Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(101,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 11 x^{10} + 60 x^{9} - 120 x^{8} - 342 x^{7} + 2709 x^{6} - 3078 x^{5} - 9720 x^{4} + 43740 x^{3} - 72171 x^{2} - 118098 x + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 401.1 | ||
Root | \(2.89597 - 0.783177i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.401 |
Dual form | 900.3.p.c.101.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.89597 | + | 0.783177i | −0.965323 | + | 0.261059i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35650 | + | 4.08158i | 0.336643 | + | 0.583083i | 0.983799 | − | 0.179274i | \(-0.0573750\pi\) |
−0.647156 | + | 0.762358i | \(0.724042\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.77327 | − | 4.53611i | 0.863696 | − | 0.504013i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.6882 | − | 9.63493i | 1.51711 | − | 0.875902i | 0.517310 | − | 0.855798i | \(-0.326934\pi\) |
0.999798 | − | 0.0201041i | \(-0.00639976\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.68482 | + | 8.11434i | −0.360370 | + | 0.624180i | −0.988022 | − | 0.154315i | \(-0.950683\pi\) |
0.627651 | + | 0.778495i | \(0.284016\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 16.2489i | − | 0.955816i | −0.878410 | − | 0.477908i | \(-0.841395\pi\) | ||
0.878410 | − | 0.477908i | \(-0.158605\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0505 | −1.00266 | −0.501328 | − | 0.865257i | \(-0.667155\pi\) | ||||
−0.501328 | + | 0.865257i | \(0.667155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.0210 | − | 9.97458i | −0.477189 | − | 0.474980i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −14.3817 | − | 8.30327i | −0.625290 | − | 0.361012i | 0.153635 | − | 0.988128i | \(-0.450902\pi\) |
−0.778926 | + | 0.627116i | \(0.784235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −18.9586 | + | 19.2243i | −0.702169 | + | 0.712011i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.87581 | + | 2.23770i | −0.133649 | + | 0.0771621i | −0.565334 | − | 0.824862i | \(-0.691253\pi\) |
0.431685 | + | 0.902024i | \(0.357919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.19383 | + | 12.4601i | −0.232059 | + | 0.401938i | −0.958414 | − | 0.285382i | \(-0.907880\pi\) |
0.726355 | + | 0.687320i | \(0.241213\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −40.7826 | + | 40.9723i | −1.23584 | + | 1.24158i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 55.6092 | 1.50295 | 0.751476 | − | 0.659761i | \(-0.229342\pi\) | ||||
0.751476 | + | 0.659761i | \(0.229342\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.21211 | − | 27.1679i | 0.184926 | − | 0.696613i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 26.7067 | + | 15.4191i | 0.651384 | + | 0.376077i | 0.788986 | − | 0.614411i | \(-0.210606\pi\) |
−0.137602 | + | 0.990488i | \(0.543940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.5538 | − | 37.3322i | −0.501250 | − | 0.868191i | −0.999999 | − | 0.00144406i | \(-0.999540\pi\) |
0.498749 | − | 0.866747i | \(-0.333793\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 35.9308 | − | 20.7446i | 0.764484 | − | 0.441375i | −0.0664192 | − | 0.997792i | \(-0.521157\pi\) |
0.830903 | + | 0.556417i | \(0.187824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.3938 | − | 23.1987i | 0.273343 | − | 0.473443i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.7257 | + | 47.0562i | 0.249524 | + | 0.922671i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 30.7037i | − | 0.579316i | −0.957130 | − | 0.289658i | \(-0.906458\pi\) | ||
0.957130 | − | 0.289658i | \(-0.0935415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 55.1696 | − | 14.9199i | 0.967887 | − | 0.261753i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 74.4236 | + | 42.9685i | 1.26142 | + | 0.728279i | 0.973348 | − | 0.229331i | \(-0.0736538\pi\) |
0.288068 | + | 0.957610i | \(0.406987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −51.7462 | − | 89.6270i | −0.848298 | − | 1.46930i | −0.882726 | − | 0.469889i | \(-0.844294\pi\) |
0.0344274 | − | 0.999407i | \(-0.489039\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 36.8323 | + | 21.0379i | 0.584639 | + | 0.333934i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 61.7879 | − | 107.020i | 0.922207 | − | 1.59731i | 0.126215 | − | 0.992003i | \(-0.459717\pi\) |
0.795992 | − | 0.605307i | \(-0.206950\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48.1518 | + | 12.7826i | 0.697853 | + | 0.185255i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 111.409i | 1.56914i | 0.620043 | + | 0.784568i | \(0.287115\pi\) | ||||
−0.620043 | + | 0.784568i | \(0.712885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 90.5781 | 1.24080 | 0.620398 | − | 0.784287i | \(-0.286971\pi\) | ||||
0.620398 | + | 0.784287i | \(0.286971\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 78.6515 | + | 45.4095i | 1.02145 | + | 0.589733i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 41.6569 | + | 72.1519i | 0.527302 | + | 0.913315i | 0.999494 | + | 0.0318185i | \(0.0101299\pi\) |
−0.472191 | + | 0.881496i | \(0.656537\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 39.8473 | − | 70.5208i | 0.491942 | − | 0.870628i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −31.0471 | + | 17.9251i | −0.374062 | + | 0.215965i | −0.675231 | − | 0.737606i | \(-0.735956\pi\) |
0.301170 | + | 0.953571i | \(0.402623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.47171 | − | 9.51576i | 0.108870 | − | 0.109377i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 84.9144i | − | 0.954095i | −0.878878 | − | 0.477047i | \(-0.841707\pi\) | ||
0.878878 | − | 0.477047i | \(-0.158293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −44.1591 | −0.485265 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.0747 | − | 41.7181i | 0.119082 | − | 0.448581i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.6259 | − | 91.1508i | −0.542535 | − | 0.939699i | −0.998758 | − | 0.0498329i | \(-0.984131\pi\) |
0.456222 | − | 0.889866i | \(-0.349202\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 86.0166 | − | 150.594i | 0.868854 | − | 1.52116i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 69.4641 | − | 40.1051i | 0.687763 | − | 0.397080i | −0.115010 | − | 0.993364i | \(-0.536690\pi\) |
0.802773 | + | 0.596284i | \(0.203357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −65.2103 | + | 112.947i | −0.633109 | + | 1.09658i | 0.353803 | + | 0.935320i | \(0.384888\pi\) |
−0.986912 | + | 0.161258i | \(0.948445\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 49.8390i | 0.465785i | 0.972502 | + | 0.232893i | \(0.0748191\pi\) | ||||
−0.972502 | + | 0.232893i | \(0.925181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 121.431 | 1.11404 | 0.557022 | − | 0.830498i | \(-0.311944\pi\) | ||||
0.557022 | + | 0.830498i | \(0.311944\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −161.043 | + | 43.5519i | −1.45083 | + | 0.392359i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 24.4862 | + | 14.1371i | 0.216692 | + | 0.125107i | 0.604418 | − | 0.796668i | \(-0.293406\pi\) |
