Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.69422 | −0.978156 | −0.489078 | − | 0.872240i | \(-0.662667\pi\) | ||||
−0.489078 | + | 0.872240i | \(0.662667\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.76480 | 1.68367 | 0.841836 | − | 0.539734i | \(-0.181475\pi\) | ||||
0.841836 | + | 0.539734i | \(0.181475\pi\) | |||||||
\(6\) | 1.69422 | 0.691660 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.129635 | −0.0432115 | ||||||||
\(10\) | −3.76480 | −1.19054 | ||||||||
\(11\) | 5.13106 | 1.54707 | 0.773536 | − | 0.633753i | \(-0.218486\pi\) | ||||
0.773536 | + | 0.633753i | \(0.218486\pi\) | |||||||
\(12\) | −1.69422 | −0.489078 | ||||||||
\(13\) | 2.53139 | 0.702082 | 0.351041 | − | 0.936360i | \(-0.385828\pi\) | ||||
0.351041 | + | 0.936360i | \(0.385828\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −6.37839 | −1.64689 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.63388 | 0.396273 | 0.198137 | − | 0.980174i | \(-0.436511\pi\) | ||||
0.198137 | + | 0.980174i | \(0.436511\pi\) | |||||||
\(18\) | 0.129635 | 0.0305552 | ||||||||
\(19\) | 2.24224 | 0.514404 | 0.257202 | − | 0.966358i | \(-0.417199\pi\) | ||||
0.257202 | + | 0.966358i | \(0.417199\pi\) | |||||||
\(20\) | 3.76480 | 0.841836 | ||||||||
\(21\) | 1.69422 | 0.369708 | ||||||||
\(22\) | −5.13106 | −1.09394 | ||||||||
\(23\) | 4.75107 | 0.990668 | 0.495334 | − | 0.868703i | \(-0.335046\pi\) | ||||
0.495334 | + | 0.868703i | \(0.335046\pi\) | |||||||
\(24\) | 1.69422 | 0.345830 | ||||||||
\(25\) | 9.17374 | 1.83475 | ||||||||
\(26\) | −2.53139 | −0.496447 | ||||||||
\(27\) | 5.30227 | 1.02042 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 3.82147 | 0.709628 | 0.354814 | − | 0.934937i | \(-0.384544\pi\) | ||||
0.354814 | + | 0.934937i | \(0.384544\pi\) | |||||||
\(30\) | 6.37839 | 1.16453 | ||||||||
\(31\) | 7.14240 | 1.28281 | 0.641406 | − | 0.767202i | \(-0.278351\pi\) | ||||
0.641406 | + | 0.767202i | \(0.278351\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −8.69311 | −1.51328 | ||||||||
\(34\) | −1.63388 | −0.280208 | ||||||||
\(35\) | −3.76480 | −0.636368 | ||||||||
\(36\) | −0.129635 | −0.0216058 | ||||||||
\(37\) | 2.28449 | 0.375568 | 0.187784 | − | 0.982210i | \(-0.439870\pi\) | ||||
0.187784 | + | 0.982210i | \(0.439870\pi\) | |||||||
\(38\) | −2.24224 | −0.363739 | ||||||||
\(39\) | −4.28873 | −0.686746 | ||||||||
\(40\) | −3.76480 | −0.595268 | ||||||||
\(41\) | −6.10878 | −0.954031 | −0.477015 | − | 0.878895i | \(-0.658281\pi\) | ||||
−0.477015 | + | 0.878895i | \(0.658281\pi\) | |||||||
\(42\) | −1.69422 | −0.261423 | ||||||||
\(43\) | −7.09119 | −1.08140 | −0.540698 | − | 0.841217i | \(-0.681840\pi\) | ||||
−0.540698 | + | 0.841217i | \(0.681840\pi\) | |||||||
\(44\) | 5.13106 | 0.773536 | ||||||||
\(45\) | −0.488049 | −0.0727540 | ||||||||
\(46\) | −4.75107 | −0.700508 | ||||||||
\(47\) | 1.29990 | 0.189610 | 0.0948048 | − | 0.995496i | \(-0.469777\pi\) | ||||
0.0948048 | + | 0.995496i | \(0.469777\pi\) | |||||||
\(48\) | −1.69422 | −0.244539 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.17374 | −1.29736 | ||||||||
\(51\) | −2.76814 | −0.387617 | ||||||||
\(52\) | 2.53139 | 0.351041 | ||||||||
\(53\) | 1.88649 | 0.259129 | 0.129564 | − | 0.991571i | \(-0.458642\pi\) | ||||
0.129564 | + | 0.991571i | \(0.458642\pi\) | |||||||
\(54\) | −5.30227 | −0.721548 | ||||||||
\(55\) | 19.3174 | 2.60476 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −3.79883 | −0.503167 | ||||||||
\(58\) | −3.82147 | −0.501783 | ||||||||
\(59\) | 7.44350 | 0.969061 | 0.484530 | − | 0.874774i | \(-0.338991\pi\) | ||||
0.484530 | + | 0.874774i | \(0.338991\pi\) | |||||||
\(60\) | −6.37839 | −0.823446 | ||||||||
\(61\) | −0.00800210 | −0.00102456 | −0.000512282 | − | 1.00000i | \(-0.500163\pi\) | ||||
−0.000512282 | 1.00000i | \(0.500163\pi\) | ||||||||
\(62\) | −7.14240 | −0.907085 | ||||||||
\(63\) | 0.129635 | 0.0163324 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.53020 | 1.18208 | ||||||||
\(66\) | 8.69311 | 1.07005 | ||||||||
\(67\) | 0.701020 | 0.0856432 | 0.0428216 | − | 0.999083i | \(-0.486365\pi\) | ||||
0.0428216 | + | 0.999083i | \(0.486365\pi\) | |||||||
\(68\) | 1.63388 | 0.198137 | ||||||||
\(69\) | −8.04934 | −0.969027 | ||||||||
\(70\) | 3.76480 | 0.449980 | ||||||||
\(71\) | −3.28126 | −0.389414 | −0.194707 | − | 0.980861i | \(-0.562376\pi\) | ||||
−0.194707 | + | 0.980861i | \(0.562376\pi\) | |||||||
\(72\) | 0.129635 | 0.0152776 | ||||||||
\(73\) | −2.75032 | −0.321900 | −0.160950 | − | 0.986963i | \(-0.551456\pi\) | ||||
−0.160950 | + | 0.986963i | \(0.551456\pi\) | |||||||
\(74\) | −2.28449 | −0.265567 | ||||||||
\(75\) | −15.5423 | −1.79467 | ||||||||
\(76\) | 2.24224 | 0.257202 | ||||||||
\(77\) | −5.13106 | −0.584738 | ||||||||
\(78\) | 4.28873 | 0.485603 | ||||||||
\(79\) | 3.70673 | 0.417040 | 0.208520 | − | 0.978018i | \(-0.433135\pi\) | ||||
0.208520 | + | 0.978018i | \(0.433135\pi\) | |||||||
\(80\) | 3.76480 | 0.420918 | ||||||||
\(81\) | −8.59429 | −0.954921 | ||||||||
\(82\) | 6.10878 | 0.674601 | ||||||||
\(83\) | 7.74981 | 0.850653 | 0.425326 | − | 0.905040i | \(-0.360159\pi\) | ||||
0.425326 | + | 0.905040i | \(0.360159\pi\) | |||||||
\(84\) | 1.69422 | 0.184854 | ||||||||
\(85\) | 6.15123 | 0.667194 | ||||||||
\(86\) | 7.09119 | 0.764663 | ||||||||
\(87\) | −6.47438 | −0.694127 | ||||||||
\(88\) | −5.13106 | −0.546972 | ||||||||
\(89\) | −8.90310 | −0.943727 | −0.471864 | − | 0.881672i | \(-0.656419\pi\) | ||||
−0.471864 | + | 0.881672i | \(0.656419\pi\) | |||||||
\(90\) | 0.488049 | 0.0514449 | ||||||||
\(91\) | −2.53139 | −0.265362 | ||||||||
\(92\) | 4.75107 | 0.495334 | ||||||||
\(93\) | −12.1008 | −1.25479 | ||||||||
\(94\) | −1.29990 | −0.134074 | ||||||||
\(95\) | 8.44158 | 0.866088 | ||||||||
\(96\) | 1.69422 | 0.172915 | ||||||||
\(97\) | −8.92397 | −0.906092 | −0.453046 | − | 0.891487i | \(-0.649663\pi\) | ||||
−0.453046 | + | 0.891487i | \(0.649663\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −0.665163 | −0.0668514 | ||||||||
\(100\) | 9.17374 | 0.917374 | ||||||||
\(101\) | −10.5709 | −1.05185 | −0.525924 | − | 0.850532i | \(-0.676280\pi\) | ||||
−0.525924 | + | 0.850532i | \(0.676280\pi\) | |||||||
\(102\) | 2.76814 | 0.274087 | ||||||||
\(103\) | 0.247124 | 0.0243498 | 0.0121749 | − | 0.999926i | \(-0.496125\pi\) | ||||
0.0121749 | + | 0.999926i | \(0.496125\pi\) | |||||||
\(104\) | −2.53139 | −0.248224 | ||||||||
\(105\) | 6.37839 | 0.622467 | ||||||||
\(106\) | −1.88649 | −0.183232 | ||||||||
\(107\) | 4.44791 | 0.429996 | 0.214998 | − | 0.976614i | \(-0.431026\pi\) | ||||
0.214998 | + | 0.976614i | \(0.431026\pi\) | |||||||
\(108\) | 5.30227 | 0.510212 | ||||||||
\(109\) | 4.93957 | 0.473125 | 0.236563 | − | 0.971616i | \(-0.423979\pi\) | ||||
0.236563 | + | 0.971616i | \(0.423979\pi\) | |||||||
\(110\) | −19.3174 | −1.84184 | ||||||||
\(111\) | −3.87042 | −0.367364 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 3.76323 | 0.354015 | 0.177008 | − | 0.984209i | \(-0.443358\pi\) | ||||
0.177008 | + | 0.984209i | \(0.443358\pi\) | |||||||
\(114\) | 3.79883 | 0.355793 | ||||||||
