Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.72329.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 2x + 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.46917\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.31071 | −1.48059 | −0.740297 | − | 0.672280i | \(-0.765315\pi\) | ||||
−0.740297 | + | 0.672280i | \(0.765315\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.84154 | 1.45197 | 0.725983 | − | 0.687713i | \(-0.241385\pi\) | ||||
0.725983 | + | 0.687713i | \(0.241385\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.31071 | −1.04694 | ||||||||
\(11\) | 5.49163 | 1.65579 | 0.827894 | − | 0.560885i | \(-0.189539\pi\) | ||||
0.827894 | + | 0.560885i | \(0.189539\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.84154 | 1.02669 | ||||||||
\(15\) | −3.31071 | −0.854821 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.938340 | 0.215270 | 0.107635 | − | 0.994190i | \(-0.465672\pi\) | ||||
0.107635 | + | 0.994190i | \(0.465672\pi\) | |||||||
\(20\) | −3.31071 | −0.740297 | ||||||||
\(21\) | 3.84154 | 0.838293 | ||||||||
\(22\) | 5.49163 | 1.17082 | ||||||||
\(23\) | 3.93834 | 0.821201 | 0.410600 | − | 0.911815i | \(-0.365319\pi\) | ||||
0.410600 | + | 0.911815i | \(0.365319\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 5.96080 | 1.19216 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.84154 | 0.725983 | ||||||||
\(29\) | 2.02246 | 0.375561 | 0.187780 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187780 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(30\) | −3.31071 | −0.604450 | ||||||||
\(31\) | −0.938340 | −0.168531 | −0.0842654 | − | 0.996443i | \(-0.526854\pi\) | ||||
−0.0842654 | + | 0.996443i | \(0.526854\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.49163 | 0.955969 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −12.7182 | −2.14977 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.49163 | −1.23162 | −0.615808 | − | 0.787896i | \(-0.711170\pi\) | ||||
−0.615808 | + | 0.787896i | \(0.711170\pi\) | |||||||
\(38\) | 0.938340 | 0.152219 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −3.31071 | −0.523469 | ||||||||
\(41\) | 11.6214 | 1.81496 | 0.907480 | − | 0.420095i | \(-0.138003\pi\) | ||||
0.907480 | + | 0.420095i | \(0.138003\pi\) | |||||||
\(42\) | 3.84154 | 0.592762 | ||||||||
\(43\) | 2.50837 | 0.382523 | 0.191262 | − | 0.981539i | \(-0.438742\pi\) | ||||
0.191262 | + | 0.981539i | \(0.438742\pi\) | |||||||
\(44\) | 5.49163 | 0.827894 | ||||||||
\(45\) | −3.31071 | −0.493531 | ||||||||
\(46\) | 3.93834 | 0.580677 | ||||||||
\(47\) | −5.51408 | −0.804312 | −0.402156 | − | 0.915571i | \(-0.631739\pi\) | ||||
−0.402156 | + | 0.915571i | \(0.631739\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 7.75742 | 1.10820 | ||||||||
\(50\) | 5.96080 | 0.842984 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −9.60467 | −1.31930 | −0.659651 | − | 0.751572i | \(-0.729296\pi\) | ||||
−0.659651 | + | 0.751572i | \(0.729296\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −18.1812 | −2.45155 | ||||||||
\(56\) | 3.84154 | 0.513347 | ||||||||
\(57\) | 0.938340 | 0.124286 | ||||||||
\(58\) | 2.02246 | 0.265561 | ||||||||
\(59\) | 4.34991 | 0.566310 | 0.283155 | − | 0.959074i | \(-0.408619\pi\) | ||||
0.283155 | + | 0.959074i | \(0.408619\pi\) | |||||||
\(60\) | −3.31071 | −0.427411 | ||||||||
\(61\) | −1.44671 | −0.185233 | −0.0926164 | − | 0.995702i | \(-0.529523\pi\) | ||||
−0.0926164 | + | 0.995702i | \(0.529523\pi\) | |||||||
\(62\) | −0.938340 | −0.119169 | ||||||||
\(63\) | 3.84154 | 0.483988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.31071 | −0.410643 | ||||||||
\(66\) | 5.49163 | 0.675972 | ||||||||
\(67\) | −4.24905 | −0.519104 | −0.259552 | − | 0.965729i | \(-0.583575\pi\) | ||||
−0.259552 | + | 0.965729i | \(0.583575\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | 3.93834 | 0.474120 | ||||||||
\(70\) | −12.7182 | −1.52012 | ||||||||
\(71\) | −9.79180 | −1.16207 | −0.581036 | − | 0.813878i | \(-0.697353\pi\) | ||||
−0.581036 | + | 0.813878i | \(0.697353\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 2.33938 | 0.273803 | 0.136902 | − | 0.990585i | \(-0.456286\pi\) | ||||
0.136902 | + | 0.990585i | \(0.456286\pi\) | |||||||
\(74\) | −7.49163 | −0.870884 | ||||||||
\(75\) | 5.96080 | 0.688293 | ||||||||
\(76\) | 0.938340 | 0.107635 | ||||||||
\(77\) | 21.0963 | 2.40415 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −15.5598 | −1.75061 | −0.875305 | − | 0.483572i | \(-0.839339\pi\) | ||||
−0.875305 | + | 0.483572i | \(0.839339\pi\) | |||||||
\(80\) | −3.31071 | −0.370149 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.6214 | 1.28337 | ||||||||
\(83\) | −0.689291 | −0.0756595 | −0.0378297 | − | 0.999284i | \(-0.512044\pi\) | ||||
−0.0378297 | + | 0.999284i | \(0.512044\pi\) | |||||||
\(84\) | 3.84154 | 0.419146 | ||||||||
\(85\) | −6.62142 | −0.718194 | ||||||||
\(86\) | 2.50837 | 0.270485 | ||||||||
\(87\) | 2.02246 | 0.216830 | ||||||||
\(88\) | 5.49163 | 0.585409 | ||||||||
\(89\) | −2.36183 | −0.250354 | −0.125177 | − | 0.992134i | \(-0.539950\pi\) | ||||
−0.125177 | + | 0.992134i | \(0.539950\pi\) | |||||||
\(90\) | −3.31071 | −0.348979 | ||||||||
\(91\) | 3.84154 | 0.402703 | ||||||||
\(92\) | 3.93834 | 0.410600 | ||||||||
\(93\) | −0.938340 | −0.0973013 | ||||||||
\(94\) | −5.51408 | −0.568734 | ||||||||
\(95\) | −3.10657 | −0.318728 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −19.1644 | −1.94585 | −0.972927 | − | 0.231115i | \(-0.925763\pi\) | ||||
−0.972927 | + | 0.231115i | \(0.925763\pi\) | |||||||
\(98\) | 7.75742 | 0.783618 | ||||||||
\(99\) | 5.49163 | 0.551929 | ||||||||
\(100\) | 5.96080 | 0.596080 | ||||||||
\(101\) | 7.08488 | 0.704972 | 0.352486 | − | 0.935817i | \(-0.385336\pi\) | ||||
0.352486 | + | 0.935817i | \(0.385336\pi\) | |||||||
\(102\) | 2.00000 | 0.198030 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −12.7182 | −1.24117 | ||||||||
\(106\) | −9.60467 | −0.932888 | ||||||||
\(107\) | 16.9833 | 1.64183 | 0.820916 | − | 0.571048i | \(-0.193463\pi\) | ||||
0.820916 | + | 0.571048i | \(0.193463\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 19.6279 | 1.88001 | 0.940006 | − | 0.341159i | \(-0.110820\pi\) | ||||
0.940006 | + | 0.341159i | \(0.110820\pi\) | |||||||
\(110\) | −18.1812 | −1.73351 | ||||||||
\(111\) | −7.49163 | −0.711074 | ||||||||
\(112\) | 3.84154 | 0.362991 | ||||||||
\(113\) | −4.16900 | −0.392186 | −0.196093 | − | 0.980585i | \(-0.562825\pi\) | ||||
−0.196093 | + | 0.980585i | \(0.562825\pi\) | |||||||
\(114\) | 0.938340 | 0.0878836 | ||||||||
\(115\) | −13.0387 | −1.21587 | ||||||||
\(116\) | 2.02246 | 0.187780 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 4.34991 | 0.400442 | ||||||||
\(119\) | 7.68308 | 0.704307 | ||||||||
\(120\) | −3.31071 | −0.302225 | ||||||||
\(121\) | 19.1580 | 1.74163 | ||||||||
\(122\) | −1.44671 | −0.130979 | ||||||||
\(123\) | 11.6214 | 1.04787 | ||||||||
\(124\) | −0.938340 | −0.0842654 | ||||||||
