | −0.370929 | ||||||||
\(156\) | 1.38197 | 0.110646 | ||||||||
\(157\) | −16.0902 | −1.28414 | −0.642068 | − | 0.766648i | \(-0.721923\pi\) | ||||
−0.642068 | + | 0.766648i | \(0.721923\pi\) | |||||||
\(158\) | 10.2361 | 0.814338 | ||||||||
\(159\) | 4.09017 | 0.324372 | ||||||||
\(160\) | 0.618034 | 0.0488599 | ||||||||
\(161\) | −24.0344 | −1.89418 | ||||||||
\(162\) | 5.70820 | 0.448479 | ||||||||
\(163\) | −6.47214 | −0.506937 | −0.253468 | − | 0.967344i | \(-0.581571\pi\) | ||||
−0.253468 | + | 0.967344i | \(0.581571\pi\) | |||||||
\(164\) | −9.70820 | −0.758083 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.09017 | −0.0846136 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | −2.38197 | −0.183773 | ||||||||
\(169\) | −8.00000 | −0.615385 | ||||||||
\(170\) | −0.618034 | −0.0474010 | ||||||||
\(171\) | 16.9443 | 1.29576 | ||||||||
\(172\) | −4.38197 | −0.334122 | ||||||||
\(173\) | −13.2361 | −1.00632 | −0.503160 | − | 0.864193i | \(-0.667829\pi\) | ||||
−0.503160 | + | 0.864193i | \(0.667829\pi\) | |||||||
\(174\) | 5.70820 | 0.432738 | ||||||||
\(175\) | −17.7984 | −1.34543 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.79837 | 0.360668 | ||||||||
\(178\) | 14.4164 | 1.08056 | ||||||||
\(179\) | −3.29180 | −0.246040 | −0.123020 | − | 0.992404i | \(-0.539258\pi\) | ||||
−0.123020 | + | 0.992404i | \(0.539258\pi\) | |||||||
\(180\) | −1.61803 | −0.120601 | ||||||||
\(181\) | 2.23607 | 0.166206 | 0.0831028 | − | 0.996541i | \(-0.473517\pi\) | ||||
0.0831028 | + | 0.996541i | \(0.473517\pi\) | |||||||
\(182\) | −8.61803 | −0.638811 | ||||||||
\(183\) | −8.61803 | −0.637063 | ||||||||
\(184\) | −6.23607 | −0.459729 | ||||||||
\(185\) | 4.61803 | 0.339525 | ||||||||
\(186\) | 4.61803 | 0.338611 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.32624 | 0.461388 | ||||||||
\(189\) | 13.3820 | 0.973395 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 14.2705 | 1.03258 | 0.516289 | − | 0.856414i | \(-0.327313\pi\) | ||||
0.516289 | + | 0.856414i | \(0.327313\pi\) | |||||||
\(192\) | −0.618034 | −0.0446028 | ||||||||
\(193\) | −17.6525 | −1.27065 | −0.635327 | − | 0.772244i | \(-0.719134\pi\) | ||||
−0.635327 | + | 0.772244i | \(0.719134\pi\) | |||||||
\(194\) | 5.47214 | 0.392876 | ||||||||
\(195\) | 0.854102 | 0.0611635 | ||||||||
\(196\) | 7.85410 | 0.561007 | ||||||||
\(197\) | −12.0344 | −0.857418 | −0.428709 | − | 0.903443i | \(-0.641032\pi\) | ||||
−0.428709 | + | 0.903443i | \(0.641032\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.03444 | −0.569546 | −0.284773 | − | 0.958595i | \(-0.591918\pi\) | ||||
−0.284773 | + | 0.958595i | \(0.591918\pi\) | |||||||
\(200\) | −4.61803 | −0.326544 | ||||||||
\(201\) | −8.09017 | −0.570637 | ||||||||
\(202\) | 13.4721 | 0.947896 | ||||||||
\(203\) | −35.5967 | −2.49840 | ||||||||
\(204\) | 0.618034 | 0.0432710 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | −11.4721 | −0.799302 | ||||||||
\(207\) | 16.3262 | 1.13475 | ||||||||
\(208\) | −2.23607 | −0.155043 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.47214 | −0.101587 | ||||||||
\(211\) | −10.2705 | −0.707051 | −0.353526 | − | 0.935425i | \(-0.615017\pi\) | ||||
−0.353526 | + | 0.935425i | \(0.615017\pi\) | |||||||
\(212\) | −6.61803 | −0.454528 | ||||||||
\(213\) | 9.61803 | 0.659017 | ||||||||
\(214\) | 2.70820 | 0.185129 | ||||||||
\(215\) | −2.70820 | −0.184698 | ||||||||
\(216\) | 3.47214 | 0.236249 | ||||||||
\(217\) | −28.7984 | −1.95496 | ||||||||
\(218\) | 14.3820 | 0.974070 | ||||||||
\(219\) | 4.70820 | 0.318151 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.23607 | 0.150414 | ||||||||
\(222\) | −4.61803 | −0.309942 | ||||||||
\(223\) | 27.7082 | 1.85548 | 0.927739 | − | 0.373229i | \(-0.121749\pi\) | ||||
0.927739 | + | 0.373229i | \(0.121749\pi\) | |||||||
\(224\) | 3.85410 | 0.257513 | ||||||||
\(225\) | 12.0902 | 0.806011 | ||||||||
\(226\) | −7.94427 | −0.528445 | ||||||||
\(227\) | 2.23607 | 0.148413 | 0.0742065 | − | 0.997243i | \(-0.476358\pi\) | ||||
0.0742065 | + | 0.997243i | \(0.476358\pi\) | |||||||
\(228\) | 4.00000 | 0.264906 | ||||||||
\(229\) | −17.5623 | −1.16055 | −0.580275 | − | 0.814421i | \(-0.697055\pi\) | ||||
−0.580275 | + | 0.814421i | \(0.697055\pi\) | |||||||
\(230\) | −3.85410 | −0.254132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.23607 | −0.606378 | ||||||||
\(233\) | 17.1803 | 1.12552 | 0.562761 | − | 0.826620i | \(-0.309739\pi\) | ||||
0.562761 | + | 0.826620i | \(0.309739\pi\) | |||||||
\(234\) | 5.85410 | 0.382695 | ||||||||
\(235\) | 3.90983 | 0.255049 | ||||||||
\(236\) | −7.76393 | −0.505389 | ||||||||
\(237\) | −6.32624 | −0.410933 | ||||||||
\(238\) | −3.85410 | −0.249824 | ||||||||
\(239\) | −21.1803 | −1.37004 | −0.685021 | − | 0.728523i | \(-0.740207\pi\) | ||||
−0.685021 | + | 0.728523i | \(0.740207\pi\) | |||||||
\(240\) | −0.381966 | −0.0246558 | ||||||||
\(241\) | 13.9443 | 0.898230 | 0.449115 | − | 0.893474i | \(-0.351739\pi\) | ||||
0.449115 | + | 0.893474i | \(0.351739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.9443 | −0.894525 | ||||||||
\(244\) | 13.9443 | 0.892691 | ||||||||
\(245\) | 4.85410 | 0.310117 | ||||||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | 14.4721 | 0.920840 | ||||||||
\(248\) | −7.47214 | −0.474481 | ||||||||
\(249\) | 0.673762 | 0.0426979 | ||||||||
\(250\) | −5.94427 | −0.375949 | ||||||||
\(251\) | −16.4721 | −1.03971 | −0.519856 | − | 0.854254i | \(-0.674014\pi\) | ||||
−0.519856 | + | 0.854254i | \(0.674014\pi\) | |||||||
\(252\) | −10.0902 | −0.635621 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.32624 | −0.522435 | ||||||||
\(255\) | 0.381966 | 0.0239196 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.4164 | −0.961649 | −0.480825 | − | 0.876817i | \(-0.659663\pi\) | ||||
−0.480825 | + | 0.876817i | \(0.659663\pi\) | |||||||
