Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (of order \(4\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} + 6x^{12} - 12x^{10} + 36x^{8} - 48x^{6} + 96x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1007.1 | ||
Root | \(-1.24570 - 0.669507i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1007 |
Dual form | 1600.2.j.c.143.8 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.07455i | − | 1.77509i | −0.460717 | − | 0.887547i | \(-0.652408\pi\) | ||
0.460717 | − | 0.887547i | \(-0.347592\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.47763 | + | 1.47763i | 0.558491 | + | 0.558491i | 0.928878 | − | 0.370386i | \(-0.120775\pi\) |
−0.370386 | + | 0.928878i | \(0.620775\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.45288 | −2.15096 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.20704 | + | 1.20704i | 0.363937 | + | 0.363937i | 0.865260 | − | 0.501323i | \(-0.167153\pi\) |
−0.501323 | + | 0.865260i | \(0.667153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.63329 | 1.56239 | 0.781196 | − | 0.624285i | \(-0.214610\pi\) | ||||
0.781196 | + | 0.624285i | \(0.214610\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.22693 | + | 4.22693i | 1.02518 | + | 1.02518i | 0.999675 | + | 0.0255073i | \(0.00812009\pi\) |
0.0255073 | + | 0.999675i | \(0.491880\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.11687 | + | 3.11687i | 0.715059 | + | 0.715059i | 0.967589 | − | 0.252530i | \(-0.0812626\pi\) |
−0.252530 | + | 0.967589i | \(0.581263\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.54305 | − | 4.54305i | 0.991375 | − | 0.991375i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.08110 | + | 1.08110i | −0.225426 | + | 0.225426i | −0.810779 | − | 0.585353i | \(-0.800956\pi\) |
0.585353 | + | 0.810779i | \(0.300956\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.6161i | 2.04306i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.32391 | − | 5.32391i | 0.988626 | − | 0.988626i | −0.0113103 | − | 0.999936i | \(-0.503600\pi\) |
0.999936 | + | 0.0113103i | \(0.00360026\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.67202i | − | 0.839120i | −0.907728 | − | 0.419560i | \(-0.862184\pi\) | ||
0.907728 | − | 0.419560i | \(-0.137816\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.71111 | − | 3.71111i | 0.646022 | − | 0.646022i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.51171 | −0.248523 | −0.124262 | − | 0.992249i | \(-0.539656\pi\) | ||||
−0.124262 | + | 0.992249i | \(0.539656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 17.3198i | − | 2.77340i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.19494i | 0.498966i | 0.968379 | + | 0.249483i | \(0.0802607\pi\) | ||||
−0.968379 | + | 0.249483i | \(0.919739\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.42405 | 0.369665 | 0.184832 | − | 0.982770i | \(-0.440826\pi\) | ||||
0.184832 | + | 0.982770i | \(0.440826\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.827129 | − | 0.827129i | 0.120649 | − | 0.120649i | −0.644204 | − | 0.764853i | \(-0.722811\pi\) |
0.764853 | + | 0.644204i | \(0.222811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2.63322i | − | 0.376175i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.9959 | − | 12.9959i | 1.81979 | − | 1.81979i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.17664i | 1.12315i | 0.827427 | + | 0.561574i | \(0.189804\pi\) | ||||
−0.827427 | + | 0.561574i | \(0.810196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.58299 | − | 9.58299i | 1.26930 | − | 1.26930i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.78889 | + | 7.78889i | −1.01403 | + | 1.01403i | −0.0141274 | + | 0.999900i | \(0.504497\pi\) |
−0.999900 | + | 0.0141274i | \(0.995503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.03880 | − | 3.03880i | −0.389079 | − | 0.389079i | 0.485280 | − | 0.874359i | \(-0.338718\pi\) |
−0.874359 | + | 0.485280i | \(0.838718\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.53497 | − | 9.53497i | −1.20129 | − | 1.20129i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.93200 | 0.358201 | 0.179101 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179101 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.32391 | + | 3.32391i | 0.400152 | + | 0.400152i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.180339 | 0.0214023 | 0.0107011 | − | 0.999943i | \(-0.496594\pi\) | ||||
0.0107011 | + | 0.999943i | \(0.496594\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.19941 | + | 2.19941i | 0.257421 | + | 0.257421i | 0.824004 | − | 0.566583i | \(-0.191735\pi\) |
−0.566583 | + | 0.824004i | \(0.691735\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.56712i | 0.406511i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.4917 | −1.40542 | −0.702712 | − | 0.711474i | \(-0.748028\pi\) | ||||
−0.702712 | + | 0.711474i | \(0.748028\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.2810 | 1.47567 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.33457i | 0.914838i | 0.889251 | + | 0.457419i | \(0.151226\pi\) | ||||
−0.889251 | + | 0.457419i | \(0.848774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.3687 | − | 16.3687i | −1.75490 | − | 1.75490i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.08610 | −0.963125 | −0.481563 | − | 0.876412i | \(-0.659931\pi\) | ||||
−0.481563 | + | 0.876412i | \(0.659931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.32391 | + | 8.32391i | 0.872583 | + | 0.872583i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.3644 | −1.48952 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.04376 | − | 6.04376i | −0.613650 | − | 0.613650i | 0.330245 | − | 0.943895i | \(-0.392869\pi\) |
−0.943895 | + | 0.330245i | \(0.892869\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.78889 | − | 7.78889i | −0.782813 | − | 0.782813i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.58185 | − | 9.58185i | 0.953430 | − | 0.953430i | −0.0455329 | − | 0.998963i | \(-0.514499\pi\) |
0.998963 | + | 0.0455329i | \(0.0144986\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.57971 | + | 6.57971i | −0.648318 | + | 0.648318i | −0.952586 | − | 0.304268i | \(-0.901588\pi\) |
0.304268 | + | 0.952586i | \(0.401588\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.980501i | 0.0947886i | 0.998876 | + | 0.0473943i | \(0.0150917\pi\) | ||||
−0.998876 | + | 0.0473943i | \(0.984908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | − | 2.00000i | 0.191565 | − | 0.191565i | −0.604807 | − | 0.796372i | \(-0.706750\pi\) |
