Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(121,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.q (of order \(3\), degree \(2\), 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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
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: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 241.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.241 |
Dual form | 360.2.q.b.121.2 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.133975 | + | 0.232051i | −0.0506376 | + | 0.0877070i | −0.890233 | − | 0.455505i | \(-0.849459\pi\) |
0.839596 | + | 0.543212i | \(0.182792\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.732051 | − | 1.26795i | 0.220722 | − | 0.382301i | −0.734306 | − | 0.678819i | \(-0.762492\pi\) |
0.955027 | + | 0.296518i | \(0.0958254\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.73205 | + | 4.73205i | 0.757735 | + | 1.31243i | 0.944003 | + | 0.329936i | \(0.107027\pi\) |
−0.186269 | + | 0.982499i | \(0.559640\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.866025 | + | 1.50000i | −0.223607 | + | 0.387298i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.535898 | 0.129974 | 0.0649872 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649872 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.464102 | −0.101275 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.86603 | − | 3.23205i | −0.389093 | − | 0.673929i | 0.603235 | − | 0.797564i | \(-0.293878\pi\) |
−0.992328 | + | 0.123635i | \(0.960545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.767949 | + | 1.33013i | −0.142605 | + | 0.246998i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) |
0.785872 | + | 0.618389i | \(0.212214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | + | 1.73205i | 0.179605 | + | 0.311086i | 0.941745 | − | 0.336327i | \(-0.109185\pi\) |
−0.762140 | + | 0.647412i | \(0.775851\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.53590 | 0.441443 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.267949 | −0.0452917 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.3923 | 1.70848 | 0.854242 | − | 0.519875i | \(-0.174022\pi\) | ||||
0.854242 | + | 0.519875i | \(0.174022\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.73205 | + | 8.19615i | −0.757735 | + | 1.31243i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.96410 | − | 8.59808i | −0.775262 | − | 1.34279i | −0.934647 | − | 0.355577i | \(-0.884284\pi\) |
0.159384 | − | 0.987217i | \(-0.449049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.26795 | − | 3.92820i | 0.345859 | − | 0.599045i | −0.639650 | − | 0.768666i | \(-0.720921\pi\) |
0.985509 | + | 0.169621i | \(0.0542542\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.133975 | + | 0.232051i | −0.0195422 | + | 0.0338481i | −0.875631 | − | 0.482980i | \(-0.839554\pi\) |
0.856089 | + | 0.516829i | \(0.172888\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.46410 | + | 6.00000i | 0.494872 | + | 0.857143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.464102 | + | 0.803848i | 0.0649872 | + | 0.112561i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.46410 | 0.197419 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.73205 | − | 3.00000i | −0.229416 | − | 0.397360i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.19615 | − | 12.4641i | −0.936859 | − | 1.62269i | −0.771284 | − | 0.636491i | \(-0.780385\pi\) |
−0.165575 | − | 0.986197i | \(-0.552948\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.23205 | − | 7.33013i | 0.541859 | − | 0.938527i | −0.456939 | − | 0.889498i | \(-0.651054\pi\) |
0.998797 | − | 0.0490285i | \(-0.0156125\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.401924 | − | 0.696152i | −0.0506376 | − | 0.0877070i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.73205 | + | 4.73205i | −0.338869 | + | 0.586939i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.13397 | − | 5.42820i | −0.382876 | − | 0.663161i | 0.608596 | − | 0.793480i | \(-0.291733\pi\) |
−0.991472 | + | 0.130320i | \(0.958400\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.23205 | − | 5.59808i | 0.389093 | − | 0.673929i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.46410 | 1.12318 | 0.561591 | − | 0.827415i | \(-0.310189\pi\) | ||||
0.561591 | + | 0.827415i | \(0.310189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820 | 0.810885 | 0.405442 | − | 0.914121i | \(-0.367117\pi\) | ||||
0.405442 | + | 0.914121i | \(0.367117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.73205 | −0.200000 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.196152 | + | 0.339746i | 0.0223536 | + | 0.0387176i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.73205 | + | 13.3923i | −0.869924 | + | 1.50675i | −0.00784992 | + | 0.999969i | \(0.502499\pi\) |
−0.862074 | + | 0.506783i | \(0.830835\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.59808 | − | 11.4282i | 0.724233 | − | 1.25441i | −0.235056 | − | 0.971982i | \(-0.575527\pi\) |
0.959289 | − | 0.282426i | \(-0.0911393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.267949 | + | 0.464102i | 0.0290632 | + | 0.0503389i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.66025 | −0.285209 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.92820 | −1.05239 | −0.526194 | − | 0.850365i | \(-0.676381\pi\) | ||||
−0.526194 | + | 0.850365i | \(0.676381\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.46410 | −0.153480 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.73205 | + | 3.00000i | −0.179605 | + | 0.311086i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | − | 1.73205i | −0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.46410 | − | 7.73205i | 0.453261 | − | 0.785071i | −0.545326 | − | 0.838224i | \(-0.683594\pi\) |
0.998586 | + | 0.0531536i | \(0.0169273\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.19615 | + | 3.80385i | 0.220722 | + | 0.382301i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.464102 | + | 0.803848i | −0.0461798 | + | 0.0799858i | −0.888191 | − | 0.459474i | \(-0.848038\pi\) |
0.842012 | + | 0.539459i | \(0.181371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.19615 | − | 12.4641i | −0.709058 | − | 1.22812i | −0.965207 | − | 0.261487i | \(-0.915787\pi\) |
0.256149 | − | 0.966637i | \(-0.417546\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.232051 | − | 0.401924i | −0.0226458 | − | 0.0392237i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.19615 | 0.502331 | 0.251166 | − | 0.967944i | \(-0.419186\pi\) | ||||
0.251166 | + | 0.967944i | \(0.419186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3923 | −1.66588 | −0.832940 | − | 0.553363i | \(-0.813344\pi\) | ||||
−0.832940 | + | 0.553363i | \(0.813344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.00000 | + | 15.5885i | 0.854242 | + | 1.47959i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.92820 | − | 12.0000i | −0.651751 | − | 1.12887i | −0.982698 | − | 0.185216i | \(-0.940702\pi\) |
0.330947 | − | 0.943649i | \(-0.392632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.86603 | − | 3.23205i | 0.174008 | − | 0.301390i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.3923 | −1.51547 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0717968 | + | 0.124356i | −0.00658160 | + | 0.0113997i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.42820 | + | 7.66987i | 0.402564 | + | 0.697261i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.59808 | − | 14.8923i | 0.775262 | − | 1.34279i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.2679 | 1.44355 | 0.721774 | − | 0.692129i | \(-0.243327\pi\) | ||||