\(258\) | 2.70820 | 0.168605 | ||||||||
\(259\) | 28.7984 | 1.78944 | ||||||||
\(260\) | −1.38197 | −0.0857059 | ||||||||
\(261\) | 24.1803 | 1.49673 | ||||||||
\(262\) | 7.23607 | 0.447046 | ||||||||
\(263\) | 8.14590 | 0.502298 | 0.251149 | − | 0.967948i | \(-0.419192\pi\) | ||||
0.251149 | + | 0.967948i | \(0.419192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.09017 | −0.251257 | ||||||||
\(266\) | −24.9443 | −1.52943 | ||||||||
\(267\) | −8.90983 | −0.545273 | ||||||||
\(268\) | 13.0902 | 0.799609 | ||||||||
\(269\) | 9.88854 | 0.602915 | 0.301458 | − | 0.953480i | \(-0.402527\pi\) | ||||
0.301458 | + | 0.953480i | \(0.402527\pi\) | |||||||
\(270\) | 2.14590 | 0.130595 | ||||||||
\(271\) | 5.85410 | 0.355611 | 0.177806 | − | 0.984066i | \(-0.443100\pi\) | ||||
0.177806 | + | 0.984066i | \(0.443100\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 5.32624 | 0.322359 | ||||||||
\(274\) | 7.18034 | 0.433780 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.85410 | 0.231990 | ||||||||
\(277\) | −20.1246 | −1.20917 | −0.604585 | − | 0.796540i | \(-0.706661\pi\) | ||||
−0.604585 | + | 0.796540i | \(0.706661\pi\) | |||||||
\(278\) | −1.29180 | −0.0774768 | ||||||||
\(279\) | 19.5623 | 1.17116 | ||||||||
\(280\) | 2.38197 | 0.142350 | ||||||||
\(281\) | 18.4721 | 1.10196 | 0.550978 | − | 0.834520i | \(-0.314255\pi\) | ||||
0.550978 | + | 0.834520i | \(0.314255\pi\) | |||||||
\(282\) | −3.90983 | −0.232827 | ||||||||
\(283\) | 9.27051 | 0.551075 | 0.275537 | − | 0.961290i | \(-0.411144\pi\) | ||||
0.275537 | + | 0.961290i | \(0.411144\pi\) | |||||||
\(284\) | −15.5623 | −0.923453 | ||||||||
\(285\) | 2.47214 | 0.146437 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.4164 | −2.20862 | ||||||||
\(288\) | −2.61803 | −0.154269 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −5.70820 | −0.335197 | ||||||||
\(291\) | −3.38197 | −0.198254 | ||||||||
\(292\) | −7.61803 | −0.445812 | ||||||||
\(293\) | −8.88854 | −0.519274 | −0.259637 | − | 0.965706i | \(-0.583603\pi\) | ||||
−0.259637 | + | 0.965706i | \(0.583603\pi\) | |||||||
\(294\) | −4.85410 | −0.283097 | ||||||||
\(295\) | −4.79837 | −0.279372 | ||||||||
\(296\) | 7.47214 | 0.434309 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.0344 | 1.16056 | ||||||||
\(299\) | 13.9443 | 0.806418 | ||||||||
\(300\) | 2.85410 | 0.164782 | ||||||||
\(301\) | −16.8885 | −0.973439 | ||||||||
\(302\) | 14.8885 | 0.856739 | ||||||||
\(303\) | −8.32624 | −0.478330 | ||||||||
\(304\) | −6.47214 | −0.371202 | ||||||||
\(305\) | 8.61803 | 0.493467 | ||||||||
\(306\) | 2.61803 | 0.149663 | ||||||||
\(307\) | 8.94427 | 0.510477 | 0.255238 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255238 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.09017 | 0.403346 | ||||||||
\(310\) | −4.61803 | −0.262287 | ||||||||
\(311\) | −4.27051 | −0.242158 | −0.121079 | − | 0.992643i | \(-0.538636\pi\) | ||||
−0.121079 | + | 0.992643i | \(0.538636\pi\) | |||||||
\(312\) | 1.38197 | 0.0782384 | ||||||||
\(313\) | 8.14590 | 0.460433 | 0.230217 | − | 0.973139i | \(-0.426057\pi\) | ||||
0.230217 | + | 0.973139i | \(0.426057\pi\) | |||||||
\(314\) | −16.0902 | −0.908021 | ||||||||
\(315\) | −6.23607 | −0.351363 | ||||||||
\(316\) | 10.2361 | 0.575824 | ||||||||
\(317\) | −14.1803 | −0.796447 | −0.398224 | − | 0.917288i | \(-0.630373\pi\) | ||||
−0.398224 | + | 0.917288i | \(0.630373\pi\) | |||||||
\(318\) | 4.09017 | 0.229365 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.618034 | 0.0345492 | ||||||||
\(321\) | −1.67376 | −0.0934203 | ||||||||
\(322\) | −24.0344 | −1.33939 | ||||||||
\(323\) | 6.47214 | 0.360119 | ||||||||
\(324\) | 5.70820 | 0.317122 | ||||||||
\(325\) | 10.3262 | 0.572797 | ||||||||
\(326\) | −6.47214 | −0.358458 | ||||||||
\(327\) | −8.88854 | −0.491538 | ||||||||
\(328\) | −9.70820 | −0.536046 | ||||||||
\(329\) | 24.3820 | 1.34422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.7426 | −0.755364 | −0.377682 | − | 0.925935i | \(-0.623279\pi\) | ||||
−0.377682 | + | 0.925935i | \(0.623279\pi\) | |||||||
\(332\) | −1.09017 | −0.0598308 | ||||||||
\(333\) | −19.5623 | −1.07201 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 8.09017 | 0.442013 | ||||||||
\(336\) | −2.38197 | −0.129947 | ||||||||
\(337\) | 5.56231 | 0.302998 | 0.151499 | − | 0.988457i | \(-0.451590\pi\) | ||||
0.151499 | + | 0.988457i | \(0.451590\pi\) | |||||||
\(338\) | −8.00000 | −0.435143 | ||||||||
\(339\) | 4.90983 | 0.266665 | ||||||||
\(340\) | −0.618034 | −0.0335176 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 16.9443 | 0.916241 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | −4.38197 | −0.236260 | ||||||||
\(345\) | 2.38197 | 0.128241 | ||||||||
\(346\) | −13.2361 | −0.711575 | ||||||||
\(347\) | 14.8541 | 0.797410 | 0.398705 | − | 0.917079i | \(-0.369460\pi\) | ||||
0.398705 | + | 0.917079i | \(0.369460\pi\) | |||||||
\(348\) | 5.70820 | 0.305992 | ||||||||
\(349\) | −12.5279 | −0.670601 | −0.335301 | − | 0.942111i | \(-0.608838\pi\) | ||||
−0.335301 | + | 0.942111i | \(0.608838\pi\) | |||||||
\(350\) | −17.7984 | −0.951363 | ||||||||
\(351\) | −7.76393 | −0.414408 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.96556 | −0.104616 | −0.0523081 | − | 0.998631i | \(-0.516658\pi\) | ||||
−0.0523081 | + | 0.998631i | \(0.516658\pi\) | |||||||
\(354\) | 4.79837 | 0.255031 | ||||||||
\(355\) | −9.61803 | −0.510472 | ||||||||
\(356\) | 14.4164 | 0.764068 | ||||||||
\(357\) | 2.38197 | 0.126067 | ||||||||
\(358\) | −3.29180 | −0.173977 | ||||||||
\(359\) | −9.70820 | −0.512379 | −0.256190 | − | 0.966627i | \(-0.582467\pi\) | ||||
−0.256190 | + | 0.966627i | \(0.582467\pi\) | |||||||
\(360\) | −1.61803 | −0.0852779 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | 2.23607 | 0.117525 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.61803 | −0.451708 | ||||||||
