Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), 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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.2 | ||
Root | \(-3.38526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.19 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.38526i | − | 1.69263i | −0.532684 | − | 0.846315i | \(-0.678816\pi\) | ||
0.532684 | − | 0.846315i | \(-0.321184\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −7.45997 | −1.86499 | ||||||||
\(5\) | 9.27487 | 1.85497 | 0.927487 | − | 0.373855i | \(-0.121964\pi\) | ||||
0.927487 | + | 0.373855i | \(0.121964\pi\) | |||||||
\(6\) | − | 5.86344i | − | 0.977240i | ||||||
\(7\) | −9.96030 | −1.42290 | −0.711450 | − | 0.702736i | \(-0.751961\pi\) | ||||
−0.711450 | + | 0.702736i | \(0.751961\pi\) | |||||||
\(8\) | 11.7129i | 1.46411i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 31.3978i | − | 3.13978i | ||||||
\(11\) | − | 20.5213i | − | 1.86557i | −0.360434 | − | 0.932785i | \(-0.617371\pi\) | ||
0.360434 | − | 0.932785i | \(-0.382629\pi\) | |||||||
\(12\) | −12.9211 | −1.07675 | ||||||||
\(13\) | − | 4.19899i | − | 0.323000i | −0.986873 | − | 0.161500i | \(-0.948367\pi\) | ||
0.986873 | − | 0.161500i | \(-0.0516331\pi\) | |||||||
\(14\) | 33.7182i | 2.40844i | ||||||||
\(15\) | 16.0645 | 1.07097 | ||||||||
\(16\) | 9.81130 | 0.613206 | ||||||||
\(17\) | 0.362285 | 0.0213109 | 0.0106554 | − | 0.999943i | \(-0.496608\pi\) | ||||
0.0106554 | + | 0.999943i | \(0.496608\pi\) | |||||||
\(18\) | − | 10.1558i | − | 0.564210i | ||||||
\(19\) | 11.7217 | 0.616930 | 0.308465 | − | 0.951236i | \(-0.400185\pi\) | ||||
0.308465 | + | 0.951236i | \(0.400185\pi\) | |||||||
\(20\) | −69.1903 | −3.45951 | ||||||||
\(21\) | −17.2518 | −0.821512 | ||||||||
\(22\) | −69.4698 | −3.15772 | ||||||||
\(23\) | 21.5797i | 0.938249i | 0.883132 | + | 0.469125i | \(0.155431\pi\) | ||||
−0.883132 | + | 0.469125i | \(0.844569\pi\) | |||||||
\(24\) | 20.2873i | 0.845306i | ||||||||
\(25\) | 61.0232 | 2.44093 | ||||||||
\(26\) | −14.2147 | −0.546718 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 74.3036 | 2.65370 | ||||||||
\(29\) | 18.1338 | 0.625303 | 0.312651 | − | 0.949868i | \(-0.398783\pi\) | ||||
0.312651 | + | 0.949868i | \(0.398783\pi\) | |||||||
\(30\) | − | 54.3826i | − | 1.81275i | ||||||
\(31\) | 42.6196i | 1.37483i | 0.726266 | + | 0.687414i | \(0.241254\pi\) | ||||
−0.726266 | + | 0.687414i | \(0.758746\pi\) | |||||||
\(32\) | 13.6378i | 0.426182i | ||||||||
\(33\) | − | 35.5439i | − | 1.07709i | ||||||
\(34\) | − | 1.22643i | − | 0.0360714i | ||||||
\(35\) | −92.3805 | −2.63944 | ||||||||
\(36\) | −22.3799 | −0.621664 | ||||||||
\(37\) | 46.4991i | 1.25673i | 0.777917 | + | 0.628367i | \(0.216276\pi\) | ||||
−0.777917 | + | 0.628367i | \(0.783724\pi\) | |||||||
\(38\) | − | 39.6809i | − | 1.04423i | ||||||
\(39\) | − | 7.27287i | − | 0.186484i | ||||||
\(40\) | 108.636i | 2.71589i | ||||||||
\(41\) | 16.1117 | 0.392968 | 0.196484 | − | 0.980507i | \(-0.437048\pi\) | ||||
0.196484 | + | 0.980507i | \(0.437048\pi\) | |||||||
\(42\) | 58.4016i | 1.39052i | ||||||||
\(43\) | − | 30.4120i | − | 0.707257i | −0.935386 | − | 0.353628i | \(-0.884948\pi\) | ||
0.935386 | − | 0.353628i | \(-0.115052\pi\) | |||||||
\(44\) | 153.088i | 3.47927i | ||||||||
\(45\) | 27.8246 | 0.618325 | ||||||||
\(46\) | 73.0530 | 1.58811 | ||||||||
\(47\) | 5.06360i | 0.107736i | 0.998548 | + | 0.0538681i | \(0.0171551\pi\) | ||||
−0.998548 | + | 0.0538681i | \(0.982845\pi\) | |||||||
\(48\) | 16.9937 | 0.354035 | ||||||||
\(49\) | 50.2077 | 1.02465 | ||||||||
\(50\) | − | 206.579i | − | 4.13159i | ||||||
\(51\) | 0.627496 | 0.0123038 | ||||||||
\(52\) | 31.3244i | 0.602392i | ||||||||
\(53\) | 36.6918 | 0.692299 | 0.346149 | − | 0.938179i | \(-0.387489\pi\) | ||||
0.346149 | + | 0.938179i | \(0.387489\pi\) | |||||||
\(54\) | − | 17.5903i | − | 0.325747i | ||||||
\(55\) | − | 190.332i | − | 3.46058i | ||||||
\(56\) | − | 116.664i | − | 2.08329i | ||||||
\(57\) | 20.3025 | 0.356185 | ||||||||
\(58\) | − | 61.3875i | − | 1.05841i | ||||||
\(59\) | −52.1348 | + | 27.6217i | −0.883641 | + | 0.468164i | ||||
\(60\) | −119.841 | −1.99735 | ||||||||
\(61\) | 32.0930i | 0.526115i | 0.964780 | + | 0.263058i | \(0.0847309\pi\) | ||||
−0.964780 | + | 0.263058i | \(0.915269\pi\) | |||||||
\(62\) | 144.279 | 2.32707 | ||||||||
\(63\) | −29.8809 | −0.474300 | ||||||||
\(64\) | 85.4127 | 1.33457 | ||||||||
\(65\) | − | 38.9451i | − | 0.599156i | ||||||
\(66\) | −120.325 | −1.82311 | ||||||||
\(67\) | − | 81.4723i | − | 1.21600i | −0.793936 | − | 0.608002i | \(-0.791971\pi\) | ||
0.793936 | − | 0.608002i | \(-0.208029\pi\) | |||||||
\(68\) | −2.70263 | −0.0397446 | ||||||||
\(69\) | 37.3772i | 0.541699i | ||||||||
\(70\) | 312.732i | 4.46760i | ||||||||
\(71\) | 9.92600 | 0.139803 | 0.0699014 | − | 0.997554i | \(-0.477732\pi\) | ||||
0.0699014 | + | 0.997554i | \(0.477732\pi\) | |||||||
\(72\) | 35.1387i | 0.488038i | ||||||||
\(73\) | − | 43.0824i | − | 0.590170i | −0.955471 | − | 0.295085i | \(-0.904652\pi\) | ||
0.955471 | − | 0.295085i | \(-0.0953480\pi\) | |||||||
\(74\) | 157.412 | 2.12718 | ||||||||
\(75\) | 105.695 | 1.40927 | ||||||||
\(76\) | −87.4433 | −1.15057 | ||||||||
\(77\) | 204.398i | 2.65452i | ||||||||
\(78\) | −24.6205 | −0.315648 | ||||||||
\(79\) | −104.049 | −1.31708 | −0.658541 | − | 0.752545i | \(-0.728826\pi\) | ||||
−0.658541 | + | 0.752545i | \(0.728826\pi\) | |||||||
\(80\) | 90.9985 | 1.13748 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 54.5422i | − | 0.665149i | ||||||
\(83\) | 118.124i | 1.42318i | 0.702597 | + | 0.711588i | \(0.252023\pi\) | ||||
−0.702597 | + | 0.711588i | \(0.747977\pi\) | |||||||
\(84\) | 128.698 | 1.53211 | ||||||||
\(85\) | 3.36014 | 0.0395311 | ||||||||
\(86\) | −102.953 | −1.19712 | ||||||||
\(87\) | 31.4086 | 0.361019 | ||||||||
\(88\) | 240.364 | 2.73140 | ||||||||
\(89\) | − | 48.1069i | − | 0.540527i | −0.962786 | − | 0.270264i | \(-0.912889\pi\) | ||
0.962786 | − | 0.270264i | \(-0.0871108\pi\) | |||||||
\(90\) | − | 94.1935i | − | 1.04659i | ||||||
\(91\) | 41.8233i | 0.459596i | ||||||||
\(92\) | − | 160.984i | − | 1.74983i | ||||||
\(93\) | 73.8194i | 0.793757i | ||||||||
\(94\) | 17.1416 | 0.182358 | ||||||||
\(95\) | 108.717 | 1.14439 | ||||||||
\(96\) | 23.6214i | 0.246056i | ||||||||
\(97\) | 125.543i | 1.29426i | 0.762379 | + | 0.647130i | \(0.224031\pi\) | ||||
−0.762379 | + | 0.647130i | \(0.775969\pi\) | |||||||
\(98\) | − | 169.966i | − | 1.73435i | ||||||
\(99\) | − | 61.5638i | − | 0.621856i | ||||||
\(100\) | −455.232 | −4.55232 | ||||||||
\(101\) | 34.1908i | 0.338523i | 0.985571 | + | 0.169261i | \(0.0541382\pi\) | ||||
−0.985571 | + | 0.169261i | \(0.945862\pi\) | |||||||
\(102\) | − | 2.12424i | − | 0.0208258i | ||||||
\(103\) | 119.958i | 1.16464i | 0.812959 | + | 0.582321i | \(0.197855\pi\) | ||||
−0.812959 | + | 0.582321i | \(0.802145\pi\) | |||||||
\(104\) | 49.1824 | 0.472908 | ||||||||
\(105\) | −160.008 | −1.52388 | ||||||||
\(106\) | − | 124.211i | − | 1.17180i | ||||||
\(107\) | 39.8153 | 0.372106 | 0.186053 | − | 0.982540i | \(-0.440430\pi\) | ||||
0.186053 | + | 0.982540i | \(0.440430\pi\) | |||||||
\(108\) | −38.7632 | −0.358918 | ||||||||
\(109\) | − | 168.447i | − | 1.54538i | −0.634781 | − | 0.772692i | \(-0.718910\pi\) | ||
0.634781 | − | 0.772692i | \(-0.281090\pi\) | |||||||
\(110\) | −644.323 | −5.85748 | ||||||||
\(111\) | 80.5389i | 0.725575i | ||||||||
