Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,3,Mod(949,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.949");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.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: | \(25.8856251142\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 949.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.949 |
Dual form | 950.3.d.a.949.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 2.82843 | 0.942809 | 0.471405 | − | 0.881917i | \(-0.343747\pi\) | ||||
0.471405 | + | 0.881917i | \(0.343747\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.00000 | −0.666667 | ||||||||
\(7\) | 5.00000i | 0.714286i | 0.934050 | + | 0.357143i | \(0.116249\pi\) | ||||
−0.934050 | + | 0.357143i | \(0.883751\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −1.00000 | −0.111111 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.00000 | 0.454545 | 0.227273 | − | 0.973831i | \(-0.427019\pi\) | ||||
0.227273 | + | 0.973831i | \(0.427019\pi\) | |||||||
\(12\) | 5.65685 | 0.471405 | ||||||||
\(13\) | −16.9706 | −1.30543 | −0.652714 | − | 0.757604i | \(-0.726370\pi\) | ||||
−0.652714 | + | 0.757604i | \(0.726370\pi\) | |||||||
\(14\) | − 7.07107i | − 0.505076i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 25.0000i | − 1.47059i | −0.677748 | − | 0.735294i | \(-0.737044\pi\) | ||||
0.677748 | − | 0.735294i | \(-0.262956\pi\) | |||||||
\(18\) | 1.41421 | 0.0785674 | ||||||||
\(19\) | −19.0000 | −1.00000 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.1421i | 0.673435i | ||||||||
\(22\) | −7.07107 | −0.321412 | ||||||||
\(23\) | 10.0000i | 0.434783i | 0.976085 | + | 0.217391i | \(0.0697548\pi\) | ||||
−0.976085 | + | 0.217391i | \(0.930245\pi\) | |||||||
\(24\) | −8.00000 | −0.333333 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 24.0000 | 0.923077 | ||||||||
\(27\) | −28.2843 | −1.04757 | ||||||||
\(28\) | 10.0000i | 0.357143i | ||||||||
\(29\) | − 42.4264i | − 1.46298i | −0.681852 | − | 0.731490i | \(-0.738825\pi\) | ||||
0.681852 | − | 0.731490i | \(-0.261175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 42.4264i | − 1.36859i | −0.729204 | − | 0.684297i | \(-0.760109\pi\) | ||||
0.729204 | − | 0.684297i | \(-0.239891\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 14.1421 | 0.428550 | ||||||||
\(34\) | 35.3553i | 1.03986i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.0555556 | ||||||||
\(37\) | 25.4558 | 0.687996 | 0.343998 | − | 0.938970i | \(-0.388219\pi\) | ||||
0.343998 | + | 0.938970i | \(0.388219\pi\) | |||||||
\(38\) | 26.8701 | 0.707107 | ||||||||
\(39\) | −48.0000 | −1.23077 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 42.4264i | − 1.03479i | −0.855747 | − | 0.517395i | \(-0.826902\pi\) | ||||
0.855747 | − | 0.517395i | \(-0.173098\pi\) | |||||||
\(42\) | − 20.0000i | − 0.476190i | ||||||||
\(43\) | − 5.00000i | − 0.116279i | −0.998308 | − | 0.0581395i | \(-0.981483\pi\) | ||||
0.998308 | − | 0.0581395i | \(-0.0185168\pi\) | |||||||
\(44\) | 10.0000 | 0.227273 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 14.1421i | − 0.307438i | ||||||||
\(47\) | 5.00000i | 0.106383i | 0.998584 | + | 0.0531915i | \(0.0169394\pi\) | ||||
−0.998584 | + | 0.0531915i | \(0.983061\pi\) | |||||||
\(48\) | 11.3137 | 0.235702 | ||||||||
\(49\) | 24.0000 | 0.489796 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 70.7107i | − 1.38648i | ||||||||
\(52\) | −33.9411 | −0.652714 | ||||||||
\(53\) | −25.4558 | −0.480299 | −0.240149 | − | 0.970736i | \(-0.577196\pi\) | ||||
−0.240149 | + | 0.970736i | \(0.577196\pi\) | |||||||
\(54\) | 40.0000 | 0.740741 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 14.1421i | − 0.252538i | ||||||||
\(57\) | −53.7401 | −0.942809 | ||||||||
\(58\) | 60.0000i | 1.03448i | ||||||||
\(59\) | − 84.8528i | − 1.43818i | −0.694915 | − | 0.719092i | \(-0.744558\pi\) | ||||
0.694915 | − | 0.719092i | \(-0.255442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 95.0000 | 1.55738 | 0.778689 | − | 0.627411i | \(-0.215885\pi\) | ||||
0.778689 | + | 0.627411i | \(0.215885\pi\) | |||||||
\(62\) | 60.0000i | 0.967742i | ||||||||
\(63\) | − 5.00000i | − 0.0793651i | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −20.0000 | −0.303030 | ||||||||
\(67\) | −110.309 | −1.64640 | −0.823199 | − | 0.567753i | \(-0.807813\pi\) | ||||
−0.823199 | + | 0.567753i | \(0.807813\pi\) | |||||||
\(68\) | − 50.0000i | − 0.735294i | ||||||||
\(69\) | 28.2843i | 0.409917i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 2.82843 | 0.0392837 | ||||||||
\(73\) | 25.0000i | 0.342466i | 0.985231 | + | 0.171233i | \(0.0547750\pi\) | ||||
−0.985231 | + | 0.171233i | \(0.945225\pi\) | |||||||
\(74\) | −36.0000 | −0.486486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −38.0000 | −0.500000 | ||||||||
\(77\) | 25.0000i | 0.324675i | ||||||||
\(78\) | 67.8823 | 0.870285 | ||||||||
\(79\) | − 42.4264i | − 0.537043i | −0.963274 | − | 0.268522i | \(-0.913465\pi\) | ||||
0.963274 | − | 0.268522i | \(-0.0865351\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −71.0000 | −0.876543 | ||||||||
\(82\) | 60.0000i | 0.731707i | ||||||||
\(83\) | 130.000i | 1.56627i | 0.621855 | + | 0.783133i | \(0.286379\pi\) | ||||
−0.621855 | + | 0.783133i | \(0.713621\pi\) | |||||||
\(84\) | 28.2843i | 0.336718i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.07107i | 0.0822217i | ||||||||
\(87\) | − 120.000i | − 1.37931i | ||||||||
\(88\) | −14.1421 | −0.160706 | ||||||||
\(89\) | 127.279i | 1.43010i | 0.699071 | + | 0.715052i | \(0.253597\pi\) | ||||
−0.699071 | + | 0.715052i | \(0.746403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 84.8528i | − 0.932449i | ||||||||
\(92\) | 20.0000i | 0.217391i | ||||||||
\(93\) | − 120.000i | − 1.29032i | ||||||||
\(94\) | − 7.07107i | − 0.0752241i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −16.0000 | −0.166667 | ||||||||
\(97\) | −16.9706 | −0.174954 | −0.0874771 | − | 0.996167i | \(-0.527880\pi\) | ||||
−0.0874771 | + | 0.996167i | \(0.527880\pi\) | |||||||
\(98\) | −33.9411 | −0.346338 | ||||||||
\(99\) | −5.00000 | −0.0505051 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 50.0000 | 0.495050 | 0.247525 | − | 0.968882i | \(-0.420383\pi\) | ||||
0.247525 | + | 0.968882i | \(0.420383\pi\) | |||||||
\(102\) | 100.000i | 0.980392i | ||||||||
\(103\) | −16.9706 | −0.164763 | −0.0823814 | − | 0.996601i | \(-0.526253\pi\) | ||||
−0.0823814 | + | 0.996601i | \(0.526253\pi\) | |||||||
\(104\) | 48.0000 | 0.461538 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 36.0000 | 0.339623 | ||||||||
\(107\) | 101.823 | 0.951620 | 0.475810 | − | 0.879548i | \(-0.342155\pi\) | ||||
0.475810 | + | 0.879548i | \(0.342155\pi\) | |||||||
\(108\) | −56.5685 | −0.523783 | ||||||||
\(109\) | − 127.279i | − 1.16770i | −0.811862 | − | 0.583850i | \(-0.801546\pi\) | ||||
0.811862 | − | 0.583850i | \(-0.198454\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 72.0000 | 0.648649 | ||||||||
\(112\) | 20.0000i | 0.178571i | ||||||||
\(113\) | 110.309 | 0.976183 | 0.488091 | − | 0.872793i | \(-0.337693\pi\) | ||||
0.488091 | + | 0.872793i | \(0.337693\pi\) | |||||||
