Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1450,2,Mod(1,1450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1450, 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("1450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1450 = 2 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1450.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: | \(11.5783082931\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
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 | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1450.1 |
$q$-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 | ||||||||
\(3\) | −2.44949 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44949 | −1.00000 | ||||||||
\(7\) | 4.44949 | 1.68175 | 0.840875 | − | 0.541230i | \(-0.182041\pi\) | ||||
0.840875 | + | 0.541230i | \(0.182041\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −2.44949 | −0.707107 | ||||||||
\(13\) | −2.44949 | −0.679366 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(14\) | 4.44949 | 1.18918 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | 6.44949 | 1.47961 | 0.739807 | − | 0.672819i | \(-0.234917\pi\) | ||||
0.739807 | + | 0.672819i | \(0.234917\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.8990 | −2.37835 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −2.44949 | −0.510754 | −0.255377 | − | 0.966842i | \(-0.582200\pi\) | ||||
−0.255377 | + | 0.966842i | \(0.582200\pi\) | |||||||
\(24\) | −2.44949 | −0.500000 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.44949 | −0.480384 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.44949 | 0.840875 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.89898 | −0.852803 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −3.44949 | −0.567093 | −0.283546 | − | 0.958959i | \(-0.591511\pi\) | ||||
−0.283546 | + | 0.958959i | \(0.591511\pi\) | |||||||
\(38\) | 6.44949 | 1.04625 | ||||||||
\(39\) | 6.00000 | 0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3485 | 1.77233 | 0.886167 | − | 0.463367i | \(-0.153359\pi\) | ||||
0.886167 | + | 0.463367i | \(0.153359\pi\) | |||||||
\(42\) | −10.8990 | −1.68175 | ||||||||
\(43\) | −8.89898 | −1.35708 | −0.678541 | − | 0.734563i | \(-0.737387\pi\) | ||||
−0.678541 | + | 0.734563i | \(0.737387\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.44949 | −0.361158 | ||||||||
\(47\) | 5.89898 | 0.860455 | 0.430227 | − | 0.902721i | \(-0.358433\pi\) | ||||
0.430227 | + | 0.902721i | \(0.358433\pi\) | |||||||
\(48\) | −2.44949 | −0.353553 | ||||||||
\(49\) | 12.7980 | 1.82828 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.89898 | 0.685994 | ||||||||
\(52\) | −2.44949 | −0.339683 | ||||||||
\(53\) | 10.4495 | 1.43535 | 0.717674 | − | 0.696379i | \(-0.245207\pi\) | ||||
0.717674 | + | 0.696379i | \(0.245207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.44949 | 0.594588 | ||||||||
\(57\) | −15.7980 | −2.09249 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 8.55051 | 1.11318 | 0.556591 | − | 0.830787i | \(-0.312109\pi\) | ||||
0.556591 | + | 0.830787i | \(0.312109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.44949 | 0.441662 | 0.220831 | − | 0.975312i | \(-0.429123\pi\) | ||||
0.220831 | + | 0.975312i | \(0.429123\pi\) | |||||||
\(62\) | −3.00000 | −0.381000 | ||||||||
\(63\) | 13.3485 | 1.68175 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.89898 | −0.603023 | ||||||||
\(67\) | −13.4495 | −1.64312 | −0.821558 | − | 0.570124i | \(-0.806895\pi\) | ||||
−0.821558 | + | 0.570124i | \(0.806895\pi\) | |||||||
\(68\) | −2.00000 | −0.242536 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3485 | 1.34682 | 0.673408 | − | 0.739271i | \(-0.264830\pi\) | ||||
0.673408 | + | 0.739271i | \(0.264830\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | 13.3485 | 1.56232 | 0.781160 | − | 0.624331i | \(-0.214628\pi\) | ||||
0.781160 | + | 0.624331i | \(0.214628\pi\) | |||||||
\(74\) | −3.44949 | −0.400995 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.44949 | 0.739807 | ||||||||
\(77\) | 8.89898 | 1.01413 | ||||||||
\(78\) | 6.00000 | 0.679366 | ||||||||
\(79\) | −2.89898 | −0.326161 | −0.163080 | − | 0.986613i | \(-0.552143\pi\) | ||||
−0.163080 | + | 0.986613i | \(0.552143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 11.3485 | 1.25323 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | −10.8990 | −1.18918 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.89898 | −0.959602 | ||||||||
\(87\) | 2.44949 | 0.262613 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 3.55051 | 0.376353 | 0.188177 | − | 0.982135i | \(-0.439742\pi\) | ||||
0.188177 | + | 0.982135i | \(0.439742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8990 | −1.14252 | ||||||||
\(92\) | −2.44949 | −0.255377 | ||||||||
\(93\) | 7.34847 | 0.762001 | ||||||||
\(94\) | 5.89898 | 0.608433 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.44949 | −0.250000 | ||||||||
\(97\) | 7.34847 | 0.746124 | 0.373062 | − | 0.927806i | \(-0.378308\pi\) | ||||
0.373062 | + | 0.927806i | \(0.378308\pi\) | |||||||
\(98\) | 12.7980 | 1.29279 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4495 | 1.33827 | 0.669137 | − | 0.743139i | \(-0.266664\pi\) | ||||
0.669137 | + | 0.743139i | \(0.266664\pi\) | |||||||
\(102\) | 4.89898 | 0.485071 | ||||||||
\(103\) | −2.44949 | −0.241355 | −0.120678 | − | 0.992692i | \(-0.538507\pi\) | ||||
−0.120678 | + | 0.992692i | \(0.538507\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.4495 | 1.01494 | ||||||||
\(107\) | 5.24745 | 0.507290 | 0.253645 | − | 0.967297i | \(-0.418370\pi\) | ||||
0.253645 | + | 0.967297i | \(0.418370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.34847 | −0.895421 | −0.447710 | − | 0.894179i | \(-0.647760\pi\) | ||||
−0.447710 | + | 0.894179i | \(0.647760\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.44949 | 0.801990 | ||||||||
\(112\) | 4.44949 | 0.420437 | ||||||||
\(113\) | 6.24745 | 0.587711 | 0.293855 | − | 0.955850i | \(-0.405062\pi\) | ||||
0.293855 | + | 0.955850i | \(0.405062\pi\) | |||||||
\(114\) | −15.7980 | −1.47961 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −7.34847 | −0.679366 | ||||||||
\(118\) | 8.55051 | 0.787138 | ||||||||
\(119\) | −8.89898 | −0.815768 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 3.44949 | 0.312302 | ||||||||
\(123\) | −27.7980 | −2.50646 | ||||||||
\(124\) | −3.00000 | −0.269408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.3485 | 1.18918 | ||||||||
