Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(521,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.u (of order \(6\), degree \(2\), not 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: | \(9.39040727770\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.4 | ||
Root | \(-0.601642 - 1.62420i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.521 |
Dual form | 1176.2.u.b.1097.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | −0.291063 | − | 1.70742i | −0.168045 | − | 0.985779i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0726693 | + | 0.125867i | 0.0324987 | + | 0.0562894i | 0.881817 | − | 0.471591i | \(-0.156320\pi\) |
−0.849319 | + | 0.527881i | \(0.822987\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.83056 | + | 0.993934i | −0.943521 | + | 0.331311i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.13889 | + | 1.23489i | 0.644899 | + | 0.372332i | 0.786499 | − | 0.617592i | \(-0.211891\pi\) |
−0.141600 | + | 0.989924i | \(0.545225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.04143i | 0.566191i | 0.959092 | + | 0.283096i | \(0.0913613\pi\) | ||||
−0.959092 | + | 0.283096i | \(0.908639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.193756 | − | 0.160712i | 0.0500276 | − | 0.0414957i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.878419 | − | 1.52147i | 0.213048 | − | 0.369010i | −0.739619 | − | 0.673026i | \(-0.764994\pi\) |
0.952667 | + | 0.304016i | \(0.0983276\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.68319 | − | 2.12649i | 0.844983 | − | 0.487851i | −0.0139720 | − | 0.999902i | \(-0.504448\pi\) |
0.858955 | + | 0.512051i | \(0.171114\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.46351 | − | 4.30906i | 1.55625 | − | 0.898501i | 0.558640 | − | 0.829410i | \(-0.311323\pi\) |
0.997610 | − | 0.0690910i | \(-0.0220099\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.48944 | − | 4.31183i | 0.497888 | − | 0.862367i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.52094 | + | 4.54366i | 0.485154 | + | 0.874429i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.08790i | − | 1.31619i | −0.752935 | − | 0.658095i | \(-0.771363\pi\) | ||
0.752935 | − | 0.658095i | \(-0.228637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.11812 | − | 1.80025i | −0.560031 | − | 0.323334i | 0.193127 | − | 0.981174i | \(-0.438137\pi\) |
−0.753158 | + | 0.657840i | \(0.771470\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.48592 | − | 4.01141i | 0.258665 | − | 0.698296i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.93493 | − | 5.08345i | −0.482499 | − | 0.835713i | 0.517299 | − | 0.855805i | \(-0.326938\pi\) |
−0.999798 | + | 0.0200916i | \(0.993604\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.48558 | − | 0.594185i | 0.558139 | − | 0.0951458i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.33255 | −0.832804 | −0.416402 | − | 0.909181i | \(-0.636709\pi\) | ||||
−0.416402 | + | 0.909181i | \(0.636709\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.19692 | −1.40252 | −0.701258 | − | 0.712907i | \(-0.747378\pi\) | ||||
−0.701258 | + | 0.712907i | \(0.747378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.330798 | − | 0.284046i | −0.0493125 | − | 0.0423431i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.65190 | + | 8.05733i | 0.678549 | + | 1.17528i | 0.975418 | + | 0.220364i | \(0.0707244\pi\) |
−0.296868 | + | 0.954918i | \(0.595942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.85346 | − | 1.05699i | −0.399564 | − | 0.148008i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.49578 | + | 2.59564i | 0.617543 | + | 0.356539i | 0.775912 | − | 0.630841i | \(-0.217290\pi\) |
−0.158369 | + | 0.987380i | \(0.550623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.358953i | 0.0484013i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.70286 | − | 5.66982i | −0.622909 | − | 0.750985i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.60299 | − | 9.70466i | 0.729447 | − | 1.26344i | −0.227670 | − | 0.973738i | \(-0.573111\pi\) |
0.957117 | − | 0.289701i | \(-0.0935558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.66353 | + | 2.69249i | −0.597104 | + | 0.344738i | −0.767901 | − | 0.640568i | \(-0.778699\pi\) |
0.170798 | + | 0.985306i | \(0.445366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.256949 | + | 0.148349i | −0.0318705 | + | 0.0184005i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.57417 | − | 4.45860i | 0.314485 | − | 0.544705i | −0.664843 | − | 0.746984i | \(-0.731501\pi\) |
0.979328 | + | 0.202279i | \(0.0648347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.52973 | − | 11.4891i | −1.14724 | − | 1.38313i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.79323i | 0.924886i | 0.886649 | + | 0.462443i | \(0.153027\pi\) | ||||
−0.886649 | + | 0.462443i | \(0.846973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3013 | − | 6.52482i | −1.32272 | − | 0.763672i | −0.338558 | − | 0.940946i | \(-0.609939\pi\) |
−0.984162 | + | 0.177273i | \(0.943272\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.08669 | − | 2.99550i | −0.933771 | − | 0.345891i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.86075 | + | 4.95497i | 0.321860 | + | 0.557478i | 0.980872 | − | 0.194655i | \(-0.0623586\pi\) |
−0.659012 | + | 0.752133i | \(0.729025\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.02419 | − | 5.62679i | 0.780466 | − | 0.625199i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.9818 | 1.75423 | 0.877115 | − | 0.480280i | \(-0.159465\pi\) | ||||
0.877115 | + | 0.480280i | \(0.159465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.255336 | 0.0276951 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.1020 | + | 2.06303i | −1.29747 | + | 0.221180i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.34252 | + | 7.52147i | 0.460306 | + | 0.797274i | 0.998976 | − | 0.0452432i | \(-0.0144063\pi\) |
−0.538670 | + | 0.842517i | \(0.681073\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.16621 | + | 5.84793i | −0.224626 | + | 0.606402i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.535310 | + | 0.309061i | 0.0549217 | + | 0.0317090i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.65337i | − | 0.675547i | −0.941227 | − | 0.337774i | \(-0.890326\pi\) | ||
0.941227 | − | 0.337774i | \(-0.109674\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.28165 | − | 1.36951i | −0.731834 | − | 0.137641i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.06357 | − | 13.9665i | 0.802355 | − | 1.38972i | −0.115707 | − | 0.993283i | \(-0.536913\pi\) |
0.918062 | − | 0.396437i | \(-0.129753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.147333 | − | 0.0850626i | 0.0145171 | − | 0.00838147i | −0.492724 | − | 0.870186i | \(-0.663999\pi\) |
0.507241 | + | 0.861804i | \(0.330665\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.03900 | − | 3.48662i | 0.583813 | − | 0.337064i | −0.178835 | − | 0.983879i | \(-0.557233\pi\) |
0.762647 | + | 0.646815i | \(0.223899\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.677559 | + | 1.17357i | −0.0648984 | + | 0.112407i | −0.896649 | − | 0.442742i | \(-0.854006\pi\) |
