Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} + \cdots + 1552 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.05100\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.05100 | −0.917235 | −0.458617 | − | 0.888634i | \(-0.651655\pi\) | ||||
−0.458617 | + | 0.888634i | \(0.651655\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 5.03739 | 1.90396 | 0.951978 | − | 0.306167i | \(-0.0990467\pi\) | ||||
0.951978 | + | 0.306167i | \(0.0990467\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.05100 | 0.648583 | ||||||||
\(11\) | 3.25636 | 0.981831 | 0.490915 | − | 0.871207i | \(-0.336662\pi\) | ||||
0.490915 | + | 0.871207i | \(0.336662\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −5.03739 | −1.34630 | ||||||||
\(15\) | 2.05100 | 0.529566 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.479851 | 0.116381 | 0.0581905 | − | 0.998305i | \(-0.481467\pi\) | ||||
0.0581905 | + | 0.998305i | \(0.481467\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.58203 | 1.28061 | 0.640303 | − | 0.768123i | \(-0.278809\pi\) | ||||
0.640303 | + | 0.768123i | \(0.278809\pi\) | |||||||
\(20\) | −2.05100 | −0.458617 | ||||||||
\(21\) | −5.03739 | −1.09925 | ||||||||
\(22\) | −3.25636 | −0.694259 | ||||||||
\(23\) | −6.13582 | −1.27941 | −0.639703 | − | 0.768622i | \(-0.720943\pi\) | ||||
−0.639703 | + | 0.768622i | \(0.720943\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −0.793401 | −0.158680 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 5.03739 | 0.951978 | ||||||||
\(29\) | 3.21614 | 0.597222 | 0.298611 | − | 0.954375i | \(-0.403477\pi\) | ||||
0.298611 | + | 0.954375i | \(0.403477\pi\) | |||||||
\(30\) | −2.05100 | −0.374460 | ||||||||
\(31\) | 8.30084 | 1.49087 | 0.745437 | − | 0.666576i | \(-0.232241\pi\) | ||||
0.745437 | + | 0.666576i | \(0.232241\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.25636 | −0.566860 | ||||||||
\(34\) | −0.479851 | −0.0822938 | ||||||||
\(35\) | −10.3317 | −1.74637 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.88622 | −0.638891 | −0.319445 | − | 0.947605i | \(-0.603497\pi\) | ||||
−0.319445 | + | 0.947605i | \(0.603497\pi\) | |||||||
\(38\) | −5.58203 | −0.905525 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 2.05100 | 0.324291 | ||||||||
\(41\) | 5.27024 | 0.823073 | 0.411536 | − | 0.911393i | \(-0.364992\pi\) | ||||
0.411536 | + | 0.911393i | \(0.364992\pi\) | |||||||
\(42\) | 5.03739 | 0.777287 | ||||||||
\(43\) | 3.12359 | 0.476343 | 0.238171 | − | 0.971223i | \(-0.423452\pi\) | ||||
0.238171 | + | 0.971223i | \(0.423452\pi\) | |||||||
\(44\) | 3.25636 | 0.490915 | ||||||||
\(45\) | −2.05100 | −0.305745 | ||||||||
\(46\) | 6.13582 | 0.904677 | ||||||||
\(47\) | 3.55585 | 0.518674 | 0.259337 | − | 0.965787i | \(-0.416496\pi\) | ||||
0.259337 | + | 0.965787i | \(0.416496\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 18.3753 | 2.62505 | ||||||||
\(50\) | 0.793401 | 0.112204 | ||||||||
\(51\) | −0.479851 | −0.0671926 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −6.76178 | −0.928802 | −0.464401 | − | 0.885625i | \(-0.653730\pi\) | ||||
−0.464401 | + | 0.885625i | \(0.653730\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −6.67880 | −0.900570 | ||||||||
\(56\) | −5.03739 | −0.673150 | ||||||||
\(57\) | −5.58203 | −0.739358 | ||||||||
\(58\) | −3.21614 | −0.422300 | ||||||||
\(59\) | 13.1023 | 1.70577 | 0.852887 | − | 0.522096i | \(-0.174850\pi\) | ||||
0.852887 | + | 0.522096i | \(0.174850\pi\) | |||||||
\(60\) | 2.05100 | 0.264783 | ||||||||
\(61\) | 6.84529 | 0.876450 | 0.438225 | − | 0.898865i | \(-0.355607\pi\) | ||||
0.438225 | + | 0.898865i | \(0.355607\pi\) | |||||||
\(62\) | −8.30084 | −1.05421 | ||||||||
\(63\) | 5.03739 | 0.634652 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.05100 | −0.254395 | ||||||||
\(66\) | 3.25636 | 0.400831 | ||||||||
\(67\) | −3.51638 | −0.429594 | −0.214797 | − | 0.976659i | \(-0.568909\pi\) | ||||
−0.214797 | + | 0.976659i | \(0.568909\pi\) | |||||||
\(68\) | 0.479851 | 0.0581905 | ||||||||
\(69\) | 6.13582 | 0.738666 | ||||||||
\(70\) | 10.3317 | 1.23487 | ||||||||
\(71\) | 0.616815 | 0.0732025 | 0.0366013 | − | 0.999330i | \(-0.488347\pi\) | ||||
0.0366013 | + | 0.999330i | \(0.488347\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 13.2386 | 1.54946 | 0.774731 | − | 0.632292i | \(-0.217885\pi\) | ||||
0.774731 | + | 0.632292i | \(0.217885\pi\) | |||||||
\(74\) | 3.88622 | 0.451764 | ||||||||
\(75\) | 0.793401 | 0.0916140 | ||||||||
\(76\) | 5.58203 | 0.640303 | ||||||||
\(77\) | 16.4036 | 1.86936 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 2.05078 | 0.230730 | 0.115365 | − | 0.993323i | \(-0.463196\pi\) | ||||
0.115365 | + | 0.993323i | \(0.463196\pi\) | |||||||
\(80\) | −2.05100 | −0.229309 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.27024 | −0.582000 | ||||||||
\(83\) | −2.18812 | −0.240178 | −0.120089 | − | 0.992763i | \(-0.538318\pi\) | ||||
−0.120089 | + | 0.992763i | \(0.538318\pi\) | |||||||
\(84\) | −5.03739 | −0.549625 | ||||||||
\(85\) | −0.984174 | −0.106749 | ||||||||
\(86\) | −3.12359 | −0.336825 | ||||||||
\(87\) | −3.21614 | −0.344806 | ||||||||
\(88\) | −3.25636 | −0.347130 | ||||||||
\(89\) | −3.35651 | −0.355789 | −0.177895 | − | 0.984050i | \(-0.556929\pi\) | ||||
−0.177895 | + | 0.984050i | \(0.556929\pi\) | |||||||
\(90\) | 2.05100 | 0.216194 | ||||||||
\(91\) | 5.03739 | 0.528062 | ||||||||
\(92\) | −6.13582 | −0.639703 | ||||||||
\(93\) | −8.30084 | −0.860757 | ||||||||
\(94\) | −3.55585 | −0.366758 | ||||||||
\(95\) | −11.4487 | −1.17462 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.04552 | −0.106156 | −0.0530780 | − | 0.998590i | \(-0.516903\pi\) | ||||
−0.0530780 | + | 0.998590i | \(0.516903\pi\) | |||||||
\(98\) | −18.3753 | −1.85619 | ||||||||
\(99\) | 3.25636 | 0.327277 | ||||||||
\(100\) | −0.793401 | −0.0793401 | ||||||||
\(101\) | 6.17717 | 0.614651 | 0.307326 | − | 0.951604i | \(-0.400566\pi\) | ||||
0.307326 | + | 0.951604i | \(0.400566\pi\) | |||||||
\(102\) | 0.479851 | 0.0475123 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 10.3317 | 1.00827 | ||||||||
\(106\) | 6.76178 | 0.656762 | ||||||||
\(107\) | −18.0835 | −1.74819 | −0.874097 | − | 0.485752i | \(-0.838546\pi\) | ||||
−0.874097 | + | 0.485752i | \(0.838546\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −1.59970 | −0.153224 | −0.0766120 | − | 0.997061i | \(-0.524410\pi\) | ||||
−0.0766120 | + | 0.997061i | \(0.524410\pi\) | |||||||
\(110\) | 6.67880 | 0.636799 | ||||||||
\(111\) | 3.88622 | 0.368864 | ||||||||
\(112\) | 5.03739 | 0.475989 | ||||||||
\(113\) | 2.73914 | 0.257676 | 0.128838 | − | 0.991666i | \(-0.458875\pi\) | ||||
0.128838 | + | 0.991666i | \(0.458875\pi\) | |||||||
\(114\) | 5.58203 | 0.522805 | ||||||||
\(115\) | 12.5846 | 1.17352 | ||||||||
\(116\) | 3.21614 | 0.298611 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −13.1023 | −1.20616 | ||||||||
\(119\) | 2.41720 | 0.221584 | ||||||||
\(120\) | −2.05100 | −0.187230 | ||||||||
\(121\) | −0.396088 | −0.0360080 | ||||||||
