Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,2,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.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: | \(9.18279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.546295\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.40815 | −1.39034 | −0.695172 | − | 0.718843i | \(-0.744672\pi\) | ||||
−0.695172 | + | 0.718843i | \(0.744672\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.40815 | −0.983122 | ||||||||
\(7\) | 0.706585 | 0.267064 | 0.133532 | − | 0.991044i | \(-0.457368\pi\) | ||||
0.133532 | + | 0.991044i | \(0.457368\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.79917 | 0.933058 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.747120 | 0.225265 | 0.112633 | − | 0.993637i | \(-0.464072\pi\) | ||||
0.112633 | + | 0.993637i | \(0.464072\pi\) | |||||||
\(12\) | −2.40815 | −0.695172 | ||||||||
\(13\) | 1.29341 | 0.358729 | 0.179364 | − | 0.983783i | \(-0.442596\pi\) | ||||
0.179364 | + | 0.983783i | \(0.442596\pi\) | |||||||
\(14\) | 0.706585 | 0.188843 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.50074 | −1.33412 | −0.667062 | − | 0.745002i | \(-0.732449\pi\) | ||||
−0.667062 | + | 0.745002i | \(0.732449\pi\) | |||||||
\(18\) | 2.79917 | 0.659772 | ||||||||
\(19\) | 2.44868 | 0.561766 | 0.280883 | − | 0.959742i | \(-0.409373\pi\) | ||||
0.280883 | + | 0.959742i | \(0.409373\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.70156 | −0.371311 | ||||||||
\(22\) | 0.747120 | 0.159286 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.40815 | −0.491561 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.29341 | 0.253659 | ||||||||
\(27\) | 0.483617 | 0.0930721 | ||||||||
\(28\) | 0.706585 | 0.133532 | ||||||||
\(29\) | 5.72371 | 1.06287 | 0.531433 | − | 0.847100i | \(-0.321654\pi\) | ||||
0.531433 | + | 0.847100i | \(0.321654\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.52288 | 1.35115 | 0.675575 | − | 0.737292i | \(-0.263896\pi\) | ||||
0.675575 | + | 0.737292i | \(0.263896\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.79917 | −0.313196 | ||||||||
\(34\) | −5.50074 | −0.943369 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.79917 | 0.466529 | ||||||||
\(37\) | −5.07420 | −0.834193 | −0.417097 | − | 0.908862i | \(-0.636952\pi\) | ||||
−0.417097 | + | 0.908862i | \(0.636952\pi\) | |||||||
\(38\) | 2.44868 | 0.397229 | ||||||||
\(39\) | −3.11473 | −0.498756 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0876 | 1.57541 | 0.787707 | − | 0.616051i | \(-0.211268\pi\) | ||||
0.787707 | + | 0.616051i | \(0.211268\pi\) | |||||||
\(42\) | −1.70156 | −0.262557 | ||||||||
\(43\) | −5.34045 | −0.814410 | −0.407205 | − | 0.913337i | \(-0.633497\pi\) | ||||
−0.407205 | + | 0.913337i | \(0.633497\pi\) | |||||||
\(44\) | 0.747120 | 0.112633 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 7.90888 | 1.15363 | 0.576815 | − | 0.816875i | \(-0.304295\pi\) | ||||
0.576815 | + | 0.816875i | \(0.304295\pi\) | |||||||
\(48\) | −2.40815 | −0.347586 | ||||||||
\(49\) | −6.50074 | −0.928677 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.2466 | 1.85489 | ||||||||
\(52\) | 1.29341 | 0.179364 | ||||||||
\(53\) | 5.84621 | 0.803038 | 0.401519 | − | 0.915851i | \(-0.368482\pi\) | ||||
0.401519 | + | 0.915851i | \(0.368482\pi\) | |||||||
\(54\) | 0.483617 | 0.0658119 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.706585 | 0.0944215 | ||||||||
\(57\) | −5.89679 | −0.781049 | ||||||||
\(58\) | 5.72371 | 0.751559 | ||||||||
\(59\) | 12.4146 | 1.61625 | 0.808125 | − | 0.589012i | \(-0.200483\pi\) | ||||
0.808125 | + | 0.589012i | \(0.200483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.57346 | 0.201461 | 0.100731 | − | 0.994914i | \(-0.467882\pi\) | ||||
0.100731 | + | 0.994914i | \(0.467882\pi\) | |||||||
\(62\) | 7.52288 | 0.955407 | ||||||||
\(63\) | 1.97786 | 0.249186 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.79917 | −0.221463 | ||||||||
\(67\) | 5.25938 | 0.642535 | 0.321268 | − | 0.946988i | \(-0.395891\pi\) | ||||
0.321268 | + | 0.946988i | \(0.395891\pi\) | |||||||
\(68\) | −5.50074 | −0.667062 | ||||||||
\(69\) | −2.40815 | −0.289907 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.68444 | 0.318585 | 0.159292 | − | 0.987231i | \(-0.449079\pi\) | ||||
0.159292 | + | 0.987231i | \(0.449079\pi\) | |||||||
\(72\) | 2.79917 | 0.329886 | ||||||||
\(73\) | 10.4589 | 1.22413 | 0.612063 | − | 0.790809i | \(-0.290340\pi\) | ||||
0.612063 | + | 0.790809i | \(0.290340\pi\) | |||||||
\(74\) | −5.07420 | −0.589864 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.44868 | 0.280883 | ||||||||
\(77\) | 0.527904 | 0.0601602 | ||||||||
\(78\) | −3.11473 | −0.352674 | ||||||||
\(79\) | −6.55005 | −0.736938 | −0.368469 | − | 0.929640i | \(-0.620118\pi\) | ||||
−0.368469 | + | 0.929640i | \(0.620118\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.56214 | −1.06246 | ||||||||
\(82\) | 10.0876 | 1.11399 | ||||||||
\(83\) | 12.7068 | 1.39475 | 0.697376 | − | 0.716706i | \(-0.254351\pi\) | ||||
0.697376 | + | 0.716706i | \(0.254351\pi\) | |||||||
\(84\) | −1.70156 | −0.185656 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.34045 | −0.575875 | ||||||||
\(87\) | −13.7835 | −1.47775 | ||||||||
\(88\) | 0.747120 | 0.0796432 | ||||||||
\(89\) | 13.6426 | 1.44612 | 0.723058 | − | 0.690787i | \(-0.242736\pi\) | ||||
0.723058 | + | 0.690787i | \(0.242736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.913908 | 0.0958036 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −18.1162 | −1.87856 | ||||||||
\(94\) | 7.90888 | 0.815739 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.40815 | −0.245781 | ||||||||
\(97\) | 1.50074 | 0.152377 | 0.0761884 | − | 0.997093i | \(-0.475725\pi\) | ||||
0.0761884 | + | 0.997093i | \(0.475725\pi\) | |||||||
\(98\) | −6.50074 | −0.656674 | ||||||||
\(99\) | 2.09132 | 0.210185 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.0472 | −1.59676 | −0.798380 | − | 0.602154i | \(-0.794309\pi\) | ||||
−0.798380 | + | 0.602154i | \(0.794309\pi\) | |||||||
\(102\) | 13.2466 | 1.31161 | ||||||||
\(103\) | 9.49069 | 0.935145 | 0.467573 | − | 0.883955i | \(-0.345129\pi\) | ||||
0.467573 | + | 0.883955i | \(0.345129\pi\) | |||||||
\(104\) | 1.29341 | 0.126830 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.84621 | 0.567834 | ||||||||
\(107\) | 1.38473 | 0.133867 | 0.0669336 | − | 0.997757i | \(-0.478678\pi\) | ||||
0.0669336 | + | 0.997757i | \(0.478678\pi\) | |||||||
\(108\) | 0.483617 | 0.0465360 | ||||||||
\(109\) | −14.0370 | −1.34450 | −0.672250 | − | 0.740325i | \(-0.734672\pi\) | ||||
−0.672250 | + | 0.740325i | \(0.734672\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.2194 | 1.15982 | ||||||||
\(112\) | 0.706585 | 0.0667661 | ||||||||
\(113\) | −16.3105 | −1.53437 | −0.767183 | − | 0.641428i | \(-0.778342\pi\) | ||||
−0.767183 | + | 0.641428i | \(0.778342\pi\) | |||||||
