Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1849,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.c (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: | \(30.7424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 17x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 770) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.4 | ||
Root | \(-3.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1849 |
Dual form | 3850.2.c.y.1849.1 |
$q$-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 \(\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times\).
\(n\) | \(1751\) | \(2201\) | \(2927\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 2.00000i | − 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.00000i | 0.577350i | ||||||||
\(13\) | 4.74456i | 1.31590i | 0.753059 | + | 0.657952i | \(0.228577\pi\) | ||||
−0.753059 | + | 0.657952i | \(0.771423\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.74456i | 1.15073i | 0.817898 | + | 0.575363i | \(0.195139\pi\) | ||||
−0.817898 | + | 0.575363i | \(0.804861\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | −4.74456 | −1.08848 | −0.544239 | − | 0.838930i | \(-0.683181\pi\) | ||||
−0.544239 | + | 0.838930i | \(0.683181\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | − 1.00000i | − 0.213201i | ||||||||
\(23\) | − 4.74456i | − 0.989310i | −0.869090 | − | 0.494655i | \(-0.835294\pi\) | ||||
0.869090 | − | 0.494655i | \(-0.164706\pi\) | |||||||
\(24\) | −2.00000 | −0.408248 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.74456 | −0.930485 | ||||||||
\(27\) | − 4.00000i | − 0.769800i | ||||||||
\(28\) | − 1.00000i | − 0.188982i | ||||||||
\(29\) | 2.74456 | 0.509652 | 0.254826 | − | 0.966987i | \(-0.417982\pi\) | ||||
0.254826 | + | 0.966987i | \(0.417982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.74456 | −1.21136 | −0.605680 | − | 0.795709i | \(-0.707099\pi\) | ||||
−0.605680 | + | 0.795709i | \(0.707099\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | −4.74456 | −0.813686 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 10.7446i | − 1.76640i | −0.469001 | − | 0.883198i | \(-0.655386\pi\) | ||||
0.469001 | − | 0.883198i | \(-0.344614\pi\) | |||||||
\(38\) | − 4.74456i | − 0.769670i | ||||||||
\(39\) | 9.48913 | 1.51948 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 2.00000i | 0.308607i | ||||||||
\(43\) | − 4.00000i | − 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.74456 | 0.699548 | ||||||||
\(47\) | − 6.74456i | − 0.983796i | −0.870653 | − | 0.491898i | \(-0.836303\pi\) | ||||
0.870653 | − | 0.491898i | \(-0.163697\pi\) | |||||||
\(48\) | − 2.00000i | − 0.288675i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.48913 | 1.32874 | ||||||||
\(52\) | − 4.74456i | − 0.657952i | ||||||||
\(53\) | 1.25544i | 0.172448i | 0.996276 | + | 0.0862238i | \(0.0274800\pi\) | ||||
−0.996276 | + | 0.0862238i | \(0.972520\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 9.48913i | 1.25687i | ||||||||
\(58\) | 2.74456i | 0.360379i | ||||||||
\(59\) | −2.74456 | −0.357312 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7446 | 1.63177 | 0.815887 | − | 0.578211i | \(-0.196249\pi\) | ||||
0.815887 | + | 0.578211i | \(0.196249\pi\) | |||||||
\(62\) | − 6.74456i | − 0.856560i | ||||||||
\(63\) | − 1.00000i | − 0.125988i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.00000 | −0.246183 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | − 4.74456i | − 0.575363i | ||||||||
\(69\) | −9.48913 | −1.14236 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 0.744563i | 0.0871445i | 0.999050 | + | 0.0435722i | \(0.0138739\pi\) | ||||
−0.999050 | + | 0.0435722i | \(0.986126\pi\) | |||||||
\(74\) | 10.7446 | 1.24903 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.74456 | 0.544239 | ||||||||
\(77\) | − 1.00000i | − 0.113961i | ||||||||
\(78\) | 9.48913i | 1.07443i | ||||||||
\(79\) | 4.74456 | 0.533805 | 0.266903 | − | 0.963724i | \(-0.414000\pi\) | ||||
0.266903 | + | 0.963724i | \(0.414000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | − 4.00000i | − 0.441726i | ||||||||
\(83\) | − 8.00000i | − 0.878114i | −0.898459 | − | 0.439057i | \(-0.855313\pi\) | ||||
0.898459 | − | 0.439057i | \(-0.144687\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | − 5.48913i | − 0.588496i | ||||||||
\(88\) | 1.00000i | 0.106600i | ||||||||
\(89\) | 7.48913 | 0.793846 | 0.396923 | − | 0.917852i | \(-0.370078\pi\) | ||||
0.396923 | + | 0.917852i | \(0.370078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.74456 | −0.497365 | ||||||||
\(92\) | 4.74456i | 0.494655i | ||||||||
\(93\) | 13.4891i | 1.39876i | ||||||||
\(94\) | 6.74456 | 0.695649 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.00000 | 0.204124 | ||||||||
\(97\) | − 5.25544i | − 0.533609i | −0.963751 | − | 0.266804i | \(-0.914032\pi\) | ||||
0.963751 | − | 0.266804i | \(-0.0859678\pi\) | |||||||
\(98\) | − 1.00000i | − 0.101015i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.74456 | −0.870117 | −0.435058 | − | 0.900402i | \(-0.643272\pi\) | ||||
−0.435058 | + | 0.900402i | \(0.643272\pi\) | |||||||
\(102\) | 9.48913i | 0.939563i | ||||||||
\(103\) | − 10.7446i | − 1.05869i | −0.848406 | − | 0.529347i | \(-0.822437\pi\) | ||||
0.848406 | − | 0.529347i | \(-0.177563\pi\) | |||||||
\(104\) | 4.74456 | 0.465243 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.25544 | −0.121939 | ||||||||
\(107\) | − 12.0000i | − 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 4.00000i | 0.384900i | ||||||||
\(109\) | −16.2337 | −1.55491 | −0.777453 | − | 0.628941i | \(-0.783489\pi\) | ||||
−0.777453 | + | 0.628941i | \(0.783489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.4891 | −2.03966 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | − 10.0000i | − 0.940721i | −0.882474 | − | 0.470360i | \(-0.844124\pi\) | ||||
0.882474 | − | 0.470360i | \(-0.155876\pi\) | |||||||
\(114\) | −9.48913 | −0.888738 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.74456 | −0.254826 | ||||||||
\(117\) | − 4.74456i | − 0.438635i | ||||||||
\(118\) | − 2.74456i | − 0.252657i | ||||||||
\(119\) | −4.74456 | −0.434933 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 12.7446i | 1.15384i | ||||||||
\(123\) | 8.00000i | 0.721336i | ||||||||
\(124\) | 6.74456 | 0.605680 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.74456 | 0.764016 | 0.382008 | − | 0.924159i | \(-0.375233\pi\) | ||||
