Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.48749 | −1.43616 | −0.718078 | − | 0.695963i | \(-0.754978\pi\) | ||||
−0.718078 | + | 0.695963i | \(0.754978\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.32783 | 0.593823 | 0.296911 | − | 0.954905i | \(-0.404043\pi\) | ||||
0.296911 | + | 0.954905i | \(0.404043\pi\) | |||||||
\(6\) | −2.48749 | −1.01552 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.18763 | 1.06254 | ||||||||
\(10\) | 1.32783 | 0.419896 | ||||||||
\(11\) | 1.36398 | 0.411257 | 0.205628 | − | 0.978630i | \(-0.434076\pi\) | ||||
0.205628 | + | 0.978630i | \(0.434076\pi\) | |||||||
\(12\) | −2.48749 | −0.718078 | ||||||||
\(13\) | 0.281781 | 0.0781519 | 0.0390759 | − | 0.999236i | \(-0.487559\pi\) | ||||
0.0390759 | + | 0.999236i | \(0.487559\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.30297 | −0.852822 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.670158 | −0.162537 | −0.0812685 | − | 0.996692i | \(-0.525897\pi\) | ||||
−0.0812685 | + | 0.996692i | \(0.525897\pi\) | |||||||
\(18\) | 3.18763 | 0.751332 | ||||||||
\(19\) | −2.87655 | −0.659927 | −0.329963 | − | 0.943994i | \(-0.607036\pi\) | ||||
−0.329963 | + | 0.943994i | \(0.607036\pi\) | |||||||
\(20\) | 1.32783 | 0.296911 | ||||||||
\(21\) | −2.48749 | −0.542816 | ||||||||
\(22\) | 1.36398 | 0.290802 | ||||||||
\(23\) | −1.59928 | −0.333474 | −0.166737 | − | 0.986001i | \(-0.553323\pi\) | ||||
−0.166737 | + | 0.986001i | \(0.553323\pi\) | |||||||
\(24\) | −2.48749 | −0.507758 | ||||||||
\(25\) | −3.23687 | −0.647374 | ||||||||
\(26\) | 0.281781 | 0.0552617 | ||||||||
\(27\) | −0.466731 | −0.0898224 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.25930 | −0.233846 | −0.116923 | − | 0.993141i | \(-0.537303\pi\) | ||||
−0.116923 | + | 0.993141i | \(0.537303\pi\) | |||||||
\(30\) | −3.30297 | −0.603036 | ||||||||
\(31\) | −1.39495 | −0.250541 | −0.125270 | − | 0.992123i | \(-0.539980\pi\) | ||||
−0.125270 | + | 0.992123i | \(0.539980\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.39290 | −0.590629 | ||||||||
\(34\) | −0.670158 | −0.114931 | ||||||||
\(35\) | 1.32783 | 0.224444 | ||||||||
\(36\) | 3.18763 | 0.531272 | ||||||||
\(37\) | −9.31561 | −1.53148 | −0.765739 | − | 0.643152i | \(-0.777626\pi\) | ||||
−0.765739 | + | 0.643152i | \(0.777626\pi\) | |||||||
\(38\) | −2.87655 | −0.466639 | ||||||||
\(39\) | −0.700928 | −0.112238 | ||||||||
\(40\) | 1.32783 | 0.209948 | ||||||||
\(41\) | −6.42674 | −1.00369 | −0.501844 | − | 0.864958i | \(-0.667345\pi\) | ||||
−0.501844 | + | 0.864958i | \(0.667345\pi\) | |||||||
\(42\) | −2.48749 | −0.383829 | ||||||||
\(43\) | −12.7746 | −1.94811 | −0.974055 | − | 0.226313i | \(-0.927333\pi\) | ||||
−0.974055 | + | 0.226313i | \(0.927333\pi\) | |||||||
\(44\) | 1.36398 | 0.205628 | ||||||||
\(45\) | 4.23263 | 0.630963 | ||||||||
\(46\) | −1.59928 | −0.235802 | ||||||||
\(47\) | 8.45192 | 1.23284 | 0.616420 | − | 0.787418i | \(-0.288583\pi\) | ||||
0.616420 | + | 0.787418i | \(0.288583\pi\) | |||||||
\(48\) | −2.48749 | −0.359039 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.23687 | −0.457763 | ||||||||
\(51\) | 1.66701 | 0.233429 | ||||||||
\(52\) | 0.281781 | 0.0390759 | ||||||||
\(53\) | −3.58042 | −0.491809 | −0.245905 | − | 0.969294i | \(-0.579085\pi\) | ||||
−0.245905 | + | 0.969294i | \(0.579085\pi\) | |||||||
\(54\) | −0.466731 | −0.0635140 | ||||||||
\(55\) | 1.81114 | 0.244214 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 7.15541 | 0.947757 | ||||||||
\(58\) | −1.25930 | −0.165354 | ||||||||
\(59\) | 1.26320 | 0.164455 | 0.0822274 | − | 0.996614i | \(-0.473797\pi\) | ||||
0.0822274 | + | 0.996614i | \(0.473797\pi\) | |||||||
\(60\) | −3.30297 | −0.426411 | ||||||||
\(61\) | −2.22784 | −0.285246 | −0.142623 | − | 0.989777i | \(-0.545554\pi\) | ||||
−0.142623 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(62\) | −1.39495 | −0.177159 | ||||||||
\(63\) | 3.18763 | 0.401604 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.374156 | 0.0464084 | ||||||||
\(66\) | −3.39290 | −0.417637 | ||||||||
\(67\) | −2.81723 | −0.344180 | −0.172090 | − | 0.985081i | \(-0.555052\pi\) | ||||
−0.172090 | + | 0.985081i | \(0.555052\pi\) | |||||||
\(68\) | −0.670158 | −0.0812685 | ||||||||
\(69\) | 3.97821 | 0.478921 | ||||||||
\(70\) | 1.32783 | 0.158706 | ||||||||
\(71\) | 11.6926 | 1.38766 | 0.693829 | − | 0.720139i | \(-0.255922\pi\) | ||||
0.693829 | + | 0.720139i | \(0.255922\pi\) | |||||||
\(72\) | 3.18763 | 0.375666 | ||||||||
\(73\) | 2.26070 | 0.264595 | 0.132298 | − | 0.991210i | \(-0.457765\pi\) | ||||
0.132298 | + | 0.991210i | \(0.457765\pi\) | |||||||
\(74\) | −9.31561 | −1.08292 | ||||||||
\(75\) | 8.05170 | 0.929730 | ||||||||
\(76\) | −2.87655 | −0.329963 | ||||||||
\(77\) | 1.36398 | 0.155440 | ||||||||
\(78\) | −0.700928 | −0.0793644 | ||||||||
\(79\) | −7.76845 | −0.874019 | −0.437010 | − | 0.899457i | \(-0.643962\pi\) | ||||
−0.437010 | + | 0.899457i | \(0.643962\pi\) | |||||||
\(80\) | 1.32783 | 0.148456 | ||||||||
\(81\) | −8.40190 | −0.933545 | ||||||||
\(82\) | −6.42674 | −0.709714 | ||||||||
\(83\) | −0.662846 | −0.0727568 | −0.0363784 | − | 0.999338i | \(-0.511582\pi\) | ||||
−0.0363784 | + | 0.999338i | \(0.511582\pi\) | |||||||
\(84\) | −2.48749 | −0.271408 | ||||||||
\(85\) | −0.889854 | −0.0965183 | ||||||||
\(86\) | −12.7746 | −1.37752 | ||||||||
\(87\) | 3.13250 | 0.335839 | ||||||||
\(88\) | 1.36398 | 0.145401 | ||||||||
\(89\) | −2.92269 | −0.309805 | −0.154902 | − | 0.987930i | \(-0.549506\pi\) | ||||
−0.154902 | + | 0.987930i | \(0.549506\pi\) | |||||||
\(90\) | 4.23263 | 0.446158 | ||||||||
\(91\) | 0.281781 | 0.0295386 | ||||||||
\(92\) | −1.59928 | −0.166737 | ||||||||
\(93\) | 3.46993 | 0.359815 | ||||||||
\(94\) | 8.45192 | 0.871749 | ||||||||
\(95\) | −3.81957 | −0.391880 | ||||||||
\(96\) | −2.48749 | −0.253879 | ||||||||
\(97\) | 14.5527 | 1.47761 | 0.738803 | − | 0.673921i | \(-0.235391\pi\) | ||||
0.738803 | + | 0.673921i | \(0.235391\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 4.34788 | 0.436978 | ||||||||
\(100\) | −3.23687 | −0.323687 | ||||||||
\(101\) | 14.1058 | 1.40358 | 0.701792 | − | 0.712382i | \(-0.252384\pi\) | ||||
0.701792 | + | 0.712382i | \(0.252384\pi\) | |||||||
\(102\) | 1.66701 | 0.165059 | ||||||||
\(103\) | 5.20884 | 0.513242 | 0.256621 | − | 0.966512i | \(-0.417391\pi\) | ||||
0.256621 | + | 0.966512i | \(0.417391\pi\) | |||||||
\(104\) | 0.281781 | 0.0276309 | ||||||||
\(105\) | −3.30297 | −0.322337 | ||||||||
\(106\) | −3.58042 | −0.347761 | ||||||||
\(107\) | −0.703567 | −0.0680164 | −0.0340082 | − | 0.999422i | \(-0.510827\pi\) | ||||
−0.0340082 | + | 0.999422i | \(0.510827\pi\) | |||||||
\(108\) | −0.466731 | −0.0449112 | ||||||||
\(109\) | −9.64219 | −0.923554 | −0.461777 | − | 0.886996i | \(-0.652788\pi\) | ||||
−0.461777 | + | 0.886996i | \(0.652788\pi\) | |||||||
\(110\) | 1.81114 | 0.172685 | ||||||||
\(111\) | 23.1725 | 2.19944 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −4.14750 | −0.390164 | −0.195082 | − | 0.980787i | \(-0.562497\pi\) | ||||
−0.195082 | + | 0.980787i | \(0.562497\pi\) | |||||||
\(114\) | 7.15541 | 0.670166 | ||||||||
