Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.24319 | 1.58618 | 0.793088 | − | 0.609107i | \(-0.208472\pi\) | ||||
0.793088 | + | 0.609107i | \(0.208472\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.03191 | 1.51596 | ||||||||
\(5\) | −4.27976 | −1.91397 | −0.956984 | − | 0.290140i | \(-0.906298\pi\) | ||||
−0.956984 | + | 0.290140i | \(0.906298\pi\) | |||||||
\(6\) | 2.24319 | 0.915779 | ||||||||
\(7\) | −0.0653339 | −0.0246939 | −0.0123469 | − | 0.999924i | \(-0.503930\pi\) | ||||
−0.0123469 | + | 0.999924i | \(0.503930\pi\) | |||||||
\(8\) | 2.31477 | 0.818396 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −9.60033 | −3.03589 | ||||||||
\(11\) | 3.23018 | 0.973936 | 0.486968 | − | 0.873420i | \(-0.338103\pi\) | ||||
0.486968 | + | 0.873420i | \(0.338103\pi\) | |||||||
\(12\) | 3.03191 | 0.875237 | ||||||||
\(13\) | −2.88004 | −0.798779 | −0.399389 | − | 0.916781i | \(-0.630778\pi\) | ||||
−0.399389 | + | 0.916781i | \(0.630778\pi\) | |||||||
\(14\) | −0.146556 | −0.0391688 | ||||||||
\(15\) | −4.27976 | −1.10503 | ||||||||
\(16\) | −0.871339 | −0.217835 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 2.24319 | 0.528725 | ||||||||
\(19\) | 7.45327 | 1.70990 | 0.854948 | − | 0.518713i | \(-0.173589\pi\) | ||||
0.854948 | + | 0.518713i | \(0.173589\pi\) | |||||||
\(20\) | −12.9759 | −2.90149 | ||||||||
\(21\) | −0.0653339 | −0.0142570 | ||||||||
\(22\) | 7.24592 | 1.54483 | ||||||||
\(23\) | −1.14406 | −0.238552 | −0.119276 | − | 0.992861i | \(-0.538057\pi\) | ||||
−0.119276 | + | 0.992861i | \(0.538057\pi\) | |||||||
\(24\) | 2.31477 | 0.472501 | ||||||||
\(25\) | 13.3164 | 2.66328 | ||||||||
\(26\) | −6.46048 | −1.26700 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.198086 | −0.0374348 | ||||||||
\(29\) | 7.28872 | 1.35348 | 0.676740 | − | 0.736222i | \(-0.263392\pi\) | ||||
0.676740 | + | 0.736222i | \(0.263392\pi\) | |||||||
\(30\) | −9.60033 | −1.75277 | ||||||||
\(31\) | 3.60094 | 0.646747 | 0.323374 | − | 0.946271i | \(-0.395183\pi\) | ||||
0.323374 | + | 0.946271i | \(0.395183\pi\) | |||||||
\(32\) | −6.58413 | −1.16392 | ||||||||
\(33\) | 3.23018 | 0.562302 | ||||||||
\(34\) | 2.24319 | 0.384704 | ||||||||
\(35\) | 0.279613 | 0.0472633 | ||||||||
\(36\) | 3.03191 | 0.505318 | ||||||||
\(37\) | −2.70010 | −0.443893 | −0.221947 | − | 0.975059i | \(-0.571241\pi\) | ||||
−0.221947 | + | 0.975059i | \(0.571241\pi\) | |||||||
\(38\) | 16.7191 | 2.71220 | ||||||||
\(39\) | −2.88004 | −0.461175 | ||||||||
\(40\) | −9.90668 | −1.56638 | ||||||||
\(41\) | 12.7049 | 1.98418 | 0.992089 | − | 0.125533i | \(-0.0400641\pi\) | ||||
0.992089 | + | 0.125533i | \(0.0400641\pi\) | |||||||
\(42\) | −0.146556 | −0.0226141 | ||||||||
\(43\) | 2.63923 | 0.402479 | 0.201239 | − | 0.979542i | \(-0.435503\pi\) | ||||
0.201239 | + | 0.979542i | \(0.435503\pi\) | |||||||
\(44\) | 9.79362 | 1.47644 | ||||||||
\(45\) | −4.27976 | −0.637990 | ||||||||
\(46\) | −2.56634 | −0.378386 | ||||||||
\(47\) | 5.16451 | 0.753321 | 0.376661 | − | 0.926351i | \(-0.377072\pi\) | ||||
0.376661 | + | 0.926351i | \(0.377072\pi\) | |||||||
\(48\) | −0.871339 | −0.125767 | ||||||||
\(49\) | −6.99573 | −0.999390 | ||||||||
\(50\) | 29.8712 | 4.22442 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −8.73202 | −1.21091 | ||||||||
\(53\) | −8.09202 | −1.11152 | −0.555762 | − | 0.831341i | \(-0.687573\pi\) | ||||
−0.555762 | + | 0.831341i | \(0.687573\pi\) | |||||||
\(54\) | 2.24319 | 0.305260 | ||||||||
\(55\) | −13.8244 | −1.86408 | ||||||||
\(56\) | −0.151233 | −0.0202094 | ||||||||
\(57\) | 7.45327 | 0.987209 | ||||||||
\(58\) | 16.3500 | 2.14686 | ||||||||
\(59\) | 12.2898 | 1.60000 | 0.800001 | − | 0.599999i | \(-0.204832\pi\) | ||||
0.800001 | + | 0.599999i | \(0.204832\pi\) | |||||||
\(60\) | −12.9759 | −1.67518 | ||||||||
\(61\) | 4.85946 | 0.622190 | 0.311095 | − | 0.950379i | \(-0.399304\pi\) | ||||
0.311095 | + | 0.950379i | \(0.399304\pi\) | |||||||
\(62\) | 8.07759 | 1.02585 | ||||||||
\(63\) | −0.0653339 | −0.00823129 | ||||||||
\(64\) | −13.0268 | −1.62835 | ||||||||
\(65\) | 12.3259 | 1.52884 | ||||||||
\(66\) | 7.24592 | 0.891911 | ||||||||
\(67\) | −7.91890 | −0.967448 | −0.483724 | − | 0.875221i | \(-0.660716\pi\) | ||||
−0.483724 | + | 0.875221i | \(0.660716\pi\) | |||||||
\(68\) | 3.03191 | 0.367673 | ||||||||
\(69\) | −1.14406 | −0.137728 | ||||||||
\(70\) | 0.627227 | 0.0749679 | ||||||||
\(71\) | 1.84117 | 0.218507 | 0.109253 | − | 0.994014i | \(-0.465154\pi\) | ||||
0.109253 | + | 0.994014i | \(0.465154\pi\) | |||||||
\(72\) | 2.31477 | 0.272799 | ||||||||
\(73\) | −2.31371 | −0.270799 | −0.135400 | − | 0.990791i | \(-0.543232\pi\) | ||||
−0.135400 | + | 0.990791i | \(0.543232\pi\) | |||||||
\(74\) | −6.05684 | −0.704093 | ||||||||
\(75\) | 13.3164 | 1.53764 | ||||||||
\(76\) | 22.5976 | 2.59213 | ||||||||
\(77\) | −0.211040 | −0.0240503 | ||||||||
\(78\) | −6.46048 | −0.731505 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 3.72913 | 0.416929 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 28.4996 | 3.14726 | ||||||||
\(83\) | 11.4658 | 1.25853 | 0.629265 | − | 0.777191i | \(-0.283356\pi\) | ||||
0.629265 | + | 0.777191i | \(0.283356\pi\) | |||||||
\(84\) | −0.198086 | −0.0216130 | ||||||||
\(85\) | −4.27976 | −0.464206 | ||||||||
\(86\) | 5.92030 | 0.638402 | ||||||||
\(87\) | 7.28872 | 0.781432 | ||||||||
\(88\) | 7.47714 | 0.797066 | ||||||||
\(89\) | −6.86540 | −0.727731 | −0.363866 | − | 0.931451i | \(-0.618543\pi\) | ||||
−0.363866 | + | 0.931451i | \(0.618543\pi\) | |||||||
\(90\) | −9.60033 | −1.01196 | ||||||||
\(91\) | 0.188164 | 0.0197249 | ||||||||
\(92\) | −3.46868 | −0.361635 | ||||||||
\(93\) | 3.60094 | 0.373400 | ||||||||
\(94\) | 11.5850 | 1.19490 | ||||||||
\(95\) | −31.8982 | −3.27269 | ||||||||
\(96\) | −6.58413 | −0.671990 | ||||||||
\(97\) | 8.64709 | 0.877979 | 0.438990 | − | 0.898492i | \(-0.355337\pi\) | ||||
0.438990 | + | 0.898492i | \(0.355337\pi\) | |||||||
\(98\) | −15.6928 | −1.58521 | ||||||||
\(99\) | 3.23018 | 0.324645 | ||||||||
\(100\) | 40.3741 | 4.03741 | ||||||||
\(101\) | −13.6386 | −1.35710 | −0.678548 | − | 0.734556i | \(-0.737390\pi\) | ||||
−0.678548 | + | 0.734556i | \(0.737390\pi\) | |||||||
\(102\) | 2.24319 | 0.222109 | ||||||||
\(103\) | 7.16588 | 0.706075 | 0.353038 | − | 0.935609i | \(-0.385149\pi\) | ||||
0.353038 | + | 0.935609i | \(0.385149\pi\) | |||||||
\(104\) | −6.66663 | −0.653717 | ||||||||
\(105\) | 0.279613 | 0.0272875 | ||||||||
\(106\) | −18.1520 | −1.76307 | ||||||||
\(107\) | 9.38280 | 0.907070 | 0.453535 | − | 0.891238i | \(-0.350163\pi\) | ||||
0.453535 | + | 0.891238i | \(0.350163\pi\) | |||||||
\(108\) | 3.03191 | 0.291746 | ||||||||
\(109\) | 8.45836 | 0.810164 | 0.405082 | − | 0.914280i | \(-0.367243\pi\) | ||||
0.405082 | + | 0.914280i | \(0.367243\pi\) | |||||||
\(110\) | −31.0108 | −2.95676 | ||||||||
\(111\) | −2.70010 | −0.256282 | ||||||||
\(112\) | 0.0569280 | 0.00537919 | ||||||||
\(113\) | −3.94608 | −0.371216 | −0.185608 | − | 0.982624i | \(-0.559425\pi\) | ||||
−0.185608 | + | 0.982624i | \(0.559425\pi\) | |||||||
\(114\) | 16.7191 | 1.56589 | ||||||||
