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 | 417.24 | ||
Character | \(\chi\) | \(=\) | 1216.417 |
Dual form | 1216.3.g.e.417.21 |
$q$-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 | \(-0.558030\pi\) | ||||
−0.181299 | + | 0.983428i | \(0.558030\pi\) | |||||||
\(4\) | 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 | \(-0.585640\pi\) | ||||
−0.265812 | + | 0.964025i | \(0.585640\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.81670 | −0.868522 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.64392i | − | 0.603993i | −0.953309 | − | 0.301996i | \(-0.902347\pi\) | ||
0.953309 | − | 0.301996i | \(-0.0976530\pi\) | |||||||
\(12\) | 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 | \(-0.553810\pi\) | ||||
−0.168245 | + | 0.985745i | \(0.553810\pi\) | |||||||
\(24\) | 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 | \(0.203791\pi\) | ||||
−0.801959 | + | 0.597379i | \(0.796209\pi\) | |||||||
\(32\) | 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 | \(0.106785\pi\) | ||||
−0.944254 | + | 0.329219i | \(0.893215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16.3653i | 0.363672i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −73.9638 | −1.57370 | −0.786849 | − | 0.617146i | \(-0.788289\pi\) | ||||
−0.786849 | + | 0.617146i | \(0.788289\pi\) | |||||||
\(48\) | 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 | \(-0.330112\pi\) | ||||
0.508740 | + | 0.860920i | \(0.330112\pi\) | |||||||
\(60\) | 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 | \(-0.261082\pi\) | ||||
0.682066 | + | 0.731291i | \(0.261082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.41877 | 0.122011 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 83.7992i | 1.18027i | 0.807304 | + | 0.590135i | \(0.200926\pi\) | ||||
−0.807304 | + | 0.590135i | \(0.799074\pi\) | |||||||
\(72\) | 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 | \(0.121495\pi\) | ||||
−0.928037 | + | 0.372488i | \(0.878505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 50.4511 | 0.622853 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.17199i | 0.0623131i | 0.999515 | + | 0.0311566i | \(0.00991905\pi\) | ||||
−0.999515 | + | 0.0311566i | \(0.990081\pi\) | |||||||
\(84\) | 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 | \(0.00942668\pi\) | ||||
−0.999562 | + | 0.0296104i | \(0.990573\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 8.47519i | − | 0.0807161i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −23.4079 | −0.218765 | −0.109383 | − | 0.994000i | \(-0.534887\pi\) | ||||
−0.109383 | + | 0.994000i | \(0.534887\pi\) | |||||||
\(108\) | 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 | \(0.182846\pi\) | ||||
−0.839504 | + | 0.543354i | \(0.817154\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 30.7986i | − | 0.238749i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 11.8847i | − | 0.0907231i | −0.998971 | − | 0.0453616i | \(-0.985556\pi\) | ||
0.998971 | − | 0.0453616i | \(-0.0144440\pi\) | |||||||
\(132\) | 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 | \(-0.733672\pi\) | ||
0.669920 | − | 0.742433i | \(-0.266328\pi\) | |||||||
\(140\) | 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 | \(0.161979\pi\) | ||||
−0.873295 | + | 0.487192i | \(0.838021\pi\) | |||||||
\(152\) | 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 | \(0.181889\pi\) | ||||
−0.841133 | + | 0.540828i | \(0.818111\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.1311 | 0.0917038 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 216.583i | 1.29690i | 0.761257 | + | 0.648451i | \(0.224583\pi\) | ||||
−0.761257 | + | 0.648451i | \(0.775417\pi\) | |||||||
\(168\) | 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 | \(-0.478360\pi\) | ||||
0.0679328 | + | 0.997690i | \(0.478360\pi\) | |||||||
\(180\) | 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 | \(-0.422409\pi\) | ||||
