Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
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.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 3781.1 | ||
Character | \(\chi\) | \(=\) | 4020.3781 |
Dual form | 4020.2.q.m.841.1 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.18663 | − | 3.78736i | −0.826470 | − | 1.43149i | −0.900791 | − | 0.434254i | \(-0.857012\pi\) |
0.0743207 | − | 0.997234i | \(-0.476321\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.49547 | + | 2.59023i | 0.450900 | + | 0.780982i | 0.998442 | − | 0.0557959i | \(-0.0177696\pi\) |
−0.547542 | + | 0.836778i | \(0.684436\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.04087 | + | 1.80283i | −0.288684 | + | 0.500016i | −0.973496 | − | 0.228704i | \(-0.926551\pi\) |
0.684812 | + | 0.728720i | \(0.259884\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.454199 | + | 0.786696i | −0.110159 | + | 0.190802i | −0.915834 | − | 0.401556i | \(-0.868469\pi\) |
0.805675 | + | 0.592358i | \(0.201803\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.53072 | − | 6.11538i | 0.810002 | − | 1.40297i | −0.102859 | − | 0.994696i | \(-0.532799\pi\) |
0.912862 | − | 0.408269i | \(-0.133868\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.18663 | − | 3.78736i | −0.477163 | − | 0.826470i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.49083 | − | 6.04630i | 0.727889 | − | 1.26074i | −0.229884 | − | 0.973218i | \(-0.573835\pi\) |
0.957774 | − | 0.287523i | \(-0.0928319\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.93896 | + | 6.82248i | 0.731447 | + | 1.26690i | 0.956265 | + | 0.292502i | \(0.0944879\pi\) |
−0.224818 | + | 0.974401i | \(0.572179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.83972 | − | 6.65058i | −0.689633 | − | 1.19448i | −0.971957 | − | 0.235161i | \(-0.924438\pi\) |
0.282323 | − | 0.959319i | \(-0.408895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.49547 | + | 2.59023i | 0.260327 | + | 0.450900i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.18663 | − | 3.78736i | −0.369609 | − | 0.640181i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.417228 | + | 0.722660i | −0.0685919 | + | 0.118805i | −0.898282 | − | 0.439420i | \(-0.855184\pi\) |
0.829690 | + | 0.558225i | \(0.188517\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.04087 | + | 1.80283i | −0.166672 | + | 0.288684i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.33572 | − | 2.31353i | −0.208604 | − | 0.361313i | 0.742671 | − | 0.669657i | \(-0.233559\pi\) |
−0.951275 | + | 0.308343i | \(0.900225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.0882 | −1.84343 | −0.921713 | − | 0.387872i | \(-0.873210\pi\) | ||||
−0.921713 | + | 0.387872i | \(0.873210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.436600 | + | 0.756213i | 0.0636846 | + | 0.110305i | 0.896110 | − | 0.443833i | \(-0.146382\pi\) |
−0.832425 | + | 0.554138i | \(0.813048\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.06274 | + | 10.5010i | −0.866105 | + | 1.50014i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.454199 | + | 0.786696i | −0.0636006 | + | 0.110159i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.39196 | 1.01536 | 0.507682 | − | 0.861545i | \(-0.330502\pi\) | ||||
0.507682 | + | 0.861545i | \(0.330502\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.49547 | + | 2.59023i | 0.201649 | + | 0.349266i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.53072 | − | 6.11538i | 0.467655 | − | 0.810002i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.81848 | −0.236746 | −0.118373 | − | 0.992969i | \(-0.537768\pi\) | ||||
−0.118373 | + | 0.992969i | \(0.537768\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.99000 | − | 3.44678i | 0.254793 | − | 0.441315i | −0.710046 | − | 0.704155i | \(-0.751326\pi\) |
0.964839 | + | 0.262840i | \(0.0846592\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.18663 | − | 3.78736i | −0.275490 | − | 0.477163i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.04087 | + | 1.80283i | −0.129104 | + | 0.223614i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.50950 | − | 7.79118i | 0.306584 | − | 0.951844i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.49083 | − | 6.04630i | 0.420247 | − | 0.727889i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0217755 | + | 0.0377163i | 0.00258428 | + | 0.00447610i | 0.867315 | − | 0.497760i | \(-0.165844\pi\) |
−0.864730 | + | 0.502236i | \(0.832511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.49932 | − | 7.79305i | 0.526606 | − | 0.912108i | −0.472914 | − | 0.881109i | \(-0.656798\pi\) |
0.999519 | − | 0.0309989i | \(-0.00986884\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.54008 | − | 11.3278i | 0.745311 | − | 1.29092i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.453494 | − | 0.785474i | −0.0510221 | − | 0.0883728i | 0.839386 | − | 0.543535i | \(-0.182915\pi\) |
−0.890408 | + | 0.455162i | \(0.849581\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.41204 | − | 2.44573i | 0.154992 | − | 0.268454i | −0.778064 | − | 0.628185i | \(-0.783798\pi\) |
0.933056 | + | 0.359731i | \(0.117132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.454199 | + | 0.786696i | −0.0492648 | + | 0.0853291i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.93896 | + | 6.82248i | 0.422301 | + | 0.731447i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.76333 | 0.292912 | 0.146456 | − | 0.989217i | \(-0.453213\pi\) | ||||
0.146456 | + | 0.989217i | \(0.453213\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.10397 | 0.954356 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.83972 | − | 6.65058i | −0.398160 | − | 0.689633i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.53072 | − | 6.11538i | 0.362244 | − | 0.627425i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.274039 | − | 0.474649i | 0.0278244 | − | 0.0481933i | −0.851778 | − | 0.523903i | \(-0.824475\pi\) |
0.879602 | + | 0.475710i | \(0.157809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.49547 | + | 2.59023i | 0.150300 | + | 0.260327i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.346371 | + | 0.599931i | 0.0344652 | + | 0.0596954i | 0.882743 | − | 0.469855i | \(-0.155694\pi\) |
−0.848278 | + | 0.529551i | \(0.822361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.65401 | − | 13.2571i | −0.754172 | − | 1.30626i | −0.945785 | − | 0.324794i | \(-0.894705\pi\) |
0.191613 | − | 0.981471i | \(-0.438628\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.18663 | − | 3.78736i | −0.213394 | − | 0.369609i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.42328 | 0.620962 | 0.310481 | − | 0.950580i | \(-0.399510\pi\) | ||||
0.310481 | + | 0.950580i | \(0.399510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.66310 | 0.159296 | 0.0796481 | − | 0.996823i | \(-0.474620\pi\) | ||||
0.0796481 | + | 0.996823i | \(0.474620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.417228 | + | 0.722660i | −0.0396015 | + | 0.0685919i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.20189 | − | 12.4740i | −0.677496 | − | 1.17346i | −0.975732 | − | 0.218966i | \(-0.929732\pi\) |
0.298236 | − | 0.954492i | \(-0.403602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.49083 | − | 6.04630i | 0.325522 | − | 0.563821i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.04087 | + | 1.80283i | −0.0962281 | + | 0.166672i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.97267 | 0.364174 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.02715 | − | 1.77908i | 0.0933776 | − | 0.161735i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.33572 | − | 2.31353i | −0.120438 | − | 0.208604i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.44194 | + | 7.69366i | 0.394158 | + | 0.682702i | 0.992993 | − | 0.118171i | \(-0.0377029\pi\) |
