Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(145,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.bc (of order \(12\), degree \(4\), 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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.145 |
Dual form | 1728.2.bc.c.1585.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.133975 | + | 0.500000i | 0.0599153 | + | 0.223607i | 0.989391 | − | 0.145276i | \(-0.0464070\pi\) |
−0.929476 | + | 0.368883i | \(0.879740\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.13397 | + | 1.23205i | −0.806567 | + | 0.465671i | −0.845762 | − | 0.533560i | \(-0.820854\pi\) |
0.0391956 | + | 0.999232i | \(0.487520\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.133975i | −0.150756 | − | 0.0403949i | 0.182652 | − | 0.983178i | \(-0.441532\pi\) |
−0.333408 | + | 0.942783i | \(0.608199\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.59808 | − | 1.23205i | 1.27528 | − | 0.341709i | 0.443227 | − | 0.896410i | \(-0.353834\pi\) |
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 3.00000i | 0.688247 | + | 0.688247i | 0.961844 | − | 0.273597i | \(-0.0882135\pi\) |
−0.273597 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.401924 | − | 0.232051i | −0.0838069 | − | 0.0483859i | 0.457511 | − | 0.889204i | \(-0.348741\pi\) |
−0.541318 | + | 0.840818i | \(0.682074\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.09808 | − | 2.36603i | 0.819615 | − | 0.473205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.866025 | + | 3.23205i | −0.160817 | + | 0.600177i | 0.837720 | + | 0.546100i | \(0.183888\pi\) |
−0.998537 | + | 0.0540766i | \(0.982778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.598076 | + | 1.03590i | −0.107418 | + | 0.186053i | −0.914723 | − | 0.404081i | \(-0.867592\pi\) |
0.807306 | + | 0.590133i | \(0.200925\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.901924 | − | 0.901924i | −0.152453 | − | 0.152453i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.73205 | + | 7.73205i | −1.27114 | + | 1.27114i | −0.325651 | + | 0.945490i | \(0.605584\pi\) |
−0.945490 | + | 0.325651i | \(0.894416\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.69615 | + | 5.59808i | 1.51428 | + | 0.874273i | 0.999860 | + | 0.0167371i | \(0.00532782\pi\) |
0.514425 | + | 0.857536i | \(0.328006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.69615 | − | 2.33013i | −1.32615 | − | 0.355341i | −0.474872 | − | 0.880055i | \(-0.657506\pi\) |
−0.851279 | + | 0.524714i | \(0.824172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.59808 | + | 7.96410i | 0.670698 | + | 1.16168i | 0.977706 | + | 0.209977i | \(0.0673388\pi\) |
−0.307008 | + | 0.951707i | \(0.599328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.464102 | + | 0.803848i | −0.0663002 | + | 0.114835i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.26795 | + | 2.26795i | −0.311527 | + | 0.311527i | −0.845501 | − | 0.533974i | \(-0.820698\pi\) |
0.533974 | + | 0.845501i | \(0.320698\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.267949i | − | 0.0361303i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | − | 5.59808i | −0.195283 | − | 0.728807i | −0.992193 | − | 0.124709i | \(-0.960200\pi\) |
0.796910 | − | 0.604098i | \(-0.206467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.86603 | + | 14.4282i | −0.494994 | + | 1.84734i | 0.0350707 | + | 0.999385i | \(0.488834\pi\) |
−0.530065 | + | 0.847957i | \(0.677832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.23205 | + | 2.13397i | 0.152817 | + | 0.264687i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.23205 | + | 0.330127i | −0.150519 | + | 0.0403314i | −0.333292 | − | 0.942824i | \(-0.608159\pi\) |
0.182773 | + | 0.983155i | \(0.441493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9282i | 1.29694i | 0.761241 | + | 0.648470i | \(0.224591\pi\) | ||||
−0.761241 | + | 0.648470i | \(0.775409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.535898i | 0.0627222i | 0.999508 | + | 0.0313611i | \(0.00998418\pi\) | ||||
−0.999508 | + | 0.0313611i | \(0.990016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.23205 | − | 0.330127i | 0.140405 | − | 0.0376215i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.866025 | − | 1.50000i | −0.0974355 | − | 0.168763i | 0.813187 | − | 0.582003i | \(-0.197731\pi\) |
−0.910622 | + | 0.413239i | \(0.864397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.16025 | − | 11.7942i | 0.346883 | − | 1.29458i | −0.543514 | − | 0.839400i | \(-0.682907\pi\) |
0.890397 | − | 0.455185i | \(-0.150427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.535898 | − | 2.00000i | −0.0581263 | − | 0.216930i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8564i | 1.25678i | 0.777900 | + | 0.628388i | \(0.216285\pi\) | ||||
−0.777900 | + | 0.628388i | \(0.783715\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.29423 | + | 8.29423i | −0.869471 | + | 0.869471i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.09808 | + | 1.90192i | −0.112660 | + | 0.195133i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.86603 | + | 0.500000i | 0.185676 | + | 0.0497519i | 0.350459 | − | 0.936578i | \(-0.386026\pi\) |
−0.164783 | + | 0.986330i | \(0.552692\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.79423 | + | 1.03590i | 0.176791 | + | 0.102070i | 0.585784 | − | 0.810467i | \(-0.300787\pi\) |
−0.408993 | + | 0.912537i | \(0.634120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.3923 | + | 11.3923i | −1.10134 | + | 1.10134i | −0.107086 | + | 0.994250i | \(0.534152\pi\) |
−0.994250 | + | 0.107086i | \(0.965848\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.73205 | + | 1.73205i | 0.165900 | + | 0.165900i | 0.785175 | − | 0.619274i | \(-0.212573\pi\) |
−0.619274 | + | 0.785175i | \(0.712573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.76795 | − | 4.79423i | 0.260387 | − | 0.451003i | −0.705958 | − | 0.708254i | \(-0.749483\pi\) |
