Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,2,Mod(1,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, 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("65.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.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: | \(0.519027613138\) |
Analytic rank: | \(0\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 3.41421 | 1.39385 | ||||||||
\(7\) | 4.82843 | 1.82497 | 0.912487 | − | 0.409106i | \(-0.134159\pi\) | ||||
0.912487 | + | 0.409106i | \(0.134159\pi\) | |||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.41421 | −0.763441 | ||||||||
\(11\) | 3.41421 | 1.02942 | 0.514712 | − | 0.857363i | \(-0.327899\pi\) | ||||
0.514712 | + | 0.857363i | \(0.327899\pi\) | |||||||
\(12\) | −5.41421 | −1.56295 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −11.6569 | −3.11543 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 0.828427 | 0.200923 | 0.100462 | − | 0.994941i | \(-0.467968\pi\) | ||||
0.100462 | + | 0.994941i | \(0.467968\pi\) | |||||||
\(18\) | 2.41421 | 0.569036 | ||||||||
\(19\) | 0.585786 | 0.134389 | 0.0671943 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671943 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | −6.82843 | −1.49008 | ||||||||
\(22\) | −8.24264 | −1.75734 | ||||||||
\(23\) | 1.41421 | 0.294884 | 0.147442 | − | 0.989071i | \(-0.452896\pi\) | ||||
0.147442 | + | 0.989071i | \(0.452896\pi\) | |||||||
\(24\) | 6.24264 | 1.27427 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.41421 | 0.473466 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 18.4853 | 3.49339 | ||||||||
\(29\) | −5.65685 | −1.05045 | −0.525226 | − | 0.850963i | \(-0.676019\pi\) | ||||
−0.525226 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(30\) | 3.41421 | 0.623347 | ||||||||
\(31\) | 1.75736 | 0.315631 | 0.157816 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157816 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | −4.82843 | −0.840521 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 4.82843 | 0.816153 | ||||||||
\(36\) | −3.82843 | −0.638071 | ||||||||
\(37\) | −8.48528 | −1.39497 | −0.697486 | − | 0.716599i | \(-0.745698\pi\) | ||||
−0.697486 | + | 0.716599i | \(0.745698\pi\) | |||||||
\(38\) | −1.41421 | −0.229416 | ||||||||
\(39\) | 1.41421 | 0.226455 | ||||||||
\(40\) | −4.41421 | −0.697948 | ||||||||
\(41\) | −3.17157 | −0.495316 | −0.247658 | − | 0.968847i | \(-0.579661\pi\) | ||||
−0.247658 | + | 0.968847i | \(0.579661\pi\) | |||||||
\(42\) | 16.4853 | 2.54373 | ||||||||
\(43\) | −11.0711 | −1.68832 | −0.844161 | − | 0.536090i | \(-0.819901\pi\) | ||||
−0.844161 | + | 0.536090i | \(0.819901\pi\) | |||||||
\(44\) | 13.0711 | 1.97054 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −3.41421 | −0.503398 | ||||||||
\(47\) | −4.82843 | −0.704298 | −0.352149 | − | 0.935944i | \(-0.614549\pi\) | ||||
−0.352149 | + | 0.935944i | \(0.614549\pi\) | |||||||
\(48\) | −4.24264 | −0.612372 | ||||||||
\(49\) | 16.3137 | 2.33053 | ||||||||
\(50\) | −2.41421 | −0.341421 | ||||||||
\(51\) | −1.17157 | −0.164053 | ||||||||
\(52\) | −3.82843 | −0.530907 | ||||||||
\(53\) | 2.48528 | 0.341380 | 0.170690 | − | 0.985325i | \(-0.445400\pi\) | ||||
0.170690 | + | 0.985325i | \(0.445400\pi\) | |||||||
\(54\) | −13.6569 | −1.85846 | ||||||||
\(55\) | 3.41421 | 0.460372 | ||||||||
\(56\) | −21.3137 | −2.84816 | ||||||||
\(57\) | −0.828427 | −0.109728 | ||||||||
\(58\) | 13.6569 | 1.79323 | ||||||||
\(59\) | 1.75736 | 0.228789 | 0.114394 | − | 0.993435i | \(-0.463507\pi\) | ||||
0.114394 | + | 0.993435i | \(0.463507\pi\) | |||||||
\(60\) | −5.41421 | −0.698972 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | −4.24264 | −0.538816 | ||||||||
\(63\) | −4.82843 | −0.608325 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 11.6569 | 1.43486 | ||||||||
\(67\) | −2.00000 | −0.244339 | −0.122169 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122169 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(68\) | 3.17157 | 0.384610 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | −11.6569 | −1.39326 | ||||||||
\(71\) | 11.8995 | 1.41221 | 0.706105 | − | 0.708107i | \(-0.250451\pi\) | ||||
0.706105 | + | 0.708107i | \(0.250451\pi\) | |||||||
\(72\) | 4.41421 | 0.520220 | ||||||||
\(73\) | 8.48528 | 0.993127 | 0.496564 | − | 0.868000i | \(-0.334595\pi\) | ||||
0.496564 | + | 0.868000i | \(0.334595\pi\) | |||||||
\(74\) | 20.4853 | 2.38137 | ||||||||
\(75\) | −1.41421 | −0.163299 | ||||||||
\(76\) | 2.24264 | 0.257249 | ||||||||
\(77\) | 16.4853 | 1.87867 | ||||||||
\(78\) | −3.41421 | −0.386584 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 7.65685 | 0.845558 | ||||||||
\(83\) | −3.17157 | −0.348125 | −0.174063 | − | 0.984735i | \(-0.555690\pi\) | ||||
−0.174063 | + | 0.984735i | \(0.555690\pi\) | |||||||
\(84\) | −26.1421 | −2.85234 | ||||||||
\(85\) | 0.828427 | 0.0898555 | ||||||||
\(86\) | 26.7279 | 2.88215 | ||||||||
\(87\) | 8.00000 | 0.857690 | ||||||||
\(88\) | −15.0711 | −1.60658 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 2.41421 | 0.254480 | ||||||||
\(91\) | −4.82843 | −0.506157 | ||||||||
\(92\) | 5.41421 | 0.564471 | ||||||||
\(93\) | −2.48528 | −0.257712 | ||||||||
\(94\) | 11.6569 | 1.20231 | ||||||||
\(95\) | 0.585786 | 0.0601004 | ||||||||
\(96\) | −2.24264 | −0.228889 | ||||||||
\(97\) | −7.65685 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(98\) | −39.3848 | −3.97846 | ||||||||
\(99\) | −3.41421 | −0.343141 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | −3.65685 | −0.363871 | −0.181935 | − | 0.983311i | \(-0.558236\pi\) | ||||
−0.181935 | + | 0.983311i | \(0.558236\pi\) | |||||||
\(102\) | 2.82843 | 0.280056 | ||||||||
\(103\) | 14.5858 | 1.43718 | 0.718590 | − | 0.695434i | \(-0.244788\pi\) | ||||
0.718590 | + | 0.695434i | \(0.244788\pi\) | |||||||
\(104\) | 4.41421 | 0.432849 | ||||||||
\(105\) | −6.82843 | −0.666386 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −9.41421 | −0.910106 | −0.455053 | − | 0.890464i | \(-0.650380\pi\) | ||||
−0.455053 | + | 0.890464i | \(0.650380\pi\) | |||||||
\(108\) | 21.6569 | 2.08393 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −8.24264 | −0.785905 | ||||||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | 14.4853 | 1.36873 | ||||||||
\(113\) | −8.82843 | −0.830509 | −0.415254 | − | 0.909705i | \(-0.636307\pi\) | ||||
−0.415254 | + | 0.909705i | \(0.636307\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | 1.41421 | 0.131876 | ||||||||
\(116\) | −21.6569 | −2.01079 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −4.24264 | −0.390567 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 6.24264 | 0.569873 | ||||||||
\(121\) | 0.656854 | 0.0597140 | ||||||||
\(122\) | 19.3137 | 1.74858 | ||||||||
\(123\) | 4.48528 | 0.404424 | ||||||||
\(124\) | 6.72792 | 0.604185 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 11.6569 | 1.03848 | ||||||||
\(127\) | −6.58579 | −0.584394 | −0.292197 | − | 0.956358i | \(-0.594386\pi\) | ||||
−0.292197 | + | 0.956358i | \(0.594386\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | 15.6569 | 1.37851 | ||||||||
\(130\) | 2.41421 | 0.211741 | ||||||||
\(131\) | −16.9706 | −1.48272 | −0.741362 | − | 0.671105i | \(-0.765820\pi\) | ||||
