Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 22 x^{12} + 18 x^{11} + 187 x^{10} - 118 x^{9} - 772 x^{8} + 346 x^{7} + 1581 x^{6} - 443 x^{5} - 1429 x^{4} + 193 x^{3} + 386 x^{2} - 3 x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.76659\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.76659 | 1.24917 | 0.624583 | − | 0.780959i | \(-0.285269\pi\) | ||||
0.624583 | + | 0.780959i | \(0.285269\pi\) | |||||||
\(3\) | 0.991358 | 0.572361 | 0.286180 | − | 0.958176i | \(-0.407614\pi\) | ||||
0.286180 | + | 0.958176i | \(0.407614\pi\) | |||||||
\(4\) | 1.12083 | 0.560413 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.75132 | 0.714973 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.55314 | −0.549116 | ||||||||
\(9\) | −2.01721 | −0.672403 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.44676 | 1.03924 | 0.519619 | − | 0.854398i | \(-0.326074\pi\) | ||||
0.519619 | + | 0.854398i | \(0.326074\pi\) | |||||||
\(12\) | 1.11114 | 0.320759 | ||||||||
\(13\) | 1.76768 | 0.490266 | 0.245133 | − | 0.969489i | \(-0.421168\pi\) | ||||
0.245133 | + | 0.969489i | \(0.421168\pi\) | |||||||
\(14\) | −1.76659 | −0.472140 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98540 | −1.24635 | ||||||||
\(17\) | −3.70284 | −0.898070 | −0.449035 | − | 0.893514i | \(-0.648232\pi\) | ||||
−0.449035 | + | 0.893514i | \(0.648232\pi\) | |||||||
\(18\) | −3.56357 | −0.839942 | ||||||||
\(19\) | −8.16438 | −1.87304 | −0.936519 | − | 0.350618i | \(-0.885972\pi\) | ||||
−0.936519 | + | 0.350618i | \(0.885972\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.991358 | −0.216332 | ||||||||
\(22\) | 6.08900 | 1.29818 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.53971 | −0.314293 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.12276 | 0.612423 | ||||||||
\(27\) | −4.97385 | −0.957218 | ||||||||
\(28\) | −1.12083 | −0.211816 | ||||||||
\(29\) | 1.63532 | 0.303672 | 0.151836 | − | 0.988406i | \(-0.451481\pi\) | ||||
0.151836 | + | 0.988406i | \(0.451481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.49337 | −1.16624 | −0.583122 | − | 0.812384i | \(-0.698169\pi\) | ||||
−0.583122 | + | 0.812384i | \(0.698169\pi\) | |||||||
\(32\) | −5.70087 | −1.00778 | ||||||||
\(33\) | 3.41697 | 0.594819 | ||||||||
\(34\) | −6.54138 | −1.12184 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.26094 | −0.376824 | ||||||||
\(37\) | −1.57716 | −0.259284 | −0.129642 | − | 0.991561i | \(-0.541383\pi\) | ||||
−0.129642 | + | 0.991561i | \(0.541383\pi\) | |||||||
\(38\) | −14.4231 | −2.33973 | ||||||||
\(39\) | 1.75240 | 0.280609 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.67517 | 0.886312 | 0.443156 | − | 0.896444i | \(-0.353859\pi\) | ||||
0.443156 | + | 0.896444i | \(0.353859\pi\) | |||||||
\(42\) | −1.75132 | −0.270234 | ||||||||
\(43\) | −12.0844 | −1.84285 | −0.921427 | − | 0.388552i | \(-0.872975\pi\) | ||||
−0.921427 | + | 0.388552i | \(0.872975\pi\) | |||||||
\(44\) | 3.86322 | 0.582402 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76659 | 0.260469 | ||||||||
\(47\) | −8.58989 | −1.25296 | −0.626482 | − | 0.779436i | \(-0.715506\pi\) | ||||
−0.626482 | + | 0.779436i | \(0.715506\pi\) | |||||||
\(48\) | −4.94232 | −0.713362 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.67084 | −0.514020 | ||||||||
\(52\) | 1.98126 | 0.274752 | ||||||||
\(53\) | 11.1369 | 1.52977 | 0.764884 | − | 0.644168i | \(-0.222796\pi\) | ||||
0.764884 | + | 0.644168i | \(0.222796\pi\) | |||||||
\(54\) | −8.78674 | −1.19572 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.55314 | 0.207546 | ||||||||
\(57\) | −8.09382 | −1.07205 | ||||||||
\(58\) | 2.88894 | 0.379337 | ||||||||
\(59\) | −0.498851 | −0.0649448 | −0.0324724 | − | 0.999473i | \(-0.510338\pi\) | ||||
−0.0324724 | + | 0.999473i | \(0.510338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.17193 | 0.534161 | 0.267080 | − | 0.963674i | \(-0.413941\pi\) | ||||
0.267080 | + | 0.963674i | \(0.413941\pi\) | |||||||
\(62\) | −11.4711 | −1.45683 | ||||||||
\(63\) | 2.01721 | 0.254144 | ||||||||
\(64\) | −0.100276 | −0.0125345 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.03638 | 0.743027 | ||||||||
\(67\) | −0.0800684 | −0.00978191 | −0.00489096 | − | 0.999988i | \(-0.501557\pi\) | ||||
−0.00489096 | + | 0.999988i | \(0.501557\pi\) | |||||||
\(68\) | −4.15024 | −0.503291 | ||||||||
\(69\) | 0.991358 | 0.119345 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.21407 | −1.09351 | −0.546754 | − | 0.837293i | \(-0.684137\pi\) | ||||
−0.546754 | + | 0.837293i | \(0.684137\pi\) | |||||||
\(72\) | 3.13300 | 0.369227 | ||||||||
\(73\) | 16.3786 | 1.91697 | 0.958486 | − | 0.285139i | \(-0.0920398\pi\) | ||||
0.958486 | + | 0.285139i | \(0.0920398\pi\) | |||||||
\(74\) | −2.78619 | −0.323888 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.15085 | −1.04968 | ||||||||
\(77\) | −3.44676 | −0.392795 | ||||||||
\(78\) | 3.09577 | 0.350527 | ||||||||
\(79\) | −4.09934 | −0.461212 | −0.230606 | − | 0.973047i | \(-0.574071\pi\) | ||||
−0.230606 | + | 0.973047i | \(0.574071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.12076 | 0.124529 | ||||||||
\(82\) | 10.0257 | 1.10715 | ||||||||
\(83\) | −14.8510 | −1.63011 | −0.815055 | − | 0.579383i | \(-0.803293\pi\) | ||||
−0.815055 | + | 0.579383i | \(0.803293\pi\) | |||||||
\(84\) | −1.11114 | −0.121235 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −21.3481 | −2.30203 | ||||||||
\(87\) | 1.62119 | 0.173810 | ||||||||
\(88\) | −5.35328 | −0.570662 | ||||||||
\(89\) | −7.81583 | −0.828476 | −0.414238 | − | 0.910169i | \(-0.635952\pi\) | ||||
−0.414238 | + | 0.910169i | \(0.635952\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.76768 | −0.185303 | ||||||||
\(92\) | 1.12083 | 0.116854 | ||||||||
\(93\) | −6.43726 | −0.667513 | ||||||||
\(94\) | −15.1748 | −1.56516 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.65160 | −0.576814 | ||||||||
\(97\) | 4.40745 | 0.447509 | 0.223754 | − | 0.974646i | \(-0.428169\pi\) | ||||
0.223754 | + | 0.974646i | \(0.428169\pi\) | |||||||
\(98\) | 1.76659 | 0.178452 | ||||||||
\(99\) | −6.95283 | −0.698786 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.153094 | −0.0152334 | −0.00761671 | − | 0.999971i | \(-0.502424\pi\) | ||||
−0.00761671 | + | 0.999971i | \(0.502424\pi\) | |||||||
\(102\) | −6.48485 | −0.642096 | ||||||||
\(103\) | 9.09068 | 0.895732 | 0.447866 | − | 0.894101i | \(-0.352184\pi\) | ||||
0.447866 | + | 0.894101i | \(0.352184\pi\) | |||||||
\(104\) | −2.74545 | −0.269213 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.6743 | 1.91093 | ||||||||
\(107\) | −3.62325 | −0.350272 | −0.175136 | − | 0.984544i | \(-0.556037\pi\) | ||||
−0.175136 | + | 0.984544i | \(0.556037\pi\) | |||||||
\(108\) | −5.57483 | −0.536438 | ||||||||
\(109\) | 16.3042 | 1.56166 | 0.780828 | − | 0.624746i | \(-0.214798\pi\) | ||||
