Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4830,2,Mod(1,4830)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4830, 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("4830.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4830.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: | \(38.5677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4830.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 6.74456 | 1.87061 | 0.935303 | − | 0.353849i | \(-0.115127\pi\) | ||||
0.935303 | + | 0.353849i | \(0.115127\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.74456 | 1.08848 | 0.544239 | − | 0.838930i | \(-0.316819\pi\) | ||||
0.544239 | + | 0.838930i | \(0.316819\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 4.00000 | 0.852803 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.74456 | −1.32272 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 4.74456 | 0.881043 | 0.440522 | − | 0.897742i | \(-0.354794\pi\) | ||||
0.440522 | + | 0.897742i | \(0.354794\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 4.74456 | 0.852149 | 0.426074 | − | 0.904688i | \(-0.359896\pi\) | ||||
0.426074 | + | 0.904688i | \(0.359896\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −4.74456 | −0.769670 | ||||||||
\(39\) | −6.74456 | −1.07999 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.74456 | −1.36567 | −0.682836 | − | 0.730572i | \(-0.739253\pi\) | ||||
−0.682836 | + | 0.730572i | \(0.739253\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −12.7446 | −1.85899 | −0.929493 | − | 0.368840i | \(-0.879755\pi\) | ||||
−0.929493 | + | 0.368840i | \(0.879755\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.74456 | 0.935303 | ||||||||
\(53\) | 12.7446 | 1.75060 | 0.875300 | − | 0.483580i | \(-0.160664\pi\) | ||||
0.875300 | + | 0.483580i | \(0.160664\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −4.74456 | −0.628433 | ||||||||
\(58\) | −4.74456 | −0.622992 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −11.4891 | −1.47103 | −0.735516 | − | 0.677507i | \(-0.763060\pi\) | ||||
−0.735516 | + | 0.677507i | \(0.763060\pi\) | |||||||
\(62\) | −4.74456 | −0.602560 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.74456 | 0.836560 | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −0.744563 | −0.0871445 | −0.0435722 | − | 0.999050i | \(-0.513874\pi\) | ||||
−0.0435722 | + | 0.999050i | \(0.513874\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.74456 | 0.544239 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 6.74456 | 0.763671 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.74456 | 0.965675 | ||||||||
\(83\) | 16.7446 | 1.83795 | 0.918977 | − | 0.394311i | \(-0.129017\pi\) | ||||
0.918977 | + | 0.394311i | \(0.129017\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.74456 | −0.508671 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | −14.7446 | −1.56292 | −0.781460 | − | 0.623955i | \(-0.785525\pi\) | ||||
−0.781460 | + | 0.623955i | \(0.785525\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −6.74456 | −0.707022 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −4.74456 | −0.491988 | ||||||||
\(94\) | 12.7446 | 1.31450 | ||||||||
\(95\) | 4.74456 | 0.486782 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.25544 | 0.127470 | 0.0637352 | − | 0.997967i | \(-0.479699\pi\) | ||||
0.0637352 | + | 0.997967i | \(0.479699\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 18.7446 | 1.86515 | 0.932577 | − | 0.360971i | \(-0.117555\pi\) | ||||
0.932577 | + | 0.360971i | \(0.117555\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | −6.74456 | −0.661359 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | −12.7446 | −1.23786 | ||||||||
\(107\) | −6.74456 | −0.652021 | −0.326011 | − | 0.945366i | \(-0.605705\pi\) | ||||
−0.326011 | + | 0.945366i | \(0.605705\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 12.7446 | 1.22071 | 0.610354 | − | 0.792129i | \(-0.291027\pi\) | ||||
0.610354 | + | 0.792129i | \(0.291027\pi\) | |||||||
\(110\) | 4.00000 | 0.381385 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 4.74456 | 0.444369 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 4.74456 | 0.440522 | ||||||||
\(117\) | 6.74456 | 0.623535 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 11.4891 | 1.04018 | ||||||||
\(123\) | 8.74456 | 0.788471 | ||||||||
\(124\) | 4.74456 | 0.426074 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.74456 | −0.591537 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | −4.74456 | −0.411406 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4891 | 0.981582 | 0.490791 | − | 0.871277i | \(-0.336708\pi\) | ||||
0.490791 | + | 0.871277i | \(0.336708\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −13.4891 | −1.14413 | −0.572066 | − | 0.820207i | \(-0.693858\pi\) | ||||
−0.572066 | + | 0.820207i | \(0.693858\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 12.7446 | 1.07329 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | −26.9783 | −2.25603 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.74456 | 0.394014 | ||||||||
\(146\) | 0.744563 | 0.0616204 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 7.48913 | 0.613533 | 0.306767 | − | 0.951785i | \(-0.400753\pi\) | ||||
0.306767 | + | 0.951785i | \(0.400753\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −9.48913 | −0.772214 | −0.386107 | − | 0.922454i | \(-0.626180\pi\) | ||||
−0.386107 | + | 0.922454i | \(0.626180\pi\) | |||||||
\(152\) | −4.74456 | −0.384835 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.00000 | −0.322329 | ||||||||
\(155\) | 4.74456 | 0.381092 | ||||||||
\(156\) | −6.74456 | −0.539997 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | −12.7446 | −1.01071 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −10.7446 | −0.841579 | −0.420790 | − | 0.907158i | \(-0.638247\pi\) | ||||
−0.420790 | + | 0.907158i | \(0.638247\pi\) | |||||||
\(164\) | −8.74456 | −0.682836 | ||||||||
