Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,2,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.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: | \(16.1697064093\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 405) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.73205 | 1.93185 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.46410 | 2.73205 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.26795 | 0.479240 | 0.239620 | − | 0.970867i | \(-0.422977\pi\) | ||||
0.239620 | + | 0.970867i | \(0.422977\pi\) | |||||||
\(8\) | 9.46410 | 3.34607 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.26795 | −0.683812 | −0.341906 | − | 0.939734i | \(-0.611073\pi\) | ||||
−0.341906 | + | 0.939734i | \(0.611073\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.46410 | 1.51547 | 0.757735 | − | 0.652563i | \(-0.226306\pi\) | ||||
0.757735 | + | 0.652563i | \(0.226306\pi\) | |||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.9282 | 3.73205 | ||||||||
\(17\) | −0.732051 | −0.177548 | −0.0887742 | − | 0.996052i | \(-0.528295\pi\) | ||||
−0.0887742 | + | 0.996052i | \(0.528295\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.46410 | −0.565304 | −0.282652 | − | 0.959223i | \(-0.591214\pi\) | ||||
−0.282652 | + | 0.959223i | \(0.591214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.19615 | −1.32102 | ||||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.9282 | 2.92766 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.92820 | 1.30931 | ||||||||
\(29\) | −7.19615 | −1.33629 | −0.668146 | − | 0.744030i | \(-0.732912\pi\) | ||||
−0.668146 | + | 0.744030i | \(0.732912\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 21.8564 | 3.86370 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.732051 | −0.120348 | −0.0601742 | − | 0.998188i | \(-0.519166\pi\) | ||||
−0.0601742 | + | 0.998188i | \(0.519166\pi\) | |||||||
\(38\) | −6.73205 | −1.09208 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.19615 | 0.499155 | 0.249578 | − | 0.968355i | \(-0.419708\pi\) | ||||
0.249578 | + | 0.968355i | \(0.419708\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1962 | 1.55490 | 0.777449 | − | 0.628946i | \(-0.216513\pi\) | ||||
0.777449 | + | 0.628946i | \(0.216513\pi\) | |||||||
\(44\) | −12.3923 | −1.86821 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.46410 | −1.39541 | ||||||||
\(47\) | 5.26795 | 0.768409 | 0.384205 | − | 0.923248i | \(-0.374476\pi\) | ||||
0.384205 | + | 0.923248i | \(0.374476\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.39230 | −0.770329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 29.8564 | 4.14034 | ||||||||
\(53\) | −3.26795 | −0.448887 | −0.224444 | − | 0.974487i | \(-0.572056\pi\) | ||||
−0.224444 | + | 0.974487i | \(0.572056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.0000 | 1.60357 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.6603 | −2.58152 | ||||||||
\(59\) | −11.7321 | −1.52738 | −0.763691 | − | 0.645581i | \(-0.776615\pi\) | ||||
−0.763691 | + | 0.645581i | \(0.776615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | −8.19615 | −1.04091 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 29.8564 | 3.73205 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46410 | 0.423207 | 0.211604 | − | 0.977356i | \(-0.432131\pi\) | ||||
0.211604 | + | 0.977356i | \(0.432131\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.267949 | −0.0317997 | −0.0158999 | − | 0.999874i | \(-0.505061\pi\) | ||||
−0.0158999 | + | 0.999874i | \(0.505061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.66025 | −1.13065 | −0.565324 | − | 0.824869i | \(-0.691249\pi\) | ||||
−0.565324 | + | 0.824869i | \(0.691249\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.4641 | −1.54444 | ||||||||
\(77\) | −2.87564 | −0.327710 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.53590 | 0.960364 | 0.480182 | − | 0.877169i | \(-0.340571\pi\) | ||||
0.480182 | + | 0.877169i | \(0.340571\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.73205 | 0.964294 | ||||||||
\(83\) | 8.19615 | 0.899645 | 0.449822 | − | 0.893118i | \(-0.351487\pi\) | ||||
0.449822 | + | 0.893118i | \(0.351487\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 27.8564 | 3.00383 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −21.4641 | −2.28808 | ||||||||
\(89\) | −5.19615 | −0.550791 | −0.275396 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.92820 | 0.726273 | ||||||||
\(92\) | −18.9282 | −1.97340 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.3923 | 1.48445 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.66025 | −0.777781 | −0.388890 | − | 0.921284i | \(-0.627142\pi\) | ||||
−0.388890 | + | 0.921284i | \(0.627142\pi\) | |||||||
\(98\) | −14.7321 | −1.48816 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.6603 | 1.45875 | 0.729375 | − | 0.684114i | \(-0.239811\pi\) | ||||
0.729375 | + | 0.684114i | \(0.239811\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.46410 | 0.735460 | 0.367730 | − | 0.929933i | \(-0.380135\pi\) | ||||
0.367730 | + | 0.929933i | \(0.380135\pi\) | |||||||
\(104\) | 51.7128 | 5.07086 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.92820 | −0.867184 | ||||||||
\(107\) | 15.4641 | 1.49497 | 0.747486 | − | 0.664278i | \(-0.231261\pi\) | ||||
0.747486 | + | 0.664278i | \(0.231261\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.9282 | −1.90878 | −0.954388 | − | 0.298570i | \(-0.903490\pi\) | ||||
−0.954388 | + | 0.298570i | \(0.903490\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 18.9282 | 1.78855 | ||||||||
\(113\) | −5.12436 | −0.482059 | −0.241029 | − | 0.970518i | \(-0.577485\pi\) | ||||
−0.241029 | + | 0.970518i | \(0.577485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −39.3205 | −3.65082 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −32.0526 | −2.95068 | ||||||||
\(119\) | −0.928203 | −0.0850883 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.85641 | −0.532401 | ||||||||
