Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2535) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.80194 | 1.27416 | 0.637081 | − | 0.770797i | \(-0.280142\pi\) | ||||
0.637081 | + | 0.770797i | \(0.280142\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.24698 | 0.623490 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.80194 | 1.05903 | 0.529516 | − | 0.848300i | \(-0.322373\pi\) | ||||
0.529516 | + | 0.848300i | \(0.322373\pi\) | |||||||
\(8\) | −1.35690 | −0.479735 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.80194 | 0.569823 | ||||||||
\(11\) | −3.49396 | −1.05347 | −0.526734 | − | 0.850030i | \(-0.676584\pi\) | ||||
−0.526734 | + | 0.850030i | \(0.676584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 5.04892 | 1.34938 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.93900 | −1.23475 | ||||||||
\(17\) | 7.60388 | 1.84421 | 0.922105 | − | 0.386939i | \(-0.126468\pi\) | ||||
0.922105 | + | 0.386939i | \(0.126468\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.75302 | 0.402170 | 0.201085 | − | 0.979574i | \(-0.435553\pi\) | ||||
0.201085 | + | 0.979574i | \(0.435553\pi\) | |||||||
\(20\) | 1.24698 | 0.278833 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.29590 | −1.34229 | ||||||||
\(23\) | 6.44504 | 1.34388 | 0.671942 | − | 0.740604i | \(-0.265460\pi\) | ||||
0.671942 | + | 0.740604i | \(0.265460\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.49396 | 0.660296 | ||||||||
\(29\) | 9.74094 | 1.80885 | 0.904423 | − | 0.426636i | \(-0.140301\pi\) | ||||
0.904423 | + | 0.426636i | \(0.140301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.59179 | −1.72274 | −0.861369 | − | 0.507981i | \(-0.830392\pi\) | ||||
−0.861369 | + | 0.507981i | \(0.830392\pi\) | |||||||
\(32\) | −6.18598 | −1.09354 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.7017 | 2.34982 | ||||||||
\(35\) | 2.80194 | 0.473614 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.85086 | −1.12627 | −0.563137 | − | 0.826364i | \(-0.690406\pi\) | ||||
−0.563137 | + | 0.826364i | \(0.690406\pi\) | |||||||
\(38\) | 3.15883 | 0.512430 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.35690 | −0.214544 | ||||||||
\(41\) | 1.19806 | 0.187106 | 0.0935529 | − | 0.995614i | \(-0.470178\pi\) | ||||
0.0935529 | + | 0.995614i | \(0.470178\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00969 | 0.611472 | 0.305736 | − | 0.952116i | \(-0.401098\pi\) | ||||
0.305736 | + | 0.952116i | \(0.401098\pi\) | |||||||
\(44\) | −4.35690 | −0.656827 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.6136 | 1.71233 | ||||||||
\(47\) | 2.97823 | 0.434419 | 0.217210 | − | 0.976125i | \(-0.430304\pi\) | ||||
0.217210 | + | 0.976125i | \(0.430304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.850855 | 0.121551 | ||||||||
\(50\) | 1.80194 | 0.254832 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.51573 | −0.620283 | −0.310142 | − | 0.950690i | \(-0.600376\pi\) | ||||
−0.310142 | + | 0.950690i | \(0.600376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.49396 | −0.471125 | ||||||||
\(56\) | −3.80194 | −0.508055 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 17.5526 | 2.30476 | ||||||||
\(59\) | 7.18598 | 0.935535 | 0.467767 | − | 0.883852i | \(-0.345058\pi\) | ||||
0.467767 | + | 0.883852i | \(0.345058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.43296 | 0.567582 | 0.283791 | − | 0.958886i | \(-0.408408\pi\) | ||||
0.283791 | + | 0.958886i | \(0.408408\pi\) | |||||||
\(62\) | −17.2838 | −2.19505 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.26875 | −0.158594 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.45712 | −0.300185 | −0.150093 | − | 0.988672i | \(-0.547957\pi\) | ||||
−0.150093 | + | 0.988672i | \(0.547957\pi\) | |||||||
\(68\) | 9.48188 | 1.14985 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.04892 | 0.603461 | ||||||||
\(71\) | −13.5090 | −1.60323 | −0.801613 | − | 0.597843i | \(-0.796025\pi\) | ||||
−0.801613 | + | 0.597843i | \(0.796025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.75302 | 0.205176 | 0.102588 | − | 0.994724i | \(-0.467288\pi\) | ||||
0.102588 | + | 0.994724i | \(0.467288\pi\) | |||||||
\(74\) | −12.3448 | −1.43506 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.18598 | 0.250749 | ||||||||
\(77\) | −9.78986 | −1.11566 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.85623 | 0.546369 | 0.273184 | − | 0.961962i | \(-0.411923\pi\) | ||||
0.273184 | + | 0.961962i | \(0.411923\pi\) | |||||||
\(80\) | −4.93900 | −0.552197 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.15883 | 0.238403 | ||||||||
\(83\) | 12.0586 | 1.32360 | 0.661802 | − | 0.749679i | \(-0.269792\pi\) | ||||
0.661802 | + | 0.749679i | \(0.269792\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.60388 | 0.824756 | ||||||||
\(86\) | 7.22521 | 0.779114 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.74094 | 0.505386 | ||||||||
\(89\) | 4.12498 | 0.437247 | 0.218624 | − | 0.975809i | \(-0.429843\pi\) | ||||
0.218624 | + | 0.975809i | \(0.429843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.03684 | 0.837898 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.36658 | 0.553521 | ||||||||
\(95\) | 1.75302 | 0.179856 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.32975 | 0.236550 | 0.118275 | − | 0.992981i | \(-0.462264\pi\) | ||||
0.118275 | + | 0.992981i | \(0.462264\pi\) | |||||||
\(98\) | 1.53319 | 0.154875 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.24698 | 0.124698 | ||||||||
\(101\) | 11.4058 | 1.13492 | 0.567460 | − | 0.823401i | \(-0.307926\pi\) | ||||
0.567460 | + | 0.823401i | \(0.307926\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.46011 | −0.538000 | −0.269000 | − | 0.963140i | \(-0.586693\pi\) | ||||
−0.269000 | + | 0.963140i | \(0.586693\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.13706 | −0.790341 | ||||||||
\(107\) | 13.9879 | 1.35226 | 0.676132 | − | 0.736781i | \(-0.263655\pi\) | ||||
0.676132 | + | 0.736781i | \(0.263655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.21983 | 0.787317 | 0.393659 | − | 0.919257i | \(-0.371209\pi\) | ||||
0.393659 | + | 0.919257i | \(0.371209\pi\) | |||||||
\(110\) | −6.29590 | −0.600290 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.8388 | −1.30764 | ||||||||
\(113\) | 1.85325 | 0.174339 | 0.0871695 | − | 0.996193i | \(-0.472218\pi\) | ||||
