Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [104,4,Mod(17,104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(104, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("104.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 104 = 2^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 104.o (of order \(6\), degree \(2\), 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: | \(6.13619864060\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 340 x^{18} + 48278 x^{16} + 3724852 x^{14} + 170209937 x^{12} + 4703455168 x^{10} + \cdots + 549543481344 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{40} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Root | \(0.769882i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 104.17 |
Dual form | 104.4.o.a.49.5 |
$q$-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 \(\left(\mathbb{Z}/104\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(53\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.884941 | + | 1.53276i | −0.170307 | + | 0.294980i | −0.938527 | − | 0.345205i | \(-0.887809\pi\) |
0.768220 | + | 0.640186i | \(0.221143\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.308172i | − | 0.0275637i | −0.999905 | − | 0.0137819i | \(-0.995613\pi\) | ||
0.999905 | − | 0.0137819i | \(-0.00438704\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.0872 | − | 6.40118i | 0.598651 | − | 0.345631i | −0.169860 | − | 0.985468i | \(-0.554331\pi\) |
0.768511 | + | 0.639837i | \(0.220998\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.9338 | + | 20.6699i | 0.441991 | + | 0.765551i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.0972 | + | 11.0258i | 0.523456 | + | 0.302217i | 0.738347 | − | 0.674421i | \(-0.235607\pi\) |
−0.214892 | + | 0.976638i | \(0.568940\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.7828 | + | 45.6150i | 0.230047 | + | 0.973179i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.472354 | + | 0.272714i | 0.00813075 | + | 0.00469429i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 35.0294 | + | 60.6726i | 0.499757 | + | 0.865605i | 1.00000 | 0.000280522i | \(-8.92928e-5\pi\) | |
−0.500243 | + | 0.865885i | \(0.666756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.4302 | − | 10.0633i | 0.210461 | − | 0.121510i | −0.391065 | − | 0.920363i | \(-0.627893\pi\) |
0.601526 | + | 0.798853i | \(0.294560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 22.6587i | 0.235454i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 15.5865 | − | 26.9966i | 0.141305 | − | 0.244747i | −0.786683 | − | 0.617357i | \(-0.788204\pi\) |
0.927988 | + | 0.372610i | \(0.121537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 124.905 | 0.999240 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −90.0295 | −0.641710 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −42.8445 | + | 74.2088i | −0.274346 | + | 0.475180i | −0.969970 | − | 0.243225i | \(-0.921795\pi\) |
0.695624 | + | 0.718406i | \(0.255128\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 167.593i | − | 0.970987i | −0.874240 | − | 0.485493i | \(-0.838640\pi\) | ||
0.874240 | − | 0.485493i | \(-0.161360\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −33.7997 | + | 19.5143i | −0.178296 | + | 0.102939i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.97266 | − | 3.41675i | −0.00952688 | − | 0.0165010i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.3333 | − | 11.1621i | −0.0859021 | − | 0.0495956i | 0.456434 | − | 0.889757i | \(-0.349127\pi\) |
−0.542336 | + | 0.840162i | \(0.682460\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −79.4592 | − | 23.8391i | −0.326247 | − | 0.0978798i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −124.007 | − | 71.5954i | −0.472356 | − | 0.272715i | 0.244869 | − | 0.969556i | \(-0.421255\pi\) |
−0.717226 | + | 0.696841i | \(0.754588\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −170.423 | − | 295.181i | −0.604401 | − | 1.04685i | −0.992146 | − | 0.125087i | \(-0.960079\pi\) |
0.387745 | − | 0.921767i | \(-0.373254\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.36987 | − | 3.67765i | 0.0211014 | − | 0.0121829i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 224.686i | − | 0.697314i | −0.937250 | − | 0.348657i | \(-0.886638\pi\) | ||
0.937250 | − | 0.348657i | \(-0.113362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −89.5497 | + | 155.105i | −0.261078 | + | 0.452200i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −123.996 | −0.340448 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.40240 | 0.00622632 | 0.00311316 | − | 0.999995i | \(-0.499009\pi\) | ||||
0.00311316 | + | 0.999995i | \(0.499009\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.39782 | − | 5.88520i | 0.00833023 | − | 0.0144284i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 35.6218i | 0.0827758i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −353.820 | + | 204.278i | −0.780736 | + | 0.450758i | −0.836691 | − | 0.547675i | \(-0.815513\pi\) |
0.0559550 | + | 0.998433i | \(0.482180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −231.775 | − | 401.446i | −0.486487 | − | 0.842620i | 0.513392 | − | 0.858154i | \(-0.328389\pi\) |
−0.999879 | + | 0.0155338i | \(0.995055\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 264.623 | + | 152.780i | 0.529197 | + | 0.305532i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.0573 | − | 3.32296i | 0.0268244 | − | 0.00634095i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 169.791 | + | 98.0287i | 0.309601 | + | 0.178748i | 0.646748 | − | 0.762704i | \(-0.276129\pi\) |
−0.337147 | + | 0.941452i | \(0.609462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 27.5862 | + | 47.7808i | 0.0481303 | + | 0.0833642i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 530.234 | − | 306.131i | 0.886298 | − | 0.511705i | 0.0135685 | − | 0.999908i | \(-0.495681\pi\) |
0.872730 | + | 0.488203i | \(0.162348\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 575.520i | − | 0.922734i | −0.887210 | − | 0.461367i | \(-0.847359\pi\) | ||
0.887210 | − | 0.461367i | \(-0.152641\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −110.534 | + | 191.450i | −0.170178 | + | 0.294756i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 282.311 | 0.417823 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 272.157 | 0.387595 | 0.193798 | − | 0.981042i | \(-0.437919\pi\) | ||||
0.193798 | + | 0.981042i | \(0.437919\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −242.541 | + | 420.093i | −0.332703 | + | 0.576259i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1416.78i | 1.87363i | 0.349819 | + | 0.936817i | \(0.386243\pi\) | ||||
−0.349819 | + | 0.936817i | \(0.613757\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.6976 | − | 10.7951i | 0.0238593 | − | 0.0137752i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −75.8297 | − | 131.341i | −0.0934459 | − | 0.161853i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 358.036 | + | 206.712i | 0.426424 | + | 0.246196i | 0.697822 | − | 0.716271i | \(-0.254153\pi\) |
−0.271398 | + | 0.962467i | \(0.587486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 411.541 | + | 436.719i | 0.474079 | + | 0.503083i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 256.880 | + | 148.310i | 0.286422 | + | 0.165366i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.10123 | − | 5.37149i | −0.00334926 | − | 0.00580109i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 726.870 | − | 419.659i | 0.760851 | − | 0.439277i | −0.0687504 | − | 0.997634i | \(-0.521901\pi\) |
0.829601 | + | 0.558357i | \(0.188568\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 526.315i | 0.534309i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −47.3809 | + | 82.0662i | −0.0466790 | + | 0.0808504i | −0.888421 | − | 0.459030i | \(-0.848197\pi\) |
0.841742 | + | 0.539880i | \(0.181530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 894.718 | 0.855915 | 0.427957 | − | 0.903799i | \(-0.359233\pi\) | ||||
