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 | 1585.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1585 |
Dual form | 1728.2.bc.c.145.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.133975 | − | 0.500000i | 0.0599153 | − | 0.223607i | −0.929476 | − | 0.368883i | \(-0.879740\pi\) |
0.989391 | + | 0.145276i | \(0.0464070\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.13397 | − | 1.23205i | −0.806567 | − | 0.465671i | 0.0391956 | − | 0.999232i | \(-0.487520\pi\) |
−0.845762 | + | 0.533560i | \(0.820854\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.133975i | −0.150756 | + | 0.0403949i | −0.333408 | − | 0.942783i | \(-0.608199\pi\) |
0.182652 | + | 0.983178i | \(0.441532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.59808 | + | 1.23205i | 1.27528 | + | 0.341709i | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
0.443227 | + | 0.896410i | \(0.353834\pi\) | |||||||
\(14\) | 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 | −0.273597 | − | 0.961844i | \(-0.588214\pi\) |
0.961844 | + | 0.273597i | \(0.0882135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.401924 | + | 0.232051i | −0.0838069 | + | 0.0483859i | −0.541318 | − | 0.840818i | \(-0.682074\pi\) |
0.457511 | + | 0.889204i | \(0.348741\pi\) | |||||||
\(24\) | 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 | −0.998537 | − | 0.0540766i | \(-0.982778\pi\) |
0.837720 | − | 0.546100i | \(-0.183888\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.598076 | − | 1.03590i | −0.107418 | − | 0.186053i | 0.807306 | − | 0.590133i | \(-0.200925\pi\) |
−0.914723 | + | 0.404081i | \(0.867592\pi\) | |||||||
\(32\) | 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 | −0.945490 | − | 0.325651i | \(-0.894416\pi\) |
−0.325651 | − | 0.945490i | \(-0.605584\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.69615 | − | 5.59808i | 1.51428 | − | 0.874273i | 0.514425 | − | 0.857536i | \(-0.328006\pi\) |
0.999860 | − | 0.0167371i | \(-0.00532782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.69615 | + | 2.33013i | −1.32615 | + | 0.355341i | −0.851279 | − | 0.524714i | \(-0.824172\pi\) |
−0.474872 | + | 0.880055i | \(0.657506\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.59808 | − | 7.96410i | 0.670698 | − | 1.16168i | −0.307008 | − | 0.951707i | \(-0.599328\pi\) |
0.977706 | − | 0.209977i | \(-0.0673388\pi\) | |||||||
\(48\) | 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 | 0.533974 | − | 0.845501i | \(-0.320698\pi\) |
−0.845501 | + | 0.533974i | \(0.820698\pi\) | |||||||
\(54\) | 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 | 0.796910 | + | 0.604098i | \(0.206467\pi\) |
−0.992193 | + | 0.124709i | \(0.960200\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.86603 | − | 14.4282i | −0.494994 | − | 1.84734i | −0.530065 | − | 0.847957i | \(-0.677832\pi\) |
0.0350707 | − | 0.999385i | \(-0.488834\pi\) | |||||||
\(62\) | 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 | 0.182773 | − | 0.983155i | \(-0.441493\pi\) |
−0.333292 | + | 0.942824i | \(0.608159\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.9282i | − | 1.29694i | −0.761241 | − | 0.648470i | \(-0.775409\pi\) | ||
0.761241 | − | 0.648470i | \(-0.224591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.535898i | − | 0.0627222i | −0.999508 | − | 0.0313611i | \(-0.990016\pi\) | ||
0.999508 | − | 0.0313611i | \(-0.00998418\pi\) | |||||||
\(74\) | 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 | −0.910622 | − | 0.413239i | \(-0.864397\pi\) |