−0.387725 | + | 0.921775i | \(0.626739\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.391246 | + | 84.3258i | 0.00334398 | + | 0.720733i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 66.3211 | − | 38.2905i | 0.557320 | − | 0.321769i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 125.164 | − | 216.790i | 1.03441 | − | 1.79165i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −89.4178 | − | 23.7372i | −0.726974 | − | 0.192986i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 44.8753 | 0.353349 | 0.176674 | − | 0.984269i | \(-0.443466\pi\) | ||||
0.176674 | + | 0.984269i | \(0.443466\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 91.6567 | + | 91.2324i | 0.710517 | + | 0.707228i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 63.7326 | + | 36.7960i | 0.486508 | + | 0.280886i | 0.723125 | − | 0.690717i | \(-0.242705\pi\) |
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −44.8925 | − | 77.7561i | −0.337538 | − | 0.584632i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 188.952 | − | 109.091i | 1.37921 | − | 0.796286i | 0.387144 | − | 0.922019i | \(-0.373461\pi\) |
0.992064 | + | 0.125733i | \(0.0401282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 33.0004 | − | 57.1584i | 0.237413 | − | 0.411212i | −0.722558 | − | 0.691310i | \(-0.757034\pi\) |
0.959971 | + | 0.280099i | \(0.0903672\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −87.8076 | + | 88.2160i | −0.622749 | + | 0.625645i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 180.551i | 1.26260i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20.6193 | + | 77.6725i | −0.140267 | + | 0.528384i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −169.401 | − | 97.8035i | −1.13692 | − | 0.656399i | −0.191252 | − | 0.981541i | \(-0.561255\pi\) |
−0.945665 | + | 0.325142i | \(0.894588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 79.5523 | + | 137.789i | 0.526836 | + | 0.912507i | 0.999511 | + | 0.0312701i | \(0.00995522\pi\) |
−0.472675 | + | 0.881237i | \(0.656711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −73.7067 | − | 126.307i | −0.481743 | − | 0.825534i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −64.1927 | + | 111.185i | −0.408871 | + | 0.708185i | −0.994764 | − | 0.102204i | \(-0.967411\pi\) |
0.585893 | + | 0.810389i | \(0.300744\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.0465 | + | 88.9170i | 0.151236 | + | 0.559227i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 78.2667i | − | 0.486129i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.6963 | −0.133106 | −0.0665531 | − | 0.997783i | \(-0.521200\pi\) | ||||
−0.0665531 | + | 0.997783i | \(0.521200\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 219.896 | + | 126.957i | 1.31674 | + | 0.760223i | 0.983204 | − | 0.182513i | \(-0.0584230\pi\) |
0.333541 | + | 0.942736i | \(0.391756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 40.6050 | + | 70.3299i | 0.240266 | + | 0.416153i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −148.084 | + | 86.4151i | −0.865991 | + | 0.505352i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 51.4018 | − | 29.6768i | 0.297120 | − | 0.171542i | −0.344028 | − | 0.938959i | \(-0.611792\pi\) |
0.641148 | + | 0.767417i | \(0.278458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −249.180 | − | 66.1485i | −1.40780 | − | 0.373720i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.43887i | 0.0303848i | 0.999885 | + | 0.0151924i | \(0.00483607\pi\) | ||||
−0.999885 | + | 0.0151924i | \(0.995164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 45.4874 | 0.251312 | 0.125656 | − | 0.992074i | \(-0.459896\pi\) | ||||
0.125656 | + | 0.992074i | \(0.459896\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 220.049 | + | 219.031i | 1.20245 | + | 1.19689i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −156.557 | − | 271.164i | −0.837201 | − | 1.45007i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −123.141 | − | 32.0788i | −0.651542 | − | 0.169729i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 199.987 | − | 115.463i | 1.04705 | − | 0.604516i | 0.125230 | − | 0.992128i | \(-0.460033\pi\) |
0.921823 | + | 0.387612i | \(0.126700\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 36.4441 | − | 63.1231i | 0.188830 | − | 0.327063i | −0.756031 | − | 0.654536i | \(-0.772864\pi\) |
0.944860 | + | 0.327474i | \(0.106197\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 39.2251i | 0.199112i | 0.995032 | + | 0.0995561i | \(0.0317423\pi\) | ||||
−0.995032 | + | 0.0995561i | \(0.968258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −268.068 | −1.34707 | −0.673537 | − | 0.739154i | \(-0.735226\pi\) | ||||
−0.673537 | + | 0.739154i | \(0.735226\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −95.1203 | + | 358.317i | −0.473235 | + | 1.78267i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.2667 | − | 10.5463i | −0.0899838 | − | 0.0519522i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −149.457 | + | 0.693436i | −0.722015 | + | 0.00334993i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −317.918 | + | 183.550i | −1.52114 | + | 0.878229i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 173.445 | − | 300.416i | 0.822015 | − | 1.42377i | −0.0821652 | − | 0.996619i | \(-0.526184\pi\) |
0.904180 | − | 0.427152i | \(-0.140483\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −87.2527 | − | 322.636i | −0.409637 | − | 1.51472i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −67.8092 | −0.312485 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −262.311 | + | 70.9387i | −1.19777 | + | 0.323921i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 131.849 | + | 76.1229i | 0.596601 | + | 0.344448i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −35.3838 | − | 61.2866i | −0.158672 | − | 0.274828i | 0.775718 | − | 0.631080i | \(-0.217388\pi\) |
−0.934390 | + | 0.356252i | \(0.884055\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −232.838 | + | 134.429i | −1.02572 | + | 0.592199i | −0.915755 | − | 0.401737i | \(-0.868407\pi\) |
−0.109963 | + | 0.993936i | \(0.535073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −103.497 | + | 179.261i | −0.451950 | + | 0.782801i | −0.998507 | − | 0.0546210i | \(-0.982605\pi\) |
0.546557 | + | 0.837422i | \(0.315938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −263.336 | − | 69.9063i | −1.13998 | − | 0.302625i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 47.4893i | − | 0.203817i | −0.994794 | − | 0.101908i | \(-0.967505\pi\) | ||
0.994794 | − | 0.101908i | \(-0.0324948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −177.145 | − | 176.325i | −0.747446 | − | 0.743986i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −288.824 | − | 166.753i | −1.20847 | − | 0.697710i | −0.246045 | − | 0.969258i | \(-0.579131\pi\) |
