Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.a (trivial) |
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: | yes |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 5.65685 | 1.70561 | 0.852803 | − | 0.522233i | \(-0.174901\pi\) | ||||
0.852803 | + | 0.522233i | \(0.174901\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.82843 | 0.755929 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.82843 | −1.17107 | −0.585533 | − | 0.810649i | \(-0.699115\pi\) | ||||
−0.585533 | + | 0.810649i | \(0.699115\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | −5.65685 | −1.20605 | ||||||||
\(23\) | 8.48528 | 1.76930 | 0.884652 | − | 0.466252i | \(-0.154396\pi\) | ||||
0.884652 | + | 0.466252i | \(0.154396\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.82843 | −0.534522 | ||||||||
\(29\) | −3.17157 | −0.588946 | −0.294473 | − | 0.955660i | \(-0.595144\pi\) | ||||
−0.294473 | + | 0.955660i | \(0.595144\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.65685 | 0.984732 | ||||||||
\(34\) | 4.82843 | 0.828068 | ||||||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.343146 | 0.0564128 | 0.0282064 | − | 0.999602i | \(-0.491020\pi\) | ||||
0.0282064 | + | 0.999602i | \(0.491020\pi\) | |||||||
\(38\) | −2.82843 | −0.458831 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.65685 | −0.571105 | −0.285552 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285552 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(42\) | 2.82843 | 0.436436 | ||||||||
\(43\) | −1.65685 | −0.252668 | −0.126334 | − | 0.991988i | \(-0.540321\pi\) | ||||
−0.126334 | + | 0.991988i | \(0.540321\pi\) | |||||||
\(44\) | 5.65685 | 0.852803 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −8.48528 | −1.25109 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −4.82843 | −0.676115 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.31371 | −1.27934 | −0.639668 | − | 0.768651i | \(-0.720928\pi\) | ||||
−0.639668 | + | 0.768651i | \(0.720928\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 2.82843 | 0.377964 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | 3.17157 | 0.416448 | ||||||||
\(59\) | 13.6569 | 1.77797 | 0.888985 | − | 0.457935i | \(-0.151411\pi\) | ||||
0.888985 | + | 0.457935i | \(0.151411\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | −2.82843 | −0.356348 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.65685 | −0.696311 | ||||||||
\(67\) | 5.65685 | 0.691095 | 0.345547 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345547 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(68\) | −4.82843 | −0.585533 | ||||||||
\(69\) | 8.48528 | 1.02151 | ||||||||
\(70\) | −2.82843 | −0.338062 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.48528 | −0.290880 | −0.145440 | − | 0.989367i | \(-0.546460\pi\) | ||||
−0.145440 | + | 0.989367i | \(0.546460\pi\) | |||||||
\(74\) | −0.343146 | −0.0398899 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 2.82843 | 0.324443 | ||||||||
\(77\) | −16.0000 | −1.82337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6569 | 1.53652 | 0.768258 | − | 0.640140i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640140i | \(0.221124\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.65685 | 0.403832 | ||||||||
\(83\) | −17.6569 | −1.93809 | −0.969046 | − | 0.246881i | \(-0.920594\pi\) | ||||
−0.969046 | + | 0.246881i | \(0.920594\pi\) | |||||||
\(84\) | −2.82843 | −0.308607 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | 1.65685 | 0.178663 | ||||||||
\(87\) | −3.17157 | −0.340028 | ||||||||
\(88\) | −5.65685 | −0.603023 | ||||||||
\(89\) | 4.34315 | 0.460373 | 0.230186 | − | 0.973147i | \(-0.426066\pi\) | ||||
0.230186 | + | 0.973147i | \(0.426066\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.48528 | 0.884652 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.82843 | 0.896391 | 0.448195 | − | 0.893936i | \(-0.352067\pi\) | ||||
0.448195 | + | 0.893936i | \(0.352067\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 5.65685 | 0.568535 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.1421 | −1.20819 | −0.604094 | − | 0.796913i | \(-0.706465\pi\) | ||||
−0.604094 | + | 0.796913i | \(0.706465\pi\) | |||||||
\(102\) | 4.82843 | 0.478086 | ||||||||
\(103\) | 9.65685 | 0.951518 | 0.475759 | − | 0.879576i | \(-0.342173\pi\) | ||||
0.475759 | + | 0.879576i | \(0.342173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.82843 | 0.276026 | ||||||||
\(106\) | 9.31371 | 0.904627 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.17157 | −0.303782 | −0.151891 | − | 0.988397i | \(-0.548536\pi\) | ||||
−0.151891 | + | 0.988397i | \(0.548536\pi\) | |||||||
\(110\) | 5.65685 | 0.539360 | ||||||||
\(111\) | 0.343146 | 0.0325700 | ||||||||
\(112\) | −2.82843 | −0.267261 | ||||||||
\(113\) | −10.4853 | −0.986372 | −0.493186 | − | 0.869924i | \(-0.664168\pi\) | ||||
−0.493186 | + | 0.869924i | \(0.664168\pi\) | |||||||
\(114\) | −2.82843 | −0.264906 | ||||||||
\(115\) | −8.48528 | −0.791257 | ||||||||
\(116\) | −3.17157 | −0.294473 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.6569 | −1.25722 | ||||||||
\(119\) | 13.6569 | 1.25192 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | −3.65685 | −0.329727 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.82843 | 0.251976 | ||||||||
\(127\) | −1.65685 | −0.147022 | −0.0735110 | − | 0.997294i | \(-0.523420\pi\) | ||||
−0.0735110 | + | 0.997294i | \(0.523420\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.65685 | −0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.1421 | 1.93457 | 0.967284 | − | 0.253697i | \(-0.0816467\pi\) | ||||
0.967284 | + | 0.253697i | \(0.0816467\pi\) | |||||||
\(132\) | 5.65685 | 0.492366 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | −5.65685 | −0.488678 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 4.82843 | 0.414034 | ||||||||
\(137\) | −5.31371 | −0.453981 | −0.226990 | − | 0.973897i | \(-0.572889\pi\) | ||||
−0.226990 | + | 0.973897i | \(0.572889\pi\) | |||||||
\(138\) | −8.48528 | −0.722315 | ||||||||
\(139\) | 17.6569 | 1.49763 | 0.748817 | − | 0.662776i | \(-0.230622\pi\) | ||||
0.748817 | + | 0.662776i | \(0.230622\pi\) | |||||||
\(140\) | 2.82843 | 0.239046 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 5.65685 | 0.474713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.17157 | 0.263385 | ||||||||
\(146\) | 2.48528 | 0.205683 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0.343146 | 0.0282064 | ||||||||
