Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 \) |
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 | 1.6 | ||
Root | \(-0.267165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.267165 | 0.188914 | 0.0944571 | − | 0.995529i | \(-0.469888\pi\) | ||||
0.0944571 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.92862 | −0.964311 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.267165 | 0.109070 | ||||||||
\(7\) | −0.207232 | −0.0783262 | −0.0391631 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391631 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(8\) | −1.04959 | −0.371086 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.27329 | −0.383912 | −0.191956 | − | 0.981404i | \(-0.561483\pi\) | ||||
−0.191956 | + | 0.981404i | \(0.561483\pi\) | |||||||
\(12\) | −1.92862 | −0.556745 | ||||||||
\(13\) | −5.37648 | −1.49117 | −0.745584 | − | 0.666412i | \(-0.767829\pi\) | ||||
−0.745584 | + | 0.666412i | \(0.767829\pi\) | |||||||
\(14\) | −0.0553651 | −0.0147969 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.57683 | 0.894208 | ||||||||
\(17\) | 0.969832 | 0.235219 | 0.117609 | − | 0.993060i | \(-0.462477\pi\) | ||||
0.117609 | + | 0.993060i | \(0.462477\pi\) | |||||||
\(18\) | 0.267165 | 0.0629714 | ||||||||
\(19\) | 6.42820 | 1.47473 | 0.737365 | − | 0.675494i | \(-0.236070\pi\) | ||||
0.737365 | + | 0.675494i | \(0.236070\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.207232 | −0.0452216 | ||||||||
\(22\) | −0.340179 | −0.0725265 | ||||||||
\(23\) | 5.87315 | 1.22464 | 0.612318 | − | 0.790611i | \(-0.290237\pi\) | ||||
0.612318 | + | 0.790611i | \(0.290237\pi\) | |||||||
\(24\) | −1.04959 | −0.214247 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.43641 | −0.281703 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.399672 | 0.0755308 | ||||||||
\(29\) | −9.93423 | −1.84474 | −0.922370 | − | 0.386307i | \(-0.873751\pi\) | ||||
−0.922370 | + | 0.386307i | \(0.873751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.97938 | 1.07393 | 0.536964 | − | 0.843605i | \(-0.319571\pi\) | ||||
0.536964 | + | 0.843605i | \(0.319571\pi\) | |||||||
\(32\) | 3.05479 | 0.540015 | ||||||||
\(33\) | −1.27329 | −0.221652 | ||||||||
\(34\) | 0.259105 | 0.0444362 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.92862 | −0.321437 | ||||||||
\(37\) | −1.19082 | −0.195769 | −0.0978846 | − | 0.995198i | \(-0.531208\pi\) | ||||
−0.0978846 | + | 0.995198i | \(0.531208\pi\) | |||||||
\(38\) | 1.71739 | 0.278598 | ||||||||
\(39\) | −5.37648 | −0.860926 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.24060 | 0.349923 | 0.174962 | − | 0.984575i | \(-0.444020\pi\) | ||||
0.174962 | + | 0.984575i | \(0.444020\pi\) | |||||||
\(42\) | −0.0553651 | −0.00854301 | ||||||||
\(43\) | −6.20192 | −0.945783 | −0.472892 | − | 0.881121i | \(-0.656790\pi\) | ||||
−0.472892 | + | 0.881121i | \(0.656790\pi\) | |||||||
\(44\) | 2.45570 | 0.370211 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.56910 | 0.231351 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 3.57683 | 0.516271 | ||||||||
\(49\) | −6.95706 | −0.993865 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.969832 | 0.135804 | ||||||||
\(52\) | 10.3692 | 1.43795 | ||||||||
\(53\) | −8.64084 | −1.18691 | −0.593455 | − | 0.804867i | \(-0.702237\pi\) | ||||
−0.593455 | + | 0.804867i | \(0.702237\pi\) | |||||||
\(54\) | 0.267165 | 0.0363566 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.217508 | 0.0290658 | ||||||||
\(57\) | 6.42820 | 0.851436 | ||||||||
\(58\) | −2.65408 | −0.348498 | ||||||||
\(59\) | −9.70796 | −1.26387 | −0.631934 | − | 0.775022i | \(-0.717739\pi\) | ||||
−0.631934 | + | 0.775022i | \(0.717739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.1014 | −1.29335 | −0.646676 | − | 0.762765i | \(-0.723841\pi\) | ||||
−0.646676 | + | 0.762765i | \(0.723841\pi\) | |||||||
\(62\) | 1.59748 | 0.202880 | ||||||||
\(63\) | −0.207232 | −0.0261087 | ||||||||
\(64\) | −6.33753 | −0.792191 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.340179 | −0.0418732 | ||||||||
\(67\) | 4.36482 | 0.533248 | 0.266624 | − | 0.963801i | \(-0.414092\pi\) | ||||
0.266624 | + | 0.963801i | \(0.414092\pi\) | |||||||
\(68\) | −1.87044 | −0.226824 | ||||||||
\(69\) | 5.87315 | 0.707044 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.54225 | 1.13246 | 0.566229 | − | 0.824248i | \(-0.308402\pi\) | ||||
0.566229 | + | 0.824248i | \(0.308402\pi\) | |||||||
\(72\) | −1.04959 | −0.123695 | ||||||||
\(73\) | −11.7305 | −1.37295 | −0.686476 | − | 0.727153i | \(-0.740843\pi\) | ||||
−0.686476 | + | 0.727153i | \(0.740843\pi\) | |||||||
\(74\) | −0.318145 | −0.0369836 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.3976 | −1.42210 | ||||||||
\(77\) | 0.263866 | 0.0300704 | ||||||||
\(78\) | −1.43641 | −0.162641 | ||||||||
\(79\) | −15.7821 | −1.77563 | −0.887814 | − | 0.460202i | \(-0.847777\pi\) | ||||
−0.887814 | + | 0.460202i | \(0.847777\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.598611 | 0.0661055 | ||||||||
\(83\) | 1.79347 | 0.196859 | 0.0984295 | − | 0.995144i | \(-0.468618\pi\) | ||||
0.0984295 | + | 0.995144i | \(0.468618\pi\) | |||||||
\(84\) | 0.399672 | 0.0436077 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.65694 | −0.178672 | ||||||||
\(87\) | −9.93423 | −1.06506 | ||||||||
\(88\) | 1.33644 | 0.142465 | ||||||||
\(89\) | −7.28256 | −0.771949 | −0.385975 | − | 0.922509i | \(-0.626135\pi\) | ||||
−0.385975 | + | 0.922509i | \(0.626135\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.11418 | 0.116797 | ||||||||
\(92\) | −11.3271 | −1.18093 | ||||||||
\(93\) | 5.97938 | 0.620033 | ||||||||
\(94\) | −0.267165 | −0.0275560 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.05479 | 0.311778 | ||||||||
\(97\) | −0.290073 | −0.0294524 | −0.0147262 | − | 0.999892i | \(-0.504688\pi\) | ||||
−0.0147262 | + | 0.999892i | \(0.504688\pi\) | |||||||
\(98\) | −1.85868 | −0.187755 | ||||||||
\(99\) | −1.27329 | −0.127971 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.63344 | −0.560548 | −0.280274 | − | 0.959920i | \(-0.590425\pi\) | ||||
−0.280274 | + | 0.959920i | \(0.590425\pi\) | |||||||
\(102\) | 0.259105 | 0.0256552 | ||||||||
\(103\) | −11.3273 | −1.11612 | −0.558058 | − | 0.829802i | \(-0.688453\pi\) | ||||
−0.558058 | + | 0.829802i | \(0.688453\pi\) | |||||||
\(104\) | 5.64311 | 0.553352 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.30853 | −0.224224 | ||||||||
\(107\) | −8.10431 | −0.783474 | −0.391737 | − | 0.920077i | \(-0.628126\pi\) | ||||
−0.391737 | + | 0.920077i | \(0.628126\pi\) | |||||||
\(108\) | −1.92862 | −0.185582 | ||||||||
\(109\) | 13.2362 | 1.26780 | 0.633899 | − | 0.773416i | \(-0.281454\pi\) | ||||
0.633899 | + | 0.773416i | \(0.281454\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.19082 | −0.113027 | ||||||||
\(112\) | −0.741232 | −0.0700399 | ||||||||