\(127\) | 8.79796 | 0.780693 | 0.390346 | − | 0.920668i | \(-0.372355\pi\) | ||||
0.390346 | + | 0.920668i | \(0.372355\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 21.7980 | 1.91920 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.34847 | −0.642039 | −0.321019 | − | 0.947073i | \(-0.604025\pi\) | ||||
−0.321019 | + | 0.947073i | \(0.604025\pi\) | |||||||
\(132\) | −4.89898 | −0.426401 | ||||||||
\(133\) | 28.6969 | 2.48834 | ||||||||
\(134\) | −13.4495 | −1.16186 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 0.898979 | 0.0768050 | 0.0384025 | − | 0.999262i | \(-0.487773\pi\) | ||||
0.0384025 | + | 0.999262i | \(0.487773\pi\) | |||||||
\(138\) | 6.00000 | 0.510754 | ||||||||
\(139\) | −11.4495 | −0.971133 | −0.485567 | − | 0.874200i | \(-0.661387\pi\) | ||||
−0.485567 | + | 0.874200i | \(0.661387\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.4495 | −1.21687 | ||||||||
\(142\) | 11.3485 | 0.952342 | ||||||||
\(143\) | −4.89898 | −0.409673 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.3485 | 1.10473 | ||||||||
\(147\) | −31.3485 | −2.58558 | ||||||||
\(148\) | −3.44949 | −0.283546 | ||||||||
\(149\) | 15.7980 | 1.29422 | 0.647110 | − | 0.762397i | \(-0.275978\pi\) | ||||
0.647110 | + | 0.762397i | \(0.275978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3485 | 0.923525 | 0.461763 | − | 0.887004i | \(-0.347217\pi\) | ||||
0.461763 | + | 0.887004i | \(0.347217\pi\) | |||||||
\(152\) | 6.44949 | 0.523123 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 8.89898 | 0.717100 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | 12.3485 | 0.985515 | 0.492758 | − | 0.870167i | \(-0.335989\pi\) | ||||
0.492758 | + | 0.870167i | \(0.335989\pi\) | |||||||
\(158\) | −2.89898 | −0.230630 | ||||||||
\(159\) | −25.5959 | −2.02989 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8990 | −0.858960 | ||||||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −12.4495 | −0.975119 | −0.487560 | − | 0.873090i | \(-0.662113\pi\) | ||||
−0.487560 | + | 0.873090i | \(0.662113\pi\) | |||||||
\(164\) | 11.3485 | 0.886167 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | −17.7980 | −1.37725 | −0.688624 | − | 0.725119i | \(-0.741785\pi\) | ||||
−0.688624 | + | 0.725119i | \(0.741785\pi\) | |||||||
\(168\) | −10.8990 | −0.840875 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.3485 | 1.47961 | ||||||||
\(172\) | −8.89898 | −0.678541 | ||||||||
\(173\) | −16.0000 | −1.21646 | −0.608229 | − | 0.793762i | \(-0.708120\pi\) | ||||
−0.608229 | + | 0.793762i | \(0.708120\pi\) | |||||||
\(174\) | 2.44949 | 0.185695 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | −20.9444 | −1.57428 | ||||||||
\(178\) | 3.55051 | 0.266122 | ||||||||
\(179\) | −17.2474 | −1.28913 | −0.644567 | − | 0.764547i | \(-0.722962\pi\) | ||||
−0.644567 | + | 0.764547i | \(0.722962\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.0454 | −1.93594 | −0.967970 | − | 0.251066i | \(-0.919219\pi\) | ||||
−0.967970 | + | 0.251066i | \(0.919219\pi\) | |||||||
\(182\) | −10.8990 | −0.807886 | ||||||||
\(183\) | −8.44949 | −0.624604 | ||||||||
\(184\) | −2.44949 | −0.180579 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.34847 | 0.538816 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | 5.89898 | 0.430227 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.6969 | −0.846361 | −0.423180 | − | 0.906045i | \(-0.639086\pi\) | ||||
−0.423180 | + | 0.906045i | \(0.639086\pi\) | |||||||
\(192\) | −2.44949 | −0.176777 | ||||||||
\(193\) | −5.34847 | −0.384991 | −0.192496 | − | 0.981298i | \(-0.561658\pi\) | ||||
−0.192496 | + | 0.981298i | \(0.561658\pi\) | |||||||
\(194\) | 7.34847 | 0.527589 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.7980 | 0.914140 | ||||||||
\(197\) | 5.10102 | 0.363433 | 0.181716 | − | 0.983351i | \(-0.441835\pi\) | ||||
0.181716 | + | 0.983351i | \(0.441835\pi\) | |||||||
\(198\) | 6.00000 | 0.426401 | ||||||||
\(199\) | −0.651531 | −0.0461858 | −0.0230929 | − | 0.999733i | \(-0.507351\pi\) | ||||
−0.0230929 | + | 0.999733i | \(0.507351\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.9444 | 2.32372 | ||||||||
\(202\) | 13.4495 | 0.946303 | ||||||||
\(203\) | −4.44949 | −0.312293 | ||||||||
\(204\) | 4.89898 | 0.342997 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.44949 | −0.170664 | ||||||||
\(207\) | −7.34847 | −0.510754 | ||||||||
\(208\) | −2.44949 | −0.169842 | ||||||||
\(209\) | 12.8990 | 0.892241 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4949 | −1.54861 | −0.774306 | − | 0.632811i | \(-0.781901\pi\) | ||||
−0.774306 | + | 0.632811i | \(0.781901\pi\) | |||||||
\(212\) | 10.4495 | 0.717674 | ||||||||
\(213\) | −27.7980 | −1.90468 | ||||||||
\(214\) | 5.24745 | 0.358708 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.3485 | −0.906153 | ||||||||
\(218\) | −9.34847 | −0.633158 | ||||||||
\(219\) | −32.6969 | −2.20945 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.89898 | 0.329541 | ||||||||
\(222\) | 8.44949 | 0.567093 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 4.44949 | 0.297294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.24745 | 0.415574 | ||||||||
\(227\) | 15.2474 | 1.01201 | 0.506004 | − | 0.862531i | \(-0.331122\pi\) | ||||
0.506004 | + | 0.862531i | \(0.331122\pi\) | |||||||
\(228\) | −15.7980 | −1.04625 | ||||||||
\(229\) | −17.1010 | −1.13007 | −0.565034 | − | 0.825068i | \(-0.691137\pi\) | ||||
−0.565034 | + | 0.825068i | \(0.691137\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.7980 | −1.43420 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −11.0000 | −0.720634 | −0.360317 | − | 0.932830i | \(-0.617331\pi\) | ||||
−0.360317 | + | 0.932830i | \(0.617331\pi\) | |||||||
\(234\) | −7.34847 | −0.480384 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.55051 | 0.556591 | ||||||||
\(237\) | 7.10102 | 0.461261 | ||||||||
\(238\) | −8.89898 | −0.576835 | ||||||||
\(239\) | 21.5959 | 1.39692 | 0.698462 | − | 0.715647i | \(-0.253868\pi\) | ||||
0.698462 | + | 0.715647i | \(0.253868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0000 | 1.09507 | 0.547533 | − | 0.836784i | \(-0.315567\pi\) | ||||
0.547533 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | 22.0454 | 1.41421 | ||||||||
\(244\) | 3.44949 | 0.220831 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −27.7980 | −1.77233 | ||||||||
\(247\) | −15.7980 | −1.00520 | ||||||||
\(248\) | −3.00000 | −0.190500 | ||||||||