\(115\) | 4.89629 | 0.456582 | ||||||||
\(116\) | 22.0987 | 2.05182 | ||||||||
\(117\) | −2.88004 | −0.266260 | ||||||||
\(118\) | 27.5685 | 2.53789 | ||||||||
\(119\) | −0.0653339 | −0.00598914 | ||||||||
\(120\) | −9.90668 | −0.904352 | ||||||||
\(121\) | −0.565931 | −0.0514483 | ||||||||
\(122\) | 10.9007 | 0.986902 | ||||||||
\(123\) | 12.7049 | 1.14557 | ||||||||
\(124\) | 10.9177 | 0.980440 | ||||||||
\(125\) | −35.5921 | −3.18346 | ||||||||
\(126\) | −0.146556 | −0.0130563 | ||||||||
\(127\) | −17.7999 | −1.57948 | −0.789741 | − | 0.613440i | \(-0.789785\pi\) | ||||
−0.789741 | + | 0.613440i | \(0.789785\pi\) | |||||||
\(128\) | −16.0533 | −1.41893 | ||||||||
\(129\) | 2.63923 | 0.232371 | ||||||||
\(130\) | 27.6493 | 2.42501 | ||||||||
\(131\) | 15.1266 | 1.32162 | 0.660809 | − | 0.750554i | \(-0.270213\pi\) | ||||
0.660809 | + | 0.750554i | \(0.270213\pi\) | |||||||
\(132\) | 9.79362 | 0.852425 | ||||||||
\(133\) | −0.486951 | −0.0422240 | ||||||||
\(134\) | −17.7636 | −1.53454 | ||||||||
\(135\) | −4.27976 | −0.368343 | ||||||||
\(136\) | 2.31477 | 0.198490 | ||||||||
\(137\) | 10.9459 | 0.935168 | 0.467584 | − | 0.883949i | \(-0.345125\pi\) | ||||
0.467584 | + | 0.883949i | \(0.345125\pi\) | |||||||
\(138\) | −2.56634 | −0.218461 | ||||||||
\(139\) | −5.85835 | −0.496898 | −0.248449 | − | 0.968645i | \(-0.579921\pi\) | ||||
−0.248449 | + | 0.968645i | \(0.579921\pi\) | |||||||
\(140\) | 0.847763 | 0.0716491 | ||||||||
\(141\) | 5.16451 | 0.434930 | ||||||||
\(142\) | 4.13010 | 0.346590 | ||||||||
\(143\) | −9.30304 | −0.777959 | ||||||||
\(144\) | −0.871339 | −0.0726116 | ||||||||
\(145\) | −31.1940 | −2.59052 | ||||||||
\(146\) | −5.19010 | −0.429536 | ||||||||
\(147\) | −6.99573 | −0.576998 | ||||||||
\(148\) | −8.18645 | −0.672922 | ||||||||
\(149\) | 22.3310 | 1.82943 | 0.914714 | − | 0.404103i | \(-0.132416\pi\) | ||||
0.914714 | + | 0.404103i | \(0.132416\pi\) | |||||||
\(150\) | 29.8712 | 2.43897 | ||||||||
\(151\) | −5.35488 | −0.435774 | −0.217887 | − | 0.975974i | \(-0.569916\pi\) | ||||
−0.217887 | + | 0.975974i | \(0.569916\pi\) | |||||||
\(152\) | 17.2526 | 1.39937 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −0.473404 | −0.0381480 | ||||||||
\(155\) | −15.4112 | −1.23785 | ||||||||
\(156\) | −8.73202 | −0.699121 | ||||||||
\(157\) | −17.8963 | −1.42828 | −0.714141 | − | 0.700002i | \(-0.753183\pi\) | ||||
−0.714141 | + | 0.700002i | \(0.753183\pi\) | |||||||
\(158\) | 2.24319 | 0.178459 | ||||||||
\(159\) | −8.09202 | −0.641739 | ||||||||
\(160\) | 28.1785 | 2.22771 | ||||||||
\(161\) | 0.0747457 | 0.00589078 | ||||||||
\(162\) | 2.24319 | 0.176242 | ||||||||
\(163\) | 11.0501 | 0.865511 | 0.432756 | − | 0.901511i | \(-0.357541\pi\) | ||||
0.432756 | + | 0.901511i | \(0.357541\pi\) | |||||||
\(164\) | 38.5203 | 3.00793 | ||||||||
\(165\) | −13.8244 | −1.07623 | ||||||||
\(166\) | 25.7199 | 1.99625 | ||||||||
\(167\) | −11.6924 | −0.904789 | −0.452394 | − | 0.891818i | \(-0.649430\pi\) | ||||
−0.452394 | + | 0.891818i | \(0.649430\pi\) | |||||||
\(168\) | −0.151233 | −0.0116679 | ||||||||
\(169\) | −4.70538 | −0.361953 | ||||||||
\(170\) | −9.60033 | −0.736312 | ||||||||
\(171\) | 7.45327 | 0.569966 | ||||||||
\(172\) | 8.00191 | 0.610140 | ||||||||
\(173\) | −10.3964 | −0.790424 | −0.395212 | − | 0.918590i | \(-0.629329\pi\) | ||||
−0.395212 | + | 0.918590i | \(0.629329\pi\) | |||||||
\(174\) | 16.3500 | 1.23949 | ||||||||
\(175\) | −0.870010 | −0.0657666 | ||||||||
\(176\) | −2.81458 | −0.212157 | ||||||||
\(177\) | 12.2898 | 0.923762 | ||||||||
\(178\) | −15.4004 | −1.15431 | ||||||||
\(179\) | −26.6599 | −1.99265 | −0.996326 | − | 0.0856454i | \(-0.972705\pi\) | ||||
−0.996326 | + | 0.0856454i | \(0.972705\pi\) | |||||||
\(180\) | −12.9759 | −0.967164 | ||||||||
\(181\) | −14.5419 | −1.08089 | −0.540446 | − | 0.841379i | \(-0.681744\pi\) | ||||
−0.540446 | + | 0.841379i | \(0.681744\pi\) | |||||||
\(182\) | 0.422088 | 0.0312872 | ||||||||
\(183\) | 4.85946 | 0.359221 | ||||||||
\(184\) | −2.64823 | −0.195230 | ||||||||
\(185\) | 11.5558 | 0.849598 | ||||||||
\(186\) | 8.07759 | 0.592278 | ||||||||
\(187\) | 3.23018 | 0.236214 | ||||||||
\(188\) | 15.6583 | 1.14200 | ||||||||
\(189\) | −0.0653339 | −0.00475234 | ||||||||
\(190\) | −71.5538 | −5.19106 | ||||||||
\(191\) | 10.3079 | 0.745853 | 0.372927 | − | 0.927861i | \(-0.378354\pi\) | ||||
0.372927 | + | 0.927861i | \(0.378354\pi\) | |||||||
\(192\) | −13.0268 | −0.940127 | ||||||||
\(193\) | 1.90532 | 0.137148 | 0.0685741 | − | 0.997646i | \(-0.478155\pi\) | ||||
0.0685741 | + | 0.997646i | \(0.478155\pi\) | |||||||
\(194\) | 19.3971 | 1.39263 | ||||||||
\(195\) | 12.3259 | 0.882675 | ||||||||
\(196\) | −21.2104 | −1.51503 | ||||||||
\(197\) | 5.83384 | 0.415644 | 0.207822 | − | 0.978167i | \(-0.433363\pi\) | ||||
0.207822 | + | 0.978167i | \(0.433363\pi\) | |||||||
\(198\) | 7.24592 | 0.514945 | ||||||||
\(199\) | 5.83516 | 0.413643 | 0.206822 | − | 0.978379i | \(-0.433688\pi\) | ||||
0.206822 | + | 0.978379i | \(0.433688\pi\) | |||||||
\(200\) | 30.8244 | 2.17961 | ||||||||
\(201\) | −7.91890 | −0.558556 | ||||||||
\(202\) | −30.5941 | −2.15259 | ||||||||
\(203\) | −0.476200 | −0.0334227 | ||||||||
\(204\) | 3.03191 | 0.212276 | ||||||||
\(205\) | −54.3742 | −3.79766 | ||||||||
\(206\) | 16.0744 | 1.11996 | ||||||||
\(207\) | −1.14406 | −0.0795175 | ||||||||
\(208\) | 2.50949 | 0.174002 | ||||||||
\(209\) | 24.0754 | 1.66533 | ||||||||
\(210\) | 0.627227 | 0.0432828 | ||||||||
\(211\) | −7.24857 | −0.499012 | −0.249506 | − | 0.968373i | \(-0.580268\pi\) | ||||
−0.249506 | + | 0.968373i | \(0.580268\pi\) | |||||||
\(212\) | −24.5343 | −1.68502 | ||||||||
\(213\) | 1.84117 | 0.126155 | ||||||||
\(214\) | 21.0474 | 1.43877 | ||||||||
\(215\) | −11.2953 | −0.770331 | ||||||||
\(216\) | 2.31477 | 0.157500 | ||||||||
\(217\) | −0.235263 | −0.0159707 | ||||||||
\(218\) | 18.9737 | 1.28506 | ||||||||
\(219\) | −2.31371 | −0.156346 | ||||||||
\(220\) | −41.9144 | −2.82587 | ||||||||
\(221\) | −2.88004 | −0.193732 | ||||||||
\(222\) | −6.05684 | −0.406508 | ||||||||
\(223\) | −15.7699 | −1.05603 | −0.528014 | − | 0.849235i | \(-0.677063\pi\) | ||||
−0.528014 | + | 0.849235i | \(0.677063\pi\) | |||||||
\(224\) | 0.430167 | 0.0287417 | ||||||||
\(225\) | 13.3164 | 0.887759 | ||||||||
\(226\) | −8.85181 | −0.588813 | ||||||||
\(227\) | −11.1561 | −0.740457 | −0.370228 | − | 0.928941i | \(-0.620721\pi\) | ||||
−0.370228 | + | 0.928941i | \(0.620721\pi\) | |||||||
\(228\) | 22.5976 | 1.49657 | ||||||||
\(229\) | −2.46171 | −0.162674 | −0.0813370 | − | 0.996687i | \(-0.525919\pi\) | ||||
−0.0813370 | + | 0.996687i | \(0.525919\pi\) | |||||||
\(230\) | 10.9833 | 0.724219 | ||||||||
\(231\) | −0.211040 | −0.0138854 | ||||||||
\(232\) | 16.8717 | 1.10768 | ||||||||
\(233\) | 6.94093 | 0.454716 | 0.227358 | − | 0.973811i | \(-0.426991\pi\) | ||||
0.227358 | + | 0.973811i | \(0.426991\pi\) | |||||||
\(234\) | −6.46048 | −0.422335 | ||||||||
\(235\) | −22.1029 | −1.44183 | ||||||||
\(236\) | 37.2617 | 2.42553 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | −0.146556 | −0.00949984 | ||||||||