\(115\) | −2.12358 | −0.198024 | ||||||||
\(116\) | −1.25930 | −0.116923 | ||||||||
\(117\) | 0.898213 | 0.0830398 | ||||||||
\(118\) | 1.26320 | 0.116287 | ||||||||
\(119\) | −0.670158 | −0.0614332 | ||||||||
\(120\) | −3.30297 | −0.301518 | ||||||||
\(121\) | −9.13955 | −0.830868 | ||||||||
\(122\) | −2.22784 | −0.201700 | ||||||||
\(123\) | 15.9865 | 1.44145 | ||||||||
\(124\) | −1.39495 | −0.125270 | ||||||||
\(125\) | −10.9372 | −0.978249 | ||||||||
\(126\) | 3.18763 | 0.283977 | ||||||||
\(127\) | −19.2644 | −1.70944 | −0.854721 | − | 0.519088i | \(-0.826272\pi\) | ||||
−0.854721 | + | 0.519088i | \(0.826272\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 31.7768 | 2.79779 | ||||||||
\(130\) | 0.374156 | 0.0328157 | ||||||||
\(131\) | −14.3216 | −1.25129 | −0.625644 | − | 0.780109i | \(-0.715164\pi\) | ||||
−0.625644 | + | 0.780109i | \(0.715164\pi\) | |||||||
\(132\) | −3.39290 | −0.295314 | ||||||||
\(133\) | −2.87655 | −0.249429 | ||||||||
\(134\) | −2.81723 | −0.243372 | ||||||||
\(135\) | −0.619739 | −0.0533386 | ||||||||
\(136\) | −0.670158 | −0.0574655 | ||||||||
\(137\) | 18.3309 | 1.56611 | 0.783057 | − | 0.621950i | \(-0.213659\pi\) | ||||
0.783057 | + | 0.621950i | \(0.213659\pi\) | |||||||
\(138\) | 3.97821 | 0.338648 | ||||||||
\(139\) | −9.54684 | −0.809752 | −0.404876 | − | 0.914372i | \(-0.632685\pi\) | ||||
−0.404876 | + | 0.914372i | \(0.632685\pi\) | |||||||
\(140\) | 1.32783 | 0.112222 | ||||||||
\(141\) | −21.0241 | −1.77055 | ||||||||
\(142\) | 11.6926 | 0.981223 | ||||||||
\(143\) | 0.384344 | 0.0321405 | ||||||||
\(144\) | 3.18763 | 0.265636 | ||||||||
\(145\) | −1.67213 | −0.138863 | ||||||||
\(146\) | 2.26070 | 0.187097 | ||||||||
\(147\) | −2.48749 | −0.205165 | ||||||||
\(148\) | −9.31561 | −0.765739 | ||||||||
\(149\) | −17.0618 | −1.39775 | −0.698877 | − | 0.715242i | \(-0.746316\pi\) | ||||
−0.698877 | + | 0.715242i | \(0.746316\pi\) | |||||||
\(150\) | 8.05170 | 0.657419 | ||||||||
\(151\) | −10.8435 | −0.882434 | −0.441217 | − | 0.897400i | \(-0.645453\pi\) | ||||
−0.441217 | + | 0.897400i | \(0.645453\pi\) | |||||||
\(152\) | −2.87655 | −0.233319 | ||||||||
\(153\) | −2.13621 | −0.172703 | ||||||||
\(154\) | 1.36398 | 0.109913 | ||||||||
\(155\) | −1.85226 | −0.148777 | ||||||||
\(156\) | −0.700928 | −0.0561191 | ||||||||
\(157\) | 12.8469 | 1.02530 | 0.512648 | − | 0.858599i | \(-0.328665\pi\) | ||||
0.512648 | + | 0.858599i | \(0.328665\pi\) | |||||||
\(158\) | −7.76845 | −0.618025 | ||||||||
\(159\) | 8.90629 | 0.706314 | ||||||||
\(160\) | 1.32783 | 0.104974 | ||||||||
\(161\) | −1.59928 | −0.126041 | ||||||||
\(162\) | −8.40190 | −0.660116 | ||||||||
\(163\) | 10.9064 | 0.854252 | 0.427126 | − | 0.904192i | \(-0.359526\pi\) | ||||
0.427126 | + | 0.904192i | \(0.359526\pi\) | |||||||
\(164\) | −6.42674 | −0.501844 | ||||||||
\(165\) | −4.50519 | −0.350729 | ||||||||
\(166\) | −0.662846 | −0.0514468 | ||||||||
\(167\) | −5.03627 | −0.389719 | −0.194859 | − | 0.980831i | \(-0.562425\pi\) | ||||
−0.194859 | + | 0.980831i | \(0.562425\pi\) | |||||||
\(168\) | −2.48749 | −0.191914 | ||||||||
\(169\) | −12.9206 | −0.993892 | ||||||||
\(170\) | −0.889854 | −0.0682487 | ||||||||
\(171\) | −9.16939 | −0.701201 | ||||||||
\(172\) | −12.7746 | −0.974055 | ||||||||
\(173\) | −17.8313 | −1.35569 | −0.677846 | − | 0.735204i | \(-0.737086\pi\) | ||||
−0.677846 | + | 0.735204i | \(0.737086\pi\) | |||||||
\(174\) | 3.13250 | 0.237474 | ||||||||
\(175\) | −3.23687 | −0.244684 | ||||||||
\(176\) | 1.36398 | 0.102814 | ||||||||
\(177\) | −3.14221 | −0.236183 | ||||||||
\(178\) | −2.92269 | −0.219065 | ||||||||
\(179\) | 19.2812 | 1.44115 | 0.720573 | − | 0.693379i | \(-0.243879\pi\) | ||||
0.720573 | + | 0.693379i | \(0.243879\pi\) | |||||||
\(180\) | 4.23263 | 0.315481 | ||||||||
\(181\) | −0.943125 | −0.0701019 | −0.0350510 | − | 0.999386i | \(-0.511159\pi\) | ||||
−0.0350510 | + | 0.999386i | \(0.511159\pi\) | |||||||
\(182\) | 0.281781 | 0.0208870 | ||||||||
\(183\) | 5.54175 | 0.409658 | ||||||||
\(184\) | −1.59928 | −0.117901 | ||||||||
\(185\) | −12.3695 | −0.909426 | ||||||||
\(186\) | 3.46993 | 0.254428 | ||||||||
\(187\) | −0.914084 | −0.0668444 | ||||||||
\(188\) | 8.45192 | 0.616420 | ||||||||
\(189\) | −0.466731 | −0.0339497 | ||||||||
\(190\) | −3.81957 | −0.277101 | ||||||||
\(191\) | 20.2936 | 1.46840 | 0.734198 | − | 0.678936i | \(-0.237558\pi\) | ||||
0.734198 | + | 0.678936i | \(0.237558\pi\) | |||||||
\(192\) | −2.48749 | −0.179519 | ||||||||
\(193\) | −18.4467 | −1.32782 | −0.663910 | − | 0.747813i | \(-0.731104\pi\) | ||||
−0.663910 | + | 0.747813i | \(0.731104\pi\) | |||||||
\(194\) | 14.5527 | 1.04483 | ||||||||
\(195\) | −0.930712 | −0.0666497 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 8.74474 | 0.623037 | 0.311519 | − | 0.950240i | \(-0.399162\pi\) | ||||
0.311519 | + | 0.950240i | \(0.399162\pi\) | |||||||
\(198\) | 4.34788 | 0.308990 | ||||||||
\(199\) | 25.9588 | 1.84017 | 0.920085 | − | 0.391719i | \(-0.128119\pi\) | ||||
0.920085 | + | 0.391719i | \(0.128119\pi\) | |||||||
\(200\) | −3.23687 | −0.228881 | ||||||||
\(201\) | 7.00785 | 0.494296 | ||||||||
\(202\) | 14.1058 | 0.992484 | ||||||||
\(203\) | −1.25930 | −0.0883855 | ||||||||
\(204\) | 1.66701 | 0.116714 | ||||||||
\(205\) | −8.53360 | −0.596013 | ||||||||
\(206\) | 5.20884 | 0.362917 | ||||||||
\(207\) | −5.09793 | −0.354331 | ||||||||
\(208\) | 0.281781 | 0.0195380 | ||||||||
\(209\) | −3.92357 | −0.271399 | ||||||||
\(210\) | −3.30297 | −0.227926 | ||||||||
\(211\) | 18.3688 | 1.26456 | 0.632280 | − | 0.774740i | \(-0.282119\pi\) | ||||
0.632280 | + | 0.774740i | \(0.282119\pi\) | |||||||
\(212\) | −3.58042 | −0.245905 | ||||||||
\(213\) | −29.0853 | −1.99289 | ||||||||
\(214\) | −0.703567 | −0.0480948 | ||||||||
\(215\) | −16.9625 | −1.15683 | ||||||||
\(216\) | −0.466731 | −0.0317570 | ||||||||
\(217\) | −1.39495 | −0.0946954 | ||||||||
\(218\) | −9.64219 | −0.653051 | ||||||||
\(219\) | −5.62349 | −0.380000 | ||||||||
\(220\) | 1.81114 | 0.122107 | ||||||||
\(221\) | −0.188837 | −0.0127026 | ||||||||
\(222\) | 23.1725 | 1.55524 | ||||||||
\(223\) | 2.02562 | 0.135645 | 0.0678227 | − | 0.997697i | \(-0.478395\pi\) | ||||
0.0678227 | + | 0.997697i | \(0.478395\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −10.3180 | −0.687863 | ||||||||
\(226\) | −4.14750 | −0.275888 | ||||||||
\(227\) | −4.94194 | −0.328008 | −0.164004 | − | 0.986460i | \(-0.552441\pi\) | ||||
−0.164004 | + | 0.986460i | \(0.552441\pi\) | |||||||
\(228\) | 7.15541 | 0.473879 | ||||||||
\(229\) | −21.2745 | −1.40586 | −0.702931 | − | 0.711258i | \(-0.748126\pi\) | ||||
−0.702931 | + | 0.711258i | \(0.748126\pi\) | |||||||
\(230\) | −2.12358 | −0.140024 | ||||||||
\(231\) | −3.39290 | −0.223237 | ||||||||
\(232\) | −1.25930 | −0.0826771 | ||||||||
\(233\) | 9.01899 | 0.590854 | 0.295427 | − | 0.955365i | \(-0.404538\pi\) | ||||
0.295427 | + | 0.955365i | \(0.404538\pi\) | |||||||
\(234\) | 0.898213 | 0.0587180 | ||||||||
\(235\) | 11.2227 | 0.732088 | ||||||||
\(236\) | 1.26320 | 0.0822274 | ||||||||
\(237\) | 19.3240 | 1.25523 | ||||||||
