Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3700,2,Mod(149,3700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3700, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3700.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3700.d (of order \(2\), degree \(1\), not 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: | \(29.5446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{6} + 139x^{4} + 273x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 740) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.6 | ||
Root | \(1.51951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3700.149 |
Dual form | 3700.2.d.i.149.3 |
$q$-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 \(\left(\mathbb{Z}/3700\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) | \(1851\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.51951i | 1.45464i | 0.686299 | + | 0.727320i | \(0.259234\pi\) | ||||
−0.686299 | + | 0.727320i | \(0.740766\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.519509i | − 0.196356i | −0.995169 | − | 0.0981780i | \(-0.968699\pi\) | ||||
0.995169 | − | 0.0981780i | \(-0.0313015\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.34793 | −1.11598 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.16241 | 1.85804 | 0.929019 | − | 0.370033i | \(-0.120654\pi\) | ||||
0.929019 | + | 0.370033i | \(0.120654\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.51034i | − 1.80564i | −0.430015 | − | 0.902822i | \(-0.641492\pi\) | ||||
0.430015 | − | 0.902822i | \(-0.358508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.51034i | 0.608847i | 0.952537 | + | 0.304423i | \(0.0984638\pi\) | ||||
−0.952537 | + | 0.304423i | \(0.901536\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.68192 | −1.53294 | −0.766469 | − | 0.642281i | \(-0.777988\pi\) | ||||
−0.766469 | + | 0.642281i | \(0.777988\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30891 | 0.285627 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.03902i | − 0.633679i | −0.948479 | − | 0.316840i | \(-0.897378\pi\) | ||||
0.948479 | − | 0.316840i | \(-0.102622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 0.876607i | − 0.168703i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.03902 | 0.564332 | 0.282166 | − | 0.959366i | \(-0.408947\pi\) | ||||
0.282166 | + | 0.959366i | \(0.408947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.33876 | −0.779264 | −0.389632 | − | 0.920971i | \(-0.627398\pi\) | ||||
−0.389632 | + | 0.920971i | \(0.627398\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.5263i | 2.70277i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.00000i | − 0.164399i | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.4029 | 2.62656 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.1624 | 1.89945 | 0.949725 | − | 0.313086i | \(-0.101363\pi\) | ||||
0.949725 | + | 0.313086i | \(0.101363\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.34316i | − 0.357329i | −0.983910 | − | 0.178665i | \(-0.942822\pi\) | ||||
0.983910 | − | 0.178665i | \(-0.0571777\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 9.54019i | − 1.39158i | −0.718245 | − | 0.695790i | \(-0.755055\pi\) | ||||
0.718245 | − | 0.695790i | \(-0.244945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.73011 | 0.961444 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.32482 | −0.885653 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.20143i | − 1.26391i | −0.775004 | − | 0.631957i | \(-0.782252\pi\) | ||||
0.775004 | − | 0.631957i | \(-0.217748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 16.8352i | − 2.22987i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.37778 | 1.22088 | 0.610441 | − | 0.792062i | \(-0.290992\pi\) | ||||
0.610441 | + | 0.792062i | \(0.290992\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.73928i | 0.219129i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.357097i | − 0.0436264i | −0.999762 | − | 0.0218132i | \(-0.993056\pi\) | ||||
0.999762 | − | 0.0218132i | \(-0.00694390\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.65684 | 0.921775 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.87661 | −0.341390 | −0.170695 | − | 0.985324i | \(-0.554601\pi\) | ||||
−0.170695 | + | 0.985324i | \(0.554601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 10.2404i | − 1.19855i | −0.800542 | − | 0.599277i | \(-0.795455\pi\) | ||||
0.800542 | − | 0.599277i | \(-0.204545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.20143i | − 0.364837i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.681922 | −0.0767222 | −0.0383611 | − | 0.999264i | \(-0.512214\pi\) | ||||
−0.0383611 | + | 0.999264i | \(0.512214\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.83516 | −0.870574 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.17635i | 0.677942i | 0.940797 | + | 0.338971i | \(0.110079\pi\) | ||||
−0.940797 | + | 0.338971i | \(0.889921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.65684i | 0.820899i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.0207 | 1.16819 | 0.584095 | − | 0.811685i | \(-0.301450\pi\) | ||||
0.584095 | + | 0.811685i | \(0.301450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.38218 | −0.354549 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 10.9315i | − 1.13355i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 6.34316i | − 0.644051i | −0.946731 | − | 0.322025i | \(-0.895636\pi\) | ||||
0.946731 | − | 0.322025i | \(-0.104364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.6313 | −2.07352 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.4466 | 1.93501 | 0.967507 | − | 0.252845i | \(-0.0813664\pi\) | ||||