0.966345 | + | 0.257251i | \(0.0828166\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0621778 | − | 0.232051i | 0.00579811 | − | 0.0216388i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.53590 | − | 4.92820i | 0.782485 | − | 0.451768i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.29423 | − | 5.36603i | −0.844930 | − | 0.487820i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.56218 | + | 3.56218i | 0.318611 | + | 0.318611i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.3923 | 1.80952 | 0.904762 | − | 0.425917i | \(-0.140048\pi\) | ||||
0.904762 | + | 0.425917i | \(0.140048\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6962 | − | 3.13397i | 1.02190 | − | 0.273817i | 0.291305 | − | 0.956630i | \(-0.405911\pi\) |
0.730593 | + | 0.682814i | \(0.239244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.0981 | − | 2.70577i | −0.875614 | − | 0.234620i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4282 | − | 8.33013i | 1.23268 | − | 0.711691i | 0.265096 | − | 0.964222i | \(-0.414596\pi\) |
0.967589 | + | 0.252531i | \(0.0812631\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.16025 | + | 4.33013i | 0.0984115 | + | 0.367277i | 0.997515 | − | 0.0704603i | \(-0.0224468\pi\) |
−0.899103 | + | 0.437737i | \(0.855780\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.46410 | −0.206059 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.73205 | −0.143839 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.93782 | − | 14.6962i | −0.322599 | − | 1.20396i | −0.916704 | − | 0.399568i | \(-0.869160\pi\) |
0.594105 | − | 0.804388i | \(-0.297507\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.06218 | + | 3.50000i | −0.493333 | + | 0.284826i | −0.725956 | − | 0.687741i | \(-0.758602\pi\) |
0.232623 | + | 0.972567i | \(0.425269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.598076 | − | 0.160254i | −0.0480386 | − | 0.0128719i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.866025 | − | 0.232051i | 0.0691164 | − | 0.0185197i | −0.224095 | − | 0.974567i | \(-0.571943\pi\) |
0.293212 | + | 0.956048i | \(0.405276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.14359 | 0.0901278 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.9282 | − | 11.9282i | −0.934289 | − | 0.934289i | 0.0636813 | − | 0.997970i | \(-0.479716\pi\) |
−0.997970 | + | 0.0636813i | \(0.979716\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.25833 | + | 4.76795i | 0.639049 | + | 0.368955i | 0.784248 | − | 0.620447i | \(-0.213049\pi\) |
−0.145199 | + | 0.989402i | \(0.546382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.36603 | − | 4.83013i | 0.643540 | − | 0.371548i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.40192 | + | 8.96410i | −0.182615 | + | 0.681528i | 0.812514 | + | 0.582942i | \(0.198099\pi\) |
−0.995129 | + | 0.0985859i | \(0.968568\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.83013 | + | 10.0981i | −0.440716 | + | 0.763343i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.92820 | + | 7.92820i | 0.592582 | + | 0.592582i | 0.938328 | − | 0.345746i | \(-0.112374\pi\) |
−0.345746 | + | 0.938328i | \(0.612374\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.26795 | + | 4.26795i | −0.317234 | + | 0.317234i | −0.847704 | − | 0.530470i | \(-0.822016\pi\) |
0.530470 | + | 0.847704i | \(0.322016\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.90192 | − | 2.83013i | −0.360397 | − | 0.208075i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | + | 0.535898i | 0.146254 | + | 0.0391888i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.59808 | + | 11.4282i | 0.477420 | + | 0.826916i | 0.999665 | − | 0.0258797i | \(-0.00823869\pi\) |
−0.522245 | + | 0.852795i | \(0.674905\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.23205 | + | 2.13397i | −0.0886850 | + | 0.153607i | −0.906956 | − | 0.421226i | \(-0.861600\pi\) |
0.818271 | + | 0.574833i | \(0.194933\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4641 | + | 10.4641i | −0.745536 | + | 0.745536i | −0.973637 | − | 0.228101i | \(-0.926748\pi\) |
0.228101 | + | 0.973637i | \(0.426748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.85641i | − | 0.415150i | −0.978219 | − | 0.207575i | \(-0.933443\pi\) | ||
0.978219 | − | 0.207575i | \(-0.0665570\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.13397 | − | 7.96410i | −0.149776 | − | 0.558970i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50000 | + | 5.59808i | −0.104765 | + | 0.390987i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.09808 | − | 1.90192i | −0.0759555 | − | 0.131559i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.96410 | + | 0.526279i | −0.135214 | + | 0.0362306i | −0.325791 | − | 0.945442i | \(-0.605631\pi\) |
0.190577 | + | 0.981672i | \(0.438964\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.66025i | − | 0.317827i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.94744i | − | 0.200085i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.3923 | + | 4.92820i | −1.23720 | + | 0.331507i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.79423 | + | 13.5000i | 0.521940 | + | 0.904027i | 0.999674 | + | 0.0255224i | \(0.00812491\pi\) |
−0.477734 | + | 0.878504i | \(0.658542\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.62436 | + | 17.2583i | −0.306929 | + | 1.14548i | 0.624343 | + | 0.781151i | \(0.285367\pi\) |
−0.931272 | + | 0.364325i | \(0.881300\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.52628 | − | 9.42820i | −0.166941 | − | 0.623033i | −0.997785 | − | 0.0665269i | \(-0.978808\pi\) |
0.830843 | − | 0.556506i | \(-0.187858\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 22.9282i | − | 1.50208i | −0.660259 | − | 0.751038i | \(-0.729553\pi\) | ||
0.660259 | − | 0.751038i | \(-0.270447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.36603 | + | 3.36603i | −0.219575 | + | 0.219575i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.59808 | + | 9.69615i | −0.362109 | + | 0.627192i | −0.988308 | − | 0.152472i | \(-0.951277\pi\) |
0.626198 | + | 0.779664i | \(0.284610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.23205 | − | 10.7942i | −0.401442 | − | 0.695317i | 0.592458 | − | 0.805601i | \(-0.298157\pi\) |
