Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(8.34436701122\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.68251\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.37279 | −0.970706 | −0.485353 | − | 0.874318i | \(-0.661309\pi\) | ||||
−0.485353 | + | 0.874318i | \(0.661309\pi\) | |||||||
\(3\) | −1.23648 | −0.713881 | −0.356941 | − | 0.934127i | \(-0.616180\pi\) | ||||
−0.356941 | + | 0.934127i | \(0.616180\pi\) | |||||||
\(4\) | −0.115460 | −0.0577299 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.69742 | 0.692969 | ||||||||
\(7\) | 2.43232 | 0.919332 | 0.459666 | − | 0.888092i | \(-0.347969\pi\) | ||||
0.459666 | + | 0.888092i | \(0.347969\pi\) | |||||||
\(8\) | 2.90407 | 1.02674 | ||||||||
\(9\) | −1.47112 | −0.490373 | ||||||||
\(10\) | −1.37279 | −0.434113 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.142763 | 0.0412123 | ||||||||
\(13\) | −4.84815 | −1.34463 | −0.672317 | − | 0.740263i | \(-0.734701\pi\) | ||||
−0.672317 | + | 0.740263i | \(0.734701\pi\) | |||||||
\(14\) | −3.33906 | −0.892401 | ||||||||
\(15\) | −1.23648 | −0.319257 | ||||||||
\(16\) | −3.75575 | −0.938937 | ||||||||
\(17\) | −1.04001 | −0.252238 | −0.126119 | − | 0.992015i | \(-0.540252\pi\) | ||||
−0.126119 | + | 0.992015i | \(0.540252\pi\) | |||||||
\(18\) | 2.01953 | 0.476008 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.115460 | −0.0258176 | ||||||||
\(21\) | −3.00752 | −0.656294 | ||||||||
\(22\) | 1.37279 | 0.292679 | ||||||||
\(23\) | 0.377030 | 0.0786163 | 0.0393081 | − | 0.999227i | \(-0.487485\pi\) | ||||
0.0393081 | + | 0.999227i | \(0.487485\pi\) | |||||||
\(24\) | −3.59082 | −0.732974 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.65547 | 1.30525 | ||||||||
\(27\) | 5.52845 | 1.06395 | ||||||||
\(28\) | −0.280835 | −0.0530729 | ||||||||
\(29\) | 4.50688 | 0.836907 | 0.418453 | − | 0.908238i | \(-0.362572\pi\) | ||||
0.418453 | + | 0.908238i | \(0.362572\pi\) | |||||||
\(30\) | 1.69742 | 0.309905 | ||||||||
\(31\) | 4.76341 | 0.855535 | 0.427767 | − | 0.903889i | \(-0.359300\pi\) | ||||
0.427767 | + | 0.903889i | \(0.359300\pi\) | |||||||
\(32\) | −0.652306 | −0.115313 | ||||||||
\(33\) | 1.23648 | 0.215243 | ||||||||
\(34\) | 1.42770 | 0.244849 | ||||||||
\(35\) | 2.43232 | 0.411138 | ||||||||
\(36\) | 0.169855 | 0.0283092 | ||||||||
\(37\) | 3.01428 | 0.495545 | 0.247773 | − | 0.968818i | \(-0.420301\pi\) | ||||
0.247773 | + | 0.968818i | \(0.420301\pi\) | |||||||
\(38\) | −1.37279 | −0.222695 | ||||||||
\(39\) | 5.99464 | 0.959910 | ||||||||
\(40\) | 2.90407 | 0.459174 | ||||||||
\(41\) | 0.790451 | 0.123448 | 0.0617238 | − | 0.998093i | \(-0.480340\pi\) | ||||
0.0617238 | + | 0.998093i | \(0.480340\pi\) | |||||||
\(42\) | 4.12867 | 0.637068 | ||||||||
\(43\) | −7.46777 | −1.13882 | −0.569412 | − | 0.822052i | \(-0.692829\pi\) | ||||
−0.569412 | + | 0.822052i | \(0.692829\pi\) | |||||||
\(44\) | 0.115460 | 0.0174062 | ||||||||
\(45\) | −1.47112 | −0.219302 | ||||||||
\(46\) | −0.517582 | −0.0763133 | ||||||||
\(47\) | −9.67305 | −1.41096 | −0.705479 | − | 0.708730i | \(-0.749268\pi\) | ||||
−0.705479 | + | 0.708730i | \(0.749268\pi\) | |||||||
\(48\) | 4.64391 | 0.670290 | ||||||||
\(49\) | −1.08380 | −0.154829 | ||||||||
\(50\) | −1.37279 | −0.194141 | ||||||||
\(51\) | 1.28594 | 0.180068 | ||||||||
\(52\) | 0.559766 | 0.0776256 | ||||||||
\(53\) | −12.7465 | −1.75087 | −0.875435 | − | 0.483336i | \(-0.839425\pi\) | ||||
−0.875435 | + | 0.483336i | \(0.839425\pi\) | |||||||
\(54\) | −7.58937 | −1.03278 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 7.06364 | 0.943919 | ||||||||
\(57\) | −1.23648 | −0.163776 | ||||||||
\(58\) | −6.18698 | −0.812390 | ||||||||
\(59\) | 1.32111 | 0.171994 | 0.0859968 | − | 0.996295i | \(-0.472593\pi\) | ||||
0.0859968 | + | 0.996295i | \(0.472593\pi\) | |||||||
\(60\) | 0.142763 | 0.0184307 | ||||||||
\(61\) | −5.58779 | −0.715443 | −0.357721 | − | 0.933828i | \(-0.616446\pi\) | ||||
−0.357721 | + | 0.933828i | \(0.616446\pi\) | |||||||
\(62\) | −6.53915 | −0.830472 | ||||||||
\(63\) | −3.57824 | −0.450816 | ||||||||
\(64\) | 8.40698 | 1.05087 | ||||||||
\(65\) | −4.84815 | −0.601339 | ||||||||
\(66\) | −1.69742 | −0.208938 | ||||||||
\(67\) | −1.20728 | −0.147493 | −0.0737465 | − | 0.997277i | \(-0.523496\pi\) | ||||
−0.0737465 | + | 0.997277i | \(0.523496\pi\) | |||||||
\(68\) | 0.120079 | 0.0145617 | ||||||||
\(69\) | −0.466190 | −0.0561227 | ||||||||
\(70\) | −3.33906 | −0.399094 | ||||||||
\(71\) | −0.259538 | −0.0308015 | −0.0154007 | − | 0.999881i | \(-0.504902\pi\) | ||||
−0.0154007 | + | 0.999881i | \(0.504902\pi\) | |||||||
\(72\) | −4.27224 | −0.503488 | ||||||||
\(73\) | −6.27686 | −0.734651 | −0.367325 | − | 0.930093i | \(-0.619726\pi\) | ||||
−0.367325 | + | 0.930093i | \(0.619726\pi\) | |||||||
\(74\) | −4.13797 | −0.481029 | ||||||||
\(75\) | −1.23648 | −0.142776 | ||||||||
\(76\) | −0.115460 | −0.0132441 | ||||||||
\(77\) | −2.43232 | −0.277189 | ||||||||
\(78\) | −8.22935 | −0.931790 | ||||||||
\(79\) | −9.16926 | −1.03162 | −0.515811 | − | 0.856702i | \(-0.672509\pi\) | ||||
−0.515811 | + | 0.856702i | \(0.672509\pi\) | |||||||
\(80\) | −3.75575 | −0.419906 | ||||||||
\(81\) | −2.42245 | −0.269161 | ||||||||
\(82\) | −1.08512 | −0.119831 | ||||||||
\(83\) | −14.2430 | −1.56337 | −0.781686 | − | 0.623673i | \(-0.785640\pi\) | ||||
−0.781686 | + | 0.623673i | \(0.785640\pi\) | |||||||
\(84\) | 0.347247 | 0.0378877 | ||||||||
\(85\) | −1.04001 | −0.112804 | ||||||||
\(86\) | 10.2517 | 1.10546 | ||||||||
\(87\) | −5.57266 | −0.597452 | ||||||||
\(88\) | −2.90407 | −0.309575 | ||||||||
\(89\) | −1.23983 | −0.131421 | −0.0657107 | − | 0.997839i | \(-0.520931\pi\) | ||||
−0.0657107 | + | 0.997839i | \(0.520931\pi\) | |||||||
\(90\) | 2.01953 | 0.212877 | ||||||||
\(91\) | −11.7923 | −1.23617 | ||||||||
\(92\) | −0.0435318 | −0.00453851 | ||||||||
\(93\) | −5.88986 | −0.610750 | ||||||||
\(94\) | 13.2790 | 1.36963 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0.806563 | 0.0823195 | ||||||||
\(97\) | 2.95633 | 0.300170 | 0.150085 | − | 0.988673i | \(-0.452045\pi\) | ||||
0.150085 | + | 0.988673i | \(0.452045\pi\) | |||||||
\(98\) | 1.48783 | 0.150294 | ||||||||
\(99\) | 1.47112 | 0.147853 | ||||||||
\(100\) | −0.115460 | −0.0115460 | ||||||||
\(101\) | −1.55010 | −0.154241 | −0.0771204 | − | 0.997022i | \(-0.524573\pi\) | ||||
−0.0771204 | + | 0.997022i | \(0.524573\pi\) | |||||||
\(102\) | −1.76533 | −0.174793 | ||||||||
\(103\) | −0.339313 | −0.0334335 | −0.0167168 | − | 0.999860i | \(-0.505321\pi\) | ||||
−0.0167168 | + | 0.999860i | \(0.505321\pi\) | |||||||
\(104\) | −14.0794 | −1.38060 | ||||||||
\(105\) | −3.00752 | −0.293504 | ||||||||
\(106\) | 17.4982 | 1.69958 | ||||||||
\(107\) | −9.05124 | −0.875017 | −0.437508 | − | 0.899214i | \(-0.644139\pi\) | ||||
−0.437508 | + | 0.899214i | \(0.644139\pi\) | |||||||
\(108\) | −0.638313 | −0.0614217 | ||||||||
\(109\) | 14.7515 | 1.41294 | 0.706471 | − | 0.707742i | \(-0.250286\pi\) | ||||
0.706471 | + | 0.707742i | \(0.250286\pi\) | |||||||
\(110\) | 1.37279 | 0.130890 | ||||||||
\(111\) | −3.72710 | −0.353761 | ||||||||
\(112\) | −9.13520 | −0.863195 | ||||||||
\(113\) | −4.71030 | −0.443108 | −0.221554 | − | 0.975148i | \(-0.571113\pi\) | ||||
