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: | 8.0.3317760000.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1241.2 | ||
Root | \(1.40294 + 1.01575i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1241 |
Dual form | 1620.3.o.f.701.2 |
$q$-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 | ||||||||
\(7\) | 6.74342 | − | 11.6799i | 0.963345 | − | 1.66856i | 0.249348 | − | 0.968414i | \(-0.419784\pi\) |
0.713997 | − | 0.700149i | \(-0.246883\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.2932 | + | 8.82952i | 1.39029 | + | 0.802684i | 0.993347 | − | 0.115159i | \(-0.0367379\pi\) |
0.396942 | + | 0.917843i | \(0.370071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.74342 | + | 6.48379i | 0.287955 | + | 0.498753i | 0.973322 | − | 0.229446i | \(-0.0736913\pi\) |
−0.685366 | + | 0.728198i | \(0.740358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.9706i | 0.998268i | 0.866525 | + | 0.499134i | \(0.166349\pi\) | ||||
−0.866525 | + | 0.499134i | \(0.833651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.9737 | −0.577561 | −0.288781 | − | 0.957395i | \(-0.593250\pi\) | ||||
−0.288781 | + | 0.957395i | \(0.593250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.9674 | + | 10.9508i | −0.824670 | + | 0.476124i | −0.852024 | − | 0.523502i | \(-0.824625\pi\) |
0.0273540 | + | 0.999626i | \(0.491292\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.0128 | + | 23.6788i | 1.41424 | + | 0.816509i | 0.995784 | − | 0.0917300i | \(-0.0292397\pi\) |
0.418451 | + | 0.908239i | \(0.362573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48683 | + | 14.6996i | 0.273769 | + | 0.474181i | 0.969824 | − | 0.243807i | \(-0.0783964\pi\) |
−0.696055 | + | 0.717989i | \(0.745063\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 30.1575i | 0.861642i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.53950 | −0.149716 | −0.0748581 | − | 0.997194i | \(-0.523850\pi\) | ||||
−0.0748581 | + | 0.997194i | \(0.523850\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 57.4985 | − | 33.1968i | 1.40240 | − | 0.809677i | 0.407764 | − | 0.913087i | \(-0.366309\pi\) |
0.994639 | + | 0.103410i | \(0.0329754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19.4868 | + | 33.7522i | −0.453182 | + | 0.784935i | −0.998582 | − | 0.0532417i | \(-0.983045\pi\) |
0.545399 | + | 0.838176i | \(0.316378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −28.2014 | − | 16.2821i | −0.600029 | − | 0.346427i | 0.169024 | − | 0.985612i | \(-0.445939\pi\) |
−0.769053 | + | 0.639185i | \(0.779272\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −66.4473 | − | 115.090i | −1.35607 | − | 2.34878i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2392i | 0.212061i | 0.994363 | + | 0.106030i | \(0.0338141\pi\) | ||||
−0.994363 | + | 0.106030i | \(0.966186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −39.4868 | −0.717942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −27.6051 | + | 15.9378i | −0.467884 | + | 0.270133i | −0.715353 | − | 0.698763i | \(-0.753734\pi\) |
0.247470 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23.4605 | + | 40.6348i | −0.384598 | + | 0.666144i | −0.991713 | − | 0.128470i | \(-0.958993\pi\) |
0.607115 | + | 0.794614i | \(0.292327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.4982 | − | 8.37053i | −0.223049 | − | 0.128777i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 38.0000 | + | 65.8179i | 0.567164 | + | 0.982357i | 0.996845 | + | 0.0793762i | \(0.0252928\pi\) |
−0.429681 | + | 0.902981i | \(0.641374\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 77.7445i | − | 1.09499i | −0.836808 | − | 0.547497i | \(-0.815581\pi\) | ||
0.836808 | − | 0.547497i | \(-0.184419\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 94.9210 | 1.30029 | 0.650144 | − | 0.759811i | \(-0.274709\pi\) | ||||
0.650144 | + | 0.759811i | \(0.274709\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 206.257 | − | 119.082i | 2.67866 | − | 1.54652i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46050 | − | 5.99376i | 0.0438038 | − | 0.0758704i | −0.843292 | − | 0.537455i | \(-0.819386\pi\) |
0.887096 | + | 0.461585i | \(0.152719\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 53.8243 | + | 31.0755i | 0.648485 | + | 0.374403i | 0.787876 | − | 0.615834i | \(-0.211181\pi\) |
−0.139390 | + | 0.990237i | \(0.544514\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.9737 | − | 32.8634i | −0.223220 | − | 0.386628i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 62.2626i | − | 0.699580i | −0.936828 | − | 0.349790i | \(-0.886253\pi\) | ||
0.936828 | − | 0.349790i | \(-0.113747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 100.974 | 1.10960 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.2504 | − | 12.2689i | 0.223689 | − | 0.129147i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 62.4868 | − | 108.230i | 0.644194 | − | 1.11578i | −0.340293 | − | 0.940320i | \(-0.610526\pi\) |
0.984487 | − | 0.175457i | \(-0.0561405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 97.2221 | + | 56.1312i | 0.962595 | + | 0.555754i | 0.896971 | − | 0.442090i | \(-0.145763\pi\) |
0.0656242 | + | 0.997844i | \(0.479096\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 85.1512 | + | 147.486i | 0.826711 | + | 1.43191i | 0.900604 | + | 0.434640i | \(0.143124\pi\) |
−0.0738934 | + | 0.997266i | \(0.523542\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 93.3381i | 0.872319i | 0.899869 | + | 0.436159i | \(0.143662\pi\) | ||||
−0.899869 | + | 0.436159i | \(0.856338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −68.8683 | −0.631820 | −0.315910 | − | 0.948789i | \(-0.602310\pi\) | ||||
−0.315910 | + | 0.948789i | \(0.602310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −95.5301 | + | 55.1543i | −0.845399 | + | 0.488091i | −0.859096 | − | 0.511815i | \(-0.828973\pi\) |
