Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, 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("845.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(6.74735897080\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.414214 | −0.292893 | −0.146447 | − | 0.989219i | \(-0.546784\pi\) | ||||
−0.146447 | + | 0.989219i | \(0.546784\pi\) | |||||||
\(3\) | 1.41421 | 0.816497 | 0.408248 | − | 0.912871i | \(-0.366140\pi\) | ||||
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.585786 | −0.239146 | ||||||||
\(7\) | 0.828427 | 0.313116 | 0.156558 | − | 0.987669i | \(-0.449960\pi\) | ||||
0.156558 | + | 0.987669i | \(0.449960\pi\) | |||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.414214 | 0.130986 | ||||||||
\(11\) | −0.585786 | −0.176621 | −0.0883106 | − | 0.996093i | \(-0.528147\pi\) | ||||
−0.0883106 | + | 0.996093i | \(0.528147\pi\) | |||||||
\(12\) | −2.58579 | −0.746452 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.343146 | −0.0917096 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −4.82843 | −1.17107 | −0.585533 | − | 0.810649i | \(-0.699115\pi\) | ||||
−0.585533 | + | 0.810649i | \(0.699115\pi\) | |||||||
\(18\) | 0.414214 | 0.0976311 | ||||||||
\(19\) | −3.41421 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(20\) | 1.82843 | 0.408849 | ||||||||
\(21\) | 1.17157 | 0.255658 | ||||||||
\(22\) | 0.242641 | 0.0517312 | ||||||||
\(23\) | −1.41421 | −0.294884 | −0.147442 | − | 0.989071i | \(-0.547104\pi\) | ||||
−0.147442 | + | 0.989071i | \(0.547104\pi\) | |||||||
\(24\) | 2.24264 | 0.457777 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | −1.51472 | −0.286255 | ||||||||
\(29\) | 5.65685 | 1.05045 | 0.525226 | − | 0.850963i | \(-0.323981\pi\) | ||||
0.525226 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(30\) | 0.585786 | 0.106949 | ||||||||
\(31\) | −10.2426 | −1.83963 | −0.919816 | − | 0.392349i | \(-0.871662\pi\) | ||||
−0.919816 | + | 0.392349i | \(0.871662\pi\) | |||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | −0.828427 | −0.144211 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −0.828427 | −0.140030 | ||||||||
\(36\) | 1.82843 | 0.304738 | ||||||||
\(37\) | −8.48528 | −1.39497 | −0.697486 | − | 0.716599i | \(-0.745698\pi\) | ||||
−0.697486 | + | 0.716599i | \(0.745698\pi\) | |||||||
\(38\) | 1.41421 | 0.229416 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.58579 | −0.250735 | ||||||||
\(41\) | 8.82843 | 1.37877 | 0.689384 | − | 0.724396i | \(-0.257881\pi\) | ||||
0.689384 | + | 0.724396i | \(0.257881\pi\) | |||||||
\(42\) | −0.485281 | −0.0748805 | ||||||||
\(43\) | 3.07107 | 0.468333 | 0.234167 | − | 0.972196i | \(-0.424764\pi\) | ||||
0.234167 | + | 0.972196i | \(0.424764\pi\) | |||||||
\(44\) | 1.07107 | 0.161470 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0.585786 | 0.0863695 | ||||||||
\(47\) | −0.828427 | −0.120839 | −0.0604193 | − | 0.998173i | \(-0.519244\pi\) | ||||
−0.0604193 | + | 0.998173i | \(0.519244\pi\) | |||||||
\(48\) | 4.24264 | 0.612372 | ||||||||
\(49\) | −6.31371 | −0.901958 | ||||||||
\(50\) | −0.414214 | −0.0585786 | ||||||||
\(51\) | −6.82843 | −0.956171 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.4853 | −1.98971 | −0.994853 | − | 0.101327i | \(-0.967691\pi\) | ||||
−0.994853 | + | 0.101327i | \(0.967691\pi\) | |||||||
\(54\) | 2.34315 | 0.318862 | ||||||||
\(55\) | 0.585786 | 0.0789874 | ||||||||
\(56\) | 1.31371 | 0.175552 | ||||||||
\(57\) | −4.82843 | −0.639541 | ||||||||
\(58\) | −2.34315 | −0.307670 | ||||||||
\(59\) | −10.2426 | −1.33348 | −0.666739 | − | 0.745291i | \(-0.732310\pi\) | ||||
−0.666739 | + | 0.745291i | \(0.732310\pi\) | |||||||
\(60\) | 2.58579 | 0.333824 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 4.24264 | 0.538816 | ||||||||
\(63\) | −0.828427 | −0.104372 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.343146 | 0.0422383 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 8.82843 | 1.07060 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0.343146 | 0.0410138 | ||||||||
\(71\) | 7.89949 | 0.937498 | 0.468749 | − | 0.883332i | \(-0.344705\pi\) | ||||
0.468749 | + | 0.883332i | \(0.344705\pi\) | |||||||
\(72\) | −1.58579 | −0.186887 | ||||||||
\(73\) | 8.48528 | 0.993127 | 0.496564 | − | 0.868000i | \(-0.334595\pi\) | ||||
0.496564 | + | 0.868000i | \(0.334595\pi\) | |||||||
\(74\) | 3.51472 | 0.408578 | ||||||||
\(75\) | 1.41421 | 0.163299 | ||||||||
\(76\) | 6.24264 | 0.716080 | ||||||||
\(77\) | −0.485281 | −0.0553029 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.48528 | 0.954669 | 0.477334 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477334 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −3.65685 | −0.403832 | ||||||||
\(83\) | 8.82843 | 0.969046 | 0.484523 | − | 0.874779i | \(-0.338993\pi\) | ||||
0.484523 | + | 0.874779i | \(0.338993\pi\) | |||||||
\(84\) | −2.14214 | −0.233726 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | −1.27208 | −0.137172 | ||||||||
\(87\) | 8.00000 | 0.857690 | ||||||||
\(88\) | −0.928932 | −0.0990245 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | −0.414214 | −0.0436619 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.58579 | 0.269587 | ||||||||
\(93\) | −14.4853 | −1.50205 | ||||||||
\(94\) | 0.343146 | 0.0353928 | ||||||||
\(95\) | 3.41421 | 0.350291 | ||||||||
\(96\) | −6.24264 | −0.637137 | ||||||||
\(97\) | −3.65685 | −0.371297 | −0.185649 | − | 0.982616i | \(-0.559439\pi\) | ||||
−0.185649 | + | 0.982616i | \(0.559439\pi\) | |||||||
\(98\) | 2.61522 | 0.264177 | ||||||||
\(99\) | 0.585786 | 0.0588738 | ||||||||
\(100\) | −1.82843 | −0.182843 | ||||||||
\(101\) | 7.65685 | 0.761885 | 0.380943 | − | 0.924599i | \(-0.375599\pi\) | ||||
0.380943 | + | 0.924599i | \(0.375599\pi\) | |||||||
\(102\) | 2.82843 | 0.280056 | ||||||||
\(103\) | 17.4142 | 1.71587 | 0.857937 | − | 0.513755i | \(-0.171746\pi\) | ||||
0.857937 | + | 0.513755i | \(0.171746\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.17157 | −0.114334 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −6.58579 | −0.636672 | −0.318336 | − | 0.947978i | \(-0.603124\pi\) | ||||
−0.318336 | + | 0.947978i | \(0.603124\pi\) | |||||||
\(108\) | 10.3431 | 0.995270 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | −0.242641 | −0.0231349 | ||||||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 2.48528 | 0.234837 | ||||||||
\(113\) | −3.17157 | −0.298356 | −0.149178 | − | 0.988810i | \(-0.547663\pi\) | ||||
−0.149178 | + | 0.988810i | \(0.547663\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | 1.41421 | 0.131876 | ||||||||
\(116\) | −10.3431 | −0.960337 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.24264 | 0.390567 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | −2.24264 | −0.204724 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | 3.31371 | 0.300009 | ||||||||
\(123\) | 12.4853 | 1.12576 | ||||||||
\(124\) | 18.7279 | 1.68182 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.343146 | 0.0305699 | ||||||||
\(127\) | −9.41421 | −0.835376 | −0.417688 | − | 0.908590i | \(-0.637160\pi\) | ||||
−0.417688 | + | 0.908590i | \(0.637160\pi\) | |||||||
\(128\) | 10.5563 | 0.933058 | ||||||||