−0.221554 | + | 0.975148i | \(0.571113\pi\) | |||||||
\(114\) | 1.69742 | 0.158978 | ||||||||
\(115\) | 0.377030 | 0.0351583 | ||||||||
\(116\) | −0.520363 | −0.0483145 | ||||||||
\(117\) | 7.13221 | 0.659373 | ||||||||
\(118\) | −1.81360 | −0.166955 | ||||||||
\(119\) | −2.52963 | −0.231891 | ||||||||
\(120\) | −3.59082 | −0.327796 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.67083 | 0.694485 | ||||||||
\(123\) | −0.977376 | −0.0881270 | ||||||||
\(124\) | −0.549982 | −0.0493899 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.91215 | 0.437610 | ||||||||
\(127\) | 14.7860 | 1.31205 | 0.656024 | − | 0.754740i | \(-0.272237\pi\) | ||||
0.656024 | + | 0.754740i | \(0.272237\pi\) | |||||||
\(128\) | −10.2364 | −0.904775 | ||||||||
\(129\) | 9.23374 | 0.812986 | ||||||||
\(130\) | 6.65547 | 0.583723 | ||||||||
\(131\) | −7.82065 | −0.683294 | −0.341647 | − | 0.939828i | \(-0.610985\pi\) | ||||
−0.341647 | + | 0.939828i | \(0.610985\pi\) | |||||||
\(132\) | −0.142763 | −0.0124260 | ||||||||
\(133\) | 2.43232 | 0.210909 | ||||||||
\(134\) | 1.65734 | 0.143172 | ||||||||
\(135\) | 5.52845 | 0.475813 | ||||||||
\(136\) | −3.02025 | −0.258984 | ||||||||
\(137\) | −7.70625 | −0.658389 | −0.329195 | − | 0.944262i | \(-0.606777\pi\) | ||||
−0.329195 | + | 0.944262i | \(0.606777\pi\) | |||||||
\(138\) | 0.639979 | 0.0544786 | ||||||||
\(139\) | 14.3953 | 1.22099 | 0.610495 | − | 0.792020i | \(-0.290970\pi\) | ||||
0.610495 | + | 0.792020i | \(0.290970\pi\) | |||||||
\(140\) | −0.280835 | −0.0237349 | ||||||||
\(141\) | 11.9605 | 1.00726 | ||||||||
\(142\) | 0.356290 | 0.0298992 | ||||||||
\(143\) | 4.84815 | 0.405423 | ||||||||
\(144\) | 5.52516 | 0.460430 | ||||||||
\(145\) | 4.50688 | 0.374276 | ||||||||
\(146\) | 8.61678 | 0.713130 | ||||||||
\(147\) | 1.34010 | 0.110530 | ||||||||
\(148\) | −0.348028 | −0.0286078 | ||||||||
\(149\) | −13.8399 | −1.13381 | −0.566906 | − | 0.823783i | \(-0.691860\pi\) | ||||
−0.566906 | + | 0.823783i | \(0.691860\pi\) | |||||||
\(150\) | 1.69742 | 0.138594 | ||||||||
\(151\) | −8.10281 | −0.659398 | −0.329699 | − | 0.944086i | \(-0.606947\pi\) | ||||
−0.329699 | + | 0.944086i | \(0.606947\pi\) | |||||||
\(152\) | 2.90407 | 0.235551 | ||||||||
\(153\) | 1.52997 | 0.123691 | ||||||||
\(154\) | 3.33906 | 0.269069 | ||||||||
\(155\) | 4.76341 | 0.382607 | ||||||||
\(156\) | −0.692139 | −0.0554155 | ||||||||
\(157\) | −7.13378 | −0.569338 | −0.284669 | − | 0.958626i | \(-0.591884\pi\) | ||||
−0.284669 | + | 0.958626i | \(0.591884\pi\) | |||||||
\(158\) | 12.5874 | 1.00140 | ||||||||
\(159\) | 15.7608 | 1.24991 | ||||||||
\(160\) | −0.652306 | −0.0515693 | ||||||||
\(161\) | 0.917060 | 0.0722744 | ||||||||
\(162\) | 3.32550 | 0.261276 | ||||||||
\(163\) | −23.8705 | −1.86968 | −0.934840 | − | 0.355068i | \(-0.884458\pi\) | ||||
−0.934840 | + | 0.355068i | \(0.884458\pi\) | |||||||
\(164\) | −0.0912652 | −0.00712661 | ||||||||
\(165\) | 1.23648 | 0.0962598 | ||||||||
\(166\) | 19.5526 | 1.51757 | ||||||||
\(167\) | −8.49981 | −0.657735 | −0.328868 | − | 0.944376i | \(-0.606667\pi\) | ||||
−0.328868 | + | 0.944376i | \(0.606667\pi\) | |||||||
\(168\) | −8.73405 | −0.673846 | ||||||||
\(169\) | 10.5046 | 0.808043 | ||||||||
\(170\) | 1.42770 | 0.109500 | ||||||||
\(171\) | −1.47112 | −0.112499 | ||||||||
\(172\) | 0.862227 | 0.0657442 | ||||||||
\(173\) | −3.76732 | −0.286424 | −0.143212 | − | 0.989692i | \(-0.545743\pi\) | ||||
−0.143212 | + | 0.989692i | \(0.545743\pi\) | |||||||
\(174\) | 7.65007 | 0.579950 | ||||||||
\(175\) | 2.43232 | 0.183866 | ||||||||
\(176\) | 3.75575 | 0.283100 | ||||||||
\(177\) | −1.63352 | −0.122783 | ||||||||
\(178\) | 1.70202 | 0.127571 | ||||||||
\(179\) | −12.0321 | −0.899323 | −0.449661 | − | 0.893199i | \(-0.648455\pi\) | ||||
−0.449661 | + | 0.893199i | \(0.648455\pi\) | |||||||
\(180\) | 0.169855 | 0.0126602 | ||||||||
\(181\) | −9.01903 | −0.670380 | −0.335190 | − | 0.942151i | \(-0.608800\pi\) | ||||
−0.335190 | + | 0.942151i | \(0.608800\pi\) | |||||||
\(182\) | 16.1883 | 1.19995 | ||||||||
\(183\) | 6.90918 | 0.510741 | ||||||||
\(184\) | 1.09492 | 0.0807188 | ||||||||
\(185\) | 3.01428 | 0.221615 | ||||||||
\(186\) | 8.08552 | 0.592859 | ||||||||
\(187\) | 1.04001 | 0.0760527 | ||||||||
\(188\) | 1.11685 | 0.0814544 | ||||||||
\(189\) | 13.4470 | 0.978123 | ||||||||
\(190\) | −1.37279 | −0.0995923 | ||||||||
\(191\) | −15.2598 | −1.10416 | −0.552079 | − | 0.833792i | \(-0.686165\pi\) | ||||
−0.552079 | + | 0.833792i | \(0.686165\pi\) | |||||||
\(192\) | −10.3950 | −0.750198 | ||||||||
\(193\) | 3.17246 | 0.228359 | 0.114179 | − | 0.993460i | \(-0.463576\pi\) | ||||
0.114179 | + | 0.993460i | \(0.463576\pi\) | |||||||
\(194\) | −4.05841 | −0.291377 | ||||||||
\(195\) | 5.99464 | 0.429285 | ||||||||
\(196\) | 0.125136 | 0.00893827 | ||||||||
\(197\) | −6.09397 | −0.434178 | −0.217089 | − | 0.976152i | \(-0.569656\pi\) | ||||
−0.217089 | + | 0.976152i | \(0.569656\pi\) | |||||||
\(198\) | −2.01953 | −0.143522 | ||||||||
\(199\) | −15.8148 | −1.12108 | −0.560541 | − | 0.828127i | \(-0.689407\pi\) | ||||
−0.560541 | + | 0.828127i | \(0.689407\pi\) | |||||||
\(200\) | 2.90407 | 0.205349 | ||||||||
\(201\) | 1.49278 | 0.105292 | ||||||||
\(202\) | 2.12796 | 0.149723 | ||||||||
\(203\) | 10.9622 | 0.769395 | ||||||||
\(204\) | −0.148475 | −0.0103953 | ||||||||
\(205\) | 0.790451 | 0.0552075 | ||||||||
\(206\) | 0.465805 | 0.0324541 | ||||||||
\(207\) | −0.554657 | −0.0385513 | ||||||||
\(208\) | 18.2084 | 1.26253 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 4.12867 | 0.284906 | ||||||||
\(211\) | 10.4371 | 0.718522 | 0.359261 | − | 0.933237i | \(-0.383029\pi\) | ||||
0.359261 | + | 0.933237i | \(0.383029\pi\) | |||||||
\(212\) | 1.47171 | 0.101077 | ||||||||
\(213\) | 0.320913 | 0.0219886 | ||||||||
\(214\) | 12.4254 | 0.849384 | ||||||||
\(215\) | −7.46777 | −0.509298 | ||||||||
\(216\) | 16.0550 | 1.09240 | ||||||||
\(217\) | 11.5862 | 0.786520 | ||||||||
\(218\) | −20.2507 | −1.37155 | ||||||||
\(219\) | 7.76120 | 0.524453 | ||||||||
\(220\) | 0.115460 | 0.00778429 | ||||||||
\(221\) | 5.04210 | 0.339168 | ||||||||
\(222\) | 5.11651 | 0.343397 | ||||||||
\(223\) | −15.2161 | −1.01895 | −0.509474 | − | 0.860486i | \(-0.670160\pi\) | ||||
−0.509474 | + | 0.860486i | \(0.670160\pi\) | |||||||
\(224\) | −1.58662 | −0.106010 | ||||||||
\(225\) | −1.47112 | −0.0980747 | ||||||||
\(226\) | 6.46623 | 0.430127 | ||||||||
\(227\) | −15.4170 | −1.02326 | −0.511630 | − | 0.859206i | \(-0.670958\pi\) | ||||
−0.511630 | + | 0.859206i | \(0.670958\pi\) | |||||||
\(228\) | 0.142763 | 0.00945474 | ||||||||
\(229\) | 18.2529 | 1.20618 | 0.603091 | − | 0.797672i | \(-0.293935\pi\) | ||||
0.603091 | + | 0.797672i | \(0.293935\pi\) | |||||||
\(230\) | −0.517582 | −0.0341283 | ||||||||
\(231\) | 3.00752 | 0.197880 | ||||||||
\(232\) | 13.0883 | 0.859289 | ||||||||
\(233\) | 19.1041 | 1.25155 | 0.625776 | − | 0.780003i | \(-0.284782\pi\) | ||||
0.625776 | + | 0.780003i | \(0.284782\pi\) | |||||||
\(234\) | −9.79100 | −0.640057 | ||||||||
\(235\) | −9.67305 | −0.631000 | ||||||||
\(236\) | −0.152535 | −0.00992917 | ||||||||
\(237\) | 11.3376 | 0.736456 | ||||||||