\(365\) | −4.70820 | −0.246439 | ||||||||
\(366\) | −8.61803 | −0.450472 | ||||||||
\(367\) | −21.7082 | −1.13316 | −0.566580 | − | 0.824007i | \(-0.691734\pi\) | ||||
−0.566580 | + | 0.824007i | \(0.691734\pi\) | |||||||
\(368\) | −6.23607 | −0.325078 | ||||||||
\(369\) | 25.4164 | 1.32313 | ||||||||
\(370\) | 4.61803 | 0.240080 | ||||||||
\(371\) | −25.5066 | −1.32424 | ||||||||
\(372\) | 4.61803 | 0.239434 | ||||||||
\(373\) | −22.3607 | −1.15779 | −0.578896 | − | 0.815401i | \(-0.696516\pi\) | ||||
−0.578896 | + | 0.815401i | \(0.696516\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.67376 | 0.189712 | ||||||||
\(376\) | 6.32624 | 0.326251 | ||||||||
\(377\) | 20.6525 | 1.06366 | ||||||||
\(378\) | 13.3820 | 0.688294 | ||||||||
\(379\) | 7.29180 | 0.374554 | 0.187277 | − | 0.982307i | \(-0.440034\pi\) | ||||
0.187277 | + | 0.982307i | \(0.440034\pi\) | |||||||
\(380\) | −4.00000 | −0.205196 | ||||||||
\(381\) | 5.14590 | 0.263632 | ||||||||
\(382\) | 14.2705 | 0.730143 | ||||||||
\(383\) | −14.5066 | −0.741251 | −0.370626 | − | 0.928782i | \(-0.620857\pi\) | ||||
−0.370626 | + | 0.928782i | \(0.620857\pi\) | |||||||
\(384\) | −0.618034 | −0.0315389 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.6525 | −0.898487 | ||||||||
\(387\) | 11.4721 | 0.583161 | ||||||||
\(388\) | 5.47214 | 0.277806 | ||||||||
\(389\) | −30.4164 | −1.54217 | −0.771087 | − | 0.636730i | \(-0.780286\pi\) | ||||
−0.771087 | + | 0.636730i | \(0.780286\pi\) | |||||||
\(390\) | 0.854102 | 0.0432491 | ||||||||
\(391\) | 6.23607 | 0.315372 | ||||||||
\(392\) | 7.85410 | 0.396692 | ||||||||
\(393\) | −4.47214 | −0.225589 | ||||||||
\(394\) | −12.0344 | −0.606286 | ||||||||
\(395\) | 6.32624 | 0.318308 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.9787 | −1.45440 | −0.727200 | − | 0.686426i | \(-0.759179\pi\) | ||||
−0.727200 | + | 0.686426i | \(0.759179\pi\) | |||||||
\(398\) | −8.03444 | −0.402730 | ||||||||
\(399\) | 15.4164 | 0.771786 | ||||||||
\(400\) | −4.61803 | −0.230902 | ||||||||
\(401\) | −8.32624 | −0.415792 | −0.207896 | − | 0.978151i | \(-0.566662\pi\) | ||||
−0.207896 | + | 0.978151i | \(0.566662\pi\) | |||||||
\(402\) | −8.09017 | −0.403501 | ||||||||
\(403\) | 16.7082 | 0.832295 | ||||||||
\(404\) | 13.4721 | 0.670264 | ||||||||
\(405\) | 3.52786 | 0.175301 | ||||||||
\(406\) | −35.5967 | −1.76664 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.618034 | 0.0305972 | ||||||||
\(409\) | 10.8885 | 0.538404 | 0.269202 | − | 0.963084i | \(-0.413240\pi\) | ||||
0.269202 | + | 0.963084i | \(0.413240\pi\) | |||||||
\(410\) | −6.00000 | −0.296319 | ||||||||
\(411\) | −4.43769 | −0.218895 | ||||||||
\(412\) | −11.4721 | −0.565192 | ||||||||
\(413\) | −29.9230 | −1.47241 | ||||||||
\(414\) | 16.3262 | 0.802391 | ||||||||
\(415\) | −0.673762 | −0.0330737 | ||||||||
\(416\) | −2.23607 | −0.109632 | ||||||||
\(417\) | 0.798374 | 0.0390965 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.1803 | −1.42555 | −0.712776 | − | 0.701391i | \(-0.752563\pi\) | ||||
−0.712776 | + | 0.701391i | \(0.752563\pi\) | |||||||
\(420\) | −1.47214 | −0.0718329 | ||||||||
\(421\) | 1.79837 | 0.0876474 | 0.0438237 | − | 0.999039i | \(-0.486046\pi\) | ||||
0.0438237 | + | 0.999039i | \(0.486046\pi\) | |||||||
\(422\) | −10.2705 | −0.499961 | ||||||||
\(423\) | −16.5623 | −0.805287 | ||||||||
\(424\) | −6.61803 | −0.321400 | ||||||||
\(425\) | 4.61803 | 0.224008 | ||||||||
\(426\) | 9.61803 | 0.465995 | ||||||||
\(427\) | 53.7426 | 2.60079 | ||||||||
\(428\) | 2.70820 | 0.130906 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.70820 | −0.130601 | ||||||||
\(431\) | 12.9443 | 0.623504 | 0.311752 | − | 0.950164i | \(-0.399084\pi\) | ||||
0.311752 | + | 0.950164i | \(0.399084\pi\) | |||||||
\(432\) | 3.47214 | 0.167053 | ||||||||
\(433\) | 3.85410 | 0.185216 | 0.0926082 | − | 0.995703i | \(-0.470480\pi\) | ||||
0.0926082 | + | 0.995703i | \(0.470480\pi\) | |||||||
\(434\) | −28.7984 | −1.38237 | ||||||||
\(435\) | 3.52786 | 0.169148 | ||||||||
\(436\) | 14.3820 | 0.688771 | ||||||||
\(437\) | 40.3607 | 1.93071 | ||||||||
\(438\) | 4.70820 | 0.224967 | ||||||||
\(439\) | 30.0902 | 1.43613 | 0.718063 | − | 0.695978i | \(-0.245029\pi\) | ||||
0.718063 | + | 0.695978i | \(0.245029\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.5623 | −0.979157 | ||||||||
\(442\) | 2.23607 | 0.106359 | ||||||||
\(443\) | −22.4164 | −1.06504 | −0.532518 | − | 0.846419i | \(-0.678754\pi\) | ||||
−0.532518 | + | 0.846419i | \(0.678754\pi\) | |||||||
\(444\) | −4.61803 | −0.219162 | ||||||||
\(445\) | 8.90983 | 0.422366 | ||||||||
\(446\) | 27.7082 | 1.31202 | ||||||||
\(447\) | −12.3820 | −0.585647 | ||||||||
\(448\) | 3.85410 | 0.182089 | ||||||||
\(449\) | −10.6738 | −0.503726 | −0.251863 | − | 0.967763i | \(-0.581043\pi\) | ||||
−0.251863 | + | 0.967763i | \(0.581043\pi\) | |||||||
\(450\) | 12.0902 | 0.569936 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.94427 | −0.373667 | ||||||||
\(453\) | −9.20163 | −0.432330 | ||||||||
\(454\) | 2.23607 | 0.104944 | ||||||||
\(455\) | −5.32624 | −0.249698 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | −18.0689 | −0.845227 | −0.422613 | − | 0.906310i | \(-0.638887\pi\) | ||||
−0.422613 | + | 0.906310i | \(0.638887\pi\) | |||||||
\(458\) | −17.5623 | −0.820633 | ||||||||
\(459\) | −3.47214 | −0.162065 | ||||||||
\(460\) | −3.85410 | −0.179698 | ||||||||
\(461\) | −20.5967 | −0.959286 | −0.479643 | − | 0.877464i | \(-0.659234\pi\) | ||||
−0.479643 | + | 0.877464i | \(0.659234\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.4508 | 1.46164 | 0.730822 | − | 0.682568i | \(-0.239137\pi\) | ||||
0.730822 | + | 0.682568i | \(0.239137\pi\) | |||||||
\(464\) | −9.23607 | −0.428774 | ||||||||
\(465\) | 2.85410 | 0.132356 | ||||||||