0.780828 | + | 0.624746i | \(0.214798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.56353 | −0.148404 | ||||||||
\(112\) | 4.98540 | 0.471076 | ||||||||
\(113\) | −8.05224 | −0.757491 | −0.378746 | − | 0.925501i | \(-0.623644\pi\) | ||||
−0.378746 | + | 0.925501i | \(0.623644\pi\) | |||||||
\(114\) | −14.2984 | −1.33917 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.83292 | 0.170182 | ||||||||
\(117\) | −3.56578 | −0.329656 | ||||||||
\(118\) | −0.881263 | −0.0811268 | ||||||||
\(119\) | 3.70284 | 0.339439 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.880150 | 0.0800137 | ||||||||
\(122\) | 7.37007 | 0.667255 | ||||||||
\(123\) | 5.62612 | 0.507291 | ||||||||
\(124\) | −7.27795 | −0.653579 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.56357 | 0.317468 | ||||||||
\(127\) | −9.41174 | −0.835157 | −0.417578 | − | 0.908641i | \(-0.637121\pi\) | ||||
−0.417578 | + | 0.908641i | \(0.637121\pi\) | |||||||
\(128\) | 11.2246 | 0.992123 | ||||||||
\(129\) | −11.9800 | −1.05478 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.8642 | −1.29869 | −0.649345 | − | 0.760494i | \(-0.724957\pi\) | ||||
−0.649345 | + | 0.760494i | \(0.724957\pi\) | |||||||
\(132\) | 3.82983 | 0.333344 | ||||||||
\(133\) | 8.16438 | 0.707941 | ||||||||
\(134\) | −0.141448 | −0.0122192 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.75101 | 0.493145 | ||||||||
\(137\) | −9.55643 | −0.816461 | −0.408231 | − | 0.912879i | \(-0.633854\pi\) | ||||
−0.408231 | + | 0.912879i | \(0.633854\pi\) | |||||||
\(138\) | 1.75132 | 0.149082 | ||||||||
\(139\) | −4.27083 | −0.362247 | −0.181124 | − | 0.983460i | \(-0.557973\pi\) | ||||
−0.181124 | + | 0.983460i | \(0.557973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.51566 | −0.717148 | ||||||||
\(142\) | −16.2774 | −1.36597 | ||||||||
\(143\) | 6.09277 | 0.509503 | ||||||||
\(144\) | 10.0566 | 0.838050 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 28.9342 | 2.39461 | ||||||||
\(147\) | 0.991358 | 0.0817658 | ||||||||
\(148\) | −1.76772 | −0.145306 | ||||||||
\(149\) | −8.75790 | −0.717475 | −0.358738 | − | 0.933438i | \(-0.616793\pi\) | ||||
−0.358738 | + | 0.933438i | \(0.616793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.8015 | 1.12315 | 0.561575 | − | 0.827426i | \(-0.310196\pi\) | ||||
0.561575 | + | 0.827426i | \(0.310196\pi\) | |||||||
\(152\) | 12.6804 | 1.02852 | ||||||||
\(153\) | 7.46940 | 0.603865 | ||||||||
\(154\) | −6.08900 | −0.490665 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.96414 | 0.157257 | ||||||||
\(157\) | −0.268103 | −0.0213969 | −0.0106985 | − | 0.999943i | \(-0.503405\pi\) | ||||
−0.0106985 | + | 0.999943i | \(0.503405\pi\) | |||||||
\(158\) | −7.24183 | −0.576129 | ||||||||
\(159\) | 11.0406 | 0.875579 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 1.97992 | 0.155557 | ||||||||
\(163\) | 11.9784 | 0.938218 | 0.469109 | − | 0.883140i | \(-0.344575\pi\) | ||||
0.469109 | + | 0.883140i | \(0.344575\pi\) | |||||||
\(164\) | 6.36088 | 0.496701 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.2356 | −2.03628 | ||||||||
\(167\) | 4.20255 | 0.325203 | 0.162602 | − | 0.986692i | \(-0.448011\pi\) | ||||
0.162602 | + | 0.986692i | \(0.448011\pi\) | |||||||
\(168\) | 1.53971 | 0.118791 | ||||||||
\(169\) | −9.87531 | −0.759639 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.4693 | 1.25944 | ||||||||
\(172\) | −13.5445 | −1.03276 | ||||||||
\(173\) | −19.1127 | −1.45311 | −0.726556 | − | 0.687107i | \(-0.758880\pi\) | ||||
−0.726556 | + | 0.687107i | \(0.758880\pi\) | |||||||
\(174\) | 2.86398 | 0.217117 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −17.1835 | −1.29525 | ||||||||
\(177\) | −0.494540 | −0.0371719 | ||||||||
\(178\) | −13.8073 | −1.03490 | ||||||||
\(179\) | −4.53066 | −0.338638 | −0.169319 | − | 0.985561i | \(-0.554157\pi\) | ||||
−0.169319 | + | 0.985561i | \(0.554157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3314 | 1.21390 | 0.606952 | − | 0.794739i | \(-0.292392\pi\) | ||||
0.606952 | + | 0.794739i | \(0.292392\pi\) | |||||||
\(182\) | −3.12276 | −0.231474 | ||||||||
\(183\) | 4.13587 | 0.305733 | ||||||||
\(184\) | −1.55314 | −0.114499 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.3720 | −0.833833 | ||||||||
\(187\) | −12.7628 | −0.933308 | ||||||||
\(188\) | −9.62778 | −0.702178 | ||||||||
\(189\) | 4.97385 | 0.361794 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.74923 | 0.343642 | 0.171821 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171821 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(192\) | −0.0994097 | −0.00717428 | ||||||||
\(193\) | −26.8798 | −1.93485 | −0.967423 | − | 0.253164i | \(-0.918529\pi\) | ||||
−0.967423 | + | 0.253164i | \(0.918529\pi\) | |||||||
\(194\) | 7.78614 | 0.559012 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.12083 | 0.0800591 | ||||||||
\(197\) | 25.7687 | 1.83594 | 0.917972 | − | 0.396646i | \(-0.129826\pi\) | ||||
0.917972 | + | 0.396646i | \(0.129826\pi\) | |||||||
\(198\) | −12.2828 | −0.872899 | ||||||||
\(199\) | −24.5630 | −1.74123 | −0.870614 | − | 0.491968i | \(-0.836278\pi\) | ||||
−0.870614 | + | 0.491968i | \(0.836278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0793764 | −0.00559878 | ||||||||
\(202\) | −0.270454 | −0.0190290 | ||||||||
\(203\) | −1.63532 | −0.114777 | ||||||||
\(204\) | −4.11437 | −0.288064 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.0595 | 1.11892 | ||||||||
\(207\) | −2.01721 | −0.140206 | ||||||||
\(208\) | −8.81259 | −0.611043 | ||||||||
\(209\) | −28.1407 | −1.94653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6762 | 1.28573 | 0.642863 | − | 0.765981i | \(-0.277747\pi\) | ||||
0.642863 | + | 0.765981i | \(0.277747\pi\) | |||||||
\(212\) | 12.4825 | 0.857303 | ||||||||
\(213\) | −9.13444 | −0.625882 | ||||||||
\(214\) | −6.40078 | −0.437548 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.72506 | 0.525624 | ||||||||
\(217\) | 6.49337 | 0.440799 | ||||||||
\(218\) | 28.8027 | 1.95077 | ||||||||
\(219\) | 16.2371 | 1.09720 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.54543 | −0.440293 | ||||||||
\(222\) | −2.76211 | −0.185381 | ||||||||
\(223\) | −5.74937 | −0.385006 | −0.192503 | − | 0.981296i | \(-0.561661\pi\) | ||||
−0.192503 | + | 0.981296i | \(0.561661\pi\) | |||||||
\(224\) | 5.70087 | 0.380905 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.2250 | −0.946232 | ||||||||
\(227\) | 4.73284 | 0.314130 | 0.157065 | − | 0.987588i | \(-0.449797\pi\) | ||||
0.157065 | + | 0.987588i | \(0.449797\pi\) | |||||||
\(228\) | −9.07177 | −0.600793 | ||||||||
\(229\) | 11.2504 | 0.743445 | 0.371723 | − | 0.928344i | \(-0.378767\pi\) | ||||
0.371723 | + | 0.928344i | \(0.378767\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.41697 | −0.224820 | ||||||||
\(232\) | −2.53988 | −0.166751 | ||||||||
\(233\) | −12.6822 | −0.830839 | −0.415419 | − | 0.909630i | \(-0.636365\pi\) | ||||
