Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6022,2,Mod(1,6022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6022 = 2 \cdot 3011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6022.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: | \(48.0859120972\) |
Analytic rank: | \(0\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6022.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.13476 | −0.655156 | −0.327578 | − | 0.944824i | \(-0.606232\pi\) | ||||
−0.327578 | + | 0.944824i | \(0.606232\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.93476 | 1.75968 | 0.879839 | − | 0.475272i | \(-0.157650\pi\) | ||||
0.879839 | + | 0.475272i | \(0.157650\pi\) | |||||||
\(6\) | 1.13476 | 0.463265 | ||||||||
\(7\) | 4.57427 | 1.72891 | 0.864455 | − | 0.502710i | \(-0.167664\pi\) | ||||
0.864455 | + | 0.502710i | \(0.167664\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.71231 | −0.570770 | ||||||||
\(10\) | −3.93476 | −1.24428 | ||||||||
\(11\) | 0.0153971 | 0.00464241 | 0.00232120 | − | 0.999997i | \(-0.499261\pi\) | ||||
0.00232120 | + | 0.999997i | \(0.499261\pi\) | |||||||
\(12\) | −1.13476 | −0.327578 | ||||||||
\(13\) | 3.92451 | 1.08846 | 0.544231 | − | 0.838935i | \(-0.316821\pi\) | ||||
0.544231 | + | 0.838935i | \(0.316821\pi\) | |||||||
\(14\) | −4.57427 | −1.22252 | ||||||||
\(15\) | −4.46502 | −1.15286 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.90653 | 1.43254 | 0.716272 | − | 0.697821i | \(-0.245847\pi\) | ||||
0.716272 | + | 0.697821i | \(0.245847\pi\) | |||||||
\(18\) | 1.71231 | 0.403596 | ||||||||
\(19\) | 7.86873 | 1.80521 | 0.902606 | − | 0.430468i | \(-0.141652\pi\) | ||||
0.902606 | + | 0.430468i | \(0.141652\pi\) | |||||||
\(20\) | 3.93476 | 0.879839 | ||||||||
\(21\) | −5.19071 | −1.13271 | ||||||||
\(22\) | −0.0153971 | −0.00328268 | ||||||||
\(23\) | −1.42378 | −0.296880 | −0.148440 | − | 0.988921i | \(-0.547425\pi\) | ||||
−0.148440 | + | 0.988921i | \(0.547425\pi\) | |||||||
\(24\) | 1.13476 | 0.231633 | ||||||||
\(25\) | 10.4823 | 2.09647 | ||||||||
\(26\) | −3.92451 | −0.769659 | ||||||||
\(27\) | 5.34736 | 1.02910 | ||||||||
\(28\) | 4.57427 | 0.864455 | ||||||||
\(29\) | 3.86000 | 0.716784 | 0.358392 | − | 0.933571i | \(-0.383325\pi\) | ||||
0.358392 | + | 0.933571i | \(0.383325\pi\) | |||||||
\(30\) | 4.46502 | 0.815198 | ||||||||
\(31\) | −8.70807 | −1.56402 | −0.782008 | − | 0.623269i | \(-0.785804\pi\) | ||||
−0.782008 | + | 0.623269i | \(0.785804\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.0174721 | −0.00304150 | ||||||||
\(34\) | −5.90653 | −1.01296 | ||||||||
\(35\) | 17.9986 | 3.04232 | ||||||||
\(36\) | −1.71231 | −0.285385 | ||||||||
\(37\) | −1.84306 | −0.302997 | −0.151498 | − | 0.988458i | \(-0.548410\pi\) | ||||
−0.151498 | + | 0.988458i | \(0.548410\pi\) | |||||||
\(38\) | −7.86873 | −1.27648 | ||||||||
\(39\) | −4.45339 | −0.713113 | ||||||||
\(40\) | −3.93476 | −0.622140 | ||||||||
\(41\) | 1.78213 | 0.278321 | 0.139161 | − | 0.990270i | \(-0.455560\pi\) | ||||
0.139161 | + | 0.990270i | \(0.455560\pi\) | |||||||
\(42\) | 5.19071 | 0.800944 | ||||||||
\(43\) | 1.71782 | 0.261965 | 0.130982 | − | 0.991385i | \(-0.458187\pi\) | ||||
0.130982 | + | 0.991385i | \(0.458187\pi\) | |||||||
\(44\) | 0.0153971 | 0.00232120 | ||||||||
\(45\) | −6.73753 | −1.00437 | ||||||||
\(46\) | 1.42378 | 0.209926 | ||||||||
\(47\) | 4.03816 | 0.589026 | 0.294513 | − | 0.955647i | \(-0.404843\pi\) | ||||
0.294513 | + | 0.955647i | \(0.404843\pi\) | |||||||
\(48\) | −1.13476 | −0.163789 | ||||||||
\(49\) | 13.9239 | 1.98913 | ||||||||
\(50\) | −10.4823 | −1.48243 | ||||||||
\(51\) | −6.70252 | −0.938541 | ||||||||
\(52\) | 3.92451 | 0.544231 | ||||||||
\(53\) | −8.24660 | −1.13276 | −0.566379 | − | 0.824145i | \(-0.691656\pi\) | ||||
−0.566379 | + | 0.824145i | \(0.691656\pi\) | |||||||
\(54\) | −5.34736 | −0.727684 | ||||||||
\(55\) | 0.0605840 | 0.00816914 | ||||||||
\(56\) | −4.57427 | −0.611262 | ||||||||
\(57\) | −8.92916 | −1.18270 | ||||||||
\(58\) | −3.86000 | −0.506843 | ||||||||
\(59\) | 2.88671 | 0.375818 | 0.187909 | − | 0.982186i | \(-0.439829\pi\) | ||||
0.187909 | + | 0.982186i | \(0.439829\pi\) | |||||||
\(60\) | −4.46502 | −0.576432 | ||||||||
\(61\) | −7.58440 | −0.971083 | −0.485542 | − | 0.874213i | \(-0.661378\pi\) | ||||
−0.485542 | + | 0.874213i | \(0.661378\pi\) | |||||||
\(62\) | 8.70807 | 1.10593 | ||||||||
\(63\) | −7.83257 | −0.986811 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 15.4420 | 1.91534 | ||||||||
\(66\) | 0.0174721 | 0.00215067 | ||||||||
\(67\) | −7.27185 | −0.888398 | −0.444199 | − | 0.895928i | \(-0.646512\pi\) | ||||
−0.444199 | + | 0.895928i | \(0.646512\pi\) | |||||||
\(68\) | 5.90653 | 0.716272 | ||||||||
\(69\) | 1.61566 | 0.194502 | ||||||||
\(70\) | −17.9986 | −2.15125 | ||||||||
\(71\) | 0.785801 | 0.0932574 | 0.0466287 | − | 0.998912i | \(-0.485152\pi\) | ||||
0.0466287 | + | 0.998912i | \(0.485152\pi\) | |||||||
\(72\) | 1.71231 | 0.201798 | ||||||||
\(73\) | 5.91895 | 0.692761 | 0.346380 | − | 0.938094i | \(-0.387411\pi\) | ||||
0.346380 | + | 0.938094i | \(0.387411\pi\) | |||||||
\(74\) | 1.84306 | 0.214251 | ||||||||
\(75\) | −11.8950 | −1.37351 | ||||||||
\(76\) | 7.86873 | 0.902606 | ||||||||
\(77\) | 0.0704305 | 0.00802631 | ||||||||
\(78\) | 4.45339 | 0.504247 | ||||||||
\(79\) | −4.17465 | −0.469685 | −0.234842 | − | 0.972033i | \(-0.575457\pi\) | ||||
−0.234842 | + | 0.972033i | \(0.575457\pi\) | |||||||
\(80\) | 3.93476 | 0.439920 | ||||||||
\(81\) | −0.931057 | −0.103451 | ||||||||
\(82\) | −1.78213 | −0.196803 | ||||||||
\(83\) | 5.21858 | 0.572814 | 0.286407 | − | 0.958108i | \(-0.407539\pi\) | ||||
0.286407 | + | 0.958108i | \(0.407539\pi\) | |||||||
\(84\) | −5.19071 | −0.566353 | ||||||||
\(85\) | 23.2408 | 2.52082 | ||||||||
\(86\) | −1.71782 | −0.185237 | ||||||||
\(87\) | −4.38019 | −0.469605 | ||||||||
\(88\) | −0.0153971 | −0.00164134 | ||||||||
\(89\) | 11.0328 | 1.16948 | 0.584738 | − | 0.811222i | \(-0.301197\pi\) | ||||
0.584738 | + | 0.811222i | \(0.301197\pi\) | |||||||
\(90\) | 6.73753 | 0.710198 | ||||||||
\(91\) | 17.9517 | 1.88185 | ||||||||
\(92\) | −1.42378 | −0.148440 | ||||||||
\(93\) | 9.88160 | 1.02467 | ||||||||
\(94\) | −4.03816 | −0.416504 | ||||||||
\(95\) | 30.9616 | 3.17659 | ||||||||
\(96\) | 1.13476 | 0.115816 | ||||||||
\(97\) | −3.27956 | −0.332989 | −0.166495 | − | 0.986042i | \(-0.553245\pi\) | ||||
−0.166495 | + | 0.986042i | \(0.553245\pi\) | |||||||
\(98\) | −13.9239 | −1.40653 | ||||||||
\(99\) | −0.0263647 | −0.00264975 | ||||||||
\(100\) | 10.4823 | 1.04823 | ||||||||
\(101\) | 1.40859 | 0.140160 | 0.0700799 | − | 0.997541i | \(-0.477675\pi\) | ||||
0.0700799 | + | 0.997541i | \(0.477675\pi\) | |||||||
\(102\) | 6.70252 | 0.663648 | ||||||||
\(103\) | −3.38461 | −0.333496 | −0.166748 | − | 0.986000i | \(-0.553327\pi\) | ||||
−0.166748 | + | 0.986000i | \(0.553327\pi\) | |||||||
\(104\) | −3.92451 | −0.384830 | ||||||||
\(105\) | −20.4242 | −1.99320 | ||||||||
\(106\) | 8.24660 | 0.800981 | ||||||||
\(107\) | −14.3324 | −1.38557 | −0.692785 | − | 0.721145i | \(-0.743616\pi\) | ||||
−0.692785 | + | 0.721145i | \(0.743616\pi\) | |||||||
\(108\) | 5.34736 | 0.514550 | ||||||||