\(122\) | −6.84529 | −0.619744 | ||||||||
\(123\) | −5.27024 | −0.475201 | ||||||||
\(124\) | 8.30084 | 0.745437 | ||||||||
\(125\) | 11.8823 | 1.06278 | ||||||||
\(126\) | −5.03739 | −0.448767 | ||||||||
\(127\) | −11.9402 | −1.05952 | −0.529762 | − | 0.848146i | \(-0.677719\pi\) | ||||
−0.529762 | + | 0.848146i | \(0.677719\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.12359 | −0.275017 | ||||||||
\(130\) | 2.05100 | 0.179885 | ||||||||
\(131\) | 3.36895 | 0.294347 | 0.147173 | − | 0.989111i | \(-0.452982\pi\) | ||||
0.147173 | + | 0.989111i | \(0.452982\pi\) | |||||||
\(132\) | −3.25636 | −0.283430 | ||||||||
\(133\) | 28.1189 | 2.43822 | ||||||||
\(134\) | 3.51638 | 0.303769 | ||||||||
\(135\) | 2.05100 | 0.176522 | ||||||||
\(136\) | −0.479851 | −0.0411469 | ||||||||
\(137\) | −1.91274 | −0.163416 | −0.0817082 | − | 0.996656i | \(-0.526038\pi\) | ||||
−0.0817082 | + | 0.996656i | \(0.526038\pi\) | |||||||
\(138\) | −6.13582 | −0.522315 | ||||||||
\(139\) | −20.1841 | −1.71199 | −0.855996 | − | 0.516983i | \(-0.827055\pi\) | ||||
−0.855996 | + | 0.516983i | \(0.827055\pi\) | |||||||
\(140\) | −10.3317 | −0.873187 | ||||||||
\(141\) | −3.55585 | −0.299457 | ||||||||
\(142\) | −0.616815 | −0.0517620 | ||||||||
\(143\) | 3.25636 | 0.272311 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.59630 | −0.547793 | ||||||||
\(146\) | −13.2386 | −1.09563 | ||||||||
\(147\) | −18.3753 | −1.51557 | ||||||||
\(148\) | −3.88622 | −0.319445 | ||||||||
\(149\) | −0.778189 | −0.0637517 | −0.0318759 | − | 0.999492i | \(-0.510148\pi\) | ||||
−0.0318759 | + | 0.999492i | \(0.510148\pi\) | |||||||
\(150\) | −0.793401 | −0.0647809 | ||||||||
\(151\) | 20.3436 | 1.65554 | 0.827771 | − | 0.561066i | \(-0.189608\pi\) | ||||
0.827771 | + | 0.561066i | \(0.189608\pi\) | |||||||
\(152\) | −5.58203 | −0.452763 | ||||||||
\(153\) | 0.479851 | 0.0387937 | ||||||||
\(154\) | −16.4036 | −1.32184 | ||||||||
\(155\) | −17.0250 | −1.36748 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −21.3836 | −1.70660 | −0.853300 | − | 0.521420i | \(-0.825403\pi\) | ||||
−0.853300 | + | 0.521420i | \(0.825403\pi\) | |||||||
\(158\) | −2.05078 | −0.163151 | ||||||||
\(159\) | 6.76178 | 0.536244 | ||||||||
\(160\) | 2.05100 | 0.162146 | ||||||||
\(161\) | −30.9085 | −2.43593 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −14.8949 | −1.16666 | −0.583328 | − | 0.812236i | \(-0.698250\pi\) | ||||
−0.583328 | + | 0.812236i | \(0.698250\pi\) | |||||||
\(164\) | 5.27024 | 0.411536 | ||||||||
\(165\) | 6.67880 | 0.519944 | ||||||||
\(166\) | 2.18812 | 0.169831 | ||||||||
\(167\) | 6.70885 | 0.519146 | 0.259573 | − | 0.965723i | \(-0.416418\pi\) | ||||
0.259573 | + | 0.965723i | \(0.416418\pi\) | |||||||
\(168\) | 5.03739 | 0.388643 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.984174 | 0.0754827 | ||||||||
\(171\) | 5.58203 | 0.426869 | ||||||||
\(172\) | 3.12359 | 0.238171 | ||||||||
\(173\) | −14.8394 | −1.12822 | −0.564110 | − | 0.825699i | \(-0.690781\pi\) | ||||
−0.564110 | + | 0.825699i | \(0.690781\pi\) | |||||||
\(174\) | 3.21614 | 0.243815 | ||||||||
\(175\) | −3.99667 | −0.302120 | ||||||||
\(176\) | 3.25636 | 0.245458 | ||||||||
\(177\) | −13.1023 | −0.984829 | ||||||||
\(178\) | 3.35651 | 0.251581 | ||||||||
\(179\) | 8.75510 | 0.654387 | 0.327193 | − | 0.944957i | \(-0.393897\pi\) | ||||
0.327193 | + | 0.944957i | \(0.393897\pi\) | |||||||
\(180\) | −2.05100 | −0.152872 | ||||||||
\(181\) | 26.8429 | 1.99522 | 0.997610 | − | 0.0691034i | \(-0.0220138\pi\) | ||||
0.997610 | + | 0.0691034i | \(0.0220138\pi\) | |||||||
\(182\) | −5.03739 | −0.373396 | ||||||||
\(183\) | −6.84529 | −0.506019 | ||||||||
\(184\) | 6.13582 | 0.452338 | ||||||||
\(185\) | 7.97064 | 0.586013 | ||||||||
\(186\) | 8.30084 | 0.608647 | ||||||||
\(187\) | 1.56257 | 0.114266 | ||||||||
\(188\) | 3.55585 | 0.259337 | ||||||||
\(189\) | −5.03739 | −0.366416 | ||||||||
\(190\) | 11.4487 | 0.830579 | ||||||||
\(191\) | −18.2739 | −1.32225 | −0.661125 | − | 0.750275i | \(-0.729921\pi\) | ||||
−0.661125 | + | 0.750275i | \(0.729921\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 9.22242 | 0.663844 | 0.331922 | − | 0.943307i | \(-0.392303\pi\) | ||||
0.331922 | + | 0.943307i | \(0.392303\pi\) | |||||||
\(194\) | 1.04552 | 0.0750637 | ||||||||
\(195\) | 2.05100 | 0.146875 | ||||||||
\(196\) | 18.3753 | 1.31252 | ||||||||
\(197\) | 21.2145 | 1.51147 | 0.755734 | − | 0.654878i | \(-0.227280\pi\) | ||||
0.755734 | + | 0.654878i | \(0.227280\pi\) | |||||||
\(198\) | −3.25636 | −0.231420 | ||||||||
\(199\) | −21.4058 | −1.51742 | −0.758708 | − | 0.651431i | \(-0.774169\pi\) | ||||
−0.758708 | + | 0.651431i | \(0.774169\pi\) | |||||||
\(200\) | 0.793401 | 0.0561019 | ||||||||
\(201\) | 3.51638 | 0.248026 | ||||||||
\(202\) | −6.17717 | −0.434624 | ||||||||
\(203\) | 16.2009 | 1.13708 | ||||||||
\(204\) | −0.479851 | −0.0335963 | ||||||||
\(205\) | −10.8093 | −0.754951 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −6.13582 | −0.426469 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 18.1771 | 1.25734 | ||||||||
\(210\) | −10.3317 | −0.712954 | ||||||||
\(211\) | 3.59640 | 0.247586 | 0.123793 | − | 0.992308i | \(-0.460494\pi\) | ||||
0.123793 | + | 0.992308i | \(0.460494\pi\) | |||||||
\(212\) | −6.76178 | −0.464401 | ||||||||
\(213\) | −0.616815 | −0.0422635 | ||||||||
\(214\) | 18.0835 | 1.23616 | ||||||||
\(215\) | −6.40648 | −0.436918 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 41.8146 | 2.83856 | ||||||||
\(218\) | 1.59970 | 0.108346 | ||||||||
\(219\) | −13.2386 | −0.894582 | ||||||||
\(220\) | −6.67880 | −0.450285 | ||||||||
\(221\) | 0.479851 | 0.0322783 | ||||||||
\(222\) | −3.88622 | −0.260826 | ||||||||
\(223\) | −27.5119 | −1.84233 | −0.921167 | − | 0.389168i | \(-0.872763\pi\) | ||||
−0.921167 | + | 0.389168i | \(0.872763\pi\) | |||||||
\(224\) | −5.03739 | −0.336575 | ||||||||
\(225\) | −0.793401 | −0.0528934 | ||||||||
\(226\) | −2.73914 | −0.182205 | ||||||||
\(227\) | 0.778045 | 0.0516407 | 0.0258203 | − | 0.999667i | \(-0.491780\pi\) | ||||
0.0258203 | + | 0.999667i | \(0.491780\pi\) | |||||||
\(228\) | −5.58203 | −0.369679 | ||||||||
\(229\) | 8.61245 | 0.569126 | 0.284563 | − | 0.958657i | \(-0.408151\pi\) | ||||
0.284563 | + | 0.958657i | \(0.408151\pi\) | |||||||
\(230\) | −12.5846 | −0.829801 | ||||||||
\(231\) | −16.4036 | −1.07928 | ||||||||
\(232\) | −3.21614 | −0.211150 | ||||||||
\(233\) | −18.5994 | −1.21849 | −0.609243 | − | 0.792984i | \(-0.708527\pi\) | ||||
−0.609243 | + | 0.792984i | \(0.708527\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −7.29305 | −0.475746 | ||||||||
\(236\) | 13.1023 | 0.852887 | ||||||||
\(237\) | −2.05078 | −0.133212 | ||||||||
\(238\) | −2.41720 | −0.156684 | ||||||||
\(239\) | 6.01961 | 0.389376 | 0.194688 | − | 0.980865i | \(-0.437631\pi\) | ||||
0.194688 | + | 0.980865i | \(0.437631\pi\) | |||||||
\(240\) | 2.05100 | 0.132391 | ||||||||
\(241\) | 8.74673 | 0.563426 | 0.281713 | − | 0.959499i | \(-0.409097\pi\) | ||||
