Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,2,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, 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("2166.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(17.2955970778\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
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 | 1.4 | ||
Root | \(1.90211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 | ||||||||
\(5\) | 3.90211 | 1.74508 | 0.872539 | − | 0.488544i | \(-0.162472\pi\) | ||||
0.872539 | + | 0.488544i | \(0.162472\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.61803 | 0.989524 | 0.494762 | − | 0.869029i | \(-0.335255\pi\) | ||||
0.494762 | + | 0.869029i | \(0.335255\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.90211 | −1.23396 | ||||||||
\(11\) | 4.06050 | 1.22429 | 0.612143 | − | 0.790747i | \(-0.290308\pi\) | ||||
0.612143 | + | 0.790747i | \(0.290308\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.58721 | −0.994913 | −0.497456 | − | 0.867489i | \(-0.665733\pi\) | ||||
−0.497456 | + | 0.867489i | \(0.665733\pi\) | |||||||
\(14\) | −2.61803 | −0.699699 | ||||||||
\(15\) | 3.90211 | 1.00752 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.39144 | −1.79269 | −0.896343 | − | 0.443361i | \(-0.853786\pi\) | ||||
−0.896343 | + | 0.443361i | \(0.853786\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 3.90211 | 0.872539 | ||||||||
\(21\) | 2.61803 | 0.571302 | ||||||||
\(22\) | −4.06050 | −0.865701 | ||||||||
\(23\) | 3.11507 | 0.649538 | 0.324769 | − | 0.945793i | \(-0.394714\pi\) | ||||
0.324769 | + | 0.945793i | \(0.394714\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 10.2265 | 2.04530 | ||||||||
\(26\) | 3.58721 | 0.703510 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.61803 | 0.494762 | ||||||||
\(29\) | −2.95012 | −0.547824 | −0.273912 | − | 0.961755i | \(-0.588318\pi\) | ||||
−0.273912 | + | 0.961755i | \(0.588318\pi\) | |||||||
\(30\) | −3.90211 | −0.712425 | ||||||||
\(31\) | 5.01905 | 0.901448 | 0.450724 | − | 0.892663i | \(-0.351166\pi\) | ||||
0.450724 | + | 0.892663i | \(0.351166\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.06050 | 0.706842 | ||||||||
\(34\) | 7.39144 | 1.26762 | ||||||||
\(35\) | 10.2159 | 1.72680 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.60845 | 0.922024 | 0.461012 | − | 0.887394i | \(-0.347487\pi\) | ||||
0.461012 | + | 0.887394i | \(0.347487\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.58721 | −0.574413 | ||||||||
\(40\) | −3.90211 | −0.616978 | ||||||||
\(41\) | 10.5065 | 1.64084 | 0.820420 | − | 0.571761i | \(-0.193739\pi\) | ||||
0.820420 | + | 0.571761i | \(0.193739\pi\) | |||||||
\(42\) | −2.61803 | −0.403971 | ||||||||
\(43\) | −2.33801 | −0.356543 | −0.178272 | − | 0.983981i | \(-0.557051\pi\) | ||||
−0.178272 | + | 0.983981i | \(0.557051\pi\) | |||||||
\(44\) | 4.06050 | 0.612143 | ||||||||
\(45\) | 3.90211 | 0.581693 | ||||||||
\(46\) | −3.11507 | −0.459292 | ||||||||
\(47\) | −9.51243 | −1.38753 | −0.693765 | − | 0.720201i | \(-0.744049\pi\) | ||||
−0.693765 | + | 0.720201i | \(0.744049\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −0.145898 | −0.0208426 | ||||||||
\(50\) | −10.2265 | −1.44624 | ||||||||
\(51\) | −7.39144 | −1.03501 | ||||||||
\(52\) | −3.58721 | −0.497456 | ||||||||
\(53\) | 2.95012 | 0.405231 | 0.202615 | − | 0.979258i | \(-0.435056\pi\) | ||||
0.202615 | + | 0.979258i | \(0.435056\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 15.8445 | 2.13647 | ||||||||
\(56\) | −2.61803 | −0.349850 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.95012 | 0.387370 | ||||||||
\(59\) | 5.75216 | 0.748867 | 0.374434 | − | 0.927254i | \(-0.377837\pi\) | ||||
0.374434 | + | 0.927254i | \(0.377837\pi\) | |||||||
\(60\) | 3.90211 | 0.503761 | ||||||||
\(61\) | −6.49338 | −0.831392 | −0.415696 | − | 0.909504i | \(-0.636462\pi\) | ||||
−0.415696 | + | 0.909504i | \(0.636462\pi\) | |||||||
\(62\) | −5.01905 | −0.637420 | ||||||||
\(63\) | 2.61803 | 0.329841 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −13.9977 | −1.73620 | ||||||||
\(66\) | −4.06050 | −0.499813 | ||||||||
\(67\) | −4.45089 | −0.543763 | −0.271882 | − | 0.962331i | \(-0.587646\pi\) | ||||
−0.271882 | + | 0.962331i | \(0.587646\pi\) | |||||||
\(68\) | −7.39144 | −0.896343 | ||||||||
\(69\) | 3.11507 | 0.375011 | ||||||||
\(70\) | −10.2159 | −1.22103 | ||||||||
\(71\) | 7.49119 | 0.889040 | 0.444520 | − | 0.895769i | \(-0.353374\pi\) | ||||
0.444520 | + | 0.895769i | \(0.353374\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −13.4626 | −1.57567 | −0.787836 | − | 0.615885i | \(-0.788799\pi\) | ||||
−0.787836 | + | 0.615885i | \(0.788799\pi\) | |||||||
\(74\) | −5.60845 | −0.651969 | ||||||||
\(75\) | 10.2265 | 1.18085 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.6305 | 1.21146 | ||||||||
\(78\) | 3.58721 | 0.406171 | ||||||||
\(79\) | −1.56712 | −0.176315 | −0.0881573 | − | 0.996107i | \(-0.528098\pi\) | ||||
−0.0881573 | + | 0.996107i | \(0.528098\pi\) | |||||||
\(80\) | 3.90211 | 0.436269 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.5065 | −1.16025 | ||||||||
\(83\) | 6.69102 | 0.734435 | 0.367217 | − | 0.930135i | \(-0.380311\pi\) | ||||
0.367217 | + | 0.930135i | \(0.380311\pi\) | |||||||
\(84\) | 2.61803 | 0.285651 | ||||||||
\(85\) | −28.8422 | −3.12838 | ||||||||
\(86\) | 2.33801 | 0.252114 | ||||||||
\(87\) | −2.95012 | −0.316287 | ||||||||
\(88\) | −4.06050 | −0.432850 | ||||||||
\(89\) | 1.64886 | 0.174779 | 0.0873894 | − | 0.996174i | \(-0.472148\pi\) | ||||
0.0873894 | + | 0.996174i | \(0.472148\pi\) | |||||||
\(90\) | −3.90211 | −0.411319 | ||||||||
\(91\) | −9.39144 | −0.984490 | ||||||||
\(92\) | 3.11507 | 0.324769 | ||||||||
\(93\) | 5.01905 | 0.520451 | ||||||||
\(94\) | 9.51243 | 0.981132 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 2.93243 | 0.297743 | 0.148871 | − | 0.988857i | \(-0.452436\pi\) | ||||
0.148871 | + | 0.988857i | \(0.452436\pi\) | |||||||
\(98\) | 0.145898 | 0.0147379 | ||||||||
\(99\) | 4.06050 | 0.408095 | ||||||||
\(100\) | 10.2265 | 1.02265 | ||||||||
\(101\) | 9.83860 | 0.978977 | 0.489489 | − | 0.872010i | \(-0.337183\pi\) | ||||
0.489489 | + | 0.872010i | \(0.337183\pi\) | |||||||
\(102\) | 7.39144 | 0.731861 | ||||||||
\(103\) | 7.76870 | 0.765473 | 0.382736 | − | 0.923858i | \(-0.374982\pi\) | ||||
0.382736 | + | 0.923858i | \(0.374982\pi\) | |||||||
\(104\) | 3.58721 | 0.351755 | ||||||||
\(105\) | 10.2159 | 0.996966 | ||||||||
\(106\) | −2.95012 | −0.286541 | ||||||||
\(107\) | −16.3819 | −1.58369 | −0.791847 | − | 0.610720i | \(-0.790880\pi\) | ||||
−0.791847 | + | 0.610720i | \(0.790880\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −10.8445 | −1.03872 | −0.519358 | − | 0.854557i | \(-0.673829\pi\) | ||||
−0.519358 | + | 0.854557i | \(0.673829\pi\) | |||||||
\(110\) | −15.8445 | −1.51072 | ||||||||
\(111\) | 5.60845 | 0.532331 | ||||||||
\(112\) | 2.61803 | 0.247381 | ||||||||
\(113\) | −4.82328 | −0.453736 | −0.226868 | − | 0.973926i | \(-0.572849\pi\) | ||||
