Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(701,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.o (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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1241.4 | ||
Root | \(-0.535233 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1241 |
Dual form | 1620.3.o.e.701.4 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.93649 | − | 1.11803i | 0.387298 | − | 0.223607i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.854102 | − | 1.47935i | 0.122015 | − | 0.211335i | −0.798547 | − | 0.601932i | \(-0.794398\pi\) |
0.920562 | + | 0.390596i | \(0.127731\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.21140 | + | 1.85410i | 0.291945 | + | 0.168555i | 0.638819 | − | 0.769357i | \(-0.279423\pi\) |
−0.346873 | + | 0.937912i | \(0.612757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.85410 | + | 11.8717i | 0.527239 | + | 0.913204i | 0.999496 | + | 0.0317434i | \(0.0101059\pi\) |
−0.472257 | + | 0.881461i | \(0.656561\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.0000i | 0.882353i | 0.897420 | + | 0.441176i | \(0.145439\pi\) | ||||
−0.897420 | + | 0.441176i | \(0.854561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.4164 | −0.758758 | −0.379379 | − | 0.925241i | \(-0.623862\pi\) | ||||
−0.379379 | + | 0.925241i | \(0.623862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.56758 | + | 3.79180i | −0.285547 | + | 0.164861i | −0.635932 | − | 0.771745i | \(-0.719384\pi\) |
0.350385 | + | 0.936606i | \(0.386051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.40755 | + | 4.85410i | 0.289916 | + | 0.167383i | 0.637904 | − | 0.770116i | \(-0.279802\pi\) |
−0.347988 | + | 0.937499i | \(0.613135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2082 | + | 17.6811i | 0.329297 | + | 0.570359i | 0.982373 | − | 0.186934i | \(-0.0598550\pi\) |
−0.653076 | + | 0.757293i | \(0.726522\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.81966i | − | 0.109133i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −56.2492 | −1.52025 | −0.760125 | − | 0.649777i | \(-0.774862\pi\) | ||||
−0.760125 | + | 0.649777i | \(0.774862\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −36.8416 | + | 21.2705i | −0.898576 | + | 0.518793i | −0.876738 | − | 0.480969i | \(-0.840285\pi\) |
−0.0218379 | + | 0.999762i | \(0.506952\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.97871 | − | 15.5516i | 0.208807 | − | 0.361665i | −0.742532 | − | 0.669811i | \(-0.766375\pi\) |
0.951339 | + | 0.308146i | \(0.0997085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.22665 | + | 0.708204i | 0.0260988 | + | 0.0150682i | 0.512993 | − | 0.858393i | \(-0.328537\pi\) |
−0.486894 | + | 0.873461i | \(0.661870\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.0410 | + | 39.9082i | 0.470225 | + | 0.814453i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 70.0820i | 1.32230i | 0.750253 | + | 0.661151i | \(0.229932\pi\) | ||||
−0.750253 | + | 0.661151i | \(0.770068\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.29180 | 0.150760 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 26.7389 | − | 15.4377i | 0.453201 | − | 0.261656i | −0.255980 | − | 0.966682i | \(-0.582398\pi\) |
0.709181 | + | 0.705026i | \(0.249065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40.7492 | − | 70.5797i | 0.668020 | − | 1.15704i | −0.310437 | − | 0.950594i | \(-0.600475\pi\) |
0.978457 | − | 0.206451i | \(-0.0661913\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 26.5458 | + | 15.3262i | 0.408397 | + | 0.235788i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 12.1244i | −0.104478 | − | 0.180961i | 0.809047 | − | 0.587744i | \(-0.199984\pi\) |
−0.913525 | + | 0.406783i | \(0.866650\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.95743i | 0.0275694i | 0.999905 | + | 0.0137847i | \(0.00438795\pi\) | ||||
−0.999905 | + | 0.0137847i | \(0.995612\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −27.1246 | −0.371570 | −0.185785 | − | 0.982590i | \(-0.559483\pi\) | ||||
−0.185785 | + | 0.982590i | \(0.559483\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.48572 | − | 3.16718i | 0.0712432 | − | 0.0411323i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.74922 | + | 11.6900i | −0.0854332 | + | 0.147975i | −0.905576 | − | 0.424185i | \(-0.860561\pi\) |
0.820143 | + | 0.572159i | \(0.193894\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 64.3728 | + | 37.1656i | 0.775575 | + | 0.447779i | 0.834860 | − | 0.550462i | \(-0.185549\pi\) |
−0.0592845 | + | 0.998241i | \(0.518882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.7705 | + | 29.0474i | 0.197300 | + | 0.341734i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 123.039i | 1.38247i | 0.722632 | + | 0.691233i | \(0.242932\pi\) | ||||
−0.722632 | + | 0.691233i | \(0.757068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.4164 | 0.257323 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27.9173 | + | 16.1180i | −0.293866 | + | 0.169664i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.70820 | − | 9.88690i | 0.0588475 | − | 0.101927i | −0.835101 | − | 0.550097i | \(-0.814591\pi\) |
0.893948 | + | 0.448170i | \(0.147924\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 145.492 | + | 84.0000i | 1.44052 | + | 0.831683i | 0.997884 | − | 0.0650194i | \(-0.0207109\pi\) |
0.442634 | + | 0.896703i | \(0.354044\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.75078 | + | 16.8888i | 0.0946677 | + | 0.163969i | 0.909470 | − | 0.415770i | \(-0.136488\pi\) |
−0.814802 | + | 0.579739i | \(0.803154\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 202.997i | 1.89717i | 0.316527 | + | 0.948584i | \(0.397483\pi\) | ||||
−0.316527 | + | 0.948584i | \(0.602517\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −32.0820 | −0.294331 | −0.147165 | − | 0.989112i | \(-0.547015\pi\) | ||||