0.382008 | + | 0.924159i | \(0.375233\pi\) | |||||||
\(132\) | − 2.00000i | − 0.174078i | ||||||||
\(133\) | − 4.74456i | − 0.411406i | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.74456 | 0.406843 | ||||||||
\(137\) | − 19.4891i | − 1.66507i | −0.553974 | − | 0.832534i | \(-0.686889\pi\) | ||||
0.553974 | − | 0.832534i | \(-0.313111\pi\) | |||||||
\(138\) | − 9.48913i | − 0.807768i | ||||||||
\(139\) | −3.25544 | −0.276123 | −0.138061 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138061 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.4891 | −1.13599 | ||||||||
\(142\) | − 4.00000i | − 0.335673i | ||||||||
\(143\) | − 4.74456i | − 0.396760i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.744563 | −0.0616204 | ||||||||
\(147\) | 2.00000i | 0.164957i | ||||||||
\(148\) | 10.7446i | 0.883198i | ||||||||
\(149\) | −10.7446 | −0.880229 | −0.440114 | − | 0.897942i | \(-0.645062\pi\) | ||||
−0.440114 | + | 0.897942i | \(0.645062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.7446 | −1.68817 | −0.844084 | − | 0.536211i | \(-0.819855\pi\) | ||||
−0.844084 | + | 0.536211i | \(0.819855\pi\) | |||||||
\(152\) | 4.74456i | 0.384835i | ||||||||
\(153\) | − 4.74456i | − 0.383575i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.48913 | −0.759738 | ||||||||
\(157\) | 23.4891i | 1.87464i | 0.348475 | + | 0.937318i | \(0.386700\pi\) | ||||
−0.348475 | + | 0.937318i | \(0.613300\pi\) | |||||||
\(158\) | 4.74456i | 0.377457i | ||||||||
\(159\) | 2.51087 | 0.199125 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.74456 | 0.373924 | ||||||||
\(162\) | − 11.0000i | − 0.864242i | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00000 | 0.620920 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | − 2.00000i | − 0.154303i | ||||||||
\(169\) | −9.51087 | −0.731606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.74456 | 0.362826 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | 14.2337i | 1.08217i | 0.840969 | + | 0.541084i | \(0.181986\pi\) | ||||
−0.840969 | + | 0.541084i | \(0.818014\pi\) | |||||||
\(174\) | 5.48913 | 0.416130 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 5.48913i | 0.412588i | ||||||||
\(178\) | 7.48913i | 0.561334i | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.48913 | 0.259345 | 0.129672 | − | 0.991557i | \(-0.458607\pi\) | ||||
0.129672 | + | 0.991557i | \(0.458607\pi\) | |||||||
\(182\) | − 4.74456i | − 0.351690i | ||||||||
\(183\) | − 25.4891i | − 1.88421i | ||||||||
\(184\) | −4.74456 | −0.349774 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.4891 | −0.989071 | ||||||||
\(187\) | − 4.74456i | − 0.346957i | ||||||||
\(188\) | 6.74456i | 0.491898i | ||||||||
\(189\) | 4.00000 | 0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 2.00000i | 0.144338i | ||||||||
\(193\) | 2.00000i | 0.143963i | 0.997406 | + | 0.0719816i | \(0.0229323\pi\) | ||||
−0.997406 | + | 0.0719816i | \(0.977068\pi\) | |||||||
\(194\) | 5.25544 | 0.377318 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 10.0000i | 0.712470i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(198\) | 1.00000i | 0.0710669i | ||||||||
\(199\) | −14.7446 | −1.04521 | −0.522607 | − | 0.852574i | \(-0.675041\pi\) | ||||
−0.522607 | + | 0.852574i | \(0.675041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | − 8.74456i | − 0.615265i | ||||||||
\(203\) | 2.74456i | 0.192631i | ||||||||
\(204\) | −9.48913 | −0.664372 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.7446 | 0.748609 | ||||||||
\(207\) | 4.74456i | 0.329770i | ||||||||
\(208\) | 4.74456i | 0.328976i | ||||||||
\(209\) | 4.74456 | 0.328188 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | − 1.25544i | − 0.0862238i | ||||||||
\(213\) | 8.00000i | 0.548151i | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | − 6.74456i | − 0.457851i | ||||||||
\(218\) | − 16.2337i | − 1.09948i | ||||||||
\(219\) | 1.48913 | 0.100626 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.5109 | −1.51425 | ||||||||
\(222\) | − 21.4891i | − 1.44226i | ||||||||
\(223\) | − 26.7446i | − 1.79095i | −0.445113 | − | 0.895474i | \(-0.646837\pi\) | ||||
0.445113 | − | 0.895474i | \(-0.353163\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.0000 | 0.665190 | ||||||||
\(227\) | 20.0000i | 1.32745i | 0.747978 | + | 0.663723i | \(0.231025\pi\) | ||||
−0.747978 | + | 0.663723i | \(0.768975\pi\) | |||||||
\(228\) | − 9.48913i | − 0.628433i | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | − 2.74456i | − 0.180189i | ||||||||
\(233\) | − 20.9783i | − 1.37433i | −0.726501 | − | 0.687165i | \(-0.758855\pi\) | ||||
0.726501 | − | 0.687165i | \(-0.241145\pi\) | |||||||
\(234\) | 4.74456 | 0.310162 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.74456 | 0.178656 | ||||||||
\(237\) | − 9.48913i | − 0.616385i | ||||||||
\(238\) | − 4.74456i | − 0.307544i | ||||||||
\(239\) | 3.25544 | 0.210577 | 0.105288 | − | 0.994442i | \(-0.466423\pi\) | ||||
0.105288 | + | 0.994442i | \(0.466423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0000 | 1.28831 | 0.644157 | − | 0.764894i | \(-0.277208\pi\) | ||||
0.644157 | + | 0.764894i | \(0.277208\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | −12.7446 | −0.815887 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.00000 | −0.510061 | ||||||||
\(247\) | − 22.5109i | − 1.43233i | ||||||||
\(248\) | 6.74456i | 0.428280i | ||||||||
\(249\) | −16.0000 | −1.01396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.23369 | 0.519706 | 0.259853 | − | 0.965648i | \(-0.416326\pi\) | ||||
0.259853 | + | 0.965648i | \(0.416326\pi\) | |||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | 4.74456i | 0.298288i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.2337i | 1.51166i | 0.654770 | + | 0.755828i | \(0.272765\pi\) | ||||
−0.654770 | + | 0.755828i | \(0.727235\pi\) | |||||||
\(258\) | − 8.00000i | − 0.498058i | ||||||||
\(259\) | 10.7446 | 0.667635 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.74456 | −0.169884 | ||||||||
\(262\) | 8.74456i | 0.540241i | ||||||||
\(263\) | 18.9783i | 1.17025i | 0.810943 | + | 0.585125i | \(0.198954\pi\) | ||||
−0.810943 | + | 0.585125i | \(0.801046\pi\) | |||||||
\(264\) | 2.00000 | 0.123091 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.74456 | 0.290908 | ||||||||
\(267\) | − 14.9783i | − 0.916654i | ||||||||
