Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(417,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.417");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.g (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: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 417.28 | ||
Character | \(\chi\) | \(=\) | 1216.417 |
Dual form | 1216.3.g.e.417.25 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.08780 | 0.362599 | 0.181299 | − | 0.983428i | \(-0.441970\pi\) | ||||
0.181299 | + | 0.983428i | \(0.441970\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.09363i | − | 0.418725i | −0.977838 | − | 0.209363i | \(-0.932861\pi\) | ||
0.977838 | − | 0.209363i | \(-0.0671389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.72137 | 0.531624 | 0.265812 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265812 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.81670 | −0.868522 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.64392i | 0.603993i | 0.953309 | + | 0.301996i | \(0.0976530\pi\) | ||||
−0.953309 | + | 0.301996i | \(0.902347\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.32905 | −0.717619 | −0.358810 | − | 0.933411i | \(-0.616817\pi\) | ||||
−0.358810 | + | 0.933411i | \(0.616817\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.27744i | − | 0.151829i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.02233 | −0.118961 | −0.0594804 | − | 0.998229i | \(-0.518944\pi\) | ||||
−0.0594804 | + | 0.998229i | \(0.518944\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.3333 | − | 7.78179i | 0.912280 | − | 0.409568i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.04809 | 0.192766 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.73929 | 0.336491 | 0.168245 | − | 0.985745i | \(-0.446190\pi\) | ||||
0.168245 | + | 0.985745i | \(0.446190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.6167 | 0.824669 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −18.2931 | −0.677524 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 35.3394 | 1.21860 | 0.609300 | − | 0.792939i | \(-0.291450\pi\) | ||||
0.609300 | + | 0.792939i | \(0.291450\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 37.0375i | − | 1.19476i | −0.801959 | − | 0.597379i | \(-0.796209\pi\) | ||
0.801959 | − | 0.597379i | \(-0.203791\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.22723i | 0.219007i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 7.79115i | − | 0.222604i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 33.2473 | 0.898577 | 0.449288 | − | 0.893387i | \(-0.351678\pi\) | ||||
0.449288 | + | 0.893387i | \(0.351678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.1481 | −0.260208 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 57.3302i | − | 1.39830i | −0.714977 | − | 0.699148i | \(-0.753563\pi\) | ||
0.714977 | − | 0.699148i | \(-0.246437\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 28.3128i | − | 0.658437i | −0.944254 | − | 0.329219i | \(-0.893215\pi\) | ||
0.944254 | − | 0.329219i | \(-0.106785\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16.3653i | 0.363672i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 73.9638 | 1.57370 | 0.786849 | − | 0.617146i | \(-0.211711\pi\) | ||||
0.786849 | + | 0.617146i | \(0.211711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −35.1514 | −0.717376 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.19989 | −0.0431350 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 59.7645 | 1.12763 | 0.563816 | − | 0.825900i | \(-0.309333\pi\) | ||||
0.563816 | + | 0.825900i | \(0.309333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.9099 | 0.252907 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.8551 | − | 8.46500i | 0.330792 | − | 0.148509i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −60.0313 | −1.01748 | −0.508740 | − | 0.860920i | \(-0.669888\pi\) | ||||
−0.508740 | + | 0.860920i | \(0.669888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.9084i | 0.309974i | 0.987917 | + | 0.154987i | \(0.0495335\pi\) | ||||
−0.987917 | + | 0.154987i | \(0.950466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −29.0888 | −0.461727 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.5316i | 0.300485i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −91.3968 | −1.36413 | −0.682066 | − | 0.731291i | \(-0.738918\pi\) | ||||
−0.682066 | + | 0.731291i | \(0.738918\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.41877 | 0.122011 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 83.7992i | − | 1.18027i | −0.807304 | − | 0.590135i | \(-0.799074\pi\) | ||
0.807304 | − | 0.590135i | \(-0.200926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2134 | 0.139910 | 0.0699551 | − | 0.997550i | \(-0.477714\pi\) | ||||
0.0699551 | + | 0.997550i | \(0.477714\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22.4268 | 0.299024 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.7245i | 0.321097i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 58.8531i | − | 0.744976i | −0.928037 | − | 0.372488i | \(-0.878505\pi\) | ||
0.928037 | − | 0.372488i | \(-0.121495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 50.4511 | 0.622853 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.17199i | − | 0.0623131i | −0.999515 | − | 0.0311566i | \(-0.990081\pi\) | ||
0.999515 | − | 0.0311566i | \(-0.00991905\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.23401i | 0.0498119i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 38.4421 | 0.441863 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 145.970i | − | 1.64011i | −0.572284 | − | 0.820056i | \(-0.693942\pi\) | ||
0.572284 | − | 0.820056i | \(-0.306058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −34.7168 | −0.381503 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 40.2893i | − | 0.433218i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.2922 | − | 36.2895i | −0.171496 | − | 0.381995i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39.3499i | 0.405669i | 0.979213 | + | 0.202835i | \(0.0650154\pi\) | ||||
−0.979213 | + | 0.202835i | \(0.934985\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 51.9335i | − | 0.524581i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 137.581i | 1.36219i | 0.732195 | + | 0.681095i | \(0.238496\pi\) | ||||
−0.732195 | + | 0.681095i | \(0.761504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.09975i | − | 0.0592209i | −0.999562 | − | 0.0296104i | \(-0.990573\pi\) | ||
0.999562 | − | 0.0296104i | \(-0.00942668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 8.47519i | − | 0.0807161i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 23.4079 | 0.218765 | 0.109383 | − | 0.994000i | \(-0.465113\pi\) | ||||
0.109383 | + | 0.994000i | \(0.465113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 98.8964 | 0.907306 | 0.453653 | − | 0.891178i | \(-0.350121\pi\) | ||||
