Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1249,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.e (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: | \(15.5708283941\) |
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: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.4 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1249 |
Dual form | 1950.2.e.o.1249.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.65685 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | −2.82843 | −0.755929 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 4.82843i | − 1.17107i | −0.810649 | − | 0.585533i | \(-0.800885\pi\) | ||||
0.810649 | − | 0.585533i | \(-0.199115\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | − 5.65685i | − 1.20605i | ||||||||
\(23\) | − 8.48528i | − 1.76930i | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||||
0.466252 | − | 0.884652i | \(-0.345604\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 2.82843i | − 0.534522i | ||||||||
\(29\) | 3.17157 | 0.588946 | 0.294473 | − | 0.955660i | \(-0.404856\pi\) | ||||
0.294473 | + | 0.955660i | \(0.404856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 5.65685i | 0.984732i | ||||||||
\(34\) | 4.82843 | 0.828068 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 0.343146i | − 0.0564128i | −0.999602 | − | 0.0282064i | \(-0.991020\pi\) | ||||
0.999602 | − | 0.0282064i | \(-0.00897957\pi\) | |||||||
\(38\) | 2.82843i | 0.458831i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.65685 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(42\) | 2.82843i | 0.436436i | ||||||||
\(43\) | 1.65685i | 0.252668i | 0.991988 | + | 0.126334i | \(0.0403211\pi\) | ||||
−0.991988 | + | 0.126334i | \(0.959679\pi\) | |||||||
\(44\) | 5.65685 | 0.852803 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.48528 | 1.25109 | ||||||||
\(47\) | − 8.00000i | − 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.82843 | −0.676115 | ||||||||
\(52\) | − 1.00000i | − 0.138675i | ||||||||
\(53\) | 9.31371i | 1.27934i | 0.768651 | + | 0.639668i | \(0.220928\pi\) | ||||
−0.768651 | + | 0.639668i | \(0.779072\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.82843 | 0.377964 | ||||||||
\(57\) | − 2.82843i | − 0.374634i | ||||||||
\(58\) | 3.17157i | 0.416448i | ||||||||
\(59\) | 13.6569 | 1.77797 | 0.888985 | − | 0.457935i | \(-0.151411\pi\) | ||||
0.888985 | + | 0.457935i | \(0.151411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 4.00000i | 0.508001i | ||||||||
\(63\) | − 2.82843i | − 0.356348i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.65685 | −0.696311 | ||||||||
\(67\) | − 5.65685i | − 0.691095i | −0.938401 | − | 0.345547i | \(-0.887693\pi\) | ||||
0.938401 | − | 0.345547i | \(-0.112307\pi\) | |||||||
\(68\) | 4.82843i | 0.585533i | ||||||||
\(69\) | −8.48528 | −1.02151 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685 | 0.671345 | 0.335673 | − | 0.941979i | \(-0.391036\pi\) | ||||
0.335673 | + | 0.941979i | \(0.391036\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 2.48528i | − 0.290880i | −0.989367 | − | 0.145440i | \(-0.953540\pi\) | ||||
0.989367 | − | 0.145440i | \(-0.0464598\pi\) | |||||||
\(74\) | 0.343146 | 0.0398899 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | − 16.0000i | − 1.82337i | ||||||||
\(78\) | 1.00000i | 0.113228i | ||||||||
\(79\) | −13.6569 | −1.53652 | −0.768258 | − | 0.640140i | \(-0.778876\pi\) | ||||
−0.768258 | + | 0.640140i | \(0.778876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.65685i | 0.403832i | ||||||||
\(83\) | − 17.6569i | − 1.93809i | −0.246881 | − | 0.969046i | \(-0.579406\pi\) | ||||
0.246881 | − | 0.969046i | \(-0.420594\pi\) | |||||||
\(84\) | −2.82843 | −0.308607 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.65685 | −0.178663 | ||||||||
\(87\) | − 3.17157i | − 0.340028i | ||||||||
\(88\) | 5.65685i | 0.603023i | ||||||||
\(89\) | 4.34315 | 0.460373 | 0.230186 | − | 0.973147i | \(-0.426066\pi\) | ||||
0.230186 | + | 0.973147i | \(0.426066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 8.48528i | 0.884652i | ||||||||
\(93\) | − 4.00000i | − 0.414781i | ||||||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − 8.82843i | − 0.896391i | −0.893936 | − | 0.448195i | \(-0.852067\pi\) | ||||
0.893936 | − | 0.448195i | \(-0.147933\pi\) | |||||||
\(98\) | − 1.00000i | − 0.101015i | ||||||||
\(99\) | 5.65685 | 0.568535 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.1421 | −1.20819 | −0.604094 | − | 0.796913i | \(-0.706465\pi\) | ||||
−0.604094 | + | 0.796913i | \(0.706465\pi\) | |||||||
\(102\) | − 4.82843i | − 0.478086i | ||||||||
\(103\) | − 9.65685i | − 0.951518i | −0.879576 | − | 0.475759i | \(-0.842173\pi\) | ||||
0.879576 | − | 0.475759i | \(-0.157827\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.31371 | −0.904627 | ||||||||
\(107\) | − 4.00000i | − 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | −3.17157 | −0.303782 | −0.151891 | − | 0.988397i | \(-0.548536\pi\) | ||||
−0.151891 | + | 0.988397i | \(0.548536\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.343146 | −0.0325700 | ||||||||
\(112\) | 2.82843i | 0.267261i | ||||||||
\(113\) | 10.4853i | 0.986372i | 0.869924 | + | 0.493186i | \(0.164168\pi\) | ||||
−0.869924 | + | 0.493186i | \(0.835832\pi\) | |||||||
\(114\) | 2.82843 | 0.264906 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.17157 | −0.294473 | ||||||||
\(117\) | − 1.00000i | − 0.0924500i | ||||||||
\(118\) | 13.6569i | 1.25722i | ||||||||
\(119\) | 13.6569 | 1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | 6.00000i | 0.543214i | ||||||||
\(123\) | − 3.65685i | − 0.329727i | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.82843 | 0.251976 | ||||||||
\(127\) | − 1.65685i | − 0.147022i | −0.997294 | − | 0.0735110i | \(-0.976580\pi\) | ||||
0.997294 | − | 0.0735110i | \(-0.0234204\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 1.65685 | 0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.1421 | 1.93457 | 0.967284 | − | 0.253697i | \(-0.0816467\pi\) | ||||
0.967284 | + | 0.253697i | \(0.0816467\pi\) | |||||||
\(132\) | − 5.65685i | − 0.492366i | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | 5.65685 | 0.488678 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.82843 | −0.414034 | ||||||||
\(137\) | 5.31371i | 0.453981i | 0.973897 | + | 0.226990i | \(0.0728886\pi\) | ||||
−0.973897 | + | 0.226990i | \(0.927111\pi\) | |||||||
\(138\) | − 8.48528i | − 0.722315i | ||||||||