\(165\) | 4.00000 | 0.311400 | ||||||||
\(166\) | −16.7446 | −1.29963 | ||||||||
\(167\) | −16.7446 | −1.29573 | −0.647867 | − | 0.761754i | \(-0.724339\pi\) | ||||
−0.647867 | + | 0.761754i | \(0.724339\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 32.4891 | 2.49916 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.74456 | 0.362826 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.74456 | 0.512780 | 0.256390 | − | 0.966573i | \(-0.417467\pi\) | ||||
0.256390 | + | 0.966573i | \(0.417467\pi\) | |||||||
\(174\) | 4.74456 | 0.359684 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 14.7446 | 1.10515 | ||||||||
\(179\) | 10.7446 | 0.803086 | 0.401543 | − | 0.915840i | \(-0.368474\pi\) | ||||
0.401543 | + | 0.915840i | \(0.368474\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 6.74456 | 0.499940 | ||||||||
\(183\) | 11.4891 | 0.849301 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 2.00000 | 0.147043 | ||||||||
\(186\) | 4.74456 | 0.347888 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.7446 | −0.929493 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −4.74456 | −0.344207 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | −1.25544 | −0.0901351 | ||||||||
\(195\) | −6.74456 | −0.482988 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 19.4891 | 1.38854 | 0.694271 | − | 0.719713i | \(-0.255727\pi\) | ||||
0.694271 | + | 0.719713i | \(0.255727\pi\) | |||||||
\(198\) | 4.00000 | 0.284268 | ||||||||
\(199\) | 24.2337 | 1.71788 | 0.858940 | − | 0.512076i | \(-0.171123\pi\) | ||||
0.858940 | + | 0.512076i | \(0.171123\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | −18.7446 | −1.31886 | ||||||||
\(203\) | −4.74456 | −0.333003 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.74456 | −0.610747 | ||||||||
\(206\) | −4.00000 | −0.278693 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 6.74456 | 0.467651 | ||||||||
\(209\) | −18.9783 | −1.31275 | ||||||||
\(210\) | −1.00000 | −0.0690066 | ||||||||
\(211\) | 9.48913 | 0.653258 | 0.326629 | − | 0.945153i | \(-0.394087\pi\) | ||||
0.326629 | + | 0.945153i | \(0.394087\pi\) | |||||||
\(212\) | 12.7446 | 0.875300 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 6.74456 | 0.461049 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.74456 | −0.322082 | ||||||||
\(218\) | −12.7446 | −0.863171 | ||||||||
\(219\) | 0.744563 | 0.0503129 | ||||||||
\(220\) | −4.00000 | −0.269680 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.00000 | 0.134231 | ||||||||
\(223\) | 19.4891 | 1.30509 | 0.652544 | − | 0.757751i | \(-0.273702\pi\) | ||||
0.652544 | + | 0.757751i | \(0.273702\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −2.00000 | −0.133038 | ||||||||
\(227\) | 4.74456 | 0.314908 | 0.157454 | − | 0.987526i | \(-0.449671\pi\) | ||||
0.157454 | + | 0.987526i | \(0.449671\pi\) | |||||||
\(228\) | −4.74456 | −0.314216 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | −4.00000 | −0.263181 | ||||||||
\(232\) | −4.74456 | −0.311496 | ||||||||
\(233\) | −23.4891 | −1.53882 | −0.769412 | − | 0.638753i | \(-0.779451\pi\) | ||||
−0.769412 | + | 0.638753i | \(0.779451\pi\) | |||||||
\(234\) | −6.74456 | −0.440906 | ||||||||
\(235\) | −12.7446 | −0.831364 | ||||||||
\(236\) | 4.00000 | 0.260378 | ||||||||
\(237\) | 8.00000 | 0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −13.4891 | −0.868911 | −0.434455 | − | 0.900693i | \(-0.643059\pi\) | ||||
−0.434455 | + | 0.900693i | \(0.643059\pi\) | |||||||
\(242\) | −5.00000 | −0.321412 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.4891 | −0.735516 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −8.74456 | −0.557533 | ||||||||
\(247\) | 32.0000 | 2.03611 | ||||||||
\(248\) | −4.74456 | −0.301280 | ||||||||
\(249\) | −16.7446 | −1.06114 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 18.2337 | 1.15090 | 0.575450 | − | 0.817837i | \(-0.304827\pi\) | ||||
0.575450 | + | 0.817837i | \(0.304827\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 6.74456 | 0.418280 | ||||||||
\(261\) | 4.74456 | 0.293681 | ||||||||
\(262\) | −4.00000 | −0.247121 | ||||||||
\(263\) | −8.00000 | −0.493301 | −0.246651 | − | 0.969104i | \(-0.579330\pi\) | ||||
−0.246651 | + | 0.969104i | \(0.579330\pi\) | |||||||
\(264\) | −4.00000 | −0.246183 | ||||||||
\(265\) | 12.7446 | 0.782892 | ||||||||
\(266\) | 4.74456 | 0.290908 | ||||||||
\(267\) | 14.7446 | 0.902353 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | −26.7446 | −1.63064 | −0.815322 | − | 0.579007i | \(-0.803440\pi\) | ||||
−0.815322 | + | 0.579007i | \(0.803440\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 12.7446 | 0.774177 | 0.387089 | − | 0.922043i | \(-0.373481\pi\) | ||||
0.387089 | + | 0.922043i | \(0.373481\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.74456 | 0.408200 | ||||||||
\(274\) | −11.4891 | −0.694083 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 32.7446 | 1.96743 | 0.983715 | − | 0.179735i | \(-0.0575241\pi\) | ||||
0.983715 | + | 0.179735i | \(0.0575241\pi\) | |||||||
\(278\) | 13.4891 | 0.809024 | ||||||||
\(279\) | 4.74456 | 0.284050 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −3.48913 | −0.208144 | −0.104072 | − | 0.994570i | \(-0.533187\pi\) | ||||
−0.104072 | + | 0.994570i | \(0.533187\pi\) | |||||||
\(282\) | −12.7446 | −0.758928 | ||||||||
\(283\) | −7.25544 | −0.431291 | −0.215645 | − | 0.976472i | \(-0.569186\pi\) | ||||
−0.215645 | + | 0.976472i | \(0.569186\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | −4.74456 | −0.281044 | ||||||||
\(286\) | 26.9783 | 1.59526 | ||||||||
\(287\) | 8.74456 | 0.516175 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −4.74456 | −0.278610 | ||||||||
\(291\) | −1.25544 | −0.0735950 | ||||||||
\(292\) | −0.744563 | −0.0435722 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | −7.48913 | −0.433833 | ||||||||
\(299\) | −6.74456 | −0.390048 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.48913 | 0.546038 | ||||||||