\(125\) | −3.18092 | −0.284510 | ||||||||
\(126\) | 3.84154 | 0.342232 | ||||||||
\(127\) | 1.23851 | 0.109900 | 0.0549502 | − | 0.998489i | \(-0.482500\pi\) | ||||
0.0549502 | + | 0.998489i | \(0.482500\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.50837 | 0.220850 | ||||||||
\(130\) | −3.31071 | −0.290368 | ||||||||
\(131\) | −3.30017 | −0.288338 | −0.144169 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144169 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(132\) | 5.49163 | 0.477985 | ||||||||
\(133\) | 3.60467 | 0.312565 | ||||||||
\(134\) | −4.24905 | −0.367062 | ||||||||
\(135\) | −3.31071 | −0.284940 | ||||||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | 3.71822 | 0.317669 | 0.158834 | − | 0.987305i | \(-0.449226\pi\) | ||||
0.158834 | + | 0.987305i | \(0.449226\pi\) | |||||||
\(138\) | 3.93834 | 0.335254 | ||||||||
\(139\) | 18.9897 | 1.61069 | 0.805344 | − | 0.592808i | \(-0.201981\pi\) | ||||
0.805344 | + | 0.592808i | \(0.201981\pi\) | |||||||
\(140\) | −12.7182 | −1.07489 | ||||||||
\(141\) | −5.51408 | −0.464369 | ||||||||
\(142\) | −9.79180 | −0.821710 | ||||||||
\(143\) | 5.49163 | 0.459233 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.69576 | −0.556053 | ||||||||
\(146\) | 2.33938 | 0.193608 | ||||||||
\(147\) | 7.75742 | 0.639822 | ||||||||
\(148\) | −7.49163 | −0.615808 | ||||||||
\(149\) | −5.12979 | −0.420249 | −0.210124 | − | 0.977675i | \(-0.567387\pi\) | ||||
−0.210124 | + | 0.977675i | \(0.567387\pi\) | |||||||
\(150\) | 5.96080 | 0.486697 | ||||||||
\(151\) | 14.1363 | 1.15039 | 0.575196 | − | 0.818015i | \(-0.304926\pi\) | ||||
0.575196 | + | 0.818015i | \(0.304926\pi\) | |||||||
\(152\) | 0.938340 | 0.0761094 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 21.0963 | 1.69999 | ||||||||
\(155\) | 3.10657 | 0.249526 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −10.2820 | −0.820596 | −0.410298 | − | 0.911951i | \(-0.634575\pi\) | ||||
−0.410298 | + | 0.911951i | \(0.634575\pi\) | |||||||
\(158\) | −15.5598 | −1.23787 | ||||||||
\(159\) | −9.60467 | −0.761700 | ||||||||
\(160\) | −3.31071 | −0.261735 | ||||||||
\(161\) | 15.1293 | 1.19235 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −17.1298 | −1.34171 | −0.670854 | − | 0.741589i | \(-0.734072\pi\) | ||||
−0.670854 | + | 0.741589i | \(0.734072\pi\) | |||||||
\(164\) | 11.6214 | 0.907480 | ||||||||
\(165\) | −18.1812 | −1.41540 | ||||||||
\(166\) | −0.689291 | −0.0534993 | ||||||||
\(167\) | −19.1979 | −1.48558 | −0.742790 | − | 0.669524i | \(-0.766498\pi\) | ||||
−0.742790 | + | 0.669524i | \(0.766498\pi\) | |||||||
\(168\) | 3.84154 | 0.296381 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −6.62142 | −0.507840 | ||||||||
\(171\) | 0.938340 | 0.0717567 | ||||||||
\(172\) | 2.50837 | 0.191262 | ||||||||
\(173\) | −8.55329 | −0.650294 | −0.325147 | − | 0.945663i | \(-0.605414\pi\) | ||||
−0.325147 | + | 0.945663i | \(0.605414\pi\) | |||||||
\(174\) | 2.02246 | 0.153322 | ||||||||
\(175\) | 22.8986 | 1.73097 | ||||||||
\(176\) | 5.49163 | 0.413947 | ||||||||
\(177\) | 4.34991 | 0.326959 | ||||||||
\(178\) | −2.36183 | −0.177027 | ||||||||
\(179\) | 18.0346 | 1.34797 | 0.673986 | − | 0.738744i | \(-0.264581\pi\) | ||||
0.673986 | + | 0.738744i | \(0.264581\pi\) | |||||||
\(180\) | −3.31071 | −0.246766 | ||||||||
\(181\) | −15.2428 | −1.13299 | −0.566496 | − | 0.824065i | \(-0.691701\pi\) | ||||
−0.566496 | + | 0.824065i | \(0.691701\pi\) | |||||||
\(182\) | 3.84154 | 0.284754 | ||||||||
\(183\) | −1.44671 | −0.106944 | ||||||||
\(184\) | 3.93834 | 0.290338 | ||||||||
\(185\) | 24.8026 | 1.82352 | ||||||||
\(186\) | −0.938340 | −0.0688024 | ||||||||
\(187\) | 10.9833 | 0.803175 | ||||||||
\(188\) | −5.51408 | −0.402156 | ||||||||
\(189\) | 3.84154 | 0.279431 | ||||||||
\(190\) | −3.10657 | −0.225374 | ||||||||
\(191\) | 12.0449 | 0.871539 | 0.435770 | − | 0.900058i | \(-0.356476\pi\) | ||||
0.435770 | + | 0.900058i | \(0.356476\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 20.0801 | 1.44539 | 0.722697 | − | 0.691165i | \(-0.242902\pi\) | ||||
0.722697 | + | 0.691165i | \(0.242902\pi\) | |||||||
\(194\) | −19.1644 | −1.37593 | ||||||||
\(195\) | −3.31071 | −0.237085 | ||||||||
\(196\) | 7.75742 | 0.554102 | ||||||||
\(197\) | 16.6439 | 1.18583 | 0.592913 | − | 0.805266i | \(-0.297978\pi\) | ||||
0.592913 | + | 0.805266i | \(0.297978\pi\) | |||||||
\(198\) | 5.49163 | 0.390273 | ||||||||
\(199\) | 4.77988 | 0.338837 | 0.169418 | − | 0.985544i | \(-0.445811\pi\) | ||||
0.169418 | + | 0.985544i | \(0.445811\pi\) | |||||||
\(200\) | 5.96080 | 0.421492 | ||||||||
\(201\) | −4.24905 | −0.299705 | ||||||||
\(202\) | 7.08488 | 0.498490 | ||||||||
\(203\) | 7.76934 | 0.545301 | ||||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | −38.4751 | −2.68722 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 3.93834 | 0.273734 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 5.15301 | 0.356441 | ||||||||
\(210\) | −12.7182 | −0.877641 | ||||||||
\(211\) | 14.6446 | 1.00818 | 0.504089 | − | 0.863652i | \(-0.331828\pi\) | ||||
0.504089 | + | 0.863652i | \(0.331828\pi\) | |||||||
\(212\) | −9.60467 | −0.659651 | ||||||||
\(213\) | −9.79180 | −0.670923 | ||||||||
\(214\) | 16.9833 | 1.16095 | ||||||||
\(215\) | −8.30450 | −0.566362 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −3.60467 | −0.244701 | ||||||||
\(218\) | 19.6279 | 1.32937 | ||||||||
\(219\) | 2.33938 | 0.158080 | ||||||||
\(220\) | −18.1812 | −1.22577 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | −7.49163 | −0.502805 | ||||||||
\(223\) | 18.8802 | 1.26431 | 0.632157 | − | 0.774840i | \(-0.282170\pi\) | ||||
0.632157 | + | 0.774840i | \(0.282170\pi\) | |||||||
\(224\) | 3.84154 | 0.256674 | ||||||||
\(225\) | 5.96080 | 0.397386 | ||||||||
\(226\) | −4.16900 | −0.277318 | ||||||||
\(227\) | 6.57651 | 0.436498 | 0.218249 | − | 0.975893i | \(-0.429965\pi\) | ||||
0.218249 | + | 0.975893i | \(0.429965\pi\) | |||||||
\(228\) | 0.938340 | 0.0621431 | ||||||||
\(229\) | −19.6896 | −1.30112 | −0.650561 | − | 0.759454i | \(-0.725466\pi\) | ||||
−0.650561 | + | 0.759454i | \(0.725466\pi\) | |||||||
\(230\) | −13.0387 | −0.859746 | ||||||||
\(231\) | 21.0963 | 1.38803 | ||||||||
\(232\) | 2.02246 | 0.132781 | ||||||||
\(233\) | −23.8026 | −1.55936 | −0.779680 | − | 0.626178i | \(-0.784618\pi\) | ||||
−0.779680 | + | 0.626178i | \(0.784618\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 18.2555 | 1.19086 | ||||||||
\(236\) | 4.34991 | 0.283155 | ||||||||
\(237\) | −15.5598 | −1.01071 | ||||||||
\(238\) | 7.68308 | 0.498020 | ||||||||
\(239\) | 28.9962 | 1.87561 | 0.937804 | − | 0.347165i | \(-0.112856\pi\) | ||||
0.937804 | + | 0.347165i | \(0.112856\pi\) | |||||||
\(240\) | −3.31071 | −0.213705 | ||||||||
\(241\) | −11.4278 | −0.736130 | −0.368065 | − | 0.929800i | \(-0.619980\pi\) | ||||
−0.368065 | + | 0.929800i | \(0.619980\pi\) | |||||||
\(242\) | 19.1580 | 1.23152 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.44671 | −0.0926164 | ||||||||