\(249\) | 14.6969 | 0.931381 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.14643 | −0.198601 | −0.0993004 | − | 0.995058i | \(-0.531660\pi\) | ||||
−0.0993004 | + | 0.995058i | \(0.531660\pi\) | |||||||
\(252\) | 13.3485 | 0.840875 | ||||||||
\(253\) | −4.89898 | −0.307996 | ||||||||
\(254\) | 8.79796 | 0.552033 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.6969 | 1.66531 | 0.832655 | − | 0.553793i | \(-0.186820\pi\) | ||||
0.832655 | + | 0.553793i | \(0.186820\pi\) | |||||||
\(258\) | 21.7980 | 1.35708 | ||||||||
\(259\) | −15.3485 | −0.953707 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | −7.34847 | −0.453990 | ||||||||
\(263\) | −16.7980 | −1.03581 | −0.517903 | − | 0.855439i | \(-0.673287\pi\) | ||||
−0.517903 | + | 0.855439i | \(0.673287\pi\) | |||||||
\(264\) | −4.89898 | −0.301511 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 28.6969 | 1.75952 | ||||||||
\(267\) | −8.69694 | −0.532244 | ||||||||
\(268\) | −13.4495 | −0.821558 | ||||||||
\(269\) | 24.3485 | 1.48455 | 0.742276 | − | 0.670094i | \(-0.233746\pi\) | ||||
0.742276 | + | 0.670094i | \(0.233746\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6969 | 0.953521 | 0.476761 | − | 0.879033i | \(-0.341811\pi\) | ||||
0.476761 | + | 0.879033i | \(0.341811\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 26.6969 | 1.61577 | ||||||||
\(274\) | 0.898979 | 0.0543093 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | −22.9444 | −1.37859 | −0.689297 | − | 0.724479i | \(-0.742081\pi\) | ||||
−0.689297 | + | 0.724479i | \(0.742081\pi\) | |||||||
\(278\) | −11.4495 | −0.686695 | ||||||||
\(279\) | −9.00000 | −0.538816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.7980 | −1.71794 | −0.858971 | − | 0.512024i | \(-0.828896\pi\) | ||||
−0.858971 | + | 0.512024i | \(0.828896\pi\) | |||||||
\(282\) | −14.4495 | −0.860455 | ||||||||
\(283\) | 24.0000 | 1.42665 | 0.713326 | − | 0.700832i | \(-0.247188\pi\) | ||||
0.713326 | + | 0.700832i | \(0.247188\pi\) | |||||||
\(284\) | 11.3485 | 0.673408 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.89898 | −0.289683 | ||||||||
\(287\) | 50.4949 | 2.98062 | ||||||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.0000 | −1.05518 | ||||||||
\(292\) | 13.3485 | 0.781160 | ||||||||
\(293\) | −7.44949 | −0.435204 | −0.217602 | − | 0.976038i | \(-0.569823\pi\) | ||||
−0.217602 | + | 0.976038i | \(0.569823\pi\) | |||||||
\(294\) | −31.3485 | −1.82828 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.44949 | −0.200498 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.7980 | 0.915151 | ||||||||
\(299\) | 6.00000 | 0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −39.5959 | −2.28227 | ||||||||
\(302\) | 11.3485 | 0.653031 | ||||||||
\(303\) | −32.9444 | −1.89261 | ||||||||
\(304\) | 6.44949 | 0.369904 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.00000 | −0.342997 | ||||||||
\(307\) | 25.3939 | 1.44931 | 0.724653 | − | 0.689114i | \(-0.242000\pi\) | ||||
0.724653 | + | 0.689114i | \(0.242000\pi\) | |||||||
\(308\) | 8.89898 | 0.507066 | ||||||||
\(309\) | 6.00000 | 0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.5959 | −1.11118 | −0.555591 | − | 0.831456i | \(-0.687508\pi\) | ||||
−0.555591 | + | 0.831456i | \(0.687508\pi\) | |||||||
\(312\) | 6.00000 | 0.339683 | ||||||||
\(313\) | −32.5959 | −1.84243 | −0.921215 | − | 0.389054i | \(-0.872802\pi\) | ||||
−0.921215 | + | 0.389054i | \(0.872802\pi\) | |||||||
\(314\) | 12.3485 | 0.696864 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.89898 | −0.163080 | ||||||||
\(317\) | 13.6515 | 0.766746 | 0.383373 | − | 0.923594i | \(-0.374762\pi\) | ||||
0.383373 | + | 0.923594i | \(0.374762\pi\) | |||||||
\(318\) | −25.5959 | −1.43535 | ||||||||
\(319\) | −2.00000 | −0.111979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8536 | −0.717416 | ||||||||
\(322\) | −10.8990 | −0.607376 | ||||||||
\(323\) | −12.8990 | −0.717718 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.4495 | −0.689513 | ||||||||
\(327\) | 22.8990 | 1.26632 | ||||||||
\(328\) | 11.3485 | 0.626614 | ||||||||
\(329\) | 26.2474 | 1.44707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.2474 | −1.66255 | −0.831275 | − | 0.555861i | \(-0.812389\pi\) | ||||
−0.831275 | + | 0.555861i | \(0.812389\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | −10.3485 | −0.567093 | ||||||||
\(334\) | −17.7980 | −0.973861 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.8990 | −0.594588 | ||||||||
\(337\) | 23.7980 | 1.29636 | 0.648179 | − | 0.761488i | \(-0.275531\pi\) | ||||
0.648179 | + | 0.761488i | \(0.275531\pi\) | |||||||
\(338\) | −7.00000 | −0.380750 | ||||||||
\(339\) | −15.3031 | −0.831148 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 19.3485 | 1.04625 | ||||||||
\(343\) | 25.7980 | 1.39296 | ||||||||
\(344\) | −8.89898 | −0.479801 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.0000 | −0.860165 | ||||||||
\(347\) | −25.0454 | −1.34451 | −0.672254 | − | 0.740321i | \(-0.734674\pi\) | ||||
−0.672254 | + | 0.740321i | \(0.734674\pi\) | |||||||
\(348\) | 2.44949 | 0.131306 | ||||||||
\(349\) | −30.9444 | −1.65642 | −0.828208 | − | 0.560422i | \(-0.810639\pi\) | ||||
−0.828208 | + | 0.560422i | \(0.810639\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | −16.7980 | −0.894065 | −0.447033 | − | 0.894518i | \(-0.647519\pi\) | ||||
−0.447033 | + | 0.894518i | \(0.647519\pi\) | |||||||
\(354\) | −20.9444 | −1.11318 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.55051 | 0.188177 | ||||||||
\(357\) | 21.7980 | 1.15367 | ||||||||
\(358\) | −17.2474 | −0.911556 | ||||||||
\(359\) | −16.5959 | −0.875899 | −0.437950 | − | 0.899000i | \(-0.644295\pi\) | ||||
−0.437950 | + | 0.899000i | \(0.644295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5959 | 1.18926 | ||||||||
\(362\) | −26.0454 | −1.36892 | ||||||||
\(363\) | 17.1464 | 0.899954 | ||||||||
\(364\) | −10.8990 | −0.571262 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.44949 | −0.441662 | ||||||||
\(367\) | −1.20204 | −0.0627460 | −0.0313730 | − | 0.999508i | \(-0.509988\pi\) | ||||
−0.0313730 | + | 0.999508i | \(0.509988\pi\) | |||||||
\(368\) | −2.44949 | −0.127688 | ||||||||
\(369\) | 34.0454 | 1.77233 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.4949 | 2.41389 | ||||||||
\(372\) | 7.34847 | 0.381000 | ||||||||
\(373\) | 28.4949 | 1.47541 | 0.737705 | − | 0.675123i | \(-0.235910\pi\) | ||||
0.737705 | + | 0.675123i | \(0.235910\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.89898 | 0.304217 | ||||||||