\(139\) | −17.6569 | −1.49763 | −0.748817 | − | 0.662776i | \(-0.769378\pi\) | ||||
−0.748817 | + | 0.662776i | \(0.769378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 5.65685i | 0.474713i | ||||||||
\(143\) | − 5.65685i | − 0.473050i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.48528 | 0.205683 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0.343146i | 0.0282064i | ||||||||
\(149\) | 7.65685 | 0.627274 | 0.313637 | − | 0.949543i | \(-0.398453\pi\) | ||||
0.313637 | + | 0.949543i | \(0.398453\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | − 2.82843i | − 0.229416i | ||||||||
\(153\) | 4.82843i | 0.390355i | ||||||||
\(154\) | 16.0000 | 1.28932 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | − 17.3137i | − 1.38178i | −0.722958 | − | 0.690892i | \(-0.757218\pi\) | ||||
0.722958 | − | 0.690892i | \(-0.242782\pi\) | |||||||
\(158\) | − 13.6569i | − 1.08648i | ||||||||
\(159\) | 9.31371 | 0.738625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0000 | 1.89146 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 11.3137i | 0.886158i | 0.896483 | + | 0.443079i | \(0.146114\pi\) | ||||
−0.896483 | + | 0.443079i | \(0.853886\pi\) | |||||||
\(164\) | −3.65685 | −0.285552 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.6569 | 1.37044 | ||||||||
\(167\) | − 24.9706i | − 1.93228i | −0.258018 | − | 0.966140i | \(-0.583069\pi\) | ||||
0.258018 | − | 0.966140i | \(-0.416931\pi\) | |||||||
\(168\) | − 2.82843i | − 0.218218i | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | − 1.65685i | − 0.126334i | ||||||||
\(173\) | − 13.3137i | − 1.01222i | −0.862468 | − | 0.506111i | \(-0.831083\pi\) | ||||
0.862468 | − | 0.506111i | \(-0.168917\pi\) | |||||||
\(174\) | 3.17157 | 0.240436 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.65685 | −0.426401 | ||||||||
\(177\) | − 13.6569i | − 1.02651i | ||||||||
\(178\) | 4.34315i | 0.325533i | ||||||||
\(179\) | −24.4853 | −1.83012 | −0.915058 | − | 0.403322i | \(-0.867855\pi\) | ||||
−0.915058 | + | 0.403322i | \(0.867855\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.65685 | 0.271812 | 0.135906 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135906 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(182\) | − 2.82843i | − 0.209657i | ||||||||
\(183\) | − 6.00000i | − 0.443533i | ||||||||
\(184\) | −8.48528 | −0.625543 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | 27.3137i | 1.99738i | ||||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3137 | −0.818631 | −0.409316 | − | 0.912393i | \(-0.634232\pi\) | ||||
−0.409316 | + | 0.912393i | \(0.634232\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 14.4853i | 1.04267i | 0.853351 | + | 0.521337i | \(0.174566\pi\) | ||||
−0.853351 | + | 0.521337i | \(0.825434\pi\) | |||||||
\(194\) | 8.82843 | 0.633844 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 9.31371i | 0.663574i | 0.943354 | + | 0.331787i | \(0.107652\pi\) | ||||
−0.943354 | + | 0.331787i | \(0.892348\pi\) | |||||||
\(198\) | 5.65685i | 0.402015i | ||||||||
\(199\) | −21.6569 | −1.53521 | −0.767607 | − | 0.640921i | \(-0.778553\pi\) | ||||
−0.767607 | + | 0.640921i | \(0.778553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.65685 | −0.399004 | ||||||||
\(202\) | − 12.1421i | − 0.854318i | ||||||||
\(203\) | 8.97056i | 0.629610i | ||||||||
\(204\) | 4.82843 | 0.338058 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.65685 | 0.672825 | ||||||||
\(207\) | 8.48528i | 0.589768i | ||||||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3137 | 1.60498 | 0.802491 | − | 0.596664i | \(-0.203508\pi\) | ||||
0.802491 | + | 0.596664i | \(0.203508\pi\) | |||||||
\(212\) | − 9.31371i | − 0.639668i | ||||||||
\(213\) | − 5.65685i | − 0.387601i | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 11.3137i | 0.768025i | ||||||||
\(218\) | − 3.17157i | − 0.214806i | ||||||||
\(219\) | −2.48528 | −0.167940 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.82843 | 0.324795 | ||||||||
\(222\) | − 0.343146i | − 0.0230304i | ||||||||
\(223\) | − 5.17157i | − 0.346314i | −0.984894 | − | 0.173157i | \(-0.944603\pi\) | ||||
0.984894 | − | 0.173157i | \(-0.0553968\pi\) | |||||||
\(224\) | −2.82843 | −0.188982 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.4853 | −0.697471 | ||||||||
\(227\) | 4.00000i | 0.265489i | 0.991150 | + | 0.132745i | \(0.0423790\pi\) | ||||
−0.991150 | + | 0.132745i | \(0.957621\pi\) | |||||||
\(228\) | 2.82843i | 0.187317i | ||||||||
\(229\) | 24.1421 | 1.59536 | 0.797679 | − | 0.603083i | \(-0.206061\pi\) | ||||
0.797679 | + | 0.603083i | \(0.206061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.0000 | −1.05272 | ||||||||
\(232\) | − 3.17157i | − 0.208224i | ||||||||
\(233\) | − 22.4853i | − 1.47306i | −0.676405 | − | 0.736530i | \(-0.736463\pi\) | ||||
0.676405 | − | 0.736530i | \(-0.263537\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.6569 | −0.888985 | ||||||||
\(237\) | 13.6569i | 0.887108i | ||||||||
\(238\) | 13.6569i | 0.885242i | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.3137 | −1.11527 | −0.557637 | − | 0.830085i | \(-0.688292\pi\) | ||||
−0.557637 | + | 0.830085i | \(0.688292\pi\) | |||||||
\(242\) | 21.0000i | 1.34993i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.65685 | 0.233153 | ||||||||
\(247\) | 2.82843i | 0.179969i | ||||||||
\(248\) | − 4.00000i | − 0.254000i | ||||||||
\(249\) | −17.6569 | −1.11896 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.17157 | 0.326427 | 0.163213 | − | 0.986591i | \(-0.447814\pi\) | ||||
0.163213 | + | 0.986591i | \(0.447814\pi\) | |||||||
\(252\) | 2.82843i | 0.178174i | ||||||||
\(253\) | 48.0000i | 3.01773i | ||||||||
\(254\) | 1.65685 | 0.103960 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.828427i | 0.0516759i | 0.999666 | + | 0.0258379i | \(0.00822538\pi\) | ||||
−0.999666 | + | 0.0258379i | \(0.991775\pi\) | |||||||
\(258\) | 1.65685i | 0.103151i | ||||||||
\(259\) | 0.970563 | 0.0603078 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.17157 | −0.196315 | ||||||||
\(262\) | 22.1421i | 1.36795i | ||||||||
\(263\) | 0.485281i | 0.0299237i | 0.999888 | + | 0.0149619i | \(0.00476269\pi\) | ||||
−0.999888 | + | 0.0149619i | \(0.995237\pi\) | |||||||
\(264\) | 5.65685 | 0.348155 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.00000 | −0.490511 | ||||||||
\(267\) | − 4.34315i | − 0.265796i | ||||||||
\(268\) | 5.65685i | 0.345547i | ||||||||
\(269\) | −2.48528 | −0.151530 | −0.0757651 | − | 0.997126i | \(-0.524140\pi\) | ||||