0.0871695 | + | 0.996193i | \(0.472218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.44504 | 0.601003 | ||||||||
\(116\) | 12.1468 | 1.12780 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.9487 | 1.19202 | ||||||||
\(119\) | 21.3056 | 1.95308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.20775 | 0.109796 | ||||||||
\(122\) | 7.98792 | 0.723192 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.9608 | −1.07411 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.24027 | 0.819942 | 0.409971 | − | 0.912099i | \(-0.365539\pi\) | ||||
0.409971 | + | 0.912099i | \(0.365539\pi\) | |||||||
\(128\) | 10.0858 | 0.891463 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.4886 | 1.09113 | 0.545566 | − | 0.838068i | \(-0.316315\pi\) | ||||
0.545566 | + | 0.838068i | \(0.316315\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.91185 | 0.425912 | ||||||||
\(134\) | −4.42758 | −0.382485 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.3177 | −0.884733 | ||||||||
\(137\) | 1.10454 | 0.0943672 | 0.0471836 | − | 0.998886i | \(-0.484975\pi\) | ||||
0.0471836 | + | 0.998886i | \(0.484975\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1903 | −0.864329 | −0.432165 | − | 0.901795i | \(-0.642250\pi\) | ||||
−0.432165 | + | 0.901795i | \(0.642250\pi\) | |||||||
\(140\) | 3.49396 | 0.295293 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −24.3424 | −2.04277 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.74094 | 0.808941 | ||||||||
\(146\) | 3.15883 | 0.261427 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.54288 | −0.702220 | ||||||||
\(149\) | −19.2403 | −1.57622 | −0.788112 | − | 0.615531i | \(-0.788941\pi\) | ||||
−0.788112 | + | 0.615531i | \(0.788941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.8267 | 1.69485 | 0.847426 | − | 0.530913i | \(-0.178151\pi\) | ||||
0.847426 | + | 0.530913i | \(0.178151\pi\) | |||||||
\(152\) | −2.37867 | −0.192935 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −17.6407 | −1.42153 | ||||||||
\(155\) | −9.59179 | −0.770431 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.6722 | −1.88924 | −0.944622 | − | 0.328159i | \(-0.893572\pi\) | ||||
−0.944622 | + | 0.328159i | \(0.893572\pi\) | |||||||
\(158\) | 8.75063 | 0.696163 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.18598 | −0.489045 | ||||||||
\(161\) | 18.0586 | 1.42322 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.79954 | 0.532581 | 0.266291 | − | 0.963893i | \(-0.414202\pi\) | ||||
0.266291 | + | 0.963893i | \(0.414202\pi\) | |||||||
\(164\) | 1.49396 | 0.116659 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.7289 | 1.68649 | ||||||||
\(167\) | 13.0194 | 1.00747 | 0.503735 | − | 0.863858i | \(-0.331959\pi\) | ||||
0.503735 | + | 0.863858i | \(0.331959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.7017 | 1.05087 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.00000 | 0.381246 | ||||||||
\(173\) | −21.5459 | −1.63810 | −0.819051 | − | 0.573721i | \(-0.805499\pi\) | ||||
−0.819051 | + | 0.573721i | \(0.805499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.80194 | 0.211807 | ||||||||
\(176\) | 17.2567 | 1.30077 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.43296 | 0.557124 | ||||||||
\(179\) | 18.9051 | 1.41304 | 0.706519 | − | 0.707694i | \(-0.250265\pi\) | ||||
0.706519 | + | 0.707694i | \(0.250265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9487 | 0.962469 | 0.481234 | − | 0.876592i | \(-0.340189\pi\) | ||||
0.481234 | + | 0.876592i | \(0.340189\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.74525 | −0.644708 | ||||||||
\(185\) | −6.85086 | −0.503685 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.5676 | −1.94282 | ||||||||
\(188\) | 3.71379 | 0.270856 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.15883 | 0.229166 | ||||||||
\(191\) | 0.660563 | 0.0477966 | 0.0238983 | − | 0.999714i | \(-0.492392\pi\) | ||||
0.0238983 | + | 0.999714i | \(0.492392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0325239 | 0.00234112 | 0.00117056 | − | 0.999999i | \(-0.499627\pi\) | ||||
0.00117056 | + | 0.999999i | \(0.499627\pi\) | |||||||
\(194\) | 4.19806 | 0.301403 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.06100 | 0.0757856 | ||||||||
\(197\) | −14.4426 | −1.02900 | −0.514498 | − | 0.857492i | \(-0.672022\pi\) | ||||
−0.514498 | + | 0.857492i | \(0.672022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.06398 | −0.146312 | −0.0731559 | − | 0.997321i | \(-0.523307\pi\) | ||||
−0.0731559 | + | 0.997321i | \(0.523307\pi\) | |||||||
\(200\) | −1.35690 | −0.0959470 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.5526 | 1.44607 | ||||||||
\(203\) | 27.2935 | 1.91563 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.19806 | 0.0836763 | ||||||||
\(206\) | −9.83877 | −0.685500 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.12498 | −0.423674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5080 | 1.61835 | 0.809177 | − | 0.587564i | \(-0.199913\pi\) | ||||
0.809177 | + | 0.587564i | \(0.199913\pi\) | |||||||
\(212\) | −5.63102 | −0.386740 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.2054 | 1.72300 | ||||||||
\(215\) | 4.00969 | 0.273458 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.8756 | −1.82444 | ||||||||
\(218\) | 14.8116 | 1.00317 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.35690 | −0.293742 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6213 | −0.845187 | −0.422594 | − | 0.906319i | \(-0.638880\pi\) | ||||
−0.422594 | + | 0.906319i | \(0.638880\pi\) | |||||||
\(224\) | −17.3327 | −1.15809 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.33944 | 0.222136 | ||||||||
\(227\) | 23.4088 | 1.55370 | 0.776848 | − | 0.629688i | \(-0.216817\pi\) | ||||
0.776848 | + | 0.629688i | \(0.216817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.0640 | 1.52411 | 0.762055 | − | 0.647512i | \(-0.224190\pi\) | ||||
0.762055 | + | 0.647512i | \(0.224190\pi\) | |||||||
\(230\) | 11.6136 | 0.765776 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.2174 | −0.867767 | ||||||||
\(233\) | −0.945706 | −0.0619553 | −0.0309776 | − | 0.999520i | \(-0.509862\pi\) | ||||
−0.0309776 | + | 0.999520i | \(0.509862\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.97823 | 0.194278 | ||||||||
\(236\) | 8.96077 | 0.583297 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 38.3913 | 2.48854 | ||||||||
