Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(949,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.l (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.4 | ||
Character | \(\chi\) | \(=\) | 1764.961 |
Dual form | 1764.2.l.j.949.4 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.755620 | − | 1.55854i | −0.436257 | − | 0.899822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.47961 | −1.55613 | −0.778065 | − | 0.628184i | \(-0.783798\pi\) | ||||
−0.778065 | + | 0.628184i | \(0.783798\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.85808 | + | 2.35532i | −0.619359 | + | 0.785108i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.51576 | 0.758530 | 0.379265 | − | 0.925288i | \(-0.376177\pi\) | ||||
0.379265 | + | 0.925288i | \(0.376177\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.292110 | + | 0.505949i | 0.0810167 | + | 0.140325i | 0.903687 | − | 0.428194i | \(-0.140850\pi\) |
−0.822670 | + | 0.568519i | \(0.807517\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.62926 | + | 5.42310i | 0.678873 | + | 1.40024i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.547519 | + | 0.948331i | 0.132793 | + | 0.230004i | 0.924752 | − | 0.380570i | \(-0.124272\pi\) |
−0.791959 | + | 0.610574i | \(0.790939\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.96834 | + | 5.14132i | −0.680984 | + | 1.17950i | 0.293696 | + | 0.955899i | \(0.405115\pi\) |
−0.974681 | + | 0.223601i | \(0.928219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.38528 | 1.33142 | 0.665712 | − | 0.746209i | \(-0.268128\pi\) | ||||
0.665712 | + | 0.746209i | \(0.268128\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.10769 | 1.42154 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.07486 | + | 1.11616i | 0.976657 | + | 0.214804i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.918333 | − | 1.59060i | 0.170530 | − | 0.295367i | −0.768075 | − | 0.640360i | \(-0.778785\pi\) |
0.938605 | + | 0.344993i | \(0.112119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.51872 | − | 6.09459i | 0.631980 | − | 1.09462i | −0.355166 | − | 0.934803i | \(-0.615576\pi\) |
0.987146 | − | 0.159818i | \(-0.0510909\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.90096 | − | 3.92091i | −0.330914 | − | 0.682542i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.702576 | − | 1.21690i | 0.115503 | − | 0.200057i | −0.802478 | − | 0.596682i | \(-0.796485\pi\) |
0.917981 | + | 0.396625i | \(0.129819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.567817 | − | 0.837570i | 0.0909235 | − | 0.134118i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.37855 | − | 9.31593i | −0.839989 | − | 1.45490i | −0.889903 | − | 0.456150i | \(-0.849228\pi\) |
0.0499141 | − | 0.998754i | \(-0.484105\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.67879 | + | 9.83596i | −0.866008 | + | 1.49997i | 3.53909e−5 | 1.00000i | \(0.499989\pi\) | |
−0.866043 | + | 0.499969i | \(0.833345\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.46539 | − | 8.19561i | 0.963803 | − | 1.22173i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.76565 | − | 6.52229i | −0.549276 | − | 0.951374i | −0.998324 | − | 0.0578664i | \(-0.981570\pi\) |
0.449048 | − | 0.893507i | \(-0.351763\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.06429 | − | 1.56991i | 0.149031 | − | 0.219831i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.82285 | − | 10.0855i | −0.799830 | − | 1.38535i | −0.919727 | − | 0.392560i | \(-0.871590\pi\) |
0.119897 | − | 0.992786i | \(-0.461744\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.75386 | −1.18037 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.2559 | + | 0.741391i | 1.35842 | + | 0.0981996i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.22775 | + | 3.85858i | −0.290029 | + | 0.502345i | −0.973816 | − | 0.227337i | \(-0.926998\pi\) |
0.683787 | + | 0.729681i | \(0.260332\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.17622 | + | 10.6975i | 0.790784 | + | 1.36968i | 0.925482 | + | 0.378792i | \(0.123660\pi\) |
−0.134698 | + | 0.990887i | \(0.543006\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.01643 | − | 1.76051i | −0.126072 | − | 0.218364i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.33536 | − | 10.9732i | 0.773988 | − | 1.34059i | −0.161374 | − | 0.986893i | \(-0.551593\pi\) |
0.935362 | − | 0.353693i | \(-0.115074\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.82485 | − | 9.95170i | −0.580843 | − | 1.19804i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.93390 | −0.585546 | −0.292773 | − | 0.956182i | \(-0.594578\pi\) | ||||
−0.292773 | + | 0.956182i | \(0.594578\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.35558 | + | 7.54408i | 0.509782 | + | 0.882968i | 0.999936 | + | 0.0113320i | \(0.00360715\pi\) |
−0.490154 | + | 0.871636i | \(0.663060\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.37071 | − | 11.0776i | −0.620156 | − | 1.27913i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.280206 | + | 0.485330i | 0.0315256 | + | 0.0546039i | 0.881358 | − | 0.472450i | \(-0.156630\pi\) |
−0.849832 | + | 0.527053i | \(0.823297\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.09509 | − | 8.75275i | −0.232788 | − | 0.972528i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.68472 | − | 6.38212i | 0.404451 | − | 0.700529i | −0.589807 | − | 0.807544i | \(-0.700796\pi\) |
0.994257 | + | 0.107015i | \(0.0341294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.90515 | − | 3.29982i | −0.206643 | − | 0.357916i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.17292 | − | 0.229368i | −0.340173 | − | 0.0245909i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.07256 | − | 10.5180i | 0.643690 | − | 1.11490i | −0.340913 | − | 0.940095i | \(-0.610736\pi\) |
