Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.73205 | 1.57735 | 0.788675 | − | 0.614810i | \(-0.210767\pi\) | ||||
0.788675 | + | 0.614810i | \(0.210767\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.73205 | −1.11536 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.73205 | 0.788675 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.73205 | −0.705412 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.535898 | 0.129974 | 0.0649872 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649872 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(18\) | −4.46410 | −1.05220 | ||||||||
\(19\) | −0.732051 | −0.167944 | −0.0839720 | − | 0.996468i | \(-0.526761\pi\) | ||||
−0.0839720 | + | 0.996468i | \(0.526761\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.73205 | 0.596182 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.19615 | 1.70902 | 0.854508 | − | 0.519438i | \(-0.173859\pi\) | ||||
0.854508 | + | 0.519438i | \(0.173859\pi\) | |||||||
\(24\) | −2.73205 | −0.557678 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −7.66025 | −1.42247 | −0.711237 | − | 0.702953i | \(-0.751865\pi\) | ||||
−0.711237 | + | 0.702953i | \(0.751865\pi\) | |||||||
\(30\) | 2.73205 | 0.498802 | ||||||||
\(31\) | 0.535898 | 0.0962502 | 0.0481251 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481251 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.535898 | −0.0919058 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 4.46410 | 0.744017 | ||||||||
\(37\) | −2.73205 | −0.449146 | −0.224573 | − | 0.974457i | \(-0.572099\pi\) | ||||
−0.224573 | + | 0.974457i | \(0.572099\pi\) | |||||||
\(38\) | 0.732051 | 0.118754 | ||||||||
\(39\) | 10.9282 | 1.74991 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.19615 | 0.342981 | 0.171491 | − | 0.985186i | \(-0.445142\pi\) | ||||
0.171491 | + | 0.985186i | \(0.445142\pi\) | |||||||
\(42\) | −2.73205 | −0.421565 | ||||||||
\(43\) | −4.92820 | −0.751544 | −0.375772 | − | 0.926712i | \(-0.622622\pi\) | ||||
−0.375772 | + | 0.926712i | \(0.622622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.46410 | −0.665469 | ||||||||
\(46\) | −8.19615 | −1.20846 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 2.73205 | 0.394338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 1.46410 | 0.205015 | ||||||||
\(52\) | 4.00000 | 0.554700 | ||||||||
\(53\) | 5.26795 | 0.723608 | 0.361804 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361804 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 7.66025 | 1.00584 | ||||||||
\(59\) | 8.39230 | 1.09259 | 0.546293 | − | 0.837594i | \(-0.316039\pi\) | ||||
0.546293 | + | 0.837594i | \(0.316039\pi\) | |||||||
\(60\) | −2.73205 | −0.352706 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | −0.535898 | −0.0680592 | ||||||||
\(63\) | 4.46410 | 0.562424 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.8564 | 1.93717 | 0.968584 | − | 0.248686i | \(-0.0799987\pi\) | ||||
0.968584 | + | 0.248686i | \(0.0799987\pi\) | |||||||
\(68\) | 0.535898 | 0.0649872 | ||||||||
\(69\) | 22.3923 | 2.69572 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 1.07180 | 0.127199 | 0.0635994 | − | 0.997976i | \(-0.479742\pi\) | ||||
0.0635994 | + | 0.997976i | \(0.479742\pi\) | |||||||
\(72\) | −4.46410 | −0.526099 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 2.73205 | 0.317594 | ||||||||
\(75\) | 2.73205 | 0.315470 | ||||||||
\(76\) | −0.732051 | −0.0839720 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −10.9282 | −1.23738 | ||||||||
\(79\) | 7.66025 | 0.861846 | 0.430923 | − | 0.902389i | \(-0.358188\pi\) | ||||
0.430923 | + | 0.902389i | \(0.358188\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | −2.19615 | −0.242524 | ||||||||
\(83\) | 14.9282 | 1.63858 | 0.819292 | − | 0.573377i | \(-0.194367\pi\) | ||||
0.819292 | + | 0.573377i | \(0.194367\pi\) | |||||||
\(84\) | 2.73205 | 0.298091 | ||||||||
\(85\) | −0.535898 | −0.0581263 | ||||||||
\(86\) | 4.92820 | 0.531422 | ||||||||
\(87\) | −20.9282 | −2.24374 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.92820 | −0.946388 | −0.473194 | − | 0.880958i | \(-0.656899\pi\) | ||||
−0.473194 | + | 0.880958i | \(0.656899\pi\) | |||||||
\(90\) | 4.46410 | 0.470558 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 8.19615 | 0.854508 | ||||||||
\(93\) | 1.46410 | 0.151820 | ||||||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | 0.732051 | 0.0751068 | ||||||||
\(96\) | −2.73205 | −0.278839 | ||||||||
\(97\) | 2.73205 | 0.277398 | 0.138699 | − | 0.990335i | \(-0.455708\pi\) | ||||
0.138699 | + | 0.990335i | \(0.455708\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 8.00000 | 0.796030 | 0.398015 | − | 0.917379i | \(-0.369699\pi\) | ||||
0.398015 | + | 0.917379i | \(0.369699\pi\) | |||||||
\(102\) | −1.46410 | −0.144968 | ||||||||
\(103\) | 2.39230 | 0.235721 | 0.117860 | − | 0.993030i | \(-0.462396\pi\) | ||||
0.117860 | + | 0.993030i | \(0.462396\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | −2.73205 | −0.266621 | ||||||||
\(106\) | −5.26795 | −0.511668 | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | −16.7321 | −1.60264 | −0.801320 | − | 0.598236i | \(-0.795868\pi\) | ||||
−0.801320 | + | 0.598236i | \(0.795868\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.46410 | −0.708461 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | −8.19615 | −0.764295 | ||||||||
\(116\) | −7.66025 | −0.711237 | ||||||||
\(117\) | 17.8564 | 1.65083 | ||||||||
\(118\) | −8.39230 | −0.772574 | ||||||||
\(119\) | 0.535898 | 0.0491257 | ||||||||
\(120\) | 2.73205 | 0.249401 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 8.00000 | 0.724286 | ||||||||
\(123\) | 6.00000 | 0.541002 | ||||||||
\(124\) | 0.535898 | 0.0481251 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.46410 | −0.397694 | ||||||||
\(127\) | 8.39230 | 0.744697 | 0.372348 | − | 0.928093i | \(-0.378553\pi\) | ||||
0.372348 | + | 0.928093i | \(0.378553\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −13.4641 | −1.18545 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | 10.1962 | 0.890842 | 0.445421 | − | 0.895321i | \(-0.353054\pi\) | ||||
0.445421 | + | 0.895321i | \(0.353054\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.732051 | −0.0634769 | ||||||||
\(134\) | −15.8564 | −1.36978 | ||||||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | −0.535898 | −0.0459529 | ||||||||
\(137\) | −7.85641 | −0.671218 | −0.335609 | − | 0.942001i | \(-0.608942\pi\) | ||||
−0.335609 | + | 0.942001i | \(0.608942\pi\) | |||||||
\(138\) | −22.3923 | −1.90616 | ||||||||