0.796372 | + | 0.604807i | \(0.206750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.64783i | 0.441152i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.54335 | − | 2.54335i | 0.239258 | − | 0.239258i | −0.577285 | − | 0.816543i | \(-0.695888\pi\) |
0.816543 | + | 0.577285i | \(0.195888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −36.3509 | −3.36065 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.4917i | 1.14511i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 8.08610i | − | 0.735100i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.82302 | 0.885712 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0019 | − | 14.0019i | 1.24247 | − | 1.24247i | 0.283498 | − | 0.958973i | \(-0.408505\pi\) |
0.958973 | − | 0.283498i | \(-0.0914950\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.45288i | − | 0.656190i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.11687 | + | 7.11687i | −0.621804 | + | 0.621804i | −0.945992 | − | 0.324189i | \(-0.894909\pi\) |
0.324189 | + | 0.945992i | \(0.394909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.21116i | 0.798709i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.995887 | − | 0.995887i | 0.0850843 | − | 0.0850843i | −0.663284 | − | 0.748368i | \(-0.730838\pi\) |
0.748368 | + | 0.663284i | \(0.230838\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1128 | − | 12.1128i | 1.02739 | − | 1.02739i | 0.0277808 | − | 0.999614i | \(-0.491156\pi\) |
0.999614 | − | 0.0277808i | \(-0.00884403\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.54305 | − | 2.54305i | −0.214164 | − | 0.214164i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.79961 | + | 6.79961i | 0.568612 | + | 0.568612i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.09598 | −0.667745 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.86696 | − | 9.86696i | −0.808333 | − | 0.808333i | 0.176048 | − | 0.984382i | \(-0.443669\pi\) |
−0.984382 | + | 0.176048i | \(0.943669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.31985 | 0.758438 | 0.379219 | − | 0.925307i | \(-0.376193\pi\) | ||||
0.379219 | + | 0.925307i | \(0.376193\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27.2759 | − | 27.2759i | −2.20513 | − | 2.20513i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.9394i | − | 1.43172i | −0.698245 | − | 0.715859i | \(-0.746035\pi\) | ||
0.698245 | − | 0.715859i | \(-0.253965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 25.1395 | 1.99369 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.19494 | −0.251797 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.39897i | − | 0.579532i | −0.957098 | − | 0.289766i | \(-0.906423\pi\) | ||
0.957098 | − | 0.289766i | \(-0.0935775\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.74192 | − | 8.74192i | −0.676470 | − | 0.676470i | 0.282730 | − | 0.959200i | \(-0.408760\pi\) |
−0.959200 | + | 0.282730i | \(0.908760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.7339 | 1.44107 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.1128 | − | 20.1128i | −1.53806 | − | 1.53806i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.7865 | 0.820083 | 0.410042 | − | 0.912067i | \(-0.365514\pi\) | ||||
0.410042 | + | 0.912067i | \(0.365514\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.9474 | + | 23.9474i | 1.79999 | + | 1.79999i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.535019 | − | 0.535019i | −0.0399892 | − | 0.0399892i | 0.686829 | − | 0.726819i | \(-0.259002\pi\) |
−0.726819 | + | 0.686829i | \(0.759002\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.58185 | + | 7.58185i | −0.563555 | + | 0.563555i | −0.930315 | − | 0.366761i | \(-0.880467\pi\) |
0.366761 | + | 0.930315i | \(0.380467\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.34296 | + | 9.34296i | −0.690651 | + | 0.690651i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.2042i | 0.746202i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.6866 | + | 15.6866i | −1.14103 | + | 1.14103i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.46749i | − | 0.323256i | −0.986852 | − | 0.161628i | \(-0.948326\pi\) | ||
0.986852 | − | 0.161628i | \(-0.0516745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9115 | + | 12.9115i | −0.929391 | + | 0.929391i | −0.997667 | − | 0.0682750i | \(-0.978250\pi\) |
0.0682750 | + | 0.997667i | \(0.478250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.8764 | 0.988656 | 0.494328 | − | 0.869275i | \(-0.335414\pi\) | ||||
0.494328 | + | 0.869275i | \(0.335414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.47599i | 0.671735i | 0.941909 | + | 0.335868i | \(0.109029\pi\) | ||||
−0.941909 | + | 0.335868i | \(0.890971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 9.01460i | − | 0.635841i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.7335 | 1.10428 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.97624 | − | 6.97624i | 0.484882 | − | 0.484882i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.52438i | 0.520472i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.20298 | + | 6.20298i | −0.427030 | + | 0.427030i | −0.887616 | − | 0.460585i | \(-0.847640\pi\) |
0.460585 | + | 0.887616i | \(0.347640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 0.554462i | − | 0.0379911i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.90352 | − | 6.90352i | 0.468641 | − | 0.468641i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.76219 | − | 6.76219i | 0.456947 | − | 0.456947i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.8115 | + | 23.8115i | 1.60174 | + | 1.60174i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3793 | + | 13.3793i | 0.895946 | + | 0.895946i | 0.995075 | − | 0.0991290i | \(-0.0316057\pi\) |
−0.0991290 | + | 0.995075i | \(0.531606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.22366 | 0.612196 | 0.306098 | − | 0.952000i | \(-0.400976\pi\) | ||||
0.306098 | + | 0.952000i | \(0.400976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.2297 | − | 12.2297i | −0.808160 | − | 0.808160i | 0.176195 | − | 0.984355i | \(-0.443621\pi\) |
−0.984355 | + | 0.176195i | \(0.943621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.9673 | 0.721595 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.6533 | + | 10.6533i | 0.697919 | + | 0.697919i | 0.963961 | − | 0.266042i | \(-0.0857161\pi\) |