0.0136967 | + | 0.999906i | \(0.495640\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.4868 | − | 42.4124i | 0.212929 | − | 0.368804i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 198.215 | + | 114.440i | 1.66567 | + | 0.961677i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 95.4210 | + | 165.274i | 0.788603 | + | 1.36590i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −65.3815 | −0.514815 | −0.257407 | − | 0.966303i | \(-0.582868\pi\) | ||||
−0.257407 | + | 0.966303i | \(0.582868\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 40.9161 | − | 23.6229i | 0.312336 | − | 0.180328i | −0.335635 | − | 0.941992i | \(-0.608951\pi\) |
0.647972 | + | 0.761665i | \(0.275618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −74.0000 | + | 128.172i | −0.556391 | + | 0.963697i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 187.096 | + | 108.020i | 1.36566 | + | 0.788465i | 0.990371 | − | 0.138442i | \(-0.0442093\pi\) |
0.375291 | + | 0.926907i | \(0.377543\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −105.921 | − | 183.461i | −0.762022 | − | 1.31986i | −0.941807 | − | 0.336154i | \(-0.890874\pi\) |
0.179785 | − | 0.983706i | \(-0.442460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 132.210i | 0.924548i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −105.895 | −0.730308 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 80.1402 | − | 46.2689i | 0.537853 | − | 0.310530i | −0.206355 | − | 0.978477i | \(-0.566160\pi\) |
0.744209 | + | 0.667947i | \(0.232827\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 61.9210 | − | 107.250i | 0.410073 | − | 0.710267i | −0.584824 | − | 0.811160i | \(-0.698837\pi\) |
0.994897 | + | 0.100893i | \(0.0321699\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −32.8694 | − | 18.9771i | −0.212060 | − | 0.122433i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7434 | + | 27.2684i | 0.100277 | + | 0.173684i | 0.911799 | − | 0.410638i | \(-0.134694\pi\) |
−0.811522 | + | 0.584322i | \(0.801361\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 295.384i | 1.83469i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −101.132 | −0.620440 | −0.310220 | − | 0.950665i | \(-0.600403\pi\) | ||||
−0.310220 | + | 0.950665i | \(0.600403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −128.002 | + | 73.9020i | −0.766479 | + | 0.442527i | −0.831617 | − | 0.555349i | \(-0.812584\pi\) |
0.0651382 | + | 0.997876i | \(0.479251\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 56.4737 | − | 97.8153i | 0.334164 | − | 0.578789i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 287.589 | + | 166.040i | 1.66237 | + | 0.959767i | 0.971581 | + | 0.236707i | \(0.0760681\pi\) |
0.690785 | + | 0.723061i | \(0.257265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33.7171 | − | 58.3997i | −0.192669 | − | 0.333713i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 45.8688i | 0.256250i | 0.991758 | + | 0.128125i | \(0.0408959\pi\) | ||||
−0.991758 | + | 0.128125i | \(0.959104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 132.868 | 0.734079 | 0.367040 | − | 0.930205i | \(-0.380371\pi\) | ||||
0.367040 | + | 0.930205i | \(0.380371\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.7272 | − | 6.19335i | 0.0579849 | − | 0.0334776i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −149.842 | + | 259.534i | −0.801294 | + | 1.38788i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 142.006 | + | 81.9871i | 0.743486 | + | 0.429252i | 0.823336 | − | 0.567555i | \(-0.192111\pi\) |
−0.0798492 | + | 0.996807i | \(0.525444\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −55.0000 | − | 95.2628i | −0.284974 | − | 0.493590i | 0.687629 | − | 0.726062i | \(-0.258652\pi\) |
−0.972603 | + | 0.232473i | \(0.925318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 211.108i | 1.07162i | 0.844340 | + | 0.535808i | \(0.179993\pi\) | ||||
−0.844340 | + | 0.535808i | \(0.820007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1053 | −0.0909816 | −0.0454908 | − | 0.998965i | \(-0.514485\pi\) | ||||
−0.0454908 | + | 0.998965i | \(0.514485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 553.133 | − | 319.352i | 2.72479 | − | 1.57316i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −74.2302 | + | 128.571i | −0.362099 | + | 0.627173i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −167.822 | − | 96.8923i | −0.802978 | − | 0.463599i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −170.789 | − | 295.816i | −0.809428 | − | 1.40197i | −0.913261 | − | 0.407376i | \(-0.866444\pi\) |
0.103833 | − | 0.994595i | \(-0.466889\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 87.1478i | − | 0.405338i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 228.921 | 1.05494 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −110.034 | + | 63.5279i | −0.497889 | + | 0.287456i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.6644 | + | 51.3803i | −0.133024 | + | 0.230405i | −0.924841 | − | 0.380354i | \(-0.875802\pi\) |
0.791817 | + | 0.610759i | \(0.209135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −100.107 | − | 57.7965i | −0.440998 | − | 0.254610i | 0.263023 | − | 0.964790i | \(-0.415281\pi\) |
−0.704021 | + | 0.710179i | \(0.748614\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 126.947 | + | 219.879i | 0.554355 | + | 0.960171i | 0.997953 | + | 0.0639455i | \(0.0203684\pi\) |
−0.443598 | + | 0.896226i | \(0.646298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 206.401i | − | 0.885840i | −0.896561 | − | 0.442920i | \(-0.853943\pi\) | ||
0.896561 | − | 0.442920i | \(-0.146057\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 72.8157 | 0.309854 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 299.901 | − | 173.148i | 1.25482 | − | 0.724469i | 0.282755 | − | 0.959192i | \(-0.408752\pi\) |
0.972062 | + | 0.234723i | \(0.0754184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 91.0263 | − | 157.662i | 0.377703 | − | 0.654200i | −0.613025 | − | 0.790064i | \(-0.710047\pi\) |