0.831751 | + | 0.555150i | \(0.187339\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.82532 | + | 6.49076i | −0.742747 | + | 0.616076i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000i | 0.376288i | 0.982141 | + | 0.188144i | \(0.0602472\pi\) | ||||
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.08474 | + | 0.626273i | 0.101152 | + | 0.0584002i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.02905 | − | 5.77840i | −0.187586 | − | 0.534213i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.45011 | − | 4.24371i | −0.222737 | − | 0.385792i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.55211 | + | 9.10490i | 0.139949 | + | 0.820961i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.45032 | 0.129720 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.33399 | −0.650787 | −0.325393 | − | 0.945579i | \(-0.605497\pi\) | ||||
−0.325393 | + | 0.945579i | \(0.605497\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.67688 | + | 15.7030i | 0.235687 | + | 1.38257i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.04832 | − | 5.27985i | −0.266333 | − | 0.461303i | 0.701579 | − | 0.712592i | \(-0.252479\pi\) |
−0.967912 | + | 0.251289i | \(0.919146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.388702 | + | 0.647487i | −0.0334542 | + | 0.0557268i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.3832 | − | 10.0362i | −1.48515 | − | 0.857451i | −0.485291 | − | 0.874353i | \(-0.661286\pi\) |
−0.999857 | + | 0.0169018i | \(0.994620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.117694i | 0.00998266i | 0.999988 | + | 0.00499133i | \(0.00158880\pi\) | ||||
−0.999988 | + | 0.00499133i | \(0.998411\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.4032 | − | 10.2879i | 1.04454 | − | 0.866401i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.52094 | + | 4.36639i | −0.210811 | + | 0.365136i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.892131 | − | 0.515072i | 0.0740875 | − | 0.0427744i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.75705 | − | 4.47853i | 0.635482 | − | 0.366896i | −0.147390 | − | 0.989078i | \(-0.547087\pi\) |
0.782872 | + | 0.622183i | \(0.213754\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.37132 | − | 2.37519i | 0.111596 | − | 0.193290i | −0.804818 | − | 0.593522i | \(-0.797737\pi\) |
0.916414 | + | 0.400232i | \(0.131070\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.974184 | + | 5.17970i | −0.0787581 | + | 0.418754i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.523291i | − | 0.0420318i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7303 | + | 6.77249i | 0.936180 | + | 0.540504i | 0.888761 | − | 0.458371i | \(-0.151567\pi\) |
0.0474193 | + | 0.998875i | \(0.484900\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.12329 | − | 8.43168i | 0.247693 | − | 0.668676i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.02428 | + | 3.50616i | 0.158554 | + | 0.274624i | 0.934347 | − | 0.356363i | \(-0.115983\pi\) |
−0.775793 | + | 0.630987i | \(0.782650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.612884 | − | 0.104478i | 0.0477130 | − | 0.00813361i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.70521 | −0.286717 | −0.143359 | − | 0.989671i | \(-0.545790\pi\) | ||||
−0.143359 | + | 0.989671i | \(0.545790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.83256 | 0.679428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.31193 | + | 9.68003i | −0.635629 | + | 0.740250i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2370 | + | 19.4630i | 0.854333 | + | 1.47975i | 0.877263 | + | 0.480011i | \(0.159367\pi\) |
−0.0229296 | + | 0.999737i | \(0.507299\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.2008 | − | 6.74198i | −1.36805 | − | 0.506758i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.18574 | + | 1.83929i | 0.238113 | + | 0.137475i | 0.614309 | − | 0.789065i | \(-0.289435\pi\) |
−0.376196 | + | 0.926540i | \(0.622768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.01062i | 0.595425i | 0.954656 | + | 0.297712i | \(0.0962237\pi\) | ||||
−0.954656 | + | 0.297712i | \(0.903776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.95459 | + | 7.17892i | 0.440176 | + | 0.530681i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.426558 | − | 0.738821i | 0.0313612 | − | 0.0543192i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.75768 | − | 2.16950i | 0.274789 | − | 0.158649i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.971326 | + | 0.560795i | −0.0702827 | + | 0.0405777i | −0.534730 | − | 0.845023i | \(-0.679587\pi\) |
0.464447 | + | 0.885601i | \(0.346253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.18421 | + | 15.9075i | −0.661094 | + | 1.14505i | 0.319235 | + | 0.947676i | \(0.396574\pi\) |
−0.980329 | + | 0.197373i | \(0.936759\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.328083 | + | 0.395540i | 0.0234945 | + | 0.0283252i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.296699i | − | 0.0211389i | −0.999944 | − | 0.0105695i | \(-0.996636\pi\) | ||
0.999944 | − | 0.0105695i | \(-0.00336442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.6874 | + | 13.6759i | 1.67915 | + | 0.969460i | 0.962202 | + | 0.272336i | \(0.0877962\pi\) |
0.716951 | + | 0.697124i | \(0.245537\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.36195 | − | 3.09746i | −0.589807 | − | 0.218478i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.387513 | − | 0.671191i | −0.0270650 | − | 0.0468780i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.8430 | + | 19.6153i | −1.17067 | + | 1.36336i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5039 | 0.726571 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.0295 | 1.44773 | 0.723864 | − | 0.689942i | \(-0.242364\pi\) | ||||
0.723864 | + | 0.689942i | \(0.242364\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.3063 | − | 2.26832i | 0.911734 | − | 0.155423i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.668333 | − | 1.15759i | −0.0455800 | − | 0.0789468i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.85121 | + | 21.1952i | −0.530535 | + | 1.43224i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.10597 | + | 1.79323i | 0.208930 | + | 0.120626i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.89447i | 0.461688i | 0.972991 | + | 0.230844i | \(0.0741487\pi\) | ||||
−0.972991 | + | 0.230844i | \(0.925851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.76084 | + | 14.6793i | −0.184056 | + | 0.978617i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.70734 | + | 11.6174i | −0.445182 | + | 0.771077i | −0.998065 | − | 0.0621816i | \(-0.980194\pi\) |
0.552883 | + | 0.833259i | \(0.313528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.51012 | − | 3.18127i | 0.364119 | − | 0.210224i | −0.306767 | − | 0.951785i | \(-0.599247\pi\) |
0.670886 | + | 0.741560i | \(0.265914\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.29295 | − | 2.47853i | 0.281240 | − | 0.162374i | −0.352744 | − | 0.935720i | \(-0.614752\pi\) |
0.633985 | + | 0.773346i | \(0.281418\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.676100 | + | 1.17104i | −0.0441039 | + | 0.0763903i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.62755 | − | 6.32672i | 0.495463 | − | 0.410964i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.3756i | 1.12394i | 0.827159 | + | 0.561968i | \(0.189956\pi\) | ||||