0.967507 | + | 0.252845i | \(0.0813664\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.0251i | 1.45253i | 0.687415 | + | 0.726265i | \(0.258745\pi\) | ||||
−0.687415 | + | 0.726265i | \(0.741255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.7070 | −1.50446 | −0.752229 | − | 0.658902i | \(-0.771021\pi\) | ||||
−0.752229 | + | 0.658902i | \(0.771021\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.51951 | 0.239141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.18552i | − 0.205596i | −0.994702 | − | 0.102798i | \(-0.967220\pi\) | ||||
0.994702 | − | 0.102798i | \(-0.0327795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 21.7961i | 2.01505i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.30414 | 0.119551 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.9753 | 2.45230 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30.6433i | 2.76301i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.17635i | − 0.193119i | −0.995327 | − | 0.0965597i | \(-0.969216\pi\) | ||||
0.995327 | − | 0.0965597i | \(-0.0307839\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.90362 | 0.519785 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7416 | −1.11324 | −0.556620 | − | 0.830767i | \(-0.687902\pi\) | ||||
−0.556620 | + | 0.830767i | \(0.687902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.47132i | 0.301002i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.26513i | 0.364394i | 0.983262 | + | 0.182197i | \(0.0583209\pi\) | ||||
−0.983262 | + | 0.182197i | \(0.941679\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6290 | 0.986356 | 0.493178 | − | 0.869928i | \(-0.335835\pi\) | ||||
0.493178 | + | 0.869928i | \(0.335835\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.0366 | 2.02425 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 40.1194i | − 3.35495i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.9566i | 1.39855i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.3591 | 1.42211 | 0.711056 | − | 0.703136i | \(-0.248217\pi\) | ||||
0.711056 | + | 0.703136i | \(0.248217\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.343164 | 0.0279263 | 0.0139631 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139631 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 8.40444i | − 0.679458i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.16241i | 0.332197i | 0.986109 | + | 0.166098i | \(0.0531169\pi\) | ||||
−0.986109 | + | 0.166098i | \(0.946883\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.1831 | 1.83854 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.57880 | −0.124427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.3455i | 1.51526i | 0.652686 | + | 0.757628i | \(0.273642\pi\) | ||||
−0.652686 | + | 0.757628i | \(0.726358\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.979321i | 0.0757821i | 0.999282 | + | 0.0378911i | \(0.0120640\pi\) | ||||
−0.999282 | + | 0.0378911i | \(0.987936\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −29.3845 | −2.26035 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.3706 | 1.71072 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.9363i | − 1.74381i | −0.489671 | − | 0.871907i | \(-0.662883\pi\) | ||||
0.489671 | − | 0.871907i | \(-0.337117\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.6274i | 1.77594i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.7600 | 1.25270 | 0.626349 | − | 0.779543i | \(-0.284548\pi\) | ||||
0.626349 | + | 0.779543i | \(0.284548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4466 | −0.850822 | −0.425411 | − | 0.905000i | \(-0.639871\pi\) | ||||
−0.425411 | + | 0.905000i | \(0.639871\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.03902i | 0.372495i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.4697i | 1.13126i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.455405 | −0.0331259 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4351 | −0.755060 | −0.377530 | − | 0.925997i | \(-0.623226\pi\) | ||||
−0.377530 | + | 0.925997i | \(0.623226\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4029i | 1.46863i | 0.678809 | + | 0.734315i | \(0.262497\pi\) | ||||
−0.678809 | + | 0.734315i | \(0.737503\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1051i | 0.791202i | 0.918422 | + | 0.395601i | \(0.129464\pi\) | ||||
−0.918422 | + | 0.395601i | \(0.870536\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.622223 | 0.0441083 | 0.0220541 | − | 0.999757i | \(-0.492979\pi\) | ||||
0.0220541 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.899710 | 0.0634606 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.57880i | − 0.110810i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.1744i | 0.707171i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.1768 | −2.84826 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.3001 | −1.25983 | −0.629917 | − | 0.776662i | \(-0.716911\pi\) | ||||
−0.629917 | + | 0.776662i | \(0.716911\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 7.24764i | − 0.496600i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.25403i | 0.153013i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 25.8009 | 1.74346 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3432 | 1.09936 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 0.784636i | − 0.0525431i | −0.999655 | − | 0.0262715i | \(-0.991637\pi\) | ||||
0.999655 | − | 0.0262715i | \(-0.00836345\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 6.32482i | − 0.419793i | −0.977724 | − | 0.209897i | \(-0.932687\pi\) | ||||
0.977724 | − | 0.209897i | \(-0.0673128\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.08437 | −0.137739 | −0.0688697 | − | 0.997626i | \(-0.521939\pi\) | ||||