0.721774 | + | 0.692129i | \(0.243327\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.85641 | 0.691718 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.73205 | + | 3.00000i | 0.151330 | + | 0.262111i | 0.931717 | − | 0.363186i | \(-0.118311\pi\) |
−0.780387 | + | 0.625297i | \(0.784978\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.267949 | − | 0.464102i | 0.0232341 | − | 0.0402427i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.59808 | − | 4.50000i | −0.223607 | − | 0.387298i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.9282 | + | 18.9282i | −0.933659 | + | 1.61715i | −0.156652 | + | 0.987654i | \(0.550070\pi\) |
−0.777007 | + | 0.629492i | \(0.783263\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.464102 | −0.0390844 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.53590 | −0.127549 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.00000 | + | 10.3923i | −0.494872 | + | 0.857143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.23205 | + | 2.13397i | 0.100934 | + | 0.174822i | 0.912070 | − | 0.410036i | \(-0.134484\pi\) |
−0.811136 | + | 0.584858i | \(0.801150\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.73205 | + | 4.73205i | −0.222331 | + | 0.385089i | −0.955515 | − | 0.294941i | \(-0.904700\pi\) |
0.733184 | + | 0.680030i | \(0.238033\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.803848 | + | 1.39230i | −0.0649872 | + | 0.112561i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | + | 1.73205i | −0.0803219 | + | 0.139122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.46410 | − | 4.26795i | −0.196657 | − | 0.340619i | 0.750786 | − | 0.660546i | \(-0.229675\pi\) |
−0.947442 | + | 0.319926i | \(0.896342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.19615 | + | 9.00000i | 0.412082 | + | 0.713746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.3205 | −1.04334 | −0.521671 | − | 0.853147i | \(-0.674691\pi\) | ||||
−0.521671 | + | 0.853147i | \(0.674691\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.26795 | + | 2.19615i | 0.0987097 | + | 0.170970i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.7942 | + | 18.6962i | 0.835282 | + | 1.44675i | 0.893800 | + | 0.448465i | \(0.148029\pi\) |
−0.0585177 | + | 0.998286i | \(0.518637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.42820 | + | 14.5981i | −0.648323 | + | 1.12293i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 5.19615i | 0.229416 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.53590 | + | 7.85641i | −0.344858 | + | 0.597312i | −0.985328 | − | 0.170672i | \(-0.945406\pi\) |
0.640470 | + | 0.767983i | \(0.278740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.133975 | − | 0.232051i | −0.0101275 | − | 0.0175414i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.4641 | − | 21.5885i | 0.936859 | − | 1.62269i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.4641 | 1.00635 | 0.503177 | − | 0.864183i | \(-0.332164\pi\) | ||||
0.503177 | + | 0.864183i | \(0.332164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.53590 | −0.708798 | −0.354399 | − | 0.935094i | \(-0.615314\pi\) | ||||
−0.354399 | + | 0.935094i | \(0.615314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.6603 | 1.08372 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.19615 | + | 9.00000i | 0.382029 | + | 0.661693i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.392305 | − | 0.679492i | 0.0286882 | − | 0.0496894i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.696152 | − | 1.20577i | 0.0506376 | − | 0.0877070i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.46410 | + | 14.6603i | −0.612441 | + | 1.06078i | 0.378387 | + | 0.925648i | \(0.376479\pi\) |
−0.990828 | + | 0.135131i | \(0.956854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.73205 | + | 15.1244i | 0.628547 | + | 1.08867i | 0.987844 | + | 0.155452i | \(0.0496833\pi\) |
−0.359297 | + | 0.933223i | \(0.616983\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.46410 | −0.677738 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.9282 | 1.06359 | 0.531795 | − | 0.846873i | \(-0.321518\pi\) | ||||
0.531795 | + | 0.846873i | \(0.321518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.07180 | 0.501306 | 0.250653 | − | 0.968077i | \(-0.419355\pi\) | ||||
0.250653 | + | 0.968077i | \(0.419355\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.42820 | − | 9.40192i | 0.382876 | − | 0.663161i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.205771 | − | 0.356406i | −0.0144423 | − | 0.0250148i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.96410 | − | 8.59808i | 0.346708 | − | 0.600516i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.1962 | 0.778186 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.46410 | + | 2.53590i | −0.101274 | + | 0.175412i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.196152 | − | 0.339746i | −0.0135037 | − | 0.0233891i | 0.859195 | − | 0.511649i | \(-0.170965\pi\) |
−0.872698 | + | 0.488260i | \(0.837632\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.19615 | + | 14.1962i | 0.561591 | + | 0.972704i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.53590 | 0.309346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.535898 | −0.0363792 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | + | 10.3923i | 0.405442 | + | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.46410 | + | 2.53590i | 0.0984861 | + | 0.170583i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3301 | + | 19.6244i | −0.758721 | + | 1.31414i | 0.184781 | + | 0.982780i | \(0.440842\pi\) |
−0.943503 | + | 0.331364i | \(0.892491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.50000 | − | 2.59808i | −0.100000 | − | 0.173205i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.1244 | + | 21.0000i | −0.804722 | + | 1.39382i | 0.111757 | + | 0.993736i | \(0.464352\pi\) |
−0.916479 | + | 0.400083i | \(0.868981\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.6244 | − | 21.8660i | −0.834241 | − | 1.44495i | −0.894647 | − | 0.446774i | \(-0.852573\pi\) |
0.0604061 | − | 0.998174i | \(-0.480760\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.339746 | + | 0.588457i | −0.0223536 | + | 0.0387176i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.3923 | −0.680823 | −0.340411 | − | 0.940277i | \(-0.610566\pi\) | ||||
−0.340411 | + | 0.940277i | \(0.610566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.267949 | −0.0174791 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.7846 | −1.73985 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.3923 | − | 18.0000i | −0.672222 | − | 1.16432i | −0.977273 | − | 0.211987i | \(-0.932007\pi\) |
0.305050 | − | 0.952336i | \(-0.401327\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.03590 | − | 5.25833i | 0.195559 | − | 0.338719i | −0.751524 | − | 0.659705i | \(-0.770681\pi\) |
0.947084 | + | 0.320987i | \(0.104014\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.46410 | + | 6.00000i | −0.221313 | + | 0.383326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.46410 | − | 9.46410i | −0.347672 | − | 0.602186i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.8564 | 1.44847 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.85641 | −0.495892 | −0.247946 | − | 0.968774i | \(-0.579756\pi\) | ||||