\(109\) | −5.03433 | −0.482202 | −0.241101 | − | 0.970500i | \(-0.577508\pi\) | ||||
−0.241101 | + | 0.970500i | \(0.577508\pi\) | |||||||
\(110\) | −0.0605840 | −0.00577646 | ||||||||
\(111\) | 2.09143 | 0.198510 | ||||||||
\(112\) | 4.57427 | 0.432227 | ||||||||
\(113\) | −14.3578 | −1.35067 | −0.675333 | − | 0.737513i | \(-0.736000\pi\) | ||||
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(114\) | 8.92916 | 0.836292 | ||||||||
\(115\) | −5.60225 | −0.522412 | ||||||||
\(116\) | 3.86000 | 0.358392 | ||||||||
\(117\) | −6.71998 | −0.621262 | ||||||||
\(118\) | −2.88671 | −0.265743 | ||||||||
\(119\) | 27.0181 | 2.47674 | ||||||||
\(120\) | 4.46502 | 0.407599 | ||||||||
\(121\) | −10.9998 | −0.999978 | ||||||||
\(122\) | 7.58440 | 0.686660 | ||||||||
\(123\) | −2.02229 | −0.182344 | ||||||||
\(124\) | −8.70807 | −0.782008 | ||||||||
\(125\) | 21.5717 | 1.92943 | ||||||||
\(126\) | 7.83257 | 0.697780 | ||||||||
\(127\) | −19.4224 | −1.72346 | −0.861732 | − | 0.507364i | \(-0.830620\pi\) | ||||
−0.861732 | + | 0.507364i | \(0.830620\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.94932 | −0.171628 | ||||||||
\(130\) | −15.4420 | −1.35435 | ||||||||
\(131\) | 14.4036 | 1.25845 | 0.629224 | − | 0.777224i | \(-0.283373\pi\) | ||||
0.629224 | + | 0.777224i | \(0.283373\pi\) | |||||||
\(132\) | −0.0174721 | −0.00152075 | ||||||||
\(133\) | 35.9937 | 3.12105 | ||||||||
\(134\) | 7.27185 | 0.628192 | ||||||||
\(135\) | 21.0406 | 1.81088 | ||||||||
\(136\) | −5.90653 | −0.506481 | ||||||||
\(137\) | 9.57782 | 0.818288 | 0.409144 | − | 0.912470i | \(-0.365827\pi\) | ||||
0.409144 | + | 0.912470i | \(0.365827\pi\) | |||||||
\(138\) | −1.61566 | −0.137534 | ||||||||
\(139\) | −4.53977 | −0.385059 | −0.192529 | − | 0.981291i | \(-0.561669\pi\) | ||||
−0.192529 | + | 0.981291i | \(0.561669\pi\) | |||||||
\(140\) | 17.9986 | 1.52116 | ||||||||
\(141\) | −4.58236 | −0.385904 | ||||||||
\(142\) | −0.785801 | −0.0659429 | ||||||||
\(143\) | 0.0604261 | 0.00505309 | ||||||||
\(144\) | −1.71231 | −0.142693 | ||||||||
\(145\) | 15.1882 | 1.26131 | ||||||||
\(146\) | −5.91895 | −0.489856 | ||||||||
\(147\) | −15.8003 | −1.30319 | ||||||||
\(148\) | −1.84306 | −0.151498 | ||||||||
\(149\) | −9.69003 | −0.793838 | −0.396919 | − | 0.917854i | \(-0.629921\pi\) | ||||
−0.396919 | + | 0.917854i | \(0.629921\pi\) | |||||||
\(150\) | 11.8950 | 0.971220 | ||||||||
\(151\) | 4.27467 | 0.347868 | 0.173934 | − | 0.984757i | \(-0.444352\pi\) | ||||
0.173934 | + | 0.984757i | \(0.444352\pi\) | |||||||
\(152\) | −7.86873 | −0.638239 | ||||||||
\(153\) | −10.1138 | −0.817654 | ||||||||
\(154\) | −0.0704305 | −0.00567546 | ||||||||
\(155\) | −34.2642 | −2.75216 | ||||||||
\(156\) | −4.45339 | −0.356557 | ||||||||
\(157\) | −11.7306 | −0.936206 | −0.468103 | − | 0.883674i | \(-0.655062\pi\) | ||||
−0.468103 | + | 0.883674i | \(0.655062\pi\) | |||||||
\(158\) | 4.17465 | 0.332117 | ||||||||
\(159\) | 9.35795 | 0.742133 | ||||||||
\(160\) | −3.93476 | −0.311070 | ||||||||
\(161\) | −6.51277 | −0.513278 | ||||||||
\(162\) | 0.931057 | 0.0731507 | ||||||||
\(163\) | −23.4773 | −1.83889 | −0.919443 | − | 0.393223i | \(-0.871360\pi\) | ||||
−0.919443 | + | 0.393223i | \(0.871360\pi\) | |||||||
\(164\) | 1.78213 | 0.139161 | ||||||||
\(165\) | −0.0687485 | −0.00535206 | ||||||||
\(166\) | −5.21858 | −0.405041 | ||||||||
\(167\) | −13.1562 | −1.01806 | −0.509028 | − | 0.860750i | \(-0.669995\pi\) | ||||
−0.509028 | + | 0.860750i | \(0.669995\pi\) | |||||||
\(168\) | 5.19071 | 0.400472 | ||||||||
\(169\) | 2.40176 | 0.184751 | ||||||||
\(170\) | −23.2408 | −1.78249 | ||||||||
\(171\) | −13.4737 | −1.03036 | ||||||||
\(172\) | 1.71782 | 0.130982 | ||||||||
\(173\) | 4.68002 | 0.355815 | 0.177908 | − | 0.984047i | \(-0.443067\pi\) | ||||
0.177908 | + | 0.984047i | \(0.443067\pi\) | |||||||
\(174\) | 4.38019 | 0.332061 | ||||||||
\(175\) | 47.9490 | 3.62460 | ||||||||
\(176\) | 0.0153971 | 0.00116060 | ||||||||
\(177\) | −3.27573 | −0.246219 | ||||||||
\(178\) | −11.0328 | −0.826944 | ||||||||
\(179\) | 10.9632 | 0.819430 | 0.409715 | − | 0.912213i | \(-0.365628\pi\) | ||||
0.409715 | + | 0.912213i | \(0.365628\pi\) | |||||||
\(180\) | −6.73753 | −0.502186 | ||||||||
\(181\) | −4.64220 | −0.345052 | −0.172526 | − | 0.985005i | \(-0.555193\pi\) | ||||
−0.172526 | + | 0.985005i | \(0.555193\pi\) | |||||||
\(182\) | −17.9517 | −1.33067 | ||||||||
\(183\) | 8.60651 | 0.636211 | ||||||||
\(184\) | 1.42378 | 0.104963 | ||||||||
\(185\) | −7.25198 | −0.533177 | ||||||||
\(186\) | −9.88160 | −0.724554 | ||||||||
\(187\) | 0.0909437 | 0.00665046 | ||||||||
\(188\) | 4.03816 | 0.294513 | ||||||||
\(189\) | 24.4602 | 1.77922 | ||||||||
\(190\) | −30.9616 | −2.24619 | ||||||||
\(191\) | −6.21455 | −0.449669 | −0.224834 | − | 0.974397i | \(-0.572184\pi\) | ||||
−0.224834 | + | 0.974397i | \(0.572184\pi\) | |||||||
\(192\) | −1.13476 | −0.0818945 | ||||||||
\(193\) | 18.3019 | 1.31740 | 0.658699 | − | 0.752407i | \(-0.271107\pi\) | ||||
0.658699 | + | 0.752407i | \(0.271107\pi\) | |||||||
\(194\) | 3.27956 | 0.235459 | ||||||||
\(195\) | −17.5230 | −1.25485 | ||||||||
\(196\) | 13.9239 | 0.994565 | ||||||||
\(197\) | 15.7263 | 1.12045 | 0.560224 | − | 0.828341i | \(-0.310715\pi\) | ||||
0.560224 | + | 0.828341i | \(0.310715\pi\) | |||||||
\(198\) | 0.0263647 | 0.00187366 | ||||||||
\(199\) | −23.4087 | −1.65940 | −0.829701 | − | 0.558208i | \(-0.811489\pi\) | ||||
−0.829701 | + | 0.558208i | \(0.811489\pi\) | |||||||
\(200\) | −10.4823 | −0.741213 | ||||||||
\(201\) | 8.25183 | 0.582039 | ||||||||
\(202\) | −1.40859 | −0.0991080 | ||||||||
\(203\) | 17.6567 | 1.23925 | ||||||||
\(204\) | −6.70252 | −0.469270 | ||||||||
\(205\) | 7.01223 | 0.489756 | ||||||||
\(206\) | 3.38461 | 0.235817 | ||||||||
\(207\) | 2.43796 | 0.169450 | ||||||||
\(208\) | 3.92451 | 0.272116 | ||||||||
\(209\) | 0.121156 | 0.00838053 | ||||||||
\(210\) | 20.4242 | 1.40940 | ||||||||
\(211\) | −19.2508 | −1.32528 | −0.662639 | − | 0.748939i | \(-0.730564\pi\) | ||||
−0.662639 | + | 0.748939i | \(0.730564\pi\) | |||||||
\(212\) | −8.24660 | −0.566379 | ||||||||
\(213\) | −0.891698 | −0.0610982 | ||||||||
\(214\) | 14.3324 | 0.979745 | ||||||||
\(215\) | 6.75920 | 0.460973 | ||||||||
\(216\) | −5.34736 | −0.363842 | ||||||||
\(217\) | −39.8330 | −2.70404 | ||||||||
\(218\) | 5.03433 | 0.340968 | ||||||||
\(219\) | −6.71661 | −0.453866 | ||||||||
\(220\) | 0.0605840 | 0.00408457 | ||||||||
\(221\) | 23.1802 | 1.55927 | ||||||||
\(222\) | −2.09143 | −0.140368 | ||||||||
\(223\) | −12.4118 | −0.831157 | −0.415578 | − | 0.909557i | \(-0.636421\pi\) | ||||
−0.415578 | + | 0.909557i | \(0.636421\pi\) | |||||||
\(224\) | −4.57427 | −0.305631 | ||||||||
\(225\) | −17.9490 | −1.19660 | ||||||||
\(226\) | 14.3578 | 0.955065 | ||||||||
\(227\) | 11.2467 | 0.746468 | 0.373234 | − | 0.927737i | \(-0.378249\pi\) | ||||
0.373234 | + | 0.927737i | \(0.378249\pi\) | |||||||
\(228\) | −8.92916 | −0.591348 | ||||||||
\(229\) | 8.89434 | 0.587754 | 0.293877 | − | 0.955843i | \(-0.405054\pi\) | ||||
0.293877 | + | 0.955843i | \(0.405054\pi\) | |||||||
\(230\) | 5.60225 | 0.369401 | ||||||||
\(231\) | −0.0799220 | −0.00525848 | ||||||||
