Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.6 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.f.2591.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.896575i | 0.400961i | 0.979698 | + | 0.200480i | \(0.0642503\pi\) | ||||
−0.979698 | + | 0.200480i | \(0.935750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.34607 | −1.00888 | −0.504438 | − | 0.863448i | \(-0.668300\pi\) | ||||
−0.504438 | + | 0.863448i | \(0.668300\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.48477i | 0.845180i | 0.906321 | + | 0.422590i | \(0.138879\pi\) | ||||
−0.906321 | + | 0.422590i | \(0.861121\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) | ||||
0.993399 | − | 0.114708i | \(-0.0365932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.138701 | −0.0289211 | −0.0144605 | − | 0.999895i | \(-0.504603\pi\) | ||||
−0.0144605 | + | 0.999895i | \(0.504603\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.19615 | 0.839230 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.07055i | 0.384492i | 0.981347 | + | 0.192246i | \(0.0615771\pi\) | ||||
−0.981347 | + | 0.192246i | \(0.938423\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.267949i | − 0.0481251i | −0.999710 | − | 0.0240625i | \(-0.992340\pi\) | ||||
0.999710 | − | 0.0240625i | \(-0.00766009\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.896575 | −0.151549 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.26795 | −1.35924 | −0.679621 | − | 0.733563i | \(-0.737856\pi\) | ||||
−0.679621 | + | 0.733563i | \(0.737856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.28032i | 1.44934i | 0.689095 | + | 0.724671i | \(0.258008\pi\) | ||||
−0.689095 | + | 0.724671i | \(0.741992\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.535898i | − 0.0817237i | −0.999165 | − | 0.0408619i | \(-0.986990\pi\) | ||||
0.999165 | − | 0.0408619i | \(-0.0130104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.93426 | −0.865600 | −0.432800 | − | 0.901490i | \(-0.642474\pi\) | ||||
−0.432800 | + | 0.901490i | \(0.642474\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.82843i | − 0.388514i | −0.980951 | − | 0.194257i | \(-0.937770\pi\) | ||||
0.980951 | − | 0.194257i | \(-0.0622296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.00000i | − 0.404520i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.03528 | 0.134781 | 0.0673907 | − | 0.997727i | \(-0.478533\pi\) | ||||
0.0673907 | + | 0.997727i | \(0.478533\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.39230 | 1.07452 | 0.537262 | − | 0.843415i | \(-0.319459\pi\) | ||||
0.537262 | + | 0.843415i | \(0.319459\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.58630i | 0.444826i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.92820i | 0.357737i | 0.983873 | + | 0.178868i | \(0.0572437\pi\) | ||||
−0.983873 | + | 0.178868i | \(0.942756\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.55291 | −0.184297 | −0.0921485 | − | 0.995745i | \(-0.529373\pi\) | ||||
−0.0921485 | + | 0.995745i | \(0.529373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.39230 | 0.748163 | 0.374081 | − | 0.927396i | \(-0.377958\pi\) | ||||
0.374081 | + | 0.927396i | \(0.377958\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.34607i | − 0.381320i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.535898i | 0.0602933i | 0.999545 | + | 0.0301466i | \(0.00959743\pi\) | ||||
−0.999545 | + | 0.0301466i | \(0.990403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.6264 | 1.38593 | 0.692963 | − | 0.720973i | \(-0.256305\pi\) | ||||
0.692963 | + | 0.720973i | \(0.256305\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.12436 | −0.338884 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 10.7961i | − 1.14438i | −0.820121 | − | 0.572191i | \(-0.806094\pi\) | ||||
0.820121 | − | 0.572191i | \(-0.193906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000i | 0.419314i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.896575 | 0.0919867 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.9282 | −1.10959 | −0.554795 | − | 0.831987i | \(-0.687203\pi\) | ||||
−0.554795 | + | 0.831987i | \(0.687203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.14162i | 0.909625i | 0.890587 | + | 0.454813i | \(0.150294\pi\) | ||||
−0.890587 | + | 0.454813i | \(0.849706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.12436i | 0.603451i | 0.953395 | + | 0.301725i | \(0.0975626\pi\) | ||||
−0.953395 | + | 0.301725i | \(0.902437\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.1769 | −0.983838 | −0.491919 | − | 0.870641i | \(-0.663704\pi\) | ||||
−0.491919 | + | 0.870641i | \(0.663704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4641 | −1.00228 | −0.501140 | − | 0.865366i | \(-0.667086\pi\) | ||||
−0.501140 | + | 0.865366i | \(0.667086\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.62158i | 0.434761i | 0.976087 | + | 0.217381i | \(0.0697513\pi\) | ||||