0.427957 | + | 0.903799i | \(0.359233\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.98276 | 0.00648998 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −773.013 | + | 1338.90i | −0.698411 | + | 1.20968i | 0.270606 | + | 0.962690i | \(0.412776\pi\) |
−0.969017 | + | 0.246994i | \(0.920557\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 772.962i | − | 0.679232i | −0.940564 | − | 0.339616i | \(-0.889703\pi\) | ||
0.940564 | − | 0.339616i | \(-0.110297\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.2177 | − | 19.7556i | 0.0292595 | − | 0.0168930i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −541.576 | − | 938.038i | −0.450860 | − | 0.780913i | 0.547579 | − | 0.836754i | \(-0.315549\pi\) |
−0.998440 | + | 0.0558408i | \(0.982216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.31959 | − | 4.80331i | −0.00674613 | − | 0.00389488i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −814.178 | + | 767.238i | −0.643340 | + | 0.606250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 776.753 | + | 448.459i | 0.598360 | + | 0.345463i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −422.366 | − | 731.559i | −0.317330 | − | 0.549631i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 219.477 | − | 126.715i | 0.160891 | − | 0.0928906i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 77.0136i | − | 0.0551065i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 744.855 | − | 1290.13i | 0.520434 | − | 0.901419i | −0.479283 | − | 0.877660i | \(-0.659103\pi\) |
0.999718 | − | 0.0237586i | \(-0.00756330\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 603.257 | 0.411735 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2017.26 | −1.34541 | −0.672705 | − | 0.739911i | \(-0.734868\pi\) | ||||
−0.672705 | + | 0.739911i | \(0.734868\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 128.834 | − | 223.148i | 0.0839952 | − | 0.145484i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.7445i | 0.0176879i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1085.51 | + | 626.717i | −0.676942 | + | 0.390833i | −0.798702 | − | 0.601727i | \(-0.794480\pi\) |
0.121760 | + | 0.992560i | \(0.461146\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1412.92 | − | 2447.25i | −0.862176 | − | 1.49333i | −0.869824 | − | 0.493362i | \(-0.835768\pi\) |
0.00764755 | − | 0.999971i | \(-0.497566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 344.390 | + | 198.833i | 0.205694 | + | 0.118757i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −297.019 | + | 990.006i | −0.173692 | + | 0.578940i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.8691 | + | 13.2035i | 0.0130977 | + | 0.00756198i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −158.492 | − | 274.517i | −0.0889268 | − | 0.154026i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2041.42 | − | 1178.61i | 1.12241 | − | 0.648025i | 0.180396 | − | 0.983594i | \(-0.442262\pi\) |
0.942016 | + | 0.335569i | \(0.108929\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3522.71i | − | 1.89851i | −0.314514 | − | 0.949253i | \(-0.601842\pi\) | ||
0.314514 | − | 0.949253i | \(-0.398158\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −836.064 | + | 1448.11i | −0.441776 | + | 0.765179i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −51.6474 | −0.0267640 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3294.99 | −1.67496 | −0.837480 | − | 0.546467i | \(-0.815972\pi\) | ||||
−0.837480 | + | 0.546467i | \(0.815972\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.12598 | + | 3.68231i | −0.00106038 | + | 0.00183664i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 399.088i | − | 0.195357i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −264.163 | + | 152.515i | −0.126938 | + | 0.0732875i | −0.562124 | − | 0.827053i | \(-0.690016\pi\) |
0.435187 | + | 0.900340i | \(0.356682\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.01375 | + | 10.4161i | 0.00283739 | + | 0.00491451i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −745.246 | − | 430.268i | −0.345322 | − | 0.199372i | 0.317301 | − | 0.948325i | \(-0.397224\pi\) |
−0.662623 | + | 0.748953i | \(0.730557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1964.46 | + | 983.716i | −0.894157 | + | 0.447754i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 416.016 | + | 240.187i | 0.186044 | + | 0.107412i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 790.927 | + | 1369.93i | 0.347590 | + | 0.602043i | 0.985821 | − | 0.167802i | \(-0.0536668\pi\) |
−0.638231 | + | 0.769845i | \(0.720334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1384.84 | − | 799.540i | 0.598196 | − | 0.345369i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 723.096i | − | 0.307069i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −939.937 | + | 1628.02i | −0.392482 | + | 0.679798i | −0.992776 | − | 0.119981i | \(-0.961717\pi\) |
0.600295 | + | 0.799779i | \(0.295050\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2800.78 | 1.15017 | 0.575083 | − | 0.818095i | \(-0.304970\pi\) | ||||
0.575083 | + | 0.818095i | \(0.304970\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 820.427 | 0.331408 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.43984 | + | 5.95798i | −0.00136704 | + | 0.00236778i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1544.90i | 0.604141i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −998.173 | + | 576.295i | −0.384161 | + | 0.221795i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1792.03 | − | 3103.89i | −0.678885 | − | 1.17586i | −0.975317 | − | 0.220809i | \(-0.929130\pi\) |
0.296432 | − | 0.955054i | \(-0.404203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4464.23 | + | 2577.43i | 1.66499 | + | 0.961280i | 0.970279 | + | 0.241988i | \(0.0777994\pi\) |
0.694707 | + | 0.719293i | \(0.255534\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.34654 | + | 24.4871i | −0.00269793 | + | 0.00899259i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1806.08 | + | 1042.74i | 0.653188 | + | 0.377119i | 0.789677 | − | 0.613523i | \(-0.210248\pi\) |
−0.136488 | + | 0.990642i | \(0.543582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1362.49 | − | 2359.91i | −0.485350 | − | 0.840651i | 0.514508 | − | 0.857485i | \(-0.327974\pi\) |
−0.999858 | + | 0.0168348i | \(0.994641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −300.509 | + | 173.499i | −0.105454 | + | 0.0608840i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1097.02i | 0.379290i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.0637 | + | 38.2154i | −0.00751704 | + | 0.0130199i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 744.022 | 0.249822 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 443.823 | 0.146889 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −153.840 | + | 266.458i | −0.0501931 | + | 0.0869370i | −0.890030 | − | 0.455901i | \(-0.849317\pi\) |
0.839837 | + | 0.542838i | \(0.182650\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1083.63i | 0.348587i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −90.9664 | + | 52.5195i | −0.0288552 | + | 0.0166595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1072.79 | − | 1858.13i | −0.335603 | − | 0.581282i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 882.136 | + | 509.301i | 0.272188 | + | 0.157148i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2389.87 | + | 2252.09i | −0.727421 | + | 0.685483i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4548.19 | + | 2625.90i | 1.36578 | + | 0.788535i | 0.990386 | − | 0.138329i | \(-0.0441732\pi\) |
0.375397 | + | 0.926864i | \(0.377506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1490.59 | + | 2581.77i | 0.441655 | + | 0.764969i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3156.55 | − | 1822.44i | 0.922942 | − | 0.532861i | 0.0383694 | − | 0.999264i | \(-0.487784\pi\) |