\(232\) | −3.86000 | −0.253421 | ||||||||
\(233\) | −23.7665 | −1.55699 | −0.778496 | − | 0.627649i | \(-0.784017\pi\) | ||||
−0.778496 | + | 0.627649i | \(0.784017\pi\) | |||||||
\(234\) | 6.71998 | 0.439299 | ||||||||
\(235\) | 15.8892 | 1.03650 | ||||||||
\(236\) | 2.88671 | 0.187909 | ||||||||
\(237\) | 4.73724 | 0.307717 | ||||||||
\(238\) | −27.0181 | −1.75132 | ||||||||
\(239\) | −2.63371 | −0.170361 | −0.0851804 | − | 0.996366i | \(-0.527147\pi\) | ||||
−0.0851804 | + | 0.996366i | \(0.527147\pi\) | |||||||
\(240\) | −4.46502 | −0.288216 | ||||||||
\(241\) | −26.1494 | −1.68443 | −0.842215 | − | 0.539142i | \(-0.818748\pi\) | ||||
−0.842215 | + | 0.539142i | \(0.818748\pi\) | |||||||
\(242\) | 10.9998 | 0.707092 | ||||||||
\(243\) | −14.9856 | −0.961324 | ||||||||
\(244\) | −7.58440 | −0.485542 | ||||||||
\(245\) | 54.7872 | 3.50023 | ||||||||
\(246\) | 2.02229 | 0.128937 | ||||||||
\(247\) | 30.8809 | 1.96491 | ||||||||
\(248\) | 8.70807 | 0.552963 | ||||||||
\(249\) | −5.92186 | −0.375282 | ||||||||
\(250\) | −21.5717 | −1.36431 | ||||||||
\(251\) | −13.8676 | −0.875315 | −0.437657 | − | 0.899142i | \(-0.644192\pi\) | ||||
−0.437657 | + | 0.899142i | \(0.644192\pi\) | |||||||
\(252\) | −7.83257 | −0.493405 | ||||||||
\(253\) | −0.0219222 | −0.00137824 | ||||||||
\(254\) | 19.4224 | 1.21867 | ||||||||
\(255\) | −26.3728 | −1.65153 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.6328 | −1.03753 | −0.518763 | − | 0.854918i | \(-0.673607\pi\) | ||||
−0.518763 | + | 0.854918i | \(0.673607\pi\) | |||||||
\(258\) | 1.94932 | 0.121359 | ||||||||
\(259\) | −8.43063 | −0.523854 | ||||||||
\(260\) | 15.4420 | 0.957672 | ||||||||
\(261\) | −6.60952 | −0.409119 | ||||||||
\(262\) | −14.4036 | −0.889857 | ||||||||
\(263\) | 1.92911 | 0.118954 | 0.0594771 | − | 0.998230i | \(-0.481057\pi\) | ||||
0.0594771 | + | 0.998230i | \(0.481057\pi\) | |||||||
\(264\) | 0.0174721 | 0.00107533 | ||||||||
\(265\) | −32.4484 | −1.99329 | ||||||||
\(266\) | −35.9937 | −2.20691 | ||||||||
\(267\) | −12.5196 | −0.766189 | ||||||||
\(268\) | −7.27185 | −0.444199 | ||||||||
\(269\) | 16.3692 | 0.998047 | 0.499023 | − | 0.866588i | \(-0.333692\pi\) | ||||
0.499023 | + | 0.866588i | \(0.333692\pi\) | |||||||
\(270\) | −21.0406 | −1.28049 | ||||||||
\(271\) | 0.0530257 | 0.00322108 | 0.00161054 | − | 0.999999i | \(-0.499487\pi\) | ||||
0.00161054 | + | 0.999999i | \(0.499487\pi\) | |||||||
\(272\) | 5.90653 | 0.358136 | ||||||||
\(273\) | −20.3710 | −1.23291 | ||||||||
\(274\) | −9.57782 | −0.578617 | ||||||||
\(275\) | 0.161398 | 0.00973265 | ||||||||
\(276\) | 1.61566 | 0.0972512 | ||||||||
\(277\) | −6.36466 | −0.382415 | −0.191208 | − | 0.981550i | \(-0.561240\pi\) | ||||
−0.191208 | + | 0.981550i | \(0.561240\pi\) | |||||||
\(278\) | 4.53977 | 0.272278 | ||||||||
\(279\) | 14.9109 | 0.892694 | ||||||||
\(280\) | −17.9986 | −1.07562 | ||||||||
\(281\) | −14.0335 | −0.837169 | −0.418585 | − | 0.908178i | \(-0.637474\pi\) | ||||
−0.418585 | + | 0.908178i | \(0.637474\pi\) | |||||||
\(282\) | 4.58236 | 0.272875 | ||||||||
\(283\) | −10.4681 | −0.622262 | −0.311131 | − | 0.950367i | \(-0.600708\pi\) | ||||
−0.311131 | + | 0.950367i | \(0.600708\pi\) | |||||||
\(284\) | 0.785801 | 0.0466287 | ||||||||
\(285\) | −35.1341 | −2.08116 | ||||||||
\(286\) | −0.0604261 | −0.00357307 | ||||||||
\(287\) | 8.15191 | 0.481192 | ||||||||
\(288\) | 1.71231 | 0.100899 | ||||||||
\(289\) | 17.8871 | 1.05219 | ||||||||
\(290\) | −15.1882 | −0.891880 | ||||||||
\(291\) | 3.72153 | 0.218160 | ||||||||
\(292\) | 5.91895 | 0.346380 | ||||||||
\(293\) | −23.4894 | −1.37226 | −0.686131 | − | 0.727478i | \(-0.740693\pi\) | ||||
−0.686131 | + | 0.727478i | \(0.740693\pi\) | |||||||
\(294\) | 15.8003 | 0.921495 | ||||||||
\(295\) | 11.3585 | 0.661318 | ||||||||
\(296\) | 1.84306 | 0.107125 | ||||||||
\(297\) | 0.0823340 | 0.00477750 | ||||||||
\(298\) | 9.69003 | 0.561329 | ||||||||
\(299\) | −5.58765 | −0.323142 | ||||||||
\(300\) | −11.8950 | −0.686757 | ||||||||
\(301\) | 7.85775 | 0.452913 | ||||||||
\(302\) | −4.27467 | −0.245980 | ||||||||
\(303\) | −1.59842 | −0.0918266 | ||||||||
\(304\) | 7.86873 | 0.451303 | ||||||||
\(305\) | −29.8428 | −1.70879 | ||||||||
\(306\) | 10.1138 | 0.578169 | ||||||||
\(307\) | −32.0967 | −1.83186 | −0.915928 | − | 0.401342i | \(-0.868544\pi\) | ||||
−0.915928 | + | 0.401342i | \(0.868544\pi\) | |||||||
\(308\) | 0.0704305 | 0.00401315 | ||||||||
\(309\) | 3.84073 | 0.218492 | ||||||||
\(310\) | 34.2642 | 1.94607 | ||||||||
\(311\) | −26.5241 | −1.50404 | −0.752022 | − | 0.659138i | \(-0.770921\pi\) | ||||
−0.752022 | + | 0.659138i | \(0.770921\pi\) | |||||||
\(312\) | 4.45339 | 0.252124 | ||||||||
\(313\) | 28.6176 | 1.61756 | 0.808782 | − | 0.588108i | \(-0.200127\pi\) | ||||
0.808782 | + | 0.588108i | \(0.200127\pi\) | |||||||
\(314\) | 11.7306 | 0.661997 | ||||||||
\(315\) | −30.8193 | −1.73647 | ||||||||
\(316\) | −4.17465 | −0.234842 | ||||||||
\(317\) | −26.1274 | −1.46746 | −0.733729 | − | 0.679442i | \(-0.762222\pi\) | ||||
−0.733729 | + | 0.679442i | \(0.762222\pi\) | |||||||
\(318\) | −9.35795 | −0.524768 | ||||||||
\(319\) | 0.0594329 | 0.00332760 | ||||||||
\(320\) | 3.93476 | 0.219960 | ||||||||
\(321\) | 16.2639 | 0.907764 | ||||||||
\(322\) | 6.51277 | 0.362942 | ||||||||
\(323\) | 46.4770 | 2.58605 | ||||||||
\(324\) | −0.931057 | −0.0517254 | ||||||||
\(325\) | 41.1380 | 2.28193 | ||||||||
\(326\) | 23.4773 | 1.30029 | ||||||||
\(327\) | 5.71278 | 0.315917 | ||||||||
\(328\) | −1.78213 | −0.0984014 | ||||||||
\(329\) | 18.4716 | 1.01837 | ||||||||
\(330\) | 0.0687485 | 0.00378448 | ||||||||
\(331\) | −18.5023 | −1.01698 | −0.508488 | − | 0.861069i | \(-0.669795\pi\) | ||||
−0.508488 | + | 0.861069i | \(0.669795\pi\) | |||||||
\(332\) | 5.21858 | 0.286407 | ||||||||
\(333\) | 3.15589 | 0.172942 | ||||||||
\(334\) | 13.1562 | 0.719875 | ||||||||
\(335\) | −28.6130 | −1.56329 | ||||||||
\(336\) | −5.19071 | −0.283176 | ||||||||
\(337\) | 33.6511 | 1.83309 | 0.916547 | − | 0.399927i | \(-0.130965\pi\) | ||||
0.916547 | + | 0.399927i | \(0.130965\pi\) | |||||||
\(338\) | −2.40176 | −0.130639 | ||||||||
\(339\) | 16.2927 | 0.884897 | ||||||||
\(340\) | 23.2408 | 1.26041 | ||||||||
\(341\) | −0.134079 | −0.00726080 | ||||||||
\(342\) | 13.4737 | 0.728575 | ||||||||
\(343\) | 31.6718 | 1.71012 | ||||||||
\(344\) | −1.71782 | −0.0926185 | ||||||||
\(345\) | 6.35723 | 0.342262 | ||||||||
\(346\) | −4.68002 | −0.251599 | ||||||||
\(347\) | −34.4206 | −1.84779 | −0.923897 | − | 0.382641i | \(-0.875015\pi\) | ||||
−0.923897 | + | 0.382641i | \(0.875015\pi\) | |||||||
\(348\) | −4.38019 | −0.234803 | ||||||||
\(349\) | −0.751923 | −0.0402495 | −0.0201248 | − | 0.999797i | \(-0.506406\pi\) | ||||
−0.0201248 | + | 0.999797i | \(0.506406\pi\) | |||||||
\(350\) | −47.9490 | −2.56298 | ||||||||
\(351\) | 20.9858 | 1.12014 | ||||||||
\(352\) | −0.0153971 | −0.000820670 0 | ||||||||
\(353\) | 1.93776 | 0.103137 | 0.0515684 | − | 0.998669i | \(-0.483578\pi\) | ||||
0.0515684 | + | 0.998669i | \(0.483578\pi\) | |||||||
\(354\) | 3.27573 | 0.174103 | ||||||||
\(355\) | 3.09194 | 0.164103 | ||||||||
\(356\) | 11.0328 | 0.584738 | ||||||||
\(357\) | −30.6591 | −1.62265 | ||||||||
