Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4608,2,Mod(1153,4608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4608, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4608.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4608 = 2^{9} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4608.k (of order \(4\), 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: | \(36.7950652514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 1536) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3457.4 | ||
Root | \(-0.437016 - 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4608.3457 |
Dual form | 4608.2.k.bg.1153.3 |
$q$-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 \(\left(\mathbb{Z}/4608\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(3583\) | \(4097\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | + | 2.23607i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.74806i | 0.660706i | 0.943857 | + | 0.330353i | \(0.107168\pi\) | ||||
−0.943857 | + | 0.330353i | \(0.892832\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.57649 | − | 4.57649i | −1.37986 | − | 1.37986i | −0.844831 | − | 0.535033i | \(-0.820299\pi\) |
−0.535033 | − | 0.844831i | \(-0.679701\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.00000i | 0.277350 | − | 0.277350i | −0.554700 | − | 0.832050i | \(-0.687167\pi\) |
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47214 | 0.599581 | 0.299791 | − | 0.954005i | \(-0.403083\pi\) | ||||
0.299791 | + | 0.954005i | \(0.403083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.57649 | − | 4.57649i | 1.04992 | − | 1.04992i | 0.0512323 | − | 0.998687i | \(-0.483685\pi\) |
0.998687 | − | 0.0512323i | \(-0.0163149\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685i | 1.17954i | 0.807573 | + | 0.589768i | \(0.200781\pi\) | ||||
−0.807573 | + | 0.589768i | \(0.799219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000i | 1.00000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.23607 | + | 4.23607i | −0.786618 | + | 0.786618i | −0.980938 | − | 0.194320i | \(-0.937750\pi\) |
0.194320 | + | 0.980938i | \(0.437750\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.90879 | −0.702039 | −0.351020 | − | 0.936368i | \(-0.614165\pi\) | ||||
−0.351020 | + | 0.936368i | \(0.614165\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.90879 | + | 3.90879i | −0.660706 | + | 0.660706i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.47214 | + | 7.47214i | 1.22841 | + | 1.22841i | 0.964565 | + | 0.263847i | \(0.0849914\pi\) |
0.263847 | + | 0.964565i | \(0.415009\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.47214i | − | 0.386083i | −0.981191 | − | 0.193041i | \(-0.938165\pi\) | ||
0.981191 | − | 0.193041i | \(-0.0618352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.08036 | + | 1.08036i | 0.164754 | + | 0.164754i | 0.784669 | − | 0.619915i | \(-0.212833\pi\) |
−0.619915 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.94427 | 0.563467 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.23607 | + | 8.23607i | 1.13131 | + | 1.13131i | 0.989959 | + | 0.141351i | \(0.0451448\pi\) |
0.141351 | + | 0.989959i | \(0.454855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 20.4667i | − | 2.75973i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.32456 | + | 6.32456i | 0.823387 | + | 0.823387i | 0.986592 | − | 0.163205i | \(-0.0521833\pi\) |
−0.163205 | + | 0.986592i | \(0.552183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.47214 | + | 1.47214i | −0.188488 | + | 0.188488i | −0.795042 | − | 0.606554i | \(-0.792551\pi\) |
0.606554 | + | 0.795042i | \(0.292551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47214 | 0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.48528 | − | 8.48528i | 1.03664 | − | 1.03664i | 0.0373395 | − | 0.999303i | \(-0.488112\pi\) |
0.999303 | − | 0.0373395i | \(-0.0118883\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.15298i | 1.08626i | 0.839649 | + | 0.543130i | \(0.182761\pi\) | ||||
−0.839649 | + | 0.543130i | \(0.817239\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.94427i | − | 0.344601i | −0.985044 | − | 0.172300i | \(-0.944880\pi\) | ||
0.985044 | − | 0.172300i | \(-0.0551200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.00000 | − | 8.00000i | 0.911685 | − | 0.911685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.40492 | 0.833118 | 0.416559 | − | 0.909109i | \(-0.363236\pi\) | ||||
0.416559 | + | 0.909109i | \(0.363236\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.57649 | + | 4.57649i | −0.502335 | + | 0.502335i | −0.912163 | − | 0.409828i | \(-0.865589\pi\) |
0.409828 | + | 0.912163i | \(0.365589\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.52786 | + | 5.52786i | 0.599581 | + | 0.599581i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000i | 1.06000i | 0.847998 | + | 0.529999i | \(0.177808\pi\) | ||||
−0.847998 | + | 0.529999i | \(0.822192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.74806 | + | 1.74806i | 0.183247 | + | 0.183247i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.4667 | 2.09984 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9443 | −1.31429 | −0.657146 | − | 0.753763i | \(-0.728236\pi\) | ||||
−0.657146 | + | 0.753763i | \(0.728236\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.236068 | + | 0.236068i | 0.0234896 | + | 0.0234896i | 0.718754 | − | 0.695264i | \(-0.244713\pi\) |
−0.695264 | + | 0.718754i | \(0.744713\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.74806i | − | 0.172242i | −0.996285 | − | 0.0861209i | \(-0.972553\pi\) | ||
0.996285 | − | 0.0861209i | \(-0.0274471\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.667701 | + | 0.667701i | 0.0645491 | + | 0.0645491i | 0.738644 | − | 0.674095i | \(-0.235466\pi\) |
