Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7360,2,Mod(1,7360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7360 = 2^{6} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7360.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: | \(58.7698958877\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7360.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.56155 | 0.901563 | 0.450781 | − | 0.892634i | \(-0.351145\pi\) | ||||
0.450781 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56155 | 0.968176 | 0.484088 | − | 0.875019i | \(-0.339151\pi\) | ||||
0.484088 | + | 0.875019i | \(0.339151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.56155 | 0.987797 | 0.493899 | − | 0.869520i | \(-0.335571\pi\) | ||||
0.493899 | + | 0.869520i | \(0.335571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.56155 | 0.621268 | 0.310634 | − | 0.950530i | \(-0.399459\pi\) | ||||
0.310634 | + | 0.950530i | \(0.399459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.56155 | −1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.12311 | −1.13703 | −0.568516 | − | 0.822672i | \(-0.692482\pi\) | ||||
−0.568516 | + | 0.822672i | \(0.692482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.24621 | 1.30146 | 0.650729 | − | 0.759310i | \(-0.274463\pi\) | ||||
0.650729 | + | 0.759310i | \(0.274463\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.12311 | −0.543663 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.56155 | −0.432981 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.56155 | 0.749915 | 0.374957 | − | 0.927042i | \(-0.377657\pi\) | ||||
0.374957 | + | 0.927042i | \(0.377657\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.56155 | 0.890561 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.12311 | 0.643921 | 0.321960 | − | 0.946753i | \(-0.395658\pi\) | ||||
0.321960 | + | 0.946753i | \(0.395658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.561553 | 0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.68466 | 0.683328 | 0.341664 | − | 0.939822i | \(-0.389010\pi\) | ||||
0.341664 | + | 0.939822i | \(0.389010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.438447 | −0.0626353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.56155 | 0.626577 | 0.313289 | − | 0.949658i | \(-0.398569\pi\) | ||||
0.313289 | + | 0.949658i | \(0.398569\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.36932 | −1.24100 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.68466 | 0.479702 | 0.239851 | − | 0.970810i | \(-0.422901\pi\) | ||||
0.239851 | + | 0.970810i | \(0.422901\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.12311 | 0.912020 | 0.456010 | − | 0.889975i | \(-0.349278\pi\) | ||||
0.456010 | + | 0.889975i | \(0.349278\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.43845 | −0.181227 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.56155 | −0.441756 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.56155 | 1.04596 | 0.522980 | − | 0.852345i | \(-0.324820\pi\) | ||||
0.522980 | + | 0.852345i | \(0.324820\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.56155 | 0.187989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1231 | 1.20139 | 0.600696 | − | 0.799478i | \(-0.294890\pi\) | ||||
0.600696 | + | 0.799478i | \(0.294890\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.43845 | −0.519481 | −0.259740 | − | 0.965678i | \(-0.583637\pi\) | ||||
−0.259740 | + | 0.965678i | \(0.583637\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.56155 | 0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.12311 | −0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.87689 | 0.548693 | 0.274347 | − | 0.961631i | \(-0.411538\pi\) | ||||
0.274347 | + | 0.961631i | \(0.411538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.9309 | 1.52911 | 0.764556 | − | 0.644558i | \(-0.222958\pi\) | ||||
0.764556 | + | 0.644558i | \(0.222958\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.56155 | −0.277839 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.56155 | −1.02511 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.2462 | 1.51010 | 0.755048 | − | 0.655670i | \(-0.227614\pi\) | ||||
0.755048 | + | 0.655670i | \(0.227614\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.12311 | 0.956361 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.3153 | 1.17335 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1231 | −1.33245 | −0.666225 | − | 0.745751i | \(-0.732091\pi\) | ||||
−0.666225 | + | 0.745751i | \(0.732091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.12311 | 0.112876 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.6847 | 1.75969 | 0.879845 | − | 0.475261i | \(-0.157647\pi\) | ||||
0.879845 | + | 0.475261i | \(0.157647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.43845 | −0.332407 | −0.166204 | − | 0.986091i | \(-0.553151\pi\) | ||||
−0.166204 | + | 0.986091i | \(0.553151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.3693 | −1.47211 | −0.736057 | − | 0.676920i | \(-0.763314\pi\) | ||||
−0.736057 | + | 0.676920i | \(0.763314\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.12311 | 0.676095 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.8078 | 1.20485 | 0.602427 | − | 0.798174i | \(-0.294201\pi\) | ||||
0.602427 | + | 0.798174i | \(0.294201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.56155 | 0.601497 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.43845 | 0.580535 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.80776 | 0.692827 | 0.346414 | − | 0.938082i | \(-0.387399\pi\) | ||||
0.346414 | + | 0.938082i | \(0.387399\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.192236 | −0.0167957 | −0.00839787 | − | 0.999965i | \(-0.502673\pi\) | ||||
−0.00839787 | + | 0.999965i | \(0.502673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.3693 | −1.33269 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.56155 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.87689 | 0.587533 | 0.293766 | − | 0.955877i | \(-0.405091\pi\) | ||||