\(115\) | 17.8869 | 1.66796 | ||||||||
\(116\) | 3.82147 | 0.354814 | ||||||||
\(117\) | −0.328156 | −0.0303381 | ||||||||
\(118\) | −7.44350 | −0.685229 | ||||||||
\(119\) | −1.63388 | −0.149777 | ||||||||
\(120\) | 6.37839 | 0.582264 | ||||||||
\(121\) | 15.3277 | 1.39343 | ||||||||
\(122\) | 0.00800210 | 0.000724476 0 | ||||||||
\(123\) | 10.3496 | 0.933190 | ||||||||
\(124\) | 7.14240 | 0.641406 | ||||||||
\(125\) | 15.7133 | 1.40544 | ||||||||
\(126\) | −0.129635 | −0.0115488 | ||||||||
\(127\) | −2.90453 | −0.257735 | −0.128868 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128868 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.0140 | 1.05777 | ||||||||
\(130\) | −9.53020 | −0.835854 | ||||||||
\(131\) | −7.95468 | −0.695003 | −0.347502 | − | 0.937679i | \(-0.612970\pi\) | ||||
−0.347502 | + | 0.937679i | \(0.612970\pi\) | |||||||
\(132\) | −8.69311 | −0.756638 | ||||||||
\(133\) | −2.24224 | −0.194427 | ||||||||
\(134\) | −0.701020 | −0.0605589 | ||||||||
\(135\) | 19.9620 | 1.71806 | ||||||||
\(136\) | −1.63388 | −0.140104 | ||||||||
\(137\) | −0.336958 | −0.0287883 | −0.0143941 | − | 0.999896i | \(-0.504582\pi\) | ||||
−0.0143941 | + | 0.999896i | \(0.504582\pi\) | |||||||
\(138\) | 8.04934 | 0.685206 | ||||||||
\(139\) | 13.2883 | 1.12709 | 0.563547 | − | 0.826084i | \(-0.309436\pi\) | ||||
0.563547 | + | 0.826084i | \(0.309436\pi\) | |||||||
\(140\) | −3.76480 | −0.318184 | ||||||||
\(141\) | −2.20231 | −0.185468 | ||||||||
\(142\) | 3.28126 | 0.275358 | ||||||||
\(143\) | 12.9887 | 1.08617 | ||||||||
\(144\) | −0.129635 | −0.0108029 | ||||||||
\(145\) | 14.3871 | 1.19478 | ||||||||
\(146\) | 2.75032 | 0.227618 | ||||||||
\(147\) | −1.69422 | −0.139737 | ||||||||
\(148\) | 2.28449 | 0.187784 | ||||||||
\(149\) | −2.03542 | −0.166748 | −0.0833742 | − | 0.996518i | \(-0.526570\pi\) | ||||
−0.0833742 | + | 0.996518i | \(0.526570\pi\) | |||||||
\(150\) | 15.5423 | 1.26902 | ||||||||
\(151\) | 1.78140 | 0.144968 | 0.0724842 | − | 0.997370i | \(-0.476907\pi\) | ||||
0.0724842 | + | 0.997370i | \(0.476907\pi\) | |||||||
\(152\) | −2.24224 | −0.181869 | ||||||||
\(153\) | −0.211807 | −0.0171236 | ||||||||
\(154\) | 5.13106 | 0.413472 | ||||||||
\(155\) | 26.8897 | 2.15983 | ||||||||
\(156\) | −4.28873 | −0.343373 | ||||||||
\(157\) | 4.79958 | 0.383049 | 0.191524 | − | 0.981488i | \(-0.438657\pi\) | ||||
0.191524 | + | 0.981488i | \(0.438657\pi\) | |||||||
\(158\) | −3.70673 | −0.294892 | ||||||||
\(159\) | −3.19612 | −0.253468 | ||||||||
\(160\) | −3.76480 | −0.297634 | ||||||||
\(161\) | −4.75107 | −0.374437 | ||||||||
\(162\) | 8.59429 | 0.675231 | ||||||||
\(163\) | 2.74208 | 0.214776 | 0.107388 | − | 0.994217i | \(-0.465751\pi\) | ||||
0.107388 | + | 0.994217i | \(0.465751\pi\) | |||||||
\(164\) | −6.10878 | −0.477015 | ||||||||
\(165\) | −32.7279 | −2.54786 | ||||||||
\(166\) | −7.74981 | −0.601502 | ||||||||
\(167\) | −17.5930 | −1.36139 | −0.680693 | − | 0.732569i | \(-0.738321\pi\) | ||||
−0.680693 | + | 0.732569i | \(0.738321\pi\) | |||||||
\(168\) | −1.69422 | −0.130712 | ||||||||
\(169\) | −6.59204 | −0.507080 | ||||||||
\(170\) | −6.15123 | −0.471778 | ||||||||
\(171\) | −0.290672 | −0.0222282 | ||||||||
\(172\) | −7.09119 | −0.540698 | ||||||||
\(173\) | −14.4727 | −1.10034 | −0.550168 | − | 0.835054i | \(-0.685436\pi\) | ||||
−0.550168 | + | 0.835054i | \(0.685436\pi\) | |||||||
\(174\) | 6.47438 | 0.490822 | ||||||||
\(175\) | −9.17374 | −0.693470 | ||||||||
\(176\) | 5.13106 | 0.386768 | ||||||||
\(177\) | −12.6109 | −0.947892 | ||||||||
\(178\) | 8.90310 | 0.667316 | ||||||||
\(179\) | −16.2018 | −1.21098 | −0.605491 | − | 0.795852i | \(-0.707023\pi\) | ||||
−0.605491 | + | 0.795852i | \(0.707023\pi\) | |||||||
\(180\) | −0.488049 | −0.0363770 | ||||||||
\(181\) | 3.75290 | 0.278951 | 0.139475 | − | 0.990226i | \(-0.455458\pi\) | ||||
0.139475 | + | 0.990226i | \(0.455458\pi\) | |||||||
\(182\) | 2.53139 | 0.187639 | ||||||||
\(183\) | 0.0135573 | 0.00100218 | ||||||||
\(184\) | −4.75107 | −0.350254 | ||||||||
\(185\) | 8.60066 | 0.632333 | ||||||||
\(186\) | 12.1008 | 0.887270 | ||||||||
\(187\) | 8.38352 | 0.613063 | ||||||||
\(188\) | 1.29990 | 0.0948048 | ||||||||
\(189\) | −5.30227 | −0.385684 | ||||||||
\(190\) | −8.44158 | −0.612416 | ||||||||
\(191\) | 15.4237 | 1.11602 | 0.558010 | − | 0.829834i | \(-0.311565\pi\) | ||||
0.558010 | + | 0.829834i | \(0.311565\pi\) | |||||||
\(192\) | −1.69422 | −0.122269 | ||||||||
\(193\) | −24.4004 | −1.75638 | −0.878191 | − | 0.478310i | \(-0.841250\pi\) | ||||
−0.878191 | + | 0.478310i | \(0.841250\pi\) | |||||||
\(194\) | 8.92397 | 0.640704 | ||||||||
\(195\) | −16.1462 | −1.15625 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −14.1409 | −1.00750 | −0.503750 | − | 0.863849i | \(-0.668047\pi\) | ||||
−0.503750 | + | 0.863849i | \(0.668047\pi\) | |||||||
\(198\) | 0.665163 | 0.0472710 | ||||||||
\(199\) | 5.58283 | 0.395756 | 0.197878 | − | 0.980227i | \(-0.436595\pi\) | ||||
0.197878 | + | 0.980227i | \(0.436595\pi\) | |||||||
\(200\) | −9.17374 | −0.648682 | ||||||||
\(201\) | −1.18768 | −0.0837724 | ||||||||
\(202\) | 10.5709 | 0.743768 | ||||||||
\(203\) | −3.82147 | −0.268214 | ||||||||
\(204\) | −2.76814 | −0.193809 | ||||||||
\(205\) | −22.9983 | −1.60627 | ||||||||
\(206\) | −0.247124 | −0.0172179 | ||||||||
\(207\) | −0.615904 | −0.0428083 | ||||||||
\(208\) | 2.53139 | 0.175521 | ||||||||
\(209\) | 11.5050 | 0.795820 | ||||||||
\(210\) | −6.37839 | −0.440151 | ||||||||
\(211\) | 19.1382 | 1.31753 | 0.658765 | − | 0.752349i | \(-0.271079\pi\) | ||||
0.658765 | + | 0.752349i | \(0.271079\pi\) | |||||||
\(212\) | 1.88649 | 0.129564 | ||||||||
\(213\) | 5.55917 | 0.380908 | ||||||||
\(214\) | −4.44791 | −0.304053 | ||||||||
\(215\) | −26.6969 | −1.82072 | ||||||||
\(216\) | −5.30227 | −0.360774 | ||||||||
\(217\) | −7.14240 | −0.484857 | ||||||||
\(218\) | −4.93957 | −0.334550 | ||||||||
\(219\) | 4.65963 | 0.314868 | ||||||||
\(220\) | 19.3174 | 1.30238 | ||||||||
\(221\) | 4.13599 | 0.278217 | ||||||||
\(222\) | 3.87042 | 0.259766 | ||||||||
\(223\) | −8.10489 | −0.542744 | −0.271372 | − | 0.962475i | \(-0.587477\pi\) | ||||
−0.271372 | + | 0.962475i | \(0.587477\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −1.18923 | −0.0792823 | ||||||||
\(226\) | −3.76323 | −0.250327 | ||||||||
\(227\) | −11.5098 | −0.763934 | −0.381967 | − | 0.924176i | \(-0.624753\pi\) | ||||
−0.381967 | + | 0.924176i | \(0.624753\pi\) | |||||||
\(228\) | −3.79883 | −0.251584 | ||||||||
\(229\) | −7.41334 | −0.489887 | −0.244944 | − | 0.969537i | \(-0.578769\pi\) | ||||
−0.244944 | + | 0.969537i | \(0.578769\pi\) | |||||||
\(230\) | −17.8869 | −1.17942 | ||||||||
\(231\) | 8.69311 | 0.571965 | ||||||||
\(232\) | −3.82147 | −0.250891 | ||||||||
\(233\) | −26.0542 | −1.70687 | −0.853433 | − | 0.521202i | \(-0.825484\pi\) | ||||
−0.853433 | + | 0.521202i | \(0.825484\pi\) | |||||||
\(234\) | 0.328156 | 0.0214523 | ||||||||
\(235\) | 4.89386 | 0.319240 | ||||||||
\(236\) | 7.44350 | 0.484530 | ||||||||
\(237\) | −6.28000 | −0.407930 | ||||||||
\(238\) | 1.63388 | 0.105909 | ||||||||