\(122\) | 10.9282 | 0.989393 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.3923 | −1.47207 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.5885 | −1.47199 | −0.735994 | − | 0.676988i | \(-0.763285\pi\) | ||||
−0.735994 | + | 0.676988i | \(0.763285\pi\) | |||||||
\(128\) | 37.8564 | 3.34607 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5885 | −1.36197 | −0.680985 | − | 0.732297i | \(-0.738448\pi\) | ||||
−0.680985 | + | 0.732297i | \(0.738448\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.12436 | −0.270916 | ||||||||
\(134\) | 9.46410 | 0.817574 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.92820 | −0.594089 | ||||||||
\(137\) | −9.46410 | −0.808573 | −0.404286 | − | 0.914632i | \(-0.632480\pi\) | ||||
−0.404286 | + | 0.914632i | \(0.632480\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.3923 | 1.81447 | 0.907236 | − | 0.420622i | \(-0.138188\pi\) | ||||
0.907236 | + | 0.420622i | \(0.138188\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.732051 | −0.0614323 | ||||||||
\(143\) | −12.3923 | −1.03630 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −26.3923 | −2.18424 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | −8.00000 | −0.655386 | −0.327693 | − | 0.944784i | \(-0.606271\pi\) | ||||
−0.327693 | + | 0.944784i | \(0.606271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.3923 | −1.25261 | −0.626304 | − | 0.779579i | \(-0.715433\pi\) | ||||
−0.626304 | + | 0.779579i | \(0.715433\pi\) | |||||||
\(152\) | −23.3205 | −1.89154 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.85641 | −0.633087 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.12436 | −0.408968 | −0.204484 | − | 0.978870i | \(-0.565552\pi\) | ||||
−0.204484 | + | 0.978870i | \(0.565552\pi\) | |||||||
\(158\) | 23.3205 | 1.85528 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.39230 | −0.346162 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.26795 | −0.725922 | −0.362961 | − | 0.931804i | \(-0.618234\pi\) | ||||
−0.362961 | + | 0.931804i | \(0.618234\pi\) | |||||||
\(164\) | 17.4641 | 1.36372 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.3923 | 1.73798 | ||||||||
\(167\) | 0.339746 | 0.0262903 | 0.0131452 | − | 0.999914i | \(-0.495816\pi\) | ||||
0.0131452 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 55.7128 | 4.24806 | ||||||||
\(173\) | −15.4641 | −1.17571 | −0.587857 | − | 0.808965i | \(-0.700028\pi\) | ||||
−0.587857 | + | 0.808965i | \(0.700028\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −33.8564 | −2.55202 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.1962 | −1.06405 | ||||||||
\(179\) | −16.1244 | −1.20519 | −0.602595 | − | 0.798047i | \(-0.705867\pi\) | ||||
−0.602595 | + | 0.798047i | \(0.705867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.5359 | 1.45209 | 0.726046 | − | 0.687646i | \(-0.241356\pi\) | ||||
0.726046 | + | 0.687646i | \(0.241356\pi\) | |||||||
\(182\) | 18.9282 | 1.40305 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −32.7846 | −2.41691 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.66025 | 0.121410 | ||||||||
\(188\) | 28.7846 | 2.09933 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1244 | 1.16672 | 0.583359 | − | 0.812215i | \(-0.301738\pi\) | ||||
0.583359 | + | 0.812215i | \(0.301738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.73205 | 0.628547 | 0.314273 | − | 0.949333i | \(-0.398239\pi\) | ||||
0.314273 | + | 0.949333i | \(0.398239\pi\) | |||||||
\(194\) | −20.9282 | −1.50256 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.4641 | −2.10458 | ||||||||
\(197\) | −13.8564 | −0.987228 | −0.493614 | − | 0.869681i | \(-0.664324\pi\) | ||||
−0.493614 | + | 0.869681i | \(0.664324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 40.0526 | 2.81809 | ||||||||
\(203\) | −9.12436 | −0.640404 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 20.3923 | 1.42080 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 81.5692 | 5.65581 | ||||||||
\(209\) | 5.58846 | 0.386562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.8564 | 1.29813 | 0.649064 | − | 0.760734i | \(-0.275161\pi\) | ||||
0.649064 | + | 0.760734i | \(0.275161\pi\) | |||||||
\(212\) | −17.8564 | −1.22638 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 42.2487 | 2.88806 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.80385 | −0.258222 | ||||||||
\(218\) | −54.4449 | −3.68747 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.7846 | 1.65970 | 0.829850 | − | 0.557986i | \(-0.188426\pi\) | ||||
0.829850 | + | 0.557986i | \(0.188426\pi\) | |||||||
\(224\) | 27.7128 | 1.85164 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | −20.0526 | −1.33094 | −0.665468 | − | 0.746427i | \(-0.731768\pi\) | ||||
−0.665468 | + | 0.746427i | \(0.731768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −68.1051 | −4.47132 | ||||||||
\(233\) | −10.0526 | −0.658565 | −0.329283 | − | 0.944231i | \(-0.606807\pi\) | ||||
−0.329283 | + | 0.944231i | \(0.606807\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −64.1051 | −4.17289 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.53590 | −0.164378 | ||||||||
\(239\) | −7.46410 | −0.482813 | −0.241406 | − | 0.970424i | \(-0.577609\pi\) | ||||
−0.241406 | + | 0.970424i | \(0.577609\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3205 | 1.18013 | 0.590064 | − | 0.807357i | \(-0.299103\pi\) | ||||
0.590064 | + | 0.807357i | \(0.299103\pi\) | |||||||
\(242\) | −16.0000 | −1.02852 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 21.8564 | 1.39921 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.4641 | −0.856700 | ||||||||
\(248\) | −28.3923 | −1.80291 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3923 | 0.655956 | 0.327978 | − | 0.944685i | \(-0.393633\pi\) | ||||
0.327978 | + | 0.944685i | \(0.393633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.85641 | 0.493928 | ||||||||