\(245\) | −25.6826 | −1.64080 | ||||||||
\(246\) | 11.6214 | 0.740955 | ||||||||
\(247\) | 0.938340 | 0.0597052 | ||||||||
\(248\) | −0.938340 | −0.0595847 | ||||||||
\(249\) | −0.689291 | −0.0436820 | ||||||||
\(250\) | −3.18092 | −0.201179 | ||||||||
\(251\) | −4.92780 | −0.311040 | −0.155520 | − | 0.987833i | \(-0.549705\pi\) | ||||
−0.155520 | + | 0.987833i | \(0.549705\pi\) | |||||||
\(252\) | 3.84154 | 0.241994 | ||||||||
\(253\) | 21.6279 | 1.35973 | ||||||||
\(254\) | 1.23851 | 0.0777113 | ||||||||
\(255\) | −6.62142 | −0.414649 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.1649 | 1.07072 | 0.535360 | − | 0.844624i | \(-0.320176\pi\) | ||||
0.535360 | + | 0.844624i | \(0.320176\pi\) | |||||||
\(258\) | 2.50837 | 0.156165 | ||||||||
\(259\) | −28.7794 | −1.78826 | ||||||||
\(260\) | −3.31071 | −0.205321 | ||||||||
\(261\) | 2.02246 | 0.125187 | ||||||||
\(262\) | −3.30017 | −0.203885 | ||||||||
\(263\) | −31.3327 | −1.93205 | −0.966027 | − | 0.258440i | \(-0.916792\pi\) | ||||
−0.966027 | + | 0.258440i | \(0.916792\pi\) | |||||||
\(264\) | 5.49163 | 0.337986 | ||||||||
\(265\) | 31.7983 | 1.95335 | ||||||||
\(266\) | 3.60467 | 0.221017 | ||||||||
\(267\) | −2.36183 | −0.144542 | ||||||||
\(268\) | −4.24905 | −0.259552 | ||||||||
\(269\) | 9.96562 | 0.607615 | 0.303807 | − | 0.952733i | \(-0.401742\pi\) | ||||
0.303807 | + | 0.952733i | \(0.401742\pi\) | |||||||
\(270\) | −3.31071 | −0.201483 | ||||||||
\(271\) | −11.6382 | −0.706968 | −0.353484 | − | 0.935441i | \(-0.615003\pi\) | ||||
−0.353484 | + | 0.935441i | \(0.615003\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 3.84154 | 0.232501 | ||||||||
\(274\) | 3.71822 | 0.224626 | ||||||||
\(275\) | 32.7345 | 1.97396 | ||||||||
\(276\) | 3.93834 | 0.237060 | ||||||||
\(277\) | −2.27151 | −0.136482 | −0.0682408 | − | 0.997669i | \(-0.521739\pi\) | ||||
−0.0682408 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(278\) | 18.9897 | 1.13893 | ||||||||
\(279\) | −0.938340 | −0.0561770 | ||||||||
\(280\) | −12.7182 | −0.760059 | ||||||||
\(281\) | −0.486683 | −0.0290331 | −0.0145165 | − | 0.999895i | \(-0.504621\pi\) | ||||
−0.0145165 | + | 0.999895i | \(0.504621\pi\) | |||||||
\(282\) | −5.51408 | −0.328359 | ||||||||
\(283\) | −21.8410 | −1.29831 | −0.649157 | − | 0.760654i | \(-0.724878\pi\) | ||||
−0.649157 | + | 0.760654i | \(0.724878\pi\) | |||||||
\(284\) | −9.79180 | −0.581036 | ||||||||
\(285\) | −3.10657 | −0.184017 | ||||||||
\(286\) | 5.49163 | 0.324727 | ||||||||
\(287\) | 44.6441 | 2.63526 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −6.69576 | −0.393189 | ||||||||
\(291\) | −19.1644 | −1.12344 | ||||||||
\(292\) | 2.33938 | 0.136902 | ||||||||
\(293\) | −0.470555 | −0.0274901 | −0.0137451 | − | 0.999906i | \(-0.504375\pi\) | ||||
−0.0137451 | + | 0.999906i | \(0.504375\pi\) | |||||||
\(294\) | 7.75742 | 0.452422 | ||||||||
\(295\) | −14.4013 | −0.838476 | ||||||||
\(296\) | −7.49163 | −0.435442 | ||||||||
\(297\) | 5.49163 | 0.318656 | ||||||||
\(298\) | −5.12979 | −0.297161 | ||||||||
\(299\) | 3.93834 | 0.227760 | ||||||||
\(300\) | 5.96080 | 0.344147 | ||||||||
\(301\) | 9.63602 | 0.555411 | ||||||||
\(302\) | 14.1363 | 0.813451 | ||||||||
\(303\) | 7.08488 | 0.407016 | ||||||||
\(304\) | 0.938340 | 0.0538175 | ||||||||
\(305\) | 4.78965 | 0.274255 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | 3.66848 | 0.209371 | 0.104686 | − | 0.994505i | \(-0.466616\pi\) | ||||
0.104686 | + | 0.994505i | \(0.466616\pi\) | |||||||
\(308\) | 21.0963 | 1.20207 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 3.10657 | 0.176441 | ||||||||
\(311\) | 21.1517 | 1.19941 | 0.599703 | − | 0.800223i | \(-0.295286\pi\) | ||||
0.599703 | + | 0.800223i | \(0.295286\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 3.14171 | 0.177580 | 0.0887901 | − | 0.996050i | \(-0.471700\pi\) | ||||
0.0887901 | + | 0.996050i | \(0.471700\pi\) | |||||||
\(314\) | −10.2820 | −0.580249 | ||||||||
\(315\) | −12.7182 | −0.716590 | ||||||||
\(316\) | −15.5598 | −0.875305 | ||||||||
\(317\) | 11.2877 | 0.633983 | 0.316992 | − | 0.948428i | \(-0.397327\pi\) | ||||
0.316992 | + | 0.948428i | \(0.397327\pi\) | |||||||
\(318\) | −9.60467 | −0.538603 | ||||||||
\(319\) | 11.1066 | 0.621849 | ||||||||
\(320\) | −3.31071 | −0.185074 | ||||||||
\(321\) | 16.9833 | 0.947913 | ||||||||
\(322\) | 15.1293 | 0.843122 | ||||||||
\(323\) | 1.87668 | 0.104421 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.96080 | 0.330645 | ||||||||
\(326\) | −17.1298 | −0.948731 | ||||||||
\(327\) | 19.6279 | 1.08542 | ||||||||
\(328\) | 11.6214 | 0.641685 | ||||||||
\(329\) | −21.1826 | −1.16783 | ||||||||
\(330\) | −18.1812 | −1.00084 | ||||||||
\(331\) | 1.45890 | 0.0801881 | 0.0400941 | − | 0.999196i | \(-0.487234\pi\) | ||||
0.0400941 | + | 0.999196i | \(0.487234\pi\) | |||||||
\(332\) | −0.689291 | −0.0378297 | ||||||||
\(333\) | −7.49163 | −0.410539 | ||||||||
\(334\) | −19.1979 | −1.05046 | ||||||||
\(335\) | 14.0674 | 0.768582 | ||||||||
\(336\) | 3.84154 | 0.209573 | ||||||||
\(337\) | −20.8767 | −1.13723 | −0.568613 | − | 0.822605i | \(-0.692520\pi\) | ||||
−0.568613 | + | 0.822605i | \(0.692520\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −4.16900 | −0.226429 | ||||||||
\(340\) | −6.62142 | −0.359097 | ||||||||
\(341\) | −5.15301 | −0.279051 | ||||||||
\(342\) | 0.938340 | 0.0507396 | ||||||||
\(343\) | 2.90967 | 0.157108 | ||||||||
\(344\) | 2.50837 | 0.135242 | ||||||||
\(345\) | −13.0387 | −0.701980 | ||||||||
\(346\) | −8.55329 | −0.459827 | ||||||||
\(347\) | 5.73827 | 0.308046 | 0.154023 | − | 0.988067i | \(-0.450777\pi\) | ||||
0.154023 | + | 0.988067i | \(0.450777\pi\) | |||||||
\(348\) | 2.02246 | 0.108415 | ||||||||
\(349\) | −28.2022 | −1.50963 | −0.754816 | − | 0.655937i | \(-0.772274\pi\) | ||||
−0.754816 | + | 0.655937i | \(0.772274\pi\) | |||||||
\(350\) | 22.8986 | 1.22398 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 5.49163 | 0.292705 | ||||||||
\(353\) | −13.3212 | −0.709018 | −0.354509 | − | 0.935053i | \(-0.615352\pi\) | ||||
−0.354509 | + | 0.935053i | \(0.615352\pi\) | |||||||
\(354\) | 4.34991 | 0.231195 | ||||||||
\(355\) | 32.4178 | 1.72056 | ||||||||
\(356\) | −2.36183 | −0.125177 | ||||||||
\(357\) | 7.68308 | 0.406632 | ||||||||
\(358\) | 18.0346 | 0.953160 | ||||||||
\(359\) | 0.868058 | 0.0458143 | 0.0229072 | − | 0.999738i | \(-0.492708\pi\) | ||||
0.0229072 | + | 0.999738i | \(0.492708\pi\) | |||||||
\(360\) | −3.31071 | −0.174490 | ||||||||
\(361\) | −18.1195 | −0.953659 | ||||||||
\(362\) | −15.2428 | −0.801146 | ||||||||
\(363\) | 19.1580 | 1.00553 | ||||||||
\(364\) | 3.84154 | 0.201351 | ||||||||
\(365\) | −7.74500 | −0.405392 | ||||||||
\(366\) | −1.44671 | −0.0756210 | ||||||||
\(367\) | −27.9345 | −1.45817 | −0.729086 | − | 0.684423i | \(-0.760054\pi\) | ||||
−0.729086 | + | 0.684423i | \(0.760054\pi\) | |||||||
\(368\) | 3.93834 | 0.205300 | ||||||||
\(369\) | 11.6214 | 0.604987 | ||||||||
\(370\) | 24.8026 | 1.28943 | ||||||||
