Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(207,1600)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.207");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.s (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 | 207.8 | ||
Root | \(1.24570 + 0.669507i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.207 |
Dual form | 1600.2.s.c.943.8 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 3.07455 | 1.77509 | 0.887547 | − | 0.460717i | \(-0.152408\pi\) | ||||
0.887547 | + | 0.460717i | \(0.152408\pi\) | |||||||
\(4\) | 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 | −0.501323 | − | 0.865260i | \(-0.667153\pi\) |
0.865260 | + | 0.501323i | \(0.167153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.63329i | − | 1.56239i | −0.624285 | − | 0.781196i | \(-0.714610\pi\) | ||
0.624285 | − | 0.781196i | \(-0.285390\pi\) | |||||||
\(14\) | 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 | \(-0.918737\pi\) |
0.252530 | + | 0.967589i | \(0.418737\pi\) | |||||||
\(20\) | 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 | ||||||||
\(27\) | 10.6161 | 2.04306 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.32391 | − | 5.32391i | −0.988626 | − | 0.988626i | 0.0113103 | − | 0.999936i | \(-0.496400\pi\) |
−0.999936 | + | 0.0113103i | \(0.996400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.67202i | 0.839120i | 0.907728 | + | 0.419560i | \(0.137816\pi\) | ||||
−0.907728 | + | 0.419560i | \(0.862184\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.71111 | − | 3.71111i | 0.646022 | − | 0.646022i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.51171i | − | 0.248523i | −0.992249 | − | 0.124262i | \(-0.960344\pi\) | ||
0.992249 | − | 0.124262i | \(-0.0396562\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 17.3198i | − | 2.77340i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.19494i | − | 0.498966i | −0.968379 | − | 0.249483i | \(-0.919739\pi\) | ||
0.968379 | − | 0.249483i | \(-0.0802607\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.42405i | − | 0.369665i | −0.982770 | − | 0.184832i | \(-0.940826\pi\) | ||
0.982770 | − | 0.184832i | \(-0.0591742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.827129 | + | 0.827129i | −0.120649 | + | 0.120649i | −0.764853 | − | 0.644204i | \(-0.777189\pi\) |
0.644204 | + | 0.764853i | \(0.277189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2.63322i | − | 0.376175i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.9959 | + | 12.9959i | 1.81979 | + | 1.81979i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.17664 | −1.12315 | −0.561574 | − | 0.827427i | \(-0.689804\pi\) | ||||
−0.561574 | + | 0.827427i | \(0.689804\pi\) | |||||||
\(54\) | 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 | 0.999900 | + | 0.0141274i | \(0.00449704\pi\) |
0.0141274 | + | 0.999900i | \(0.495503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.03880 | + | 3.03880i | −0.389079 | + | 0.389079i | −0.874359 | − | 0.485280i | \(-0.838718\pi\) |
0.485280 | + | 0.874359i | \(0.338718\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.53497 | + | 9.53497i | 1.20129 | + | 1.20129i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.93200i | 0.358201i | 0.983831 | + | 0.179101i | \(0.0573188\pi\) | ||||
−0.983831 | + | 0.179101i | \(0.942681\pi\) | |||||||
\(68\) | 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 | 0.566583 | − | 0.824004i | \(-0.308265\pi\) |
−0.824004 | + | 0.566583i | \(0.808265\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.56712 | 0.406511 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4917 | 1.40542 | 0.702712 | − | 0.711474i | \(-0.251972\pi\) | ||||
0.702712 | + | 0.711474i | \(0.251972\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.2810 | 1.47567 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.33457 | −0.914838 | −0.457419 | − | 0.889251i | \(-0.651226\pi\) | ||||
−0.457419 | + | 0.889251i | \(0.651226\pi\) | |||||||
\(84\) | 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 | \(-0.340069\pi\) | ||||