\(139\) | −3.66025 | −0.310459 | −0.155229 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155229 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 16.3923 | 1.38048 | ||||||||
\(142\) | −1.07180 | −0.0899432 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.46410 | 0.372008 | ||||||||
\(145\) | 7.66025 | 0.636149 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | 2.73205 | 0.225336 | ||||||||
\(148\) | −2.73205 | −0.224573 | ||||||||
\(149\) | 1.80385 | 0.147777 | 0.0738885 | − | 0.997267i | \(-0.476459\pi\) | ||||
0.0738885 | + | 0.997267i | \(0.476459\pi\) | |||||||
\(150\) | −2.73205 | −0.223071 | ||||||||
\(151\) | −1.80385 | −0.146795 | −0.0733975 | − | 0.997303i | \(-0.523384\pi\) | ||||
−0.0733975 | + | 0.997303i | \(0.523384\pi\) | |||||||
\(152\) | 0.732051 | 0.0593772 | ||||||||
\(153\) | 2.39230 | 0.193406 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.535898 | −0.0430444 | ||||||||
\(156\) | 10.9282 | 0.874957 | ||||||||
\(157\) | −16.5359 | −1.31971 | −0.659854 | − | 0.751394i | \(-0.729382\pi\) | ||||
−0.659854 | + | 0.751394i | \(0.729382\pi\) | |||||||
\(158\) | −7.66025 | −0.609417 | ||||||||
\(159\) | 14.3923 | 1.14138 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 8.19615 | 0.645947 | ||||||||
\(162\) | 2.46410 | 0.193598 | ||||||||
\(163\) | 12.9282 | 1.01262 | 0.506308 | − | 0.862353i | \(-0.331010\pi\) | ||||
0.506308 | + | 0.862353i | \(0.331010\pi\) | |||||||
\(164\) | 2.19615 | 0.171491 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.9282 | −1.15865 | ||||||||
\(167\) | 5.07180 | 0.392467 | 0.196234 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196234 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(168\) | −2.73205 | −0.210782 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0.535898 | 0.0411015 | ||||||||
\(171\) | −3.26795 | −0.249906 | ||||||||
\(172\) | −4.92820 | −0.375772 | ||||||||
\(173\) | 4.92820 | 0.374684 | 0.187342 | − | 0.982295i | \(-0.440013\pi\) | ||||
0.187342 | + | 0.982295i | \(0.440013\pi\) | |||||||
\(174\) | 20.9282 | 1.58656 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.9282 | 1.72339 | ||||||||
\(178\) | 8.92820 | 0.669197 | ||||||||
\(179\) | 6.39230 | 0.477783 | 0.238892 | − | 0.971046i | \(-0.423216\pi\) | ||||
0.238892 | + | 0.971046i | \(0.423216\pi\) | |||||||
\(180\) | −4.46410 | −0.332734 | ||||||||
\(181\) | −4.92820 | −0.366310 | −0.183155 | − | 0.983084i | \(-0.558631\pi\) | ||||
−0.183155 | + | 0.983084i | \(0.558631\pi\) | |||||||
\(182\) | −4.00000 | −0.296500 | ||||||||
\(183\) | −21.8564 | −1.61567 | ||||||||
\(184\) | −8.19615 | −0.604228 | ||||||||
\(185\) | 2.73205 | 0.200864 | ||||||||
\(186\) | −1.46410 | −0.107353 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 4.00000 | 0.290957 | ||||||||
\(190\) | −0.732051 | −0.0531085 | ||||||||
\(191\) | −20.3923 | −1.47554 | −0.737768 | − | 0.675055i | \(-0.764120\pi\) | ||||
−0.737768 | + | 0.675055i | \(0.764120\pi\) | |||||||
\(192\) | 2.73205 | 0.197169 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | −2.73205 | −0.196150 | ||||||||
\(195\) | −10.9282 | −0.782585 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −3.46410 | −0.246807 | −0.123404 | − | 0.992357i | \(-0.539381\pi\) | ||||
−0.123404 | + | 0.992357i | \(0.539381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.85641 | −0.131597 | −0.0657986 | − | 0.997833i | \(-0.520959\pi\) | ||||
−0.0657986 | + | 0.997833i | \(0.520959\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 43.3205 | 3.05559 | ||||||||
\(202\) | −8.00000 | −0.562878 | ||||||||
\(203\) | −7.66025 | −0.537644 | ||||||||
\(204\) | 1.46410 | 0.102508 | ||||||||
\(205\) | −2.19615 | −0.153386 | ||||||||
\(206\) | −2.39230 | −0.166680 | ||||||||
\(207\) | 36.5885 | 2.54307 | ||||||||
\(208\) | 4.00000 | 0.277350 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.73205 | 0.188529 | ||||||||
\(211\) | −13.8564 | −0.953914 | −0.476957 | − | 0.878927i | \(-0.658260\pi\) | ||||
−0.476957 | + | 0.878927i | \(0.658260\pi\) | |||||||
\(212\) | 5.26795 | 0.361804 | ||||||||
\(213\) | 2.92820 | 0.200637 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 4.92820 | 0.336101 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 0.535898 | 0.0363792 | ||||||||
\(218\) | 16.7321 | 1.13324 | ||||||||
\(219\) | −16.3923 | −1.10769 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.14359 | 0.144194 | ||||||||
\(222\) | 7.46410 | 0.500958 | ||||||||
\(223\) | −11.4641 | −0.767693 | −0.383847 | − | 0.923397i | \(-0.625401\pi\) | ||||
−0.383847 | + | 0.923397i | \(0.625401\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | −23.3205 | −1.54784 | −0.773918 | − | 0.633286i | \(-0.781706\pi\) | ||||
−0.773918 | + | 0.633286i | \(0.781706\pi\) | |||||||
\(228\) | −2.00000 | −0.132453 | ||||||||
\(229\) | 23.3205 | 1.54106 | 0.770531 | − | 0.637402i | \(-0.219991\pi\) | ||||
0.770531 | + | 0.637402i | \(0.219991\pi\) | |||||||
\(230\) | 8.19615 | 0.540438 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.66025 | 0.502920 | ||||||||
\(233\) | 23.8564 | 1.56289 | 0.781443 | − | 0.623977i | \(-0.214484\pi\) | ||||
0.781443 | + | 0.623977i | \(0.214484\pi\) | |||||||
\(234\) | −17.8564 | −1.16731 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 8.39230 | 0.546293 | ||||||||
\(237\) | 20.9282 | 1.35943 | ||||||||
\(238\) | −0.535898 | −0.0347371 | ||||||||
\(239\) | 20.0526 | 1.29709 | 0.648546 | − | 0.761175i | \(-0.275377\pi\) | ||||
0.648546 | + | 0.761175i | \(0.275377\pi\) | |||||||
\(240\) | −2.73205 | −0.176353 | ||||||||
\(241\) | −22.9808 | −1.48032 | −0.740161 | − | 0.672430i | \(-0.765251\pi\) | ||||
−0.740161 | + | 0.672430i | \(0.765251\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.7321 | −1.20166 | ||||||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | −2.92820 | −0.186317 | ||||||||
\(248\) | −0.535898 | −0.0340296 | ||||||||
\(249\) | 40.7846 | 2.58462 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −24.7846 | −1.56439 | −0.782195 | − | 0.623033i | \(-0.785900\pi\) | ||||
−0.782195 | + | 0.623033i | \(0.785900\pi\) | |||||||
\(252\) | 4.46410 | 0.281212 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.39230 | −0.526580 | ||||||||
\(255\) | −1.46410 | −0.0916856 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.80385 | −0.486791 | −0.243395 | − | 0.969927i | \(-0.578261\pi\) | ||||
−0.243395 | + | 0.969927i | \(0.578261\pi\) | |||||||
\(258\) | 13.4641 | 0.838238 | ||||||||
\(259\) | −2.73205 | −0.169761 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | −34.1962 | −2.11669 | ||||||||
\(262\) | −10.1962 | −0.629920 | ||||||||