−0.674095 | + | 0.738644i | \(0.735466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9443 | − | 11.9443i | 1.14405 | − | 1.14405i | 0.156352 | − | 0.987701i | \(-0.450026\pi\) |
0.987701 | − | 0.156352i | \(-0.0499736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6491 | + | 12.6491i | −1.17954 | + | 1.17954i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.32145i | 0.396147i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.8885i | 2.80805i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9010 | −0.967311 | −0.483656 | − | 0.875258i | \(-0.660691\pi\) | ||||
−0.483656 | + | 0.875258i | \(0.660691\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.9814 | + | 11.9814i | −1.04682 | + | 1.04682i | −0.0479719 | + | 0.998849i | \(0.515276\pi\) |
−0.998849 | + | 0.0479719i | \(0.984724\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | + | 8.00000i | 0.693688 | + | 0.693688i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.47214i | 0.211209i | 0.994408 | + | 0.105604i | \(0.0336777\pi\) | ||||
−0.994408 | + | 0.105604i | \(0.966322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9814 | + | 11.9814i | 1.01625 | + | 1.01625i | 0.999866 | + | 0.0163841i | \(0.00521546\pi\) |
0.0163841 | + | 0.999866i | \(0.494785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.15298 | −0.765411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.9443 | −1.57324 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.70820 | − | 2.70820i | −0.221865 | − | 0.221865i | 0.587419 | − | 0.809283i | \(-0.300144\pi\) |
−0.809283 | + | 0.587419i | \(0.800144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0540i | 1.63197i | 0.578070 | + | 0.815987i | \(0.303806\pi\) | ||||
−0.578070 | + | 0.815987i | \(0.696194\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.74032 | − | 8.74032i | −0.702039 | − | 0.702039i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.47214 | + | 9.47214i | −0.755959 | + | 0.755959i | −0.975584 | − | 0.219626i | \(-0.929516\pi\) |
0.219626 | + | 0.975584i | \(0.429516\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.88854 | −0.779326 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2333 | − | 10.2333i | 0.801537 | − | 0.801537i | −0.181798 | − | 0.983336i | \(-0.558192\pi\) |
0.983336 | + | 0.181798i | \(0.0581918\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.4667i | − | 1.58376i | −0.610677 | − | 0.791880i | \(-0.709102\pi\) | ||
0.610677 | − | 0.791880i | \(-0.290898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.70820 | − | 6.70820i | 0.510015 | − | 0.510015i | −0.404516 | − | 0.914531i | \(-0.632560\pi\) |
0.914531 | + | 0.404516i | \(0.132560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.74032 | −0.660706 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.48528 | − | 8.48528i | 0.634220 | − | 0.634220i | −0.314904 | − | 0.949124i | \(-0.601972\pi\) |
0.949124 | + | 0.314904i | \(0.101972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0000 | + | 11.0000i | 0.817624 | + | 0.817624i | 0.985763 | − | 0.168140i | \(-0.0537759\pi\) |
−0.168140 | + | 0.985763i | \(0.553776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.4164i | 2.45682i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3137 | − | 11.3137i | −0.827340 | − | 0.827340i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.8098 | −1.07160 | −0.535801 | − | 0.844344i | \(-0.679990\pi\) | ||||
−0.535801 | + | 0.844344i | \(0.679990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.94427 | 0.355896 | 0.177948 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177948 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.18034 | − | 5.18034i | −0.369084 | − | 0.369084i | 0.498059 | − | 0.867143i | \(-0.334046\pi\) |
−0.867143 | + | 0.498059i | \(0.834046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.24419i | − | 0.371751i | −0.982573 | − | 0.185875i | \(-0.940488\pi\) | ||
0.982573 | − | 0.185875i | \(-0.0595121\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.40492 | − | 7.40492i | −0.519723 | − | 0.519723i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.52786 | − | 5.52786i | 0.386083 | − | 0.386083i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.8885 | −2.89749 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.98915 | + | 4.98915i | −0.343467 | + | 0.343467i | −0.857669 | − | 0.514202i | \(-0.828088\pi\) |
0.514202 | + | 0.857669i | \(0.328088\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.83153i | 0.329508i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.83282i | − | 0.463842i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.47214 | − | 2.47214i | 0.166294 | − | 0.166294i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.90879 | −0.261752 | −0.130876 | − | 0.991399i | \(-0.541779\pi\) | ||||
−0.130876 | + | 0.991399i | \(0.541779\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.2333 | − | 10.2333i | 0.679211 | − | 0.679211i | −0.280611 | − | 0.959822i | \(-0.590537\pi\) |
0.959822 | + | 0.280611i | \(0.0905370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.94427 | − | 9.94427i | −0.657136 | − | 0.657136i | 0.297565 | − | 0.954701i | \(-0.403825\pi\) |
−0.954701 | + | 0.297565i | \(0.903825\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.0000i | − | 0.655122i | −0.944830 | − | 0.327561i | \(-0.893773\pi\) | ||
0.944830 | − | 0.327561i | \(-0.106227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.1235 | −1.68979 | −0.844896 | − | 0.534931i | \(-0.820338\pi\) | ||||