−0.415419 | + | 0.909630i | \(0.636365\pi\) | |||||||
\(234\) | −6.29926 | −0.411795 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.559125 | −0.0363960 | ||||||||
\(237\) | −4.06391 | −0.263979 | ||||||||
\(238\) | 6.54138 | 0.424015 | ||||||||
\(239\) | 8.19034 | 0.529789 | 0.264895 | − | 0.964277i | \(-0.414663\pi\) | ||||
0.264895 | + | 0.964277i | \(0.414663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.26668 | 0.210425 | 0.105213 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105213 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(242\) | 1.55486 | 0.0999503 | ||||||||
\(243\) | 16.0326 | 1.02849 | ||||||||
\(244\) | 4.67601 | 0.299351 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.93903 | 0.633690 | ||||||||
\(247\) | −14.4320 | −0.918287 | ||||||||
\(248\) | 10.0851 | 0.640404 | ||||||||
\(249\) | −14.7227 | −0.933011 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.14200 | −0.513918 | −0.256959 | − | 0.966422i | \(-0.582721\pi\) | ||||
−0.256959 | + | 0.966422i | \(0.582721\pi\) | |||||||
\(252\) | 2.26094 | 0.142426 | ||||||||
\(253\) | 3.44676 | 0.216696 | ||||||||
\(254\) | −16.6266 | −1.04325 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.0298 | 1.25186 | ||||||||
\(257\) | −6.24425 | −0.389506 | −0.194753 | − | 0.980852i | \(-0.562390\pi\) | ||||
−0.194753 | + | 0.980852i | \(0.562390\pi\) | |||||||
\(258\) | −21.1636 | −1.31759 | ||||||||
\(259\) | 1.57716 | 0.0980000 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.29879 | −0.204190 | ||||||||
\(262\) | −26.2589 | −1.62228 | ||||||||
\(263\) | 2.46177 | 0.151799 | 0.0758997 | − | 0.997115i | \(-0.475817\pi\) | ||||
0.0758997 | + | 0.997115i | \(0.475817\pi\) | |||||||
\(264\) | −5.30702 | −0.326625 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.4231 | 0.884336 | ||||||||
\(267\) | −7.74828 | −0.474187 | ||||||||
\(268\) | −0.0897428 | −0.00548191 | ||||||||
\(269\) | 6.46545 | 0.394205 | 0.197103 | − | 0.980383i | \(-0.436847\pi\) | ||||
0.197103 | + | 0.980383i | \(0.436847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.9101 | 1.51318 | 0.756589 | − | 0.653891i | \(-0.226864\pi\) | ||||
0.756589 | + | 0.653891i | \(0.226864\pi\) | |||||||
\(272\) | 18.4601 | 1.11931 | ||||||||
\(273\) | −1.75240 | −0.106060 | ||||||||
\(274\) | −16.8823 | −1.01989 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.11114 | 0.0668828 | ||||||||
\(277\) | −27.1737 | −1.63271 | −0.816355 | − | 0.577551i | \(-0.804009\pi\) | ||||
−0.816355 | + | 0.577551i | \(0.804009\pi\) | |||||||
\(278\) | −7.54479 | −0.452506 | ||||||||
\(279\) | 13.0985 | 0.784186 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.2788 | 0.971112 | 0.485556 | − | 0.874206i | \(-0.338617\pi\) | ||||
0.485556 | + | 0.874206i | \(0.338617\pi\) | |||||||
\(282\) | −15.0436 | −0.895836 | ||||||||
\(283\) | −18.1155 | −1.07685 | −0.538427 | − | 0.842672i | \(-0.680981\pi\) | ||||
−0.538427 | + | 0.842672i | \(0.680981\pi\) | |||||||
\(284\) | −10.3274 | −0.612817 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.7634 | 0.636453 | ||||||||
\(287\) | −5.67517 | −0.334995 | ||||||||
\(288\) | 11.4998 | 0.677635 | ||||||||
\(289\) | −3.28899 | −0.193470 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.36936 | 0.256136 | ||||||||
\(292\) | 18.3576 | 1.07430 | ||||||||
\(293\) | −20.7733 | −1.21359 | −0.606796 | − | 0.794858i | \(-0.707545\pi\) | ||||
−0.606796 | + | 0.794858i | \(0.707545\pi\) | |||||||
\(294\) | 1.75132 | 0.102139 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.44954 | 0.142377 | ||||||||
\(297\) | −17.1437 | −0.994776 | ||||||||
\(298\) | −15.4716 | −0.896245 | ||||||||
\(299\) | 1.76768 | 0.102228 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0844 | 0.696533 | ||||||||
\(302\) | 24.3815 | 1.40300 | ||||||||
\(303\) | −0.151771 | −0.00871901 | ||||||||
\(304\) | 40.7027 | 2.33446 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.1953 | 0.754327 | ||||||||
\(307\) | 5.15026 | 0.293941 | 0.146970 | − | 0.989141i | \(-0.453048\pi\) | ||||
0.146970 | + | 0.989141i | \(0.453048\pi\) | |||||||
\(308\) | −3.86322 | −0.220127 | ||||||||
\(309\) | 9.01212 | 0.512682 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1433 | 0.745287 | 0.372643 | − | 0.927975i | \(-0.378451\pi\) | ||||
0.372643 | + | 0.927975i | \(0.378451\pi\) | |||||||
\(312\) | −2.72172 | −0.154087 | ||||||||
\(313\) | 31.3762 | 1.77349 | 0.886744 | − | 0.462261i | \(-0.152962\pi\) | ||||
0.886744 | + | 0.462261i | \(0.152962\pi\) | |||||||
\(314\) | −0.473626 | −0.0267283 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.59465 | −0.258469 | ||||||||
\(317\) | 9.97763 | 0.560399 | 0.280200 | − | 0.959942i | \(-0.409599\pi\) | ||||
0.280200 | + | 0.959942i | \(0.409599\pi\) | |||||||
\(318\) | 19.5042 | 1.09374 | ||||||||
\(319\) | 5.63657 | 0.315587 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.59193 | −0.200482 | ||||||||
\(322\) | −1.76659 | −0.0984480 | ||||||||
\(323\) | 30.2314 | 1.68212 | ||||||||
\(324\) | 1.25618 | 0.0697877 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.1608 | 1.17199 | ||||||||
\(327\) | 16.1633 | 0.893830 | ||||||||
\(328\) | −8.81431 | −0.486689 | ||||||||
\(329\) | 8.58989 | 0.473576 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.3591 | 1.66869 | 0.834344 | − | 0.551245i | \(-0.185847\pi\) | ||||
0.834344 | + | 0.551245i | \(0.185847\pi\) | |||||||
\(332\) | −16.6454 | −0.913536 | ||||||||
\(333\) | 3.18146 | 0.174343 | ||||||||
\(334\) | 7.42417 | 0.406232 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.94232 | 0.269626 | ||||||||
\(337\) | 32.0709 | 1.74701 | 0.873506 | − | 0.486814i | \(-0.161841\pi\) | ||||
0.873506 | + | 0.486814i | \(0.161841\pi\) | |||||||
\(338\) | −17.4456 | −0.948915 | ||||||||
\(339\) | −7.98265 | −0.433558 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.3811 | −1.21200 | ||||||||
\(342\) | 29.0944 | 1.57324 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 18.7687 | 1.01194 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.7642 | −1.81518 | ||||||||
\(347\) | 17.5315 | 0.941141 | 0.470571 | − | 0.882362i | \(-0.344048\pi\) | ||||
0.470571 | + | 0.882362i | \(0.344048\pi\) | |||||||
\(348\) | 1.81708 | 0.0974055 | ||||||||
\(349\) | −14.7333 | −0.788657 | −0.394329 | − | 0.918970i | \(-0.629023\pi\) | ||||
−0.394329 | + | 0.918970i | \(0.629023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.79218 | −0.469292 | ||||||||
\(352\) | −19.6495 | −1.04732 | ||||||||
\(353\) | 11.2457 | 0.598546 | 0.299273 | − | 0.954167i | \(-0.403256\pi\) | ||||
0.299273 | + | 0.954167i | \(0.403256\pi\) | |||||||
\(354\) | −0.873647 | −0.0464338 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.76019 | −0.464289 | ||||||||
\(357\) | 3.67084 | 0.194281 | ||||||||
\(358\) | −8.00380 | −0.423014 | ||||||||
\(359\) | 29.1214 | 1.53697 | 0.768485 | − | 0.639868i | \(-0.221011\pi\) | ||||
