Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45725 | 1.73754 | 0.868768 | − | 0.495219i | \(-0.164912\pi\) | ||||
0.868768 | + | 0.495219i | \(0.164912\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.03807 | 2.01903 | ||||||||
\(5\) | 1.82467 | 0.816016 | 0.408008 | − | 0.912978i | \(-0.366224\pi\) | ||||
0.408008 | + | 0.912978i | \(0.366224\pi\) | |||||||
\(6\) | −2.45725 | −1.00317 | ||||||||
\(7\) | 1.71478 | 0.648127 | 0.324064 | − | 0.946035i | \(-0.394951\pi\) | ||||
0.324064 | + | 0.946035i | \(0.394951\pi\) | |||||||
\(8\) | 5.00803 | 1.77061 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.48366 | 1.41786 | ||||||||
\(11\) | −2.47217 | −0.745389 | −0.372694 | − | 0.927954i | \(-0.621566\pi\) | ||||
−0.372694 | + | 0.927954i | \(0.621566\pi\) | |||||||
\(12\) | −4.03807 | −1.16569 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 4.21365 | 1.12614 | ||||||||
\(15\) | −1.82467 | −0.471127 | ||||||||
\(16\) | 4.22984 | 1.05746 | ||||||||
\(17\) | 2.10209 | 0.509831 | 0.254916 | − | 0.966963i | \(-0.417952\pi\) | ||||
0.254916 | + | 0.966963i | \(0.417952\pi\) | |||||||
\(18\) | 2.45725 | 0.579179 | ||||||||
\(19\) | 5.03790 | 1.15577 | 0.577887 | − | 0.816117i | \(-0.303878\pi\) | ||||
0.577887 | + | 0.816117i | \(0.303878\pi\) | |||||||
\(20\) | 7.36812 | 1.64756 | ||||||||
\(21\) | −1.71478 | −0.374196 | ||||||||
\(22\) | −6.07475 | −1.29514 | ||||||||
\(23\) | −4.48018 | −0.934183 | −0.467091 | − | 0.884209i | \(-0.654698\pi\) | ||||
−0.467091 | + | 0.884209i | \(0.654698\pi\) | |||||||
\(24\) | −5.00803 | −1.02226 | ||||||||
\(25\) | −1.67059 | −0.334119 | ||||||||
\(26\) | 2.45725 | 0.481906 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 6.92441 | 1.30859 | ||||||||
\(29\) | 2.41624 | 0.448685 | 0.224343 | − | 0.974510i | \(-0.427977\pi\) | ||||
0.224343 | + | 0.974510i | \(0.427977\pi\) | |||||||
\(30\) | −4.48366 | −0.818600 | ||||||||
\(31\) | 8.42140 | 1.51253 | 0.756264 | − | 0.654266i | \(-0.227022\pi\) | ||||
0.756264 | + | 0.654266i | \(0.227022\pi\) | |||||||
\(32\) | 0.377710 | 0.0667704 | ||||||||
\(33\) | 2.47217 | 0.430350 | ||||||||
\(34\) | 5.16535 | 0.885850 | ||||||||
\(35\) | 3.12891 | 0.528882 | ||||||||
\(36\) | 4.03807 | 0.673011 | ||||||||
\(37\) | 5.69321 | 0.935957 | 0.467979 | − | 0.883740i | \(-0.344982\pi\) | ||||
0.467979 | + | 0.883740i | \(0.344982\pi\) | |||||||
\(38\) | 12.3794 | 2.00820 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 9.13799 | 1.44484 | ||||||||
\(41\) | 11.1071 | 1.73464 | 0.867319 | − | 0.497752i | \(-0.165841\pi\) | ||||
0.867319 | + | 0.497752i | \(0.165841\pi\) | |||||||
\(42\) | −4.21365 | −0.650180 | ||||||||
\(43\) | −2.64739 | −0.403723 | −0.201862 | − | 0.979414i | \(-0.564699\pi\) | ||||
−0.201862 | + | 0.979414i | \(0.564699\pi\) | |||||||
\(44\) | −9.98280 | −1.50496 | ||||||||
\(45\) | 1.82467 | 0.272005 | ||||||||
\(46\) | −11.0089 | −1.62318 | ||||||||
\(47\) | 6.04114 | 0.881190 | 0.440595 | − | 0.897706i | \(-0.354767\pi\) | ||||
0.440595 | + | 0.897706i | \(0.354767\pi\) | |||||||
\(48\) | −4.22984 | −0.610525 | ||||||||
\(49\) | −4.05952 | −0.579931 | ||||||||
\(50\) | −4.10506 | −0.580543 | ||||||||
\(51\) | −2.10209 | −0.294351 | ||||||||
\(52\) | 4.03807 | 0.559979 | ||||||||
\(53\) | −1.63456 | −0.224525 | −0.112262 | − | 0.993679i | \(-0.535810\pi\) | ||||
−0.112262 | + | 0.993679i | \(0.535810\pi\) | |||||||
\(54\) | −2.45725 | −0.334389 | ||||||||
\(55\) | −4.51089 | −0.608249 | ||||||||
\(56\) | 8.58769 | 1.14758 | ||||||||
\(57\) | −5.03790 | −0.667286 | ||||||||
\(58\) | 5.93731 | 0.779607 | ||||||||
\(59\) | 2.39601 | 0.311934 | 0.155967 | − | 0.987762i | \(-0.450151\pi\) | ||||
0.155967 | + | 0.987762i | \(0.450151\pi\) | |||||||
\(60\) | −7.36812 | −0.951221 | ||||||||
\(61\) | −10.8292 | −1.38654 | −0.693270 | − | 0.720678i | \(-0.743831\pi\) | ||||
−0.693270 | + | 0.720678i | \(0.743831\pi\) | |||||||
\(62\) | 20.6935 | 2.62807 | ||||||||
\(63\) | 1.71478 | 0.216042 | ||||||||
\(64\) | −7.53156 | −0.941445 | ||||||||
\(65\) | 1.82467 | 0.226322 | ||||||||
\(66\) | 6.07475 | 0.747749 | ||||||||
\(67\) | −7.49568 | −0.915743 | −0.457872 | − | 0.889018i | \(-0.651388\pi\) | ||||
−0.457872 | + | 0.889018i | \(0.651388\pi\) | |||||||
\(68\) | 8.48837 | 1.02937 | ||||||||
\(69\) | 4.48018 | 0.539351 | ||||||||
\(70\) | 7.68850 | 0.918952 | ||||||||
\(71\) | −1.28480 | −0.152478 | −0.0762389 | − | 0.997090i | \(-0.524291\pi\) | ||||
−0.0762389 | + | 0.997090i | \(0.524291\pi\) | |||||||
\(72\) | 5.00803 | 0.590202 | ||||||||
\(73\) | 4.77967 | 0.559418 | 0.279709 | − | 0.960085i | \(-0.409762\pi\) | ||||
0.279709 | + | 0.960085i | \(0.409762\pi\) | |||||||
\(74\) | 13.9896 | 1.62626 | ||||||||
\(75\) | 1.67059 | 0.192903 | ||||||||
\(76\) | 20.3434 | 2.33354 | ||||||||
\(77\) | −4.23924 | −0.483107 | ||||||||
\(78\) | −2.45725 | −0.278229 | ||||||||
\(79\) | 10.3906 | 1.16904 | 0.584519 | − | 0.811380i | \(-0.301283\pi\) | ||||
0.584519 | + | 0.811380i | \(0.301283\pi\) | |||||||
\(80\) | 7.71805 | 0.862905 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 27.2929 | 3.01400 | ||||||||
\(83\) | 5.09703 | 0.559471 | 0.279736 | − | 0.960077i | \(-0.409753\pi\) | ||||
0.279736 | + | 0.960077i | \(0.409753\pi\) | |||||||
\(84\) | −6.92441 | −0.755515 | ||||||||
\(85\) | 3.83561 | 0.416030 | ||||||||
\(86\) | −6.50529 | −0.701484 | ||||||||
\(87\) | −2.41624 | −0.259048 | ||||||||
\(88\) | −12.3807 | −1.31979 | ||||||||
\(89\) | −5.25191 | −0.556702 | −0.278351 | − | 0.960479i | \(-0.589788\pi\) | ||||
−0.278351 | + | 0.960479i | \(0.589788\pi\) | |||||||
\(90\) | 4.48366 | 0.472619 | ||||||||
\(91\) | 1.71478 | 0.179758 | ||||||||
\(92\) | −18.0913 | −1.88615 | ||||||||
\(93\) | −8.42140 | −0.873259 | ||||||||
\(94\) | 14.8446 | 1.53110 | ||||||||
\(95\) | 9.19248 | 0.943129 | ||||||||
\(96\) | −0.377710 | −0.0385499 | ||||||||
\(97\) | −13.6887 | −1.38988 | −0.694940 | − | 0.719068i | \(-0.744569\pi\) | ||||
−0.694940 | + | 0.719068i | \(0.744569\pi\) | |||||||
\(98\) | −9.97524 | −1.00765 | ||||||||
\(99\) | −2.47217 | −0.248463 | ||||||||
\(100\) | −6.74596 | −0.674596 | ||||||||
\(101\) | −1.97292 | −0.196313 | −0.0981566 | − | 0.995171i | \(-0.531295\pi\) | ||||
−0.0981566 | + | 0.995171i | \(0.531295\pi\) | |||||||
\(102\) | −5.16535 | −0.511446 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 5.00803 | 0.491078 | ||||||||
\(105\) | −3.12891 | −0.305350 | ||||||||
\(106\) | −4.01653 | −0.390120 | ||||||||
\(107\) | 15.1982 | 1.46927 | 0.734634 | − | 0.678463i | \(-0.237354\pi\) | ||||
0.734634 | + | 0.678463i | \(0.237354\pi\) | |||||||
\(108\) | −4.03807 | −0.388563 | ||||||||
\(109\) | −18.2958 | −1.75242 | −0.876208 | − | 0.481933i | \(-0.839935\pi\) | ||||
−0.876208 | + | 0.481933i | \(0.839935\pi\) | |||||||
\(110\) | −11.0844 | −1.05685 | ||||||||
\(111\) | −5.69321 | −0.540375 | ||||||||
\(112\) | 7.25327 | 0.685369 | ||||||||
\(113\) | −10.9011 | −1.02549 | −0.512743 | − | 0.858542i | \(-0.671371\pi\) | ||||
−0.512743 | + | 0.858542i | \(0.671371\pi\) | |||||||
\(114\) | −12.3794 | −1.15943 | ||||||||