\(238\) | 3.47264 | 0.225098 | ||||||||
\(239\) | 20.6551 | 1.33607 | 0.668034 | − | 0.744131i | \(-0.267136\pi\) | ||||
0.668034 | + | 0.744131i | \(0.267136\pi\) | |||||||
\(240\) | 4.64391 | 0.299763 | ||||||||
\(241\) | 15.9963 | 1.03042 | 0.515208 | − | 0.857065i | \(-0.327715\pi\) | ||||
0.515208 | + | 0.857065i | \(0.327715\pi\) | |||||||
\(242\) | −1.37279 | −0.0882460 | ||||||||
\(243\) | −13.5900 | −0.871801 | ||||||||
\(244\) | 0.645164 | 0.0413024 | ||||||||
\(245\) | −1.08380 | −0.0692417 | ||||||||
\(246\) | 1.34173 | 0.0855454 | ||||||||
\(247\) | −4.84815 | −0.308480 | ||||||||
\(248\) | 13.8333 | 0.878416 | ||||||||
\(249\) | 17.6112 | 1.11606 | ||||||||
\(250\) | −1.37279 | −0.0868226 | ||||||||
\(251\) | −11.3379 | −0.715639 | −0.357820 | − | 0.933791i | \(-0.616480\pi\) | ||||
−0.357820 | + | 0.933791i | \(0.616480\pi\) | |||||||
\(252\) | 0.413142 | 0.0260255 | ||||||||
\(253\) | −0.377030 | −0.0237037 | ||||||||
\(254\) | −20.2981 | −1.27361 | ||||||||
\(255\) | 1.28594 | 0.0805290 | ||||||||
\(256\) | −2.76162 | −0.172601 | ||||||||
\(257\) | 9.80023 | 0.611322 | 0.305661 | − | 0.952140i | \(-0.401123\pi\) | ||||
0.305661 | + | 0.952140i | \(0.401123\pi\) | |||||||
\(258\) | −12.6759 | −0.789170 | ||||||||
\(259\) | 7.33171 | 0.455570 | ||||||||
\(260\) | 0.559766 | 0.0347152 | ||||||||
\(261\) | −6.63016 | −0.410397 | ||||||||
\(262\) | 10.7361 | 0.663277 | ||||||||
\(263\) | −21.2899 | −1.31279 | −0.656395 | − | 0.754418i | \(-0.727919\pi\) | ||||
−0.656395 | + | 0.754418i | \(0.727919\pi\) | |||||||
\(264\) | 3.59082 | 0.221000 | ||||||||
\(265\) | −12.7465 | −0.783013 | ||||||||
\(266\) | −3.33906 | −0.204731 | ||||||||
\(267\) | 1.53302 | 0.0938192 | ||||||||
\(268\) | 0.139392 | 0.00851475 | ||||||||
\(269\) | −18.2788 | −1.11448 | −0.557240 | − | 0.830352i | \(-0.688140\pi\) | ||||
−0.557240 | + | 0.830352i | \(0.688140\pi\) | |||||||
\(270\) | −7.58937 | −0.461874 | ||||||||
\(271\) | 19.7872 | 1.20199 | 0.600994 | − | 0.799253i | \(-0.294772\pi\) | ||||
0.600994 | + | 0.799253i | \(0.294772\pi\) | |||||||
\(272\) | 3.90600 | 0.236836 | ||||||||
\(273\) | 14.5809 | 0.882476 | ||||||||
\(274\) | 10.5790 | 0.639103 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0.0538262 | 0.00323995 | ||||||||
\(277\) | 24.5658 | 1.47602 | 0.738008 | − | 0.674792i | \(-0.235767\pi\) | ||||
0.738008 | + | 0.674792i | \(0.235767\pi\) | |||||||
\(278\) | −19.7616 | −1.18522 | ||||||||
\(279\) | −7.00755 | −0.419531 | ||||||||
\(280\) | 7.06364 | 0.422133 | ||||||||
\(281\) | 14.0898 | 0.840524 | 0.420262 | − | 0.907403i | \(-0.361938\pi\) | ||||
0.420262 | + | 0.907403i | \(0.361938\pi\) | |||||||
\(282\) | −16.4192 | −0.977751 | ||||||||
\(283\) | −18.8367 | −1.11973 | −0.559863 | − | 0.828585i | \(-0.689146\pi\) | ||||
−0.559863 | + | 0.828585i | \(0.689146\pi\) | |||||||
\(284\) | 0.0299662 | 0.00177816 | ||||||||
\(285\) | −1.23648 | −0.0732427 | ||||||||
\(286\) | −6.65547 | −0.393546 | ||||||||
\(287\) | 1.92263 | 0.113489 | ||||||||
\(288\) | 0.959621 | 0.0565462 | ||||||||
\(289\) | −15.9184 | −0.936376 | ||||||||
\(290\) | −6.18698 | −0.363312 | ||||||||
\(291\) | −3.65544 | −0.214286 | ||||||||
\(292\) | 0.724724 | 0.0424113 | ||||||||
\(293\) | 2.08270 | 0.121673 | 0.0608364 | − | 0.998148i | \(-0.480623\pi\) | ||||
0.0608364 | + | 0.998148i | \(0.480623\pi\) | |||||||
\(294\) | −1.83967 | −0.107292 | ||||||||
\(295\) | 1.32111 | 0.0769179 | ||||||||
\(296\) | 8.75370 | 0.508798 | ||||||||
\(297\) | −5.52845 | −0.320793 | ||||||||
\(298\) | 18.9993 | 1.10060 | ||||||||
\(299\) | −1.82790 | −0.105710 | ||||||||
\(300\) | 0.142763 | 0.00824245 | ||||||||
\(301\) | −18.1640 | −1.04696 | ||||||||
\(302\) | 11.1234 | 0.640081 | ||||||||
\(303\) | 1.91667 | 0.110110 | ||||||||
\(304\) | −3.75575 | −0.215407 | ||||||||
\(305\) | −5.58779 | −0.319956 | ||||||||
\(306\) | −2.10032 | −0.120068 | ||||||||
\(307\) | 19.8442 | 1.13257 | 0.566284 | − | 0.824210i | \(-0.308381\pi\) | ||||
0.566284 | + | 0.824210i | \(0.308381\pi\) | |||||||
\(308\) | 0.280835 | 0.0160021 | ||||||||
\(309\) | 0.419554 | 0.0238676 | ||||||||
\(310\) | −6.53915 | −0.371399 | ||||||||
\(311\) | 3.71814 | 0.210836 | 0.105418 | − | 0.994428i | \(-0.466382\pi\) | ||||
0.105418 | + | 0.994428i | \(0.466382\pi\) | |||||||
\(312\) | 17.4089 | 0.985582 | ||||||||
\(313\) | 27.0866 | 1.53102 | 0.765511 | − | 0.643423i | \(-0.222486\pi\) | ||||
0.765511 | + | 0.643423i | \(0.222486\pi\) | |||||||
\(314\) | 9.79316 | 0.552660 | ||||||||
\(315\) | −3.57824 | −0.201611 | ||||||||
\(316\) | 1.05868 | 0.0595554 | ||||||||
\(317\) | 9.50445 | 0.533823 | 0.266911 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266911 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(318\) | −21.6362 | −1.21330 | ||||||||
\(319\) | −4.50688 | −0.252337 | ||||||||
\(320\) | 8.40698 | 0.469964 | ||||||||
\(321\) | 11.1917 | 0.624658 | ||||||||
\(322\) | −1.25893 | −0.0701572 | ||||||||
\(323\) | −1.04001 | −0.0578674 | ||||||||
\(324\) | 0.279695 | 0.0155386 | ||||||||
\(325\) | −4.84815 | −0.268927 | ||||||||
\(326\) | 32.7691 | 1.81491 | ||||||||
\(327\) | −18.2400 | −1.00867 | ||||||||
\(328\) | 2.29553 | 0.126749 | ||||||||
\(329\) | −23.5280 | −1.29714 | ||||||||
\(330\) | −1.69742 | −0.0934399 | ||||||||
\(331\) | 7.27869 | 0.400073 | 0.200036 | − | 0.979788i | \(-0.435894\pi\) | ||||
0.200036 | + | 0.979788i | \(0.435894\pi\) | |||||||
\(332\) | 1.64449 | 0.0902532 | ||||||||
\(333\) | −4.43437 | −0.243002 | ||||||||
\(334\) | 11.6684 | 0.638467 | ||||||||
\(335\) | −1.20728 | −0.0659609 | ||||||||
\(336\) | 11.2955 | 0.616219 | ||||||||
\(337\) | 29.3790 | 1.60037 | 0.800187 | − | 0.599750i | \(-0.204733\pi\) | ||||
0.800187 | + | 0.599750i | \(0.204733\pi\) | |||||||
\(338\) | −14.4205 | −0.784372 | ||||||||
\(339\) | 5.82419 | 0.316326 | ||||||||
\(340\) | 0.120079 | 0.00651218 | ||||||||
\(341\) | −4.76341 | −0.257953 | ||||||||
\(342\) | 2.01953 | 0.109204 | ||||||||
\(343\) | −19.6624 | −1.06167 | ||||||||
\(344\) | −21.6870 | −1.16928 | ||||||||
\(345\) | −0.466190 | −0.0250988 | ||||||||
\(346\) | 5.17173 | 0.278034 | ||||||||
\(347\) | 28.1028 | 1.50864 | 0.754318 | − | 0.656509i | \(-0.227968\pi\) | ||||
0.754318 | + | 0.656509i | \(0.227968\pi\) | |||||||
\(348\) | 0.643418 | 0.0344908 | ||||||||
\(349\) | 20.9948 | 1.12383 | 0.561913 | − | 0.827196i | \(-0.310065\pi\) | ||||
0.561913 | + | 0.827196i | \(0.310065\pi\) | |||||||
\(350\) | −3.33906 | −0.178480 | ||||||||
\(351\) | −26.8027 | −1.43062 | ||||||||
\(352\) | 0.652306 | 0.0347680 | ||||||||
\(353\) | 15.1874 | 0.808345 | 0.404172 | − | 0.914683i | \(-0.367560\pi\) | ||||
0.404172 | + | 0.914683i | \(0.367560\pi\) | |||||||
\(354\) | 2.24248 | 0.119186 | ||||||||
\(355\) | −0.259538 | −0.0137748 | ||||||||
\(356\) | 0.143150 | 0.00758693 | ||||||||
\(357\) | 3.12783 | 0.165542 | ||||||||
\(358\) | 16.5175 | 0.872978 | ||||||||
\(359\) | 11.5028 | 0.607093 | 0.303546 | − | 0.952817i | \(-0.401829\pi\) | ||||
0.303546 | + | 0.952817i | \(0.401829\pi\) | |||||||
\(360\) | −4.27224 | −0.225167 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 12.3812 | 0.650741 | ||||||||
\(363\) | −1.23648 | −0.0648983 | ||||||||