\(239\) | −4.13675 | −0.267584 | −0.133792 | − | 0.991009i | \(-0.542715\pi\) | ||||
−0.133792 | + | 0.991009i | \(0.542715\pi\) | |||||||
\(240\) | −6.37839 | −0.411723 | ||||||||
\(241\) | 14.4204 | 0.928897 | 0.464448 | − | 0.885600i | \(-0.346253\pi\) | ||||
0.464448 | + | 0.885600i | \(0.346253\pi\) | |||||||
\(242\) | −15.3277 | −0.985304 | ||||||||
\(243\) | −1.34625 | −0.0863617 | ||||||||
\(244\) | −0.00800210 | −0.000512282 0 | ||||||||
\(245\) | 3.76480 | 0.240524 | ||||||||
\(246\) | −10.3496 | −0.659865 | ||||||||
\(247\) | 5.67598 | 0.361154 | ||||||||
\(248\) | −7.14240 | −0.453543 | ||||||||
\(249\) | −13.1299 | −0.832071 | ||||||||
\(250\) | −15.7133 | −0.993798 | ||||||||
\(251\) | 13.2145 | 0.834091 | 0.417046 | − | 0.908886i | \(-0.363066\pi\) | ||||
0.417046 | + | 0.908886i | \(0.363066\pi\) | |||||||
\(252\) | 0.129635 | 0.00816622 | ||||||||
\(253\) | 24.3780 | 1.53263 | ||||||||
\(254\) | 2.90453 | 0.182246 | ||||||||
\(255\) | −10.4215 | −0.652620 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.32744 | 0.207560 | 0.103780 | − | 0.994600i | \(-0.466906\pi\) | ||||
0.103780 | + | 0.994600i | \(0.466906\pi\) | |||||||
\(258\) | −12.0140 | −0.747959 | ||||||||
\(259\) | −2.28449 | −0.141951 | ||||||||
\(260\) | 9.53020 | 0.591038 | ||||||||
\(261\) | −0.495394 | −0.0306641 | ||||||||
\(262\) | 7.95468 | 0.491442 | ||||||||
\(263\) | −22.8100 | −1.40653 | −0.703264 | − | 0.710929i | \(-0.748275\pi\) | ||||
−0.703264 | + | 0.710929i | \(0.748275\pi\) | |||||||
\(264\) | 8.69311 | 0.535024 | ||||||||
\(265\) | 7.10225 | 0.436288 | ||||||||
\(266\) | 2.24224 | 0.137480 | ||||||||
\(267\) | 15.0838 | 0.923112 | ||||||||
\(268\) | 0.701020 | 0.0428216 | ||||||||
\(269\) | −2.36176 | −0.143999 | −0.0719995 | − | 0.997405i | \(-0.522938\pi\) | ||||
−0.0719995 | + | 0.997405i | \(0.522938\pi\) | |||||||
\(270\) | −19.9620 | −1.21485 | ||||||||
\(271\) | −6.66509 | −0.404875 | −0.202438 | − | 0.979295i | \(-0.564886\pi\) | ||||
−0.202438 | + | 0.979295i | \(0.564886\pi\) | |||||||
\(272\) | 1.63388 | 0.0990684 | ||||||||
\(273\) | 4.28873 | 0.259566 | ||||||||
\(274\) | 0.336958 | 0.0203564 | ||||||||
\(275\) | 47.0710 | 2.83849 | ||||||||
\(276\) | −8.04934 | −0.484514 | ||||||||
\(277\) | −25.7492 | −1.54712 | −0.773560 | − | 0.633723i | \(-0.781526\pi\) | ||||
−0.773560 | + | 0.633723i | \(0.781526\pi\) | |||||||
\(278\) | −13.2883 | −0.796976 | ||||||||
\(279\) | −0.925902 | −0.0554323 | ||||||||
\(280\) | 3.76480 | 0.224990 | ||||||||
\(281\) | 7.24230 | 0.432040 | 0.216020 | − | 0.976389i | \(-0.430692\pi\) | ||||
0.216020 | + | 0.976389i | \(0.430692\pi\) | |||||||
\(282\) | 2.20231 | 0.131146 | ||||||||
\(283\) | −5.52079 | −0.328177 | −0.164089 | − | 0.986446i | \(-0.552468\pi\) | ||||
−0.164089 | + | 0.986446i | \(0.552468\pi\) | |||||||
\(284\) | −3.28126 | −0.194707 | ||||||||
\(285\) | −14.3019 | −0.847169 | ||||||||
\(286\) | −12.9887 | −0.768039 | ||||||||
\(287\) | 6.10878 | 0.360590 | ||||||||
\(288\) | 0.129635 | 0.00763879 | ||||||||
\(289\) | −14.3304 | −0.842967 | ||||||||
\(290\) | −14.3871 | −0.844838 | ||||||||
\(291\) | 15.1191 | 0.886299 | ||||||||
\(292\) | −2.75032 | −0.160950 | ||||||||
\(293\) | 4.12082 | 0.240741 | 0.120370 | − | 0.992729i | \(-0.461592\pi\) | ||||
0.120370 | + | 0.992729i | \(0.461592\pi\) | |||||||
\(294\) | 1.69422 | 0.0988086 | ||||||||
\(295\) | 28.0233 | 1.63158 | ||||||||
\(296\) | −2.28449 | −0.132783 | ||||||||
\(297\) | 27.2063 | 1.57867 | ||||||||
\(298\) | 2.03542 | 0.117909 | ||||||||
\(299\) | 12.0268 | 0.695530 | ||||||||
\(300\) | −15.5423 | −0.897335 | ||||||||
\(301\) | 7.09119 | 0.408729 | ||||||||
\(302\) | −1.78140 | −0.102508 | ||||||||
\(303\) | 17.9094 | 1.02887 | ||||||||
\(304\) | 2.24224 | 0.128601 | ||||||||
\(305\) | −0.0301263 | −0.00172503 | ||||||||
\(306\) | 0.211807 | 0.0121082 | ||||||||
\(307\) | 15.1726 | 0.865944 | 0.432972 | − | 0.901407i | \(-0.357465\pi\) | ||||
0.432972 | + | 0.901407i | \(0.357465\pi\) | |||||||
\(308\) | −5.13106 | −0.292369 | ||||||||
\(309\) | −0.418681 | −0.0238179 | ||||||||
\(310\) | −26.8897 | −1.52723 | ||||||||
\(311\) | −4.58694 | −0.260101 | −0.130051 | − | 0.991507i | \(-0.541514\pi\) | ||||
−0.130051 | + | 0.991507i | \(0.541514\pi\) | |||||||
\(312\) | 4.28873 | 0.242801 | ||||||||
\(313\) | −0.591030 | −0.0334070 | −0.0167035 | − | 0.999860i | \(-0.505317\pi\) | ||||
−0.0167035 | + | 0.999860i | \(0.505317\pi\) | |||||||
\(314\) | −4.79958 | −0.270856 | ||||||||
\(315\) | 0.488049 | 0.0274984 | ||||||||
\(316\) | 3.70673 | 0.208520 | ||||||||
\(317\) | 18.1207 | 1.01776 | 0.508881 | − | 0.860837i | \(-0.330059\pi\) | ||||
0.508881 | + | 0.860837i | \(0.330059\pi\) | |||||||
\(318\) | 3.19612 | 0.179229 | ||||||||
\(319\) | 19.6082 | 1.09785 | ||||||||
\(320\) | 3.76480 | 0.210459 | ||||||||
\(321\) | −7.53572 | −0.420603 | ||||||||
\(322\) | 4.75107 | 0.264767 | ||||||||
\(323\) | 3.66354 | 0.203845 | ||||||||
\(324\) | −8.59429 | −0.477461 | ||||||||
\(325\) | 23.2224 | 1.28814 | ||||||||
\(326\) | −2.74208 | −0.151870 | ||||||||
\(327\) | −8.36870 | −0.462790 | ||||||||
\(328\) | 6.10878 | 0.337301 | ||||||||
\(329\) | −1.29990 | −0.0716657 | ||||||||
\(330\) | 32.7279 | 1.80161 | ||||||||
\(331\) | 24.2633 | 1.33363 | 0.666816 | − | 0.745223i | \(-0.267657\pi\) | ||||
0.666816 | + | 0.745223i | \(0.267657\pi\) | |||||||
\(332\) | 7.74981 | 0.425326 | ||||||||
\(333\) | −0.296149 | −0.0162289 | ||||||||
\(334\) | 17.5930 | 0.962645 | ||||||||
\(335\) | 2.63920 | 0.144195 | ||||||||
\(336\) | 1.69422 | 0.0924270 | ||||||||
\(337\) | 20.5308 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(338\) | 6.59204 | 0.358560 | ||||||||
\(339\) | −6.37573 | −0.346282 | ||||||||
\(340\) | 6.15123 | 0.333597 | ||||||||
\(341\) | 36.6480 | 1.98460 | ||||||||
\(342\) | 0.290672 | 0.0157177 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.09119 | 0.382331 | ||||||||
\(345\) | −30.3042 | −1.63152 | ||||||||
\(346\) | 14.4727 | 0.778055 | ||||||||
\(347\) | 0.619877 | 0.0332767 | 0.0166384 | − | 0.999862i | \(-0.494704\pi\) | ||||
0.0166384 | + | 0.999862i | \(0.494704\pi\) | |||||||
\(348\) | −6.47438 | −0.347063 | ||||||||
\(349\) | 0.293252 | 0.0156974 | 0.00784871 | − | 0.999969i | \(-0.497502\pi\) | ||||
0.00784871 | + | 0.999969i | \(0.497502\pi\) | |||||||
\(350\) | 9.17374 | 0.490357 | ||||||||
\(351\) | 13.4221 | 0.716421 | ||||||||
\(352\) | −5.13106 | −0.273486 | ||||||||
\(353\) | −30.7987 | −1.63925 | −0.819625 | − | 0.572900i | \(-0.805818\pi\) | ||||
−0.819625 | + | 0.572900i | \(0.805818\pi\) | |||||||
\(354\) | 12.6109 | 0.670261 | ||||||||
\(355\) | −12.3533 | −0.655646 | ||||||||
\(356\) | −8.90310 | −0.471864 | ||||||||
\(357\) | 2.76814 | 0.146505 | ||||||||
\(358\) | 16.2018 | 0.856294 | ||||||||
\(359\) | −13.9496 | −0.736231 | −0.368116 | − | 0.929780i | \(-0.619997\pi\) | ||||
−0.368116 | + | 0.929780i | \(0.619997\pi\) | |||||||
\(360\) | 0.488049 | 0.0257224 | ||||||||
\(361\) | −13.9724 | −0.735388 | ||||||||
\(362\) | −3.75290 | −0.197248 | ||||||||
\(363\) | −25.9685 | −1.36299 | ||||||||