−0.827159 | + | 0.561968i | \(0.810044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5626 | − | 7.25302i | −0.809228 | − | 0.467208i | 0.0374597 | − | 0.999298i | \(-0.488073\pi\) |
−0.846688 | + | 0.532090i | \(0.821407\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.6518 | − | 10.3555i | −0.747462 | − | 0.664305i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.34109 | + | 7.51899i | 0.276217 | + | 0.478422i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.65171 | − | 27.2876i | −0.294790 | − | 1.72928i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.49783 | 0.220781 | 0.110391 | − | 0.993888i | \(-0.464790\pi\) | ||||
0.110391 | + | 0.993888i | \(0.464790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.2848 | 1.33816 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0743190 | − | 0.435966i | −0.00465404 | − | 0.0273013i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.96781 | − | 13.8006i | −0.497018 | − | 0.860861i | 0.502976 | − | 0.864300i | \(-0.332238\pi\) |
−0.999994 | + | 0.00343985i | \(0.998905\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.04490 | + | 20.0627i | 0.436069 | + | 1.24185i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.4343 | − | 7.17892i | −0.766729 | − | 0.442671i | 0.0649777 | − | 0.997887i | \(-0.479302\pi\) |
−0.831706 | + | 0.555216i | \(0.812636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.754493i | 0.0463482i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.5784 | − | 9.60373i | 0.708584 | − | 0.587739i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.68211 | + | 6.37760i | −0.224502 | + | 0.388849i | −0.956170 | − | 0.292812i | \(-0.905409\pi\) |
0.731668 | + | 0.681661i | \(0.238742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8537 | + | 6.26636i | −0.659313 | + | 0.380654i | −0.792015 | − | 0.610501i | \(-0.790968\pi\) |
0.132702 | + | 0.991156i | \(0.457635\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.6493 | − | 6.14835i | 0.642174 | − | 0.370759i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2409 | + | 28.1300i | −0.975819 | + | 1.69017i | −0.298614 | + | 0.954374i | \(0.596524\pi\) |
−0.677205 | + | 0.735794i | \(0.736809\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.6154 | + | 1.99651i | 0.635526 | + | 0.119528i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1758i | 0.607037i | 0.952826 | + | 0.303518i | \(0.0981614\pi\) | ||||
−0.952826 | + | 0.303518i | \(0.901839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.18666 | + | 0.685120i | 0.0705397 | + | 0.0407261i | 0.534855 | − | 0.844944i | \(-0.320366\pi\) |
−0.464315 | + | 0.885670i | \(0.653700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.371889 | − | 1.00396i | 0.0220288 | − | 0.0594692i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.95676 | + | 12.0495i | 0.409221 | + | 0.708792i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.3601 | + | 1.93655i | −0.665941 | + | 0.113523i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.9961 | −0.992923 | −0.496461 | − | 0.868059i | \(-0.665368\pi\) | ||||
−0.496461 | + | 0.868059i | \(0.665368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.62866 | 0.0948243 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.218914 | + | 12.8315i | −0.0127027 | + | 0.744556i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.79665 | + | 15.2362i | 0.508723 | + | 0.881135i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.1937 | − | 9.70276i | −1.50479 | − | 0.557409i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.677791 | − | 0.391323i | −0.0388102 | − | 0.0224071i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.9023i | − | 1.19296i | −0.802629 | − | 0.596479i | \(-0.796566\pi\) | ||
0.802629 | − | 0.596479i | \(-0.203434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.188121 | − | 0.226800i | −0.0107018 | − | 0.0129022i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.74040 | − | 9.94267i | 0.325508 | − | 0.563797i | −0.656107 | − | 0.754668i | \(-0.727798\pi\) |
0.981615 | + | 0.190871i | \(0.0611312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.57172 | + | 4.94889i | −0.484502 | + | 0.279728i | −0.722291 | − | 0.691589i | \(-0.756911\pi\) |
0.237788 | + | 0.971317i | \(0.423577\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.74547 | − | 3.31715i | 0.322698 | − | 0.186310i | −0.329897 | − | 0.944017i | \(-0.607014\pi\) |
0.652594 | + | 0.757707i | \(0.273681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.75275 | − | 15.1602i | 0.490060 | − | 0.848809i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.71086 | − | 9.29629i | −0.430378 | − | 0.518868i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.47181i | − | 0.415742i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.80231 | + | 5.08202i | 0.488264 | + | 0.281900i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.20098 | + | 0.815296i | 0.121715 | + | 0.0450860i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.36537 | − | 12.7572i | −0.404837 | − | 0.701199i | 0.589465 | − | 0.807794i | \(-0.299339\pi\) |
−0.994303 | + | 0.106595i | \(0.966005\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.3601 | + | 11.4719i | 0.732130 | + | 0.628656i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.748254 | 0.0408815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.7209 | −1.67347 | −0.836737 | − | 0.547605i | \(-0.815540\pi\) | ||||
−0.836737 | + | 0.547605i | \(0.815540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.82968 | − | 1.16425i | 0.370937 | − | 0.0632335i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.44621 | − | 7.70106i | −0.240776 | − | 0.417036i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.753584 | − | 2.03439i | 0.0405716 | − | 0.109528i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.5124 | − | 8.37875i | −0.779068 | − | 0.449795i | 0.0570320 | − | 0.998372i | \(-0.481836\pi\) |
−0.836100 | + | 0.548577i | \(0.815170\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.12385i | − | 0.167216i | −0.996499 | − | 0.0836080i | \(-0.973356\pi\) | ||
0.996499 | − | 0.0836080i | \(-0.0266443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.27558 | + | 5.14632i | −0.495094 | + | 0.274690i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.7450 | + | 30.7353i | −0.944473 | + | 1.63587i | −0.187669 | + | 0.982232i | \(0.560093\pi\) |
−0.756804 | + | 0.653642i | \(0.773240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.980910 | + | 0.566328i | −0.0520613 | + | 0.0300576i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.42817 | + | 3.13395i | −0.286488 | + | 0.165404i | −0.636357 | − | 0.771395i | \(-0.719559\pi\) |
0.349869 | + | 0.936799i | \(0.386226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.456052 | + | 0.789905i | −0.0240027 | + | 0.0415739i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.53266 | + | 5.41855i | −0.342876 | + | 0.284400i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.89662i | − | 0.0992734i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.5823 | + | 8.41907i | 0.761188 | + | 0.439472i | 0.829722 | − | 0.558177i | \(-0.188499\pi\) |