\(113\) | −16.4518 | −1.54766 | −0.773830 | − | 0.633394i | \(-0.781661\pi\) | ||||
−0.773830 | + | 0.633394i | \(0.781661\pi\) | |||||||
\(114\) | 1.71739 | 0.160848 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 19.1594 | 1.77890 | ||||||||
\(117\) | −5.37648 | −0.497056 | ||||||||
\(118\) | −2.59363 | −0.238763 | ||||||||
\(119\) | −0.200980 | −0.0184238 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.37873 | −0.852611 | ||||||||
\(122\) | −2.69874 | −0.244333 | ||||||||
\(123\) | 2.24060 | 0.202028 | ||||||||
\(124\) | −11.5320 | −1.03560 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.0553651 | −0.00493231 | ||||||||
\(127\) | 4.51985 | 0.401072 | 0.200536 | − | 0.979686i | \(-0.435732\pi\) | ||||
0.200536 | + | 0.979686i | \(0.435732\pi\) | |||||||
\(128\) | −7.80274 | −0.689671 | ||||||||
\(129\) | −6.20192 | −0.546048 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.5471 | 1.79520 | 0.897602 | − | 0.440806i | \(-0.145307\pi\) | ||||
0.897602 | + | 0.440806i | \(0.145307\pi\) | |||||||
\(132\) | 2.45570 | 0.213741 | ||||||||
\(133\) | −1.33213 | −0.115510 | ||||||||
\(134\) | 1.16613 | 0.100738 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.01793 | −0.0872865 | ||||||||
\(137\) | −14.7837 | −1.26306 | −0.631528 | − | 0.775353i | \(-0.717572\pi\) | ||||
−0.631528 | + | 0.775353i | \(0.717572\pi\) | |||||||
\(138\) | 1.56910 | 0.133571 | ||||||||
\(139\) | 18.5218 | 1.57100 | 0.785500 | − | 0.618862i | \(-0.212406\pi\) | ||||
0.785500 | + | 0.618862i | \(0.212406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | 2.54936 | 0.213937 | ||||||||
\(143\) | 6.84583 | 0.572477 | ||||||||
\(144\) | 3.57683 | 0.298069 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.13398 | −0.259370 | ||||||||
\(147\) | −6.95706 | −0.573808 | ||||||||
\(148\) | 2.29664 | 0.188783 | ||||||||
\(149\) | −1.52423 | −0.124870 | −0.0624349 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624349 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.2961 | 1.81443 | 0.907215 | − | 0.420666i | \(-0.138204\pi\) | ||||
0.907215 | + | 0.420666i | \(0.138204\pi\) | |||||||
\(152\) | −6.74698 | −0.547252 | ||||||||
\(153\) | 0.969832 | 0.0784063 | ||||||||
\(154\) | 0.0704959 | 0.00568072 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.3692 | 0.830201 | ||||||||
\(157\) | −16.4590 | −1.31357 | −0.656787 | − | 0.754076i | \(-0.728085\pi\) | ||||
−0.656787 | + | 0.754076i | \(0.728085\pi\) | |||||||
\(158\) | −4.21644 | −0.335442 | ||||||||
\(159\) | −8.64084 | −0.685263 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.21710 | −0.0959211 | ||||||||
\(162\) | 0.267165 | 0.0209905 | ||||||||
\(163\) | −7.71004 | −0.603897 | −0.301948 | − | 0.953324i | \(-0.597637\pi\) | ||||
−0.301948 | + | 0.953324i | \(0.597637\pi\) | |||||||
\(164\) | −4.32128 | −0.337435 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.479153 | 0.0371895 | ||||||||
\(167\) | 10.0987 | 0.781458 | 0.390729 | − | 0.920506i | \(-0.372223\pi\) | ||||
0.390729 | + | 0.920506i | \(0.372223\pi\) | |||||||
\(168\) | 0.217508 | 0.0167811 | ||||||||
\(169\) | 15.9066 | 1.22358 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.42820 | 0.491577 | ||||||||
\(172\) | 11.9612 | 0.912030 | ||||||||
\(173\) | 19.8597 | 1.50990 | 0.754952 | − | 0.655781i | \(-0.227660\pi\) | ||||
0.754952 | + | 0.655781i | \(0.227660\pi\) | |||||||
\(174\) | −2.65408 | −0.201205 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.55435 | −0.343297 | ||||||||
\(177\) | −9.70796 | −0.729695 | ||||||||
\(178\) | −1.94565 | −0.145832 | ||||||||
\(179\) | −12.2276 | −0.913931 | −0.456966 | − | 0.889484i | \(-0.651064\pi\) | ||||
−0.456966 | + | 0.889484i | \(0.651064\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1323 | −0.753126 | −0.376563 | − | 0.926391i | \(-0.622894\pi\) | ||||
−0.376563 | + | 0.926391i | \(0.622894\pi\) | |||||||
\(182\) | 0.297669 | 0.0220647 | ||||||||
\(183\) | −10.1014 | −0.746717 | ||||||||
\(184\) | −6.16441 | −0.454446 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.59748 | 0.117133 | ||||||||
\(187\) | −1.23488 | −0.0903034 | ||||||||
\(188\) | 1.92862 | 0.140659 | ||||||||
\(189\) | −0.207232 | −0.0150739 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.90791 | −0.355124 | −0.177562 | − | 0.984110i | \(-0.556821\pi\) | ||||
−0.177562 | + | 0.984110i | \(0.556821\pi\) | |||||||
\(192\) | −6.33753 | −0.457372 | ||||||||
\(193\) | −3.01983 | −0.217372 | −0.108686 | − | 0.994076i | \(-0.534664\pi\) | ||||
−0.108686 | + | 0.994076i | \(0.534664\pi\) | |||||||
\(194\) | −0.0774974 | −0.00556399 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4175 | 0.958395 | ||||||||
\(197\) | 7.63855 | 0.544224 | 0.272112 | − | 0.962266i | \(-0.412278\pi\) | ||||
0.272112 | + | 0.962266i | \(0.412278\pi\) | |||||||
\(198\) | −0.340179 | −0.0241755 | ||||||||
\(199\) | 14.8893 | 1.05547 | 0.527737 | − | 0.849408i | \(-0.323041\pi\) | ||||
0.527737 | + | 0.849408i | \(0.323041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.36482 | 0.307871 | ||||||||
\(202\) | −1.50506 | −0.105896 | ||||||||
\(203\) | 2.05869 | 0.144491 | ||||||||
\(204\) | −1.87044 | −0.130957 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.02627 | −0.210850 | ||||||||
\(207\) | 5.87315 | 0.408212 | ||||||||
\(208\) | −19.2308 | −1.33341 | ||||||||
\(209\) | −8.18498 | −0.566167 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.94144 | −0.340183 | −0.170091 | − | 0.985428i | \(-0.554406\pi\) | ||||
−0.170091 | + | 0.985428i | \(0.554406\pi\) | |||||||
\(212\) | 16.6649 | 1.14455 | ||||||||
\(213\) | 9.54225 | 0.653824 | ||||||||
\(214\) | −2.16519 | −0.148009 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.04959 | −0.0714156 | ||||||||
\(217\) | −1.23912 | −0.0841167 | ||||||||
\(218\) | 3.53625 | 0.239505 | ||||||||
\(219\) | −11.7305 | −0.792674 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.21428 | −0.350751 | ||||||||
\(222\) | −0.318145 | −0.0213525 | ||||||||
\(223\) | 18.3690 | 1.23008 | 0.615041 | − | 0.788495i | \(-0.289140\pi\) | ||||
0.615041 | + | 0.788495i | \(0.289140\pi\) | |||||||
\(224\) | −0.633048 | −0.0422973 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.39536 | −0.292375 | ||||||||
\(227\) | −29.0700 | −1.92944 | −0.964721 | − | 0.263274i | \(-0.915198\pi\) | ||||
−0.964721 | + | 0.263274i | \(0.915198\pi\) | |||||||
\(228\) | −12.3976 | −0.821049 | ||||||||
\(229\) | −0.499997 | −0.0330407 | −0.0165204 | − | 0.999864i | \(-0.505259\pi\) | ||||
−0.0165204 | + | 0.999864i | \(0.505259\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.263866 | 0.0173611 | ||||||||
\(232\) | 10.4269 | 0.684558 | ||||||||
\(233\) | −27.0992 | −1.77533 | −0.887663 | − | 0.460494i | \(-0.847672\pi\) | ||||
−0.887663 | + | 0.460494i | \(0.847672\pi\) | |||||||
\(234\) | −1.43641 | −0.0939010 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.7230 | 1.21876 | ||||||||