\(377\) | 2.44949 | 0.126155 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1464 | 1.29169 | 0.645843 | − | 0.763471i | \(-0.276506\pi\) | ||||
0.645843 | + | 0.763471i | \(0.276506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.5505 | −1.10407 | ||||||||
\(382\) | −11.6969 | −0.598467 | ||||||||
\(383\) | −11.7980 | −0.602848 | −0.301424 | − | 0.953490i | \(-0.597462\pi\) | ||||
−0.301424 | + | 0.953490i | \(0.597462\pi\) | |||||||
\(384\) | −2.44949 | −0.125000 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.34847 | −0.272230 | ||||||||
\(387\) | −26.6969 | −1.35708 | ||||||||
\(388\) | 7.34847 | 0.373062 | ||||||||
\(389\) | −24.3485 | −1.23452 | −0.617258 | − | 0.786761i | \(-0.711757\pi\) | ||||
−0.617258 | + | 0.786761i | \(0.711757\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.89898 | 0.247752 | ||||||||
\(392\) | 12.7980 | 0.646395 | ||||||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | 5.10102 | 0.256986 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.00000 | 0.301511 | ||||||||
\(397\) | 13.1464 | 0.659800 | 0.329900 | − | 0.944016i | \(-0.392985\pi\) | ||||
0.329900 | + | 0.944016i | \(0.392985\pi\) | |||||||
\(398\) | −0.651531 | −0.0326583 | ||||||||
\(399\) | −70.2929 | −3.51904 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.5959 | 1.92739 | 0.963694 | − | 0.267009i | \(-0.0860353\pi\) | ||||
0.963694 | + | 0.267009i | \(0.0860353\pi\) | |||||||
\(402\) | 32.9444 | 1.64312 | ||||||||
\(403\) | 7.34847 | 0.366053 | ||||||||
\(404\) | 13.4495 | 0.669137 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.44949 | −0.220824 | ||||||||
\(407\) | −6.89898 | −0.341970 | ||||||||
\(408\) | 4.89898 | 0.242536 | ||||||||
\(409\) | −5.79796 | −0.286691 | −0.143345 | − | 0.989673i | \(-0.545786\pi\) | ||||
−0.143345 | + | 0.989673i | \(0.545786\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.20204 | −0.108619 | ||||||||
\(412\) | −2.44949 | −0.120678 | ||||||||
\(413\) | 38.0454 | 1.87209 | ||||||||
\(414\) | −7.34847 | −0.361158 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.44949 | −0.120096 | ||||||||
\(417\) | 28.0454 | 1.37339 | ||||||||
\(418\) | 12.8990 | 0.630910 | ||||||||
\(419\) | −10.1464 | −0.495685 | −0.247843 | − | 0.968800i | \(-0.579722\pi\) | ||||
−0.247843 | + | 0.968800i | \(0.579722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4495 | 0.655488 | 0.327744 | − | 0.944767i | \(-0.393712\pi\) | ||||
0.327744 | + | 0.944767i | \(0.393712\pi\) | |||||||
\(422\) | −22.4949 | −1.09503 | ||||||||
\(423\) | 17.6969 | 0.860455 | ||||||||
\(424\) | 10.4495 | 0.507472 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −27.7980 | −1.34682 | ||||||||
\(427\) | 15.3485 | 0.742764 | ||||||||
\(428\) | 5.24745 | 0.253645 | ||||||||
\(429\) | 12.0000 | 0.579365 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4495 | 0.888681 | 0.444340 | − | 0.895858i | \(-0.353438\pi\) | ||||
0.444340 | + | 0.895858i | \(0.353438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.4495 | 1.46331 | 0.731655 | − | 0.681676i | \(-0.238748\pi\) | ||||
0.731655 | + | 0.681676i | \(0.238748\pi\) | |||||||
\(434\) | −13.3485 | −0.640747 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.34847 | −0.447710 | ||||||||
\(437\) | −15.7980 | −0.755719 | ||||||||
\(438\) | −32.6969 | −1.56232 | ||||||||
\(439\) | 18.6969 | 0.892356 | 0.446178 | − | 0.894944i | \(-0.352785\pi\) | ||||
0.446178 | + | 0.894944i | \(0.352785\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 38.3939 | 1.82828 | ||||||||
\(442\) | 4.89898 | 0.233021 | ||||||||
\(443\) | −13.1010 | −0.622448 | −0.311224 | − | 0.950337i | \(-0.600739\pi\) | ||||
−0.311224 | + | 0.950337i | \(0.600739\pi\) | |||||||
\(444\) | 8.44949 | 0.400995 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | −38.6969 | −1.83030 | ||||||||
\(448\) | 4.44949 | 0.210219 | ||||||||
\(449\) | 25.7980 | 1.21748 | 0.608740 | − | 0.793369i | \(-0.291675\pi\) | ||||
0.608740 | + | 0.793369i | \(0.291675\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.6969 | 1.06876 | ||||||||
\(452\) | 6.24745 | 0.293855 | ||||||||
\(453\) | −27.7980 | −1.30606 | ||||||||
\(454\) | 15.2474 | 0.715598 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.7980 | −0.739807 | ||||||||
\(457\) | −17.7980 | −0.832553 | −0.416277 | − | 0.909238i | \(-0.636665\pi\) | ||||
−0.416277 | + | 0.909238i | \(0.636665\pi\) | |||||||
\(458\) | −17.1010 | −0.799078 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.2929 | −1.31773 | −0.658865 | − | 0.752261i | \(-0.728963\pi\) | ||||
−0.658865 | + | 0.752261i | \(0.728963\pi\) | |||||||
\(462\) | −21.7980 | −1.01413 | ||||||||
\(463\) | −3.10102 | −0.144117 | −0.0720583 | − | 0.997400i | \(-0.522957\pi\) | ||||
−0.0720583 | + | 0.997400i | \(0.522957\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.0000 | −0.509565 | ||||||||
\(467\) | −22.9444 | −1.06174 | −0.530870 | − | 0.847453i | \(-0.678135\pi\) | ||||
−0.530870 | + | 0.847453i | \(0.678135\pi\) | |||||||
\(468\) | −7.34847 | −0.339683 | ||||||||
\(469\) | −59.8434 | −2.76331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.2474 | −1.39373 | ||||||||
\(472\) | 8.55051 | 0.393569 | ||||||||
\(473\) | −17.7980 | −0.818351 | ||||||||
\(474\) | 7.10102 | 0.326161 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.89898 | −0.407884 | ||||||||
\(477\) | 31.3485 | 1.43535 | ||||||||
\(478\) | 21.5959 | 0.987774 | ||||||||
\(479\) | −4.20204 | −0.191996 | −0.0959981 | − | 0.995382i | \(-0.530604\pi\) | ||||
−0.0959981 | + | 0.995382i | \(0.530604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.44949 | 0.385264 | ||||||||
\(482\) | 17.0000 | 0.774329 | ||||||||
\(483\) | 26.6969 | 1.21475 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454 | 1.00000 | ||||||||
\(487\) | −9.10102 | −0.412407 | −0.206203 | − | 0.978509i | \(-0.566111\pi\) | ||||
−0.206203 | + | 0.978509i | \(0.566111\pi\) | |||||||
\(488\) | 3.44949 | 0.156151 | ||||||||
\(489\) | 30.4949 | 1.37903 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.4949 | 1.19570 | 0.597849 | − | 0.801609i | \(-0.296022\pi\) | ||||
0.597849 | + | 0.801609i | \(0.296022\pi\) | |||||||
\(492\) | −27.7980 | −1.25323 | ||||||||
\(493\) | 2.00000 | 0.0900755 | ||||||||
\(494\) | −15.7980 | −0.710784 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | −0.134704 | ||||||||
\(497\) | 50.4949 | 2.26501 | ||||||||
\(498\) | 14.6969 | 0.658586 | ||||||||