\(358\) | −10.9632 | −0.579425 | ||||||||
\(359\) | 34.5060 | 1.82116 | 0.910578 | − | 0.413336i | \(-0.135637\pi\) | ||||
0.910578 | + | 0.413336i | \(0.135637\pi\) | |||||||
\(360\) | 6.73753 | 0.355099 | ||||||||
\(361\) | 42.9170 | 2.25879 | ||||||||
\(362\) | 4.64220 | 0.243988 | ||||||||
\(363\) | 12.4821 | 0.655142 | ||||||||
\(364\) | 17.9517 | 0.940927 | ||||||||
\(365\) | 23.2896 | 1.21904 | ||||||||
\(366\) | −8.60651 | −0.449869 | ||||||||
\(367\) | −11.9224 | −0.622345 | −0.311173 | − | 0.950353i | \(-0.600722\pi\) | ||||
−0.311173 | + | 0.950353i | \(0.600722\pi\) | |||||||
\(368\) | −1.42378 | −0.0742199 | ||||||||
\(369\) | −3.05155 | −0.158857 | ||||||||
\(370\) | 7.25198 | 0.377013 | ||||||||
\(371\) | −37.7221 | −1.95844 | ||||||||
\(372\) | 9.88160 | 0.512337 | ||||||||
\(373\) | −18.2778 | −0.946390 | −0.473195 | − | 0.880958i | \(-0.656899\pi\) | ||||
−0.473195 | + | 0.880958i | \(0.656899\pi\) | |||||||
\(374\) | −0.0909437 | −0.00470258 | ||||||||
\(375\) | −24.4787 | −1.26408 | ||||||||
\(376\) | −4.03816 | −0.208252 | ||||||||
\(377\) | 15.1486 | 0.780192 | ||||||||
\(378\) | −24.4602 | −1.25810 | ||||||||
\(379\) | −5.50543 | −0.282795 | −0.141398 | − | 0.989953i | \(-0.545160\pi\) | ||||
−0.141398 | + | 0.989953i | \(0.545160\pi\) | |||||||
\(380\) | 30.9616 | 1.58830 | ||||||||
\(381\) | 22.0399 | 1.12914 | ||||||||
\(382\) | 6.21455 | 0.317964 | ||||||||
\(383\) | 26.0096 | 1.32903 | 0.664515 | − | 0.747274i | \(-0.268638\pi\) | ||||
0.664515 | + | 0.747274i | \(0.268638\pi\) | |||||||
\(384\) | 1.13476 | 0.0579082 | ||||||||
\(385\) | 0.277127 | 0.0141237 | ||||||||
\(386\) | −18.3019 | −0.931541 | ||||||||
\(387\) | −2.94144 | −0.149522 | ||||||||
\(388\) | −3.27956 | −0.166495 | ||||||||
\(389\) | −1.85343 | −0.0939726 | −0.0469863 | − | 0.998896i | \(-0.514962\pi\) | ||||
−0.0469863 | + | 0.998896i | \(0.514962\pi\) | |||||||
\(390\) | 17.5230 | 0.887312 | ||||||||
\(391\) | −8.40963 | −0.425293 | ||||||||
\(392\) | −13.9239 | −0.703263 | ||||||||
\(393\) | −16.3447 | −0.824480 | ||||||||
\(394\) | −15.7263 | −0.792277 | ||||||||
\(395\) | −16.4262 | −0.826494 | ||||||||
\(396\) | −0.0263647 | −0.00132487 | ||||||||
\(397\) | 19.7166 | 0.989549 | 0.494774 | − | 0.869022i | \(-0.335251\pi\) | ||||
0.494774 | + | 0.869022i | \(0.335251\pi\) | |||||||
\(398\) | 23.4087 | 1.17337 | ||||||||
\(399\) | −40.8443 | −2.04477 | ||||||||
\(400\) | 10.4823 | 0.524117 | ||||||||
\(401\) | 33.8736 | 1.69157 | 0.845783 | − | 0.533527i | \(-0.179134\pi\) | ||||
0.845783 | + | 0.533527i | \(0.179134\pi\) | |||||||
\(402\) | −8.25183 | −0.411564 | ||||||||
\(403\) | −34.1749 | −1.70237 | ||||||||
\(404\) | 1.40859 | 0.0700799 | ||||||||
\(405\) | −3.66348 | −0.182040 | ||||||||
\(406\) | −17.6567 | −0.876285 | ||||||||
\(407\) | −0.0283778 | −0.00140663 | ||||||||
\(408\) | 6.70252 | 0.331824 | ||||||||
\(409\) | −18.3199 | −0.905861 | −0.452931 | − | 0.891546i | \(-0.649621\pi\) | ||||
−0.452931 | + | 0.891546i | \(0.649621\pi\) | |||||||
\(410\) | −7.01223 | −0.346310 | ||||||||
\(411\) | −10.8686 | −0.536107 | ||||||||
\(412\) | −3.38461 | −0.166748 | ||||||||
\(413\) | 13.2046 | 0.649755 | ||||||||
\(414\) | −2.43796 | −0.119819 | ||||||||
\(415\) | 20.5339 | 1.00797 | ||||||||
\(416\) | −3.92451 | −0.192415 | ||||||||
\(417\) | 5.15157 | 0.252274 | ||||||||
\(418\) | −0.121156 | −0.00592593 | ||||||||
\(419\) | 6.86468 | 0.335362 | 0.167681 | − | 0.985841i | \(-0.446372\pi\) | ||||
0.167681 | + | 0.985841i | \(0.446372\pi\) | |||||||
\(420\) | −20.4242 | −0.996599 | ||||||||
\(421\) | 36.7808 | 1.79259 | 0.896293 | − | 0.443463i | \(-0.146250\pi\) | ||||
0.896293 | + | 0.443463i | \(0.146250\pi\) | |||||||
\(422\) | 19.2508 | 0.937113 | ||||||||
\(423\) | −6.91458 | −0.336199 | ||||||||
\(424\) | 8.24660 | 0.400490 | ||||||||
\(425\) | 61.9143 | 3.00328 | ||||||||
\(426\) | 0.891698 | 0.0432029 | ||||||||
\(427\) | −34.6931 | −1.67892 | ||||||||
\(428\) | −14.3324 | −0.692785 | ||||||||
\(429\) | −0.0685694 | −0.00331056 | ||||||||
\(430\) | −6.75920 | −0.325957 | ||||||||
\(431\) | 25.5159 | 1.22906 | 0.614528 | − | 0.788895i | \(-0.289346\pi\) | ||||
0.614528 | + | 0.788895i | \(0.289346\pi\) | |||||||
\(432\) | 5.34736 | 0.257275 | ||||||||
\(433\) | 5.51689 | 0.265125 | 0.132562 | − | 0.991175i | \(-0.457680\pi\) | ||||
0.132562 | + | 0.991175i | \(0.457680\pi\) | |||||||
\(434\) | 39.8330 | 1.91205 | ||||||||
\(435\) | −17.2350 | −0.826354 | ||||||||
\(436\) | −5.03433 | −0.241101 | ||||||||
\(437\) | −11.2034 | −0.535930 | ||||||||
\(438\) | 6.71661 | 0.320932 | ||||||||
\(439\) | 35.0980 | 1.67514 | 0.837568 | − | 0.546333i | \(-0.183977\pi\) | ||||
0.837568 | + | 0.546333i | \(0.183977\pi\) | |||||||
\(440\) | −0.0605840 | −0.00288823 | ||||||||
\(441\) | −23.8421 | −1.13534 | ||||||||
\(442\) | −23.1802 | −1.10257 | ||||||||
\(443\) | 27.3957 | 1.30161 | 0.650805 | − | 0.759245i | \(-0.274432\pi\) | ||||
0.650805 | + | 0.759245i | \(0.274432\pi\) | |||||||
\(444\) | 2.09143 | 0.0992551 | ||||||||
\(445\) | 43.4115 | 2.05790 | ||||||||
\(446\) | 12.4118 | 0.587717 | ||||||||
\(447\) | 10.9959 | 0.520088 | ||||||||
\(448\) | 4.57427 | 0.216114 | ||||||||
\(449\) | −9.48377 | −0.447567 | −0.223783 | − | 0.974639i | \(-0.571841\pi\) | ||||
−0.223783 | + | 0.974639i | \(0.571841\pi\) | |||||||
\(450\) | 17.9490 | 0.846125 | ||||||||
\(451\) | 0.0274396 | 0.00129208 | ||||||||
\(452\) | −14.3578 | −0.675333 | ||||||||
\(453\) | −4.85074 | −0.227908 | ||||||||
\(454\) | −11.2467 | −0.527832 | ||||||||
\(455\) | 70.6358 | 3.31146 | ||||||||
\(456\) | 8.92916 | 0.418146 | ||||||||
\(457\) | 9.36207 | 0.437939 | 0.218969 | − | 0.975732i | \(-0.429730\pi\) | ||||
0.218969 | + | 0.975732i | \(0.429730\pi\) | |||||||
\(458\) | −8.89434 | −0.415605 | ||||||||
\(459\) | 31.5844 | 1.47423 | ||||||||
\(460\) | −5.60225 | −0.261206 | ||||||||
\(461\) | −23.8236 | −1.10958 | −0.554788 | − | 0.831992i | \(-0.687201\pi\) | ||||
−0.554788 | + | 0.831992i | \(0.687201\pi\) | |||||||
\(462\) | 0.0799220 | 0.00371831 | ||||||||
\(463\) | −26.9978 | −1.25470 | −0.627348 | − | 0.778739i | \(-0.715860\pi\) | ||||
−0.627348 | + | 0.778739i | \(0.715860\pi\) | |||||||
\(464\) | 3.86000 | 0.179196 | ||||||||
\(465\) | 38.8817 | 1.80310 | ||||||||
\(466\) | 23.7665 | 1.10096 | ||||||||
\(467\) | 18.3814 | 0.850590 | 0.425295 | − | 0.905055i | \(-0.360170\pi\) | ||||
0.425295 | + | 0.905055i | \(0.360170\pi\) | |||||||
\(468\) | −6.71998 | −0.310631 | ||||||||
\(469\) | −33.2634 | −1.53596 | ||||||||
\(470\) | −15.8892 | −0.732913 | ||||||||
\(471\) | 13.3115 | 0.613361 | ||||||||
\(472\) | −2.88671 | −0.132872 | ||||||||
\(473\) | 0.0264494 | 0.00121615 | ||||||||
\(474\) | −4.73724 | −0.217589 | ||||||||
\(475\) | 82.4827 | 3.78457 | ||||||||
\(476\) | 27.0181 | 1.23837 | ||||||||
\(477\) | 14.1207 | 0.646545 | ||||||||
\(478\) | 2.63371 | 0.120463 | ||||||||
\(479\) | −6.54219 | −0.298920 | −0.149460 | − | 0.988768i | \(-0.547754\pi\) | ||||
−0.149460 | + | 0.988768i | \(0.547754\pi\) | |||||||
\(480\) | 4.46502 | 0.203799 | ||||||||
\(481\) | −7.23309 | −0.329801 | ||||||||
\(482\) | 26.1494 | 1.19107 | ||||||||
\(483\) | 7.39045 | 0.336277 | ||||||||