−0.598835 | + | 0.800872i | \(0.704370\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0882 | −1.06430 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.70567 | −0.323766 | −0.161883 | − | 0.986810i | \(-0.551757\pi\) | ||||
−0.161883 | + | 0.986810i | \(0.551757\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −30.8816 | −2.67777 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.0338 | −1.45530 | −0.727648 | − | 0.685951i | \(-0.759386\pi\) | ||||
−0.727648 | + | 0.685951i | \(0.759386\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.20074 | 0.356302 | 0.178151 | − | 0.984003i | \(-0.442988\pi\) | ||||
0.178151 | + | 0.984003i | \(0.442988\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.436600 | + | 0.756213i | 0.0367683 | + | 0.0636846i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.22633 | −0.520671 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93896 | + | 6.82248i | 0.327113 | + | 0.566576i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.06274 | + | 10.5010i | −0.500046 | + | 0.866105i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5719 | 0.866084 | 0.433042 | − | 0.901374i | \(-0.357440\pi\) | ||||
0.433042 | + | 0.901374i | \(0.357440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.55070 | − | 13.0782i | 0.614468 | − | 1.06429i | −0.376010 | − | 0.926616i | \(-0.622704\pi\) |
0.990478 | − | 0.137673i | \(-0.0439625\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.454199 | + | 0.786696i | −0.0367198 | + | 0.0636006i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.83972 | − | 6.65058i | −0.308413 | − | 0.534188i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.40208 | − | 9.35667i | 0.431133 | − | 0.746744i | −0.565838 | − | 0.824516i | \(-0.691447\pi\) |
0.996971 | + | 0.0777723i | \(0.0247807\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.39196 | 0.586221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.5327 | −2.40631 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.42050 | − | 11.1206i | −0.502893 | − | 0.871036i | −0.999994 | − | 0.00334341i | \(-0.998936\pi\) |
0.497102 | − | 0.867692i | \(-0.334398\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.49547 | + | 2.59023i | 0.116422 | + | 0.201649i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.1268 | + | 17.5401i | 0.783635 | + | 1.35730i | 0.929811 | + | 0.368037i | \(0.119970\pi\) |
−0.146176 | + | 0.989259i | \(0.546697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.33320 | + | 7.50532i | 0.333323 | + | 0.577332i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.53072 | − | 6.11538i | 0.270001 | − | 0.467655i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.68539 | − | 2.91918i | 0.128138 | − | 0.221941i | −0.794817 | − | 0.606849i | \(-0.792433\pi\) |
0.922955 | + | 0.384908i | \(0.125767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.18663 | − | 3.78736i | −0.165294 | − | 0.286298i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.81848 | −0.136685 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.54970 | −0.639035 | −0.319517 | − | 0.947580i | \(-0.603521\pi\) | ||||
−0.319517 | + | 0.947580i | \(0.603521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.30488 | + | 3.99218i | 0.171321 | + | 0.296736i | 0.938882 | − | 0.344240i | \(-0.111863\pi\) |
−0.767561 | + | 0.640976i | \(0.778530\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.99000 | − | 3.44678i | 0.147105 | − | 0.254793i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.417228 | + | 0.722660i | −0.0306752 | + | 0.0531310i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.71696 | −0.198684 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.18663 | − | 3.78736i | −0.159054 | − | 0.275490i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.49218 | + | 11.2448i | −0.469758 | + | 0.813645i | −0.999402 | − | 0.0345753i | \(-0.988992\pi\) |
0.529644 | + | 0.848220i | \(0.322325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.1932 | −0.733722 | −0.366861 | − | 0.930276i | \(-0.619568\pi\) | ||||
−0.366861 | + | 0.930276i | \(0.619568\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.04087 | + | 1.80283i | −0.0745380 | + | 0.129104i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.06345 | − | 15.6984i | −0.645744 | − | 1.11846i | −0.984129 | − | 0.177454i | \(-0.943214\pi\) |
0.338385 | − | 0.941008i | \(-0.390119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.84561 | − | 17.0531i | 0.697937 | − | 1.20886i | −0.271244 | − | 0.962511i | \(-0.587435\pi\) |
0.969181 | − | 0.246351i | \(-0.0792317\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.50950 | − | 7.79118i | 0.177006 | − | 0.549547i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.2261 | − | 29.8365i | 1.20904 | − | 2.09411i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.33572 | − | 2.31353i | −0.0932907 | − | 0.161584i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.49083 | − | 6.04630i | 0.242630 | − | 0.420247i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.1203 | 1.46092 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5249 | + | 18.2296i | −0.724563 | + | 1.25498i | 0.234590 | + | 0.972094i | \(0.424625\pi\) |
−0.959153 | + | 0.282886i | \(0.908708\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0217755 | + | 0.0377163i | 0.00149203 | + | 0.00258428i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0882 | −0.824405 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.7921 | + | 29.0848i | −1.13992 | + | 1.97440i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.49932 | − | 7.79305i | 0.304036 | − | 0.526606i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.945520 | − | 1.63769i | −0.0636026 | − | 0.110163i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4616 | −0.834488 | −0.417244 | − | 0.908794i | \(-0.637004\pi\) | ||||
−0.417244 | + | 0.908794i | \(0.637004\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.36483 | − | 9.29216i | −0.356076 | − | 0.616742i | 0.631225 | − | 0.775600i | \(-0.282552\pi\) |
−0.987302 | + | 0.158857i | \(0.949219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.19516 | + | 12.4624i | −0.475469 | + | 0.823537i | −0.999605 | − | 0.0280976i | \(-0.991055\pi\) |
0.524136 | + | 0.851635i | \(0.324388\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.54008 | − | 11.3278i | 0.430306 | − | 0.745311i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.88321 | − | 3.26182i | −0.123373 | − | 0.213689i | 0.797723 | − | 0.603025i | \(-0.206038\pi\) |
−0.921096 | + | 0.389336i | \(0.872705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.436600 | + | 0.756213i | 0.0284806 | + | 0.0493299i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.453494 | − | 0.785474i | −0.0294576 | − | 0.0510221i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.447416 | + | 0.774947i | 0.0289409 | + | 0.0501272i | 0.880133 | − | 0.474727i | \(-0.157453\pi\) |
−0.851192 | + | 0.524854i | \(0.824120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3244 | −1.30921 | −0.654603 | − | 0.755972i | \(-0.727164\pi\) | ||||