0.481563 | + | 0.876412i | \(0.340069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.32391 | − | 8.32391i | 0.872583 | − | 0.872583i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.3644i | 1.48952i | ||||||||
\(94\) | 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 | 0.998963 | − | 0.0455329i | \(-0.0144986\pi\) |
−0.0455329 | + | 0.998963i | \(0.514499\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | 0.980501 | 0.0947886 | 0.0473943 | − | 0.998876i | \(-0.484908\pi\) | ||||
0.0473943 | + | 0.998876i | \(0.484908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | − | 2.00000i | −0.191565 | − | 0.191565i | 0.604807 | − | 0.796372i | \(-0.293250\pi\) |
−0.796372 | + | 0.604807i | \(0.793250\pi\) | |||||||
\(110\) | 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 | ||||||||
\(117\) | − | 36.3509i | − | 3.36065i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.4917i | 1.14511i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.08610i | 0.735100i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 9.82302i | − | 0.885712i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.0019 | + | 14.0019i | −1.24247 | + | 1.24247i | −0.283498 | + | 0.958973i | \(0.591495\pi\) |
−0.958973 | + | 0.283498i | \(0.908505\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7.45288i | − | 0.656190i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.11687 | − | 7.11687i | −0.621804 | − | 0.621804i | 0.324189 | − | 0.945992i | \(-0.394909\pi\) |
−0.945992 | + | 0.324189i | \(0.894909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.21116 | −0.798709 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.995887 | + | 0.995887i | −0.0850843 | + | 0.0850843i | −0.748368 | − | 0.663284i | \(-0.769162\pi\) |
0.663284 | + | 0.748368i | \(0.269162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1128 | − | 12.1128i | −1.02739 | − | 1.02739i | −0.999614 | − | 0.0277808i | \(-0.991156\pi\) |
−0.0277808 | − | 0.999614i | \(-0.508844\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | − | 8.09598i | − | 0.667745i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.86696 | − | 9.86696i | 0.808333 | − | 0.808333i | −0.176048 | − | 0.984382i | \(-0.556331\pi\) |
0.984382 | + | 0.176048i | \(0.0563315\pi\) | |||||||
\(150\) | 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 | ||||||||
\(157\) | −17.9394 | −1.43172 | −0.715859 | − | 0.698245i | \(-0.753965\pi\) | ||||
−0.715859 | + | 0.698245i | \(0.753965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25.1395 | −1.99369 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.19494 | −0.251797 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.39897 | 0.579532 | 0.289766 | − | 0.957098i | \(-0.406423\pi\) | ||||
0.289766 | + | 0.957098i | \(0.406423\pi\) | |||||||
\(164\) | 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 | ||||||||
\(173\) | − | 10.7865i | − | 0.820083i | −0.912067 | − | 0.410042i | \(-0.865514\pi\) | ||
0.912067 | − | 0.410042i | \(-0.134486\pi\) | |||||||
\(174\) | 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 | \(-0.740998\pi\) |
0.726819 | + | 0.686829i | \(0.240998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.58185 | − | 7.58185i | −0.563555 | − | 0.563555i | 0.366761 | − | 0.930315i | \(-0.380467\pi\) |
−0.930315 | + | 0.366761i | \(0.880467\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.34296 | + | 9.34296i | −0.690651 | + | 0.690651i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.2042 | 0.746202 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.6866 | + | 15.6866i | 1.14103 | + | 1.14103i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.46749i | 0.323256i | 0.986852 | + | 0.161628i | \(0.0516745\pi\) | ||||
−0.986852 | + | 0.161628i | \(0.948326\pi\) | |||||||
\(192\) | 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 | ||||||||
\(197\) | 13.8764i | 0.988656i | 0.869275 | + | 0.494328i | \(0.164586\pi\) | ||||
−0.869275 | + | 0.494328i | \(0.835414\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | − | 15.7335i | − | 1.10428i | ||||||
\(204\) | 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 | 0.460585 | − | 0.887616i | \(-0.347640\pi\) |
