Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.41421 | 0.392232 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.41421 | −0.342997 | −0.171499 | − | 0.985184i | \(-0.554861\pi\) | ||||
−0.171499 | + | 0.985184i | \(0.554861\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.41421 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 1.41421 | 0.277350 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.757359 | −0.140638 | −0.0703190 | − | 0.997525i | \(-0.522402\pi\) | ||||
−0.0703190 | + | 0.997525i | \(0.522402\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 4.65685 | 0.836396 | 0.418198 | − | 0.908356i | \(-0.362662\pi\) | ||||
0.418198 | + | 0.908356i | \(0.362662\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.00000 | −0.522233 | ||||||||
\(34\) | −1.41421 | −0.242536 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.07107 | −1.49127 | −0.745637 | − | 0.666352i | \(-0.767855\pi\) | ||||
−0.745637 | + | 0.666352i | \(0.767855\pi\) | |||||||
\(38\) | −3.41421 | −0.553859 | ||||||||
\(39\) | 1.41421 | 0.226455 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 1.75736 | 0.274453 | 0.137227 | − | 0.990540i | \(-0.456181\pi\) | ||||
0.137227 | + | 0.990540i | \(0.456181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.65685 | −1.16766 | −0.583830 | − | 0.811876i | \(-0.698446\pi\) | ||||
−0.583830 | + | 0.811876i | \(0.698446\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −9.31371 | −1.35854 | −0.679272 | − | 0.733887i | \(-0.737704\pi\) | ||||
−0.679272 | + | 0.733887i | \(0.737704\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | −1.41421 | −0.198030 | ||||||||
\(52\) | 1.41421 | 0.196116 | ||||||||
\(53\) | −2.17157 | −0.298288 | −0.149144 | − | 0.988815i | \(-0.547652\pi\) | ||||
−0.149144 | + | 0.988815i | \(0.547652\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.41421 | −0.452224 | ||||||||
\(58\) | −0.757359 | −0.0994461 | ||||||||
\(59\) | −0.757359 | −0.0985998 | −0.0492999 | − | 0.998784i | \(-0.515699\pi\) | ||||
−0.0492999 | + | 0.998784i | \(0.515699\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 4.65685 | 0.591421 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.41421 | −0.175412 | ||||||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | −4.34315 | −0.530600 | −0.265300 | − | 0.964166i | \(-0.585471\pi\) | ||||
−0.265300 | + | 0.964166i | \(0.585471\pi\) | |||||||
\(68\) | −1.41421 | −0.171499 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.89949 | 0.700141 | 0.350071 | − | 0.936723i | \(-0.386158\pi\) | ||||
0.350071 | + | 0.936723i | \(0.386158\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 5.65685 | 0.662085 | 0.331042 | − | 0.943616i | \(-0.392600\pi\) | ||||
0.331042 | + | 0.943616i | \(0.392600\pi\) | |||||||
\(74\) | −9.07107 | −1.05449 | ||||||||
\(75\) | −4.00000 | −0.461880 | ||||||||
\(76\) | −3.41421 | −0.391637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.41421 | 0.160128 | ||||||||
\(79\) | −0.414214 | −0.0466027 | −0.0233013 | − | 0.999728i | \(-0.507418\pi\) | ||||
−0.0233013 | + | 0.999728i | \(0.507418\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.75736 | 0.194068 | ||||||||
\(83\) | 12.3137 | 1.35161 | 0.675803 | − | 0.737083i | \(-0.263797\pi\) | ||||
0.675803 | + | 0.737083i | \(0.263797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41421 | 0.153393 | ||||||||
\(86\) | −7.65685 | −0.825660 | ||||||||
\(87\) | −0.757359 | −0.0811974 | ||||||||
\(88\) | −3.00000 | −0.319801 | ||||||||
\(89\) | 14.7279 | 1.56116 | 0.780578 | − | 0.625058i | \(-0.214925\pi\) | ||||
0.780578 | + | 0.625058i | \(0.214925\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 4.65685 | 0.482893 | ||||||||
\(94\) | −9.31371 | −0.960636 | ||||||||
\(95\) | 3.41421 | 0.350291 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −3.58579 | −0.364081 | −0.182041 | − | 0.983291i | \(-0.558270\pi\) | ||||
−0.182041 | + | 0.983291i | \(0.558270\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | −4.48528 | −0.446302 | −0.223151 | − | 0.974784i | \(-0.571634\pi\) | ||||
−0.223151 | + | 0.974784i | \(0.571634\pi\) | |||||||
\(102\) | −1.41421 | −0.140028 | ||||||||
\(103\) | −13.6569 | −1.34565 | −0.672825 | − | 0.739802i | \(-0.734919\pi\) | ||||
−0.672825 | + | 0.739802i | \(0.734919\pi\) | |||||||
\(104\) | 1.41421 | 0.138675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.17157 | −0.210922 | ||||||||
\(107\) | −7.48528 | −0.723629 | −0.361815 | − | 0.932250i | \(-0.617843\pi\) | ||||
−0.361815 | + | 0.932250i | \(0.617843\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 5.31371 | 0.508961 | 0.254480 | − | 0.967078i | \(-0.418096\pi\) | ||||
0.254480 | + | 0.967078i | \(0.418096\pi\) | |||||||
\(110\) | 3.00000 | 0.286039 | ||||||||
\(111\) | −9.07107 | −0.860988 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.4142 | −1.63819 | −0.819096 | − | 0.573657i | \(-0.805524\pi\) | ||||
−0.819096 | + | 0.573657i | \(0.805524\pi\) | |||||||
\(114\) | −3.41421 | −0.319770 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | −0.757359 | −0.0703190 | ||||||||
\(117\) | 1.41421 | 0.130744 | ||||||||
\(118\) | −0.757359 | −0.0697206 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | 1.75736 | 0.158456 | ||||||||
\(124\) | 4.65685 | 0.418198 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.82843 | −0.517189 | −0.258595 | − | 0.965986i | \(-0.583259\pi\) | ||||
−0.258595 | + | 0.965986i | \(0.583259\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.65685 | −0.674148 | ||||||||
\(130\) | −1.41421 | −0.124035 | ||||||||
\(131\) | −1.24264 | −0.108570 | −0.0542850 | − | 0.998525i | \(-0.517288\pi\) | ||||
−0.0542850 | + | 0.998525i | \(0.517288\pi\) | |||||||
\(132\) | −3.00000 | −0.261116 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.34315 | −0.375191 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −1.41421 | −0.121268 | ||||||||
\(137\) | −18.9706 | −1.62076 | −0.810382 | − | 0.585901i | \(-0.800741\pi\) | ||||
−0.810382 | + | 0.585901i | \(0.800741\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −5.31371 | −0.450703 | −0.225351 | − | 0.974278i | \(-0.572353\pi\) | ||||
−0.225351 | + | 0.974278i | \(0.572353\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.31371 | −0.784356 | ||||||||
\(142\) | 5.89949 | 0.495075 | ||||||||
\(143\) | −4.24264 | −0.354787 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.757359 | 0.0628953 | ||||||||