\(254\) | −45.3205 | −2.84366 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 43.7128 | 2.73205 | ||||||||
\(257\) | 10.3923 | 0.648254 | 0.324127 | − | 0.946014i | \(-0.394929\pi\) | ||||
0.324127 | + | 0.946014i | \(0.394929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.928203 | −0.0576757 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −42.5885 | −2.63112 | ||||||||
\(263\) | 13.3205 | 0.821378 | 0.410689 | − | 0.911776i | \(-0.365288\pi\) | ||||
0.410689 | + | 0.911776i | \(0.365288\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.53590 | −0.523370 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.9282 | 1.15622 | ||||||||
\(269\) | −6.66025 | −0.406083 | −0.203041 | − | 0.979170i | \(-0.565083\pi\) | ||||
−0.203041 | + | 0.979170i | \(0.565083\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9282 | 0.663841 | 0.331921 | − | 0.943307i | \(-0.392303\pi\) | ||||
0.331921 | + | 0.943307i | \(0.392303\pi\) | |||||||
\(272\) | −10.9282 | −0.662620 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.8564 | −1.56204 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1962 | −0.852964 | −0.426482 | − | 0.904496i | \(-0.640247\pi\) | ||||
−0.426482 | + | 0.904496i | \(0.640247\pi\) | |||||||
\(278\) | 58.4449 | 3.50529 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.53590 | 0.509209 | 0.254605 | − | 0.967045i | \(-0.418055\pi\) | ||||
0.254605 | + | 0.967045i | \(0.418055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.32051 | −0.316271 | −0.158136 | − | 0.987417i | \(-0.550548\pi\) | ||||
−0.158136 | + | 0.987417i | \(0.550548\pi\) | |||||||
\(284\) | −1.46410 | −0.0868784 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −33.8564 | −2.00197 | ||||||||
\(287\) | 4.05256 | 0.239215 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4641 | −0.968477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −52.7846 | −3.08899 | ||||||||
\(293\) | −25.2679 | −1.47617 | −0.738085 | − | 0.674708i | \(-0.764270\pi\) | ||||
−0.738085 | + | 0.674708i | \(0.764270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.92820 | −0.402694 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.8564 | −1.26611 | ||||||||
\(299\) | −18.9282 | −1.09465 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.9282 | 0.745169 | ||||||||
\(302\) | −42.0526 | −2.41985 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −36.7846 | −2.10974 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0526 | 1.37275 | 0.686376 | − | 0.727247i | \(-0.259200\pi\) | ||||
0.686376 | + | 0.727247i | \(0.259200\pi\) | |||||||
\(308\) | −15.7128 | −0.895321 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.2679 | 0.922471 | 0.461235 | − | 0.887278i | \(-0.347406\pi\) | ||||
0.461235 | + | 0.887278i | \(0.347406\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9282 | 1.29598 | 0.647989 | − | 0.761649i | \(-0.275610\pi\) | ||||
0.647989 | + | 0.761649i | \(0.275610\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 46.6410 | 2.62376 | ||||||||
\(317\) | 4.19615 | 0.235679 | 0.117840 | − | 0.993033i | \(-0.462403\pi\) | ||||
0.117840 | + | 0.993033i | \(0.462403\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.3205 | 0.913773 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | −0.668734 | ||||||||
\(323\) | 1.80385 | 0.100369 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −25.3205 | −1.40237 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 30.2487 | 1.67021 | ||||||||
\(329\) | 6.67949 | 0.368252 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.46410 | 0.355299 | 0.177650 | − | 0.984094i | \(-0.443151\pi\) | ||||
0.177650 | + | 0.984094i | \(0.443151\pi\) | |||||||
\(332\) | 44.7846 | 2.45787 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.928203 | 0.0507890 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.32051 | 0.398773 | 0.199387 | − | 0.979921i | \(-0.436105\pi\) | ||||
0.199387 | + | 0.979921i | \(0.436105\pi\) | |||||||
\(338\) | 46.0526 | 2.50493 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.80385 | 0.368449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7128 | −0.848412 | ||||||||
\(344\) | 96.4974 | 5.20279 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −42.2487 | −2.27130 | ||||||||
\(347\) | −2.58846 | −0.138956 | −0.0694778 | − | 0.997583i | \(-0.522133\pi\) | ||||
−0.0694778 | + | 0.997583i | \(0.522133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.85641 | 0.474073 | 0.237036 | − | 0.971501i | \(-0.423824\pi\) | ||||
0.237036 | + | 0.971501i | \(0.423824\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −49.5692 | −2.64205 | ||||||||
\(353\) | 19.5167 | 1.03877 | 0.519384 | − | 0.854541i | \(-0.326162\pi\) | ||||
0.519384 | + | 0.854541i | \(0.326162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −28.3923 | −1.50479 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −44.0526 | −2.32825 | ||||||||
\(359\) | 18.1244 | 0.956567 | 0.478283 | − | 0.878206i | \(-0.341259\pi\) | ||||
0.478283 | + | 0.878206i | \(0.341259\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9282 | −0.680432 | ||||||||
\(362\) | 53.3731 | 2.80523 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 37.8564 | 1.98421 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.1769 | 1.62742 | 0.813711 | − | 0.581270i | \(-0.197444\pi\) | ||||
0.813711 | + | 0.581270i | \(0.197444\pi\) | |||||||
\(368\) | −51.7128 | −2.69572 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.14359 | −0.215125 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0526 | 0.934726 | 0.467363 | − | 0.884065i | \(-0.345204\pi\) | ||||
0.467363 | + | 0.884065i | \(0.345204\pi\) | |||||||
\(374\) | 4.53590 | 0.234546 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 49.8564 | 2.57115 | ||||||||
\(377\) | −39.3205 | −2.02511 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.3923 | −0.944749 | −0.472375 | − | 0.881398i | \(-0.656603\pi\) | ||||