\(263\) | 28.3923 | 1.75074 | 0.875372 | − | 0.483449i | \(-0.160616\pi\) | ||||
0.875372 | + | 0.483449i | \(0.160616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.26795 | −0.323608 | ||||||||
\(266\) | 0.732051 | 0.0448849 | ||||||||
\(267\) | −24.3923 | −1.49278 | ||||||||
\(268\) | 15.8564 | 0.968584 | ||||||||
\(269\) | −4.39230 | −0.267804 | −0.133902 | − | 0.990995i | \(-0.542751\pi\) | ||||
−0.133902 | + | 0.990995i | \(0.542751\pi\) | |||||||
\(270\) | 4.00000 | 0.243432 | ||||||||
\(271\) | 32.3923 | 1.96769 | 0.983846 | − | 0.179016i | \(-0.0572913\pi\) | ||||
0.983846 | + | 0.179016i | \(0.0572913\pi\) | |||||||
\(272\) | 0.535898 | 0.0324936 | ||||||||
\(273\) | 10.9282 | 0.661405 | ||||||||
\(274\) | 7.85641 | 0.474623 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 22.3923 | 1.34786 | ||||||||
\(277\) | −17.3205 | −1.04069 | −0.520344 | − | 0.853957i | \(-0.674196\pi\) | ||||
−0.520344 | + | 0.853957i | \(0.674196\pi\) | |||||||
\(278\) | 3.66025 | 0.219527 | ||||||||
\(279\) | 2.39230 | 0.143224 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −23.3205 | −1.39118 | −0.695592 | − | 0.718437i | \(-0.744858\pi\) | ||||
−0.695592 | + | 0.718437i | \(0.744858\pi\) | |||||||
\(282\) | −16.3923 | −0.976148 | ||||||||
\(283\) | −9.46410 | −0.562582 | −0.281291 | − | 0.959622i | \(-0.590763\pi\) | ||||
−0.281291 | + | 0.959622i | \(0.590763\pi\) | |||||||
\(284\) | 1.07180 | 0.0635994 | ||||||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.19615 | 0.129635 | ||||||||
\(288\) | −4.46410 | −0.263050 | ||||||||
\(289\) | −16.7128 | −0.983107 | ||||||||
\(290\) | −7.66025 | −0.449826 | ||||||||
\(291\) | 7.46410 | 0.437553 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | 27.7128 | 1.61900 | 0.809500 | − | 0.587120i | \(-0.199738\pi\) | ||||
0.809500 | + | 0.587120i | \(0.199738\pi\) | |||||||
\(294\) | −2.73205 | −0.159336 | ||||||||
\(295\) | −8.39230 | −0.488619 | ||||||||
\(296\) | 2.73205 | 0.158797 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.80385 | −0.104494 | ||||||||
\(299\) | 32.7846 | 1.89598 | ||||||||
\(300\) | 2.73205 | 0.157735 | ||||||||
\(301\) | −4.92820 | −0.284057 | ||||||||
\(302\) | 1.80385 | 0.103800 | ||||||||
\(303\) | 21.8564 | 1.25562 | ||||||||
\(304\) | −0.732051 | −0.0419860 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | −2.39230 | −0.136759 | ||||||||
\(307\) | 13.4641 | 0.768437 | 0.384218 | − | 0.923242i | \(-0.374471\pi\) | ||||
0.384218 | + | 0.923242i | \(0.374471\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.53590 | 0.371814 | ||||||||
\(310\) | 0.535898 | 0.0304370 | ||||||||
\(311\) | 17.3205 | 0.982156 | 0.491078 | − | 0.871116i | \(-0.336603\pi\) | ||||
0.491078 | + | 0.871116i | \(0.336603\pi\) | |||||||
\(312\) | −10.9282 | −0.618688 | ||||||||
\(313\) | −2.73205 | −0.154425 | −0.0772123 | − | 0.997015i | \(-0.524602\pi\) | ||||
−0.0772123 | + | 0.997015i | \(0.524602\pi\) | |||||||
\(314\) | 16.5359 | 0.933175 | ||||||||
\(315\) | −4.46410 | −0.251524 | ||||||||
\(316\) | 7.66025 | 0.430923 | ||||||||
\(317\) | −4.58846 | −0.257713 | −0.128857 | − | 0.991663i | \(-0.541131\pi\) | ||||
−0.128857 | + | 0.991663i | \(0.541131\pi\) | |||||||
\(318\) | −14.3923 | −0.807080 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −5.46410 | −0.304976 | ||||||||
\(322\) | −8.19615 | −0.456754 | ||||||||
\(323\) | −0.392305 | −0.0218284 | ||||||||
\(324\) | −2.46410 | −0.136895 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | −12.9282 | −0.716027 | ||||||||
\(327\) | −45.7128 | −2.52792 | ||||||||
\(328\) | −2.19615 | −0.121262 | ||||||||
\(329\) | 6.00000 | 0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.60770 | 0.308227 | 0.154113 | − | 0.988053i | \(-0.450748\pi\) | ||||
0.154113 | + | 0.988053i | \(0.450748\pi\) | |||||||
\(332\) | 14.9282 | 0.819292 | ||||||||
\(333\) | −12.1962 | −0.668345 | ||||||||
\(334\) | −5.07180 | −0.277516 | ||||||||
\(335\) | −15.8564 | −0.866328 | ||||||||
\(336\) | 2.73205 | 0.149046 | ||||||||
\(337\) | 27.8564 | 1.51744 | 0.758718 | − | 0.651420i | \(-0.225826\pi\) | ||||
0.758718 | + | 0.651420i | \(0.225826\pi\) | |||||||
\(338\) | −3.00000 | −0.163178 | ||||||||
\(339\) | 49.1769 | 2.67092 | ||||||||
\(340\) | −0.535898 | −0.0290632 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.26795 | 0.176710 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.92820 | 0.265711 | ||||||||
\(345\) | −22.3923 | −1.20556 | ||||||||
\(346\) | −4.92820 | −0.264942 | ||||||||
\(347\) | 4.92820 | 0.264560 | 0.132280 | − | 0.991212i | \(-0.457770\pi\) | ||||
0.132280 | + | 0.991212i | \(0.457770\pi\) | |||||||
\(348\) | −20.9282 | −1.12187 | ||||||||
\(349\) | 5.46410 | 0.292487 | 0.146243 | − | 0.989249i | \(-0.453282\pi\) | ||||
0.146243 | + | 0.989249i | \(0.453282\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 16.0000 | 0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9808 | 1.32959 | 0.664796 | − | 0.747025i | \(-0.268519\pi\) | ||||
0.664796 | + | 0.747025i | \(0.268519\pi\) | |||||||
\(354\) | −22.9282 | −1.21862 | ||||||||
\(355\) | −1.07180 | −0.0568851 | ||||||||
\(356\) | −8.92820 | −0.473194 | ||||||||
\(357\) | 1.46410 | 0.0774885 | ||||||||
\(358\) | −6.39230 | −0.337844 | ||||||||
\(359\) | 24.4449 | 1.29015 | 0.645075 | − | 0.764119i | \(-0.276826\pi\) | ||||
0.645075 | + | 0.764119i | \(0.276826\pi\) | |||||||
\(360\) | 4.46410 | 0.235279 | ||||||||
\(361\) | −18.4641 | −0.971795 | ||||||||
\(362\) | 4.92820 | 0.259021 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 21.8564 | 1.14245 | ||||||||
\(367\) | −14.3923 | −0.751272 | −0.375636 | − | 0.926767i | \(-0.622576\pi\) | ||||
−0.375636 | + | 0.926767i | \(0.622576\pi\) | |||||||
\(368\) | 8.19615 | 0.427254 | ||||||||
\(369\) | 9.80385 | 0.510368 | ||||||||
\(370\) | −2.73205 | −0.142033 | ||||||||
\(371\) | 5.26795 | 0.273498 | ||||||||
\(372\) | 1.46410 | 0.0759101 | ||||||||
\(373\) | 33.3205 | 1.72527 | 0.862635 | − | 0.505826i | \(-0.168812\pi\) | ||||
0.862635 | + | 0.505826i | \(0.168812\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.73205 | −0.141082 | ||||||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | −30.6410 | −1.57809 | ||||||||
\(378\) | −4.00000 | −0.205738 | ||||||||
\(379\) | 29.8564 | 1.53362 | 0.766810 | − | 0.641874i | \(-0.221843\pi\) | ||||
0.766810 | + | 0.641874i | \(0.221843\pi\) | |||||||
\(380\) | 0.732051 | 0.0375534 | ||||||||
\(381\) | 22.9282 | 1.17465 | ||||||||
\(382\) | 20.3923 | 1.04336 | ||||||||
\(383\) | 3.46410 | 0.177007 | 0.0885037 | − | 0.996076i | \(-0.471792\pi\) | ||||