−0.0685342 | + | 0.997649i | \(0.521832\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.0941 | − | 5.30020i | 0.785769 | − | 0.275918i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.617106 | + | 1.06886i | 0.0319526 | + | 0.0553435i | 0.881559 | − | 0.472073i | \(-0.156494\pi\) |
−0.849607 | + | 0.527416i | \(0.823161\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.422134 | − | 2.47630i | −0.0217989 | − | 0.127875i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.4695 | 0.745215 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.3895 | −0.739141 | −0.369571 | − | 0.929203i | \(-0.620495\pi\) | ||||
−0.369571 | + | 0.929203i | \(0.620495\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.13466 | + | 12.5222i | 0.109362 | + | 0.641532i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.95842 | + | 8.58824i | 0.253364 | + | 0.438839i | 0.964450 | − | 0.264266i | \(-0.0851298\pi\) |
−0.711086 | + | 0.703105i | \(0.751796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.0325 | − | 9.14113i | 1.32330 | − | 0.464670i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.5061 | + | 6.64306i | 0.583383 | + | 0.336816i | 0.762477 | − | 0.647016i | \(-0.223983\pi\) |
−0.179094 | + | 0.983832i | \(0.557317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15.1406i | − | 0.765695i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.12767 | + | 6.74154i | −0.409987 | + | 0.340066i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.415778 | + | 0.720148i | −0.0209201 | + | 0.0362346i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0410 | + | 12.1480i | −1.05602 | + | 0.609693i | −0.924328 | − | 0.381598i | \(-0.875374\pi\) |
−0.131691 | + | 0.991291i | \(0.542041\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.4125 | + | 7.16635i | −0.619850 | + | 0.357870i | −0.776810 | − | 0.629735i | \(-0.783164\pi\) |
0.156961 | + | 0.987605i | \(0.449830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.67508 | − | 6.36543i | 0.183069 | − | 0.317085i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.21867 | + | 0.475218i | 0.0605562 | + | 0.0236138i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14.4972i | − | 0.718600i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.3256 | − | 10.0029i | −0.856695 | − | 0.494613i | 0.00620937 | − | 0.999981i | \(-0.498023\pi\) |
−0.862904 | + | 0.505368i | \(0.831357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0764 | + | 32.6016i | −0.595685 | + | 1.60812i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.16139 | + | 2.01158i | 0.0570102 | + | 0.0987446i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.200953 | − | 0.0342563i | 0.00984070 | − | 0.00167754i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.7445 | −1.35541 | −0.677704 | − | 0.735335i | \(-0.737025\pi\) | ||||
−0.677704 | + | 0.735335i | \(0.737025\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.53586 | −0.0748533 | −0.0374267 | − | 0.999299i | \(-0.511916\pi\) | ||||
−0.0374267 | + | 0.999299i | \(0.511916\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.1760 | − | 18.1831i | −1.02961 | − | 0.884093i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.37354 | − | 7.57519i | −0.212148 | − | 0.367451i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.18901 | + | 3.03340i | 0.395369 | + | 0.146454i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8277 | + | 8.56080i | 0.714227 | + | 0.412359i | 0.812624 | − | 0.582788i | \(-0.198038\pi\) |
−0.0983974 | + | 0.995147i | \(0.531372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.5219i | 1.32262i | 0.750113 | + | 0.661310i | \(0.229999\pi\) | ||||
−0.750113 | + | 0.661310i | \(0.770001\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.13911 | − | 1.37332i | −0.0546162 | − | 0.0658459i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.3264 | − | 31.7422i | 0.876670 | − | 1.51844i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9922 | − | 10.9651i | 0.906446 | − | 0.523337i | 0.0271602 | − | 0.999631i | \(-0.491354\pi\) |
0.879286 | + | 0.476294i | \(0.158020\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.7589 | + | 10.2531i | −0.843750 | + | 0.487139i | −0.858537 | − | 0.512752i | \(-0.828626\pi\) |
0.0147873 | + | 0.999891i | \(0.495293\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.631136 | + | 1.09316i | −0.0299187 | + | 0.0518207i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.90453 | − | 11.9410i | −0.468468 | − | 0.564790i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.7692i | 0.885773i | 0.896578 | + | 0.442886i | \(0.146046\pi\) | ||||
−0.896578 | + | 0.442886i | \(0.853954\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4057 | − | 6.58509i | −0.537074 | − | 0.310080i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.45458 | − | 1.65008i | −0.209295 | − | 0.0775276i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.79670 | − | 6.57607i | −0.177602 | − | 0.307616i | 0.763457 | − | 0.645859i | \(-0.223501\pi\) |
−0.941059 | + | 0.338243i | \(0.890167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.12747 | + | 0.155721i | 0.426034 | + | 0.00726845i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.2727 | 1.36337 | 0.681683 | − | 0.731648i | \(-0.261248\pi\) | ||||
0.681683 | + | 0.731648i | \(0.261248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8326 | 0.549906 | 0.274953 | − | 0.961458i | \(-0.411338\pi\) | ||||
0.274953 | + | 0.961458i | \(0.411338\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.893478 | + | 0.152311i | −0.0414340 | + | 0.00706325i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.58282 | − | 4.47358i | −0.119519 | − | 0.207013i | 0.800058 | − | 0.599922i | \(-0.204802\pi\) |
−0.919577 | + | 0.392910i | \(0.871469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.14923 | − | 21.9998i | 0.375497 | − | 1.01370i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.6712 | − | 11.3572i | −0.904481 | − | 0.522202i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 21.1751i | − | 0.971580i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.3055 | − | 2.87862i | −0.700790 | − | 0.131803i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.85496 | − | 17.0693i | 0.450284 | − | 0.779915i | −0.548119 | − | 0.836400i | \(-0.684656\pi\) |
0.998403 | + | 0.0564848i | \(0.0179893\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3775 | − | 5.99145i | 0.473173 | − | 0.273187i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.837439 | − | 0.483496i | 0.0380261 | − | 0.0219544i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.50360 | − | 4.33637i | 0.113449 | − | 0.196500i | −0.803710 | − | 0.595022i | \(-0.797143\pi\) |
0.917159 | + | 0.398522i | \(0.130477\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.39730 | − | 4.47682i | 0.244074 | − | 0.202449i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.55902i | 0.160616i | 0.996770 | + | 0.0803081i | \(0.0255904\pi\) | ||||
−0.996770 | + | 0.0803081i | \(0.974410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.7840 | − | 6.22614i | −0.485687 | − | 0.280411i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.356776 | − | 1.01604i | −0.0160359 | − | 0.0456676i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.404702 | + | 0.700965i | 0.0181170 | + | 0.0313795i | 0.874942 | − | 0.484228i | \(-0.160900\pi\) |