\(114\) | 76.0000 | 0.666667 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − 84.8528i | − 0.731490i | ||||||||
\(117\) | 16.9706 | 0.145048 | ||||||||
\(118\) | 120.000i | 1.01695i | ||||||||
\(119\) | 125.000 | 1.05042 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −96.0000 | −0.793388 | ||||||||
\(122\) | −134.350 | −1.10123 | ||||||||
\(123\) | − 120.000i | − 0.975610i | ||||||||
\(124\) | − 84.8528i | − 0.684297i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.07107i | 0.0561196i | ||||||||
\(127\) | −229.103 | −1.80396 | −0.901979 | − | 0.431780i | \(-0.857886\pi\) | ||||
−0.901979 | + | 0.431780i | \(0.857886\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | − 14.1421i | − 0.109629i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −163.000 | −1.24427 | −0.622137 | − | 0.782908i | \(-0.713735\pi\) | ||||
−0.622137 | + | 0.782908i | \(0.713735\pi\) | |||||||
\(132\) | 28.2843 | 0.214275 | ||||||||
\(133\) | − 95.0000i | − 0.714286i | ||||||||
\(134\) | 156.000 | 1.16418 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 70.7107i | 0.519931i | ||||||||
\(137\) | 95.0000i | 0.693431i | 0.937970 | + | 0.346715i | \(0.112703\pi\) | ||||
−0.937970 | + | 0.346715i | \(0.887297\pi\) | |||||||
\(138\) | − 40.0000i | − 0.289855i | ||||||||
\(139\) | −125.000 | −0.899281 | −0.449640 | − | 0.893210i | \(-0.648448\pi\) | ||||
−0.449640 | + | 0.893210i | \(0.648448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.1421i | 0.100299i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −84.8528 | −0.593376 | ||||||||
\(144\) | −4.00000 | −0.0277778 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 35.3553i | − 0.242160i | ||||||||
\(147\) | 67.8823 | 0.461784 | ||||||||
\(148\) | 50.9117 | 0.343998 | ||||||||
\(149\) | −215.000 | −1.44295 | −0.721477 | − | 0.692439i | \(-0.756536\pi\) | ||||
−0.721477 | + | 0.692439i | \(0.756536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 84.8528i | − 0.561939i | −0.959717 | − | 0.280970i | \(-0.909344\pi\) | ||||
0.959717 | − | 0.280970i | \(-0.0906560\pi\) | |||||||
\(152\) | 53.7401 | 0.353553 | ||||||||
\(153\) | 25.0000i | 0.163399i | ||||||||
\(154\) | − 35.3553i | − 0.229580i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −96.0000 | −0.615385 | ||||||||
\(157\) | − 190.000i | − 1.21019i | −0.796153 | − | 0.605096i | \(-0.793135\pi\) | ||||
0.796153 | − | 0.605096i | \(-0.206865\pi\) | |||||||
\(158\) | 60.0000i | 0.379747i | ||||||||
\(159\) | −72.0000 | −0.452830 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −50.0000 | −0.310559 | ||||||||
\(162\) | 100.409 | 0.619810 | ||||||||
\(163\) | − 110.000i | − 0.674847i | −0.941353 | − | 0.337423i | \(-0.890445\pi\) | ||||
0.941353 | − | 0.337423i | \(-0.109555\pi\) | |||||||
\(164\) | − 84.8528i | − 0.517395i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 183.848i | − 1.10752i | ||||||||
\(167\) | −59.3970 | −0.355670 | −0.177835 | − | 0.984060i | \(-0.556909\pi\) | ||||
−0.177835 | + | 0.984060i | \(0.556909\pi\) | |||||||
\(168\) | − 40.0000i | − 0.238095i | ||||||||
\(169\) | 119.000 | 0.704142 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.0000 | 0.111111 | ||||||||
\(172\) | − 10.0000i | − 0.0581395i | ||||||||
\(173\) | −186.676 | −1.07905 | −0.539527 | − | 0.841969i | \(-0.681397\pi\) | ||||
−0.539527 | + | 0.841969i | \(0.681397\pi\) | |||||||
\(174\) | 169.706i | 0.975320i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.0000 | 0.113636 | ||||||||
\(177\) | − 240.000i | − 1.35593i | ||||||||
\(178\) | − 180.000i | − 1.01124i | ||||||||
\(179\) | 127.279i | 0.711057i | 0.934665 | + | 0.355529i | \(0.115699\pi\) | ||||
−0.934665 | + | 0.355529i | \(0.884301\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 254.558i | − 1.40640i | −0.710992 | − | 0.703200i | \(-0.751754\pi\) | ||||
0.710992 | − | 0.703200i | \(-0.248246\pi\) | |||||||
\(182\) | 120.000i | 0.659341i | ||||||||
\(183\) | 268.701 | 1.46831 | ||||||||
\(184\) | − 28.2843i | − 0.153719i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 169.706i | 0.912396i | ||||||||
\(187\) | − 125.000i | − 0.668449i | ||||||||
\(188\) | 10.0000i | 0.0531915i | ||||||||
\(189\) | − 141.421i | − 0.748261i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 293.000 | 1.53403 | 0.767016 | − | 0.641628i | \(-0.221741\pi\) | ||||
0.767016 | + | 0.641628i | \(0.221741\pi\) | |||||||
\(192\) | 22.6274 | 0.117851 | ||||||||
\(193\) | 59.3970 | 0.307756 | 0.153878 | − | 0.988090i | \(-0.450824\pi\) | ||||
0.153878 | + | 0.988090i | \(0.450824\pi\) | |||||||
\(194\) | 24.0000 | 0.123711 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 48.0000 | 0.244898 | ||||||||
\(197\) | − 70.0000i | − 0.355330i | −0.984091 | − | 0.177665i | \(-0.943146\pi\) | ||||
0.984091 | − | 0.177665i | \(-0.0568543\pi\) | |||||||
\(198\) | 7.07107 | 0.0357125 | ||||||||
\(199\) | −173.000 | −0.869347 | −0.434673 | − | 0.900588i | \(-0.643136\pi\) | ||||
−0.434673 | + | 0.900588i | \(0.643136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −312.000 | −1.55224 | ||||||||
\(202\) | −70.7107 | −0.350053 | ||||||||
\(203\) | 212.132 | 1.04499 | ||||||||
\(204\) | − 141.421i | − 0.693242i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 24.0000 | 0.116505 | ||||||||
\(207\) | − 10.0000i | − 0.0483092i | ||||||||
\(208\) | −67.8823 | −0.326357 | ||||||||
\(209\) | −95.0000 | −0.454545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 84.8528i | 0.402146i | 0.979576 | + | 0.201073i | \(0.0644429\pi\) | ||||
−0.979576 | + | 0.201073i | \(0.935557\pi\) | |||||||
\(212\) | −50.9117 | −0.240149 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −144.000 | −0.672897 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 80.0000 | 0.370370 | ||||||||
\(217\) | 212.132 | 0.977567 | ||||||||
\(218\) | 180.000i | 0.825688i | ||||||||
\(219\) | 70.7107i | 0.322880i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 424.264i | 1.91975i | ||||||||
\(222\) | −101.823 | −0.458664 | ||||||||
\(223\) | −364.867 | −1.63618 | −0.818088 | − | 0.575094i | \(-0.804966\pi\) | ||||
−0.818088 | + | 0.575094i | \(0.804966\pi\) | |||||||
\(224\) | − 28.2843i | − 0.126269i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −156.000 | −0.690265 | ||||||||
\(227\) | −67.8823 | −0.299041 | −0.149520 | − | 0.988759i | \(-0.547773\pi\) | ||||
−0.149520 | + | 0.988759i | \(0.547773\pi\) | |||||||
\(228\) | −107.480 | −0.471405 | ||||||||
\(229\) | 145.000 | 0.633188 | 0.316594 | − | 0.948561i | \(-0.397461\pi\) | ||||
0.316594 | + | 0.948561i | \(0.397461\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 70.7107i | 0.306107i | ||||||||
\(232\) | 120.000i | 0.517241i | ||||||||
\(233\) | − 335.000i | − 1.43777i | −0.695130 | − | 0.718884i | \(-0.744653\pi\) | ||||
0.695130 | − | 0.718884i | \(-0.255347\pi\) | |||||||
\(234\) | −24.0000 | −0.102564 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − 169.706i | − 0.719092i | ||||||||
\(237\) | − 120.000i | − 0.506329i | ||||||||
\(238\) | −176.777 | −0.742759 | ||||||||
\(239\) | −197.000 | −0.824268 | −0.412134 | − | 0.911123i | \(-0.635216\pi\) | ||||
−0.412134 | + | 0.911123i | \(0.635216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 296.985i | 1.23230i | 0.787628 | + | 0.616151i | \(0.211309\pi\) | ||||