−0.247946 | + | 0.968774i | \(0.579756\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.46410 | −0.343525 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.464102 | + | 0.803848i | −0.0290632 | + | 0.0503389i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.464102 | + | 0.803848i | 0.0289499 | + | 0.0501426i | 0.880137 | − | 0.474719i | \(-0.157450\pi\) |
−0.851187 | + | 0.524862i | \(0.824117\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.39230 | + | 2.41154i | −0.0865136 | + | 0.149846i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.30385 | − | 3.99038i | −0.142605 | − | 0.246998i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.1962 | + | 19.3923i | −0.690384 | + | 1.19578i | 0.281328 | + | 0.959612i | \(0.409225\pi\) |
−0.971712 | + | 0.236169i | \(0.924108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | + | 5.19615i | 0.184289 | + | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.59808 | − | 14.8923i | −0.526194 | − | 0.911394i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3923 | 0.694601 | 0.347301 | − | 0.937754i | \(-0.387098\pi\) | ||||
0.347301 | + | 0.937754i | \(0.387098\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8564 | −1.20619 | −0.603095 | − | 0.797669i | \(-0.706066\pi\) | ||||
−0.603095 | + | 0.797669i | \(0.706066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.26795 | − | 2.19615i | −0.0767398 | − | 0.132917i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.732051 | + | 1.26795i | 0.0441443 | + | 0.0764602i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.19615 | − | 12.4641i | 0.432375 | − | 0.748895i | −0.564702 | − | 0.825295i | \(-0.691009\pi\) |
0.997077 | + | 0.0763993i | \(0.0243424\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.42820 | − | 12.8660i | 0.443129 | − | 0.767523i | −0.554790 | − | 0.831990i | \(-0.687202\pi\) |
0.997920 | + | 0.0644675i | \(0.0205349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.8660 | − | 18.8205i | −0.645918 | − | 1.11876i | −0.984089 | − | 0.177678i | \(-0.943141\pi\) |
0.338170 | − | 0.941085i | \(-0.390192\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.73205 | − | 3.00000i | 0.102598 | − | 0.177705i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.66025 | 0.157030 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7128 | −0.983107 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.4641 | 0.906522 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.73205 | + | 6.46410i | 0.218029 | + | 0.377637i | 0.954205 | − | 0.299153i | \(-0.0967040\pi\) |
−0.736176 | + | 0.676790i | \(0.763371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.19615 | − | 12.4641i | 0.418976 | − | 0.725688i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.80385 | + | 6.58846i | −0.220722 | + | 0.382301i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.1962 | − | 17.6603i | 0.589659 | − | 1.02132i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.607695 | + | 1.05256i | 0.0350270 | + | 0.0606685i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.60770 | −0.0923597 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.46410 | 0.484653 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.12436 | 0.235389 | 0.117695 | − | 0.993050i | \(-0.462450\pi\) | ||||
0.117695 | + | 0.993050i | \(0.462450\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.4641 | − | 21.5885i | 0.709058 | − | 1.22812i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.53590 | − | 2.66025i | −0.0870928 | − | 0.150849i | 0.819188 | − | 0.573525i | \(-0.194424\pi\) |
−0.906281 | + | 0.422676i | \(0.861091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.19615 | + | 10.7321i | −0.350227 | + | 0.606611i | −0.986289 | − | 0.165027i | \(-0.947229\pi\) |
0.636062 | + | 0.771638i | \(0.280562\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.401924 | − | 0.696152i | 0.0226458 | − | 0.0392237i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.26795 | + | 2.19615i | −0.0712151 | + | 0.123348i | −0.899434 | − | 0.437056i | \(-0.856021\pi\) |
0.828219 | + | 0.560405i | \(0.189354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.12436 | + | 1.94744i | 0.0629518 | + | 0.109036i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50000 | + | 7.79423i | 0.251166 | + | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.07180 | −0.0596364 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.46410 | −0.303094 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.0622 | − | 26.0885i | −0.832940 | − | 1.44269i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.0358984 | − | 0.0621778i | −0.00197914 | − | 0.00342797i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.73205 | − | 3.00000i | 0.0952021 | − | 0.164895i | −0.814491 | − | 0.580176i | \(-0.802984\pi\) |
0.909693 | + | 0.415282i | \(0.136317\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.5885 | + | 27.0000i | −0.854242 | + | 1.47959i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.13397 | − | 5.42820i | 0.171227 | − | 0.296574i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.53590 | − | 7.85641i | −0.247086 | − | 0.427966i | 0.715630 | − | 0.698480i | \(-0.246140\pi\) |
−0.962716 | + | 0.270514i | \(0.912806\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.0000 | − | 20.7846i | 0.651751 | − | 1.12887i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.92820 | 0.158571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.73205 | −0.201512 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.46410 | 0.348016 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.19615 | + | 15.9282i | 0.493675 | + | 0.855071i | 0.999973 | − | 0.00728777i | \(-0.00231979\pi\) |
−0.506298 | + | 0.862359i | \(0.668986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.232051 | + | 0.401924i | −0.0124214 | + | 0.0215145i | −0.872169 | − | 0.489204i | \(-0.837287\pi\) |
0.859748 | + | 0.510719i | \(0.170621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.1962 | − | 24.5885i | −0.757735 | − | 1.31243i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.9282 | − | 18.9282i | 0.581650 | − | 1.00745i | −0.413634 | − | 0.910443i | \(-0.635741\pi\) |
0.995284 | − | 0.0970036i | \(-0.0309258\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.73205 | + | 8.19615i | 0.251151 | + | 0.435007i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.248711 | −0.0131632 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.9282 | −0.682324 | −0.341162 | − | 0.940004i | \(-0.610821\pi\) | ||||
−0.341162 | + | 0.940004i | \(0.610821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.66987 | + | 13.2846i | −0.402564 | + | 0.697261i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.46410 | + | 6.00000i | 0.181319 | + | 0.314054i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.19615 | − | 12.4641i | 0.375636 | − | 0.650621i | −0.614786 | − | 0.788694i | \(-0.710758\pi\) |
0.990422 | + | 0.138073i | \(0.0440909\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.7846 | 1.55052 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.803848 | + | 1.39230i | −0.0417337 | + | 0.0722849i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.46410 | + | 7.73205i | 0.231142 | + | 0.400350i | 0.958145 | − | 0.286285i | \(-0.0924203\pi\) |