−0.856825 | + | 0.515608i | \(0.827566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.07845 | + | 6.32634i | 0.0481815 | + | 0.282640i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.47070 | 0.422278 | 0.211139 | − | 0.977456i | \(-0.432283\pi\) | ||||
0.211139 | + | 0.977456i | \(0.432283\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.34390 | 0.104302 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.57083 | − | 15.0809i | −0.114175 | − | 0.669766i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.24404 | − | 9.08294i | −0.232438 | − | 0.402594i | 0.726087 | − | 0.687603i | \(-0.241337\pi\) |
−0.958525 | + | 0.285009i | \(0.908004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.9472 | + | 11.3744i | 0.836538 | + | 0.502194i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.0214131 | + | 0.0123629i | 0.000943576 | + | 0.000544774i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.9783i | 1.01058i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.9609 | − | 24.8512i | 1.31514 | − | 1.09085i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.77854 | + | 8.27667i | −0.209351 | + | 0.362607i | −0.951510 | − | 0.307617i | \(-0.900469\pi\) |
0.742159 | + | 0.670224i | \(0.233802\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.0305 | − | 13.8740i | 1.05078 | − | 0.606668i | 0.127912 | − | 0.991785i | \(-0.459172\pi\) |
0.922868 | + | 0.385117i | \(0.125839\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.47804 | + | 3.16275i | −0.238627 | + | 0.137771i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.6360 | − | 44.4029i | 1.11461 | − | 1.93056i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.21383 | + | 33.0387i | −0.269657 | + | 1.43376i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.8860i | − | 0.471526i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.877700 | + | 0.506740i | 0.0379463 | + | 0.0219083i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.21318 | − | 5.97474i | 0.0955060 | − | 0.257829i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.577777 | + | 1.00074i | 0.0248406 | + | 0.0430251i | 0.878178 | − | 0.478333i | \(-0.158759\pi\) |
−0.853338 | + | 0.521358i | \(0.825426\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.6775 | − | 2.33160i | 0.586958 | − | 0.100058i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.196951 | −0.00843645 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1394 | 0.690070 | 0.345035 | − | 0.938590i | \(-0.387867\pi\) | ||||
0.345035 | + | 0.938590i | \(0.387867\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5243 | − | 12.2565i | 0.449165 | − | 0.523095i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0724 | − | 26.1061i | −0.642104 | − | 1.11216i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.38563 | − | 0.513271i | −0.0588168 | − | 0.0217871i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.1074 | + | 18.5372i | 1.36043 | + | 0.785447i | 0.989682 | − | 0.143284i | \(-0.0457663\pi\) |
0.370753 | + | 0.928732i | \(0.379100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18.7749i | − | 0.794092i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.79796 | − | 5.78447i | −0.202570 | − | 0.244221i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.79584 | − | 13.5028i | 0.328556 | − | 0.569075i | −0.653670 | − | 0.756780i | \(-0.726772\pi\) |
0.982225 | + | 0.187705i | \(0.0601049\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.503468 | + | 0.290677i | −0.0211810 | + | 0.0122289i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.0276 | + | 7.52147i | −0.546144 | + | 0.315316i | −0.747565 | − | 0.664188i | \(-0.768777\pi\) |
0.201421 | + | 0.979505i | \(0.435444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.81334 | + | 4.87284i | −0.117735 | + | 0.203922i | −0.918870 | − | 0.394561i | \(-0.870897\pi\) |
0.801135 | + | 0.598484i | \(0.204230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.24023 | + | 1.49523i | 0.0518114 | + | 0.0624643i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 42.9086i | − | 1.78941i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.2278 | − | 11.1012i | −0.800465 | − | 0.462149i | 0.0431688 | − | 0.999068i | \(-0.486255\pi\) |
−0.843634 | + | 0.536919i | \(0.819588\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.8340 | + | 11.0512i | 1.23986 | + | 0.459273i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.41064 | + | 11.1036i | 0.265502 | + | 0.459863i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.579860 | − | 0.675302i | 0.0239743 | − | 0.0279203i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.9245 | −0.863648 | −0.431824 | − | 0.901958i | \(-0.642130\pi\) | ||||
−0.431824 | + | 0.901958i | \(0.642130\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.3129 | −0.630956 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.506589 | + | 0.0863581i | −0.0208383 | + | 0.00355230i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5845 | + | 18.3329i | 0.434654 | + | 0.752842i | 0.997267 | − | 0.0738778i | \(-0.0235375\pi\) |
−0.562614 | + | 0.826720i | \(0.690204\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.4560 | − | 44.4248i | 0.673499 | − | 1.81819i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.58648 | − | 2.64801i | −0.187399 | − | 0.108195i | 0.403366 | − | 0.915039i | \(-0.367840\pi\) |
−0.590764 | + | 0.806844i | \(0.701174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.5346i | 1.53107i | 0.643396 | + | 0.765533i | \(0.277525\pi\) | ||||
−0.643396 | + | 0.765533i | \(0.722475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.85481 | + | 15.1789i | −0.116257 | + | 0.618133i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.356095 | − | 0.616775i | 0.0144773 | − | 0.0250755i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.2123 | + | 19.7525i | −1.38864 | + | 0.801729i | −0.993162 | − | 0.116748i | \(-0.962753\pi\) |
−0.395474 | + | 0.918477i | \(0.629420\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4485 | + | 9.49653i | −0.665434 | + | 0.384189i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.19736 | + | 12.4662i | −0.290699 | + | 0.503505i | −0.973975 | − | 0.226655i | \(-0.927221\pi\) |
0.683277 | + | 0.730160i | \(0.260554\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.03321 | + | 0.857006i | −0.0416632 | + | 0.0345578i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1573i | 0.489435i | 0.969594 | + | 0.244718i | \(0.0786952\pi\) | ||||
−0.969594 | + | 0.244718i | \(0.921305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.8732 | + | 9.74173i | 0.678190 | + | 0.391553i | 0.799173 | − | 0.601101i | \(-0.205271\pi\) |
−0.120983 | + | 0.992655i | \(0.538605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 38.3940 | + | 23.0488i | 1.54070 | + | 0.924918i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.3418 | − | 21.3766i | −0.493672 | − | 0.855065i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.05730 | − | 17.9346i | −0.122097 | − | 0.716239i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.3124 | −0.411182 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.3846 | −1.24940 | −0.624701 | − | 0.780864i | \(-0.714779\pi\) | ||||