−0.787628 | + | 0.616151i | \(0.788691\pi\) | |||||||
\(242\) | 135.765 | 0.561010 | ||||||||
\(243\) | 53.7401 | 0.221153 | ||||||||
\(244\) | 190.000 | 0.778689 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 169.706i | 0.689860i | ||||||||
\(247\) | 322.441 | 1.30543 | ||||||||
\(248\) | 120.000i | 0.483871i | ||||||||
\(249\) | 367.696i | 1.47669i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 173.000 | 0.689243 | 0.344622 | − | 0.938742i | \(-0.388007\pi\) | ||||
0.344622 | + | 0.938742i | \(0.388007\pi\) | |||||||
\(252\) | − 10.0000i | − 0.0396825i | ||||||||
\(253\) | 50.0000i | 0.197628i | ||||||||
\(254\) | 324.000 | 1.27559 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 67.8823 | 0.264133 | 0.132067 | − | 0.991241i | \(-0.457839\pi\) | ||||
0.132067 | + | 0.991241i | \(0.457839\pi\) | |||||||
\(258\) | 20.0000i | 0.0775194i | ||||||||
\(259\) | 127.279i | 0.491426i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 42.4264i | 0.162553i | ||||||||
\(262\) | 230.517 | 0.879835 | ||||||||
\(263\) | 355.000i | 1.34981i | 0.737905 | + | 0.674905i | \(0.235815\pi\) | ||||
−0.737905 | + | 0.674905i | \(0.764185\pi\) | |||||||
\(264\) | −40.0000 | −0.151515 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 134.350i | 0.505076i | ||||||||
\(267\) | 360.000i | 1.34831i | ||||||||
\(268\) | −220.617 | −0.823199 | ||||||||
\(269\) | 381.838i | 1.41947i | 0.704468 | + | 0.709735i | \(0.251186\pi\) | ||||
−0.704468 | + | 0.709735i | \(0.748814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 110.000 | 0.405904 | 0.202952 | − | 0.979189i | \(-0.434946\pi\) | ||||
0.202952 | + | 0.979189i | \(0.434946\pi\) | |||||||
\(272\) | − 100.000i | − 0.367647i | ||||||||
\(273\) | − 240.000i | − 0.879121i | ||||||||
\(274\) | − 134.350i | − 0.490330i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 56.5685i | 0.204958i | ||||||||
\(277\) | − 265.000i | − 0.956679i | −0.878175 | − | 0.478339i | \(-0.841239\pi\) | ||||
0.878175 | − | 0.478339i | \(-0.158761\pi\) | |||||||
\(278\) | 176.777 | 0.635887 | ||||||||
\(279\) | 42.4264i | 0.152066i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 424.264i | 1.50984i | 0.655819 | + | 0.754918i | \(0.272323\pi\) | ||||
−0.655819 | + | 0.754918i | \(0.727677\pi\) | |||||||
\(282\) | − 20.0000i | − 0.0709220i | ||||||||
\(283\) | − 125.000i | − 0.441696i | −0.975308 | − | 0.220848i | \(-0.929118\pi\) | ||||
0.975308 | − | 0.220848i | \(-0.0708825\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 120.000 | 0.419580 | ||||||||
\(287\) | 212.132 | 0.739136 | ||||||||
\(288\) | 5.65685 | 0.0196419 | ||||||||
\(289\) | −336.000 | −1.16263 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −48.0000 | −0.164948 | ||||||||
\(292\) | 50.0000i | 0.171233i | ||||||||
\(293\) | 186.676 | 0.637120 | 0.318560 | − | 0.947903i | \(-0.396801\pi\) | ||||
0.318560 | + | 0.947903i | \(0.396801\pi\) | |||||||
\(294\) | −96.0000 | −0.326531 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −72.0000 | −0.243243 | ||||||||
\(297\) | −141.421 | −0.476166 | ||||||||
\(298\) | 304.056 | 1.02032 | ||||||||
\(299\) | − 169.706i | − 0.567577i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.0000 | 0.0830565 | ||||||||
\(302\) | 120.000i | 0.397351i | ||||||||
\(303\) | 141.421 | 0.466737 | ||||||||
\(304\) | −76.0000 | −0.250000 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − 35.3553i | − 0.115540i | ||||||||
\(307\) | −280.014 | −0.912099 | −0.456049 | − | 0.889955i | \(-0.650736\pi\) | ||||
−0.456049 | + | 0.889955i | \(0.650736\pi\) | |||||||
\(308\) | 50.0000i | 0.162338i | ||||||||
\(309\) | −48.0000 | −0.155340 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −235.000 | −0.755627 | −0.377814 | − | 0.925882i | \(-0.623324\pi\) | ||||
−0.377814 | + | 0.925882i | \(0.623324\pi\) | |||||||
\(312\) | 135.765 | 0.435143 | ||||||||
\(313\) | 310.000i | 0.990415i | 0.868775 | + | 0.495208i | \(0.164908\pi\) | ||||
−0.868775 | + | 0.495208i | \(0.835092\pi\) | |||||||
\(314\) | 268.701i | 0.855734i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 84.8528i | − 0.268522i | ||||||||
\(317\) | 186.676 | 0.588884 | 0.294442 | − | 0.955669i | \(-0.404866\pi\) | ||||
0.294442 | + | 0.955669i | \(0.404866\pi\) | |||||||
\(318\) | 101.823 | 0.320199 | ||||||||
\(319\) | − 212.132i | − 0.664991i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 288.000 | 0.897196 | ||||||||
\(322\) | 70.7107 | 0.219598 | ||||||||
\(323\) | 475.000i | 1.47059i | ||||||||
\(324\) | −142.000 | −0.438272 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 155.563i | 0.477189i | ||||||||
\(327\) | − 360.000i | − 1.10092i | ||||||||
\(328\) | 120.000i | 0.365854i | ||||||||
\(329\) | −25.0000 | −0.0759878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 296.985i | 0.897235i | 0.893724 | + | 0.448618i | \(0.148083\pi\) | ||||
−0.893724 | + | 0.448618i | \(0.851917\pi\) | |||||||
\(332\) | 260.000i | 0.783133i | ||||||||
\(333\) | −25.4558 | −0.0764440 | ||||||||
\(334\) | 84.0000 | 0.251497 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 56.5685i | 0.168359i | ||||||||
\(337\) | 526.087 | 1.56109 | 0.780545 | − | 0.625099i | \(-0.214942\pi\) | ||||
0.780545 | + | 0.625099i | \(0.214942\pi\) | |||||||
\(338\) | −168.291 | −0.497904 | ||||||||
\(339\) | 312.000 | 0.920354 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 212.132i | − 0.622088i | ||||||||
\(342\) | −26.8701 | −0.0785674 | ||||||||
\(343\) | 365.000i | 1.06414i | ||||||||
\(344\) | 14.1421i | 0.0411109i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 264.000 | 0.763006 | ||||||||
\(347\) | 125.000i | 0.360231i | 0.983646 | + | 0.180115i | \(0.0576471\pi\) | ||||
−0.983646 | + | 0.180115i | \(0.942353\pi\) | |||||||
\(348\) | − 240.000i | − 0.689655i | ||||||||
\(349\) | −23.0000 | −0.0659026 | −0.0329513 | − | 0.999457i | \(-0.510491\pi\) | ||||
−0.0329513 | + | 0.999457i | \(0.510491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 480.000 | 1.36752 | ||||||||
\(352\) | −28.2843 | −0.0803530 | ||||||||
\(353\) | − 410.000i | − 1.16147i | −0.814092 | − | 0.580737i | \(-0.802765\pi\) | ||||
0.814092 | − | 0.580737i | \(-0.197235\pi\) | |||||||
\(354\) | 339.411i | 0.958789i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 254.558i | 0.715052i | ||||||||
\(357\) | 353.553 | 0.990346 | ||||||||
\(358\) | − 180.000i | − 0.502793i | ||||||||
\(359\) | 475.000 | 1.32312 | 0.661560 | − | 0.749892i | \(-0.269895\pi\) | ||||
0.661560 | + | 0.749892i | \(0.269895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 1.00000 | ||||||||
\(362\) | 360.000i | 0.994475i | ||||||||
\(363\) | −271.529 | −0.748014 | ||||||||
\(364\) | − 169.706i | − 0.466224i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −380.000 | −1.03825 | ||||||||
\(367\) | 230.000i | 0.626703i | 0.949637 | + | 0.313351i | \(0.101452\pi\) | ||||
−0.949637 | + | 0.313351i | \(0.898548\pi\) | |||||||
\(368\) | 40.0000i | 0.108696i | ||||||||
\(369\) | 42.4264i | 0.114977i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 127.279i | − 0.343071i | ||||||||
\(372\) | − 240.000i | − 0.645161i | ||||||||
