Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(89\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | −2.39406 | −1.38221 | −0.691104 | − | 0.722755i | \(-0.742875\pi\) | ||||
−0.691104 | + | 0.722755i | \(0.742875\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.62374 | 1.62059 | 0.810294 | − | 0.586024i | \(-0.199308\pi\) | ||||
0.810294 | + | 0.586024i | \(0.199308\pi\) | |||||||
\(6\) | 2.39406 | 0.977369 | ||||||||
\(7\) | −4.52806 | −1.71145 | −0.855724 | − | 0.517433i | \(-0.826888\pi\) | ||||
−0.855724 | + | 0.517433i | \(0.826888\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.73150 | 0.910501 | ||||||||
\(10\) | −3.62374 | −1.14593 | ||||||||
\(11\) | 2.26084 | 0.681669 | 0.340835 | − | 0.940123i | \(-0.389290\pi\) | ||||
0.340835 | + | 0.940123i | \(0.389290\pi\) | |||||||
\(12\) | −2.39406 | −0.691104 | ||||||||
\(13\) | 4.69364 | 1.30178 | 0.650891 | − | 0.759171i | \(-0.274395\pi\) | ||||
0.650891 | + | 0.759171i | \(0.274395\pi\) | |||||||
\(14\) | 4.52806 | 1.21018 | ||||||||
\(15\) | −8.67544 | −2.23999 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.55658 | 0.862597 | 0.431299 | − | 0.902209i | \(-0.358056\pi\) | ||||
0.431299 | + | 0.902209i | \(0.358056\pi\) | |||||||
\(18\) | −2.73150 | −0.643821 | ||||||||
\(19\) | −3.26930 | −0.750029 | −0.375014 | − | 0.927019i | \(-0.622362\pi\) | ||||
−0.375014 | + | 0.927019i | \(0.622362\pi\) | |||||||
\(20\) | 3.62374 | 0.810294 | ||||||||
\(21\) | 10.8404 | 2.36558 | ||||||||
\(22\) | −2.26084 | −0.482013 | ||||||||
\(23\) | 0.716528 | 0.149406 | 0.0747032 | − | 0.997206i | \(-0.476199\pi\) | ||||
0.0747032 | + | 0.997206i | \(0.476199\pi\) | |||||||
\(24\) | 2.39406 | 0.488685 | ||||||||
\(25\) | 8.13152 | 1.62630 | ||||||||
\(26\) | −4.69364 | −0.920499 | ||||||||
\(27\) | 0.642799 | 0.123707 | ||||||||
\(28\) | −4.52806 | −0.855724 | ||||||||
\(29\) | −0.534178 | −0.0991944 | −0.0495972 | − | 0.998769i | \(-0.515794\pi\) | ||||
−0.0495972 | + | 0.998769i | \(0.515794\pi\) | |||||||
\(30\) | 8.67544 | 1.58391 | ||||||||
\(31\) | −1.14211 | −0.205130 | −0.102565 | − | 0.994726i | \(-0.532705\pi\) | ||||
−0.102565 | + | 0.994726i | \(0.532705\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.41258 | −0.942209 | ||||||||
\(34\) | −3.55658 | −0.609949 | ||||||||
\(35\) | −16.4085 | −2.77355 | ||||||||
\(36\) | 2.73150 | 0.455250 | ||||||||
\(37\) | −10.8724 | −1.78741 | −0.893706 | − | 0.448654i | \(-0.851904\pi\) | ||||
−0.893706 | + | 0.448654i | \(0.851904\pi\) | |||||||
\(38\) | 3.26930 | 0.530351 | ||||||||
\(39\) | −11.2368 | −1.79934 | ||||||||
\(40\) | −3.62374 | −0.572964 | ||||||||
\(41\) | −1.11139 | −0.173569 | −0.0867847 | − | 0.996227i | \(-0.527659\pi\) | ||||
−0.0867847 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(42\) | −10.8404 | −1.67272 | ||||||||
\(43\) | −10.6887 | −1.63001 | −0.815005 | − | 0.579454i | \(-0.803266\pi\) | ||||
−0.815005 | + | 0.579454i | \(0.803266\pi\) | |||||||
\(44\) | 2.26084 | 0.340835 | ||||||||
\(45\) | 9.89826 | 1.47555 | ||||||||
\(46\) | −0.716528 | −0.105646 | ||||||||
\(47\) | −9.03883 | −1.31845 | −0.659225 | − | 0.751946i | \(-0.729115\pi\) | ||||
−0.659225 | + | 0.751946i | \(0.729115\pi\) | |||||||
\(48\) | −2.39406 | −0.345552 | ||||||||
\(49\) | 13.5034 | 1.92905 | ||||||||
\(50\) | −8.13152 | −1.14997 | ||||||||
\(51\) | −8.51465 | −1.19229 | ||||||||
\(52\) | 4.69364 | 0.650891 | ||||||||
\(53\) | −4.68525 | −0.643569 | −0.321784 | − | 0.946813i | \(-0.604283\pi\) | ||||
−0.321784 | + | 0.946813i | \(0.604283\pi\) | |||||||
\(54\) | −0.642799 | −0.0874738 | ||||||||
\(55\) | 8.19271 | 1.10470 | ||||||||
\(56\) | 4.52806 | 0.605088 | ||||||||
\(57\) | 7.82689 | 1.03670 | ||||||||
\(58\) | 0.534178 | 0.0701410 | ||||||||
\(59\) | 12.6910 | 1.65222 | 0.826112 | − | 0.563506i | \(-0.190548\pi\) | ||||
0.826112 | + | 0.563506i | \(0.190548\pi\) | |||||||
\(60\) | −8.67544 | −1.11999 | ||||||||
\(61\) | 3.60034 | 0.460977 | 0.230488 | − | 0.973075i | \(-0.425968\pi\) | ||||
0.230488 | + | 0.973075i | \(0.425968\pi\) | |||||||
\(62\) | 1.14211 | 0.145049 | ||||||||
\(63\) | −12.3684 | −1.55827 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 17.0086 | 2.10965 | ||||||||
\(66\) | 5.41258 | 0.666242 | ||||||||
\(67\) | −1.78990 | −0.218671 | −0.109336 | − | 0.994005i | \(-0.534872\pi\) | ||||
−0.109336 | + | 0.994005i | \(0.534872\pi\) | |||||||
\(68\) | 3.55658 | 0.431299 | ||||||||
\(69\) | −1.71541 | −0.206511 | ||||||||
\(70\) | 16.4085 | 1.96120 | ||||||||
\(71\) | −5.04234 | −0.598415 | −0.299208 | − | 0.954188i | \(-0.596722\pi\) | ||||
−0.299208 | + | 0.954188i | \(0.596722\pi\) | |||||||
\(72\) | −2.73150 | −0.321911 | ||||||||
\(73\) | −2.10107 | −0.245911 | −0.122956 | − | 0.992412i | \(-0.539237\pi\) | ||||
−0.122956 | + | 0.992412i | \(0.539237\pi\) | |||||||
\(74\) | 10.8724 | 1.26389 | ||||||||
\(75\) | −19.4673 | −2.24789 | ||||||||
\(76\) | −3.26930 | −0.375014 | ||||||||
\(77\) | −10.2372 | −1.16664 | ||||||||
\(78\) | 11.2368 | 1.27232 | ||||||||
\(79\) | −3.34115 | −0.375909 | −0.187954 | − | 0.982178i | \(-0.560186\pi\) | ||||
−0.187954 | + | 0.982178i | \(0.560186\pi\) | |||||||
\(80\) | 3.62374 | 0.405147 | ||||||||
\(81\) | −9.73340 | −1.08149 | ||||||||
\(82\) | 1.11139 | 0.122732 | ||||||||
\(83\) | 13.3227 | 1.46235 | 0.731176 | − | 0.682189i | \(-0.238972\pi\) | ||||
0.731176 | + | 0.682189i | \(0.238972\pi\) | |||||||
\(84\) | 10.8404 | 1.18279 | ||||||||
\(85\) | 12.8881 | 1.39791 | ||||||||
\(86\) | 10.6887 | 1.15259 | ||||||||
\(87\) | 1.27885 | 0.137107 | ||||||||
\(88\) | −2.26084 | −0.241006 | ||||||||
\(89\) | −12.8692 | −1.36414 | −0.682068 | − | 0.731288i | \(-0.738919\pi\) | ||||
−0.682068 | + | 0.731288i | \(0.738919\pi\) | |||||||
\(90\) | −9.89826 | −1.04337 | ||||||||
\(91\) | −21.2531 | −2.22793 | ||||||||
\(92\) | 0.716528 | 0.0747032 | ||||||||
\(93\) | 2.73428 | 0.283532 | ||||||||
\(94\) | 9.03883 | 0.932284 | ||||||||
\(95\) | −11.8471 | −1.21549 | ||||||||
\(96\) | 2.39406 | 0.244342 | ||||||||
\(97\) | 0.0981843 | 0.00996910 | 0.00498455 | − | 0.999988i | \(-0.498413\pi\) | ||||
0.00498455 | + | 0.999988i | \(0.498413\pi\) | |||||||
\(98\) | −13.5034 | −1.36405 | ||||||||
\(99\) | 6.17549 | 0.620660 | ||||||||
\(100\) | 8.13152 | 0.813152 | ||||||||
\(101\) | 14.2187 | 1.41481 | 0.707406 | − | 0.706808i | \(-0.249865\pi\) | ||||
0.707406 | + | 0.706808i | \(0.249865\pi\) | |||||||
\(102\) | 8.51465 | 0.843076 | ||||||||
\(103\) | −17.2899 | −1.70362 | −0.851812 | − | 0.523848i | \(-0.824496\pi\) | ||||
−0.851812 | + | 0.523848i | \(0.824496\pi\) | |||||||
\(104\) | −4.69364 | −0.460250 | ||||||||
\(105\) | 39.2830 | 3.83363 | ||||||||
\(106\) | 4.68525 | 0.455072 | ||||||||
\(107\) | 11.2384 | 1.08646 | 0.543229 | − | 0.839585i | \(-0.317202\pi\) | ||||
0.543229 | + | 0.839585i | \(0.317202\pi\) | |||||||
\(108\) | 0.642799 | 0.0618533 | ||||||||
\(109\) | −1.44304 | −0.138218 | −0.0691091 | − | 0.997609i | \(-0.522016\pi\) | ||||
−0.0691091 | + | 0.997609i | \(0.522016\pi\) | |||||||
\(110\) | −8.19271 | −0.781144 | ||||||||
\(111\) | 26.0291 | 2.47058 | ||||||||
