Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.23 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.4 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.02556 | + | 0.947153i | −0.905859 | + | 0.423580i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.95752i | − | 1.11784i | −0.829222 | − | 0.558919i | \(-0.811216\pi\) | ||
0.829222 | − | 0.558919i | \(-0.188784\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.74672 | 0.828169 | 0.414084 | − | 0.910239i | \(-0.364102\pi\) | ||||
0.414084 | + | 0.910239i | \(0.364102\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.48947i | 1.52251i | 0.648455 | + | 0.761253i | \(0.275416\pi\) | ||||
−0.648455 | + | 0.761253i | \(0.724584\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.947153 | − | 2.02556i | −0.244554 | − | 0.522998i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.836518i | 0.202885i | 0.994841 | + | 0.101443i | \(0.0323458\pi\) | ||||
−0.994841 | + | 0.101443i | \(0.967654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.78037 | −1.78494 | −0.892469 | − | 0.451108i | \(-0.851029\pi\) | ||||
−0.892469 | + | 0.451108i | \(0.851029\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.95752 | 0.645384 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.14420i | 0.238583i | 0.992859 | + | 0.119291i | \(0.0380623\pi\) | ||||
−0.992859 | + | 0.119291i | \(0.961938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.20580 | − | 3.83703i | 0.641160 | − | 0.767407i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.28812 | 0.610589 | 0.305295 | − | 0.952258i | \(-0.401245\pi\) | ||||
0.305295 | + | 0.952258i | \(0.401245\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.40904 | 0.971493 | 0.485746 | − | 0.874100i | \(-0.338548\pi\) | ||||
0.485746 | + | 0.874100i | \(0.338548\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.74672i | 0.478143i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.80122 | + | 5.99064i | 0.473493 | + | 1.01260i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.63135i | − | 0.761389i | −0.924701 | − | 0.380695i | \(-0.875685\pi\) | ||
0.924701 | − | 0.380695i | \(-0.124315\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.48947 | −0.879019 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.97291 | 0.308117 | 0.154059 | − | 0.988062i | \(-0.450766\pi\) | ||||
0.154059 | + | 0.988062i | \(0.450766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.74443i | 0.876017i | 0.898971 | + | 0.438009i | \(0.144316\pi\) | ||||
−0.898971 | + | 0.438009i | \(0.855684\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.02556 | − | 0.947153i | 0.301953 | − | 0.141193i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.67357i | 0.389980i | 0.980805 | + | 0.194990i | \(0.0624675\pi\) | ||||
−0.980805 | + | 0.194990i | \(0.937533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74693 | −0.249561 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.836518 | −0.117136 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.93268i | − | 0.540196i | −0.962833 | − | 0.270098i | \(-0.912944\pi\) | ||
0.962833 | − | 0.270098i | \(-0.0870561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.56366 | + | 2.60157i | −0.750204 | + | 0.350796i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.78037i | − | 1.03053i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.2982 | −1.60109 | −0.800543 | − | 0.599276i | \(-0.795455\pi\) | ||||
−0.800543 | + | 0.599276i | \(0.795455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.93068 | −1.14346 | −0.571728 | − | 0.820443i | \(-0.693727\pi\) | ||||
−0.571728 | + | 0.820443i | \(0.693727\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.95752i | 0.372613i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.19937 | − | 11.1193i | −0.644903 | − | 1.37918i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.14420 | −0.137746 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.94317 | −0.705325 | −0.352662 | − | 0.935751i | \(-0.614724\pi\) | ||||
−0.352662 | + | 0.935751i | \(0.614724\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.964685i | − | 0.112908i | −0.998405 | − | 0.0564539i | \(-0.982021\pi\) | ||
0.998405 | − | 0.0564539i | \(-0.0179794\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.83703 | + | 3.20580i | 0.443063 | + | 0.370174i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 8.12349i | − | 0.925758i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7034 | −1.42924 | −0.714621 | − | 0.699512i | \(-0.753401\pi\) | ||||
−0.714621 | + | 0.699512i | \(0.753401\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.18552i | 1.00824i | 0.863633 | + | 0.504121i | \(0.168183\pi\) | ||||
−0.863633 | + | 0.504121i | \(0.831817\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.792310 | − | 1.69442i | −0.0859381 | − | 0.183785i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.28812i | 0.352524i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.47078 | 0.897901 | 0.448950 | − | 0.893557i | \(-0.351798\pi\) | ||||
0.448950 | + | 0.893557i | \(0.351798\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.2352 | 1.70191 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.40904i | 0.560892i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.7596 | − | 7.36920i | 1.61690 | − | 0.756064i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.98952i | 0.303539i | 0.988416 | + | 0.151770i | \(0.0484972\pi\) | ||||
−0.988416 | + | 0.151770i | \(0.951503\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.74672 | −0.276056 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.23279 | −0.819194 | −0.409597 | − | 0.912267i | \(-0.634331\pi\) | ||||
−0.409597 | + | 0.912267i | \(0.634331\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.19798i | 0.413639i | 0.978379 | + | 0.206819i | \(0.0663113\pi\) | ||||
−0.978379 | + | 0.206819i | \(0.933689\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.99064 | + | 2.80122i | −0.584627 | + | 0.273372i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.91266i | − | 0.184904i | −0.995717 | − | 0.0924519i | \(-0.970530\pi\) | ||
0.995717 | − | 0.0924519i | \(-0.0294704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.87248 | −0.754047 | −0.377024 | − | 0.926204i | \(-0.623052\pi\) | ||||
−0.377024 | + | 0.926204i | \(0.623052\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.63135 | 0.439588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 18.9099i | − | 1.77890i | −0.457036 | − | 0.889448i | \(-0.651089\pi\) | ||
0.457036 | − | 0.889448i | \(-0.348911\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.08374 | − | 2.31765i | −0.101059 | − | 0.216122i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.48947i | − | 0.507502i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.47402 | 0.226793 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.45550 | −0.314137 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.97291i | 0.177892i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.85929 | + | 10.8085i | −0.255743 | + | 0.966745i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.152806i | 0.0135593i | 0.999977 | + | 0.00677966i | \(0.00215805\pi\) | ||||
−0.999977 | + | 0.00677966i | \(0.997842\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.74443 | −0.505769 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4130 | −1.08453 | −0.542265 | − | 0.840208i | \(-0.682433\pi\) | ||||
−0.542265 | + | 0.840208i | \(0.682433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.0106i | 1.99527i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.947153 | + | 2.02556i | 0.0815180 | + | 0.174333i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.99009i | − | 0.768075i | −0.923317 | − | 0.384038i | \(-0.874533\pi\) | ||
0.923317 | − | 0.384038i | \(-0.125467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.8040 | −1.93421 | −0.967104 | − | 0.254380i | \(-0.918128\pi\) | ||||
−0.967104 | + | 0.254380i | \(0.918128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.67357 | −0.225155 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.0781i | 1.26089i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.66030 | + | 3.11436i | −0.553108 | + | 0.258633i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.74693i | − | 0.144084i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.72732 | 0.469200 | 0.234600 | − | 0.972092i | \(-0.424622\pi\) | ||||
0.234600 | + | 0.972092i | \(0.424622\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3074 | −1.08294 | −0.541471 | − | 0.840720i | \(-0.682132\pi\) | ||||
−0.541471 | + | 0.840720i | \(0.682132\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.836518i | − | 0.0676284i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.9564 | + | 5.12319i | −0.880035 | + | 0.411505i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.9141i | 1.42970i | 0.699276 | + | 0.714852i | \(0.253506\pi\) | ||||
−0.699276 | + | 0.714852i | \(0.746494\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.93268 | 0.311882 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.38400 | 0.266697 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.5544i | − | 1.06167i | −0.847476 | − | 0.530833i | \(-0.821879\pi\) | ||
0.847476 | − | 0.530833i | \(-0.178121\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.60157 | − | 5.56366i | −0.202532 | − | 0.433130i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 14.9256i | − | 1.15498i | −0.816398 | − | 0.577490i | \(-0.804032\pi\) | ||
0.816398 | − | 0.577490i | \(-0.195968\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.1343 | −1.31802 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.78037 | 0.594980 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 15.4705i | − | 1.17620i | −0.808787 | − | 0.588102i | \(-0.799875\pi\) | ||
0.808787 | − | 0.588102i | \(-0.200125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3481 | − | 9.48122i | −0.857836 | − | 0.716713i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.2982i | − | 0.924387i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.5415 | 1.23637 | 0.618185 | − | 0.786032i | \(-0.287868\pi\) | ||||
0.618185 | + | 0.786032i | \(0.287868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.9855 | −1.18819 | −0.594096 | − | 0.804394i | \(-0.702490\pi\) | ||||
−0.594096 | + | 0.804394i | \(0.702490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.93068i | − | 0.660175i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.38660 | + | 9.38108i | 0.322509 | + | 0.689711i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.29768i | 0.168023i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.95752 | −0.215128 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.89989 | −0.716331 | −0.358166 | − | 0.933658i | \(-0.616598\pi\) | ||||
−0.358166 | + | 0.933658i | \(0.616598\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.9755i | 1.00598i | 0.864292 | + | 0.502990i | \(0.167767\pi\) | ||||
−0.864292 | + | 0.502990i | \(0.832233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.1193 | − | 5.19937i | 0.796267 | − | 0.372335i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.47194i | − | 0.389859i | −0.980817 | − | 0.194930i | \(-0.937552\pi\) | ||
0.980817 | − | 0.194930i | \(-0.0624479\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.21401 | 0.156947 | 0.0784736 | − | 0.996916i | \(-0.474995\pi\) | ||||
0.0784736 | + | 0.996916i | \(0.474995\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.72469i | − | 0.682540i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.99626 | + | 1.86865i | −0.279111 | + | 0.130512i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.14420i | − | 0.0795276i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.3705 | −1.47823 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.0506 | −1.93108 | −0.965542 | − | 0.260249i | \(-0.916195\pi\) | ||||
−0.965542 | + | 0.260249i | \(0.916195\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 5.94317i | − | 0.407219i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.44086 | − | 11.6357i | −0.371063 | − | 0.793548i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 15.9974i | − | 1.08597i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.964685 | 0.0651873 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.59204 | −0.308894 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.83158i | 0.122652i | 0.998118 | + | 0.0613258i | \(0.0195329\pi\) | ||||
−0.998118 | + | 0.0613258i | \(0.980467\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.20580 | + | 3.83703i | −0.213720 | + | 0.255802i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2018i | 0.876232i | 0.898919 | + | 0.438116i | \(0.144354\pi\) | ||||
−0.898919 | + | 0.438116i | \(0.855646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7004 | −0.839269 | −0.419634 | − | 0.907693i | \(-0.637842\pi\) | ||||
−0.419634 | + | 0.907693i | \(0.637842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.12349 | 0.534487 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.7551i | − | 0.901129i | −0.892744 | − | 0.450564i | \(-0.851223\pi\) | ||
0.892744 | − | 0.450564i | \(-0.148777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.53228 | − | 5.41548i | −0.165188 | − | 0.353267i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 12.7034i | − | 0.825173i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.29614 | 0.213210 | 0.106605 | − | 0.994301i | \(-0.466002\pi\) | ||||
0.106605 | + | 0.994301i | \(0.466002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.789127 | 0.0508321 | 0.0254161 | − | 0.999677i | \(-0.491909\pi\) | ||||
0.0254161 | + | 0.999677i | \(0.491909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.53851 | − | 1.65461i | 0.226067 | − | 0.105709i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 42.7101i | − | 2.71758i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.18552 | −0.582108 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.4247 | 1.16295 | 0.581477 | − | 0.813563i | \(-0.302475\pi\) | ||||
0.581477 | + | 0.813563i | \(0.302475\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.14281i | 0.197587i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.69442 | − | 0.792310i | 0.106109 | − | 0.0496164i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 24.3790i | − | 1.52072i | −0.649502 | − | 0.760360i | \(-0.725023\pi\) | ||
0.649502 | − | 0.760360i | \(-0.274977\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.6973 | −0.851109 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.28812 | −0.203530 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.1653i | − | 0.996796i | −0.866948 | − | 0.498398i | \(-0.833922\pi\) | ||
0.866948 | − | 0.498398i | \(-0.166078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.72485 | + | 7.96589i | 0.228816 | + | 0.489341i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.47078i | 0.518403i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.3842 | 0.998961 | 0.499481 | − | 0.866325i | \(-0.333524\pi\) | ||||
0.499481 | + | 0.866325i | \(0.333524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4620 | 0.757015 | 0.378508 | − | 0.925598i | \(-0.376437\pi\) | ||||
0.378508 | + | 0.925598i | \(0.376437\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.2352i | 0.982601i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.80545 | − | 10.5393i | 0.530989 | − | 0.635542i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.7278i | 1.00507i | 0.864556 | + | 0.502537i | \(0.167600\pi\) | ||||
−0.864556 | + | 0.502537i | \(0.832400\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.40904 | −0.323831 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.16809 | −0.308302 | −0.154151 | − | 0.988047i | \(-0.549264\pi\) | ||||
−0.154151 | + | 0.988047i | \(0.549264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1242i | 0.720707i | 0.932816 | + | 0.360354i | \(0.117344\pi\) | ||||
−0.932816 | + | 0.360354i | \(0.882656\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.36920 | + | 15.7596i | 0.436514 | + | 0.933519i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5.83493i | − | 0.344425i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3002 | 0.958838 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.98952 | −0.175248 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 30.9443i | − | 1.80779i | −0.427759 | − | 0.903893i | \(-0.640697\pi\) | ||
0.427759 | − | 0.903893i | \(-0.359303\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.9107 | − | 11.6483i | 1.45036 | − | 0.678188i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.74672i | − | 0.159381i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.28107 | −0.363244 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.9893 | 0.979245 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 8.23279i | − | 0.472962i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.0896 | − | 8.45872i | 1.03581 | − | 0.484345i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.72403i | 0.554980i | 0.960729 | + | 0.277490i | \(0.0895025\pi\) | ||||
−0.960729 | + | 0.277490i | \(0.910497\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.19798 | −0.238815 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.3633 | −1.89186 | −0.945929 | − | 0.324373i | \(-0.894847\pi\) | ||||
−0.945929 | + | 0.324373i | \(0.894847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.42253i | − | 0.419546i | −0.977750 | − | 0.209773i | \(-0.932727\pi\) | ||
0.977750 | − | 0.209773i | \(-0.0672726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.80122 | − | 5.99064i | −0.157831 | − | 0.337534i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.8359i | 1.90041i | 0.311623 | + | 0.950206i | \(0.399127\pi\) | ||||
−0.311623 | + | 0.950206i | \(0.600873\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.03157 | 0.505671 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.91266 | 0.106754 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.50842i | − | 0.362138i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.0633 | + | 17.5982i | 1.16838 | + | 0.976171i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.87248i | − | 0.435349i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.90713 | 0.435934 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2746 | −0.564746 | −0.282373 | − | 0.959305i | \(-0.591122\pi\) | ||||
−0.282373 | + | 0.959305i | \(0.591122\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.63135i | 0.253796i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.947153 | − | 2.02556i | −0.0517485 | − | 0.110668i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.3148i | 1.16109i | 0.814228 | + | 0.580546i | \(0.197161\pi\) | ||||
−0.814228 | + | 0.580546i | \(0.802839\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.9099 | 1.02705 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.8572 | 0.804560 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.5361i | − | 0.838869i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.31765 | − | 1.08374i | 0.124778 | − | 0.0583464i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.7129i | − | 0.736149i | −0.929796 | − | 0.368075i | \(-0.880017\pi\) | ||
0.929796 | − | 0.368075i | \(-0.119983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.67969 | −0.357556 | −0.178778 | − | 0.983889i | \(-0.557214\pi\) | ||||
−0.178778 | + | 0.983889i | \(0.557214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.48947 | 0.293006 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.46529i | 0.290888i | 0.989367 | + | 0.145444i | \(0.0464610\pi\) | ||||
−0.989367 | + | 0.145444i | \(0.953539\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0383 | − | 5.62909i | 0.638925 | − | 0.298761i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.47402i | 0.130939i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4078 | −1.28819 | −0.644097 | − | 0.764944i | \(-0.722767\pi\) | ||||
−0.644097 | + | 0.764944i | \(0.722767\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.5341 | 2.18601 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.45550i | − | 0.181367i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.913704 | + | 1.95403i | 0.0478255 | + | 0.102279i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 33.8706i | − | 1.76803i | −0.467456 | − | 0.884016i | \(-0.654829\pi\) | ||
0.467456 | − | 0.884016i | \(-0.345171\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.97291 | −0.102706 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.6310 | −0.603851 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.71356i | 0.192281i | 0.995368 | + | 0.0961403i | \(0.0306498\pi\) | ||||
−0.995368 | + | 0.0961403i | \(0.969350\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.8085 | − | 2.85929i | −0.558150 | − | 0.147653i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.0501i | 0.929626i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.9135 | −0.663322 | −0.331661 | − | 0.943399i | \(-0.607609\pi\) | ||||
−0.331661 | + | 0.943399i | \(0.607609\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.152806 | −0.00782848 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.5864i | 1.81838i | 0.416380 | + | 0.909191i | \(0.363299\pi\) | ||||
−0.416380 | + | 0.909191i | \(0.636701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.69419 | + | 16.4546i | 0.392132 | + | 0.838606i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 5.74443i | − | 0.292006i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.159135 | −0.00806848 | −0.00403424 | − | 0.999992i | \(-0.501284\pi\) | ||||
−0.00403424 | + | 0.999992i | \(0.501284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.957146 | −0.0484050 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.4130i | − | 0.626153i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.7315 | − | 12.0320i | 1.29469 | − | 0.605398i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.4448i | 0.975904i | 0.872870 | + | 0.487952i | \(0.162256\pi\) | ||||
−0.872870 | + | 0.487952i | \(0.837744\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23.0106 | −1.15197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.15915 | −0.457386 | −0.228693 | − | 0.973499i | \(-0.573445\pi\) | ||||
−0.228693 | + | 0.973499i | \(0.573445\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.6928i | 1.47910i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.02556 | + | 0.947153i | −0.100651 | + | 0.0470644i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 12.7210i | − | 0.630559i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3811 | 1.30446 | 0.652232 | − | 0.758020i | \(-0.273833\pi\) | ||||
0.652232 | + | 0.758020i | \(0.273833\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.99009 | 0.443448 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.3721i | 1.78975i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.70009 | − | 18.6058i | −0.427071 | − | 0.913324i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 22.8040i | − | 1.11672i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.0978 | −0.786430 | −0.393215 | − | 0.919447i | \(-0.628637\pi\) | ||||
−0.393215 | + | 0.919447i | \(0.628637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.554657 | 0.0270323 | 0.0135162 | − | 0.999909i | \(-0.495698\pi\) | ||||
0.0135162 | + | 0.999909i | \(0.495698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.67357i | − | 0.129993i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.20975 | + | 2.68171i | 0.155696 | + | 0.130082i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.4127i | 1.27820i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.0781 | −0.727976 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.64879 | 0.320261 | 0.160130 | − | 0.987096i | \(-0.448809\pi\) | ||||
0.160130 | + | 0.987096i | \(0.448809\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.5054i | − | 0.504856i | −0.967616 | − | 0.252428i | \(-0.918771\pi\) | ||
0.967616 | − | 0.252428i | \(-0.0812290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.11436 | − | 6.66030i | −0.149322 | − | 0.319337i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 8.90232i | − | 0.425856i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.56850 | −0.361225 | −0.180612 | − | 0.983554i | \(-0.557808\pi\) | ||||
−0.180612 | + | 0.983554i | \(0.557808\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.74693 | 0.0831870 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 33.0123i | − | 1.56846i | −0.620469 | − | 0.784231i | \(-0.713058\pi\) | ||
0.620469 | − | 0.784231i | \(-0.286942\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.1581 | + | 8.02313i | −0.813371 | + | 0.380333i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.72732i | 0.270893i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.62923 | 0.124081 | 0.0620405 | − | 0.998074i | \(-0.480239\pi\) | ||||
0.0620405 | + | 0.998074i | \(0.480239\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.41905 | 0.255173 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 13.3074i | − | 0.625237i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.8855 | + | 15.3773i | −1.54169 | + | 0.720897i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.9731i | 1.02786i | 0.857833 | + | 0.513929i | \(0.171810\pi\) | ||||
−0.857833 | + | 0.513929i | \(0.828190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.836518 | 0.0390453 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.4409 | −1.74380 | −0.871899 | − | 0.489686i | \(-0.837111\pi\) | ||||
−0.871899 | + | 0.489686i | \(0.837111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.7261i | − | 0.777326i | −0.921380 | − | 0.388663i | \(-0.872937\pi\) | ||
0.921380 | − | 0.388663i | \(-0.127063\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.12319 | − | 10.9564i | −0.237582 | − | 0.508089i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.5719i | 0.720583i | 0.932840 | + | 0.360291i | \(0.117323\pi\) | ||||
−0.932840 | + | 0.360291i | \(0.882677\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.95752 | 0.136566 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.9141 | −0.825440 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.7784i | 0.725490i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.9423 | + | 29.8535i | −1.14443 | + | 1.36977i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.93268i | 0.180065i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.6312 | −0.622824 | −0.311412 | − | 0.950275i | \(-0.600802\pi\) | ||||
−0.311412 | + | 0.950275i | \(0.600802\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.4237 | 1.15922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.38400i | 0.153978i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.83153 | − | 6.05545i | −0.128573 | − | 0.274964i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.3372i | 1.01219i | 0.862477 | + | 0.506097i | \(0.168912\pi\) | ||||
−0.862477 | + | 0.506097i | \(0.831088\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.5544 | 0.612953 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.4758 | 0.878928 | 0.439464 | − | 0.898260i | \(-0.355168\pi\) | ||||
0.439464 | + | 0.898260i | \(0.355168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.75057i | 0.123880i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.56366 | − | 2.60157i | 0.250068 | − | 0.116932i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.5771i | 0.788438i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.1507 | 0.588708 | 0.294354 | − | 0.955696i | \(-0.404895\pi\) | ||||
0.294354 | + | 0.955696i | \(0.404895\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.9256 | 0.666828 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.16789i | 0.408776i | 0.978890 | + | 0.204388i | \(0.0655204\pi\) | ||||
−0.978890 | + | 0.204388i | \(0.934480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.6760 | − | 7.79772i | 0.742074 | − | 0.346994i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 17.1343i | − | 0.760962i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.688601 | 0.0305217 | 0.0152609 | − | 0.999884i | \(-0.495142\pi\) | ||||
0.0152609 | + | 0.999884i | \(0.495142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.85307 | −0.126213 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.78037i | 0.343512i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.97613 | − | 8.50326i | −0.175209 | − | 0.374698i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.34356i | 0.322969i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.4705 | 0.679082 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.5420 | 1.68856 | 0.844278 | − | 0.535905i | \(-0.180029\pi\) | ||||
0.844278 | + | 0.535905i | \(0.180029\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14.7842i | − | 0.646468i | −0.946319 | − | 0.323234i | \(-0.895230\pi\) | ||
0.946319 | − | 0.323234i | \(-0.104770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.48122 | − | 11.3481i | 0.413795 | − | 0.495272i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.52476i | 0.197102i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6908 | 0.943078 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.2982 | 0.533695 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.8303i | 0.469110i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.81158 | + | 3.87421i | 0.0783215 | + | 0.167497i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.5415i | 0.713819i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.79833 | −0.206679 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.1951 | −0.997235 | −0.498617 | − | 0.866822i | \(-0.666159\pi\) | ||||
−0.498617 | + | 0.866822i | \(0.666159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 15.9855i | − | 0.686003i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.9462 | − | 7.45645i | 0.683060 | − | 0.319399i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.5999i | 1.18009i | 0.807371 | + | 0.590044i | \(0.200890\pi\) | ||||
−0.807371 | + | 0.590044i | \(0.799110\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.93068 | 0.381152 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.5828 | −1.08986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.5705i | 1.59766i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.38108 | + | 4.38660i | −0.398205 | + | 0.186201i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 2.27768i | − | 0.0965086i | −0.998835 | − | 0.0482543i | \(-0.984634\pi\) | ||
0.998835 | − | 0.0482543i | \(-0.0153658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.5339 | −1.33374 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.29768 | −0.0970083 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.1148i | 1.22704i | 0.789679 | + | 0.613521i | \(0.210247\pi\) | ||||
−0.789679 | + | 0.613521i | \(0.789753\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.9106 | + | 38.3032i | 0.753504 | + | 1.61143i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.95752i | − | 0.124204i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.2631 | −1.56215 | −0.781075 | − | 0.624437i | \(-0.785329\pi\) | ||||
−0.781075 | + | 0.624437i | \(0.785329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.77045 | −0.325183 | −0.162592 | − | 0.986693i | \(-0.551985\pi\) | ||||
−0.162592 | + | 0.986693i | \(0.551985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 9.89989i | − | 0.413574i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.39035 | + | 3.66809i | 0.183090 | + | 0.152970i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.9697i | 1.66396i | 0.554806 | + | 0.831980i | \(0.312793\pi\) | ||||
−0.554806 | + | 0.831980i | \(0.687207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.9755 | −0.580802 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.1664 | 1.12705 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10.8020i | − | 0.447373i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.19937 | + | 11.1193i | 0.214968 | + | 0.459725i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 32.4241i | − | 1.33829i | −0.743134 | − | 0.669143i | \(-0.766661\pi\) | ||
0.743134 | − | 0.669143i | \(-0.233339\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.0844 | −1.73406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.47194 | 0.225085 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 27.3374i | − | 1.12261i | −0.827608 | − | 0.561306i | \(-0.810299\pi\) | ||
0.827608 | − | 0.561306i | \(-0.189701\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.01128 | + | 2.34327i | −0.205442 | + | 0.0960649i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.21401i | 0.0906135i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.1243 | −1.80287 | −0.901435 | − | 0.432915i | \(-0.857485\pi\) | ||||
−0.901435 | + | 0.432915i | \(0.857485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.9423 | 1.18058 | 0.590290 | − | 0.807191i | \(-0.299014\pi\) | ||||
0.590290 | + | 0.807191i | \(0.299014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.99934 | − | 3.27289i | 0.284563 | − | 0.133062i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.5954i | 1.16065i | 0.814384 | + | 0.580326i | \(0.197075\pi\) | ||||
−0.814384 | + | 0.580326i | \(0.802925\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.72469 | 0.394064 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.6765 | −0.593747 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21.3445i | − | 0.862096i | −0.902329 | − | 0.431048i | \(-0.858144\pi\) | ||
0.902329 | − | 0.431048i | \(-0.141856\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.86865 | − | 3.99626i | −0.0753513 | − | 0.161145i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.0558i | 0.525608i | 0.964849 | + | 0.262804i | \(0.0846473\pi\) | ||||
−0.964849 | + | 0.262804i | \(0.915353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0190092 | −0.000764043 | −0.000382021 | − | 1.00000i | \(-0.500122\pi\) | ||||
−0.000382021 | 1.00000i | \(0.500122\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.14420 | 0.0459153 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 25.0525i | − | 1.00371i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.44567 | − | 24.6015i | −0.177827 | − | 0.984062i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 21.3705i | − | 0.853457i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.87421 | 0.154475 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.3875 | 0.493138 | 0.246569 | − | 0.969125i | \(-0.420697\pi\) | ||||
0.246569 | + | 0.969125i | \(0.420697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 28.0506i | − | 1.11491i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.144730 | − | 0.309517i | −0.00574345 | − | 0.0122828i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 9.58971i | − | 0.379958i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.94317 | 0.235108 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.3167 | 1.03945 | 0.519723 | − | 0.854335i | \(-0.326035\pi\) | ||||
0.519723 | + | 0.854335i | \(0.326035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.6412i | 1.68161i | 0.541342 | + | 0.840803i | \(0.317916\pi\) | ||||
−0.541342 | + | 0.840803i | \(0.682084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.6357 | − | 5.44086i | 0.458155 | − | 0.214233i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.1030i | 1.81250i | 0.422747 | + | 0.906248i | \(0.361066\pi\) | ||||
−0.422747 | + | 0.906248i | \(0.638934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.7797 | −1.32597 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.9974 | 0.626986 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.8854i | 1.87390i | 0.349460 | + | 0.936951i | \(0.386365\pi\) | ||||
−0.349460 | + | 0.936951i | \(0.613635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.1433 | − | 11.7570i | 0.982430 | − | 0.459385i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.964685i | 0.0376359i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.9626 | 1.63463 | 0.817315 | − | 0.576192i | \(-0.195462\pi\) | ||||
0.817315 | + | 0.576192i | \(0.195462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.99221 | 0.155279 | 0.0776394 | − | 0.996982i | \(-0.475262\pi\) | ||||
0.0776394 | + | 0.996982i | \(0.475262\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 4.59204i | − | 0.178340i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.7946 | − | 46.6094i | −0.845157 | − | 1.80743i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.76228i | 0.145676i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.83158 | −0.0708129 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.5301 | −0.946974 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6406i | 0.718543i | 0.933233 | + | 0.359271i | \(0.116975\pi\) | ||||
−0.933233 | + | 0.359271i | \(0.883025\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.83703 | − | 3.20580i | −0.147688 | − | 0.123391i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.6577i | 0.563342i | 0.959511 | + | 0.281671i | \(0.0908887\pi\) | ||||
−0.959511 | + | 0.281671i | \(0.909111\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.84155 | 0.339308 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.2018 | −0.505893 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0897i | 1.38094i | 0.723363 | + | 0.690468i | \(0.242595\pi\) | ||||
−0.723363 | + | 0.690468i | \(0.757405\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.51499 | + | 18.2100i | 0.325341 | + | 0.695768i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 12.7004i | − | 0.484552i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.5884 | 0.822451 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5459 | 0.591396 | 0.295698 | − | 0.955282i | \(-0.404448\pi\) | ||||
0.295698 | + | 0.955282i | \(0.404448\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.12349i | 0.308586i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46.1909 | − | 21.5989i | 1.75212 | − | 0.819292i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.65038i | 0.0625125i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.7551 | 0.520267 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1326 | 1.36471 | 0.682355 | − | 0.731021i | \(-0.260956\pi\) | ||||
0.682355 | + | 0.731021i | \(0.260956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.0336i | 1.35903i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.41548 | − | 2.53228i | 0.203959 | − | 0.0953712i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.3487i | 0.915725i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.2485 | −1.58668 | −0.793338 | − | 0.608781i | \(-0.791659\pi\) | ||||
−0.793338 | + | 0.608781i | \(0.791659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.7034 | 0.476414 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.18904i | 0.231782i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.2812 | − | 30.5416i | −0.534088 | − | 1.14219i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.29614i | 0.123097i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.7436 | 0.512551 | 0.256275 | − | 0.966604i | \(-0.417505\pi\) | ||||
0.256275 | + | 0.966604i | \(0.417505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.4156 | 0.462381 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.789127i | 0.0293479i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.5411 | − | 12.6166i | 0.391486 | − | 0.468570i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.6271i | − | 0.876281i | −0.898907 | − | 0.438140i | \(-0.855637\pi\) | ||
0.898907 | − | 0.438140i | \(-0.144363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.80532 | −0.177731 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 41.9518i | − | 1.54953i | −0.632252 | − | 0.774763i | \(-0.717869\pi\) | ||
0.632252 | − | 0.774763i | \(-0.282131\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.65461 | + | 3.53851i | 0.0610311 | + | 0.130520i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.74672i | 0.101177i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.3488 | 0.711758 | 0.355879 | − | 0.934532i | \(-0.384181\pi\) | ||||
0.355879 | + | 0.934532i | \(0.384181\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.7101 | 1.56900 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.54217i | − | 0.313382i | −0.987648 | − | 0.156691i | \(-0.949917\pi\) | ||
0.987648 | − | 0.156691i | \(-0.0500827\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.6010 | + | 5.42465i | −0.425029 | + | 0.198744i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 9.18552i | − | 0.336080i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.65673 | −0.206692 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.22485 | 0.336620 | 0.168310 | − | 0.985734i | \(-0.446169\pi\) | ||||
0.168310 | + | 0.985734i | \(0.446169\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.4247i | 0.671432i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.9550 | − | 12.6042i | 0.980992 | − | 0.458712i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 16.6768i | − | 0.606129i | −0.952970 | − | 0.303064i | \(-0.901990\pi\) | ||
0.952970 | − | 0.303064i | \(-0.0980097\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.14281 | −0.114077 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.6354 | 1.36428 | 0.682142 | − | 0.731220i | \(-0.261049\pi\) | ||||
0.682142 | + | 0.731220i | \(0.261049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.2830i | 0.842902i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.792310 | + | 1.69442i | 0.0286460 | + | 0.0612618i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 67.5105i | − | 2.43766i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.7260 | −1.54074 | −0.770369 | − | 0.637598i | \(-0.779928\pi\) | ||||
−0.770369 | + | 0.637598i | \(0.779928\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.3790 | 0.877988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.98882i | 0.0715330i | 0.999360 | + | 0.0357665i | \(0.0113873\pi\) | ||||
−0.999360 | + | 0.0357665i | \(0.988613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3403 | − | 20.7547i | 0.622883 | − | 0.745530i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 13.6973i | − | 0.491388i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.3500 | −0.549970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.3243 | −0.584128 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.28812i | − | 0.117508i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.9674 | − | 36.2862i | −0.605594 | − | 1.29511i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0279170i | 0.000995132i | 1.00000 | 0.000497566i | \(0.000158380\pi\) | |||||
−1.00000 | 0.000497566i | \(0.999842\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.1653 | 0.575500 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −55.9265 | −1.98852 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 49.0247i | − | 1.74092i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.96589 | + | 3.72485i | −0.282521 | + | 0.132107i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.5883i | 0.587589i | 0.955869 | + | 0.293794i | \(0.0949181\pi\) | ||||
−0.955869 | + | 0.293794i | \(0.905082\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.23649 | −0.0791213 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.47078 | −0.299300 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.64972i | − | 0.0935067i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.85451 | + | 3.20517i | −0.241590 | + | 0.112967i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.3842i | 0.576751i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.4267 | 0.683007 | 0.341503 | − | 0.939881i | \(-0.389064\pi\) | ||||
0.341503 | + | 0.939881i | \(0.389064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.0189 | 1.01899 | 0.509495 | − | 0.860474i | \(-0.329832\pi\) | ||||
0.509495 | + | 0.860474i | \(0.329832\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.4620i | 0.437063i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.8381 | + | 27.4554i | 0.449700 | + | 0.961720i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 44.6938i | − | 1.56364i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.2352 | −0.567305 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.29024 | −0.0799300 | −0.0399650 | − | 0.999201i | \(-0.512725\pi\) | ||||
−0.0399650 | + | 0.999201i | \(0.512725\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.9274i | 0.659769i | 0.944021 | + | 0.329884i | \(0.107010\pi\) | ||||
−0.944021 | + | 0.329884i | \(0.892990\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.5393 | + | 8.80545i | 0.366931 | + | 0.306567i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 4.13628i | − | 0.143832i | −0.997411 | − | 0.0719162i | \(-0.977089\pi\) | ||
0.997411 | − | 0.0719162i | \(-0.0229114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.0018 | 0.868348 | 0.434174 | − | 0.900829i | \(-0.357040\pi\) | ||||
0.434174 | + | 0.900829i | \(0.357040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.7278 | −0.580280 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.46133i | − | 0.0506323i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.1369 | + | 30.2328i | 0.489226 | + | 1.04625i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.40904i | − | 0.186964i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.72466 | 0.335733 | 0.167866 | − | 0.985810i | \(-0.446312\pi\) | ||||
0.167866 | + | 0.985810i | \(0.446312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1882 | −0.627181 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5.16809i | − | 0.177998i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.7066 | − | 16.2288i | 1.19394 | − | 0.558289i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.2197i | 0.351154i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.1242 | −0.416101 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.29920 | 0.181654 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.4876i | 0.804201i | 0.915596 | + | 0.402100i | \(0.131720\pi\) | ||||
−0.915596 | + | 0.402100i | \(0.868280\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.7596 | + | 7.36920i | −0.538968 | + | 0.252021i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.5598i | 0.531512i | 0.964040 | + | 0.265756i | \(0.0856216\pi\) | ||||
−0.964040 | + | 0.265756i | \(0.914378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.0903 | −1.67494 | −0.837470 | − | 0.546484i | \(-0.815966\pi\) | ||||
−0.837470 | + | 0.546484i | \(0.815966\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.83493 | 0.198854 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.5921i | 0.735002i | 0.930023 | + | 0.367501i | \(0.119787\pi\) | ||||
−0.930023 | + | 0.367501i | \(0.880213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.6530 | + | 31.3366i | 0.498216 | + | 1.06547i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.3002i | 0.553585i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.8927 | −1.18365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.48947 | −0.186004 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.98952i | − | 0.101180i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.9665 | + | 8.45641i | 1.08066 | + | 0.285879i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 2.27099i | − | 0.0766857i | −0.999265 | − | 0.0383429i | \(-0.987792\pi\) | ||
0.999265 | − | 0.0383429i | \(-0.0122079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.9443 | 1.04373 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3030 | 0.987242 | 0.493621 | − | 0.869677i | \(-0.335673\pi\) | ||||
0.493621 | + | 0.869677i | \(0.335673\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.7790i | − | 1.54059i | −0.637690 | − | 0.770293i | \(-0.720110\pi\) | ||
0.637690 | − | 0.770293i | \(-0.279890\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.6483 | + | 24.9107i | 0.391552 | + | 0.837364i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.7876i | 1.10090i | 0.834868 | + | 0.550450i | \(0.185544\pi\) | ||||
−0.834868 | + | 0.550450i | \(0.814456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.451926 | 0.0151571 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.74672 | 0.0920187 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 20.8014i | − | 0.696091i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.5059 | + | 15.6673i | −1.11998 | + | 0.523702i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.28107i | − | 0.209719i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.7856 | 0.593183 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.28976 | 0.109598 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.9893i | 0.565368i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.3796 | − | 15.1407i | 1.07633 | − | 0.503294i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 21.1709i | − | 0.702970i | −0.936194 | − | 0.351485i | \(-0.885677\pi\) | ||
0.936194 | − | 0.351485i | \(-0.114323\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.23279 | 0.273065 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.3820 | −0.343970 | −0.171985 | − | 0.985100i | \(-0.555018\pi\) | ||||
−0.171985 | + | 0.985100i | \(0.555018\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.2301i | 0.834994i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.45872 | + | 18.0896i | 0.279637 | + | 0.598025i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.7117i | 1.21233i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.7376 | −1.34381 | −0.671905 | − | 0.740637i | \(-0.734524\pi\) | ||||
−0.671905 | + | 0.740637i | \(0.734524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.72403 | −0.320418 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 32.6249i | − | 1.07386i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.7706 | − | 14.8472i | −0.584295 | − | 0.488172i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 4.19798i | − | 0.137880i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.29322 | −0.206474 | −0.103237 | − | 0.994657i | \(-0.532920\pi\) | ||||
−0.103237 | + | 0.994657i | \(0.532920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.5917 | 0.445451 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 33.3633i | − | 1.09226i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.17626 | − | 4.65410i | −0.0711713 | − | 0.152205i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6773i | 0.479487i | 0.970836 | + | 0.239744i | \(0.0770634\pi\) | ||||
−0.970836 | + | 0.239744i | \(0.922937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.42253 | 0.242225 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.5443 | −0.800120 | −0.400060 | − | 0.916489i | \(-0.631011\pi\) | ||||
−0.400060 | + | 0.916489i | \(0.631011\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.25741i | 0.0735115i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.99064 | − | 2.80122i | 0.194876 | − | 0.0911239i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.2631i | 0.333505i | 0.985999 | + | 0.166753i | \(0.0533281\pi\) | ||||
−0.985999 | + | 0.166753i | \(0.946672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.29561 | 0.171903 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.8359 | −1.09720 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 15.5361i | − | 0.503263i | −0.967823 | − | 0.251631i | \(-0.919033\pi\) | ||
0.967823 | − | 0.251631i | \(-0.0809670\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.0528 | − | 9.37671i | 0.648895 | − | 0.303423i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.03157i | 0.291949i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.5884 | −0.858583 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.74225 | −0.0562016 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.91266i | 0.0616346i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.2370 | − | 28.3083i | −0.426113 | − | 0.911275i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.2910i | − | 1.68157i | −0.541372 | − | 0.840783i | \(-0.682095\pi\) | ||
0.541372 | − | 0.840783i | \(-0.317905\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.50842 | 0.209080 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.4265 | 1.87499 | 0.937497 | − | 0.347993i | \(-0.113137\pi\) | ||||
0.937497 | + | 0.347993i | \(0.113137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 67.4432i | 2.16213i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.5982 | + | 21.0633i | −0.563592 | + | 0.674566i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.4260i | 1.38932i | 0.719338 | + | 0.694660i | \(0.244445\pi\) | ||||
−0.719338 | + | 0.694660i | \(0.755555\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.2669 | 0.743613 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.87248 | 0.251349 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 14.4108i | − | 0.459632i | −0.973234 | − | 0.229816i | \(-0.926188\pi\) | ||
0.973234 | − | 0.229816i | \(-0.0738124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.18276 | + | 11.0837i | 0.165137 | + | 0.353158i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.90713i | 0.251687i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.57280 | −0.209003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.8742 | −1.36194 | −0.680972 | − | 0.732310i | \(-0.738442\pi\) | ||||
−0.680972 | + | 0.732310i | \(0.738442\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 10.2746i | − | 0.326056i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.48462 | + | 2.09701i | −0.142172 | + | 0.0664797i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.02882i | 0.222605i | 0.993787 | + | 0.111303i | \(0.0355023\pi\) | ||||
−0.993787 | + | 0.111303i | \(0.964498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.63135 | −0.146529 |
(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 | 4020.2.g.c.1609.23 | yes | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.4 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.4 | ✓ | 38 | 5.4 | even | 2 | inner | |
4020.2.g.c.1609.23 | yes | 38 | 1.1 | even | 1 | trivial |