\(129\) | 4.34315 | 0.382393 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9706 | 1.48272 | 0.741362 | − | 0.671105i | \(-0.234180\pi\) | ||||
0.741362 | + | 0.671105i | \(0.234180\pi\) | |||||||
\(132\) | 1.51472 | 0.131839 | ||||||||
\(133\) | −2.82843 | −0.245256 | ||||||||
\(134\) | −0.828427 | −0.0715652 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | −7.65685 | −0.656570 | ||||||||
\(137\) | −5.31371 | −0.453981 | −0.226990 | − | 0.973897i | \(-0.572889\pi\) | ||||
−0.226990 | + | 0.973897i | \(0.572889\pi\) | |||||||
\(138\) | 0.828427 | 0.0705204 | ||||||||
\(139\) | −12.4853 | −1.05899 | −0.529494 | − | 0.848314i | \(-0.677618\pi\) | ||||
−0.529494 | + | 0.848314i | \(0.677618\pi\) | |||||||
\(140\) | 1.51472 | 0.128017 | ||||||||
\(141\) | −1.17157 | −0.0986642 | ||||||||
\(142\) | −3.27208 | −0.274587 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −5.65685 | −0.469776 | ||||||||
\(146\) | −3.51472 | −0.290880 | ||||||||
\(147\) | −8.92893 | −0.736446 | ||||||||
\(148\) | 15.5147 | 1.27530 | ||||||||
\(149\) | 0.343146 | 0.0281116 | 0.0140558 | − | 0.999901i | \(-0.495526\pi\) | ||||
0.0140558 | + | 0.999901i | \(0.495526\pi\) | |||||||
\(150\) | −0.585786 | −0.0478293 | ||||||||
\(151\) | −18.2426 | −1.48457 | −0.742283 | − | 0.670087i | \(-0.766257\pi\) | ||||
−0.742283 | + | 0.670087i | \(0.766257\pi\) | |||||||
\(152\) | −5.41421 | −0.439151 | ||||||||
\(153\) | 4.82843 | 0.390355 | ||||||||
\(154\) | 0.201010 | 0.0161979 | ||||||||
\(155\) | 10.2426 | 0.822709 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0000 | 1.43656 | 0.718278 | − | 0.695756i | \(-0.244931\pi\) | ||||
0.718278 | + | 0.695756i | \(0.244931\pi\) | |||||||
\(158\) | −3.51472 | −0.279616 | ||||||||
\(159\) | −20.4853 | −1.62459 | ||||||||
\(160\) | 4.41421 | 0.348974 | ||||||||
\(161\) | −1.17157 | −0.0923329 | ||||||||
\(162\) | 2.07107 | 0.162718 | ||||||||
\(163\) | 14.9706 | 1.17258 | 0.586292 | − | 0.810099i | \(-0.300587\pi\) | ||||
0.586292 | + | 0.810099i | \(0.300587\pi\) | |||||||
\(164\) | −16.1421 | −1.26049 | ||||||||
\(165\) | 0.828427 | 0.0644930 | ||||||||
\(166\) | −3.65685 | −0.283827 | ||||||||
\(167\) | 8.82843 | 0.683164 | 0.341582 | − | 0.939852i | \(-0.389037\pi\) | ||||
0.341582 | + | 0.939852i | \(0.389037\pi\) | |||||||
\(168\) | 1.85786 | 0.143337 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | 3.41421 | 0.261091 | ||||||||
\(172\) | −5.61522 | −0.428157 | ||||||||
\(173\) | 11.1716 | 0.849359 | 0.424679 | − | 0.905344i | \(-0.360387\pi\) | ||||
0.424679 | + | 0.905344i | \(0.360387\pi\) | |||||||
\(174\) | −3.31371 | −0.251212 | ||||||||
\(175\) | 0.828427 | 0.0626232 | ||||||||
\(176\) | −1.75736 | −0.132466 | ||||||||
\(177\) | −14.4853 | −1.08878 | ||||||||
\(178\) | 2.48528 | 0.186280 | ||||||||
\(179\) | −5.65685 | −0.422813 | −0.211407 | − | 0.977398i | \(-0.567804\pi\) | ||||
−0.211407 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(180\) | −1.82843 | −0.136283 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3137 | −0.836333 | ||||||||
\(184\) | −2.24264 | −0.165330 | ||||||||
\(185\) | 8.48528 | 0.623850 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 2.82843 | 0.206835 | ||||||||
\(188\) | 1.51472 | 0.110472 | ||||||||
\(189\) | −4.68629 | −0.340878 | ||||||||
\(190\) | −1.41421 | −0.102598 | ||||||||
\(191\) | 13.6569 | 0.988175 | 0.494088 | − | 0.869412i | \(-0.335502\pi\) | ||||
0.494088 | + | 0.869412i | \(0.335502\pi\) | |||||||
\(192\) | −5.89949 | −0.425759 | ||||||||
\(193\) | −15.6569 | −1.12701 | −0.563503 | − | 0.826114i | \(-0.690546\pi\) | ||||
−0.563503 | + | 0.826114i | \(0.690546\pi\) | |||||||
\(194\) | 1.51472 | 0.108750 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.5442 | 0.824583 | ||||||||
\(197\) | 22.9706 | 1.63658 | 0.818292 | − | 0.574802i | \(-0.194921\pi\) | ||||
0.818292 | + | 0.574802i | \(0.194921\pi\) | |||||||
\(198\) | −0.242641 | −0.0172437 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | 1.58579 | 0.112132 | ||||||||
\(201\) | 2.82843 | 0.199502 | ||||||||
\(202\) | −3.17157 | −0.223151 | ||||||||
\(203\) | 4.68629 | 0.328913 | ||||||||
\(204\) | 12.4853 | 0.874145 | ||||||||
\(205\) | −8.82843 | −0.616604 | ||||||||
\(206\) | −7.21320 | −0.502568 | ||||||||
\(207\) | 1.41421 | 0.0982946 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0.485281 | 0.0334876 | ||||||||
\(211\) | −19.3137 | −1.32961 | −0.664805 | − | 0.747017i | \(-0.731485\pi\) | ||||
−0.664805 | + | 0.747017i | \(0.731485\pi\) | |||||||
\(212\) | 26.4853 | 1.81902 | ||||||||
\(213\) | 11.1716 | 0.765464 | ||||||||
\(214\) | 2.72792 | 0.186477 | ||||||||
\(215\) | −3.07107 | −0.209445 | ||||||||
\(216\) | −8.97056 | −0.610369 | ||||||||
\(217\) | −8.48528 | −0.576018 | ||||||||
\(218\) | −0.828427 | −0.0561082 | ||||||||
\(219\) | 12.0000 | 0.810885 | ||||||||
\(220\) | −1.07107 | −0.0722114 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.97056 | 0.333602 | ||||||||
\(223\) | −26.4853 | −1.77359 | −0.886793 | − | 0.462167i | \(-0.847072\pi\) | ||||
−0.886793 | + | 0.462167i | \(0.847072\pi\) | |||||||
\(224\) | −3.65685 | −0.244334 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 1.31371 | 0.0873866 | ||||||||
\(227\) | 27.6569 | 1.83565 | 0.917825 | − | 0.396985i | \(-0.129944\pi\) | ||||
0.917825 | + | 0.396985i | \(0.129944\pi\) | |||||||
\(228\) | 8.82843 | 0.584677 | ||||||||
\(229\) | −0.828427 | −0.0547440 | −0.0273720 | − | 0.999625i | \(-0.508714\pi\) | ||||
−0.0273720 | + | 0.999625i | \(0.508714\pi\) | |||||||
\(230\) | −0.585786 | −0.0386256 | ||||||||
\(231\) | −0.686292 | −0.0451547 | ||||||||
\(232\) | 8.97056 | 0.588946 | ||||||||
\(233\) | 24.6274 | 1.61340 | 0.806698 | − | 0.590964i | \(-0.201253\pi\) | ||||
0.806698 | + | 0.590964i | \(0.201253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.828427 | 0.0540406 | ||||||||
\(236\) | 18.7279 | 1.21908 | ||||||||
\(237\) | 12.0000 | 0.779484 | ||||||||
\(238\) | 1.65685 | 0.107398 | ||||||||
\(239\) | 0.585786 | 0.0378914 | 0.0189457 | − | 0.999821i | \(-0.493969\pi\) | ||||
0.0189457 | + | 0.999821i | \(0.493969\pi\) | |||||||
\(240\) | −4.24264 | −0.273861 | ||||||||
\(241\) | −2.48528 | −0.160091 | −0.0800455 | − | 0.996791i | \(-0.525507\pi\) | ||||
−0.0800455 | + | 0.996791i | \(0.525507\pi\) | |||||||
\(242\) | 4.41421 | 0.283756 | ||||||||
\(243\) | 9.89949 | 0.635053 | ||||||||
\(244\) | 14.6274 | 0.936424 | ||||||||
\(245\) | 6.31371 | 0.403368 | ||||||||
\(246\) | −5.17157 | −0.329727 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.2426 | −1.03141 | ||||||||
\(249\) | 12.4853 | 0.791223 | ||||||||
\(250\) | 0.414214 | 0.0261972 | ||||||||
\(251\) | −19.7990 | −1.24970 | −0.624851 | − | 0.780744i | \(-0.714840\pi\) | ||||
−0.624851 | + | 0.780744i | \(0.714840\pi\) | |||||||
\(252\) | 1.51472 | 0.0954183 | ||||||||
\(253\) | 0.828427 | 0.0520828 | ||||||||
\(254\) | 3.89949 | 0.244676 | ||||||||
\(255\) | 6.82843 | 0.427613 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 16.3431 | 1.01946 | 0.509729 | − | 0.860335i | \(-0.329746\pi\) | ||||
0.509729 | + | 0.860335i | \(0.329746\pi\) | |||||||