0.813187 | + | 0.582003i | \(0.197731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.16025 | + | 11.7942i | 0.346883 | + | 1.29458i | 0.890397 | + | 0.455185i | \(0.150427\pi\) |
−0.543514 | + | 0.839400i | \(0.682907\pi\) | |||||||
\(84\) | 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 | \(-0.783715\pi\) | ||
0.777900 | − | 0.628388i | \(-0.216285\pi\) | |||||||
\(90\) | 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 | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.86603 | − | 0.500000i | 0.185676 | − | 0.0497519i | −0.164783 | − | 0.986330i | \(-0.552692\pi\) |
0.350459 | + | 0.936578i | \(0.386026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.79423 | − | 1.03590i | 0.176791 | − | 0.102070i | −0.408993 | − | 0.912537i | \(-0.634120\pi\) |
0.585784 | + | 0.810467i | \(0.300787\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.3923 | − | 11.3923i | −1.10134 | − | 1.10134i | −0.994250 | − | 0.107086i | \(-0.965848\pi\) |
−0.107086 | − | 0.994250i | \(-0.534152\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.73205 | − | 1.73205i | 0.165900 | − | 0.165900i | −0.619274 | − | 0.785175i | \(-0.712573\pi\) |
0.785175 | + | 0.619274i | \(0.212573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.76795 | + | 4.79423i | 0.260387 | + | 0.451003i | 0.966345 | − | 0.257251i | \(-0.0828166\pi\) |
−0.705958 | + | 0.708254i | \(0.749483\pi\) | |||||||
\(114\) | 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 | 0.730593 | − | 0.682814i | \(-0.239244\pi\) |
0.291305 | + | 0.956630i | \(0.405911\pi\) | |||||||
\(132\) | 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 | 0.967589 | − | 0.252531i | \(-0.0812631\pi\) |
0.265096 | + | 0.964222i | \(0.414596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.16025 | − | 4.33013i | 0.0984115 | − | 0.367277i | −0.899103 | − | 0.437737i | \(-0.855780\pi\) |
0.997515 | + | 0.0704603i | \(0.0224468\pi\) | |||||||
\(140\) | 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 | 0.594105 | + | 0.804388i | \(0.297507\pi\) |
−0.916704 | + | 0.399568i | \(0.869160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.06218 | − | 3.50000i | −0.493333 | − | 0.284826i | 0.232623 | − | 0.972567i | \(-0.425269\pi\) |
−0.725956 | + | 0.687741i | \(0.758602\pi\) | |||||||
\(152\) | 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 | 0.293212 | − | 0.956048i | \(-0.405276\pi\) |
−0.224095 | + | 0.974567i | \(0.571943\pi\) | |||||||
\(158\) | 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 | −0.997970 | − | 0.0636813i | \(-0.979716\pi\) |
0.0636813 | + | 0.997970i | \(0.479716\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.25833 | − | 4.76795i | 0.639049 | − | 0.368955i | −0.145199 | − | 0.989402i | \(-0.546382\pi\) |
0.784248 | + | 0.620447i | \(0.213049\pi\) | |||||||
\(168\) | 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 | −0.995129 | − | 0.0985859i | \(-0.968568\pi\) |
0.812514 | − | 0.582942i | \(-0.198099\pi\) | |||||||
\(174\) | 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 | −0.345746 | − | 0.938328i | \(-0.612374\pi\) |
0.938328 | + | 0.345746i | \(0.112374\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.26795 | − | 4.26795i | −0.317234 | − | 0.317234i | 0.530470 | − | 0.847704i | \(-0.322016\pi\) |
−0.847704 | + | 0.530470i | \(0.822016\pi\) | |||||||
\(182\) | 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 | −0.522245 | − | 0.852795i | \(-0.674905\pi\) |
0.999665 | + | 0.0258797i | \(0.00823869\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.23205 | − | 2.13397i | −0.0886850 | − | 0.153607i | 0.818271 | − | 0.574833i | \(-0.194933\pi\) |