−0.976087 | + | 0.217381i | \(0.930249\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.124356i | − 0.0115962i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.48477 | −0.319448 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.196152 | 0.0178320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.24504i | 0.737459i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.39230i | 0.389754i | 0.980828 | + | 0.194877i | \(0.0624308\pi\) | ||||
−0.980828 | + | 0.194877i | \(0.937569\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.0764 | −1.75408 | −0.877041 | − | 0.480415i | \(-0.840486\pi\) | ||||
−0.877041 | + | 0.480415i | \(0.840486\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.2832i | 1.56204i | 0.624504 | + | 0.781021i | \(0.285301\pi\) | ||||
−0.624504 | + | 0.781021i | \(0.714699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 7.46410i | − 0.633097i | −0.948576 | − | 0.316548i | \(-0.897476\pi\) | ||||
0.948576 | − | 0.316548i | \(-0.102524\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.3843 | −1.11925 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.85641 | −0.154166 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1.79315i | − 0.146901i | −0.997299 | − | 0.0734503i | \(-0.976599\pi\) | ||||
0.997299 | − | 0.0734503i | \(-0.0234010\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3205i | 1.40952i | 0.709444 | + | 0.704761i | \(0.248946\pi\) | ||||
−0.709444 | + | 0.704761i | \(0.751054\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.240237 | 0.0192963 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.46410 | 0.436083 | 0.218041 | − | 0.975940i | \(-0.430033\pi\) | ||||
0.218041 | + | 0.975940i | \(0.430033\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 0.138701i | − 0.0109311i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 15.3205i | − 1.19999i | −0.800002 | − | 0.599997i | \(-0.795168\pi\) | ||||
0.800002 | − | 0.599997i | \(-0.204832\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.6617 | −1.05717 | −0.528586 | − | 0.848880i | \(-0.677277\pi\) | ||||
−0.528586 | + | 0.848880i | \(0.677277\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0735i | 0.841900i | 0.907084 | + | 0.420950i | \(0.138303\pi\) | ||||
−0.907084 | + | 0.420950i | \(0.861697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.19615i | 0.317199i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.20736 | 0.239730 | 0.119865 | − | 0.992790i | \(-0.461754\pi\) | ||||
0.119865 | + | 0.992790i | \(0.461754\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.46410 | −0.257485 | −0.128742 | − | 0.991678i | \(-0.541094\pi\) | ||||
−0.128742 | + | 0.991678i | \(0.541094\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 7.41284i | − 0.545003i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 11.6603i | − 0.852682i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.8709 | −1.14838 | −0.574190 | − | 0.818722i | \(-0.694683\pi\) | ||||
−0.574190 | + | 0.818722i | \(0.694683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.07180 | 0.0771496 | 0.0385748 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385748 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.93426i | 0.422798i | 0.977400 | + | 0.211399i | \(0.0678020\pi\) | ||||
−0.977400 | + | 0.211399i | \(0.932198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5359i | 1.38486i | 0.721484 | + | 0.692432i | \(0.243461\pi\) | ||||
−0.721484 | + | 0.692432i | \(0.756539\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.07055 | −0.145324 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.32051 | −0.581129 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.34607i | 0.231452i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 21.3205i | − 1.46776i | −0.679277 | − | 0.733882i | \(-0.737706\pi\) | ||||
0.679277 | − | 0.733882i | \(-0.262294\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.480473 | 0.0327680 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.267949 | 0.0181896 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.9391i | 0.937643i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.4641i | 0.968588i | 0.874905 | + | 0.484294i | \(0.160923\pi\) | ||||
−0.874905 | + | 0.484294i | \(0.839077\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.37945 | 0.357047 | 0.178523 | − | 0.983936i | \(-0.442868\pi\) | ||||
0.178523 | + | 0.983936i | \(0.442868\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.3205 | 1.54106 | 0.770531 | − | 0.637402i | \(-0.219991\pi\) | ||||
0.770531 | + | 0.637402i | \(0.219991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 4.62158i | − 0.302770i | −0.988475 | − | 0.151385i | \(-0.951627\pi\) | ||||