0.281713 | + | 0.959499i | \(0.409097\pi\) | |||||||
\(242\) | 0.396088 | 0.0254615 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.84529 | 0.438225 | ||||||||
\(245\) | −37.6878 | −2.40778 | ||||||||
\(246\) | 5.27024 | 0.336018 | ||||||||
\(247\) | 5.58203 | 0.355176 | ||||||||
\(248\) | −8.30084 | −0.527104 | ||||||||
\(249\) | 2.18812 | 0.138667 | ||||||||
\(250\) | −11.8823 | −0.751500 | ||||||||
\(251\) | −2.31076 | −0.145854 | −0.0729268 | − | 0.997337i | \(-0.523234\pi\) | ||||
−0.0729268 | + | 0.997337i | \(0.523234\pi\) | |||||||
\(252\) | 5.03739 | 0.317326 | ||||||||
\(253\) | −19.9805 | −1.25616 | ||||||||
\(254\) | 11.9402 | 0.749197 | ||||||||
\(255\) | 0.984174 | 0.0616314 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −30.3838 | −1.89529 | −0.947645 | − | 0.319326i | \(-0.896544\pi\) | ||||
−0.947645 | + | 0.319326i | \(0.896544\pi\) | |||||||
\(258\) | 3.12359 | 0.194466 | ||||||||
\(259\) | −19.5764 | −1.21642 | ||||||||
\(260\) | −2.05100 | −0.127198 | ||||||||
\(261\) | 3.21614 | 0.199074 | ||||||||
\(262\) | −3.36895 | −0.208135 | ||||||||
\(263\) | 15.0290 | 0.926730 | 0.463365 | − | 0.886168i | \(-0.346642\pi\) | ||||
0.463365 | + | 0.886168i | \(0.346642\pi\) | |||||||
\(264\) | 3.25636 | 0.200415 | ||||||||
\(265\) | 13.8684 | 0.851929 | ||||||||
\(266\) | −28.1189 | −1.72408 | ||||||||
\(267\) | 3.35651 | 0.205415 | ||||||||
\(268\) | −3.51638 | −0.214797 | ||||||||
\(269\) | −19.3049 | −1.17704 | −0.588519 | − | 0.808483i | \(-0.700289\pi\) | ||||
−0.588519 | + | 0.808483i | \(0.700289\pi\) | |||||||
\(270\) | −2.05100 | −0.124820 | ||||||||
\(271\) | 5.46064 | 0.331710 | 0.165855 | − | 0.986150i | \(-0.446962\pi\) | ||||
0.165855 | + | 0.986150i | \(0.446962\pi\) | |||||||
\(272\) | 0.479851 | 0.0290952 | ||||||||
\(273\) | −5.03739 | −0.304877 | ||||||||
\(274\) | 1.91274 | 0.115553 | ||||||||
\(275\) | −2.58360 | −0.155797 | ||||||||
\(276\) | 6.13582 | 0.369333 | ||||||||
\(277\) | −18.3298 | −1.10133 | −0.550665 | − | 0.834726i | \(-0.685626\pi\) | ||||
−0.550665 | + | 0.834726i | \(0.685626\pi\) | |||||||
\(278\) | 20.1841 | 1.21056 | ||||||||
\(279\) | 8.30084 | 0.496958 | ||||||||
\(280\) | 10.3317 | 0.617437 | ||||||||
\(281\) | 7.86816 | 0.469375 | 0.234688 | − | 0.972071i | \(-0.424593\pi\) | ||||
0.234688 | + | 0.972071i | \(0.424593\pi\) | |||||||
\(282\) | 3.55585 | 0.211748 | ||||||||
\(283\) | 14.4497 | 0.858943 | 0.429472 | − | 0.903080i | \(-0.358700\pi\) | ||||
0.429472 | + | 0.903080i | \(0.358700\pi\) | |||||||
\(284\) | 0.616815 | 0.0366013 | ||||||||
\(285\) | 11.4487 | 0.678165 | ||||||||
\(286\) | −3.25636 | −0.192553 | ||||||||
\(287\) | 26.5483 | 1.56709 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.7697 | −0.986455 | ||||||||
\(290\) | 6.59630 | 0.387348 | ||||||||
\(291\) | 1.04552 | 0.0612892 | ||||||||
\(292\) | 13.2386 | 0.774731 | ||||||||
\(293\) | 7.67257 | 0.448236 | 0.224118 | − | 0.974562i | \(-0.428050\pi\) | ||||
0.224118 | + | 0.974562i | \(0.428050\pi\) | |||||||
\(294\) | 18.3753 | 1.07167 | ||||||||
\(295\) | −26.8728 | −1.56460 | ||||||||
\(296\) | 3.88622 | 0.225882 | ||||||||
\(297\) | −3.25636 | −0.188953 | ||||||||
\(298\) | 0.778189 | 0.0450793 | ||||||||
\(299\) | −6.13582 | −0.354843 | ||||||||
\(300\) | 0.793401 | 0.0458070 | ||||||||
\(301\) | 15.7347 | 0.906936 | ||||||||
\(302\) | −20.3436 | −1.17065 | ||||||||
\(303\) | −6.17717 | −0.354869 | ||||||||
\(304\) | 5.58203 | 0.320151 | ||||||||
\(305\) | −14.0397 | −0.803910 | ||||||||
\(306\) | −0.479851 | −0.0274313 | ||||||||
\(307\) | 8.31383 | 0.474495 | 0.237248 | − | 0.971449i | \(-0.423755\pi\) | ||||
0.237248 | + | 0.971449i | \(0.423755\pi\) | |||||||
\(308\) | 16.4036 | 0.934681 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 17.0250 | 0.966956 | ||||||||
\(311\) | −18.2570 | −1.03526 | −0.517630 | − | 0.855605i | \(-0.673186\pi\) | ||||
−0.517630 | + | 0.855605i | \(0.673186\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 28.5611 | 1.61437 | 0.807186 | − | 0.590298i | \(-0.200990\pi\) | ||||
0.807186 | + | 0.590298i | \(0.200990\pi\) | |||||||
\(314\) | 21.3836 | 1.20675 | ||||||||
\(315\) | −10.3317 | −0.582125 | ||||||||
\(316\) | 2.05078 | 0.115365 | ||||||||
\(317\) | 18.8153 | 1.05677 | 0.528387 | − | 0.849004i | \(-0.322797\pi\) | ||||
0.528387 | + | 0.849004i | \(0.322797\pi\) | |||||||
\(318\) | −6.76178 | −0.379182 | ||||||||
\(319\) | 10.4729 | 0.586371 | ||||||||
\(320\) | −2.05100 | −0.114654 | ||||||||
\(321\) | 18.0835 | 1.00932 | ||||||||
\(322\) | 30.9085 | 1.72246 | ||||||||
\(323\) | 2.67854 | 0.149038 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.793401 | −0.0440100 | ||||||||
\(326\) | 14.8949 | 0.824951 | ||||||||
\(327\) | 1.59970 | 0.0884639 | ||||||||
\(328\) | −5.27024 | −0.291000 | ||||||||
\(329\) | 17.9122 | 0.987533 | ||||||||
\(330\) | −6.67880 | −0.367656 | ||||||||
\(331\) | −23.2918 | −1.28023 | −0.640115 | − | 0.768279i | \(-0.721113\pi\) | ||||
−0.640115 | + | 0.768279i | \(0.721113\pi\) | |||||||
\(332\) | −2.18812 | −0.120089 | ||||||||
\(333\) | −3.88622 | −0.212964 | ||||||||
\(334\) | −6.70885 | −0.367092 | ||||||||
\(335\) | 7.21210 | 0.394039 | ||||||||
\(336\) | −5.03739 | −0.274812 | ||||||||
\(337\) | 31.2626 | 1.70298 | 0.851490 | − | 0.524371i | \(-0.175699\pi\) | ||||
0.851490 | + | 0.524371i | \(0.175699\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −2.73914 | −0.148769 | ||||||||
\(340\) | −0.984174 | −0.0533743 | ||||||||
\(341\) | 27.0305 | 1.46379 | ||||||||
\(342\) | −5.58203 | −0.301842 | ||||||||
\(343\) | 57.3020 | 3.09401 | ||||||||
\(344\) | −3.12359 | −0.168413 | ||||||||
\(345\) | −12.5846 | −0.677530 | ||||||||
\(346\) | 14.8394 | 0.797772 | ||||||||
\(347\) | −26.8471 | −1.44123 | −0.720613 | − | 0.693338i | \(-0.756139\pi\) | ||||
−0.720613 | + | 0.693338i | \(0.756139\pi\) | |||||||
\(348\) | −3.21614 | −0.172403 | ||||||||
\(349\) | 8.81086 | 0.471635 | 0.235817 | − | 0.971797i | \(-0.424223\pi\) | ||||
0.235817 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(350\) | 3.99667 | 0.213631 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −3.25636 | −0.173565 | ||||||||
\(353\) | −18.6641 | −0.993392 | −0.496696 | − | 0.867925i | \(-0.665454\pi\) | ||||
−0.496696 | + | 0.867925i | \(0.665454\pi\) | |||||||
\(354\) | 13.1023 | 0.696379 | ||||||||
\(355\) | −1.26509 | −0.0671439 | ||||||||
\(356\) | −3.35651 | −0.177895 | ||||||||
\(357\) | −2.41720 | −0.127932 | ||||||||
\(358\) | −8.75510 | −0.462721 | ||||||||
\(359\) | 34.4613 | 1.81880 | 0.909398 | − | 0.415926i | \(-0.136543\pi\) | ||||
0.909398 | + | 0.415926i | \(0.136543\pi\) | |||||||
\(360\) | 2.05100 | 0.108097 | ||||||||
\(361\) | 12.1591 | 0.639951 | ||||||||
\(362\) | −26.8429 | −1.41083 | ||||||||
\(363\) | 0.396088 | 0.0207892 | ||||||||
\(364\) | 5.03739 | 0.264031 | ||||||||
\(365\) | −27.1524 | −1.42122 | ||||||||
\(366\) | 6.84529 | 0.357809 | ||||||||
\(367\) | 34.7488 | 1.81387 | 0.906936 | − | 0.421268i | \(-0.138415\pi\) | ||||
0.906936 | + | 0.421268i | \(0.138415\pi\) | |||||||