−0.0757651 | + | 0.997126i | \(0.524140\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3137 | −0.930242 | −0.465121 | − | 0.885247i | \(-0.653989\pi\) | ||||
−0.465121 | + | 0.885247i | \(0.653989\pi\) | |||||||
\(272\) | − 4.82843i | − 0.292766i | ||||||||
\(273\) | 2.82843i | 0.171184i | ||||||||
\(274\) | −5.31371 | −0.321013 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.48528 | 0.510754 | ||||||||
\(277\) | 26.0000i | 1.56219i | 0.624413 | + | 0.781094i | \(0.285338\pi\) | ||||
−0.624413 | + | 0.781094i | \(0.714662\pi\) | |||||||
\(278\) | − 17.6569i | − 1.05899i | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.6569 | 1.17263 | 0.586315 | − | 0.810083i | \(-0.300578\pi\) | ||||
0.586315 | + | 0.810083i | \(0.300578\pi\) | |||||||
\(282\) | − 8.00000i | − 0.476393i | ||||||||
\(283\) | 6.34315i | 0.377061i | 0.982067 | + | 0.188530i | \(0.0603724\pi\) | ||||
−0.982067 | + | 0.188530i | \(0.939628\pi\) | |||||||
\(284\) | −5.65685 | −0.335673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.65685 | 0.334497 | ||||||||
\(287\) | 10.3431i | 0.610537i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −6.31371 | −0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.82843 | −0.517532 | ||||||||
\(292\) | 2.48528i | 0.145440i | ||||||||
\(293\) | − 28.6274i | − 1.67243i | −0.548401 | − | 0.836216i | \(-0.684763\pi\) | ||||
0.548401 | − | 0.836216i | \(-0.315237\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.343146 | −0.0199449 | ||||||||
\(297\) | − 5.65685i | − 0.328244i | ||||||||
\(298\) | 7.65685i | 0.443550i | ||||||||
\(299\) | 8.48528 | 0.490716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.68629 | −0.270113 | ||||||||
\(302\) | 12.0000i | 0.690522i | ||||||||
\(303\) | 12.1421i | 0.697547i | ||||||||
\(304\) | 2.82843 | 0.162221 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.82843 | −0.276023 | ||||||||
\(307\) | − 10.3431i | − 0.590315i | −0.955449 | − | 0.295157i | \(-0.904628\pi\) | ||||
0.955449 | − | 0.295157i | \(-0.0953720\pi\) | |||||||
\(308\) | 16.0000i | 0.911685i | ||||||||
\(309\) | −9.65685 | −0.549359 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | − 1.00000i | − 0.0566139i | ||||||||
\(313\) | − 2.97056i | − 0.167906i | −0.996470 | − | 0.0839531i | \(-0.973245\pi\) | ||||
0.996470 | − | 0.0839531i | \(-0.0267546\pi\) | |||||||
\(314\) | 17.3137 | 0.977069 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.6569 | 0.768258 | ||||||||
\(317\) | 2.68629i | 0.150877i | 0.997150 | + | 0.0754386i | \(0.0240357\pi\) | ||||
−0.997150 | + | 0.0754386i | \(0.975964\pi\) | |||||||
\(318\) | 9.31371i | 0.522287i | ||||||||
\(319\) | −17.9411 | −1.00451 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 24.0000i | 1.33747i | ||||||||
\(323\) | − 13.6569i | − 0.759888i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.3137 | −0.626608 | ||||||||
\(327\) | 3.17157i | 0.175388i | ||||||||
\(328\) | − 3.65685i | − 0.201916i | ||||||||
\(329\) | 22.6274 | 1.24749 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.48528 | 0.466393 | 0.233197 | − | 0.972430i | \(-0.425081\pi\) | ||||
0.233197 | + | 0.972430i | \(0.425081\pi\) | |||||||
\(332\) | 17.6569i | 0.969046i | ||||||||
\(333\) | 0.343146i | 0.0188043i | ||||||||
\(334\) | 24.9706 | 1.36633 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.82843 | 0.154303 | ||||||||
\(337\) | − 22.9706i | − 1.25129i | −0.780109 | − | 0.625643i | \(-0.784837\pi\) | ||||
0.780109 | − | 0.625643i | \(-0.215163\pi\) | |||||||
\(338\) | − 1.00000i | − 0.0543928i | ||||||||
\(339\) | 10.4853 | 0.569482 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.6274 | −1.22534 | ||||||||
\(342\) | − 2.82843i | − 0.152944i | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 1.65685 | 0.0893316 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.3137 | 0.715749 | ||||||||
\(347\) | 1.65685i | 0.0889446i | 0.999011 | + | 0.0444723i | \(0.0141606\pi\) | ||||
−0.999011 | + | 0.0444723i | \(0.985839\pi\) | |||||||
\(348\) | 3.17157i | 0.170014i | ||||||||
\(349\) | 16.1421 | 0.864069 | 0.432034 | − | 0.901857i | \(-0.357796\pi\) | ||||
0.432034 | + | 0.901857i | \(0.357796\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | − 5.65685i | − 0.301511i | ||||||||
\(353\) | 17.3137i | 0.921516i | 0.887526 | + | 0.460758i | \(0.152422\pi\) | ||||
−0.887526 | + | 0.460758i | \(0.847578\pi\) | |||||||
\(354\) | 13.6569 | 0.725854 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.34315 | −0.230186 | ||||||||
\(357\) | − 13.6569i | − 0.722797i | ||||||||
\(358\) | − 24.4853i | − 1.29409i | ||||||||
\(359\) | −28.2843 | −1.49279 | −0.746393 | − | 0.665505i | \(-0.768216\pi\) | ||||
−0.746393 | + | 0.665505i | \(0.768216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 3.65685i | 0.192200i | ||||||||
\(363\) | − 21.0000i | − 1.10221i | ||||||||
\(364\) | 2.82843 | 0.148250 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.00000 | 0.313625 | ||||||||
\(367\) | 14.3431i | 0.748706i | 0.927286 | + | 0.374353i | \(0.122135\pi\) | ||||
−0.927286 | + | 0.374353i | \(0.877865\pi\) | |||||||
\(368\) | − 8.48528i | − 0.442326i | ||||||||
\(369\) | −3.65685 | −0.190368 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.3431 | −1.36767 | ||||||||
\(372\) | 4.00000i | 0.207390i | ||||||||
\(373\) | 25.3137i | 1.31069i | 0.755328 | + | 0.655347i | \(0.227478\pi\) | ||||
−0.755328 | + | 0.655347i | \(0.772522\pi\) | |||||||
\(374\) | −27.3137 | −1.41236 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 3.17157i | 0.163344i | ||||||||
\(378\) | − 2.82843i | − 0.145479i | ||||||||
\(379\) | 24.4853 | 1.25772 | 0.628862 | − | 0.777517i | \(-0.283521\pi\) | ||||
0.628862 | + | 0.777517i | \(0.283521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.65685 | −0.0848832 | ||||||||
\(382\) | − 11.3137i | − 0.578860i | ||||||||
\(383\) | 18.3431i | 0.937291i | 0.883386 | + | 0.468645i | \(0.155258\pi\) | ||||
−0.883386 | + | 0.468645i | \(0.844742\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.4853 | −0.737281 | ||||||||
\(387\) | − 1.65685i | − 0.0842226i | ||||||||
\(388\) | 8.82843i | 0.448195i | ||||||||
\(389\) | −10.4853 | −0.531625 | −0.265812 | − | 0.964025i | \(-0.585640\pi\) | ||||
−0.265812 | + | 0.964025i | \(0.585640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.9706 | −2.07197 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | − 22.1421i | − 1.11692i | ||||||||