−0.993900 | + | 0.110284i | \(0.964824\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.464102 | − | 0.124356i | −0.0296504 | − | 0.00794479i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.4904 | + | 10.0981i | 1.11289 | + | 0.642525i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.39230 | − | 7.39230i | 0.466598 | − | 0.466598i | −0.434212 | − | 0.900811i | \(-0.642973\pi\) |
0.900811 | + | 0.434212i | \(0.142973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.169873 | + | 0.169873i | 0.0106798 | + | 0.0106798i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.16025 | − | 8.93782i | 0.321888 | − | 0.557526i | −0.658990 | − | 0.752152i | \(-0.729016\pi\) |
0.980878 | + | 0.194626i | \(0.0623493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.97372 | − | 26.0263i | 0.433326 | − | 1.61719i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.40192 | + | 1.96410i | −0.209772 | + | 0.121112i | −0.601205 | − | 0.799095i | \(-0.705313\pi\) |
0.391434 | + | 0.920206i | \(0.371979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.43782 | − | 0.830127i | −0.0883247 | − | 0.0509943i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.73205 | − | 7.73205i | −0.471431 | − | 0.471431i | 0.430946 | − | 0.902378i | \(-0.358180\pi\) |
−0.902378 | + | 0.430946i | \(0.858180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9282 | 0.906824 | 0.453412 | − | 0.891301i | \(-0.350207\pi\) | ||||
0.453412 | + | 0.891301i | \(0.350207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.36603 | + | 0.633975i | −0.142677 | + | 0.0382301i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.7942 | + | 3.69615i | 0.828815 | + | 0.222080i | 0.648197 | − | 0.761473i | \(-0.275523\pi\) |
0.180618 | + | 0.983553i | \(0.442190\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9641 | − | 9.79423i | 1.01199 | − | 0.584275i | 0.100219 | − | 0.994965i | \(-0.468046\pi\) |
0.911775 | + | 0.410691i | \(0.134712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.16025 | − | 15.5263i | −0.247301 | − | 0.922942i | −0.972213 | − | 0.234099i | \(-0.924786\pi\) |
0.724911 | − | 0.688842i | \(-0.241881\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.5885 | −1.62850 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.86603 | − | 14.4282i | −0.225856 | − | 0.842905i | −0.982060 | − | 0.188569i | \(-0.939615\pi\) |
0.756204 | − | 0.654336i | \(-0.227052\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.59808 | − | 1.50000i | 0.151266 | − | 0.0873334i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.13397 | − | 0.571797i | −0.123411 | − | 0.0330679i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.4282 | − | 5.74167i | 1.23510 | − | 0.330944i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.73205 | −0.442736 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.92820 | + | 5.92820i | 0.338340 | + | 0.338340i | 0.855742 | − | 0.517402i | \(-0.173101\pi\) |
−0.517402 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.1865 | − | 15.6962i | −1.54161 | − | 0.890047i | −0.998738 | − | 0.0502299i | \(-0.984005\pi\) |
−0.542869 | − | 0.839817i | \(-0.682662\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.83975 | − | 4.52628i | 0.443129 | − | 0.255840i | −0.261795 | − | 0.965123i | \(-0.584314\pi\) |
0.704924 | + | 0.709283i | \(0.250981\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.545517 | − | 2.03590i | 0.0306393 | − | 0.114347i | −0.948913 | − | 0.315539i | \(-0.897815\pi\) |
0.979552 | + | 0.201192i | \(0.0644814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.866025 | − | 1.50000i | 0.0484881 | − | 0.0839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.0000 | − | 12.0000i | −0.667698 | − | 0.667698i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.9282 | − | 15.9282i | 0.883538 | − | 0.883538i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.6244 | − | 11.3301i | −1.08193 | − | 0.624650i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3564 | + | 7.06218i | 1.44868 | + | 0.388172i | 0.895564 | − | 0.444933i | \(-0.146772\pi\) |
0.553115 | + | 0.833105i | \(0.313439\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.330127 | − | 0.571797i | −0.0180368 | − | 0.0312406i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.696152 | − | 1.20577i | 0.0379218 | − | 0.0656826i | −0.846442 | − | 0.532482i | \(-0.821260\pi\) |
0.884363 | + | 0.466799i | \(0.154593\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.437822 | − | 0.437822i | 0.0237094 | − | 0.0237094i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.5359i | − | 1.05484i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.23205 | − | 19.5263i | −0.280871 | − | 1.04823i | −0.951804 | − | 0.306707i | \(-0.900773\pi\) |
0.670933 | − | 0.741518i | \(-0.265894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.13397 | + | 7.96410i | −0.114229 | + | 0.426309i | −0.999228 | − | 0.0392843i | \(-0.987492\pi\) |
0.884999 | + | 0.465593i | \(0.154159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.2321 | + | 26.3827i | 0.810720 | + | 1.40421i | 0.912361 | + | 0.409387i | \(0.134258\pi\) |
−0.101640 | + | 0.994821i | \(0.532409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.46410 | + | 1.46410i | −0.290004 | + | 0.0777064i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 15.0718i | − | 0.795459i | −0.917503 | − | 0.397730i | \(-0.869798\pi\) | ||
0.917503 | − | 0.397730i | \(-0.130202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.267949 | + | 0.0717968i | −0.0140251 | + | 0.00375801i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.4545 | − | 26.7679i | −0.806717 | − | 1.39728i | −0.915125 | − | 0.403169i | \(-0.867909\pi\) |
0.108408 | − | 0.994106i | \(-0.465425\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.04552 | − | 7.63397i | 0.106198 | − | 0.396336i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.59808 | + | 13.4282i | 0.186301 | + | 0.695286i | 0.994348 | + | 0.106168i | \(0.0338581\pi\) |