\(268\) | 4.00000i | 0.244339i | ||||||||
\(269\) | 24.9783 | 1.52295 | 0.761475 | − | 0.648194i | \(-0.224475\pi\) | ||||
0.761475 | + | 0.648194i | \(0.224475\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.9783 | −1.88179 | −0.940897 | − | 0.338692i | \(-0.890016\pi\) | ||||
−0.940897 | + | 0.338692i | \(0.890016\pi\) | |||||||
\(272\) | 4.74456i | 0.287681i | ||||||||
\(273\) | 9.48913i | 0.574308i | ||||||||
\(274\) | 19.4891 | 1.17738 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.48913 | 0.571178 | ||||||||
\(277\) | − 7.48913i | − 0.449978i | −0.974361 | − | 0.224989i | \(-0.927765\pi\) | ||||
0.974361 | − | 0.224989i | \(-0.0722346\pi\) | |||||||
\(278\) | − 3.25544i | − 0.195248i | ||||||||
\(279\) | 6.74456 | 0.403786 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0000 | 0.835170 | 0.417585 | − | 0.908638i | \(-0.362877\pi\) | ||||
0.417585 | + | 0.908638i | \(0.362877\pi\) | |||||||
\(282\) | − 13.4891i | − 0.803266i | ||||||||
\(283\) | − 28.0000i | − 1.66443i | −0.554455 | − | 0.832214i | \(-0.687073\pi\) | ||||
0.554455 | − | 0.832214i | \(-0.312927\pi\) | |||||||
\(284\) | 4.00000 | 0.237356 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.74456 | 0.280552 | ||||||||
\(287\) | − 4.00000i | − 0.236113i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −5.51087 | −0.324169 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.5109 | −0.616158 | ||||||||
\(292\) | − 0.744563i | − 0.0435722i | ||||||||
\(293\) | − 24.7446i | − 1.44559i | −0.691061 | − | 0.722796i | \(-0.742856\pi\) | ||||
0.691061 | − | 0.722796i | \(-0.257144\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.7446 | −0.624515 | ||||||||
\(297\) | 4.00000i | 0.232104i | ||||||||
\(298\) | − 10.7446i | − 0.622416i | ||||||||
\(299\) | 22.5109 | 1.30184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | − 20.7446i | − 1.19372i | ||||||||
\(303\) | 17.4891i | 1.00472i | ||||||||
\(304\) | −4.74456 | −0.272119 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.74456 | 0.271229 | ||||||||
\(307\) | 21.4891i | 1.22645i | 0.789909 | + | 0.613225i | \(0.210128\pi\) | ||||
−0.789909 | + | 0.613225i | \(0.789872\pi\) | |||||||
\(308\) | 1.00000i | 0.0569803i | ||||||||
\(309\) | −21.4891 | −1.22247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.25544 | −0.524828 | −0.262414 | − | 0.964955i | \(-0.584519\pi\) | ||||
−0.262414 | + | 0.964955i | \(0.584519\pi\) | |||||||
\(312\) | − 9.48913i | − 0.537216i | ||||||||
\(313\) | − 32.2337i | − 1.82196i | −0.412455 | − | 0.910978i | \(-0.635329\pi\) | ||||
0.412455 | − | 0.910978i | \(-0.364671\pi\) | |||||||
\(314\) | −23.4891 | −1.32557 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.74456 | −0.266903 | ||||||||
\(317\) | − 32.2337i | − 1.81042i | −0.424960 | − | 0.905212i | \(-0.639712\pi\) | ||||
0.424960 | − | 0.905212i | \(-0.360288\pi\) | |||||||
\(318\) | 2.51087i | 0.140803i | ||||||||
\(319\) | −2.74456 | −0.153666 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | 4.74456i | 0.264404i | ||||||||
\(323\) | − 22.5109i | − 1.25254i | ||||||||
\(324\) | 11.0000 | 0.611111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 32.4674i | 1.79545i | ||||||||
\(328\) | 4.00000i | 0.220863i | ||||||||
\(329\) | 6.74456 | 0.371840 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.9783 | −1.70272 | −0.851359 | − | 0.524583i | \(-0.824221\pi\) | ||||
−0.851359 | + | 0.524583i | \(0.824221\pi\) | |||||||
\(332\) | 8.00000i | 0.439057i | ||||||||
\(333\) | 10.7446i | 0.588798i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | 0.109109 | ||||||||
\(337\) | 26.0000i | 1.41631i | 0.706057 | + | 0.708155i | \(0.250472\pi\) | ||||
−0.706057 | + | 0.708155i | \(0.749528\pi\) | |||||||
\(338\) | − 9.51087i | − 0.517323i | ||||||||
\(339\) | −20.0000 | −1.08625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.74456 | 0.365239 | ||||||||
\(342\) | 4.74456i | 0.256557i | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.2337 | −0.765208 | ||||||||
\(347\) | 22.9783i | 1.23354i | 0.787145 | + | 0.616769i | \(0.211559\pi\) | ||||
−0.787145 | + | 0.616769i | \(0.788441\pi\) | |||||||
\(348\) | 5.48913i | 0.294248i | ||||||||
\(349\) | −19.2554 | −1.03072 | −0.515360 | − | 0.856974i | \(-0.672342\pi\) | ||||
−0.515360 | + | 0.856974i | \(0.672342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9783 | 1.01298 | ||||||||
\(352\) | − 1.00000i | − 0.0533002i | ||||||||
\(353\) | 2.74456i | 0.146078i | 0.997329 | + | 0.0730392i | \(0.0232698\pi\) | ||||
−0.997329 | + | 0.0730392i | \(0.976730\pi\) | |||||||
\(354\) | −5.48913 | −0.291744 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.48913 | −0.396923 | ||||||||
\(357\) | 9.48913i | 0.502218i | ||||||||
\(358\) | 4.00000i | 0.211407i | ||||||||
\(359\) | 12.7446 | 0.672632 | 0.336316 | − | 0.941749i | \(-0.390819\pi\) | ||||
0.336316 | + | 0.941749i | \(0.390819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.51087 | 0.184783 | ||||||||
\(362\) | 3.48913i | 0.183384i | ||||||||
\(363\) | − 2.00000i | − 0.104973i | ||||||||
\(364\) | 4.74456 | 0.248683 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.4891 | 1.33234 | ||||||||
\(367\) | 2.74456i | 0.143265i | 0.997431 | + | 0.0716325i | \(0.0228209\pi\) | ||||
−0.997431 | + | 0.0716325i | \(0.977179\pi\) | |||||||
\(368\) | − 4.74456i | − 0.247327i | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.25544 | −0.0651791 | ||||||||
\(372\) | − 13.4891i | − 0.699379i | ||||||||
\(373\) | − 28.9783i | − 1.50044i | −0.661190 | − | 0.750218i | \(-0.729948\pi\) | ||||
0.661190 | − | 0.750218i | \(-0.270052\pi\) | |||||||
\(374\) | 4.74456 | 0.245335 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.74456 | −0.347824 | ||||||||
\(377\) | 13.0217i | 0.670654i | ||||||||
\(378\) | 4.00000i | 0.205738i | ||||||||
\(379\) | 14.5109 | 0.745374 | 0.372687 | − | 0.927957i | \(-0.378437\pi\) | ||||
0.372687 | + | 0.927957i | \(0.378437\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 16.0000i | − 0.818631i | ||||||||
\(383\) | 37.7228i | 1.92755i | 0.266724 | + | 0.963773i | \(0.414059\pi\) | ||||
−0.266724 | + | 0.963773i | \(0.585941\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | 5.25544i | 0.266804i | ||||||||
\(389\) | −15.4891 | −0.785330 | −0.392665 | − | 0.919682i | \(-0.628447\pi\) | ||||