0.768485 | + | 0.639868i | \(0.221011\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47.6571 | 2.50827 | ||||||||
\(362\) | 28.8508 | 1.51637 | ||||||||
\(363\) | 0.872544 | 0.0457967 | ||||||||
\(364\) | −1.98126 | −0.103846 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.30638 | 0.381910 | ||||||||
\(367\) | −26.7214 | −1.39484 | −0.697422 | − | 0.716660i | \(-0.745670\pi\) | ||||
−0.697422 | + | 0.716660i | \(0.745670\pi\) | |||||||
\(368\) | −4.98540 | −0.259882 | ||||||||
\(369\) | −11.4480 | −0.595959 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.1369 | −0.578198 | ||||||||
\(372\) | −7.21505 | −0.374083 | ||||||||
\(373\) | 10.2153 | 0.528930 | 0.264465 | − | 0.964395i | \(-0.414805\pi\) | ||||
0.264465 | + | 0.964395i | \(0.414805\pi\) | |||||||
\(374\) | −22.5466 | −1.16586 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.3413 | 0.688023 | ||||||||
\(377\) | 2.89073 | 0.148880 | ||||||||
\(378\) | 8.78674 | 0.451941 | ||||||||
\(379\) | 27.7864 | 1.42729 | 0.713646 | − | 0.700506i | \(-0.247042\pi\) | ||||
0.713646 | + | 0.700506i | \(0.247042\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.33040 | −0.478011 | ||||||||
\(382\) | 8.38992 | 0.429266 | ||||||||
\(383\) | −10.8751 | −0.555692 | −0.277846 | − | 0.960626i | \(-0.589620\pi\) | ||||
−0.277846 | + | 0.960626i | \(0.589620\pi\) | |||||||
\(384\) | 11.1276 | 0.567852 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −47.4854 | −2.41694 | ||||||||
\(387\) | 24.3768 | 1.23914 | ||||||||
\(388\) | 4.93999 | 0.250790 | ||||||||
\(389\) | 31.8089 | 1.61277 | 0.806387 | − | 0.591388i | \(-0.201420\pi\) | ||||
0.806387 | + | 0.591388i | \(0.201420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.70284 | −0.187261 | ||||||||
\(392\) | −1.55314 | −0.0784452 | ||||||||
\(393\) | −14.7357 | −0.743320 | ||||||||
\(394\) | 45.5226 | 2.29340 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.79292 | −0.391609 | ||||||||
\(397\) | −4.64600 | −0.233176 | −0.116588 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116588 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(398\) | −43.3927 | −2.17508 | ||||||||
\(399\) | 8.09382 | 0.405198 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.00993722 | −0.000496241 0 | −0.000248120 | − | 1.00000i | \(-0.500079\pi\) | ||||
−0.000248120 | 1.00000i | \(0.500079\pi\) | ||||||||
\(402\) | −0.140225 | −0.00699380 | ||||||||
\(403\) | −11.4782 | −0.571770 | ||||||||
\(404\) | −0.171592 | −0.00853701 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.88894 | −0.143376 | ||||||||
\(407\) | −5.43609 | −0.269457 | ||||||||
\(408\) | 5.70131 | 0.282257 | ||||||||
\(409\) | 28.9009 | 1.42906 | 0.714529 | − | 0.699606i | \(-0.246641\pi\) | ||||
0.714529 | + | 0.699606i | \(0.246641\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.47385 | −0.467310 | ||||||||
\(412\) | 10.1891 | 0.501980 | ||||||||
\(413\) | 0.498851 | 0.0245468 | ||||||||
\(414\) | −3.56357 | −0.175140 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.0773 | −0.494081 | ||||||||
\(417\) | −4.23392 | −0.207336 | ||||||||
\(418\) | −49.7129 | −2.43154 | ||||||||
\(419\) | −34.8023 | −1.70020 | −0.850101 | − | 0.526620i | \(-0.823459\pi\) | ||||
−0.850101 | + | 0.526620i | \(0.823459\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.9555 | −1.31373 | −0.656865 | − | 0.754008i | \(-0.728118\pi\) | ||||
−0.656865 | + | 0.754008i | \(0.728118\pi\) | |||||||
\(422\) | 32.9932 | 1.60608 | ||||||||
\(423\) | 17.3276 | 0.842497 | ||||||||
\(424\) | −17.2971 | −0.840020 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.1368 | −0.781830 | ||||||||
\(427\) | −4.17193 | −0.201894 | ||||||||
\(428\) | −4.06103 | −0.196297 | ||||||||
\(429\) | 6.04011 | 0.291619 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.9939 | 0.529557 | 0.264779 | − | 0.964309i | \(-0.414701\pi\) | ||||
0.264779 | + | 0.964309i | \(0.414701\pi\) | |||||||
\(432\) | 24.7966 | 1.19303 | ||||||||
\(433\) | −36.7288 | −1.76508 | −0.882538 | − | 0.470241i | \(-0.844167\pi\) | ||||
−0.882538 | + | 0.470241i | \(0.844167\pi\) | |||||||
\(434\) | 11.4711 | 0.550631 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.2741 | 0.875173 | ||||||||
\(437\) | −8.16438 | −0.390555 | ||||||||
\(438\) | 28.6842 | 1.37058 | ||||||||
\(439\) | 17.8485 | 0.851865 | 0.425932 | − | 0.904755i | \(-0.359946\pi\) | ||||
0.425932 | + | 0.904755i | \(0.359946\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.01721 | −0.0960576 | ||||||||
\(442\) | −11.5631 | −0.549999 | ||||||||
\(443\) | 14.5466 | 0.691128 | 0.345564 | − | 0.938395i | \(-0.387688\pi\) | ||||
0.345564 | + | 0.938395i | \(0.387688\pi\) | |||||||
\(444\) | −1.75245 | −0.0831674 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.1568 | −0.480936 | ||||||||
\(447\) | −8.68221 | −0.410655 | ||||||||
\(448\) | 0.100276 | 0.00473761 | ||||||||
\(449\) | 2.58177 | 0.121841 | 0.0609207 | − | 0.998143i | \(-0.480596\pi\) | ||||
0.0609207 | + | 0.998143i | \(0.480596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5609 | 0.921089 | ||||||||
\(452\) | −9.02517 | −0.424508 | ||||||||
\(453\) | 13.6822 | 0.642847 | ||||||||
\(454\) | 8.36098 | 0.392400 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.5708 | 0.588682 | ||||||||
\(457\) | −36.1923 | −1.69300 | −0.846502 | − | 0.532385i | \(-0.821296\pi\) | ||||
−0.846502 | + | 0.532385i | \(0.821296\pi\) | |||||||
\(458\) | 19.8747 | 0.928686 | ||||||||
\(459\) | 18.4174 | 0.859649 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.30197 | 0.153788 | 0.0768939 | − | 0.997039i | \(-0.475500\pi\) | ||||
0.0768939 | + | 0.997039i | \(0.475500\pi\) | |||||||
\(462\) | −6.03638 | −0.280838 | ||||||||
\(463\) | −28.8596 | −1.34122 | −0.670610 | − | 0.741810i | \(-0.733968\pi\) | ||||
−0.670610 | + | 0.741810i | \(0.733968\pi\) | |||||||
\(464\) | −8.15275 | −0.378482 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.4042 | −1.03785 | ||||||||
\(467\) | −38.2124 | −1.76826 | −0.884130 | − | 0.467240i | \(-0.845248\pi\) | ||||
−0.884130 | + | 0.467240i | \(0.845248\pi\) | |||||||
\(468\) | −3.99662 | −0.184744 | ||||||||
\(469\) | 0.0800684 | 0.00369721 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.265786 | −0.0122468 | ||||||||
\(472\) | 0.774783 | 0.0356623 | ||||||||
\(473\) | −41.6520 | −1.91516 | ||||||||
\(474\) | −7.17925 | −0.329754 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.15024 | 0.190226 | ||||||||
\(477\) | −22.4654 | −1.02862 | ||||||||
\(478\) | 14.4689 | 0.661794 | ||||||||
\(479\) | −4.22746 | −0.193158 | −0.0965788 | − | 0.995325i | \(-0.530790\pi\) | ||||
−0.0965788 | + | 0.995325i | \(0.530790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.78791 | −0.127118 | ||||||||
\(482\) | 5.77086 | 0.262856 | ||||||||
\(483\) | −0.991358 | −0.0451084 | ||||||||
\(484\) | 0.986496 | 0.0448407 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 28.3230 | 1.28476 | ||||||||