−0.808047 | + | 0.589118i | \(0.799475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.9282i | 0.820344i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.5885 | + | 15.5885i | −0.800725 | + | 0.800725i | −0.983209 | − | 0.182484i | \(-0.941586\pi\) |
0.182484 | + | 0.983209i | \(0.441586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.3301 | − | 21.3564i | 0.630040 | − | 1.09126i | −0.357503 | − | 0.933912i | \(-0.616372\pi\) |
0.987543 | − | 0.157349i | \(-0.0502949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.330127 | + | 0.571797i | 0.0168248 | + | 0.0291415i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.59808 | − | 2.03590i | −0.385238 | − | 0.103224i | 0.0610019 | − | 0.998138i | \(-0.480570\pi\) |
−0.446240 | + | 0.894914i | \(0.647237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.60770 | + | 0.928203i | 0.0813046 | + | 0.0469413i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.633975 | − | 0.633975i | 0.0318987 | − | 0.0318987i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0526 | − | 21.0526i | −1.05660 | − | 1.05660i | −0.998299 | − | 0.0582984i | \(-0.981433\pi\) |
−0.0582984 | − | 0.998299i | \(-0.518567\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.16025 | + | 2.00962i | −0.0579403 | + | 0.100356i | −0.893541 | − | 0.448982i | \(-0.851787\pi\) |
0.835600 | + | 0.549338i | \(0.185120\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.47372 | + | 5.50000i | −0.0734112 | + | 0.273975i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.90192 | − | 2.83013i | 0.242979 | − | 0.140284i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.62436 | + | 2.66987i | 0.228660 | + | 0.132017i | 0.609954 | − | 0.792437i | \(-0.291188\pi\) |
−0.381294 | + | 0.924454i | \(0.624521\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.0981 | + | 10.0981i | 0.496894 | + | 0.496894i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.32051 | 0.310262 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.96410 | − | 0.526279i | 0.0959526 | − | 0.0257104i | −0.210523 | − | 0.977589i | \(-0.567517\pi\) |
0.306476 | + | 0.951878i | \(0.400850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7942 | + | 2.89230i | 0.526079 | + | 0.140962i | 0.512077 | − | 0.858940i | \(-0.328876\pi\) |
0.0140017 | + | 0.999902i | \(0.495543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.3923 | + | 9.46410i | −0.795144 | + | 0.459076i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.52628 | − | 35.5526i | −0.461009 | − | 1.72051i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.3205 | 1.50866 | 0.754328 | − | 0.656498i | \(-0.227963\pi\) | ||||
0.754328 | + | 0.656498i | \(0.227963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3923 | 1.17222 | 0.586110 | − | 0.810232i | \(-0.300659\pi\) | ||||
0.586110 | + | 0.810232i | \(0.300659\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.509619 | − | 1.90192i | −0.0243784 | − | 0.0909814i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.0622 | + | 10.4282i | −0.862061 | + | 0.497711i | −0.864702 | − | 0.502286i | \(-0.832493\pi\) |
0.00264111 | + | 0.999997i | \(0.499159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.1603 | + | 4.33013i | 0.767797 | + | 0.205731i | 0.621398 | − | 0.783495i | \(-0.286565\pi\) |
0.146399 | + | 0.989226i | \(0.453232\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.92820 | + | 1.58846i | −0.281024 | + | 0.0753001i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.679492 | −0.0320672 | −0.0160336 | − | 0.999871i | \(-0.505104\pi\) | ||||
−0.0160336 | + | 0.999871i | \(0.505104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.09808 | − | 4.09808i | −0.192971 | − | 0.192971i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.25833 | − | 3.03590i | −0.246514 | − | 0.142325i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0359 | − | 10.9904i | 0.890462 | − | 0.514108i | 0.0163683 | − | 0.999866i | \(-0.494790\pi\) |
0.874094 | + | 0.485758i | \(0.161456\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.598076 | − | 2.23205i | 0.0278552 | − | 0.103957i | −0.950599 | − | 0.310423i | \(-0.899529\pi\) |
0.978454 | + | 0.206466i | \(0.0661961\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.33013 | + | 5.76795i | −0.154764 | + | 0.268059i | −0.932973 | − | 0.359946i | \(-0.882795\pi\) |
0.778209 | + | 0.628005i | \(0.216128\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7846 | − | 19.7846i | −0.915523 | − | 0.915523i | 0.0811771 | − | 0.996700i | \(-0.474132\pi\) |
−0.996700 | + | 0.0811771i | \(0.974132\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.22243 | − | 2.22243i | 0.102622 | − | 0.102622i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.03590 | + | 2.33013i | 0.185571 | + | 0.107139i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.3923 | + | 5.19615i | 0.889780 | + | 0.238416i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.669873 | + | 1.16025i | 0.0306073 | + | 0.0530134i | 0.880923 | − | 0.473259i | \(-0.156923\pi\) |
−0.850316 | + | 0.526272i | \(0.823589\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.0263 | + | 45.0788i | −1.18670 | + | 2.05542i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.366025 | − | 0.366025i | 0.0166204 | − | 0.0166204i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 34.7846i | − | 1.57624i | −0.615521 | − | 0.788121i | \(-0.711054\pi\) | ||
0.615521 | − | 0.788121i | \(-0.288946\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.500000 | + | 1.86603i | 0.0225647 | + | 0.0842125i | 0.976290 | − | 0.216467i | \(-0.0694533\pi\) |
−0.953725 | + | 0.300679i | \(0.902787\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.46410 | − | 12.9282i | 0.156015 | − | 0.582257i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.4641 | − | 23.3205i | −0.603947 | − | 1.04607i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50000 | − | 0.669873i | 0.111915 | − | 0.0299876i | −0.202427 | − | 0.979297i | \(-0.564883\pi\) |