\(499\) | −24.3485 | −1.08999 | −0.544994 | − | 0.838440i | \(-0.683468\pi\) | ||||
−0.544994 | + | 0.838440i | \(0.683468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.5959 | 1.94772 | ||||||||
\(502\) | −3.14643 | −0.140432 | ||||||||
\(503\) | 4.79796 | 0.213930 | 0.106965 | − | 0.994263i | \(-0.465887\pi\) | ||||
0.106965 | + | 0.994263i | \(0.465887\pi\) | |||||||
\(504\) | 13.3485 | 0.594588 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.89898 | −0.217786 | ||||||||
\(507\) | 17.1464 | 0.761500 | ||||||||
\(508\) | 8.79796 | 0.390346 | ||||||||
\(509\) | −17.3939 | −0.770970 | −0.385485 | − | 0.922714i | \(-0.625966\pi\) | ||||
−0.385485 | + | 0.922714i | \(0.625966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 59.3939 | 2.62743 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.6969 | 1.17755 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.7980 | 0.959602 | ||||||||
\(517\) | 11.7980 | 0.518874 | ||||||||
\(518\) | −15.3485 | −0.674373 | ||||||||
\(519\) | 39.1918 | 1.72033 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.1010 | −0.442534 | −0.221267 | − | 0.975213i | \(-0.571019\pi\) | ||||
−0.221267 | + | 0.975213i | \(0.571019\pi\) | |||||||
\(522\) | −3.00000 | −0.131306 | ||||||||
\(523\) | −27.4495 | −1.20028 | −0.600141 | − | 0.799894i | \(-0.704889\pi\) | ||||
−0.600141 | + | 0.799894i | \(0.704889\pi\) | |||||||
\(524\) | −7.34847 | −0.321019 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.7980 | −0.732426 | ||||||||
\(527\) | 6.00000 | 0.261364 | ||||||||
\(528\) | −4.89898 | −0.213201 | ||||||||
\(529\) | −17.0000 | −0.739130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.6515 | 1.11318 | ||||||||
\(532\) | 28.6969 | 1.24417 | ||||||||
\(533\) | −27.7980 | −1.20406 | ||||||||
\(534\) | −8.69694 | −0.376353 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.4495 | −0.580929 | ||||||||
\(537\) | 42.2474 | 1.82311 | ||||||||
\(538\) | 24.3485 | 1.04974 | ||||||||
\(539\) | 25.5959 | 1.10249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0454 | −0.904813 | −0.452406 | − | 0.891812i | \(-0.649434\pi\) | ||||
−0.452406 | + | 0.891812i | \(0.649434\pi\) | |||||||
\(542\) | 15.6969 | 0.674241 | ||||||||
\(543\) | 63.7980 | 2.73783 | ||||||||
\(544\) | −2.00000 | −0.0857493 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 26.6969 | 1.14252 | ||||||||
\(547\) | −22.0000 | −0.940652 | −0.470326 | − | 0.882493i | \(-0.655864\pi\) | ||||
−0.470326 | + | 0.882493i | \(0.655864\pi\) | |||||||
\(548\) | 0.898979 | 0.0384025 | ||||||||
\(549\) | 10.3485 | 0.441662 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.44949 | −0.274758 | ||||||||
\(552\) | 6.00000 | 0.255377 | ||||||||
\(553\) | −12.8990 | −0.548520 | ||||||||
\(554\) | −22.9444 | −0.974814 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.4495 | −0.485567 | ||||||||
\(557\) | −6.49490 | −0.275198 | −0.137599 | − | 0.990488i | \(-0.543938\pi\) | ||||
−0.137599 | + | 0.990488i | \(0.543938\pi\) | |||||||
\(558\) | −9.00000 | −0.381000 | ||||||||
\(559\) | 21.7980 | 0.921955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.79796 | 0.413670 | ||||||||
\(562\) | −28.7980 | −1.21477 | ||||||||
\(563\) | −21.7980 | −0.918674 | −0.459337 | − | 0.888262i | \(-0.651913\pi\) | ||||
−0.459337 | + | 0.888262i | \(0.651913\pi\) | |||||||
\(564\) | −14.4495 | −0.608433 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | −40.0454 | −1.68175 | ||||||||
\(568\) | 11.3485 | 0.476171 | ||||||||
\(569\) | −8.69694 | −0.364595 | −0.182297 | − | 0.983243i | \(-0.558353\pi\) | ||||
−0.182297 | + | 0.983243i | \(0.558353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.0454 | 1.04812 | 0.524059 | − | 0.851682i | \(-0.324417\pi\) | ||||
0.524059 | + | 0.851682i | \(0.324417\pi\) | |||||||
\(572\) | −4.89898 | −0.204837 | ||||||||
\(573\) | 28.6515 | 1.19693 | ||||||||
\(574\) | 50.4949 | 2.10762 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | 28.9444 | 1.20497 | 0.602485 | − | 0.798130i | \(-0.294177\pi\) | ||||
0.602485 | + | 0.798130i | \(0.294177\pi\) | |||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | 13.1010 | 0.544460 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.6969 | −1.10758 | ||||||||
\(582\) | −18.0000 | −0.746124 | ||||||||
\(583\) | 20.8990 | 0.865547 | ||||||||
\(584\) | 13.3485 | 0.552364 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.44949 | −0.307736 | ||||||||
\(587\) | −14.7526 | −0.608903 | −0.304451 | − | 0.952528i | \(-0.598473\pi\) | ||||
−0.304451 | + | 0.952528i | \(0.598473\pi\) | |||||||
\(588\) | −31.3485 | −1.29279 | ||||||||
\(589\) | −19.3485 | −0.797240 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4949 | −0.513971 | ||||||||
\(592\) | −3.44949 | −0.141773 | ||||||||
\(593\) | −18.3939 | −0.755346 | −0.377673 | − | 0.925939i | \(-0.623276\pi\) | ||||
−0.377673 | + | 0.925939i | \(0.623276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.7980 | 0.647110 | ||||||||
\(597\) | 1.59592 | 0.0653166 | ||||||||
\(598\) | 6.00000 | 0.245358 | ||||||||
\(599\) | −12.1010 | −0.494434 | −0.247217 | − | 0.968960i | \(-0.579516\pi\) | ||||
−0.247217 | + | 0.968960i | \(0.579516\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.69694 | −0.273174 | −0.136587 | − | 0.990628i | \(-0.543613\pi\) | ||||
−0.136587 | + | 0.990628i | \(0.543613\pi\) | |||||||
\(602\) | −39.5959 | −1.61381 | ||||||||
\(603\) | −40.3485 | −1.64312 | ||||||||
\(604\) | 11.3485 | 0.461763 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −32.9444 | −1.33827 | ||||||||
\(607\) | −34.3939 | −1.39600 | −0.698002 | − | 0.716096i | \(-0.745927\pi\) | ||||
−0.698002 | + | 0.716096i | \(0.745927\pi\) | |||||||
\(608\) | 6.44949 | 0.261561 | ||||||||
\(609\) | 10.8990 | 0.441649 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.4495 | −0.584564 | ||||||||
\(612\) | −6.00000 | −0.242536 | ||||||||
\(613\) | 46.8990 | 1.89423 | 0.947116 | − | 0.320891i | \(-0.103982\pi\) | ||||
0.947116 | + | 0.320891i | \(0.103982\pi\) | |||||||
\(614\) | 25.3939 | 1.02481 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.89898 | 0.358550 | ||||||||
\(617\) | 14.4495 | 0.581715 | 0.290857 | − | 0.956766i | \(-0.406060\pi\) | ||||
0.290857 | + | 0.956766i | \(0.406060\pi\) | |||||||
\(618\) | 6.00000 | 0.241355 | ||||||||
\(619\) | 2.89898 | 0.116520 | 0.0582599 | − | 0.998301i | \(-0.481445\pi\) | ||||
0.0582599 | + | 0.998301i | \(0.481445\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.5959 | −0.785725 | ||||||||