0.984602 | − | 0.174808i | \(-0.0559306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.1575 | − | 0.878855i | −1.26067 | − | 0.0911331i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.3287 | − | 17.8898i | 1.05970 | − | 1.83545i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.98486 | − | 12.0981i | 0.709205 | − | 1.22838i | −0.255947 | − | 0.966691i | \(-0.582387\pi\) |
0.965152 | − | 0.261688i | \(-0.0842793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.67448 | + | 5.92543i | −0.469803 | + | 0.595528i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.17649 | 0.913095 | 0.456548 | − | 0.889699i | \(-0.349086\pi\) | ||||
0.456548 | + | 0.889699i | \(0.349086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.479075 | 0.0472047 | 0.0236024 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236024 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.67882 | − | 4.63986i | 0.258972 | − | 0.448552i | −0.706995 | − | 0.707219i | \(-0.749950\pi\) |
0.965967 | + | 0.258666i | \(0.0832830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.87535 | + | 13.6405i | 0.754322 | + | 1.30652i | 0.945711 | + | 0.325009i | \(0.105367\pi\) |
−0.191389 | + | 0.981514i | \(0.561299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.42746 | − | 0.175480i | −0.230404 | − | 0.0166558i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.92483 | − | 11.9942i | −0.651433 | − | 1.12832i | −0.982775 | − | 0.184804i | \(-0.940835\pi\) |
0.331342 | − | 0.943511i | \(-0.392499\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −22.2183 | −2.07187 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.73444 | − | 0.252080i | −0.160349 | − | 0.0233048i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.67095 | −0.424632 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.4551 | + | 15.4220i | −0.942703 | + | 1.39055i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.33394 | −0.655968 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.7533 | 1.84156 | 0.920780 | − | 0.390083i | \(-0.127554\pi\) | ||||
0.920780 | + | 0.390083i | \(0.127554\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.6207 | + | 1.41837i | 1.72751 | + | 0.124880i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.59898 | 0.139704 | 0.0698518 | − | 0.997557i | \(-0.477747\pi\) | ||||
0.0698518 | + | 0.997557i | \(0.477747\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.6585 | − | 3.88379i | −1.51980 | − | 0.334263i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.65220 | −0.653771 | −0.326886 | − | 0.945064i | \(-0.605999\pi\) | ||||
−0.326886 | + | 0.945064i | \(0.605999\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.99424 | − | 13.8464i | −0.678062 | − | 1.17444i | −0.975564 | − | 0.219717i | \(-0.929487\pi\) |
0.297501 | − | 0.954721i | \(-0.403847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.31984 | + | 10.7973i | −0.616442 | + | 0.909294i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.734878 | + | 1.27285i | 0.0614536 | + | 0.106441i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.19544 | + | 5.53467i | −0.265367 | + | 0.459629i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.87468 | −0.235503 | −0.117752 | − | 0.993043i | \(-0.537569\pi\) | ||||
−0.117752 | + | 0.993043i | \(0.537569\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.16152 | 0.745554 | 0.372777 | − | 0.927921i | \(-0.378406\pi\) | ||||
0.372777 | + | 0.927921i | \(0.378406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.25096 | − | 0.472488i | −0.262824 | − | 0.0381984i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.2438 | + | 21.2068i | −0.983443 | + | 1.70337i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.39409 | − | 11.0749i | 0.510304 | − | 0.883873i | −0.489625 | − | 0.871933i | \(-0.662866\pi\) |
0.999929 | − | 0.0119393i | \(-0.00380048\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.3187 | + | 16.6959i | −0.897633 | + | 1.32407i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.18390 | + | 12.4429i | −0.562686 | + | 0.974601i | 0.434575 | + | 0.900636i | \(0.356899\pi\) |
−0.997261 | + | 0.0739653i | \(0.976435\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.61459 | + | 13.6432i | 0.514945 | + | 1.06212i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.38280 | − | 4.12714i | −0.184387 | − | 0.319367i | 0.758983 | − | 0.651111i | \(-0.225697\pi\) |
−0.943370 | + | 0.331743i | \(0.892363\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.32934 | − | 10.9627i | 0.486873 | − | 0.843288i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.59406 | − | 16.5444i | −0.504260 | − | 1.26518i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.5583 | + | 21.7517i | 0.954792 | + | 1.65375i | 0.734844 | + | 0.678237i | \(0.237256\pi\) |
0.219948 | + | 0.975512i | \(0.429411\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.69708 | + | 0.556417i | 0.578548 | + | 0.0418229i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.41168 | − | 5.90920i | −0.255001 | − | 0.441675i | 0.709895 | − | 0.704308i | \(-0.248742\pi\) |
−0.964896 | + | 0.262633i | \(0.915409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4735 | 1.00148 | 0.500739 | − | 0.865598i | \(-0.333062\pi\) | ||||
0.500739 | + | 0.865598i | \(0.333062\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0056 | − | 17.7091i | 0.887481 | − | 1.30910i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.44469 | + | 4.23433i | −0.179737 | + | 0.311314i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.37743 | + | 2.38577i | 0.100727 | + | 0.174465i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.10318 | − | 12.3031i | −0.513968 | − | 0.890218i | −0.999869 | − | 0.0162045i | \(-0.994842\pi\) |
0.485901 | − | 0.874014i | \(-0.338492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.39260 | − | 5.87616i | 0.244205 | − | 0.422975i | −0.717703 | − | 0.696349i | \(-0.754806\pi\) |
0.961908 | + | 0.273374i | \(0.0881397\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.97578 | + | 2.91442i | −0.141489 | + | 0.208706i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.5287 | 1.32011 | 0.660057 | − | 0.751215i | \(-0.270532\pi\) | ||||