\(487\) | −29.1490 | −1.32087 | −0.660433 | − | 0.750885i | \(-0.729627\pi\) | ||||
−0.660433 | + | 0.750885i | \(0.729627\pi\) | |||||||
\(488\) | −6.47957 | −0.293316 | ||||||||
\(489\) | 11.8748 | 0.536999 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.13897 | −0.231918 | −0.115959 | − | 0.993254i | \(-0.536994\pi\) | ||||
−0.115959 | + | 0.993254i | \(0.536994\pi\) | |||||||
\(492\) | 6.30591 | 0.284292 | ||||||||
\(493\) | −6.05534 | −0.272719 | ||||||||
\(494\) | −25.4954 | −1.14709 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.3721 | 1.45355 | ||||||||
\(497\) | 9.21407 | 0.413308 | ||||||||
\(498\) | −26.0089 | −1.16549 | ||||||||
\(499\) | 15.8487 | 0.709483 | 0.354742 | − | 0.934964i | \(-0.384569\pi\) | ||||
0.354742 | + | 0.934964i | \(0.384569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.16623 | 0.186133 | ||||||||
\(502\) | −14.3835 | −0.641969 | ||||||||
\(503\) | −20.9422 | −0.933766 | −0.466883 | − | 0.884319i | \(-0.654623\pi\) | ||||
−0.466883 | + | 0.884319i | \(0.654623\pi\) | |||||||
\(504\) | −3.13300 | −0.139555 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.08900 | 0.270689 | ||||||||
\(507\) | −9.78997 | −0.434788 | ||||||||
\(508\) | −10.5489 | −0.468033 | ||||||||
\(509\) | 22.2352 | 0.985558 | 0.492779 | − | 0.870154i | \(-0.335981\pi\) | ||||
0.492779 | + | 0.870154i | \(0.335981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3786 | −0.724547 | ||||||||
\(512\) | 12.9351 | 0.571657 | ||||||||
\(513\) | 40.6084 | 1.79290 | ||||||||
\(514\) | −11.0310 | −0.486557 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.4275 | −0.591111 | ||||||||
\(517\) | −29.6073 | −1.30213 | ||||||||
\(518\) | 2.78619 | 0.122418 | ||||||||
\(519\) | −18.9475 | −0.831704 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.9572 | −1.00577 | −0.502886 | − | 0.864353i | \(-0.667728\pi\) | ||||
−0.502886 | + | 0.864353i | \(0.667728\pi\) | |||||||
\(522\) | −5.82760 | −0.255067 | ||||||||
\(523\) | −11.5417 | −0.504682 | −0.252341 | − | 0.967638i | \(-0.581200\pi\) | ||||
−0.252341 | + | 0.967638i | \(0.581200\pi\) | |||||||
\(524\) | −16.6602 | −0.727804 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.34894 | 0.189623 | ||||||||
\(527\) | 24.0439 | 1.04737 | ||||||||
\(528\) | −17.0350 | −0.741352 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.00629 | 0.0436691 | ||||||||
\(532\) | 9.15085 | 0.396740 | ||||||||
\(533\) | 10.0319 | 0.434529 | ||||||||
\(534\) | −13.6880 | −0.592338 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.124357 | 0.00537141 | ||||||||
\(537\) | −4.49151 | −0.193823 | ||||||||
\(538\) | 11.4218 | 0.492428 | ||||||||
\(539\) | 3.44676 | 0.148462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.7878 | −1.23768 | −0.618841 | − | 0.785516i | \(-0.712398\pi\) | ||||
−0.618841 | + | 0.785516i | \(0.712398\pi\) | |||||||
\(542\) | 44.0058 | 1.89021 | ||||||||
\(543\) | 16.1903 | 0.694791 | ||||||||
\(544\) | 21.1094 | 0.905058 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.09577 | −0.132487 | ||||||||
\(547\) | 24.8991 | 1.06461 | 0.532304 | − | 0.846553i | \(-0.321326\pi\) | ||||
0.532304 | + | 0.846553i | \(0.321326\pi\) | |||||||
\(548\) | −10.7111 | −0.457556 | ||||||||
\(549\) | −8.41565 | −0.359171 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.3514 | −0.568789 | ||||||||
\(552\) | −1.53971 | −0.0655345 | ||||||||
\(553\) | 4.09934 | 0.174322 | ||||||||
\(554\) | −48.0047 | −2.03952 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.78686 | −0.203008 | ||||||||
\(557\) | −12.5854 | −0.533262 | −0.266631 | − | 0.963799i | \(-0.585910\pi\) | ||||
−0.266631 | + | 0.963799i | \(0.585910\pi\) | |||||||
\(558\) | 23.1396 | 0.979578 | ||||||||
\(559\) | −21.3614 | −0.903489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.6525 | −0.534189 | ||||||||
\(562\) | 28.7579 | 1.21308 | ||||||||
\(563\) | −16.9502 | −0.714366 | −0.357183 | − | 0.934034i | \(-0.616263\pi\) | ||||
−0.357183 | + | 0.934034i | \(0.616263\pi\) | |||||||
\(564\) | −9.54458 | −0.401899 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −32.0025 | −1.34517 | ||||||||
\(567\) | −1.12076 | −0.0470675 | ||||||||
\(568\) | 14.3107 | 0.600464 | ||||||||
\(569\) | 17.9630 | 0.753049 | 0.376525 | − | 0.926407i | \(-0.377119\pi\) | ||||
0.376525 | + | 0.926407i | \(0.377119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.3483 | −0.977097 | −0.488549 | − | 0.872537i | \(-0.662474\pi\) | ||||
−0.488549 | + | 0.872537i | \(0.662474\pi\) | |||||||
\(572\) | 6.82894 | 0.285532 | ||||||||
\(573\) | 4.70819 | 0.196687 | ||||||||
\(574\) | −10.0257 | −0.418464 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.202278 | 0.00842826 | ||||||||
\(577\) | 26.0419 | 1.08414 | 0.542068 | − | 0.840334i | \(-0.317641\pi\) | ||||
0.542068 | + | 0.840334i | \(0.317641\pi\) | |||||||
\(578\) | −5.81028 | −0.241676 | ||||||||
\(579\) | −26.6475 | −1.10743 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.8510 | 0.616124 | ||||||||
\(582\) | 7.71885 | 0.319957 | ||||||||
\(583\) | 38.3861 | 1.58979 | ||||||||
\(584\) | −25.4382 | −1.05264 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.6979 | −1.51598 | ||||||||
\(587\) | 23.4126 | 0.966339 | 0.483170 | − | 0.875527i | \(-0.339485\pi\) | ||||
0.483170 | + | 0.875527i | \(0.339485\pi\) | |||||||
\(588\) | 1.11114 | 0.0458227 | ||||||||
\(589\) | 53.0144 | 2.18442 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.5460 | 1.05082 | ||||||||
\(592\) | 7.86277 | 0.323158 | ||||||||
\(593\) | −13.8008 | −0.566732 | −0.283366 | − | 0.959012i | \(-0.591451\pi\) | ||||
−0.283366 | + | 0.959012i | \(0.591451\pi\) | |||||||
\(594\) | −30.2858 | −1.24264 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.81609 | −0.402083 | ||||||||
\(597\) | −24.3508 | −0.996610 | ||||||||
\(598\) | 3.12276 | 0.127699 | ||||||||
\(599\) | 45.7819 | 1.87060 | 0.935298 | − | 0.353860i | \(-0.115131\pi\) | ||||
0.935298 | + | 0.353860i | \(0.115131\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.844411 | −0.0344442 | −0.0172221 | − | 0.999852i | \(-0.505482\pi\) | ||||
−0.0172221 | + | 0.999852i | \(0.505482\pi\) | |||||||
\(602\) | 21.3481 | 0.870085 | ||||||||
\(603\) | 0.161515 | 0.00657739 | ||||||||
\(604\) | 15.4691 | 0.629428 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.268116 | −0.0108915 | ||||||||
\(607\) | −20.8458 | −0.846105 | −0.423052 | − | 0.906105i | \(-0.639041\pi\) | ||||
−0.423052 | + | 0.906105i | \(0.639041\pi\) | |||||||
\(608\) | 46.5441 | 1.88761 | ||||||||
\(609\) | −1.62119 | −0.0656940 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.1842 | −0.614286 | ||||||||
\(612\) | 8.37190 | 0.338414 | ||||||||
\(613\) | −14.1486 | −0.571458 | −0.285729 | − | 0.958310i | \(-0.592236\pi\) | ||||
−0.285729 | + | 0.958310i | \(0.592236\pi\) | |||||||