−0.727002 | + | 0.686635i | \(0.759087\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.866025 | − | 1.50000i | −0.0447214 | − | 0.0774597i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.39230 | −0.432226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.1769 | 1.80692 | 0.903458 | − | 0.428676i | \(-0.141020\pi\) | ||||
0.903458 | + | 0.428676i | \(0.141020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.0885 | + | 24.4019i | 0.721774 | + | 1.25015i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.73205 | − | 3.00000i | −0.0885037 | − | 0.153293i | 0.818375 | − | 0.574684i | \(-0.194875\pi\) |
−0.906879 | + | 0.421392i | \(0.861542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.196152 | + | 0.339746i | −0.00999685 | + | 0.0173151i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.80385 | + | 11.7846i | 0.345859 | + | 0.599045i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.7679 | − | 20.3827i | 0.596659 | − | 1.03344i | −0.396652 | − | 0.917969i | \(-0.629828\pi\) |
0.993310 | − | 0.115474i | \(-0.0368387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | − | 1.73205i | −0.0505722 | − | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.00000 | + | 5.19615i | −0.151330 | + | 0.262111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.4641 | −0.778083 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | 0.501886 | 0.250943 | − | 0.968002i | \(-0.419259\pi\) | ||||
0.250943 | + | 0.968002i | \(0.419259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.928203 | 0.0464683 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.39230 | − | 12.8038i | −0.369154 | − | 0.639394i | 0.620279 | − | 0.784381i | \(-0.287019\pi\) |
−0.989434 | + | 0.144987i | \(0.953686\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.46410 | + | 9.46410i | −0.272186 | + | 0.471440i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.50000 | − | 7.79423i | 0.223607 | − | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.60770 | − | 13.1769i | 0.377099 | − | 0.653155i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.46410 | − | 4.26795i | −0.121842 | − | 0.211037i | 0.798652 | − | 0.601793i | \(-0.205547\pi\) |
−0.920494 | + | 0.390757i | \(0.872213\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −37.8564 | −1.86732 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.85641 | 0.189761 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.1962 | 0.647774 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.1244 | − | 26.1962i | −0.738873 | − | 1.27977i | −0.953003 | − | 0.302961i | \(-0.902025\pi\) |
0.214130 | − | 0.976805i | \(-0.431308\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4641 | − | 31.9808i | 0.899885 | − | 1.55865i | 0.0722458 | − | 0.997387i | \(-0.476983\pi\) |
0.827639 | − | 0.561260i | \(-0.189683\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.401924 | − | 0.696152i | −0.0195422 | − | 0.0338481i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.267949 | + | 0.464102i | −0.0129974 | + | 0.0225122i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.13397 | + | 1.96410i | 0.0548769 | + | 0.0950495i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.92820 | + | 12.0000i | 0.334497 | + | 0.579365i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.53590 | −0.218487 | −0.109243 | − | 0.994015i | \(-0.534843\pi\) | ||||
−0.109243 | + | 0.994015i | \(0.534843\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.5359 | −0.602437 | −0.301218 | − | 0.953555i | \(-0.597393\pi\) | ||||
−0.301218 | + | 0.953555i | \(0.597393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.33013 | − | 2.30385i | −0.0637747 | − | 0.110461i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.73205 | + | 6.46410i | 0.178528 | + | 0.309220i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.5359 | + | 18.2487i | −0.502851 | + | 0.870963i | 0.497144 | + | 0.867668i | \(0.334382\pi\) |
−0.999995 | + | 0.00329518i | \(0.998951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7846 | −0.989743 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2583 | + | 29.8923i | −0.819968 | + | 1.42023i | 0.0857370 | + | 0.996318i | \(0.472676\pi\) |
−0.905705 | + | 0.423908i | \(0.860658\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.96410 | − | 8.59808i | −0.235321 | − | 0.407588i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.13397 | + | 3.69615i | −0.100934 | + | 0.174822i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.14359 | 0.195548 | 0.0977741 | − | 0.995209i | \(-0.468828\pi\) | ||||
0.0977741 | + | 0.995209i | \(0.468828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.5359 | −0.684469 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.46410 | −0.444662 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.732051 | − | 1.26795i | −0.0343191 | − | 0.0594424i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.80385 | + | 4.85641i | −0.131158 | + | 0.227173i | −0.924123 | − | 0.382094i | \(-0.875203\pi\) |
0.792965 | + | 0.609267i | \(0.208536\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.78461 | −0.129974 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.30385 | + | 3.99038i | −0.107301 | + | 0.185851i | −0.914676 | − | 0.404188i | \(-0.867554\pi\) |
0.807375 | + | 0.590039i | \(0.200887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.73205 | + | 3.00000i | 0.0804952 | + | 0.139422i | 0.903463 | − | 0.428667i | \(-0.141016\pi\) |
−0.822968 | + | 0.568088i | \(0.807683\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.46410 | −0.160644 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.3923 | −1.40639 | −0.703194 | − | 0.710998i | \(-0.748243\pi\) | ||||
−0.703194 | + | 0.710998i | \(0.748243\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.67949 | 0.0775517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.26795 | − | 7.39230i | 0.196657 | − | 0.340619i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.32051 | − | 5.75129i | −0.152677 | − | 0.264445i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | − | 1.73205i | 0.0458831 | − | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.00000 | + | 15.5885i | −0.412082 | + | 0.713746i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.19615 | − | 12.4641i | 0.328801 | − | 0.569499i | −0.653474 | − | 0.756949i | \(-0.726689\pi\) |
0.982274 | + | 0.187450i | \(0.0600223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.3923 | + | 49.1769i | 1.29458 | + | 2.24227i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.866025 | + | 1.50000i | 0.0394055 | + | 0.0682524i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.92820 | 0.405409 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.2487 | 1.82384 | 0.911922 | − | 0.410364i | \(-0.134599\pi\) | ||||
0.911922 | + | 0.410364i | \(0.134599\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.5359 | − | 19.9808i | −0.521671 | − | 0.903561i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9282 | + | 22.3923i | 0.583442 | + | 1.01055i | 0.995068 | + | 0.0991978i | \(0.0316276\pi\) |
−0.411626 | + | 0.911353i | \(0.635039\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.411543 | + | 0.712813i | −0.0185350 | + | 0.0321035i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.19615 | + | 3.80385i | −0.0987097 | + | 0.170970i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.26795 | + | 2.19615i | −0.0568753 | + | 0.0985109i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.92820 | + | 15.4641i | 0.399681 | + | 0.692268i | 0.993686 | − | 0.112193i | \(-0.0357875\pi\) |