−0.147165 | + | 0.989112i | \(0.547015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.16372 | + | 1.24922i | −0.0191480 | + | 0.0110551i | −0.509543 | − | 0.860445i | \(-0.670186\pi\) |
0.490395 | + | 0.871500i | \(0.336852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.47871 | + | 14.6856i | −0.0737279 | + | 0.127701i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.1902 | + | 12.8115i | 0.186472 | + | 0.107660i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.6246 | − | 92.8806i | −0.443179 | − | 0.767608i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 104.748 | 0.824785 | 0.412392 | − | 0.911006i | \(-0.364693\pi\) | ||||
0.412392 | + | 0.911006i | \(0.364693\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −158.627 | + | 91.5836i | −1.21090 | + | 0.699111i | −0.962955 | − | 0.269664i | \(-0.913088\pi\) |
−0.247942 | + | 0.968775i | \(0.579754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.3131 | + | 21.3269i | −0.0925796 | + | 0.160353i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −78.3766 | − | 45.2508i | −0.572092 | − | 0.330298i | 0.185892 | − | 0.982570i | \(-0.440482\pi\) |
−0.757985 | + | 0.652272i | \(0.773816\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −89.2492 | − | 154.584i | −0.642081 | − | 1.11212i | −0.984968 | − | 0.172740i | \(-0.944738\pi\) |
0.342887 | − | 0.939377i | \(-0.388595\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 50.8328i | 0.355474i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.7082 | 0.149712 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −126.403 | + | 72.9787i | −0.848341 | + | 0.489790i | −0.860091 | − | 0.510141i | \(-0.829593\pi\) |
0.0117496 | + | 0.999931i | \(0.496260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −75.4984 | + | 130.767i | −0.499990 | + | 0.866008i | −1.00000 | 1.18743e-5i | \(-0.999996\pi\) | |
0.500010 | + | 0.866019i | \(0.333330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 39.5362 | + | 22.8262i | 0.255072 | + | 0.147266i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.14590 | − | 14.1091i | −0.0518847 | − | 0.0898669i | 0.838917 | − | 0.544260i | \(-0.183189\pi\) |
−0.890801 | + | 0.454393i | \(0.849856\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9543i | 0.0804616i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 297.830 | 1.82718 | 0.913588 | − | 0.406641i | \(-0.133300\pi\) | ||||
0.913588 | + | 0.406641i | \(0.133300\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 180.204 | − | 104.041i | 1.07907 | − | 0.623000i | 0.148423 | − | 0.988924i | \(-0.452580\pi\) |
0.930645 | + | 0.365924i | \(0.119247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.45743 | + | 16.3807i | −0.0559611 | + | 0.0969275i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 28.2893 | + | 16.3328i | 0.163522 | + | 0.0944093i | 0.579528 | − | 0.814953i | \(-0.303237\pi\) |
−0.416006 | + | 0.909362i | \(0.636570\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.27051 | − | 7.39674i | −0.0244029 | − | 0.0422671i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 257.666i | 1.43947i | 0.694247 | + | 0.719736i | \(0.255737\pi\) | ||||
−0.694247 | + | 0.719736i | \(0.744263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −191.918 | −1.06032 | −0.530160 | − | 0.847898i | \(-0.677868\pi\) | ||||
−0.530160 | + | 0.847898i | \(0.677868\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −108.926 | + | 62.8885i | −0.588790 | + | 0.339938i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.8115 | + | 48.1710i | −0.148725 | + | 0.257599i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 282.177 | + | 162.915i | 1.47737 | + | 0.852957i | 0.999673 | − | 0.0255698i | \(-0.00814000\pi\) |
0.477692 | + | 0.878527i | \(0.341473\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 54.3131 | + | 94.0730i | 0.281415 | + | 0.487425i | 0.971733 | − | 0.236081i | \(-0.0758629\pi\) |
−0.690319 | + | 0.723506i | \(0.742530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 308.666i | 1.56683i | 0.621499 | + | 0.783415i | \(0.286524\pi\) | ||||
−0.621499 | + | 0.783415i | \(0.713476\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 134.413 | 0.675444 | 0.337722 | − | 0.941246i | \(-0.390344\pi\) | ||||
0.337722 | + | 0.941246i | \(0.390344\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.3618 | − | 8.29180i | 0.0707478 | − | 0.0408463i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −47.5623 | + | 82.3803i | −0.232011 | + | 0.401855i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −46.2968 | − | 26.7295i | −0.221516 | − | 0.127892i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −166.831 | − | 288.960i | −0.790669 | − | 1.36948i | −0.925553 | − | 0.378618i | \(-0.876399\pi\) |
0.134883 | − | 0.990861i | \(-0.456934\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 40.1540i | − | 0.186763i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 34.8754 | 0.160716 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −178.075 | + | 102.812i | −0.805768 | + | 0.465211i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −113.790 | + | 197.090i | −0.510270 | + | 0.883814i | 0.489659 | + | 0.871914i | \(0.337121\pi\) |
−0.999929 | + | 0.0118998i | \(0.996212\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 57.6604 | + | 33.2902i | 0.254011 | + | 0.146653i | 0.621599 | − | 0.783335i | \(-0.286483\pi\) |
−0.367589 | + | 0.929988i | \(0.619817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 84.3328 | + | 146.069i | 0.368266 | + | 0.637855i | 0.989294 | − | 0.145933i | \(-0.0466184\pi\) |
−0.621029 | + | 0.783788i | \(0.713285\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 254.912i | 1.09404i | 0.837119 | + | 0.547021i | \(0.184238\pi\) | ||||
−0.837119 | + | 0.547021i | \(0.815762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.16718 | 0.0134774 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 267.457 | − | 154.416i | 1.11907 | − | 0.646094i | 0.177905 | − | 0.984048i | \(-0.443068\pi\) |