−0.392665 | + | 0.919682i | \(0.628447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.5109 | 1.13842 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | − 17.4891i | − 0.882210i | ||||||||
\(394\) | −10.0000 | −0.503793 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 12.5109i | 0.627903i | 0.949439 | + | 0.313951i | \(0.101653\pi\) | ||||
−0.949439 | + | 0.313951i | \(0.898347\pi\) | |||||||
\(398\) | − 14.7446i | − 0.739078i | ||||||||
\(399\) | −9.48913 | −0.475050 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.510875 | 0.0255119 | 0.0127559 | − | 0.999919i | \(-0.495940\pi\) | ||||
0.0127559 | + | 0.999919i | \(0.495940\pi\) | |||||||
\(402\) | − 8.00000i | − 0.399004i | ||||||||
\(403\) | − 32.0000i | − 1.59403i | ||||||||
\(404\) | 8.74456 | 0.435058 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.74456 | −0.136210 | ||||||||
\(407\) | 10.7446i | 0.532588i | ||||||||
\(408\) | − 9.48913i | − 0.469782i | ||||||||
\(409\) | −1.48913 | −0.0736325 | −0.0368163 | − | 0.999322i | \(-0.511722\pi\) | ||||
−0.0368163 | + | 0.999322i | \(0.511722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −38.9783 | −1.92266 | ||||||||
\(412\) | 10.7446i | 0.529347i | ||||||||
\(413\) | − 2.74456i | − 0.135051i | ||||||||
\(414\) | −4.74456 | −0.233183 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.74456 | −0.232621 | ||||||||
\(417\) | 6.51087i | 0.318839i | ||||||||
\(418\) | 4.74456i | 0.232064i | ||||||||
\(419\) | −10.7446 | −0.524906 | −0.262453 | − | 0.964945i | \(-0.584532\pi\) | ||||
−0.262453 | + | 0.964945i | \(0.584532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4891 | 1.33974 | 0.669869 | − | 0.742479i | \(-0.266350\pi\) | ||||
0.669869 | + | 0.742479i | \(0.266350\pi\) | |||||||
\(422\) | − 12.0000i | − 0.584151i | ||||||||
\(423\) | 6.74456i | 0.327932i | ||||||||
\(424\) | 1.25544 | 0.0609694 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 12.7446i | 0.616753i | ||||||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | −9.48913 | −0.458139 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.7446 | −1.38458 | −0.692288 | − | 0.721621i | \(-0.743397\pi\) | ||||
−0.692288 | + | 0.721621i | \(0.743397\pi\) | |||||||
\(432\) | − 4.00000i | − 0.192450i | ||||||||
\(433\) | − 25.2554i | − 1.21370i | −0.794817 | − | 0.606849i | \(-0.792433\pi\) | ||||
0.794817 | − | 0.606849i | \(-0.207567\pi\) | |||||||
\(434\) | 6.74456 | 0.323749 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.2337 | 0.777453 | ||||||||
\(437\) | 22.5109i | 1.07684i | ||||||||
\(438\) | 1.48913i | 0.0711532i | ||||||||
\(439\) | 30.9783 | 1.47851 | 0.739256 | − | 0.673425i | \(-0.235178\pi\) | ||||
0.739256 | + | 0.673425i | \(0.235178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − 22.5109i | − 1.07073i | ||||||||
\(443\) | 6.51087i | 0.309341i | 0.987966 | + | 0.154670i | \(0.0494316\pi\) | ||||
−0.987966 | + | 0.154670i | \(0.950568\pi\) | |||||||
\(444\) | 21.4891 | 1.01983 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.7446 | 1.26639 | ||||||||
\(447\) | 21.4891i | 1.01640i | ||||||||
\(448\) | − 1.00000i | − 0.0472456i | ||||||||
\(449\) | −40.9783 | −1.93388 | −0.966942 | − | 0.254998i | \(-0.917925\pi\) | ||||
−0.966942 | + | 0.254998i | \(0.917925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 10.0000i | 0.470360i | ||||||||
\(453\) | 41.4891i | 1.94933i | ||||||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.48913 | 0.444369 | ||||||||
\(457\) | − 19.4891i | − 0.911663i | −0.890066 | − | 0.455831i | \(-0.849342\pi\) | ||||
0.890066 | − | 0.455831i | \(-0.150658\pi\) | |||||||
\(458\) | 6.00000i | 0.280362i | ||||||||
\(459\) | 18.9783 | 0.885829 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.7228 | −1.10488 | −0.552441 | − | 0.833552i | \(-0.686303\pi\) | ||||
−0.552441 | + | 0.833552i | \(0.686303\pi\) | |||||||
\(462\) | − 2.00000i | − 0.0930484i | ||||||||
\(463\) | − 12.7446i | − 0.592290i | −0.955143 | − | 0.296145i | \(-0.904299\pi\) | ||||
0.955143 | − | 0.296145i | \(-0.0957012\pi\) | |||||||
\(464\) | 2.74456 | 0.127413 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.9783 | 0.971799 | ||||||||
\(467\) | − 28.9783i | − 1.34095i | −0.741931 | − | 0.670477i | \(-0.766090\pi\) | ||||
0.741931 | − | 0.670477i | \(-0.233910\pi\) | |||||||
\(468\) | 4.74456i | 0.219317i | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.9783 | 2.16464 | ||||||||
\(472\) | 2.74456i | 0.126329i | ||||||||
\(473\) | 4.00000i | 0.183920i | ||||||||
\(474\) | 9.48913 | 0.435850 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.74456 | 0.217467 | ||||||||
\(477\) | − 1.25544i | − 0.0574825i | ||||||||
\(478\) | 3.25544i | 0.148900i | ||||||||
\(479\) | 18.5109 | 0.845783 | 0.422892 | − | 0.906180i | \(-0.361015\pi\) | ||||
0.422892 | + | 0.906180i | \(0.361015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.9783 | 2.32441 | ||||||||
\(482\) | 20.0000i | 0.910975i | ||||||||
\(483\) | − 9.48913i | − 0.431770i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.0000 | −0.453609 | ||||||||
\(487\) | 20.7446i | 0.940026i | 0.882660 | + | 0.470013i | \(0.155751\pi\) | ||||
−0.882660 | + | 0.470013i | \(0.844249\pi\) | |||||||
\(488\) | − 12.7446i | − 0.576919i | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.9783 | −0.675959 | −0.337979 | − | 0.941153i | \(-0.609743\pi\) | ||||
−0.337979 | + | 0.941153i | \(0.609743\pi\) | |||||||
\(492\) | − 8.00000i | − 0.360668i | ||||||||
\(493\) | 13.0217i | 0.586470i | ||||||||
\(494\) | 22.5109 | 1.01281 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.74456 | −0.302840 | ||||||||
\(497\) | − 4.00000i | − 0.179425i | ||||||||
\(498\) | − 16.0000i | − 0.716977i | ||||||||
\(499\) | −9.48913 | −0.424792 | −0.212396 | − | 0.977184i | \(-0.568127\pi\) | ||||
−0.212396 | + | 0.977184i | \(0.568127\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.23369i | 0.367487i | ||||||||
\(503\) | − 29.4891i | − 1.31486i | −0.753518 | − | 0.657428i | \(-0.771645\pi\) | ||||
0.753518 | − | 0.657428i | \(-0.228355\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.74456 | −0.210922 | ||||||||
\(507\) | 19.0217i | 0.844786i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.5109 | 0.554535 | 0.277267 | − | 0.960793i | \(-0.410571\pi\) | ||||
0.277267 | + | 0.960793i | \(0.410571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.744563 | −0.0329375 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 18.9783i | 0.837910i | ||||||||