\(112\) | −4.52806 | −0.427862 | ||||||||
\(113\) | 6.87791 | 0.647020 | 0.323510 | − | 0.946225i | \(-0.395137\pi\) | ||||
0.323510 | + | 0.946225i | \(0.395137\pi\) | |||||||
\(114\) | −7.82689 | −0.733055 | ||||||||
\(115\) | 2.59651 | 0.242126 | ||||||||
\(116\) | −0.534178 | −0.0495972 | ||||||||
\(117\) | 12.8207 | 1.18527 | ||||||||
\(118\) | −12.6910 | −1.16830 | ||||||||
\(119\) | −16.1044 | −1.47629 | ||||||||
\(120\) | 8.67544 | 0.791956 | ||||||||
\(121\) | −5.88860 | −0.535327 | ||||||||
\(122\) | −3.60034 | −0.325960 | ||||||||
\(123\) | 2.66072 | 0.239909 | ||||||||
\(124\) | −1.14211 | −0.102565 | ||||||||
\(125\) | 11.3478 | 1.01498 | ||||||||
\(126\) | 12.3684 | 1.10187 | ||||||||
\(127\) | −9.27798 | −0.823288 | −0.411644 | − | 0.911345i | \(-0.635045\pi\) | ||||
−0.411644 | + | 0.911345i | \(0.635045\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 25.5893 | 2.25301 | ||||||||
\(130\) | −17.0086 | −1.49175 | ||||||||
\(131\) | −1.62186 | −0.141703 | −0.0708513 | − | 0.997487i | \(-0.522572\pi\) | ||||
−0.0708513 | + | 0.997487i | \(0.522572\pi\) | |||||||
\(132\) | −5.41258 | −0.471105 | ||||||||
\(133\) | 14.8036 | 1.28364 | ||||||||
\(134\) | 1.78990 | 0.154624 | ||||||||
\(135\) | 2.32934 | 0.200477 | ||||||||
\(136\) | −3.55658 | −0.304974 | ||||||||
\(137\) | 13.8541 | 1.18363 | 0.591817 | − | 0.806073i | \(-0.298411\pi\) | ||||
0.591817 | + | 0.806073i | \(0.298411\pi\) | |||||||
\(138\) | 1.71541 | 0.146025 | ||||||||
\(139\) | 6.13120 | 0.520041 | 0.260021 | − | 0.965603i | \(-0.416271\pi\) | ||||
0.260021 | + | 0.965603i | \(0.416271\pi\) | |||||||
\(140\) | −16.4085 | −1.38678 | ||||||||
\(141\) | 21.6395 | 1.82237 | ||||||||
\(142\) | 5.04234 | 0.423143 | ||||||||
\(143\) | 10.6116 | 0.887385 | ||||||||
\(144\) | 2.73150 | 0.227625 | ||||||||
\(145\) | −1.93572 | −0.160753 | ||||||||
\(146\) | 2.10107 | 0.173886 | ||||||||
\(147\) | −32.3278 | −2.66635 | ||||||||
\(148\) | −10.8724 | −0.893706 | ||||||||
\(149\) | −19.9991 | −1.63839 | −0.819197 | − | 0.573512i | \(-0.805580\pi\) | ||||
−0.819197 | + | 0.573512i | \(0.805580\pi\) | |||||||
\(150\) | 19.4673 | 1.58950 | ||||||||
\(151\) | −6.38314 | −0.519452 | −0.259726 | − | 0.965682i | \(-0.583632\pi\) | ||||
−0.259726 | + | 0.965682i | \(0.583632\pi\) | |||||||
\(152\) | 3.26930 | 0.265175 | ||||||||
\(153\) | 9.71481 | 0.785396 | ||||||||
\(154\) | 10.2372 | 0.824940 | ||||||||
\(155\) | −4.13873 | −0.332431 | ||||||||
\(156\) | −11.2368 | −0.899668 | ||||||||
\(157\) | −12.8240 | −1.02347 | −0.511735 | − | 0.859143i | \(-0.670997\pi\) | ||||
−0.511735 | + | 0.859143i | \(0.670997\pi\) | |||||||
\(158\) | 3.34115 | 0.265808 | ||||||||
\(159\) | 11.2168 | 0.889547 | ||||||||
\(160\) | −3.62374 | −0.286482 | ||||||||
\(161\) | −3.24449 | −0.255701 | ||||||||
\(162\) | 9.73340 | 0.764728 | ||||||||
\(163\) | −14.6654 | −1.14869 | −0.574343 | − | 0.818615i | \(-0.694742\pi\) | ||||
−0.574343 | + | 0.818615i | \(0.694742\pi\) | |||||||
\(164\) | −1.11139 | −0.0867847 | ||||||||
\(165\) | −19.6138 | −1.52693 | ||||||||
\(166\) | −13.3227 | −1.03404 | ||||||||
\(167\) | 14.2266 | 1.10089 | 0.550443 | − | 0.834873i | \(-0.314459\pi\) | ||||
0.550443 | + | 0.834873i | \(0.314459\pi\) | |||||||
\(168\) | −10.8404 | −0.836358 | ||||||||
\(169\) | 9.03029 | 0.694638 | ||||||||
\(170\) | −12.8881 | −0.988475 | ||||||||
\(171\) | −8.93010 | −0.682902 | ||||||||
\(172\) | −10.6887 | −0.815005 | ||||||||
\(173\) | −4.18903 | −0.318486 | −0.159243 | − | 0.987239i | \(-0.550905\pi\) | ||||
−0.159243 | + | 0.987239i | \(0.550905\pi\) | |||||||
\(174\) | −1.27885 | −0.0969495 | ||||||||
\(175\) | −36.8200 | −2.78333 | ||||||||
\(176\) | 2.26084 | 0.170417 | ||||||||
\(177\) | −30.3829 | −2.28372 | ||||||||
\(178\) | 12.8692 | 0.964590 | ||||||||
\(179\) | 18.4418 | 1.37840 | 0.689202 | − | 0.724569i | \(-0.257961\pi\) | ||||
0.689202 | + | 0.724569i | \(0.257961\pi\) | |||||||
\(180\) | 9.89826 | 0.737773 | ||||||||
\(181\) | −4.43507 | −0.329656 | −0.164828 | − | 0.986322i | \(-0.552707\pi\) | ||||
−0.164828 | + | 0.986322i | \(0.552707\pi\) | |||||||
\(182\) | 21.2531 | 1.57539 | ||||||||
\(183\) | −8.61942 | −0.637166 | ||||||||
\(184\) | −0.716528 | −0.0528232 | ||||||||
\(185\) | −39.3988 | −2.89666 | ||||||||
\(186\) | −2.73428 | −0.200487 | ||||||||
\(187\) | 8.04086 | 0.588006 | ||||||||
\(188\) | −9.03883 | −0.659225 | ||||||||
\(189\) | −2.91063 | −0.211717 | ||||||||
\(190\) | 11.8471 | 0.859479 | ||||||||
\(191\) | 14.7216 | 1.06522 | 0.532610 | − | 0.846361i | \(-0.321211\pi\) | ||||
0.532610 | + | 0.846361i | \(0.321211\pi\) | |||||||
\(192\) | −2.39406 | −0.172776 | ||||||||
\(193\) | 19.3196 | 1.39066 | 0.695329 | − | 0.718691i | \(-0.255259\pi\) | ||||
0.695329 | + | 0.718691i | \(0.255259\pi\) | |||||||
\(194\) | −0.0981843 | −0.00704922 | ||||||||
\(195\) | −40.7194 | −2.91598 | ||||||||
\(196\) | 13.5034 | 0.964526 | ||||||||
\(197\) | −24.2286 | −1.72621 | −0.863107 | − | 0.505021i | \(-0.831485\pi\) | ||||
−0.863107 | + | 0.505021i | \(0.831485\pi\) | |||||||
\(198\) | −6.17549 | −0.438873 | ||||||||
\(199\) | 0.365447 | 0.0259059 | 0.0129529 | − | 0.999916i | \(-0.495877\pi\) | ||||
0.0129529 | + | 0.999916i | \(0.495877\pi\) | |||||||
\(200\) | −8.13152 | −0.574985 | ||||||||
\(201\) | 4.28513 | 0.302249 | ||||||||
\(202\) | −14.2187 | −1.00042 | ||||||||
\(203\) | 2.41879 | 0.169766 | ||||||||
\(204\) | −8.51465 | −0.596145 | ||||||||
\(205\) | −4.02738 | −0.281284 | ||||||||
\(206\) | 17.2899 | 1.20464 | ||||||||
\(207\) | 1.95720 | 0.136035 | ||||||||
\(208\) | 4.69364 | 0.325446 | ||||||||
\(209\) | −7.39137 | −0.511272 | ||||||||
\(210\) | −39.2830 | −2.71078 | ||||||||
\(211\) | −11.2593 | −0.775120 | −0.387560 | − | 0.921844i | \(-0.626682\pi\) | ||||
−0.387560 | + | 0.921844i | \(0.626682\pi\) | |||||||
\(212\) | −4.68525 | −0.321784 | ||||||||
\(213\) | 12.0716 | 0.827135 | ||||||||
\(214\) | −11.2384 | −0.768242 | ||||||||
\(215\) | −38.7331 | −2.64157 | ||||||||
\(216\) | −0.642799 | −0.0437369 | ||||||||
\(217\) | 5.17157 | 0.351069 | ||||||||
\(218\) | 1.44304 | 0.0977350 | ||||||||
\(219\) | 5.03007 | 0.339901 | ||||||||
\(220\) | 8.19271 | 0.552352 | ||||||||
\(221\) | 16.6933 | 1.12291 | ||||||||
\(222\) | −26.0291 | −1.74696 | ||||||||
\(223\) | −12.7748 | −0.855461 | −0.427731 | − | 0.903906i | \(-0.640687\pi\) | ||||
−0.427731 | + | 0.903906i | \(0.640687\pi\) | |||||||
\(224\) | 4.52806 | 0.302544 | ||||||||
\(225\) | 22.2113 | 1.48075 | ||||||||
\(226\) | −6.87791 | −0.457512 | ||||||||
\(227\) | 18.6882 | 1.24038 | 0.620191 | − | 0.784451i | \(-0.287055\pi\) | ||||
0.620191 | + | 0.784451i | \(0.287055\pi\) | |||||||
\(228\) | 7.82689 | 0.518348 | ||||||||
\(229\) | 11.3690 | 0.751283 | 0.375642 | − | 0.926765i | \(-0.377422\pi\) | ||||
0.375642 | + | 0.926765i | \(0.377422\pi\) | |||||||
\(230\) | −2.59651 | −0.171209 | ||||||||
\(231\) | 24.5085 | 1.61254 | ||||||||
\(232\) | 0.534178 | 0.0350705 | ||||||||
\(233\) | −24.7164 | −1.61922 | −0.809612 | − | 0.586965i | \(-0.800323\pi\) | ||||
−0.809612 | + | 0.586965i | \(0.800323\pi\) | |||||||
\(234\) | −12.8207 | −0.838115 | ||||||||