−0.844896 | + | 0.534931i | \(0.820338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.81966 | + | 8.81966i | 0.563467 | + | 0.563467i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 9.15298i | − | 0.582390i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.07262 | + | 8.07262i | 0.509539 | + | 0.509539i | 0.914385 | − | 0.404846i | \(-0.132675\pi\) |
−0.404846 | + | 0.914385i | \(0.632675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.8885 | − | 25.8885i | 1.62760 | − | 1.62760i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0000 | 0.873296 | 0.436648 | − | 0.899632i | \(-0.356166\pi\) | ||||
0.436648 | + | 0.899632i | \(0.356166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.0618 | + | 13.0618i | −0.811619 | + | 0.811619i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.6491i | − | 0.779978i | −0.920820 | − | 0.389989i | \(-0.872479\pi\) | ||
0.920820 | − | 0.389989i | \(-0.127521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.8328i | 2.26262i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.76393 | − | 3.76393i | 0.229491 | − | 0.229491i | −0.582989 | − | 0.812480i | \(-0.698117\pi\) |
0.812480 | + | 0.582989i | \(0.198117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9010 | 0.662191 | 0.331096 | − | 0.943597i | \(-0.392582\pi\) | ||||
0.331096 | + | 0.943597i | \(0.392582\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.8825 | − | 22.8825i | 1.37986 | − | 1.37986i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0000 | + | 13.0000i | 0.781094 | + | 0.781094i | 0.980015 | − | 0.198921i | \(-0.0637438\pi\) |
−0.198921 | + | 0.980015i | \(0.563744\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.88854i | − | 0.231971i | −0.993251 | − | 0.115986i | \(-0.962997\pi\) | ||
0.993251 | − | 0.115986i | \(-0.0370026\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.9737 | − | 18.9737i | −1.12787 | − | 1.12787i | −0.990523 | − | 0.137344i | \(-0.956143\pi\) |
−0.137344 | − | 0.990523i | \(-0.543857\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.32145 | 0.255087 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.2361 | − | 16.2361i | −0.948521 | − | 0.948521i | 0.0502171 | − | 0.998738i | \(-0.484009\pi\) |
−0.998738 | + | 0.0502171i | \(0.984009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.2843i | 1.64677i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.65685 | + | 5.65685i | 0.327144 | + | 0.327144i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.88854 | + | 1.88854i | −0.108854 | + | 0.108854i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.58359 | −0.376975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.16383 | − | 4.16383i | 0.237642 | − | 0.237642i | −0.578231 | − | 0.815873i | \(-0.696257\pi\) |
0.815873 | + | 0.578231i | \(0.196257\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6414i | 1.11376i | 0.830593 | + | 0.556880i | \(0.188002\pi\) | ||||
−0.830593 | + | 0.556880i | \(0.811998\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.9443i | 1.18384i | 0.805997 | + | 0.591920i | \(0.201630\pi\) | ||||
−0.805997 | + | 0.591920i | \(0.798370\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2361 | + | 12.2361i | −0.687246 | + | 0.687246i | −0.961622 | − | 0.274376i | \(-0.911529\pi\) |
0.274376 | + | 0.961622i | \(0.411529\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38.7727 | 2.17085 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.3137 | − | 11.3137i | 0.629512 | − | 0.629512i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.00000 | + | 5.00000i | 0.277350 | + | 0.277350i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9814 | − | 11.9814i | −0.658558 | − | 0.658558i | 0.296481 | − | 0.955039i | \(-0.404187\pi\) |
−0.955039 | + | 0.296481i | \(0.904187\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 37.9473 | 2.07328 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.9443 | −0.814066 | −0.407033 | − | 0.913413i | \(-0.633437\pi\) | ||||
−0.407033 | + | 0.913413i | \(0.633437\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.8885 | + | 17.8885i | 0.968719 | + | 0.968719i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1313i | 1.03299i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.8902 | + | 15.8902i | 0.853031 | + | 0.853031i | 0.990505 | − | 0.137475i | \(-0.0438986\pi\) |
−0.137475 | + | 0.990505i | \(0.543899\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.52786 | + | 6.52786i | −0.349429 | + | 0.349429i | −0.859897 | − | 0.510468i | \(-0.829472\pi\) |
0.510468 | + | 0.859897i | \(0.329472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.8885 | 0.632763 | 0.316382 | − | 0.948632i | \(-0.397532\pi\) | ||||
0.316382 | + | 0.948632i | \(0.397532\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.4667 | + | 20.4667i | −1.08626 | + | 1.08626i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.4744i | − | 0.711153i | −0.934647 | − | 0.355577i | \(-0.884284\pi\) | ||
0.934647 | − | 0.355577i | \(-0.115716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 22.8885i | − | 1.20466i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.58359 | − | 6.58359i | 0.344601 | − | 0.344601i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8933 | 0.934023 | 0.467011 | − | 0.884251i | \(-0.345331\pi\) | ||||
0.467011 | + | 0.884251i | \(0.345331\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.3972 | + | 14.3972i | −0.747464 | + | 0.747464i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.4721 | + | 15.4721i | 0.801117 | + | 0.801117i | 0.983270 | − | 0.182153i | \(-0.0583067\pi\) |
−0.182153 | + | 0.983270i | \(0.558307\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.47214i | 0.436337i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.3863 | + | 19.3863i | 0.995809 | + | 0.995809i | 0.999991 | − | 0.00418248i | \(-0.00133133\pi\) |