\(146\) | 5.65685 | 0.468165 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.07107 | −0.745637 | ||||||||
\(149\) | 13.6569 | 1.11881 | 0.559407 | − | 0.828893i | \(-0.311029\pi\) | ||||
0.559407 | + | 0.828893i | \(0.311029\pi\) | |||||||
\(150\) | −4.00000 | −0.326599 | ||||||||
\(151\) | −1.34315 | −0.109304 | −0.0546518 | − | 0.998505i | \(-0.517405\pi\) | ||||
−0.0546518 | + | 0.998505i | \(0.517405\pi\) | |||||||
\(152\) | −3.41421 | −0.276929 | ||||||||
\(153\) | −1.41421 | −0.114332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.65685 | −0.374048 | ||||||||
\(156\) | 1.41421 | 0.113228 | ||||||||
\(157\) | −3.89949 | −0.311214 | −0.155607 | − | 0.987819i | \(-0.549733\pi\) | ||||
−0.155607 | + | 0.987819i | \(0.549733\pi\) | |||||||
\(158\) | −0.414214 | −0.0329531 | ||||||||
\(159\) | −2.17157 | −0.172217 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −1.41421 | −0.110770 | −0.0553849 | − | 0.998465i | \(-0.517639\pi\) | ||||
−0.0553849 | + | 0.998465i | \(0.517639\pi\) | |||||||
\(164\) | 1.75736 | 0.137227 | ||||||||
\(165\) | 3.00000 | 0.233550 | ||||||||
\(166\) | 12.3137 | 0.955729 | ||||||||
\(167\) | 18.4853 | 1.43043 | 0.715217 | − | 0.698902i | \(-0.246328\pi\) | ||||
0.715217 | + | 0.698902i | \(0.246328\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 1.41421 | 0.108465 | ||||||||
\(171\) | −3.41421 | −0.261091 | ||||||||
\(172\) | −7.65685 | −0.583830 | ||||||||
\(173\) | 4.82843 | 0.367099 | 0.183549 | − | 0.983011i | \(-0.441241\pi\) | ||||
0.183549 | + | 0.983011i | \(0.441241\pi\) | |||||||
\(174\) | −0.757359 | −0.0574153 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | −0.757359 | −0.0569266 | ||||||||
\(178\) | 14.7279 | 1.10390 | ||||||||
\(179\) | 16.0000 | 1.19590 | 0.597948 | − | 0.801535i | \(-0.295983\pi\) | ||||
0.597948 | + | 0.801535i | \(0.295983\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −12.4853 | −0.928024 | −0.464012 | − | 0.885829i | \(-0.653590\pi\) | ||||
−0.464012 | + | 0.885829i | \(0.653590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 9.07107 | 0.666918 | ||||||||
\(186\) | 4.65685 | 0.341457 | ||||||||
\(187\) | 4.24264 | 0.310253 | ||||||||
\(188\) | −9.31371 | −0.679272 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.41421 | 0.247693 | ||||||||
\(191\) | 1.41421 | 0.102329 | 0.0511645 | − | 0.998690i | \(-0.483707\pi\) | ||||
0.0511645 | + | 0.998690i | \(0.483707\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −19.6274 | −1.41281 | −0.706406 | − | 0.707807i | \(-0.749685\pi\) | ||||
−0.706406 | + | 0.707807i | \(0.749685\pi\) | |||||||
\(194\) | −3.58579 | −0.257444 | ||||||||
\(195\) | −1.41421 | −0.101274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.17157 | −0.225965 | −0.112983 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112983 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(198\) | −3.00000 | −0.213201 | ||||||||
\(199\) | 5.31371 | 0.376679 | 0.188339 | − | 0.982104i | \(-0.439690\pi\) | ||||
0.188339 | + | 0.982104i | \(0.439690\pi\) | |||||||
\(200\) | −4.00000 | −0.282843 | ||||||||
\(201\) | −4.34315 | −0.306342 | ||||||||
\(202\) | −4.48528 | −0.315583 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.41421 | −0.0990148 | ||||||||
\(205\) | −1.75736 | −0.122739 | ||||||||
\(206\) | −13.6569 | −0.951518 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 1.41421 | 0.0980581 | ||||||||
\(209\) | 10.2426 | 0.708498 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.82843 | 0.332403 | 0.166201 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166201 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(212\) | −2.17157 | −0.149144 | ||||||||
\(213\) | 5.89949 | 0.404227 | ||||||||
\(214\) | −7.48528 | −0.511683 | ||||||||
\(215\) | 7.65685 | 0.522193 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.31371 | 0.359890 | ||||||||
\(219\) | 5.65685 | 0.382255 | ||||||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | −2.00000 | −0.134535 | ||||||||
\(222\) | −9.07107 | −0.608810 | ||||||||
\(223\) | −10.1716 | −0.681139 | −0.340569 | − | 0.940219i | \(-0.610620\pi\) | ||||
−0.340569 | + | 0.940219i | \(0.610620\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | −17.4142 | −1.15838 | ||||||||
\(227\) | −7.82843 | −0.519591 | −0.259795 | − | 0.965664i | \(-0.583655\pi\) | ||||
−0.259795 | + | 0.965664i | \(0.583655\pi\) | |||||||
\(228\) | −3.41421 | −0.226112 | ||||||||
\(229\) | 22.7279 | 1.50190 | 0.750952 | − | 0.660357i | \(-0.229595\pi\) | ||||
0.750952 | + | 0.660357i | \(0.229595\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.757359 | −0.0497231 | ||||||||
\(233\) | 15.2132 | 0.996650 | 0.498325 | − | 0.866990i | \(-0.333949\pi\) | ||||
0.498325 | + | 0.866990i | \(0.333949\pi\) | |||||||
\(234\) | 1.41421 | 0.0924500 | ||||||||
\(235\) | 9.31371 | 0.607559 | ||||||||
\(236\) | −0.757359 | −0.0492999 | ||||||||
\(237\) | −0.414214 | −0.0269061 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3137 | −1.50804 | −0.754019 | − | 0.656852i | \(-0.771887\pi\) | ||||
−0.754019 | + | 0.656852i | \(0.771887\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −9.92893 | −0.639579 | −0.319789 | − | 0.947489i | \(-0.603612\pi\) | ||||
−0.319789 | + | 0.947489i | \(0.603612\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.75736 | 0.112045 | ||||||||
\(247\) | −4.82843 | −0.307225 | ||||||||
\(248\) | 4.65685 | 0.295711 | ||||||||
\(249\) | 12.3137 | 0.780350 | ||||||||
\(250\) | 9.00000 | 0.569210 | ||||||||
\(251\) | 25.8284 | 1.63028 | 0.815138 | − | 0.579267i | \(-0.196661\pi\) | ||||
0.815138 | + | 0.579267i | \(0.196661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00000 | 0.188608 | ||||||||
\(254\) | −5.82843 | −0.365708 | ||||||||
\(255\) | 1.41421 | 0.0885615 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.41421 | −0.0882162 | −0.0441081 | − | 0.999027i | \(-0.514045\pi\) | ||||
−0.0441081 | + | 0.999027i | \(0.514045\pi\) | |||||||
\(258\) | −7.65685 | −0.476695 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.41421 | −0.0877058 | ||||||||
\(261\) | −0.757359 | −0.0468794 | ||||||||
\(262\) | −1.24264 | −0.0767706 | ||||||||
\(263\) | 10.9706 | 0.676474 | 0.338237 | − | 0.941061i | \(-0.390169\pi\) | ||||
0.338237 | + | 0.941061i | \(0.390169\pi\) | |||||||
\(264\) | −3.00000 | −0.184637 | ||||||||
\(265\) | 2.17157 | 0.133399 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.7279 | 0.901334 | ||||||||
\(268\) | −4.34315 | −0.265300 | ||||||||