\(364\) | −2.53139 | −0.132681 | ||||||||
\(365\) | −10.3544 | −0.541974 | ||||||||
\(366\) | −0.0135573 | −0.000708650 0 | ||||||||
\(367\) | −18.7430 | −0.978376 | −0.489188 | − | 0.872178i | \(-0.662707\pi\) | ||||
−0.489188 | + | 0.872178i | \(0.662707\pi\) | |||||||
\(368\) | 4.75107 | 0.247667 | ||||||||
\(369\) | 0.791909 | 0.0412251 | ||||||||
\(370\) | −8.60066 | −0.447127 | ||||||||
\(371\) | −1.88649 | −0.0979416 | ||||||||
\(372\) | −12.1008 | −0.627395 | ||||||||
\(373\) | 0.233693 | 0.0121002 | 0.00605009 | − | 0.999982i | \(-0.498074\pi\) | ||||
0.00605009 | + | 0.999982i | \(0.498074\pi\) | |||||||
\(374\) | −8.38352 | −0.433501 | ||||||||
\(375\) | −26.6217 | −1.37474 | ||||||||
\(376\) | −1.29990 | −0.0670372 | ||||||||
\(377\) | 9.67364 | 0.498218 | ||||||||
\(378\) | 5.30227 | 0.272720 | ||||||||
\(379\) | 22.0112 | 1.13064 | 0.565319 | − | 0.824873i | \(-0.308753\pi\) | ||||
0.565319 | + | 0.824873i | \(0.308753\pi\) | |||||||
\(380\) | 8.44158 | 0.433044 | ||||||||
\(381\) | 4.92090 | 0.252105 | ||||||||
\(382\) | −15.4237 | −0.789145 | ||||||||
\(383\) | 6.39092 | 0.326561 | 0.163280 | − | 0.986580i | \(-0.447792\pi\) | ||||
0.163280 | + | 0.986580i | \(0.447792\pi\) | |||||||
\(384\) | 1.69422 | 0.0864576 | ||||||||
\(385\) | −19.3174 | −0.984507 | ||||||||
\(386\) | 24.4004 | 1.24195 | ||||||||
\(387\) | 0.919264 | 0.0467288 | ||||||||
\(388\) | −8.92397 | −0.453046 | ||||||||
\(389\) | 26.6128 | 1.34932 | 0.674662 | − | 0.738127i | \(-0.264289\pi\) | ||||
0.674662 | + | 0.738127i | \(0.264289\pi\) | |||||||
\(390\) | 16.1462 | 0.817595 | ||||||||
\(391\) | 7.76267 | 0.392575 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 13.4769 | 0.679821 | ||||||||
\(394\) | 14.1409 | 0.712411 | ||||||||
\(395\) | 13.9551 | 0.702158 | ||||||||
\(396\) | −0.665163 | −0.0334257 | ||||||||
\(397\) | −6.68899 | −0.335711 | −0.167856 | − | 0.985812i | \(-0.553684\pi\) | ||||
−0.167856 | + | 0.985812i | \(0.553684\pi\) | |||||||
\(398\) | −5.58283 | −0.279842 | ||||||||
\(399\) | 3.79883 | 0.190179 | ||||||||
\(400\) | 9.17374 | 0.458687 | ||||||||
\(401\) | −8.28110 | −0.413538 | −0.206769 | − | 0.978390i | \(-0.566295\pi\) | ||||
−0.206769 | + | 0.978390i | \(0.566295\pi\) | |||||||
\(402\) | 1.18768 | 0.0592360 | ||||||||
\(403\) | 18.0802 | 0.900640 | ||||||||
\(404\) | −10.5709 | −0.525924 | ||||||||
\(405\) | −32.3558 | −1.60777 | ||||||||
\(406\) | 3.82147 | 0.189656 | ||||||||
\(407\) | 11.7218 | 0.581031 | ||||||||
\(408\) | 2.76814 | 0.137043 | ||||||||
\(409\) | 3.04974 | 0.150800 | 0.0753999 | − | 0.997153i | \(-0.475977\pi\) | ||||
0.0753999 | + | 0.997153i | \(0.475977\pi\) | |||||||
\(410\) | 22.9983 | 1.13581 | ||||||||
\(411\) | 0.570880 | 0.0281594 | ||||||||
\(412\) | 0.247124 | 0.0121749 | ||||||||
\(413\) | −7.44350 | −0.366271 | ||||||||
\(414\) | 0.615904 | 0.0302700 | ||||||||
\(415\) | 29.1765 | 1.43222 | ||||||||
\(416\) | −2.53139 | −0.124112 | ||||||||
\(417\) | −22.5132 | −1.10247 | ||||||||
\(418\) | −11.5050 | −0.562730 | ||||||||
\(419\) | 33.0604 | 1.61511 | 0.807554 | − | 0.589794i | \(-0.200791\pi\) | ||||
0.807554 | + | 0.589794i | \(0.200791\pi\) | |||||||
\(420\) | 6.37839 | 0.311233 | ||||||||
\(421\) | 26.2130 | 1.27754 | 0.638771 | − | 0.769397i | \(-0.279443\pi\) | ||||
0.638771 | + | 0.769397i | \(0.279443\pi\) | |||||||
\(422\) | −19.1382 | −0.931635 | ||||||||
\(423\) | −0.168512 | −0.00819333 | ||||||||
\(424\) | −1.88649 | −0.0916159 | ||||||||
\(425\) | 14.9888 | 0.727062 | ||||||||
\(426\) | −5.55917 | −0.269342 | ||||||||
\(427\) | 0.00800210 | 0.000387249 0 | ||||||||
\(428\) | 4.44791 | 0.214998 | ||||||||
\(429\) | −22.0057 | −1.06245 | ||||||||
\(430\) | 26.6969 | 1.28744 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | 5.30227 | 0.255106 | ||||||||
\(433\) | 15.9959 | 0.768713 | 0.384356 | − | 0.923185i | \(-0.374423\pi\) | ||||
0.384356 | + | 0.923185i | \(0.374423\pi\) | |||||||
\(434\) | 7.14240 | 0.342846 | ||||||||
\(435\) | −24.3748 | −1.16868 | ||||||||
\(436\) | 4.93957 | 0.236563 | ||||||||
\(437\) | 10.6530 | 0.509604 | ||||||||
\(438\) | −4.65963 | −0.222646 | ||||||||
\(439\) | −31.2755 | −1.49270 | −0.746350 | − | 0.665554i | \(-0.768195\pi\) | ||||
−0.746350 | + | 0.665554i | \(0.768195\pi\) | |||||||
\(440\) | −19.3174 | −0.920922 | ||||||||
\(441\) | −0.129635 | −0.00617308 | ||||||||
\(442\) | −4.13599 | −0.196729 | ||||||||
\(443\) | −26.1389 | −1.24190 | −0.620949 | − | 0.783851i | \(-0.713253\pi\) | ||||
−0.620949 | + | 0.783851i | \(0.713253\pi\) | |||||||
\(444\) | −3.87042 | −0.183682 | ||||||||
\(445\) | −33.5184 | −1.58893 | ||||||||
\(446\) | 8.10489 | 0.383778 | ||||||||
\(447\) | 3.44845 | 0.163106 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 14.1690 | 0.668678 | 0.334339 | − | 0.942453i | \(-0.391487\pi\) | ||||
0.334339 | + | 0.942453i | \(0.391487\pi\) | |||||||
\(450\) | 1.18923 | 0.0560611 | ||||||||
\(451\) | −31.3445 | −1.47595 | ||||||||
\(452\) | 3.76323 | 0.177008 | ||||||||
\(453\) | −3.01808 | −0.141802 | ||||||||
\(454\) | 11.5098 | 0.540183 | ||||||||
\(455\) | −9.53020 | −0.446783 | ||||||||
\(456\) | 3.79883 | 0.177897 | ||||||||
\(457\) | 14.2280 | 0.665557 | 0.332779 | − | 0.943005i | \(-0.392014\pi\) | ||||
0.332779 | + | 0.943005i | \(0.392014\pi\) | |||||||
\(458\) | 7.41334 | 0.346402 | ||||||||
\(459\) | 8.66327 | 0.404367 | ||||||||
\(460\) | 17.8869 | 0.833979 | ||||||||
\(461\) | 19.6352 | 0.914504 | 0.457252 | − | 0.889337i | \(-0.348834\pi\) | ||||
0.457252 | + | 0.889337i | \(0.348834\pi\) | |||||||
\(462\) | −8.69311 | −0.404440 | ||||||||
\(463\) | −12.0254 | −0.558867 | −0.279433 | − | 0.960165i | \(-0.590147\pi\) | ||||
−0.279433 | + | 0.960165i | \(0.590147\pi\) | |||||||
\(464\) | 3.82147 | 0.177407 | ||||||||
\(465\) | −45.5570 | −2.11265 | ||||||||
\(466\) | 26.0542 | 1.20694 | ||||||||
\(467\) | −2.49381 | −0.115400 | −0.0576998 | − | 0.998334i | \(-0.518377\pi\) | ||||
−0.0576998 | + | 0.998334i | \(0.518377\pi\) | |||||||
\(468\) | −0.328156 | −0.0151690 | ||||||||
\(469\) | −0.701020 | −0.0323701 | ||||||||
\(470\) | −4.89386 | −0.225737 | ||||||||
\(471\) | −8.13153 | −0.374681 | ||||||||
\(472\) | −7.44350 | −0.342615 | ||||||||
\(473\) | −36.3853 | −1.67300 | ||||||||
\(474\) | 6.28000 | 0.288450 | ||||||||
\(475\) | 20.5697 | 0.943803 | ||||||||
\(476\) | −1.63388 | −0.0748886 | ||||||||
\(477\) | −0.244554 | −0.0111974 | ||||||||
\(478\) | 4.13675 | 0.189210 | ||||||||
\(479\) | 23.9177 | 1.09283 | 0.546415 | − | 0.837515i | \(-0.315992\pi\) | ||||
0.546415 | + | 0.837515i | \(0.315992\pi\) | |||||||
\(480\) | 6.37839 | 0.291132 | ||||||||
\(481\) | 5.78295 | 0.263680 | ||||||||
\(482\) | −14.4204 | −0.656829 | ||||||||
\(483\) | 8.04934 | 0.366258 | ||||||||
\(484\) | 15.3277 | 0.696715 | ||||||||
\(485\) | −33.5970 | −1.52556 | ||||||||
\(486\) | 1.34625 | 0.0610669 | ||||||||
\(487\) | 13.4212 | 0.608171 | 0.304085 | − | 0.952645i | \(-0.401649\pi\) | ||||
0.304085 | + | 0.952645i | \(0.401649\pi\) | |||||||
\(488\) | 0.00800210 | 0.000362238 0 | ||||||||
\(489\) | −4.64567 | −0.210084 | ||||||||
\(490\) | −3.76480 | −0.170076 | ||||||||