0.660057 | + | 0.751215i | \(0.270532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.39804 | − | 14.5458i | −0.595321 | − | 1.03113i | −0.993501 | − | 0.113819i | \(-0.963691\pi\) |
0.398180 | − | 0.917307i | \(-0.369642\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.8892 | − | 1.58236i | −1.54395 | − | 0.111611i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.7153 | + | 32.4158i | 1.30713 | + | 2.26402i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.8644 | + | 15.0394i | −0.824630 | + | 1.04531i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.46763 | + | 12.9343i | −0.516547 | + | 0.894686i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.7912 | − | 18.6909i | −0.742896 | − | 1.28673i | −0.951171 | − | 0.308664i | \(-0.900118\pi\) |
0.208275 | − | 0.978070i | \(-0.433215\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.72815 | + | 7.68967i | 0.255449 | + | 0.526888i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.7600 | − | 34.2253i | 1.34762 | − | 2.33415i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.46657 | − | 12.4888i | 0.572118 | − | 0.843914i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.319872 | + | 0.554034i | −0.0215169 | + | 0.0372683i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.495791 | − | 0.858736i | 0.0332006 | − | 0.0575052i | −0.848948 | − | 0.528477i | \(-0.822763\pi\) |
0.882148 | + | 0.470972i | \(0.156097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.2066 | + | 16.7409i | −0.880443 | + | 1.11606i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.93134 | 0.194560 | 0.0972799 | − | 0.995257i | \(-0.468986\pi\) | ||||
0.0972799 | + | 0.995257i | \(0.468986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.38401 | −0.289704 | −0.144852 | − | 0.989453i | \(-0.546271\pi\) | ||||
−0.144852 | + | 0.989453i | \(0.546271\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.543158 | − | 0.940778i | 0.0355835 | − | 0.0616324i | −0.847685 | − | 0.530500i | \(-0.822004\pi\) |
0.883269 | + | 0.468867i | \(0.155338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.1030 | + | 22.6950i | 0.854744 | + | 1.48046i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.544677 | − | 0.803436i | 0.0353805 | − | 0.0521888i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.91423 | + | 3.31554i | 0.123821 | + | 0.214464i | 0.921271 | − | 0.388920i | \(-0.127152\pi\) |
−0.797450 | + | 0.603384i | \(0.793818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9254 | −0.832599 | −0.416300 | − | 0.909227i | \(-0.636673\pi\) | ||||
−0.416300 | + | 0.909227i | \(0.636673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.0584 | + | 9.87903i | −0.773546 | + | 0.633740i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.46833 | −0.220685 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.7310 | − | 0.920317i | −0.806796 | − | 0.0583227i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.6654 | 1.24127 | 0.620634 | − | 0.784101i | \(-0.286875\pi\) | ||||
0.620634 | + | 0.784101i | \(0.286875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0638 | 1.00992 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.70332 | + | 5.46266i | −0.231911 | + | 0.342085i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.3597 | 1.58190 | 0.790948 | − | 0.611884i | \(-0.209588\pi\) | ||||
0.790948 | + | 0.611884i | \(0.209588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.04004 | + | 5.11843i | 0.126275 | + | 0.316823i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.87595 | 0.547315 | 0.273657 | − | 0.961827i | \(-0.411767\pi\) | ||||
0.273657 | + | 0.961827i | \(0.411767\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.2612 | + | 35.0935i | 1.24464 | + | 2.15578i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.9812 | − | 1.51672i | −1.28403 | − | 0.0928216i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.15338 | + | 15.8541i | 0.558092 | + | 0.966643i | 0.997656 | + | 0.0684319i | \(0.0217996\pi\) |
−0.439564 | + | 0.898211i | \(0.644867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.34465 | − | 4.06106i | 0.142427 | − | 0.246692i | −0.785983 | − | 0.618248i | \(-0.787843\pi\) |
0.928410 | + | 0.371557i | \(0.121176\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.8812 | 1.07828 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.65614 | 0.339845 | 0.169922 | − | 0.985457i | \(-0.445648\pi\) | ||||
0.169922 | + | 0.985457i | \(0.445648\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.81669 | + | 19.6119i | 0.467973 | + | 1.17414i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.36370 | + | 9.29020i | −0.319971 | + | 0.554207i | −0.980482 | − | 0.196610i | \(-0.937007\pi\) |
0.660510 | + | 0.750817i | \(0.270340\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.9053 | + | 20.6206i | −0.707697 | + | 1.22577i | 0.258013 | + | 0.966141i | \(0.416932\pi\) |
−0.965710 | + | 0.259625i | \(0.916401\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −35.6865 | − | 2.57975i | −2.11388 | − | 0.152811i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.90045 | − | 13.6840i | 0.464732 | − | 0.804940i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.1333 | − | 1.74458i | −1.41472 | − | 0.102269i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3315 | + | 17.8946i | 0.603570 | + | 1.04541i | 0.992276 | + | 0.124052i | \(0.0395889\pi\) |
−0.388706 | + | 0.921362i | \(0.627078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.75171 | − | 13.4264i | 0.451322 | − | 0.781713i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.7671 | + | 2.80798i | 0.740824 | + | 0.162936i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.86521 | + | 3.23063i | 0.107868 | + | 0.186832i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.93394 | − | 14.3019i | −0.398344 | − | 0.821623i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.4908 | − | 37.2232i | −1.23056 | − | 2.13140i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9227 | −0.680464 | −0.340232 | − | 0.940342i | \(-0.610506\pi\) | ||||