0.314342 | + | 0.949310i | \(0.398216\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 13.8564i | − | 0.617827i | −0.951090 | − | 0.308913i | \(-0.900035\pi\) | ||
0.951090 | − | 0.308913i | \(-0.0999653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.00000i | 0.0444994i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.2583 | − | 5.69615i | 0.942259 | − | 0.252478i | 0.245185 | − | 0.969476i | \(-0.421151\pi\) |
0.697074 | + | 0.716999i | \(0.254485\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.660254 | − | 1.14359i | −0.0292079 | − | 0.0505896i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.277568 | + | 1.03590i | −0.0122311 | + | 0.0456471i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.23205 | − | 4.59808i | −0.0541855 | − | 0.202223i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.1436i | 0.619642i | 0.950795 | + | 0.309821i | \(0.100269\pi\) | ||||
−0.950795 | + | 0.309821i | \(0.899731\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.12436 | − | 2.12436i | 0.0928916 | − | 0.0928916i | −0.659134 | − | 0.752026i | \(-0.729077\pi\) |
0.752026 | + | 0.659134i | \(0.229077\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.39230 | − | 4.14359i | 0.104210 | − | 0.180498i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3923 | − | 19.7321i | −0.495318 | − | 0.857915i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.4808 | + | 13.7942i | 2.22988 | + | 0.597494i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.22243 | − | 4.16987i | −0.312253 | − | 0.180279i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.339746 | − | 0.339746i | 0.0146339 | − | 0.0146339i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0000 | − | 15.0000i | −0.644900 | − | 0.644900i | 0.306856 | − | 0.951756i | \(-0.400723\pi\) |
−0.951756 | + | 0.306856i | \(0.900723\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.633975 | + | 1.09808i | −0.0271565 | + | 0.0470364i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.57180 | + | 28.2583i | −0.323747 | + | 1.20824i | 0.591819 | + | 0.806071i | \(0.298410\pi\) |
−0.915566 | + | 0.402168i | \(0.868257\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.2942 | + | 7.09808i | −0.523752 | + | 0.302388i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.69615 | + | 2.13397i | 0.157176 | + | 0.0907458i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.9808 | − | 27.9808i | −1.18558 | − | 1.18558i | −0.978276 | − | 0.207307i | \(-0.933530\pi\) |
−0.207307 | − | 0.978276i | \(-0.566470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.8564 | −1.81263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.3564 | + | 7.86603i | −1.23723 | + | 0.331513i | −0.817389 | − | 0.576086i | \(-0.804579\pi\) |
−0.419836 | + | 0.907600i | \(0.637912\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.76795 | + | 0.741670i | 0.116448 | + | 0.0312023i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.4808 | + | 14.1340i | −1.02629 | + | 0.592527i | −0.915919 | − | 0.401364i | \(-0.868536\pi\) |
−0.110368 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.44744 | − | 5.40192i | −0.0605735 | − | 0.226063i | 0.929003 | − | 0.370073i | \(-0.120667\pi\) |
−0.989576 | + | 0.144009i | \(0.954001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.19615 | −0.0915859 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.1769 | 1.54770 | 0.773848 | − | 0.633372i | \(-0.218330\pi\) | ||||
0.773848 | + | 0.633372i | \(0.218330\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.78719 | + | 29.0622i | 0.323067 | + | 1.20570i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.43782 | − | 0.830127i | 0.0595485 | − | 0.0343803i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.96410 | − | 0.794229i | −0.122342 | − | 0.0327813i | 0.197129 | − | 0.980378i | \(-0.436838\pi\) |
−0.319470 | + | 0.947596i | \(0.603505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.90192 | + | 1.31347i | −0.201980 | + | 0.0541204i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.46410 | −0.0601234 | −0.0300617 | − | 0.999548i | \(-0.509570\pi\) | ||||
−0.0300617 | + | 0.999548i | \(0.509570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.60770 | + | 3.60770i | 0.147901 | + | 0.147901i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.3109 | + | 17.5000i | 1.23847 | + | 0.715031i | 0.968781 | − | 0.247917i | \(-0.0797461\pi\) |
0.269688 | + | 0.962948i | \(0.413079\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.2321 | + | 17.4545i | −1.23319 | + | 0.711983i | −0.967694 | − | 0.252128i | \(-0.918869\pi\) |
−0.265497 | + | 0.964112i | \(0.585536\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.43782 | − | 5.36603i | 0.0584558 | − | 0.218160i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.59808 | − | 7.96410i | 0.186630 | − | 0.323253i | −0.757494 | − | 0.652842i | \(-0.773577\pi\) |
0.944125 | + | 0.329589i | \(0.106910\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9545 | + | 30.9545i | 1.25228 | + | 1.25228i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.58846 | + | 7.58846i | −0.306495 | + | 0.306495i | −0.843548 | − | 0.537053i | \(-0.819537\pi\) |
0.537053 | + | 0.843548i | \(0.319537\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.08846 | + | 4.66987i | 0.325629 | + | 0.188002i | 0.653899 | − | 0.756582i | \(-0.273132\pi\) |
−0.328270 | + | 0.944584i | \(0.606466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.0885 | + | 8.86603i | 1.32994 | + | 0.356356i | 0.852692 | − | 0.522414i | \(-0.174969\pi\) |
0.477246 | + | 0.878770i | \(0.341635\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.6077 | − | 25.3013i | −0.585245 | − | 1.01367i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.5263 | − | 18.2321i | 0.421051 | − | 0.729282i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.9282 | − | 30.9282i | 1.23319 | − | 1.23319i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2487i | 1.28380i | 0.766788 | + | 0.641900i | \(0.221854\pi\) | ||||