0.293766 | + | 0.955877i | \(0.405091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2462 | 0.953891 | 0.476946 | − | 0.878933i | \(-0.341744\pi\) | ||||
0.476946 | + | 0.878933i | \(0.341744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.31534 | 0.616063 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.12311 | −0.595664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.12311 | 0.508496 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.684658 | −0.0564697 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.36932 | 0.767564 | 0.383782 | − | 0.923424i | \(-0.374621\pi\) | ||||
0.383782 | + | 0.923424i | \(0.374621\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0540 | −1.14370 | −0.571848 | − | 0.820359i | \(-0.693773\pi\) | ||||
−0.571848 | + | 0.820359i | \(0.693773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.43845 | −0.116292 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.24621 | −0.582030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.31534 | 0.344402 | 0.172201 | − | 0.985062i | \(-0.444912\pi\) | ||||
0.172201 | + | 0.985062i | \(0.444912\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.12311 | 0.564899 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.56155 | 0.201879 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9309 | −1.32613 | −0.663064 | − | 0.748563i | \(-0.730744\pi\) | ||||
−0.663064 | + | 0.748563i | \(0.730744\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.12311 | 0.243133 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.315342 | −0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.36932 | 0.257658 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.36932 | −0.408222 | −0.204111 | − | 0.978948i | \(-0.565430\pi\) | ||||
−0.204111 | + | 0.978948i | \(0.565430\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.56155 | 0.193635 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.75379 | 0.432481 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.93087 | 0.518038 | 0.259019 | − | 0.965872i | \(-0.416601\pi\) | ||||
0.259019 | + | 0.965872i | \(0.416601\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.36932 | 0.399098 | 0.199549 | − | 0.979888i | \(-0.436052\pi\) | ||||
0.199549 | + | 0.979888i | \(0.436052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.1231 | 0.822244 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.56155 | −0.335372 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.12311 | −0.374639 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.2462 | −1.03626 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3693 | 1.25680 | 0.628400 | − | 0.777891i | \(-0.283710\pi\) | ||||
0.628400 | + | 0.777891i | \(0.283710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.43845 | 0.175523 | 0.0877616 | − | 0.996142i | \(-0.472029\pi\) | ||||
0.0877616 | + | 0.996142i | \(0.472029\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.56155 | −0.398271 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.6847 | 1.33123 | 0.665613 | − | 0.746297i | \(-0.268170\pi\) | ||||
0.665613 | + | 0.746297i | \(0.268170\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | −0.708881 | −0.354441 | − | 0.935079i | \(-0.615329\pi\) | ||||
−0.354441 | + | 0.935079i | \(0.615329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.3693 | 0.942999 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.6847 | −1.10085 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.12311 | −0.287970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.561553 | −0.0390306 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.315342 | −0.0217090 | −0.0108545 | − | 0.999941i | \(-0.503455\pi\) | ||||
−0.0108545 | + | 0.999941i | \(0.503455\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.8078 | 1.08313 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.5616 | 1.26004 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.93087 | −0.468345 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.12311 | 0.613686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6155 | −1.17962 | −0.589812 | − | 0.807541i | \(-0.700798\pi\) | ||||
−0.589812 | + | 0.807541i | \(0.700798\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.2462 | −1.74202 | −0.871011 | − | 0.491263i | \(-0.836535\pi\) | ||||
−0.871011 | + | 0.491263i | \(0.836535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.7386 | 1.76694 | 0.883469 | − | 0.468489i | \(-0.155201\pi\) | ||||
0.883469 | + | 0.468489i | \(0.155201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.684658 | −0.0448535 | −0.0224267 | − | 0.999748i | \(-0.507139\pi\) | ||||
−0.0224267 | + | 0.999748i | \(0.507139\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.68466 | −0.305593 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.61553 | 0.494682 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.75379 | 0.178128 | 0.0890639 | − | 0.996026i | \(-0.471612\pi\) | ||||
0.0890639 | + | 0.996026i | \(0.471612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.75379 | 0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.438447 | 0.0280114 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.3693 | −1.35970 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.7538 | 1.37859 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.36932 | 0.465147 | 0.232574 | − | 0.972579i | \(-0.425285\pi\) | ||||
0.232574 | + | 0.972579i | \(0.425285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.8078 | 1.98411 | 0.992057 | − | 0.125790i | \(-0.0401465\pi\) | ||||
0.992057 | + | 0.125790i | \(0.0401465\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6847 | 0.726049 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.43845 | 0.212835 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0691303 | 0.00426276 | 0.00213138 | − | 0.999998i | \(-0.499322\pi\) | ||||