\(373\) | −67.8823 | −0.181990 | −0.0909950 | − | 0.995851i | \(-0.529005\pi\) | ||||
−0.0909950 | + | 0.995851i | \(0.529005\pi\) | |||||||
\(374\) | 176.777i | 0.472665i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 14.1421i | − 0.0376121i | ||||||||
\(377\) | 720.000i | 1.90981i | ||||||||
\(378\) | 200.000i | 0.529101i | ||||||||
\(379\) | 254.558i | 0.671658i | 0.941923 | + | 0.335829i | \(0.109016\pi\) | ||||
−0.941923 | + | 0.335829i | \(0.890984\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −648.000 | −1.70079 | ||||||||
\(382\) | −414.365 | −1.08472 | ||||||||
\(383\) | −144.250 | −0.376631 | −0.188316 | − | 0.982109i | \(-0.560303\pi\) | ||||
−0.188316 | + | 0.982109i | \(0.560303\pi\) | |||||||
\(384\) | −32.0000 | −0.0833333 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −84.0000 | −0.217617 | ||||||||
\(387\) | 5.00000i | 0.0129199i | ||||||||
\(388\) | −33.9411 | −0.0874771 | ||||||||
\(389\) | 553.000 | 1.42159 | 0.710797 | − | 0.703397i | \(-0.248334\pi\) | ||||
0.710797 | + | 0.703397i | \(0.248334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 250.000 | 0.639386 | ||||||||
\(392\) | −67.8823 | −0.173169 | ||||||||
\(393\) | −461.034 | −1.17311 | ||||||||
\(394\) | 98.9949i | 0.251256i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.0000 | −0.0252525 | ||||||||
\(397\) | 335.000i | 0.843829i | 0.906636 | + | 0.421914i | \(0.138642\pi\) | ||||
−0.906636 | + | 0.421914i | \(0.861358\pi\) | |||||||
\(398\) | 244.659 | 0.614721 | ||||||||
\(399\) | − 268.701i | − 0.673435i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 212.132i | 0.529008i | 0.964385 | + | 0.264504i | \(0.0852082\pi\) | ||||
−0.964385 | + | 0.264504i | \(0.914792\pi\) | |||||||
\(402\) | 441.235 | 1.09760 | ||||||||
\(403\) | 720.000i | 1.78660i | ||||||||
\(404\) | 100.000 | 0.247525 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −300.000 | −0.738916 | ||||||||
\(407\) | 127.279 | 0.312725 | ||||||||
\(408\) | 200.000i | 0.490196i | ||||||||
\(409\) | − 721.249i | − 1.76344i | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
0.471769 | − | 0.881722i | \(-0.343616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 268.701i | 0.653773i | ||||||||
\(412\) | −33.9411 | −0.0823814 | ||||||||
\(413\) | 424.264 | 1.02727 | ||||||||
\(414\) | 14.1421i | 0.0341597i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 96.0000 | 0.230769 | ||||||||
\(417\) | −353.553 | −0.847850 | ||||||||
\(418\) | 134.350 | 0.321412 | ||||||||
\(419\) | −62.0000 | −0.147971 | −0.0739857 | − | 0.997259i | \(-0.523572\pi\) | ||||
−0.0739857 | + | 0.997259i | \(0.523572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 296.985i | 0.705427i | 0.935731 | + | 0.352714i | \(0.114741\pi\) | ||||
−0.935731 | + | 0.352714i | \(0.885259\pi\) | |||||||
\(422\) | − 120.000i | − 0.284360i | ||||||||
\(423\) | − 5.00000i | − 0.0118203i | ||||||||
\(424\) | 72.0000 | 0.169811 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 475.000i | 1.11241i | ||||||||
\(428\) | 203.647 | 0.475810 | ||||||||
\(429\) | −240.000 | −0.559441 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 509.117i | − 1.18125i | −0.806948 | − | 0.590623i | \(-0.798882\pi\) | ||||
0.806948 | − | 0.590623i | \(-0.201118\pi\) | |||||||
\(432\) | −113.137 | −0.261891 | ||||||||
\(433\) | −229.103 | −0.529105 | −0.264553 | − | 0.964371i | \(-0.585224\pi\) | ||||
−0.264553 | + | 0.964371i | \(0.585224\pi\) | |||||||
\(434\) | −300.000 | −0.691244 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 254.558i | − 0.583850i | ||||||||
\(437\) | − 190.000i | − 0.434783i | ||||||||
\(438\) | − 100.000i | − 0.228311i | ||||||||
\(439\) | − 806.102i | − 1.83622i | −0.396323 | − | 0.918111i | \(-0.629714\pi\) | ||||
0.396323 | − | 0.918111i | \(-0.370286\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.0000 | −0.0544218 | ||||||||
\(442\) | − 600.000i | − 1.35747i | ||||||||
\(443\) | − 365.000i | − 0.823928i | −0.911200 | − | 0.411964i | \(-0.864843\pi\) | ||||
0.911200 | − | 0.411964i | \(-0.135157\pi\) | |||||||
\(444\) | 144.000 | 0.324324 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 516.000 | 1.15695 | ||||||||
\(447\) | −608.112 | −1.36043 | ||||||||
\(448\) | 40.0000i | 0.0892857i | ||||||||
\(449\) | 763.675i | 1.70084i | 0.526108 | + | 0.850418i | \(0.323651\pi\) | ||||
−0.526108 | + | 0.850418i | \(0.676349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 212.132i | − 0.470359i | ||||||||
\(452\) | 220.617 | 0.488091 | ||||||||
\(453\) | − 240.000i | − 0.529801i | ||||||||
\(454\) | 96.0000 | 0.211454 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 152.000 | 0.333333 | ||||||||
\(457\) | − 265.000i | − 0.579869i | −0.957047 | − | 0.289934i | \(-0.906367\pi\) | ||||
0.957047 | − | 0.289934i | \(-0.0936335\pi\) | |||||||
\(458\) | −205.061 | −0.447731 | ||||||||
\(459\) | 707.107i | 1.54054i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −553.000 | −1.19957 | −0.599783 | − | 0.800163i | \(-0.704746\pi\) | ||||
−0.599783 | + | 0.800163i | \(0.704746\pi\) | |||||||
\(462\) | − 100.000i | − 0.216450i | ||||||||
\(463\) | − 485.000i | − 1.04752i | −0.851867 | − | 0.523758i | \(-0.824530\pi\) | ||||
0.851867 | − | 0.523758i | \(-0.175470\pi\) | |||||||
\(464\) | − 169.706i | − 0.365745i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 473.762i | 1.01666i | ||||||||
\(467\) | − 115.000i | − 0.246253i | −0.992391 | − | 0.123126i | \(-0.960708\pi\) | ||||
0.992391 | − | 0.123126i | \(-0.0392920\pi\) | |||||||
\(468\) | 33.9411 | 0.0725238 | ||||||||
\(469\) | − 551.543i | − 1.17600i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 537.401i | − 1.14098i | ||||||||
\(472\) | 240.000i | 0.508475i | ||||||||
\(473\) | − 25.0000i | − 0.0528541i | ||||||||
\(474\) | 169.706i | 0.358029i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 250.000 | 0.525210 | ||||||||
\(477\) | 25.4558 | 0.0533665 | ||||||||
\(478\) | 278.600 | 0.582845 | ||||||||
\(479\) | 490.000 | 1.02296 | 0.511482 | − | 0.859294i | \(-0.329097\pi\) | ||||
0.511482 | + | 0.859294i | \(0.329097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −432.000 | −0.898129 | ||||||||
\(482\) | − 420.000i | − 0.871369i | ||||||||
\(483\) | −141.421 | −0.292798 | ||||||||
\(484\) | −192.000 | −0.396694 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −76.0000 | −0.156379 | ||||||||
\(487\) | 610.940 | 1.25450 | 0.627249 | − | 0.778819i | \(-0.284181\pi\) | ||||
0.627249 | + | 0.778819i | \(0.284181\pi\) | |||||||
\(488\) | −268.701 | −0.550616 | ||||||||
\(489\) | − 311.127i | − 0.636252i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −82.0000 | −0.167006 | −0.0835031 | − | 0.996508i | \(-0.526611\pi\) | ||||
−0.0835031 | + | 0.996508i | \(0.526611\pi\) | |||||||
\(492\) | − 240.000i | − 0.487805i | ||||||||
\(493\) | −1060.66 | −2.15144 | ||||||||
\(494\) | −456.000 | −0.923077 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 169.706i | − 0.342148i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − 520.000i | − 1.04418i | ||||||||
\(499\) | −485.000 | −0.971944 | −0.485972 | − | 0.873974i | \(-0.661534\pi\) | ||||