−0.0688697 | + | 0.997626i | \(0.521939\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.06604 | 0.530706 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.4626i | 1.73362i | 0.498639 | + | 0.866810i | \(0.333833\pi\) | ||||
−0.498639 | + | 0.866810i | \(0.666167\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.71811i | − 0.111603i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.6636 | −1.20725 | −0.603623 | − | 0.797270i | \(-0.706277\pi\) | ||||
−0.603623 | + | 0.797270i | \(0.706277\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0596981 | −0.00384549 | −0.00192274 | − | 0.999998i | \(-0.500612\pi\) | ||||
−0.00192274 | + | 0.999998i | \(0.500612\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 22.3706i | − 1.43507i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.5016i | 2.76794i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.5614 | −0.986161 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.05295 | 0.192701 | 0.0963503 | − | 0.995347i | \(-0.469283\pi\) | ||||
0.0963503 | + | 0.995347i | \(0.469283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 18.7277i | − 1.17740i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.9132i | 1.30453i | 0.757991 | + | 0.652265i | \(0.226181\pi\) | ||||
−0.757991 | + | 0.652265i | \(0.773819\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.519509 | −0.0322807 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.1744 | −0.629780 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 7.91122i | − 0.487827i | −0.969797 | − | 0.243913i | \(-0.921569\pi\) | ||||
0.969797 | − | 0.243913i | \(-0.0784312\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.7667i | 1.69929i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.606717 | 0.0369922 | 0.0184961 | − | 0.999829i | \(-0.494112\pi\) | ||||
0.0184961 | + | 0.999829i | \(0.494112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5931 | 1.25094 | 0.625472 | − | 0.780247i | \(-0.284906\pi\) | ||||
0.625472 | + | 0.780247i | \(0.284906\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 8.52144i | − 0.515741i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 21.2842i | − 1.27885i | −0.768855 | − | 0.639423i | \(-0.779173\pi\) | ||||
0.768855 | − | 0.639423i | \(-0.220827\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.5258 | 0.869640 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3432 | −0.617021 | −0.308511 | − | 0.951221i | \(-0.599831\pi\) | ||||
−0.308511 | + | 0.951221i | \(0.599831\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.67518i | 0.0995789i | 0.998760 | + | 0.0497894i | \(0.0158550\pi\) | ||||
−0.998760 | + | 0.0497894i | \(0.984145\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 6.31849i | − 0.372969i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.6982 | 0.629306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.9817 | 0.936862 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.96332i | 0.582063i | 0.956713 | + | 0.291032i | \(0.0939985\pi\) | ||||
−0.956713 | + | 0.291032i | \(0.906001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 5.40201i | − 0.313456i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.7850 | −1.14420 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.21730 | −0.0701637 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 48.9960i | 2.81475i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 26.2265i | − 1.49683i | −0.663233 | − | 0.748413i | \(-0.730816\pi\) | ||||
0.663233 | − | 0.748413i | \(-0.269184\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.03902 | −0.286660 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.74881 | 0.0991658 | 0.0495829 | − | 0.998770i | \(-0.484211\pi\) | ||||
0.0495829 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 21.7762i | − 1.23087i | −0.788189 | − | 0.615433i | \(-0.788981\pi\) | ||||
0.788189 | − | 0.615433i | \(-0.211019\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 4.42120i | − 0.248319i | −0.992262 | − | 0.124160i | \(-0.960376\pi\) | ||||
0.992262 | − | 0.124160i | \(-0.0396235\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.7277 | 1.04855 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.8558 | −2.11291 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 16.7739i | − 0.933324i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 39.5740i | − 2.18844i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.95622 | −0.273245 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.4168 | 1.78179 | 0.890894 | − | 0.454211i | \(-0.150079\pi\) | ||||
0.890894 | + | 0.454211i | \(0.150079\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.34793i | 0.183465i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 29.8789i | − 1.62761i | −0.581138 | − | 0.813805i | \(-0.697392\pi\) | ||||
0.581138 | − | 0.813805i | \(-0.302608\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.50643 | 0.299068 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.7372 | −1.44790 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 7.13292i | − 0.385142i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.88294i | − 0.154765i | −0.997001 | − | 0.0773823i | \(-0.975344\pi\) | ||||
0.997001 | − | 0.0773823i | \(-0.0246562\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.5494 | −1.68880 | −0.844399 | − | 0.535714i | \(-0.820042\pi\) | ||||
−0.844399 | + | 0.535714i | \(0.820042\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.70701 | −0.304617 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2.68633i | − 0.142979i | −0.997441 | − | 0.0714894i | \(-0.977225\pi\) | ||||