0.990728 | + | 0.135863i | \(0.0433808\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 257.349 | + | 148.581i | 1.05041 | + | 0.606452i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −41.0790 | − | 71.1509i | −0.166312 | − | 0.288060i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 140.807i | − | 0.560985i | −0.959856 | − | 0.280493i | \(-0.909502\pi\) | ||
0.959856 | − | 0.280493i | \(-0.0904979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −386.763 | −1.52871 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −253.425 | + | 146.315i | −0.986091 | + | 0.569320i | −0.904104 | − | 0.427313i | \(-0.859460\pi\) |
−0.0819876 | + | 0.996633i | \(0.526127\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −37.3552 | + | 64.7010i | −0.144228 | + | 0.249811i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −234.652 | − | 135.476i | −0.892211 | − | 0.515118i | −0.0175460 | − | 0.999846i | \(-0.505585\pi\) |
−0.874665 | + | 0.484728i | \(0.838919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.5658 | − | 21.7647i | −0.0474182 | − | 0.0821308i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 275.083i | 1.02261i | 0.859398 | + | 0.511307i | \(0.170838\pi\) | ||||
−0.859398 | + | 0.511307i | \(0.829162\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 248.158 | 0.915712 | 0.457856 | − | 0.889026i | \(-0.348617\pi\) | ||||
0.457856 | + | 0.889026i | \(0.348617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 76.4659 | − | 44.1476i | 0.278058 | − | 0.160537i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 171.020 | − | 296.215i | 0.617399 | − | 1.06937i | −0.372559 | − | 0.928008i | \(-0.621520\pi\) |
0.989958 | − | 0.141358i | \(-0.0451470\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −304.961 | − | 176.070i | −1.08527 | − | 0.626582i | −0.152958 | − | 0.988233i | \(-0.548880\pi\) |
−0.932314 | + | 0.361650i | \(0.882213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −124.816 | − | 216.187i | −0.441045 | − | 0.763912i | 0.556723 | − | 0.830699i | \(-0.312059\pi\) |
−0.997767 | + | 0.0667866i | \(0.978725\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 895.439i | − | 3.12000i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.00346021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.4719 | + | 18.7476i | −0.110825 | + | 0.0639851i | −0.554388 | − | 0.832258i | \(-0.687048\pi\) |
0.443563 | + | 0.896243i | \(0.353714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.6381 | − | 61.7270i | 0.120807 | − | 0.209244i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −142.006 | − | 81.9871i | −0.474936 | − | 0.274204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 262.816 | + | 455.210i | 0.873142 | + | 1.51233i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 104.919i | − | 0.343995i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 457.842 | 1.49134 | 0.745671 | − | 0.666314i | \(-0.232129\pi\) | ||||
0.745671 | + | 0.666314i | \(0.232129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.34847 | + | 4.24264i | −0.0236285 | + | 0.0136419i | −0.511768 | − | 0.859124i | \(-0.671009\pi\) |
0.488139 | + | 0.872766i | \(0.337676\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.789328 | − | 1.36716i | 0.00252181 | − | 0.00436791i | −0.864762 | − | 0.502182i | \(-0.832531\pi\) |
0.867284 | + | 0.497814i | \(0.165864\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 458.296 | + | 264.597i | 1.44573 | + | 0.834692i | 0.998223 | − | 0.0595890i | \(-0.0189790\pi\) |
0.447506 | + | 0.894281i | \(0.352312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 418.144 | + | 724.248i | 1.31080 | + | 2.27037i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 186.229i | − | 0.576561i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.4342 | 0.115182 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −380.347 | + | 219.594i | −1.15607 | + | 0.667458i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 195.381 | − | 338.411i | 0.590276 | − | 1.02239i | −0.403919 | − | 0.914795i | \(-0.632352\pi\) |
0.994195 | − | 0.107594i | \(-0.0343146\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −147.173 | − | 84.9706i | −0.439323 | − | 0.253644i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −207.355 | − | 359.150i | −0.615297 | − | 1.06573i | −0.990332 | − | 0.138715i | \(-0.955703\pi\) |
0.375035 | − | 0.927011i | \(-0.377631\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 299.739i | 0.878999i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1131.47 | −3.29876 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −111.420 | + | 64.3281i | −0.321094 | + | 0.185384i | −0.651880 | − | 0.758322i | \(-0.726019\pi\) |
0.330786 | + | 0.943706i | \(0.392686\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.5395 | − | 32.1114i | 0.0531218 | − | 0.0920096i | −0.838242 | − | 0.545299i | \(-0.816416\pi\) |
0.891364 | + | 0.453289i | \(0.149750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −165.050 | − | 95.2918i | −0.467565 | − | 0.269949i | 0.247655 | − | 0.968848i | \(-0.420340\pi\) |
−0.715220 | + | 0.698900i | \(0.753673\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 86.9210 | + | 150.552i | 0.244848 | + | 0.424089i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 254.782i | 0.709699i | 0.934923 | + | 0.354849i | \(0.115468\pi\) | ||||
−0.934923 | + | 0.354849i | \(0.884532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −240.579 | −0.666423 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −183.814 | + | 106.125i | −0.503599 | + | 0.290753i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −150.230 | + | 260.206i | −0.409347 | + | 0.709009i | −0.994817 | − | 0.101685i | \(-0.967577\pi\) |
0.585470 | + | 0.810694i | \(0.300910\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 131.273 | + | 75.7908i | 0.353837 | + | 0.204288i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −352.046 | − | 609.761i | −0.943823 | − | 1.63475i | −0.758091 | − | 0.652149i | \(-0.773868\pi\) |
−0.185732 | − | 0.982601i | \(-0.559466\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 354.558i | 0.940472i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 333.789 | 0.880711 | 0.440355 | − | 0.897824i | \(-0.354852\pi\) | ||||