\(115\) | −8.17484 | −0.762308 | ||||||||
\(116\) | 9.75695 | 0.905910 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 5.88758 | 0.541996 | ||||||||
\(119\) | 3.60463 | 0.330436 | ||||||||
\(120\) | −9.13799 | −0.834180 | ||||||||
\(121\) | −4.88835 | −0.444396 | ||||||||
\(122\) | −26.6101 | −2.40916 | ||||||||
\(123\) | −11.1071 | −1.00149 | ||||||||
\(124\) | 34.0062 | 3.05384 | ||||||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | 4.21365 | 0.375382 | ||||||||
\(127\) | 18.0296 | 1.59987 | 0.799934 | − | 0.600088i | \(-0.204868\pi\) | ||||
0.799934 | + | 0.600088i | \(0.204868\pi\) | |||||||
\(128\) | −19.2623 | −1.70257 | ||||||||
\(129\) | 2.64739 | 0.233090 | ||||||||
\(130\) | 4.48366 | 0.393243 | ||||||||
\(131\) | 7.05989 | 0.616826 | 0.308413 | − | 0.951253i | \(-0.400202\pi\) | ||||
0.308413 | + | 0.951253i | \(0.400202\pi\) | |||||||
\(132\) | 9.98280 | 0.868892 | ||||||||
\(133\) | 8.63891 | 0.749088 | ||||||||
\(134\) | −18.4187 | −1.59114 | ||||||||
\(135\) | −1.82467 | −0.157042 | ||||||||
\(136\) | 10.5273 | 0.902711 | ||||||||
\(137\) | 18.8311 | 1.60885 | 0.804424 | − | 0.594055i | \(-0.202474\pi\) | ||||
0.804424 | + | 0.594055i | \(0.202474\pi\) | |||||||
\(138\) | 11.0089 | 0.937141 | ||||||||
\(139\) | −15.2404 | −1.29268 | −0.646339 | − | 0.763051i | \(-0.723701\pi\) | ||||
−0.646339 | + | 0.763051i | \(0.723701\pi\) | |||||||
\(140\) | 12.6347 | 1.06783 | ||||||||
\(141\) | −6.04114 | −0.508756 | ||||||||
\(142\) | −3.15707 | −0.264936 | ||||||||
\(143\) | −2.47217 | −0.206734 | ||||||||
\(144\) | 4.22984 | 0.352487 | ||||||||
\(145\) | 4.40884 | 0.366134 | ||||||||
\(146\) | 11.7448 | 0.972009 | ||||||||
\(147\) | 4.05952 | 0.334823 | ||||||||
\(148\) | 22.9895 | 1.88973 | ||||||||
\(149\) | −9.62177 | −0.788246 | −0.394123 | − | 0.919058i | \(-0.628952\pi\) | ||||
−0.394123 | + | 0.919058i | \(0.628952\pi\) | |||||||
\(150\) | 4.10506 | 0.335177 | ||||||||
\(151\) | −5.21999 | −0.424797 | −0.212398 | − | 0.977183i | \(-0.568127\pi\) | ||||
−0.212398 | + | 0.977183i | \(0.568127\pi\) | |||||||
\(152\) | 25.2300 | 2.04642 | ||||||||
\(153\) | 2.10209 | 0.169944 | ||||||||
\(154\) | −10.4169 | −0.839416 | ||||||||
\(155\) | 15.3662 | 1.23425 | ||||||||
\(156\) | −4.03807 | −0.323304 | ||||||||
\(157\) | 2.11215 | 0.168568 | 0.0842841 | − | 0.996442i | \(-0.473140\pi\) | ||||
0.0842841 | + | 0.996442i | \(0.473140\pi\) | |||||||
\(158\) | 25.5324 | 2.03125 | ||||||||
\(159\) | 1.63456 | 0.129629 | ||||||||
\(160\) | 0.689195 | 0.0544856 | ||||||||
\(161\) | −7.68254 | −0.605469 | ||||||||
\(162\) | 2.45725 | 0.193060 | ||||||||
\(163\) | −22.7611 | −1.78279 | −0.891393 | − | 0.453231i | \(-0.850271\pi\) | ||||
−0.891393 | + | 0.453231i | \(0.850271\pi\) | |||||||
\(164\) | 44.8512 | 3.50229 | ||||||||
\(165\) | 4.51089 | 0.351173 | ||||||||
\(166\) | 12.5247 | 0.972102 | ||||||||
\(167\) | 6.01129 | 0.465168 | 0.232584 | − | 0.972576i | \(-0.425282\pi\) | ||||
0.232584 | + | 0.972576i | \(0.425282\pi\) | |||||||
\(168\) | −8.58769 | −0.662555 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 9.42504 | 0.722868 | ||||||||
\(171\) | 5.03790 | 0.385258 | ||||||||
\(172\) | −10.6903 | −0.815131 | ||||||||
\(173\) | 2.03881 | 0.155008 | 0.0775038 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775038 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(174\) | −5.93731 | −0.450106 | ||||||||
\(175\) | −2.86471 | −0.216551 | ||||||||
\(176\) | −10.4569 | −0.788220 | ||||||||
\(177\) | −2.39601 | −0.180095 | ||||||||
\(178\) | −12.9053 | −0.967290 | ||||||||
\(179\) | 25.5086 | 1.90661 | 0.953303 | − | 0.302016i | \(-0.0976596\pi\) | ||||
0.953303 | + | 0.302016i | \(0.0976596\pi\) | |||||||
\(180\) | 7.36812 | 0.549187 | ||||||||
\(181\) | 10.2267 | 0.760147 | 0.380073 | − | 0.924956i | \(-0.375899\pi\) | ||||
0.380073 | + | 0.924956i | \(0.375899\pi\) | |||||||
\(182\) | 4.21365 | 0.312336 | ||||||||
\(183\) | 10.8292 | 0.800519 | ||||||||
\(184\) | −22.4369 | −1.65407 | ||||||||
\(185\) | 10.3882 | 0.763756 | ||||||||
\(186\) | −20.6935 | −1.51732 | ||||||||
\(187\) | −5.19673 | −0.380022 | ||||||||
\(188\) | 24.3945 | 1.77915 | ||||||||
\(189\) | −1.71478 | −0.124732 | ||||||||
\(190\) | 22.5882 | 1.63872 | ||||||||
\(191\) | −8.37666 | −0.606114 | −0.303057 | − | 0.952972i | \(-0.598007\pi\) | ||||
−0.303057 | + | 0.952972i | \(0.598007\pi\) | |||||||
\(192\) | 7.53156 | 0.543544 | ||||||||
\(193\) | −15.6923 | −1.12956 | −0.564779 | − | 0.825242i | \(-0.691039\pi\) | ||||
−0.564779 | + | 0.825242i | \(0.691039\pi\) | |||||||
\(194\) | −33.6366 | −2.41497 | ||||||||
\(195\) | −1.82467 | −0.130667 | ||||||||
\(196\) | −16.3926 | −1.17090 | ||||||||
\(197\) | −11.2707 | −0.803001 | −0.401501 | − | 0.915859i | \(-0.631511\pi\) | ||||
−0.401501 | + | 0.915859i | \(0.631511\pi\) | |||||||
\(198\) | −6.07475 | −0.431713 | ||||||||
\(199\) | −0.778082 | −0.0551567 | −0.0275784 | − | 0.999620i | \(-0.508780\pi\) | ||||
−0.0275784 | + | 0.999620i | \(0.508780\pi\) | |||||||
\(200\) | −8.36638 | −0.591593 | ||||||||
\(201\) | 7.49568 | 0.528705 | ||||||||
\(202\) | −4.84796 | −0.341101 | ||||||||
\(203\) | 4.14333 | 0.290805 | ||||||||
\(204\) | −8.48837 | −0.594305 | ||||||||
\(205\) | 20.2668 | 1.41549 | ||||||||
\(206\) | −2.45725 | −0.171205 | ||||||||
\(207\) | −4.48018 | −0.311394 | ||||||||
\(208\) | 4.22984 | 0.293287 | ||||||||
\(209\) | −12.4546 | −0.861500 | ||||||||
\(210\) | −7.68850 | −0.530557 | ||||||||
\(211\) | 27.4762 | 1.89154 | 0.945769 | − | 0.324840i | \(-0.105311\pi\) | ||||
0.945769 | + | 0.324840i | \(0.105311\pi\) | |||||||
\(212\) | −6.60047 | −0.453322 | ||||||||
\(213\) | 1.28480 | 0.0880331 | ||||||||
\(214\) | 37.3458 | 2.55291 | ||||||||
\(215\) | −4.83060 | −0.329444 | ||||||||
\(216\) | −5.00803 | −0.340753 | ||||||||
\(217\) | 14.4409 | 0.980311 | ||||||||
\(218\) | −44.9572 | −3.04489 | ||||||||
\(219\) | −4.77967 | −0.322980 | ||||||||
\(220\) | −18.2153 | −1.22807 | ||||||||
\(221\) | 2.10209 | 0.141402 | ||||||||
\(222\) | −13.9896 | −0.938922 | ||||||||
\(223\) | 21.7022 | 1.45329 | 0.726643 | − | 0.687015i | \(-0.241079\pi\) | ||||
0.726643 | + | 0.687015i | \(0.241079\pi\) | |||||||
\(224\) | 0.647691 | 0.0432757 | ||||||||
\(225\) | −1.67059 | −0.111373 | ||||||||
\(226\) | −26.7866 | −1.78182 | ||||||||
\(227\) | −6.41324 | −0.425662 | −0.212831 | − | 0.977089i | \(-0.568268\pi\) | ||||
−0.212831 | + | 0.977089i | \(0.568268\pi\) | |||||||
\(228\) | −20.3434 | −1.34727 | ||||||||
\(229\) | −18.9532 | −1.25247 | −0.626233 | − | 0.779636i | \(-0.715404\pi\) | ||||
−0.626233 | + | 0.779636i | \(0.715404\pi\) | |||||||
\(230\) | −20.0876 | −1.32454 | ||||||||
\(231\) | 4.23924 | 0.278922 | ||||||||
\(232\) | 12.1006 | 0.794445 | ||||||||
\(233\) | −13.3023 | −0.871460 | −0.435730 | − | 0.900077i | \(-0.643510\pi\) | ||||
−0.435730 | + | 0.900077i | \(0.643510\pi\) | |||||||
\(234\) | 2.45725 | 0.160635 | ||||||||
\(235\) | 11.0231 | 0.719065 | ||||||||
\(236\) | 9.67524 | 0.629804 | ||||||||
\(237\) | −10.3906 | −0.674944 | ||||||||