0.884572 | + | 0.466403i | \(0.154450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1142.45i | − | 0.329673i | −0.986321 | − | 0.164837i | \(-0.947290\pi\) | ||
0.986321 | − | 0.164837i | \(-0.0527097\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −249.829 | + | 432.716i | −0.0711582 | + | 0.123250i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5012.43 | 1.40934 | 0.704668 | − | 0.709537i | \(-0.251096\pi\) | ||||
0.704668 | + | 0.709537i | \(0.251096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −69.2417 | −0.0192206 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −240.843 | + | 417.152i | −0.0660102 | + | 0.114333i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6333.82i | 1.71423i | 0.515126 | + | 0.857114i | \(0.327745\pi\) | ||||
−0.515126 | + | 0.857114i | \(0.672255\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1206.67 | + | 696.670i | −0.322524 | + | 0.186209i | −0.652517 | − | 0.757774i | \(-0.726287\pi\) |
0.329993 | + | 0.943983i | \(0.392954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1644.67 | − | 2848.65i | −0.434179 | − | 0.752019i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 47.7989 | + | 27.5967i | 0.0124643 | + | 0.00719628i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 646.985 | + | 686.568i | 0.166667 | + | 0.176863i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2171.59 | − | 1253.77i | −0.552685 | − | 0.319093i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −898.814 | − | 1556.79i | −0.226027 | − | 0.391489i | 0.730600 | − | 0.682805i | \(-0.239240\pi\) |
−0.956627 | + | 0.291316i | \(0.905907\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 595.316 | − | 343.706i | 0.147933 | − | 0.0854094i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 38.2119i | 0.00938402i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 691.477 | − | 1197.67i | 0.167833 | − | 0.290696i | −0.769825 | − | 0.638255i | \(-0.779656\pi\) |
0.937658 | + | 0.347560i | \(0.112990\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −285.803 | −0.0685672 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2045.18 | −0.485033 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2800.87 | + | 4851.25i | −0.656688 | + | 1.13742i | 0.324780 | + | 0.945790i | \(0.394710\pi\) |
−0.981468 | + | 0.191628i | \(0.938623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.740351i | − | 0.000171620i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −633.681 | + | 365.856i | −0.145246 | + | 0.0838577i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2213.85 | − | 3834.50i | −0.501788 | − | 0.869122i | −0.999998 | − | 0.00206531i | \(-0.999343\pi\) |
0.498210 | − | 0.867056i | \(-0.333991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2571.05 | − | 1484.39i | −0.576309 | − | 0.332732i | 0.183356 | − | 0.983047i | \(-0.441304\pi\) |
−0.759665 | + | 0.650314i | \(0.774637\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1033.58 | + | 244.324i | −0.229139 | + | 0.0541654i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2385.33 | + | 1377.17i | 0.523058 | + | 0.301988i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1072.92 | − | 1858.36i | −0.232728 | − | 0.403097i | 0.725882 | − | 0.687819i | \(-0.241432\pi\) |
−0.958610 | + | 0.284723i | \(0.908098\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3464.13 | − | 2000.01i | 0.743340 | − | 0.429167i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4898.16i | − | 1.03986i | −0.854210 | − | 0.519928i | \(-0.825959\pi\) | ||
0.854210 | − | 0.519928i | \(-0.174041\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1212.14 | − | 2099.48i | 0.254608 | − | 0.440994i | −0.710181 | − | 0.704019i | \(-0.751387\pi\) |
0.964789 | + | 0.263025i | \(0.0847202\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.9776 | 0.00228161 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1833.18 | −0.377036 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.38673 | − | 4.13394i | 0.000485799 | − | 0.000841429i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1485.49i | 0.299248i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1870.33 | − | 1079.84i | 0.372921 | − | 0.215306i | −0.301813 | − | 0.953367i | \(-0.597592\pi\) |
0.674734 | + | 0.738061i | \(0.264258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 62.9527 | + | 109.037i | 0.0124246 | + | 0.0215200i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1719.31 | − | 992.643i | −0.335907 | − | 0.193936i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1399.52 | + | 419.879i | 0.270689 | + | 0.0812115i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3779.02 | − | 2181.82i | −0.723651 | − | 0.417800i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −83.8586 | − | 145.247i | −0.0158995 | − | 0.0275388i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −123.714 | + | 71.4264i | −0.0232257 | + | 0.0134094i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 885.266i | − | 0.164576i | −0.996609 | − | 0.0822880i | \(-0.973777\pi\) | ||
0.996609 | − | 0.0822880i | \(-0.0262227\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −791.773 | + | 1371.39i | −0.145768 | + | 0.252478i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9880.11 | −1.80145 | −0.900723 | − | 0.434395i | \(-0.856962\pi\) | ||||
−0.900723 | + | 0.434395i | \(0.856962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5644.55 | −1.01933 | −0.509663 | − | 0.860374i | \(-0.670230\pi\) | ||||
−0.509663 | + | 0.860374i | \(0.670230\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 47.0826 | − | 81.5494i | 0.00842159 | − | 0.0145866i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 11147.7i | − | 1.97513i | −0.157202 | − | 0.987566i | \(-0.550247\pi\) | ||
0.157202 | − | 0.987566i | \(-0.449753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1636.42 | + | 944.785i | −0.287215 | + | 0.165824i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1368.14 | − | 2369.69i | −0.237889 | − | 0.412035i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1221.14 | + | 705.024i | 0.210359 | + | 0.121451i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1346.83 | + | 5697.55i | 0.229872 | + | 0.972440i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1184.77 | + | 684.025i | 0.200360 | + | 0.115678i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1438.25 | − | 2491.13i | −0.241014 | − | 0.417448i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3981.54 | − | 2298.74i | 0.661164 | − | 0.381723i | −0.131556 | − | 0.991309i | \(-0.541997\pi\) |
0.792720 | + | 0.609585i | \(0.208664\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 532.823i | − | 0.0876833i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 30.2097 | − | 52.3247i | 0.00492696 | − | 0.00853374i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4309.91 | 0.696663 | 0.348332 | − | 0.937371i | \(-0.386748\pi\) | ||||
0.348332 | + | 0.937371i | \(0.386748\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1917.05 | 0.307139 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1847.84 | − | 3200.55i | 0.293449 | − | 0.508268i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6684.11i | 1.05221i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.7247 | − | 8.50130i | 0.00229783 | − | 0.00132665i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −932.598 | − | 1615.31i | −0.144278 | − | 0.249897i | 0.784825 | − | 0.619717i | \(-0.212753\pi\) |
−0.929103 | + | 0.369820i | \(0.879419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1715.81 | + | 990.623i | 0.263167 | + | 0.151939i | 0.625778 | − | 0.780001i | \(-0.284782\pi\) |
−0.362612 | + | 0.931940i | \(0.618115\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −970.771 | − | 4106.70i | −0.147624 | − | 0.624499i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2955.95 | + | 1706.62i | 0.445693 | + | 0.257321i | 0.706009 | − | 0.708202i | \(-0.250494\pi\) |