\(491\) | −12.6746 | −0.571995 | −0.285998 | − | 0.958230i | \(-0.592325\pi\) | ||||
−0.285998 | + | 0.958230i | \(0.592325\pi\) | |||||||
\(492\) | 10.3496 | 0.466595 | ||||||||
\(493\) | 6.24381 | 0.281207 | ||||||||
\(494\) | −5.67598 | −0.255375 | ||||||||
\(495\) | −2.50421 | −0.112556 | ||||||||
\(496\) | 7.14240 | 0.320703 | ||||||||
\(497\) | 3.28126 | 0.147185 | ||||||||
\(498\) | 13.1299 | 0.588363 | ||||||||
\(499\) | 30.7009 | 1.37436 | 0.687181 | − | 0.726486i | \(-0.258848\pi\) | ||||
0.687181 | + | 0.726486i | \(0.258848\pi\) | |||||||
\(500\) | 15.7133 | 0.702721 | ||||||||
\(501\) | 29.8063 | 1.33165 | ||||||||
\(502\) | −13.2145 | −0.589792 | ||||||||
\(503\) | −5.63591 | −0.251293 | −0.125646 | − | 0.992075i | \(-0.540100\pi\) | ||||
−0.125646 | + | 0.992075i | \(0.540100\pi\) | |||||||
\(504\) | −0.129635 | −0.00577439 | ||||||||
\(505\) | −39.7975 | −1.77096 | ||||||||
\(506\) | −24.3780 | −1.08374 | ||||||||
\(507\) | 11.1683 | 0.496003 | ||||||||
\(508\) | −2.90453 | −0.128868 | ||||||||
\(509\) | 40.0652 | 1.77586 | 0.887930 | − | 0.459979i | \(-0.152143\pi\) | ||||
0.887930 | + | 0.459979i | \(0.152143\pi\) | |||||||
\(510\) | 10.4215 | 0.461472 | ||||||||
\(511\) | 2.75032 | 0.121667 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 11.8890 | 0.524910 | ||||||||
\(514\) | −3.32744 | −0.146767 | ||||||||
\(515\) | 0.930373 | 0.0409971 | ||||||||
\(516\) | 12.0140 | 0.528887 | ||||||||
\(517\) | 6.66985 | 0.293340 | ||||||||
\(518\) | 2.28449 | 0.100375 | ||||||||
\(519\) | 24.5198 | 1.07630 | ||||||||
\(520\) | −9.53020 | −0.417927 | ||||||||
\(521\) | −12.7582 | −0.558947 | −0.279474 | − | 0.960153i | \(-0.590160\pi\) | ||||
−0.279474 | + | 0.960153i | \(0.590160\pi\) | |||||||
\(522\) | 0.495394 | 0.0216828 | ||||||||
\(523\) | −22.1792 | −0.969829 | −0.484915 | − | 0.874561i | \(-0.661149\pi\) | ||||
−0.484915 | + | 0.874561i | \(0.661149\pi\) | |||||||
\(524\) | −7.95468 | −0.347502 | ||||||||
\(525\) | 15.5423 | 0.678321 | ||||||||
\(526\) | 22.8100 | 0.994565 | ||||||||
\(527\) | 11.6698 | 0.508344 | ||||||||
\(528\) | −8.69311 | −0.378319 | ||||||||
\(529\) | −0.427289 | −0.0185778 | ||||||||
\(530\) | −7.10225 | −0.308502 | ||||||||
\(531\) | −0.964935 | −0.0418746 | ||||||||
\(532\) | −2.24224 | −0.0972133 | ||||||||
\(533\) | −15.4637 | −0.669808 | ||||||||
\(534\) | −15.0838 | −0.652739 | ||||||||
\(535\) | 16.7455 | 0.723972 | ||||||||
\(536\) | −0.701020 | −0.0302794 | ||||||||
\(537\) | 27.4494 | 1.18453 | ||||||||
\(538\) | 2.36176 | 0.101823 | ||||||||
\(539\) | 5.13106 | 0.221010 | ||||||||
\(540\) | 19.9620 | 0.859029 | ||||||||
\(541\) | −6.75570 | −0.290450 | −0.145225 | − | 0.989399i | \(-0.546391\pi\) | ||||
−0.145225 | + | 0.989399i | \(0.546391\pi\) | |||||||
\(542\) | 6.66509 | 0.286290 | ||||||||
\(543\) | −6.35821 | −0.272857 | ||||||||
\(544\) | −1.63388 | −0.0700519 | ||||||||
\(545\) | 18.5965 | 0.796587 | ||||||||
\(546\) | −4.28873 | −0.183541 | ||||||||
\(547\) | 20.5399 | 0.878221 | 0.439110 | − | 0.898433i | \(-0.355294\pi\) | ||||
0.439110 | + | 0.898433i | \(0.355294\pi\) | |||||||
\(548\) | −0.336958 | −0.0143941 | ||||||||
\(549\) | 0.00103735 | 4.42730e−5 0 | ||||||||
\(550\) | −47.0710 | −2.00711 | ||||||||
\(551\) | 8.56863 | 0.365036 | ||||||||
\(552\) | 8.04934 | 0.342603 | ||||||||
\(553\) | −3.70673 | −0.157626 | ||||||||
\(554\) | 25.7492 | 1.09398 | ||||||||
\(555\) | −14.5714 | −0.618520 | ||||||||
\(556\) | 13.2883 | 0.563547 | ||||||||
\(557\) | 30.3295 | 1.28510 | 0.642550 | − | 0.766244i | \(-0.277876\pi\) | ||||
0.642550 | + | 0.766244i | \(0.277876\pi\) | |||||||
\(558\) | 0.925902 | 0.0391966 | ||||||||
\(559\) | −17.9506 | −0.759230 | ||||||||
\(560\) | −3.76480 | −0.159092 | ||||||||
\(561\) | −14.2035 | −0.599671 | ||||||||
\(562\) | −7.24230 | −0.305498 | ||||||||
\(563\) | 34.3651 | 1.44831 | 0.724157 | − | 0.689635i | \(-0.242229\pi\) | ||||
0.724157 | + | 0.689635i | \(0.242229\pi\) | |||||||
\(564\) | −2.20231 | −0.0927339 | ||||||||
\(565\) | 14.1678 | 0.596045 | ||||||||
\(566\) | 5.52079 | 0.232056 | ||||||||
\(567\) | 8.59429 | 0.360926 | ||||||||
\(568\) | 3.28126 | 0.137679 | ||||||||
\(569\) | 37.0801 | 1.55448 | 0.777240 | − | 0.629204i | \(-0.216619\pi\) | ||||
0.777240 | + | 0.629204i | \(0.216619\pi\) | |||||||
\(570\) | 14.3019 | 0.599039 | ||||||||
\(571\) | 4.16167 | 0.174161 | 0.0870803 | − | 0.996201i | \(-0.472246\pi\) | ||||
0.0870803 | + | 0.996201i | \(0.472246\pi\) | |||||||
\(572\) | 12.9887 | 0.543086 | ||||||||
\(573\) | −26.1311 | −1.09164 | ||||||||
\(574\) | −6.10878 | −0.254975 | ||||||||
\(575\) | 43.5851 | 1.81763 | ||||||||
\(576\) | −0.129635 | −0.00540144 | ||||||||
\(577\) | 2.02887 | 0.0844628 | 0.0422314 | − | 0.999108i | \(-0.486553\pi\) | ||||
0.0422314 | + | 0.999108i | \(0.486553\pi\) | |||||||
\(578\) | 14.3304 | 0.596068 | ||||||||
\(579\) | 41.3396 | 1.71801 | ||||||||
\(580\) | 14.3871 | 0.597390 | ||||||||
\(581\) | −7.74981 | −0.321516 | ||||||||
\(582\) | −15.1191 | −0.626708 | ||||||||
\(583\) | 9.67967 | 0.400891 | ||||||||
\(584\) | 2.75032 | 0.113809 | ||||||||
\(585\) | −1.23544 | −0.0510793 | ||||||||
\(586\) | −4.12082 | −0.170229 | ||||||||
\(587\) | 6.09047 | 0.251380 | 0.125690 | − | 0.992070i | \(-0.459885\pi\) | ||||
0.125690 | + | 0.992070i | \(0.459885\pi\) | |||||||
\(588\) | −1.69422 | −0.0698683 | ||||||||
\(589\) | 16.0149 | 0.659884 | ||||||||
\(590\) | −28.0233 | −1.15370 | ||||||||
\(591\) | 23.9578 | 0.985492 | ||||||||
\(592\) | 2.28449 | 0.0938920 | ||||||||
\(593\) | −6.16953 | −0.253352 | −0.126676 | − | 0.991944i | \(-0.540431\pi\) | ||||
−0.126676 | + | 0.991944i | \(0.540431\pi\) | |||||||
\(594\) | −27.2063 | −1.11629 | ||||||||
\(595\) | −6.15123 | −0.252176 | ||||||||
\(596\) | −2.03542 | −0.0833742 | ||||||||
\(597\) | −9.45852 | −0.387111 | ||||||||
\(598\) | −12.0268 | −0.491814 | ||||||||
\(599\) | 11.2936 | 0.461444 | 0.230722 | − | 0.973020i | \(-0.425891\pi\) | ||||
0.230722 | + | 0.973020i | \(0.425891\pi\) | |||||||
\(600\) | 15.5423 | 0.634512 | ||||||||
\(601\) | −18.5052 | −0.754844 | −0.377422 | − | 0.926041i | \(-0.623189\pi\) | ||||
−0.377422 | + | 0.926041i | \(0.623189\pi\) | |||||||
\(602\) | −7.09119 | −0.289015 | ||||||||
\(603\) | −0.0908764 | −0.00370077 | ||||||||
\(604\) | 1.78140 | 0.0724842 | ||||||||
\(605\) | 57.7059 | 2.34608 | ||||||||
\(606\) | −17.9094 | −0.727521 | ||||||||
\(607\) | 32.3535 | 1.31319 | 0.656593 | − | 0.754245i | \(-0.271997\pi\) | ||||
0.656593 | + | 0.754245i | \(0.271997\pi\) | |||||||
\(608\) | −2.24224 | −0.0909347 | ||||||||
\(609\) | 6.47438 | 0.262355 | ||||||||
\(610\) | 0.0301263 | 0.00121978 | ||||||||
\(611\) | 3.29056 | 0.133122 | ||||||||
\(612\) | −0.211807 | −0.00856179 | ||||||||
\(613\) | −33.5095 | −1.35344 | −0.676718 | − | 0.736243i | \(-0.736598\pi\) | ||||
−0.676718 | + | 0.736243i | \(0.736598\pi\) | |||||||
\(614\) | −15.1726 | −0.612315 | ||||||||
\(615\) | 38.9641 | 1.57119 | ||||||||
\(616\) | 5.13106 | 0.206736 | ||||||||
\(617\) | −41.2052 | −1.65886 | −0.829429 | − | 0.558612i | \(-0.811334\pi\) | ||||