\(149\) | 7.65685 | 0.627274 | 0.313637 | − | 0.949543i | \(-0.398453\pi\) | ||||
0.313637 | + | 0.949543i | \(0.398453\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | −2.82843 | −0.229416 | ||||||||
\(153\) | −4.82843 | −0.390355 | ||||||||
\(154\) | 16.0000 | 1.28932 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3137 | −1.38178 | −0.690892 | − | 0.722958i | \(-0.742782\pi\) | ||||
−0.690892 | + | 0.722958i | \(0.742782\pi\) | |||||||
\(158\) | −13.6569 | −1.08648 | ||||||||
\(159\) | −9.31371 | −0.738625 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 11.3137 | 0.886158 | 0.443079 | − | 0.896483i | \(-0.353886\pi\) | ||||
0.443079 | + | 0.896483i | \(0.353886\pi\) | |||||||
\(164\) | −3.65685 | −0.285552 | ||||||||
\(165\) | −5.65685 | −0.440386 | ||||||||
\(166\) | 17.6569 | 1.37044 | ||||||||
\(167\) | 24.9706 | 1.93228 | 0.966140 | − | 0.258018i | \(-0.0830694\pi\) | ||||
0.966140 | + | 0.258018i | \(0.0830694\pi\) | |||||||
\(168\) | 2.82843 | 0.218218 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.82843 | −0.370323 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | −1.65685 | −0.126334 | ||||||||
\(173\) | 13.3137 | 1.01222 | 0.506111 | − | 0.862468i | \(-0.331083\pi\) | ||||
0.506111 | + | 0.862468i | \(0.331083\pi\) | |||||||
\(174\) | 3.17157 | 0.240436 | ||||||||
\(175\) | −2.82843 | −0.213809 | ||||||||
\(176\) | 5.65685 | 0.426401 | ||||||||
\(177\) | 13.6569 | 1.02651 | ||||||||
\(178\) | −4.34315 | −0.325533 | ||||||||
\(179\) | 24.4853 | 1.83012 | 0.915058 | − | 0.403322i | \(-0.132145\pi\) | ||||
0.915058 | + | 0.403322i | \(0.132145\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 3.65685 | 0.271812 | 0.135906 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135906 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | −8.48528 | −0.625543 | ||||||||
\(185\) | −0.343146 | −0.0252286 | ||||||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | −27.3137 | −1.99738 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | 2.82843 | 0.205196 | ||||||||
\(191\) | −11.3137 | −0.818631 | −0.409316 | − | 0.912393i | \(-0.634232\pi\) | ||||
−0.409316 | + | 0.912393i | \(0.634232\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 14.4853 | 1.04267 | 0.521337 | − | 0.853351i | \(-0.325434\pi\) | ||||
0.521337 | + | 0.853351i | \(0.325434\pi\) | |||||||
\(194\) | −8.82843 | −0.633844 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −9.31371 | −0.663574 | −0.331787 | − | 0.943354i | \(-0.607652\pi\) | ||||
−0.331787 | + | 0.943354i | \(0.607652\pi\) | |||||||
\(198\) | −5.65685 | −0.402015 | ||||||||
\(199\) | 21.6569 | 1.53521 | 0.767607 | − | 0.640921i | \(-0.221447\pi\) | ||||
0.767607 | + | 0.640921i | \(0.221447\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 5.65685 | 0.399004 | ||||||||
\(202\) | 12.1421 | 0.854318 | ||||||||
\(203\) | 8.97056 | 0.629610 | ||||||||
\(204\) | −4.82843 | −0.338058 | ||||||||
\(205\) | 3.65685 | 0.255406 | ||||||||
\(206\) | −9.65685 | −0.672825 | ||||||||
\(207\) | 8.48528 | 0.589768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | −2.82843 | −0.195180 | ||||||||
\(211\) | 23.3137 | 1.60498 | 0.802491 | − | 0.596664i | \(-0.203508\pi\) | ||||
0.802491 | + | 0.596664i | \(0.203508\pi\) | |||||||
\(212\) | −9.31371 | −0.639668 | ||||||||
\(213\) | −5.65685 | −0.387601 | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | 1.65685 | 0.112997 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 11.3137 | 0.768025 | ||||||||
\(218\) | 3.17157 | 0.214806 | ||||||||
\(219\) | −2.48528 | −0.167940 | ||||||||
\(220\) | −5.65685 | −0.381385 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.343146 | −0.0230304 | ||||||||
\(223\) | −5.17157 | −0.346314 | −0.173157 | − | 0.984894i | \(-0.555397\pi\) | ||||
−0.173157 | + | 0.984894i | \(0.555397\pi\) | |||||||
\(224\) | 2.82843 | 0.188982 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 10.4853 | 0.697471 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 2.82843 | 0.187317 | ||||||||
\(229\) | 24.1421 | 1.59536 | 0.797679 | − | 0.603083i | \(-0.206061\pi\) | ||||
0.797679 | + | 0.603083i | \(0.206061\pi\) | |||||||
\(230\) | 8.48528 | 0.559503 | ||||||||
\(231\) | −16.0000 | −1.05272 | ||||||||
\(232\) | 3.17157 | 0.208224 | ||||||||
\(233\) | 22.4853 | 1.47306 | 0.736530 | − | 0.676405i | \(-0.236463\pi\) | ||||
0.736530 | + | 0.676405i | \(0.236463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 13.6569 | 0.888985 | ||||||||
\(237\) | 13.6569 | 0.887108 | ||||||||
\(238\) | −13.6569 | −0.885242 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 17.3137 | 1.11527 | 0.557637 | − | 0.830085i | \(-0.311708\pi\) | ||||
0.557637 | + | 0.830085i | \(0.311708\pi\) | |||||||
\(242\) | −21.0000 | −1.34993 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 3.65685 | 0.233153 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −17.6569 | −1.11896 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 5.17157 | 0.326427 | 0.163213 | − | 0.986591i | \(-0.447814\pi\) | ||||
0.163213 | + | 0.986591i | \(0.447814\pi\) | |||||||
\(252\) | −2.82843 | −0.178174 | ||||||||
\(253\) | 48.0000 | 3.01773 | ||||||||
\(254\) | 1.65685 | 0.103960 | ||||||||
\(255\) | 4.82843 | 0.302368 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.828427 | 0.0516759 | 0.0258379 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258379 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(258\) | 1.65685 | 0.103151 | ||||||||
\(259\) | −0.970563 | −0.0603078 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.17157 | −0.196315 | ||||||||
\(262\) | −22.1421 | −1.36795 | ||||||||
\(263\) | −0.485281 | −0.0299237 | −0.0149619 | − | 0.999888i | \(-0.504763\pi\) | ||||
−0.0149619 | + | 0.999888i | \(0.504763\pi\) | |||||||
\(264\) | −5.65685 | −0.348155 | ||||||||
\(265\) | 9.31371 | 0.572137 | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 4.34315 | 0.265796 | ||||||||
\(268\) | 5.65685 | 0.345547 | ||||||||
\(269\) | 2.48528 | 0.151530 | 0.0757651 | − | 0.997126i | \(-0.475860\pi\) | ||||
0.0757651 | + | 0.997126i | \(0.475860\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 15.3137 | 0.930242 | 0.465121 | − | 0.885247i | \(-0.346011\pi\) | ||||
0.465121 | + | 0.885247i | \(0.346011\pi\) | |||||||
\(272\) | −4.82843 | −0.292766 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.31371 | 0.321013 | ||||||||