0.00213138 | + | 0.999998i | \(0.499322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.56155 | −0.280214 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.2462 | 1.36145 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.2462 | −1.41735 | −0.708673 | − | 0.705537i | \(-0.750706\pi\) | ||||
−0.708673 | + | 0.705537i | \(0.750706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9309 | 1.33221 | 0.666103 | − | 0.745860i | \(-0.267961\pi\) | ||||
0.666103 | + | 0.745860i | \(0.267961\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.2462 | 0.862220 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.68466 | 0.401642 | 0.200821 | − | 0.979628i | \(-0.435639\pi\) | ||||
0.200821 | + | 0.979628i | \(0.435639\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.06913 | −0.243612 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.87689 | −0.410241 | −0.205121 | − | 0.978737i | \(-0.565759\pi\) | ||||
−0.205121 | + | 0.978737i | \(0.565759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.8078 | −0.880230 | −0.440115 | − | 0.897941i | \(-0.645062\pi\) | ||||
−0.440115 | + | 0.897941i | \(0.645062\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.36932 | 0.554990 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.5616 | 0.623429 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4384 | −0.614026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.4924 | −1.20129 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.8078 | 0.981920 | 0.490960 | − | 0.871182i | \(-0.336646\pi\) | ||||
0.490960 | + | 0.871182i | \(0.336646\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.68466 | −0.214529 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1231 | 0.645428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.56155 | 0.205970 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.6155 | 1.58647 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.12311 | −0.407868 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.1231 | 1.20556 | 0.602780 | − | 0.797908i | \(-0.294060\pi\) | ||||
0.602780 | + | 0.797908i | \(0.294060\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.9848 | −1.42134 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.68466 | 0.492462 | 0.246231 | − | 0.969211i | \(-0.420808\pi\) | ||||
0.246231 | + | 0.969211i | \(0.420808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.807764 | −0.0456575 | −0.0228288 | − | 0.999739i | \(-0.507267\pi\) | ||||
−0.0228288 | + | 0.999739i | \(0.507267\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.43845 | 0.0810473 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1231 | −0.849398 | −0.424699 | − | 0.905335i | \(-0.639620\pi\) | ||||
−0.424699 | + | 0.905335i | \(0.639620\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.2462 | 0.685656 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.36932 | −0.299686 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.3693 | −0.855172 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.56155 | 0.197559 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.0000 | −1.32720 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.6155 | −1.57285 | −0.786426 | − | 0.617685i | \(-0.788071\pi\) | ||||
−0.786426 | + | 0.617685i | \(0.788071\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.56155 | −0.140372 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.56155 | −0.467768 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6155 | 0.741685 | 0.370843 | − | 0.928696i | \(-0.379069\pi\) | ||||
0.370843 | + | 0.928696i | \(0.379069\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.0000 | 1.08625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.4924 | −0.784809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0540 | −1.02882 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.56155 | −0.0840712 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.4924 | −0.885360 | −0.442680 | − | 0.896680i | \(-0.645972\pi\) | ||||
−0.442680 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.3693 | 1.41152 | 0.705759 | − | 0.708452i | \(-0.250606\pi\) | ||||
0.705759 | + | 0.708452i | \(0.250606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.8078 | −1.05726 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.05398 | −0.109322 | −0.0546610 | − | 0.998505i | \(-0.517408\pi\) | ||||
−0.0546610 | + | 0.998505i | \(0.517408\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.1231 | −0.537279 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.2462 | 0.542287 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.6155 | 0.824156 | 0.412078 | − | 0.911149i | \(-0.364803\pi\) | ||||
0.412078 | + | 0.911149i | \(0.364803\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9309 | −0.573722 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.43845 | 0.232319 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.5616 | −1.17770 | −0.588852 | − | 0.808241i | \(-0.700420\pi\) | ||||
−0.588852 | + | 0.808241i | \(0.700420\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.31534 | −0.120532 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.6847 | 0.606637 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.2462 | 1.04831 | 0.524155 | − | 0.851623i | \(-0.324381\pi\) | ||||
0.524155 | + | 0.851623i | \(0.324381\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56155 | −0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.8078 | −1.12316 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.4924 | 1.87449 | 0.937245 | − | 0.348672i | \(-0.113367\pi\) | ||||
0.937245 | + | 0.348672i | \(0.113367\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.1922 | 0.624627 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.19224 | 0.163116 | 0.0815578 | − | 0.996669i | \(-0.474010\pi\) | ||||
0.0815578 | + | 0.996669i | \(0.474010\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.12311 | 0.261098 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.8769 | 0.551480 | 0.275740 | − | 0.961232i | \(-0.411077\pi\) | ||||