\(239\) | −20.2567 | −1.31029 | −0.655147 | − | 0.755501i | \(-0.727394\pi\) | ||||
−0.655147 | + | 0.755501i | \(0.727394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.75840 | −0.499762 | −0.249881 | − | 0.968277i | \(-0.580392\pi\) | ||||
−0.249881 | + | 0.968277i | \(0.580392\pi\) | |||||||
\(242\) | 2.17629 | 0.139897 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.52781 | 0.353882 | ||||||||
\(245\) | 0.850855 | 0.0543591 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 13.0151 | 0.826457 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.80194 | 0.113965 | ||||||||
\(251\) | 10.1021 | 0.637642 | 0.318821 | − | 0.947815i | \(-0.396713\pi\) | ||||
0.318821 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.5187 | −1.41574 | ||||||||
\(254\) | 16.6504 | 1.04474 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.7114 | 1.29446 | ||||||||
\(257\) | 23.9801 | 1.49584 | 0.747920 | − | 0.663789i | \(-0.231053\pi\) | ||||
0.747920 | + | 0.663789i | \(0.231053\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.1957 | −1.19276 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.5036 | 1.39028 | ||||||||
\(263\) | −31.9028 | −1.96721 | −0.983604 | − | 0.180341i | \(-0.942280\pi\) | ||||
−0.983604 | + | 0.180341i | \(0.942280\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.51573 | −0.277399 | ||||||||
\(266\) | 8.85086 | 0.542681 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.06398 | −0.187163 | ||||||||
\(269\) | −14.4004 | −0.878010 | −0.439005 | − | 0.898485i | \(-0.644669\pi\) | ||||
−0.439005 | + | 0.898485i | \(0.644669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.22414 | −0.135107 | −0.0675536 | − | 0.997716i | \(-0.521519\pi\) | ||||
−0.0675536 | + | 0.997716i | \(0.521519\pi\) | |||||||
\(272\) | −37.5555 | −2.27714 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.99031 | 0.120239 | ||||||||
\(275\) | −3.49396 | −0.210694 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.8853 | −1.49521 | −0.747606 | − | 0.664142i | \(-0.768797\pi\) | ||||
−0.747606 | + | 0.664142i | \(0.768797\pi\) | |||||||
\(278\) | −18.3623 | −1.10130 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.80194 | −0.227209 | ||||||||
\(281\) | −13.8834 | −0.828213 | −0.414106 | − | 0.910228i | \(-0.635906\pi\) | ||||
−0.414106 | + | 0.910228i | \(0.635906\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.44504 | 0.0858988 | 0.0429494 | − | 0.999077i | \(-0.486325\pi\) | ||||
0.0429494 | + | 0.999077i | \(0.486325\pi\) | |||||||
\(284\) | −16.8455 | −0.999595 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.35690 | 0.198151 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.8189 | 2.40111 | ||||||||
\(290\) | 17.5526 | 1.03072 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.18598 | 0.127925 | ||||||||
\(293\) | 11.2741 | 0.658642 | 0.329321 | − | 0.944218i | \(-0.393180\pi\) | ||||
0.329321 | + | 0.944218i | \(0.393180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.18598 | 0.418384 | ||||||||
\(296\) | 9.29590 | 0.540313 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −34.6698 | −2.00837 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.2349 | 0.647569 | ||||||||
\(302\) | 37.5284 | 2.15952 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.65817 | −0.496580 | ||||||||
\(305\) | 4.43296 | 0.253831 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.90754 | 0.223015 | 0.111508 | − | 0.993764i | \(-0.464432\pi\) | ||||
0.111508 | + | 0.993764i | \(0.464432\pi\) | |||||||
\(308\) | −12.2078 | −0.695601 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.2838 | −0.981655 | ||||||||
\(311\) | 14.1347 | 0.801504 | 0.400752 | − | 0.916187i | \(-0.368749\pi\) | ||||
0.400752 | + | 0.916187i | \(0.368749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4470 | 0.816591 | 0.408295 | − | 0.912850i | \(-0.366123\pi\) | ||||
0.408295 | + | 0.912850i | \(0.366123\pi\) | |||||||
\(314\) | −42.6558 | −2.40720 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.05562 | 0.340655 | ||||||||
\(317\) | −4.28919 | −0.240905 | −0.120453 | − | 0.992719i | \(-0.538435\pi\) | ||||
−0.120453 | + | 0.992719i | \(0.538435\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.0344 | −1.90556 | ||||||||
\(320\) | −1.26875 | −0.0709253 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 32.5405 | 1.81341 | ||||||||
\(323\) | 13.3297 | 0.741687 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.2524 | 0.678595 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.62565 | −0.0897613 | ||||||||
\(329\) | 8.34481 | 0.460065 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.9420 | −1.37094 | −0.685468 | − | 0.728103i | \(-0.740402\pi\) | ||||
−0.685468 | + | 0.728103i | \(0.740402\pi\) | |||||||
\(332\) | 15.0368 | 0.825254 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.4601 | 1.28368 | ||||||||
\(335\) | −2.45712 | −0.134247 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.1226 | −1.64088 | −0.820441 | − | 0.571731i | \(-0.806272\pi\) | ||||
−0.820441 | + | 0.571731i | \(0.806272\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.48188 | 0.514227 | ||||||||
\(341\) | 33.5133 | 1.81485 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2295 | −0.930307 | ||||||||
\(344\) | −5.44073 | −0.293345 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38.8243 | −2.08721 | ||||||||
\(347\) | 21.3230 | 1.14468 | 0.572340 | − | 0.820016i | \(-0.306036\pi\) | ||||
0.572340 | + | 0.820016i | \(0.306036\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2218 | 1.45715 | 0.728573 | − | 0.684968i | \(-0.240184\pi\) | ||||
0.728573 | + | 0.684968i | \(0.240184\pi\) | |||||||
\(350\) | 5.04892 | 0.269876 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.6136 | 1.15201 | ||||||||
\(353\) | −12.0871 | −0.643330 | −0.321665 | − | 0.946853i | \(-0.604243\pi\) | ||||
−0.321665 | + | 0.946853i | \(0.604243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.5090 | −0.716985 | ||||||||
\(356\) | 5.14377 | 0.272619 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 34.0659 | 1.80044 | ||||||||
\(359\) | −4.21014 | −0.222203 | −0.111101 | − | 0.993809i | \(-0.535438\pi\) | ||||
−0.111101 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.9269 | −0.838259 | ||||||||