\(114\) | −5.89679 | −0.552285 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.72371 | 0.531433 | ||||||||
\(117\) | 3.62049 | 0.334715 | ||||||||
\(118\) | 12.4146 | 1.14286 | ||||||||
\(119\) | −3.88674 | −0.356297 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4418 | −0.949256 | ||||||||
\(122\) | 1.57346 | 0.142455 | ||||||||
\(123\) | −24.2923 | −2.19037 | ||||||||
\(124\) | 7.52288 | 0.675575 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.97786 | 0.176201 | ||||||||
\(127\) | −2.73523 | −0.242712 | −0.121356 | − | 0.992609i | \(-0.538724\pi\) | ||||
−0.121356 | + | 0.992609i | \(0.538724\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 12.8606 | 1.13231 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.21942 | −0.718134 | −0.359067 | − | 0.933312i | \(-0.616905\pi\) | ||||
−0.359067 | + | 0.933312i | \(0.616905\pi\) | |||||||
\(132\) | −1.79917 | −0.156598 | ||||||||
\(133\) | 1.73020 | 0.150028 | ||||||||
\(134\) | 5.25938 | 0.454341 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.50074 | −0.471684 | ||||||||
\(137\) | −22.8449 | −1.95177 | −0.975887 | − | 0.218275i | \(-0.929957\pi\) | ||||
−0.975887 | + | 0.218275i | \(0.929957\pi\) | |||||||
\(138\) | −2.40815 | −0.204995 | ||||||||
\(139\) | 3.76049 | 0.318960 | 0.159480 | − | 0.987201i | \(-0.449018\pi\) | ||||
0.159480 | + | 0.987201i | \(0.449018\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.0458 | −1.60394 | ||||||||
\(142\) | 2.68444 | 0.225273 | ||||||||
\(143\) | 0.966336 | 0.0808090 | ||||||||
\(144\) | 2.79917 | 0.233265 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.4589 | 0.865587 | ||||||||
\(147\) | 15.6547 | 1.29118 | ||||||||
\(148\) | −5.07420 | −0.417097 | ||||||||
\(149\) | −1.90614 | −0.156157 | −0.0780785 | − | 0.996947i | \(-0.524878\pi\) | ||||
−0.0780785 | + | 0.996947i | \(0.524878\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.41967 | −0.766562 | −0.383281 | − | 0.923632i | \(-0.625206\pi\) | ||||
−0.383281 | + | 0.923632i | \(0.625206\pi\) | |||||||
\(152\) | 2.44868 | 0.198614 | ||||||||
\(153\) | −15.3975 | −1.24482 | ||||||||
\(154\) | 0.527904 | 0.0425397 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.11473 | −0.249378 | ||||||||
\(157\) | 4.43304 | 0.353795 | 0.176897 | − | 0.984229i | \(-0.443394\pi\) | ||||
0.176897 | + | 0.984229i | \(0.443394\pi\) | |||||||
\(158\) | −6.55005 | −0.521094 | ||||||||
\(159\) | −14.0785 | −1.11650 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.706585 | 0.0556867 | ||||||||
\(162\) | −9.56214 | −0.751273 | ||||||||
\(163\) | 9.92453 | 0.777349 | 0.388675 | − | 0.921375i | \(-0.372933\pi\) | ||||
0.388675 | + | 0.921375i | \(0.372933\pi\) | |||||||
\(164\) | 10.0876 | 0.787707 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.7068 | 0.986238 | ||||||||
\(167\) | −11.9089 | −0.921537 | −0.460769 | − | 0.887520i | \(-0.652426\pi\) | ||||
−0.460769 | + | 0.887520i | \(0.652426\pi\) | |||||||
\(168\) | −1.70156 | −0.131278 | ||||||||
\(169\) | −11.3271 | −0.871314 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.85429 | 0.524161 | ||||||||
\(172\) | −5.34045 | −0.407205 | ||||||||
\(173\) | 2.91391 | 0.221540 | 0.110770 | − | 0.993846i | \(-0.464668\pi\) | ||||
0.110770 | + | 0.993846i | \(0.464668\pi\) | |||||||
\(174\) | −13.7835 | −1.04493 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.747120 | 0.0563163 | ||||||||
\(177\) | −29.8963 | −2.24714 | ||||||||
\(178\) | 13.6426 | 1.02256 | ||||||||
\(179\) | 19.3663 | 1.44751 | 0.723754 | − | 0.690058i | \(-0.242415\pi\) | ||||
0.723754 | + | 0.690058i | \(0.242415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.5986 | 1.30809 | 0.654045 | − | 0.756456i | \(-0.273071\pi\) | ||||
0.654045 | + | 0.756456i | \(0.273071\pi\) | |||||||
\(182\) | 0.913908 | 0.0677434 | ||||||||
\(183\) | −3.78913 | −0.280100 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −18.1162 | −1.32834 | ||||||||
\(187\) | −4.10971 | −0.300532 | ||||||||
\(188\) | 7.90888 | 0.576815 | ||||||||
\(189\) | 0.341716 | 0.0248562 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.3578 | 1.47304 | 0.736518 | − | 0.676418i | \(-0.236469\pi\) | ||||
0.736518 | + | 0.676418i | \(0.236469\pi\) | |||||||
\(192\) | −2.40815 | −0.173793 | ||||||||
\(193\) | −1.41317 | −0.101722 | −0.0508611 | − | 0.998706i | \(-0.516197\pi\) | ||||
−0.0508611 | + | 0.998706i | \(0.516197\pi\) | |||||||
\(194\) | 1.50074 | 0.107747 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50074 | −0.464338 | ||||||||
\(197\) | 4.92395 | 0.350817 | 0.175409 | − | 0.984496i | \(-0.443875\pi\) | ||||
0.175409 | + | 0.984496i | \(0.443875\pi\) | |||||||
\(198\) | 2.09132 | 0.148624 | ||||||||
\(199\) | −10.3105 | −0.730894 | −0.365447 | − | 0.930832i | \(-0.619084\pi\) | ||||
−0.365447 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.6654 | −0.893345 | ||||||||
\(202\) | −16.0472 | −1.12908 | ||||||||
\(203\) | 4.04429 | 0.283853 | ||||||||
\(204\) | 13.2466 | 0.927447 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.49069 | 0.661248 | ||||||||
\(207\) | 2.79917 | 0.194556 | ||||||||
\(208\) | 1.29341 | 0.0896822 | ||||||||
\(209\) | 1.82946 | 0.126546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4161 | 0.785918 | 0.392959 | − | 0.919556i | \(-0.371451\pi\) | ||||
0.392959 | + | 0.919556i | \(0.371451\pi\) | |||||||
\(212\) | 5.84621 | 0.401519 | ||||||||
\(213\) | −6.46453 | −0.442942 | ||||||||
\(214\) | 1.38473 | 0.0946584 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.483617 | 0.0329059 | ||||||||
\(217\) | 5.31556 | 0.360844 | ||||||||
\(218\) | −14.0370 | −0.950705 | ||||||||
\(219\) | −25.1867 | −1.70196 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.11473 | −0.478589 | ||||||||
\(222\) | 12.2194 | 0.820114 | ||||||||
\(223\) | −18.2094 | −1.21939 | −0.609695 | − | 0.792636i | \(-0.708708\pi\) | ||||
−0.609695 | + | 0.792636i | \(0.708708\pi\) | |||||||
\(224\) | 0.706585 | 0.0472107 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.3105 | −1.08496 | ||||||||
\(227\) | −18.9363 | −1.25684 | −0.628422 | − | 0.777873i | \(-0.716299\pi\) | ||||
−0.628422 | + | 0.777873i | \(0.716299\pi\) | |||||||
\(228\) | −5.89679 | −0.390524 | ||||||||
\(229\) | −8.46433 | −0.559339 | −0.279669 | − | 0.960096i | \(-0.590225\pi\) | ||||
−0.279669 | + | 0.960096i | \(0.590225\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.27127 | −0.0836435 | ||||||||
\(232\) | 5.72371 | 0.375780 | ||||||||
\(233\) | 16.6341 | 1.08973 | 0.544867 | − | 0.838523i | \(-0.316580\pi\) | ||||
0.544867 | + | 0.838523i | \(0.316580\pi\) | |||||||
\(234\) | 3.62049 | 0.236679 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.4146 | 0.808125 | ||||||||
\(237\) | 15.7735 | 1.02460 | ||||||||
\(238\) | −3.88674 | −0.251940 | ||||||||
\(239\) | −16.0840 | −1.04039 | −0.520194 | − | 0.854048i | \(-0.674140\pi\) | ||||