−0.00418248 | + | 0.999991i | \(0.501331\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.1313 | −0.977563 | −0.488782 | − | 0.872406i | \(-0.662559\pi\) | ||||
−0.488782 | + | 0.872406i | \(0.662559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.7771 | 1.82337 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.6525 | + | 23.6525i | 1.19923 | + | 1.19923i | 0.974398 | + | 0.224830i | \(0.0721827\pi\) |
0.224830 | + | 0.974398i | \(0.427817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.9845i | 0.707227i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.5579 | + | 16.5579i | 0.833118 | + | 0.833118i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.41641 | − | 6.41641i | 0.322030 | − | 0.322030i | −0.527515 | − | 0.849546i | \(-0.676876\pi\) |
0.849546 | + | 0.527515i | \(0.176876\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5279 | 0.675549 | 0.337775 | − | 0.941227i | \(-0.390326\pi\) | ||||
0.337775 | + | 0.941227i | \(0.390326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.90879 | + | 3.90879i | −0.194711 | + | 0.194711i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 68.3923i | − | 3.39008i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.9443i | − | 0.640053i | −0.947409 | − | 0.320027i | \(-0.896308\pi\) | ||
0.947409 | − | 0.320027i | \(-0.103692\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.0557 | + | 11.0557i | −0.544017 | + | 0.544017i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.4667 | −1.00467 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.08036 | − | 1.08036i | 0.0527792 | − | 0.0527792i | −0.680225 | − | 0.733004i | \(-0.738118\pi\) |
0.733004 | + | 0.680225i | \(0.238118\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | − | 5.00000i | −0.243685 | − | 0.243685i | 0.574688 | − | 0.818373i | \(-0.305124\pi\) |
−0.818373 | + | 0.574688i | \(0.805124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.3607i | 0.599581i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.57339 | − | 2.57339i | −0.124535 | − | 0.124535i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3060 | 0.881767 | 0.440884 | − | 0.897564i | \(-0.354665\pi\) | ||||
0.440884 | + | 0.897564i | \(0.354665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.0000 | −1.15337 | −0.576683 | − | 0.816968i | \(-0.695653\pi\) | ||||
−0.576683 | + | 0.816968i | \(0.695653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.8885 | + | 25.8885i | 1.23842 | + | 1.23842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.06952i | − | 0.289682i | −0.989455 | − | 0.144841i | \(-0.953733\pi\) | ||
0.989455 | − | 0.144841i | \(-0.0462671\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.07262 | − | 8.07262i | −0.383542 | − | 0.383542i | 0.488835 | − | 0.872376i | \(-0.337422\pi\) |
−0.872376 | + | 0.488835i | \(0.837422\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.3607 | + | 22.3607i | −1.06000 | + | 1.06000i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.4164 | 1.10509 | 0.552544 | − | 0.833484i | \(-0.313657\pi\) | ||||
0.552544 | + | 0.833484i | \(0.313657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3137 | + | 11.3137i | −0.532742 | + | 0.532742i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.81758i | 0.366494i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.05573i | − | 0.142941i | −0.997443 | − | 0.0714705i | \(-0.977231\pi\) | ||
0.997443 | − | 0.0714705i | \(-0.0227692\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.23607 | − | 6.23607i | 0.290443 | − | 0.290443i | −0.546812 | − | 0.837255i | \(-0.684159\pi\) |
0.837255 | + | 0.546812i | \(0.184159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.40492 | −0.344136 | −0.172068 | − | 0.985085i | \(-0.555045\pi\) | ||||
−0.172068 | + | 0.985085i | \(0.555045\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.24109 | + | 3.24109i | −0.149980 | + | 0.149980i | −0.778109 | − | 0.628129i | \(-0.783821\pi\) |
0.628129 | + | 0.778109i | \(0.283821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8328 | + | 14.8328i | 0.684916 | + | 0.684916i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.88854i | − | 0.454676i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.8825 | + | 22.8825i | 1.04992 | + | 1.04992i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.49613 | 0.159742 | 0.0798711 | − | 0.996805i | \(-0.474549\pi\) | ||||
0.0798711 | + | 0.996805i | \(0.474549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.9443 | 0.681400 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.9443 | − | 28.9443i | −1.31429 | − | 1.31429i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5579i | 0.750310i | 0.926962 | + | 0.375155i | \(0.122411\pi\) | ||||
−0.926962 | + | 0.375155i | \(0.877589\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.4775 | − | 15.4775i | −0.698492 | − | 0.698492i | 0.265594 | − | 0.964085i | \(-0.414432\pi\) |
−0.964085 | + | 0.265594i | \(0.914432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.4721 | + | 10.4721i | −0.471641 | + | 0.471641i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.6383 | − | 17.6383i | 0.789597 | − | 0.789597i | −0.191831 | − | 0.981428i | \(-0.561443\pi\) |
0.981428 | + | 0.191831i | \(0.0614425\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 4.83153i | − | 0.215427i | −0.994182 | − | 0.107714i | \(-0.965647\pi\) | ||
0.994182 | − | 0.107714i | \(-0.0343530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.05573i | 0.0469793i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2361 | − | 28.2361i | 1.25154 | − | 1.25154i | 0.296513 | − | 0.955029i | \(-0.404176\pi\) |