\(362\) | 23.3327 | 1.22634 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.75302 | 0.0917573 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.9071 | −1.40454 | −0.702269 | − | 0.711912i | \(-0.747830\pi\) | ||||
−0.702269 | + | 0.711912i | \(0.747830\pi\) | |||||||
\(368\) | −31.8321 | −1.65936 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.3448 | −0.641776 | ||||||||
\(371\) | −12.6528 | −0.656900 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.8461 | −1.49359 | −0.746796 | − | 0.665053i | \(-0.768409\pi\) | ||||
−0.746796 | + | 0.665053i | \(0.768409\pi\) | |||||||
\(374\) | −47.8732 | −2.47547 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.04115 | −0.208406 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.57135 | −0.440281 | −0.220140 | − | 0.975468i | \(-0.570652\pi\) | ||||
−0.220140 | + | 0.975468i | \(0.570652\pi\) | |||||||
\(380\) | 2.18598 | 0.112138 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.19029 | 0.0609007 | ||||||||
\(383\) | −7.28382 | −0.372186 | −0.186093 | − | 0.982532i | \(-0.559583\pi\) | ||||
−0.186093 | + | 0.982532i | \(0.559583\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.78986 | −0.498937 | ||||||||
\(386\) | 0.0586060 | 0.00298297 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.90515 | 0.147487 | ||||||||
\(389\) | −15.5840 | −0.790141 | −0.395071 | − | 0.918651i | \(-0.629280\pi\) | ||||
−0.395071 | + | 0.918651i | \(0.629280\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49.0073 | 2.47841 | ||||||||
\(392\) | −1.15452 | −0.0583122 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.0248 | −1.31111 | ||||||||
\(395\) | 4.85623 | 0.244344 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.0538 | −1.60874 | −0.804368 | − | 0.594132i | \(-0.797496\pi\) | ||||
−0.804368 | + | 0.594132i | \(0.797496\pi\) | |||||||
\(398\) | −3.71917 | −0.186425 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.93900 | −0.246950 | ||||||||
\(401\) | −14.0073 | −0.699491 | −0.349745 | − | 0.936845i | \(-0.613732\pi\) | ||||
−0.349745 | + | 0.936845i | \(0.613732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.2228 | 0.707612 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 49.1812 | 2.44082 | ||||||||
\(407\) | 23.9366 | 1.18649 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0707 | 0.992432 | 0.496216 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496216 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(410\) | 2.15883 | 0.106617 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.80864 | −0.335438 | ||||||||
\(413\) | 20.1347 | 0.990762 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0586 | 0.591934 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.0368 | −0.539829 | ||||||||
\(419\) | −36.1299 | −1.76506 | −0.882530 | − | 0.470256i | \(-0.844162\pi\) | ||||
−0.882530 | + | 0.470256i | \(0.844162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.708415 | −0.0345260 | −0.0172630 | − | 0.999851i | \(-0.505495\pi\) | ||||
−0.0172630 | + | 0.999851i | \(0.505495\pi\) | |||||||
\(422\) | 42.3599 | 2.06205 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.12737 | 0.297572 | ||||||||
\(425\) | 7.60388 | 0.368842 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4209 | 0.601088 | ||||||||
\(428\) | 17.4426 | 0.843122 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.22521 | 0.348431 | ||||||||
\(431\) | 23.6286 | 1.13815 | 0.569076 | − | 0.822285i | \(-0.307301\pi\) | ||||
0.569076 | + | 0.822285i | \(0.307301\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.6450 | −0.511567 | −0.255784 | − | 0.966734i | \(-0.582333\pi\) | ||||
−0.255784 | + | 0.966734i | \(0.582333\pi\) | |||||||
\(434\) | −48.4282 | −2.32463 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.2500 | 0.490884 | ||||||||
\(437\) | 11.2983 | 0.540470 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.4832 | 0.548064 | 0.274032 | − | 0.961721i | \(-0.411643\pi\) | ||||
0.274032 | + | 0.961721i | \(0.411643\pi\) | |||||||
\(440\) | 4.74094 | 0.226015 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.73423 | 0.177419 | 0.0887094 | − | 0.996058i | \(-0.471726\pi\) | ||||
0.0887094 | + | 0.996058i | \(0.471726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.12498 | 0.195543 | ||||||||
\(446\) | −22.7429 | −1.07691 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.55496 | −0.167956 | ||||||||
\(449\) | −4.52052 | −0.213336 | −0.106668 | − | 0.994295i | \(-0.534018\pi\) | ||||
−0.106668 | + | 0.994295i | \(0.534018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.18598 | −0.197110 | ||||||||
\(452\) | 2.31096 | 0.108699 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 42.1812 | 1.97966 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.3860 | 0.766503 | 0.383251 | − | 0.923644i | \(-0.374804\pi\) | ||||
0.383251 | + | 0.923644i | \(0.374804\pi\) | |||||||
\(458\) | 41.5599 | 1.94196 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.03684 | 0.374719 | ||||||||
\(461\) | −13.8769 | −0.646313 | −0.323157 | − | 0.946345i | \(-0.604744\pi\) | ||||
−0.323157 | + | 0.946345i | \(0.604744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.9530 | −1.06672 | −0.533358 | − | 0.845889i | \(-0.679070\pi\) | ||||
−0.533358 | + | 0.845889i | \(0.679070\pi\) | |||||||
\(464\) | −48.1105 | −2.23347 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.70410 | −0.0789410 | ||||||||
\(467\) | 5.15346 | 0.238474 | 0.119237 | − | 0.992866i | \(-0.461955\pi\) | ||||
0.119237 | + | 0.992866i | \(0.461955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.88471 | −0.317906 | ||||||||
\(470\) | 5.36658 | 0.247542 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.75063 | −0.448809 | ||||||||
\(473\) | −14.0097 | −0.644166 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.75302 | 0.0804341 | ||||||||
\(476\) | 26.5676 | 1.21773 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −36.5013 | −1.66953 | ||||||||
\(479\) | 16.2252 | 0.741349 | 0.370674 | − | 0.928763i | \(-0.379127\pi\) | ||||
0.370674 | + | 0.928763i | \(0.379127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −13.9801 | −0.636778 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.50604 | 0.0684564 | ||||||||
\(485\) | 2.32975 | 0.105788 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.2543 | 1.46158 | 0.730790 | − | 0.682602i | \(-0.239152\pi\) | ||||
0.730790 | + | 0.682602i | \(0.239152\pi\) | |||||||