−0.962425 | + | 0.271548i | \(0.912464\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −213.356 | − | 369.544i | −0.885296 | − | 1.53338i | −0.845374 | − | 0.534176i | \(-0.820622\pi\) |
−0.0399229 | − | 0.999203i | \(-0.512711\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −60.1663 | + | 235.434i | −0.247598 | + | 0.968863i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 89.2480 | − | 154.582i | 0.361328 | − | 0.625838i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 75.8730 | − | 76.2258i | 0.304711 | − | 0.306128i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 394.340i | 1.57107i | 0.618814 | + | 0.785537i | \(0.287613\pi\) | ||||
−0.618814 | + | 0.785537i | \(0.712387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −320.005 | −1.26484 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 313.600 | + | 181.057i | 1.22023 | + | 0.704503i | 0.964968 | − | 0.262368i | \(-0.0845033\pi\) |
0.255267 | + | 0.966871i | \(0.417837\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 131.043 | + | 226.974i | 0.505959 | + | 0.876346i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.9772 | + | 34.9754i | −0.0765412 | + | 0.134005i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 294.065 | − | 169.779i | 1.11812 | − | 0.645546i | 0.177198 | − | 0.984175i | \(-0.443297\pi\) |
0.940920 | + | 0.338630i | \(0.109963\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 66.5031 | + | 245.910i | 0.249075 | + | 0.921010i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.2060i | 0.0862678i | 0.999069 | + | 0.0431339i | \(0.0137342\pi\) | ||||
−0.999069 | + | 0.0431339i | \(0.986266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −433.939 | −1.60125 | −0.800626 | − | 0.599165i | \(-0.795499\pi\) | ||||
−0.800626 | + | 0.599165i | \(0.795499\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 127.883 | − | 34.5844i | 0.468438 | − | 0.126683i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −170.725 | − | 295.704i | −0.616336 | − | 1.06752i | −0.990149 | − | 0.140021i | \(-0.955283\pi\) |
0.373813 | − | 0.927504i | \(-0.378050\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.600783 | + | 129.488i | 0.00215334 | + | 0.464113i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 175.833 | − | 101.517i | 0.625741 | − | 0.361272i | −0.153360 | − | 0.988170i | \(-0.549009\pi\) |
0.779101 | + | 0.626899i | \(0.215676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 78.4126 | − | 135.815i | 0.277076 | − | 0.479910i | −0.693581 | − | 0.720379i | \(-0.743968\pi\) |
0.970657 | + | 0.240469i | \(0.0773012\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 145.341i | 0.506415i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.9744 | 0.0864167 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 223.790 | + | 222.754i | 0.769039 | + | 0.765479i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −54.9412 | − | 31.7203i | −0.187513 | − | 0.108260i | 0.403305 | − | 0.915066i | \(-0.367861\pi\) |
−0.590818 | + | 0.806805i | \(0.701195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −131.159 | + | 503.483i | −0.441613 | + | 1.69523i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 134.751 | − | 77.7986i | 0.450672 | − | 0.260196i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 101.583 | − | 175.947i | 0.337485 | − | 0.584541i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −169.756 | + | 170.546i | −0.560252 | + | 0.562857i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −183.760 | −0.598568 | −0.299284 | − | 0.954164i | \(-0.596748\pi\) | ||||
−0.299284 | + | 0.954164i | \(0.596748\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 100.389 | − | 378.164i | 0.324883 | − | 1.22383i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 328.599 | + | 189.717i | 1.05659 | + | 0.610021i | 0.924486 | − | 0.381215i | \(-0.124494\pi\) |
0.132101 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 204.306 | + | 353.868i | 0.652734 | + | 1.13057i | 0.982457 | + | 0.186491i | \(0.0597115\pi\) |
−0.329723 | + | 0.944078i | \(0.606955\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −449.330 | + | 259.421i | −1.41744 | + | 0.818362i | −0.996074 | − | 0.0885271i | \(-0.971784\pi\) |
−0.421370 | + | 0.906889i | \(0.638451\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.1202 | + | 74.6863i | −0.135173 | + | 0.234126i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.0328 | − | 144.332i | −0.121597 | − | 0.449633i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 309.549i | 0.958355i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −351.660 | + | 95.1019i | −1.07541 | + | 0.290831i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 169.342 | + | 97.7696i | 0.514717 | + | 0.297172i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −147.622 | − | 255.689i | −0.445988 | − | 0.772474i | 0.552133 | − | 0.833756i | \(-0.313814\pi\) |
−0.998120 | + | 0.0612827i | \(0.980481\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 432.265 | − | 252.250i | 1.29809 | − | 0.757507i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −53.8810 | + | 93.3245i | −0.159884 | + | 0.276927i | −0.934827 | − | 0.355104i | \(-0.884445\pi\) |
0.774943 | + | 0.632032i | \(0.217779\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −81.9833 | − | 21.7636i | −0.241839 | − | 0.0641995i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 277.248i | 0.813045i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 357.187 | 1.04136 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −382.308 | − | 220.726i | −1.10175 | − | 0.636097i | −0.165071 | − | 0.986282i | \(-0.552785\pi\) |
−0.936681 | + | 0.350185i | \(0.886119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −94.7382 | − | 164.091i | −0.271456 | − | 0.470176i | 0.697779 | − | 0.716313i | \(-0.254172\pi\) |
−0.969235 | + | 0.246138i | \(0.920839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −67.1751 | − | 243.898i | −0.191382 | − | 0.694867i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 435.490 | − | 251.430i | 1.23368 | − | 0.712267i | 0.265887 | − | 0.964004i | \(-0.414335\pi\) |
0.967796 | + | 0.251737i | \(0.0810018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −162.076 | + | 162.829i | −0.453993 | + | 0.456104i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2.93084i | − | 0.00816391i | −0.999992 | − | 0.00408196i | \(-0.998701\pi\) | ||
0.999992 | − | 0.00408196i | \(-0.00129933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.92045 | 0.00531981 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −192.685 | + | 725.842i | −0.530813 | + | 1.99956i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3696 | + | 47.4055i | 0.0745765 | + | 0.129170i | 0.900902 | − | 0.434023i | \(-0.142906\pi\) |
−0.826326 | + | 0.563193i | \(0.809573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 277.542 | − | 1.28771i | 0.752145 | − | 0.00348973i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 125.320 | − | 72.3534i | 0.337789 | − | 0.195023i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 338.735 | − | 586.707i | 0.908138 | − | 1.57294i | 0.0914894 | − | 0.995806i | \(-0.470837\pi\) |