−0.485972 | + | 0.873974i | \(0.661534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −168.000 | −0.335329 | ||||||||
\(502\) | −244.659 | −0.487368 | ||||||||
\(503\) | 250.000i | 0.497018i | 0.968630 | + | 0.248509i | \(0.0799405\pi\) | ||||
−0.968630 | + | 0.248509i | \(0.920059\pi\) | |||||||
\(504\) | 14.1421i | 0.0280598i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − 70.7107i | − 0.139744i | ||||||||
\(507\) | 336.583 | 0.663871 | ||||||||
\(508\) | −458.205 | −0.901979 | ||||||||
\(509\) | 169.706i | 0.333410i | 0.986007 | + | 0.166705i | \(0.0533127\pi\) | ||||
−0.986007 | + | 0.166705i | \(0.946687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −125.000 | −0.244618 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 537.401 | 1.04757 | ||||||||
\(514\) | −96.0000 | −0.186770 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − 28.2843i | − 0.0548145i | ||||||||
\(517\) | 25.0000i | 0.0483559i | ||||||||
\(518\) | − 180.000i | − 0.347490i | ||||||||
\(519\) | −528.000 | −1.01734 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 127.279i | − 0.244298i | −0.992512 | − | 0.122149i | \(-0.961021\pi\) | ||||
0.992512 | − | 0.122149i | \(-0.0389786\pi\) | |||||||
\(522\) | − 60.0000i | − 0.114943i | ||||||||
\(523\) | 356.382 | 0.681418 | 0.340709 | − | 0.940169i | \(-0.389333\pi\) | ||||
0.340709 | + | 0.940169i | \(0.389333\pi\) | |||||||
\(524\) | −326.000 | −0.622137 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − 502.046i | − 0.954460i | ||||||||
\(527\) | −1060.66 | −2.01264 | ||||||||
\(528\) | 56.5685 | 0.107137 | ||||||||
\(529\) | 429.000 | 0.810964 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 84.8528i | 0.159798i | ||||||||
\(532\) | − 190.000i | − 0.357143i | ||||||||
\(533\) | 720.000i | 1.35084i | ||||||||
\(534\) | − 509.117i | − 0.953402i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 312.000 | 0.582090 | ||||||||
\(537\) | 360.000i | 0.670391i | ||||||||
\(538\) | − 540.000i | − 1.00372i | ||||||||
\(539\) | 120.000 | 0.222635 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0000 | −0.0462107 | −0.0231054 | − | 0.999733i | \(-0.507355\pi\) | ||||
−0.0231054 | + | 0.999733i | \(0.507355\pi\) | |||||||
\(542\) | −155.563 | −0.287018 | ||||||||
\(543\) | − 720.000i | − 1.32597i | ||||||||
\(544\) | 141.421i | 0.259966i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 339.411i | 0.621632i | ||||||||
\(547\) | −16.9706 | −0.0310248 | −0.0155124 | − | 0.999880i | \(-0.504938\pi\) | ||||
−0.0155124 | + | 0.999880i | \(0.504938\pi\) | |||||||
\(548\) | 190.000i | 0.346715i | ||||||||
\(549\) | −95.0000 | −0.173042 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 806.102i | 1.46298i | ||||||||
\(552\) | − 80.0000i | − 0.144928i | ||||||||
\(553\) | 212.132 | 0.383602 | ||||||||
\(554\) | 374.767i | 0.676474i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −250.000 | −0.449640 | ||||||||
\(557\) | − 745.000i | − 1.33752i | −0.743477 | − | 0.668761i | \(-0.766825\pi\) | ||||
0.743477 | − | 0.668761i | \(-0.233175\pi\) | |||||||
\(558\) | − 60.0000i | − 0.107527i | ||||||||
\(559\) | 84.8528i | 0.151794i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − 353.553i | − 0.630220i | ||||||||
\(562\) | − 600.000i | − 1.06762i | ||||||||
\(563\) | 313.955 | 0.557647 | 0.278824 | − | 0.960342i | \(-0.410056\pi\) | ||||
0.278824 | + | 0.960342i | \(0.410056\pi\) | |||||||
\(564\) | 28.2843i | 0.0501494i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 176.777i | 0.312326i | ||||||||
\(567\) | − 355.000i | − 0.626102i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 424.264i | − 0.745631i | −0.927905 | − | 0.372816i | \(-0.878392\pi\) | ||||
0.927905 | − | 0.372816i | \(-0.121608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1070.00 | 1.87391 | 0.936953 | − | 0.349456i | \(-0.113634\pi\) | ||||
0.936953 | + | 0.349456i | \(0.113634\pi\) | |||||||
\(572\) | −169.706 | −0.296688 | ||||||||
\(573\) | 828.729 | 1.44630 | ||||||||
\(574\) | −300.000 | −0.522648 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.00000 | −0.0138889 | ||||||||
\(577\) | − 25.0000i | − 0.0433276i | −0.999765 | − | 0.0216638i | \(-0.993104\pi\) | ||||
0.999765 | − | 0.0216638i | \(-0.00689633\pi\) | |||||||
\(578\) | 475.176 | 0.822103 | ||||||||
\(579\) | 168.000 | 0.290155 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −650.000 | −1.11876 | ||||||||
\(582\) | 67.8823 | 0.116636 | ||||||||
\(583\) | −127.279 | −0.218318 | ||||||||
\(584\) | − 70.7107i | − 0.121080i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −264.000 | −0.450512 | ||||||||
\(587\) | 725.000i | 1.23509i | 0.786534 | + | 0.617547i | \(0.211873\pi\) | ||||
−0.786534 | + | 0.617547i | \(0.788127\pi\) | |||||||
\(588\) | 135.765 | 0.230892 | ||||||||
\(589\) | 806.102i | 1.36859i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 197.990i | − 0.335008i | ||||||||
\(592\) | 101.823 | 0.171999 | ||||||||
\(593\) | − 650.000i | − 1.09612i | −0.836439 | − | 0.548061i | \(-0.815366\pi\) | ||||
0.836439 | − | 0.548061i | \(-0.184634\pi\) | |||||||
\(594\) | 200.000 | 0.336700 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −430.000 | −0.721477 | ||||||||
\(597\) | −489.318 | −0.819628 | ||||||||
\(598\) | 240.000i | 0.401338i | ||||||||
\(599\) | 296.985i | 0.495801i | 0.968785 | + | 0.247901i | \(0.0797406\pi\) | ||||
−0.968785 | + | 0.247901i | \(0.920259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 848.528i | − 1.41186i | −0.708281 | − | 0.705930i | \(-0.750529\pi\) | ||||
0.708281 | − | 0.705930i | \(-0.249471\pi\) | |||||||
\(602\) | −35.3553 | −0.0587298 | ||||||||
\(603\) | 110.309 | 0.182933 | ||||||||
\(604\) | − 169.706i | − 0.280970i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −200.000 | −0.330033 | ||||||||
\(607\) | 271.529 | 0.447329 | 0.223665 | − | 0.974666i | \(-0.428198\pi\) | ||||
0.223665 | + | 0.974666i | \(0.428198\pi\) | |||||||
\(608\) | 107.480 | 0.176777 | ||||||||
\(609\) | 600.000 | 0.985222 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 84.8528i | − 0.138875i | ||||||||
\(612\) | 50.0000i | 0.0816993i | ||||||||
\(613\) | − 1055.00i | − 1.72104i | −0.509413 | − | 0.860522i | \(-0.670138\pi\) | ||||
0.509413 | − | 0.860522i | \(-0.329862\pi\) | |||||||
\(614\) | 396.000 | 0.644951 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − 70.7107i | − 0.114790i | ||||||||
\(617\) | − 505.000i | − 0.818476i | −0.912428 | − | 0.409238i | \(-0.865794\pi\) | ||||
0.912428 | − | 0.409238i | \(-0.134206\pi\) | |||||||
\(618\) | 67.8823 | 0.109842 | ||||||||
\(619\) | 130.000 | 0.210016 | 0.105008 | − | 0.994471i | \(-0.466513\pi\) | ||||
0.105008 | + | 0.994471i | \(0.466513\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 282.843i | − 0.455463i | ||||||||
\(622\) | 332.340 | 0.534309 | ||||||||
\(623\) | −636.396 | −1.02150 | ||||||||
\(624\) | −192.000 | −0.307692 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 438.406i | − 0.700329i | ||||||||
\(627\) | −268.701 | −0.428550 | ||||||||
\(628\) | − 380.000i | − 0.605096i | ||||||||
\(629\) | − 636.396i | − 1.01176i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −475.000 | −0.752773 | −0.376387 | − | 0.926463i | \(-0.622834\pi\) | ||||