\(371\) | −36.8967 | −1.91558 | ||||||||
\(372\) | −0.938340 | −0.0486507 | ||||||||
\(373\) | −22.7583 | −1.17838 | −0.589190 | − | 0.807994i | \(-0.700553\pi\) | ||||
−0.589190 | + | 0.807994i | \(0.700553\pi\) | |||||||
\(374\) | 10.9833 | 0.567930 | ||||||||
\(375\) | −3.18092 | −0.164262 | ||||||||
\(376\) | −5.51408 | −0.284367 | ||||||||
\(377\) | 2.02246 | 0.104162 | ||||||||
\(378\) | 3.84154 | 0.197587 | ||||||||
\(379\) | 0.735587 | 0.0377846 | 0.0188923 | − | 0.999822i | \(-0.493986\pi\) | ||||
0.0188923 | + | 0.999822i | \(0.493986\pi\) | |||||||
\(380\) | −3.10657 | −0.159364 | ||||||||
\(381\) | 1.23851 | 0.0634510 | ||||||||
\(382\) | 12.0449 | 0.616271 | ||||||||
\(383\) | −24.8167 | −1.26807 | −0.634036 | − | 0.773303i | \(-0.718603\pi\) | ||||
−0.634036 | + | 0.773303i | \(0.718603\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −69.8437 | −3.55956 | ||||||||
\(386\) | 20.0801 | 1.02205 | ||||||||
\(387\) | 2.50837 | 0.127508 | ||||||||
\(388\) | −19.1644 | −0.972927 | ||||||||
\(389\) | −4.85778 | −0.246299 | −0.123150 | − | 0.992388i | \(-0.539300\pi\) | ||||
−0.123150 | + | 0.992388i | \(0.539300\pi\) | |||||||
\(390\) | −3.31071 | −0.167644 | ||||||||
\(391\) | 7.87668 | 0.398341 | ||||||||
\(392\) | 7.75742 | 0.391809 | ||||||||
\(393\) | −3.30017 | −0.166472 | ||||||||
\(394\) | 16.6439 | 0.838506 | ||||||||
\(395\) | 51.5138 | 2.59194 | ||||||||
\(396\) | 5.49163 | 0.275965 | ||||||||
\(397\) | 16.6663 | 0.836459 | 0.418230 | − | 0.908341i | \(-0.362651\pi\) | ||||
0.418230 | + | 0.908341i | \(0.362651\pi\) | |||||||
\(398\) | 4.77988 | 0.239594 | ||||||||
\(399\) | 3.60467 | 0.180459 | ||||||||
\(400\) | 5.96080 | 0.298040 | ||||||||
\(401\) | −1.52462 | −0.0761358 | −0.0380679 | − | 0.999275i | \(-0.512120\pi\) | ||||
−0.0380679 | + | 0.999275i | \(0.512120\pi\) | |||||||
\(402\) | −4.24905 | −0.211923 | ||||||||
\(403\) | −0.938340 | −0.0467421 | ||||||||
\(404\) | 7.08488 | 0.352486 | ||||||||
\(405\) | −3.31071 | −0.164510 | ||||||||
\(406\) | 7.76934 | 0.385586 | ||||||||
\(407\) | −41.1412 | −2.03929 | ||||||||
\(408\) | 2.00000 | 0.0990148 | ||||||||
\(409\) | −17.4814 | −0.864397 | −0.432199 | − | 0.901778i | \(-0.642262\pi\) | ||||
−0.432199 | + | 0.901778i | \(0.642262\pi\) | |||||||
\(410\) | −38.4751 | −1.90015 | ||||||||
\(411\) | 3.71822 | 0.183406 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 16.7104 | 0.822263 | ||||||||
\(414\) | 3.93834 | 0.193559 | ||||||||
\(415\) | 2.28204 | 0.112021 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 18.9897 | 0.929931 | ||||||||
\(418\) | 5.15301 | 0.252042 | ||||||||
\(419\) | 21.8200 | 1.06597 | 0.532987 | − | 0.846123i | \(-0.321069\pi\) | ||||
0.532987 | + | 0.846123i | \(0.321069\pi\) | |||||||
\(420\) | −12.7182 | −0.620586 | ||||||||
\(421\) | −4.33938 | −0.211488 | −0.105744 | − | 0.994393i | \(-0.533722\pi\) | ||||
−0.105744 | + | 0.994393i | \(0.533722\pi\) | |||||||
\(422\) | 14.6446 | 0.712890 | ||||||||
\(423\) | −5.51408 | −0.268104 | ||||||||
\(424\) | −9.60467 | −0.466444 | ||||||||
\(425\) | 11.9216 | 0.578282 | ||||||||
\(426\) | −9.79180 | −0.474414 | ||||||||
\(427\) | −5.55761 | −0.268952 | ||||||||
\(428\) | 16.9833 | 0.820916 | ||||||||
\(429\) | 5.49163 | 0.265138 | ||||||||
\(430\) | −8.30450 | −0.400478 | ||||||||
\(431\) | 8.16823 | 0.393450 | 0.196725 | − | 0.980459i | \(-0.436969\pi\) | ||||
0.196725 | + | 0.980459i | \(0.436969\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 13.0731 | 0.628252 | 0.314126 | − | 0.949381i | \(-0.398289\pi\) | ||||
0.314126 | + | 0.949381i | \(0.398289\pi\) | |||||||
\(434\) | −3.60467 | −0.173030 | ||||||||
\(435\) | −6.69576 | −0.321037 | ||||||||
\(436\) | 19.6279 | 0.940006 | ||||||||
\(437\) | 3.69550 | 0.176780 | ||||||||
\(438\) | 2.33938 | 0.111780 | ||||||||
\(439\) | −4.23687 | −0.202215 | −0.101107 | − | 0.994876i | \(-0.532239\pi\) | ||||
−0.101107 | + | 0.994876i | \(0.532239\pi\) | |||||||
\(440\) | −18.1812 | −0.866754 | ||||||||
\(441\) | 7.75742 | 0.369401 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | 8.15872 | 0.387633 | 0.193816 | − | 0.981038i | \(-0.437913\pi\) | ||||
0.193816 | + | 0.981038i | \(0.437913\pi\) | |||||||
\(444\) | −7.49163 | −0.355537 | ||||||||
\(445\) | 7.81934 | 0.370672 | ||||||||
\(446\) | 18.8802 | 0.894005 | ||||||||
\(447\) | −5.12979 | −0.242631 | ||||||||
\(448\) | 3.84154 | 0.181496 | ||||||||
\(449\) | 9.11952 | 0.430377 | 0.215188 | − | 0.976573i | \(-0.430963\pi\) | ||||
0.215188 | + | 0.976573i | \(0.430963\pi\) | |||||||
\(450\) | 5.96080 | 0.280995 | ||||||||
\(451\) | 63.8205 | 3.00519 | ||||||||
\(452\) | −4.16900 | −0.196093 | ||||||||
\(453\) | 14.1363 | 0.664180 | ||||||||
\(454\) | 6.57651 | 0.308651 | ||||||||
\(455\) | −12.7182 | −0.596239 | ||||||||
\(456\) | 0.938340 | 0.0439418 | ||||||||
\(457\) | 8.74550 | 0.409097 | 0.204549 | − | 0.978856i | \(-0.434427\pi\) | ||||
0.204549 | + | 0.978856i | \(0.434427\pi\) | |||||||
\(458\) | −19.6896 | −0.920032 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | −13.0387 | −0.607933 | ||||||||
\(461\) | 27.8859 | 1.29878 | 0.649389 | − | 0.760456i | \(-0.275025\pi\) | ||||
0.649389 | + | 0.760456i | \(0.275025\pi\) | |||||||
\(462\) | 21.0963 | 0.981489 | ||||||||
\(463\) | −2.60035 | −0.120848 | −0.0604242 | − | 0.998173i | \(-0.519245\pi\) | ||||
−0.0604242 | + | 0.998173i | \(0.519245\pi\) | |||||||
\(464\) | 2.02246 | 0.0938902 | ||||||||
\(465\) | 3.10657 | 0.144064 | ||||||||
\(466\) | −23.8026 | −1.10263 | ||||||||
\(467\) | 0.519790 | 0.0240530 | 0.0120265 | − | 0.999928i | \(-0.496172\pi\) | ||||
0.0120265 | + | 0.999928i | \(0.496172\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −16.3229 | −0.753721 | ||||||||
\(470\) | 18.2555 | 0.842064 | ||||||||
\(471\) | −10.2820 | −0.473771 | ||||||||
\(472\) | 4.34991 | 0.200221 | ||||||||
\(473\) | 13.7751 | 0.633378 | ||||||||
\(474\) | −15.5598 | −0.714683 | ||||||||
\(475\) | 5.59325 | 0.256636 | ||||||||
\(476\) | 7.68308 | 0.352153 | ||||||||
\(477\) | −9.60467 | −0.439768 | ||||||||
\(478\) | 28.9962 | 1.32626 | ||||||||
\(479\) | 25.9892 | 1.18748 | 0.593739 | − | 0.804658i | \(-0.297651\pi\) | ||||
0.593739 | + | 0.804658i | \(0.297651\pi\) | |||||||
\(480\) | −3.31071 | −0.151113 | ||||||||
\(481\) | −7.49163 | −0.341589 | ||||||||
\(482\) | −11.4278 | −0.520523 | ||||||||
\(483\) | 15.1293 | 0.688406 | ||||||||
\(484\) | 19.1580 | 0.870816 | ||||||||
\(485\) | 63.4479 | 2.88102 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −7.15301 | −0.324134 | −0.162067 | − | 0.986780i | \(-0.551816\pi\) | ||||
−0.162067 | + | 0.986780i | \(0.551816\pi\) | |||||||
\(488\) | −1.44671 | −0.0654897 | ||||||||
\(489\) | −17.1298 | −0.774636 | ||||||||
\(490\) | −25.6826 | −1.16022 | ||||||||
\(491\) | 35.0157 | 1.58024 | 0.790119 | − | 0.612953i | \(-0.210019\pi\) | ||||
0.790119 | + | 0.612953i | \(0.210019\pi\) | |||||||
\(492\) | 11.6214 | 0.523934 | ||||||||
\(493\) | 4.04491 | 0.182174 | ||||||||