−0.654603 | + | 0.755972i | \(0.727164\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.06274 | + | 10.5010i | −0.387334 | + | 0.670882i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.35001 | + | 12.7306i | 0.467670 | + | 0.810028i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.41204 | − | 2.44573i | 0.0894845 | − | 0.154992i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.24998 | − | 14.2894i | 0.520734 | − | 0.901938i | −0.478975 | − | 0.877828i | \(-0.658992\pi\) |
0.999709 | − | 0.0241096i | \(-0.00767508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.8817 | 1.31282 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.454199 | + | 0.786696i | −0.0284430 | + | 0.0492648i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.99116 | − | 17.3052i | −0.623231 | − | 1.07947i | −0.988880 | − | 0.148715i | \(-0.952486\pi\) |
0.365649 | − | 0.930753i | \(-0.380847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.64930 | 0.226757 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.93896 | + | 6.82248i | 0.243816 | + | 0.422301i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0971 | 1.36257 | 0.681284 | − | 0.732019i | \(-0.261422\pi\) | ||||
0.681284 | + | 0.732019i | \(0.261422\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.39196 | 0.454085 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.76333 | 0.169113 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.1061 | 1.16492 | 0.582459 | − | 0.812860i | \(-0.302091\pi\) | ||||
0.582459 | + | 0.812860i | \(0.302091\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1078 | 0.917736 | 0.458868 | − | 0.888504i | \(-0.348255\pi\) | ||||
0.458868 | + | 0.888504i | \(0.348255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.10397 | 0.550997 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.49547 | + | 2.59023i | 0.0901801 | + | 0.156196i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5221 | 0.812465 | 0.406233 | − | 0.913770i | \(-0.366842\pi\) | ||||
0.406233 | + | 0.913770i | \(0.366842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.83972 | − | 6.65058i | −0.229878 | − | 0.398160i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.59295 | + | 9.68728i | −0.333648 | + | 0.577895i | −0.983224 | − | 0.182402i | \(-0.941613\pi\) |
0.649577 | + | 0.760296i | \(0.274946\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.3977 | 1.86640 | 0.933201 | − | 0.359356i | \(-0.117004\pi\) | ||||
0.933201 | + | 0.359356i | \(0.117004\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.53072 | − | 6.11538i | 0.209142 | − | 0.362244i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.84146 | + | 10.1177i | −0.344810 | + | 0.597229i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.08741 | + | 14.0078i | 0.475730 | + | 0.823988i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.274039 | − | 0.474649i | 0.0160644 | − | 0.0278244i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.857561 | 0.0500992 | 0.0250496 | − | 0.999686i | \(-0.492026\pi\) | ||||
0.0250496 | + | 0.999686i | \(0.492026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.81848 | −0.105876 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.49547 | + | 2.59023i | 0.0867758 | + | 0.150300i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.26698 | + | 12.5868i | 0.420260 | + | 0.727912i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.4324 | + | 45.7822i | 1.52354 | + | 2.63884i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.346371 | + | 0.599931i | 0.0198985 | + | 0.0344652i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.99000 | − | 3.44678i | 0.113947 | − | 0.197362i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.19008 | + | 5.52538i | −0.182067 | + | 0.315350i | −0.942584 | − | 0.333968i | \(-0.891612\pi\) |
0.760517 | + | 0.649318i | \(0.224946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.65401 | − | 13.2571i | −0.435421 | − | 0.754172i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.0122 | 1.19150 | 0.595748 | − | 0.803172i | \(-0.296856\pi\) | ||||
0.595748 | + | 0.803172i | \(0.296856\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.7198 | −0.775489 | −0.387745 | − | 0.921767i | \(-0.626746\pi\) | ||||
−0.387745 | + | 0.921767i | \(0.626746\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.18663 | − | 3.78736i | −0.123203 | − | 0.213394i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.53972 | − | 7.86302i | 0.254976 | − | 0.441631i | −0.709913 | − | 0.704289i | \(-0.751266\pi\) |
0.964889 | + | 0.262658i | \(0.0845991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7812 | + | 20.4056i | −0.659619 | + | 1.14249i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.42328 | 0.358512 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.20730 | + | 5.55520i | 0.178459 | + | 0.309100i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.04087 | + | 1.80283i | −0.0577369 | + | 0.100003i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.66310 | 0.0919697 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.90937 | − | 3.30712i | 0.105267 | − | 0.182327i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.36593 | − | 7.56201i | −0.239973 | − | 0.415646i | 0.720733 | − | 0.693213i | \(-0.243805\pi\) |
−0.960706 | + | 0.277567i | \(0.910472\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.417228 | + | 0.722660i | −0.0228640 | + | 0.0396015i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.50950 | − | 7.79118i | 0.137109 | − | 0.425677i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.1782 | + | 26.2894i | −0.826807 | + | 1.43207i | 0.0737229 | + | 0.997279i | \(0.476512\pi\) |
−0.900530 | + | 0.434793i | \(0.856821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.20189 | − | 12.4740i | −0.391153 | − | 0.677496i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.4843 | − | 19.8915i | 0.621912 | − | 1.07718i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.4151 | 1.21030 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.49083 | − | 6.04630i | 0.187940 | − | 0.325522i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.79561 | − | 4.84214i | −0.150076 | − | 0.259940i | 0.781179 | − | 0.624307i | \(-0.214619\pi\) |
−0.931255 | + | 0.364367i | \(0.881285\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.7337 | 1.96631 | 0.983154 | − | 0.182781i | \(-0.0585098\pi\) | ||||
0.983154 | + | 0.182781i | \(0.0585098\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.04087 | + | 1.80283i | −0.0555573 | + | 0.0962281i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.21593 | + | 3.83811i | −0.117942 | + | 0.204282i | −0.918952 | − | 0.394369i | \(-0.870963\pi\) |
0.801010 | + | 0.598651i | \(0.204296\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0217755 | + | 0.0377163i | 0.00115572 | + | 0.00200177i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.97267 | 0.210256 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.95476 | −0.472614 | −0.236307 | − | 0.971678i | \(-0.575937\pi\) | ||||
−0.236307 | + | 0.971678i | \(0.575937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4319 | − | 26.7289i | −0.812208 | − | 1.40678i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.02715 | − | 1.77908i | 0.0539116 | − | 0.0933776i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.49932 | − | 7.79305i | 0.235505 | − | 0.407907i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.80302 | + | 15.2473i | 0.459514 | + | 0.795901i | 0.998935 | − | 0.0461347i | \(-0.0146903\pi\) |