\(466\) | 17.1803 | 0.795864 | ||||||||
\(467\) | 1.61803 | 0.0748737 | 0.0374368 | − | 0.999299i | \(-0.488081\pi\) | ||||
0.0374368 | + | 0.999299i | \(0.488081\pi\) | |||||||
\(468\) | 5.85410 | 0.270606 | ||||||||
\(469\) | 50.4508 | 2.32960 | ||||||||
\(470\) | 3.90983 | 0.180347 | ||||||||
\(471\) | 9.94427 | 0.458208 | ||||||||
\(472\) | −7.76393 | −0.357364 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.32624 | −0.290574 | ||||||||
\(475\) | 29.8885 | 1.37138 | ||||||||
\(476\) | −3.85410 | −0.176652 | ||||||||
\(477\) | 17.3262 | 0.793314 | ||||||||
\(478\) | −21.1803 | −0.968766 | ||||||||
\(479\) | 14.5967 | 0.666942 | 0.333471 | − | 0.942760i | \(-0.391780\pi\) | ||||
0.333471 | + | 0.942760i | \(0.391780\pi\) | |||||||
\(480\) | −0.381966 | −0.0174343 | ||||||||
\(481\) | −16.7082 | −0.761829 | ||||||||
\(482\) | 13.9443 | 0.635144 | ||||||||
\(483\) | 14.8541 | 0.675885 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.38197 | 0.153567 | ||||||||
\(486\) | −13.9443 | −0.632525 | ||||||||
\(487\) | −40.1803 | −1.82074 | −0.910372 | − | 0.413790i | \(-0.864205\pi\) | ||||
−0.910372 | + | 0.413790i | \(0.864205\pi\) | |||||||
\(488\) | 13.9443 | 0.631228 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 4.85410 | 0.219286 | ||||||||
\(491\) | 33.9443 | 1.53188 | 0.765942 | − | 0.642910i | \(-0.222273\pi\) | ||||
0.765942 | + | 0.642910i | \(0.222273\pi\) | |||||||
\(492\) | 6.00000 | 0.270501 | ||||||||
\(493\) | 9.23607 | 0.415972 | ||||||||
\(494\) | 14.4721 | 0.651132 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.47214 | −0.335509 | ||||||||
\(497\) | −59.9787 | −2.69041 | ||||||||
\(498\) | 0.673762 | 0.0301920 | ||||||||
\(499\) | −13.3607 | −0.598106 | −0.299053 | − | 0.954236i | \(-0.596671\pi\) | ||||
−0.299053 | + | 0.954236i | \(0.596671\pi\) | |||||||
\(500\) | −5.94427 | −0.265836 | ||||||||
\(501\) | −7.41641 | −0.331341 | ||||||||
\(502\) | −16.4721 | −0.735187 | ||||||||
\(503\) | 25.3262 | 1.12924 | 0.564621 | − | 0.825351i | \(-0.309023\pi\) | ||||
0.564621 | + | 0.825351i | \(0.309023\pi\) | |||||||
\(504\) | −10.0902 | −0.449452 | ||||||||
\(505\) | 8.32624 | 0.370513 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.94427 | 0.219583 | ||||||||
\(508\) | −8.32624 | −0.369417 | ||||||||
\(509\) | 7.58359 | 0.336137 | 0.168068 | − | 0.985775i | \(-0.446247\pi\) | ||||
0.168068 | + | 0.985775i | \(0.446247\pi\) | |||||||
\(510\) | 0.381966 | 0.0169137 | ||||||||
\(511\) | −29.3607 | −1.29884 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −22.4721 | −0.992169 | ||||||||
\(514\) | −15.4164 | −0.679989 | ||||||||
\(515\) | −7.09017 | −0.312430 | ||||||||
\(516\) | 2.70820 | 0.119222 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 28.7984 | 1.26533 | ||||||||
\(519\) | 8.18034 | 0.359077 | ||||||||
\(520\) | −1.38197 | −0.0606032 | ||||||||
\(521\) | 24.5623 | 1.07609 | 0.538047 | − | 0.842915i | \(-0.319162\pi\) | ||||
0.538047 | + | 0.842915i | \(0.319162\pi\) | |||||||
\(522\) | 24.1803 | 1.05834 | ||||||||
\(523\) | −5.05573 | −0.221072 | −0.110536 | − | 0.993872i | \(-0.535257\pi\) | ||||
−0.110536 | + | 0.993872i | \(0.535257\pi\) | |||||||
\(524\) | 7.23607 | 0.316109 | ||||||||
\(525\) | 11.0000 | 0.480079 | ||||||||
\(526\) | 8.14590 | 0.355178 | ||||||||
\(527\) | 7.47214 | 0.325491 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.8885 | 0.690806 | ||||||||
\(530\) | −4.09017 | −0.177666 | ||||||||
\(531\) | 20.3262 | 0.882084 | ||||||||
\(532\) | −24.9443 | −1.08147 | ||||||||
\(533\) | 21.7082 | 0.940287 | ||||||||
\(534\) | −8.90983 | −0.385566 | ||||||||
\(535\) | 1.67376 | 0.0723630 | ||||||||
\(536\) | 13.0902 | 0.565409 | ||||||||
\(537\) | 2.03444 | 0.0877926 | ||||||||
\(538\) | 9.88854 | 0.426325 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.14590 | 0.0923447 | ||||||||
\(541\) | −20.9443 | −0.900465 | −0.450232 | − | 0.892911i | \(-0.648659\pi\) | ||||
−0.450232 | + | 0.892911i | \(0.648659\pi\) | |||||||
\(542\) | 5.85410 | 0.251455 | ||||||||
\(543\) | −1.38197 | −0.0593058 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 8.88854 | 0.380743 | ||||||||
\(546\) | 5.32624 | 0.227942 | ||||||||
\(547\) | 32.1246 | 1.37355 | 0.686775 | − | 0.726870i | \(-0.259026\pi\) | ||||
0.686775 | + | 0.726870i | \(0.259026\pi\) | |||||||
\(548\) | 7.18034 | 0.306729 | ||||||||
\(549\) | −36.5066 | −1.55806 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 59.7771 | 2.54659 | ||||||||
\(552\) | 3.85410 | 0.164041 | ||||||||
\(553\) | 39.4508 | 1.67762 | ||||||||
\(554\) | −20.1246 | −0.855013 | ||||||||
\(555\) | −2.85410 | −0.121150 | ||||||||
\(556\) | −1.29180 | −0.0547844 | ||||||||
\(557\) | 14.5066 | 0.614663 | 0.307332 | − | 0.951602i | \(-0.400564\pi\) | ||||
0.307332 | + | 0.951602i | \(0.400564\pi\) | |||||||
\(558\) | 19.5623 | 0.828138 | ||||||||
\(559\) | 9.79837 | 0.414427 | ||||||||
\(560\) | 2.38197 | 0.100656 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.4721 | 0.779200 | ||||||||
\(563\) | −19.1803 | −0.808355 | −0.404177 | − | 0.914681i | \(-0.632442\pi\) | ||||
−0.404177 | + | 0.914681i | \(0.632442\pi\) | |||||||
\(564\) | −3.90983 | −0.164634 | ||||||||
\(565\) | −4.90983 | −0.206558 | ||||||||
\(566\) | 9.27051 | 0.389669 | ||||||||
\(567\) | 22.0000 | 0.923913 | ||||||||
\(568\) | −15.5623 | −0.652980 | ||||||||
\(569\) | −37.7082 | −1.58081 | −0.790405 | − | 0.612585i | \(-0.790130\pi\) | ||||
−0.790405 | + | 0.612585i | \(0.790130\pi\) | |||||||
\(570\) | 2.47214 | 0.103546 | ||||||||
\(571\) | −36.1803 | −1.51410 | −0.757050 | − | 0.653357i | \(-0.773360\pi\) | ||||
−0.757050 | + | 0.653357i | \(0.773360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.81966 | −0.368447 | ||||||||
\(574\) | −37.4164 | −1.56173 | ||||||||
\(575\) | 28.7984 | 1.20098 | ||||||||