\(484\) | −10.9998 | −0.499989 | ||||||||
\(485\) | −12.9043 | −0.585954 | ||||||||
\(486\) | 14.9856 | 0.679758 | ||||||||
\(487\) | 15.0683 | 0.682808 | 0.341404 | − | 0.939917i | \(-0.389098\pi\) | ||||
0.341404 | + | 0.939917i | \(0.389098\pi\) | |||||||
\(488\) | 7.58440 | 0.343330 | ||||||||
\(489\) | 26.6412 | 1.20476 | ||||||||
\(490\) | −54.7872 | −2.47503 | ||||||||
\(491\) | −11.2325 | −0.506918 | −0.253459 | − | 0.967346i | \(-0.581568\pi\) | ||||
−0.253459 | + | 0.967346i | \(0.581568\pi\) | |||||||
\(492\) | −2.02229 | −0.0911719 | ||||||||
\(493\) | 22.7992 | 1.02682 | ||||||||
\(494\) | −30.8809 | −1.38940 | ||||||||
\(495\) | −0.103739 | −0.00466271 | ||||||||
\(496\) | −8.70807 | −0.391004 | ||||||||
\(497\) | 3.59446 | 0.161234 | ||||||||
\(498\) | 5.92186 | 0.265365 | ||||||||
\(499\) | −30.2317 | −1.35336 | −0.676678 | − | 0.736279i | \(-0.736581\pi\) | ||||
−0.676678 | + | 0.736279i | \(0.736581\pi\) | |||||||
\(500\) | 21.5717 | 0.964714 | ||||||||
\(501\) | 14.9292 | 0.666986 | ||||||||
\(502\) | 13.8676 | 0.618941 | ||||||||
\(503\) | 30.7138 | 1.36946 | 0.684730 | − | 0.728797i | \(-0.259920\pi\) | ||||
0.684730 | + | 0.728797i | \(0.259920\pi\) | |||||||
\(504\) | 7.83257 | 0.348890 | ||||||||
\(505\) | 5.54246 | 0.246636 | ||||||||
\(506\) | 0.0219222 | 0.000974560 0 | ||||||||
\(507\) | −2.72543 | −0.121041 | ||||||||
\(508\) | −19.4224 | −0.861732 | ||||||||
\(509\) | 11.8801 | 0.526574 | 0.263287 | − | 0.964717i | \(-0.415193\pi\) | ||||
0.263287 | + | 0.964717i | \(0.415193\pi\) | |||||||
\(510\) | 26.3728 | 1.16781 | ||||||||
\(511\) | 27.0748 | 1.19772 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 42.0770 | 1.85774 | ||||||||
\(514\) | 16.6328 | 0.733642 | ||||||||
\(515\) | −13.3176 | −0.586845 | ||||||||
\(516\) | −1.94932 | −0.0858139 | ||||||||
\(517\) | 0.0621760 | 0.00273450 | ||||||||
\(518\) | 8.43063 | 0.370421 | ||||||||
\(519\) | −5.31071 | −0.233114 | ||||||||
\(520\) | −15.4420 | −0.677176 | ||||||||
\(521\) | −13.0180 | −0.570327 | −0.285164 | − | 0.958479i | \(-0.592048\pi\) | ||||
−0.285164 | + | 0.958479i | \(0.592048\pi\) | |||||||
\(522\) | 6.60952 | 0.289291 | ||||||||
\(523\) | −22.9101 | −1.00179 | −0.500894 | − | 0.865508i | \(-0.666996\pi\) | ||||
−0.500894 | + | 0.865508i | \(0.666996\pi\) | |||||||
\(524\) | 14.4036 | 0.629224 | ||||||||
\(525\) | −54.4108 | −2.37468 | ||||||||
\(526\) | −1.92911 | −0.0841134 | ||||||||
\(527\) | −51.4345 | −2.24052 | ||||||||
\(528\) | −0.0174721 | −0.000760376 0 | ||||||||
\(529\) | −20.9728 | −0.911863 | ||||||||
\(530\) | 32.4484 | 1.40947 | ||||||||
\(531\) | −4.94294 | −0.214506 | ||||||||
\(532\) | 35.9937 | 1.56052 | ||||||||
\(533\) | 6.99396 | 0.302942 | ||||||||
\(534\) | 12.5196 | 0.541777 | ||||||||
\(535\) | −56.3947 | −2.43816 | ||||||||
\(536\) | 7.27185 | 0.314096 | ||||||||
\(537\) | −12.4407 | −0.536855 | ||||||||
\(538\) | −16.3692 | −0.705726 | ||||||||
\(539\) | 0.214388 | 0.00923435 | ||||||||
\(540\) | 21.0406 | 0.905442 | ||||||||
\(541\) | 33.4048 | 1.43619 | 0.718093 | − | 0.695947i | \(-0.245015\pi\) | ||||
0.718093 | + | 0.695947i | \(0.245015\pi\) | |||||||
\(542\) | −0.0530257 | −0.00227765 | ||||||||
\(543\) | 5.26780 | 0.226063 | ||||||||
\(544\) | −5.90653 | −0.253241 | ||||||||
\(545\) | −19.8089 | −0.848519 | ||||||||
\(546\) | 20.3710 | 0.871798 | ||||||||
\(547\) | 31.6261 | 1.35223 | 0.676116 | − | 0.736795i | \(-0.263662\pi\) | ||||
0.676116 | + | 0.736795i | \(0.263662\pi\) | |||||||
\(548\) | 9.57782 | 0.409144 | ||||||||
\(549\) | 12.9869 | 0.554266 | ||||||||
\(550\) | −0.161398 | −0.00688203 | ||||||||
\(551\) | 30.3733 | 1.29395 | ||||||||
\(552\) | −1.61566 | −0.0687670 | ||||||||
\(553\) | −19.0960 | −0.812043 | ||||||||
\(554\) | 6.36466 | 0.270408 | ||||||||
\(555\) | 8.22929 | 0.349314 | ||||||||
\(556\) | −4.53977 | −0.192529 | ||||||||
\(557\) | −16.2622 | −0.689052 | −0.344526 | − | 0.938777i | \(-0.611960\pi\) | ||||
−0.344526 | + | 0.938777i | \(0.611960\pi\) | |||||||
\(558\) | −14.9109 | −0.631230 | ||||||||
\(559\) | 6.74159 | 0.285139 | ||||||||
\(560\) | 17.9986 | 0.760581 | ||||||||
\(561\) | −0.103200 | −0.00435709 | ||||||||
\(562\) | 14.0335 | 0.591968 | ||||||||
\(563\) | 13.3378 | 0.562123 | 0.281062 | − | 0.959690i | \(-0.409313\pi\) | ||||
0.281062 | + | 0.959690i | \(0.409313\pi\) | |||||||
\(564\) | −4.58236 | −0.192952 | ||||||||
\(565\) | −56.4944 | −2.37674 | ||||||||
\(566\) | 10.4681 | 0.440006 | ||||||||
\(567\) | −4.25890 | −0.178857 | ||||||||
\(568\) | −0.785801 | −0.0329715 | ||||||||
\(569\) | 10.7055 | 0.448798 | 0.224399 | − | 0.974497i | \(-0.427958\pi\) | ||||
0.224399 | + | 0.974497i | \(0.427958\pi\) | |||||||
\(570\) | 35.1341 | 1.47160 | ||||||||
\(571\) | −16.5837 | −0.694004 | −0.347002 | − | 0.937864i | \(-0.612800\pi\) | ||||
−0.347002 | + | 0.937864i | \(0.612800\pi\) | |||||||
\(572\) | 0.0604261 | 0.00252654 | ||||||||
\(573\) | 7.05204 | 0.294603 | ||||||||
\(574\) | −8.15191 | −0.340254 | ||||||||
\(575\) | −14.9246 | −0.622398 | ||||||||
\(576\) | −1.71231 | −0.0713463 | ||||||||
\(577\) | 37.1052 | 1.54471 | 0.772354 | − | 0.635192i | \(-0.219079\pi\) | ||||
0.772354 | + | 0.635192i | \(0.219079\pi\) | |||||||
\(578\) | −17.8871 | −0.744007 | ||||||||
\(579\) | −20.7683 | −0.863101 | ||||||||
\(580\) | 15.1882 | 0.630654 | ||||||||
\(581\) | 23.8712 | 0.990343 | ||||||||
\(582\) | −3.72153 | −0.154262 | ||||||||
\(583\) | −0.126974 | −0.00525872 | ||||||||
\(584\) | −5.91895 | −0.244928 | ||||||||
\(585\) | −26.4415 | −1.09322 | ||||||||
\(586\) | 23.4894 | 0.970336 | ||||||||
\(587\) | 19.3061 | 0.796849 | 0.398425 | − | 0.917201i | \(-0.369557\pi\) | ||||
0.398425 | + | 0.917201i | \(0.369557\pi\) | |||||||
\(588\) | −15.8003 | −0.651595 | ||||||||
\(589\) | −68.5215 | −2.82338 | ||||||||
\(590\) | −11.3585 | −0.467622 | ||||||||
\(591\) | −17.8456 | −0.734069 | ||||||||
\(592\) | −1.84306 | −0.0757492 | ||||||||
\(593\) | 5.11908 | 0.210216 | 0.105108 | − | 0.994461i | \(-0.466481\pi\) | ||||
0.105108 | + | 0.994461i | \(0.466481\pi\) | |||||||
\(594\) | −0.0823340 | −0.00337820 | ||||||||
\(595\) | 106.310 | 4.35827 | ||||||||
\(596\) | −9.69003 | −0.396919 | ||||||||
\(597\) | 26.5634 | 1.08717 | ||||||||
\(598\) | 5.58765 | 0.228496 | ||||||||
\(599\) | −0.421438 | −0.0172195 | −0.00860974 | − | 0.999963i | \(-0.502741\pi\) | ||||
−0.00860974 | + | 0.999963i | \(0.502741\pi\) | |||||||
\(600\) | 11.8950 | 0.485610 | ||||||||
\(601\) | −2.73482 | −0.111556 | −0.0557779 | − | 0.998443i | \(-0.517764\pi\) | ||||
−0.0557779 | + | 0.998443i | \(0.517764\pi\) | |||||||
\(602\) | −7.85775 | −0.320258 | ||||||||
\(603\) | 12.4517 | 0.507071 | ||||||||
\(604\) | 4.27467 | 0.173934 | ||||||||
\(605\) | −43.2814 | −1.75964 | ||||||||
\(606\) | 1.59842 | 0.0649312 | ||||||||
\(607\) | −7.14117 | −0.289851 | −0.144925 | − | 0.989443i | \(-0.546294\pi\) | ||||
−0.144925 | + | 0.989443i | \(0.546294\pi\) | |||||||
\(608\) | −7.86873 | −0.319119 | ||||||||
\(609\) | −20.0361 | −0.811905 | ||||||||
\(610\) | 29.8428 | 1.20830 | ||||||||
\(611\) | 15.8478 | 0.641133 | ||||||||
\(612\) | −10.1138 | −0.408827 | ||||||||
\(613\) | 35.9204 | 1.45081 | 0.725405 | − | 0.688323i | \(-0.241653\pi\) | ||||