\(239\) | 10.5045 | 0.679479 | 0.339739 | − | 0.940520i | \(-0.389661\pi\) | ||||
0.339739 | + | 0.940520i | \(0.389661\pi\) | |||||||
\(240\) | 3.72913 | 0.240714 | ||||||||
\(241\) | 25.0266 | 1.61210 | 0.806052 | − | 0.591844i | \(-0.201600\pi\) | ||||
0.806052 | + | 0.591844i | \(0.201600\pi\) | |||||||
\(242\) | −1.26949 | −0.0816061 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 14.7334 | 0.943212 | ||||||||
\(245\) | 29.9401 | 1.91280 | ||||||||
\(246\) | 28.4996 | 1.81707 | ||||||||
\(247\) | −21.4657 | −1.36583 | ||||||||
\(248\) | 8.33535 | 0.529295 | ||||||||
\(249\) | 11.4658 | 0.726612 | ||||||||
\(250\) | −79.8400 | −5.04952 | ||||||||
\(251\) | −17.4686 | −1.10261 | −0.551303 | − | 0.834305i | \(-0.685869\pi\) | ||||
−0.551303 | + | 0.834305i | \(0.685869\pi\) | |||||||
\(252\) | −0.198086 | −0.0124783 | ||||||||
\(253\) | −3.69551 | −0.232335 | ||||||||
\(254\) | −39.9285 | −2.50534 | ||||||||
\(255\) | −4.27976 | −0.268009 | ||||||||
\(256\) | −9.95712 | −0.622320 | ||||||||
\(257\) | 16.5472 | 1.03219 | 0.516094 | − | 0.856532i | \(-0.327386\pi\) | ||||
0.516094 | + | 0.856532i | \(0.327386\pi\) | |||||||
\(258\) | 5.92030 | 0.368582 | ||||||||
\(259\) | 0.176408 | 0.0109614 | ||||||||
\(260\) | 37.3710 | 2.31765 | ||||||||
\(261\) | 7.28872 | 0.451160 | ||||||||
\(262\) | 33.9319 | 2.09632 | ||||||||
\(263\) | 1.84760 | 0.113928 | 0.0569640 | − | 0.998376i | \(-0.481858\pi\) | ||||
0.0569640 | + | 0.998376i | \(0.481858\pi\) | |||||||
\(264\) | 7.47714 | 0.460186 | ||||||||
\(265\) | 34.6319 | 2.12742 | ||||||||
\(266\) | −1.09232 | −0.0669747 | ||||||||
\(267\) | −6.86540 | −0.420156 | ||||||||
\(268\) | −24.0094 | −1.46661 | ||||||||
\(269\) | 25.0351 | 1.52642 | 0.763209 | − | 0.646152i | \(-0.223623\pi\) | ||||
0.763209 | + | 0.646152i | \(0.223623\pi\) | |||||||
\(270\) | −9.60033 | −0.584258 | ||||||||
\(271\) | −0.0889911 | −0.00540583 | −0.00270291 | − | 0.999996i | \(-0.500860\pi\) | ||||
−0.00270291 | + | 0.999996i | \(0.500860\pi\) | |||||||
\(272\) | −0.871339 | −0.0528327 | ||||||||
\(273\) | 0.188164 | 0.0113882 | ||||||||
\(274\) | 24.5537 | 1.48334 | ||||||||
\(275\) | 43.0143 | 2.59386 | ||||||||
\(276\) | −3.46868 | −0.208790 | ||||||||
\(277\) | 3.46495 | 0.208189 | 0.104094 | − | 0.994567i | \(-0.466806\pi\) | ||||
0.104094 | + | 0.994567i | \(0.466806\pi\) | |||||||
\(278\) | −13.1414 | −0.788168 | ||||||||
\(279\) | 3.60094 | 0.215582 | ||||||||
\(280\) | 0.647242 | 0.0386801 | ||||||||
\(281\) | −20.4218 | −1.21826 | −0.609131 | − | 0.793070i | \(-0.708482\pi\) | ||||
−0.609131 | + | 0.793070i | \(0.708482\pi\) | |||||||
\(282\) | 11.5850 | 0.689876 | ||||||||
\(283\) | 10.7287 | 0.637755 | 0.318878 | − | 0.947796i | \(-0.396694\pi\) | ||||
0.318878 | + | 0.947796i | \(0.396694\pi\) | |||||||
\(284\) | 5.58227 | 0.331247 | ||||||||
\(285\) | −31.8982 | −1.88949 | ||||||||
\(286\) | −20.8685 | −1.23398 | ||||||||
\(287\) | −0.830063 | −0.0489971 | ||||||||
\(288\) | −6.58413 | −0.387974 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −69.9741 | −4.10902 | ||||||||
\(291\) | 8.64709 | 0.506901 | ||||||||
\(292\) | −7.01497 | −0.410520 | ||||||||
\(293\) | 31.7647 | 1.85571 | 0.927857 | − | 0.372937i | \(-0.121649\pi\) | ||||
0.927857 | + | 0.372937i | \(0.121649\pi\) | |||||||
\(294\) | −15.6928 | −0.915221 | ||||||||
\(295\) | −52.5977 | −3.06235 | ||||||||
\(296\) | −6.25011 | −0.363281 | ||||||||
\(297\) | 3.23018 | 0.187434 | ||||||||
\(298\) | 50.0927 | 2.90179 | ||||||||
\(299\) | 3.29493 | 0.190551 | ||||||||
\(300\) | 40.3741 | 2.33100 | ||||||||
\(301\) | −0.172431 | −0.00993876 | ||||||||
\(302\) | −12.0120 | −0.691214 | ||||||||
\(303\) | −13.6386 | −0.783520 | ||||||||
\(304\) | −6.49432 | −0.372475 | ||||||||
\(305\) | −20.7973 | −1.19085 | ||||||||
\(306\) | 2.24319 | 0.128235 | ||||||||
\(307\) | −24.8838 | −1.42019 | −0.710097 | − | 0.704104i | \(-0.751349\pi\) | ||||
−0.710097 | + | 0.704104i | \(0.751349\pi\) | |||||||
\(308\) | −0.639855 | −0.0364591 | ||||||||
\(309\) | 7.16588 | 0.407653 | ||||||||
\(310\) | −34.5702 | −1.96345 | ||||||||
\(311\) | 1.31464 | 0.0745465 | 0.0372732 | − | 0.999305i | \(-0.488133\pi\) | ||||
0.0372732 | + | 0.999305i | \(0.488133\pi\) | |||||||
\(312\) | −6.66663 | −0.377424 | ||||||||
\(313\) | −25.5573 | −1.44459 | −0.722293 | − | 0.691588i | \(-0.756912\pi\) | ||||
−0.722293 | + | 0.691588i | \(0.756912\pi\) | |||||||
\(314\) | −40.1449 | −2.26551 | ||||||||
\(315\) | 0.279613 | 0.0157544 | ||||||||
\(316\) | 3.03191 | 0.170558 | ||||||||
\(317\) | −15.9302 | −0.894730 | −0.447365 | − | 0.894351i | \(-0.647638\pi\) | ||||
−0.447365 | + | 0.894351i | \(0.647638\pi\) | |||||||
\(318\) | −18.1520 | −1.01791 | ||||||||
\(319\) | 23.5439 | 1.31820 | ||||||||
\(320\) | 55.7516 | 3.11661 | ||||||||
\(321\) | 9.38280 | 0.523697 | ||||||||
\(322\) | 0.167669 | 0.00934382 | ||||||||
\(323\) | 7.45327 | 0.414711 | ||||||||
\(324\) | 3.03191 | 0.168439 | ||||||||
\(325\) | −38.3517 | −2.12737 | ||||||||
\(326\) | 24.7875 | 1.37285 | ||||||||
\(327\) | 8.45836 | 0.467748 | ||||||||
\(328\) | 29.4091 | 1.62384 | ||||||||
\(329\) | −0.337417 | −0.0186024 | ||||||||
\(330\) | −31.0108 | −1.70709 | ||||||||
\(331\) | 14.8737 | 0.817534 | 0.408767 | − | 0.912639i | \(-0.365959\pi\) | ||||
0.408767 | + | 0.912639i | \(0.365959\pi\) | |||||||
\(332\) | 34.7631 | 1.90787 | ||||||||
\(333\) | −2.70010 | −0.147964 | ||||||||
\(334\) | −26.2284 | −1.43515 | ||||||||
\(335\) | 33.8910 | 1.85166 | ||||||||
\(336\) | 0.0569280 | 0.00310567 | ||||||||
\(337\) | −1.91722 | −0.104437 | −0.0522187 | − | 0.998636i | \(-0.516629\pi\) | ||||
−0.0522187 | + | 0.998636i | \(0.516629\pi\) | |||||||
\(338\) | −10.5551 | −0.574121 | ||||||||
\(339\) | −3.94608 | −0.214321 | ||||||||
\(340\) | −12.9759 | −0.703715 | ||||||||
\(341\) | 11.6317 | 0.629890 | ||||||||
\(342\) | 16.7191 | 0.904066 | ||||||||
\(343\) | 0.914395 | 0.0493727 | ||||||||
\(344\) | 6.10922 | 0.329387 | ||||||||
\(345\) | 4.89629 | 0.263608 | ||||||||
\(346\) | −23.3211 | −1.25375 | ||||||||
\(347\) | −23.3849 | −1.25537 | −0.627685 | − | 0.778468i | \(-0.715997\pi\) | ||||
−0.627685 | + | 0.778468i | \(0.715997\pi\) | |||||||
\(348\) | 22.0987 | 1.18462 | ||||||||
\(349\) | 24.9527 | 1.33569 | 0.667844 | − | 0.744301i | \(-0.267217\pi\) | ||||
0.667844 | + | 0.744301i | \(0.267217\pi\) | |||||||
\(350\) | −1.95160 | −0.104317 | ||||||||
\(351\) | −2.88004 | −0.153725 | ||||||||
\(352\) | −21.2679 | −1.13358 | ||||||||
\(353\) | 13.0410 | 0.694102 | 0.347051 | − | 0.937846i | \(-0.387183\pi\) | ||||
0.347051 | + | 0.937846i | \(0.387183\pi\) | |||||||
\(354\) | 27.5685 | 1.46525 | ||||||||
\(355\) | −7.87978 | −0.418215 | ||||||||
\(356\) | −20.8153 | −1.10321 | ||||||||
\(357\) | −0.0653339 | −0.00345783 | ||||||||
\(358\) | −59.8032 | −3.16070 | ||||||||
\(359\) | −21.4840 | −1.13388 | −0.566941 | − | 0.823758i | \(-0.691873\pi\) | ||||
−0.566941 | + | 0.823758i | \(0.691873\pi\) | |||||||
\(360\) | −9.90668 | −0.522128 | ||||||||
\(361\) | 36.5512 | 1.92375 | ||||||||
\(362\) | −32.6203 | −1.71449 | ||||||||