\(303\) | −18.7446 | −1.07685 | ||||||||
\(304\) | 4.74456 | 0.272119 | ||||||||
\(305\) | −11.4891 | −0.657865 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9783 | −1.08315 | −0.541573 | − | 0.840654i | \(-0.682171\pi\) | ||||
−0.541573 | + | 0.840654i | \(0.682171\pi\) | |||||||
\(308\) | 4.00000 | 0.227921 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | −4.74456 | −0.269473 | ||||||||
\(311\) | 3.48913 | 0.197850 | 0.0989251 | − | 0.995095i | \(-0.468460\pi\) | ||||
0.0989251 | + | 0.995095i | \(0.468460\pi\) | |||||||
\(312\) | 6.74456 | 0.381836 | ||||||||
\(313\) | 5.25544 | 0.297055 | 0.148527 | − | 0.988908i | \(-0.452547\pi\) | ||||
0.148527 | + | 0.988908i | \(0.452547\pi\) | |||||||
\(314\) | 2.00000 | 0.112867 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 16.9783 | 0.953594 | 0.476797 | − | 0.879014i | \(-0.341798\pi\) | ||||
0.476797 | + | 0.879014i | \(0.341798\pi\) | |||||||
\(318\) | 12.7446 | 0.714680 | ||||||||
\(319\) | −18.9783 | −1.06258 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 6.74456 | 0.376445 | ||||||||
\(322\) | −1.00000 | −0.0557278 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 6.74456 | 0.374121 | ||||||||
\(326\) | 10.7446 | 0.595086 | ||||||||
\(327\) | −12.7446 | −0.704776 | ||||||||
\(328\) | 8.74456 | 0.482838 | ||||||||
\(329\) | 12.7446 | 0.702630 | ||||||||
\(330\) | −4.00000 | −0.220193 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 16.7446 | 0.918977 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | 16.7446 | 0.916222 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 10.0000 | 0.544735 | 0.272367 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272367 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(338\) | −32.4891 | −1.76718 | ||||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9783 | −1.02773 | ||||||||
\(342\) | −4.74456 | −0.256557 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | −6.74456 | −0.362590 | ||||||||
\(347\) | −22.9783 | −1.23354 | −0.616769 | − | 0.787145i | \(-0.711559\pi\) | ||||
−0.616769 | + | 0.787145i | \(0.711559\pi\) | |||||||
\(348\) | −4.74456 | −0.254335 | ||||||||
\(349\) | 9.25544 | 0.495432 | 0.247716 | − | 0.968833i | \(-0.420320\pi\) | ||||
0.247716 | + | 0.968833i | \(0.420320\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −6.74456 | −0.359998 | ||||||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | 19.4891 | 1.03730 | 0.518651 | − | 0.854986i | \(-0.326435\pi\) | ||||
0.518651 | + | 0.854986i | \(0.326435\pi\) | |||||||
\(354\) | 4.00000 | 0.212598 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | −14.7446 | −0.781460 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.7446 | −0.567868 | ||||||||
\(359\) | −26.9783 | −1.42386 | −0.711929 | − | 0.702252i | \(-0.752178\pi\) | ||||
−0.711929 | + | 0.702252i | \(0.752178\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 3.51087 | 0.184783 | ||||||||
\(362\) | 14.0000 | 0.735824 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | −6.74456 | −0.353511 | ||||||||
\(365\) | −0.744563 | −0.0389722 | ||||||||
\(366\) | −11.4891 | −0.600546 | ||||||||
\(367\) | 6.51087 | 0.339865 | 0.169932 | − | 0.985456i | \(-0.445645\pi\) | ||||
0.169932 | + | 0.985456i | \(0.445645\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −8.74456 | −0.455224 | ||||||||
\(370\) | −2.00000 | −0.103975 | ||||||||
\(371\) | −12.7446 | −0.661665 | ||||||||
\(372\) | −4.74456 | −0.245994 | ||||||||
\(373\) | 23.4891 | 1.21622 | 0.608110 | − | 0.793852i | \(-0.291928\pi\) | ||||
0.608110 | + | 0.793852i | \(0.291928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 12.7446 | 0.657251 | ||||||||
\(377\) | 32.0000 | 1.64808 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −6.74456 | −0.346445 | −0.173222 | − | 0.984883i | \(-0.555418\pi\) | ||||
−0.173222 | + | 0.984883i | \(0.555418\pi\) | |||||||
\(380\) | 4.74456 | 0.243391 | ||||||||
\(381\) | −8.00000 | −0.409852 | ||||||||
\(382\) | 16.0000 | 0.818631 | ||||||||
\(383\) | 38.7446 | 1.97975 | 0.989877 | − | 0.141926i | \(-0.0453294\pi\) | ||||
0.989877 | + | 0.141926i | \(0.0453294\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.25544 | 0.0637352 | ||||||||
\(389\) | 3.48913 | 0.176906 | 0.0884528 | − | 0.996080i | \(-0.471808\pi\) | ||||
0.0884528 | + | 0.996080i | \(0.471808\pi\) | |||||||
\(390\) | 6.74456 | 0.341524 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | −19.4891 | −0.981848 | ||||||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | −4.00000 | −0.201008 | ||||||||
\(397\) | 33.7228 | 1.69250 | 0.846250 | − | 0.532786i | \(-0.178855\pi\) | ||||
0.846250 | + | 0.532786i | \(0.178855\pi\) | |||||||
\(398\) | −24.2337 | −1.21473 | ||||||||
\(399\) | 4.74456 | 0.237525 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 36.9783 | 1.84661 | 0.923303 | − | 0.384073i | \(-0.125479\pi\) | ||||
0.923303 | + | 0.384073i | \(0.125479\pi\) | |||||||
\(402\) | 8.00000 | 0.399004 | ||||||||
\(403\) | 32.0000 | 1.59403 | ||||||||
\(404\) | 18.7446 | 0.932577 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 4.74456 | 0.235469 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.97825 | −0.443946 | −0.221973 | − | 0.975053i | \(-0.571250\pi\) | ||||
−0.221973 | + | 0.975053i | \(0.571250\pi\) | |||||||
\(410\) | 8.74456 | 0.431863 | ||||||||
\(411\) | −11.4891 | −0.566717 | ||||||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 16.7446 | 0.821958 | ||||||||
\(416\) | −6.74456 | −0.330679 | ||||||||
\(417\) | 13.4891 | 0.660565 | ||||||||
\(418\) | 18.9783 | 0.928257 | ||||||||
\(419\) | 26.2337 | 1.28160 | 0.640800 | − | 0.767708i | \(-0.278603\pi\) | ||||
0.640800 | + | 0.767708i | \(0.278603\pi\) | |||||||
\(420\) | 1.00000 | 0.0487950 | ||||||||
\(421\) | 15.2554 | 0.743505 | 0.371752 | − | 0.928332i | \(-0.378757\pi\) | ||||
0.371752 | + | 0.928332i | \(0.378757\pi\) | |||||||