\(614\) | 9.09838 | 0.367181 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.35328 | 0.215690 | ||||||||
\(617\) | 5.61486 | 0.226046 | 0.113023 | − | 0.993592i | \(-0.463947\pi\) | ||||
0.113023 | + | 0.993592i | \(0.463947\pi\) | |||||||
\(618\) | 15.9207 | 0.640424 | ||||||||
\(619\) | −21.2289 | −0.853261 | −0.426631 | − | 0.904426i | \(-0.640300\pi\) | ||||
−0.426631 | + | 0.904426i | \(0.640300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.97385 | −0.199594 | ||||||||
\(622\) | 23.2187 | 0.930986 | ||||||||
\(623\) | 7.81583 | 0.313134 | ||||||||
\(624\) | −8.73643 | −0.349737 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 55.4288 | 2.21538 | ||||||||
\(627\) | −27.8975 | −1.11412 | ||||||||
\(628\) | −0.300496 | −0.0119911 | ||||||||
\(629\) | 5.83997 | 0.232855 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.1170 | −0.522181 | −0.261090 | − | 0.965314i | \(-0.584082\pi\) | ||||
−0.261090 | + | 0.965314i | \(0.584082\pi\) | |||||||
\(632\) | 6.36683 | 0.253259 | ||||||||
\(633\) | 18.5148 | 0.735899 | ||||||||
\(634\) | 17.6263 | 0.700031 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.3746 | 0.490686 | ||||||||
\(637\) | 1.76768 | 0.0700380 | ||||||||
\(638\) | 9.95749 | 0.394221 | ||||||||
\(639\) | 18.5867 | 0.735279 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.1415 | −0.400566 | −0.200283 | − | 0.979738i | \(-0.564186\pi\) | ||||
−0.200283 | + | 0.979738i | \(0.564186\pi\) | |||||||
\(642\) | −6.34546 | −0.250435 | ||||||||
\(643\) | −21.4125 | −0.844428 | −0.422214 | − | 0.906496i | \(-0.638747\pi\) | ||||
−0.422214 | + | 0.906496i | \(0.638747\pi\) | |||||||
\(644\) | −1.12083 | −0.0441668 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 53.4063 | 2.10124 | ||||||||
\(647\) | 25.0768 | 0.985872 | 0.492936 | − | 0.870066i | \(-0.335924\pi\) | ||||
0.492936 | + | 0.870066i | \(0.335924\pi\) | |||||||
\(648\) | −1.74069 | −0.0683809 | ||||||||
\(649\) | −1.71942 | −0.0674931 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.43726 | 0.252296 | ||||||||
\(652\) | 13.4257 | 0.525790 | ||||||||
\(653\) | 21.5701 | 0.844102 | 0.422051 | − | 0.906572i | \(-0.361310\pi\) | ||||
0.422051 | + | 0.906572i | \(0.361310\pi\) | |||||||
\(654\) | 28.5538 | 1.11654 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −28.2930 | −1.10466 | ||||||||
\(657\) | −33.0391 | −1.28898 | ||||||||
\(658\) | 15.1748 | 0.591575 | ||||||||
\(659\) | 35.9704 | 1.40121 | 0.700604 | − | 0.713550i | \(-0.252914\pi\) | ||||
0.700604 | + | 0.713550i | \(0.252914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.66323 | −0.220274 | −0.110137 | − | 0.993916i | \(-0.535129\pi\) | ||||
−0.110137 | + | 0.993916i | \(0.535129\pi\) | |||||||
\(662\) | 53.6320 | 2.08447 | ||||||||
\(663\) | −6.48887 | −0.252007 | ||||||||
\(664\) | 23.0656 | 0.895120 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.62033 | 0.217783 | ||||||||
\(667\) | 1.63532 | 0.0633200 | ||||||||
\(668\) | 4.71033 | 0.182248 | ||||||||
\(669\) | −5.69968 | −0.220363 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.3796 | 0.555119 | ||||||||
\(672\) | 5.65160 | 0.218015 | ||||||||
\(673\) | 6.36930 | 0.245519 | 0.122759 | − | 0.992436i | \(-0.460826\pi\) | ||||
0.122759 | + | 0.992436i | \(0.460826\pi\) | |||||||
\(674\) | 56.6559 | 2.18231 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0685 | −0.425712 | ||||||||
\(677\) | −23.2321 | −0.892881 | −0.446440 | − | 0.894813i | \(-0.647309\pi\) | ||||
−0.446440 | + | 0.894813i | \(0.647309\pi\) | |||||||
\(678\) | −14.1020 | −0.541586 | ||||||||
\(679\) | −4.40745 | −0.169142 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.69194 | 0.179796 | ||||||||
\(682\) | −39.5381 | −1.51399 | ||||||||
\(683\) | −35.9894 | −1.37710 | −0.688548 | − | 0.725191i | \(-0.741751\pi\) | ||||
−0.688548 | + | 0.725191i | \(0.741751\pi\) | |||||||
\(684\) | 18.4592 | 0.705805 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.76659 | −0.0674486 | ||||||||
\(687\) | 11.1531 | 0.425519 | ||||||||
\(688\) | 60.2456 | 2.29684 | ||||||||
\(689\) | 19.6864 | 0.749994 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.3624 | −1.15504 | −0.577519 | − | 0.816377i | \(-0.695979\pi\) | ||||
−0.577519 | + | 0.816377i | \(0.695979\pi\) | |||||||
\(692\) | −21.4220 | −0.814343 | ||||||||
\(693\) | 6.95283 | 0.264116 | ||||||||
\(694\) | 30.9709 | 1.17564 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.51793 | −0.0954419 | ||||||||
\(697\) | −21.0142 | −0.795971 | ||||||||
\(698\) | −26.0277 | −0.985163 | ||||||||
\(699\) | −12.5726 | −0.475539 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.5382 | −1.07787 | −0.538936 | − | 0.842347i | \(-0.681174\pi\) | ||||
−0.538936 | + | 0.842347i | \(0.681174\pi\) | |||||||
\(702\) | −15.5321 | −0.586223 | ||||||||
\(703\) | 12.8765 | 0.485648 | ||||||||
\(704\) | −0.345628 | −0.0130264 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.8664 | 0.747683 | ||||||||
\(707\) | 0.153094 | 0.00575769 | ||||||||
\(708\) | −0.554293 | −0.0208316 | ||||||||
\(709\) | −7.71848 | −0.289874 | −0.144937 | − | 0.989441i | \(-0.546298\pi\) | ||||
−0.144937 | + | 0.989441i | \(0.546298\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.26922 | 0.310120 | ||||||||
\(712\) | 12.1390 | 0.454930 | ||||||||
\(713\) | −6.49337 | −0.243179 | ||||||||
\(714\) | 6.48485 | 0.242689 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.07809 | −0.189777 | ||||||||
\(717\) | 8.11956 | 0.303231 | ||||||||
\(718\) | 51.4455 | 1.91993 | ||||||||
\(719\) | −17.4122 | −0.649366 | −0.324683 | − | 0.945823i | \(-0.605258\pi\) | ||||
−0.324683 | + | 0.945823i | \(0.605258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.09068 | −0.338555 | ||||||||
\(722\) | 84.1904 | 3.13324 | ||||||||
\(723\) | 3.23845 | 0.120439 | ||||||||
\(724\) | 18.3047 | 0.680288 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.54142 | 0.0572076 | ||||||||
\(727\) | 1.06900 | 0.0396470 | 0.0198235 | − | 0.999803i | \(-0.493690\pi\) | ||||
0.0198235 | + | 0.999803i | \(0.493690\pi\) | |||||||
\(728\) | 2.74545 | 0.101753 | ||||||||
\(729\) | 12.5318 | 0.464140 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44.7466 | 1.65501 | ||||||||
\(732\) | 4.63560 | 0.171337 | ||||||||
\(733\) | −26.2852 | −0.970866 | −0.485433 | − | 0.874274i | \(-0.661338\pi\) | ||||
−0.485433 | + | 0.874274i | \(0.661338\pi\) | |||||||
\(734\) | −47.2056 | −1.74239 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.70087 | −0.210137 | ||||||||
\(737\) | −0.275976 | −0.0101657 | ||||||||
\(738\) | −20.2239 | −0.744451 | ||||||||
\(739\) | −26.6622 | −0.980783 | −0.490392 | − | 0.871502i | \(-0.663146\pi\) | ||||
−0.490392 | + | 0.871502i | \(0.663146\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.3073 | −0.525591 | ||||||||
\(742\) | −19.6743 | −0.722265 | ||||||||
\(743\) | −28.5431 | −1.04714 | −0.523572 | − | 0.851981i | \(-0.675401\pi\) | ||||