0.241352 | + | 0.970438i | \(0.422409\pi\) | |||||||
\(192\) | 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 | \(-0.646374\pi\) | ||||
−0.443811 | + | 0.896121i | \(0.646374\pi\) | |||||||
\(200\) | 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 | \(-0.547726\pi\) | ||||
−0.149374 | + | 0.988781i | \(0.547726\pi\) | |||||||
\(212\) | 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 | \(-0.674112\pi\) | ||
0.520117 | − | 0.854095i | \(-0.325888\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −161.155 | −0.716243 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 223.454 | 0.984378 | 0.492189 | − | 0.870488i | \(-0.336197\pi\) | ||||
0.492189 | + | 0.870488i | \(0.336197\pi\) | |||||||
\(228\) | 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 | \(-0.552594\pi\) | ||||
−0.164477 | + | 0.986381i | \(0.552594\pi\) | |||||||
\(240\) | 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 | \(0.0765772\pi\) | ||||
−0.971201 | + | 0.238261i | \(0.923423\pi\) | |||||||
\(252\) | 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 | \(-0.536673\pi\) | ||||
−0.114958 | + | 0.993370i | \(0.536673\pi\) | |||||||
\(264\) | 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 | \(-0.332900\pi\) | ||||
0.501180 | + | 0.865343i | \(0.332900\pi\) | |||||||
\(272\) | 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 | \(-0.720950\pi\) | ||
0.639720 | − | 0.768608i | \(-0.279050\pi\) | |||||||
\(284\) | 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 | \(-0.614727\pi\) | ||||
−0.352673 | + | 0.935747i | \(0.614727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.63529i | − | 0.0214734i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −353.673 | −1.13721 | −0.568606 | − | 0.822610i | \(-0.692517\pi\) | ||||
−0.568606 | + | 0.822610i | \(0.692517\pi\) | |||||||
\(312\) | 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 | \(-0.608348\pi\) | ||||
−0.333852 | + | 0.942626i | \(0.608348\pi\) | |||||||
\(332\) | 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 | \(0.163097\pi\) | ||||
−0.871578 | + | 0.490257i | \(0.836903\pi\) | |||||||
\(348\) | 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 | \(-0.355310\pi\) | ||||
0.439065 | + | 0.898455i | \(0.355310\pi\) | |||||||
\(360\) | 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 | \(-0.451335\pi\) | ||||
0.152292 | + | 0.988336i | \(0.451335\pi\) | |||||||
\(368\) | 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 | \(-0.598943\pi\) | ||||
−0.305856 | + | 0.952078i | \(0.598943\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 150.129i | − | 0.394039i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 180.106i | − | 0.470250i | −0.971965 | − | 0.235125i | \(-0.924450\pi\) | ||
0.971965 | − | 0.235125i | \(-0.0755500\pi\) | |||||||
\(384\) | 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 | \(0.0532495\pi\) | ||||
−0.986040 | + | 0.166509i | \(0.946750\pi\) | |||||||
\(420\) | 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 | \(0.0525035\pi\) | ||||
−0.986427 | + | 0.164198i | \(0.947496\pi\) | |||||||
\(432\) | 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 | \(-0.672852\pi\) | ||
0.516732 | − | 0.856147i | \(-0.327148\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 274.768 | 0.623057 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 415.267i | − | 0.937397i | −0.883358 | − | 0.468698i | \(-0.844723\pi\) | ||
0.883358 | − | 0.468698i | \(-0.155277\pi\) | |||||||
\(444\) | 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 | \(-0.494924\pi\) | ||||
0.0159450 | + | 0.999873i | \(0.494924\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −84.3507 | −0.181399 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 273.231i | 0.585078i | 0.956254 | + | 0.292539i | \(0.0945001\pi\) | ||||
−0.956254 | + | 0.292539i | \(0.905500\pi\) | |||||||
\(468\) | 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 | \(-0.295770\pi\) | ||||
0.598485 | + | 0.801134i | \(0.295770\pi\) | |||||||
\(480\) | 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 | \(-0.966702\pi\) | ||
0.994533 | − | 0.104419i | \(-0.0332984\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 191.789i | − | 0.392207i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 157.940i | − | 0.321670i | −0.986981 | − | 0.160835i | \(-0.948581\pi\) | ||
0.986981 | − | 0.160835i | \(-0.0514187\pi\) | |||||||
\(492\) | 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 | \(-0.785351\pi\) | ||
0.781119 | − | 0.624382i | \(-0.214649\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 235.598i | − | 0.470255i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 253.778 | 0.504528 | 0.252264 | − | 0.967658i | \(-0.418825\pi\) | ||||
0.252264 | + | 0.967658i | \(0.418825\pi\) | |||||||
\(504\) | 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 | \(-0.492551\pi\) | ||||
0.0233994 | + | 0.999726i | \(0.492551\pi\) | |||||||
\(524\) | 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 | \(-0.213599\pi\) | ||||
0.783174 | + | 0.621802i | \(0.213599\pi\) | |||||||
\(548\) | 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 | \(-0.447793\pi\) | ||||
0.163279 | + | 0.986580i | \(0.447793\pi\) | |||||||
\(564\) | 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 | \(0.0175632\pi\) | ||||
−0.998478 | + | 0.0551484i | \(0.982437\pi\) | |||||||
\(572\) | 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 | \(-0.923216\pi\) | ||
0.971046 | − | 0.238892i | \(-0.0767843\pi\) | |||||||
\(588\) | 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 | \(0.443358\pi\) | ||||
−0.177007 | + | 0.984210i | \(0.556642\pi\) | |||||||
\(600\) | 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 | \(0.194047\pi\) | ||||
−0.819868 | + | 0.572553i | \(0.805953\pi\) | |||||||
\(608\) | 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 | \(0.164031\pi\) | ||||
−0.870135 | + | 0.492813i | \(0.835969\pi\) | |||||||
\(620\) | 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 | \(-0.189039\pi\) | ||||
0.828774 | + | 0.559583i | \(0.189039\pi\) | |||||||
\(632\) | 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 | \(0.323179\pi\) | ||||
−0.527368 | + | 0.849637i | \(0.676821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −64.4807 | −0.0999701 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −712.381 | −1.10105 | −0.550526 | − | 0.834818i | \(-0.685573\pi\) | ||||
−0.550526 | + | 0.834818i | \(0.685573\pi\) | |||||||
\(648\) | 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 | \(-0.616019\pi\) | ||||
−0.356469 | + | 0.934307i | \(0.616019\pi\) | |||||||
\(660\) | 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 | \(-0.142578\pi\) | ||||
0.901349 | + | 0.433093i | \(0.142578\pi\) | |||||||
\(684\) | 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 | \(-0.939370\pi\) | ||
0.981914 | − | 0.189325i | \(-0.0606301\pi\) | |||||||
\(692\) | 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 | \(-0.670798\pi\) | ||||
−0.511197 | + | 0.859464i | \(0.670798\pi\) | |||||||
\(720\) | 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 | \(-0.524956\pi\) | ||||
−0.0783205 | + | 0.996928i | \(0.524956\pi\) | |||||||
\(728\) | 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 | \(0.0909952\pi\) | ||||
−0.959417 | + | 0.281992i | \(0.909005\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −175.900 | + | 78.9704i | −0.237382 | + | 0.106573i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 528.231i | 0.710943i | 0.934687 | + | 0.355472i | \(0.115680\pi\) | ||||
−0.934687 | + | 0.355472i | \(0.884320\pi\) | |||||||
\(744\) | 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 | \(-0.931255\pi\) | ||
0.976769 | − | 0.214294i | \(-0.0687450\pi\) | |||||||
\(752\) | 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 | \(-0.632660\pi\) | ||||
−0.404804 | + | 0.914404i | \(0.632660\pi\) | |||||||
\(788\) | 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 | \(-0.335202\pi\) | ||||
0.494907 | + | 0.868946i | \(0.335202\pi\) | |||||||
\(812\) | 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 | \(-0.555100\pi\) | ||||
−0.172238 | + | 0.985055i | \(0.555100\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 149.002i | 0.180608i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 174.686 | 0.211228 | 0.105614 | − | 0.994407i | \(-0.466319\pi\) | ||||
0.105614 | + | 0.994407i | \(0.466319\pi\) | |||||||
\(828\) | 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 | \(0.231410\pi\) | ||||
−0.747175 | + | 0.664628i | \(0.768590\pi\) | |||||||
\(840\) | 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 | \(-0.788233\pi\) | ||
0.786740 | − | 0.617284i | \(-0.211767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 232.078i | − | 0.269544i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1211.79i | 1.40416i | 0.712096 | + | 0.702082i | \(0.247746\pi\) | ||||
−0.712096 | + | 0.702082i | \(0.752254\pi\) | |||||||
\(864\) | 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 | \(0.00814372\pi\) | ||||
−0.999673 | + | 0.0255815i | \(0.991856\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 136.718i | 0.154483i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1667.14i | 1.87952i | 0.341829 | + | 0.939762i | \(0.388954\pi\) | ||||
−0.341829 | + | 0.939762i | \(0.611046\pi\) | |||||||
\(888\) | 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 | \(-0.320963\pi\) | ||||
0.533271 | + | 0.845945i | \(0.320963\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1075.43i | − | 1.18309i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 759.283i | 0.833461i | 0.909030 | + | 0.416730i | \(0.136824\pi\) | ||||
−0.909030 | + | 0.416730i | \(0.863176\pi\) | |||||||
\(912\) | 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 | \(-0.829414\pi\) | ||||
−0.859804 | + | 0.510624i | \(0.829414\pi\) | |||||||
\(920\) | 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 | \(0.261399\pi\) | ||||
−0.681336 | + | 0.731971i | \(0.738601\pi\) | |||||||
\(948\) | 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 | \(-0.249811\pi\) | ||||
0.707527 | + | 0.706686i | \(0.249811\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.1313 | + | 17.1191i | −0.0393512 | + | 0.0176667i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 87.5512 | 0.0901660 | 0.0450830 | − | 0.998983i | \(-0.485645\pi\) | ||||
0.0450830 | + | 0.998983i | \(0.485645\pi\) | |||||||
\(972\) | 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 | \(-0.932591\pi\) | ||
0.977660 | − | 0.210192i | \(-0.0674090\pi\) | |||||||
\(984\) | 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 | \(-0.929457\pi\) | ||
0.975543 | − | 0.219808i | \(-0.0705429\pi\) | |||||||
\(992\) | 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.417.24 | yes | 48 | |
4.3 | odd | 2 | inner | 1216.3.g.e.417.28 | yes | 48 | |
8.3 | odd | 2 | inner | 1216.3.g.e.417.23 | yes | 48 | |
8.5 | even | 2 | inner | 1216.3.g.e.417.27 | yes | 48 | |
19.18 | odd | 2 | inner | 1216.3.g.e.417.26 | yes | 48 | |
76.75 | even | 2 | inner | 1216.3.g.e.417.22 | yes | 48 | |
152.37 | odd | 2 | inner | 1216.3.g.e.417.21 | ✓ | 48 | |
152.75 | even | 2 | inner | 1216.3.g.e.417.25 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.3.g.e.417.21 | ✓ | 48 | 152.37 | odd | 2 | inner | |
1216.3.g.e.417.22 | yes | 48 | 76.75 | even | 2 | inner | |
1216.3.g.e.417.23 | yes | 48 | 8.3 | odd | 2 | inner | |
1216.3.g.e.417.24 | yes | 48 | 1.1 | even | 1 | trivial | |
1216.3.g.e.417.25 | yes | 48 | 152.75 | even | 2 | inner | |
1216.3.g.e.417.26 | yes | 48 | 19.18 | odd | 2 | inner | |
1216.3.g.e.417.27 | yes | 48 | 8.5 | even | 2 | inner | |
1216.3.g.e.417.28 | yes | 48 | 4.3 | odd | 2 | inner |