\(494\) | 0.938340 | 0.0422179 | ||||||||
\(495\) | −18.1812 | −0.817183 | ||||||||
\(496\) | −0.938340 | −0.0421327 | ||||||||
\(497\) | −37.6156 | −1.68729 | ||||||||
\(498\) | −0.689291 | −0.0308879 | ||||||||
\(499\) | 17.2813 | 0.773616 | 0.386808 | − | 0.922160i | \(-0.373578\pi\) | ||||
0.386808 | + | 0.922160i | \(0.373578\pi\) | |||||||
\(500\) | −3.18092 | −0.142255 | ||||||||
\(501\) | −19.1979 | −0.857700 | ||||||||
\(502\) | −4.92780 | −0.219939 | ||||||||
\(503\) | 43.1858 | 1.92556 | 0.962779 | − | 0.270290i | \(-0.0871196\pi\) | ||||
0.962779 | + | 0.270290i | \(0.0871196\pi\) | |||||||
\(504\) | 3.84154 | 0.171116 | ||||||||
\(505\) | −23.4560 | −1.04378 | ||||||||
\(506\) | 21.6279 | 0.961477 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 1.23851 | 0.0549502 | ||||||||
\(509\) | 1.73014 | 0.0766871 | 0.0383436 | − | 0.999265i | \(-0.487792\pi\) | ||||
0.0383436 | + | 0.999265i | \(0.487792\pi\) | |||||||
\(510\) | −6.62142 | −0.293201 | ||||||||
\(511\) | 8.98681 | 0.397553 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.938340 | 0.0414287 | ||||||||
\(514\) | 17.1649 | 0.757113 | ||||||||
\(515\) | 3.31071 | 0.145887 | ||||||||
\(516\) | 2.50837 | 0.110425 | ||||||||
\(517\) | −30.2813 | −1.33177 | ||||||||
\(518\) | −28.7794 | −1.26449 | ||||||||
\(519\) | −8.55329 | −0.375448 | ||||||||
\(520\) | −3.31071 | −0.145184 | ||||||||
\(521\) | 17.7870 | 0.779261 | 0.389631 | − | 0.920971i | \(-0.372603\pi\) | ||||
0.389631 | + | 0.920971i | \(0.372603\pi\) | |||||||
\(522\) | 2.02246 | 0.0885205 | ||||||||
\(523\) | −14.8824 | −0.650761 | −0.325381 | − | 0.945583i | \(-0.605492\pi\) | ||||
−0.325381 | + | 0.945583i | \(0.605492\pi\) | |||||||
\(524\) | −3.30017 | −0.144169 | ||||||||
\(525\) | 22.8986 | 0.999378 | ||||||||
\(526\) | −31.3327 | −1.36617 | ||||||||
\(527\) | −1.87668 | −0.0817495 | ||||||||
\(528\) | 5.49163 | 0.238992 | ||||||||
\(529\) | −7.48948 | −0.325629 | ||||||||
\(530\) | 31.7983 | 1.38123 | ||||||||
\(531\) | 4.34991 | 0.188770 | ||||||||
\(532\) | 3.60467 | 0.156282 | ||||||||
\(533\) | 11.6214 | 0.503380 | ||||||||
\(534\) | −2.36183 | −0.102207 | ||||||||
\(535\) | −56.2266 | −2.43089 | ||||||||
\(536\) | −4.24905 | −0.183531 | ||||||||
\(537\) | 18.0346 | 0.778252 | ||||||||
\(538\) | 9.96562 | 0.429649 | ||||||||
\(539\) | 42.6009 | 1.83495 | ||||||||
\(540\) | −3.31071 | −0.142470 | ||||||||
\(541\) | 23.8872 | 1.02699 | 0.513496 | − | 0.858092i | \(-0.328350\pi\) | ||||
0.513496 | + | 0.858092i | \(0.328350\pi\) | |||||||
\(542\) | −11.6382 | −0.499902 | ||||||||
\(543\) | −15.2428 | −0.654133 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | −64.9822 | −2.78353 | ||||||||
\(546\) | 3.84154 | 0.164403 | ||||||||
\(547\) | 30.0235 | 1.28371 | 0.641856 | − | 0.766825i | \(-0.278165\pi\) | ||||
0.641856 | + | 0.766825i | \(0.278165\pi\) | |||||||
\(548\) | 3.71822 | 0.158834 | ||||||||
\(549\) | −1.44671 | −0.0617443 | ||||||||
\(550\) | 32.7345 | 1.39580 | ||||||||
\(551\) | 1.89775 | 0.0808469 | ||||||||
\(552\) | 3.93834 | 0.167627 | ||||||||
\(553\) | −59.7734 | −2.54182 | ||||||||
\(554\) | −2.27151 | −0.0965070 | ||||||||
\(555\) | 24.8026 | 1.05281 | ||||||||
\(556\) | 18.9897 | 0.805344 | ||||||||
\(557\) | 15.9665 | 0.676522 | 0.338261 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338261 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(558\) | −0.938340 | −0.0397231 | ||||||||
\(559\) | 2.50837 | 0.106093 | ||||||||
\(560\) | −12.7182 | −0.537443 | ||||||||
\(561\) | 10.9833 | 0.463713 | ||||||||
\(562\) | −0.486683 | −0.0205295 | ||||||||
\(563\) | 20.3838 | 0.859074 | 0.429537 | − | 0.903049i | \(-0.358677\pi\) | ||||
0.429537 | + | 0.903049i | \(0.358677\pi\) | |||||||
\(564\) | −5.51408 | −0.232185 | ||||||||
\(565\) | 13.8023 | 0.580669 | ||||||||
\(566\) | −21.8410 | −0.918047 | ||||||||
\(567\) | 3.84154 | 0.161329 | ||||||||
\(568\) | −9.79180 | −0.410855 | ||||||||
\(569\) | 2.14604 | 0.0899665 | 0.0449833 | − | 0.998988i | \(-0.485677\pi\) | ||||
0.0449833 | + | 0.998988i | \(0.485677\pi\) | |||||||
\(570\) | −3.10657 | −0.130120 | ||||||||
\(571\) | 27.1306 | 1.13538 | 0.567689 | − | 0.823243i | \(-0.307838\pi\) | ||||
0.567689 | + | 0.823243i | \(0.307838\pi\) | |||||||
\(572\) | 5.49163 | 0.229616 | ||||||||
\(573\) | 12.0449 | 0.503183 | ||||||||
\(574\) | 44.6441 | 1.86341 | ||||||||
\(575\) | 23.4756 | 0.979002 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −29.4476 | −1.22592 | −0.612960 | − | 0.790114i | \(-0.710021\pi\) | ||||
−0.612960 | + | 0.790114i | \(0.710021\pi\) | |||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | 20.0801 | 0.834499 | ||||||||
\(580\) | −6.69576 | −0.278026 | ||||||||
\(581\) | −2.64794 | −0.109855 | ||||||||
\(582\) | −19.1644 | −0.794391 | ||||||||
\(583\) | −52.7453 | −2.18449 | ||||||||
\(584\) | 2.33938 | 0.0968041 | ||||||||
\(585\) | −3.31071 | −0.136881 | ||||||||
\(586\) | −0.470555 | −0.0194384 | ||||||||
\(587\) | 27.4140 | 1.13150 | 0.565748 | − | 0.824578i | \(-0.308587\pi\) | ||||
0.565748 | + | 0.824578i | \(0.308587\pi\) | |||||||
\(588\) | 7.75742 | 0.319911 | ||||||||
\(589\) | −0.880482 | −0.0362796 | ||||||||
\(590\) | −14.4013 | −0.592892 | ||||||||
\(591\) | 16.6439 | 0.684638 | ||||||||
\(592\) | −7.49163 | −0.307904 | ||||||||
\(593\) | 1.77443 | 0.0728672 | 0.0364336 | − | 0.999336i | \(-0.488400\pi\) | ||||
0.0364336 | + | 0.999336i | \(0.488400\pi\) | |||||||
\(594\) | 5.49163 | 0.225324 | ||||||||
\(595\) | −25.4364 | −1.04279 | ||||||||
\(596\) | −5.12979 | −0.210124 | ||||||||
\(597\) | 4.77988 | 0.195627 | ||||||||
\(598\) | 3.93834 | 0.161051 | ||||||||
\(599\) | 36.0693 | 1.47375 | 0.736875 | − | 0.676029i | \(-0.236300\pi\) | ||||
0.736875 | + | 0.676029i | \(0.236300\pi\) | |||||||
\(600\) | 5.96080 | 0.243348 | ||||||||
\(601\) | 7.15301 | 0.291778 | 0.145889 | − | 0.989301i | \(-0.453396\pi\) | ||||
0.145889 | + | 0.989301i | \(0.453396\pi\) | |||||||
\(602\) | 9.63602 | 0.392735 | ||||||||
\(603\) | −4.24905 | −0.173035 | ||||||||
\(604\) | 14.1363 | 0.575196 | ||||||||
\(605\) | −63.4264 | −2.57865 | ||||||||
\(606\) | 7.08488 | 0.287804 | ||||||||
\(607\) | −28.8150 | −1.16957 | −0.584783 | − | 0.811190i | \(-0.698820\pi\) | ||||
−0.584783 | + | 0.811190i | \(0.698820\pi\) | |||||||
\(608\) | 0.938340 | 0.0380547 | ||||||||
\(609\) | 7.76934 | 0.314830 | ||||||||
\(610\) | 4.78965 | 0.193927 | ||||||||
\(611\) | −5.51408 | −0.223076 | ||||||||
\(612\) | 2.00000 | 0.0808452 | ||||||||
\(613\) | −23.5327 | −0.950478 | −0.475239 | − | 0.879857i | \(-0.657638\pi\) | ||||
−0.475239 | + | 0.879857i | \(0.657638\pi\) | |||||||
\(614\) | 3.66848 | 0.148048 | ||||||||
\(615\) | −38.4751 | −1.55147 | ||||||||
\(616\) | 21.0963 | 0.849994 | ||||||||
\(617\) | −17.9427 | −0.722344 | −0.361172 | − | 0.932499i | \(-0.617623\pi\) | ||||
−0.361172 | + | 0.932499i | \(0.617623\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 4.11090 | 0.165231 | 0.0826154 | − | 0.996582i | \(-0.473673\pi\) | ||||