\(422\) | −9.48913 | −0.461923 | ||||||||
\(423\) | −12.7446 | −0.619662 | ||||||||
\(424\) | −12.7446 | −0.618931 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 11.4891 | 0.555998 | ||||||||
\(428\) | −6.74456 | −0.326011 | ||||||||
\(429\) | 26.9783 | 1.30252 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.0000 | 1.54139 | 0.770693 | − | 0.637207i | \(-0.219910\pi\) | ||||
0.770693 | + | 0.637207i | \(0.219910\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 4.23369 | 0.203458 | 0.101729 | − | 0.994812i | \(-0.467563\pi\) | ||||
0.101729 | + | 0.994812i | \(0.467563\pi\) | |||||||
\(434\) | 4.74456 | 0.227746 | ||||||||
\(435\) | −4.74456 | −0.227484 | ||||||||
\(436\) | 12.7446 | 0.610354 | ||||||||
\(437\) | −4.74456 | −0.226963 | ||||||||
\(438\) | −0.744563 | −0.0355766 | ||||||||
\(439\) | 19.2554 | 0.919012 | 0.459506 | − | 0.888175i | \(-0.348026\pi\) | ||||
0.459506 | + | 0.888175i | \(0.348026\pi\) | |||||||
\(440\) | 4.00000 | 0.190693 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.0000 | −1.33032 | −0.665160 | − | 0.746701i | \(-0.731637\pi\) | ||||
−0.665160 | + | 0.746701i | \(0.731637\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | −14.7446 | −0.698959 | ||||||||
\(446\) | −19.4891 | −0.922837 | ||||||||
\(447\) | −7.48913 | −0.354223 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −28.9783 | −1.36757 | −0.683784 | − | 0.729684i | \(-0.739667\pi\) | ||||
−0.683784 | + | 0.729684i | \(0.739667\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 34.9783 | 1.64706 | ||||||||
\(452\) | 2.00000 | 0.0940721 | ||||||||
\(453\) | 9.48913 | 0.445838 | ||||||||
\(454\) | −4.74456 | −0.222673 | ||||||||
\(455\) | −6.74456 | −0.316190 | ||||||||
\(456\) | 4.74456 | 0.222185 | ||||||||
\(457\) | 27.4891 | 1.28589 | 0.642944 | − | 0.765914i | \(-0.277713\pi\) | ||||
0.642944 | + | 0.765914i | \(0.277713\pi\) | |||||||
\(458\) | −2.00000 | −0.0934539 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | 32.2337 | 1.50127 | 0.750636 | − | 0.660716i | \(-0.229747\pi\) | ||||
0.750636 | + | 0.660716i | \(0.229747\pi\) | |||||||
\(462\) | 4.00000 | 0.186097 | ||||||||
\(463\) | 36.4674 | 1.69478 | 0.847391 | − | 0.530969i | \(-0.178172\pi\) | ||||
0.847391 | + | 0.530969i | \(0.178172\pi\) | |||||||
\(464\) | 4.74456 | 0.220261 | ||||||||
\(465\) | −4.74456 | −0.220024 | ||||||||
\(466\) | 23.4891 | 1.08811 | ||||||||
\(467\) | 31.7228 | 1.46796 | 0.733978 | − | 0.679173i | \(-0.237661\pi\) | ||||
0.733978 | + | 0.679173i | \(0.237661\pi\) | |||||||
\(468\) | 6.74456 | 0.311768 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 12.7446 | 0.587863 | ||||||||
\(471\) | 2.00000 | 0.0921551 | ||||||||
\(472\) | −4.00000 | −0.184115 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −8.00000 | −0.367452 | ||||||||
\(475\) | 4.74456 | 0.217695 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.7446 | 0.583533 | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | −6.51087 | −0.297489 | −0.148745 | − | 0.988876i | \(-0.547523\pi\) | ||||
−0.148745 | + | 0.988876i | \(0.547523\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 13.4891 | 0.615051 | ||||||||
\(482\) | 13.4891 | 0.614413 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | 1.25544 | 0.0570065 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −14.9783 | −0.678729 | −0.339365 | − | 0.940655i | \(-0.610212\pi\) | ||||
−0.339365 | + | 0.940655i | \(0.610212\pi\) | |||||||
\(488\) | 11.4891 | 0.520088 | ||||||||
\(489\) | 10.7446 | 0.485886 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −13.7228 | −0.619302 | −0.309651 | − | 0.950850i | \(-0.600212\pi\) | ||||
−0.309651 | + | 0.950850i | \(0.600212\pi\) | |||||||
\(492\) | 8.74456 | 0.394235 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −32.0000 | −1.43975 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 4.74456 | 0.213037 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 16.7446 | 0.750342 | ||||||||
\(499\) | 36.4674 | 1.63250 | 0.816252 | − | 0.577696i | \(-0.196048\pi\) | ||||
0.816252 | + | 0.577696i | \(0.196048\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 16.7446 | 0.748092 | ||||||||
\(502\) | −18.2337 | −0.813809 | ||||||||
\(503\) | 25.7228 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 18.7446 | 0.834122 | ||||||||
\(506\) | −4.00000 | −0.177822 | ||||||||
\(507\) | −32.4891 | −1.44289 | ||||||||
\(508\) | 8.00000 | 0.354943 | ||||||||
\(509\) | −37.7228 | −1.67203 | −0.836017 | − | 0.548703i | \(-0.815122\pi\) | ||||
−0.836017 | + | 0.548703i | \(0.815122\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.744563 | 0.0329375 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.74456 | −0.209478 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 4.00000 | 0.176261 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 50.9783 | 2.24202 | ||||||||
\(518\) | 2.00000 | 0.0878750 | ||||||||
\(519\) | −6.74456 | −0.296053 | ||||||||
\(520\) | −6.74456 | −0.295769 | ||||||||
\(521\) | −20.2337 | −0.886454 | −0.443227 | − | 0.896409i | \(-0.646166\pi\) | ||||
−0.443227 | + | 0.896409i | \(0.646166\pi\) | |||||||
\(522\) | −4.74456 | −0.207664 | ||||||||
\(523\) | −10.2337 | −0.447488 | −0.223744 | − | 0.974648i | \(-0.571828\pi\) | ||||
−0.223744 | + | 0.974648i | \(0.571828\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 8.00000 | 0.348817 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −12.7446 | −0.553588 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | −4.74456 | −0.205703 | ||||||||
\(533\) | −58.9783 | −2.55463 | ||||||||
\(534\) | −14.7446 | −0.638060 | ||||||||
\(535\) | −6.74456 | −0.291593 | ||||||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | −10.7446 | −0.463662 | ||||||||
\(538\) | 26.7446 | 1.15304 | ||||||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 8.97825 | 0.386005 | 0.193003 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193003 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(542\) | −12.7446 | −0.547426 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.7446 | 0.545917 | ||||||||
