Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(5,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 11, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.s (of order \(22\), degree \(10\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 581.1 | ||
Root | \(0.0475819 + 0.998867i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.581 |
Dual form | 804.2.s.a.137.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{9}{22}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.71442 | + | 0.246497i | −0.989821 | + | 0.142315i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.43029 | − | 4.87111i | −0.540597 | − | 1.84111i | −0.540871 | − | 0.841105i | \(-0.681905\pi\) |
0.000273951 | − | 1.00000i | \(-0.499913\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.87848 | − | 0.845198i | 0.959493 | − | 0.281733i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.44973 | + | 4.72222i | −1.51148 | + | 1.30971i | −0.752753 | + | 0.658303i | \(0.771274\pi\) |
−0.758731 | + | 0.651404i | \(0.774180\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19755 | + | 0.645259i | 0.504152 | + | 0.148032i | 0.523912 | − | 0.851772i | \(-0.324472\pi\) |
−0.0197599 | + | 0.999805i | \(0.506290\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.65282 | + | 7.99857i | 0.797111 | + | 1.74543i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.27430 | + | 3.77875i | 0.654861 | + | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.72659 | + | 2.15856i | −0.909632 | + | 0.415415i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.512845 | − | 0.444383i | −0.0921097 | − | 0.0798135i | 0.607589 | − | 0.794252i | \(-0.292137\pi\) |
−0.699699 | + | 0.714438i | \(0.746682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.7846 | −1.93738 | −0.968688 | − | 0.248283i | \(-0.920134\pi\) | ||||
−0.968688 | + | 0.248283i | \(0.920134\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.17912 | − | 9.43921i | 1.30971 | − | 1.51148i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.94805 | + | 10.8114i | −1.05957 | + | 1.64872i | −0.362039 | + | 0.932163i | \(0.617919\pi\) |
−0.697529 | + | 0.716557i | \(0.745717\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.7932 | + | 10.1497i | −2.25617 | + | 1.44995i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.92658 | − | 0.564557i | −0.520088 | − | 0.0747774i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7083 | + | 5.34702i | −1.49910 | + | 0.684616i | −0.984911 | − | 0.173061i | \(-0.944634\pi\) |
−0.514188 | + | 0.857677i | \(0.671907\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.23410 | − | 12.8125i | −1.03740 | − | 1.61422i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.92989 | − | 7.18025i | −0.480112 | − | 0.877207i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.96168 | + | 15.2440i | 0.814803 | + | 1.78417i | 0.585206 | + | 0.810885i | \(0.301014\pi\) |
0.229598 | + | 0.973286i | \(0.426259\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.54498 | − | 5.67126i | −0.755750 | − | 0.654861i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8567 | − | 9.40741i | 1.22148 | − | 1.05842i | 0.225018 | − | 0.974355i | \(-0.427756\pi\) |
0.996461 | − | 0.0840621i | \(-0.0267894\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.57128 | − | 4.86577i | 0.841254 | − | 0.540641i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.7971 | + | 19.7921i | 3.22841 | + | 2.07478i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.988771 | + | 0.635445i | 0.102531 | + | 0.0658926i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.8295i | − | 1.60724i | −0.595143 | − | 0.803620i | \(-0.702905\pi\) | ||
0.595143 | − | 0.803620i | \(-0.297095\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2058 | + | 15.2403i | −1.30121 | + | 1.50167i | −0.564562 | + | 0.825391i | \(0.690955\pi\) |
−0.736644 | + | 0.676281i | \(0.763591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.90023 | − | 6.84559i | 0.756705 | − | 0.655688i | −0.188534 | − | 0.982067i | \(-0.560374\pi\) |
0.945239 | + | 0.326378i | \(0.105828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.2038 | − | 2.90486i | 1.91766 | − | 0.275717i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.6957 | + | 18.1989i | −1.08127 | + | 1.68249i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.20347 | + | 8.31325i | 0.654861 | + | 0.755750i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.03085 | + | 1.47719i | −0.446415 | + | 0.131079i | −0.497211 | − | 0.867630i | \(-0.665643\pi\) |