\(488\) | −6.01507 | −0.272289 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.53319 | 0.0692624 | ||||||||
\(491\) | −12.1497 | −0.548310 | −0.274155 | − | 0.961686i | \(-0.588398\pi\) | ||||
−0.274155 | + | 0.961686i | \(0.588398\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 74.0689 | 3.33589 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 47.3739 | 2.12715 | ||||||||
\(497\) | −37.8514 | −1.69787 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.9202 | −1.38418 | −0.692089 | − | 0.721812i | \(-0.743310\pi\) | ||||
−0.692089 | + | 0.721812i | \(0.743310\pi\) | |||||||
\(500\) | 1.24698 | 0.0557666 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.2034 | 0.812459 | ||||||||
\(503\) | −22.0737 | −0.984216 | −0.492108 | − | 0.870534i | \(-0.663774\pi\) | ||||
−0.492108 | + | 0.870534i | \(0.663774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4058 | 0.507552 | ||||||||
\(506\) | −40.5773 | −1.80388 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.5224 | 0.511225 | ||||||||
\(509\) | 1.64071 | 0.0727232 | 0.0363616 | − | 0.999339i | \(-0.488423\pi\) | ||||
0.0363616 | + | 0.999339i | \(0.488423\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.91185 | 0.217288 | ||||||||
\(512\) | 17.1491 | 0.757892 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 43.2107 | 1.90594 | ||||||||
\(515\) | −5.46011 | −0.240601 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4058 | −0.457647 | ||||||||
\(518\) | −34.5894 | −1.51977 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.1390 | −1.49566 | −0.747828 | − | 0.663893i | \(-0.768903\pi\) | ||||
−0.747828 | + | 0.663893i | \(0.768903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5104 | 0.547040 | 0.273520 | − | 0.961866i | \(-0.411812\pi\) | ||||
0.273520 | + | 0.961866i | \(0.411812\pi\) | |||||||
\(524\) | 15.5730 | 0.680310 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −57.4868 | −2.50654 | ||||||||
\(527\) | −72.9348 | −3.17709 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.5386 | 0.806025 | ||||||||
\(530\) | −8.13706 | −0.353451 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.12498 | 0.265552 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.9879 | 0.604750 | ||||||||
\(536\) | 3.33406 | 0.144009 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.9487 | −1.11873 | ||||||||
\(539\) | −2.97285 | −0.128050 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.5254 | −1.26940 | −0.634698 | − | 0.772760i | \(-0.718876\pi\) | ||||
−0.634698 | + | 0.772760i | \(0.718876\pi\) | |||||||
\(542\) | −4.00777 | −0.172148 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −47.0374 | −2.01671 | ||||||||
\(545\) | 8.21983 | 0.352099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.07367 | −0.259691 | −0.129846 | − | 0.991534i | \(-0.541448\pi\) | ||||
−0.129846 | + | 0.991534i | \(0.541448\pi\) | |||||||
\(548\) | 1.37734 | 0.0588370 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.29590 | −0.268458 | ||||||||
\(551\) | 17.0761 | 0.727465 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.6069 | 0.578623 | ||||||||
\(554\) | −44.8418 | −1.90514 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.7071 | −0.538901 | ||||||||
\(557\) | −20.0291 | −0.848659 | −0.424329 | − | 0.905508i | \(-0.639490\pi\) | ||||
−0.424329 | + | 0.905508i | \(0.639490\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −13.8388 | −0.584795 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.0170 | −1.05528 | ||||||||
\(563\) | 7.47219 | 0.314915 | 0.157458 | − | 0.987526i | \(-0.449670\pi\) | ||||
0.157458 | + | 0.987526i | \(0.449670\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.85325 | 0.0779667 | ||||||||
\(566\) | 2.60388 | 0.109449 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.3303 | 0.769124 | ||||||||
\(569\) | −0.428911 | −0.0179809 | −0.00899045 | − | 0.999960i | \(-0.502862\pi\) | ||||
−0.00899045 | + | 0.999960i | \(0.502862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.00298391 | −0.000124873 0 | −6.24363e−5 | − | 1.00000i | \(-0.500020\pi\) | ||||
−6.24363e−5 | 1.00000i | \(0.500020\pi\) | ||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.04892 | 0.252477 | ||||||||
\(575\) | 6.44504 | 0.268777 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5743 | −0.606738 | −0.303369 | − | 0.952873i | \(-0.598111\pi\) | ||||
−0.303369 | + | 0.952873i | \(0.598111\pi\) | |||||||
\(578\) | 73.5532 | 3.05941 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.1468 | 0.504366 | ||||||||
\(581\) | 33.7875 | 1.40174 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.7778 | 0.653449 | ||||||||
\(584\) | −2.37867 | −0.0984299 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.3153 | 0.839216 | ||||||||
\(587\) | −20.6329 | −0.851613 | −0.425806 | − | 0.904814i | \(-0.640010\pi\) | ||||
−0.425806 | + | 0.904814i | \(0.640010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.8146 | −0.692834 | ||||||||
\(590\) | 12.9487 | 0.533089 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 33.8364 | 1.39067 | ||||||||
\(593\) | 30.0901 | 1.23565 | 0.617825 | − | 0.786315i | \(-0.288014\pi\) | ||||
0.617825 | + | 0.786315i | \(0.288014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.3056 | 0.873444 | ||||||||
\(596\) | −23.9922 | −0.982760 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.72481 | 0.111333 | 0.0556663 | − | 0.998449i | \(-0.482272\pi\) | ||||
0.0556663 | + | 0.998449i | \(0.482272\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.9584 | −1.22203 | −0.611014 | − | 0.791620i | \(-0.709238\pi\) | ||||
−0.611014 | + | 0.791620i | \(0.709238\pi\) | |||||||
\(602\) | 20.2446 | 0.825108 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 25.9705 | 1.05672 | ||||||||
\(605\) | 1.20775 | 0.0491021 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.1116 | 1.42513 | 0.712567 | − | 0.701604i | \(-0.247532\pi\) | ||||
0.712567 | + | 0.701604i | \(0.247532\pi\) | |||||||
\(608\) | −10.8442 | −0.439788 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.98792 | 0.323421 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.4142 | −1.67270 | −0.836351 | − | 0.548194i | \(-0.815316\pi\) | ||||
−0.836351 | + | 0.548194i | \(0.815316\pi\) | |||||||
\(614\) | 7.04115 | 0.284158 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.2838 | 0.535220 | ||||||||
\(617\) | 21.1575 | 0.851769 | 0.425885 | − | 0.904778i | \(-0.359963\pi\) | ||||