\(258\) | −1.79899 | −0.112000 | ||||||||
\(259\) | −7.02944 | −0.436788 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.65685 | −0.350150 | ||||||||
\(262\) | −7.02944 | −0.434280 | ||||||||
\(263\) | −13.4142 | −0.827156 | −0.413578 | − | 0.910469i | \(-0.635721\pi\) | ||||
−0.413578 | + | 0.910469i | \(0.635721\pi\) | |||||||
\(264\) | −1.31371 | −0.0808532 | ||||||||
\(265\) | 14.4853 | 0.889824 | ||||||||
\(266\) | 1.17157 | 0.0718337 | ||||||||
\(267\) | −8.48528 | −0.519291 | ||||||||
\(268\) | −3.65685 | −0.223378 | ||||||||
\(269\) | −2.68629 | −0.163786 | −0.0818930 | − | 0.996641i | \(-0.526097\pi\) | ||||
−0.0818930 | + | 0.996641i | \(0.526097\pi\) | |||||||
\(270\) | −2.34315 | −0.142599 | ||||||||
\(271\) | −1.27208 | −0.0772732 | −0.0386366 | − | 0.999253i | \(-0.512301\pi\) | ||||
−0.0386366 | + | 0.999253i | \(0.512301\pi\) | |||||||
\(272\) | −14.4853 | −0.878299 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.20101 | 0.132968 | ||||||||
\(275\) | −0.585786 | −0.0353243 | ||||||||
\(276\) | 3.65685 | 0.220117 | ||||||||
\(277\) | −7.17157 | −0.430898 | −0.215449 | − | 0.976515i | \(-0.569122\pi\) | ||||
−0.215449 | + | 0.976515i | \(0.569122\pi\) | |||||||
\(278\) | 5.17157 | 0.310170 | ||||||||
\(279\) | 10.2426 | 0.613211 | ||||||||
\(280\) | −1.31371 | −0.0785091 | ||||||||
\(281\) | 17.7990 | 1.06180 | 0.530899 | − | 0.847435i | \(-0.321854\pi\) | ||||
0.530899 | + | 0.847435i | \(0.321854\pi\) | |||||||
\(282\) | 0.485281 | 0.0288981 | ||||||||
\(283\) | 8.72792 | 0.518821 | 0.259411 | − | 0.965767i | \(-0.416472\pi\) | ||||
0.259411 | + | 0.965767i | \(0.416472\pi\) | |||||||
\(284\) | −14.4437 | −0.857073 | ||||||||
\(285\) | 4.82843 | 0.286011 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.31371 | 0.431715 | ||||||||
\(288\) | 4.41421 | 0.260110 | ||||||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | 2.34315 | 0.137594 | ||||||||
\(291\) | −5.17157 | −0.303163 | ||||||||
\(292\) | −15.5147 | −0.907930 | ||||||||
\(293\) | 2.14214 | 0.125145 | 0.0625724 | − | 0.998040i | \(-0.480070\pi\) | ||||
0.0625724 | + | 0.998040i | \(0.480070\pi\) | |||||||
\(294\) | 3.69848 | 0.215700 | ||||||||
\(295\) | 10.2426 | 0.596350 | ||||||||
\(296\) | −13.4558 | −0.782105 | ||||||||
\(297\) | 3.31371 | 0.192281 | ||||||||
\(298\) | −0.142136 | −0.00823370 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.58579 | −0.149290 | ||||||||
\(301\) | 2.54416 | 0.146643 | ||||||||
\(302\) | 7.55635 | 0.434819 | ||||||||
\(303\) | 10.8284 | 0.622077 | ||||||||
\(304\) | −10.2426 | −0.587456 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | −2.00000 | −0.114332 | ||||||||
\(307\) | −19.1716 | −1.09418 | −0.547090 | − | 0.837074i | \(-0.684264\pi\) | ||||
−0.547090 | + | 0.837074i | \(0.684264\pi\) | |||||||
\(308\) | 0.887302 | 0.0505587 | ||||||||
\(309\) | 24.6274 | 1.40100 | ||||||||
\(310\) | −4.24264 | −0.240966 | ||||||||
\(311\) | −8.48528 | −0.481156 | −0.240578 | − | 0.970630i | \(-0.577337\pi\) | ||||
−0.240578 | + | 0.970630i | \(0.577337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.828427 | 0.0468255 | 0.0234127 | − | 0.999726i | \(-0.492547\pi\) | ||||
0.0234127 | + | 0.999726i | \(0.492547\pi\) | |||||||
\(314\) | −7.45584 | −0.420758 | ||||||||
\(315\) | 0.828427 | 0.0466766 | ||||||||
\(316\) | −15.5147 | −0.872771 | ||||||||
\(317\) | −26.1421 | −1.46829 | −0.734144 | − | 0.678993i | \(-0.762416\pi\) | ||||
−0.734144 | + | 0.678993i | \(0.762416\pi\) | |||||||
\(318\) | 8.48528 | 0.475831 | ||||||||
\(319\) | −3.31371 | −0.185532 | ||||||||
\(320\) | 4.17157 | 0.233198 | ||||||||
\(321\) | −9.31371 | −0.519841 | ||||||||
\(322\) | 0.485281 | 0.0270437 | ||||||||
\(323\) | 16.4853 | 0.917266 | ||||||||
\(324\) | 9.14214 | 0.507896 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.20101 | −0.343442 | ||||||||
\(327\) | 2.82843 | 0.156412 | ||||||||
\(328\) | 14.0000 | 0.773021 | ||||||||
\(329\) | −0.686292 | −0.0378365 | ||||||||
\(330\) | −0.343146 | −0.0188896 | ||||||||
\(331\) | −22.0416 | −1.21152 | −0.605759 | − | 0.795648i | \(-0.707130\pi\) | ||||
−0.605759 | + | 0.795648i | \(0.707130\pi\) | |||||||
\(332\) | −16.1421 | −0.885915 | ||||||||
\(333\) | 8.48528 | 0.464991 | ||||||||
\(334\) | −3.65685 | −0.200094 | ||||||||
\(335\) | −2.00000 | −0.109272 | ||||||||
\(336\) | 3.51472 | 0.191744 | ||||||||
\(337\) | 7.17157 | 0.390660 | 0.195330 | − | 0.980738i | \(-0.437422\pi\) | ||||
0.195330 | + | 0.980738i | \(0.437422\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.48528 | −0.243607 | ||||||||
\(340\) | −8.82843 | −0.478789 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | −1.41421 | −0.0764719 | ||||||||
\(343\) | −11.0294 | −0.595534 | ||||||||
\(344\) | 4.87006 | 0.262576 | ||||||||
\(345\) | 2.00000 | 0.107676 | ||||||||
\(346\) | −4.62742 | −0.248771 | ||||||||
\(347\) | 4.24264 | 0.227757 | 0.113878 | − | 0.993495i | \(-0.463673\pi\) | ||||
0.113878 | + | 0.993495i | \(0.463673\pi\) | |||||||
\(348\) | −14.6274 | −0.784112 | ||||||||
\(349\) | −1.51472 | −0.0810810 | −0.0405405 | − | 0.999178i | \(-0.512908\pi\) | ||||
−0.0405405 | + | 0.999178i | \(0.512908\pi\) | |||||||
\(350\) | −0.343146 | −0.0183419 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.58579 | 0.137823 | ||||||||
\(353\) | −9.17157 | −0.488154 | −0.244077 | − | 0.969756i | \(-0.578485\pi\) | ||||
−0.244077 | + | 0.969756i | \(0.578485\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | −7.89949 | −0.419262 | ||||||||
\(356\) | 10.9706 | 0.581439 | ||||||||
\(357\) | −5.65685 | −0.299392 | ||||||||
\(358\) | 2.34315 | 0.123839 | ||||||||
\(359\) | 27.8995 | 1.47248 | 0.736240 | − | 0.676721i | \(-0.236600\pi\) | ||||
0.736240 | + | 0.676721i | \(0.236600\pi\) | |||||||
\(360\) | 1.58579 | 0.0835783 | ||||||||
\(361\) | −7.34315 | −0.386481 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.0711 | −0.791026 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.48528 | −0.444140 | ||||||||
\(366\) | 4.68629 | 0.244956 | ||||||||
\(367\) | 4.44365 | 0.231957 | 0.115978 | − | 0.993252i | \(-0.463000\pi\) | ||||
0.115978 | + | 0.993252i | \(0.463000\pi\) | |||||||
\(368\) | −4.24264 | −0.221163 | ||||||||
\(369\) | −8.82843 | −0.459590 | ||||||||
\(370\) | −3.51472 | −0.182722 | ||||||||
\(371\) | −12.0000 | −0.623009 | ||||||||
\(372\) | 26.4853 | 1.37320 | ||||||||
\(373\) | −25.3137 | −1.31069 | −0.655347 | − | 0.755328i | \(-0.727478\pi\) | ||||
−0.655347 | + | 0.755328i | \(0.727478\pi\) | |||||||
\(374\) | −1.17157 | −0.0605806 | ||||||||
\(375\) | −1.41421 | −0.0730297 | ||||||||
\(376\) | −1.31371 | −0.0677493 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.94113 | 0.0998407 | ||||||||
\(379\) | −14.9289 | −0.766848 | −0.383424 | − | 0.923572i | \(-0.625255\pi\) | ||||
−0.383424 | + | 0.923572i | \(0.625255\pi\) | |||||||
\(380\) | −6.24264 | −0.320241 | ||||||||
\(381\) | −13.3137 | −0.682082 | ||||||||
\(382\) | −5.65685 | −0.289430 | ||||||||
\(383\) | −33.1127 | −1.69198 | −0.845990 | − | 0.533199i | \(-0.820990\pi\) | ||||
−0.845990 | + | 0.533199i | \(0.820990\pi\) | |||||||
\(384\) | 14.9289 | 0.761839 | ||||||||
\(385\) | 0.485281 | 0.0247322 | ||||||||