−0.887616 | + | 0.460585i | \(0.847640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.554462 | 0.0379911 | ||||||||
\(214\) | 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 | 0.0991290 | − | 0.995075i | \(-0.468394\pi\) |
−0.995075 | + | 0.0991290i | \(0.968394\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.22366i | 0.612196i | 0.952000 | + | 0.306098i | \(0.0990235\pi\) | ||||
−0.952000 | + | 0.306098i | \(0.900976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.2297 | − | 12.2297i | 0.808160 | − | 0.808160i | −0.176195 | − | 0.984355i | \(-0.556379\pi\) |
0.984355 | + | 0.176195i | \(0.0563790\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.9673 | 0.721595 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.6533 | − | 10.6533i | −0.697919 | − | 0.697919i | 0.266042 | − | 0.963961i | \(-0.414284\pi\) |
−0.963961 | + | 0.266042i | \(0.914284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 38.4064 | 2.49476 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3284 | 1.44430 | 0.722150 | − | 0.691736i | \(-0.243154\pi\) | ||||
0.722150 | + | 0.691736i | \(0.243154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.1868 | −1.75126 | −0.875628 | − | 0.482986i | \(-0.839552\pi\) | ||||
−0.875628 | + | 0.482986i | \(0.839552\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.98507 | 0.576393 | ||||||||
\(244\) | 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 | −0.245686 | − | 0.969349i | \(-0.579013\pi\) |
0.969349 | + | 0.245686i | \(0.0790133\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.60987i | 0.164081i | ||||||||
\(254\) | 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 | ||||||||
\(267\) | 27.9357 | 1.70964 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8670 | + | 15.8670i | 0.967426 | + | 0.967426i | 0.999486 | − | 0.0320600i | \(-0.0102068\pi\) |
−0.0320600 | + | 0.999486i | \(0.510207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8040i | 1.26375i | 0.775070 | + | 0.631875i | \(0.217715\pi\) | ||||
−0.775070 | + | 0.631875i | \(0.782285\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.5923 | − | 25.5923i | 1.54892 | − | 1.54892i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 20.4670i | − | 1.22974i | −0.788628 | − | 0.614871i | \(-0.789208\pi\) | ||
0.788628 | − | 0.614871i | \(-0.210792\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.1480i | 1.80491i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.89116i | − | 0.351437i | −0.984440 | − | 0.175719i | \(-0.943775\pi\) | ||
0.984440 | − | 0.175719i | \(-0.0562249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 14.6262i | − | 0.869439i | −0.900566 | − | 0.434720i | \(-0.856847\pi\) | ||
0.900566 | − | 0.434720i | \(-0.143153\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | 12.2982 | 0.718469 | 0.359235 | − | 0.933247i | \(-0.383038\pi\) | ||||
0.359235 | + | 0.933247i | \(0.383038\pi\) | |||||||
\(294\) | 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 | ||||||||
\(307\) | 20.6636i | 1.17933i | 0.807647 | + | 0.589666i | \(0.200741\pi\) | ||||
−0.807647 | + | 0.589666i | \(0.799259\pi\) | |||||||
\(308\) | 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 | 0.639207 | − | 0.769035i | \(-0.279263\pi\) |
−0.769035 | + | 0.639207i | \(0.779263\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.05541 | −0.115443 | −0.0577217 | − | 0.998333i | \(-0.518384\pi\) | ||||
−0.0577217 | + | 0.998333i | \(0.518384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.8524 | −0.719594 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.01460 | 0.168259 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.3496 | −1.46613 | ||||||||
\(324\) | 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 | −0.975157 | − | 0.221516i | \(-0.928900\pi\) |
0.221516 | + | 0.975157i | \(0.428900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 9.75487i | − | 0.534563i | ||||||
\(334\) | 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 | ||||||||
\(347\) | −8.81175 | −0.473040 | −0.236520 | − | 0.971627i | \(-0.576007\pi\) | ||||