−0.741362 | + | 0.671105i | \(0.765820\pi\) | |||||||
\(132\) | −18.4853 | −1.60894 | ||||||||
\(133\) | 2.82843 | 0.245256 | ||||||||
\(134\) | 4.82843 | 0.417113 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | −3.65685 | −0.313573 | ||||||||
\(137\) | −17.3137 | −1.47921 | −0.739605 | − | 0.673041i | \(-0.764988\pi\) | ||||
−0.739605 | + | 0.673041i | \(0.764988\pi\) | |||||||
\(138\) | 4.82843 | 0.411023 | ||||||||
\(139\) | 4.48528 | 0.380437 | 0.190218 | − | 0.981742i | \(-0.439080\pi\) | ||||
0.190218 | + | 0.981742i | \(0.439080\pi\) | |||||||
\(140\) | 18.4853 | 1.56229 | ||||||||
\(141\) | 6.82843 | 0.575057 | ||||||||
\(142\) | −28.7279 | −2.41079 | ||||||||
\(143\) | −3.41421 | −0.285511 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | −5.65685 | −0.469776 | ||||||||
\(146\) | −20.4853 | −1.69537 | ||||||||
\(147\) | −23.0711 | −1.90287 | ||||||||
\(148\) | −32.4853 | −2.67027 | ||||||||
\(149\) | −11.6569 | −0.954967 | −0.477483 | − | 0.878641i | \(-0.658451\pi\) | ||||
−0.477483 | + | 0.878641i | \(0.658451\pi\) | |||||||
\(150\) | 3.41421 | 0.278769 | ||||||||
\(151\) | 9.75736 | 0.794043 | 0.397021 | − | 0.917809i | \(-0.370044\pi\) | ||||
0.397021 | + | 0.917809i | \(0.370044\pi\) | |||||||
\(152\) | −2.58579 | −0.209735 | ||||||||
\(153\) | −0.828427 | −0.0669744 | ||||||||
\(154\) | −39.7990 | −3.20709 | ||||||||
\(155\) | 1.75736 | 0.141154 | ||||||||
\(156\) | 5.41421 | 0.433484 | ||||||||
\(157\) | 18.0000 | 1.43656 | 0.718278 | − | 0.695756i | \(-0.244931\pi\) | ||||
0.718278 | + | 0.695756i | \(0.244931\pi\) | |||||||
\(158\) | 20.4853 | 1.62972 | ||||||||
\(159\) | −3.51472 | −0.278735 | ||||||||
\(160\) | 1.58579 | 0.125367 | ||||||||
\(161\) | 6.82843 | 0.538155 | ||||||||
\(162\) | 12.0711 | 0.948393 | ||||||||
\(163\) | 18.9706 | 1.48589 | 0.742945 | − | 0.669353i | \(-0.233429\pi\) | ||||
0.742945 | + | 0.669353i | \(0.233429\pi\) | |||||||
\(164\) | −12.1421 | −0.948141 | ||||||||
\(165\) | −4.82843 | −0.375893 | ||||||||
\(166\) | 7.65685 | 0.594287 | ||||||||
\(167\) | −3.17157 | −0.245424 | −0.122712 | − | 0.992442i | \(-0.539159\pi\) | ||||
−0.122712 | + | 0.992442i | \(0.539159\pi\) | |||||||
\(168\) | 30.1421 | 2.32552 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | −0.585786 | −0.0447962 | ||||||||
\(172\) | −42.3848 | −3.23181 | ||||||||
\(173\) | 16.8284 | 1.27944 | 0.639721 | − | 0.768607i | \(-0.279050\pi\) | ||||
0.639721 | + | 0.768607i | \(0.279050\pi\) | |||||||
\(174\) | −19.3137 | −1.46417 | ||||||||
\(175\) | 4.82843 | 0.364995 | ||||||||
\(176\) | 10.2426 | 0.772068 | ||||||||
\(177\) | −2.48528 | −0.186805 | ||||||||
\(178\) | −14.4853 | −1.08572 | ||||||||
\(179\) | 5.65685 | 0.422813 | 0.211407 | − | 0.977398i | \(-0.432196\pi\) | ||||
0.211407 | + | 0.977398i | \(0.432196\pi\) | |||||||
\(180\) | −3.82843 | −0.285354 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 11.6569 | 0.864064 | ||||||||
\(183\) | 11.3137 | 0.836333 | ||||||||
\(184\) | −6.24264 | −0.460214 | ||||||||
\(185\) | −8.48528 | −0.623850 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 2.82843 | 0.206835 | ||||||||
\(188\) | −18.4853 | −1.34818 | ||||||||
\(189\) | 27.3137 | 1.98678 | ||||||||
\(190\) | −1.41421 | −0.102598 | ||||||||
\(191\) | 2.34315 | 0.169544 | 0.0847720 | − | 0.996400i | \(-0.472984\pi\) | ||||
0.0847720 | + | 0.996400i | \(0.472984\pi\) | |||||||
\(192\) | 13.8995 | 1.00311 | ||||||||
\(193\) | 4.34315 | 0.312626 | 0.156313 | − | 0.987708i | \(-0.450039\pi\) | ||||
0.156313 | + | 0.987708i | \(0.450039\pi\) | |||||||
\(194\) | 18.4853 | 1.32717 | ||||||||
\(195\) | 1.41421 | 0.101274 | ||||||||
\(196\) | 62.4558 | 4.46113 | ||||||||
\(197\) | 10.9706 | 0.781620 | 0.390810 | − | 0.920471i | \(-0.372195\pi\) | ||||
0.390810 | + | 0.920471i | \(0.372195\pi\) | |||||||
\(198\) | 8.24264 | 0.585779 | ||||||||
\(199\) | 4.00000 | 0.283552 | 0.141776 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141776 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(200\) | −4.41421 | −0.312132 | ||||||||
\(201\) | 2.82843 | 0.199502 | ||||||||
\(202\) | 8.82843 | 0.621166 | ||||||||
\(203\) | −27.3137 | −1.91705 | ||||||||
\(204\) | −4.48528 | −0.314033 | ||||||||
\(205\) | −3.17157 | −0.221512 | ||||||||
\(206\) | −35.2132 | −2.45342 | ||||||||
\(207\) | −1.41421 | −0.0982946 | ||||||||
\(208\) | −3.00000 | −0.208013 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 16.4853 | 1.13759 | ||||||||
\(211\) | 3.31371 | 0.228125 | 0.114063 | − | 0.993474i | \(-0.463614\pi\) | ||||
0.114063 | + | 0.993474i | \(0.463614\pi\) | |||||||
\(212\) | 9.51472 | 0.653474 | ||||||||
\(213\) | −16.8284 | −1.15306 | ||||||||
\(214\) | 22.7279 | 1.55365 | ||||||||
\(215\) | −11.0711 | −0.755041 | ||||||||
\(216\) | −24.9706 | −1.69903 | ||||||||
\(217\) | 8.48528 | 0.576018 | ||||||||
\(218\) | 4.82843 | 0.327022 | ||||||||
\(219\) | −12.0000 | −0.810885 | ||||||||
\(220\) | 13.0711 | 0.881251 | ||||||||
\(221\) | −0.828427 | −0.0557260 | ||||||||
\(222\) | −28.9706 | −1.94438 | ||||||||
\(223\) | 9.51472 | 0.637153 | 0.318576 | − | 0.947897i | \(-0.396795\pi\) | ||||
0.318576 | + | 0.947897i | \(0.396795\pi\) | |||||||
\(224\) | 7.65685 | 0.511595 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 21.3137 | 1.41777 | ||||||||
\(227\) | −16.3431 | −1.08473 | −0.542366 | − | 0.840142i | \(-0.682472\pi\) | ||||
−0.542366 | + | 0.840142i | \(0.682472\pi\) | |||||||
\(228\) | −3.17157 | −0.210043 | ||||||||
\(229\) | −4.82843 | −0.319071 | −0.159536 | − | 0.987192i | \(-0.551000\pi\) | ||||
−0.159536 | + | 0.987192i | \(0.551000\pi\) | |||||||
\(230\) | −3.41421 | −0.225127 | ||||||||
\(231\) | −23.3137 | −1.53393 | ||||||||
\(232\) | 24.9706 | 1.63940 | ||||||||
\(233\) | −20.6274 | −1.35135 | −0.675674 | − | 0.737201i | \(-0.736147\pi\) | ||||
−0.675674 | + | 0.737201i | \(0.736147\pi\) | |||||||
\(234\) | −2.41421 | −0.157822 | ||||||||
\(235\) | −4.82843 | −0.314972 | ||||||||
\(236\) | 6.72792 | 0.437950 | ||||||||
\(237\) | 12.0000 | 0.779484 | ||||||||
\(238\) | −9.65685 | −0.625961 | ||||||||
\(239\) | −3.41421 | −0.220847 | −0.110424 | − | 0.993885i | \(-0.535221\pi\) | ||||
−0.110424 | + | 0.993885i | \(0.535221\pi\) | |||||||
\(240\) | −4.24264 | −0.273861 | ||||||||
\(241\) | −14.4853 | −0.933079 | −0.466539 | − | 0.884500i | \(-0.654499\pi\) | ||||
−0.466539 | + | 0.884500i | \(0.654499\pi\) | |||||||
\(242\) | −1.58579 | −0.101938 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | −30.6274 | −1.96072 | ||||||||
\(245\) | 16.3137 | 1.04224 | ||||||||
\(246\) | −10.8284 | −0.690395 | ||||||||
\(247\) | −0.585786 | −0.0372727 | ||||||||
\(248\) | −7.75736 | −0.492593 | ||||||||
\(249\) | 4.48528 | 0.284243 | ||||||||
\(250\) | −2.41421 | −0.152688 | ||||||||
\(251\) | 19.7990 | 1.24970 | 0.624851 | − | 0.780744i | \(-0.285160\pi\) | ||||
0.624851 | + | 0.780744i | \(0.285160\pi\) | |||||||
\(252\) | −18.4853 | −1.16446 | ||||||||
\(253\) | 4.82843 | 0.303561 | ||||||||
\(254\) | 15.8995 | 0.997623 | ||||||||
\(255\) | −1.17157 | −0.0733667 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 27.6569 | 1.72519 | 0.862594 | − | 0.505898i | \(-0.168839\pi\) | ||||