−0.472375 | + | 0.881398i | \(0.656603\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 44.0526 | 2.25392 | ||||||||
\(383\) | −9.46410 | −0.483593 | −0.241797 | − | 0.970327i | \(-0.577737\pi\) | ||||
−0.241797 | + | 0.970327i | \(0.577737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.8564 | 1.21426 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −41.8564 | −2.12494 | ||||||||
\(389\) | 20.5359 | 1.04121 | 0.520606 | − | 0.853797i | \(-0.325706\pi\) | ||||
0.520606 | + | 0.853797i | \(0.325706\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.53590 | 0.128246 | ||||||||
\(392\) | −51.0333 | −2.57757 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −37.8564 | −1.90718 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.39230 | 0.320821 | 0.160410 | − | 0.987050i | \(-0.448718\pi\) | ||||
0.160410 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(398\) | −5.46410 | −0.273891 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.0718 | 0.552899 | 0.276450 | − | 0.961028i | \(-0.410842\pi\) | ||||
0.276450 | + | 0.961028i | \(0.410842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.3923 | −0.816559 | ||||||||
\(404\) | 80.1051 | 3.98538 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.9282 | −1.23717 | ||||||||
\(407\) | 1.66025 | 0.0822957 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.85641 | 0.487368 | 0.243684 | − | 0.969855i | \(-0.421644\pi\) | ||||
0.243684 | + | 0.969855i | \(0.421644\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 40.7846 | 2.00931 | ||||||||
\(413\) | −14.8756 | −0.731983 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 119.426 | 5.85532 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.2679 | 0.746780 | ||||||||
\(419\) | −0.392305 | −0.0191653 | −0.00958267 | − | 0.999954i | \(-0.503050\pi\) | ||||
−0.00958267 | + | 0.999954i | \(0.503050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.78461 | −0.379399 | −0.189699 | − | 0.981842i | \(-0.560751\pi\) | ||||
−0.189699 | + | 0.981842i | \(0.560751\pi\) | |||||||
\(422\) | 51.5167 | 2.50779 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.9282 | −1.50201 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.07180 | 0.245441 | ||||||||
\(428\) | 84.4974 | 4.08434 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.6603 | −1.86220 | −0.931099 | − | 0.364765i | \(-0.881149\pi\) | ||||
−0.931099 | + | 0.364765i | \(0.881149\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.5359 | 1.37135 | 0.685674 | − | 0.727909i | \(-0.259508\pi\) | ||||
0.685674 | + | 0.727909i | \(0.259508\pi\) | |||||||
\(434\) | −10.3923 | −0.498847 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −108.890 | −5.21487 | ||||||||
\(437\) | 8.53590 | 0.408327 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3923 | −0.734635 | −0.367317 | − | 0.930096i | \(-0.619724\pi\) | ||||
−0.367317 | + | 0.930096i | \(0.619724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.9282 | −0.519802 | ||||||||
\(443\) | 17.6603 | 0.839064 | 0.419532 | − | 0.907741i | \(-0.362194\pi\) | ||||
0.419532 | + | 0.907741i | \(0.362194\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 67.7128 | 3.20629 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 37.8564 | 1.78855 | ||||||||
\(449\) | −16.1244 | −0.760955 | −0.380478 | − | 0.924790i | \(-0.624240\pi\) | ||||
−0.380478 | + | 0.924790i | \(0.624240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.24871 | −0.341328 | ||||||||
\(452\) | −28.0000 | −1.31701 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −54.7846 | −2.57117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.732051 | 0.0342439 | 0.0171219 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171219 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(458\) | −32.7846 | −1.53192 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.05256 | 0.0490226 | 0.0245113 | − | 0.999700i | \(-0.492197\pi\) | ||||
0.0245113 | + | 0.999700i | \(0.492197\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3923 | −0.482971 | −0.241486 | − | 0.970404i | \(-0.577635\pi\) | ||||
−0.241486 | + | 0.970404i | \(0.577635\pi\) | |||||||
\(464\) | −107.426 | −4.98711 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.4641 | −1.27225 | ||||||||
\(467\) | 35.3731 | 1.63687 | 0.818435 | − | 0.574599i | \(-0.194842\pi\) | ||||
0.818435 | + | 0.574599i | \(0.194842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.39230 | 0.202818 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −111.033 | −5.11072 | ||||||||
\(473\) | −23.1244 | −1.06326 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.07180 | −0.232465 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.3923 | −0.932722 | ||||||||
\(479\) | −36.1244 | −1.65056 | −0.825282 | − | 0.564721i | \(-0.808984\pi\) | ||||
−0.825282 | + | 0.564721i | \(0.808984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 50.0526 | 2.27983 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −32.0000 | −1.45455 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.60770 | −0.163480 | −0.0817401 | − | 0.996654i | \(-0.526048\pi\) | ||||
−0.0817401 | + | 0.996654i | \(0.526048\pi\) | |||||||
\(488\) | 37.8564 | 1.71368 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.1244 | −1.72053 | −0.860264 | − | 0.509849i | \(-0.829701\pi\) | ||||
−0.860264 | + | 0.509849i | \(0.829701\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.26795 | 0.237256 | ||||||||
\(494\) | −36.7846 | −1.65502 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −44.7846 | −2.01089 | ||||||||
\(497\) | −0.339746 | −0.0152397 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.3205 | −0.462009 | −0.231005 | − | 0.972953i | \(-0.574201\pi\) | ||||
−0.231005 | + | 0.972953i | \(0.574201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.3923 | 1.26721 | ||||||||
\(503\) | −27.3205 | −1.21816 | −0.609081 | − | 0.793108i | \(-0.708461\pi\) | ||||