\(238\) | 8.85746 | 0.574144 | ||||||||
\(239\) | 3.37996 | 0.218631 | 0.109316 | − | 0.994007i | \(-0.465134\pi\) | ||||
0.109316 | + | 0.994007i | \(0.465134\pi\) | |||||||
\(240\) | −7.71805 | −0.498198 | ||||||||
\(241\) | −6.02414 | −0.388049 | −0.194025 | − | 0.980997i | \(-0.562154\pi\) | ||||
−0.194025 | + | 0.980997i | \(0.562154\pi\) | |||||||
\(242\) | −12.0119 | −0.772154 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −43.7291 | −2.79947 | ||||||||
\(245\) | −7.40726 | −0.473233 | ||||||||
\(246\) | −27.2929 | −1.74013 | ||||||||
\(247\) | 5.03790 | 0.320554 | ||||||||
\(248\) | 42.1747 | 2.67809 | ||||||||
\(249\) | −5.09703 | −0.323011 | ||||||||
\(250\) | −29.9087 | −1.89159 | ||||||||
\(251\) | 6.55153 | 0.413529 | 0.206764 | − | 0.978391i | \(-0.433707\pi\) | ||||
0.206764 | + | 0.978391i | \(0.433707\pi\) | |||||||
\(252\) | 6.92441 | 0.436197 | ||||||||
\(253\) | 11.0758 | 0.696329 | ||||||||
\(254\) | 44.3032 | 2.77983 | ||||||||
\(255\) | −3.83561 | −0.240195 | ||||||||
\(256\) | −32.2692 | −2.01682 | ||||||||
\(257\) | 20.5033 | 1.27896 | 0.639482 | − | 0.768806i | \(-0.279149\pi\) | ||||
0.639482 | + | 0.768806i | \(0.279149\pi\) | |||||||
\(258\) | 6.50529 | 0.405002 | ||||||||
\(259\) | 9.76262 | 0.606619 | ||||||||
\(260\) | 7.36812 | 0.456952 | ||||||||
\(261\) | 2.41624 | 0.149562 | ||||||||
\(262\) | 17.3479 | 1.07176 | ||||||||
\(263\) | −17.7020 | −1.09155 | −0.545775 | − | 0.837932i | \(-0.683765\pi\) | ||||
−0.545775 | + | 0.837932i | \(0.683765\pi\) | |||||||
\(264\) | 12.3807 | 0.761981 | ||||||||
\(265\) | −2.98253 | −0.183216 | ||||||||
\(266\) | 21.2279 | 1.30157 | ||||||||
\(267\) | 5.25191 | 0.321412 | ||||||||
\(268\) | −30.2681 | −1.84892 | ||||||||
\(269\) | −24.5061 | −1.49417 | −0.747083 | − | 0.664731i | \(-0.768546\pi\) | ||||
−0.747083 | + | 0.664731i | \(0.768546\pi\) | |||||||
\(270\) | −4.48366 | −0.272867 | ||||||||
\(271\) | −26.9728 | −1.63848 | −0.819240 | − | 0.573451i | \(-0.805604\pi\) | ||||
−0.819240 | + | 0.573451i | \(0.805604\pi\) | |||||||
\(272\) | 8.89151 | 0.539127 | ||||||||
\(273\) | −1.71478 | −0.103783 | ||||||||
\(274\) | 46.2727 | 2.79543 | ||||||||
\(275\) | 4.13000 | 0.249048 | ||||||||
\(276\) | 18.0913 | 1.08897 | ||||||||
\(277\) | 24.0323 | 1.44396 | 0.721980 | − | 0.691914i | \(-0.243232\pi\) | ||||
0.721980 | + | 0.691914i | \(0.243232\pi\) | |||||||
\(278\) | −37.4495 | −2.24607 | ||||||||
\(279\) | 8.42140 | 0.504176 | ||||||||
\(280\) | 15.6697 | 0.936442 | ||||||||
\(281\) | 12.5280 | 0.747359 | 0.373679 | − | 0.927558i | \(-0.378096\pi\) | ||||
0.373679 | + | 0.927558i | \(0.378096\pi\) | |||||||
\(282\) | −14.8446 | −0.883981 | ||||||||
\(283\) | −30.3643 | −1.80497 | −0.902485 | − | 0.430721i | \(-0.858259\pi\) | ||||
−0.902485 | + | 0.430721i | \(0.858259\pi\) | |||||||
\(284\) | −5.18811 | −0.307858 | ||||||||
\(285\) | −9.19248 | −0.544516 | ||||||||
\(286\) | −6.07475 | −0.359207 | ||||||||
\(287\) | 19.0463 | 1.12427 | ||||||||
\(288\) | 0.377710 | 0.0222568 | ||||||||
\(289\) | −12.5812 | −0.740072 | ||||||||
\(290\) | 10.8336 | 0.636171 | ||||||||
\(291\) | 13.6887 | 0.802448 | ||||||||
\(292\) | 19.3006 | 1.12948 | ||||||||
\(293\) | −29.0186 | −1.69529 | −0.847644 | − | 0.530566i | \(-0.821979\pi\) | ||||
−0.847644 | + | 0.530566i | \(0.821979\pi\) | |||||||
\(294\) | 9.97524 | 0.581768 | ||||||||
\(295\) | 4.37191 | 0.254543 | ||||||||
\(296\) | 28.5118 | 1.65721 | ||||||||
\(297\) | 2.47217 | 0.143450 | ||||||||
\(298\) | −23.6431 | −1.36961 | ||||||||
\(299\) | −4.48018 | −0.259096 | ||||||||
\(300\) | 6.74596 | 0.389478 | ||||||||
\(301\) | −4.53970 | −0.261664 | ||||||||
\(302\) | −12.8268 | −0.738100 | ||||||||
\(303\) | 1.97292 | 0.113341 | ||||||||
\(304\) | 21.3095 | 1.22219 | ||||||||
\(305\) | −19.7597 | −1.13144 | ||||||||
\(306\) | 5.16535 | 0.295283 | ||||||||
\(307\) | −30.0178 | −1.71321 | −0.856603 | − | 0.515976i | \(-0.827429\pi\) | ||||
−0.856603 | + | 0.515976i | \(0.827429\pi\) | |||||||
\(308\) | −17.1183 | −0.975409 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 37.7587 | 2.14455 | ||||||||
\(311\) | 17.9357 | 1.01704 | 0.508521 | − | 0.861050i | \(-0.330192\pi\) | ||||
0.508521 | + | 0.861050i | \(0.330192\pi\) | |||||||
\(312\) | −5.00803 | −0.283524 | ||||||||
\(313\) | 5.61280 | 0.317254 | 0.158627 | − | 0.987339i | \(-0.449293\pi\) | ||||
0.158627 | + | 0.987339i | \(0.449293\pi\) | |||||||
\(314\) | 5.19009 | 0.292894 | ||||||||
\(315\) | 3.12891 | 0.176294 | ||||||||
\(316\) | 41.9581 | 2.36033 | ||||||||
\(317\) | 21.9236 | 1.23135 | 0.615677 | − | 0.787999i | \(-0.288883\pi\) | ||||
0.615677 | + | 0.787999i | \(0.288883\pi\) | |||||||
\(318\) | 4.01653 | 0.225236 | ||||||||
\(319\) | −5.97338 | −0.334445 | ||||||||
\(320\) | −13.7426 | −0.768234 | ||||||||
\(321\) | −15.1982 | −0.848282 | ||||||||
\(322\) | −18.8779 | −1.05202 | ||||||||
\(323\) | 10.5901 | 0.589249 | ||||||||
\(324\) | 4.03807 | 0.224337 | ||||||||
\(325\) | −1.67059 | −0.0926678 | ||||||||
\(326\) | −55.9296 | −3.09766 | ||||||||
\(327\) | 18.2958 | 1.01176 | ||||||||
\(328\) | 55.6247 | 3.07136 | ||||||||
\(329\) | 10.3592 | 0.571124 | ||||||||
\(330\) | 11.0844 | 0.610175 | ||||||||
\(331\) | −2.09911 | −0.115377 | −0.0576887 | − | 0.998335i | \(-0.518373\pi\) | ||||
−0.0576887 | + | 0.998335i | \(0.518373\pi\) | |||||||
\(332\) | 20.5821 | 1.12959 | ||||||||
\(333\) | 5.69321 | 0.311986 | ||||||||
\(334\) | 14.7712 | 0.808246 | ||||||||
\(335\) | −13.6771 | −0.747261 | ||||||||
\(336\) | −7.25327 | −0.395698 | ||||||||
\(337\) | −0.810195 | −0.0441342 | −0.0220671 | − | 0.999756i | \(-0.507025\pi\) | ||||
−0.0220671 | + | 0.999756i | \(0.507025\pi\) | |||||||
\(338\) | 2.45725 | 0.133657 | ||||||||
\(339\) | 10.9011 | 0.592065 | ||||||||
\(340\) | 15.4884 | 0.839979 | ||||||||
\(341\) | −20.8192 | −1.12742 | ||||||||
\(342\) | 12.3794 | 0.669399 | ||||||||
\(343\) | −18.9647 | −1.02400 | ||||||||
\(344\) | −13.2582 | −0.714835 | ||||||||
\(345\) | 8.17484 | 0.440118 | ||||||||
\(346\) | 5.00986 | 0.269331 | ||||||||
\(347\) | −20.7820 | −1.11564 | −0.557818 | − | 0.829963i | \(-0.688361\pi\) | ||||
−0.557818 | + | 0.829963i | \(0.688361\pi\) | |||||||
\(348\) | −9.75695 | −0.523027 | ||||||||
\(349\) | 11.4654 | 0.613731 | 0.306865 | − | 0.951753i | \(-0.400720\pi\) | ||||
0.306865 | + | 0.951753i | \(0.400720\pi\) | |||||||
\(350\) | −7.03929 | −0.376266 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −0.933765 | −0.0497699 | ||||||||
\(353\) | 16.0880 | 0.856278 | 0.428139 | − | 0.903713i | \(-0.359169\pi\) | ||||
0.428139 | + | 0.903713i | \(0.359169\pi\) | |||||||
\(354\) | −5.88758 | −0.312922 | ||||||||
\(355\) | −2.34433 | −0.124424 | ||||||||
\(356\) | −21.2076 | −1.12400 | ||||||||
\(357\) | −3.60463 | −0.190777 | ||||||||
\(358\) | 62.6811 | 3.31280 | ||||||||
\(359\) | −9.74393 | −0.514265 | −0.257133 | − | 0.966376i | \(-0.582778\pi\) | ||||
−0.257133 | + | 0.966376i | \(0.582778\pi\) | |||||||
\(360\) | 9.13799 | 0.481614 | ||||||||
\(361\) | 6.38042 | 0.335811 | ||||||||
\(362\) | 25.1296 | 1.32078 | ||||||||