−0.376387 | + | 0.926463i | \(0.622834\pi\) | |||||||
\(632\) | 120.000i | 0.189873i | ||||||||
\(633\) | 240.000i | 0.379147i | ||||||||
\(634\) | −264.000 | −0.416404 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −144.000 | −0.226415 | ||||||||
\(637\) | −407.294 | −0.639393 | ||||||||
\(638\) | 300.000i | 0.470219i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 848.528i | − 1.32376i | −0.749611 | − | 0.661878i | \(-0.769760\pi\) | ||||
0.749611 | − | 0.661878i | \(-0.230240\pi\) | |||||||
\(642\) | −407.294 | −0.634414 | ||||||||
\(643\) | 955.000i | 1.48523i | 0.669721 | + | 0.742613i | \(0.266414\pi\) | ||||
−0.669721 | + | 0.742613i | \(0.733586\pi\) | |||||||
\(644\) | −100.000 | −0.155280 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − 671.751i | − 1.03986i | ||||||||
\(647\) | 965.000i | 1.49150i | 0.666226 | + | 0.745750i | \(0.267908\pi\) | ||||
−0.666226 | + | 0.745750i | \(0.732092\pi\) | |||||||
\(648\) | 200.818 | 0.309905 | ||||||||
\(649\) | − 424.264i | − 0.653720i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 600.000 | 0.921659 | ||||||||
\(652\) | − 220.000i | − 0.337423i | ||||||||
\(653\) | − 935.000i | − 1.43185i | −0.698176 | − | 0.715926i | \(-0.746005\pi\) | ||||
0.698176 | − | 0.715926i | \(-0.253995\pi\) | |||||||
\(654\) | 509.117i | 0.778466i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 169.706i | − 0.258698i | ||||||||
\(657\) | − 25.0000i | − 0.0380518i | ||||||||
\(658\) | 35.3553 | 0.0537315 | ||||||||
\(659\) | 84.8528i | 0.128760i | 0.997925 | + | 0.0643800i | \(0.0205070\pi\) | ||||
−0.997925 | + | 0.0643800i | \(0.979493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 678.823i | − 1.02696i | −0.858101 | − | 0.513481i | \(-0.828356\pi\) | ||||
0.858101 | − | 0.513481i | \(-0.171644\pi\) | |||||||
\(662\) | − 420.000i | − 0.634441i | ||||||||
\(663\) | 1200.00i | 1.80995i | ||||||||
\(664\) | − 367.696i | − 0.553758i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 36.0000 | 0.0540541 | ||||||||
\(667\) | 424.264 | 0.636078 | ||||||||
\(668\) | −118.794 | −0.177835 | ||||||||
\(669\) | −1032.00 | −1.54260 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 475.000 | 0.707899 | ||||||||
\(672\) | − 80.0000i | − 0.119048i | ||||||||
\(673\) | −186.676 | −0.277379 | −0.138690 | − | 0.990336i | \(-0.544289\pi\) | ||||
−0.138690 | + | 0.990336i | \(0.544289\pi\) | |||||||
\(674\) | −744.000 | −1.10386 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 238.000 | 0.352071 | ||||||||
\(677\) | −907.925 | −1.34110 | −0.670550 | − | 0.741864i | \(-0.733942\pi\) | ||||
−0.670550 | + | 0.741864i | \(0.733942\pi\) | |||||||
\(678\) | −441.235 | −0.650789 | ||||||||
\(679\) | − 84.8528i | − 0.124967i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −192.000 | −0.281938 | ||||||||
\(682\) | 300.000i | 0.439883i | ||||||||
\(683\) | 1120.06 | 1.63991 | 0.819954 | − | 0.572429i | \(-0.193999\pi\) | ||||
0.819954 | + | 0.572429i | \(0.193999\pi\) | |||||||
\(684\) | 38.0000 | 0.0555556 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − 516.188i | − 0.752461i | ||||||||
\(687\) | 410.122 | 0.596975 | ||||||||
\(688\) | − 20.0000i | − 0.0290698i | ||||||||
\(689\) | 432.000 | 0.626996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −715.000 | −1.03473 | −0.517366 | − | 0.855764i | \(-0.673087\pi\) | ||||
−0.517366 | + | 0.855764i | \(0.673087\pi\) | |||||||
\(692\) | −373.352 | −0.539527 | ||||||||
\(693\) | − 25.0000i | − 0.0360750i | ||||||||
\(694\) | − 176.777i | − 0.254721i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 339.411i | 0.487660i | ||||||||
\(697\) | −1060.66 | −1.52175 | ||||||||
\(698\) | 32.5269 | 0.0466002 | ||||||||
\(699\) | − 947.523i | − 1.35554i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −430.000 | −0.613409 | −0.306705 | − | 0.951805i | \(-0.599226\pi\) | ||||
−0.306705 | + | 0.951805i | \(0.599226\pi\) | |||||||
\(702\) | −678.823 | −0.966984 | ||||||||
\(703\) | −483.661 | −0.687996 | ||||||||
\(704\) | 40.0000 | 0.0568182 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 579.828i | 0.821285i | ||||||||
\(707\) | 250.000i | 0.353607i | ||||||||
\(708\) | − 480.000i | − 0.677966i | ||||||||
\(709\) | 382.000 | 0.538787 | 0.269394 | − | 0.963030i | \(-0.413177\pi\) | ||||
0.269394 | + | 0.963030i | \(0.413177\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.4264i | 0.0596715i | ||||||||
\(712\) | − 360.000i | − 0.505618i | ||||||||
\(713\) | 424.264 | 0.595041 | ||||||||
\(714\) | −500.000 | −0.700280 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 254.558i | 0.355529i | ||||||||
\(717\) | −557.200 | −0.777127 | ||||||||
\(718\) | −671.751 | −0.935587 | ||||||||
\(719\) | 115.000 | 0.159944 | 0.0799722 | − | 0.996797i | \(-0.474517\pi\) | ||||
0.0799722 | + | 0.996797i | \(0.474517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 84.8528i | − 0.117688i | ||||||||
\(722\) | −510.531 | −0.707107 | ||||||||
\(723\) | 840.000i | 1.16183i | ||||||||
\(724\) | − 509.117i | − 0.703200i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 384.000 | 0.528926 | ||||||||
\(727\) | − 1075.00i | − 1.47868i | −0.673333 | − | 0.739340i | \(-0.735138\pi\) | ||||
0.673333 | − | 0.739340i | \(-0.264862\pi\) | |||||||
\(728\) | 240.000i | 0.329670i | ||||||||
\(729\) | 791.000 | 1.08505 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −125.000 | −0.170999 | ||||||||
\(732\) | 537.401 | 0.734155 | ||||||||
\(733\) | − 530.000i | − 0.723056i | −0.932361 | − | 0.361528i | \(-0.882255\pi\) | ||||
0.932361 | − | 0.361528i | \(-0.117745\pi\) | |||||||
\(734\) | − 325.269i | − 0.443146i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 56.5685i | − 0.0768594i | ||||||||
\(737\) | −551.543 | −0.748363 | ||||||||
\(738\) | − 60.0000i | − 0.0813008i | ||||||||
\(739\) | 547.000 | 0.740189 | 0.370095 | − | 0.928994i | \(-0.379325\pi\) | ||||
0.370095 | + | 0.928994i | \(0.379325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 912.000 | 1.23077 | ||||||||
\(742\) | 180.000i | 0.242588i | ||||||||
\(743\) | −958.837 | −1.29049 | −0.645247 | − | 0.763974i | \(-0.723245\pi\) | ||||
−0.645247 | + | 0.763974i | \(0.723245\pi\) | |||||||
\(744\) | 339.411i | 0.456198i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 96.0000 | 0.128686 | ||||||||
\(747\) | − 130.000i | − 0.174029i | ||||||||
\(748\) | − 250.000i | − 0.334225i | ||||||||
\(749\) | 509.117i | 0.679729i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 169.706i | − 0.225973i | −0.993597 | − | 0.112986i | \(-0.963958\pi\) | ||||
0.993597 | − | 0.112986i | \(-0.0360417\pi\) | |||||||
\(752\) | 20.0000i | 0.0265957i | ||||||||
\(753\) | 489.318 | 0.649825 | ||||||||
\(754\) | − 1018.23i | − 1.35044i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − 282.843i | − 0.374131i | ||||||||
\(757\) | 1055.00i | 1.39366i | 0.717237 | + | 0.696830i | \(0.245407\pi\) | ||||
−0.717237 | + | 0.696830i | \(0.754593\pi\) | |||||||
\(758\) | − 360.000i | − 0.474934i | ||||||||
\(759\) | 141.421i | 0.186326i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 215.000 | 0.282523 | 0.141261 | − | 0.989972i | \(-0.454884\pi\) | ||||
0.141261 | + | 0.989972i | \(0.454884\pi\) | |||||||