\(238\) | −0.670158 | −0.0434399 | ||||||||
\(239\) | −5.91684 | −0.382729 | −0.191364 | − | 0.981519i | \(-0.561291\pi\) | ||||
−0.191364 | + | 0.981519i | \(0.561291\pi\) | |||||||
\(240\) | −3.30297 | −0.213206 | ||||||||
\(241\) | −8.37298 | −0.539351 | −0.269675 | − | 0.962951i | \(-0.586916\pi\) | ||||
−0.269675 | + | 0.962951i | \(0.586916\pi\) | |||||||
\(242\) | −9.13955 | −0.587512 | ||||||||
\(243\) | 22.2999 | 1.43054 | ||||||||
\(244\) | −2.22784 | −0.142623 | ||||||||
\(245\) | 1.32783 | 0.0848319 | ||||||||
\(246\) | 15.9865 | 1.01926 | ||||||||
\(247\) | −0.810557 | −0.0515745 | ||||||||
\(248\) | −1.39495 | −0.0885795 | ||||||||
\(249\) | 1.64883 | 0.104490 | ||||||||
\(250\) | −10.9372 | −0.691726 | ||||||||
\(251\) | −25.7847 | −1.62752 | −0.813759 | − | 0.581202i | \(-0.802583\pi\) | ||||
−0.813759 | + | 0.581202i | \(0.802583\pi\) | |||||||
\(252\) | 3.18763 | 0.200802 | ||||||||
\(253\) | −2.18140 | −0.137143 | ||||||||
\(254\) | −19.2644 | −1.20876 | ||||||||
\(255\) | 2.21351 | 0.138615 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.2012 | −1.13536 | −0.567681 | − | 0.823248i | \(-0.692159\pi\) | ||||
−0.567681 | + | 0.823248i | \(0.692159\pi\) | |||||||
\(258\) | 31.7768 | 1.97834 | ||||||||
\(259\) | −9.31561 | −0.578844 | ||||||||
\(260\) | 0.374156 | 0.0232042 | ||||||||
\(261\) | −4.01418 | −0.248472 | ||||||||
\(262\) | −14.3216 | −0.884794 | ||||||||
\(263\) | −8.76899 | −0.540719 | −0.270359 | − | 0.962759i | \(-0.587143\pi\) | ||||
−0.270359 | + | 0.962759i | \(0.587143\pi\) | |||||||
\(264\) | −3.39290 | −0.208819 | ||||||||
\(265\) | −4.75419 | −0.292047 | ||||||||
\(266\) | −2.87655 | −0.176373 | ||||||||
\(267\) | 7.27018 | 0.444928 | ||||||||
\(268\) | −2.81723 | −0.172090 | ||||||||
\(269\) | −2.09481 | −0.127723 | −0.0638613 | − | 0.997959i | \(-0.520342\pi\) | ||||
−0.0638613 | + | 0.997959i | \(0.520342\pi\) | |||||||
\(270\) | −0.619739 | −0.0377161 | ||||||||
\(271\) | 28.2295 | 1.71482 | 0.857411 | − | 0.514632i | \(-0.172072\pi\) | ||||
0.857411 | + | 0.514632i | \(0.172072\pi\) | |||||||
\(272\) | −0.670158 | −0.0406343 | ||||||||
\(273\) | −0.700928 | −0.0424221 | ||||||||
\(274\) | 18.3309 | 1.10741 | ||||||||
\(275\) | −4.41504 | −0.266237 | ||||||||
\(276\) | 3.97821 | 0.239460 | ||||||||
\(277\) | −21.9882 | −1.32114 | −0.660571 | − | 0.750764i | \(-0.729686\pi\) | ||||
−0.660571 | + | 0.750764i | \(0.729686\pi\) | |||||||
\(278\) | −9.54684 | −0.572581 | ||||||||
\(279\) | −4.44659 | −0.266210 | ||||||||
\(280\) | 1.32783 | 0.0793529 | ||||||||
\(281\) | 1.37003 | 0.0817290 | 0.0408645 | − | 0.999165i | \(-0.486989\pi\) | ||||
0.0408645 | + | 0.999165i | \(0.486989\pi\) | |||||||
\(282\) | −21.0241 | −1.25197 | ||||||||
\(283\) | 22.6165 | 1.34441 | 0.672205 | − | 0.740365i | \(-0.265347\pi\) | ||||
0.672205 | + | 0.740365i | \(0.265347\pi\) | |||||||
\(284\) | 11.6926 | 0.693829 | ||||||||
\(285\) | 9.50116 | 0.562800 | ||||||||
\(286\) | 0.384344 | 0.0227267 | ||||||||
\(287\) | −6.42674 | −0.379358 | ||||||||
\(288\) | 3.18763 | 0.187833 | ||||||||
\(289\) | −16.5509 | −0.973582 | ||||||||
\(290\) | −1.67213 | −0.0981911 | ||||||||
\(291\) | −36.1999 | −2.12207 | ||||||||
\(292\) | 2.26070 | 0.132298 | ||||||||
\(293\) | 12.8871 | 0.752872 | 0.376436 | − | 0.926443i | \(-0.377149\pi\) | ||||
0.376436 | + | 0.926443i | \(0.377149\pi\) | |||||||
\(294\) | −2.48749 | −0.145074 | ||||||||
\(295\) | 1.67731 | 0.0976570 | ||||||||
\(296\) | −9.31561 | −0.541459 | ||||||||
\(297\) | −0.636614 | −0.0369401 | ||||||||
\(298\) | −17.0618 | −0.988361 | ||||||||
\(299\) | −0.450647 | −0.0260616 | ||||||||
\(300\) | 8.05170 | 0.464865 | ||||||||
\(301\) | −12.7746 | −0.736316 | ||||||||
\(302\) | −10.8435 | −0.623975 | ||||||||
\(303\) | −35.0882 | −2.01577 | ||||||||
\(304\) | −2.87655 | −0.164982 | ||||||||
\(305\) | −2.95820 | −0.169386 | ||||||||
\(306\) | −2.13621 | −0.122119 | ||||||||
\(307\) | 18.5453 | 1.05843 | 0.529217 | − | 0.848486i | \(-0.322486\pi\) | ||||
0.529217 | + | 0.848486i | \(0.322486\pi\) | |||||||
\(308\) | 1.36398 | 0.0777202 | ||||||||
\(309\) | −12.9570 | −0.737095 | ||||||||
\(310\) | −1.85226 | −0.105201 | ||||||||
\(311\) | −26.7289 | −1.51566 | −0.757829 | − | 0.652453i | \(-0.773740\pi\) | ||||
−0.757829 | + | 0.652453i | \(0.773740\pi\) | |||||||
\(312\) | −0.700928 | −0.0396822 | ||||||||
\(313\) | −26.7284 | −1.51078 | −0.755388 | − | 0.655277i | \(-0.772552\pi\) | ||||
−0.755388 | + | 0.655277i | \(0.772552\pi\) | |||||||
\(314\) | 12.8469 | 0.724993 | ||||||||
\(315\) | 4.23263 | 0.238482 | ||||||||
\(316\) | −7.76845 | −0.437010 | ||||||||
\(317\) | −3.61201 | −0.202871 | −0.101435 | − | 0.994842i | \(-0.532344\pi\) | ||||
−0.101435 | + | 0.994842i | \(0.532344\pi\) | |||||||
\(318\) | 8.90629 | 0.499440 | ||||||||
\(319\) | −1.71766 | −0.0961707 | ||||||||
\(320\) | 1.32783 | 0.0742279 | ||||||||
\(321\) | 1.75012 | 0.0976821 | ||||||||
\(322\) | −1.59928 | −0.0891247 | ||||||||
\(323\) | 1.92774 | 0.107263 | ||||||||
\(324\) | −8.40190 | −0.466772 | ||||||||
\(325\) | −0.912088 | −0.0505935 | ||||||||
\(326\) | 10.9064 | 0.604047 | ||||||||
\(327\) | 23.9849 | 1.32637 | ||||||||
\(328\) | −6.42674 | −0.354857 | ||||||||
\(329\) | 8.45192 | 0.465969 | ||||||||
\(330\) | −4.50519 | −0.248003 | ||||||||
\(331\) | 5.82013 | 0.319903 | 0.159952 | − | 0.987125i | \(-0.448866\pi\) | ||||
0.159952 | + | 0.987125i | \(0.448866\pi\) | |||||||
\(332\) | −0.662846 | −0.0363784 | ||||||||
\(333\) | −29.6947 | −1.62726 | ||||||||
\(334\) | −5.03627 | −0.275573 | ||||||||
\(335\) | −3.74080 | −0.204382 | ||||||||
\(336\) | −2.48749 | −0.135704 | ||||||||
\(337\) | 6.61801 | 0.360506 | 0.180253 | − | 0.983620i | \(-0.442308\pi\) | ||||
0.180253 | + | 0.983620i | \(0.442308\pi\) | |||||||
\(338\) | −12.9206 | −0.702788 | ||||||||
\(339\) | 10.3169 | 0.560337 | ||||||||
\(340\) | −0.889854 | −0.0482591 | ||||||||
\(341\) | −1.90269 | −0.103036 | ||||||||
\(342\) | −9.16939 | −0.495824 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.7746 | −0.688761 | ||||||||
\(345\) | 5.28238 | 0.284394 | ||||||||
\(346\) | −17.8313 | −0.958619 | ||||||||
\(347\) | 15.5183 | 0.833064 | 0.416532 | − | 0.909121i | \(-0.363245\pi\) | ||||
0.416532 | + | 0.909121i | \(0.363245\pi\) | |||||||
\(348\) | 3.13250 | 0.167920 | ||||||||
\(349\) | −7.42938 | −0.397685 | −0.198843 | − | 0.980031i | \(-0.563718\pi\) | ||||
−0.198843 | + | 0.980031i | \(0.563718\pi\) | |||||||
\(350\) | −3.23687 | −0.173018 | ||||||||
\(351\) | −0.131516 | −0.00701979 | ||||||||
\(352\) | 1.36398 | 0.0727006 | ||||||||
\(353\) | 13.6875 | 0.728510 | 0.364255 | − | 0.931299i | \(-0.381324\pi\) | ||||
0.364255 | + | 0.931299i | \(0.381324\pi\) | |||||||
\(354\) | −3.14221 | −0.167006 | ||||||||
\(355\) | 15.5258 | 0.824024 | ||||||||
\(356\) | −2.92269 | −0.154902 | ||||||||
\(357\) | 1.66701 | 0.0882277 | ||||||||
\(358\) | 19.2812 | 1.01904 | ||||||||
\(359\) | −35.3180 | −1.86401 | −0.932005 | − | 0.362445i | \(-0.881942\pi\) | ||||
−0.932005 | + | 0.362445i | \(0.881942\pi\) | |||||||
\(360\) | 4.23263 | 0.223079 | ||||||||
\(361\) | −10.7254 | −0.564497 | ||||||||