\(363\) | 4.88835 | 0.256572 | ||||||||
\(364\) | 6.92441 | 0.362938 | ||||||||
\(365\) | 8.72130 | 0.456494 | ||||||||
\(366\) | 26.6101 | 1.39093 | ||||||||
\(367\) | 4.49956 | 0.234875 | 0.117437 | − | 0.993080i | \(-0.462532\pi\) | ||||
0.117437 | + | 0.993080i | \(0.462532\pi\) | |||||||
\(368\) | −18.9505 | −0.987862 | ||||||||
\(369\) | 11.1071 | 0.578213 | ||||||||
\(370\) | 25.5264 | 1.32705 | ||||||||
\(371\) | −2.80292 | −0.145520 | ||||||||
\(372\) | −34.0062 | −1.76314 | ||||||||
\(373\) | 29.6861 | 1.53709 | 0.768543 | − | 0.639798i | \(-0.220982\pi\) | ||||
0.768543 | + | 0.639798i | \(0.220982\pi\) | |||||||
\(374\) | −12.7696 | −0.660303 | ||||||||
\(375\) | 12.1716 | 0.628539 | ||||||||
\(376\) | 30.2542 | 1.56024 | ||||||||
\(377\) | 2.41624 | 0.124443 | ||||||||
\(378\) | −4.21365 | −0.216727 | ||||||||
\(379\) | −24.5787 | −1.26252 | −0.631262 | − | 0.775569i | \(-0.717463\pi\) | ||||
−0.631262 | + | 0.775569i | \(0.717463\pi\) | |||||||
\(380\) | 37.1198 | 1.90421 | ||||||||
\(381\) | −18.0296 | −0.923684 | ||||||||
\(382\) | −20.5835 | −1.05314 | ||||||||
\(383\) | −18.1584 | −0.927849 | −0.463925 | − | 0.885875i | \(-0.653559\pi\) | ||||
−0.463925 | + | 0.885875i | \(0.653559\pi\) | |||||||
\(384\) | 19.2623 | 0.982977 | ||||||||
\(385\) | −7.73521 | −0.394223 | ||||||||
\(386\) | −38.5599 | −1.96265 | ||||||||
\(387\) | −2.64739 | −0.134574 | ||||||||
\(388\) | −55.2760 | −2.80621 | ||||||||
\(389\) | 0.0830578 | 0.00421120 | 0.00210560 | − | 0.999998i | \(-0.499330\pi\) | ||||
0.00210560 | + | 0.999998i | \(0.499330\pi\) | |||||||
\(390\) | −4.48366 | −0.227039 | ||||||||
\(391\) | −9.41774 | −0.476275 | ||||||||
\(392\) | −20.3302 | −1.02683 | ||||||||
\(393\) | −7.05989 | −0.356125 | ||||||||
\(394\) | −27.6948 | −1.39524 | ||||||||
\(395\) | 18.9594 | 0.953953 | ||||||||
\(396\) | −9.98280 | −0.501655 | ||||||||
\(397\) | 13.2343 | 0.664212 | 0.332106 | − | 0.943242i | \(-0.392241\pi\) | ||||
0.332106 | + | 0.943242i | \(0.392241\pi\) | |||||||
\(398\) | −1.91194 | −0.0958368 | ||||||||
\(399\) | −8.63891 | −0.432486 | ||||||||
\(400\) | −7.06635 | −0.353317 | ||||||||
\(401\) | −9.78535 | −0.488657 | −0.244329 | − | 0.969693i | \(-0.578568\pi\) | ||||
−0.244329 | + | 0.969693i | \(0.578568\pi\) | |||||||
\(402\) | 18.4187 | 0.918644 | ||||||||
\(403\) | 8.42140 | 0.419500 | ||||||||
\(404\) | −7.96679 | −0.396363 | ||||||||
\(405\) | 1.82467 | 0.0906684 | ||||||||
\(406\) | 10.1812 | 0.505284 | ||||||||
\(407\) | −14.0746 | −0.697652 | ||||||||
\(408\) | −10.5273 | −0.521180 | ||||||||
\(409\) | 32.2133 | 1.59284 | 0.796422 | − | 0.604742i | \(-0.206724\pi\) | ||||
0.796422 | + | 0.604742i | \(0.206724\pi\) | |||||||
\(410\) | 49.8004 | 2.45947 | ||||||||
\(411\) | −18.8311 | −0.928869 | ||||||||
\(412\) | −4.03807 | −0.198941 | ||||||||
\(413\) | 4.10863 | 0.202173 | ||||||||
\(414\) | −11.0089 | −0.541059 | ||||||||
\(415\) | 9.30037 | 0.456537 | ||||||||
\(416\) | 0.377710 | 0.0185188 | ||||||||
\(417\) | 15.2404 | 0.746328 | ||||||||
\(418\) | −30.6039 | −1.49689 | ||||||||
\(419\) | −20.8448 | −1.01833 | −0.509167 | − | 0.860668i | \(-0.670046\pi\) | ||||
−0.509167 | + | 0.860668i | \(0.670046\pi\) | |||||||
\(420\) | −12.6347 | −0.616512 | ||||||||
\(421\) | −26.9078 | −1.31141 | −0.655704 | − | 0.755018i | \(-0.727628\pi\) | ||||
−0.655704 | + | 0.755018i | \(0.727628\pi\) | |||||||
\(422\) | 67.5158 | 3.28662 | ||||||||
\(423\) | 6.04114 | 0.293730 | ||||||||
\(424\) | −8.18595 | −0.397545 | ||||||||
\(425\) | −3.51173 | −0.170344 | ||||||||
\(426\) | 3.15707 | 0.152961 | ||||||||
\(427\) | −18.5698 | −0.898654 | ||||||||
\(428\) | 61.3715 | 2.96650 | ||||||||
\(429\) | 2.47217 | 0.119358 | ||||||||
\(430\) | −11.8700 | −0.572422 | ||||||||
\(431\) | 25.2765 | 1.21753 | 0.608763 | − | 0.793352i | \(-0.291666\pi\) | ||||
0.608763 | + | 0.793352i | \(0.291666\pi\) | |||||||
\(432\) | −4.22984 | −0.203508 | ||||||||
\(433\) | −33.2750 | −1.59909 | −0.799547 | − | 0.600604i | \(-0.794927\pi\) | ||||
−0.799547 | + | 0.600604i | \(0.794927\pi\) | |||||||
\(434\) | 35.4848 | 1.70333 | ||||||||
\(435\) | −4.40884 | −0.211388 | ||||||||
\(436\) | −73.8795 | −3.53819 | ||||||||
\(437\) | −22.5707 | −1.07970 | ||||||||
\(438\) | −11.7448 | −0.561190 | ||||||||
\(439\) | −27.8343 | −1.32846 | −0.664230 | − | 0.747528i | \(-0.731240\pi\) | ||||
−0.664230 | + | 0.747528i | \(0.731240\pi\) | |||||||
\(440\) | −22.5907 | −1.07697 | ||||||||
\(441\) | −4.05952 | −0.193310 | ||||||||
\(442\) | 5.16535 | 0.245691 | ||||||||
\(443\) | 13.4728 | 0.640114 | 0.320057 | − | 0.947398i | \(-0.396298\pi\) | ||||
0.320057 | + | 0.947398i | \(0.396298\pi\) | |||||||
\(444\) | −22.9895 | −1.09104 | ||||||||
\(445\) | −9.58299 | −0.454277 | ||||||||
\(446\) | 53.3276 | 2.52514 | ||||||||
\(447\) | 9.62177 | 0.455094 | ||||||||
\(448\) | −12.9150 | −0.610176 | ||||||||
\(449\) | −27.8246 | −1.31312 | −0.656561 | − | 0.754273i | \(-0.727990\pi\) | ||||
−0.656561 | + | 0.754273i | \(0.727990\pi\) | |||||||
\(450\) | −4.10506 | −0.193514 | ||||||||
\(451\) | −27.4587 | −1.29298 | ||||||||
\(452\) | −44.0192 | −2.07049 | ||||||||
\(453\) | 5.21999 | 0.245257 | ||||||||
\(454\) | −15.7589 | −0.739603 | ||||||||
\(455\) | 3.12891 | 0.146685 | ||||||||
\(456\) | −25.2300 | −1.18150 | ||||||||
\(457\) | 4.15766 | 0.194487 | 0.0972435 | − | 0.995261i | \(-0.468997\pi\) | ||||
0.0972435 | + | 0.995261i | \(0.468997\pi\) | |||||||
\(458\) | −46.5728 | −2.17620 | ||||||||
\(459\) | −2.10209 | −0.0981171 | ||||||||
\(460\) | −33.0105 | −1.53912 | ||||||||
\(461\) | −28.3340 | −1.31964 | −0.659822 | − | 0.751422i | \(-0.729368\pi\) | ||||
−0.659822 | + | 0.751422i | \(0.729368\pi\) | |||||||
\(462\) | 10.4169 | 0.484637 | ||||||||
\(463\) | −4.84265 | −0.225057 | −0.112529 | − | 0.993648i | \(-0.535895\pi\) | ||||
−0.112529 | + | 0.993648i | \(0.535895\pi\) | |||||||
\(464\) | 10.2203 | 0.474467 | ||||||||
\(465\) | −15.3662 | −0.712593 | ||||||||
\(466\) | −32.6870 | −1.51419 | ||||||||
\(467\) | 3.18012 | 0.147159 | 0.0735793 | − | 0.997289i | \(-0.476558\pi\) | ||||
0.0735793 | + | 0.997289i | \(0.476558\pi\) | |||||||
\(468\) | 4.03807 | 0.186660 | ||||||||
\(469\) | −12.8535 | −0.593518 | ||||||||
\(470\) | 27.0864 | 1.24940 | ||||||||
\(471\) | −2.11215 | −0.0973229 | ||||||||
\(472\) | 11.9993 | 0.552312 | ||||||||
\(473\) | 6.54481 | 0.300931 | ||||||||
\(474\) | −25.5324 | −1.17274 | ||||||||
\(475\) | −8.41628 | −0.386165 | ||||||||
\(476\) | 14.5557 | 0.667160 | ||||||||
\(477\) | −1.63456 | −0.0748415 | ||||||||
\(478\) | 8.30540 | 0.379880 | ||||||||
\(479\) | 15.9757 | 0.729948 | 0.364974 | − | 0.931018i | \(-0.381078\pi\) | ||||
0.364974 | + | 0.931018i | \(0.381078\pi\) | |||||||
\(480\) | −0.689195 | −0.0314573 | ||||||||
\(481\) | 5.69321 | 0.259588 | ||||||||
\(482\) | −14.8028 | −0.674250 | ||||||||
\(483\) | 7.68254 | 0.349568 | ||||||||
\(484\) | −19.7395 | −0.897250 | ||||||||
\(485\) | −24.9774 | −1.13416 | ||||||||
\(486\) | −2.45725 | −0.111463 | ||||||||
\(487\) | 6.70437 | 0.303804 | 0.151902 | − | 0.988396i | \(-0.451460\pi\) | ||||