\(269\) | 1.58579 | 0.0966871 | 0.0483436 | − | 0.998831i | \(-0.484606\pi\) | ||||
0.0483436 | + | 0.998831i | \(0.484606\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −7.00000 | −0.425220 | −0.212610 | − | 0.977137i | \(-0.568196\pi\) | ||||
−0.212610 | + | 0.977137i | \(0.568196\pi\) | |||||||
\(272\) | −1.41421 | −0.0857493 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.9706 | −1.14605 | ||||||||
\(275\) | 12.0000 | 0.723627 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −2.82843 | −0.169944 | −0.0849719 | − | 0.996383i | \(-0.527080\pi\) | ||||
−0.0849719 | + | 0.996383i | \(0.527080\pi\) | |||||||
\(278\) | −5.31371 | −0.318695 | ||||||||
\(279\) | 4.65685 | 0.278799 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.7279 | −1.59445 | −0.797227 | − | 0.603680i | \(-0.793701\pi\) | ||||
−0.797227 | + | 0.603680i | \(0.793701\pi\) | |||||||
\(282\) | −9.31371 | −0.554623 | ||||||||
\(283\) | −24.1421 | −1.43510 | −0.717551 | − | 0.696506i | \(-0.754737\pi\) | ||||
−0.717551 | + | 0.696506i | \(0.754737\pi\) | |||||||
\(284\) | 5.89949 | 0.350071 | ||||||||
\(285\) | 3.41421 | 0.202241 | ||||||||
\(286\) | −4.24264 | −0.250873 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | 0.757359 | 0.0444737 | ||||||||
\(291\) | −3.58579 | −0.210203 | ||||||||
\(292\) | 5.65685 | 0.331042 | ||||||||
\(293\) | −21.6274 | −1.26349 | −0.631744 | − | 0.775177i | \(-0.717660\pi\) | ||||
−0.631744 | + | 0.775177i | \(0.717660\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.757359 | 0.0440952 | ||||||||
\(296\) | −9.07107 | −0.527245 | ||||||||
\(297\) | −3.00000 | −0.174078 | ||||||||
\(298\) | 13.6569 | 0.791120 | ||||||||
\(299\) | −1.41421 | −0.0817861 | ||||||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.34315 | −0.0772894 | ||||||||
\(303\) | −4.48528 | −0.257673 | ||||||||
\(304\) | −3.41421 | −0.195819 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | −1.41421 | −0.0808452 | ||||||||
\(307\) | 25.8995 | 1.47816 | 0.739081 | − | 0.673616i | \(-0.235260\pi\) | ||||
0.739081 | + | 0.673616i | \(0.235260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6569 | −0.776911 | ||||||||
\(310\) | −4.65685 | −0.264492 | ||||||||
\(311\) | 3.41421 | 0.193602 | 0.0968011 | − | 0.995304i | \(-0.469139\pi\) | ||||
0.0968011 | + | 0.995304i | \(0.469139\pi\) | |||||||
\(312\) | 1.41421 | 0.0800641 | ||||||||
\(313\) | 16.7574 | 0.947182 | 0.473591 | − | 0.880745i | \(-0.342958\pi\) | ||||
0.473591 | + | 0.880745i | \(0.342958\pi\) | |||||||
\(314\) | −3.89949 | −0.220061 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.414214 | −0.0233013 | ||||||||
\(317\) | 9.92893 | 0.557664 | 0.278832 | − | 0.960340i | \(-0.410053\pi\) | ||||
0.278832 | + | 0.960340i | \(0.410053\pi\) | |||||||
\(318\) | −2.17157 | −0.121776 | ||||||||
\(319\) | 2.27208 | 0.127212 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −7.48528 | −0.417788 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.82843 | 0.268661 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −5.65685 | −0.313786 | ||||||||
\(326\) | −1.41421 | −0.0783260 | ||||||||
\(327\) | 5.31371 | 0.293849 | ||||||||
\(328\) | 1.75736 | 0.0970339 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.00000 | 0.165145 | ||||||||
\(331\) | 25.8995 | 1.42356 | 0.711782 | − | 0.702400i | \(-0.247888\pi\) | ||||
0.711782 | + | 0.702400i | \(0.247888\pi\) | |||||||
\(332\) | 12.3137 | 0.675803 | ||||||||
\(333\) | −9.07107 | −0.497091 | ||||||||
\(334\) | 18.4853 | 1.01147 | ||||||||
\(335\) | 4.34315 | 0.237291 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.9289 | −0.758757 | −0.379379 | − | 0.925242i | \(-0.623862\pi\) | ||||
−0.379379 | + | 0.925242i | \(0.623862\pi\) | |||||||
\(338\) | −11.0000 | −0.598321 | ||||||||
\(339\) | −17.4142 | −0.945810 | ||||||||
\(340\) | 1.41421 | 0.0766965 | ||||||||
\(341\) | −13.9706 | −0.756548 | ||||||||
\(342\) | −3.41421 | −0.184620 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.65685 | −0.412830 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 4.82843 | 0.259578 | ||||||||
\(347\) | −14.6274 | −0.785241 | −0.392620 | − | 0.919701i | \(-0.628431\pi\) | ||||
−0.392620 | + | 0.919701i | \(0.628431\pi\) | |||||||
\(348\) | −0.757359 | −0.0405987 | ||||||||
\(349\) | 26.0416 | 1.39398 | 0.696988 | − | 0.717083i | \(-0.254523\pi\) | ||||
0.696988 | + | 0.717083i | \(0.254523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41421 | 0.0754851 | ||||||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | −22.7279 | −1.20969 | −0.604843 | − | 0.796345i | \(-0.706764\pi\) | ||||
−0.604843 | + | 0.796345i | \(0.706764\pi\) | |||||||
\(354\) | −0.757359 | −0.0402532 | ||||||||
\(355\) | −5.89949 | −0.313113 | ||||||||
\(356\) | 14.7279 | 0.780578 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.0000 | 0.845626 | ||||||||
\(359\) | 2.00000 | 0.105556 | 0.0527780 | − | 0.998606i | \(-0.483192\pi\) | ||||
0.0527780 | + | 0.998606i | \(0.483192\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −7.34315 | −0.386481 | ||||||||
\(362\) | −12.4853 | −0.656212 | ||||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.65685 | −0.296093 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | −34.6985 | −1.81125 | −0.905623 | − | 0.424084i | \(-0.860596\pi\) | ||||
−0.905623 | + | 0.424084i | \(0.860596\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 1.75736 | 0.0914845 | ||||||||
\(370\) | 9.07107 | 0.471582 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.65685 | 0.241447 | ||||||||
\(373\) | −14.3431 | −0.742660 | −0.371330 | − | 0.928501i | \(-0.621098\pi\) | ||||
−0.371330 | + | 0.928501i | \(0.621098\pi\) | |||||||
\(374\) | 4.24264 | 0.219382 | ||||||||
\(375\) | 9.00000 | 0.464758 | ||||||||
\(376\) | −9.31371 | −0.480318 | ||||||||
\(377\) | −1.07107 | −0.0551628 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.9706 | 1.48812 | 0.744059 | − | 0.668114i | \(-0.232898\pi\) | ||||
0.744059 | + | 0.668114i | \(0.232898\pi\) | |||||||
\(380\) | 3.41421 | 0.175145 | ||||||||
\(381\) | −5.82843 | −0.298599 | ||||||||
\(382\) | 1.41421 | 0.0723575 | ||||||||
\(383\) | −1.27208 | −0.0650001 | −0.0325001 | − | 0.999472i | \(-0.510347\pi\) | ||||
−0.0325001 | + | 0.999472i | \(0.510347\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.6274 | −0.999009 | ||||||||
\(387\) | −7.65685 | −0.389220 | ||||||||
\(388\) | −3.58579 | −0.182041 | ||||||||
\(389\) | −1.17157 | −0.0594011 | −0.0297006 | − | 0.999559i | \(-0.509455\pi\) | ||||