0.0885037 | + | 0.996076i | \(0.471792\pi\) | |||||||
\(384\) | −2.73205 | −0.139419 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | −22.0000 | −1.11832 | ||||||||
\(388\) | 2.73205 | 0.138699 | ||||||||
\(389\) | 26.3923 | 1.33814 | 0.669071 | − | 0.743198i | \(-0.266692\pi\) | ||||
0.669071 | + | 0.743198i | \(0.266692\pi\) | |||||||
\(390\) | 10.9282 | 0.553371 | ||||||||
\(391\) | 4.39230 | 0.222128 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 27.8564 | 1.40517 | ||||||||
\(394\) | 3.46410 | 0.174519 | ||||||||
\(395\) | −7.66025 | −0.385429 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.46410 | 0.374613 | 0.187306 | − | 0.982302i | \(-0.440024\pi\) | ||||
0.187306 | + | 0.982302i | \(0.440024\pi\) | |||||||
\(398\) | 1.85641 | 0.0930532 | ||||||||
\(399\) | −2.00000 | −0.100125 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 20.3923 | 1.01834 | 0.509172 | − | 0.860665i | \(-0.329952\pi\) | ||||
0.509172 | + | 0.860665i | \(0.329952\pi\) | |||||||
\(402\) | −43.3205 | −2.16063 | ||||||||
\(403\) | 2.14359 | 0.106780 | ||||||||
\(404\) | 8.00000 | 0.398015 | ||||||||
\(405\) | 2.46410 | 0.122442 | ||||||||
\(406\) | 7.66025 | 0.380172 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.46410 | −0.0724838 | ||||||||
\(409\) | 30.1962 | 1.49310 | 0.746552 | − | 0.665327i | \(-0.231708\pi\) | ||||
0.746552 | + | 0.665327i | \(0.231708\pi\) | |||||||
\(410\) | 2.19615 | 0.108460 | ||||||||
\(411\) | −21.4641 | −1.05875 | ||||||||
\(412\) | 2.39230 | 0.117860 | ||||||||
\(413\) | 8.39230 | 0.412958 | ||||||||
\(414\) | −36.5885 | −1.79822 | ||||||||
\(415\) | −14.9282 | −0.732797 | ||||||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | −10.0000 | −0.489702 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.8564 | 1.84941 | 0.924703 | − | 0.380689i | \(-0.124313\pi\) | ||||
0.924703 | + | 0.380689i | \(0.124313\pi\) | |||||||
\(420\) | −2.73205 | −0.133310 | ||||||||
\(421\) | 24.2487 | 1.18181 | 0.590905 | − | 0.806741i | \(-0.298771\pi\) | ||||
0.590905 | + | 0.806741i | \(0.298771\pi\) | |||||||
\(422\) | 13.8564 | 0.674519 | ||||||||
\(423\) | 26.7846 | 1.30231 | ||||||||
\(424\) | −5.26795 | −0.255834 | ||||||||
\(425\) | 0.535898 | 0.0259949 | ||||||||
\(426\) | −2.92820 | −0.141872 | ||||||||
\(427\) | −8.00000 | −0.387147 | ||||||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.92820 | −0.237659 | ||||||||
\(431\) | −16.7321 | −0.805955 | −0.402977 | − | 0.915210i | \(-0.632025\pi\) | ||||
−0.402977 | + | 0.915210i | \(0.632025\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | −29.2679 | −1.40653 | −0.703264 | − | 0.710929i | \(-0.748275\pi\) | ||||
−0.703264 | + | 0.710929i | \(0.748275\pi\) | |||||||
\(434\) | −0.535898 | −0.0257239 | ||||||||
\(435\) | 20.9282 | 1.00343 | ||||||||
\(436\) | −16.7321 | −0.801320 | ||||||||
\(437\) | −6.00000 | −0.287019 | ||||||||
\(438\) | 16.3923 | 0.783255 | ||||||||
\(439\) | −29.4641 | −1.40624 | −0.703122 | − | 0.711069i | \(-0.748211\pi\) | ||||
−0.703122 | + | 0.711069i | \(0.748211\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.46410 | 0.212576 | ||||||||
\(442\) | −2.14359 | −0.101960 | ||||||||
\(443\) | −28.9282 | −1.37442 | −0.687210 | − | 0.726459i | \(-0.741165\pi\) | ||||
−0.687210 | + | 0.726459i | \(0.741165\pi\) | |||||||
\(444\) | −7.46410 | −0.354231 | ||||||||
\(445\) | 8.92820 | 0.423237 | ||||||||
\(446\) | 11.4641 | 0.542841 | ||||||||
\(447\) | 4.92820 | 0.233096 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −10.2487 | −0.483667 | −0.241833 | − | 0.970318i | \(-0.577749\pi\) | ||||
−0.241833 | + | 0.970318i | \(0.577749\pi\) | |||||||
\(450\) | −4.46410 | −0.210440 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 18.0000 | 0.846649 | ||||||||
\(453\) | −4.92820 | −0.231547 | ||||||||
\(454\) | 23.3205 | 1.09449 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | −15.8564 | −0.741731 | −0.370866 | − | 0.928687i | \(-0.620939\pi\) | ||||
−0.370866 | + | 0.928687i | \(0.620939\pi\) | |||||||
\(458\) | −23.3205 | −1.08970 | ||||||||
\(459\) | 2.14359 | 0.100054 | ||||||||
\(460\) | −8.19615 | −0.382148 | ||||||||
\(461\) | −4.67949 | −0.217946 | −0.108973 | − | 0.994045i | \(-0.534756\pi\) | ||||
−0.108973 | + | 0.994045i | \(0.534756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.41154 | 0.344444 | 0.172222 | − | 0.985058i | \(-0.444905\pi\) | ||||
0.172222 | + | 0.985058i | \(0.444905\pi\) | |||||||
\(464\) | −7.66025 | −0.355618 | ||||||||
\(465\) | −1.46410 | −0.0678961 | ||||||||
\(466\) | −23.8564 | −1.10513 | ||||||||
\(467\) | 40.5885 | 1.87821 | 0.939105 | − | 0.343631i | \(-0.111657\pi\) | ||||
0.939105 | + | 0.343631i | \(0.111657\pi\) | |||||||
\(468\) | 17.8564 | 0.825413 | ||||||||
\(469\) | 15.8564 | 0.732181 | ||||||||
\(470\) | 6.00000 | 0.276759 | ||||||||
\(471\) | −45.1769 | −2.08164 | ||||||||
\(472\) | −8.39230 | −0.386287 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −20.9282 | −0.961264 | ||||||||
\(475\) | −0.732051 | −0.0335888 | ||||||||
\(476\) | 0.535898 | 0.0245629 | ||||||||
\(477\) | 23.5167 | 1.07675 | ||||||||
\(478\) | −20.0526 | −0.917183 | ||||||||
\(479\) | −19.7128 | −0.900701 | −0.450351 | − | 0.892852i | \(-0.648701\pi\) | ||||
−0.450351 | + | 0.892852i | \(0.648701\pi\) | |||||||
\(480\) | 2.73205 | 0.124700 | ||||||||
\(481\) | −10.9282 | −0.498283 | ||||||||
\(482\) | 22.9808 | 1.04675 | ||||||||
\(483\) | 22.3923 | 1.01889 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.73205 | −0.124056 | ||||||||
\(486\) | 18.7321 | 0.849703 | ||||||||
\(487\) | −30.0526 | −1.36181 | −0.680906 | − | 0.732371i | \(-0.738414\pi\) | ||||
−0.680906 | + | 0.732371i | \(0.738414\pi\) | |||||||
\(488\) | 8.00000 | 0.362143 | ||||||||
\(489\) | 35.3205 | 1.59725 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −9.07180 | −0.409404 | −0.204702 | − | 0.978824i | \(-0.565623\pi\) | ||||
−0.204702 | + | 0.978824i | \(0.565623\pi\) | |||||||
\(492\) | 6.00000 | 0.270501 | ||||||||
\(493\) | −4.10512 | −0.184885 | ||||||||
\(494\) | 2.92820 | 0.131746 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.535898 | 0.0240625 | ||||||||
\(497\) | 1.07180 | 0.0480767 | ||||||||
\(498\) | −40.7846 | −1.82760 | ||||||||
\(499\) | −22.3923 | −1.00242 | −0.501209 | − | 0.865326i | \(-0.667111\pi\) | ||||
−0.501209 | + | 0.865326i | \(0.667111\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 13.8564 | 0.619059 | ||||||||
\(502\) | 24.7846 | 1.10619 | ||||||||
\(503\) | −10.1436 | −0.452280 | −0.226140 | − | 0.974095i | \(-0.572611\pi\) | ||||