0.453653 | + | 0.891178i | \(0.350121\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 36.1663 | 0.325823 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 51.2397i | − | 0.453449i | −0.973959 | − | 0.226724i | \(-0.927198\pi\) | ||
0.973959 | − | 0.226724i | \(-0.0728017\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 16.2032i | − | 0.140897i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 72.9224 | 0.623268 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.52584 | −0.0632424 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 76.8583 | 0.635193 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 62.3635i | − | 0.507021i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 95.5044i | − | 0.764035i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 138.012i | − | 1.08671i | −0.839504 | − | 0.543354i | \(-0.817154\pi\) | ||
0.839504 | − | 0.543354i | \(-0.182846\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 30.7986i | − | 0.238749i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.8847i | 0.0907231i | 0.998971 | + | 0.0453616i | \(0.0144440\pi\) | ||||
−0.998971 | + | 0.0453616i | \(0.985556\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 64.5036 | − | 28.9589i | 0.484989 | − | 0.217736i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 38.2990i | 0.283697i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 83.3482 | 0.608381 | 0.304190 | − | 0.952611i | \(-0.401614\pi\) | ||||
0.304190 | + | 0.952611i | \(0.401614\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 206.396i | 1.48487i | 0.669920 | + | 0.742433i | \(0.266328\pi\) | ||||
−0.669920 | + | 0.742433i | \(0.733672\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 80.4576 | 0.570621 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 61.9814i | − | 0.433437i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 73.9876i | − | 0.510259i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −38.2376 | −0.260120 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 219.150i | 1.47081i | 0.677631 | + | 0.735403i | \(0.263007\pi\) | ||||
−0.677631 | + | 0.735403i | \(0.736993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 147.132i | − | 0.974383i | −0.873295 | − | 0.487192i | \(-0.838021\pi\) | ||
0.873295 | − | 0.487192i | \(-0.161979\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.8080 | 0.103320 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −77.5427 | −0.500276 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 247.777i | 1.57820i | 0.614266 | + | 0.789099i | \(0.289452\pi\) | ||||
−0.614266 | + | 0.789099i | \(0.710548\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 65.0116 | 0.408878 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.8007 | 0.178886 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 176.310i | − | 1.08166i | −0.841133 | − | 0.540828i | \(-0.818111\pi\) | ||
0.841133 | − | 0.540828i | \(-0.181889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.1311 | 0.0917038 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 216.583i | − | 1.29690i | −0.761257 | − | 0.648451i | \(-0.775417\pi\) | ||
0.761257 | − | 0.648451i | \(-0.224583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −81.9689 | −0.485023 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −135.489 | + | 60.8279i | −0.792335 | + | 0.355719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 130.712 | 0.755563 | 0.377781 | − | 0.925895i | \(-0.376687\pi\) | ||||
0.377781 | + | 0.925895i | \(0.376687\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 76.7224 | 0.438413 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −65.3018 | −0.368937 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.3199 | −0.135866 | −0.0679328 | − | 0.997690i | \(-0.521640\pi\) | ||||
−0.0679328 | + | 0.997690i | \(0.521640\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 98.1544 | 0.542290 | 0.271145 | − | 0.962539i | \(-0.412598\pi\) | ||||
0.271145 | + | 0.962539i | \(0.412598\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.5685i | 0.112396i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 69.6076i | − | 0.376257i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 13.4362i | − | 0.0718515i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −68.0755 | −0.360188 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −92.1966 | −0.482705 | −0.241352 | − | 0.970438i | \(-0.577591\pi\) | ||||
−0.241352 | + | 0.970438i | \(0.577591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 168.238i | 0.871697i | 0.900020 | + | 0.435848i | \(0.143552\pi\) | ||||
−0.900020 | + | 0.435848i | \(0.856448\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 21.2464i | 0.108956i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 223.927i | − | 1.13668i | −0.822793 | − | 0.568341i | \(-0.807585\pi\) | ||
0.822793 | − | 0.568341i | \(-0.192415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 176.637 | 0.887621 | 0.443811 | − | 0.896121i | \(-0.353626\pi\) | ||||
0.443811 | + | 0.896121i | \(0.353626\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −99.4211 | −0.494632 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 131.511 | 0.647837 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −120.028 | −0.585502 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −60.4957 | −0.292250 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 51.7016 | + | 115.161i | 0.247376 | + | 0.551010i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 63.0357 | 0.298747 | 0.149374 | − | 0.988781i | \(-0.452274\pi\) | ||||
0.149374 | + | 0.988781i | \(0.452274\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 91.1565i | − | 0.427965i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −59.2765 | −0.275704 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 137.830i | − | 0.635162i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1101 | 0.0507313 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.8664 | 0.0853685 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 380.926i | 1.70819i | 0.520117 | + | 0.854095i | \(0.325888\pi\) | ||||
−0.520117 | + | 0.854095i | \(0.674112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −161.155 | −0.716243 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −223.454 | −0.984378 | −0.492189 | − | 0.870488i | \(-0.663803\pi\) | ||||
−0.492189 | + | 0.870488i | \(0.663803\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 70.1574i | − | 0.306364i | −0.988198 | − | 0.153182i | \(-0.951048\pi\) | ||
0.988198 | − | 0.153182i | \(-0.0489521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26.8952i | 0.116429i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 254.338 | 1.09158 | 0.545789 | − | 0.837923i | \(-0.316230\pi\) | ||||