\(762\) | 916.410 | 1.20264 | ||||||||
\(763\) | 636.396 | 0.834071 | ||||||||
\(764\) | 586.000 | 0.767016 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 204.000 | 0.266319 | ||||||||
\(767\) | 1440.00i | 1.87744i | ||||||||
\(768\) | 45.2548 | 0.0589256 | ||||||||
\(769\) | 145.000 | 0.188557 | 0.0942783 | − | 0.995546i | \(-0.469946\pi\) | ||||
0.0942783 | + | 0.995546i | \(0.469946\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 192.000 | 0.249027 | ||||||||
\(772\) | 118.794 | 0.153878 | ||||||||
\(773\) | 407.294 | 0.526900 | 0.263450 | − | 0.964673i | \(-0.415140\pi\) | ||||
0.263450 | + | 0.964673i | \(0.415140\pi\) | |||||||
\(774\) | − 7.07107i | − 0.00913575i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 48.0000 | 0.0618557 | ||||||||
\(777\) | 360.000i | 0.463320i | ||||||||
\(778\) | −782.060 | −1.00522 | ||||||||
\(779\) | 806.102i | 1.03479i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −353.553 | −0.452114 | ||||||||
\(783\) | 1200.00i | 1.53257i | ||||||||
\(784\) | 96.0000 | 0.122449 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 652.000 | 0.829517 | ||||||||
\(787\) | −186.676 | −0.237200 | −0.118600 | − | 0.992942i | \(-0.537841\pi\) | ||||
−0.118600 | + | 0.992942i | \(0.537841\pi\) | |||||||
\(788\) | − 140.000i | − 0.177665i | ||||||||
\(789\) | 1004.09i | 1.27261i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 551.543i | 0.697273i | ||||||||
\(792\) | 14.1421 | 0.0178562 | ||||||||
\(793\) | −1612.20 | −2.03304 | ||||||||
\(794\) | − 473.762i | − 0.596677i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −346.000 | −0.434673 | ||||||||
\(797\) | 704.278 | 0.883662 | 0.441831 | − | 0.897098i | \(-0.354329\pi\) | ||||
0.441831 | + | 0.897098i | \(0.354329\pi\) | |||||||
\(798\) | 380.000i | 0.476190i | ||||||||
\(799\) | 125.000 | 0.156446 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 127.279i | − 0.158900i | ||||||||
\(802\) | − 300.000i | − 0.374065i | ||||||||
\(803\) | 125.000i | 0.155666i | ||||||||
\(804\) | −624.000 | −0.776119 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 1018.23i | − 1.26332i | ||||||||
\(807\) | 1080.00i | 1.33829i | ||||||||
\(808\) | −141.421 | −0.175026 | ||||||||
\(809\) | 457.000 | 0.564895 | 0.282447 | − | 0.959283i | \(-0.408854\pi\) | ||||
0.282447 | + | 0.959283i | \(0.408854\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 509.117i | 0.627764i | 0.949462 | + | 0.313882i | \(0.101630\pi\) | ||||
−0.949462 | + | 0.313882i | \(0.898370\pi\) | |||||||
\(812\) | 424.264 | 0.522493 | ||||||||
\(813\) | 311.127 | 0.382690 | ||||||||
\(814\) | −180.000 | −0.221130 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − 282.843i | − 0.346621i | ||||||||
\(817\) | 95.0000i | 0.116279i | ||||||||
\(818\) | 1020.00i | 1.24694i | ||||||||
\(819\) | 84.8528i | 0.103605i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 167.000 | 0.203410 | 0.101705 | − | 0.994815i | \(-0.467570\pi\) | ||||
0.101705 | + | 0.994815i | \(0.467570\pi\) | |||||||
\(822\) | − 380.000i | − 0.462287i | ||||||||
\(823\) | 1315.00i | 1.59781i | 0.601455 | + | 0.798906i | \(0.294588\pi\) | ||||
−0.601455 | + | 0.798906i | \(0.705412\pi\) | |||||||
\(824\) | 48.0000 | 0.0582524 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −600.000 | −0.726392 | ||||||||
\(827\) | 534.573 | 0.646400 | 0.323200 | − | 0.946331i | \(-0.395241\pi\) | ||||
0.323200 | + | 0.946331i | \(0.395241\pi\) | |||||||
\(828\) | − 20.0000i | − 0.0241546i | ||||||||
\(829\) | − 763.675i | − 0.921201i | −0.887608 | − | 0.460600i | \(-0.847634\pi\) | ||||
0.887608 | − | 0.460600i | \(-0.152366\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 749.533i | − 0.901965i | ||||||||
\(832\) | −135.765 | −0.163178 | ||||||||
\(833\) | − 600.000i | − 0.720288i | ||||||||
\(834\) | 500.000 | 0.599520 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −190.000 | −0.227273 | ||||||||
\(837\) | 1200.00i | 1.43369i | ||||||||
\(838\) | 87.6812 | 0.104632 | ||||||||
\(839\) | 339.411i | 0.404543i | 0.979330 | + | 0.202271i | \(0.0648323\pi\) | ||||
−0.979330 | + | 0.202271i | \(0.935168\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −959.000 | −1.14031 | ||||||||
\(842\) | − 420.000i | − 0.498812i | ||||||||
\(843\) | 1200.00i | 1.42349i | ||||||||
\(844\) | 169.706i | 0.201073i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.07107i | 0.00835824i | ||||||||
\(847\) | − 480.000i | − 0.566706i | ||||||||
\(848\) | −101.823 | −0.120075 | ||||||||
\(849\) | − 353.553i | − 0.416435i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 254.558i | 0.299129i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 770.000i | − 0.902696i | −0.892348 | − | 0.451348i | \(-0.850943\pi\) | ||||
0.892348 | − | 0.451348i | \(-0.149057\pi\) | |||||||
\(854\) | − 671.751i | − 0.786594i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −288.000 | −0.336449 | ||||||||
\(857\) | 1255.82 | 1.46537 | 0.732685 | − | 0.680568i | \(-0.238267\pi\) | ||||
0.732685 | + | 0.680568i | \(0.238267\pi\) | |||||||
\(858\) | 339.411 | 0.395584 | ||||||||
\(859\) | −557.000 | −0.648428 | −0.324214 | − | 0.945984i | \(-0.605100\pi\) | ||||
−0.324214 | + | 0.945984i | \(0.605100\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 600.000 | 0.696864 | ||||||||
\(862\) | 720.000i | 0.835267i | ||||||||
\(863\) | 992.778 | 1.15038 | 0.575190 | − | 0.818020i | \(-0.304928\pi\) | ||||
0.575190 | + | 0.818020i | \(0.304928\pi\) | |||||||
\(864\) | 160.000 | 0.185185 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 324.000 | 0.374134 | ||||||||
\(867\) | −950.352 | −1.09614 | ||||||||
\(868\) | 424.264 | 0.488783 | ||||||||
\(869\) | − 212.132i | − 0.244111i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1872.00 | 2.14925 | ||||||||
\(872\) | 360.000i | 0.412844i | ||||||||
\(873\) | 16.9706 | 0.0194394 | ||||||||
\(874\) | 268.701i | 0.307438i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 141.421i | 0.161440i | ||||||||
\(877\) | −186.676 | −0.212858 | −0.106429 | − | 0.994320i | \(-0.533942\pi\) | ||||
−0.106429 | + | 0.994320i | \(0.533942\pi\) | |||||||
\(878\) | 1140.00i | 1.29841i | ||||||||
\(879\) | 528.000 | 0.600683 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0000 | −0.0283768 | −0.0141884 | − | 0.999899i | \(-0.504516\pi\) | ||||
−0.0141884 | + | 0.999899i | \(0.504516\pi\) | |||||||
\(882\) | 33.9411 | 0.0384820 | ||||||||
\(883\) | − 965.000i | − 1.09287i | −0.837503 | − | 0.546433i | \(-0.815985\pi\) | ||||
0.837503 | − | 0.546433i | \(-0.184015\pi\) | |||||||
\(884\) | 848.528i | 0.959873i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 516.188i | 0.582605i | ||||||||
\(887\) | 780.646 | 0.880097 | 0.440048 | − | 0.897974i | \(-0.354961\pi\) | ||||
0.440048 | + | 0.897974i | \(0.354961\pi\) | |||||||
\(888\) | −203.647 | −0.229332 | ||||||||
\(889\) | − 1145.51i | − 1.28854i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −355.000 | −0.398429 | ||||||||
\(892\) | −729.734 | −0.818088 | ||||||||
\(893\) | − 95.0000i | − 0.106383i | ||||||||
\(894\) | 860.000 | 0.961969 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 56.5685i | − 0.0631345i | ||||||||