\(386\) | 6.48528 | 0.330092 | ||||||||
\(387\) | −3.07107 | −0.156111 | ||||||||
\(388\) | 6.68629 | 0.339445 | ||||||||
\(389\) | −16.6274 | −0.843044 | −0.421522 | − | 0.906818i | \(-0.638504\pi\) | ||||
−0.421522 | + | 0.906818i | \(0.638504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.82843 | 0.345328 | ||||||||
\(392\) | −10.0122 | −0.505692 | ||||||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | −9.51472 | −0.479345 | ||||||||
\(395\) | −8.48528 | −0.426941 | ||||||||
\(396\) | −1.07107 | −0.0538232 | ||||||||
\(397\) | 27.7990 | 1.39519 | 0.697596 | − | 0.716492i | \(-0.254253\pi\) | ||||
0.697596 | + | 0.716492i | \(0.254253\pi\) | |||||||
\(398\) | −1.65685 | −0.0830506 | ||||||||
\(399\) | −4.00000 | −0.200250 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | −17.3137 | −0.864605 | −0.432303 | − | 0.901729i | \(-0.642299\pi\) | ||||
−0.432303 | + | 0.901729i | \(0.642299\pi\) | |||||||
\(402\) | −1.17157 | −0.0584327 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 5.00000 | 0.248452 | ||||||||
\(406\) | −1.94113 | −0.0963364 | ||||||||
\(407\) | 4.97056 | 0.246382 | ||||||||
\(408\) | −10.8284 | −0.536087 | ||||||||
\(409\) | −12.8284 | −0.634325 | −0.317162 | − | 0.948371i | \(-0.602730\pi\) | ||||
−0.317162 | + | 0.948371i | \(0.602730\pi\) | |||||||
\(410\) | 3.65685 | 0.180599 | ||||||||
\(411\) | −7.51472 | −0.370674 | ||||||||
\(412\) | −31.8406 | −1.56867 | ||||||||
\(413\) | −8.48528 | −0.417533 | ||||||||
\(414\) | −0.585786 | −0.0287898 | ||||||||
\(415\) | −8.82843 | −0.433370 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.6569 | −0.864660 | ||||||||
\(418\) | −0.828427 | −0.0405197 | ||||||||
\(419\) | 5.17157 | 0.252648 | 0.126324 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126324 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(420\) | 2.14214 | 0.104526 | ||||||||
\(421\) | 1.02944 | 0.0501717 | 0.0250859 | − | 0.999685i | \(-0.492014\pi\) | ||||
0.0250859 | + | 0.999685i | \(0.492014\pi\) | |||||||
\(422\) | 8.00000 | 0.389434 | ||||||||
\(423\) | 0.828427 | 0.0402795 | ||||||||
\(424\) | −22.9706 | −1.11555 | ||||||||
\(425\) | −4.82843 | −0.234213 | ||||||||
\(426\) | −4.62742 | −0.224199 | ||||||||
\(427\) | −6.62742 | −0.320723 | ||||||||
\(428\) | 12.0416 | 0.582054 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.27208 | 0.0613450 | ||||||||
\(431\) | −3.61522 | −0.174139 | −0.0870696 | − | 0.996202i | \(-0.527750\pi\) | ||||
−0.0870696 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(432\) | −16.9706 | −0.816497 | ||||||||
\(433\) | −3.65685 | −0.175737 | −0.0878686 | − | 0.996132i | \(-0.528006\pi\) | ||||
−0.0878686 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(434\) | 3.51472 | 0.168712 | ||||||||
\(435\) | −8.00000 | −0.383571 | ||||||||
\(436\) | −3.65685 | −0.175132 | ||||||||
\(437\) | 4.82843 | 0.230975 | ||||||||
\(438\) | −4.97056 | −0.237503 | ||||||||
\(439\) | −32.9706 | −1.57360 | −0.786800 | − | 0.617209i | \(-0.788263\pi\) | ||||
−0.786800 | + | 0.617209i | \(0.788263\pi\) | |||||||
\(440\) | 0.928932 | 0.0442851 | ||||||||
\(441\) | 6.31371 | 0.300653 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.58579 | −0.312900 | −0.156450 | − | 0.987686i | \(-0.550005\pi\) | ||||
−0.156450 | + | 0.987686i | \(0.550005\pi\) | |||||||
\(444\) | 21.9411 | 1.04128 | ||||||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | 10.9706 | 0.519471 | ||||||||
\(447\) | 0.485281 | 0.0229530 | ||||||||
\(448\) | −3.45584 | −0.163273 | ||||||||
\(449\) | −29.1127 | −1.37391 | −0.686957 | − | 0.726698i | \(-0.741054\pi\) | ||||
−0.686957 | + | 0.726698i | \(0.741054\pi\) | |||||||
\(450\) | 0.414214 | 0.0195262 | ||||||||
\(451\) | −5.17157 | −0.243520 | ||||||||
\(452\) | 5.79899 | 0.272762 | ||||||||
\(453\) | −25.7990 | −1.21214 | ||||||||
\(454\) | −11.4558 | −0.537649 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.65685 | −0.358565 | ||||||||
\(457\) | 18.0000 | 0.842004 | 0.421002 | − | 0.907060i | \(-0.361678\pi\) | ||||
0.421002 | + | 0.907060i | \(0.361678\pi\) | |||||||
\(458\) | 0.343146 | 0.0160341 | ||||||||
\(459\) | 27.3137 | 1.27489 | ||||||||
\(460\) | −2.58579 | −0.120563 | ||||||||
\(461\) | −26.4853 | −1.23354 | −0.616771 | − | 0.787142i | \(-0.711560\pi\) | ||||
−0.616771 | + | 0.787142i | \(0.711560\pi\) | |||||||
\(462\) | 0.284271 | 0.0132255 | ||||||||
\(463\) | 15.6569 | 0.727636 | 0.363818 | − | 0.931470i | \(-0.381473\pi\) | ||||
0.363818 | + | 0.931470i | \(0.381473\pi\) | |||||||
\(464\) | 16.9706 | 0.787839 | ||||||||
\(465\) | 14.4853 | 0.671739 | ||||||||
\(466\) | −10.2010 | −0.472553 | ||||||||
\(467\) | −10.5858 | −0.489852 | −0.244926 | − | 0.969542i | \(-0.578764\pi\) | ||||
−0.244926 | + | 0.969542i | \(0.578764\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.65685 | 0.0765064 | ||||||||
\(470\) | −0.343146 | −0.0158281 | ||||||||
\(471\) | 25.4558 | 1.17294 | ||||||||
\(472\) | −16.2426 | −0.747628 | ||||||||
\(473\) | −1.79899 | −0.0827176 | ||||||||
\(474\) | −4.97056 | −0.228306 | ||||||||
\(475\) | −3.41421 | −0.156655 | ||||||||
\(476\) | 7.31371 | 0.335223 | ||||||||
\(477\) | 14.4853 | 0.663235 | ||||||||
\(478\) | −0.242641 | −0.0110981 | ||||||||
\(479\) | 5.27208 | 0.240887 | 0.120444 | − | 0.992720i | \(-0.461568\pi\) | ||||
0.120444 | + | 0.992720i | \(0.461568\pi\) | |||||||
\(480\) | 6.24264 | 0.284936 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.02944 | 0.0468896 | ||||||||
\(483\) | −1.65685 | −0.0753895 | ||||||||
\(484\) | 19.4853 | 0.885695 | ||||||||
\(485\) | 3.65685 | 0.166049 | ||||||||
\(486\) | −4.10051 | −0.186003 | ||||||||
\(487\) | −22.9706 | −1.04090 | −0.520448 | − | 0.853894i | \(-0.674235\pi\) | ||||
−0.520448 | + | 0.853894i | \(0.674235\pi\) | |||||||
\(488\) | −12.6863 | −0.574281 | ||||||||
\(489\) | 21.1716 | 0.957412 | ||||||||
\(490\) | −2.61522 | −0.118144 | ||||||||
\(491\) | 10.8284 | 0.488680 | 0.244340 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244340 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(492\) | −22.8284 | −1.02918 | ||||||||
\(493\) | −27.3137 | −1.23015 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.585786 | −0.0263291 | ||||||||
\(496\) | −30.7279 | −1.37972 | ||||||||
\(497\) | 6.54416 | 0.293546 | ||||||||
\(498\) | −5.17157 | −0.231744 | ||||||||
\(499\) | −10.4437 | −0.467522 | −0.233761 | − | 0.972294i | \(-0.575103\pi\) | ||||
−0.233761 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(500\) | 1.82843 | 0.0817697 | ||||||||
\(501\) | 12.4853 | 0.557801 | ||||||||
\(502\) | 8.20101 | 0.366029 | ||||||||
\(503\) | 18.1005 | 0.807062 | 0.403531 | − | 0.914966i | \(-0.367783\pi\) | ||||
0.403531 | + | 0.914966i | \(0.367783\pi\) | |||||||
\(504\) | −1.31371 | −0.0585172 | ||||||||
\(505\) | −7.65685 | −0.340726 | ||||||||
\(506\) | −0.343146 | −0.0152547 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.2132 | 0.763712 | ||||||||
\(509\) | 21.1127 | 0.935804 | 0.467902 | − | 0.883780i | \(-0.345010\pi\) | ||||
0.467902 | + | 0.883780i | \(0.345010\pi\) | |||||||
\(510\) | −2.82843 | −0.125245 | ||||||||