−0.906956 | + | 0.421226i | \(0.861600\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.4641 | − | 10.4641i | −0.745536 | − | 0.745536i | 0.228101 | − | 0.973637i | \(-0.426748\pi\) |
−0.973637 | + | 0.228101i | \(0.926748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.85641i | 0.415150i | 0.978219 | + | 0.207575i | \(0.0665570\pi\) | ||||
−0.978219 | + | 0.207575i | \(0.933443\pi\) | |||||||
\(200\) | 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 | 0.190577 | − | 0.981672i | \(-0.438964\pi\) |
−0.325791 | + | 0.945442i | \(0.605631\pi\) | |||||||
\(212\) | 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 | −0.477734 | − | 0.878504i | \(-0.658542\pi\) |
0.999674 | − | 0.0255224i | \(-0.00812491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.62436 | − | 17.2583i | −0.306929 | − | 1.14548i | −0.931272 | − | 0.364325i | \(-0.881300\pi\) |
0.624343 | − | 0.781151i | \(-0.285367\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.52628 | + | 9.42820i | −0.166941 | + | 0.623033i | 0.830843 | + | 0.556506i | \(0.187858\pi\) |
−0.997785 | + | 0.0665269i | \(0.978808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.9282i | 1.50208i | 0.660259 | + | 0.751038i | \(0.270447\pi\) | ||||
−0.660259 | + | 0.751038i | \(0.729553\pi\) | |||||||
\(234\) | 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 | 0.626198 | − | 0.779664i | \(-0.284610\pi\) |
−0.988308 | + | 0.152472i | \(0.951277\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.23205 | + | 10.7942i | −0.401442 | + | 0.695317i | −0.993900 | − | 0.110284i | \(-0.964824\pi\) |
0.592458 | + | 0.805601i | \(0.298157\pi\) | |||||||
\(242\) | 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 | 0.900811 | − | 0.434212i | \(-0.142973\pi\) |
−0.434212 | + | 0.900811i | \(0.642973\pi\) | |||||||
\(252\) | 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 | 0.980878 | − | 0.194626i | \(-0.0623493\pi\) |
−0.658990 | + | 0.752152i | \(0.729016\pi\) | |||||||
\(258\) | 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 | 0.391434 | − | 0.920206i | \(-0.371979\pi\) |
−0.601205 | + | 0.799095i | \(0.705313\pi\) | |||||||
\(264\) | 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 | −0.902378 | − | 0.430946i | \(-0.858180\pi\) |
0.430946 | + | 0.902378i | \(0.358180\pi\) | |||||||
\(270\) | 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 | 0.180618 | − | 0.983553i | \(-0.442190\pi\) |
0.648197 | + | 0.761473i | \(0.275523\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9641 | + | 9.79423i | 1.01199 | + | 0.584275i | 0.911775 | − | 0.410691i | \(-0.134712\pi\) |
0.100219 | + | 0.994965i | \(0.468046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.16025 | + | 15.5263i | −0.247301 | + | 0.922942i | 0.724911 | + | 0.688842i | \(0.241881\pi\) |
−0.972213 | + | 0.234099i | \(0.924786\pi\) | |||||||
\(284\) | 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 | 0.756204 | + | 0.654336i | \(0.227052\pi\) |
−0.982060 | + | 0.188569i | \(0.939615\pi\) | |||||||
\(294\) | 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 | −0.517402 | − | 0.855742i | \(-0.673101\pi\) |
0.855742 | + | 0.517402i | \(0.173101\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.1865 | + | 15.6962i | −1.54161 | + | 0.890047i | −0.542869 | + | 0.839817i | \(0.682662\pi\) |
−0.998738 | + | 0.0502299i | \(0.984005\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.83975 | + | 4.52628i | 0.443129 | + | 0.255840i | 0.704924 | − | 0.709283i | \(-0.250981\pi\) |