\(368\) | −6.13582 | −0.319852 | ||||||||
\(369\) | 5.27024 | 0.274358 | ||||||||
\(370\) | −7.97064 | −0.414374 | ||||||||
\(371\) | −34.0617 | −1.76840 | ||||||||
\(372\) | −8.30084 | −0.430378 | ||||||||
\(373\) | 16.4025 | 0.849291 | 0.424645 | − | 0.905360i | \(-0.360399\pi\) | ||||
0.424645 | + | 0.905360i | \(0.360399\pi\) | |||||||
\(374\) | −1.56257 | −0.0807986 | ||||||||
\(375\) | −11.8823 | −0.613597 | ||||||||
\(376\) | −3.55585 | −0.183379 | ||||||||
\(377\) | 3.21614 | 0.165640 | ||||||||
\(378\) | 5.03739 | 0.259096 | ||||||||
\(379\) | −21.1040 | −1.08404 | −0.542019 | − | 0.840366i | \(-0.682340\pi\) | ||||
−0.542019 | + | 0.840366i | \(0.682340\pi\) | |||||||
\(380\) | −11.4487 | −0.587308 | ||||||||
\(381\) | 11.9402 | 0.611717 | ||||||||
\(382\) | 18.2739 | 0.934973 | ||||||||
\(383\) | 26.8489 | 1.37191 | 0.685957 | − | 0.727642i | \(-0.259384\pi\) | ||||
0.685957 | + | 0.727642i | \(0.259384\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −33.6437 | −1.71464 | ||||||||
\(386\) | −9.22242 | −0.469409 | ||||||||
\(387\) | 3.12359 | 0.158781 | ||||||||
\(388\) | −1.04552 | −0.0530780 | ||||||||
\(389\) | 0.453851 | 0.0230111 | 0.0115056 | − | 0.999934i | \(-0.496338\pi\) | ||||
0.0115056 | + | 0.999934i | \(0.496338\pi\) | |||||||
\(390\) | −2.05100 | −0.103856 | ||||||||
\(391\) | −2.94428 | −0.148899 | ||||||||
\(392\) | −18.3753 | −0.928094 | ||||||||
\(393\) | −3.36895 | −0.169941 | ||||||||
\(394\) | −21.2145 | −1.06877 | ||||||||
\(395\) | −4.20614 | −0.211634 | ||||||||
\(396\) | 3.25636 | 0.163638 | ||||||||
\(397\) | −10.5105 | −0.527507 | −0.263754 | − | 0.964590i | \(-0.584961\pi\) | ||||
−0.263754 | + | 0.964590i | \(0.584961\pi\) | |||||||
\(398\) | 21.4058 | 1.07298 | ||||||||
\(399\) | −28.1189 | −1.40770 | ||||||||
\(400\) | −0.793401 | −0.0396700 | ||||||||
\(401\) | 19.8785 | 0.992685 | 0.496342 | − | 0.868127i | \(-0.334676\pi\) | ||||
0.496342 | + | 0.868127i | \(0.334676\pi\) | |||||||
\(402\) | −3.51638 | −0.175381 | ||||||||
\(403\) | 8.30084 | 0.413494 | ||||||||
\(404\) | 6.17717 | 0.307326 | ||||||||
\(405\) | −2.05100 | −0.101915 | ||||||||
\(406\) | −16.2009 | −0.804040 | ||||||||
\(407\) | −12.6550 | −0.627283 | ||||||||
\(408\) | 0.479851 | 0.0237562 | ||||||||
\(409\) | −11.4709 | −0.567198 | −0.283599 | − | 0.958943i | \(-0.591528\pi\) | ||||
−0.283599 | + | 0.958943i | \(0.591528\pi\) | |||||||
\(410\) | 10.8093 | 0.533831 | ||||||||
\(411\) | 1.91274 | 0.0943485 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 66.0014 | 3.24772 | ||||||||
\(414\) | 6.13582 | 0.301559 | ||||||||
\(415\) | 4.48784 | 0.220300 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 20.1841 | 0.988419 | ||||||||
\(418\) | −18.1771 | −0.889072 | ||||||||
\(419\) | −34.7936 | −1.69978 | −0.849889 | − | 0.526961i | \(-0.823331\pi\) | ||||
−0.849889 | + | 0.526961i | \(0.823331\pi\) | |||||||
\(420\) | 10.3317 | 0.504135 | ||||||||
\(421\) | −6.18218 | −0.301301 | −0.150650 | − | 0.988587i | \(-0.548137\pi\) | ||||
−0.150650 | + | 0.988587i | \(0.548137\pi\) | |||||||
\(422\) | −3.59640 | −0.175070 | ||||||||
\(423\) | 3.55585 | 0.172891 | ||||||||
\(424\) | 6.76178 | 0.328381 | ||||||||
\(425\) | −0.380714 | −0.0184674 | ||||||||
\(426\) | 0.616815 | 0.0298848 | ||||||||
\(427\) | 34.4824 | 1.66872 | ||||||||
\(428\) | −18.0835 | −0.874097 | ||||||||
\(429\) | −3.25636 | −0.157219 | ||||||||
\(430\) | 6.40648 | 0.308948 | ||||||||
\(431\) | 2.84511 | 0.137044 | 0.0685220 | − | 0.997650i | \(-0.478172\pi\) | ||||
0.0685220 | + | 0.997650i | \(0.478172\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −5.12180 | −0.246138 | −0.123069 | − | 0.992398i | \(-0.539274\pi\) | ||||
−0.123069 | + | 0.992398i | \(0.539274\pi\) | |||||||
\(434\) | −41.8146 | −2.00716 | ||||||||
\(435\) | 6.59630 | 0.316268 | ||||||||
\(436\) | −1.59970 | −0.0766120 | ||||||||
\(437\) | −34.2503 | −1.63842 | ||||||||
\(438\) | 13.2386 | 0.632565 | ||||||||
\(439\) | −8.67259 | −0.413920 | −0.206960 | − | 0.978349i | \(-0.566357\pi\) | ||||
−0.206960 | + | 0.978349i | \(0.566357\pi\) | |||||||
\(440\) | 6.67880 | 0.318399 | ||||||||
\(441\) | 18.3753 | 0.875015 | ||||||||
\(442\) | −0.479851 | −0.0228242 | ||||||||
\(443\) | −5.13670 | −0.244052 | −0.122026 | − | 0.992527i | \(-0.538939\pi\) | ||||
−0.122026 | + | 0.992527i | \(0.538939\pi\) | |||||||
\(444\) | 3.88622 | 0.184432 | ||||||||
\(445\) | 6.88420 | 0.326342 | ||||||||
\(446\) | 27.5119 | 1.30273 | ||||||||
\(447\) | 0.778189 | 0.0368071 | ||||||||
\(448\) | 5.03739 | 0.237994 | ||||||||
\(449\) | 0.593133 | 0.0279917 | 0.0139958 | − | 0.999902i | \(-0.495545\pi\) | ||||
0.0139958 | + | 0.999902i | \(0.495545\pi\) | |||||||
\(450\) | 0.793401 | 0.0374013 | ||||||||
\(451\) | 17.1618 | 0.808118 | ||||||||
\(452\) | 2.73914 | 0.128838 | ||||||||
\(453\) | −20.3436 | −0.955828 | ||||||||
\(454\) | −0.778045 | −0.0365155 | ||||||||
\(455\) | −10.3317 | −0.484357 | ||||||||
\(456\) | 5.58203 | 0.261403 | ||||||||
\(457\) | −21.1234 | −0.988113 | −0.494056 | − | 0.869430i | \(-0.664486\pi\) | ||||
−0.494056 | + | 0.869430i | \(0.664486\pi\) | |||||||
\(458\) | −8.61245 | −0.402433 | ||||||||
\(459\) | −0.479851 | −0.0223975 | ||||||||
\(460\) | 12.5846 | 0.586758 | ||||||||
\(461\) | 21.7463 | 1.01283 | 0.506413 | − | 0.862291i | \(-0.330971\pi\) | ||||
0.506413 | + | 0.862291i | \(0.330971\pi\) | |||||||
\(462\) | 16.4036 | 0.763164 | ||||||||
\(463\) | 31.9048 | 1.48274 | 0.741371 | − | 0.671096i | \(-0.234176\pi\) | ||||
0.741371 | + | 0.671096i | \(0.234176\pi\) | |||||||
\(464\) | 3.21614 | 0.149305 | ||||||||
\(465\) | 17.0250 | 0.789516 | ||||||||
\(466\) | 18.5994 | 0.861599 | ||||||||
\(467\) | 0.266545 | 0.0123342 | 0.00616711 | − | 0.999981i | \(-0.498037\pi\) | ||||
0.00616711 | + | 0.999981i | \(0.498037\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −17.7134 | −0.817929 | ||||||||
\(470\) | 7.29305 | 0.336403 | ||||||||
\(471\) | 21.3836 | 0.985306 | ||||||||
\(472\) | −13.1023 | −0.603082 | ||||||||
\(473\) | 10.1715 | 0.467688 | ||||||||
\(474\) | 2.05078 | 0.0941952 | ||||||||
\(475\) | −4.42879 | −0.203207 | ||||||||
\(476\) | 2.41720 | 0.110792 | ||||||||
\(477\) | −6.76178 | −0.309601 | ||||||||
\(478\) | −6.01961 | −0.275331 | ||||||||
\(479\) | −21.6179 | −0.987748 | −0.493874 | − | 0.869533i | \(-0.664420\pi\) | ||||
−0.493874 | + | 0.869533i | \(0.664420\pi\) | |||||||
\(480\) | −2.05100 | −0.0936149 | ||||||||
\(481\) | −3.88622 | −0.177196 | ||||||||
\(482\) | −8.74673 | −0.398403 | ||||||||
\(483\) | 30.9085 | 1.40639 | ||||||||
\(484\) | −0.396088 | −0.0180040 | ||||||||
\(485\) | 2.14435 | 0.0973701 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −15.2920 | −0.692946 | −0.346473 | − | 0.938060i | \(-0.612621\pi\) | ||||
−0.346473 | + | 0.938060i | \(0.612621\pi\) | |||||||
\(488\) | −6.84529 | −0.309872 | ||||||||
\(489\) | 14.8949 | 0.673570 | ||||||||
\(490\) | 37.6878 | 1.70256 | ||||||||
\(491\) | 29.3696 | 1.32543 | 0.662715 | − | 0.748871i | \(-0.269404\pi\) | ||||