−0.829429 | + | 0.558612i | \(0.811334\pi\) | |||||||
\(618\) | 0.418681 | 0.0168418 | ||||||||
\(619\) | −20.2632 | −0.814448 | −0.407224 | − | 0.913328i | \(-0.633503\pi\) | ||||
−0.407224 | + | 0.913328i | \(0.633503\pi\) | |||||||
\(620\) | 26.8897 | 1.07992 | ||||||||
\(621\) | 25.1915 | 1.01090 | ||||||||
\(622\) | 4.58694 | 0.183919 | ||||||||
\(623\) | 8.90310 | 0.356695 | ||||||||
\(624\) | −4.28873 | −0.171686 | ||||||||
\(625\) | 13.2888 | 0.531554 | ||||||||
\(626\) | 0.591030 | 0.0236223 | ||||||||
\(627\) | −19.4920 | −0.778436 | ||||||||
\(628\) | 4.79958 | 0.191524 | ||||||||
\(629\) | 3.73258 | 0.148828 | ||||||||
\(630\) | −0.488049 | −0.0194443 | ||||||||
\(631\) | −22.9496 | −0.913610 | −0.456805 | − | 0.889567i | \(-0.651006\pi\) | ||||
−0.456805 | + | 0.889567i | \(0.651006\pi\) | |||||||
\(632\) | −3.70673 | −0.147446 | ||||||||
\(633\) | −32.4243 | −1.28875 | ||||||||
\(634\) | −18.1207 | −0.719666 | ||||||||
\(635\) | −10.9350 | −0.433941 | ||||||||
\(636\) | −3.19612 | −0.126734 | ||||||||
\(637\) | 2.53139 | 0.100297 | ||||||||
\(638\) | −19.6082 | −0.776294 | ||||||||
\(639\) | 0.425365 | 0.0168272 | ||||||||
\(640\) | −3.76480 | −0.148817 | ||||||||
\(641\) | −24.5916 | −0.971310 | −0.485655 | − | 0.874151i | \(-0.661419\pi\) | ||||
−0.485655 | + | 0.874151i | \(0.661419\pi\) | |||||||
\(642\) | 7.53572 | 0.297411 | ||||||||
\(643\) | 34.8580 | 1.37467 | 0.687333 | − | 0.726342i | \(-0.258781\pi\) | ||||
0.687333 | + | 0.726342i | \(0.258781\pi\) | |||||||
\(644\) | −4.75107 | −0.187219 | ||||||||
\(645\) | 45.2304 | 1.78094 | ||||||||
\(646\) | −3.66354 | −0.144140 | ||||||||
\(647\) | 16.9996 | 0.668322 | 0.334161 | − | 0.942516i | \(-0.391547\pi\) | ||||
0.334161 | + | 0.942516i | \(0.391547\pi\) | |||||||
\(648\) | 8.59429 | 0.337616 | ||||||||
\(649\) | 38.1930 | 1.49921 | ||||||||
\(650\) | −23.2224 | −0.910856 | ||||||||
\(651\) | 12.1008 | 0.474266 | ||||||||
\(652\) | 2.74208 | 0.107388 | ||||||||
\(653\) | 20.4074 | 0.798602 | 0.399301 | − | 0.916820i | \(-0.369253\pi\) | ||||
0.399301 | + | 0.916820i | \(0.369253\pi\) | |||||||
\(654\) | 8.36870 | 0.327242 | ||||||||
\(655\) | −29.9478 | −1.17016 | ||||||||
\(656\) | −6.10878 | −0.238508 | ||||||||
\(657\) | 0.356536 | 0.0139098 | ||||||||
\(658\) | 1.29990 | 0.0506753 | ||||||||
\(659\) | 32.3364 | 1.25965 | 0.629824 | − | 0.776738i | \(-0.283127\pi\) | ||||
0.629824 | + | 0.776738i | \(0.283127\pi\) | |||||||
\(660\) | −32.7279 | −1.27393 | ||||||||
\(661\) | −33.5586 | −1.30528 | −0.652639 | − | 0.757669i | \(-0.726338\pi\) | ||||
−0.652639 | + | 0.757669i | \(0.726338\pi\) | |||||||
\(662\) | −24.2633 | −0.943020 | ||||||||
\(663\) | −7.00725 | −0.272139 | ||||||||
\(664\) | −7.74981 | −0.300751 | ||||||||
\(665\) | −8.44158 | −0.327350 | ||||||||
\(666\) | 0.296149 | 0.0114755 | ||||||||
\(667\) | 18.1561 | 0.703006 | ||||||||
\(668\) | −17.5930 | −0.680693 | ||||||||
\(669\) | 13.7314 | 0.530888 | ||||||||
\(670\) | −2.63920 | −0.101961 | ||||||||
\(671\) | −0.0410592 | −0.00158507 | ||||||||
\(672\) | −1.69422 | −0.0653558 | ||||||||
\(673\) | 18.8291 | 0.725810 | 0.362905 | − | 0.931826i | \(-0.381785\pi\) | ||||
0.362905 | + | 0.931826i | \(0.381785\pi\) | |||||||
\(674\) | −20.5308 | −0.790818 | ||||||||
\(675\) | 48.6417 | 1.87222 | ||||||||
\(676\) | −6.59204 | −0.253540 | ||||||||
\(677\) | 23.0258 | 0.884954 | 0.442477 | − | 0.896780i | \(-0.354100\pi\) | ||||
0.442477 | + | 0.896780i | \(0.354100\pi\) | |||||||
\(678\) | 6.37573 | 0.244858 | ||||||||
\(679\) | 8.92397 | 0.342471 | ||||||||
\(680\) | −6.15123 | −0.235889 | ||||||||
\(681\) | 19.5001 | 0.747247 | ||||||||
\(682\) | −36.6480 | −1.40333 | ||||||||
\(683\) | 18.5392 | 0.709381 | 0.354690 | − | 0.934984i | \(-0.384586\pi\) | ||||
0.354690 | + | 0.934984i | \(0.384586\pi\) | |||||||
\(684\) | −0.290672 | −0.0111141 | ||||||||
\(685\) | −1.26858 | −0.0484700 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 12.5598 | 0.479186 | ||||||||
\(688\) | −7.09119 | −0.270349 | ||||||||
\(689\) | 4.77544 | 0.181930 | ||||||||
\(690\) | 30.3042 | 1.15366 | ||||||||
\(691\) | 1.70733 | 0.0649497 | 0.0324749 | − | 0.999473i | \(-0.489661\pi\) | ||||
0.0324749 | + | 0.999473i | \(0.489661\pi\) | |||||||
\(692\) | −14.4727 | −0.550168 | ||||||||
\(693\) | 0.665163 | 0.0252674 | ||||||||
\(694\) | −0.619877 | −0.0235302 | ||||||||
\(695\) | 50.0277 | 1.89766 | ||||||||
\(696\) | 6.47438 | 0.245411 | ||||||||
\(697\) | −9.98099 | −0.378057 | ||||||||
\(698\) | −0.293252 | −0.0110997 | ||||||||
\(699\) | 44.1414 | 1.66958 | ||||||||
\(700\) | −9.17374 | −0.346735 | ||||||||
\(701\) | −8.58039 | −0.324077 | −0.162039 | − | 0.986784i | \(-0.551807\pi\) | ||||
−0.162039 | + | 0.986784i | \(0.551807\pi\) | |||||||
\(702\) | −13.4221 | −0.506586 | ||||||||
\(703\) | 5.12237 | 0.193194 | ||||||||
\(704\) | 5.13106 | 0.193384 | ||||||||
\(705\) | −8.29126 | −0.312267 | ||||||||
\(706\) | 30.7987 | 1.15912 | ||||||||
\(707\) | 10.5709 | 0.397561 | ||||||||
\(708\) | −12.6109 | −0.473946 | ||||||||
\(709\) | −40.6934 | −1.52827 | −0.764136 | − | 0.645055i | \(-0.776834\pi\) | ||||
−0.764136 | + | 0.645055i | \(0.776834\pi\) | |||||||
\(710\) | 12.3533 | 0.463611 | ||||||||
\(711\) | −0.480521 | −0.0180209 | ||||||||
\(712\) | 8.90310 | 0.333658 | ||||||||
\(713\) | 33.9341 | 1.27084 | ||||||||
\(714\) | −2.76814 | −0.103595 | ||||||||
\(715\) | 48.9000 | 1.82876 | ||||||||
\(716\) | −16.2018 | −0.605491 | ||||||||
\(717\) | 7.00854 | 0.261739 | ||||||||
\(718\) | 13.9496 | 0.520594 | ||||||||
\(719\) | 1.09263 | 0.0407482 | 0.0203741 | − | 0.999792i | \(-0.493514\pi\) | ||||
0.0203741 | + | 0.999792i | \(0.493514\pi\) | |||||||
\(720\) | −0.488049 | −0.0181885 | ||||||||
\(721\) | −0.247124 | −0.00920338 | ||||||||
\(722\) | 13.9724 | 0.519998 | ||||||||
\(723\) | −24.4312 | −0.908605 | ||||||||
\(724\) | 3.75290 | 0.139475 | ||||||||
\(725\) | 35.0571 | 1.30199 | ||||||||
\(726\) | 25.9685 | 0.963781 | ||||||||
\(727\) | −1.68744 | −0.0625837 | −0.0312918 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312918 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(728\) | 2.53139 | 0.0938197 | ||||||||
\(729\) | 28.0637 | 1.03940 | ||||||||
\(730\) | 10.3544 | 0.383234 | ||||||||
\(731\) | −11.5861 | −0.428529 | ||||||||
\(732\) | 0.0135573 | 0.000501092 0 | ||||||||
\(733\) | 7.42652 | 0.274305 | 0.137152 | − | 0.990550i | \(-0.456205\pi\) | ||||
0.137152 | + | 0.990550i | \(0.456205\pi\) | |||||||
\(734\) | 18.7430 | 0.691817 | ||||||||
\(735\) | −6.37839 | −0.235270 | ||||||||
\(736\) | −4.75107 | −0.175127 | ||||||||
\(737\) | 3.59697 | 0.132496 | ||||||||
\(738\) | −0.791909 | −0.0291506 | ||||||||
\(739\) | −32.7878 | −1.20612 | −0.603060 | − | 0.797696i | \(-0.706052\pi\) | ||||
−0.603060 | + | 0.797696i | \(0.706052\pi\) | |||||||
\(740\) | 8.60066 | 0.316166 | ||||||||
\(741\) | −9.61634 | −0.353265 | ||||||||
\(742\) | 1.88649 | 0.0692551 | ||||||||
\(743\) | −21.9863 | −0.806599 | −0.403299 | − | 0.915068i | \(-0.632137\pi\) | ||||
−0.403299 | + | 0.915068i | \(0.632137\pi\) | |||||||