0.440355 | + | 0.897824i | \(0.354852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −226.030 | + | 130.498i | −0.590155 | + | 0.340726i | −0.765159 | − | 0.643841i | \(-0.777340\pi\) |
0.175004 | + | 0.984568i | \(0.444006\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −266.276 | + | 461.204i | −0.691626 | + | 1.19793i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.0859 | − | 17.9474i | −0.0799122 | − | 0.0461373i | 0.459511 | − | 0.888172i | \(-0.348025\pi\) |
−0.539424 | + | 0.842035i | \(0.681358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −185.842 | − | 321.888i | −0.475299 | − | 0.823242i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.4758i | 0.0391793i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −90.3552 | −0.227595 | −0.113797 | − | 0.993504i | \(-0.536301\pi\) | ||||
−0.113797 | + | 0.993504i | \(0.536301\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.8381 | + | 21.8458i | −0.0943593 | + | 0.0544784i | −0.546437 | − | 0.837500i | \(-0.684016\pi\) |
0.452078 | + | 0.891978i | \(0.350683\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −63.5395 | + | 110.054i | −0.157666 | + | 0.273086i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −84.7166 | − | 48.9112i | −0.208149 | − | 0.120175i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 130.026 | + | 225.212i | 0.317913 | + | 0.550641i | 0.980052 | − | 0.198739i | \(-0.0636847\pi\) |
−0.662140 | + | 0.749381i | \(0.730351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 429.902i | 1.04092i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −138.974 | −0.334876 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 228.012 | − | 131.643i | 0.544181 | − | 0.314183i | −0.202591 | − | 0.979263i | \(-0.564936\pi\) |
0.746772 | + | 0.665081i | \(0.231603\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −183.605 | + | 318.013i | −0.436116 | + | 0.755376i | −0.997386 | − | 0.0722573i | \(-0.976980\pi\) |
0.561270 | + | 0.827633i | \(0.310313\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 73.4847 | + | 42.4264i | 0.172905 | + | 0.0998268i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 316.408 | + | 548.034i | 0.741002 | + | 1.28345i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 690.768i | − | 1.60271i | −0.598189 | − | 0.801355i | \(-0.704113\pi\) | ||
0.598189 | − | 0.801355i | \(-0.295887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −117.500 | −0.271363 | −0.135682 | − | 0.990752i | \(-0.543322\pi\) | ||||
−0.135682 | + | 0.990752i | \(0.543322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 208.142 | − | 120.171i | 0.476298 | − | 0.274991i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0000 | + | 43.3013i | −0.0569476 | + | 0.0986362i | −0.893094 | − | 0.449871i | \(-0.851470\pi\) |
0.836146 | + | 0.548507i | \(0.184803\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −456.217 | − | 263.397i | −1.02984 | − | 0.594576i | −0.112898 | − | 0.993607i | \(-0.536013\pi\) |
−0.916937 | + | 0.399031i | \(0.869347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 69.6117 | + | 120.571i | 0.156431 | + | 0.270946i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 321.882i | 0.716887i | 0.933552 | + | 0.358443i | \(0.116692\pi\) | ||||
−0.933552 | + | 0.358443i | \(0.883308\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1172.45 | 2.59966 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −195.535 | + | 112.892i | −0.429747 | + | 0.248114i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 216.540 | − | 375.057i | 0.473828 | − | 0.820695i | −0.525723 | − | 0.850656i | \(-0.676205\pi\) |
0.999551 | + | 0.0299614i | \(0.00953842\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −421.554 | − | 243.384i | −0.914433 | − | 0.527948i | −0.0325783 | − | 0.999469i | \(-0.510372\pi\) |
−0.881855 | + | 0.471521i | \(0.843705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −211.612 | − | 366.522i | −0.457045 | − | 0.791625i | 0.541758 | − | 0.840534i | \(-0.317759\pi\) |
−0.998803 | + | 0.0489094i | \(0.984425\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 295.831i | 0.633472i | 0.948514 | + | 0.316736i | \(0.102587\pi\) | ||||
−0.948514 | + | 0.316736i | \(0.897413\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1025.00 | 2.18550 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −596.031 | + | 344.119i | −1.26011 | + | 0.727524i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.4342 | + | 47.5174i | −0.0577561 | + | 0.100037i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −230.993 | − | 133.364i | −0.482240 | − | 0.278421i | 0.239109 | − | 0.970993i | \(-0.423145\pi\) |
−0.721350 | + | 0.692571i | \(0.756478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7367 | − | 35.9169i | −0.0431116 | − | 0.0746714i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 279.450i | 0.576185i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 247.750 | 0.508727 | 0.254364 | − | 0.967109i | \(-0.418134\pi\) | ||||
0.254364 | + | 0.967109i | \(0.418134\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −147.566 | + | 85.1971i | −0.300541 | + | 0.173517i | −0.642686 | − | 0.766130i | \(-0.722180\pi\) |
0.342145 | + | 0.939647i | \(0.388847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −401.842 | + | 696.011i | −0.815095 | + | 1.41179i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −908.051 | − | 524.264i | −1.82706 | − | 1.05486i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.6975 | − | 41.0453i | −0.0474900 | − | 0.0822551i | 0.841303 | − | 0.540563i | \(-0.181789\pi\) |
−0.888793 | + | 0.458308i | \(0.848456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 321.064i | 0.638298i | 0.947705 | + | 0.319149i | \(0.103397\pi\) | ||||
−0.947705 | + | 0.319149i | \(0.896603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −251.026 | −0.497082 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −105.763 | + | 61.0623i | −0.207786 | + | 0.119965i | −0.600282 | − | 0.799788i | \(-0.704945\pi\) |