−0.340232 | + | 0.940342i | \(0.610506\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.361999 | − | 0.746657i | −0.0205934 | − | 0.0424758i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.56635 | + | 7.90916i | −0.258934 | + | 0.448487i | −0.965957 | − | 0.258704i | \(-0.916705\pi\) |
0.707022 | + | 0.707191i | \(0.250038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.91980 | + | 11.9854i | 0.391130 | + | 0.677457i | 0.992599 | − | 0.121439i | \(-0.0387509\pi\) |
−0.601469 | + | 0.798896i | \(0.705418\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.915786 | − | 1.58619i | −0.0514357 | − | 0.0890892i | 0.839161 | − | 0.543883i | \(-0.183046\pi\) |
−0.890597 | + | 0.454794i | \(0.849713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.31031 | − | 4.00157i | 0.129352 | − | 0.224045i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.25557 | − | 0.669079i | −0.516595 | − | 0.0373444i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.50089 | −0.361719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.07623 | + | 3.59613i | 0.115168 | + | 0.199477i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.3085 | − | 22.5811i | 0.846560 | − | 1.24874i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.103132 | + | 0.178630i | 0.00566864 | + | 0.00981838i | 0.868846 | − | 0.495083i | \(-0.164862\pi\) |
−0.863177 | + | 0.504901i | \(0.831529\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.56075 | + | 3.91589i | 0.0855284 | + | 0.214589i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.0446 | + | 38.1824i | −1.20442 | + | 2.08613i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.756536 | + | 1.31036i | 0.0412111 | + | 0.0713798i | 0.885895 | − | 0.463885i | \(-0.153545\pi\) |
−0.844684 | + | 0.535265i | \(0.820212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.4608 | + | 19.8556i | −0.731090 | + | 1.07841i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.85224 | − | 15.3325i | 0.479376 | − | 0.830303i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.7886 | + | 34.6281i | 0.903867 | + | 1.86431i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.60907 | − | 2.78698i | 0.0863792 | − | 0.149613i | −0.819599 | − | 0.572938i | \(-0.805804\pi\) |
0.905978 | + | 0.423325i | \(0.139137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.04006 | − | 12.1937i | 0.376846 | − | 0.652716i | −0.613756 | − | 0.789496i | \(-0.710342\pi\) |
0.990601 | + | 0.136780i | \(0.0436753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.917699 | + | 2.89366i | 0.0489831 | + | 0.154452i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.36930 | 0.179330 | 0.0896648 | − | 0.995972i | \(-0.471420\pi\) | ||||
0.0896648 | + | 0.995972i | \(0.471420\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.1681 | 0.911186 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.28913 | − | 12.6251i | 0.384706 | − | 0.666330i | −0.607023 | − | 0.794685i | \(-0.707636\pi\) |
0.991728 | + | 0.128355i | \(0.0409696\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.12211 | − | 14.0679i | −0.427479 | − | 0.740416i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.52946 | + | 7.27986i | 0.185249 | + | 0.382093i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.1557 | − | 26.2505i | −0.793286 | − | 1.37401i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.736734 | 0.0384572 | 0.0192286 | − | 0.999815i | \(-0.493879\pi\) | ||||
0.0192286 | + | 0.999815i | \(0.493879\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.9358 | + | 4.64149i | 1.66251 | + | 0.241626i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.9029 | 1.49653 | 0.748267 | − | 0.663397i | \(-0.230886\pi\) | ||||
0.748267 | + | 0.663397i | \(0.230886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.54167 | + | 11.4302i | 0.286171 | + | 0.590254i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.07302 | 0.0552632 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.88267 | −0.456272 | −0.228136 | − | 0.973629i | \(-0.573263\pi\) | ||||
−0.228136 | + | 0.973629i | \(0.573263\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.6816 | − | 32.3448i | −0.803394 | − | 1.65708i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.4055 | −0.787182 | −0.393591 | − | 0.919286i | \(-0.628767\pi\) | ||||
−0.393591 | + | 0.919286i | \(0.628767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.6152 | − | 31.6514i | −0.641267 | − | 1.60893i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.3139 | −1.02996 | −0.514978 | − | 0.857204i | \(-0.672200\pi\) | ||||
−0.514978 | + | 0.857204i | \(0.672200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.49606 | + | 6.05536i | 0.176804 | + | 0.306233i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.20822 | − | 2.49207i | −0.0609467 | − | 0.125708i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.975006 | − | 1.68876i | −0.0490579 | − | 0.0849708i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.32895 | + | 7.49796i | −0.217264 | + | 0.376312i | −0.953970 | − | 0.299901i | \(-0.903047\pi\) |
0.736707 | + | 0.676212i | \(0.236380\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.0546 | 1.75054 | 0.875272 | − | 0.483631i | \(-0.160682\pi\) | ||||
0.875272 | + | 0.483631i | \(0.160682\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.11141 | 0.204804 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.29010 | + | 30.4562i | 0.362248 | + | 1.51338i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.76751 | − | 3.06142i | 0.0876124 | − | 0.151749i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.61681 | + | 11.4607i | −0.327180 | + | 0.566693i | −0.981951 | − | 0.189135i | \(-0.939432\pi\) |