−0.261795 | + | 0.965123i | \(0.584314\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.545517 | + | 2.03590i | 0.0306393 | + | 0.114347i | 0.979552 | − | 0.201192i | \(-0.0644814\pi\) |
−0.948913 | + | 0.315539i | \(0.897815\pi\) | |||||||
\(318\) | 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 | 0.553115 | − | 0.833105i | \(-0.313439\pi\) |
0.895564 | + | 0.444933i | \(0.146772\pi\) | |||||||
\(332\) | 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 | 0.884363 | − | 0.466799i | \(-0.154593\pi\) |
−0.846442 | + | 0.532482i | \(0.821260\pi\) | |||||||
\(338\) | 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 | 0.670933 | + | 0.741518i | \(0.265894\pi\) |
−0.951804 | + | 0.306707i | \(0.900773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.13397 | − | 7.96410i | −0.114229 | − | 0.426309i | 0.884999 | − | 0.465593i | \(-0.154159\pi\) |
−0.999228 | + | 0.0392843i | \(0.987492\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.2321 | − | 26.3827i | 0.810720 | − | 1.40421i | −0.101640 | − | 0.994821i | \(-0.532409\pi\) |
0.912361 | − | 0.409387i | \(-0.134258\pi\) | |||||||
\(354\) | 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 | \(0.130202\pi\) | ||||
−0.917503 | + | 0.397730i | \(0.869798\pi\) | |||||||
\(360\) | 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 | 0.108408 | + | 0.994106i | \(0.465425\pi\) |
−0.915125 | + | 0.403169i | \(0.867909\pi\) | |||||||
\(368\) | 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 | −0.808047 | − | 0.589118i | \(-0.799475\pi\) |
0.994348 | − | 0.106168i | \(-0.0338581\pi\) | |||||||
\(374\) | 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 | 0.182484 | − | 0.983209i | \(-0.441586\pi\) |
−0.983209 | + | 0.182484i | \(0.941586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.3301 | + | 21.3564i | 0.630040 | + | 1.09126i | 0.987543 | + | 0.157349i | \(0.0502949\pi\) |
−0.357503 | + | 0.933912i | \(0.616372\pi\) | |||||||
\(384\) | 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 | −0.446240 | − | 0.894914i | \(-0.647237\pi\) |
0.0610019 | + | 0.998138i | \(0.480570\pi\) | |||||||
\(390\) | 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 | −0.0582984 | + | 0.998299i | \(0.518567\pi\) |
−0.998299 | + | 0.0582984i | \(0.981433\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.16025 | − | 2.00962i | −0.0579403 | − | 0.100356i | 0.835600 | − | 0.549338i | \(-0.185120\pi\) |
−0.893541 | + | 0.448982i | \(0.851787\pi\) | |||||||
\(402\) | 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 | −0.381294 | − | 0.924454i | \(-0.624521\pi\) |
0.609954 | + | 0.792437i | \(0.291188\pi\) | |||||||
\(410\) | 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 | 0.306476 | − | 0.951878i | \(-0.400850\pi\) |
−0.210523 | + | 0.977589i | \(0.567517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7942 | − | 2.89230i | 0.526079 | − | 0.140962i | 0.0140017 | − | 0.999902i | \(-0.495543\pi\) |
0.512077 | + | 0.858940i | \(0.328876\pi\) | |||||||
\(422\) | 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 | 0.00264111 | − | 0.999997i | \(-0.499159\pi\) |
−0.864702 | + | 0.502286i | \(0.832493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.1603 | − | 4.33013i | 0.767797 | − | 0.205731i | 0.146399 | − | 0.989226i | \(-0.453232\pi\) |
0.621398 | + | 0.783495i | \(0.286565\pi\) | |||||||
\(444\) | 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 | 0.874094 | − | 0.485758i | \(-0.161456\pi\) |
0.0163683 | + | 0.999866i | \(0.494790\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.598076 | + | 2.23205i | 0.0278552 | + | 0.103957i | 0.978454 | − | 0.206466i | \(-0.0661961\pi\) |