0.997441 | − | 0.0714894i | \(-0.0227752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.28581i | 0.173903i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.9570 | −1.15885 | −0.579423 | − | 0.815027i | \(-0.696722\pi\) | ||||
−0.579423 | + | 0.815027i | \(0.696722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.6481 | 1.34990 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 67.9646i | 3.56722i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.3499i | 1.32325i | 0.749833 | + | 0.661627i | \(0.230134\pi\) | ||||
−0.749833 | + | 0.661627i | \(0.769866\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −40.7189 | −2.11974 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.78023 | −0.248177 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.6322i | 1.22363i | 0.791002 | + | 0.611813i | \(0.209560\pi\) | ||||
−0.791002 | + | 0.611813i | \(0.790440\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 19.7850i | − 1.01898i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8216 | 0.966800 | 0.483400 | − | 0.875400i | \(-0.339402\pi\) | ||||
0.483400 | + | 0.875400i | \(0.339402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.48332 | 0.280919 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.0485i | 0.564554i | 0.959333 | + | 0.282277i | \(0.0910898\pi\) | ||||
−0.959333 | + | 0.282277i | \(0.908910\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.84474i | 0.398771i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.4235 | −1.49183 | −0.745916 | − | 0.666040i | \(-0.767988\pi\) | ||||
−0.745916 | + | 0.666040i | \(0.767988\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.62897 | 0.385814 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 32.1026i | − 1.61936i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 17.2014i | − 0.863315i | −0.902038 | − | 0.431658i | \(-0.857929\pi\) | ||||
0.902038 | − | 0.431658i | \(-0.142071\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.74603 | −0.437849 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.6496 | 0.931319 | 0.465660 | − | 0.884964i | \(-0.345817\pi\) | ||||
0.465660 | + | 0.884964i | \(0.345817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.2468i | 1.40707i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6.16241i | − 0.305459i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0390 | −0.545844 | −0.272922 | − | 0.962036i | \(-0.587990\pi\) | ||||
−0.272922 | + | 0.962036i | \(0.587990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7460 | −0.530062 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.87184i | − 0.239728i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.2993i | 1.43479i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.95698 | 0.486430 | 0.243215 | − | 0.969972i | \(-0.421798\pi\) | ||||
0.243215 | + | 0.969972i | \(0.421798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.8153 | 1.11195 | 0.555974 | − | 0.831200i | \(-0.312346\pi\) | ||||
0.555974 | + | 0.831200i | \(0.312346\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.9399i | 1.55297i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.03902i | − 0.0502816i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 101.081 | 4.88025 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.67239 | 0.417735 | 0.208867 | − | 0.977944i | \(-0.433022\pi\) | ||||
0.208867 | + | 0.977944i | \(0.433022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 5.38852i | − 0.258956i | −0.991582 | − | 0.129478i | \(-0.958670\pi\) | ||||
0.991582 | − | 0.129478i | \(-0.0413301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.3065i | 0.971391i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.603884 | −0.0288218 | −0.0144109 | − | 0.999896i | \(-0.504587\pi\) | ||||
−0.0144109 | + | 0.999896i | \(0.504587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.5319 | −1.07295 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.2655i | 1.29542i | 0.761885 | + | 0.647712i | \(0.224274\pi\) | ||||
−0.761885 | + | 0.647712i | \(0.775726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 43.7364i | 2.06866i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.28581 | −0.438224 | −0.219112 | − | 0.975700i | \(-0.570316\pi\) | ||||
−0.219112 | + | 0.975700i | \(0.570316\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 74.9498 | 3.52925 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.864604i | 0.0406227i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 12.2651i | − 0.573738i | −0.957970 | − | 0.286869i | \(-0.907385\pi\) | ||||
0.957970 | − | 0.286869i | \(-0.0926145\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.20058 | 0.102714 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.81291 | 0.0844357 | 0.0422178 | − | 0.999108i | \(-0.486558\pi\) | ||||
0.0422178 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 23.7349i | − 1.10305i | −0.834157 | − | 0.551527i | \(-0.814046\pi\) | ||||
0.834157 | − | 0.551527i | \(-0.185954\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 6.00000i | − 0.277647i | −0.990317 | − | 0.138823i | \(-0.955668\pi\) | ||||
0.990317 | − | 0.138823i | \(-0.0443321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.185515 | −0.00856630 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4872 | −0.483226 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 14.4395i | − 0.663931i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.8057i | 1.41050i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.62456 | 0.439758 | 0.219879 | − | 0.975527i | \(-0.429434\pi\) | ||||
0.219879 | + | 0.975527i | \(0.429434\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.51034 | −0.296846 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 3.97780i | − 0.180996i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.7165i | 1.43721i | 0.695417 | + | 0.718607i | \(0.255220\pi\) | ||||