0.725405 | + | 0.688323i | \(0.241653\pi\) | |||||||
\(614\) | 32.0967 | 1.29532 | ||||||||
\(615\) | −7.95723 | −0.320866 | ||||||||
\(616\) | −0.0704305 | −0.00283773 | ||||||||
\(617\) | −1.35429 | −0.0545218 | −0.0272609 | − | 0.999628i | \(-0.508678\pi\) | ||||
−0.0272609 | + | 0.999628i | \(0.508678\pi\) | |||||||
\(618\) | −3.84073 | −0.154497 | ||||||||
\(619\) | 40.1091 | 1.61212 | 0.806061 | − | 0.591833i | \(-0.201595\pi\) | ||||
0.806061 | + | 0.591833i | \(0.201595\pi\) | |||||||
\(620\) | −34.2642 | −1.37608 | ||||||||
\(621\) | −7.61349 | −0.305519 | ||||||||
\(622\) | 26.5241 | 1.06352 | ||||||||
\(623\) | 50.4670 | 2.02192 | ||||||||
\(624\) | −4.45339 | −0.178278 | ||||||||
\(625\) | 32.4677 | 1.29871 | ||||||||
\(626\) | −28.6176 | −1.14379 | ||||||||
\(627\) | −0.137483 | −0.00549056 | ||||||||
\(628\) | −11.7306 | −0.468103 | ||||||||
\(629\) | −10.8861 | −0.434056 | ||||||||
\(630\) | 30.8193 | 1.22787 | ||||||||
\(631\) | −10.7738 | −0.428898 | −0.214449 | − | 0.976735i | \(-0.568796\pi\) | ||||
−0.214449 | + | 0.976735i | \(0.568796\pi\) | |||||||
\(632\) | 4.17465 | 0.166059 | ||||||||
\(633\) | 21.8451 | 0.868264 | ||||||||
\(634\) | 26.1274 | 1.03765 | ||||||||
\(635\) | −76.4227 | −3.03274 | ||||||||
\(636\) | 9.35795 | 0.371067 | ||||||||
\(637\) | 54.6445 | 2.16509 | ||||||||
\(638\) | −0.0594329 | −0.00235297 | ||||||||
\(639\) | −1.34554 | −0.0532286 | ||||||||
\(640\) | −3.93476 | −0.155535 | ||||||||
\(641\) | 33.3826 | 1.31853 | 0.659266 | − | 0.751909i | \(-0.270867\pi\) | ||||
0.659266 | + | 0.751909i | \(0.270867\pi\) | |||||||
\(642\) | −16.2639 | −0.641886 | ||||||||
\(643\) | 16.0681 | 0.633662 | 0.316831 | − | 0.948482i | \(-0.397381\pi\) | ||||
0.316831 | + | 0.948482i | \(0.397381\pi\) | |||||||
\(644\) | −6.51277 | −0.256639 | ||||||||
\(645\) | −7.67009 | −0.302010 | ||||||||
\(646\) | −46.4770 | −1.82861 | ||||||||
\(647\) | 29.8593 | 1.17389 | 0.586944 | − | 0.809627i | \(-0.300331\pi\) | ||||
0.586944 | + | 0.809627i | \(0.300331\pi\) | |||||||
\(648\) | 0.931057 | 0.0365754 | ||||||||
\(649\) | 0.0444470 | 0.00174470 | ||||||||
\(650\) | −41.1380 | −1.61357 | ||||||||
\(651\) | 45.2011 | 1.77157 | ||||||||
\(652\) | −23.4773 | −0.919443 | ||||||||
\(653\) | −16.6227 | −0.650497 | −0.325248 | − | 0.945629i | \(-0.605448\pi\) | ||||
−0.325248 | + | 0.945629i | \(0.605448\pi\) | |||||||
\(654\) | −5.71278 | −0.223387 | ||||||||
\(655\) | 56.6747 | 2.21446 | ||||||||
\(656\) | 1.78213 | 0.0695803 | ||||||||
\(657\) | −10.1351 | −0.395407 | ||||||||
\(658\) | −18.4716 | −0.720098 | ||||||||
\(659\) | 3.72529 | 0.145117 | 0.0725584 | − | 0.997364i | \(-0.476884\pi\) | ||||
0.0725584 | + | 0.997364i | \(0.476884\pi\) | |||||||
\(660\) | −0.0687485 | −0.00267603 | ||||||||
\(661\) | 18.0109 | 0.700542 | 0.350271 | − | 0.936648i | \(-0.386089\pi\) | ||||
0.350271 | + | 0.936648i | \(0.386089\pi\) | |||||||
\(662\) | 18.5023 | 0.719111 | ||||||||
\(663\) | −26.3041 | −1.02157 | ||||||||
\(664\) | −5.21858 | −0.202520 | ||||||||
\(665\) | 141.626 | 5.49204 | ||||||||
\(666\) | −3.15589 | −0.122288 | ||||||||
\(667\) | −5.49581 | −0.212798 | ||||||||
\(668\) | −13.1562 | −0.509028 | ||||||||
\(669\) | 14.0845 | 0.544538 | ||||||||
\(670\) | 28.6130 | 1.10542 | ||||||||
\(671\) | −0.116778 | −0.00450817 | ||||||||
\(672\) | 5.19071 | 0.200236 | ||||||||
\(673\) | 22.8335 | 0.880167 | 0.440084 | − | 0.897957i | \(-0.354949\pi\) | ||||
0.440084 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(674\) | −33.6511 | −1.29619 | ||||||||
\(675\) | 56.0528 | 2.15747 | ||||||||
\(676\) | 2.40176 | 0.0923755 | ||||||||
\(677\) | −36.1136 | −1.38796 | −0.693980 | − | 0.719995i | \(-0.744144\pi\) | ||||
−0.693980 | + | 0.719995i | \(0.744144\pi\) | |||||||
\(678\) | −16.2927 | −0.625717 | ||||||||
\(679\) | −15.0016 | −0.575708 | ||||||||
\(680\) | −23.2408 | −0.891244 | ||||||||
\(681\) | −12.7623 | −0.489053 | ||||||||
\(682\) | 0.134079 | 0.00513416 | ||||||||
\(683\) | −30.2375 | −1.15701 | −0.578503 | − | 0.815681i | \(-0.696363\pi\) | ||||
−0.578503 | + | 0.815681i | \(0.696363\pi\) | |||||||
\(684\) | −13.4737 | −0.515181 | ||||||||
\(685\) | 37.6864 | 1.43992 | ||||||||
\(686\) | −31.6718 | −1.20923 | ||||||||
\(687\) | −10.0930 | −0.385071 | ||||||||
\(688\) | 1.71782 | 0.0654912 | ||||||||
\(689\) | −32.3639 | −1.23296 | ||||||||
\(690\) | −6.35723 | −0.242016 | ||||||||
\(691\) | 4.28207 | 0.162898 | 0.0814488 | − | 0.996678i | \(-0.474045\pi\) | ||||
0.0814488 | + | 0.996678i | \(0.474045\pi\) | |||||||
\(692\) | 4.68002 | 0.177908 | ||||||||
\(693\) | −0.120599 | −0.00458118 | ||||||||
\(694\) | 34.4206 | 1.30659 | ||||||||
\(695\) | −17.8629 | −0.677579 | ||||||||
\(696\) | 4.38019 | 0.166031 | ||||||||
\(697\) | 10.5262 | 0.398708 | ||||||||
\(698\) | 0.751923 | 0.0284607 | ||||||||
\(699\) | 26.9693 | 1.02007 | ||||||||
\(700\) | 47.9490 | 1.81230 | ||||||||
\(701\) | 13.2695 | 0.501182 | 0.250591 | − | 0.968093i | \(-0.419375\pi\) | ||||
0.250591 | + | 0.968093i | \(0.419375\pi\) | |||||||
\(702\) | −20.9858 | −0.792056 | ||||||||
\(703\) | −14.5025 | −0.546973 | ||||||||
\(704\) | 0.0153971 | 0.000580301 0 | ||||||||
\(705\) | −18.0305 | −0.679067 | ||||||||
\(706\) | −1.93776 | −0.0729287 | ||||||||
\(707\) | 6.44326 | 0.242324 | ||||||||
\(708\) | −3.27573 | −0.123110 | ||||||||
\(709\) | −33.0471 | −1.24111 | −0.620554 | − | 0.784163i | \(-0.713092\pi\) | ||||
−0.620554 | + | 0.784163i | \(0.713092\pi\) | |||||||
\(710\) | −3.09194 | −0.116038 | ||||||||
\(711\) | 7.14830 | 0.268082 | ||||||||
\(712\) | −11.0328 | −0.413472 | ||||||||
\(713\) | 12.3984 | 0.464324 | ||||||||
\(714\) | 30.6591 | 1.14739 | ||||||||
\(715\) | 0.237762 | 0.00889181 | ||||||||
\(716\) | 10.9632 | 0.409715 | ||||||||
\(717\) | 2.98864 | 0.111613 | ||||||||
\(718\) | −34.5060 | −1.28775 | ||||||||
\(719\) | 20.1907 | 0.752985 | 0.376493 | − | 0.926420i | \(-0.377130\pi\) | ||||
0.376493 | + | 0.926420i | \(0.377130\pi\) | |||||||
\(720\) | −6.73753 | −0.251093 | ||||||||
\(721\) | −15.4821 | −0.576584 | ||||||||
\(722\) | −42.9170 | −1.59720 | ||||||||
\(723\) | 29.6734 | 1.10356 | ||||||||
\(724\) | −4.64220 | −0.172526 | ||||||||
\(725\) | 40.4618 | 1.50271 | ||||||||
\(726\) | −12.4821 | −0.463255 | ||||||||
\(727\) | −15.0651 | −0.558733 | −0.279366 | − | 0.960185i | \(-0.590124\pi\) | ||||
−0.279366 | + | 0.960185i | \(0.590124\pi\) | |||||||
\(728\) | −17.9517 | −0.665336 | ||||||||
\(729\) | 19.7982 | 0.733268 | ||||||||
\(730\) | −23.2896 | −0.861988 | ||||||||
\(731\) | 10.1463 | 0.375276 | ||||||||
\(732\) | 8.60651 | 0.318106 | ||||||||
\(733\) | 53.2618 | 1.96727 | 0.983635 | − | 0.180174i | \(-0.0576660\pi\) | ||||
0.983635 | + | 0.180174i | \(0.0576660\pi\) | |||||||
\(734\) | 11.9224 | 0.440064 | ||||||||
\(735\) | −62.1706 | −2.29320 | ||||||||
\(736\) | 1.42378 | 0.0524814 | ||||||||
\(737\) | −0.111966 | −0.00412430 | ||||||||
\(738\) | 3.05155 | 0.112329 | ||||||||
\(739\) | −51.5016 | −1.89452 | −0.947259 | − | 0.320470i | \(-0.896159\pi\) | ||||
−0.947259 | + | 0.320470i | \(0.896159\pi\) | |||||||
\(740\) | −7.25198 | −0.266588 | ||||||||
\(741\) | −35.0425 | −1.28732 | ||||||||