\(237\) | −15.7821 | −1.02516 | ||||||||
\(238\) | −0.0536948 | −0.00348052 | ||||||||
\(239\) | 25.1215 | 1.62497 | 0.812487 | − | 0.582979i | \(-0.198113\pi\) | ||||
0.812487 | + | 0.582979i | \(0.198113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.98036 | −0.514060 | −0.257030 | − | 0.966403i | \(-0.582744\pi\) | ||||
−0.257030 | + | 0.966403i | \(0.582744\pi\) | |||||||
\(242\) | −2.50567 | −0.161070 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 19.4818 | 1.24719 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.598611 | 0.0381660 | ||||||||
\(247\) | −34.5611 | −2.19907 | ||||||||
\(248\) | −6.27590 | −0.398520 | ||||||||
\(249\) | 1.79347 | 0.113657 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.7735 | −1.87929 | −0.939645 | − | 0.342151i | \(-0.888844\pi\) | ||||
−0.939645 | + | 0.342151i | \(0.888844\pi\) | |||||||
\(252\) | 0.399672 | 0.0251769 | ||||||||
\(253\) | −7.47824 | −0.470153 | ||||||||
\(254\) | 1.20755 | 0.0757682 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.5904 | 0.661902 | ||||||||
\(257\) | 3.24067 | 0.202148 | 0.101074 | − | 0.994879i | \(-0.467772\pi\) | ||||
0.101074 | + | 0.994879i | \(0.467772\pi\) | |||||||
\(258\) | −1.65694 | −0.103156 | ||||||||
\(259\) | 0.246775 | 0.0153339 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.93423 | −0.614914 | ||||||||
\(262\) | 5.48946 | 0.339140 | ||||||||
\(263\) | −14.9421 | −0.921367 | −0.460684 | − | 0.887564i | \(-0.652396\pi\) | ||||
−0.460684 | + | 0.887564i | \(0.652396\pi\) | |||||||
\(264\) | 1.33644 | 0.0822520 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.355898 | −0.0218215 | ||||||||
\(267\) | −7.28256 | −0.445685 | ||||||||
\(268\) | −8.41809 | −0.514217 | ||||||||
\(269\) | 12.7592 | 0.777941 | 0.388970 | − | 0.921250i | \(-0.372831\pi\) | ||||
0.388970 | + | 0.921250i | \(0.372831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.13747 | 0.555062 | 0.277531 | − | 0.960717i | \(-0.410484\pi\) | ||||
0.277531 | + | 0.960717i | \(0.410484\pi\) | |||||||
\(272\) | 3.46893 | 0.210334 | ||||||||
\(273\) | 1.11418 | 0.0674331 | ||||||||
\(274\) | −3.94968 | −0.238609 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.3271 | −0.681811 | ||||||||
\(277\) | −3.04812 | −0.183144 | −0.0915720 | − | 0.995798i | \(-0.529189\pi\) | ||||
−0.0915720 | + | 0.995798i | \(0.529189\pi\) | |||||||
\(278\) | 4.94838 | 0.296784 | ||||||||
\(279\) | 5.97938 | 0.357976 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.19048 | −0.488603 | −0.244302 | − | 0.969699i | \(-0.578559\pi\) | ||||
−0.244302 | + | 0.969699i | \(0.578559\pi\) | |||||||
\(282\) | −0.267165 | −0.0159095 | ||||||||
\(283\) | −6.63076 | −0.394158 | −0.197079 | − | 0.980388i | \(-0.563146\pi\) | ||||
−0.197079 | + | 0.980388i | \(0.563146\pi\) | |||||||
\(284\) | −18.4034 | −1.09204 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.82897 | 0.108149 | ||||||||
\(287\) | −0.464324 | −0.0274082 | ||||||||
\(288\) | 3.05479 | 0.180005 | ||||||||
\(289\) | −16.0594 | −0.944672 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.290073 | −0.0170044 | ||||||||
\(292\) | 22.6237 | 1.32395 | ||||||||
\(293\) | 18.2716 | 1.06744 | 0.533719 | − | 0.845662i | \(-0.320794\pi\) | ||||
0.533719 | + | 0.845662i | \(0.320794\pi\) | |||||||
\(294\) | −1.85868 | −0.108401 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.24987 | 0.0726473 | ||||||||
\(297\) | −1.27329 | −0.0738839 | ||||||||
\(298\) | −0.407221 | −0.0235897 | ||||||||
\(299\) | −31.5769 | −1.82614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.28523 | 0.0740796 | ||||||||
\(302\) | 5.95674 | 0.342772 | ||||||||
\(303\) | −5.63344 | −0.323633 | ||||||||
\(304\) | 22.9926 | 1.31872 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.259105 | 0.0148121 | ||||||||
\(307\) | −18.1634 | −1.03664 | −0.518319 | − | 0.855187i | \(-0.673442\pi\) | ||||
−0.518319 | + | 0.855187i | \(0.673442\pi\) | |||||||
\(308\) | −0.508899 | −0.0289972 | ||||||||
\(309\) | −11.3273 | −0.644389 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.0180 | 1.58876 | 0.794379 | − | 0.607423i | \(-0.207797\pi\) | ||||
0.794379 | + | 0.607423i | \(0.207797\pi\) | |||||||
\(312\) | 5.64311 | 0.319478 | ||||||||
\(313\) | −12.6852 | −0.717009 | −0.358504 | − | 0.933528i | \(-0.616713\pi\) | ||||
−0.358504 | + | 0.933528i | \(0.616713\pi\) | |||||||
\(314\) | −4.39728 | −0.248153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 30.4378 | 1.71226 | ||||||||
\(317\) | −34.8739 | −1.95871 | −0.979355 | − | 0.202146i | \(-0.935208\pi\) | ||||
−0.979355 | + | 0.202146i | \(0.935208\pi\) | |||||||
\(318\) | −2.30853 | −0.129456 | ||||||||
\(319\) | 12.6492 | 0.708218 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.10431 | −0.452339 | ||||||||
\(322\) | −0.325167 | −0.0181209 | ||||||||
\(323\) | 6.23427 | 0.346884 | ||||||||
\(324\) | −1.92862 | −0.107146 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.05985 | −0.114085 | ||||||||
\(327\) | 13.2362 | 0.731963 | ||||||||
\(328\) | −2.35172 | −0.129852 | ||||||||
\(329\) | 0.207232 | 0.0114250 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.3577 | 1.11896 | 0.559480 | − | 0.828844i | \(-0.311001\pi\) | ||||
0.559480 | + | 0.828844i | \(0.311001\pi\) | |||||||
\(332\) | −3.45893 | −0.189833 | ||||||||
\(333\) | −1.19082 | −0.0652564 | ||||||||
\(334\) | 2.69801 | 0.147629 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.741232 | −0.0404375 | ||||||||
\(337\) | 29.3333 | 1.59789 | 0.798943 | − | 0.601407i | \(-0.205393\pi\) | ||||
0.798943 | + | 0.601407i | \(0.205393\pi\) | |||||||
\(338\) | 4.24968 | 0.231152 | ||||||||
\(339\) | −16.4518 | −0.893542 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.61350 | −0.412294 | ||||||||
\(342\) | 1.71739 | 0.0928659 | ||||||||
\(343\) | 2.89234 | 0.156172 | ||||||||
\(344\) | 6.50948 | 0.350967 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.30581 | 0.285242 | ||||||||
\(347\) | −29.5486 | −1.58625 | −0.793127 | − | 0.609057i | \(-0.791548\pi\) | ||||
−0.793127 | + | 0.609057i | \(0.791548\pi\) | |||||||
\(348\) | 19.1594 | 1.02705 | ||||||||
\(349\) | 0.661771 | 0.0354238 | 0.0177119 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177119 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.37648 | −0.286975 | ||||||||
\(352\) | −3.88964 | −0.207318 | ||||||||
\(353\) | 4.99309 | 0.265756 | 0.132878 | − | 0.991132i | \(-0.457578\pi\) | ||||
0.132878 | + | 0.991132i | \(0.457578\pi\) | |||||||
\(354\) | −2.59363 | −0.137850 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0453 | 0.744400 | ||||||||
\(357\) | −0.200980 | −0.0106370 | ||||||||
\(358\) | −3.26678 | −0.172655 | ||||||||
\(359\) | −17.0698 | −0.900910 | −0.450455 | − | 0.892799i | \(-0.648738\pi\) | ||||
−0.450455 | + | 0.892799i | \(0.648738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.3218 | 1.17483 | ||||||||