0.392496 | + | 0.919754i | \(0.371612\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 640.092 | − | 1108.67i | 1.25263 | − | 2.16961i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −329.789 | − | 190.404i | −0.640368 | − | 0.369716i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −287.526 | − | 498.010i | −0.556143 | − | 0.963268i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 79.4567i | − | 0.152508i | −0.997088 | − | 0.0762540i | \(-0.975704\pi\) | ||
0.997088 | − | 0.0762540i | \(-0.0242960\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −864.605 | −1.65316 | −0.826582 | − | 0.562816i | \(-0.809718\pi\) | ||||
−0.826582 | + | 0.562816i | \(0.809718\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −249.461 | + | 144.026i | −0.473360 | + | 0.273295i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.6580 | + | 42.7089i | −0.0466125 | + | 0.0807352i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 430.482 | + | 248.539i | 0.807658 | + | 0.466302i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −104.355 | − | 180.748i | −0.195056 | − | 0.337848i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 2346.79i | − | 4.35398i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.6057 | 0.0621177 | 0.0310589 | − | 0.999518i | \(-0.490112\pi\) | ||||
0.0310589 | + | 0.999518i | \(0.490112\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 133.363 | − | 76.9971i | 0.244703 | − | 0.141279i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 279.540 | − | 484.177i | 0.511041 | − | 0.885149i | −0.488877 | − | 0.872353i | \(-0.662593\pi\) |
0.999918 | − | 0.0127965i | \(-0.00407336\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −450.061 | − | 259.843i | −0.816808 | − | 0.471584i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −46.6712 | − | 80.8368i | −0.0843963 | − | 0.146179i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 310.308i | − | 0.557105i | −0.960421 | − | 0.278553i | \(-0.910145\pi\) | ||
0.960421 | − | 0.278553i | \(-0.0898547\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −291.789 | −0.521984 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −490.768 | + | 283.345i | −0.871701 | + | 0.503277i | −0.867913 | − | 0.496716i | \(-0.834539\pi\) |
−0.00378817 | + | 0.999993i | \(0.501206\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 123.329 | − | 213.612i | 0.218281 | − | 0.378074i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −116.093 | − | 67.0262i | −0.204029 | − | 0.117796i | 0.394504 | − | 0.918894i | \(-0.370916\pi\) |
−0.598534 | + | 0.801098i | \(0.704250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 330.960 | + | 573.240i | 0.579615 | + | 1.00392i | 0.995523 | + | 0.0945161i | \(0.0301304\pi\) |
−0.415908 | + | 0.909407i | \(0.636536\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 109.508i | 0.190449i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 76.7630 | 0.133038 | 0.0665191 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665191 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 725.919 | − | 419.109i | 1.24943 | − | 0.721359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −99.2370 | + | 171.884i | −0.170218 | + | 0.294826i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −592.841 | − | 342.277i | −1.00995 | − | 0.583095i | −0.0987734 | − | 0.995110i | \(-0.531492\pi\) |
−0.911177 | + | 0.412015i | \(0.864825\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −93.1317 | − | 161.309i | −0.158118 | − | 0.273869i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 592.146i | − | 0.998560i | −0.866441 | − | 0.499280i | \(-0.833598\pi\) | ||
0.866441 | − | 0.499280i | \(-0.166402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −511.789 | −0.860150 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −877.078 | + | 506.381i | −1.46424 | + | 0.845377i | −0.999203 | − | 0.0399156i | \(-0.987291\pi\) |
−0.465034 | + | 0.885293i | \(0.653958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −161.789 | + | 280.227i | −0.269200 | + | 0.466268i | −0.968656 | − | 0.248408i | \(-0.920093\pi\) |
0.699455 | + | 0.714676i | \(0.253426\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −369.564 | − | 213.368i | −0.610849 | − | 0.352674i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 399.914 | + | 692.672i | 0.658837 | + | 1.14114i | 0.980917 | + | 0.194427i | \(0.0622848\pi\) |
−0.322080 | + | 0.946713i | \(0.604382\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 243.802i | − | 0.399022i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −680.302 | −1.10979 | −0.554896 | − | 0.831920i | \(-0.687242\pi\) | ||||
−0.554896 | + | 0.831920i | \(0.687242\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 229.382 | − | 132.434i | 0.371770 | − | 0.214641i | −0.302461 | − | 0.953162i | \(-0.597808\pi\) |
0.674231 | + | 0.738520i | \(0.264475\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −267.921 | + | 464.053i | −0.432829 | + | 0.749681i | −0.997116 | − | 0.0758974i | \(-0.975818\pi\) |
0.564287 | + | 0.825579i | \(0.309151\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −727.224 | − | 419.863i | −1.16729 | − | 0.673937i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 94.0085i | − | 0.149457i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 307.026 | 0.486571 | 0.243286 | − | 0.969955i | \(-0.421775\pi\) | ||||
0.243286 | + | 0.969955i | \(0.421775\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 126.611 | − | 73.0987i | 0.199387 | − | 0.115116i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 497.480 | − | 861.661i | 0.780973 | − | 1.35269i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1079.35 | + | 623.165i | 1.68386 | + | 0.972177i | 0.959054 | + | 0.283224i | \(0.0914040\pi\) |
0.724806 | + | 0.688953i | \(0.241929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −77.6975 | − | 134.576i | −0.120836 | − | 0.209294i | 0.799262 | − | 0.600983i | \(-0.205224\pi\) |