0.545789 | + | 0.837923i | \(0.316230\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 154.853i | − | 0.658947i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 64.0202i | − | 0.270127i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 78.6199 | 0.328954 | 0.164477 | − | 0.986381i | \(-0.447406\pi\) | ||||
0.164477 | + | 0.986381i | \(0.447406\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 273.046i | 1.13297i | 0.824072 | + | 0.566485i | \(0.191697\pi\) | ||||
−0.824072 | + | 0.566485i | \(0.808303\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 219.519 | 0.903370 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 73.5940i | 0.300384i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −161.703 | + | 72.5967i | −0.654669 | + | 0.293914i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 5.62607i | − | 0.0225947i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 119.607i | − | 0.476521i | −0.971201 | − | 0.238261i | \(-0.923423\pi\) | ||
0.971201 | − | 0.238261i | \(-0.0765772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 51.4192i | 0.203238i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.60574i | 0.0180617i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 151.484i | 0.589434i | 0.955585 | + | 0.294717i | \(0.0952253\pi\) | ||||
−0.955585 | + | 0.294717i | \(0.904775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 123.726 | 0.477705 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −276.238 | −1.05838 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 60.4679 | 0.229916 | 0.114958 | − | 0.993370i | \(-0.463327\pi\) | ||||
0.114958 | + | 0.993370i | \(0.463327\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 125.125i | − | 0.472168i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 158.786i | − | 0.594702i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −43.9742 | −0.163473 | −0.0817365 | − | 0.996654i | \(-0.526047\pi\) | ||||
−0.0817365 | + | 0.996654i | \(0.526047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −271.639 | −1.00236 | −0.501180 | − | 0.865343i | \(-0.667100\pi\) | ||||
−0.501180 | + | 0.865343i | \(0.667100\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −37.7648 | −0.138333 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 136.976i | 0.498094i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 202.731i | − | 0.731880i | −0.930638 | − | 0.365940i | \(-0.880747\pi\) | ||
0.930638 | − | 0.365940i | \(-0.119253\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 289.511i | 1.03767i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 352.493i | − | 1.25443i | −0.778848 | − | 0.627213i | \(-0.784196\pi\) | ||
0.778848 | − | 0.627213i | \(-0.215804\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 435.032i | 1.53722i | 0.639720 | + | 0.768608i | \(0.279050\pi\) | ||||
−0.639720 | + | 0.768608i | \(0.720950\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.7226 | − | 39.4756i | −0.0621844 | − | 0.138511i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 213.346i | − | 0.743367i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −284.910 | −0.985848 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 42.8047i | 0.147095i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −223.976 | −0.764425 | −0.382212 | − | 0.924075i | \(-0.624838\pi\) | ||||
−0.382212 | + | 0.924075i | \(0.624838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 125.683i | 0.426045i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 121.538i | − | 0.409219i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −72.2002 | −0.241472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 105.362i | − | 0.350041i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 149.660i | 0.493928i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.5871 | 0.129794 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 216.541 | 0.705346 | 0.352673 | − | 0.935747i | \(-0.385273\pi\) | ||||
0.352673 | + | 0.935747i | \(0.385273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.63529i | − | 0.0214734i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 353.673 | 1.13721 | 0.568606 | − | 0.822610i | \(-0.307483\pi\) | ||||
0.568606 | + | 0.822610i | \(0.307483\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.55967 | 0.0305421 | 0.0152710 | − | 0.999883i | \(-0.495139\pi\) | ||||
0.0152710 | + | 0.999883i | \(0.495139\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 60.9011i | 0.193337i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 53.9855 | 0.170301 | 0.0851507 | − | 0.996368i | \(-0.472863\pi\) | ||||
0.0851507 | + | 0.996368i | \(0.472863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 234.792i | 0.736026i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.4630 | 0.0793241 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.0537 | + | 15.7374i | −0.108526 | + | 0.0487225i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −192.334 | −0.591798 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 107.579 | 0.328988 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 275.246 | 0.836615 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 221.010 | 0.667703 | 0.333852 | − | 0.942626i | \(-0.391652\pi\) | ||||
0.333852 | + | 0.942626i | \(0.391652\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −259.884 | −0.780434 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 191.351i | 0.571196i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 481.993i | 1.43025i | 0.698998 | + | 0.715124i | \(0.253630\pi\) | ||||
−0.698998 | + | 0.715124i | \(0.746370\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 55.7384i | − | 0.164420i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 246.074 | 0.721625 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −313.158 | −0.912998 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 17.6258i | − | 0.0510892i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 340.238i | − | 0.980514i | −0.871578 | − | 0.490257i | \(-0.836903\pi\) | ||
0.871578 | − | 0.490257i | \(-0.163097\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 293.467i | − | 0.840880i | −0.907320 | − | 0.420440i | \(-0.861876\pi\) | ||
0.907320 | − | 0.420440i | \(-0.138124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 170.658 | 0.486204 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −545.177 | −1.54441 | −0.772206 | − | 0.635372i | \(-0.780847\pi\) | ||||
−0.772206 | + | 0.635372i | \(0.780847\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −175.444 | −0.494209 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.18658 | −0.0229316 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −315.249 | −0.878130 | −0.439065 | − | 0.898455i | \(-0.644690\pi\) | ||||