0.151902 | + | 0.988396i | \(0.451460\pi\) | |||||||
\(488\) | −54.2331 | −2.45502 | ||||||||
\(489\) | 22.7611 | 1.02929 | ||||||||
\(490\) | −18.2015 | −0.822259 | ||||||||
\(491\) | 20.3061 | 0.916402 | 0.458201 | − | 0.888849i | \(-0.348494\pi\) | ||||
0.458201 | + | 0.888849i | \(0.348494\pi\) | |||||||
\(492\) | −44.8512 | −2.02205 | ||||||||
\(493\) | 5.07916 | 0.228754 | ||||||||
\(494\) | 12.3794 | 0.556974 | ||||||||
\(495\) | −4.51089 | −0.202750 | ||||||||
\(496\) | 35.6212 | 1.59944 | ||||||||
\(497\) | −2.20315 | −0.0988250 | ||||||||
\(498\) | −12.5247 | −0.561243 | ||||||||
\(499\) | 6.47947 | 0.290061 | 0.145030 | − | 0.989427i | \(-0.453672\pi\) | ||||
0.145030 | + | 0.989427i | \(0.453672\pi\) | |||||||
\(500\) | −49.1497 | −2.19804 | ||||||||
\(501\) | −6.01129 | −0.268565 | ||||||||
\(502\) | 16.0987 | 0.718521 | ||||||||
\(503\) | −23.7928 | −1.06087 | −0.530434 | − | 0.847726i | \(-0.677971\pi\) | ||||
−0.530434 | + | 0.847726i | \(0.677971\pi\) | |||||||
\(504\) | 8.58769 | 0.382526 | ||||||||
\(505\) | −3.59992 | −0.160195 | ||||||||
\(506\) | 27.2160 | 1.20990 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 72.8047 | 3.23019 | ||||||||
\(509\) | 28.2482 | 1.25208 | 0.626040 | − | 0.779791i | \(-0.284675\pi\) | ||||
0.626040 | + | 0.779791i | \(0.284675\pi\) | |||||||
\(510\) | −9.42504 | −0.417348 | ||||||||
\(511\) | 8.19610 | 0.362574 | ||||||||
\(512\) | −40.7687 | −1.80174 | ||||||||
\(513\) | −5.03790 | −0.222429 | ||||||||
\(514\) | 50.3818 | 2.22225 | ||||||||
\(515\) | −1.82467 | −0.0804044 | ||||||||
\(516\) | 10.6903 | 0.470616 | ||||||||
\(517\) | −14.9347 | −0.656829 | ||||||||
\(518\) | 23.9892 | 1.05402 | ||||||||
\(519\) | −2.03881 | −0.0894937 | ||||||||
\(520\) | 9.13799 | 0.400727 | ||||||||
\(521\) | −44.1567 | −1.93454 | −0.967271 | − | 0.253746i | \(-0.918337\pi\) | ||||
−0.967271 | + | 0.253746i | \(0.918337\pi\) | |||||||
\(522\) | 5.93731 | 0.259869 | ||||||||
\(523\) | 31.6452 | 1.38375 | 0.691875 | − | 0.722017i | \(-0.256785\pi\) | ||||
0.691875 | + | 0.722017i | \(0.256785\pi\) | |||||||
\(524\) | 28.5083 | 1.24539 | ||||||||
\(525\) | 2.86471 | 0.125026 | ||||||||
\(526\) | −43.4981 | −1.89661 | ||||||||
\(527\) | 17.7025 | 0.771134 | ||||||||
\(528\) | 10.4569 | 0.455079 | ||||||||
\(529\) | −2.92797 | −0.127303 | ||||||||
\(530\) | −7.32882 | −0.318344 | ||||||||
\(531\) | 2.39601 | 0.103978 | ||||||||
\(532\) | 34.8845 | 1.51243 | ||||||||
\(533\) | 11.1071 | 0.481102 | ||||||||
\(534\) | 12.9053 | 0.558465 | ||||||||
\(535\) | 27.7317 | 1.19895 | ||||||||
\(536\) | −37.5386 | −1.62142 | ||||||||
\(537\) | −25.5086 | −1.10078 | ||||||||
\(538\) | −60.2176 | −2.59617 | ||||||||
\(539\) | 10.0358 | 0.432274 | ||||||||
\(540\) | −7.36812 | −0.317074 | ||||||||
\(541\) | −42.7803 | −1.83927 | −0.919634 | − | 0.392775i | \(-0.871515\pi\) | ||||
−0.919634 | + | 0.392775i | \(0.871515\pi\) | |||||||
\(542\) | −66.2788 | −2.84692 | ||||||||
\(543\) | −10.2267 | −0.438871 | ||||||||
\(544\) | 0.793980 | 0.0340416 | ||||||||
\(545\) | −33.3837 | −1.43000 | ||||||||
\(546\) | −4.21365 | −0.180327 | ||||||||
\(547\) | 16.3747 | 0.700131 | 0.350066 | − | 0.936725i | \(-0.386159\pi\) | ||||
0.350066 | + | 0.936725i | \(0.386159\pi\) | |||||||
\(548\) | 76.0412 | 3.24832 | ||||||||
\(549\) | −10.8292 | −0.462180 | ||||||||
\(550\) | 10.1484 | 0.432730 | ||||||||
\(551\) | 12.1728 | 0.518578 | ||||||||
\(552\) | 22.4369 | 0.954978 | ||||||||
\(553\) | 17.8177 | 0.757685 | ||||||||
\(554\) | 59.0533 | 2.50893 | ||||||||
\(555\) | −10.3882 | −0.440955 | ||||||||
\(556\) | −61.5419 | −2.60996 | ||||||||
\(557\) | 33.3832 | 1.41449 | 0.707245 | − | 0.706969i | \(-0.249938\pi\) | ||||
0.707245 | + | 0.706969i | \(0.249938\pi\) | |||||||
\(558\) | 20.6935 | 0.876024 | ||||||||
\(559\) | −2.64739 | −0.111973 | ||||||||
\(560\) | 13.2348 | 0.559272 | ||||||||
\(561\) | 5.19673 | 0.219406 | ||||||||
\(562\) | 30.7844 | 1.29856 | ||||||||
\(563\) | 14.3656 | 0.605439 | 0.302719 | − | 0.953080i | \(-0.402105\pi\) | ||||
0.302719 | + | 0.953080i | \(0.402105\pi\) | |||||||
\(564\) | −24.3945 | −1.02719 | ||||||||
\(565\) | −19.8908 | −0.836813 | ||||||||
\(566\) | −74.6126 | −3.13620 | ||||||||
\(567\) | 1.71478 | 0.0720141 | ||||||||
\(568\) | −6.43432 | −0.269978 | ||||||||
\(569\) | 12.0211 | 0.503949 | 0.251975 | − | 0.967734i | \(-0.418920\pi\) | ||||
0.251975 | + | 0.967734i | \(0.418920\pi\) | |||||||
\(570\) | −22.5882 | −0.946116 | ||||||||
\(571\) | 18.0344 | 0.754718 | 0.377359 | − | 0.926067i | \(-0.376832\pi\) | ||||
0.377359 | + | 0.926067i | \(0.376832\pi\) | |||||||
\(572\) | −9.98280 | −0.417402 | ||||||||
\(573\) | 8.37666 | 0.349940 | ||||||||
\(574\) | 46.8014 | 1.95345 | ||||||||
\(575\) | 7.48456 | 0.312128 | ||||||||
\(576\) | −7.53156 | −0.313815 | ||||||||
\(577\) | 10.8638 | 0.452266 | 0.226133 | − | 0.974096i | \(-0.427392\pi\) | ||||
0.226133 | + | 0.974096i | \(0.427392\pi\) | |||||||
\(578\) | −30.9152 | −1.28590 | ||||||||
\(579\) | 15.6923 | 0.652151 | ||||||||
\(580\) | 17.8032 | 0.739237 | ||||||||
\(581\) | 8.74030 | 0.362609 | ||||||||
\(582\) | 33.6366 | 1.39428 | ||||||||
\(583\) | 4.04093 | 0.167358 | ||||||||
\(584\) | 23.9367 | 0.990509 | ||||||||
\(585\) | 1.82467 | 0.0754407 | ||||||||
\(586\) | −71.3060 | −2.94562 | ||||||||
\(587\) | 4.52036 | 0.186575 | 0.0932877 | − | 0.995639i | \(-0.470262\pi\) | ||||
0.0932877 | + | 0.995639i | \(0.470262\pi\) | |||||||
\(588\) | 16.3926 | 0.676019 | ||||||||
\(589\) | 42.4262 | 1.74814 | ||||||||
\(590\) | 10.7429 | 0.442277 | ||||||||
\(591\) | 11.2707 | 0.463613 | ||||||||
\(592\) | 24.0814 | 0.989738 | ||||||||
\(593\) | −31.7623 | −1.30432 | −0.652160 | − | 0.758081i | \(-0.726137\pi\) | ||||
−0.652160 | + | 0.758081i | \(0.726137\pi\) | |||||||
\(594\) | 6.07475 | 0.249250 | ||||||||
\(595\) | 6.57724 | 0.269641 | ||||||||
\(596\) | −38.8534 | −1.59150 | ||||||||
\(597\) | 0.778082 | 0.0318448 | ||||||||
\(598\) | −11.0089 | −0.450188 | ||||||||
\(599\) | −22.3684 | −0.913948 | −0.456974 | − | 0.889480i | \(-0.651067\pi\) | ||||
−0.456974 | + | 0.889480i | \(0.651067\pi\) | |||||||
\(600\) | 8.36638 | 0.341556 | ||||||||
\(601\) | −12.7059 | −0.518284 | −0.259142 | − | 0.965839i | \(-0.583440\pi\) | ||||
−0.259142 | + | 0.965839i | \(0.583440\pi\) | |||||||
\(602\) | −11.1552 | −0.454651 | ||||||||
\(603\) | −7.49568 | −0.305248 | ||||||||
\(604\) | −21.0787 | −0.857679 | ||||||||
\(605\) | −8.91961 | −0.362634 | ||||||||
\(606\) | 4.84796 | 0.196935 | ||||||||
\(607\) | 13.8752 | 0.563176 | 0.281588 | − | 0.959535i | \(-0.409139\pi\) | ||||
0.281588 | + | 0.959535i | \(0.409139\pi\) | |||||||
\(608\) | 1.90287 | 0.0771714 | ||||||||
\(609\) | −4.14333 | −0.167896 | ||||||||
\(610\) | −48.5545 | −1.96591 | ||||||||
\(611\) | 6.04114 | 0.244398 | ||||||||
\(612\) | 8.48837 | 0.343122 | ||||||||
\(613\) | 20.2055 | 0.816094 | 0.408047 | − | 0.912961i | \(-0.366210\pi\) | ||||
0.408047 | + | 0.912961i | \(0.366210\pi\) | |||||||
\(614\) | −73.7612 | −2.97676 | ||||||||