\(363\) | −0.565931 | −0.0297037 | ||||||||
\(364\) | 0.570496 | 0.0299021 | ||||||||
\(365\) | 9.90214 | 0.518302 | ||||||||
\(366\) | 10.9007 | 0.569788 | ||||||||
\(367\) | −10.7360 | −0.560415 | −0.280208 | − | 0.959939i | \(-0.590403\pi\) | ||||
−0.280208 | + | 0.959939i | \(0.590403\pi\) | |||||||
\(368\) | 0.996862 | 0.0519650 | ||||||||
\(369\) | 12.7049 | 0.661393 | ||||||||
\(370\) | 25.9218 | 1.34761 | ||||||||
\(371\) | 0.528683 | 0.0274478 | ||||||||
\(372\) | 10.9177 | 0.566057 | ||||||||
\(373\) | −19.7906 | −1.02472 | −0.512359 | − | 0.858772i | \(-0.671228\pi\) | ||||
−0.512359 | + | 0.858772i | \(0.671228\pi\) | |||||||
\(374\) | 7.24592 | 0.374677 | ||||||||
\(375\) | −35.5921 | −1.83797 | ||||||||
\(376\) | 11.9547 | 0.616515 | ||||||||
\(377\) | −20.9918 | −1.08113 | ||||||||
\(378\) | −0.146556 | −0.00753805 | ||||||||
\(379\) | 3.13241 | 0.160901 | 0.0804505 | − | 0.996759i | \(-0.474364\pi\) | ||||
0.0804505 | + | 0.996759i | \(0.474364\pi\) | |||||||
\(380\) | −96.7125 | −4.96125 | ||||||||
\(381\) | −17.7999 | −0.911915 | ||||||||
\(382\) | 23.1226 | 1.18305 | ||||||||
\(383\) | 22.7645 | 1.16321 | 0.581606 | − | 0.813471i | \(-0.302425\pi\) | ||||
0.581606 | + | 0.813471i | \(0.302425\pi\) | |||||||
\(384\) | −16.0533 | −0.819218 | ||||||||
\(385\) | 0.903202 | 0.0460314 | ||||||||
\(386\) | 4.27401 | 0.217541 | ||||||||
\(387\) | 2.63923 | 0.134160 | ||||||||
\(388\) | 26.2172 | 1.33098 | ||||||||
\(389\) | 28.5165 | 1.44584 | 0.722921 | − | 0.690931i | \(-0.242799\pi\) | ||||
0.722921 | + | 0.690931i | \(0.242799\pi\) | |||||||
\(390\) | 27.6493 | 1.40008 | ||||||||
\(391\) | −1.14406 | −0.0578575 | ||||||||
\(392\) | −16.1935 | −0.817897 | ||||||||
\(393\) | 15.1266 | 0.763037 | ||||||||
\(394\) | 13.0864 | 0.659285 | ||||||||
\(395\) | −4.27976 | −0.215338 | ||||||||
\(396\) | 9.79362 | 0.492148 | ||||||||
\(397\) | 36.9626 | 1.85510 | 0.927550 | − | 0.373699i | \(-0.121911\pi\) | ||||
0.927550 | + | 0.373699i | \(0.121911\pi\) | |||||||
\(398\) | 13.0894 | 0.656111 | ||||||||
\(399\) | −0.486951 | −0.0243780 | ||||||||
\(400\) | −11.6031 | −0.580154 | ||||||||
\(401\) | −14.5668 | −0.727430 | −0.363715 | − | 0.931510i | \(-0.618492\pi\) | ||||
−0.363715 | + | 0.931510i | \(0.618492\pi\) | |||||||
\(402\) | −17.7636 | −0.885969 | ||||||||
\(403\) | −10.3708 | −0.516608 | ||||||||
\(404\) | −41.3512 | −2.05730 | ||||||||
\(405\) | −4.27976 | −0.212663 | ||||||||
\(406\) | −1.06821 | −0.0530143 | ||||||||
\(407\) | −8.72180 | −0.432324 | ||||||||
\(408\) | 2.31477 | 0.114598 | ||||||||
\(409\) | −37.0354 | −1.83128 | −0.915640 | − | 0.401998i | \(-0.868316\pi\) | ||||
−0.915640 | + | 0.401998i | \(0.868316\pi\) | |||||||
\(410\) | −121.972 | −6.02375 | ||||||||
\(411\) | 10.9459 | 0.539919 | ||||||||
\(412\) | 21.7263 | 1.07038 | ||||||||
\(413\) | −0.802943 | −0.0395103 | ||||||||
\(414\) | −2.56634 | −0.126129 | ||||||||
\(415\) | −49.0707 | −2.40879 | ||||||||
\(416\) | 18.9625 | 0.929715 | ||||||||
\(417\) | −5.85835 | −0.286884 | ||||||||
\(418\) | 54.0057 | 2.64151 | ||||||||
\(419\) | 38.5543 | 1.88350 | 0.941751 | − | 0.336311i | \(-0.109179\pi\) | ||||
0.941751 | + | 0.336311i | \(0.109179\pi\) | |||||||
\(420\) | 0.847763 | 0.0413666 | ||||||||
\(421\) | 11.8642 | 0.578223 | 0.289112 | − | 0.957295i | \(-0.406640\pi\) | ||||
0.289112 | + | 0.957295i | \(0.406640\pi\) | |||||||
\(422\) | −16.2599 | −0.791522 | ||||||||
\(423\) | 5.16451 | 0.251107 | ||||||||
\(424\) | −18.7312 | −0.909667 | ||||||||
\(425\) | 13.3164 | 0.645939 | ||||||||
\(426\) | 4.13010 | 0.200104 | ||||||||
\(427\) | −0.317487 | −0.0153643 | ||||||||
\(428\) | 28.4478 | 1.37508 | ||||||||
\(429\) | −9.30304 | −0.449155 | ||||||||
\(430\) | −25.3375 | −1.22188 | ||||||||
\(431\) | −36.6782 | −1.76672 | −0.883362 | − | 0.468691i | \(-0.844726\pi\) | ||||
−0.883362 | + | 0.468691i | \(0.844726\pi\) | |||||||
\(432\) | −0.871339 | −0.0419223 | ||||||||
\(433\) | 5.95020 | 0.285948 | 0.142974 | − | 0.989726i | \(-0.454333\pi\) | ||||
0.142974 | + | 0.989726i | \(0.454333\pi\) | |||||||
\(434\) | −0.527740 | −0.0253323 | ||||||||
\(435\) | −31.1940 | −1.49564 | ||||||||
\(436\) | 25.6450 | 1.22817 | ||||||||
\(437\) | −8.52696 | −0.407900 | ||||||||
\(438\) | −5.19010 | −0.247993 | ||||||||
\(439\) | 8.10451 | 0.386807 | 0.193404 | − | 0.981119i | \(-0.438047\pi\) | ||||
0.193404 | + | 0.981119i | \(0.438047\pi\) | |||||||
\(440\) | −32.0004 | −1.52556 | ||||||||
\(441\) | −6.99573 | −0.333130 | ||||||||
\(442\) | −6.46048 | −0.307294 | ||||||||
\(443\) | −7.36079 | −0.349722 | −0.174861 | − | 0.984593i | \(-0.555948\pi\) | ||||
−0.174861 | + | 0.984593i | \(0.555948\pi\) | |||||||
\(444\) | −8.18645 | −0.388512 | ||||||||
\(445\) | 29.3823 | 1.39285 | ||||||||
\(446\) | −35.3749 | −1.67505 | ||||||||
\(447\) | 22.3310 | 1.05622 | ||||||||
\(448\) | 0.851090 | 0.0402102 | ||||||||
\(449\) | 7.87811 | 0.371791 | 0.185895 | − | 0.982570i | \(-0.440481\pi\) | ||||
0.185895 | + | 0.982570i | \(0.440481\pi\) | |||||||
\(450\) | 29.8712 | 1.40814 | ||||||||
\(451\) | 41.0393 | 1.93246 | ||||||||
\(452\) | −11.9642 | −0.562746 | ||||||||
\(453\) | −5.35488 | −0.251594 | ||||||||
\(454\) | −25.0253 | −1.17450 | ||||||||
\(455\) | −0.805297 | −0.0377529 | ||||||||
\(456\) | 17.2526 | 0.807928 | ||||||||
\(457\) | −29.7161 | −1.39006 | −0.695030 | − | 0.718981i | \(-0.744609\pi\) | ||||
−0.695030 | + | 0.718981i | \(0.744609\pi\) | |||||||
\(458\) | −5.52208 | −0.258030 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 14.8451 | 0.692158 | ||||||||
\(461\) | 29.8469 | 1.39011 | 0.695053 | − | 0.718958i | \(-0.255381\pi\) | ||||
0.695053 | + | 0.718958i | \(0.255381\pi\) | |||||||
\(462\) | −0.473404 | −0.0220247 | ||||||||
\(463\) | −21.1974 | −0.985126 | −0.492563 | − | 0.870277i | \(-0.663940\pi\) | ||||
−0.492563 | + | 0.870277i | \(0.663940\pi\) | |||||||
\(464\) | −6.35095 | −0.294835 | ||||||||
\(465\) | −15.4112 | −0.714675 | ||||||||
\(466\) | 15.5698 | 0.721259 | ||||||||
\(467\) | −35.0045 | −1.61982 | −0.809908 | − | 0.586557i | \(-0.800483\pi\) | ||||
−0.809908 | + | 0.586557i | \(0.800483\pi\) | |||||||
\(468\) | −8.73202 | −0.403638 | ||||||||
\(469\) | 0.517372 | 0.0238900 | ||||||||
\(470\) | −49.5810 | −2.28700 | ||||||||
\(471\) | −17.8963 | −0.824619 | ||||||||
\(472\) | 28.4482 | 1.30944 | ||||||||
\(473\) | 8.52519 | 0.391988 | ||||||||
\(474\) | 2.24319 | 0.103033 | ||||||||
\(475\) | 99.2505 | 4.55393 | ||||||||
\(476\) | −0.198086 | −0.00907928 | ||||||||
\(477\) | −8.09202 | −0.370508 | ||||||||
\(478\) | 23.5636 | 1.07777 | ||||||||
\(479\) | −9.11379 | −0.416419 | −0.208210 | − | 0.978084i | \(-0.566764\pi\) | ||||
−0.208210 | + | 0.978084i | \(0.566764\pi\) | |||||||
\(480\) | 28.1785 | 1.28617 | ||||||||
\(481\) | 7.77638 | 0.354572 | ||||||||
\(482\) | 56.1395 | 2.55708 | ||||||||
\(483\) | 0.0747457 | 0.00340105 | ||||||||
\(484\) | −1.71585 | −0.0779933 | ||||||||
\(485\) | −37.0075 | −1.68042 | ||||||||
\(486\) | 2.24319 | 0.101753 | ||||||||
\(487\) | 8.56392 | 0.388068 | 0.194034 | − | 0.980995i | \(-0.437843\pi\) | ||||