−0.695417 | + | 0.718607i | \(0.744780\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −48.7412 | −2.20415 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.02068 | −0.226580 | −0.113290 | − | 0.993562i | \(-0.536139\pi\) | ||||
−0.113290 | + | 0.993562i | \(0.536139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.62897i | 0.343591i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.49442i | 0.0670341i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.8794 | −1.56141 | −0.780707 | − | 0.624897i | \(-0.785141\pi\) | ||||
−0.780707 | + | 0.624897i | \(0.785141\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.46741 | −0.110236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.2158i | 0.901377i | 0.892681 | + | 0.450688i | \(0.148821\pi\) | ||||
−0.892681 | + | 0.450688i | \(0.851179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 74.0346i | − 3.28799i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.18075 | −0.185309 | −0.0926543 | − | 0.995698i | \(-0.529535\pi\) | ||||
−0.0926543 | + | 0.995698i | \(0.529535\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.32001 | −0.235343 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.85742i | 0.258611i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 58.7906i | − 2.58561i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.7882 | 2.53662 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.26036 | −0.274271 | −0.137136 | − | 0.990552i | \(-0.543790\pi\) | ||||
−0.137136 | + | 0.990552i | \(0.543790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.3432i | 1.32681i | 0.748259 | + | 0.663407i | \(0.230890\pi\) | ||||
−0.748259 | + | 0.663407i | \(0.769110\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 10.8918i | − 0.474452i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.7644 | 0.598451 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.3961 | −1.36248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 79.1814i | − 3.42973i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 42.2269i | 1.82222i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.4737 | 1.78640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0502 | −0.690051 | −0.345025 | − | 0.938593i | \(-0.612130\pi\) | ||||
−0.345025 | + | 0.938593i | \(0.612130\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 28.8399i | − 1.23764i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 21.0804i | − 0.901332i | −0.892693 | − | 0.450666i | \(-0.851187\pi\) | ||||
0.892693 | − | 0.450666i | \(-0.148813\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.69586 | −0.285772 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.3065 | −0.865085 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.354265i | 0.0150649i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 0.959408i | − 0.0406514i | −0.999793 | − | 0.0203257i | \(-0.993530\pi\) | ||||
0.999793 | − | 0.0203257i | \(-0.00647032\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.2548 | −0.645209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.9762 | −1.64558 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 41.3957i | − 1.74462i | −0.488954 | − | 0.872310i | \(-0.662621\pi\) | ||||
0.488954 | − | 0.872310i | \(-0.337379\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.07044i | 0.170942i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.4626 | 1.10937 | 0.554684 | − | 0.832061i | \(-0.312839\pi\) | ||||
0.554684 | + | 0.832061i | \(0.312839\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4482 | 0.730185 | 0.365093 | − | 0.930971i | \(-0.381037\pi\) | ||||
0.365093 | + | 0.930971i | \(0.381037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 26.2914i | − 1.09834i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 30.2954i | − 1.26121i | −0.776103 | − | 0.630607i | \(-0.782806\pi\) | ||||
0.776103 | − | 0.630607i | \(-0.217194\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −51.4052 | −2.13633 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.20867 | 0.133118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 56.7030i | − 2.34840i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 21.2858i | − 0.878559i | −0.898350 | − | 0.439280i | \(-0.855234\pi\) | ||||
0.898350 | − | 0.439280i | \(-0.144766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.9912 | 1.19456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.9793 | −1.15091 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 17.5629i | − 0.721223i | −0.932716 | − | 0.360612i | \(-0.882568\pi\) | ||||
0.932716 | − | 0.360612i | \(-0.117432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.56770i | 0.0641616i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.8901 | 0.526675 | 0.263338 | − | 0.964704i | \(-0.415177\pi\) | ||||
0.263338 | + | 0.964704i | \(0.415177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.8424 | −0.564641 | −0.282321 | − | 0.959320i | \(-0.591104\pi\) | ||||
−0.282321 | + | 0.959320i | \(0.591104\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.19554i | 0.0486860i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.7460i | − 1.00441i | −0.864749 | − | 0.502205i | \(-0.832522\pi\) | ||||
0.864749 | − | 0.502205i | \(-0.167478\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.97780 | 0.161189 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.1099 | −2.51270 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 11.9753i | − 0.483679i | −0.970316 | − | 0.241839i | \(-0.922249\pi\) | ||||