\(394\) | −9.31371 | −0.469218 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.65685 | −0.284268 | ||||||||
\(397\) | − 26.2843i | − 1.31917i | −0.751630 | − | 0.659585i | \(-0.770732\pi\) | ||||
0.751630 | − | 0.659585i | \(-0.229268\pi\) | |||||||
\(398\) | − 21.6569i | − 1.08556i | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.97056 | 0.348093 | 0.174047 | − | 0.984737i | \(-0.444316\pi\) | ||||
0.174047 | + | 0.984737i | \(0.444316\pi\) | |||||||
\(402\) | − 5.65685i | − 0.282138i | ||||||||
\(403\) | 4.00000i | 0.199254i | ||||||||
\(404\) | 12.1421 | 0.604094 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.97056 | −0.445202 | ||||||||
\(407\) | 1.94113i | 0.0962180i | ||||||||
\(408\) | 4.82843i | 0.239043i | ||||||||
\(409\) | −7.65685 | −0.378607 | −0.189304 | − | 0.981919i | \(-0.560623\pi\) | ||||
−0.189304 | + | 0.981919i | \(0.560623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.31371 | 0.262106 | ||||||||
\(412\) | 9.65685i | 0.475759i | ||||||||
\(413\) | 38.6274i | 1.90073i | ||||||||
\(414\) | −8.48528 | −0.417029 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 17.6569i | 0.864660i | ||||||||
\(418\) | − 16.0000i | − 0.782586i | ||||||||
\(419\) | 5.17157 | 0.252648 | 0.126324 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126324 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.14214 | 0.201875 | 0.100938 | − | 0.994893i | \(-0.467816\pi\) | ||||
0.100938 | + | 0.994893i | \(0.467816\pi\) | |||||||
\(422\) | 23.3137i | 1.13489i | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | 9.31371 | 0.452314 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.65685 | 0.274075 | ||||||||
\(427\) | 16.9706i | 0.821263i | ||||||||
\(428\) | 4.00000i | 0.193347i | ||||||||
\(429\) | −5.65685 | −0.273115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − 10.9706i | − 0.527212i | −0.964630 | − | 0.263606i | \(-0.915088\pi\) | ||||
0.964630 | − | 0.263606i | \(-0.0849118\pi\) | |||||||
\(434\) | −11.3137 | −0.543075 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.17157 | 0.151891 | ||||||||
\(437\) | − 24.0000i | − 1.14808i | ||||||||
\(438\) | − 2.48528i | − 0.118751i | ||||||||
\(439\) | 22.6274 | 1.07995 | 0.539974 | − | 0.841682i | \(-0.318434\pi\) | ||||
0.539974 | + | 0.841682i | \(0.318434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 4.82843i | 0.229665i | ||||||||
\(443\) | − 41.6569i | − 1.97918i | −0.143926 | − | 0.989588i | \(-0.545973\pi\) | ||||
0.143926 | − | 0.989588i | \(-0.454027\pi\) | |||||||
\(444\) | 0.343146 | 0.0162850 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.17157 | 0.244881 | ||||||||
\(447\) | − 7.65685i | − 0.362157i | ||||||||
\(448\) | − 2.82843i | − 0.133631i | ||||||||
\(449\) | 30.2843 | 1.42920 | 0.714602 | − | 0.699532i | \(-0.246608\pi\) | ||||
0.714602 | + | 0.699532i | \(0.246608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.6863 | −0.974079 | ||||||||
\(452\) | − 10.4853i | − 0.493186i | ||||||||
\(453\) | − 12.0000i | − 0.563809i | ||||||||
\(454\) | −4.00000 | −0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.82843 | −0.132453 | ||||||||
\(457\) | 15.1716i | 0.709696i | 0.934924 | + | 0.354848i | \(0.115467\pi\) | ||||
−0.934924 | + | 0.354848i | \(0.884533\pi\) | |||||||
\(458\) | 24.1421i | 1.12809i | ||||||||
\(459\) | 4.82843 | 0.225372 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | − 16.0000i | − 0.744387i | ||||||||
\(463\) | − 35.7990i | − 1.66372i | −0.554985 | − | 0.831860i | \(-0.687276\pi\) | ||||
0.554985 | − | 0.831860i | \(-0.312724\pi\) | |||||||
\(464\) | 3.17157 | 0.147237 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.4853 | 1.04161 | ||||||||
\(467\) | − 15.3137i | − 0.708634i | −0.935125 | − | 0.354317i | \(-0.884713\pi\) | ||||
0.935125 | − | 0.354317i | \(-0.115287\pi\) | |||||||
\(468\) | 1.00000i | 0.0462250i | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.3137 | −0.797774 | ||||||||
\(472\) | − 13.6569i | − 0.628608i | ||||||||
\(473\) | − 9.37258i | − 0.430952i | ||||||||
\(474\) | −13.6569 | −0.627280 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.6569 | −0.625961 | ||||||||
\(477\) | − 9.31371i | − 0.426445i | ||||||||
\(478\) | − 16.0000i | − 0.731823i | ||||||||
\(479\) | −11.3137 | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.343146 | 0.0156461 | ||||||||
\(482\) | − 17.3137i | − 0.788618i | ||||||||
\(483\) | − 24.0000i | − 1.09204i | ||||||||
\(484\) | −21.0000 | −0.954545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − 0.485281i | − 0.0219902i | −0.999940 | − | 0.0109951i | \(-0.996500\pi\) | ||||
0.999940 | − | 0.0109951i | \(-0.00349992\pi\) | |||||||
\(488\) | − 6.00000i | − 0.271607i | ||||||||
\(489\) | 11.3137 | 0.511624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.85786 | −0.444879 | −0.222440 | − | 0.974946i | \(-0.571402\pi\) | ||||
−0.222440 | + | 0.974946i | \(0.571402\pi\) | |||||||
\(492\) | 3.65685i | 0.164864i | ||||||||
\(493\) | − 15.3137i | − 0.689695i | ||||||||
\(494\) | −2.82843 | −0.127257 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 16.0000i | 0.717698i | ||||||||
\(498\) | − 17.6569i | − 0.791223i | ||||||||
\(499\) | 16.4853 | 0.737983 | 0.368991 | − | 0.929433i | \(-0.379703\pi\) | ||||
0.368991 | + | 0.929433i | \(0.379703\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.9706 | −1.11560 | ||||||||
\(502\) | 5.17157i | 0.230819i | ||||||||
\(503\) | 40.4853i | 1.80515i | 0.430533 | + | 0.902575i | \(0.358326\pi\) | ||||
−0.430533 | + | 0.902575i | \(0.641674\pi\) | |||||||
\(504\) | −2.82843 | −0.125988 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −48.0000 | −2.13386 | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | 1.65685i | 0.0735110i | ||||||||
\(509\) | 14.6863 | 0.650958 | 0.325479 | − | 0.945549i | \(-0.394474\pi\) | ||||
0.325479 | + | 0.945549i | \(0.394474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.02944 | 0.310964 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.82843i | 0.124878i | ||||||||
\(514\) | −0.828427 | −0.0365404 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.65685 | −0.0729389 | ||||||||
\(517\) | 45.2548i | 1.99031i | ||||||||
\(518\) | 0.970563i | 0.0426441i | ||||||||
\(519\) | −13.3137 | −0.584407 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.97056 | −0.305386 | −0.152693 | − | 0.988274i | \(-0.548795\pi\) | ||||
−0.152693 | + | 0.988274i | \(0.548795\pi\) | |||||||
\(522\) | − 3.17157i | − 0.138816i | ||||||||