−0.523572 | + | 0.851981i | \(0.675401\pi\) | |||||||
\(744\) | 9.99793 | 0.366542 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.0463 | 0.660721 | ||||||||
\(747\) | 29.9576 | 1.09609 | ||||||||
\(748\) | −14.3049 | −0.523038 | ||||||||
\(749\) | 3.62325 | 0.132391 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0773 | 0.367728 | 0.183864 | − | 0.982952i | \(-0.441139\pi\) | ||||
0.183864 | + | 0.982952i | \(0.441139\pi\) | |||||||
\(752\) | 42.8240 | 1.56163 | ||||||||
\(753\) | −8.07163 | −0.294147 | ||||||||
\(754\) | 5.10672 | 0.185976 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.57483 | 0.202754 | ||||||||
\(757\) | 26.3007 | 0.955916 | 0.477958 | − | 0.878383i | \(-0.341377\pi\) | ||||
0.477958 | + | 0.878383i | \(0.341377\pi\) | |||||||
\(758\) | 49.0871 | 1.78292 | ||||||||
\(759\) | 3.41697 | 0.124028 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.2702 | −0.517294 | −0.258647 | − | 0.965972i | \(-0.583277\pi\) | ||||
−0.258647 | + | 0.965972i | \(0.583277\pi\) | |||||||
\(762\) | −16.4830 | −0.597115 | ||||||||
\(763\) | −16.3042 | −0.590250 | ||||||||
\(764\) | 5.32306 | 0.192582 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.2118 | −0.694151 | ||||||||
\(767\) | −0.881809 | −0.0318403 | ||||||||
\(768\) | 19.8567 | 0.716516 | ||||||||
\(769\) | 6.90481 | 0.248994 | 0.124497 | − | 0.992220i | \(-0.460268\pi\) | ||||
0.124497 | + | 0.992220i | \(0.460268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.19029 | −0.222938 | ||||||||
\(772\) | −30.1275 | −1.08431 | ||||||||
\(773\) | 14.5844 | 0.524565 | 0.262283 | − | 0.964991i | \(-0.415525\pi\) | ||||
0.262283 | + | 0.964991i | \(0.415525\pi\) | |||||||
\(774\) | 43.0637 | 1.54789 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.84537 | −0.245734 | ||||||||
\(777\) | 1.56353 | 0.0560913 | ||||||||
\(778\) | 56.1931 | 2.01462 | ||||||||
\(779\) | −46.3342 | −1.66010 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.7587 | −1.13641 | ||||||||
\(782\) | −6.54138 | −0.233919 | ||||||||
\(783\) | −8.13386 | −0.290680 | ||||||||
\(784\) | −4.98540 | −0.178050 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −26.0320 | −0.928529 | ||||||||
\(787\) | −35.9750 | −1.28237 | −0.641186 | − | 0.767386i | \(-0.721557\pi\) | ||||
−0.641186 | + | 0.767386i | \(0.721557\pi\) | |||||||
\(788\) | 28.8822 | 1.02889 | ||||||||
\(789\) | 2.44050 | 0.0868841 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.05224 | 0.286305 | ||||||||
\(792\) | 10.7987 | 0.383715 | ||||||||
\(793\) | 7.37463 | 0.261881 | ||||||||
\(794\) | −8.20755 | −0.291275 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.5309 | −0.975807 | ||||||||
\(797\) | −48.5020 | −1.71803 | −0.859014 | − | 0.511951i | \(-0.828923\pi\) | ||||
−0.859014 | + | 0.511951i | \(0.828923\pi\) | |||||||
\(798\) | 14.2984 | 0.506159 | ||||||||
\(799\) | 31.8070 | 1.12525 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.7662 | 0.557070 | ||||||||
\(802\) | −0.0175550 | −0.000619887 0 | ||||||||
\(803\) | 56.4532 | 1.99219 | ||||||||
\(804\) | −0.0889672 | −0.00313763 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.2772 | −0.714235 | ||||||||
\(807\) | 6.40957 | 0.225628 | ||||||||
\(808\) | 0.237776 | 0.00836491 | ||||||||
\(809\) | 32.9628 | 1.15891 | 0.579455 | − | 0.815004i | \(-0.303265\pi\) | ||||
0.579455 | + | 0.815004i | \(0.303265\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.93536 | −0.348878 | −0.174439 | − | 0.984668i | \(-0.555811\pi\) | ||||
−0.174439 | + | 0.984668i | \(0.555811\pi\) | |||||||
\(812\) | −1.83292 | −0.0643227 | ||||||||
\(813\) | 24.6948 | 0.866084 | ||||||||
\(814\) | −9.60332 | −0.336596 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 18.3006 | 0.640649 | ||||||||
\(817\) | 98.6616 | 3.45173 | ||||||||
\(818\) | 51.0559 | 1.78513 | ||||||||
\(819\) | 3.56578 | 0.124598 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.56735 | −0.159402 | −0.0797008 | − | 0.996819i | \(-0.525396\pi\) | ||||
−0.0797008 | + | 0.996819i | \(0.525396\pi\) | |||||||
\(822\) | −16.7364 | −0.583748 | ||||||||
\(823\) | 17.7786 | 0.619721 | 0.309861 | − | 0.950782i | \(-0.399718\pi\) | ||||
0.309861 | + | 0.950782i | \(0.399718\pi\) | |||||||
\(824\) | −14.1191 | −0.491861 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.881263 | 0.0306631 | ||||||||
\(827\) | −43.2668 | −1.50453 | −0.752266 | − | 0.658859i | \(-0.771039\pi\) | ||||
−0.752266 | + | 0.658859i | \(0.771039\pi\) | |||||||
\(828\) | −2.26094 | −0.0785732 | ||||||||
\(829\) | 13.1864 | 0.457983 | 0.228992 | − | 0.973428i | \(-0.426457\pi\) | ||||
0.228992 | + | 0.973428i | \(0.426457\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.9389 | −0.934499 | ||||||||
\(832\) | −0.177256 | −0.00614526 | ||||||||
\(833\) | −3.70284 | −0.128296 | ||||||||
\(834\) | −7.47959 | −0.258997 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −31.5408 | −1.09086 | ||||||||
\(837\) | 32.2971 | 1.11635 | ||||||||
\(838\) | −61.4812 | −2.12383 | ||||||||
\(839\) | −50.7869 | −1.75336 | −0.876679 | − | 0.481077i | \(-0.840246\pi\) | ||||
−0.876679 | + | 0.481077i | \(0.840246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3257 | −0.907783 | ||||||||
\(842\) | −47.6192 | −1.64106 | ||||||||
\(843\) | 16.1381 | 0.555826 | ||||||||
\(844\) | 20.9328 | 0.720538 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 30.6107 | 1.05242 | ||||||||
\(847\) | −0.880150 | −0.0302423 | ||||||||
\(848\) | −55.5218 | −1.90663 | ||||||||
\(849\) | −17.9589 | −0.616349 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.57716 | −0.0540643 | ||||||||
\(852\) | −10.2381 | −0.350752 | ||||||||
\(853\) | 3.62258 | 0.124035 | 0.0620174 | − | 0.998075i | \(-0.480247\pi\) | ||||
0.0620174 | + | 0.998075i | \(0.480247\pi\) | |||||||
\(854\) | −7.37007 | −0.252199 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.62739 | 0.192340 | ||||||||
\(857\) | 23.6336 | 0.807310 | 0.403655 | − | 0.914911i | \(-0.367740\pi\) | ||||
0.403655 | + | 0.914911i | \(0.367740\pi\) | |||||||
\(858\) | 10.6704 | 0.364281 | ||||||||
\(859\) | −50.9839 | −1.73955 | −0.869774 | − | 0.493450i | \(-0.835736\pi\) | ||||
−0.869774 | + | 0.493450i | \(0.835736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.62612 | −0.191738 | ||||||||
\(862\) | 19.4217 | 0.661505 | ||||||||
\(863\) | −44.8025 | −1.52509 | −0.762547 | − | 0.646933i | \(-0.776051\pi\) | ||||
−0.762547 | + | 0.646933i | \(0.776051\pi\) | |||||||
\(864\) | 28.3553 | 0.964666 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −64.8847 | −2.20487 | ||||||||
\(867\) | −3.26057 | −0.110735 | ||||||||
\(868\) | 7.27795 | 0.247030 | ||||||||
\(869\) | −14.1294 | −0.479308 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.141535 | −0.00479574 | ||||||||
\(872\) | −25.3226 | −0.857530 | ||||||||
\(873\) | −8.89075 | −0.300906 | ||||||||