−0.950599 | + | 0.310423i | \(0.899529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.33013 | − | 5.76795i | −0.154764 | − | 0.268059i | 0.778209 | − | 0.628005i | \(-0.216128\pi\) |
−0.932973 | + | 0.359946i | \(0.882795\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7846 | + | 19.7846i | −0.915523 | + | 0.915523i | −0.996700 | − | 0.0811771i | \(-0.974132\pi\) |
0.0811771 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(468\) | 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 | −0.850316 | − | 0.526272i | \(-0.823589\pi\) |
0.880923 | + | 0.473259i | \(0.156923\pi\) | |||||||
\(480\) | 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 | \(0.288946\pi\) | ||||
−0.615521 | + | 0.788121i | \(0.711054\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.500000 | − | 1.86603i | 0.0225647 | − | 0.0842125i | −0.953725 | − | 0.300679i | \(-0.902787\pi\) |
0.976290 | + | 0.216467i | \(0.0694533\pi\) | |||||||
\(492\) | 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 | 0.314342 | − | 0.949310i | \(-0.398216\pi\) |
−0.202427 | + | 0.979297i | \(0.564883\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.8564i | 0.617827i | 0.951090 | + | 0.308913i | \(0.0999653\pi\) | ||||
−0.951090 | + | 0.308913i | \(0.900035\pi\) | |||||||
\(504\) | 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 | 0.697074 | − | 0.716999i | \(-0.254485\pi\) |
0.245185 | + | 0.969476i | \(0.421151\pi\) | |||||||
\(510\) | 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 | \(-0.899731\pi\) | ||
0.950795 | − | 0.309821i | \(-0.100269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.12436 | + | 2.12436i | 0.0928916 | + | 0.0928916i | 0.752026 | − | 0.659134i | \(-0.229077\pi\) |
−0.659134 | + | 0.752026i | \(0.729077\pi\) | |||||||
\(524\) | 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 | −0.951756 | − | 0.306856i | \(-0.900723\pi\) |
0.306856 | + | 0.951756i | \(0.400723\pi\) | |||||||
\(542\) | 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 | −0.915566 | − | 0.402168i | \(-0.868257\pi\) |
0.591819 | − | 0.806071i | \(-0.298410\pi\) | |||||||
\(548\) | 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 | −0.207307 | + | 0.978276i | \(0.566470\pi\) |
−0.978276 | + | 0.207307i | \(0.933530\pi\) | |||||||
\(558\) | 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 | −0.419836 | − | 0.907600i | \(-0.637912\pi\) |
−0.817389 | + | 0.576086i | \(0.804579\pi\) | |||||||
\(564\) | 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 | −0.110368 | − | 0.993891i | \(-0.535203\pi\) |
−0.915919 | + | 0.401364i | \(0.868536\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.44744 | + | 5.40192i | −0.0605735 | + | 0.226063i | −0.989576 | − | 0.144009i | \(-0.954001\pi\) |
0.929003 | + | 0.370073i | \(0.120667\pi\) | |||||||
\(572\) | 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 | −0.319470 | − | 0.947596i | \(-0.603505\pi\) |
0.197129 | + | 0.980378i | \(0.436838\pi\) | |||||||
\(588\) | 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 | 0.269688 | − | 0.962948i | \(-0.413079\pi\) |
0.968781 | + | 0.247917i | \(0.0797461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.2321 | − | 17.4545i | −1.23319 | − | 0.711983i | −0.265497 | − | 0.964112i | \(-0.585536\pi\) |
−0.967694 | + | 0.252128i | \(0.918869\pi\) | |||||||
\(602\) | 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 | 0.944125 | − | 0.329589i | \(-0.106910\pi\) |
−0.757494 | + | 0.652842i | \(0.773577\pi\) | |||||||