0.662715 | + | 0.748871i | \(0.269404\pi\) | |||||||
\(492\) | −5.27024 | −0.237601 | ||||||||
\(493\) | 1.54327 | 0.0695053 | ||||||||
\(494\) | −5.58203 | −0.251147 | ||||||||
\(495\) | −6.67880 | −0.300190 | ||||||||
\(496\) | 8.30084 | 0.372719 | ||||||||
\(497\) | 3.10714 | 0.139374 | ||||||||
\(498\) | −2.18812 | −0.0980522 | ||||||||
\(499\) | 19.4220 | 0.869450 | 0.434725 | − | 0.900563i | \(-0.356846\pi\) | ||||
0.434725 | + | 0.900563i | \(0.356846\pi\) | |||||||
\(500\) | 11.8823 | 0.531391 | ||||||||
\(501\) | −6.70885 | −0.299729 | ||||||||
\(502\) | 2.31076 | 0.103134 | ||||||||
\(503\) | 12.2856 | 0.547789 | 0.273895 | − | 0.961760i | \(-0.411688\pi\) | ||||
0.273895 | + | 0.961760i | \(0.411688\pi\) | |||||||
\(504\) | −5.03739 | −0.224383 | ||||||||
\(505\) | −12.6694 | −0.563780 | ||||||||
\(506\) | 19.9805 | 0.888240 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −11.9402 | −0.529762 | ||||||||
\(509\) | −3.08185 | −0.136600 | −0.0683002 | − | 0.997665i | \(-0.521758\pi\) | ||||
−0.0683002 | + | 0.997665i | \(0.521758\pi\) | |||||||
\(510\) | −0.984174 | −0.0435800 | ||||||||
\(511\) | 66.6880 | 2.95010 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.58203 | −0.246453 | ||||||||
\(514\) | 30.3838 | 1.34017 | ||||||||
\(515\) | 2.05100 | 0.0903778 | ||||||||
\(516\) | −3.12359 | −0.137508 | ||||||||
\(517\) | 11.5792 | 0.509250 | ||||||||
\(518\) | 19.5764 | 0.860139 | ||||||||
\(519\) | 14.8394 | 0.651378 | ||||||||
\(520\) | 2.05100 | 0.0899423 | ||||||||
\(521\) | 13.3801 | 0.586191 | 0.293096 | − | 0.956083i | \(-0.405315\pi\) | ||||
0.293096 | + | 0.956083i | \(0.405315\pi\) | |||||||
\(522\) | −3.21614 | −0.140767 | ||||||||
\(523\) | −42.4084 | −1.85439 | −0.927194 | − | 0.374581i | \(-0.877787\pi\) | ||||
−0.927194 | + | 0.374581i | \(0.877787\pi\) | |||||||
\(524\) | 3.36895 | 0.147173 | ||||||||
\(525\) | 3.99667 | 0.174429 | ||||||||
\(526\) | −15.0290 | −0.655297 | ||||||||
\(527\) | 3.98316 | 0.173509 | ||||||||
\(528\) | −3.25636 | −0.141715 | ||||||||
\(529\) | 14.6483 | 0.636881 | ||||||||
\(530\) | −13.8684 | −0.602405 | ||||||||
\(531\) | 13.1023 | 0.568591 | ||||||||
\(532\) | 28.1189 | 1.21911 | ||||||||
\(533\) | 5.27024 | 0.228279 | ||||||||
\(534\) | −3.35651 | −0.145250 | ||||||||
\(535\) | 37.0891 | 1.60350 | ||||||||
\(536\) | 3.51638 | 0.151885 | ||||||||
\(537\) | −8.75510 | −0.377810 | ||||||||
\(538\) | 19.3049 | 0.832292 | ||||||||
\(539\) | 59.8368 | 2.57735 | ||||||||
\(540\) | 2.05100 | 0.0882610 | ||||||||
\(541\) | 8.14551 | 0.350203 | 0.175101 | − | 0.984550i | \(-0.443975\pi\) | ||||
0.175101 | + | 0.984550i | \(0.443975\pi\) | |||||||
\(542\) | −5.46064 | −0.234555 | ||||||||
\(543\) | −26.8429 | −1.15194 | ||||||||
\(544\) | −0.479851 | −0.0205734 | ||||||||
\(545\) | 3.28099 | 0.140542 | ||||||||
\(546\) | 5.03739 | 0.215580 | ||||||||
\(547\) | −10.4160 | −0.445354 | −0.222677 | − | 0.974892i | \(-0.571480\pi\) | ||||
−0.222677 | + | 0.974892i | \(0.571480\pi\) | |||||||
\(548\) | −1.91274 | −0.0817082 | ||||||||
\(549\) | 6.84529 | 0.292150 | ||||||||
\(550\) | 2.58360 | 0.110165 | ||||||||
\(551\) | 17.9526 | 0.764806 | ||||||||
\(552\) | −6.13582 | −0.261158 | ||||||||
\(553\) | 10.3306 | 0.439300 | ||||||||
\(554\) | 18.3298 | 0.778758 | ||||||||
\(555\) | −7.97064 | −0.338335 | ||||||||
\(556\) | −20.1841 | −0.855996 | ||||||||
\(557\) | −11.9603 | −0.506774 | −0.253387 | − | 0.967365i | \(-0.581545\pi\) | ||||
−0.253387 | + | 0.967365i | \(0.581545\pi\) | |||||||
\(558\) | −8.30084 | −0.351402 | ||||||||
\(559\) | 3.12359 | 0.132114 | ||||||||
\(560\) | −10.3317 | −0.436594 | ||||||||
\(561\) | −1.56257 | −0.0659718 | ||||||||
\(562\) | −7.86816 | −0.331898 | ||||||||
\(563\) | 35.2621 | 1.48612 | 0.743060 | − | 0.669224i | \(-0.233373\pi\) | ||||
0.743060 | + | 0.669224i | \(0.233373\pi\) | |||||||
\(564\) | −3.55585 | −0.149728 | ||||||||
\(565\) | −5.61797 | −0.236350 | ||||||||
\(566\) | −14.4497 | −0.607365 | ||||||||
\(567\) | 5.03739 | 0.211551 | ||||||||
\(568\) | −0.616815 | −0.0258810 | ||||||||
\(569\) | −37.9481 | −1.59087 | −0.795433 | − | 0.606042i | \(-0.792756\pi\) | ||||
−0.795433 | + | 0.606042i | \(0.792756\pi\) | |||||||
\(570\) | −11.4487 | −0.479535 | ||||||||
\(571\) | −13.8437 | −0.579342 | −0.289671 | − | 0.957126i | \(-0.593546\pi\) | ||||
−0.289671 | + | 0.957126i | \(0.593546\pi\) | |||||||
\(572\) | 3.25636 | 0.136155 | ||||||||
\(573\) | 18.2739 | 0.763402 | ||||||||
\(574\) | −26.5483 | −1.10810 | ||||||||
\(575\) | 4.86816 | 0.203016 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 45.6191 | 1.89915 | 0.949574 | − | 0.313543i | \(-0.101516\pi\) | ||||
0.949574 | + | 0.313543i | \(0.101516\pi\) | |||||||
\(578\) | 16.7697 | 0.697529 | ||||||||
\(579\) | −9.22242 | −0.383271 | ||||||||
\(580\) | −6.59630 | −0.273896 | ||||||||
\(581\) | −11.0224 | −0.457288 | ||||||||
\(582\) | −1.04552 | −0.0433380 | ||||||||
\(583\) | −22.0188 | −0.911926 | ||||||||
\(584\) | −13.2386 | −0.547817 | ||||||||
\(585\) | −2.05100 | −0.0847984 | ||||||||
\(586\) | −7.67257 | −0.316951 | ||||||||
\(587\) | −1.92423 | −0.0794217 | −0.0397108 | − | 0.999211i | \(-0.512644\pi\) | ||||
−0.0397108 | + | 0.999211i | \(0.512644\pi\) | |||||||
\(588\) | −18.3753 | −0.757785 | ||||||||
\(589\) | 46.3355 | 1.90922 | ||||||||
\(590\) | 26.8728 | 1.10634 | ||||||||
\(591\) | −21.2145 | −0.872647 | ||||||||
\(592\) | −3.88622 | −0.159723 | ||||||||
\(593\) | 20.6977 | 0.849951 | 0.424975 | − | 0.905205i | \(-0.360283\pi\) | ||||
0.424975 | + | 0.905205i | \(0.360283\pi\) | |||||||
\(594\) | 3.25636 | 0.133610 | ||||||||
\(595\) | −4.95767 | −0.203245 | ||||||||
\(596\) | −0.778189 | −0.0318759 | ||||||||
\(597\) | 21.4058 | 0.876081 | ||||||||
\(598\) | 6.13582 | 0.250912 | ||||||||
\(599\) | 16.4988 | 0.674124 | 0.337062 | − | 0.941482i | \(-0.390567\pi\) | ||||
0.337062 | + | 0.941482i | \(0.390567\pi\) | |||||||
\(600\) | −0.793401 | −0.0323905 | ||||||||
\(601\) | 8.49981 | 0.346715 | 0.173357 | − | 0.984859i | \(-0.444538\pi\) | ||||
0.173357 | + | 0.984859i | \(0.444538\pi\) | |||||||
\(602\) | −15.7347 | −0.641300 | ||||||||
\(603\) | −3.51638 | −0.143198 | ||||||||
\(604\) | 20.3436 | 0.827771 | ||||||||
\(605\) | 0.812376 | 0.0330278 | ||||||||
\(606\) | 6.17717 | 0.250930 | ||||||||
\(607\) | 26.9659 | 1.09451 | 0.547256 | − | 0.836965i | \(-0.315673\pi\) | ||||
0.547256 | + | 0.836965i | \(0.315673\pi\) | |||||||
\(608\) | −5.58203 | −0.226381 | ||||||||
\(609\) | −16.2009 | −0.656496 | ||||||||
\(610\) | 14.0397 | 0.568451 | ||||||||
\(611\) | 3.55585 | 0.143854 | ||||||||
\(612\) | 0.479851 | 0.0193968 | ||||||||
\(613\) | −22.8824 | −0.924213 | −0.462107 | − | 0.886824i | \(-0.652906\pi\) | ||||
−0.462107 | + | 0.886824i | \(0.652906\pi\) | |||||||
\(614\) | −8.31383 | −0.335519 | ||||||||
\(615\) | 10.8093 | 0.435871 | ||||||||
\(616\) | −16.4036 | −0.660919 | ||||||||
\(617\) | 40.8773 | 1.64566 | 0.822829 | − | 0.568289i | \(-0.192394\pi\) | ||||