\(235\) | −32.7544 | −2.13666 | ||||||||
\(236\) | 12.6910 | 0.826112 | ||||||||
\(237\) | 7.99890 | 0.519584 | ||||||||
\(238\) | 16.1044 | 1.04389 | ||||||||
\(239\) | 7.14402 | 0.462108 | 0.231054 | − | 0.972941i | \(-0.425783\pi\) | ||||
0.231054 | + | 0.972941i | \(0.425783\pi\) | |||||||
\(240\) | −8.67544 | −0.559997 | ||||||||
\(241\) | 9.92812 | 0.639527 | 0.319763 | − | 0.947497i | \(-0.396397\pi\) | ||||
0.319763 | + | 0.947497i | \(0.396397\pi\) | |||||||
\(242\) | 5.88860 | 0.378533 | ||||||||
\(243\) | 21.3739 | 1.37114 | ||||||||
\(244\) | 3.60034 | 0.230488 | ||||||||
\(245\) | 48.9328 | 3.12620 | ||||||||
\(246\) | −2.66072 | −0.169641 | ||||||||
\(247\) | −15.3449 | −0.976375 | ||||||||
\(248\) | 1.14211 | 0.0725243 | ||||||||
\(249\) | −31.8952 | −2.02127 | ||||||||
\(250\) | −11.3478 | −0.717699 | ||||||||
\(251\) | 14.1361 | 0.892262 | 0.446131 | − | 0.894968i | \(-0.352802\pi\) | ||||
0.446131 | + | 0.894968i | \(0.352802\pi\) | |||||||
\(252\) | −12.3684 | −0.779137 | ||||||||
\(253\) | 1.61996 | 0.101846 | ||||||||
\(254\) | 9.27798 | 0.582152 | ||||||||
\(255\) | −30.8549 | −1.93221 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.0786 | 1.19009 | 0.595044 | − | 0.803693i | \(-0.297135\pi\) | ||||
0.595044 | + | 0.803693i | \(0.297135\pi\) | |||||||
\(258\) | −25.5893 | −1.59312 | ||||||||
\(259\) | 49.2309 | 3.05906 | ||||||||
\(260\) | 17.0086 | 1.05483 | ||||||||
\(261\) | −1.45911 | −0.0903165 | ||||||||
\(262\) | 1.62186 | 0.100199 | ||||||||
\(263\) | −31.2966 | −1.92983 | −0.964915 | − | 0.262564i | \(-0.915432\pi\) | ||||
−0.964915 | + | 0.262564i | \(0.915432\pi\) | |||||||
\(264\) | 5.41258 | 0.333121 | ||||||||
\(265\) | −16.9782 | −1.04296 | ||||||||
\(266\) | −14.8036 | −0.907667 | ||||||||
\(267\) | 30.8097 | 1.88552 | ||||||||
\(268\) | −1.78990 | −0.109336 | ||||||||
\(269\) | 4.49940 | 0.274333 | 0.137167 | − | 0.990548i | \(-0.456200\pi\) | ||||
0.137167 | + | 0.990548i | \(0.456200\pi\) | |||||||
\(270\) | −2.32934 | −0.141759 | ||||||||
\(271\) | −13.7538 | −0.835484 | −0.417742 | − | 0.908566i | \(-0.637178\pi\) | ||||
−0.417742 | + | 0.908566i | \(0.637178\pi\) | |||||||
\(272\) | 3.55658 | 0.215649 | ||||||||
\(273\) | 50.8812 | 3.07947 | ||||||||
\(274\) | −13.8541 | −0.836955 | ||||||||
\(275\) | 18.3841 | 1.10860 | ||||||||
\(276\) | −1.71541 | −0.103255 | ||||||||
\(277\) | −11.0106 | −0.661561 | −0.330781 | − | 0.943708i | \(-0.607312\pi\) | ||||
−0.330781 | + | 0.943708i | \(0.607312\pi\) | |||||||
\(278\) | −6.13120 | −0.367725 | ||||||||
\(279\) | −3.11969 | −0.186771 | ||||||||
\(280\) | 16.4085 | 0.980598 | ||||||||
\(281\) | 30.8707 | 1.84159 | 0.920797 | − | 0.390042i | \(-0.127540\pi\) | ||||
0.920797 | + | 0.390042i | \(0.127540\pi\) | |||||||
\(282\) | −21.6395 | −1.28861 | ||||||||
\(283\) | 2.08025 | 0.123658 | 0.0618290 | − | 0.998087i | \(-0.480307\pi\) | ||||
0.0618290 | + | 0.998087i | \(0.480307\pi\) | |||||||
\(284\) | −5.04234 | −0.299208 | ||||||||
\(285\) | 28.3626 | 1.68006 | ||||||||
\(286\) | −10.6116 | −0.627476 | ||||||||
\(287\) | 5.03243 | 0.297055 | ||||||||
\(288\) | −2.73150 | −0.160955 | ||||||||
\(289\) | −4.35074 | −0.255926 | ||||||||
\(290\) | 1.93572 | 0.113670 | ||||||||
\(291\) | −0.235059 | −0.0137794 | ||||||||
\(292\) | −2.10107 | −0.122956 | ||||||||
\(293\) | −8.00119 | −0.467434 | −0.233717 | − | 0.972305i | \(-0.575089\pi\) | ||||
−0.233717 | + | 0.972305i | \(0.575089\pi\) | |||||||
\(294\) | 32.3278 | 1.88540 | ||||||||
\(295\) | 45.9888 | 2.67757 | ||||||||
\(296\) | 10.8724 | 0.631945 | ||||||||
\(297\) | 1.45327 | 0.0843270 | ||||||||
\(298\) | 19.9991 | 1.15852 | ||||||||
\(299\) | 3.36313 | 0.194495 | ||||||||
\(300\) | −19.4673 | −1.12395 | ||||||||
\(301\) | 48.3991 | 2.78968 | ||||||||
\(302\) | 6.38314 | 0.367308 | ||||||||
\(303\) | −34.0403 | −1.95556 | ||||||||
\(304\) | −3.26930 | −0.187507 | ||||||||
\(305\) | 13.0467 | 0.747053 | ||||||||
\(306\) | −9.71481 | −0.555359 | ||||||||
\(307\) | −24.1519 | −1.37842 | −0.689210 | − | 0.724561i | \(-0.742042\pi\) | ||||
−0.689210 | + | 0.724561i | \(0.742042\pi\) | |||||||
\(308\) | −10.2372 | −0.583321 | ||||||||
\(309\) | 41.3930 | 2.35476 | ||||||||
\(310\) | 4.13873 | 0.235064 | ||||||||
\(311\) | 12.5984 | 0.714391 | 0.357195 | − | 0.934030i | \(-0.383733\pi\) | ||||
0.357195 | + | 0.934030i | \(0.383733\pi\) | |||||||
\(312\) | 11.2368 | 0.636161 | ||||||||
\(313\) | 19.9674 | 1.12863 | 0.564313 | − | 0.825561i | \(-0.309141\pi\) | ||||
0.564313 | + | 0.825561i | \(0.309141\pi\) | |||||||
\(314\) | 12.8240 | 0.723703 | ||||||||
\(315\) | −44.8200 | −2.52532 | ||||||||
\(316\) | −3.34115 | −0.187954 | ||||||||
\(317\) | 1.53264 | 0.0860815 | 0.0430407 | − | 0.999073i | \(-0.486295\pi\) | ||||
0.0430407 | + | 0.999073i | \(0.486295\pi\) | |||||||
\(318\) | −11.2168 | −0.629004 | ||||||||
\(319\) | −1.20769 | −0.0676177 | ||||||||
\(320\) | 3.62374 | 0.202573 | ||||||||
\(321\) | −26.9054 | −1.50171 | ||||||||
\(322\) | 3.24449 | 0.180808 | ||||||||
\(323\) | −11.6275 | −0.646973 | ||||||||
\(324\) | −9.73340 | −0.540745 | ||||||||
\(325\) | 38.1664 | 2.11709 | ||||||||
\(326\) | 14.6654 | 0.812243 | ||||||||
\(327\) | 3.45472 | 0.191046 | ||||||||
\(328\) | 1.11139 | 0.0613661 | ||||||||
\(329\) | 40.9284 | 2.25646 | ||||||||
\(330\) | 19.6138 | 1.07970 | ||||||||
\(331\) | −10.4917 | −0.576676 | −0.288338 | − | 0.957529i | \(-0.593103\pi\) | ||||
−0.288338 | + | 0.957529i | \(0.593103\pi\) | |||||||
\(332\) | 13.3227 | 0.731176 | ||||||||
\(333\) | −29.6980 | −1.62744 | ||||||||
\(334\) | −14.2266 | −0.778444 | ||||||||
\(335\) | −6.48615 | −0.354376 | ||||||||
\(336\) | 10.8404 | 0.591394 | ||||||||
\(337\) | −23.2031 | −1.26395 | −0.631976 | − | 0.774988i | \(-0.717756\pi\) | ||||
−0.631976 | + | 0.774988i | \(0.717756\pi\) | |||||||
\(338\) | −9.03029 | −0.491183 | ||||||||
\(339\) | −16.4661 | −0.894316 | ||||||||
\(340\) | 12.8881 | 0.698957 | ||||||||
\(341\) | −2.58214 | −0.139831 | ||||||||
\(342\) | 8.93010 | 0.482885 | ||||||||
\(343\) | −29.4477 | −1.59003 | ||||||||
\(344\) | 10.6887 | 0.576295 | ||||||||
\(345\) | −6.21620 | −0.334669 | ||||||||
\(346\) | 4.18903 | 0.225203 | ||||||||
\(347\) | 3.54059 | 0.190069 | 0.0950344 | − | 0.995474i | \(-0.469704\pi\) | ||||
0.0950344 | + | 0.995474i | \(0.469704\pi\) | |||||||
\(348\) | 1.27885 | 0.0685537 | ||||||||
\(349\) | −32.6885 | −1.74978 | −0.874888 | − | 0.484326i | \(-0.839065\pi\) | ||||
−0.874888 | + | 0.484326i | \(0.839065\pi\) | |||||||
\(350\) | 36.8200 | 1.96811 | ||||||||
\(351\) | 3.01707 | 0.161039 | ||||||||
\(352\) | −2.26084 | −0.120503 | ||||||||
\(353\) | 20.9819 | 1.11675 | 0.558377 | − | 0.829587i | \(-0.311424\pi\) | ||||
0.558377 | + | 0.829587i | \(0.311424\pi\) | |||||||
\(354\) | 30.3829 | 1.61483 | ||||||||
\(355\) | −18.2721 | −0.969784 | ||||||||
\(356\) | −12.8692 | −0.682068 | ||||||||
\(357\) | 38.5549 | 2.04054 | ||||||||
\(358\) | −18.4418 | −0.974679 | ||||||||
\(359\) | 32.3869 | 1.70932 | 0.854658 | − | 0.519191i | \(-0.173767\pi\) | ||||
0.854658 | + | 0.519191i | \(0.173767\pi\) | |||||||