−0.226140 | + | 0.974095i | \(0.572611\pi\) | |||||||
\(504\) | −4.46410 | −0.198847 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.19615 | 0.364004 | ||||||||
\(508\) | 8.39230 | 0.372348 | ||||||||
\(509\) | −0.928203 | −0.0411419 | −0.0205709 | − | 0.999788i | \(-0.506548\pi\) | ||||
−0.0205709 | + | 0.999788i | \(0.506548\pi\) | |||||||
\(510\) | 1.46410 | 0.0648315 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.92820 | −0.129283 | ||||||||
\(514\) | 7.80385 | 0.344213 | ||||||||
\(515\) | −2.39230 | −0.105418 | ||||||||
\(516\) | −13.4641 | −0.592724 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.73205 | 0.120039 | ||||||||
\(519\) | 13.4641 | 0.591008 | ||||||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | −24.2487 | −1.06236 | −0.531178 | − | 0.847260i | \(-0.678250\pi\) | ||||
−0.531178 | + | 0.847260i | \(0.678250\pi\) | |||||||
\(522\) | 34.1962 | 1.49672 | ||||||||
\(523\) | −14.5359 | −0.635610 | −0.317805 | − | 0.948156i | \(-0.602946\pi\) | ||||
−0.317805 | + | 0.948156i | \(0.602946\pi\) | |||||||
\(524\) | 10.1962 | 0.445421 | ||||||||
\(525\) | 2.73205 | 0.119236 | ||||||||
\(526\) | −28.3923 | −1.23796 | ||||||||
\(527\) | 0.287187 | 0.0125101 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.1769 | 1.92074 | ||||||||
\(530\) | 5.26795 | 0.228825 | ||||||||
\(531\) | 37.4641 | 1.62580 | ||||||||
\(532\) | −0.732051 | −0.0317384 | ||||||||
\(533\) | 8.78461 | 0.380504 | ||||||||
\(534\) | 24.3923 | 1.05556 | ||||||||
\(535\) | 2.00000 | 0.0864675 | ||||||||
\(536\) | −15.8564 | −0.684892 | ||||||||
\(537\) | 17.4641 | 0.753632 | ||||||||
\(538\) | 4.39230 | 0.189366 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | −12.7321 | −0.547394 | −0.273697 | − | 0.961816i | \(-0.588246\pi\) | ||||
−0.273697 | + | 0.961816i | \(0.588246\pi\) | |||||||
\(542\) | −32.3923 | −1.39137 | ||||||||
\(543\) | −13.4641 | −0.577800 | ||||||||
\(544\) | −0.535898 | −0.0229765 | ||||||||
\(545\) | 16.7321 | 0.716722 | ||||||||
\(546\) | −10.9282 | −0.467684 | ||||||||
\(547\) | 23.7128 | 1.01389 | 0.506943 | − | 0.861979i | \(-0.330775\pi\) | ||||
0.506943 | + | 0.861979i | \(0.330775\pi\) | |||||||
\(548\) | −7.85641 | −0.335609 | ||||||||
\(549\) | −35.7128 | −1.52419 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.60770 | 0.238896 | ||||||||
\(552\) | −22.3923 | −0.953080 | ||||||||
\(553\) | 7.66025 | 0.325747 | ||||||||
\(554\) | 17.3205 | 0.735878 | ||||||||
\(555\) | 7.46410 | 0.316833 | ||||||||
\(556\) | −3.66025 | −0.155229 | ||||||||
\(557\) | 3.07180 | 0.130156 | 0.0650781 | − | 0.997880i | \(-0.479270\pi\) | ||||
0.0650781 | + | 0.997880i | \(0.479270\pi\) | |||||||
\(558\) | −2.39230 | −0.101274 | ||||||||
\(559\) | −19.7128 | −0.833763 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.3205 | 0.983716 | ||||||||
\(563\) | 39.7128 | 1.67370 | 0.836848 | − | 0.547436i | \(-0.184396\pi\) | ||||
0.836848 | + | 0.547436i | \(0.184396\pi\) | |||||||
\(564\) | 16.3923 | 0.690241 | ||||||||
\(565\) | −18.0000 | −0.757266 | ||||||||
\(566\) | 9.46410 | 0.397806 | ||||||||
\(567\) | −2.46410 | −0.103483 | ||||||||
\(568\) | −1.07180 | −0.0449716 | ||||||||
\(569\) | −33.8564 | −1.41933 | −0.709667 | − | 0.704537i | \(-0.751155\pi\) | ||||
−0.709667 | + | 0.704537i | \(0.751155\pi\) | |||||||
\(570\) | −2.00000 | −0.0837708 | ||||||||
\(571\) | 19.3205 | 0.808538 | 0.404269 | − | 0.914640i | \(-0.367526\pi\) | ||||
0.404269 | + | 0.914640i | \(0.367526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −55.7128 | −2.32744 | ||||||||
\(574\) | −2.19615 | −0.0916656 | ||||||||
\(575\) | 8.19615 | 0.341803 | ||||||||
\(576\) | 4.46410 | 0.186004 | ||||||||
\(577\) | 1.26795 | 0.0527854 | 0.0263927 | − | 0.999652i | \(-0.491598\pi\) | ||||
0.0263927 | + | 0.999652i | \(0.491598\pi\) | |||||||
\(578\) | 16.7128 | 0.695161 | ||||||||
\(579\) | −43.7128 | −1.81664 | ||||||||
\(580\) | 7.66025 | 0.318075 | ||||||||
\(581\) | 14.9282 | 0.619326 | ||||||||
\(582\) | −7.46410 | −0.309397 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | −17.8564 | −0.738272 | ||||||||
\(586\) | −27.7128 | −1.14481 | ||||||||
\(587\) | 26.7321 | 1.10335 | 0.551675 | − | 0.834059i | \(-0.313989\pi\) | ||||
0.551675 | + | 0.834059i | \(0.313989\pi\) | |||||||
\(588\) | 2.73205 | 0.112668 | ||||||||
\(589\) | −0.392305 | −0.0161646 | ||||||||
\(590\) | 8.39230 | 0.345506 | ||||||||
\(591\) | −9.46410 | −0.389301 | ||||||||
\(592\) | −2.73205 | −0.112287 | ||||||||
\(593\) | −28.6410 | −1.17615 | −0.588073 | − | 0.808808i | \(-0.700113\pi\) | ||||
−0.588073 | + | 0.808808i | \(0.700113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.535898 | −0.0219697 | ||||||||
\(596\) | 1.80385 | 0.0738885 | ||||||||
\(597\) | −5.07180 | −0.207575 | ||||||||
\(598\) | −32.7846 | −1.34066 | ||||||||
\(599\) | −46.9282 | −1.91743 | −0.958717 | − | 0.284361i | \(-0.908218\pi\) | ||||
−0.958717 | + | 0.284361i | \(0.908218\pi\) | |||||||
\(600\) | −2.73205 | −0.111536 | ||||||||
\(601\) | 2.87564 | 0.117300 | 0.0586500 | − | 0.998279i | \(-0.481320\pi\) | ||||
0.0586500 | + | 0.998279i | \(0.481320\pi\) | |||||||
\(602\) | 4.92820 | 0.200859 | ||||||||
\(603\) | 70.7846 | 2.88257 | ||||||||
\(604\) | −1.80385 | −0.0733975 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −21.8564 | −0.887856 | ||||||||
\(607\) | 10.0000 | 0.405887 | 0.202944 | − | 0.979190i | \(-0.434949\pi\) | ||||
0.202944 | + | 0.979190i | \(0.434949\pi\) | |||||||
\(608\) | 0.732051 | 0.0296886 | ||||||||
\(609\) | −20.9282 | −0.848054 | ||||||||
\(610\) | −8.00000 | −0.323911 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | 2.39230 | 0.0967032 | ||||||||
\(613\) | 41.7128 | 1.68476 | 0.842382 | − | 0.538880i | \(-0.181153\pi\) | ||||
0.842382 | + | 0.538880i | \(0.181153\pi\) | |||||||
\(614\) | −13.4641 | −0.543367 | ||||||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.3923 | 1.54562 | 0.772808 | − | 0.634640i | \(-0.218852\pi\) | ||||
0.772808 | + | 0.634640i | \(0.218852\pi\) | |||||||
\(618\) | −6.53590 | −0.262912 | ||||||||
\(619\) | 5.07180 | 0.203853 | 0.101926 | − | 0.994792i | \(-0.467499\pi\) | ||||
0.101926 | + | 0.994792i | \(0.467499\pi\) | |||||||
\(620\) | −0.535898 | −0.0215222 | ||||||||
\(621\) | 32.7846 | 1.31560 | ||||||||
\(622\) | −17.3205 | −0.694489 | ||||||||
\(623\) | −8.92820 | −0.357701 | ||||||||
\(624\) | 10.9282 | 0.437478 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.73205 | 0.109195 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.5359 | −0.659854 | ||||||||
\(629\) | −1.46410 | −0.0583776 | ||||||||