0.862594 | + | 0.505898i | \(0.168839\pi\) | |||||||
\(258\) | −37.7990 | −2.35326 | ||||||||
\(259\) | −40.9706 | −2.54579 | ||||||||
\(260\) | −3.82843 | −0.237429 | ||||||||
\(261\) | 5.65685 | 0.350150 | ||||||||
\(262\) | 40.9706 | 2.53117 | ||||||||
\(263\) | −10.5858 | −0.652748 | −0.326374 | − | 0.945241i | \(-0.605827\pi\) | ||||
−0.326374 | + | 0.945241i | \(0.605827\pi\) | |||||||
\(264\) | 21.3137 | 1.31177 | ||||||||
\(265\) | 2.48528 | 0.152670 | ||||||||
\(266\) | −6.82843 | −0.418678 | ||||||||
\(267\) | −8.48528 | −0.519291 | ||||||||
\(268\) | −7.65685 | −0.467717 | ||||||||
\(269\) | −25.3137 | −1.54340 | −0.771702 | − | 0.635984i | \(-0.780594\pi\) | ||||
−0.771702 | + | 0.635984i | \(0.780594\pi\) | |||||||
\(270\) | −13.6569 | −0.831130 | ||||||||
\(271\) | 26.7279 | 1.62361 | 0.811803 | − | 0.583932i | \(-0.198486\pi\) | ||||
0.811803 | + | 0.583932i | \(0.198486\pi\) | |||||||
\(272\) | 2.48528 | 0.150692 | ||||||||
\(273\) | 6.82843 | 0.413275 | ||||||||
\(274\) | 41.7990 | 2.52517 | ||||||||
\(275\) | 3.41421 | 0.205885 | ||||||||
\(276\) | −7.65685 | −0.460888 | ||||||||
\(277\) | −12.8284 | −0.770785 | −0.385393 | − | 0.922753i | \(-0.625934\pi\) | ||||
−0.385393 | + | 0.922753i | \(0.625934\pi\) | |||||||
\(278\) | −10.8284 | −0.649446 | ||||||||
\(279\) | −1.75736 | −0.105210 | ||||||||
\(280\) | −21.3137 | −1.27374 | ||||||||
\(281\) | 21.7990 | 1.30042 | 0.650209 | − | 0.759755i | \(-0.274681\pi\) | ||||
0.650209 | + | 0.759755i | \(0.274681\pi\) | |||||||
\(282\) | −16.4853 | −0.981684 | ||||||||
\(283\) | −16.7279 | −0.994372 | −0.497186 | − | 0.867644i | \(-0.665633\pi\) | ||||
−0.497186 | + | 0.867644i | \(0.665633\pi\) | |||||||
\(284\) | 45.5563 | 2.70327 | ||||||||
\(285\) | −0.828427 | −0.0490718 | ||||||||
\(286\) | 8.24264 | 0.487398 | ||||||||
\(287\) | −15.3137 | −0.903940 | ||||||||
\(288\) | −1.58579 | −0.0934434 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 13.6569 | 0.801958 | ||||||||
\(291\) | 10.8284 | 0.634774 | ||||||||
\(292\) | 32.4853 | 1.90106 | ||||||||
\(293\) | 26.1421 | 1.52724 | 0.763620 | − | 0.645666i | \(-0.223420\pi\) | ||||
0.763620 | + | 0.645666i | \(0.223420\pi\) | |||||||
\(294\) | 55.6985 | 3.24840 | ||||||||
\(295\) | 1.75736 | 0.102317 | ||||||||
\(296\) | 37.4558 | 2.17708 | ||||||||
\(297\) | 19.3137 | 1.12070 | ||||||||
\(298\) | 28.1421 | 1.63023 | ||||||||
\(299\) | −1.41421 | −0.0817861 | ||||||||
\(300\) | −5.41421 | −0.312590 | ||||||||
\(301\) | −53.4558 | −3.08114 | ||||||||
\(302\) | −23.5563 | −1.35552 | ||||||||
\(303\) | 5.17157 | 0.297099 | ||||||||
\(304\) | 1.75736 | 0.100791 | ||||||||
\(305\) | −8.00000 | −0.458079 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | 24.8284 | 1.41703 | 0.708517 | − | 0.705694i | \(-0.249365\pi\) | ||||
0.708517 | + | 0.705694i | \(0.249365\pi\) | |||||||
\(308\) | 63.1127 | 3.59618 | ||||||||
\(309\) | −20.6274 | −1.17345 | ||||||||
\(310\) | −4.24264 | −0.240966 | ||||||||
\(311\) | 8.48528 | 0.481156 | 0.240578 | − | 0.970630i | \(-0.422663\pi\) | ||||
0.240578 | + | 0.970630i | \(0.422663\pi\) | |||||||
\(312\) | −6.24264 | −0.353420 | ||||||||
\(313\) | −4.82843 | −0.272919 | −0.136459 | − | 0.990646i | \(-0.543572\pi\) | ||||
−0.136459 | + | 0.990646i | \(0.543572\pi\) | |||||||
\(314\) | −43.4558 | −2.45236 | ||||||||
\(315\) | −4.82843 | −0.272051 | ||||||||
\(316\) | −32.4853 | −1.82744 | ||||||||
\(317\) | −2.14214 | −0.120314 | −0.0601572 | − | 0.998189i | \(-0.519160\pi\) | ||||
−0.0601572 | + | 0.998189i | \(0.519160\pi\) | |||||||
\(318\) | 8.48528 | 0.475831 | ||||||||
\(319\) | −19.3137 | −1.08136 | ||||||||
\(320\) | −9.82843 | −0.549426 | ||||||||
\(321\) | 13.3137 | 0.743099 | ||||||||
\(322\) | −16.4853 | −0.918689 | ||||||||
\(323\) | 0.485281 | 0.0270018 | ||||||||
\(324\) | −19.1421 | −1.06345 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −45.7990 | −2.53657 | ||||||||
\(327\) | 2.82843 | 0.156412 | ||||||||
\(328\) | 14.0000 | 0.773021 | ||||||||
\(329\) | −23.3137 | −1.28533 | ||||||||
\(330\) | 11.6569 | 0.641689 | ||||||||
\(331\) | −26.0416 | −1.43138 | −0.715689 | − | 0.698419i | \(-0.753887\pi\) | ||||
−0.715689 | + | 0.698419i | \(0.753887\pi\) | |||||||
\(332\) | −12.1421 | −0.666386 | ||||||||
\(333\) | 8.48528 | 0.464991 | ||||||||
\(334\) | 7.65685 | 0.418964 | ||||||||
\(335\) | −2.00000 | −0.109272 | ||||||||
\(336\) | −20.4853 | −1.11756 | ||||||||
\(337\) | 12.8284 | 0.698809 | 0.349404 | − | 0.936972i | \(-0.386384\pi\) | ||||
0.349404 | + | 0.936972i | \(0.386384\pi\) | |||||||
\(338\) | −2.41421 | −0.131316 | ||||||||
\(339\) | 12.4853 | 0.678107 | ||||||||
\(340\) | 3.17157 | 0.172003 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 1.41421 | 0.0764719 | ||||||||
\(343\) | 44.9706 | 2.42818 | ||||||||
\(344\) | 48.8701 | 2.63490 | ||||||||
\(345\) | −2.00000 | −0.107676 | ||||||||
\(346\) | −40.6274 | −2.18414 | ||||||||
\(347\) | −4.24264 | −0.227757 | −0.113878 | − | 0.993495i | \(-0.536327\pi\) | ||||
−0.113878 | + | 0.993495i | \(0.536327\pi\) | |||||||
\(348\) | 30.6274 | 1.64180 | ||||||||
\(349\) | 18.4853 | 0.989494 | 0.494747 | − | 0.869037i | \(-0.335261\pi\) | ||||
0.494747 | + | 0.869037i | \(0.335261\pi\) | |||||||
\(350\) | −11.6569 | −0.623085 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | 5.41421 | 0.288579 | ||||||||
\(353\) | 14.8284 | 0.789238 | 0.394619 | − | 0.918845i | \(-0.370877\pi\) | ||||
0.394619 | + | 0.918845i | \(0.370877\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | 11.8995 | 0.631560 | ||||||||
\(356\) | 22.9706 | 1.21744 | ||||||||
\(357\) | −5.65685 | −0.299392 | ||||||||
\(358\) | −13.6569 | −0.721787 | ||||||||
\(359\) | −8.10051 | −0.427528 | −0.213764 | − | 0.976885i | \(-0.568572\pi\) | ||||
−0.213764 | + | 0.976885i | \(0.568572\pi\) | |||||||
\(360\) | 4.41421 | 0.232649 | ||||||||
\(361\) | −18.6569 | −0.981940 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.928932 | −0.0487563 | ||||||||
\(364\) | −18.4853 | −0.968892 | ||||||||
\(365\) | 8.48528 | 0.444140 | ||||||||
\(366\) | −27.3137 | −1.42771 | ||||||||
\(367\) | 35.5563 | 1.85603 | 0.928013 | − | 0.372547i | \(-0.121516\pi\) | ||||
0.928013 | + | 0.372547i | \(0.121516\pi\) | |||||||
\(368\) | 4.24264 | 0.221163 | ||||||||
\(369\) | 3.17157 | 0.165105 | ||||||||
\(370\) | 20.4853 | 1.06498 | ||||||||
\(371\) | 12.0000 | 0.623009 | ||||||||
\(372\) | −9.51472 | −0.493315 | ||||||||
\(373\) | −2.68629 | −0.139091 | −0.0695455 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695455 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(374\) | −6.82843 | −0.353090 | ||||||||
\(375\) | −1.41421 | −0.0730297 | ||||||||
\(376\) | 21.3137 | 1.09917 | ||||||||
\(377\) | 5.65685 | 0.291343 | ||||||||
\(378\) | −65.9411 | −3.39165 | ||||||||
\(379\) | 29.0711 | 1.49328 | 0.746640 | − | 0.665228i | \(-0.231666\pi\) | ||||
0.746640 | + | 0.665228i | \(0.231666\pi\) | |||||||
\(380\) | 2.24264 | 0.115045 | ||||||||
\(381\) | 9.31371 | 0.477156 | ||||||||
\(382\) | −5.65685 | −0.289430 | ||||||||
\(383\) | −29.1127 | −1.48759 | −0.743795 | − | 0.668408i | \(-0.766976\pi\) | ||||
−0.743795 | + | 0.668408i | \(0.766976\pi\) | |||||||
\(384\) | −29.0711 | −1.48353 | ||||||||