−0.609081 | + | 0.793108i | \(0.708461\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 21.4641 | 0.954196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −90.6410 | −4.02154 | ||||||||
\(509\) | 34.7846 | 1.54180 | 0.770900 | − | 0.636956i | \(-0.219807\pi\) | ||||
0.770900 | + | 0.636956i | \(0.219807\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.2487 | −0.541851 | ||||||||
\(512\) | 43.7128 | 1.93185 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.3923 | 1.25233 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.9474 | −0.525448 | ||||||||
\(518\) | −2.53590 | −0.111421 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5359 | 0.549208 | 0.274604 | − | 0.961557i | \(-0.411453\pi\) | ||||
0.274604 | + | 0.961557i | \(0.411453\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2487 | 1.14778 | 0.573888 | − | 0.818934i | \(-0.305434\pi\) | ||||
0.573888 | + | 0.818934i | \(0.305434\pi\) | |||||||
\(524\) | −85.1769 | −3.72097 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 36.3923 | 1.58678 | ||||||||
\(527\) | 2.19615 | 0.0956659 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.0718 | −0.740156 | ||||||||
\(533\) | 17.4641 | 0.756454 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 32.7846 | 1.41608 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.1962 | −0.784492 | ||||||||
\(539\) | 12.2295 | 0.526761 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5359 | −0.753927 | −0.376964 | − | 0.926228i | \(-0.623032\pi\) | ||||
−0.376964 | + | 0.926228i | \(0.623032\pi\) | |||||||
\(542\) | 29.8564 | 1.28244 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.0000 | −0.685994 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.14359 | 0.262681 | 0.131341 | − | 0.991337i | \(-0.458072\pi\) | ||||
0.131341 | + | 0.991337i | \(0.458072\pi\) | |||||||
\(548\) | −51.7128 | −2.20906 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.7321 | 0.755411 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8231 | 0.460244 | ||||||||
\(554\) | −38.7846 | −1.64780 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 116.890 | 4.95723 | ||||||||
\(557\) | 9.46410 | 0.401007 | 0.200503 | − | 0.979693i | \(-0.435742\pi\) | ||||
0.200503 | + | 0.979693i | \(0.435742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.7128 | 2.35640 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.3205 | 0.983716 | ||||||||
\(563\) | 13.2679 | 0.559177 | 0.279589 | − | 0.960120i | \(-0.409802\pi\) | ||||
0.279589 | + | 0.960120i | \(0.409802\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.5359 | −0.610989 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.53590 | −0.106404 | ||||||||
\(569\) | 32.9090 | 1.37962 | 0.689808 | − | 0.723993i | \(-0.257695\pi\) | ||||
0.689808 | + | 0.723993i | \(0.257695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.78461 | 0.0746836 | 0.0373418 | − | 0.999303i | \(-0.488111\pi\) | ||||
0.0373418 | + | 0.999303i | \(0.488111\pi\) | |||||||
\(572\) | −67.7128 | −2.83121 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.0718 | 0.462128 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7321 | −0.779825 | −0.389913 | − | 0.920852i | \(-0.627495\pi\) | ||||
−0.389913 | + | 0.920852i | \(0.627495\pi\) | |||||||
\(578\) | −44.9808 | −1.87095 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3923 | 0.431145 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.41154 | 0.306955 | ||||||||
\(584\) | −91.4256 | −3.78322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −69.0333 | −2.85174 | ||||||||
\(587\) | −5.66025 | −0.233624 | −0.116812 | − | 0.993154i | \(-0.537267\pi\) | ||||
−0.116812 | + | 0.993154i | \(0.537267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.39230 | 0.304595 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.9282 | −0.449146 | ||||||||
\(593\) | 27.8564 | 1.14393 | 0.571963 | − | 0.820280i | \(-0.306182\pi\) | ||||
0.571963 | + | 0.820280i | \(0.306182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −43.7128 | −1.79055 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −51.7128 | −2.11469 | ||||||||
\(599\) | 16.8038 | 0.686587 | 0.343293 | − | 0.939228i | \(-0.388458\pi\) | ||||
0.343293 | + | 0.939228i | \(0.388458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2487 | 0.703590 | 0.351795 | − | 0.936077i | \(-0.385571\pi\) | ||||
0.351795 | + | 0.936077i | \(0.385571\pi\) | |||||||
\(602\) | 35.3205 | 1.43956 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −84.1051 | −3.42219 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.80385 | 0.235571 | 0.117785 | − | 0.993039i | \(-0.462420\pi\) | ||||
0.117785 | + | 0.993039i | \(0.462420\pi\) | |||||||
\(608\) | −53.8564 | −2.18417 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.7846 | 1.16450 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.46410 | 0.220693 | 0.110346 | − | 0.993893i | \(-0.464804\pi\) | ||||
0.110346 | + | 0.993893i | \(0.464804\pi\) | |||||||
\(614\) | 65.7128 | 2.65195 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −27.2154 | −1.09654 | ||||||||
\(617\) | −6.92820 | −0.278919 | −0.139459 | − | 0.990228i | \(-0.544536\pi\) | ||||
−0.139459 | + | 0.990228i | \(0.544536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.8564 | 0.637323 | 0.318661 | − | 0.947869i | \(-0.396767\pi\) | ||||
0.318661 | + | 0.947869i | \(0.396767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 44.4449 | 1.78208 | ||||||||
\(623\) | −6.58846 | −0.263961 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 62.6410 | 2.50364 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.0000 | −1.11732 | ||||||||
\(629\) | 0.535898 | 0.0213677 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7128 | 0.904183 | 0.452091 | − | 0.891972i | \(-0.350678\pi\) | ||||
0.452091 | + | 0.891972i | \(0.350678\pi\) | |||||||
\(632\) | 80.7846 | 3.21344 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.4641 | 0.455298 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.4641 | −1.16741 | ||||||||