−0.539421 | + | 0.842036i | \(0.681357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.33572 | − | 2.31353i | −0.0695348 | − | 0.120438i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.1635 | − | 27.9960i | −0.839168 | − | 1.45348i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.17950 | + | 7.23911i | 0.216406 | + | 0.374827i | 0.953707 | − | 0.300738i | \(-0.0972331\pi\) |
−0.737300 | + | 0.675565i | \(0.763900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.3997 | −0.844629 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.77956 | + | 11.7425i | −0.348243 | + | 0.603174i | −0.985937 | − | 0.167115i | \(-0.946555\pi\) |
0.637695 | + | 0.770289i | \(0.279888\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.44194 | + | 7.69366i | 0.227567 | + | 0.394158i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.07543 | + | 8.79091i | −0.259343 | + | 0.449195i | −0.966066 | − | 0.258295i | \(-0.916839\pi\) |
0.706723 | + | 0.707490i | \(0.250173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.54008 | − | 11.3278i | 0.333313 | − | 0.577316i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.0882 | −0.614476 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.92875 | + | 6.80480i | −0.199196 | + | 0.345017i | −0.948268 | − | 0.317471i | \(-0.897166\pi\) |
0.749072 | + | 0.662488i | \(0.230500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.17107 | + | 5.49245i | 0.160368 | + | 0.277765i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.70567 | −0.186926 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.453494 | − | 0.785474i | −0.0228178 | − | 0.0395215i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.6770 | 0.535861 | 0.267931 | − | 0.963438i | \(-0.413660\pi\) | ||||
0.267931 | + | 0.963438i | \(0.413660\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.8816 | −1.54601 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0544 | −1.15128 | −0.575641 | − | 0.817703i | \(-0.695247\pi\) | ||||
−0.575641 | + | 0.817703i | \(0.695247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.9865 | 0.796345 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.49580 | −0.123712 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.74620 | − | 16.8809i | −0.481918 | − | 0.834707i | 0.517866 | − | 0.855462i | \(-0.326726\pi\) |
−0.999785 | + | 0.0207545i | \(0.993393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0338 | −0.840215 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.97635 | + | 6.88724i | 0.195663 | + | 0.338899i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.41204 | − | 2.44573i | 0.0693144 | − | 0.120056i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.20074 | 0.205711 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4661 | + | 23.3240i | −0.657863 | + | 1.13945i | 0.323304 | + | 0.946295i | \(0.395206\pi\) |
−0.981168 | + | 0.193158i | \(0.938127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5808 | + | 20.0585i | −0.564411 | + | 0.977589i | 0.432693 | + | 0.901541i | \(0.357563\pi\) |
−0.997104 | + | 0.0760477i | \(0.975770\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.436600 | + | 0.756213i | 0.0212282 | + | 0.0367683i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.454199 | + | 0.786696i | −0.0220319 | + | 0.0381603i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.4056 | −0.842316 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.22633 | −0.300610 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.01576 | − | 8.68755i | −0.241601 | − | 0.418465i | 0.719570 | − | 0.694420i | \(-0.244339\pi\) |
−0.961170 | + | 0.275956i | \(0.911006\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.20238 | + | 10.7428i | 0.298067 | + | 0.516267i | 0.975694 | − | 0.219139i | \(-0.0703247\pi\) |
−0.677627 | + | 0.735406i | \(0.736991\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.93896 | + | 6.82248i | 0.188859 | + | 0.327113i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.6503 | − | 42.6956i | −1.17918 | − | 2.04241i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.61849 | + | 7.99945i | −0.220428 | + | 0.381793i | −0.954938 | − | 0.296805i | \(-0.904079\pi\) |
0.734510 | + | 0.678598i | \(0.237412\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.06274 | + | 10.5010i | −0.288702 | + | 0.500046i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.837559 | − | 1.45070i | −0.0397937 | − | 0.0689246i | 0.845443 | − | 0.534066i | \(-0.179337\pi\) |
−0.885236 | + | 0.465142i | \(0.846003\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.76333 | 0.130994 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5719 | 0.500034 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4119 | − | 18.0339i | −0.491366 | − | 0.851071i | 0.508584 | − | 0.861012i | \(-0.330169\pi\) |
−0.999951 | + | 0.00994101i | \(0.996836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.99505 | − | 6.91963i | 0.188120 | − | 0.325833i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.55070 | − | 13.0782i | 0.354763 | − | 0.614468i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.10397 | 0.426801 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9737 | + | 31.1314i | 0.840774 | + | 1.45626i | 0.889241 | + | 0.457439i | \(0.151233\pi\) |
−0.0484666 | + | 0.998825i | \(0.515433\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.454199 | + | 0.786696i | −0.0212002 | + | 0.0367198i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.9362 | 0.835370 | 0.417685 | − | 0.908592i | \(-0.362842\pi\) | ||||
0.417685 | + | 0.908592i | \(0.362842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.88693 | − | 3.26826i | 0.0876932 | − | 0.151889i | −0.818842 | − | 0.574018i | \(-0.805384\pi\) |
0.906536 | + | 0.422129i | \(0.138717\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.83972 | − | 6.65058i | −0.178063 | − | 0.308413i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.6753 | + | 25.4183i | −0.679091 | + | 1.17622i | 0.296165 | + | 0.955137i | \(0.404292\pi\) |
−0.975255 | + | 0.221082i | \(0.929041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.9954 | + | 7.53207i | −1.61594 | + | 0.347799i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.40208 | − | 9.35667i | 0.248915 | − | 0.431133i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.0774 | − | 31.3111i | −0.831202 | − | 1.43968i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.53072 | − | 6.11538i | 0.162000 | − | 0.280593i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.39196 | 0.338455 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.28475 | + | 12.6176i | −0.332849 | + | 0.576511i | −0.983069 | − | 0.183234i | \(-0.941343\pi\) |
0.650220 | + | 0.759746i | \(0.274677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.868557 | − | 1.50439i | −0.0396028 | − | 0.0685941i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.5327 | −1.38929 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.274039 | − | 0.474649i | 0.0124435 | − | 0.0215527i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.94405 | + | 5.09925i | −0.133408 | + | 0.231069i | −0.924988 | − | 0.379996i | \(-0.875925\pi\) |
0.791580 | + | 0.611065i | \(0.209259\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.42050 | − | 11.1206i | −0.290345 | − | 0.502893i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8188 | 0.894410 | 0.447205 | − | 0.894431i | \(-0.352419\pi\) | ||||