\(874\) | −14.4231 | −0.487868 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18.1989 | 0.614886 | ||||||||
\(877\) | −10.3876 | −0.350763 | −0.175381 | − | 0.984501i | \(-0.556116\pi\) | ||||
−0.175381 | + | 0.984501i | \(0.556116\pi\) | |||||||
\(878\) | 31.5310 | 1.06412 | ||||||||
\(879\) | −20.5938 | −0.694612 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.08491 | −0.272388 | −0.136194 | − | 0.990682i | \(-0.543487\pi\) | ||||
−0.136194 | + | 0.990682i | \(0.543487\pi\) | |||||||
\(882\) | −3.56357 | −0.119992 | ||||||||
\(883\) | −4.95000 | −0.166581 | −0.0832903 | − | 0.996525i | \(-0.526543\pi\) | ||||
−0.0832903 | + | 0.996525i | \(0.526543\pi\) | |||||||
\(884\) | −7.33630 | −0.246746 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.6978 | 0.863333 | ||||||||
\(887\) | 12.0450 | 0.404431 | 0.202215 | − | 0.979341i | \(-0.435186\pi\) | ||||
0.202215 | + | 0.979341i | \(0.435186\pi\) | |||||||
\(888\) | 2.42837 | 0.0814909 | ||||||||
\(889\) | 9.41174 | 0.315660 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.86299 | 0.129415 | ||||||||
\(892\) | −6.44405 | −0.215763 | ||||||||
\(893\) | 70.1311 | 2.34685 | ||||||||
\(894\) | −15.3379 | −0.512975 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.2246 | −0.374987 | ||||||||
\(897\) | 1.75240 | 0.0585111 | ||||||||
\(898\) | 4.56092 | 0.152200 | ||||||||
\(899\) | −10.6188 | −0.354156 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.2381 | −1.37384 | ||||||||
\(902\) | 34.5561 | 1.15059 | ||||||||
\(903\) | 11.9800 | 0.398668 | ||||||||
\(904\) | 12.5062 | 0.415951 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.1708 | 0.803022 | ||||||||
\(907\) | −50.9499 | −1.69176 | −0.845881 | − | 0.533372i | \(-0.820925\pi\) | ||||
−0.845881 | + | 0.533372i | \(0.820925\pi\) | |||||||
\(908\) | 5.30470 | 0.176043 | ||||||||
\(909\) | 0.308822 | 0.0102430 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.3203 | 1.23648 | 0.618239 | − | 0.785990i | \(-0.287846\pi\) | ||||
0.618239 | + | 0.785990i | \(0.287846\pi\) | |||||||
\(912\) | 40.3510 | 1.33615 | ||||||||
\(913\) | −51.1879 | −1.69407 | ||||||||
\(914\) | −63.9368 | −2.11484 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.6097 | 0.416637 | ||||||||
\(917\) | 14.8642 | 0.490859 | ||||||||
\(918\) | 32.5359 | 1.07384 | ||||||||
\(919\) | 42.6489 | 1.40686 | 0.703429 | − | 0.710766i | \(-0.251651\pi\) | ||||
0.703429 | + | 0.710766i | \(0.251651\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.10575 | 0.168240 | ||||||||
\(922\) | 5.83321 | 0.192106 | ||||||||
\(923\) | −16.2875 | −0.536110 | ||||||||
\(924\) | −3.82983 | −0.125992 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −50.9830 | −1.67541 | ||||||||
\(927\) | −18.3378 | −0.602293 | ||||||||
\(928\) | −9.32277 | −0.306035 | ||||||||
\(929\) | 23.8363 | 0.782044 | 0.391022 | − | 0.920381i | \(-0.372122\pi\) | ||||
0.391022 | + | 0.920381i | \(0.372122\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.16438 | −0.267577 | ||||||||
\(932\) | −14.2145 | −0.465613 | ||||||||
\(933\) | 13.0297 | 0.426573 | ||||||||
\(934\) | −67.5056 | −2.20885 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.53814 | 0.181020 | ||||||||
\(937\) | −33.5831 | −1.09711 | −0.548555 | − | 0.836114i | \(-0.684822\pi\) | ||||
−0.548555 | + | 0.836114i | \(0.684822\pi\) | |||||||
\(938\) | 0.141448 | 0.00461843 | ||||||||
\(939\) | 31.1050 | 1.01507 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.1410 | 0.526183 | 0.263092 | − | 0.964771i | \(-0.415258\pi\) | ||||
0.263092 | + | 0.964771i | \(0.415258\pi\) | |||||||
\(942\) | −0.469533 | −0.0152982 | ||||||||
\(943\) | 5.67517 | 0.184809 | ||||||||
\(944\) | 2.48697 | 0.0809440 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −73.5819 | −2.39235 | ||||||||
\(947\) | 54.8866 | 1.78358 | 0.891788 | − | 0.452454i | \(-0.149451\pi\) | ||||
0.891788 | + | 0.452454i | \(0.149451\pi\) | |||||||
\(948\) | −4.55494 | −0.147938 | ||||||||
\(949\) | 28.9522 | 0.939827 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.89140 | 0.320751 | ||||||||
\(952\) | −5.75101 | −0.186391 | ||||||||
\(953\) | −18.3821 | −0.595455 | −0.297728 | − | 0.954651i | \(-0.596229\pi\) | ||||
−0.297728 | + | 0.954651i | \(0.596229\pi\) | |||||||
\(954\) | −39.6871 | −1.28492 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.17995 | 0.296901 | ||||||||
\(957\) | 5.58786 | 0.180630 | ||||||||
\(958\) | −7.46817 | −0.241286 | ||||||||
\(959\) | 9.55643 | 0.308593 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.1639 | 0.360126 | ||||||||
\(962\) | −4.92509 | −0.158791 | ||||||||
\(963\) | 7.30885 | 0.235524 | ||||||||
\(964\) | 3.66138 | 0.117925 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.75132 | −0.0563478 | ||||||||
\(967\) | −5.46628 | −0.175784 | −0.0878918 | − | 0.996130i | \(-0.528013\pi\) | ||||
−0.0878918 | + | 0.996130i | \(0.528013\pi\) | |||||||
\(968\) | −1.36699 | −0.0439368 | ||||||||
\(969\) | 29.9701 | 0.962779 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.4172 | −0.398486 | −0.199243 | − | 0.979950i | \(-0.563848\pi\) | ||||
−0.199243 | + | 0.979950i | \(0.563848\pi\) | |||||||
\(972\) | 17.9698 | 0.576382 | ||||||||
\(973\) | 4.27083 | 0.136917 | ||||||||
\(974\) | −51.4942 | −1.64998 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.7987 | −0.665751 | ||||||||
\(977\) | 8.42191 | 0.269441 | 0.134720 | − | 0.990884i | \(-0.456986\pi\) | ||||
0.134720 | + | 0.990884i | \(0.456986\pi\) | |||||||
\(978\) | 20.9779 | 0.670801 | ||||||||
\(979\) | −26.9393 | −0.860983 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32.8889 | −1.05006 | ||||||||
\(982\) | −9.07843 | −0.289704 | ||||||||
\(983\) | 28.0046 | 0.893207 | 0.446603 | − | 0.894732i | \(-0.352633\pi\) | ||||
0.446603 | + | 0.894732i | \(0.352633\pi\) | |||||||
\(984\) | −8.73813 | −0.278561 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.6973 | −0.340671 | ||||||||
\(987\) | 8.51566 | 0.271056 | ||||||||
\(988\) | −16.1758 | −0.514620 | ||||||||
\(989\) | −12.0844 | −0.384262 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.4173 | −1.02977 | −0.514885 | − | 0.857259i | \(-0.672165\pi\) | ||||
−0.514885 | + | 0.857259i | \(0.672165\pi\) | |||||||
\(992\) | 37.0179 | 1.17532 | ||||||||
\(993\) | 30.0967 | 0.955091 | ||||||||
\(994\) | 16.2774 | 0.516289 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −16.5016 | −0.522872 | ||||||||
\(997\) | −11.6906 | −0.370244 | −0.185122 | − | 0.982716i | \(-0.559268\pi\) | ||||
−0.185122 | + | 0.982716i | \(0.559268\pi\) | |||||||
\(998\) | 27.9980 | 0.886262 | ||||||||
\(999\) | 7.84456 | 0.248191 |
(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 | 4025.2.a.ba.1.11 | ✓ | 14 | |
5.4 | even | 2 | 4025.2.a.bb.1.4 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.ba.1.11 | ✓ | 14 | 1.1 | even | 1 | trivial | |
4025.2.a.bb.1.4 | yes | 14 | 5.4 | even | 2 |