0.0826154 | + | 0.996582i | \(0.473673\pi\) | |||||||
\(620\) | 3.10657 | 0.124763 | ||||||||
\(621\) | 3.93834 | 0.158040 | ||||||||
\(622\) | 21.1517 | 0.848108 | ||||||||
\(623\) | −9.07308 | −0.363505 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −19.2729 | −0.770916 | ||||||||
\(626\) | 3.14171 | 0.125568 | ||||||||
\(627\) | 5.15301 | 0.205792 | ||||||||
\(628\) | −10.2820 | −0.410298 | ||||||||
\(629\) | −14.9833 | −0.597421 | ||||||||
\(630\) | −12.7182 | −0.506706 | ||||||||
\(631\) | 0.915119 | 0.0364303 | 0.0182152 | − | 0.999834i | \(-0.494202\pi\) | ||||
0.0182152 | + | 0.999834i | \(0.494202\pi\) | |||||||
\(632\) | −15.5598 | −0.618934 | ||||||||
\(633\) | 14.6446 | 0.582072 | ||||||||
\(634\) | 11.2877 | 0.448294 | ||||||||
\(635\) | −4.10036 | −0.162718 | ||||||||
\(636\) | −9.60467 | −0.380850 | ||||||||
\(637\) | 7.75742 | 0.307360 | ||||||||
\(638\) | 11.1066 | 0.439713 | ||||||||
\(639\) | −9.79180 | −0.387358 | ||||||||
\(640\) | −3.31071 | −0.130867 | ||||||||
\(641\) | −12.6679 | −0.500350 | −0.250175 | − | 0.968201i | \(-0.580488\pi\) | ||||
−0.250175 | + | 0.968201i | \(0.580488\pi\) | |||||||
\(642\) | 16.9833 | 0.670275 | ||||||||
\(643\) | −24.1130 | −0.950926 | −0.475463 | − | 0.879736i | \(-0.657719\pi\) | ||||
−0.475463 | + | 0.879736i | \(0.657719\pi\) | |||||||
\(644\) | 15.1293 | 0.596177 | ||||||||
\(645\) | −8.30450 | −0.326989 | ||||||||
\(646\) | 1.87668 | 0.0738370 | ||||||||
\(647\) | −23.8783 | −0.938754 | −0.469377 | − | 0.882998i | \(-0.655521\pi\) | ||||
−0.469377 | + | 0.882998i | \(0.655521\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 23.8881 | 0.937690 | ||||||||
\(650\) | 5.96080 | 0.233802 | ||||||||
\(651\) | −3.60467 | −0.141278 | ||||||||
\(652\) | −17.1298 | −0.670854 | ||||||||
\(653\) | −25.1747 | −0.985162 | −0.492581 | − | 0.870267i | \(-0.663947\pi\) | ||||
−0.492581 | + | 0.870267i | \(0.663947\pi\) | |||||||
\(654\) | 19.6279 | 0.767511 | ||||||||
\(655\) | 10.9259 | 0.426911 | ||||||||
\(656\) | 11.6214 | 0.453740 | ||||||||
\(657\) | 2.33938 | 0.0912678 | ||||||||
\(658\) | −21.1826 | −0.825782 | ||||||||
\(659\) | −27.9541 | −1.08894 | −0.544468 | − | 0.838782i | \(-0.683268\pi\) | ||||
−0.544468 | + | 0.838782i | \(0.683268\pi\) | |||||||
\(660\) | −18.1812 | −0.707701 | ||||||||
\(661\) | −16.6793 | −0.648749 | −0.324374 | − | 0.945929i | \(-0.605154\pi\) | ||||
−0.324374 | + | 0.945929i | \(0.605154\pi\) | |||||||
\(662\) | 1.45890 | 0.0567016 | ||||||||
\(663\) | 2.00000 | 0.0776736 | ||||||||
\(664\) | −0.689291 | −0.0267497 | ||||||||
\(665\) | −11.9340 | −0.462781 | ||||||||
\(666\) | −7.49163 | −0.290295 | ||||||||
\(667\) | 7.96512 | 0.308411 | ||||||||
\(668\) | −19.1979 | −0.742790 | ||||||||
\(669\) | 18.8802 | 0.729952 | ||||||||
\(670\) | 14.0674 | 0.543470 | ||||||||
\(671\) | −7.94481 | −0.306706 | ||||||||
\(672\) | 3.84154 | 0.148191 | ||||||||
\(673\) | 24.9835 | 0.963044 | 0.481522 | − | 0.876434i | \(-0.340084\pi\) | ||||
0.481522 | + | 0.876434i | \(0.340084\pi\) | |||||||
\(674\) | −20.8767 | −0.804140 | ||||||||
\(675\) | 5.96080 | 0.229431 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 5.84369 | 0.224591 | 0.112296 | − | 0.993675i | \(-0.464180\pi\) | ||||
0.112296 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(678\) | −4.16900 | −0.160109 | ||||||||
\(679\) | −73.6209 | −2.82531 | ||||||||
\(680\) | −6.62142 | −0.253920 | ||||||||
\(681\) | 6.57651 | 0.252012 | ||||||||
\(682\) | −5.15301 | −0.197319 | ||||||||
\(683\) | −23.7084 | −0.907179 | −0.453589 | − | 0.891211i | \(-0.649857\pi\) | ||||
−0.453589 | + | 0.891211i | \(0.649857\pi\) | |||||||
\(684\) | 0.938340 | 0.0358783 | ||||||||
\(685\) | −12.3099 | −0.470339 | ||||||||
\(686\) | 2.90967 | 0.111092 | ||||||||
\(687\) | −19.6896 | −0.751203 | ||||||||
\(688\) | 2.50837 | 0.0956309 | ||||||||
\(689\) | −9.60467 | −0.365909 | ||||||||
\(690\) | −13.0387 | −0.496375 | ||||||||
\(691\) | −30.2366 | −1.15026 | −0.575128 | − | 0.818064i | \(-0.695048\pi\) | ||||
−0.575128 | + | 0.818064i | \(0.695048\pi\) | |||||||
\(692\) | −8.55329 | −0.325147 | ||||||||
\(693\) | 21.0963 | 0.801382 | ||||||||
\(694\) | 5.73827 | 0.217822 | ||||||||
\(695\) | −62.8695 | −2.38477 | ||||||||
\(696\) | 2.02246 | 0.0766610 | ||||||||
\(697\) | 23.2428 | 0.880385 | ||||||||
\(698\) | −28.2022 | −1.06747 | ||||||||
\(699\) | −23.8026 | −0.900297 | ||||||||
\(700\) | 22.8986 | 0.865487 | ||||||||
\(701\) | −14.4637 | −0.546287 | −0.273144 | − | 0.961973i | \(-0.588063\pi\) | ||||
−0.273144 | + | 0.961973i | \(0.588063\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −7.02969 | −0.265130 | ||||||||
\(704\) | 5.49163 | 0.206973 | ||||||||
\(705\) | 18.2555 | 0.687543 | ||||||||
\(706\) | −13.3212 | −0.501352 | ||||||||
\(707\) | 27.2168 | 1.02359 | ||||||||
\(708\) | 4.34991 | 0.163480 | ||||||||
\(709\) | 0.159226 | 0.00597985 | 0.00298992 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00298992 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(710\) | 32.4178 | 1.21662 | ||||||||
\(711\) | −15.5598 | −0.583537 | ||||||||
\(712\) | −2.36183 | −0.0885135 | ||||||||
\(713\) | −3.69550 | −0.138398 | ||||||||
\(714\) | 7.68308 | 0.287532 | ||||||||
\(715\) | −18.1812 | −0.679937 | ||||||||
\(716\) | 18.0346 | 0.673986 | ||||||||
\(717\) | 28.9962 | 1.08288 | ||||||||
\(718\) | 0.868058 | 0.0323956 | ||||||||
\(719\) | −23.3776 | −0.871836 | −0.435918 | − | 0.899986i | \(-0.643576\pi\) | ||||
−0.435918 | + | 0.899986i | \(0.643576\pi\) | |||||||
\(720\) | −3.31071 | −0.123383 | ||||||||
\(721\) | −3.84154 | −0.143066 | ||||||||
\(722\) | −18.1195 | −0.674339 | ||||||||
\(723\) | −11.4278 | −0.425005 | ||||||||
\(724\) | −15.2428 | −0.566496 | ||||||||
\(725\) | 12.0554 | 0.447728 | ||||||||
\(726\) | 19.1580 | 0.711018 | ||||||||
\(727\) | 17.8313 | 0.661325 | 0.330662 | − | 0.943749i | \(-0.392728\pi\) | ||||
0.330662 | + | 0.943749i | \(0.392728\pi\) | |||||||
\(728\) | 3.84154 | 0.142377 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.74500 | −0.286655 | ||||||||
\(731\) | 5.01675 | 0.185551 | ||||||||
\(732\) | −1.44671 | −0.0534721 | ||||||||
\(733\) | −21.7063 | −0.801740 | −0.400870 | − | 0.916135i | \(-0.631292\pi\) | ||||
−0.400870 | + | 0.916135i | \(0.631292\pi\) | |||||||
\(734\) | −27.9345 | −1.03108 | ||||||||
\(735\) | −25.6826 | −0.947316 | ||||||||
\(736\) | 3.93834 | 0.145169 | ||||||||
\(737\) | −23.3342 | −0.859526 | ||||||||
\(738\) | 11.6214 | 0.427790 | ||||||||
\(739\) | −16.2617 | −0.598198 | −0.299099 | − | 0.954222i | \(-0.596686\pi\) | ||||
−0.299099 | + | 0.954222i | \(0.596686\pi\) | |||||||
\(740\) | 24.8026 | 0.911762 | ||||||||
\(741\) | 0.938340 | 0.0344708 | ||||||||
\(742\) | −36.8967 | −1.35452 | ||||||||
\(743\) | 2.65871 | 0.0975386 | 0.0487693 | − | 0.998810i | \(-0.484470\pi\) | ||||
0.0487693 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(744\) | −0.938340 | −0.0344012 | ||||||||
\(745\) | 16.9833 | 0.622218 | ||||||||