0.194034 | + | 0.980995i | \(0.437843\pi\) | |||||||
\(488\) | 11.2485 | 0.509197 | ||||||||
\(489\) | 11.0501 | 0.499703 | ||||||||
\(490\) | 67.1613 | 3.03404 | ||||||||
\(491\) | −13.8472 | −0.624917 | −0.312458 | − | 0.949931i | \(-0.601152\pi\) | ||||
−0.312458 | + | 0.949931i | \(0.601152\pi\) | |||||||
\(492\) | 38.5203 | 1.73663 | ||||||||
\(493\) | 7.28872 | 0.328267 | ||||||||
\(494\) | −48.1517 | −2.16645 | ||||||||
\(495\) | −13.8244 | −0.621361 | ||||||||
\(496\) | −3.13764 | −0.140884 | ||||||||
\(497\) | −0.120291 | −0.00539578 | ||||||||
\(498\) | 25.7199 | 1.15254 | ||||||||
\(499\) | −41.5122 | −1.85834 | −0.929171 | − | 0.369650i | \(-0.879478\pi\) | ||||
−0.929171 | + | 0.369650i | \(0.879478\pi\) | |||||||
\(500\) | −107.912 | −4.82598 | ||||||||
\(501\) | −11.6924 | −0.522380 | ||||||||
\(502\) | −39.1853 | −1.74893 | ||||||||
\(503\) | 17.2207 | 0.767833 | 0.383917 | − | 0.923368i | \(-0.374575\pi\) | ||||
0.383917 | + | 0.923368i | \(0.374575\pi\) | |||||||
\(504\) | −0.151233 | −0.00673646 | ||||||||
\(505\) | 58.3702 | 2.59744 | ||||||||
\(506\) | −8.28974 | −0.368524 | ||||||||
\(507\) | −4.70538 | −0.208973 | ||||||||
\(508\) | −53.9676 | −2.39442 | ||||||||
\(509\) | −33.8186 | −1.49898 | −0.749491 | − | 0.662014i | \(-0.769702\pi\) | ||||
−0.749491 | + | 0.662014i | \(0.769702\pi\) | |||||||
\(510\) | −9.60033 | −0.425110 | ||||||||
\(511\) | 0.151164 | 0.00668709 | ||||||||
\(512\) | 9.77092 | 0.431818 | ||||||||
\(513\) | 7.45327 | 0.329070 | ||||||||
\(514\) | 37.1186 | 1.63723 | ||||||||
\(515\) | −30.6683 | −1.35141 | ||||||||
\(516\) | 8.00191 | 0.352264 | ||||||||
\(517\) | 16.6823 | 0.733687 | ||||||||
\(518\) | 0.395717 | 0.0173868 | ||||||||
\(519\) | −10.3964 | −0.456351 | ||||||||
\(520\) | 28.5316 | 1.25119 | ||||||||
\(521\) | 1.22209 | 0.0535409 | 0.0267705 | − | 0.999642i | \(-0.491478\pi\) | ||||
0.0267705 | + | 0.999642i | \(0.491478\pi\) | |||||||
\(522\) | 16.3500 | 0.715620 | ||||||||
\(523\) | −16.2375 | −0.710017 | −0.355009 | − | 0.934863i | \(-0.615522\pi\) | ||||
−0.355009 | + | 0.934863i | \(0.615522\pi\) | |||||||
\(524\) | 45.8626 | 2.00351 | ||||||||
\(525\) | −0.870010 | −0.0379704 | ||||||||
\(526\) | 4.14453 | 0.180710 | ||||||||
\(527\) | 3.60094 | 0.156859 | ||||||||
\(528\) | −2.81458 | −0.122489 | ||||||||
\(529\) | −21.6911 | −0.943093 | ||||||||
\(530\) | 77.6861 | 3.37447 | ||||||||
\(531\) | 12.2898 | 0.533334 | ||||||||
\(532\) | −1.47639 | −0.0640097 | ||||||||
\(533\) | −36.5907 | −1.58492 | ||||||||
\(534\) | −15.4004 | −0.666441 | ||||||||
\(535\) | −40.1562 | −1.73610 | ||||||||
\(536\) | −18.3305 | −0.791755 | ||||||||
\(537\) | −26.6599 | −1.15046 | ||||||||
\(538\) | 56.1586 | 2.42117 | ||||||||
\(539\) | −22.5975 | −0.973342 | ||||||||
\(540\) | −12.9759 | −0.558392 | ||||||||
\(541\) | −31.0112 | −1.33328 | −0.666638 | − | 0.745382i | \(-0.732267\pi\) | ||||
−0.666638 | + | 0.745382i | \(0.732267\pi\) | |||||||
\(542\) | −0.199624 | −0.00857459 | ||||||||
\(543\) | −14.5419 | −0.624053 | ||||||||
\(544\) | −6.58413 | −0.282292 | ||||||||
\(545\) | −36.1998 | −1.55063 | ||||||||
\(546\) | 0.422088 | 0.0180637 | ||||||||
\(547\) | −7.23456 | −0.309328 | −0.154664 | − | 0.987967i | \(-0.549429\pi\) | ||||
−0.154664 | + | 0.987967i | \(0.549429\pi\) | |||||||
\(548\) | 33.1869 | 1.41767 | ||||||||
\(549\) | 4.85946 | 0.207397 | ||||||||
\(550\) | 96.4894 | 4.11432 | ||||||||
\(551\) | 54.3247 | 2.31431 | ||||||||
\(552\) | −2.64823 | −0.112716 | ||||||||
\(553\) | −0.0653339 | −0.00277828 | ||||||||
\(554\) | 7.77255 | 0.330224 | ||||||||
\(555\) | 11.5558 | 0.490516 | ||||||||
\(556\) | −17.7620 | −0.753276 | ||||||||
\(557\) | 16.7212 | 0.708501 | 0.354250 | − | 0.935151i | \(-0.384736\pi\) | ||||
0.354250 | + | 0.935151i | \(0.384736\pi\) | |||||||
\(558\) | 8.07759 | 0.341952 | ||||||||
\(559\) | −7.60108 | −0.321491 | ||||||||
\(560\) | −0.243638 | −0.0102956 | ||||||||
\(561\) | 3.23018 | 0.136378 | ||||||||
\(562\) | −45.8100 | −1.93238 | ||||||||
\(563\) | 8.37738 | 0.353064 | 0.176532 | − | 0.984295i | \(-0.443512\pi\) | ||||
0.176532 | + | 0.984295i | \(0.443512\pi\) | |||||||
\(564\) | 15.6583 | 0.659335 | ||||||||
\(565\) | 16.8883 | 0.710495 | ||||||||
\(566\) | 24.0665 | 1.01159 | ||||||||
\(567\) | −0.0653339 | −0.00274376 | ||||||||
\(568\) | 4.26189 | 0.178825 | ||||||||
\(569\) | −6.47451 | −0.271426 | −0.135713 | − | 0.990748i | \(-0.543332\pi\) | ||||
−0.135713 | + | 0.990748i | \(0.543332\pi\) | |||||||
\(570\) | −71.5538 | −2.99706 | ||||||||
\(571\) | −5.08808 | −0.212930 | −0.106465 | − | 0.994316i | \(-0.533953\pi\) | ||||
−0.106465 | + | 0.994316i | \(0.533953\pi\) | |||||||
\(572\) | −28.2060 | −1.17935 | ||||||||
\(573\) | 10.3079 | 0.430619 | ||||||||
\(574\) | −1.86199 | −0.0777180 | ||||||||
\(575\) | −15.2347 | −0.635331 | ||||||||
\(576\) | −13.0268 | −0.542783 | ||||||||
\(577\) | 26.9593 | 1.12233 | 0.561166 | − | 0.827703i | \(-0.310353\pi\) | ||||
0.561166 | + | 0.827703i | \(0.310353\pi\) | |||||||
\(578\) | 2.24319 | 0.0933045 | ||||||||
\(579\) | 1.90532 | 0.0791825 | ||||||||
\(580\) | −94.5774 | −3.92711 | ||||||||
\(581\) | −0.749102 | −0.0310780 | ||||||||
\(582\) | 19.3971 | 0.804035 | ||||||||
\(583\) | −26.1387 | −1.08255 | ||||||||
\(584\) | −5.35572 | −0.221621 | ||||||||
\(585\) | 12.3259 | 0.509612 | ||||||||
\(586\) | 71.2543 | 2.94349 | ||||||||
\(587\) | −7.56818 | −0.312372 | −0.156186 | − | 0.987728i | \(-0.549920\pi\) | ||||
−0.156186 | + | 0.987728i | \(0.549920\pi\) | |||||||
\(588\) | −21.2104 | −0.874703 | ||||||||
\(589\) | 26.8387 | 1.10587 | ||||||||
\(590\) | −117.987 | −4.85743 | ||||||||
\(591\) | 5.83384 | 0.239972 | ||||||||
\(592\) | 2.35270 | 0.0966954 | ||||||||
\(593\) | 33.8791 | 1.39125 | 0.695624 | − | 0.718406i | \(-0.255128\pi\) | ||||
0.695624 | + | 0.718406i | \(0.255128\pi\) | |||||||
\(594\) | 7.24592 | 0.297304 | ||||||||
\(595\) | 0.279613 | 0.0114630 | ||||||||
\(596\) | 67.7056 | 2.77333 | ||||||||
\(597\) | 5.83516 | 0.238817 | ||||||||
\(598\) | 7.39115 | 0.302247 | ||||||||
\(599\) | −30.1074 | −1.23015 | −0.615077 | − | 0.788467i | \(-0.710875\pi\) | ||||
−0.615077 | + | 0.788467i | \(0.710875\pi\) | |||||||
\(600\) | 30.8244 | 1.25840 | ||||||||
\(601\) | −5.03682 | −0.205456 | −0.102728 | − | 0.994709i | \(-0.532757\pi\) | ||||
−0.102728 | + | 0.994709i | \(0.532757\pi\) | |||||||
\(602\) | −0.386796 | −0.0157646 | ||||||||
\(603\) | −7.91890 | −0.322483 | ||||||||
\(604\) | −16.2355 | −0.660614 | ||||||||
\(605\) | 2.42205 | 0.0984705 | ||||||||
\(606\) | −30.5941 | −1.24280 | ||||||||
\(607\) | −10.2109 | −0.414448 | −0.207224 | − | 0.978294i | \(-0.566443\pi\) | ||||
−0.207224 | + | 0.978294i | \(0.566443\pi\) | |||||||
\(608\) | −49.0733 | −1.99018 | ||||||||
\(609\) | −0.476200 | −0.0192966 | ||||||||
\(610\) | −46.6524 | −1.88890 | ||||||||
\(611\) | −14.8740 | −0.601737 | ||||||||
\(612\) | 3.03191 | 0.122558 | ||||||||
\(613\) | 5.75216 | 0.232328 | 0.116164 | − | 0.993230i | \(-0.462940\pi\) | ||||
0.116164 | + | 0.993230i | \(0.462940\pi\) | |||||||
\(614\) | −55.8192 | −2.25268 | ||||||||