\(360\) | −9.89826 | −0.521684 | ||||||||
\(361\) | −8.31168 | −0.437457 | ||||||||
\(362\) | 4.43507 | 0.233102 | ||||||||
\(363\) | 14.0976 | 0.739934 | ||||||||
\(364\) | −21.2531 | −1.11397 | ||||||||
\(365\) | −7.61373 | −0.398521 | ||||||||
\(366\) | 8.61942 | 0.450544 | ||||||||
\(367\) | −21.3339 | −1.11362 | −0.556809 | − | 0.830640i | \(-0.687975\pi\) | ||||
−0.556809 | + | 0.830640i | \(0.687975\pi\) | |||||||
\(368\) | 0.716528 | 0.0373516 | ||||||||
\(369\) | −3.03576 | −0.158035 | ||||||||
\(370\) | 39.3988 | 2.04825 | ||||||||
\(371\) | 21.2151 | 1.10143 | ||||||||
\(372\) | 2.73428 | 0.141766 | ||||||||
\(373\) | −8.68720 | −0.449806 | −0.224903 | − | 0.974381i | \(-0.572207\pi\) | ||||
−0.224903 | + | 0.974381i | \(0.572207\pi\) | |||||||
\(374\) | −8.04086 | −0.415783 | ||||||||
\(375\) | −27.1673 | −1.40291 | ||||||||
\(376\) | 9.03883 | 0.466142 | ||||||||
\(377\) | −2.50724 | −0.129130 | ||||||||
\(378\) | 2.91063 | 0.149707 | ||||||||
\(379\) | −7.77342 | −0.399294 | −0.199647 | − | 0.979868i | \(-0.563980\pi\) | ||||
−0.199647 | + | 0.979868i | \(0.563980\pi\) | |||||||
\(380\) | −11.8471 | −0.607744 | ||||||||
\(381\) | 22.2120 | 1.13796 | ||||||||
\(382\) | −14.7216 | −0.753225 | ||||||||
\(383\) | 31.5159 | 1.61039 | 0.805193 | − | 0.593013i | \(-0.202062\pi\) | ||||
0.805193 | + | 0.593013i | \(0.202062\pi\) | |||||||
\(384\) | 2.39406 | 0.122171 | ||||||||
\(385\) | −37.0971 | −1.89064 | ||||||||
\(386\) | −19.3196 | −0.983344 | ||||||||
\(387\) | −29.1962 | −1.48412 | ||||||||
\(388\) | 0.0981843 | 0.00498455 | ||||||||
\(389\) | −17.4550 | −0.885006 | −0.442503 | − | 0.896767i | \(-0.645909\pi\) | ||||
−0.442503 | + | 0.896767i | \(0.645909\pi\) | |||||||
\(390\) | 40.7194 | 2.06191 | ||||||||
\(391\) | 2.54839 | 0.128878 | ||||||||
\(392\) | −13.5034 | −0.682023 | ||||||||
\(393\) | 3.88283 | 0.195863 | ||||||||
\(394\) | 24.2286 | 1.22062 | ||||||||
\(395\) | −12.1075 | −0.609193 | ||||||||
\(396\) | 6.17549 | 0.310330 | ||||||||
\(397\) | −20.1859 | −1.01310 | −0.506550 | − | 0.862211i | \(-0.669079\pi\) | ||||
−0.506550 | + | 0.862211i | \(0.669079\pi\) | |||||||
\(398\) | −0.365447 | −0.0183182 | ||||||||
\(399\) | −35.4406 | −1.77425 | ||||||||
\(400\) | 8.13152 | 0.406576 | ||||||||
\(401\) | −30.9339 | −1.54477 | −0.772383 | − | 0.635157i | \(-0.780935\pi\) | ||||
−0.772383 | + | 0.635157i | \(0.780935\pi\) | |||||||
\(402\) | −4.28513 | −0.213723 | ||||||||
\(403\) | −5.36068 | −0.267034 | ||||||||
\(404\) | 14.2187 | 0.707406 | ||||||||
\(405\) | −35.2714 | −1.75265 | ||||||||
\(406\) | −2.41879 | −0.120043 | ||||||||
\(407\) | −24.5808 | −1.21842 | ||||||||
\(408\) | 8.51465 | 0.421538 | ||||||||
\(409\) | 20.7917 | 1.02808 | 0.514041 | − | 0.857765i | \(-0.328148\pi\) | ||||
0.514041 | + | 0.857765i | \(0.328148\pi\) | |||||||
\(410\) | 4.02738 | 0.198898 | ||||||||
\(411\) | −33.1674 | −1.63603 | ||||||||
\(412\) | −17.2899 | −0.851812 | ||||||||
\(413\) | −57.4656 | −2.82770 | ||||||||
\(414\) | −1.95720 | −0.0961910 | ||||||||
\(415\) | 48.2779 | 2.36987 | ||||||||
\(416\) | −4.69364 | −0.230125 | ||||||||
\(417\) | −14.6784 | −0.718805 | ||||||||
\(418\) | 7.39137 | 0.361524 | ||||||||
\(419\) | 30.4461 | 1.48739 | 0.743694 | − | 0.668520i | \(-0.233072\pi\) | ||||
0.743694 | + | 0.668520i | \(0.233072\pi\) | |||||||
\(420\) | 39.2830 | 1.91681 | ||||||||
\(421\) | −13.9994 | −0.682289 | −0.341145 | − | 0.940011i | \(-0.610815\pi\) | ||||
−0.341145 | + | 0.940011i | \(0.610815\pi\) | |||||||
\(422\) | 11.2593 | 0.548093 | ||||||||
\(423\) | −24.6896 | −1.20045 | ||||||||
\(424\) | 4.68525 | 0.227536 | ||||||||
\(425\) | 28.9204 | 1.40285 | ||||||||
\(426\) | −12.0716 | −0.584873 | ||||||||
\(427\) | −16.3026 | −0.788937 | ||||||||
\(428\) | 11.2384 | 0.543229 | ||||||||
\(429\) | −25.4047 | −1.22655 | ||||||||
\(430\) | 38.7331 | 1.86787 | ||||||||
\(431\) | −27.9060 | −1.34419 | −0.672093 | − | 0.740467i | \(-0.734605\pi\) | ||||
−0.672093 | + | 0.740467i | \(0.734605\pi\) | |||||||
\(432\) | 0.642799 | 0.0309267 | ||||||||
\(433\) | 12.0911 | 0.581059 | 0.290530 | − | 0.956866i | \(-0.406169\pi\) | ||||
0.290530 | + | 0.956866i | \(0.406169\pi\) | |||||||
\(434\) | −5.17157 | −0.248243 | ||||||||
\(435\) | 4.63423 | 0.222194 | ||||||||
\(436\) | −1.44304 | −0.0691091 | ||||||||
\(437\) | −2.34255 | −0.112059 | ||||||||
\(438\) | −5.03007 | −0.240346 | ||||||||
\(439\) | 14.8967 | 0.710980 | 0.355490 | − | 0.934680i | \(-0.384314\pi\) | ||||
0.355490 | + | 0.934680i | \(0.384314\pi\) | |||||||
\(440\) | −8.19271 | −0.390572 | ||||||||
\(441\) | 36.8845 | 1.75640 | ||||||||
\(442\) | −16.6933 | −0.794020 | ||||||||
\(443\) | −27.9427 | −1.32760 | −0.663798 | − | 0.747912i | \(-0.731057\pi\) | ||||
−0.663798 | + | 0.747912i | \(0.731057\pi\) | |||||||
\(444\) | 26.0291 | 1.23529 | ||||||||
\(445\) | −46.6348 | −2.21070 | ||||||||
\(446\) | 12.7748 | 0.604902 | ||||||||
\(447\) | 47.8791 | 2.26460 | ||||||||
\(448\) | −4.52806 | −0.213931 | ||||||||
\(449\) | 24.5693 | 1.15950 | 0.579749 | − | 0.814795i | \(-0.303151\pi\) | ||||
0.579749 | + | 0.814795i | \(0.303151\pi\) | |||||||
\(450\) | −22.2113 | −1.04705 | ||||||||
\(451\) | −2.51267 | −0.118317 | ||||||||
\(452\) | 6.87791 | 0.323510 | ||||||||
\(453\) | 15.2816 | 0.717992 | ||||||||
\(454\) | −18.6882 | −0.877083 | ||||||||
\(455\) | −77.0159 | −3.61056 | ||||||||
\(456\) | −7.82689 | −0.366528 | ||||||||
\(457\) | −9.00593 | −0.421280 | −0.210640 | − | 0.977564i | \(-0.567555\pi\) | ||||
−0.210640 | + | 0.977564i | \(0.567555\pi\) | |||||||
\(458\) | −11.3690 | −0.531238 | ||||||||
\(459\) | 2.28617 | 0.106709 | ||||||||
\(460\) | 2.59651 | 0.121063 | ||||||||
\(461\) | −24.8496 | −1.15736 | −0.578681 | − | 0.815554i | \(-0.696432\pi\) | ||||
−0.578681 | + | 0.815554i | \(0.696432\pi\) | |||||||
\(462\) | −24.5085 | −1.14024 | ||||||||
\(463\) | 1.19650 | 0.0556060 | 0.0278030 | − | 0.999613i | \(-0.491149\pi\) | ||||
0.0278030 | + | 0.999613i | \(0.491149\pi\) | |||||||
\(464\) | −0.534178 | −0.0247986 | ||||||||
\(465\) | 9.90834 | 0.459488 | ||||||||
\(466\) | 24.7164 | 1.14496 | ||||||||
\(467\) | 5.50533 | 0.254756 | 0.127378 | − | 0.991854i | \(-0.459344\pi\) | ||||
0.127378 | + | 0.991854i | \(0.459344\pi\) | |||||||
\(468\) | 12.8207 | 0.592637 | ||||||||
\(469\) | 8.10479 | 0.374245 | ||||||||
\(470\) | 32.7544 | 1.51085 | ||||||||
\(471\) | 30.7015 | 1.41465 | ||||||||
\(472\) | −12.6910 | −0.584149 | ||||||||
\(473\) | −24.1654 | −1.11113 | ||||||||
\(474\) | −7.99890 | −0.367402 | ||||||||
\(475\) | −26.5844 | −1.21977 | ||||||||
\(476\) | −16.1044 | −0.738145 | ||||||||
\(477\) | −12.7978 | −0.585970 | ||||||||
\(478\) | −7.14402 | −0.326760 | ||||||||
\(479\) | 8.58037 | 0.392047 | 0.196024 | − | 0.980599i | \(-0.437197\pi\) | ||||
0.196024 | + | 0.980599i | \(0.437197\pi\) | |||||||
\(480\) | 8.67544 | 0.395978 | ||||||||
\(481\) | −51.0312 | −2.32682 | ||||||||
\(482\) | −9.92812 | −0.452214 | ||||||||
\(483\) | 7.76748 | 0.353433 | ||||||||
\(484\) | −5.88860 | −0.267664 | ||||||||
\(485\) | 0.355795 | 0.0161558 | ||||||||
\(486\) | −21.3739 | −0.969540 | ||||||||