0.275740 | + | 0.961232i | \(0.411077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.56155 | 0.129543 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.300187 | −0.0151424 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.87689 | −0.245383 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.5464 | −1.73383 | −0.866917 | − | 0.498453i | \(-0.833902\pi\) | ||||
−0.866917 | + | 0.498453i | \(0.833902\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −24.0000 | −1.20150 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.8078 | 1.28558 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | 0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.12311 | −0.452216 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.9848 | −1.77934 | −0.889668 | − | 0.456608i | \(-0.849064\pi\) | ||||
−0.889668 | + | 0.456608i | \(0.849064\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.7386 | 0.529698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.43845 | 0.464436 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.9309 | −0.683839 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.5616 | 0.859993 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.8769 | 0.922197 | 0.461098 | − | 0.887349i | \(-0.347456\pi\) | ||||
0.461098 | + | 0.887349i | \(0.347456\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.1231 | −1.22443 | −0.612213 | − | 0.790693i | \(-0.709720\pi\) | ||||
−0.612213 | + | 0.790693i | \(0.709720\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.63068 | −0.127908 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.56155 | 0.124254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.2462 | 0.882996 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.1231 | −0.537029 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.2462 | −0.493543 | −0.246771 | − | 0.969074i | \(-0.579370\pi\) | ||||
−0.246771 | + | 0.969074i | \(0.579370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.9309 | 1.91896 | 0.959478 | − | 0.281785i | \(-0.0909265\pi\) | ||||
0.959478 | + | 0.281785i | \(0.0909265\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.56155 | 0.458441 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.00000 | −0.287019 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.8078 | 0.945373 | 0.472686 | − | 0.881231i | \(-0.343284\pi\) | ||||
0.472686 | + | 0.881231i | \(0.343284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.246211 | 0.0117243 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.8078 | 0.561004 | 0.280502 | − | 0.959853i | \(-0.409499\pi\) | ||||
0.280502 | + | 0.959853i | \(0.409499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.2462 | −0.675335 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.6307 | 0.692008 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.6847 | −1.02336 | −0.511681 | − | 0.859175i | \(-0.670977\pi\) | ||||
−0.511681 | + | 0.859175i | \(0.670977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.24621 | −0.388299 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.9460 | −1.03111 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.12311 | −0.427698 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.43845 | 0.441512 | 0.220756 | − | 0.975329i | \(-0.429148\pi\) | ||||
0.220756 | + | 0.975329i | \(0.429148\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.2462 | −0.664956 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.9309 | 1.90634 | 0.953170 | − | 0.302434i | \(-0.0977992\pi\) | ||||
0.953170 | + | 0.302434i | \(0.0977992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.3693 | −1.45786 | −0.728928 | − | 0.684590i | \(-0.759981\pi\) | ||||
−0.728928 | + | 0.684590i | \(0.759981\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.3153 | −0.524736 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.3153 | 1.03263 | 0.516315 | − | 0.856398i | \(-0.327303\pi\) | ||||
0.516315 | + | 0.856398i | \(0.327303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.9309 | 1.01267 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.73863 | 0.310500 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | −0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.56155 | −0.117285 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −43.2311 | −1.97528 | −0.987639 | − | 0.156748i | \(-0.949899\pi\) | ||||
−0.987639 | + | 0.156748i | \(0.949899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2462 | 0.740763 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | 0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.1231 | 0.595890 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.80776 | 0.353804 | 0.176902 | − | 0.984229i | \(-0.443393\pi\) | ||||
0.176902 | + | 0.984229i | \(0.443393\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.4384 | −1.19559 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4924 | −0.518646 | −0.259323 | − | 0.965791i | \(-0.583499\pi\) | ||||
−0.259323 | + | 0.965791i | \(0.583499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.6847 | −0.706401 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.12311 | −0.0504798 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.9309 | 1.16316 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.6155 | −1.01241 | −0.506205 | − | 0.862413i | \(-0.668952\pi\) | ||||
−0.506205 | + | 0.862413i | \(0.668952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.4924 | −0.558120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.93087 | −0.175269 | −0.0876344 | − | 0.996153i | \(-0.527931\pi\) | ||||
−0.0876344 | + | 0.996153i | \(0.527931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6847 | −0.786957 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.492423 | −0.0218693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.1771 | 1.20460 | 0.602301 | − | 0.798269i | \(-0.294251\pi\) | ||||