−0.520194 | + | 0.854048i | \(0.674140\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.1283 | −1.81190 | −0.905952 | − | 0.423381i | \(-0.860843\pi\) | ||||
−0.905952 | + | 0.423381i | \(0.860843\pi\) | |||||||
\(242\) | −10.4418 | −0.671225 | ||||||||
\(243\) | 21.5762 | 1.38411 | ||||||||
\(244\) | 1.57346 | 0.100731 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.2923 | −1.54882 | ||||||||
\(247\) | 3.16716 | 0.201522 | ||||||||
\(248\) | 7.52288 | 0.477703 | ||||||||
\(249\) | −30.5998 | −1.93919 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5770 | −1.29881 | −0.649404 | − | 0.760444i | \(-0.724982\pi\) | ||||
−0.649404 | + | 0.760444i | \(0.724982\pi\) | |||||||
\(252\) | 1.97786 | 0.124593 | ||||||||
\(253\) | 0.747120 | 0.0469710 | ||||||||
\(254\) | −2.73523 | −0.171623 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.8505 | 1.05111 | 0.525554 | − | 0.850760i | \(-0.323858\pi\) | ||||
0.525554 | + | 0.850760i | \(0.323858\pi\) | |||||||
\(258\) | 12.8606 | 0.800665 | ||||||||
\(259\) | −3.58536 | −0.222783 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.0217 | 0.991715 | ||||||||
\(262\) | −8.21942 | −0.507797 | ||||||||
\(263\) | 24.7630 | 1.52695 | 0.763475 | − | 0.645837i | \(-0.223492\pi\) | ||||
0.763475 | + | 0.645837i | \(0.223492\pi\) | |||||||
\(264\) | −1.79917 | −0.110732 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.73020 | 0.106086 | ||||||||
\(267\) | −32.8535 | −2.01060 | ||||||||
\(268\) | 5.25938 | 0.321268 | ||||||||
\(269\) | −3.55152 | −0.216540 | −0.108270 | − | 0.994122i | \(-0.534531\pi\) | ||||
−0.108270 | + | 0.994122i | \(0.534531\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.4761 | −1.66905 | −0.834526 | − | 0.550969i | \(-0.814258\pi\) | ||||
−0.834526 | + | 0.550969i | \(0.814258\pi\) | |||||||
\(272\) | −5.50074 | −0.333531 | ||||||||
\(273\) | −2.20083 | −0.133200 | ||||||||
\(274\) | −22.8449 | −1.38011 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.40815 | −0.144953 | ||||||||
\(277\) | 11.1001 | 0.666940 | 0.333470 | − | 0.942761i | \(-0.391780\pi\) | ||||
0.333470 | + | 0.942761i | \(0.391780\pi\) | |||||||
\(278\) | 3.76049 | 0.225539 | ||||||||
\(279\) | 21.0579 | 1.26070 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0458 | 0.778245 | 0.389122 | − | 0.921186i | \(-0.372778\pi\) | ||||
0.389122 | + | 0.921186i | \(0.372778\pi\) | |||||||
\(282\) | −19.0458 | −1.13416 | ||||||||
\(283\) | −3.35049 | −0.199166 | −0.0995831 | − | 0.995029i | \(-0.531751\pi\) | ||||
−0.0995831 | + | 0.995029i | \(0.531751\pi\) | |||||||
\(284\) | 2.68444 | 0.159292 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.966336 | 0.0571406 | ||||||||
\(287\) | 7.12773 | 0.420736 | ||||||||
\(288\) | 2.79917 | 0.164943 | ||||||||
\(289\) | 13.2581 | 0.779889 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.61400 | −0.211856 | ||||||||
\(292\) | 10.4589 | 0.612063 | ||||||||
\(293\) | −8.89197 | −0.519474 | −0.259737 | − | 0.965679i | \(-0.583636\pi\) | ||||
−0.259737 | + | 0.965679i | \(0.583636\pi\) | |||||||
\(294\) | 15.6547 | 0.913003 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.07420 | −0.294932 | ||||||||
\(297\) | 0.361320 | 0.0209659 | ||||||||
\(298\) | −1.90614 | −0.110420 | ||||||||
\(299\) | 1.29341 | 0.0748001 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.77348 | −0.217500 | ||||||||
\(302\) | −9.41967 | −0.542041 | ||||||||
\(303\) | 38.6441 | 2.22005 | ||||||||
\(304\) | 2.44868 | 0.140442 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −15.3975 | −0.880218 | ||||||||
\(307\) | 28.4111 | 1.62151 | 0.810753 | − | 0.585388i | \(-0.199058\pi\) | ||||
0.810753 | + | 0.585388i | \(0.199058\pi\) | |||||||
\(308\) | 0.527904 | 0.0300801 | ||||||||
\(309\) | −22.8550 | −1.30017 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.0105 | −1.58833 | −0.794164 | − | 0.607704i | \(-0.792091\pi\) | ||||
−0.794164 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(312\) | −3.11473 | −0.176337 | ||||||||
\(313\) | −7.42882 | −0.419902 | −0.209951 | − | 0.977712i | \(-0.567330\pi\) | ||||
−0.209951 | + | 0.977712i | \(0.567330\pi\) | |||||||
\(314\) | 4.43304 | 0.250171 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.55005 | −0.368469 | ||||||||
\(317\) | 13.1480 | 0.738463 | 0.369232 | − | 0.929337i | \(-0.379621\pi\) | ||||
0.369232 | + | 0.929337i | \(0.379621\pi\) | |||||||
\(318\) | −14.0785 | −0.789485 | ||||||||
\(319\) | 4.27629 | 0.239427 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.33464 | −0.186122 | ||||||||
\(322\) | 0.706585 | 0.0393765 | ||||||||
\(323\) | −13.4696 | −0.749466 | ||||||||
\(324\) | −9.56214 | −0.531230 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.92453 | 0.549669 | ||||||||
\(327\) | 33.8031 | 1.86932 | ||||||||
\(328\) | 10.0876 | 0.556993 | ||||||||
\(329\) | 5.58830 | 0.308093 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6225 | −0.858693 | −0.429346 | − | 0.903140i | \(-0.641256\pi\) | ||||
−0.429346 | + | 0.903140i | \(0.641256\pi\) | |||||||
\(332\) | 12.7068 | 0.697376 | ||||||||
\(333\) | −14.2036 | −0.778351 | ||||||||
\(334\) | −11.9089 | −0.651625 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.70156 | −0.0928278 | ||||||||
\(337\) | −16.6965 | −0.909518 | −0.454759 | − | 0.890614i | \(-0.650275\pi\) | ||||
−0.454759 | + | 0.890614i | \(0.650275\pi\) | |||||||
\(338\) | −11.3271 | −0.616112 | ||||||||
\(339\) | 39.2782 | 2.13330 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.62049 | 0.304367 | ||||||||
\(342\) | 6.85429 | 0.370637 | ||||||||
\(343\) | −9.53942 | −0.515081 | ||||||||
\(344\) | −5.34045 | −0.287938 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.91391 | 0.156653 | ||||||||
\(347\) | 16.3981 | 0.880296 | 0.440148 | − | 0.897925i | \(-0.354926\pi\) | ||||
0.440148 | + | 0.897925i | \(0.354926\pi\) | |||||||
\(348\) | −13.7835 | −0.738875 | ||||||||
\(349\) | −1.86165 | −0.0996518 | −0.0498259 | − | 0.998758i | \(-0.515867\pi\) | ||||
−0.0498259 | + | 0.998758i | \(0.515867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.625517 | 0.0333876 | ||||||||
\(352\) | 0.747120 | 0.0398216 | ||||||||
\(353\) | −25.8408 | −1.37537 | −0.687684 | − | 0.726010i | \(-0.741372\pi\) | ||||
−0.687684 | + | 0.726010i | \(0.741372\pi\) | |||||||
\(354\) | −29.8963 | −1.58897 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.6426 | 0.723058 | ||||||||
\(357\) | 9.35985 | 0.495376 | ||||||||
\(358\) | 19.3663 | 1.02354 | ||||||||
\(359\) | 8.72223 | 0.460342 | 0.230171 | − | 0.973150i | \(-0.426071\pi\) | ||||
0.230171 | + | 0.973150i | \(0.426071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0040 | −0.684419 | ||||||||
\(362\) | 17.5986 | 0.924959 | ||||||||
\(363\) | 25.1454 | 1.31979 | ||||||||
\(364\) | 0.913908 | 0.0479018 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.78913 | −0.198061 | ||||||||
\(367\) | 25.5958 | 1.33609 | 0.668045 | − | 0.744121i | \(-0.267131\pi\) | ||||