\(511\) | 7.02944 | 0.310964 | ||||||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | 19.3137 | 0.852721 | ||||||||
\(514\) | −6.76955 | −0.298592 | ||||||||
\(515\) | −17.4142 | −0.767362 | ||||||||
\(516\) | −7.94113 | −0.349589 | ||||||||
\(517\) | 0.485281 | 0.0213427 | ||||||||
\(518\) | 2.91169 | 0.127932 | ||||||||
\(519\) | 15.7990 | 0.693499 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.34315 | −0.277898 | −0.138949 | − | 0.990300i | \(-0.544372\pi\) | ||||
−0.138949 | + | 0.990300i | \(0.544372\pi\) | |||||||
\(522\) | 2.34315 | 0.102557 | ||||||||
\(523\) | −28.2426 | −1.23496 | −0.617482 | − | 0.786585i | \(-0.711847\pi\) | ||||
−0.617482 | + | 0.786585i | \(0.711847\pi\) | |||||||
\(524\) | −31.0294 | −1.35553 | ||||||||
\(525\) | 1.17157 | 0.0511316 | ||||||||
\(526\) | 5.55635 | 0.242268 | ||||||||
\(527\) | 49.4558 | 2.15433 | ||||||||
\(528\) | −2.48528 | −0.108158 | ||||||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | 10.2426 | 0.444493 | ||||||||
\(532\) | 5.17157 | 0.224216 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.51472 | 0.152097 | ||||||||
\(535\) | 6.58579 | 0.284728 | ||||||||
\(536\) | 3.17157 | 0.136991 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | 1.11270 | 0.0479718 | ||||||||
\(539\) | 3.69848 | 0.159305 | ||||||||
\(540\) | −10.3431 | −0.445098 | ||||||||
\(541\) | 12.8284 | 0.551537 | 0.275769 | − | 0.961224i | \(-0.411068\pi\) | ||||
0.275769 | + | 0.961224i | \(0.411068\pi\) | |||||||
\(542\) | 0.526912 | 0.0226328 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.3137 | 0.913818 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.2132 | −1.24907 | −0.624533 | − | 0.780998i | \(-0.714711\pi\) | ||||
−0.624533 | + | 0.780998i | \(0.714711\pi\) | |||||||
\(548\) | 9.71573 | 0.415035 | ||||||||
\(549\) | 8.00000 | 0.341432 | ||||||||
\(550\) | 0.242641 | 0.0103462 | ||||||||
\(551\) | −19.3137 | −0.822792 | ||||||||
\(552\) | −3.17157 | −0.134991 | ||||||||
\(553\) | 7.02944 | 0.298922 | ||||||||
\(554\) | 2.97056 | 0.126207 | ||||||||
\(555\) | 12.0000 | 0.509372 | ||||||||
\(556\) | 22.8284 | 0.968141 | ||||||||
\(557\) | −3.79899 | −0.160968 | −0.0804842 | − | 0.996756i | \(-0.525647\pi\) | ||||
−0.0804842 | + | 0.996756i | \(0.525647\pi\) | |||||||
\(558\) | −4.24264 | −0.179605 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.48528 | −0.105022 | ||||||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | −7.37258 | −0.310994 | ||||||||
\(563\) | −16.2426 | −0.684546 | −0.342273 | − | 0.939601i | \(-0.611197\pi\) | ||||
−0.342273 | + | 0.939601i | \(0.611197\pi\) | |||||||
\(564\) | 2.14214 | 0.0902002 | ||||||||
\(565\) | 3.17157 | 0.133429 | ||||||||
\(566\) | −3.61522 | −0.151959 | ||||||||
\(567\) | −4.14214 | −0.173953 | ||||||||
\(568\) | 12.5269 | 0.525618 | ||||||||
\(569\) | −21.6569 | −0.907903 | −0.453951 | − | 0.891027i | \(-0.649986\pi\) | ||||
−0.453951 | + | 0.891027i | \(0.649986\pi\) | |||||||
\(570\) | −2.00000 | −0.0837708 | ||||||||
\(571\) | −28.4853 | −1.19207 | −0.596036 | − | 0.802958i | \(-0.703258\pi\) | ||||
−0.596036 | + | 0.802958i | \(0.703258\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.3137 | 0.806842 | ||||||||
\(574\) | −3.02944 | −0.126446 | ||||||||
\(575\) | −1.41421 | −0.0589768 | ||||||||
\(576\) | 4.17157 | 0.173816 | ||||||||
\(577\) | 29.1716 | 1.21443 | 0.607214 | − | 0.794538i | \(-0.292287\pi\) | ||||
0.607214 | + | 0.794538i | \(0.292287\pi\) | |||||||
\(578\) | −2.61522 | −0.108779 | ||||||||
\(579\) | −22.1421 | −0.920196 | ||||||||
\(580\) | 10.3431 | 0.429476 | ||||||||
\(581\) | 7.31371 | 0.303424 | ||||||||
\(582\) | 2.14214 | 0.0887944 | ||||||||
\(583\) | 8.48528 | 0.351424 | ||||||||
\(584\) | 13.4558 | 0.556807 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.887302 | −0.0366541 | ||||||||
\(587\) | −31.6569 | −1.30662 | −0.653309 | − | 0.757091i | \(-0.726620\pi\) | ||||
−0.653309 | + | 0.757091i | \(0.726620\pi\) | |||||||
\(588\) | 16.3259 | 0.673269 | ||||||||
\(589\) | 34.9706 | 1.44094 | ||||||||
\(590\) | −4.24264 | −0.174667 | ||||||||
\(591\) | 32.4853 | 1.33627 | ||||||||
\(592\) | −25.4558 | −1.04623 | ||||||||
\(593\) | −20.6274 | −0.847066 | −0.423533 | − | 0.905881i | \(-0.639210\pi\) | ||||
−0.423533 | + | 0.905881i | \(0.639210\pi\) | |||||||
\(594\) | −1.37258 | −0.0563178 | ||||||||
\(595\) | 4.00000 | 0.163984 | ||||||||
\(596\) | −0.627417 | −0.0257000 | ||||||||
\(597\) | 5.65685 | 0.231520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.4558 | −1.04010 | −0.520049 | − | 0.854137i | \(-0.674086\pi\) | ||||
−0.520049 | + | 0.854137i | \(0.674086\pi\) | |||||||
\(600\) | 2.24264 | 0.0915554 | ||||||||
\(601\) | 0.627417 | 0.0255929 | 0.0127964 | − | 0.999918i | \(-0.495927\pi\) | ||||
0.0127964 | + | 0.999918i | \(0.495927\pi\) | |||||||
\(602\) | −1.05382 | −0.0429507 | ||||||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | 33.3553 | 1.35721 | ||||||||
\(605\) | 10.6569 | 0.433263 | ||||||||
\(606\) | −4.48528 | −0.182202 | ||||||||
\(607\) | 40.2426 | 1.63340 | 0.816699 | − | 0.577064i | \(-0.195802\pi\) | ||||
0.816699 | + | 0.577064i | \(0.195802\pi\) | |||||||
\(608\) | 15.0711 | 0.611213 | ||||||||
\(609\) | 6.62742 | 0.268556 | ||||||||
\(610\) | −3.31371 | −0.134168 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8.82843 | −0.356868 | ||||||||
\(613\) | 37.3137 | 1.50709 | 0.753543 | − | 0.657398i | \(-0.228343\pi\) | ||||
0.753543 | + | 0.657398i | \(0.228343\pi\) | |||||||
\(614\) | 7.94113 | 0.320478 | ||||||||
\(615\) | −12.4853 | −0.503455 | ||||||||
\(616\) | −0.769553 | −0.0310062 | ||||||||
\(617\) | 22.9706 | 0.924760 | 0.462380 | − | 0.886682i | \(-0.346996\pi\) | ||||
0.462380 | + | 0.886682i | \(0.346996\pi\) | |||||||
\(618\) | −10.2010 | −0.410345 | ||||||||
\(619\) | −10.2426 | −0.411686 | −0.205843 | − | 0.978585i | \(-0.565994\pi\) | ||||
−0.205843 | + | 0.978585i | \(0.565994\pi\) | |||||||
\(620\) | −18.7279 | −0.752131 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 3.51472 | 0.140927 | ||||||||
\(623\) | −4.97056 | −0.199141 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.343146 | −0.0137149 | ||||||||
\(627\) | 2.82843 | 0.112956 | ||||||||
\(628\) | −32.9117 | −1.31332 | ||||||||
\(629\) | 40.9706 | 1.63360 | ||||||||
\(630\) | −0.343146 | −0.0136713 | ||||||||
\(631\) | 18.2426 | 0.726228 | 0.363114 | − | 0.931745i | \(-0.381714\pi\) | ||||
0.363114 | + | 0.931745i | \(0.381714\pi\) | |||||||
\(632\) | 13.4558 | 0.535245 | ||||||||
\(633\) | −27.3137 | −1.08562 | ||||||||
\(634\) | 10.8284 | 0.430052 | ||||||||
\(635\) | 9.41421 | 0.373592 | ||||||||
\(636\) | 37.4558 | 1.48522 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.37258 | 0.0543411 | ||||||||
\(639\) | −7.89949 | −0.312499 | ||||||||
\(640\) | −10.5563 | −0.417276 | ||||||||
\(641\) | 36.3431 | 1.43547 | 0.717734 | − | 0.696317i | \(-0.245179\pi\) | ||||
0.717734 | + | 0.696317i | \(0.245179\pi\) | |||||||
\(642\) | 3.85786 | 0.152258 | ||||||||
\(643\) | −26.4853 | −1.04448 | −0.522239 | − | 0.852799i | \(-0.674903\pi\) | ||||
−0.522239 | + | 0.852799i | \(0.674903\pi\) | |||||||
\(644\) | 2.14214 | 0.0844120 | ||||||||
\(645\) | −4.34315 | −0.171011 | ||||||||