−0.920098 | + | 0.391689i | \(0.871891\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 142.649i | − | 0.220478i | −0.993905 | − | 0.110239i | \(-0.964838\pi\) | ||
0.993905 | − | 0.110239i | \(-0.0351617\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −562.894 | −0.867325 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −800.709 | + | 462.289i | −1.22620 | + | 0.707947i | −0.966233 | − | 0.257671i | \(-0.917045\pi\) |
−0.259967 | + | 0.965617i | \(0.583712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52.8224 | + | 91.4911i | −0.0806449 | + | 0.139681i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −304.880 | − | 176.023i | −0.462641 | − | 0.267106i | 0.250513 | − | 0.968113i | \(-0.419401\pi\) |
−0.713154 | + | 0.701007i | \(0.752734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 321.460 | + | 556.786i | 0.486325 | + | 0.842339i | 0.999876 | − | 0.0157198i | \(-0.00500396\pi\) |
−0.513552 | + | 0.858059i | \(0.671671\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 330.938i | − | 0.497651i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1037.21 | −1.55504 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −717.571 | + | 414.290i | −1.06941 | + | 0.617422i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −491.302 | + | 850.961i | −0.730019 | + | 1.26443i | 0.226856 | + | 0.973928i | \(0.427155\pi\) |
−0.956875 | + | 0.290501i | \(0.906178\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −334.952 | − | 193.384i | −0.494759 | − | 0.285649i | 0.231788 | − | 0.972766i | \(-0.425542\pi\) |
−0.726546 | + | 0.687117i | \(0.758876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −842.749 | − | 1459.68i | −1.24116 | − | 2.14976i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 504.539i | − | 0.738710i | −0.929288 | − | 0.369355i | \(-0.879579\pi\) | ||
0.929288 | − | 0.369355i | \(-0.120421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −483.079 | −0.705225 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −72.8727 | + | 42.0731i | −0.105766 | + | 0.0610640i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 135.540 | − | 234.761i | 0.196150 | − | 0.339741i | −0.751127 | − | 0.660158i | \(-0.770489\pi\) |
0.947277 | + | 0.320416i | \(0.103823\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 410.230 | + | 236.847i | 0.590259 | + | 0.340786i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 563.368 | + | 975.782i | 0.808275 | + | 1.39997i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 358.559i | − | 0.511496i | −0.966743 | − | 0.255748i | \(-0.917678\pi\) | ||
0.966743 | − | 0.255748i | \(-0.0823218\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.7886 | 0.0864703 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1311.22 | − | 757.032i | 1.85462 | − | 1.07077i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 366.789 | − | 635.298i | 0.517333 | − | 0.896048i | −0.482464 | − | 0.875916i | \(-0.660258\pi\) |
0.999797 | − | 0.0201318i | \(-0.00640859\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −321.947 | − | 185.876i | −0.451538 | − | 0.260696i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −147.816 | − | 256.024i | −0.206735 | − | 0.358076i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1108.37i | 1.54155i | 0.637110 | + | 0.770773i | \(0.280130\pi\) | ||||
−0.637110 | + | 0.770773i | \(0.719870\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2296.84 | 3.18563 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 205.064 | − | 118.394i | 0.282847 | − | 0.163302i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −632.519 | + | 1095.56i | −0.870040 | + | 1.50695i | −0.00808623 | + | 0.999967i | \(0.502574\pi\) |
−0.861954 | + | 0.506987i | \(0.830759\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −572.794 | − | 330.703i | −0.783575 | − | 0.452397i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 293.375 | + | 508.140i | 0.400238 | + | 0.693233i | 0.993754 | − | 0.111589i | \(-0.0355940\pi\) |
−0.593516 | + | 0.804822i | \(0.702261\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1342.09i | 1.82101i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −215.973 | −0.292250 | −0.146125 | − | 0.989266i | \(-0.546680\pi\) | ||||
−0.146125 | + | 0.989266i | \(0.546680\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 519.581 | − | 299.980i | 0.699302 | − | 0.403742i | −0.107786 | − | 0.994174i | \(-0.534376\pi\) |
0.807087 | + | 0.590432i | \(0.201043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −103.460 | + | 179.199i | −0.138873 | + | 0.240535i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1090.18 | + | 629.418i | 1.45552 | + | 0.840344i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −406.828 | − | 704.648i | −0.541716 | − | 0.938279i | −0.998806 | − | 0.0488587i | \(-0.984442\pi\) |
0.457090 | − | 0.889420i | \(-0.348892\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 276.919i | 0.366780i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1070.43 | 1.41405 | 0.707023 | − | 0.707190i | \(-0.250038\pi\) | ||||
0.707023 | + | 0.707190i | \(0.250038\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −567.153 | + | 327.446i | −0.745273 | + | 0.430284i | −0.823983 | − | 0.566614i | \(-0.808253\pi\) |
0.0787104 | + | 0.996898i | \(0.474920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −464.408 | + | 804.378i | −0.608660 | + | 1.05423i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −206.675 | − | 119.324i | −0.269459 | − | 0.155572i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −341.315 | − | 591.175i | −0.443843 | − | 0.768759i | 0.554128 | − | 0.832432i | \(-0.313052\pi\) |
−0.997971 | + | 0.0636729i | \(0.979719\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 770.690i | 0.997012i | 0.866886 | + | 0.498506i | \(0.166118\pi\) | ||||