0.822829 | + | 0.568289i | \(0.192394\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −15.2553 | −0.613161 | −0.306580 | − | 0.951845i | \(-0.599185\pi\) | ||||
−0.306580 | + | 0.951845i | \(0.599185\pi\) | |||||||
\(620\) | −17.0250 | −0.683741 | ||||||||
\(621\) | 6.13582 | 0.246222 | ||||||||
\(622\) | 18.2570 | 0.732039 | ||||||||
\(623\) | −16.9081 | −0.677407 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −20.4035 | −0.816140 | ||||||||
\(626\) | −28.5611 | −1.14153 | ||||||||
\(627\) | −18.1771 | −0.725925 | ||||||||
\(628\) | −21.3836 | −0.853300 | ||||||||
\(629\) | −1.86481 | −0.0743547 | ||||||||
\(630\) | 10.3317 | 0.411624 | ||||||||
\(631\) | −31.9766 | −1.27297 | −0.636485 | − | 0.771289i | \(-0.719612\pi\) | ||||
−0.636485 | + | 0.771289i | \(0.719612\pi\) | |||||||
\(632\) | −2.05078 | −0.0815755 | ||||||||
\(633\) | −3.59640 | −0.142944 | ||||||||
\(634\) | −18.8153 | −0.747252 | ||||||||
\(635\) | 24.4894 | 0.971833 | ||||||||
\(636\) | 6.76178 | 0.268122 | ||||||||
\(637\) | 18.3753 | 0.728057 | ||||||||
\(638\) | −10.4729 | −0.414627 | ||||||||
\(639\) | 0.616815 | 0.0244008 | ||||||||
\(640\) | 2.05100 | 0.0810729 | ||||||||
\(641\) | 30.5631 | 1.20717 | 0.603584 | − | 0.797299i | \(-0.293739\pi\) | ||||
0.603584 | + | 0.797299i | \(0.293739\pi\) | |||||||
\(642\) | −18.0835 | −0.713697 | ||||||||
\(643\) | −34.1633 | −1.34727 | −0.673634 | − | 0.739066i | \(-0.735267\pi\) | ||||
−0.673634 | + | 0.739066i | \(0.735267\pi\) | |||||||
\(644\) | −30.9085 | −1.21797 | ||||||||
\(645\) | 6.40648 | 0.252255 | ||||||||
\(646\) | −2.67854 | −0.105386 | ||||||||
\(647\) | 35.6220 | 1.40045 | 0.700223 | − | 0.713924i | \(-0.253084\pi\) | ||||
0.700223 | + | 0.713924i | \(0.253084\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 42.6659 | 1.67478 | ||||||||
\(650\) | 0.793401 | 0.0311197 | ||||||||
\(651\) | −41.8146 | −1.63884 | ||||||||
\(652\) | −14.8949 | −0.583328 | ||||||||
\(653\) | −21.1952 | −0.829432 | −0.414716 | − | 0.909951i | \(-0.636119\pi\) | ||||
−0.414716 | + | 0.909951i | \(0.636119\pi\) | |||||||
\(654\) | −1.59970 | −0.0625534 | ||||||||
\(655\) | −6.90972 | −0.269985 | ||||||||
\(656\) | 5.27024 | 0.205768 | ||||||||
\(657\) | 13.2386 | 0.516487 | ||||||||
\(658\) | −17.9122 | −0.698291 | ||||||||
\(659\) | 0.843335 | 0.0328516 | 0.0164258 | − | 0.999865i | \(-0.494771\pi\) | ||||
0.0164258 | + | 0.999865i | \(0.494771\pi\) | |||||||
\(660\) | 6.67880 | 0.259972 | ||||||||
\(661\) | −0.0808243 | −0.00314370 | −0.00157185 | − | 0.999999i | \(-0.500500\pi\) | ||||
−0.00157185 | + | 0.999999i | \(0.500500\pi\) | |||||||
\(662\) | 23.2918 | 0.905260 | ||||||||
\(663\) | −0.479851 | −0.0186359 | ||||||||
\(664\) | 2.18812 | 0.0849157 | ||||||||
\(665\) | −57.6718 | −2.23642 | ||||||||
\(666\) | 3.88622 | 0.150588 | ||||||||
\(667\) | −19.7336 | −0.764089 | ||||||||
\(668\) | 6.70885 | 0.259573 | ||||||||
\(669\) | 27.5119 | 1.06367 | ||||||||
\(670\) | −7.21210 | −0.278628 | ||||||||
\(671\) | 22.2908 | 0.860526 | ||||||||
\(672\) | 5.03739 | 0.194322 | ||||||||
\(673\) | 11.5783 | 0.446310 | 0.223155 | − | 0.974783i | \(-0.428364\pi\) | ||||
0.223155 | + | 0.974783i | \(0.428364\pi\) | |||||||
\(674\) | −31.2626 | −1.20419 | ||||||||
\(675\) | 0.793401 | 0.0305380 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 8.07324 | 0.310280 | 0.155140 | − | 0.987893i | \(-0.450417\pi\) | ||||
0.155140 | + | 0.987893i | \(0.450417\pi\) | |||||||
\(678\) | 2.73914 | 0.105196 | ||||||||
\(679\) | −5.26668 | −0.202116 | ||||||||
\(680\) | 0.984174 | 0.0377414 | ||||||||
\(681\) | −0.778045 | −0.0298147 | ||||||||
\(682\) | −27.0305 | −1.03505 | ||||||||
\(683\) | −46.8207 | −1.79154 | −0.895772 | − | 0.444513i | \(-0.853377\pi\) | ||||
−0.895772 | + | 0.444513i | \(0.853377\pi\) | |||||||
\(684\) | 5.58203 | 0.213434 | ||||||||
\(685\) | 3.92303 | 0.149891 | ||||||||
\(686\) | −57.3020 | −2.18780 | ||||||||
\(687\) | −8.61245 | −0.328585 | ||||||||
\(688\) | 3.12359 | 0.119086 | ||||||||
\(689\) | −6.76178 | −0.257603 | ||||||||
\(690\) | 12.5846 | 0.479086 | ||||||||
\(691\) | 0.322636 | 0.0122737 | 0.00613683 | − | 0.999981i | \(-0.498047\pi\) | ||||
0.00613683 | + | 0.999981i | \(0.498047\pi\) | |||||||
\(692\) | −14.8394 | −0.564110 | ||||||||
\(693\) | 16.4036 | 0.623121 | ||||||||
\(694\) | 26.8471 | 1.01910 | ||||||||
\(695\) | 41.3975 | 1.57030 | ||||||||
\(696\) | 3.21614 | 0.121907 | ||||||||
\(697\) | 2.52893 | 0.0957900 | ||||||||
\(698\) | −8.81086 | −0.333496 | ||||||||
\(699\) | 18.5994 | 0.703493 | ||||||||
\(700\) | −3.99667 | −0.151060 | ||||||||
\(701\) | −1.11915 | −0.0422698 | −0.0211349 | − | 0.999777i | \(-0.506728\pi\) | ||||
−0.0211349 | + | 0.999777i | \(0.506728\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −21.6930 | −0.818167 | ||||||||
\(704\) | 3.25636 | 0.122729 | ||||||||
\(705\) | 7.29305 | 0.274672 | ||||||||
\(706\) | 18.6641 | 0.702434 | ||||||||
\(707\) | 31.1168 | 1.17027 | ||||||||
\(708\) | −13.1023 | −0.492415 | ||||||||
\(709\) | −31.9614 | −1.20034 | −0.600168 | − | 0.799874i | \(-0.704900\pi\) | ||||
−0.600168 | + | 0.799874i | \(0.704900\pi\) | |||||||
\(710\) | 1.26509 | 0.0474779 | ||||||||
\(711\) | 2.05078 | 0.0769101 | ||||||||
\(712\) | 3.35651 | 0.125791 | ||||||||
\(713\) | −50.9324 | −1.90743 | ||||||||
\(714\) | 2.41720 | 0.0904614 | ||||||||
\(715\) | −6.67880 | −0.249773 | ||||||||
\(716\) | 8.75510 | 0.327193 | ||||||||
\(717\) | −6.01961 | −0.224806 | ||||||||
\(718\) | −34.4613 | −1.28608 | ||||||||
\(719\) | −11.8588 | −0.442260 | −0.221130 | − | 0.975244i | \(-0.570974\pi\) | ||||
−0.221130 | + | 0.975244i | \(0.570974\pi\) | |||||||
\(720\) | −2.05100 | −0.0764362 | ||||||||
\(721\) | −5.03739 | −0.187602 | ||||||||
\(722\) | −12.1591 | −0.452514 | ||||||||
\(723\) | −8.74673 | −0.325294 | ||||||||
\(724\) | 26.8429 | 0.997610 | ||||||||
\(725\) | −2.55169 | −0.0947673 | ||||||||
\(726\) | −0.396088 | −0.0147002 | ||||||||
\(727\) | 6.51833 | 0.241752 | 0.120876 | − | 0.992668i | \(-0.461430\pi\) | ||||
0.120876 | + | 0.992668i | \(0.461430\pi\) | |||||||
\(728\) | −5.03739 | −0.186698 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 27.1524 | 1.00495 | ||||||||
\(731\) | 1.49886 | 0.0554373 | ||||||||
\(732\) | −6.84529 | −0.253009 | ||||||||
\(733\) | 25.8385 | 0.954368 | 0.477184 | − | 0.878803i | \(-0.341658\pi\) | ||||
0.477184 | + | 0.878803i | \(0.341658\pi\) | |||||||
\(734\) | −34.7488 | −1.28260 | ||||||||
\(735\) | 37.6878 | 1.39013 | ||||||||
\(736\) | 6.13582 | 0.226169 | ||||||||
\(737\) | −11.4506 | −0.421789 | ||||||||
\(738\) | −5.27024 | −0.194000 | ||||||||
\(739\) | 18.6136 | 0.684711 | 0.342356 | − | 0.939570i | \(-0.388775\pi\) | ||||
0.342356 | + | 0.939570i | \(0.388775\pi\) | |||||||
\(740\) | 7.97064 | 0.293006 | ||||||||
\(741\) | −5.58203 | −0.205061 | ||||||||
\(742\) | 34.0617 | 1.25045 | ||||||||
\(743\) | −17.1841 | −0.630423 | −0.315212 | − | 0.949021i | \(-0.602076\pi\) | ||||
−0.315212 | + | 0.949021i | \(0.602076\pi\) | |||||||
\(744\) | 8.30084 | 0.304323 | ||||||||