−0.0297006 | + | 0.999559i | \(0.509455\pi\) | |||||||
\(390\) | −1.41421 | −0.0716115 | ||||||||
\(391\) | 1.41421 | 0.0715199 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.24264 | −0.0626829 | ||||||||
\(394\) | −3.17157 | −0.159782 | ||||||||
\(395\) | 0.414214 | 0.0208413 | ||||||||
\(396\) | −3.00000 | −0.150756 | ||||||||
\(397\) | 0.443651 | 0.0222662 | 0.0111331 | − | 0.999938i | \(-0.496456\pi\) | ||||
0.0111331 | + | 0.999938i | \(0.496456\pi\) | |||||||
\(398\) | 5.31371 | 0.266352 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −0.485281 | −0.0242338 | −0.0121169 | − | 0.999927i | \(-0.503857\pi\) | ||||
−0.0121169 | + | 0.999927i | \(0.503857\pi\) | |||||||
\(402\) | −4.34315 | −0.216616 | ||||||||
\(403\) | 6.58579 | 0.328061 | ||||||||
\(404\) | −4.48528 | −0.223151 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.2132 | 1.34891 | ||||||||
\(408\) | −1.41421 | −0.0700140 | ||||||||
\(409\) | −13.3431 | −0.659776 | −0.329888 | − | 0.944020i | \(-0.607011\pi\) | ||||
−0.329888 | + | 0.944020i | \(0.607011\pi\) | |||||||
\(410\) | −1.75736 | −0.0867898 | ||||||||
\(411\) | −18.9706 | −0.935749 | ||||||||
\(412\) | −13.6569 | −0.672825 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −12.3137 | −0.604456 | ||||||||
\(416\) | 1.41421 | 0.0693375 | ||||||||
\(417\) | −5.31371 | −0.260213 | ||||||||
\(418\) | 10.2426 | 0.500984 | ||||||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.4558 | 1.53306 | 0.766532 | − | 0.642206i | \(-0.221981\pi\) | ||||
0.766532 | + | 0.642206i | \(0.221981\pi\) | |||||||
\(422\) | 4.82843 | 0.235044 | ||||||||
\(423\) | −9.31371 | −0.452848 | ||||||||
\(424\) | −2.17157 | −0.105461 | ||||||||
\(425\) | 5.65685 | 0.274398 | ||||||||
\(426\) | 5.89949 | 0.285831 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.48528 | −0.361815 | ||||||||
\(429\) | −4.24264 | −0.204837 | ||||||||
\(430\) | 7.65685 | 0.369246 | ||||||||
\(431\) | 6.34315 | 0.305539 | 0.152769 | − | 0.988262i | \(-0.451181\pi\) | ||||
0.152769 | + | 0.988262i | \(0.451181\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 30.0000 | 1.44171 | 0.720854 | − | 0.693087i | \(-0.243750\pi\) | ||||
0.720854 | + | 0.693087i | \(0.243750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.757359 | 0.0363126 | ||||||||
\(436\) | 5.31371 | 0.254480 | ||||||||
\(437\) | 3.41421 | 0.163324 | ||||||||
\(438\) | 5.65685 | 0.270295 | ||||||||
\(439\) | 11.1421 | 0.531785 | 0.265893 | − | 0.964003i | \(-0.414333\pi\) | ||||
0.265893 | + | 0.964003i | \(0.414333\pi\) | |||||||
\(440\) | 3.00000 | 0.143019 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.00000 | −0.0951303 | ||||||||
\(443\) | 10.2721 | 0.488041 | 0.244021 | − | 0.969770i | \(-0.421534\pi\) | ||||
0.244021 | + | 0.969770i | \(0.421534\pi\) | |||||||
\(444\) | −9.07107 | −0.430494 | ||||||||
\(445\) | −14.7279 | −0.698170 | ||||||||
\(446\) | −10.1716 | −0.481638 | ||||||||
\(447\) | 13.6569 | 0.645947 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.75736 | −0.0829349 | −0.0414675 | − | 0.999140i | \(-0.513203\pi\) | ||||
−0.0414675 | + | 0.999140i | \(0.513203\pi\) | |||||||
\(450\) | −4.00000 | −0.188562 | ||||||||
\(451\) | −5.27208 | −0.248252 | ||||||||
\(452\) | −17.4142 | −0.819096 | ||||||||
\(453\) | −1.34315 | −0.0631065 | ||||||||
\(454\) | −7.82843 | −0.367406 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.41421 | −0.159885 | ||||||||
\(457\) | 20.2132 | 0.945534 | 0.472767 | − | 0.881188i | \(-0.343255\pi\) | ||||
0.472767 | + | 0.881188i | \(0.343255\pi\) | |||||||
\(458\) | 22.7279 | 1.06201 | ||||||||
\(459\) | −1.41421 | −0.0660098 | ||||||||
\(460\) | 1.00000 | 0.0466252 | ||||||||
\(461\) | 30.9706 | 1.44244 | 0.721221 | − | 0.692705i | \(-0.243581\pi\) | ||||
0.721221 | + | 0.692705i | \(0.243581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.7990 | −0.641293 | −0.320647 | − | 0.947199i | \(-0.603900\pi\) | ||||
−0.320647 | + | 0.947199i | \(0.603900\pi\) | |||||||
\(464\) | −0.757359 | −0.0351595 | ||||||||
\(465\) | −4.65685 | −0.215956 | ||||||||
\(466\) | 15.2132 | 0.704738 | ||||||||
\(467\) | 28.8284 | 1.33402 | 0.667010 | − | 0.745049i | \(-0.267574\pi\) | ||||
0.667010 | + | 0.745049i | \(0.267574\pi\) | |||||||
\(468\) | 1.41421 | 0.0653720 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.31371 | 0.429609 | ||||||||
\(471\) | −3.89949 | −0.179679 | ||||||||
\(472\) | −0.757359 | −0.0348603 | ||||||||
\(473\) | 22.9706 | 1.05619 | ||||||||
\(474\) | −0.414214 | −0.0190255 | ||||||||
\(475\) | 13.6569 | 0.626619 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.17157 | −0.0994295 | ||||||||
\(478\) | −23.3137 | −1.06634 | ||||||||
\(479\) | 30.5269 | 1.39481 | 0.697405 | − | 0.716677i | \(-0.254338\pi\) | ||||
0.697405 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −12.8284 | −0.584926 | ||||||||
\(482\) | −9.92893 | −0.452250 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 3.58579 | 0.162822 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −29.4853 | −1.33611 | −0.668053 | − | 0.744114i | \(-0.732872\pi\) | ||||
−0.668053 | + | 0.744114i | \(0.732872\pi\) | |||||||
\(488\) | −6.00000 | −0.271607 | ||||||||
\(489\) | −1.41421 | −0.0639529 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.10051 | −0.410700 | −0.205350 | − | 0.978689i | \(-0.565833\pi\) | ||||
−0.205350 | + | 0.978689i | \(0.565833\pi\) | |||||||
\(492\) | 1.75736 | 0.0792279 | ||||||||
\(493\) | 1.07107 | 0.0482385 | ||||||||
\(494\) | −4.82843 | −0.217241 | ||||||||
\(495\) | 3.00000 | 0.134840 | ||||||||
\(496\) | 4.65685 | 0.209099 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.3137 | 0.551790 | ||||||||
\(499\) | −13.7990 | −0.617728 | −0.308864 | − | 0.951106i | \(-0.599949\pi\) | ||||
−0.308864 | + | 0.951106i | \(0.599949\pi\) | |||||||
\(500\) | 9.00000 | 0.402492 | ||||||||
\(501\) | 18.4853 | 0.825861 | ||||||||
\(502\) | 25.8284 | 1.15278 | ||||||||
\(503\) | −6.82843 | −0.304465 | −0.152232 | − | 0.988345i | \(-0.548646\pi\) | ||||
−0.152232 | + | 0.988345i | \(0.548646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.48528 | 0.199592 | ||||||||
\(506\) | 3.00000 | 0.133366 | ||||||||
\(507\) | −11.0000 | −0.488527 | ||||||||
\(508\) | −5.82843 | −0.258595 | ||||||||
\(509\) | 41.7279 | 1.84956 | 0.924779 | − | 0.380505i | \(-0.124250\pi\) | ||||
0.924779 | + | 0.380505i | \(0.124250\pi\) | |||||||
\(510\) | 1.41421 | 0.0626224 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.41421 | −0.150741 | ||||||||