\(630\) | 4.46410 | 0.177854 | ||||||||
\(631\) | −25.8564 | −1.02933 | −0.514664 | − | 0.857392i | \(-0.672083\pi\) | ||||
−0.514664 | + | 0.857392i | \(0.672083\pi\) | |||||||
\(632\) | −7.66025 | −0.304709 | ||||||||
\(633\) | −37.8564 | −1.50466 | ||||||||
\(634\) | 4.58846 | 0.182231 | ||||||||
\(635\) | −8.39230 | −0.333038 | ||||||||
\(636\) | 14.3923 | 0.570692 | ||||||||
\(637\) | 4.00000 | 0.158486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.78461 | 0.189276 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −23.8564 | −0.942271 | −0.471136 | − | 0.882061i | \(-0.656156\pi\) | ||||
−0.471136 | + | 0.882061i | \(0.656156\pi\) | |||||||
\(642\) | 5.46410 | 0.215651 | ||||||||
\(643\) | 4.19615 | 0.165480 | 0.0827400 | − | 0.996571i | \(-0.473633\pi\) | ||||
0.0827400 | + | 0.996571i | \(0.473633\pi\) | |||||||
\(644\) | 8.19615 | 0.322974 | ||||||||
\(645\) | 13.4641 | 0.530148 | ||||||||
\(646\) | 0.392305 | 0.0154350 | ||||||||
\(647\) | −5.60770 | −0.220461 | −0.110231 | − | 0.993906i | \(-0.535159\pi\) | ||||
−0.110231 | + | 0.993906i | \(0.535159\pi\) | |||||||
\(648\) | 2.46410 | 0.0967991 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | −0.156893 | ||||||||
\(651\) | 1.46410 | 0.0573827 | ||||||||
\(652\) | 12.9282 | 0.506308 | ||||||||
\(653\) | −34.7321 | −1.35917 | −0.679585 | − | 0.733597i | \(-0.737840\pi\) | ||||
−0.679585 | + | 0.733597i | \(0.737840\pi\) | |||||||
\(654\) | 45.7128 | 1.78751 | ||||||||
\(655\) | −10.1962 | −0.398397 | ||||||||
\(656\) | 2.19615 | 0.0857453 | ||||||||
\(657\) | −26.7846 | −1.04497 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | 40.3923 | 1.57346 | 0.786730 | − | 0.617297i | \(-0.211772\pi\) | ||||
0.786730 | + | 0.617297i | \(0.211772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | −5.60770 | −0.217949 | ||||||||
\(663\) | 5.85641 | 0.227444 | ||||||||
\(664\) | −14.9282 | −0.579327 | ||||||||
\(665\) | 0.732051 | 0.0283877 | ||||||||
\(666\) | 12.1962 | 0.472591 | ||||||||
\(667\) | −62.7846 | −2.43103 | ||||||||
\(668\) | 5.07180 | 0.196234 | ||||||||
\(669\) | −31.3205 | −1.21092 | ||||||||
\(670\) | 15.8564 | 0.612586 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.73205 | −0.105391 | ||||||||
\(673\) | −43.8564 | −1.69054 | −0.845270 | − | 0.534339i | \(-0.820560\pi\) | ||||
−0.845270 | + | 0.534339i | \(0.820560\pi\) | |||||||
\(674\) | −27.8564 | −1.07299 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −12.9282 | −0.496871 | −0.248436 | − | 0.968648i | \(-0.579916\pi\) | ||||
−0.248436 | + | 0.968648i | \(0.579916\pi\) | |||||||
\(678\) | −49.1769 | −1.88863 | ||||||||
\(679\) | 2.73205 | 0.104846 | ||||||||
\(680\) | 0.535898 | 0.0205508 | ||||||||
\(681\) | −63.7128 | −2.44148 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.60770 | 0.0615167 | 0.0307584 | − | 0.999527i | \(-0.490208\pi\) | ||||
0.0307584 | + | 0.999527i | \(0.490208\pi\) | |||||||
\(684\) | −3.26795 | −0.124953 | ||||||||
\(685\) | 7.85641 | 0.300178 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 63.7128 | 2.43080 | ||||||||
\(688\) | −4.92820 | −0.187886 | ||||||||
\(689\) | 21.0718 | 0.802772 | ||||||||
\(690\) | 22.3923 | 0.852460 | ||||||||
\(691\) | −14.9282 | −0.567896 | −0.283948 | − | 0.958840i | \(-0.591644\pi\) | ||||
−0.283948 | + | 0.958840i | \(0.591644\pi\) | |||||||
\(692\) | 4.92820 | 0.187342 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.92820 | −0.187072 | ||||||||
\(695\) | 3.66025 | 0.138841 | ||||||||
\(696\) | 20.9282 | 0.793281 | ||||||||
\(697\) | 1.17691 | 0.0445788 | ||||||||
\(698\) | −5.46410 | −0.206819 | ||||||||
\(699\) | 65.1769 | 2.46522 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 31.2679 | 1.18097 | 0.590487 | − | 0.807047i | \(-0.298936\pi\) | ||||
0.590487 | + | 0.807047i | \(0.298936\pi\) | |||||||
\(702\) | −16.0000 | −0.603881 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.3923 | −0.617370 | ||||||||
\(706\) | −24.9808 | −0.940163 | ||||||||
\(707\) | 8.00000 | 0.300871 | ||||||||
\(708\) | 22.9282 | 0.861695 | ||||||||
\(709\) | −3.85641 | −0.144830 | −0.0724152 | − | 0.997375i | \(-0.523071\pi\) | ||||
−0.0724152 | + | 0.997375i | \(0.523071\pi\) | |||||||
\(710\) | 1.07180 | 0.0402238 | ||||||||
\(711\) | 34.1962 | 1.28246 | ||||||||
\(712\) | 8.92820 | 0.334599 | ||||||||
\(713\) | 4.39230 | 0.164493 | ||||||||
\(714\) | −1.46410 | −0.0547926 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.39230 | 0.238892 | ||||||||
\(717\) | 54.7846 | 2.04597 | ||||||||
\(718\) | −24.4449 | −0.912274 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | −4.46410 | −0.166367 | ||||||||
\(721\) | 2.39230 | 0.0890941 | ||||||||
\(722\) | 18.4641 | 0.687163 | ||||||||
\(723\) | −62.7846 | −2.33498 | ||||||||
\(724\) | −4.92820 | −0.183155 | ||||||||
\(725\) | −7.66025 | −0.284495 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.7128 | −1.69539 | −0.847697 | − | 0.530480i | \(-0.822012\pi\) | ||||
−0.847697 | + | 0.530480i | \(0.822012\pi\) | |||||||
\(728\) | −4.00000 | −0.148250 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | −2.64102 | −0.0976815 | ||||||||
\(732\) | −21.8564 | −0.807836 | ||||||||
\(733\) | 51.8564 | 1.91536 | 0.957680 | − | 0.287835i | \(-0.0929354\pi\) | ||||
0.957680 | + | 0.287835i | \(0.0929354\pi\) | |||||||
\(734\) | 14.3923 | 0.531230 | ||||||||
\(735\) | −2.73205 | −0.100773 | ||||||||
\(736\) | −8.19615 | −0.302114 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −9.80385 | −0.360885 | ||||||||
\(739\) | −9.85641 | −0.362574 | −0.181287 | − | 0.983430i | \(-0.558026\pi\) | ||||
−0.181287 | + | 0.983430i | \(0.558026\pi\) | |||||||
\(740\) | 2.73205 | 0.100432 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | −5.26795 | −0.193392 | ||||||||
\(743\) | −3.60770 | −0.132353 | −0.0661767 | − | 0.997808i | \(-0.521080\pi\) | ||||
−0.0661767 | + | 0.997808i | \(0.521080\pi\) | |||||||
\(744\) | −1.46410 | −0.0536766 | ||||||||
\(745\) | −1.80385 | −0.0660879 | ||||||||
\(746\) | −33.3205 | −1.21995 | ||||||||
\(747\) | 66.6410 | 2.43827 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.00000 | −0.0730784 | ||||||||
\(750\) | 2.73205 | 0.0997604 | ||||||||
\(751\) | 22.1436 | 0.808031 | 0.404016 | − | 0.914752i | \(-0.367614\pi\) | ||||
0.404016 | + | 0.914752i | \(0.367614\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | −67.7128 | −2.46759 | ||||||||
\(754\) | 30.6410 | 1.11588 | ||||||||
\(755\) | 1.80385 | 0.0656487 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | −10.3397 | −0.375804 | −0.187902 | − | 0.982188i | \(-0.560169\pi\) | ||||