\(523\) | − 34.6274i | − 1.51415i | −0.653327 | − | 0.757076i | \(-0.726627\pi\) | ||||
0.653327 | − | 0.757076i | \(-0.273373\pi\) | |||||||
\(524\) | −22.1421 | −0.967284 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.485281 | −0.0211593 | ||||||||
\(527\) | − 19.3137i | − 0.841318i | ||||||||
\(528\) | 5.65685i | 0.246183i | ||||||||
\(529\) | −49.0000 | −2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.6569 | −0.592657 | ||||||||
\(532\) | − 8.00000i | − 0.346844i | ||||||||
\(533\) | 3.65685i | 0.158396i | ||||||||
\(534\) | 4.34315 | 0.187946 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.65685 | −0.244339 | ||||||||
\(537\) | 24.4853i | 1.05662i | ||||||||
\(538\) | − 2.48528i | − 0.107148i | ||||||||
\(539\) | 5.65685 | 0.243658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.48528 | −0.106851 | −0.0534253 | − | 0.998572i | \(-0.517014\pi\) | ||||
−0.0534253 | + | 0.998572i | \(0.517014\pi\) | |||||||
\(542\) | − 15.3137i | − 0.657780i | ||||||||
\(543\) | − 3.65685i | − 0.156931i | ||||||||
\(544\) | 4.82843 | 0.207017 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.82843 | −0.121046 | ||||||||
\(547\) | 23.3137i | 0.996822i | 0.866941 | + | 0.498411i | \(0.166083\pi\) | ||||
−0.866941 | + | 0.498411i | \(0.833917\pi\) | |||||||
\(548\) | − 5.31371i | − 0.226990i | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.97056 | 0.382159 | ||||||||
\(552\) | 8.48528i | 0.361158i | ||||||||
\(553\) | − 38.6274i | − 1.64260i | ||||||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.6569 | 0.748817 | ||||||||
\(557\) | 33.3137i | 1.41155i | 0.708437 | + | 0.705774i | \(0.249400\pi\) | ||||
−0.708437 | + | 0.705774i | \(0.750600\pi\) | |||||||
\(558\) | − 4.00000i | − 0.169334i | ||||||||
\(559\) | −1.65685 | −0.0700775 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.3137 | 1.15319 | ||||||||
\(562\) | 19.6569i | 0.829174i | ||||||||
\(563\) | 41.6569i | 1.75563i | 0.479002 | + | 0.877814i | \(0.340998\pi\) | ||||
−0.479002 | + | 0.877814i | \(0.659002\pi\) | |||||||
\(564\) | 8.00000 | 0.336861 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.34315 | −0.266622 | ||||||||
\(567\) | 2.82843i | 0.118783i | ||||||||
\(568\) | − 5.65685i | − 0.237356i | ||||||||
\(569\) | −20.3431 | −0.852829 | −0.426415 | − | 0.904528i | \(-0.640224\pi\) | ||||
−0.426415 | + | 0.904528i | \(0.640224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9706 | −0.542801 | −0.271401 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271401 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(572\) | 5.65685i | 0.236525i | ||||||||
\(573\) | 11.3137i | 0.472637i | ||||||||
\(574\) | −10.3431 | −0.431715 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 27.4558i | 1.14300i | 0.820601 | + | 0.571501i | \(0.193639\pi\) | ||||
−0.820601 | + | 0.571501i | \(0.806361\pi\) | |||||||
\(578\) | − 6.31371i | − 0.262616i | ||||||||
\(579\) | 14.4853 | 0.601988 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 49.9411 | 2.07191 | ||||||||
\(582\) | − 8.82843i | − 0.365950i | ||||||||
\(583\) | − 52.6863i | − 2.18204i | ||||||||
\(584\) | −2.48528 | −0.102842 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.6274 | 1.18259 | ||||||||
\(587\) | − 42.6274i | − 1.75942i | −0.475509 | − | 0.879711i | \(-0.657736\pi\) | ||||
0.475509 | − | 0.879711i | \(-0.342264\pi\) | |||||||
\(588\) | − 1.00000i | − 0.0412393i | ||||||||
\(589\) | 11.3137 | 0.466173 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.31371 | 0.383115 | ||||||||
\(592\) | − 0.343146i | − 0.0141032i | ||||||||
\(593\) | 11.6569i | 0.478690i | 0.970935 | + | 0.239345i | \(0.0769326\pi\) | ||||
−0.970935 | + | 0.239345i | \(0.923067\pi\) | |||||||
\(594\) | 5.65685 | 0.232104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.65685 | −0.313637 | ||||||||
\(597\) | 21.6569i | 0.886356i | ||||||||
\(598\) | 8.48528i | 0.346989i | ||||||||
\(599\) | −40.0000 | −1.63436 | −0.817178 | − | 0.576386i | \(-0.804463\pi\) | ||||
−0.817178 | + | 0.576386i | \(0.804463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.68629 | 0.272740 | 0.136370 | − | 0.990658i | \(-0.456456\pi\) | ||||
0.136370 | + | 0.990658i | \(0.456456\pi\) | |||||||
\(602\) | − 4.68629i | − 0.190999i | ||||||||
\(603\) | 5.65685i | 0.230365i | ||||||||
\(604\) | −12.0000 | −0.488273 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.1421 | −0.493241 | ||||||||
\(607\) | − 4.97056i | − 0.201749i | −0.994899 | − | 0.100874i | \(-0.967836\pi\) | ||||
0.994899 | − | 0.100874i | \(-0.0321640\pi\) | |||||||
\(608\) | 2.82843i | 0.114708i | ||||||||
\(609\) | 8.97056 | 0.363506 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | − 4.82843i | − 0.195178i | ||||||||
\(613\) | 34.2843i | 1.38473i | 0.721548 | + | 0.692364i | \(0.243431\pi\) | ||||
−0.721548 | + | 0.692364i | \(0.756569\pi\) | |||||||
\(614\) | 10.3431 | 0.417415 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.0000 | −0.644658 | ||||||||
\(617\) | 2.00000i | 0.0805170i | 0.999189 | + | 0.0402585i | \(0.0128181\pi\) | ||||
−0.999189 | + | 0.0402585i | \(0.987182\pi\) | |||||||
\(618\) | − 9.65685i | − 0.388456i | ||||||||
\(619\) | 29.1716 | 1.17250 | 0.586252 | − | 0.810129i | \(-0.300603\pi\) | ||||
0.586252 | + | 0.810129i | \(0.300603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.48528 | 0.340503 | ||||||||
\(622\) | − 24.0000i | − 0.962312i | ||||||||
\(623\) | 12.2843i | 0.492159i | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.97056 | 0.118728 | ||||||||
\(627\) | 16.0000i | 0.638978i | ||||||||
\(628\) | 17.3137i | 0.690892i | ||||||||
\(629\) | −1.65685 | −0.0660631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.3431 | −0.889467 | −0.444733 | − | 0.895663i | \(-0.646702\pi\) | ||||
−0.444733 | + | 0.895663i | \(0.646702\pi\) | |||||||
\(632\) | 13.6569i | 0.543240i | ||||||||
\(633\) | − 23.3137i | − 0.926637i | ||||||||
\(634\) | −2.68629 | −0.106686 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.31371 | −0.369313 | ||||||||
\(637\) | − 1.00000i | − 0.0396214i | ||||||||
\(638\) | − 17.9411i | − 0.710296i | ||||||||
\(639\) | −5.65685 | −0.223782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.6274 | 1.60469 | 0.802343 | − | 0.596863i | \(-0.203586\pi\) | ||||
0.802343 | + | 0.596863i | \(0.203586\pi\) | |||||||
\(642\) | − 4.00000i | − 0.157867i | ||||||||
\(643\) | 39.5980i | 1.56159i | 0.624786 | + | 0.780796i | \(0.285186\pi\) | ||||
−0.624786 | + | 0.780796i | \(0.714814\pi\) | |||||||