0.447205 | + | 0.894431i | \(0.352419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.15629 | −0.322303 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.49547 | + | 2.59023i | 0.0672163 | + | 0.116422i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0952302 | − | 0.164944i | 0.00427166 | − | 0.00739873i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.09991 | − | 8.83331i | 0.228304 | − | 0.395433i | −0.729002 | − | 0.684512i | \(-0.760015\pi\) |
0.957305 | + | 0.289078i | \(0.0933488\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1268 | + | 17.5401i | 0.452432 | + | 0.783635i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.2004 | − | 19.3996i | −0.499401 | − | 0.864987i | 0.500599 | − | 0.865679i | \(-0.333113\pi\) |
−1.00000 | 0.000691938i | \(0.999780\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.346371 | + | 0.599931i | 0.0154133 | + | 0.0266966i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.33320 | + | 7.50532i | 0.192444 | + | 0.333323i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.4309 | 1.17153 | 0.585765 | − | 0.810481i | \(-0.300794\pi\) | ||||
0.585765 | + | 0.810481i | \(0.300794\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.3535 | −1.74089 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.53072 | − | 6.11538i | 0.155885 | − | 0.270001i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.65401 | − | 13.2571i | −0.337276 | − | 0.584179i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.30584 | + | 2.26178i | −0.0574308 | + | 0.0994731i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.68539 | − | 2.91918i | 0.0739803 | − | 0.128138i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.0477 | 0.878304 | 0.439152 | − | 0.898413i | \(-0.355279\pi\) | ||||
0.439152 | + | 0.898413i | \(0.355279\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.3772 | + | 17.9739i | −0.453764 | + | 0.785943i | −0.998616 | − | 0.0525894i | \(-0.983253\pi\) |
0.544852 | + | 0.838532i | \(0.316586\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.18663 | − | 3.78736i | −0.0954325 | − | 0.165294i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.97598 | 0.303878 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.8719 | − | 22.2947i | −0.559646 | − | 0.969335i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.81848 | −0.0789153 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.56122 | 0.240883 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.42328 | 0.277702 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.54970 | −0.368947 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.2665 | −1.56211 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.500503 | 0.0215183 | 0.0107592 | − | 0.999942i | \(-0.496575\pi\) | ||||
0.0107592 | + | 0.999942i | \(0.496575\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.30488 | + | 3.99218i | 0.0989120 | + | 0.171321i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.66310 | 0.0712395 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.1918 | + | 29.7771i | 0.735070 | + | 1.27318i | 0.954693 | + | 0.297594i | \(0.0961842\pi\) |
−0.219622 | + | 0.975585i | \(0.570483\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.99000 | − | 3.44678i | 0.0849311 | − | 0.147105i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 55.6295 | 2.36989 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.98325 | + | 3.43509i | −0.0843364 | + | 0.146075i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.417228 | + | 0.722660i | −0.0177103 | + | 0.0306752i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.7577 | − | 20.3650i | −0.498192 | − | 0.862894i | 0.501806 | − | 0.864980i | \(-0.332669\pi\) |
−0.999998 | + | 0.00208665i | \(0.999336\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5822 | − | 21.7929i | 0.532168 | − | 0.921743i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.71696 | −0.114710 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.3432 | 1.82670 | 0.913350 | − | 0.407176i | \(-0.133487\pi\) | ||||
0.913350 | + | 0.407176i | \(0.133487\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.20189 | − | 12.4740i | −0.302986 | − | 0.524786i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.18663 | − | 3.78736i | −0.0918300 | − | 0.159054i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.3419 | + | 23.1088i | 0.559320 | + | 0.968770i | 0.997553 | + | 0.0699088i | \(0.0222708\pi\) |
−0.438234 | + | 0.898861i | \(0.644396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.527129 | − | 0.913015i | −0.0220597 | − | 0.0382085i | 0.854785 | − | 0.518983i | \(-0.173689\pi\) |
−0.876844 | + | 0.480774i | \(0.840356\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.49218 | + | 11.2448i | −0.271215 | + | 0.469758i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.49083 | − | 6.04630i | 0.145578 | − | 0.252148i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.28518 | + | 16.0824i | 0.386547 | + | 0.669519i | 0.991983 | − | 0.126375i | \(-0.0403343\pi\) |
−0.605435 | + | 0.795894i | \(0.707001\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.1932 | −0.423615 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.3505 | −0.512384 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.0544 | + | 19.1469i | 0.457828 | + | 0.792982i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.04087 | + | 1.80283i | −0.0430345 | + | 0.0745380i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.8014 | + | 18.7086i | −0.445821 | + | 0.772185i | −0.998109 | − | 0.0614687i | \(-0.980422\pi\) |
0.552288 | + | 0.833653i | \(0.313755\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −54.2278 | −2.23442 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.06345 | − | 15.6984i | −0.372821 | − | 0.645744i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.1278 | − | 41.7906i | 0.990811 | − | 1.71614i | 0.378275 | − | 0.925693i | \(-0.376517\pi\) |
0.612537 | − | 0.790442i | \(-0.290149\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.97267 | 0.162863 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.84561 | − | 17.0531i | 0.402954 | − | 0.697937i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0066 | − | 22.5281i | −0.531436 | − | 0.920474i | −0.999327 | − | 0.0366878i | \(-0.988319\pi\) |
0.467891 | − | 0.883786i | \(-0.345014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.4264 | + | 18.0590i | −0.425302 | + | 0.736644i | −0.996449 | − | 0.0842039i | \(-0.973165\pi\) |
0.571147 | + | 0.820848i | \(0.306499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.50950 | − | 7.79118i | 0.102195 | − | 0.317281i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.02715 | − | 1.77908i | 0.0417597 | − | 0.0723300i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.02951 | − | 5.24727i | −0.122964 | − | 0.212980i | 0.797971 | − | 0.602696i | \(-0.205907\pi\) |
−0.920935 | + | 0.389715i | \(0.872573\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.2261 | − | 29.8365i | 0.698038 | − | 1.20904i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.81777 | −0.0735390 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.3261 | − | 23.0815i | 0.538236 | − | 0.932251i | −0.460764 | − | 0.887523i | \(-0.652424\pi\) |
0.998999 | − | 0.0447284i | \(-0.0142423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.33572 | − | 2.31353i | −0.0538614 | − | 0.0932907i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.4714 | −0.944924 | −0.472462 | − | 0.881351i | \(-0.656635\pi\) | ||||
−0.472462 | + | 0.881351i | \(0.656635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.97219 | + | 6.88003i | −0.159656 | + | 0.276532i | −0.934745 | − | 0.355321i | \(-0.884372\pi\) |