\(364\) | 1.36153 | 0.0713637 | ||||||||
\(365\) | −6.27686 | −0.328546 | ||||||||
\(366\) | −9.48483 | −0.495780 | ||||||||
\(367\) | −1.52355 | −0.0795284 | −0.0397642 | − | 0.999209i | \(-0.512661\pi\) | ||||
−0.0397642 | + | 0.999209i | \(0.512661\pi\) | |||||||
\(368\) | −1.41603 | −0.0738158 | ||||||||
\(369\) | −1.16285 | −0.0605354 | ||||||||
\(370\) | −4.13797 | −0.215123 | ||||||||
\(371\) | −31.0037 | −1.60963 | ||||||||
\(372\) | 0.680042 | 0.0352585 | ||||||||
\(373\) | 16.5646 | 0.857682 | 0.428841 | − | 0.903380i | \(-0.358922\pi\) | ||||
0.428841 | + | 0.903380i | \(0.358922\pi\) | |||||||
\(374\) | −1.42770 | −0.0738248 | ||||||||
\(375\) | −1.23648 | −0.0638515 | ||||||||
\(376\) | −28.0912 | −1.44869 | ||||||||
\(377\) | −21.8500 | −1.12533 | ||||||||
\(378\) | −18.4598 | −0.949470 | ||||||||
\(379\) | −0.0190602 | −0.000979058 0 | −0.000489529 | − | 1.00000i | \(-0.500156\pi\) | ||||
−0.000489529 | 1.00000i | \(0.500156\pi\) | ||||||||
\(380\) | −0.115460 | −0.00592296 | ||||||||
\(381\) | −18.2826 | −0.936647 | ||||||||
\(382\) | 20.9484 | 1.07181 | ||||||||
\(383\) | 18.2085 | 0.930412 | 0.465206 | − | 0.885202i | \(-0.345980\pi\) | ||||
0.465206 | + | 0.885202i | \(0.345980\pi\) | |||||||
\(384\) | 12.6570 | 0.645902 | ||||||||
\(385\) | −2.43232 | −0.123963 | ||||||||
\(386\) | −4.35511 | −0.221669 | ||||||||
\(387\) | 10.9860 | 0.558449 | ||||||||
\(388\) | −0.341337 | −0.0173288 | ||||||||
\(389\) | −31.4031 | −1.59220 | −0.796099 | − | 0.605166i | \(-0.793107\pi\) | ||||
−0.796099 | + | 0.605166i | \(0.793107\pi\) | |||||||
\(390\) | −8.22935 | −0.416709 | ||||||||
\(391\) | −0.392114 | −0.0198300 | ||||||||
\(392\) | −3.14745 | −0.158970 | ||||||||
\(393\) | 9.67007 | 0.487791 | ||||||||
\(394\) | 8.36572 | 0.421459 | ||||||||
\(395\) | −9.16926 | −0.461355 | ||||||||
\(396\) | −0.169855 | −0.00853554 | ||||||||
\(397\) | −25.8619 | −1.29797 | −0.648985 | − | 0.760801i | \(-0.724806\pi\) | ||||
−0.648985 | + | 0.760801i | \(0.724806\pi\) | |||||||
\(398\) | 21.7103 | 1.08824 | ||||||||
\(399\) | −3.00752 | −0.150564 | ||||||||
\(400\) | −3.75575 | −0.187787 | ||||||||
\(401\) | −15.5141 | −0.774737 | −0.387369 | − | 0.921925i | \(-0.626616\pi\) | ||||
−0.387369 | + | 0.921925i | \(0.626616\pi\) | |||||||
\(402\) | −2.04926 | −0.102208 | ||||||||
\(403\) | −23.0938 | −1.15038 | ||||||||
\(404\) | 0.178974 | 0.00890430 | ||||||||
\(405\) | −2.42245 | −0.120372 | ||||||||
\(406\) | −15.0487 | −0.746856 | ||||||||
\(407\) | −3.01428 | −0.149412 | ||||||||
\(408\) | 3.73448 | 0.184884 | ||||||||
\(409\) | 20.7451 | 1.02578 | 0.512889 | − | 0.858455i | \(-0.328575\pi\) | ||||
0.512889 | + | 0.858455i | \(0.328575\pi\) | |||||||
\(410\) | −1.08512 | −0.0535902 | ||||||||
\(411\) | 9.52862 | 0.470012 | ||||||||
\(412\) | 0.0391770 | 0.00193011 | ||||||||
\(413\) | 3.21336 | 0.158119 | ||||||||
\(414\) | 0.761425 | 0.0374220 | ||||||||
\(415\) | −14.2430 | −0.699161 | ||||||||
\(416\) | 3.16248 | 0.155053 | ||||||||
\(417\) | −17.7994 | −0.871643 | ||||||||
\(418\) | 1.37279 | 0.0671451 | ||||||||
\(419\) | 6.94955 | 0.339508 | 0.169754 | − | 0.985487i | \(-0.445703\pi\) | ||||
0.169754 | + | 0.985487i | \(0.445703\pi\) | |||||||
\(420\) | 0.347247 | 0.0169439 | ||||||||
\(421\) | 17.0486 | 0.830897 | 0.415448 | − | 0.909617i | \(-0.363625\pi\) | ||||
0.415448 | + | 0.909617i | \(0.363625\pi\) | |||||||
\(422\) | −14.3280 | −0.697474 | ||||||||
\(423\) | 14.2302 | 0.691897 | ||||||||
\(424\) | −37.0168 | −1.79770 | ||||||||
\(425\) | −1.04001 | −0.0504477 | ||||||||
\(426\) | −0.440545 | −0.0213445 | ||||||||
\(427\) | −13.5913 | −0.657729 | ||||||||
\(428\) | 1.04505 | 0.0505146 | ||||||||
\(429\) | −5.99464 | −0.289424 | ||||||||
\(430\) | 10.2517 | 0.494378 | ||||||||
\(431\) | 10.6174 | 0.511421 | 0.255711 | − | 0.966753i | \(-0.417691\pi\) | ||||
0.255711 | + | 0.966753i | \(0.417691\pi\) | |||||||
\(432\) | −20.7635 | −0.998982 | ||||||||
\(433\) | −5.21952 | −0.250834 | −0.125417 | − | 0.992104i | \(-0.540027\pi\) | ||||
−0.125417 | + | 0.992104i | \(0.540027\pi\) | |||||||
\(434\) | −15.9053 | −0.763480 | ||||||||
\(435\) | −5.57266 | −0.267189 | ||||||||
\(436\) | −1.70321 | −0.0815689 | ||||||||
\(437\) | 0.377030 | 0.0180358 | ||||||||
\(438\) | −10.6545 | −0.509090 | ||||||||
\(439\) | −25.8096 | −1.23182 | −0.615912 | − | 0.787815i | \(-0.711212\pi\) | ||||
−0.615912 | + | 0.787815i | \(0.711212\pi\) | |||||||
\(440\) | −2.90407 | −0.138446 | ||||||||
\(441\) | 1.59441 | 0.0759241 | ||||||||
\(442\) | −6.92172 | −0.329233 | ||||||||
\(443\) | −30.3917 | −1.44395 | −0.721977 | − | 0.691917i | \(-0.756766\pi\) | ||||
−0.721977 | + | 0.691917i | \(0.756766\pi\) | |||||||
\(444\) | 0.430330 | 0.0204225 | ||||||||
\(445\) | −1.23983 | −0.0587734 | ||||||||
\(446\) | 20.8885 | 0.989099 | ||||||||
\(447\) | 17.1128 | 0.809407 | ||||||||
\(448\) | 20.4485 | 0.966100 | ||||||||
\(449\) | 10.8574 | 0.512394 | 0.256197 | − | 0.966625i | \(-0.417530\pi\) | ||||
0.256197 | + | 0.966625i | \(0.417530\pi\) | |||||||
\(450\) | 2.01953 | 0.0952017 | ||||||||
\(451\) | −0.790451 | −0.0372209 | ||||||||
\(452\) | 0.543850 | 0.0255805 | ||||||||
\(453\) | 10.0190 | 0.470732 | ||||||||
\(454\) | 21.1642 | 0.993285 | ||||||||
\(455\) | −11.7923 | −0.552830 | ||||||||
\(456\) | −3.59082 | −0.168156 | ||||||||
\(457\) | 18.3849 | 0.860008 | 0.430004 | − | 0.902827i | \(-0.358512\pi\) | ||||
0.430004 | + | 0.902827i | \(0.358512\pi\) | |||||||
\(458\) | −25.0573 | −1.17085 | ||||||||
\(459\) | −5.74961 | −0.268369 | ||||||||
\(460\) | −0.0435318 | −0.00202968 | ||||||||
\(461\) | −28.2662 | −1.31649 | −0.658245 | − | 0.752804i | \(-0.728701\pi\) | ||||
−0.658245 | + | 0.752804i | \(0.728701\pi\) | |||||||
\(462\) | −4.12867 | −0.192083 | ||||||||
\(463\) | 33.4266 | 1.55346 | 0.776732 | − | 0.629831i | \(-0.216876\pi\) | ||||
0.776732 | + | 0.629831i | \(0.216876\pi\) | |||||||
\(464\) | −16.9267 | −0.785803 | ||||||||
\(465\) | −5.88986 | −0.273136 | ||||||||
\(466\) | −26.2258 | −1.21489 | ||||||||
\(467\) | −1.21297 | −0.0561297 | −0.0280648 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280648 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(468\) | −0.823483 | −0.0380655 | ||||||||
\(469\) | −2.93650 | −0.135595 | ||||||||
\(470\) | 13.2790 | 0.612515 | ||||||||
\(471\) | 8.82077 | 0.406440 | ||||||||
\(472\) | 3.83659 | 0.176594 | ||||||||
\(473\) | 7.46777 | 0.343369 | ||||||||
\(474\) | −15.5641 | −0.714882 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0.292070 | 0.0133870 | ||||||||
\(477\) | 18.7517 | 0.858580 | ||||||||
\(478\) | −28.3550 | −1.29693 | ||||||||
\(479\) | −25.9098 | −1.18385 | −0.591923 | − | 0.805994i | \(-0.701631\pi\) | ||||
−0.591923 | + | 0.805994i | \(0.701631\pi\) | |||||||
\(480\) | 0.806563 | 0.0368144 | ||||||||
\(481\) | −14.6137 | −0.666327 | ||||||||
\(482\) | −21.9596 | −1.00023 | ||||||||
\(483\) | −1.13392 | −0.0515954 | ||||||||
\(484\) | −0.115460 | −0.00524817 | ||||||||
\(485\) | 2.95633 | 0.134240 | ||||||||
\(486\) | 18.6562 | 0.846262 | ||||||||
\(487\) | −3.09538 | −0.140265 | −0.0701326 | − | 0.997538i | \(-0.522342\pi\) | ||||
−0.0701326 | + | 0.997538i | \(0.522342\pi\) | |||||||