−0.187902 | + | 0.982188i | \(0.560169\pi\) | |||||||
\(758\) | −29.8564 | −1.08443 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.732051 | −0.0265543 | ||||||||
\(761\) | −34.5885 | −1.25383 | −0.626915 | − | 0.779087i | \(-0.715683\pi\) | ||||
−0.626915 | + | 0.779087i | \(0.715683\pi\) | |||||||
\(762\) | −22.9282 | −0.830601 | ||||||||
\(763\) | −16.7321 | −0.605741 | ||||||||
\(764\) | −20.3923 | −0.737768 | ||||||||
\(765\) | −2.39230 | −0.0864940 | ||||||||
\(766\) | −3.46410 | −0.125163 | ||||||||
\(767\) | 33.5692 | 1.21211 | ||||||||
\(768\) | 2.73205 | 0.0985844 | ||||||||
\(769\) | 3.26795 | 0.117845 | 0.0589226 | − | 0.998263i | \(-0.481233\pi\) | ||||
0.0589226 | + | 0.998263i | \(0.481233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.3205 | −0.767839 | ||||||||
\(772\) | −16.0000 | −0.575853 | ||||||||
\(773\) | −45.7128 | −1.64418 | −0.822088 | − | 0.569361i | \(-0.807191\pi\) | ||||
−0.822088 | + | 0.569361i | \(0.807191\pi\) | |||||||
\(774\) | 22.0000 | 0.790774 | ||||||||
\(775\) | 0.535898 | 0.0192500 | ||||||||
\(776\) | −2.73205 | −0.0980749 | ||||||||
\(777\) | −7.46410 | −0.267773 | ||||||||
\(778\) | −26.3923 | −0.946210 | ||||||||
\(779\) | −1.60770 | −0.0576017 | ||||||||
\(780\) | −10.9282 | −0.391292 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.39230 | −0.157069 | ||||||||
\(783\) | −30.6410 | −1.09502 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 16.5359 | 0.590192 | ||||||||
\(786\) | −27.8564 | −0.993605 | ||||||||
\(787\) | 4.78461 | 0.170553 | 0.0852765 | − | 0.996357i | \(-0.472823\pi\) | ||||
0.0852765 | + | 0.996357i | \(0.472823\pi\) | |||||||
\(788\) | −3.46410 | −0.123404 | ||||||||
\(789\) | 77.5692 | 2.76154 | ||||||||
\(790\) | 7.66025 | 0.272540 | ||||||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.0000 | −1.13635 | ||||||||
\(794\) | −7.46410 | −0.264891 | ||||||||
\(795\) | −14.3923 | −0.510442 | ||||||||
\(796\) | −1.85641 | −0.0657986 | ||||||||
\(797\) | 18.3923 | 0.651489 | 0.325744 | − | 0.945458i | \(-0.394385\pi\) | ||||
0.325744 | + | 0.945458i | \(0.394385\pi\) | |||||||
\(798\) | 2.00000 | 0.0707992 | ||||||||
\(799\) | 3.21539 | 0.113752 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −39.8564 | −1.40826 | ||||||||
\(802\) | −20.3923 | −0.720077 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 43.3205 | 1.52780 | ||||||||
\(805\) | −8.19615 | −0.288876 | ||||||||
\(806\) | −2.14359 | −0.0755049 | ||||||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | −8.00000 | −0.281439 | ||||||||
\(809\) | −44.1051 | −1.55065 | −0.775327 | − | 0.631560i | \(-0.782415\pi\) | ||||
−0.775327 | + | 0.631560i | \(0.782415\pi\) | |||||||
\(810\) | −2.46410 | −0.0865797 | ||||||||
\(811\) | 3.26795 | 0.114753 | 0.0573766 | − | 0.998353i | \(-0.481726\pi\) | ||||
0.0573766 | + | 0.998353i | \(0.481726\pi\) | |||||||
\(812\) | −7.66025 | −0.268822 | ||||||||
\(813\) | 88.4974 | 3.10374 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.9282 | −0.452855 | ||||||||
\(816\) | 1.46410 | 0.0512538 | ||||||||
\(817\) | 3.60770 | 0.126217 | ||||||||
\(818\) | −30.1962 | −1.05578 | ||||||||
\(819\) | 17.8564 | 0.623953 | ||||||||
\(820\) | −2.19615 | −0.0766930 | ||||||||
\(821\) | −23.3731 | −0.815726 | −0.407863 | − | 0.913043i | \(-0.633726\pi\) | ||||
−0.407863 | + | 0.913043i | \(0.633726\pi\) | |||||||
\(822\) | 21.4641 | 0.748647 | ||||||||
\(823\) | 1.94744 | 0.0678835 | 0.0339418 | − | 0.999424i | \(-0.489194\pi\) | ||||
0.0339418 | + | 0.999424i | \(0.489194\pi\) | |||||||
\(824\) | −2.39230 | −0.0833399 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.39230 | −0.292006 | ||||||||
\(827\) | −20.7846 | −0.722752 | −0.361376 | − | 0.932420i | \(-0.617693\pi\) | ||||
−0.361376 | + | 0.932420i | \(0.617693\pi\) | |||||||
\(828\) | 36.5885 | 1.27154 | ||||||||
\(829\) | 3.60770 | 0.125300 | 0.0626502 | − | 0.998036i | \(-0.480045\pi\) | ||||
0.0626502 | + | 0.998036i | \(0.480045\pi\) | |||||||
\(830\) | 14.9282 | 0.518165 | ||||||||
\(831\) | −47.3205 | −1.64153 | ||||||||
\(832\) | 4.00000 | 0.138675 | ||||||||
\(833\) | 0.535898 | 0.0185678 | ||||||||
\(834\) | 10.0000 | 0.346272 | ||||||||
\(835\) | −5.07180 | −0.175517 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.14359 | 0.0740934 | ||||||||
\(838\) | −37.8564 | −1.30773 | ||||||||
\(839\) | −28.2487 | −0.975254 | −0.487627 | − | 0.873052i | \(-0.662137\pi\) | ||||
−0.487627 | + | 0.873052i | \(0.662137\pi\) | |||||||
\(840\) | 2.73205 | 0.0942647 | ||||||||
\(841\) | 29.6795 | 1.02343 | ||||||||
\(842\) | −24.2487 | −0.835666 | ||||||||
\(843\) | −63.7128 | −2.19439 | ||||||||
\(844\) | −13.8564 | −0.476957 | ||||||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | −26.7846 | −0.920874 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.26795 | 0.180902 | ||||||||
\(849\) | −25.8564 | −0.887390 | ||||||||
\(850\) | −0.535898 | −0.0183812 | ||||||||
\(851\) | −22.3923 | −0.767598 | ||||||||
\(852\) | 2.92820 | 0.100319 | ||||||||
\(853\) | −24.6410 | −0.843692 | −0.421846 | − | 0.906667i | \(-0.638618\pi\) | ||||
−0.421846 | + | 0.906667i | \(0.638618\pi\) | |||||||
\(854\) | 8.00000 | 0.273754 | ||||||||
\(855\) | 3.26795 | 0.111762 | ||||||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | −24.9282 | −0.851531 | −0.425766 | − | 0.904833i | \(-0.639995\pi\) | ||||
−0.425766 | + | 0.904833i | \(0.639995\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.0718 | 0.446004 | 0.223002 | − | 0.974818i | \(-0.428414\pi\) | ||||
0.223002 | + | 0.974818i | \(0.428414\pi\) | |||||||
\(860\) | 4.92820 | 0.168050 | ||||||||
\(861\) | 6.00000 | 0.204479 | ||||||||
\(862\) | 16.7321 | 0.569896 | ||||||||
\(863\) | 5.66025 | 0.192677 | 0.0963386 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963386 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(864\) | −4.00000 | −0.136083 | ||||||||
\(865\) | −4.92820 | −0.167564 | ||||||||
\(866\) | 29.2679 | 0.994565 | ||||||||
\(867\) | −45.6603 | −1.55070 | ||||||||
\(868\) | 0.535898 | 0.0181896 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −20.9282 | −0.709533 | ||||||||
\(871\) | 63.4256 | 2.14910 | ||||||||
\(872\) | 16.7321 | 0.566619 | ||||||||
\(873\) | 12.1962 | 0.412777 | ||||||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −16.3923 | −0.553845 | ||||||||
\(877\) | −38.3923 | −1.29642 | −0.648208 | − | 0.761463i | \(-0.724481\pi\) | ||||
−0.648208 | + | 0.761463i | \(0.724481\pi\) | |||||||
\(878\) | 29.4641 | 0.994365 | ||||||||
\(879\) | 75.7128 | 2.55373 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.28719 | 0.0770573 | 0.0385286 | − | 0.999257i | \(-0.487733\pi\) | ||||