0.668045 | + | 0.744121i | \(0.267131\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 28.2369 | 1.46995 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.13084 | 0.214463 | ||||||||
\(372\) | −18.1162 | −0.939282 | ||||||||
\(373\) | −17.2125 | −0.891232 | −0.445616 | − | 0.895224i | \(-0.647015\pi\) | ||||
−0.445616 | + | 0.895224i | \(0.647015\pi\) | |||||||
\(374\) | −4.10971 | −0.212508 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.90888 | 0.407870 | ||||||||
\(377\) | 7.40312 | 0.381280 | ||||||||
\(378\) | 0.341716 | 0.0175760 | ||||||||
\(379\) | 23.0339 | 1.18317 | 0.591585 | − | 0.806243i | \(-0.298502\pi\) | ||||
0.591585 | + | 0.806243i | \(0.298502\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.58683 | 0.337453 | ||||||||
\(382\) | 20.3578 | 1.04159 | ||||||||
\(383\) | 3.81777 | 0.195079 | 0.0975394 | − | 0.995232i | \(-0.468903\pi\) | ||||
0.0975394 | + | 0.995232i | \(0.468903\pi\) | |||||||
\(384\) | −2.40815 | −0.122890 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.41317 | −0.0719285 | ||||||||
\(387\) | −14.9488 | −0.759892 | ||||||||
\(388\) | 1.50074 | 0.0761884 | ||||||||
\(389\) | −8.25435 | −0.418512 | −0.209256 | − | 0.977861i | \(-0.567104\pi\) | ||||
−0.209256 | + | 0.977861i | \(0.567104\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.50074 | −0.278184 | ||||||||
\(392\) | −6.50074 | −0.328337 | ||||||||
\(393\) | 19.7936 | 0.998454 | ||||||||
\(394\) | 4.92395 | 0.248065 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.09132 | 0.105093 | ||||||||
\(397\) | 12.4967 | 0.627193 | 0.313596 | − | 0.949556i | \(-0.398466\pi\) | ||||
0.313596 | + | 0.949556i | \(0.398466\pi\) | |||||||
\(398\) | −10.3105 | −0.516820 | ||||||||
\(399\) | −4.16658 | −0.208590 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.5660 | 1.72614 | 0.863072 | − | 0.505082i | \(-0.168538\pi\) | ||||
0.863072 | + | 0.505082i | \(0.168538\pi\) | |||||||
\(402\) | −12.6654 | −0.631691 | ||||||||
\(403\) | 9.73020 | 0.484696 | ||||||||
\(404\) | −16.0472 | −0.798380 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.04429 | 0.200715 | ||||||||
\(407\) | −3.79103 | −0.187915 | ||||||||
\(408\) | 13.2466 | 0.655804 | ||||||||
\(409\) | 12.0499 | 0.595829 | 0.297914 | − | 0.954593i | \(-0.403709\pi\) | ||||
0.297914 | + | 0.954593i | \(0.403709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 55.0140 | 2.71364 | ||||||||
\(412\) | 9.49069 | 0.467573 | ||||||||
\(413\) | 8.77201 | 0.431642 | ||||||||
\(414\) | 2.79917 | 0.137572 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.29341 | 0.0634149 | ||||||||
\(417\) | −9.05581 | −0.443465 | ||||||||
\(418\) | 1.82946 | 0.0894818 | ||||||||
\(419\) | 38.6157 | 1.88650 | 0.943250 | − | 0.332085i | \(-0.107752\pi\) | ||||
0.943250 | + | 0.332085i | \(0.107752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.7384 | 1.59557 | 0.797785 | − | 0.602941i | \(-0.206005\pi\) | ||||
0.797785 | + | 0.602941i | \(0.206005\pi\) | |||||||
\(422\) | 11.4161 | 0.555728 | ||||||||
\(423\) | 22.1384 | 1.07640 | ||||||||
\(424\) | 5.84621 | 0.283917 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.46453 | −0.313208 | ||||||||
\(427\) | 1.11179 | 0.0538031 | ||||||||
\(428\) | 1.38473 | 0.0669336 | ||||||||
\(429\) | −2.32708 | −0.112352 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.7739 | −1.72317 | −0.861584 | − | 0.507615i | \(-0.830527\pi\) | ||||
−0.861584 | + | 0.507615i | \(0.830527\pi\) | |||||||
\(432\) | 0.483617 | 0.0232680 | ||||||||
\(433\) | −10.5682 | −0.507877 | −0.253938 | − | 0.967220i | \(-0.581726\pi\) | ||||
−0.253938 | + | 0.967220i | \(0.581726\pi\) | |||||||
\(434\) | 5.31556 | 0.255155 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.0370 | −0.672250 | ||||||||
\(437\) | 2.44868 | 0.117136 | ||||||||
\(438\) | −25.1867 | −1.20346 | ||||||||
\(439\) | −27.6642 | −1.32034 | −0.660170 | − | 0.751117i | \(-0.729516\pi\) | ||||
−0.660170 | + | 0.751117i | \(0.729516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.1967 | −0.866509 | ||||||||
\(442\) | −7.11473 | −0.338413 | ||||||||
\(443\) | 36.8082 | 1.74881 | 0.874404 | − | 0.485198i | \(-0.161253\pi\) | ||||
0.874404 | + | 0.485198i | \(0.161253\pi\) | |||||||
\(444\) | 12.2194 | 0.579908 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.2094 | −0.862239 | ||||||||
\(447\) | 4.59027 | 0.217112 | ||||||||
\(448\) | 0.706585 | 0.0333830 | ||||||||
\(449\) | 18.2711 | 0.862267 | 0.431133 | − | 0.902288i | \(-0.358114\pi\) | ||||
0.431133 | + | 0.902288i | \(0.358114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.53662 | 0.354886 | ||||||||
\(452\) | −16.3105 | −0.767183 | ||||||||
\(453\) | 22.6840 | 1.06579 | ||||||||
\(454\) | −18.9363 | −0.888722 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.89679 | −0.276142 | ||||||||
\(457\) | −27.6326 | −1.29260 | −0.646299 | − | 0.763084i | \(-0.723684\pi\) | ||||
−0.646299 | + | 0.763084i | \(0.723684\pi\) | |||||||
\(458\) | −8.46433 | −0.395512 | ||||||||
\(459\) | −2.66025 | −0.124170 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.5515 | 1.65580 | 0.827900 | − | 0.560876i | \(-0.189536\pi\) | ||||
0.827900 | + | 0.560876i | \(0.189536\pi\) | |||||||
\(462\) | −1.27127 | −0.0591449 | ||||||||
\(463\) | −23.9331 | −1.11226 | −0.556132 | − | 0.831094i | \(-0.687715\pi\) | ||||
−0.556132 | + | 0.831094i | \(0.687715\pi\) | |||||||
\(464\) | 5.72371 | 0.265716 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.6341 | 0.770558 | ||||||||
\(467\) | −19.9035 | −0.921024 | −0.460512 | − | 0.887654i | \(-0.652334\pi\) | ||||
−0.460512 | + | 0.887654i | \(0.652334\pi\) | |||||||
\(468\) | 3.62049 | 0.167357 | ||||||||
\(469\) | 3.71620 | 0.171598 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.6754 | −0.491897 | ||||||||
\(472\) | 12.4146 | 0.571430 | ||||||||
\(473\) | −3.98995 | −0.183458 | ||||||||
\(474\) | 15.7735 | 0.724500 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.88674 | −0.178148 | ||||||||
\(477\) | 16.3646 | 0.749281 | ||||||||
\(478\) | −16.0840 | −0.735666 | ||||||||
\(479\) | −3.86206 | −0.176462 | −0.0882309 | − | 0.996100i | \(-0.528121\pi\) | ||||
−0.0882309 | + | 0.996100i | \(0.528121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.56304 | −0.299249 | ||||||||
\(482\) | −28.1283 | −1.28121 | ||||||||
\(483\) | −1.70156 | −0.0774238 | ||||||||
\(484\) | −10.4418 | −0.474628 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 21.5762 | 0.978717 | ||||||||
\(487\) | −15.1499 | −0.686506 | −0.343253 | − | 0.939243i | \(-0.611529\pi\) | ||||
−0.343253 | + | 0.939243i | \(0.611529\pi\) | |||||||
\(488\) | 1.57346 | 0.0712273 | ||||||||
\(489\) | −23.8997 | −1.08078 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.86312 | −0.309728 | −0.154864 | − | 0.987936i | \(-0.549494\pi\) | ||||
−0.154864 | + | 0.987936i | \(0.549494\pi\) | |||||||
\(492\) | −24.2923 | −1.09518 | ||||||||
\(493\) | −31.4846 | −1.41800 | ||||||||