\(362\) | −2.70699 | −0.142276 | ||||||||
\(363\) | −9.37873 | −0.492255 | ||||||||
\(364\) | −2.14883 | −0.112629 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.69874 | −0.141065 | ||||||||
\(367\) | −6.07188 | −0.316949 | −0.158475 | − | 0.987363i | \(-0.550658\pi\) | ||||
−0.158475 | + | 0.987363i | \(0.550658\pi\) | |||||||
\(368\) | 21.0073 | 1.09508 | ||||||||
\(369\) | 2.24060 | 0.116641 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.79065 | 0.0929661 | ||||||||
\(372\) | −11.5320 | −0.597905 | ||||||||
\(373\) | −19.3121 | −0.999944 | −0.499972 | − | 0.866042i | \(-0.666656\pi\) | ||||
−0.499972 | + | 0.866042i | \(0.666656\pi\) | |||||||
\(374\) | −0.329917 | −0.0170596 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.04959 | 0.0541285 | ||||||||
\(377\) | 53.4112 | 2.75082 | ||||||||
\(378\) | −0.0553651 | −0.00284767 | ||||||||
\(379\) | −4.68181 | −0.240488 | −0.120244 | − | 0.992744i | \(-0.538368\pi\) | ||||
−0.120244 | + | 0.992744i | \(0.538368\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.51985 | 0.231559 | ||||||||
\(382\) | −1.31122 | −0.0670880 | ||||||||
\(383\) | 5.78171 | 0.295432 | 0.147716 | − | 0.989030i | \(-0.452808\pi\) | ||||
0.147716 | + | 0.989030i | \(0.452808\pi\) | |||||||
\(384\) | −7.80274 | −0.398182 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.806794 | −0.0410647 | ||||||||
\(387\) | −6.20192 | −0.315261 | ||||||||
\(388\) | 0.559441 | 0.0284013 | ||||||||
\(389\) | 1.93198 | 0.0979553 | 0.0489777 | − | 0.998800i | \(-0.484404\pi\) | ||||
0.0489777 | + | 0.998800i | \(0.484404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.69597 | 0.288058 | ||||||||
\(392\) | 7.30206 | 0.368810 | ||||||||
\(393\) | 20.5471 | 1.03646 | ||||||||
\(394\) | 2.04076 | 0.102812 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.45570 | 0.123404 | ||||||||
\(397\) | 30.9953 | 1.55561 | 0.777805 | − | 0.628506i | \(-0.216333\pi\) | ||||
0.777805 | + | 0.628506i | \(0.216333\pi\) | |||||||
\(398\) | 3.97790 | 0.199394 | ||||||||
\(399\) | −1.33213 | −0.0666897 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.2628 | 1.81088 | 0.905438 | − | 0.424478i | \(-0.139542\pi\) | ||||
0.905438 | + | 0.424478i | \(0.139542\pi\) | |||||||
\(402\) | 1.16613 | 0.0581612 | ||||||||
\(403\) | −32.1480 | −1.60141 | ||||||||
\(404\) | 10.8648 | 0.540543 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.550009 | 0.0272965 | ||||||||
\(407\) | 1.51626 | 0.0751582 | ||||||||
\(408\) | −1.01793 | −0.0503949 | ||||||||
\(409\) | −0.0369376 | −0.00182645 | −0.000913223 | − | 1.00000i | \(-0.500291\pi\) | ||||
−0.000913223 | 1.00000i | \(0.500291\pi\) | ||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.7837 | −0.729225 | ||||||||
\(412\) | 21.8462 | 1.07628 | ||||||||
\(413\) | 2.01180 | 0.0989940 | ||||||||
\(414\) | 1.56910 | 0.0771171 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.4240 | −0.805253 | ||||||||
\(417\) | 18.5218 | 0.907017 | ||||||||
\(418\) | −2.18674 | −0.106957 | ||||||||
\(419\) | 0.362309 | 0.0176999 | 0.00884997 | − | 0.999961i | \(-0.497183\pi\) | ||||
0.00884997 | + | 0.999961i | \(0.497183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.6406 | 0.616063 | 0.308032 | − | 0.951376i | \(-0.400330\pi\) | ||||
0.308032 | + | 0.951376i | \(0.400330\pi\) | |||||||
\(422\) | −1.32018 | −0.0642654 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | 9.06934 | 0.440446 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.54936 | 0.123517 | ||||||||
\(427\) | 2.09333 | 0.101303 | ||||||||
\(428\) | 15.6302 | 0.755513 | ||||||||
\(429\) | 6.84583 | 0.330520 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.98498 | 0.336455 | 0.168227 | − | 0.985748i | \(-0.446196\pi\) | ||||
0.168227 | + | 0.985748i | \(0.446196\pi\) | |||||||
\(432\) | 3.57683 | 0.172090 | ||||||||
\(433\) | 22.4312 | 1.07797 | 0.538987 | − | 0.842314i | \(-0.318807\pi\) | ||||
0.538987 | + | 0.842314i | \(0.318807\pi\) | |||||||
\(434\) | −0.331049 | −0.0158908 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −25.5276 | −1.22255 | ||||||||
\(437\) | 37.7538 | 1.80601 | ||||||||
\(438\) | −3.13398 | −0.149747 | ||||||||
\(439\) | 19.9828 | 0.953726 | 0.476863 | − | 0.878978i | \(-0.341774\pi\) | ||||
0.476863 | + | 0.878978i | \(0.341774\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.95706 | −0.331288 | ||||||||
\(442\) | −1.39307 | −0.0662618 | ||||||||
\(443\) | −0.382306 | −0.0181639 | −0.00908196 | − | 0.999959i | \(-0.502891\pi\) | ||||
−0.00908196 | + | 0.999959i | \(0.502891\pi\) | |||||||
\(444\) | 2.29664 | 0.108994 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.90756 | 0.232380 | ||||||||
\(447\) | −1.52423 | −0.0720936 | ||||||||
\(448\) | 1.31334 | 0.0620493 | ||||||||
\(449\) | 33.6928 | 1.59006 | 0.795030 | − | 0.606570i | \(-0.207455\pi\) | ||||
0.795030 | + | 0.606570i | \(0.207455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.85294 | −0.134340 | ||||||||
\(452\) | 31.7294 | 1.49243 | ||||||||
\(453\) | 22.2961 | 1.04756 | ||||||||
\(454\) | −7.76648 | −0.364499 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.74698 | −0.315956 | ||||||||
\(457\) | −10.9263 | −0.511110 | −0.255555 | − | 0.966795i | \(-0.582258\pi\) | ||||
−0.255555 | + | 0.966795i | \(0.582258\pi\) | |||||||
\(458\) | −0.133582 | −0.00624186 | ||||||||
\(459\) | 0.969832 | 0.0452679 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.9233 | −1.67311 | −0.836557 | − | 0.547880i | \(-0.815435\pi\) | ||||
−0.836557 | + | 0.547880i | \(0.815435\pi\) | |||||||
\(462\) | 0.0704959 | 0.00327977 | ||||||||
\(463\) | 25.5389 | 1.18690 | 0.593448 | − | 0.804873i | \(-0.297766\pi\) | ||||
0.593448 | + | 0.804873i | \(0.297766\pi\) | |||||||
\(464\) | −35.5331 | −1.64958 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.23996 | −0.335384 | ||||||||
\(467\) | −27.9327 | −1.29257 | −0.646285 | − | 0.763096i | \(-0.723678\pi\) | ||||
−0.646285 | + | 0.763096i | \(0.723678\pi\) | |||||||
\(468\) | 10.3692 | 0.479317 | ||||||||
\(469\) | −0.904529 | −0.0417673 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.4590 | −0.758393 | ||||||||
\(472\) | 10.1894 | 0.469005 | ||||||||
\(473\) | 7.89685 | 0.363098 | ||||||||
\(474\) | −4.21644 | −0.193667 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.387614 | 0.0177663 | ||||||||
\(477\) | −8.64084 | −0.395637 | ||||||||
\(478\) | 6.71159 | 0.306981 | ||||||||
\(479\) | 17.2921 | 0.790096 | 0.395048 | − | 0.918660i | \(-0.370728\pi\) | ||||
0.395048 | + | 0.918660i | \(0.370728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.40241 | 0.291925 | ||||||||
\(482\) | −2.13207 | −0.0971133 | ||||||||
\(483\) | −1.21710 | −0.0553801 | ||||||||
\(484\) | 18.0880 | 0.822183 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.267165 | 0.0121189 | ||||||||
\(487\) | −5.99955 | −0.271866 | −0.135933 | − | 0.990718i | \(-0.543403\pi\) | ||||