0.941163 | + | 0.337954i | \(0.109735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.45743 | − | 14.6487i | 0.0350931 | − | 0.0607830i | −0.847945 | − | 0.530084i | \(-0.822161\pi\) |
0.883039 | + | 0.469301i | \(0.155494\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 89.2375 | + | 51.5213i | 0.364235 | + | 0.210291i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −98.8115 | − | 171.147i | −0.400047 | − | 0.692901i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 433.082i | − | 1.72543i | −0.505693 | − | 0.862713i | \(-0.668763\pi\) | ||
0.505693 | − | 0.862713i | \(-0.331237\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.1215 | −0.111152 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.9978 | + | 12.1231i | −0.0817033 | + | 0.0471714i | −0.540295 | − | 0.841476i | \(-0.681687\pi\) |
0.458592 | + | 0.888647i | \(0.348354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −48.0426 | + | 83.2122i | −0.185493 | + | 0.321283i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −44.0909 | − | 25.4559i | −0.167646 | − | 0.0967904i | 0.413829 | − | 0.910354i | \(-0.364191\pi\) |
−0.581475 | + | 0.813564i | \(0.697524\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 78.3541 | + | 135.713i | 0.295676 | + | 0.512126i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 78.4133i | 0.291499i | 0.989322 | + | 0.145750i | \(0.0465594\pi\) | ||||
−0.989322 | + | 0.145750i | \(0.953441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −208.246 | −0.768436 | −0.384218 | − | 0.923242i | \(-0.625529\pi\) | ||||
−0.384218 | + | 0.923242i | \(0.625529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.0570 | − | 9.27051i | 0.0583891 | − | 0.0337109i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 93.5197 | − | 161.981i | 0.337616 | − | 0.584769i | −0.646367 | − | 0.763026i | \(-0.723713\pi\) |
0.983984 | + | 0.178258i | \(0.0570460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 185.435 | + | 107.061i | 0.659910 | + | 0.380999i | 0.792243 | − | 0.610206i | \(-0.208913\pi\) |
−0.132333 | + | 0.991205i | \(0.542247\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 213.520 | + | 369.827i | 0.754487 | + | 1.30681i | 0.945629 | + | 0.325247i | \(0.105447\pi\) |
−0.191142 | + | 0.981562i | \(0.561219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 72.6687i | 0.253201i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 64.0000 | 0.221453 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −120.304 | + | 69.4574i | −0.410593 | + | 0.237056i | −0.691045 | − | 0.722812i | \(-0.742849\pi\) |
0.280451 | + | 0.959868i | \(0.409516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.5197 | − | 59.7899i | 0.117016 | − | 0.202678i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −90.0298 | − | 51.9787i | −0.301103 | − | 0.173842i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.3375 | − | 26.5653i | −0.0509551 | − | 0.0882568i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 182.236i | − | 0.597495i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −169.502 | −0.552122 | −0.276061 | − | 0.961140i | \(-0.589029\pi\) | ||||
−0.276061 | + | 0.961140i | \(0.589029\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −152.963 | + | 88.3131i | −0.491842 | + | 0.283965i | −0.725338 | − | 0.688393i | \(-0.758317\pi\) |
0.233497 | + | 0.972358i | \(0.424983\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 42.5836 | − | 73.7569i | 0.136050 | − | 0.235645i | −0.789948 | − | 0.613174i | \(-0.789893\pi\) |
0.925998 | + | 0.377528i | \(0.123226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −414.679 | − | 239.415i | −1.30813 | − | 0.755252i | −0.326350 | − | 0.945249i | \(-0.605819\pi\) |
−0.981785 | + | 0.189997i | \(0.939152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.0000 | + | 31.1769i | 0.0564263 | + | 0.0977333i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 216.246i | − | 0.669493i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 68.5410 | 0.210895 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.09536 | − | 1.20976i | 0.00636888 | − | 0.00367707i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 157.626 | − | 273.017i | 0.476212 | − | 0.824823i | −0.523417 | − | 0.852077i | \(-0.675343\pi\) |
0.999629 | + | 0.0272536i | \(0.00867616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −27.1109 | − | 15.6525i | −0.0809280 | − | 0.0467238i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −45.7295 | − | 79.2058i | −0.135696 | − | 0.235032i | 0.790167 | − | 0.612891i | \(-0.209994\pi\) |
−0.925863 | + | 0.377859i | \(0.876660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 75.7082i | 0.222018i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 162.420 | 0.473526 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 365.315 | − | 210.915i | 1.05278 | − | 0.607824i | 0.129355 | − | 0.991598i | \(-0.458709\pi\) |
0.923427 | + | 0.383775i | \(0.125376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 209.871 | − | 363.507i | 0.601349 | − | 1.04157i | −0.391268 | − | 0.920277i | \(-0.627964\pi\) |
0.992617 | − | 0.121290i | \(-0.0387031\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −334.717 | − | 193.249i | −0.948208 | − | 0.547448i | −0.0556843 | − | 0.998448i | \(-0.517734\pi\) |
−0.892524 | + | 0.451000i | \(0.851067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.18847 | + | 3.79054i | 0.00616471 | + | 0.0106776i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 344.991i | − | 0.960977i | −0.877001 | − | 0.480488i | \(-0.840459\pi\) | ||
0.877001 | − | 0.480488i | \(-0.159541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −153.167 | −0.424286 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −52.5266 | + | 30.3262i | −0.143908 | + | 0.0830856i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 114.185 | − | 197.775i | 0.311132 | − | 0.538896i | −0.667476 | − | 0.744631i | \(-0.732625\pi\) |