−0.266042 | + | 0.963961i | \(0.585716\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 38.4064i | 2.49476i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.3284 | −1.44430 | −0.722150 | − | 0.691736i | \(-0.756846\pi\) | ||||
−0.722150 | + | 0.691736i | \(0.756846\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.1868 | −1.75126 | −0.875628 | − | 0.482986i | \(-0.839552\pi\) | ||||
−0.875628 | + | 0.482986i | \(0.839552\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 8.98507i | − | 0.576393i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.5582 | + | 17.5582i | 1.11720 | + | 1.11720i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.6251 | 1.62392 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4650 | + | 11.4650i | 0.723663 | + | 0.723663i | 0.969349 | − | 0.245686i | \(-0.0790133\pi\) |
−0.245686 | + | 0.969349i | \(0.579013\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.60987 | −0.164081 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.36017 | − | 4.36017i | −0.271980 | − | 0.271980i | 0.557917 | − | 0.829897i | \(-0.311601\pi\) |
−0.829897 | + | 0.557917i | \(0.811601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.23374 | − | 2.23374i | −0.138798 | − | 0.138798i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −34.3546 | + | 34.3546i | −2.12650 | + | 2.12650i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.93150 | − | 9.93150i | 0.612402 | − | 0.612402i | −0.331169 | − | 0.943571i | \(-0.607443\pi\) |
0.943571 | + | 0.331169i | \(0.107443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.9357i | 1.70964i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.8670 | + | 15.8670i | −0.967426 | + | 0.967426i | −0.999486 | − | 0.0320600i | \(-0.989793\pi\) |
0.0320600 | + | 0.999486i | \(0.489793\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.8040i | − | 1.26375i | −0.775070 | − | 0.631875i | \(-0.782285\pi\) | ||
0.775070 | − | 0.631875i | \(-0.217715\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.5923 | − | 25.5923i | 1.54892 | − | 1.54892i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.4670 | −1.22974 | −0.614871 | − | 0.788628i | \(-0.710792\pi\) | ||||
−0.614871 | + | 0.788628i | \(0.710792\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.1480i | 1.80491i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.89116i | 0.351437i | 0.984440 | + | 0.175719i | \(0.0562249\pi\) | ||||
−0.984440 | + | 0.175719i | \(0.943775\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6262 | 0.869439 | 0.434720 | − | 0.900566i | \(-0.356847\pi\) | ||||
0.434720 | + | 0.900566i | \(0.356847\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.72094 | + | 4.72094i | −0.278668 | + | 0.278668i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.7339i | 1.10200i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.5819 | + | 18.5819i | −1.08929 | + | 1.08929i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 12.2982i | − | 0.718469i | −0.933247 | − | 0.359235i | \(-0.883038\pi\) | ||
0.933247 | − | 0.359235i | \(-0.116962\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.8140 | + | 12.8140i | −0.743546 | + | 0.743546i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.09017 | + | 6.09017i | −0.352204 | + | 0.352204i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.58185 | + | 3.58185i | 0.206455 | + | 0.206455i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.4599 | − | 29.4599i | −1.69243 | − | 1.69243i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.6636 | 1.17933 | 0.589666 | − | 0.807647i | \(-0.299259\pi\) | ||||
0.589666 | + | 0.807647i | \(0.299259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.2297 | + | 20.2297i | 1.15083 | + | 1.15083i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1561 | −0.916131 | −0.458065 | − | 0.888919i | \(-0.651457\pi\) | ||||
−0.458065 | + | 0.888919i | \(0.651457\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.29689 | + | 2.29689i | 0.129828 | + | 0.129828i | 0.769035 | − | 0.639207i | \(-0.220737\pi\) |
−0.639207 | + | 0.769035i | \(0.720737\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.05541i | − | 0.115443i | −0.998333 | − | 0.0577217i | \(-0.981616\pi\) | ||
0.998333 | − | 0.0577217i | \(-0.0183836\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8524 | 0.719594 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.01460 | 0.168259 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.3496i | 1.46613i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.14911 | − | 6.14911i | −0.340046 | − | 0.340046i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.44438 | 0.134763 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.7113 | − | 13.7113i | −0.753641 | − | 0.753641i | 0.221516 | − | 0.975157i | \(-0.428900\pi\) |
−0.975157 | + | 0.221516i | \(0.928900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.75487 | 0.534563 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8140 | + | 12.8140i | 0.698025 | + | 0.698025i | 0.963984 | − | 0.265959i | \(-0.0856887\pi\) |
−0.265959 | + | 0.963984i | \(0.585689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.81966 | − | 7.81966i | −0.424706 | − | 0.424706i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.63932 | − | 5.63932i | 0.305386 | − | 0.305386i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2343 | − | 14.2343i | 0.768582 | − | 0.768582i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8.81175i | − | 0.473040i | −0.971627 | − | 0.236520i | \(-0.923993\pi\) | ||
0.971627 | − | 0.236520i | \(-0.0760068\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8398 | − | 15.8398i | 0.847885 | − | 0.847885i | −0.141984 | − | 0.989869i | \(-0.545348\pi\) |
0.989869 | + | 0.141984i | \(0.0453482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 59.8034i | 3.19207i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.2349 | − | 10.2349i | 0.544751 | − | 0.544751i | −0.380167 | − | 0.924918i | \(-0.624134\pi\) |
0.924918 | + | 0.380167i | \(0.124134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 38.4064 | 2.03268 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.18790i | 0.484919i | 0.970162 | + | 0.242459i | \(0.0779541\pi\) | ||||
−0.970162 | + | 0.242459i | \(0.922046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.429776i | 0.0226198i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.8612 | −1.30487 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.40440 | + | 8.40440i | −0.438706 | + | 0.438706i | −0.891576 | − | 0.452870i | \(-0.850400\pi\) |