−0.236520 | + | 0.971627i | \(0.576007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.8398 | − | 15.8398i | −0.847885 | − | 0.847885i | 0.141984 | − | 0.989869i | \(-0.454652\pi\) |
−0.989869 | + | 0.141984i | \(0.954652\pi\) | |||||||
\(350\) | 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 | ||||||||
\(357\) | 38.4064i | 2.03268i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 24.8612i | 1.30487i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.40440 | − | 8.40440i | 0.438706 | − | 0.438706i | −0.452870 | − | 0.891576i | \(-0.649600\pi\) |
0.891576 | + | 0.452870i | \(0.149600\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 20.6166i | − | 1.07326i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0820 | − | 12.0820i | −0.627268 | − | 0.627268i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.6942 | −1.43395 | −0.716977 | − | 0.697097i | \(-0.754475\pi\) | ||||
−0.716977 | + | 0.697097i | \(0.754475\pi\) | |||||||
\(374\) | 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 | \(-0.472247\pi\) |
−0.996201 | + | 0.0870790i | \(0.972247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.0497 | + | 43.0497i | −2.20550 | + | 2.20550i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.11930 | + | 8.11930i | 0.414877 | + | 0.414877i | 0.883434 | − | 0.468557i | \(-0.155226\pi\) |
−0.468557 | + | 0.883434i | \(0.655226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 15.6421i | − | 0.795134i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.38285 | + | 6.38285i | −0.323623 | + | 0.323623i | −0.850155 | − | 0.526532i | \(-0.823492\pi\) |
0.526532 | + | 0.850155i | \(0.323492\pi\) | |||||||
\(390\) | 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 | ||||||||
\(397\) | −8.65670 | −0.434467 | −0.217234 | − | 0.976120i | \(-0.569703\pi\) | ||||
−0.217234 | + | 0.976120i | \(0.569703\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 26.3188 | 1.31104 | ||||||||
\(404\) | 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 | \(-0.474831\pi\) | ||||
0.0789899 | + | 0.996875i | \(0.474831\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.06191 | + | 3.06191i | −0.151033 | + | 0.151033i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.0182i | 1.13265i | ||||||||
\(414\) | 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 | −0.352473 | + | 0.935822i | \(0.614659\pi\) |
−0.935822 | + | 0.352473i | \(0.885341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.3345 | + | 28.3345i | 1.38094 | + | 1.38094i | 0.842959 | + | 0.537977i | \(0.180811\pi\) |
0.537977 | + | 0.842959i | \(0.319189\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.33736 | + | 5.33736i | −0.259512 | + | 0.259512i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.98044 | −0.434594 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.9058 | − | 20.9058i | −1.00934 | − | 1.00934i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.49981i | 0.313085i | 0.987671 | + | 0.156543i | \(0.0500348\pi\) | ||||
−0.987671 | + | 0.156543i | \(0.949965\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | − | 6.73932i | − | 0.322386i | ||||||
\(438\) | 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 | ||||||||
\(443\) | 35.3347i | 1.67880i | 0.543513 | + | 0.839401i | \(0.317094\pi\) | ||||
−0.543513 | + | 0.839401i | \(0.682906\pi\) | |||||||
\(444\) | 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 | ||||||||
\(453\) | 28.6544 | 1.34630 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.1040 | − | 27.1040i | 1.26787 | − | 1.26787i | 0.320688 | − | 0.947185i | \(-0.396086\pi\) |
0.947185 | − | 0.320688i | \(-0.103914\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 44.8734 | + | 44.8734i | 2.09451 | + | 2.09451i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.94253 | − | 3.94253i | 0.183622 | − | 0.183622i | −0.609310 | − | 0.792932i | \(-0.708554\pi\) |
0.792932 | + | 0.609310i | \(0.208554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.8625 | − | 18.8625i | −0.876617 | − | 0.876617i | 0.116566 | − | 0.993183i | \(-0.462811\pi\) |
−0.993183 | + | 0.116566i | \(0.962811\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 17.2282i | − | 0.797228i | −0.917119 | − | 0.398614i | \(-0.869491\pi\) | ||