\(744\) | 12.1008 | 0.443635 | ||||||||
\(745\) | −7.66297 | −0.280750 | ||||||||
\(746\) | −0.233693 | −0.00855613 | ||||||||
\(747\) | −1.00464 | −0.0367580 | ||||||||
\(748\) | 8.38352 | 0.306532 | ||||||||
\(749\) | −4.44791 | −0.162523 | ||||||||
\(750\) | 26.6217 | 0.972089 | ||||||||
\(751\) | −20.6369 | −0.753051 | −0.376525 | − | 0.926406i | \(-0.622881\pi\) | ||||
−0.376525 | + | 0.926406i | \(0.622881\pi\) | |||||||
\(752\) | 1.29990 | 0.0474024 | ||||||||
\(753\) | −22.3882 | −0.815871 | ||||||||
\(754\) | −9.67364 | −0.352293 | ||||||||
\(755\) | 6.70663 | 0.244079 | ||||||||
\(756\) | −5.30227 | −0.192842 | ||||||||
\(757\) | 23.4349 | 0.851756 | 0.425878 | − | 0.904781i | \(-0.359965\pi\) | ||||
0.425878 | + | 0.904781i | \(0.359965\pi\) | |||||||
\(758\) | −22.0112 | −0.799481 | ||||||||
\(759\) | −41.3016 | −1.49915 | ||||||||
\(760\) | −8.44158 | −0.306208 | ||||||||
\(761\) | 32.1036 | 1.16375 | 0.581876 | − | 0.813277i | \(-0.302319\pi\) | ||||
0.581876 | + | 0.813277i | \(0.302319\pi\) | |||||||
\(762\) | −4.92090 | −0.178265 | ||||||||
\(763\) | −4.93957 | −0.178824 | ||||||||
\(764\) | 15.4237 | 0.558010 | ||||||||
\(765\) | −0.797412 | −0.0288305 | ||||||||
\(766\) | −6.39092 | −0.230913 | ||||||||
\(767\) | 18.8424 | 0.680361 | ||||||||
\(768\) | −1.69422 | −0.0611347 | ||||||||
\(769\) | −28.6301 | −1.03243 | −0.516214 | − | 0.856459i | \(-0.672659\pi\) | ||||
−0.516214 | + | 0.856459i | \(0.672659\pi\) | |||||||
\(770\) | 19.3174 | 0.696151 | ||||||||
\(771\) | −5.63740 | −0.203026 | ||||||||
\(772\) | −24.4004 | −0.878191 | ||||||||
\(773\) | −12.4854 | −0.449070 | −0.224535 | − | 0.974466i | \(-0.572086\pi\) | ||||
−0.224535 | + | 0.974466i | \(0.572086\pi\) | |||||||
\(774\) | −0.919264 | −0.0330423 | ||||||||
\(775\) | 65.5225 | 2.35364 | ||||||||
\(776\) | 8.92397 | 0.320352 | ||||||||
\(777\) | 3.87042 | 0.138851 | ||||||||
\(778\) | −26.6128 | −0.954116 | ||||||||
\(779\) | −13.6973 | −0.490757 | ||||||||
\(780\) | −16.1462 | −0.578127 | ||||||||
\(781\) | −16.8363 | −0.602452 | ||||||||
\(782\) | −7.76267 | −0.277593 | ||||||||
\(783\) | 20.2625 | 0.724121 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 18.0695 | 0.644928 | ||||||||
\(786\) | −13.4769 | −0.480706 | ||||||||
\(787\) | −34.2854 | −1.22214 | −0.611071 | − | 0.791576i | \(-0.709261\pi\) | ||||
−0.611071 | + | 0.791576i | \(0.709261\pi\) | |||||||
\(788\) | −14.1409 | −0.503750 | ||||||||
\(789\) | 38.6451 | 1.37580 | ||||||||
\(790\) | −13.9551 | −0.496501 | ||||||||
\(791\) | −3.76323 | −0.133805 | ||||||||
\(792\) | 0.665163 | 0.0236355 | ||||||||
\(793\) | −0.0202565 | −0.000719328 0 | ||||||||
\(794\) | 6.68899 | 0.237384 | ||||||||
\(795\) | −12.0327 | −0.426758 | ||||||||
\(796\) | 5.58283 | 0.197878 | ||||||||
\(797\) | 24.7988 | 0.878419 | 0.439209 | − | 0.898385i | \(-0.355259\pi\) | ||||
0.439209 | + | 0.898385i | \(0.355259\pi\) | |||||||
\(798\) | −3.79883 | −0.134477 | ||||||||
\(799\) | 2.12387 | 0.0751373 | ||||||||
\(800\) | −9.17374 | −0.324341 | ||||||||
\(801\) | 1.15415 | 0.0407799 | ||||||||
\(802\) | 8.28110 | 0.292416 | ||||||||
\(803\) | −14.1120 | −0.498003 | ||||||||
\(804\) | −1.18768 | −0.0418862 | ||||||||
\(805\) | −17.8869 | −0.630429 | ||||||||
\(806\) | −18.0802 | −0.636849 | ||||||||
\(807\) | 4.00133 | 0.140853 | ||||||||
\(808\) | 10.5709 | 0.371884 | ||||||||
\(809\) | −29.1838 | −1.02605 | −0.513024 | − | 0.858374i | \(-0.671475\pi\) | ||||
−0.513024 | + | 0.858374i | \(0.671475\pi\) | |||||||
\(810\) | 32.3558 | 1.13687 | ||||||||
\(811\) | 36.1041 | 1.26778 | 0.633892 | − | 0.773421i | \(-0.281456\pi\) | ||||
0.633892 | + | 0.773421i | \(0.281456\pi\) | |||||||
\(812\) | −3.82147 | −0.134107 | ||||||||
\(813\) | 11.2921 | 0.396031 | ||||||||
\(814\) | −11.7218 | −0.410851 | ||||||||
\(815\) | 10.3234 | 0.361612 | ||||||||
\(816\) | −2.76814 | −0.0969043 | ||||||||
\(817\) | −15.9001 | −0.556275 | ||||||||
\(818\) | −3.04974 | −0.106632 | ||||||||
\(819\) | 0.328156 | 0.0114667 | ||||||||
\(820\) | −22.9983 | −0.803137 | ||||||||
\(821\) | 39.8232 | 1.38984 | 0.694920 | − | 0.719087i | \(-0.255440\pi\) | ||||
0.694920 | + | 0.719087i | \(0.255440\pi\) | |||||||
\(822\) | −0.570880 | −0.0199117 | ||||||||
\(823\) | −17.9944 | −0.627244 | −0.313622 | − | 0.949548i | \(-0.601542\pi\) | ||||
−0.313622 | + | 0.949548i | \(0.601542\pi\) | |||||||
\(824\) | −0.247124 | −0.00860897 | ||||||||
\(825\) | −79.7484 | −2.77648 | ||||||||
\(826\) | 7.44350 | 0.258992 | ||||||||
\(827\) | −12.4662 | −0.433493 | −0.216747 | − | 0.976228i | \(-0.569545\pi\) | ||||
−0.216747 | + | 0.976228i | \(0.569545\pi\) | |||||||
\(828\) | −0.615904 | −0.0214041 | ||||||||
\(829\) | −48.1453 | −1.67215 | −0.836077 | − | 0.548612i | \(-0.815157\pi\) | ||||
−0.836077 | + | 0.548612i | \(0.815157\pi\) | |||||||
\(830\) | −29.1765 | −1.01273 | ||||||||
\(831\) | 43.6247 | 1.51332 | ||||||||
\(832\) | 2.53139 | 0.0877603 | ||||||||
\(833\) | 1.63388 | 0.0566105 | ||||||||
\(834\) | 22.5132 | 0.779567 | ||||||||
\(835\) | −66.2341 | −2.29213 | ||||||||
\(836\) | 11.5050 | 0.397910 | ||||||||
\(837\) | 37.8709 | 1.30901 | ||||||||
\(838\) | −33.0604 | −1.14205 | ||||||||
\(839\) | −18.6641 | −0.644358 | −0.322179 | − | 0.946679i | \(-0.604415\pi\) | ||||
−0.322179 | + | 0.946679i | \(0.604415\pi\) | |||||||
\(840\) | −6.37839 | −0.220075 | ||||||||
\(841\) | −14.3964 | −0.496428 | ||||||||
\(842\) | −26.2130 | −0.903358 | ||||||||
\(843\) | −12.2700 | −0.422602 | ||||||||
\(844\) | 19.1382 | 0.658765 | ||||||||
\(845\) | −24.8177 | −0.853756 | ||||||||
\(846\) | 0.168512 | 0.00579356 | ||||||||
\(847\) | −15.3277 | −0.526667 | ||||||||
\(848\) | 1.88649 | 0.0647822 | ||||||||
\(849\) | 9.35341 | 0.321008 | ||||||||
\(850\) | −14.9888 | −0.514111 | ||||||||
\(851\) | 10.8538 | 0.372063 | ||||||||
\(852\) | 5.55917 | 0.190454 | ||||||||
\(853\) | 34.9018 | 1.19502 | 0.597508 | − | 0.801863i | \(-0.296158\pi\) | ||||
0.597508 | + | 0.801863i | \(0.296158\pi\) | |||||||
\(854\) | −0.00800210 | −0.000273826 0 | ||||||||
\(855\) | −1.09432 | −0.0374250 | ||||||||
\(856\) | −4.44791 | −0.152027 | ||||||||
\(857\) | −35.3858 | −1.20876 | −0.604378 | − | 0.796697i | \(-0.706578\pi\) | ||||
−0.604378 | + | 0.796697i | \(0.706578\pi\) | |||||||
\(858\) | 22.0057 | 0.751262 | ||||||||
\(859\) | −16.8970 | −0.576518 | −0.288259 | − | 0.957552i | \(-0.593076\pi\) | ||||
−0.288259 | + | 0.957552i | \(0.593076\pi\) | |||||||
\(860\) | −26.6969 | −0.910358 | ||||||||
\(861\) | −10.3496 | −0.352713 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −13.6174 | −0.463543 | −0.231772 | − | 0.972770i | \(-0.574452\pi\) | ||||
−0.231772 | + | 0.972770i | \(0.574452\pi\) | |||||||
\(864\) | −5.30227 | −0.180387 | ||||||||
\(865\) | −54.4867 | −1.85260 | ||||||||
\(866\) | −15.9959 | −0.543562 | ||||||||
\(867\) | 24.2789 | 0.824553 | ||||||||
\(868\) | −7.14240 | −0.242429 | ||||||||
\(869\) | 19.0194 | 0.645190 | ||||||||
\(870\) | 24.3748 | 0.826383 | ||||||||
\(871\) | 1.77456 | 0.0601286 | ||||||||
\(872\) | −4.93957 | −0.167275 | ||||||||
\(873\) | 1.15686 | 0.0391536 | ||||||||