0.978608 | + | 0.205735i | \(0.0659586\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 103.676 | + | 59.8572i | 0.279449 | + | 0.161340i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 320.079 | + | 554.393i | 0.858120 | + | 1.48631i | 0.873720 | + | 0.486430i | \(0.161701\pi\) |
−0.0155991 | + | 0.999878i | \(0.504966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 133.082i | 0.353003i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −537.164 | −1.41732 | −0.708660 | − | 0.705550i | \(-0.750700\pi\) | ||||
−0.708660 | + | 0.705550i | \(0.750700\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 135.671 | − | 78.3297i | 0.354232 | − | 0.204516i | −0.312315 | − | 0.949978i | \(-0.601105\pi\) |
0.666548 | + | 0.745462i | \(0.267771\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.08204 | − | 12.2665i | 0.0183949 | − | 0.0318609i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 164.003 | + | 94.6869i | 0.421600 | + | 0.243411i | 0.695762 | − | 0.718273i | \(-0.255067\pi\) |
−0.274161 | + | 0.961684i | \(0.588400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −56.8769 | − | 98.5138i | −0.145465 | − | 0.251953i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.1834i | 0.0764138i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −708.529 | −1.78471 | −0.892353 | − | 0.451337i | \(-0.850947\pi\) | ||||
−0.892353 | + | 0.451337i | \(0.850947\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −354.565 | + | 204.708i | −0.884202 | + | 0.510494i | −0.872042 | − | 0.489432i | \(-0.837204\pi\) |
−0.0121604 | + | 0.999926i | \(0.503871\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −139.936 | + | 242.377i | −0.347236 | + | 0.601431i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −180.639 | − | 104.292i | −0.443830 | − | 0.256245i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −196.664 | − | 340.632i | −0.480841 | − | 0.832842i | 0.518917 | − | 0.854825i | \(-0.326335\pi\) |
−0.999758 | + | 0.0219831i | \(0.993002\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 52.7415i | − | 0.127703i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 166.210 | 0.400505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 409.585 | − | 236.474i | 0.977530 | − | 0.564377i | 0.0760065 | − | 0.997107i | \(-0.475783\pi\) |
0.901524 | + | 0.432730i | \(0.142450\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 278.123 | − | 481.723i | 0.660625 | − | 1.14424i | −0.319827 | − | 0.947476i | \(-0.603625\pi\) |
0.980452 | − | 0.196760i | \(-0.0630419\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 64.9519 | + | 37.5000i | 0.152828 | + | 0.0882353i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −69.6080 | − | 120.565i | −0.163016 | − | 0.282353i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 453.866i | − | 1.05305i | −0.850159 | − | 0.526527i | \(-0.823494\pi\) | ||
0.850159 | − | 0.526527i | \(-0.176506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 564.043 | 1.30264 | 0.651319 | − | 0.758804i | \(-0.274216\pi\) | ||||
0.651319 | + | 0.758804i | \(0.274216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 94.6810 | − | 54.6641i | 0.216661 | − | 0.125089i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 94.9953 | − | 164.537i | 0.216390 | − | 0.374799i | −0.737311 | − | 0.675553i | \(-0.763905\pi\) |
0.953702 | + | 0.300754i | \(0.0972383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 393.673 | + | 227.287i | 0.888652 | + | 0.513064i | 0.873501 | − | 0.486822i | \(-0.161844\pi\) |
0.0151507 | + | 0.999885i | \(0.495177\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 137.562 | + | 238.265i | 0.309129 | + | 0.535427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 246.875i | − | 0.549834i | −0.961468 | − | 0.274917i | \(-0.911350\pi\) | ||
0.961468 | − | 0.274917i | \(-0.0886503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −157.751 | −0.349780 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 45.3457 | − | 26.1803i | 0.0996608 | − | 0.0575392i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −178.620 | + | 309.379i | −0.390853 | + | 0.676978i | −0.992562 | − | 0.121738i | \(-0.961153\pi\) |
0.601709 | + | 0.798715i | \(0.294487\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −506.975 | − | 292.702i | −1.09973 | − | 0.634928i | −0.163579 | − | 0.986530i | \(-0.552304\pi\) |
−0.936150 | + | 0.351602i | \(0.885637\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 409.498 | + | 709.272i | 0.884446 | + | 1.53191i | 0.846347 | + | 0.532631i | \(0.178797\pi\) |
0.0380985 | + | 0.999274i | \(0.487870\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 675.906i | − | 1.44734i | −0.690149 | − | 0.723668i | \(-0.742455\pi\) | ||
0.690149 | − | 0.723668i | \(-0.257545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.9149 | −0.0509912 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 57.6685 | − | 33.2949i | 0.121921 | − | 0.0703909i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.0410 | + | 62.4249i | −0.0758758 | + | 0.131421i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −822.824 | − | 475.058i | −1.71780 | − | 0.991770i | −0.922915 | − | 0.385003i | \(-0.874200\pi\) |
−0.794880 | − | 0.606767i | \(-0.792466\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −385.538 | − | 667.771i | −0.801534 | − | 1.38830i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 25.5279i | − | 0.0526348i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −66.2129 | −0.135961 | −0.0679804 | − | 0.997687i | \(-0.521656\pi\) | ||||
−0.0679804 | + | 0.997687i | \(0.521656\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 723.697 | − | 417.827i | 1.47392 | − | 0.850971i | 0.474356 | − | 0.880333i | \(-0.342681\pi\) |