\(514\) | −24.2337 | −1.06890 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 6.74456i | 0.296626i | ||||||||
\(518\) | 10.7446i | 0.472089i | ||||||||
\(519\) | 28.4674 | 1.24958 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.00000 | −0.0876216 | −0.0438108 | − | 0.999040i | \(-0.513950\pi\) | ||||
−0.0438108 | + | 0.999040i | \(0.513950\pi\) | |||||||
\(522\) | − 2.74456i | − 0.120126i | ||||||||
\(523\) | − 5.48913i | − 0.240023i | −0.992773 | − | 0.120011i | \(-0.961707\pi\) | ||||
0.992773 | − | 0.120011i | \(-0.0382931\pi\) | |||||||
\(524\) | −8.74456 | −0.382008 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.9783 | −0.827491 | ||||||||
\(527\) | − 32.0000i | − 1.39394i | ||||||||
\(528\) | 2.00000i | 0.0870388i | ||||||||
\(529\) | 0.489125 | 0.0212663 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.74456 | 0.119104 | ||||||||
\(532\) | 4.74456i | 0.205703i | ||||||||
\(533\) | − 18.9783i | − 0.822039i | ||||||||
\(534\) | 14.9783 | 0.648172 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | − 8.00000i | − 0.345225i | ||||||||
\(538\) | 24.9783i | 1.07689i | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.2337 | 1.55781 | 0.778904 | − | 0.627143i | \(-0.215776\pi\) | ||||
0.778904 | + | 0.627143i | \(0.215776\pi\) | |||||||
\(542\) | − 30.9783i | − 1.33063i | ||||||||
\(543\) | − 6.97825i | − 0.299465i | ||||||||
\(544\) | −4.74456 | −0.203421 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.48913 | −0.406097 | ||||||||
\(547\) | − 30.9783i | − 1.32453i | −0.749268 | − | 0.662267i | \(-0.769594\pi\) | ||||
0.749268 | − | 0.662267i | \(-0.230406\pi\) | |||||||
\(548\) | 19.4891i | 0.832534i | ||||||||
\(549\) | −12.7446 | −0.543925 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.0217 | −0.554745 | ||||||||
\(552\) | 9.48913i | 0.403884i | ||||||||
\(553\) | 4.74456i | 0.201759i | ||||||||
\(554\) | 7.48913 | 0.318182 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.25544 | 0.138061 | ||||||||
\(557\) | 44.9783i | 1.90579i | 0.303301 | + | 0.952895i | \(0.401911\pi\) | ||||
−0.303301 | + | 0.952895i | \(0.598089\pi\) | |||||||
\(558\) | 6.74456i | 0.285520i | ||||||||
\(559\) | 18.9783 | 0.802694 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.48913 | −0.400631 | ||||||||
\(562\) | 14.0000i | 0.590554i | ||||||||
\(563\) | 17.4891i | 0.737079i | 0.929612 | + | 0.368539i | \(0.120142\pi\) | ||||
−0.929612 | + | 0.368539i | \(0.879858\pi\) | |||||||
\(564\) | 13.4891 | 0.567995 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 28.0000 | 1.17693 | ||||||||
\(567\) | − 11.0000i | − 0.461957i | ||||||||
\(568\) | 4.00000i | 0.167836i | ||||||||
\(569\) | −39.4891 | −1.65547 | −0.827735 | − | 0.561119i | \(-0.810371\pi\) | ||||
−0.827735 | + | 0.561119i | \(0.810371\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.48913 | 0.229713 | 0.114856 | − | 0.993382i | \(-0.463359\pi\) | ||||
0.114856 | + | 0.993382i | \(0.463359\pi\) | |||||||
\(572\) | 4.74456i | 0.198380i | ||||||||
\(573\) | 32.0000i | 1.33682i | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 2.74456i | 0.114258i | 0.998367 | + | 0.0571288i | \(0.0181946\pi\) | ||||
−0.998367 | + | 0.0571288i | \(0.981805\pi\) | |||||||
\(578\) | − 5.51087i | − 0.229222i | ||||||||
\(579\) | 4.00000 | 0.166234 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | − 10.5109i | − 0.435690i | ||||||||
\(583\) | − 1.25544i | − 0.0519949i | ||||||||
\(584\) | 0.744563 | 0.0308102 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.7446 | 1.02219 | ||||||||
\(587\) | 40.9783i | 1.69135i | 0.533696 | + | 0.845677i | \(0.320803\pi\) | ||||
−0.533696 | + | 0.845677i | \(0.679197\pi\) | |||||||
\(588\) | − 2.00000i | − 0.0824786i | ||||||||
\(589\) | 32.0000 | 1.31854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.0000 | 0.822690 | ||||||||
\(592\) | − 10.7446i | − 0.441599i | ||||||||
\(593\) | 5.76631i | 0.236794i | 0.992966 | + | 0.118397i | \(0.0377756\pi\) | ||||
−0.992966 | + | 0.118397i | \(0.962224\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.7446 | 0.440114 | ||||||||
\(597\) | 29.4891i | 1.20691i | ||||||||
\(598\) | 22.5109i | 0.920538i | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.5109 | −0.428748 | −0.214374 | − | 0.976752i | \(-0.568771\pi\) | ||||
−0.214374 | + | 0.976752i | \(0.568771\pi\) | |||||||
\(602\) | 4.00000i | 0.163028i | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 20.7446 | 0.844084 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.4891 | −0.710447 | ||||||||
\(607\) | 8.00000i | 0.324710i | 0.986732 | + | 0.162355i | \(0.0519090\pi\) | ||||
−0.986732 | + | 0.162355i | \(0.948091\pi\) | |||||||
\(608\) | − 4.74456i | − 0.192417i | ||||||||
\(609\) | 5.48913 | 0.222431 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.0000 | 1.29458 | ||||||||
\(612\) | 4.74456i | 0.191788i | ||||||||
\(613\) | 11.4891i | 0.464041i | 0.972711 | + | 0.232021i | \(0.0745337\pi\) | ||||
−0.972711 | + | 0.232021i | \(0.925466\pi\) | |||||||
\(614\) | −21.4891 | −0.867231 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | − 10.0000i | − 0.402585i | −0.979531 | − | 0.201292i | \(-0.935486\pi\) | ||||
0.979531 | − | 0.201292i | \(-0.0645141\pi\) | |||||||
\(618\) | − 21.4891i | − 0.864419i | ||||||||
\(619\) | 10.7446 | 0.431860 | 0.215930 | − | 0.976409i | \(-0.430722\pi\) | ||||
0.215930 | + | 0.976409i | \(0.430722\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.9783 | −0.761571 | ||||||||
\(622\) | − 9.25544i | − 0.371109i | ||||||||
\(623\) | 7.48913i | 0.300045i | ||||||||
\(624\) | 9.48913 | 0.379869 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.2337 | 1.28832 | ||||||||
\(627\) | − 9.48913i | − 0.378959i | ||||||||
\(628\) | − 23.4891i | − 0.937318i | ||||||||
\(629\) | 50.9783 | 2.03264 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.9783 | 1.71094 | 0.855469 | − | 0.517855i | \(-0.173269\pi\) | ||||
0.855469 | + | 0.517855i | \(0.173269\pi\) | |||||||
\(632\) | − 4.74456i | − 0.188729i | ||||||||
\(633\) | 24.0000i | 0.953914i | ||||||||
\(634\) | 32.2337 | 1.28016 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.51087 | −0.0995627 | ||||||||
\(637\) | − 4.74456i | − 0.187986i | ||||||||
\(638\) | − 2.74456i | − 0.108658i | ||||||||