\(644\) | −24.0000 | −0.945732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.6569 | 0.537322 | ||||||||
\(647\) | − 8.48528i | − 0.333591i | −0.985992 | − | 0.166795i | \(-0.946658\pi\) | ||||
0.985992 | − | 0.166795i | \(-0.0533419\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | −77.2548 | −3.03252 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3137 | 0.443419 | ||||||||
\(652\) | − 11.3137i | − 0.443079i | ||||||||
\(653\) | − 14.2843i | − 0.558987i | −0.960148 | − | 0.279493i | \(-0.909834\pi\) | ||||
0.960148 | − | 0.279493i | \(-0.0901665\pi\) | |||||||
\(654\) | −3.17157 | −0.124018 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.65685 | 0.142776 | ||||||||
\(657\) | 2.48528i | 0.0969601i | ||||||||
\(658\) | 22.6274i | 0.882109i | ||||||||
\(659\) | 24.4853 | 0.953811 | 0.476906 | − | 0.878955i | \(-0.341758\pi\) | ||||
0.476906 | + | 0.878955i | \(0.341758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.1421 | 0.783438 | 0.391719 | − | 0.920085i | \(-0.371880\pi\) | ||||
0.391719 | + | 0.920085i | \(0.371880\pi\) | |||||||
\(662\) | 8.48528i | 0.329790i | ||||||||
\(663\) | − 4.82843i | − 0.187521i | ||||||||
\(664\) | −17.6569 | −0.685219 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.343146 | −0.0132966 | ||||||||
\(667\) | − 26.9117i | − 1.04202i | ||||||||
\(668\) | 24.9706i | 0.966140i | ||||||||
\(669\) | −5.17157 | −0.199945 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.9411 | −1.31028 | ||||||||
\(672\) | 2.82843i | 0.109109i | ||||||||
\(673\) | 12.6274i | 0.486751i | 0.969932 | + | 0.243376i | \(0.0782548\pi\) | ||||
−0.969932 | + | 0.243376i | \(0.921745\pi\) | |||||||
\(674\) | 22.9706 | 0.884793 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 23.6569i | 0.909207i | 0.890694 | + | 0.454603i | \(0.150219\pi\) | ||||
−0.890694 | + | 0.454603i | \(0.849781\pi\) | |||||||
\(678\) | 10.4853i | 0.402685i | ||||||||
\(679\) | 24.9706 | 0.958282 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | 0.153280 | ||||||||
\(682\) | − 22.6274i | − 0.866449i | ||||||||
\(683\) | − 22.3431i | − 0.854937i | −0.904030 | − | 0.427468i | \(-0.859406\pi\) | ||||
0.904030 | − | 0.427468i | \(-0.140594\pi\) | |||||||
\(684\) | 2.82843 | 0.108148 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.9706 | −0.647939 | ||||||||
\(687\) | − 24.1421i | − 0.921080i | ||||||||
\(688\) | 1.65685i | 0.0631670i | ||||||||
\(689\) | −9.31371 | −0.354824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7990 | 0.448855 | 0.224427 | − | 0.974491i | \(-0.427949\pi\) | ||||
0.224427 | + | 0.974491i | \(0.427949\pi\) | |||||||
\(692\) | 13.3137i | 0.506111i | ||||||||
\(693\) | 16.0000i | 0.607790i | ||||||||
\(694\) | −1.65685 | −0.0628933 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.17157 | −0.120218 | ||||||||
\(697\) | − 17.6569i | − 0.668801i | ||||||||
\(698\) | 16.1421i | 0.610989i | ||||||||
\(699\) | −22.4853 | −0.850471 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.1421 | −1.06291 | −0.531457 | − | 0.847085i | \(-0.678355\pi\) | ||||
−0.531457 | + | 0.847085i | \(0.678355\pi\) | |||||||
\(702\) | − 1.00000i | − 0.0377426i | ||||||||
\(703\) | − 0.970563i | − 0.0366055i | ||||||||
\(704\) | 5.65685 | 0.213201 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.3137 | −0.651610 | ||||||||
\(707\) | − 34.3431i | − 1.29161i | ||||||||
\(708\) | 13.6569i | 0.513256i | ||||||||
\(709\) | 12.8284 | 0.481782 | 0.240891 | − | 0.970552i | \(-0.422560\pi\) | ||||
0.240891 | + | 0.970552i | \(0.422560\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6569 | 0.512172 | ||||||||
\(712\) | − 4.34315i | − 0.162766i | ||||||||
\(713\) | − 33.9411i | − 1.27111i | ||||||||
\(714\) | 13.6569 | 0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.4853 | 0.915058 | ||||||||
\(717\) | 16.0000i | 0.597531i | ||||||||
\(718\) | − 28.2843i | − 1.05556i | ||||||||
\(719\) | 18.3431 | 0.684084 | 0.342042 | − | 0.939685i | \(-0.388882\pi\) | ||||
0.342042 | + | 0.939685i | \(0.388882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.3137 | 1.01722 | ||||||||
\(722\) | − 11.0000i | − 0.409378i | ||||||||
\(723\) | 17.3137i | 0.643904i | ||||||||
\(724\) | −3.65685 | −0.135906 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 21.0000 | 0.779383 | ||||||||
\(727\) | 21.9411i | 0.813751i | 0.913484 | + | 0.406876i | \(0.133382\pi\) | ||||
−0.913484 | + | 0.406876i | \(0.866618\pi\) | |||||||
\(728\) | 2.82843i | 0.104828i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 6.00000i | 0.221766i | ||||||||
\(733\) | 11.6569i | 0.430556i | 0.976553 | + | 0.215278i | \(0.0690657\pi\) | ||||
−0.976553 | + | 0.215278i | \(0.930934\pi\) | |||||||
\(734\) | −14.3431 | −0.529415 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.48528 | 0.312772 | ||||||||
\(737\) | 32.0000i | 1.17874i | ||||||||
\(738\) | − 3.65685i | − 0.134611i | ||||||||
\(739\) | −14.1421 | −0.520227 | −0.260113 | − | 0.965578i | \(-0.583760\pi\) | ||||
−0.260113 | + | 0.965578i | \(0.583760\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.82843 | 0.103905 | ||||||||
\(742\) | − 26.3431i | − 0.967087i | ||||||||
\(743\) | − 20.2843i | − 0.744158i | −0.928201 | − | 0.372079i | \(-0.878645\pi\) | ||||
0.928201 | − | 0.372079i | \(-0.121355\pi\) | |||||||
\(744\) | −4.00000 | −0.146647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25.3137 | −0.926801 | ||||||||
\(747\) | 17.6569i | 0.646031i | ||||||||
\(748\) | − 27.3137i | − 0.998688i | ||||||||
\(749\) | 11.3137 | 0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3137 | −0.412843 | −0.206422 | − | 0.978463i | \(-0.566182\pi\) | ||||
−0.206422 | + | 0.978463i | \(0.566182\pi\) | |||||||
\(752\) | − 8.00000i | − 0.291730i | ||||||||
\(753\) | − 5.17157i | − 0.188463i | ||||||||
\(754\) | −3.17157 | −0.115502 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.82843 | 0.102869 | ||||||||
\(757\) | − 47.9411i | − 1.74245i | −0.490884 | − | 0.871225i | \(-0.663326\pi\) | ||||
0.490884 | − | 0.871225i | \(-0.336674\pi\) | |||||||
\(758\) | 24.4853i | 0.889345i | ||||||||
\(759\) | 48.0000 | 1.74229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3431 | 0.592439 | 0.296219 | − | 0.955120i | \(-0.404274\pi\) | ||||
0.296219 | + | 0.955120i | \(0.404274\pi\) | |||||||
\(762\) | − 1.65685i | − 0.0600215i | ||||||||
\(763\) | − 8.97056i | − 0.324756i | ||||||||
\(764\) | 11.3137 | 0.409316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.3431 | −0.662765 | ||||||||