0.654771 | + | 0.755827i | \(0.272765\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.78215 | + | 11.9262i | 0.285212 | + | 0.588278i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.8214 | + | 22.2073i | −0.629377 | + | 1.09011i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.5396 | + | 22.9219i | −0.760976 | + | 1.12249i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.43952 | − | 7.68947i | −0.216885 | − | 0.375655i | 0.736969 | − | 0.675926i | \(-0.236256\pi\) |
−0.953854 | + | 0.300271i | \(0.902923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00273 | − | 3.46884i | 0.0976073 | − | 0.169061i | −0.813087 | − | 0.582143i | \(-0.802214\pi\) |
0.910694 | + | 0.413082i | \(0.135548\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.3590 | + | 3.24961i | 1.08713 | + | 0.158002i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.89160 | + | 6.74044i | 0.188770 | + | 0.326959i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.42849 | − | 2.10712i | 0.0689682 | − | 0.101733i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.48548 | + | 12.9652i | 0.360563 | + | 0.624513i | 0.988054 | − | 0.154111i | \(-0.0492513\pi\) |
−0.627491 | + | 0.778624i | \(0.715918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3215 | 0.736304 | 0.368152 | − | 0.929766i | \(-0.379991\pi\) | ||||
0.368152 | + | 0.929766i | \(0.379991\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.0405 | + | 0.798113i | 0.529353 | + | 0.0382666i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.9537 | + | 32.8288i | −0.906679 | + | 1.57041i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.03657 | + | 10.4556i | 0.288110 | + | 0.499021i | 0.973359 | − | 0.229288i | \(-0.0736399\pi\) |
−0.685249 | + | 0.728309i | \(0.740307\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.02894 | − | 10.4424i | −0.286444 | − | 0.496135i | 0.686515 | − | 0.727116i | \(-0.259140\pi\) |
−0.972958 | + | 0.230981i | \(0.925806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.1301 | + | 36.5985i | −1.00166 | + | 1.73493i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.17217 | + | 4.48030i | 0.102740 | + | 0.211911i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.9502 | −0.799928 | −0.399964 | − | 0.916531i | \(-0.630977\pi\) | ||||
−0.399964 | + | 0.916531i | \(0.630977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5311 | − | 23.4366i | −0.637157 | − | 1.10359i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.92263 | − | 14.2786i | −0.325253 | − | 0.670866i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.88323 | − | 4.99390i | −0.134872 | − | 0.233605i | 0.790677 | − | 0.612234i | \(-0.209729\pi\) |
−0.925548 | + | 0.378629i | \(0.876396\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.72010 | + | 5.42376i | 0.0802872 | + | 0.253160i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.9138 | − | 31.0277i | 0.834330 | − | 1.44510i | −0.0602447 | − | 0.998184i | \(-0.519188\pi\) |
0.894575 | − | 0.446918i | \(-0.147479\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.53947 | + | 2.66645i | 0.0715455 | + | 0.123920i | 0.899579 | − | 0.436758i | \(-0.143874\pi\) |
−0.828033 | + | 0.560679i | \(0.810540\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 42.3032 | + | 3.05807i | 1.96177 | + | 0.141815i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.42738 | − | 2.47230i | 0.0660515 | − | 0.114404i | −0.831108 | − | 0.556110i | \(-0.812293\pi\) |
0.897160 | + | 0.441706i | \(0.145627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.0921 | − | 1.59703i | −1.01795 | − | 0.0735871i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.2865 | + | 24.7449i | −0.656893 | + | 1.13777i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.0981 | + | 36.5429i | −0.968045 | + | 1.67670i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.5738 | + | 5.02490i | 1.58303 | + | 0.230074i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.37376 | 0.199842 | 0.0999211 | − | 0.994995i | \(-0.468141\pi\) | ||||
0.0999211 | + | 0.994995i | \(0.468141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.820918 | 0.0374307 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.3046 | + | 42.0968i | −1.10361 | + | 1.91152i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.2678 | + | 26.4447i | 0.691852 | + | 1.19832i | 0.971230 | + | 0.238142i | \(0.0765383\pi\) |
−0.279378 | + | 0.960181i | \(0.590128\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.8210 | + | 1.79429i | 1.12244 | + | 0.0811407i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.3502 | − | 36.9797i | −0.963522 | − | 1.66887i | −0.713534 | − | 0.700621i | \(-0.752906\pi\) |
−0.249989 | − | 0.968249i | \(-0.580427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.01122 | 0.0905808 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.2654 | − | 20.6182i | 0.731074 | − | 0.926718i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.7703 | −1.01934 | −0.509670 | − | 0.860370i | \(-0.670232\pi\) | ||||
−0.509670 | + | 0.860370i | \(0.670232\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.63180 | + | 6.83223i | −0.206934 | + | 0.305242i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0843 | 1.07387 | 0.536933 | − | 0.843625i | \(-0.319583\pi\) | ||||
0.536933 | + | 0.843625i | \(0.319583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.9306 | −1.42089 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.8684 | − | 1.58085i | −0.971211 | − | 0.0702082i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.4700 | −1.08461 | −0.542307 | − | 0.840180i | \(-0.682449\pi\) | ||||
−0.542307 | + | 0.840180i | \(0.682449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.8024 | + | 22.7783i | −0.918450 | + | 1.00569i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.66700 | −0.0734566 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.47346 | − | 16.4085i | −0.416642 | − | 0.721646i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.4115 | − | 36.0086i | 1.07154 | − | 1.58060i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.3743 | − | 33.5573i | −0.848805 | − | 1.47017i | −0.882276 | − | 0.470733i | \(-0.843989\pi\) |