\(623\) | 15.7980 | 0.632932 | ||||||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −32.5959 | −1.30279 | ||||||||
\(627\) | −31.5959 | −1.26182 | ||||||||
\(628\) | 12.3485 | 0.492758 | ||||||||
\(629\) | 6.89898 | 0.275080 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | −2.89898 | −0.115315 | ||||||||
\(633\) | 55.1010 | 2.19007 | ||||||||
\(634\) | 13.6515 | 0.542172 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −25.5959 | −1.01494 | ||||||||
\(637\) | −31.3485 | −1.24207 | ||||||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | 34.0454 | 1.34682 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.2474 | 0.957717 | 0.478858 | − | 0.877892i | \(-0.341051\pi\) | ||||
0.478858 | + | 0.877892i | \(0.341051\pi\) | |||||||
\(642\) | −12.8536 | −0.507290 | ||||||||
\(643\) | −24.8434 | −0.979727 | −0.489863 | − | 0.871799i | \(-0.662953\pi\) | ||||
−0.489863 | + | 0.871799i | \(0.662953\pi\) | |||||||
\(644\) | −10.8990 | −0.429480 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.8990 | −0.507504 | ||||||||
\(647\) | 39.5959 | 1.55668 | 0.778338 | − | 0.627845i | \(-0.216063\pi\) | ||||
0.778338 | + | 0.627845i | \(0.216063\pi\) | |||||||
\(648\) | −9.00000 | −0.353553 | ||||||||
\(649\) | 17.1010 | 0.671274 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.6969 | 1.28149 | ||||||||
\(652\) | −12.4495 | −0.487560 | ||||||||
\(653\) | 11.2474 | 0.440147 | 0.220073 | − | 0.975483i | \(-0.429370\pi\) | ||||
0.220073 | + | 0.975483i | \(0.429370\pi\) | |||||||
\(654\) | 22.8990 | 0.895421 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.3485 | 0.443083 | ||||||||
\(657\) | 40.0454 | 1.56232 | ||||||||
\(658\) | 26.2474 | 1.02323 | ||||||||
\(659\) | −38.6969 | −1.50742 | −0.753709 | − | 0.657208i | \(-0.771737\pi\) | ||||
−0.753709 | + | 0.657208i | \(0.771737\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.75255 | 0.379330 | 0.189665 | − | 0.981849i | \(-0.439260\pi\) | ||||
0.189665 | + | 0.981849i | \(0.439260\pi\) | |||||||
\(662\) | −30.2474 | −1.17560 | ||||||||
\(663\) | −12.0000 | −0.466041 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.3485 | −0.400995 | ||||||||
\(667\) | 2.44949 | 0.0948446 | ||||||||
\(668\) | −17.7980 | −0.688624 | ||||||||
\(669\) | −9.79796 | −0.378811 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.89898 | 0.266332 | ||||||||
\(672\) | −10.8990 | −0.420437 | ||||||||
\(673\) | −16.7980 | −0.647514 | −0.323757 | − | 0.946140i | \(-0.604946\pi\) | ||||
−0.323757 | + | 0.946140i | \(0.604946\pi\) | |||||||
\(674\) | 23.7980 | 0.916663 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | −25.0454 | −0.962573 | −0.481287 | − | 0.876563i | \(-0.659830\pi\) | ||||
−0.481287 | + | 0.876563i | \(0.659830\pi\) | |||||||
\(678\) | −15.3031 | −0.587711 | ||||||||
\(679\) | 32.6969 | 1.25479 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −37.3485 | −1.43120 | ||||||||
\(682\) | −6.00000 | −0.229752 | ||||||||
\(683\) | 11.1010 | 0.424769 | 0.212384 | − | 0.977186i | \(-0.431877\pi\) | ||||
0.212384 | + | 0.977186i | \(0.431877\pi\) | |||||||
\(684\) | 19.3485 | 0.739807 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25.7980 | 0.984971 | ||||||||
\(687\) | 41.8888 | 1.59816 | ||||||||
\(688\) | −8.89898 | −0.339270 | ||||||||
\(689\) | −25.5959 | −0.975127 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.9444 | −1.67172 | −0.835862 | − | 0.548940i | \(-0.815031\pi\) | ||||
−0.835862 | + | 0.548940i | \(0.815031\pi\) | |||||||
\(692\) | −16.0000 | −0.608229 | ||||||||
\(693\) | 26.6969 | 1.01413 | ||||||||
\(694\) | −25.0454 | −0.950711 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.44949 | 0.0928477 | ||||||||
\(697\) | −22.6969 | −0.859708 | ||||||||
\(698\) | −30.9444 | −1.17126 | ||||||||
\(699\) | 26.9444 | 1.01913 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.3939 | −0.959113 | −0.479557 | − | 0.877511i | \(-0.659203\pi\) | ||||
−0.479557 | + | 0.877511i | \(0.659203\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.2474 | −0.839078 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.7980 | −0.632200 | ||||||||
\(707\) | 59.8434 | 2.25064 | ||||||||
\(708\) | −20.9444 | −0.787138 | ||||||||
\(709\) | −27.3939 | −1.02880 | −0.514399 | − | 0.857551i | \(-0.671985\pi\) | ||||
−0.514399 | + | 0.857551i | \(0.671985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.69694 | −0.326161 | ||||||||
\(712\) | 3.55051 | 0.133061 | ||||||||
\(713\) | 7.34847 | 0.275202 | ||||||||
\(714\) | 21.7980 | 0.815768 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.2474 | −0.644567 | ||||||||
\(717\) | −52.8990 | −1.97555 | ||||||||
\(718\) | −16.5959 | −0.619354 | ||||||||
\(719\) | −36.7423 | −1.37026 | −0.685129 | − | 0.728422i | \(-0.740254\pi\) | ||||
−0.685129 | + | 0.728422i | \(0.740254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8990 | −0.405899 | ||||||||
\(722\) | 22.5959 | 0.840933 | ||||||||
\(723\) | −41.6413 | −1.54866 | ||||||||
\(724\) | −26.0454 | −0.967970 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.1464 | 0.636364 | ||||||||
\(727\) | −33.5959 | −1.24600 | −0.623002 | − | 0.782220i | \(-0.714087\pi\) | ||||
−0.623002 | + | 0.782220i | \(0.714087\pi\) | |||||||
\(728\) | −10.8990 | −0.403943 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.7980 | 0.658281 | ||||||||
\(732\) | −8.44949 | −0.312302 | ||||||||
\(733\) | 1.10102 | 0.0406671 | 0.0203336 | − | 0.999793i | \(-0.493527\pi\) | ||||
0.0203336 | + | 0.999793i | \(0.493527\pi\) | |||||||
\(734\) | −1.20204 | −0.0443681 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.44949 | −0.0902894 | ||||||||
\(737\) | −26.8990 | −0.990837 | ||||||||
\(738\) | 34.0454 | 1.25323 | ||||||||
\(739\) | 10.0000 | 0.367856 | 0.183928 | − | 0.982940i | \(-0.441119\pi\) | ||||
0.183928 | + | 0.982940i | \(0.441119\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.6969 | 1.42157 | ||||||||
\(742\) | 46.4949 | 1.70688 | ||||||||
\(743\) | 12.6969 | 0.465805 | 0.232903 | − | 0.972500i | \(-0.425178\pi\) | ||||
0.232903 | + | 0.972500i | \(0.425178\pi\) | |||||||
\(744\) | 7.34847 | 0.269408 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 28.4949 | 1.04327 | ||||||||
\(747\) | −18.0000 | −0.658586 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | 23.3485 | 0.853134 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.1010 | 0.879459 | 0.439729 | − | 0.898130i | \(-0.355074\pi\) | ||||
0.439729 | + | 0.898130i | \(0.355074\pi\) | |||||||