−0.226868 | + | 0.973926i | \(0.572849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.1554 | 1.13349 | ||||||||
\(116\) | −2.95012 | −0.273912 | ||||||||
\(117\) | −3.58721 | −0.331638 | ||||||||
\(118\) | −5.75216 | −0.529529 | ||||||||
\(119\) | −19.3510 | −1.77391 | ||||||||
\(120\) | −3.90211 | −0.356213 | ||||||||
\(121\) | 5.48764 | 0.498876 | ||||||||
\(122\) | 6.49338 | 0.587883 | ||||||||
\(123\) | 10.5065 | 0.947340 | ||||||||
\(124\) | 5.01905 | 0.450724 | ||||||||
\(125\) | 20.3943 | 1.82413 | ||||||||
\(126\) | −2.61803 | −0.233233 | ||||||||
\(127\) | −18.3119 | −1.62492 | −0.812459 | − | 0.583019i | \(-0.801871\pi\) | ||||
−0.812459 | + | 0.583019i | \(0.801871\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.33801 | −0.205850 | ||||||||
\(130\) | 13.9977 | 1.22768 | ||||||||
\(131\) | 16.0919 | 1.40595 | 0.702976 | − | 0.711214i | \(-0.251854\pi\) | ||||
0.702976 | + | 0.711214i | \(0.251854\pi\) | |||||||
\(132\) | 4.06050 | 0.353421 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.45089 | 0.384499 | ||||||||
\(135\) | 3.90211 | 0.335840 | ||||||||
\(136\) | 7.39144 | 0.633810 | ||||||||
\(137\) | −13.0653 | −1.11624 | −0.558121 | − | 0.829760i | \(-0.688477\pi\) | ||||
−0.558121 | + | 0.829760i | \(0.688477\pi\) | |||||||
\(138\) | −3.11507 | −0.265173 | ||||||||
\(139\) | −5.83860 | −0.495223 | −0.247612 | − | 0.968859i | \(-0.579646\pi\) | ||||
−0.247612 | + | 0.968859i | \(0.579646\pi\) | |||||||
\(140\) | 10.2159 | 0.863398 | ||||||||
\(141\) | −9.51243 | −0.801091 | ||||||||
\(142\) | −7.49119 | −0.628646 | ||||||||
\(143\) | −14.5659 | −1.21806 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −11.5117 | −0.955996 | ||||||||
\(146\) | 13.4626 | 1.11417 | ||||||||
\(147\) | −0.145898 | −0.0120335 | ||||||||
\(148\) | 5.60845 | 0.461012 | ||||||||
\(149\) | 7.00406 | 0.573795 | 0.286897 | − | 0.957961i | \(-0.407376\pi\) | ||||
0.286897 | + | 0.957961i | \(0.407376\pi\) | |||||||
\(150\) | −10.2265 | −0.834989 | ||||||||
\(151\) | −20.5920 | −1.67575 | −0.837876 | − | 0.545861i | \(-0.816203\pi\) | ||||
−0.837876 | + | 0.545861i | \(0.816203\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.39144 | −0.597562 | ||||||||
\(154\) | −10.6305 | −0.856632 | ||||||||
\(155\) | 19.5849 | 1.57310 | ||||||||
\(156\) | −3.58721 | −0.287207 | ||||||||
\(157\) | −11.0272 | −0.880064 | −0.440032 | − | 0.897982i | \(-0.645033\pi\) | ||||
−0.440032 | + | 0.897982i | \(0.645033\pi\) | |||||||
\(158\) | 1.56712 | 0.124673 | ||||||||
\(159\) | 2.95012 | 0.233960 | ||||||||
\(160\) | −3.90211 | −0.308489 | ||||||||
\(161\) | 8.15537 | 0.642733 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 6.50651 | 0.509629 | 0.254815 | − | 0.966990i | \(-0.417986\pi\) | ||||
0.254815 | + | 0.966990i | \(0.417986\pi\) | |||||||
\(164\) | 10.5065 | 0.820420 | ||||||||
\(165\) | 15.8445 | 1.23349 | ||||||||
\(166\) | −6.69102 | −0.519324 | ||||||||
\(167\) | 11.3783 | 0.880480 | 0.440240 | − | 0.897880i | \(-0.354893\pi\) | ||||
0.440240 | + | 0.897880i | \(0.354893\pi\) | |||||||
\(168\) | −2.61803 | −0.201986 | ||||||||
\(169\) | −0.131932 | −0.0101486 | ||||||||
\(170\) | 28.8422 | 2.21210 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.33801 | −0.178272 | ||||||||
\(173\) | 5.22660 | 0.397371 | 0.198685 | − | 0.980063i | \(-0.436333\pi\) | ||||
0.198685 | + | 0.980063i | \(0.436333\pi\) | |||||||
\(174\) | 2.95012 | 0.223648 | ||||||||
\(175\) | 26.7733 | 2.02387 | ||||||||
\(176\) | 4.06050 | 0.306072 | ||||||||
\(177\) | 5.75216 | 0.432359 | ||||||||
\(178\) | −1.64886 | −0.123587 | ||||||||
\(179\) | 14.4969 | 1.08355 | 0.541776 | − | 0.840523i | \(-0.317752\pi\) | ||||
0.541776 | + | 0.840523i | \(0.317752\pi\) | |||||||
\(180\) | 3.90211 | 0.290846 | ||||||||
\(181\) | −17.3510 | −1.28969 | −0.644846 | − | 0.764313i | \(-0.723078\pi\) | ||||
−0.644846 | + | 0.764313i | \(0.723078\pi\) | |||||||
\(182\) | 9.39144 | 0.696139 | ||||||||
\(183\) | −6.49338 | −0.480004 | ||||||||
\(184\) | −3.11507 | −0.229646 | ||||||||
\(185\) | 21.8848 | 1.60900 | ||||||||
\(186\) | −5.01905 | −0.368015 | ||||||||
\(187\) | −30.0129 | −2.19476 | ||||||||
\(188\) | −9.51243 | −0.693765 | ||||||||
\(189\) | 2.61803 | 0.190434 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.99177 | −0.650622 | −0.325311 | − | 0.945607i | \(-0.605469\pi\) | ||||
−0.325311 | + | 0.945607i | \(0.605469\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 17.1227 | 1.23252 | 0.616261 | − | 0.787542i | \(-0.288647\pi\) | ||||
0.616261 | + | 0.787542i | \(0.288647\pi\) | |||||||
\(194\) | −2.93243 | −0.210536 | ||||||||
\(195\) | −13.9977 | −1.00240 | ||||||||
\(196\) | −0.145898 | −0.0104213 | ||||||||
\(197\) | −3.81851 | −0.272057 | −0.136029 | − | 0.990705i | \(-0.543434\pi\) | ||||
−0.136029 | + | 0.990705i | \(0.543434\pi\) | |||||||
\(198\) | −4.06050 | −0.288567 | ||||||||
\(199\) | 14.1283 | 1.00153 | 0.500763 | − | 0.865584i | \(-0.333053\pi\) | ||||
0.500763 | + | 0.865584i | \(0.333053\pi\) | |||||||
\(200\) | −10.2265 | −0.723122 | ||||||||
\(201\) | −4.45089 | −0.313942 | ||||||||
\(202\) | −9.83860 | −0.692241 | ||||||||
\(203\) | −7.72353 | −0.542085 | ||||||||
\(204\) | −7.39144 | −0.517504 | ||||||||
\(205\) | 40.9976 | 2.86340 | ||||||||
\(206\) | −7.76870 | −0.541271 | ||||||||
\(207\) | 3.11507 | 0.216513 | ||||||||
\(208\) | −3.58721 | −0.248728 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −10.2159 | −0.704962 | ||||||||
\(211\) | −11.4508 | −0.788304 | −0.394152 | − | 0.919045i | \(-0.628962\pi\) | ||||
−0.394152 | + | 0.919045i | \(0.628962\pi\) | |||||||
\(212\) | 2.95012 | 0.202615 | ||||||||
\(213\) | 7.49119 | 0.513288 | ||||||||
\(214\) | 16.3819 | 1.11984 | ||||||||
\(215\) | −9.12319 | −0.622196 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 13.1400 | 0.892004 | ||||||||
\(218\) | 10.8445 | 0.734484 | ||||||||
\(219\) | −13.4626 | −0.909715 | ||||||||
\(220\) | 15.8445 | 1.06824 | ||||||||
\(221\) | 26.5146 | 1.78357 | ||||||||
\(222\) | −5.60845 | −0.376415 | ||||||||
\(223\) | −11.2319 | −0.752144 | −0.376072 | − | 0.926591i | \(-0.622725\pi\) | ||||
−0.376072 | + | 0.926591i | \(0.622725\pi\) | |||||||
\(224\) | −2.61803 | −0.174925 | ||||||||
\(225\) | 10.2265 | 0.681766 | ||||||||
\(226\) | 4.82328 | 0.320840 | ||||||||
\(227\) | −15.3878 | −1.02132 | −0.510661 | − | 0.859782i | \(-0.670599\pi\) | ||||
−0.510661 | + | 0.859782i | \(0.670599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6750 | 0.837588 | 0.418794 | − | 0.908081i | \(-0.362453\pi\) | ||||
0.418794 | + | 0.908081i | \(0.362453\pi\) | |||||||
\(230\) | −12.1554 | −0.801501 | ||||||||
\(231\) | 10.6305 | 0.699437 | ||||||||
\(232\) | 2.95012 | 0.193685 | ||||||||
\(233\) | 16.2147 | 1.06226 | 0.531131 | − | 0.847290i | \(-0.321767\pi\) | ||||
0.531131 | + | 0.847290i | \(0.321767\pi\) | |||||||
\(234\) | 3.58721 | 0.234503 | ||||||||
\(235\) | −37.1186 | −2.42135 | ||||||||
\(236\) | 5.75216 | 0.374434 | ||||||||
\(237\) | −1.56712 | −0.101795 | ||||||||
\(238\) | 19.3510 | 1.25434 | ||||||||