0.988475 | − | 0.151385i | \(-0.0483733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 5.32051i | − 0.347072i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3495 | −1.12225 | −0.561123 | − | 0.827732i | \(-0.689631\pi\) | ||||
−0.561123 | + | 0.827732i | \(0.689631\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.928203 | 0.0597908 | 0.0298954 | − | 0.999553i | \(-0.490483\pi\) | ||||
0.0298954 | + | 0.999553i | \(0.490483\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 0.896575i | − 0.0572801i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.00000i | − 0.254514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.3538 | −1.28472 | −0.642360 | − | 0.766403i | \(-0.722045\pi\) | ||||
−0.642360 | + | 0.766403i | \(0.722045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.464102 | 0.0291778 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.51815i | 0.344213i | 0.985078 | + | 0.172106i | \(0.0550573\pi\) | ||||
−0.985078 | + | 0.172106i | \(0.944943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 8.26795i | − 0.513745i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0072 | 0.740396 | 0.370198 | − | 0.928953i | \(-0.379290\pi\) | ||||
0.370198 | + | 0.928953i | \(0.379290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.53590 | 0.155779 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.9382i | 1.52051i | 0.649625 | + | 0.760255i | \(0.274926\pi\) | ||||
−0.649625 | + | 0.760255i | \(0.725074\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.535898i | 0.0325535i | 0.999868 | + | 0.0162768i | \(0.00518128\pi\) | ||||
−0.999868 | + | 0.0162768i | \(0.994819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.0406 | −0.846680 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1962 | −0.672712 | −0.336356 | − | 0.941735i | \(-0.609194\pi\) | ||||
−0.336356 | + | 0.941735i | \(0.609194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3185i | 1.15245i | 0.817292 | + | 0.576223i | \(0.195474\pi\) | ||||
−0.817292 | + | 0.576223i | \(0.804526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 9.85641i | − 0.585903i | −0.956127 | − | 0.292951i | \(-0.905363\pi\) | ||||
0.956127 | − | 0.292951i | \(-0.0946374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.28032 | −0.547800 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.85641 | 0.285671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 11.9700i | − 0.699298i | −0.936881 | − | 0.349649i | \(-0.886301\pi\) | ||||
0.936881 | − | 0.349649i | \(-0.113699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.928203i | 0.0540421i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.554803 | −0.0320851 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.535898 | 0.0308887 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.52433i | 0.430842i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.00000i | − 0.285365i | −0.989769 | − | 0.142683i | \(-0.954427\pi\) | ||||
0.989769 | − | 0.142683i | \(-0.0455728\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.14110 | −0.234821 | −0.117410 | − | 0.993083i | \(-0.537459\pi\) | ||||
−0.117410 | + | 0.993083i | \(0.537459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.39230 | −0.474361 | −0.237181 | − | 0.971466i | \(-0.576223\pi\) | ||||
−0.237181 | + | 0.971466i | \(0.576223\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.6312i | 1.15876i | 0.815056 | + | 0.579382i | \(0.196706\pi\) | ||||
−0.815056 | + | 0.579382i | \(0.803294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 6.92820i | − 0.387905i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.48477 | 0.193898 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.7846 | 0.931043 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 5.93426i | − 0.327166i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 26.2487i | − 1.44276i | −0.692540 | − | 0.721380i | \(-0.743508\pi\) | ||||
0.692540 | − | 0.721380i | \(-0.256492\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.62536 | −0.143438 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.7128 | −1.78198 | −0.890990 | − | 0.454022i | \(-0.849989\pi\) | ||||
−0.890990 | + | 0.454022i | \(0.849989\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.896575i | 0.0485523i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.3220 | −1.78882 | −0.894408 | − | 0.447252i | \(-0.852403\pi\) | ||||
−0.894408 | + | 0.447252i | \(0.852403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3205 | −1.14126 | −0.570630 | − | 0.821207i | \(-0.693301\pi\) | ||||
−0.570630 | + | 0.821207i | \(0.693301\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.5235i | 0.985905i | 0.870056 | + | 0.492953i | \(0.164082\pi\) | ||||
−0.870056 | + | 0.492953i | \(0.835918\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.39230i | − 0.0738959i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.96524 | −0.209277 | −0.104639 | − | 0.994510i | \(-0.533369\pi\) | ||||
