Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(109,1620)]
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, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.r (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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 3x^{14} - 11x^{12} - 90x^{10} - 450x^{8} - 2250x^{6} - 6875x^{4} + 46875x^{2} + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1189.8 | ||
Root | \(-2.23368 + 0.103355i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1189 |
Dual form | 1620.2.r.h.109.8 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 2.23368 | + | 0.103355i | 0.998931 | + | 0.0462217i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.10979 | − | 0.640739i | −0.419462 | − | 0.242176i | 0.275385 | − | 0.961334i | \(-0.411195\pi\) |
−0.694847 | + | 0.719158i | \(0.744528\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.07237 | − | 3.58945i | 0.624844 | − | 1.08226i | −0.363727 | − | 0.931505i | \(-0.618496\pi\) |
0.988571 | − | 0.150756i | \(-0.0481707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.64823 | − | 3.26101i | 1.56654 | − | 0.904441i | 0.569970 | − | 0.821666i | \(-0.306955\pi\) |
0.996568 | − | 0.0827757i | \(-0.0263785\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.98507i | − | 1.45159i | −0.687909 | − | 0.725797i | \(-0.741471\pi\) | ||
0.687909 | − | 0.725797i | \(-0.258529\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.17891 | −1.64695 | −0.823477 | − | 0.567349i | \(-0.807969\pi\) | ||||
−0.823477 | + | 0.567349i | \(0.807969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.52202 | + | 3.76549i | −1.35993 | + | 0.785159i | −0.989615 | − | 0.143745i | \(-0.954085\pi\) |
−0.370320 | + | 0.928904i | \(0.620752\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.97864 | + | 0.461723i | 0.995727 | + | 0.0923445i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.59808 | + | 4.50000i | −0.482451 | + | 0.835629i | −0.999797 | − | 0.0201471i | \(-0.993587\pi\) |
0.517346 | + | 0.855776i | \(0.326920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.58945 | − | 4.48507i | −0.465080 | − | 0.805542i | 0.534125 | − | 0.845405i | \(-0.320641\pi\) |
−0.999205 | + | 0.0398636i | \(0.987308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.41269 | − | 1.54591i | −0.407820 | − | 0.261306i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.24054i | − | 0.861540i | −0.902462 | − | 0.430770i | \(-0.858242\pi\) | ||
0.902462 | − | 0.430770i | \(-0.141758\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.340322 | + | 0.589454i | 0.0531493 | + | 0.0920573i | 0.891376 | − | 0.453265i | \(-0.149741\pi\) |
−0.838227 | + | 0.545322i | \(0.816407\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.10979 | + | 0.640739i | 0.169242 | + | 0.0977117i | 0.582228 | − | 0.813025i | \(-0.302181\pi\) |
−0.412987 | + | 0.910737i | \(0.635514\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.59980 | + | 2.65570i | 0.670950 | + | 0.387373i | 0.796437 | − | 0.604722i | \(-0.206716\pi\) |
−0.125486 | + | 0.992095i | \(0.540049\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.67891 | − | 4.64001i | −0.382701 | − | 0.662858i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.21958i | 0.304883i | 0.988312 | + | 0.152442i | \(0.0487136\pi\) | ||||
−0.988312 | + | 0.152442i | \(0.951286\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | − | 7.80350i | 0.674200 | − | 1.05222i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.80442 | + | 6.58945i | 0.495294 | + | 0.857874i | 0.999985 | − | 0.00542586i | \(-0.00172711\pi\) |
−0.504692 | + | 0.863300i | \(0.668394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.08945 | − | 1.88699i | 0.139490 | − | 0.241604i | −0.787813 | − | 0.615914i | \(-0.788787\pi\) |
0.927304 | + | 0.374310i | \(0.122120\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.9534 | − | 6.70027i | 1.60667 | − | 0.831067i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5161 | − | 7.80350i | 1.65125 | − | 0.953349i | 0.674689 | − | 0.738103i | \(-0.264278\pi\) |
0.976560 | − | 0.215246i | \(-0.0690554\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.50603 | −0.653446 | −0.326723 | − | 0.945120i | \(-0.605944\pi\) | ||||
−0.326723 | + | 0.945120i | \(0.605944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.80350i | − | 0.913330i | −0.889639 | − | 0.456665i | \(-0.849044\pi\) | ||
0.889639 | − | 0.456665i | \(-0.150956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.59980 | + | 2.65570i | −0.524196 | + | 0.302645i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00000 | − | 5.19615i | 0.337526 | − | 0.584613i | −0.646440 | − | 0.762964i | \(-0.723743\pi\) |
0.983967 | + | 0.178352i | \(0.0570765\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.44423 | + | 4.87528i | 0.926875 | + | 0.535132i | 0.885822 | − | 0.464025i | \(-0.153595\pi\) |
0.0410532 | + | 0.999157i | \(0.486929\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.618586 | − | 13.3687i | 0.0670951 | − | 1.45004i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0215 | −1.06228 | −0.531141 | − | 0.847284i | \(-0.678236\pi\) | ||||
−0.531141 | + | 0.847284i | \(0.678236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.35782 | −0.876137 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.0354 | − | 0.741975i | −1.64519 | − | 0.0761250i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4063 | + | 7.16276i | 1.25966 | + | 0.727268i | 0.973009 | − | 0.230766i | \(-0.0741232\pi\) |
0.286655 | + | 0.958034i | \(0.407457\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.340322 | + | 0.589454i | −0.0338633 | + | 0.0586529i | −0.882460 | − | 0.470387i | \(-0.844114\pi\) |
0.848597 | + | 0.529040i | \(0.177448\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.21958 | + | 1.28148i | −0.218702 | + | 0.126268i | −0.605349 | − | 0.795960i | \(-0.706966\pi\) |