0.0507955 | + | 0.998709i | \(0.483824\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.24692 | − | 20.2479i | 0.814146 | − | 1.78273i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 11.6274i | − | 1.00822i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1638 | − | 5.55500i | −1.03172 | − | 0.471169i | −0.173704 | − | 0.984798i | \(-0.555574\pi\) |
−0.858013 | + | 0.513629i | \(0.828301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.5743 | − | 21.2938i | 2.02686 | − | 1.75628i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.9537 | − | 12.8235i | −1.62381 | − | 1.04356i | −0.953460 | − | 0.301518i | \(-0.902507\pi\) |
−0.670352 | − | 0.742043i | \(-0.733857\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.07835 | + | 7.50008i | 0.0860615 | + | 0.598571i | 0.986521 | + | 0.163632i | \(0.0523210\pi\) |
−0.900460 | + | 0.434939i | \(0.856770\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.8399 | 1.55398 | 0.776989 | − | 0.629514i | \(-0.216746\pi\) | ||||
0.776989 | + | 0.629514i | \(0.216746\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.55012 | − | 38.6020i | 0.426933 | − | 2.96938i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.87097 | 0.525436 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.7235 | − | 21.3542i | 1.03740 | − | 1.61422i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.50254 | + | 10.4504i | 0.111683 | + | 0.776773i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) |
−0.854599 | + | 0.519288i | \(0.826197\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.7550 | − | 12.0531i | 1.38641 | − | 0.890991i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.2749 | + | 19.9364i | 1.25657 | + | 1.45016i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.85622 | + | 4.45032i | −0.277577 | + | 0.320341i | −0.877370 | − | 0.479814i | \(-0.840704\pi\) |
0.599793 | + | 0.800155i | \(0.295250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.8040 | + | 6.10860i | −1.47476 | + | 0.433027i | −0.917642 | − | 0.397409i | \(-0.869909\pi\) |
−0.557114 | + | 0.830436i | \(0.688091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.50739 | + | 11.3413i | 0.600065 | + | 0.799951i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.19318 | − | 15.2539i | 0.150985 | − | 1.05012i | −0.763589 | − | 0.645703i | \(-0.776565\pi\) |
0.914574 | − | 0.404419i | \(-0.132526\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.43112 | + | 3.13372i | −0.0971508 | + | 0.212731i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.6928 | − | 24.4185i | −1.06042 | − | 1.65005i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.896827 | − | 6.23757i | 0.0600560 | − | 0.417698i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) |
0.997565 | − | 0.0697384i | \(-0.0222164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.6188 | + | 8.10961i | 0.841254 | + | 0.540641i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.27894 | − | 1.97471i | −0.150596 | − | 0.130493i | 0.576304 | − | 0.817235i | \(-0.304494\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.2941 | + | 18.8044i | −1.05842 | + | 1.22148i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.89188 | + | 10.7117i | 0.315114 | + | 0.690003i | 0.999225 | − | 0.0393750i | \(-0.0125367\pi\) |
−0.684111 | + | 0.729378i | \(0.739809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.7810 | + | 10.2083i | −0.755750 | + | 0.654861i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.0231 | + | 6.86082i | −0.955897 | + | 0.436544i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.8553 | + | 57.4040i | 1.04734 | + | 3.56691i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.2580 | + | 3.48777i | −1.47357 | + | 0.211867i | −0.831818 | − | 0.555048i | \(-0.812700\pi\) |
−0.641748 | + | 0.766915i | \(0.721791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −57.6779 | − | 26.3406i | −3.49082 | − | 1.59421i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.7684 | − | 9.32805i | 1.90878 | − | 0.560468i | 0.925372 | − | 0.379060i | \(-0.123753\pi\) |
0.983408 | − | 0.181408i | \(-0.0580655\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.85181 | − | 0.845691i | −0.110865 | − | 0.0506302i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.8251 | − | 6.40842i | −1.29737 | − | 0.380941i | −0.441091 | − | 0.897462i | \(-0.645408\pi\) |