\(752\) | 5.89898 | 0.215114 | ||||||||
\(753\) | 7.70714 | 0.280864 | ||||||||
\(754\) | 2.44949 | 0.0892052 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.3939 | −0.704882 | −0.352441 | − | 0.935834i | \(-0.614648\pi\) | ||||
−0.352441 | + | 0.935834i | \(0.614648\pi\) | |||||||
\(758\) | 25.1464 | 0.913359 | ||||||||
\(759\) | 12.0000 | 0.435572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.1010 | 0.511162 | 0.255581 | − | 0.966788i | \(-0.417733\pi\) | ||||
0.255581 | + | 0.966788i | \(0.417733\pi\) | |||||||
\(762\) | −21.5505 | −0.780693 | ||||||||
\(763\) | −41.5959 | −1.50587 | ||||||||
\(764\) | −11.6969 | −0.423180 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.7980 | −0.426278 | ||||||||
\(767\) | −20.9444 | −0.756258 | ||||||||
\(768\) | −2.44949 | −0.0883883 | ||||||||
\(769\) | −3.55051 | −0.128035 | −0.0640173 | − | 0.997949i | \(-0.520391\pi\) | ||||
−0.0640173 | + | 0.997949i | \(0.520391\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −65.3939 | −2.35510 | ||||||||
\(772\) | −5.34847 | −0.192496 | ||||||||
\(773\) | −17.4495 | −0.627615 | −0.313807 | − | 0.949487i | \(-0.601605\pi\) | ||||
−0.313807 | + | 0.949487i | \(0.601605\pi\) | |||||||
\(774\) | −26.6969 | −0.959602 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.34847 | 0.263795 | ||||||||
\(777\) | 37.5959 | 1.34875 | ||||||||
\(778\) | −24.3485 | −0.872935 | ||||||||
\(779\) | 73.1918 | 2.62237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6969 | 0.812160 | ||||||||
\(782\) | 4.89898 | 0.175187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.7980 | 0.457070 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.0000 | 0.642039 | ||||||||
\(787\) | −40.5505 | −1.44547 | −0.722735 | − | 0.691125i | \(-0.757115\pi\) | ||||
−0.722735 | + | 0.691125i | \(0.757115\pi\) | |||||||
\(788\) | 5.10102 | 0.181716 | ||||||||
\(789\) | 41.1464 | 1.46485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.7980 | 0.988382 | ||||||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | −8.44949 | −0.300050 | ||||||||
\(794\) | 13.1464 | 0.466549 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.651531 | −0.0230929 | ||||||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | −70.2929 | −2.48834 | ||||||||
\(799\) | −11.7980 | −0.417382 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.6515 | 0.376353 | ||||||||
\(802\) | 38.5959 | 1.36287 | ||||||||
\(803\) | 26.6969 | 0.942114 | ||||||||
\(804\) | 32.9444 | 1.16186 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.34847 | 0.258839 | ||||||||
\(807\) | −59.6413 | −2.09947 | ||||||||
\(808\) | 13.4495 | 0.473151 | ||||||||
\(809\) | 31.5959 | 1.11085 | 0.555427 | − | 0.831566i | \(-0.312555\pi\) | ||||
0.555427 | + | 0.831566i | \(0.312555\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.4495 | −1.03411 | −0.517056 | − | 0.855952i | \(-0.672972\pi\) | ||||
−0.517056 | + | 0.855952i | \(0.672972\pi\) | |||||||
\(812\) | −4.44949 | −0.156146 | ||||||||
\(813\) | −38.4495 | −1.34848 | ||||||||
\(814\) | −6.89898 | −0.241809 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.89898 | 0.171499 | ||||||||
\(817\) | −57.3939 | −2.00796 | ||||||||
\(818\) | −5.79796 | −0.202721 | ||||||||
\(819\) | −32.6969 | −1.14252 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.7526 | 0.689369 | 0.344684 | − | 0.938719i | \(-0.387986\pi\) | ||||
0.344684 | + | 0.938719i | \(0.387986\pi\) | |||||||
\(822\) | −2.20204 | −0.0768050 | ||||||||
\(823\) | −11.7980 | −0.411251 | −0.205625 | − | 0.978631i | \(-0.565923\pi\) | ||||
−0.205625 | + | 0.978631i | \(0.565923\pi\) | |||||||
\(824\) | −2.44949 | −0.0853320 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 38.0454 | 1.32377 | ||||||||
\(827\) | 19.3031 | 0.671233 | 0.335617 | − | 0.941999i | \(-0.391055\pi\) | ||||
0.335617 | + | 0.941999i | \(0.391055\pi\) | |||||||
\(828\) | −7.34847 | −0.255377 | ||||||||
\(829\) | 14.4949 | 0.503429 | 0.251714 | − | 0.967802i | \(-0.419006\pi\) | ||||
0.251714 | + | 0.967802i | \(0.419006\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 56.2020 | 1.94963 | ||||||||
\(832\) | −2.44949 | −0.0849208 | ||||||||
\(833\) | −25.5959 | −0.886846 | ||||||||
\(834\) | 28.0454 | 0.971133 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.8990 | 0.446121 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.1464 | −0.350503 | ||||||||
\(839\) | −30.7980 | −1.06326 | −0.531632 | − | 0.846976i | \(-0.678421\pi\) | ||||
−0.531632 | + | 0.846976i | \(0.678421\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 13.4495 | 0.463500 | ||||||||
\(843\) | 70.5403 | 2.42954 | ||||||||
\(844\) | −22.4949 | −0.774306 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.6969 | 0.608433 | ||||||||
\(847\) | −31.1464 | −1.07020 | ||||||||
\(848\) | 10.4495 | 0.358837 | ||||||||
\(849\) | −58.7878 | −2.01759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.44949 | 0.289645 | ||||||||
\(852\) | −27.7980 | −0.952342 | ||||||||
\(853\) | 8.20204 | 0.280833 | 0.140416 | − | 0.990093i | \(-0.455156\pi\) | ||||
0.140416 | + | 0.990093i | \(0.455156\pi\) | |||||||
\(854\) | 15.3485 | 0.525214 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.24745 | 0.179354 | ||||||||
\(857\) | −39.3939 | −1.34567 | −0.672835 | − | 0.739793i | \(-0.734923\pi\) | ||||
−0.672835 | + | 0.739793i | \(0.734923\pi\) | |||||||
\(858\) | 12.0000 | 0.409673 | ||||||||
\(859\) | 22.8990 | 0.781303 | 0.390652 | − | 0.920539i | \(-0.372250\pi\) | ||||
0.390652 | + | 0.920539i | \(0.372250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −123.687 | −4.21523 | ||||||||
\(862\) | 18.4495 | 0.628392 | ||||||||
\(863\) | 11.7526 | 0.400061 | 0.200031 | − | 0.979790i | \(-0.435896\pi\) | ||||
0.200031 | + | 0.979790i | \(0.435896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.4495 | 1.03472 | ||||||||
\(867\) | 31.8434 | 1.08146 | ||||||||
\(868\) | −13.3485 | −0.453077 | ||||||||
\(869\) | −5.79796 | −0.196682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.9444 | 1.11628 | ||||||||
\(872\) | −9.34847 | −0.316579 | ||||||||
\(873\) | 22.0454 | 0.746124 | ||||||||
\(874\) | −15.7980 | −0.534374 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.6969 | −1.10473 | ||||||||
\(877\) | 8.00000 | 0.270141 | 0.135070 | − | 0.990836i | \(-0.456874\pi\) | ||||
0.135070 | + | 0.990836i | \(0.456874\pi\) | |||||||
\(878\) | 18.6969 | 0.630991 | ||||||||
\(879\) | 18.2474 | 0.615471 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | 38.3939 | 1.29279 | ||||||||