0.775089 | + | 0.631852i | \(0.217705\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.49083 | − | 6.04630i | 0.140082 | − | 0.242630i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.04239 | − | 10.4657i | −0.242083 | − | 0.419300i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.1203 | 0.843463 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.379009 | − | 0.656463i | −0.0151121 | − | 0.0261749i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0072 | + | 36.3856i | −0.836285 | + | 1.44849i | 0.0566945 | + | 0.998392i | \(0.481944\pi\) |
−0.892980 | + | 0.450097i | \(0.851389\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.5249 | + | 18.2296i | −0.418327 | + | 0.724563i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.44194 | + | 7.69366i | 0.176273 | + | 0.305313i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.6210 | − | 21.8602i | −0.500062 | − | 0.866133i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.0217755 | + | 0.0377163i | 0.000861426 | + | 0.00149203i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.1762 | + | 34.9462i | 0.796912 | + | 1.38029i | 0.921618 | + | 0.388098i | \(0.126868\pi\) |
−0.124707 | + | 0.992194i | \(0.539799\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.4834 | 0.452862 | 0.226431 | − | 0.974027i | \(-0.427294\pi\) | ||||
0.226431 | + | 0.974027i | \(0.427294\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.0882 | −0.475971 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.0745 | + | 29.5740i | −0.671270 | + | 1.16267i | 0.306275 | + | 0.951943i | \(0.400917\pi\) |
−0.977544 | + | 0.210730i | \(0.932416\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.71948 | − | 4.71027i | −0.106749 | − | 0.184894i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.7921 | + | 29.0848i | −0.658135 | + | 1.13992i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.30873 | + | 12.6591i | −0.286013 | + | 0.495388i | −0.972854 | − | 0.231419i | \(-0.925663\pi\) |
0.686842 | + | 0.726807i | \(0.258997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.70567 | −0.144793 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.49932 | − | 7.79305i | 0.175535 | − | 0.304036i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.49306 | + | 16.4425i | 0.369797 | + | 0.640507i | 0.989534 | − | 0.144303i | \(-0.0460939\pi\) |
−0.619736 | + | 0.784810i | \(0.712761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.42342 | −0.327633 | −0.163817 | − | 0.986491i | \(-0.552381\pi\) | ||||
−0.163817 | + | 0.986491i | \(0.552381\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.945520 | − | 1.63769i | −0.0367210 | − | 0.0636026i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30.8816 | −1.19754 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.0011 | 2.12965 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.4616 | −0.481792 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9039 | 0.459546 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6687 | 0.873814 | 0.436907 | − | 0.899507i | \(-0.356074\pi\) | ||||
0.436907 | + | 0.899507i | \(0.356074\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.3304 | + | 31.7491i | 0.704493 | + | 1.22022i | 0.966874 | + | 0.255253i | \(0.0821589\pi\) |
−0.262381 | + | 0.964964i | \(0.584508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.39689 | −0.0919842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.36483 | − | 9.29216i | −0.205581 | − | 0.356076i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.2991 | − | 28.2309i | 0.623668 | − | 1.08023i | −0.365128 | − | 0.930957i | \(-0.618975\pi\) |
0.988797 | − | 0.149268i | \(-0.0476918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.0338 | −0.650828 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.19516 | + | 12.4624i | −0.274512 | + | 0.475469i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.69404 | + | 13.3265i | −0.293120 | + | 0.507698i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.9651 | + | 24.1882i | 0.531257 | + | 0.920164i | 0.999335 | + | 0.0364767i | \(0.0116135\pi\) |
−0.468077 | + | 0.883687i | \(0.655053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.54008 | − | 11.3278i | 0.248437 | − | 0.430306i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.20074 | 0.159343 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.42673 | 0.0919189 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.88321 | − | 3.26182i | −0.0712297 | − | 0.123373i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.4378 | + | 31.9352i | 0.696386 | + | 1.20618i | 0.969711 | + | 0.244254i | \(0.0785431\pi\) |
−0.273325 | + | 0.961922i | \(0.588124\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.94623 | + | 5.10302i | 0.111119 | + | 0.192464i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.436600 | + | 0.756213i | 0.0164433 | + | 0.0284806i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.51477 | − | 2.62366i | 0.0569688 | − | 0.0986729i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.62600 | + | 14.9407i | −0.323956 | + | 0.561109i | −0.981301 | − | 0.192482i | \(-0.938346\pi\) |
0.657344 | + | 0.753590i | \(0.271680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.453494 | − | 0.785474i | −0.0170074 | − | 0.0294576i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −53.6152 | −2.00791 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.22633 | −0.232851 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.447416 | + | 0.774947i | 0.0167091 | + | 0.0289409i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.7156 | + | 28.9523i | −0.623387 | + | 1.07974i | 0.365464 | + | 0.930825i | \(0.380910\pi\) |
−0.988850 | + | 0.148912i | \(0.952423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.4730 | + | 57.9770i | −1.24660 | + | 2.15918i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.3244 | −0.755871 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.93896 | + | 6.82248i | 0.146289 | + | 0.253381i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.3419 | − | 40.4294i | 0.865703 | − | 1.49944i | −0.000643607 | − | 1.00000i | \(-0.500205\pi\) |
0.866347 | − | 0.499443i | \(-0.166462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.49043 | − | 9.50970i | 0.203071 | − | 0.351729i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.73972 | − | 13.4056i | −0.285873 | − | 0.495147i | 0.686947 | − | 0.726707i | \(-0.258950\pi\) |
−0.972821 | + | 0.231560i | \(0.925617\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.06274 | + | 10.5010i | −0.223627 | + | 0.387334i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.9338 | − | 5.15128i | 0.881612 | − | 0.189750i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0656 | − | 29.5585i | 0.627769 | − | 1.08733i | −0.360230 | − | 0.932864i | \(-0.617302\pi\) |
0.987998 | − | 0.154464i | \(-0.0493649\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.35001 | + | 12.7306i | 0.270009 | + | 0.467670i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.3705 | − | 30.0866i | 0.637262 | − | 1.10377i | −0.348769 | − | 0.937209i | \(-0.613400\pi\) |
0.986031 | − | 0.166561i | \(-0.0532664\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5719 | 0.387325 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.41204 | − | 2.44573i | 0.0516639 | − | 0.0894845i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.0454 | − | 24.3273i | −0.513206 | − | 0.888899i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.8526 | 1.38126 | 0.690630 | − | 0.723208i | \(-0.257333\pi\) | ||||