\(487\) | 6.92054 | 0.313600 | 0.156800 | − | 0.987630i | \(-0.449882\pi\) | ||||
0.156800 | + | 0.987630i | \(0.449882\pi\) | |||||||
\(488\) | −3.60034 | −0.162980 | ||||||||
\(489\) | 35.1099 | 1.58772 | ||||||||
\(490\) | −48.9328 | −2.21056 | ||||||||
\(491\) | −32.7740 | −1.47907 | −0.739536 | − | 0.673117i | \(-0.764955\pi\) | ||||
−0.739536 | + | 0.673117i | \(0.764955\pi\) | |||||||
\(492\) | 2.66072 | 0.119955 | ||||||||
\(493\) | −1.89985 | −0.0855648 | ||||||||
\(494\) | 15.3449 | 0.690401 | ||||||||
\(495\) | 22.3784 | 1.00583 | ||||||||
\(496\) | −1.14211 | −0.0512824 | ||||||||
\(497\) | 22.8320 | 1.02416 | ||||||||
\(498\) | 31.8952 | 1.42926 | ||||||||
\(499\) | −19.5945 | −0.877172 | −0.438586 | − | 0.898689i | \(-0.644521\pi\) | ||||
−0.438586 | + | 0.898689i | \(0.644521\pi\) | |||||||
\(500\) | 11.3478 | 0.507490 | ||||||||
\(501\) | −34.0592 | −1.52165 | ||||||||
\(502\) | −14.1361 | −0.630924 | ||||||||
\(503\) | −22.8431 | −1.01852 | −0.509261 | − | 0.860612i | \(-0.670081\pi\) | ||||
−0.509261 | + | 0.860612i | \(0.670081\pi\) | |||||||
\(504\) | 12.3684 | 0.550933 | ||||||||
\(505\) | 51.5248 | 2.29283 | ||||||||
\(506\) | −1.61996 | −0.0720158 | ||||||||
\(507\) | −21.6190 | −0.960134 | ||||||||
\(508\) | −9.27798 | −0.411644 | ||||||||
\(509\) | −9.89769 | −0.438707 | −0.219354 | − | 0.975645i | \(-0.570395\pi\) | ||||
−0.219354 | + | 0.975645i | \(0.570395\pi\) | |||||||
\(510\) | 30.8549 | 1.36628 | ||||||||
\(511\) | 9.51377 | 0.420864 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.10150 | −0.0927836 | ||||||||
\(514\) | −19.0786 | −0.841519 | ||||||||
\(515\) | −62.6541 | −2.76087 | ||||||||
\(516\) | 25.5893 | 1.12651 | ||||||||
\(517\) | −20.4354 | −0.898746 | ||||||||
\(518\) | −49.2309 | −2.16308 | ||||||||
\(519\) | 10.0288 | 0.440214 | ||||||||
\(520\) | −17.0086 | −0.745875 | ||||||||
\(521\) | −10.7629 | −0.471529 | −0.235765 | − | 0.971810i | \(-0.575759\pi\) | ||||
−0.235765 | + | 0.971810i | \(0.575759\pi\) | |||||||
\(522\) | 1.45911 | 0.0638634 | ||||||||
\(523\) | −0.766585 | −0.0335204 | −0.0167602 | − | 0.999860i | \(-0.505335\pi\) | ||||
−0.0167602 | + | 0.999860i | \(0.505335\pi\) | |||||||
\(524\) | −1.62186 | −0.0708513 | ||||||||
\(525\) | 88.1492 | 3.84715 | ||||||||
\(526\) | 31.2966 | 1.36460 | ||||||||
\(527\) | −4.06202 | −0.176944 | ||||||||
\(528\) | −5.41258 | −0.235552 | ||||||||
\(529\) | −22.4866 | −0.977678 | ||||||||
\(530\) | 16.9782 | 0.737484 | ||||||||
\(531\) | 34.6654 | 1.50435 | ||||||||
\(532\) | 14.8036 | 0.641818 | ||||||||
\(533\) | −5.21645 | −0.225950 | ||||||||
\(534\) | −30.8097 | −1.33327 | ||||||||
\(535\) | 40.7251 | 1.76070 | ||||||||
\(536\) | 1.78990 | 0.0773120 | ||||||||
\(537\) | −44.1507 | −1.90524 | ||||||||
\(538\) | −4.49940 | −0.193983 | ||||||||
\(539\) | 30.5290 | 1.31498 | ||||||||
\(540\) | 2.32934 | 0.100239 | ||||||||
\(541\) | 22.4906 | 0.966947 | 0.483473 | − | 0.875359i | \(-0.339375\pi\) | ||||
0.483473 | + | 0.875359i | \(0.339375\pi\) | |||||||
\(542\) | 13.7538 | 0.590776 | ||||||||
\(543\) | 10.6178 | 0.455653 | ||||||||
\(544\) | −3.55658 | −0.152487 | ||||||||
\(545\) | −5.22921 | −0.223995 | ||||||||
\(546\) | −50.8812 | −2.17751 | ||||||||
\(547\) | −7.74802 | −0.331282 | −0.165641 | − | 0.986186i | \(-0.552969\pi\) | ||||
−0.165641 | + | 0.986186i | \(0.552969\pi\) | |||||||
\(548\) | 13.8541 | 0.591817 | ||||||||
\(549\) | 9.83435 | 0.419720 | ||||||||
\(550\) | −18.3841 | −0.783899 | ||||||||
\(551\) | 1.74639 | 0.0743986 | ||||||||
\(552\) | 1.71541 | 0.0730126 | ||||||||
\(553\) | 15.1289 | 0.643348 | ||||||||
\(554\) | 11.0106 | 0.467794 | ||||||||
\(555\) | 94.3229 | 4.00378 | ||||||||
\(556\) | 6.13120 | 0.260021 | ||||||||
\(557\) | −30.6954 | −1.30061 | −0.650303 | − | 0.759675i | \(-0.725358\pi\) | ||||
−0.650303 | + | 0.759675i | \(0.725358\pi\) | |||||||
\(558\) | 3.11969 | 0.132067 | ||||||||
\(559\) | −50.1689 | −2.12192 | ||||||||
\(560\) | −16.4085 | −0.693388 | ||||||||
\(561\) | −19.2503 | −0.812747 | ||||||||
\(562\) | −30.8707 | −1.30220 | ||||||||
\(563\) | −3.54795 | −0.149528 | −0.0747641 | − | 0.997201i | \(-0.523820\pi\) | ||||
−0.0747641 | + | 0.997201i | \(0.523820\pi\) | |||||||
\(564\) | 21.6395 | 0.911186 | ||||||||
\(565\) | 24.9238 | 1.04855 | ||||||||
\(566\) | −2.08025 | −0.0874394 | ||||||||
\(567\) | 44.0735 | 1.85091 | ||||||||
\(568\) | 5.04234 | 0.211572 | ||||||||
\(569\) | 42.1066 | 1.76520 | 0.882601 | − | 0.470123i | \(-0.155790\pi\) | ||||
0.882601 | + | 0.470123i | \(0.155790\pi\) | |||||||
\(570\) | −28.3626 | −1.18798 | ||||||||
\(571\) | −25.3353 | −1.06025 | −0.530124 | − | 0.847920i | \(-0.677855\pi\) | ||||
−0.530124 | + | 0.847920i | \(0.677855\pi\) | |||||||
\(572\) | 10.6116 | 0.443693 | ||||||||
\(573\) | −35.2444 | −1.47236 | ||||||||
\(574\) | −5.03243 | −0.210050 | ||||||||
\(575\) | 5.82646 | 0.242980 | ||||||||
\(576\) | 2.73150 | 0.113813 | ||||||||
\(577\) | −29.6274 | −1.23341 | −0.616703 | − | 0.787196i | \(-0.711532\pi\) | ||||
−0.616703 | + | 0.787196i | \(0.711532\pi\) | |||||||
\(578\) | 4.35074 | 0.180967 | ||||||||
\(579\) | −46.2523 | −1.92218 | ||||||||
\(580\) | −1.93572 | −0.0803766 | ||||||||
\(581\) | −60.3258 | −2.50274 | ||||||||
\(582\) | 0.235059 | 0.00974349 | ||||||||
\(583\) | −10.5926 | −0.438701 | ||||||||
\(584\) | 2.10107 | 0.0869428 | ||||||||
\(585\) | 46.4589 | 1.92084 | ||||||||
\(586\) | 8.00119 | 0.330526 | ||||||||
\(587\) | −5.10598 | −0.210746 | −0.105373 | − | 0.994433i | \(-0.533604\pi\) | ||||
−0.105373 | + | 0.994433i | \(0.533604\pi\) | |||||||
\(588\) | −32.3278 | −1.33318 | ||||||||
\(589\) | 3.73391 | 0.153853 | ||||||||
\(590\) | −45.9888 | −1.89333 | ||||||||
\(591\) | 58.0045 | 2.38599 | ||||||||
\(592\) | −10.8724 | −0.446853 | ||||||||
\(593\) | 3.49206 | 0.143402 | 0.0717009 | − | 0.997426i | \(-0.477157\pi\) | ||||
0.0717009 | + | 0.997426i | \(0.477157\pi\) | |||||||
\(594\) | −1.45327 | −0.0596282 | ||||||||
\(595\) | −58.3583 | −2.39246 | ||||||||
\(596\) | −19.9991 | −0.819197 | ||||||||
\(597\) | −0.874901 | −0.0358073 | ||||||||
\(598\) | −3.36313 | −0.137529 | ||||||||
\(599\) | 28.4802 | 1.16367 | 0.581835 | − | 0.813307i | \(-0.302335\pi\) | ||||
0.581835 | + | 0.813307i | \(0.302335\pi\) | |||||||
\(600\) | 19.4673 | 0.794749 | ||||||||
\(601\) | −38.5141 | −1.57102 | −0.785512 | − | 0.618847i | \(-0.787600\pi\) | ||||
−0.785512 | + | 0.618847i | \(0.787600\pi\) | |||||||
\(602\) | −48.3991 | −1.97260 | ||||||||
\(603\) | −4.88912 | −0.199100 | ||||||||
\(604\) | −6.38314 | −0.259726 | ||||||||
\(605\) | −21.3388 | −0.867544 | ||||||||
\(606\) | 34.0403 | 1.38279 | ||||||||
\(607\) | −29.4426 | −1.19504 | −0.597519 | − | 0.801855i | \(-0.703847\pi\) | ||||
−0.597519 | + | 0.801855i | \(0.703847\pi\) | |||||||
\(608\) | 3.26930 | 0.132588 | ||||||||
\(609\) | −5.79072 | −0.234652 | ||||||||
\(610\) | −13.0467 | −0.528246 | ||||||||
\(611\) | −42.4251 | −1.71633 | ||||||||
\(612\) | 9.71481 | 0.392698 | ||||||||
\(613\) | 29.5501 | 1.19352 | 0.596759 | − | 0.802421i | \(-0.296455\pi\) | ||||
0.596759 | + | 0.802421i | \(0.296455\pi\) | |||||||