\(745\) | 1.59607 | 0.0584753 | ||||||||
\(746\) | −16.4025 | −0.600539 | ||||||||
\(747\) | −2.18812 | −0.0800593 | ||||||||
\(748\) | 1.56257 | 0.0571332 | ||||||||
\(749\) | −91.0934 | −3.32848 | ||||||||
\(750\) | 11.8823 | 0.433879 | ||||||||
\(751\) | 40.1392 | 1.46470 | 0.732350 | − | 0.680929i | \(-0.238424\pi\) | ||||
0.732350 | + | 0.680929i | \(0.238424\pi\) | |||||||
\(752\) | 3.55585 | 0.129669 | ||||||||
\(753\) | 2.31076 | 0.0842086 | ||||||||
\(754\) | −3.21614 | −0.117125 | ||||||||
\(755\) | −41.7248 | −1.51852 | ||||||||
\(756\) | −5.03739 | −0.183208 | ||||||||
\(757\) | 50.7558 | 1.84475 | 0.922375 | − | 0.386295i | \(-0.126245\pi\) | ||||
0.922375 | + | 0.386295i | \(0.126245\pi\) | |||||||
\(758\) | 21.1040 | 0.766530 | ||||||||
\(759\) | 19.9805 | 0.725245 | ||||||||
\(760\) | 11.4487 | 0.415290 | ||||||||
\(761\) | 34.2737 | 1.24242 | 0.621210 | − | 0.783644i | \(-0.286641\pi\) | ||||
0.621210 | + | 0.783644i | \(0.286641\pi\) | |||||||
\(762\) | −11.9402 | −0.432549 | ||||||||
\(763\) | −8.05834 | −0.291732 | ||||||||
\(764\) | −18.2739 | −0.661125 | ||||||||
\(765\) | −0.984174 | −0.0355829 | ||||||||
\(766\) | −26.8489 | −0.970090 | ||||||||
\(767\) | 13.1023 | 0.473097 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −50.1599 | −1.80881 | −0.904406 | − | 0.426672i | \(-0.859686\pi\) | ||||
−0.904406 | + | 0.426672i | \(0.859686\pi\) | |||||||
\(770\) | 33.6437 | 1.21244 | ||||||||
\(771\) | 30.3838 | 1.09425 | ||||||||
\(772\) | 9.22242 | 0.331922 | ||||||||
\(773\) | 35.1265 | 1.26341 | 0.631705 | − | 0.775208i | \(-0.282355\pi\) | ||||
0.631705 | + | 0.775208i | \(0.282355\pi\) | |||||||
\(774\) | −3.12359 | −0.112275 | ||||||||
\(775\) | −6.58589 | −0.236572 | ||||||||
\(776\) | 1.04552 | 0.0375318 | ||||||||
\(777\) | 19.5764 | 0.702300 | ||||||||
\(778\) | −0.453851 | −0.0162713 | ||||||||
\(779\) | 29.4186 | 1.05403 | ||||||||
\(780\) | 2.05100 | 0.0734376 | ||||||||
\(781\) | 2.00858 | 0.0718725 | ||||||||
\(782\) | 2.94428 | 0.105287 | ||||||||
\(783\) | −3.21614 | −0.114935 | ||||||||
\(784\) | 18.3753 | 0.656261 | ||||||||
\(785\) | 43.8579 | 1.56535 | ||||||||
\(786\) | 3.36895 | 0.120167 | ||||||||
\(787\) | 7.10009 | 0.253091 | 0.126545 | − | 0.991961i | \(-0.459611\pi\) | ||||
0.126545 | + | 0.991961i | \(0.459611\pi\) | |||||||
\(788\) | 21.2145 | 0.755734 | ||||||||
\(789\) | −15.0290 | −0.535048 | ||||||||
\(790\) | 4.20614 | 0.149648 | ||||||||
\(791\) | 13.7981 | 0.490604 | ||||||||
\(792\) | −3.25636 | −0.115710 | ||||||||
\(793\) | 6.84529 | 0.243083 | ||||||||
\(794\) | 10.5105 | 0.373004 | ||||||||
\(795\) | −13.8684 | −0.491862 | ||||||||
\(796\) | −21.4058 | −0.758708 | ||||||||
\(797\) | 43.3628 | 1.53599 | 0.767995 | − | 0.640455i | \(-0.221254\pi\) | ||||
0.767995 | + | 0.640455i | \(0.221254\pi\) | |||||||
\(798\) | 28.1189 | 0.995398 | ||||||||
\(799\) | 1.70628 | 0.0603638 | ||||||||
\(800\) | 0.793401 | 0.0280510 | ||||||||
\(801\) | −3.35651 | −0.118596 | ||||||||
\(802\) | −19.8785 | −0.701934 | ||||||||
\(803\) | 43.1097 | 1.52131 | ||||||||
\(804\) | 3.51638 | 0.124013 | ||||||||
\(805\) | 63.3934 | 2.23432 | ||||||||
\(806\) | −8.30084 | −0.292384 | ||||||||
\(807\) | 19.3049 | 0.679563 | ||||||||
\(808\) | −6.17717 | −0.217312 | ||||||||
\(809\) | −4.30489 | −0.151352 | −0.0756760 | − | 0.997132i | \(-0.524111\pi\) | ||||
−0.0756760 | + | 0.997132i | \(0.524111\pi\) | |||||||
\(810\) | 2.05100 | 0.0720648 | ||||||||
\(811\) | 12.6095 | 0.442779 | 0.221390 | − | 0.975185i | \(-0.428941\pi\) | ||||
0.221390 | + | 0.975185i | \(0.428941\pi\) | |||||||
\(812\) | 16.2009 | 0.568542 | ||||||||
\(813\) | −5.46064 | −0.191513 | ||||||||
\(814\) | 12.6550 | 0.443556 | ||||||||
\(815\) | 30.5494 | 1.07010 | ||||||||
\(816\) | −0.479851 | −0.0167981 | ||||||||
\(817\) | 17.4360 | 0.610008 | ||||||||
\(818\) | 11.4709 | 0.401069 | ||||||||
\(819\) | 5.03739 | 0.176021 | ||||||||
\(820\) | −10.8093 | −0.377476 | ||||||||
\(821\) | −28.7016 | −1.00169 | −0.500847 | − | 0.865536i | \(-0.666978\pi\) | ||||
−0.500847 | + | 0.865536i | \(0.666978\pi\) | |||||||
\(822\) | −1.91274 | −0.0667145 | ||||||||
\(823\) | 1.62898 | 0.0567828 | 0.0283914 | − | 0.999597i | \(-0.490962\pi\) | ||||
0.0283914 | + | 0.999597i | \(0.490962\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 2.58360 | 0.0899495 | ||||||||
\(826\) | −66.0014 | −2.29648 | ||||||||
\(827\) | 16.5940 | 0.577031 | 0.288516 | − | 0.957475i | \(-0.406838\pi\) | ||||
0.288516 | + | 0.957475i | \(0.406838\pi\) | |||||||
\(828\) | −6.13582 | −0.213234 | ||||||||
\(829\) | −18.9337 | −0.657593 | −0.328797 | − | 0.944401i | \(-0.606643\pi\) | ||||
−0.328797 | + | 0.944401i | \(0.606643\pi\) | |||||||
\(830\) | −4.48784 | −0.155775 | ||||||||
\(831\) | 18.3298 | 0.635853 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 8.81742 | 0.305505 | ||||||||
\(834\) | −20.1841 | −0.698917 | ||||||||
\(835\) | −13.7598 | −0.476179 | ||||||||
\(836\) | 18.1771 | 0.628669 | ||||||||
\(837\) | −8.30084 | −0.286919 | ||||||||
\(838\) | 34.7936 | 1.20192 | ||||||||
\(839\) | −2.03863 | −0.0703812 | −0.0351906 | − | 0.999381i | \(-0.511204\pi\) | ||||
−0.0351906 | + | 0.999381i | \(0.511204\pi\) | |||||||
\(840\) | −10.3317 | −0.356477 | ||||||||
\(841\) | −18.6565 | −0.643326 | ||||||||
\(842\) | 6.18218 | 0.213052 | ||||||||
\(843\) | −7.86816 | −0.270994 | ||||||||
\(844\) | 3.59640 | 0.123793 | ||||||||
\(845\) | −2.05100 | −0.0705565 | ||||||||
\(846\) | −3.55585 | −0.122253 | ||||||||
\(847\) | −1.99525 | −0.0685576 | ||||||||
\(848\) | −6.76178 | −0.232200 | ||||||||
\(849\) | −14.4497 | −0.495911 | ||||||||
\(850\) | 0.380714 | 0.0130584 | ||||||||
\(851\) | 23.8451 | 0.817401 | ||||||||
\(852\) | −0.616815 | −0.0211317 | ||||||||
\(853\) | 0.868769 | 0.0297461 | 0.0148730 | − | 0.999889i | \(-0.495266\pi\) | ||||
0.0148730 | + | 0.999889i | \(0.495266\pi\) | |||||||
\(854\) | −34.4824 | −1.17996 | ||||||||
\(855\) | −11.4487 | −0.391539 | ||||||||
\(856\) | 18.0835 | 0.618080 | ||||||||
\(857\) | −7.49315 | −0.255961 | −0.127981 | − | 0.991777i | \(-0.540850\pi\) | ||||
−0.127981 | + | 0.991777i | \(0.540850\pi\) | |||||||
\(858\) | 3.25636 | 0.111170 | ||||||||
\(859\) | 35.6824 | 1.21747 | 0.608734 | − | 0.793374i | \(-0.291678\pi\) | ||||
0.608734 | + | 0.793374i | \(0.291678\pi\) | |||||||
\(860\) | −6.40648 | −0.218459 | ||||||||
\(861\) | −26.5483 | −0.904762 | ||||||||
\(862\) | −2.84511 | −0.0969048 | ||||||||
\(863\) | 17.3230 | 0.589682 | 0.294841 | − | 0.955546i | \(-0.404733\pi\) | ||||
0.294841 | + | 0.955546i | \(0.404733\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 30.4357 | 1.03484 | ||||||||
\(866\) | 5.12180 | 0.174046 | ||||||||
\(867\) | 16.7697 | 0.569530 | ||||||||
\(868\) | 41.8146 | 1.41928 | ||||||||
\(869\) | 6.67807 | 0.226538 | ||||||||
\(870\) | −6.59630 | −0.223635 | ||||||||
\(871\) | −3.51638 | −0.119148 | ||||||||
\(872\) | 1.59970 | 0.0541728 | ||||||||
\(873\) | −1.04552 | −0.0353854 | ||||||||
\(874\) | 34.2503 | 1.15853 | ||||||||