\(608\) | 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 | 0.537053 | − | 0.843548i | \(-0.319537\pi\) |
−0.843548 | + | 0.537053i | \(0.819537\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.08846 | − | 4.66987i | 0.325629 | − | 0.188002i | −0.328270 | − | 0.944584i | \(-0.606466\pi\) |
0.653899 | + | 0.756582i | \(0.273132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.0885 | − | 8.86603i | 1.32994 | − | 0.356356i | 0.477246 | − | 0.878770i | \(-0.341635\pi\) |
0.852692 | + | 0.522414i | \(0.174969\pi\) | |||||||
\(620\) | 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 | \(-0.778146\pi\) | ||
0.766788 | − | 0.641900i | \(-0.221854\pi\) | |||||||
\(632\) | 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 | −0.957162 | − | 0.289553i | \(-0.906493\pi\) |
0.729342 | + | 0.684150i | \(0.239827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.03590 | − | 0.277568i | −0.0408518 | − | 0.0109462i | 0.238335 | − | 0.971183i | \(-0.423398\pi\) |
−0.279187 | + | 0.960237i | \(0.590065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.3923i | − | 1.82387i | −0.410335 | − | 0.911935i | \(-0.634588\pi\) | ||
0.410335 | − | 0.911935i | \(-0.365412\pi\) | |||||||
\(648\) | 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 | 0.650768 | − | 0.759276i | \(-0.274447\pi\) |
0.183944 | + | 0.982937i | \(0.441114\pi\) | |||||||
\(654\) | 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 | 0.908728 | − | 0.417390i | \(-0.137055\pi\) |
−0.995676 | + | 0.0928939i | \(0.970388\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.20577 | − | 15.6962i | 0.163586 | − | 0.610510i | −0.834631 | − | 0.550810i | \(-0.814319\pi\) |
0.998216 | − | 0.0596998i | \(-0.0190143\pi\) | |||||||
\(662\) | 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 | −0.782481 | − | 0.622674i | \(-0.786046\pi\) |
0.930492 | + | 0.366311i | \(0.119379\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.6506 | + | 12.2321i | −1.75450 | + | 0.470116i | −0.985577 | − | 0.169229i | \(-0.945872\pi\) |
−0.768920 | + | 0.639345i | \(0.779205\pi\) | |||||||
\(678\) | 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 | 0.596375 | − | 0.802706i | \(-0.296607\pi\) |
−0.802706 | + | 0.596375i | \(0.796607\pi\) | |||||||
\(684\) | 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 | −0.993775 | − | 0.111405i | \(-0.964465\pi\) |
0.804932 | − | 0.593367i | \(-0.202202\pi\) | |||||||
\(692\) | 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 | −0.187181 | − | 0.982325i | \(-0.559935\pi\) |
0.982325 | + | 0.187181i | \(0.0599352\pi\) | |||||||
\(702\) | 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 | −0.915285 | − | 0.402808i | \(-0.868034\pi\) |
−0.591256 | + | 0.806484i | \(0.701368\pi\) | |||||||
\(710\) | 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 | 0.658545 | − | 0.752541i | \(-0.271172\pi\) |
−0.322447 | + | 0.946587i | \(0.604506\pi\) | |||||||
\(728\) | 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 | 0.728429 | − | 0.685121i | \(-0.240251\pi\) |
0.288277 | + | 0.957547i | \(0.406917\pi\) | |||||||
\(734\) | 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 | 0.0985823 | − | 0.995129i | \(-0.468569\pi\) |
0.995129 | − | 0.0985823i | \(-0.0314308\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1147 | + | 14.5000i | −0.921370 | + | 0.531953i | −0.884072 | − | 0.467351i | \(-0.845209\pi\) |
−0.0372984 | + | 0.999304i | \(0.511875\pi\) | |||||||
\(744\) | 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 | 0.766908 | − | 0.641757i | \(-0.221794\pi\) |