\(615\) | −20.2668 | −0.817235 | ||||||||
\(616\) | −21.2303 | −0.855392 | ||||||||
\(617\) | −25.7238 | −1.03560 | −0.517802 | − | 0.855501i | \(-0.673249\pi\) | ||||
−0.517802 | + | 0.855501i | \(0.673249\pi\) | |||||||
\(618\) | 2.45725 | 0.0988450 | ||||||||
\(619\) | −19.3588 | −0.778094 | −0.389047 | − | 0.921218i | \(-0.627196\pi\) | ||||
−0.389047 | + | 0.921218i | \(0.627196\pi\) | |||||||
\(620\) | 62.0499 | 2.49198 | ||||||||
\(621\) | 4.48018 | 0.179784 | ||||||||
\(622\) | 44.0725 | 1.76715 | ||||||||
\(623\) | −9.00590 | −0.360814 | ||||||||
\(624\) | −4.22984 | −0.169329 | ||||||||
\(625\) | −13.8562 | −0.554246 | ||||||||
\(626\) | 13.7920 | 0.551241 | ||||||||
\(627\) | 12.4546 | 0.497387 | ||||||||
\(628\) | 8.52902 | 0.340345 | ||||||||
\(629\) | 11.9676 | 0.477180 | ||||||||
\(630\) | 7.68850 | 0.306317 | ||||||||
\(631\) | −30.4519 | −1.21227 | −0.606136 | − | 0.795361i | \(-0.707281\pi\) | ||||
−0.606136 | + | 0.795361i | \(0.707281\pi\) | |||||||
\(632\) | 52.0366 | 2.06991 | ||||||||
\(633\) | −27.4762 | −1.09208 | ||||||||
\(634\) | 53.8718 | 2.13952 | ||||||||
\(635\) | 32.8980 | 1.30552 | ||||||||
\(636\) | 6.60047 | 0.261726 | ||||||||
\(637\) | −4.05952 | −0.160844 | ||||||||
\(638\) | −14.6781 | −0.581110 | ||||||||
\(639\) | −1.28480 | −0.0508259 | ||||||||
\(640\) | −35.1473 | −1.38932 | ||||||||
\(641\) | 8.91397 | 0.352081 | 0.176040 | − | 0.984383i | \(-0.443671\pi\) | ||||
0.176040 | + | 0.984383i | \(0.443671\pi\) | |||||||
\(642\) | −37.3458 | −1.47392 | ||||||||
\(643\) | 11.9688 | 0.472005 | 0.236002 | − | 0.971752i | \(-0.424163\pi\) | ||||
0.236002 | + | 0.971752i | \(0.424163\pi\) | |||||||
\(644\) | −31.0226 | −1.22246 | ||||||||
\(645\) | 4.83060 | 0.190205 | ||||||||
\(646\) | 26.0225 | 1.02384 | ||||||||
\(647\) | −4.78523 | −0.188127 | −0.0940634 | − | 0.995566i | \(-0.529986\pi\) | ||||
−0.0940634 | + | 0.995566i | \(0.529986\pi\) | |||||||
\(648\) | 5.00803 | 0.196734 | ||||||||
\(649\) | −5.92335 | −0.232512 | ||||||||
\(650\) | −4.10506 | −0.161014 | ||||||||
\(651\) | −14.4409 | −0.565983 | ||||||||
\(652\) | −91.9108 | −3.59950 | ||||||||
\(653\) | −24.9769 | −0.977422 | −0.488711 | − | 0.872446i | \(-0.662533\pi\) | ||||
−0.488711 | + | 0.872446i | \(0.662533\pi\) | |||||||
\(654\) | 44.9572 | 1.75797 | ||||||||
\(655\) | 12.8820 | 0.503339 | ||||||||
\(656\) | 46.9813 | 1.83431 | ||||||||
\(657\) | 4.77967 | 0.186473 | ||||||||
\(658\) | 25.4552 | 0.992348 | ||||||||
\(659\) | 10.8201 | 0.421490 | 0.210745 | − | 0.977541i | \(-0.432411\pi\) | ||||
0.210745 | + | 0.977541i | \(0.432411\pi\) | |||||||
\(660\) | 18.2153 | 0.709029 | ||||||||
\(661\) | −7.22917 | −0.281182 | −0.140591 | − | 0.990068i | \(-0.544900\pi\) | ||||
−0.140591 | + | 0.990068i | \(0.544900\pi\) | |||||||
\(662\) | −5.15802 | −0.200472 | ||||||||
\(663\) | −2.10209 | −0.0816383 | ||||||||
\(664\) | 25.5261 | 0.990604 | ||||||||
\(665\) | 15.7631 | 0.611268 | ||||||||
\(666\) | 13.9896 | 0.542087 | ||||||||
\(667\) | −10.8252 | −0.419154 | ||||||||
\(668\) | 24.2740 | 0.939189 | ||||||||
\(669\) | −21.7022 | −0.839055 | ||||||||
\(670\) | −33.6081 | −1.29839 | ||||||||
\(671\) | 26.7717 | 1.03351 | ||||||||
\(672\) | −0.647691 | −0.0249852 | ||||||||
\(673\) | 26.7146 | 1.02977 | 0.514886 | − | 0.857259i | \(-0.327834\pi\) | ||||
0.514886 | + | 0.857259i | \(0.327834\pi\) | |||||||
\(674\) | −1.99085 | −0.0766847 | ||||||||
\(675\) | 1.67059 | 0.0643012 | ||||||||
\(676\) | 4.03807 | 0.155310 | ||||||||
\(677\) | 17.6487 | 0.678294 | 0.339147 | − | 0.940733i | \(-0.389862\pi\) | ||||
0.339147 | + | 0.940733i | \(0.389862\pi\) | |||||||
\(678\) | 26.7866 | 1.02873 | ||||||||
\(679\) | −23.4732 | −0.900819 | ||||||||
\(680\) | 19.2089 | 0.736626 | ||||||||
\(681\) | 6.41324 | 0.245756 | ||||||||
\(682\) | −51.1579 | −1.95894 | ||||||||
\(683\) | −22.1422 | −0.847247 | −0.423623 | − | 0.905838i | \(-0.639242\pi\) | ||||
−0.423623 | + | 0.905838i | \(0.639242\pi\) | |||||||
\(684\) | 20.3434 | 0.777848 | ||||||||
\(685\) | 34.3605 | 1.31285 | ||||||||
\(686\) | −46.6009 | −1.77923 | ||||||||
\(687\) | 18.9532 | 0.723111 | ||||||||
\(688\) | −11.1981 | −0.426922 | ||||||||
\(689\) | −1.63456 | −0.0622719 | ||||||||
\(690\) | 20.0876 | 0.764722 | ||||||||
\(691\) | 26.0769 | 0.992011 | 0.496006 | − | 0.868319i | \(-0.334800\pi\) | ||||
0.496006 | + | 0.868319i | \(0.334800\pi\) | |||||||
\(692\) | 8.23284 | 0.312966 | ||||||||
\(693\) | −4.23924 | −0.161036 | ||||||||
\(694\) | −51.0665 | −1.93846 | ||||||||
\(695\) | −27.8087 | −1.05484 | ||||||||
\(696\) | −12.1006 | −0.458673 | ||||||||
\(697\) | 23.3481 | 0.884373 | ||||||||
\(698\) | 28.1734 | 1.06638 | ||||||||
\(699\) | 13.3023 | 0.503138 | ||||||||
\(700\) | −11.5679 | −0.437224 | ||||||||
\(701\) | −13.9609 | −0.527297 | −0.263648 | − | 0.964619i | \(-0.584926\pi\) | ||||
−0.263648 | + | 0.964619i | \(0.584926\pi\) | |||||||
\(702\) | −2.45725 | −0.0927428 | ||||||||
\(703\) | 28.6818 | 1.08175 | ||||||||
\(704\) | 18.6193 | 0.701743 | ||||||||
\(705\) | −11.0231 | −0.415152 | ||||||||
\(706\) | 39.5322 | 1.48781 | ||||||||
\(707\) | −3.38313 | −0.127236 | ||||||||
\(708\) | −9.67524 | −0.363618 | ||||||||
\(709\) | −16.0197 | −0.601632 | −0.300816 | − | 0.953682i | \(-0.597259\pi\) | ||||
−0.300816 | + | 0.953682i | \(0.597259\pi\) | |||||||
\(710\) | −5.76060 | −0.216192 | ||||||||
\(711\) | 10.3906 | 0.389679 | ||||||||
\(712\) | −26.3018 | −0.985700 | ||||||||
\(713\) | −37.7294 | −1.41298 | ||||||||
\(714\) | −8.85746 | −0.331482 | ||||||||
\(715\) | −4.51089 | −0.168698 | ||||||||
\(716\) | 103.006 | 3.84950 | ||||||||
\(717\) | −3.37996 | −0.126227 | ||||||||
\(718\) | −23.9433 | −0.893555 | ||||||||
\(719\) | −8.82899 | −0.329266 | −0.164633 | − | 0.986355i | \(-0.552644\pi\) | ||||
−0.164633 | + | 0.986355i | \(0.552644\pi\) | |||||||
\(720\) | 7.71805 | 0.287635 | ||||||||
\(721\) | −1.71478 | −0.0638619 | ||||||||
\(722\) | 15.6783 | 0.583484 | ||||||||
\(723\) | 6.02414 | 0.224040 | ||||||||
\(724\) | 41.2962 | 1.53476 | ||||||||
\(725\) | −4.03656 | −0.149914 | ||||||||
\(726\) | 12.0119 | 0.445803 | ||||||||
\(727\) | 19.1342 | 0.709649 | 0.354825 | − | 0.934933i | \(-0.384541\pi\) | ||||
0.354825 | + | 0.934933i | \(0.384541\pi\) | |||||||
\(728\) | 8.58769 | 0.318281 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.4304 | 0.793174 | ||||||||
\(731\) | −5.56505 | −0.205831 | ||||||||
\(732\) | 43.7291 | 1.61627 | ||||||||
\(733\) | −11.8488 | −0.437644 | −0.218822 | − | 0.975765i | \(-0.570221\pi\) | ||||
−0.218822 | + | 0.975765i | \(0.570221\pi\) | |||||||
\(734\) | 11.0565 | 0.408104 | ||||||||
\(735\) | 7.40726 | 0.273221 | ||||||||
\(736\) | −1.69221 | −0.0623757 | ||||||||
\(737\) | 18.5306 | 0.682585 | ||||||||
\(738\) | 27.2929 | 1.00467 | ||||||||
\(739\) | 35.6420 | 1.31111 | 0.655555 | − | 0.755147i | \(-0.272435\pi\) | ||||
0.655555 | + | 0.755147i | \(0.272435\pi\) | |||||||
\(740\) | 41.9482 | 1.54205 | ||||||||
\(741\) | −5.03790 | −0.185072 | ||||||||
\(742\) | −6.88748 | −0.252847 | ||||||||