0.917119 | − | 0.398614i | \(-0.130509\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | −52.7629 | −2.41585 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.2875 | 1.79509 | 0.897546 | − | 0.440920i | \(-0.145348\pi\) | ||||
0.897546 | + | 0.440920i | \(0.145348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.51588 | −0.388291 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.82302 | −0.446963 | ||||||||
\(484\) | 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 | 0.315277 | − | 0.949000i | \(-0.397902\pi\) |
0.949000 | − | 0.315277i | \(-0.102098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 45.0076i | − | 2.02704i | ||||||
\(494\) | 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 | \(-0.761921\pi\) |
0.680135 | + | 0.733087i | \(0.261921\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | −57.5985 | −2.55804 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.1062 | + | 23.1062i | 1.02417 | + | 1.02417i | 0.999701 | + | 0.0244652i | \(0.00778830\pi\) |
0.0244652 | + | 0.999701i | \(0.492212\pi\) | |||||||
\(510\) | 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 | ||||||||
\(517\) | 1.99676i | 0.0878173i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 33.1637i | − | 1.45573i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 31.3733i | − | 1.37449i | −0.726427 | − | 0.687244i | \(-0.758821\pi\) | ||
0.726427 | − | 0.687244i | \(-0.241179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.6926i | 0.511282i | 0.966772 | + | 0.255641i | \(0.0822866\pi\) | ||||
−0.966772 | + | 0.255641i | \(0.917713\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | −17.9980 | −0.779581 | ||||||||
\(534\) | 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 | −0.257437 | − | 0.966295i | \(-0.582878\pi\) |
0.966295 | + | 0.257437i | \(0.0828780\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.3108 | − | 23.3108i | −1.00036 | − | 1.00036i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 36.0505i | − | 1.54141i | −0.637194 | − | 0.770703i | \(-0.719905\pi\) | ||
0.637194 | − | 0.770703i | \(-0.280095\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | 5.64116 | 0.239024 | 0.119512 | − | 0.992833i | \(-0.461867\pi\) | ||||
0.119512 | + | 0.992833i | \(0.461867\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6554 | −0.577561 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.3733 | 1.32458 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.69143 | 0.197720 | 0.0988601 | − | 0.995101i | \(-0.468480\pi\) | ||||
0.0988601 | + | 0.995101i | \(0.468480\pi\) | |||||||
\(564\) | 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 | \(-0.0761000\pi\) | ||||
0.971557 | + | 0.236804i | \(0.0761000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.27708 | − | 6.27708i | 0.262688 | − | 0.262688i | −0.563457 | − | 0.826145i | \(-0.690529\pi\) |
0.826145 | + | 0.563457i | \(0.190529\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.7355i | 0.573810i | ||||||||
\(574\) | 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 | ||||||||
\(587\) | −17.4298 | −0.719405 | −0.359703 | − | 0.933067i | \(-0.617122\pi\) | ||||
−0.359703 | + | 0.933067i | \(0.617122\pi\) | |||||||
\(588\) | 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 | ||||||||
\(597\) | 29.1344i | 1.19239i | ||||||||
\(598\) | 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 | \(-0.875648\pi\) | ||
0.924657 | − | 0.380802i | \(-0.124352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.9199i | 0.770477i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.9446 | + | 21.9446i | −0.890704 | + | 0.890704i | −0.994589 | − | 0.103885i | \(-0.966873\pi\) |
0.103885 | + | 0.994589i | \(0.466873\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 48.3736i | − | 1.96020i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.65945 | + | 4.65945i | 0.188501 | + | 0.188501i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.7731 | 1.32369 | 0.661846 | − | 0.749640i | \(-0.269773\pi\) | ||||
0.661846 | + | 0.749640i | \(0.269773\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.6044 | − | 30.6044i | 1.23209 | − | 1.23209i | 0.268928 | − | 0.963160i | \(-0.413331\pi\) |