\(275\) | 5.65685 | 0.341121 | ||||||||
\(276\) | 8.48528 | 0.510754 | ||||||||
\(277\) | 26.0000 | 1.56219 | 0.781094 | − | 0.624413i | \(-0.214662\pi\) | ||||
0.781094 | + | 0.624413i | \(0.214662\pi\) | |||||||
\(278\) | −17.6569 | −1.05899 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | −2.82843 | −0.169031 | ||||||||
\(281\) | −19.6569 | −1.17263 | −0.586315 | − | 0.810083i | \(-0.699422\pi\) | ||||
−0.586315 | + | 0.810083i | \(0.699422\pi\) | |||||||
\(282\) | −8.00000 | −0.476393 | ||||||||
\(283\) | −6.34315 | −0.377061 | −0.188530 | − | 0.982067i | \(-0.560372\pi\) | ||||
−0.188530 | + | 0.982067i | \(0.560372\pi\) | |||||||
\(284\) | −5.65685 | −0.335673 | ||||||||
\(285\) | −2.82843 | −0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3431 | 0.610537 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 6.31371 | 0.371395 | ||||||||
\(290\) | −3.17157 | −0.186241 | ||||||||
\(291\) | 8.82843 | 0.517532 | ||||||||
\(292\) | −2.48528 | −0.145440 | ||||||||
\(293\) | −28.6274 | −1.67243 | −0.836216 | − | 0.548401i | \(-0.815237\pi\) | ||||
−0.836216 | + | 0.548401i | \(0.815237\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −13.6569 | −0.795133 | ||||||||
\(296\) | −0.343146 | −0.0199449 | ||||||||
\(297\) | 5.65685 | 0.328244 | ||||||||
\(298\) | −7.65685 | −0.443550 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 4.68629 | 0.270113 | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | −12.1421 | −0.697547 | ||||||||
\(304\) | 2.82843 | 0.162221 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 4.82843 | 0.276023 | ||||||||
\(307\) | 10.3431 | 0.590315 | 0.295157 | − | 0.955449i | \(-0.404628\pi\) | ||||
0.295157 | + | 0.955449i | \(0.404628\pi\) | |||||||
\(308\) | −16.0000 | −0.911685 | ||||||||
\(309\) | 9.65685 | 0.549359 | ||||||||
\(310\) | −4.00000 | −0.227185 | ||||||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.97056 | 0.167906 | 0.0839531 | − | 0.996470i | \(-0.473245\pi\) | ||||
0.0839531 | + | 0.996470i | \(0.473245\pi\) | |||||||
\(314\) | 17.3137 | 0.977069 | ||||||||
\(315\) | 2.82843 | 0.159364 | ||||||||
\(316\) | 13.6569 | 0.768258 | ||||||||
\(317\) | −2.68629 | −0.150877 | −0.0754386 | − | 0.997150i | \(-0.524036\pi\) | ||||
−0.0754386 | + | 0.997150i | \(0.524036\pi\) | |||||||
\(318\) | 9.31371 | 0.522287 | ||||||||
\(319\) | −17.9411 | −1.00451 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 24.0000 | 1.33747 | ||||||||
\(323\) | −13.6569 | −0.759888 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.3137 | −0.626608 | ||||||||
\(327\) | −3.17157 | −0.175388 | ||||||||
\(328\) | 3.65685 | 0.201916 | ||||||||
\(329\) | −22.6274 | −1.24749 | ||||||||
\(330\) | 5.65685 | 0.311400 | ||||||||
\(331\) | −8.48528 | −0.466393 | −0.233197 | − | 0.972430i | \(-0.574919\pi\) | ||||
−0.233197 | + | 0.972430i | \(0.574919\pi\) | |||||||
\(332\) | −17.6569 | −0.969046 | ||||||||
\(333\) | 0.343146 | 0.0188043 | ||||||||
\(334\) | −24.9706 | −1.36633 | ||||||||
\(335\) | −5.65685 | −0.309067 | ||||||||
\(336\) | −2.82843 | −0.154303 | ||||||||
\(337\) | −22.9706 | −1.25129 | −0.625643 | − | 0.780109i | \(-0.715163\pi\) | ||||
−0.625643 | + | 0.780109i | \(0.715163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.4853 | −0.569482 | ||||||||
\(340\) | 4.82843 | 0.261858 | ||||||||
\(341\) | −22.6274 | −1.22534 | ||||||||
\(342\) | −2.82843 | −0.152944 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 1.65685 | 0.0893316 | ||||||||
\(345\) | −8.48528 | −0.456832 | ||||||||
\(346\) | −13.3137 | −0.715749 | ||||||||
\(347\) | 1.65685 | 0.0889446 | 0.0444723 | − | 0.999011i | \(-0.485839\pi\) | ||||
0.0444723 | + | 0.999011i | \(0.485839\pi\) | |||||||
\(348\) | −3.17157 | −0.170014 | ||||||||
\(349\) | 16.1421 | 0.864069 | 0.432034 | − | 0.901857i | \(-0.357796\pi\) | ||||
0.432034 | + | 0.901857i | \(0.357796\pi\) | |||||||
\(350\) | 2.82843 | 0.151186 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.65685 | −0.301511 | ||||||||
\(353\) | 17.3137 | 0.921516 | 0.460758 | − | 0.887526i | \(-0.347578\pi\) | ||||
0.460758 | + | 0.887526i | \(0.347578\pi\) | |||||||
\(354\) | −13.6569 | −0.725854 | ||||||||
\(355\) | 5.65685 | 0.300235 | ||||||||
\(356\) | 4.34315 | 0.230186 | ||||||||
\(357\) | 13.6569 | 0.722797 | ||||||||
\(358\) | −24.4853 | −1.29409 | ||||||||
\(359\) | −28.2843 | −1.49279 | −0.746393 | − | 0.665505i | \(-0.768216\pi\) | ||||
−0.746393 | + | 0.665505i | \(0.768216\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | −3.65685 | −0.192200 | ||||||||
\(363\) | 21.0000 | 1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.48528 | 0.130086 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | 14.3431 | 0.748706 | 0.374353 | − | 0.927286i | \(-0.377865\pi\) | ||||
0.374353 | + | 0.927286i | \(0.377865\pi\) | |||||||
\(368\) | 8.48528 | 0.442326 | ||||||||
\(369\) | −3.65685 | −0.190368 | ||||||||
\(370\) | 0.343146 | 0.0178393 | ||||||||
\(371\) | 26.3431 | 1.36767 | ||||||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | −25.3137 | −1.31069 | −0.655347 | − | 0.755328i | \(-0.727478\pi\) | ||||
−0.655347 | + | 0.755328i | \(0.727478\pi\) | |||||||
\(374\) | 27.3137 | 1.41236 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.82843 | 0.145479 | ||||||||
\(379\) | 24.4853 | 1.25772 | 0.628862 | − | 0.777517i | \(-0.283521\pi\) | ||||
0.628862 | + | 0.777517i | \(0.283521\pi\) | |||||||
\(380\) | −2.82843 | −0.145095 | ||||||||
\(381\) | −1.65685 | −0.0848832 | ||||||||
\(382\) | 11.3137 | 0.578860 | ||||||||
\(383\) | 18.3431 | 0.937291 | 0.468645 | − | 0.883386i | \(-0.344742\pi\) | ||||
0.468645 | + | 0.883386i | \(0.344742\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | −14.4853 | −0.737281 | ||||||||
\(387\) | −1.65685 | −0.0842226 | ||||||||
\(388\) | 8.82843 | 0.448195 | ||||||||
\(389\) | 10.4853 | 0.531625 | 0.265812 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265812 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40.9706 | −2.07197 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 22.1421 | 1.11692 | ||||||||
\(394\) | 9.31371 | 0.469218 | ||||||||
\(395\) | −13.6569 | −0.687151 | ||||||||
\(396\) | 5.65685 | 0.284268 | ||||||||
\(397\) | 26.2843 | 1.31917 | 0.659585 | − | 0.751630i | \(-0.270732\pi\) | ||||
0.659585 | + | 0.751630i | \(0.270732\pi\) | |||||||
\(398\) | −21.6569 | −1.08556 | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −6.97056 | −0.348093 | −0.174047 | − | 0.984737i | \(-0.555684\pi\) | ||||