0.452870 | + | 0.891576i | \(0.350400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 20.6166i | − | 1.07326i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0820 | + | 12.0820i | −0.627268 | + | 0.627268i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.6942i | 1.43395i | 0.697097 | + | 0.716977i | \(0.254475\pi\) | ||||
−0.697097 | + | 0.716977i | \(0.745525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.9911 | − | 29.9911i | 1.54462 | − | 1.54462i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6987 | − | 17.6987i | 0.909122 | − | 0.909122i | −0.0870790 | − | 0.996201i | \(-0.527753\pi\) |
0.996201 | + | 0.0870790i | \(0.0277533\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.0497 | − | 43.0497i | −2.20550 | − | 2.20550i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.11930 | − | 8.11930i | −0.414877 | − | 0.414877i | 0.468557 | − | 0.883434i | \(-0.344774\pi\) |
−0.883434 | + | 0.468557i | \(0.844774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.6421 | −0.795134 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.38285 | + | 6.38285i | 0.323623 | + | 0.323623i | 0.850155 | − | 0.526532i | \(-0.176508\pi\) |
−0.526532 | + | 0.850155i | \(0.676508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.13951 | −0.462205 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.8812 | + | 21.8812i | 1.10376 | + | 1.10376i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.65670i | − | 0.434467i | −0.976120 | − | 0.217234i | \(-0.930297\pi\) | ||
0.976120 | − | 0.217234i | \(-0.0697034\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 28.3202 | 1.41778 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.57022 | −0.328101 | −0.164051 | − | 0.986452i | \(-0.552456\pi\) | ||||
−0.164051 | + | 0.986452i | \(0.552456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 26.3188i | − | 1.31104i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.82469 | − | 1.82469i | −0.0904466 | − | 0.0904466i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.19494 | −0.157980 | −0.0789899 | − | 0.996875i | \(-0.525169\pi\) | ||||
−0.0789899 | + | 0.996875i | \(0.525169\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.06191 | − | 3.06191i | −0.151033 | − | 0.151033i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.0182 | −1.13265 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.2415 | − | 37.2415i | −1.82372 | − | 1.82372i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.3707 | + | 26.3707i | 1.28830 | + | 1.28830i | 0.935822 | + | 0.352473i | \(0.114659\pi\) |
0.352473 | + | 0.935822i | \(0.385341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.3345 | − | 28.3345i | 1.38094 | − | 1.38094i | 0.537977 | − | 0.842959i | \(-0.319189\pi\) |
0.842959 | − | 0.537977i | \(-0.180811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.33736 | + | 5.33736i | −0.259512 | + | 0.259512i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.98044i | − | 0.434594i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.9058 | − | 20.9058i | 1.00934 | − | 1.00934i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6.49981i | − | 0.313085i | −0.987671 | − | 0.156543i | \(-0.949965\pi\) | ||
0.987671 | − | 0.156543i | \(-0.0500348\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.5486 | + | 19.5486i | −0.939444 | + | 0.939444i | −0.998268 | − | 0.0588243i | \(-0.981265\pi\) |
0.0588243 | + | 0.998268i | \(0.481265\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.73932 | −0.322386 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 23.3117i | − | 1.11261i | −0.830979 | − | 0.556304i | \(-0.812219\pi\) | ||
0.830979 | − | 0.556304i | \(-0.187781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.9919i | 0.809137i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.3347 | −1.67880 | −0.839401 | − | 0.543513i | \(-0.817094\pi\) | ||||
−0.839401 | + | 0.543513i | \(0.817094\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.3365 | + | 30.3365i | −1.43487 | + | 1.43487i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.5305i | 0.827315i | 0.910433 | + | 0.413657i | \(0.135749\pi\) | ||||
−0.910433 | + | 0.413657i | \(0.864251\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.85643 | + | 3.85643i | −0.181592 | + | 0.181592i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 28.6544i | − | 1.34630i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.1040 | + | 27.1040i | −1.26787 | + | 1.26787i | −0.320688 | + | 0.947185i | \(0.603914\pi\) |
−0.947185 | + | 0.320688i | \(0.896086\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −44.8734 | + | 44.8734i | −2.09451 | + | 2.09451i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.94253 | + | 3.94253i | 0.183622 | + | 0.183622i | 0.792932 | − | 0.609310i | \(-0.208554\pi\) |
−0.609310 | + | 0.792932i | \(0.708554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.8625 | + | 18.8625i | 0.876617 | + | 0.876617i | 0.993183 | − | 0.116566i | \(-0.0371887\pi\) |
−0.116566 | + | 0.993183i | \(0.537189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.2282 | −0.797228 | −0.398614 | − | 0.917119i | \(-0.630509\pi\) | ||||
−0.398614 | + | 0.917119i | \(0.630509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.33242 | + | 4.33242i | 0.200052 | + | 0.200052i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −55.1556 | −2.54143 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.92593 | + | 2.92593i | 0.134534 | + | 0.134534i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 52.7629i | − | 2.41585i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.2875 | −1.79509 | −0.897546 | − | 0.440920i | \(-0.854652\pi\) | ||||
−0.897546 | + | 0.440920i | \(0.854652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.51588 | −0.388291 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.82302i | 0.446963i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.39013 | + | 5.39013i | 0.244250 | + | 0.244250i | 0.818606 | − | 0.574356i | \(-0.194747\pi\) |
−0.574356 | + | 0.818606i | \(0.694747\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.7485 | −1.02872 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.0145 | + | 28.0145i | 1.26428 | + | 1.26428i | 0.949000 | + | 0.315277i | \(0.102098\pi\) |
0.315277 | + | 0.949000i | \(0.397902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.0076 | 2.02704 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.266474 | + | 0.266474i | 0.0119530 | + | 0.0119530i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.18284 | + | 1.18284i | 0.0529514 | + | 0.0529514i | 0.733087 | − | 0.680135i | \(-0.238079\pi\) |