0.999569 | + | 0.0293626i | \(0.00934776\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −72.8115 | + | 126.113i | −0.147691 | + | 0.255808i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.89572 | + | 1.67184i | 0.00582639 | + | 0.00336387i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 52.3754 | + | 90.7168i | 0.104961 | + | 0.181797i | 0.913722 | − | 0.406340i | \(-0.133195\pi\) |
−0.808761 | + | 0.588137i | \(0.799862\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 743.912i | − | 1.47895i | −0.673184 | − | 0.739475i | \(-0.735074\pi\) | ||
0.673184 | − | 0.739475i | \(-0.264926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 375.659 | 0.743880 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −632.551 | + | 365.204i | −1.24273 | + | 0.717492i | −0.969650 | − | 0.244498i | \(-0.921377\pi\) |
−0.273083 | + | 0.961990i | \(0.588043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.1672 | + | 40.1267i | −0.0453370 | + | 0.0785259i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.7646 | + | 21.8034i | 0.0733293 | + | 0.0423367i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.62616 | + | 4.54865i | 0.00507962 | + | 0.00879816i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 490.200i | − | 0.940884i | −0.882431 | − | 0.470442i | \(-0.844095\pi\) | ||
0.882431 | − | 0.470442i | \(-0.155905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.12772 | 0.0155406 | 0.00777028 | − | 0.999970i | \(-0.497527\pi\) | ||||
0.00777028 | + | 0.999970i | \(0.497527\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −265.217 | + | 153.123i | −0.503258 | + | 0.290556i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −235.745 | + | 408.322i | −0.445642 | + | 0.771874i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −505.032 | − | 291.580i | −0.947528 | − | 0.547055i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 226.957 | + | 393.102i | 0.424219 | + | 0.734770i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 170.882i | 0.317035i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −98.8390 | −0.182697 | −0.0913485 | − | 0.995819i | \(-0.529118\pi\) | ||||
−0.0913485 | + | 0.995819i | \(0.529118\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −62.1266 | + | 35.8688i | −0.113994 | + | 0.0658143i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 110.310 | − | 191.062i | 0.201664 | − | 0.349292i | −0.747401 | − | 0.664373i | \(-0.768699\pi\) |
0.949065 | + | 0.315082i | \(0.102032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −121.207 | − | 69.9787i | −0.219976 | − | 0.127003i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.5291 | + | 19.9689i | 0.0208482 | + | 0.0361101i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 440.164i | − | 0.790241i | −0.918629 | − | 0.395120i | \(-0.870703\pi\) | ||
0.918629 | − | 0.395120i | \(-0.129297\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 246.164 | 0.440365 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 351.311 | − | 202.830i | 0.623999 | − | 0.360266i | −0.154425 | − | 0.988004i | \(-0.549353\pi\) |
0.778424 | + | 0.627739i | \(0.216019\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.79335 | + | 4.83822i | −0.00494398 | + | 0.00856323i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.9640 | + | 23.6506i | 0.0719929 | + | 0.0415651i | 0.535564 | − | 0.844494i | \(-0.320099\pi\) |
−0.463571 | + | 0.886060i | \(0.653432\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −352.959 | − | 611.343i | −0.618142 | − | 1.07065i | −0.989825 | − | 0.142293i | \(-0.954552\pi\) |
0.371683 | − | 0.928360i | \(-0.378781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.9180i | 0.0659443i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 537.860 | 0.932166 | 0.466083 | − | 0.884741i | \(-0.345665\pi\) | ||||
0.466083 | + | 0.884741i | \(0.345665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 109.962 | − | 63.4865i | 0.189263 | − | 0.109271i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −129.939 | + | 225.061i | −0.222880 | + | 0.386040i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −108.395 | − | 62.5820i | −0.184660 | − | 0.106613i | 0.404820 | − | 0.914396i | \(-0.367334\pi\) |
−0.589480 | + | 0.807783i | \(0.700667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −147.166 | − | 254.898i | −0.249857 | − | 0.432765i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 357.413i | 0.602721i | 0.953510 | + | 0.301360i | \(0.0974407\pi\) | ||||
−0.953510 | + | 0.301360i | \(0.902559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 57.2949 | 0.0962940 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 489.402 | − | 282.556i | 0.817031 | − | 0.471713i | −0.0323606 | − | 0.999476i | \(-0.510303\pi\) |
0.849392 | + | 0.527763i | \(0.176969\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −230.953 | + | 400.022i | −0.384281 | + | 0.665594i | −0.991669 | − | 0.128811i | \(-0.958884\pi\) |
0.607388 | + | 0.794405i | \(0.292217\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −207.687 | − | 119.908i | −0.343285 | − | 0.198195i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −364.310 | − | 631.003i | −0.600181 | − | 1.03954i | −0.992793 | − | 0.119840i | \(-0.961762\pi\) |
0.392612 | − | 0.919704i | \(-0.371572\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.4164i | 0.0317781i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 912.741 | 1.48897 | 0.744487 | − | 0.667637i | \(-0.232694\pi\) | ||||
0.744487 | + | 0.667637i | \(0.232694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −84.2887 | + | 48.6641i | −0.136610 | + | 0.0788721i | −0.566748 | − | 0.823891i | \(-0.691799\pi\) |
0.430137 | + | 0.902764i | \(0.358465\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −171.371 | + | 296.823i | −0.276851 | + | 0.479520i | −0.970600 | − | 0.240696i | \(-0.922624\pi\) |
0.693749 | + | 0.720216i | \(0.255957\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 182.018 | + | 105.088i | 0.292164 | + | 0.168681i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 843.738i | − | 1.34140i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1002.15 | −1.58820 | −0.794100 | − | 0.607787i | \(-0.792058\pi\) | ||||