−0.260317 | + | 0.965523i | \(0.583827\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −94.3408 | − | 163.403i | −0.0141045 | − | 0.0244297i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1374.76 | + | 793.719i | −0.203810 | + | 0.117670i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5042.77i | 0.741357i | 0.928761 | + | 0.370678i | \(0.120875\pi\) | ||||
−0.928761 | + | 0.370678i | \(0.879125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3226.96 | + | 5589.26i | −0.470471 | + | 0.814879i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1495.07 | 0.216174 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −177.359 | −0.0254340 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5363.87 | + | 9290.49i | −0.762920 | + | 1.32142i | 0.178420 | + | 0.983954i | \(0.442901\pi\) |
−0.941340 | + | 0.337461i | \(0.890432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 3417.61i | − | 0.482151i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.6358 | − | 15.3782i | 0.00372739 | − | 0.00215201i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6338.32 | + | 10978.3i | 0.879855 | + | 1.52395i | 0.851500 | + | 0.524355i | \(0.175694\pi\) |
0.0283552 | + | 0.999598i | \(0.490973\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 118.044 | + | 68.1525i | 0.0162553 | + | 0.00938501i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3847.02 | − | 1154.17i | −0.525548 | − | 0.157674i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 882.953 | + | 509.773i | 0.119668 | + | 0.0690905i | 0.558639 | − | 0.829411i | \(-0.311324\pi\) |
−0.438971 | + | 0.898501i | \(0.644657\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1318.30 | + | 2283.37i | 0.177267 | + | 0.307036i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2190.46 | − | 1264.66i | 0.292239 | − | 0.168724i | −0.346712 | − | 0.937971i | \(-0.612702\pi\) |
0.638951 | + | 0.769247i | \(0.279369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 87.0004i | − | 0.0115168i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4067.57 | − | 7045.24i | 0.534280 | − | 0.925400i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13051.8 | 1.70117 | 0.850584 | − | 0.525839i | \(-0.176249\pi\) | ||||
0.850584 | + | 0.525839i | \(0.176249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2183.94 | 0.282472 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1785.15 | − | 3091.98i | 0.229133 | − | 0.396869i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 83.8710i | − | 0.0106836i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8030.23 | + | 4636.26i | −1.01518 | + | 0.586114i | −0.912704 | − | 0.408622i | \(-0.866009\pi\) |
−0.102475 | + | 0.994736i | \(0.532676\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 228.022 | + | 394.945i | 0.0286099 | + | 0.0495538i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8913.94 | + | 5146.46i | 1.11008 | + | 0.640903i | 0.938849 | − | 0.344329i | \(-0.111893\pi\) |
0.171227 | + | 0.985232i | \(0.445227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7644.76 | − | 1807.12i | 0.944944 | − | 0.223373i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 129.461 | + | 74.7442i | 0.0158838 | + | 0.00917054i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −246.141 | − | 426.329i | −0.0299773 | − | 0.0519222i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9969.25 | + | 5755.75i | −1.20525 | + | 0.695852i | −0.961718 | − | 0.274040i | \(-0.911640\pi\) |
−0.243533 | + | 0.969893i | \(0.578306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2218.43i | − | 0.266246i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2615.24 | + | 4529.73i | −0.311592 | + | 0.539694i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 436.611 | 0.0516443 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5001.41 | 0.587338 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2813.49 | − | 4873.10i | 0.328038 | − | 0.568178i | −0.654085 | − | 0.756421i | \(-0.726946\pi\) |
0.982122 | + | 0.188243i | \(0.0602794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2770.00i | − | 0.320668i | −0.987063 | − | 0.160334i | \(-0.948743\pi\) | ||
0.987063 | − | 0.160334i | \(-0.0512572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4644.22 | − | 2681.34i | 0.533830 | − | 0.308207i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4375.34 | + | 7578.32i | 0.499377 | + | 0.864947i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5139.45 | − | 2967.26i | −0.582472 | − | 0.336290i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1254.60 | − | 1331.36i | −0.141195 | − | 0.149833i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11092.2 | − | 6404.07i | −1.23966 | − | 0.715715i | −0.270632 | − | 0.962683i | \(-0.587233\pi\) |
−0.969024 | + | 0.246968i | \(0.920566\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5516.87 | + | 9555.50i | 0.612295 | + | 1.06053i | 0.990853 | + | 0.134949i | \(0.0430870\pi\) |
−0.378557 | + | 0.925578i | \(0.623580\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −40.4755 | + | 23.3686i | −0.00446127 | + | 0.00257572i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 627.408i | − | 0.0686796i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2386.20 | + | 4133.02i | −0.259424 | + | 0.449335i | −0.966088 | − | 0.258214i | \(-0.916866\pi\) |
0.706664 | + | 0.707549i | \(0.250199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4274.66 | −0.461576 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12949.0 | 1.38877 | 0.694385 | − | 0.719604i | \(-0.255676\pi\) | ||||
0.694385 | + | 0.719604i | \(0.255676\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 63.7028 | − | 110.336i | 0.00678607 | − | 0.0117538i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4172.01i | 0.441452i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2773.33 | − | 1601.18i | 0.291496 | − | 0.168295i | −0.347120 | − | 0.937821i | \(-0.612840\pi\) |
0.638616 | + | 0.769525i | \(0.279507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1578.79 | − | 2734.54i | −0.164838 | − | 0.285509i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5399.48 | + | 3117.39i | 0.560022 | + | 0.323329i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 134.584 | − | 126.825i | 0.0138668 | − | 0.0130674i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4450.84 | − | 2569.69i | −0.455583 | − | 0.263031i | 0.254602 | − | 0.967046i | \(-0.418056\pi\) |
−0.710185 | + | 0.704015i | \(0.751389\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3153.68 | − | 5462.33i | −0.320699 | − | 0.555468i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6393.22 | + | 3691.13i | −0.645904 | + | 0.372913i | −0.786885 | − | 0.617099i | \(-0.788308\pi\) |
0.140981 | + | 0.990012i | \(0.454974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6264.13i | 0.628766i | 0.949296 | + | 0.314383i | \(0.101798\pi\) | ||||
−0.949296 | + | 0.314383i | \(0.898202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 45.7049 | − | 79.1632i | 0.00455809 | − | 0.00789485i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14540.3 | −1.44078 | −0.720390 | − | 0.693569i | \(-0.756037\pi\) | ||||
−0.720390 | + | 0.693569i | \(0.756037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2510.00 | 0.247124 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2915.87 | − | 5050.44i | 0.285257 | − | 0.494080i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7516.16i | − | 0.730642i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2177.12 | − | 1256.96i | 0.210301 | − | 0.121417i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.6696 | + | 49.6573i | 0.00275198 | + | 0.00476656i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11438.9 | − | 6604.24i | −1.09114 | − | 0.629970i | −0.157260 | − | 0.987557i | \(-0.550266\pi\) |
−0.933880 | + | 0.357588i | \(0.883599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 300.692 | − | 1002.25i | 0.0285039 | − | 0.0950075i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 611.707 | + | 353.169i | 0.0576266 | + | 0.0332707i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −129.327 | − | 224.001i | −0.0121081 | − | 0.0209719i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6333.27 | + | 3656.51i | −0.589297 | + | 0.340231i | −0.764820 | − | 0.644245i | \(-0.777172\pi\) |