\(742\) | 37.7221 | 1.38482 | ||||||||
\(743\) | −6.83169 | −0.250630 | −0.125315 | − | 0.992117i | \(-0.539994\pi\) | ||||
−0.125315 | + | 0.992117i | \(0.539994\pi\) | |||||||
\(744\) | −9.88160 | −0.362277 | ||||||||
\(745\) | −38.1280 | −1.39690 | ||||||||
\(746\) | 18.2778 | 0.669199 | ||||||||
\(747\) | −8.93584 | −0.326945 | ||||||||
\(748\) | 0.0909437 | 0.00332523 | ||||||||
\(749\) | −65.5604 | −2.39552 | ||||||||
\(750\) | 24.4787 | 0.893837 | ||||||||
\(751\) | 50.2187 | 1.83250 | 0.916252 | − | 0.400601i | \(-0.131199\pi\) | ||||
0.916252 | + | 0.400601i | \(0.131199\pi\) | |||||||
\(752\) | 4.03816 | 0.147257 | ||||||||
\(753\) | 15.7364 | 0.573468 | ||||||||
\(754\) | −15.1486 | −0.551679 | ||||||||
\(755\) | 16.8198 | 0.612135 | ||||||||
\(756\) | 24.4602 | 0.889611 | ||||||||
\(757\) | 0.465410 | 0.0169156 | 0.00845780 | − | 0.999964i | \(-0.497308\pi\) | ||||
0.00845780 | + | 0.999964i | \(0.497308\pi\) | |||||||
\(758\) | 5.50543 | 0.199966 | ||||||||
\(759\) | 0.0248765 | 0.000902960 0 | ||||||||
\(760\) | −30.9616 | −1.12309 | ||||||||
\(761\) | −31.2635 | −1.13330 | −0.566650 | − | 0.823959i | \(-0.691761\pi\) | ||||
−0.566650 | + | 0.823959i | \(0.691761\pi\) | |||||||
\(762\) | −22.0399 | −0.798421 | ||||||||
\(763\) | −23.0284 | −0.833683 | ||||||||
\(764\) | −6.21455 | −0.224834 | ||||||||
\(765\) | −39.7955 | −1.43881 | ||||||||
\(766\) | −26.0096 | −0.939767 | ||||||||
\(767\) | 11.3289 | 0.409063 | ||||||||
\(768\) | −1.13476 | −0.0409473 | ||||||||
\(769\) | −32.3655 | −1.16713 | −0.583566 | − | 0.812066i | \(-0.698343\pi\) | ||||
−0.583566 | + | 0.812066i | \(0.698343\pi\) | |||||||
\(770\) | −0.277127 | −0.00998697 | ||||||||
\(771\) | 18.8743 | 0.679742 | ||||||||
\(772\) | 18.3019 | 0.658699 | ||||||||
\(773\) | 12.5276 | 0.450586 | 0.225293 | − | 0.974291i | \(-0.427666\pi\) | ||||
0.225293 | + | 0.974291i | \(0.427666\pi\) | |||||||
\(774\) | 2.94144 | 0.105728 | ||||||||
\(775\) | −91.2809 | −3.27891 | ||||||||
\(776\) | 3.27956 | 0.117729 | ||||||||
\(777\) | 9.56677 | 0.343206 | ||||||||
\(778\) | 1.85343 | 0.0664487 | ||||||||
\(779\) | 14.0231 | 0.502429 | ||||||||
\(780\) | −17.5230 | −0.627425 | ||||||||
\(781\) | 0.0120991 | 0.000432939 0 | ||||||||
\(782\) | 8.40963 | 0.300728 | ||||||||
\(783\) | 20.6408 | 0.737642 | ||||||||
\(784\) | 13.9239 | 0.497282 | ||||||||
\(785\) | −46.1572 | −1.64742 | ||||||||
\(786\) | 16.3447 | 0.582996 | ||||||||
\(787\) | 8.07383 | 0.287801 | 0.143901 | − | 0.989592i | \(-0.454035\pi\) | ||||
0.143901 | + | 0.989592i | \(0.454035\pi\) | |||||||
\(788\) | 15.7263 | 0.560224 | ||||||||
\(789\) | −2.18909 | −0.0779336 | ||||||||
\(790\) | 16.4262 | 0.584419 | ||||||||
\(791\) | −65.6763 | −2.33518 | ||||||||
\(792\) | 0.0263647 | 0.000936828 0 | ||||||||
\(793\) | −29.7651 | −1.05699 | ||||||||
\(794\) | −19.7166 | −0.699716 | ||||||||
\(795\) | 36.8213 | 1.30592 | ||||||||
\(796\) | −23.4087 | −0.829701 | ||||||||
\(797\) | −13.3274 | −0.472080 | −0.236040 | − | 0.971743i | \(-0.575850\pi\) | ||||
−0.236040 | + | 0.971743i | \(0.575850\pi\) | |||||||
\(798\) | 40.8443 | 1.44587 | ||||||||
\(799\) | 23.8515 | 0.843806 | ||||||||
\(800\) | −10.4823 | −0.370606 | ||||||||
\(801\) | −18.8916 | −0.667502 | ||||||||
\(802\) | −33.8736 | −1.19612 | ||||||||
\(803\) | 0.0911348 | 0.00321608 | ||||||||
\(804\) | 8.25183 | 0.291020 | ||||||||
\(805\) | −25.6262 | −0.903204 | ||||||||
\(806\) | 34.1749 | 1.20376 | ||||||||
\(807\) | −18.5752 | −0.653877 | ||||||||
\(808\) | −1.40859 | −0.0495540 | ||||||||
\(809\) | −23.1318 | −0.813272 | −0.406636 | − | 0.913590i | \(-0.633298\pi\) | ||||
−0.406636 | + | 0.913590i | \(0.633298\pi\) | |||||||
\(810\) | 3.66348 | 0.128722 | ||||||||
\(811\) | 2.19604 | 0.0771136 | 0.0385568 | − | 0.999256i | \(-0.487724\pi\) | ||||
0.0385568 | + | 0.999256i | \(0.487724\pi\) | |||||||
\(812\) | 17.6567 | 0.619627 | ||||||||
\(813\) | −0.0601716 | −0.00211031 | ||||||||
\(814\) | 0.0283778 | 0.000994640 0 | ||||||||
\(815\) | −92.3777 | −3.23585 | ||||||||
\(816\) | −6.70252 | −0.234635 | ||||||||
\(817\) | 13.5170 | 0.472902 | ||||||||
\(818\) | 18.3199 | 0.640541 | ||||||||
\(819\) | −30.7390 | −1.07411 | ||||||||
\(820\) | 7.01223 | 0.244878 | ||||||||
\(821\) | 45.8469 | 1.60007 | 0.800034 | − | 0.599955i | \(-0.204815\pi\) | ||||
0.800034 | + | 0.599955i | \(0.204815\pi\) | |||||||
\(822\) | 10.8686 | 0.379085 | ||||||||
\(823\) | 49.4167 | 1.72256 | 0.861279 | − | 0.508133i | \(-0.169664\pi\) | ||||
0.861279 | + | 0.508133i | \(0.169664\pi\) | |||||||
\(824\) | 3.38461 | 0.117909 | ||||||||
\(825\) | −0.183148 | −0.00637641 | ||||||||
\(826\) | −13.2046 | −0.459446 | ||||||||
\(827\) | 4.04297 | 0.140588 | 0.0702940 | − | 0.997526i | \(-0.477606\pi\) | ||||
0.0702940 | + | 0.997526i | \(0.477606\pi\) | |||||||
\(828\) | 2.43796 | 0.0847250 | ||||||||
\(829\) | −25.8554 | −0.897997 | −0.448998 | − | 0.893533i | \(-0.648219\pi\) | ||||
−0.448998 | + | 0.893533i | \(0.648219\pi\) | |||||||
\(830\) | −20.5339 | −0.712741 | ||||||||
\(831\) | 7.22238 | 0.250542 | ||||||||
\(832\) | 3.92451 | 0.136058 | ||||||||
\(833\) | 82.2420 | 2.84952 | ||||||||
\(834\) | −5.15157 | −0.178384 | ||||||||
\(835\) | −51.7664 | −1.79145 | ||||||||
\(836\) | 0.121156 | 0.00419026 | ||||||||
\(837\) | −46.5652 | −1.60953 | ||||||||
\(838\) | −6.86468 | −0.237136 | ||||||||
\(839\) | −2.60424 | −0.0899082 | −0.0449541 | − | 0.998989i | \(-0.514314\pi\) | ||||
−0.0449541 | + | 0.998989i | \(0.514314\pi\) | |||||||
\(840\) | 20.4242 | 0.704702 | ||||||||
\(841\) | −14.1004 | −0.486221 | ||||||||
\(842\) | −36.7808 | −1.26755 | ||||||||
\(843\) | 15.9247 | 0.548476 | ||||||||
\(844\) | −19.2508 | −0.662639 | ||||||||
\(845\) | 9.45036 | 0.325102 | ||||||||
\(846\) | 6.91458 | 0.237728 | ||||||||
\(847\) | −50.3158 | −1.72887 | ||||||||
\(848\) | −8.24660 | −0.283189 | ||||||||
\(849\) | 11.8788 | 0.407679 | ||||||||
\(850\) | −61.9143 | −2.12364 | ||||||||
\(851\) | 2.62412 | 0.0899535 | ||||||||
\(852\) | −0.891698 | −0.0305491 | ||||||||
\(853\) | −2.10284 | −0.0719999 | −0.0360000 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360000 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(854\) | 34.6931 | 1.18717 | ||||||||
\(855\) | −53.0159 | −1.81310 | ||||||||
\(856\) | 14.3324 | 0.489873 | ||||||||
\(857\) | 12.1540 | 0.415172 | 0.207586 | − | 0.978217i | \(-0.433439\pi\) | ||||
0.207586 | + | 0.978217i | \(0.433439\pi\) | |||||||
\(858\) | 0.0685694 | 0.00234092 | ||||||||
\(859\) | −55.1342 | −1.88116 | −0.940578 | − | 0.339579i | \(-0.889716\pi\) | ||||
−0.940578 | + | 0.339579i | \(0.889716\pi\) | |||||||
\(860\) | 6.75920 | 0.230487 | ||||||||
\(861\) | −9.25050 | −0.315256 | ||||||||
\(862\) | −25.5159 | −0.869075 | ||||||||
\(863\) | −35.8069 | −1.21888 | −0.609441 | − | 0.792832i | \(-0.708606\pi\) | ||||
−0.609441 | + | 0.792832i | \(0.708606\pi\) | |||||||
\(864\) | −5.34736 | −0.181921 | ||||||||
\(865\) | 18.4147 | 0.626120 | ||||||||
\(866\) | −5.51689 | −0.187471 | ||||||||
\(867\) | −20.2977 | −0.689346 | ||||||||
\(868\) | −39.8330 | −1.35202 | ||||||||
\(869\) | −0.0642776 | −0.00218047 | ||||||||
\(870\) | 17.2350 | 0.584321 | ||||||||
\(871\) | −28.5384 | −0.966988 | ||||||||