0.970316 | − | 0.241839i | \(-0.0777507\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.5167i | 1.02726i | 0.858010 | + | 0.513632i | \(0.171700\pi\) | ||||
−0.858010 | + | 0.513632i | \(0.828300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0660 | 0.967296 | 0.483648 | − | 0.875263i | \(-0.339312\pi\) | ||||
0.483648 | + | 0.875263i | \(0.339312\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.66402 | −0.106904 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5.72535i | − 0.229381i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 103.745i | − 4.14318i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.51034 | 0.100094 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5545 | −0.977500 | −0.488750 | − | 0.872424i | \(-0.662547\pi\) | ||||
−0.488750 | + | 0.872424i | \(0.662547\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 46.1074i | − 1.83260i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 43.8153i | − 1.73603i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.63067 | 0.380983 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.20300 | −0.205506 | −0.102753 | − | 0.994707i | \(-0.532765\pi\) | ||||
−0.102753 | + | 0.994707i | \(0.532765\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 0.0875650i | − 0.00345323i | −0.999999 | − | 0.00172661i | \(-0.999450\pi\) | ||||
0.999999 | − | 0.00172661i | \(-0.000549599\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.81606i | 0.228653i | 0.993443 | + | 0.114326i | \(0.0364710\pi\) | ||||
−0.993443 | + | 0.114326i | \(0.963529\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.7897 | 2.26845 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.67904 | −0.222579 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.5716i | 0.491965i | 0.969274 | + | 0.245983i | \(0.0791106\pi\) | ||||
−0.969274 | + | 0.245983i | \(0.920889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.2843i | 1.33756i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.7730 | −0.848157 | −0.424079 | − | 0.905625i | \(-0.639402\pi\) | ||||
−0.424079 | + | 0.905625i | \(0.639402\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.29462 | −0.361519 | −0.180759 | − | 0.983527i | \(-0.557856\pi\) | ||||
−0.180759 | + | 0.983527i | \(0.557856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 41.1768i | 1.59917i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.23563i | − 0.357605i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.97690 | 0.0764312 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.3248 | 0.475795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2221i | 1.31917i | 0.751632 | + | 0.659583i | \(0.229267\pi\) | ||||
−0.751632 | + | 0.659583i | \(0.770733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 15.4761i | − 0.594794i | −0.954754 | − | 0.297397i | \(-0.903881\pi\) | ||||
0.954754 | − | 0.297397i | \(-0.0961185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.29533 | −0.126463 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.9355 | 0.610648 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.3750i | 0.473516i | 0.971569 | + | 0.236758i | \(0.0760849\pi\) | ||||
−0.971569 | + | 0.236758i | \(0.923915\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 5.25160i | − 0.200361i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −59.9044 | −2.28218 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.69819 | 0.0646024 | 0.0323012 | − | 0.999478i | \(-0.489716\pi\) | ||||
0.0323012 | + | 0.999478i | \(0.489716\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.7182i | 0.407149i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.5318i | 1.15647i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −66.6727 | −2.52179 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3869 | 1.26100 | 0.630502 | − | 0.776187i | \(-0.282849\pi\) | ||||
0.630502 | + | 0.776187i | \(0.282849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.68192i | 0.252013i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 10.1027i | − 0.379952i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.9403 | 0.748874 | 0.374437 | − | 0.927252i | \(-0.377836\pi\) | ||||
0.374437 | + | 0.927252i | \(0.377836\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.28302 | 0.0856201 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.1856i | 0.493803i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 47.0231i | − 1.75611i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −43.8694 | −1.63605 | −0.818027 | − | 0.575180i | \(-0.804932\pi\) | ||||
−0.818027 | + | 0.575180i | \(0.804932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.03902 | 0.0386951 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 0.150410i | − 0.00559380i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.4052i | 1.53563i | 0.640669 | + | 0.767817i | \(0.278657\pi\) | ||||
−0.640669 | + | 0.767817i | \(0.721343\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.8574 | 1.21694 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.88214 | 0.217559 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.6919i | 0.948950i | 0.880269 | + | 0.474475i | \(0.157362\pi\) | ||||
−0.880269 | + | 0.474475i | \(0.842638\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2.20058i | − 0.0810594i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.4195 | 1.70757 | 0.853785 | − | 0.520625i | \(-0.174301\pi\) | ||||
0.853785 | + | 0.520625i | \(0.174301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −109.603 | −4.02635 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.86501i | 0.361912i | 0.983491 | + | 0.180956i | \(0.0579192\pi\) | ||||