−0.794100 | + | 0.607787i | \(0.792058\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 202.843 | − | 117.111i | 0.319438 | − | 0.184427i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −315.851 | + | 547.070i | −0.495841 | + | 0.858823i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −868.405 | − | 501.374i | −1.35477 | − | 0.782174i | −0.365853 | − | 0.930673i | \(-0.619223\pi\) |
−0.988913 | + | 0.148498i | \(0.952556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 265.188 | + | 459.320i | 0.412424 | + | 0.714339i | 0.995154 | − | 0.0983266i | \(-0.0313490\pi\) |
−0.582730 | + | 0.812666i | \(0.698016\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 450.325i | − | 0.696020i | −0.937491 | − | 0.348010i | \(-0.886857\pi\) | ||
0.937491 | − | 0.348010i | \(-0.113143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 114.492 | 0.176413 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 497.885 | − | 287.454i | 0.762459 | − | 0.440206i | −0.0677192 | − | 0.997704i | \(-0.521572\pi\) |
0.830178 | + | 0.557499i | \(0.188239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −204.787 | + | 354.702i | −0.312652 | + | 0.541529i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 472.007 | + | 272.514i | 0.716248 | + | 0.413526i | 0.813370 | − | 0.581747i | \(-0.197630\pi\) |
−0.0971223 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −395.249 | − | 684.592i | −0.597956 | − | 1.03569i | −0.993122 | − | 0.117081i | \(-0.962646\pi\) |
0.395166 | − | 0.918610i | \(-0.370687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55.0658i | 0.0828057i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −73.6231 | −0.110379 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 261.724 | − | 151.106i | 0.390051 | − | 0.225196i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −526.684 | + | 912.243i | −0.782591 | + | 1.35549i | 0.147837 | + | 0.989012i | \(0.452769\pi\) |
−0.930428 | + | 0.366476i | \(0.880564\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 439.220 | + | 253.584i | 0.648774 | + | 0.374570i | 0.787986 | − | 0.615693i | \(-0.211124\pi\) |
−0.139213 | + | 0.990263i | \(0.544457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.75078 | − | 16.8888i | −0.0143605 | − | 0.0248731i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1322.49i | − | 1.93629i | −0.250382 | − | 0.968147i | \(-0.580556\pi\) | ||
0.250382 | − | 0.968147i | \(-0.419444\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −202.368 | −0.295427 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −831.990 | + | 480.349i | −1.20753 | + | 0.697169i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 244.749 | − | 423.918i | 0.354196 | − | 0.613485i | −0.632784 | − | 0.774328i | \(-0.718088\pi\) |
0.986980 | + | 0.160843i | \(0.0514213\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −345.661 | − | 199.567i | −0.497354 | − | 0.287147i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −319.058 | − | 552.624i | −0.457758 | − | 0.792861i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1063.50i | 1.51711i | 0.651608 | + | 0.758556i | \(0.274095\pi\) | ||||
−0.651608 | + | 0.758556i | \(0.725905\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 810.912 | 1.15350 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 248.530 | − | 143.489i | 0.351528 | − | 0.202955i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 206.836 | − | 358.250i | 0.291729 | − | 0.505290i | −0.682490 | − | 0.730895i | \(-0.739103\pi\) |
0.974219 | + | 0.225606i | \(0.0724361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −134.086 | − | 77.4149i | −0.188060 | − | 0.108576i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56.8328 | + | 98.4373i | 0.0794865 | + | 0.137675i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 69.0883i | − | 0.0960894i | −0.998845 | − | 0.0480447i | \(-0.984701\pi\) | ||
0.998845 | − | 0.0480447i | \(-0.0152990\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.3126 | 0.0462034 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42.0378 | − | 24.2705i | 0.0579831 | − | 0.0334766i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 712.498 | − | 1234.08i | 0.980053 | − | 1.69750i | 0.317915 | − | 0.948119i | \(-0.397017\pi\) |
0.662138 | − | 0.749382i | \(-0.269649\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 233.274 | + | 134.681i | 0.319116 | + | 0.184242i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 648.249 | + | 1122.80i | 0.884378 | + | 1.53179i | 0.846425 | + | 0.532508i | \(0.178751\pi\) |
0.0379535 | + | 0.999280i | \(0.487916\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 51.9149i | − | 0.0704408i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 356.246 | 0.482065 | 0.241033 | − | 0.970517i | \(-0.422514\pi\) | ||||
0.241033 | + | 0.970517i | \(0.422514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −850.584 | + | 491.085i | −1.14480 | + | 0.660949i | −0.947614 | − | 0.319418i | \(-0.896513\pi\) |
−0.197183 | + | 0.980367i | \(0.563179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −163.185 | + | 282.645i | −0.219041 | + | 0.379390i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 300.303 | + | 173.380i | 0.400939 | + | 0.231482i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −389.245 | − | 674.191i | −0.518302 | − | 0.897725i | −0.999774 | − | 0.0212635i | \(-0.993231\pi\) |
0.481472 | − | 0.876461i | \(-0.340102\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 337.639i | 0.447204i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −160.748 | −0.212348 | −0.106174 | − | 0.994348i | \(-0.533860\pi\) | ||||
−0.106174 | + | 0.994348i | \(0.533860\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 553.851 | − | 319.766i | 0.727793 | − | 0.420192i | −0.0898210 | − | 0.995958i | \(-0.528630\pi\) |