\(767\) | 13.6569i | 0.493120i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.828427 | 0.0298351 | ||||||||
\(772\) | − 14.4853i | − 0.521337i | ||||||||
\(773\) | 30.6863i | 1.10371i | 0.833940 | + | 0.551855i | \(0.186080\pi\) | ||||
−0.833940 | + | 0.551855i | \(0.813920\pi\) | |||||||
\(774\) | 1.65685 | 0.0595544 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.82843 | −0.316922 | ||||||||
\(777\) | − 0.970563i | − 0.0348187i | ||||||||
\(778\) | − 10.4853i | − 0.375916i | ||||||||
\(779\) | 10.3431 | 0.370582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | − 40.9706i | − 1.46510i | ||||||||
\(783\) | 3.17157i | 0.113343i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 22.1421 | 0.789784 | ||||||||
\(787\) | − 24.0000i | − 0.855508i | −0.903895 | − | 0.427754i | \(-0.859305\pi\) | ||||
0.903895 | − | 0.427754i | \(-0.140695\pi\) | |||||||
\(788\) | − 9.31371i | − 0.331787i | ||||||||
\(789\) | 0.485281 | 0.0172765 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.6569 | −1.05448 | ||||||||
\(792\) | − 5.65685i | − 0.201008i | ||||||||
\(793\) | 6.00000i | 0.213066i | ||||||||
\(794\) | 26.2843 | 0.932794 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.6569 | 0.767607 | ||||||||
\(797\) | − 28.6274i | − 1.01404i | −0.861936 | − | 0.507018i | \(-0.830748\pi\) | ||||
0.861936 | − | 0.507018i | \(-0.169252\pi\) | |||||||
\(798\) | 8.00000i | 0.283197i | ||||||||
\(799\) | −38.6274 | −1.36654 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.34315 | −0.153458 | ||||||||
\(802\) | 6.97056i | 0.246139i | ||||||||
\(803\) | 14.0589i | 0.496127i | ||||||||
\(804\) | 5.65685 | 0.199502 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 2.48528i | 0.0874860i | ||||||||
\(808\) | 12.1421i | 0.427159i | ||||||||
\(809\) | 9.31371 | 0.327453 | 0.163726 | − | 0.986506i | \(-0.447649\pi\) | ||||
0.163726 | + | 0.986506i | \(0.447649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.1421 | −1.05843 | −0.529217 | − | 0.848487i | \(-0.677514\pi\) | ||||
−0.529217 | + | 0.848487i | \(0.677514\pi\) | |||||||
\(812\) | − 8.97056i | − 0.314805i | ||||||||
\(813\) | 15.3137i | 0.537075i | ||||||||
\(814\) | −1.94113 | −0.0680364 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.82843 | −0.169029 | ||||||||
\(817\) | 4.68629i | 0.163953i | ||||||||
\(818\) | − 7.65685i | − 0.267716i | ||||||||
\(819\) | 2.82843 | 0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.2843 | −0.777726 | −0.388863 | − | 0.921296i | \(-0.627132\pi\) | ||||
−0.388863 | + | 0.921296i | \(0.627132\pi\) | |||||||
\(822\) | 5.31371i | 0.185337i | ||||||||
\(823\) | 19.0294i | 0.663324i | 0.943398 | + | 0.331662i | \(0.107609\pi\) | ||||
−0.943398 | + | 0.331662i | \(0.892391\pi\) | |||||||
\(824\) | −9.65685 | −0.336412 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.6274 | −1.34402 | ||||||||
\(827\) | − 1.65685i | − 0.0576145i | −0.999585 | − | 0.0288072i | \(-0.990829\pi\) | ||||
0.999585 | − | 0.0288072i | \(-0.00917090\pi\) | |||||||
\(828\) | − 8.48528i | − 0.294884i | ||||||||
\(829\) | 30.6863 | 1.06578 | 0.532889 | − | 0.846185i | \(-0.321106\pi\) | ||||
0.532889 | + | 0.846185i | \(0.321106\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.0000 | 0.901930 | ||||||||
\(832\) | − 1.00000i | − 0.0346688i | ||||||||
\(833\) | 4.82843i | 0.167295i | ||||||||
\(834\) | −17.6569 | −0.611407 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.0000 | 0.553372 | ||||||||
\(837\) | 4.00000i | 0.138260i | ||||||||
\(838\) | 5.17157i | 0.178649i | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | 4.14214i | 0.142747i | ||||||||
\(843\) | − 19.6569i | − 0.677018i | ||||||||
\(844\) | −23.3137 | −0.802491 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | 59.3970i | 2.04090i | ||||||||
\(848\) | 9.31371i | 0.319834i | ||||||||
\(849\) | 6.34315 | 0.217696 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.91169 | −0.0998114 | ||||||||
\(852\) | 5.65685i | 0.193801i | ||||||||
\(853\) | 18.2843i | 0.626042i | 0.949746 | + | 0.313021i | \(0.101341\pi\) | ||||
−0.949746 | + | 0.313021i | \(0.898659\pi\) | |||||||
\(854\) | −16.9706 | −0.580721 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | − 15.1716i | − 0.518251i | −0.965844 | − | 0.259126i | \(-0.916566\pi\) | ||||
0.965844 | − | 0.259126i | \(-0.0834343\pi\) | |||||||
\(858\) | − 5.65685i | − 0.193122i | ||||||||
\(859\) | 29.9411 | 1.02158 | 0.510789 | − | 0.859706i | \(-0.329353\pi\) | ||||
0.510789 | + | 0.859706i | \(0.329353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.3431 | 0.352493 | ||||||||
\(862\) | − 16.0000i | − 0.544962i | ||||||||
\(863\) | − 28.2843i | − 0.962808i | −0.876499 | − | 0.481404i | \(-0.840127\pi\) | ||||
0.876499 | − | 0.481404i | \(-0.159873\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.9706 | 0.372795 | ||||||||
\(867\) | 6.31371i | 0.214425i | ||||||||
\(868\) | − 11.3137i | − 0.384012i | ||||||||
\(869\) | 77.2548 | 2.62069 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.65685 | 0.191675 | ||||||||
\(872\) | 3.17157i | 0.107403i | ||||||||
\(873\) | 8.82843i | 0.298797i | ||||||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.48528 | 0.0839699 | ||||||||
\(877\) | 39.2548i | 1.32554i | 0.748822 | + | 0.662771i | \(0.230620\pi\) | ||||
−0.748822 | + | 0.662771i | \(0.769380\pi\) | |||||||
\(878\) | 22.6274i | 0.763638i | ||||||||
\(879\) | −28.6274 | −0.965579 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.2843 | 1.55936 | 0.779678 | − | 0.626180i | \(-0.215383\pi\) | ||||
0.779678 | + | 0.626180i | \(0.215383\pi\) | |||||||
\(882\) | 1.00000i | 0.0336718i | ||||||||
\(883\) | − 8.68629i | − 0.292317i | −0.989261 | − | 0.146158i | \(-0.953309\pi\) | ||||
0.989261 | − | 0.146158i | \(-0.0466909\pi\) | |||||||
\(884\) | −4.82843 | −0.162398 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 41.6569 | 1.39949 | ||||||||
\(887\) | − 23.5147i | − 0.789547i | −0.918778 | − | 0.394773i | \(-0.870823\pi\) | ||||
0.918778 | − | 0.394773i | \(-0.129177\pi\) | |||||||
\(888\) | 0.343146i | 0.0115152i | ||||||||
\(889\) | 4.68629 | 0.157173 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.65685 | −0.189512 | ||||||||
\(892\) | 5.17157i | 0.173157i | ||||||||
\(893\) | − 22.6274i | − 0.757198i | ||||||||
\(894\) | 7.65685 | 0.256084 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.82843 | 0.0944911 | ||||||||
\(897\) | − 8.48528i | − 0.283315i | ||||||||
\(898\) | 30.2843i | 1.01060i | ||||||||