\(546\) | −6.74456 | −0.288641 | ||||||||
\(547\) | −16.2337 | −0.694102 | −0.347051 | − | 0.937846i | \(-0.612817\pi\) | ||||
−0.347051 | + | 0.937846i | \(0.612817\pi\) | |||||||
\(548\) | 11.4891 | 0.490791 | ||||||||
\(549\) | −11.4891 | −0.490344 | ||||||||
\(550\) | 4.00000 | 0.170561 | ||||||||
\(551\) | 22.5109 | 0.958996 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | −32.7446 | −1.39118 | ||||||||
\(555\) | −2.00000 | −0.0848953 | ||||||||
\(556\) | −13.4891 | −0.572066 | ||||||||
\(557\) | −34.2337 | −1.45053 | −0.725264 | − | 0.688471i | \(-0.758282\pi\) | ||||
−0.725264 | + | 0.688471i | \(0.758282\pi\) | |||||||
\(558\) | −4.74456 | −0.200853 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.48913 | 0.147180 | ||||||||
\(563\) | −9.76631 | −0.411601 | −0.205800 | − | 0.978594i | \(-0.565980\pi\) | ||||
−0.205800 | + | 0.978594i | \(0.565980\pi\) | |||||||
\(564\) | 12.7446 | 0.536643 | ||||||||
\(565\) | 2.00000 | 0.0841406 | ||||||||
\(566\) | 7.25544 | 0.304969 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | −24.9783 | −1.04714 | −0.523571 | − | 0.851982i | \(-0.675401\pi\) | ||||
−0.523571 | + | 0.851982i | \(0.675401\pi\) | |||||||
\(570\) | 4.74456 | 0.198728 | ||||||||
\(571\) | 13.7228 | 0.574282 | 0.287141 | − | 0.957888i | \(-0.407295\pi\) | ||||
0.287141 | + | 0.957888i | \(0.407295\pi\) | |||||||
\(572\) | −26.9783 | −1.12802 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | −8.74456 | −0.364991 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 28.7446 | 1.19665 | 0.598326 | − | 0.801253i | \(-0.295833\pi\) | ||||
0.598326 | + | 0.801253i | \(0.295833\pi\) | |||||||
\(578\) | 17.0000 | 0.707107 | ||||||||
\(579\) | −14.0000 | −0.581820 | ||||||||
\(580\) | 4.74456 | 0.197007 | ||||||||
\(581\) | −16.7446 | −0.694682 | ||||||||
\(582\) | 1.25544 | 0.0520396 | ||||||||
\(583\) | −50.9783 | −2.11130 | ||||||||
\(584\) | 0.744563 | 0.0308102 | ||||||||
\(585\) | 6.74456 | 0.278853 | ||||||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | 29.4891 | 1.21715 | 0.608573 | − | 0.793498i | \(-0.291742\pi\) | ||||
0.608573 | + | 0.793498i | \(0.291742\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 22.5109 | 0.927544 | ||||||||
\(590\) | −4.00000 | −0.164677 | ||||||||
\(591\) | −19.4891 | −0.801675 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | 28.9783 | 1.18999 | 0.594997 | − | 0.803728i | \(-0.297153\pi\) | ||||
0.594997 | + | 0.803728i | \(0.297153\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.48913 | 0.306767 | ||||||||
\(597\) | −24.2337 | −0.991819 | ||||||||
\(598\) | 6.74456 | 0.275806 | ||||||||
\(599\) | −4.00000 | −0.163436 | −0.0817178 | − | 0.996656i | \(-0.526041\pi\) | ||||
−0.0817178 | + | 0.996656i | \(0.526041\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −42.4674 | −1.73228 | −0.866140 | − | 0.499801i | \(-0.833406\pi\) | ||||
−0.866140 | + | 0.499801i | \(0.833406\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | −9.48913 | −0.386107 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 18.7446 | 0.761446 | ||||||||
\(607\) | 47.4891 | 1.92752 | 0.963762 | − | 0.266763i | \(-0.0859542\pi\) | ||||
0.963762 | + | 0.266763i | \(0.0859542\pi\) | |||||||
\(608\) | −4.74456 | −0.192417 | ||||||||
\(609\) | 4.74456 | 0.192259 | ||||||||
\(610\) | 11.4891 | 0.465181 | ||||||||
\(611\) | −85.9565 | −3.47743 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.0000 | 0.888572 | 0.444286 | − | 0.895885i | \(-0.353457\pi\) | ||||
0.444286 | + | 0.895885i | \(0.353457\pi\) | |||||||
\(614\) | 18.9783 | 0.765900 | ||||||||
\(615\) | 8.74456 | 0.352615 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | −28.9783 | −1.16662 | −0.583310 | − | 0.812249i | \(-0.698243\pi\) | ||||
−0.583310 | + | 0.812249i | \(0.698243\pi\) | |||||||
\(618\) | 4.00000 | 0.160904 | ||||||||
\(619\) | 6.23369 | 0.250553 | 0.125277 | − | 0.992122i | \(-0.460018\pi\) | ||||
0.125277 | + | 0.992122i | \(0.460018\pi\) | |||||||
\(620\) | 4.74456 | 0.190546 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −3.48913 | −0.139901 | ||||||||
\(623\) | 14.7446 | 0.590728 | ||||||||
\(624\) | −6.74456 | −0.269999 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.25544 | −0.210050 | ||||||||
\(627\) | 18.9783 | 0.757918 | ||||||||
\(628\) | −2.00000 | −0.0798087 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.00000 | 0.0398410 | ||||||||
\(631\) | −18.9783 | −0.755512 | −0.377756 | − | 0.925905i | \(-0.623304\pi\) | ||||
−0.377756 | + | 0.925905i | \(0.623304\pi\) | |||||||
\(632\) | 8.00000 | 0.318223 | ||||||||
\(633\) | −9.48913 | −0.377159 | ||||||||
\(634\) | −16.9783 | −0.674292 | ||||||||
\(635\) | 8.00000 | 0.317470 | ||||||||
\(636\) | −12.7446 | −0.505355 | ||||||||
\(637\) | 6.74456 | 0.267229 | ||||||||
\(638\) | 18.9783 | 0.751356 | ||||||||
\(639\) | −8.00000 | −0.316475 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 12.5109 | 0.494150 | 0.247075 | − | 0.968996i | \(-0.420531\pi\) | ||||
0.247075 | + | 0.968996i | \(0.420531\pi\) | |||||||
\(642\) | −6.74456 | −0.266187 | ||||||||
\(643\) | −27.7228 | −1.09328 | −0.546641 | − | 0.837367i | \(-0.684094\pi\) | ||||
−0.546641 | + | 0.837367i | \(0.684094\pi\) | |||||||
\(644\) | 1.00000 | 0.0394055 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.744563 | −0.0292718 | −0.0146359 | − | 0.999893i | \(-0.504659\pi\) | ||||
−0.0146359 | + | 0.999893i | \(0.504659\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −16.0000 | −0.628055 | ||||||||
\(650\) | −6.74456 | −0.264544 | ||||||||
\(651\) | 4.74456 | 0.185954 | ||||||||
\(652\) | −10.7446 | −0.420790 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 12.7446 | 0.498352 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | −8.74456 | −0.341418 | ||||||||