\(576\) | −2.61803 | −0.109085 | ||||||||
\(577\) | 35.4721 | 1.47672 | 0.738362 | − | 0.674404i | \(-0.235600\pi\) | ||||
0.738362 | + | 0.674404i | \(0.235600\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 10.9098 | 0.453397 | ||||||||
\(580\) | −5.70820 | −0.237020 | ||||||||
\(581\) | −4.20163 | −0.174313 | ||||||||
\(582\) | −3.38197 | −0.140187 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −7.61803 | −0.315236 | ||||||||
\(585\) | 3.61803 | 0.149587 | ||||||||
\(586\) | −8.88854 | −0.367182 | ||||||||
\(587\) | −31.6180 | −1.30502 | −0.652508 | − | 0.757782i | \(-0.726283\pi\) | ||||
−0.652508 | + | 0.757782i | \(0.726283\pi\) | |||||||
\(588\) | −4.85410 | −0.200180 | ||||||||
\(589\) | 48.3607 | 1.99267 | ||||||||
\(590\) | −4.79837 | −0.197546 | ||||||||
\(591\) | 7.43769 | 0.305946 | ||||||||
\(592\) | 7.47214 | 0.307103 | ||||||||
\(593\) | −5.74265 | −0.235822 | −0.117911 | − | 0.993024i | \(-0.537620\pi\) | ||||
−0.117911 | + | 0.993024i | \(0.537620\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.38197 | −0.0976511 | ||||||||
\(596\) | 20.0344 | 0.820643 | ||||||||
\(597\) | 4.96556 | 0.203227 | ||||||||
\(598\) | 13.9443 | 0.570224 | ||||||||
\(599\) | −34.5623 | −1.41218 | −0.706089 | − | 0.708123i | \(-0.749542\pi\) | ||||
−0.706089 | + | 0.708123i | \(0.749542\pi\) | |||||||
\(600\) | 2.85410 | 0.116518 | ||||||||
\(601\) | 13.0000 | 0.530281 | 0.265141 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265141 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(602\) | −16.8885 | −0.688326 | ||||||||
\(603\) | −34.2705 | −1.39560 | ||||||||
\(604\) | 14.8885 | 0.605806 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.32624 | −0.338230 | ||||||||
\(607\) | 39.1591 | 1.58942 | 0.794708 | − | 0.606991i | \(-0.207624\pi\) | ||||
0.794708 | + | 0.606991i | \(0.207624\pi\) | |||||||
\(608\) | −6.47214 | −0.262480 | ||||||||
\(609\) | 22.0000 | 0.891485 | ||||||||
\(610\) | 8.61803 | 0.348934 | ||||||||
\(611\) | −14.1459 | −0.572282 | ||||||||
\(612\) | 2.61803 | 0.105828 | ||||||||
\(613\) | −4.27051 | −0.172484 | −0.0862421 | − | 0.996274i | \(-0.527486\pi\) | ||||
−0.0862421 | + | 0.996274i | \(0.527486\pi\) | |||||||
\(614\) | 8.94427 | 0.360961 | ||||||||
\(615\) | 3.70820 | 0.149529 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.6180 | −0.991085 | −0.495542 | − | 0.868584i | \(-0.665031\pi\) | ||||
−0.495542 | + | 0.868584i | \(0.665031\pi\) | |||||||
\(618\) | 7.09017 | 0.285208 | ||||||||
\(619\) | −17.7639 | −0.713993 | −0.356996 | − | 0.934106i | \(-0.616199\pi\) | ||||
−0.356996 | + | 0.934106i | \(0.616199\pi\) | |||||||
\(620\) | −4.61803 | −0.185465 | ||||||||
\(621\) | −21.6525 | −0.868884 | ||||||||
\(622\) | −4.27051 | −0.171232 | ||||||||
\(623\) | 55.5623 | 2.22606 | ||||||||
\(624\) | 1.38197 | 0.0553229 | ||||||||
\(625\) | 19.4164 | 0.776656 | ||||||||
\(626\) | 8.14590 | 0.325576 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.0902 | −0.642068 | ||||||||
\(629\) | −7.47214 | −0.297934 | ||||||||
\(630\) | −6.23607 | −0.248451 | ||||||||
\(631\) | 26.0132 | 1.03557 | 0.517784 | − | 0.855512i | \(-0.326757\pi\) | ||||
0.517784 | + | 0.855512i | \(0.326757\pi\) | |||||||
\(632\) | 10.2361 | 0.407169 | ||||||||
\(633\) | 6.34752 | 0.252291 | ||||||||
\(634\) | −14.1803 | −0.563173 | ||||||||
\(635\) | −5.14590 | −0.204209 | ||||||||
\(636\) | 4.09017 | 0.162186 | ||||||||
\(637\) | −17.5623 | −0.695844 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.7426 | 1.61175 | ||||||||
\(640\) | 0.618034 | 0.0244299 | ||||||||
\(641\) | −3.97871 | −0.157150 | −0.0785749 | − | 0.996908i | \(-0.525037\pi\) | ||||
−0.0785749 | + | 0.996908i | \(0.525037\pi\) | |||||||
\(642\) | −1.67376 | −0.0660581 | ||||||||
\(643\) | 29.6869 | 1.17074 | 0.585369 | − | 0.810767i | \(-0.300950\pi\) | ||||
0.585369 | + | 0.810767i | \(0.300950\pi\) | |||||||
\(644\) | −24.0344 | −0.947090 | ||||||||
\(645\) | 1.67376 | 0.0659043 | ||||||||
\(646\) | 6.47214 | 0.254643 | ||||||||
\(647\) | −28.3820 | −1.11581 | −0.557905 | − | 0.829905i | \(-0.688395\pi\) | ||||
−0.557905 | + | 0.829905i | \(0.688395\pi\) | |||||||
\(648\) | 5.70820 | 0.224239 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 10.3262 | 0.405028 | ||||||||
\(651\) | 17.7984 | 0.697573 | ||||||||
\(652\) | −6.47214 | −0.253468 | ||||||||
\(653\) | 5.76393 | 0.225560 | 0.112780 | − | 0.993620i | \(-0.464024\pi\) | ||||
0.112780 | + | 0.993620i | \(0.464024\pi\) | |||||||
\(654\) | −8.88854 | −0.347570 | ||||||||
\(655\) | 4.47214 | 0.174741 | ||||||||
\(656\) | −9.70820 | −0.379042 | ||||||||
\(657\) | 19.9443 | 0.778100 | ||||||||
\(658\) | 24.3820 | 0.950508 | ||||||||
\(659\) | 9.41641 | 0.366811 | 0.183406 | − | 0.983037i | \(-0.441288\pi\) | ||||
0.183406 | + | 0.983037i | \(0.441288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.5410 | 1.18791 | 0.593954 | − | 0.804499i | \(-0.297566\pi\) | ||||
0.593954 | + | 0.804499i | \(0.297566\pi\) | |||||||
\(662\) | −13.7426 | −0.534123 | ||||||||
\(663\) | −1.38197 | −0.0536711 | ||||||||
\(664\) | −1.09017 | −0.0423068 | ||||||||
\(665\) | −15.4164 | −0.597823 | ||||||||
\(666\) | −19.5623 | −0.758024 | ||||||||
\(667\) | 57.5967 | 2.23015 | ||||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | −17.1246 | −0.662076 | ||||||||
\(670\) | 8.09017 | 0.312551 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.38197 | −0.0918863 | ||||||||
\(673\) | 19.5623 | 0.754071 | 0.377036 | − | 0.926199i | \(-0.376943\pi\) | ||||
0.377036 | + | 0.926199i | \(0.376943\pi\) | |||||||
\(674\) | 5.56231 | 0.214252 | ||||||||
\(675\) | −16.0344 | −0.617166 | ||||||||
\(676\) | −8.00000 | −0.307692 | ||||||||
\(677\) | 11.3050 | 0.434485 | 0.217242 | − | 0.976118i | \(-0.430294\pi\) | ||||
0.217242 | + | 0.976118i | \(0.430294\pi\) | |||||||