\(494\) | 3.16716 | 0.142497 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.52288 | 0.337787 | ||||||||
\(497\) | 1.89679 | 0.0850826 | ||||||||
\(498\) | −30.5998 | −1.37121 | ||||||||
\(499\) | −18.6809 | −0.836272 | −0.418136 | − | 0.908385i | \(-0.637316\pi\) | ||||
−0.418136 | + | 0.908385i | \(0.637316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.6784 | 1.28125 | ||||||||
\(502\) | −20.5770 | −0.918396 | ||||||||
\(503\) | 23.1886 | 1.03393 | 0.516963 | − | 0.856008i | \(-0.327062\pi\) | ||||
0.516963 | + | 0.856008i | \(0.327062\pi\) | |||||||
\(504\) | 1.97786 | 0.0881007 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.747120 | 0.0332135 | ||||||||
\(507\) | 27.2773 | 1.21143 | ||||||||
\(508\) | −2.73523 | −0.121356 | ||||||||
\(509\) | 11.5385 | 0.511436 | 0.255718 | − | 0.966751i | \(-0.417688\pi\) | ||||
0.255718 | + | 0.966751i | \(0.417688\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.39013 | 0.326920 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.18422 | 0.0522847 | ||||||||
\(514\) | 16.8505 | 0.743245 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.8606 | 0.566156 | ||||||||
\(517\) | 5.90888 | 0.259872 | ||||||||
\(518\) | −3.58536 | −0.157531 | ||||||||
\(519\) | −7.01712 | −0.308017 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.2792 | −0.713207 | −0.356603 | − | 0.934256i | \(-0.616065\pi\) | ||||
−0.356603 | + | 0.934256i | \(0.616065\pi\) | |||||||
\(522\) | 16.0217 | 0.701249 | ||||||||
\(523\) | 30.8347 | 1.34831 | 0.674153 | − | 0.738591i | \(-0.264509\pi\) | ||||
0.674153 | + | 0.738591i | \(0.264509\pi\) | |||||||
\(524\) | −8.21942 | −0.359067 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.7630 | 1.07972 | ||||||||
\(527\) | −41.3814 | −1.80260 | ||||||||
\(528\) | −1.79917 | −0.0782990 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 34.7508 | 1.50805 | ||||||||
\(532\) | 1.73020 | 0.0750138 | ||||||||
\(533\) | 13.0474 | 0.565146 | ||||||||
\(534\) | −32.8535 | −1.42171 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.25938 | 0.227171 | ||||||||
\(537\) | −46.6370 | −2.01254 | ||||||||
\(538\) | −3.55152 | −0.153117 | ||||||||
\(539\) | −4.85683 | −0.209198 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.5199 | −1.31215 | −0.656077 | − | 0.754694i | \(-0.727785\pi\) | ||||
−0.656077 | + | 0.754694i | \(0.727785\pi\) | |||||||
\(542\) | −27.4761 | −1.18020 | ||||||||
\(543\) | −42.3799 | −1.81870 | ||||||||
\(544\) | −5.50074 | −0.235842 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.20083 | −0.0941866 | ||||||||
\(547\) | 28.0416 | 1.19897 | 0.599487 | − | 0.800385i | \(-0.295371\pi\) | ||||
0.599487 | + | 0.800385i | \(0.295371\pi\) | |||||||
\(548\) | −22.8449 | −0.975887 | ||||||||
\(549\) | 4.40439 | 0.187975 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0155 | 0.597082 | ||||||||
\(552\) | −2.40815 | −0.102498 | ||||||||
\(553\) | −4.62817 | −0.196810 | ||||||||
\(554\) | 11.1001 | 0.471598 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.76049 | 0.159480 | ||||||||
\(557\) | −4.15674 | −0.176127 | −0.0880634 | − | 0.996115i | \(-0.528068\pi\) | ||||
−0.0880634 | + | 0.996115i | \(0.528068\pi\) | |||||||
\(558\) | 21.0579 | 0.891450 | ||||||||
\(559\) | −6.90741 | −0.292152 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.89679 | 0.417843 | ||||||||
\(562\) | 13.0458 | 0.550302 | ||||||||
\(563\) | −21.3480 | −0.899709 | −0.449854 | − | 0.893102i | \(-0.648524\pi\) | ||||
−0.449854 | + | 0.893102i | \(0.648524\pi\) | |||||||
\(564\) | −19.0458 | −0.801971 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.35049 | −0.140832 | ||||||||
\(567\) | −6.75647 | −0.283745 | ||||||||
\(568\) | 2.68444 | 0.112637 | ||||||||
\(569\) | −25.6430 | −1.07501 | −0.537506 | − | 0.843260i | \(-0.680634\pi\) | ||||
−0.537506 | + | 0.843260i | \(0.680634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.10743 | −0.297437 | −0.148718 | − | 0.988880i | \(-0.547515\pi\) | ||||
−0.148718 | + | 0.988880i | \(0.547515\pi\) | |||||||
\(572\) | 0.966336 | 0.0404045 | ||||||||
\(573\) | −49.0245 | −2.04803 | ||||||||
\(574\) | 7.12773 | 0.297506 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.79917 | 0.116632 | ||||||||
\(577\) | −22.7226 | −0.945956 | −0.472978 | − | 0.881074i | \(-0.656821\pi\) | ||||
−0.472978 | + | 0.881074i | \(0.656821\pi\) | |||||||
\(578\) | 13.2581 | 0.551465 | ||||||||
\(579\) | 3.40312 | 0.141429 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.97843 | 0.372488 | ||||||||
\(582\) | −3.61400 | −0.149805 | ||||||||
\(583\) | 4.36782 | 0.180896 | ||||||||
\(584\) | 10.4589 | 0.432794 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.89197 | −0.367324 | ||||||||
\(587\) | −7.06600 | −0.291645 | −0.145822 | − | 0.989311i | \(-0.546583\pi\) | ||||
−0.145822 | + | 0.989311i | \(0.546583\pi\) | |||||||
\(588\) | 15.6547 | 0.645590 | ||||||||
\(589\) | 18.4211 | 0.759030 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.8576 | −0.487757 | ||||||||
\(592\) | −5.07420 | −0.208548 | ||||||||
\(593\) | −14.9914 | −0.615624 | −0.307812 | − | 0.951447i | \(-0.599597\pi\) | ||||
−0.307812 | + | 0.951447i | \(0.599597\pi\) | |||||||
\(594\) | 0.361320 | 0.0148251 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.90614 | −0.0780785 | ||||||||
\(597\) | 24.8293 | 1.01620 | ||||||||
\(598\) | 1.29341 | 0.0528917 | ||||||||
\(599\) | −4.03069 | −0.164690 | −0.0823448 | − | 0.996604i | \(-0.526241\pi\) | ||||
−0.0823448 | + | 0.996604i | \(0.526241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.9320 | 0.568300 | 0.284150 | − | 0.958780i | \(-0.408289\pi\) | ||||
0.284150 | + | 0.958780i | \(0.408289\pi\) | |||||||
\(602\) | −3.77348 | −0.153796 | ||||||||
\(603\) | 14.7219 | 0.599523 | ||||||||
\(604\) | −9.41967 | −0.383281 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 38.6441 | 1.56981 | ||||||||
\(607\) | 31.0588 | 1.26064 | 0.630318 | − | 0.776337i | \(-0.282925\pi\) | ||||
0.630318 | + | 0.776337i | \(0.282925\pi\) | |||||||
\(608\) | 2.44868 | 0.0993072 | ||||||||
\(609\) | −9.73924 | −0.394654 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2295 | 0.413840 | ||||||||
\(612\) | −15.3975 | −0.622408 | ||||||||
\(613\) | −19.6722 | −0.794554 | −0.397277 | − | 0.917699i | \(-0.630045\pi\) | ||||
−0.397277 | + | 0.917699i | \(0.630045\pi\) | |||||||
\(614\) | 28.4111 | 1.14658 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.527904 | 0.0212699 | ||||||||
\(617\) | 40.9043 | 1.64674 | 0.823372 | − | 0.567502i | \(-0.192090\pi\) | ||||
0.823372 | + | 0.567502i | \(0.192090\pi\) | |||||||
\(618\) | −22.8550 | −0.919362 | ||||||||
\(619\) | −3.58556 | −0.144116 | −0.0720579 | − | 0.997400i | \(-0.522957\pi\) | ||||
−0.0720579 | + | 0.997400i | \(0.522957\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.483617 | 0.0194069 | ||||||||
\(622\) | −28.0105 | −1.12312 | ||||||||
\(623\) | 9.63969 | 0.386206 | ||||||||