0.955029 | − | 0.296513i | \(-0.0958238\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.14678 | 0.227680 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.90879 | − | 3.90879i | 0.172242 | − | 0.172242i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.3607i | − | 1.24250i | −0.783611 | − | 0.621252i | \(-0.786624\pi\) | ||
0.783611 | − | 0.621252i | \(-0.213376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.5687 | − | 11.5687i | −0.505866 | − | 0.505866i | 0.407389 | − | 0.913255i | \(-0.366439\pi\) |
−0.913255 | + | 0.407389i | \(0.866439\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.66306 | −0.420930 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.47214 | − | 2.47214i | −0.107080 | − | 0.107080i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.98605i | 0.129098i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.0509 | − | 18.0509i | −0.777508 | − | 0.777508i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8885 | − | 18.8885i | 0.812082 | − | 0.812082i | −0.172864 | − | 0.984946i | \(-0.555302\pi\) |
0.984946 | + | 0.172864i | \(0.0553020\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 53.4164 | 2.28811 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.8825 | − | 22.8825i | 0.978383 | − | 0.978383i | −0.0213881 | − | 0.999771i | \(-0.506809\pi\) |
0.999771 | + | 0.0213881i | \(0.00680856\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.7727i | 1.65177i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9443i | 0.550446i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.1803 | + | 11.1803i | −0.473726 | + | 0.473726i | −0.903118 | − | 0.429392i | \(-0.858728\pi\) |
0.429392 | + | 0.903118i | \(0.358728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.16073 | 0.0913890 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.08036 | − | 1.08036i | 0.0455319 | − | 0.0455319i | −0.683974 | − | 0.729506i | \(-0.739750\pi\) |
0.729506 | + | 0.683974i | \(0.239750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.47214 | − | 4.47214i | −0.188144 | − | 0.188144i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.41641i | − | 0.310912i | −0.987843 | − | 0.155456i | \(-0.950315\pi\) | ||
0.987843 | − | 0.155456i | \(-0.0496847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.32456 | + | 6.32456i | 0.264674 | + | 0.264674i | 0.826950 | − | 0.562276i | \(-0.190074\pi\) |
−0.562276 | + | 0.826950i | \(0.690074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.2843 | −1.17954 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9443 | 1.12170 | 0.560852 | − | 0.827916i | \(-0.310474\pi\) | ||||
0.560852 | + | 0.827916i | \(0.310474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.00000 | − | 8.00000i | −0.331896 | − | 0.331896i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 75.3846i | − | 3.12211i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.2951 | + | 23.2951i | 0.961492 | + | 0.961492i | 0.999286 | − | 0.0377932i | \(-0.0120328\pi\) |
−0.0377932 | + | 0.999286i | \(0.512033\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.8885 | + | 17.8885i | −0.737085 | + | 0.737085i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.88854 | 0.323944 | 0.161972 | − | 0.986795i | \(-0.448215\pi\) | ||||
0.161972 | + | 0.986795i | \(0.448215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.66306 | + | 9.66306i | −0.396147 | + | 0.396147i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.65685i | − | 0.231133i | −0.993300 | − | 0.115566i | \(-0.963132\pi\) | ||
0.993300 | − | 0.115566i | \(-0.0368683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.94427i | − | 0.283263i | −0.989919 | − | 0.141631i | \(-0.954765\pi\) | ||
0.989919 | − | 0.141631i | \(-0.0452348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −69.0689 | + | 69.0689i | −2.80805 | + | 2.80805i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.8422 | −1.82009 | −0.910044 | − | 0.414512i | \(-0.863952\pi\) | ||||
−0.910044 | + | 0.414512i | \(0.863952\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.47214 | − | 7.47214i | −0.301797 | − | 0.301797i | 0.539920 | − | 0.841716i | \(-0.318455\pi\) |
−0.841716 | + | 0.539920i | \(0.818455\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.8885i | − | 0.639649i | −0.947477 | − | 0.319824i | \(-0.896376\pi\) | ||
0.947477 | − | 0.319824i | \(-0.103624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.16383 | − | 4.16383i | −0.167358 | − | 0.167358i | 0.618459 | − | 0.785817i | \(-0.287757\pi\) |
−0.785817 | + | 0.618459i | \(0.787757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.4806 | −0.700347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.4721 | + | 18.4721i | 0.736532 | + | 0.736532i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0463i | 1.07670i | 0.842723 | + | 0.538348i | \(0.180951\pi\) | ||||
−0.842723 | + | 0.538348i | \(0.819049\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.3755 | − | 24.3755i | −0.967311 | − | 0.967311i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.94427 | − | 3.94427i | 0.156278 | − | 0.156278i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.58359 | −0.339032 | −0.169516 | − | 0.985527i | \(-0.554220\pi\) | ||||
−0.169516 | + | 0.985527i | \(0.554220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.91189 | + | 5.91189i | −0.233142 | + | 0.233142i | −0.814003 | − | 0.580861i | \(-0.802716\pi\) |
0.580861 | + | 0.814003i | \(0.302716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.2688i | 1.66176i | 0.556454 | + | 0.830879i | \(0.312162\pi\) | ||||
−0.556454 | + | 0.830879i | \(0.687838\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 57.8885i | − | 2.27232i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.1803 | − | 27.1803i | 1.06365 | − | 1.06365i | 0.0658172 | − | 0.997832i | \(-0.479035\pi\) |