−0.939232 | + | 0.343283i | \(0.888461\pi\) | |||||||
\(752\) | 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 | 0.843991 | − | 0.536358i | \(-0.180200\pi\) |
−0.536358 | + | 0.843991i | \(0.680200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.2846 | + | 14.5981i | −0.916566 | + | 0.529180i | −0.882538 | − | 0.470241i | \(-0.844167\pi\) |
−0.0340283 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(762\) | 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 | 0.795993 | − | 0.605305i | \(-0.206949\pi\) |
−0.922207 | + | 0.386698i | \(0.873616\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.58846 | − | 7.58846i | −0.272938 | − | 0.272938i | 0.557344 | − | 0.830282i | \(-0.311821\pi\) |
−0.830282 | + | 0.557344i | \(0.811821\pi\) | |||||||
\(774\) | 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 | 0.805023 | − | 0.593244i | \(-0.202153\pi\) |
0.400548 | + | 0.916276i | \(0.368820\pi\) | |||||||
\(788\) | 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 | 0.277582 | − | 0.960702i | \(-0.410467\pi\) |
−0.239958 | + | 0.970783i | \(0.577134\pi\) | |||||||
\(798\) | 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 | \(0.194531\pi\) | ||||
−0.818997 | + | 0.573799i | \(0.805469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5359 | + | 11.5359i | 0.405080 | + | 0.405080i | 0.880019 | − | 0.474939i | \(-0.157530\pi\) |
−0.474939 | + | 0.880019i | \(0.657530\pi\) | |||||||
\(812\) | 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 | 0.0831439 | − | 0.996538i | \(-0.473504\pi\) |
0.570273 | + | 0.821455i | \(0.306837\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.65064 | − | 3.83975i | 0.231827 | − | 0.133845i | −0.379588 | − | 0.925156i | \(-0.623934\pi\) |
0.611414 | + | 0.791311i | \(0.290601\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.6077 | − | 10.6077i | −0.368866 | − | 0.368866i | 0.498198 | − | 0.867063i | \(-0.333995\pi\) |
−0.867063 | + | 0.498198i | \(0.833995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.7321 | + | 17.7321i | −0.615860 | + | 0.615860i | −0.944467 | − | 0.328607i | \(-0.893421\pi\) |
0.328607 | + | 0.944467i | \(0.393421\pi\) | |||||||
\(830\) | 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 | 0.911224 | − | 0.411912i | \(-0.135139\pi\) |
0.0988859 | + | 0.995099i | \(0.468472\pi\) | |||||||
\(840\) | 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 | −0.0824088 | − | 0.996599i | \(-0.526261\pi\) |
0.426931 | + | 0.904284i | \(0.359595\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.3564 | − | 24.4545i | −1.44687 | − | 0.835349i | −0.448574 | − | 0.893746i | \(-0.648068\pi\) |
−0.998293 | + | 0.0583966i | \(0.981401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.50000 | − | 16.7942i | 0.153538 | − | 0.573012i | −0.845688 | − | 0.533677i | \(-0.820810\pi\) |
0.999226 | − | 0.0393342i | \(-0.0125237\pi\) | |||||||
\(860\) | 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 | 0.773815 | − | 0.633411i | \(-0.218346\pi\) |
0.353438 | + | 0.935458i | \(0.385013\pi\) | |||||||
\(878\) | 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 | −0.654824 | − | 0.755782i | \(-0.727257\pi\) |
0.755782 | + | 0.654824i | \(0.227257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.0622 | − | 12.1603i | 0.707199 | − | 0.408301i | −0.102824 | − | 0.994700i | \(-0.532788\pi\) |
0.810023 | + | 0.586398i | \(0.199455\pi\) | |||||||
\(888\) | 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 | −0.443510 | − | 0.896269i | \(-0.646267\pi\) |