0.425885 | + | 0.904778i | \(0.359963\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.39134 | 0.297083 | 0.148541 | − | 0.988906i | \(-0.452542\pi\) | ||||
0.148541 | + | 0.988906i | \(0.452542\pi\) | |||||||
\(620\) | −11.9608 | −0.480356 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.4698 | 1.02125 | ||||||||
\(623\) | 11.5579 | 0.463059 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.0325 | 1.04047 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −29.5187 | −1.17792 | ||||||||
\(629\) | −52.0930 | −2.07709 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.16660 | −0.126060 | −0.0630302 | − | 0.998012i | \(-0.520076\pi\) | ||||
−0.0630302 | + | 0.998012i | \(0.520076\pi\) | |||||||
\(632\) | −6.58940 | −0.262112 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.72886 | −0.306952 | ||||||||
\(635\) | 9.24027 | 0.366689 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −61.3279 | −2.42800 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.0858 | 0.398674 | ||||||||
\(641\) | 9.94762 | 0.392908 | 0.196454 | − | 0.980513i | \(-0.437057\pi\) | ||||
0.196454 | + | 0.980513i | \(0.437057\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7211 | 1.13265 | 0.566325 | − | 0.824182i | \(-0.308365\pi\) | ||||
0.566325 | + | 0.824182i | \(0.308365\pi\) | |||||||
\(644\) | 22.5187 | 0.887362 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0194 | 0.945030 | ||||||||
\(647\) | 9.03013 | 0.355011 | 0.177506 | − | 0.984120i | \(-0.443197\pi\) | ||||
0.177506 | + | 0.984120i | \(0.443197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.1075 | −0.985557 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.47889 | 0.332059 | ||||||||
\(653\) | −8.55496 | −0.334781 | −0.167391 | − | 0.985891i | \(-0.553534\pi\) | ||||
−0.167391 | + | 0.985891i | \(0.553534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.4886 | 0.487969 | ||||||||
\(656\) | −5.91723 | −0.231029 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.0368 | 0.586197 | ||||||||
\(659\) | 24.0847 | 0.938206 | 0.469103 | − | 0.883143i | \(-0.344577\pi\) | ||||
0.469103 | + | 0.883143i | \(0.344577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5646 | 0.994350 | 0.497175 | − | 0.867650i | \(-0.334371\pi\) | ||||
0.497175 | + | 0.867650i | \(0.334371\pi\) | |||||||
\(662\) | −44.9439 | −1.74679 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.3623 | −0.634979 | ||||||||
\(665\) | 4.91185 | 0.190474 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 62.7808 | 2.43088 | ||||||||
\(668\) | 16.2349 | 0.628147 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.42758 | −0.171052 | ||||||||
\(671\) | −15.4886 | −0.597930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.9681 | 1.15518 | 0.577592 | − | 0.816326i | \(-0.303992\pi\) | ||||
0.577592 | + | 0.816326i | \(0.303992\pi\) | |||||||
\(674\) | −54.2790 | −2.09075 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.0736715 | −0.00283143 | −0.00141571 | − | 0.999999i | \(-0.500451\pi\) | ||||
−0.00141571 | + | 0.999999i | \(0.500451\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.52781 | 0.250514 | ||||||||
\(680\) | −10.3177 | −0.395664 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 60.3889 | 2.31241 | ||||||||
\(683\) | 3.58078 | 0.137015 | 0.0685073 | − | 0.997651i | \(-0.478176\pi\) | ||||
0.0685073 | + | 0.997651i | \(0.478176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.10454 | 0.0422023 | ||||||||
\(686\) | −31.0465 | −1.18536 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.8039 | −0.755015 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.1454 | −0.728326 | −0.364163 | − | 0.931335i | \(-0.618645\pi\) | ||||
−0.364163 | + | 0.931335i | \(0.618645\pi\) | |||||||
\(692\) | −26.8672 | −1.02134 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.4228 | 1.45851 | ||||||||
\(695\) | −10.1903 | −0.386540 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.10992 | 0.345063 | ||||||||
\(698\) | 49.0519 | 1.85664 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.49396 | 0.132059 | ||||||||
\(701\) | 18.3230 | 0.692052 | 0.346026 | − | 0.938225i | \(-0.387531\pi\) | ||||
0.346026 | + | 0.938225i | \(0.387531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0097 | −0.452954 | ||||||||
\(704\) | 4.43296 | 0.167073 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.7802 | −0.819707 | ||||||||
\(707\) | 31.9584 | 1.20192 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.5084 | 0.695099 | 0.347549 | − | 0.937662i | \(-0.387014\pi\) | ||||
0.347549 | + | 0.937662i | \(0.387014\pi\) | |||||||
\(710\) | −24.3424 | −0.913555 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.59717 | −0.209763 | ||||||||
\(713\) | −61.8195 | −2.31516 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23.5743 | 0.881014 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.58642 | −0.283123 | ||||||||
\(719\) | 14.8006 | 0.551970 | 0.275985 | − | 0.961162i | \(-0.410996\pi\) | ||||
0.275985 | + | 0.961162i | \(0.410996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.2989 | −0.569760 | ||||||||
\(722\) | −28.6993 | −1.06808 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.1468 | 0.600089 | ||||||||
\(725\) | 9.74094 | 0.361769 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.76749 | 0.176817 | 0.0884083 | − | 0.996084i | \(-0.471822\pi\) | ||||
0.0884083 | + | 0.996084i | \(0.471822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.15883 | 0.116914 | ||||||||
\(731\) | 30.4892 | 1.12768 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.2416 | −0.673769 | −0.336884 | − | 0.941546i | \(-0.609373\pi\) | ||||
−0.336884 | + | 0.941546i | \(0.609373\pi\) | |||||||
\(734\) | −48.4849 | −1.78961 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −39.8689 | −1.46959 | ||||||||
\(737\) | 8.58509 | 0.316236 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.2218 | −0.596727 | −0.298363 | − | 0.954452i | \(-0.596441\pi\) | ||||
−0.298363 | + | 0.954452i | \(0.596441\pi\) | |||||||
\(740\) | −8.54288 | −0.314042 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.7995 | −0.836998 | ||||||||
\(743\) | 4.19375 | 0.153854 | 0.0769269 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769269 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.2403 | −0.704909 | ||||||||
\(746\) | −51.9788 | −1.90308 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −33.1293 | −1.21133 | ||||||||