−0.174047 | + | 0.984737i | \(0.555684\pi\) | |||||||
\(402\) | −5.65685 | −0.282138 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.1421 | −0.604094 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −8.97056 | −0.445202 | ||||||||
\(407\) | 1.94113 | 0.0962180 | ||||||||
\(408\) | 4.82843 | 0.239043 | ||||||||
\(409\) | −7.65685 | −0.378607 | −0.189304 | − | 0.981919i | \(-0.560623\pi\) | ||||
−0.189304 | + | 0.981919i | \(0.560623\pi\) | |||||||
\(410\) | −3.65685 | −0.180599 | ||||||||
\(411\) | −5.31371 | −0.262106 | ||||||||
\(412\) | 9.65685 | 0.475759 | ||||||||
\(413\) | −38.6274 | −1.90073 | ||||||||
\(414\) | −8.48528 | −0.417029 | ||||||||
\(415\) | 17.6569 | 0.866741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.6569 | 0.864660 | ||||||||
\(418\) | −16.0000 | −0.782586 | ||||||||
\(419\) | −5.17157 | −0.252648 | −0.126324 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126324 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(420\) | 2.82843 | 0.138013 | ||||||||
\(421\) | −4.14214 | −0.201875 | −0.100938 | − | 0.994893i | \(-0.532184\pi\) | ||||
−0.100938 | + | 0.994893i | \(0.532184\pi\) | |||||||
\(422\) | −23.3137 | −1.13489 | ||||||||
\(423\) | 8.00000 | 0.388973 | ||||||||
\(424\) | 9.31371 | 0.452314 | ||||||||
\(425\) | −4.82843 | −0.234213 | ||||||||
\(426\) | 5.65685 | 0.274075 | ||||||||
\(427\) | −16.9706 | −0.821263 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.65685 | −0.0799006 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 10.9706 | 0.527212 | 0.263606 | − | 0.964630i | \(-0.415088\pi\) | ||||
0.263606 | + | 0.964630i | \(0.415088\pi\) | |||||||
\(434\) | −11.3137 | −0.543075 | ||||||||
\(435\) | 3.17157 | 0.152065 | ||||||||
\(436\) | −3.17157 | −0.151891 | ||||||||
\(437\) | 24.0000 | 1.14808 | ||||||||
\(438\) | 2.48528 | 0.118751 | ||||||||
\(439\) | −22.6274 | −1.07995 | −0.539974 | − | 0.841682i | \(-0.681566\pi\) | ||||
−0.539974 | + | 0.841682i | \(0.681566\pi\) | |||||||
\(440\) | 5.65685 | 0.269680 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 41.6569 | 1.97918 | 0.989588 | − | 0.143926i | \(-0.0459728\pi\) | ||||
0.989588 | + | 0.143926i | \(0.0459728\pi\) | |||||||
\(444\) | 0.343146 | 0.0162850 | ||||||||
\(445\) | −4.34315 | −0.205885 | ||||||||
\(446\) | 5.17157 | 0.244881 | ||||||||
\(447\) | 7.65685 | 0.362157 | ||||||||
\(448\) | −2.82843 | −0.133631 | ||||||||
\(449\) | 30.2843 | 1.42920 | 0.714602 | − | 0.699532i | \(-0.246608\pi\) | ||||
0.714602 | + | 0.699532i | \(0.246608\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −20.6863 | −0.974079 | ||||||||
\(452\) | −10.4853 | −0.493186 | ||||||||
\(453\) | −12.0000 | −0.563809 | ||||||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.82843 | −0.132453 | ||||||||
\(457\) | −15.1716 | −0.709696 | −0.354848 | − | 0.934924i | \(-0.615467\pi\) | ||||
−0.354848 | + | 0.934924i | \(0.615467\pi\) | |||||||
\(458\) | −24.1421 | −1.12809 | ||||||||
\(459\) | −4.82843 | −0.225372 | ||||||||
\(460\) | −8.48528 | −0.395628 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 16.0000 | 0.744387 | ||||||||
\(463\) | −35.7990 | −1.66372 | −0.831860 | − | 0.554985i | \(-0.812724\pi\) | ||||
−0.831860 | + | 0.554985i | \(0.812724\pi\) | |||||||
\(464\) | −3.17157 | −0.147237 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | −22.4853 | −1.04161 | ||||||||
\(467\) | −15.3137 | −0.708634 | −0.354317 | − | 0.935125i | \(-0.615287\pi\) | ||||
−0.354317 | + | 0.935125i | \(0.615287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 8.00000 | 0.369012 | ||||||||
\(471\) | −17.3137 | −0.797774 | ||||||||
\(472\) | −13.6569 | −0.628608 | ||||||||
\(473\) | −9.37258 | −0.430952 | ||||||||
\(474\) | −13.6569 | −0.627280 | ||||||||
\(475\) | 2.82843 | 0.129777 | ||||||||
\(476\) | 13.6569 | 0.625961 | ||||||||
\(477\) | −9.31371 | −0.426445 | ||||||||
\(478\) | 16.0000 | 0.731823 | ||||||||
\(479\) | −11.3137 | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.3137 | −0.788618 | ||||||||
\(483\) | −24.0000 | −1.09204 | ||||||||
\(484\) | 21.0000 | 0.954545 | ||||||||
\(485\) | −8.82843 | −0.400878 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 0.485281 | 0.0219902 | 0.0109951 | − | 0.999940i | \(-0.496500\pi\) | ||||
0.0109951 | + | 0.999940i | \(0.496500\pi\) | |||||||
\(488\) | −6.00000 | −0.271607 | ||||||||
\(489\) | 11.3137 | 0.511624 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −9.85786 | −0.444879 | −0.222440 | − | 0.974946i | \(-0.571402\pi\) | ||||
−0.222440 | + | 0.974946i | \(0.571402\pi\) | |||||||
\(492\) | −3.65685 | −0.164864 | ||||||||
\(493\) | 15.3137 | 0.689695 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65685 | −0.254257 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | 17.6569 | 0.791223 | ||||||||
\(499\) | 16.4853 | 0.737983 | 0.368991 | − | 0.929433i | \(-0.379703\pi\) | ||||
0.368991 | + | 0.929433i | \(0.379703\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 24.9706 | 1.11560 | ||||||||
\(502\) | −5.17157 | −0.230819 | ||||||||
\(503\) | −40.4853 | −1.80515 | −0.902575 | − | 0.430533i | \(-0.858326\pi\) | ||||
−0.902575 | + | 0.430533i | \(0.858326\pi\) | |||||||
\(504\) | 2.82843 | 0.125988 | ||||||||
\(505\) | 12.1421 | 0.540318 | ||||||||
\(506\) | −48.0000 | −2.13386 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.65685 | −0.0735110 | ||||||||
\(509\) | 14.6863 | 0.650958 | 0.325479 | − | 0.945549i | \(-0.394474\pi\) | ||||
0.325479 | + | 0.945549i | \(0.394474\pi\) | |||||||
\(510\) | −4.82843 | −0.213806 | ||||||||
\(511\) | 7.02944 | 0.310964 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.82843 | 0.124878 | ||||||||
\(514\) | −0.828427 | −0.0365404 | ||||||||
\(515\) | −9.65685 | −0.425532 | ||||||||
\(516\) | −1.65685 | −0.0729389 | ||||||||
\(517\) | 45.2548 | 1.99031 | ||||||||
\(518\) | 0.970563 | 0.0426441 | ||||||||
\(519\) | 13.3137 | 0.584407 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.97056 | −0.305386 | −0.152693 | − | 0.988274i | \(-0.548795\pi\) | ||||
−0.152693 | + | 0.988274i | \(0.548795\pi\) | |||||||
\(522\) | 3.17157 | 0.138816 | ||||||||
\(523\) | 34.6274 | 1.51415 | 0.757076 | − | 0.653327i | \(-0.226627\pi\) | ||||
0.757076 | + | 0.653327i | \(0.226627\pi\) | |||||||
\(524\) | 22.1421 | 0.967284 | ||||||||
\(525\) | −2.82843 | −0.123443 | ||||||||
\(526\) | 0.485281 | 0.0211593 | ||||||||