−0.866886 | + | 0.498506i | \(0.833882\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 84.8683 | 0.109508 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −630.969 | + | 364.290i | −0.809974 | + | 0.467638i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 686.447 | − | 1188.96i | 0.878933 | − | 1.52236i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −60.9740 | − | 35.2033i | −0.0776739 | − | 0.0448450i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 126.935 | + | 219.857i | 0.161289 | + | 0.279361i | 0.935331 | − | 0.353773i | \(-0.115102\pi\) |
−0.774042 | + | 0.633134i | \(0.781768\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1487.71i | 1.88080i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −351.290 | −0.442988 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −914.401 | + | 527.929i | −1.14730 | + | 0.662396i | −0.948229 | − | 0.317589i | \(-0.897127\pi\) |
−0.199075 | + | 0.979984i | \(0.563794\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 276.316 | − | 478.593i | 0.345827 | − | 0.598990i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1451.64 | + | 838.107i | 1.80778 | + | 1.04372i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −330.250 | − | 572.009i | −0.410248 | − | 0.710571i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 506.698i | 0.626326i | 0.949699 | + | 0.313163i | \(0.101389\pi\) | ||||
−0.949699 | + | 0.313163i | \(0.898611\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 537.473 | 0.662729 | 0.331365 | − | 0.943503i | \(-0.392491\pi\) | ||||
0.331365 | + | 0.943503i | \(0.392491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 195.841 | − | 113.069i | 0.240295 | − | 0.138735i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 213.842 | − | 370.385i | 0.261741 | − | 0.453348i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −222.758 | − | 128.609i | −0.271325 | − | 0.156650i | 0.358165 | − | 0.933658i | \(-0.383403\pi\) |
−0.629490 | + | 0.777009i | \(0.716736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 183.506 | + | 317.842i | 0.222973 | + | 0.386200i | 0.955709 | − | 0.294312i | \(-0.0950906\pi\) |
−0.732737 | + | 0.680512i | \(0.761757\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 122.254i | − | 0.147829i | −0.997265 | − | 0.0739144i | \(-0.976451\pi\) | ||
0.997265 | − | 0.0739144i | \(-0.0235492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 335.237 | 0.404387 | 0.202194 | − | 0.979346i | \(-0.435193\pi\) | ||||
0.202194 | + | 0.979346i | \(0.435193\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1953.14 | − | 1127.65i | 2.34471 | − | 1.35372i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 165.250 | − | 286.221i | 0.197904 | − | 0.342780i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −670.322 | − | 387.010i | −0.798953 | − | 0.461276i | 0.0441519 | − | 0.999025i | \(-0.485941\pi\) |
−0.843105 | + | 0.537749i | \(0.819275\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 700.868 | + | 1213.94i | 0.833375 | + | 1.44345i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 252.558i | 0.298885i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2573.85 | 3.03879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 105.070 | − | 60.6622i | 0.123467 | − | 0.0712834i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −382.296 | + | 662.156i | −0.448178 | + | 0.776267i | −0.998267 | − | 0.0588388i | \(-0.981260\pi\) |
0.550090 | + | 0.835106i | \(0.314594\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1313.02 | + | 758.074i | 1.53211 | + | 0.884567i | 0.999264 | + | 0.0383577i | \(0.0122126\pi\) |
0.532851 | + | 0.846209i | \(0.321121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −216.842 | − | 375.581i | −0.252435 | − | 0.437231i | 0.711760 | − | 0.702422i | \(-0.247898\pi\) |
−0.964196 | + | 0.265191i | \(0.914565\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1255.50i | − | 1.45481i | −0.686206 | − | 0.727407i | \(-0.740725\pi\) | ||
0.686206 | − | 0.727407i | \(-0.259275\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −742.552 | −0.858442 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 105.844 | − | 61.1091i | 0.121800 | − | 0.0703212i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −284.500 | + | 492.768i | −0.326636 | + | 0.565750i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 130.586 | + | 75.3937i | 0.149241 | + | 0.0861642i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −501.796 | − | 869.136i | −0.572173 | − | 0.991033i | −0.996342 | − | 0.0854504i | \(-0.972767\pi\) |
0.424169 | − | 0.905583i | \(-0.360566\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 737.214i | 0.836792i | 0.908265 | + | 0.418396i | \(0.137408\pi\) | ||||
−0.908265 | + | 0.418396i | \(0.862592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 336.394 | 0.380968 | 0.190484 | − | 0.981690i | \(-0.438994\pi\) | ||||
0.190484 | + | 0.981690i | \(0.438994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −686.873 | + | 396.566i | −0.774377 | + | 0.447087i | −0.834434 | − | 0.551108i | \(-0.814205\pi\) |
0.0600566 | + | 0.998195i | \(0.480872\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −440.895 | + | 763.652i | −0.495945 | + | 0.859001i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 309.473 | + | 178.674i | 0.346554 | + | 0.200083i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.2829 | − | 88.8246i | −0.0572993 | − | 0.0992454i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 803.831i | 0.894139i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −190.736 | −0.211694 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −257.298 | + | 148.551i | −0.284308 | + | 0.164145i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 539.828 | − | 935.010i | 0.595180 | − | 1.03088i | −0.398341 | − | 0.917237i | \(-0.630414\pi\) |
0.993521 | − | 0.113645i | \(-0.0362527\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1276.25 | − | 736.843i | −1.40093 | − | 0.808828i | −0.406443 | − | 0.913676i | \(-0.633231\pi\) |