\(746\) | −22.7583 | −0.833241 | ||||||||
\(747\) | −0.689291 | −0.0252198 | ||||||||
\(748\) | 10.9833 | 0.401587 | ||||||||
\(749\) | 65.2418 | 2.38388 | ||||||||
\(750\) | −3.18092 | −0.116151 | ||||||||
\(751\) | 36.2499 | 1.32278 | 0.661389 | − | 0.750043i | \(-0.269967\pi\) | ||||
0.661389 | + | 0.750043i | \(0.269967\pi\) | |||||||
\(752\) | −5.51408 | −0.201078 | ||||||||
\(753\) | −4.92780 | −0.179579 | ||||||||
\(754\) | 2.02246 | 0.0736535 | ||||||||
\(755\) | −46.8011 | −1.70327 | ||||||||
\(756\) | 3.84154 | 0.139715 | ||||||||
\(757\) | 20.3965 | 0.741322 | 0.370661 | − | 0.928768i | \(-0.379131\pi\) | ||||
0.370661 | + | 0.928768i | \(0.379131\pi\) | |||||||
\(758\) | 0.735587 | 0.0267177 | ||||||||
\(759\) | 21.6279 | 0.785043 | ||||||||
\(760\) | −3.10657 | −0.112687 | ||||||||
\(761\) | −19.5473 | −0.708590 | −0.354295 | − | 0.935134i | \(-0.615279\pi\) | ||||
−0.354295 | + | 0.935134i | \(0.615279\pi\) | |||||||
\(762\) | 1.23851 | 0.0448666 | ||||||||
\(763\) | 75.4013 | 2.72971 | ||||||||
\(764\) | 12.0449 | 0.435770 | ||||||||
\(765\) | −6.62142 | −0.239398 | ||||||||
\(766\) | −24.8167 | −0.896663 | ||||||||
\(767\) | 4.34991 | 0.157066 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −50.4056 | −1.81767 | −0.908837 | − | 0.417152i | \(-0.863028\pi\) | ||||
−0.908837 | + | 0.417152i | \(0.863028\pi\) | |||||||
\(770\) | −69.8437 | −2.51699 | ||||||||
\(771\) | 17.1649 | 0.618180 | ||||||||
\(772\) | 20.0801 | 0.722697 | ||||||||
\(773\) | 13.6614 | 0.491366 | 0.245683 | − | 0.969350i | \(-0.420988\pi\) | ||||
0.245683 | + | 0.969350i | \(0.420988\pi\) | |||||||
\(774\) | 2.50837 | 0.0901616 | ||||||||
\(775\) | −5.59325 | −0.200916 | ||||||||
\(776\) | −19.1644 | −0.687963 | ||||||||
\(777\) | −28.7794 | −1.03245 | ||||||||
\(778\) | −4.85778 | −0.174160 | ||||||||
\(779\) | 10.9048 | 0.390707 | ||||||||
\(780\) | −3.31071 | −0.118542 | ||||||||
\(781\) | −53.7729 | −1.92415 | ||||||||
\(782\) | 7.87668 | 0.281670 | ||||||||
\(783\) | 2.02246 | 0.0722767 | ||||||||
\(784\) | 7.75742 | 0.277051 | ||||||||
\(785\) | 34.0408 | 1.21497 | ||||||||
\(786\) | −3.30017 | −0.117713 | ||||||||
\(787\) | −38.7583 | −1.38158 | −0.690792 | − | 0.723053i | \(-0.742738\pi\) | ||||
−0.690792 | + | 0.723053i | \(0.742738\pi\) | |||||||
\(788\) | 16.6439 | 0.592913 | ||||||||
\(789\) | −31.3327 | −1.11547 | ||||||||
\(790\) | 51.5138 | 1.83278 | ||||||||
\(791\) | −16.0154 | −0.569441 | ||||||||
\(792\) | 5.49163 | 0.195136 | ||||||||
\(793\) | −1.44671 | −0.0513743 | ||||||||
\(794\) | 16.6663 | 0.591466 | ||||||||
\(795\) | 31.7983 | 1.12777 | ||||||||
\(796\) | 4.77988 | 0.169418 | ||||||||
\(797\) | −48.1328 | −1.70495 | −0.852476 | − | 0.522766i | \(-0.824900\pi\) | ||||
−0.852476 | + | 0.522766i | \(0.824900\pi\) | |||||||
\(798\) | 3.60467 | 0.127604 | ||||||||
\(799\) | −11.0282 | −0.390148 | ||||||||
\(800\) | 5.96080 | 0.210746 | ||||||||
\(801\) | −2.36183 | −0.0834513 | ||||||||
\(802\) | −1.52462 | −0.0538361 | ||||||||
\(803\) | 12.8470 | 0.453360 | ||||||||
\(804\) | −4.24905 | −0.149852 | ||||||||
\(805\) | −50.0887 | −1.76539 | ||||||||
\(806\) | −0.938340 | −0.0330516 | ||||||||
\(807\) | 9.96562 | 0.350807 | ||||||||
\(808\) | 7.08488 | 0.249245 | ||||||||
\(809\) | −33.8667 | −1.19069 | −0.595344 | − | 0.803471i | \(-0.702984\pi\) | ||||
−0.595344 | + | 0.803471i | \(0.702984\pi\) | |||||||
\(810\) | −3.31071 | −0.116326 | ||||||||
\(811\) | 0.767698 | 0.0269575 | 0.0134788 | − | 0.999909i | \(-0.495709\pi\) | ||||
0.0134788 | + | 0.999909i | \(0.495709\pi\) | |||||||
\(812\) | 7.76934 | 0.272651 | ||||||||
\(813\) | −11.6382 | −0.408168 | ||||||||
\(814\) | −41.1412 | −1.44200 | ||||||||
\(815\) | 56.7118 | 1.98653 | ||||||||
\(816\) | 2.00000 | 0.0700140 | ||||||||
\(817\) | 2.35371 | 0.0823458 | ||||||||
\(818\) | −17.4814 | −0.611221 | ||||||||
\(819\) | 3.84154 | 0.134234 | ||||||||
\(820\) | −38.4751 | −1.34361 | ||||||||
\(821\) | −44.1374 | −1.54041 | −0.770203 | − | 0.637799i | \(-0.779845\pi\) | ||||
−0.770203 | + | 0.637799i | \(0.779845\pi\) | |||||||
\(822\) | 3.71822 | 0.129688 | ||||||||
\(823\) | 10.2469 | 0.357184 | 0.178592 | − | 0.983923i | \(-0.442846\pi\) | ||||
0.178592 | + | 0.983923i | \(0.442846\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 32.7345 | 1.13967 | ||||||||
\(826\) | 16.7104 | 0.581428 | ||||||||
\(827\) | −13.1633 | −0.457732 | −0.228866 | − | 0.973458i | \(-0.573502\pi\) | ||||
−0.228866 | + | 0.973458i | \(0.573502\pi\) | |||||||
\(828\) | 3.93834 | 0.136867 | ||||||||
\(829\) | 5.88722 | 0.204471 | 0.102236 | − | 0.994760i | \(-0.467400\pi\) | ||||
0.102236 | + | 0.994760i | \(0.467400\pi\) | |||||||
\(830\) | 2.28204 | 0.0792108 | ||||||||
\(831\) | −2.27151 | −0.0787977 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 15.5148 | 0.537558 | ||||||||
\(834\) | 18.9897 | 0.657560 | ||||||||
\(835\) | 63.5588 | 2.19954 | ||||||||
\(836\) | 5.15301 | 0.178221 | ||||||||
\(837\) | −0.938340 | −0.0324338 | ||||||||
\(838\) | 21.8200 | 0.753758 | ||||||||
\(839\) | −55.5712 | −1.91853 | −0.959265 | − | 0.282508i | \(-0.908834\pi\) | ||||
−0.959265 | + | 0.282508i | \(0.908834\pi\) | |||||||
\(840\) | −12.7182 | −0.438820 | ||||||||
\(841\) | −24.9097 | −0.858954 | ||||||||
\(842\) | −4.33938 | −0.149545 | ||||||||
\(843\) | −0.486683 | −0.0167623 | ||||||||
\(844\) | 14.6446 | 0.504089 | ||||||||
\(845\) | −3.31071 | −0.113892 | ||||||||
\(846\) | −5.51408 | −0.189578 | ||||||||
\(847\) | 73.5960 | 2.52879 | ||||||||
\(848\) | −9.60467 | −0.329826 | ||||||||
\(849\) | −21.8410 | −0.749582 | ||||||||
\(850\) | 11.9216 | 0.408907 | ||||||||
\(851\) | −29.5046 | −1.01140 | ||||||||
\(852\) | −9.79180 | −0.335462 | ||||||||
\(853\) | 24.2701 | 0.830993 | 0.415497 | − | 0.909595i | \(-0.363608\pi\) | ||||
0.415497 | + | 0.909595i | \(0.363608\pi\) | |||||||
\(854\) | −5.55761 | −0.190177 | ||||||||
\(855\) | −3.10657 | −0.106243 | ||||||||
\(856\) | 16.9833 | 0.580476 | ||||||||
\(857\) | −29.3776 | −1.00352 | −0.501759 | − | 0.865007i | \(-0.667314\pi\) | ||||
−0.501759 | + | 0.865007i | \(0.667314\pi\) | |||||||
\(858\) | 5.49163 | 0.187481 | ||||||||
\(859\) | 30.2828 | 1.03324 | 0.516618 | − | 0.856216i | \(-0.327191\pi\) | ||||
0.516618 | + | 0.856216i | \(0.327191\pi\) | |||||||
\(860\) | −8.30450 | −0.283181 | ||||||||
\(861\) | 44.6441 | 1.52147 | ||||||||
\(862\) | 8.16823 | 0.278211 | ||||||||
\(863\) | −38.8611 | −1.32285 | −0.661423 | − | 0.750013i | \(-0.730047\pi\) | ||||
−0.661423 | + | 0.750013i | \(0.730047\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 28.3174 | 0.962822 | ||||||||
\(866\) | 13.0731 | 0.444241 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | −3.60467 | −0.122350 | ||||||||
\(869\) | −85.4484 | −2.89864 | ||||||||
\(870\) | −6.69576 | −0.227008 | ||||||||
\(871\) | −4.24905 | −0.143974 | ||||||||
\(872\) | 19.6279 | 0.664684 | ||||||||
\(873\) | −19.1644 | −0.648618 | ||||||||
\(874\) | 3.69550 | 0.125002 | ||||||||