0.602301 | + | 0.798269i | \(0.294251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3693 | −0.502949 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.3693 | 1.47329 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0000 | 0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.36932 | −0.412062 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.38447 | −0.368037 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.6155 | −0.596507 | −0.298254 | − | 0.954487i | \(-0.596404\pi\) | ||||
−0.298254 | + | 0.954487i | \(0.596404\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.7386 | 0.644475 | 0.322238 | − | 0.946659i | \(-0.395565\pi\) | ||||
0.322238 | + | 0.946659i | \(0.395565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.5616 | 0.808554 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.06913 | −0.0897926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.6847 | 0.636063 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.43845 | 0.148657 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.8229 | 0.467043 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.876894 | 0.0377705 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.68466 | 0.115422 | 0.0577112 | − | 0.998333i | \(-0.481620\pi\) | ||||
0.0577112 | + | 0.998333i | \(0.481620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.38447 | 0.359812 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.3693 | 0.658349 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.1771 | 0.905467 | 0.452733 | − | 0.891646i | \(-0.350449\pi\) | ||||
0.452733 | + | 0.891646i | \(0.350449\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | −0.170716 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.7386 | 1.56512 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.4924 | 0.531232 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.12311 | −0.302359 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.6847 | 0.664580 | 0.332290 | − | 0.943177i | \(-0.392179\pi\) | ||||
0.332290 | + | 0.943177i | \(0.392179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.6695 | −1.37686 | −0.688428 | − | 0.725305i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725305i | \(0.741699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.8078 | −0.538827 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.9309 | −0.753026 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.7386 | 0.701720 | 0.350860 | − | 0.936428i | \(-0.385889\pi\) | ||||
0.350860 | + | 0.936428i | \(0.385889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.0000 | −1.50655 | −0.753277 | − | 0.657704i | \(-0.771528\pi\) | ||||
−0.753277 | + | 0.657704i | \(0.771528\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.1231 | 1.13308 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.5616 | −1.23066 | −0.615332 | − | 0.788268i | \(-0.710978\pi\) | ||||
−0.615332 | + | 0.788268i | \(0.710978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.80776 | 0.158245 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.6847 | 1.48045 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.12311 | −0.377840 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.06913 | −0.291774 | −0.145887 | − | 0.989301i | \(-0.546604\pi\) | ||||
−0.145887 | + | 0.989301i | \(0.546604\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.4773 | −1.79145 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.1771 | 1.20018 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.6155 | 0.641253 | 0.320626 | − | 0.947206i | \(-0.396107\pi\) | ||||
0.320626 | + | 0.947206i | \(0.396107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.56155 | −0.268997 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.6155 | −0.639101 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.9848 | −1.34772 | −0.673862 | − | 0.738857i | \(-0.735366\pi\) | ||||
−0.673862 | + | 0.738857i | \(0.735366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.3693 | 1.48354 | 0.741768 | − | 0.670657i | \(-0.233988\pi\) | ||||
0.741768 | + | 0.670657i | \(0.233988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.80776 | −0.195787 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.49242 | 0.344697 | 0.172348 | − | 0.985036i | \(-0.444865\pi\) | ||||
0.172348 | + | 0.985036i | \(0.444865\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.4924 | −0.992483 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.6847 | 0.674989 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.61553 | 0.226809 | 0.113405 | − | 0.993549i | \(-0.463824\pi\) | ||||
0.113405 | + | 0.993549i | \(0.463824\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.43845 | −0.259623 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.561553 | 0.0226073 | 0.0113036 | − | 0.999936i | \(-0.496402\pi\) | ||||
0.0113036 | + | 0.999936i | \(0.496402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.4924 | −0.502113 | −0.251056 | − | 0.967972i | \(-0.580778\pi\) | ||||
−0.251056 | + | 0.967972i | \(0.580778\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.56155 | −0.223177 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.4924 | 1.46204 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.7386 | 0.748349 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.6847 | 0.465898 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.2462 | 1.20408 | 0.602041 | − | 0.798465i | \(-0.294354\pi\) | ||||
0.602041 | + | 0.798465i | \(0.294354\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.492423 | −0.0195720 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.80776 | −0.309842 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.56155 | −0.0618710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.68466 | −0.224882 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.87689 | 0.271621 | 0.135810 | − | 0.990735i | \(-0.456636\pi\) | ||||