−0.624701 | + | 0.780864i | \(0.714779\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.12091 | − | 35.9061i | −0.243284 | − | 1.42714i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.532956 | − | 0.923107i | −0.0211497 | − | 0.0366324i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.74596 | − | 22.0592i | −0.306425 | − | 0.872650i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.0118 | + | 20.7914i | 1.42238 | + | 0.821211i | 0.996502 | − | 0.0835697i | \(-0.0266321\pi\) |
0.425878 | + | 0.904781i | \(0.359965\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.5290i | 0.533531i | 0.963761 | + | 0.266766i | \(0.0859549\pi\) | ||||
−0.963761 | + | 0.266766i | \(0.914045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.78196 | + | 1.47806i | −0.0701646 | + | 0.0581984i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.0442 | + | 26.0573i | −0.591449 | + | 1.02442i | 0.402589 | + | 0.915381i | \(0.368110\pi\) |
−0.994038 | + | 0.109038i | \(0.965223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.9683 | − | 13.8381i | 0.940839 | − | 0.543193i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.3717 | − | 10.6069i | 0.718941 | − | 0.415081i | −0.0954221 | − | 0.995437i | \(-0.530420\pi\) |
0.814363 | + | 0.580356i | \(0.197087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.443039 | − | 0.767366i | 0.0173110 | − | 0.0299835i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38.4743 | + | 7.23615i | 1.50103 | + | 0.282309i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.67926i | − | 0.104369i | −0.998637 | − | 0.0521846i | \(-0.983382\pi\) | ||
0.998637 | − | 0.0521846i | \(-0.0166184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.79785 | − | 2.77004i | −0.186615 | − | 0.107742i | 0.403782 | − | 0.914855i | \(-0.367695\pi\) |
−0.590397 | + | 0.807113i | \(0.701029\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.15777 | − | 5.82513i | 0.0838007 | − | 0.226229i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.5422 | − | 52.9006i | −1.18260 | − | 2.04832i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.7718 | − | 2.00673i | 0.455123 | − | 0.0775846i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.2997 | −0.513429 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1946 | −0.662804 | −0.331402 | − | 0.943490i | \(-0.607522\pi\) | ||||
−0.331402 | + | 0.943490i | \(0.607522\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.8672 | + | 0.441314i | 0.995630 | + | 0.0169862i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.23319 | − | 12.5283i | −0.277994 | − | 0.481500i | 0.692892 | − | 0.721041i | \(-0.256336\pi\) |
−0.970886 | + | 0.239541i | \(0.923003\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.7881 | + | 8.07083i | 0.834923 | + | 0.309275i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.1356 | + | 16.2441i | 1.07658 | + | 0.621564i | 0.929972 | − | 0.367630i | \(-0.119831\pi\) |
0.146609 | + | 0.989195i | \(0.453164\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.91730i | − | 0.111464i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.03555 | − | 8.48214i | −0.268423 | − | 0.323614i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.29882 | + | 9.17783i | −0.201869 | + | 0.349647i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0961 | − | 16.2213i | 1.06883 | − | 0.617087i | 0.140966 | − | 0.990014i | \(-0.454979\pi\) |
0.927861 | + | 0.372927i | \(0.121646\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0148138 | + | 0.00855273i | −0.000561918 | + | 0.000324423i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.68421 | + | 8.11329i | −0.177427 | + | 0.307313i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.48142 | − | 6.60845i | −0.207326 | − | 0.249955i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30.3777i | − | 1.14735i | −0.819084 | − | 0.573674i | \(-0.805518\pi\) | ||
0.819084 | − | 0.573674i | \(-0.194482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.6198 | − | 12.4822i | −0.815407 | − | 0.470776i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.19625 | + | 0.813541i | 0.0827154 | + | 0.0306397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.2569 | + | 28.1578i | 0.610542 | + | 1.05749i | 0.991149 | + | 0.132753i | \(0.0423816\pi\) |
−0.380607 | + | 0.924737i | \(0.624285\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.0225 | − | 11.1820i | −0.488380 | − | 0.419356i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.0295 | −1.16207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.732778 | −0.0274044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.6675 | − | 5.05741i | 1.10795 | − | 0.188872i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.29867 | + | 9.17757i | 0.197607 | + | 0.342266i | 0.947752 | − | 0.319008i | \(-0.103350\pi\) |
−0.750145 | + | 0.661273i | \(0.770016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.72744 | + | 23.5607i | −0.324577 | + | 0.876232i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.5618 | − | 17.6449i | −1.13504 | − | 0.655314i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.3600i | 1.16308i | 0.813518 | + | 0.581540i | \(0.197549\pi\) | ||||
−0.813518 | + | 0.581540i | \(0.802451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.2898 | + | 22.9086i | −0.529251 | + | 0.848466i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.07874 | + | 13.9928i | −0.298803 | + | 0.517542i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.13184 | − | 1.80817i | 0.115677 | − | 0.0667863i | −0.441045 | − | 0.897485i | \(-0.645392\pi\) |
0.556722 | + | 0.830699i | \(0.312059\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0117 | − | 6.35763i | 0.405623 | − | 0.234186i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.3463 | − | 33.5087i | 0.711665 | − | 1.23264i | −0.252567 | − | 0.967579i | \(-0.581275\pi\) |
0.964232 | − | 0.265060i | \(-0.0853917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.5745 | − | 9.60056i | 0.425201 | − | 0.352685i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 45.1194i | − | 1.65527i | −0.561266 | − | 0.827635i | \(-0.689686\pi\) | ||
0.561266 | − | 0.827635i | \(-0.310314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.12740 | + | 0.650904i | 0.0413047 | + | 0.0238473i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.2375 | + | 15.8849i | −1.65515 | + | 0.581197i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7841 | + | 20.4107i | 0.430009 | + | 0.744797i | 0.996874 | − | 0.0790136i | \(-0.0251771\pi\) |
−0.566865 | + | 0.823811i | \(0.691844\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.01809 | − | 5.97226i | −0.0371013 | − | 0.217641i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.398610 | 0.0145069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2967 | 0.955770 | 0.477885 | − | 0.878422i | \(-0.341404\pi\) | ||||
0.477885 | + | 0.878422i | \(0.341404\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.19523 | − | 36.3421i | −0.224872 | − | 1.31914i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.9780 | − | 22.4785i | −0.470452 | − | 0.814846i | 0.528977 | − | 0.848636i | \(-0.322576\pi\) |
−0.999429 | + | 0.0337898i | \(0.989242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.722746 | + | 0.253787i | −0.0261309 | + | 0.00917570i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.8114 | + | 11.4381i | 0.715348 | + | 0.413006i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 36.9215i | − | 1.33142i | −0.746209 | − | 0.665712i | \(-0.768128\pi\) | ||