\(239\) | −5.06154 | −0.327404 | −0.163702 | − | 0.986510i | \(-0.552343\pi\) | ||||
−0.163702 | + | 0.986510i | \(0.552343\pi\) | |||||||
\(240\) | 3.90211 | 0.251880 | ||||||||
\(241\) | 15.6902 | 1.01069 | 0.505347 | − | 0.862916i | \(-0.331364\pi\) | ||||
0.505347 | + | 0.862916i | \(0.331364\pi\) | |||||||
\(242\) | −5.48764 | −0.352759 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −6.49338 | −0.415696 | ||||||||
\(245\) | −0.569311 | −0.0363719 | ||||||||
\(246\) | −10.5065 | −0.669870 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.01905 | −0.318710 | ||||||||
\(249\) | 6.69102 | 0.424026 | ||||||||
\(250\) | −20.3943 | −1.28985 | ||||||||
\(251\) | −21.1945 | −1.33779 | −0.668893 | − | 0.743359i | \(-0.733231\pi\) | ||||
−0.668893 | + | 0.743359i | \(0.733231\pi\) | |||||||
\(252\) | 2.61803 | 0.164921 | ||||||||
\(253\) | 12.6487 | 0.795220 | ||||||||
\(254\) | 18.3119 | 1.14899 | ||||||||
\(255\) | −28.8422 | −1.80617 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.7367 | 1.16876 | 0.584380 | − | 0.811480i | \(-0.301338\pi\) | ||||
0.584380 | + | 0.811480i | \(0.301338\pi\) | |||||||
\(258\) | 2.33801 | 0.145558 | ||||||||
\(259\) | 14.6831 | 0.912365 | ||||||||
\(260\) | −13.9977 | −0.868100 | ||||||||
\(261\) | −2.95012 | −0.182608 | ||||||||
\(262\) | −16.0919 | −0.994158 | ||||||||
\(263\) | 0.676024 | 0.0416854 | 0.0208427 | − | 0.999783i | \(-0.493365\pi\) | ||||
0.0208427 | + | 0.999783i | \(0.493365\pi\) | |||||||
\(264\) | −4.06050 | −0.249906 | ||||||||
\(265\) | 11.5117 | 0.707159 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.64886 | 0.100909 | ||||||||
\(268\) | −4.45089 | −0.271882 | ||||||||
\(269\) | −12.5622 | −0.765930 | −0.382965 | − | 0.923763i | \(-0.625097\pi\) | ||||
−0.382965 | + | 0.923763i | \(0.625097\pi\) | |||||||
\(270\) | −3.90211 | −0.237475 | ||||||||
\(271\) | −8.59887 | −0.522344 | −0.261172 | − | 0.965292i | \(-0.584109\pi\) | ||||
−0.261172 | + | 0.965292i | \(0.584109\pi\) | |||||||
\(272\) | −7.39144 | −0.448172 | ||||||||
\(273\) | −9.39144 | −0.568396 | ||||||||
\(274\) | 13.0653 | 0.789302 | ||||||||
\(275\) | 41.5246 | 2.50403 | ||||||||
\(276\) | 3.11507 | 0.187505 | ||||||||
\(277\) | 15.9940 | 0.960984 | 0.480492 | − | 0.876999i | \(-0.340458\pi\) | ||||
0.480492 | + | 0.876999i | \(0.340458\pi\) | |||||||
\(278\) | 5.83860 | 0.350176 | ||||||||
\(279\) | 5.01905 | 0.300483 | ||||||||
\(280\) | −10.2159 | −0.610515 | ||||||||
\(281\) | 9.70447 | 0.578920 | 0.289460 | − | 0.957190i | \(-0.406524\pi\) | ||||
0.289460 | + | 0.957190i | \(0.406524\pi\) | |||||||
\(282\) | 9.51243 | 0.566457 | ||||||||
\(283\) | 17.6143 | 1.04706 | 0.523530 | − | 0.852008i | \(-0.324615\pi\) | ||||
0.523530 | + | 0.852008i | \(0.324615\pi\) | |||||||
\(284\) | 7.49119 | 0.444520 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.5659 | 0.861297 | ||||||||
\(287\) | 27.5064 | 1.62365 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 37.6333 | 2.21372 | ||||||||
\(290\) | 11.5117 | 0.675991 | ||||||||
\(291\) | 2.93243 | 0.171902 | ||||||||
\(292\) | −13.4626 | −0.787836 | ||||||||
\(293\) | 7.16495 | 0.418581 | 0.209290 | − | 0.977854i | \(-0.432885\pi\) | ||||
0.209290 | + | 0.977854i | \(0.432885\pi\) | |||||||
\(294\) | 0.145898 | 0.00850895 | ||||||||
\(295\) | 22.4456 | 1.30683 | ||||||||
\(296\) | −5.60845 | −0.325985 | ||||||||
\(297\) | 4.06050 | 0.235614 | ||||||||
\(298\) | −7.00406 | −0.405734 | ||||||||
\(299\) | −11.1744 | −0.646233 | ||||||||
\(300\) | 10.2265 | 0.590426 | ||||||||
\(301\) | −6.12099 | −0.352808 | ||||||||
\(302\) | 20.5920 | 1.18494 | ||||||||
\(303\) | 9.83860 | 0.565213 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.3379 | −1.45084 | ||||||||
\(306\) | 7.39144 | 0.422540 | ||||||||
\(307\) | −28.5278 | −1.62816 | −0.814082 | − | 0.580749i | \(-0.802760\pi\) | ||||
−0.814082 | + | 0.580749i | \(0.802760\pi\) | |||||||
\(308\) | 10.6305 | 0.605730 | ||||||||
\(309\) | 7.76870 | 0.441946 | ||||||||
\(310\) | −19.5849 | −1.11235 | ||||||||
\(311\) | 23.1896 | 1.31496 | 0.657482 | − | 0.753471i | \(-0.271622\pi\) | ||||
0.657482 | + | 0.753471i | \(0.271622\pi\) | |||||||
\(312\) | 3.58721 | 0.203086 | ||||||||
\(313\) | −24.9975 | −1.41294 | −0.706471 | − | 0.707742i | \(-0.749714\pi\) | ||||
−0.706471 | + | 0.707742i | \(0.749714\pi\) | |||||||
\(314\) | 11.0272 | 0.622299 | ||||||||
\(315\) | 10.2159 | 0.575599 | ||||||||
\(316\) | −1.56712 | −0.0881573 | ||||||||
\(317\) | 7.67157 | 0.430878 | 0.215439 | − | 0.976517i | \(-0.430882\pi\) | ||||
0.215439 | + | 0.976517i | \(0.430882\pi\) | |||||||
\(318\) | −2.95012 | −0.165435 | ||||||||
\(319\) | −11.9790 | −0.670694 | ||||||||
\(320\) | 3.90211 | 0.218135 | ||||||||
\(321\) | −16.3819 | −0.914346 | ||||||||
\(322\) | −8.15537 | −0.454481 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −36.6845 | −2.03489 | ||||||||
\(326\) | −6.50651 | −0.360362 | ||||||||
\(327\) | −10.8445 | −0.599703 | ||||||||
\(328\) | −10.5065 | −0.580125 | ||||||||
\(329\) | −24.9039 | −1.37299 | ||||||||
\(330\) | −15.8445 | −0.872212 | ||||||||
\(331\) | −20.0806 | −1.10373 | −0.551864 | − | 0.833934i | \(-0.686083\pi\) | ||||
−0.551864 | + | 0.833934i | \(0.686083\pi\) | |||||||
\(332\) | 6.69102 | 0.367217 | ||||||||
\(333\) | 5.60845 | 0.307341 | ||||||||
\(334\) | −11.3783 | −0.622593 | ||||||||
\(335\) | −17.3679 | −0.948909 | ||||||||
\(336\) | 2.61803 | 0.142825 | ||||||||
\(337\) | 13.8386 | 0.753836 | 0.376918 | − | 0.926247i | \(-0.376984\pi\) | ||||
0.376918 | + | 0.926247i | \(0.376984\pi\) | |||||||
\(338\) | 0.131932 | 0.00717614 | ||||||||
\(339\) | −4.82328 | −0.261964 | ||||||||
\(340\) | −28.8422 | −1.56419 | ||||||||
\(341\) | 20.3798 | 1.10363 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7082 | −1.01015 | ||||||||
\(344\) | 2.33801 | 0.126057 | ||||||||
\(345\) | 12.1554 | 0.654423 | ||||||||
\(346\) | −5.22660 | −0.280984 | ||||||||
\(347\) | −17.0758 | −0.916678 | −0.458339 | − | 0.888777i | \(-0.651555\pi\) | ||||
−0.458339 | + | 0.888777i | \(0.651555\pi\) | |||||||
\(348\) | −2.95012 | −0.158143 | ||||||||
\(349\) | 2.01313 | 0.107760 | 0.0538802 | − | 0.998547i | \(-0.482841\pi\) | ||||
0.0538802 | + | 0.998547i | \(0.482841\pi\) | |||||||
\(350\) | −26.7733 | −1.43109 | ||||||||
\(351\) | −3.58721 | −0.191471 | ||||||||
\(352\) | −4.06050 | −0.216425 | ||||||||
\(353\) | −28.1187 | −1.49661 | −0.748303 | − | 0.663357i | \(-0.769131\pi\) | ||||
−0.748303 | + | 0.663357i | \(0.769131\pi\) | |||||||
\(354\) | −5.75216 | −0.305724 | ||||||||
\(355\) | 29.2315 | 1.55144 | ||||||||
\(356\) | 1.64886 | 0.0873894 | ||||||||
\(357\) | −19.3510 | −1.02417 | ||||||||
\(358\) | −14.4969 | −0.766186 | ||||||||
\(359\) | −17.5680 | −0.927206 | −0.463603 | − | 0.886043i | \(-0.653444\pi\) | ||||
−0.463603 | + | 0.886043i | \(0.653444\pi\) | |||||||
\(360\) | −3.90211 | −0.205659 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 17.3510 | 0.911950 | ||||||||
\(363\) | 5.48764 | 0.288026 | ||||||||
\(364\) | −9.39144 | −0.492245 | ||||||||
\(365\) | −52.5324 | −2.74967 | ||||||||