−0.104639 | + | 0.994510i | \(0.533369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.73118i | 0.299984i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 11.5359i | − 0.602169i | −0.953597 | − | 0.301084i | \(-0.902651\pi\) | ||||
0.953597 | − | 0.301084i | \(-0.0973486\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.82843 | 0.146845 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.39230 | −0.279203 | −0.139601 | − | 0.990208i | \(-0.544582\pi\) | ||||
−0.139601 | + | 0.990208i | \(0.544582\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.28221i | 0.426555i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3205i | 0.889695i | 0.895606 | + | 0.444847i | \(0.146742\pi\) | ||||
−0.895606 | + | 0.444847i | \(0.853258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.2784 | −0.525203 | −0.262602 | − | 0.964904i | \(-0.584581\pi\) | ||||
−0.262602 | + | 0.964904i | \(0.584581\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | 0.152894 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.6579i | 0.793886i | 0.917843 | + | 0.396943i | \(0.129929\pi\) | ||||
−0.917843 | + | 0.396943i | \(0.870071\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 0.483340i | − 0.0244435i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.480473 | −0.0241752 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 31.6675i | − 1.58140i | −0.612204 | − | 0.790700i | \(-0.709717\pi\) | ||||
0.612204 | − | 0.790700i | \(-0.290283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.07180i | − 0.0533900i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.6651 | 1.37131 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.60770 | −0.277283 | −0.138641 | − | 0.990343i | \(-0.544274\pi\) | ||||
−0.138641 | + | 0.990343i | \(0.544274\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.03528i | 0.0509426i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.3205i | 0.555702i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.3490 | −0.603287 | −0.301644 | − | 0.953421i | \(-0.597535\pi\) | ||||
−0.301644 | + | 0.953421i | \(0.597535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.5885 | 0.662261 | 0.331130 | − | 0.943585i | \(-0.392570\pi\) | ||||
0.331130 | + | 0.943585i | \(0.392570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.6226i | 0.709301i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.39230i | 0.406132i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.2819 | 1.16962 | 0.584808 | − | 0.811172i | \(-0.301170\pi\) | ||||
0.584808 | + | 0.811172i | \(0.301170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.138701i | 0.00663495i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0718i | 0.623883i | 0.950101 | + | 0.311941i | \(0.100979\pi\) | ||||
−0.950101 | + | 0.311941i | \(0.899021\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.31079 | 0.109789 | 0.0548945 | − | 0.998492i | \(-0.482518\pi\) | ||||
0.0548945 | + | 0.998492i | \(0.482518\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.67949 | 0.458852 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.76268i | 0.413537i | 0.978390 | + | 0.206768i | \(0.0662946\pi\) | ||||
−0.978390 | + | 0.206768i | \(0.933705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 31.0526i | − 1.46221i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.58630 | −0.168128 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.7846 | 1.76749 | 0.883745 | − | 0.467969i | \(-0.155014\pi\) | ||||
0.883745 | + | 0.467969i | \(0.155014\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 13.6988i | − 0.638018i | −0.947752 | − | 0.319009i | \(-0.896650\pi\) | ||||
0.947752 | − | 0.319009i | \(-0.103350\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.8564i | 1.85228i | 0.377175 | + | 0.926142i | \(0.376896\pi\) | ||||
−0.377175 | + | 0.926142i | \(0.623104\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.2480 | −0.798141 | −0.399070 | − | 0.916920i | \(-0.630667\pi\) | ||||
−0.399070 | + | 0.916920i | \(0.630667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.92820 | −0.135212 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.79315i | 0.0824492i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.19615i | − 0.192533i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.5665 | 1.67077 | 0.835383 | − | 0.549669i | \(-0.185246\pi\) | ||||
0.835383 | + | 0.549669i | \(0.185246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.0718 | −1.50794 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 9.79796i | − 0.444902i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.7128i | 1.16516i | 0.812774 | + | 0.582579i | \(0.197956\pi\) | ||||
−0.812774 | + | 0.582579i | \(0.802044\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4219 | 0.831371 | 0.415685 | − | 0.909509i | \(-0.363542\pi\) | ||||