0.963160 | − | 0.268928i | \(-0.0866693\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9365 | + | 10.9365i | 0.439576 | + | 0.439576i | 0.891869 | − | 0.452293i | \(-0.149394\pi\) |
−0.452293 | + | 0.891869i | \(0.649394\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | 23.1341i | 0.923888i | ||||||||
\(628\) | 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 | ||||||||
\(637\) | −14.8337 | −0.587732 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 36.4066 | 1.43574 | 0.717868 | − | 0.696179i | \(-0.245118\pi\) | ||||
0.717868 | + | 0.696179i | \(0.245118\pi\) | |||||||
\(644\) | 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 | ||||||||
\(653\) | 29.2010i | 1.14272i | 0.820699 | + | 0.571361i | \(0.193584\pi\) | ||||
−0.820699 | + | 0.571361i | \(0.806416\pi\) | |||||||
\(654\) | 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 | 0.355575 | − | 0.934648i | \(-0.384285\pi\) |
0.934648 | − | 0.355575i | \(-0.115715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0780 | + | 31.0780i | 1.20879 | + | 1.20879i | 0.971418 | + | 0.237375i | \(0.0762870\pi\) |
0.237375 | + | 0.971418i | \(0.423713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 73.2098 | − | 73.2098i | 2.84323 | − | 2.84323i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.5114 | 0.445723 | ||||||||
\(668\) | 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 | ||||||||
\(677\) | 25.5644i | 0.982521i | 0.871013 | + | 0.491261i | \(0.163464\pi\) | ||||
−0.871013 | + | 0.491261i | \(0.836536\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17.8609i | − | 0.685437i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.3586i | 1.08671i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 26.4968i | − | 1.01387i | −0.861984 | − | 0.506936i | \(-0.830778\pi\) | ||
0.861984 | − | 0.506936i | \(-0.169222\pi\) | |||||||
\(684\) | 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 | 0.671196 | − | 0.741280i | \(-0.265781\pi\) |
−0.741280 | + | 0.671196i | \(0.765781\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.0182 | 0.874389 | ||||||||
\(694\) | 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 | −0.700263 | − | 0.713885i | \(-0.746934\pi\) |
0.713885 | + | 0.700263i | \(0.246934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.71180 | + | 4.71180i | 0.177709 | + | 0.177709i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.3169i | 1.06497i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.03677 | − | 3.03677i | 0.114048 | − | 0.114048i | −0.647780 | − | 0.761828i | \(-0.724302\pi\) |
0.761828 | + | 0.647780i | \(0.224302\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | 68.6497 | 2.56377 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.02420 | 0.299252 | 0.149626 | − | 0.988743i | \(-0.452193\pi\) | ||||
0.149626 | + | 0.988743i | \(0.452193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.4448 | −0.724160 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −83.5873 | −3.10865 | ||||||||
\(724\) | 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 | ||||||||
\(733\) | − | 15.3403i | − | 0.566605i | −0.959031 | − | 0.283303i | \(-0.908570\pi\) | ||
0.959031 | − | 0.283303i | \(-0.0914301\pi\) | |||||||
\(734\) | 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 | \(-0.974707\pi\) |
0.0793763 | + | 0.996845i | \(0.474707\pi\) | |||||||
\(740\) | 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 | ||||||||
\(747\) | −53.7820 | −1.96778 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.44882 | + | 1.44882i | 0.0529386 | + | 0.0529386i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.3355i | 1.03398i | 0.855992 | + | 0.516989i | \(0.172947\pi\) | ||||
−0.855992 | + | 0.516989i | \(0.827053\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.2497 | − | 35.2497i | 1.28457 | − | 1.28457i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.5834i | 0.857154i | 0.903505 | + | 0.428577i | \(0.140985\pi\) | ||||