\(385\) | 16.4853 | 0.840168 | ||||||||
\(386\) | −10.4853 | −0.533687 | ||||||||
\(387\) | 11.0711 | 0.562774 | ||||||||
\(388\) | −29.3137 | −1.48818 | ||||||||
\(389\) | 28.6274 | 1.45147 | 0.725734 | − | 0.687976i | \(-0.241500\pi\) | ||||
0.725734 | + | 0.687976i | \(0.241500\pi\) | |||||||
\(390\) | −3.41421 | −0.172885 | ||||||||
\(391\) | 1.17157 | 0.0592490 | ||||||||
\(392\) | −72.0122 | −3.63717 | ||||||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | −26.4853 | −1.33431 | ||||||||
\(395\) | −8.48528 | −0.426941 | ||||||||
\(396\) | −13.0711 | −0.656846 | ||||||||
\(397\) | 11.7990 | 0.592174 | 0.296087 | − | 0.955161i | \(-0.404318\pi\) | ||||
0.296087 | + | 0.955161i | \(0.404318\pi\) | |||||||
\(398\) | −9.65685 | −0.484054 | ||||||||
\(399\) | −4.00000 | −0.200250 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | −5.31371 | −0.265354 | −0.132677 | − | 0.991159i | \(-0.542357\pi\) | ||||
−0.132677 | + | 0.991159i | \(0.542357\pi\) | |||||||
\(402\) | −6.82843 | −0.340571 | ||||||||
\(403\) | −1.75736 | −0.0875403 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | −5.00000 | −0.248452 | ||||||||
\(406\) | 65.9411 | 3.27260 | ||||||||
\(407\) | −28.9706 | −1.43602 | ||||||||
\(408\) | 5.17157 | 0.256031 | ||||||||
\(409\) | 7.17157 | 0.354611 | 0.177306 | − | 0.984156i | \(-0.443262\pi\) | ||||
0.177306 | + | 0.984156i | \(0.443262\pi\) | |||||||
\(410\) | 7.65685 | 0.378145 | ||||||||
\(411\) | 24.4853 | 1.20777 | ||||||||
\(412\) | 55.8406 | 2.75107 | ||||||||
\(413\) | 8.48528 | 0.417533 | ||||||||
\(414\) | 3.41421 | 0.167799 | ||||||||
\(415\) | −3.17157 | −0.155686 | ||||||||
\(416\) | −1.58579 | −0.0777496 | ||||||||
\(417\) | −6.34315 | −0.310625 | ||||||||
\(418\) | −4.82843 | −0.236166 | ||||||||
\(419\) | 10.8284 | 0.529003 | 0.264502 | − | 0.964385i | \(-0.414793\pi\) | ||||
0.264502 | + | 0.964385i | \(0.414793\pi\) | |||||||
\(420\) | −26.1421 | −1.27561 | ||||||||
\(421\) | −34.9706 | −1.70436 | −0.852180 | − | 0.523248i | \(-0.824720\pi\) | ||||
−0.852180 | + | 0.523248i | \(0.824720\pi\) | |||||||
\(422\) | −8.00000 | −0.389434 | ||||||||
\(423\) | 4.82843 | 0.234766 | ||||||||
\(424\) | −10.9706 | −0.532778 | ||||||||
\(425\) | 0.828427 | 0.0401846 | ||||||||
\(426\) | 40.6274 | 1.96840 | ||||||||
\(427\) | −38.6274 | −1.86931 | ||||||||
\(428\) | −36.0416 | −1.74214 | ||||||||
\(429\) | 4.82843 | 0.233119 | ||||||||
\(430\) | 26.7279 | 1.28893 | ||||||||
\(431\) | 40.3848 | 1.94527 | 0.972633 | − | 0.232346i | \(-0.0746403\pi\) | ||||
0.972633 | + | 0.232346i | \(0.0746403\pi\) | |||||||
\(432\) | 16.9706 | 0.816497 | ||||||||
\(433\) | 7.65685 | 0.367965 | 0.183982 | − | 0.982930i | \(-0.441101\pi\) | ||||
0.183982 | + | 0.982930i | \(0.441101\pi\) | |||||||
\(434\) | −20.4853 | −0.983325 | ||||||||
\(435\) | 8.00000 | 0.383571 | ||||||||
\(436\) | −7.65685 | −0.366697 | ||||||||
\(437\) | 0.828427 | 0.0396290 | ||||||||
\(438\) | 28.9706 | 1.38427 | ||||||||
\(439\) | 0.970563 | 0.0463224 | 0.0231612 | − | 0.999732i | \(-0.492627\pi\) | ||||
0.0231612 | + | 0.999732i | \(0.492627\pi\) | |||||||
\(440\) | −15.0711 | −0.718485 | ||||||||
\(441\) | −16.3137 | −0.776843 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | −9.41421 | −0.447283 | −0.223641 | − | 0.974671i | \(-0.571794\pi\) | ||||
−0.223641 | + | 0.974671i | \(0.571794\pi\) | |||||||
\(444\) | 45.9411 | 2.18027 | ||||||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | −22.9706 | −1.08769 | ||||||||
\(447\) | 16.4853 | 0.779727 | ||||||||
\(448\) | −47.4558 | −2.24208 | ||||||||
\(449\) | −33.1127 | −1.56268 | −0.781342 | − | 0.624103i | \(-0.785465\pi\) | ||||
−0.781342 | + | 0.624103i | \(0.785465\pi\) | |||||||
\(450\) | 2.41421 | 0.113807 | ||||||||
\(451\) | −10.8284 | −0.509891 | ||||||||
\(452\) | −33.7990 | −1.58977 | ||||||||
\(453\) | −13.7990 | −0.648333 | ||||||||
\(454\) | 39.4558 | 1.85175 | ||||||||
\(455\) | −4.82843 | −0.226360 | ||||||||
\(456\) | 3.65685 | 0.171248 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | 11.6569 | 0.544689 | ||||||||
\(459\) | 4.68629 | 0.218737 | ||||||||
\(460\) | 5.41421 | 0.252439 | ||||||||
\(461\) | 9.51472 | 0.443145 | 0.221572 | − | 0.975144i | \(-0.428881\pi\) | ||||
0.221572 | + | 0.975144i | \(0.428881\pi\) | |||||||
\(462\) | 56.2843 | 2.61858 | ||||||||
\(463\) | −4.34315 | −0.201843 | −0.100922 | − | 0.994894i | \(-0.532179\pi\) | ||||
−0.100922 | + | 0.994894i | \(0.532179\pi\) | |||||||
\(464\) | −16.9706 | −0.787839 | ||||||||
\(465\) | −2.48528 | −0.115252 | ||||||||
\(466\) | 49.7990 | 2.30689 | ||||||||
\(467\) | −13.4142 | −0.620736 | −0.310368 | − | 0.950617i | \(-0.600452\pi\) | ||||
−0.310368 | + | 0.950617i | \(0.600452\pi\) | |||||||
\(468\) | 3.82843 | 0.176969 | ||||||||
\(469\) | −9.65685 | −0.445912 | ||||||||
\(470\) | 11.6569 | 0.537691 | ||||||||
\(471\) | −25.4558 | −1.17294 | ||||||||
\(472\) | −7.75736 | −0.357061 | ||||||||
\(473\) | −37.7990 | −1.73800 | ||||||||
\(474\) | −28.9706 | −1.33066 | ||||||||
\(475\) | 0.585786 | 0.0268777 | ||||||||
\(476\) | 15.3137 | 0.701903 | ||||||||
\(477\) | −2.48528 | −0.113793 | ||||||||
\(478\) | 8.24264 | 0.377010 | ||||||||
\(479\) | −30.7279 | −1.40399 | −0.701997 | − | 0.712180i | \(-0.747708\pi\) | ||||
−0.701997 | + | 0.712180i | \(0.747708\pi\) | |||||||
\(480\) | −2.24264 | −0.102362 | ||||||||
\(481\) | 8.48528 | 0.386896 | ||||||||
\(482\) | 34.9706 | 1.59287 | ||||||||
\(483\) | −9.65685 | −0.439402 | ||||||||
\(484\) | 2.51472 | 0.114305 | ||||||||
\(485\) | −7.65685 | −0.347680 | ||||||||
\(486\) | 23.8995 | 1.08410 | ||||||||
\(487\) | −10.9706 | −0.497124 | −0.248562 | − | 0.968616i | \(-0.579958\pi\) | ||||
−0.248562 | + | 0.968616i | \(0.579958\pi\) | |||||||
\(488\) | 35.3137 | 1.59858 | ||||||||
\(489\) | −26.8284 | −1.21322 | ||||||||
\(490\) | −39.3848 | −1.77922 | ||||||||
\(491\) | 5.17157 | 0.233390 | 0.116695 | − | 0.993168i | \(-0.462770\pi\) | ||||
0.116695 | + | 0.993168i | \(0.462770\pi\) | |||||||
\(492\) | 17.1716 | 0.774154 | ||||||||
\(493\) | −4.68629 | −0.211060 | ||||||||
\(494\) | 1.41421 | 0.0636285 | ||||||||
\(495\) | −3.41421 | −0.153457 | ||||||||
\(496\) | 5.27208 | 0.236723 | ||||||||
\(497\) | 57.4558 | 2.57725 | ||||||||
\(498\) | −10.8284 | −0.485233 | ||||||||
\(499\) | 41.5563 | 1.86032 | 0.930159 | − | 0.367157i | \(-0.119669\pi\) | ||||
0.930159 | + | 0.367157i | \(0.119669\pi\) | |||||||
\(500\) | 3.82843 | 0.171212 | ||||||||
\(501\) | 4.48528 | 0.200388 | ||||||||
\(502\) | −47.7990 | −2.13337 | ||||||||
\(503\) | 37.8995 | 1.68985 | 0.844927 | − | 0.534881i | \(-0.179644\pi\) | ||||
0.844927 | + | 0.534881i | \(0.179644\pi\) | |||||||
\(504\) | 21.3137 | 0.949388 | ||||||||
\(505\) | −3.65685 | −0.162728 | ||||||||
\(506\) | −11.6569 | −0.518210 | ||||||||
\(507\) | −1.41421 | −0.0628074 | ||||||||
\(508\) | −25.2132 | −1.11866 | ||||||||
\(509\) | 41.1127 | 1.82229 | 0.911144 | − | 0.412088i | \(-0.135200\pi\) | ||||
0.911144 | + | 0.412088i | \(0.135200\pi\) | |||||||
\(510\) | 2.82843 | 0.125245 | ||||||||
\(511\) | 40.9706 | 1.81243 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 3.31371 | 0.146304 | ||||||||
\(514\) | −66.7696 | −2.94508 | ||||||||