\(514\) | −1.41421 | −0.0623783 | ||||||||
\(515\) | 13.6569 | 0.601793 | ||||||||
\(516\) | −7.65685 | −0.337074 | ||||||||
\(517\) | 27.9411 | 1.22885 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.82843 | 0.211944 | ||||||||
\(520\) | −1.41421 | −0.0620174 | ||||||||
\(521\) | 26.0000 | 1.13908 | 0.569540 | − | 0.821963i | \(-0.307121\pi\) | ||||
0.569540 | + | 0.821963i | \(0.307121\pi\) | |||||||
\(522\) | −0.757359 | −0.0331487 | ||||||||
\(523\) | −16.2843 | −0.712061 | −0.356031 | − | 0.934474i | \(-0.615870\pi\) | ||||
−0.356031 | + | 0.934474i | \(0.615870\pi\) | |||||||
\(524\) | −1.24264 | −0.0542850 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.9706 | 0.478339 | ||||||||
\(527\) | −6.58579 | −0.286881 | ||||||||
\(528\) | −3.00000 | −0.130558 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 2.17157 | 0.0943271 | ||||||||
\(531\) | −0.757359 | −0.0328666 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.48528 | 0.107649 | ||||||||
\(534\) | 14.7279 | 0.637340 | ||||||||
\(535\) | 7.48528 | 0.323617 | ||||||||
\(536\) | −4.34315 | −0.187595 | ||||||||
\(537\) | 16.0000 | 0.690451 | ||||||||
\(538\) | 1.58579 | 0.0683681 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −39.6985 | −1.70677 | −0.853386 | − | 0.521280i | \(-0.825455\pi\) | ||||
−0.853386 | + | 0.521280i | \(0.825455\pi\) | |||||||
\(542\) | −7.00000 | −0.300676 | ||||||||
\(543\) | −12.4853 | −0.535795 | ||||||||
\(544\) | −1.41421 | −0.0606339 | ||||||||
\(545\) | −5.31371 | −0.227614 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2426 | 1.03654 | 0.518270 | − | 0.855217i | \(-0.326576\pi\) | ||||
0.518270 | + | 0.855217i | \(0.326576\pi\) | |||||||
\(548\) | −18.9706 | −0.810382 | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 12.0000 | 0.511682 | ||||||||
\(551\) | 2.58579 | 0.110158 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.82843 | −0.120168 | ||||||||
\(555\) | 9.07107 | 0.385045 | ||||||||
\(556\) | −5.31371 | −0.225351 | ||||||||
\(557\) | −40.3137 | −1.70815 | −0.854073 | − | 0.520153i | \(-0.825875\pi\) | ||||
−0.854073 | + | 0.520153i | \(0.825875\pi\) | |||||||
\(558\) | 4.65685 | 0.197140 | ||||||||
\(559\) | −10.8284 | −0.457994 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.24264 | 0.179124 | ||||||||
\(562\) | −26.7279 | −1.12745 | ||||||||
\(563\) | −13.1421 | −0.553875 | −0.276937 | − | 0.960888i | \(-0.589319\pi\) | ||||
−0.276937 | + | 0.960888i | \(0.589319\pi\) | |||||||
\(564\) | −9.31371 | −0.392178 | ||||||||
\(565\) | 17.4142 | 0.732621 | ||||||||
\(566\) | −24.1421 | −1.01477 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.89949 | 0.247537 | ||||||||
\(569\) | −5.85786 | −0.245574 | −0.122787 | − | 0.992433i | \(-0.539183\pi\) | ||||
−0.122787 | + | 0.992433i | \(0.539183\pi\) | |||||||
\(570\) | 3.41421 | 0.143006 | ||||||||
\(571\) | 40.5269 | 1.69600 | 0.847999 | − | 0.529997i | \(-0.177807\pi\) | ||||
0.847999 | + | 0.529997i | \(0.177807\pi\) | |||||||
\(572\) | −4.24264 | −0.177394 | ||||||||
\(573\) | 1.41421 | 0.0590796 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −7.62742 | −0.317534 | −0.158767 | − | 0.987316i | \(-0.550752\pi\) | ||||
−0.158767 | + | 0.987316i | \(0.550752\pi\) | |||||||
\(578\) | −15.0000 | −0.623918 | ||||||||
\(579\) | −19.6274 | −0.815688 | ||||||||
\(580\) | 0.757359 | 0.0314476 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.58579 | −0.148636 | ||||||||
\(583\) | 6.51472 | 0.269812 | ||||||||
\(584\) | 5.65685 | 0.234082 | ||||||||
\(585\) | −1.41421 | −0.0584705 | ||||||||
\(586\) | −21.6274 | −0.893420 | ||||||||
\(587\) | −2.41421 | −0.0996453 | −0.0498226 | − | 0.998758i | \(-0.515866\pi\) | ||||
−0.0498226 | + | 0.998758i | \(0.515866\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.8995 | −0.655127 | ||||||||
\(590\) | 0.757359 | 0.0311800 | ||||||||
\(591\) | −3.17157 | −0.130461 | ||||||||
\(592\) | −9.07107 | −0.372819 | ||||||||
\(593\) | 8.97056 | 0.368377 | 0.184188 | − | 0.982891i | \(-0.441034\pi\) | ||||
0.184188 | + | 0.982891i | \(0.441034\pi\) | |||||||
\(594\) | −3.00000 | −0.123091 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.6569 | 0.559407 | ||||||||
\(597\) | 5.31371 | 0.217476 | ||||||||
\(598\) | −1.41421 | −0.0578315 | ||||||||
\(599\) | −0.928932 | −0.0379551 | −0.0189776 | − | 0.999820i | \(-0.506041\pi\) | ||||
−0.0189776 | + | 0.999820i | \(0.506041\pi\) | |||||||
\(600\) | −4.00000 | −0.163299 | ||||||||
\(601\) | −40.9411 | −1.67002 | −0.835012 | − | 0.550232i | \(-0.814539\pi\) | ||||
−0.835012 | + | 0.550232i | \(0.814539\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.34315 | −0.176867 | ||||||||
\(604\) | −1.34315 | −0.0546518 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | −4.48528 | −0.182202 | ||||||||
\(607\) | 19.2843 | 0.782724 | 0.391362 | − | 0.920237i | \(-0.372004\pi\) | ||||
0.391362 | + | 0.920237i | \(0.372004\pi\) | |||||||
\(608\) | −3.41421 | −0.138465 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −13.1716 | −0.532865 | ||||||||
\(612\) | −1.41421 | −0.0571662 | ||||||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 25.8995 | 1.04522 | ||||||||
\(615\) | −1.75736 | −0.0708636 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.9411 | −1.28590 | −0.642951 | − | 0.765908i | \(-0.722290\pi\) | ||||
−0.642951 | + | 0.765908i | \(0.722290\pi\) | |||||||
\(618\) | −13.6569 | −0.549359 | ||||||||
\(619\) | 9.89949 | 0.397894 | 0.198947 | − | 0.980010i | \(-0.436248\pi\) | ||||
0.198947 | + | 0.980010i | \(0.436248\pi\) | |||||||
\(620\) | −4.65685 | −0.187024 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 3.41421 | 0.136897 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.41421 | 0.0566139 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 16.7574 | 0.669759 | ||||||||
\(627\) | 10.2426 | 0.409052 | ||||||||
\(628\) | −3.89949 | −0.155607 | ||||||||
\(629\) | 12.8284 | 0.511503 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.41421 | 0.0961083 | 0.0480542 | − | 0.998845i | \(-0.484698\pi\) | ||||
0.0480542 | + | 0.998845i | \(0.484698\pi\) | |||||||
\(632\) | −0.414214 | −0.0164765 | ||||||||
\(633\) | 4.82843 | 0.191913 | ||||||||
\(634\) | 9.92893 | 0.394328 | ||||||||
\(635\) | 5.82843 | 0.231294 | ||||||||
\(636\) | −2.17157 | −0.0861085 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.27208 | 0.0899524 | ||||||||