\(615\) | −54.3742 | −2.19258 | ||||||||
\(616\) | −0.488510 | −0.0196826 | ||||||||
\(617\) | −40.0191 | −1.61111 | −0.805555 | − | 0.592521i | \(-0.798133\pi\) | ||||
−0.805555 | + | 0.592521i | \(0.798133\pi\) | |||||||
\(618\) | 16.0744 | 0.646609 | ||||||||
\(619\) | 6.83554 | 0.274744 | 0.137372 | − | 0.990520i | \(-0.456134\pi\) | ||||
0.137372 | + | 0.990520i | \(0.456134\pi\) | |||||||
\(620\) | −46.7252 | −1.87653 | ||||||||
\(621\) | −1.14406 | −0.0459094 | ||||||||
\(622\) | 2.94899 | 0.118244 | ||||||||
\(623\) | 0.448543 | 0.0179705 | ||||||||
\(624\) | 2.50949 | 0.100460 | ||||||||
\(625\) | 85.7440 | 3.42976 | ||||||||
\(626\) | −57.3300 | −2.29137 | ||||||||
\(627\) | 24.0754 | 0.961479 | ||||||||
\(628\) | −54.2601 | −2.16521 | ||||||||
\(629\) | −2.70010 | −0.107660 | ||||||||
\(630\) | 0.627227 | 0.0249893 | ||||||||
\(631\) | 11.9665 | 0.476378 | 0.238189 | − | 0.971219i | \(-0.423446\pi\) | ||||
0.238189 | + | 0.971219i | \(0.423446\pi\) | |||||||
\(632\) | 2.31477 | 0.0920767 | ||||||||
\(633\) | −7.24857 | −0.288105 | ||||||||
\(634\) | −35.7345 | −1.41920 | ||||||||
\(635\) | 76.1792 | 3.02308 | ||||||||
\(636\) | −24.5343 | −0.972847 | ||||||||
\(637\) | 20.1480 | 0.798292 | ||||||||
\(638\) | 52.8134 | 2.09090 | ||||||||
\(639\) | 1.84117 | 0.0728356 | ||||||||
\(640\) | 68.7044 | 2.71578 | ||||||||
\(641\) | 20.3054 | 0.802017 | 0.401008 | − | 0.916074i | \(-0.368660\pi\) | ||||
0.401008 | + | 0.916074i | \(0.368660\pi\) | |||||||
\(642\) | 21.0474 | 0.830676 | ||||||||
\(643\) | −6.76980 | −0.266975 | −0.133487 | − | 0.991051i | \(-0.542618\pi\) | ||||
−0.133487 | + | 0.991051i | \(0.542618\pi\) | |||||||
\(644\) | 0.226622 | 0.00893016 | ||||||||
\(645\) | −11.2953 | −0.444751 | ||||||||
\(646\) | 16.7191 | 0.657804 | ||||||||
\(647\) | −10.7095 | −0.421034 | −0.210517 | − | 0.977590i | \(-0.567515\pi\) | ||||
−0.210517 | + | 0.977590i | \(0.567515\pi\) | |||||||
\(648\) | 2.31477 | 0.0909329 | ||||||||
\(649\) | 39.6984 | 1.55830 | ||||||||
\(650\) | −86.0302 | −3.37438 | ||||||||
\(651\) | −0.235263 | −0.00922068 | ||||||||
\(652\) | 33.5029 | 1.31208 | ||||||||
\(653\) | 32.8301 | 1.28474 | 0.642371 | − | 0.766393i | \(-0.277951\pi\) | ||||
0.642371 | + | 0.766393i | \(0.277951\pi\) | |||||||
\(654\) | 18.9737 | 0.741932 | ||||||||
\(655\) | −64.7383 | −2.52954 | ||||||||
\(656\) | −11.0703 | −0.432223 | ||||||||
\(657\) | −2.31371 | −0.0902665 | ||||||||
\(658\) | −0.756892 | −0.0295067 | ||||||||
\(659\) | 27.9870 | 1.09022 | 0.545110 | − | 0.838365i | \(-0.316488\pi\) | ||||
0.545110 | + | 0.838365i | \(0.316488\pi\) | |||||||
\(660\) | −41.9144 | −1.63151 | ||||||||
\(661\) | 3.39998 | 0.132244 | 0.0661219 | − | 0.997812i | \(-0.478937\pi\) | ||||
0.0661219 | + | 0.997812i | \(0.478937\pi\) | |||||||
\(662\) | 33.3646 | 1.29675 | ||||||||
\(663\) | −2.88004 | −0.111851 | ||||||||
\(664\) | 26.5406 | 1.02998 | ||||||||
\(665\) | 2.08403 | 0.0808154 | ||||||||
\(666\) | −6.05684 | −0.234698 | ||||||||
\(667\) | −8.33871 | −0.322876 | ||||||||
\(668\) | −35.4504 | −1.37162 | ||||||||
\(669\) | −15.7699 | −0.609699 | ||||||||
\(670\) | 76.0241 | 2.93707 | ||||||||
\(671\) | 15.6969 | 0.605973 | ||||||||
\(672\) | 0.430167 | 0.0165940 | ||||||||
\(673\) | −34.9002 | −1.34530 | −0.672651 | − | 0.739960i | \(-0.734845\pi\) | ||||
−0.672651 | + | 0.739960i | \(0.734845\pi\) | |||||||
\(674\) | −4.30069 | −0.165656 | ||||||||
\(675\) | 13.3164 | 0.512548 | ||||||||
\(676\) | −14.2663 | −0.548704 | ||||||||
\(677\) | 44.6542 | 1.71620 | 0.858100 | − | 0.513482i | \(-0.171645\pi\) | ||||
0.858100 | + | 0.513482i | \(0.171645\pi\) | |||||||
\(678\) | −8.85181 | −0.339952 | ||||||||
\(679\) | −0.564948 | −0.0216807 | ||||||||
\(680\) | −9.90668 | −0.379904 | ||||||||
\(681\) | −11.1561 | −0.427503 | ||||||||
\(682\) | 26.0921 | 0.999117 | ||||||||
\(683\) | 0.715961 | 0.0273955 | 0.0136978 | − | 0.999906i | \(-0.495640\pi\) | ||||
0.0136978 | + | 0.999906i | \(0.495640\pi\) | |||||||
\(684\) | 22.5976 | 0.864042 | ||||||||
\(685\) | −46.8457 | −1.78988 | ||||||||
\(686\) | 2.05116 | 0.0783138 | ||||||||
\(687\) | −2.46171 | −0.0939199 | ||||||||
\(688\) | −2.29966 | −0.0876739 | ||||||||
\(689\) | 23.3053 | 0.887862 | ||||||||
\(690\) | 10.9833 | 0.418128 | ||||||||
\(691\) | 11.3132 | 0.430375 | 0.215187 | − | 0.976573i | \(-0.430964\pi\) | ||||
0.215187 | + | 0.976573i | \(0.430964\pi\) | |||||||
\(692\) | −31.5210 | −1.19825 | ||||||||
\(693\) | −0.211040 | −0.00801675 | ||||||||
\(694\) | −52.4569 | −1.99124 | ||||||||
\(695\) | 25.0723 | 0.951048 | ||||||||
\(696\) | 16.8717 | 0.639521 | ||||||||
\(697\) | 12.7049 | 0.481234 | ||||||||
\(698\) | 55.9737 | 2.11864 | ||||||||
\(699\) | 6.94093 | 0.262530 | ||||||||
\(700\) | −2.63779 | −0.0996992 | ||||||||
\(701\) | 39.4997 | 1.49188 | 0.745942 | − | 0.666011i | \(-0.231999\pi\) | ||||
0.745942 | + | 0.666011i | \(0.231999\pi\) | |||||||
\(702\) | −6.46048 | −0.243835 | ||||||||
\(703\) | −20.1245 | −0.759012 | ||||||||
\(704\) | −42.0789 | −1.58591 | ||||||||
\(705\) | −22.1029 | −0.832443 | ||||||||
\(706\) | 29.2535 | 1.10097 | ||||||||
\(707\) | 0.891065 | 0.0335120 | ||||||||
\(708\) | 37.2617 | 1.40038 | ||||||||
\(709\) | 7.83441 | 0.294227 | 0.147114 | − | 0.989120i | \(-0.453002\pi\) | ||||
0.147114 | + | 0.989120i | \(0.453002\pi\) | |||||||
\(710\) | −17.6759 | −0.663363 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −15.8919 | −0.595572 | ||||||||
\(713\) | −4.11968 | −0.154283 | ||||||||
\(714\) | −0.146556 | −0.00548473 | ||||||||
\(715\) | 39.8148 | 1.48899 | ||||||||
\(716\) | −80.8303 | −3.02077 | ||||||||
\(717\) | 10.5045 | 0.392297 | ||||||||
\(718\) | −48.1928 | −1.79854 | ||||||||
\(719\) | 0.919912 | 0.0343069 | 0.0171535 | − | 0.999853i | \(-0.494540\pi\) | ||||
0.0171535 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(720\) | 3.72913 | 0.138976 | ||||||||
\(721\) | −0.468175 | −0.0174357 | ||||||||
\(722\) | 81.9913 | 3.05140 | ||||||||
\(723\) | 25.0266 | 0.930749 | ||||||||
\(724\) | −44.0898 | −1.63858 | ||||||||
\(725\) | 97.0593 | 3.60469 | ||||||||
\(726\) | −1.26949 | −0.0471153 | ||||||||
\(727\) | 18.6452 | 0.691511 | 0.345756 | − | 0.938325i | \(-0.387623\pi\) | ||||
0.345756 | + | 0.938325i | \(0.387623\pi\) | |||||||
\(728\) | 0.435557 | 0.0161428 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 22.2124 | 0.822118 | ||||||||
\(731\) | 2.63923 | 0.0976154 | ||||||||
\(732\) | 14.7334 | 0.544563 | ||||||||
\(733\) | −42.2388 | −1.56013 | −0.780064 | − | 0.625700i | \(-0.784813\pi\) | ||||
−0.780064 | + | 0.625700i | \(0.784813\pi\) | |||||||
\(734\) | −24.0829 | −0.888917 | ||||||||
\(735\) | 29.9401 | 1.10436 | ||||||||
\(736\) | 7.53262 | 0.277656 | ||||||||
\(737\) | −25.5795 | −0.942232 | ||||||||
\(738\) | 28.4996 | 1.04909 | ||||||||
\(739\) | −42.2571 | −1.55445 | −0.777227 | − | 0.629221i | \(-0.783374\pi\) | ||||
−0.777227 | + | 0.629221i | \(0.783374\pi\) | |||||||
\(740\) | 35.0361 | 1.28795 | ||||||||
\(741\) | −21.4657 | −0.788562 | ||||||||
\(742\) | 1.18594 | 0.0435371 | ||||||||
\(743\) | 2.82361 | 0.103588 | 0.0517941 | − | 0.998658i | \(-0.483506\pi\) | ||||