\(515\) | 14.5858 | 0.642727 | ||||||||
\(516\) | 59.9411 | 2.63876 | ||||||||
\(517\) | −16.4853 | −0.725022 | ||||||||
\(518\) | 98.9117 | 4.34593 | ||||||||
\(519\) | −23.7990 | −1.04466 | ||||||||
\(520\) | 4.41421 | 0.193576 | ||||||||
\(521\) | −17.6569 | −0.773561 | −0.386780 | − | 0.922172i | \(-0.626413\pi\) | ||||
−0.386780 | + | 0.922172i | \(0.626413\pi\) | |||||||
\(522\) | −13.6569 | −0.597744 | ||||||||
\(523\) | −19.7574 | −0.863929 | −0.431965 | − | 0.901891i | \(-0.642179\pi\) | ||||
−0.431965 | + | 0.901891i | \(0.642179\pi\) | |||||||
\(524\) | −64.9706 | −2.83825 | ||||||||
\(525\) | −6.82843 | −0.298017 | ||||||||
\(526\) | 25.5563 | 1.11431 | ||||||||
\(527\) | 1.45584 | 0.0634176 | ||||||||
\(528\) | −14.4853 | −0.630391 | ||||||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | −1.75736 | −0.0762629 | ||||||||
\(532\) | 10.8284 | 0.469472 | ||||||||
\(533\) | 3.17157 | 0.137376 | ||||||||
\(534\) | 20.4853 | 0.886485 | ||||||||
\(535\) | −9.41421 | −0.407012 | ||||||||
\(536\) | 8.82843 | 0.381330 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | 61.1127 | 2.63476 | ||||||||
\(539\) | 55.6985 | 2.39910 | ||||||||
\(540\) | 21.6569 | 0.931963 | ||||||||
\(541\) | −7.17157 | −0.308330 | −0.154165 | − | 0.988045i | \(-0.549269\pi\) | ||||
−0.154165 | + | 0.988045i | \(0.549269\pi\) | |||||||
\(542\) | −64.5269 | −2.77167 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.31371 | 0.0563248 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | −16.4853 | −0.705505 | ||||||||
\(547\) | 13.2132 | 0.564956 | 0.282478 | − | 0.959274i | \(-0.408844\pi\) | ||||
0.282478 | + | 0.959274i | \(0.408844\pi\) | |||||||
\(548\) | −66.2843 | −2.83152 | ||||||||
\(549\) | 8.00000 | 0.341432 | ||||||||
\(550\) | −8.24264 | −0.351467 | ||||||||
\(551\) | −3.31371 | −0.141169 | ||||||||
\(552\) | 8.82843 | 0.375763 | ||||||||
\(553\) | −40.9706 | −1.74225 | ||||||||
\(554\) | 30.9706 | 1.31581 | ||||||||
\(555\) | 12.0000 | 0.509372 | ||||||||
\(556\) | 17.1716 | 0.728237 | ||||||||
\(557\) | −35.7990 | −1.51685 | −0.758426 | − | 0.651759i | \(-0.774031\pi\) | ||||
−0.758426 | + | 0.651759i | \(0.774031\pi\) | |||||||
\(558\) | 4.24264 | 0.179605 | ||||||||
\(559\) | 11.0711 | 0.468256 | ||||||||
\(560\) | 14.4853 | 0.612115 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | −52.6274 | −2.21995 | ||||||||
\(563\) | −7.75736 | −0.326934 | −0.163467 | − | 0.986549i | \(-0.552268\pi\) | ||||
−0.163467 | + | 0.986549i | \(0.552268\pi\) | |||||||
\(564\) | 26.1421 | 1.10078 | ||||||||
\(565\) | −8.82843 | −0.371415 | ||||||||
\(566\) | 40.3848 | 1.69750 | ||||||||
\(567\) | −24.1421 | −1.01387 | ||||||||
\(568\) | −52.5269 | −2.20398 | ||||||||
\(569\) | −10.3431 | −0.433607 | −0.216804 | − | 0.976215i | \(-0.569563\pi\) | ||||
−0.216804 | + | 0.976215i | \(0.569563\pi\) | |||||||
\(570\) | 2.00000 | 0.0837708 | ||||||||
\(571\) | −11.5147 | −0.481876 | −0.240938 | − | 0.970541i | \(-0.577455\pi\) | ||||
−0.240938 | + | 0.970541i | \(0.577455\pi\) | |||||||
\(572\) | −13.0711 | −0.546529 | ||||||||
\(573\) | −3.31371 | −0.138432 | ||||||||
\(574\) | 36.9706 | 1.54312 | ||||||||
\(575\) | 1.41421 | 0.0589768 | ||||||||
\(576\) | 9.82843 | 0.409518 | ||||||||
\(577\) | −34.8284 | −1.44993 | −0.724963 | − | 0.688788i | \(-0.758143\pi\) | ||||
−0.724963 | + | 0.688788i | \(0.758143\pi\) | |||||||
\(578\) | 39.3848 | 1.63819 | ||||||||
\(579\) | −6.14214 | −0.255258 | ||||||||
\(580\) | −21.6569 | −0.899252 | ||||||||
\(581\) | −15.3137 | −0.635320 | ||||||||
\(582\) | −26.1421 | −1.08363 | ||||||||
\(583\) | 8.48528 | 0.351424 | ||||||||
\(584\) | −37.4558 | −1.54993 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | −63.1127 | −2.60716 | ||||||||
\(587\) | 20.3431 | 0.839651 | 0.419826 | − | 0.907605i | \(-0.362091\pi\) | ||||
0.419826 | + | 0.907605i | \(0.362091\pi\) | |||||||
\(588\) | −88.3259 | −3.64250 | ||||||||
\(589\) | 1.02944 | 0.0424172 | ||||||||
\(590\) | −4.24264 | −0.174667 | ||||||||
\(591\) | −15.5147 | −0.638190 | ||||||||
\(592\) | −25.4558 | −1.04623 | ||||||||
\(593\) | −24.6274 | −1.01133 | −0.505663 | − | 0.862731i | \(-0.668752\pi\) | ||||
−0.505663 | + | 0.862731i | \(0.668752\pi\) | |||||||
\(594\) | −46.6274 | −1.91315 | ||||||||
\(595\) | 4.00000 | 0.163984 | ||||||||
\(596\) | −44.6274 | −1.82801 | ||||||||
\(597\) | −5.65685 | −0.231520 | ||||||||
\(598\) | 3.41421 | 0.139618 | ||||||||
\(599\) | 25.4558 | 1.04010 | 0.520049 | − | 0.854137i | \(-0.325914\pi\) | ||||
0.520049 | + | 0.854137i | \(0.325914\pi\) | |||||||
\(600\) | 6.24264 | 0.254855 | ||||||||
\(601\) | −44.6274 | −1.82039 | −0.910195 | − | 0.414180i | \(-0.864069\pi\) | ||||
−0.910195 | + | 0.414180i | \(0.864069\pi\) | |||||||
\(602\) | 129.054 | 5.25984 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 37.3553 | 1.51997 | ||||||||
\(605\) | 0.656854 | 0.0267049 | ||||||||
\(606\) | −12.4853 | −0.507180 | ||||||||
\(607\) | 31.7574 | 1.28899 | 0.644496 | − | 0.764608i | \(-0.277067\pi\) | ||||
0.644496 | + | 0.764608i | \(0.277067\pi\) | |||||||
\(608\) | 0.928932 | 0.0376732 | ||||||||
\(609\) | 38.6274 | 1.56526 | ||||||||
\(610\) | 19.3137 | 0.781989 | ||||||||
\(611\) | 4.82843 | 0.195337 | ||||||||
\(612\) | −3.17157 | −0.128203 | ||||||||
\(613\) | −14.6863 | −0.593174 | −0.296587 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296587 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(614\) | −59.9411 | −2.41903 | ||||||||
\(615\) | 4.48528 | 0.180864 | ||||||||
\(616\) | −72.7696 | −2.93197 | ||||||||
\(617\) | 10.9706 | 0.441658 | 0.220829 | − | 0.975313i | \(-0.429124\pi\) | ||||
0.220829 | + | 0.975313i | \(0.429124\pi\) | |||||||
\(618\) | 49.7990 | 2.00321 | ||||||||
\(619\) | 1.75736 | 0.0706342 | 0.0353171 | − | 0.999376i | \(-0.488756\pi\) | ||||
0.0353171 | + | 0.999376i | \(0.488756\pi\) | |||||||
\(620\) | 6.72792 | 0.270200 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | −20.4853 | −0.821385 | ||||||||
\(623\) | 28.9706 | 1.16068 | ||||||||
\(624\) | 4.24264 | 0.169842 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.6569 | 0.465902 | ||||||||
\(627\) | −2.82843 | −0.112956 | ||||||||
\(628\) | 68.9117 | 2.74988 | ||||||||
\(629\) | −7.02944 | −0.280282 | ||||||||
\(630\) | 11.6569 | 0.464420 | ||||||||
\(631\) | −9.75736 | −0.388434 | −0.194217 | − | 0.980959i | \(-0.562217\pi\) | ||||
−0.194217 | + | 0.980959i | \(0.562217\pi\) | |||||||
\(632\) | 37.4558 | 1.48991 | ||||||||
\(633\) | −4.68629 | −0.186263 | ||||||||
\(634\) | 5.17157 | 0.205389 | ||||||||
\(635\) | −6.58579 | −0.261349 | ||||||||
\(636\) | −13.4558 | −0.533559 | ||||||||
\(637\) | −16.3137 | −0.646373 | ||||||||
\(638\) | 46.6274 | 1.84600 | ||||||||
\(639\) | −11.8995 | −0.470737 | ||||||||
\(640\) | 20.5563 | 0.812561 | ||||||||
\(641\) | 47.6569 | 1.88233 | 0.941166 | − | 0.337944i | \(-0.109731\pi\) | ||||
0.941166 | + | 0.337944i | \(0.109731\pi\) | |||||||
\(642\) | −32.1421 | −1.26855 | ||||||||
\(643\) | 9.51472 | 0.375224 | 0.187612 | − | 0.982243i | \(-0.439925\pi\) | ||||
0.187612 | + | 0.982243i | \(0.439925\pi\) | |||||||
\(644\) | 26.1421 | 1.03014 | ||||||||
\(645\) | 15.6569 | 0.616488 | ||||||||