\(624\) | −3.11473 | −0.124689 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.42882 | −0.296915 | ||||||||
\(627\) | −4.40561 | −0.175943 | ||||||||
\(628\) | 4.43304 | 0.176897 | ||||||||
\(629\) | 27.9118 | 1.11292 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.19670 | −0.286496 | −0.143248 | − | 0.989687i | \(-0.545755\pi\) | ||||
−0.143248 | + | 0.989687i | \(0.545755\pi\) | |||||||
\(632\) | −6.55005 | −0.260547 | ||||||||
\(633\) | −27.4917 | −1.09270 | ||||||||
\(634\) | 13.1480 | 0.522172 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −14.0785 | −0.558250 | ||||||||
\(637\) | −8.40815 | −0.333143 | ||||||||
\(638\) | 4.27629 | 0.169300 | ||||||||
\(639\) | 7.51422 | 0.297258 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.3436 | −0.645534 | −0.322767 | − | 0.946478i | \(-0.604613\pi\) | ||||
−0.322767 | + | 0.946478i | \(0.604613\pi\) | |||||||
\(642\) | −3.33464 | −0.131608 | ||||||||
\(643\) | 6.55839 | 0.258638 | 0.129319 | − | 0.991603i | \(-0.458721\pi\) | ||||
0.129319 | + | 0.991603i | \(0.458721\pi\) | |||||||
\(644\) | 0.706585 | 0.0278434 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.4696 | −0.529953 | ||||||||
\(647\) | −16.5455 | −0.650470 | −0.325235 | − | 0.945633i | \(-0.605443\pi\) | ||||
−0.325235 | + | 0.945633i | \(0.605443\pi\) | |||||||
\(648\) | −9.56214 | −0.375637 | ||||||||
\(649\) | 9.27523 | 0.364085 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.8006 | −0.501697 | ||||||||
\(652\) | 9.92453 | 0.388675 | ||||||||
\(653\) | 12.7408 | 0.498587 | 0.249294 | − | 0.968428i | \(-0.419802\pi\) | ||||
0.249294 | + | 0.968428i | \(0.419802\pi\) | |||||||
\(654\) | 33.8031 | 1.32181 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.0876 | 0.393853 | ||||||||
\(657\) | 29.2764 | 1.14218 | ||||||||
\(658\) | 5.58830 | 0.217855 | ||||||||
\(659\) | −23.8094 | −0.927484 | −0.463742 | − | 0.885970i | \(-0.653493\pi\) | ||||
−0.463742 | + | 0.885970i | \(0.653493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.9323 | 0.969754 | 0.484877 | − | 0.874582i | \(-0.338864\pi\) | ||||
0.484877 | + | 0.874582i | \(0.338864\pi\) | |||||||
\(662\) | −15.6225 | −0.607187 | ||||||||
\(663\) | 17.1333 | 0.665403 | ||||||||
\(664\) | 12.7068 | 0.493119 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.2036 | −0.550377 | ||||||||
\(667\) | 5.72371 | 0.221623 | ||||||||
\(668\) | −11.9089 | −0.460769 | ||||||||
\(669\) | 43.8509 | 1.69537 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.17556 | 0.0453822 | ||||||||
\(672\) | −1.70156 | −0.0656392 | ||||||||
\(673\) | −5.48050 | −0.211258 | −0.105629 | − | 0.994406i | \(-0.533686\pi\) | ||||
−0.105629 | + | 0.994406i | \(0.533686\pi\) | |||||||
\(674\) | −16.6965 | −0.643127 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.3271 | −0.435657 | ||||||||
\(677\) | −1.75255 | −0.0673560 | −0.0336780 | − | 0.999433i | \(-0.510722\pi\) | ||||
−0.0336780 | + | 0.999433i | \(0.510722\pi\) | |||||||
\(678\) | 39.2782 | 1.50847 | ||||||||
\(679\) | 1.06040 | 0.0406944 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.6013 | 1.74745 | ||||||||
\(682\) | 5.62049 | 0.215220 | ||||||||
\(683\) | −23.5091 | −0.899552 | −0.449776 | − | 0.893141i | \(-0.648496\pi\) | ||||
−0.449776 | + | 0.893141i | \(0.648496\pi\) | |||||||
\(684\) | 6.85429 | 0.262080 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.53942 | −0.364217 | ||||||||
\(687\) | 20.3834 | 0.777673 | ||||||||
\(688\) | −5.34045 | −0.203603 | ||||||||
\(689\) | 7.56157 | 0.288073 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.4834 | −0.817269 | −0.408634 | − | 0.912698i | \(-0.633995\pi\) | ||||
−0.408634 | + | 0.912698i | \(0.633995\pi\) | |||||||
\(692\) | 2.91391 | 0.110770 | ||||||||
\(693\) | 1.47770 | 0.0561330 | ||||||||
\(694\) | 16.3981 | 0.622463 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.7835 | −0.522463 | ||||||||
\(697\) | −55.4890 | −2.10180 | ||||||||
\(698\) | −1.86165 | −0.0704645 | ||||||||
\(699\) | −40.0573 | −1.51511 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.62985 | 0.363714 | 0.181857 | − | 0.983325i | \(-0.441789\pi\) | ||||
0.181857 | + | 0.983325i | \(0.441789\pi\) | |||||||
\(702\) | 0.625517 | 0.0236086 | ||||||||
\(703\) | −12.4251 | −0.468621 | ||||||||
\(704\) | 0.747120 | 0.0281581 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.8408 | −0.972532 | ||||||||
\(707\) | −11.3387 | −0.426437 | ||||||||
\(708\) | −29.8963 | −1.12357 | ||||||||
\(709\) | 11.8970 | 0.446801 | 0.223400 | − | 0.974727i | \(-0.428284\pi\) | ||||
0.223400 | + | 0.974727i | \(0.428284\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.3347 | −0.687606 | ||||||||
\(712\) | 13.6426 | 0.511279 | ||||||||
\(713\) | 7.52288 | 0.281734 | ||||||||
\(714\) | 9.35985 | 0.350283 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.3663 | 0.723754 | ||||||||
\(717\) | 38.7327 | 1.44650 | ||||||||
\(718\) | 8.72223 | 0.325511 | ||||||||
\(719\) | 24.2949 | 0.906046 | 0.453023 | − | 0.891499i | \(-0.350345\pi\) | ||||
0.453023 | + | 0.891499i | \(0.350345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.70598 | 0.249744 | ||||||||
\(722\) | −13.0040 | −0.483957 | ||||||||
\(723\) | 67.7371 | 2.51917 | ||||||||
\(724\) | 17.5986 | 0.654045 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.1454 | 0.933234 | ||||||||
\(727\) | 6.25721 | 0.232067 | 0.116034 | − | 0.993245i | \(-0.462982\pi\) | ||||
0.116034 | + | 0.993245i | \(0.462982\pi\) | |||||||
\(728\) | 0.913908 | 0.0338717 | ||||||||
\(729\) | −23.2723 | −0.861935 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.3764 | 1.08653 | ||||||||
\(732\) | −3.78913 | −0.140050 | ||||||||
\(733\) | −37.3304 | −1.37883 | −0.689415 | − | 0.724367i | \(-0.742132\pi\) | ||||
−0.689415 | + | 0.724367i | \(0.742132\pi\) | |||||||
\(734\) | 25.5958 | 0.944759 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 3.92939 | 0.144741 | ||||||||
\(738\) | 28.2369 | 1.03941 | ||||||||
\(739\) | −26.9889 | −0.992802 | −0.496401 | − | 0.868093i | \(-0.665345\pi\) | ||||
−0.496401 | + | 0.868093i | \(0.665345\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.62699 | −0.280185 | ||||||||
\(742\) | 4.13084 | 0.151648 | ||||||||
\(743\) | −32.1544 | −1.17963 | −0.589815 | − | 0.807538i | \(-0.700799\pi\) | ||||
−0.589815 | + | 0.807538i | \(0.700799\pi\) | |||||||
\(744\) | −18.1162 | −0.664172 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.2125 | −0.630196 | ||||||||
\(747\) | 35.5685 | 1.30138 | ||||||||
\(748\) | −4.10971 | −0.150266 | ||||||||
\(749\) | 0.978433 | 0.0357512 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.7865 | 1.45183 | 0.725915 | − | 0.687785i | \(-0.241417\pi\) | ||||
0.725915 | + | 0.687785i | \(0.241417\pi\) | |||||||
\(752\) | 7.90888 | 0.288407 | ||||||||
\(753\) | 49.5524 | 1.80579 | ||||||||
\(754\) | 7.40312 | 0.269606 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.341716 | 0.0124281 | ||||||||