0.746209 | − | 0.665712i | \(-0.231872\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.2444 | + | 17.6212i | −0.765097 | + | 0.634614i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.79284 | + | 10.0335i | −0.208354 | + | 0.360879i | −0.951196 | − | 0.308587i | \(-0.900144\pi\) |
0.742842 | + | 0.669466i | \(0.233477\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.5247 | + | 8.96322i | −0.557665 | + | 0.321968i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.6408 | + | 11.3396i | −0.703705 | + | 0.406284i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.62376 | + | 16.6688i | −0.344365 | + | 0.596458i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.2050 | − | 17.8681i | 1.15091 | − | 0.638555i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.96861i | 0.0702627i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.9153 | − | 14.9622i | −0.923779 | − | 0.533344i | −0.0389406 | − | 0.999242i | \(-0.512398\pi\) |
−0.884839 | + | 0.465897i | \(0.845732\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.63827 | + | 23.3200i | −0.307531 | + | 0.830214i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.49653 | − | 9.52027i | −0.195188 | − | 0.338075i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.28824 | − | 0.219605i | 0.0456891 | − | 0.00778860i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.2866 | −0.718587 | −0.359293 | − | 0.933225i | \(-0.616982\pi\) | ||||
−0.359293 | + | 0.933225i | \(0.616982\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3453 | 0.578254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.7676 | − | 16.9738i | −0.698455 | − | 0.599740i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.1148 | − | 27.9117i | −0.568680 | − | 0.984982i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.9610 | + | 4.43062i | 0.421046 | + | 0.155965i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.15641 | − | 1.24501i | −0.0758155 | − | 0.0437721i | 0.461613 | − | 0.887081i | \(-0.347271\pi\) |
−0.537429 | + | 0.843309i | \(0.680604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.9838i | − | 0.561269i | −0.959815 | − | 0.280634i | \(-0.909455\pi\) | ||
0.959815 | − | 0.280634i | \(-0.0905448\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.8584 | + | 16.7078i | 0.486036 | + | 0.585970i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.294206 | + | 0.509581i | −0.0103056 | + | 0.0178498i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.8740 | + | 19.5572i | −1.18510 | + | 0.684219i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.38960 | − | 1.37963i | 0.0833975 | − | 0.0481495i | −0.457721 | − | 0.889096i | \(-0.651334\pi\) |
0.541119 | + | 0.840946i | \(0.318001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2212 | − | 24.6318i | 0.495720 | − | 0.858612i | −0.504268 | − | 0.863547i | \(-0.668238\pi\) |
0.999988 | + | 0.00493523i | \(0.00157094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.5974 | − | 16.3932i | −0.473401 | − | 0.570738i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.6070i | 1.06431i | 0.846647 | + | 0.532154i | \(0.178617\pi\) | ||||
−0.846647 | + | 0.532154i | \(0.821383\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.71397 | − | 5.03101i | −0.302649 | − | 0.174734i | 0.340983 | − | 0.940069i | \(-0.389240\pi\) |
−0.643632 | + | 0.765335i | \(0.722573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.7568 | + | 19.5424i | 1.83011 | + | 0.677917i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.269255 | − | 0.466363i | −0.00931794 | − | 0.0161391i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.319139 | − | 18.7060i | 0.0110310 | − | 0.646574i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.3067 | −0.459400 | −0.229700 | − | 0.973262i | \(-0.573774\pi\) | ||||
−0.229700 | + | 0.973262i | \(0.573774\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.2383 | −0.732354 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.3744 | − | 2.96180i | 0.598404 | − | 0.102010i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.641856 | + | 1.11173i | 0.0220805 | + | 0.0382446i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.824393 | − | 2.22554i | 0.0282931 | − | 0.0763805i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.8098 | − | 25.2936i | −1.50178 | − | 0.867053i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.4736i | − | 1.45427i | −0.686495 | − | 0.727134i | \(-0.740852\pi\) | ||
0.686495 | − | 0.727134i | \(-0.259148\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.82242 | − | 0.342755i | −0.0623253 | − | 0.0117220i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.77854 | + | 8.27667i | −0.163232 | + | 0.282726i | −0.936026 | − | 0.351931i | \(-0.885525\pi\) |
0.772794 | + | 0.634657i | \(0.218858\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.82940 | − | 1.05620i | 0.0624183 | − | 0.0360372i | −0.468466 | − | 0.883481i | \(-0.655193\pi\) |
0.530884 | + | 0.847444i | \(0.321860\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.5684 | + | 17.6487i | −1.04056 | + | 0.600768i | −0.919992 | − | 0.391936i | \(-0.871805\pi\) |
−0.120569 | + | 0.992705i | \(0.538472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.63317 | + | 2.82873i | −0.0555294 | + | 0.0961797i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.5486 | − | 15.3853i | 0.629945 | − | 0.522511i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.1308i | 0.479356i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.10193 | + | 5.25500i | 0.308407 | + | 0.178059i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.61301 | + | 18.8328i | 0.223817 | + | 0.637394i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.36886 | + | 14.4953i | 0.282596 | + | 0.489471i | 0.972023 | − | 0.234884i | \(-0.0754709\pi\) |
−0.689427 | + | 0.724355i | \(0.742138\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.94694 | + | 29.0195i | 0.166856 | + | 0.978803i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.6152 | 1.43574 | 0.717871 | − | 0.696176i | \(-0.245117\pi\) | ||||
0.717871 | + | 0.696176i | \(0.245117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.2392 | −0.512839 | −0.256419 | − | 0.966566i | \(-0.582543\pi\) | ||||
−0.256419 | + | 0.966566i | \(0.582543\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.474043 | − | 2.78081i | −0.0159348 | − | 0.0934758i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.0633 | − | 48.6071i | −0.942275 | − | 1.63207i | −0.761118 | − | 0.648613i | \(-0.775349\pi\) |
−0.181157 | − | 0.983454i | \(-0.557984\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.9724 | − | 3.36099i | 0.736103 | − | 0.112597i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.2677 | + | 19.7845i | 1.14673 | + | 0.662062i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.534639i | 0.0178710i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.4543 | − | 19.4543i | 0.783116 | − | 0.649560i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.7600 | + | 22.1009i | −0.425569 | + | 0.737107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.89836 | − | 4.56012i | 0.263132 | − | 0.151920i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.00827 | + | 0.582126i | −0.0335161 | + | 0.0193505i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.3625 | + | 35.2688i | −0.676124 | + | 1.17108i | 0.300015 | + | 0.953935i | \(0.403008\pi\) |