−0.594005 | + | 0.804461i | \(0.702454\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.6962 | + | 32.3827i | −0.835282 | + | 1.44675i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.1244 | −0.808125 | −0.404063 | − | 0.914731i | \(-0.632402\pi\) | ||||
−0.404063 | + | 0.914731i | \(0.632402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.928203 | −0.0413045 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.1962 | −1.29665 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3038 | + | 17.8468i | 0.456710 | + | 0.791045i | 0.998785 | − | 0.0492853i | \(-0.0156944\pi\) |
−0.542075 | + | 0.840330i | \(0.682361\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.928203 | + | 1.60770i | −0.0410613 | + | 0.0711202i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3923 | 0.458831 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.19615 | − | 12.4641i | 0.317100 | − | 0.549234i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.196152 | + | 0.339746i | 0.00862677 | + | 0.0149420i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.7128 | −0.689716 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0000 | −0.569540 | −0.284770 | − | 0.958596i | \(-0.591917\pi\) | ||||
−0.284770 | + | 0.958596i | \(0.591917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8038 | 0.472419 | 0.236210 | − | 0.971702i | \(-0.424095\pi\) | ||||
0.236210 | + | 0.971702i | \(0.424095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.232051 | − | 0.401924i | 0.0101275 | − | 0.0175414i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.535898 | + | 0.928203i | 0.0233441 | + | 0.0404332i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.53590 | − | 7.85641i | 0.197213 | − | 0.341583i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 43.1769 | 1.87372 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.1244 | − | 46.9808i | 1.17489 | − | 2.03496i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.59808 | + | 4.50000i | 0.112325 | + | 0.194552i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.6603 | + | 20.1962i | 0.503177 | + | 0.871528i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.1436 | 0.436916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.6077 | −0.800007 | −0.400004 | − | 0.916514i | \(-0.630991\pi\) | ||||
−0.400004 | + | 0.916514i | \(0.630991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.25833 | − | 14.3038i | −0.354399 | − | 0.613837i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.69615 | − | 15.0622i | −0.372502 | − | 0.645193i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.9904 | + | 39.8205i | −0.982998 | + | 1.70260i | −0.332481 | + | 0.943110i | \(0.607886\pi\) |
−0.650517 | + | 0.759492i | \(0.725448\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.6962 | + | 21.9904i | 0.541859 | + | 0.938527i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.53590 | − | 2.66025i | 0.0654315 | − | 0.113331i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.07180 | − | 3.58846i | −0.0881018 | − | 0.152597i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.00000 | + | 15.5885i | −0.382029 | + | 0.661693i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.6410 | 1.38304 | 0.691522 | − | 0.722355i | \(-0.256940\pi\) | ||||
0.691522 | + | 0.722355i | \(0.256940\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.7846 | 1.04828 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.35898 | 0.0573763 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.20577 | + | 10.7487i | 0.261542 | + | 0.453004i | 0.966652 | − | 0.256094i | \(-0.0824356\pi\) |
−0.705110 | + | 0.709098i | \(0.749102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.92820 | − | 12.0000i | 0.291472 | − | 0.504844i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.41154 | 0.101275 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3923 | + | 35.3205i | 0.853391 | + | 1.47812i | 0.878129 | + | 0.478423i | \(0.158792\pi\) |
−0.0247380 | + | 0.999694i | \(0.507875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.3205 | −1.22488 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.73205 | 0.155637 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.9282 | 1.37082 | 0.685410 | − | 0.728158i | \(-0.259623\pi\) | ||||
0.685410 | + | 0.728158i | \(0.259623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.1244 | + | 26.1962i | −0.628547 | + | 1.08867i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.76795 | + | 3.06218i | 0.0733469 | + | 0.127041i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.39230 | − | 7.60770i | 0.181911 | − | 0.315079i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.19615 | − | 14.1962i | −0.338869 | − | 0.586939i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.20577 | + | 7.28461i | −0.173591 | + | 0.300668i | −0.939673 | − | 0.342075i | \(-0.888870\pi\) |
0.766082 | + | 0.642743i | \(0.222204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | − | 3.46410i | −0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.9282 | + | 22.3923i | 0.531795 | + | 0.921096i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.4641 | −1.62060 | −0.810298 | − | 0.586018i | \(-0.800695\pi\) | ||||
−0.810298 | + | 0.586018i | \(0.800695\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.143594 | −0.00588676 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.12436 | + | 10.6077i | 0.250653 | + | 0.434144i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.803848 | − | 1.39230i | −0.0328443 | − | 0.0568880i | 0.849136 | − | 0.528174i | \(-0.177123\pi\) |
−0.881980 | + | 0.471286i | \(0.843790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3923 | + | 26.6603i | −0.627865 | + | 1.08749i | 0.360114 | + | 0.932908i | \(0.382738\pi\) |
−0.987979 | + | 0.154586i | \(0.950596\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.8038 | 0.765752 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.42820 | + | 7.66987i | −0.180032 | + | 0.311825i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.1340 | − | 34.8731i | −0.817213 | − | 1.41545i | −0.907728 | − | 0.419559i | \(-0.862185\pi\) |
0.0905152 | − | 0.995895i | \(-0.471149\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.356406 | − | 0.617314i | 0.0144423 | − | 0.0250148i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.46410 | −0.0592312 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3923 | 0.904417 | 0.452208 | − | 0.891912i | \(-0.350636\pi\) | ||||
0.452208 | + | 0.891912i | \(0.350636\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.1962 | 0.693416 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.4641 | − | 26.7846i | −0.622561 | − | 1.07831i | −0.989007 | − | 0.147868i | \(-0.952759\pi\) |
0.366446 | − | 0.930439i | \(-0.380575\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.8564 | − | 32.6603i | 0.757903 | − | 1.31273i | −0.186015 | − | 0.982547i | \(-0.559557\pi\) |
0.943918 | − | 0.330180i | \(-0.107109\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.69615 | + | 16.7942i | 0.389093 | + | 0.673929i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.33013 | − | 2.30385i | 0.0532904 | − | 0.0923017i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.07180 | −0.202548 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.56922 | 0.222059 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.7128 | 1.26247 | 0.631234 | − | 0.775593i | \(-0.282549\pi\) | ||||