\(657\) | −0.744563 | −0.0290482 | ||||||||
\(658\) | −12.7446 | −0.496835 | ||||||||
\(659\) | 34.9783 | 1.36256 | 0.681280 | − | 0.732023i | \(-0.261424\pi\) | ||||
0.681280 | + | 0.732023i | \(0.261424\pi\) | |||||||
\(660\) | 4.00000 | 0.155700 | ||||||||
\(661\) | 31.4891 | 1.22479 | 0.612393 | − | 0.790554i | \(-0.290207\pi\) | ||||
0.612393 | + | 0.790554i | \(0.290207\pi\) | |||||||
\(662\) | 12.0000 | 0.466393 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.7446 | −0.649815 | ||||||||
\(665\) | −4.74456 | −0.183986 | ||||||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | −4.74456 | −0.183710 | ||||||||
\(668\) | −16.7446 | −0.647867 | ||||||||
\(669\) | −19.4891 | −0.753493 | ||||||||
\(670\) | −8.00000 | −0.309067 | ||||||||
\(671\) | 45.9565 | 1.77413 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −4.51087 | −0.173881 | −0.0869407 | − | 0.996213i | \(-0.527709\pi\) | ||||
−0.0869407 | + | 0.996213i | \(0.527709\pi\) | |||||||
\(674\) | −10.0000 | −0.385186 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 32.4891 | 1.24958 | ||||||||
\(677\) | −7.48913 | −0.287830 | −0.143915 | − | 0.989590i | \(-0.545969\pi\) | ||||
−0.143915 | + | 0.989590i | \(0.545969\pi\) | |||||||
\(678\) | 2.00000 | 0.0768095 | ||||||||
\(679\) | −1.25544 | −0.0481793 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.74456 | −0.181812 | ||||||||
\(682\) | 18.9783 | 0.726715 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 4.74456 | 0.181413 | ||||||||
\(685\) | 11.4891 | 0.438977 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −2.00000 | −0.0763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 85.9565 | 3.27468 | ||||||||
\(690\) | −1.00000 | −0.0380693 | ||||||||
\(691\) | −32.4674 | −1.23512 | −0.617559 | − | 0.786525i | \(-0.711878\pi\) | ||||
−0.617559 | + | 0.786525i | \(0.711878\pi\) | |||||||
\(692\) | 6.74456 | 0.256390 | ||||||||
\(693\) | 4.00000 | 0.151947 | ||||||||
\(694\) | 22.9783 | 0.872242 | ||||||||
\(695\) | −13.4891 | −0.511672 | ||||||||
\(696\) | 4.74456 | 0.179842 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −9.25544 | −0.350323 | ||||||||
\(699\) | 23.4891 | 0.888440 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −40.9783 | −1.54773 | −0.773864 | − | 0.633352i | \(-0.781678\pi\) | ||||
−0.773864 | + | 0.633352i | \(0.781678\pi\) | |||||||
\(702\) | 6.74456 | 0.254557 | ||||||||
\(703\) | 9.48913 | 0.357889 | ||||||||
\(704\) | −4.00000 | −0.150756 | ||||||||
\(705\) | 12.7446 | 0.479988 | ||||||||
\(706\) | −19.4891 | −0.733483 | ||||||||
\(707\) | −18.7446 | −0.704962 | ||||||||
\(708\) | −4.00000 | −0.150329 | ||||||||
\(709\) | −17.7663 | −0.667228 | −0.333614 | − | 0.942710i | \(-0.608268\pi\) | ||||
−0.333614 | + | 0.942710i | \(0.608268\pi\) | |||||||
\(710\) | 8.00000 | 0.300235 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 14.7446 | 0.552576 | ||||||||
\(713\) | −4.74456 | −0.177685 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.9783 | −1.00893 | ||||||||
\(716\) | 10.7446 | 0.401543 | ||||||||
\(717\) | −8.00000 | −0.298765 | ||||||||
\(718\) | 26.9783 | 1.00682 | ||||||||
\(719\) | −14.0000 | −0.522112 | −0.261056 | − | 0.965324i | \(-0.584071\pi\) | ||||
−0.261056 | + | 0.965324i | \(0.584071\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | −3.51087 | −0.130661 | ||||||||
\(723\) | 13.4891 | 0.501666 | ||||||||
\(724\) | −14.0000 | −0.520306 | ||||||||
\(725\) | 4.74456 | 0.176209 | ||||||||
\(726\) | 5.00000 | 0.185567 | ||||||||
\(727\) | 44.0000 | 1.63187 | 0.815935 | − | 0.578144i | \(-0.196223\pi\) | ||||
0.815935 | + | 0.578144i | \(0.196223\pi\) | |||||||
\(728\) | 6.74456 | 0.249970 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.744563 | 0.0275575 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 11.4891 | 0.424650 | ||||||||
\(733\) | −15.4891 | −0.572104 | −0.286052 | − | 0.958214i | \(-0.592343\pi\) | ||||
−0.286052 | + | 0.958214i | \(0.592343\pi\) | |||||||
\(734\) | −6.51087 | −0.240321 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −32.0000 | −1.17874 | ||||||||
\(738\) | 8.74456 | 0.321892 | ||||||||
\(739\) | 36.4674 | 1.34147 | 0.670737 | − | 0.741695i | \(-0.265978\pi\) | ||||
0.670737 | + | 0.741695i | \(0.265978\pi\) | |||||||
\(740\) | 2.00000 | 0.0735215 | ||||||||
\(741\) | −32.0000 | −1.17555 | ||||||||
\(742\) | 12.7446 | 0.467868 | ||||||||
\(743\) | 32.0000 | 1.17397 | 0.586983 | − | 0.809599i | \(-0.300316\pi\) | ||||
0.586983 | + | 0.809599i | \(0.300316\pi\) | |||||||
\(744\) | 4.74456 | 0.173944 | ||||||||
\(745\) | 7.48913 | 0.274380 | ||||||||
\(746\) | −23.4891 | −0.859998 | ||||||||
\(747\) | 16.7446 | 0.612652 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.74456 | 0.246441 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −10.5109 | −0.383547 | −0.191774 | − | 0.981439i | \(-0.561424\pi\) | ||||
−0.191774 | + | 0.981439i | \(0.561424\pi\) | |||||||
\(752\) | −12.7446 | −0.464746 | ||||||||
\(753\) | −18.2337 | −0.664473 | ||||||||
\(754\) | −32.0000 | −1.16537 | ||||||||
\(755\) | −9.48913 | −0.345345 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | −7.48913 | −0.272197 | −0.136098 | − | 0.990695i | \(-0.543456\pi\) | ||||
−0.136098 | + | 0.990695i | \(0.543456\pi\) | |||||||
\(758\) | 6.74456 | 0.244974 | ||||||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | −4.74456 | −0.172103 | ||||||||
\(761\) | 19.7228 | 0.714951 | 0.357476 | − | 0.933922i | \(-0.383637\pi\) | ||||
0.357476 | + | 0.933922i | \(0.383637\pi\) | |||||||
\(762\) | 8.00000 | 0.289809 | ||||||||
\(763\) | −12.7446 | −0.461384 | ||||||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.7446 | −1.39990 | ||||||||
\(767\) | 26.9783 | 0.974128 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 32.0000 | 1.15395 | 0.576975 | − | 0.816762i | \(-0.304233\pi\) | ||||
0.576975 | + | 0.816762i | \(0.304233\pi\) | |||||||