0.690630 | + | 0.723208i | \(0.257333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.24998 | − | 14.2894i | 0.300646 | − | 0.520734i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.55070 | − | 13.0782i | 0.274798 | − | 0.475965i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.01713 | + | 5.22582i | 0.109659 | + | 0.189936i | 0.915632 | − | 0.402017i | \(-0.131691\pi\) |
−0.805973 | + | 0.591952i | \(0.798357\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.8817 | 0.757958 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2286 | −0.624535 | −0.312267 | − | 0.949994i | \(-0.601088\pi\) | ||||
−0.312267 | + | 0.949994i | \(0.601088\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.63660 | − | 6.29877i | −0.131654 | − | 0.228031i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.454199 | + | 0.786696i | −0.0164216 | + | 0.0284430i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.89279 | − | 3.27841i | 0.0683448 | − | 0.118377i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.61143 | + | 9.71929i | 0.202353 | + | 0.350486i | 0.949286 | − | 0.314413i | \(-0.101808\pi\) |
−0.746933 | + | 0.664900i | \(0.768474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.99116 | − | 17.3052i | −0.359823 | − | 0.623231i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.31801 | + | 9.21106i | 0.191275 | + | 0.331299i | 0.945673 | − | 0.325119i | \(-0.105404\pi\) |
−0.754398 | + | 0.656418i | \(0.772071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.83972 | − | 6.65058i | −0.137927 | − | 0.238896i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.64930 | 0.130918 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.8642 | −0.675880 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0651292 | + | 0.112807i | −0.00233050 | + | 0.00403655i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.93896 | + | 6.82248i | 0.140767 | + | 0.243816i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.40208 | − | 9.35667i | 0.192808 | − | 0.333954i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.04693 | − | 3.54538i | 0.0729650 | − | 0.126379i | −0.827235 | − | 0.561857i | \(-0.810087\pi\) |
0.900200 | + | 0.435478i | \(0.143421\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.0971 | 0.786679 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.4958 | + | 54.5523i | −1.11986 | + | 1.93966i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.14265 | + | 7.17528i | 0.147110 | + | 0.254801i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.39196 | 0.262166 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.3322 | + | 40.4126i | 0.826470 | + | 1.43149i | 0.900790 | + | 0.434254i | \(0.142988\pi\) |
−0.0743202 | + | 0.997234i | \(0.523679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.793212 | −0.0280618 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.76333 | 0.0976374 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.9143 | 0.949787 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.5327 | −1.07614 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.1061 | 0.672565 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.5590 | −0.828291 | −0.414145 | − | 0.910211i | \(-0.635919\pi\) | ||||
−0.414145 | + | 0.910211i | \(0.635919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.3750 | − | 19.7020i | −0.399429 | − | 0.691831i | 0.594227 | − | 0.804297i | \(-0.297458\pi\) |
−0.993655 | + | 0.112467i | \(0.964125\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.1078 | 0.529855 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.42050 | − | 11.1206i | −0.224900 | − | 0.389539i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.6799 | + | 73.9237i | −1.49318 | + | 2.58626i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.10397 | 0.318119 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.73838 | + | 11.6712i | −0.235171 | + | 0.407328i | −0.959322 | − | 0.282313i | \(-0.908898\pi\) |
0.724151 | + | 0.689641i | \(0.242232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.88421 | + | 8.45970i | −0.170253 | + | 0.294886i | −0.938508 | − | 0.345257i | \(-0.887792\pi\) |
0.768255 | + | 0.640143i | \(0.221125\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.49547 | + | 2.59023i | 0.0520655 | + | 0.0901801i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.467810 | + | 0.810270i | −0.0162673 | + | 0.0281759i | −0.874044 | − | 0.485846i | \(-0.838512\pi\) |
0.857777 | + | 0.514022i | \(0.171845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.4682 | −1.02347 | −0.511736 | − | 0.859143i | \(-0.670997\pi\) | ||||
−0.511736 | + | 0.859143i | \(0.670997\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.5221 | 0.469077 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.50738 | − | 9.53906i | −0.190819 | − | 0.330509i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.1268 | + | 17.5401i | 0.350452 | + | 0.607001i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.83972 | − | 6.65058i | −0.132720 | − | 0.229878i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.9506 | + | 41.4837i | 0.826867 | + | 1.43218i | 0.900484 | + | 0.434890i | \(0.143213\pi\) |
−0.0736164 | + | 0.997287i | \(0.523454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5308 | + | 28.6322i | −0.570029 | + | 0.987319i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.59295 | + | 9.68728i | −0.192632 | + | 0.333648i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.33320 | + | 7.50532i | 0.149066 | + | 0.258191i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.98404 | −0.308695 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.3977 | 1.07757 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.91295 | + | 5.04538i | 0.0998546 | + | 0.172953i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.06418 | + | 7.03937i | −0.139155 | + | 0.241024i | −0.927177 | − | 0.374624i | \(-0.877772\pi\) |
0.788022 | + | 0.615647i | \(0.211105\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.53072 | − | 6.11538i | 0.120748 | − | 0.209142i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.6205 | 1.11430 | 0.557148 | − | 0.830413i | \(-0.311896\pi\) | ||||
0.557148 | + | 0.830413i | \(0.311896\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.8967 | + | 27.5339i | 0.542388 | + | 0.939444i | 0.998766 | + | 0.0496579i | \(0.0158131\pi\) |
−0.456378 | + | 0.889786i | \(0.650854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.84146 | + | 10.1177i | −0.199076 | + | 0.344810i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.7907 | −1.86510 | −0.932549 | − | 0.361044i | \(-0.882421\pi\) | ||||
−0.932549 | + | 0.361044i | \(0.882421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.68539 | − | 2.91918i | 0.0573049 | − | 0.0992550i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.08741 | + | 14.0078i | 0.274663 | + | 0.475730i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.35637 | − | 2.34930i | 0.0460117 | − | 0.0796946i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.4341 | + | 12.6338i | 0.387431 | + | 0.428079i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.274039 | − | 0.474649i | 0.00927481 | − | 0.0160644i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.18663 | − | 3.78736i | −0.0739217 | − | 0.128036i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.01417 | − | 8.68480i | 0.169317 | − | 0.293265i | −0.768863 | − | 0.639413i | \(-0.779177\pi\) |