0.135810 | + | 0.990735i | \(0.456636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.4233 | −0.805416 | −0.402708 | − | 0.915328i | \(-0.631931\pi\) | ||||
−0.402708 | + | 0.915328i | \(0.631931\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.31534 | 0.208968 | 0.104484 | − | 0.994527i | \(-0.466681\pi\) | ||||
0.104484 | + | 0.994527i | \(0.466681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.36932 | −0.289271 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.9848 | 1.13601 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.6695 | −1.55239 | −0.776194 | − | 0.630494i | \(-0.782852\pi\) | ||||
−0.776194 | + | 0.630494i | \(0.782852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.192236 | 0.00751128 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.49242 | 0.0972387 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.3693 | −0.598704 | −0.299352 | − | 0.954143i | \(-0.596770\pi\) | ||||
−0.299352 | + | 0.954143i | \(0.596770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.49242 | 0.252526 | 0.126263 | − | 0.991997i | \(-0.459702\pi\) | ||||
0.126263 | + | 0.991997i | \(0.459702\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.2462 | 0.553277 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.3693 | 0.595997 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.12311 | −0.237088 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.5076 | −1.06350 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.2462 | −0.549969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.5464 | 1.33167 | 0.665833 | − | 0.746101i | \(-0.268076\pi\) | ||||
0.665833 | + | 0.746101i | \(0.268076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.56155 | −0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.8078 | −1.03031 | −0.515153 | − | 0.857098i | \(-0.672265\pi\) | ||||
−0.515153 | + | 0.857098i | \(0.672265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.6155 | −1.29005 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −40.9848 | −1.57054 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.0540 | −1.60915 | −0.804575 | − | 0.593851i | \(-0.797607\pi\) | ||||
−0.804575 | + | 0.593851i | \(0.797607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.87689 | −0.262753 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.7538 | 1.59301 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.2462 | 0.618931 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4924 | −0.627401 | −0.313701 | − | 0.949522i | \(-0.601569\pi\) | ||||
−0.313701 | + | 0.949522i | \(0.601569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.87689 | 0.109284 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.2462 | −0.426593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.5616 | 0.400047 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.06913 | −0.0404382 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.75379 | 0.0662397 | 0.0331198 | − | 0.999451i | \(-0.489456\pi\) | ||||
0.0331198 | + | 0.999451i | \(0.489456\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.3693 | −1.03225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.31534 | −0.275512 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.3002 | 1.70369 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.7538 | −1.11743 | −0.558713 | − | 0.829361i | \(-0.688705\pi\) | ||||
−0.558713 | + | 0.829361i | \(0.688705\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.73863 | −0.102707 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.24621 | 0.271373 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.12311 | 0.266389 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.30019 | 0.160593 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.0540 | 0.710593 | 0.355297 | − | 0.934754i | \(-0.384380\pi\) | ||||
0.355297 | + | 0.934754i | \(0.384380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.9848 | −1.52636 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.36932 | 0.348449 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.12311 | −0.227406 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.1922 | −0.785977 | −0.392988 | − | 0.919543i | \(-0.628559\pi\) | ||||
−0.392988 | + | 0.919543i | \(0.628559\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.315342 | −0.0116474 | −0.00582370 | − | 0.999983i | \(-0.501854\pi\) | ||||
−0.00582370 | + | 0.999983i | \(0.501854\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.684658 | 0.0252540 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.1231 | −0.630738 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.615528 | −0.0226426 | −0.0113213 | − | 0.999936i | \(-0.503604\pi\) | ||||
−0.0113213 | + | 0.999936i | \(0.503604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.3693 | −1.22585 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.50758 | 0.128681 | 0.0643403 | − | 0.997928i | \(-0.479506\pi\) | ||||
0.0643403 | + | 0.997928i | \(0.479506\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.36932 | −0.343265 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.82292 | −0.286226 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.80776 | −0.321829 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1231 | −0.478869 | −0.239434 | − | 0.970913i | \(-0.576962\pi\) | ||||
−0.239434 | + | 0.970913i | \(0.576962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.5076 | 0.419359 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.0540 | 0.511477 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.5616 | −0.456557 | −0.228279 | − | 0.973596i | \(-0.573310\pi\) | ||||
−0.228279 | + | 0.973596i | \(0.573310\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.12311 | −0.113362 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.9848 | −1.59445 | −0.797225 | − | 0.603683i | \(-0.793699\pi\) | ||||