\(875\) | 59.8556 | 2.02349 | ||||||||
\(876\) | −13.2386 | −0.447291 | ||||||||
\(877\) | −31.0758 | −1.04936 | −0.524678 | − | 0.851301i | \(-0.675814\pi\) | ||||
−0.524678 | + | 0.851301i | \(0.675814\pi\) | |||||||
\(878\) | 8.67259 | 0.292686 | ||||||||
\(879\) | −7.67257 | −0.258789 | ||||||||
\(880\) | −6.67880 | −0.225142 | ||||||||
\(881\) | 16.4398 | 0.553870 | 0.276935 | − | 0.960889i | \(-0.410681\pi\) | ||||
0.276935 | + | 0.960889i | \(0.410681\pi\) | |||||||
\(882\) | −18.3753 | −0.618729 | ||||||||
\(883\) | −1.87158 | −0.0629836 | −0.0314918 | − | 0.999504i | \(-0.510026\pi\) | ||||
−0.0314918 | + | 0.999504i | \(0.510026\pi\) | |||||||
\(884\) | 0.479851 | 0.0161391 | ||||||||
\(885\) | 26.8728 | 0.903320 | ||||||||
\(886\) | 5.13670 | 0.172571 | ||||||||
\(887\) | 41.3963 | 1.38995 | 0.694975 | − | 0.719034i | \(-0.255415\pi\) | ||||
0.694975 | + | 0.719034i | \(0.255415\pi\) | |||||||
\(888\) | −3.88622 | −0.130413 | ||||||||
\(889\) | −60.1477 | −2.01729 | ||||||||
\(890\) | −6.88420 | −0.230759 | ||||||||
\(891\) | 3.25636 | 0.109092 | ||||||||
\(892\) | −27.5119 | −0.921167 | ||||||||
\(893\) | 19.8489 | 0.664217 | ||||||||
\(894\) | −0.778189 | −0.0260265 | ||||||||
\(895\) | −17.9567 | −0.600227 | ||||||||
\(896\) | −5.03739 | −0.168287 | ||||||||
\(897\) | 6.13582 | 0.204869 | ||||||||
\(898\) | −0.593133 | −0.0197931 | ||||||||
\(899\) | 26.6966 | 0.890382 | ||||||||
\(900\) | −0.793401 | −0.0264467 | ||||||||
\(901\) | −3.24465 | −0.108095 | ||||||||
\(902\) | −17.1618 | −0.571426 | ||||||||
\(903\) | −15.7347 | −0.523620 | ||||||||
\(904\) | −2.73914 | −0.0911023 | ||||||||
\(905\) | −55.0548 | −1.83008 | ||||||||
\(906\) | 20.3436 | 0.675872 | ||||||||
\(907\) | 21.5957 | 0.717074 | 0.358537 | − | 0.933516i | \(-0.383276\pi\) | ||||
0.358537 | + | 0.933516i | \(0.383276\pi\) | |||||||
\(908\) | 0.778045 | 0.0258203 | ||||||||
\(909\) | 6.17717 | 0.204884 | ||||||||
\(910\) | 10.3317 | 0.342492 | ||||||||
\(911\) | −54.0446 | −1.79058 | −0.895289 | − | 0.445486i | \(-0.853031\pi\) | ||||
−0.895289 | + | 0.445486i | \(0.853031\pi\) | |||||||
\(912\) | −5.58203 | −0.184840 | ||||||||
\(913\) | −7.12533 | −0.235814 | ||||||||
\(914\) | 21.1234 | 0.698701 | ||||||||
\(915\) | 14.0397 | 0.464138 | ||||||||
\(916\) | 8.61245 | 0.284563 | ||||||||
\(917\) | 16.9707 | 0.560423 | ||||||||
\(918\) | 0.479851 | 0.0158374 | ||||||||
\(919\) | −29.4124 | −0.970227 | −0.485113 | − | 0.874451i | \(-0.661222\pi\) | ||||
−0.485113 | + | 0.874451i | \(0.661222\pi\) | |||||||
\(920\) | −12.5846 | −0.414901 | ||||||||
\(921\) | −8.31383 | −0.273950 | ||||||||
\(922\) | −21.7463 | −0.716176 | ||||||||
\(923\) | 0.616815 | 0.0203027 | ||||||||
\(924\) | −16.4036 | −0.539638 | ||||||||
\(925\) | 3.08333 | 0.101379 | ||||||||
\(926\) | −31.9048 | −1.04846 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −3.21614 | −0.105575 | ||||||||
\(929\) | −7.67002 | −0.251645 | −0.125823 | − | 0.992053i | \(-0.540157\pi\) | ||||
−0.125823 | + | 0.992053i | \(0.540157\pi\) | |||||||
\(930\) | −17.0250 | −0.558272 | ||||||||
\(931\) | 102.572 | 3.36165 | ||||||||
\(932\) | −18.5994 | −0.609243 | ||||||||
\(933\) | 18.2570 | 0.597708 | ||||||||
\(934\) | −0.266545 | −0.00872162 | ||||||||
\(935\) | −3.20483 | −0.104809 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −42.3946 | −1.38497 | −0.692485 | − | 0.721432i | \(-0.743484\pi\) | ||||
−0.692485 | + | 0.721432i | \(0.743484\pi\) | |||||||
\(938\) | 17.7134 | 0.578363 | ||||||||
\(939\) | −28.5611 | −0.932058 | ||||||||
\(940\) | −7.29305 | −0.237873 | ||||||||
\(941\) | −32.7077 | −1.06624 | −0.533120 | − | 0.846040i | \(-0.678980\pi\) | ||||
−0.533120 | + | 0.846040i | \(0.678980\pi\) | |||||||
\(942\) | −21.3836 | −0.696717 | ||||||||
\(943\) | −32.3372 | −1.05304 | ||||||||
\(944\) | 13.1023 | 0.426444 | ||||||||
\(945\) | 10.3317 | 0.336090 | ||||||||
\(946\) | −10.1715 | −0.330706 | ||||||||
\(947\) | 8.41560 | 0.273470 | 0.136735 | − | 0.990608i | \(-0.456339\pi\) | ||||
0.136735 | + | 0.990608i | \(0.456339\pi\) | |||||||
\(948\) | −2.05078 | −0.0666061 | ||||||||
\(949\) | 13.2386 | 0.429743 | ||||||||
\(950\) | 4.42879 | 0.143689 | ||||||||
\(951\) | −18.8153 | −0.610129 | ||||||||
\(952\) | −2.41720 | −0.0783418 | ||||||||
\(953\) | −6.22137 | −0.201530 | −0.100765 | − | 0.994910i | \(-0.532129\pi\) | ||||
−0.100765 | + | 0.994910i | \(0.532129\pi\) | |||||||
\(954\) | 6.76178 | 0.218921 | ||||||||
\(955\) | 37.4797 | 1.21281 | ||||||||
\(956\) | 6.01961 | 0.194688 | ||||||||
\(957\) | −10.4729 | −0.338541 | ||||||||
\(958\) | 21.6179 | 0.698443 | ||||||||
\(959\) | −9.63522 | −0.311138 | ||||||||
\(960\) | 2.05100 | 0.0661957 | ||||||||
\(961\) | 37.9039 | 1.22271 | ||||||||
\(962\) | 3.88622 | 0.125297 | ||||||||
\(963\) | −18.0835 | −0.582731 | ||||||||
\(964\) | 8.74673 | 0.281713 | ||||||||
\(965\) | −18.9152 | −0.608901 | ||||||||
\(966\) | −30.9085 | −0.994465 | ||||||||
\(967\) | 8.10148 | 0.260526 | 0.130263 | − | 0.991479i | \(-0.458418\pi\) | ||||
0.130263 | + | 0.991479i | \(0.458418\pi\) | |||||||
\(968\) | 0.396088 | 0.0127308 | ||||||||
\(969\) | −2.67854 | −0.0860472 | ||||||||
\(970\) | −2.14435 | −0.0688510 | ||||||||
\(971\) | −52.7015 | −1.69127 | −0.845636 | − | 0.533760i | \(-0.820779\pi\) | ||||
−0.845636 | + | 0.533760i | \(0.820779\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −101.675 | −3.25955 | ||||||||
\(974\) | 15.2920 | 0.489987 | ||||||||
\(975\) | 0.793401 | 0.0254092 | ||||||||
\(976\) | 6.84529 | 0.219112 | ||||||||
\(977\) | 43.3117 | 1.38567 | 0.692833 | − | 0.721098i | \(-0.256362\pi\) | ||||
0.692833 | + | 0.721098i | \(0.256362\pi\) | |||||||
\(978\) | −14.8949 | −0.476286 | ||||||||
\(979\) | −10.9300 | −0.349325 | ||||||||
\(980\) | −37.6878 | −1.20389 | ||||||||
\(981\) | −1.59970 | −0.0510746 | ||||||||
\(982\) | −29.3696 | −0.937221 | ||||||||
\(983\) | −23.0411 | −0.734896 | −0.367448 | − | 0.930044i | \(-0.619768\pi\) | ||||
−0.367448 | + | 0.930044i | \(0.619768\pi\) | |||||||
\(984\) | 5.27024 | 0.168009 | ||||||||
\(985\) | −43.5109 | −1.38637 | ||||||||
\(986\) | −1.54327 | −0.0491476 | ||||||||
\(987\) | −17.9122 | −0.570152 | ||||||||
\(988\) | 5.58203 | 0.177588 | ||||||||
\(989\) | −19.1658 | −0.609436 | ||||||||
\(990\) | 6.67880 | 0.212266 | ||||||||
\(991\) | 55.5151 | 1.76350 | 0.881748 | − | 0.471721i | \(-0.156367\pi\) | ||||
0.881748 | + | 0.471721i | \(0.156367\pi\) | |||||||
\(992\) | −8.30084 | −0.263552 | ||||||||
\(993\) | 23.2918 | 0.739142 | ||||||||
\(994\) | −3.10714 | −0.0985525 | ||||||||
\(995\) | 43.9033 | 1.39183 | ||||||||
\(996\) | 2.18812 | 0.0693334 | ||||||||
\(997\) | −51.9836 | −1.64634 | −0.823168 | − | 0.567797i | \(-0.807796\pi\) | ||||
−0.823168 | + | 0.567797i | \(0.807796\pi\) | |||||||
\(998\) | −19.4220 | −0.614794 | ||||||||
\(999\) | 3.88622 | 0.122955 |
(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 | 8034.2.a.z.1.4 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.4 | ✓ | 14 | 1.1 | even | 1 | trivial |