\(638\) | 44.5885 | 1.76527 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.6603 | 1.05302 | 0.526508 | − | 0.850170i | \(-0.323501\pi\) | ||||
0.526508 | + | 0.850170i | \(0.323501\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.3397 | −0.959866 | −0.479933 | − | 0.877305i | \(-0.659339\pi\) | ||||
−0.479933 | + | 0.877305i | \(0.659339\pi\) | |||||||
\(644\) | −24.0000 | −0.945732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.92820 | 0.193898 | ||||||||
\(647\) | −4.53590 | −0.178325 | −0.0891623 | − | 0.996017i | \(-0.528419\pi\) | ||||
−0.0891623 | + | 0.996017i | \(0.528419\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.6077 | 1.04444 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −50.6410 | −1.98326 | ||||||||
\(653\) | 10.5359 | 0.412302 | 0.206151 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206151 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 47.7128 | 1.86287 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.2487 | 0.711409 | ||||||||
\(659\) | 5.46410 | 0.212851 | 0.106426 | − | 0.994321i | \(-0.466059\pi\) | ||||
0.106426 | + | 0.994321i | \(0.466059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.3205 | −0.634794 | −0.317397 | − | 0.948293i | \(-0.602809\pi\) | ||||
−0.317397 | + | 0.948293i | \(0.602809\pi\) | |||||||
\(662\) | 17.6603 | 0.686385 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 77.5692 | 3.01027 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.9282 | 0.965224 | ||||||||
\(668\) | 1.85641 | 0.0718265 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.07180 | −0.350213 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3923 | −0.400594 | −0.200297 | − | 0.979735i | \(-0.564191\pi\) | ||||
−0.200297 | + | 0.979735i | \(0.564191\pi\) | |||||||
\(674\) | 20.0000 | 0.770371 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 92.1051 | 3.54250 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.71281 | −0.372744 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.5885 | 0.711789 | ||||||||
\(683\) | 40.3923 | 1.54557 | 0.772784 | − | 0.634669i | \(-0.218863\pi\) | ||||
0.772784 | + | 0.634669i | \(0.218863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −42.9282 | −1.63901 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 152.210 | 5.80296 | ||||||||
\(689\) | −17.8564 | −0.680275 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.7128 | 1.43466 | 0.717332 | − | 0.696732i | \(-0.245363\pi\) | ||||
0.717332 | + | 0.696732i | \(0.245363\pi\) | |||||||
\(692\) | −84.4974 | −3.21211 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.07180 | −0.268442 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.33975 | −0.0886242 | ||||||||
\(698\) | 24.1962 | 0.915838 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.1962 | −1.17826 | −0.589131 | − | 0.808037i | \(-0.700530\pi\) | ||||
−0.589131 | + | 0.808037i | \(0.700530\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.80385 | 0.0680334 | ||||||||
\(704\) | −67.7128 | −2.55202 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.3205 | 2.00674 | ||||||||
\(707\) | 18.5885 | 0.699091 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.4641 | −1.10655 | −0.553274 | − | 0.832999i | \(-0.686622\pi\) | ||||
−0.553274 | + | 0.832999i | \(0.686622\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −49.1769 | −1.84298 | ||||||||
\(713\) | 10.3923 | 0.389195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −88.1051 | −3.29264 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 49.5167 | 1.84795 | ||||||||
\(719\) | 39.5885 | 1.47640 | 0.738200 | − | 0.674582i | \(-0.235676\pi\) | ||||
0.738200 | + | 0.674582i | \(0.235676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.46410 | 0.352462 | ||||||||
\(722\) | −35.3205 | −1.31449 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 106.746 | 3.96719 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.3923 | −0.459605 | −0.229803 | − | 0.973237i | \(-0.573808\pi\) | ||||
−0.229803 | + | 0.973237i | \(0.573808\pi\) | |||||||
\(728\) | 65.5692 | 2.43016 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.46410 | −0.276070 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.78461 | 0.250595 | 0.125298 | − | 0.992119i | \(-0.460011\pi\) | ||||
0.125298 | + | 0.992119i | \(0.460011\pi\) | |||||||
\(734\) | 85.1769 | 3.14394 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −75.7128 | −2.79081 | ||||||||
\(737\) | −7.85641 | −0.289394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.5359 | 0.571497 | 0.285749 | − | 0.958305i | \(-0.407758\pi\) | ||||
0.285749 | + | 0.958305i | \(0.407758\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.3205 | −0.415589 | ||||||||
\(743\) | 45.9090 | 1.68424 | 0.842118 | − | 0.539293i | \(-0.181308\pi\) | ||||
0.842118 | + | 0.539293i | \(0.181308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 49.3205 | 1.80575 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.07180 | 0.331698 | ||||||||
\(749\) | 19.6077 | 0.716450 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.21539 | 0.263293 | 0.131647 | − | 0.991297i | \(-0.457974\pi\) | ||||
0.131647 | + | 0.991297i | \(0.457974\pi\) | |||||||
\(752\) | 78.6410 | 2.86774 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −107.426 | −3.91221 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.1769 | −1.93275 | −0.966374 | − | 0.257141i | \(-0.917220\pi\) | ||||
−0.966374 | + | 0.257141i | \(0.917220\pi\) | |||||||
\(758\) | −50.2487 | −1.82512 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.4449 | −1.28488 | −0.642438 | − | 0.766338i | \(-0.722077\pi\) | ||||
−0.642438 | + | 0.766338i | \(0.722077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.2679 | −0.914761 | ||||||||
\(764\) | 88.1051 | 3.18753 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.8564 | −0.934230 | ||||||||