0.816649 | − | 0.577135i | \(-0.195829\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 41.9329i | − | 0.111228i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −431.714 | −1.13909 | −0.569543 | − | 0.821961i | \(-0.692880\pi\) | ||||
−0.569543 | + | 0.821961i | \(0.692880\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −129.957 | + | 35.1453i | −0.341095 | + | 0.0922449i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −506.226 | − | 292.269i | −1.32174 | − | 0.763106i | −0.337732 | − | 0.941242i | \(-0.609660\pi\) |
−0.984006 | + | 0.178137i | \(0.942993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −336.886 | − | 192.423i | −0.870507 | − | 0.497217i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −49.9565 | + | 28.8424i | −0.128423 | + | 0.0741450i | −0.562835 | − | 0.826569i | \(-0.690289\pi\) |
0.434412 | + | 0.900714i | \(0.356956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −134.919 | + | 233.686i | −0.345061 | + | 0.597662i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −213.385 | − | 56.6462i | −0.542965 | − | 0.144138i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.9853 | −0.0654542 | −0.0327271 | − | 0.999464i | \(-0.510419\pi\) | ||||
−0.0327271 | + | 0.999464i | \(0.510419\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 190.904 | + | 190.020i | 0.478456 | + | 0.476242i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −229.069 | − | 132.253i | −0.571244 | − | 0.329808i | 0.186402 | − | 0.982474i | \(-0.440317\pi\) |
−0.757646 | + | 0.652666i | \(0.773651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −67.4036 | − | 116.746i | −0.167255 | − | 0.289693i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 928.017 | − | 535.791i | 2.28014 | − | 1.31644i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −154.678 | + | 267.911i | −0.378187 | + | 0.655039i | −0.990798 | − | 0.135345i | \(-0.956786\pi\) |
0.612612 | + | 0.790384i | \(0.290119\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −461.760 | + | 463.907i | −1.12350 | + | 1.12873i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 405.021i | 0.980681i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −50.8030 | + | 191.374i | −0.121830 | + | 0.458931i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −58.4329 | − | 33.7363i | −0.139458 | − | 0.0805161i | 0.428648 | − | 0.903472i | \(-0.358990\pi\) |
−0.568106 | + | 0.822956i | \(0.692324\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −101.577 | − | 175.936i | −0.241275 | − | 0.417901i | 0.719803 | − | 0.694179i | \(-0.244232\pi\) |
−0.961078 | + | 0.276278i | \(0.910899\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 185.199 | − | 324.240i | 0.437824 | − | 0.766524i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 243.880 | − | 422.413i | 0.571148 | − | 0.989257i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −141.404 | − | 522.871i | −0.329613 | − | 1.21881i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 319.947i | 0.742337i | 0.928566 | + | 0.371168i | \(0.121043\pi\) | ||||
−0.928566 | + | 0.371168i | \(0.878957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 454.101 | 1.04873 | 0.524366 | − | 0.851493i | \(-0.324303\pi\) | ||||
0.524366 | + | 0.851493i | \(0.324303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 273.978 | + | 158.181i | 0.626951 | + | 0.361971i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −45.7154 | − | 79.1813i | −0.104135 | − | 0.180367i | 0.809249 | − | 0.587465i | \(-0.199874\pi\) |
−0.913385 | + | 0.407098i | \(0.866541\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.11856 | − | 241.086i | −0.00253643 | − | 0.546679i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 188.030 | − | 108.559i | 0.424448 | − | 0.245055i | −0.272531 | − | 0.962147i | \(-0.587861\pi\) |
0.696978 | + | 0.717092i | \(0.254527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 567.176 | + | 150.565i | 1.26885 | + | 0.336835i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 832.270i | 1.85361i | 0.375545 | + | 0.926804i | \(0.377456\pi\) | ||||
−0.375545 | + | 0.926804i | \(0.622544\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 594.249 | 1.31763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −338.294 | − | 336.728i | −0.746785 | − | 0.743329i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 400.398 | + | 693.510i | 0.876145 | + | 1.51753i | 0.855538 | + | 0.517739i | \(0.173226\pi\) |
0.0206062 | + | 0.999788i | \(0.493440\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 312.373 | + | 308.055i | 0.680551 | + | 0.671144i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 504.549 | − | 291.301i | 1.09447 | − | 0.631890i | 0.159704 | − | 0.987165i | \(-0.448946\pi\) |
0.934762 | + | 0.355275i | \(0.115613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −367.120 | + | 635.871i | −0.792916 | + | 1.37337i | 0.131237 | + | 0.991351i | \(0.458105\pi\) |
−0.924154 | + | 0.382021i | \(0.875228\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 670.573i | − | 1.43592i | −0.696086 | − | 0.717958i | \(-0.745077\pi\) | ||
0.696086 | − | 0.717958i | \(-0.254923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 582.413 | 1.24182 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 98.8225 | − | 372.263i | 0.209814 | − | 0.790367i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −719.386 | − | 415.338i | −1.52090 | − | 0.878092i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −139.276 | − | 238.668i | −0.291982 | − | 0.500353i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 148.723 | − | 85.8655i | 0.310487 | − | 0.179260i | −0.336657 | − | 0.941627i | \(-0.609296\pi\) |
0.647144 | + | 0.762367i | \(0.275963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −260.519 | + | 451.232i | −0.541619 | + | 0.938112i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 61.2967 | + | 226.658i | 0.126908 | + | 0.469271i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.0906 | −0.0453606 | −0.0226803 | − | 0.999743i | \(-0.507220\pi\) | ||||
−0.0226803 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 62.8319 | − | 16.9921i | 0.128491 | − | 0.0347486i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −458.788 | − | 264.881i | −0.934395 | − | 0.539473i | −0.0461960 | − | 0.998932i | \(-0.514710\pi\) |
−0.888199 | + | 0.459459i | \(0.848043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.3601 | + | 62.9775i | 0.0737527 | + | 0.127743i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −454.724 | + | 262.535i | −0.914937 | + | 0.528239i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −84.6486 | + | 146.616i | −0.169636 | + | 0.293819i | −0.938292 | − | 0.345844i | \(-0.887593\pi\) |
0.768656 | + | 0.639663i | \(0.220926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −736.243 | − | 195.446i | −1.46955 | − | 0.390112i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.5687i | 0.0448682i | 0.999748 | + | 0.0224341i | \(0.00714159\pi\) | ||||