\(362\) | −0.943125 | −0.0495696 | ||||||||
\(363\) | 22.7346 | 1.19326 | ||||||||
\(364\) | 0.281781 | 0.0147693 | ||||||||
\(365\) | 3.00183 | 0.157123 | ||||||||
\(366\) | 5.54175 | 0.289672 | ||||||||
\(367\) | −5.49026 | −0.286589 | −0.143295 | − | 0.989680i | \(-0.545770\pi\) | ||||
−0.143295 | + | 0.989680i | \(0.545770\pi\) | |||||||
\(368\) | −1.59928 | −0.0833685 | ||||||||
\(369\) | −20.4861 | −1.06646 | ||||||||
\(370\) | −12.3695 | −0.643062 | ||||||||
\(371\) | −3.58042 | −0.185886 | ||||||||
\(372\) | 3.46993 | 0.179908 | ||||||||
\(373\) | 0.659604 | 0.0341530 | 0.0170765 | − | 0.999854i | \(-0.494564\pi\) | ||||
0.0170765 | + | 0.999854i | \(0.494564\pi\) | |||||||
\(374\) | −0.914084 | −0.0472662 | ||||||||
\(375\) | 27.2061 | 1.40492 | ||||||||
\(376\) | 8.45192 | 0.435875 | ||||||||
\(377\) | −0.354846 | −0.0182755 | ||||||||
\(378\) | −0.466731 | −0.0240061 | ||||||||
\(379\) | 10.5619 | 0.542528 | 0.271264 | − | 0.962505i | \(-0.412558\pi\) | ||||
0.271264 | + | 0.962505i | \(0.412558\pi\) | |||||||
\(380\) | −3.81957 | −0.195940 | ||||||||
\(381\) | 47.9202 | 2.45502 | ||||||||
\(382\) | 20.2936 | 1.03831 | ||||||||
\(383\) | −16.2108 | −0.828332 | −0.414166 | − | 0.910201i | \(-0.635927\pi\) | ||||
−0.414166 | + | 0.910201i | \(0.635927\pi\) | |||||||
\(384\) | −2.48749 | −0.126939 | ||||||||
\(385\) | 1.81114 | 0.0923041 | ||||||||
\(386\) | −18.4467 | −0.938910 | ||||||||
\(387\) | −40.7207 | −2.06995 | ||||||||
\(388\) | 14.5527 | 0.738803 | ||||||||
\(389\) | −9.87917 | −0.500894 | −0.250447 | − | 0.968130i | \(-0.580578\pi\) | ||||
−0.250447 | + | 0.968130i | \(0.580578\pi\) | |||||||
\(390\) | −0.930712 | −0.0471284 | ||||||||
\(391\) | 1.07177 | 0.0542019 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 35.6250 | 1.79704 | ||||||||
\(394\) | 8.74474 | 0.440554 | ||||||||
\(395\) | −10.3152 | −0.519013 | ||||||||
\(396\) | 4.34788 | 0.218489 | ||||||||
\(397\) | −32.9334 | −1.65288 | −0.826439 | − | 0.563026i | \(-0.809637\pi\) | ||||
−0.826439 | + | 0.563026i | \(0.809637\pi\) | |||||||
\(398\) | 25.9588 | 1.30120 | ||||||||
\(399\) | 7.15541 | 0.358219 | ||||||||
\(400\) | −3.23687 | −0.161844 | ||||||||
\(401\) | −33.2223 | −1.65904 | −0.829520 | − | 0.558477i | \(-0.811386\pi\) | ||||
−0.829520 | + | 0.558477i | \(0.811386\pi\) | |||||||
\(402\) | 7.00785 | 0.349520 | ||||||||
\(403\) | −0.393070 | −0.0195802 | ||||||||
\(404\) | 14.1058 | 0.701792 | ||||||||
\(405\) | −11.1563 | −0.554360 | ||||||||
\(406\) | −1.25930 | −0.0624980 | ||||||||
\(407\) | −12.7063 | −0.629830 | ||||||||
\(408\) | 1.66701 | 0.0825295 | ||||||||
\(409\) | −29.6001 | −1.46363 | −0.731815 | − | 0.681503i | \(-0.761327\pi\) | ||||
−0.731815 | + | 0.681503i | \(0.761327\pi\) | |||||||
\(410\) | −8.53360 | −0.421445 | ||||||||
\(411\) | −45.5980 | −2.24918 | ||||||||
\(412\) | 5.20884 | 0.256621 | ||||||||
\(413\) | 1.26320 | 0.0621581 | ||||||||
\(414\) | −5.09793 | −0.250550 | ||||||||
\(415\) | −0.880146 | −0.0432047 | ||||||||
\(416\) | 0.281781 | 0.0138154 | ||||||||
\(417\) | 23.7477 | 1.16293 | ||||||||
\(418\) | −3.92357 | −0.191908 | ||||||||
\(419\) | 0.686821 | 0.0335534 | 0.0167767 | − | 0.999859i | \(-0.494660\pi\) | ||||
0.0167767 | + | 0.999859i | \(0.494660\pi\) | |||||||
\(420\) | −3.30297 | −0.161168 | ||||||||
\(421\) | −6.61491 | −0.322391 | −0.161196 | − | 0.986922i | \(-0.551535\pi\) | ||||
−0.161196 | + | 0.986922i | \(0.551535\pi\) | |||||||
\(422\) | 18.3688 | 0.894179 | ||||||||
\(423\) | 26.9416 | 1.30995 | ||||||||
\(424\) | −3.58042 | −0.173881 | ||||||||
\(425\) | 2.16921 | 0.105222 | ||||||||
\(426\) | −29.0853 | −1.40919 | ||||||||
\(427\) | −2.22784 | −0.107813 | ||||||||
\(428\) | −0.703567 | −0.0340082 | ||||||||
\(429\) | −0.956054 | −0.0461587 | ||||||||
\(430\) | −16.9625 | −0.818004 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | −0.466731 | −0.0224556 | ||||||||
\(433\) | −35.6021 | −1.71093 | −0.855463 | − | 0.517864i | \(-0.826727\pi\) | ||||
−0.855463 | + | 0.517864i | \(0.826727\pi\) | |||||||
\(434\) | −1.39495 | −0.0669598 | ||||||||
\(435\) | 4.15942 | 0.199429 | ||||||||
\(436\) | −9.64219 | −0.461777 | ||||||||
\(437\) | 4.60043 | 0.220068 | ||||||||
\(438\) | −5.62349 | −0.268701 | ||||||||
\(439\) | 20.5945 | 0.982924 | 0.491462 | − | 0.870899i | \(-0.336463\pi\) | ||||
0.491462 | + | 0.870899i | \(0.336463\pi\) | |||||||
\(440\) | 1.81114 | 0.0863426 | ||||||||
\(441\) | 3.18763 | 0.151792 | ||||||||
\(442\) | −0.188837 | −0.00898208 | ||||||||
\(443\) | −38.1747 | −1.81373 | −0.906867 | − | 0.421416i | \(-0.861533\pi\) | ||||
−0.906867 | + | 0.421416i | \(0.861533\pi\) | |||||||
\(444\) | 23.1725 | 1.09972 | ||||||||
\(445\) | −3.88083 | −0.183969 | ||||||||
\(446\) | 2.02562 | 0.0959158 | ||||||||
\(447\) | 42.4410 | 2.00739 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −31.4244 | −1.48301 | −0.741504 | − | 0.670948i | \(-0.765887\pi\) | ||||
−0.741504 | + | 0.670948i | \(0.765887\pi\) | |||||||
\(450\) | −10.3180 | −0.486393 | ||||||||
\(451\) | −8.76596 | −0.412773 | ||||||||
\(452\) | −4.14750 | −0.195082 | ||||||||
\(453\) | 26.9732 | 1.26731 | ||||||||
\(454\) | −4.94194 | −0.231937 | ||||||||
\(455\) | 0.374156 | 0.0175407 | ||||||||
\(456\) | 7.15541 | 0.335083 | ||||||||
\(457\) | 22.7966 | 1.06638 | 0.533191 | − | 0.845995i | \(-0.320993\pi\) | ||||
0.533191 | + | 0.845995i | \(0.320993\pi\) | |||||||
\(458\) | −21.2745 | −0.994094 | ||||||||
\(459\) | 0.312783 | 0.0145995 | ||||||||
\(460\) | −2.12358 | −0.0990122 | ||||||||
\(461\) | −22.5292 | −1.04929 | −0.524645 | − | 0.851321i | \(-0.675802\pi\) | ||||
−0.524645 | + | 0.851321i | \(0.675802\pi\) | |||||||
\(462\) | −3.39290 | −0.157852 | ||||||||
\(463\) | −16.3115 | −0.758059 | −0.379030 | − | 0.925385i | \(-0.623742\pi\) | ||||
−0.379030 | + | 0.925385i | \(0.623742\pi\) | |||||||
\(464\) | −1.25930 | −0.0584615 | ||||||||
\(465\) | 4.60748 | 0.213667 | ||||||||
\(466\) | 9.01899 | 0.417797 | ||||||||
\(467\) | −3.99673 | −0.184947 | −0.0924734 | − | 0.995715i | \(-0.529477\pi\) | ||||
−0.0924734 | + | 0.995715i | \(0.529477\pi\) | |||||||
\(468\) | 0.898213 | 0.0415199 | ||||||||
\(469\) | −2.81723 | −0.130088 | ||||||||
\(470\) | 11.2227 | 0.517665 | ||||||||
\(471\) | −31.9566 | −1.47248 | ||||||||
\(472\) | 1.26320 | 0.0581435 | ||||||||
\(473\) | −17.4244 | −0.801173 | ||||||||
\(474\) | 19.3240 | 0.887580 | ||||||||
\(475\) | 9.31103 | 0.427219 | ||||||||
\(476\) | −0.670158 | −0.0307166 | ||||||||
\(477\) | −11.4131 | −0.522569 | ||||||||
\(478\) | −5.91684 | −0.270630 | ||||||||
\(479\) | 33.3604 | 1.52428 | 0.762139 | − | 0.647414i | \(-0.224149\pi\) | ||||
0.762139 | + | 0.647414i | \(0.224149\pi\) | |||||||
\(480\) | −3.30297 | −0.150759 | ||||||||
\(481\) | −2.62496 | −0.119688 | ||||||||
\(482\) | −8.37298 | −0.381379 | ||||||||
\(483\) | 3.97821 | 0.181015 | ||||||||
\(484\) | −9.13955 | −0.415434 | ||||||||
\(485\) | 19.3235 | 0.877437 | ||||||||
\(486\) | 22.2999 | 1.01154 | ||||||||
\(487\) | 9.68933 | 0.439065 | 0.219533 | − | 0.975605i | \(-0.429547\pi\) | ||||
0.219533 | + | 0.975605i | \(0.429547\pi\) | |||||||