−0.994488 | + | 0.104848i | \(0.966564\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 548.763 | + | 950.485i | 0.601055 | + | 1.04106i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 637.196i | − | 0.694871i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1602.92 | −1.74420 | −0.872101 | − | 0.489327i | \(-0.837243\pi\) | ||||
−0.872101 | + | 0.489327i | \(0.837243\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 504.079 | − | 291.030i | 0.546131 | − | 0.315309i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8488 | + | 23.9867i | −0.0149716 | + | 0.0259316i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 895.449 | + | 516.988i | 0.963885 | + | 0.556499i | 0.897366 | − | 0.441286i | \(-0.145478\pi\) |
0.0665183 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 729.171 | + | 1262.96i | 0.783212 | + | 1.35656i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 670.114i | − | 0.716699i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1258.05 | −1.34264 | −0.671319 | − | 0.741169i | \(-0.734272\pi\) | ||||
−0.671319 | + | 0.741169i | \(0.734272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −660.669 | + | 381.438i | −0.702093 | + | 0.405353i | −0.808126 | − | 0.589009i | \(-0.799518\pi\) |
0.106034 | + | 0.994363i | \(0.466185\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −727.065 | + | 1259.31i | −0.771013 | + | 1.33543i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 886.424 | + | 511.777i | 0.936034 | + | 0.540419i | 0.888715 | − | 0.458460i | \(-0.151599\pi\) |
0.0473191 | + | 0.998880i | \(0.484932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 355.329 | + | 615.448i | 0.374424 | + | 0.648522i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 63.7513i | 0.0668954i | 0.999440 | + | 0.0334477i | \(0.0106487\pi\) | ||||
−0.999440 | + | 0.0334477i | \(0.989351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −366.658 | −0.383935 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2523.33 | − | 1456.84i | 2.63121 | − | 1.51913i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 336.447 | − | 582.744i | 0.350101 | − | 0.606393i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 213.014 | + | 122.984i | 0.220740 | + | 0.127444i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 252.993 | + | 438.197i | 0.261627 | + | 0.453151i | 0.966674 | − | 0.256009i | \(-0.0824077\pi\) |
−0.705047 | + | 0.709160i | \(0.749074\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1803.51i | − | 1.85738i | −0.370862 | − | 0.928688i | \(-0.620938\pi\) | ||
0.370862 | − | 0.928688i | \(-0.379062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2857.08 | −2.93636 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1597.42 | + | 922.272i | −1.63503 | + | 0.943983i | −0.652517 | + | 0.757774i | \(0.726287\pi\) |
−0.982510 | + | 0.186209i | \(0.940380\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 549.749 | − | 952.194i | 0.561542 | − | 0.972619i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −512.813 | − | 296.073i | −0.521682 | − | 0.301193i | 0.215941 | − | 0.976406i | \(-0.430718\pi\) |
−0.737623 | + | 0.675213i | \(0.764052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −236.026 | − | 408.810i | −0.239621 | − | 0.415035i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 853.589i | − | 0.863083i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 961.684 | 0.970418 | 0.485209 | − | 0.874398i | \(-0.338744\pi\) | ||||
0.485209 | + | 0.874398i | \(0.338744\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.0608 | − | 20.2424i | 0.0352370 | − | 0.0203441i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −449.835 | + | 779.137i | −0.451189 | + | 0.781482i | −0.998460 | − | 0.0554733i | \(-0.982333\pi\) |
0.547271 | + | 0.836955i | \(0.315667\pi\) | |||||||
\(998\) | 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.f.1241.2 | 8 | ||
3.2 | odd | 2 | inner | 1620.3.o.f.1241.4 | 8 | ||
9.2 | odd | 6 | 180.3.g.a.161.3 | yes | 4 | ||
9.4 | even | 3 | inner | 1620.3.o.f.701.4 | 8 | ||
9.5 | odd | 6 | inner | 1620.3.o.f.701.2 | 8 | ||
9.7 | even | 3 | 180.3.g.a.161.1 | ✓ | 4 | ||
36.7 | odd | 6 | 720.3.l.c.161.2 | 4 | |||
36.11 | even | 6 | 720.3.l.c.161.4 | 4 | |||
45.2 | even | 12 | 900.3.b.b.449.2 | 8 | |||
45.7 | odd | 12 | 900.3.b.b.449.1 | 8 | |||
45.29 | odd | 6 | 900.3.g.d.701.4 | 4 | |||
45.34 | even | 6 | 900.3.g.d.701.3 | 4 | |||
45.38 | even | 12 | 900.3.b.b.449.8 | 8 | |||
45.43 | odd | 12 | 900.3.b.b.449.7 | 8 | |||
72.11 | even | 6 | 2880.3.l.f.1601.2 | 4 | |||
72.29 | odd | 6 | 2880.3.l.b.1601.1 | 4 | |||
72.43 | odd | 6 | 2880.3.l.f.1601.4 | 4 | |||
72.61 | even | 6 | 2880.3.l.b.1601.3 | 4 | |||
180.7 | even | 12 | 3600.3.c.k.449.8 | 8 | |||
180.43 | even | 12 | 3600.3.c.k.449.2 | 8 | |||
180.47 | odd | 12 | 3600.3.c.k.449.7 | 8 | |||
180.79 | odd | 6 | 3600.3.l.n.1601.2 | 4 | |||
180.83 | odd | 12 | 3600.3.c.k.449.1 | 8 | |||
180.119 | even | 6 | 3600.3.l.n.1601.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.g.a.161.1 | ✓ | 4 | 9.7 | even | 3 | ||
180.3.g.a.161.3 | yes | 4 | 9.2 | odd | 6 | ||
720.3.l.c.161.2 | 4 | 36.7 | odd | 6 | |||
720.3.l.c.161.4 | 4 | 36.11 | even | 6 | |||
900.3.b.b.449.1 | 8 | 45.7 | odd | 12 | |||
900.3.b.b.449.2 | 8 | 45.2 | even | 12 | |||
900.3.b.b.449.7 | 8 | 45.43 | odd | 12 | |||
900.3.b.b.449.8 | 8 | 45.38 | even | 12 | |||
900.3.g.d.701.3 | 4 | 45.34 | even | 6 | |||
900.3.g.d.701.4 | 4 | 45.29 | odd | 6 | |||
1620.3.o.f.701.2 | 8 | 9.5 | odd | 6 | inner | ||
1620.3.o.f.701.4 | 8 | 9.4 | even | 3 | inner | ||
1620.3.o.f.1241.2 | 8 | 1.1 | even | 1 | trivial | ||
1620.3.o.f.1241.4 | 8 | 3.2 | odd | 2 | inner | ||
2880.3.l.b.1601.1 | 4 | 72.29 | odd | 6 | |||
2880.3.l.b.1601.3 | 4 | 72.61 | even | 6 | |||
2880.3.l.f.1601.2 | 4 | 72.11 | even | 6 | |||
2880.3.l.f.1601.4 | 4 | 72.43 | odd | 6 | |||
3600.3.c.k.449.1 | 8 | 180.83 | odd | 12 | |||
3600.3.c.k.449.2 | 8 | 180.43 | even | 12 | |||
3600.3.c.k.449.7 | 8 | 180.47 | odd | 12 | |||
3600.3.c.k.449.8 | 8 | 180.7 | even | 12 | |||
3600.3.l.n.1601.1 | 4 | 180.119 | even | 6 | |||
3600.3.l.n.1601.2 | 4 | 180.79 | odd | 6 |