\(646\) | −6.82843 | −0.268661 | ||||||||
\(647\) | 6.58579 | 0.258914 | 0.129457 | − | 0.991585i | \(-0.458677\pi\) | ||||
0.129457 | + | 0.991585i | \(0.458677\pi\) | |||||||
\(648\) | −7.92893 | −0.311478 | ||||||||
\(649\) | 6.00000 | 0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | −27.3726 | −1.07199 | ||||||||
\(653\) | 13.0294 | 0.509881 | 0.254941 | − | 0.966957i | \(-0.417944\pi\) | ||||
0.254941 | + | 0.966957i | \(0.417944\pi\) | |||||||
\(654\) | −1.17157 | −0.0458121 | ||||||||
\(655\) | −16.9706 | −0.663095 | ||||||||
\(656\) | 26.4853 | 1.03408 | ||||||||
\(657\) | −8.48528 | −0.331042 | ||||||||
\(658\) | 0.284271 | 0.0110820 | ||||||||
\(659\) | 46.1421 | 1.79744 | 0.898721 | − | 0.438520i | \(-0.144497\pi\) | ||||
0.898721 | + | 0.438520i | \(0.144497\pi\) | |||||||
\(660\) | −1.51472 | −0.0589603 | ||||||||
\(661\) | 49.5980 | 1.92914 | 0.964569 | − | 0.263831i | \(-0.0849861\pi\) | ||||
0.964569 | + | 0.263831i | \(0.0849861\pi\) | |||||||
\(662\) | 9.12994 | 0.354845 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.0000 | 0.543305 | ||||||||
\(665\) | 2.82843 | 0.109682 | ||||||||
\(666\) | −3.51472 | −0.136193 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | −16.1421 | −0.624558 | ||||||||
\(669\) | −37.4558 | −1.44813 | ||||||||
\(670\) | 0.828427 | 0.0320049 | ||||||||
\(671\) | 4.68629 | 0.180912 | ||||||||
\(672\) | −5.17157 | −0.199498 | ||||||||
\(673\) | −10.4853 | −0.404178 | −0.202089 | − | 0.979367i | \(-0.564773\pi\) | ||||
−0.202089 | + | 0.979367i | \(0.564773\pi\) | |||||||
\(674\) | −2.97056 | −0.114422 | ||||||||
\(675\) | −5.65685 | −0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.14214 | 0.312928 | 0.156464 | − | 0.987684i | \(-0.449991\pi\) | ||||
0.156464 | + | 0.987684i | \(0.449991\pi\) | |||||||
\(678\) | 1.85786 | 0.0713509 | ||||||||
\(679\) | −3.02944 | −0.116259 | ||||||||
\(680\) | 7.65685 | 0.293627 | ||||||||
\(681\) | 39.1127 | 1.49880 | ||||||||
\(682\) | −2.48528 | −0.0951663 | ||||||||
\(683\) | −33.3137 | −1.27471 | −0.637357 | − | 0.770569i | \(-0.719972\pi\) | ||||
−0.637357 | + | 0.770569i | \(0.719972\pi\) | |||||||
\(684\) | −6.24264 | −0.238693 | ||||||||
\(685\) | 5.31371 | 0.203026 | ||||||||
\(686\) | 4.56854 | 0.174428 | ||||||||
\(687\) | −1.17157 | −0.0446983 | ||||||||
\(688\) | 9.21320 | 0.351250 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.828427 | −0.0315377 | ||||||||
\(691\) | −21.0711 | −0.801581 | −0.400791 | − | 0.916170i | \(-0.631265\pi\) | ||||
−0.400791 | + | 0.916170i | \(0.631265\pi\) | |||||||
\(692\) | −20.4264 | −0.776495 | ||||||||
\(693\) | 0.485281 | 0.0184343 | ||||||||
\(694\) | −1.75736 | −0.0667084 | ||||||||
\(695\) | 12.4853 | 0.473594 | ||||||||
\(696\) | 12.6863 | 0.480873 | ||||||||
\(697\) | −42.6274 | −1.61463 | ||||||||
\(698\) | 0.627417 | 0.0237481 | ||||||||
\(699\) | 34.8284 | 1.31733 | ||||||||
\(700\) | −1.51472 | −0.0572510 | ||||||||
\(701\) | 37.3137 | 1.40932 | 0.704660 | − | 0.709545i | \(-0.251100\pi\) | ||||
0.704660 | + | 0.709545i | \(0.251100\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.9706 | 1.09265 | ||||||||
\(704\) | 2.44365 | 0.0920986 | ||||||||
\(705\) | 1.17157 | 0.0441240 | ||||||||
\(706\) | 3.79899 | 0.142977 | ||||||||
\(707\) | 6.34315 | 0.238559 | ||||||||
\(708\) | 26.4853 | 0.995378 | ||||||||
\(709\) | 17.1127 | 0.642681 | 0.321340 | − | 0.946964i | \(-0.395867\pi\) | ||||
0.321340 | + | 0.946964i | \(0.395867\pi\) | |||||||
\(710\) | 3.27208 | 0.122799 | ||||||||
\(711\) | −8.48528 | −0.318223 | ||||||||
\(712\) | −9.51472 | −0.356579 | ||||||||
\(713\) | 14.4853 | 0.542478 | ||||||||
\(714\) | 2.34315 | 0.0876900 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.3431 | 0.386542 | ||||||||
\(717\) | 0.828427 | 0.0309382 | ||||||||
\(718\) | −11.5563 | −0.431279 | ||||||||
\(719\) | −4.97056 | −0.185371 | −0.0926854 | − | 0.995695i | \(-0.529545\pi\) | ||||
−0.0926854 | + | 0.995695i | \(0.529545\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | 14.4264 | 0.537267 | ||||||||
\(722\) | 3.04163 | 0.113198 | ||||||||
\(723\) | −3.51472 | −0.130714 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.65685 | 0.210090 | ||||||||
\(726\) | 6.24264 | 0.231686 | ||||||||
\(727\) | 19.3553 | 0.717850 | 0.358925 | − | 0.933366i | \(-0.383143\pi\) | ||||
0.358925 | + | 0.933366i | \(0.383143\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 3.51472 | 0.130086 | ||||||||
\(731\) | −14.8284 | −0.548449 | ||||||||
\(732\) | 20.6863 | 0.764587 | ||||||||
\(733\) | 1.31371 | 0.0485229 | 0.0242615 | − | 0.999706i | \(-0.492277\pi\) | ||||
0.0242615 | + | 0.999706i | \(0.492277\pi\) | |||||||
\(734\) | −1.84062 | −0.0679385 | ||||||||
\(735\) | 8.92893 | 0.329349 | ||||||||
\(736\) | 6.24264 | 0.230107 | ||||||||
\(737\) | −1.17157 | −0.0431554 | ||||||||
\(738\) | 3.65685 | 0.134611 | ||||||||
\(739\) | −30.7279 | −1.13034 | −0.565172 | − | 0.824973i | \(-0.691190\pi\) | ||||
−0.565172 | + | 0.824973i | \(0.691190\pi\) | |||||||
\(740\) | −15.5147 | −0.570332 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.97056 | 0.182475 | ||||||||
\(743\) | 38.4853 | 1.41189 | 0.705944 | − | 0.708268i | \(-0.250523\pi\) | ||||
0.705944 | + | 0.708268i | \(0.250523\pi\) | |||||||
\(744\) | −22.9706 | −0.842142 | ||||||||
\(745\) | −0.343146 | −0.0125719 | ||||||||
\(746\) | 10.4853 | 0.383893 | ||||||||
\(747\) | −8.82843 | −0.323015 | ||||||||
\(748\) | −5.17157 | −0.189091 | ||||||||
\(749\) | −5.45584 | −0.199352 | ||||||||
\(750\) | 0.585786 | 0.0213899 | ||||||||
\(751\) | −44.4853 | −1.62329 | −0.811645 | − | 0.584150i | \(-0.801428\pi\) | ||||
−0.811645 | + | 0.584150i | \(0.801428\pi\) | |||||||
\(752\) | −2.48528 | −0.0906289 | ||||||||
\(753\) | −28.0000 | −1.02038 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.2426 | 0.663918 | ||||||||
\(756\) | 8.56854 | 0.311635 | ||||||||
\(757\) | 4.14214 | 0.150548 | 0.0752742 | − | 0.997163i | \(-0.476017\pi\) | ||||
0.0752742 | + | 0.997163i | \(0.476017\pi\) | |||||||
\(758\) | 6.18377 | 0.224605 | ||||||||
\(759\) | 1.17157 | 0.0425254 | ||||||||
\(760\) | 5.41421 | 0.196394 | ||||||||
\(761\) | 36.6274 | 1.32774 | 0.663871 | − | 0.747847i | \(-0.268912\pi\) | ||||
0.663871 | + | 0.747847i | \(0.268912\pi\) | |||||||
\(762\) | 5.51472 | 0.199777 | ||||||||
\(763\) | 1.65685 | 0.0599822 | ||||||||
\(764\) | −24.9706 | −0.903403 | ||||||||
\(765\) | −4.82843 | −0.174572 | ||||||||
\(766\) | 13.7157 | 0.495569 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 5.61522 | 0.202622 | ||||||||
\(769\) | −10.9706 | −0.395609 | −0.197804 | − | 0.980242i | \(-0.563381\pi\) | ||||
−0.197804 | + | 0.980242i | \(0.563381\pi\) | |||||||
\(770\) | −0.201010 | −0.00724390 | ||||||||
\(771\) | 23.1127 | 0.832383 | ||||||||
\(772\) | 28.6274 | 1.03032 | ||||||||
\(773\) | −6.14214 | −0.220917 | −0.110459 | − | 0.993881i | \(-0.535232\pi\) | ||||
−0.110459 | + | 0.993881i | \(0.535232\pi\) | |||||||
\(774\) | 1.27208 | 0.0457239 | ||||||||
\(775\) | −10.2426 | −0.367927 | ||||||||
\(776\) | −5.79899 | −0.208172 | ||||||||
\(777\) | −9.94113 | −0.356636 | ||||||||
\(778\) | 6.88730 | 0.246922 | ||||||||