0.0334709 | − | 0.999440i | \(-0.489344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8473 | + | 22.2521i | −0.561771 | + | 0.973016i | 0.435571 | + | 0.900154i | \(0.356546\pi\) |
−0.997342 | + | 0.0728616i | \(0.976787\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.70626 | 0.335690 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.7719 | 0.772689 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.94887 | − | 12.4166i | −0.214763 | − | 0.538836i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.14226 | − | 5.44255i | 0.136106 | − | 0.235743i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.32127 | + | 16.1449i | −0.402993 | + | 0.698005i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.63178 | + | 9.78234i | −0.286182 | + | 0.422139i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.92878 | − | 8.53690i | 0.211905 | − | 0.367030i | −0.740406 | − | 0.672160i | \(-0.765367\pi\) |
0.952311 | + | 0.305130i | \(0.0986999\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.1809 | − | 20.9990i | −0.436902 | − | 0.901152i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.4032 | − | 47.4636i | −1.17382 | − | 2.03312i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.94133 | + | 6.82659i | −0.168519 | + | 0.291884i | −0.937899 | − | 0.346907i | \(-0.887232\pi\) |
0.769380 | + | 0.638791i | \(0.220565\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36.6720 | − | 5.32985i | −1.56512 | − | 0.227472i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.45185 | + | 9.44289i | 0.232257 | + | 0.402281i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.44662 | + | 0.610601i | 0.358539 | + | 0.0259186i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.1686 | + | 17.6125i | 0.430857 | + | 0.746266i | 0.996947 | − | 0.0780770i | \(-0.0248780\pi\) |
−0.566090 | + | 0.824343i | \(0.691545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.63533 | −0.280644 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.67750 | − | 3.94951i | 0.113044 | − | 0.166748i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.0910 | + | 17.4781i | −0.425284 | + | 0.736614i | −0.996447 | − | 0.0842230i | \(-0.973159\pi\) |
0.571163 | + | 0.820837i | \(0.306493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.0957 | + | 41.7350i | 1.01371 | + | 1.75580i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.0525 | − | 20.8755i | −0.505266 | − | 0.875146i | −0.999981 | − | 0.00609110i | \(-0.998061\pi\) |
0.494716 | − | 0.869055i | \(-0.335272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.22763 | + | 5.59042i | −0.135072 | + | 0.233952i | −0.925625 | − | 0.378442i | \(-0.876460\pi\) |
0.790553 | + | 0.612394i | \(0.209793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8075 | + | 20.3670i | −0.576816 | + | 0.850844i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 45.3846 | 1.89267 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.20385 | + | 15.9415i | 0.383161 | + | 0.663654i | 0.991512 | − | 0.130014i | \(-0.0415021\pi\) |
−0.608351 | + | 0.793668i | \(0.708169\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.7217 | − | 0.847356i | −0.487139 | − | 0.0352149i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.6489 | − | 25.3726i | −0.606695 | − | 1.05083i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.03517 | + | 0.877140i | 0.249523 | + | 0.0362653i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.8848 | + | 39.6376i | −0.944557 | + | 1.63602i | −0.187921 | + | 0.982184i | \(0.560175\pi\) |
−0.756636 | + | 0.653837i | \(0.773158\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.8895 | + | 36.1817i | 0.860737 | + | 1.49084i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.0006 | − | 28.8776i | −0.575909 | − | 1.18787i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.71630 | − | 15.0971i | 0.357935 | − | 0.619962i | −0.629680 | − | 0.776854i | \(-0.716814\pi\) |
0.987616 | + | 0.156892i | \(0.0501475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.3245 | + | 24.0798i | −0.668117 | + | 0.985520i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.72222 | + | 2.98297i | −0.0703680 | + | 0.121881i | −0.899063 | − | 0.437820i | \(-0.855751\pi\) |
0.828695 | + | 0.559701i | \(0.189084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1666 | + | 21.0731i | −0.496284 | + | 0.859590i | −0.999991 | − | 0.00428500i | \(-0.998636\pi\) |
0.503706 | + | 0.863875i | \(0.331969\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0738 | + | 35.3108i | 0.573128 | + | 1.43797i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.2531 | 0.660782 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.9215 | 0.808587 | 0.404294 | − | 0.914629i | \(-0.367517\pi\) | ||||
0.404294 | + | 0.914629i | \(0.367517\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.19997 | − | 3.81045i | 0.0890011 | − | 0.154154i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3848 | − | 35.3075i | −0.823334 | − | 1.42606i | −0.903186 | − | 0.429250i | \(-0.858778\pi\) |
0.0798515 | − | 0.996807i | \(-0.474555\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 36.3796 | − | 53.6625i | 1.46697 | − | 2.16388i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.5453 | − | 19.9970i | −0.464796 | − | 0.805050i | 0.534396 | − | 0.845234i | \(-0.320539\pi\) |
−0.999192 | + | 0.0401838i | \(0.987206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.1168 | 1.81340 | 0.906698 | − | 0.421780i | \(-0.138594\pi\) | ||||
0.906698 | + | 0.421780i | \(0.138594\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.4044 | + | 7.12697i | 1.30034 | + | 0.285996i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.0192 | −0.400768 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.8013 | + | 1.86516i | 1.03041 | + | 0.0744873i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.53870 | 0.0613518 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.7010 | −1.46104 | −0.730521 | − | 0.682890i | \(-0.760723\pi\) | ||||