\(749\) | 39.1933 | 1.43209 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.43727 | −0.344371 | −0.172185 | − | 0.985065i | \(-0.555083\pi\) | ||||
−0.172185 | + | 0.985065i | \(0.555083\pi\) | |||||||
\(752\) | −14.7095 | −0.536400 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.8267 | 0.757961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.80061 | 0.319864 | 0.159932 | − | 0.987128i | \(-0.448873\pi\) | ||||
0.159932 | + | 0.987128i | \(0.448873\pi\) | |||||||
\(758\) | −15.4450 | −0.560989 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.37867 | −0.0862833 | ||||||||
\(761\) | −44.4728 | −1.61214 | −0.806069 | − | 0.591822i | \(-0.798409\pi\) | ||||
−0.806069 | + | 0.591822i | \(0.798409\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.0315 | 0.833795 | ||||||||
\(764\) | 0.823708 | 0.0298007 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.1250 | −0.474225 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.521106 | 0.0187916 | 0.00939579 | − | 0.999956i | \(-0.497009\pi\) | ||||
0.00939579 | + | 0.999956i | \(0.497009\pi\) | |||||||
\(770\) | −17.6407 | −0.635727 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.0405566 | 0.00145966 | ||||||||
\(773\) | 10.3690 | 0.372946 | 0.186473 | − | 0.982460i | \(-0.440294\pi\) | ||||
0.186473 | + | 0.982460i | \(0.440294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.59179 | −0.344547 | ||||||||
\(776\) | −3.16123 | −0.113481 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.0814 | −1.00677 | ||||||||
\(779\) | 2.10023 | 0.0752485 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.2000 | 1.68895 | ||||||||
\(782\) | 88.3081 | 3.15789 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.20237 | −0.150085 | ||||||||
\(785\) | −23.6722 | −0.844896 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.1444 | −0.825007 | −0.412504 | − | 0.910956i | \(-0.635346\pi\) | ||||
−0.412504 | + | 0.910956i | \(0.635346\pi\) | |||||||
\(788\) | −18.0097 | −0.641569 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.75063 | 0.311333 | ||||||||
\(791\) | 5.19269 | 0.184631 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −57.7590 | −2.04979 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.57374 | −0.0912240 | ||||||||
\(797\) | −34.6292 | −1.22663 | −0.613315 | − | 0.789838i | \(-0.710164\pi\) | ||||
−0.613315 | + | 0.789838i | \(0.710164\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6461 | 0.801161 | ||||||||
\(800\) | −6.18598 | −0.218707 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −25.2403 | −0.891265 | ||||||||
\(803\) | −6.12498 | −0.216146 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0586 | 0.636482 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.4765 | −0.544461 | ||||||||
\(809\) | 42.8082 | 1.50506 | 0.752528 | − | 0.658561i | \(-0.228834\pi\) | ||||
0.752528 | + | 0.658561i | \(0.228834\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.5410 | 0.440373 | 0.220186 | − | 0.975458i | \(-0.429333\pi\) | ||||
0.220186 | + | 0.975458i | \(0.429333\pi\) | |||||||
\(812\) | 34.0344 | 1.19437 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 43.1323 | 1.51179 | ||||||||
\(815\) | 6.79954 | 0.238178 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.02907 | 0.245916 | ||||||||
\(818\) | 36.1661 | 1.26452 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.49396 | 0.0521713 | ||||||||
\(821\) | −11.4324 | −0.398992 | −0.199496 | − | 0.979899i | \(-0.563931\pi\) | ||||
−0.199496 | + | 0.979899i | \(0.563931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.2349 | 0.705344 | 0.352672 | − | 0.935747i | \(-0.385273\pi\) | ||||
0.352672 | + | 0.935747i | \(0.385273\pi\) | |||||||
\(824\) | 7.40880 | 0.258098 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36.2814 | 1.26239 | ||||||||
\(827\) | −47.0267 | −1.63528 | −0.817639 | − | 0.575731i | \(-0.804717\pi\) | ||||
−0.817639 | + | 0.575731i | \(0.804717\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.8291 | 0.619230 | 0.309615 | − | 0.950862i | \(-0.399800\pi\) | ||||
0.309615 | + | 0.950862i | \(0.399800\pi\) | |||||||
\(830\) | 21.7289 | 0.754220 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.46980 | 0.224165 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.0194 | 0.450554 | ||||||||
\(836\) | −7.63773 | −0.264156 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −65.1038 | −2.24897 | ||||||||
\(839\) | 11.8931 | 0.410594 | 0.205297 | − | 0.978700i | \(-0.434184\pi\) | ||||
0.205297 | + | 0.978700i | \(0.434184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 65.8859 | 2.27193 | ||||||||
\(842\) | −1.27652 | −0.0439918 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29.3139 | 1.00903 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.38404 | 0.116277 | ||||||||
\(848\) | 22.3032 | 0.765895 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.7017 | 0.469965 | ||||||||
\(851\) | −44.1540 | −1.51358 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5749 | 0.533275 | 0.266638 | − | 0.963797i | \(-0.414087\pi\) | ||||
0.266638 | + | 0.963797i | \(0.414087\pi\) | |||||||
\(854\) | 22.3817 | 0.765884 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.9801 | −0.648728 | ||||||||
\(857\) | −20.3327 | −0.694553 | −0.347276 | − | 0.937763i | \(-0.612893\pi\) | ||||
−0.347276 | + | 0.937763i | \(0.612893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.2965 | 0.897225 | 0.448612 | − | 0.893726i | \(-0.351918\pi\) | ||||
0.448612 | + | 0.893726i | \(0.351918\pi\) | |||||||
\(860\) | 5.00000 | 0.170499 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.5773 | 1.45019 | ||||||||
\(863\) | −28.6698 | −0.975931 | −0.487965 | − | 0.872863i | \(-0.662261\pi\) | ||||
−0.487965 | + | 0.872863i | \(0.662261\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.5459 | −0.732581 | ||||||||
\(866\) | −19.1817 | −0.651820 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33.5133 | −1.13752 | ||||||||
\(869\) | −16.9675 | −0.575582 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11.1535 | −0.377704 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.3588 | 0.688647 | ||||||||
\(875\) | 2.80194 | 0.0947228 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.8522 | −0.366452 | −0.183226 | − | 0.983071i | \(-0.558654\pi\) | ||||
−0.183226 | + | 0.983071i | \(0.558654\pi\) | |||||||