−0.999748 | + | 0.0224341i | \(0.992858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −172.672 | − | 171.872i | −0.340575 | − | 0.338999i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −654.896 | − | 378.104i | −1.28663 | − | 0.742838i | −0.308580 | − | 0.951198i | \(-0.599854\pi\) |
−0.978052 | + | 0.208361i | \(0.933187\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 213.448 | + | 369.702i | 0.417706 | + | 0.723487i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 361.169 | − | 366.232i | 0.704034 | − | 0.713902i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 399.746 | − | 692.380i | 0.773203 | − | 1.33923i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −125.616 | + | 126.200i | −0.242034 | + | 0.243160i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 157.921i | 0.303112i | 0.988449 | + | 0.151556i | \(0.0484283\pi\) | ||||
−0.988449 | + | 0.151556i | \(0.951572\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −535.341 | −1.02360 | −0.511798 | − | 0.859106i | \(-0.671021\pi\) | ||||
−0.511798 | + | 0.859106i | \(0.671021\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 202.462 | + | 116.892i | 0.384179 | + | 0.221806i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −126.612 | − | 219.298i | −0.239341 | − | 0.414551i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 773.424 | − | 3.58845i | 1.45654 | − | 0.00675791i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −250.232 | + | 144.472i | −0.469479 | + | 0.271054i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.25960 | − | 15.7508i | −0.00793222 | − | 0.0293311i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 516.193i | − | 0.957686i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 446.519 | 0.825358 | 0.412679 | − | 0.910877i | \(-0.364593\pi\) | ||||
0.412679 | + | 0.910877i | \(0.364593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −131.730 | + | 35.6247i | −0.242597 | + | 0.0656072i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −104.414 | − | 180.850i | −0.190885 | − | 0.330622i | 0.754659 | − | 0.656117i | \(-0.227802\pi\) |
−0.945544 | + | 0.325495i | \(0.894469\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −808.795 | − | 461.968i | −1.47322 | − | 0.841472i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 73.8360 | − | 42.6292i | 0.134004 | − | 0.0773671i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −196.329 | + | 340.052i | −0.355026 | + | 0.614923i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 428.915i | 0.770044i | 0.922907 | + | 0.385022i | \(0.125806\pi\) | ||||
−0.922907 | + | 0.385022i | \(0.874194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 403.901 | 0.722543 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 665.753 | + | 662.671i | 1.18672 | + | 1.18123i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 683.687 | + | 394.727i | 1.21436 | + | 0.701114i | 0.963707 | − | 0.266962i | \(-0.0860199\pi\) |
0.250657 | + | 0.968076i | \(0.419353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 381.737 | − | 3.54236i | 0.673258 | − | 0.00624756i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 153.834 | − | 88.8163i | 0.270359 | − | 0.156092i | −0.358692 | − | 0.933456i | \(-0.616777\pi\) |
0.629051 | + | 0.777364i | \(0.283444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.18137 | + | 15.9026i | −0.0160795 | + | 0.0278504i | −0.873953 | − | 0.486010i | \(-0.838452\pi\) |
0.857874 | + | 0.513861i | \(0.171785\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −488.729 | + | 491.001i | −0.852929 | + | 0.856896i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −240.588 | −0.416963 | −0.208482 | − | 0.978026i | \(-0.566852\pi\) | ||||
−0.208482 | + | 0.978026i | \(0.566852\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −56.1045 | + | 211.345i | −0.0968989 | + | 0.365017i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −146.325 | − | 84.4809i | −0.251851 | − | 0.145406i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −295.828 | − | 512.389i | −0.507424 | − | 0.878884i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −143.112 | + | 82.6260i | −0.243803 | + | 0.140760i | −0.616923 | − | 0.787023i | \(-0.711621\pi\) |
0.373120 | + | 0.927783i | \(0.378288\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 137.046 | − | 237.370i | 0.232676 | − | 0.403006i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.7202 | − | 113.595i | −0.0519801 | − | 0.192208i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 901.661i | 1.52051i | 0.649626 | + | 0.760254i | \(0.274925\pi\) | ||||
−0.649626 | + | 0.760254i | \(0.725075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 776.316 | − | 209.945i | 1.30036 | − | 0.351666i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 893.571 | + | 515.904i | 1.49177 | + | 0.861275i | 0.999956 | − | 0.00942385i | \(-0.00299975\pi\) |
0.491817 | + | 0.870699i | \(0.336333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −481.489 | − | 833.964i | −0.801147 | − | 1.38763i | −0.918862 | − | 0.394580i | \(-0.870890\pi\) |
0.117715 | − | 0.993047i | \(-0.462443\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.16013 | − | 1112.17i | −0.00855743 | − | 1.84439i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −469.609 | + | 813.387i | −0.773656 | + | 1.34001i | 0.161891 | + | 0.986809i | \(0.448241\pi\) |
−0.935547 | + | 0.353202i | \(0.885093\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 61.1595 | + | 16.2357i | 0.100426 | + | 0.0266595i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 388.739i | 0.636234i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −364.929 | −0.595316 | −0.297658 | − | 0.954673i | \(-0.596206\pi\) | ||||
−0.297658 | + | 0.954673i | \(0.596206\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 231.260 | + | 133.518i | 0.374813 | + | 0.216398i | 0.675559 | − | 0.737306i | \(-0.263902\pi\) |
−0.300746 | + | 0.953704i | \(0.597236\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −453.122 | − | 784.830i | −0.732022 | − | 1.26790i | −0.956017 | − | 0.293310i | \(-0.905243\pi\) |
0.223995 | − | 0.974590i | \(-0.428090\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 432.280 | − | 119.060i | 0.696103 | − | 0.191722i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 346.585 | − | 200.101i | 0.556317 | − | 0.321190i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 776.928 | − | 780.541i | 1.23912 | − | 1.24488i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 903.586i | − | 1.43654i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 597.193 | 0.946424 | 0.473212 | − | 0.880949i | \(-0.343095\pi\) | ||||