\(488\) | −16.2273 | −0.734577 | ||||||||
\(489\) | 29.5154 | 1.33473 | ||||||||
\(490\) | 1.48783 | 0.0672134 | ||||||||
\(491\) | 17.4687 | 0.788352 | 0.394176 | − | 0.919035i | \(-0.371030\pi\) | ||||
0.394176 | + | 0.919035i | \(0.371030\pi\) | |||||||
\(492\) | 0.112847 | 0.00508756 | ||||||||
\(493\) | −4.68718 | −0.211100 | ||||||||
\(494\) | 6.65547 | 0.299444 | ||||||||
\(495\) | 1.47112 | 0.0661219 | ||||||||
\(496\) | −17.8902 | −0.803293 | ||||||||
\(497\) | −0.631280 | −0.0283168 | ||||||||
\(498\) | −24.1763 | −1.08337 | ||||||||
\(499\) | −6.47276 | −0.289760 | −0.144880 | − | 0.989449i | \(-0.546280\pi\) | ||||
−0.144880 | + | 0.989449i | \(0.546280\pi\) | |||||||
\(500\) | −0.115460 | −0.00516351 | ||||||||
\(501\) | 10.5098 | 0.469545 | ||||||||
\(502\) | 15.5644 | 0.694675 | ||||||||
\(503\) | −15.5931 | −0.695262 | −0.347631 | − | 0.937631i | \(-0.613014\pi\) | ||||
−0.347631 | + | 0.937631i | \(0.613014\pi\) | |||||||
\(504\) | −10.3915 | −0.462873 | ||||||||
\(505\) | −1.55010 | −0.0689786 | ||||||||
\(506\) | 0.517582 | 0.0230093 | ||||||||
\(507\) | −12.9887 | −0.576847 | ||||||||
\(508\) | −1.70719 | −0.0757444 | ||||||||
\(509\) | 6.14404 | 0.272330 | 0.136165 | − | 0.990686i | \(-0.456522\pi\) | ||||
0.136165 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(510\) | −1.76533 | −0.0781699 | ||||||||
\(511\) | −15.2673 | −0.675388 | ||||||||
\(512\) | 24.2638 | 1.07232 | ||||||||
\(513\) | 5.52845 | 0.244087 | ||||||||
\(514\) | −13.4536 | −0.593414 | ||||||||
\(515\) | −0.339313 | −0.0149519 | ||||||||
\(516\) | −1.06613 | −0.0469335 | ||||||||
\(517\) | 9.67305 | 0.425420 | ||||||||
\(518\) | −10.0649 | −0.442225 | ||||||||
\(519\) | 4.65822 | 0.204473 | ||||||||
\(520\) | −14.0794 | −0.617422 | ||||||||
\(521\) | 41.4684 | 1.81676 | 0.908382 | − | 0.418141i | \(-0.137318\pi\) | ||||
0.908382 | + | 0.418141i | \(0.137318\pi\) | |||||||
\(522\) | 9.10179 | 0.398375 | ||||||||
\(523\) | 2.76287 | 0.120812 | 0.0604059 | − | 0.998174i | \(-0.480760\pi\) | ||||
0.0604059 | + | 0.998174i | \(0.480760\pi\) | |||||||
\(524\) | 0.902970 | 0.0394464 | ||||||||
\(525\) | −3.00752 | −0.131259 | ||||||||
\(526\) | 29.2264 | 1.27433 | ||||||||
\(527\) | −4.95398 | −0.215799 | ||||||||
\(528\) | −4.64391 | −0.202100 | ||||||||
\(529\) | −22.8578 | −0.993819 | ||||||||
\(530\) | 17.4982 | 0.760075 | ||||||||
\(531\) | −1.94351 | −0.0843411 | ||||||||
\(532\) | −0.280835 | −0.0121758 | ||||||||
\(533\) | −3.83222 | −0.165992 | ||||||||
\(534\) | −2.10451 | −0.0910709 | ||||||||
\(535\) | −9.05124 | −0.391319 | ||||||||
\(536\) | −3.50603 | −0.151438 | ||||||||
\(537\) | 14.8775 | 0.642010 | ||||||||
\(538\) | 25.0929 | 1.08183 | ||||||||
\(539\) | 1.08380 | 0.0466828 | ||||||||
\(540\) | −0.638313 | −0.0274686 | ||||||||
\(541\) | 29.6566 | 1.27504 | 0.637519 | − | 0.770435i | \(-0.279961\pi\) | ||||
0.637519 | + | 0.770435i | \(0.279961\pi\) | |||||||
\(542\) | −27.1636 | −1.16678 | ||||||||
\(543\) | 11.1518 | 0.478572 | ||||||||
\(544\) | 0.678402 | 0.0290862 | ||||||||
\(545\) | 14.7515 | 0.631886 | ||||||||
\(546\) | −20.0164 | −0.856624 | ||||||||
\(547\) | −21.7318 | −0.929184 | −0.464592 | − | 0.885525i | \(-0.653799\pi\) | ||||
−0.464592 | + | 0.885525i | \(0.653799\pi\) | |||||||
\(548\) | 0.889761 | 0.0380087 | ||||||||
\(549\) | 8.22031 | 0.350834 | ||||||||
\(550\) | 1.37279 | 0.0585358 | ||||||||
\(551\) | 4.50688 | 0.192000 | ||||||||
\(552\) | −1.35385 | −0.0576237 | ||||||||
\(553\) | −22.3026 | −0.948403 | ||||||||
\(554\) | −33.7236 | −1.43278 | ||||||||
\(555\) | −3.72710 | −0.158207 | ||||||||
\(556\) | −1.66207 | −0.0704876 | ||||||||
\(557\) | 8.08244 | 0.342464 | 0.171232 | − | 0.985231i | \(-0.445225\pi\) | ||||
0.171232 | + | 0.985231i | \(0.445225\pi\) | |||||||
\(558\) | 9.61987 | 0.407242 | ||||||||
\(559\) | 36.2049 | 1.53130 | ||||||||
\(560\) | −9.13520 | −0.386033 | ||||||||
\(561\) | −1.28594 | −0.0542926 | ||||||||
\(562\) | −19.3422 | −0.815902 | ||||||||
\(563\) | −25.7685 | −1.08601 | −0.543006 | − | 0.839729i | \(-0.682714\pi\) | ||||
−0.543006 | + | 0.839729i | \(0.682714\pi\) | |||||||
\(564\) | −1.38096 | −0.0581488 | ||||||||
\(565\) | −4.71030 | −0.198164 | ||||||||
\(566\) | 25.8588 | 1.08693 | ||||||||
\(567\) | −5.89217 | −0.247448 | ||||||||
\(568\) | −0.753717 | −0.0316253 | ||||||||
\(569\) | −19.2047 | −0.805102 | −0.402551 | − | 0.915398i | \(-0.631876\pi\) | ||||
−0.402551 | + | 0.915398i | \(0.631876\pi\) | |||||||
\(570\) | 1.69742 | 0.0710971 | ||||||||
\(571\) | −28.0284 | −1.17295 | −0.586477 | − | 0.809966i | \(-0.699486\pi\) | ||||
−0.586477 | + | 0.809966i | \(0.699486\pi\) | |||||||
\(572\) | −0.559766 | −0.0234050 | ||||||||
\(573\) | 18.8684 | 0.788237 | ||||||||
\(574\) | −2.63936 | −0.110165 | ||||||||
\(575\) | 0.377030 | 0.0157233 | ||||||||
\(576\) | −12.3677 | −0.515320 | ||||||||
\(577\) | −34.8547 | −1.45102 | −0.725509 | − | 0.688212i | \(-0.758396\pi\) | ||||
−0.725509 | + | 0.688212i | \(0.758396\pi\) | |||||||
\(578\) | 21.8525 | 0.908946 | ||||||||
\(579\) | −3.92268 | −0.163021 | ||||||||
\(580\) | −0.520363 | −0.0216069 | ||||||||
\(581\) | −34.6436 | −1.43726 | ||||||||
\(582\) | 5.01813 | 0.208008 | ||||||||
\(583\) | 12.7465 | 0.527907 | ||||||||
\(584\) | −18.2285 | −0.754299 | ||||||||
\(585\) | 7.13221 | 0.294881 | ||||||||
\(586\) | −2.85910 | −0.118109 | ||||||||
\(587\) | 7.98152 | 0.329433 | 0.164716 | − | 0.986341i | \(-0.447329\pi\) | ||||
0.164716 | + | 0.986341i | \(0.447329\pi\) | |||||||
\(588\) | −0.154728 | −0.00638086 | ||||||||
\(589\) | 4.76341 | 0.196273 | ||||||||
\(590\) | −1.81360 | −0.0746647 | ||||||||
\(591\) | 7.53507 | 0.309951 | ||||||||
\(592\) | −11.3209 | −0.465286 | ||||||||
\(593\) | 11.6876 | 0.479951 | 0.239976 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239976 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(594\) | 7.58937 | 0.311396 | ||||||||
\(595\) | −2.52963 | −0.103705 | ||||||||
\(596\) | 1.59796 | 0.0654548 | ||||||||
\(597\) | 19.5547 | 0.800320 | ||||||||
\(598\) | 2.50931 | 0.102614 | ||||||||
\(599\) | −20.3132 | −0.829973 | −0.414986 | − | 0.909828i | \(-0.636214\pi\) | ||||
−0.414986 | + | 0.909828i | \(0.636214\pi\) | |||||||
\(600\) | −3.59082 | −0.146595 | ||||||||
\(601\) | 32.4805 | 1.32491 | 0.662453 | − | 0.749104i | \(-0.269516\pi\) | ||||
0.662453 | + | 0.749104i | \(0.269516\pi\) | |||||||
\(602\) | 24.9353 | 1.01629 | ||||||||
\(603\) | 1.77606 | 0.0723266 | ||||||||
\(604\) | 0.935548 | 0.0380669 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −2.63117 | −0.106884 | ||||||||
\(607\) | −45.4701 | −1.84557 | −0.922787 | − | 0.385311i | \(-0.874094\pi\) | ||||
−0.922787 | + | 0.385311i | \(0.874094\pi\) | |||||||
\(608\) | −0.652306 | −0.0264545 | ||||||||
\(609\) | −13.5545 | −0.549257 | ||||||||
\(610\) | 7.67083 | 0.310583 | ||||||||
\(611\) | 46.8964 | 1.89722 | ||||||||
\(612\) | −0.176650 | −0.00714066 | ||||||||
\(613\) | 4.06460 | 0.164168 | 0.0820839 | − | 0.996625i | \(-0.473842\pi\) | ||||
0.0820839 | + | 0.996625i | \(0.473842\pi\) | |||||||
\(614\) | −27.2418 | −1.09939 | ||||||||
\(615\) | −0.977376 | −0.0394116 | ||||||||
\(616\) | −7.06364 | −0.284602 | ||||||||