−0.856274 | + | 0.516522i | \(0.827227\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.06206 | + | 15.4637i | 0.415415 | + | 0.909632i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.90191 | + | 27.1384i | 0.228734 | + | 1.59088i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 62.6011 | + | 18.3813i | 3.60827 | + | 1.05948i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8525 | − | 22.9110i | 1.13304 | − | 1.30760i | 0.187437 | − | 0.982277i | \(-0.439982\pi\) |
0.945603 | − | 0.325322i | \(-0.105473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.8836 | − | 29.3835i | 1.07425 | − | 1.67157i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1846 | − | 2.90210i | −1.14090 | − | 0.164037i | −0.454146 | − | 0.890927i | \(-0.650056\pi\) |
−0.686753 | + | 0.726891i | \(0.740965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −35.6881 | − | 5.13118i | −1.97962 | − | 0.284627i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.8569 | + | 13.6836i | −0.655688 | + | 0.756705i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.4571 | − | 28.7198i | −1.01449 | − | 1.57858i | −0.798327 | − | 0.602224i | \(-0.794281\pi\) |
−0.216166 | − | 0.976357i | \(-0.569355\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −33.9217 | + | 9.96031i | −1.85890 | + | 0.545822i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.68281 | − | 15.9482i | −0.255089 | − | 0.868753i | −0.983082 | − | 0.183168i | \(-0.941365\pi\) |
0.727993 | − | 0.685585i | \(-0.240453\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 45.1716 | + | 39.1414i | 2.43904 | + | 2.11344i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.09026 | − | 1.98599i | 0.165418 | − | 0.106308i | −0.455313 | − | 0.890332i | \(-0.650472\pi\) |
0.620730 | + | 0.784024i | \(0.286836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.5654 | − | 34.0835i | 0.830821 | − | 1.81925i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5710 | − | 7.43620i | −0.608998 | − | 0.391379i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.3990 | − | 12.4768i | −0.755750 | − | 0.654861i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2698 | − | 2.77058i | −1.00588 | − | 0.144623i | −0.380363 | − | 0.924837i | \(-0.624201\pi\) |
−0.625513 | + | 0.780214i | \(0.715110\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.3534i | − | 0.898525i | −0.893400 | − | 0.449262i | \(-0.851687\pi\) | ||
0.893400 | − | 0.449262i | \(-0.148313\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −38.4204 | + | 5.52401i | −1.97352 | + | 0.283750i | −0.975578 | + | 0.219653i | \(0.929507\pi\) |
−0.997944 | + | 0.0640964i | \(0.979583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.26087 | − | 3.77261i | 0.423217 | − | 0.193277i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.8621 | + | 36.9928i | −0.552150 | + | 1.88045i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.21394 | − | 15.7963i | 0.362057 | − | 0.792794i | −0.637690 | − | 0.770293i | \(-0.720110\pi\) |
0.999747 | − | 0.0225011i | \(-0.00716292\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.86611 | + | 19.9343i | 0.143485 | + | 0.997961i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.89334 | 0.243755 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.3601 | + | 38.6888i | 0.561719 | + | 1.91304i | 0.356332 | + | 0.934359i | \(0.384027\pi\) |
0.205387 | + | 0.978681i | \(0.434155\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.2231 | + | 6.52529i | 1.08827 | + | 0.319545i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2961 | − | 3.31684i | −0.550539 | − | 0.161653i | −0.00537983 | − | 0.999986i | \(-0.501712\pi\) |
−0.545159 | + | 0.838333i | \(0.683531\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 42.7922 | + | 49.3848i | 2.07086 | + | 2.38990i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.7154 | − | 18.8165i | −1.04357 | − | 0.904262i | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) |
−0.995517 | + | 0.0945826i | \(0.969848\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.69959 | 0.319754 | 0.159877 | − | 0.987137i | \(-0.448890\pi\) | ||||
0.159877 | + | 0.987137i | \(0.448890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.8819 | + | 42.5640i | −1.75628 | + | 2.02686i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.3701 | + | 17.0663i | 1.75580 | + | 0.801847i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.9527 | − | 16.1023i | −0.652679 | − | 0.753232i | 0.328884 | − | 0.944370i | \(-0.393327\pi\) |
−0.981563 | + | 0.191139i | \(0.938782\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.3831 | + | 17.5290i | −1.78381 | + | 0.814640i | −0.810296 | + | 0.586021i | \(0.800693\pi\) |