−0.983491 | + | 0.180956i | \(0.942081\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 20.6780i | − 0.756567i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.80567 | 0.285213 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.5860 | 1.37153 | 0.685765 | − | 0.727823i | \(-0.259468\pi\) | ||||
0.685765 | + | 0.727823i | \(0.259468\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.69194i | 0.280310i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 47.1672i | − 1.71432i | −0.515049 | − | 0.857161i | \(-0.672226\pi\) | ||||
0.515049 | − | 0.857161i | \(-0.327774\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 47.1846 | 1.71269 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0167 | −1.08810 | −0.544052 | − | 0.839052i | \(-0.683111\pi\) | ||||
−0.544052 | + | 0.839052i | \(0.683111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.15994i | 0.295410i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 61.0525i | − 2.20448i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.3662 | 1.16715 | 0.583577 | − | 0.812058i | \(-0.301653\pi\) | ||||
0.583577 | + | 0.812058i | \(0.301653\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.6910 | −1.89762 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 40.6338i | − 1.46150i | −0.682648 | − | 0.730748i | \(-0.739172\pi\) | ||||
0.682648 | − | 0.730748i | \(-0.260828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 1.30891i | − 0.0469568i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −81.2683 | −2.91174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.7268 | −0.634316 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 2.66402i | − 0.0952044i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.7089i | 0.488671i | 0.969691 | + | 0.244335i | \(0.0785698\pi\) | ||||
−0.969691 | + | 0.244335i | \(0.921430\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.9324 | 0.709612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.13540 | −0.0403700 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 13.0207i | − 0.462378i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 18.3321i | − 0.649355i | −0.945825 | − | 0.324677i | \(-0.894744\pi\) | ||||
0.945825 | − | 0.324677i | \(-0.105256\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.9491 | 0.847259 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.8964 | −1.30367 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 63.1059i | − 2.22696i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.52863i | 0.0538103i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.3248 | −0.644267 | −0.322133 | − | 0.946694i | \(-0.604400\pi\) | ||||
−0.322133 | + | 0.946694i | \(0.604400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.45775 | −0.332106 | −0.166053 | − | 0.986117i | \(-0.553102\pi\) | ||||
−0.166053 | + | 0.986117i | \(0.553102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.8846i | 1.81967i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.6568i | 0.547763i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.3233 | 0.395668 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.4689 | −1.13317 | −0.566586 | − | 0.824003i | \(-0.691736\pi\) | ||||
−0.566586 | + | 0.824003i | \(0.691736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0370i | 1.11674i | 0.829593 | + | 0.558369i | \(0.188573\pi\) | ||||
−0.829593 | + | 0.558369i | \(0.811427\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.20543i | − 0.0766903i | −0.999265 | − | 0.0383451i | \(-0.987791\pi\) | ||||
0.999265 | − | 0.0383451i | \(-0.0122086\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.9745 | −0.936862 | −0.468431 | − | 0.883500i | \(-0.655181\pi\) | ||||
−0.468431 | + | 0.883500i | \(0.655181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 53.6258 | 1.86026 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.8949i | 0.585372i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.80338i | 0.131464i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.8424 | 0.719560 | 0.359780 | − | 0.933037i | \(-0.382852\pi\) | ||||
0.359780 | + | 0.933037i | \(0.382852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.7644 | −0.681530 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 26.0597i | − 0.897544i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 14.0139i | − 0.481524i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.22062 | −0.144851 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.03902 | −0.104176 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 48.7093i | − 1.66778i | −0.551933 | − | 0.833888i | \(-0.686110\pi\) | ||||
0.551933 | − | 0.833888i | \(-0.313890\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.4212i | 0.970850i | 0.874278 | + | 0.485425i | \(0.161335\pi\) | ||||
−0.874278 | + | 0.485425i | \(0.838665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.2926 | −0.555895 | −0.277947 | − | 0.960596i | \(-0.589654\pi\) | ||||
−0.277947 | + | 0.960596i | \(0.589654\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.9195 | 0.542535 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.1333i | 0.957670i | 0.877905 | + | 0.478835i | \(0.158941\pi\) | ||||
−0.877905 | + | 0.478835i | \(0.841059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.9542i | 0.915413i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.20228 | −0.142553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.32482 | −0.0787737 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.2365i | 0.718745i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.0899i | 0.847226i | 0.905843 | + | 0.423613i | \(0.139238\pi\) | ||||
−0.905843 | + | 0.423613i | \(0.860762\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.1027 | −0.846692 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.2197 | 0.984436 | 0.492218 | − | 0.870472i | \(-0.336186\pi\) | ||||