0.0640432 | + | 0.997947i | \(0.479600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.86603 | + | 10.1603i | −0.194350 | + | 0.336624i | −0.946687 | − | 0.322154i | \(-0.895593\pi\) |
0.752337 | + | 0.658778i | \(0.228926\pi\) | |||||||
\(912\) | 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 | \(-0.745572\pi\) | ||
0.697203 | − | 0.716874i | \(-0.254428\pi\) | |||||||
\(920\) | 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 | −0.390225 | − | 0.920720i | \(-0.627603\pi\) |
0.992479 | − | 0.122415i | \(-0.0390640\pi\) | |||||||
\(930\) | 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 | \(-0.819233\pi\) | ||
0.843035 | − | 0.537859i | \(-0.180767\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.8660 | − | 2.91154i | −0.354222 | − | 0.0949136i | 0.0773199 | − | 0.997006i | \(-0.475364\pi\) |
−0.431542 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(942\) | 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 | 0.999976 | − | 0.00689497i | \(-0.00219475\pi\) |
−0.869452 | + | 0.494017i | \(0.835528\pi\) | |||||||
\(948\) | 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 | \(-0.779272\pi\) | ||
0.769054 | − | 0.639184i | \(-0.220728\pi\) | |||||||
\(954\) | 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 | −0.240202 | − | 0.970723i | \(-0.577214\pi\) |
0.720570 | + | 0.693382i | \(0.243880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.9808 | + | 27.9808i | 0.897945 | + | 0.897945i | 0.995254 | − | 0.0973088i | \(-0.0310235\pi\) |
−0.0973088 | + | 0.995254i | \(0.531023\pi\) | |||||||
\(972\) | 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 | −0.998057 | − | 0.0623018i | \(-0.980156\pi\) |
0.445074 | − | 0.895494i | \(-0.353177\pi\) | |||||||
\(978\) | 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 | −0.323826 | − | 0.946117i | \(-0.604969\pi\) |
−0.981274 | + | 0.192617i | \(0.938303\pi\) | |||||||
\(984\) | 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 | −0.0793561 | − | 0.996846i | \(-0.525286\pi\) |
0.429699 | + | 0.902972i | \(0.358620\pi\) | |||||||
\(998\) | 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.1585.1 | 4 | ||
3.2 | odd | 2 | 576.2.bb.a.241.1 | 4 | |||
4.3 | odd | 2 | 432.2.y.d.181.1 | 4 | |||
9.4 | even | 3 | 1728.2.bc.b.1009.1 | 4 | |||
9.5 | odd | 6 | 576.2.bb.b.49.1 | 4 | |||
12.11 | even | 2 | 144.2.x.a.133.1 | yes | 4 | ||
16.3 | odd | 4 | 432.2.y.a.397.1 | 4 | |||
16.13 | even | 4 | 1728.2.bc.b.721.1 | 4 | |||
36.23 | even | 6 | 144.2.x.d.85.1 | yes | 4 | ||
36.31 | odd | 6 | 432.2.y.a.37.1 | 4 | |||
48.29 | odd | 4 | 576.2.bb.b.529.1 | 4 | |||
48.35 | even | 4 | 144.2.x.d.61.1 | yes | 4 | ||
144.13 | even | 12 | inner | 1728.2.bc.c.145.1 | 4 | ||
144.67 | odd | 12 | 432.2.y.d.253.1 | 4 | |||
144.77 | odd | 12 | 576.2.bb.a.337.1 | 4 | |||
144.131 | even | 12 | 144.2.x.a.13.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.a.13.1 | ✓ | 4 | 144.131 | even | 12 | ||
144.2.x.a.133.1 | yes | 4 | 12.11 | even | 2 | ||
144.2.x.d.61.1 | yes | 4 | 48.35 | even | 4 | ||
144.2.x.d.85.1 | yes | 4 | 36.23 | even | 6 | ||
432.2.y.a.37.1 | 4 | 36.31 | odd | 6 | |||
432.2.y.a.397.1 | 4 | 16.3 | odd | 4 | |||
432.2.y.d.181.1 | 4 | 4.3 | odd | 2 | |||
432.2.y.d.253.1 | 4 | 144.67 | odd | 12 | |||
576.2.bb.a.241.1 | 4 | 3.2 | odd | 2 | |||
576.2.bb.a.337.1 | 4 | 144.77 | odd | 12 | |||
576.2.bb.b.49.1 | 4 | 9.5 | odd | 6 | |||
576.2.bb.b.529.1 | 4 | 48.29 | odd | 4 | |||
1728.2.bc.b.721.1 | 4 | 16.13 | even | 4 | |||
1728.2.bc.b.1009.1 | 4 | 9.4 | even | 3 | |||
1728.2.bc.c.145.1 | 4 | 144.13 | even | 12 | inner | ||
1728.2.bc.c.1585.1 | 4 | 1.1 | even | 1 | trivial |