−0.973516 | + | 0.228618i | \(0.926579\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.3549 | + | 29.4127i | −1.35548 | + | 1.35815i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.69749 | − | 12.5925i | −0.170371 | − | 0.580231i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.75717 | + | 10.4168i | 0.218274 | + | 0.477954i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 64.2229 | − | 55.6494i | 2.92831 | − | 2.53740i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.4364 | − | 22.4635i | −0.654176 | − | 1.01792i | −0.996915 | − | 0.0784867i | \(-0.974991\pi\) |
0.342739 | − | 0.939430i | \(-0.388645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −34.0139 | + | 4.89046i | −1.53816 | + | 0.221154i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.76745i | 0.168654i | 0.996438 | + | 0.0843271i | \(0.0268741\pi\) | ||||
−0.996438 | + | 0.0843271i | \(0.973126\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 67.5481i | 2.99992i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 64.2978 | − | 55.7143i | 2.84437 | − | 2.46466i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.7797 | + | 1.69367i | −0.520088 | + | 0.0747774i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.28177 | + | 3.78737i | 0.143502 | + | 0.165610i | 0.822951 | − | 0.568113i | \(-0.192326\pi\) |
−0.679449 | + | 0.733723i | \(0.737781\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.2641 | + | 39.9928i | −0.797111 | + | 1.74543i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0683 | + | 6.47985i | −0.959493 | + | 0.281733i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3204 | − | 7.90996i | −0.744662 | − | 0.340076i | 0.00668980 | − | 0.999978i | \(-0.497871\pi\) |
−0.751352 | + | 0.659902i | \(0.770598\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.15198 | − | 17.5460i | −0.221093 | − | 0.752972i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.2272 | + | 17.4578i | 1.63448 | + | 0.746441i | 0.999656 | − | 0.0262168i | \(-0.00834602\pi\) |
0.634822 | + | 0.772658i | \(0.281073\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.1829 | + | 25.2871i | −1.24550 | + | 1.07923i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −61.3528 | − | 39.4290i | −2.60898 | − | 1.67669i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.1887 | − | 91.7293i | −0.557822 | − | 3.87974i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −34.5308 | − | 29.9211i | −1.45016 | − | 1.25657i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.66773 | + | 46.3751i | −0.279036 | + | 1.94074i | 0.0557537 | + | 0.998445i | \(0.482244\pi\) |
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.7341 | + | 40.0430i | −1.07132 | + | 1.66701i | −0.421756 | + | 0.906709i | \(0.638586\pi\) |
−0.649568 | + | 0.760303i | \(0.725050\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.51420 | − | 8.58027i | 0.229162 | − | 0.356584i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.840261 | − | 1.30747i | −0.0346223 | − | 0.0538734i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.1610 | − | 15.6008i | 1.39812 | − | 0.638499i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.6443 | − | 13.6960i | 1.90266 | − | 0.558672i | 0.914659 | − | 0.404226i | \(-0.132459\pi\) |
0.988001 | − | 0.154446i | \(-0.0493591\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.3808 | − | 17.3467i | −0.707802 | − | 0.706411i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.47026 | + | 3.51552i | −0.222031 | + | 0.142691i | −0.646928 | − | 0.762551i | \(-0.723947\pi\) |
0.424897 | + | 0.905242i | \(0.360310\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.92868 | − | 34.2797i | 0.199067 | − | 1.38454i | −0.607930 | − | 0.793990i | \(-0.708000\pi\) |
0.806998 | − | 0.590554i | \(-0.201091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.87674 | + | 19.4373i | −0.356786 | + | 0.781253i | 0.643094 | + | 0.765787i | \(0.277650\pi\) |
−0.999880 | + | 0.0154656i | \(0.995077\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.55787 | + | 24.7455i | −0.142315 | + | 0.989821i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.3065 | + | 26.2607i | 1.20648 | + | 1.04542i | 0.997722 | + | 0.0674546i | \(0.0214878\pi\) |
0.208759 | + | 0.977967i | \(0.433058\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.6922i | 1.06092i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.1397 | − | 129.892i | 1.51115 | − | 5.14650i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.97674 | + | 15.2769i | 0.275136 | + | 0.602463i | 0.995874 | − | 0.0907437i | \(-0.0289244\pi\) |