\(488\) | −2.22784 | −0.100850 | ||||||||
\(489\) | −27.1295 | −1.22684 | ||||||||
\(490\) | 1.32783 | 0.0599852 | ||||||||
\(491\) | 23.5275 | 1.06178 | 0.530891 | − | 0.847440i | \(-0.321857\pi\) | ||||
0.530891 | + | 0.847440i | \(0.321857\pi\) | |||||||
\(492\) | 15.9865 | 0.720726 | ||||||||
\(493\) | 0.843929 | 0.0380087 | ||||||||
\(494\) | −0.810557 | −0.0364687 | ||||||||
\(495\) | 5.77324 | 0.259488 | ||||||||
\(496\) | −1.39495 | −0.0626351 | ||||||||
\(497\) | 11.6926 | 0.524486 | ||||||||
\(498\) | 1.64883 | 0.0738857 | ||||||||
\(499\) | −7.42227 | −0.332266 | −0.166133 | − | 0.986103i | \(-0.553128\pi\) | ||||
−0.166133 | + | 0.986103i | \(0.553128\pi\) | |||||||
\(500\) | −10.9372 | −0.489124 | ||||||||
\(501\) | 12.5277 | 0.559697 | ||||||||
\(502\) | −25.7847 | −1.15083 | ||||||||
\(503\) | 3.74884 | 0.167153 | 0.0835763 | − | 0.996501i | \(-0.473366\pi\) | ||||
0.0835763 | + | 0.996501i | \(0.473366\pi\) | |||||||
\(504\) | 3.18763 | 0.141988 | ||||||||
\(505\) | 18.7301 | 0.833481 | ||||||||
\(506\) | −2.18140 | −0.0969750 | ||||||||
\(507\) | 32.1399 | 1.42738 | ||||||||
\(508\) | −19.2644 | −0.854721 | ||||||||
\(509\) | −8.81025 | −0.390507 | −0.195254 | − | 0.980753i | \(-0.562553\pi\) | ||||
−0.195254 | + | 0.980753i | \(0.562553\pi\) | |||||||
\(510\) | 2.21351 | 0.0980158 | ||||||||
\(511\) | 2.26070 | 0.100008 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.34258 | 0.0592762 | ||||||||
\(514\) | −18.2012 | −0.802823 | ||||||||
\(515\) | 6.91644 | 0.304775 | ||||||||
\(516\) | 31.7768 | 1.39889 | ||||||||
\(517\) | 11.5283 | 0.507013 | ||||||||
\(518\) | −9.31561 | −0.409305 | ||||||||
\(519\) | 44.3554 | 1.94699 | ||||||||
\(520\) | 0.374156 | 0.0164078 | ||||||||
\(521\) | 41.3020 | 1.80947 | 0.904737 | − | 0.425971i | \(-0.140067\pi\) | ||||
0.904737 | + | 0.425971i | \(0.140067\pi\) | |||||||
\(522\) | −4.01418 | −0.175696 | ||||||||
\(523\) | −23.0466 | −1.00776 | −0.503878 | − | 0.863775i | \(-0.668094\pi\) | ||||
−0.503878 | + | 0.863775i | \(0.668094\pi\) | |||||||
\(524\) | −14.3216 | −0.625644 | ||||||||
\(525\) | 8.05170 | 0.351405 | ||||||||
\(526\) | −8.76899 | −0.382346 | ||||||||
\(527\) | 0.934837 | 0.0407221 | ||||||||
\(528\) | −3.39290 | −0.147657 | ||||||||
\(529\) | −20.4423 | −0.888795 | ||||||||
\(530\) | −4.75419 | −0.206509 | ||||||||
\(531\) | 4.02662 | 0.174740 | ||||||||
\(532\) | −2.87655 | −0.124714 | ||||||||
\(533\) | −1.81093 | −0.0784401 | ||||||||
\(534\) | 7.27018 | 0.314611 | ||||||||
\(535\) | −0.934216 | −0.0403897 | ||||||||
\(536\) | −2.81723 | −0.121686 | ||||||||
\(537\) | −47.9619 | −2.06971 | ||||||||
\(538\) | −2.09481 | −0.0903135 | ||||||||
\(539\) | 1.36398 | 0.0587509 | ||||||||
\(540\) | −0.619739 | −0.0266693 | ||||||||
\(541\) | 9.69628 | 0.416876 | 0.208438 | − | 0.978036i | \(-0.433162\pi\) | ||||
0.208438 | + | 0.978036i | \(0.433162\pi\) | |||||||
\(542\) | 28.2295 | 1.21256 | ||||||||
\(543\) | 2.34602 | 0.100677 | ||||||||
\(544\) | −0.670158 | −0.0287328 | ||||||||
\(545\) | −12.8032 | −0.548428 | ||||||||
\(546\) | −0.700928 | −0.0299969 | ||||||||
\(547\) | −10.0725 | −0.430667 | −0.215334 | − | 0.976541i | \(-0.569084\pi\) | ||||
−0.215334 | + | 0.976541i | \(0.569084\pi\) | |||||||
\(548\) | 18.3309 | 0.783057 | ||||||||
\(549\) | −7.10155 | −0.303087 | ||||||||
\(550\) | −4.41504 | −0.188258 | ||||||||
\(551\) | 3.62244 | 0.154321 | ||||||||
\(552\) | 3.97821 | 0.169324 | ||||||||
\(553\) | −7.76845 | −0.330348 | ||||||||
\(554\) | −21.9882 | −0.934188 | ||||||||
\(555\) | 30.7692 | 1.30608 | ||||||||
\(556\) | −9.54684 | −0.404876 | ||||||||
\(557\) | −3.24225 | −0.137379 | −0.0686894 | − | 0.997638i | \(-0.521882\pi\) | ||||
−0.0686894 | + | 0.997638i | \(0.521882\pi\) | |||||||
\(558\) | −4.44659 | −0.188239 | ||||||||
\(559\) | −3.59964 | −0.152248 | ||||||||
\(560\) | 1.32783 | 0.0561110 | ||||||||
\(561\) | 2.27378 | 0.0959990 | ||||||||
\(562\) | 1.37003 | 0.0577911 | ||||||||
\(563\) | 27.5227 | 1.15994 | 0.579971 | − | 0.814637i | \(-0.303064\pi\) | ||||
0.579971 | + | 0.814637i | \(0.303064\pi\) | |||||||
\(564\) | −21.0241 | −0.885275 | ||||||||
\(565\) | −5.50718 | −0.231689 | ||||||||
\(566\) | 22.6165 | 0.950641 | ||||||||
\(567\) | −8.40190 | −0.352847 | ||||||||
\(568\) | 11.6926 | 0.490611 | ||||||||
\(569\) | −22.6831 | −0.950924 | −0.475462 | − | 0.879736i | \(-0.657719\pi\) | ||||
−0.475462 | + | 0.879736i | \(0.657719\pi\) | |||||||
\(570\) | 9.50116 | 0.397960 | ||||||||
\(571\) | 25.9223 | 1.08481 | 0.542407 | − | 0.840116i | \(-0.317513\pi\) | ||||
0.542407 | + | 0.840116i | \(0.317513\pi\) | |||||||
\(572\) | 0.384344 | 0.0160702 | ||||||||
\(573\) | −50.4803 | −2.10884 | ||||||||
\(574\) | −6.42674 | −0.268247 | ||||||||
\(575\) | 5.17668 | 0.215882 | ||||||||
\(576\) | 3.18763 | 0.132818 | ||||||||
\(577\) | 35.5454 | 1.47977 | 0.739887 | − | 0.672731i | \(-0.234879\pi\) | ||||
0.739887 | + | 0.672731i | \(0.234879\pi\) | |||||||
\(578\) | −16.5509 | −0.688426 | ||||||||
\(579\) | 45.8860 | 1.90696 | ||||||||
\(580\) | −1.67213 | −0.0694316 | ||||||||
\(581\) | −0.662846 | −0.0274995 | ||||||||
\(582\) | −36.1999 | −1.50053 | ||||||||
\(583\) | −4.88364 | −0.202260 | ||||||||
\(584\) | 2.26070 | 0.0935486 | ||||||||
\(585\) | 1.19267 | 0.0493109 | ||||||||
\(586\) | 12.8871 | 0.532361 | ||||||||
\(587\) | 38.0738 | 1.57148 | 0.785738 | − | 0.618560i | \(-0.212284\pi\) | ||||
0.785738 | + | 0.618560i | \(0.212284\pi\) | |||||||
\(588\) | −2.48749 | −0.102583 | ||||||||
\(589\) | 4.01265 | 0.165338 | ||||||||
\(590\) | 1.67731 | 0.0690539 | ||||||||
\(591\) | −21.7525 | −0.894778 | ||||||||
\(592\) | −9.31561 | −0.382869 | ||||||||
\(593\) | 16.3486 | 0.671358 | 0.335679 | − | 0.941976i | \(-0.391034\pi\) | ||||
0.335679 | + | 0.941976i | \(0.391034\pi\) | |||||||
\(594\) | −0.636614 | −0.0261206 | ||||||||
\(595\) | −0.889854 | −0.0364805 | ||||||||
\(596\) | −17.0618 | −0.698877 | ||||||||
\(597\) | −64.5724 | −2.64277 | ||||||||
\(598\) | −0.450647 | −0.0184283 | ||||||||
\(599\) | −15.2724 | −0.624015 | −0.312008 | − | 0.950080i | \(-0.601001\pi\) | ||||
−0.312008 | + | 0.950080i | \(0.601001\pi\) | |||||||
\(600\) | 8.05170 | 0.328709 | ||||||||
\(601\) | 46.7939 | 1.90876 | 0.954381 | − | 0.298591i | \(-0.0965166\pi\) | ||||
0.954381 | + | 0.298591i | \(0.0965166\pi\) | |||||||
\(602\) | −12.7746 | −0.520654 | ||||||||
\(603\) | −8.98029 | −0.365706 | ||||||||
\(604\) | −10.8435 | −0.441217 | ||||||||
\(605\) | −12.1358 | −0.493389 | ||||||||
\(606\) | −35.0882 | −1.42536 | ||||||||
\(607\) | −0.257101 | −0.0104354 | −0.00521770 | − | 0.999986i | \(-0.501661\pi\) | ||||
−0.00521770 | + | 0.999986i | \(0.501661\pi\) | |||||||
\(608\) | −2.87655 | −0.116660 | ||||||||
\(609\) | 3.13250 | 0.126935 | ||||||||
\(610\) | −2.95820 | −0.119774 | ||||||||
\(611\) | 2.38159 | 0.0963487 | ||||||||
\(612\) | −2.13621 | −0.0863514 | ||||||||
\(613\) | 46.4767 | 1.87718 | 0.938588 | − | 0.345041i | \(-0.112135\pi\) | ||||
0.938588 | + | 0.345041i | \(0.112135\pi\) | |||||||
\(614\) | 18.5453 | 0.748426 | ||||||||
\(615\) | 21.2273 | 0.855967 | ||||||||