−0.135933 | + | 0.990718i | \(0.543403\pi\) | |||||||
\(488\) | 10.6023 | 0.479945 | ||||||||
\(489\) | −7.71004 | −0.348660 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.8555 | −0.986323 | −0.493161 | − | 0.869938i | \(-0.664159\pi\) | ||||
−0.493161 | + | 0.869938i | \(0.664159\pi\) | |||||||
\(492\) | −4.32128 | −0.194818 | ||||||||
\(493\) | −9.63454 | −0.433918 | ||||||||
\(494\) | −9.23352 | −0.415436 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.3872 | 0.960315 | ||||||||
\(497\) | −1.97746 | −0.0887010 | ||||||||
\(498\) | 0.479153 | 0.0214713 | ||||||||
\(499\) | 34.1218 | 1.52750 | 0.763752 | − | 0.645510i | \(-0.223355\pi\) | ||||
0.763752 | + | 0.645510i | \(0.223355\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.0987 | 0.451175 | ||||||||
\(502\) | −7.95445 | −0.355025 | ||||||||
\(503\) | −17.7971 | −0.793533 | −0.396767 | − | 0.917919i | \(-0.629868\pi\) | ||||
−0.396767 | + | 0.917919i | \(0.629868\pi\) | |||||||
\(504\) | 0.217508 | 0.00968860 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.99793 | −0.0888186 | ||||||||
\(507\) | 15.9066 | 0.706435 | ||||||||
\(508\) | −8.71709 | −0.386758 | ||||||||
\(509\) | −21.7120 | −0.962369 | −0.481184 | − | 0.876619i | \(-0.659793\pi\) | ||||
−0.481184 | + | 0.876619i | \(0.659793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.43093 | 0.107538 | ||||||||
\(512\) | 18.4349 | 0.814714 | ||||||||
\(513\) | 6.42820 | 0.283812 | ||||||||
\(514\) | 0.865795 | 0.0381886 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 11.9612 | 0.526561 | ||||||||
\(517\) | 1.27329 | 0.0559993 | ||||||||
\(518\) | 0.0659297 | 0.00289678 | ||||||||
\(519\) | 19.8597 | 0.871743 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.2821 | −0.976197 | −0.488099 | − | 0.872788i | \(-0.662309\pi\) | ||||
−0.488099 | + | 0.872788i | \(0.662309\pi\) | |||||||
\(522\) | −2.65408 | −0.116166 | ||||||||
\(523\) | −9.96039 | −0.435538 | −0.217769 | − | 0.976000i | \(-0.569878\pi\) | ||||
−0.217769 | + | 0.976000i | \(0.569878\pi\) | |||||||
\(524\) | −39.6275 | −1.73114 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.99200 | −0.174059 | ||||||||
\(527\) | 5.79899 | 0.252608 | ||||||||
\(528\) | −4.55435 | −0.198203 | ||||||||
\(529\) | 11.4939 | 0.499736 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.70796 | −0.421290 | ||||||||
\(532\) | 2.56917 | 0.111388 | ||||||||
\(533\) | −12.0466 | −0.521794 | ||||||||
\(534\) | −1.94565 | −0.0841963 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.58128 | −0.197881 | ||||||||
\(537\) | −12.2276 | −0.527658 | ||||||||
\(538\) | 3.40881 | 0.146964 | ||||||||
\(539\) | 8.85837 | 0.381557 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.70353 | −0.202221 | −0.101110 | − | 0.994875i | \(-0.532240\pi\) | ||||
−0.101110 | + | 0.994875i | \(0.532240\pi\) | |||||||
\(542\) | 2.44121 | 0.104859 | ||||||||
\(543\) | −10.1323 | −0.434818 | ||||||||
\(544\) | 2.96263 | 0.127022 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.297669 | 0.0127391 | ||||||||
\(547\) | 41.3316 | 1.76721 | 0.883605 | − | 0.468233i | \(-0.155109\pi\) | ||||
0.883605 | + | 0.468233i | \(0.155109\pi\) | |||||||
\(548\) | 28.5121 | 1.21798 | ||||||||
\(549\) | −10.1014 | −0.431117 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −63.8592 | −2.72049 | ||||||||
\(552\) | −6.16441 | −0.262375 | ||||||||
\(553\) | 3.27056 | 0.139078 | ||||||||
\(554\) | −0.814352 | −0.0345985 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −35.7216 | −1.51493 | ||||||||
\(557\) | −43.0480 | −1.82400 | −0.912001 | − | 0.410188i | \(-0.865463\pi\) | ||||
−0.912001 | + | 0.410188i | \(0.865463\pi\) | |||||||
\(558\) | 1.59748 | 0.0676268 | ||||||||
\(559\) | 33.3445 | 1.41032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.23488 | −0.0521367 | ||||||||
\(562\) | −2.18821 | −0.0923041 | ||||||||
\(563\) | −32.3647 | −1.36401 | −0.682006 | − | 0.731347i | \(-0.738892\pi\) | ||||
−0.682006 | + | 0.731347i | \(0.738892\pi\) | |||||||
\(564\) | 1.92862 | 0.0812097 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.77151 | −0.0744620 | ||||||||
\(567\) | −0.207232 | −0.00870291 | ||||||||
\(568\) | −10.0155 | −0.420240 | ||||||||
\(569\) | −34.4813 | −1.44553 | −0.722766 | − | 0.691093i | \(-0.757129\pi\) | ||||
−0.722766 | + | 0.691093i | \(0.757129\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.6501 | 1.53376 | 0.766879 | − | 0.641792i | \(-0.221809\pi\) | ||||
0.766879 | + | 0.641792i | \(0.221809\pi\) | |||||||
\(572\) | −13.2030 | −0.552047 | ||||||||
\(573\) | −4.90791 | −0.205031 | ||||||||
\(574\) | −0.124051 | −0.00517779 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.33753 | −0.264064 | ||||||||
\(577\) | −2.62010 | −0.109076 | −0.0545381 | − | 0.998512i | \(-0.517369\pi\) | ||||
−0.0545381 | + | 0.998512i | \(0.517369\pi\) | |||||||
\(578\) | −4.29052 | −0.178462 | ||||||||
\(579\) | −3.01983 | −0.125500 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.371664 | −0.0154192 | ||||||||
\(582\) | −0.0774974 | −0.00321237 | ||||||||
\(583\) | 11.0023 | 0.455669 | ||||||||
\(584\) | 12.3122 | 0.509484 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.88154 | 0.201654 | ||||||||
\(587\) | −2.63615 | −0.108806 | −0.0544028 | − | 0.998519i | \(-0.517326\pi\) | ||||
−0.0544028 | + | 0.998519i | \(0.517326\pi\) | |||||||
\(588\) | 13.4175 | 0.553330 | ||||||||
\(589\) | 38.4366 | 1.58375 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.63855 | 0.314208 | ||||||||
\(592\) | −4.25935 | −0.175058 | ||||||||
\(593\) | −7.63049 | −0.313347 | −0.156673 | − | 0.987650i | \(-0.550077\pi\) | ||||
−0.156673 | + | 0.987650i | \(0.550077\pi\) | |||||||
\(594\) | −0.340179 | −0.0139577 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.93967 | 0.120413 | ||||||||
\(597\) | 14.8893 | 0.609378 | ||||||||
\(598\) | −8.43625 | −0.344984 | ||||||||
\(599\) | 20.3053 | 0.829650 | 0.414825 | − | 0.909901i | \(-0.363843\pi\) | ||||
0.414825 | + | 0.909901i | \(0.363843\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.07475 | −0.0438398 | −0.0219199 | − | 0.999760i | \(-0.506978\pi\) | ||||
−0.0219199 | + | 0.999760i | \(0.506978\pi\) | |||||||
\(602\) | 0.343369 | 0.0139947 | ||||||||
\(603\) | 4.36482 | 0.177749 | ||||||||
\(604\) | −43.0008 | −1.74968 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.50506 | −0.0611389 | ||||||||
\(607\) | 17.0385 | 0.691573 | 0.345786 | − | 0.938313i | \(-0.387612\pi\) | ||||
0.345786 | + | 0.938313i | \(0.387612\pi\) | |||||||
\(608\) | 19.6368 | 0.796377 | ||||||||
\(609\) | 2.05869 | 0.0834222 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.37648 | 0.217509 | ||||||||
\(612\) | −1.87044 | −0.0756081 | ||||||||
\(613\) | 36.6117 | 1.47873 | 0.739366 | − | 0.673304i | \(-0.235126\pi\) | ||||
0.739366 | + | 0.673304i | \(0.235126\pi\) | |||||||
\(614\) | −4.85262 | −0.195836 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.276952 | −0.0111587 | ||||||||