\(639\) | 4.00000 | 0.158238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.4891 | −0.453793 | −0.226897 | − | 0.973919i | \(-0.572858\pi\) | ||||
−0.226897 | + | 0.973919i | \(0.572858\pi\) | |||||||
\(642\) | − 24.0000i | − 0.947204i | ||||||||
\(643\) | 22.4674i | 0.886027i | 0.896515 | + | 0.443013i | \(0.146091\pi\) | ||||
−0.896515 | + | 0.443013i | \(0.853909\pi\) | |||||||
\(644\) | −4.74456 | −0.186962 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.5109 | 0.885679 | ||||||||
\(647\) | − 2.74456i | − 0.107900i | −0.998544 | − | 0.0539499i | \(-0.982819\pi\) | ||||
0.998544 | − | 0.0539499i | \(-0.0171811\pi\) | |||||||
\(648\) | 11.0000i | 0.432121i | ||||||||
\(649\) | 2.74456 | 0.107734 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.4891 | −0.528681 | ||||||||
\(652\) | − 4.00000i | − 0.156652i | ||||||||
\(653\) | 41.7228i | 1.63274i | 0.577529 | + | 0.816370i | \(0.304017\pi\) | ||||
−0.577529 | + | 0.816370i | \(0.695983\pi\) | |||||||
\(654\) | −32.4674 | −1.26957 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.00000 | −0.156174 | ||||||||
\(657\) | − 0.744563i | − 0.0290482i | ||||||||
\(658\) | 6.74456i | 0.262930i | ||||||||
\(659\) | 18.5109 | 0.721081 | 0.360541 | − | 0.932744i | \(-0.382592\pi\) | ||||
0.360541 | + | 0.932744i | \(0.382592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | − 30.9783i | − 1.20400i | ||||||||
\(663\) | 45.0217i | 1.74850i | ||||||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.7446 | −0.416343 | ||||||||
\(667\) | − 13.0217i | − 0.504204i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −53.4891 | −2.06801 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.7446 | −0.491998 | ||||||||
\(672\) | 2.00000i | 0.0771517i | ||||||||
\(673\) | 24.9783i | 0.962841i | 0.876490 | + | 0.481420i | \(0.159879\pi\) | ||||
−0.876490 | + | 0.481420i | \(0.840121\pi\) | |||||||
\(674\) | −26.0000 | −1.00148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.51087 | 0.365803 | ||||||||
\(677\) | 1.76631i | 0.0678849i | 0.999424 | + | 0.0339424i | \(0.0108063\pi\) | ||||
−0.999424 | + | 0.0339424i | \(0.989194\pi\) | |||||||
\(678\) | − 20.0000i | − 0.768095i | ||||||||
\(679\) | 5.25544 | 0.201685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40.0000 | 1.53280 | ||||||||
\(682\) | 6.74456i | 0.258263i | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −4.74456 | −0.181413 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | − 12.0000i | − 0.457829i | ||||||||
\(688\) | − 4.00000i | − 0.152499i | ||||||||
\(689\) | −5.95650 | −0.226925 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.2337 | 1.37839 | 0.689197 | − | 0.724574i | \(-0.257963\pi\) | ||||
0.689197 | + | 0.724574i | \(0.257963\pi\) | |||||||
\(692\) | − 14.2337i | − 0.541084i | ||||||||
\(693\) | 1.00000i | 0.0379869i | ||||||||
\(694\) | −22.9783 | −0.872242 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.48913 | −0.208065 | ||||||||
\(697\) | − 18.9783i | − 0.718853i | ||||||||
\(698\) | − 19.2554i | − 0.728829i | ||||||||
\(699\) | −41.9565 | −1.58694 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.2337 | −0.462060 | −0.231030 | − | 0.972947i | \(-0.574210\pi\) | ||||
−0.231030 | + | 0.972947i | \(0.574210\pi\) | |||||||
\(702\) | 18.9783i | 0.716288i | ||||||||
\(703\) | 50.9783i | 1.92268i | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.74456 | −0.103293 | ||||||||
\(707\) | − 8.74456i | − 0.328873i | ||||||||
\(708\) | − 5.48913i | − 0.206294i | ||||||||
\(709\) | −23.4891 | −0.882153 | −0.441076 | − | 0.897470i | \(-0.645403\pi\) | ||||
−0.441076 | + | 0.897470i | \(0.645403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.74456 | −0.177935 | ||||||||
\(712\) | − 7.48913i | − 0.280667i | ||||||||
\(713\) | 32.0000i | 1.19841i | ||||||||
\(714\) | −9.48913 | −0.355122 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | − 6.51087i | − 0.243153i | ||||||||
\(718\) | 12.7446i | 0.475623i | ||||||||
\(719\) | 49.7228 | 1.85435 | 0.927174 | − | 0.374631i | \(-0.122231\pi\) | ||||
0.927174 | + | 0.374631i | \(0.122231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7446 | 0.400148 | ||||||||
\(722\) | 3.51087i | 0.130661i | ||||||||
\(723\) | − 40.0000i | − 1.48762i | ||||||||
\(724\) | −3.48913 | −0.129672 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.00000 | 0.0742270 | ||||||||
\(727\) | − 20.2337i | − 0.750426i | −0.926939 | − | 0.375213i | \(-0.877570\pi\) | ||||
0.926939 | − | 0.375213i | \(-0.122430\pi\) | |||||||
\(728\) | 4.74456i | 0.175845i | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.9783 | 0.701936 | ||||||||
\(732\) | 25.4891i | 0.942105i | ||||||||
\(733\) | − 18.2337i | − 0.673477i | −0.941598 | − | 0.336738i | \(-0.890676\pi\) | ||||
0.941598 | − | 0.336738i | \(-0.109324\pi\) | |||||||
\(734\) | −2.74456 | −0.101304 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.74456 | 0.174887 | ||||||||
\(737\) | 4.00000i | 0.147342i | ||||||||
\(738\) | 4.00000i | 0.147242i | ||||||||
\(739\) | −14.9783 | −0.550984 | −0.275492 | − | 0.961303i | \(-0.588841\pi\) | ||||
−0.275492 | + | 0.961303i | \(0.588841\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.0217 | −1.65392 | ||||||||
\(742\) | − 1.25544i | − 0.0460886i | ||||||||
\(743\) | 18.9783i | 0.696244i | 0.937449 | + | 0.348122i | \(0.113181\pi\) | ||||
−0.937449 | + | 0.348122i | \(0.886819\pi\) | |||||||
\(744\) | 13.4891 | 0.494535 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 28.9783 | 1.06097 | ||||||||
\(747\) | 8.00000i | 0.292705i | ||||||||
\(748\) | 4.74456i | 0.173478i | ||||||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | 0.729810 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(752\) | − 6.74456i | − 0.245949i | ||||||||
\(753\) | − 16.4674i | − 0.600105i | ||||||||
\(754\) | −13.0217 | −0.474224 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | − 30.7446i | − 1.11743i | −0.829360 | − | 0.558715i | \(-0.811295\pi\) | ||||
0.829360 | − | 0.558715i | \(-0.188705\pi\) | |||||||
\(758\) | 14.5109i | 0.527059i | ||||||||
\(759\) | 9.48913 | 0.344433 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.51087 | −0.236019 | −0.118010 | − | 0.993012i | \(-0.537651\pi\) | ||||
−0.118010 | + | 0.993012i | \(0.537651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 16.2337i | − 0.587699i | ||||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.7228 | −1.36298 | ||||||||