\(366\) | 6.49338 | 0.339414 | ||||||||
\(367\) | 21.4208 | 1.11816 | 0.559078 | − | 0.829115i | \(-0.311155\pi\) | ||||
0.559078 | + | 0.829115i | \(0.311155\pi\) | |||||||
\(368\) | 3.11507 | 0.162384 | ||||||||
\(369\) | 10.5065 | 0.546947 | ||||||||
\(370\) | −21.8848 | −1.13774 | ||||||||
\(371\) | 7.72353 | 0.400985 | ||||||||
\(372\) | 5.01905 | 0.260226 | ||||||||
\(373\) | 10.9480 | 0.566866 | 0.283433 | − | 0.958992i | \(-0.408527\pi\) | ||||
0.283433 | + | 0.958992i | \(0.408527\pi\) | |||||||
\(374\) | 30.0129 | 1.55193 | ||||||||
\(375\) | 20.3943 | 1.05316 | ||||||||
\(376\) | 9.51243 | 0.490566 | ||||||||
\(377\) | 10.5827 | 0.545037 | ||||||||
\(378\) | −2.61803 | −0.134657 | ||||||||
\(379\) | −25.6415 | −1.31712 | −0.658559 | − | 0.752529i | \(-0.728834\pi\) | ||||
−0.658559 | + | 0.752529i | \(0.728834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.3119 | −0.938146 | ||||||||
\(382\) | 8.99177 | 0.460059 | ||||||||
\(383\) | −20.1068 | −1.02741 | −0.513706 | − | 0.857966i | \(-0.671728\pi\) | ||||
−0.513706 | + | 0.857966i | \(0.671728\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 41.4815 | 2.11409 | ||||||||
\(386\) | −17.1227 | −0.871525 | ||||||||
\(387\) | −2.33801 | −0.118848 | ||||||||
\(388\) | 2.93243 | 0.148871 | ||||||||
\(389\) | −8.06874 | −0.409102 | −0.204551 | − | 0.978856i | \(-0.565573\pi\) | ||||
−0.204551 | + | 0.978856i | \(0.565573\pi\) | |||||||
\(390\) | 13.9977 | 0.708801 | ||||||||
\(391\) | −23.0249 | −1.16442 | ||||||||
\(392\) | 0.145898 | 0.00736896 | ||||||||
\(393\) | 16.0919 | 0.811727 | ||||||||
\(394\) | 3.81851 | 0.192374 | ||||||||
\(395\) | −6.11507 | −0.307683 | ||||||||
\(396\) | 4.06050 | 0.204048 | ||||||||
\(397\) | 13.1421 | 0.659584 | 0.329792 | − | 0.944054i | \(-0.393021\pi\) | ||||
0.329792 | + | 0.944054i | \(0.393021\pi\) | |||||||
\(398\) | −14.1283 | −0.708186 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.2265 | 0.511324 | ||||||||
\(401\) | 20.9905 | 1.04821 | 0.524107 | − | 0.851652i | \(-0.324399\pi\) | ||||
0.524107 | + | 0.851652i | \(0.324399\pi\) | |||||||
\(402\) | 4.45089 | 0.221990 | ||||||||
\(403\) | −18.0044 | −0.896862 | ||||||||
\(404\) | 9.83860 | 0.489489 | ||||||||
\(405\) | 3.90211 | 0.193898 | ||||||||
\(406\) | 7.72353 | 0.383312 | ||||||||
\(407\) | 22.7731 | 1.12882 | ||||||||
\(408\) | 7.39144 | 0.365931 | ||||||||
\(409\) | −4.59628 | −0.227271 | −0.113636 | − | 0.993522i | \(-0.536250\pi\) | ||||
−0.113636 | + | 0.993522i | \(0.536250\pi\) | |||||||
\(410\) | −40.9976 | −2.02473 | ||||||||
\(411\) | −13.0653 | −0.644462 | ||||||||
\(412\) | 7.76870 | 0.382736 | ||||||||
\(413\) | 15.0593 | 0.741022 | ||||||||
\(414\) | −3.11507 | −0.153097 | ||||||||
\(415\) | 26.1091 | 1.28165 | ||||||||
\(416\) | 3.58721 | 0.175877 | ||||||||
\(417\) | −5.83860 | −0.285917 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.04424 | 0.344134 | 0.172067 | − | 0.985085i | \(-0.444956\pi\) | ||||
0.172067 | + | 0.985085i | \(0.444956\pi\) | |||||||
\(420\) | 10.2159 | 0.498483 | ||||||||
\(421\) | −20.2397 | −0.986422 | −0.493211 | − | 0.869910i | \(-0.664177\pi\) | ||||
−0.493211 | + | 0.869910i | \(0.664177\pi\) | |||||||
\(422\) | 11.4508 | 0.557415 | ||||||||
\(423\) | −9.51243 | −0.462510 | ||||||||
\(424\) | −2.95012 | −0.143271 | ||||||||
\(425\) | −75.5884 | −3.66658 | ||||||||
\(426\) | −7.49119 | −0.362949 | ||||||||
\(427\) | −16.9999 | −0.822682 | ||||||||
\(428\) | −16.3819 | −0.791847 | ||||||||
\(429\) | −14.5659 | −0.703246 | ||||||||
\(430\) | 9.12319 | 0.439959 | ||||||||
\(431\) | 11.9477 | 0.575503 | 0.287751 | − | 0.957705i | \(-0.407092\pi\) | ||||
0.287751 | + | 0.957705i | \(0.407092\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −32.6322 | −1.56820 | −0.784101 | − | 0.620634i | \(-0.786875\pi\) | ||||
−0.784101 | + | 0.620634i | \(0.786875\pi\) | |||||||
\(434\) | −13.1400 | −0.630742 | ||||||||
\(435\) | −11.5117 | −0.551945 | ||||||||
\(436\) | −10.8445 | −0.519358 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 13.4626 | 0.643266 | ||||||||
\(439\) | −34.5778 | −1.65031 | −0.825155 | − | 0.564907i | \(-0.808912\pi\) | ||||
−0.825155 | + | 0.564907i | \(0.808912\pi\) | |||||||
\(440\) | −15.8445 | −0.755358 | ||||||||
\(441\) | −0.145898 | −0.00694753 | ||||||||
\(442\) | −26.5146 | −1.26117 | ||||||||
\(443\) | 29.7846 | 1.41511 | 0.707555 | − | 0.706658i | \(-0.249798\pi\) | ||||
0.707555 | + | 0.706658i | \(0.249798\pi\) | |||||||
\(444\) | 5.60845 | 0.266165 | ||||||||
\(445\) | 6.43403 | 0.305002 | ||||||||
\(446\) | 11.2319 | 0.531846 | ||||||||
\(447\) | 7.00406 | 0.331281 | ||||||||
\(448\) | 2.61803 | 0.123690 | ||||||||
\(449\) | 2.95239 | 0.139332 | 0.0696659 | − | 0.997570i | \(-0.477807\pi\) | ||||
0.0696659 | + | 0.997570i | \(0.477807\pi\) | |||||||
\(450\) | −10.2265 | −0.482081 | ||||||||
\(451\) | 42.6616 | 2.00886 | ||||||||
\(452\) | −4.82328 | −0.226868 | ||||||||
\(453\) | −20.5920 | −0.967496 | ||||||||
\(454\) | 15.3878 | 0.722184 | ||||||||
\(455\) | −36.6464 | −1.71801 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.6466 | 0.731915 | 0.365957 | − | 0.930632i | \(-0.380742\pi\) | ||||
0.365957 | + | 0.930632i | \(0.380742\pi\) | |||||||
\(458\) | −12.6750 | −0.592264 | ||||||||
\(459\) | −7.39144 | −0.345003 | ||||||||
\(460\) | 12.1554 | 0.566747 | ||||||||
\(461\) | 1.74444 | 0.0812467 | 0.0406234 | − | 0.999175i | \(-0.487066\pi\) | ||||
0.0406234 | + | 0.999175i | \(0.487066\pi\) | |||||||
\(462\) | −10.6305 | −0.494577 | ||||||||
\(463\) | −28.6429 | −1.33115 | −0.665574 | − | 0.746332i | \(-0.731813\pi\) | ||||
−0.665574 | + | 0.746332i | \(0.731813\pi\) | |||||||
\(464\) | −2.95012 | −0.136956 | ||||||||
\(465\) | 19.5849 | 0.908228 | ||||||||
\(466\) | −16.2147 | −0.751132 | ||||||||
\(467\) | −2.64480 | −0.122387 | −0.0611934 | − | 0.998126i | \(-0.519491\pi\) | ||||
−0.0611934 | + | 0.998126i | \(0.519491\pi\) | |||||||
\(468\) | −3.58721 | −0.165819 | ||||||||
\(469\) | −11.6526 | −0.538067 | ||||||||
\(470\) | 37.1186 | 1.71215 | ||||||||
\(471\) | −11.0272 | −0.508105 | ||||||||
\(472\) | −5.75216 | −0.264765 | ||||||||
\(473\) | −9.49349 | −0.436511 | ||||||||
\(474\) | 1.56712 | 0.0719801 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −19.3510 | −0.886953 | ||||||||
\(477\) | 2.95012 | 0.135077 | ||||||||
\(478\) | 5.06154 | 0.231509 | ||||||||
\(479\) | 30.9359 | 1.41350 | 0.706749 | − | 0.707464i | \(-0.250161\pi\) | ||||
0.706749 | + | 0.707464i | \(0.250161\pi\) | |||||||
\(480\) | −3.90211 | −0.178106 | ||||||||
\(481\) | −20.1187 | −0.917333 | ||||||||
\(482\) | −15.6902 | −0.714669 | ||||||||
\(483\) | 8.15537 | 0.371082 | ||||||||
\(484\) | 5.48764 | 0.249438 | ||||||||
\(485\) | 11.4427 | 0.519585 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 1.36331 | 0.0617776 | 0.0308888 | − | 0.999523i | \(-0.490166\pi\) | ||||
0.0308888 | + | 0.999523i | \(0.490166\pi\) | |||||||
\(488\) | 6.49338 | 0.293941 | ||||||||
\(489\) | 6.50651 | 0.294234 | ||||||||
\(490\) | 0.569311 | 0.0257188 | ||||||||