0.415685 | + | 0.909509i | \(0.363542\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.21539 | −0.324965 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1.55291i | − 0.0696577i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0000i | 0.805791i | 0.915246 | + | 0.402895i | \(0.131996\pi\) | ||||
−0.915246 | + | 0.402895i | \(0.868004\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.0421 | −1.29493 | −0.647463 | − | 0.762097i | \(-0.724170\pi\) | ||||
−0.647463 | + | 0.762097i | \(0.724170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.19615 | −0.364724 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 41.0122i | − 1.81783i | −0.416978 | − | 0.908917i | \(-0.636911\pi\) | ||||
0.416978 | − | 0.908917i | \(-0.363089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.39230i | 0.282779i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.49095 | −0.241960 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.8564 | 0.873284 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.8709i | 0.695317i | 0.937621 | + | 0.347659i | \(0.113023\pi\) | ||||
−0.937621 | + | 0.347659i | \(0.886977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.3397i | 0.495852i | 0.968779 | + | 0.247926i | \(0.0797491\pi\) | ||||
−0.968779 | + | 0.247926i | \(0.920251\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.933740 | 0.0406744 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9808 | −0.999164 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.1213i | 1.60790i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 9.12436i | − 0.394480i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.34607 | 0.144125 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.6603 | −1.49016 | −0.745080 | − | 0.666975i | \(-0.767589\pi\) | ||||
−0.745080 | + | 0.666975i | \(0.767589\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 9.38186i | − 0.401875i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.14359i | 0.0916534i | 0.998949 | + | 0.0458267i | \(0.0145922\pi\) | ||||
−0.998949 | + | 0.0458267i | \(0.985408\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.07055 | 0.0882085 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.535898 | −0.0227887 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 36.2891i | − 1.53762i | −0.639479 | − | 0.768809i | \(-0.720850\pi\) | ||||
0.639479 | − | 0.768809i | \(-0.279150\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 2.14359i | − 0.0906643i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7284 | 0.747165 | 0.373582 | − | 0.927597i | \(-0.378129\pi\) | ||||
0.373582 | + | 0.927597i | \(0.378129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.14359 | −0.174322 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.8343i | 0.873418i | 0.899603 | + | 0.436709i | \(0.143856\pi\) | ||||
−0.899603 | + | 0.436709i | \(0.856144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 26.3923i | − 1.10448i | −0.833684 | − | 0.552242i | \(-0.813773\pi\) | ||||
0.833684 | − | 0.552242i | \(-0.186227\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.582009 | −0.0242715 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.67949 | 0.111549 | 0.0557744 | − | 0.998443i | \(-0.482237\pi\) | ||||
0.0557744 | + | 0.998443i | \(0.482237\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.6264i | 0.523831i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.46410i | 0.391963i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.23835 | 0.0511121 | 0.0255560 | − | 0.999673i | \(-0.491864\pi\) | ||||
0.0255560 | + | 0.999673i | \(0.491864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.267949 | −0.0110407 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 11.7298i | − 0.481686i | −0.970564 | − | 0.240843i | \(-0.922576\pi\) | ||||
0.970564 | − | 0.240843i | \(-0.0774238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 3.12436i | − 0.128086i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.8367 | −1.01480 | −0.507399 | − | 0.861711i | \(-0.669393\pi\) | ||||
−0.507399 | + | 0.861711i | \(0.669393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7846 | 1.01099 | 0.505493 | − | 0.862831i | \(-0.331311\pi\) | ||||
0.505493 | + | 0.862831i | \(0.331311\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.175865i | 0.00714995i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.7846i | 0.843621i | 0.906684 | + | 0.421811i | \(0.138605\pi\) | ||||
−0.906684 | + | 0.421811i | \(0.861395\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.7370 | −0.960297 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.4641 | 1.31121 | 0.655606 | − | 0.755103i | \(-0.272413\pi\) | ||||
0.655606 | + | 0.755103i | \(0.272413\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.8439i | 1.48328i | 0.670799 | + | 0.741639i | \(0.265951\pi\) | ||||