\(883\) | 29.9444 | 1.00771 | 0.503854 | − | 0.863789i | \(-0.331915\pi\) | ||||
0.503854 | + | 0.863789i | \(0.331915\pi\) | |||||||
\(884\) | 4.89898 | 0.164771 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.1010 | −0.440137 | ||||||||
\(887\) | −47.7980 | −1.60490 | −0.802449 | − | 0.596720i | \(-0.796470\pi\) | ||||
−0.802449 | + | 0.596720i | \(0.796470\pi\) | |||||||
\(888\) | 8.44949 | 0.283546 | ||||||||
\(889\) | 39.1464 | 1.31293 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0000 | −0.603023 | ||||||||
\(892\) | 4.00000 | 0.133930 | ||||||||
\(893\) | 38.0454 | 1.27314 | ||||||||
\(894\) | −38.6969 | −1.29422 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.44949 | 0.148647 | ||||||||
\(897\) | −14.6969 | −0.490716 | ||||||||
\(898\) | 25.7980 | 0.860889 | ||||||||
\(899\) | 3.00000 | 0.100056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.8990 | −0.696246 | ||||||||
\(902\) | 22.6969 | 0.755725 | ||||||||
\(903\) | 96.9898 | 3.22762 | ||||||||
\(904\) | 6.24745 | 0.207787 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −27.7980 | −0.923525 | ||||||||
\(907\) | −21.3485 | −0.708864 | −0.354432 | − | 0.935082i | \(-0.615326\pi\) | ||||
−0.354432 | + | 0.935082i | \(0.615326\pi\) | |||||||
\(908\) | 15.2474 | 0.506004 | ||||||||
\(909\) | 40.3485 | 1.33827 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.4949 | 1.70610 | 0.853051 | − | 0.521827i | \(-0.174750\pi\) | ||||
0.853051 | + | 0.521827i | \(0.174750\pi\) | |||||||
\(912\) | −15.7980 | −0.523123 | ||||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | −17.7980 | −0.588704 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.1010 | −0.565034 | ||||||||
\(917\) | −32.6969 | −1.07975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.8536 | −0.819844 | −0.409922 | − | 0.912121i | \(-0.634444\pi\) | ||||
−0.409922 | + | 0.912121i | \(0.634444\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −62.2020 | −2.04963 | ||||||||
\(922\) | −28.2929 | −0.931776 | ||||||||
\(923\) | −27.7980 | −0.914981 | ||||||||
\(924\) | −21.7980 | −0.717100 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.10102 | −0.101906 | ||||||||
\(927\) | −7.34847 | −0.241355 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | −39.4949 | −1.29579 | −0.647893 | − | 0.761732i | \(-0.724350\pi\) | ||||
−0.647893 | + | 0.761732i | \(0.724350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 82.5403 | 2.70515 | ||||||||
\(932\) | −11.0000 | −0.360317 | ||||||||
\(933\) | 48.0000 | 1.57145 | ||||||||
\(934\) | −22.9444 | −0.750763 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.34847 | −0.240192 | ||||||||
\(937\) | 53.2929 | 1.74100 | 0.870501 | − | 0.492167i | \(-0.163795\pi\) | ||||
0.870501 | + | 0.492167i | \(0.163795\pi\) | |||||||
\(938\) | −59.8434 | −1.95396 | ||||||||
\(939\) | 79.8434 | 2.60559 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.44949 | 0.275445 | 0.137723 | − | 0.990471i | \(-0.456022\pi\) | ||||
0.137723 | + | 0.990471i | \(0.456022\pi\) | |||||||
\(942\) | −30.2474 | −0.985515 | ||||||||
\(943\) | −27.7980 | −0.905226 | ||||||||
\(944\) | 8.55051 | 0.278295 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.7980 | −0.578662 | ||||||||
\(947\) | 37.3485 | 1.21366 | 0.606831 | − | 0.794831i | \(-0.292440\pi\) | ||||
0.606831 | + | 0.794831i | \(0.292440\pi\) | |||||||
\(948\) | 7.10102 | 0.230630 | ||||||||
\(949\) | −32.6969 | −1.06139 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.4393 | −1.08434 | ||||||||
\(952\) | −8.89898 | −0.288418 | ||||||||
\(953\) | 34.2929 | 1.11085 | 0.555427 | − | 0.831565i | \(-0.312555\pi\) | ||||
0.555427 | + | 0.831565i | \(0.312555\pi\) | |||||||
\(954\) | 31.3485 | 1.01494 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21.5959 | 0.698462 | ||||||||
\(957\) | 4.89898 | 0.158362 | ||||||||
\(958\) | −4.20204 | −0.135762 | ||||||||
\(959\) | 4.00000 | 0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 8.44949 | 0.272422 | ||||||||
\(963\) | 15.7423 | 0.507290 | ||||||||
\(964\) | 17.0000 | 0.547533 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 26.6969 | 0.858960 | ||||||||
\(967\) | 28.0000 | 0.900419 | 0.450210 | − | 0.892923i | \(-0.351349\pi\) | ||||
0.450210 | + | 0.892923i | \(0.351349\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 31.5959 | 1.01501 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9444 | 0.736320 | 0.368160 | − | 0.929762i | \(-0.379988\pi\) | ||||
0.368160 | + | 0.929762i | \(0.379988\pi\) | |||||||
\(972\) | 22.0454 | 0.707107 | ||||||||
\(973\) | −50.9444 | −1.63320 | ||||||||
\(974\) | −9.10102 | −0.291616 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.44949 | 0.110415 | ||||||||
\(977\) | 0.101021 | 0.00323193 | 0.00161597 | − | 0.999999i | \(-0.499486\pi\) | ||||
0.00161597 | + | 0.999999i | \(0.499486\pi\) | |||||||
\(978\) | 30.4949 | 0.975119 | ||||||||
\(979\) | 7.10102 | 0.226950 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.0454 | −0.895421 | ||||||||
\(982\) | 26.4949 | 0.845486 | ||||||||
\(983\) | 39.0000 | 1.24391 | 0.621953 | − | 0.783054i | \(-0.286339\pi\) | ||||
0.621953 | + | 0.783054i | \(0.286339\pi\) | |||||||
\(984\) | −27.7980 | −0.886167 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.00000 | 0.0636930 | ||||||||
\(987\) | −64.2929 | −2.04646 | ||||||||
\(988\) | −15.7980 | −0.502600 | ||||||||
\(989\) | 21.7980 | 0.693135 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.50510 | −0.111343 | −0.0556716 | − | 0.998449i | \(-0.517730\pi\) | ||||
−0.0556716 | + | 0.998449i | \(0.517730\pi\) | |||||||
\(992\) | −3.00000 | −0.0952501 | ||||||||
\(993\) | 74.0908 | 2.35120 | ||||||||
\(994\) | 50.4949 | 1.60160 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14.6969 | 0.465690 | ||||||||
\(997\) | 29.7423 | 0.941950 | 0.470975 | − | 0.882147i | \(-0.343902\pi\) | ||||
0.470975 | + | 0.882147i | \(0.343902\pi\) | |||||||
\(998\) | −24.3485 | −0.770737 | ||||||||
\(999\) | 0 | 0 |
(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 | 1450.2.a.o.1.1 | yes | 2 | |
5.2 | odd | 4 | 1450.2.b.i.349.4 | 4 | |||
5.3 | odd | 4 | 1450.2.b.i.349.1 | 4 | |||
5.4 | even | 2 | 1450.2.a.j.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1450.2.a.j.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
1450.2.a.o.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1450.2.b.i.349.1 | 4 | 5.3 | odd | 4 | |||
1450.2.b.i.349.4 | 4 | 5.2 | odd | 4 |