\(491\) | −10.7173 | −0.483664 | −0.241832 | − | 0.970318i | \(-0.577748\pi\) | ||||
−0.241832 | + | 0.970318i | \(0.577748\pi\) | |||||||
\(492\) | 10.5065 | 0.473670 | ||||||||
\(493\) | 21.8057 | 0.982077 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.8445 | 0.712158 | ||||||||
\(496\) | 5.01905 | 0.225362 | ||||||||
\(497\) | 19.6122 | 0.879727 | ||||||||
\(498\) | −6.69102 | −0.299832 | ||||||||
\(499\) | −1.49119 | −0.0667547 | −0.0333773 | − | 0.999443i | \(-0.510626\pi\) | ||||
−0.0333773 | + | 0.999443i | \(0.510626\pi\) | |||||||
\(500\) | 20.3943 | 0.912063 | ||||||||
\(501\) | 11.3783 | 0.508345 | ||||||||
\(502\) | 21.1945 | 0.945957 | ||||||||
\(503\) | −44.6083 | −1.98899 | −0.994494 | − | 0.104796i | \(-0.966581\pi\) | ||||
−0.994494 | + | 0.104796i | \(0.966581\pi\) | |||||||
\(504\) | −2.61803 | −0.116617 | ||||||||
\(505\) | 38.3913 | 1.70839 | ||||||||
\(506\) | −12.6487 | −0.562305 | ||||||||
\(507\) | −0.131932 | −0.00585929 | ||||||||
\(508\) | −18.3119 | −0.812459 | ||||||||
\(509\) | −29.5563 | −1.31006 | −0.655029 | − | 0.755603i | \(-0.727344\pi\) | ||||
−0.655029 | + | 0.755603i | \(0.727344\pi\) | |||||||
\(510\) | 28.8422 | 1.27715 | ||||||||
\(511\) | −35.2454 | −1.55917 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.7367 | −0.826438 | ||||||||
\(515\) | 30.3144 | 1.33581 | ||||||||
\(516\) | −2.33801 | −0.102925 | ||||||||
\(517\) | −38.6252 | −1.69873 | ||||||||
\(518\) | −14.6831 | −0.645139 | ||||||||
\(519\) | 5.22660 | 0.229422 | ||||||||
\(520\) | 13.9977 | 0.613840 | ||||||||
\(521\) | 34.9574 | 1.53151 | 0.765756 | − | 0.643131i | \(-0.222365\pi\) | ||||
0.765756 | + | 0.643131i | \(0.222365\pi\) | |||||||
\(522\) | 2.95012 | 0.129123 | ||||||||
\(523\) | −4.98468 | −0.217965 | −0.108982 | − | 0.994044i | \(-0.534759\pi\) | ||||
−0.108982 | + | 0.994044i | \(0.534759\pi\) | |||||||
\(524\) | 16.0919 | 0.702976 | ||||||||
\(525\) | 26.7733 | 1.16848 | ||||||||
\(526\) | −0.676024 | −0.0294760 | ||||||||
\(527\) | −37.0980 | −1.61601 | ||||||||
\(528\) | 4.06050 | 0.176710 | ||||||||
\(529\) | −13.2963 | −0.578101 | ||||||||
\(530\) | −11.5117 | −0.500037 | ||||||||
\(531\) | 5.75216 | 0.249622 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.6890 | −1.63249 | ||||||||
\(534\) | −1.64886 | −0.0713531 | ||||||||
\(535\) | −63.9238 | −2.76367 | ||||||||
\(536\) | 4.45089 | 0.192249 | ||||||||
\(537\) | 14.4969 | 0.625589 | ||||||||
\(538\) | 12.5622 | 0.541595 | ||||||||
\(539\) | −0.592419 | −0.0255173 | ||||||||
\(540\) | 3.90211 | 0.167920 | ||||||||
\(541\) | 1.12692 | 0.0484499 | 0.0242250 | − | 0.999707i | \(-0.492288\pi\) | ||||
0.0242250 | + | 0.999707i | \(0.492288\pi\) | |||||||
\(542\) | 8.59887 | 0.369353 | ||||||||
\(543\) | −17.3510 | −0.744604 | ||||||||
\(544\) | 7.39144 | 0.316905 | ||||||||
\(545\) | −42.3165 | −1.81264 | ||||||||
\(546\) | 9.39144 | 0.401916 | ||||||||
\(547\) | 39.4435 | 1.68648 | 0.843240 | − | 0.537537i | \(-0.180645\pi\) | ||||
0.843240 | + | 0.537537i | \(0.180645\pi\) | |||||||
\(548\) | −13.0653 | −0.558121 | ||||||||
\(549\) | −6.49338 | −0.277131 | ||||||||
\(550\) | −41.5246 | −1.77062 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −3.11507 | −0.132586 | ||||||||
\(553\) | −4.10277 | −0.174467 | ||||||||
\(554\) | −15.9940 | −0.679518 | ||||||||
\(555\) | 21.8848 | 0.928959 | ||||||||
\(556\) | −5.83860 | −0.247612 | ||||||||
\(557\) | 7.70913 | 0.326646 | 0.163323 | − | 0.986573i | \(-0.447779\pi\) | ||||
0.163323 | + | 0.986573i | \(0.447779\pi\) | |||||||
\(558\) | −5.01905 | −0.212473 | ||||||||
\(559\) | 8.38694 | 0.354730 | ||||||||
\(560\) | 10.2159 | 0.431699 | ||||||||
\(561\) | −30.0129 | −1.26715 | ||||||||
\(562\) | −9.70447 | −0.409359 | ||||||||
\(563\) | 35.5099 | 1.49657 | 0.748283 | − | 0.663380i | \(-0.230879\pi\) | ||||
0.748283 | + | 0.663380i | \(0.230879\pi\) | |||||||
\(564\) | −9.51243 | −0.400546 | ||||||||
\(565\) | −18.8210 | −0.791804 | ||||||||
\(566\) | −17.6143 | −0.740383 | ||||||||
\(567\) | 2.61803 | 0.109947 | ||||||||
\(568\) | −7.49119 | −0.314323 | ||||||||
\(569\) | −2.74269 | −0.114979 | −0.0574897 | − | 0.998346i | \(-0.518310\pi\) | ||||
−0.0574897 | + | 0.998346i | \(0.518310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.18845 | 0.175281 | 0.0876407 | − | 0.996152i | \(-0.472067\pi\) | ||||
0.0876407 | + | 0.996152i | \(0.472067\pi\) | |||||||
\(572\) | −14.5659 | −0.609029 | ||||||||
\(573\) | −8.99177 | −0.375637 | ||||||||
\(574\) | −27.5064 | −1.14809 | ||||||||
\(575\) | 31.8563 | 1.32850 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 18.3270 | 0.762961 | 0.381481 | − | 0.924377i | \(-0.375414\pi\) | ||||
0.381481 | + | 0.924377i | \(0.375414\pi\) | |||||||
\(578\) | −37.6333 | −1.56534 | ||||||||
\(579\) | 17.1227 | 0.711597 | ||||||||
\(580\) | −11.5117 | −0.477998 | ||||||||
\(581\) | 17.5173 | 0.726741 | ||||||||
\(582\) | −2.93243 | −0.121553 | ||||||||
\(583\) | 11.9790 | 0.496118 | ||||||||
\(584\) | 13.4626 | 0.557084 | ||||||||
\(585\) | −13.9977 | −0.578733 | ||||||||
\(586\) | −7.16495 | −0.295981 | ||||||||
\(587\) | −38.7843 | −1.60080 | −0.800400 | − | 0.599467i | \(-0.795379\pi\) | ||||
−0.800400 | + | 0.599467i | \(0.795379\pi\) | |||||||
\(588\) | −0.145898 | −0.00601673 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −22.4456 | −0.924070 | ||||||||
\(591\) | −3.81851 | −0.157072 | ||||||||
\(592\) | 5.60845 | 0.230506 | ||||||||
\(593\) | 45.3687 | 1.86307 | 0.931534 | − | 0.363654i | \(-0.118471\pi\) | ||||
0.931534 | + | 0.363654i | \(0.118471\pi\) | |||||||
\(594\) | −4.06050 | −0.166604 | ||||||||
\(595\) | −75.5099 | −3.09560 | ||||||||
\(596\) | 7.00406 | 0.286897 | ||||||||
\(597\) | 14.1283 | 0.578232 | ||||||||
\(598\) | 11.1744 | 0.456956 | ||||||||
\(599\) | −3.53390 | −0.144391 | −0.0721956 | − | 0.997390i | \(-0.523001\pi\) | ||||
−0.0721956 | + | 0.997390i | \(0.523001\pi\) | |||||||
\(600\) | −10.2265 | −0.417495 | ||||||||
\(601\) | 32.0977 | 1.30929 | 0.654645 | − | 0.755936i | \(-0.272818\pi\) | ||||
0.654645 | + | 0.755936i | \(0.272818\pi\) | |||||||
\(602\) | 6.12099 | 0.249473 | ||||||||
\(603\) | −4.45089 | −0.181254 | ||||||||
\(604\) | −20.5920 | −0.837876 | ||||||||
\(605\) | 21.4134 | 0.870578 | ||||||||
\(606\) | −9.83860 | −0.399666 | ||||||||
\(607\) | −33.0018 | −1.33950 | −0.669750 | − | 0.742587i | \(-0.733599\pi\) | ||||
−0.669750 | + | 0.742587i | \(0.733599\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.72353 | −0.312973 | ||||||||
\(610\) | 25.3379 | 1.02590 | ||||||||
\(611\) | 34.1231 | 1.38047 | ||||||||
\(612\) | −7.39144 | −0.298781 | ||||||||
\(613\) | 12.3582 | 0.499144 | 0.249572 | − | 0.968356i | \(-0.419710\pi\) | ||||
0.249572 | + | 0.968356i | \(0.419710\pi\) | |||||||
\(614\) | 28.5278 | 1.15129 | ||||||||
\(615\) | 40.9976 | 1.65318 | ||||||||
\(616\) | −10.6305 | −0.428316 | ||||||||
\(617\) | −5.52054 | −0.222249 | −0.111124 | − | 0.993807i | \(-0.535445\pi\) | ||||
−0.111124 | + | 0.993807i | \(0.535445\pi\) | |||||||
\(618\) | −7.76870 | −0.312503 | ||||||||