\(767\) | − 13.0217i | − 0.470188i | ||||||||
\(768\) | − 2.00000i | − 0.0721688i | ||||||||
\(769\) | 8.00000 | 0.288487 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48.4674 | 1.74551 | ||||||||
\(772\) | − 2.00000i | − 0.0719816i | ||||||||
\(773\) | 28.5109i | 1.02546i | 0.858548 | + | 0.512732i | \(0.171367\pi\) | ||||
−0.858548 | + | 0.512732i | \(0.828633\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.25544 | −0.188659 | ||||||||
\(777\) | − 21.4891i | − 0.770918i | ||||||||
\(778\) | − 15.4891i | − 0.555312i | ||||||||
\(779\) | 18.9783 | 0.679966 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 22.5109i | 0.804987i | ||||||||
\(783\) | − 10.9783i | − 0.392331i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.4891 | 0.623816 | ||||||||
\(787\) | − 17.4891i | − 0.623420i | −0.950177 | − | 0.311710i | \(-0.899098\pi\) | ||||
0.950177 | − | 0.311710i | \(-0.100902\pi\) | |||||||
\(788\) | − 10.0000i | − 0.356235i | ||||||||
\(789\) | 37.9565 | 1.35129 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0000 | 0.355559 | ||||||||
\(792\) | − 1.00000i | − 0.0355335i | ||||||||
\(793\) | 60.4674i | 2.14726i | ||||||||
\(794\) | −12.5109 | −0.443994 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.7446 | 0.522607 | ||||||||
\(797\) | 26.4674i | 0.937523i | 0.883325 | + | 0.468761i | \(0.155300\pi\) | ||||
−0.883325 | + | 0.468761i | \(0.844700\pi\) | |||||||
\(798\) | − 9.48913i | − 0.335911i | ||||||||
\(799\) | 32.0000 | 1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.48913 | −0.264615 | ||||||||
\(802\) | 0.510875i | 0.0180396i | ||||||||
\(803\) | − 0.744563i | − 0.0262750i | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.0000 | 1.12715 | ||||||||
\(807\) | − 49.9565i | − 1.75855i | ||||||||
\(808\) | 8.74456i | 0.307633i | ||||||||
\(809\) | 34.4674 | 1.21181 | 0.605904 | − | 0.795538i | \(-0.292811\pi\) | ||||
0.605904 | + | 0.795538i | \(0.292811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.25544 | −0.254773 | −0.127386 | − | 0.991853i | \(-0.540659\pi\) | ||||
−0.127386 | + | 0.991853i | \(0.540659\pi\) | |||||||
\(812\) | − 2.74456i | − 0.0963153i | ||||||||
\(813\) | 61.9565i | 2.17291i | ||||||||
\(814\) | −10.7446 | −0.376597 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.48913 | 0.332186 | ||||||||
\(817\) | 18.9783i | 0.663965i | ||||||||
\(818\) | − 1.48913i | − 0.0520660i | ||||||||
\(819\) | 4.74456 | 0.165788 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.7228 | −1.73534 | −0.867669 | − | 0.497142i | \(-0.834383\pi\) | ||||
−0.867669 | + | 0.497142i | \(0.834383\pi\) | |||||||
\(822\) | − 38.9783i | − 1.35952i | ||||||||
\(823\) | − 42.2337i | − 1.47217i | −0.676887 | − | 0.736087i | \(-0.736671\pi\) | ||||
0.676887 | − | 0.736087i | \(-0.263329\pi\) | |||||||
\(824\) | −10.7446 | −0.374305 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.74456 | 0.0954955 | ||||||||
\(827\) | 4.00000i | 0.139094i | 0.997579 | + | 0.0695468i | \(0.0221553\pi\) | ||||
−0.997579 | + | 0.0695468i | \(0.977845\pi\) | |||||||
\(828\) | − 4.74456i | − 0.164885i | ||||||||
\(829\) | 54.4674 | 1.89173 | 0.945865 | − | 0.324560i | \(-0.105216\pi\) | ||||
0.945865 | + | 0.324560i | \(0.105216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.9783 | −0.519590 | ||||||||
\(832\) | − 4.74456i | − 0.164488i | ||||||||
\(833\) | − 4.74456i | − 0.164389i | ||||||||
\(834\) | −6.51087 | −0.225453 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.74456 | −0.164094 | ||||||||
\(837\) | 26.9783i | 0.932505i | ||||||||
\(838\) | − 10.7446i | − 0.371165i | ||||||||
\(839\) | 14.7446 | 0.509039 | 0.254519 | − | 0.967068i | \(-0.418083\pi\) | ||||
0.254519 | + | 0.967068i | \(0.418083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4674 | −0.740254 | ||||||||
\(842\) | 27.4891i | 0.947338i | ||||||||
\(843\) | − 28.0000i | − 0.964371i | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.74456 | −0.231883 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 1.25544i | 0.0431119i | ||||||||
\(849\) | −56.0000 | −1.92192 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.9783 | −1.74751 | ||||||||
\(852\) | − 8.00000i | − 0.274075i | ||||||||
\(853\) | 11.2554i | 0.385379i | 0.981260 | + | 0.192689i | \(0.0617210\pi\) | ||||
−0.981260 | + | 0.192689i | \(0.938279\pi\) | |||||||
\(854\) | −12.7446 | −0.436110 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | 37.2119i | 1.27114i | 0.772045 | + | 0.635568i | \(0.219234\pi\) | ||||
−0.772045 | + | 0.635568i | \(0.780766\pi\) | |||||||
\(858\) | − 9.48913i | − 0.323953i | ||||||||
\(859\) | −51.2119 | −1.74733 | −0.873664 | − | 0.486529i | \(-0.838263\pi\) | ||||
−0.873664 | + | 0.486529i | \(0.838263\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | − 28.7446i | − 0.979044i | ||||||||
\(863\) | 5.76631i | 0.196288i | 0.995172 | + | 0.0981438i | \(0.0312905\pi\) | ||||
−0.995172 | + | 0.0981438i | \(0.968709\pi\) | |||||||
\(864\) | 4.00000 | 0.136083 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.2554 | 0.858215 | ||||||||
\(867\) | 11.0217i | 0.374318i | ||||||||
\(868\) | 6.74456i | 0.228925i | ||||||||
\(869\) | −4.74456 | −0.160948 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9783 | 0.643053 | ||||||||
\(872\) | 16.2337i | 0.549742i | ||||||||
\(873\) | 5.25544i | 0.177870i | ||||||||
\(874\) | −22.5109 | −0.761442 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.48913 | −0.0503129 | ||||||||
\(877\) | 42.4674i | 1.43402i | 0.697062 | + | 0.717011i | \(0.254490\pi\) | ||||
−0.697062 | + | 0.717011i | \(0.745510\pi\) | |||||||
\(878\) | 30.9783i | 1.04547i | ||||||||
\(879\) | −49.4891 | −1.66923 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.5109 | −1.09532 | −0.547660 | − | 0.836701i | \(-0.684481\pi\) | ||||
−0.547660 | + | 0.836701i | \(0.684481\pi\) | |||||||
\(882\) | 1.00000i | 0.0336718i | ||||||||
\(883\) | 8.00000i | 0.269221i | 0.990899 | + | 0.134611i | \(0.0429784\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(884\) | 22.5109 | 0.757123 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.51087 | −0.218737 | ||||||||
\(887\) | − 18.5109i | − 0.621534i | −0.950486 | − | 0.310767i | \(-0.899414\pi\) | ||||
0.950486 | − | 0.310767i | \(-0.100586\pi\) | |||||||
\(888\) | 21.4891i | 0.721128i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.0000 | 0.368514 | ||||||||