\(646\) | −1.17157 | −0.0460949 | ||||||||
\(647\) | 9.41421 | 0.370111 | 0.185055 | − | 0.982728i | \(-0.440754\pi\) | ||||
0.185055 | + | 0.982728i | \(0.440754\pi\) | |||||||
\(648\) | 22.0711 | 0.867033 | ||||||||
\(649\) | 6.00000 | 0.235521 | ||||||||
\(650\) | 2.41421 | 0.0946932 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | 72.6274 | 2.84431 | ||||||||
\(653\) | 46.9706 | 1.83810 | 0.919050 | − | 0.394141i | \(-0.128958\pi\) | ||||
0.919050 | + | 0.394141i | \(0.128958\pi\) | |||||||
\(654\) | −6.82843 | −0.267013 | ||||||||
\(655\) | −16.9706 | −0.663095 | ||||||||
\(656\) | −9.51472 | −0.371487 | ||||||||
\(657\) | −8.48528 | −0.331042 | ||||||||
\(658\) | 56.2843 | 2.19419 | ||||||||
\(659\) | 17.8579 | 0.695644 | 0.347822 | − | 0.937561i | \(-0.386921\pi\) | ||||
0.347822 | + | 0.937561i | \(0.386921\pi\) | |||||||
\(660\) | −18.4853 | −0.719539 | ||||||||
\(661\) | 29.5980 | 1.15123 | 0.575614 | − | 0.817722i | \(-0.304763\pi\) | ||||
0.575614 | + | 0.817722i | \(0.304763\pi\) | |||||||
\(662\) | 62.8701 | 2.44351 | ||||||||
\(663\) | 1.17157 | 0.0455001 | ||||||||
\(664\) | 14.0000 | 0.543305 | ||||||||
\(665\) | 2.82843 | 0.109682 | ||||||||
\(666\) | −20.4853 | −0.793789 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | −12.1421 | −0.469793 | ||||||||
\(669\) | −13.4558 | −0.520233 | ||||||||
\(670\) | 4.82843 | 0.186538 | ||||||||
\(671\) | −27.3137 | −1.05443 | ||||||||
\(672\) | −10.8284 | −0.417716 | ||||||||
\(673\) | 6.48528 | 0.249989 | 0.124995 | − | 0.992157i | \(-0.460109\pi\) | ||||
0.124995 | + | 0.992157i | \(0.460109\pi\) | |||||||
\(674\) | −30.9706 | −1.19294 | ||||||||
\(675\) | 5.65685 | 0.217732 | ||||||||
\(676\) | 3.82843 | 0.147247 | ||||||||
\(677\) | −20.1421 | −0.774125 | −0.387063 | − | 0.922053i | \(-0.626510\pi\) | ||||
−0.387063 | + | 0.922053i | \(0.626510\pi\) | |||||||
\(678\) | −30.1421 | −1.15760 | ||||||||
\(679\) | −36.9706 | −1.41880 | ||||||||
\(680\) | −3.65685 | −0.140234 | ||||||||
\(681\) | 23.1127 | 0.885681 | ||||||||
\(682\) | −14.4853 | −0.554670 | ||||||||
\(683\) | 10.6863 | 0.408900 | 0.204450 | − | 0.978877i | \(-0.434459\pi\) | ||||
0.204450 | + | 0.978877i | \(0.434459\pi\) | |||||||
\(684\) | −2.24264 | −0.0857495 | ||||||||
\(685\) | −17.3137 | −0.661523 | ||||||||
\(686\) | −108.569 | −4.14517 | ||||||||
\(687\) | 6.82843 | 0.260521 | ||||||||
\(688\) | −33.2132 | −1.26624 | ||||||||
\(689\) | −2.48528 | −0.0946817 | ||||||||
\(690\) | 4.82843 | 0.183815 | ||||||||
\(691\) | 6.92893 | 0.263589 | 0.131795 | − | 0.991277i | \(-0.457926\pi\) | ||||
0.131795 | + | 0.991277i | \(0.457926\pi\) | |||||||
\(692\) | 64.4264 | 2.44912 | ||||||||
\(693\) | −16.4853 | −0.626224 | ||||||||
\(694\) | 10.2426 | 0.388805 | ||||||||
\(695\) | 4.48528 | 0.170136 | ||||||||
\(696\) | −35.3137 | −1.33856 | ||||||||
\(697\) | −2.62742 | −0.0995205 | ||||||||
\(698\) | −44.6274 | −1.68917 | ||||||||
\(699\) | 29.1716 | 1.10337 | ||||||||
\(700\) | 18.4853 | 0.698678 | ||||||||
\(701\) | 14.6863 | 0.554694 | 0.277347 | − | 0.960770i | \(-0.410545\pi\) | ||||
0.277347 | + | 0.960770i | \(0.410545\pi\) | |||||||
\(702\) | 13.6569 | 0.515445 | ||||||||
\(703\) | −4.97056 | −0.187468 | ||||||||
\(704\) | −33.5563 | −1.26470 | ||||||||
\(705\) | 6.82843 | 0.257173 | ||||||||
\(706\) | −35.7990 | −1.34731 | ||||||||
\(707\) | −17.6569 | −0.664054 | ||||||||
\(708\) | −9.51472 | −0.357585 | ||||||||
\(709\) | 45.1127 | 1.69424 | 0.847121 | − | 0.531399i | \(-0.178334\pi\) | ||||
0.847121 | + | 0.531399i | \(0.178334\pi\) | |||||||
\(710\) | −28.7279 | −1.07814 | ||||||||
\(711\) | 8.48528 | 0.318223 | ||||||||
\(712\) | −26.4853 | −0.992578 | ||||||||
\(713\) | 2.48528 | 0.0930745 | ||||||||
\(714\) | 13.6569 | 0.511095 | ||||||||
\(715\) | −3.41421 | −0.127684 | ||||||||
\(716\) | 21.6569 | 0.809355 | ||||||||
\(717\) | 4.82843 | 0.180321 | ||||||||
\(718\) | 19.5563 | 0.729836 | ||||||||
\(719\) | 28.9706 | 1.08042 | 0.540210 | − | 0.841530i | \(-0.318345\pi\) | ||||
0.540210 | + | 0.841530i | \(0.318345\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | 70.4264 | 2.62282 | ||||||||
\(722\) | 45.0416 | 1.67628 | ||||||||
\(723\) | 20.4853 | 0.761856 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.65685 | −0.210090 | ||||||||
\(726\) | 2.24264 | 0.0832322 | ||||||||
\(727\) | −51.3553 | −1.90466 | −0.952332 | − | 0.305063i | \(-0.901322\pi\) | ||||
−0.952332 | + | 0.305063i | \(0.901322\pi\) | |||||||
\(728\) | 21.3137 | 0.789939 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −20.4853 | −0.758194 | ||||||||
\(731\) | −9.17157 | −0.339223 | ||||||||
\(732\) | 43.3137 | 1.60092 | ||||||||
\(733\) | 21.3137 | 0.787240 | 0.393620 | − | 0.919273i | \(-0.371223\pi\) | ||||
0.393620 | + | 0.919273i | \(0.371223\pi\) | |||||||
\(734\) | −85.8406 | −3.16844 | ||||||||
\(735\) | −23.0711 | −0.850989 | ||||||||
\(736\) | 2.24264 | 0.0826648 | ||||||||
\(737\) | −6.82843 | −0.251528 | ||||||||
\(738\) | −7.65685 | −0.281853 | ||||||||
\(739\) | 5.27208 | 0.193937 | 0.0969683 | − | 0.995287i | \(-0.469085\pi\) | ||||
0.0969683 | + | 0.995287i | \(0.469085\pi\) | |||||||
\(740\) | −32.4853 | −1.19418 | ||||||||
\(741\) | 0.828427 | 0.0304330 | ||||||||
\(742\) | −28.9706 | −1.06354 | ||||||||
\(743\) | −21.5147 | −0.789298 | −0.394649 | − | 0.918832i | \(-0.629134\pi\) | ||||
−0.394649 | + | 0.918832i | \(0.629134\pi\) | |||||||
\(744\) | 10.9706 | 0.402200 | ||||||||
\(745\) | −11.6569 | −0.427074 | ||||||||
\(746\) | 6.48528 | 0.237443 | ||||||||
\(747\) | 3.17157 | 0.116042 | ||||||||
\(748\) | 10.8284 | 0.395927 | ||||||||
\(749\) | −45.4558 | −1.66092 | ||||||||
\(750\) | 3.41421 | 0.124669 | ||||||||
\(751\) | −27.5147 | −1.00403 | −0.502013 | − | 0.864860i | \(-0.667407\pi\) | ||||
−0.502013 | + | 0.864860i | \(0.667407\pi\) | |||||||
\(752\) | −14.4853 | −0.528224 | ||||||||
\(753\) | −28.0000 | −1.02038 | ||||||||
\(754\) | −13.6569 | −0.497353 | ||||||||
\(755\) | 9.75736 | 0.355107 | ||||||||
\(756\) | 104.569 | 3.80312 | ||||||||
\(757\) | −24.1421 | −0.877461 | −0.438730 | − | 0.898619i | \(-0.644572\pi\) | ||||
−0.438730 | + | 0.898619i | \(0.644572\pi\) | |||||||
\(758\) | −70.1838 | −2.54919 | ||||||||
\(759\) | −6.82843 | −0.247856 | ||||||||
\(760\) | −2.58579 | −0.0937963 | ||||||||
\(761\) | 8.62742 | 0.312744 | 0.156372 | − | 0.987698i | \(-0.450020\pi\) | ||||
0.156372 | + | 0.987698i | \(0.450020\pi\) | |||||||
\(762\) | −22.4853 | −0.814556 | ||||||||
\(763\) | −9.65685 | −0.349602 | ||||||||
\(764\) | 8.97056 | 0.324544 | ||||||||
\(765\) | −0.828427 | −0.0299518 | ||||||||
\(766\) | 70.2843 | 2.53947 | ||||||||
\(767\) | −1.75736 | −0.0634546 | ||||||||
\(768\) | 42.3848 | 1.52943 | ||||||||
\(769\) | −22.9706 | −0.828340 | −0.414170 | − | 0.910200i | \(-0.635928\pi\) | ||||
−0.414170 | + | 0.910200i | \(0.635928\pi\) | |||||||
\(770\) | −39.7990 | −1.43426 | ||||||||
\(771\) | −39.1127 | −1.40861 | ||||||||
\(772\) | 16.6274 | 0.598434 | ||||||||
\(773\) | −22.1421 | −0.796397 | −0.398199 | − | 0.917299i | \(-0.630365\pi\) | ||||
−0.398199 | + | 0.917299i | \(0.630365\pi\) | |||||||
\(774\) | −26.7279 | −0.960715 | ||||||||
\(775\) | 1.75736 | 0.0631262 | ||||||||