\(767\) | −64.1051 | −2.31470 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.4641 | −0.593711 | −0.296855 | − | 0.954922i | \(-0.595938\pi\) | ||||
−0.296855 | + | 0.954922i | \(0.595938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 47.7128 | 1.71722 | ||||||||
\(773\) | 43.5167 | 1.56519 | 0.782593 | − | 0.622534i | \(-0.213897\pi\) | ||||
0.782593 | + | 0.622534i | \(0.213897\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −72.4974 | −2.60251 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.1051 | 2.01147 | ||||||||
\(779\) | −7.87564 | −0.282174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.607695 | 0.0217450 | ||||||||
\(782\) | 6.92820 | 0.247752 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −80.4974 | −2.87491 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.94744 | 0.354588 | 0.177294 | − | 0.984158i | \(-0.443266\pi\) | ||||
0.177294 | + | 0.984158i | \(0.443266\pi\) | |||||||
\(788\) | −75.7128 | −2.69716 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.49742 | −0.231022 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.8564 | 0.776144 | ||||||||
\(794\) | 17.4641 | 0.619778 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.9282 | −0.387340 | ||||||||
\(797\) | 36.3923 | 1.28908 | 0.644541 | − | 0.764570i | \(-0.277049\pi\) | ||||
0.644541 | + | 0.764570i | \(0.277049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.85641 | −0.136430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.2487 | 1.06812 | ||||||||
\(803\) | 21.9090 | 0.773151 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −44.7846 | −1.57747 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 138.746 | 4.88107 | ||||||||
\(809\) | −13.4449 | −0.472696 | −0.236348 | − | 0.971668i | \(-0.575951\pi\) | ||||
−0.236348 | + | 0.971668i | \(0.575951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.5359 | −0.405080 | −0.202540 | − | 0.979274i | \(-0.564920\pi\) | ||||
−0.202540 | + | 0.979274i | \(0.564920\pi\) | |||||||
\(812\) | −49.8564 | −1.74962 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.53590 | 0.158983 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.1244 | −0.878990 | ||||||||
\(818\) | 26.9282 | 0.941523 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.2679 | −1.19596 | −0.597980 | − | 0.801511i | \(-0.704030\pi\) | ||||
−0.597980 | + | 0.801511i | \(0.704030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.8564 | 0.831582 | 0.415791 | − | 0.909460i | \(-0.363505\pi\) | ||||
0.415791 | + | 0.909460i | \(0.363505\pi\) | |||||||
\(824\) | 70.6410 | 2.46090 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −40.6410 | −1.41408 | ||||||||
\(827\) | 32.3923 | 1.12639 | 0.563195 | − | 0.826324i | \(-0.309572\pi\) | ||||
0.563195 | + | 0.826324i | \(0.309572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.7846 | 0.617685 | 0.308843 | − | 0.951113i | \(-0.400058\pi\) | ||||
0.308843 | + | 0.951113i | \(0.400058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 163.138 | 5.65581 | ||||||||
\(833\) | 3.94744 | 0.136771 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 30.5359 | 1.05611 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.07180 | −0.0370246 | ||||||||
\(839\) | 22.8038 | 0.787276 | 0.393638 | − | 0.919265i | \(-0.371216\pi\) | ||||
0.393638 | + | 0.919265i | \(0.371216\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.7846 | 0.785676 | ||||||||
\(842\) | −21.2679 | −0.732942 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 103.033 | 3.54655 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.42563 | −0.255148 | ||||||||
\(848\) | −48.7846 | −1.67527 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.53590 | 0.0869295 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −55.5167 | −1.90085 | −0.950427 | − | 0.310947i | \(-0.899354\pi\) | ||||
−0.950427 | + | 0.310947i | \(0.899354\pi\) | |||||||
\(854\) | 13.8564 | 0.474156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 146.354 | 5.00227 | ||||||||
\(857\) | 52.4974 | 1.79328 | 0.896639 | − | 0.442763i | \(-0.146002\pi\) | ||||
0.896639 | + | 0.442763i | \(0.146002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0000 | −0.375315 | −0.187658 | − | 0.982235i | \(-0.560090\pi\) | ||||
−0.187658 | + | 0.982235i | \(0.560090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −105.622 | −3.59749 | ||||||||
\(863\) | −1.12436 | −0.0382735 | −0.0191368 | − | 0.999817i | \(-0.506092\pi\) | ||||
−0.0191368 | + | 0.999817i | \(0.506092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 77.9615 | 2.64924 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −20.7846 | −0.705476 | ||||||||
\(869\) | −19.3590 | −0.656709 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9282 | 0.641358 | ||||||||
\(872\) | −188.603 | −6.38689 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.3205 | 0.788828 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.5359 | −0.896054 | −0.448027 | − | 0.894020i | \(-0.647873\pi\) | ||||
−0.448027 | + | 0.894020i | \(0.647873\pi\) | |||||||
\(878\) | −42.0526 | −1.41921 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.94744 | −0.301447 | −0.150723 | − | 0.988576i | \(-0.548160\pi\) | ||||
−0.150723 | + | 0.988576i | \(0.548160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8038 | 0.666453 | 0.333226 | − | 0.942847i | \(-0.391863\pi\) | ||||
0.333226 | + | 0.942847i | \(0.391863\pi\) | |||||||
\(884\) | −21.8564 | −0.735111 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 48.2487 | 1.62095 | ||||||||
\(887\) | −44.1962 | −1.48396 | −0.741981 | − | 0.670421i | \(-0.766113\pi\) | ||||
−0.741981 | + | 0.670421i | \(0.766113\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.0333 | −0.705435 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 135.426 | 4.53439 | ||||||||
\(893\) | −12.9808 | −0.434385 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 48.0000 | 1.60357 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −44.0526 | −1.47005 | ||||||||