0.631234 | + | 0.775593i | \(0.282549\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.339746 | − | 0.588457i | 0.0135037 | − | 0.0233891i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.13397 | + | 14.0885i | 0.322787 | + | 0.559083i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.9282 | + | 32.7846i | −0.749963 | + | 1.29897i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.1962 | + | 24.5885i | −0.561591 | + | 0.972704i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.4282 | − | 30.1865i | 0.688373 | − | 1.19230i | −0.283991 | − | 0.958827i | \(-0.591659\pi\) |
0.972364 | − | 0.233470i | \(-0.0750079\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.1340 | + | 29.6769i | 0.675698 | + | 1.17034i | 0.976264 | + | 0.216582i | \(0.0694910\pi\) |
−0.300566 | + | 0.953761i | \(0.597176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.92820 | + | 6.80385i | 0.154673 | + | 0.267901i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5167 | −0.649337 | −0.324668 | − | 0.945828i | \(-0.605253\pi\) | ||||
−0.324668 | + | 0.945828i | \(0.605253\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.0718 | −0.827140 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.464102 | − | 0.803848i | −0.0181896 | − | 0.0315053i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.7321 | − | 27.2487i | −0.615643 | − | 1.06632i | −0.990271 | − | 0.139150i | \(-0.955563\pi\) |
0.374629 | − | 0.927175i | \(-0.377770\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.73205 | + | 3.00000i | −0.0676768 | + | 0.117220i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.3923 | + | 18.0000i | −0.405442 | + | 0.702247i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3923 | − | 18.0000i | 0.404827 | − | 0.701180i | −0.589475 | − | 0.807787i | \(-0.700665\pi\) |
0.994301 | + | 0.106606i | \(0.0339985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8564 | − | 18.8038i | −0.422265 | − | 0.731385i | 0.573895 | − | 0.818929i | \(-0.305432\pi\) |
−0.996161 | + | 0.0875437i | \(0.972098\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.53590 | + | 4.39230i | −0.0984861 | + | 0.170583i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.535898 | 0.0207812 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.73205 | 0.221946 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.2487 | −1.51744 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.19615 | − | 10.7321i | −0.239200 | − | 0.414306i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.33975 | − | 10.9808i | 0.244379 | − | 0.423277i | −0.717578 | − | 0.696479i | \(-0.754749\pi\) |
0.961957 | + | 0.273201i | \(0.0880825\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.59808 | − | 4.50000i | 0.100000 | − | 0.173205i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.58846 | − | 14.8756i | 0.330081 | − | 0.571717i | −0.652446 | − | 0.757835i | \(-0.726257\pi\) |
0.982527 | + | 0.186118i | \(0.0595905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.19615 | + | 2.07180i | 0.0459041 | + | 0.0795083i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.0000 | −1.60944 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.3923 | 0.856818 | 0.428409 | − | 0.903585i | \(-0.359074\pi\) | ||||
0.428409 | + | 0.903585i | \(0.359074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.8564 | −0.835090 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.8660 | − | 37.8731i | 0.834241 | − | 1.44495i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.3923 | + | 28.3923i | 0.624497 | + | 1.08166i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.1962 | − | 43.6410i | 0.958507 | − | 1.66018i | 0.232376 | − | 0.972626i | \(-0.425350\pi\) |
0.726131 | − | 0.687556i | \(-0.241317\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.17691 | −0.0447073 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.66025 | − | 4.60770i | −0.100764 | − | 0.174529i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.00000 | − | 15.5885i | −0.340411 | − | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.1769 | −0.913149 | −0.456575 | − | 0.889685i | \(-0.650924\pi\) | ||||
−0.456575 | + | 0.889685i | \(0.650924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.7846 | −0.783906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.232051 | − | 0.401924i | −0.00873954 | − | 0.0151373i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.124356 | − | 0.215390i | −0.00467688 | − | 0.00810059i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.69615 | + | 13.3301i | −0.289035 | + | 0.500623i | −0.973580 | − | 0.228348i | \(-0.926668\pi\) |
0.684545 | + | 0.728971i | \(0.260001\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.1962 | − | 40.1769i | −0.869924 | − | 1.50675i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.73205 | − | 6.46410i | 0.139766 | − | 0.242083i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | + | 6.92820i | 0.149592 | + | 0.259100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.0000 | − | 31.1769i | 0.672222 | − | 1.16432i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.3205 | −1.24265 | −0.621323 | − | 0.783555i | \(-0.713404\pi\) | ||||
−0.621323 | + | 0.783555i | \(0.713404\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.85641 | 0.143620 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.5167 | 0.391119 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.767949 | − | 1.33013i | −0.0285209 | − | 0.0493997i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.99038 | + | 13.8397i | −0.296347 | + | 0.513288i | −0.975297 | − | 0.220896i | \(-0.929102\pi\) |
0.678950 | + | 0.734184i | \(0.262435\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.21539 | − | 2.10512i | 0.0449528 | − | 0.0778606i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.07180 | − | 13.9808i | −0.298139 | − | 0.516391i | 0.677571 | − | 0.735457i | \(-0.263032\pi\) |
−0.975710 | + | 0.219066i | \(0.929699\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.0000 | −0.442627 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.17691 | −0.338036 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.248711 | −0.00914899 | −0.00457450 | − | 0.999990i | \(-0.501456\pi\) | ||||
−0.00457450 | + | 0.999990i | \(0.501456\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.46410 | − | 16.3923i | 0.347672 | − | 0.602186i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9186 | + | 29.3038i | 0.620683 | + | 1.07505i | 0.989359 | + | 0.145496i | \(0.0464778\pi\) |
−0.368676 | + | 0.929558i | \(0.620189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.23205 | + | 2.13397i | −0.0451388 | + | 0.0781828i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.7942 | + | 34.2846i | 0.724233 | + | 1.25441i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.696152 | + | 1.20577i | −0.0254369 | + | 0.0440579i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.19615 | − | 14.1962i | −0.299082 | − | 0.518025i | 0.676844 | − | 0.736126i | \(-0.263347\pi\) |
−0.975926 | + | 0.218101i | \(0.930014\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.80385 | − | 11.7846i | −0.247946 | − | 0.429455i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.46410 | −0.198859 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3923 | −0.741171 | −0.370585 | − | 0.928798i | \(-0.620843\pi\) | ||||