−0.720738 | + | 0.693207i | \(0.756197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.68109 | − | 5.72528i | 0.0658873 | − | 0.224391i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.9232 | + | 37.9954i | 1.28446 | + | 1.48234i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.9982 | + | 47.6736i | 0.544468 | + | 1.85429i | 0.519279 | + | 0.854605i | \(0.326201\pi\) |
0.0251892 | + | 0.999683i | \(0.491981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.9149i | 0.421994i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.3211 | − | 5.65352i | 1.51572 | − | 0.217927i | 0.666314 | − | 0.745672i | \(-0.267871\pi\) |
0.849403 | + | 0.527744i | \(0.176962\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.6329 | − | 10.7928i | −0.909632 | − | 0.415415i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −77.1071 | + | 22.6407i | −2.95910 | + | 0.868869i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.39382 | + | 2.82373i | 0.167635 | + | 0.107732i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.4896 | + | 40.4866i | 0.703378 | + | 1.54018i | 0.835827 | + | 0.548994i | \(0.184989\pi\) |
−0.132448 | + | 0.991190i | \(0.542284\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.8972 | − | 7.60411i | −0.976732 | − | 0.286794i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.4861 | − | 38.6450i | 1.25760 | − | 1.45134i | 0.417714 | − | 0.908579i | \(-0.362832\pi\) |
0.839884 | − | 0.542766i | \(-0.182623\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.2998 | − | 36.2551i | 0.873809 | − | 1.35967i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 93.1252 | + | 42.5289i | 3.46816 | + | 1.58386i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.0272 | − | 17.1586i | −0.410104 | − | 0.638135i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.5068 | + | 7.11800i | 1.83611 | + | 0.263992i | 0.971256 | − | 0.238039i | \(-0.0765045\pi\) |
0.864850 | + | 0.502031i | \(0.167414\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.6812 | − | 20.4052i | 0.654861 | − | 0.755750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.16602 | − | 4.92643i | −0.116940 | − | 0.181962i | 0.777849 | − | 0.628451i | \(-0.216311\pi\) |
−0.894789 | + | 0.446489i | \(0.852674\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.87827 | + | 33.6423i | 0.363378 | + | 1.23755i | 0.914999 | + | 0.403456i | \(0.132191\pi\) |
−0.551621 | + | 0.834095i | \(0.685990\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.0648 | − | 15.4655i | 0.884041 | − | 0.568139i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.9231 | + | 18.5878i | −1.05542 | + | 0.678278i | −0.948753 | − | 0.316017i | \(-0.897654\pi\) |
−0.106667 | + | 0.994295i | \(0.534018\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.3512 | + | 6.23296i | −1.57563 | + | 0.226541i | −0.873972 | − | 0.485977i | \(-0.838464\pi\) |
−0.701654 | + | 0.712517i | \(0.747555\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.6452 | − | 28.6917i | −1.61626 | − | 1.03871i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.4305 | + | 4.95036i | 1.24160 | + | 0.178515i | 0.731643 | − | 0.681688i | \(-0.238754\pi\) |
0.509953 | + | 0.860202i | \(0.329663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.39296i | − | 0.121879i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −43.0470 | − | 94.2599i | −1.54430 | − | 3.38155i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.1074 | − | 37.5119i | 0.859337 | − | 1.33715i | −0.0809308 | − | 0.996720i | \(-0.525789\pi\) |
0.940268 | − | 0.340435i | \(-0.110574\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.5575 | − | 84.4292i | 1.36922 | − | 2.99817i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.8408 | − | 47.1375i | −0.486017 | − | 1.65522i | −0.728485 | − | 0.685062i | \(-0.759775\pi\) |
0.242469 | − | 0.970159i | \(-0.422043\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.7286 | − | 11.9590i | 1.42842 | − | 0.419421i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.2448 | + | 19.2752i | −0.778248 | + | 0.674355i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 105.377 | + | 30.9415i | 3.68217 | + | 1.08118i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.3177 | + | 12.1320i | 1.44024 | + | 0.422894i | 0.906303 | − | 0.422628i | \(-0.138892\pi\) |
0.533940 | + | 0.845522i | \(0.320711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0771 | − | 15.0918i | −0.454187 | − | 0.524160i | 0.481759 | − | 0.876304i | \(-0.339998\pi\) |