\(527\) | 19.3137 | 0.841318 | ||||||||
\(528\) | 5.65685 | 0.246183 | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | −9.31371 | −0.404562 | ||||||||
\(531\) | 13.6569 | 0.592657 | ||||||||
\(532\) | −8.00000 | −0.346844 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −4.34315 | −0.187946 | ||||||||
\(535\) | 4.00000 | 0.172935 | ||||||||
\(536\) | −5.65685 | −0.244339 | ||||||||
\(537\) | 24.4853 | 1.05662 | ||||||||
\(538\) | −2.48528 | −0.107148 | ||||||||
\(539\) | 5.65685 | 0.243658 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 2.48528 | 0.106851 | 0.0534253 | − | 0.998572i | \(-0.482986\pi\) | ||||
0.0534253 | + | 0.998572i | \(0.482986\pi\) | |||||||
\(542\) | −15.3137 | −0.657780 | ||||||||
\(543\) | 3.65685 | 0.156931 | ||||||||
\(544\) | 4.82843 | 0.207017 | ||||||||
\(545\) | 3.17157 | 0.135855 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3137 | 0.996822 | 0.498411 | − | 0.866941i | \(-0.333917\pi\) | ||||
0.498411 | + | 0.866941i | \(0.333917\pi\) | |||||||
\(548\) | −5.31371 | −0.226990 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | −5.65685 | −0.241209 | ||||||||
\(551\) | −8.97056 | −0.382159 | ||||||||
\(552\) | −8.48528 | −0.361158 | ||||||||
\(553\) | −38.6274 | −1.64260 | ||||||||
\(554\) | −26.0000 | −1.10463 | ||||||||
\(555\) | −0.343146 | −0.0145657 | ||||||||
\(556\) | 17.6569 | 0.748817 | ||||||||
\(557\) | −33.3137 | −1.41155 | −0.705774 | − | 0.708437i | \(-0.749400\pi\) | ||||
−0.705774 | + | 0.708437i | \(0.749400\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.82843 | 0.119523 | ||||||||
\(561\) | −27.3137 | −1.15319 | ||||||||
\(562\) | 19.6569 | 0.829174 | ||||||||
\(563\) | −41.6569 | −1.75563 | −0.877814 | − | 0.479002i | \(-0.840998\pi\) | ||||
−0.877814 | + | 0.479002i | \(0.840998\pi\) | |||||||
\(564\) | 8.00000 | 0.336861 | ||||||||
\(565\) | 10.4853 | 0.441119 | ||||||||
\(566\) | 6.34315 | 0.266622 | ||||||||
\(567\) | −2.82843 | −0.118783 | ||||||||
\(568\) | 5.65685 | 0.237356 | ||||||||
\(569\) | 20.3431 | 0.852829 | 0.426415 | − | 0.904528i | \(-0.359776\pi\) | ||||
0.426415 | + | 0.904528i | \(0.359776\pi\) | |||||||
\(570\) | 2.82843 | 0.118470 | ||||||||
\(571\) | −12.9706 | −0.542801 | −0.271401 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271401 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.3137 | −0.472637 | ||||||||
\(574\) | −10.3431 | −0.431715 | ||||||||
\(575\) | 8.48528 | 0.353861 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −27.4558 | −1.14300 | −0.571501 | − | 0.820601i | \(-0.693639\pi\) | ||||
−0.571501 | + | 0.820601i | \(0.693639\pi\) | |||||||
\(578\) | −6.31371 | −0.262616 | ||||||||
\(579\) | 14.4853 | 0.601988 | ||||||||
\(580\) | 3.17157 | 0.131692 | ||||||||
\(581\) | 49.9411 | 2.07191 | ||||||||
\(582\) | −8.82843 | −0.365950 | ||||||||
\(583\) | −52.6863 | −2.18204 | ||||||||
\(584\) | 2.48528 | 0.102842 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.6274 | 1.18259 | ||||||||
\(587\) | 42.6274 | 1.75942 | 0.879711 | − | 0.475509i | \(-0.157736\pi\) | ||||
0.879711 | + | 0.475509i | \(0.157736\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −11.3137 | −0.466173 | ||||||||
\(590\) | 13.6569 | 0.562244 | ||||||||
\(591\) | −9.31371 | −0.383115 | ||||||||
\(592\) | 0.343146 | 0.0141032 | ||||||||
\(593\) | 11.6569 | 0.478690 | 0.239345 | − | 0.970935i | \(-0.423067\pi\) | ||||
0.239345 | + | 0.970935i | \(0.423067\pi\) | |||||||
\(594\) | −5.65685 | −0.232104 | ||||||||
\(595\) | −13.6569 | −0.559876 | ||||||||
\(596\) | 7.65685 | 0.313637 | ||||||||
\(597\) | 21.6569 | 0.886356 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0000 | 1.63436 | 0.817178 | − | 0.576386i | \(-0.195537\pi\) | ||||
0.817178 | + | 0.576386i | \(0.195537\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 6.68629 | 0.272740 | 0.136370 | − | 0.990658i | \(-0.456456\pi\) | ||||
0.136370 | + | 0.990658i | \(0.456456\pi\) | |||||||
\(602\) | −4.68629 | −0.190999 | ||||||||
\(603\) | 5.65685 | 0.230365 | ||||||||
\(604\) | −12.0000 | −0.488273 | ||||||||
\(605\) | −21.0000 | −0.853771 | ||||||||
\(606\) | 12.1421 | 0.493241 | ||||||||
\(607\) | −4.97056 | −0.201749 | −0.100874 | − | 0.994899i | \(-0.532164\pi\) | ||||
−0.100874 | + | 0.994899i | \(0.532164\pi\) | |||||||
\(608\) | −2.82843 | −0.114708 | ||||||||
\(609\) | 8.97056 | 0.363506 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.82843 | −0.195178 | ||||||||
\(613\) | 34.2843 | 1.38473 | 0.692364 | − | 0.721548i | \(-0.256569\pi\) | ||||
0.692364 | + | 0.721548i | \(0.256569\pi\) | |||||||
\(614\) | −10.3431 | −0.417415 | ||||||||
\(615\) | 3.65685 | 0.147459 | ||||||||
\(616\) | 16.0000 | 0.644658 | ||||||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | −9.65685 | −0.388456 | ||||||||
\(619\) | 29.1716 | 1.17250 | 0.586252 | − | 0.810129i | \(-0.300603\pi\) | ||||
0.586252 | + | 0.810129i | \(0.300603\pi\) | |||||||
\(620\) | 4.00000 | 0.160644 | ||||||||
\(621\) | 8.48528 | 0.340503 | ||||||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | −12.2843 | −0.492159 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.97056 | −0.118728 | ||||||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | −17.3137 | −0.690892 | ||||||||
\(629\) | −1.65685 | −0.0660631 | ||||||||
\(630\) | −2.82843 | −0.112687 | ||||||||
\(631\) | 22.3431 | 0.889467 | 0.444733 | − | 0.895663i | \(-0.353298\pi\) | ||||
0.444733 | + | 0.895663i | \(0.353298\pi\) | |||||||
\(632\) | −13.6569 | −0.543240 | ||||||||
\(633\) | 23.3137 | 0.926637 | ||||||||
\(634\) | 2.68629 | 0.106686 | ||||||||
\(635\) | 1.65685 | 0.0657503 | ||||||||
\(636\) | −9.31371 | −0.369313 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 17.9411 | 0.710296 | ||||||||
\(639\) | −5.65685 | −0.223782 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 40.6274 | 1.60469 | 0.802343 | − | 0.596863i | \(-0.203586\pi\) | ||||
0.802343 | + | 0.596863i | \(0.203586\pi\) | |||||||
\(642\) | 4.00000 | 0.157867 | ||||||||
\(643\) | 39.5980 | 1.56159 | 0.780796 | − | 0.624786i | \(-0.214814\pi\) | ||||
0.780796 | + | 0.624786i | \(0.214814\pi\) | |||||||
\(644\) | −24.0000 | −0.945732 | ||||||||
\(645\) | 1.65685 | 0.0652386 | ||||||||
\(646\) | 13.6569 | 0.537322 | ||||||||
\(647\) | −8.48528 | −0.333591 | −0.166795 | − | 0.985992i | \(-0.553342\pi\) | ||||
−0.166795 | + | 0.985992i | \(0.553342\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 77.2548 | 3.03252 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3137 | 0.443419 | ||||||||