\(897\) | − 480.000i | − 0.535117i | ||||||||
\(898\) | − 1080.00i | − 1.20267i | ||||||||
\(899\) | −1800.00 | −2.00222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 636.396i | 0.706322i | ||||||||
\(902\) | 300.000i | 0.332594i | ||||||||
\(903\) | 70.7107 | 0.0783064 | ||||||||
\(904\) | −312.000 | −0.345133 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 339.411i | 0.374626i | ||||||||
\(907\) | 313.955 | 0.346147 | 0.173074 | − | 0.984909i | \(-0.444630\pi\) | ||||
0.173074 | + | 0.984909i | \(0.444630\pi\) | |||||||
\(908\) | −135.765 | −0.149520 | ||||||||
\(909\) | −50.0000 | −0.0550055 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 933.381i | 1.02457i | 0.858816 | + | 0.512284i | \(0.171200\pi\) | ||||
−0.858816 | + | 0.512284i | \(0.828800\pi\) | |||||||
\(912\) | −214.960 | −0.235702 | ||||||||
\(913\) | 650.000i | 0.711939i | ||||||||
\(914\) | 374.767i | 0.410029i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 290.000 | 0.316594 | ||||||||
\(917\) | − 815.000i | − 0.888768i | ||||||||
\(918\) | − 1000.00i | − 1.08932i | ||||||||
\(919\) | 538.000 | 0.585419 | 0.292709 | − | 0.956201i | \(-0.405443\pi\) | ||||
0.292709 | + | 0.956201i | \(0.405443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −792.000 | −0.859935 | ||||||||
\(922\) | 782.060 | 0.848221 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 141.421i | 0.153053i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 685.894i | 0.740706i | ||||||||
\(927\) | 16.9706 | 0.0183070 | ||||||||
\(928\) | 240.000i | 0.258621i | ||||||||
\(929\) | 742.000 | 0.798708 | 0.399354 | − | 0.916797i | \(-0.369234\pi\) | ||||
0.399354 | + | 0.916797i | \(0.369234\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −456.000 | −0.489796 | ||||||||
\(932\) | − 670.000i | − 0.718884i | ||||||||
\(933\) | −664.680 | −0.712412 | ||||||||
\(934\) | 162.635i | 0.174127i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −48.0000 | −0.0512821 | ||||||||
\(937\) | 335.000i | 0.357524i | 0.983892 | + | 0.178762i | \(0.0572092\pi\) | ||||
−0.983892 | + | 0.178762i | \(0.942791\pi\) | |||||||
\(938\) | 780.000i | 0.831557i | ||||||||
\(939\) | 876.812i | 0.933773i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 424.264i | − 0.450865i | −0.974259 | − | 0.225433i | \(-0.927620\pi\) | ||||
0.974259 | − | 0.225433i | \(-0.0723795\pi\) | |||||||
\(942\) | 760.000i | 0.806794i | ||||||||
\(943\) | 424.264 | 0.449909 | ||||||||
\(944\) | − 339.411i | − 0.359546i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.3553i | 0.0373735i | ||||||||
\(947\) | − 1210.00i | − 1.27772i | −0.769323 | − | 0.638860i | \(-0.779406\pi\) | ||||
0.769323 | − | 0.638860i | \(-0.220594\pi\) | |||||||
\(948\) | − 240.000i | − 0.253165i | ||||||||
\(949\) | − 424.264i | − 0.447064i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 528.000 | 0.555205 | ||||||||
\(952\) | −353.553 | −0.371380 | ||||||||
\(953\) | 992.778 | 1.04174 | 0.520870 | − | 0.853636i | \(-0.325608\pi\) | ||||
0.520870 | + | 0.853636i | \(0.325608\pi\) | |||||||
\(954\) | −36.0000 | −0.0377358 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −394.000 | −0.412134 | ||||||||
\(957\) | − 600.000i | − 0.626959i | ||||||||
\(958\) | −692.965 | −0.723345 | ||||||||
\(959\) | −475.000 | −0.495308 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −839.000 | −0.873049 | ||||||||
\(962\) | 610.940 | 0.635073 | ||||||||
\(963\) | −101.823 | −0.105736 | ||||||||
\(964\) | 593.970i | 0.616151i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 200.000 | 0.207039 | ||||||||
\(967\) | 350.000i | 0.361944i | 0.983488 | + | 0.180972i | \(0.0579244\pi\) | ||||
−0.983488 | + | 0.180972i | \(0.942076\pi\) | |||||||
\(968\) | 271.529 | 0.280505 | ||||||||
\(969\) | 1343.50i | 1.38648i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 254.558i | 0.262161i | 0.991372 | + | 0.131081i | \(0.0418447\pi\) | ||||
−0.991372 | + | 0.131081i | \(0.958155\pi\) | |||||||
\(972\) | 107.480 | 0.110576 | ||||||||
\(973\) | − 625.000i | − 0.642343i | ||||||||
\(974\) | −864.000 | −0.887064 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 380.000 | 0.389344 | ||||||||
\(977\) | 398.808 | 0.408197 | 0.204098 | − | 0.978950i | \(-0.434574\pi\) | ||||
0.204098 | + | 0.978950i | \(0.434574\pi\) | |||||||
\(978\) | 440.000i | 0.449898i | ||||||||
\(979\) | 636.396i | 0.650047i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 127.279i | 0.129744i | ||||||||
\(982\) | 115.966 | 0.118091 | ||||||||
\(983\) | −695.793 | −0.707826 | −0.353913 | − | 0.935278i | \(-0.615149\pi\) | ||||
−0.353913 | + | 0.935278i | \(0.615149\pi\) | |||||||
\(984\) | 339.411i | 0.344930i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1500.00 | 1.52130 | ||||||||
\(987\) | −70.7107 | −0.0716420 | ||||||||
\(988\) | 644.881 | 0.652714 | ||||||||
\(989\) | 50.0000 | 0.0505561 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 381.838i | 0.385305i | 0.981267 | + | 0.192653i | \(0.0617091\pi\) | ||||
−0.981267 | + | 0.192653i | \(0.938291\pi\) | |||||||
\(992\) | 240.000i | 0.241935i | ||||||||
\(993\) | 840.000i | 0.845921i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 735.391i | 0.738344i | ||||||||
\(997\) | − 265.000i | − 0.265797i | −0.991130 | − | 0.132899i | \(-0.957572\pi\) | ||||
0.991130 | − | 0.132899i | \(-0.0424285\pi\) | |||||||
\(998\) | 685.894 | 0.687268 | ||||||||
\(999\) | −720.000 | −0.720721 |
(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 | 950.3.d.a.949.2 | 4 | ||
5.2 | odd | 4 | 950.3.c.a.151.1 | 2 | |||
5.3 | odd | 4 | 38.3.b.a.37.2 | yes | 2 | ||
5.4 | even | 2 | inner | 950.3.d.a.949.3 | 4 | ||
15.8 | even | 4 | 342.3.d.a.37.1 | 2 | |||
19.18 | odd | 2 | inner | 950.3.d.a.949.4 | 4 | ||
20.3 | even | 4 | 304.3.e.c.113.1 | 2 | |||
40.3 | even | 4 | 1216.3.e.i.1025.2 | 2 | |||
40.13 | odd | 4 | 1216.3.e.j.1025.1 | 2 | |||
60.23 | odd | 4 | 2736.3.o.h.721.1 | 2 | |||
95.18 | even | 4 | 38.3.b.a.37.1 | ✓ | 2 | ||
95.37 | even | 4 | 950.3.c.a.151.2 | 2 | |||
95.94 | odd | 2 | inner | 950.3.d.a.949.1 | 4 | ||
285.113 | odd | 4 | 342.3.d.a.37.2 | 2 | |||
380.303 | odd | 4 | 304.3.e.c.113.2 | 2 | |||
760.493 | even | 4 | 1216.3.e.j.1025.2 | 2 | |||
760.683 | odd | 4 | 1216.3.e.i.1025.1 | 2 | |||
1140.683 | even | 4 | 2736.3.o.h.721.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.3.b.a.37.1 | ✓ | 2 | 95.18 | even | 4 | ||
38.3.b.a.37.2 | yes | 2 | 5.3 | odd | 4 | ||
304.3.e.c.113.1 | 2 | 20.3 | even | 4 | |||
304.3.e.c.113.2 | 2 | 380.303 | odd | 4 | |||
342.3.d.a.37.1 | 2 | 15.8 | even | 4 | |||
342.3.d.a.37.2 | 2 | 285.113 | odd | 4 | |||
950.3.c.a.151.1 | 2 | 5.2 | odd | 4 | |||
950.3.c.a.151.2 | 2 | 95.37 | even | 4 | |||
950.3.d.a.949.1 | 4 | 95.94 | odd | 2 | inner | ||
950.3.d.a.949.2 | 4 | 1.1 | even | 1 | trivial | ||
950.3.d.a.949.3 | 4 | 5.4 | even | 2 | inner | ||
950.3.d.a.949.4 | 4 | 19.18 | odd | 2 | inner | ||
1216.3.e.i.1025.1 | 2 | 760.683 | odd | 4 | |||
1216.3.e.i.1025.2 | 2 | 40.3 | even | 4 | |||
1216.3.e.j.1025.1 | 2 | 40.13 | odd | 4 | |||
1216.3.e.j.1025.2 | 2 | 760.493 | even | 4 | |||
2736.3.o.h.721.1 | 2 | 60.23 | odd | 4 | |||
2736.3.o.h.721.2 | 2 | 1140.683 | even | 4 |