\(616\) | 1.36398 | 0.0549565 | ||||||||
\(617\) | 43.4704 | 1.75005 | 0.875025 | − | 0.484077i | \(-0.160845\pi\) | ||||
0.875025 | + | 0.484077i | \(0.160845\pi\) | |||||||
\(618\) | −12.9570 | −0.521205 | ||||||||
\(619\) | −31.4847 | −1.26548 | −0.632738 | − | 0.774366i | \(-0.718069\pi\) | ||||
−0.632738 | + | 0.774366i | \(0.718069\pi\) | |||||||
\(620\) | −1.85226 | −0.0743884 | ||||||||
\(621\) | 0.746436 | 0.0299534 | ||||||||
\(622\) | −26.7289 | −1.07173 | ||||||||
\(623\) | −2.92269 | −0.117095 | ||||||||
\(624\) | −0.700928 | −0.0280596 | ||||||||
\(625\) | 1.66169 | 0.0664677 | ||||||||
\(626\) | −26.7284 | −1.06828 | ||||||||
\(627\) | 9.75987 | 0.389771 | ||||||||
\(628\) | 12.8469 | 0.512648 | ||||||||
\(629\) | 6.24293 | 0.248922 | ||||||||
\(630\) | 4.23263 | 0.168632 | ||||||||
\(631\) | 40.5403 | 1.61389 | 0.806943 | − | 0.590630i | \(-0.201121\pi\) | ||||
0.806943 | + | 0.590630i | \(0.201121\pi\) | |||||||
\(632\) | −7.76845 | −0.309012 | ||||||||
\(633\) | −45.6923 | −1.81611 | ||||||||
\(634\) | −3.61201 | −0.143451 | ||||||||
\(635\) | −25.5799 | −1.01511 | ||||||||
\(636\) | 8.90629 | 0.353157 | ||||||||
\(637\) | 0.281781 | 0.0111646 | ||||||||
\(638\) | −1.71766 | −0.0680030 | ||||||||
\(639\) | 37.2718 | 1.47445 | ||||||||
\(640\) | 1.32783 | 0.0524870 | ||||||||
\(641\) | 6.42650 | 0.253831 | 0.126916 | − | 0.991914i | \(-0.459492\pi\) | ||||
0.126916 | + | 0.991914i | \(0.459492\pi\) | |||||||
\(642\) | 1.75012 | 0.0690717 | ||||||||
\(643\) | −7.75535 | −0.305841 | −0.152921 | − | 0.988238i | \(-0.548868\pi\) | ||||
−0.152921 | + | 0.988238i | \(0.548868\pi\) | |||||||
\(644\) | −1.59928 | −0.0630207 | ||||||||
\(645\) | 42.1941 | 1.66139 | ||||||||
\(646\) | 1.92774 | 0.0758461 | ||||||||
\(647\) | −14.9289 | −0.586914 | −0.293457 | − | 0.955972i | \(-0.594806\pi\) | ||||
−0.293457 | + | 0.955972i | \(0.594806\pi\) | |||||||
\(648\) | −8.40190 | −0.330058 | ||||||||
\(649\) | 1.72299 | 0.0676331 | ||||||||
\(650\) | −0.912088 | −0.0357750 | ||||||||
\(651\) | 3.46993 | 0.135997 | ||||||||
\(652\) | 10.9064 | 0.427126 | ||||||||
\(653\) | 11.6313 | 0.455167 | 0.227584 | − | 0.973759i | \(-0.426917\pi\) | ||||
0.227584 | + | 0.973759i | \(0.426917\pi\) | |||||||
\(654\) | 23.9849 | 0.937884 | ||||||||
\(655\) | −19.0167 | −0.743043 | ||||||||
\(656\) | −6.42674 | −0.250922 | ||||||||
\(657\) | 7.20629 | 0.281144 | ||||||||
\(658\) | 8.45192 | 0.329490 | ||||||||
\(659\) | 34.2263 | 1.33327 | 0.666634 | − | 0.745385i | \(-0.267734\pi\) | ||||
0.666634 | + | 0.745385i | \(0.267734\pi\) | |||||||
\(660\) | −4.50519 | −0.175364 | ||||||||
\(661\) | 16.3856 | 0.637327 | 0.318663 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318663 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(662\) | 5.82013 | 0.226206 | ||||||||
\(663\) | 0.469732 | 0.0182429 | ||||||||
\(664\) | −0.662846 | −0.0257234 | ||||||||
\(665\) | −3.81957 | −0.148117 | ||||||||
\(666\) | −29.6947 | −1.15065 | ||||||||
\(667\) | 2.01398 | 0.0779816 | ||||||||
\(668\) | −5.03627 | −0.194859 | ||||||||
\(669\) | −5.03871 | −0.194808 | ||||||||
\(670\) | −3.74080 | −0.144520 | ||||||||
\(671\) | −3.03874 | −0.117309 | ||||||||
\(672\) | −2.48749 | −0.0959572 | ||||||||
\(673\) | 23.1554 | 0.892575 | 0.446288 | − | 0.894890i | \(-0.352746\pi\) | ||||
0.446288 | + | 0.894890i | \(0.352746\pi\) | |||||||
\(674\) | 6.61801 | 0.254916 | ||||||||
\(675\) | 1.51075 | 0.0581487 | ||||||||
\(676\) | −12.9206 | −0.496946 | ||||||||
\(677\) | −18.1784 | −0.698653 | −0.349326 | − | 0.937001i | \(-0.613590\pi\) | ||||
−0.349326 | + | 0.937001i | \(0.613590\pi\) | |||||||
\(678\) | 10.3169 | 0.396218 | ||||||||
\(679\) | 14.5527 | 0.558483 | ||||||||
\(680\) | −0.889854 | −0.0341244 | ||||||||
\(681\) | 12.2930 | 0.471070 | ||||||||
\(682\) | −1.90269 | −0.0728578 | ||||||||
\(683\) | −36.6838 | −1.40367 | −0.701833 | − | 0.712342i | \(-0.747635\pi\) | ||||
−0.701833 | + | 0.712342i | \(0.747635\pi\) | |||||||
\(684\) | −9.16939 | −0.350600 | ||||||||
\(685\) | 24.3403 | 0.929995 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 52.9203 | 2.01904 | ||||||||
\(688\) | −12.7746 | −0.487027 | ||||||||
\(689\) | −1.00889 | −0.0384358 | ||||||||
\(690\) | 5.28238 | 0.201097 | ||||||||
\(691\) | −22.1102 | −0.841113 | −0.420556 | − | 0.907266i | \(-0.638165\pi\) | ||||
−0.420556 | + | 0.907266i | \(0.638165\pi\) | |||||||
\(692\) | −17.8313 | −0.677846 | ||||||||
\(693\) | 4.34788 | 0.165162 | ||||||||
\(694\) | 15.5183 | 0.589065 | ||||||||
\(695\) | −12.6766 | −0.480849 | ||||||||
\(696\) | 3.13250 | 0.118737 | ||||||||
\(697\) | 4.30693 | 0.163136 | ||||||||
\(698\) | −7.42938 | −0.281206 | ||||||||
\(699\) | −22.4347 | −0.848558 | ||||||||
\(700\) | −3.23687 | −0.122342 | ||||||||
\(701\) | 16.1641 | 0.610511 | 0.305255 | − | 0.952271i | \(-0.401258\pi\) | ||||
0.305255 | + | 0.952271i | \(0.401258\pi\) | |||||||
\(702\) | −0.131516 | −0.00496374 | ||||||||
\(703\) | 26.7969 | 1.01066 | ||||||||
\(704\) | 1.36398 | 0.0514071 | ||||||||
\(705\) | −27.9164 | −1.05139 | ||||||||
\(706\) | 13.6875 | 0.515134 | ||||||||
\(707\) | 14.1058 | 0.530505 | ||||||||
\(708\) | −3.14221 | −0.118091 | ||||||||
\(709\) | −29.5183 | −1.10858 | −0.554291 | − | 0.832323i | \(-0.687011\pi\) | ||||
−0.554291 | + | 0.832323i | \(0.687011\pi\) | |||||||
\(710\) | 15.5258 | 0.582673 | ||||||||
\(711\) | −24.7630 | −0.928684 | ||||||||
\(712\) | −2.92269 | −0.109532 | ||||||||
\(713\) | 2.23092 | 0.0835488 | ||||||||
\(714\) | 1.66701 | 0.0623864 | ||||||||
\(715\) | 0.510343 | 0.0190858 | ||||||||
\(716\) | 19.2812 | 0.720573 | ||||||||
\(717\) | 14.7181 | 0.549658 | ||||||||
\(718\) | −35.3180 | −1.31805 | ||||||||
\(719\) | 43.8476 | 1.63524 | 0.817620 | − | 0.575759i | \(-0.195293\pi\) | ||||
0.817620 | + | 0.575759i | \(0.195293\pi\) | |||||||
\(720\) | 4.23263 | 0.157741 | ||||||||
\(721\) | 5.20884 | 0.193987 | ||||||||
\(722\) | −10.7254 | −0.399160 | ||||||||
\(723\) | 20.8277 | 0.774592 | ||||||||
\(724\) | −0.943125 | −0.0350510 | ||||||||
\(725\) | 4.07619 | 0.151386 | ||||||||
\(726\) | 22.7346 | 0.843759 | ||||||||
\(727\) | 28.6539 | 1.06271 | 0.531357 | − | 0.847148i | \(-0.321682\pi\) | ||||
0.531357 | + | 0.847148i | \(0.321682\pi\) | |||||||
\(728\) | 0.281781 | 0.0104435 | ||||||||
\(729\) | −30.2651 | −1.12093 | ||||||||
\(730\) | 3.00183 | 0.111103 | ||||||||
\(731\) | 8.56100 | 0.316640 | ||||||||
\(732\) | 5.54175 | 0.204829 | ||||||||
\(733\) | 33.9673 | 1.25461 | 0.627306 | − | 0.778773i | \(-0.284158\pi\) | ||||
0.627306 | + | 0.778773i | \(0.284158\pi\) | |||||||
\(734\) | −5.49026 | −0.202649 | ||||||||
\(735\) | −3.30297 | −0.121832 | ||||||||
\(736\) | −1.59928 | −0.0589504 | ||||||||
\(737\) | −3.84266 | −0.141546 | ||||||||
\(738\) | −20.4861 | −0.754102 | ||||||||
\(739\) | −36.0497 | −1.32611 | −0.663055 | − | 0.748571i | \(-0.730740\pi\) | ||||
−0.663055 | + | 0.748571i | \(0.730740\pi\) | |||||||
\(740\) | −12.3695 | −0.454713 | ||||||||
\(741\) | 2.01626 | 0.0740690 | ||||||||
\(742\) | −3.58042 | −0.131441 | ||||||||
\(743\) | 40.9311 | 1.50162 | 0.750808 | − | 0.660521i | \(-0.229665\pi\) | ||||