\(770\) | −4.00000 | −0.144150 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | −35.4891 | −1.27646 | −0.638228 | − | 0.769848i | \(-0.720332\pi\) | ||||
−0.638228 | + | 0.769848i | \(0.720332\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.74456 | 0.170430 | ||||||||
\(776\) | −1.25544 | −0.0450676 | ||||||||
\(777\) | 2.00000 | 0.0717496 | ||||||||
\(778\) | −3.48913 | −0.125091 | ||||||||
\(779\) | −41.4891 | −1.48650 | ||||||||
\(780\) | −6.74456 | −0.241494 | ||||||||
\(781\) | 32.0000 | 1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.74456 | −0.169557 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 4.00000 | 0.142675 | ||||||||
\(787\) | −11.7228 | −0.417873 | −0.208937 | − | 0.977929i | \(-0.567000\pi\) | ||||
−0.208937 | + | 0.977929i | \(0.567000\pi\) | |||||||
\(788\) | 19.4891 | 0.694271 | ||||||||
\(789\) | 8.00000 | 0.284808 | ||||||||
\(790\) | 8.00000 | 0.284627 | ||||||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 4.00000 | 0.142134 | ||||||||
\(793\) | −77.4891 | −2.75172 | ||||||||
\(794\) | −33.7228 | −1.19678 | ||||||||
\(795\) | −12.7446 | −0.452003 | ||||||||
\(796\) | 24.2337 | 0.858940 | ||||||||
\(797\) | 52.9783 | 1.87659 | 0.938293 | − | 0.345841i | \(-0.112407\pi\) | ||||
0.938293 | + | 0.345841i | \(0.112407\pi\) | |||||||
\(798\) | −4.74456 | −0.167956 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −14.7446 | −0.520974 | ||||||||
\(802\) | −36.9783 | −1.30575 | ||||||||
\(803\) | 2.97825 | 0.105100 | ||||||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 1.00000 | 0.0352454 | ||||||||
\(806\) | −32.0000 | −1.12715 | ||||||||
\(807\) | 26.7446 | 0.941453 | ||||||||
\(808\) | −18.7446 | −0.659431 | ||||||||
\(809\) | −52.9783 | −1.86262 | −0.931308 | − | 0.364233i | \(-0.881331\pi\) | ||||
−0.931308 | + | 0.364233i | \(0.881331\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −46.9783 | −1.64963 | −0.824815 | − | 0.565403i | \(-0.808721\pi\) | ||||
−0.824815 | + | 0.565403i | \(0.808721\pi\) | |||||||
\(812\) | −4.74456 | −0.166502 | ||||||||
\(813\) | −12.7446 | −0.446971 | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | −10.7446 | −0.376366 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 8.97825 | 0.313917 | ||||||||
\(819\) | −6.74456 | −0.235674 | ||||||||
\(820\) | −8.74456 | −0.305373 | ||||||||
\(821\) | 49.2119 | 1.71751 | 0.858754 | − | 0.512388i | \(-0.171239\pi\) | ||||
0.858754 | + | 0.512388i | \(0.171239\pi\) | |||||||
\(822\) | 11.4891 | 0.400729 | ||||||||
\(823\) | −45.9565 | −1.60194 | −0.800971 | − | 0.598703i | \(-0.795683\pi\) | ||||
−0.800971 | + | 0.598703i | \(0.795683\pi\) | |||||||
\(824\) | −4.00000 | −0.139347 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 4.00000 | 0.139178 | ||||||||
\(827\) | 25.7228 | 0.894470 | 0.447235 | − | 0.894417i | \(-0.352409\pi\) | ||||
0.447235 | + | 0.894417i | \(0.352409\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −45.7228 | −1.58802 | −0.794009 | − | 0.607905i | \(-0.792010\pi\) | ||||
−0.794009 | + | 0.607905i | \(0.792010\pi\) | |||||||
\(830\) | −16.7446 | −0.581212 | ||||||||
\(831\) | −32.7446 | −1.13590 | ||||||||
\(832\) | 6.74456 | 0.233826 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13.4891 | −0.467090 | ||||||||
\(835\) | −16.7446 | −0.579469 | ||||||||
\(836\) | −18.9783 | −0.656377 | ||||||||
\(837\) | −4.74456 | −0.163996 | ||||||||
\(838\) | −26.2337 | −0.906228 | ||||||||
\(839\) | 18.5109 | 0.639066 | 0.319533 | − | 0.947575i | \(-0.396474\pi\) | ||||
0.319533 | + | 0.947575i | \(0.396474\pi\) | |||||||
\(840\) | −1.00000 | −0.0345033 | ||||||||
\(841\) | −6.48913 | −0.223763 | ||||||||
\(842\) | −15.2554 | −0.525737 | ||||||||
\(843\) | 3.48913 | 0.120172 | ||||||||
\(844\) | 9.48913 | 0.326629 | ||||||||
\(845\) | 32.4891 | 1.11766 | ||||||||
\(846\) | 12.7446 | 0.438167 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | 12.7446 | 0.437650 | ||||||||
\(849\) | 7.25544 | 0.249006 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | −0.0685591 | ||||||||
\(852\) | 8.00000 | 0.274075 | ||||||||
\(853\) | −36.2337 | −1.24062 | −0.620309 | − | 0.784358i | \(-0.712993\pi\) | ||||
−0.620309 | + | 0.784358i | \(0.712993\pi\) | |||||||
\(854\) | −11.4891 | −0.393150 | ||||||||
\(855\) | 4.74456 | 0.162261 | ||||||||
\(856\) | 6.74456 | 0.230524 | ||||||||
\(857\) | −52.9783 | −1.80970 | −0.904851 | − | 0.425728i | \(-0.860018\pi\) | ||||
−0.904851 | + | 0.425728i | \(0.860018\pi\) | |||||||
\(858\) | −26.9783 | −0.921022 | ||||||||
\(859\) | 48.4674 | 1.65369 | 0.826843 | − | 0.562433i | \(-0.190135\pi\) | ||||
0.826843 | + | 0.562433i | \(0.190135\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.74456 | −0.298014 | ||||||||
\(862\) | −32.0000 | −1.08992 | ||||||||
\(863\) | −30.5109 | −1.03860 | −0.519301 | − | 0.854591i | \(-0.673808\pi\) | ||||
−0.519301 | + | 0.854591i | \(0.673808\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 6.74456 | 0.229322 | ||||||||
\(866\) | −4.23369 | −0.143867 | ||||||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | −4.74456 | −0.161041 | ||||||||
\(869\) | 32.0000 | 1.08553 | ||||||||
\(870\) | 4.74456 | 0.160856 | ||||||||
\(871\) | 53.9565 | 1.82825 | ||||||||
\(872\) | −12.7446 | −0.431585 | ||||||||
\(873\) | 1.25544 | 0.0424901 | ||||||||
\(874\) | 4.74456 | 0.160487 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0.744563 | 0.0251564 | ||||||||
\(877\) | 4.74456 | 0.160212 | 0.0801062 | − | 0.996786i | \(-0.474474\pi\) | ||||
0.0801062 | + | 0.996786i | \(0.474474\pi\) | |||||||
\(878\) | −19.2554 | −0.649840 | ||||||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | −4.00000 | −0.134840 | ||||||||
\(881\) | 26.7446 | 0.901047 | 0.450524 | − | 0.892765i | \(-0.351237\pi\) | ||||
0.450524 | + | 0.892765i | \(0.351237\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −42.7446 | −1.43847 | −0.719235 | − | 0.694767i | \(-0.755507\pi\) | ||||
−0.719235 | + | 0.694767i | \(0.755507\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.00000 | −0.134459 | ||||||||