\(899\) | 21.5885 | 0.720015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.39230 | 0.0796992 | ||||||||
\(902\) | −19.8038 | −0.659396 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −48.4974 | −1.61300 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.0000 | 0.996134 | 0.498067 | − | 0.867139i | \(-0.334043\pi\) | ||||
0.498067 | + | 0.867139i | \(0.334043\pi\) | |||||||
\(908\) | −109.569 | −3.63618 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.58846 | −0.251417 | −0.125708 | − | 0.992067i | \(-0.540120\pi\) | ||||
−0.125708 | + | 0.992067i | \(0.540120\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.5885 | −0.615188 | ||||||||
\(914\) | 2.00000 | 0.0661541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −65.5692 | −2.16647 | ||||||||
\(917\) | −19.7654 | −0.652710 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.9615 | 1.54912 | 0.774559 | − | 0.632502i | \(-0.217972\pi\) | ||||
0.774559 | + | 0.632502i | \(0.217972\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.87564 | 0.0947043 | ||||||||
\(923\) | −1.46410 | −0.0481915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −28.3923 | −0.933029 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −157.282 | −5.16304 | ||||||||
\(929\) | 28.3731 | 0.930890 | 0.465445 | − | 0.885077i | \(-0.345894\pi\) | ||||
0.465445 | + | 0.885077i | \(0.345894\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.2872 | 0.435470 | ||||||||
\(932\) | −54.9282 | −1.79923 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 96.6410 | 3.16219 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.8564 | 1.04070 | 0.520352 | − | 0.853952i | \(-0.325801\pi\) | ||||
0.520352 | + | 0.853952i | \(0.325801\pi\) | |||||||
\(938\) | 12.0000 | 0.391814 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.1769 | −0.885942 | −0.442971 | − | 0.896536i | \(-0.646076\pi\) | ||||
−0.442971 | + | 0.896536i | \(0.646076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.0718 | −0.360547 | ||||||||
\(944\) | −175.138 | −5.70027 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −63.1769 | −2.05406 | ||||||||
\(947\) | 2.28719 | 0.0743236 | 0.0371618 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371618 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.7846 | −1.71346 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.78461 | −0.284711 | ||||||||
\(953\) | −15.6077 | −0.505583 | −0.252791 | − | 0.967521i | \(-0.581349\pi\) | ||||
−0.252791 | + | 0.967521i | \(0.581349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −40.7846 | −1.31907 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −98.6936 | −3.18864 | ||||||||
\(959\) | −12.0000 | −0.387500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | −10.9282 | −0.352339 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 100.105 | 3.22417 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.1962 | 1.16399 | 0.581995 | − | 0.813192i | \(-0.302272\pi\) | ||||
0.581995 | + | 0.813192i | \(0.302272\pi\) | |||||||
\(968\) | −55.4256 | −1.78145 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.4449 | −1.33003 | −0.665014 | − | 0.746830i | \(-0.731575\pi\) | ||||
−0.665014 | + | 0.746830i | \(0.731575\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.1244 | 0.869567 | ||||||||
\(974\) | −9.85641 | −0.315820 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 59.7128 | 1.91136 | ||||||||
\(977\) | 1.46410 | 0.0468408 | 0.0234204 | − | 0.999726i | \(-0.492544\pi\) | ||||
0.0234204 | + | 0.999726i | \(0.492544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.7846 | 0.376638 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −104.158 | −3.32381 | ||||||||
\(983\) | −17.4115 | −0.555342 | −0.277671 | − | 0.960676i | \(-0.589563\pi\) | ||||
−0.277671 | + | 0.960676i | \(0.589563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.3923 | 0.458344 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −73.5692 | −2.34055 | ||||||||
\(989\) | −35.3205 | −1.12313 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.14359 | 0.0998595 | 0.0499298 | − | 0.998753i | \(-0.484100\pi\) | ||||
0.0499298 | + | 0.998753i | \(0.484100\pi\) | |||||||
\(992\) | −65.5692 | −2.08182 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.928203 | −0.0294408 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.5167 | 0.618099 | 0.309049 | − | 0.951046i | \(-0.399989\pi\) | ||||
0.309049 | + | 0.951046i | \(0.399989\pi\) | |||||||
\(998\) | −28.1962 | −0.892534 | ||||||||
\(999\) | 0 | 0 |
(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 | 2025.2.a.m.1.2 | 2 | ||
3.2 | odd | 2 | 2025.2.a.g.1.1 | 2 | |||
5.2 | odd | 4 | 2025.2.b.g.649.4 | 4 | |||
5.3 | odd | 4 | 2025.2.b.g.649.1 | 4 | |||
5.4 | even | 2 | 405.2.a.g.1.1 | ✓ | 2 | ||
15.2 | even | 4 | 2025.2.b.h.649.1 | 4 | |||
15.8 | even | 4 | 2025.2.b.h.649.4 | 4 | |||
15.14 | odd | 2 | 405.2.a.h.1.2 | yes | 2 | ||
20.19 | odd | 2 | 6480.2.a.br.1.1 | 2 | |||
45.4 | even | 6 | 405.2.e.l.136.2 | 4 | |||
45.14 | odd | 6 | 405.2.e.i.136.1 | 4 | |||
45.29 | odd | 6 | 405.2.e.i.271.1 | 4 | |||
45.34 | even | 6 | 405.2.e.l.271.2 | 4 | |||
60.59 | even | 2 | 6480.2.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.a.g.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
405.2.a.h.1.2 | yes | 2 | 15.14 | odd | 2 | ||
405.2.e.i.136.1 | 4 | 45.14 | odd | 6 | |||
405.2.e.i.271.1 | 4 | 45.29 | odd | 6 | |||
405.2.e.l.136.2 | 4 | 45.4 | even | 6 | |||
405.2.e.l.271.2 | 4 | 45.34 | even | 6 | |||
2025.2.a.g.1.1 | 2 | 3.2 | odd | 2 | |||
2025.2.a.m.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2025.2.b.g.649.1 | 4 | 5.3 | odd | 4 | |||
2025.2.b.g.649.4 | 4 | 5.2 | odd | 4 | |||
2025.2.b.h.649.1 | 4 | 15.2 | even | 4 | |||
2025.2.b.h.649.4 | 4 | 15.8 | even | 4 | |||
6480.2.a.bi.1.1 | 2 | 60.59 | even | 2 | |||
6480.2.a.br.1.1 | 2 | 20.19 | odd | 2 |