\(878\) | 20.6920 | 0.698322 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17.2567 | 0.581722 | ||||||||
\(881\) | 47.6118 | 1.60408 | 0.802041 | − | 0.597270i | \(-0.203748\pi\) | ||||
0.802041 | + | 0.597270i | \(0.203748\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.7469 | −1.00106 | −0.500532 | − | 0.865718i | \(-0.666862\pi\) | ||||
−0.500532 | + | 0.865718i | \(0.666862\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.72886 | 0.226060 | ||||||||
\(887\) | −18.1621 | −0.609823 | −0.304911 | − | 0.952381i | \(-0.598627\pi\) | ||||
−0.304911 | + | 0.952381i | \(0.598627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.8907 | 0.868345 | ||||||||
\(890\) | 7.43296 | 0.249153 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.7385 | −0.526965 | ||||||||
\(893\) | 5.22090 | 0.174711 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.9051 | 0.631929 | ||||||||
\(896\) | 28.2597 | 0.944089 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.14569 | −0.271825 | ||||||||
\(899\) | −93.4331 | −3.11617 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.3370 | −1.14393 | ||||||||
\(902\) | −7.54288 | −0.251150 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.51466 | −0.0836365 | ||||||||
\(905\) | 12.9487 | 0.430429 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.81641 | −0.0603130 | −0.0301565 | − | 0.999545i | \(-0.509601\pi\) | ||||
−0.0301565 | + | 0.999545i | \(0.509601\pi\) | |||||||
\(908\) | 29.1903 | 0.968714 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.5502 | −1.74106 | −0.870532 | − | 0.492111i | \(-0.836225\pi\) | ||||
−0.870532 | + | 0.492111i | \(0.836225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.1323 | −1.39437 | ||||||||
\(914\) | 29.5265 | 0.976649 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.7603 | 0.950268 | ||||||||
\(917\) | 34.9922 | 1.15555 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −59.3135 | −1.95657 | −0.978285 | − | 0.207262i | \(-0.933545\pi\) | ||||
−0.978285 | + | 0.207262i | \(0.933545\pi\) | |||||||
\(920\) | −8.74525 | −0.288322 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25.0054 | −0.823508 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.85086 | −0.225255 | ||||||||
\(926\) | −41.3599 | −1.35917 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −60.2573 | −1.97804 | ||||||||
\(929\) | 55.0629 | 1.80656 | 0.903278 | − | 0.429056i | \(-0.141154\pi\) | ||||
0.903278 | + | 0.429056i | \(0.141154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.49157 | 0.0488841 | ||||||||
\(932\) | −1.17928 | −0.0386285 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.28621 | 0.303854 | ||||||||
\(935\) | −26.5676 | −0.868854 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.6673 | −0.805844 | −0.402922 | − | 0.915234i | \(-0.632005\pi\) | ||||
−0.402922 | + | 0.915234i | \(0.632005\pi\) | |||||||
\(938\) | −12.4058 | −0.405064 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.71379 | 0.121131 | ||||||||
\(941\) | −48.8823 | −1.59352 | −0.796759 | − | 0.604297i | \(-0.793454\pi\) | ||||
−0.796759 | + | 0.604297i | \(0.793454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.72156 | 0.251449 | ||||||||
\(944\) | −35.4916 | −1.15515 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.2446 | −0.820772 | ||||||||
\(947\) | 10.2832 | 0.334160 | 0.167080 | − | 0.985943i | \(-0.446566\pi\) | ||||
0.167080 | + | 0.985943i | \(0.446566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.15883 | 0.102486 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −28.9095 | −0.936961 | ||||||||
\(953\) | −33.7458 | −1.09314 | −0.546568 | − | 0.837415i | \(-0.684066\pi\) | ||||
−0.546568 | + | 0.837415i | \(0.684066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.660563 | 0.0213753 | ||||||||
\(956\) | −25.2597 | −0.816956 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.2368 | 0.944599 | ||||||||
\(959\) | 3.09485 | 0.0999379 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.0025 | 1.96782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.67456 | −0.311597 | ||||||||
\(965\) | 0.0325239 | 0.00104698 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.6517 | −0.471168 | −0.235584 | − | 0.971854i | \(-0.575700\pi\) | ||||
−0.235584 | + | 0.971854i | \(0.575700\pi\) | |||||||
\(968\) | −1.63879 | −0.0526728 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.19806 | 0.134792 | ||||||||
\(971\) | 21.3884 | 0.686385 | 0.343192 | − | 0.939265i | \(-0.388492\pi\) | ||||
0.343192 | + | 0.939265i | \(0.388492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.5526 | −0.915353 | ||||||||
\(974\) | 58.1202 | 1.86229 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21.8944 | −0.700823 | ||||||||
\(977\) | 58.2049 | 1.86214 | 0.931070 | − | 0.364842i | \(-0.118877\pi\) | ||||
0.931070 | + | 0.364842i | \(0.118877\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4125 | −0.460626 | ||||||||
\(980\) | 1.06100 | 0.0338924 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.8931 | −0.698636 | ||||||||
\(983\) | 33.1855 | 1.05845 | 0.529227 | − | 0.848481i | \(-0.322482\pi\) | ||||
0.529227 | + | 0.848481i | \(0.322482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.4426 | −0.460181 | ||||||||
\(986\) | 133.468 | 4.25047 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.8426 | 0.821747 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.4166 | −0.680320 | −0.340160 | − | 0.940368i | \(-0.610481\pi\) | ||||
−0.340160 | + | 0.940368i | \(0.610481\pi\) | |||||||
\(992\) | 59.3347 | 1.88388 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −68.2059 | −2.16336 | ||||||||
\(995\) | −2.06398 | −0.0654327 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.76330 | −0.309207 | −0.154603 | − | 0.987977i | \(-0.549410\pi\) | ||||
−0.154603 | + | 0.987977i | \(0.549410\pi\) | |||||||
\(998\) | −55.7163 | −1.76367 | ||||||||
\(999\) | 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 | 7605.2.a.cb.1.3 | 3 | ||
3.2 | odd | 2 | 2535.2.a.w.1.1 | ✓ | 3 | ||
13.12 | even | 2 | 7605.2.a.bo.1.1 | 3 | |||
39.38 | odd | 2 | 2535.2.a.bf.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2535.2.a.w.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
2535.2.a.bf.1.3 | yes | 3 | 39.38 | odd | 2 | ||
7605.2.a.bo.1.1 | 3 | 13.12 | even | 2 | |||
7605.2.a.cb.1.3 | 3 | 1.1 | even | 1 | trivial |