\(776\) | 33.7990 | 1.21331 | ||||||||
\(777\) | 57.9411 | 2.07863 | ||||||||
\(778\) | −69.1127 | −2.47781 | ||||||||
\(779\) | −1.85786 | −0.0665649 | ||||||||
\(780\) | 5.41421 | 0.193860 | ||||||||
\(781\) | 40.6274 | 1.45376 | ||||||||
\(782\) | −2.82843 | −0.101144 | ||||||||
\(783\) | −32.0000 | −1.14359 | ||||||||
\(784\) | 48.9411 | 1.74790 | ||||||||
\(785\) | 18.0000 | 0.642448 | ||||||||
\(786\) | −57.9411 | −2.06669 | ||||||||
\(787\) | 22.4853 | 0.801514 | 0.400757 | − | 0.916184i | \(-0.368747\pi\) | ||||
0.400757 | + | 0.916184i | \(0.368747\pi\) | |||||||
\(788\) | 42.0000 | 1.49619 | ||||||||
\(789\) | 14.9706 | 0.532966 | ||||||||
\(790\) | 20.4853 | 0.728834 | ||||||||
\(791\) | −42.6274 | −1.51566 | ||||||||
\(792\) | 15.0711 | 0.535527 | ||||||||
\(793\) | 8.00000 | 0.284088 | ||||||||
\(794\) | −28.4853 | −1.01090 | ||||||||
\(795\) | −3.51472 | −0.124654 | ||||||||
\(796\) | 15.3137 | 0.542780 | ||||||||
\(797\) | −22.9706 | −0.813659 | −0.406830 | − | 0.913504i | \(-0.633366\pi\) | ||||
−0.406830 | + | 0.913504i | \(0.633366\pi\) | |||||||
\(798\) | 9.65685 | 0.341849 | ||||||||
\(799\) | −4.00000 | −0.141510 | ||||||||
\(800\) | 1.58579 | 0.0560660 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 12.8284 | 0.452988 | ||||||||
\(803\) | 28.9706 | 1.02235 | ||||||||
\(804\) | 10.8284 | 0.381889 | ||||||||
\(805\) | 6.82843 | 0.240670 | ||||||||
\(806\) | 4.24264 | 0.149441 | ||||||||
\(807\) | 35.7990 | 1.26018 | ||||||||
\(808\) | 16.1421 | 0.567878 | ||||||||
\(809\) | 45.2548 | 1.59108 | 0.795538 | − | 0.605904i | \(-0.207189\pi\) | ||||
0.795538 | + | 0.605904i | \(0.207189\pi\) | |||||||
\(810\) | 12.0711 | 0.424134 | ||||||||
\(811\) | −28.3848 | −0.996724 | −0.498362 | − | 0.866969i | \(-0.666065\pi\) | ||||
−0.498362 | + | 0.866969i | \(0.666065\pi\) | |||||||
\(812\) | −104.569 | −3.66964 | ||||||||
\(813\) | −37.7990 | −1.32567 | ||||||||
\(814\) | 69.9411 | 2.45144 | ||||||||
\(815\) | 18.9706 | 0.664510 | ||||||||
\(816\) | −3.51472 | −0.123040 | ||||||||
\(817\) | −6.48528 | −0.226891 | ||||||||
\(818\) | −17.3137 | −0.605360 | ||||||||
\(819\) | 4.82843 | 0.168719 | ||||||||
\(820\) | −12.1421 | −0.424022 | ||||||||
\(821\) | −51.2548 | −1.78881 | −0.894403 | − | 0.447262i | \(-0.852399\pi\) | ||||
−0.894403 | + | 0.447262i | \(0.852399\pi\) | |||||||
\(822\) | −59.1127 | −2.06179 | ||||||||
\(823\) | −2.38478 | −0.0831281 | −0.0415640 | − | 0.999136i | \(-0.513234\pi\) | ||||
−0.0415640 | + | 0.999136i | \(0.513234\pi\) | |||||||
\(824\) | −64.3848 | −2.24295 | ||||||||
\(825\) | −4.82843 | −0.168104 | ||||||||
\(826\) | −20.4853 | −0.712774 | ||||||||
\(827\) | 56.1421 | 1.95225 | 0.976127 | − | 0.217202i | \(-0.0696930\pi\) | ||||
0.976127 | + | 0.217202i | \(0.0696930\pi\) | |||||||
\(828\) | −5.41421 | −0.188157 | ||||||||
\(829\) | 40.9706 | 1.42297 | 0.711483 | − | 0.702703i | \(-0.248024\pi\) | ||||
0.711483 | + | 0.702703i | \(0.248024\pi\) | |||||||
\(830\) | 7.65685 | 0.265773 | ||||||||
\(831\) | 18.1421 | 0.629344 | ||||||||
\(832\) | 9.82843 | 0.340739 | ||||||||
\(833\) | 13.5147 | 0.468257 | ||||||||
\(834\) | 15.3137 | 0.530270 | ||||||||
\(835\) | −3.17157 | −0.109757 | ||||||||
\(836\) | 7.65685 | 0.264818 | ||||||||
\(837\) | 9.94113 | 0.343616 | ||||||||
\(838\) | −26.1421 | −0.903065 | ||||||||
\(839\) | 6.72792 | 0.232274 | 0.116137 | − | 0.993233i | \(-0.462949\pi\) | ||||
0.116137 | + | 0.993233i | \(0.462949\pi\) | |||||||
\(840\) | 30.1421 | 1.04000 | ||||||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | 84.4264 | 2.90953 | ||||||||
\(843\) | −30.8284 | −1.06179 | ||||||||
\(844\) | 12.6863 | 0.436680 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | −11.6569 | −0.400771 | ||||||||
\(847\) | 3.17157 | 0.108977 | ||||||||
\(848\) | 7.45584 | 0.256035 | ||||||||
\(849\) | 23.6569 | 0.811901 | ||||||||
\(850\) | −2.00000 | −0.0685994 | ||||||||
\(851\) | −12.0000 | −0.411355 | ||||||||
\(852\) | −64.4264 | −2.20721 | ||||||||
\(853\) | −13.4558 | −0.460719 | −0.230360 | − | 0.973106i | \(-0.573990\pi\) | ||||
−0.230360 | + | 0.973106i | \(0.573990\pi\) | |||||||
\(854\) | 93.2548 | 3.19111 | ||||||||
\(855\) | −0.585786 | −0.0200335 | ||||||||
\(856\) | 41.5563 | 1.42037 | ||||||||
\(857\) | 11.6569 | 0.398191 | 0.199095 | − | 0.979980i | \(-0.436200\pi\) | ||||
0.199095 | + | 0.979980i | \(0.436200\pi\) | |||||||
\(858\) | −11.6569 | −0.397958 | ||||||||
\(859\) | −27.7990 | −0.948489 | −0.474245 | − | 0.880393i | \(-0.657279\pi\) | ||||
−0.474245 | + | 0.880393i | \(0.657279\pi\) | |||||||
\(860\) | −42.3848 | −1.44531 | ||||||||
\(861\) | 21.6569 | 0.738064 | ||||||||
\(862\) | −97.4975 | −3.32078 | ||||||||
\(863\) | −31.4558 | −1.07077 | −0.535385 | − | 0.844608i | \(-0.679833\pi\) | ||||
−0.535385 | + | 0.844608i | \(0.679833\pi\) | |||||||
\(864\) | 8.97056 | 0.305185 | ||||||||
\(865\) | 16.8284 | 0.572184 | ||||||||
\(866\) | −18.4853 | −0.628155 | ||||||||
\(867\) | 23.0711 | 0.783535 | ||||||||
\(868\) | 32.4853 | 1.10262 | ||||||||
\(869\) | −28.9706 | −0.982759 | ||||||||
\(870\) | −19.3137 | −0.654796 | ||||||||
\(871\) | 2.00000 | 0.0677674 | ||||||||
\(872\) | 8.82843 | 0.298968 | ||||||||
\(873\) | 7.65685 | 0.259145 | ||||||||
\(874\) | −2.00000 | −0.0676510 | ||||||||
\(875\) | 4.82843 | 0.163231 | ||||||||
\(876\) | −45.9411 | −1.55221 | ||||||||
\(877\) | 25.3137 | 0.854783 | 0.427392 | − | 0.904067i | \(-0.359433\pi\) | ||||
0.427392 | + | 0.904067i | \(0.359433\pi\) | |||||||
\(878\) | −2.34315 | −0.0790773 | ||||||||
\(879\) | −36.9706 | −1.24699 | ||||||||
\(880\) | 10.2426 | 0.345279 | ||||||||
\(881\) | 19.0294 | 0.641118 | 0.320559 | − | 0.947229i | \(-0.396129\pi\) | ||||
0.320559 | + | 0.947229i | \(0.396129\pi\) | |||||||
\(882\) | 39.3848 | 1.32615 | ||||||||
\(883\) | −23.7574 | −0.799499 | −0.399749 | − | 0.916624i | \(-0.630903\pi\) | ||||
−0.399749 | + | 0.916624i | \(0.630903\pi\) | |||||||
\(884\) | −3.17157 | −0.106672 | ||||||||
\(885\) | −2.48528 | −0.0835418 | ||||||||
\(886\) | 22.7279 | 0.763559 | ||||||||
\(887\) | −22.3848 | −0.751607 | −0.375804 | − | 0.926699i | \(-0.622633\pi\) | ||||
−0.375804 | + | 0.926699i | \(0.622633\pi\) | |||||||
\(888\) | −52.9706 | −1.77758 | ||||||||
\(889\) | −31.7990 | −1.06650 | ||||||||
\(890\) | −14.4853 | −0.485548 | ||||||||
\(891\) | −17.0711 | −0.571902 | ||||||||
\(892\) | 36.4264 | 1.21965 | ||||||||
\(893\) | −2.82843 | −0.0946497 | ||||||||
\(894\) | −39.7990 | −1.33108 | ||||||||
\(895\) | 5.65685 | 0.189088 | ||||||||
\(896\) | 99.2548 | 3.31587 | ||||||||
\(897\) | 2.00000 | 0.0667781 | ||||||||
\(898\) | 79.9411 | 2.66767 | ||||||||
\(899\) | −9.94113 | −0.331555 | ||||||||
\(900\) | −3.82843 | −0.127614 | ||||||||
\(901\) | 2.05887 | 0.0685911 | ||||||||
\(902\) | 26.1421 | 0.870438 | ||||||||
\(903\) | 75.5980 | 2.51574 | ||||||||
\(904\) | 38.9706 | 1.29614 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 33.3137 | 1.10677 | ||||||||
\(907\) | 9.21320 | 0.305919 | 0.152960 | − | 0.988232i | \(-0.451120\pi\) | ||||
0.152960 | + | 0.988232i | \(0.451120\pi\) | |||||||
\(908\) | −62.5685 | −2.07641 | ||||||||
\(909\) | 3.65685 | 0.121290 | ||||||||