0.0517941 | + | 0.998658i | \(0.483506\pi\) | |||||||
\(744\) | 8.33535 | 0.305589 | ||||||||
\(745\) | −95.5714 | −3.50147 | ||||||||
\(746\) | −44.3941 | −1.62538 | ||||||||
\(747\) | 11.4658 | 0.419510 | ||||||||
\(748\) | 9.79362 | 0.358090 | ||||||||
\(749\) | −0.613015 | −0.0223991 | ||||||||
\(750\) | −79.8400 | −2.91534 | ||||||||
\(751\) | 40.7594 | 1.48733 | 0.743665 | − | 0.668552i | \(-0.233086\pi\) | ||||
0.743665 | + | 0.668552i | \(0.233086\pi\) | |||||||
\(752\) | −4.50004 | −0.164100 | ||||||||
\(753\) | −17.4686 | −0.636590 | ||||||||
\(754\) | −47.0886 | −1.71487 | ||||||||
\(755\) | 22.9176 | 0.834058 | ||||||||
\(756\) | −0.198086 | −0.00720433 | ||||||||
\(757\) | 16.7162 | 0.607560 | 0.303780 | − | 0.952742i | \(-0.401751\pi\) | ||||
0.303780 | + | 0.952742i | \(0.401751\pi\) | |||||||
\(758\) | 7.02660 | 0.255217 | ||||||||
\(759\) | −3.69551 | −0.134139 | ||||||||
\(760\) | −73.8372 | −2.67836 | ||||||||
\(761\) | −31.3212 | −1.13539 | −0.567696 | − | 0.823238i | \(-0.692165\pi\) | ||||
−0.567696 | + | 0.823238i | \(0.692165\pi\) | |||||||
\(762\) | −39.9285 | −1.44646 | ||||||||
\(763\) | −0.552617 | −0.0200061 | ||||||||
\(764\) | 31.2526 | 1.13068 | ||||||||
\(765\) | −4.27976 | −0.154735 | ||||||||
\(766\) | 51.0651 | 1.84506 | ||||||||
\(767\) | −35.3952 | −1.27805 | ||||||||
\(768\) | −9.95712 | −0.359297 | ||||||||
\(769\) | 55.1421 | 1.98848 | 0.994238 | − | 0.107199i | \(-0.0341883\pi\) | ||||
0.994238 | + | 0.107199i | \(0.0341883\pi\) | |||||||
\(770\) | 2.02606 | 0.0730140 | ||||||||
\(771\) | 16.5472 | 0.595934 | ||||||||
\(772\) | 5.77677 | 0.207910 | ||||||||
\(773\) | −20.2070 | −0.726795 | −0.363397 | − | 0.931634i | \(-0.618383\pi\) | ||||
−0.363397 | + | 0.931634i | \(0.618383\pi\) | |||||||
\(774\) | 5.92030 | 0.212801 | ||||||||
\(775\) | 47.9514 | 1.72247 | ||||||||
\(776\) | 20.0161 | 0.718535 | ||||||||
\(777\) | 0.176408 | 0.00632859 | ||||||||
\(778\) | 63.9679 | 2.29336 | ||||||||
\(779\) | 94.6933 | 3.39274 | ||||||||
\(780\) | 37.3710 | 1.33810 | ||||||||
\(781\) | 5.94732 | 0.212812 | ||||||||
\(782\) | −2.56634 | −0.0917721 | ||||||||
\(783\) | 7.28872 | 0.260477 | ||||||||
\(784\) | 6.09566 | 0.217702 | ||||||||
\(785\) | 76.5920 | 2.73369 | ||||||||
\(786\) | 33.9319 | 1.21031 | ||||||||
\(787\) | −20.9602 | −0.747151 | −0.373576 | − | 0.927600i | \(-0.621868\pi\) | ||||
−0.373576 | + | 0.927600i | \(0.621868\pi\) | |||||||
\(788\) | 17.6877 | 0.630098 | ||||||||
\(789\) | 1.84760 | 0.0657764 | ||||||||
\(790\) | −9.60033 | −0.341564 | ||||||||
\(791\) | 0.257812 | 0.00916675 | ||||||||
\(792\) | 7.47714 | 0.265689 | ||||||||
\(793\) | −13.9954 | −0.496992 | ||||||||
\(794\) | 82.9142 | 2.94252 | ||||||||
\(795\) | 34.6319 | 1.22827 | ||||||||
\(796\) | 17.6917 | 0.627065 | ||||||||
\(797\) | −16.4859 | −0.583962 | −0.291981 | − | 0.956424i | \(-0.594314\pi\) | ||||
−0.291981 | + | 0.956424i | \(0.594314\pi\) | |||||||
\(798\) | −1.09232 | −0.0386678 | ||||||||
\(799\) | 5.16451 | 0.182707 | ||||||||
\(800\) | −87.6768 | −3.09984 | ||||||||
\(801\) | −6.86540 | −0.242577 | ||||||||
\(802\) | −32.6761 | −1.15383 | ||||||||
\(803\) | −7.47371 | −0.263741 | ||||||||
\(804\) | −24.0094 | −0.846746 | ||||||||
\(805\) | −0.319894 | −0.0112748 | ||||||||
\(806\) | −23.2638 | −0.819431 | ||||||||
\(807\) | 25.0351 | 0.881278 | ||||||||
\(808\) | −31.5704 | −1.11064 | ||||||||
\(809\) | 3.19727 | 0.112410 | 0.0562050 | − | 0.998419i | \(-0.482100\pi\) | ||||
0.0562050 | + | 0.998419i | \(0.482100\pi\) | |||||||
\(810\) | −9.60033 | −0.337321 | ||||||||
\(811\) | 52.9353 | 1.85881 | 0.929404 | − | 0.369064i | \(-0.120322\pi\) | ||||
0.929404 | + | 0.369064i | \(0.120322\pi\) | |||||||
\(812\) | −1.44380 | −0.0506673 | ||||||||
\(813\) | −0.0889911 | −0.00312106 | ||||||||
\(814\) | −19.5647 | −0.685742 | ||||||||
\(815\) | −47.2919 | −1.65656 | ||||||||
\(816\) | −0.871339 | −0.0305030 | ||||||||
\(817\) | 19.6709 | 0.688197 | ||||||||
\(818\) | −83.0774 | −2.90473 | ||||||||
\(819\) | 0.188164 | 0.00657498 | ||||||||
\(820\) | −164.858 | −5.75708 | ||||||||
\(821\) | −10.3302 | −0.360528 | −0.180264 | − | 0.983618i | \(-0.557695\pi\) | ||||
−0.180264 | + | 0.983618i | \(0.557695\pi\) | |||||||
\(822\) | 24.5537 | 0.856407 | ||||||||
\(823\) | −20.5023 | −0.714665 | −0.357333 | − | 0.933977i | \(-0.616314\pi\) | ||||
−0.357333 | + | 0.933977i | \(0.616314\pi\) | |||||||
\(824\) | 16.5874 | 0.577849 | ||||||||
\(825\) | 43.0143 | 1.49757 | ||||||||
\(826\) | −1.80116 | −0.0626702 | ||||||||
\(827\) | 16.2558 | 0.565271 | 0.282636 | − | 0.959227i | \(-0.408791\pi\) | ||||
0.282636 | + | 0.959227i | \(0.408791\pi\) | |||||||
\(828\) | −3.46868 | −0.120545 | ||||||||
\(829\) | 44.2832 | 1.53802 | 0.769010 | − | 0.639237i | \(-0.220750\pi\) | ||||
0.769010 | + | 0.639237i | \(0.220750\pi\) | |||||||
\(830\) | −110.075 | −3.82076 | ||||||||
\(831\) | 3.46495 | 0.120198 | ||||||||
\(832\) | 37.5176 | 1.30069 | ||||||||
\(833\) | −6.99573 | −0.242388 | ||||||||
\(834\) | −13.1414 | −0.455049 | ||||||||
\(835\) | 50.0409 | 1.73174 | ||||||||
\(836\) | 72.9945 | 2.52457 | ||||||||
\(837\) | 3.60094 | 0.124467 | ||||||||
\(838\) | 86.4847 | 2.98757 | ||||||||
\(839\) | −3.09167 | −0.106736 | −0.0533681 | − | 0.998575i | \(-0.516996\pi\) | ||||
−0.0533681 | + | 0.998575i | \(0.516996\pi\) | |||||||
\(840\) | 0.647242 | 0.0223320 | ||||||||
\(841\) | 24.1254 | 0.831910 | ||||||||
\(842\) | 26.6136 | 0.917164 | ||||||||
\(843\) | −20.4218 | −0.703364 | ||||||||
\(844\) | −21.9770 | −0.756480 | ||||||||
\(845\) | 20.1379 | 0.692766 | ||||||||
\(846\) | 11.5850 | 0.398300 | ||||||||
\(847\) | 0.0369745 | 0.00127046 | ||||||||
\(848\) | 7.05089 | 0.242129 | ||||||||
\(849\) | 10.7287 | 0.368208 | ||||||||
\(850\) | 29.8712 | 1.02457 | ||||||||
\(851\) | 3.08907 | 0.105892 | ||||||||
\(852\) | 5.58227 | 0.191245 | ||||||||
\(853\) | −54.8783 | −1.87900 | −0.939499 | − | 0.342551i | \(-0.888709\pi\) | ||||
−0.939499 | + | 0.342551i | \(0.888709\pi\) | |||||||
\(854\) | −0.712184 | −0.0243704 | ||||||||
\(855\) | −31.8982 | −1.09090 | ||||||||
\(856\) | 21.7191 | 0.742343 | ||||||||
\(857\) | 1.62498 | 0.0555083 | 0.0277541 | − | 0.999615i | \(-0.491164\pi\) | ||||
0.0277541 | + | 0.999615i | \(0.491164\pi\) | |||||||
\(858\) | −20.8685 | −0.712439 | ||||||||
\(859\) | −8.63692 | −0.294688 | −0.147344 | − | 0.989085i | \(-0.547072\pi\) | ||||
−0.147344 | + | 0.989085i | \(0.547072\pi\) | |||||||
\(860\) | −34.2463 | −1.16779 | ||||||||
\(861\) | −0.830063 | −0.0282885 | ||||||||
\(862\) | −82.2761 | −2.80234 | ||||||||
\(863\) | −37.1114 | −1.26329 | −0.631643 | − | 0.775259i | \(-0.717619\pi\) | ||||
−0.631643 | + | 0.775259i | \(0.717619\pi\) | |||||||
\(864\) | −6.58413 | −0.223997 | ||||||||
\(865\) | 44.4941 | 1.51285 | ||||||||
\(866\) | 13.3474 | 0.453565 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −0.713296 | −0.0242109 | ||||||||
\(869\) | 3.23018 | 0.109576 | ||||||||
\(870\) | −69.9741 | −2.37234 | ||||||||
\(871\) | 22.8067 | 0.772777 | ||||||||
\(872\) | 19.5792 | 0.663035 | ||||||||