0.750808 | + | 0.660521i | \(0.229665\pi\) | |||||||
\(744\) | 3.46993 | 0.127214 | ||||||||
\(745\) | −22.6551 | −0.830018 | ||||||||
\(746\) | 0.659604 | 0.0241498 | ||||||||
\(747\) | −2.11291 | −0.0773073 | ||||||||
\(748\) | −0.914084 | −0.0334222 | ||||||||
\(749\) | −0.703567 | −0.0257078 | ||||||||
\(750\) | 27.2061 | 0.993427 | ||||||||
\(751\) | 3.96763 | 0.144781 | 0.0723904 | − | 0.997376i | \(-0.476937\pi\) | ||||
0.0723904 | + | 0.997376i | \(0.476937\pi\) | |||||||
\(752\) | 8.45192 | 0.308210 | ||||||||
\(753\) | 64.1394 | 2.33737 | ||||||||
\(754\) | −0.354846 | −0.0129227 | ||||||||
\(755\) | −14.3983 | −0.524009 | ||||||||
\(756\) | −0.466731 | −0.0169748 | ||||||||
\(757\) | 41.9368 | 1.52422 | 0.762109 | − | 0.647449i | \(-0.224164\pi\) | ||||
0.762109 | + | 0.647449i | \(0.224164\pi\) | |||||||
\(758\) | 10.5619 | 0.383625 | ||||||||
\(759\) | 5.42622 | 0.196959 | ||||||||
\(760\) | −3.81957 | −0.138550 | ||||||||
\(761\) | 39.8908 | 1.44604 | 0.723021 | − | 0.690826i | \(-0.242753\pi\) | ||||
0.723021 | + | 0.690826i | \(0.242753\pi\) | |||||||
\(762\) | 47.9202 | 1.73596 | ||||||||
\(763\) | −9.64219 | −0.349071 | ||||||||
\(764\) | 20.2936 | 0.734198 | ||||||||
\(765\) | −2.83653 | −0.102555 | ||||||||
\(766\) | −16.2108 | −0.585719 | ||||||||
\(767\) | 0.355946 | 0.0128524 | ||||||||
\(768\) | −2.48749 | −0.0897597 | ||||||||
\(769\) | 49.7943 | 1.79563 | 0.897814 | − | 0.440375i | \(-0.145155\pi\) | ||||
0.897814 | + | 0.440375i | \(0.145155\pi\) | |||||||
\(770\) | 1.81114 | 0.0652688 | ||||||||
\(771\) | 45.2755 | 1.63056 | ||||||||
\(772\) | −18.4467 | −0.663910 | ||||||||
\(773\) | 38.1563 | 1.37238 | 0.686192 | − | 0.727420i | \(-0.259281\pi\) | ||||
0.686192 | + | 0.727420i | \(0.259281\pi\) | |||||||
\(774\) | −40.7207 | −1.46368 | ||||||||
\(775\) | 4.51528 | 0.162194 | ||||||||
\(776\) | 14.5527 | 0.522413 | ||||||||
\(777\) | 23.1725 | 0.831310 | ||||||||
\(778\) | −9.87917 | −0.354186 | ||||||||
\(779\) | 18.4868 | 0.662360 | ||||||||
\(780\) | −0.930712 | −0.0333248 | ||||||||
\(781\) | 15.9485 | 0.570684 | ||||||||
\(782\) | 1.07177 | 0.0383265 | ||||||||
\(783\) | 0.587754 | 0.0210046 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 17.0585 | 0.608844 | ||||||||
\(786\) | 35.6250 | 1.27070 | ||||||||
\(787\) | −19.8666 | −0.708167 | −0.354083 | − | 0.935214i | \(-0.615207\pi\) | ||||
−0.354083 | + | 0.935214i | \(0.615207\pi\) | |||||||
\(788\) | 8.74474 | 0.311519 | ||||||||
\(789\) | 21.8128 | 0.776556 | ||||||||
\(790\) | −10.3152 | −0.366997 | ||||||||
\(791\) | −4.14750 | −0.147468 | ||||||||
\(792\) | 4.34788 | 0.154495 | ||||||||
\(793\) | −0.627763 | −0.0222925 | ||||||||
\(794\) | −32.9334 | −1.16876 | ||||||||
\(795\) | 11.8260 | 0.419426 | ||||||||
\(796\) | 25.9588 | 0.920085 | ||||||||
\(797\) | −31.9491 | −1.13170 | −0.565848 | − | 0.824510i | \(-0.691451\pi\) | ||||
−0.565848 | + | 0.824510i | \(0.691451\pi\) | |||||||
\(798\) | 7.15541 | 0.253299 | ||||||||
\(799\) | −5.66412 | −0.200382 | ||||||||
\(800\) | −3.23687 | −0.114441 | ||||||||
\(801\) | −9.31646 | −0.329181 | ||||||||
\(802\) | −33.2223 | −1.17312 | ||||||||
\(803\) | 3.08356 | 0.108817 | ||||||||
\(804\) | 7.00785 | 0.247148 | ||||||||
\(805\) | −2.12358 | −0.0748462 | ||||||||
\(806\) | −0.393070 | −0.0138453 | ||||||||
\(807\) | 5.21082 | 0.183430 | ||||||||
\(808\) | 14.1058 | 0.496242 | ||||||||
\(809\) | −9.62596 | −0.338431 | −0.169215 | − | 0.985579i | \(-0.554123\pi\) | ||||
−0.169215 | + | 0.985579i | \(0.554123\pi\) | |||||||
\(810\) | −11.1563 | −0.391992 | ||||||||
\(811\) | −21.0781 | −0.740154 | −0.370077 | − | 0.929001i | \(-0.620669\pi\) | ||||
−0.370077 | + | 0.929001i | \(0.620669\pi\) | |||||||
\(812\) | −1.25930 | −0.0441928 | ||||||||
\(813\) | −70.2208 | −2.46275 | ||||||||
\(814\) | −12.7063 | −0.445357 | ||||||||
\(815\) | 14.4818 | 0.507274 | ||||||||
\(816\) | 1.66701 | 0.0583571 | ||||||||
\(817\) | 36.7468 | 1.28561 | ||||||||
\(818\) | −29.6001 | −1.03494 | ||||||||
\(819\) | 0.898213 | 0.0313861 | ||||||||
\(820\) | −8.53360 | −0.298006 | ||||||||
\(821\) | −35.4055 | −1.23566 | −0.617830 | − | 0.786312i | \(-0.711988\pi\) | ||||
−0.617830 | + | 0.786312i | \(0.711988\pi\) | |||||||
\(822\) | −45.5980 | −1.59041 | ||||||||
\(823\) | −25.4055 | −0.885579 | −0.442789 | − | 0.896626i | \(-0.646011\pi\) | ||||
−0.442789 | + | 0.896626i | \(0.646011\pi\) | |||||||
\(824\) | 5.20884 | 0.181458 | ||||||||
\(825\) | 10.9824 | 0.382358 | ||||||||
\(826\) | 1.26320 | 0.0439524 | ||||||||
\(827\) | −18.7198 | −0.650953 | −0.325476 | − | 0.945550i | \(-0.605525\pi\) | ||||
−0.325476 | + | 0.945550i | \(0.605525\pi\) | |||||||
\(828\) | −5.09793 | −0.177165 | ||||||||
\(829\) | −16.1210 | −0.559905 | −0.279953 | − | 0.960014i | \(-0.590319\pi\) | ||||
−0.279953 | + | 0.960014i | \(0.590319\pi\) | |||||||
\(830\) | −0.880146 | −0.0305503 | ||||||||
\(831\) | 54.6955 | 1.89736 | ||||||||
\(832\) | 0.281781 | 0.00976898 | ||||||||
\(833\) | −0.670158 | −0.0232196 | ||||||||
\(834\) | 23.7477 | 0.822316 | ||||||||
\(835\) | −6.68731 | −0.231424 | ||||||||
\(836\) | −3.92357 | −0.135700 | ||||||||
\(837\) | 0.651067 | 0.0225042 | ||||||||
\(838\) | 0.686821 | 0.0237258 | ||||||||
\(839\) | −7.33478 | −0.253225 | −0.126612 | − | 0.991952i | \(-0.540410\pi\) | ||||
−0.126612 | + | 0.991952i | \(0.540410\pi\) | |||||||
\(840\) | −3.30297 | −0.113963 | ||||||||
\(841\) | −27.4142 | −0.945316 | ||||||||
\(842\) | −6.61491 | −0.227965 | ||||||||
\(843\) | −3.40794 | −0.117376 | ||||||||
\(844\) | 18.3688 | 0.632280 | ||||||||
\(845\) | −17.1563 | −0.590196 | ||||||||
\(846\) | 26.9416 | 0.926271 | ||||||||
\(847\) | −9.13955 | −0.314039 | ||||||||
\(848\) | −3.58042 | −0.122952 | ||||||||
\(849\) | −56.2584 | −1.93078 | ||||||||
\(850\) | 2.16921 | 0.0744034 | ||||||||
\(851\) | 14.8983 | 0.510708 | ||||||||
\(852\) | −29.0853 | −0.996447 | ||||||||
\(853\) | −3.53623 | −0.121078 | −0.0605392 | − | 0.998166i | \(-0.519282\pi\) | ||||
−0.0605392 | + | 0.998166i | \(0.519282\pi\) | |||||||
\(854\) | −2.22784 | −0.0762353 | ||||||||
\(855\) | −12.1754 | −0.416389 | ||||||||
\(856\) | −0.703567 | −0.0240474 | ||||||||
\(857\) | 16.3278 | 0.557747 | 0.278873 | − | 0.960328i | \(-0.410039\pi\) | ||||
0.278873 | + | 0.960328i | \(0.410039\pi\) | |||||||
\(858\) | −0.956054 | −0.0326392 | ||||||||
\(859\) | 1.20390 | 0.0410766 | 0.0205383 | − | 0.999789i | \(-0.493462\pi\) | ||||
0.0205383 | + | 0.999789i | \(0.493462\pi\) | |||||||
\(860\) | −16.9625 | −0.578416 | ||||||||
\(861\) | 15.9865 | 0.544818 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 2.40294 | 0.0817971 | 0.0408985 | − | 0.999163i | \(-0.486978\pi\) | ||||
0.0408985 | + | 0.999163i | \(0.486978\pi\) | |||||||
\(864\) | −0.466731 | −0.0158785 | ||||||||
\(865\) | −23.6770 | −0.805041 | ||||||||
\(866\) | −35.6021 | −1.20981 | ||||||||
\(867\) | 41.1703 | 1.39822 | ||||||||
\(868\) | −1.39495 | −0.0473477 | ||||||||
\(869\) | −10.5960 | −0.359446 | ||||||||
\(870\) | 4.15942 | 0.141018 | ||||||||
\(871\) | −0.793841 | −0.0268983 | ||||||||
\(872\) | −9.64219 | −0.326526 | ||||||||