\(617\) | 23.1682 | 0.932716 | 0.466358 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466358 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(618\) | −3.02627 | −0.121734 | ||||||||
\(619\) | −26.4232 | −1.06204 | −0.531018 | − | 0.847360i | \(-0.678190\pi\) | ||||
−0.531018 | + | 0.847360i | \(0.678190\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.87315 | 0.235681 | ||||||||
\(622\) | 7.48545 | 0.300139 | ||||||||
\(623\) | 1.50918 | 0.0604639 | ||||||||
\(624\) | −19.2308 | −0.769847 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.38904 | −0.135453 | ||||||||
\(627\) | −8.18498 | −0.326877 | ||||||||
\(628\) | 31.7433 | 1.26669 | ||||||||
\(629\) | −1.15489 | −0.0460486 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.2696 | −1.68273 | −0.841363 | − | 0.540471i | \(-0.818246\pi\) | ||||
−0.841363 | + | 0.540471i | \(0.818246\pi\) | |||||||
\(632\) | 16.5648 | 0.658912 | ||||||||
\(633\) | −4.94144 | −0.196405 | ||||||||
\(634\) | −9.31708 | −0.370028 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.6649 | 0.660807 | ||||||||
\(637\) | 37.4045 | 1.48202 | ||||||||
\(638\) | 3.37942 | 0.133793 | ||||||||
\(639\) | 9.54225 | 0.377486 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.47629 | −0.0978077 | −0.0489039 | − | 0.998803i | \(-0.515573\pi\) | ||||
−0.0489039 | + | 0.998803i | \(0.515573\pi\) | |||||||
\(642\) | −2.16519 | −0.0854532 | ||||||||
\(643\) | 38.6391 | 1.52378 | 0.761890 | − | 0.647707i | \(-0.224272\pi\) | ||||
0.761890 | + | 0.647707i | \(0.224272\pi\) | |||||||
\(644\) | 2.34733 | 0.0924978 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.66558 | 0.0655314 | ||||||||
\(647\) | 8.32898 | 0.327446 | 0.163723 | − | 0.986506i | \(-0.447650\pi\) | ||||
0.163723 | + | 0.986506i | \(0.447650\pi\) | |||||||
\(648\) | −1.04959 | −0.0412318 | ||||||||
\(649\) | 12.3611 | 0.485215 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.23912 | −0.0485648 | ||||||||
\(652\) | 14.8698 | 0.582345 | ||||||||
\(653\) | 18.8800 | 0.738832 | 0.369416 | − | 0.929264i | \(-0.379558\pi\) | ||||
0.369416 | + | 0.929264i | \(0.379558\pi\) | |||||||
\(654\) | 3.53625 | 0.138278 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.01426 | 0.312904 | ||||||||
\(657\) | −11.7305 | −0.457651 | ||||||||
\(658\) | 0.0553651 | 0.00215835 | ||||||||
\(659\) | −13.9987 | −0.545311 | −0.272656 | − | 0.962112i | \(-0.587902\pi\) | ||||
−0.272656 | + | 0.962112i | \(0.587902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.55730 | 0.216154 | 0.108077 | − | 0.994143i | \(-0.465531\pi\) | ||||
0.108077 | + | 0.994143i | \(0.465531\pi\) | |||||||
\(662\) | 5.43887 | 0.211388 | ||||||||
\(663\) | −5.21428 | −0.202506 | ||||||||
\(664\) | −1.88241 | −0.0730517 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.318145 | −0.0123279 | ||||||||
\(667\) | −58.3453 | −2.25914 | ||||||||
\(668\) | −19.4765 | −0.753569 | ||||||||
\(669\) | 18.3690 | 0.710188 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.8620 | 0.496533 | ||||||||
\(672\) | −0.633048 | −0.0244204 | ||||||||
\(673\) | −31.0565 | −1.19714 | −0.598569 | − | 0.801071i | \(-0.704264\pi\) | ||||
−0.598569 | + | 0.801071i | \(0.704264\pi\) | |||||||
\(674\) | 7.83683 | 0.301863 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.6777 | −1.17991 | ||||||||
\(677\) | −21.7287 | −0.835101 | −0.417550 | − | 0.908654i | \(-0.637111\pi\) | ||||
−0.417550 | + | 0.908654i | \(0.637111\pi\) | |||||||
\(678\) | −4.39536 | −0.168803 | ||||||||
\(679\) | 0.0601123 | 0.00230690 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.0700 | −1.11396 | ||||||||
\(682\) | −2.03406 | −0.0778882 | ||||||||
\(683\) | 1.85083 | 0.0708202 | 0.0354101 | − | 0.999373i | \(-0.488726\pi\) | ||||
0.0354101 | + | 0.999373i | \(0.488726\pi\) | |||||||
\(684\) | −12.3976 | −0.474033 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.772733 | 0.0295031 | ||||||||
\(687\) | −0.499997 | −0.0190761 | ||||||||
\(688\) | −22.1832 | −0.845727 | ||||||||
\(689\) | 46.4573 | 1.76988 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.56714 | 0.249826 | 0.124913 | − | 0.992168i | \(-0.460135\pi\) | ||||
0.124913 | + | 0.992168i | \(0.460135\pi\) | |||||||
\(692\) | −38.3018 | −1.45602 | ||||||||
\(693\) | 0.263866 | 0.0100235 | ||||||||
\(694\) | −7.89436 | −0.299666 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.4269 | 0.395230 | ||||||||
\(697\) | 2.17301 | 0.0823085 | ||||||||
\(698\) | 0.176802 | 0.00669206 | ||||||||
\(699\) | −27.0992 | −1.02498 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.3117 | −1.06932 | −0.534659 | − | 0.845068i | \(-0.679560\pi\) | ||||
−0.534659 | + | 0.845068i | \(0.679560\pi\) | |||||||
\(702\) | −1.43641 | −0.0542137 | ||||||||
\(703\) | −7.65482 | −0.288707 | ||||||||
\(704\) | 8.06953 | 0.304132 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.33398 | 0.0502050 | ||||||||
\(707\) | 1.16743 | 0.0439056 | ||||||||
\(708\) | 18.7230 | 0.703653 | ||||||||
\(709\) | 18.8498 | 0.707920 | 0.353960 | − | 0.935260i | \(-0.384835\pi\) | ||||
0.353960 | + | 0.935260i | \(0.384835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.7821 | −0.591876 | ||||||||
\(712\) | 7.64371 | 0.286460 | ||||||||
\(713\) | 35.1178 | 1.31517 | ||||||||
\(714\) | −0.0536948 | −0.00200948 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23.5824 | 0.881314 | ||||||||
\(717\) | 25.1215 | 0.938179 | ||||||||
\(718\) | −4.56046 | −0.170195 | ||||||||
\(719\) | −21.6400 | −0.807036 | −0.403518 | − | 0.914972i | \(-0.632213\pi\) | ||||
−0.403518 | + | 0.914972i | \(0.632213\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.34738 | 0.0874210 | ||||||||
\(722\) | 5.96360 | 0.221942 | ||||||||
\(723\) | −7.98036 | −0.296793 | ||||||||
\(724\) | 19.5413 | 0.726248 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.50567 | −0.0929941 | ||||||||
\(727\) | −2.30732 | −0.0855737 | −0.0427869 | − | 0.999084i | \(-0.513624\pi\) | ||||
−0.0427869 | + | 0.999084i | \(0.513624\pi\) | |||||||
\(728\) | −1.16943 | −0.0433420 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.01482 | −0.222466 | ||||||||
\(732\) | 19.4818 | 0.720068 | ||||||||
\(733\) | 18.9481 | 0.699863 | 0.349932 | − | 0.936775i | \(-0.386205\pi\) | ||||
0.349932 | + | 0.936775i | \(0.386205\pi\) | |||||||
\(734\) | −1.62219 | −0.0598763 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.9412 | 0.661322 | ||||||||
\(737\) | −5.55769 | −0.204720 | ||||||||
\(738\) | 0.598611 | 0.0220352 | ||||||||
\(739\) | 18.6083 | 0.684519 | 0.342259 | − | 0.939605i | \(-0.388808\pi\) | ||||
0.342259 | + | 0.939605i | \(0.388808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34.5611 | −1.26963 | ||||||||
\(742\) | 0.478400 | 0.0175626 | ||||||||
\(743\) | 4.08148 | 0.149735 | 0.0748676 | − | 0.997193i | \(-0.476147\pi\) | ||||
0.0748676 | + | 0.997193i | \(0.476147\pi\) | |||||||