0.938180 | + | 0.346148i | \(0.112511\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.857561 | 0.0289248 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.9472 | + | 36.2816i | −0.705729 | + | 1.22236i | 0.260699 | + | 0.965420i | \(0.416047\pi\) |
−0.966428 | + | 0.256938i | \(0.917286\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.01930 | − | 3.49752i | −0.0679547 | − | 0.117701i | 0.830046 | − | 0.557695i | \(-0.188314\pi\) |
−0.898001 | + | 0.439994i | \(0.854981\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.81848 | −0.0611275 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.3630 | − | 31.8056i | 0.616569 | − | 1.06793i | −0.373538 | − | 0.927615i | \(-0.621855\pi\) |
0.990107 | − | 0.140314i | \(-0.0448112\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.4258 | − | 33.6464i | 0.651520 | − | 1.12846i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.49547 | + | 2.59023i | 0.0501000 | + | 0.0867758i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.16604 | 0.206339 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.54970 | −0.285785 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.26698 | + | 12.5868i | 0.242637 | + | 0.420260i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.2490 | − | 52.3928i | 1.00886 | − | 1.74740i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.35742 | + | 5.81522i | −0.111852 | + | 0.193733i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.4324 | + | 45.7822i | 0.879614 | + | 1.52354i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.30488 | + | 3.99218i | 0.0766169 | + | 0.132704i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.42704 | − | 4.20376i | −0.0805886 | − | 0.139583i | 0.822914 | − | 0.568165i | \(-0.192347\pi\) |
−0.903503 | + | 0.428582i | \(0.859013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.346371 | + | 0.599931i | 0.0114884 | + | 0.0198985i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.1911 | 0.602697 | 0.301348 | − | 0.953514i | \(-0.402563\pi\) | ||||
0.301348 | + | 0.953514i | \(0.402563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.44665 | 0.279543 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.99000 | − | 3.44678i | 0.0657874 | − | 0.113947i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.10295 | + | 14.0347i | 0.267583 | + | 0.463467i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.8787 | + | 24.0385i | −0.457815 | + | 0.792958i | −0.998845 | − | 0.0480449i | \(-0.984701\pi\) |
0.541031 | + | 0.841003i | \(0.318034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.19008 | + | 5.52538i | −0.105117 | + | 0.182067i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0906616 | −0.00298416 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.417228 | + | 0.722660i | −0.0137184 | + | 0.0237609i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.65401 | − | 13.2571i | −0.251391 | − | 0.435421i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.8287 | 0.420897 | 0.210449 | − | 0.977605i | \(-0.432508\pi\) | ||||
0.210449 | + | 0.977605i | \(0.432508\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.8116 | + | 74.1519i | 1.40309 | + | 2.43023i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.0122 | 0.687910 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.71696 | −0.0888540 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.5470 | −1.71664 | −0.858318 | − | 0.513117i | \(-0.828491\pi\) | ||||
−0.858318 | + | 0.513117i | \(0.828491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.7198 | −0.447729 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.7928 | 1.85139 | 0.925697 | − | 0.378266i | \(-0.123480\pi\) | ||||
0.925697 | + | 0.378266i | \(0.123480\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.6511 | −0.607363 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.18663 | − | 3.78736i | −0.0711312 | − | 0.123203i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.5181 | −1.73910 | −0.869551 | − | 0.493842i | \(-0.835592\pi\) | ||||
−0.869551 | + | 0.493842i | \(0.835592\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.36638 | + | 16.2230i | 0.304046 | + | 0.526622i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.53972 | − | 7.86302i | 0.147210 | − | 0.254976i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.1650 | 1.68979 | 0.844894 | − | 0.534933i | \(-0.179663\pi\) | ||||
0.844894 | + | 0.534933i | \(0.179663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.49218 | + | 11.2448i | −0.210082 | + | 0.363873i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.7812 | + | 20.4056i | −0.380831 | + | 0.659619i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.2467 | + | 64.5132i | 1.20276 | + | 2.08324i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.9868 | + | 24.2259i | −0.451188 | + | 0.781481i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.42328 | 0.206987 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.1932 | −0.328131 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3818 | + | 52.6229i | 0.977014 | + | 1.69224i | 0.673122 | + | 0.739532i | \(0.264953\pi\) |
0.303892 | + | 0.952706i | \(0.401714\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.20730 | + | 5.55520i | 0.103033 | + | 0.178459i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.0672 | − | 45.1497i | −0.836537 | − | 1.44892i | −0.892773 | − | 0.450507i | \(-0.851243\pi\) |
0.0562365 | − | 0.998417i | \(-0.482090\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.18547 | − | 15.9097i | −0.294473 | − | 0.510042i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.04087 | + | 1.80283i | −0.0333344 | + | 0.0577369i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.462261 | + | 0.800660i | −0.0147890 | + | 0.0256154i | −0.873325 | − | 0.487138i | \(-0.838041\pi\) |
0.858536 | + | 0.512753i | \(0.171374\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.13247 | + | 7.15765i | 0.132074 | + | 0.228759i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.66310 | 0.0530988 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.6111 | 1.04013 | 0.520067 | − | 0.854126i | \(-0.325907\pi\) | ||||
0.520067 | + | 0.854126i | \(0.325907\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.06345 | − | 15.6984i | −0.288786 | − | 0.500191i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.90937 | − | 3.30712i | 0.0607758 | − | 0.105267i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.1978 | + | 73.0887i | −1.34181 | + | 2.32408i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.1668 | −0.926514 | −0.463257 | − | 0.886224i | \(-0.653319\pi\) | ||||
−0.463257 | + | 0.886224i | \(0.653319\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.36593 | − | 7.56201i | −0.138549 | − | 0.239973i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.84561 | − | 17.0531i | 0.312127 | − | 0.540619i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.4009 | 0.551092 | 0.275546 | − | 0.961288i | \(-0.411141\pi\) | ||||
0.275546 | + | 0.961288i | \(0.411141\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.417228 | + | 0.722660i | −0.0132005 | + | 0.0228640i |
(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.q.m.3781.1 | yes | 24 | |
67.37 | even | 3 | inner | 4020.2.q.m.841.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.m.841.1 | ✓ | 24 | 67.37 | even | 3 | inner | |
4020.2.q.m.3781.1 | yes | 24 | 1.1 | even | 1 | trivial |