\(652\) | 11.3137 | 0.443079 | ||||||||
\(653\) | 14.2843 | 0.558987 | 0.279493 | − | 0.960148i | \(-0.409834\pi\) | ||||
0.279493 | + | 0.960148i | \(0.409834\pi\) | |||||||
\(654\) | 3.17157 | 0.124018 | ||||||||
\(655\) | −22.1421 | −0.865165 | ||||||||
\(656\) | −3.65685 | −0.142776 | ||||||||
\(657\) | −2.48528 | −0.0969601 | ||||||||
\(658\) | 22.6274 | 0.882109 | ||||||||
\(659\) | −24.4853 | −0.953811 | −0.476906 | − | 0.878955i | \(-0.658242\pi\) | ||||
−0.476906 | + | 0.878955i | \(0.658242\pi\) | |||||||
\(660\) | −5.65685 | −0.220193 | ||||||||
\(661\) | −20.1421 | −0.783438 | −0.391719 | − | 0.920085i | \(-0.628120\pi\) | ||||
−0.391719 | + | 0.920085i | \(0.628120\pi\) | |||||||
\(662\) | 8.48528 | 0.329790 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.6569 | 0.685219 | ||||||||
\(665\) | 8.00000 | 0.310227 | ||||||||
\(666\) | −0.343146 | −0.0132966 | ||||||||
\(667\) | −26.9117 | −1.04202 | ||||||||
\(668\) | 24.9706 | 0.966140 | ||||||||
\(669\) | −5.17157 | −0.199945 | ||||||||
\(670\) | 5.65685 | 0.218543 | ||||||||
\(671\) | 33.9411 | 1.31028 | ||||||||
\(672\) | 2.82843 | 0.109109 | ||||||||
\(673\) | −12.6274 | −0.486751 | −0.243376 | − | 0.969932i | \(-0.578255\pi\) | ||||
−0.243376 | + | 0.969932i | \(0.578255\pi\) | |||||||
\(674\) | 22.9706 | 0.884793 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.6569 | 0.909207 | 0.454603 | − | 0.890694i | \(-0.349781\pi\) | ||||
0.454603 | + | 0.890694i | \(0.349781\pi\) | |||||||
\(678\) | 10.4853 | 0.402685 | ||||||||
\(679\) | −24.9706 | −0.958282 | ||||||||
\(680\) | −4.82843 | −0.185162 | ||||||||
\(681\) | −4.00000 | −0.153280 | ||||||||
\(682\) | 22.6274 | 0.866449 | ||||||||
\(683\) | −22.3431 | −0.854937 | −0.427468 | − | 0.904030i | \(-0.640594\pi\) | ||||
−0.427468 | + | 0.904030i | \(0.640594\pi\) | |||||||
\(684\) | 2.82843 | 0.108148 | ||||||||
\(685\) | 5.31371 | 0.203026 | ||||||||
\(686\) | −16.9706 | −0.647939 | ||||||||
\(687\) | 24.1421 | 0.921080 | ||||||||
\(688\) | −1.65685 | −0.0631670 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 8.48528 | 0.323029 | ||||||||
\(691\) | −11.7990 | −0.448855 | −0.224427 | − | 0.974491i | \(-0.572051\pi\) | ||||
−0.224427 | + | 0.974491i | \(0.572051\pi\) | |||||||
\(692\) | 13.3137 | 0.506111 | ||||||||
\(693\) | −16.0000 | −0.607790 | ||||||||
\(694\) | −1.65685 | −0.0628933 | ||||||||
\(695\) | −17.6569 | −0.669763 | ||||||||
\(696\) | 3.17157 | 0.120218 | ||||||||
\(697\) | 17.6569 | 0.668801 | ||||||||
\(698\) | −16.1421 | −0.610989 | ||||||||
\(699\) | 22.4853 | 0.850471 | ||||||||
\(700\) | −2.82843 | −0.106904 | ||||||||
\(701\) | −28.1421 | −1.06291 | −0.531457 | − | 0.847085i | \(-0.678355\pi\) | ||||
−0.531457 | + | 0.847085i | \(0.678355\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.970563 | 0.0366055 | ||||||||
\(704\) | 5.65685 | 0.213201 | ||||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | −17.3137 | −0.651610 | ||||||||
\(707\) | 34.3431 | 1.29161 | ||||||||
\(708\) | 13.6569 | 0.513256 | ||||||||
\(709\) | 12.8284 | 0.481782 | 0.240891 | − | 0.970552i | \(-0.422560\pi\) | ||||
0.240891 | + | 0.970552i | \(0.422560\pi\) | |||||||
\(710\) | −5.65685 | −0.212298 | ||||||||
\(711\) | 13.6569 | 0.512172 | ||||||||
\(712\) | −4.34315 | −0.162766 | ||||||||
\(713\) | −33.9411 | −1.27111 | ||||||||
\(714\) | −13.6569 | −0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.4853 | 0.915058 | ||||||||
\(717\) | −16.0000 | −0.597531 | ||||||||
\(718\) | 28.2843 | 1.05556 | ||||||||
\(719\) | −18.3431 | −0.684084 | −0.342042 | − | 0.939685i | \(-0.611118\pi\) | ||||
−0.342042 | + | 0.939685i | \(0.611118\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −27.3137 | −1.01722 | ||||||||
\(722\) | 11.0000 | 0.409378 | ||||||||
\(723\) | 17.3137 | 0.643904 | ||||||||
\(724\) | 3.65685 | 0.135906 | ||||||||
\(725\) | −3.17157 | −0.117789 | ||||||||
\(726\) | −21.0000 | −0.779383 | ||||||||
\(727\) | 21.9411 | 0.813751 | 0.406876 | − | 0.913484i | \(-0.366618\pi\) | ||||
0.406876 | + | 0.913484i | \(0.366618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.48528 | −0.0919844 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 6.00000 | 0.221766 | ||||||||
\(733\) | 11.6569 | 0.430556 | 0.215278 | − | 0.976553i | \(-0.430934\pi\) | ||||
0.215278 | + | 0.976553i | \(0.430934\pi\) | |||||||
\(734\) | −14.3431 | −0.529415 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | −8.48528 | −0.312772 | ||||||||
\(737\) | 32.0000 | 1.17874 | ||||||||
\(738\) | 3.65685 | 0.134611 | ||||||||
\(739\) | −14.1421 | −0.520227 | −0.260113 | − | 0.965578i | \(-0.583760\pi\) | ||||
−0.260113 | + | 0.965578i | \(0.583760\pi\) | |||||||
\(740\) | −0.343146 | −0.0126143 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.3431 | −0.967087 | ||||||||
\(743\) | −20.2843 | −0.744158 | −0.372079 | − | 0.928201i | \(-0.621355\pi\) | ||||
−0.372079 | + | 0.928201i | \(0.621355\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | −7.65685 | −0.280525 | ||||||||
\(746\) | 25.3137 | 0.926801 | ||||||||
\(747\) | −17.6569 | −0.646031 | ||||||||
\(748\) | −27.3137 | −0.998688 | ||||||||
\(749\) | 11.3137 | 0.413394 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −11.3137 | −0.412843 | −0.206422 | − | 0.978463i | \(-0.566182\pi\) | ||||
−0.206422 | + | 0.978463i | \(0.566182\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 5.17157 | 0.188463 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | −2.82843 | −0.102869 | ||||||||
\(757\) | −47.9411 | −1.74245 | −0.871225 | − | 0.490884i | \(-0.836674\pi\) | ||||
−0.871225 | + | 0.490884i | \(0.836674\pi\) | |||||||
\(758\) | −24.4853 | −0.889345 | ||||||||
\(759\) | 48.0000 | 1.74229 | ||||||||
\(760\) | 2.82843 | 0.102598 | ||||||||
\(761\) | −16.3431 | −0.592439 | −0.296219 | − | 0.955120i | \(-0.595726\pi\) | ||||
−0.296219 | + | 0.955120i | \(0.595726\pi\) | |||||||
\(762\) | 1.65685 | 0.0600215 | ||||||||
\(763\) | 8.97056 | 0.324756 | ||||||||
\(764\) | −11.3137 | −0.409316 | ||||||||
\(765\) | 4.82843 | 0.174572 | ||||||||
\(766\) | −18.3431 | −0.662765 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | −16.0000 | −0.576600 | ||||||||
\(771\) | 0.828427 | 0.0298351 | ||||||||
\(772\) | 14.4853 | 0.521337 | ||||||||
\(773\) | 30.6863 | 1.10371 | 0.551855 | − | 0.833940i | \(-0.313920\pi\) | ||||