0.386647 | + | 0.922228i | \(0.373633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.86081 | − | 4.53844i | 0.739483 | − | 0.426941i | −0.0823983 | − | 0.996599i | \(-0.526258\pi\) |
0.821881 | + | 0.569659i | \(0.192925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.9573 | + | 7.73681i | −1.39477 | + | 0.721461i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.83487 | + | 6.64218i | −0.351542 | + | 0.608888i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.08945 | − | 5.35109i | −0.280859 | − | 0.486463i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0729 | + | 1.54591i | 0.990395 | + | 0.138270i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.28148i | 0.113713i | 0.998382 | + | 0.0568563i | \(0.0181077\pi\) | ||||
−0.998382 | + | 0.0568563i | \(0.981892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.75302 | + | 4.76836i | 0.240532 | + | 0.416614i | 0.960866 | − | 0.277014i | \(-0.0893447\pi\) |
−0.720334 | + | 0.693627i | \(0.756011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.96709 | + | 4.59980i | 0.690835 | + | 0.398854i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.78303 | − | 5.64823i | −0.835820 | − | 0.482561i | 0.0200209 | − | 0.999800i | \(-0.493627\pi\) |
−0.855841 | + | 0.517238i | \(0.826960\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.58945 | + | 14.8774i | 0.728548 | + | 1.26188i | 0.957497 | + | 0.288444i | \(0.0931378\pi\) |
−0.228949 | + | 0.973438i | \(0.573529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 27.0321i | − | 2.26054i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.26836 | + | 9.78303i | −0.520559 | + | 0.812436i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.86660 | + | 17.0895i | 0.808303 | + | 1.40002i | 0.914038 | + | 0.405628i | \(0.132947\pi\) |
−0.105735 | + | 0.994394i | \(0.533719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.58945 | + | 4.48507i | −0.210727 | + | 0.364990i | −0.951942 | − | 0.306278i | \(-0.900916\pi\) |
0.741215 | + | 0.671267i | \(0.234250\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.32045 | − | 10.2858i | −0.427349 | − | 0.826177i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.53844 | − | 2.62027i | 0.362207 | − | 0.209120i | −0.307841 | − | 0.951438i | \(-0.599607\pi\) |
0.670049 | + | 0.742317i | \(0.266273\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.65078 | 0.760588 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.7626i | − | 0.921315i | −0.887578 | − | 0.460657i | \(-0.847614\pi\) | ||
0.887578 | − | 0.460657i | \(-0.152386\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.92222 | + | 1.10979i | −0.148746 | + | 0.0858783i | −0.572526 | − | 0.819887i | \(-0.694036\pi\) |
0.423780 | + | 0.905765i | \(0.360703\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.7684 | − | 25.5796i | 1.13603 | − | 1.96766i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.583422 | − | 0.336839i | −0.0443567 | − | 0.0256094i | 0.477658 | − | 0.878546i | \(-0.341486\pi\) |
−0.522014 | + | 0.852937i | \(0.674819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.22940 | − | 3.70242i | −0.395306 | − | 0.279877i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.5370 | −1.08655 | −0.543275 | − | 0.839555i | \(-0.682816\pi\) | ||||
−0.543275 | + | 0.839555i | \(0.682816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.1789 | 1.12824 | 0.564120 | − | 0.825693i | \(-0.309216\pi\) | ||||
0.564120 | + | 0.825693i | \(0.309216\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.541635 | − | 11.7057i | 0.0398218 | − | 0.860619i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.4831 | − | 12.4033i | −1.57100 | − | 0.907019i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.1453 | − | 22.7684i | 0.951162 | − | 1.64746i | 0.208246 | − | 0.978077i | \(-0.433225\pi\) |
0.742916 | − | 0.669384i | \(-0.233442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.1972 | − | 6.46470i | 0.805992 | − | 0.465339i | −0.0395704 | − | 0.999217i | \(-0.512599\pi\) |
0.845562 | + | 0.533877i | \(0.179266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.20466i | 0.584558i | 0.956333 | + | 0.292279i | \(0.0944135\pi\) | ||||
−0.956333 | + | 0.292279i | \(0.905586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.35782 | 0.167141 | 0.0835706 | − | 0.996502i | \(-0.473368\pi\) | ||||
0.0835706 | + | 0.996502i | \(0.473368\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.76665 | − | 3.32937i | 0.404739 | − | 0.233676i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.699246 | + | 1.35182i | 0.0488374 | + | 0.0944155i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.8774 | + | 25.7684i | −1.02909 | + | 1.78243i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.41055 | − | 4.17519i | −0.165949 | − | 0.287432i | 0.771043 | − | 0.636783i | \(-0.219735\pi\) |
−0.936992 | + | 0.349351i | \(0.886402\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.41269 | + | 1.54591i | 0.164544 | + | 0.105430i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.63665i | 0.450525i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.5174 | − | 33.8051i | −1.31288 | − | 2.27398i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.85730 | − | 3.95906i | −0.459199 | − | 0.265119i | 0.252508 | − | 0.967595i | \(-0.418744\pi\) |
−0.711707 | + | 0.702476i | \(0.752078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.8107 | + | 10.8604i | 1.24851 | + | 0.720827i | 0.970812 | − | 0.239842i | \(-0.0770956\pi\) |
0.277697 | + | 0.960669i | \(0.410429\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.08945 | + | 15.7434i | 0.600648 | + | 1.04035i | 0.992723 | + | 0.120420i | \(0.0384240\pi\) |
−0.392075 | + | 0.919933i | \(0.628243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.0470i | 1.37884i | 0.724363 | + | 0.689418i | \(0.242134\pi\) | ||||
−0.724363 | + | 0.689418i | \(0.757866\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0000 | + | 6.40739i | 0.652328 | + | 0.417972i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0729 | + | 19.1789i | 0.716249 | + | 1.24058i | 0.962476 | + | 0.271368i | \(0.0874761\pi\) |