−0.670799 | + | 0.741639i | \(0.734049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.1244i | 0.487319i | 0.969861 | + | 0.243659i | \(0.0783479\pi\) | ||||
−0.969861 | + | 0.243659i | \(0.921652\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.7961 | 0.432535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.5885 | 0.543538 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 28.8119i | − 1.14880i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.78461i | 0.110854i | 0.998463 | + | 0.0554268i | \(0.0176519\pi\) | ||||
−0.998463 | + | 0.0554268i | \(0.982348\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.93803 | −0.156276 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | −0.158486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.1774i | 0.599472i | 0.954022 | + | 0.299736i | \(0.0968986\pi\) | ||||
−0.954022 | + | 0.299736i | \(0.903101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0718i | 0.397193i | 0.980081 | + | 0.198596i | \(0.0636383\pi\) | ||||
−0.980081 | + | 0.198596i | \(0.936362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.3901 | −1.23407 | −0.617036 | − | 0.786935i | \(-0.711667\pi\) | ||||
−0.617036 | + | 0.786935i | \(0.711667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.46410 | −0.135978 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.2480i | 0.674965i | 0.941332 | + | 0.337482i | \(0.109575\pi\) | ||||
−0.941332 | + | 0.337482i | \(0.890425\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 18.0000i | − 0.703318i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.4673 | 1.57638 | 0.788192 | − | 0.615429i | \(-0.211017\pi\) | ||||
0.788192 | + | 0.615429i | \(0.211017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.7846 | 0.964010 | 0.482005 | − | 0.876169i | \(-0.339909\pi\) | ||||
0.482005 | + | 0.876169i | \(0.339909\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.896575i | 0.0347677i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 0.287187i | − 0.0111199i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.0812 | −1.08406 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.34658i | 0.320785i | 0.987053 | + | 0.160393i | \(0.0512760\pi\) | ||||
−0.987053 | + | 0.160393i | \(0.948724\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 10.9282i | − 0.419386i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.27551 | −0.0488061 | −0.0244031 | − | 0.999702i | \(-0.507769\pi\) | ||||
−0.0244031 | + | 0.999702i | \(0.507769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.3923 | −0.626318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 11.3137i | − 0.431018i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 31.4641i | − 1.19695i | −0.801141 | − | 0.598475i | \(-0.795773\pi\) | ||||
0.801141 | − | 0.598475i | \(-0.204227\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.69213 | 0.253847 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.3397 | −1.22496 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.0908i | 1.66529i | 0.553809 | + | 0.832644i | \(0.313174\pi\) | ||||
−0.553809 | + | 0.832644i | \(0.686826\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.26795i | 0.311832i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.14162 | −0.343806 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.3923 | 0.803405 | 0.401702 | − | 0.915770i | \(-0.368419\pi\) | ||||
0.401702 | + | 0.915770i | \(0.368419\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0371647i | 0.00139183i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 12.0000i | − 0.448775i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.8038 | −1.03691 | −0.518453 | − | 0.855106i | \(-0.673492\pi\) | ||||
−0.518453 | + | 0.855106i | \(0.673492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.12436 | −0.228083 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.68835i | 0.322677i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.3205i | 1.82920i | 0.404364 | + | 0.914598i | \(0.367493\pi\) | ||||
−0.404364 | + | 0.914598i | \(0.632507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.86748 | 0.0690713 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0000 | −0.517102 | −0.258551 | − | 0.965998i | \(-0.583245\pi\) | ||||
−0.258551 | + | 0.965998i | \(0.583245\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 9.79796i | − 0.360912i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 8.14359i | − 0.299567i | −0.988719 | − | 0.149783i | \(-0.952142\pi\) | ||||
0.988719 | − | 0.149783i | \(-0.0478577\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.4625 | 1.19094 | 0.595468 | − | 0.803379i | \(-0.296967\pi\) | ||||
0.595468 | + | 0.803379i | \(0.296967\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.60770 | 0.0589014 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 10.1769i | − 0.371856i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.9282i | 1.34753i | 0.738946 | + | 0.673765i | \(0.235324\pi\) | ||||