\(873\) | 8.64709 | 0.292660 | ||||||||
\(874\) | −19.1276 | −0.647001 | ||||||||
\(875\) | 2.32537 | 0.0786119 | ||||||||
\(876\) | −7.01497 | −0.237014 | ||||||||
\(877\) | 9.62427 | 0.324989 | 0.162494 | − | 0.986709i | \(-0.448046\pi\) | ||||
0.162494 | + | 0.986709i | \(0.448046\pi\) | |||||||
\(878\) | 18.1800 | 0.613544 | ||||||||
\(879\) | 31.7647 | 1.07140 | ||||||||
\(880\) | 12.0458 | 0.406062 | ||||||||
\(881\) | 16.4726 | 0.554977 | 0.277489 | − | 0.960729i | \(-0.410498\pi\) | ||||
0.277489 | + | 0.960729i | \(0.410498\pi\) | |||||||
\(882\) | −15.6928 | −0.528403 | ||||||||
\(883\) | 23.4669 | 0.789724 | 0.394862 | − | 0.918741i | \(-0.370792\pi\) | ||||
0.394862 | + | 0.918741i | \(0.370792\pi\) | |||||||
\(884\) | −8.73202 | −0.293689 | ||||||||
\(885\) | −52.5977 | −1.76805 | ||||||||
\(886\) | −16.5117 | −0.554720 | ||||||||
\(887\) | 46.3409 | 1.55598 | 0.777988 | − | 0.628279i | \(-0.216240\pi\) | ||||
0.777988 | + | 0.628279i | \(0.216240\pi\) | |||||||
\(888\) | −6.25011 | −0.209740 | ||||||||
\(889\) | 1.16293 | 0.0390035 | ||||||||
\(890\) | 65.9101 | 2.20931 | ||||||||
\(891\) | 3.23018 | 0.108215 | ||||||||
\(892\) | −47.8129 | −1.60089 | ||||||||
\(893\) | 38.4925 | 1.28810 | ||||||||
\(894\) | 50.0927 | 1.67535 | ||||||||
\(895\) | 114.098 | 3.81387 | ||||||||
\(896\) | 1.04883 | 0.0350388 | ||||||||
\(897\) | 3.29493 | 0.110014 | ||||||||
\(898\) | 17.6721 | 0.589726 | ||||||||
\(899\) | 26.2462 | 0.875360 | ||||||||
\(900\) | 40.3741 | 1.34580 | ||||||||
\(901\) | −8.09202 | −0.269584 | ||||||||
\(902\) | 92.0590 | 3.06523 | ||||||||
\(903\) | −0.172431 | −0.00573814 | ||||||||
\(904\) | −9.13427 | −0.303801 | ||||||||
\(905\) | 62.2360 | 2.06879 | ||||||||
\(906\) | −12.0120 | −0.399073 | ||||||||
\(907\) | 18.7815 | 0.623631 | 0.311815 | − | 0.950143i | \(-0.399063\pi\) | ||||
0.311815 | + | 0.950143i | \(0.399063\pi\) | |||||||
\(908\) | −33.8243 | −1.12250 | ||||||||
\(909\) | −13.6386 | −0.452365 | ||||||||
\(910\) | −1.80644 | −0.0598828 | ||||||||
\(911\) | 10.9307 | 0.362152 | 0.181076 | − | 0.983469i | \(-0.442042\pi\) | ||||
0.181076 | + | 0.983469i | \(0.442042\pi\) | |||||||
\(912\) | −6.49432 | −0.215049 | ||||||||
\(913\) | 37.0365 | 1.22573 | ||||||||
\(914\) | −66.6589 | −2.20488 | ||||||||
\(915\) | −20.7973 | −0.687538 | ||||||||
\(916\) | −7.46367 | −0.246607 | ||||||||
\(917\) | −0.988280 | −0.0326359 | ||||||||
\(918\) | 2.24319 | 0.0740364 | ||||||||
\(919\) | 18.8356 | 0.621330 | 0.310665 | − | 0.950519i | \(-0.399448\pi\) | ||||
0.310665 | + | 0.950519i | \(0.399448\pi\) | |||||||
\(920\) | 11.3338 | 0.373665 | ||||||||
\(921\) | −24.8838 | −0.819949 | ||||||||
\(922\) | 66.9522 | 2.20495 | ||||||||
\(923\) | −5.30264 | −0.174539 | ||||||||
\(924\) | −0.639855 | −0.0210497 | ||||||||
\(925\) | −35.9555 | −1.18221 | ||||||||
\(926\) | −47.5498 | −1.56258 | ||||||||
\(927\) | 7.16588 | 0.235358 | ||||||||
\(928\) | −47.9899 | −1.57534 | ||||||||
\(929\) | 13.5613 | 0.444933 | 0.222466 | − | 0.974940i | \(-0.428589\pi\) | ||||
0.222466 | + | 0.974940i | \(0.428589\pi\) | |||||||
\(930\) | −34.5702 | −1.13360 | ||||||||
\(931\) | −52.1410 | −1.70885 | ||||||||
\(932\) | 21.0443 | 0.689328 | ||||||||
\(933\) | 1.31464 | 0.0430394 | ||||||||
\(934\) | −78.5218 | −2.56931 | ||||||||
\(935\) | −13.8244 | −0.452107 | ||||||||
\(936\) | −6.66663 | −0.217906 | ||||||||
\(937\) | −37.2320 | −1.21632 | −0.608158 | − | 0.793816i | \(-0.708091\pi\) | ||||
−0.608158 | + | 0.793816i | \(0.708091\pi\) | |||||||
\(938\) | 1.16057 | 0.0378938 | ||||||||
\(939\) | −25.5573 | −0.834032 | ||||||||
\(940\) | −67.0140 | −2.18575 | ||||||||
\(941\) | 52.2433 | 1.70308 | 0.851542 | − | 0.524287i | \(-0.175668\pi\) | ||||
0.851542 | + | 0.524287i | \(0.175668\pi\) | |||||||
\(942\) | −40.1449 | −1.30799 | ||||||||
\(943\) | −14.5352 | −0.473331 | ||||||||
\(944\) | −10.7086 | −0.348536 | ||||||||
\(945\) | 0.279613 | 0.00909583 | ||||||||
\(946\) | 19.1236 | 0.621763 | ||||||||
\(947\) | −23.1081 | −0.750912 | −0.375456 | − | 0.926840i | \(-0.622514\pi\) | ||||
−0.375456 | + | 0.926840i | \(0.622514\pi\) | |||||||
\(948\) | 3.03191 | 0.0984719 | ||||||||
\(949\) | 6.66357 | 0.216309 | ||||||||
\(950\) | 222.638 | 7.22333 | ||||||||
\(951\) | −15.9302 | −0.516573 | ||||||||
\(952\) | −0.151233 | −0.00490149 | ||||||||
\(953\) | −30.5266 | −0.988855 | −0.494427 | − | 0.869219i | \(-0.664622\pi\) | ||||
−0.494427 | + | 0.869219i | \(0.664622\pi\) | |||||||
\(954\) | −18.1520 | −0.587691 | ||||||||
\(955\) | −44.1154 | −1.42754 | ||||||||
\(956\) | 31.8487 | 1.03006 | ||||||||
\(957\) | 23.5439 | 0.761065 | ||||||||
\(958\) | −20.4440 | −0.660515 | ||||||||
\(959\) | −0.715135 | −0.0230929 | ||||||||
\(960\) | 55.7516 | 1.79937 | ||||||||
\(961\) | −18.0333 | −0.581718 | ||||||||
\(962\) | 17.4439 | 0.562414 | ||||||||
\(963\) | 9.38280 | 0.302357 | ||||||||
\(964\) | 75.8784 | 2.44388 | ||||||||
\(965\) | −8.15433 | −0.262497 | ||||||||
\(966\) | 0.167669 | 0.00539466 | ||||||||
\(967\) | −28.5510 | −0.918137 | −0.459069 | − | 0.888401i | \(-0.651817\pi\) | ||||
−0.459069 | + | 0.888401i | \(0.651817\pi\) | |||||||
\(968\) | −1.31000 | −0.0421051 | ||||||||
\(969\) | 7.45327 | 0.239433 | ||||||||
\(970\) | −83.0150 | −2.66545 | ||||||||
\(971\) | −57.0453 | −1.83067 | −0.915336 | − | 0.402691i | \(-0.868075\pi\) | ||||
−0.915336 | + | 0.402691i | \(0.868075\pi\) | |||||||
\(972\) | 3.03191 | 0.0972486 | ||||||||
\(973\) | 0.382748 | 0.0122703 | ||||||||
\(974\) | 19.2105 | 0.615545 | ||||||||
\(975\) | −38.3517 | −1.22824 | ||||||||
\(976\) | −4.23424 | −0.135535 | ||||||||
\(977\) | 13.8746 | 0.443889 | 0.221945 | − | 0.975059i | \(-0.428760\pi\) | ||||
0.221945 | + | 0.975059i | \(0.428760\pi\) | |||||||
\(978\) | 24.7875 | 0.792617 | ||||||||
\(979\) | −22.1765 | −0.708764 | ||||||||
\(980\) | 90.7756 | 2.89972 | ||||||||
\(981\) | 8.45836 | 0.270055 | ||||||||
\(982\) | −31.0620 | −0.991228 | ||||||||
\(983\) | −24.8229 | −0.791728 | −0.395864 | − | 0.918309i | \(-0.629555\pi\) | ||||
−0.395864 | + | 0.918309i | \(0.629555\pi\) | |||||||
\(984\) | 29.4091 | 0.937527 | ||||||||
\(985\) | −24.9675 | −0.795530 | ||||||||
\(986\) | 16.3500 | 0.520690 | ||||||||
\(987\) | −0.337417 | −0.0107401 | ||||||||
\(988\) | −65.0820 | −2.07054 | ||||||||
\(989\) | −3.01943 | −0.0960122 | ||||||||
\(990\) | −31.0108 | −0.985588 | ||||||||
\(991\) | 38.1462 | 1.21175 | 0.605877 | − | 0.795558i | \(-0.292822\pi\) | ||||
0.605877 | + | 0.795558i | \(0.292822\pi\) | |||||||
\(992\) | −23.7090 | −0.752762 | ||||||||
\(993\) | 14.8737 | 0.472003 | ||||||||
\(994\) | −0.269835 | −0.00855866 | ||||||||
\(995\) | −24.9731 | −0.791701 | ||||||||
\(996\) | 34.7631 | 1.10151 | ||||||||
\(997\) | −7.97553 | −0.252588 | −0.126294 | − | 0.991993i | \(-0.540308\pi\) | ||||
−0.126294 | + | 0.991993i | \(0.540308\pi\) | |||||||
\(998\) | −93.1199 | −2.94766 | ||||||||
\(999\) | −2.70010 | −0.0854273 |
(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 | 4029.2.a.k.1.26 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.26 | ✓ | 31 | 1.1 | even | 1 | trivial |