−0.246226 | + | 0.969212i | \(0.579191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50000 | + | 16.4545i | −0.611949 | + | 1.05993i | 0.378963 | + | 0.925412i | \(0.376281\pi\) |
−0.990912 | + | 0.134515i | \(0.957053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.50425 | − | 10.6412i | −0.351654 | − | 0.679839i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −40.5482 | + | 23.4105i | −2.58002 | + | 1.48957i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.3205 | 1.09326 | 0.546630 | − | 0.837374i | \(-0.315910\pi\) | ||||
0.546630 | + | 0.837374i | \(0.315910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.2140i | 1.96241i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.93860 | − | 3.42865i | 0.370439 | − | 0.213873i | −0.303211 | − | 0.952923i | \(-0.598059\pi\) |
0.673650 | + | 0.739050i | \(0.264725\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.35782 | + | 5.81591i | −0.208645 | + | 0.361383i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0440 | − | 7.53098i | −0.804330 | − | 0.464380i | 0.0406531 | − | 0.999173i | \(-0.487056\pi\) |
−0.844983 | + | 0.534793i | \(0.820389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.229405 | + | 4.95783i | −0.0140922 | + | 0.304557i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.28001 | 0.565812 | 0.282906 | − | 0.959148i | \(-0.408702\pi\) | ||||
0.282906 | + | 0.959148i | \(0.408702\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.357817 | 0.0217358 | 0.0108679 | − | 0.999941i | \(-0.496541\pi\) | ||||
0.0108679 | + | 0.999941i | \(0.496541\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.9749 | − | 16.9137i | 0.722115 | − | 1.01994i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1867 | + | 5.88128i | 0.612058 | + | 0.353372i | 0.773770 | − | 0.633466i | \(-0.218368\pi\) |
−0.161712 | + | 0.986838i | \(0.551702\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.61904 | + | 6.26836i | −0.215894 | + | 0.373939i | −0.953549 | − | 0.301239i | \(-0.902600\pi\) |
0.737655 | + | 0.675178i | \(0.235933\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.8125 | + | 14.3255i | −1.47495 | + | 0.851563i | −0.999601 | − | 0.0282335i | \(-0.991012\pi\) |
−0.475350 | + | 0.879797i | \(0.657678\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.872228i | − | 0.0514860i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.8211 | −1.10712 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.5497 | + | 8.97761i | −0.908422 | + | 0.524477i | −0.879923 | − | 0.475116i | \(-0.842406\pi\) |
−0.0284987 | + | 0.999594i | \(0.509073\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.81680 | + | 15.1119i | 0.455112 | + | 0.879850i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.5586 | + | 42.5367i | −1.42026 | + | 2.45996i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.821092 | − | 1.42217i | −0.0473269 | − | 0.0819727i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.62852 | − | 4.10233i | 0.150509 | − | 0.234899i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.8885i | − | 0.963876i | −0.876205 | − | 0.481938i | \(-0.839933\pi\) | ||
0.876205 | − | 0.481938i | \(-0.160067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.48507 | + | 7.76836i | 0.254325 | + | 0.440503i | 0.964712 | − | 0.263308i | \(-0.0848135\pi\) |
−0.710387 | + | 0.703811i | \(0.751480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.86782 | − | 4.54249i | −0.444715 | − | 0.256757i | 0.260880 | − | 0.965371i | \(-0.415987\pi\) |
−0.705596 | + | 0.708615i | \(0.749321\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5384 | − | 6.08435i | −0.591895 | − | 0.341731i | 0.173951 | − | 0.984754i | \(-0.444347\pi\) |
−0.765847 | + | 0.643023i | \(0.777680\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.7684 | + | 18.6514i | 0.602913 | + | 1.04428i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.9663i | 2.39071i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.6262 | − | 13.6275i | 1.64336 | − | 0.755915i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.40322 | − | 5.89454i | −0.187625 | − | 0.324977i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.768363 | + | 1.33084i | −0.0422330 | + | 0.0731497i | −0.886369 | − | 0.462979i | \(-0.846781\pi\) |
0.844136 | + | 0.536129i | \(0.180114\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 30.9970 | − | 16.0335i | 1.69355 | − | 0.876006i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.21958 | + | 1.28148i | −0.120908 | + | 0.0698065i | −0.559234 | − | 0.829010i | \(-0.688905\pi\) |
0.438326 | + | 0.898816i | \(0.355572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.4653 | −1.16241 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.8363i | 0.855078i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.92222 | + | 1.10979i | −0.103190 | + | 0.0595767i | −0.550707 | − | 0.834699i | \(-0.685642\pi\) |
0.447517 | + | 0.894275i | \(0.352308\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.41055 | − | 7.63929i | 0.236091 | − | 0.408922i | −0.723498 | − | 0.690326i | \(-0.757467\pi\) |
0.959589 | + | 0.281405i | \(0.0908003\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.1659 | − | 13.9522i | −1.28622 | − | 0.742599i | −0.308241 | − | 0.951308i | \(-0.599740\pi\) |
−0.977978 | + | 0.208709i | \(0.933074\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.2987 | − | 0.569075i | −0.652747 | − | 0.0302034i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.3624 | −1.02191 | −0.510955 | − | 0.859607i | \(-0.670708\pi\) | ||||
−0.510955 | + | 0.859607i | \(0.670708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.5367 | 1.71246 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.806529 | − | 17.4305i | 0.0422156 | − | 0.912354i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.21958 | + | 1.28148i | 0.115861 | + | 0.0668926i | 0.556811 | − | 0.830639i | \(-0.312025\pi\) |