\(678\) | 4.90983 | 0.188561 | ||||||||
\(679\) | 21.0902 | 0.809366 | ||||||||
\(680\) | −0.618034 | −0.0237005 | ||||||||
\(681\) | −1.38197 | −0.0529571 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.6525 | 0.828509 | 0.414254 | − | 0.910161i | \(-0.364042\pi\) | ||||
0.414254 | + | 0.910161i | \(0.364042\pi\) | |||||||
\(684\) | 16.9443 | 0.647880 | ||||||||
\(685\) | 4.43769 | 0.169556 | ||||||||
\(686\) | 3.29180 | 0.125681 | ||||||||
\(687\) | 10.8541 | 0.414110 | ||||||||
\(688\) | −4.38197 | −0.167061 | ||||||||
\(689\) | 14.7984 | 0.563773 | ||||||||
\(690\) | 2.38197 | 0.0906799 | ||||||||
\(691\) | 17.5836 | 0.668911 | 0.334456 | − | 0.942411i | \(-0.391448\pi\) | ||||
0.334456 | + | 0.942411i | \(0.391448\pi\) | |||||||
\(692\) | −13.2361 | −0.503160 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.8541 | 0.563854 | ||||||||
\(695\) | −0.798374 | −0.0302840 | ||||||||
\(696\) | 5.70820 | 0.216369 | ||||||||
\(697\) | 9.70820 | 0.367724 | ||||||||
\(698\) | −12.5279 | −0.474187 | ||||||||
\(699\) | −10.6180 | −0.401611 | ||||||||
\(700\) | −17.7984 | −0.672715 | ||||||||
\(701\) | −39.1033 | −1.47691 | −0.738456 | − | 0.674302i | \(-0.764445\pi\) | ||||
−0.738456 | + | 0.674302i | \(0.764445\pi\) | |||||||
\(702\) | −7.76393 | −0.293031 | ||||||||
\(703\) | −48.3607 | −1.82396 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.41641 | −0.0910072 | ||||||||
\(706\) | −1.96556 | −0.0739748 | ||||||||
\(707\) | 51.9230 | 1.95276 | ||||||||
\(708\) | 4.79837 | 0.180334 | ||||||||
\(709\) | 8.81966 | 0.331229 | 0.165615 | − | 0.986191i | \(-0.447039\pi\) | ||||
0.165615 | + | 0.986191i | \(0.447039\pi\) | |||||||
\(710\) | −9.61803 | −0.360958 | ||||||||
\(711\) | −26.7984 | −1.00502 | ||||||||
\(712\) | 14.4164 | 0.540278 | ||||||||
\(713\) | 46.5967 | 1.74506 | ||||||||
\(714\) | 2.38197 | 0.0891428 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.29180 | −0.123020 | ||||||||
\(717\) | 13.0902 | 0.488861 | ||||||||
\(718\) | −9.70820 | −0.362307 | ||||||||
\(719\) | −15.8197 | −0.589974 | −0.294987 | − | 0.955501i | \(-0.595315\pi\) | ||||
−0.294987 | + | 0.955501i | \(0.595315\pi\) | |||||||
\(720\) | −1.61803 | −0.0603006 | ||||||||
\(721\) | −44.2148 | −1.64664 | ||||||||
\(722\) | 22.8885 | 0.851823 | ||||||||
\(723\) | −8.61803 | −0.320508 | ||||||||
\(724\) | 2.23607 | 0.0831028 | ||||||||
\(725\) | 42.6525 | 1.58407 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3607 | 1.05184 | 0.525920 | − | 0.850534i | \(-0.323721\pi\) | ||||
0.525920 | + | 0.850534i | \(0.323721\pi\) | |||||||
\(728\) | −8.61803 | −0.319406 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | −4.70820 | −0.174258 | ||||||||
\(731\) | 4.38197 | 0.162073 | ||||||||
\(732\) | −8.61803 | −0.318532 | ||||||||
\(733\) | −45.6525 | −1.68621 | −0.843106 | − | 0.537747i | \(-0.819276\pi\) | ||||
−0.843106 | + | 0.537747i | \(0.819276\pi\) | |||||||
\(734\) | −21.7082 | −0.801264 | ||||||||
\(735\) | −3.00000 | −0.110657 | ||||||||
\(736\) | −6.23607 | −0.229865 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 25.4164 | 0.935591 | ||||||||
\(739\) | −28.3607 | −1.04326 | −0.521632 | − | 0.853170i | \(-0.674677\pi\) | ||||
−0.521632 | + | 0.853170i | \(0.674677\pi\) | |||||||
\(740\) | 4.61803 | 0.169762 | ||||||||
\(741\) | −8.94427 | −0.328576 | ||||||||
\(742\) | −25.5066 | −0.936376 | ||||||||
\(743\) | −10.6180 | −0.389538 | −0.194769 | − | 0.980849i | \(-0.562396\pi\) | ||||
−0.194769 | + | 0.980849i | \(0.562396\pi\) | |||||||
\(744\) | 4.61803 | 0.169305 | ||||||||
\(745\) | 12.3820 | 0.453640 | ||||||||
\(746\) | −22.3607 | −0.818683 | ||||||||
\(747\) | 2.85410 | 0.104426 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.4377 | 0.381385 | ||||||||
\(750\) | 3.67376 | 0.134147 | ||||||||
\(751\) | 19.0000 | 0.693320 | 0.346660 | − | 0.937991i | \(-0.387316\pi\) | ||||
0.346660 | + | 0.937991i | \(0.387316\pi\) | |||||||
\(752\) | 6.32624 | 0.230694 | ||||||||
\(753\) | 10.1803 | 0.370992 | ||||||||
\(754\) | 20.6525 | 0.752119 | ||||||||
\(755\) | 9.20163 | 0.334881 | ||||||||
\(756\) | 13.3820 | 0.486697 | ||||||||
\(757\) | −25.1803 | −0.915195 | −0.457598 | − | 0.889159i | \(-0.651290\pi\) | ||||
−0.457598 | + | 0.889159i | \(0.651290\pi\) | |||||||
\(758\) | 7.29180 | 0.264850 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.00000 | −0.145095 | ||||||||
\(761\) | 5.74265 | 0.208171 | 0.104085 | − | 0.994568i | \(-0.466808\pi\) | ||||
0.104085 | + | 0.994568i | \(0.466808\pi\) | |||||||
\(762\) | 5.14590 | 0.186416 | ||||||||
\(763\) | 55.4296 | 2.00668 | ||||||||
\(764\) | 14.2705 | 0.516289 | ||||||||
\(765\) | 1.61803 | 0.0585001 | ||||||||
\(766\) | −14.5066 | −0.524144 | ||||||||
\(767\) | 17.3607 | 0.626858 | ||||||||
\(768\) | −0.618034 | −0.0223014 | ||||||||
\(769\) | 26.8328 | 0.967616 | 0.483808 | − | 0.875174i | \(-0.339253\pi\) | ||||
0.483808 | + | 0.875174i | \(0.339253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.52786 | 0.343138 | ||||||||
\(772\) | −17.6525 | −0.635327 | ||||||||
\(773\) | 3.72949 | 0.134140 | 0.0670702 | − | 0.997748i | \(-0.478635\pi\) | ||||
0.0670702 | + | 0.997748i | \(0.478635\pi\) | |||||||
\(774\) | 11.4721 | 0.412357 | ||||||||
\(775\) | 34.5066 | 1.23951 | ||||||||
\(776\) | 5.47214 | 0.196438 | ||||||||
\(777\) | −17.7984 | −0.638513 | ||||||||
\(778\) | −30.4164 | −1.09048 | ||||||||
\(779\) | 62.8328 | 2.25122 | ||||||||
\(780\) | 0.854102 | 0.0305818 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.23607 | 0.223001 | ||||||||
\(783\) | −32.0689 | −1.14605 | ||||||||
\(784\) | 7.85410 | 0.280504 | ||||||||
\(785\) | −9.94427 | −0.354926 | ||||||||
\(786\) | −4.47214 | −0.159516 | ||||||||
\(787\) | 22.6180 | 0.806246 | 0.403123 | − | 0.915146i | \(-0.367925\pi\) | ||||