\(743\) | 32.2067 | 1.18155 | 0.590774 | − | 0.806837i | \(-0.298823\pi\) | ||||
0.590774 | + | 0.806837i | \(0.298823\pi\) | |||||||
\(744\) | −42.1747 | −1.54620 | ||||||||
\(745\) | −17.5565 | −0.643221 | ||||||||
\(746\) | 72.9460 | 2.67074 | ||||||||
\(747\) | 5.09703 | 0.186490 | ||||||||
\(748\) | −20.9847 | −0.767278 | ||||||||
\(749\) | 26.0617 | 0.952273 | ||||||||
\(750\) | 29.9087 | 1.09211 | ||||||||
\(751\) | 24.8419 | 0.906494 | 0.453247 | − | 0.891385i | \(-0.350266\pi\) | ||||
0.453247 | + | 0.891385i | \(0.350266\pi\) | |||||||
\(752\) | 25.5531 | 0.931825 | ||||||||
\(753\) | −6.55153 | −0.238751 | ||||||||
\(754\) | 5.93731 | 0.216224 | ||||||||
\(755\) | −9.52474 | −0.346641 | ||||||||
\(756\) | −6.92441 | −0.251838 | ||||||||
\(757\) | −15.3497 | −0.557893 | −0.278946 | − | 0.960307i | \(-0.589985\pi\) | ||||
−0.278946 | + | 0.960307i | \(0.589985\pi\) | |||||||
\(758\) | −60.3960 | −2.19368 | ||||||||
\(759\) | −11.0758 | −0.402026 | ||||||||
\(760\) | 46.0363 | 1.66991 | ||||||||
\(761\) | 6.52172 | 0.236412 | 0.118206 | − | 0.992989i | \(-0.462286\pi\) | ||||
0.118206 | + | 0.992989i | \(0.462286\pi\) | |||||||
\(762\) | −44.3032 | −1.60493 | ||||||||
\(763\) | −31.3733 | −1.13579 | ||||||||
\(764\) | −33.8255 | −1.22376 | ||||||||
\(765\) | 3.83561 | 0.138677 | ||||||||
\(766\) | −44.6196 | −1.61217 | ||||||||
\(767\) | 2.39601 | 0.0865148 | ||||||||
\(768\) | 32.2692 | 1.16441 | ||||||||
\(769\) | −21.7203 | −0.783252 | −0.391626 | − | 0.920124i | \(-0.628087\pi\) | ||||
−0.391626 | + | 0.920124i | \(0.628087\pi\) | |||||||
\(770\) | −19.0073 | −0.684976 | ||||||||
\(771\) | −20.5033 | −0.738410 | ||||||||
\(772\) | −63.3667 | −2.28062 | ||||||||
\(773\) | −4.58871 | −0.165045 | −0.0825223 | − | 0.996589i | \(-0.526298\pi\) | ||||
−0.0825223 | + | 0.996589i | \(0.526298\pi\) | |||||||
\(774\) | −6.50529 | −0.233828 | ||||||||
\(775\) | −14.0687 | −0.505364 | ||||||||
\(776\) | −68.5536 | −2.46093 | ||||||||
\(777\) | −9.76262 | −0.350232 | ||||||||
\(778\) | 0.204094 | 0.00731711 | ||||||||
\(779\) | 55.9565 | 2.00485 | ||||||||
\(780\) | −7.36812 | −0.263821 | ||||||||
\(781\) | 3.17625 | 0.113655 | ||||||||
\(782\) | −23.1417 | −0.827546 | ||||||||
\(783\) | −2.41624 | −0.0863495 | ||||||||
\(784\) | −17.1711 | −0.613254 | ||||||||
\(785\) | 3.85398 | 0.137554 | ||||||||
\(786\) | −17.3479 | −0.618779 | ||||||||
\(787\) | 10.4885 | 0.373873 | 0.186937 | − | 0.982372i | \(-0.440144\pi\) | ||||
0.186937 | + | 0.982372i | \(0.440144\pi\) | |||||||
\(788\) | −45.5117 | −1.62129 | ||||||||
\(789\) | 17.7020 | 0.630207 | ||||||||
\(790\) | 46.5880 | 1.65753 | ||||||||
\(791\) | −18.6930 | −0.664646 | ||||||||
\(792\) | −12.3807 | −0.439930 | ||||||||
\(793\) | −10.8292 | −0.384557 | ||||||||
\(794\) | 32.5200 | 1.15409 | ||||||||
\(795\) | 2.98253 | 0.105780 | ||||||||
\(796\) | −3.14194 | −0.111363 | ||||||||
\(797\) | −19.4563 | −0.689178 | −0.344589 | − | 0.938754i | \(-0.611982\pi\) | ||||
−0.344589 | + | 0.938754i | \(0.611982\pi\) | |||||||
\(798\) | −21.2279 | −0.751461 | ||||||||
\(799\) | 12.6990 | 0.449258 | ||||||||
\(800\) | −0.631000 | −0.0223092 | ||||||||
\(801\) | −5.25191 | −0.185567 | ||||||||
\(802\) | −24.0450 | −0.849059 | ||||||||
\(803\) | −11.8162 | −0.416984 | ||||||||
\(804\) | 30.2681 | 1.06747 | ||||||||
\(805\) | −14.0181 | −0.494072 | ||||||||
\(806\) | 20.6935 | 0.728896 | ||||||||
\(807\) | 24.5061 | 0.862657 | ||||||||
\(808\) | −9.88046 | −0.347593 | ||||||||
\(809\) | −33.2176 | −1.16787 | −0.583935 | − | 0.811800i | \(-0.698488\pi\) | ||||
−0.583935 | + | 0.811800i | \(0.698488\pi\) | |||||||
\(810\) | 4.48366 | 0.157540 | ||||||||
\(811\) | 20.0974 | 0.705715 | 0.352857 | − | 0.935677i | \(-0.385210\pi\) | ||||
0.352857 | + | 0.935677i | \(0.385210\pi\) | |||||||
\(812\) | 16.7311 | 0.587145 | ||||||||
\(813\) | 26.9728 | 0.945977 | ||||||||
\(814\) | −34.5848 | −1.21220 | ||||||||
\(815\) | −41.5314 | −1.45478 | ||||||||
\(816\) | −8.89151 | −0.311265 | ||||||||
\(817\) | −13.3373 | −0.466613 | ||||||||
\(818\) | 79.1560 | 2.76762 | ||||||||
\(819\) | 1.71478 | 0.0599194 | ||||||||
\(820\) | 81.8385 | 2.85792 | ||||||||
\(821\) | −9.75001 | −0.340278 | −0.170139 | − | 0.985420i | \(-0.554422\pi\) | ||||
−0.170139 | + | 0.985420i | \(0.554422\pi\) | |||||||
\(822\) | −46.2727 | −1.61394 | ||||||||
\(823\) | −33.2226 | −1.15807 | −0.579033 | − | 0.815304i | \(-0.696570\pi\) | ||||
−0.579033 | + | 0.815304i | \(0.696570\pi\) | |||||||
\(824\) | −5.00803 | −0.174463 | ||||||||
\(825\) | −4.13000 | −0.143788 | ||||||||
\(826\) | 10.0959 | 0.351282 | ||||||||
\(827\) | −37.6560 | −1.30943 | −0.654714 | − | 0.755877i | \(-0.727211\pi\) | ||||
−0.654714 | + | 0.755877i | \(0.727211\pi\) | |||||||
\(828\) | −18.0913 | −0.628715 | ||||||||
\(829\) | 28.5745 | 0.992433 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(830\) | 22.8533 | 0.793250 | ||||||||
\(831\) | −24.0323 | −0.833670 | ||||||||
\(832\) | −7.53156 | −0.261110 | ||||||||
\(833\) | −8.53346 | −0.295667 | ||||||||
\(834\) | 37.4495 | 1.29677 | ||||||||
\(835\) | 10.9686 | 0.379584 | ||||||||
\(836\) | −50.2923 | −1.73940 | ||||||||
\(837\) | −8.42140 | −0.291086 | ||||||||
\(838\) | −51.2207 | −1.76939 | ||||||||
\(839\) | 35.7276 | 1.23346 | 0.616728 | − | 0.787177i | \(-0.288458\pi\) | ||||
0.616728 | + | 0.787177i | \(0.288458\pi\) | |||||||
\(840\) | −15.6697 | −0.540655 | ||||||||
\(841\) | −23.1618 | −0.798682 | ||||||||
\(842\) | −66.1192 | −2.27862 | ||||||||
\(843\) | −12.5280 | −0.431488 | ||||||||
\(844\) | 110.951 | 3.81908 | ||||||||
\(845\) | 1.82467 | 0.0627704 | ||||||||
\(846\) | 14.8446 | 0.510367 | ||||||||
\(847\) | −8.38247 | −0.288025 | ||||||||
\(848\) | −6.91395 | −0.237426 | ||||||||
\(849\) | 30.3643 | 1.04210 | ||||||||
\(850\) | −8.62920 | −0.295979 | ||||||||
\(851\) | −25.5066 | −0.874355 | ||||||||
\(852\) | 5.18811 | 0.177742 | ||||||||
\(853\) | −44.9199 | −1.53803 | −0.769015 | − | 0.639231i | \(-0.779253\pi\) | ||||
−0.769015 | + | 0.639231i | \(0.779253\pi\) | |||||||
\(854\) | −45.6305 | −1.56144 | ||||||||
\(855\) | 9.19248 | 0.314376 | ||||||||
\(856\) | 76.1132 | 2.60150 | ||||||||
\(857\) | 41.0855 | 1.40345 | 0.701726 | − | 0.712447i | \(-0.252413\pi\) | ||||
0.701726 | + | 0.712447i | \(0.252413\pi\) | |||||||
\(858\) | 6.07475 | 0.207388 | ||||||||
\(859\) | −50.4833 | −1.72247 | −0.861234 | − | 0.508209i | \(-0.830308\pi\) | ||||
−0.861234 | + | 0.508209i | \(0.830308\pi\) | |||||||
\(860\) | −19.5063 | −0.665159 | ||||||||
\(861\) | −19.0463 | −0.649096 | ||||||||
\(862\) | 62.1106 | 2.11550 | ||||||||
\(863\) | −36.8528 | −1.25448 | −0.627241 | − | 0.778825i | \(-0.715816\pi\) | ||||
−0.627241 | + | 0.778825i | \(0.715816\pi\) | |||||||
\(864\) | −0.377710 | −0.0128500 | ||||||||
\(865\) | 3.72014 | 0.126489 | ||||||||
\(866\) | −81.7649 | −2.77848 | ||||||||
\(867\) | 12.5812 | 0.427281 | ||||||||
\(868\) | 58.3132 | 1.97928 | ||||||||
\(869\) | −25.6875 | −0.871387 | ||||||||
\(870\) | −10.8336 | −0.367294 | ||||||||
\(871\) | −7.49568 | −0.253982 | ||||||||
\(872\) | −91.6258 | −3.10284 | ||||||||