0.473212 | + | 0.880949i | \(0.343095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −267.013 | + | 1005.83i | −0.421821 | + | 1.58899i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 125.495 | + | 217.363i | 0.197009 | + | 0.341230i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 505.362 | + | 866.009i | 0.790864 | + | 1.35526i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 78.1431 | − | 45.1160i | 0.121908 | − | 0.0703837i | −0.437806 | − | 0.899070i | \(-0.644244\pi\) |
0.559714 | + | 0.828686i | \(0.310911\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −194.434 | + | 336.770i | −0.302386 | + | 0.523748i | −0.976676 | − | 0.214719i | \(-0.931117\pi\) |
0.674290 | + | 0.738467i | \(0.264450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 607.624i | 0.939141i | 0.882895 | + | 0.469570i | \(0.155591\pi\) | ||||
−0.882895 | + | 0.469570i | \(0.844409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1655.99 | 2.55161 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 196.373 | − | 53.1066i | 0.301649 | − | 0.0815770i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −981.221 | − | 566.508i | −1.50264 | − | 0.867547i | −0.999995 | − | 0.00305096i | \(-0.999029\pi\) |
−0.502640 | − | 0.864496i | \(-0.667638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 704.088 | − | 410.873i | 1.07167 | − | 0.625377i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 772.309 | − | 445.893i | 1.17194 | − | 0.676621i | 0.217805 | − | 0.975992i | \(-0.430110\pi\) |
0.954137 | + | 0.299372i | \(0.0967771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −219.766 | + | 380.645i | −0.332474 | + | 0.575863i | −0.982996 | − | 0.183625i | \(-0.941217\pi\) |
0.650522 | + | 0.759487i | \(0.274550\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −441.448 | − | 117.189i | −0.665834 | − | 0.176755i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 74.3209 | 0.111426 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 150.469 | + | 149.772i | 0.224916 | + | 0.223875i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1727.10 | − | 997.142i | −2.57392 | − | 1.48605i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.1287 | + | 53.9165i | 0.0462537 | + | 0.0801137i | 0.888225 | − | 0.459408i | \(-0.151938\pi\) |
−0.841972 | + | 0.539522i | \(0.818605\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 116.119 | − | 67.0416i | 0.171521 | − | 0.0990275i | −0.411782 | − | 0.911282i | \(-0.635093\pi\) |
0.583303 | + | 0.812255i | \(0.301760\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 248.026 | − | 429.594i | 0.365282 | − | 0.632687i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 569.010 | − | 571.656i | 0.835550 | − | 0.839436i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 299.004i | 0.437780i | 0.975750 | + | 0.218890i | \(0.0702436\pi\) | ||||
−0.975750 | + | 0.218890i | \(0.929756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 159.329 | − | 600.192i | 0.231921 | − | 0.873641i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 249.140 | + | 143.841i | 0.361597 | + | 0.208768i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 188.288 | + | 326.124i | 0.272486 | + | 0.471960i | 0.969498 | − | 0.245100i | \(-0.0788208\pi\) |
−0.697012 | + | 0.717060i | \(0.745487\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 817.362 | − | 3.79231i | 1.17945 | − | 0.00547231i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 250.544 | − | 433.954i | 0.359460 | − | 0.622603i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 37.1925 | + | 137.527i | 0.0532082 | + | 0.196749i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 909.992i | − | 1.29813i | −0.760731 | − | 0.649067i | \(-0.775159\pi\) | ||
0.760731 | − | 0.649067i | \(-0.224841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1059.38 | −1.50694 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 327.385 | + | 189.016i | 0.463062 | + | 0.267349i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 671.694 | + | 1163.41i | 0.947382 | + | 1.64091i | 0.750911 | + | 0.660404i | \(0.229615\pi\) |
0.196471 | + | 0.980510i | \(0.437052\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 651.099 | + | 371.895i | 0.915751 | + | 0.523059i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 206.919 | − | 119.465i | 0.290209 | − | 0.167552i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 967.023 | + | 256.710i | 1.34871 | + | 0.358034i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 288.276i | 0.400940i | 0.979700 | + | 0.200470i | \(0.0642469\pi\) | ||||
−0.979700 | + | 0.200470i | \(0.935753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −614.673 | −0.852528 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 907.292 | + | 903.092i | 1.25490 | + | 1.24909i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 243.149 | + | 421.147i | 0.334456 | + | 0.579294i | 0.983380 | − | 0.181559i | \(-0.0581143\pi\) |
−0.648925 | + | 0.760853i | \(0.724781\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.1466 | − | 728.929i | −0.0139185 | − | 0.999903i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −606.606 | + | 350.224i | −0.829830 | + | 0.479103i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 629.211 | − | 1089.83i | 0.858406 | − | 1.48680i | −0.0150435 | − | 0.999887i | \(-0.504789\pi\) |
0.873449 | − | 0.486915i | \(-0.161878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2381.29i | − | 3.23105i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1192.17 | −1.61322 | −0.806609 | − | 0.591086i | \(-0.798700\pi\) | ||||
−0.806609 | + | 0.591086i | \(0.798700\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −137.394 | + | 517.562i | −0.185417 | + | 0.698464i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 170.987 | + | 98.7194i | 0.230131 | + | 0.132866i | 0.610632 | − | 0.791914i | \(-0.290915\pi\) |
−0.380502 | + | 0.924780i | \(0.624249\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −160.027 | + | 280.170i | −0.214227 | + | 0.375060i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −203.422 | + | 117.446i | −0.271592 | + | 0.156803i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.0633 | + | 43.4109i | −0.0333733 | + | 0.0578042i | −0.882230 | − | 0.470819i | \(-0.843958\pi\) |
0.848856 | + | 0.528624i | \(0.177292\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −308.838 | − | 1142.00i | −0.410143 | − | 1.51659i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 282.361 | 0.373000 | 0.186500 | − | 0.982455i | \(-0.440286\pi\) | ||||
0.186500 | + | 0.982455i | \(0.440286\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 926.726 | − | 250.621i | 1.22098 | − | 0.330199i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 89.9243 | + | 51.9178i | 0.118166 | + | 0.0682231i | 0.557918 | − | 0.829896i | \(-0.311600\pi\) |
−0.439752 | + | 0.898119i | \(0.644934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 286.152 | + | 495.630i | 0.375036 | + | 0.649581i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −697.321 | + | 402.599i | −0.909154 | + | 0.524900i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 190.567 | − | 330.073i | 0.247812 | − | 0.429223i | −0.715106 | − | 0.699016i | \(-0.753622\pi\) |