−0.439065 | + | 0.898455i | \(0.644690\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 239.888 | − | 269.768i | 0.664509 | − | 0.747281i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 83.6062 | 0.230320 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 21.3831i | − | 0.0585840i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −111.782 | −0.304583 | −0.152292 | − | 0.988336i | \(-0.548665\pi\) | ||||
−0.152292 | + | 0.988336i | \(0.548665\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 448.133i | 1.21445i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 222.406 | 0.599476 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −633.441 | −1.69823 | −0.849117 | − | 0.528205i | \(-0.822865\pi\) | ||||
−0.849117 | + | 0.528205i | \(0.822865\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 103.889i | − | 0.277038i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −329.683 | −0.874491 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 231.839 | 0.611712 | 0.305856 | − | 0.952078i | \(-0.401057\pi\) | ||||
0.305856 | + | 0.952078i | \(0.401057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 150.129i | − | 0.394039i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 180.106i | 0.470250i | 0.971965 | + | 0.235125i | \(0.0755500\pi\) | ||||
−0.971965 | + | 0.235125i | \(0.924450\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 51.7638 | 0.134451 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 221.313i | 0.571867i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 35.1789i | − | 0.0904342i | −0.998977 | − | 0.0452171i | \(-0.985602\pi\) | ||
0.998977 | − | 0.0452171i | \(-0.0143980\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.6514 | −0.0400292 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.9282i | 0.0328961i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −123.216 | −0.311940 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 341.490i | 0.860177i | 0.902787 | + | 0.430089i | \(0.141518\pi\) | ||||
−0.902787 | + | 0.430089i | \(0.858482\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 70.1668 | − | 31.5014i | 0.175857 | − | 0.0789508i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 163.382i | 0.407438i | 0.979029 | + | 0.203719i | \(0.0653028\pi\) | ||||
−0.979029 | + | 0.203719i | \(0.934697\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 345.525i | 0.857381i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 105.626i | − | 0.260804i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 220.893i | 0.542734i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 266.286i | − | 0.651065i | −0.945531 | − | 0.325533i | \(-0.894456\pi\) | ||
0.945531 | − | 0.325533i | \(-0.105544\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 90.6659 | 0.220598 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −223.398 | −0.540916 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.8282 | −0.0260921 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 224.517i | 0.538411i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 139.535i | − | 0.333018i | −0.986040 | − | 0.166509i | \(-0.946750\pi\) | ||
0.986040 | − | 0.166509i | \(-0.0532495\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −210.410 | −0.499787 | −0.249893 | − | 0.968273i | \(-0.580396\pi\) | ||||
−0.249893 | + | 0.968273i | \(0.580396\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −578.153 | −1.36679 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −41.6939 | −0.0981033 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 70.3650i | 0.164789i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 67.4232i | − | 0.157164i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 141.538i | − | 0.328395i | −0.986427 | − | 0.164198i | \(-0.947496\pi\) | ||
0.986427 | − | 0.164198i | \(-0.0525035\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 790.795i | 1.82632i | 0.407605 | + | 0.913158i | \(0.366364\pi\) | ||||
−0.407605 | + | 0.913158i | \(0.633636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 80.4834i | − | 0.185019i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 134.148 | − | 60.2255i | 0.306974 | − | 0.137816i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 751.697i | 1.71229i | 0.516732 | + | 0.856147i | \(0.327148\pi\) | ||||
−0.516732 | + | 0.856147i | \(0.672852\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 274.768 | 0.623057 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 415.267i | 0.937397i | 0.883358 | + | 0.468698i | \(0.155277\pi\) | ||||
−0.883358 | + | 0.468698i | \(0.844723\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −305.607 | −0.686756 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 238.391i | 0.533312i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 768.511i | 1.71161i | 0.517302 | + | 0.855803i | \(0.326936\pi\) | ||||
−0.517302 | + | 0.855803i | \(0.673064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 380.897 | 0.844561 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 160.050i | − | 0.353310i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 72.6840i | 0.159745i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −75.9879 | −0.166275 | −0.0831377 | − | 0.996538i | \(-0.526494\pi\) | ||||
−0.0831377 | + | 0.996538i | \(0.526494\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 36.9948 | 0.0805988 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.6371i | 0.0881499i | 0.999028 | + | 0.0440750i | \(0.0140340\pi\) | ||||
−0.999028 | + | 0.0440750i | \(0.985966\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.7651 | −0.0318901 | −0.0159450 | − | 0.999873i | \(-0.505076\pi\) | ||||
−0.0159450 | + | 0.999873i | \(0.505076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −84.3507 | −0.181399 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 273.231i | − | 0.585078i | −0.956254 | − | 0.292539i | \(-0.905500\pi\) | ||
0.956254 | − | 0.292539i | \(-0.0945001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −340.121 | −0.725204 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 269.531i | 0.572253i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 188.108 | 0.397691 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 357.356 | − | 160.435i | 0.752329 | − | 0.337758i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −467.161 | −0.979374 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −573.348 | −1.19697 | −0.598485 | − | 0.801134i | \(-0.704230\pi\) | ||||
−0.598485 | + | 0.801134i | \(0.704230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −310.166 | −0.644836 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 31.3293 | 0.0648640 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 82.3840 | 0.169864 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 101.704i | 0.208838i | 0.994533 | + | 0.104419i | \(0.0332984\pi\) | ||||
−0.994533 | + | 0.104419i | \(0.966702\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 191.789i | − | 0.392207i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 157.940i | 0.321670i | 0.986981 | + | 0.160835i | \(0.0514187\pi\) | ||||