\(892\) | 26.7446i | 0.895474i | ||||||||
\(893\) | 32.0000i | 1.07084i | ||||||||
\(894\) | −21.4891 | −0.718704 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | − 45.0217i | − 1.50323i | ||||||||
\(898\) | − 40.9783i | − 1.36746i | ||||||||
\(899\) | −18.5109 | −0.617372 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.95650 | −0.198440 | ||||||||
\(902\) | 4.00000i | 0.133185i | ||||||||
\(903\) | − 8.00000i | − 0.266223i | ||||||||
\(904\) | −10.0000 | −0.332595 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −41.4891 | −1.37838 | ||||||||
\(907\) | − 37.4891i | − 1.24481i | −0.782697 | − | 0.622403i | \(-0.786157\pi\) | ||||
0.782697 | − | 0.622403i | \(-0.213843\pi\) | |||||||
\(908\) | − 20.0000i | − 0.663723i | ||||||||
\(909\) | 8.74456 | 0.290039 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.0000 | 0.662630 | 0.331315 | − | 0.943520i | \(-0.392508\pi\) | ||||
0.331315 | + | 0.943520i | \(0.392508\pi\) | |||||||
\(912\) | 9.48913i | 0.314216i | ||||||||
\(913\) | 8.00000i | 0.264761i | ||||||||
\(914\) | 19.4891 | 0.644643 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.00000 | −0.198246 | ||||||||
\(917\) | 8.74456i | 0.288771i | ||||||||
\(918\) | 18.9783i | 0.626376i | ||||||||
\(919\) | −25.2119 | −0.831665 | −0.415833 | − | 0.909441i | \(-0.636510\pi\) | ||||
−0.415833 | + | 0.909441i | \(0.636510\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.9783 | 1.41618 | ||||||||
\(922\) | − 23.7228i | − 0.781269i | ||||||||
\(923\) | − 18.9783i | − 0.624677i | ||||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.7446 | 0.418812 | ||||||||
\(927\) | 10.7446i | 0.352898i | ||||||||
\(928\) | 2.74456i | 0.0900947i | ||||||||
\(929\) | −16.9783 | −0.557038 | −0.278519 | − | 0.960431i | \(-0.589844\pi\) | ||||
−0.278519 | + | 0.960431i | \(0.589844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.74456 | 0.155497 | ||||||||
\(932\) | 20.9783i | 0.687165i | ||||||||
\(933\) | 18.5109i | 0.606019i | ||||||||
\(934\) | 28.9783 | 0.948197 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.74456 | −0.155081 | ||||||||
\(937\) | − 7.25544i | − 0.237025i | −0.992953 | − | 0.118512i | \(-0.962187\pi\) | ||||
0.992953 | − | 0.118512i | \(-0.0378125\pi\) | |||||||
\(938\) | 4.00000i | 0.130605i | ||||||||
\(939\) | −64.4674 | −2.10381 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.2337 | −0.724798 | −0.362399 | − | 0.932023i | \(-0.618042\pi\) | ||||
−0.362399 | + | 0.932023i | \(0.618042\pi\) | |||||||
\(942\) | 46.9783i | 1.53063i | ||||||||
\(943\) | 18.9783i | 0.618017i | ||||||||
\(944\) | −2.74456 | −0.0893279 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | − 8.00000i | − 0.259965i | −0.991516 | − | 0.129983i | \(-0.958508\pi\) | ||||
0.991516 | − | 0.129983i | \(-0.0414921\pi\) | |||||||
\(948\) | 9.48913i | 0.308192i | ||||||||
\(949\) | −3.53262 | −0.114674 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −64.4674 | −2.09050 | ||||||||
\(952\) | 4.74456i | 0.153772i | ||||||||
\(953\) | − 6.00000i | − 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 1.25544 | 0.0406463 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.25544 | −0.105288 | ||||||||
\(957\) | 5.48913i | 0.177438i | ||||||||
\(958\) | 18.5109i | 0.598059i | ||||||||
\(959\) | 19.4891 | 0.629337 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4891 | 0.467391 | ||||||||
\(962\) | 50.9783i | 1.64360i | ||||||||
\(963\) | 12.0000i | 0.386695i | ||||||||
\(964\) | −20.0000 | −0.644157 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.48913 | 0.305308 | ||||||||
\(967\) | − 5.02175i | − 0.161489i | −0.996735 | − | 0.0807443i | \(-0.974270\pi\) | ||||
0.996735 | − | 0.0807443i | \(-0.0257297\pi\) | |||||||
\(968\) | − 1.00000i | − 0.0321412i | ||||||||
\(969\) | −45.0217 | −1.44631 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.7228 | −1.21058 | −0.605291 | − | 0.796004i | \(-0.706943\pi\) | ||||
−0.605291 | + | 0.796004i | \(0.706943\pi\) | |||||||
\(972\) | − 10.0000i | − 0.320750i | ||||||||
\(973\) | − 3.25544i | − 0.104365i | ||||||||
\(974\) | −20.7446 | −0.664699 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.7446 | 0.407944 | ||||||||
\(977\) | − 32.9783i | − 1.05507i | −0.849534 | − | 0.527534i | \(-0.823117\pi\) | ||||
0.849534 | − | 0.527534i | \(-0.176883\pi\) | |||||||
\(978\) | 8.00000i | 0.255812i | ||||||||
\(979\) | −7.48913 | −0.239353 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.2337 | 0.518302 | ||||||||
\(982\) | − 14.9783i | − 0.477975i | ||||||||
\(983\) | 32.2337i | 1.02809i | 0.857762 | + | 0.514047i | \(0.171854\pi\) | ||||
−0.857762 | + | 0.514047i | \(0.828146\pi\) | |||||||
\(984\) | 8.00000 | 0.255031 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.0217 | −0.414697 | ||||||||
\(987\) | − 13.4891i | − 0.429364i | ||||||||
\(988\) | 22.5109i | 0.716166i | ||||||||
\(989\) | −18.9783 | −0.603473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.4891 | −0.682625 | −0.341312 | − | 0.939950i | \(-0.610871\pi\) | ||||
−0.341312 | + | 0.939950i | \(0.610871\pi\) | |||||||
\(992\) | − 6.74456i | − 0.214140i | ||||||||
\(993\) | 61.9565i | 1.96613i | ||||||||
\(994\) | 4.00000 | 0.126872 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.0000 | 0.506979 | ||||||||
\(997\) | − 41.2119i | − 1.30520i | −0.757705 | − | 0.652598i | \(-0.773679\pi\) | ||||
0.757705 | − | 0.652598i | \(-0.226321\pi\) | |||||||
\(998\) | − 9.48913i | − 0.300373i | ||||||||
\(999\) | −42.9783 | −1.35977 |
(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 | 3850.2.c.y.1849.4 | 4 | ||
5.2 | odd | 4 | 3850.2.a.bc.1.2 | 2 | |||
5.3 | odd | 4 | 770.2.a.k.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 3850.2.c.y.1849.1 | 4 | ||
15.8 | even | 4 | 6930.2.a.bo.1.1 | 2 | |||
20.3 | even | 4 | 6160.2.a.r.1.1 | 2 | |||
35.13 | even | 4 | 5390.2.a.bq.1.2 | 2 | |||
55.43 | even | 4 | 8470.2.a.bu.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.k.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
3850.2.a.bc.1.2 | 2 | 5.2 | odd | 4 | |||
3850.2.c.y.1849.1 | 4 | 5.4 | even | 2 | inner | ||
3850.2.c.y.1849.4 | 4 | 1.1 | even | 1 | trivial | ||
5390.2.a.bq.1.2 | 2 | 35.13 | even | 4 | |||
6160.2.a.r.1.1 | 2 | 20.3 | even | 4 | |||
6930.2.a.bo.1.1 | 2 | 15.8 | even | 4 | |||
8470.2.a.bu.1.2 | 2 | 55.43 | even | 4 |