\(619\) | −39.9843 | −1.60711 | −0.803553 | − | 0.595233i | \(-0.797060\pi\) | ||||
−0.803553 | + | 0.595233i | \(0.797060\pi\) | |||||||
\(620\) | 19.5849 | 0.786549 | ||||||||
\(621\) | 3.11507 | 0.125004 | ||||||||
\(622\) | −23.1896 | −0.929819 | ||||||||
\(623\) | 4.31677 | 0.172948 | ||||||||
\(624\) | −3.58721 | −0.143603 | ||||||||
\(625\) | 28.4486 | 1.13794 | ||||||||
\(626\) | 24.9975 | 0.999102 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0272 | −0.440032 | ||||||||
\(629\) | −41.4545 | −1.65290 | ||||||||
\(630\) | −10.2159 | −0.407010 | ||||||||
\(631\) | 27.3628 | 1.08930 | 0.544648 | − | 0.838665i | \(-0.316663\pi\) | ||||
0.544648 | + | 0.838665i | \(0.316663\pi\) | |||||||
\(632\) | 1.56712 | 0.0623366 | ||||||||
\(633\) | −11.4508 | −0.455128 | ||||||||
\(634\) | −7.67157 | −0.304677 | ||||||||
\(635\) | −71.4551 | −2.83561 | ||||||||
\(636\) | 2.95012 | 0.116980 | ||||||||
\(637\) | 0.523367 | 0.0207365 | ||||||||
\(638\) | 11.9790 | 0.474252 | ||||||||
\(639\) | 7.49119 | 0.296347 | ||||||||
\(640\) | −3.90211 | −0.154245 | ||||||||
\(641\) | −6.36054 | −0.251226 | −0.125613 | − | 0.992079i | \(-0.540090\pi\) | ||||
−0.125613 | + | 0.992079i | \(0.540090\pi\) | |||||||
\(642\) | 16.3819 | 0.646540 | ||||||||
\(643\) | −1.15548 | −0.0455677 | −0.0227838 | − | 0.999740i | \(-0.507253\pi\) | ||||
−0.0227838 | + | 0.999740i | \(0.507253\pi\) | |||||||
\(644\) | 8.15537 | 0.321366 | ||||||||
\(645\) | −9.12319 | −0.359225 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.81026 | −0.0711687 | −0.0355843 | − | 0.999367i | \(-0.511329\pi\) | ||||
−0.0355843 | + | 0.999367i | \(0.511329\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 23.3566 | 0.916828 | ||||||||
\(650\) | 36.6845 | 1.43889 | ||||||||
\(651\) | 13.1400 | 0.514999 | ||||||||
\(652\) | 6.50651 | 0.254815 | ||||||||
\(653\) | 10.1285 | 0.396360 | 0.198180 | − | 0.980166i | \(-0.436497\pi\) | ||||
0.198180 | + | 0.980166i | \(0.436497\pi\) | |||||||
\(654\) | 10.8445 | 0.424054 | ||||||||
\(655\) | 62.7922 | 2.45350 | ||||||||
\(656\) | 10.5065 | 0.410210 | ||||||||
\(657\) | −13.4626 | −0.525224 | ||||||||
\(658\) | 24.9039 | 0.970854 | ||||||||
\(659\) | 9.41056 | 0.366583 | 0.183292 | − | 0.983059i | \(-0.441325\pi\) | ||||
0.183292 | + | 0.983059i | \(0.441325\pi\) | |||||||
\(660\) | 15.8445 | 0.616747 | ||||||||
\(661\) | −43.1611 | −1.67877 | −0.839385 | − | 0.543537i | \(-0.817085\pi\) | ||||
−0.839385 | + | 0.543537i | \(0.817085\pi\) | |||||||
\(662\) | 20.0806 | 0.780454 | ||||||||
\(663\) | 26.5146 | 1.02974 | ||||||||
\(664\) | −6.69102 | −0.259662 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.60845 | −0.217323 | ||||||||
\(667\) | −9.18985 | −0.355832 | ||||||||
\(668\) | 11.3783 | 0.440240 | ||||||||
\(669\) | −11.2319 | −0.434250 | ||||||||
\(670\) | 17.3679 | 0.670980 | ||||||||
\(671\) | −26.3663 | −1.01786 | ||||||||
\(672\) | −2.61803 | −0.100993 | ||||||||
\(673\) | 25.6466 | 0.988602 | 0.494301 | − | 0.869291i | \(-0.335424\pi\) | ||||
0.494301 | + | 0.869291i | \(0.335424\pi\) | |||||||
\(674\) | −13.8386 | −0.533043 | ||||||||
\(675\) | 10.2265 | 0.393618 | ||||||||
\(676\) | −0.131932 | −0.00507430 | ||||||||
\(677\) | 1.60260 | 0.0615929 | 0.0307965 | − | 0.999526i | \(-0.490196\pi\) | ||||
0.0307965 | + | 0.999526i | \(0.490196\pi\) | |||||||
\(678\) | 4.82328 | 0.185237 | ||||||||
\(679\) | 7.67720 | 0.294624 | ||||||||
\(680\) | 28.8422 | 1.10605 | ||||||||
\(681\) | −15.3878 | −0.589661 | ||||||||
\(682\) | −20.3798 | −0.780385 | ||||||||
\(683\) | −14.0357 | −0.537062 | −0.268531 | − | 0.963271i | \(-0.586538\pi\) | ||||
−0.268531 | + | 0.963271i | \(0.586538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50.9821 | −1.94793 | ||||||||
\(686\) | 18.7082 | 0.714283 | ||||||||
\(687\) | 12.6750 | 0.483582 | ||||||||
\(688\) | −2.33801 | −0.0891359 | ||||||||
\(689\) | −10.5827 | −0.403169 | ||||||||
\(690\) | −12.1554 | −0.462747 | ||||||||
\(691\) | −8.97363 | −0.341373 | −0.170686 | − | 0.985325i | \(-0.554599\pi\) | ||||
−0.170686 | + | 0.985325i | \(0.554599\pi\) | |||||||
\(692\) | 5.22660 | 0.198685 | ||||||||
\(693\) | 10.6305 | 0.403820 | ||||||||
\(694\) | 17.0758 | 0.648189 | ||||||||
\(695\) | −22.7829 | −0.864204 | ||||||||
\(696\) | 2.95012 | 0.111824 | ||||||||
\(697\) | −77.6582 | −2.94151 | ||||||||
\(698\) | −2.01313 | −0.0761981 | ||||||||
\(699\) | 16.2147 | 0.613297 | ||||||||
\(700\) | 26.7733 | 1.01194 | ||||||||
\(701\) | −39.0756 | −1.47586 | −0.737932 | − | 0.674875i | \(-0.764198\pi\) | ||||
−0.737932 | + | 0.674875i | \(0.764198\pi\) | |||||||
\(702\) | 3.58721 | 0.135390 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.06050 | 0.153036 | ||||||||
\(705\) | −37.1186 | −1.39797 | ||||||||
\(706\) | 28.1187 | 1.05826 | ||||||||
\(707\) | 25.7578 | 0.968721 | ||||||||
\(708\) | 5.75216 | 0.216179 | ||||||||
\(709\) | 47.4377 | 1.78156 | 0.890779 | − | 0.454436i | \(-0.150159\pi\) | ||||
0.890779 | + | 0.454436i | \(0.150159\pi\) | |||||||
\(710\) | −29.2315 | −1.09704 | ||||||||
\(711\) | −1.56712 | −0.0587715 | ||||||||
\(712\) | −1.64886 | −0.0617936 | ||||||||
\(713\) | 15.6347 | 0.585524 | ||||||||
\(714\) | 19.3510 | 0.724194 | ||||||||
\(715\) | −56.8376 | −2.12561 | ||||||||
\(716\) | 14.4969 | 0.541776 | ||||||||
\(717\) | −5.06154 | −0.189027 | ||||||||
\(718\) | 17.5680 | 0.655634 | ||||||||
\(719\) | −6.07349 | −0.226503 | −0.113252 | − | 0.993566i | \(-0.536127\pi\) | ||||
−0.113252 | + | 0.993566i | \(0.536127\pi\) | |||||||
\(720\) | 3.90211 | 0.145423 | ||||||||
\(721\) | 20.3387 | 0.757454 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.6902 | 0.583525 | ||||||||
\(724\) | −17.3510 | −0.644846 | ||||||||
\(725\) | −30.1694 | −1.12046 | ||||||||
\(726\) | −5.48764 | −0.203665 | ||||||||
\(727\) | 33.2148 | 1.23187 | 0.615934 | − | 0.787798i | \(-0.288779\pi\) | ||||
0.615934 | + | 0.787798i | \(0.288779\pi\) | |||||||
\(728\) | 9.39144 | 0.348070 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 52.5324 | 1.94431 | ||||||||
\(731\) | 17.2813 | 0.639171 | ||||||||
\(732\) | −6.49338 | −0.240002 | ||||||||
\(733\) | −3.72967 | −0.137759 | −0.0688793 | − | 0.997625i | \(-0.521942\pi\) | ||||
−0.0688793 | + | 0.997625i | \(0.521942\pi\) | |||||||
\(734\) | −21.4208 | −0.790656 | ||||||||
\(735\) | −0.569311 | −0.0209993 | ||||||||
\(736\) | −3.11507 | −0.114823 | ||||||||
\(737\) | −18.0728 | −0.665722 | ||||||||
\(738\) | −10.5065 | −0.386750 | ||||||||
\(739\) | 2.52337 | 0.0928235 | 0.0464118 | − | 0.998922i | \(-0.485221\pi\) | ||||
0.0464118 | + | 0.998922i | \(0.485221\pi\) | |||||||
\(740\) | 21.8848 | 0.804502 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.72353 | −0.283540 | ||||||||
\(743\) | 23.7403 | 0.870946 | 0.435473 | − | 0.900202i | \(-0.356581\pi\) | ||||
0.435473 | + | 0.900202i | \(0.356581\pi\) | |||||||
\(744\) | −5.01905 | −0.184007 | ||||||||
\(745\) | 27.3306 | 1.00132 | ||||||||
\(746\) | −10.9480 | −0.400835 | ||||||||
\(747\) | 6.69102 | 0.244812 | ||||||||
\(748\) | −30.0129 | −1.09738 | ||||||||
\(749\) | −42.8882 | −1.56710 | ||||||||
\(750\) | −20.3943 | −0.744696 | ||||||||
\(751\) | −35.9804 | −1.31294 | −0.656472 | − | 0.754351i | \(-0.727952\pi\) | ||||
−0.656472 | + | 0.754351i | \(0.727952\pi\) | |||||||
\(752\) | −9.51243 | −0.346883 | ||||||||
\(753\) | −21.1945 | −0.772371 | ||||||||
\(754\) | −10.5827 | −0.385400 | ||||||||
\(755\) | −80.3522 | −2.92432 | ||||||||
\(756\) | 2.61803 | 0.0952170 | ||||||||
\(757\) | 27.2398 | 0.990047 | 0.495024 | − | 0.868880i | \(-0.335159\pi\) | ||||
0.495024 | + | 0.868880i | \(0.335159\pi\) | |||||||
\(758\) | 25.6415 | 0.931343 | ||||||||
\(759\) | 12.6487 | 0.459120 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0592 | −0.690897 | −0.345448 | − | 0.938438i | \(-0.612273\pi\) | ||||
−0.345448 | + | 0.938438i | \(0.612273\pi\) | |||||||
\(762\) | 18.3119 | 0.663370 | ||||||||
\(763\) | −28.3913 | −1.02783 | ||||||||
\(764\) | −8.99177 | −0.325311 | ||||||||
\(765\) | −28.8422 | −1.04279 | ||||||||
\(766\) | 20.1068 | 0.726490 | ||||||||
\(767\) | −20.6342 | −0.745058 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 2.38906 | 0.0861517 | 0.0430759 | − | 0.999072i | \(-0.486284\pi\) | ||||
0.0430759 | + | 0.999072i | \(0.486284\pi\) | |||||||
\(770\) | −41.4815 | −1.49489 | ||||||||
\(771\) | 18.7367 | 0.674784 | ||||||||
\(772\) | 17.1227 | 0.616261 | ||||||||
\(773\) | 9.92888 | 0.357117 | 0.178559 | − | 0.983929i | \(-0.442857\pi\) | ||||
0.178559 | + | 0.983929i | \(0.442857\pi\) | |||||||
\(774\) | 2.33801 | 0.0840381 | ||||||||
\(775\) | 51.3273 | 1.84373 | ||||||||
\(776\) | −2.93243 | −0.105268 | ||||||||
\(777\) | 14.6831 | 0.526754 | ||||||||
\(778\) | 8.06874 | 0.289278 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −13.9977 | −0.501198 | ||||||||
\(781\) | 30.4179 | 1.08844 | ||||||||
\(782\) | 23.0249 | 0.823367 | ||||||||
\(783\) | −2.95012 | −0.105429 | ||||||||
\(784\) | −0.145898 | −0.00521064 | ||||||||
\(785\) | −43.0292 | −1.53578 | ||||||||
\(786\) | −16.0919 | −0.573977 | ||||||||
\(787\) | −16.6942 | −0.595083 | −0.297541 | − | 0.954709i | \(-0.596167\pi\) | ||||
−0.297541 | + | 0.954709i | \(0.596167\pi\) | |||||||
\(788\) | −3.81851 | −0.136029 | ||||||||
\(789\) | 0.676024 | 0.0240671 | ||||||||
\(790\) | 6.11507 | 0.217565 | ||||||||
\(791\) | −12.6275 | −0.448982 | ||||||||
\(792\) | −4.06050 | −0.144283 | ||||||||
\(793\) | 23.2931 | 0.827163 | ||||||||
\(794\) | −13.1421 | −0.466397 | ||||||||
\(795\) | 11.5117 | 0.408279 | ||||||||
\(796\) | 14.1283 | 0.500763 | ||||||||
\(797\) | −40.6596 | −1.44024 | −0.720118 | − | 0.693852i | \(-0.755912\pi\) | ||||
−0.720118 | + | 0.693852i | \(0.755912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 70.3105 | 2.48741 | ||||||||
\(800\) | −10.2265 | −0.361561 | ||||||||
\(801\) | 1.64886 | 0.0582596 | ||||||||
\(802\) | −20.9905 | −0.741200 | ||||||||
\(803\) | −54.6647 | −1.92907 | ||||||||
\(804\) | −4.45089 | −0.156971 | ||||||||
\(805\) | 31.8232 | 1.12162 | ||||||||
\(806\) | 18.0044 | 0.634177 | ||||||||
\(807\) | −12.5622 | −0.442210 | ||||||||
\(808\) | −9.83860 | −0.346121 | ||||||||
\(809\) | 17.5974 | 0.618692 | 0.309346 | − | 0.950950i | \(-0.399890\pi\) | ||||
0.309346 | + | 0.950950i | \(0.399890\pi\) | |||||||
\(810\) | −3.90211 | −0.137106 | ||||||||
\(811\) | 15.6607 | 0.549922 | 0.274961 | − | 0.961455i | \(-0.411335\pi\) | ||||
0.274961 | + | 0.961455i | \(0.411335\pi\) | |||||||
\(812\) | −7.72353 | −0.271043 | ||||||||
\(813\) | −8.59887 | −0.301576 | ||||||||
\(814\) | −22.7731 | −0.798197 | ||||||||
\(815\) | 25.3891 | 0.889342 | ||||||||
\(816\) | −7.39144 | −0.258752 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4.59628 | 0.160705 | ||||||||
\(819\) | −9.39144 | −0.328163 | ||||||||
\(820\) | 40.9976 | 1.43170 | ||||||||
\(821\) | −25.9393 | −0.905287 | −0.452644 | − | 0.891692i | \(-0.649519\pi\) | ||||
−0.452644 | + | 0.891692i | \(0.649519\pi\) | |||||||
\(822\) | 13.0653 | 0.455704 | ||||||||
\(823\) | 19.7806 | 0.689509 | 0.344754 | − | 0.938693i | \(-0.387962\pi\) | ||||
0.344754 | + | 0.938693i | \(0.387962\pi\) | |||||||
\(824\) | −7.76870 | −0.270636 | ||||||||
\(825\) | 41.5246 | 1.44570 | ||||||||
\(826\) | −15.0593 | −0.523982 | ||||||||
\(827\) | 23.2683 | 0.809119 | 0.404559 | − | 0.914512i | \(-0.367425\pi\) | ||||
0.404559 | + | 0.914512i | \(0.367425\pi\) | |||||||
\(828\) | 3.11507 | 0.108256 | ||||||||
\(829\) | −33.9142 | −1.17789 | −0.588944 | − | 0.808174i | \(-0.700456\pi\) | ||||
−0.588944 | + | 0.808174i | \(0.700456\pi\) | |||||||
\(830\) | −26.1091 | −0.906260 | ||||||||
\(831\) | 15.9940 | 0.554825 | ||||||||
\(832\) | −3.58721 | −0.124364 | ||||||||
\(833\) | 1.07840 | 0.0373642 | ||||||||
\(834\) | 5.83860 | 0.202174 | ||||||||
\(835\) | 44.3994 | 1.53651 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.01905 | 0.173484 | ||||||||
\(838\) | −7.04424 | −0.243339 | ||||||||
\(839\) | −29.9933 | −1.03548 | −0.517742 | − | 0.855537i | \(-0.673227\pi\) | ||||
−0.517742 | + | 0.855537i | \(0.673227\pi\) | |||||||
\(840\) | −10.2159 | −0.352481 | ||||||||
\(841\) | −20.2968 | −0.699889 | ||||||||
\(842\) | 20.2397 | 0.697506 | ||||||||
\(843\) | 9.70447 | 0.334240 | ||||||||
\(844\) | −11.4508 | −0.394152 | ||||||||
\(845\) | −0.514812 | −0.0177101 | ||||||||
\(846\) | 9.51243 | 0.327044 | ||||||||
\(847\) | 14.3668 | 0.493650 | ||||||||
\(848\) | 2.95012 | 0.101308 | ||||||||
\(849\) | 17.6143 | 0.604520 | ||||||||
\(850\) | 75.5884 | 2.59266 | ||||||||
\(851\) | 17.4707 | 0.598889 | ||||||||
\(852\) | 7.49119 | 0.256644 | ||||||||
\(853\) | 14.3703 | 0.492030 | 0.246015 | − | 0.969266i | \(-0.420879\pi\) | ||||
0.246015 | + | 0.969266i | \(0.420879\pi\) | |||||||
\(854\) | 16.9999 | 0.581724 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.3819 | 0.559920 | ||||||||
\(857\) | −47.2918 | −1.61546 | −0.807729 | − | 0.589554i | \(-0.799304\pi\) | ||||
−0.807729 | + | 0.589554i | \(0.799304\pi\) | |||||||
\(858\) | 14.5659 | 0.497270 | ||||||||
\(859\) | −14.1920 | −0.484226 | −0.242113 | − | 0.970248i | \(-0.577841\pi\) | ||||
−0.242113 | + | 0.970248i | \(0.577841\pi\) | |||||||
\(860\) | −9.12319 | −0.311098 | ||||||||
\(861\) | 27.5064 | 0.937415 | ||||||||
\(862\) | −11.9477 | −0.406942 | ||||||||
\(863\) | −21.9917 | −0.748605 | −0.374302 | − | 0.927307i | \(-0.622118\pi\) | ||||
−0.374302 | + | 0.927307i | \(0.622118\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 20.3948 | 0.693443 | ||||||||
\(866\) | 32.6322 | 1.10889 | ||||||||
\(867\) | 37.6333 | 1.27809 | ||||||||
\(868\) | 13.1400 | 0.446002 | ||||||||
\(869\) | −6.36328 | −0.215859 | ||||||||
\(870\) | 11.5117 | 0.390284 | ||||||||
\(871\) | 15.9663 | 0.540997 | ||||||||
\(872\) | 10.8445 | 0.367242 | ||||||||
\(873\) | 2.93243 | 0.0992477 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 53.3931 | 1.80502 | ||||||||
\(876\) | −13.4626 | −0.454858 | ||||||||
\(877\) | 24.0900 | 0.813461 | 0.406731 | − | 0.913548i | \(-0.366669\pi\) | ||||
0.406731 | + | 0.913548i | \(0.366669\pi\) | |||||||
\(878\) | 34.5778 | 1.16695 | ||||||||
\(879\) | 7.16495 | 0.241668 | ||||||||
\(880\) | 15.8445 | 0.534119 | ||||||||
\(881\) | 19.5381 | 0.658254 | 0.329127 | − | 0.944286i | \(-0.393246\pi\) | ||||
0.329127 | + | 0.944286i | \(0.393246\pi\) | |||||||
\(882\) | 0.145898 | 0.00491264 | ||||||||
\(883\) | 14.6238 | 0.492129 | 0.246065 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246065 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(884\) | 26.5146 | 0.891783 | ||||||||
\(885\) | 22.4456 | 0.754500 | ||||||||
\(886\) | −29.7846 | −1.00063 | ||||||||
\(887\) | −10.5395 | −0.353880 | −0.176940 | − | 0.984222i | \(-0.556620\pi\) | ||||
−0.176940 | + | 0.984222i | \(0.556620\pi\) | |||||||
\(888\) | −5.60845 | −0.188207 | ||||||||
\(889\) | −47.9411 | −1.60789 | ||||||||
\(890\) | −6.43403 | −0.215669 | ||||||||
\(891\) | 4.06050 | 0.136032 | ||||||||
\(892\) | −11.2319 | −0.376072 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −7.00406 | −0.234251 | ||||||||
\(895\) | 56.5686 | 1.89088 | ||||||||
\(896\) | −2.61803 | −0.0874624 | ||||||||
\(897\) | −11.1744 | −0.373103 | ||||||||
\(898\) | −2.95239 | −0.0985224 | ||||||||
\(899\) | −14.8068 | −0.493835 | ||||||||
\(900\) | 10.2265 | 0.340883 | ||||||||
\(901\) | −21.8057 | −0.726452 | ||||||||
\(902\) | −42.6616 | −1.42048 | ||||||||
\(903\) | −6.12099 | −0.203694 | ||||||||
\(904\) | 4.82328 | 0.160420 | ||||||||
\(905\) | −67.7057 | −2.25061 | ||||||||
\(906\) | 20.5920 | 0.684123 | ||||||||
\(907\) | 2.96782 | 0.0985448 | 0.0492724 | − | 0.998785i | \(-0.484310\pi\) | ||||
0.0492724 | + | 0.998785i | \(0.484310\pi\) | |||||||
\(908\) | −15.3878 | −0.510661 | ||||||||
\(909\) | 9.83860 | 0.326326 | ||||||||
\(910\) | 36.6464 | 1.21482 | ||||||||
\(911\) | −16.0402 | −0.531435 | −0.265717 | − | 0.964051i | \(-0.585609\pi\) | ||||
−0.265717 | + | 0.964051i | \(0.585609\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.1689 | 0.899158 | ||||||||
\(914\) | −15.6466 | −0.517542 | ||||||||
\(915\) | −25.3379 | −0.837645 | ||||||||
\(916\) | 12.6750 | 0.418794 | ||||||||
\(917\) | 42.1290 | 1.39122 | ||||||||
\(918\) | 7.39144 | 0.243954 | ||||||||
\(919\) | 42.0666 | 1.38765 | 0.693825 | − | 0.720144i | \(-0.255924\pi\) | ||||
0.693825 | + | 0.720144i | \(0.255924\pi\) | |||||||
\(920\) | −12.1554 | −0.400751 | ||||||||
\(921\) | −28.5278 | −0.940021 | ||||||||
\(922\) | −1.74444 | −0.0574501 | ||||||||
\(923\) | −26.8725 | −0.884518 | ||||||||
\(924\) | 10.6305 | 0.349718 | ||||||||
\(925\) | 57.3548 | 1.88581 | ||||||||
\(926\) | 28.6429 | 0.941264 | ||||||||
\(927\) | 7.76870 | 0.255158 | ||||||||
\(928\) | 2.95012 | 0.0968426 | ||||||||
\(929\) | 24.4355 | 0.801701 | 0.400851 | − | 0.916143i | \(-0.368715\pi\) | ||||
0.400851 | + | 0.916143i | \(0.368715\pi\) | |||||||
\(930\) | −19.5849 | −0.642214 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.2147 | 0.531131 | ||||||||
\(933\) | 23.1896 | 0.759194 | ||||||||
\(934\) | 2.64480 | 0.0865406 | ||||||||
\(935\) | −117.114 | −3.83003 | ||||||||
\(936\) | 3.58721 | 0.117252 | ||||||||
\(937\) | −40.8774 | −1.33541 | −0.667704 | − | 0.744427i | \(-0.732723\pi\) | ||||
−0.667704 | + | 0.744427i | \(0.732723\pi\) | |||||||
\(938\) | 11.6526 | 0.380471 | ||||||||
\(939\) | −24.9975 | −0.815763 | ||||||||
\(940\) | −37.1186 | −1.21067 | ||||||||
\(941\) | 24.9003 | 0.811727 | 0.405864 | − | 0.913934i | \(-0.366971\pi\) | ||||
0.405864 | + | 0.913934i | \(0.366971\pi\) | |||||||
\(942\) | 11.0272 | 0.359284 | ||||||||
\(943\) | 32.7285 | 1.06579 | ||||||||
\(944\) | 5.75216 | 0.187217 | ||||||||
\(945\) | 10.2159 | 0.332322 | ||||||||
\(946\) | 9.49349 | 0.308660 | ||||||||
\(947\) | −8.67917 | −0.282035 | −0.141018 | − | 0.990007i | \(-0.545037\pi\) | ||||
−0.141018 | + | 0.990007i | \(0.545037\pi\) | |||||||
\(948\) | −1.56712 | −0.0508976 | ||||||||
\(949\) | 48.2930 | 1.56766 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.67157 | 0.248768 | ||||||||
\(952\) | 19.3510 | 0.627170 | ||||||||
\(953\) | 26.2814 | 0.851337 | 0.425669 | − | 0.904879i | \(-0.360039\pi\) | ||||
0.425669 | + | 0.904879i | \(0.360039\pi\) | |||||||
\(954\) | −2.95012 | −0.0955138 | ||||||||
\(955\) | −35.0869 | −1.13539 | ||||||||
\(956\) | −5.06154 | −0.163702 | ||||||||
\(957\) | −11.9790 | −0.387225 | ||||||||
\(958\) | −30.9359 | −0.999495 | ||||||||
\(959\) | −34.2053 | −1.10455 | ||||||||
\(960\) | 3.90211 | 0.125940 | ||||||||
\(961\) | −5.80913 | −0.187391 | ||||||||
\(962\) | 20.1187 | 0.648653 | ||||||||
\(963\) | −16.3819 | −0.527898 | ||||||||
\(964\) | 15.6902 | 0.505347 | ||||||||
\(965\) | 66.8149 | 2.15085 | ||||||||
\(966\) | −8.15537 | −0.262395 | ||||||||
\(967\) | −22.4390 | −0.721590 | −0.360795 | − | 0.932645i | \(-0.617495\pi\) | ||||
−0.360795 | + | 0.932645i | \(0.617495\pi\) | |||||||
\(968\) | −5.48764 | −0.176379 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.4427 | −0.367402 | ||||||||
\(971\) | −2.51700 | −0.0807743 | −0.0403871 | − | 0.999184i | \(-0.512859\pi\) | ||||
−0.0403871 | + | 0.999184i | \(0.512859\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −15.2856 | −0.490035 | ||||||||
\(974\) | −1.36331 | −0.0436833 | ||||||||
\(975\) | −36.6845 | −1.17485 | ||||||||
\(976\) | −6.49338 | −0.207848 | ||||||||
\(977\) | 23.6369 | 0.756212 | 0.378106 | − | 0.925762i | \(-0.376575\pi\) | ||||
0.378106 | + | 0.925762i | \(0.376575\pi\) | |||||||
\(978\) | −6.50651 | −0.208055 | ||||||||
\(979\) | 6.69519 | 0.213979 | ||||||||
\(980\) | −0.569311 | −0.0181860 | ||||||||
\(981\) | −10.8445 | −0.346239 | ||||||||
\(982\) | 10.7173 | 0.342002 | ||||||||
\(983\) | 11.2242 | 0.357997 | 0.178999 | − | 0.983849i | \(-0.442714\pi\) | ||||
0.178999 | + | 0.983849i | \(0.442714\pi\) | |||||||
\(984\) | −10.5065 | −0.334935 | ||||||||
\(985\) | −14.9002 | −0.474761 | ||||||||
\(986\) | −21.8057 | −0.694433 | ||||||||
\(987\) | −24.9039 | −0.792699 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.28308 | −0.231588 | ||||||||
\(990\) | −15.8445 | −0.503572 | ||||||||
\(991\) | 45.9723 | 1.46036 | 0.730179 | − | 0.683256i | \(-0.239437\pi\) | ||||
0.730179 | + | 0.683256i | \(0.239437\pi\) | |||||||
\(992\) | −5.01905 | −0.159355 | ||||||||
\(993\) | −20.0806 | −0.637238 | ||||||||
\(994\) | −19.6122 | −0.622061 | ||||||||
\(995\) | 55.1301 | 1.74774 | ||||||||
\(996\) | 6.69102 | 0.212013 | ||||||||
\(997\) | 20.1291 | 0.637495 | 0.318748 | − | 0.947840i | \(-0.396738\pi\) | ||||
0.318748 | + | 0.947840i | \(0.396738\pi\) | |||||||
\(998\) | 1.49119 | 0.0472027 | ||||||||
\(999\) | 5.60845 | 0.177444 |
(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 | 2166.2.a.w.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 6498.2.a.by.1.1 | 4 | |||
19.18 | odd | 2 | 2166.2.a.x.1.4 | yes | 4 | ||
57.56 | even | 2 | 6498.2.a.bv.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2166.2.a.w.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2166.2.a.x.1.4 | yes | 4 | 19.18 | odd | 2 | ||
6498.2.a.bv.1.1 | 4 | 57.56 | even | 2 | |||
6498.2.a.by.1.1 | 4 | 3.2 | odd | 2 |