−0.935946 | + | 0.352144i | \(0.885453\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −52.1651 | + | 23.8230i | −1.80959 | + | 0.826411i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.38323 | + | 0.993407i | 0.116942 | + | 0.0343372i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.1917 | − | 46.9792i | 1.03740 | − | 1.61422i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38.9970 | + | 5.60692i | 1.33837 | + | 0.192429i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.5476 | − | 17.7038i | 0.943213 | − | 0.606166i | 0.0239089 | − | 0.999714i | \(-0.492389\pi\) |
0.919304 | + | 0.393548i | \(0.128752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.5873 | + | 37.6077i | 1.11186 | + | 1.28316i | 0.955348 | + | 0.295484i | \(0.0954809\pi\) |
0.156516 | + | 0.987675i | \(0.449974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.9191 | − | 24.7706i | −0.540641 | − | 0.841254i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.3235 | + | 20.5726i | 1.87457 | + | 0.697077i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.3790 | − | 45.5648i | −0.452812 | − | 1.54213i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.2279 | − | 42.1033i | −0.649281 | − | 1.42173i | −0.892182 | − | 0.451676i | \(-0.850826\pi\) |
0.242901 | − | 0.970051i | \(-0.421901\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.3183 | + | 10.6739i | −0.414544 | + | 0.359204i | −0.837022 | − | 0.547169i | \(-0.815706\pi\) |
0.422478 | + | 0.906373i | \(0.361160\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3911 | + | 22.3930i | 0.482662 | + | 0.751037i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −111.856 | − | 16.0824i | −3.72232 | − | 0.535189i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.9440 | + | 18.4003i | −0.529412 | + | 0.610974i | −0.955962 | − | 0.293490i | \(-0.905183\pi\) |
0.426551 | + | 0.904464i | \(0.359729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9750 | + | 57.8116i | −0.559954 | + | 1.90703i | −0.173030 | + | 0.984917i | \(0.555356\pi\) |
−0.386924 | + | 0.922112i | \(0.626462\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.3880 | + | 44.1726i | −0.935417 | + | 1.45554i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.5863 | − | 44.5310i | −1.26871 | − | 1.46417i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.1315 | + | 55.0304i | −0.825428 | + | 1.80744i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.2555 | + | 12.1137i | −1.35209 | + | 0.397010i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.5703i | − | 1.06403i | −0.846736 | − | 0.532013i | \(-0.821436\pi\) | ||
0.846736 | − | 0.532013i | \(-0.178564\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.3202 | 1.15263 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −109.925 | − | 50.2009i | −3.56830 | − | 1.62959i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.34623 | − | 30.2287i | −0.140201 | − | 0.975118i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61.1366 | 1.96602 | 0.983010 | − | 0.183550i | \(-0.0587588\pi\) | ||||
0.983010 | + | 0.183550i | \(0.0587588\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.66136 | + | 67.1962i | −0.309729 | + | 2.15421i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 62.4493 | 1.99998 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.9548 | − | 26.3821i | 0.541324 | − | 0.842317i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.5245 | − | 17.9324i | −0.366086 | − | 0.569642i | 0.608528 | − | 0.793533i | \(-0.291760\pi\) |
−0.974614 | + | 0.223891i | \(0.928124\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.7225 | + | 44.6882i | 1.22882 | + | 1.41814i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.4855 | + | 45.5687i | −1.25052 | + | 1.44317i | −0.400606 | + | 0.916251i | \(0.631200\pi\) |
−0.849912 | + | 0.526924i | \(0.823345\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 55.7009 | − | 25.4377i | 1.76230 | − | 0.804815i |
(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 | 804.2.s.a.581.1 | yes | 20 | |
3.2 | odd | 2 | CM | 804.2.s.a.581.1 | yes | 20 | |
67.3 | odd | 22 | inner | 804.2.s.a.137.1 | ✓ | 20 | |
201.137 | even | 22 | inner | 804.2.s.a.137.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.s.a.137.1 | ✓ | 20 | 67.3 | odd | 22 | inner | |
804.2.s.a.137.1 | ✓ | 20 | 201.137 | even | 22 | inner | |
804.2.s.a.581.1 | yes | 20 | 1.1 | even | 1 | trivial | |
804.2.s.a.581.1 | yes | 20 | 3.2 | odd | 2 | CM |