\(614\) | 24.1519 | 0.974691 | ||||||||
\(615\) | 9.64177 | 0.388794 | ||||||||
\(616\) | 10.2372 | 0.412470 | ||||||||
\(617\) | 18.7791 | 0.756019 | 0.378009 | − | 0.925802i | \(-0.376609\pi\) | ||||
0.378009 | + | 0.925802i | \(0.376609\pi\) | |||||||
\(618\) | −41.3930 | −1.66507 | ||||||||
\(619\) | 36.6843 | 1.47447 | 0.737234 | − | 0.675637i | \(-0.236131\pi\) | ||||
0.737234 | + | 0.675637i | \(0.236131\pi\) | |||||||
\(620\) | −4.13873 | −0.166215 | ||||||||
\(621\) | 0.460583 | 0.0184826 | ||||||||
\(622\) | −12.5984 | −0.505151 | ||||||||
\(623\) | 58.2728 | 2.33465 | ||||||||
\(624\) | −11.2368 | −0.449834 | ||||||||
\(625\) | 0.463985 | 0.0185594 | ||||||||
\(626\) | −19.9674 | −0.798059 | ||||||||
\(627\) | 17.6953 | 0.706684 | ||||||||
\(628\) | −12.8240 | −0.511735 | ||||||||
\(629\) | −38.6686 | −1.54182 | ||||||||
\(630\) | 44.8200 | 1.78567 | ||||||||
\(631\) | −30.5770 | −1.21725 | −0.608625 | − | 0.793458i | \(-0.708278\pi\) | ||||
−0.608625 | + | 0.793458i | \(0.708278\pi\) | |||||||
\(632\) | 3.34115 | 0.132904 | ||||||||
\(633\) | 26.9553 | 1.07138 | ||||||||
\(634\) | −1.53264 | −0.0608688 | ||||||||
\(635\) | −33.6210 | −1.33421 | ||||||||
\(636\) | 11.2168 | 0.444773 | ||||||||
\(637\) | 63.3800 | 2.51121 | ||||||||
\(638\) | 1.20769 | 0.0478130 | ||||||||
\(639\) | −13.7732 | −0.544858 | ||||||||
\(640\) | −3.62374 | −0.143241 | ||||||||
\(641\) | 14.5656 | 0.575305 | 0.287653 | − | 0.957735i | \(-0.407125\pi\) | ||||
0.287653 | + | 0.957735i | \(0.407125\pi\) | |||||||
\(642\) | 26.9054 | 1.06187 | ||||||||
\(643\) | 36.1814 | 1.42686 | 0.713428 | − | 0.700728i | \(-0.247141\pi\) | ||||
0.713428 | + | 0.700728i | \(0.247141\pi\) | |||||||
\(644\) | −3.24449 | −0.127851 | ||||||||
\(645\) | 92.7291 | 3.65120 | ||||||||
\(646\) | 11.6275 | 0.457479 | ||||||||
\(647\) | −45.1311 | −1.77429 | −0.887144 | − | 0.461493i | \(-0.847314\pi\) | ||||
−0.887144 | + | 0.461493i | \(0.847314\pi\) | |||||||
\(648\) | 9.73340 | 0.382364 | ||||||||
\(649\) | 28.6923 | 1.12627 | ||||||||
\(650\) | −38.1664 | −1.49701 | ||||||||
\(651\) | −12.3810 | −0.485250 | ||||||||
\(652\) | −14.6654 | −0.574343 | ||||||||
\(653\) | −5.37003 | −0.210146 | −0.105073 | − | 0.994465i | \(-0.533508\pi\) | ||||
−0.105073 | + | 0.994465i | \(0.533508\pi\) | |||||||
\(654\) | −3.45472 | −0.135090 | ||||||||
\(655\) | −5.87721 | −0.229642 | ||||||||
\(656\) | −1.11139 | −0.0433924 | ||||||||
\(657\) | −5.73907 | −0.223902 | ||||||||
\(658\) | −40.9284 | −1.59556 | ||||||||
\(659\) | 5.88129 | 0.229102 | 0.114551 | − | 0.993417i | \(-0.463457\pi\) | ||||
0.114551 | + | 0.993417i | \(0.463457\pi\) | |||||||
\(660\) | −19.6138 | −0.763466 | ||||||||
\(661\) | −19.0357 | −0.740402 | −0.370201 | − | 0.928952i | \(-0.620711\pi\) | ||||
−0.370201 | + | 0.928952i | \(0.620711\pi\) | |||||||
\(662\) | 10.4917 | 0.407772 | ||||||||
\(663\) | −39.9647 | −1.55210 | ||||||||
\(664\) | −13.3227 | −0.517019 | ||||||||
\(665\) | 53.6445 | 2.08024 | ||||||||
\(666\) | 29.6980 | 1.15077 | ||||||||
\(667\) | −0.382754 | −0.0148203 | ||||||||
\(668\) | 14.2266 | 0.550443 | ||||||||
\(669\) | 30.5835 | 1.18243 | ||||||||
\(670\) | 6.48615 | 0.250582 | ||||||||
\(671\) | 8.13980 | 0.314234 | ||||||||
\(672\) | −10.8404 | −0.418179 | ||||||||
\(673\) | 8.65779 | 0.333733 | 0.166867 | − | 0.985979i | \(-0.446635\pi\) | ||||
0.166867 | + | 0.985979i | \(0.446635\pi\) | |||||||
\(674\) | 23.2031 | 0.893749 | ||||||||
\(675\) | 5.22693 | 0.201185 | ||||||||
\(676\) | 9.03029 | 0.347319 | ||||||||
\(677\) | −10.2663 | −0.394566 | −0.197283 | − | 0.980347i | \(-0.563212\pi\) | ||||
−0.197283 | + | 0.980347i | \(0.563212\pi\) | |||||||
\(678\) | 16.4661 | 0.632377 | ||||||||
\(679\) | −0.444585 | −0.0170616 | ||||||||
\(680\) | −12.8881 | −0.494237 | ||||||||
\(681\) | −44.7407 | −1.71447 | ||||||||
\(682\) | 2.58214 | 0.0988752 | ||||||||
\(683\) | −31.8049 | −1.21698 | −0.608490 | − | 0.793561i | \(-0.708225\pi\) | ||||
−0.608490 | + | 0.793561i | \(0.708225\pi\) | |||||||
\(684\) | −8.93010 | −0.341451 | ||||||||
\(685\) | 50.2036 | 1.91818 | ||||||||
\(686\) | 29.4477 | 1.12432 | ||||||||
\(687\) | −27.2180 | −1.03843 | ||||||||
\(688\) | −10.6887 | −0.407502 | ||||||||
\(689\) | −21.9909 | −0.837787 | ||||||||
\(690\) | 6.21620 | 0.236647 | ||||||||
\(691\) | −2.89440 | −0.110108 | −0.0550541 | − | 0.998483i | \(-0.517533\pi\) | ||||
−0.0550541 | + | 0.998483i | \(0.517533\pi\) | |||||||
\(692\) | −4.18903 | −0.159243 | ||||||||
\(693\) | −27.9630 | −1.06223 | ||||||||
\(694\) | −3.54059 | −0.134399 | ||||||||
\(695\) | 22.2179 | 0.842772 | ||||||||
\(696\) | −1.27885 | −0.0484748 | ||||||||
\(697\) | −3.95274 | −0.149721 | ||||||||
\(698\) | 32.6885 | 1.23728 | ||||||||
\(699\) | 59.1724 | 2.23811 | ||||||||
\(700\) | −36.8200 | −1.39167 | ||||||||
\(701\) | 27.8401 | 1.05151 | 0.525753 | − | 0.850637i | \(-0.323784\pi\) | ||||
0.525753 | + | 0.850637i | \(0.323784\pi\) | |||||||
\(702\) | −3.01707 | −0.113872 | ||||||||
\(703\) | 35.5451 | 1.34061 | ||||||||
\(704\) | 2.26084 | 0.0852087 | ||||||||
\(705\) | 78.4159 | 2.95331 | ||||||||
\(706\) | −20.9819 | −0.789665 | ||||||||
\(707\) | −64.3831 | −2.42138 | ||||||||
\(708\) | −30.3829 | −1.14186 | ||||||||
\(709\) | −17.3183 | −0.650402 | −0.325201 | − | 0.945645i | \(-0.605432\pi\) | ||||
−0.325201 | + | 0.945645i | \(0.605432\pi\) | |||||||
\(710\) | 18.2721 | 0.685741 | ||||||||
\(711\) | −9.12636 | −0.342265 | ||||||||
\(712\) | 12.8692 | 0.482295 | ||||||||
\(713\) | −0.818357 | −0.0306477 | ||||||||
\(714\) | −38.5549 | −1.44288 | ||||||||
\(715\) | 38.4537 | 1.43809 | ||||||||
\(716\) | 18.4418 | 0.689202 | ||||||||
\(717\) | −17.1032 | −0.638730 | ||||||||
\(718\) | −32.3869 | −1.20867 | ||||||||
\(719\) | 3.79195 | 0.141416 | 0.0707080 | − | 0.997497i | \(-0.477474\pi\) | ||||
0.0707080 | + | 0.997497i | \(0.477474\pi\) | |||||||
\(720\) | 9.89826 | 0.368886 | ||||||||
\(721\) | 78.2897 | 2.91566 | ||||||||
\(722\) | 8.31168 | 0.309329 | ||||||||
\(723\) | −23.7685 | −0.883959 | ||||||||
\(724\) | −4.43507 | −0.164828 | ||||||||
\(725\) | −4.34368 | −0.161320 | ||||||||
\(726\) | −14.0976 | −0.523212 | ||||||||
\(727\) | 3.60482 | 0.133695 | 0.0668477 | − | 0.997763i | \(-0.478706\pi\) | ||||
0.0668477 | + | 0.997763i | \(0.478706\pi\) | |||||||
\(728\) | 21.2531 | 0.787693 | ||||||||
\(729\) | −21.9701 | −0.813708 | ||||||||
\(730\) | 7.61373 | 0.281797 | ||||||||
\(731\) | −38.0152 | −1.40604 | ||||||||
\(732\) | −8.61942 | −0.318583 | ||||||||
\(733\) | 10.4879 | 0.387379 | 0.193690 | − | 0.981063i | \(-0.437954\pi\) | ||||
0.193690 | + | 0.981063i | \(0.437954\pi\) | |||||||
\(734\) | 21.3339 | 0.787447 | ||||||||
\(735\) | −117.148 | −4.32106 | ||||||||
\(736\) | −0.716528 | −0.0264116 | ||||||||
\(737\) | −4.04668 | −0.149062 | ||||||||
\(738\) | 3.03576 | 0.111748 | ||||||||
\(739\) | −42.9737 | −1.58081 | −0.790407 | − | 0.612582i | \(-0.790131\pi\) | ||||
−0.790407 | + | 0.612582i | \(0.790131\pi\) | |||||||
\(740\) | −39.3988 | −1.44833 | ||||||||
\(741\) | 36.7366 | 1.34955 | ||||||||
\(742\) | −21.2151 | −0.778832 | ||||||||