\(639\) | 5.89949 | 0.233380 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 39.6985 | 1.56800 | 0.783998 | − | 0.620763i | \(-0.213177\pi\) | ||||
0.783998 | + | 0.620763i | \(0.213177\pi\) | |||||||
\(642\) | −7.48528 | −0.295420 | ||||||||
\(643\) | −10.5858 | −0.417463 | −0.208731 | − | 0.977973i | \(-0.566933\pi\) | ||||
−0.208731 | + | 0.977973i | \(0.566933\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.65685 | 0.301488 | ||||||||
\(646\) | 4.82843 | 0.189972 | ||||||||
\(647\) | −0.828427 | −0.0325688 | −0.0162844 | − | 0.999867i | \(-0.505184\pi\) | ||||
−0.0162844 | + | 0.999867i | \(0.505184\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 2.27208 | 0.0891869 | ||||||||
\(650\) | −5.65685 | −0.221880 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.41421 | −0.0553849 | ||||||||
\(653\) | 45.7279 | 1.78947 | 0.894736 | − | 0.446596i | \(-0.147364\pi\) | ||||
0.894736 | + | 0.446596i | \(0.147364\pi\) | |||||||
\(654\) | 5.31371 | 0.207782 | ||||||||
\(655\) | 1.24264 | 0.0485540 | ||||||||
\(656\) | 1.75736 | 0.0686134 | ||||||||
\(657\) | 5.65685 | 0.220695 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.9411 | −1.71170 | −0.855852 | − | 0.517221i | \(-0.826966\pi\) | ||||
−0.855852 | + | 0.517221i | \(0.826966\pi\) | |||||||
\(660\) | 3.00000 | 0.116775 | ||||||||
\(661\) | 10.9706 | 0.426705 | 0.213353 | − | 0.976975i | \(-0.431562\pi\) | ||||
0.213353 | + | 0.976975i | \(0.431562\pi\) | |||||||
\(662\) | 25.8995 | 1.00661 | ||||||||
\(663\) | −2.00000 | −0.0776736 | ||||||||
\(664\) | 12.3137 | 0.477865 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.07107 | −0.351497 | ||||||||
\(667\) | 0.757359 | 0.0293251 | ||||||||
\(668\) | 18.4853 | 0.715217 | ||||||||
\(669\) | −10.1716 | −0.393256 | ||||||||
\(670\) | 4.34315 | 0.167790 | ||||||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0294 | 0.386606 | 0.193303 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193303 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(674\) | −13.9289 | −0.536522 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | −11.0000 | −0.423077 | ||||||||
\(677\) | −42.6569 | −1.63944 | −0.819718 | − | 0.572767i | \(-0.805870\pi\) | ||||
−0.819718 | + | 0.572767i | \(0.805870\pi\) | |||||||
\(678\) | −17.4142 | −0.668789 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.41421 | 0.0542326 | ||||||||
\(681\) | −7.82843 | −0.299986 | ||||||||
\(682\) | −13.9706 | −0.534960 | ||||||||
\(683\) | −7.04163 | −0.269441 | −0.134720 | − | 0.990884i | \(-0.543014\pi\) | ||||
−0.134720 | + | 0.990884i | \(0.543014\pi\) | |||||||
\(684\) | −3.41421 | −0.130546 | ||||||||
\(685\) | 18.9706 | 0.724828 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.7279 | 0.867124 | ||||||||
\(688\) | −7.65685 | −0.291915 | ||||||||
\(689\) | −3.07107 | −0.116998 | ||||||||
\(690\) | 1.00000 | 0.0380693 | ||||||||
\(691\) | −46.5858 | −1.77221 | −0.886103 | − | 0.463488i | \(-0.846598\pi\) | ||||
−0.886103 | + | 0.463488i | \(0.846598\pi\) | |||||||
\(692\) | 4.82843 | 0.183549 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.6274 | −0.555249 | ||||||||
\(695\) | 5.31371 | 0.201560 | ||||||||
\(696\) | −0.757359 | −0.0287076 | ||||||||
\(697\) | −2.48528 | −0.0941367 | ||||||||
\(698\) | 26.0416 | 0.985690 | ||||||||
\(699\) | 15.2132 | 0.575416 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.514719 | 0.0194407 | 0.00972033 | − | 0.999953i | \(-0.496906\pi\) | ||||
0.00972033 | + | 0.999953i | \(0.496906\pi\) | |||||||
\(702\) | 1.41421 | 0.0533761 | ||||||||
\(703\) | 30.9706 | 1.16808 | ||||||||
\(704\) | −3.00000 | −0.113067 | ||||||||
\(705\) | 9.31371 | 0.350775 | ||||||||
\(706\) | −22.7279 | −0.855377 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.757359 | −0.0284633 | ||||||||
\(709\) | −6.58579 | −0.247334 | −0.123667 | − | 0.992324i | \(-0.539466\pi\) | ||||
−0.123667 | + | 0.992324i | \(0.539466\pi\) | |||||||
\(710\) | −5.89949 | −0.221404 | ||||||||
\(711\) | −0.414214 | −0.0155342 | ||||||||
\(712\) | 14.7279 | 0.551952 | ||||||||
\(713\) | −4.65685 | −0.174401 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.24264 | 0.158666 | ||||||||
\(716\) | 16.0000 | 0.597948 | ||||||||
\(717\) | −23.3137 | −0.870666 | ||||||||
\(718\) | 2.00000 | 0.0746393 | ||||||||
\(719\) | −0.142136 | −0.00530076 | −0.00265038 | − | 0.999996i | \(-0.500844\pi\) | ||||
−0.00265038 | + | 0.999996i | \(0.500844\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.34315 | −0.273284 | ||||||||
\(723\) | −9.92893 | −0.369261 | ||||||||
\(724\) | −12.4853 | −0.464012 | ||||||||
\(725\) | 3.02944 | 0.112510 | ||||||||
\(726\) | −2.00000 | −0.0742270 | ||||||||
\(727\) | −5.44365 | −0.201894 | −0.100947 | − | 0.994892i | \(-0.532187\pi\) | ||||
−0.100947 | + | 0.994892i | \(0.532187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.65685 | −0.209370 | ||||||||
\(731\) | 10.8284 | 0.400504 | ||||||||
\(732\) | −6.00000 | −0.221766 | ||||||||
\(733\) | 15.5563 | 0.574587 | 0.287293 | − | 0.957843i | \(-0.407245\pi\) | ||||
0.287293 | + | 0.957843i | \(0.407245\pi\) | |||||||
\(734\) | −34.6985 | −1.28074 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 13.0294 | 0.479945 | ||||||||
\(738\) | 1.75736 | 0.0646893 | ||||||||
\(739\) | 20.8284 | 0.766186 | 0.383093 | − | 0.923710i | \(-0.374859\pi\) | ||||
0.383093 | + | 0.923710i | \(0.374859\pi\) | |||||||
\(740\) | 9.07107 | 0.333459 | ||||||||
\(741\) | −4.82843 | −0.177377 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.24264 | −0.229020 | −0.114510 | − | 0.993422i | \(-0.536530\pi\) | ||||
−0.114510 | + | 0.993422i | \(0.536530\pi\) | |||||||
\(744\) | 4.65685 | 0.170729 | ||||||||
\(745\) | −13.6569 | −0.500348 | ||||||||
\(746\) | −14.3431 | −0.525140 | ||||||||
\(747\) | 12.3137 | 0.450535 | ||||||||
\(748\) | 4.24264 | 0.155126 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.00000 | 0.328634 | ||||||||
\(751\) | 35.5269 | 1.29640 | 0.648198 | − | 0.761472i | \(-0.275523\pi\) | ||||
0.648198 | + | 0.761472i | \(0.275523\pi\) | |||||||
\(752\) | −9.31371 | −0.339636 | ||||||||
\(753\) | 25.8284 | 0.941240 | ||||||||
\(754\) | −1.07107 | −0.0390060 | ||||||||
\(755\) | 1.34315 | 0.0488821 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.0711 | 1.42006 | 0.710031 | − | 0.704170i | \(-0.248681\pi\) | ||||
0.710031 | + | 0.704170i | \(0.248681\pi\) | |||||||
\(758\) | 28.9706 | 1.05226 | ||||||||
\(759\) | 3.00000 | 0.108893 | ||||||||
\(760\) | 3.41421 | 0.123847 | ||||||||