0.817614 | + | 0.575766i | \(0.195296\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.4013 | + | 47.4605i | −0.0359126 | + | 0.0622025i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 366.542 | + | 211.623i | 0.477890 | + | 0.275910i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −276.336 | − | 478.628i | −0.359345 | − | 0.622403i | 0.628507 | − | 0.777804i | \(-0.283666\pi\) |
−0.987851 | + | 0.155401i | \(0.950333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 934.909i | 1.20945i | 0.796432 | + | 0.604727i | \(0.206718\pi\) | ||||
−0.796432 | + | 0.604727i | \(0.793282\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 102.082 | 0.131719 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 531.124 | − | 306.644i | 0.681802 | − | 0.393638i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.62927 | + | 6.28608i | −0.00464695 | + | 0.00804876i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31.5489 | − | 18.2148i | −0.0401897 | − | 0.0232035i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.5623 | − | 89.3085i | −0.0655175 | − | 0.113480i | 0.831406 | − | 0.555666i | \(-0.187536\pi\) |
−0.896923 | + | 0.442186i | \(0.854203\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.26786i | 0.00539552i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1117.20 | 1.40882 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1289.71 | + | 744.615i | −1.61821 | + | 0.934273i | −0.630824 | + | 0.775926i | \(0.717283\pi\) |
−0.987384 | + | 0.158347i | \(0.949384\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.6231 | + | 18.3997i | −0.0132954 | + | 0.0230284i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −87.1079 | − | 50.2918i | −0.108478 | − | 0.0626299i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.4834 | + | 25.0859i | 0.0179918 | + | 0.0311627i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 278.213i | − | 0.343897i | −0.985106 | − | 0.171949i | \(-0.944994\pi\) | ||
0.985106 | − | 0.171949i | \(-0.0550063\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −838.158 | −1.03349 | −0.516743 | − | 0.856140i | \(-0.672856\pi\) | ||||
−0.516743 | + | 0.856140i | \(0.672856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 576.745 | − | 332.984i | 0.707662 | − | 0.408569i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −129.441 | + | 224.198i | −0.158434 | + | 0.274416i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −464.774 | − | 268.337i | −0.566107 | − | 0.326842i | 0.189486 | − | 0.981883i | \(-0.439318\pi\) |
−0.755593 | + | 0.655041i | \(0.772651\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 586.602 | + | 1016.02i | 0.712760 | + | 1.23454i | 0.963817 | + | 0.266565i | \(0.0858886\pi\) |
−0.251057 | + | 0.967972i | \(0.580778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 677.754i | − | 0.819533i | −0.912190 | − | 0.409767i | \(-0.865610\pi\) | ||
0.912190 | − | 0.409767i | \(-0.134390\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −141.234 | −0.170366 | −0.0851832 | − | 0.996365i | \(-0.527148\pi\) | ||||
−0.0851832 | + | 0.996365i | \(0.527148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −598.623 | + | 345.615i | −0.718635 | + | 0.414904i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 232.643 | − | 402.949i | 0.278614 | − | 0.482574i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −351.464 | − | 202.918i | −0.418908 | − | 0.241857i | 0.275702 | − | 0.961243i | \(-0.411090\pi\) |
−0.694610 | + | 0.719386i | \(0.744423\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −373.375 | − | 646.705i | −0.443966 | − | 0.768972i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.2949i | 0.0500531i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −183.204 | −0.216297 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 369.421 | − | 213.286i | 0.434103 | − | 0.250629i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 428.492 | − | 742.170i | 0.502336 | − | 0.870071i | −0.497661 | − | 0.867372i | \(-0.665808\pi\) |
0.999996 | − | 0.00269898i | \(-0.000859113\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 148.159 | + | 85.5395i | 0.172881 | + | 0.0998127i | 0.583943 | − | 0.811794i | \(-0.301509\pi\) |
−0.411063 | + | 0.911607i | \(0.634842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 668.861 | + | 1158.50i | 0.778651 | + | 1.34866i | 0.932719 | + | 0.360603i | \(0.117429\pi\) |
−0.154068 | + | 0.988060i | \(0.549238\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 768.659i | 0.890683i | 0.895361 | + | 0.445341i | \(0.146918\pi\) | ||||
−0.895361 | + | 0.445341i | \(0.853082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 73.0426 | 0.0844423 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.3489 | + | 25.0275i | −0.0498837 | + | 0.0288003i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 95.9574 | − | 166.203i | 0.110169 | − | 0.190819i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.5396 | − | 9.54915i | −0.0189024 | − | 0.0109133i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −103.526 | − | 179.312i | −0.118046 | − | 0.204461i | 0.800948 | − | 0.598735i | \(-0.204330\pi\) |
−0.918993 | + | 0.394274i | \(0.870996\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1384.61i | 1.57164i | 0.618456 | + | 0.785819i | \(0.287758\pi\) | ||||
−0.618456 | + | 0.785819i | \(0.712242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −317.525 | −0.359599 | −0.179799 | − | 0.983703i | \(-0.557545\pi\) | ||||
−0.179799 | + | 0.983703i | \(0.557545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −688.201 | + | 397.333i | −0.775874 | + | 0.447951i | −0.834966 | − | 0.550301i | \(-0.814513\pi\) |