\(744\) | −6.27590 | −0.230086 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.15953 | −0.188904 | ||||||||
\(747\) | 1.79347 | 0.0656196 | ||||||||
\(748\) | 2.38162 | 0.0870806 | ||||||||
\(749\) | 1.67947 | 0.0613665 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.378534 | −0.0138129 | −0.00690645 | − | 0.999976i | \(-0.502198\pi\) | ||||
−0.00690645 | + | 0.999976i | \(0.502198\pi\) | |||||||
\(752\) | −3.57683 | −0.130434 | ||||||||
\(753\) | −29.7735 | −1.08501 | ||||||||
\(754\) | 14.2696 | 0.519669 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.399672 | 0.0145359 | ||||||||
\(757\) | −24.9727 | −0.907649 | −0.453825 | − | 0.891091i | \(-0.649941\pi\) | ||||
−0.453825 | + | 0.891091i | \(0.649941\pi\) | |||||||
\(758\) | −1.25082 | −0.0454317 | ||||||||
\(759\) | −7.47824 | −0.271443 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.0020 | −0.471322 | −0.235661 | − | 0.971835i | \(-0.575725\pi\) | ||||
−0.235661 | + | 0.971835i | \(0.575725\pi\) | |||||||
\(762\) | 1.20755 | 0.0437448 | ||||||||
\(763\) | −2.74296 | −0.0993018 | ||||||||
\(764\) | 9.46551 | 0.342450 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.54467 | 0.0558113 | ||||||||
\(767\) | 52.1947 | 1.88464 | ||||||||
\(768\) | 10.5904 | 0.382150 | ||||||||
\(769\) | 30.0353 | 1.08310 | 0.541550 | − | 0.840669i | \(-0.317838\pi\) | ||||
0.541550 | + | 0.840669i | \(0.317838\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.24067 | 0.116710 | ||||||||
\(772\) | 5.82412 | 0.209615 | ||||||||
\(773\) | 40.8899 | 1.47071 | 0.735354 | − | 0.677683i | \(-0.237016\pi\) | ||||
0.735354 | + | 0.677683i | \(0.237016\pi\) | |||||||
\(774\) | −1.65694 | −0.0595573 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.304458 | 0.0109294 | ||||||||
\(777\) | 0.246775 | 0.00885301 | ||||||||
\(778\) | 0.516158 | 0.0185052 | ||||||||
\(779\) | 14.4030 | 0.516042 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1501 | −0.434764 | ||||||||
\(782\) | 1.52176 | 0.0544182 | ||||||||
\(783\) | −9.93423 | −0.355021 | ||||||||
\(784\) | −24.8842 | −0.888722 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.48946 | 0.195802 | ||||||||
\(787\) | −11.3769 | −0.405543 | −0.202772 | − | 0.979226i | \(-0.564995\pi\) | ||||
−0.202772 | + | 0.979226i | \(0.564995\pi\) | |||||||
\(788\) | −14.7319 | −0.524802 | ||||||||
\(789\) | −14.9421 | −0.531952 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.40934 | 0.121222 | ||||||||
\(792\) | 1.33644 | 0.0474882 | ||||||||
\(793\) | 54.3100 | 1.92860 | ||||||||
\(794\) | 8.28086 | 0.293877 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −28.7158 | −1.01780 | ||||||||
\(797\) | −7.09623 | −0.251361 | −0.125681 | − | 0.992071i | \(-0.540111\pi\) | ||||
−0.125681 | + | 0.992071i | \(0.540111\pi\) | |||||||
\(798\) | −0.355898 | −0.0125986 | ||||||||
\(799\) | −0.969832 | −0.0343102 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.28256 | −0.257316 | ||||||||
\(802\) | 9.68815 | 0.342100 | ||||||||
\(803\) | 14.9364 | 0.527093 | ||||||||
\(804\) | −8.41809 | −0.296883 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.58883 | −0.302529 | ||||||||
\(807\) | 12.7592 | 0.449144 | ||||||||
\(808\) | 5.91281 | 0.208012 | ||||||||
\(809\) | 11.6552 | 0.409776 | 0.204888 | − | 0.978785i | \(-0.434317\pi\) | ||||
0.204888 | + | 0.978785i | \(0.434317\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0224294 | 0.000787602 0 | 0.000393801 | − | 1.00000i | \(-0.499875\pi\) | ||||
0.000393801 | 1.00000i | \(0.499875\pi\) | ||||||||
\(812\) | −3.97043 | −0.139335 | ||||||||
\(813\) | 9.13747 | 0.320465 | ||||||||
\(814\) | 0.405092 | 0.0141985 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.46893 | 0.121437 | ||||||||
\(817\) | −39.8672 | −1.39478 | ||||||||
\(818\) | −0.00986844 | −0.000345042 0 | ||||||||
\(819\) | 1.11418 | 0.0389325 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.9487 | −1.46402 | −0.732009 | − | 0.681294i | \(-0.761417\pi\) | ||||
−0.732009 | + | 0.681294i | \(0.761417\pi\) | |||||||
\(822\) | −3.94968 | −0.137761 | ||||||||
\(823\) | 30.5936 | 1.06643 | 0.533213 | − | 0.845981i | \(-0.320985\pi\) | ||||
0.533213 | + | 0.845981i | \(0.320985\pi\) | |||||||
\(824\) | 11.8891 | 0.414175 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.537482 | 0.0187014 | ||||||||
\(827\) | −33.5561 | −1.16686 | −0.583430 | − | 0.812163i | \(-0.698290\pi\) | ||||
−0.583430 | + | 0.812163i | \(0.698290\pi\) | |||||||
\(828\) | −11.3271 | −0.393644 | ||||||||
\(829\) | 33.2808 | 1.15589 | 0.577945 | − | 0.816076i | \(-0.303855\pi\) | ||||
0.577945 | + | 0.816076i | \(0.303855\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.04812 | −0.105738 | ||||||||
\(832\) | 34.0736 | 1.18129 | ||||||||
\(833\) | −6.74717 | −0.233776 | ||||||||
\(834\) | 4.94838 | 0.171348 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15.7857 | 0.545961 | ||||||||
\(837\) | 5.97938 | 0.206678 | ||||||||
\(838\) | 0.0967963 | 0.00334377 | ||||||||
\(839\) | 30.8908 | 1.06647 | 0.533235 | − | 0.845967i | \(-0.320976\pi\) | ||||
0.533235 | + | 0.845967i | \(0.320976\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69.6890 | 2.40307 | ||||||||
\(842\) | 3.37712 | 0.116383 | ||||||||
\(843\) | −8.19048 | −0.282095 | ||||||||
\(844\) | 9.53018 | 0.328042 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.267165 | −0.00918533 | ||||||||
\(847\) | 1.94357 | 0.0667818 | ||||||||
\(848\) | −30.9068 | −1.06134 | ||||||||
\(849\) | −6.63076 | −0.227567 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.99385 | −0.239746 | ||||||||
\(852\) | −18.4034 | −0.630490 | ||||||||
\(853\) | 11.9094 | 0.407772 | 0.203886 | − | 0.978995i | \(-0.434643\pi\) | ||||
0.203886 | + | 0.978995i | \(0.434643\pi\) | |||||||
\(854\) | 0.559264 | 0.0191376 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.50622 | 0.290736 | ||||||||
\(857\) | −1.29588 | −0.0442665 | −0.0221332 | − | 0.999755i | \(-0.507046\pi\) | ||||
−0.0221332 | + | 0.999755i | \(0.507046\pi\) | |||||||
\(858\) | 1.82897 | 0.0624400 | ||||||||
\(859\) | 15.9383 | 0.543808 | 0.271904 | − | 0.962324i | \(-0.412347\pi\) | ||||
0.271904 | + | 0.962324i | \(0.412347\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.464324 | −0.0158241 | ||||||||
\(862\) | 1.86614 | 0.0635611 | ||||||||
\(863\) | −4.41860 | −0.150411 | −0.0752054 | − | 0.997168i | \(-0.523961\pi\) | ||||
−0.0752054 | + | 0.997168i | \(0.523961\pi\) | |||||||
\(864\) | 3.05479 | 0.103926 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.99283 | 0.203645 | ||||||||
\(867\) | −16.0594 | −0.545407 | ||||||||
\(868\) | 2.38979 | 0.0811147 | ||||||||
\(869\) | 20.0953 | 0.681685 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.4674 | −0.795162 | ||||||||
\(872\) | −13.8926 | −0.470463 | ||||||||
\(873\) | −0.290073 | −0.00981748 | ||||||||