\(886\) | 28.0000 | 0.940678 | ||||||||
\(887\) | −14.2337 | −0.477920 | −0.238960 | − | 0.971029i | \(-0.576807\pi\) | ||||
−0.238960 | + | 0.971029i | \(0.576807\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 14.7446 | 0.494239 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 19.4891 | 0.652544 | ||||||||
\(893\) | −60.4674 | −2.02346 | ||||||||
\(894\) | 7.48913 | 0.250474 | ||||||||
\(895\) | 10.7446 | 0.359151 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 6.74456 | 0.225194 | ||||||||
\(898\) | 28.9783 | 0.967017 | ||||||||
\(899\) | 22.5109 | 0.750780 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −34.9783 | −1.16465 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.00000 | −0.0665190 | ||||||||
\(905\) | −14.0000 | −0.465376 | ||||||||
\(906\) | −9.48913 | −0.315255 | ||||||||
\(907\) | 33.4891 | 1.11199 | 0.555994 | − | 0.831186i | \(-0.312338\pi\) | ||||
0.555994 | + | 0.831186i | \(0.312338\pi\) | |||||||
\(908\) | 4.74456 | 0.157454 | ||||||||
\(909\) | 18.7446 | 0.621718 | ||||||||
\(910\) | 6.74456 | 0.223580 | ||||||||
\(911\) | 10.9783 | 0.363726 | 0.181863 | − | 0.983324i | \(-0.441787\pi\) | ||||
0.181863 | + | 0.983324i | \(0.441787\pi\) | |||||||
\(912\) | −4.74456 | −0.157108 | ||||||||
\(913\) | −66.9783 | −2.21666 | ||||||||
\(914\) | −27.4891 | −0.909259 | ||||||||
\(915\) | 11.4891 | 0.379819 | ||||||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.4891 | −0.708861 | −0.354430 | − | 0.935082i | \(-0.615325\pi\) | ||||
−0.354430 | + | 0.935082i | \(0.615325\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | 18.9783 | 0.625355 | ||||||||
\(922\) | −32.2337 | −1.06156 | ||||||||
\(923\) | −53.9565 | −1.77600 | ||||||||
\(924\) | −4.00000 | −0.131590 | ||||||||
\(925\) | 2.00000 | 0.0657596 | ||||||||
\(926\) | −36.4674 | −1.19839 | ||||||||
\(927\) | 4.00000 | 0.131377 | ||||||||
\(928\) | −4.74456 | −0.155748 | ||||||||
\(929\) | −3.25544 | −0.106807 | −0.0534037 | − | 0.998573i | \(-0.517007\pi\) | ||||
−0.0534037 | + | 0.998573i | \(0.517007\pi\) | |||||||
\(930\) | 4.74456 | 0.155580 | ||||||||
\(931\) | 4.74456 | 0.155497 | ||||||||
\(932\) | −23.4891 | −0.769412 | ||||||||
\(933\) | −3.48913 | −0.114229 | ||||||||
\(934\) | −31.7228 | −1.03800 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.74456 | −0.220453 | ||||||||
\(937\) | −2.74456 | −0.0896610 | −0.0448305 | − | 0.998995i | \(-0.514275\pi\) | ||||
−0.0448305 | + | 0.998995i | \(0.514275\pi\) | |||||||
\(938\) | 8.00000 | 0.261209 | ||||||||
\(939\) | −5.25544 | −0.171505 | ||||||||
\(940\) | −12.7446 | −0.415682 | ||||||||
\(941\) | −15.4891 | −0.504931 | −0.252466 | − | 0.967606i | \(-0.581241\pi\) | ||||
−0.252466 | + | 0.967606i | \(0.581241\pi\) | |||||||
\(942\) | −2.00000 | −0.0651635 | ||||||||
\(943\) | 8.74456 | 0.284762 | ||||||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.48913 | 0.308355 | 0.154178 | − | 0.988043i | \(-0.450727\pi\) | ||||
0.154178 | + | 0.988043i | \(0.450727\pi\) | |||||||
\(948\) | 8.00000 | 0.259828 | ||||||||
\(949\) | −5.02175 | −0.163013 | ||||||||
\(950\) | −4.74456 | −0.153934 | ||||||||
\(951\) | −16.9783 | −0.550557 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.4891 | −0.890460 | −0.445230 | − | 0.895416i | \(-0.646878\pi\) | ||||
−0.445230 | + | 0.895416i | \(0.646878\pi\) | |||||||
\(954\) | −12.7446 | −0.412620 | ||||||||
\(955\) | −16.0000 | −0.517748 | ||||||||
\(956\) | 8.00000 | 0.258738 | ||||||||
\(957\) | 18.9783 | 0.613480 | ||||||||
\(958\) | 6.51087 | 0.210357 | ||||||||
\(959\) | −11.4891 | −0.371003 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −8.48913 | −0.273843 | ||||||||
\(962\) | −13.4891 | −0.434907 | ||||||||
\(963\) | −6.74456 | −0.217340 | ||||||||
\(964\) | −13.4891 | −0.434455 | ||||||||
\(965\) | 14.0000 | 0.450676 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | −9.02175 | −0.290120 | −0.145060 | − | 0.989423i | \(-0.546338\pi\) | ||||
−0.145060 | + | 0.989423i | \(0.546338\pi\) | |||||||
\(968\) | −5.00000 | −0.160706 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.25544 | −0.0403097 | ||||||||
\(971\) | −21.7663 | −0.698514 | −0.349257 | − | 0.937027i | \(-0.613566\pi\) | ||||
−0.349257 | + | 0.937027i | \(0.613566\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 13.4891 | 0.432442 | ||||||||
\(974\) | 14.9783 | 0.479934 | ||||||||
\(975\) | −6.74456 | −0.215999 | ||||||||
\(976\) | −11.4891 | −0.367758 | ||||||||
\(977\) | −7.48913 | −0.239598 | −0.119799 | − | 0.992798i | \(-0.538225\pi\) | ||||
−0.119799 | + | 0.992798i | \(0.538225\pi\) | |||||||
\(978\) | −10.7446 | −0.343573 | ||||||||
\(979\) | 58.9783 | 1.88495 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 12.7446 | 0.406903 | ||||||||
\(982\) | 13.7228 | 0.437913 | ||||||||
\(983\) | −31.2119 | −0.995506 | −0.497753 | − | 0.867319i | \(-0.665841\pi\) | ||||
−0.497753 | + | 0.867319i | \(0.665841\pi\) | |||||||
\(984\) | −8.74456 | −0.278766 | ||||||||
\(985\) | 19.4891 | 0.620975 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.7446 | −0.405664 | ||||||||
\(988\) | 32.0000 | 1.01806 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 4.00000 | 0.127128 | ||||||||
\(991\) | 20.4674 | 0.650168 | 0.325084 | − | 0.945685i | \(-0.394607\pi\) | ||||
0.325084 | + | 0.945685i | \(0.394607\pi\) | |||||||
\(992\) | −4.74456 | −0.150640 | ||||||||
\(993\) | 12.0000 | 0.380808 | ||||||||
\(994\) | −8.00000 | −0.253745 | ||||||||
\(995\) | 24.2337 | 0.768260 | ||||||||
\(996\) | −16.7446 | −0.530572 | ||||||||
\(997\) | −9.72281 | −0.307925 | −0.153962 | − | 0.988077i | \(-0.549203\pi\) | ||||
−0.153962 | + | 0.988077i | \(0.549203\pi\) | |||||||
\(998\) | −36.4674 | −1.15435 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 4830.2.a.bm.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4830.2.a.bm.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |