Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.13 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.14 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.07570 | −0.621058 | −0.310529 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310529 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.26058i | − | 1.45818i | −0.684420 | − | 0.729088i | \(-0.739944\pi\) | ||
0.684420 | − | 0.729088i | \(-0.260056\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.84286 | −0.614287 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.30427 | − | 3.36138i | 0.361739 | − | 0.932279i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.50742i | 0.905612i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.05222 | 0.740271 | 0.370136 | − | 0.928978i | \(-0.379311\pi\) | ||||
0.370136 | + | 0.928978i | \(0.379311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.15929i | 0.724791i | 0.932024 | + | 0.362395i | \(0.118041\pi\) | ||||
−0.932024 | + | 0.362395i | \(0.881959\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.07570i | − | 0.234738i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.49538 | 1.14587 | 0.572933 | − | 0.819602i | \(-0.305806\pi\) | ||||
0.572933 | + | 0.819602i | \(0.305806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.63139 | −1.12628 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.20948 | 1.00257 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.12550 | 0.766085 | 0.383043 | − | 0.923731i | \(-0.374876\pi\) | ||||
0.383043 | + | 0.923731i | \(0.374876\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.96290i | − | 1.25057i | −0.780395 | − | 0.625287i | \(-0.784982\pi\) | ||
0.780395 | − | 0.625287i | \(-0.215018\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.07570i | 0.187256i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.26058 | 0.551139 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1344i | 1.66608i | 0.553211 | + | 0.833041i | \(0.313402\pi\) | ||||
−0.553211 | + | 0.833041i | \(0.686598\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.40301 | + | 3.61585i | −0.224661 | + | 0.578999i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.829912i | 0.129611i | 0.997898 | + | 0.0648053i | \(0.0206426\pi\) | ||||
−0.997898 | + | 0.0648053i | \(0.979357\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0236 | 1.52858 | 0.764292 | − | 0.644870i | \(-0.223089\pi\) | ||||
0.764292 | + | 0.644870i | \(0.223089\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00880i | 0.895739i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.75979i | − | 1.42361i | −0.702377 | − | 0.711806i | \(-0.747878\pi\) | ||
0.702377 | − | 0.711806i | \(-0.252122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.28328 | −0.459751 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.58699 | 1.04215 | 0.521077 | − | 0.853510i | \(-0.325530\pi\) | ||||
0.521077 | + | 0.853510i | \(0.325530\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.26058 | −0.439657 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.39846i | − | 0.450137i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 15.0400i | − | 1.95804i | −0.203773 | − | 0.979018i | \(-0.565320\pi\) | ||
0.203773 | − | 0.979018i | \(-0.434680\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.7376 | −1.88696 | −0.943478 | − | 0.331434i | \(-0.892468\pi\) | ||||
−0.943478 | + | 0.331434i | \(0.892468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.84286i | − | 0.232179i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.9601 | − | 4.25268i | −1.35943 | − | 0.527479i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.94155i | 1.21455i | 0.794490 | + | 0.607277i | \(0.207738\pi\) | ||||
−0.794490 | + | 0.607277i | \(0.792262\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.91140 | −0.711649 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.2258i | − | 1.68829i | −0.536111 | − | 0.844147i | \(-0.680107\pi\) | ||
0.536111 | − | 0.844147i | \(-0.319893\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.06972i | 0.827448i | 0.910402 | + | 0.413724i | \(0.135772\pi\) | ||||
−0.910402 | + | 0.413724i | \(0.864228\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.05771 | 0.699484 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7487 | 1.32183 | 0.660916 | − | 0.750459i | \(-0.270168\pi\) | ||||
0.660916 | + | 0.750459i | \(0.270168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.0752765 | −0.00836405 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.295776i | − | 0.0324656i | −0.999868 | − | 0.0162328i | \(-0.994833\pi\) | ||
0.999868 | − | 0.0162328i | \(-0.00516728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 9.95200i | − | 1.07945i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.43781 | −0.475783 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.17825i | 0.866893i | 0.901179 | + | 0.433446i | \(0.142703\pi\) | ||||
−0.901179 | + | 0.433446i | \(0.857297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.36138 | + | 1.30427i | 0.352368 | + | 0.136725i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.49002i | 0.776679i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.3011 | 1.05687 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.48378i | − | 0.962932i | −0.876465 | − | 0.481466i | \(-0.840104\pi\) | ||
0.876465 | − | 0.481466i | \(-0.159896\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.84286i | 0.185215i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.77226 | −0.474858 | −0.237429 | − | 0.971405i | \(-0.576305\pi\) | ||||
−0.237429 | + | 0.971405i | \(0.576305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.53648 | 0.545526 | 0.272763 | − | 0.962081i | \(-0.412063\pi\) | ||||
0.272763 | + | 0.962081i | \(0.412063\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.50742 | −0.342289 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8337 | −1.04733 | −0.523665 | − | 0.851924i | \(-0.675436\pi\) | ||||
−0.523665 | + | 0.851924i | \(0.675436\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.525322i | 0.0503167i | 0.999683 | + | 0.0251583i | \(0.00800900\pi\) | ||||
−0.999683 | + | 0.0251583i | \(0.991991\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 10.9016i | − | 1.03473i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.688371 | 0.0647565 | 0.0323782 | − | 0.999476i | \(-0.489692\pi\) | ||||
0.0323782 | + | 0.999476i | \(0.489692\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 17.9181i | − | 1.67087i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.40359 | + | 6.19456i | −0.222212 | + | 0.572687i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.05222i | 0.279796i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.892740i | − | 0.0804956i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.05871i | 0.184136i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4996 | −1.02042 | −0.510211 | − | 0.860050i | \(-0.670433\pi\) | ||||
−0.510211 | + | 0.860050i | \(0.670433\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.7824 | −0.949339 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.4533 | −0.913312 | −0.456656 | − | 0.889643i | \(-0.650953\pi\) | ||||
−0.456656 | + | 0.889643i | \(0.650953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.15929 | −0.273945 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 16.9859i | − | 1.46192i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.34884i | 0.200675i | 0.994953 | + | 0.100338i | \(0.0319923\pi\) | ||||
−0.994953 | + | 0.100338i | \(0.968008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.95608 | 0.165912 | 0.0829561 | − | 0.996553i | \(-0.473564\pi\) | ||||
0.0829561 | + | 0.996553i | \(0.473564\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4986i | 0.884145i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.36138 | − | 1.30427i | −0.281093 | − | 0.109068i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 13.4515i | − | 1.11709i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.07570 | 0.0887225 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 15.3388i | − | 1.25661i | −0.777969 | − | 0.628303i | \(-0.783750\pi\) | ||
0.777969 | − | 0.628303i | \(-0.216250\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.941516i | − | 0.0766195i | −0.999266 | − | 0.0383097i | \(-0.987803\pi\) | ||
0.999266 | − | 0.0383097i | \(-0.0121974\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.62481 | −0.454739 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.7031 | −1.82356 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.14676 | −0.570373 | −0.285187 | − | 0.958472i | \(-0.592056\pi\) | ||||
−0.285187 | + | 0.958472i | \(0.592056\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.16136 | −0.647238 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.49538i | 0.433097i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.15590i | − | 0.560494i | −0.959928 | − | 0.280247i | \(-0.909584\pi\) | ||
0.959928 | − | 0.280247i | \(-0.0904163\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.50742 | 0.273052 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.7620i | 1.14232i | 0.820838 | + | 0.571160i | \(0.193507\pi\) | ||||
−0.820838 | + | 0.571160i | \(0.806493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.59776 | − | 8.76829i | −0.738290 | − | 0.674484i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 5.82213i | − | 0.445230i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0494 | −0.840073 | −0.420037 | − | 0.907507i | \(-0.637983\pi\) | ||||
−0.420037 | + | 0.907507i | \(0.637983\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.63139i | − | 0.425693i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.1785i | 1.21605i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.24627 | −0.691099 | −0.345549 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345549 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8299 | 1.32528 | 0.662642 | − | 0.748937i | \(-0.269435\pi\) | ||||
0.662642 | + | 0.748937i | \(0.269435\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.8533 | 1.17191 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.0440 | 2.42944 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.05222i | − | 0.223200i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.20948i | 0.378934i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.87147 | 0.207772 | 0.103886 | − | 0.994589i | \(-0.466872\pi\) | ||||
0.103886 | + | 0.994589i | \(0.466872\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.4001i | 1.03654i | 0.855216 | + | 0.518272i | \(0.173425\pi\) | ||||
−0.855216 | + | 0.518272i | \(0.826575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.7898 | + | 4.57462i | 0.844283 | + | 0.327595i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.69489i | − | 0.548238i | −0.961696 | − | 0.274119i | \(-0.911614\pi\) | ||
0.961696 | − | 0.274119i | \(-0.0883862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.11257 | −0.433309 | −0.216654 | − | 0.976248i | \(-0.569514\pi\) | ||||
−0.216654 | + | 0.976248i | \(0.569514\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 10.6942i | − | 0.754308i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.12550i | 0.289553i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.70600 | 0.188995 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.1272 | −0.703891 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.15929 | 0.218533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.4170 | −1.13019 | −0.565095 | − | 0.825026i | \(-0.691161\pi\) | ||||
−0.565095 | + | 0.825026i | \(0.691161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.3028i | 1.04853i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 32.6827i | − | 2.22894i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.96290 | 0.472673 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 7.60493i | − | 0.513893i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.98091 | − | 10.2597i | 0.267785 | − | 0.690140i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.7760i | − | 1.72609i | −0.505126 | − | 0.863046i | \(-0.668554\pi\) | ||
0.505126 | − | 0.863046i | \(-0.331446\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.3779 | 0.691858 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.5995i | 1.30087i | 0.759563 | + | 0.650433i | \(0.225413\pi\) | ||||
−0.759563 | + | 0.650433i | \(0.774587\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.9163i | − | 0.985699i | −0.870114 | − | 0.492850i | \(-0.835955\pi\) | ||
0.870114 | − | 0.492850i | \(-0.164045\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.07570 | −0.0707761 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8515 | 0.710903 | 0.355452 | − | 0.934695i | \(-0.384327\pi\) | ||||
0.355452 | + | 0.934695i | \(0.384327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.8226 | −2.07588 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.6381 | −0.820935 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 11.4325i | − | 0.739505i | −0.929130 | − | 0.369752i | \(-0.879443\pi\) | ||
0.929130 | − | 0.369752i | \(-0.120557\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.20504i | 0.335286i | 0.985848 | + | 0.167643i | \(0.0536156\pi\) | ||||
−0.985848 | + | 0.167643i | \(0.946384\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5475 | −0.997371 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.26058i | 0.208311i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.6196 | + | 4.12056i | 0.675707 | + | 0.262185i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.318167i | 0.0201630i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.8773 | 1.06529 | 0.532643 | − | 0.846340i | \(-0.321199\pi\) | ||||
0.532643 | + | 0.846340i | \(0.321199\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.49538i | − | 0.345491i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.7054i | 0.670398i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.3254 | 0.955970 | 0.477985 | − | 0.878368i | \(-0.341367\pi\) | ||||
0.477985 | + | 0.878368i | \(0.341367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1344 | −0.629720 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.60272 | −0.470596 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3305 | 0.883658 | 0.441829 | − | 0.897099i | \(-0.354330\pi\) | ||||
0.441829 | + | 0.897099i | \(0.354330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 24.7380i | − | 1.51964i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.79737i | − | 0.538390i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.3313 | −1.05671 | −0.528353 | − | 0.849025i | \(-0.677190\pi\) | ||||
−0.528353 | + | 0.849025i | \(0.677190\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.614183i | 0.0373090i | 0.999826 | + | 0.0186545i | \(0.00593825\pi\) | ||||
−0.999826 | + | 0.0186545i | \(0.994062\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.61585 | − | 1.40301i | −0.218841 | − | 0.0849138i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.63139i | 0.339586i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.1543 | −1.21095 | −0.605477 | − | 0.795863i | \(-0.707018\pi\) | ||||
−0.605477 | + | 0.795863i | \(0.707018\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.8317i | 0.768212i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.01985i | 0.239804i | 0.992786 | + | 0.119902i | \(0.0382580\pi\) | ||||
−0.992786 | + | 0.119902i | \(0.961742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0278 | 0.655537 | 0.327768 | − | 0.944758i | \(-0.393703\pi\) | ||||
0.327768 | + | 0.944758i | \(0.393703\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.0810 | −0.656379 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.829912 | −0.0489882 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.68397 | −0.451998 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.2017i | 0.598037i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 32.5830i | − | 1.90352i | −0.306849 | − | 0.951758i | \(-0.599275\pi\) | ||
0.306849 | − | 0.951758i | \(-0.400725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49.0390 | −2.85516 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.20948i | − | 0.302285i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.16745 | − | 18.4721i | 0.414504 | − | 1.06827i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0236i | 0.577750i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.13354 | 0.294914 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48.0532i | 2.75152i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.18948i | − | 0.410325i | −0.978728 | − | 0.205163i | \(-0.934228\pi\) | ||
0.978728 | − | 0.205163i | \(-0.0657723\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.95561 | −0.338803 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7964 | 1.00914 | 0.504572 | − | 0.863370i | \(-0.331650\pi\) | ||||
0.504572 | + | 0.863370i | \(0.331650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.2818 | −1.08987 | −0.544937 | − | 0.838477i | \(-0.683446\pi\) | ||||
−0.544937 | + | 0.838477i | \(0.683446\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.00880 | −0.338558 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.78137i | 0.156217i | 0.996945 | + | 0.0781086i | \(0.0248881\pi\) | ||||
−0.996945 | + | 0.0781086i | \(0.975112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.12550i | − | 0.230983i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6538 | 0.650453 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.64283i | 0.536542i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.34485 | + | 18.9293i | −0.407419 | + | 1.05001i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 0.565090i | − | 0.0312496i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.75979 | 0.538074 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.67645i | 0.0921461i | 0.998938 | + | 0.0460731i | \(0.0146707\pi\) | ||||
−0.998938 | + | 0.0460731i | \(0.985329\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 18.6763i | − | 1.02345i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.4152 | 1.77103 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.32141 | −0.0719818 | −0.0359909 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359909 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.740483 | −0.0402175 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.96290 | −0.377062 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.2746i | 1.03771i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.1529 | −0.974500 | −0.487250 | − | 0.873262i | \(-0.662000\pi\) | ||||
−0.487250 | + | 0.873262i | \(0.662000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.08323i | − | 0.218570i | −0.994010 | − | 0.109285i | \(-0.965144\pi\) | ||
0.994010 | − | 0.109285i | \(-0.0348561\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.79457 | − | 17.5111i | 0.362667 | − | 0.934671i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 28.2106i | − | 1.50150i | −0.660587 | − | 0.750750i | \(-0.729693\pi\) | ||
0.660587 | − | 0.750750i | \(-0.270307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −46.3845 | −2.46183 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.28328i | − | 0.173770i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.7635i | 0.568077i | 0.958813 | + | 0.284039i | \(0.0916744\pi\) | ||||
−0.958813 | + | 0.284039i | \(0.908326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.01889 | 0.474679 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.07570 | 0.0564598 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.0514 | 1.20657 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.9220 | 1.45752 | 0.728758 | − | 0.684771i | \(-0.240098\pi\) | ||||
0.728758 | + | 0.684771i | \(0.240098\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.52941i | − | 0.0796181i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.58699i | 0.393897i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.95262 | 0.463549 | 0.231775 | − | 0.972770i | \(-0.425547\pi\) | ||||
0.231775 | + | 0.972770i | \(0.425547\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 2.21456i | − | 0.114359i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.38076 | − | 13.8674i | 0.277123 | − | 0.714206i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 31.9416i | − | 1.64073i | −0.571841 | − | 0.820364i | \(-0.693771\pi\) | ||
0.571841 | − | 0.820364i | \(-0.306229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.3701 | 0.633740 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 22.0246i | − | 1.12540i | −0.826660 | − | 0.562701i | \(-0.809762\pi\) | ||
0.826660 | − | 0.562701i | \(-0.190238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 3.26058i | − | 0.166175i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.4721 | −0.938990 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.17862 | −0.211865 | −0.105932 | − | 0.994373i | \(-0.533783\pi\) | ||||
−0.105932 | + | 0.994373i | \(0.533783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7731 | 0.848251 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.2447 | 0.567220 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 38.3076i | − | 1.92747i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.0538i | − | 0.604962i | −0.953155 | − | 0.302481i | \(-0.902185\pi\) | ||
0.953155 | − | 0.302481i | \(-0.0978149\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.39846 | 0.170136 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.3073i | 1.06403i | 0.846734 | + | 0.532017i | \(0.178566\pi\) | ||||
−0.846734 | + | 0.532017i | \(0.821434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.4050 | − | 9.08150i | −1.16588 | − | 0.452382i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.245445i | 0.0121963i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.1344 | 0.502343 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.7180i | − | 0.925544i | −0.886477 | − | 0.462772i | \(-0.846855\pi\) | ||
0.886477 | − | 0.462772i | \(-0.153145\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.52666i | − | 0.124631i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.0400 | 0.740068 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.964400 | −0.0473405 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.10416 | −0.103041 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.6971 | 1.45080 | 0.725399 | − | 0.688329i | \(-0.241655\pi\) | ||||
0.725399 | + | 0.688329i | \(0.241655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.2123i | − | 0.546456i | −0.961949 | − | 0.273228i | \(-0.911909\pi\) | ||
0.961949 | − | 0.273228i | \(-0.0880914\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.9859i | 0.874506i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.1882 | −0.833752 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 14.7376i | − | 0.713203i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.61585 | + | 1.40301i | 0.174575 | + | 0.0677378i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 0.176475i | − | 0.00850050i | −0.999991 | − | 0.00425025i | \(-0.998647\pi\) | ||
0.999991 | − | 0.00425025i | \(-0.00135290\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.1279 | −0.486714 | −0.243357 | − | 0.969937i | \(-0.578249\pi\) | ||||
−0.243357 | + | 0.969937i | \(0.578249\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.4698i | 0.693776i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.3615i | 0.830513i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1287 | 0.578869 | 0.289435 | − | 0.957198i | \(-0.406533\pi\) | ||||
0.289435 | + | 0.957198i | \(0.406533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.84286 | 0.0877553 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.685413 | 0.0325650 | 0.0162825 | − | 0.999867i | \(-0.494817\pi\) | ||||
0.0162825 | + | 0.999867i | \(0.494817\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.6658 | 1.26408 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.5000i | 0.780425i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.4568i | 1.67331i | 0.547732 | + | 0.836654i | \(0.315491\pi\) | ||||
−0.547732 | + | 0.836654i | \(0.684509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.829912 | 0.0390790 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.01279i | 0.0475851i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.25268 | − | 10.9601i | 0.199369 | − | 0.513815i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.7743i | 1.20567i | 0.797865 | + | 0.602836i | \(0.205963\pi\) | ||||
−0.797865 | + | 0.602836i | \(0.794037\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.9005 | 0.742171 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.29626i | 0.106947i | 0.998569 | + | 0.0534737i | \(0.0170293\pi\) | ||||
−0.998569 | + | 0.0534737i | \(0.982971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.2474i | − | 0.476239i | −0.971236 | − | 0.238119i | \(-0.923469\pi\) | ||
0.971236 | − | 0.238119i | \(-0.0765310\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.4218 | 1.13253 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.7823 | −1.65581 | −0.827904 | − | 0.560870i | \(-0.810467\pi\) | ||||
−0.827904 | + | 0.560870i | \(0.810467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.94155 | −0.459058 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.68779 | 0.354235 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.0236i | − | 0.460885i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 17.7912i | − | 0.816316i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.9818 | −0.640182 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 11.4723i | − | 0.524184i | −0.965043 | − | 0.262092i | \(-0.915588\pi\) | ||
0.965043 | − | 0.262092i | \(-0.0844123\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.0655 | + | 13.2180i | 1.55325 | + | 0.602687i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 5.91140i | − | 0.268978i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.9226 | −1.40412 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.6514i | − | 1.38895i | −0.719519 | − | 0.694473i | \(-0.755638\pi\) | ||
0.719519 | − | 0.694473i | \(-0.244362\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.69763i | 0.348099i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.3578 | 1.59567 | 0.797837 | − | 0.602873i | \(-0.205978\pi\) | ||||
0.797837 | + | 0.602873i | \(0.205978\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.5919 | 0.567111 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.00880 | 0.270075 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.2258 | 0.638115 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.19506i | − | 0.366861i | −0.983033 | − | 0.183431i | \(-0.941280\pi\) | ||
0.983033 | − | 0.183431i | \(-0.0587202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 15.8796i | − | 0.709447i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2611 | 0.546698 | 0.273349 | − | 0.961915i | \(-0.411869\pi\) | ||||
0.273349 | + | 0.961915i | \(0.411869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5603i | 0.692426i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.3244 | + | 9.43208i | 0.458521 | + | 0.418893i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.8793i | 0.836810i | 0.908261 | + | 0.418405i | \(0.137411\pi\) | ||||
−0.908261 | + | 0.418405i | \(0.862589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.06972 | −0.312746 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.4583i | 0.726650i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 18.0521i | − | 0.795473i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.75979 | −0.429235 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.8859 | 0.521734 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.1763 | 0.664885 | 0.332443 | − | 0.943123i | \(-0.392127\pi\) | ||||
0.332443 | + | 0.943123i | \(0.392127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.6123 | −1.16368 | −0.581838 | − | 0.813305i | \(-0.697666\pi\) | ||||
−0.581838 | + | 0.813305i | \(0.697666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.05771i | 0.264380i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 21.2523i | − | 0.925764i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.19919 | 0.313008 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.7166i | 1.20280i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.78965 | + | 1.08243i | 0.120833 | + | 0.0468852i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.3241i | 1.52719i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.94625 | 0.429212 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.1326i | 0.994546i | 0.867594 | + | 0.497273i | \(0.165665\pi\) | ||||
−0.867594 | + | 0.497273i | \(0.834335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.1796 | −0.823078 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.71285 | 0.0733706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.88107 | 0.294213 | 0.147107 | − | 0.989121i | \(-0.453004\pi\) | ||||
0.147107 | + | 0.989121i | \(0.453004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.1594 | 1.15913 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.0336i | 0.555251i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7487i | 0.499606i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −35.5455 | −1.50882 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.3101i | 1.24191i | 0.783846 | + | 0.620955i | \(0.213255\pi\) | ||||
−0.783846 | + | 0.620955i | \(0.786745\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.0735 | − | 33.6931i | 0.552949 | − | 1.42507i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.28328i | 0.138620i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.0739 | 1.35176 | 0.675878 | − | 0.737014i | \(-0.263765\pi\) | ||||
0.675878 | + | 0.737014i | \(0.263765\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.24449i | − | 0.0944263i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.0752765i | − | 0.00316131i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.1986 | −1.43368 | −0.716841 | − | 0.697237i | \(-0.754413\pi\) | ||||
−0.716841 | + | 0.697237i | \(0.754413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.6809 | −1.24211 | −0.621054 | − | 0.783767i | \(-0.713295\pi\) | ||||
−0.621054 | + | 0.783767i | \(0.713295\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.08885 | −0.129039 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.9466 | −1.29056 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.4269i | − | 0.600601i | −0.953845 | − | 0.300300i | \(-0.902913\pi\) | ||
0.953845 | − | 0.300300i | \(-0.0970870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 15.4903i | − | 0.643754i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.295776 | 0.0122708 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.58699i | − | 0.314221i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20.1979 | + | 7.83709i | 0.835079 | + | 0.324024i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.2819i | 1.20859i | 0.796759 | + | 0.604297i | \(0.206546\pi\) | ||||
−0.796759 | + | 0.604297i | \(0.793454\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.9978 | 0.906404 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.27742i | 0.340488i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.9708i | 1.88780i | 0.330239 | + | 0.943898i | \(0.392871\pi\) | ||||
−0.330239 | + | 0.943898i | \(0.607129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.95200 | 0.407992 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.57531 | 0.269110 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.54448 | −0.185682 | −0.0928411 | − | 0.995681i | \(-0.529595\pi\) | ||||
−0.0928411 | + | 0.995681i | \(0.529595\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.93195 | −0.119597 | −0.0597984 | − | 0.998210i | \(-0.519046\pi\) | ||||
−0.0597984 | + | 0.998210i | \(0.519046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 18.3209i | − | 0.746085i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.26058i | 0.132561i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.9586 | 1.78422 | 0.892112 | − | 0.451815i | \(-0.149223\pi\) | ||||
0.892112 | + | 0.451815i | \(0.149223\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 4.43781i | − | 0.179829i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.8064 | − | 12.7294i | −1.32720 | − | 0.514976i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21.5218i | − | 0.869257i | −0.900610 | − | 0.434628i | \(-0.856880\pi\) | ||
0.900610 | − | 0.434628i | \(-0.143120\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.91085 | −0.117377 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.3070i | − | 1.01882i | −0.860523 | − | 0.509412i | \(-0.829863\pi\) | ||
0.860523 | − | 0.509412i | \(-0.170137\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8075i | 0.836324i | 0.908373 | + | 0.418162i | \(0.137326\pi\) | ||||
−0.908373 | + | 0.418162i | \(0.862674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.6281 | 1.14881 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.17825 | −0.327655 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.4444 | −0.857775 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.39846 | −0.135721 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.9323i | 1.23335i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.3787i | 0.771455i | 0.922613 | + | 0.385727i | \(0.126049\pi\) | ||||
−0.922613 | + | 0.385727i | \(0.873951\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.6598 | 0.701914 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.4953i | 1.48795i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.30427 | + | 3.36138i | −0.0516770 | + | 0.133183i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.2162i | 1.03710i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7551 | 0.780279 | 0.390140 | − | 0.920756i | \(-0.372427\pi\) | ||||
0.390140 | + | 0.920756i | \(0.372427\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 45.6637i | − | 1.80080i | −0.435063 | − | 0.900400i | \(-0.643274\pi\) | ||
0.435063 | − | 0.900400i | \(-0.356726\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 35.1570i | 1.38430i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.6121 | 0.535145 | 0.267573 | − | 0.963538i | \(-0.413778\pi\) | ||||
0.267573 | + | 0.963538i | \(0.413778\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.0400 | −0.590370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.49002 | −0.293557 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.97739 | 0.273046 | 0.136523 | − | 0.990637i | \(-0.456407\pi\) | ||||
0.136523 | + | 0.990637i | \(0.456407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.0840i | 1.33177i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 13.0285i | − | 0.508291i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.333655 | 0.0129974 | 0.00649869 | − | 0.999979i | \(-0.497931\pi\) | ||||
0.00649869 | + | 0.999979i | \(0.497931\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.0873i | 1.52032i | 0.649737 | + | 0.760159i | \(0.274879\pi\) | ||||
−0.649737 | + | 0.760159i | \(0.725121\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.28228 | + | 11.0364i | −0.166310 | + | 0.428617i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.3011i | 0.399460i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.6712 | 0.877831 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.7274i | 1.07200i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.7376i | 0.568939i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.7921 | 1.18695 | 0.593474 | − | 0.804853i | \(-0.297756\pi\) | ||||
0.593474 | + | 0.804853i | \(0.297756\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −29.3366 | −1.12917 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.8179 | −1.14599 | −0.572997 | − | 0.819557i | \(-0.694219\pi\) | ||||
−0.572997 | + | 0.819557i | \(0.694219\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.48378 | 0.363954 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 21.0833i | − | 0.807913i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.9745i | 0.879093i | 0.898220 | + | 0.439547i | \(0.144861\pi\) | ||||
−0.898220 | + | 0.439547i | \(0.855139\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.65860 | 0.292620 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.0456i | 0.612176i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.89548 | − | 25.5028i | 0.376988 | − | 0.971579i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.75760i | − | 0.371197i | −0.982626 | − | 0.185598i | \(-0.940578\pi\) | ||
0.982626 | − | 0.185598i | \(-0.0594223\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.84286 | −0.0700045 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.37794i | − | 0.241929i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.53307i | 0.0959469i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.6730 | −0.441512 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.23964 | 0.0468207 | 0.0234104 | − | 0.999726i | \(-0.492548\pi\) | ||||
0.0234104 | + | 0.999726i | \(0.492548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.0174 | −1.20756 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 34.2317 | 1.28924 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.77226i | − | 0.179479i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.9775i | 0.449825i | 0.974379 | + | 0.224912i | \(0.0722096\pi\) | ||||
−0.974379 | + | 0.224912i | \(0.927790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.6512 | −0.811985 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 38.2638i | − | 1.43299i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.25268 | + | 10.9601i | −0.159041 | + | 0.409883i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.2979i | 0.459275i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.9151 | −0.481653 | −0.240826 | − | 0.970568i | \(-0.577418\pi\) | ||||
−0.240826 | + | 0.970568i | \(0.577418\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.53648i | 0.206189i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.59908i | − | 0.208232i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.2323 | −0.862825 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.8067 | −1.77305 | −0.886527 | − | 0.462678i | \(-0.846889\pi\) | ||||
−0.886527 | + | 0.462678i | \(0.846889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.9503 | 0.627789 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.5942 | 1.13157 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.43540i | 0.0899534i | 0.998988 | + | 0.0449767i | \(0.0143214\pi\) | ||||
−0.998988 | + | 0.0449767i | \(0.985679\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 3.50742i | − | 0.129373i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.94155 | 0.366202 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.76085i | 0.0647739i | 0.999475 | + | 0.0323870i | \(0.0103109\pi\) | ||||
−0.999475 | + | 0.0323870i | \(0.989689\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.4235 | − | 4.43250i | −0.419653 | − | 0.162832i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.7004i | 1.41978i | 0.704312 | + | 0.709890i | \(0.251256\pi\) | ||||
−0.704312 | + | 0.709890i | \(0.748744\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −50.0135 | −1.83235 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.545073i | 0.0199432i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 10.8337i | − | 0.395854i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.5856 | −1.33503 | −0.667514 | − | 0.744597i | \(-0.732642\pi\) | ||||
−0.667514 | + | 0.744597i | \(0.732642\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.1550 | −0.661604 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.06989 | −0.111725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.9777 | 0.435336 | 0.217668 | − | 0.976023i | \(-0.430155\pi\) | ||||
0.217668 | + | 0.976023i | \(0.430155\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.91140i | 0.214570i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.4044i | 1.57341i | 0.617331 | + | 0.786703i | \(0.288214\pi\) | ||||
−0.617331 | + | 0.786703i | \(0.711786\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.525322 | −0.0190179 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.3402i | 0.663090i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.5550 | − | 19.6162i | −1.82544 | − | 0.708298i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.2992i | 0.695946i | 0.937504 | + | 0.347973i | \(0.113130\pi\) | ||||
−0.937504 | + | 0.347973i | \(0.886870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.4856 | −0.593713 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 15.9785i | − | 0.574706i | −0.957825 | − | 0.287353i | \(-0.907225\pi\) | ||
0.957825 | − | 0.287353i | \(-0.0927752\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.2108i | 1.40849i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.9016 | 0.391092 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.62193 | −0.0939405 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.2258 | −0.509040 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.4917 | 0.768051 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.3026i | 0.831705i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16.4732i | − | 0.587206i | −0.955927 | − | 0.293603i | \(-0.905146\pi\) | ||
0.955927 | − | 0.293603i | \(-0.0948543\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.4154 | −0.548803 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.688371i | 0.0244756i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.2218 | + | 49.5387i | −0.682586 | + | 1.75917i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.6108i | 0.943787i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.7578 | 1.83336 | 0.916678 | − | 0.399628i | \(-0.130861\pi\) | ||||
0.916678 | + | 0.399628i | \(0.130861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 29.7890i | − | 1.05386i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 15.0714i | − | 0.532521i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.06972 | 0.249485 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.9181 | 0.631531 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.6433 | 0.656275 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.9055 | −1.71943 | −0.859713 | − | 0.510777i | \(-0.829358\pi\) | ||||
−0.859713 | + | 0.510777i | \(0.829358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.0535i | 1.19578i | 0.801578 | + | 0.597891i | \(0.203994\pi\) | ||||
−0.801578 | + | 0.597891i | \(0.796006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 0.660679i | − | 0.0231710i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.3324 | −0.817299 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.6674i | 1.10790i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.19456 | − | 2.40359i | −0.216455 | − | 0.0839881i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 22.2785i | − | 0.777524i | −0.921338 | − | 0.388762i | \(-0.872903\pi\) | ||
0.921338 | − | 0.388762i | \(-0.127097\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.20464 | −0.285996 | −0.142998 | − | 0.989723i | \(-0.545674\pi\) | ||||
−0.142998 | + | 0.989723i | \(0.545674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.05771i | − | 0.210902i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.8256i | 0.724178i | 0.932144 | + | 0.362089i | \(0.117936\pi\) | ||||
−0.932144 | + | 0.362089i | \(0.882064\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.9023 | −1.24694 | −0.623469 | − | 0.781848i | \(-0.714277\pi\) | ||||
−0.623469 | + | 0.781848i | \(0.714277\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.6801 | 0.752073 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.05222 | −0.105753 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.1328 | 1.66571 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 36.2731i | − | 1.25378i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.9442i | 1.20641i | 0.797587 | + | 0.603203i | \(0.206109\pi\) | ||||
−0.797587 | + | 0.603203i | \(0.793891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.9803 | −0.413113 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 4.32416i | − | 0.148932i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.5897 | + | 31.2943i | −0.983516 | + | 1.07656i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.8627 | −0.407126 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 55.6923i | 1.90911i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.0942i | 0.585295i | 0.956220 | + | 0.292648i | \(0.0945363\pi\) | ||||
−0.956220 | + | 0.292648i | \(0.905464\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.9835 | −0.649223 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0481 | 0.753149 | 0.376575 | − | 0.926386i | \(-0.377102\pi\) | ||||
0.376575 | + | 0.926386i | \(0.377102\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.39652 | 0.0476485 | 0.0238243 | − | 0.999716i | \(-0.492416\pi\) | ||||
0.0238243 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.892740 | 0.0304245 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 11.7720i | − | 0.400723i | −0.979722 | − | 0.200361i | \(-0.935788\pi\) | ||
0.979722 | − | 0.200361i | \(-0.0642116\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0276i | 1.22497i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.26568 | 0.280717 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 11.7487i | − | 0.398548i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.4173 | + | 12.9665i | 1.13230 | + | 0.439352i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.4773i | 0.591517i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.05871 | −0.0695970 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.9307i | 1.11199i | 0.831185 | + | 0.555996i | \(0.187663\pi\) | ||||
−0.831185 | + | 0.555996i | \(0.812337\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.0496i | 1.18219i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.4056 | 1.29392 | 0.646959 | − | 0.762525i | \(-0.276040\pi\) | ||||
0.646959 | + | 0.762525i | \(0.276040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.8657 | −1.20698 | −0.603489 | − | 0.797372i | \(-0.706223\pi\) | ||||
−0.603489 | + | 0.797372i | \(0.706223\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 52.7515 | 1.77322 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.4089 | 1.12176 | 0.560880 | − | 0.827897i | \(-0.310463\pi\) | ||||
0.560880 | + | 0.827897i | \(0.310463\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 11.4996i | − | 0.385683i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0752765i | 0.00252186i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.8340 | 1.03182 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.1482i | 1.00774i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.71005 | + | 19.8705i | −0.257431 | + | 0.663456i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 28.7254i | − | 0.958047i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.1572 | 0.771477 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 10.7824i | − | 0.358816i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 58.1357i | − | 1.93250i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.3125 | 1.23894 | 0.619471 | − | 0.785020i | \(-0.287347\pi\) | ||||
0.619471 | + | 0.785020i | \(0.287347\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.79461 | 0.291699 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3137 | 0.341708 | 0.170854 | − | 0.985296i | \(-0.445347\pi\) | ||||
0.170854 | + | 0.985296i | \(0.445347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.295776 | −0.00978874 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 51.6910i | − | 1.70885i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 10.4533i | − | 0.345200i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.6879 | −1.67204 | −0.836020 | − | 0.548698i | \(-0.815124\pi\) | ||||
−0.836020 | + | 0.548698i | \(0.815124\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.73375i | 0.254836i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −47.8184 | − | 18.5543i | −1.57396 | − | 0.610722i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 57.0707i | − | 1.87647i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.2030 | −0.335109 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 42.6892i | − | 1.40059i | −0.713854 | − | 0.700294i | \(-0.753052\pi\) | ||
0.713854 | − | 0.700294i | \(-0.246948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.15929i | − | 0.103542i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.1437 | −0.626736 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.95200 | −0.325465 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0612 | 1.14540 | 0.572700 | − | 0.819765i | \(-0.305896\pi\) | ||||
0.572700 | + | 0.819765i | \(0.305896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.7415 | 0.676874 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 24.5597i | − | 0.800622i | −0.916379 | − | 0.400311i | \(-0.868902\pi\) | ||
0.916379 | − | 0.400311i | \(-0.131098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.56068i | 0.148516i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.9859 | 0.552553 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 4.78250i | − | 0.155410i | −0.996976 | − | 0.0777052i | \(-0.975241\pi\) | ||
0.996976 | − | 0.0777052i | \(-0.0247593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.7640 | + | 9.22082i | 0.771413 | + | 0.299320i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2.99193i | − | 0.0970199i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.08287 | −0.0674707 | −0.0337354 | − | 0.999431i | \(-0.510740\pi\) | ||||
−0.0337354 | + | 0.999431i | \(0.510740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 9.36266i | − | 0.302969i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.43781i | 0.143454i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.34884 | −0.0758481 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.4820 | −0.563936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.9650 | 0.643362 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 46.9528 | 1.51146 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 43.2917i | − | 1.39217i | −0.717960 | − | 0.696084i | \(-0.754924\pi\) | ||
0.717960 | − | 0.696084i | \(-0.245076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 10.3728i | − | 0.333223i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.9334 | −0.511329 | −0.255664 | − | 0.966766i | \(-0.582294\pi\) | ||||
−0.255664 | + | 0.966766i | \(0.582294\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.95608i | 0.0627089i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.90088 | − | 20.3623i | 0.253031 | − | 0.652115i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.6064i | 1.26712i | 0.773693 | + | 0.633561i | \(0.218407\pi\) | ||||
−0.773693 | + | 0.633561i | \(0.781593\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.17825 | 0.261378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 0.968095i | − | 0.0309089i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.16239i | − | 0.0370746i | −0.999828 | − | 0.0185373i | \(-0.994099\pi\) | ||
0.999828 | − | 0.0185373i | \(-0.00590095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.0898 | −0.799428 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.4986 | −0.334175 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.0834 | 1.75155 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.551130 | 0.0175072 | 0.00875362 | − | 0.999962i | \(-0.497214\pi\) | ||||
0.00875362 | + | 0.999962i | \(0.497214\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1.80337i | − | 0.0572281i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.9305i | 0.631840i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.9259 | 1.64451 | 0.822255 | − | 0.569120i | \(-0.192716\pi\) | ||||
0.822255 | + | 0.569120i | \(0.192716\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 52.7949i | 1.67036i |
(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 | 4004.2.m.c.2157.13 | ✓ | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.14 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.13 | ✓ | 36 | 1.1 | even | 1 | trivial | |
4004.2.m.c.2157.14 | yes | 36 | 13.12 | even | 2 | inner |