−0.370585 | + | 0.928798i | \(0.620843\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.73205 | − | 8.19615i | −0.171763 | − | 0.297501i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5000 | + | 18.1865i | 0.380625 | + | 0.659261i | 0.991152 | − | 0.132734i | \(-0.0423756\pi\) |
−0.610527 | + | 0.791995i | \(0.709042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.33013 | − | 4.03590i | 0.0843563 | − | 0.146109i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.60770 | −0.0581263 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.3205 | − | 68.1051i | 1.41978 | − | 2.45913i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.8923 | − | 29.2583i | −0.609152 | − | 1.05508i | −0.991380 | − | 0.131014i | \(-0.958177\pi\) |
0.382228 | − | 0.924068i | \(-0.375157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.803848 | + | 1.39230i | −0.0289499 | + | 0.0501426i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.78461 | −0.315960 | −0.157980 | − | 0.987442i | \(-0.550498\pi\) | ||||
−0.157980 | + | 0.987442i | \(0.550498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.82309 | −0.173027 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.92820 | + | 17.1962i | 0.355715 | + | 0.616116i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.92820 | − | 12.0000i | 0.247911 | − | 0.429394i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.99038 | − | 6.91154i | 0.142605 | − | 0.246998i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.46410 | − | 4.26795i | 0.0879476 | − | 0.152330i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.660254 | − | 1.14359i | −0.0235355 | − | 0.0407647i | 0.854018 | − | 0.520244i | \(-0.174159\pi\) |
−0.877553 | + | 0.479479i | \(0.840826\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.7846 | −1.38077 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.71281 | 0.132012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.2487 | 1.64234 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.19615 | + | 9.00000i | −0.184289 | + | 0.319197i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.80385 | + | 6.58846i | 0.134739 | + | 0.233375i | 0.925498 | − | 0.378753i | \(-0.123647\pi\) |
−0.790759 | + | 0.612128i | \(0.790314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0717968 | + | 0.124356i | −0.00253999 | + | 0.00439939i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.8923 | − | 25.7942i | 0.526194 | − | 0.911394i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.07180 | − | 8.78461i | 0.178980 | − | 0.310002i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.500000 | + | 0.866025i | 0.0176227 | + | 0.0305234i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.86603 | + | 17.0885i | 0.347301 | + | 0.601542i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.9282 | −1.72022 | −0.860112 | − | 0.510105i | \(-0.829606\pi\) | ||||
−0.860112 | + | 0.510105i | \(0.829606\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.3923 | −1.76951 | −0.884757 | − | 0.466053i | \(-0.845675\pi\) | ||||
−0.884757 | + | 0.466053i | \(0.845675\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.1962 | − | 29.7846i | −0.603095 | − | 1.04459i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.66025 | − | 11.5359i | −0.233299 | − | 0.404085i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.53590 | + | 7.85641i | −0.158691 | + | 0.274861i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.19615 | − | 3.80385i | 0.0767398 | − | 0.132917i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.6244 | + | 20.1340i | −0.405693 | + | 0.702681i | −0.994402 | − | 0.105664i | \(-0.966303\pi\) |
0.588709 | + | 0.808345i | \(0.299636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.8660 | − | 20.5526i | −0.413624 | − | 0.716417i | 0.581659 | − | 0.813433i | \(-0.302404\pi\) |
−0.995283 | + | 0.0970154i | \(0.969070\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.26795 | + | 2.19615i | −0.0441443 | + | 0.0764602i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.9474 | −0.589320 | −0.294660 | − | 0.955602i | \(-0.595206\pi\) | ||||
−0.294660 | + | 0.955602i | \(0.595206\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3923 | 0.395671 | 0.197836 | − | 0.980235i | \(-0.436609\pi\) | ||||
0.197836 | + | 0.980235i | \(0.436609\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.9282 | 0.864750 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.85641 | + | 3.21539i | 0.0643207 | + | 0.111407i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.7942 | + | 18.6962i | −0.373550 | + | 0.647007i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.19615 | − | 9.00000i | −0.179605 | − | 0.311086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.9282 | + | 31.0526i | −0.618950 | + | 1.07205i | 0.370727 | + | 0.928742i | \(0.379108\pi\) |
−0.989678 | + | 0.143312i | \(0.954225\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.3205 | + | 23.0718i | 0.459328 | + | 0.795579i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.7321 | 0.886259 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.8564 | −0.579878 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.37307 | −0.0815395 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.8205 | − | 32.5981i | 0.645918 | − | 1.11876i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.3923 | − | 33.5885i | −0.664760 | − | 1.15140i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.7321 | − | 42.8372i | 0.846809 | − | 1.46672i | −0.0372313 | − | 0.999307i | \(-0.511854\pi\) |
0.884041 | − | 0.467410i | \(-0.154813\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.12436 | + | 15.8038i | −0.311682 | + | 0.539849i | −0.978727 | − | 0.205169i | \(-0.934226\pi\) |
0.667045 | + | 0.745018i | \(0.267559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.1962 | + | 17.6603i | 0.347888 | + | 0.602560i | 0.985874 | − | 0.167488i | \(-0.0535655\pi\) |
−0.637986 | + | 0.770048i | \(0.720232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.30385 | + | 3.99038i | 0.0785149 | + | 0.135992i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.6603 | 0.907526 | 0.453763 | − | 0.891123i | \(-0.350081\pi\) | ||||
0.453763 | + | 0.891123i | \(0.350081\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.07180 | −0.308450 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.4737 | − | 25.0692i | −0.491553 | − | 0.851395i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3205 | + | 19.6077i | 0.384022 | + | 0.665146i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.1244 | − | 29.6603i | 0.580237 | − | 1.00500i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.3923 | + | 23.1962i | 0.453261 | + | 0.785071i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.133975 | − | 0.232051i | 0.00452917 | − | 0.00784475i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.80385 | − | 10.0526i | −0.195982 | − | 0.339451i | 0.751240 | − | 0.660029i | \(-0.229456\pi\) |
−0.947222 | + | 0.320578i | \(0.896123\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.46410 | + | 11.1962i | −0.218029 | + | 0.377637i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.6410 | 1.26816 | 0.634079 | − | 0.773268i | \(-0.281379\pi\) | ||||
0.634079 | + | 0.773268i | \(0.281379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.19615 | −0.309475 | −0.154738 | − | 0.987956i | \(-0.549453\pi\) | ||||
−0.154738 | + | 0.987956i | \(0.549453\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.9282 | 0.837952 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.66025 | + | 8.07180i | 0.156476 | + | 0.271024i | 0.933596 | − | 0.358329i | \(-0.116653\pi\) |