−0.440949 | + | 0.897532i | \(0.645358\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.42217 | − | 2.46327i | 0.0738355 | − | 0.127887i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.6258 | + | 8.44423i | −0.757297 | + | 0.437226i | −0.828325 | − | 0.560249i | \(-0.810706\pi\) |
0.0710272 | + | 0.997474i | \(0.477372\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 33.8894i | 1.74539i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3578 | −1.14844 | −0.574222 | − | 0.818700i | \(-0.694695\pi\) | ||||
−0.574222 | + | 0.818700i | \(0.694695\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3664 | − | 5.98507i | 0.529701 | − | 0.305823i | −0.211194 | − | 0.977444i | \(-0.567735\pi\) |
0.740895 | + | 0.671621i | \(0.234402\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5490 | + | 5.45656i | −0.537625 | + | 0.278092i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.24756 | + | 10.8211i | −0.316764 | + | 0.548651i | −0.979811 | − | 0.199927i | \(-0.935930\pi\) |
0.663047 | + | 0.748578i | \(0.269263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.5367 | + | 39.0348i | 1.13973 | + | 1.97407i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.23808 | − | 11.2965i | 0.364187 | − | 0.568387i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.6920i | 1.23925i | 0.784896 | + | 0.619627i | \(0.212716\pi\) | ||||
−0.784896 | + | 0.619627i | \(0.787284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.03173 | + | 10.4473i | 0.301210 | + | 0.521712i | 0.976410 | − | 0.215923i | \(-0.0692760\pi\) |
−0.675200 | + | 0.737635i | \(0.735943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.2517 | − | 16.8885i | −1.45713 | − | 0.841275i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.8107 | − | 10.8604i | −0.932411 | − | 0.538328i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.08945 | + | 15.7434i | 0.449445 | + | 0.778461i | 0.998350 | − | 0.0574237i | \(-0.0182886\pi\) |
−0.548905 | + | 0.835885i | \(0.684955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9.75056i | − | 0.479794i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.3578 | + | 11.7626i | 0.901150 | + | 0.577401i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.82539 | − | 8.35782i | −0.235736 | − | 0.408306i | 0.723751 | − | 0.690062i | \(-0.242417\pi\) |
−0.959486 | + | 0.281756i | \(0.909083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.85782 | − | 13.6101i | 0.382967 | − | 0.663318i | −0.608518 | − | 0.793540i | \(-0.708236\pi\) |
0.991485 | + | 0.130222i | \(0.0415691\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.76344 | − | 29.7975i | 0.134047 | − | 1.44539i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.41813 | + | 1.39611i | −0.117022 | + | 0.0675625i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.1160 | 1.49881 | 0.749403 | − | 0.662114i | \(-0.230341\pi\) | ||||
0.749403 | + | 0.662114i | \(0.230341\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.7738i | 0.806099i | 0.915178 | + | 0.403050i | \(0.132050\pi\) | ||||
−0.915178 | + | 0.403050i | \(0.867950\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 46.8210 | − | 27.0321i | 2.23975 | − | 1.29312i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.76836 | + | 13.4552i | −0.370764 | + | 0.642182i | −0.989683 | − | 0.143273i | \(-0.954237\pi\) |
0.618920 | + | 0.785454i | \(0.287571\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.6438 | + | 10.1867i | 0.838284 | + | 0.483984i | 0.856681 | − | 0.515847i | \(-0.172523\pi\) |
−0.0183965 | + | 0.999831i | \(0.505856\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.3849 | − | 1.03577i | −1.06115 | − | 0.0491004i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.8386 | 1.59694 | 0.798471 | − | 0.602033i | \(-0.205642\pi\) | ||||
0.798471 | + | 0.602033i | \(0.205642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.82109 | 0.132840 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.6687 | − | 0.863821i | −0.875201 | − | 0.0404965i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0992755 | − | 0.0573167i | −0.00464391 | − | 0.00268116i | 0.497676 | − | 0.867363i | \(-0.334187\pi\) |
−0.502320 | + | 0.864682i | \(0.667520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.48507 | + | 7.76836i | −0.208890 | + | 0.361809i | −0.951365 | − | 0.308065i | \(-0.900319\pi\) |
0.742475 | + | 0.669874i | \(0.233652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.65875 | − | 3.84443i | 0.309458 | − | 0.178666i | −0.337226 | − | 0.941424i | \(-0.609489\pi\) |
0.646684 | + | 0.762758i | \(0.276155\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 29.2517i | − | 1.35361i | −0.736164 | − | 0.676803i | \(-0.763365\pi\) | ||
0.736164 | − | 0.676803i | \(-0.236635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.0000 | −0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.59980 | − | 2.65570i | 0.211499 | − | 0.122109i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.7412 | − | 3.31467i | −1.63992 | − | 0.152087i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.9288 | + | 27.5895i | −0.727804 | + | 1.26059i | 0.230005 | + | 0.973190i | \(0.426126\pi\) |
−0.957809 | + | 0.287405i | \(0.907207\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.0895 | − | 29.5998i | −0.779212 | − | 1.34963i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.9713 | + | 17.2815i | 1.22470 | + | 0.784714i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.7769i | 1.53058i | 0.643686 | + | 0.765290i | \(0.277404\pi\) | ||||
−0.643686 | + | 0.765290i | \(0.722596\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.7231 | − | 20.3051i | −0.529058 | − | 0.916356i | −0.999426 | − | 0.0338851i | \(-0.989212\pi\) |
0.470367 | − | 0.882471i | \(-0.344121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.9328 | + | 15.5497i | 1.21299 | + | 0.700322i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.11055 | + | 3.52793i | 0.274095 | + | 0.158249i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.58945 | − | 6.21712i | −0.160686 | − | 0.278316i | 0.774429 | − | 0.632661i | \(-0.218037\pi\) |