\(617\) | −27.7980 | −1.11911 | −0.559554 | − | 0.828794i | \(-0.689027\pi\) | ||||
−0.559554 | + | 0.828794i | \(0.689027\pi\) | |||||||
\(618\) | −0.575958 | −0.0231684 | ||||||||
\(619\) | 31.8288 | 1.27931 | 0.639654 | − | 0.768663i | \(-0.279077\pi\) | ||||
0.639654 | + | 0.768663i | \(0.279077\pi\) | |||||||
\(620\) | −0.549982 | −0.0220878 | ||||||||
\(621\) | 2.08439 | 0.0836438 | ||||||||
\(622\) | −5.10420 | −0.204660 | ||||||||
\(623\) | −3.01566 | −0.120820 | ||||||||
\(624\) | −22.5144 | −0.901295 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −37.1840 | −1.48617 | ||||||||
\(627\) | 1.23648 | 0.0493802 | ||||||||
\(628\) | 0.823665 | 0.0328678 | ||||||||
\(629\) | −3.13487 | −0.124995 | ||||||||
\(630\) | 4.91215 | 0.195705 | ||||||||
\(631\) | 32.8526 | 1.30784 | 0.653920 | − | 0.756564i | \(-0.273123\pi\) | ||||
0.653920 | + | 0.756564i | \(0.273123\pi\) | |||||||
\(632\) | −26.6282 | −1.05921 | ||||||||
\(633\) | −12.9053 | −0.512940 | ||||||||
\(634\) | −13.0476 | −0.518185 | ||||||||
\(635\) | 14.7860 | 0.586766 | ||||||||
\(636\) | −1.81974 | −0.0721573 | ||||||||
\(637\) | 5.25445 | 0.208189 | ||||||||
\(638\) | 6.18698 | 0.244945 | ||||||||
\(639\) | 0.381811 | 0.0151042 | ||||||||
\(640\) | −10.2364 | −0.404628 | ||||||||
\(641\) | 31.2727 | 1.23520 | 0.617599 | − | 0.786493i | \(-0.288106\pi\) | ||||
0.617599 | + | 0.786493i | \(0.288106\pi\) | |||||||
\(642\) | −15.3638 | −0.606359 | ||||||||
\(643\) | −13.7579 | −0.542557 | −0.271279 | − | 0.962501i | \(-0.587446\pi\) | ||||
−0.271279 | + | 0.962501i | \(0.587446\pi\) | |||||||
\(644\) | −0.105883 | −0.00417239 | ||||||||
\(645\) | 9.23374 | 0.363578 | ||||||||
\(646\) | 1.42770 | 0.0561723 | ||||||||
\(647\) | 20.3525 | 0.800140 | 0.400070 | − | 0.916485i | \(-0.368986\pi\) | ||||
0.400070 | + | 0.916485i | \(0.368986\pi\) | |||||||
\(648\) | −7.03496 | −0.276359 | ||||||||
\(649\) | −1.32111 | −0.0518580 | ||||||||
\(650\) | 6.65547 | 0.261049 | ||||||||
\(651\) | −14.3260 | −0.561482 | ||||||||
\(652\) | 2.75608 | 0.107936 | ||||||||
\(653\) | −4.04869 | −0.158437 | −0.0792187 | − | 0.996857i | \(-0.525243\pi\) | ||||
−0.0792187 | + | 0.996857i | \(0.525243\pi\) | |||||||
\(654\) | 25.0396 | 0.979124 | ||||||||
\(655\) | −7.82065 | −0.305578 | ||||||||
\(656\) | −2.96873 | −0.115910 | ||||||||
\(657\) | 9.23401 | 0.360253 | ||||||||
\(658\) | 32.2989 | 1.25914 | ||||||||
\(659\) | −13.0892 | −0.509882 | −0.254941 | − | 0.966957i | \(-0.582056\pi\) | ||||
−0.254941 | + | 0.966957i | \(0.582056\pi\) | |||||||
\(660\) | −0.142763 | −0.00555706 | ||||||||
\(661\) | 9.55227 | 0.371540 | 0.185770 | − | 0.982593i | \(-0.440522\pi\) | ||||
0.185770 | + | 0.982593i | \(0.440522\pi\) | |||||||
\(662\) | −9.99208 | −0.388353 | ||||||||
\(663\) | −6.23445 | −0.242126 | ||||||||
\(664\) | −41.3627 | −1.60518 | ||||||||
\(665\) | 2.43232 | 0.0943214 | ||||||||
\(666\) | 6.08744 | 0.235884 | ||||||||
\(667\) | 1.69923 | 0.0657945 | ||||||||
\(668\) | 0.981386 | 0.0379710 | ||||||||
\(669\) | 18.8144 | 0.727408 | ||||||||
\(670\) | 1.65734 | 0.0640286 | ||||||||
\(671\) | 5.58779 | 0.215714 | ||||||||
\(672\) | 1.96182 | 0.0756789 | ||||||||
\(673\) | 31.4730 | 1.21320 | 0.606598 | − | 0.795009i | \(-0.292534\pi\) | ||||
0.606598 | + | 0.795009i | \(0.292534\pi\) | |||||||
\(674\) | −40.3310 | −1.55349 | ||||||||
\(675\) | 5.52845 | 0.212790 | ||||||||
\(676\) | −1.21285 | −0.0466482 | ||||||||
\(677\) | −35.4776 | −1.36352 | −0.681758 | − | 0.731578i | \(-0.738784\pi\) | ||||
−0.681758 | + | 0.731578i | \(0.738784\pi\) | |||||||
\(678\) | −7.99536 | −0.307060 | ||||||||
\(679\) | 7.19075 | 0.275956 | ||||||||
\(680\) | −3.02025 | −0.115821 | ||||||||
\(681\) | 19.0628 | 0.730487 | ||||||||
\(682\) | 6.53915 | 0.250397 | ||||||||
\(683\) | −40.6216 | −1.55434 | −0.777171 | − | 0.629289i | \(-0.783346\pi\) | ||||
−0.777171 | + | 0.629289i | \(0.783346\pi\) | |||||||
\(684\) | 0.169855 | 0.00649457 | ||||||||
\(685\) | −7.70625 | −0.294441 | ||||||||
\(686\) | 26.9923 | 1.03057 | ||||||||
\(687\) | −22.5693 | −0.861072 | ||||||||
\(688\) | 28.0471 | 1.06929 | ||||||||
\(689\) | 61.7971 | 2.35428 | ||||||||
\(690\) | 0.639979 | 0.0243636 | ||||||||
\(691\) | −12.5025 | −0.475616 | −0.237808 | − | 0.971312i | \(-0.576429\pi\) | ||||
−0.237808 | + | 0.971312i | \(0.576429\pi\) | |||||||
\(692\) | 0.434974 | 0.0165352 | ||||||||
\(693\) | 3.57824 | 0.135926 | ||||||||
\(694\) | −38.5791 | −1.46444 | ||||||||
\(695\) | 14.3953 | 0.546044 | ||||||||
\(696\) | −16.1834 | −0.613431 | ||||||||
\(697\) | −0.822073 | −0.0311382 | ||||||||
\(698\) | −28.8214 | −1.09091 | ||||||||
\(699\) | −23.6218 | −0.893460 | ||||||||
\(700\) | −0.280835 | −0.0106146 | ||||||||
\(701\) | −22.1578 | −0.836887 | −0.418443 | − | 0.908243i | \(-0.637424\pi\) | ||||
−0.418443 | + | 0.908243i | \(0.637424\pi\) | |||||||
\(702\) | 36.7944 | 1.38872 | ||||||||
\(703\) | 3.01428 | 0.113686 | ||||||||
\(704\) | −8.40698 | −0.316850 | ||||||||
\(705\) | 11.9605 | 0.450459 | ||||||||
\(706\) | −20.8491 | −0.784665 | ||||||||
\(707\) | −3.77035 | −0.141798 | ||||||||
\(708\) | 0.188606 | 0.00708825 | ||||||||
\(709\) | −32.1717 | −1.20824 | −0.604118 | − | 0.796895i | \(-0.706474\pi\) | ||||
−0.604118 | + | 0.796895i | \(0.706474\pi\) | |||||||
\(710\) | 0.356290 | 0.0133713 | ||||||||
\(711\) | 13.4891 | 0.505880 | ||||||||
\(712\) | −3.60055 | −0.134936 | ||||||||
\(713\) | 1.79595 | 0.0672589 | ||||||||
\(714\) | −4.29384 | −0.160693 | ||||||||
\(715\) | 4.84815 | 0.181311 | ||||||||
\(716\) | 1.38922 | 0.0519178 | ||||||||
\(717\) | −25.5396 | −0.953794 | ||||||||
\(718\) | −15.7908 | −0.589308 | ||||||||
\(719\) | 4.63511 | 0.172860 | 0.0864302 | − | 0.996258i | \(-0.472454\pi\) | ||||
0.0864302 | + | 0.996258i | \(0.472454\pi\) | |||||||
\(720\) | 5.52516 | 0.205910 | ||||||||
\(721\) | −0.825320 | −0.0307365 | ||||||||
\(722\) | −1.37279 | −0.0510898 | ||||||||
\(723\) | −19.7791 | −0.735594 | ||||||||
\(724\) | 1.04134 | 0.0387009 | ||||||||
\(725\) | 4.50688 | 0.167381 | ||||||||
\(726\) | 1.69742 | 0.0629972 | ||||||||
\(727\) | −29.6755 | −1.10060 | −0.550302 | − | 0.834966i | \(-0.685487\pi\) | ||||
−0.550302 | + | 0.834966i | \(0.685487\pi\) | |||||||
\(728\) | −34.2456 | −1.26923 | ||||||||
\(729\) | 24.0711 | 0.891523 | ||||||||
\(730\) | 8.61678 | 0.318921 | ||||||||
\(731\) | 7.76652 | 0.287255 | ||||||||
\(732\) | −0.797732 | −0.0294850 | ||||||||
\(733\) | 36.0642 | 1.33206 | 0.666031 | − | 0.745924i | \(-0.267992\pi\) | ||||
0.666031 | + | 0.745924i | \(0.267992\pi\) | |||||||
\(734\) | 2.09150 | 0.0771987 | ||||||||
\(735\) | 1.34010 | 0.0494304 | ||||||||
\(736\) | −0.245939 | −0.00906544 | ||||||||
\(737\) | 1.20728 | 0.0444708 | ||||||||
\(738\) | 1.59634 | 0.0587621 | ||||||||
\(739\) | 13.1048 | 0.482066 | 0.241033 | − | 0.970517i | \(-0.422514\pi\) | ||||
0.241033 | + | 0.970517i | \(0.422514\pi\) | |||||||
\(740\) | −0.348028 | −0.0127938 | ||||||||
\(741\) | 5.99464 | 0.220218 | ||||||||
\(742\) | 42.5614 | 1.56248 | ||||||||
\(743\) | 49.4215 | 1.81310 | 0.906550 | − | 0.422098i | \(-0.138706\pi\) | ||||
0.906550 | + | 0.422098i | \(0.138706\pi\) | |||||||