−0.986981 | + | 0.160835i | \(0.948581\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −71.4681 | −0.144966 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −108.729 | −0.219655 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 311.848i | − | 0.627460i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 623.133i | 1.24876i | 0.781119 | + | 0.624382i | \(0.214649\pi\) | ||||
−0.781119 | + | 0.624382i | \(0.785351\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 235.598i | − | 0.470255i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −253.778 | −0.504528 | −0.252264 | − | 0.967658i | \(-0.581175\pi\) | ||||
−0.252264 | + | 0.967658i | \(0.581175\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 288.044 | 0.570383 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −89.1654 | −0.175869 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 523.377 | 1.02825 | 0.514123 | − | 0.857717i | \(-0.328118\pi\) | ||||
0.514123 | + | 0.857717i | \(0.328118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.0080 | 0.0743796 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −317.081 | + | 142.353i | −0.618091 | + | 0.277492i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.7706 | −0.0247973 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 491.410i | 0.950502i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 142.188 | 0.273966 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 277.898i | − | 0.533394i | −0.963780 | − | 0.266697i | \(-0.914068\pi\) | ||
0.963780 | − | 0.266697i | \(-0.0859323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.4757 | −0.0467987 | −0.0233994 | − | 0.999726i | \(-0.507449\pi\) | ||||
−0.0233994 | + | 0.999726i | \(0.507449\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 83.4583 | 0.158968 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 74.9022i | 0.142129i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −469.103 | −0.886774 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 469.247 | 0.883704 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 534.836i | 1.00344i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 49.0074i | − | 0.0916026i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.4552 | −0.0492647 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 233.543i | − | 0.433290i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 495.925i | − | 0.916682i | −0.888776 | − | 0.458341i | \(-0.848444\pi\) | ||
0.888776 | − | 0.458341i | \(-0.151556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 106.772 | 0.196634 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 207.052i | − | 0.379912i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −856.793 | −1.56635 | −0.783174 | − | 0.621802i | \(-0.786401\pi\) | ||||
−0.783174 | + | 0.621802i | \(0.786401\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 147.801i | − | 0.269219i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 612.549 | − | 275.004i | 1.11170 | − | 0.499100i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 219.014i | − | 0.396047i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 75.7189i | − | 0.136430i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 528.791i | 0.949356i | 0.880159 | + | 0.474678i | \(0.157436\pi\) | ||||
−0.880159 | + | 0.474678i | \(0.842564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 264.131i | 0.472507i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 14.6159i | − | 0.0260533i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −183.852 | −0.326557 | −0.163279 | − | 0.986580i | \(-0.552207\pi\) | ||||
−0.163279 | + | 0.986580i | \(0.552207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −107.277 | −0.189871 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 187.747 | 0.331123 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 12.6119i | − | 0.0221650i | −0.999939 | − | 0.0110825i | \(-0.996472\pi\) | ||
0.999939 | − | 0.0110825i | \(-0.00352775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 62.9795i | − | 0.110297i | −0.998478 | − | 0.0551484i | \(-0.982437\pi\) | ||
0.998478 | − | 0.0551484i | \(-0.0175632\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −100.291 | −0.175028 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 159.559 | 0.277494 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 333.803 | 0.578515 | 0.289257 | − | 0.957251i | \(-0.406592\pi\) | ||||
0.289257 | + | 0.957251i | \(0.406592\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 183.008i | 0.316076i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 19.2469i | − | 0.0331271i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 397.071i | 0.681082i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 152.672i | − | 0.260978i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 280.459i | 0.477784i | 0.971046 | + | 0.238892i | \(0.0767843\pi\) | ||||
−0.971046 | + | 0.238892i | \(0.923216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −288.218 | − | 641.983i | −0.489334 | − | 1.08995i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 243.586i | − | 0.412160i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 562.285 | 0.948204 | 0.474102 | − | 0.880470i | \(-0.342773\pi\) | ||||
0.474102 | + | 0.880470i | \(0.342773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.7563i | 0.0264812i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 192.145 | 0.321850 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1179.08i | − | 1.96842i | −0.177007 | − | 0.984210i | \(-0.556642\pi\) | ||
0.177007 | − | 0.984210i | \(-0.443358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.6269i | 0.0642711i | 0.999484 | + | 0.0321356i | \(0.0102308\pi\) | ||||
−0.999484 | + | 0.0321356i | \(0.989769\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 714.421 | 1.18478 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 160.913i | − | 0.265971i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 695.079i | − | 1.14511i | −0.819868 | − | 0.572553i | \(-0.805953\pi\) | ||
0.819868 | − | 0.572553i | \(-0.194047\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 143.057 | 0.234905 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −690.012 | −1.12932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 84.3445i | 0.137593i | 0.997631 | + | 0.0687965i | \(0.0219159\pi\) | ||||
−0.997631 | + | 0.0687965i | \(0.978084\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −130.566 | −0.212302 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 244.410 | 0.396126 | 0.198063 | − | 0.980189i | \(-0.436535\pi\) | ||||
0.198063 | + | 0.980189i | \(0.436535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 610.103i | − | 0.985626i | −0.870135 | − | 0.492813i | \(-0.835969\pi\) | ||
0.870135 | − | 0.492813i | \(-0.164031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −141.576 | −0.227981 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 543.207i | − | 0.871922i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 315.467 | 0.504748 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 56.2408 | + | 125.272i | 0.0896982 | + | 0.199796i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −67.2372 | −0.106895 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1045.91 | −1.65755 | −0.828774 | − | 0.559583i | \(-0.810961\pi\) | ||||
−0.828774 | + | 0.559583i | \(0.810961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 68.5700 | 0.108325 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −288.946 | −0.455032 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 327.930 | 0.514803 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 655.033i | 1.02509i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 323.515i | − | 0.504704i | −0.967635 | − | 0.252352i | \(-0.918796\pi\) | ||
0.967635 | − | 0.252352i | \(-0.0812041\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1092.63i | − | 1.69927i | −0.527368 | − | 0.849637i | \(-0.676821\pi\) | ||
0.527368 | − | 0.849637i | \(-0.323179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −64.4807 | −0.0999701 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 712.381 | 1.10105 | 0.550526 | − | 0.834818i | \(-0.314427\pi\) | ||||
0.550526 | + | 0.834818i | \(0.314427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 398.843i | − | 0.614550i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 149.931i | − | 0.230309i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 219.109i | − | 0.335542i | −0.985826 | − | 0.167771i | \(-0.946343\pi\) | ||
0.985826 | − | 0.167771i | \(-0.0536569\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.8822 | 0.0379881 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −79.8354 | −0.121515 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 469.826 | 0.712938 | 0.356469 | − | 0.934307i | \(-0.383981\pi\) | ||||
0.356469 | + | 0.934307i | \(0.383981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 152.275 | 0.230371 | 0.115186 | − | 0.993344i | \(-0.463254\pi\) | ||||
0.115186 | + | 0.993344i | \(0.463254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.5229 | 0.0309545 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −60.6291 | − | 135.046i | −0.0911715 | − | 0.203077i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 273.502 | 0.410048 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 414.370i | 0.619387i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −125.626 | −0.187222 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 366.022i | 0.543866i | 0.962316 | + | 0.271933i | \(0.0876630\pi\) | ||||
−0.962316 | + | 0.271933i | \(0.912337\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −377.145 | −0.558733 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1245.19 | 1.83927 | 0.919636 | − | 0.392772i | \(-0.128484\pi\) | ||||
0.919636 | + | 0.392772i | \(0.128484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 146.435i | 0.215663i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −243.072 | −0.356934 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1231.24 | −1.80270 | −0.901349 | − | 0.433093i | \(-0.857422\pi\) | ||||
−0.901349 | + | 0.433093i | \(0.857422\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 174.500i | − | 0.254745i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 76.3169i | − | 0.111087i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −557.546 | −0.809211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 261.648i | 0.378651i | 0.981914 | + | 0.189325i | \(0.0606301\pi\) | ||||
−0.981914 | + | 0.189325i | \(0.939370\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 193.264i | − | 0.278880i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 432.117 | 0.621751 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 115.941i | 0.166342i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 276.667 | 0.395805 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1082.48i | 1.54420i | 0.635503 | + | 0.772098i | \(0.280793\pi\) | ||||
−0.635503 | + | 0.772098i | \(0.719207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 576.287 | − | 258.724i | 0.819754 | − | 0.368028i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 168.448i | − | 0.238934i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 511.990i | 0.724172i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 252.694i | − | 0.356409i | −0.983993 | − | 0.178204i | \(-0.942971\pi\) | ||
0.983993 | − | 0.178204i | \(-0.0570288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 460.037i | 0.647028i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 286.644i | − | 0.402025i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −129.766 | −0.181491 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 85.5224 | 0.119278 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 735.101 | 1.02239 | 0.511197 | − | 0.859464i | \(-0.329202\pi\) | ||||
0.511197 | + | 0.859464i | \(0.329202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 22.6994i | − | 0.0314832i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 297.018i | 0.410813i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 728.583 | 1.00494 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 113.878 | 0.156641 | 0.0783205 | − | 0.996928i | \(-0.475044\pi\) | ||||
0.0783205 | + | 0.996928i | \(0.475044\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −215.268 | −0.295292 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 57.2579i | 0.0783282i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 645.099i | 0.880081i | 0.897978 | + | 0.440040i | \(0.145036\pi\) | ||||
−0.897978 | + | 0.440040i | \(0.854964\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 80.0553i | 0.108919i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 607.233i | − | 0.823925i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 416.784i | − | 0.563984i | −0.959417 | − | 0.281992i | \(-0.909005\pi\) | ||
0.959417 | − | 0.281992i | \(-0.0909952\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −175.900 | + | 78.9704i | −0.237382 | + | 0.106573i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 528.231i | − | 0.710943i | −0.934687 | − | 0.355472i | \(-0.884320\pi\) | ||
0.934687 | − | 0.355472i | \(-0.115680\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 458.818 | 0.615864 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.4279i | 0.0541203i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 87.1093 | 0.116301 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 321.869i | 0.428588i | 0.976769 | + | 0.214294i | \(0.0687450\pi\) | ||||