−0.777119 | + | 0.629353i | \(0.783320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.17949 | + | 3.77499i | −0.0730978 | + | 0.126609i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.1769 | −0.441443 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.267949 | − | 0.464102i | 0.00896658 | − | 0.0155306i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.73205 | + | 11.6603i | 0.225028 | + | 0.389759i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 35.3205 | 1.17932 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.07180 | −0.102450 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.21539 | 0.107120 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.05256 | + | 1.82309i | −0.0350270 | + | 0.0606685i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.76795 | − | 8.25833i | −0.158492 | − | 0.274516i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.86603 | − | 11.8923i | 0.227983 | − | 0.394878i | −0.729227 | − | 0.684271i | \(-0.760120\pi\) |
0.957210 | + | 0.289394i | \(0.0934537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.39230 | − | 2.41154i | −0.0461798 | − | 0.0799858i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.26795 | − | 10.8564i | 0.207666 | − | 0.359689i | −0.743313 | − | 0.668944i | \(-0.766746\pi\) |
0.950979 | + | 0.309255i | \(0.100080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.66025 | − | 16.7321i | −0.319708 | − | 0.553750i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.33013 | + | 12.6962i | 0.242327 | + | 0.419722i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.928203 | −0.0306520 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.6077 | −0.580824 | −0.290412 | − | 0.956902i | \(-0.593792\pi\) | ||||
−0.290412 | + | 0.956902i | \(0.593792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.57180 | + | 6.18653i | 0.117695 | + | 0.203853i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.8564 | + | 44.7846i | 0.851074 | + | 1.47410i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.19615 | + | 9.00000i | −0.170848 | + | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.1769 | 1.41812 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.3205 | + | 21.3397i | −0.404223 | + | 0.700134i | −0.994231 | − | 0.107263i | \(-0.965791\pi\) |
0.590008 | + | 0.807397i | \(0.299125\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.92820 | − | 12.0000i | −0.227063 | − | 0.393284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.66025 | − | 4.60770i | 0.0870928 | − | 0.150849i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.784610 | 0.0256595 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.7128 | −0.382641 | −0.191320 | − | 0.981528i | \(-0.561277\pi\) | ||||
−0.191320 | + | 0.981528i | \(0.561277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.4641 | −0.700454 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.6962 | + | 20.2583i | 0.381284 | + | 0.660403i | 0.991246 | − | 0.132028i | \(-0.0421488\pi\) |
−0.609962 | + | 0.792430i | \(0.708815\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.5263 | + | 32.0885i | −0.603299 | + | 1.04494i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.39230 | 0.0452917 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.25833 | − | 12.5718i | 0.235864 | − | 0.408529i | −0.723659 | − | 0.690157i | \(-0.757541\pi\) |
0.959523 | + | 0.281629i | \(0.0908747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.9282 | + | 32.7846i | 0.614435 | + | 1.06423i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.39230 | −0.142430 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.3923 | 1.30844 | 0.654218 | − | 0.756306i | \(-0.272998\pi\) | ||||
0.654218 | + | 0.756306i | \(0.272998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.9282 | −0.547784 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.94744 | + | 3.37307i | −0.0629518 | + | 0.109036i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.92820 | − | 5.07180i | −0.0945566 | − | 0.163777i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.79423 | + | 13.5000i | −0.251166 | + | 0.435031i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.73205 | + | 15.1244i | −0.281095 | + | 0.486870i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.6699 | − | 18.4808i | −0.343120 | − | 0.594301i | 0.641890 | − | 0.766796i | \(-0.278150\pi\) |
−0.985010 | + | 0.172495i | \(0.944817\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.928203 | − | 1.60770i | −0.0298182 | − | 0.0516466i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.7128 | 0.825163 | 0.412582 | − | 0.910921i | \(-0.364627\pi\) | ||||
0.412582 | + | 0.910921i | \(0.364627\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.73205 | − | 8.19615i | −0.151547 | − | 0.262487i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.58846 | − | 14.8756i | −0.274769 | − | 0.475914i | 0.695308 | − | 0.718712i | \(-0.255268\pi\) |
−0.970077 | + | 0.242798i | \(0.921935\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.26795 | + | 12.5885i | −0.232285 | + | 0.402329i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.0885 | − | 45.1865i | 0.832940 | − | 1.44269i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.2583 | + | 35.0885i | −0.646140 | + | 1.11915i | 0.337896 | + | 0.941183i | \(0.390285\pi\) |
−0.984037 | + | 0.177965i | \(0.943049\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.46410 | + | 12.9282i | 0.237826 | + | 0.411927i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0621778 | − | 0.107695i | 0.00197914 | − | 0.00342797i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.9282 | −0.538286 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.0333 | −1.17640 | −0.588201 | − | 0.808715i | \(-0.700164\pi\) | ||||
−0.588201 | + | 0.808715i | \(0.700164\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.00000 | 0.190404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.53590 | + | 6.12436i | 0.112096 | + | 0.194155i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.7846 | + | 41.1962i | −0.753266 | + | 1.30470i | 0.192966 | + | 0.981206i | \(0.438189\pi\) |
−0.946232 | + | 0.323490i | \(0.895144\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −54.0000 | −1.70848 |
(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 | 360.2.q.b.241.2 | yes | 4 | |
3.2 | odd | 2 | 1080.2.q.b.721.2 | 4 | |||
4.3 | odd | 2 | 720.2.q.h.241.1 | 4 | |||
9.2 | odd | 6 | 3240.2.a.p.1.1 | 2 | |||
9.4 | even | 3 | inner | 360.2.q.b.121.2 | ✓ | 4 | |
9.5 | odd | 6 | 1080.2.q.b.361.2 | 4 | |||
9.7 | even | 3 | 3240.2.a.k.1.1 | 2 | |||
12.11 | even | 2 | 2160.2.q.h.721.1 | 4 | |||
36.7 | odd | 6 | 6480.2.a.ba.1.2 | 2 | |||
36.11 | even | 6 | 6480.2.a.bk.1.2 | 2 | |||
36.23 | even | 6 | 2160.2.q.h.1441.1 | 4 | |||
36.31 | odd | 6 | 720.2.q.h.481.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.b.121.2 | ✓ | 4 | 9.4 | even | 3 | inner | |
360.2.q.b.241.2 | yes | 4 | 1.1 | even | 1 | trivial | |
720.2.q.h.241.1 | 4 | 4.3 | odd | 2 | |||
720.2.q.h.481.1 | 4 | 36.31 | odd | 6 | |||
1080.2.q.b.361.2 | 4 | 9.5 | odd | 6 | |||
1080.2.q.b.721.2 | 4 | 3.2 | odd | 2 | |||
2160.2.q.h.721.1 | 4 | 12.11 | even | 2 | |||
2160.2.q.h.1441.1 | 4 | 36.23 | even | 6 | |||
3240.2.a.k.1.1 | 2 | 9.7 | even | 3 | |||
3240.2.a.p.1.1 | 2 | 9.2 | odd | 6 | |||
6480.2.a.ba.1.2 | 2 | 36.7 | odd | 6 | |||
6480.2.a.bk.1.2 | 2 | 36.11 | even | 6 |