\(875\) | −12.2196 | −0.413098 | ||||||||
\(876\) | 2.33938 | 0.0790402 | ||||||||
\(877\) | −19.6165 | −0.662401 | −0.331201 | − | 0.943560i | \(-0.607454\pi\) | ||||
−0.331201 | + | 0.943560i | \(0.607454\pi\) | |||||||
\(878\) | −4.23687 | −0.142987 | ||||||||
\(879\) | −0.470555 | −0.0158714 | ||||||||
\(880\) | −18.1812 | −0.612887 | ||||||||
\(881\) | −15.6111 | −0.525953 | −0.262976 | − | 0.964802i | \(-0.584704\pi\) | ||||
−0.262976 | + | 0.964802i | \(0.584704\pi\) | |||||||
\(882\) | 7.75742 | 0.261206 | ||||||||
\(883\) | 37.8583 | 1.27403 | 0.637017 | − | 0.770850i | \(-0.280168\pi\) | ||||
0.637017 | + | 0.770850i | \(0.280168\pi\) | |||||||
\(884\) | 2.00000 | 0.0672673 | ||||||||
\(885\) | −14.4013 | −0.484094 | ||||||||
\(886\) | 8.15872 | 0.274098 | ||||||||
\(887\) | −19.1160 | −0.641852 | −0.320926 | − | 0.947104i | \(-0.603994\pi\) | ||||
−0.320926 | + | 0.947104i | \(0.603994\pi\) | |||||||
\(888\) | −7.49163 | −0.251403 | ||||||||
\(889\) | 4.75780 | 0.159571 | ||||||||
\(890\) | 7.81934 | 0.262105 | ||||||||
\(891\) | 5.49163 | 0.183976 | ||||||||
\(892\) | 18.8802 | 0.632157 | ||||||||
\(893\) | −5.17408 | −0.173144 | ||||||||
\(894\) | −5.12979 | −0.171566 | ||||||||
\(895\) | −59.7074 | −1.99580 | ||||||||
\(896\) | 3.84154 | 0.128337 | ||||||||
\(897\) | 3.93834 | 0.131497 | ||||||||
\(898\) | 9.11952 | 0.304322 | ||||||||
\(899\) | −1.89775 | −0.0632936 | ||||||||
\(900\) | 5.96080 | 0.198693 | ||||||||
\(901\) | −19.2093 | −0.639956 | ||||||||
\(902\) | 63.8205 | 2.12499 | ||||||||
\(903\) | 9.63602 | 0.320667 | ||||||||
\(904\) | −4.16900 | −0.138659 | ||||||||
\(905\) | 50.4646 | 1.67750 | ||||||||
\(906\) | 14.1363 | 0.469646 | ||||||||
\(907\) | 33.4800 | 1.11168 | 0.555842 | − | 0.831288i | \(-0.312396\pi\) | ||||
0.555842 | + | 0.831288i | \(0.312396\pi\) | |||||||
\(908\) | 6.57651 | 0.218249 | ||||||||
\(909\) | 7.08488 | 0.234991 | ||||||||
\(910\) | −12.7182 | −0.421605 | ||||||||
\(911\) | 54.6247 | 1.80980 | 0.904899 | − | 0.425627i | \(-0.139946\pi\) | ||||
0.904899 | + | 0.425627i | \(0.139946\pi\) | |||||||
\(912\) | 0.938340 | 0.0310715 | ||||||||
\(913\) | −3.78533 | −0.125276 | ||||||||
\(914\) | 8.74550 | 0.289276 | ||||||||
\(915\) | 4.78965 | 0.158341 | ||||||||
\(916\) | −19.6896 | −0.650561 | ||||||||
\(917\) | −12.6777 | −0.418656 | ||||||||
\(918\) | 2.00000 | 0.0660098 | ||||||||
\(919\) | −15.3578 | −0.506606 | −0.253303 | − | 0.967387i | \(-0.581517\pi\) | ||||
−0.253303 | + | 0.967387i | \(0.581517\pi\) | |||||||
\(920\) | −13.0387 | −0.429873 | ||||||||
\(921\) | 3.66848 | 0.120881 | ||||||||
\(922\) | 27.8859 | 0.918375 | ||||||||
\(923\) | −9.79180 | −0.322301 | ||||||||
\(924\) | 21.0963 | 0.694017 | ||||||||
\(925\) | −44.6561 | −1.46828 | ||||||||
\(926\) | −2.60035 | −0.0854527 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 2.02246 | 0.0663904 | ||||||||
\(929\) | −0.822381 | −0.0269814 | −0.0134907 | − | 0.999909i | \(-0.504294\pi\) | ||||
−0.0134907 | + | 0.999909i | \(0.504294\pi\) | |||||||
\(930\) | 3.10657 | 0.101868 | ||||||||
\(931\) | 7.27910 | 0.238563 | ||||||||
\(932\) | −23.8026 | −0.779680 | ||||||||
\(933\) | 21.1517 | 0.692477 | ||||||||
\(934\) | 0.519790 | 0.0170080 | ||||||||
\(935\) | −36.3624 | −1.18918 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −32.4661 | −1.06062 | −0.530311 | − | 0.847803i | \(-0.677925\pi\) | ||||
−0.530311 | + | 0.847803i | \(0.677925\pi\) | |||||||
\(938\) | −16.3229 | −0.532961 | ||||||||
\(939\) | 3.14171 | 0.102526 | ||||||||
\(940\) | 18.2555 | 0.595429 | ||||||||
\(941\) | 59.3667 | 1.93530 | 0.967649 | − | 0.252299i | \(-0.0811868\pi\) | ||||
0.967649 | + | 0.252299i | \(0.0811868\pi\) | |||||||
\(942\) | −10.2820 | −0.335007 | ||||||||
\(943\) | 45.7691 | 1.49045 | ||||||||
\(944\) | 4.34991 | 0.141578 | ||||||||
\(945\) | −12.7182 | −0.413724 | ||||||||
\(946\) | 13.7751 | 0.447866 | ||||||||
\(947\) | −58.5203 | −1.90165 | −0.950827 | − | 0.309722i | \(-0.899764\pi\) | ||||
−0.950827 | + | 0.309722i | \(0.899764\pi\) | |||||||
\(948\) | −15.5598 | −0.505357 | ||||||||
\(949\) | 2.33938 | 0.0759394 | ||||||||
\(950\) | 5.59325 | 0.181469 | ||||||||
\(951\) | 11.2877 | 0.366030 | ||||||||
\(952\) | 7.68308 | 0.249010 | ||||||||
\(953\) | 35.0411 | 1.13509 | 0.567546 | − | 0.823341i | \(-0.307893\pi\) | ||||
0.567546 | + | 0.823341i | \(0.307893\pi\) | |||||||
\(954\) | −9.60467 | −0.310963 | ||||||||
\(955\) | −39.8772 | −1.29040 | ||||||||
\(956\) | 28.9962 | 0.937804 | ||||||||
\(957\) | 11.1066 | 0.359024 | ||||||||
\(958\) | 25.9892 | 0.839674 | ||||||||
\(959\) | 14.2837 | 0.461244 | ||||||||
\(960\) | −3.31071 | −0.106853 | ||||||||
\(961\) | −30.1195 | −0.971597 | ||||||||
\(962\) | −7.49163 | −0.241540 | ||||||||
\(963\) | 16.9833 | 0.547278 | ||||||||
\(964\) | −11.4278 | −0.368065 | ||||||||
\(965\) | −66.4792 | −2.14004 | ||||||||
\(966\) | 15.1293 | 0.486777 | ||||||||
\(967\) | 37.4354 | 1.20384 | 0.601921 | − | 0.798556i | \(-0.294402\pi\) | ||||
0.601921 | + | 0.798556i | \(0.294402\pi\) | |||||||
\(968\) | 19.1580 | 0.615760 | ||||||||
\(969\) | 1.87668 | 0.0602877 | ||||||||
\(970\) | 63.4479 | 2.03719 | ||||||||
\(971\) | −6.55493 | −0.210358 | −0.105179 | − | 0.994453i | \(-0.533542\pi\) | ||||
−0.105179 | + | 0.994453i | \(0.533542\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 72.9498 | 2.33866 | ||||||||
\(974\) | −7.15301 | −0.229197 | ||||||||
\(975\) | 5.96080 | 0.190898 | ||||||||
\(976\) | −1.44671 | −0.0463082 | ||||||||
\(977\) | 56.7409 | 1.81530 | 0.907652 | − | 0.419724i | \(-0.137873\pi\) | ||||
0.907652 | + | 0.419724i | \(0.137873\pi\) | |||||||
\(978\) | −17.1298 | −0.547750 | ||||||||
\(979\) | −12.9703 | −0.414533 | ||||||||
\(980\) | −25.6826 | −0.820400 | ||||||||
\(981\) | 19.6279 | 0.626670 | ||||||||
\(982\) | 35.0157 | 1.11740 | ||||||||
\(983\) | −35.7280 | −1.13955 | −0.569773 | − | 0.821802i | \(-0.692969\pi\) | ||||
−0.569773 | + | 0.821802i | \(0.692969\pi\) | |||||||
\(984\) | 11.6214 | 0.370477 | ||||||||
\(985\) | −55.1030 | −1.75573 | ||||||||
\(986\) | 4.04491 | 0.128816 | ||||||||
\(987\) | −21.1826 | −0.674248 | ||||||||
\(988\) | 0.938340 | 0.0298526 | ||||||||
\(989\) | 9.87883 | 0.314129 | ||||||||
\(990\) | −18.1812 | −0.577836 | ||||||||
\(991\) | 19.2413 | 0.611220 | 0.305610 | − | 0.952157i | \(-0.401140\pi\) | ||||
0.305610 | + | 0.952157i | \(0.401140\pi\) | |||||||
\(992\) | −0.938340 | −0.0297923 | ||||||||
\(993\) | 1.45890 | 0.0462966 | ||||||||
\(994\) | −37.6156 | −1.19309 | ||||||||
\(995\) | −15.8248 | −0.501680 | ||||||||
\(996\) | −0.689291 | −0.0218410 | ||||||||
\(997\) | −26.5903 | −0.842124 | −0.421062 | − | 0.907032i | \(-0.638343\pi\) | ||||
−0.421062 | + | 0.907032i | \(0.638343\pi\) | |||||||
\(998\) | 17.2813 | 0.547029 | ||||||||
\(999\) | −7.49163 | −0.237025 |
(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 | 8034.2.a.n.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.n.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |