Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(1,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, 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("605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.27433728.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 15x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.480901\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.480901 | −0.340048 | −0.170024 | − | 0.985440i | \(-0.554385\pi\) | ||||
−0.170024 | + | 0.985440i | \(0.554385\pi\) | |||||||
\(3\) | −1.60168 | −0.924730 | −0.462365 | − | 0.886690i | \(-0.652999\pi\) | ||||
−0.462365 | + | 0.886690i | \(0.652999\pi\) | |||||||
\(4\) | −1.76873 | −0.884367 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.770249 | 0.314453 | ||||||||
\(7\) | 0.480901 | 0.181763 | 0.0908817 | − | 0.995862i | \(-0.471031\pi\) | ||||
0.0908817 | + | 0.995862i | \(0.471031\pi\) | |||||||
\(8\) | 1.81239 | 0.640776 | ||||||||
\(9\) | −0.434624 | −0.144875 | ||||||||
\(10\) | −0.480901 | −0.152074 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.83294 | 0.817801 | ||||||||
\(13\) | −4.79559 | −1.33006 | −0.665028 | − | 0.746818i | \(-0.731581\pi\) | ||||
−0.665028 | + | 0.746818i | \(0.731581\pi\) | |||||||
\(14\) | −0.231266 | −0.0618084 | ||||||||
\(15\) | −1.60168 | −0.413552 | ||||||||
\(16\) | 2.66589 | 0.666472 | ||||||||
\(17\) | 2.50230 | 0.606897 | 0.303448 | − | 0.952848i | \(-0.401862\pi\) | ||||
0.303448 | + | 0.952848i | \(0.401862\pi\) | |||||||
\(18\) | 0.209011 | 0.0492644 | ||||||||
\(19\) | −5.75739 | −1.32084 | −0.660418 | − | 0.750898i | \(-0.729621\pi\) | ||||
−0.660418 | + | 0.750898i | \(0.729621\pi\) | |||||||
\(20\) | −1.76873 | −0.395501 | ||||||||
\(21\) | −0.770249 | −0.168082 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43462 | 0.924683 | 0.462342 | − | 0.886702i | \(-0.347009\pi\) | ||||
0.462342 | + | 0.886702i | \(0.347009\pi\) | |||||||
\(24\) | −2.90286 | −0.592545 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.30620 | 0.452284 | ||||||||
\(27\) | 5.50117 | 1.05870 | ||||||||
\(28\) | −0.850586 | −0.160746 | ||||||||
\(29\) | 9.01248 | 1.67358 | 0.836788 | − | 0.547527i | \(-0.184431\pi\) | ||||
0.836788 | + | 0.547527i | \(0.184431\pi\) | |||||||
\(30\) | 0.770249 | 0.140628 | ||||||||
\(31\) | 7.97209 | 1.43183 | 0.715915 | − | 0.698187i | \(-0.246010\pi\) | ||||
0.715915 | + | 0.698187i | \(0.246010\pi\) | |||||||
\(32\) | −4.90680 | −0.867409 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.20336 | −0.206374 | ||||||||
\(35\) | 0.480901 | 0.0812871 | ||||||||
\(36\) | 0.768734 | 0.128122 | ||||||||
\(37\) | 5.20336 | 0.855427 | 0.427713 | − | 0.903914i | \(-0.359319\pi\) | ||||
0.427713 | + | 0.903914i | \(0.359319\pi\) | |||||||
\(38\) | 2.76873 | 0.449148 | ||||||||
\(39\) | 7.68099 | 1.22994 | ||||||||
\(40\) | 1.81239 | 0.286564 | ||||||||
\(41\) | −8.45124 | −1.31986 | −0.659931 | − | 0.751326i | \(-0.729415\pi\) | ||||
−0.659931 | + | 0.751326i | \(0.729415\pi\) | |||||||
\(42\) | 0.370413 | 0.0571560 | ||||||||
\(43\) | 8.53158 | 1.30105 | 0.650527 | − | 0.759483i | \(-0.274548\pi\) | ||||
0.650527 | + | 0.759483i | \(0.274548\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.434624 | −0.0647899 | ||||||||
\(46\) | −2.13261 | −0.314437 | ||||||||
\(47\) | 9.60168 | 1.40055 | 0.700274 | − | 0.713874i | \(-0.253061\pi\) | ||||
0.700274 | + | 0.713874i | \(0.253061\pi\) | |||||||
\(48\) | −4.26990 | −0.616307 | ||||||||
\(49\) | −6.76873 | −0.966962 | ||||||||
\(50\) | −0.480901 | −0.0680097 | ||||||||
\(51\) | −4.00788 | −0.561216 | ||||||||
\(52\) | 8.48212 | 1.17626 | ||||||||
\(53\) | 6.10051 | 0.837970 | 0.418985 | − | 0.907993i | \(-0.362386\pi\) | ||||
0.418985 | + | 0.907993i | \(0.362386\pi\) | |||||||
\(54\) | −2.64552 | −0.360009 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.871579 | 0.116470 | ||||||||
\(57\) | 9.22149 | 1.22142 | ||||||||
\(58\) | −4.33411 | −0.569097 | ||||||||
\(59\) | 2.76873 | 0.360459 | 0.180229 | − | 0.983625i | \(-0.442316\pi\) | ||||
0.180229 | + | 0.983625i | \(0.442316\pi\) | |||||||
\(60\) | 2.83294 | 0.365732 | ||||||||
\(61\) | 4.02534 | 0.515392 | 0.257696 | − | 0.966226i | \(-0.417037\pi\) | ||||
0.257696 | + | 0.966226i | \(0.417037\pi\) | |||||||
\(62\) | −3.83379 | −0.486891 | ||||||||
\(63\) | −0.209011 | −0.0263329 | ||||||||
\(64\) | −2.97209 | −0.371512 | ||||||||
\(65\) | −4.79559 | −0.594820 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.60168 | 0.928693 | 0.464346 | − | 0.885654i | \(-0.346289\pi\) | ||||
0.464346 | + | 0.885654i | \(0.346289\pi\) | |||||||
\(68\) | −4.42590 | −0.536720 | ||||||||
\(69\) | −7.10284 | −0.855082 | ||||||||
\(70\) | −0.231266 | −0.0276415 | ||||||||
\(71\) | −2.76873 | −0.328588 | −0.164294 | − | 0.986411i | \(-0.552535\pi\) | ||||
−0.164294 | + | 0.986411i | \(0.552535\pi\) | |||||||
\(72\) | −0.787707 | −0.0928322 | ||||||||
\(73\) | −5.00460 | −0.585744 | −0.292872 | − | 0.956152i | \(-0.594611\pi\) | ||||
−0.292872 | + | 0.956152i | \(0.594611\pi\) | |||||||
\(74\) | −2.50230 | −0.290886 | ||||||||
\(75\) | −1.60168 | −0.184946 | ||||||||
\(76\) | 10.1833 | 1.16810 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.69380 | −0.418240 | ||||||||
\(79\) | −3.62478 | −0.407819 | −0.203910 | − | 0.978990i | \(-0.565365\pi\) | ||||
−0.203910 | + | 0.978990i | \(0.565365\pi\) | |||||||
\(80\) | 2.66589 | 0.298056 | ||||||||
\(81\) | −7.50723 | −0.834137 | ||||||||
\(82\) | 4.06421 | 0.448817 | ||||||||
\(83\) | −1.71459 | −0.188201 | −0.0941005 | − | 0.995563i | \(-0.529998\pi\) | ||||
−0.0941005 | + | 0.995563i | \(0.529998\pi\) | |||||||
\(84\) | 1.36237 | 0.148646 | ||||||||
\(85\) | 2.50230 | 0.271413 | ||||||||
\(86\) | −4.10284 | −0.442421 | ||||||||
\(87\) | −14.4351 | −1.54761 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.7408 | −1.66852 | −0.834262 | − | 0.551368i | \(-0.814106\pi\) | ||||
−0.834262 | + | 0.551368i | \(0.814106\pi\) | |||||||
\(90\) | 0.209011 | 0.0220317 | ||||||||
\(91\) | −2.30620 | −0.241756 | ||||||||
\(92\) | −7.84367 | −0.817759 | ||||||||
\(93\) | −12.7687 | −1.32406 | ||||||||
\(94\) | −4.61746 | −0.476254 | ||||||||
\(95\) | −5.75739 | −0.590696 | ||||||||
\(96\) | 7.85913 | 0.802119 | ||||||||
\(97\) | −3.63798 | −0.369381 | −0.184691 | − | 0.982797i | \(-0.559128\pi\) | ||||
−0.184691 | + | 0.982797i | \(0.559128\pi\) | |||||||
\(98\) | 3.25509 | 0.328814 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.76873 | −0.176873 | ||||||||
\(101\) | 7.69845 | 0.766025 | 0.383012 | − | 0.923743i | \(-0.374887\pi\) | ||||
0.383012 | + | 0.923743i | \(0.374887\pi\) | |||||||
\(102\) | 1.92739 | 0.190840 | ||||||||
\(103\) | 9.10284 | 0.896930 | 0.448465 | − | 0.893800i | \(-0.351971\pi\) | ||||
0.448465 | + | 0.893800i | \(0.351971\pi\) | |||||||
\(104\) | −8.69147 | −0.852268 | ||||||||
\(105\) | −0.770249 | −0.0751686 | ||||||||
\(106\) | −2.93374 | −0.284950 | ||||||||
\(107\) | 16.7913 | 1.62327 | 0.811637 | − | 0.584163i | \(-0.198577\pi\) | ||||
0.811637 | + | 0.584163i | \(0.198577\pi\) | |||||||
\(108\) | −9.73010 | −0.936279 | ||||||||
\(109\) | 17.8817 | 1.71276 | 0.856380 | − | 0.516346i | \(-0.172708\pi\) | ||||
0.856380 | + | 0.516346i | \(0.172708\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.33411 | −0.791039 | ||||||||
\(112\) | 1.28203 | 0.121140 | ||||||||
\(113\) | −0.462531 | −0.0435113 | −0.0217556 | − | 0.999763i | \(-0.506926\pi\) | ||||
−0.0217556 | + | 0.999763i | \(0.506926\pi\) | |||||||
\(114\) | −4.43462 | −0.415341 | ||||||||
\(115\) | 4.43462 | 0.413531 | ||||||||
\(116\) | −15.9407 | −1.48006 | ||||||||
\(117\) | 2.08428 | 0.192692 | ||||||||
\(118\) | −1.33149 | −0.122573 | ||||||||
\(119\) | 1.20336 | 0.110312 | ||||||||
\(120\) | −2.90286 | −0.264994 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.93579 | −0.175258 | ||||||||
\(123\) | 13.5362 | 1.22052 | ||||||||
\(124\) | −14.1005 | −1.26626 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.100514 | 0.00895446 | ||||||||
\(127\) | −15.8295 | −1.40464 | −0.702319 | − | 0.711862i | \(-0.747852\pi\) | ||||
−0.702319 | + | 0.711862i | \(0.747852\pi\) | |||||||
\(128\) | 11.2429 | 0.993741 | ||||||||
\(129\) | −13.6649 | −1.20312 | ||||||||
\(130\) | 2.30620 | 0.202267 | ||||||||
\(131\) | −9.60460 | −0.839158 | −0.419579 | − | 0.907719i | \(-0.637822\pi\) | ||||
−0.419579 | + | 0.907719i | \(0.637822\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.76873 | −0.240080 | ||||||||
\(134\) | −3.65565 | −0.315800 | ||||||||
\(135\) | 5.50117 | 0.473465 | ||||||||
\(136\) | 4.53514 | 0.388885 | ||||||||
\(137\) | 3.97209 | 0.339359 | 0.169679 | − | 0.985499i | \(-0.445727\pi\) | ||||
0.169679 | + | 0.985499i | \(0.445727\pi\) | |||||||
\(138\) | 3.41576 | 0.290769 | ||||||||
\(139\) | −9.22149 | −0.782157 | −0.391078 | − | 0.920357i | \(-0.627898\pi\) | ||||
−0.391078 | + | 0.920357i | \(0.627898\pi\) | |||||||
\(140\) | −0.850586 | −0.0718876 | ||||||||
\(141\) | −15.3788 | −1.29513 | ||||||||
\(142\) | 1.33149 | 0.111736 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.15866 | −0.0965550 | ||||||||
\(145\) | 9.01248 | 0.748446 | ||||||||
\(146\) | 2.40672 | 0.199181 | ||||||||
\(147\) | 10.8413 | 0.894179 | ||||||||
\(148\) | −9.20336 | −0.756511 | ||||||||
\(149\) | −7.65012 | −0.626722 | −0.313361 | − | 0.949634i | \(-0.601455\pi\) | ||||
−0.313361 | + | 0.949634i | \(0.601455\pi\) | |||||||
\(150\) | 0.770249 | 0.0628906 | ||||||||
\(151\) | 2.87198 | 0.233719 | 0.116859 | − | 0.993148i | \(-0.462717\pi\) | ||||
0.116859 | + | 0.993148i | \(0.462717\pi\) | |||||||
\(152\) | −10.4346 | −0.846360 | ||||||||
\(153\) | −1.08756 | −0.0879240 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.97209 | 0.640334 | ||||||||
\(156\) | −13.5856 | −1.08772 | ||||||||
\(157\) | 17.4817 | 1.39519 | 0.697594 | − | 0.716493i | \(-0.254254\pi\) | ||||
0.697594 | + | 0.716493i | \(0.254254\pi\) | |||||||
\(158\) | 1.74316 | 0.138678 | ||||||||
\(159\) | −9.77107 | −0.774896 | ||||||||
\(160\) | −4.90680 | −0.387917 | ||||||||
\(161\) | 2.13261 | 0.168074 | ||||||||
\(162\) | 3.61023 | 0.283647 | ||||||||
\(163\) | 13.1671 | 1.03132 | 0.515662 | − | 0.856792i | \(-0.327546\pi\) | ||||
0.515662 | + | 0.856792i | \(0.327546\pi\) | |||||||
\(164\) | 14.9480 | 1.16724 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.824549 | 0.0639974 | ||||||||
\(167\) | 15.8778 | 1.22866 | 0.614331 | − | 0.789049i | \(-0.289426\pi\) | ||||
0.614331 | + | 0.789049i | \(0.289426\pi\) | |||||||
\(168\) | −1.39599 | −0.107703 | ||||||||
\(169\) | 9.99767 | 0.769051 | ||||||||
\(170\) | −1.20336 | −0.0922934 | ||||||||
\(171\) | 2.50230 | 0.191356 | ||||||||
\(172\) | −15.0901 | −1.15061 | ||||||||
\(173\) | −22.8206 | −1.73501 | −0.867507 | − | 0.497425i | \(-0.834279\pi\) | ||||
−0.867507 | + | 0.497425i | \(0.834279\pi\) | |||||||
\(174\) | 6.94185 | 0.526261 | ||||||||
\(175\) | 0.480901 | 0.0363527 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.43462 | −0.333327 | ||||||||
\(178\) | 7.56978 | 0.567379 | ||||||||
\(179\) | −0.462531 | −0.0345712 | −0.0172856 | − | 0.999851i | \(-0.505502\pi\) | ||||
−0.0172856 | + | 0.999851i | \(0.505502\pi\) | |||||||
\(180\) | 0.768734 | 0.0572981 | ||||||||
\(181\) | −3.12842 | −0.232534 | −0.116267 | − | 0.993218i | \(-0.537093\pi\) | ||||
−0.116267 | + | 0.993218i | \(0.537093\pi\) | |||||||
\(182\) | 1.10906 | 0.0822086 | ||||||||
\(183\) | −6.44730 | −0.476598 | ||||||||
\(184\) | 8.03726 | 0.592515 | ||||||||
\(185\) | 5.20336 | 0.382559 | ||||||||
\(186\) | 6.14050 | 0.450243 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −16.9828 | −1.23860 | ||||||||
\(189\) | 2.64552 | 0.192433 | ||||||||
\(190\) | 2.76873 | 0.200865 | ||||||||
\(191\) | −5.43695 | −0.393404 | −0.196702 | − | 0.980463i | \(-0.563023\pi\) | ||||
−0.196702 | + | 0.980463i | \(0.563023\pi\) | |||||||
\(192\) | 4.76034 | 0.343548 | ||||||||
\(193\) | 3.20675 | 0.230827 | 0.115414 | − | 0.993318i | \(-0.463181\pi\) | ||||
0.115414 | + | 0.993318i | \(0.463181\pi\) | |||||||
\(194\) | 1.74951 | 0.125607 | ||||||||
\(195\) | 7.68099 | 0.550047 | ||||||||
\(196\) | 11.9721 | 0.855149 | ||||||||
\(197\) | −19.4048 | −1.38253 | −0.691267 | − | 0.722600i | \(-0.742947\pi\) | ||||
−0.691267 | + | 0.722600i | \(0.742947\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3509 | 1.44264 | 0.721319 | − | 0.692603i | \(-0.243536\pi\) | ||||
0.721319 | + | 0.692603i | \(0.243536\pi\) | |||||||
\(200\) | 1.81239 | 0.128155 | ||||||||
\(201\) | −12.1755 | −0.858790 | ||||||||
\(202\) | −3.70219 | −0.260485 | ||||||||
\(203\) | 4.33411 | 0.304195 | ||||||||
\(204\) | 7.08888 | 0.496321 | ||||||||
\(205\) | −8.45124 | −0.590260 | ||||||||
\(206\) | −4.37757 | −0.305000 | ||||||||
\(207\) | −1.92739 | −0.133963 | ||||||||
\(208\) | −12.7845 | −0.886446 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.370413 | 0.0255610 | ||||||||
\(211\) | 6.87987 | 0.473630 | 0.236815 | − | 0.971555i | \(-0.423897\pi\) | ||||
0.236815 | + | 0.971555i | \(0.423897\pi\) | |||||||
\(212\) | −10.7902 | −0.741073 | ||||||||
\(213\) | 4.43462 | 0.303855 | ||||||||
\(214\) | −8.07494 | −0.551991 | ||||||||
\(215\) | 8.53158 | 0.581849 | ||||||||
\(216\) | 9.97025 | 0.678389 | ||||||||
\(217\) | 3.83379 | 0.260254 | ||||||||
\(218\) | −8.59935 | −0.582421 | ||||||||
\(219\) | 8.01576 | 0.541655 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 4.00788 | 0.268991 | ||||||||
\(223\) | −1.03863 | −0.0695521 | −0.0347760 | − | 0.999395i | \(-0.511072\pi\) | ||||
−0.0347760 | + | 0.999395i | \(0.511072\pi\) | |||||||
\(224\) | −2.35969 | −0.157663 | ||||||||
\(225\) | −0.434624 | −0.0289749 | ||||||||
\(226\) | 0.222432 | 0.0147959 | ||||||||
\(227\) | 0.480901 | 0.0319185 | 0.0159593 | − | 0.999873i | \(-0.494920\pi\) | ||||
0.0159593 | + | 0.999873i | \(0.494920\pi\) | |||||||
\(228\) | −16.3104 | −1.08018 | ||||||||
\(229\) | 13.5398 | 0.894735 | 0.447368 | − | 0.894350i | \(-0.352362\pi\) | ||||
0.447368 | + | 0.894350i | \(0.352362\pi\) | |||||||
\(230\) | −2.13261 | −0.140620 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.3341 | 1.07239 | ||||||||
\(233\) | −21.1543 | −1.38586 | −0.692932 | − | 0.721003i | \(-0.743681\pi\) | ||||
−0.692932 | + | 0.721003i | \(0.743681\pi\) | |||||||
\(234\) | −1.00233 | −0.0655244 | ||||||||
\(235\) | 9.60168 | 0.626344 | ||||||||
\(236\) | −4.89716 | −0.318778 | ||||||||
\(237\) | 5.80573 | 0.377123 | ||||||||
\(238\) | −0.578696 | −0.0375113 | ||||||||
\(239\) | 2.67639 | 0.173122 | 0.0865608 | − | 0.996247i | \(-0.472412\pi\) | ||||
0.0865608 | + | 0.996247i | \(0.472412\pi\) | |||||||
\(240\) | −4.26990 | −0.275621 | ||||||||
\(241\) | −4.56912 | −0.294323 | −0.147161 | − | 0.989112i | \(-0.547014\pi\) | ||||
−0.147161 | + | 0.989112i | \(0.547014\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.47932 | −0.287349 | ||||||||
\(244\) | −7.11976 | −0.455796 | ||||||||
\(245\) | −6.76873 | −0.432439 | ||||||||
\(246\) | −6.50956 | −0.415034 | ||||||||
\(247\) | 27.6101 | 1.75679 | ||||||||
\(248\) | 14.4485 | 0.917482 | ||||||||
\(249\) | 2.74623 | 0.174035 | ||||||||
\(250\) | −0.480901 | −0.0304148 | ||||||||
\(251\) | −11.4370 | −0.721894 | −0.360947 | − | 0.932586i | \(-0.617547\pi\) | ||||
−0.360947 | + | 0.932586i | \(0.617547\pi\) | |||||||
\(252\) | 0.369685 | 0.0232880 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 7.61241 | 0.477645 | ||||||||
\(255\) | −4.00788 | −0.250983 | ||||||||
\(256\) | 0.537469 | 0.0335918 | ||||||||
\(257\) | −20.0447 | −1.25035 | −0.625177 | − | 0.780483i | \(-0.714973\pi\) | ||||
−0.625177 | + | 0.780483i | \(0.714973\pi\) | |||||||
\(258\) | 6.57144 | 0.409120 | ||||||||
\(259\) | 2.50230 | 0.155485 | ||||||||
\(260\) | 8.48212 | 0.526039 | ||||||||
\(261\) | −3.91704 | −0.242459 | ||||||||
\(262\) | 4.61886 | 0.285354 | ||||||||
\(263\) | −6.55852 | −0.404416 | −0.202208 | − | 0.979343i | \(-0.564812\pi\) | ||||
−0.202208 | + | 0.979343i | \(0.564812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.10051 | 0.374752 | ||||||||
\(266\) | 1.33149 | 0.0816387 | ||||||||
\(267\) | 25.2118 | 1.54293 | ||||||||
\(268\) | −13.4454 | −0.821306 | ||||||||
\(269\) | 1.89716 | 0.115672 | 0.0578358 | − | 0.998326i | \(-0.481580\pi\) | ||||
0.0578358 | + | 0.998326i | \(0.481580\pi\) | |||||||
\(270\) | −2.64552 | −0.161001 | ||||||||
\(271\) | 11.3541 | 0.689713 | 0.344856 | − | 0.938655i | \(-0.387928\pi\) | ||||
0.344856 | + | 0.938655i | \(0.387928\pi\) | |||||||
\(272\) | 6.67086 | 0.404480 | ||||||||
\(273\) | 3.69380 | 0.223559 | ||||||||
\(274\) | −1.91018 | −0.115398 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.5630 | 0.756206 | ||||||||
\(277\) | −22.8340 | −1.37196 | −0.685980 | − | 0.727620i | \(-0.740626\pi\) | ||||
−0.685980 | + | 0.727620i | \(0.740626\pi\) | |||||||
\(278\) | 4.43462 | 0.265971 | ||||||||
\(279\) | −3.46486 | −0.207436 | ||||||||
\(280\) | 0.871579 | 0.0520868 | ||||||||
\(281\) | 22.6115 | 1.34889 | 0.674446 | − | 0.738324i | \(-0.264383\pi\) | ||||
0.674446 | + | 0.738324i | \(0.264383\pi\) | |||||||
\(282\) | 7.39568 | 0.440407 | ||||||||
\(283\) | 27.5667 | 1.63867 | 0.819335 | − | 0.573316i | \(-0.194343\pi\) | ||||
0.819335 | + | 0.573316i | \(0.194343\pi\) | |||||||
\(284\) | 4.89716 | 0.290593 | ||||||||
\(285\) | 9.22149 | 0.546234 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.06421 | −0.239903 | ||||||||
\(288\) | 2.13261 | 0.125666 | ||||||||
\(289\) | −10.7385 | −0.631676 | ||||||||
\(290\) | −4.33411 | −0.254508 | ||||||||
\(291\) | 5.82688 | 0.341578 | ||||||||
\(292\) | 8.85181 | 0.518013 | ||||||||
\(293\) | 21.8587 | 1.27700 | 0.638501 | − | 0.769621i | \(-0.279555\pi\) | ||||
0.638501 | + | 0.769621i | \(0.279555\pi\) | |||||||
\(294\) | −5.21361 | −0.304064 | ||||||||
\(295\) | 2.76873 | 0.161202 | ||||||||
\(296\) | 9.43050 | 0.548137 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.67895 | 0.213116 | ||||||||
\(299\) | −21.2666 | −1.22988 | ||||||||
\(300\) | 2.83294 | 0.163560 | ||||||||
\(301\) | 4.10284 | 0.236484 | ||||||||
\(302\) | −1.38114 | −0.0794757 | ||||||||
\(303\) | −12.3305 | −0.708366 | ||||||||
\(304\) | −15.3486 | −0.880301 | ||||||||
\(305\) | 4.02534 | 0.230490 | ||||||||
\(306\) | 0.523008 | 0.0298984 | ||||||||
\(307\) | 9.80019 | 0.559326 | 0.279663 | − | 0.960098i | \(-0.409777\pi\) | ||||
0.279663 | + | 0.960098i | \(0.409777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.5798 | −0.829418 | ||||||||
\(310\) | −3.83379 | −0.217744 | ||||||||
\(311\) | 9.77107 | 0.554066 | 0.277033 | − | 0.960860i | \(-0.410649\pi\) | ||||
0.277033 | + | 0.960860i | \(0.410649\pi\) | |||||||
\(312\) | 13.9209 | 0.788118 | ||||||||
\(313\) | −0.897155 | −0.0507102 | −0.0253551 | − | 0.999679i | \(-0.508072\pi\) | ||||
−0.0253551 | + | 0.999679i | \(0.508072\pi\) | |||||||
\(314\) | −8.40694 | −0.474431 | ||||||||
\(315\) | −0.209011 | −0.0117764 | ||||||||
\(316\) | 6.41126 | 0.360662 | ||||||||
\(317\) | −2.66822 | −0.149862 | −0.0749311 | − | 0.997189i | \(-0.523874\pi\) | ||||
−0.0749311 | + | 0.997189i | \(0.523874\pi\) | |||||||
\(318\) | 4.69891 | 0.263502 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.97209 | −0.166145 | ||||||||
\(321\) | −26.8942 | −1.50109 | ||||||||
\(322\) | −1.02558 | −0.0571531 | ||||||||
\(323\) | −14.4067 | −0.801611 | ||||||||
\(324\) | 13.2783 | 0.737683 | ||||||||
\(325\) | −4.79559 | −0.266011 | ||||||||
\(326\) | −6.33205 | −0.350700 | ||||||||
\(327\) | −28.6408 | −1.58384 | ||||||||
\(328\) | −15.3169 | −0.845736 | ||||||||
\(329\) | 4.61746 | 0.254569 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9744 | 1.04293 | 0.521464 | − | 0.853273i | \(-0.325386\pi\) | ||||
0.521464 | + | 0.853273i | \(0.325386\pi\) | |||||||
\(332\) | 3.03266 | 0.166439 | ||||||||
\(333\) | −2.26150 | −0.123930 | ||||||||
\(334\) | −7.63565 | −0.417804 | ||||||||
\(335\) | 7.60168 | 0.415324 | ||||||||
\(336\) | −2.05340 | −0.112022 | ||||||||
\(337\) | 4.79559 | 0.261232 | 0.130616 | − | 0.991433i | \(-0.458304\pi\) | ||||
0.130616 | + | 0.991433i | \(0.458304\pi\) | |||||||
\(338\) | −4.80789 | −0.261515 | ||||||||
\(339\) | 0.740827 | 0.0402362 | ||||||||
\(340\) | −4.42590 | −0.240028 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.20336 | −0.0650702 | ||||||||
\(343\) | −6.62140 | −0.357522 | ||||||||
\(344\) | 15.4625 | 0.833684 | ||||||||
\(345\) | −7.10284 | −0.382404 | ||||||||
\(346\) | 10.9744 | 0.589989 | ||||||||
\(347\) | 0.258469 | 0.0138754 | 0.00693768 | − | 0.999976i | \(-0.497792\pi\) | ||||
0.00693768 | + | 0.999976i | \(0.497792\pi\) | |||||||
\(348\) | 25.5319 | 1.36865 | ||||||||
\(349\) | −1.34491 | −0.0719913 | −0.0359956 | − | 0.999352i | \(-0.511460\pi\) | ||||
−0.0359956 | + | 0.999352i | \(0.511460\pi\) | |||||||
\(350\) | −0.231266 | −0.0123617 | ||||||||
\(351\) | −26.3813 | −1.40813 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.4537 | 1.88701 | 0.943506 | − | 0.331355i | \(-0.107506\pi\) | ||||
0.943506 | + | 0.331355i | \(0.107506\pi\) | |||||||
\(354\) | 2.13261 | 0.113347 | ||||||||
\(355\) | −2.76873 | −0.146949 | ||||||||
\(356\) | 27.8413 | 1.47559 | ||||||||
\(357\) | −1.92739 | −0.102008 | ||||||||
\(358\) | 0.222432 | 0.0117559 | ||||||||
\(359\) | 7.84167 | 0.413867 | 0.206934 | − | 0.978355i | \(-0.433652\pi\) | ||||
0.206934 | + | 0.978355i | \(0.433652\pi\) | |||||||
\(360\) | −0.787707 | −0.0415158 | ||||||||
\(361\) | 14.1475 | 0.744608 | ||||||||
\(362\) | 1.50446 | 0.0790727 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.07906 | 0.213801 | ||||||||
\(365\) | −5.00460 | −0.261953 | ||||||||
\(366\) | 3.10051 | 0.162066 | ||||||||
\(367\) | 1.06654 | 0.0556730 | 0.0278365 | − | 0.999612i | \(-0.491138\pi\) | ||||
0.0278365 | + | 0.999612i | \(0.491138\pi\) | |||||||
\(368\) | 11.8222 | 0.616276 | ||||||||
\(369\) | 3.67311 | 0.191215 | ||||||||
\(370\) | −2.50230 | −0.130088 | ||||||||
\(371\) | 2.93374 | 0.152312 | ||||||||
\(372\) | 22.5845 | 1.17095 | ||||||||
\(373\) | 37.6388 | 1.94886 | 0.974431 | − | 0.224689i | \(-0.0721366\pi\) | ||||
0.974431 | + | 0.224689i | \(0.0721366\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.60168 | −0.0827104 | ||||||||
\(376\) | 17.4020 | 0.897438 | ||||||||
\(377\) | −43.2201 | −2.22595 | ||||||||
\(378\) | −1.27223 | −0.0654365 | ||||||||
\(379\) | 35.1475 | 1.80541 | 0.902704 | − | 0.430262i | \(-0.141579\pi\) | ||||
0.902704 | + | 0.430262i | \(0.141579\pi\) | |||||||
\(380\) | 10.1833 | 0.522392 | ||||||||
\(381\) | 25.3537 | 1.29891 | ||||||||
\(382\) | 2.61464 | 0.133776 | ||||||||
\(383\) | 0.824549 | 0.0421325 | 0.0210662 | − | 0.999778i | \(-0.493294\pi\) | ||||
0.0210662 | + | 0.999778i | \(0.493294\pi\) | |||||||
\(384\) | −18.0075 | −0.918942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.54213 | −0.0784924 | ||||||||
\(387\) | −3.70803 | −0.188490 | ||||||||
\(388\) | 6.43462 | 0.326669 | ||||||||
\(389\) | 4.84367 | 0.245584 | 0.122792 | − | 0.992432i | \(-0.460815\pi\) | ||||
0.122792 | + | 0.992432i | \(0.460815\pi\) | |||||||
\(390\) | −3.69380 | −0.187043 | ||||||||
\(391\) | 11.0968 | 0.561187 | ||||||||
\(392\) | −12.2676 | −0.619606 | ||||||||
\(393\) | 15.3835 | 0.775994 | ||||||||
\(394\) | 9.33178 | 0.470128 | ||||||||
\(395\) | −3.62478 | −0.182382 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.33178 | −0.367971 | −0.183986 | − | 0.982929i | \(-0.558900\pi\) | ||||
−0.183986 | + | 0.982929i | \(0.558900\pi\) | |||||||
\(398\) | −9.78677 | −0.490566 | ||||||||
\(399\) | 4.43462 | 0.222009 | ||||||||
\(400\) | 2.66589 | 0.133294 | ||||||||
\(401\) | −31.1499 | −1.55555 | −0.777775 | − | 0.628542i | \(-0.783652\pi\) | ||||
−0.777775 | + | 0.628542i | \(0.783652\pi\) | |||||||
\(402\) | 5.85519 | 0.292030 | ||||||||
\(403\) | −38.2309 | −1.90442 | ||||||||
\(404\) | −13.6165 | −0.677447 | ||||||||
\(405\) | −7.50723 | −0.373037 | ||||||||
\(406\) | −2.08428 | −0.103441 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.26384 | −0.359613 | ||||||||
\(409\) | 7.23209 | 0.357604 | 0.178802 | − | 0.983885i | \(-0.442778\pi\) | ||||
0.178802 | + | 0.983885i | \(0.442778\pi\) | |||||||
\(410\) | 4.06421 | 0.200717 | ||||||||
\(411\) | −6.36202 | −0.313815 | ||||||||
\(412\) | −16.1005 | −0.793215 | ||||||||
\(413\) | 1.33149 | 0.0655182 | ||||||||
\(414\) | 0.926885 | 0.0455539 | ||||||||
\(415\) | −1.71459 | −0.0841660 | ||||||||
\(416\) | 23.5310 | 1.15370 | ||||||||
\(417\) | 14.7699 | 0.723284 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.30620 | −0.112665 | −0.0563327 | − | 0.998412i | \(-0.517941\pi\) | ||||
−0.0563327 | + | 0.998412i | \(0.517941\pi\) | |||||||
\(420\) | 1.36237 | 0.0664766 | ||||||||
\(421\) | 6.63798 | 0.323515 | 0.161758 | − | 0.986831i | \(-0.448284\pi\) | ||||
0.161758 | + | 0.986831i | \(0.448284\pi\) | |||||||
\(422\) | −3.30853 | −0.161057 | ||||||||
\(423\) | −4.17312 | −0.202904 | ||||||||
\(424\) | 11.0565 | 0.536951 | ||||||||
\(425\) | 2.50230 | 0.121379 | ||||||||
\(426\) | −2.13261 | −0.103326 | ||||||||
\(427\) | 1.93579 | 0.0936794 | ||||||||
\(428\) | −29.6993 | −1.43557 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.10284 | −0.197857 | ||||||||
\(431\) | 32.8432 | 1.58200 | 0.791000 | − | 0.611816i | \(-0.209561\pi\) | ||||
0.791000 | + | 0.611816i | \(0.209561\pi\) | |||||||
\(432\) | 14.6655 | 0.705594 | ||||||||
\(433\) | 2.36202 | 0.113511 | 0.0567557 | − | 0.998388i | \(-0.481924\pi\) | ||||
0.0567557 | + | 0.998388i | \(0.481924\pi\) | |||||||
\(434\) | −1.84367 | −0.0884991 | ||||||||
\(435\) | −14.4351 | −0.692110 | ||||||||
\(436\) | −31.6281 | −1.51471 | ||||||||
\(437\) | −25.5319 | −1.22135 | ||||||||
\(438\) | −3.85479 | −0.184189 | ||||||||
\(439\) | −30.8847 | −1.47404 | −0.737022 | − | 0.675869i | \(-0.763769\pi\) | ||||
−0.737022 | + | 0.675869i | \(0.763769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.94185 | 0.140088 | ||||||||
\(442\) | 5.77081 | 0.274489 | ||||||||
\(443\) | −13.7748 | −0.654460 | −0.327230 | − | 0.944945i | \(-0.606115\pi\) | ||||
−0.327230 | + | 0.944945i | \(0.606115\pi\) | |||||||
\(444\) | 14.7408 | 0.699569 | ||||||||
\(445\) | −15.7408 | −0.746187 | ||||||||
\(446\) | 0.499480 | 0.0236511 | ||||||||
\(447\) | 12.2530 | 0.579548 | ||||||||
\(448\) | −1.42928 | −0.0675272 | ||||||||
\(449\) | −38.9163 | −1.83657 | −0.918286 | − | 0.395917i | \(-0.870427\pi\) | ||||
−0.918286 | + | 0.395917i | \(0.870427\pi\) | |||||||
\(450\) | 0.209011 | 0.00985288 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.818095 | 0.0384800 | ||||||||
\(453\) | −4.60000 | −0.216127 | ||||||||
\(454\) | −0.231266 | −0.0108538 | ||||||||
\(455\) | −2.30620 | −0.108116 | ||||||||
\(456\) | 16.7129 | 0.782654 | ||||||||
\(457\) | 1.33149 | 0.0622843 | 0.0311422 | − | 0.999515i | \(-0.490086\pi\) | ||||
0.0311422 | + | 0.999515i | \(0.490086\pi\) | |||||||
\(458\) | −6.51130 | −0.304253 | ||||||||
\(459\) | 13.7656 | 0.642522 | ||||||||
\(460\) | −7.84367 | −0.365713 | ||||||||
\(461\) | 5.73993 | 0.267335 | 0.133668 | − | 0.991026i | \(-0.457325\pi\) | ||||
0.133668 | + | 0.991026i | \(0.457325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.44535 | −0.160119 | −0.0800595 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800595 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(464\) | 24.0263 | 1.11539 | ||||||||
\(465\) | −12.7687 | −0.592136 | ||||||||
\(466\) | 10.1731 | 0.471261 | ||||||||
\(467\) | −27.2164 | −1.25943 | −0.629713 | − | 0.776828i | \(-0.716827\pi\) | ||||
−0.629713 | + | 0.776828i | \(0.716827\pi\) | |||||||
\(468\) | −3.68653 | −0.170410 | ||||||||
\(469\) | 3.65565 | 0.168802 | ||||||||
\(470\) | −4.61746 | −0.212987 | ||||||||
\(471\) | −28.0000 | −1.29017 | ||||||||
\(472\) | 5.01802 | 0.230973 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.79198 | −0.128240 | ||||||||
\(475\) | −5.75739 | −0.264167 | ||||||||
\(476\) | −2.12842 | −0.0975560 | ||||||||
\(477\) | −2.65143 | −0.121401 | ||||||||
\(478\) | −1.28708 | −0.0588697 | ||||||||
\(479\) | 13.9822 | 0.638861 | 0.319431 | − | 0.947610i | \(-0.396508\pi\) | ||||
0.319431 | + | 0.947610i | \(0.396508\pi\) | |||||||
\(480\) | 7.85913 | 0.358718 | ||||||||
\(481\) | −24.9532 | −1.13777 | ||||||||
\(482\) | 2.19729 | 0.100084 | ||||||||
\(483\) | −3.41576 | −0.155423 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.63798 | −0.165192 | ||||||||
\(486\) | 2.15411 | 0.0977124 | ||||||||
\(487\) | −7.45375 | −0.337761 | −0.168881 | − | 0.985636i | \(-0.554015\pi\) | ||||
−0.168881 | + | 0.985636i | \(0.554015\pi\) | |||||||
\(488\) | 7.29548 | 0.330251 | ||||||||
\(489\) | −21.0894 | −0.953696 | ||||||||
\(490\) | 3.25509 | 0.147050 | ||||||||
\(491\) | −15.9756 | −0.720969 | −0.360484 | − | 0.932765i | \(-0.617389\pi\) | ||||
−0.360484 | + | 0.932765i | \(0.617389\pi\) | |||||||
\(492\) | −23.9419 | −1.07938 | ||||||||
\(493\) | 22.5519 | 1.01569 | ||||||||
\(494\) | −13.2777 | −0.597392 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.2527 | 0.954275 | ||||||||
\(497\) | −1.33149 | −0.0597253 | ||||||||
\(498\) | −1.32066 | −0.0591803 | ||||||||
\(499\) | −24.3509 | −1.09010 | −0.545048 | − | 0.838405i | \(-0.683489\pi\) | ||||
−0.545048 | + | 0.838405i | \(0.683489\pi\) | |||||||
\(500\) | −1.76873 | −0.0791002 | ||||||||
\(501\) | −25.4311 | −1.13618 | ||||||||
\(502\) | 5.50004 | 0.245479 | ||||||||
\(503\) | 27.5667 | 1.22914 | 0.614569 | − | 0.788863i | \(-0.289330\pi\) | ||||
0.614569 | + | 0.788863i | \(0.289330\pi\) | |||||||
\(504\) | −0.378809 | −0.0168735 | ||||||||
\(505\) | 7.69845 | 0.342577 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.0131 | −0.711165 | ||||||||
\(508\) | 27.9981 | 1.24222 | ||||||||
\(509\) | 17.6850 | 0.783874 | 0.391937 | − | 0.919992i | \(-0.371805\pi\) | ||||
0.391937 | + | 0.919992i | \(0.371805\pi\) | |||||||
\(510\) | 1.92739 | 0.0853464 | ||||||||
\(511\) | −2.40672 | −0.106467 | ||||||||
\(512\) | −22.7443 | −1.00516 | ||||||||
\(513\) | −31.6724 | −1.39837 | ||||||||
\(514\) | 9.63951 | 0.425181 | ||||||||
\(515\) | 9.10284 | 0.401119 | ||||||||
\(516\) | 24.1695 | 1.06400 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.20336 | −0.0528725 | ||||||||
\(519\) | 36.5512 | 1.60442 | ||||||||
\(520\) | −8.69147 | −0.381146 | ||||||||
\(521\) | −5.38993 | −0.236137 | −0.118068 | − | 0.993005i | \(-0.537670\pi\) | ||||
−0.118068 | + | 0.993005i | \(0.537670\pi\) | |||||||
\(522\) | 1.88371 | 0.0824477 | ||||||||
\(523\) | −37.6737 | −1.64735 | −0.823677 | − | 0.567059i | \(-0.808081\pi\) | ||||
−0.823677 | + | 0.567059i | \(0.808081\pi\) | |||||||
\(524\) | 16.9880 | 0.742123 | ||||||||
\(525\) | −0.770249 | −0.0336164 | ||||||||
\(526\) | 3.15400 | 0.137521 | ||||||||
\(527\) | 19.9486 | 0.868973 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.33411 | −0.144961 | ||||||||
\(530\) | −2.93374 | −0.127434 | ||||||||
\(531\) | −1.20336 | −0.0522213 | ||||||||
\(532\) | 4.89716 | 0.212319 | ||||||||
\(533\) | 40.5287 | 1.75549 | ||||||||
\(534\) | −12.1244 | −0.524672 | ||||||||
\(535\) | 16.7913 | 0.725950 | ||||||||
\(536\) | 13.7772 | 0.595084 | ||||||||
\(537\) | 0.740827 | 0.0319690 | ||||||||
\(538\) | −0.912344 | −0.0393339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.73010 | −0.418717 | ||||||||
\(541\) | −28.9651 | −1.24531 | −0.622653 | − | 0.782498i | \(-0.713945\pi\) | ||||
−0.622653 | + | 0.782498i | \(0.713945\pi\) | |||||||
\(542\) | −5.46020 | −0.234536 | ||||||||
\(543\) | 5.01073 | 0.215031 | ||||||||
\(544\) | −12.2783 | −0.526428 | ||||||||
\(545\) | 17.8817 | 0.765970 | ||||||||
\(546\) | −1.77635 | −0.0760208 | ||||||||
\(547\) | 19.7396 | 0.844002 | 0.422001 | − | 0.906595i | \(-0.361328\pi\) | ||||
0.422001 | + | 0.906595i | \(0.361328\pi\) | |||||||
\(548\) | −7.02558 | −0.300118 | ||||||||
\(549\) | −1.74951 | −0.0746672 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.8884 | −2.21052 | ||||||||
\(552\) | −12.8731 | −0.547916 | ||||||||
\(553\) | −1.74316 | −0.0741266 | ||||||||
\(554\) | 10.9809 | 0.466533 | ||||||||
\(555\) | −8.33411 | −0.353763 | ||||||||
\(556\) | 16.3104 | 0.691714 | ||||||||
\(557\) | −16.6801 | −0.706757 | −0.353378 | − | 0.935481i | \(-0.614967\pi\) | ||||
−0.353378 | + | 0.935481i | \(0.614967\pi\) | |||||||
\(558\) | 1.66626 | 0.0705382 | ||||||||
\(559\) | −40.9139 | −1.73048 | ||||||||
\(560\) | 1.28203 | 0.0541756 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.8739 | −0.458688 | ||||||||
\(563\) | 4.90680 | 0.206797 | 0.103399 | − | 0.994640i | \(-0.467028\pi\) | ||||
0.103399 | + | 0.994640i | \(0.467028\pi\) | |||||||
\(564\) | 27.2010 | 1.14537 | ||||||||
\(565\) | −0.462531 | −0.0194588 | ||||||||
\(566\) | −13.2568 | −0.557227 | ||||||||
\(567\) | −3.61023 | −0.151616 | ||||||||
\(568\) | −5.01802 | −0.210551 | ||||||||
\(569\) | 22.4334 | 0.940457 | 0.470229 | − | 0.882545i | \(-0.344171\pi\) | ||||
0.470229 | + | 0.882545i | \(0.344171\pi\) | |||||||
\(570\) | −4.43462 | −0.185746 | ||||||||
\(571\) | −0.195590 | −0.00818520 | −0.00409260 | − | 0.999992i | \(-0.501303\pi\) | ||||
−0.00409260 | + | 0.999992i | \(0.501303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.70826 | 0.363793 | ||||||||
\(574\) | 1.95448 | 0.0815785 | ||||||||
\(575\) | 4.43462 | 0.184937 | ||||||||
\(576\) | 1.29174 | 0.0538226 | ||||||||
\(577\) | −41.2481 | −1.71718 | −0.858590 | − | 0.512664i | \(-0.828659\pi\) | ||||
−0.858590 | + | 0.512664i | \(0.828659\pi\) | |||||||
\(578\) | 5.16415 | 0.214800 | ||||||||
\(579\) | −5.13619 | −0.213453 | ||||||||
\(580\) | −15.9407 | −0.661901 | ||||||||
\(581\) | −0.824549 | −0.0342081 | ||||||||
\(582\) | −2.80215 | −0.116153 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.07028 | −0.375331 | ||||||||
\(585\) | 2.08428 | 0.0861743 | ||||||||
\(586\) | −10.5119 | −0.434242 | ||||||||
\(587\) | −1.77480 | −0.0732538 | −0.0366269 | − | 0.999329i | \(-0.511661\pi\) | ||||
−0.0366269 | + | 0.999329i | \(0.511661\pi\) | |||||||
\(588\) | −19.1755 | −0.790782 | ||||||||
\(589\) | −45.8984 | −1.89121 | ||||||||
\(590\) | −1.33149 | −0.0548164 | ||||||||
\(591\) | 31.0802 | 1.27847 | ||||||||
\(592\) | 13.8716 | 0.570118 | ||||||||
\(593\) | 29.0094 | 1.19127 | 0.595636 | − | 0.803254i | \(-0.296900\pi\) | ||||
0.595636 | + | 0.803254i | \(0.296900\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.20336 | 0.0493329 | ||||||||
\(596\) | 13.5310 | 0.554252 | ||||||||
\(597\) | −32.5956 | −1.33405 | ||||||||
\(598\) | 10.2271 | 0.418219 | ||||||||
\(599\) | 40.2672 | 1.64527 | 0.822636 | − | 0.568568i | \(-0.192502\pi\) | ||||
0.822636 | + | 0.568568i | \(0.192502\pi\) | |||||||
\(600\) | −2.90286 | −0.118509 | ||||||||
\(601\) | 13.6957 | 0.558661 | 0.279330 | − | 0.960195i | \(-0.409888\pi\) | ||||
0.279330 | + | 0.960195i | \(0.409888\pi\) | |||||||
\(602\) | −1.97306 | −0.0804160 | ||||||||
\(603\) | −3.30387 | −0.134544 | ||||||||
\(604\) | −5.07978 | −0.206693 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.92972 | 0.240879 | ||||||||
\(607\) | −21.1543 | −0.858626 | −0.429313 | − | 0.903156i | \(-0.641244\pi\) | ||||
−0.429313 | + | 0.903156i | \(0.641244\pi\) | |||||||
\(608\) | 28.2504 | 1.14570 | ||||||||
\(609\) | −6.94185 | −0.281298 | ||||||||
\(610\) | −1.93579 | −0.0783778 | ||||||||
\(611\) | −46.0457 | −1.86281 | ||||||||
\(612\) | 1.92360 | 0.0777571 | ||||||||
\(613\) | 23.2520 | 0.939139 | 0.469570 | − | 0.882895i | \(-0.344409\pi\) | ||||
0.469570 | + | 0.882895i | \(0.344409\pi\) | |||||||
\(614\) | −4.71292 | −0.190198 | ||||||||
\(615\) | 13.5362 | 0.545831 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1028 | −0.527501 | −0.263750 | − | 0.964591i | \(-0.584960\pi\) | ||||
−0.263750 | + | 0.964591i | \(0.584960\pi\) | |||||||
\(618\) | 7.01146 | 0.282042 | ||||||||
\(619\) | 16.6682 | 0.669952 | 0.334976 | − | 0.942227i | \(-0.391272\pi\) | ||||
0.334976 | + | 0.942227i | \(0.391272\pi\) | |||||||
\(620\) | −14.1005 | −0.566290 | ||||||||
\(621\) | 24.3956 | 0.978962 | ||||||||
\(622\) | −4.69891 | −0.188409 | ||||||||
\(623\) | −7.56978 | −0.303277 | ||||||||
\(624\) | 20.4767 | 0.819723 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.431443 | 0.0172439 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.9204 | −1.23386 | ||||||||
\(629\) | 13.0204 | 0.519156 | ||||||||
\(630\) | 0.100514 | 0.00400456 | ||||||||
\(631\) | −2.66356 | −0.106035 | −0.0530173 | − | 0.998594i | \(-0.516884\pi\) | ||||
−0.0530173 | + | 0.998594i | \(0.516884\pi\) | |||||||
\(632\) | −6.56950 | −0.261321 | ||||||||
\(633\) | −11.0193 | −0.437979 | ||||||||
\(634\) | 1.28315 | 0.0509604 | ||||||||
\(635\) | −15.8295 | −0.628173 | ||||||||
\(636\) | 17.2824 | 0.685292 | ||||||||
\(637\) | 32.4601 | 1.28611 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.20336 | 0.0476041 | ||||||||
\(640\) | 11.2429 | 0.444414 | ||||||||
\(641\) | −0.462531 | −0.0182689 | −0.00913445 | − | 0.999958i | \(-0.502908\pi\) | ||||
−0.00913445 | + | 0.999958i | \(0.502908\pi\) | |||||||
\(642\) | 12.9335 | 0.510443 | ||||||||
\(643\) | −33.4621 | −1.31962 | −0.659809 | − | 0.751433i | \(-0.729363\pi\) | ||||
−0.659809 | + | 0.751433i | \(0.729363\pi\) | |||||||
\(644\) | −3.77203 | −0.148639 | ||||||||
\(645\) | −13.6649 | −0.538053 | ||||||||
\(646\) | 6.92820 | 0.272587 | ||||||||
\(647\) | −40.2588 | −1.58274 | −0.791368 | − | 0.611340i | \(-0.790631\pi\) | ||||
−0.791368 | + | 0.611340i | \(0.790631\pi\) | |||||||
\(648\) | −13.6060 | −0.534495 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.30620 | 0.0904567 | ||||||||
\(651\) | −6.14050 | −0.240665 | ||||||||
\(652\) | −23.2890 | −0.912068 | ||||||||
\(653\) | 15.3486 | 0.600636 | 0.300318 | − | 0.953839i | \(-0.402907\pi\) | ||||
0.300318 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(654\) | 13.7734 | 0.538582 | ||||||||
\(655\) | −9.60460 | −0.375283 | ||||||||
\(656\) | −22.5301 | −0.879652 | ||||||||
\(657\) | 2.17512 | 0.0848595 | ||||||||
\(658\) | −2.22054 | −0.0865656 | ||||||||
\(659\) | −36.6635 | −1.42821 | −0.714104 | − | 0.700039i | \(-0.753166\pi\) | ||||
−0.714104 | + | 0.700039i | \(0.753166\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.03024 | −0.312340 | −0.156170 | − | 0.987730i | \(-0.549915\pi\) | ||||
−0.156170 | + | 0.987730i | \(0.549915\pi\) | |||||||
\(662\) | −9.12482 | −0.354646 | ||||||||
\(663\) | 19.2201 | 0.746449 | ||||||||
\(664\) | −3.10751 | −0.120595 | ||||||||
\(665\) | −2.76873 | −0.107367 | ||||||||
\(666\) | 1.08756 | 0.0421421 | ||||||||
\(667\) | 39.9670 | 1.54753 | ||||||||
\(668\) | −28.0836 | −1.08659 | ||||||||
\(669\) | 1.66356 | 0.0643169 | ||||||||
\(670\) | −3.65565 | −0.141230 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.77946 | 0.145796 | ||||||||
\(673\) | 11.7587 | 0.453265 | 0.226632 | − | 0.973980i | \(-0.427228\pi\) | ||||
0.226632 | + | 0.973980i | \(0.427228\pi\) | |||||||
\(674\) | −2.30620 | −0.0888316 | ||||||||
\(675\) | 5.50117 | 0.211740 | ||||||||
\(676\) | −17.6832 | −0.680124 | ||||||||
\(677\) | 27.2948 | 1.04902 | 0.524512 | − | 0.851403i | \(-0.324248\pi\) | ||||
0.524512 | + | 0.851403i | \(0.324248\pi\) | |||||||
\(678\) | −0.356264 | −0.0136822 | ||||||||
\(679\) | −1.74951 | −0.0671400 | ||||||||
\(680\) | 4.53514 | 0.173915 | ||||||||
\(681\) | −0.770249 | −0.0295160 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.5738 | 1.89689 | 0.948444 | − | 0.316945i | \(-0.102657\pi\) | ||||
0.948444 | + | 0.316945i | \(0.102657\pi\) | |||||||
\(684\) | −4.42590 | −0.169229 | ||||||||
\(685\) | 3.97209 | 0.151766 | ||||||||
\(686\) | 3.18424 | 0.121575 | ||||||||
\(687\) | −21.6864 | −0.827388 | ||||||||
\(688\) | 22.7443 | 0.867116 | ||||||||
\(689\) | −29.2556 | −1.11455 | ||||||||
\(690\) | 3.41576 | 0.130036 | ||||||||
\(691\) | −25.3253 | −0.963421 | −0.481710 | − | 0.876330i | \(-0.659984\pi\) | ||||
−0.481710 | + | 0.876330i | \(0.659984\pi\) | |||||||
\(692\) | 40.3635 | 1.53439 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.124298 | −0.00471829 | ||||||||
\(695\) | −9.22149 | −0.349791 | ||||||||
\(696\) | −26.1620 | −0.991668 | ||||||||
\(697\) | −21.1475 | −0.801020 | ||||||||
\(698\) | 0.646767 | 0.0244805 | ||||||||
\(699\) | 33.8824 | 1.28155 | ||||||||
\(700\) | −0.850586 | −0.0321491 | ||||||||
\(701\) | 18.2555 | 0.689500 | 0.344750 | − | 0.938695i | \(-0.387964\pi\) | ||||
0.344750 | + | 0.938695i | \(0.387964\pi\) | |||||||
\(702\) | 12.6868 | 0.478833 | ||||||||
\(703\) | −29.9578 | −1.12988 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.3788 | −0.579199 | ||||||||
\(706\) | −17.0497 | −0.641675 | ||||||||
\(707\) | 3.70219 | 0.139235 | ||||||||
\(708\) | 7.84367 | 0.294783 | ||||||||
\(709\) | 4.33178 | 0.162683 | 0.0813417 | − | 0.996686i | \(-0.474079\pi\) | ||||
0.0813417 | + | 0.996686i | \(0.474079\pi\) | |||||||
\(710\) | 1.33149 | 0.0499698 | ||||||||
\(711\) | 1.57541 | 0.0590827 | ||||||||
\(712\) | −28.5285 | −1.06915 | ||||||||
\(713\) | 35.3532 | 1.32399 | ||||||||
\(714\) | 0.926885 | 0.0346878 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.818095 | 0.0305737 | ||||||||
\(717\) | −4.28673 | −0.160091 | ||||||||
\(718\) | −3.77107 | −0.140735 | ||||||||
\(719\) | −24.1005 | −0.898797 | −0.449399 | − | 0.893331i | \(-0.648362\pi\) | ||||
−0.449399 | + | 0.893331i | \(0.648362\pi\) | |||||||
\(720\) | −1.15866 | −0.0431807 | ||||||||
\(721\) | 4.37757 | 0.163029 | ||||||||
\(722\) | −6.80357 | −0.253203 | ||||||||
\(723\) | 7.31826 | 0.272169 | ||||||||
\(724\) | 5.53335 | 0.205645 | ||||||||
\(725\) | 9.01248 | 0.334715 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.1066 | −0.931151 | −0.465576 | − | 0.885008i | \(-0.654153\pi\) | ||||
−0.465576 | + | 0.885008i | \(0.654153\pi\) | |||||||
\(728\) | −4.17973 | −0.154911 | ||||||||
\(729\) | 29.6961 | 1.09986 | ||||||||
\(730\) | 2.40672 | 0.0890766 | ||||||||
\(731\) | 21.3486 | 0.789605 | ||||||||
\(732\) | 11.4036 | 0.421488 | ||||||||
\(733\) | 17.4463 | 0.644393 | 0.322196 | − | 0.946673i | \(-0.395579\pi\) | ||||
0.322196 | + | 0.946673i | \(0.395579\pi\) | |||||||
\(734\) | −0.512901 | −0.0189315 | ||||||||
\(735\) | 10.8413 | 0.399889 | ||||||||
\(736\) | −21.7598 | −0.802078 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.76640 | −0.0650222 | ||||||||
\(739\) | 5.20019 | 0.191292 | 0.0956460 | − | 0.995415i | \(-0.469508\pi\) | ||||
0.0956460 | + | 0.995415i | \(0.469508\pi\) | |||||||
\(740\) | −9.20336 | −0.338322 | ||||||||
\(741\) | −44.2225 | −1.62455 | ||||||||
\(742\) | −1.41084 | −0.0517935 | ||||||||
\(743\) | 37.1928 | 1.36447 | 0.682235 | − | 0.731133i | \(-0.261008\pi\) | ||||
0.682235 | + | 0.731133i | \(0.261008\pi\) | |||||||
\(744\) | −23.1419 | −0.848423 | ||||||||
\(745\) | −7.65012 | −0.280279 | ||||||||
\(746\) | −18.1005 | −0.662707 | ||||||||
\(747\) | 0.745203 | 0.0272656 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.07494 | 0.295052 | ||||||||
\(750\) | 0.770249 | 0.0281255 | ||||||||
\(751\) | 41.4212 | 1.51148 | 0.755740 | − | 0.654872i | \(-0.227277\pi\) | ||||
0.755740 | + | 0.654872i | \(0.227277\pi\) | |||||||
\(752\) | 25.5970 | 0.933427 | ||||||||
\(753\) | 18.3183 | 0.667557 | ||||||||
\(754\) | 20.7846 | 0.756931 | ||||||||
\(755\) | 2.87198 | 0.104522 | ||||||||
\(756\) | −4.67921 | −0.170181 | ||||||||
\(757\) | 3.91628 | 0.142340 | 0.0711698 | − | 0.997464i | \(-0.477327\pi\) | ||||
0.0711698 | + | 0.997464i | \(0.477327\pi\) | |||||||
\(758\) | −16.9025 | −0.613926 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.4346 | −0.378504 | ||||||||
\(761\) | 39.1309 | 1.41849 | 0.709247 | − | 0.704960i | \(-0.249035\pi\) | ||||
0.709247 | + | 0.704960i | \(0.249035\pi\) | |||||||
\(762\) | −12.1926 | −0.441692 | ||||||||
\(763\) | 8.59935 | 0.311317 | ||||||||
\(764\) | 9.61653 | 0.347914 | ||||||||
\(765\) | −1.08756 | −0.0393208 | ||||||||
\(766\) | −0.396526 | −0.0143271 | ||||||||
\(767\) | −13.2777 | −0.479430 | ||||||||
\(768\) | −0.860852 | −0.0310633 | ||||||||
\(769\) | −11.6755 | −0.421028 | −0.210514 | − | 0.977591i | \(-0.567514\pi\) | ||||
−0.210514 | + | 0.977591i | \(0.567514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.1052 | 1.15624 | ||||||||
\(772\) | −5.67189 | −0.204136 | ||||||||
\(773\) | −7.76640 | −0.279338 | −0.139669 | − | 0.990198i | \(-0.544604\pi\) | ||||
−0.139669 | + | 0.990198i | \(0.544604\pi\) | |||||||
\(774\) | 1.78319 | 0.0640956 | ||||||||
\(775\) | 7.97209 | 0.286366 | ||||||||
\(776\) | −6.59343 | −0.236691 | ||||||||
\(777\) | −4.00788 | −0.143782 | ||||||||
\(778\) | −2.32933 | −0.0835104 | ||||||||
\(779\) | 48.6571 | 1.74332 | ||||||||
\(780\) | −13.5856 | −0.486444 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.33644 | −0.190831 | ||||||||
\(783\) | 49.5791 | 1.77181 | ||||||||
\(784\) | −18.0447 | −0.644454 | ||||||||
\(785\) | 17.4817 | 0.623947 | ||||||||
\(786\) | −7.39793 | −0.263875 | ||||||||
\(787\) | 1.42928 | 0.0509484 | 0.0254742 | − | 0.999675i | \(-0.491890\pi\) | ||||
0.0254742 | + | 0.999675i | \(0.491890\pi\) | |||||||
\(788\) | 34.3219 | 1.22267 | ||||||||
\(789\) | 10.5046 | 0.373975 | ||||||||
\(790\) | 1.74316 | 0.0620188 | ||||||||
\(791\) | −0.222432 | −0.00790876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.3039 | −0.685501 | ||||||||
\(794\) | 3.52586 | 0.125128 | ||||||||
\(795\) | −9.77107 | −0.346544 | ||||||||
\(796\) | −35.9953 | −1.27582 | ||||||||
\(797\) | −36.3788 | −1.28860 | −0.644302 | − | 0.764771i | \(-0.722852\pi\) | ||||
−0.644302 | + | 0.764771i | \(0.722852\pi\) | |||||||
\(798\) | −2.13261 | −0.0754937 | ||||||||
\(799\) | 24.0263 | 0.849989 | ||||||||
\(800\) | −4.90680 | −0.173482 | ||||||||
\(801\) | 6.84134 | 0.241727 | ||||||||
\(802\) | 14.9800 | 0.528962 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.5351 | 0.759486 | ||||||||
\(805\) | 2.13261 | 0.0751648 | ||||||||
\(806\) | 18.3853 | 0.647593 | ||||||||
\(807\) | −3.03863 | −0.106965 | ||||||||
\(808\) | 13.9526 | 0.490850 | ||||||||
\(809\) | −27.8735 | −0.979980 | −0.489990 | − | 0.871728i | \(-0.663000\pi\) | ||||
−0.489990 | + | 0.871728i | \(0.663000\pi\) | |||||||
\(810\) | 3.61023 | 0.126851 | ||||||||
\(811\) | −39.1793 | −1.37577 | −0.687885 | − | 0.725820i | \(-0.741461\pi\) | ||||
−0.687885 | + | 0.725820i | \(0.741461\pi\) | |||||||
\(812\) | −7.66589 | −0.269020 | ||||||||
\(813\) | −18.1856 | −0.637798 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.1671 | 0.461222 | ||||||||
\(816\) | −10.6846 | −0.374035 | ||||||||
\(817\) | −49.1196 | −1.71848 | ||||||||
\(818\) | −3.47792 | −0.121603 | ||||||||
\(819\) | 1.00233 | 0.0350243 | ||||||||
\(820\) | 14.9480 | 0.522007 | ||||||||
\(821\) | 13.7772 | 0.480827 | 0.240414 | − | 0.970671i | \(-0.422717\pi\) | ||||
0.240414 | + | 0.970671i | \(0.422717\pi\) | |||||||
\(822\) | 3.05950 | 0.106712 | ||||||||
\(823\) | −19.8800 | −0.692972 | −0.346486 | − | 0.938055i | \(-0.612625\pi\) | ||||
−0.346486 | + | 0.938055i | \(0.612625\pi\) | |||||||
\(824\) | 16.4979 | 0.574731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.640313 | −0.0222793 | ||||||||
\(827\) | −13.3272 | −0.463431 | −0.231716 | − | 0.972784i | \(-0.574434\pi\) | ||||
−0.231716 | + | 0.972784i | \(0.574434\pi\) | |||||||
\(828\) | 3.40905 | 0.118473 | ||||||||
\(829\) | 51.1899 | 1.77790 | 0.888950 | − | 0.458005i | \(-0.151436\pi\) | ||||
0.888950 | + | 0.458005i | \(0.151436\pi\) | |||||||
\(830\) | 0.824549 | 0.0286205 | ||||||||
\(831\) | 36.5727 | 1.26869 | ||||||||
\(832\) | 14.2529 | 0.494132 | ||||||||
\(833\) | −16.9374 | −0.586846 | ||||||||
\(834\) | −7.10284 | −0.245951 | ||||||||
\(835\) | 15.8778 | 0.549474 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 43.8558 | 1.51588 | ||||||||
\(838\) | 1.10906 | 0.0383117 | ||||||||
\(839\) | −16.8739 | −0.582552 | −0.291276 | − | 0.956639i | \(-0.594080\pi\) | ||||
−0.291276 | + | 0.956639i | \(0.594080\pi\) | |||||||
\(840\) | −1.39599 | −0.0481662 | ||||||||
\(841\) | 52.2248 | 1.80086 | ||||||||
\(842\) | −3.19221 | −0.110011 | ||||||||
\(843\) | −36.2164 | −1.24736 | ||||||||
\(844\) | −12.1687 | −0.418862 | ||||||||
\(845\) | 9.99767 | 0.343930 | ||||||||
\(846\) | 2.00686 | 0.0689972 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.2633 | 0.558484 | ||||||||
\(849\) | −44.1530 | −1.51533 | ||||||||
\(850\) | −1.20336 | −0.0412748 | ||||||||
\(851\) | 23.0749 | 0.790999 | ||||||||
\(852\) | −7.84367 | −0.268720 | ||||||||
\(853\) | −5.42262 | −0.185667 | −0.0928335 | − | 0.995682i | \(-0.529592\pi\) | ||||
−0.0928335 | + | 0.995682i | \(0.529592\pi\) | |||||||
\(854\) | −0.930923 | −0.0318555 | ||||||||
\(855\) | 2.50230 | 0.0855768 | ||||||||
\(856\) | 30.4323 | 1.04015 | ||||||||
\(857\) | −27.8386 | −0.950947 | −0.475474 | − | 0.879730i | \(-0.657723\pi\) | ||||
−0.475474 | + | 0.879730i | \(0.657723\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.1899 | 1.64422 | 0.822109 | − | 0.569330i | \(-0.192797\pi\) | ||||
0.822109 | + | 0.569330i | \(0.192797\pi\) | |||||||
\(860\) | −15.0901 | −0.514568 | ||||||||
\(861\) | 6.50956 | 0.221845 | ||||||||
\(862\) | −15.7943 | −0.537956 | ||||||||
\(863\) | 26.8609 | 0.914354 | 0.457177 | − | 0.889376i | \(-0.348861\pi\) | ||||
0.457177 | + | 0.889376i | \(0.348861\pi\) | |||||||
\(864\) | −26.9931 | −0.918325 | ||||||||
\(865\) | −22.8206 | −0.775922 | ||||||||
\(866\) | −1.13590 | −0.0385993 | ||||||||
\(867\) | 17.1996 | 0.584130 | ||||||||
\(868\) | −6.78095 | −0.230160 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 6.94185 | 0.235351 | ||||||||
\(871\) | −36.4545 | −1.23521 | ||||||||
\(872\) | 32.4087 | 1.09750 | ||||||||
\(873\) | 1.58115 | 0.0535140 | ||||||||
\(874\) | 12.2783 | 0.415320 | ||||||||
\(875\) | 0.480901 | 0.0162574 | ||||||||
\(876\) | −14.1778 | −0.479022 | ||||||||
\(877\) | −39.8837 | −1.34678 | −0.673389 | − | 0.739289i | \(-0.735162\pi\) | ||||
−0.673389 | + | 0.739289i | \(0.735162\pi\) | |||||||
\(878\) | 14.8525 | 0.501246 | ||||||||
\(879\) | −35.0107 | −1.18088 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.82222 | −0.0950829 | −0.0475415 | − | 0.998869i | \(-0.515139\pi\) | ||||
−0.0475415 | + | 0.998869i | \(0.515139\pi\) | |||||||
\(882\) | −1.41474 | −0.0476368 | ||||||||
\(883\) | 50.5287 | 1.70043 | 0.850213 | − | 0.526439i | \(-0.176473\pi\) | ||||
0.850213 | + | 0.526439i | \(0.176473\pi\) | |||||||
\(884\) | 21.2248 | 0.713868 | ||||||||
\(885\) | −4.43462 | −0.149068 | ||||||||
\(886\) | 6.62431 | 0.222548 | ||||||||
\(887\) | 28.3195 | 0.950875 | 0.475437 | − | 0.879750i | \(-0.342290\pi\) | ||||
0.475437 | + | 0.879750i | \(0.342290\pi\) | |||||||
\(888\) | −15.1046 | −0.506879 | ||||||||
\(889\) | −7.61241 | −0.255312 | ||||||||
\(890\) | 7.56978 | 0.253740 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.83707 | 0.0615096 | ||||||||
\(893\) | −55.2806 | −1.84990 | ||||||||
\(894\) | −5.89249 | −0.197074 | ||||||||
\(895\) | −0.462531 | −0.0154607 | ||||||||
\(896\) | 5.40672 | 0.180626 | ||||||||
\(897\) | 34.0623 | 1.13731 | ||||||||
\(898\) | 18.7149 | 0.624523 | ||||||||
\(899\) | 71.8483 | 2.39628 | ||||||||
\(900\) | 0.768734 | 0.0256245 | ||||||||
\(901\) | 15.2653 | 0.508561 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.57144 | −0.218684 | ||||||||
\(904\) | −0.838286 | −0.0278810 | ||||||||
\(905\) | −3.12842 | −0.103992 | ||||||||
\(906\) | 2.21214 | 0.0734935 | ||||||||
\(907\) | 51.0508 | 1.69511 | 0.847556 | − | 0.530705i | \(-0.178073\pi\) | ||||
0.847556 | + | 0.530705i | \(0.178073\pi\) | |||||||
\(908\) | −0.850586 | −0.0282277 | ||||||||
\(909\) | −3.34593 | −0.110978 | ||||||||
\(910\) | 1.10906 | 0.0367648 | ||||||||
\(911\) | −25.1429 | −0.833021 | −0.416510 | − | 0.909131i | \(-0.636747\pi\) | ||||
−0.416510 | + | 0.909131i | \(0.636747\pi\) | |||||||
\(912\) | 24.5835 | 0.814040 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.640313 | −0.0211797 | ||||||||
\(915\) | −6.44730 | −0.213141 | ||||||||
\(916\) | −23.9483 | −0.791274 | ||||||||
\(917\) | −4.61886 | −0.152528 | ||||||||
\(918\) | −6.61987 | −0.218488 | ||||||||
\(919\) | 25.6151 | 0.844965 | 0.422482 | − | 0.906371i | \(-0.361159\pi\) | ||||
0.422482 | + | 0.906371i | \(0.361159\pi\) | |||||||
\(920\) | 8.03726 | 0.264981 | ||||||||
\(921\) | −15.6968 | −0.517226 | ||||||||
\(922\) | −2.76034 | −0.0909069 | ||||||||
\(923\) | 13.2777 | 0.437041 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.20336 | 0.171085 | ||||||||
\(926\) | 1.65687 | 0.0544482 | ||||||||
\(927\) | −3.95631 | −0.129942 | ||||||||
\(928\) | −44.2225 | −1.45167 | ||||||||
\(929\) | −8.60774 | −0.282411 | −0.141205 | − | 0.989980i | \(-0.545098\pi\) | ||||
−0.141205 | + | 0.989980i | \(0.545098\pi\) | |||||||
\(930\) | 6.14050 | 0.201355 | ||||||||
\(931\) | 38.9702 | 1.27720 | ||||||||
\(932\) | 37.4163 | 1.22561 | ||||||||
\(933\) | −15.6501 | −0.512362 | ||||||||
\(934\) | 13.0884 | 0.428266 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.77752 | 0.123472 | ||||||||
\(937\) | −5.96640 | −0.194914 | −0.0974569 | − | 0.995240i | \(-0.531071\pi\) | ||||
−0.0974569 | + | 0.995240i | \(0.531071\pi\) | |||||||
\(938\) | −1.75801 | −0.0574010 | ||||||||
\(939\) | 1.43695 | 0.0468933 | ||||||||
\(940\) | −16.9828 | −0.553918 | ||||||||
\(941\) | −22.8380 | −0.744498 | −0.372249 | − | 0.928133i | \(-0.621413\pi\) | ||||
−0.372249 | + | 0.928133i | \(0.621413\pi\) | |||||||
\(942\) | 13.4652 | 0.438721 | ||||||||
\(943\) | −37.4781 | −1.22045 | ||||||||
\(944\) | 7.38114 | 0.240236 | ||||||||
\(945\) | 2.64552 | 0.0860586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.30620 | −0.0749415 | −0.0374708 | − | 0.999298i | \(-0.511930\pi\) | ||||
−0.0374708 | + | 0.999298i | \(0.511930\pi\) | |||||||
\(948\) | −10.2688 | −0.333515 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 2.76873 | 0.0898296 | ||||||||
\(951\) | 4.27363 | 0.138582 | ||||||||
\(952\) | 2.18095 | 0.0706851 | ||||||||
\(953\) | 28.6129 | 0.926861 | 0.463431 | − | 0.886133i | \(-0.346618\pi\) | ||||
0.463431 | + | 0.886133i | \(0.346618\pi\) | |||||||
\(954\) | 1.27507 | 0.0412821 | ||||||||
\(955\) | −5.43695 | −0.175936 | ||||||||
\(956\) | −4.73383 | −0.153103 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.72404 | −0.217244 | ||||||||
\(959\) | 1.91018 | 0.0616830 | ||||||||
\(960\) | 4.76034 | 0.153639 | ||||||||
\(961\) | 32.5543 | 1.05014 | ||||||||
\(962\) | 12.0000 | 0.386896 | ||||||||
\(963\) | −7.29789 | −0.235171 | ||||||||
\(964\) | 8.08156 | 0.260289 | ||||||||
\(965\) | 3.20675 | 0.103229 | ||||||||
\(966\) | 1.64264 | 0.0528512 | ||||||||
\(967\) | −31.7422 | −1.02076 | −0.510380 | − | 0.859949i | \(-0.670495\pi\) | ||||
−0.510380 | + | 0.859949i | \(0.670495\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.0749 | 0.741274 | ||||||||
\(970\) | 1.74951 | 0.0561733 | ||||||||
\(971\) | −37.0023 | −1.18746 | −0.593731 | − | 0.804664i | \(-0.702346\pi\) | ||||
−0.593731 | + | 0.804664i | \(0.702346\pi\) | |||||||
\(972\) | 7.92273 | 0.254122 | ||||||||
\(973\) | −4.43462 | −0.142168 | ||||||||
\(974\) | 3.58451 | 0.114855 | ||||||||
\(975\) | 7.68099 | 0.245989 | ||||||||
\(976\) | 10.7311 | 0.343494 | ||||||||
\(977\) | 33.8716 | 1.08365 | 0.541824 | − | 0.840492i | \(-0.317734\pi\) | ||||
0.541824 | + | 0.840492i | \(0.317734\pi\) | |||||||
\(978\) | 10.1419 | 0.324303 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 11.9721 | 0.382434 | ||||||||
\(981\) | −7.77184 | −0.248136 | ||||||||
\(982\) | 7.68268 | 0.245164 | ||||||||
\(983\) | −37.7516 | −1.20409 | −0.602044 | − | 0.798463i | \(-0.705647\pi\) | ||||
−0.602044 | + | 0.798463i | \(0.705647\pi\) | |||||||
\(984\) | 24.5328 | 0.782077 | ||||||||
\(985\) | −19.4048 | −0.618288 | ||||||||
\(986\) | −10.8452 | −0.345383 | ||||||||
\(987\) | −7.39568 | −0.235407 | ||||||||
\(988\) | −48.8349 | −1.55364 | ||||||||
\(989\) | 37.8343 | 1.20306 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.9354 | −1.42742 | −0.713710 | − | 0.700441i | \(-0.752987\pi\) | ||||
−0.713710 | + | 0.700441i | \(0.752987\pi\) | |||||||
\(992\) | −39.1175 | −1.24198 | ||||||||
\(993\) | −30.3909 | −0.964427 | ||||||||
\(994\) | 0.640313 | 0.0203095 | ||||||||
\(995\) | 20.3509 | 0.645167 | ||||||||
\(996\) | −4.85735 | −0.153911 | ||||||||
\(997\) | −0.396526 | −0.0125581 | −0.00627906 | − | 0.999980i | \(-0.501999\pi\) | ||||
−0.00627906 | + | 0.999980i | \(0.501999\pi\) | |||||||
\(998\) | 11.7104 | 0.370685 | ||||||||
\(999\) | 28.6245 | 0.905640 |
(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 | 605.2.a.m.1.3 | ✓ | 6 | |
3.2 | odd | 2 | 5445.2.a.bx.1.4 | 6 | |||
4.3 | odd | 2 | 9680.2.a.cw.1.5 | 6 | |||
5.4 | even | 2 | 3025.2.a.bg.1.4 | 6 | |||
11.2 | odd | 10 | 605.2.g.q.81.3 | 24 | |||
11.3 | even | 5 | 605.2.g.q.251.3 | 24 | |||
11.4 | even | 5 | 605.2.g.q.511.3 | 24 | |||
11.5 | even | 5 | 605.2.g.q.366.4 | 24 | |||
11.6 | odd | 10 | 605.2.g.q.366.3 | 24 | |||
11.7 | odd | 10 | 605.2.g.q.511.4 | 24 | |||
11.8 | odd | 10 | 605.2.g.q.251.4 | 24 | |||
11.9 | even | 5 | 605.2.g.q.81.4 | 24 | |||
11.10 | odd | 2 | inner | 605.2.a.m.1.4 | yes | 6 | |
33.32 | even | 2 | 5445.2.a.bx.1.3 | 6 | |||
44.43 | even | 2 | 9680.2.a.cw.1.6 | 6 | |||
55.54 | odd | 2 | 3025.2.a.bg.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.m.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
605.2.a.m.1.4 | yes | 6 | 11.10 | odd | 2 | inner | |
605.2.g.q.81.3 | 24 | 11.2 | odd | 10 | |||
605.2.g.q.81.4 | 24 | 11.9 | even | 5 | |||
605.2.g.q.251.3 | 24 | 11.3 | even | 5 | |||
605.2.g.q.251.4 | 24 | 11.8 | odd | 10 | |||
605.2.g.q.366.3 | 24 | 11.6 | odd | 10 | |||
605.2.g.q.366.4 | 24 | 11.5 | even | 5 | |||
605.2.g.q.511.3 | 24 | 11.4 | even | 5 | |||
605.2.g.q.511.4 | 24 | 11.7 | odd | 10 | |||
3025.2.a.bg.1.3 | 6 | 55.54 | odd | 2 | |||
3025.2.a.bg.1.4 | 6 | 5.4 | even | 2 | |||
5445.2.a.bx.1.3 | 6 | 33.32 | even | 2 | |||
5445.2.a.bx.1.4 | 6 | 3.2 | odd | 2 | |||
9680.2.a.cw.1.5 | 6 | 4.3 | odd | 2 | |||
9680.2.a.cw.1.6 | 6 | 44.43 | even | 2 |