−0.766788 | + | 0.641900i | \(0.778146\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.73205 | + | 10.1962i | 0.108418 | + | 0.404622i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.14359 | + | 4.26795i | −0.0453108 | + | 0.169102i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.76795 | − | 9.99038i | −0.227820 | − | 0.394596i | 0.729342 | − | 0.684150i | \(-0.239827\pi\) |
−0.957162 | + | 0.289553i | \(0.906493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.03590 | + | 0.277568i | −0.0408518 | + | 0.0109462i | −0.279187 | − | 0.960237i | \(-0.590065\pi\) |
0.238335 | + | 0.971183i | \(0.423398\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.3923i | 1.82387i | 0.410335 | + | 0.911935i | \(0.365412\pi\) | ||||
−0.410335 | + | 0.911935i | \(0.634588\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000i | 0.117760i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.3301 | − | 5.71539i | 0.834712 | − | 0.223661i | 0.183944 | − | 0.982937i | \(-0.441114\pi\) |
0.650768 | + | 0.759276i | \(0.274447\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.13397 | + | 5.42820i | 0.122455 | + | 0.212097i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.23205 | + | 8.33013i | −0.0869484 | + | 0.324496i | −0.995676 | − | 0.0928939i | \(-0.970388\pi\) |
0.908728 | + | 0.417390i | \(0.137055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.20577 | + | 15.6962i | 0.163586 | + | 0.610510i | 0.998216 | + | 0.0596998i | \(0.0190143\pi\) |
−0.834631 | + | 0.550810i | \(0.814319\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 5.41154i | − | 0.209851i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.09808 | − | 1.09808i | 0.0425177 | − | 0.0425177i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.86603 | − | 6.69615i | 0.149246 | − | 0.258502i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.83975 | + | 6.65064i | 0.148011 | + | 0.256363i | 0.930492 | − | 0.366311i | \(-0.119379\pi\) |
−0.782481 | + | 0.622674i | \(0.786046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.6506 | − | 12.2321i | −1.75450 | − | 0.470116i | −0.768920 | − | 0.639345i | \(-0.779205\pi\) |
−0.985577 | + | 0.169229i | \(0.945872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.13397 | + | 1.23205i | 0.0818944 | + | 0.0472818i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.39230 | + | 5.39230i | −0.206331 | + | 0.206331i | −0.802706 | − | 0.596375i | \(-0.796607\pi\) |
0.596375 | + | 0.802706i | \(0.296607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.09808 | + | 6.09808i | 0.232996 | + | 0.232996i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.63397 | + | 13.2224i | −0.290831 | + | 0.503735i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.96410 | + | 18.5263i | −0.188843 | + | 0.704773i | 0.804932 | + | 0.593367i | \(0.202202\pi\) |
−0.993775 | + | 0.111405i | \(0.964465\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.00962 | + | 1.16025i | −0.0762292 | + | 0.0440109i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.7846 | − | 22.3923i | −1.46907 | − | 0.848169i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0526 | + | 21.0526i | 0.795144 | + | 0.795144i | 0.982325 | − | 0.187181i | \(-0.0599352\pi\) |
−0.187181 | + | 0.982325i | \(0.559935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.3923 | −1.74972 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.59808 | + | 1.23205i | −0.172928 | + | 0.0463360i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.1147 | − | 10.7487i | −1.50654 | − | 0.403676i | −0.591256 | − | 0.806484i | \(-0.701368\pi\) |
−0.915285 | + | 0.402808i | \(0.868034\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.480762 | − | 0.277568i | 0.0180047 | − | 0.0103950i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.330127 | − | 1.23205i | −0.0123461 | − | 0.0460761i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.3205 | 0.869708 | 0.434854 | − | 0.900501i | \(-0.356800\pi\) | ||||
0.434854 | + | 0.900501i | \(0.356800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.10512 | −0.190125 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.09808 | + | 15.2942i | 0.152199 | + | 0.568013i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.06218 | − | 5.23205i | 0.336098 | − | 0.194046i | −0.322447 | − | 0.946587i | \(-0.604506\pi\) |
0.658545 | + | 0.752541i | \(0.271172\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.7846 | + | 9.32051i | 1.28656 | + | 0.344731i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.5263 | − | 7.37564i | 1.01671 | − | 0.272426i | 0.288277 | − | 0.957547i | \(-0.406917\pi\) |
0.728429 | + | 0.685121i | \(0.240251\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.660254 | 0.0243208 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7321 | + | 29.7321i | 1.09371 | + | 1.09371i | 0.995129 | + | 0.0985823i | \(0.0314308\pi\) |
0.0985823 | + | 0.995129i | \(0.468569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1147 | − | 14.5000i | −0.921370 | − | 0.531953i | −0.0372984 | − | 0.999304i | \(-0.511875\pi\) |
−0.884072 | + | 0.467351i | \(0.845209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.82051 | − | 3.93782i | 0.249884 | − | 0.144271i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.2750 | − | 38.3468i | 0.375440 | − | 1.40116i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.72243 | + | 8.17949i | −0.172324 | + | 0.298474i | −0.939232 | − | 0.343283i | \(-0.888461\pi\) |
0.766908 | + | 0.641757i | \(0.221794\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.56218 | − | 2.56218i | −0.0932472 | − | 0.0932472i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.46410 | − | 8.46410i | 0.307633 | − | 0.307633i | −0.536358 | − | 0.843991i | \(-0.680200\pi\) |
0.843991 | + | 0.536358i | \(0.180200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.2846 | − | 14.5981i | −0.916566 | − | 0.529180i | −0.0340283 | − | 0.999421i | \(-0.510834\pi\) |