0.403123 | + | 0.915146i | \(0.367925\pi\) | |||||||
\(788\) | −12.0344 | −0.428709 | ||||||||
\(789\) | −5.03444 | −0.179231 | ||||||||
\(790\) | 6.32624 | 0.225077 | ||||||||
\(791\) | −30.6180 | −1.08865 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.1803 | −1.10725 | ||||||||
\(794\) | −28.9787 | −1.02842 | ||||||||
\(795\) | 2.52786 | 0.0896541 | ||||||||
\(796\) | −8.03444 | −0.284773 | ||||||||
\(797\) | −24.8885 | −0.881597 | −0.440799 | − | 0.897606i | \(-0.645305\pi\) | ||||
−0.440799 | + | 0.897606i | \(0.645305\pi\) | |||||||
\(798\) | 15.4164 | 0.545735 | ||||||||
\(799\) | −6.32624 | −0.223806 | ||||||||
\(800\) | −4.61803 | −0.163272 | ||||||||
\(801\) | −37.7426 | −1.33357 | ||||||||
\(802\) | −8.32624 | −0.294010 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −8.09017 | −0.285318 | ||||||||
\(805\) | −14.8541 | −0.523538 | ||||||||
\(806\) | 16.7082 | 0.588521 | ||||||||
\(807\) | −6.11146 | −0.215133 | ||||||||
\(808\) | 13.4721 | 0.473948 | ||||||||
\(809\) | −26.2016 | −0.921200 | −0.460600 | − | 0.887608i | \(-0.652366\pi\) | ||||
−0.460600 | + | 0.887608i | \(0.652366\pi\) | |||||||
\(810\) | 3.52786 | 0.123957 | ||||||||
\(811\) | −1.47214 | −0.0516937 | −0.0258468 | − | 0.999666i | \(-0.508228\pi\) | ||||
−0.0258468 | + | 0.999666i | \(0.508228\pi\) | |||||||
\(812\) | −35.5967 | −1.24920 | ||||||||
\(813\) | −3.61803 | −0.126890 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | 0.618034 | 0.0216355 | ||||||||
\(817\) | 28.3607 | 0.992215 | ||||||||
\(818\) | 10.8885 | 0.380709 | ||||||||
\(819\) | 22.5623 | 0.788391 | ||||||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | −2.63932 | −0.0921129 | −0.0460565 | − | 0.998939i | \(-0.514665\pi\) | ||||
−0.0460565 | + | 0.998939i | \(0.514665\pi\) | |||||||
\(822\) | −4.43769 | −0.154782 | ||||||||
\(823\) | 21.1459 | 0.737100 | 0.368550 | − | 0.929608i | \(-0.379854\pi\) | ||||
0.368550 | + | 0.929608i | \(0.379854\pi\) | |||||||
\(824\) | −11.4721 | −0.399651 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.9230 | −1.04115 | ||||||||
\(827\) | −17.6738 | −0.614577 | −0.307288 | − | 0.951616i | \(-0.599422\pi\) | ||||
−0.307288 | + | 0.951616i | \(0.599422\pi\) | |||||||
\(828\) | 16.3262 | 0.567376 | ||||||||
\(829\) | −34.1803 | −1.18713 | −0.593566 | − | 0.804785i | \(-0.702280\pi\) | ||||
−0.593566 | + | 0.804785i | \(0.702280\pi\) | |||||||
\(830\) | −0.673762 | −0.0233866 | ||||||||
\(831\) | 12.4377 | 0.431459 | ||||||||
\(832\) | −2.23607 | −0.0775217 | ||||||||
\(833\) | −7.85410 | −0.272129 | ||||||||
\(834\) | 0.798374 | 0.0276454 | ||||||||
\(835\) | 7.41641 | 0.256655 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.9443 | −0.896765 | ||||||||
\(838\) | −29.1803 | −1.00802 | ||||||||
\(839\) | 6.29180 | 0.217217 | 0.108608 | − | 0.994085i | \(-0.465361\pi\) | ||||
0.108608 | + | 0.994085i | \(0.465361\pi\) | |||||||
\(840\) | −1.47214 | −0.0507935 | ||||||||
\(841\) | 56.3050 | 1.94155 | ||||||||
\(842\) | 1.79837 | 0.0619761 | ||||||||
\(843\) | −11.4164 | −0.393202 | ||||||||
\(844\) | −10.2705 | −0.353526 | ||||||||
\(845\) | −4.94427 | −0.170088 | ||||||||
\(846\) | −16.5623 | −0.569424 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.61803 | −0.227264 | ||||||||
\(849\) | −5.72949 | −0.196636 | ||||||||
\(850\) | 4.61803 | 0.158397 | ||||||||
\(851\) | −46.5967 | −1.59732 | ||||||||
\(852\) | 9.61803 | 0.329508 | ||||||||
\(853\) | −5.78522 | −0.198082 | −0.0990411 | − | 0.995083i | \(-0.531578\pi\) | ||||
−0.0990411 | + | 0.995083i | \(0.531578\pi\) | |||||||
\(854\) | 53.7426 | 1.83904 | ||||||||
\(855\) | 10.4721 | 0.358139 | ||||||||
\(856\) | 2.70820 | 0.0925645 | ||||||||
\(857\) | 7.09017 | 0.242196 | 0.121098 | − | 0.992641i | \(-0.461359\pi\) | ||||
0.121098 | + | 0.992641i | \(0.461359\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.3475 | 0.557770 | 0.278885 | − | 0.960324i | \(-0.410035\pi\) | ||||
0.278885 | + | 0.960324i | \(0.410035\pi\) | |||||||
\(860\) | −2.70820 | −0.0923490 | ||||||||
\(861\) | 23.1246 | 0.788085 | ||||||||
\(862\) | 12.9443 | 0.440884 | ||||||||
\(863\) | −36.2361 | −1.23349 | −0.616745 | − | 0.787163i | \(-0.711549\pi\) | ||||
−0.616745 | + | 0.787163i | \(0.711549\pi\) | |||||||
\(864\) | 3.47214 | 0.118124 | ||||||||
\(865\) | −8.18034 | −0.278140 | ||||||||
\(866\) | 3.85410 | 0.130968 | ||||||||
\(867\) | −0.618034 | −0.0209895 | ||||||||
\(868\) | −28.7984 | −0.977481 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.52786 | 0.119606 | ||||||||
\(871\) | −29.2705 | −0.991793 | ||||||||
\(872\) | 14.3820 | 0.487035 | ||||||||
\(873\) | −14.3262 | −0.484870 | ||||||||
\(874\) | 40.3607 | 1.36522 | ||||||||
\(875\) | −22.9098 | −0.774494 | ||||||||
\(876\) | 4.70820 | 0.159075 | ||||||||
\(877\) | −23.5623 | −0.795643 | −0.397821 | − | 0.917463i | \(-0.630234\pi\) | ||||
−0.397821 | + | 0.917463i | \(0.630234\pi\) | |||||||
\(878\) | 30.0902 | 1.01549 | ||||||||
\(879\) | 5.49342 | 0.185289 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.8328 | −1.91475 | −0.957373 | − | 0.288854i | \(-0.906726\pi\) | ||||
−0.957373 | + | 0.288854i | \(0.906726\pi\) | |||||||
\(882\) | −20.5623 | −0.692369 | ||||||||
\(883\) | 24.8197 | 0.835248 | 0.417624 | − | 0.908620i | \(-0.362863\pi\) | ||||
0.417624 | + | 0.908620i | \(0.362863\pi\) | |||||||
\(884\) | 2.23607 | 0.0752071 | ||||||||
\(885\) | 2.96556 | 0.0996861 | ||||||||
\(886\) | −22.4164 | −0.753094 | ||||||||
\(887\) | −1.14590 | −0.0384755 | −0.0192377 | − | 0.999815i | \(-0.506124\pi\) | ||||
−0.0192377 | + | 0.999815i | \(0.506124\pi\) | |||||||
\(888\) | −4.61803 | −0.154971 | ||||||||
\(889\) | −32.0902 | −1.07627 | ||||||||
\(890\) | 8.90983 | 0.298658 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.7082 | 0.927739 | ||||||||
\(893\) | −40.9443 | −1.37015 | ||||||||