\(112\) | −97.7235 | −0.872532 | ||||||||
\(113\) | − | 23.4960i | − | 0.207929i | −0.994581 | − | 0.103965i | \(-0.966847\pi\) | ||
0.994581 | − | 0.103965i | \(-0.0331529\pi\) | |||||||
\(114\) | − | 68.7293i | − | 0.602888i | ||||||
\(115\) | 200.149i | 1.74043i | ||||||||
\(116\) | −135.278 | −1.16619 | ||||||||
\(117\) | − | 12.5970i | − | 0.107667i | ||||||
\(118\) | 93.5065 | + | 176.490i | 0.792428 | + | 1.49568i | ||||
\(119\) | −3.60847 | −0.0303233 | ||||||||
\(120\) | 188.162i | 1.56802i | ||||||||
\(121\) | −300.122 | −2.48035 | ||||||||
\(122\) | 108.643 | 0.890518 | ||||||||
\(123\) | 27.9062 | 0.226880 | ||||||||
\(124\) | − | 317.941i | − | 2.56404i | ||||||
\(125\) | 334.111 | 2.67289 | ||||||||
\(126\) | 101.155i | 0.802814i | ||||||||
\(127\) | −40.6699 | −0.320236 | −0.160118 | − | 0.987098i | \(-0.551187\pi\) | ||||
−0.160118 | + | 0.987098i | \(0.551187\pi\) | |||||||
\(128\) | − | 234.593i | − | 1.83276i | ||||||
\(129\) | − | 52.6752i | − | 0.408335i | ||||||
\(130\) | −131.839 | −1.01415 | ||||||||
\(131\) | − | 121.173i | − | 0.924988i | −0.886622 | − | 0.462494i | \(-0.846955\pi\) | ||
0.886622 | − | 0.462494i | \(-0.153045\pi\) | |||||||
\(132\) | 265.156i | 2.00876i | ||||||||
\(133\) | −116.751 | −0.877830 | ||||||||
\(134\) | −275.805 | −2.05824 | ||||||||
\(135\) | 48.1936 | 0.356990 | ||||||||
\(136\) | 4.24341i | 0.0312015i | ||||||||
\(137\) | −198.510 | −1.44898 | −0.724489 | − | 0.689286i | \(-0.757924\pi\) | ||||
−0.724489 | + | 0.689286i | \(0.757924\pi\) | |||||||
\(138\) | 126.531 | 0.916895 | ||||||||
\(139\) | 228.034 | 1.64053 | 0.820267 | − | 0.571981i | \(-0.193825\pi\) | ||||
0.820267 | + | 0.571981i | \(0.193825\pi\) | |||||||
\(140\) | 689.156 | 4.92254 | ||||||||
\(141\) | 8.77042i | 0.0622016i | ||||||||
\(142\) | − | 33.6021i | − | 0.236634i | ||||||
\(143\) | −86.1687 | −0.602578 | ||||||||
\(144\) | 29.4339 | 0.204402 | ||||||||
\(145\) | 168.188 | 1.15992 | ||||||||
\(146\) | −145.845 | −0.998940 | ||||||||
\(147\) | 86.9622 | 0.591580 | ||||||||
\(148\) | − | 346.882i | − | 2.34380i | ||||||
\(149\) | 95.3536i | 0.639957i | 0.947425 | + | 0.319979i | \(0.103676\pi\) | ||||
−0.947425 | + | 0.319979i | \(0.896324\pi\) | |||||||
\(150\) | − | 357.806i | − | 2.38537i | ||||||
\(151\) | − | 262.692i | − | 1.73968i | −0.493333 | − | 0.869841i | \(-0.664221\pi\) | ||
0.493333 | − | 0.869841i | \(-0.335779\pi\) | |||||||
\(152\) | 137.295i | 0.903255i | ||||||||
\(153\) | 1.08685 | 0.00710362 | ||||||||
\(154\) | 691.940 | 4.49312 | ||||||||
\(155\) | 395.292i | 2.55027i | ||||||||
\(156\) | 54.2554i | 0.347791i | ||||||||
\(157\) | 23.3960i | 0.149019i | 0.997220 | + | 0.0745096i | \(0.0237392\pi\) | ||||
−0.997220 | + | 0.0745096i | \(0.976261\pi\) | |||||||
\(158\) | 352.234i | 2.22933i | ||||||||
\(159\) | 63.5521 | 0.399699 | ||||||||
\(160\) | 126.489i | 0.790556i | ||||||||
\(161\) | − | 214.941i | − | 1.33504i | ||||||
\(162\) | − | 30.4673i | − | 0.188070i | ||||||
\(163\) | −29.9339 | −0.183644 | −0.0918218 | − | 0.995775i | \(-0.529269\pi\) | ||||
−0.0918218 | + | 0.995775i | \(0.529269\pi\) | |||||||
\(164\) | −120.193 | −0.732882 | ||||||||
\(165\) | − | 329.665i | − | 1.99797i | ||||||
\(166\) | 399.879 | 2.40891 | ||||||||
\(167\) | −140.361 | −0.840485 | −0.420242 | − | 0.907412i | \(-0.638055\pi\) | ||||
−0.420242 | + | 0.907412i | \(0.638055\pi\) | |||||||
\(168\) | − | 202.068i | − | 1.20279i | ||||||
\(169\) | 151.368 | 0.895671 | ||||||||
\(170\) | − | 11.3750i | − | 0.0669115i | ||||||
\(171\) | 35.1650 | 0.205643 | ||||||||
\(172\) | 226.873i | 1.31903i | ||||||||
\(173\) | 122.872i | 0.710245i | 0.934820 | + | 0.355123i | \(0.115561\pi\) | ||||
−0.934820 | + | 0.355123i | \(0.884439\pi\) | |||||||
\(174\) | − | 106.326i | − | 0.611071i | ||||||
\(175\) | −607.810 | −3.47320 | ||||||||
\(176\) | − | 201.340i | − | 1.14398i | ||||||
\(177\) | −90.3002 | + | 47.8422i | −0.510171 | + | 0.270295i | ||||
\(178\) | −162.854 | −0.914912 | ||||||||
\(179\) | 13.1743i | 0.0735996i | 0.999323 | + | 0.0367998i | \(0.0117164\pi\) | ||||
−0.999323 | + | 0.0367998i | \(0.988284\pi\) | |||||||
\(180\) | −207.571 | −1.15317 | ||||||||
\(181\) | −194.551 | −1.07487 | −0.537433 | − | 0.843307i | \(-0.680606\pi\) | ||||
−0.537433 | + | 0.843307i | \(0.680606\pi\) | |||||||
\(182\) | 141.583 | 0.777926 | ||||||||
\(183\) | 55.5867i | 0.303753i | ||||||||
\(184\) | −252.761 | −1.37370 | ||||||||
\(185\) | 431.274i | 2.33121i | ||||||||
\(186\) | 249.898 | 1.34354 | ||||||||
\(187\) | − | 7.43454i | − | 0.0397569i | ||||||
\(188\) | − | 37.7743i | − | 0.200927i | ||||||
\(189\) | −51.7553 | −0.273837 | ||||||||
\(190\) | − | 368.035i | − | 1.93703i | ||||||
\(191\) | − | 299.916i | − | 1.57024i | −0.619342 | − | 0.785121i | \(-0.712601\pi\) | ||
0.619342 | − | 0.785121i | \(-0.287399\pi\) | |||||||
\(192\) | 147.939 | 0.770517 | ||||||||
\(193\) | −27.4449 | −0.142202 | −0.0711008 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0711008 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(194\) | 424.996 | 2.19070 | ||||||||
\(195\) | − | 67.4549i | − | 0.345923i | ||||||
\(196\) | −374.548 | −1.91096 | ||||||||
\(197\) | 82.5430 | 0.419000 | 0.209500 | − | 0.977809i | \(-0.432816\pi\) | ||||
0.209500 | + | 0.977809i | \(0.432816\pi\) | |||||||
\(198\) | −208.409 | −1.05257 | ||||||||
\(199\) | −41.4291 | −0.208186 | −0.104093 | − | 0.994568i | \(-0.533194\pi\) | ||||
−0.104093 | + | 0.994568i | \(0.533194\pi\) | |||||||
\(200\) | 714.759i | 3.57379i | ||||||||
\(201\) | − | 141.114i | − | 0.702060i | ||||||
\(202\) | 115.745 | 0.572994 | ||||||||
\(203\) | −180.618 | −0.889744 | ||||||||
\(204\) | −4.68110 | −0.0229466 | ||||||||
\(205\) | 149.434 | 0.728945 | ||||||||
\(206\) | 406.089 | 1.97131 | ||||||||
\(207\) | 64.7392i | 0.312750i | ||||||||
\(208\) | − | 41.1976i | − | 0.198065i | ||||||
\(209\) | − | 240.543i | − | 1.15093i | ||||||
\(210\) | 541.668i | 2.57937i | ||||||||
\(211\) | − | 241.695i | − | 1.14547i | −0.819740 | − | 0.572736i | \(-0.805882\pi\) | ||
0.819740 | − | 0.572736i | \(-0.194118\pi\) | |||||||
\(212\) | −273.720 | −1.29113 | ||||||||
\(213\) | 17.1923 | 0.0807152 | ||||||||
\(214\) | − | 134.785i | − | 0.629837i | ||||||
\(215\) | − | 282.068i | − | 1.31194i | ||||||
\(216\) | 60.8620i | 0.281769i | ||||||||
\(217\) | − | 424.505i | − | 1.95624i | ||||||
\(218\) | −570.236 | −2.61576 | ||||||||
\(219\) | − | 74.6210i | − | 0.340735i | ||||||
\(220\) | 1419.87i | 6.45396i | ||||||||
\(221\) | − | 1.52123i | − | 0.00688340i | ||||||
\(222\) | 272.645 | 1.22813 | ||||||||
\(223\) | 200.733 | 0.900148 | 0.450074 | − | 0.892991i | \(-0.351398\pi\) | ||||
0.450074 | + | 0.892991i | \(0.351398\pi\) | |||||||
\(224\) | − | 135.837i | − | 0.606414i | ||||||
\(225\) | 183.070 | 0.813643 | ||||||||
\(226\) | −79.5400 | −0.351947 | ||||||||
\(227\) | 221.780i | 0.977002i | 0.872563 | + | 0.488501i | \(0.162456\pi\) | ||||
−0.872563 | + | 0.488501i | \(0.837544\pi\) | |||||||
\(228\) | −151.456 | −0.664282 | ||||||||
\(229\) | 169.854i | 0.741720i | 0.928689 | + | 0.370860i | \(0.120937\pi\) | ||||
−0.928689 | + | 0.370860i | \(0.879063\pi\) | |||||||
\(230\) | 677.557 | 2.94590 | ||||||||
\(231\) | 354.028i | 1.53259i | ||||||||
\(232\) | 212.399i | 0.915514i | ||||||||
\(233\) | 56.1420i | 0.240953i | 0.992716 | + | 0.120476i | \(0.0384422\pi\) | ||||
−0.992716 | + | 0.120476i | \(0.961558\pi\) | |||||||
\(234\) | −42.6440 | −0.182239 | ||||||||
\(235\) | 46.9643i | 0.199848i | ||||||||
\(236\) | 388.925 | − | 206.057i | 1.64799 | − | 0.873123i | ||||
\(237\) | −180.219 | −0.760417 | ||||||||
\(238\) | 12.2156i | 0.0513260i | ||||||||
\(239\) | −282.703 | −1.18286 | −0.591429 | − | 0.806357i | \(-0.701436\pi\) | ||||
−0.591429 | + | 0.806357i | \(0.701436\pi\) | |||||||
\(240\) | 157.614 | 0.656725 | ||||||||
\(241\) | 90.4885 | 0.375471 | 0.187736 | − | 0.982220i | \(-0.439885\pi\) | ||||
0.187736 | + | 0.982220i | \(0.439885\pi\) | |||||||
\(242\) | 1015.99i | 4.19831i | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 239.413i | − | 0.981201i | ||||||
\(245\) | 465.669 | 1.90069 | ||||||||
\(246\) | − | 94.4698i | − | 0.384024i | ||||||
\(247\) | − | 49.2192i | − | 0.199268i | ||||||
\(248\) | −499.200 | −2.01290 | ||||||||
\(249\) | 204.596i | 0.821671i | ||||||||
\(250\) | − | 1131.05i | − | 4.52420i | ||||||
\(251\) | 90.8848 | 0.362091 | 0.181045 | − | 0.983475i | \(-0.442052\pi\) | ||||
0.181045 | + | 0.983475i | \(0.442052\pi\) | |||||||
\(252\) | 222.911 | 0.884567 | ||||||||
\(253\) | 442.843 | 1.75037 | ||||||||
\(254\) | 137.678i | 0.542040i | ||||||||
\(255\) | 5.81994 | 0.0228233 | ||||||||
\(256\) | −452.507 | −1.76760 | ||||||||
\(257\) | −75.3044 | −0.293013 | −0.146507 | − | 0.989210i | \(-0.546803\pi\) | ||||
−0.146507 | + | 0.989210i | \(0.546803\pi\) | |||||||
\(258\) | −178.319 | −0.691160 | ||||||||
\(259\) | − | 463.146i | − | 1.78821i | ||||||
\(260\) | 290.530i | 1.11742i | ||||||||
\(261\) | 54.4013 | 0.208434 | ||||||||
\(262\) | −410.203 | −1.56566 | ||||||||
\(263\) | 366.374 | 1.39306 | 0.696528 | − | 0.717530i | \(-0.254727\pi\) | ||||
0.696528 | + | 0.717530i | \(0.254727\pi\) | |||||||
\(264\) | 416.322 | 1.57698 | ||||||||
\(265\) | 340.312 | 1.28420 | ||||||||
\(266\) | 395.234i | 1.48584i | ||||||||
\(267\) | − | 83.3236i | − | 0.312073i | ||||||
\(268\) | 607.781i | 2.26784i | ||||||||
\(269\) | − | 0.373353i | − | 0.00138793i | −1.00000 | 0.000693966i | \(-0.999779\pi\) | |||
1.00000 | 0.000693966i | \(-0.000220896\pi\) | ||||||||
\(270\) | − | 163.148i | − | 0.604252i | ||||||
\(271\) | −375.056 | −1.38397 | −0.691986 | − | 0.721911i | \(-0.743264\pi\) | ||||
−0.691986 | + | 0.721911i | \(0.743264\pi\) | |||||||
\(272\) | 3.55449 | 0.0130680 | ||||||||
\(273\) | 72.4400i | 0.265348i | ||||||||
\(274\) | 672.008i | 2.45258i | ||||||||
\(275\) | − | 1252.27i | − | 4.55372i | ||||||
\(276\) | − | 278.833i | − | 1.01026i | ||||||
\(277\) | 87.9624 | 0.317554 | 0.158777 | − | 0.987314i | \(-0.449245\pi\) | ||||
0.158777 | + | 0.987314i | \(0.449245\pi\) | |||||||
\(278\) | − | 771.955i | − | 2.77682i | ||||||
\(279\) | 127.859i | 0.458276i | ||||||||
\(280\) | − | 1082.04i | − | 3.86444i | ||||||
\(281\) | −358.335 | −1.27521 | −0.637607 | − | 0.770362i | \(-0.720076\pi\) | ||||
−0.637607 | + | 0.770362i | \(0.720076\pi\) | |||||||
\(282\) | 29.6901 | 0.105284 | ||||||||
\(283\) | 372.886i | 1.31762i | 0.752311 | + | 0.658808i | \(0.228939\pi\) | ||||
−0.752311 | + | 0.658808i | \(0.771061\pi\) | |||||||
\(284\) | −74.0477 | −0.260731 | ||||||||
\(285\) | 188.303 | 0.660713 | ||||||||
\(286\) | 291.703i | 1.01994i | ||||||||
\(287\) | −160.477 | −0.559154 | ||||||||
\(288\) | 40.9135i | 0.142061i | ||||||||
\(289\) | −288.869 | −0.999546 | ||||||||
\(290\) | − | 569.361i | − | 1.96332i | ||||||
\(291\) | 217.447i | 0.747242i | ||||||||
\(292\) | 321.394i | 1.10066i | ||||||||
\(293\) | −82.4199 | −0.281297 | −0.140648 | − | 0.990060i | \(-0.544919\pi\) | ||||
−0.140648 | + | 0.990060i | \(0.544919\pi\) | |||||||
\(294\) | − | 294.390i | − | 1.00132i | ||||||
\(295\) | −483.544 | + | 256.188i | −1.63913 | + | 0.868432i | ||||
\(296\) | −544.640 | −1.84000 | ||||||||
\(297\) | − | 106.632i | − | 0.359029i | ||||||
\(298\) | 322.797 | 1.08321 | ||||||||
\(299\) | 90.6132 | 0.303054 | ||||||||
\(300\) | −788.484 | −2.62828 | ||||||||
\(301\) | 302.913i | 1.00636i | ||||||||
\(302\) | −889.280 | −2.94464 | ||||||||
\(303\) | 59.2202i | 0.195446i | ||||||||
\(304\) | 115.005 | 0.378305 | ||||||||
\(305\) | 297.659i | 0.975930i | ||||||||
\(306\) | − | 3.67928i | − | 0.0120238i | ||||||
\(307\) | −469.709 | −1.53000 | −0.764999 | − | 0.644032i | \(-0.777260\pi\) | ||||
−0.764999 | + | 0.644032i | \(0.777260\pi\) | |||||||
\(308\) | − | 1524.80i | − | 4.95066i | ||||||
\(309\) | 207.774i | 0.672406i | ||||||||
\(310\) | 1338.16 | 4.31666 | ||||||||
\(311\) | 53.4334 | 0.171812 | 0.0859058 | − | 0.996303i | \(-0.472622\pi\) | ||||
0.0859058 | + | 0.996303i | \(0.472622\pi\) | |||||||
\(312\) | 85.1864 | 0.273033 | ||||||||
\(313\) | − | 8.38179i | − | 0.0267789i | −0.999910 | − | 0.0133894i | \(-0.995738\pi\) | ||
0.999910 | − | 0.0133894i | \(-0.00426212\pi\) | |||||||
\(314\) | 79.2016 | 0.252234 | ||||||||
\(315\) | −277.142 | −0.879815 | ||||||||
\(316\) | 776.206 | 2.45635 | ||||||||
\(317\) | −400.493 | −1.26338 | −0.631692 | − | 0.775219i | \(-0.717639\pi\) | ||||
−0.631692 | + | 0.775219i | \(0.717639\pi\) | |||||||
\(318\) | − | 215.140i | − | 0.676542i | ||||||
\(319\) | − | 372.128i | − | 1.16655i | ||||||
\(320\) | 792.192 | 2.47560 | ||||||||
\(321\) | 68.9622 | 0.214836 | ||||||||
\(322\) | −727.630 | −2.25972 | ||||||||
\(323\) | 4.24658 | 0.0131473 | ||||||||
\(324\) | −67.1398 | −0.207221 | ||||||||
\(325\) | − | 256.236i | − | 0.788419i | ||||||
\(326\) | 101.334i | 0.310840i | ||||||||
\(327\) | − | 291.759i | − | 0.892228i | ||||||
\(328\) | 188.714i | 0.575349i | ||||||||
\(329\) | − | 50.4350i | − | 0.153298i | ||||||
\(330\) | −1116.00 | −3.38182 | ||||||||
\(331\) | −29.6370 | −0.0895377 | −0.0447688 | − | 0.998997i | \(-0.514255\pi\) | ||||
−0.0447688 | + | 0.998997i | \(0.514255\pi\) | |||||||
\(332\) | − | 881.198i | − | 2.65421i | ||||||
\(333\) | 139.497i | 0.418911i | ||||||||
\(334\) | 475.158i | 1.42263i | ||||||||
\(335\) | − | 755.645i | − | 2.25566i | ||||||
\(336\) | −169.262 | −0.503756 | ||||||||
\(337\) | − | 112.535i | − | 0.333932i | −0.985963 | − | 0.166966i | \(-0.946603\pi\) | ||
0.985963 | − | 0.166966i | \(-0.0533971\pi\) | |||||||
\(338\) | − | 512.421i | − | 1.51604i | ||||||
\(339\) | − | 40.6963i | − | 0.120048i | ||||||
\(340\) | −25.0666 | −0.0737253 | ||||||||
\(341\) | 874.609 | 2.56484 | ||||||||
\(342\) | − | 119.043i | − | 0.348078i | ||||||
\(343\) | −12.0286 | −0.0350687 | ||||||||
\(344\) | 356.213 | 1.03550 | ||||||||
\(345\) | 346.669i | 1.00484i | ||||||||
\(346\) | 415.955 | 1.20218 | ||||||||
\(347\) | 388.058i | 1.11832i | 0.829059 | + | 0.559161i | \(0.188877\pi\) | ||||
−0.829059 | + | 0.559161i | \(0.811123\pi\) | |||||||
\(348\) | −234.308 | −0.673297 | ||||||||
\(349\) | 542.368i | 1.55406i | 0.629462 | + | 0.777031i | \(0.283275\pi\) | ||||
−0.629462 | + | 0.777031i | \(0.716725\pi\) | |||||||
\(350\) | 2057.59i | 5.87884i | ||||||||
\(351\) | − | 21.8186i | − | 0.0621613i | ||||||
\(352\) | 279.865 | 0.795072 | ||||||||
\(353\) | − | 102.916i | − | 0.291546i | −0.989318 | − | 0.145773i | \(-0.953433\pi\) | ||
0.989318 | − | 0.145773i | \(-0.0465669\pi\) | |||||||
\(354\) | 161.958 | + | 305.690i | 0.457509 | + | 0.863530i | ||||
\(355\) | 92.0624 | 0.259331 | ||||||||
\(356\) | 358.876i | 1.00808i | ||||||||
\(357\) | −6.25005 | −0.0175071 | ||||||||
\(358\) | 44.5985 | 0.124577 | ||||||||
\(359\) | 281.215 | 0.783328 | 0.391664 | − | 0.920108i | \(-0.371899\pi\) | ||||
0.391664 | + | 0.920108i | \(0.371899\pi\) | |||||||
\(360\) | 325.907i | 0.905297i | ||||||||
\(361\) | −223.603 | −0.619398 | ||||||||
\(362\) | 658.604i | 1.81935i | ||||||||
\(363\) | −519.827 | −1.43203 | ||||||||
\(364\) | − | 312.000i | − | 0.857144i | ||||||
\(365\) | − | 399.584i | − | 1.09475i | ||||||
\(366\) | 188.175 | 0.514141 | ||||||||
\(367\) | 22.4570i | 0.0611907i | 0.999532 | + | 0.0305953i | \(0.00974032\pi\) | ||||
−0.999532 | + | 0.0305953i | \(0.990260\pi\) | |||||||
\(368\) | 211.725i | 0.575340i | ||||||||
\(369\) | 48.3350 | 0.130989 | ||||||||
\(370\) | 1459.97 | 3.94587 | ||||||||
\(371\) | −365.462 | −0.985072 | ||||||||
\(372\) | − | 550.691i | − | 1.48035i | ||||||
\(373\) | 70.8071 | 0.189831 | 0.0949157 | − | 0.995485i | \(-0.469742\pi\) | ||||
0.0949157 | + | 0.995485i | \(0.469742\pi\) | |||||||
\(374\) | −25.1678 | −0.0672937 | ||||||||
\(375\) | 578.697 | 1.54319 | ||||||||
\(376\) | −59.3095 | −0.157738 | ||||||||
\(377\) | − | 76.1436i | − | 0.201973i | ||||||
\(378\) | 175.205i | 0.463505i | ||||||||
\(379\) | −249.514 | −0.658349 | −0.329174 | − | 0.944269i | \(-0.606770\pi\) | ||||
−0.329174 | + | 0.944269i | \(0.606770\pi\) | |||||||
\(380\) | −811.025 | −2.13428 | ||||||||
\(381\) | −70.4424 | −0.184888 | ||||||||
\(382\) | −1015.29 | −2.65784 | ||||||||
\(383\) | −674.681 | −1.76157 | −0.880785 | − | 0.473516i | \(-0.842985\pi\) | ||||
−0.880785 | + | 0.473516i | \(0.842985\pi\) | |||||||
\(384\) | − | 406.327i | − | 1.05814i | ||||||
\(385\) | 1895.77i | 4.92407i | ||||||||
\(386\) | 92.9081i | 0.240694i | ||||||||
\(387\) | − | 91.2361i | − | 0.235752i | ||||||
\(388\) | − | 936.549i | − | 2.41379i | ||||||
\(389\) | 493.759 | 1.26930 | 0.634651 | − | 0.772799i | \(-0.281144\pi\) | ||||
0.634651 | + | 0.772799i | \(0.281144\pi\) | |||||||
\(390\) | −228.352 | −0.585519 | ||||||||
\(391\) | 7.81801i | 0.0199949i | ||||||||
\(392\) | 588.077i | 1.50020i | ||||||||
\(393\) | − | 209.879i | − | 0.534042i | ||||||
\(394\) | − | 279.429i | − | 0.709212i | ||||||
\(395\) | −965.045 | −2.44315 | ||||||||
\(396\) | 459.264i | 1.15976i | ||||||||
\(397\) | − | 648.987i | − | 1.63473i | −0.576122 | − | 0.817364i | \(-0.695435\pi\) | ||
0.576122 | − | 0.817364i | \(-0.304565\pi\) | |||||||
\(398\) | 140.248i | 0.352382i | ||||||||
\(399\) | −202.219 | −0.506815 | ||||||||
\(400\) | 598.717 | 1.49679 | ||||||||
\(401\) | 59.8224i | 0.149183i | 0.997214 | + | 0.0745915i | \(0.0237653\pi\) | ||||
−0.997214 | + | 0.0745915i | \(0.976235\pi\) | |||||||
\(402\) | −477.708 | −1.18833 | ||||||||
\(403\) | 178.960 | 0.444069 | ||||||||
\(404\) | − | 255.063i | − | 0.631343i | ||||||
\(405\) | 83.4738 | 0.206108 | ||||||||
\(406\) | 611.438i | 1.50601i | ||||||||
\(407\) | 954.221 | 2.34452 | ||||||||
\(408\) | 7.34979i | 0.0180142i | ||||||||
\(409\) | − | 279.180i | − | 0.682591i | −0.939956 | − | 0.341296i | \(-0.889134\pi\) | ||
0.939956 | − | 0.341296i | \(-0.110866\pi\) | |||||||
\(410\) | − | 505.872i | − | 1.23383i | ||||||
\(411\) | −343.830 | −0.836568 | ||||||||
\(412\) | − | 894.884i | − | 2.17205i | ||||||
\(413\) | 519.279 | − | 275.120i | 1.25733 | − | 0.666151i | ||||
\(414\) | 219.159 | 0.529369 | ||||||||
\(415\) | 1095.58i | 2.63995i | ||||||||
\(416\) | 57.2651 | 0.137657 | ||||||||
\(417\) | 394.967 | 0.947163 | ||||||||
\(418\) | −814.302 | −1.94809 | ||||||||
\(419\) | 442.679i | 1.05651i | 0.849085 | + | 0.528256i | \(0.177154\pi\) | ||||
−0.849085 | + | 0.528256i | \(0.822846\pi\) | |||||||
\(420\) | 1193.65 | 2.84203 | ||||||||
\(421\) | 73.7045i | 0.175070i | 0.996161 | + | 0.0875350i | \(0.0278990\pi\) | ||||
−0.996161 | + | 0.0875350i | \(0.972101\pi\) | |||||||
\(422\) | −818.198 | −1.93886 | ||||||||
\(423\) | 15.1908i | 0.0359121i | ||||||||
\(424\) | 429.768i | 1.01360i | ||||||||
\(425\) | 22.1078 | 0.0520183 | ||||||||
\(426\) | − | 58.2005i | − | 0.136621i | ||||||
\(427\) | − | 319.656i | − | 0.748609i | ||||||
\(428\) | −297.021 | −0.693975 | ||||||||
\(429\) | −149.249 | −0.347899 | ||||||||
\(430\) | −954.872 | −2.22063 | ||||||||
\(431\) | 25.3259i | 0.0587607i | 0.999568 | + | 0.0293804i | \(0.00935340\pi\) | ||||
−0.999568 | + | 0.0293804i | \(0.990647\pi\) | |||||||
\(432\) | 50.9810 | 0.118012 | ||||||||
\(433\) | 374.398 | 0.864659 | 0.432330 | − | 0.901716i | \(-0.357692\pi\) | ||||
0.432330 | + | 0.901716i | \(0.357692\pi\) | |||||||
\(434\) | −1437.06 | −3.31119 | ||||||||
\(435\) | 291.311 | 0.669680 | ||||||||
\(436\) | 1256.61i | 2.88213i | ||||||||
\(437\) | 252.950i | 0.578834i | ||||||||
\(438\) | −252.611 | −0.576738 | ||||||||
\(439\) | −282.618 | −0.643776 | −0.321888 | − | 0.946778i | \(-0.604318\pi\) | ||||
−0.321888 | + | 0.946778i | \(0.604318\pi\) | |||||||
\(440\) | 2229.34 | 5.06668 | ||||||||
\(441\) | 150.623 | 0.341549 | ||||||||
\(442\) | −5.14976 | −0.0116510 | ||||||||
\(443\) | 543.714i | 1.22735i | 0.789560 | + | 0.613673i | \(0.210309\pi\) | ||||
−0.789560 | + | 0.613673i | \(0.789691\pi\) | |||||||
\(444\) | − | 600.818i | − | 1.35319i | ||||||
\(445\) | − | 446.185i | − | 1.00266i | ||||||
\(446\) | − | 679.533i | − | 1.52362i | ||||||
\(447\) | 165.157i | 0.369479i | ||||||||
\(448\) | −850.737 | −1.89897 | ||||||||
\(449\) | 369.058 | 0.821955 | 0.410977 | − | 0.911646i | \(-0.365188\pi\) | ||||
0.410977 | + | 0.911646i | \(0.365188\pi\) | |||||||
\(450\) | − | 619.738i | − | 1.37720i | ||||||
\(451\) | − | 330.632i | − | 0.733109i | ||||||
\(452\) | 175.279i | 0.387786i | ||||||||
\(453\) | − | 454.996i | − | 1.00441i | ||||||
\(454\) | 750.781 | 1.65370 | ||||||||
\(455\) | 387.905i | 0.852539i | ||||||||
\(456\) | 237.801i | 0.521494i | ||||||||
\(457\) | − | 529.971i | − | 1.15967i | −0.814732 | − | 0.579837i | \(-0.803116\pi\) | ||
0.814732 | − | 0.579837i | \(-0.196884\pi\) | |||||||
\(458\) | 574.999 | 1.25546 | ||||||||
\(459\) | 1.88249 | 0.00410128 | ||||||||
\(460\) | − | 1493.11i | − | 3.24589i | ||||||
\(461\) | −131.591 | −0.285448 | −0.142724 | − | 0.989763i | \(-0.545586\pi\) | ||||
−0.142724 | + | 0.989763i | \(0.545586\pi\) | |||||||
\(462\) | 1198.48 | 2.59410 | ||||||||
\(463\) | − | 489.009i | − | 1.05618i | −0.849190 | − | 0.528088i | \(-0.822909\pi\) | ||
0.849190 | − | 0.528088i | \(-0.177091\pi\) | |||||||
\(464\) | 177.916 | 0.383440 | ||||||||
\(465\) | 684.665i | 1.47240i | ||||||||
\(466\) | 190.055 | 0.407844 | ||||||||
\(467\) | − | 58.5903i | − | 0.125461i | −0.998031 | − | 0.0627305i | \(-0.980019\pi\) | ||
0.998031 | − | 0.0627305i | \(-0.0199808\pi\) | |||||||
\(468\) | 93.9732i | 0.200797i | ||||||||
\(469\) | 811.488i | 1.73025i | ||||||||
\(470\) | 158.986 | 0.338268 | ||||||||
\(471\) | 40.5231i | 0.0860363i | ||||||||
\(472\) | −323.530 | − | 610.650i | −0.685445 | − | 1.29375i | ||||
\(473\) | −624.094 | −1.31944 | ||||||||
\(474\) | 610.087i | 1.28710i | ||||||||
\(475\) | 715.294 | 1.50588 | ||||||||
\(476\) | 26.9191 | 0.0565527 | ||||||||
\(477\) | 110.075 | 0.230766 | ||||||||
\(478\) | 957.023i | 2.00214i | ||||||||
\(479\) | 571.506 | 1.19312 | 0.596562 | − | 0.802567i | \(-0.296533\pi\) | ||||
0.596562 | + | 0.802567i | \(0.296533\pi\) | |||||||
\(480\) | 219.085i | 0.456428i | ||||||||
\(481\) | 195.250 | 0.405924 | ||||||||
\(482\) | − | 306.327i | − | 0.635533i | ||||||
\(483\) | − | 372.288i | − | 0.770783i | ||||||
\(484\) | 2238.90 | 4.62583 | ||||||||
\(485\) | 1164.40i | 2.40082i | ||||||||
\(486\) | − | 52.7710i | − | 0.108582i | ||||||
\(487\) | 420.688 | 0.863836 | 0.431918 | − | 0.901913i | \(-0.357837\pi\) | ||||
0.431918 | + | 0.901913i | \(0.357837\pi\) | |||||||
\(488\) | −375.902 | −0.770292 | ||||||||
\(489\) | −51.8470 | −0.106027 | ||||||||
\(490\) | − | 1576.41i | − | 3.21717i | ||||||
\(491\) | 880.226 | 1.79272 | 0.896360 | − | 0.443326i | \(-0.146202\pi\) | ||||
0.896360 | + | 0.443326i | \(0.146202\pi\) | |||||||
\(492\) | −208.180 | −0.423130 | ||||||||
\(493\) | 6.56959 | 0.0133257 | ||||||||
\(494\) | −166.620 | −0.337287 | ||||||||
\(495\) | − | 570.996i | − | 1.15353i | ||||||
\(496\) | 418.154i | 0.843053i | ||||||||
\(497\) | −98.8660 | −0.198925 | ||||||||
\(498\) | 692.610 | 1.39078 | ||||||||
\(499\) | −232.423 | −0.465778 | −0.232889 | − | 0.972503i | \(-0.574818\pi\) | ||||
−0.232889 | + | 0.972503i | \(0.574818\pi\) | |||||||
\(500\) | −2492.46 | −4.98491 | ||||||||
\(501\) | −243.112 | −0.485254 | ||||||||
\(502\) | − | 307.668i | − | 0.612885i | ||||||
\(503\) | 769.859i | 1.53053i | 0.643713 | + | 0.765267i | \(0.277393\pi\) | ||||
−0.643713 | + | 0.765267i | \(0.722607\pi\) | |||||||
\(504\) | − | 349.992i | − | 0.694429i | ||||||
\(505\) | 317.115i | 0.627951i | ||||||||
\(506\) | − | 1499.14i | − | 2.96273i | ||||||
\(507\) | 262.178 | 0.517116 | ||||||||
\(508\) | 303.397 | 0.597237 | ||||||||
\(509\) | − | 237.299i | − | 0.466207i | −0.972452 | − | 0.233103i | \(-0.925112\pi\) | ||
0.972452 | − | 0.233103i | \(-0.0748881\pi\) | |||||||
\(510\) | − | 19.7020i | − | 0.0386314i | ||||||
\(511\) | 429.114i | 0.839754i | ||||||||
\(512\) | 593.480i | 1.15914i | ||||||||
\(513\) | 60.9076 | 0.118728 | ||||||||
\(514\) | 254.925i | 0.495963i | ||||||||
\(515\) | 1112.60i | 2.16038i | ||||||||
\(516\) | 392.956i | 0.761542i | ||||||||
\(517\) | 103.912 | 0.200989 | ||||||||
\(518\) | −1567.87 | −3.02677 | ||||||||
\(519\) | 212.821i | 0.410060i | ||||||||
\(520\) | 456.160 | 0.877232 | ||||||||
\(521\) | −28.9394 | −0.0555459 | −0.0277730 | − | 0.999614i | \(-0.508842\pi\) | ||||
−0.0277730 | + | 0.999614i | \(0.508842\pi\) | |||||||
\(522\) | − | 184.163i | − | 0.352802i | ||||||
\(523\) | −390.540 | −0.746730 | −0.373365 | − | 0.927684i | \(-0.621796\pi\) | ||||
−0.373365 | + | 0.927684i | \(0.621796\pi\) | |||||||
\(524\) | 903.951i | 1.72510i | ||||||||
\(525\) | −1052.76 | −2.00525 | ||||||||
\(526\) | − | 1240.27i | − | 2.35793i | ||||||
\(527\) | 15.4405i | 0.0292988i | ||||||||
\(528\) | − | 348.732i | − | 0.660476i | ||||||
\(529\) | 63.3150 | 0.119688 | ||||||||
\(530\) | − | 1152.04i | − | 2.17367i | ||||||
\(531\) | −156.405 | + | 82.8651i | −0.294547 | + | 0.156055i | ||||
\(532\) | 870.962 | 1.63715 | ||||||||
\(533\) | − | 67.6528i | − | 0.126928i | ||||||
\(534\) | −282.072 | −0.528225 | ||||||||
\(535\) | 369.282 | 0.690247 | ||||||||
\(536\) | 954.276 | 1.78037 | ||||||||
\(537\) | 22.8186i | 0.0424927i | ||||||||
\(538\) | −1.26390 | −0.00234925 | ||||||||
\(539\) | − | 1030.32i | − | 1.91155i | ||||||
\(540\) | −359.523 | −0.665784 | ||||||||
\(541\) | − | 639.799i | − | 1.18262i | −0.806443 | − | 0.591311i | \(-0.798610\pi\) | ||
0.806443 | − | 0.591311i | \(-0.201390\pi\) | |||||||
\(542\) | 1269.66i | 2.34255i | ||||||||
\(543\) | −336.971 | −0.620574 | ||||||||
\(544\) | 4.94077i | 0.00908231i | ||||||||
\(545\) | − | 1562.32i | − | 2.86665i | ||||||
\(546\) | 245.228 | 0.449136 | ||||||||
\(547\) | −33.9867 | −0.0621329 | −0.0310664 | − | 0.999517i | \(-0.509890\pi\) | ||||
−0.0310664 | + | 0.999517i | \(0.509890\pi\) | |||||||
\(548\) | 1480.88 | 2.70234 | ||||||||
\(549\) | 96.2791i | 0.175372i | ||||||||
\(550\) | −4239.27 | −7.70776 | ||||||||
\(551\) | 212.558 | 0.385768 | ||||||||
\(552\) | −437.795 | −0.793108 | ||||||||
\(553\) | 1036.36 | 1.87408 | ||||||||
\(554\) | − | 297.776i | − | 0.537501i | ||||||
\(555\) | 746.988i | 1.34592i | ||||||||
\(556\) | −1701.13 | −3.05958 | ||||||||
\(557\) | −587.282 | −1.05437 | −0.527183 | − | 0.849752i | \(-0.676752\pi\) | ||||
−0.527183 | + | 0.849752i | \(0.676752\pi\) | |||||||
\(558\) | 432.836 | 0.775691 | ||||||||
\(559\) | −127.700 | −0.228444 | ||||||||
\(560\) | −906.373 | −1.61852 | ||||||||
\(561\) | − | 12.8770i | − | 0.0229537i | ||||||
\(562\) | 1213.06i | 2.15846i | ||||||||
\(563\) | 416.727i | 0.740190i | 0.928994 | + | 0.370095i | \(0.120675\pi\) | ||||
−0.928994 | + | 0.370095i | \(0.879325\pi\) | |||||||
\(564\) | − | 65.4271i | − | 0.116005i | ||||||
\(565\) | − | 217.922i | − | 0.385703i | ||||||
\(566\) | 1262.31 | 2.23024 | ||||||||
\(567\) | −89.6427 | −0.158100 | ||||||||
\(568\) | 116.262i | 0.204687i | ||||||||
\(569\) | − | 429.645i | − | 0.755089i | −0.925992 | − | 0.377544i | \(-0.876769\pi\) | ||
0.925992 | − | 0.377544i | \(-0.123231\pi\) | |||||||
\(570\) | − | 637.455i | − | 1.11834i | ||||||
\(571\) | − | 783.544i | − | 1.37223i | −0.727492 | − | 0.686116i | \(-0.759314\pi\) | ||
0.727492 | − | 0.686116i | \(-0.240686\pi\) | |||||||
\(572\) | 642.816 | 1.12380 | ||||||||
\(573\) | − | 519.470i | − | 0.906580i | ||||||
\(574\) | 543.257i | 0.946440i | ||||||||
\(575\) | 1316.87i | 2.29020i | ||||||||
\(576\) | 256.238 | 0.444858 | ||||||||
\(577\) | 14.6938 | 0.0254659 | 0.0127330 | − | 0.999919i | \(-0.495947\pi\) | ||||
0.0127330 | + | 0.999919i | \(0.495947\pi\) | |||||||
\(578\) | 977.895i | 1.69186i | ||||||||
\(579\) | −47.5360 | −0.0821001 | ||||||||
\(580\) | −1254.68 | −2.16324 | ||||||||
\(581\) | − | 1176.55i | − | 2.02504i | ||||||
\(582\) | 736.115 | 1.26480 | ||||||||
\(583\) | − | 752.963i | − | 1.29153i | ||||||
\(584\) | 504.620 | 0.864076 | ||||||||
\(585\) | − | 116.835i | − | 0.199719i | ||||||
\(586\) | 279.013i | 0.476131i | ||||||||
\(587\) | − | 847.153i | − | 1.44319i | −0.692315 | − | 0.721596i | \(-0.743409\pi\) | ||
0.692315 | − | 0.721596i | \(-0.256591\pi\) | |||||||
\(588\) | −648.736 | −1.10329 | ||||||||
\(589\) | 499.573i | 0.848172i | ||||||||
\(590\) | 867.261 | + | 1636.92i | 1.46993 | + | 2.77444i | ||||
\(591\) | 142.969 | 0.241910 | ||||||||
\(592\) | 456.217i | 0.770637i | ||||||||
\(593\) | −669.594 | −1.12916 | −0.564582 | − | 0.825377i | \(-0.690963\pi\) | ||||
−0.564582 | + | 0.825377i | \(0.690963\pi\) | |||||||
\(594\) | −360.976 | −0.607703 | ||||||||
\(595\) | −33.4681 | −0.0562488 | ||||||||
\(596\) | − | 711.335i | − | 1.19352i | ||||||
\(597\) | −71.7573 | −0.120196 | ||||||||
\(598\) | − | 306.749i | − | 0.512958i | ||||||
\(599\) | 666.722 | 1.11306 | 0.556529 | − | 0.830828i | \(-0.312133\pi\) | ||||
0.556529 | + | 0.830828i | \(0.312133\pi\) | |||||||
\(600\) | 1238.00i | 2.06333i | ||||||||
\(601\) | 341.243i | 0.567792i | 0.958855 | + | 0.283896i | \(0.0916270\pi\) | ||||
−0.958855 | + | 0.283896i | \(0.908373\pi\) | |||||||
\(602\) | 1025.44 | 1.70339 | ||||||||
\(603\) | − | 244.417i | − | 0.405335i | ||||||
\(604\) | 1959.67i | 3.24449i | ||||||||
\(605\) | −2783.59 | −4.60098 | ||||||||
\(606\) | 200.476 | 0.330818 | ||||||||
\(607\) | −137.196 | −0.226023 | −0.113011 | − | 0.993594i | \(-0.536050\pi\) | ||||
−0.113011 | + | 0.993594i | \(0.536050\pi\) | |||||||
\(608\) | 159.858i | 0.262924i | ||||||||
\(609\) | −312.839 | −0.513694 | ||||||||
\(610\) | 1007.65 | 1.65189 | ||||||||
\(611\) | 21.2620 | 0.0347988 | ||||||||
\(612\) | −8.10790 | −0.0132482 | ||||||||
\(613\) | 583.317i | 0.951577i | 0.879560 | + | 0.475788i | \(0.157837\pi\) | ||||
−0.879560 | + | 0.475788i | \(0.842163\pi\) | |||||||
\(614\) | 1590.09i | 2.58972i | ||||||||
\(615\) | 258.827 | 0.420857 | ||||||||
\(616\) | −2394.09 | −3.88652 | ||||||||
\(617\) | 775.180 | 1.25637 | 0.628185 | − | 0.778064i | \(-0.283798\pi\) | ||||
0.628185 | + | 0.778064i | \(0.283798\pi\) | |||||||
\(618\) | 703.367 | 1.13813 | ||||||||
\(619\) | 297.409 | 0.480467 | 0.240233 | − | 0.970715i | \(-0.422776\pi\) | ||||
0.240233 | + | 0.970715i | \(0.422776\pi\) | |||||||
\(620\) | − | 2948.87i | − | 4.75623i | ||||||
\(621\) | 112.132i | 0.180566i | ||||||||
\(622\) | − | 180.886i | − | 0.290813i | ||||||
\(623\) | 479.159i | 0.769116i | ||||||||
\(624\) | − | 71.3563i | − | 0.114353i | ||||||
\(625\) | 1573.25 | 2.51721 | ||||||||
\(626\) | −28.3745 | −0.0453267 | ||||||||
\(627\) | − | 416.633i | − | 0.664487i | ||||||
\(628\) | − | 174.534i | − | 0.277920i | ||||||
\(629\) | 16.8459i | 0.0267821i | ||||||||
\(630\) | 938.196i | 1.48920i | ||||||||
\(631\) | 172.413 | 0.273238 | 0.136619 | − | 0.990624i | \(-0.456376\pi\) | ||||
0.136619 | + | 0.990624i | \(0.456376\pi\) | |||||||
\(632\) | − | 1218.72i | − | 1.92836i | ||||||
\(633\) | − | 418.627i | − | 0.661338i | ||||||
\(634\) | 1355.77i | 2.13844i | ||||||||
\(635\) | −377.208 | −0.594029 | ||||||||
\(636\) | −474.097 | −0.745435 | ||||||||
\(637\) | − | 210.822i | − | 0.330960i | ||||||
\(638\) | −1259.75 | −1.97453 | ||||||||
\(639\) | 29.7780 | 0.0466009 | ||||||||
\(640\) | − | 2175.82i | − | 3.39972i | ||||||
\(641\) | 219.920 | 0.343089 | 0.171544 | − | 0.985176i | \(-0.445124\pi\) | ||||
0.171544 | + | 0.985176i | \(0.445124\pi\) | |||||||
\(642\) | − | 233.455i | − | 0.363637i | ||||||
\(643\) | −930.457 | −1.44706 | −0.723528 | − | 0.690295i | \(-0.757481\pi\) | ||||
−0.723528 | + | 0.690295i | \(0.757481\pi\) | |||||||
\(644\) | 1603.45i | 2.48983i | ||||||||
\(645\) | − | 488.556i | − | 0.757451i | ||||||
\(646\) | − | 14.3758i | − | 0.0222535i | ||||||
\(647\) | 748.437 | 1.15678 | 0.578390 | − | 0.815760i | \(-0.303681\pi\) | ||||
0.578390 | + | 0.815760i | \(0.303681\pi\) | |||||||
\(648\) | 105.416i | 0.162679i | ||||||||
\(649\) | 566.832 | + | 1069.87i | 0.873393 | + | 1.64849i | ||||
\(650\) | −867.426 | −1.33450 | ||||||||
\(651\) | − | 735.264i | − | 1.12944i | ||||||
\(652\) | 223.306 | 0.342494 | ||||||||
\(653\) | −172.727 | −0.264514 | −0.132257 | − | 0.991215i | \(-0.542222\pi\) | ||||
−0.132257 | + | 0.991215i | \(0.542222\pi\) | |||||||
\(654\) | −987.678 | −1.51021 | ||||||||
\(655\) | − | 1123.87i | − | 1.71583i | ||||||
\(656\) | 158.077 | 0.240970 | ||||||||
\(657\) | − | 129.247i | − | 0.196723i | ||||||
\(658\) | −170.736 | −0.259477 | ||||||||
\(659\) | − | 552.763i | − | 0.838790i | −0.907804 | − | 0.419395i | \(-0.862242\pi\) | ||
0.907804 | − | 0.419395i | \(-0.137758\pi\) | |||||||
\(660\) | 2459.29i | 3.72620i | ||||||||
\(661\) | 890.466 | 1.34715 | 0.673575 | − | 0.739119i | \(-0.264758\pi\) | ||||
0.673575 | + | 0.739119i | \(0.264758\pi\) | |||||||
\(662\) | 100.329i | 0.151554i | ||||||||
\(663\) | − | 2.63485i | − | 0.00397413i | ||||||
\(664\) | −1383.57 | −2.08369 | ||||||||
\(665\) | −1082.85 | −1.62835 | ||||||||
\(666\) | 472.235 | 0.709061 | ||||||||
\(667\) | 391.322i | 0.586690i | ||||||||
\(668\) | 1047.09 | 1.56750 | ||||||||
\(669\) | 347.680 | 0.519701 | ||||||||
\(670\) | −2558.05 | −3.81799 | ||||||||
\(671\) | 658.589 | 0.981504 | ||||||||
\(672\) | − | 235.276i | − | 0.350113i | ||||||
\(673\) | 136.255i | 0.202459i | 0.994863 | + | 0.101230i | \(0.0322777\pi\) | ||||
−0.994863 | + | 0.101230i | \(0.967722\pi\) | |||||||
\(674\) | −380.961 | −0.565223 | ||||||||
\(675\) | 317.086 | 0.469757 | ||||||||
\(676\) | −1129.20 | −1.67042 | ||||||||
\(677\) | 265.723 | 0.392501 | 0.196251 | − | 0.980554i | \(-0.437123\pi\) | ||||
0.196251 | + | 0.980554i | \(0.437123\pi\) | |||||||
\(678\) | −137.767 | −0.203197 | ||||||||
\(679\) | − | 1250.45i | − | 1.84160i | ||||||
\(680\) | 39.3570i | 0.0578780i | ||||||||
\(681\) | 384.133i | 0.564073i | ||||||||
\(682\) | − | 2960.78i | − | 4.34132i | ||||||
\(683\) | 445.533i | 0.652318i | 0.945315 | + | 0.326159i | \(0.105754\pi\) | ||||
−0.945315 | + | 0.326159i | \(0.894246\pi\) | |||||||
\(684\) | −262.330 | −0.383523 | ||||||||
\(685\) | −1841.16 | −2.68782 | ||||||||
\(686\) | 40.7198i | 0.0593583i | ||||||||
\(687\) | 294.196i | 0.428232i | ||||||||
\(688\) | − | 298.382i | − | 0.433694i | ||||||
\(689\) | − | 154.069i | − | 0.223612i | ||||||
\(690\) | 1173.56 | 1.70082 | ||||||||
\(691\) | 370.939i | 0.536815i | 0.963306 | + | 0.268407i | \(0.0864973\pi\) | ||||
−0.963306 | + | 0.268407i | \(0.913503\pi\) | |||||||
\(692\) | − | 916.625i | − | 1.32460i | ||||||
\(693\) | 613.194i | 0.884840i | ||||||||
\(694\) | 1313.68 | 1.89290 | ||||||||
\(695\) | 2114.99 | 3.04315 | ||||||||
\(696\) | 367.886i | 0.528572i | ||||||||
\(697\) | 5.83702 | 0.00837449 | ||||||||
\(698\) | 1836.05 | 2.63045 | ||||||||
\(699\) | 97.2409i | 0.139114i | ||||||||
\(700\) | 4534.24 | 6.47749 | ||||||||
\(701\) | − | 416.398i | − | 0.594006i | −0.954877 | − | 0.297003i | \(-0.904013\pi\) | ||
0.954877 | − | 0.297003i | \(-0.0959871\pi\) | |||||||
\(702\) | −73.8616 | −0.105216 | ||||||||
\(703\) | 545.047i | 0.775316i | ||||||||
\(704\) | − | 1752.78i | − | 2.48974i | ||||||
\(705\) | 81.3445i | 0.115382i | ||||||||
\(706\) | −348.397 | −0.493480 | ||||||||
\(707\) | − | 340.551i | − | 0.481684i | ||||||
\(708\) | 673.637 | − | 356.901i | 0.951465 | − | 0.504098i | ||||
\(709\) | −751.459 | −1.05989 | −0.529943 | − | 0.848033i | \(-0.677787\pi\) | ||||
−0.529943 | + | 0.848033i | \(0.677787\pi\) | |||||||
\(710\) | − | 311.655i | − | 0.438951i | ||||||
\(711\) | −312.148 | −0.439027 | ||||||||
\(712\) | 563.471 | 0.791392 | ||||||||
\(713\) | −919.721 | −1.28993 | ||||||||
\(714\) | 21.1580i | 0.0296331i | ||||||||
\(715\) | −799.203 | −1.11777 | ||||||||
\(716\) | − | 98.2801i | − | 0.137263i | ||||||
\(717\) | −489.656 | −0.682923 | ||||||||
\(718\) | − | 951.985i | − | 1.32588i | ||||||
\(719\) | 869.723i | 1.20963i | 0.796367 | + | 0.604814i | \(0.206753\pi\) | ||||
−0.796367 | + | 0.604814i | \(0.793247\pi\) | |||||||
\(720\) | 272.996 | 0.379161 | ||||||||
\(721\) | − | 1194.82i | − | 1.65717i | ||||||
\(722\) | 756.952i | 1.04841i | ||||||||
\(723\) | 156.731 | 0.216778 | ||||||||
\(724\) | 1451.34 | 2.00462 | ||||||||
\(725\) | 1106.58 | 1.52632 | ||||||||
\(726\) | 1759.75i | 2.42390i | ||||||||
\(727\) | 1392.73 | 1.91572 | 0.957859 | − | 0.287238i | \(-0.0927370\pi\) | ||||
0.957859 | + | 0.287238i | \(0.0927370\pi\) | |||||||
\(728\) | −489.872 | −0.672901 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −1352.70 | −1.85301 | ||||||||
\(731\) | − | 11.0178i | − | 0.0150723i | ||||||
\(732\) | − | 414.676i | − | 0.566497i | ||||||
\(733\) | −57.5400 | −0.0784993 | −0.0392497 | − | 0.999229i | \(-0.512497\pi\) | ||||
−0.0392497 | + | 0.999229i | \(0.512497\pi\) | |||||||
\(734\) | 76.0226 | 0.103573 | ||||||||
\(735\) | 806.563 | 1.09736 | ||||||||
\(736\) | −294.300 | −0.399865 | ||||||||
\(737\) | −1671.91 | −2.26854 | ||||||||
\(738\) | − | 163.627i | − | 0.221716i | ||||||
\(739\) | − | 194.224i | − | 0.262820i | −0.991328 | − | 0.131410i | \(-0.958049\pi\) | ||
0.991328 | − | 0.131410i | \(-0.0419505\pi\) | |||||||
\(740\) | − | 3217.29i | − | 4.34769i | ||||||
\(741\) | − | 85.2502i | − | 0.115047i | ||||||
\(742\) | 1237.18i | 1.66736i | ||||||||
\(743\) | −365.950 | −0.492531 | −0.246265 | − | 0.969202i | \(-0.579203\pi\) | ||||
−0.246265 | + | 0.969202i | \(0.579203\pi\) | |||||||
\(744\) | −864.639 | −1.16215 | ||||||||
\(745\) | 884.392i | 1.18710i | ||||||||
\(746\) | − | 239.700i | − | 0.321314i | ||||||
\(747\) | 354.371i | 0.474392i | ||||||||
\(748\) | 55.4615i | 0.0741464i | ||||||||
\(749\) | −396.573 | −0.529470 | ||||||||
\(750\) | − | 1959.04i | − | 2.61205i | ||||||
\(751\) | − | 196.887i | − | 0.262166i | −0.991371 | − | 0.131083i | \(-0.958155\pi\) | ||
0.991371 | − | 0.131083i | \(-0.0418455\pi\) | |||||||
\(752\) | 49.6805i | 0.0660645i | ||||||||
\(753\) | 157.417 | 0.209053 | ||||||||
\(754\) | −257.766 | −0.341865 | ||||||||
\(755\) | − | 2436.43i | − | 3.22706i | ||||||
\(756\) | 386.093 | 0.510705 | ||||||||
\(757\) | 581.124 | 0.767667 | 0.383834 | − | 0.923402i | \(-0.374604\pi\) | ||||
0.383834 | + | 0.923402i | \(0.374604\pi\) | |||||||
\(758\) | 844.670i | 1.11434i | ||||||||
\(759\) | 767.027 | 1.01058 | ||||||||
\(760\) | 1273.39i | 1.67551i | ||||||||
\(761\) | −1257.55 | −1.65249 | −0.826246 | − | 0.563310i | \(-0.809528\pi\) | ||||
−0.826246 | + | 0.563310i | \(0.809528\pi\) | |||||||
\(762\) | 238.466i | 0.312947i | ||||||||
\(763\) | 1677.78i | 2.19893i | ||||||||
\(764\) | 2237.37i | 2.92849i | ||||||||
\(765\) | 10.0804 | 0.0131770 | ||||||||
\(766\) | 2283.97i | 2.98168i | ||||||||
\(767\) | 115.983 | + | 218.914i | 0.151217 | + | 0.285416i | ||||
\(768\) | −783.764 | −1.02053 | ||||||||
\(769\) | − | 865.286i | − | 1.12521i | −0.826726 | − | 0.562605i | \(-0.809799\pi\) | ||
0.826726 | − | 0.562605i | \(-0.190201\pi\) | |||||||
\(770\) | 6417.65 | 8.33462 | ||||||||
\(771\) | −130.431 | −0.169171 | ||||||||
\(772\) | 204.738 | 0.265205 | ||||||||
\(773\) | 1118.01i | 1.44633i | 0.690675 | + | 0.723165i | \(0.257313\pi\) | ||||
−0.690675 | + | 0.723165i | \(0.742687\pi\) | |||||||
\(774\) | −308.858 | −0.399041 | ||||||||
\(775\) | 2600.79i | 3.35586i | ||||||||
\(776\) | −1470.48 | −1.89494 | ||||||||
\(777\) | − | 802.192i | − | 1.03242i | ||||||
\(778\) | − | 1671.50i | − | 2.14846i | ||||||
\(779\) | 188.856 | 0.242434 | ||||||||
\(780\) | 503.212i | 0.645144i | ||||||||
\(781\) | − | 203.694i | − | 0.260812i | ||||||
\(782\) | 26.4660 | 0.0338440 | ||||||||
\(783\) | 94.2259 | 0.120340 | ||||||||
\(784\) | 492.602 | 0.628319 | ||||||||
\(785\) | 216.995i | 0.276427i | ||||||||
\(786\) | −710.493 | −0.903935 | ||||||||
\(787\) | −1066.39 | −1.35501 | −0.677506 | − | 0.735517i | \(-0.736939\pi\) | ||||
−0.677506 | + | 0.735517i | \(0.736939\pi\) | |||||||
\(788\) | −615.769 | −0.781432 | ||||||||
\(789\) | 634.578 | 0.804281 | ||||||||
\(790\) | 3266.93i | 4.13535i | ||||||||
\(791\) | 234.027i | 0.295862i | ||||||||
\(792\) | 721.091 | 0.910468 | ||||||||
\(793\) | 134.758 | 0.169935 | ||||||||
\(794\) | −2196.99 | −2.76699 | ||||||||
\(795\) | 589.438 | 0.741431 | ||||||||
\(796\) | 309.060 | 0.388266 | ||||||||
\(797\) | 464.166i | 0.582392i | 0.956663 | + | 0.291196i | \(0.0940531\pi\) | ||||
−0.956663 | + | 0.291196i | \(0.905947\pi\) | |||||||
\(798\) | 684.565i | 0.857850i | ||||||||
\(799\) | 1.83447i | 0.00229595i | ||||||||
\(800\) | 832.224i | 1.04028i | ||||||||
\(801\) | − | 144.321i | − | 0.180176i | ||||||
\(802\) | 202.514 | 0.252512 | ||||||||
\(803\) | −884.106 | −1.10100 | ||||||||
\(804\) | 1052.71i | 1.30934i | ||||||||
\(805\) | − | 1993.55i | − | 2.47646i | ||||||
\(806\) | − | 605.825i | − | 0.751644i | ||||||
\(807\) | − | 0.646667i | − | 0.000801322i | ||||||
\(808\) | −400.474 | −0.495636 | ||||||||
\(809\) | 376.680i | 0.465612i | 0.972523 | + | 0.232806i | \(0.0747907\pi\) | ||||
−0.972523 | + | 0.232806i | \(0.925209\pi\) | |||||||
\(810\) | − | 282.580i | − | 0.348865i | ||||||
\(811\) | 356.067i | 0.439047i | 0.975607 | + | 0.219524i | \(0.0704503\pi\) | ||||
−0.975607 | + | 0.219524i | \(0.929550\pi\) | |||||||
\(812\) | 1347.41 | 1.65937 | ||||||||
\(813\) | −649.617 | −0.799037 | ||||||||
\(814\) | − | 3230.28i | − | 3.96841i | ||||||
\(815\) | −277.633 | −0.340654 | ||||||||
\(816\) | 6.15655 | 0.00754479 | ||||||||
\(817\) | − | 356.480i | − | 0.436328i | ||||||
\(818\) | −945.096 | −1.15537 | ||||||||
\(819\) | 125.470i | 0.153199i | ||||||||
\(820\) | −1114.77 | −1.35948 | ||||||||
\(821\) | 7.62665i | 0.00928946i | 0.999989 | + | 0.00464473i | \(0.00147847\pi\) | ||||
−0.999989 | + | 0.00464473i | \(0.998522\pi\) | |||||||
\(822\) | 1163.95i | 1.41600i | ||||||||
\(823\) | − | 846.755i | − | 1.02886i | −0.857531 | − | 0.514432i | \(-0.828003\pi\) | ||
0.857531 | − | 0.514432i | \(-0.171997\pi\) | |||||||
\(824\) | −1405.06 | −1.70517 | ||||||||
\(825\) | − | 2169.00i | − | 2.62909i | ||||||
\(826\) | −931.354 | − | 1757.89i | −1.12755 | − | 2.12820i | ||||
\(827\) | 1039.36 | 1.25679 | 0.628393 | − | 0.777896i | \(-0.283713\pi\) | ||||
0.628393 | + | 0.777896i | \(0.283713\pi\) | |||||||
\(828\) | − | 482.953i | − | 0.583276i | ||||||
\(829\) | −528.130 | −0.637069 | −0.318535 | − | 0.947911i | \(-0.603191\pi\) | ||||
−0.318535 | + | 0.947911i | \(0.603191\pi\) | |||||||
\(830\) | 3708.82 | 4.46846 | ||||||||
\(831\) | 152.355 | 0.183340 | ||||||||
\(832\) | − | 358.648i | − | 0.431067i | ||||||
\(833\) | 18.1895 | 0.0218361 | ||||||||
\(834\) | − | 1337.06i | − | 1.60320i | ||||||
\(835\) | −1301.83 | −1.55908 | ||||||||
\(836\) | 1794.45i | 2.14647i | ||||||||
\(837\) | 221.458i | 0.264586i | ||||||||
\(838\) | 1498.58 | 1.78828 | ||||||||
\(839\) | 814.378i | 0.970653i | 0.874333 | + | 0.485327i | \(0.161299\pi\) | ||||
−0.874333 | + | 0.485327i | \(0.838701\pi\) | |||||||
\(840\) | − | 1874.16i | − | 2.23114i | ||||||
\(841\) | −512.166 | −0.608996 | ||||||||
\(842\) | 249.509 | 0.296329 | ||||||||
\(843\) | −620.655 | −0.736245 | ||||||||
\(844\) | 1803.03i | 2.13630i | ||||||||
\(845\) | 1403.92 | 1.66145 | ||||||||
\(846\) | 51.4248 | 0.0607858 | ||||||||
\(847\) | 2989.31 | 3.52929 | ||||||||
\(848\) | 359.995 | 0.424522 | ||||||||
\(849\) | 645.857i | 0.760726i | ||||||||
\(850\) | − | 74.8406i | − | 0.0880477i | ||||||
\(851\) | −1003.44 | −1.17913 | ||||||||
\(852\) | −128.254 | −0.150533 | ||||||||
\(853\) | 186.085 | 0.218153 | 0.109077 | − | 0.994033i | \(-0.465211\pi\) | ||||
0.109077 | + | 0.994033i | \(0.465211\pi\) | |||||||
\(854\) | −1082.12 | −1.26712 | ||||||||
\(855\) | 326.151 | 0.381463 | ||||||||
\(856\) | 466.353i | 0.544805i | ||||||||
\(857\) | − | 1618.09i | − | 1.88809i | −0.329816 | − | 0.944045i | \(-0.606987\pi\) | ||
0.329816 | − | 0.944045i | \(-0.393013\pi\) | |||||||
\(858\) | 505.245i | 0.588863i | ||||||||
\(859\) | − | 718.693i | − | 0.836662i | −0.908295 | − | 0.418331i | \(-0.862615\pi\) | ||
0.908295 | − | 0.418331i | \(-0.137385\pi\) | |||||||
\(860\) | 2104.22i | 2.44677i | ||||||||
\(861\) | −277.955 | −0.322828 | ||||||||
\(862\) | 85.7346 | 0.0994601 | ||||||||
\(863\) | 1217.22i | 1.41045i | 0.708981 | + | 0.705227i | \(0.249155\pi\) | ||||
−0.708981 | + | 0.705227i | \(0.750845\pi\) | |||||||
\(864\) | 70.8642i | 0.0820187i | ||||||||
\(865\) | 1139.63i | 1.31749i | ||||||||
\(866\) | − | 1267.43i | − | 1.46355i | ||||||
\(867\) | −500.335 | −0.577088 | ||||||||
\(868\) | 3166.79i | 3.64838i | ||||||||
\(869\) | 2135.23i | 2.45711i | ||||||||
\(870\) | − | 986.163i | − | 1.13352i | ||||||
\(871\) | −342.102 | −0.392769 | ||||||||
\(872\) | 1973.00 | 2.26262 | ||||||||
\(873\) | 376.630i | 0.431420i | ||||||||
\(874\) | 856.303 | 0.979751 | ||||||||
\(875\) | −3327.84 | −3.80325 | ||||||||
\(876\) | 556.670i | 0.635468i | ||||||||
\(877\) | 1635.00 | 1.86431 | 0.932154 | − | 0.362061i | \(-0.117927\pi\) | ||||
0.932154 | + | 0.362061i | \(0.117927\pi\) | |||||||
\(878\) | 956.734i | 1.08967i | ||||||||
\(879\) | −142.755 | −0.162407 | ||||||||
\(880\) | − | 1867.40i | − | 2.12205i | ||||||
\(881\) | − | 842.026i | − | 0.955762i | −0.878425 | − | 0.477881i | \(-0.841405\pi\) | ||
0.878425 | − | 0.477881i | \(-0.158595\pi\) | |||||||
\(882\) | − | 509.898i | − | 0.578115i | ||||||
\(883\) | −306.069 | −0.346624 | −0.173312 | − | 0.984867i | \(-0.555447\pi\) | ||||
−0.173312 | + | 0.984867i | \(0.555447\pi\) | |||||||
\(884\) | 11.3483i | 0.0128375i | ||||||||
\(885\) | −837.523 | + | 443.730i | −0.946353 | + | 0.501390i | ||||
\(886\) | 1840.61 | 2.07744 | ||||||||
\(887\) | 910.611i | 1.02662i | 0.858204 | + | 0.513309i | \(0.171581\pi\) | ||||
−0.858204 | + | 0.513309i | \(0.828419\pi\) | |||||||
\(888\) | −943.344 | −1.06232 | ||||||||
\(889\) | 405.085 | 0.455663 | ||||||||
\(890\) | −1510.45 | −1.69714 | ||||||||
\(891\) | − | 184.691i | − | 0.207285i | ||||||
\(892\) | −1497.46 | −1.67877 | ||||||||
\(893\) | 59.3539i | 0.0664657i | ||||||||
\(894\) | 559.100 | 0.625392 | ||||||||
\(895\) | 122.190i | 0.136525i | ||||||||
\(896\) | 2336.62i | 2.60783i | ||||||||
\(897\) | 156.947 | 0.174968 | ||||||||
\(898\) | − | 1249.36i | − | 1.39126i | ||||||
\(899\) | 772.855i | 0.859683i | ||||||||
\(900\) | −1365.69 | −1.51744 | ||||||||
\(901\) | 13.2929 | 0.0147535 | ||||||||
\(902\) | −1119.27 | −1.24088 | ||||||||
\(903\) | 524.661i | 0.581020i | ||||||||
\(904\) | 275.206 | 0.304432 | ||||||||
\(905\) | −1804.43 | −1.99385 | ||||||||
\(906\) | −1540.28 | −1.70009 | ||||||||
\(907\) | −1445.12 | −1.59330 | −0.796648 | − | 0.604444i | \(-0.793395\pi\) | ||||
−0.796648 | + | 0.604444i | \(0.793395\pi\) | |||||||
\(908\) | − | 1654.47i | − | 1.82210i | ||||||
\(909\) | 102.572i | 0.112841i | ||||||||
\(910\) | 1313.16 | 1.44303 | ||||||||
\(911\) | −884.175 | −0.970554 | −0.485277 | − | 0.874360i | \(-0.661281\pi\) | ||||
−0.485277 | + | 0.874360i | \(0.661281\pi\) | |||||||
\(912\) | 199.194 | 0.218415 | ||||||||
\(913\) | 2424.04 | 2.65503 | ||||||||
\(914\) | −1794.09 | −1.96290 | ||||||||
\(915\) | 515.560i | 0.563453i | ||||||||
\(916\) | − | 1267.11i | − | 1.38330i | ||||||
\(917\) | 1206.92i | 1.31617i | ||||||||
\(918\) | − | 6.37271i | − | 0.00694194i | ||||||
\(919\) | − | 1285.28i | − | 1.39856i | −0.714848 | − | 0.699280i | \(-0.753504\pi\) | ||
0.714848 | − | 0.699280i | \(-0.246496\pi\) | |||||||
\(920\) | −2344.33 | −2.54818 | ||||||||
\(921\) | −813.560 | −0.883344 | ||||||||
\(922\) | 445.471i | 0.483157i | ||||||||
\(923\) | − | 41.6792i | − | 0.0451563i | ||||||
\(924\) | − | 2641.04i | − | 2.85827i | ||||||
\(925\) | 2837.53i | 3.06760i | ||||||||
\(926\) | −1655.42 | −1.78771 | ||||||||
\(927\) | 359.874i | 0.388214i | ||||||||
\(928\) | 247.305i | 0.266493i | ||||||||
\(929\) | − | 1119.46i | − | 1.20502i | −0.798113 | − | 0.602508i | \(-0.794168\pi\) | ||
0.798113 | − | 0.602508i | \(-0.205832\pi\) | |||||||
\(930\) | 2317.77 | 2.49222 | ||||||||
\(931\) | 588.517 | 0.632135 | ||||||||
\(932\) | − | 418.818i | − | 0.449376i | ||||||
\(933\) | 92.5493 | 0.0991954 | ||||||||
\(934\) | −198.343 | −0.212359 | ||||||||
\(935\) | − | 68.9544i | − | 0.0737480i | ||||||
\(936\) | 147.547 | 0.157636 | ||||||||
\(937\) | − | 1417.82i | − | 1.51315i | −0.653908 | − | 0.756574i | \(-0.726872\pi\) | ||
0.653908 | − | 0.756574i | \(-0.273128\pi\) | |||||||
\(938\) | 2747.10 | 2.92868 | ||||||||
\(939\) | − | 14.5177i | − | 0.0154608i | ||||||
\(940\) | − | 350.352i | − | 0.372715i | ||||||
\(941\) | − | 698.423i | − | 0.742214i | −0.928590 | − | 0.371107i | \(-0.878978\pi\) | ||
0.928590 | − | 0.371107i | \(-0.121022\pi\) | |||||||
\(942\) | 137.181 | 0.145628 | ||||||||
\(943\) | 347.686i | 0.368702i | ||||||||
\(944\) | −511.511 | + | 271.005i | −0.541855 | + | 0.287081i | ||||
\(945\) | −480.023 | −0.507961 | ||||||||
\(946\) | 2112.72i | 2.23332i | ||||||||
\(947\) | 210.515 | 0.222297 | 0.111149 | − | 0.993804i | \(-0.464547\pi\) | ||||
0.111149 | + | 0.993804i | \(0.464547\pi\) | |||||||
\(948\) | 1344.43 | 1.41817 | ||||||||
\(949\) | −180.903 | −0.190625 | ||||||||
\(950\) | − | 2421.45i | − | 2.54890i | ||||||
\(951\) | −693.674 | −0.729416 | ||||||||
\(952\) | − | 42.2656i | − | 0.0443967i | ||||||
\(953\) | −681.588 | −0.715202 | −0.357601 | − | 0.933874i | \(-0.616405\pi\) | ||||
−0.357601 | + | 0.933874i | \(0.616405\pi\) | |||||||
\(954\) | − | 372.634i | − | 0.390602i | ||||||
\(955\) | − | 2781.69i | − | 2.91276i | ||||||
\(956\) | 2108.96 | 2.20602 | ||||||||
\(957\) | − | 644.545i | − | 0.673505i | ||||||
\(958\) | − | 1934.70i | − | 2.01952i | ||||||
\(959\) | 1977.22 | 2.06175 | ||||||||
\(960\) | 1372.12 | 1.42929 | ||||||||
\(961\) | −855.434 | −0.890150 | ||||||||
\(962\) | − | 660.970i | − | 0.687080i | ||||||
\(963\) | 119.446 | 0.124035 | ||||||||
\(964\) | −675.042 | −0.700251 | ||||||||
\(965\) | −254.548 | −0.263780 | ||||||||
\(966\) | −1260.29 | −1.30465 | ||||||||
\(967\) | 1165.11i | 1.20487i | 0.798168 | + | 0.602435i | \(0.205803\pi\) | ||||
−0.798168 | + | 0.602435i | \(0.794197\pi\) | |||||||
\(968\) | − | 3515.30i | − | 3.63151i | ||||||
\(969\) | 7.35530 | 0.00759060 | ||||||||
\(970\) | 3941.79 | 4.06370 | ||||||||
\(971\) | −393.936 | −0.405701 | −0.202850 | − | 0.979210i | \(-0.565021\pi\) | ||||
−0.202850 | + | 0.979210i | \(0.565021\pi\) | |||||||
\(972\) | −116.289 | −0.119639 | ||||||||
\(973\) | −2271.29 | −2.33432 | ||||||||
\(974\) | − | 1424.14i | − | 1.46215i | ||||||
\(975\) | − | 443.814i | − | 0.455194i | ||||||
\(976\) | 314.874i | 0.322617i | ||||||||
\(977\) | 1020.38i | 1.04440i | 0.852822 | + | 0.522202i | \(0.174889\pi\) | ||||
−0.852822 | + | 0.522202i | \(0.825111\pi\) | |||||||
\(978\) | 175.516i | 0.179464i | ||||||||
\(979\) | −987.214 | −1.00839 | ||||||||
\(980\) | −3473.88 | −3.54478 | ||||||||
\(981\) | − | 505.341i | − | 0.515128i | ||||||
\(982\) | − | 2979.79i | − | 3.03441i | ||||||
\(983\) | − | 464.597i | − | 0.472632i | −0.971676 | − | 0.236316i | \(-0.924060\pi\) | ||
0.971676 | − | 0.236316i | \(-0.0759401\pi\) | |||||||
\(984\) | 326.863i | 0.332178i | ||||||||
\(985\) | 765.576 | 0.777234 | ||||||||
\(986\) | − | 22.2398i | − | 0.0225555i | ||||||
\(987\) | − | 87.3560i | − | 0.0885066i | ||||||
\(988\) | 367.174i | 0.371634i | ||||||||
\(989\) | 656.284 | 0.663583 | ||||||||
\(990\) | −1932.97 | −1.95249 | ||||||||
\(991\) | 512.343i | 0.516996i | 0.966012 | + | 0.258498i | \(0.0832276\pi\) | ||||
−0.966012 | + | 0.258498i | \(0.916772\pi\) | |||||||
\(992\) | −581.239 | −0.585926 | ||||||||
\(993\) | −51.3327 | −0.0516946 | ||||||||
\(994\) | 334.687i | 0.336707i | ||||||||
\(995\) | −384.249 | −0.386180 | ||||||||
\(996\) | − | 1526.28i | − | 1.53241i | ||||||
\(997\) | −174.174 | −0.174698 | −0.0873491 | − | 0.996178i | \(-0.527840\pi\) | ||||
−0.0873491 | + | 0.996178i | \(0.527840\pi\) | |||||||
\(998\) | 786.813i | 0.788390i | ||||||||
\(999\) | 241.617i | 0.241858i |
(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 | 177.3.c.a.58.2 | ✓ | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.19 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.19 | yes | 20 | |
177.176 | even | 2 | 531.3.c.c.235.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
177.3.c.a.58.19 | yes | 20 | 59.58 | odd | 2 | inner | |
531.3.c.c.235.2 | 20 | 177.176 | even | 2 | |||
531.3.c.c.235.19 | 20 | 3.2 | odd | 2 |