\(779\) | −30.1421 | −1.07995 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.62742 | −0.165582 | ||||||||
\(782\) | −2.82843 | −0.101144 | ||||||||
\(783\) | −32.0000 | −1.14359 | ||||||||
\(784\) | −18.9411 | −0.676469 | ||||||||
\(785\) | −18.0000 | −0.642448 | ||||||||
\(786\) | −9.94113 | −0.354588 | ||||||||
\(787\) | −5.51472 | −0.196578 | −0.0982892 | − | 0.995158i | \(-0.531337\pi\) | ||||
−0.0982892 | + | 0.995158i | \(0.531337\pi\) | |||||||
\(788\) | −42.0000 | −1.49619 | ||||||||
\(789\) | −18.9706 | −0.675370 | ||||||||
\(790\) | 3.51472 | 0.125048 | ||||||||
\(791\) | −2.62742 | −0.0934202 | ||||||||
\(792\) | 0.928932 | 0.0330082 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −11.5147 | −0.408642 | ||||||||
\(795\) | 20.4853 | 0.726538 | ||||||||
\(796\) | −7.31371 | −0.259228 | ||||||||
\(797\) | 10.9706 | 0.388597 | 0.194299 | − | 0.980942i | \(-0.437757\pi\) | ||||
0.194299 | + | 0.980942i | \(0.437757\pi\) | |||||||
\(798\) | 1.65685 | 0.0586520 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | −4.41421 | −0.156066 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 7.17157 | 0.253237 | ||||||||
\(803\) | −4.97056 | −0.175407 | ||||||||
\(804\) | −5.17157 | −0.182387 | ||||||||
\(805\) | 1.17157 | 0.0412925 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.79899 | −0.133731 | ||||||||
\(808\) | 12.1421 | 0.427159 | ||||||||
\(809\) | −45.2548 | −1.59108 | −0.795538 | − | 0.605904i | \(-0.792811\pi\) | ||||
−0.795538 | + | 0.605904i | \(0.792811\pi\) | |||||||
\(810\) | −2.07107 | −0.0727699 | ||||||||
\(811\) | −8.38478 | −0.294429 | −0.147215 | − | 0.989105i | \(-0.547031\pi\) | ||||
−0.147215 | + | 0.989105i | \(0.547031\pi\) | |||||||
\(812\) | −8.56854 | −0.300697 | ||||||||
\(813\) | −1.79899 | −0.0630933 | ||||||||
\(814\) | −2.05887 | −0.0721635 | ||||||||
\(815\) | −14.9706 | −0.524396 | ||||||||
\(816\) | −20.4853 | −0.717128 | ||||||||
\(817\) | −10.4853 | −0.366834 | ||||||||
\(818\) | 5.31371 | 0.185789 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.1421 | 0.563708 | ||||||||
\(821\) | −39.2548 | −1.37000 | −0.685002 | − | 0.728542i | \(-0.740199\pi\) | ||||
−0.685002 | + | 0.728542i | \(0.740199\pi\) | |||||||
\(822\) | 3.11270 | 0.108568 | ||||||||
\(823\) | 34.3848 | 1.19858 | 0.599289 | − | 0.800533i | \(-0.295450\pi\) | ||||
0.599289 | + | 0.800533i | \(0.295450\pi\) | |||||||
\(824\) | 27.6152 | 0.962022 | ||||||||
\(825\) | −0.828427 | −0.0288421 | ||||||||
\(826\) | 3.51472 | 0.122293 | ||||||||
\(827\) | −27.8579 | −0.968713 | −0.484356 | − | 0.874871i | \(-0.660946\pi\) | ||||
−0.484356 | + | 0.874871i | \(0.660946\pi\) | |||||||
\(828\) | −2.58579 | −0.0898623 | ||||||||
\(829\) | 7.02944 | 0.244142 | 0.122071 | − | 0.992521i | \(-0.461046\pi\) | ||||
0.122071 | + | 0.992521i | \(0.461046\pi\) | |||||||
\(830\) | 3.65685 | 0.126931 | ||||||||
\(831\) | −10.1421 | −0.351827 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.4853 | 1.05625 | ||||||||
\(834\) | 7.31371 | 0.253253 | ||||||||
\(835\) | −8.82843 | −0.305520 | ||||||||
\(836\) | −3.65685 | −0.126475 | ||||||||
\(837\) | 57.9411 | 2.00274 | ||||||||
\(838\) | −2.14214 | −0.0739988 | ||||||||
\(839\) | 18.7279 | 0.646560 | 0.323280 | − | 0.946303i | \(-0.395214\pi\) | ||||
0.323280 | + | 0.946303i | \(0.395214\pi\) | |||||||
\(840\) | −1.85786 | −0.0641024 | ||||||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | −0.426407 | −0.0146950 | ||||||||
\(843\) | 25.1716 | 0.866955 | ||||||||
\(844\) | 35.3137 | 1.21555 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.343146 | −0.0117976 | ||||||||
\(847\) | −8.82843 | −0.303348 | ||||||||
\(848\) | −43.4558 | −1.49228 | ||||||||
\(849\) | 12.3431 | 0.423616 | ||||||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | 12.0000 | 0.411355 | ||||||||
\(852\) | −20.4264 | −0.699797 | ||||||||
\(853\) | −37.4558 | −1.28246 | −0.641232 | − | 0.767347i | \(-0.721576\pi\) | ||||
−0.641232 | + | 0.767347i | \(0.721576\pi\) | |||||||
\(854\) | 2.74517 | 0.0939376 | ||||||||
\(855\) | −3.41421 | −0.116764 | ||||||||
\(856\) | −10.4437 | −0.356957 | ||||||||
\(857\) | 0.343146 | 0.0117216 | 0.00586082 | − | 0.999983i | \(-0.498134\pi\) | ||||
0.00586082 | + | 0.999983i | \(0.498134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.7990 | 0.402576 | 0.201288 | − | 0.979532i | \(-0.435487\pi\) | ||||
0.201288 | + | 0.979532i | \(0.435487\pi\) | |||||||
\(860\) | 5.61522 | 0.191478 | ||||||||
\(861\) | 10.3431 | 0.352493 | ||||||||
\(862\) | 1.49747 | 0.0510042 | ||||||||
\(863\) | −19.4558 | −0.662285 | −0.331142 | − | 0.943581i | \(-0.607434\pi\) | ||||
−0.331142 | + | 0.943581i | \(0.607434\pi\) | |||||||
\(864\) | 24.9706 | 0.849516 | ||||||||
\(865\) | −11.1716 | −0.379845 | ||||||||
\(866\) | 1.51472 | 0.0514722 | ||||||||
\(867\) | 8.92893 | 0.303242 | ||||||||
\(868\) | 15.5147 | 0.526604 | ||||||||
\(869\) | −4.97056 | −0.168615 | ||||||||
\(870\) | 3.31371 | 0.112345 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.17157 | 0.107403 | ||||||||
\(873\) | 3.65685 | 0.123766 | ||||||||
\(874\) | −2.00000 | −0.0676510 | ||||||||
\(875\) | −0.828427 | −0.0280059 | ||||||||
\(876\) | −21.9411 | −0.741322 | ||||||||
\(877\) | −2.68629 | −0.0907096 | −0.0453548 | − | 0.998971i | \(-0.514442\pi\) | ||||
−0.0453548 | + | 0.998971i | \(0.514442\pi\) | |||||||
\(878\) | 13.6569 | 0.460897 | ||||||||
\(879\) | 3.02944 | 0.102180 | ||||||||
\(880\) | 1.75736 | 0.0592406 | ||||||||
\(881\) | 52.9706 | 1.78462 | 0.892312 | − | 0.451420i | \(-0.149082\pi\) | ||||
0.892312 | + | 0.451420i | \(0.149082\pi\) | |||||||
\(882\) | −2.61522 | −0.0880592 | ||||||||
\(883\) | −32.2426 | −1.08505 | −0.542526 | − | 0.840039i | \(-0.682532\pi\) | ||||
−0.542526 | + | 0.840039i | \(0.682532\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.4853 | 0.486917 | ||||||||
\(886\) | 2.72792 | 0.0916463 | ||||||||
\(887\) | 14.3848 | 0.482994 | 0.241497 | − | 0.970402i | \(-0.422362\pi\) | ||||
0.241497 | + | 0.970402i | \(0.422362\pi\) | |||||||
\(888\) | −19.0294 | −0.638586 | ||||||||
\(889\) | −7.79899 | −0.261570 | ||||||||
\(890\) | −2.48528 | −0.0833068 | ||||||||
\(891\) | 2.92893 | 0.0981229 | ||||||||
\(892\) | 48.4264 | 1.62144 | ||||||||
\(893\) | 2.82843 | 0.0946497 | ||||||||
\(894\) | −0.201010 | −0.00672278 | ||||||||
\(895\) | 5.65685 | 0.189088 | ||||||||
\(896\) | 8.74517 | 0.292155 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.0589 | 0.402410 | ||||||||
\(899\) | −57.9411 | −1.93244 | ||||||||
\(900\) | 1.82843 | 0.0609476 | ||||||||
\(901\) | 69.9411 | 2.33008 | ||||||||
\(902\) | 2.14214 | 0.0713253 | ||||||||
\(903\) | 3.59798 | 0.119733 | ||||||||
\(904\) | −5.02944 | −0.167277 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.6863 | 0.355028 | ||||||||
\(907\) | −33.2132 | −1.10283 | −0.551413 | − | 0.834232i | \(-0.685911\pi\) | ||||
−0.551413 | + | 0.834232i | \(0.685911\pi\) | |||||||
\(908\) | −50.5685 | −1.67818 | ||||||||
\(909\) | −7.65685 | −0.253962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | −14.4853 | −0.479656 | ||||||||
\(913\) | −5.17157 | −0.171154 | ||||||||
\(914\) | −7.45584 | −0.246617 | ||||||||