\(894\) | −12.3820 | −0.414115 | ||||||||
\(895\) | −2.03444 | −0.0680039 | ||||||||
\(896\) | 3.85410 | 0.128757 | ||||||||
\(897\) | −8.61803 | −0.287748 | ||||||||
\(898\) | −10.6738 | −0.356188 | ||||||||
\(899\) | 69.0132 | 2.30172 | ||||||||
\(900\) | 12.0902 | 0.403006 | ||||||||
\(901\) | 6.61803 | 0.220479 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.4377 | 0.347345 | ||||||||
\(904\) | −7.94427 | −0.264223 | ||||||||
\(905\) | 1.38197 | 0.0459381 | ||||||||
\(906\) | −9.20163 | −0.305704 | ||||||||
\(907\) | 38.0689 | 1.26406 | 0.632028 | − | 0.774945i | \(-0.282223\pi\) | ||||
0.632028 | + | 0.774945i | \(0.282223\pi\) | |||||||
\(908\) | 2.23607 | 0.0742065 | ||||||||
\(909\) | −35.2705 | −1.16985 | ||||||||
\(910\) | −5.32624 | −0.176563 | ||||||||
\(911\) | −16.1115 | −0.533796 | −0.266898 | − | 0.963725i | \(-0.585999\pi\) | ||||
−0.266898 | + | 0.963725i | \(0.585999\pi\) | |||||||
\(912\) | 4.00000 | 0.132453 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −18.0689 | −0.597666 | ||||||||
\(915\) | −5.32624 | −0.176080 | ||||||||
\(916\) | −17.5623 | −0.580275 | ||||||||
\(917\) | 27.8885 | 0.920961 | ||||||||
\(918\) | −3.47214 | −0.114598 | ||||||||
\(919\) | −37.4508 | −1.23539 | −0.617695 | − | 0.786418i | \(-0.711933\pi\) | ||||
−0.617695 | + | 0.786418i | \(0.711933\pi\) | |||||||
\(920\) | −3.85410 | −0.127066 | ||||||||
\(921\) | −5.52786 | −0.182149 | ||||||||
\(922\) | −20.5967 | −0.678318 | ||||||||
\(923\) | 34.7984 | 1.14540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.5066 | −1.13457 | ||||||||
\(926\) | 31.4508 | 1.03354 | ||||||||
\(927\) | 30.0344 | 0.986460 | ||||||||
\(928\) | −9.23607 | −0.303189 | ||||||||
\(929\) | −23.6738 | −0.776711 | −0.388355 | − | 0.921510i | \(-0.626957\pi\) | ||||
−0.388355 | + | 0.921510i | \(0.626957\pi\) | |||||||
\(930\) | 2.85410 | 0.0935897 | ||||||||
\(931\) | −50.8328 | −1.66598 | ||||||||
\(932\) | 17.1803 | 0.562761 | ||||||||
\(933\) | 2.63932 | 0.0864075 | ||||||||
\(934\) | 1.61803 | 0.0529437 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.85410 | 0.191347 | ||||||||
\(937\) | −25.8885 | −0.845742 | −0.422871 | − | 0.906190i | \(-0.638978\pi\) | ||||
−0.422871 | + | 0.906190i | \(0.638978\pi\) | |||||||
\(938\) | 50.4508 | 1.64728 | ||||||||
\(939\) | −5.03444 | −0.164293 | ||||||||
\(940\) | 3.90983 | 0.127525 | ||||||||
\(941\) | −33.7639 | −1.10067 | −0.550336 | − | 0.834943i | \(-0.685501\pi\) | ||||
−0.550336 | + | 0.834943i | \(0.685501\pi\) | |||||||
\(942\) | 9.94427 | 0.324002 | ||||||||
\(943\) | 60.5410 | 1.97149 | ||||||||
\(944\) | −7.76393 | −0.252694 | ||||||||
\(945\) | 8.27051 | 0.269040 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.70820 | 0.217987 | 0.108994 | − | 0.994042i | \(-0.465237\pi\) | ||||
0.108994 | + | 0.994042i | \(0.465237\pi\) | |||||||
\(948\) | −6.32624 | −0.205467 | ||||||||
\(949\) | 17.0344 | 0.552961 | ||||||||
\(950\) | 29.8885 | 0.969712 | ||||||||
\(951\) | 8.76393 | 0.284190 | ||||||||
\(952\) | −3.85410 | −0.124912 | ||||||||
\(953\) | 45.7214 | 1.48106 | 0.740530 | − | 0.672023i | \(-0.234575\pi\) | ||||
0.740530 | + | 0.672023i | \(0.234575\pi\) | |||||||
\(954\) | 17.3262 | 0.560958 | ||||||||
\(955\) | 8.81966 | 0.285397 | ||||||||
\(956\) | −21.1803 | −0.685021 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.5967 | 0.471600 | ||||||||
\(959\) | 27.6738 | 0.893632 | ||||||||
\(960\) | −0.381966 | −0.0123279 | ||||||||
\(961\) | 24.8328 | 0.801059 | ||||||||
\(962\) | −16.7082 | −0.538694 | ||||||||
\(963\) | −7.09017 | −0.228478 | ||||||||
\(964\) | 13.9443 | 0.449115 | ||||||||
\(965\) | −10.9098 | −0.351200 | ||||||||
\(966\) | 14.8541 | 0.477923 | ||||||||
\(967\) | 22.5623 | 0.725555 | 0.362777 | − | 0.931876i | \(-0.381829\pi\) | ||||
0.362777 | + | 0.931876i | \(0.381829\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | 3.38197 | 0.108588 | ||||||||
\(971\) | 4.16718 | 0.133731 | 0.0668657 | − | 0.997762i | \(-0.478700\pi\) | ||||
0.0668657 | + | 0.997762i | \(0.478700\pi\) | |||||||
\(972\) | −13.9443 | −0.447263 | ||||||||
\(973\) | −4.97871 | −0.159610 | ||||||||
\(974\) | −40.1803 | −1.28746 | ||||||||
\(975\) | −6.38197 | −0.204386 | ||||||||
\(976\) | 13.9443 | 0.446345 | ||||||||
\(977\) | −33.0000 | −1.05576 | −0.527882 | − | 0.849318i | \(-0.677014\pi\) | ||||
−0.527882 | + | 0.849318i | \(0.677014\pi\) | |||||||
\(978\) | 4.00000 | 0.127906 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.85410 | 0.155059 | ||||||||
\(981\) | −37.6525 | −1.20215 | ||||||||
\(982\) | 33.9443 | 1.08321 | ||||||||
\(983\) | 3.29180 | 0.104992 | 0.0524960 | − | 0.998621i | \(-0.483282\pi\) | ||||
0.0524960 | + | 0.998621i | \(0.483282\pi\) | |||||||
\(984\) | 6.00000 | 0.191273 | ||||||||
\(985\) | −7.43769 | −0.236985 | ||||||||
\(986\) | 9.23607 | 0.294136 | ||||||||
\(987\) | −15.0689 | −0.479648 | ||||||||
\(988\) | 14.4721 | 0.460420 | ||||||||
\(989\) | 27.3262 | 0.868924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.4164 | 1.95096 | 0.975478 | − | 0.220096i | \(-0.0706370\pi\) | ||||
0.975478 | + | 0.220096i | \(0.0706370\pi\) | |||||||
\(992\) | −7.47214 | −0.237241 | ||||||||
\(993\) | 8.49342 | 0.269531 | ||||||||
\(994\) | −59.9787 | −1.90241 | ||||||||
\(995\) | −4.96556 | −0.157419 | ||||||||
\(996\) | 0.673762 | 0.0213490 | ||||||||
\(997\) | 37.1803 | 1.17751 | 0.588757 | − | 0.808310i | \(-0.299618\pi\) | ||||
0.588757 | + | 0.808310i | \(0.299618\pi\) | |||||||
\(998\) | −13.3607 | −0.422925 | ||||||||
\(999\) | 25.9443 | 0.820840 |
(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 | 4114.2.a.m.1.1 | yes | 2 | |
11.10 | odd | 2 | 4114.2.a.h.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4114.2.a.h.1.1 | ✓ | 2 | 11.10 | odd | 2 | ||
4114.2.a.m.1.1 | yes | 2 | 1.1 | even | 1 | trivial |