\(761\) | 4.58579 | 0.166235 | 0.0831173 | − | 0.996540i | \(-0.473512\pi\) | ||||
0.0831173 | + | 0.996540i | \(0.473512\pi\) | |||||||
\(762\) | −5.82843 | −0.211142 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.41421 | 0.0511645 | ||||||||
\(765\) | 1.41421 | 0.0511310 | ||||||||
\(766\) | −1.27208 | −0.0459620 | ||||||||
\(767\) | −1.07107 | −0.0386740 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −42.0122 | −1.51500 | −0.757499 | − | 0.652836i | \(-0.773579\pi\) | ||||
−0.757499 | + | 0.652836i | \(0.773579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.41421 | −0.0509317 | ||||||||
\(772\) | −19.6274 | −0.706406 | ||||||||
\(773\) | 22.8284 | 0.821081 | 0.410541 | − | 0.911842i | \(-0.365340\pi\) | ||||
0.410541 | + | 0.911842i | \(0.365340\pi\) | |||||||
\(774\) | −7.65685 | −0.275220 | ||||||||
\(775\) | −18.6274 | −0.669117 | ||||||||
\(776\) | −3.58579 | −0.128722 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.17157 | −0.0420029 | ||||||||
\(779\) | −6.00000 | −0.214972 | ||||||||
\(780\) | −1.41421 | −0.0506370 | ||||||||
\(781\) | −17.6985 | −0.633302 | ||||||||
\(782\) | 1.41421 | 0.0505722 | ||||||||
\(783\) | −0.757359 | −0.0270658 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.89949 | 0.139179 | ||||||||
\(786\) | −1.24264 | −0.0443235 | ||||||||
\(787\) | 23.4558 | 0.836111 | 0.418055 | − | 0.908422i | \(-0.362712\pi\) | ||||
0.418055 | + | 0.908422i | \(0.362712\pi\) | |||||||
\(788\) | −3.17157 | −0.112983 | ||||||||
\(789\) | 10.9706 | 0.390562 | ||||||||
\(790\) | 0.414214 | 0.0147371 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.00000 | −0.106600 | ||||||||
\(793\) | −8.48528 | −0.301321 | ||||||||
\(794\) | 0.443651 | 0.0157446 | ||||||||
\(795\) | 2.17157 | 0.0770178 | ||||||||
\(796\) | 5.31371 | 0.188339 | ||||||||
\(797\) | −3.97056 | −0.140645 | −0.0703223 | − | 0.997524i | \(-0.522403\pi\) | ||||
−0.0703223 | + | 0.997524i | \(0.522403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.1716 | 0.465977 | ||||||||
\(800\) | −4.00000 | −0.141421 | ||||||||
\(801\) | 14.7279 | 0.520386 | ||||||||
\(802\) | −0.485281 | −0.0171359 | ||||||||
\(803\) | −16.9706 | −0.598878 | ||||||||
\(804\) | −4.34315 | −0.153171 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.58579 | 0.231974 | ||||||||
\(807\) | 1.58579 | 0.0558223 | ||||||||
\(808\) | −4.48528 | −0.157792 | ||||||||
\(809\) | 50.5269 | 1.77643 | 0.888216 | − | 0.459426i | \(-0.151945\pi\) | ||||
0.888216 | + | 0.459426i | \(0.151945\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −42.2843 | −1.48480 | −0.742401 | − | 0.669956i | \(-0.766313\pi\) | ||||
−0.742401 | + | 0.669956i | \(0.766313\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.00000 | −0.245501 | ||||||||
\(814\) | 27.2132 | 0.953822 | ||||||||
\(815\) | 1.41421 | 0.0495377 | ||||||||
\(816\) | −1.41421 | −0.0495074 | ||||||||
\(817\) | 26.1421 | 0.914598 | ||||||||
\(818\) | −13.3431 | −0.466532 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.75736 | −0.0613696 | ||||||||
\(821\) | 14.7574 | 0.515035 | 0.257518 | − | 0.966274i | \(-0.417095\pi\) | ||||
0.257518 | + | 0.966274i | \(0.417095\pi\) | |||||||
\(822\) | −18.9706 | −0.661674 | ||||||||
\(823\) | 46.6274 | 1.62533 | 0.812665 | − | 0.582731i | \(-0.198016\pi\) | ||||
0.812665 | + | 0.582731i | \(0.198016\pi\) | |||||||
\(824\) | −13.6569 | −0.475759 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7990 | 0.723252 | 0.361626 | − | 0.932323i | \(-0.382222\pi\) | ||||
0.361626 | + | 0.932323i | \(0.382222\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −27.5147 | −0.955626 | −0.477813 | − | 0.878462i | \(-0.658570\pi\) | ||||
−0.477813 | + | 0.878462i | \(0.658570\pi\) | |||||||
\(830\) | −12.3137 | −0.427415 | ||||||||
\(831\) | −2.82843 | −0.0981170 | ||||||||
\(832\) | 1.41421 | 0.0490290 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.31371 | −0.183999 | ||||||||
\(835\) | −18.4853 | −0.639710 | ||||||||
\(836\) | 10.2426 | 0.354249 | ||||||||
\(837\) | 4.65685 | 0.160964 | ||||||||
\(838\) | −6.00000 | −0.207267 | ||||||||
\(839\) | −17.6985 | −0.611020 | −0.305510 | − | 0.952189i | \(-0.598827\pi\) | ||||
−0.305510 | + | 0.952189i | \(0.598827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4264 | −0.980221 | ||||||||
\(842\) | 31.4558 | 1.08404 | ||||||||
\(843\) | −26.7279 | −0.920559 | ||||||||
\(844\) | 4.82843 | 0.166201 | ||||||||
\(845\) | 11.0000 | 0.378412 | ||||||||
\(846\) | −9.31371 | −0.320212 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.17157 | −0.0745721 | ||||||||
\(849\) | −24.1421 | −0.828556 | ||||||||
\(850\) | 5.65685 | 0.194029 | ||||||||
\(851\) | 9.07107 | 0.310952 | ||||||||
\(852\) | 5.89949 | 0.202113 | ||||||||
\(853\) | −28.1421 | −0.963568 | −0.481784 | − | 0.876290i | \(-0.660011\pi\) | ||||
−0.481784 | + | 0.876290i | \(0.660011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.41421 | 0.116764 | ||||||||
\(856\) | −7.48528 | −0.255842 | ||||||||
\(857\) | 26.8701 | 0.917864 | 0.458932 | − | 0.888471i | \(-0.348232\pi\) | ||||
0.458932 | + | 0.888471i | \(0.348232\pi\) | |||||||
\(858\) | −4.24264 | −0.144841 | ||||||||
\(859\) | 19.4142 | 0.662404 | 0.331202 | − | 0.943560i | \(-0.392546\pi\) | ||||
0.331202 | + | 0.943560i | \(0.392546\pi\) | |||||||
\(860\) | 7.65685 | 0.261097 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.34315 | 0.216048 | ||||||||
\(863\) | 38.8701 | 1.32315 | 0.661576 | − | 0.749878i | \(-0.269888\pi\) | ||||
0.661576 | + | 0.749878i | \(0.269888\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −4.82843 | −0.164171 | ||||||||
\(866\) | 30.0000 | 1.01944 | ||||||||
\(867\) | −15.0000 | −0.509427 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.24264 | 0.0421537 | ||||||||
\(870\) | 0.757359 | 0.0256769 | ||||||||
\(871\) | −6.14214 | −0.208118 | ||||||||
\(872\) | 5.31371 | 0.179945 | ||||||||
\(873\) | −3.58579 | −0.121360 | ||||||||
\(874\) | 3.41421 | 0.115487 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.65685 | 0.191127 | ||||||||
\(877\) | 37.8995 | 1.27978 | 0.639888 | − | 0.768469i | \(-0.278981\pi\) | ||||
0.639888 | + | 0.768469i | \(0.278981\pi\) | |||||||
\(878\) | 11.1421 | 0.376029 | ||||||||
\(879\) | −21.6274 | −0.729475 | ||||||||
\(880\) | 3.00000 | 0.101130 | ||||||||
\(881\) | 8.14214 | 0.274316 | 0.137158 | − | 0.990549i | \(-0.456203\pi\) | ||||
0.137158 | + | 0.990549i | \(0.456203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.6985 | 1.80710 | 0.903549 | − | 0.428485i | \(-0.140952\pi\) | ||||