\(744\) | −17.1046 | −0.627085 | ||||||||
\(745\) | −13.8399 | −0.507056 | ||||||||
\(746\) | −22.7396 | −0.832557 | ||||||||
\(747\) | 20.9531 | 0.766636 | ||||||||
\(748\) | −0.120079 | −0.00439051 | ||||||||
\(749\) | −22.0155 | −0.804431 | ||||||||
\(750\) | 1.69742 | 0.0619810 | ||||||||
\(751\) | 5.10832 | 0.186405 | 0.0932026 | − | 0.995647i | \(-0.470290\pi\) | ||||
0.0932026 | + | 0.995647i | \(0.470290\pi\) | |||||||
\(752\) | 36.3295 | 1.32480 | ||||||||
\(753\) | 14.0190 | 0.510882 | ||||||||
\(754\) | 29.9954 | 1.09237 | ||||||||
\(755\) | −8.10281 | −0.294892 | ||||||||
\(756\) | −1.55258 | −0.0564669 | ||||||||
\(757\) | −38.3696 | −1.39457 | −0.697283 | − | 0.716796i | \(-0.745608\pi\) | ||||
−0.697283 | + | 0.716796i | \(0.745608\pi\) | |||||||
\(758\) | 0.0261656 | 0.000950378 0 | ||||||||
\(759\) | 0.466190 | 0.0169216 | ||||||||
\(760\) | 2.90407 | 0.105342 | ||||||||
\(761\) | −34.9845 | −1.26819 | −0.634093 | − | 0.773257i | \(-0.718626\pi\) | ||||
−0.634093 | + | 0.773257i | \(0.718626\pi\) | |||||||
\(762\) | 25.0981 | 0.909209 | ||||||||
\(763\) | 35.8805 | 1.29896 | ||||||||
\(764\) | 1.76189 | 0.0637428 | ||||||||
\(765\) | 1.52997 | 0.0553163 | ||||||||
\(766\) | −24.9964 | −0.903157 | ||||||||
\(767\) | −6.40493 | −0.231269 | ||||||||
\(768\) | 3.41468 | 0.123217 | ||||||||
\(769\) | 4.72143 | 0.170259 | 0.0851296 | − | 0.996370i | \(-0.472870\pi\) | ||||
0.0851296 | + | 0.996370i | \(0.472870\pi\) | |||||||
\(770\) | 3.33906 | 0.120331 | ||||||||
\(771\) | −12.1178 | −0.436411 | ||||||||
\(772\) | −0.366292 | −0.0131831 | ||||||||
\(773\) | 47.5946 | 1.71186 | 0.855930 | − | 0.517092i | \(-0.172986\pi\) | ||||
0.855930 | + | 0.517092i | \(0.172986\pi\) | |||||||
\(774\) | −15.0814 | −0.542090 | ||||||||
\(775\) | 4.76341 | 0.171107 | ||||||||
\(776\) | 8.58539 | 0.308198 | ||||||||
\(777\) | −9.06551 | −0.325223 | ||||||||
\(778\) | 43.1097 | 1.54556 | ||||||||
\(779\) | 0.790451 | 0.0283208 | ||||||||
\(780\) | −0.692139 | −0.0247825 | ||||||||
\(781\) | 0.259538 | 0.00928700 | ||||||||
\(782\) | 0.538288 | 0.0192491 | ||||||||
\(783\) | 24.9160 | 0.890427 | ||||||||
\(784\) | 4.07050 | 0.145375 | ||||||||
\(785\) | −7.13378 | −0.254616 | ||||||||
\(786\) | −13.2749 | −0.473501 | ||||||||
\(787\) | 1.02158 | 0.0364154 | 0.0182077 | − | 0.999834i | \(-0.494204\pi\) | ||||
0.0182077 | + | 0.999834i | \(0.494204\pi\) | |||||||
\(788\) | 0.703608 | 0.0250650 | ||||||||
\(789\) | 26.3245 | 0.937176 | ||||||||
\(790\) | 12.5874 | 0.447841 | ||||||||
\(791\) | −11.4570 | −0.407363 | ||||||||
\(792\) | 4.27224 | 0.151807 | ||||||||
\(793\) | 27.0904 | 0.962010 | ||||||||
\(794\) | 35.5028 | 1.25995 | ||||||||
\(795\) | 15.7608 | 0.558978 | ||||||||
\(796\) | 1.82597 | 0.0647199 | ||||||||
\(797\) | −37.8469 | −1.34061 | −0.670304 | − | 0.742087i | \(-0.733836\pi\) | ||||
−0.670304 | + | 0.742087i | \(0.733836\pi\) | |||||||
\(798\) | 4.12867 | 0.146154 | ||||||||
\(799\) | 10.0600 | 0.355898 | ||||||||
\(800\) | −0.652306 | −0.0230625 | ||||||||
\(801\) | 1.82393 | 0.0644455 | ||||||||
\(802\) | 21.2975 | 0.752042 | ||||||||
\(803\) | 6.27686 | 0.221506 | ||||||||
\(804\) | −0.172356 | −0.00607852 | ||||||||
\(805\) | 0.917060 | 0.0323221 | ||||||||
\(806\) | 31.7028 | 1.11668 | ||||||||
\(807\) | 22.6014 | 0.795606 | ||||||||
\(808\) | −4.50161 | −0.158366 | ||||||||
\(809\) | 25.6686 | 0.902461 | 0.451231 | − | 0.892407i | \(-0.350985\pi\) | ||||
0.451231 | + | 0.892407i | \(0.350985\pi\) | |||||||
\(810\) | 3.32550 | 0.116846 | ||||||||
\(811\) | −6.16852 | −0.216606 | −0.108303 | − | 0.994118i | \(-0.534542\pi\) | ||||
−0.108303 | + | 0.994118i | \(0.534542\pi\) | |||||||
\(812\) | −1.26569 | −0.0444170 | ||||||||
\(813\) | −24.4665 | −0.858077 | ||||||||
\(814\) | 4.13797 | 0.145036 | ||||||||
\(815\) | −23.8705 | −0.836147 | ||||||||
\(816\) | −4.82969 | −0.169073 | ||||||||
\(817\) | −7.46777 | −0.261264 | ||||||||
\(818\) | −28.4785 | −0.995729 | ||||||||
\(819\) | 17.3478 | 0.606183 | ||||||||
\(820\) | −0.0912652 | −0.00318712 | ||||||||
\(821\) | −30.9910 | −1.08159 | −0.540796 | − | 0.841154i | \(-0.681877\pi\) | ||||
−0.540796 | + | 0.841154i | \(0.681877\pi\) | |||||||
\(822\) | −13.0807 | −0.456243 | ||||||||
\(823\) | −40.7706 | −1.42117 | −0.710587 | − | 0.703609i | \(-0.751571\pi\) | ||||
−0.710587 | + | 0.703609i | \(0.751571\pi\) | |||||||
\(824\) | −0.985391 | −0.0343277 | ||||||||
\(825\) | 1.23648 | 0.0430487 | ||||||||
\(826\) | −4.41126 | −0.153487 | ||||||||
\(827\) | 46.2940 | 1.60980 | 0.804900 | − | 0.593410i | \(-0.202219\pi\) | ||||
0.804900 | + | 0.593410i | \(0.202219\pi\) | |||||||
\(828\) | 0.0640405 | 0.00222556 | ||||||||
\(829\) | −14.8471 | −0.515660 | −0.257830 | − | 0.966190i | \(-0.583007\pi\) | ||||
−0.257830 | + | 0.966190i | \(0.583007\pi\) | |||||||
\(830\) | 19.5526 | 0.678680 | ||||||||
\(831\) | −30.3751 | −1.05370 | ||||||||
\(832\) | −40.7583 | −1.41304 | ||||||||
\(833\) | 1.12716 | 0.0390539 | ||||||||
\(834\) | 24.4348 | 0.846109 | ||||||||
\(835\) | −8.49981 | −0.294148 | ||||||||
\(836\) | 0.115460 | 0.00399326 | ||||||||
\(837\) | 26.3343 | 0.910246 | ||||||||
\(838\) | −9.54024 | −0.329562 | ||||||||
\(839\) | 36.8854 | 1.27343 | 0.636713 | − | 0.771101i | \(-0.280294\pi\) | ||||
0.636713 | + | 0.771101i | \(0.280294\pi\) | |||||||
\(840\) | −8.73405 | −0.301353 | ||||||||
\(841\) | −8.68803 | −0.299587 | ||||||||
\(842\) | −23.4040 | −0.806556 | ||||||||
\(843\) | −17.4217 | −0.600035 | ||||||||
\(844\) | −1.20507 | −0.0414802 | ||||||||
\(845\) | 10.5046 | 0.361368 | ||||||||
\(846\) | −19.5350 | −0.671628 | ||||||||
\(847\) | 2.43232 | 0.0835756 | ||||||||
\(848\) | 47.8728 | 1.64396 | ||||||||
\(849\) | 23.2912 | 0.799352 | ||||||||
\(850\) | 1.42770 | 0.0489698 | ||||||||
\(851\) | 1.13648 | 0.0389579 | ||||||||
\(852\) | −0.0370525 | −0.00126940 | ||||||||
\(853\) | 9.84716 | 0.337160 | 0.168580 | − | 0.985688i | \(-0.446082\pi\) | ||||
0.168580 | + | 0.985688i | \(0.446082\pi\) | |||||||
\(854\) | 18.6579 | 0.638462 | ||||||||
\(855\) | −1.47112 | −0.0503112 | ||||||||
\(856\) | −26.2855 | −0.898419 | ||||||||
\(857\) | −25.6874 | −0.877464 | −0.438732 | − | 0.898618i | \(-0.644572\pi\) | ||||
−0.438732 | + | 0.898618i | \(0.644572\pi\) | |||||||
\(858\) | 8.22935 | 0.280945 | ||||||||
\(859\) | 48.4118 | 1.65179 | 0.825894 | − | 0.563825i | \(-0.190671\pi\) | ||||
0.825894 | + | 0.563825i | \(0.190671\pi\) | |||||||
\(860\) | 0.862227 | 0.0294017 | ||||||||
\(861\) | −2.37729 | −0.0810179 | ||||||||
\(862\) | −14.5754 | −0.496439 | ||||||||
\(863\) | 15.3028 | 0.520913 | 0.260457 | − | 0.965486i | \(-0.416127\pi\) | ||||
0.260457 | + | 0.965486i | \(0.416127\pi\) | |||||||
\(864\) | −3.60624 | −0.122687 | ||||||||
\(865\) | −3.76732 | −0.128093 | ||||||||
\(866\) | 7.16528 | 0.243486 | ||||||||
\(867\) | 19.6828 | 0.668461 | ||||||||
\(868\) | −1.33773 | −0.0454057 | ||||||||
\(869\) | 9.16926 | 0.311046 | ||||||||
\(870\) | 7.65007 | 0.259362 | ||||||||
\(871\) | 5.85308 | 0.198324 | ||||||||
\(872\) | 42.8395 | 1.45073 | ||||||||
\(873\) | −4.34911 | −0.147195 | ||||||||
\(874\) | −0.517582 | −0.0175075 | ||||||||
\(875\) | 2.43232 | 0.0822275 | ||||||||
\(876\) | −0.896106 | −0.0302766 | ||||||||