\(874\) | 10.0865 | 0.341181 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 22.6237 | 0.764385 | ||||||||
\(877\) | 24.5208 | 0.828007 | 0.414004 | − | 0.910275i | \(-0.364130\pi\) | ||||
0.414004 | + | 0.910275i | \(0.364130\pi\) | |||||||
\(878\) | 5.33870 | 0.180172 | ||||||||
\(879\) | 18.2716 | 0.616286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.7702 | 0.969293 | 0.484646 | − | 0.874710i | \(-0.338948\pi\) | ||||
0.484646 | + | 0.874710i | \(0.338948\pi\) | |||||||
\(882\) | −1.85868 | −0.0625851 | ||||||||
\(883\) | 10.7916 | 0.363167 | 0.181584 | − | 0.983375i | \(-0.441878\pi\) | ||||
0.181584 | + | 0.983375i | \(0.441878\pi\) | |||||||
\(884\) | 10.0564 | 0.338233 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.102139 | −0.00343142 | ||||||||
\(887\) | −30.3740 | −1.01986 | −0.509930 | − | 0.860216i | \(-0.670329\pi\) | ||||
−0.509930 | + | 0.860216i | \(0.670329\pi\) | |||||||
\(888\) | 1.24987 | 0.0419430 | ||||||||
\(889\) | −0.936656 | −0.0314144 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.27329 | −0.0426569 | ||||||||
\(892\) | −35.4269 | −1.18618 | ||||||||
\(893\) | −6.42820 | −0.215112 | ||||||||
\(894\) | −0.407221 | −0.0136195 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.61697 | 0.0540193 | ||||||||
\(897\) | −31.5769 | −1.05432 | ||||||||
\(898\) | 9.00153 | 0.300385 | ||||||||
\(899\) | −59.4005 | −1.98112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.38016 | −0.279184 | ||||||||
\(902\) | −0.762207 | −0.0253787 | ||||||||
\(903\) | 1.28523 | 0.0427699 | ||||||||
\(904\) | 17.2677 | 0.574316 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.95674 | 0.197899 | ||||||||
\(907\) | −34.6143 | −1.14935 | −0.574674 | − | 0.818382i | \(-0.694871\pi\) | ||||
−0.574674 | + | 0.818382i | \(0.694871\pi\) | |||||||
\(908\) | 56.0650 | 1.86058 | ||||||||
\(909\) | −5.63344 | −0.186849 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.9342 | 0.925502 | 0.462751 | − | 0.886488i | \(-0.346862\pi\) | ||||
0.462751 | + | 0.886488i | \(0.346862\pi\) | |||||||
\(912\) | 22.9926 | 0.761361 | ||||||||
\(913\) | −2.28361 | −0.0755765 | ||||||||
\(914\) | −2.91912 | −0.0965560 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.964305 | 0.0318615 | ||||||||
\(917\) | −4.25800 | −0.140612 | ||||||||
\(918\) | 0.259105 | 0.00855175 | ||||||||
\(919\) | 22.8657 | 0.754269 | 0.377135 | − | 0.926158i | \(-0.376909\pi\) | ||||
0.377135 | + | 0.926158i | \(0.376909\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.1634 | −0.598504 | ||||||||
\(922\) | −9.59745 | −0.316075 | ||||||||
\(923\) | −51.3038 | −1.68868 | ||||||||
\(924\) | −0.508899 | −0.0167415 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.82311 | 0.224221 | ||||||||
\(927\) | −11.3273 | −0.372038 | ||||||||
\(928\) | −30.3470 | −0.996188 | ||||||||
\(929\) | −19.6394 | −0.644348 | −0.322174 | − | 0.946680i | \(-0.604414\pi\) | ||||
−0.322174 | + | 0.946680i | \(0.604414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.7213 | −1.46568 | ||||||||
\(932\) | 52.2641 | 1.71197 | ||||||||
\(933\) | 28.0180 | 0.917270 | ||||||||
\(934\) | −7.46263 | −0.244185 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.64311 | 0.184451 | ||||||||
\(937\) | −19.3312 | −0.631521 | −0.315761 | − | 0.948839i | \(-0.602260\pi\) | ||||
−0.315761 | + | 0.948839i | \(0.602260\pi\) | |||||||
\(938\) | −0.241659 | −0.00789043 | ||||||||
\(939\) | −12.6852 | −0.413965 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.7500 | −0.546034 | −0.273017 | − | 0.962009i | \(-0.588021\pi\) | ||||
−0.273017 | + | 0.962009i | \(0.588021\pi\) | |||||||
\(942\) | −4.39728 | −0.143271 | ||||||||
\(943\) | 13.1594 | 0.428529 | ||||||||
\(944\) | −34.7237 | −1.13016 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.10976 | 0.0685943 | ||||||||
\(947\) | 51.3618 | 1.66903 | 0.834517 | − | 0.550982i | \(-0.185747\pi\) | ||||
0.834517 | + | 0.550982i | \(0.185747\pi\) | |||||||
\(948\) | 30.4378 | 0.988573 | ||||||||
\(949\) | 63.0688 | 2.04730 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.8739 | −1.13086 | ||||||||
\(952\) | 0.210947 | 0.00683682 | ||||||||
\(953\) | 18.3541 | 0.594548 | 0.297274 | − | 0.954792i | \(-0.403922\pi\) | ||||
0.297274 | + | 0.954792i | \(0.403922\pi\) | |||||||
\(954\) | −2.30853 | −0.0747414 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −48.4499 | −1.56698 | ||||||||
\(957\) | 12.6492 | 0.408890 | ||||||||
\(958\) | 4.61985 | 0.149260 | ||||||||
\(959\) | 3.06365 | 0.0989303 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.75296 | 0.153321 | ||||||||
\(962\) | 1.71050 | 0.0551488 | ||||||||
\(963\) | −8.10431 | −0.261158 | ||||||||
\(964\) | 15.3911 | 0.495714 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.325167 | −0.0104621 | ||||||||
\(967\) | 47.6325 | 1.53176 | 0.765879 | − | 0.642985i | \(-0.222304\pi\) | ||||
0.765879 | + | 0.642985i | \(0.222304\pi\) | |||||||
\(968\) | 9.84383 | 0.316393 | ||||||||
\(969\) | 6.23427 | 0.200274 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0570 | −0.483203 | −0.241601 | − | 0.970376i | \(-0.577673\pi\) | ||||
−0.241601 | + | 0.970376i | \(0.577673\pi\) | |||||||
\(972\) | −1.92862 | −0.0618606 | ||||||||
\(973\) | −3.83830 | −0.123050 | ||||||||
\(974\) | −1.60287 | −0.0513593 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.1310 | −1.15653 | ||||||||
\(977\) | −57.6863 | −1.84555 | −0.922774 | − | 0.385342i | \(-0.874083\pi\) | ||||
−0.922774 | + | 0.385342i | \(0.874083\pi\) | |||||||
\(978\) | −2.05985 | −0.0658669 | ||||||||
\(979\) | 9.27283 | 0.296361 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.2362 | 0.422599 | ||||||||
\(982\) | −5.83902 | −0.186330 | ||||||||
\(983\) | −27.1491 | −0.865920 | −0.432960 | − | 0.901413i | \(-0.642531\pi\) | ||||
−0.432960 | + | 0.901413i | \(0.642531\pi\) | |||||||
\(984\) | −2.35172 | −0.0749700 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.57401 | −0.0819732 | ||||||||
\(987\) | 0.207232 | 0.00659625 | ||||||||
\(988\) | 66.6553 | 2.12059 | ||||||||
\(989\) | −36.4248 | −1.15824 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.3572 | 0.487837 | 0.243918 | − | 0.969796i | \(-0.421567\pi\) | ||||
0.243918 | + | 0.969796i | \(0.421567\pi\) | |||||||
\(992\) | 18.2657 | 0.579937 | ||||||||
\(993\) | 20.3577 | 0.646032 | ||||||||
\(994\) | −0.528307 | −0.0167569 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.45893 | −0.109600 | ||||||||
\(997\) | 50.5126 | 1.59975 | 0.799876 | − | 0.600166i | \(-0.204899\pi\) | ||||
0.799876 | + | 0.600166i | \(0.204899\pi\) | |||||||
\(998\) | 9.11617 | 0.288567 | ||||||||
\(999\) | −1.19082 | −0.0376758 |
(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 | 3525.2.a.bd.1.6 | ✓ | 8 | |
5.4 | even | 2 | 3525.2.a.be.1.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.2.a.bd.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial | |
3525.2.a.be.1.3 | yes | 8 | 5.4 | even | 2 |