\(743\) | −47.9697 | −1.75984 | −0.879918 | − | 0.475125i | \(-0.842403\pi\) | ||||
−0.879918 | + | 0.475125i | \(0.842403\pi\) | |||||||
\(744\) | −2.73428 | −0.100244 | ||||||||
\(745\) | −72.4718 | −2.65516 | ||||||||
\(746\) | 8.68720 | 0.318061 | ||||||||
\(747\) | 36.3909 | 1.33147 | ||||||||
\(748\) | 8.04086 | 0.294003 | ||||||||
\(749\) | −50.8882 | −1.85942 | ||||||||
\(750\) | 27.1673 | 0.992010 | ||||||||
\(751\) | −20.3145 | −0.741288 | −0.370644 | − | 0.928775i | \(-0.620863\pi\) | ||||
−0.370644 | + | 0.928775i | \(0.620863\pi\) | |||||||
\(752\) | −9.03883 | −0.329612 | ||||||||
\(753\) | −33.8426 | −1.23329 | ||||||||
\(754\) | 2.50724 | 0.0913083 | ||||||||
\(755\) | −23.1309 | −0.841818 | ||||||||
\(756\) | −2.91063 | −0.105859 | ||||||||
\(757\) | −49.1717 | −1.78718 | −0.893588 | − | 0.448888i | \(-0.851820\pi\) | ||||
−0.893588 | + | 0.448888i | \(0.851820\pi\) | |||||||
\(758\) | 7.77342 | 0.282343 | ||||||||
\(759\) | −3.87827 | −0.140772 | ||||||||
\(760\) | 11.8471 | 0.429740 | ||||||||
\(761\) | 42.8577 | 1.55359 | 0.776795 | − | 0.629754i | \(-0.216844\pi\) | ||||
0.776795 | + | 0.629754i | \(0.216844\pi\) | |||||||
\(762\) | −22.2120 | −0.804656 | ||||||||
\(763\) | 6.53418 | 0.236553 | ||||||||
\(764\) | 14.7216 | 0.532610 | ||||||||
\(765\) | 35.2040 | 1.27280 | ||||||||
\(766\) | −31.5159 | −1.13871 | ||||||||
\(767\) | 59.5669 | 2.15084 | ||||||||
\(768\) | −2.39406 | −0.0863880 | ||||||||
\(769\) | −11.8690 | −0.428008 | −0.214004 | − | 0.976833i | \(-0.568651\pi\) | ||||
−0.214004 | + | 0.976833i | \(0.568651\pi\) | |||||||
\(770\) | 37.0971 | 1.33689 | ||||||||
\(771\) | −45.6751 | −1.64495 | ||||||||
\(772\) | 19.3196 | 0.695329 | ||||||||
\(773\) | −19.0584 | −0.685483 | −0.342741 | − | 0.939430i | \(-0.611355\pi\) | ||||
−0.342741 | + | 0.939430i | \(0.611355\pi\) | |||||||
\(774\) | 29.1962 | 1.04943 | ||||||||
\(775\) | −9.28712 | −0.333603 | ||||||||
\(776\) | −0.0981843 | −0.00352461 | ||||||||
\(777\) | −117.862 | −4.22826 | ||||||||
\(778\) | 17.4550 | 0.625794 | ||||||||
\(779\) | 3.63346 | 0.130182 | ||||||||
\(780\) | −40.7194 | −1.45799 | ||||||||
\(781\) | −11.3999 | −0.407921 | ||||||||
\(782\) | −2.54839 | −0.0911302 | ||||||||
\(783\) | −0.343369 | −0.0122710 | ||||||||
\(784\) | 13.5034 | 0.482263 | ||||||||
\(785\) | −46.4711 | −1.65862 | ||||||||
\(786\) | −3.88283 | −0.138496 | ||||||||
\(787\) | 18.7130 | 0.667048 | 0.333524 | − | 0.942742i | \(-0.391762\pi\) | ||||
0.333524 | + | 0.942742i | \(0.391762\pi\) | |||||||
\(788\) | −24.2286 | −0.863107 | ||||||||
\(789\) | 74.9257 | 2.66743 | ||||||||
\(790\) | 12.1075 | 0.430765 | ||||||||
\(791\) | −31.1436 | −1.10734 | ||||||||
\(792\) | −6.17549 | −0.219437 | ||||||||
\(793\) | 16.8987 | 0.600091 | ||||||||
\(794\) | 20.1859 | 0.716370 | ||||||||
\(795\) | 40.6466 | 1.44159 | ||||||||
\(796\) | 0.365447 | 0.0129529 | ||||||||
\(797\) | −40.9899 | −1.45194 | −0.725968 | − | 0.687729i | \(-0.758608\pi\) | ||||
−0.725968 | + | 0.687729i | \(0.758608\pi\) | |||||||
\(798\) | 35.4406 | 1.25459 | ||||||||
\(799\) | −32.1473 | −1.13729 | ||||||||
\(800\) | −8.13152 | −0.287493 | ||||||||
\(801\) | −35.1524 | −1.24205 | ||||||||
\(802\) | 30.9339 | 1.09231 | ||||||||
\(803\) | −4.75018 | −0.167630 | ||||||||
\(804\) | 4.28513 | 0.151125 | ||||||||
\(805\) | −11.7572 | −0.414386 | ||||||||
\(806\) | 5.36068 | 0.188822 | ||||||||
\(807\) | −10.7718 | −0.379186 | ||||||||
\(808\) | −14.2187 | −0.500211 | ||||||||
\(809\) | −16.0225 | −0.563321 | −0.281660 | − | 0.959514i | \(-0.590885\pi\) | ||||
−0.281660 | + | 0.959514i | \(0.590885\pi\) | |||||||
\(810\) | 35.2714 | 1.23931 | ||||||||
\(811\) | 21.8834 | 0.768432 | 0.384216 | − | 0.923243i | \(-0.374472\pi\) | ||||
0.384216 | + | 0.923243i | \(0.374472\pi\) | |||||||
\(812\) | 2.41879 | 0.0848830 | ||||||||
\(813\) | 32.9274 | 1.15481 | ||||||||
\(814\) | 24.5808 | 0.861555 | ||||||||
\(815\) | −53.1438 | −1.86155 | ||||||||
\(816\) | −8.51465 | −0.298072 | ||||||||
\(817\) | 34.9445 | 1.22255 | ||||||||
\(818\) | −20.7917 | −0.726964 | ||||||||
\(819\) | −58.0530 | −2.02853 | ||||||||
\(820\) | −4.02738 | −0.140642 | ||||||||
\(821\) | −40.6855 | −1.41993 | −0.709966 | − | 0.704236i | \(-0.751290\pi\) | ||||
−0.709966 | + | 0.704236i | \(0.751290\pi\) | |||||||
\(822\) | 33.1674 | 1.15685 | ||||||||
\(823\) | −28.6666 | −0.999254 | −0.499627 | − | 0.866241i | \(-0.666530\pi\) | ||||
−0.499627 | + | 0.866241i | \(0.666530\pi\) | |||||||
\(824\) | 17.2899 | 0.602322 | ||||||||
\(825\) | −44.0125 | −1.53232 | ||||||||
\(826\) | 57.4656 | 1.99948 | ||||||||
\(827\) | −9.37183 | −0.325890 | −0.162945 | − | 0.986635i | \(-0.552099\pi\) | ||||
−0.162945 | + | 0.986635i | \(0.552099\pi\) | |||||||
\(828\) | 1.95720 | 0.0680173 | ||||||||
\(829\) | −3.33811 | −0.115937 | −0.0579687 | − | 0.998318i | \(-0.518462\pi\) | ||||
−0.0579687 | + | 0.998318i | \(0.518462\pi\) | |||||||
\(830\) | −48.2779 | −1.67575 | ||||||||
\(831\) | 26.3599 | 0.914416 | ||||||||
\(832\) | 4.69364 | 0.162723 | ||||||||
\(833\) | 48.0258 | 1.66400 | ||||||||
\(834\) | 14.6784 | 0.508272 | ||||||||
\(835\) | 51.5535 | 1.78408 | ||||||||
\(836\) | −7.39137 | −0.255636 | ||||||||
\(837\) | −0.734149 | −0.0253759 | ||||||||
\(838\) | −30.4461 | −1.05174 | ||||||||
\(839\) | 38.3835 | 1.32514 | 0.662572 | − | 0.748998i | \(-0.269465\pi\) | ||||
0.662572 | + | 0.748998i | \(0.269465\pi\) | |||||||
\(840\) | −39.2830 | −1.35539 | ||||||||
\(841\) | −28.7147 | −0.990160 | ||||||||
\(842\) | 13.9994 | 0.482451 | ||||||||
\(843\) | −73.9063 | −2.54547 | ||||||||
\(844\) | −11.2593 | −0.387560 | ||||||||
\(845\) | 32.7235 | 1.12572 | ||||||||
\(846\) | 24.6896 | 0.848846 | ||||||||
\(847\) | 26.6640 | 0.916184 | ||||||||
\(848\) | −4.68525 | −0.160892 | ||||||||
\(849\) | −4.98023 | −0.170921 | ||||||||
\(850\) | −28.9204 | −0.991961 | ||||||||
\(851\) | −7.79038 | −0.267051 | ||||||||
\(852\) | 12.0716 | 0.413567 | ||||||||
\(853\) | −48.6331 | −1.66516 | −0.832582 | − | 0.553901i | \(-0.813138\pi\) | ||||
−0.832582 | + | 0.553901i | \(0.813138\pi\) | |||||||
\(854\) | 16.3026 | 0.557863 | ||||||||
\(855\) | −32.3604 | −1.10670 | ||||||||
\(856\) | −11.2384 | −0.384121 | ||||||||
\(857\) | 11.9410 | 0.407898 | 0.203949 | − | 0.978982i | \(-0.434622\pi\) | ||||
0.203949 | + | 0.978982i | \(0.434622\pi\) | |||||||
\(858\) | 25.4047 | 0.867303 | ||||||||
\(859\) | −11.2099 | −0.382476 | −0.191238 | − | 0.981544i | \(-0.561250\pi\) | ||||
−0.191238 | + | 0.981544i | \(0.561250\pi\) | |||||||
\(860\) | −38.7331 | −1.32079 | ||||||||
\(861\) | −12.0479 | −0.410592 | ||||||||
\(862\) | 27.9060 | 0.950483 | ||||||||
\(863\) | 43.0231 | 1.46452 | 0.732261 | − | 0.681024i | \(-0.238465\pi\) | ||||
0.732261 | + | 0.681024i | \(0.238465\pi\) | |||||||
\(864\) | −0.642799 | −0.0218685 | ||||||||
\(865\) | −15.1800 | −0.516134 | ||||||||
\(866\) | −12.0911 | −0.410871 | ||||||||
\(867\) | 10.4159 | 0.353743 | ||||||||
\(868\) | 5.17157 | 0.175534 | ||||||||
\(869\) | −7.55381 | −0.256245 | ||||||||
\(870\) | −4.63423 | −0.157115 | ||||||||
\(871\) | −8.40116 | −0.284663 | ||||||||
\(872\) | 1.44304 | 0.0488675 | ||||||||