−0.680135 | + | 0.733087i | \(0.738079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.8775 | + | 26.8775i | −1.20080 | + | 1.20080i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.0763 | + | 30.0763i | −1.34104 | + | 1.34104i | −0.446010 | + | 0.895028i | \(0.647155\pi\) |
−0.895028 | + | 0.446010i | \(0.852845\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 57.5985i | − | 2.55804i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.1062 | + | 23.1062i | −1.02417 | + | 1.02417i | −0.0244652 | + | 0.999701i | \(0.507788\pi\) |
−0.999701 | + | 0.0244652i | \(0.992212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.49981i | 0.287535i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −33.0889 | + | 33.0889i | −1.46091 | + | 1.46091i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.99676 | 0.0878173 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 33.1637i | − | 1.45573i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.3733i | 1.37449i | 0.726427 | + | 0.687244i | \(0.241179\pi\) | ||||
−0.726427 | + | 0.687244i | \(0.758821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.6926 | −0.511282 | −0.255641 | − | 0.966772i | \(-0.582287\pi\) | ||||
−0.255641 | + | 0.966772i | \(0.582287\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.7483 | − | 19.7483i | 0.860251 | − | 0.860251i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.6624i | 0.898366i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 50.2608 | − | 50.2608i | 2.18113 | − | 2.18113i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.9980i | 0.779581i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.64494 | + | 1.64494i | −0.0709846 | + | 0.0709846i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.17841 | − | 3.17841i | 0.136904 | − | 0.136904i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.4876 | + | 16.4876i | 0.708858 | + | 0.708858i | 0.966295 | − | 0.257437i | \(-0.0828780\pi\) |
−0.257437 | + | 0.966295i | \(0.582878\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.3108 | + | 23.3108i | 1.00036 | + | 1.00036i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.0505 | −1.54141 | −0.770703 | − | 0.637194i | \(-0.780095\pi\) | ||||
−0.770703 | + | 0.637194i | \(0.780095\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.6090 | + | 19.6090i | 0.836893 | + | 0.836893i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.1879 | 1.41385 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.4581 | − | 18.4581i | −0.784917 | − | 0.784917i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.64116i | 0.239024i | 0.992833 | + | 0.119512i | \(0.0381329\pi\) | ||||
−0.992833 | + | 0.119512i | \(0.961867\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6554 | 0.577561 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.3733 | 1.32458 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 4.69143i | − | 0.197720i | −0.995101 | − | 0.0988601i | \(-0.968480\pi\) | ||
0.995101 | − | 0.0988601i | \(-0.0315196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.6245 | + | 19.6245i | 0.824150 | + | 0.824150i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.3505 | −1.94311 | −0.971557 | − | 0.236804i | \(-0.923900\pi\) | ||||
−0.971557 | + | 0.236804i | \(0.923900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.27708 | + | 6.27708i | 0.262688 | + | 0.262688i | 0.826145 | − | 0.563457i | \(-0.190529\pi\) |
−0.563457 | + | 0.826145i | \(0.690529\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.7355 | −0.573810 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.5833 | − | 12.5833i | −0.523850 | − | 0.523850i | 0.394882 | − | 0.918732i | \(-0.370786\pi\) |
−0.918732 | + | 0.394882i | \(0.870786\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.6972 | + | 39.6972i | 1.64976 | + | 1.64976i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.3154 | + | 12.3154i | −0.510929 | + | 0.510929i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.86953 | + | 9.86953i | −0.408754 | + | 0.408754i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 17.4298i | − | 0.719405i | −0.933067 | − | 0.359703i | \(-0.882878\pi\) | ||
0.933067 | − | 0.359703i | \(-0.117122\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.5621 | − | 14.5621i | 0.600021 | − | 0.600021i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 42.6639i | − | 1.75496i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.81682 | − | 1.81682i | 0.0746079 | − | 0.0746079i | −0.668818 | − | 0.743426i | \(-0.733200\pi\) |
0.743426 | + | 0.668818i | \(0.233200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.1344 | 1.19239 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 34.2790i | − | 1.40060i | −0.713847 | − | 0.700301i | \(-0.753049\pi\) | ||
0.713847 | − | 0.700301i | \(-0.246951\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6709i | 0.761603i | 0.924657 | + | 0.380802i | \(0.124352\pi\) | ||||
−0.924657 | + | 0.380802i | \(0.875648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.9199 | −0.770477 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.9446 | − | 21.9446i | 0.890704 | − | 0.890704i | −0.103885 | − | 0.994589i | \(-0.533127\pi\) |
0.994589 | + | 0.103885i | \(0.0331274\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 48.3736i | − | 1.96020i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.65945 | − | 4.65945i | 0.188501 | − | 0.188501i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 32.7731i | − | 1.32369i | −0.749640 | − | 0.661846i | \(-0.769773\pi\) | ||
0.749640 | − | 0.661846i | \(-0.230227\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.6044 | + | 30.6044i | −1.23209 | + | 1.23209i | −0.268928 | + | 0.963160i | \(0.586669\pi\) |
−0.963160 | + | 0.268928i | \(0.913331\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.9365 | + | 10.9365i | −0.439576 | + | 0.439576i | −0.891869 | − | 0.452293i | \(-0.850606\pi\) |
0.452293 | + | 0.891869i | \(0.350606\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.4771 | − | 11.4771i | −0.460559 | − | 0.460559i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.4259 | − | 13.4259i | −0.537897 | − | 0.537897i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.1341 | 0.923888 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.38988 | − | 6.38988i | −0.254781 | − | 0.254781i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6639 | −1.69842 | −0.849211 | − | 0.528053i | \(-0.822922\pi\) | ||||