−0.903505 | + | 0.428577i | \(0.859015\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.02420i | 0.291260i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.8891i | 0.793480i | 0.917931 | + | 0.396740i | \(0.129859\pi\) | ||||
−0.917931 | + | 0.396740i | \(0.870141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 5.91052i | − | 0.213975i | ||||||
\(764\) | 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 | ||||||||
\(773\) | 37.4599 | 1.34734 | 0.673669 | − | 0.739033i | \(-0.264717\pi\) | ||||
0.673669 | + | 0.739033i | \(0.264717\pi\) | |||||||
\(774\) | 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 | ||||||||
\(787\) | − | 5.74760i | − | 0.204880i | −0.994739 | − | 0.102440i | \(-0.967335\pi\) | ||
0.994739 | − | 0.102440i | \(-0.0326649\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | 48.1720 | 1.70634 | 0.853170 | − | 0.521634i | \(-0.174677\pi\) | ||||
0.853170 | + | 0.521634i | \(0.174677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.99244 | −0.247375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 58.6316 | 2.07164 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.30955 | −0.187370 | ||||||||
\(804\) | 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 | \(-0.385078\pi\) | ||||
0.353244 | + | 0.935531i | \(0.385078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.14513 | + | 2.14513i | −0.0753258 | + | 0.0753258i | −0.743766 | − | 0.668440i | \(-0.766962\pi\) |
0.668440 | + | 0.743766i | \(0.266962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 63.9629i | 2.24328i | ||||||||
\(814\) | 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 | 0.804013 | − | 0.594612i | \(-0.202694\pi\) |
−0.594612 | + | 0.804013i | \(0.702694\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | 15.2302 | 0.529607 | 0.264803 | − | 0.964302i | \(-0.414693\pi\) | ||||
0.264803 | + | 0.964302i | \(0.414693\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6005 | + | 14.6005i | 0.507097 | + | 0.507097i | 0.913634 | − | 0.406537i | \(-0.133264\pi\) |
−0.406537 | + | 0.913634i | \(0.633264\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | 49.5985i | 1.71438i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | − | 18.1127i | − | 0.623834i | ||||||
\(844\) | 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 | ||||||||
\(853\) | 27.0575 | 0.926432 | 0.463216 | − | 0.886246i | \(-0.346695\pi\) | ||||
0.463216 | + | 0.886246i | \(0.346695\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.28577 | − | 4.28577i | 0.146399 | − | 0.146399i | −0.630108 | − | 0.776507i | \(-0.716989\pi\) |
0.776507 | + | 0.630108i | \(0.216989\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.19447 | + | 1.19447i | 0.0407549 | + | 0.0407549i | 0.727191 | − | 0.686436i | \(-0.240826\pi\) |
−0.686436 | + | 0.727191i | \(0.740826\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.5148 | − | 14.5148i | 0.494663 | − | 0.494663i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.7360 | + | 14.7360i | 0.501619 | + | 0.501619i | 0.911941 | − | 0.410322i | \(-0.134584\pi\) |
−0.410322 | + | 0.911941i | \(0.634584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 57.5985i | 1.95615i | ||||||||
\(868\) | 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 | ||||||||
\(877\) | −19.8539 | −0.670417 | −0.335209 | − | 0.942144i | \(-0.608807\pi\) | ||||
−0.335209 | + | 0.942144i | \(0.608807\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 26.5836 | 0.894609 | 0.447304 | − | 0.894382i | \(-0.352384\pi\) | ||||
0.447304 | + | 0.894382i | \(0.352384\pi\) | |||||||
\(884\) | 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 | ||||||||
\(893\) | − | 5.15611i | − | 0.172543i | ||||||
\(894\) | 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 | ||||||||
\(907\) | −0.472551 | −0.0156908 | −0.00784539 | − | 0.999969i | \(-0.502497\pi\) | ||||
−0.00784539 | + | 0.999969i | \(0.502497\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 61.8306 | + | 61.8306i | 2.05079 | + | 2.05079i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.03233i | 0.0673340i | 0.999433 | + | 0.0336670i | \(0.0107186\pi\) | ||||