\(873\) | 46.3888 | 1.57002 | ||||||||
\(874\) | 4.60043 | 0.155612 | ||||||||
\(875\) | −10.9372 | −0.369743 | ||||||||
\(876\) | −5.62349 | −0.190000 | ||||||||
\(877\) | 36.4502 | 1.23084 | 0.615418 | − | 0.788201i | \(-0.288987\pi\) | ||||
0.615418 | + | 0.788201i | \(0.288987\pi\) | |||||||
\(878\) | 20.5945 | 0.695032 | ||||||||
\(879\) | −32.0566 | −1.08124 | ||||||||
\(880\) | 1.81114 | 0.0610534 | ||||||||
\(881\) | −26.2306 | −0.883732 | −0.441866 | − | 0.897081i | \(-0.645683\pi\) | ||||
−0.441866 | + | 0.897081i | \(0.645683\pi\) | |||||||
\(882\) | 3.18763 | 0.107333 | ||||||||
\(883\) | −31.1098 | −1.04693 | −0.523464 | − | 0.852048i | \(-0.675361\pi\) | ||||
−0.523464 | + | 0.852048i | \(0.675361\pi\) | |||||||
\(884\) | −0.188837 | −0.00635129 | ||||||||
\(885\) | −4.17231 | −0.140251 | ||||||||
\(886\) | −38.1747 | −1.28250 | ||||||||
\(887\) | −11.0909 | −0.372397 | −0.186199 | − | 0.982512i | \(-0.559617\pi\) | ||||
−0.186199 | + | 0.982512i | \(0.559617\pi\) | |||||||
\(888\) | 23.1725 | 0.777619 | ||||||||
\(889\) | −19.2644 | −0.646108 | ||||||||
\(890\) | −3.88083 | −0.130086 | ||||||||
\(891\) | −11.4601 | −0.383926 | ||||||||
\(892\) | 2.02562 | 0.0678227 | ||||||||
\(893\) | −24.3124 | −0.813583 | ||||||||
\(894\) | 42.4410 | 1.41944 | ||||||||
\(895\) | 25.6021 | 0.855785 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 1.12098 | 0.0374285 | ||||||||
\(898\) | −31.4244 | −1.04864 | ||||||||
\(899\) | 1.75666 | 0.0585879 | ||||||||
\(900\) | −10.3180 | −0.343932 | ||||||||
\(901\) | 2.39945 | 0.0799372 | ||||||||
\(902\) | −8.76596 | −0.291875 | ||||||||
\(903\) | 31.7768 | 1.05746 | ||||||||
\(904\) | −4.14750 | −0.137944 | ||||||||
\(905\) | −1.25231 | −0.0416281 | ||||||||
\(906\) | 26.9732 | 0.896125 | ||||||||
\(907\) | 45.9040 | 1.52422 | 0.762109 | − | 0.647449i | \(-0.224164\pi\) | ||||
0.762109 | + | 0.647449i | \(0.224164\pi\) | |||||||
\(908\) | −4.94194 | −0.164004 | ||||||||
\(909\) | 44.9642 | 1.49137 | ||||||||
\(910\) | 0.374156 | 0.0124032 | ||||||||
\(911\) | −0.905177 | −0.0299898 | −0.0149949 | − | 0.999888i | \(-0.504773\pi\) | ||||
−0.0149949 | + | 0.999888i | \(0.504773\pi\) | |||||||
\(912\) | 7.15541 | 0.236939 | ||||||||
\(913\) | −0.904112 | −0.0299217 | ||||||||
\(914\) | 22.7966 | 0.754046 | ||||||||
\(915\) | 7.35850 | 0.243264 | ||||||||
\(916\) | −21.2745 | −0.702931 | ||||||||
\(917\) | −14.3216 | −0.472942 | ||||||||
\(918\) | 0.312783 | 0.0103234 | ||||||||
\(919\) | −14.8043 | −0.488350 | −0.244175 | − | 0.969731i | \(-0.578517\pi\) | ||||
−0.244175 | + | 0.969731i | \(0.578517\pi\) | |||||||
\(920\) | −2.12358 | −0.0700122 | ||||||||
\(921\) | −46.1313 | −1.52008 | ||||||||
\(922\) | −22.5292 | −0.741960 | ||||||||
\(923\) | 3.29475 | 0.108448 | ||||||||
\(924\) | −3.39290 | −0.111618 | ||||||||
\(925\) | 30.1534 | 0.991439 | ||||||||
\(926\) | −16.3115 | −0.536029 | ||||||||
\(927\) | 16.6038 | 0.545342 | ||||||||
\(928\) | −1.25930 | −0.0413385 | ||||||||
\(929\) | −26.8808 | −0.881930 | −0.440965 | − | 0.897524i | \(-0.645364\pi\) | ||||
−0.440965 | + | 0.897524i | \(0.645364\pi\) | |||||||
\(930\) | 4.60748 | 0.151085 | ||||||||
\(931\) | −2.87655 | −0.0942752 | ||||||||
\(932\) | 9.01899 | 0.295427 | ||||||||
\(933\) | 66.4880 | 2.17672 | ||||||||
\(934\) | −3.99673 | −0.130777 | ||||||||
\(935\) | −1.21375 | −0.0396938 | ||||||||
\(936\) | 0.898213 | 0.0293590 | ||||||||
\(937\) | −38.8813 | −1.27020 | −0.635098 | − | 0.772432i | \(-0.719040\pi\) | ||||
−0.635098 | + | 0.772432i | \(0.719040\pi\) | |||||||
\(938\) | −2.81723 | −0.0919859 | ||||||||
\(939\) | 66.4867 | 2.16971 | ||||||||
\(940\) | 11.2227 | 0.366044 | ||||||||
\(941\) | 40.3202 | 1.31440 | 0.657200 | − | 0.753716i | \(-0.271741\pi\) | ||||
0.657200 | + | 0.753716i | \(0.271741\pi\) | |||||||
\(942\) | −31.9566 | −1.04120 | ||||||||
\(943\) | 10.2782 | 0.334704 | ||||||||
\(944\) | 1.26320 | 0.0411137 | ||||||||
\(945\) | −0.619739 | −0.0201601 | ||||||||
\(946\) | −17.4244 | −0.566515 | ||||||||
\(947\) | −58.4984 | −1.90094 | −0.950471 | − | 0.310814i | \(-0.899398\pi\) | ||||
−0.950471 | + | 0.310814i | \(0.899398\pi\) | |||||||
\(948\) | 19.3240 | 0.627614 | ||||||||
\(949\) | 0.637022 | 0.0206786 | ||||||||
\(950\) | 9.31103 | 0.302090 | ||||||||
\(951\) | 8.98486 | 0.291354 | ||||||||
\(952\) | −0.670158 | −0.0217199 | ||||||||
\(953\) | 17.9630 | 0.581878 | 0.290939 | − | 0.956742i | \(-0.406032\pi\) | ||||
0.290939 | + | 0.956742i | \(0.406032\pi\) | |||||||
\(954\) | −11.4131 | −0.369512 | ||||||||
\(955\) | 26.9465 | 0.871967 | ||||||||
\(956\) | −5.91684 | −0.191364 | ||||||||
\(957\) | 4.27268 | 0.138116 | ||||||||
\(958\) | 33.3604 | 1.07783 | ||||||||
\(959\) | 18.3309 | 0.591936 | ||||||||
\(960\) | −3.30297 | −0.106603 | ||||||||
\(961\) | −29.0541 | −0.937229 | ||||||||
\(962\) | −2.62496 | −0.0846321 | ||||||||
\(963\) | −2.24271 | −0.0722704 | ||||||||
\(964\) | −8.37298 | −0.269675 | ||||||||
\(965\) | −24.4940 | −0.788490 | ||||||||
\(966\) | 3.97821 | 0.127997 | ||||||||
\(967\) | 7.26690 | 0.233688 | 0.116844 | − | 0.993150i | \(-0.462722\pi\) | ||||
0.116844 | + | 0.993150i | \(0.462722\pi\) | |||||||
\(968\) | −9.13955 | −0.293756 | ||||||||
\(969\) | −4.79525 | −0.154046 | ||||||||
\(970\) | 19.3235 | 0.620442 | ||||||||
\(971\) | −30.5015 | −0.978839 | −0.489420 | − | 0.872048i | \(-0.662791\pi\) | ||||
−0.489420 | + | 0.872048i | \(0.662791\pi\) | |||||||
\(972\) | 22.2999 | 0.715269 | ||||||||
\(973\) | −9.54684 | −0.306058 | ||||||||
\(974\) | 9.68933 | 0.310466 | ||||||||
\(975\) | 2.26881 | 0.0726602 | ||||||||
\(976\) | −2.22784 | −0.0713116 | ||||||||
\(977\) | −48.6210 | −1.55552 | −0.777761 | − | 0.628560i | \(-0.783645\pi\) | ||||
−0.777761 | + | 0.628560i | \(0.783645\pi\) | |||||||
\(978\) | −27.1295 | −0.867506 | ||||||||
\(979\) | −3.98650 | −0.127409 | ||||||||
\(980\) | 1.32783 | 0.0424159 | ||||||||
\(981\) | −30.7357 | −0.981317 | ||||||||
\(982\) | 23.5275 | 0.750793 | ||||||||
\(983\) | 8.05361 | 0.256870 | 0.128435 | − | 0.991718i | \(-0.459005\pi\) | ||||
0.128435 | + | 0.991718i | \(0.459005\pi\) | |||||||
\(984\) | 15.9865 | 0.509630 | ||||||||
\(985\) | 11.6115 | 0.369974 | ||||||||
\(986\) | 0.843929 | 0.0268762 | ||||||||
\(987\) | −21.0241 | −0.669205 | ||||||||
\(988\) | −0.810557 | −0.0257872 | ||||||||
\(989\) | 20.4302 | 0.649644 | ||||||||
\(990\) | 5.77324 | 0.183485 | ||||||||
\(991\) | −25.0665 | −0.796262 | −0.398131 | − | 0.917329i | \(-0.630341\pi\) | ||||
−0.398131 | + | 0.917329i | \(0.630341\pi\) | |||||||
\(992\) | −1.39495 | −0.0442897 | ||||||||
\(993\) | −14.4776 | −0.459431 | ||||||||
\(994\) | 11.6926 | 0.370867 | ||||||||
\(995\) | 34.4688 | 1.09274 | ||||||||
\(996\) | 1.64883 | 0.0522451 | ||||||||
\(997\) | −39.8864 | −1.26321 | −0.631607 | − | 0.775289i | \(-0.717604\pi\) | ||||
−0.631607 | + | 0.775289i | \(0.717604\pi\) | |||||||
\(998\) | −7.42227 | −0.234948 | ||||||||
\(999\) | 4.34788 | 0.137561 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6034.2.a.m.1.2 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.m.1.2 | ✓ | 21 | 1.1 | even | 1 | trivial |