−0.882538 | + | 0.470241i | \(0.844167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.83013 | − | 1.56218i | −0.211065 | − | 0.0565546i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.7942 | − | 23.8923i | −0.498081 | − | 0.862701i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.50000 | + | 6.06218i | −0.126213 | + | 0.218608i | −0.922207 | − | 0.386698i | \(-0.873616\pi\) |
0.795993 | + | 0.605305i | \(0.206949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.58846 | + | 7.58846i | −0.272938 | + | 0.272938i | −0.830282 | − | 0.557344i | \(-0.811821\pi\) |
0.557344 | + | 0.830282i | \(0.311821\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.66025i | 0.203322i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.2942 | + | 45.8827i | 0.440486 | + | 1.64392i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.46410 | − | 5.46410i | 0.0523897 | − | 0.195521i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.232051 | + | 0.401924i | 0.00828225 | + | 0.0143453i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.8205 | − | 9.06218i | 1.20557 | − | 0.323032i | 0.400548 | − | 0.916276i | \(-0.368820\pi\) |
0.805023 | + | 0.593244i | \(0.202153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6410i | 0.485019i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 71.1051i | 2.52502i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.06218 | − | 0.284610i | 0.0376243 | − | 0.0100814i | −0.239958 | − | 0.970783i | \(-0.577134\pi\) |
0.277582 | + | 0.960702i | \(0.410467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.3923 | − | 31.8564i | −0.650673 | − | 1.12700i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0717968 | − | 0.267949i | 0.00253365 | − | 0.00945572i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.153212 | + | 0.571797i | 0.00540003 | + | 0.0201532i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.6410i | − | 1.14760i | −0.818997 | − | 0.573799i | \(-0.805469\pi\) | ||
0.818997 | − | 0.573799i | \(-0.194531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5359 | − | 11.5359i | 0.405080 | − | 0.405080i | −0.474939 | − | 0.880019i | \(-0.657530\pi\) |
0.880019 | + | 0.474939i | \(0.157530\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.36603 | − | 7.56218i | 0.152935 | − | 0.264892i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.0981 | − | 33.0788i | −0.668157 | − | 1.15728i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.7224 | + | 5.01666i | 0.653417 | + | 0.175083i | 0.570273 | − | 0.821455i | \(-0.306837\pi\) |
0.0831439 | + | 0.996538i | \(0.473504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.65064 | + | 3.83975i | 0.231827 | + | 0.133845i | 0.611414 | − | 0.791311i | \(-0.290601\pi\) |
−0.379588 | + | 0.925156i | \(0.623934\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.6077 | + | 10.6077i | −0.368866 | + | 0.368866i | −0.867063 | − | 0.498198i | \(-0.833995\pi\) |
0.498198 | + | 0.867063i | \(0.333995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.7321 | − | 17.7321i | −0.615860 | − | 0.615860i | 0.328607 | − | 0.944467i | \(-0.393421\pi\) |
−0.944467 | + | 0.328607i | \(0.893421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.85641 | − | 3.21539i | 0.0643207 | − | 0.111407i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.27757 | + | 4.76795i | −0.0442121 | + | 0.165002i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.2583 | − | 16.8923i | 1.01011 | − | 0.583187i | 0.0988859 | − | 0.995099i | \(-0.468472\pi\) |
0.911224 | + | 0.411912i | \(0.135139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.4186 | + | 8.90192i | 0.531675 | + | 0.306963i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.53590 | + | 3.53590i | 0.121639 | + | 0.121639i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.4449 | 0.908656 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.90192 | − | 1.31347i | 0.168036 | − | 0.0450251i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0622 | + | 2.69615i | 0.344522 | + | 0.0923145i | 0.426931 | − | 0.904284i | \(-0.359595\pi\) |
−0.0824088 | + | 0.996599i | \(0.526261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.3564 | + | 24.4545i | −1.44687 | + | 0.835349i | −0.998293 | − | 0.0583966i | \(-0.981401\pi\) |
−0.448574 | + | 0.893746i | \(0.648068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.50000 | + | 16.7942i | 0.153538 | + | 0.573012i | 0.999226 | + | 0.0393342i | \(0.0125237\pi\) |
−0.845688 | + | 0.533677i | \(0.820810\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.4641 | −1.13913 | −0.569566 | − | 0.821946i | \(-0.692889\pi\) | ||||
−0.569566 | + | 0.821946i | \(0.692889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.80385 | −0.163336 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.232051 | + | 0.866025i | 0.00787178 | + | 0.0293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.25833 | + | 3.03590i | −0.178172 | + | 0.102867i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.9904 | − | 3.21281i | −0.405349 | − | 0.108613i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.3827 | − | 8.94486i | 1.12725 | − | 0.302047i | 0.353438 | − | 0.935458i | \(-0.385013\pi\) |
0.773815 | + | 0.633411i | \(0.218346\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.32051 | 0.111871 | 0.0559354 | − | 0.998434i | \(-0.482186\pi\) | ||||
0.0559354 | + | 0.998434i | \(0.482186\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.00000 | + | 3.00000i | 0.100958 | + | 0.100958i | 0.755782 | − | 0.654824i | \(-0.227257\pi\) |
−0.654824 | + | 0.755782i | \(0.727257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.0622 | + | 12.1603i | 0.707199 | + | 0.408301i | 0.810023 | − | 0.586398i | \(-0.199455\pi\) |
−0.102824 | + | 0.994700i | \(0.532788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.5167 | + | 25.1244i | −1.45950 | + | 0.842644i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.0981 | + | 37.6865i | −0.337919 | + | 1.26113i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.90192 | + | 5.02628i | −0.0970006 | + | 0.168010i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.83013 | − | 2.83013i | −0.0943900 | − | 0.0943900i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.07180 | − | 9.07180i | 0.302225 | − | 0.302225i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.70577 | − | 1.56218i | −0.0899429 | − | 0.0519285i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.4282 | − | 3.06218i | −0.379467 | − | 0.101678i | 0.0640432 | − | 0.997947i | \(-0.479600\pi\) |