0.551855 | + | 0.833940i | \(0.313920\pi\) | |||||||
\(774\) | 1.65685 | 0.0595544 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | −8.82843 | −0.316922 | ||||||||
\(777\) | −0.970563 | −0.0348187 | ||||||||
\(778\) | −10.4853 | −0.375916 | ||||||||
\(779\) | −10.3431 | −0.370582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 40.9706 | 1.46510 | ||||||||
\(783\) | −3.17157 | −0.113343 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 17.3137 | 0.617953 | ||||||||
\(786\) | −22.1421 | −0.789784 | ||||||||
\(787\) | 24.0000 | 0.855508 | 0.427754 | − | 0.903895i | \(-0.359305\pi\) | ||||
0.427754 | + | 0.903895i | \(0.359305\pi\) | |||||||
\(788\) | −9.31371 | −0.331787 | ||||||||
\(789\) | −0.485281 | −0.0172765 | ||||||||
\(790\) | 13.6569 | 0.485889 | ||||||||
\(791\) | 29.6569 | 1.05448 | ||||||||
\(792\) | −5.65685 | −0.201008 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −26.2843 | −0.932794 | ||||||||
\(795\) | 9.31371 | 0.330323 | ||||||||
\(796\) | 21.6569 | 0.767607 | ||||||||
\(797\) | −28.6274 | −1.01404 | −0.507018 | − | 0.861936i | \(-0.669252\pi\) | ||||
−0.507018 | + | 0.861936i | \(0.669252\pi\) | |||||||
\(798\) | 8.00000 | 0.283197 | ||||||||
\(799\) | −38.6274 | −1.36654 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 4.34315 | 0.153458 | ||||||||
\(802\) | 6.97056 | 0.246139 | ||||||||
\(803\) | −14.0589 | −0.496127 | ||||||||
\(804\) | 5.65685 | 0.199502 | ||||||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.48528 | 0.0874860 | ||||||||
\(808\) | 12.1421 | 0.427159 | ||||||||
\(809\) | −9.31371 | −0.327453 | −0.163726 | − | 0.986506i | \(-0.552351\pi\) | ||||
−0.163726 | + | 0.986506i | \(0.552351\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 30.1421 | 1.05843 | 0.529217 | − | 0.848487i | \(-0.322486\pi\) | ||||
0.529217 | + | 0.848487i | \(0.322486\pi\) | |||||||
\(812\) | 8.97056 | 0.314805 | ||||||||
\(813\) | 15.3137 | 0.537075 | ||||||||
\(814\) | −1.94113 | −0.0680364 | ||||||||
\(815\) | −11.3137 | −0.396302 | ||||||||
\(816\) | −4.82843 | −0.169029 | ||||||||
\(817\) | −4.68629 | −0.163953 | ||||||||
\(818\) | 7.65685 | 0.267716 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.65685 | 0.127703 | ||||||||
\(821\) | 22.2843 | 0.777726 | 0.388863 | − | 0.921296i | \(-0.372868\pi\) | ||||
0.388863 | + | 0.921296i | \(0.372868\pi\) | |||||||
\(822\) | 5.31371 | 0.185337 | ||||||||
\(823\) | −19.0294 | −0.663324 | −0.331662 | − | 0.943398i | \(-0.607609\pi\) | ||||
−0.331662 | + | 0.943398i | \(0.607609\pi\) | |||||||
\(824\) | −9.65685 | −0.336412 | ||||||||
\(825\) | 5.65685 | 0.196946 | ||||||||
\(826\) | 38.6274 | 1.34402 | ||||||||
\(827\) | 1.65685 | 0.0576145 | 0.0288072 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288072 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(828\) | 8.48528 | 0.294884 | ||||||||
\(829\) | −30.6863 | −1.06578 | −0.532889 | − | 0.846185i | \(-0.678894\pi\) | ||||
−0.532889 | + | 0.846185i | \(0.678894\pi\) | |||||||
\(830\) | −17.6569 | −0.612878 | ||||||||
\(831\) | 26.0000 | 0.901930 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.82843 | −0.167295 | ||||||||
\(834\) | −17.6569 | −0.611407 | ||||||||
\(835\) | −24.9706 | −0.864142 | ||||||||
\(836\) | 16.0000 | 0.553372 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 5.17157 | 0.178649 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | −2.82843 | −0.0975900 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | 4.14214 | 0.142747 | ||||||||
\(843\) | −19.6569 | −0.677018 | ||||||||
\(844\) | 23.3137 | 0.802491 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | −59.3970 | −2.04090 | ||||||||
\(848\) | −9.31371 | −0.319834 | ||||||||
\(849\) | −6.34315 | −0.217696 | ||||||||
\(850\) | 4.82843 | 0.165614 | ||||||||
\(851\) | 2.91169 | 0.0998114 | ||||||||
\(852\) | −5.65685 | −0.193801 | ||||||||
\(853\) | 18.2843 | 0.626042 | 0.313021 | − | 0.949746i | \(-0.398659\pi\) | ||||
0.313021 | + | 0.949746i | \(0.398659\pi\) | |||||||
\(854\) | 16.9706 | 0.580721 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | 4.00000 | 0.136717 | ||||||||
\(857\) | −15.1716 | −0.518251 | −0.259126 | − | 0.965844i | \(-0.583434\pi\) | ||||
−0.259126 | + | 0.965844i | \(0.583434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.9411 | −1.02158 | −0.510789 | − | 0.859706i | \(-0.670647\pi\) | ||||
−0.510789 | + | 0.859706i | \(0.670647\pi\) | |||||||
\(860\) | 1.65685 | 0.0564983 | ||||||||
\(861\) | 10.3431 | 0.352493 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | −28.2843 | −0.962808 | −0.481404 | − | 0.876499i | \(-0.659873\pi\) | ||||
−0.481404 | + | 0.876499i | \(0.659873\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −13.3137 | −0.452680 | ||||||||
\(866\) | −10.9706 | −0.372795 | ||||||||
\(867\) | 6.31371 | 0.214425 | ||||||||
\(868\) | 11.3137 | 0.384012 | ||||||||
\(869\) | 77.2548 | 2.62069 | ||||||||
\(870\) | −3.17157 | −0.107526 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.17157 | 0.107403 | ||||||||
\(873\) | 8.82843 | 0.298797 | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | 2.82843 | 0.0956183 | ||||||||
\(876\) | −2.48528 | −0.0839699 | ||||||||
\(877\) | −39.2548 | −1.32554 | −0.662771 | − | 0.748822i | \(-0.730620\pi\) | ||||
−0.662771 | + | 0.748822i | \(0.730620\pi\) | |||||||
\(878\) | 22.6274 | 0.763638 | ||||||||
\(879\) | −28.6274 | −0.965579 | ||||||||
\(880\) | −5.65685 | −0.190693 | ||||||||
\(881\) | 46.2843 | 1.55936 | 0.779678 | − | 0.626180i | \(-0.215383\pi\) | ||||
0.779678 | + | 0.626180i | \(0.215383\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 8.68629 | 0.292317 | 0.146158 | − | 0.989261i | \(-0.453309\pi\) | ||||
0.146158 | + | 0.989261i | \(0.453309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.6569 | −0.459070 | ||||||||
\(886\) | −41.6569 | −1.39949 | ||||||||
\(887\) | −23.5147 | −0.789547 | −0.394773 | − | 0.918778i | \(-0.629177\pi\) | ||||
−0.394773 | + | 0.918778i | \(0.629177\pi\) | |||||||
\(888\) | −0.343146 | −0.0115152 | ||||||||
\(889\) | 4.68629 | 0.157173 | ||||||||
\(890\) | 4.34315 | 0.145583 | ||||||||
\(891\) | 5.65685 | 0.189512 | ||||||||
\(892\) | −5.17157 | −0.173157 | ||||||||
\(893\) | 22.6274 | 0.757198 | ||||||||
\(894\) | −7.65685 | −0.256084 | ||||||||
\(895\) | −24.4853 | −0.818453 | ||||||||
\(896\) | 2.82843 | 0.0944911 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.2843 | −1.01060 | ||||||||