\(757\) | −26.9961 | −0.981189 | −0.490595 | − | 0.871388i | \(-0.663220\pi\) | ||||
−0.490595 | + | 0.871388i | \(0.663220\pi\) | |||||||
\(758\) | 23.0339 | 0.836628 | ||||||||
\(759\) | −1.79917 | −0.0653059 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.21529 | −0.261554 | −0.130777 | − | 0.991412i | \(-0.541747\pi\) | ||||
−0.130777 | + | 0.991412i | \(0.541747\pi\) | |||||||
\(762\) | 6.58683 | 0.238616 | ||||||||
\(763\) | −9.91833 | −0.359068 | ||||||||
\(764\) | 20.3578 | 0.736518 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.81777 | 0.137942 | ||||||||
\(767\) | 16.0573 | 0.579795 | ||||||||
\(768\) | −2.40815 | −0.0868965 | ||||||||
\(769\) | 6.40916 | 0.231120 | 0.115560 | − | 0.993300i | \(-0.463134\pi\) | ||||
0.115560 | + | 0.993300i | \(0.463134\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.5786 | −1.46140 | ||||||||
\(772\) | −1.41317 | −0.0508611 | ||||||||
\(773\) | −50.2483 | −1.80730 | −0.903652 | − | 0.428267i | \(-0.859124\pi\) | ||||
−0.903652 | + | 0.428267i | \(0.859124\pi\) | |||||||
\(774\) | −14.9488 | −0.537325 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.50074 | 0.0538733 | ||||||||
\(777\) | 8.63406 | 0.309745 | ||||||||
\(778\) | −8.25435 | −0.295933 | ||||||||
\(779\) | 24.7012 | 0.885014 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00560 | 0.0717660 | ||||||||
\(782\) | −5.50074 | −0.196706 | ||||||||
\(783\) | 2.76808 | 0.0989231 | ||||||||
\(784\) | −6.50074 | −0.232169 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.7936 | 0.706013 | ||||||||
\(787\) | −2.70933 | −0.0965772 | −0.0482886 | − | 0.998833i | \(-0.515377\pi\) | ||||
−0.0482886 | + | 0.998833i | \(0.515377\pi\) | |||||||
\(788\) | 4.92395 | 0.175409 | ||||||||
\(789\) | −59.6329 | −2.12299 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.5248 | −0.409774 | ||||||||
\(792\) | 2.09132 | 0.0743118 | ||||||||
\(793\) | 2.03514 | 0.0722699 | ||||||||
\(794\) | 12.4967 | 0.443492 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.3105 | −0.365447 | ||||||||
\(797\) | 15.1452 | 0.536471 | 0.268236 | − | 0.963353i | \(-0.413559\pi\) | ||||
0.268236 | + | 0.963353i | \(0.413559\pi\) | |||||||
\(798\) | −4.16658 | −0.147495 | ||||||||
\(799\) | −43.5047 | −1.53909 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.1881 | 1.34931 | ||||||||
\(802\) | 34.5660 | 1.22057 | ||||||||
\(803\) | 7.81408 | 0.275753 | ||||||||
\(804\) | −12.6654 | −0.446673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.73020 | 0.342732 | ||||||||
\(807\) | 8.55259 | 0.301065 | ||||||||
\(808\) | −16.0472 | −0.564540 | ||||||||
\(809\) | −3.94373 | −0.138654 | −0.0693270 | − | 0.997594i | \(-0.522085\pi\) | ||||
−0.0693270 | + | 0.997594i | \(0.522085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1521 | −0.496947 | −0.248474 | − | 0.968639i | \(-0.579929\pi\) | ||||
−0.248474 | + | 0.968639i | \(0.579929\pi\) | |||||||
\(812\) | 4.04429 | 0.141927 | ||||||||
\(813\) | 66.1664 | 2.32056 | ||||||||
\(814\) | −3.79103 | −0.132876 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.2466 | 0.463723 | ||||||||
\(817\) | −13.0771 | −0.457508 | ||||||||
\(818\) | 12.0499 | 0.421314 | ||||||||
\(819\) | 2.55819 | 0.0893903 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.0094 | 1.29164 | 0.645818 | − | 0.763491i | \(-0.276516\pi\) | ||||
0.645818 | + | 0.763491i | \(0.276516\pi\) | |||||||
\(822\) | 55.0140 | 1.91883 | ||||||||
\(823\) | 18.1208 | 0.631651 | 0.315826 | − | 0.948817i | \(-0.397719\pi\) | ||||
0.315826 | + | 0.948817i | \(0.397719\pi\) | |||||||
\(824\) | 9.49069 | 0.330624 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.77201 | 0.305217 | ||||||||
\(827\) | 41.5398 | 1.44448 | 0.722240 | − | 0.691643i | \(-0.243113\pi\) | ||||
0.722240 | + | 0.691643i | \(0.243113\pi\) | |||||||
\(828\) | 2.79917 | 0.0972781 | ||||||||
\(829\) | 21.3976 | 0.743171 | 0.371585 | − | 0.928399i | \(-0.378814\pi\) | ||||
0.371585 | + | 0.928399i | \(0.378814\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.7307 | −0.927277 | ||||||||
\(832\) | 1.29341 | 0.0448411 | ||||||||
\(833\) | 35.7588 | 1.23897 | ||||||||
\(834\) | −9.05581 | −0.313577 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.82946 | 0.0632732 | ||||||||
\(837\) | 3.63819 | 0.125754 | ||||||||
\(838\) | 38.6157 | 1.33396 | ||||||||
\(839\) | −41.3437 | −1.42734 | −0.713672 | − | 0.700480i | \(-0.752969\pi\) | ||||
−0.713672 | + | 0.700480i | \(0.752969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.76081 | 0.129683 | ||||||||
\(842\) | 32.7384 | 1.12824 | ||||||||
\(843\) | −31.4161 | −1.08203 | ||||||||
\(844\) | 11.4161 | 0.392959 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 22.1384 | 0.761132 | ||||||||
\(847\) | −7.37803 | −0.253512 | ||||||||
\(848\) | 5.84621 | 0.200760 | ||||||||
\(849\) | 8.06848 | 0.276910 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.07420 | −0.173941 | ||||||||
\(852\) | −6.46453 | −0.221471 | ||||||||
\(853\) | 56.0373 | 1.91868 | 0.959340 | − | 0.282252i | \(-0.0910814\pi\) | ||||
0.959340 | + | 0.282252i | \(0.0910814\pi\) | |||||||
\(854\) | 1.11179 | 0.0380445 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.38473 | 0.0473292 | ||||||||
\(857\) | 43.4734 | 1.48502 | 0.742512 | − | 0.669833i | \(-0.233634\pi\) | ||||
0.742512 | + | 0.669833i | \(0.233634\pi\) | |||||||
\(858\) | −2.32708 | −0.0794452 | ||||||||
\(859\) | 11.1599 | 0.380771 | 0.190386 | − | 0.981709i | \(-0.439026\pi\) | ||||
0.190386 | + | 0.981709i | \(0.439026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.1646 | −0.584969 | ||||||||
\(862\) | −35.7739 | −1.21846 | ||||||||
\(863\) | −32.2767 | −1.09871 | −0.549356 | − | 0.835589i | \(-0.685127\pi\) | ||||
−0.549356 | + | 0.835589i | \(0.685127\pi\) | |||||||
\(864\) | 0.483617 | 0.0164530 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.5682 | −0.359123 | ||||||||
\(867\) | −31.9275 | −1.08431 | ||||||||
\(868\) | 5.31556 | 0.180422 | ||||||||
\(869\) | −4.89367 | −0.166006 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.80256 | 0.230496 | ||||||||
\(872\) | −14.0370 | −0.475352 | ||||||||
\(873\) | 4.20083 | 0.142176 | ||||||||
\(874\) | 2.44868 | 0.0828279 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −25.1867 | −0.850978 | ||||||||
\(877\) | 9.52493 | 0.321634 | 0.160817 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160817 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(878\) | −27.6642 | −0.933621 | ||||||||
\(879\) | 21.4132 | 0.722248 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.1585 | 1.65619 | 0.828096 | − | 0.560586i | \(-0.189424\pi\) | ||||
0.828096 | + | 0.560586i | \(0.189424\pi\) | |||||||
\(882\) | −18.1967 | −0.612715 | ||||||||
\(883\) | −33.1379 | −1.11518 | −0.557590 | − | 0.830117i | \(-0.688274\pi\) | ||||
−0.557590 | + | 0.830117i | \(0.688274\pi\) | |||||||