−0.730521 | + | 0.682890i | \(0.760723\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.9764 | + | 30.9417i | −0.833738 | + | 1.22982i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −72.2135 | −2.86570 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.16757 | − | 11.6209i | 0.362664 | − | 0.459717i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.2449 | 0.562640 | 0.281320 | − | 0.959614i | \(-0.409228\pi\) | ||||
0.281320 | + | 0.959614i | \(0.409228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.0592 | − | 31.2795i | −0.712187 | − | 1.23354i | −0.964035 | − | 0.265777i | \(-0.914372\pi\) |
0.251848 | − | 0.967767i | \(-0.418962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −68.2724 | − | 4.93537i | −2.68822 | − | 0.194330i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.73327 | − | 6.46622i | −0.146770 | − | 0.254213i | 0.783262 | − | 0.621692i | \(-0.213554\pi\) |
−0.930032 | + | 0.367479i | \(0.880221\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.60449 | + | 9.70727i | −0.219996 | + | 0.381043i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.1090 | −1.56959 | −0.784794 | − | 0.619757i | \(-0.787231\pi\) | ||||
−0.784794 | + | 0.619757i | \(0.787231\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.56383 | −0.217397 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25.8617 | − | 3.75870i | −1.00896 | − | 0.146641i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.96459 | + | 6.86688i | −0.154439 | + | 0.267496i | −0.932855 | − | 0.360253i | \(-0.882690\pi\) |
0.778416 | + | 0.627749i | \(0.216024\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0643 | − | 19.1640i | 0.430352 | − | 0.745392i | −0.566551 | − | 0.824026i | \(-0.691723\pi\) |
0.996904 | + | 0.0786346i | \(0.0250560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.10518 | + | 0.0798930i | 0.0429218 | + | 0.00310279i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.86382 | − | 10.1564i | 0.227048 | − | 0.393259i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.71300 | − | 0.123832i | −0.0662285 | − | 0.00478761i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.5379 | + | 26.9124i | 0.599834 | + | 1.03894i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.60773 | − | 11.4449i | 0.254709 | − | 0.441169i | −0.710107 | − | 0.704094i | \(-0.751354\pi\) |
0.964817 | + | 0.262924i | \(0.0846869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 36.0705 | + | 7.93329i | 1.38836 | + | 0.305353i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0105 | + | 17.3387i | 0.384736 | + | 0.666382i | 0.991732 | − | 0.128323i | \(-0.0409593\pi\) |
−0.606997 | + | 0.794704i | \(0.707626\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.21498 | − | 4.56860i | −0.0848781 | − | 0.175069i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.7716 | − | 18.6569i | −0.412162 | − | 0.713886i | 0.582964 | − | 0.812498i | \(-0.301893\pi\) |
−0.995126 | + | 0.0986124i | \(0.968560\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.6267 | 1.01735 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.31265 | + | 6.83265i | 0.126385 | + | 0.260682i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.40182 | − | 5.89213i | 0.129599 | − | 0.224472i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.8693 | − | 37.8787i | −0.831947 | − | 1.44097i | −0.896492 | − | 0.443060i | \(-0.853893\pi\) |
0.0645449 | − | 0.997915i | \(-0.479440\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.8168 | + | 48.1802i | 1.05515 | + | 1.82758i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.88972 | − | 10.2013i | 0.223089 | − | 0.386402i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.87666 | − | 0.135662i | −0.0709818 | − | 0.00513123i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.2894 | 0.615244 | 0.307622 | − | 0.951509i | \(-0.400467\pi\) | ||||
0.307622 | + | 0.951509i | \(0.400467\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.17097 | + | 7.22434i | 0.157311 | + | 0.272471i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.4702 | − | 37.5703i | 0.959263 | − | 1.41498i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.4050 | − | 31.8784i | −0.691214 | − | 1.19722i | −0.971440 | − | 0.237284i | \(-0.923743\pi\) |
0.280226 | − | 0.959934i | \(-0.409591\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.66375 | − | 0.241807i | −0.0623956 | − | 0.00906847i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.4680 | − | 38.9157i | 0.841433 | − | 1.45741i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.55709 | − | 4.42901i | −0.0956298 | − | 0.165636i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.72096 | − | 5.48868i | 0.138962 | − | 0.204978i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.8787 | − | 27.5028i | 0.592177 | − | 1.02568i | −0.401762 | − | 0.915744i | \(-0.631602\pi\) |
0.993939 | − | 0.109936i | \(-0.0350646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.76670 | + | 20.1447i | 0.363227 | + | 0.749191i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.52723 | − | 11.3055i | 0.242415 | − | 0.419875i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.83596 | − | 4.91203i | 0.105180 | − | 0.182177i | −0.808632 | − | 0.588315i | \(-0.799791\pi\) |
0.913812 | + | 0.406138i | \(0.133125\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.5084 | + | 11.3287i | 0.907718 | + | 0.419580i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4370 | −0.459999 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.9853 | −0.885917 | −0.442958 | − | 0.896542i | \(-0.646071\pi\) | ||||
−0.442958 | + | 0.896542i | \(0.646071\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.9382 | − | 27.6059i | 0.587093 | − | 1.01687i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.162996 | + | 0.282317i | 0.00599590 | + | 0.0103852i | 0.869008 | − | 0.494798i | \(-0.164758\pi\) |