−0.797225 | + | 0.603683i | \(0.793699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.3693 | −1.42526 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.43845 | 0.0520072 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.1231 | 0.473848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.6307 | −0.383352 | −0.191676 | − | 0.981458i | \(-0.561392\pi\) | ||||
−0.191676 | + | 0.981458i | \(0.561392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 49.6695 | 1.78880 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.1231 | 1.47910 | 0.739548 | − | 0.673104i | \(-0.235039\pi\) | ||||
0.739548 | + | 0.673104i | \(0.235039\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.24621 | 0.260292 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.2462 | 0.654579 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.7386 | −0.886354 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.2462 | −0.724466 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.0540 | 1.21699 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.31534 | −0.154021 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.6847 | 1.41461 | 0.707303 | − | 0.706911i | \(-0.249912\pi\) | ||||
0.707303 | + | 0.706911i | \(0.249912\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.107951 | 0.00384314 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.8078 | 1.16651 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.3693 | 0.900891 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.12311 | −0.252631 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 52.4233 | 1.85693 | 0.928464 | − | 0.371422i | \(-0.121130\pi\) | ||||
0.928464 | + | 0.371422i | \(0.121130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.00000 | −0.282666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.87689 | 0.313259 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56155 | −0.0902829 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.3002 | −1.27783 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −54.1771 | −1.90476 | −0.952382 | − | 0.304906i | \(-0.901375\pi\) | ||||
−0.952382 | + | 0.304906i | \(0.901375\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.2462 | −1.65904 | −0.829519 | − | 0.558478i | \(-0.811386\pi\) | ||||
−0.829519 | + | 0.558478i | \(0.811386\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.2462 | 1.20107 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.9309 | 0.593062 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.12311 | −0.179016 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.4924 | 1.20379 | 0.601897 | − | 0.798574i | \(-0.294412\pi\) | ||||
0.601897 | + | 0.798574i | \(0.294412\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.0540 | −1.32648 | −0.663239 | − | 0.748408i | \(-0.730819\pi\) | ||||
−0.663239 | + | 0.748408i | \(0.730819\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.12311 | −0.108733 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.6847 | −0.684503 | −0.342251 | − | 0.939608i | \(-0.611189\pi\) | ||||
−0.342251 | + | 0.939608i | \(0.611189\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5464 | 1.02619 | 0.513094 | − | 0.858332i | \(-0.328499\pi\) | ||||
0.513094 | + | 0.858332i | \(0.328499\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.4384 | 0.362106 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.12311 | −0.0389133 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.3002 | −1.39298 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.8769 | −1.48027 | −0.740137 | − | 0.672456i | \(-0.765240\pi\) | ||||
−0.740137 | + | 0.672456i | \(0.765240\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.49242 | 0.292842 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.7386 | −0.369858 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.315342 | 0.0108481 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.9309 | −0.616112 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.1231 | −0.793583 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.56155 | 0.156368 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2462 | 0.693217 | 0.346609 | − | 0.938010i | \(-0.387333\pi\) | ||||
0.346609 | + | 0.938010i | \(0.387333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.36932 | −0.115228 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.3153 | −1.13803 | −0.569015 | − | 0.822327i | \(-0.692675\pi\) | ||||
−0.569015 | + | 0.822327i | \(0.692675\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.5076 | 0.494992 | 0.247496 | − | 0.968889i | \(-0.420392\pi\) | ||||
0.247496 | + | 0.968889i | \(0.420392\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.4924 | 0.562060 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.56155 | −0.257398 | −0.128699 | − | 0.991684i | \(-0.541080\pi\) | ||||
−0.128699 | + | 0.991684i | \(0.541080\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.36932 | 0.182562 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.3002 | −0.553583 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.75379 | −0.330875 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.4924 | 1.03320 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.36932 | 0.249414 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.56155 | −0.0865963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9848 | 0.641073 | 0.320536 | − | 0.947236i | \(-0.396137\pi\) | ||||
0.320536 | + | 0.947236i | \(0.396137\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.2462 | 0.885263 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.4773 | 1.39740 | 0.698702 | − | 0.715413i | \(-0.253761\pi\) | ||||
0.698702 | + | 0.715413i | \(0.253761\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.7386 | −0.361384 | −0.180692 | − | 0.983540i | \(-0.557834\pi\) | ||||
−0.180692 | + | 0.983540i | \(0.557834\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.75379 | −0.193411 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.7926 | 1.43684 | 0.718418 | − | 0.695612i | \(-0.244867\pi\) | ||||