\(884\) | −7.11473 | −0.239294 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.8082 | 1.23659 | ||||||||
\(887\) | 1.59084 | 0.0534153 | 0.0267076 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267076 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(888\) | 12.2194 | 0.410057 | ||||||||
\(889\) | −1.93267 | −0.0648197 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.14407 | −0.239335 | ||||||||
\(892\) | −18.2094 | −0.609695 | ||||||||
\(893\) | 19.3663 | 0.648070 | ||||||||
\(894\) | 4.59027 | 0.153522 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.706585 | 0.0236054 | ||||||||
\(897\) | −3.11473 | −0.103998 | ||||||||
\(898\) | 18.2711 | 0.609715 | ||||||||
\(899\) | 43.0588 | 1.43609 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.1584 | −1.07135 | ||||||||
\(902\) | 7.53662 | 0.250942 | ||||||||
\(903\) | 9.08710 | 0.302400 | ||||||||
\(904\) | −16.3105 | −0.542480 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 22.6840 | 0.753624 | ||||||||
\(907\) | −17.4658 | −0.579942 | −0.289971 | − | 0.957035i | \(-0.593646\pi\) | ||||
−0.289971 | + | 0.957035i | \(0.593646\pi\) | |||||||
\(908\) | −18.9363 | −0.628422 | ||||||||
\(909\) | −44.9190 | −1.48987 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.6050 | −0.715805 | −0.357903 | − | 0.933759i | \(-0.616508\pi\) | ||||
−0.357903 | + | 0.933759i | \(0.616508\pi\) | |||||||
\(912\) | −5.89679 | −0.195262 | ||||||||
\(913\) | 9.49349 | 0.314189 | ||||||||
\(914\) | −27.6326 | −0.914005 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.46433 | −0.279669 | ||||||||
\(917\) | −5.80772 | −0.191788 | ||||||||
\(918\) | −2.66025 | −0.0878013 | ||||||||
\(919\) | −41.7396 | −1.37686 | −0.688432 | − | 0.725301i | \(-0.741701\pi\) | ||||
−0.688432 | + | 0.725301i | \(0.741701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −68.4181 | −2.25445 | ||||||||
\(922\) | 35.5515 | 1.17083 | ||||||||
\(923\) | 3.47210 | 0.114285 | ||||||||
\(924\) | −1.27127 | −0.0418217 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23.9331 | −0.786490 | ||||||||
\(927\) | 26.5661 | 0.872545 | ||||||||
\(928\) | 5.72371 | 0.187890 | ||||||||
\(929\) | 38.8505 | 1.27464 | 0.637322 | − | 0.770597i | \(-0.280042\pi\) | ||||
0.637322 | + | 0.770597i | \(0.280042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.9182 | −0.521699 | ||||||||
\(932\) | 16.6341 | 0.544867 | ||||||||
\(933\) | 67.4533 | 2.20832 | ||||||||
\(934\) | −19.9035 | −0.651262 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.62049 | 0.118340 | ||||||||
\(937\) | −33.1555 | −1.08314 | −0.541571 | − | 0.840655i | \(-0.682170\pi\) | ||||
−0.541571 | + | 0.840655i | \(0.682170\pi\) | |||||||
\(938\) | 3.71620 | 0.121338 | ||||||||
\(939\) | 17.8897 | 0.583808 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.8004 | −1.10186 | −0.550931 | − | 0.834551i | \(-0.685727\pi\) | ||||
−0.550931 | + | 0.834551i | \(0.685727\pi\) | |||||||
\(942\) | −10.6754 | −0.347823 | ||||||||
\(943\) | 10.0876 | 0.328496 | ||||||||
\(944\) | 12.4146 | 0.404062 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.98995 | −0.129725 | ||||||||
\(947\) | 20.2406 | 0.657730 | 0.328865 | − | 0.944377i | \(-0.393334\pi\) | ||||
0.328865 | + | 0.944377i | \(0.393334\pi\) | |||||||
\(948\) | 15.7735 | 0.512299 | ||||||||
\(949\) | 13.5277 | 0.439129 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.6622 | −1.02672 | ||||||||
\(952\) | −3.88674 | −0.125970 | ||||||||
\(953\) | −28.3885 | −0.919592 | −0.459796 | − | 0.888024i | \(-0.652078\pi\) | ||||
−0.459796 | + | 0.888024i | \(0.652078\pi\) | |||||||
\(954\) | 16.3646 | 0.529822 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −16.0840 | −0.520194 | ||||||||
\(957\) | −10.2979 | −0.332885 | ||||||||
\(958\) | −3.86206 | −0.124777 | ||||||||
\(959\) | −16.1419 | −0.521249 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5937 | 0.825604 | ||||||||
\(962\) | −6.56304 | −0.211601 | ||||||||
\(963\) | 3.87611 | 0.124906 | ||||||||
\(964\) | −28.1283 | −0.905952 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.70156 | −0.0547469 | ||||||||
\(967\) | −57.6163 | −1.85282 | −0.926408 | − | 0.376522i | \(-0.877120\pi\) | ||||
−0.926408 | + | 0.376522i | \(0.877120\pi\) | |||||||
\(968\) | −10.4418 | −0.335613 | ||||||||
\(969\) | 32.4367 | 1.04202 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.47686 | −0.0473946 | −0.0236973 | − | 0.999719i | \(-0.507544\pi\) | ||||
−0.0236973 | + | 0.999719i | \(0.507544\pi\) | |||||||
\(972\) | 21.5762 | 0.692057 | ||||||||
\(973\) | 2.65711 | 0.0851829 | ||||||||
\(974\) | −15.1499 | −0.485433 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.57346 | 0.0503653 | ||||||||
\(977\) | −11.5709 | −0.370185 | −0.185092 | − | 0.982721i | \(-0.559258\pi\) | ||||
−0.185092 | + | 0.982721i | \(0.559258\pi\) | |||||||
\(978\) | −23.8997 | −0.764229 | ||||||||
\(979\) | 10.1927 | 0.325760 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.2920 | −1.25450 | ||||||||
\(982\) | −6.86312 | −0.219011 | ||||||||
\(983\) | 37.5275 | 1.19694 | 0.598470 | − | 0.801145i | \(-0.295775\pi\) | ||||
0.598470 | + | 0.801145i | \(0.295775\pi\) | |||||||
\(984\) | −24.2923 | −0.774412 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −31.4846 | −1.00267 | ||||||||
\(987\) | −13.4575 | −0.428356 | ||||||||
\(988\) | 3.16716 | 0.100761 | ||||||||
\(989\) | −5.34045 | −0.169816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.87860 | 0.313804 | 0.156902 | − | 0.987614i | \(-0.449849\pi\) | ||||
0.156902 | + | 0.987614i | \(0.449849\pi\) | |||||||
\(992\) | 7.52288 | 0.238852 | ||||||||
\(993\) | 37.6214 | 1.19388 | ||||||||
\(994\) | 1.89679 | 0.0601624 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −30.5998 | −0.969593 | ||||||||
\(997\) | −53.6506 | −1.69913 | −0.849565 | − | 0.527484i | \(-0.823135\pi\) | ||||
−0.849565 | + | 0.527484i | \(0.823135\pi\) | |||||||
\(998\) | −18.6809 | −0.591333 | ||||||||
\(999\) | −2.45397 | −0.0776401 |
(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 | 1150.2.a.s.1.1 | 4 | ||
4.3 | odd | 2 | 9200.2.a.cj.1.4 | 4 | |||
5.2 | odd | 4 | 230.2.b.b.139.8 | yes | 8 | ||
5.3 | odd | 4 | 230.2.b.b.139.1 | ✓ | 8 | ||
5.4 | even | 2 | 1150.2.a.r.1.4 | 4 | |||
15.2 | even | 4 | 2070.2.d.f.829.1 | 8 | |||
15.8 | even | 4 | 2070.2.d.f.829.5 | 8 | |||
20.3 | even | 4 | 1840.2.e.e.369.7 | 8 | |||
20.7 | even | 4 | 1840.2.e.e.369.2 | 8 | |||
20.19 | odd | 2 | 9200.2.a.cr.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.b.139.1 | ✓ | 8 | 5.3 | odd | 4 | ||
230.2.b.b.139.8 | yes | 8 | 5.2 | odd | 4 | ||
1150.2.a.r.1.4 | 4 | 5.4 | even | 2 | |||
1150.2.a.s.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1840.2.e.e.369.2 | 8 | 20.7 | even | 4 | |||
1840.2.e.e.369.7 | 8 | 20.3 | even | 4 | |||
2070.2.d.f.829.1 | 8 | 15.2 | even | 4 | |||
2070.2.d.f.829.5 | 8 | 15.8 | even | 4 | |||
9200.2.a.cj.1.4 | 4 | 4.3 | odd | 2 | |||
9200.2.a.cr.1.1 | 4 | 20.19 | odd | 2 |