\(915\) | 11.3137 | 0.374020 | ||||||||
\(916\) | 1.51472 | 0.0500477 | ||||||||
\(917\) | 14.0589 | 0.464265 | ||||||||
\(918\) | −11.3137 | −0.373408 | ||||||||
\(919\) | −16.4853 | −0.543799 | −0.271900 | − | 0.962326i | \(-0.587652\pi\) | ||||
−0.271900 | + | 0.962326i | \(0.587652\pi\) | |||||||
\(920\) | 2.24264 | 0.0739377 | ||||||||
\(921\) | −27.1127 | −0.893394 | ||||||||
\(922\) | 10.9706 | 0.361296 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.25483 | 0.0412810 | ||||||||
\(925\) | −8.48528 | −0.278994 | ||||||||
\(926\) | −6.48528 | −0.213120 | ||||||||
\(927\) | −17.4142 | −0.571958 | ||||||||
\(928\) | −24.9706 | −0.819699 | ||||||||
\(929\) | −11.1716 | −0.366527 | −0.183264 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183264 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(930\) | −6.00000 | −0.196748 | ||||||||
\(931\) | 21.5563 | 0.706481 | ||||||||
\(932\) | −45.0294 | −1.47499 | ||||||||
\(933\) | −12.0000 | −0.392862 | ||||||||
\(934\) | 4.38478 | 0.143474 | ||||||||
\(935\) | −2.82843 | −0.0924995 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.9706 | 0.358393 | 0.179196 | − | 0.983813i | \(-0.442650\pi\) | ||||
0.179196 | + | 0.983813i | \(0.442650\pi\) | |||||||
\(938\) | −0.686292 | −0.0224082 | ||||||||
\(939\) | 1.17157 | 0.0382328 | ||||||||
\(940\) | −1.51472 | −0.0494047 | ||||||||
\(941\) | 54.7696 | 1.78544 | 0.892718 | − | 0.450615i | \(-0.148795\pi\) | ||||
0.892718 | + | 0.450615i | \(0.148795\pi\) | |||||||
\(942\) | −10.5442 | −0.343547 | ||||||||
\(943\) | −12.4853 | −0.406577 | ||||||||
\(944\) | −30.7279 | −1.00011 | ||||||||
\(945\) | 4.68629 | 0.152445 | ||||||||
\(946\) | 0.745166 | 0.0242274 | ||||||||
\(947\) | 45.1127 | 1.46597 | 0.732983 | − | 0.680247i | \(-0.238128\pi\) | ||||
0.732983 | + | 0.680247i | \(0.238128\pi\) | |||||||
\(948\) | −21.9411 | −0.712615 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.41421 | 0.0458831 | ||||||||
\(951\) | −36.9706 | −1.19885 | ||||||||
\(952\) | −6.34315 | −0.205583 | ||||||||
\(953\) | −55.2548 | −1.78988 | −0.894940 | − | 0.446187i | \(-0.852782\pi\) | ||||
−0.894940 | + | 0.446187i | \(0.852782\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | −13.6569 | −0.441925 | ||||||||
\(956\) | −1.07107 | −0.0346408 | ||||||||
\(957\) | −4.68629 | −0.151486 | ||||||||
\(958\) | −2.18377 | −0.0705543 | ||||||||
\(959\) | −4.40202 | −0.142149 | ||||||||
\(960\) | 5.89949 | 0.190405 | ||||||||
\(961\) | 73.9117 | 2.38425 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.58579 | 0.212224 | ||||||||
\(964\) | 4.54416 | 0.146357 | ||||||||
\(965\) | 15.6569 | 0.504012 | ||||||||
\(966\) | 0.686292 | 0.0220811 | ||||||||
\(967\) | 19.9411 | 0.641263 | 0.320632 | − | 0.947204i | \(-0.396105\pi\) | ||||
0.320632 | + | 0.947204i | \(0.396105\pi\) | |||||||
\(968\) | −16.8995 | −0.543170 | ||||||||
\(969\) | 23.3137 | 0.748944 | ||||||||
\(970\) | −1.51472 | −0.0486347 | ||||||||
\(971\) | −12.2843 | −0.394221 | −0.197111 | − | 0.980381i | \(-0.563156\pi\) | ||||
−0.197111 | + | 0.980381i | \(0.563156\pi\) | |||||||
\(972\) | −18.1005 | −0.580574 | ||||||||
\(973\) | −10.3431 | −0.331586 | ||||||||
\(974\) | 9.51472 | 0.304871 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.0000 | −0.768221 | ||||||||
\(977\) | 56.4853 | 1.80712 | 0.903562 | − | 0.428457i | \(-0.140943\pi\) | ||||
0.903562 | + | 0.428457i | \(0.140943\pi\) | |||||||
\(978\) | −8.76955 | −0.280419 | ||||||||
\(979\) | 3.51472 | 0.112331 | ||||||||
\(980\) | −11.5442 | −0.368765 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | −4.48528 | −0.143131 | ||||||||
\(983\) | 34.9706 | 1.11539 | 0.557694 | − | 0.830047i | \(-0.311686\pi\) | ||||
0.557694 | + | 0.830047i | \(0.311686\pi\) | |||||||
\(984\) | 19.7990 | 0.631169 | ||||||||
\(985\) | −22.9706 | −0.731903 | ||||||||
\(986\) | 11.3137 | 0.360302 | ||||||||
\(987\) | −0.970563 | −0.0308934 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.34315 | −0.138104 | ||||||||
\(990\) | 0.242641 | 0.00771163 | ||||||||
\(991\) | 15.0294 | 0.477426 | 0.238713 | − | 0.971090i | \(-0.423275\pi\) | ||||
0.238713 | + | 0.971090i | \(0.423275\pi\) | |||||||
\(992\) | 45.2132 | 1.43552 | ||||||||
\(993\) | −31.1716 | −0.989200 | ||||||||
\(994\) | −2.71068 | −0.0859775 | ||||||||
\(995\) | −4.00000 | −0.126809 | ||||||||
\(996\) | −22.8284 | −0.723346 | ||||||||
\(997\) | 23.1716 | 0.733851 | 0.366926 | − | 0.930250i | \(-0.380410\pi\) | ||||
0.366926 | + | 0.930250i | \(0.380410\pi\) | |||||||
\(998\) | 4.32590 | 0.136934 | ||||||||
\(999\) | 48.0000 | 1.51865 |
(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 | 845.2.a.g.1.1 | 2 | ||
3.2 | odd | 2 | 7605.2.a.x.1.2 | 2 | |||
5.4 | even | 2 | 4225.2.a.r.1.2 | 2 | |||
13.2 | odd | 12 | 845.2.m.f.316.2 | 8 | |||
13.3 | even | 3 | 845.2.e.c.191.2 | 4 | |||
13.4 | even | 6 | 845.2.e.h.146.1 | 4 | |||
13.5 | odd | 4 | 845.2.c.b.506.3 | 4 | |||
13.6 | odd | 12 | 845.2.m.f.361.3 | 8 | |||
13.7 | odd | 12 | 845.2.m.f.361.2 | 8 | |||
13.8 | odd | 4 | 845.2.c.b.506.2 | 4 | |||
13.9 | even | 3 | 845.2.e.c.146.2 | 4 | |||
13.10 | even | 6 | 845.2.e.h.191.1 | 4 | |||
13.11 | odd | 12 | 845.2.m.f.316.3 | 8 | |||
13.12 | even | 2 | 65.2.a.b.1.2 | ✓ | 2 | ||
39.38 | odd | 2 | 585.2.a.m.1.1 | 2 | |||
52.51 | odd | 2 | 1040.2.a.j.1.1 | 2 | |||
65.12 | odd | 4 | 325.2.b.f.274.3 | 4 | |||
65.38 | odd | 4 | 325.2.b.f.274.2 | 4 | |||
65.64 | even | 2 | 325.2.a.i.1.1 | 2 | |||
91.90 | odd | 2 | 3185.2.a.j.1.2 | 2 | |||
104.51 | odd | 2 | 4160.2.a.z.1.2 | 2 | |||
104.77 | even | 2 | 4160.2.a.bf.1.1 | 2 | |||
143.142 | odd | 2 | 7865.2.a.j.1.1 | 2 | |||
156.155 | even | 2 | 9360.2.a.cd.1.2 | 2 | |||
195.38 | even | 4 | 2925.2.c.r.2224.3 | 4 | |||
195.77 | even | 4 | 2925.2.c.r.2224.2 | 4 | |||
195.194 | odd | 2 | 2925.2.a.u.1.2 | 2 | |||
260.259 | odd | 2 | 5200.2.a.bu.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.b.1.2 | ✓ | 2 | 13.12 | even | 2 | ||
325.2.a.i.1.1 | 2 | 65.64 | even | 2 | |||
325.2.b.f.274.2 | 4 | 65.38 | odd | 4 | |||
325.2.b.f.274.3 | 4 | 65.12 | odd | 4 | |||
585.2.a.m.1.1 | 2 | 39.38 | odd | 2 | |||
845.2.a.g.1.1 | 2 | 1.1 | even | 1 | trivial | ||
845.2.c.b.506.2 | 4 | 13.8 | odd | 4 | |||
845.2.c.b.506.3 | 4 | 13.5 | odd | 4 | |||
845.2.e.c.146.2 | 4 | 13.9 | even | 3 | |||
845.2.e.c.191.2 | 4 | 13.3 | even | 3 | |||
845.2.e.h.146.1 | 4 | 13.4 | even | 6 | |||
845.2.e.h.191.1 | 4 | 13.10 | even | 6 | |||
845.2.m.f.316.2 | 8 | 13.2 | odd | 12 | |||
845.2.m.f.316.3 | 8 | 13.11 | odd | 12 | |||
845.2.m.f.361.2 | 8 | 13.7 | odd | 12 | |||
845.2.m.f.361.3 | 8 | 13.6 | odd | 12 | |||
1040.2.a.j.1.1 | 2 | 52.51 | odd | 2 | |||
2925.2.a.u.1.2 | 2 | 195.194 | odd | 2 | |||
2925.2.c.r.2224.2 | 4 | 195.77 | even | 4 | |||
2925.2.c.r.2224.3 | 4 | 195.38 | even | 4 | |||
3185.2.a.j.1.2 | 2 | 91.90 | odd | 2 | |||
4160.2.a.z.1.2 | 2 | 104.51 | odd | 2 | |||
4160.2.a.bf.1.1 | 2 | 104.77 | even | 2 | |||
4225.2.a.r.1.2 | 2 | 5.4 | even | 2 | |||
5200.2.a.bu.1.2 | 2 | 260.259 | odd | 2 | |||
7605.2.a.x.1.2 | 2 | 3.2 | odd | 2 | |||
7865.2.a.j.1.1 | 2 | 143.142 | odd | 2 | |||
9360.2.a.cd.1.2 | 2 | 156.155 | even | 2 |