0.0590918 | + | 0.998253i | \(0.481180\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 89.4652 | − | 154.958i | 0.100636 | − | 0.174306i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.6838 | − | 10.2098i | −0.0198027 | − | 0.0114331i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 288.079 | + | 498.967i | 0.321876 | + | 0.557505i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 198.207i | 0.220475i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1051.23 | −1.16674 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −371.648 | + | 214.571i | −0.410660 | + | 0.237095i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 268.371 | − | 464.832i | 0.295888 | − | 0.512494i | −0.679303 | − | 0.733858i | \(-0.737718\pi\) |
0.975191 | + | 0.221364i | \(0.0710510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −773.384 | − | 446.514i | −0.848940 | − | 0.490136i | 0.0113532 | − | 0.999936i | \(-0.496386\pi\) |
−0.860293 | + | 0.509800i | \(0.829719\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 137.818 | + | 238.707i | 0.150950 | + | 0.261454i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 312.887i | 0.341207i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −965.988 | −1.05113 | −0.525565 | − | 0.850754i | \(-0.676146\pi\) | ||||
−0.525565 | + | 0.850754i | \(0.676146\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.2379 | + | 13.4164i | −0.0251765 | + | 0.0145357i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −140.623 | + | 243.566i | −0.152025 | + | 0.263315i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1115.10 | + | 643.805i | 1.20033 | + | 0.693009i | 0.960628 | − | 0.277838i | \(-0.0896180\pi\) |
0.239699 | + | 0.970847i | \(0.422951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −332.169 | − | 575.333i | −0.356787 | − | 0.617973i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 124.377i | 0.133023i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −932.328 | −0.995014 | −0.497507 | − | 0.867460i | \(-0.665751\pi\) | ||||
−0.497507 | + | 0.867460i | \(0.665751\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 615.173 | − | 355.170i | 0.653744 | − | 0.377439i | −0.136145 | − | 0.990689i | \(-0.543471\pi\) |
0.789889 | + | 0.613250i | \(0.210138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 161.307 | − | 279.392i | 0.171057 | − | 0.296280i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1405.41 | + | 811.412i | 1.48406 | + | 0.856823i | 0.999836 | − | 0.0181197i | \(-0.00576799\pi\) |
0.484226 | + | 0.874943i | \(0.339101\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −185.915 | − | 322.014i | −0.195906 | − | 0.339319i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33.2461i | − | 0.0348857i | −0.999848 | − | 0.0174429i | \(-0.994447\pi\) | ||
0.999848 | − | 0.0174429i | \(-0.00555252\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 728.577 | 0.762908 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −133.883 | + | 77.2976i | −0.139607 | + | 0.0806022i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 272.085 | − | 471.265i | 0.283127 | − | 0.490391i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 210.354 | + | 121.448i | 0.217983 | + | 0.125853i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 132.240 | + | 229.046i | 0.136753 | + | 0.236863i | 0.926266 | − | 0.376871i | \(-0.123000\pi\) |
−0.789513 | + | 0.613734i | \(0.789667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1477.22i | 1.52134i | 0.649139 | + | 0.760670i | \(0.275129\pi\) | ||||
−0.649139 | + | 0.760670i | \(0.724871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −304.912 | −0.313373 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 332.980 | − | 192.246i | 0.340819 | − | 0.196772i | −0.319815 | − | 0.947480i | \(-0.603621\pi\) |
0.660634 | + | 0.750708i | \(0.270288\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −228.128 | + | 395.129i | −0.233021 | + | 0.403604i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 925.912 | + | 534.576i | 0.941925 | + | 0.543821i | 0.890563 | − | 0.454859i | \(-0.150310\pi\) |
0.0513619 | + | 0.998680i | \(0.483644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 345.099 | + | 597.728i | 0.350354 | + | 0.606831i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 136.182i | 0.137696i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −233.012 | −0.235129 | −0.117564 | − | 0.993065i | \(-0.537509\pi\) | ||||
−0.117564 | + | 0.993065i | \(0.537509\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 260.290 | − | 150.279i | 0.261598 | − | 0.151034i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 124.061 | − | 214.880i | 0.124434 | − | 0.215526i | −0.797078 | − | 0.603877i | \(-0.793622\pi\) |
0.921512 | + | 0.388351i | \(0.126955\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1620.3.o.e.1241.4 | 8 | ||
3.2 | odd | 2 | inner | 1620.3.o.e.1241.2 | 8 | ||
9.2 | odd | 6 | 540.3.g.d.161.1 | ✓ | 4 | ||
9.4 | even | 3 | inner | 1620.3.o.e.701.2 | 8 | ||
9.5 | odd | 6 | inner | 1620.3.o.e.701.4 | 8 | ||
9.7 | even | 3 | 540.3.g.d.161.3 | yes | 4 | ||
36.7 | odd | 6 | 2160.3.l.e.161.4 | 4 | |||
36.11 | even | 6 | 2160.3.l.e.161.2 | 4 | |||
45.2 | even | 12 | 2700.3.b.l.1349.2 | 4 | |||
45.7 | odd | 12 | 2700.3.b.g.1349.2 | 4 | |||
45.29 | odd | 6 | 2700.3.g.n.701.4 | 4 | |||
45.34 | even | 6 | 2700.3.g.n.701.3 | 4 | |||
45.38 | even | 12 | 2700.3.b.g.1349.3 | 4 | |||
45.43 | odd | 12 | 2700.3.b.l.1349.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.3.g.d.161.1 | ✓ | 4 | 9.2 | odd | 6 | ||
540.3.g.d.161.3 | yes | 4 | 9.7 | even | 3 | ||
1620.3.o.e.701.2 | 8 | 9.4 | even | 3 | inner | ||
1620.3.o.e.701.4 | 8 | 9.5 | odd | 6 | inner | ||
1620.3.o.e.1241.2 | 8 | 3.2 | odd | 2 | inner | ||
1620.3.o.e.1241.4 | 8 | 1.1 | even | 1 | trivial | ||
2160.3.l.e.161.2 | 4 | 36.11 | even | 6 | |||
2160.3.l.e.161.4 | 4 | 36.7 | odd | 6 | |||
2700.3.b.g.1349.2 | 4 | 45.7 | odd | 12 | |||
2700.3.b.g.1349.3 | 4 | 45.38 | even | 12 | |||
2700.3.b.l.1349.2 | 4 | 45.2 | even | 12 | |||
2700.3.b.l.1349.3 | 4 | 45.43 | odd | 12 | |||
2700.3.g.n.701.3 | 4 | 45.34 | even | 6 | |||
2700.3.g.n.701.4 | 4 | 45.29 | odd | 6 |