−0.738946 | + | 0.673765i | \(0.764676\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.5291 | −0.565163 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 22.5259i | − 0.816563i | −0.912856 | − | 0.408281i | \(-0.866128\pi\) | ||||
0.912856 | − | 0.408281i | \(-0.133872\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 10.4641i | − 0.378826i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.14110 | 0.149527 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.2487 | 0.369578 | 0.184789 | − | 0.982778i | \(-0.440840\pi\) | ||||
0.184789 | + | 0.982778i | \(0.440840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 10.1397i | − 0.364701i | −0.983234 | − | 0.182350i | \(-0.941629\pi\) | ||||
0.983234 | − | 0.182350i | \(-0.0583705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.12436i | − 0.0403880i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.28032 | 0.332502 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.19615 | 0.185933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.89898i | 0.174852i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 26.3923i | − 0.940784i | −0.882458 | − | 0.470392i | \(-0.844113\pi\) | ||||
0.882458 | − | 0.470392i | \(-0.155887\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.62158 | −0.164324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.5692 | 1.19208 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 28.7747i | − 1.01925i | −0.860396 | − | 0.509626i | \(-0.829784\pi\) | ||||
0.860396 | − | 0.509626i | \(-0.170216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 20.6795i | − 0.731588i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.3891 | −0.754804 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.124356 | 0.00438296 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 42.2233i | − 1.48449i | −0.670127 | − | 0.742247i | \(-0.733760\pi\) | ||||
0.670127 | − | 0.742247i | \(-0.266240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 46.5167i | − 1.63342i | −0.577048 | − | 0.816710i | \(-0.695795\pi\) | ||||
0.577048 | − | 0.816710i | \(-0.304205\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7360 | 0.481151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.535898 | −0.0187487 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 17.0449i | − 0.594871i | −0.954742 | − | 0.297435i | \(-0.903869\pi\) | ||||
0.954742 | − | 0.297435i | \(-0.0961313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.7128i | 0.617430i | 0.951155 | + | 0.308715i | \(0.0998989\pi\) | ||||
−0.951155 | + | 0.308715i | \(0.900101\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.7042 | 0.928594 | 0.464297 | − | 0.885679i | \(-0.346307\pi\) | ||||
0.464297 | + | 0.885679i | \(0.346307\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.1769 | −0.527116 | −0.263558 | − | 0.964644i | \(-0.584896\pi\) | ||||
−0.263558 | + | 0.964644i | \(0.584896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.48477i | − 0.120740i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 12.2487i | − 0.423884i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.4158 | 0.566735 | 0.283367 | − | 0.959011i | \(-0.408548\pi\) | ||||
0.283367 | + | 0.959011i | \(0.408548\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.7128 | 0.852166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.68973i | 0.0925294i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.196152i | 0.00673988i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.14677 | 0.0393108 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.8564 | −0.611392 | −0.305696 | − | 0.952129i | \(-0.598889\pi\) | ||||
−0.305696 | + | 0.952129i | \(0.598889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.8981i | 0.543069i | 0.962429 | + | 0.271535i | \(0.0875312\pi\) | ||||
−0.962429 | + | 0.271535i | \(0.912469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 12.7128i | − 0.433756i | −0.976199 | − | 0.216878i | \(-0.930413\pi\) | ||||
0.976199 | − | 0.216878i | \(-0.0695873\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.3896 | 0.898312 | 0.449156 | − | 0.893453i | \(-0.351725\pi\) | ||||
0.449156 | + | 0.893453i | \(0.351725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.92820 | −0.337569 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.79315i | − 0.0608285i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7128i | 0.396874i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.24504 | −0.278733 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.21539 | 0.311182 | 0.155591 | − | 0.987822i | \(-0.450272\pi\) | ||||
0.155591 | + | 0.987822i | \(0.450272\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 41.2252i | − 1.38891i | −0.719535 | − | 0.694457i | \(-0.755645\pi\) | ||||