\(873\) | 0.268190 | 0.00907687 | ||||||||
\(874\) | 2.34255 | 0.0792378 | ||||||||
\(875\) | −51.3836 | −1.73708 | ||||||||
\(876\) | 5.03007 | 0.169950 | ||||||||
\(877\) | 42.5092 | 1.43543 | 0.717716 | − | 0.696336i | \(-0.245187\pi\) | ||||
0.717716 | + | 0.696336i | \(0.245187\pi\) | |||||||
\(878\) | −14.8967 | −0.502738 | ||||||||
\(879\) | 19.1553 | 0.646092 | ||||||||
\(880\) | 8.19271 | 0.276176 | ||||||||
\(881\) | −19.1034 | −0.643610 | −0.321805 | − | 0.946806i | \(-0.604290\pi\) | ||||
−0.321805 | + | 0.946806i | \(0.604290\pi\) | |||||||
\(882\) | −36.8845 | −1.24197 | ||||||||
\(883\) | 56.3436 | 1.89611 | 0.948057 | − | 0.318100i | \(-0.103045\pi\) | ||||
0.948057 | + | 0.318100i | \(0.103045\pi\) | |||||||
\(884\) | 16.6933 | 0.561457 | ||||||||
\(885\) | −110.100 | −3.70097 | ||||||||
\(886\) | 27.9427 | 0.938752 | ||||||||
\(887\) | −20.0143 | −0.672013 | −0.336006 | − | 0.941860i | \(-0.609076\pi\) | ||||
−0.336006 | + | 0.941860i | \(0.609076\pi\) | |||||||
\(888\) | −26.0291 | −0.873480 | ||||||||
\(889\) | 42.0113 | 1.40901 | ||||||||
\(890\) | 46.6348 | 1.56320 | ||||||||
\(891\) | −22.0057 | −0.737218 | ||||||||
\(892\) | −12.7748 | −0.427731 | ||||||||
\(893\) | 29.5507 | 0.988875 | ||||||||
\(894\) | −47.8791 | −1.60132 | ||||||||
\(895\) | 66.8283 | 2.23382 | ||||||||
\(896\) | 4.52806 | 0.151272 | ||||||||
\(897\) | −8.05152 | −0.268832 | ||||||||
\(898\) | −24.5693 | −0.819889 | ||||||||
\(899\) | 0.610092 | 0.0203477 | ||||||||
\(900\) | 22.2113 | 0.740375 | ||||||||
\(901\) | −16.6635 | −0.555141 | ||||||||
\(902\) | 2.51267 | 0.0836627 | ||||||||
\(903\) | −115.870 | −3.85591 | ||||||||
\(904\) | −6.87791 | −0.228756 | ||||||||
\(905\) | −16.0715 | −0.534236 | ||||||||
\(906\) | −15.2816 | −0.507697 | ||||||||
\(907\) | 45.2561 | 1.50270 | 0.751352 | − | 0.659901i | \(-0.229402\pi\) | ||||
0.751352 | + | 0.659901i | \(0.229402\pi\) | |||||||
\(908\) | 18.6882 | 0.620191 | ||||||||
\(909\) | 38.8384 | 1.28819 | ||||||||
\(910\) | 77.0159 | 2.55305 | ||||||||
\(911\) | 13.3220 | 0.441376 | 0.220688 | − | 0.975344i | \(-0.429170\pi\) | ||||
0.220688 | + | 0.975344i | \(0.429170\pi\) | |||||||
\(912\) | 7.82689 | 0.259174 | ||||||||
\(913\) | 30.1204 | 0.996840 | ||||||||
\(914\) | 9.00593 | 0.297890 | ||||||||
\(915\) | −31.2346 | −1.03258 | ||||||||
\(916\) | 11.3690 | 0.375642 | ||||||||
\(917\) | 7.34389 | 0.242517 | ||||||||
\(918\) | −2.28617 | −0.0754547 | ||||||||
\(919\) | 18.5089 | 0.610553 | 0.305277 | − | 0.952264i | \(-0.401251\pi\) | ||||
0.305277 | + | 0.952264i | \(0.401251\pi\) | |||||||
\(920\) | −2.59651 | −0.0856045 | ||||||||
\(921\) | 57.8209 | 1.90526 | ||||||||
\(922\) | 24.8496 | 0.818379 | ||||||||
\(923\) | −23.6669 | −0.779007 | ||||||||
\(924\) | 24.5085 | 0.806271 | ||||||||
\(925\) | −88.4091 | −2.90687 | ||||||||
\(926\) | −1.19650 | −0.0393194 | ||||||||
\(927\) | −47.2274 | −1.55115 | ||||||||
\(928\) | 0.534178 | 0.0175353 | ||||||||
\(929\) | 29.0552 | 0.953270 | 0.476635 | − | 0.879101i | \(-0.341856\pi\) | ||||
0.476635 | + | 0.879101i | \(0.341856\pi\) | |||||||
\(930\) | −9.90834 | −0.324907 | ||||||||
\(931\) | −44.1466 | −1.44685 | ||||||||
\(932\) | −24.7164 | −0.809612 | ||||||||
\(933\) | −30.1613 | −0.987437 | ||||||||
\(934\) | −5.50533 | −0.180140 | ||||||||
\(935\) | 29.1380 | 0.952915 | ||||||||
\(936\) | −12.8207 | −0.419058 | ||||||||
\(937\) | 2.93807 | 0.0959826 | 0.0479913 | − | 0.998848i | \(-0.484718\pi\) | ||||
0.0479913 | + | 0.998848i | \(0.484718\pi\) | |||||||
\(938\) | −8.10479 | −0.264631 | ||||||||
\(939\) | −47.8031 | −1.56000 | ||||||||
\(940\) | −32.7544 | −1.06833 | ||||||||
\(941\) | 53.4754 | 1.74325 | 0.871624 | − | 0.490176i | \(-0.163067\pi\) | ||||
0.871624 | + | 0.490176i | \(0.163067\pi\) | |||||||
\(942\) | −30.7015 | −1.00031 | ||||||||
\(943\) | −0.796340 | −0.0259324 | ||||||||
\(944\) | 12.6910 | 0.413056 | ||||||||
\(945\) | −10.5474 | −0.343107 | ||||||||
\(946\) | 24.1654 | 0.785686 | ||||||||
\(947\) | −39.3678 | −1.27928 | −0.639641 | − | 0.768674i | \(-0.720917\pi\) | ||||
−0.639641 | + | 0.768674i | \(0.720917\pi\) | |||||||
\(948\) | 7.99890 | 0.259792 | ||||||||
\(949\) | −9.86166 | −0.320123 | ||||||||
\(950\) | 26.5844 | 0.862511 | ||||||||
\(951\) | −3.66922 | −0.118983 | ||||||||
\(952\) | 16.1044 | 0.521947 | ||||||||
\(953\) | −22.3747 | −0.724789 | −0.362394 | − | 0.932025i | \(-0.618041\pi\) | ||||
−0.362394 | + | 0.932025i | \(0.618041\pi\) | |||||||
\(954\) | 12.7978 | 0.414343 | ||||||||
\(955\) | 53.3474 | 1.72628 | ||||||||
\(956\) | 7.14402 | 0.231054 | ||||||||
\(957\) | 2.89128 | 0.0934618 | ||||||||
\(958\) | −8.58037 | −0.277219 | ||||||||
\(959\) | −62.7321 | −2.02573 | ||||||||
\(960\) | −8.67544 | −0.279999 | ||||||||
\(961\) | −29.6956 | −0.957922 | ||||||||
\(962\) | 51.0312 | 1.64531 | ||||||||
\(963\) | 30.6977 | 0.989221 | ||||||||
\(964\) | 9.92812 | 0.319763 | ||||||||
\(965\) | 70.0094 | 2.25368 | ||||||||
\(966\) | −7.76748 | −0.249915 | ||||||||
\(967\) | −40.5707 | −1.30467 | −0.652334 | − | 0.757932i | \(-0.726210\pi\) | ||||
−0.652334 | + | 0.757932i | \(0.726210\pi\) | |||||||
\(968\) | 5.88860 | 0.189267 | ||||||||
\(969\) | 27.8370 | 0.894252 | ||||||||
\(970\) | −0.355795 | −0.0114239 | ||||||||
\(971\) | −14.0961 | −0.452366 | −0.226183 | − | 0.974085i | \(-0.572625\pi\) | ||||
−0.226183 | + | 0.974085i | \(0.572625\pi\) | |||||||
\(972\) | 21.3739 | 0.685568 | ||||||||
\(973\) | −27.7625 | −0.890023 | ||||||||
\(974\) | −6.92054 | −0.221749 | ||||||||
\(975\) | −91.3726 | −2.92626 | ||||||||
\(976\) | 3.60034 | 0.115244 | ||||||||
\(977\) | −45.9679 | −1.47064 | −0.735321 | − | 0.677719i | \(-0.762969\pi\) | ||||
−0.735321 | + | 0.677719i | \(0.762969\pi\) | |||||||
\(978\) | −35.1099 | −1.12269 | ||||||||
\(979\) | −29.0953 | −0.929890 | ||||||||
\(980\) | 48.9328 | 1.56310 | ||||||||
\(981\) | −3.94167 | −0.125848 | ||||||||
\(982\) | 32.7740 | 1.04586 | ||||||||
\(983\) | −22.4337 | −0.715523 | −0.357762 | − | 0.933813i | \(-0.616460\pi\) | ||||
−0.357762 | + | 0.933813i | \(0.616460\pi\) | |||||||
\(984\) | −2.66072 | −0.0848207 | ||||||||
\(985\) | −87.7981 | −2.79748 | ||||||||
\(986\) | 1.89985 | 0.0605035 | ||||||||
\(987\) | −97.9849 | −3.11889 | ||||||||
\(988\) | −15.3449 | −0.488187 | ||||||||
\(989\) | −7.65875 | −0.243534 | ||||||||
\(990\) | −22.3784 | −0.711232 | ||||||||
\(991\) | −14.4829 | −0.460064 | −0.230032 | − | 0.973183i | \(-0.573883\pi\) | ||||
−0.230032 | + | 0.973183i | \(0.573883\pi\) | |||||||
\(992\) | 1.14211 | 0.0362622 | ||||||||
\(993\) | 25.1177 | 0.797087 | ||||||||
\(994\) | −22.8320 | −0.724188 | ||||||||
\(995\) | 1.32429 | 0.0419827 | ||||||||
\(996\) | −31.8952 | −1.01064 | ||||||||
\(997\) | −0.0104048 | −0.000329524 0 | −0.000164762 | − | 1.00000i | \(-0.500052\pi\) | ||||
−0.000164762 | 1.00000i | \(0.500052\pi\) | ||||||||
\(998\) | 19.5945 | 0.620254 | ||||||||
\(999\) | −6.98876 | −0.221115 |
(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 | 8002.2.a.f.1.15 | ✓ | 89 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.f.1.15 | ✓ | 89 | 1.1 | even | 1 | trivial |