\(873\) | −13.6887 | −0.463293 | ||||||||
\(874\) | −55.4618 | −1.87602 | ||||||||
\(875\) | −20.8717 | −0.705591 | ||||||||
\(876\) | −19.3006 | −0.652107 | ||||||||
\(877\) | 7.42795 | 0.250824 | 0.125412 | − | 0.992105i | \(-0.459975\pi\) | ||||
0.125412 | + | 0.992105i | \(0.459975\pi\) | |||||||
\(878\) | −68.3958 | −2.30825 | ||||||||
\(879\) | 29.0186 | 0.978775 | ||||||||
\(880\) | −19.0804 | −0.643199 | ||||||||
\(881\) | −23.2794 | −0.784302 | −0.392151 | − | 0.919901i | \(-0.628269\pi\) | ||||
−0.392151 | + | 0.919901i | \(0.628269\pi\) | |||||||
\(882\) | −9.97524 | −0.335884 | ||||||||
\(883\) | 3.87577 | 0.130430 | 0.0652149 | − | 0.997871i | \(-0.479227\pi\) | ||||
0.0652149 | + | 0.997871i | \(0.479227\pi\) | |||||||
\(884\) | 8.48837 | 0.285495 | ||||||||
\(885\) | −4.37191 | −0.146960 | ||||||||
\(886\) | 33.1061 | 1.11222 | ||||||||
\(887\) | 47.3370 | 1.58942 | 0.794711 | − | 0.606988i | \(-0.207623\pi\) | ||||
0.794711 | + | 0.606988i | \(0.207623\pi\) | |||||||
\(888\) | −28.5118 | −0.956792 | ||||||||
\(889\) | 30.9168 | 1.03692 | ||||||||
\(890\) | −23.5478 | −0.789323 | ||||||||
\(891\) | −2.47217 | −0.0828210 | ||||||||
\(892\) | 87.6349 | 2.93423 | ||||||||
\(893\) | 30.4346 | 1.01846 | ||||||||
\(894\) | 23.6431 | 0.790743 | ||||||||
\(895\) | 46.5448 | 1.55582 | ||||||||
\(896\) | −33.0307 | −1.10348 | ||||||||
\(897\) | 4.48018 | 0.149589 | ||||||||
\(898\) | −68.3719 | −2.28160 | ||||||||
\(899\) | 20.3482 | 0.678649 | ||||||||
\(900\) | −6.74596 | −0.224865 | ||||||||
\(901\) | −3.43600 | −0.114470 | ||||||||
\(902\) | −67.4728 | −2.24660 | ||||||||
\(903\) | 4.53970 | 0.151072 | ||||||||
\(904\) | −54.5929 | −1.81573 | ||||||||
\(905\) | 18.6604 | 0.620292 | ||||||||
\(906\) | 12.8268 | 0.426142 | ||||||||
\(907\) | −33.1774 | −1.10164 | −0.550818 | − | 0.834625i | \(-0.685684\pi\) | ||||
−0.550818 | + | 0.834625i | \(0.685684\pi\) | |||||||
\(908\) | −25.8971 | −0.859426 | ||||||||
\(909\) | −1.97292 | −0.0654377 | ||||||||
\(910\) | 7.68850 | 0.254871 | ||||||||
\(911\) | 38.9751 | 1.29130 | 0.645651 | − | 0.763633i | \(-0.276586\pi\) | ||||
0.645651 | + | 0.763633i | \(0.276586\pi\) | |||||||
\(912\) | −21.3095 | −0.705629 | ||||||||
\(913\) | −12.6007 | −0.417024 | ||||||||
\(914\) | 10.2164 | 0.337928 | ||||||||
\(915\) | 19.7597 | 0.653236 | ||||||||
\(916\) | −76.5344 | −2.52877 | ||||||||
\(917\) | 12.1062 | 0.399782 | ||||||||
\(918\) | −5.16535 | −0.170482 | ||||||||
\(919\) | −33.4095 | −1.10208 | −0.551038 | − | 0.834480i | \(-0.685768\pi\) | ||||
−0.551038 | + | 0.834480i | \(0.685768\pi\) | |||||||
\(920\) | −40.9399 | −1.34975 | ||||||||
\(921\) | 30.0178 | 0.989120 | ||||||||
\(922\) | −69.6236 | −2.29293 | ||||||||
\(923\) | −1.28480 | −0.0422897 | ||||||||
\(924\) | 17.1183 | 0.563152 | ||||||||
\(925\) | −9.51103 | −0.312721 | ||||||||
\(926\) | −11.8996 | −0.391045 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 0.912640 | 0.0299589 | ||||||||
\(929\) | 40.9112 | 1.34225 | 0.671126 | − | 0.741344i | \(-0.265811\pi\) | ||||
0.671126 | + | 0.741344i | \(0.265811\pi\) | |||||||
\(930\) | −37.7587 | −1.23816 | ||||||||
\(931\) | −20.4514 | −0.670269 | ||||||||
\(932\) | −53.7154 | −1.75951 | ||||||||
\(933\) | −17.9357 | −0.587189 | ||||||||
\(934\) | 7.81435 | 0.255693 | ||||||||
\(935\) | −9.48230 | −0.310104 | ||||||||
\(936\) | 5.00803 | 0.163693 | ||||||||
\(937\) | 32.3748 | 1.05764 | 0.528820 | − | 0.848734i | \(-0.322635\pi\) | ||||
0.528820 | + | 0.848734i | \(0.322635\pi\) | |||||||
\(938\) | −31.5842 | −1.03126 | ||||||||
\(939\) | −5.61280 | −0.183167 | ||||||||
\(940\) | 44.5118 | 1.45182 | ||||||||
\(941\) | 2.27246 | 0.0740801 | 0.0370401 | − | 0.999314i | \(-0.488207\pi\) | ||||
0.0370401 | + | 0.999314i | \(0.488207\pi\) | |||||||
\(942\) | −5.19009 | −0.169102 | ||||||||
\(943\) | −49.7619 | −1.62047 | ||||||||
\(944\) | 10.1347 | 0.329858 | ||||||||
\(945\) | −3.12891 | −0.101783 | ||||||||
\(946\) | 16.0822 | 0.522878 | ||||||||
\(947\) | 35.5665 | 1.15575 | 0.577877 | − | 0.816124i | \(-0.303881\pi\) | ||||
0.577877 | + | 0.816124i | \(0.303881\pi\) | |||||||
\(948\) | −41.9581 | −1.36273 | ||||||||
\(949\) | 4.77967 | 0.155155 | ||||||||
\(950\) | −20.6809 | −0.670976 | ||||||||
\(951\) | −21.9236 | −0.710922 | ||||||||
\(952\) | 18.0521 | 0.585071 | ||||||||
\(953\) | 58.0872 | 1.88163 | 0.940814 | − | 0.338924i | \(-0.110063\pi\) | ||||
0.940814 | + | 0.338924i | \(0.110063\pi\) | |||||||
\(954\) | −4.01653 | −0.130040 | ||||||||
\(955\) | −15.2846 | −0.494598 | ||||||||
\(956\) | 13.6485 | 0.441424 | ||||||||
\(957\) | 5.97338 | 0.193092 | ||||||||
\(958\) | 39.2562 | 1.26831 | ||||||||
\(959\) | 32.2912 | 1.04274 | ||||||||
\(960\) | 13.7426 | 0.443540 | ||||||||
\(961\) | 39.9200 | 1.28774 | ||||||||
\(962\) | 13.9896 | 0.451043 | ||||||||
\(963\) | 15.1982 | 0.489756 | ||||||||
\(964\) | −24.3259 | −0.783484 | ||||||||
\(965\) | −28.6333 | −0.921737 | ||||||||
\(966\) | 18.8779 | 0.607387 | ||||||||
\(967\) | −31.2378 | −1.00454 | −0.502269 | − | 0.864711i | \(-0.667501\pi\) | ||||
−0.502269 | + | 0.864711i | \(0.667501\pi\) | |||||||
\(968\) | −24.4810 | −0.786850 | ||||||||
\(969\) | −10.5901 | −0.340203 | ||||||||
\(970\) | −61.3756 | −1.97065 | ||||||||
\(971\) | −23.6040 | −0.757487 | −0.378743 | − | 0.925502i | \(-0.623644\pi\) | ||||
−0.378743 | + | 0.925502i | \(0.623644\pi\) | |||||||
\(972\) | −4.03807 | −0.129521 | ||||||||
\(973\) | −26.1341 | −0.837820 | ||||||||
\(974\) | 16.4743 | 0.527871 | ||||||||
\(975\) | 1.67059 | 0.0535018 | ||||||||
\(976\) | −45.8059 | −1.46621 | ||||||||
\(977\) | −21.7135 | −0.694678 | −0.347339 | − | 0.937740i | \(-0.612915\pi\) | ||||
−0.347339 | + | 0.937740i | \(0.612915\pi\) | |||||||
\(978\) | 55.9296 | 1.78843 | ||||||||
\(979\) | 12.9836 | 0.414959 | ||||||||
\(980\) | −29.9110 | −0.955472 | ||||||||
\(981\) | −18.2958 | −0.584139 | ||||||||
\(982\) | 49.8971 | 1.59228 | ||||||||
\(983\) | 48.1433 | 1.53553 | 0.767766 | − | 0.640730i | \(-0.221368\pi\) | ||||
0.767766 | + | 0.640730i | \(0.221368\pi\) | |||||||
\(984\) | −55.6247 | −1.77325 | ||||||||
\(985\) | −20.5652 | −0.655262 | ||||||||
\(986\) | 12.4807 | 0.397468 | ||||||||
\(987\) | −10.3592 | −0.329738 | ||||||||
\(988\) | 20.3434 | 0.647209 | ||||||||
\(989\) | 11.8608 | 0.377151 | ||||||||
\(990\) | −11.0844 | −0.352285 | ||||||||
\(991\) | 12.3184 | 0.391308 | 0.195654 | − | 0.980673i | \(-0.437317\pi\) | ||||
0.195654 | + | 0.980673i | \(0.437317\pi\) | |||||||
\(992\) | 3.18085 | 0.100992 | ||||||||
\(993\) | 2.09911 | 0.0666131 | ||||||||
\(994\) | −5.41370 | −0.171712 | ||||||||
\(995\) | −1.41974 | −0.0450088 | ||||||||
\(996\) | −20.5821 | −0.652170 | ||||||||
\(997\) | −9.40592 | −0.297889 | −0.148944 | − | 0.988846i | \(-0.547588\pi\) | ||||
−0.148944 | + | 0.988846i | \(0.547588\pi\) | |||||||
\(998\) | 15.9217 | 0.503991 | ||||||||
\(999\) | −5.69321 | −0.180125 |
(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 | 4017.2.a.j.1.22 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.22 | ✓ | 25 | 1.1 | even | 1 | trivial |