0.492218 | + | 0.870472i | \(0.336186\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9745i | 0.907763i | 0.891062 | + | 0.453882i | \(0.149961\pi\) | ||||
−0.891062 | + | 0.453882i | \(0.850039\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.2839i | 1.05041i | 0.850976 | + | 0.525205i | \(0.176011\pi\) | ||||
−0.850976 | + | 0.525205i | \(0.823989\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.13063 | −0.0379202 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −48.2835 | −1.61756 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 63.7468i | 2.13321i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 49.8486i | − 1.66440i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.1856 | −0.439763 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.0987 | 0.769530 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3.06699i | − 0.102063i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 17.4697i | − 0.580073i | −0.957016 | − | 0.290037i | \(-0.906332\pi\) | ||||
0.957016 | − | 0.290037i | \(-0.0936675\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −65.1060 | −2.15943 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.6659 | −1.24793 | −0.623964 | − | 0.781453i | \(-0.714479\pi\) | ||||
−0.623964 | + | 0.781453i | \(0.714479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.0612i | 1.25964i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.61939i | 0.218592i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.6119 | 1.43862 | 0.719312 | − | 0.694687i | \(-0.244457\pi\) | ||||
0.719312 | + | 0.694687i | \(0.244457\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 66.0780 | 2.17734 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.7277i | 0.616429i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 6.69586i | − 0.219921i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.8367 | −0.749249 | −0.374625 | − | 0.927177i | \(-0.622228\pi\) | ||||
−0.374625 | + | 0.927177i | \(0.622228\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.9701 | −1.47383 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.40614i | 0.144250i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.2309i | 0.464904i | 0.972608 | + | 0.232452i | \(0.0746749\pi\) | ||||
−0.972608 | + | 0.232452i | \(0.925325\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.8654 | 1.79047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4140 | 0.535080 | 0.267540 | − | 0.963547i | \(-0.413789\pi\) | ||||
0.267540 | + | 0.963547i | \(0.413789\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 36.9618i | − 1.20364i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.9506i | 1.10325i | 0.834093 | + | 0.551624i | \(0.185992\pi\) | ||||
−0.834093 | + | 0.551624i | \(0.814008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −66.6688 | −2.16416 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.1393 | 0.361215 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 41.5358i | − 1.34548i | −0.739881 | − | 0.672738i | \(-0.765118\pi\) | ||||
0.739881 | − | 0.672738i | \(-0.234882\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47.1846i | 1.52526i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.21577 | 0.0715510 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1752 | −0.392748 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 50.3029i | − 1.62099i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.2341i | 0.522054i | 0.965332 | + | 0.261027i | \(0.0840611\pi\) | ||||
−0.965332 | + | 0.261027i | \(0.915939\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42.2620 | 1.35765 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.7277 | 0.986098 | 0.493049 | − | 0.870001i | \(-0.335882\pi\) | ||||
0.493049 | + | 0.870001i | \(0.335882\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 6.04136i | − 0.193677i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.8654i | 0.667544i | 0.942654 | + | 0.333772i | \(0.108322\pi\) | ||||
−0.942654 | + | 0.333772i | \(0.891678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 67.9140 | 2.17054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 52.5859 | 1.67894 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 20.2360i | − 0.645430i | −0.946496 | − | 0.322715i | \(-0.895405\pi\) | ||||
0.946496 | − | 0.322715i | \(-0.104595\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 12.4872i | − 0.397473i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.12092 | −0.226432 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.33642 | −0.296581 | −0.148291 | − | 0.988944i | \(-0.547377\pi\) | ||||
−0.148291 | + | 0.988944i | \(0.547377\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 81.6744i | 2.59186i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.9506i | 0.441821i | 0.975294 | + | 0.220911i | \(0.0709029\pi\) | ||||
−0.975294 | + | 0.220911i | \(0.929097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.876607 | −0.0277346 |
(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 | 3700.2.d.i.149.6 | 8 | ||
5.2 | odd | 4 | 740.2.a.f.1.3 | ✓ | 4 | ||
5.3 | odd | 4 | 3700.2.a.j.1.2 | 4 | |||
5.4 | even | 2 | inner | 3700.2.d.i.149.3 | 8 | ||
15.2 | even | 4 | 6660.2.a.r.1.3 | 4 | |||
20.7 | even | 4 | 2960.2.a.v.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
740.2.a.f.1.3 | ✓ | 4 | 5.2 | odd | 4 | ||
2960.2.a.v.1.2 | 4 | 20.7 | even | 4 | |||
3700.2.a.j.1.2 | 4 | 5.3 | odd | 4 | |||
3700.2.d.i.149.3 | 8 | 5.4 | even | 2 | inner | ||
3700.2.d.i.149.6 | 8 | 1.1 | even | 1 | trivial | ||
6660.2.a.r.1.3 | 4 | 15.2 | even | 4 |