0.0385286 | + | 0.999257i | \(0.487733\pi\) | |||||||
\(882\) | −4.46410 | −0.150314 | ||||||||
\(883\) | −57.3205 | −1.92899 | −0.964494 | − | 0.264104i | \(-0.914924\pi\) | ||||
−0.964494 | + | 0.264104i | \(0.914924\pi\) | |||||||
\(884\) | 2.14359 | 0.0720969 | ||||||||
\(885\) | −22.9282 | −0.770723 | ||||||||
\(886\) | 28.9282 | 0.971862 | ||||||||
\(887\) | −46.6410 | −1.56605 | −0.783026 | − | 0.621989i | \(-0.786325\pi\) | ||||
−0.783026 | + | 0.621989i | \(0.786325\pi\) | |||||||
\(888\) | 7.46410 | 0.250479 | ||||||||
\(889\) | 8.39230 | 0.281469 | ||||||||
\(890\) | −8.92820 | −0.299274 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.4641 | −0.383847 | ||||||||
\(893\) | −4.39230 | −0.146983 | ||||||||
\(894\) | −4.92820 | −0.164824 | ||||||||
\(895\) | −6.39230 | −0.213671 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 89.5692 | 2.99063 | ||||||||
\(898\) | 10.2487 | 0.342004 | ||||||||
\(899\) | −4.10512 | −0.136913 | ||||||||
\(900\) | 4.46410 | 0.148803 | ||||||||
\(901\) | 2.82309 | 0.0940506 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.4641 | −0.448057 | ||||||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 4.92820 | 0.163819 | ||||||||
\(906\) | 4.92820 | 0.163729 | ||||||||
\(907\) | −9.32051 | −0.309482 | −0.154741 | − | 0.987955i | \(-0.549454\pi\) | ||||
−0.154741 | + | 0.987955i | \(0.549454\pi\) | |||||||
\(908\) | −23.3205 | −0.773918 | ||||||||
\(909\) | 35.7128 | 1.18452 | ||||||||
\(910\) | 4.00000 | 0.132599 | ||||||||
\(911\) | 43.0333 | 1.42576 | 0.712879 | − | 0.701287i | \(-0.247391\pi\) | ||||
0.712879 | + | 0.701287i | \(0.247391\pi\) | |||||||
\(912\) | −2.00000 | −0.0662266 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 15.8564 | 0.524483 | ||||||||
\(915\) | 21.8564 | 0.722551 | ||||||||
\(916\) | 23.3205 | 0.770531 | ||||||||
\(917\) | 10.1962 | 0.336707 | ||||||||
\(918\) | −2.14359 | −0.0707491 | ||||||||
\(919\) | −35.3731 | −1.16685 | −0.583425 | − | 0.812167i | \(-0.698288\pi\) | ||||
−0.583425 | + | 0.812167i | \(0.698288\pi\) | |||||||
\(920\) | 8.19615 | 0.270219 | ||||||||
\(921\) | 36.7846 | 1.21209 | ||||||||
\(922\) | 4.67949 | 0.154111 | ||||||||
\(923\) | 4.28719 | 0.141114 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.73205 | −0.0898293 | ||||||||
\(926\) | −7.41154 | −0.243558 | ||||||||
\(927\) | 10.6795 | 0.350761 | ||||||||
\(928\) | 7.66025 | 0.251460 | ||||||||
\(929\) | −36.2487 | −1.18928 | −0.594641 | − | 0.803991i | \(-0.702706\pi\) | ||||
−0.594641 | + | 0.803991i | \(0.702706\pi\) | |||||||
\(930\) | 1.46410 | 0.0480098 | ||||||||
\(931\) | −0.732051 | −0.0239920 | ||||||||
\(932\) | 23.8564 | 0.781443 | ||||||||
\(933\) | 47.3205 | 1.54920 | ||||||||
\(934\) | −40.5885 | −1.32809 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −17.8564 | −0.583655 | ||||||||
\(937\) | −6.67949 | −0.218209 | −0.109105 | − | 0.994030i | \(-0.534798\pi\) | ||||
−0.109105 | + | 0.994030i | \(0.534798\pi\) | |||||||
\(938\) | −15.8564 | −0.517730 | ||||||||
\(939\) | −7.46410 | −0.243582 | ||||||||
\(940\) | −6.00000 | −0.195698 | ||||||||
\(941\) | −6.92820 | −0.225853 | −0.112926 | − | 0.993603i | \(-0.536022\pi\) | ||||
−0.112926 | + | 0.993603i | \(0.536022\pi\) | |||||||
\(942\) | 45.1769 | 1.47194 | ||||||||
\(943\) | 18.0000 | 0.586161 | ||||||||
\(944\) | 8.39230 | 0.273146 | ||||||||
\(945\) | −4.00000 | −0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.39230 | 0.0777395 | 0.0388697 | − | 0.999244i | \(-0.487624\pi\) | ||||
0.0388697 | + | 0.999244i | \(0.487624\pi\) | |||||||
\(948\) | 20.9282 | 0.679716 | ||||||||
\(949\) | −24.0000 | −0.779073 | ||||||||
\(950\) | 0.732051 | 0.0237509 | ||||||||
\(951\) | −12.5359 | −0.406504 | ||||||||
\(952\) | −0.535898 | −0.0173686 | ||||||||
\(953\) | 22.6410 | 0.733414 | 0.366707 | − | 0.930336i | \(-0.380485\pi\) | ||||
0.366707 | + | 0.930336i | \(0.380485\pi\) | |||||||
\(954\) | −23.5167 | −0.761380 | ||||||||
\(955\) | 20.3923 | 0.659879 | ||||||||
\(956\) | 20.0526 | 0.648546 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.7128 | 0.636892 | ||||||||
\(959\) | −7.85641 | −0.253697 | ||||||||
\(960\) | −2.73205 | −0.0881766 | ||||||||
\(961\) | −30.7128 | −0.990736 | ||||||||
\(962\) | 10.9282 | 0.352339 | ||||||||
\(963\) | −8.92820 | −0.287707 | ||||||||
\(964\) | −22.9808 | −0.740161 | ||||||||
\(965\) | 16.0000 | 0.515058 | ||||||||
\(966\) | −22.3923 | −0.720461 | ||||||||
\(967\) | 36.3923 | 1.17030 | 0.585149 | − | 0.810926i | \(-0.301036\pi\) | ||||
0.585149 | + | 0.810926i | \(0.301036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.07180 | −0.0344311 | ||||||||
\(970\) | 2.73205 | 0.0877209 | ||||||||
\(971\) | 3.60770 | 0.115776 | 0.0578882 | − | 0.998323i | \(-0.481563\pi\) | ||||
0.0578882 | + | 0.998323i | \(0.481563\pi\) | |||||||
\(972\) | −18.7321 | −0.600831 | ||||||||
\(973\) | −3.66025 | −0.117342 | ||||||||
\(974\) | 30.0526 | 0.962946 | ||||||||
\(975\) | 10.9282 | 0.349983 | ||||||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 31.8564 | 1.01918 | 0.509588 | − | 0.860418i | \(-0.329798\pi\) | ||||
0.509588 | + | 0.860418i | \(0.329798\pi\) | |||||||
\(978\) | −35.3205 | −1.12943 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −74.6936 | −2.38478 | ||||||||
\(982\) | 9.07180 | 0.289493 | ||||||||
\(983\) | 27.4641 | 0.875969 | 0.437984 | − | 0.898983i | \(-0.355693\pi\) | ||||
0.437984 | + | 0.898983i | \(0.355693\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | 3.46410 | 0.110375 | ||||||||
\(986\) | 4.10512 | 0.130734 | ||||||||
\(987\) | 16.3923 | 0.521773 | ||||||||
\(988\) | −2.92820 | −0.0931586 | ||||||||
\(989\) | −40.3923 | −1.28440 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.60770 | −0.114602 | −0.0573011 | − | 0.998357i | \(-0.518250\pi\) | ||||
−0.0573011 | + | 0.998357i | \(0.518250\pi\) | |||||||
\(992\) | −0.535898 | −0.0170148 | ||||||||
\(993\) | 15.3205 | 0.486182 | ||||||||
\(994\) | −1.07180 | −0.0339953 | ||||||||
\(995\) | 1.85641 | 0.0588520 | ||||||||
\(996\) | 40.7846 | 1.29231 | ||||||||
\(997\) | 23.8564 | 0.755540 | 0.377770 | − | 0.925899i | \(-0.376691\pi\) | ||||
0.377770 | + | 0.925899i | \(0.376691\pi\) | |||||||
\(998\) | 22.3923 | 0.708816 | ||||||||
\(999\) | −10.9282 | −0.345753 |
(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 | 8470.2.a.bs.1.2 | ✓ | 2 | |
11.10 | odd | 2 | 8470.2.a.cd.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bs.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8470.2.a.cd.1.2 | yes | 2 | 11.10 | odd | 2 |