0.903549 | + | 0.428485i | \(0.140952\pi\) | |||||||
\(884\) | −2.00000 | −0.0672673 | ||||||||
\(885\) | 0.757359 | 0.0254584 | ||||||||
\(886\) | 10.2721 | 0.345097 | ||||||||
\(887\) | −45.6569 | −1.53301 | −0.766504 | − | 0.642240i | \(-0.778005\pi\) | ||||
−0.766504 | + | 0.642240i | \(0.778005\pi\) | |||||||
\(888\) | −9.07107 | −0.304405 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.7279 | −0.493681 | ||||||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | −10.1716 | −0.340569 | ||||||||
\(893\) | 31.7990 | 1.06411 | ||||||||
\(894\) | 13.6569 | 0.456754 | ||||||||
\(895\) | −16.0000 | −0.534821 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.41421 | −0.0472192 | ||||||||
\(898\) | −1.75736 | −0.0586438 | ||||||||
\(899\) | −3.52691 | −0.117629 | ||||||||
\(900\) | −4.00000 | −0.133333 | ||||||||
\(901\) | 3.07107 | 0.102312 | ||||||||
\(902\) | −5.27208 | −0.175541 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.4142 | −0.579188 | ||||||||
\(905\) | 12.4853 | 0.415025 | ||||||||
\(906\) | −1.34315 | −0.0446230 | ||||||||
\(907\) | −25.0711 | −0.832471 | −0.416236 | − | 0.909257i | \(-0.636651\pi\) | ||||
−0.416236 | + | 0.909257i | \(0.636651\pi\) | |||||||
\(908\) | −7.82843 | −0.259795 | ||||||||
\(909\) | −4.48528 | −0.148767 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.34315 | −0.143895 | −0.0719474 | − | 0.997408i | \(-0.522921\pi\) | ||||
−0.0719474 | + | 0.997408i | \(0.522921\pi\) | |||||||
\(912\) | −3.41421 | −0.113056 | ||||||||
\(913\) | −36.9411 | −1.22257 | ||||||||
\(914\) | 20.2132 | 0.668593 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | 22.7279 | 0.750952 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.41421 | −0.0466760 | ||||||||
\(919\) | 36.2843 | 1.19691 | 0.598454 | − | 0.801157i | \(-0.295782\pi\) | ||||
0.598454 | + | 0.801157i | \(0.295782\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | 25.8995 | 0.853417 | ||||||||
\(922\) | 30.9706 | 1.01996 | ||||||||
\(923\) | 8.34315 | 0.274618 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.2843 | 1.19302 | ||||||||
\(926\) | −13.7990 | −0.453463 | ||||||||
\(927\) | −13.6569 | −0.448550 | ||||||||
\(928\) | −0.757359 | −0.0248615 | ||||||||
\(929\) | 0.727922 | 0.0238823 | 0.0119412 | − | 0.999929i | \(-0.496199\pi\) | ||||
0.0119412 | + | 0.999929i | \(0.496199\pi\) | |||||||
\(930\) | −4.65685 | −0.152704 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.2132 | 0.498325 | ||||||||
\(933\) | 3.41421 | 0.111776 | ||||||||
\(934\) | 28.8284 | 0.943295 | ||||||||
\(935\) | −4.24264 | −0.138749 | ||||||||
\(936\) | 1.41421 | 0.0462250 | ||||||||
\(937\) | 47.1838 | 1.54143 | 0.770713 | − | 0.637182i | \(-0.219900\pi\) | ||||
0.770713 | + | 0.637182i | \(0.219900\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.7574 | 0.546856 | ||||||||
\(940\) | 9.31371 | 0.303780 | ||||||||
\(941\) | 35.4853 | 1.15679 | 0.578394 | − | 0.815758i | \(-0.303680\pi\) | ||||
0.578394 | + | 0.815758i | \(0.303680\pi\) | |||||||
\(942\) | −3.89949 | −0.127052 | ||||||||
\(943\) | −1.75736 | −0.0572275 | ||||||||
\(944\) | −0.757359 | −0.0246499 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9706 | 0.746837 | ||||||||
\(947\) | −6.28427 | −0.204211 | −0.102106 | − | 0.994774i | \(-0.532558\pi\) | ||||
−0.102106 | + | 0.994774i | \(0.532558\pi\) | |||||||
\(948\) | −0.414214 | −0.0134530 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | 13.6569 | 0.443087 | ||||||||
\(951\) | 9.92893 | 0.321968 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.7990 | −1.22443 | −0.612215 | − | 0.790692i | \(-0.709721\pi\) | ||||
−0.612215 | + | 0.790692i | \(0.709721\pi\) | |||||||
\(954\) | −2.17157 | −0.0703073 | ||||||||
\(955\) | −1.41421 | −0.0457629 | ||||||||
\(956\) | −23.3137 | −0.754019 | ||||||||
\(957\) | 2.27208 | 0.0734458 | ||||||||
\(958\) | 30.5269 | 0.986280 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −9.31371 | −0.300442 | ||||||||
\(962\) | −12.8284 | −0.413605 | ||||||||
\(963\) | −7.48528 | −0.241210 | ||||||||
\(964\) | −9.92893 | −0.319789 | ||||||||
\(965\) | 19.6274 | 0.631829 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.9706 | −1.15674 | −0.578368 | − | 0.815776i | \(-0.696310\pi\) | ||||
−0.578368 | + | 0.815776i | \(0.696310\pi\) | |||||||
\(968\) | −2.00000 | −0.0642824 | ||||||||
\(969\) | 4.82843 | 0.155111 | ||||||||
\(970\) | 3.58579 | 0.115133 | ||||||||
\(971\) | 3.97056 | 0.127421 | 0.0637107 | − | 0.997968i | \(-0.479707\pi\) | ||||
0.0637107 | + | 0.997968i | \(0.479707\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.4853 | −0.944769 | ||||||||
\(975\) | −5.65685 | −0.181164 | ||||||||
\(976\) | −6.00000 | −0.192055 | ||||||||
\(977\) | 34.9706 | 1.11881 | 0.559404 | − | 0.828895i | \(-0.311030\pi\) | ||||
0.559404 | + | 0.828895i | \(0.311030\pi\) | |||||||
\(978\) | −1.41421 | −0.0452216 | ||||||||
\(979\) | −44.1838 | −1.41212 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.31371 | 0.169654 | ||||||||
\(982\) | −9.10051 | −0.290409 | ||||||||
\(983\) | 6.58579 | 0.210054 | 0.105027 | − | 0.994469i | \(-0.466507\pi\) | ||||
0.105027 | + | 0.994469i | \(0.466507\pi\) | |||||||
\(984\) | 1.75736 | 0.0560226 | ||||||||
\(985\) | 3.17157 | 0.101055 | ||||||||
\(986\) | 1.07107 | 0.0341097 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.82843 | −0.153613 | ||||||||
\(989\) | 7.65685 | 0.243474 | ||||||||
\(990\) | 3.00000 | 0.0953463 | ||||||||
\(991\) | −35.7696 | −1.13626 | −0.568129 | − | 0.822940i | \(-0.692332\pi\) | ||||
−0.568129 | + | 0.822940i | \(0.692332\pi\) | |||||||
\(992\) | 4.65685 | 0.147855 | ||||||||
\(993\) | 25.8995 | 0.821896 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.31371 | −0.168456 | ||||||||
\(996\) | 12.3137 | 0.390175 | ||||||||
\(997\) | −44.8701 | −1.42105 | −0.710524 | − | 0.703672i | \(-0.751542\pi\) | ||||
−0.710524 | + | 0.703672i | \(0.751542\pi\) | |||||||
\(998\) | −13.7990 | −0.436799 | ||||||||
\(999\) | −9.07107 | −0.286996 |
(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 | 6762.2.a.cc.1.2 | 2 | ||
7.2 | even | 3 | 966.2.i.h.277.2 | ✓ | 4 | ||
7.4 | even | 3 | 966.2.i.h.415.2 | yes | 4 | ||
7.6 | odd | 2 | 6762.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.h.277.2 | ✓ | 4 | 7.2 | even | 3 | ||
966.2.i.h.415.2 | yes | 4 | 7.4 | even | 3 | ||
6762.2.a.ca.1.1 | 2 | 7.6 | odd | 2 | |||
6762.2.a.cc.1.2 | 2 | 1.1 | even | 1 | trivial |