−0.976769 | + | 0.214294i | \(0.931255\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 130.108i | − | 0.172786i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −308.039 | −0.407999 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1443.50i | − | 1.90687i | −0.301606 | − | 0.953433i | \(-0.597523\pi\) | ||
0.301606 | − | 0.953433i | \(-0.402477\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 55.9336i | 0.0736939i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −371.415 | −0.488062 | −0.244031 | − | 0.969767i | \(-0.578470\pi\) | ||||
−0.244031 | + | 0.969767i | \(0.578470\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 368.030 | 0.482345 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 33.0960i | − | 0.0432628i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 560.035 | 0.730163 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −642.327 | −0.835276 | −0.417638 | − | 0.908614i | \(-0.637142\pi\) | ||||
−0.417638 | + | 0.908614i | \(0.637142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 164.784i | 0.213728i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 838.133 | 1.08426 | 0.542130 | − | 0.840295i | \(-0.317618\pi\) | ||||
0.542130 | + | 0.840295i | \(0.317618\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 763.592i | − | 0.985280i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 134.588 | 0.173215 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −446.131 | − | 993.722i | −0.572697 | − | 1.27564i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 556.755 | 0.712875 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −646.469 | −0.825631 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 518.753 | 0.660832 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 637.161 | 0.809608 | 0.404804 | − | 0.914404i | \(-0.367340\pi\) | ||||
0.404804 | + | 0.914404i | \(0.367340\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 65.7768 | 0.0833673 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 190.682i | − | 0.241064i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 176.397i | − | 0.222443i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 136.110i | − | 0.171208i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1233.71 | 1.54795 | 0.773973 | − | 0.633218i | \(-0.218267\pi\) | ||||
0.773973 | + | 0.633218i | \(0.218267\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −149.579 | −0.187208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1141.00i | 1.42447i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 67.8573i | 0.0845047i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 60.2980i | − | 0.0749043i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.8350 | −0.0592751 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 296.868 | 0.366956 | 0.183478 | − | 0.983024i | \(-0.441264\pi\) | ||||
0.183478 | + | 0.983024i | \(0.441264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −802.739 | −0.989814 | −0.494907 | − | 0.868946i | \(-0.664798\pi\) | ||||
−0.494907 | + | 0.868946i | \(0.664798\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −295.488 | −0.363454 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −369.127 | −0.452917 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −220.324 | − | 490.755i | −0.269675 | − | 0.600679i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 271.371 | 0.331344 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1590.22i | 1.93693i | 0.249148 | + | 0.968465i | \(0.419849\pi\) | ||||
−0.249148 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 283.504 | 0.344476 | 0.172238 | − | 0.985055i | \(-0.444900\pi\) | ||||
0.172238 | + | 0.985055i | \(0.444900\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 149.002i | 0.180608i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −174.686 | −0.211228 | −0.105614 | − | 0.994407i | \(-0.533681\pi\) | ||||
−0.105614 | + | 0.994407i | \(0.533681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1044.05 | −1.25940 | −0.629702 | − | 0.776837i | \(-0.716823\pi\) | ||||
−0.629702 | + | 0.776837i | \(0.716823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 220.530i | − | 0.265379i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 71.0879 | 0.0853397 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −453.443 | −0.543046 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 677.533i | 0.809477i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1115.25i | − | 1.32926i | −0.747175 | − | 0.664628i | \(-0.768590\pi\) | ||
0.747175 | − | 0.664628i | \(-0.231410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 407.875 | 0.484988 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 383.441i | − | 0.454853i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 171.612i | 0.203091i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 286.018 | 0.337683 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 473.227i | 0.557393i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 257.311 | 0.302363 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 812.448i | 0.952459i | 0.879321 | + | 0.476230i | \(0.157997\pi\) | ||||
−0.879321 | + | 0.476230i | \(0.842003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 127.351 | + | 283.664i | 0.148948 | + | 0.331771i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 619.864i | − | 0.723295i | −0.932315 | − | 0.361648i | \(-0.882214\pi\) | ||
0.932315 | − | 0.361648i | \(-0.117786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1060.49i | 1.23457i | 0.786740 | + | 0.617284i | \(0.211767\pi\) | ||||
−0.786740 | + | 0.617284i | \(0.788233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 232.078i | − | 0.269544i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1211.79i | − | 1.40416i | −0.712096 | − | 0.702082i | \(-0.752254\pi\) | ||
0.712096 | − | 0.702082i | \(-0.247746\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 273.663i | − | 0.316373i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −309.924 | −0.357467 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 391.015 | 0.449960 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 852.645 | 0.978927 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 307.586i | − | 0.352333i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 355.407i | − | 0.406179i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 505.369 | 0.576247 | 0.288124 | − | 0.957593i | \(-0.406969\pi\) | ||||
0.288124 | + | 0.957593i | \(0.406969\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −243.641 | −0.277180 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −381.023 | −0.432489 | −0.216245 | − | 0.976339i | \(-0.569381\pi\) | ||||
−0.216245 | + | 0.976339i | \(0.569381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.1768i | − | 0.0511629i | −0.999673 | − | 0.0255815i | \(-0.991856\pi\) | ||