0.962918 | + | 0.269793i | \(0.0869551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1049.98 | − | 278.731i | −1.36184 | − | 0.361519i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 276.633i | 0.357870i | 0.983861 | + | 0.178935i | \(0.0572651\pi\) | ||||
−0.983861 | + | 0.178935i | \(0.942735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −557.258 | − | 554.678i | −0.717191 | − | 0.713872i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −508.776 | − | 293.742i | −0.653114 | − | 0.377076i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1073.41 | + | 1859.21i | 1.37441 | + | 2.38055i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.4616 | − | 116.933i | 0.0389037 | − | 0.149340i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −666.067 | + | 1153.66i | −0.846336 | + | 1.46590i | 0.0381190 | + | 0.999273i | \(0.487863\pi\) |
−0.884455 | + | 0.466625i | \(0.845470\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −718.636 | + | 721.978i | −0.910819 | + | 0.915055i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 133.257i | 0.168466i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 969.686 | 1.22281 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −571.372 | − | 329.882i | −0.716903 | − | 0.413904i | 0.0967084 | − | 0.995313i | \(-0.469169\pi\) |
−0.813612 | + | 0.581408i | \(0.802502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −337.077 | − | 583.834i | −0.421873 | − | 0.730706i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −385.182 | − | 660.063i | −0.480876 | − | 0.824048i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1511.58 | − | 872.713i | 1.88242 | − | 1.08682i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.1744 | − | 67.2039i | −0.0225210 | − | 0.0832762i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 654.023i | 0.808433i | 0.914663 | + | 0.404217i | \(0.132456\pi\) | ||||
−0.914663 | + | 0.404217i | \(0.867544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −408.003 | −0.503086 | −0.251543 | − | 0.967846i | \(-0.580938\pi\) | ||||
−0.251543 | + | 0.967846i | \(0.580938\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1256.67 | − | 339.851i | 1.54572 | − | 0.418021i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 410.609 | + | 711.196i | 0.502582 | + | 0.870497i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −343.261 | + | 200.311i | −0.419122 | + | 0.244580i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 762.425 | − | 440.186i | 0.928654 | − | 0.536158i | 0.0422680 | − | 0.999106i | \(-0.486542\pi\) |
0.886385 | + | 0.462948i | \(0.153208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 64.8244 | − | 112.279i | 0.0787660 | − | 0.136427i | −0.823952 | − | 0.566660i | \(-0.808235\pi\) |
0.902718 | + | 0.430233i | \(0.141569\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 646.300i | − | 0.781499i | −0.920497 | − | 0.390750i | \(-0.872216\pi\) | ||
0.920497 | − | 0.390750i | \(-0.127784\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −416.080 | −0.501906 | −0.250953 | − | 0.967999i | \(-0.580744\pi\) | ||||
−0.250953 | + | 0.967999i | \(0.580744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 726.003 | + | 722.642i | 0.873650 | + | 0.869606i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −376.953 | − | 217.634i | −0.452524 | − | 0.261265i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −103.152 | − | 374.522i | −0.123240 | − | 0.447457i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 240.544 | − | 138.878i | 0.286703 | − | 0.165528i | −0.349751 | − | 0.936843i | \(-0.613734\pi\) |
0.636454 | + | 0.771315i | \(0.280400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −410.485 | + | 710.982i | −0.488092 | + | 0.845400i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −429.701 | + | 431.700i | −0.509729 | + | 0.512099i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1179.79 | 1.39291 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −120.714 | + | 454.726i | −0.142183 | + | 0.535602i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −799.754 | − | 461.738i | −0.939781 | − | 0.542583i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 658.042 | + | 1139.76i | 0.771444 | + | 1.33618i | 0.936771 | + | 0.349942i | \(0.113799\pi\) |
−0.165327 | + | 0.986239i | \(0.552868\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −830.857 | + | 479.696i | −0.969495 | + | 0.559738i | −0.899082 | − | 0.437780i | \(-0.855765\pi\) |
−0.0704129 | + | 0.997518i | \(0.522432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 439.753 | − | 761.675i | 0.511936 | − | 0.886699i | −0.487968 | − | 0.872861i | \(-0.662262\pi\) |
0.999904 | − | 0.0138379i | \(-0.00440487\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −113.828 | − | 420.903i | −0.132204 | − | 0.488854i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 326.481i | − | 0.378310i | −0.981947 | − | 0.189155i | \(-0.939425\pi\) | ||
0.981947 | − | 0.189155i | \(-0.0605748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −72.3251 | + | 19.5594i | −0.0834200 | + | 0.0225599i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1390.36 | + | 802.722i | 1.59995 | + | 0.923731i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 578.930 | + | 1002.74i | 0.664673 | + | 1.15125i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −822.546 | − | 469.822i | −0.942206 | − | 0.538170i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.1834 | + | 99.0445i | −0.0652034 | + | 0.112936i | −0.896784 | − | 0.442468i | \(-0.854103\pi\) |
0.831581 | + | 0.555404i | \(0.187436\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 183.951 | + | 48.8323i | 0.209273 | + | 0.0555544i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 429.252i | 0.487233i | 0.969872 | + | 0.243617i | \(0.0783338\pi\) | ||||
−0.969872 | + | 0.243617i | \(0.921666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −294.993 | −0.334080 | −0.167040 | − | 0.985950i | \(-0.553421\pi\) | ||||
−0.167040 | + | 0.985950i | \(0.553421\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −347.848 | − | 200.830i | −0.392162 | − | 0.226415i | 0.290934 | − | 0.956743i | \(-0.406034\pi\) |
−0.683097 | + | 0.730328i | \(0.739367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 105.749 | + | 183.162i | 0.118952 | + | 0.206032i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.4835 | − | 1560.79i | −0.0162553 | − | 1.75173i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −684.498 | + | 395.195i | −0.766515 | + | 0.442548i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −329.305 | + | 330.836i | −0.367118 | + | 0.368825i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 64.3906i | − | 0.0716247i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −498.901 | −0.553719 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −156.383 | + | 589.094i | −0.173182 | + | 0.652374i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 211.939 | + | 367.089i | 0.233670 | + | 0.404729i | 0.958885 | − | 0.283794i | \(-0.0915931\pi\) |