\(899\) | 12.6863 | 0.423112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.9706 | 1.49819 | ||||||||
\(902\) | − 20.6863i | − 0.688778i | ||||||||
\(903\) | 4.68629i | 0.155950i | ||||||||
\(904\) | 10.4853 | 0.348735 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.0000 | 0.398673 | ||||||||
\(907\) | − 48.2843i | − 1.60325i | −0.597825 | − | 0.801626i | \(-0.703968\pi\) | ||||
0.597825 | − | 0.801626i | \(-0.296032\pi\) | |||||||
\(908\) | − 4.00000i | − 0.132745i | ||||||||
\(909\) | 12.1421 | 0.402729 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.97056 | −0.297208 | −0.148604 | − | 0.988897i | \(-0.547478\pi\) | ||||
−0.148604 | + | 0.988897i | \(0.547478\pi\) | |||||||
\(912\) | − 2.82843i | − 0.0936586i | ||||||||
\(913\) | 99.8823i | 3.30562i | ||||||||
\(914\) | −15.1716 | −0.501831 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.1421 | −0.797679 | ||||||||
\(917\) | 62.6274i | 2.06814i | ||||||||
\(918\) | 4.82843i | 0.159362i | ||||||||
\(919\) | 25.9411 | 0.855719 | 0.427859 | − | 0.903845i | \(-0.359268\pi\) | ||||
0.427859 | + | 0.903845i | \(0.359268\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.3431 | −0.340818 | ||||||||
\(922\) | 14.0000i | 0.461065i | ||||||||
\(923\) | 5.65685i | 0.186198i | ||||||||
\(924\) | 16.0000 | 0.526361 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.7990 | 1.17643 | ||||||||
\(927\) | 9.65685i | 0.317173i | ||||||||
\(928\) | 3.17157i | 0.104112i | ||||||||
\(929\) | −45.5980 | −1.49602 | −0.748011 | − | 0.663687i | \(-0.768991\pi\) | ||||
−0.748011 | + | 0.663687i | \(0.768991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | 22.4853i | 0.736530i | ||||||||
\(933\) | 24.0000i | 0.785725i | ||||||||
\(934\) | 15.3137 | 0.501080 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | − 28.6274i | − 0.935217i | −0.883936 | − | 0.467608i | \(-0.845116\pi\) | ||||
0.883936 | − | 0.467608i | \(-0.154884\pi\) | |||||||
\(938\) | 16.0000i | 0.522419i | ||||||||
\(939\) | −2.97056 | −0.0969407 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0294 | 0.685540 | 0.342770 | − | 0.939419i | \(-0.388635\pi\) | ||||
0.342770 | + | 0.939419i | \(0.388635\pi\) | |||||||
\(942\) | − 17.3137i | − 0.564111i | ||||||||
\(943\) | − 31.0294i | − 1.01046i | ||||||||
\(944\) | 13.6569 | 0.444493 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.37258 | 0.304729 | ||||||||
\(947\) | 41.6569i | 1.35367i | 0.736137 | + | 0.676833i | \(0.236648\pi\) | ||||
−0.736137 | + | 0.676833i | \(0.763352\pi\) | |||||||
\(948\) | − 13.6569i | − 0.443554i | ||||||||
\(949\) | 2.48528 | 0.0806756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.68629 | 0.0871090 | ||||||||
\(952\) | − 13.6569i | − 0.442621i | ||||||||
\(953\) | 56.1421i | 1.81862i | 0.416117 | + | 0.909311i | \(0.363391\pi\) | ||||
−0.416117 | + | 0.909311i | \(0.636609\pi\) | |||||||
\(954\) | 9.31371 | 0.301542 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.0000 | 0.517477 | ||||||||
\(957\) | 17.9411i | 0.579954i | ||||||||
\(958\) | − 11.3137i | − 0.365529i | ||||||||
\(959\) | −15.0294 | −0.485326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0.343146i | 0.0110635i | ||||||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | 17.3137 | 0.557637 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 24.0000 | 0.772187 | ||||||||
\(967\) | − 24.4853i | − 0.787394i | −0.919240 | − | 0.393697i | \(-0.871196\pi\) | ||||
0.919240 | − | 0.393697i | \(-0.128804\pi\) | |||||||
\(968\) | − 21.0000i | − 0.674966i | ||||||||
\(969\) | −13.6569 | −0.438721 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.4853 | 1.04250 | 0.521251 | − | 0.853403i | \(-0.325465\pi\) | ||||
0.521251 | + | 0.853403i | \(0.325465\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − 49.9411i | − 1.60104i | ||||||||
\(974\) | 0.485281 | 0.0155494 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | − 19.6569i | − 0.628878i | −0.949278 | − | 0.314439i | \(-0.898184\pi\) | ||||
0.949278 | − | 0.314439i | \(-0.101816\pi\) | |||||||
\(978\) | 11.3137i | 0.361773i | ||||||||
\(979\) | −24.5685 | −0.785214 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.17157 | 0.101261 | ||||||||
\(982\) | − 9.85786i | − 0.314577i | ||||||||
\(983\) | 13.6569i | 0.435586i | 0.975995 | + | 0.217793i | \(0.0698858\pi\) | ||||
−0.975995 | + | 0.217793i | \(0.930114\pi\) | |||||||
\(984\) | −3.65685 | −0.116576 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.3137 | 0.487688 | ||||||||
\(987\) | − 22.6274i | − 0.720239i | ||||||||
\(988\) | − 2.82843i | − 0.0899843i | ||||||||
\(989\) | 14.0589 | 0.447046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.9117 | 1.87139 | 0.935696 | − | 0.352808i | \(-0.114773\pi\) | ||||
0.935696 | + | 0.352808i | \(0.114773\pi\) | |||||||
\(992\) | 4.00000i | 0.127000i | ||||||||
\(993\) | − 8.48528i | − 0.269272i | ||||||||
\(994\) | −16.0000 | −0.507489 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.6569 | 0.559479 | ||||||||
\(997\) | 38.6863i | 1.22521i | 0.790390 | + | 0.612604i | \(0.209878\pi\) | ||||
−0.790390 | + | 0.612604i | \(0.790122\pi\) | |||||||
\(998\) | 16.4853i | 0.521832i | ||||||||
\(999\) | 0.343146 | 0.0108567 |
(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 | 1950.2.e.o.1249.4 | 4 | ||
3.2 | odd | 2 | 5850.2.e.bk.5149.2 | 4 | |||
5.2 | odd | 4 | 1950.2.a.bd.1.1 | 2 | |||
5.3 | odd | 4 | 390.2.a.h.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1950.2.e.o.1249.1 | 4 | ||
15.2 | even | 4 | 5850.2.a.cl.1.1 | 2 | |||
15.8 | even | 4 | 1170.2.a.o.1.2 | 2 | |||
15.14 | odd | 2 | 5850.2.e.bk.5149.3 | 4 | |||
20.3 | even | 4 | 3120.2.a.bc.1.1 | 2 | |||
60.23 | odd | 4 | 9360.2.a.ch.1.1 | 2 | |||
65.8 | even | 4 | 5070.2.b.q.1351.3 | 4 | |||
65.18 | even | 4 | 5070.2.b.q.1351.2 | 4 | |||
65.38 | odd | 4 | 5070.2.a.bc.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.a.h.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
1170.2.a.o.1.2 | 2 | 15.8 | even | 4 | |||
1950.2.a.bd.1.1 | 2 | 5.2 | odd | 4 | |||
1950.2.e.o.1249.1 | 4 | 5.4 | even | 2 | inner | ||
1950.2.e.o.1249.4 | 4 | 1.1 | even | 1 | trivial | ||
3120.2.a.bc.1.1 | 2 | 20.3 | even | 4 | |||
5070.2.a.bc.1.1 | 2 | 65.38 | odd | 4 | |||
5070.2.b.q.1351.2 | 4 | 65.18 | even | 4 | |||
5070.2.b.q.1351.3 | 4 | 65.8 | even | 4 | |||
5850.2.a.cl.1.1 | 2 | 15.2 | even | 4 | |||
5850.2.e.bk.5149.2 | 4 | 3.2 | odd | 2 | |||
5850.2.e.bk.5149.3 | 4 | 15.14 | odd | 2 | |||
9360.2.a.ch.1.1 | 2 | 60.23 | odd | 4 |