−0.935115 | + | 0.354345i | \(0.884704\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 40.7467i | − | 1.81681i | −0.418096 | − | 0.908403i | \(-0.637302\pi\) | ||
0.418096 | − | 0.908403i | \(-0.362698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.821092 | + | 1.28148i | −0.0365381 | + | 0.0570250i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.8983 | + | 27.5367i | 0.704681 | + | 1.22054i | 0.966806 | + | 0.255510i | \(0.0822434\pi\) |
−0.262125 | + | 0.965034i | \(0.584423\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.00000 | + | 8.66025i | −0.221187 | + | 0.383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.09028 | + | 2.63300i | −0.224305 | + | 0.116024i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.0650 | − | 11.0072i | 0.838478 | − | 0.484096i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.1459 | −0.970229 | −0.485115 | − | 0.874451i | \(-0.661222\pi\) | ||||
−0.485115 | + | 0.874451i | \(0.661222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 41.6951i | − | 1.82320i | −0.411081 | − | 0.911599i | \(-0.634849\pi\) | ||
0.411081 | − | 0.911599i | \(-0.365151\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.8434 | + | 15.4981i | −1.16932 | + | 0.675107i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.8578 | − | 29.1986i | 0.732949 | − | 1.26950i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.84443 | + | 2.21958i | 0.166521 | + | 0.0961408i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.2068 | −0.956514 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.3578 | −0.832258 | −0.416129 | − | 0.909306i | \(-0.636613\pi\) | ||||
−0.416129 | + | 0.909306i | \(0.636613\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.6357 | − | 0.723484i | −0.669762 | − | 0.0309906i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.43917 | − | 2.56295i | −0.189805 | − | 0.109584i | 0.402086 | − | 0.915602i | \(-0.368285\pi\) |
−0.591891 | + | 0.806018i | \(0.701619\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.6514 | − | 32.3051i | 0.794574 | − | 1.37624i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.65875 | + | 3.84443i | −0.283159 | + | 0.163482i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.41813i | 0.102460i | 0.998687 | + | 0.0512298i | \(0.0163141\pi\) | ||||
−0.998687 | + | 0.0512298i | \(0.983686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.35782 | 0.353498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.59980 | − | 2.65570i | 0.193859 | − | 0.111924i | −0.399929 | − | 0.916546i | \(-0.630965\pi\) |
0.593788 | + | 0.804622i | \(0.297632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0276 | − | 9.32497i | 0.758427 | − | 0.392304i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.8876 | + | 18.8578i | −0.456430 | + | 0.790561i | −0.998769 | − | 0.0495991i | \(-0.984206\pi\) |
0.542339 | + | 0.840160i | \(0.317539\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.41055 | + | 5.90724i | 0.142727 | + | 0.247210i | 0.928523 | − | 0.371276i | \(-0.121080\pi\) |
−0.785796 | + | 0.618486i | \(0.787746\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.2094 | + | 15.7356i | −1.42663 | + | 0.656221i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 5.24054i | − | 0.218167i | −0.994033 | − | 0.109083i | \(-0.965208\pi\) | ||
0.994033 | − | 0.109083i | \(-0.0347915\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.24756 | − | 10.8211i | −0.259192 | − | 0.448935i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.96709 | + | 4.59980i | 0.329963 | + | 0.190504i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.0543 | − | 23.7027i | −1.69449 | − | 0.978316i | −0.950805 | − | 0.309790i | \(-0.899741\pi\) |
−0.743688 | − | 0.668527i | \(-0.766925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.5895 | + | 32.1979i | 0.765965 | + | 1.32669i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.2965i | − | 0.463890i | −0.972729 | − | 0.231945i | \(-0.925491\pi\) | ||
0.972729 | − | 0.231945i | \(-0.0745090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.25236 | + | 14.4401i | −0.379310 | + | 0.591988i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.3415 | + | 31.7684i | 0.749412 | + | 1.29802i | 0.948105 | + | 0.317958i | \(0.102997\pi\) |
−0.198692 | + | 0.980062i | \(0.563669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.67891 | + | 16.7644i | −0.394811 | + | 0.683833i | −0.993077 | − | 0.117465i | \(-0.962523\pi\) |
0.598266 | + | 0.801297i | \(0.295857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.34779 | − | 12.2719i | −0.258074 | − | 0.498925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.10979 | + | 0.640739i | −0.0450451 | + | 0.0260068i | −0.522353 | − | 0.852729i | \(-0.674946\pi\) |
0.477308 | + | 0.878736i | \(0.341612\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.6410 | 1.40143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 38.9028i | − | 1.57127i | −0.618690 | − | 0.785636i | \(-0.712336\pi\) | ||
0.618690 | − | 0.785636i | \(-0.287664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.6715 | + | 15.3988i | −1.07375 | + | 0.619932i | −0.929205 | − | 0.369565i | \(-0.879507\pi\) |
−0.144549 | + | 0.989498i | \(0.546173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.1789 | − | 29.7547i | 0.690479 | − | 1.19594i | −0.281203 | − | 0.959648i | \(-0.590733\pi\) |
0.971681 | − | 0.236296i | \(-0.0759334\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.1218 | + | 6.42119i | 0.445586 | + | 0.257259i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5736 | + | 4.59750i | 0.982945 | + | 0.183900i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.3650 | −1.25061 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.5367 | 0.459270 | 0.229635 | − | 0.973277i | \(-0.426247\pi\) | ||||
0.229635 | + | 0.973277i | \(0.426247\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.132447 | + | 2.86241i | −0.00525599 | + | 0.113591i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.2622 | − | 17.4719i | −1.19903 | − | 0.692261i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.95936 | − | 6.85782i | 0.156385 | − | 0.270867i | −0.777177 | − | 0.629282i | \(-0.783349\pi\) |
0.933563 | + | 0.358414i | \(0.116682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.96709 | − | 4.59980i | 0.314191 | − | 0.181399i | −0.334609 | − | 0.942357i | \(-0.608604\pi\) |
0.648801 | + | 0.760958i | \(0.275271\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.7146i | 0.539177i | 0.962976 | + | 0.269588i | \(0.0868876\pi\) | ||||
−0.962976 | + | 0.269588i | \(0.913112\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.5367 | 1.23792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.4545 | − | 21.0470i | 1.42658 | − | 0.823634i | 0.429727 | − | 0.902959i | \(-0.358610\pi\) |
0.996849 | + | 0.0793250i | \(0.0252765\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.65652 | + | 10.9355i | 0.221018 | + | 0.427286i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0635 | − | 20.8945i | 0.469926 | − | 0.813936i | −0.529483 | − | 0.848321i | \(-0.677614\pi\) |
0.999409 | + | 0.0343850i | \(0.0109472\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.2156 | − | 38.4786i | −0.864088 | − | 1.49664i | −0.867950 | − | 0.496652i | \(-0.834563\pi\) |
0.00386191 | − | 0.999993i | \(-0.498771\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.3205 | + | 11.0979i | 0.671660 | + | 0.430359i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 39.1321i | − | 1.51520i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.51551 | − | 7.82109i | −0.174319 | − | 0.301930i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.2412 | + | 16.3050i | 1.08862 | + | 0.628513i | 0.933208 | − | 0.359337i | \(-0.116997\pi\) |
0.155409 | + | 0.987850i | \(0.450330\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.1434 | + | 25.4862i | 1.69657 | + | 0.979514i | 0.948972 | + | 0.315360i | \(0.102125\pi\) |
0.747596 | + | 0.664154i | \(0.231208\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.17891 | − | 15.8983i | −0.352254 | − | 0.610122i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.3795i | 1.08591i | 0.839762 | + | 0.542955i | \(0.182695\pi\) | ||||
−0.839762 | + | 0.542955i | \(0.817305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.2684 | − | 13.6275i | −0.812622 | − | 0.520678i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.23808 | + | 12.5367i | 0.275749 | + | 0.477611i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.35782 | + | 12.7441i | −0.279905 | + | 0.484809i | −0.971361 | − | 0.237609i | \(-0.923636\pi\) |
0.691456 | + | 0.722418i | \(0.256969\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.6484 | + | 34.1190i | 0.669443 | + | 1.29421i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.52793 | − | 2.03685i | 0.133630 | − | 0.0771512i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2272 | −0.537353 | −0.268676 | − | 0.963230i | \(-0.586586\pi\) | ||||
−0.268676 | + | 0.963230i | \(0.586586\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.6214i | 1.41892i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.755372 | − | 0.436114i | 0.0284087 | − | 0.0164018i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.26836 | + | 16.0533i | −0.348081 | + | 0.602893i | −0.985908 | − | 0.167286i | \(-0.946500\pi\) |
0.637828 | + | 0.770179i | \(0.279833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.7769 | + | 19.5011i | 1.26496 | + | 0.730323i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.79390 | − | 60.3810i | 0.104486 | − | 2.25812i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.7358 | −1.18355 | −0.591773 | − | 0.806105i | \(-0.701572\pi\) | ||||
−0.591773 | + | 0.806105i | \(0.701572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.28437 | 0.122316 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.0126 | + | 21.2043i | −0.557555 | + | 0.787507i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.2307 | + | 15.7216i | 1.00993 | + | 0.583083i | 0.911171 | − | 0.412029i | \(-0.135180\pi\) |
0.0987581 | + | 0.995111i | \(0.468513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.83487 | − | 6.64218i | 0.141838 | − | 0.245670i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.43917 | − | 2.56295i | 0.163964 | − | 0.0946649i | −0.415772 | − | 0.909469i | \(-0.636489\pi\) |
0.579737 | + | 0.814804i | \(0.303155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 64.6870i | − | 2.38278i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.8945 | −1.24683 | −0.623415 | − | 0.781891i | \(-0.714255\pi\) | ||||
−0.623415 | + | 0.781891i | \(0.714255\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.0216 | + | 19.0650i | −1.21144 | + | 0.699427i | −0.963074 | − | 0.269238i | \(-0.913228\pi\) |
−0.248370 | + | 0.968665i | \(0.579895\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.2725 | + | 39.1921i | 0.742728 | + | 1.43589i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.17891 | − | 14.1663i | −0.298453 | − | 0.516935i | 0.677330 | − | 0.735680i | \(-0.263137\pi\) |
−0.975782 | + | 0.218745i | \(0.929804\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.24756 | + | 9.75056i | −0.227372 | + | 0.354859i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 28.6510i | − | 1.04134i | −0.853758 | − | 0.520670i | \(-0.825682\pi\) | ||
0.853758 | − | 0.520670i | \(-0.174318\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.866025 | + | 1.50000i | 0.0313934 | + | 0.0543750i | 0.881295 | − | 0.472566i | \(-0.156672\pi\) |
−0.849902 | + | 0.526941i | \(0.823339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.76854 | + | 4.48517i | 0.281240 | + | 0.162374i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.9765 | + | 24.8125i | 1.55179 | + | 0.895928i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.85782 | − | 17.0742i | −0.355482 | − | 0.615713i | 0.631718 | − | 0.775198i | \(-0.282350\pi\) |
−0.987200 | + | 0.159485i | \(0.949017\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.63772i | 0.166807i | 0.996516 | + | 0.0834036i | \(0.0265791\pi\) | ||||
−0.996516 | + | 0.0834036i | \(0.973421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.8211 | − | 23.5251i | −0.388705 | − | 0.845047i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.44314 | − | 4.23164i | −0.0875345 | − | 0.151614i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4105 | + | 19.7636i | −0.408301 | + | 0.707199i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.4082 | − | 5.38377i | 0.371486 | − | 0.192155i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.6369 | − | 22.8844i | 1.41290 | − | 0.815740i | 0.417242 | − | 0.908795i | \(-0.362997\pi\) |
0.995661 | + | 0.0930552i | \(0.0296633\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.6318 | −0.413580 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 14.2109i | − | 0.504643i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.8271 | + | 13.1792i | −0.808576 | + | 0.466832i | −0.846461 | − | 0.532450i | \(-0.821271\pi\) |
0.0378850 | + | 0.999282i | \(0.487938\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.8945 | − | 27.5302i | 0.562308 | − | 0.973947i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.0103 | − | 16.1717i | −0.988462 | − | 0.570689i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.5567 | + | 0.997454i | 0.759775 | + | 0.0351556i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.19615 | 0.182687 | 0.0913435 | − | 0.995819i | \(-0.470884\pi\) | ||||
0.0913435 | + | 0.995819i | \(0.470884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.8945 | −1.75203 | −0.876017 | − | 0.482280i | \(-0.839809\pi\) | ||||
−0.876017 | + | 0.482280i | \(0.839809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.21572 | − | 26.2738i | 0.0425847 | − | 0.920330i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.96709 | − | 4.59980i | −0.278733 | − | 0.160927i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.124496 | − | 0.215633i | 0.00434494 | − | 0.00752566i | −0.863845 | − | 0.503758i | \(-0.831950\pi\) |
0.868190 | + | 0.496232i | \(0.165284\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.5929 | − | 13.0440i | 0.787540 | − | 0.454687i | −0.0515557 | − | 0.998670i | \(-0.516418\pi\) |
0.839096 | + | 0.543984i | \(0.183085\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.9701i | 0.416243i | 0.978103 | + | 0.208121i | \(0.0667349\pi\) | ||||
−0.978103 | + | 0.208121i | \(0.933265\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.17891 | −0.249334 | −0.124667 | − | 0.992199i | \(-0.539786\pi\) | ||||
−0.124667 | + | 0.992199i | \(0.539786\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.7708 | + | 16.0335i | −0.962200 | + | 0.555526i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.40831 | + | 2.28025i | −0.152556 | + | 0.0789112i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.0425 | − | 19.1262i | 0.381230 | − | 0.660309i | −0.610009 | − | 0.792395i | \(-0.708834\pi\) |
0.991238 | + | 0.132086i | \(0.0421674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | + | 1.73205i | 0.0344828 | + | 0.0597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.6315 | − | 55.6101i | 1.22576 | − | 1.91305i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.91813i | 0.272070i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.7332 | + | 34.1789i | 0.676445 | + | 1.17164i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.9992 | − | 20.2068i | −1.19835 | − | 0.691867i | −0.238163 | − | 0.971225i | \(-0.576545\pi\) |
−0.960187 | + | 0.279358i | \(0.909878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.75027 | − | 1.01052i | −0.0597879 | − | 0.0345186i | 0.469808 | − | 0.882769i | \(-0.344323\pi\) |
−0.529596 | + | 0.848250i | \(0.677656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.23164 | + | 3.86531i | 0.0761425 | + | 0.131883i | 0.901583 | − | 0.432607i | \(-0.142406\pi\) |
−0.825440 | + | 0.564490i | \(0.809073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.21958i | − | 0.0755555i | −0.999286 | − | 0.0377777i | \(-0.987972\pi\) | ||
0.999286 | − | 0.0377777i | \(-0.0120279\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.26836 | − | 0.812689i | −0.0431256 | − | 0.0276322i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.4342 | − | 21.5367i | −0.421802 | − | 0.730583i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.8945 | − | 88.1519i | 1.72450 | − | 2.98691i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.2981 | − | 8.81050i | −0.381947 | − | 0.297849i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.06637 | + | 4.65712i | −0.272382 | + | 0.157260i | −0.629970 | − | 0.776620i | \(-0.716933\pi\) |
0.357588 | + | 0.933880i | \(0.383599\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.6111 | −1.46930 | −0.734648 | − | 0.678448i | \(-0.762653\pi\) | ||||
−0.734648 | + | 0.678448i | \(0.762653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.51074i | − | 0.0508406i | −0.999677 | − | 0.0254203i | \(-0.991908\pi\) | ||
0.999677 | − | 0.0254203i | \(-0.00809240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.76665 | − | 3.32937i | 0.193625 | − | 0.111789i | −0.400053 | − | 0.916492i | \(-0.631008\pi\) |
0.593678 | + | 0.804702i | \(0.297675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.821092 | − | 1.42217i | 0.0275385 | − | 0.0476981i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.0216 | − | 19.0650i | −1.10502 | − | 0.637986i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.4711 | − | 1.50247i | −1.08539 | − | 0.0502222i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.9104 | 0.897512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.2844 | 0.442566 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.9048 | + | 1.56881i | 1.12703 | + | 0.0521491i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3175 | + | 7.68886i | 0.442200 | + | 0.255304i | 0.704531 | − | 0.709674i | \(-0.251158\pi\) |
−0.262330 | + | 0.964978i | \(0.584491\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.7231 | + | 20.3051i | −0.388405 | + | 0.672738i | −0.992235 | − | 0.124376i | \(-0.960307\pi\) |
0.603830 | + | 0.797113i | \(0.293641\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.9992 | − | 20.2068i | 1.15830 | − | 0.668747i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.05585i | − | 0.233005i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.1789 | 1.02850 | 0.514249 | − | 0.857641i | \(-0.328071\pi\) | ||||
0.514249 | + | 0.857641i | \(0.328071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.0993 | + | 17.9552i | −1.02365 | + | 0.591003i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.41968 | − | 26.0907i | 0.0795585 | − | 0.857858i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.3003 | − | 23.0367i | 0.436367 | − | 0.755810i | −0.561039 | − | 0.827790i | \(-0.689598\pi\) |
0.997406 | + | 0.0719791i | \(0.0229315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.2316 | + | 33.3102i | 0.630291 | + | 1.09170i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −46.7045 | − | 29.9254i | −1.52740 | − | 0.978664i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.95906i | − | 0.129337i | −0.997907 | − | 0.0646685i | \(-0.979401\pi\) | ||
0.997907 | − | 0.0646685i | \(-0.0205990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.6825 | + | 27.1629i | 0.511235 | + | 0.885485i | 0.999915 | + | 0.0130223i | \(0.00414523\pi\) |
−0.488680 | + | 0.872463i | \(0.662521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.43917 | − | 2.56295i | −0.144559 | − | 0.0834613i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.4105 | − | 13.5161i | −0.760739 | − | 0.439213i | 0.0688223 | − | 0.997629i | \(-0.478076\pi\) |
−0.829561 | + | 0.558416i | \(0.811409\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.4473 | − | 44.0760i | −0.826053 | − | 1.43077i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26.3584i | − | 0.853833i | −0.904291 | − | 0.426917i | \(-0.859600\pi\) | ||
0.904291 | − | 0.426917i | \(-0.140400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.7156 | − | 49.4986i | 1.02629 | − | 1.60174i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.23808 | + | 12.5367i | 0.233730 | + | 0.404832i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.08945 | − | 3.61904i | 0.0674017 | − | 0.116743i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.6791 | − | 13.2828i | 0.826639 | − | 0.427588i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.1419 | − | 16.2477i | 0.904982 | − | 0.522492i | 0.0261690 | − | 0.999658i | \(-0.491669\pi\) |
0.878813 | + | 0.477166i | \(0.158336\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.3027 | 1.19710 | 0.598550 | − | 0.801085i | \(-0.295744\pi\) | ||||
0.598550 | + | 0.801085i | \(0.295744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 22.0144i | − | 0.705748i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.7216 | − | 9.07688i | 0.502979 | − | 0.290395i | −0.226964 | − | 0.973903i | \(-0.572880\pi\) |
0.729943 | + | 0.683508i | \(0.239547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.7684 | + | 35.9719i | −0.663760 | + | 1.14967i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.2212 | + | 24.3764i | 1.34665 | + | 0.777487i | 0.987773 | − | 0.155900i | \(-0.0498277\pi\) |
0.358873 | + | 0.933386i | \(0.383161\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.847991 | + | 18.3266i | −0.0270192 | + | 0.583933i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.65078 | −0.306877 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.53673 | 0.0488157 | 0.0244078 | − | 0.999702i | \(-0.492230\pi\) | ||||
0.0244078 | + | 0.999702i | \(0.492230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.26660 | + | 0.243692i | 0.166963 | + | 0.00772555i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.2293 | + | 22.0717i | 1.21073 | + | 0.699018i | 0.962919 | − | 0.269790i | \(-0.0869543\pi\) |
0.247815 | + | 0.968807i | \(0.420288\pi\) | |||||||
\(998\) | 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 | 1620.2.r.h.1189.8 | 16 | ||
3.2 | odd | 2 | inner | 1620.2.r.h.1189.1 | 16 | ||
5.4 | even | 2 | inner | 1620.2.r.h.1189.3 | 16 | ||
9.2 | odd | 6 | 1620.2.d.e.649.5 | yes | 8 | ||
9.4 | even | 3 | inner | 1620.2.r.h.109.3 | 16 | ||
9.5 | odd | 6 | inner | 1620.2.r.h.109.6 | 16 | ||
9.7 | even | 3 | 1620.2.d.e.649.4 | yes | 8 | ||
15.14 | odd | 2 | inner | 1620.2.r.h.1189.6 | 16 | ||
45.2 | even | 12 | 8100.2.a.be.1.4 | 8 | |||
45.4 | even | 6 | inner | 1620.2.r.h.109.8 | 16 | ||
45.7 | odd | 12 | 8100.2.a.be.1.3 | 8 | |||
45.14 | odd | 6 | inner | 1620.2.r.h.109.1 | 16 | ||
45.29 | odd | 6 | 1620.2.d.e.649.6 | yes | 8 | ||
45.34 | even | 6 | 1620.2.d.e.649.3 | ✓ | 8 | ||
45.38 | even | 12 | 8100.2.a.be.1.6 | 8 | |||
45.43 | odd | 12 | 8100.2.a.be.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.2.d.e.649.3 | ✓ | 8 | 45.34 | even | 6 | ||
1620.2.d.e.649.4 | yes | 8 | 9.7 | even | 3 | ||
1620.2.d.e.649.5 | yes | 8 | 9.2 | odd | 6 | ||
1620.2.d.e.649.6 | yes | 8 | 45.29 | odd | 6 | ||
1620.2.r.h.109.1 | 16 | 45.14 | odd | 6 | inner | ||
1620.2.r.h.109.3 | 16 | 9.4 | even | 3 | inner | ||
1620.2.r.h.109.6 | 16 | 9.5 | odd | 6 | inner | ||
1620.2.r.h.109.8 | 16 | 45.4 | even | 6 | inner | ||
1620.2.r.h.1189.1 | 16 | 3.2 | odd | 2 | inner | ||
1620.2.r.h.1189.3 | 16 | 5.4 | even | 2 | inner | ||
1620.2.r.h.1189.6 | 16 | 15.14 | odd | 2 | inner | ||
1620.2.r.h.1189.8 | 16 | 1.1 | even | 1 | trivial | ||
8100.2.a.be.1.3 | 8 | 45.7 | odd | 12 | |||
8100.2.a.be.1.4 | 8 | 45.2 | even | 12 | |||
8100.2.a.be.1.5 | 8 | 45.43 | odd | 12 | |||
8100.2.a.be.1.6 | 8 | 45.38 | even | 12 |