0.997832 | − | 0.0658172i | \(-0.0209654\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −53.5825 | −2.09364 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.82843 | + | 2.82843i | −0.110180 | + | 0.110180i | −0.760047 | − | 0.649868i | \(-0.774824\pi\) |
0.649868 | + | 0.760047i | \(0.274824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.4164 | − | 28.4164i | −1.10527 | − | 1.10527i | −0.993764 | − | 0.111506i | \(-0.964432\pi\) |
−0.111506 | − | 0.993764i | \(-0.535568\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.7771i | 1.38738i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.9628 | − | 23.9628i | −0.927844 | − | 0.927844i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.4744 | 0.520175 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.8885 | −0.689553 | −0.344776 | − | 0.938685i | \(-0.612045\pi\) | ||||
−0.344776 | + | 0.938685i | \(0.612045\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.347524 | − | 0.347524i | −0.0133564 | − | 0.0133564i | 0.700397 | − | 0.713753i | \(-0.253006\pi\) |
−0.713753 | + | 0.700397i | \(0.753006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 22.6274i | − | 0.868361i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.41577 | − | 2.41577i | −0.0924367 | − | 0.0924367i | 0.659376 | − | 0.751813i | \(-0.270820\pi\) |
−0.751813 | + | 0.659376i | \(0.770820\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.52786 | + | 5.52786i | −0.211209 | + | 0.211209i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.4721 | 0.627538 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.0509 | − | 18.0509i | 0.686690 | − | 0.686690i | −0.274809 | − | 0.961499i | \(-0.588615\pi\) |
0.961499 | + | 0.274809i | \(0.0886147\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.5825i | 2.03250i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.11146i | − | 0.231488i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1803 | − | 25.1803i | 0.951048 | − | 0.951048i | −0.0478082 | − | 0.998857i | \(-0.515224\pi\) |
0.998857 | + | 0.0478082i | \(0.0152236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.3923 | 2.57947 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.412662 | + | 0.412662i | −0.0155198 | + | 0.0155198i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.9443 | − | 23.9443i | −0.899246 | − | 0.899246i | 0.0961234 | − | 0.995369i | \(-0.469356\pi\) |
−0.995369 | + | 0.0961234i | \(0.969356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 22.1115i | − | 0.828081i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.4667 | − | 20.4667i | −0.765411 | − | 0.765411i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.8021 | −0.813081 | −0.406540 | − | 0.913633i | \(-0.633265\pi\) | ||||
−0.406540 | + | 0.913633i | \(0.633265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.05573 | 0.113801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.1803 | − | 21.1803i | −0.786618 | − | 0.786618i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 20.0540i | − | 0.743763i | −0.928280 | − | 0.371881i | \(-0.878713\pi\) | ||
0.928280 | − | 0.371881i | \(-0.121287\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.67080 | + | 2.67080i | 0.0987833 | + | 0.0987833i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.9443 | + | 21.9443i | −0.810530 | + | 0.810530i | −0.984713 | − | 0.174183i | \(-0.944272\pi\) |
0.174183 | + | 0.984713i | \(0.444272\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −77.6656 | −2.86085 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.2951 | + | 23.2951i | −0.856925 | + | 0.856925i | −0.990975 | − | 0.134050i | \(-0.957202\pi\) |
0.134050 | + | 0.990975i | \(0.457202\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.16073i | 0.0792694i | 0.999214 | + | 0.0396347i | \(0.0126194\pi\) | ||||
−0.999214 | + | 0.0396347i | \(0.987381\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 12.1115i | − | 0.443729i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.16718 | + | 1.16718i | −0.0426480 | + | 0.0426480i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.40492 | −0.270209 | −0.135105 | − | 0.990831i | \(-0.543137\pi\) | ||||
−0.135105 | + | 0.990831i | \(0.543137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.8422 | + | 44.8422i | −1.63197 | + | 1.63197i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.94427 | − | 9.94427i | −0.361431 | − | 0.361431i | 0.502909 | − | 0.864339i | \(-0.332263\pi\) |
−0.864339 | + | 0.502909i | \(0.832263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.41641i | 0.268845i | 0.990924 | + | 0.134422i | \(0.0429179\pi\) | ||||
−0.990924 | + | 0.134422i | \(0.957082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.8794 | + | 20.8794i | 0.755883 | + | 0.755883i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.6491 | 0.456733 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.8328 | −1.11186 | −0.555930 | − | 0.831229i | \(-0.687638\pi\) | ||||
−0.555930 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.70820 | − | 4.70820i | −0.169342 | − | 0.169342i | 0.617348 | − | 0.786690i | \(-0.288207\pi\) |
−0.786690 | + | 0.617348i | \(0.788207\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 19.5440i | − | 0.702039i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.3137 | − | 11.3137i | −0.405356 | − | 0.405356i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.8885 | − | 41.8885i | 1.49889 | − | 1.49889i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.3607 | −1.51192 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2333 | − | 10.2333i | 0.364779 | − | 0.364779i | −0.500790 | − | 0.865569i | \(-0.666957\pi\) |