\(872\) | 5.03433 | 0.170484 | ||||||||
\(873\) | 5.61563 | 0.190060 | ||||||||
\(874\) | 11.2034 | 0.378960 | ||||||||
\(875\) | 98.6745 | 3.33581 | ||||||||
\(876\) | −6.71661 | −0.226933 | ||||||||
\(877\) | 37.3172 | 1.26011 | 0.630055 | − | 0.776550i | \(-0.283032\pi\) | ||||
0.630055 | + | 0.776550i | \(0.283032\pi\) | |||||||
\(878\) | −35.0980 | −1.18450 | ||||||||
\(879\) | 26.6549 | 0.899046 | ||||||||
\(880\) | 0.0605840 | 0.00204229 | ||||||||
\(881\) | 23.1784 | 0.780900 | 0.390450 | − | 0.920624i | \(-0.372319\pi\) | ||||
0.390450 | + | 0.920624i | \(0.372319\pi\) | |||||||
\(882\) | 23.8421 | 0.802804 | ||||||||
\(883\) | −9.88240 | −0.332569 | −0.166285 | − | 0.986078i | \(-0.553177\pi\) | ||||
−0.166285 | + | 0.986078i | \(0.553177\pi\) | |||||||
\(884\) | 23.1802 | 0.779636 | ||||||||
\(885\) | −12.8892 | −0.433266 | ||||||||
\(886\) | −27.3957 | −0.920377 | ||||||||
\(887\) | −37.9263 | −1.27344 | −0.636721 | − | 0.771095i | \(-0.719710\pi\) | ||||
−0.636721 | + | 0.771095i | \(0.719710\pi\) | |||||||
\(888\) | −2.09143 | −0.0701839 | ||||||||
\(889\) | −88.8434 | −2.97971 | ||||||||
\(890\) | −43.4115 | −1.45516 | ||||||||
\(891\) | −0.0143356 | −0.000480261 0 | ||||||||
\(892\) | −12.4118 | −0.415578 | ||||||||
\(893\) | 31.7752 | 1.06332 | ||||||||
\(894\) | −10.9959 | −0.367758 | ||||||||
\(895\) | 43.1377 | 1.44193 | ||||||||
\(896\) | −4.57427 | −0.152815 | ||||||||
\(897\) | 6.34067 | 0.211709 | ||||||||
\(898\) | 9.48377 | 0.316477 | ||||||||
\(899\) | −33.6131 | −1.12106 | ||||||||
\(900\) | −17.9490 | −0.598301 | ||||||||
\(901\) | −48.7088 | −1.62273 | ||||||||
\(902\) | −0.0274396 | −0.000913639 0 | ||||||||
\(903\) | −8.91669 | −0.296729 | ||||||||
\(904\) | 14.3578 | 0.477532 | ||||||||
\(905\) | −18.2659 | −0.607180 | ||||||||
\(906\) | 4.85074 | 0.161155 | ||||||||
\(907\) | −17.3341 | −0.575569 | −0.287785 | − | 0.957695i | \(-0.592919\pi\) | ||||
−0.287785 | + | 0.957695i | \(0.592919\pi\) | |||||||
\(908\) | 11.2467 | 0.373234 | ||||||||
\(909\) | −2.41194 | −0.0799991 | ||||||||
\(910\) | −70.6358 | −2.34155 | ||||||||
\(911\) | −25.7278 | −0.852401 | −0.426201 | − | 0.904629i | \(-0.640148\pi\) | ||||
−0.426201 | + | 0.904629i | \(0.640148\pi\) | |||||||
\(912\) | −8.92916 | −0.295674 | ||||||||
\(913\) | 0.0803512 | 0.00265924 | ||||||||
\(914\) | −9.36207 | −0.309670 | ||||||||
\(915\) | 33.8645 | 1.11953 | ||||||||
\(916\) | 8.89434 | 0.293877 | ||||||||
\(917\) | 65.8859 | 2.17574 | ||||||||
\(918\) | −31.5844 | −1.04244 | ||||||||
\(919\) | 40.5308 | 1.33699 | 0.668495 | − | 0.743717i | \(-0.266939\pi\) | ||||
0.668495 | + | 0.743717i | \(0.266939\pi\) | |||||||
\(920\) | 5.60225 | 0.184701 | ||||||||
\(921\) | 36.4222 | 1.20015 | ||||||||
\(922\) | 23.8236 | 0.784589 | ||||||||
\(923\) | 3.08388 | 0.101507 | ||||||||
\(924\) | −0.0799220 | −0.00262924 | ||||||||
\(925\) | −19.3195 | −0.635222 | ||||||||
\(926\) | 26.9978 | 0.887204 | ||||||||
\(927\) | 5.79551 | 0.190349 | ||||||||
\(928\) | −3.86000 | −0.126711 | ||||||||
\(929\) | 41.3151 | 1.35550 | 0.677752 | − | 0.735290i | \(-0.262954\pi\) | ||||
0.677752 | + | 0.735290i | \(0.262954\pi\) | |||||||
\(930\) | −38.8817 | −1.27498 | ||||||||
\(931\) | 109.564 | 3.59080 | ||||||||
\(932\) | −23.7665 | −0.778496 | ||||||||
\(933\) | 30.0986 | 0.985383 | ||||||||
\(934\) | −18.3814 | −0.601458 | ||||||||
\(935\) | 0.357841 | 0.0117027 | ||||||||
\(936\) | 6.71998 | 0.219649 | ||||||||
\(937\) | 38.7579 | 1.26617 | 0.633083 | − | 0.774084i | \(-0.281789\pi\) | ||||
0.633083 | + | 0.774084i | \(0.281789\pi\) | |||||||
\(938\) | 33.2634 | 1.08609 | ||||||||
\(939\) | −32.4743 | −1.05976 | ||||||||
\(940\) | 15.8892 | 0.518248 | ||||||||
\(941\) | −9.13597 | −0.297824 | −0.148912 | − | 0.988850i | \(-0.547577\pi\) | ||||
−0.148912 | + | 0.988850i | \(0.547577\pi\) | |||||||
\(942\) | −13.3115 | −0.433712 | ||||||||
\(943\) | −2.53736 | −0.0826279 | ||||||||
\(944\) | 2.88671 | 0.0939544 | ||||||||
\(945\) | 96.2452 | 3.13086 | ||||||||
\(946\) | −0.0264494 | −0.000859946 0 | ||||||||
\(947\) | 22.1900 | 0.721079 | 0.360540 | − | 0.932744i | \(-0.382593\pi\) | ||||
0.360540 | + | 0.932744i | \(0.382593\pi\) | |||||||
\(948\) | 4.73724 | 0.153858 | ||||||||
\(949\) | 23.2290 | 0.754044 | ||||||||
\(950\) | −82.4827 | −2.67609 | ||||||||
\(951\) | 29.6484 | 0.961414 | ||||||||
\(952\) | −27.0181 | −0.875660 | ||||||||
\(953\) | 3.75124 | 0.121515 | 0.0607573 | − | 0.998153i | \(-0.480648\pi\) | ||||
0.0607573 | + | 0.998153i | \(0.480648\pi\) | |||||||
\(954\) | −14.1207 | −0.457176 | ||||||||
\(955\) | −24.4527 | −0.791272 | ||||||||
\(956\) | −2.63371 | −0.0851804 | ||||||||
\(957\) | −0.0674423 | −0.00218010 | ||||||||
\(958\) | 6.54219 | 0.211369 | ||||||||
\(959\) | 43.8115 | 1.41475 | ||||||||
\(960\) | −4.46502 | −0.144108 | ||||||||
\(961\) | 44.8304 | 1.44614 | ||||||||
\(962\) | 7.23309 | 0.233204 | ||||||||
\(963\) | 24.5416 | 0.790842 | ||||||||
\(964\) | −26.1494 | −0.842215 | ||||||||
\(965\) | 72.0135 | 2.31820 | ||||||||
\(966\) | −7.39045 | −0.237784 | ||||||||
\(967\) | −18.6184 | −0.598728 | −0.299364 | − | 0.954139i | \(-0.596774\pi\) | ||||
−0.299364 | + | 0.954139i | \(0.596774\pi\) | |||||||
\(968\) | 10.9998 | 0.353546 | ||||||||
\(969\) | −52.7404 | −1.69426 | ||||||||
\(970\) | 12.9043 | 0.414332 | ||||||||
\(971\) | −4.07975 | −0.130926 | −0.0654628 | − | 0.997855i | \(-0.520852\pi\) | ||||
−0.0654628 | + | 0.997855i | \(0.520852\pi\) | |||||||
\(972\) | −14.9856 | −0.480662 | ||||||||
\(973\) | −20.7661 | −0.665732 | ||||||||
\(974\) | −15.0683 | −0.482818 | ||||||||
\(975\) | −46.6819 | −1.49502 | ||||||||
\(976\) | −7.58440 | −0.242771 | ||||||||
\(977\) | 34.5710 | 1.10603 | 0.553013 | − | 0.833173i | \(-0.313478\pi\) | ||||
0.553013 | + | 0.833173i | \(0.313478\pi\) | |||||||
\(978\) | −26.6412 | −0.851892 | ||||||||
\(979\) | 0.169874 | 0.00542918 | ||||||||
\(980\) | 54.7872 | 1.75011 | ||||||||
\(981\) | 8.62034 | 0.275226 | ||||||||
\(982\) | 11.2325 | 0.358445 | ||||||||
\(983\) | −21.6223 | −0.689643 | −0.344821 | − | 0.938668i | \(-0.612061\pi\) | ||||
−0.344821 | + | 0.938668i | \(0.612061\pi\) | |||||||
\(984\) | 2.02229 | 0.0644683 | ||||||||
\(985\) | 61.8790 | 1.97163 | ||||||||
\(986\) | −22.7992 | −0.726075 | ||||||||
\(987\) | −20.9609 | −0.667193 | ||||||||
\(988\) | 30.8809 | 0.982453 | ||||||||
\(989\) | −2.44580 | −0.0777719 | ||||||||
\(990\) | 0.103739 | 0.00329703 | ||||||||
\(991\) | −32.2418 | −1.02420 | −0.512098 | − | 0.858927i | \(-0.671132\pi\) | ||||
−0.512098 | + | 0.858927i | \(0.671132\pi\) | |||||||
\(992\) | 8.70807 | 0.276481 | ||||||||
\(993\) | 20.9957 | 0.666278 | ||||||||
\(994\) | −3.59446 | −0.114009 | ||||||||
\(995\) | −92.1078 | −2.92001 | ||||||||
\(996\) | −5.92186 | −0.187641 | ||||||||
\(997\) | −28.6048 | −0.905922 | −0.452961 | − | 0.891530i | \(-0.649632\pi\) | ||||
−0.452961 | + | 0.891530i | \(0.649632\pi\) | |||||||
\(998\) | 30.2317 | 0.956968 | ||||||||
\(999\) | −9.85549 | −0.311814 |
(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 | 6022.2.a.c.1.20 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6022.2.a.c.1.20 | ✓ | 61 | 1.1 | even | 1 | trivial |