\(877\) | −34.7213 | −1.17245 | −0.586227 | − | 0.810147i | \(-0.699387\pi\) | ||||
−0.586227 | + | 0.810147i | \(0.699387\pi\) | |||||||
\(878\) | 35.4310 | 1.19574 | ||||||||
\(879\) | −2.57522 | −0.0868600 | ||||||||
\(880\) | 3.75575 | 0.126606 | ||||||||
\(881\) | 33.7901 | 1.13842 | 0.569208 | − | 0.822194i | \(-0.307250\pi\) | ||||
0.569208 | + | 0.822194i | \(0.307250\pi\) | |||||||
\(882\) | −2.18878 | −0.0737000 | ||||||||
\(883\) | 54.4286 | 1.83167 | 0.915835 | − | 0.401556i | \(-0.131530\pi\) | ||||
0.915835 | + | 0.401556i | \(0.131530\pi\) | |||||||
\(884\) | −0.582160 | −0.0195801 | ||||||||
\(885\) | −1.63352 | −0.0549103 | ||||||||
\(886\) | 41.7213 | 1.40166 | ||||||||
\(887\) | 14.5748 | 0.489373 | 0.244686 | − | 0.969602i | \(-0.421315\pi\) | ||||
0.244686 | + | 0.969602i | \(0.421315\pi\) | |||||||
\(888\) | −10.8238 | −0.363222 | ||||||||
\(889\) | 35.9644 | 1.20621 | ||||||||
\(890\) | 1.70202 | 0.0570517 | ||||||||
\(891\) | 2.42245 | 0.0811550 | ||||||||
\(892\) | 1.75685 | 0.0588237 | ||||||||
\(893\) | −9.67305 | −0.323696 | ||||||||
\(894\) | −23.4922 | −0.785696 | ||||||||
\(895\) | −12.0321 | −0.402189 | ||||||||
\(896\) | −24.8981 | −0.831789 | ||||||||
\(897\) | 2.26016 | 0.0754645 | ||||||||
\(898\) | −14.9049 | −0.497384 | ||||||||
\(899\) | 21.4681 | 0.716003 | ||||||||
\(900\) | 0.169855 | 0.00566184 | ||||||||
\(901\) | 13.2565 | 0.441636 | ||||||||
\(902\) | 1.08512 | 0.0361305 | ||||||||
\(903\) | 22.4594 | 0.747404 | ||||||||
\(904\) | −13.6791 | −0.454959 | ||||||||
\(905\) | −9.01903 | −0.299803 | ||||||||
\(906\) | −13.7539 | −0.456942 | ||||||||
\(907\) | −36.7115 | −1.21898 | −0.609492 | − | 0.792792i | \(-0.708627\pi\) | ||||
−0.609492 | + | 0.792792i | \(0.708627\pi\) | |||||||
\(908\) | 1.78004 | 0.0590727 | ||||||||
\(909\) | 2.28038 | 0.0756356 | ||||||||
\(910\) | 16.1883 | 0.536635 | ||||||||
\(911\) | 18.5321 | 0.613997 | 0.306999 | − | 0.951710i | \(-0.400675\pi\) | ||||
0.306999 | + | 0.951710i | \(0.400675\pi\) | |||||||
\(912\) | 4.64391 | 0.153775 | ||||||||
\(913\) | 14.2430 | 0.471374 | ||||||||
\(914\) | −25.2385 | −0.834815 | ||||||||
\(915\) | 6.90918 | 0.228411 | ||||||||
\(916\) | −2.10747 | −0.0696328 | ||||||||
\(917\) | −19.0224 | −0.628173 | ||||||||
\(918\) | 7.89298 | 0.260507 | ||||||||
\(919\) | −30.1650 | −0.995052 | −0.497526 | − | 0.867449i | \(-0.665758\pi\) | ||||
−0.497526 | + | 0.867449i | \(0.665758\pi\) | |||||||
\(920\) | 1.09492 | 0.0360986 | ||||||||
\(921\) | −24.5369 | −0.808519 | ||||||||
\(922\) | 38.8035 | 1.27792 | ||||||||
\(923\) | 1.25828 | 0.0414167 | ||||||||
\(924\) | −0.347247 | −0.0114236 | ||||||||
\(925\) | 3.01428 | 0.0991090 | ||||||||
\(926\) | −45.8875 | −1.50796 | ||||||||
\(927\) | 0.499171 | 0.0163949 | ||||||||
\(928\) | −2.93987 | −0.0965058 | ||||||||
\(929\) | −53.1253 | −1.74298 | −0.871492 | − | 0.490409i | \(-0.836847\pi\) | ||||
−0.871492 | + | 0.490409i | \(0.836847\pi\) | |||||||
\(930\) | 8.08552 | 0.265135 | ||||||||
\(931\) | −1.08380 | −0.0355203 | ||||||||
\(932\) | −2.20575 | −0.0722519 | ||||||||
\(933\) | −4.59740 | −0.150512 | ||||||||
\(934\) | 1.66515 | 0.0544854 | ||||||||
\(935\) | 1.04001 | 0.0340118 | ||||||||
\(936\) | 20.7125 | 0.677008 | ||||||||
\(937\) | 46.9097 | 1.53247 | 0.766237 | − | 0.642558i | \(-0.222127\pi\) | ||||
0.766237 | + | 0.642558i | \(0.222127\pi\) | |||||||
\(938\) | 4.03118 | 0.131623 | ||||||||
\(939\) | −33.4919 | −1.09297 | ||||||||
\(940\) | 1.11685 | 0.0364275 | ||||||||
\(941\) | 36.0038 | 1.17369 | 0.586845 | − | 0.809699i | \(-0.300370\pi\) | ||||
0.586845 | + | 0.809699i | \(0.300370\pi\) | |||||||
\(942\) | −12.1090 | −0.394534 | ||||||||
\(943\) | 0.298024 | 0.00970499 | ||||||||
\(944\) | −4.96175 | −0.161491 | ||||||||
\(945\) | 13.4470 | 0.437430 | ||||||||
\(946\) | −10.2517 | −0.333310 | ||||||||
\(947\) | −21.3336 | −0.693249 | −0.346625 | − | 0.938004i | \(-0.612672\pi\) | ||||
−0.346625 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(948\) | −1.30904 | −0.0425155 | ||||||||
\(949\) | 30.4312 | 0.987837 | ||||||||
\(950\) | −1.37279 | −0.0445390 | ||||||||
\(951\) | −11.7520 | −0.381086 | ||||||||
\(952\) | −7.34622 | −0.238093 | ||||||||
\(953\) | 0.777926 | 0.0251995 | 0.0125997 | − | 0.999921i | \(-0.495989\pi\) | ||||
0.0125997 | + | 0.999921i | \(0.495989\pi\) | |||||||
\(954\) | −25.7420 | −0.833429 | ||||||||
\(955\) | −15.2598 | −0.493794 | ||||||||
\(956\) | −2.38483 | −0.0771310 | ||||||||
\(957\) | 5.57266 | 0.180139 | ||||||||
\(958\) | 35.5685 | 1.14917 | ||||||||
\(959\) | −18.7441 | −0.605278 | ||||||||
\(960\) | −10.3950 | −0.335499 | ||||||||
\(961\) | −8.30988 | −0.268061 | ||||||||
\(962\) | 20.0615 | 0.646808 | ||||||||
\(963\) | 13.3155 | 0.429085 | ||||||||
\(964\) | −1.84693 | −0.0594857 | ||||||||
\(965\) | 3.17246 | 0.102125 | ||||||||
\(966\) | 1.55664 | 0.0500839 | ||||||||
\(967\) | 41.5502 | 1.33616 | 0.668082 | − | 0.744088i | \(-0.267116\pi\) | ||||
0.668082 | + | 0.744088i | \(0.267116\pi\) | |||||||
\(968\) | 2.90407 | 0.0933404 | ||||||||
\(969\) | 1.28594 | 0.0413105 | ||||||||
\(970\) | −4.05841 | −0.130308 | ||||||||
\(971\) | 41.5722 | 1.33412 | 0.667058 | − | 0.745006i | \(-0.267553\pi\) | ||||
0.667058 | + | 0.745006i | \(0.267553\pi\) | |||||||
\(972\) | 1.56910 | 0.0503289 | ||||||||
\(973\) | 35.0139 | 1.12250 | ||||||||
\(974\) | 4.24930 | 0.136156 | ||||||||
\(975\) | 5.99464 | 0.191982 | ||||||||
\(976\) | 20.9863 | 0.671756 | ||||||||
\(977\) | −4.43754 | −0.141969 | −0.0709847 | − | 0.997477i | \(-0.522614\pi\) | ||||
−0.0709847 | + | 0.997477i | \(0.522614\pi\) | |||||||
\(978\) | −40.5183 | −1.29563 | ||||||||
\(979\) | 1.23983 | 0.0396250 | ||||||||
\(980\) | 0.125136 | 0.00399732 | ||||||||
\(981\) | −21.7013 | −0.692869 | ||||||||
\(982\) | −23.9808 | −0.765258 | ||||||||
\(983\) | 4.98576 | 0.159021 | 0.0795106 | − | 0.996834i | \(-0.474664\pi\) | ||||
0.0795106 | + | 0.996834i | \(0.474664\pi\) | |||||||
\(984\) | −2.83837 | −0.0904839 | ||||||||
\(985\) | −6.09397 | −0.194170 | ||||||||
\(986\) | 6.43449 | 0.204916 | ||||||||
\(987\) | 29.0918 | 0.926004 | ||||||||
\(988\) | 0.559766 | 0.0178085 | ||||||||
\(989\) | −2.81558 | −0.0895301 | ||||||||
\(990\) | −2.01953 | −0.0641850 | ||||||||
\(991\) | −39.9837 | −1.27012 | −0.635062 | − | 0.772461i | \(-0.719025\pi\) | ||||
−0.635062 | + | 0.772461i | \(0.719025\pi\) | |||||||
\(992\) | −3.10720 | −0.0986539 | ||||||||
\(993\) | −8.99994 | −0.285605 | ||||||||
\(994\) | 0.866612 | 0.0274873 | ||||||||
\(995\) | −15.8148 | −0.501363 | ||||||||
\(996\) | −2.03338 | −0.0644301 | ||||||||
\(997\) | −31.3940 | −0.994258 | −0.497129 | − | 0.867677i | \(-0.665612\pi\) | ||||
−0.497129 | + | 0.867677i | \(0.665612\pi\) | |||||||
\(998\) | 8.88571 | 0.281272 | ||||||||
\(999\) | 16.6643 | 0.527235 |
(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 | 1045.2.a.d.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 9405.2.a.v.1.3 | 5 | |||
5.4 | even | 2 | 5225.2.a.j.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.a.d.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
5225.2.a.j.1.3 | 5 | 5.4 | even | 2 | |||
9405.2.a.v.1.3 | 5 | 3.2 | odd | 2 |