−0.849211 | + | 0.528053i | \(0.822922\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.0714 | + | 19.0714i | 0.758019 | + | 0.758019i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 14.8337i | − | 0.587732i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.16371 | −0.0460355 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.4821 | −0.532511 | −0.266255 | − | 0.963903i | \(-0.585786\pi\) | ||||
−0.266255 | + | 0.963903i | \(0.585786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.4066i | − | 1.43574i | −0.696179 | − | 0.717868i | \(-0.745118\pi\) | ||
0.696179 | − | 0.717868i | \(-0.254882\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.88954 | − | 1.88954i | −0.0742855 | − | 0.0742855i | 0.668988 | − | 0.743273i | \(-0.266728\pi\) |
−0.743273 | + | 0.668988i | \(0.766728\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.8030 | −0.738083 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.2252 | − | 21.2252i | −0.831883 | − | 0.831883i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.2010 | −1.14272 | −0.571361 | − | 0.820699i | \(-0.693584\pi\) | ||||
−0.571361 | + | 0.820699i | \(0.693584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.1925 | − | 14.1925i | −0.553702 | − | 0.553702i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.1213 | − | 33.1213i | −1.29022 | − | 1.29022i | −0.934648 | − | 0.355575i | \(-0.884285\pi\) |
−0.355575 | − | 0.934648i | \(-0.615715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0780 | − | 31.0780i | 1.20879 | − | 1.20879i | 0.237375 | − | 0.971418i | \(-0.423713\pi\) |
0.971418 | − | 0.237375i | \(-0.0762870\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 73.2098 | − | 73.2098i | 2.84323 | − | 2.84323i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.5114i | 0.445723i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 41.1354 | − | 41.1354i | 1.59039 | − | 1.59039i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 7.33591i | − | 0.283200i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.6450 | + | 12.6450i | −0.487431 | + | 0.487431i | −0.907495 | − | 0.420064i | \(-0.862008\pi\) |
0.420064 | + | 0.907495i | \(0.362008\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.5644 | 0.982521 | 0.491261 | − | 0.871013i | \(-0.336536\pi\) | ||||
0.491261 | + | 0.871013i | \(0.336536\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17.8609i | − | 0.685437i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 28.3586i | − | 1.08671i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.4968 | 1.01387 | 0.506936 | − | 0.861984i | \(-0.330778\pi\) | ||||
0.506936 | + | 0.861984i | \(0.330778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37.6008 | + | 37.6008i | −1.43456 | + | 1.43456i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 46.0613i | 1.75480i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.84230 | + | 1.84230i | −0.0700843 | + | 0.0700843i | −0.741280 | − | 0.671196i | \(-0.765781\pi\) |
0.671196 | + | 0.741280i | \(0.265781\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 23.0182i | − | 0.874389i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.5048 | + | 13.5048i | −0.511531 | + | 0.511531i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.7541 | − | 32.7541i | 1.23887 | − | 1.23887i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.360678 | + | 0.360678i | 0.0136226 | + | 0.0136226i | 0.713885 | − | 0.700263i | \(-0.246934\pi\) |
−0.700263 | + | 0.713885i | \(0.746934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.71180 | − | 4.71180i | −0.177709 | − | 0.177709i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.3169 | 1.06497 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.03677 | − | 3.03677i | −0.114048 | − | 0.114048i | 0.647780 | − | 0.761828i | \(-0.275698\pi\) |
−0.761828 | + | 0.647780i | \(0.775698\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 80.6074 | 3.02301 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.05094 | + | 5.05094i | 0.189159 | + | 0.189159i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 68.6497i | 2.56377i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.02420 | −0.299252 | −0.149626 | − | 0.988743i | \(-0.547807\pi\) | ||||
−0.149626 | + | 0.988743i | \(0.547807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.4448 | −0.724160 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 83.5873i | 3.10865i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.46006 | + | 8.46006i | 0.313766 | + | 0.313766i | 0.846367 | − | 0.532601i | \(-0.178785\pi\) |
−0.532601 | + | 0.846367i | \(0.678785\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.2180 | 0.452520 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.2463 | + | 10.2463i | 0.378974 | + | 0.378974i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3403 | 0.566605 | 0.283303 | − | 0.959031i | \(-0.408570\pi\) | ||||
0.283303 | + | 0.959031i | \(0.408570\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.53905 | + | 3.53905i | 0.130363 | + | 0.130363i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.9410 | + | 24.9410i | 0.917468 | + | 0.917468i | 0.996845 | − | 0.0793763i | \(-0.0252929\pi\) |
−0.0793763 | + | 0.996845i | \(0.525293\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.9837 | − | 53.9837i | 1.98314 | − | 1.98314i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.4908 | − | 24.4908i | 0.898482 | − | 0.898482i | −0.0968199 | − | 0.995302i | \(-0.530867\pi\) |
0.995302 | + | 0.0968199i | \(0.0308671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 53.7820i | − | 1.96778i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.44882 | + | 1.44882i | −0.0529386 | + | 0.0529386i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28.3355i | − | 1.03398i | −0.855992 | − | 0.516989i | \(-0.827053\pi\) | ||
0.855992 | − | 0.516989i | \(-0.172947\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.2497 | − | 35.2497i | 1.28457 | − | 1.28457i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.5834 | 0.857154 | 0.428577 | − | 0.903505i | \(-0.359015\pi\) | ||||
0.428577 | + | 0.903505i | \(0.359015\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.02420i | 0.291260i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 21.8891i | − | 0.793480i | −0.917931 | − | 0.396740i | \(-0.870141\pi\) | ||