0.865569 | + | 0.500790i | \(0.166957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.49613i | − | 0.124308i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.94427i | 0.104554i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.65248 | − | 3.65248i | 0.129377 | − | 0.129377i | −0.639453 | − | 0.768830i | \(-0.720839\pi\) |
0.768830 | + | 0.639453i | \(0.220839\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.4744 | + | 13.4744i | −0.475502 | + | 0.475502i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.1115 | − | 22.1115i | −0.779326 | − | 0.779326i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 23.4164i | − | 0.823277i | −0.911347 | − | 0.411639i | \(-0.864957\pi\) | ||
0.911347 | − | 0.411639i | \(-0.135043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7217 | + | 20.7217i | 0.727638 | + | 0.727638i | 0.970149 | − | 0.242510i | \(-0.0779709\pi\) |
−0.242510 | + | 0.970149i | \(0.577971\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45.7649 | 1.60307 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.88854 | 0.345956 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.5410 | − | 35.5410i | −1.24039 | − | 1.24039i | −0.959839 | − | 0.280551i | \(-0.909483\pi\) |
−0.280551 | − | 0.959839i | \(-0.590517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.74806i | 0.0609337i | 0.999536 | + | 0.0304668i | \(0.00969940\pi\) | ||||
−0.999536 | + | 0.0304668i | \(0.990301\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.8067 | + | 12.8067i | 0.445334 | + | 0.445334i | 0.893800 | − | 0.448466i | \(-0.148030\pi\) |
−0.448466 | + | 0.893800i | \(0.648030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.94427 | + | 3.94427i | −0.136990 | + | 0.136990i | −0.772277 | − | 0.635286i | \(-0.780882\pi\) |
0.635286 | + | 0.772277i | \(0.280882\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.75078 | 0.337844 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.7649 | − | 45.7649i | 1.58376 | − | 1.58376i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.48218i | 0.223790i | 0.993720 | + | 0.111895i | \(0.0356920\pi\) | ||||
−0.993720 | + | 0.111895i | \(0.964308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 6.88854i | − | 0.237536i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.5967 | + | 24.5967i | −0.846154 | + | 0.846154i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.9952 | −1.85530 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −42.2688 | + | 42.2688i | −1.44896 | + | 1.44896i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.4721 | − | 21.4721i | −0.735192 | − | 0.735192i | 0.236451 | − | 0.971643i | \(-0.424016\pi\) |
−0.971643 | + | 0.236451i | \(0.924016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 55.4164i | − | 1.89299i | −0.322721 | − | 0.946494i | \(-0.604597\pi\) | ||
0.322721 | − | 0.946494i | \(-0.395403\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.5176 | + | 38.5176i | 1.31420 | + | 1.31420i | 0.918286 | + | 0.395918i | \(0.129574\pi\) |
0.395918 | + | 0.918286i | \(0.370426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.7943 | 0.980171 | 0.490086 | − | 0.871674i | \(-0.336966\pi\) | ||||
0.490086 | + | 0.871674i | \(0.336966\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.0000 | 1.02003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.8885 | − | 33.8885i | −1.14959 | − | 1.14959i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 16.9706i | − | 0.575026i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.3607 | − | 19.3607i | 0.653764 | − | 0.653764i | −0.300134 | − | 0.953897i | \(-0.597031\pi\) |
0.953897 | + | 0.300134i | \(0.0970312\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.88854 | −0.265772 | −0.132886 | − | 0.991131i | \(-0.542424\pi\) | ||||
−0.132886 | + | 0.991131i | \(0.542424\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.73722 | + | 6.73722i | −0.226725 | + | 0.226725i | −0.811323 | − | 0.584598i | \(-0.801252\pi\) |
0.584598 | + | 0.811323i | \(0.301252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 8.32766i | − | 0.279615i | −0.990179 | − | 0.139808i | \(-0.955352\pi\) | ||
0.990179 | − | 0.139808i | \(-0.0446484\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 19.0557i | − | 0.639109i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.9473 | 1.26844 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.5579 | − | 16.5579i | 0.552237 | − | 0.552237i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.3607 | + | 20.3607i | 0.678313 | + | 0.678313i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49.1935i | 1.63525i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3708 | + | 33.3708i | 1.10806 | + | 1.10806i | 0.993405 | + | 0.114655i | \(0.0365763\pi\) |
0.114655 | + | 0.993405i | \(0.463424\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8098 | 0.490672 | 0.245336 | − | 0.969438i | \(-0.421102\pi\) | ||||
0.245336 | + | 0.969438i | \(0.421102\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.8885 | 1.38631 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.9443 | − | 20.9443i | −0.691641 | − | 0.691641i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.57339i | − | 0.0848882i | −0.999099 | − | 0.0424441i | \(-0.986486\pi\) | ||
0.999099 | − | 0.0424441i | \(-0.0135144\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.15298 | + | 9.15298i | 0.301274 | + | 0.301274i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.3607 | + | 37.3607i | −1.22841 | + | 1.22841i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.47214 | 0.0811081 | 0.0405541 | − | 0.999177i | \(-0.487088\pi\) | ||||