0.175522 | + | 0.984475i | \(0.443839\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 539.865i | − | 0.0499255i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4354.04 | − | 7541.42i | 0.400194 | − | 0.693156i | −0.593555 | − | 0.804793i | \(-0.702276\pi\) |
0.993749 | + | 0.111637i | \(0.0356095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6003.26 | −0.548425 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 162.195 | 0.0147275 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3919.20 | − | 6788.25i | 0.353722 | − | 0.612665i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 932.041i | − | 0.0836150i | −0.999126 | − | 0.0418075i | \(-0.986688\pi\) | ||
0.999126 | − | 0.0418075i | \(-0.0133116\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1319.00 | − | 761.523i | 0.117622 | − | 0.0679088i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1811.68 | + | 3137.92i | 0.160594 | + | 0.278157i | 0.935082 | − | 0.354432i | \(-0.115326\pi\) |
−0.774488 | + | 0.632589i | \(0.781992\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.2905 | + | 14.6015i | 0.00222854 | + | 0.00128665i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 230.629 | − | 3881.58i | 0.0202024 | − | 0.340014i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11862.7 | − | 6848.91i | −1.03301 | − | 0.596410i | −0.115167 | − | 0.993346i | \(-0.536740\pi\) |
−0.917846 | + | 0.396936i | \(0.870074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3684.01 | − | 6380.89i | −0.318926 | − | 0.552395i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1569.23 | + | 905.996i | −0.135055 | + | 0.0779741i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 275.727i | − | 0.0235922i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2477.33 | − | 4290.86i | 0.210740 | − | 0.365013i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2799.69 | −0.236788 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17030.4 | −1.43209 | −0.716043 | − | 0.698056i | \(-0.754049\pi\) | ||||
−0.716043 | + | 0.698056i | \(0.754049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6084.81 | + | 10539.2i | −0.508738 | + | 0.881160i | 0.491211 | + | 0.871041i | \(0.336554\pi\) |
−0.999949 | + | 0.0101193i | \(0.996779\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2830.18i | 0.235275i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10168.3 | − | 5870.68i | 0.840490 | − | 0.485257i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5597.62 | + | 9695.37i | 0.460066 | + | 0.796858i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8444.80 | − | 4875.61i | −0.690157 | − | 0.398462i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1928.68 | − | 6428.58i | 0.156737 | − | 0.522425i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 412.610 | + | 238.221i | 0.0333434 | + | 0.0192508i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1663.58 | − | 2881.40i | −0.133685 | − | 0.231549i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3420.29 | + | 1974.71i | −0.273325 | + | 0.157804i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4027.65i | 0.320078i | 0.987111 | + | 0.160039i | \(0.0511620\pi\) | ||||
−0.987111 | + | 0.160039i | \(0.948838\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2478.52 | + | 4292.92i | −0.195881 | + | 0.339276i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −238.205 | −0.0187222 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11525.4 | 0.900895 | 0.450447 | − | 0.892803i | \(-0.351264\pi\) | ||||
0.450447 | + | 0.892803i | \(0.351264\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5531.89 | − | 9581.51i | 0.430046 | − | 0.744861i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1724.63i | 0.133343i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3017.45 | − | 1742.13i | 0.232034 | − | 0.133965i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.08811 | − | 10.5449i | −0.000465633 | − | 0.000806499i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14371.4 | − | 8297.31i | −1.09324 | − | 0.631182i | −0.158802 | − | 0.987310i | \(-0.550763\pi\) |
−0.934437 | + | 0.356129i | \(0.884096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11627.1 | − | 10956.7i | 0.879736 | − | 0.829016i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2367.97 | − | 1367.15i | −0.178210 | − | 0.102889i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8891.95 | + | 15401.3i | 0.665633 | + | 1.15291i | 0.979113 | + | 0.203315i | \(0.0651716\pi\) |
−0.313481 | + | 0.949595i | \(0.601495\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −289.077 | + | 166.898i | −0.0215249 | + | 0.0124274i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6210.19i | 0.459971i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7831.97 | − | 13565.4i | 0.577036 | − | 0.999455i | −0.418782 | − | 0.908087i | \(-0.637543\pi\) |
0.995817 | − | 0.0913679i | \(-0.0291239\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24046.3 | −1.76236 | −0.881179 | − | 0.472783i | \(-0.843250\pi\) | ||||
−0.881179 | + | 0.472783i | \(0.843250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6343.37 | 0.462475 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1946.83 | − | 3372.01i | 0.141197 | − | 0.244561i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18975.5i | − | 1.36908i | −0.728975 | − | 0.684541i | \(-0.760003\pi\) | ||
0.728975 | − | 0.684541i | \(-0.239997\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7901.16 | + | 4561.74i | −0.567117 | + | 0.327425i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9069.06 | + | 15708.1i | 0.647587 | + | 1.12165i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.8790 | + | 26.4882i | 0.00325920 | + | 0.00188170i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 236.441 | + | 250.906i | 0.0167105 | + | 0.0177328i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20733.6 | + | 11970.5i | 1.45786 | + | 0.841699i | 0.998906 | − | 0.0467588i | \(-0.0148892\pi\) |
0.458959 | + | 0.888458i | \(0.348223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1686.54 | − | 2921.18i | −0.117984 | − | 0.204355i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3196.55 | + | 1845.53i | −0.222485 | + | 0.128452i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16015.7i | 1.10908i | 0.832156 | + | 0.554542i | \(0.187106\pi\) | ||||
−0.832156 | + | 0.554542i | \(0.812894\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 138.202 | − | 239.373i | 0.00952225 | − | 0.0164930i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4822.90 | 0.330634 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5201.91 | −0.354832 | −0.177416 | − | 0.984136i | \(-0.556774\pi\) | ||||
−0.177416 | + | 0.984136i | \(0.556774\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 408.881 | − | 708.203i | 0.0277514 | − | 0.0480669i | −0.851816 | − | 0.523841i | \(-0.824499\pi\) |
0.879568 | + | 0.475774i | \(0.157832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4679.41i | 0.316020i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −225.446 | + | 130.161i | −0.0151499 | + | 0.00874678i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12019.2 | + | 20817.9i | 0.803699 | + | 1.39205i | 0.917166 | + | 0.398505i | \(0.130471\pi\) |
−0.113467 | + | 0.993542i | \(0.536196\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1681.47 | − | 970.799i | −0.111883 | − | 0.0645957i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10249.0 | − | 2422.74i | 0.678612 | − | 0.160415i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4778.79 | − | 2759.04i | −0.314867 | − | 0.181789i | 0.334235 | − | 0.942490i | \(-0.391522\pi\) |