−0.725215 | + | 0.688522i | \(0.758260\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 358.041 | − | 626.844i | 0.393885 | − | 0.689598i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.7248 | + | 29.8633i | −0.0567780 | + | 0.0327808i | −0.528120 | − | 0.849170i | \(-0.677103\pi\) |
0.471342 | + | 0.881950i | \(0.343770\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −345.413 | + | 598.273i | −0.378328 | + | 0.655283i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 346.840i | 0.378233i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −522.062 | −0.568077 | −0.284038 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284038 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 532.164 | − | 143.917i | 0.577811 | − | 0.156262i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −904.008 | − | 521.929i | −0.979423 | − | 0.565470i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.44595 | + | 1173.77i | 0.00587481 | + | 1.26621i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1309.83 | + | 756.229i | −1.40993 | + | 0.814025i | −0.995381 | − | 0.0960006i | \(-0.969395\pi\) |
−0.414552 | + | 0.910026i | \(0.636062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −255.158 | + | 441.947i | −0.274069 | + | 0.474701i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1100.19 | − | 292.062i | −1.17920 | − | 0.313036i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −272.803 | −0.291145 | −0.145573 | − | 0.989348i | \(-0.546502\pi\) | ||||
−0.145573 | + | 0.989348i | \(0.546502\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −868.805 | − | 864.783i | −0.925245 | − | 0.920962i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1149.68 | − | 663.770i | −1.22177 | − | 0.705388i | −0.256473 | − | 0.966551i | \(-0.582560\pi\) |
−0.965295 | + | 0.261164i | \(0.915894\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −256.059 | − | 443.506i | −0.271536 | − | 0.470314i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.7310 | + | 11.3917i | −0.0208352 | + | 0.0120292i | −0.510381 | − | 0.859948i | \(-0.670496\pi\) |
0.489546 | + | 0.871977i | \(0.337162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −424.342 | + | 734.981i | −0.447146 | + | 0.774480i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1098.07 | − | 1103.18i | 1.15465 | − | 1.16002i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 563.843i | 0.591650i | 0.955242 | + | 0.295825i | \(0.0955946\pi\) | ||||
−0.955242 | + | 0.295825i | \(0.904405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 66.3820 | − | 250.060i | 0.0693647 | − | 0.261296i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 890.530 | + | 514.148i | 0.928603 | + | 0.536129i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 376.998 | + | 652.979i | 0.392297 | + | 0.679479i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 226.075 | + | 387.412i | 0.234762 | + | 0.402297i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −637.165 | + | 1103.60i | −0.658909 | + | 1.14126i | 0.321990 | + | 0.946743i | \(0.395648\pi\) |
−0.980899 | + | 0.194520i | \(0.937685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −242.431 | − | 896.443i | −0.250187 | − | 0.925121i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 119.681i | 0.123255i | 0.998099 | + | 0.0616276i | \(0.0196291\pi\) | ||||
−0.998099 | + | 0.0616276i | \(0.980371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 311.062 | 0.319694 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1307.00 | − | 754.597i | −1.33777 | − | 0.772361i | −0.351293 | − | 0.936266i | \(-0.614258\pi\) |
−0.986476 | + | 0.163905i | \(0.947591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −818.144 | − | 1417.07i | −0.835694 | − | 1.44746i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 943.914 | − | 550.824i | 0.962196 | − | 0.561492i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −448.144 | + | 258.736i | −0.455894 | + | 0.263211i | −0.710316 | − | 0.703883i | \(-0.751448\pi\) |
0.254422 | + | 0.967093i | \(0.418115\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −566.980 | − | 150.513i | −0.574448 | − | 0.152495i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 715.866i | 0.723828i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −201.958 | −0.203793 | −0.101896 | − | 0.994795i | \(-0.532491\pi\) | ||||
−0.101896 | + | 0.994795i | \(0.532491\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 627.758 | + | 624.852i | 0.632184 | + | 0.629257i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −104.672 | − | 181.297i | −0.104987 | − | 0.181842i | 0.808746 | − | 0.588158i | \(-0.200147\pi\) |
−0.913733 | + | 0.406316i | \(0.866813\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1054.27 | + | 1069.05i | −1.05533 | + | 1.07012i |
(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 | 900.3.p.c.401.1 | 12 | ||
3.2 | odd | 2 | 2700.3.p.c.2501.5 | 12 | |||
5.2 | odd | 4 | 900.3.u.c.149.8 | 24 | |||
5.3 | odd | 4 | 900.3.u.c.149.5 | 24 | |||
5.4 | even | 2 | 180.3.o.b.41.6 | ✓ | 12 | ||
9.2 | odd | 6 | inner | 900.3.p.c.101.1 | 12 | ||
9.7 | even | 3 | 2700.3.p.c.1601.5 | 12 | |||
15.2 | even | 4 | 2700.3.u.c.449.3 | 24 | |||
15.8 | even | 4 | 2700.3.u.c.449.10 | 24 | |||
15.14 | odd | 2 | 540.3.o.b.341.4 | 12 | |||
20.19 | odd | 2 | 720.3.bs.b.401.1 | 12 | |||
45.2 | even | 12 | 900.3.u.c.749.5 | 24 | |||
45.4 | even | 6 | 1620.3.g.b.161.11 | 12 | |||
45.7 | odd | 12 | 2700.3.u.c.2249.10 | 24 | |||
45.14 | odd | 6 | 1620.3.g.b.161.5 | 12 | |||
45.29 | odd | 6 | 180.3.o.b.101.6 | yes | 12 | ||
45.34 | even | 6 | 540.3.o.b.521.4 | 12 | |||
45.38 | even | 12 | 900.3.u.c.749.8 | 24 | |||
45.43 | odd | 12 | 2700.3.u.c.2249.3 | 24 | |||
60.59 | even | 2 | 2160.3.bs.b.881.6 | 12 | |||
180.79 | odd | 6 | 2160.3.bs.b.1601.6 | 12 | |||
180.119 | even | 6 | 720.3.bs.b.641.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.o.b.41.6 | ✓ | 12 | 5.4 | even | 2 | ||
180.3.o.b.101.6 | yes | 12 | 45.29 | odd | 6 | ||
540.3.o.b.341.4 | 12 | 15.14 | odd | 2 | |||
540.3.o.b.521.4 | 12 | 45.34 | even | 6 | |||
720.3.bs.b.401.1 | 12 | 20.19 | odd | 2 | |||
720.3.bs.b.641.1 | 12 | 180.119 | even | 6 | |||
900.3.p.c.101.1 | 12 | 9.2 | odd | 6 | inner | ||
900.3.p.c.401.1 | 12 | 1.1 | even | 1 | trivial | ||
900.3.u.c.149.5 | 24 | 5.3 | odd | 4 | |||
900.3.u.c.149.8 | 24 | 5.2 | odd | 4 | |||
900.3.u.c.749.5 | 24 | 45.2 | even | 12 | |||
900.3.u.c.749.8 | 24 | 45.38 | even | 12 | |||
1620.3.g.b.161.5 | 12 | 45.14 | odd | 6 | |||
1620.3.g.b.161.11 | 12 | 45.4 | even | 6 | |||
2160.3.bs.b.881.6 | 12 | 60.59 | even | 2 | |||
2160.3.bs.b.1601.6 | 12 | 180.79 | odd | 6 | |||
2700.3.p.c.1601.5 | 12 | 9.7 | even | 3 | |||
2700.3.p.c.2501.5 | 12 | 3.2 | odd | 2 | |||
2700.3.u.c.449.3 | 24 | 15.2 | even | 4 | |||
2700.3.u.c.449.10 | 24 | 15.8 | even | 4 | |||
2700.3.u.c.2249.3 | 24 | 45.43 | odd | 12 | |||
2700.3.u.c.2249.10 | 24 | 45.7 | odd | 12 |