0.0405541 | + | 0.999177i | \(0.487088\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0509 | − | 18.0509i | 0.591595 | − | 0.591595i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 50.5964i | − | 1.65468i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.0000i | − | 0.718709i | −0.933201 | − | 0.359354i | \(-0.882997\pi\) | ||
0.933201 | − | 0.359354i | \(-0.117003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.2361 | − | 22.2361i | 0.724875 | − | 0.724875i | −0.244719 | − | 0.969594i | \(-0.578696\pi\) |
0.969594 | + | 0.244719i | \(0.0786957\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.9845 | 0.455398 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.8129 | − | 16.8129i | 0.546347 | − | 0.546347i | −0.379035 | − | 0.925382i | \(-0.623744\pi\) |
0.925382 | + | 0.379035i | \(0.123744\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.94427 | − | 2.94427i | −0.0955751 | − | 0.0955751i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.4721i | 0.598371i | 0.954195 | + | 0.299186i | \(0.0967150\pi\) | ||||
−0.954195 | + | 0.299186i | \(0.903285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.1158 | − | 33.1158i | −1.07160 | − | 1.07160i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.32145 | −0.139547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.7214 | −0.507141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0557 | + | 11.0557i | 0.355896 | + | 0.355896i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.3600i | 1.23357i | 0.787130 | + | 0.616787i | \(0.211566\pi\) | ||||
−0.787130 | + | 0.616787i | \(0.788434\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.2256 | − | 17.2256i | −0.552796 | − | 0.552796i | 0.374451 | − | 0.927247i | \(-0.377831\pi\) |
−0.927247 | + | 0.374451i | \(0.877831\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.9443 | + | 20.9443i | −0.671443 | + | 0.671443i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.4164 | 1.26104 | 0.630521 | − | 0.776172i | \(-0.282841\pi\) | ||||
0.630521 | + | 0.776172i | \(0.282841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.7649 | − | 45.7649i | 1.46265 | − | 1.46265i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.98605i | − | 0.0952402i | −0.998866 | − | 0.0476201i | \(-0.984836\pi\) | ||
0.998866 | − | 0.0476201i | \(-0.0151637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 23.1672i | − | 0.738168i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.11146 | + | 6.11146i | −0.194333 | + | 0.194333i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3972 | 0.457341 | 0.228671 | − | 0.973504i | \(-0.426562\pi\) | ||||
0.228671 | + | 0.973504i | \(0.426562\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.7264 | − | 11.7264i | 0.371751 | − | 0.371751i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.4721 | − | 29.4721i | −0.933392 | − | 0.933392i | 0.0645242 | − | 0.997916i | \(-0.479447\pi\) |
−0.997916 | + | 0.0645242i | \(0.979447\pi\) | |||||||
\(998\) | 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 | 4608.2.k.bg.3457.4 | 8 | ||
3.2 | odd | 2 | 1536.2.j.h.385.3 | yes | 8 | ||
4.3 | odd | 2 | inner | 4608.2.k.bg.3457.3 | 8 | ||
8.3 | odd | 2 | 4608.2.k.bf.3457.1 | 8 | |||
8.5 | even | 2 | 4608.2.k.bf.3457.2 | 8 | |||
12.11 | even | 2 | 1536.2.j.h.385.1 | yes | 8 | ||
16.3 | odd | 4 | inner | 4608.2.k.bg.1153.4 | 8 | ||
16.5 | even | 4 | 4608.2.k.bf.1153.1 | 8 | |||
16.11 | odd | 4 | 4608.2.k.bf.1153.2 | 8 | |||
16.13 | even | 4 | inner | 4608.2.k.bg.1153.3 | 8 | ||
24.5 | odd | 2 | 1536.2.j.g.385.2 | ✓ | 8 | ||
24.11 | even | 2 | 1536.2.j.g.385.4 | yes | 8 | ||
32.3 | odd | 8 | 9216.2.a.bj.1.2 | 4 | |||
32.13 | even | 8 | 9216.2.a.bj.1.3 | 4 | |||
32.19 | odd | 8 | 9216.2.a.bd.1.4 | 4 | |||
32.29 | even | 8 | 9216.2.a.bd.1.1 | 4 | |||
48.5 | odd | 4 | 1536.2.j.g.1153.2 | yes | 8 | ||
48.11 | even | 4 | 1536.2.j.g.1153.4 | yes | 8 | ||
48.29 | odd | 4 | 1536.2.j.h.1153.3 | yes | 8 | ||
48.35 | even | 4 | 1536.2.j.h.1153.1 | yes | 8 | ||
96.5 | odd | 8 | 3072.2.d.g.1537.6 | 8 | |||
96.11 | even | 8 | 3072.2.d.g.1537.7 | 8 | |||
96.29 | odd | 8 | 3072.2.a.q.1.3 | 4 | |||
96.35 | even | 8 | 3072.2.a.k.1.4 | 4 | |||
96.53 | odd | 8 | 3072.2.d.g.1537.4 | 8 | |||
96.59 | even | 8 | 3072.2.d.g.1537.1 | 8 | |||
96.77 | odd | 8 | 3072.2.a.k.1.1 | 4 | |||
96.83 | even | 8 | 3072.2.a.q.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.g.385.2 | ✓ | 8 | 24.5 | odd | 2 | ||
1536.2.j.g.385.4 | yes | 8 | 24.11 | even | 2 | ||
1536.2.j.g.1153.2 | yes | 8 | 48.5 | odd | 4 | ||
1536.2.j.g.1153.4 | yes | 8 | 48.11 | even | 4 | ||
1536.2.j.h.385.1 | yes | 8 | 12.11 | even | 2 | ||
1536.2.j.h.385.3 | yes | 8 | 3.2 | odd | 2 | ||
1536.2.j.h.1153.1 | yes | 8 | 48.35 | even | 4 | ||
1536.2.j.h.1153.3 | yes | 8 | 48.29 | odd | 4 | ||
3072.2.a.k.1.1 | 4 | 96.77 | odd | 8 | |||
3072.2.a.k.1.4 | 4 | 96.35 | even | 8 | |||
3072.2.a.q.1.2 | 4 | 96.83 | even | 8 | |||
3072.2.a.q.1.3 | 4 | 96.29 | odd | 8 | |||
3072.2.d.g.1537.1 | 8 | 96.59 | even | 8 | |||
3072.2.d.g.1537.4 | 8 | 96.53 | odd | 8 | |||
3072.2.d.g.1537.6 | 8 | 96.5 | odd | 8 | |||
3072.2.d.g.1537.7 | 8 | 96.11 | even | 8 | |||
4608.2.k.bf.1153.1 | 8 | 16.5 | even | 4 | |||
4608.2.k.bf.1153.2 | 8 | 16.11 | odd | 4 | |||
4608.2.k.bf.3457.1 | 8 | 8.3 | odd | 2 | |||
4608.2.k.bf.3457.2 | 8 | 8.5 | even | 2 | |||
4608.2.k.bg.1153.3 | 8 | 16.13 | even | 4 | inner | ||
4608.2.k.bg.1153.4 | 8 | 16.3 | odd | 4 | inner | ||
4608.2.k.bg.3457.3 | 8 | 4.3 | odd | 2 | inner | ||
4608.2.k.bg.3457.4 | 8 | 1.1 | even | 1 | trivial | ||
9216.2.a.bd.1.1 | 4 | 32.29 | even | 8 | |||
9216.2.a.bd.1.4 | 4 | 32.19 | odd | 8 | |||
9216.2.a.bj.1.2 | 4 | 32.3 | odd | 8 | |||
9216.2.a.bj.1.3 | 4 | 32.13 | even | 8 |