\(910\) | 11.6569 | 0.386421 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | −2.48528 | −0.0822959 | ||||||||
\(913\) | −10.8284 | −0.358369 | ||||||||
\(914\) | 43.4558 | 1.43739 | ||||||||
\(915\) | 11.3137 | 0.374020 | ||||||||
\(916\) | −18.4853 | −0.610771 | ||||||||
\(917\) | −81.9411 | −2.70593 | ||||||||
\(918\) | −11.3137 | −0.373408 | ||||||||
\(919\) | 0.485281 | 0.0160080 | 0.00800398 | − | 0.999968i | \(-0.497452\pi\) | ||||
0.00800398 | + | 0.999968i | \(0.497452\pi\) | |||||||
\(920\) | −6.24264 | −0.205814 | ||||||||
\(921\) | −35.1127 | −1.15700 | ||||||||
\(922\) | −22.9706 | −0.756495 | ||||||||
\(923\) | −11.8995 | −0.391677 | ||||||||
\(924\) | −89.2548 | −2.93627 | ||||||||
\(925\) | −8.48528 | −0.278994 | ||||||||
\(926\) | 10.4853 | 0.344568 | ||||||||
\(927\) | −14.5858 | −0.479060 | ||||||||
\(928\) | −8.97056 | −0.294473 | ||||||||
\(929\) | 16.8284 | 0.552123 | 0.276061 | − | 0.961140i | \(-0.410971\pi\) | ||||
0.276061 | + | 0.961140i | \(0.410971\pi\) | |||||||
\(930\) | 6.00000 | 0.196748 | ||||||||
\(931\) | 9.55635 | 0.313197 | ||||||||
\(932\) | −78.9706 | −2.58677 | ||||||||
\(933\) | −12.0000 | −0.392862 | ||||||||
\(934\) | 32.3848 | 1.05966 | ||||||||
\(935\) | 2.82843 | 0.0924995 | ||||||||
\(936\) | −4.41421 | −0.144283 | ||||||||
\(937\) | −22.9706 | −0.750416 | −0.375208 | − | 0.926941i | \(-0.622429\pi\) | ||||
−0.375208 | + | 0.926941i | \(0.622429\pi\) | |||||||
\(938\) | 23.3137 | 0.761220 | ||||||||
\(939\) | 6.82843 | 0.222837 | ||||||||
\(940\) | −18.4853 | −0.602923 | ||||||||
\(941\) | 18.7696 | 0.611870 | 0.305935 | − | 0.952052i | \(-0.401031\pi\) | ||||
0.305935 | + | 0.952052i | \(0.401031\pi\) | |||||||
\(942\) | 61.4558 | 2.00234 | ||||||||
\(943\) | −4.48528 | −0.146061 | ||||||||
\(944\) | 5.27208 | 0.171592 | ||||||||
\(945\) | 27.3137 | 0.888515 | ||||||||
\(946\) | 91.2548 | 2.96695 | ||||||||
\(947\) | 17.1127 | 0.556088 | 0.278044 | − | 0.960568i | \(-0.410314\pi\) | ||||
0.278044 | + | 0.960568i | \(0.410314\pi\) | |||||||
\(948\) | 45.9411 | 1.49210 | ||||||||
\(949\) | −8.48528 | −0.275444 | ||||||||
\(950\) | −1.41421 | −0.0458831 | ||||||||
\(951\) | 3.02944 | 0.0982362 | ||||||||
\(952\) | −17.6569 | −0.572262 | ||||||||
\(953\) | 35.2548 | 1.14202 | 0.571008 | − | 0.820944i | \(-0.306553\pi\) | ||||
0.571008 | + | 0.820944i | \(0.306553\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | 2.34315 | 0.0758224 | ||||||||
\(956\) | −13.0711 | −0.422749 | ||||||||
\(957\) | 27.3137 | 0.882927 | ||||||||
\(958\) | 74.1838 | 2.39677 | ||||||||
\(959\) | −83.5980 | −2.69952 | ||||||||
\(960\) | 13.8995 | 0.448604 | ||||||||
\(961\) | −27.9117 | −0.900377 | ||||||||
\(962\) | −20.4853 | −0.660472 | ||||||||
\(963\) | 9.41421 | 0.303369 | ||||||||
\(964\) | −55.4558 | −1.78611 | ||||||||
\(965\) | 4.34315 | 0.139811 | ||||||||
\(966\) | 23.3137 | 0.750106 | ||||||||
\(967\) | 47.9411 | 1.54168 | 0.770841 | − | 0.637027i | \(-0.219836\pi\) | ||||
0.770841 | + | 0.637027i | \(0.219836\pi\) | |||||||
\(968\) | −2.89949 | −0.0931933 | ||||||||
\(969\) | −0.686292 | −0.0220469 | ||||||||
\(970\) | 18.4853 | 0.593527 | ||||||||
\(971\) | 44.2843 | 1.42115 | 0.710575 | − | 0.703622i | \(-0.248435\pi\) | ||||
0.710575 | + | 0.703622i | \(0.248435\pi\) | |||||||
\(972\) | −37.8995 | −1.21563 | ||||||||
\(973\) | 21.6569 | 0.694287 | ||||||||
\(974\) | 26.4853 | 0.848643 | ||||||||
\(975\) | 1.41421 | 0.0452911 | ||||||||
\(976\) | −24.0000 | −0.768221 | ||||||||
\(977\) | −39.5147 | −1.26419 | −0.632094 | − | 0.774892i | \(-0.717804\pi\) | ||||
−0.632094 | + | 0.774892i | \(0.717804\pi\) | |||||||
\(978\) | 64.7696 | 2.07110 | ||||||||
\(979\) | 20.4853 | 0.654712 | ||||||||
\(980\) | 62.4558 | 1.99508 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | −12.4853 | −0.398421 | ||||||||
\(983\) | −1.02944 | −0.0328339 | −0.0164170 | − | 0.999865i | \(-0.505226\pi\) | ||||
−0.0164170 | + | 0.999865i | \(0.505226\pi\) | |||||||
\(984\) | −19.7990 | −0.631169 | ||||||||
\(985\) | 10.9706 | 0.349551 | ||||||||
\(986\) | 11.3137 | 0.360302 | ||||||||
\(987\) | 32.9706 | 1.04946 | ||||||||
\(988\) | −2.24264 | −0.0713479 | ||||||||
\(989\) | −15.6569 | −0.497859 | ||||||||
\(990\) | 8.24264 | 0.261968 | ||||||||
\(991\) | 48.9706 | 1.55560 | 0.777801 | − | 0.628511i | \(-0.216335\pi\) | ||||
0.777801 | + | 0.628511i | \(0.216335\pi\) | |||||||
\(992\) | 2.78680 | 0.0884809 | ||||||||
\(993\) | 36.8284 | 1.16871 | ||||||||
\(994\) | −138.711 | −4.39964 | ||||||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | 17.1716 | 0.544102 | ||||||||
\(997\) | 28.8284 | 0.913005 | 0.456503 | − | 0.889722i | \(-0.349102\pi\) | ||||
0.456503 | + | 0.889722i | \(0.349102\pi\) | |||||||
\(998\) | −100.326 | −3.17576 | ||||||||
\(999\) | −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 | 65.2.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 585.2.a.m.1.2 | 2 | |||
4.3 | odd | 2 | 1040.2.a.j.1.2 | 2 | |||
5.2 | odd | 4 | 325.2.b.f.274.1 | 4 | |||
5.3 | odd | 4 | 325.2.b.f.274.4 | 4 | |||
5.4 | even | 2 | 325.2.a.i.1.2 | 2 | |||
7.6 | odd | 2 | 3185.2.a.j.1.1 | 2 | |||
8.3 | odd | 2 | 4160.2.a.z.1.1 | 2 | |||
8.5 | even | 2 | 4160.2.a.bf.1.2 | 2 | |||
11.10 | odd | 2 | 7865.2.a.j.1.2 | 2 | |||
12.11 | even | 2 | 9360.2.a.cd.1.1 | 2 | |||
13.2 | odd | 12 | 845.2.m.f.316.1 | 8 | |||
13.3 | even | 3 | 845.2.e.h.191.2 | 4 | |||
13.4 | even | 6 | 845.2.e.c.146.1 | 4 | |||
13.5 | odd | 4 | 845.2.c.b.506.4 | 4 | |||
13.6 | odd | 12 | 845.2.m.f.361.4 | 8 | |||
13.7 | odd | 12 | 845.2.m.f.361.1 | 8 | |||
13.8 | odd | 4 | 845.2.c.b.506.1 | 4 | |||
13.9 | even | 3 | 845.2.e.h.146.2 | 4 | |||
13.10 | even | 6 | 845.2.e.c.191.1 | 4 | |||
13.11 | odd | 12 | 845.2.m.f.316.4 | 8 | |||
13.12 | even | 2 | 845.2.a.g.1.2 | 2 | |||
15.2 | even | 4 | 2925.2.c.r.2224.4 | 4 | |||
15.8 | even | 4 | 2925.2.c.r.2224.1 | 4 | |||
15.14 | odd | 2 | 2925.2.a.u.1.1 | 2 | |||
20.19 | odd | 2 | 5200.2.a.bu.1.1 | 2 | |||
39.38 | odd | 2 | 7605.2.a.x.1.1 | 2 | |||
65.64 | even | 2 | 4225.2.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
325.2.a.i.1.2 | 2 | 5.4 | even | 2 | |||
325.2.b.f.274.1 | 4 | 5.2 | odd | 4 | |||
325.2.b.f.274.4 | 4 | 5.3 | odd | 4 | |||
585.2.a.m.1.2 | 2 | 3.2 | odd | 2 | |||
845.2.a.g.1.2 | 2 | 13.12 | even | 2 | |||
845.2.c.b.506.1 | 4 | 13.8 | odd | 4 | |||
845.2.c.b.506.4 | 4 | 13.5 | odd | 4 | |||
845.2.e.c.146.1 | 4 | 13.4 | even | 6 | |||
845.2.e.c.191.1 | 4 | 13.10 | even | 6 | |||
845.2.e.h.146.2 | 4 | 13.9 | even | 3 | |||
845.2.e.h.191.2 | 4 | 13.3 | even | 3 | |||
845.2.m.f.316.1 | 8 | 13.2 | odd | 12 | |||
845.2.m.f.316.4 | 8 | 13.11 | odd | 12 | |||
845.2.m.f.361.1 | 8 | 13.7 | odd | 12 | |||
845.2.m.f.361.4 | 8 | 13.6 | odd | 12 | |||
1040.2.a.j.1.2 | 2 | 4.3 | odd | 2 | |||
2925.2.a.u.1.1 | 2 | 15.14 | odd | 2 | |||
2925.2.c.r.2224.1 | 4 | 15.8 | even | 4 | |||
2925.2.c.r.2224.4 | 4 | 15.2 | even | 4 | |||
3185.2.a.j.1.1 | 2 | 7.6 | odd | 2 | |||
4160.2.a.z.1.1 | 2 | 8.3 | odd | 2 | |||
4160.2.a.bf.1.2 | 2 | 8.5 | even | 2 | |||
4225.2.a.r.1.1 | 2 | 65.64 | even | 2 | |||
5200.2.a.bu.1.1 | 2 | 20.19 | odd | 2 | |||
7605.2.a.x.1.1 | 2 | 39.38 | odd | 2 | |||
7865.2.a.j.1.2 | 2 | 11.10 | odd | 2 | |||
9360.2.a.cd.1.1 | 2 | 12.11 | even | 2 |