\(874\) | −10.6530 | −0.360344 | ||||||||
\(875\) | −15.7133 | −0.531207 | ||||||||
\(876\) | 4.65963 | 0.157434 | ||||||||
\(877\) | 55.3170 | 1.86792 | 0.933961 | − | 0.357376i | \(-0.116328\pi\) | ||||
0.933961 | + | 0.357376i | \(0.116328\pi\) | |||||||
\(878\) | 31.2755 | 1.05550 | ||||||||
\(879\) | −6.98156 | −0.235482 | ||||||||
\(880\) | 19.3174 | 0.651190 | ||||||||
\(881\) | 37.1653 | 1.25213 | 0.626066 | − | 0.779770i | \(-0.284664\pi\) | ||||
0.626066 | + | 0.779770i | \(0.284664\pi\) | |||||||
\(882\) | 0.129635 | 0.00436503 | ||||||||
\(883\) | 20.0043 | 0.673199 | 0.336599 | − | 0.941648i | \(-0.390723\pi\) | ||||
0.336599 | + | 0.941648i | \(0.390723\pi\) | |||||||
\(884\) | 4.13599 | 0.139108 | ||||||||
\(885\) | −47.4775 | −1.59594 | ||||||||
\(886\) | 26.1389 | 0.878155 | ||||||||
\(887\) | 35.2378 | 1.18317 | 0.591585 | − | 0.806242i | \(-0.298502\pi\) | ||||
0.591585 | + | 0.806242i | \(0.298502\pi\) | |||||||
\(888\) | 3.87042 | 0.129883 | ||||||||
\(889\) | 2.90453 | 0.0974148 | ||||||||
\(890\) | 33.5184 | 1.12354 | ||||||||
\(891\) | −44.0978 | −1.47733 | ||||||||
\(892\) | −8.10489 | −0.271372 | ||||||||
\(893\) | 2.91468 | 0.0975360 | ||||||||
\(894\) | −3.44845 | −0.115333 | ||||||||
\(895\) | −60.9967 | −2.03890 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −20.3761 | −0.680337 | ||||||||
\(898\) | −14.1690 | −0.472827 | ||||||||
\(899\) | 27.2944 | 0.910320 | ||||||||
\(900\) | −1.18923 | −0.0396412 | ||||||||
\(901\) | 3.08229 | 0.102686 | ||||||||
\(902\) | 31.3445 | 1.04366 | ||||||||
\(903\) | −12.0140 | −0.399801 | ||||||||
\(904\) | −3.76323 | −0.125163 | ||||||||
\(905\) | 14.1289 | 0.469661 | ||||||||
\(906\) | 3.01808 | 0.100269 | ||||||||
\(907\) | −16.3214 | −0.541943 | −0.270972 | − | 0.962587i | \(-0.587345\pi\) | ||||
−0.270972 | + | 0.962587i | \(0.587345\pi\) | |||||||
\(908\) | −11.5098 | −0.381967 | ||||||||
\(909\) | 1.37036 | 0.0454519 | ||||||||
\(910\) | 9.53020 | 0.315923 | ||||||||
\(911\) | −12.9312 | −0.428430 | −0.214215 | − | 0.976787i | \(-0.568719\pi\) | ||||
−0.214215 | + | 0.976787i | \(0.568719\pi\) | |||||||
\(912\) | −3.79883 | −0.125792 | ||||||||
\(913\) | 39.7647 | 1.31602 | ||||||||
\(914\) | −14.2280 | −0.470620 | ||||||||
\(915\) | 0.0510405 | 0.00168735 | ||||||||
\(916\) | −7.41334 | −0.244944 | ||||||||
\(917\) | 7.95468 | 0.262687 | ||||||||
\(918\) | −8.66327 | −0.285930 | ||||||||
\(919\) | 4.11729 | 0.135817 | 0.0679085 | − | 0.997692i | \(-0.478367\pi\) | ||||
0.0679085 | + | 0.997692i | \(0.478367\pi\) | |||||||
\(920\) | −17.8869 | −0.589712 | ||||||||
\(921\) | −25.7056 | −0.847028 | ||||||||
\(922\) | −19.6352 | −0.646652 | ||||||||
\(923\) | −8.30617 | −0.273401 | ||||||||
\(924\) | 8.69311 | 0.285982 | ||||||||
\(925\) | 20.9573 | 0.689073 | ||||||||
\(926\) | 12.0254 | 0.395179 | ||||||||
\(927\) | −0.0320358 | −0.00105219 | ||||||||
\(928\) | −3.82147 | −0.125446 | ||||||||
\(929\) | 21.3527 | 0.700559 | 0.350280 | − | 0.936645i | \(-0.386087\pi\) | ||||
0.350280 | + | 0.936645i | \(0.386087\pi\) | |||||||
\(930\) | 45.5570 | 1.49387 | ||||||||
\(931\) | 2.24224 | 0.0734863 | ||||||||
\(932\) | −26.0542 | −0.853433 | ||||||||
\(933\) | 7.77126 | 0.254420 | ||||||||
\(934\) | 2.49381 | 0.0815998 | ||||||||
\(935\) | 31.5623 | 1.03220 | ||||||||
\(936\) | 0.328156 | 0.0107261 | ||||||||
\(937\) | −19.5021 | −0.637104 | −0.318552 | − | 0.947905i | \(-0.603197\pi\) | ||||
−0.318552 | + | 0.947905i | \(0.603197\pi\) | |||||||
\(938\) | 0.701020 | 0.0228891 | ||||||||
\(939\) | 1.00133 | 0.0326772 | ||||||||
\(940\) | 4.89386 | 0.159620 | ||||||||
\(941\) | −5.14134 | −0.167603 | −0.0838014 | − | 0.996482i | \(-0.526706\pi\) | ||||
−0.0838014 | + | 0.996482i | \(0.526706\pi\) | |||||||
\(942\) | 8.13153 | 0.264940 | ||||||||
\(943\) | −29.0233 | −0.945127 | ||||||||
\(944\) | 7.44350 | 0.242265 | ||||||||
\(945\) | −19.9620 | −0.649365 | ||||||||
\(946\) | 36.3853 | 1.18299 | ||||||||
\(947\) | 57.8513 | 1.87991 | 0.939957 | − | 0.341293i | \(-0.110865\pi\) | ||||
0.939957 | + | 0.341293i | \(0.110865\pi\) | |||||||
\(948\) | −6.28000 | −0.203965 | ||||||||
\(949\) | −6.96214 | −0.226000 | ||||||||
\(950\) | −20.5697 | −0.667369 | ||||||||
\(951\) | −30.7004 | −0.995529 | ||||||||
\(952\) | 1.63388 | 0.0529543 | ||||||||
\(953\) | −43.7561 | −1.41740 | −0.708700 | − | 0.705510i | \(-0.750718\pi\) | ||||
−0.708700 | + | 0.705510i | \(0.750718\pi\) | |||||||
\(954\) | 0.244554 | 0.00791773 | ||||||||
\(955\) | 58.0672 | 1.87901 | ||||||||
\(956\) | −4.13675 | −0.133792 | ||||||||
\(957\) | −33.2204 | −1.07386 | ||||||||
\(958\) | −23.9177 | −0.772747 | ||||||||
\(959\) | 0.336958 | 0.0108809 | ||||||||
\(960\) | −6.37839 | −0.205862 | ||||||||
\(961\) | 20.0138 | 0.645607 | ||||||||
\(962\) | −5.78295 | −0.186450 | ||||||||
\(963\) | −0.576604 | −0.0185808 | ||||||||
\(964\) | 14.4204 | 0.464448 | ||||||||
\(965\) | −91.8628 | −2.95717 | ||||||||
\(966\) | −8.04934 | −0.258983 | ||||||||
\(967\) | −33.2809 | −1.07024 | −0.535121 | − | 0.844775i | \(-0.679734\pi\) | ||||
−0.535121 | + | 0.844775i | \(0.679734\pi\) | |||||||
\(968\) | −15.3277 | −0.492652 | ||||||||
\(969\) | −6.20682 | −0.199392 | ||||||||
\(970\) | 33.5970 | 1.07873 | ||||||||
\(971\) | 3.31961 | 0.106531 | 0.0532657 | − | 0.998580i | \(-0.483037\pi\) | ||||
0.0532657 | + | 0.998580i | \(0.483037\pi\) | |||||||
\(972\) | −1.34625 | −0.0431808 | ||||||||
\(973\) | −13.2883 | −0.426002 | ||||||||
\(974\) | −13.4212 | −0.430042 | ||||||||
\(975\) | −39.3437 | −1.26001 | ||||||||
\(976\) | −0.00800210 | −0.000256141 0 | ||||||||
\(977\) | 4.02190 | 0.128672 | 0.0643360 | − | 0.997928i | \(-0.479507\pi\) | ||||
0.0643360 | + | 0.997928i | \(0.479507\pi\) | |||||||
\(978\) | 4.64567 | 0.148552 | ||||||||
\(979\) | −45.6823 | −1.46001 | ||||||||
\(980\) | 3.76480 | 0.120262 | ||||||||
\(981\) | −0.640339 | −0.0204445 | ||||||||
\(982\) | 12.6746 | 0.404462 | ||||||||
\(983\) | −23.2274 | −0.740838 | −0.370419 | − | 0.928865i | \(-0.620786\pi\) | ||||
−0.370419 | + | 0.928865i | \(0.620786\pi\) | |||||||
\(984\) | −10.3496 | −0.329933 | ||||||||
\(985\) | −53.2379 | −1.69630 | ||||||||
\(986\) | −6.24381 | −0.198843 | ||||||||
\(987\) | 2.20231 | 0.0701002 | ||||||||
\(988\) | 5.67598 | 0.180577 | ||||||||
\(989\) | −33.6908 | −1.07130 | ||||||||
\(990\) | 2.50421 | 0.0795889 | ||||||||
\(991\) | 39.7385 | 1.26234 | 0.631168 | − | 0.775646i | \(-0.282576\pi\) | ||||
0.631168 | + | 0.775646i | \(0.282576\pi\) | |||||||
\(992\) | −7.14240 | −0.226771 | ||||||||
\(993\) | −41.1072 | −1.30450 | ||||||||
\(994\) | −3.28126 | −0.104075 | ||||||||
\(995\) | 21.0183 | 0.666324 | ||||||||
\(996\) | −13.1299 | −0.416035 | ||||||||
\(997\) | −4.20588 | −0.133202 | −0.0666009 | − | 0.997780i | \(-0.521215\pi\) | ||||
−0.0666009 | + | 0.997780i | \(0.521215\pi\) | |||||||
\(998\) | −30.7009 | −0.971821 | ||||||||
\(999\) | 12.1130 | 0.383238 |
(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 | 6034.2.a.n.1.6 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.n.1.6 | ✓ | 24 | 1.1 | even | 1 | trivial |