0.999673 | − | 0.0255815i | \(-0.00814372\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 136.718i | 0.154483i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1667.14i | − | 1.87952i | −0.341829 | − | 0.939762i | \(-0.611046\pi\) | ||
0.341829 | − | 0.939762i | \(-0.388954\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 513.593i | − | 0.577720i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 335.193i | 0.376199i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1282.04 | − | 575.571i | 1.43565 | − | 0.644536i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.9169i | 0.0568904i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −78.5391 | −0.0875575 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1308.88i | − | 1.45593i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −120.864 | −0.134144 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 114.613i | − | 0.126924i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 205.499i | − | 0.227070i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −967.353 | −1.06654 | −0.533271 | − | 0.845945i | \(-0.679037\pi\) | ||||
−0.533271 | + | 0.845945i | \(0.679037\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1075.43i | − | 1.18309i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 759.283i | − | 0.833461i | −0.909030 | − | 0.416730i | \(-0.863176\pi\) | ||
0.909030 | − | 0.416730i | \(-0.136824\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.3623 | 0.0376367 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 43.0627 | 0.0470631 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.2274i | 0.0482306i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1580.32 | 1.71961 | 0.859804 | − | 0.510624i | \(-0.170586\pi\) | ||||
0.859804 | + | 0.510624i | \(0.170586\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 235.553 | 0.255758 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 781.767i | 0.846985i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 685.451 | 0.741029 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.6799i | 0.0514347i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1629.32 | 1.75384 | 0.876921 | − | 0.480634i | \(-0.159594\pi\) | ||||
0.876921 | + | 0.480634i | \(0.159594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −609.291 | + | 273.541i | −0.654448 | + | 0.293814i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 384.724 | 0.412352 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −28.1304 | −0.0300860 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 794.022 | 0.847409 | 0.423705 | − | 0.905800i | \(-0.360729\pi\) | ||||
0.423705 | + | 0.905800i | \(0.360729\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.3990 | 0.0110745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 802.627 | 0.852951 | 0.426475 | − | 0.904499i | \(-0.359755\pi\) | ||||
0.426475 | + | 0.904499i | \(0.359755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 443.695i | − | 0.470514i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 142.525i | 0.150820i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1386.35i | − | 1.46394i | −0.681336 | − | 0.731971i | \(-0.738601\pi\) | ||
0.681336 | − | 0.731971i | \(-0.261399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −95.2817 | −0.100402 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 58.7253 | 0.0617511 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 431.148i | − | 0.452411i | −0.974080 | − | 0.226205i | \(-0.927368\pi\) | ||
0.974080 | − | 0.226205i | \(-0.0726321\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 193.025i | 0.202121i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 255.406i | 0.266882i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 310.169 | 0.323430 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −410.777 | −0.427448 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −182.972 | −0.190003 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 352.227 | 0.365002 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1368.36 | −1.41505 | −0.707527 | − | 0.706686i | \(-0.750189\pi\) | ||||
−0.707527 | + | 0.706686i | \(0.750189\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.1313 | + | 17.1191i | −0.0393512 | + | 0.0176667i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −87.5512 | −0.0901660 | −0.0450830 | − | 0.998983i | \(-0.514355\pi\) | ||||
−0.0450830 | + | 0.998983i | \(0.514355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 768.076i | 0.789390i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −209.221 | −0.214585 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1674.52i | − | 1.71394i | −0.515368 | − | 0.856969i | \(-0.672345\pi\) | ||
0.515368 | − | 0.856969i | \(-0.327655\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 969.812 | 0.990615 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −773.043 | −0.788015 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 413.238i | 0.420385i | 0.977660 | + | 0.210192i | \(0.0674090\pi\) | ||||
−0.977660 | + | 0.210192i | \(0.932591\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −468.819 | −0.475958 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 299.412 | 0.303356 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 219.121i | − | 0.221558i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 435.659i | 0.439615i | 0.975543 | + | 0.219808i | \(0.0705429\pi\) | ||||
−0.975543 | + | 0.219808i | \(0.929457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 240.414 | 0.242108 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 369.811i | − | 0.371670i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 569.052i | 0.570764i | 0.958414 | + | 0.285382i | \(0.0921204\pi\) | ||||
−0.958414 | + | 0.285382i | \(0.907880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −608.199 | −0.608807 |
(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 | 1216.3.g.e.417.28 | yes | 48 | |
4.3 | odd | 2 | inner | 1216.3.g.e.417.24 | yes | 48 | |
8.3 | odd | 2 | inner | 1216.3.g.e.417.27 | yes | 48 | |
8.5 | even | 2 | inner | 1216.3.g.e.417.23 | yes | 48 | |
19.18 | odd | 2 | inner | 1216.3.g.e.417.22 | yes | 48 | |
76.75 | even | 2 | inner | 1216.3.g.e.417.26 | yes | 48 | |
152.37 | odd | 2 | inner | 1216.3.g.e.417.25 | yes | 48 | |
152.75 | even | 2 | inner | 1216.3.g.e.417.21 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.3.g.e.417.21 | ✓ | 48 | 152.75 | even | 2 | inner | |
1216.3.g.e.417.22 | yes | 48 | 19.18 | odd | 2 | inner | |
1216.3.g.e.417.23 | yes | 48 | 8.5 | even | 2 | inner | |
1216.3.g.e.417.24 | yes | 48 | 4.3 | odd | 2 | inner | |
1216.3.g.e.417.25 | yes | 48 | 152.37 | odd | 2 | inner | |
1216.3.g.e.417.26 | yes | 48 | 76.75 | even | 2 | inner | |
1216.3.g.e.417.27 | yes | 48 | 8.3 | odd | 2 | inner | |
1216.3.g.e.417.28 | yes | 48 | 1.1 | even | 1 | trivial |