−0.999433 | + | 0.0336670i | \(0.989281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0602 | + | 10.0602i | −0.332943 | + | 0.332943i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 21.0322i | − | 0.694544i | ||||||
\(918\) | 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 | ||||||||
\(923\) | − | 1.01590i | − | 0.0334388i | ||||||
\(924\) | 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 | ||||||||
\(933\) | −49.6729 | −1.62622 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.41422 | − | 1.41422i | 0.0462007 | − | 0.0462007i | −0.683629 | − | 0.729830i | \(-0.739599\pi\) |
0.729830 | + | 0.683629i | \(0.239599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.06191 | − | 7.06191i | −0.230457 | − | 0.230457i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.4961 | − | 17.4961i | 0.570357 | − | 0.570357i | −0.361871 | − | 0.932228i | \(-0.617862\pi\) |
0.932228 | + | 0.361871i | \(0.117862\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.45406 | + | 3.45406i | 0.112480 | + | 0.112480i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 13.6441i | − | 0.443374i | −0.975118 | − | 0.221687i | \(-0.928844\pi\) | ||
0.975118 | − | 0.221687i | \(-0.0711564\pi\) | |||||||
\(948\) | 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 | 0.789063 | − | 0.614312i | \(-0.210566\pi\) |
−0.614312 | + | 0.789063i | \(0.710566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −39.5153 | −1.27735 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.94310 | −0.0950377 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.17221 | 0.295878 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.32706 | 0.203887 | ||||||||
\(964\) | 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 | −0.855992 | − | 0.516989i | \(-0.827053\pi\) |
0.516989 | + | 0.855992i | \(0.327053\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 35.7965i | − | 1.14758i | ||||||
\(974\) | 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 | ||||||||
\(987\) | −7.51538 | −0.239217 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.62065 | + | 2.62065i | 0.0833319 | + | 0.0833319i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.9183i | 1.07745i | 0.842481 | + | 0.538726i | \(0.181094\pi\) | ||||
−0.842481 | + | 0.538726i | \(0.818906\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −42.1561 | + | 42.1561i | −1.33778 | + | 1.33778i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 29.7497i | − | 0.942181i | −0.882085 | − | 0.471090i | \(-0.843861\pi\) | ||
0.882085 | − | 0.471090i | \(-0.156139\pi\) | |||||||
\(998\) | 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.s.c.207.8 | 16 | ||
4.3 | odd | 2 | 400.2.s.c.107.6 | yes | 16 | ||
5.2 | odd | 4 | 1600.2.j.c.143.1 | 16 | |||
5.3 | odd | 4 | 1600.2.j.c.143.8 | 16 | |||
5.4 | even | 2 | inner | 1600.2.s.c.207.1 | 16 | ||
16.3 | odd | 4 | 1600.2.j.c.1007.1 | 16 | |||
16.13 | even | 4 | 400.2.j.c.307.7 | yes | 16 | ||
20.3 | even | 4 | 400.2.j.c.43.7 | yes | 16 | ||
20.7 | even | 4 | 400.2.j.c.43.2 | ✓ | 16 | ||
20.19 | odd | 2 | 400.2.s.c.107.3 | yes | 16 | ||
80.3 | even | 4 | inner | 1600.2.s.c.943.8 | 16 | ||
80.13 | odd | 4 | 400.2.s.c.243.6 | yes | 16 | ||
80.19 | odd | 4 | 1600.2.j.c.1007.8 | 16 | |||
80.29 | even | 4 | 400.2.j.c.307.2 | yes | 16 | ||
80.67 | even | 4 | inner | 1600.2.s.c.943.1 | 16 | ||
80.77 | odd | 4 | 400.2.s.c.243.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.c.43.2 | ✓ | 16 | 20.7 | even | 4 | ||
400.2.j.c.43.7 | yes | 16 | 20.3 | even | 4 | ||
400.2.j.c.307.2 | yes | 16 | 80.29 | even | 4 | ||
400.2.j.c.307.7 | yes | 16 | 16.13 | even | 4 | ||
400.2.s.c.107.3 | yes | 16 | 20.19 | odd | 2 | ||
400.2.s.c.107.6 | yes | 16 | 4.3 | odd | 2 | ||
400.2.s.c.243.3 | yes | 16 | 80.77 | odd | 4 | ||
400.2.s.c.243.6 | yes | 16 | 80.13 | odd | 4 | ||
1600.2.j.c.143.1 | 16 | 5.2 | odd | 4 | |||
1600.2.j.c.143.8 | 16 | 5.3 | odd | 4 | |||
1600.2.j.c.1007.1 | 16 | 16.3 | odd | 4 | |||
1600.2.j.c.1007.8 | 16 | 80.19 | odd | 4 | |||
1600.2.s.c.207.1 | 16 | 5.4 | even | 2 | inner | ||
1600.2.s.c.207.8 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.s.c.943.1 | 16 | 80.67 | even | 4 | inner | ||
1600.2.s.c.943.8 | 16 | 80.3 | even | 4 | inner |