\(899\) | 12.6863 | 0.423112 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 44.9706 | 1.49819 | ||||||||
\(902\) | 20.6863 | 0.688778 | ||||||||
\(903\) | 4.68629 | 0.155950 | ||||||||
\(904\) | 10.4853 | 0.348735 | ||||||||
\(905\) | −3.65685 | −0.121558 | ||||||||
\(906\) | 12.0000 | 0.398673 | ||||||||
\(907\) | −48.2843 | −1.60325 | −0.801626 | − | 0.597825i | \(-0.796032\pi\) | ||||
−0.801626 | + | 0.597825i | \(0.796032\pi\) | |||||||
\(908\) | −4.00000 | −0.132745 | ||||||||
\(909\) | −12.1421 | −0.402729 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.97056 | −0.297208 | −0.148604 | − | 0.988897i | \(-0.547478\pi\) | ||||
−0.148604 | + | 0.988897i | \(0.547478\pi\) | |||||||
\(912\) | 2.82843 | 0.0936586 | ||||||||
\(913\) | −99.8823 | −3.30562 | ||||||||
\(914\) | 15.1716 | 0.501831 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | 24.1421 | 0.797679 | ||||||||
\(917\) | −62.6274 | −2.06814 | ||||||||
\(918\) | 4.82843 | 0.159362 | ||||||||
\(919\) | −25.9411 | −0.855719 | −0.427859 | − | 0.903845i | \(-0.640732\pi\) | ||||
−0.427859 | + | 0.903845i | \(0.640732\pi\) | |||||||
\(920\) | 8.48528 | 0.279751 | ||||||||
\(921\) | 10.3431 | 0.340818 | ||||||||
\(922\) | 14.0000 | 0.461065 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −16.0000 | −0.526361 | ||||||||
\(925\) | 0.343146 | 0.0112826 | ||||||||
\(926\) | 35.7990 | 1.17643 | ||||||||
\(927\) | 9.65685 | 0.317173 | ||||||||
\(928\) | 3.17157 | 0.104112 | ||||||||
\(929\) | −45.5980 | −1.49602 | −0.748011 | − | 0.663687i | \(-0.768991\pi\) | ||||
−0.748011 | + | 0.663687i | \(0.768991\pi\) | |||||||
\(930\) | −4.00000 | −0.131165 | ||||||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | 22.4853 | 0.736530 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 15.3137 | 0.501080 | ||||||||
\(935\) | 27.3137 | 0.893254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.6274 | −0.935217 | −0.467608 | − | 0.883936i | \(-0.654884\pi\) | ||||
−0.467608 | + | 0.883936i | \(0.654884\pi\) | |||||||
\(938\) | 16.0000 | 0.522419 | ||||||||
\(939\) | 2.97056 | 0.0969407 | ||||||||
\(940\) | −8.00000 | −0.260931 | ||||||||
\(941\) | −21.0294 | −0.685540 | −0.342770 | − | 0.939419i | \(-0.611365\pi\) | ||||
−0.342770 | + | 0.939419i | \(0.611365\pi\) | |||||||
\(942\) | 17.3137 | 0.564111 | ||||||||
\(943\) | −31.0294 | −1.01046 | ||||||||
\(944\) | 13.6569 | 0.444493 | ||||||||
\(945\) | 2.82843 | 0.0920087 | ||||||||
\(946\) | 9.37258 | 0.304729 | ||||||||
\(947\) | −41.6569 | −1.35367 | −0.676833 | − | 0.736137i | \(-0.736648\pi\) | ||||
−0.676833 | + | 0.736137i | \(0.736648\pi\) | |||||||
\(948\) | 13.6569 | 0.443554 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.82843 | −0.0917663 | ||||||||
\(951\) | −2.68629 | −0.0871090 | ||||||||
\(952\) | −13.6569 | −0.442621 | ||||||||
\(953\) | −56.1421 | −1.81862 | −0.909311 | − | 0.416117i | \(-0.863391\pi\) | ||||
−0.909311 | + | 0.416117i | \(0.863391\pi\) | |||||||
\(954\) | 9.31371 | 0.301542 | ||||||||
\(955\) | 11.3137 | 0.366103 | ||||||||
\(956\) | −16.0000 | −0.517477 | ||||||||
\(957\) | −17.9411 | −0.579954 | ||||||||
\(958\) | 11.3137 | 0.365529 | ||||||||
\(959\) | 15.0294 | 0.485326 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | 17.3137 | 0.557637 | ||||||||
\(965\) | −14.4853 | −0.466298 | ||||||||
\(966\) | 24.0000 | 0.772187 | ||||||||
\(967\) | 24.4853 | 0.787394 | 0.393697 | − | 0.919240i | \(-0.371196\pi\) | ||||
0.393697 | + | 0.919240i | \(0.371196\pi\) | |||||||
\(968\) | −21.0000 | −0.674966 | ||||||||
\(969\) | −13.6569 | −0.438721 | ||||||||
\(970\) | 8.82843 | 0.283464 | ||||||||
\(971\) | 32.4853 | 1.04250 | 0.521251 | − | 0.853403i | \(-0.325465\pi\) | ||||
0.521251 | + | 0.853403i | \(0.325465\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −49.9411 | −1.60104 | ||||||||
\(974\) | −0.485281 | −0.0155494 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 19.6569 | 0.628878 | 0.314439 | − | 0.949278i | \(-0.398184\pi\) | ||||
0.314439 | + | 0.949278i | \(0.398184\pi\) | |||||||
\(978\) | −11.3137 | −0.361773 | ||||||||
\(979\) | 24.5685 | 0.785214 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −3.17157 | −0.101261 | ||||||||
\(982\) | 9.85786 | 0.314577 | ||||||||
\(983\) | 13.6569 | 0.435586 | 0.217793 | − | 0.975995i | \(-0.430114\pi\) | ||||
0.217793 | + | 0.975995i | \(0.430114\pi\) | |||||||
\(984\) | 3.65685 | 0.116576 | ||||||||
\(985\) | 9.31371 | 0.296759 | ||||||||
\(986\) | −15.3137 | −0.487688 | ||||||||
\(987\) | −22.6274 | −0.720239 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.0589 | −0.447046 | ||||||||
\(990\) | 5.65685 | 0.179787 | ||||||||
\(991\) | 58.9117 | 1.87139 | 0.935696 | − | 0.352808i | \(-0.114773\pi\) | ||||
0.935696 | + | 0.352808i | \(0.114773\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | −8.48528 | −0.269272 | ||||||||
\(994\) | −16.0000 | −0.507489 | ||||||||
\(995\) | −21.6569 | −0.686568 | ||||||||
\(996\) | −17.6569 | −0.559479 | ||||||||
\(997\) | 38.6863 | 1.22521 | 0.612604 | − | 0.790390i | \(-0.290122\pi\) | ||||
0.612604 | + | 0.790390i | \(0.290122\pi\) | |||||||
\(998\) | −16.4853 | −0.521832 | ||||||||
\(999\) | 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 | 5070.2.a.bc.1.1 | 2 | ||
13.5 | odd | 4 | 5070.2.b.q.1351.3 | 4 | |||
13.8 | odd | 4 | 5070.2.b.q.1351.2 | 4 | |||
13.12 | even | 2 | 390.2.a.h.1.2 | ✓ | 2 | ||
39.38 | odd | 2 | 1170.2.a.o.1.2 | 2 | |||
52.51 | odd | 2 | 3120.2.a.bc.1.1 | 2 | |||
65.12 | odd | 4 | 1950.2.e.o.1249.4 | 4 | |||
65.38 | odd | 4 | 1950.2.e.o.1249.1 | 4 | |||
65.64 | even | 2 | 1950.2.a.bd.1.1 | 2 | |||
156.155 | even | 2 | 9360.2.a.ch.1.1 | 2 | |||
195.38 | even | 4 | 5850.2.e.bk.5149.3 | 4 | |||
195.77 | even | 4 | 5850.2.e.bk.5149.2 | 4 | |||
195.194 | odd | 2 | 5850.2.a.cl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.a.h.1.2 | ✓ | 2 | 13.12 | even | 2 | ||
1170.2.a.o.1.2 | 2 | 39.38 | odd | 2 | |||
1950.2.a.bd.1.1 | 2 | 65.64 | even | 2 | |||
1950.2.e.o.1249.1 | 4 | 65.38 | odd | 4 | |||
1950.2.e.o.1249.4 | 4 | 65.12 | odd | 4 | |||
3120.2.a.bc.1.1 | 2 | 52.51 | odd | 2 | |||
5070.2.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5070.2.b.q.1351.2 | 4 | 13.8 | odd | 4 | |||
5070.2.b.q.1351.3 | 4 | 13.5 | odd | 4 | |||
5850.2.a.cl.1.1 | 2 | 195.194 | odd | 2 | |||
5850.2.e.bk.5149.2 | 4 | 195.77 | even | 4 | |||
5850.2.e.bk.5149.3 | 4 | 195.38 | even | 4 | |||
9360.2.a.ch.1.1 | 2 | 156.155 | even | 2 |