−0.649102 | + | 0.760701i | \(0.724855\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −39.0501 | − | 67.6367i | −0.00256041 | − | 0.00443476i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15743.8 | + | 9089.68i | −1.02726 | + | 0.593090i | −0.916199 | − | 0.400723i | \(-0.868759\pi\) |
−0.111063 | + | 0.993813i | \(0.535426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25821.4i | 1.67666i | 0.545164 | + | 0.838329i | \(0.316467\pi\) | ||||
−0.545164 | + | 0.838329i | \(0.683533\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1403.24 | + | 2430.49i | −0.0906767 | + | 0.157057i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5292.81 | 0.340372 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15589.4 | 0.997721 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −392.757 | + | 680.275i | −0.0250163 | + | 0.0433295i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1564.01i | − | 0.0991430i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18315.1 | − | 10574.2i | 1.15549 | − | 0.667122i | 0.205271 | − | 0.978705i | \(-0.434193\pi\) |
0.950219 | + | 0.311583i | \(0.100859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −272.278 | − | 471.599i | −0.0170965 | − | 0.0296120i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −397.580 | − | 229.543i | −0.0248464 | − | 0.0143451i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8040.70 | − | 2412.35i | −0.500132 | − | 0.150048i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12655.4 | + | 7306.58i | 0.783472 | + | 0.452338i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8029.05 | + | 13906.7i | 0.494740 | + | 0.856915i | 0.999982 | − | 0.00606294i | \(-0.00192991\pi\) |
−0.505241 | + | 0.862978i | \(0.668597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5959.36 | + | 3440.64i | −0.365497 | + | 0.211020i | −0.671489 | − | 0.741014i | \(-0.734345\pi\) |
0.305993 | + | 0.952034i | \(0.401012\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 185.907i | − | 0.0113489i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −512.640 | + | 887.918i | −0.0311499 | + | 0.0539531i | −0.881180 | − | 0.472781i | \(-0.843250\pi\) |
0.850030 | + | 0.526734i | \(0.176584\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9009.27 | −0.544908 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3797.43 | 0.228622 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7950.27 | − | 13770.3i | 0.476444 | − | 0.825226i | −0.523191 | − | 0.852215i | \(-0.675259\pi\) |
0.999636 | + | 0.0269894i | \(0.00859205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 621.662i | 0.0370845i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11895.9 | − | 6868.12i | 0.706400 | − | 0.407840i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5361.28 | + | 9286.01i | 0.316913 | + | 0.548910i | 0.979842 | − | 0.199772i | \(-0.0640202\pi\) |
−0.662929 | + | 0.748682i | \(0.730687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5405.10 | + | 3120.64i | 0.318054 | + | 0.183629i | 0.650525 | − | 0.759485i | \(-0.274549\pi\) |
−0.332471 | + | 0.943114i | \(0.607882\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1337.02 | − | 5656.07i | −0.0783192 | − | 0.331317i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −68.7678 | − | 39.7031i | −0.00401008 | − | 0.00231522i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1335.59 | + | 2313.31i | 0.0775326 | + | 0.134290i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8049.76 | + | 4647.53i | −0.465205 | + | 0.268586i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10222.0i | − | 0.588099i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 393.479 | − | 681.526i | 0.0225371 | − | 0.0390355i | −0.854537 | − | 0.519391i | \(-0.826159\pi\) |
0.877074 | + | 0.480355i | \(0.159492\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11245.1 | −0.641223 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10335.7 | 0.586755 | 0.293377 | − | 0.955997i | \(-0.405221\pi\) | ||||
0.293377 | + | 0.955997i | \(0.405221\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5372.63 | − | 9305.66i | 0.303656 | − | 0.525948i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6450.99i | 0.362999i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7210.96 | + | 4163.25i | −0.403982 | + | 0.233239i | −0.688201 | − | 0.725520i | \(-0.741599\pi\) |
0.284219 | + | 0.958759i | \(0.408266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 193.137 | + | 334.522i | 0.0107728 | + | 0.0186590i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1751.10 | + | 1011.00i | 0.0972471 | + | 0.0561456i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.9046 | + | 109.585i | 0.00143235 | + | 0.00605932i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25859.9 | − | 14930.2i | −1.42367 | − | 0.821957i | −0.427060 | − | 0.904223i | \(-0.640451\pi\) |
−0.996610 | + | 0.0822667i | \(0.973784\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3369.04 | + | 5835.34i | 0.184674 | + | 0.319865i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −754.174 | + | 435.423i | −0.0411618 | + | 0.0237648i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10031.8i | − | 0.545165i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4435.71 | + | 7682.87i | −0.240020 | + | 0.415726i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9140.89 | −0.492506 | −0.246253 | − | 0.969206i | \(-0.579199\pi\) | ||||
−0.246253 | + | 0.969206i | \(0.579199\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −449.312 | −0.0241054 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 61.2748 | − | 106.131i | 0.00327340 | − | 0.00566969i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1213.18i | 0.0645349i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8070.16 | − | 4659.31i | 0.427477 | − | 0.246804i | −0.270794 | − | 0.962637i | \(-0.587286\pi\) |
0.698271 | + | 0.715833i | \(0.253953\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3247.85 | + | 5625.45i | 0.171314 | + | 0.296724i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4524.44 | − | 2612.19i | −0.237646 | − | 0.137205i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 305.092 | + | 91.5328i | 0.0159577 | + | 0.00478760i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9708.24 | − | 5605.05i | −0.505664 | − | 0.291945i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2452.15 | − | 4247.25i | −0.127190 | − | 0.220300i | 0.795397 | − | 0.606089i | \(-0.207263\pi\) |
−0.922587 | + | 0.385789i | \(0.873929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9919.90 | − | 5727.26i | 0.512394 | − | 0.295831i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2466.05i | − | 0.126851i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5351.49 | + | 9269.06i | −0.274137 | + | 0.474819i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12039.6 | 0.614199 | 0.307100 | − | 0.951677i | \(-0.400642\pi\) | ||||
0.307100 | + | 0.951677i | \(0.400642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7275.47 | −0.369632 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11939.6 | − | 20680.0i | 0.604107 | − | 1.04634i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 15050.7i | − | 0.758402i | −0.925314 | − | 0.379201i | \(-0.876199\pi\) | ||
0.925314 | − | 0.379201i | \(-0.123801\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −84.5983 | + | 48.8429i | −0.00424552 | + | 0.00245115i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2161.68 | + | 3744.14i | 0.108041 | + | 0.187133i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1357.29 | − | 783.630i | −0.0675624 | − | 0.0390072i | 0.465838 | − | 0.884870i | \(-0.345753\pi\) |
−0.533401 | + | 0.845863i | \(0.679086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1624.89 | + | 384.103i | −0.0805557 | + | 0.0190423i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18172.2 | − | 10491.7i | −0.897272 | − | 0.518040i | −0.0209580 | − | 0.999780i | \(-0.506672\pi\) |
−0.876314 | + | 0.481740i | \(0.840005\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −363.215 | − | 629.107i | −0.0178620 | − | 0.0309378i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29284.6 | + | 16907.5i | −1.43436 | + | 0.828130i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19792.8i | 0.965571i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11597.6 | − | 20087.6i | 0.563517 | − | 0.976041i | −0.433669 | − | 0.901072i | \(-0.642781\pi\) |
0.997186 | − | 0.0749681i | \(-0.0238855\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3181.59 | 0.153976 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1085.60 | −0.0523299 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1357.75 | − | 2351.68i | 0.0651890 | − | 0.112911i | −0.831589 | − | 0.555392i | \(-0.812568\pi\) |
0.896778 | + | 0.442481i | \(0.145902\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1216.64i | 0.0581833i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5511.96 | + | 3182.33i | −0.262561 | + | 0.151589i | −0.625502 | − | 0.780223i | \(-0.715106\pi\) |
0.362942 | + | 0.931812i | \(0.381772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4947.87 | − | 8569.96i | −0.234764 | − | 0.406623i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 446.265 | + | 257.651i | 0.0210912 | + | 0.0121770i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13133.3 | − | 13936.8i | −0.618275 | − | 0.656101i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14492.8 | − | 8367.40i | −0.679613 | − | 0.392375i | 0.120096 | − | 0.992762i | \(-0.461680\pi\) |
−0.799709 | + | 0.600388i | \(0.795013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1223.83 | + | 2119.74i | 0.0571663 | + | 0.0990149i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28226.6 | + | 16296.7i | −1.31338 | + | 0.758279i | −0.982654 | − | 0.185448i | \(-0.940626\pi\) |
−0.330724 | + | 0.943728i | \(0.607293\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20933.2i | − | 0.970249i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 252.918 | − | 438.067i | 0.0116775 | − | 0.0202260i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2881.95 | −0.132550 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13501.3 | 0.618584 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3857.27 | − | 6680.98i | 0.176050 | − | 0.304928i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1015.42i | 0.0461681i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29768.0 | + | 17186.6i | −1.34830 | + | 0.778444i | −0.988009 | − | 0.154394i | \(-0.950657\pi\) |
−0.360295 | + | 0.932838i | \(0.617324\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4957.21 | − | 8586.13i | −0.223677 | − | 0.387420i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12009.1 | − | 6933.46i | −0.539816 | − | 0.311663i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15812.8 | − | 14901.1i | 0.708106 | − | 0.667282i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.13478 | + | 0.655167i | 5.06246e−5 | + | 2.92281e-5i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1428.91 | + | 2474.95i | 0.0635066 | + | 0.109997i | 0.896031 | − | 0.443992i | \(-0.146438\pi\) |
−0.832524 | + | 0.553989i | \(0.813105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13632.3 | − | 7870.60i | 0.603598 | − | 0.348488i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9867.41i | 0.435265i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6345.54 | − | 10990.8i | 0.278866 | − | 0.483010i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −122.988 | −0.00538477 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7836.51 | 0.341832 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12203.9 | + | 21137.8i | −0.530366 | + | 0.918621i | 0.469006 | + | 0.883195i | \(0.344612\pi\) |
−0.999372 | + | 0.0354263i | \(0.988721\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31138.1i | − | 1.34822i | −0.738631 | − | 0.674110i | \(-0.764527\pi\) | ||
0.738631 | − | 0.674110i | \(-0.235473\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4550.45 | − | 2627.20i | 0.196299 | − | 0.113333i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.0007 | + | 81.4075i | 0.00202008 | + | 0.00349887i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5941.01 | − | 3430.04i | −0.254406 | − | 0.146881i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4115.70 | + | 13718.2i | −0.175597 | + | 0.585290i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30329.4 | + | 17510.7i | 1.28928 | + | 0.744369i | 0.978527 | − | 0.206120i | \(-0.0660837\pi\) |
0.310758 | + | 0.950489i | \(0.399417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11993.1 | − | 20772.6i | −0.507962 | − | 0.879816i | −0.999958 | − | 0.00921810i | \(-0.997066\pi\) |
0.491996 | − | 0.870598i | \(-0.336268\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4221.75 | + | 2437.43i | −0.178161 | + | 0.102861i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14919.3i | 0.627320i | 0.949535 | + | 0.313660i | \(0.101555\pi\) | ||||
−0.949535 | + | 0.313660i | \(0.898445\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8096.41 | + | 14023.4i | −0.339204 | + | 0.587518i | −0.984283 | − | 0.176597i | \(-0.943491\pi\) |
0.645079 | + | 0.764115i | \(0.276824\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3797.89 | 0.158541 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12547.5 | −0.521902 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −132.596 | + | 229.664i | −0.00549543 | + | 0.00951836i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15088.3i | 0.623092i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37765.8 | − | 21804.1i | 1.55402 | − | 0.897213i | 0.556210 | − | 0.831042i | \(-0.312255\pi\) |
0.997808 | − | 0.0661708i | \(-0.0210782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8523.20 | + | 14762.6i | 0.349469 | + | 0.605298i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7507.72 | + | 4334.58i | 0.306737 | + | 0.177095i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 303.153 | + | 605.391i | 0.0123418 | + | 0.0246463i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9365.68 | − | 5407.28i | −0.379939 | − | 0.219358i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2145.34 | + | 3715.84i | 0.0867231 | + | 0.150209i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −602.677 | + | 347.956i | −0.0242768 | + | 0.0140162i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12671.8i | − | 0.508644i | −0.967120 | − | 0.254322i | \(-0.918148\pi\) | ||
0.967120 | − | 0.254322i | \(-0.0818523\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 74.0187 | − | 128.204i | 0.00296069 | − | 0.00512806i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11021.6 | −0.439314 | −0.219657 | − | 0.975577i | \(-0.570494\pi\) | ||||
−0.219657 | + | 0.975577i | \(0.570494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2679.73 | −0.106439 | −0.0532195 | − | 0.998583i | \(-0.516948\pi\) | ||||
−0.0532195 | + | 0.998583i | \(0.516948\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1622.26 | − | 2809.83i | 0.0642118 | − | 0.111218i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9500.93i | 0.374757i | 0.982288 | + | 0.187378i | \(0.0599991\pi\) | ||||
−0.982288 | + | 0.187378i | \(0.940001\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 422.172 | − | 243.741i | 0.0165945 | − | 0.00958086i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.22423 | + | 7.31658i | 0.000165470 | + | 0.000286602i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5197.42 | + | 3000.73i | 0.202889 | + | 0.117138i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2640.76 | + | 8802.03i | −0.102731 | + | 0.342417i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17348.6 | + | 10016.2i | 0.672578 | + | 0.388313i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −492.978 | − | 853.864i | −0.0190465 | − | 0.0329896i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44593.9 | − | 25746.3i | 1.71702 | − | 0.991323i | 0.792786 | − | 0.609499i | \(-0.208630\pi\) |
0.924235 | − | 0.381823i | \(-0.124704\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3822.37i | 0.146673i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6046.76 | + | 10473.3i | −0.231238 | + | 0.400515i | −0.958173 | − | 0.286191i | \(-0.907611\pi\) |
0.726935 | + | 0.686706i | \(0.240944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13875.0 | 0.528802 | 0.264401 | − | 0.964413i | \(-0.414826\pi\) | ||||
0.264401 | + | 0.964413i | \(0.414826\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −222.838 | −0.00846396 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12632.1 | + | 21879.4i | −0.478179 | + | 0.828230i | −0.999687 | − | 0.0250165i | \(-0.992036\pi\) |
0.521508 | + | 0.853246i | \(0.325369\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19071.8i | − | 0.719514i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9263.68 | + | 5348.39i | −0.348311 | + | 0.201097i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2261.09 | − | 3916.31i | −0.0847305 | − | 0.146758i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 501.709 | + | 289.662i | 0.0187378 | + | 0.0108182i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1882.06 | + | 1773.56i | −0.0700561 | + | 0.0660172i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12436.9 | + | 7180.43i | 0.461394 | + | 0.266386i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 84.1545 | + | 145.760i | 0.00311165 | + | 0.00538953i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6688.41 | − | 3861.56i | 0.246485 | − | 0.142308i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 863.119i | − | 0.0317028i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1172.04 | − | 2030.03i | 0.0429073 | − | 0.0743177i | −0.843774 | − | 0.536698i | \(-0.819671\pi\) |
0.886682 | + | 0.462381i | \(0.153005\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2261.73 | −0.0825268 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4870.47 | −0.177131 | −0.0885653 | − | 0.996070i | \(-0.528228\pi\) | ||||
−0.0885653 | + | 0.996070i | \(0.528228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15621.1 | + | 27056.5i | −0.566245 | + | 0.980765i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 252.832i | − | 0.00913485i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22365.7 | + | 12912.8i | −0.805431 | + | 0.465016i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14502.0 | + | 25118.2i | 0.520541 | + | 0.901604i | 0.999715 | + | 0.0238835i | \(0.00760307\pi\) |
−0.479174 | + | 0.877720i | \(0.659064\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1356.90 | + | 783.408i | 0.0485467 | + | 0.0280284i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19681.6 | + | 20885.7i | 0.701871 | + | 0.744811i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2414.83 | − | 1394.20i | −0.0858369 | − | 0.0495579i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10677.4 | + | 18493.7i | 0.378307 | + | 0.655246i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24834.8 | − | 14338.4i | 0.877075 | − | 0.506379i | 0.00738211 | − | 0.999973i | \(-0.497650\pi\) |
0.869693 | + | 0.493593i | \(0.164317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3604.67i | 0.126894i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8743.31 | − | 15143.9i | 0.306799 | − | 0.531391i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 476.095 | 0.0166524 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18265.9 | 0.636842 | 0.318421 | − | 0.947949i | \(-0.396847\pi\) | ||||
0.318421 | + | 0.947949i | \(0.396847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4995.10 | − | 8651.76i | 0.173598 | − | 0.300681i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45277.4i | 1.56855i | 0.620415 | + | 0.784273i | \(0.286964\pi\) | ||||
−0.620415 | + | 0.784273i | \(0.713036\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3865.66 | + | 2231.84i | −0.133492 | + | 0.0770719i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 177.598 | + | 307.608i | 0.00611350 | + | 0.0105889i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44615.8 | + | 25759.0i | 1.53096 | + | 0.883900i | 0.999318 | + | 0.0369314i | \(0.0117583\pi\) |
0.531642 | + | 0.846969i | \(0.321575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26252.4 | − | 6205.72i | 0.897985 | − | 0.212272i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17086.8 | + | 9865.05i | 0.582625 | + | 0.336379i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12223.9 | − | 21172.4i | −0.415499 | − | 0.719666i | 0.579982 | − | 0.814630i | \(-0.303060\pi\) |
−0.995481 | + | 0.0949640i | \(0.969726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −956.532 | + | 552.254i | −0.0324111 | + | 0.0187126i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3344.32i | − | 0.112964i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8023.46 | + | 13897.0i | −0.270168 | + | 0.467945i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1703.60 | 0.0571850 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36899.8 | −1.23477 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 794.289 | − | 1375.75i | 0.0264965 | − | 0.0458932i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6835.07i | 0.227302i | 0.993521 | + | 0.113651i | \(0.0362546\pi\) | ||||
−0.993521 | + | 0.113651i | \(0.963745\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2161.27 | + | 1247.81i | −0.0716511 | + | 0.0413678i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14656.6 | − | 25386.0i | −0.484400 | − | 0.839005i | 0.515439 | − | 0.856926i | \(-0.327629\pi\) |
−0.999839 | + | 0.0179207i | \(0.994295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31330.6 | − | 18088.7i | −1.03229 | − | 0.595990i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9924.85 | − | 2977.63i | −0.325999 | − | 0.0978055i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11633.2 | + | 6716.45i | 0.380942 | + | 0.219937i | 0.678228 | − | 0.734852i | \(-0.262748\pi\) |
−0.297286 | + | 0.954788i | \(0.596082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4558.31 | + | 7895.23i | 0.148809 | + | 0.257745i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15977.0 | − | 9224.34i | 0.519987 | − | 0.300215i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20535.8i | − | 0.666316i | −0.942871 | − | 0.333158i | \(-0.891886\pi\) | ||
0.942871 | − | 0.333158i | \(-0.108114\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 321.344 | − | 556.584i | 0.0103948 | − | 0.0180043i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5091.08 | 0.164185 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10625.2 | −0.341619 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23130.6 | + | 40063.4i | −0.741442 | + | 1.28422i | 0.210397 | + | 0.977616i | \(0.432524\pi\) |
−0.951839 | + | 0.306599i | \(0.900809\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8137.01i | 0.260040i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −727.257 | + | 419.882i | −0.0231714 | + | 0.0133780i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16096.9 | − | 27880.6i | −0.511326 | − | 0.885643i | −0.999914 | − | 0.0131284i | \(-0.995821\pi\) |
0.488587 | − | 0.872515i | \(-0.337512\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1740.57 | + | 1004.92i | 0.0551243 | + | 0.0318260i |
(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 | 104.4.o.a.17.5 | ✓ | 20 | |
4.3 | odd | 2 | 208.4.w.e.17.6 | 20 | |||
13.6 | odd | 12 | 1352.4.a.p.1.6 | 10 | |||
13.7 | odd | 12 | 1352.4.a.o.1.6 | 10 | |||
13.10 | even | 6 | inner | 104.4.o.a.49.5 | yes | 20 | |
52.23 | odd | 6 | 208.4.w.e.49.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
104.4.o.a.17.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
104.4.o.a.49.5 | yes | 20 | 13.10 | even | 6 | inner | |
208.4.w.e.17.6 | 20 | 4.3 | odd | 2 | |||
208.4.w.e.49.6 | 20 | 52.23 | odd | 6 | |||
1352.4.a.o.1.6 | 10 | 13.7 | odd | 12 | |||
1352.4.a.p.1.6 | 10 | 13.6 | odd | 12 |