−0.443510 | + | 0.896269i | \(0.646267\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.86603 | − | 10.1603i | −0.194350 | − | 0.336624i | 0.752337 | − | 0.658778i | \(-0.228926\pi\) |
−0.946687 | + | 0.322154i | \(0.895593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.16025 | + | 5.47372i | −0.104589 | + | 0.181154i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.0981 | + | 21.0981i | −0.696720 | + | 0.696720i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.4641i | 1.43375i | 0.697203 | + | 0.716874i | \(0.254428\pi\) | ||||
−0.697203 | + | 0.716874i | \(0.745572\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.4641 | + | 50.2487i | 0.443176 | + | 1.65396i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.3923 | + | 49.9808i | −0.440336 | + | 1.64336i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3564 | + | 31.7942i | 0.602254 | + | 1.04313i | 0.992479 | + | 0.122415i | \(0.0390640\pi\) |
−0.390225 | + | 0.920720i | \(0.627603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.80385 | + | 1.01924i | −0.124666 | + | 0.0334042i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.07180i | 0.0350515i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.9282i | 1.07572i | 0.843035 | + | 0.537859i | \(0.180767\pi\) | ||||
−0.843035 | + | 0.537859i | \(0.819233\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.8660 | + | 2.91154i | −0.354222 | + | 0.0949136i | −0.431542 | − | 0.902093i | \(-0.642030\pi\) |
0.0773199 | + | 0.997006i | \(0.475364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.59808 | − | 4.50000i | −0.0846050 | − | 0.146540i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.01666 | − | 14.9904i | 0.130524 | − | 0.487122i | −0.869452 | − | 0.494017i | \(-0.835528\pi\) |
0.999976 | + | 0.00689497i | \(0.00219475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.660254 | + | 2.46410i | 0.0214328 | + | 0.0799881i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.4641i | 1.27837i | 0.769054 | + | 0.639184i | \(0.220728\pi\) | ||||
−0.769054 | + | 0.639184i | \(0.779272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.83013 | + | 4.83013i | −0.156299 | + | 0.156299i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.5263 | + | 35.5526i | −0.662828 | + | 1.14805i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7846 | + | 25.6077i | 0.476923 | + | 0.826055i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.23205 | − | 0.330127i | −0.0396611 | − | 0.0106272i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.9378 | + | 8.62436i | 0.480368 | + | 0.277341i | 0.720570 | − | 0.693382i | \(-0.243880\pi\) |
−0.240202 | + | 0.970723i | \(0.577214\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.9808 | − | 27.9808i | 0.897945 | − | 0.897945i | −0.0973088 | − | 0.995254i | \(-0.531023\pi\) |
0.995254 | + | 0.0973088i | \(0.0310235\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.81089 | − | 7.81089i | −0.250406 | − | 0.250406i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.2846 | + | 29.9378i | −0.552984 | + | 0.957796i | 0.445074 | + | 0.895494i | \(0.353177\pi\) |
−0.998057 | + | 0.0623018i | \(0.980156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.58846 | − | 5.92820i | 0.0507673 | − | 0.189466i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.9186 | + | 23.6244i | −1.30510 | + | 0.753500i | −0.981274 | − | 0.192617i | \(-0.938303\pi\) |
−0.323826 | + | 0.946117i | \(0.604969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.63397 | − | 3.83013i | −0.211376 | − | 0.122038i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.95448 | + | 2.95448i | 0.0939471 | + | 0.0939471i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6077 | 0.749923 | 0.374962 | − | 0.927040i | \(-0.377656\pi\) | ||||
0.374962 | + | 0.927040i | \(0.377656\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.92820 | − | 0.784610i | 0.0928303 | − | 0.0248738i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0622 | + | 2.96410i | 0.350343 | + | 0.0938740i | 0.429699 | − | 0.902972i | \(-0.358620\pi\) |
−0.0793561 | + | 0.996846i | \(0.525286\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.bc.c.145.1 | 4 | ||
3.2 | odd | 2 | 576.2.bb.a.337.1 | 4 | |||
4.3 | odd | 2 | 432.2.y.d.253.1 | 4 | |||
9.2 | odd | 6 | 576.2.bb.b.529.1 | 4 | |||
9.7 | even | 3 | 1728.2.bc.b.721.1 | 4 | |||
12.11 | even | 2 | 144.2.x.a.13.1 | ✓ | 4 | ||
16.5 | even | 4 | 1728.2.bc.b.1009.1 | 4 | |||
16.11 | odd | 4 | 432.2.y.a.37.1 | 4 | |||
36.7 | odd | 6 | 432.2.y.a.397.1 | 4 | |||
36.11 | even | 6 | 144.2.x.d.61.1 | yes | 4 | ||
48.5 | odd | 4 | 576.2.bb.b.49.1 | 4 | |||
48.11 | even | 4 | 144.2.x.d.85.1 | yes | 4 | ||
144.11 | even | 12 | 144.2.x.a.133.1 | yes | 4 | ||
144.43 | odd | 12 | 432.2.y.d.181.1 | 4 | |||
144.101 | odd | 12 | 576.2.bb.a.241.1 | 4 | |||
144.133 | even | 12 | inner | 1728.2.bc.c.1585.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.a.13.1 | ✓ | 4 | 12.11 | even | 2 | ||
144.2.x.a.133.1 | yes | 4 | 144.11 | even | 12 | ||
144.2.x.d.61.1 | yes | 4 | 36.11 | even | 6 | ||
144.2.x.d.85.1 | yes | 4 | 48.11 | even | 4 | ||
432.2.y.a.37.1 | 4 | 16.11 | odd | 4 | |||
432.2.y.a.397.1 | 4 | 36.7 | odd | 6 | |||
432.2.y.d.181.1 | 4 | 144.43 | odd | 12 | |||
432.2.y.d.253.1 | 4 | 4.3 | odd | 2 | |||
576.2.bb.a.241.1 | 4 | 144.101 | odd | 12 | |||
576.2.bb.a.337.1 | 4 | 3.2 | odd | 2 | |||
576.2.bb.b.49.1 | 4 | 48.5 | odd | 4 | |||
576.2.bb.b.529.1 | 4 | 9.2 | odd | 6 | |||
1728.2.bc.b.721.1 | 4 | 9.7 | even | 3 | |||
1728.2.bc.b.1009.1 | 4 | 16.5 | even | 4 | |||
1728.2.bc.c.145.1 | 4 | 1.1 | even | 1 | trivial | ||
1728.2.bc.c.1585.1 | 4 | 144.133 | even | 12 | inner |