0.719535 | − | 0.694457i | \(-0.244355\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 35.3205i | − 1.18863i | −0.804232 | − | 0.594315i | \(-0.797423\pi\) | ||||
0.804232 | − | 0.594315i | \(-0.202577\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.5873 | 0.456218 | 0.228109 | − | 0.973636i | \(-0.426746\pi\) | ||||
0.228109 | + | 0.973636i | \(0.426746\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.39230 | −0.147313 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.93426i | 0.198582i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.87564i | 0.0961222i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.554803 | 0.0185037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.85641 | 0.328365 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 3.10583i | − 0.103241i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.78461i | − 0.0924614i | −0.998931 | − | 0.0462307i | \(-0.985279\pi\) | ||||
0.998931 | − | 0.0462307i | \(-0.0147209\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.5328 | 1.67422 | 0.837112 | − | 0.547031i | \(-0.184242\pi\) | ||||
0.837112 | + | 0.547031i | \(0.184242\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.2487 | −1.39823 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 20.0764i | − 0.662981i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 37.0718i | − 1.22289i | −0.791289 | − | 0.611443i | \(-0.790589\pi\) | ||||
0.791289 | − | 0.611443i | \(-0.209411\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.21166 | −0.204459 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.6936 | −1.14072 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 23.0807i | − 0.757253i | −0.925550 | − | 0.378626i | \(-0.876397\pi\) | ||||
0.925550 | − | 0.378626i | \(-0.123603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000i | 0.0327737i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.4543 | 0.341892 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.3205 | 0.369825 | 0.184912 | − | 0.982755i | \(-0.440800\pi\) | ||||
0.184912 | + | 0.982755i | \(0.440800\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 44.9131i | − 1.46412i | −0.681238 | − | 0.732062i | \(-0.738558\pi\) | ||||
0.681238 | − | 0.732062i | \(-0.261442\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.28719i | − 0.0419166i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.1905 | 1.46849 | 0.734246 | − | 0.678883i | \(-0.237536\pi\) | ||||
0.734246 | + | 0.678883i | \(0.237536\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.5692 | 0.830012 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 15.6579i | − 0.507209i | −0.967308 | − | 0.253604i | \(-0.918384\pi\) | ||||
0.967308 | − | 0.253604i | \(-0.0816161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 14.2295i | − 0.460455i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.2832 | −0.590397 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9282 | 0.997684 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.960947i | 0.0309340i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.4641i | 0.625923i | 0.949766 | + | 0.312962i | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312962i | \(0.898679\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.45378 | 0.175020 | 0.0875101 | − | 0.996164i | \(-0.472109\pi\) | ||||
0.0875101 | + | 0.996164i | \(0.472109\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.46410 | 0.239288 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 5.10205i | − 0.163229i | −0.996664 | − | 0.0816145i | \(-0.973992\pi\) | ||||
0.996664 | − | 0.0816145i | \(-0.0260076\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.1244i | 1.15454i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.4815 | 0.334308 | 0.167154 | − | 0.985931i | \(-0.446542\pi\) | ||||
0.167154 | + | 0.985931i | \(0.446542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.32051 | −0.169525 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0743295i | 0.00236354i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.60770i | 0.114602i | 0.998357 | + | 0.0573011i | \(0.0182495\pi\) | ||||
−0.998357 | + | 0.0573011i | \(0.981750\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.5154 | −0.555276 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.2487 | 0.387921 | 0.193960 | − | 0.981009i | \(-0.437867\pi\) | ||||
0.193960 | + | 0.981009i | \(0.437867\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6048.2.h.f.2591.6 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.f.2591.4 | yes | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.f.2591.5 | yes | 8 | |
12.11 | even | 2 | inner | 6048.2.h.f.2591.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.f.2591.3 | ✓ | 8 | 12.11 | even | 2 | inner | |
6048.2.h.f.2591.4 | yes | 8 | 3.2 | odd | 2 | inner | |
6048.2.h.f.2591.5 | yes | 8 | 4.3 | odd | 2 | inner | |
6048.2.h.f.2591.6 | yes | 8 | 1.1 | even | 1 | trivial |