−0.976139 | + | 0.217147i | \(0.930325\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.94266 | + | 47.5478i | −0.296609 | + | 1.57706i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.0308i | 1.02810i | 0.857761 | + | 0.514049i | \(0.171855\pi\) | ||||
−0.857761 | + | 0.514049i | \(0.828145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.1833 | + | 19.7357i | 1.13130 | + | 0.653157i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.470872 | + | 1.27117i | −0.0155666 | + | 0.0420237i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.6178 | + | 44.3713i | 0.845053 | + | 1.46367i | 0.885575 | + | 0.464496i | \(0.153765\pi\) |
−0.0405222 | + | 0.999179i | \(0.512902\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −35.6890 | + | 6.08389i | −1.17599 | + | 0.200471i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.9093 | −0.523662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.2253 | −0.960922 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.332488 | + | 0.387214i | −0.0109203 | + | 0.0127178i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.87116 | + | 3.24094i | 0.0613907 | + | 0.106332i | 0.895087 | − | 0.445891i | \(-0.147113\pi\) |
−0.833697 | + | 0.552223i | \(0.813780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.6471 | − | 6.90733i | −0.610480 | − | 0.226136i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.546135 | + | 0.315311i | 0.0178605 | + | 0.0103118i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.23951i | − | 0.105830i | −0.998599 | − | 0.0529150i | \(-0.983149\pi\) | ||
0.998599 | − | 0.0529150i | \(-0.0168512\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.9447 | + | 13.1951i | 0.357168 | + | 0.430606i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.0342 | − | 19.1117i | 0.359703 | − | 0.623024i | −0.628208 | − | 0.778046i | \(-0.716211\pi\) |
0.987911 | + | 0.155021i | \(0.0495446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.7996 | + | 22.9783i | −1.29605 | + | 0.748276i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.4016 | − | 18.1297i | 1.02042 | − | 0.589137i | 0.106191 | − | 0.994346i | \(-0.466134\pi\) |
0.914224 | + | 0.405208i | \(0.132801\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.3200 | − | 23.0709i | 0.432384 | − | 0.748912i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.33606 | − | 8.84443i | −0.237888 | − | 0.286800i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.4656i | − | 0.436192i | −0.975927 | − | 0.218096i | \(-0.930015\pi\) | ||
0.975927 | − | 0.218096i | \(-0.0699846\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.141171 | − | 0.0815052i | −0.00456819 | − | 0.00263745i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28.4324 | − | 10.5320i | −0.919090 | − | 0.340452i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.01821 | − | 15.6200i | −0.290910 | − | 0.503871i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.6283 | + | 15.8715i | −0.439166 | + | 0.511451i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.66964 | −0.0859388 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.25940 | −0.297762 | −0.148881 | − | 0.988855i | \(-0.547567\pi\) | ||||
−0.148881 | + | 0.988855i | \(0.547567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.7575 | + | 2.17477i | −0.409830 | + | 0.0698636i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.9645 | + | 34.5795i | 0.640691 | + | 1.10971i | 0.985279 | + | 0.170956i | \(0.0546856\pi\) |
−0.344587 | + | 0.938754i | \(0.611981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.11511 | − | 16.5084i | 0.195840 | − | 0.528693i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.4299 | − | 30.2704i | −1.67738 | − | 0.968436i | −0.963321 | − | 0.268352i | \(-0.913521\pi\) |
−0.714060 | − | 0.700084i | \(-0.753146\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.4501i | 0.685548i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.751427 | − | 3.99531i | 0.0239912 | − | 0.127560i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.7027 | + | 34.1261i | −0.628419 | + | 1.08845i | 0.359450 | + | 0.933164i | \(0.382964\pi\) |
−0.987869 | + | 0.155289i | \(0.950369\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0373445 | − | 0.0215609i | 0.00118990 | − | 0.000686987i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −68.6413 | + | 39.6301i | −2.18267 | + | 1.26016i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.0507 | + | 26.0686i | −0.478102 | + | 0.828098i | −0.999685 | − | 0.0251033i | \(-0.992009\pi\) |
0.521583 | + | 0.853201i | \(0.325342\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.6381 | + | 16.2889i | −0.623196 | + | 0.516914i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.97527i | 0.126025i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.10467 | + | 3.52453i | 0.193337 | + | 0.111623i | 0.593544 | − | 0.804802i | \(-0.297728\pi\) |
−0.400207 | + | 0.916425i | \(0.631062\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.6987 | − | 26.1504i | 0.496685 | − | 0.827361i |
(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 | 1176.2.u.b.521.4 | 16 | ||
3.2 | odd | 2 | inner | 1176.2.u.b.521.2 | 16 | ||
7.2 | even | 3 | 168.2.u.a.89.7 | yes | 16 | ||
7.3 | odd | 6 | 1176.2.k.a.881.13 | 16 | |||
7.4 | even | 3 | 1176.2.k.a.881.4 | 16 | |||
7.5 | odd | 6 | inner | 1176.2.u.b.1097.2 | 16 | ||
7.6 | odd | 2 | 168.2.u.a.17.5 | ✓ | 16 | ||
21.2 | odd | 6 | 168.2.u.a.89.5 | yes | 16 | ||
21.5 | even | 6 | inner | 1176.2.u.b.1097.4 | 16 | ||
21.11 | odd | 6 | 1176.2.k.a.881.14 | 16 | |||
21.17 | even | 6 | 1176.2.k.a.881.3 | 16 | |||
21.20 | even | 2 | 168.2.u.a.17.7 | yes | 16 | ||
28.3 | even | 6 | 2352.2.k.i.881.4 | 16 | |||
28.11 | odd | 6 | 2352.2.k.i.881.13 | 16 | |||
28.23 | odd | 6 | 336.2.bc.f.257.2 | 16 | |||
28.27 | even | 2 | 336.2.bc.f.17.4 | 16 | |||
84.11 | even | 6 | 2352.2.k.i.881.3 | 16 | |||
84.23 | even | 6 | 336.2.bc.f.257.4 | 16 | |||
84.59 | odd | 6 | 2352.2.k.i.881.14 | 16 | |||
84.83 | odd | 2 | 336.2.bc.f.17.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.u.a.17.5 | ✓ | 16 | 7.6 | odd | 2 | ||
168.2.u.a.17.7 | yes | 16 | 21.20 | even | 2 | ||
168.2.u.a.89.5 | yes | 16 | 21.2 | odd | 6 | ||
168.2.u.a.89.7 | yes | 16 | 7.2 | even | 3 | ||
336.2.bc.f.17.2 | 16 | 84.83 | odd | 2 | |||
336.2.bc.f.17.4 | 16 | 28.27 | even | 2 | |||
336.2.bc.f.257.2 | 16 | 28.23 | odd | 6 | |||
336.2.bc.f.257.4 | 16 | 84.23 | even | 6 | |||
1176.2.k.a.881.3 | 16 | 21.17 | even | 6 | |||
1176.2.k.a.881.4 | 16 | 7.4 | even | 3 | |||
1176.2.k.a.881.13 | 16 | 7.3 | odd | 6 | |||
1176.2.k.a.881.14 | 16 | 21.11 | odd | 6 | |||
1176.2.u.b.521.2 | 16 | 3.2 | odd | 2 | inner | ||
1176.2.u.b.521.4 | 16 | 1.1 | even | 1 | trivial | ||
1176.2.u.b.1097.2 | 16 | 7.5 | odd | 6 | inner | ||
1176.2.u.b.1097.4 | 16 | 21.5 | even | 6 | inner | ||
2352.2.k.i.881.3 | 16 | 84.11 | even | 6 | |||
2352.2.k.i.881.4 | 16 | 28.3 | even | 6 | |||
2352.2.k.i.881.13 | 16 | 28.11 | odd | 6 | |||
2352.2.k.i.881.14 | 16 | 84.59 | odd | 6 |