0.917931 | − | 0.396740i | \(-0.129859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.91052 | 0.213975 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −43.8771 | + | 43.8771i | −1.58431 | + | 1.58431i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 29.2413i | − | 1.05447i | −0.849720 | − | 0.527234i | \(-0.823229\pi\) | ||
0.849720 | − | 0.527234i | \(-0.176771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.4056 | + | 13.4056i | −0.482790 | + | 0.482790i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 37.4599i | − | 1.34734i | −0.739033 | − | 0.673669i | \(-0.764717\pi\) | ||
0.739033 | − | 0.673669i | \(-0.235283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.86776 | + | 6.86776i | −0.246380 | + | 0.246380i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.95822 | + | 9.95822i | −0.356790 | + | 0.356790i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.217676 | + | 0.217676i | 0.00778907 | + | 0.00778907i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 56.5191 | + | 56.5191i | 2.01983 | + | 2.01983i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.74760 | −0.204880 | −0.102440 | − | 0.994739i | \(-0.532665\pi\) | ||||
−0.102440 | + | 0.994739i | \(0.532665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.5349 | − | 30.5349i | −1.08707 | − | 1.08707i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.51625 | 0.267247 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.1184 | − | 17.1184i | −0.607894 | − | 0.607894i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.1720i | 1.70634i | 0.521634 | + | 0.853170i | \(0.325323\pi\) | ||||
−0.521634 | + | 0.853170i | \(0.674677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.99244 | 0.247375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 58.6316 | 2.07164 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.30955i | 0.187370i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.7838 | + | 48.7838i | 1.71727 | + | 1.71727i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.0946 | −0.706489 | −0.353244 | − | 0.935531i | \(-0.614922\pi\) | ||||
−0.353244 | + | 0.935531i | \(0.614922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.14513 | − | 2.14513i | −0.0753258 | − | 0.0753258i | 0.668440 | − | 0.743766i | \(-0.266962\pi\) |
−0.743766 | + | 0.668440i | \(0.766962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −63.9629 | −2.24328 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.55546 | + | 7.55546i | 0.264332 | + | 0.264332i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −53.7132 | − | 53.7132i | −1.87689 | − | 1.87689i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | − | 6.00000i | 0.209401 | − | 0.209401i | −0.594612 | − | 0.804013i | \(-0.702694\pi\) |
0.804013 | + | 0.594612i | \(0.202694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.2525 | + | 29.2525i | −1.01968 | + | 1.01968i | −0.0198765 | + | 0.999802i | \(0.506327\pi\) |
−0.999802 | + | 0.0198765i | \(0.993673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.2302i | 0.529607i | 0.964302 | + | 0.264803i | \(0.0853070\pi\) | ||||
−0.964302 | + | 0.264803i | \(0.914693\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.6005 | + | 14.6005i | −0.507097 | + | 0.507097i | −0.913634 | − | 0.406537i | \(-0.866736\pi\) |
0.406537 | + | 0.913634i | \(0.366736\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 62.9268i | 2.18291i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.1305 | − | 11.1305i | 0.385647 | − | 0.385647i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.5985 | 1.71438 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.4754i | 1.67356i | 0.547541 | + | 0.836779i | \(0.315564\pi\) | ||||
−0.547541 | + | 0.836779i | \(0.684436\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 27.6881i | − | 0.954762i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.1127 | 0.623834 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.9483 | − | 11.9483i | 0.410547 | − | 0.410547i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 44.9691i | − | 1.54334i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.63431 | − | 1.63431i | 0.0560235 | − | 0.0560235i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.0575i | − | 0.926432i | −0.886246 | − | 0.463216i | \(-0.846695\pi\) | ||
0.886246 | − | 0.463216i | \(-0.153305\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.28577 | + | 4.28577i | −0.146399 | + | 0.146399i | −0.776507 | − | 0.630108i | \(-0.783011\pi\) |
0.630108 | + | 0.776507i | \(0.283011\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.19447 | + | 1.19447i | −0.0407549 | + | 0.0407549i | −0.727191 | − | 0.686436i | \(-0.759174\pi\) |
0.686436 | + | 0.727191i | \(0.259174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.5148 | + | 14.5148i | 0.494663 | + | 0.494663i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.7360 | − | 14.7360i | −0.501619 | − | 0.501619i | 0.410322 | − | 0.911941i | \(-0.365416\pi\) |
−0.911941 | + | 0.410322i | \(0.865416\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 57.5985 | 1.95615 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.0780 | − | 15.0780i | −0.511485 | − | 0.511485i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.5168 | 0.559651 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 38.9996 | + | 38.9996i | 1.31994 | + | 1.31994i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 19.8539i | − | 0.670417i | −0.942144 | − | 0.335209i | \(-0.891193\pi\) | ||
0.942144 | − | 0.335209i | \(-0.108807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −37.8115 | −1.27535 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0235 | 1.04521 | 0.522604 | − | 0.852576i | \(-0.324961\pi\) | ||||
0.522604 | + | 0.852576i | \(0.324961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26.5836i | − | 0.894609i | −0.894382 | − | 0.447304i | \(-0.852384\pi\) | ||
0.894382 | − | 0.447304i | \(-0.147616\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.53715 | + | 2.53715i | 0.0851893 | + | 0.0851893i | 0.748417 | − | 0.663228i | \(-0.230814\pi\) |
−0.663228 | + | 0.748417i | \(0.730814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.3794 | 1.38782 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.0308 | + | 16.0308i | 0.537051 | + | 0.537051i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.15611 | 0.172543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.7246 | + | 18.7246i | 0.625195 | + | 0.625195i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.8734 | − | 24.8734i | −0.829576 | − | 0.829576i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.5621 | + | 34.5621i | −1.15143 | + | 1.15143i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.0126 | − | 11.0126i | 0.366476 | − | 0.366476i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 0.472551i | − | 0.0156908i | −0.999969 | − | 0.00784539i | \(-0.997503\pi\) | ||