0.718418 | + | 0.695612i | \(0.244867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | 0.670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.0000 | 0.469018 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.1080 | −0.940597 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.93087 | −0.231673 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.56155 | 0.185695 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −44.3693 | −1.47980 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.6847 | 0.389272 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.36932 | −0.178482 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.6847 | −0.720027 | −0.360014 | − | 0.932947i | \(-0.617228\pi\) | ||||
−0.360014 | + | 0.932947i | \(0.617228\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.93087 | −0.329386 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.12311 | −0.103473 | −0.0517366 | − | 0.998661i | \(-0.516476\pi\) | ||||
−0.0517366 | + | 0.998661i | \(0.516476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.8617 | −0.922089 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.1231 | −0.367719 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.492423 | −0.0162612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.7386 | 1.54177 | 0.770883 | − | 0.636977i | \(-0.219815\pi\) | ||||
0.770883 | + | 0.636977i | \(0.219815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.9848 | 1.08689 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0540 | 1.18673 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.56155 | 0.149983 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.98485 | 0.295101 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.7235 | −1.86104 | −0.930518 | − | 0.366245i | \(-0.880643\pi\) | ||||
−0.930518 | + | 0.366245i | \(0.880643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.63068 | 0.0862172 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.5616 | 0.443985 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.12311 | 0.167543 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.2462 | −0.530741 | −0.265370 | − | 0.964147i | \(-0.585494\pi\) | ||||
−0.265370 | + | 0.964147i | \(0.585494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.26137 | −0.0411631 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.7538 | 1.23074 | 0.615369 | − | 0.788239i | \(-0.289007\pi\) | ||||
0.615369 | + | 0.788239i | \(0.289007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.12311 | 0.134267 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.2462 | 0.463429 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −56.6847 | −1.84200 | −0.921002 | − | 0.389558i | \(-0.872628\pi\) | ||||
−0.921002 | + | 0.389558i | \(0.872628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.8078 | −0.513142 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.6155 | −0.765786 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.4924 | −1.24689 | −0.623446 | − | 0.781866i | \(-0.714268\pi\) | ||||
−0.623446 | + | 0.781866i | \(0.714268\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.3693 | −0.562058 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.1231 | 0.618162 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.6155 | 0.568835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.5076 | 0.693793 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.93087 | 0.0622214 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.43845 | −0.0784964 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.6847 | −1.82286 | −0.911428 | − | 0.411460i | \(-0.865019\pi\) | ||||
−0.911428 | + | 0.411460i | \(0.865019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.6307 | 0.726253 | 0.363127 | − | 0.931740i | \(-0.381709\pi\) | ||||
0.363127 | + | 0.931740i | \(0.381709\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.8078 | 0.923535 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.56155 | 0.178112 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 59.7926 | 1.91294 | 0.956468 | − | 0.291839i | \(-0.0942671\pi\) | ||||
0.956468 | + | 0.291839i | \(0.0942671\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.4924 | −0.910622 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.63068 | 0.275557 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.0540 | −1.18184 | −0.590919 | − | 0.806731i | \(-0.701235\pi\) | ||||
−0.590919 | + | 0.806731i | \(0.701235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.6847 | −0.595343 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.7386 | 0.596457 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.3002 | 1.69314 | 0.846568 | − | 0.532280i | \(-0.178665\pi\) | ||||
0.846568 | + | 0.532280i | \(0.178665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −44.6847 | −1.41802 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | 0.317021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.6155 | −1.76136 | −0.880681 | − | 0.473710i | \(-0.842914\pi\) | ||||
−0.880681 | + | 0.473710i | \(0.842914\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.3693 | −0.802650 |
(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 | 7360.2.a.bi.1.2 | 2 | ||
4.3 | odd | 2 | 7360.2.a.bo.1.1 | 2 | |||
8.3 | odd | 2 | 1840.2.a.m.1.2 | 2 | |||
8.5 | even | 2 | 460.2.a.e.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 4140.2.a.m.1.2 | 2 | |||
40.13 | odd | 4 | 2300.2.c.h.1749.2 | 4 | |||
40.19 | odd | 2 | 9200.2.a.bv.1.1 | 2 | |||
40.29 | even | 2 | 2300.2.a.i.1.2 | 2 | |||
40.37 | odd | 4 | 2300.2.c.h.1749.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.a.e.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
1840.2.a.m.1.2 | 2 | 8.3 | odd | 2 | |||
2300.2.a.i.1.2 | 2 | 40.29 | even | 2 | |||
2300.2.c.h.1749.2 | 4 | 40.13 | odd | 4 | |||
2300.2.c.h.1749.3 | 4 | 40.37 | odd | 4 | |||
4140.2.a.m.1.2 | 2 | 24.5 | odd | 2 | |||
7360.2.a.bi.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7360.2.a.bo.1.1 | 2 | 4.3 | odd | 2 | |||
9200.2.a.bv.1.1 | 2 | 40.19 | odd | 2 |