0.999969 | − | 0.00784539i | \(-0.00249729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −61.8306 | + | 61.8306i | −2.05079 | + | 2.05079i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.03233i | − | 0.0673340i | −0.999433 | − | 0.0336670i | \(-0.989281\pi\) | ||
0.999433 | − | 0.0336670i | \(-0.0107186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0602 | + | 10.0602i | −0.332943 | + | 0.332943i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.0322 | −0.694544 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.1234i | 0.630824i | 0.948955 | + | 0.315412i | \(0.102143\pi\) | ||||
−0.948955 | + | 0.315412i | \(0.897857\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 63.5312i | − | 2.09343i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.01590 | 0.0334388 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42.4581 | − | 42.4581i | 1.39451 | − | 1.39451i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.7803i | 1.10830i | 0.832418 | + | 0.554148i | \(0.186956\pi\) | ||||
−0.832418 | + | 0.554148i | \(0.813044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.20741 | − | 8.20741i | 0.268987 | − | 0.268987i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 49.6729i | 1.62622i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.41422 | + | 1.41422i | −0.0462007 | + | 0.0462007i | −0.729830 | − | 0.683629i | \(-0.760401\pi\) |
0.683629 | + | 0.729830i | \(0.260401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.06191 | − | 7.06191i | 0.230457 | − | 0.230457i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.4961 | + | 17.4961i | 0.570357 | + | 0.570357i | 0.932228 | − | 0.361871i | \(-0.117862\pi\) |
−0.361871 | + | 0.932228i | \(0.617862\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.45406 | − | 3.45406i | −0.112480 | − | 0.112480i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.6441 | −0.443374 | −0.221687 | − | 0.975118i | \(-0.571156\pi\) | ||||
−0.221687 | + | 0.975118i | \(0.571156\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.3899 | + | 12.3899i | 0.402193 | + | 0.402193i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.31948 | −0.204923 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.39470 | − | 5.39470i | −0.174751 | − | 0.174751i | 0.614312 | − | 0.789063i | \(-0.289434\pi\) |
−0.789063 | + | 0.614312i | \(0.789434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 39.5153i | − | 1.27735i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.94310 | 0.0950377 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.17221 | 0.295878 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 6.32706i | − | 0.203887i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.15383 | + | 9.15383i | 0.294367 | + | 0.294367i | 0.838803 | − | 0.544435i | \(-0.183256\pi\) |
−0.544435 | + | 0.838803i | \(0.683256\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 81.0133 | 2.60252 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5637 | − | 10.5637i | −0.339004 | − | 0.339004i | 0.516989 | − | 0.855992i | \(-0.327053\pi\) |
−0.855992 | + | 0.516989i | \(0.827053\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.7965 | 1.14758 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.0480 | − | 16.0480i | −0.513420 | − | 0.513420i | 0.402153 | − | 0.915573i | \(-0.368262\pi\) |
−0.915573 | + | 0.402153i | \(0.868262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.9673 | − | 10.9673i | −0.350516 | − | 0.350516i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.9058 | + | 12.9058i | −0.412049 | + | 0.412049i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.9855 | − | 32.9855i | 1.05207 | − | 1.05207i | 0.0535049 | − | 0.998568i | \(-0.482961\pi\) |
0.998568 | − | 0.0535049i | \(-0.0170393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 7.51538i | − | 0.239217i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.62065 | + | 2.62065i | −0.0833319 | + | 0.0833319i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 33.9183i | − | 1.07745i | −0.842481 | − | 0.538726i | \(-0.818906\pi\) | ||
0.842481 | − | 0.538726i | \(-0.181094\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −42.1561 | + | 42.1561i | −1.33778 | + | 1.33778i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.7497 | −0.942181 | −0.471090 | − | 0.882085i | \(-0.656139\pi\) | ||||
−0.471090 | + | 0.882085i | \(0.656139\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 16.0484i | − | 0.507749i |
(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 | 1600.2.j.c.1007.1 | 16 | ||
4.3 | odd | 2 | 400.2.j.c.307.7 | yes | 16 | ||
5.2 | odd | 4 | 1600.2.s.c.943.1 | 16 | |||
5.3 | odd | 4 | 1600.2.s.c.943.8 | 16 | |||
5.4 | even | 2 | inner | 1600.2.j.c.1007.8 | 16 | ||
16.5 | even | 4 | 400.2.s.c.107.6 | yes | 16 | ||
16.11 | odd | 4 | 1600.2.s.c.207.8 | 16 | |||
20.3 | even | 4 | 400.2.s.c.243.6 | yes | 16 | ||
20.7 | even | 4 | 400.2.s.c.243.3 | yes | 16 | ||
20.19 | odd | 2 | 400.2.j.c.307.2 | yes | 16 | ||
80.27 | even | 4 | inner | 1600.2.j.c.143.1 | 16 | ||
80.37 | odd | 4 | 400.2.j.c.43.2 | ✓ | 16 | ||
80.43 | even | 4 | inner | 1600.2.j.c.143.8 | 16 | ||
80.53 | odd | 4 | 400.2.j.c.43.7 | yes | 16 | ||
80.59 | odd | 4 | 1600.2.s.c.207.1 | 16 | |||
80.69 | even | 4 | 400.2.s.c.107.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.c.43.2 | ✓ | 16 | 80.37 | odd | 4 | ||
400.2.j.c.43.7 | yes | 16 | 80.53 | odd | 4 | ||
400.2.j.c.307.2 | yes | 16 | 20.19 | odd | 2 | ||
400.2.j.c.307.7 | yes | 16 | 4.3 | odd | 2 | ||
400.2.s.c.107.3 | yes | 16 | 80.69 | even | 4 | ||
400.2.s.c.107.6 | yes | 16 | 16.5 | even | 4 | ||
400.2.s.c.243.3 | yes | 16 | 20.7 | even | 4 | ||
400.2.s.c.243.6 | yes | 16 | 20.3 | even | 4 | ||
1600.2.j.c.143.1 | 16 | 80.27 | even | 4 | inner | ||
1600.2.j.c.143.8 | 16 | 80.43 | even | 4 | inner | ||
1600.2.j.c.1007.1 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.j.c.1007.8 | 16 | 5.4 | even | 2 | inner | ||
1600.2.s.c.207.1 | 16 | 80.59 | odd | 4 | |||
1600.2.s.c.207.8 | 16 | 16.11 | odd | 4 | |||
1600.2.s.c.943.1 | 16 | 5.2 | odd | 4 | |||
1600.2.s.c.943.8 | 16 | 5.3 | odd | 4 |