−0.863012 | + | 0.505184i | \(0.831425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.62074 | + | 5.40552i | 0.0962752 | + | 0.198577i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.3464 | + | 23.1166i | 0.489631 | + | 0.848066i | 0.999929 | − | 0.0119319i | \(-0.00379815\pi\) |
−0.510298 | + | 0.859998i | \(0.670465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0028 | 0.366473 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.18546 | + | 20.5372i | 0.299490 | + | 0.751416i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.3955 | 1.14564 | 0.572820 | − | 0.819681i | \(-0.305850\pi\) | ||||
0.572820 | + | 0.819681i | \(0.305850\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.8595 | − | 30.6492i | −0.541512 | − | 1.11692i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.8785 | −1.16018 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.144979 | −0.00526933 | −0.00263467 | − | 0.999997i | \(-0.500839\pi\) | ||||
−0.00263467 | + | 0.999997i | \(0.500839\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.1382 | − | 25.0361i | −0.440587 | − | 0.908753i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3801 | 0.485028 | 0.242514 | − | 0.970148i | \(-0.422028\pi\) | ||||
0.242514 | + | 0.970148i | \(0.422028\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.3121 | + | 1.64408i | 0.408989 | + | 0.0594417i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.60300 | −0.0939887 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.98750 | − | 10.3707i | −0.215915 | − | 0.373975i | 0.737640 | − | 0.675194i | \(-0.235940\pi\) |
−0.953555 | + | 0.301218i | \(0.902607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.1623 | − | 39.5241i | −0.690113 | − | 1.42342i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.9471 | + | 24.1571i | 0.501642 | + | 0.868869i | 0.999998 | + | 0.00189699i | \(0.000603830\pi\) |
−0.498356 | + | 0.866972i | \(0.666063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.0099 | − | 43.3185i | 0.898384 | − | 1.55605i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 63.8615 | 2.28808 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4125 | −0.444155 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.43577 | − | 7.04707i | 0.229996 | − | 0.251842i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.2489 | + | 38.5363i | −0.794099 | + | 1.37542i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0522535 | − | 0.0905057i | 0.00186264 | − | 0.00322618i | −0.865093 | − | 0.501612i | \(-0.832740\pi\) |
0.866955 | + | 0.498386i | \(0.166074\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.70684 | − | 13.8335i | −0.238770 | − | 0.492486i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.60827 | + | 6.24971i | −0.128133 | + | 0.221934i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 39.3848 | − | 58.0953i | 1.39683 | − | 2.06043i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.5235 | − | 30.3516i | −0.620715 | − | 1.07511i | −0.989353 | − | 0.145537i | \(-0.953509\pi\) |
0.368638 | − | 0.929573i | \(-0.379824\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.12353 | − | 7.14216i | 0.145880 | − | 0.252671i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.4899 | + | 33.8461i | 0.476644 | + | 1.19589i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.9576 | + | 18.9791i | 0.386685 | + | 0.669758i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.7928 | − | 26.2456i | 0.626335 | − | 0.923888i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.1259 | + | 38.3233i | 0.777907 | + | 1.34737i | 0.933146 | + | 0.359497i | \(0.117052\pi\) |
−0.155239 | + | 0.987877i | \(0.549615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.903637 | −0.0317310 | −0.0158655 | − | 0.999874i | \(-0.505050\pi\) | ||||
−0.0158655 | + | 0.999874i | \(0.505050\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.10098 | − | 0.585614i | −0.284114 | − | 0.0205384i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.9972 | − | 43.2964i | 0.875613 | − | 1.51661i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.7132 | − | 58.3930i | −1.17948 | − | 2.04291i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.1783 | − | 40.1459i | −0.808927 | − | 1.40110i | −0.913608 | − | 0.406596i | \(-0.866716\pi\) |
0.104681 | − | 0.994506i | \(-0.466618\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.4915 | − | 26.8320i | 0.539998 | − | 0.935305i | −0.458905 | − | 0.888485i | \(-0.651758\pi\) |
0.998903 | − | 0.0468193i | \(-0.0149085\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.5114 | − | 27.8686i | −0.470407 | − | 0.970259i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.0923 | 0.872544 | 0.436272 | − | 0.899815i | \(-0.356299\pi\) | ||||
0.436272 | + | 0.899815i | \(0.356299\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.1853 | − | 36.6941i | −0.735798 | − | 1.27444i | −0.954373 | − | 0.298619i | \(-0.903474\pi\) |
0.218575 | − | 0.975820i | \(-0.429859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.27389 | − | 8.81531i | −0.148260 | − | 0.305800i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.29123 | + | 14.3608i | 0.286930 | + | 0.496977i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.6595 | − | 27.0018i | 0.852357 | − | 0.933318i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.36843 | + | 2.37020i | −0.0472435 | + | 0.0818282i | −0.888680 | − | 0.458528i | \(-0.848377\pi\) |
0.841437 | + | 0.540356i | \(0.181710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8133 | + | 22.1933i | 0.441839 | + | 0.765287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.5320 | + | 1.33967i | 0.638277 | + | 0.0461407i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.0237 | + | 38.1461i | −0.757637 | + | 1.31227i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.1338 | + | 2.97354i | 1.41171 | + | 0.102052i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.48615 | − | 7.77024i | 0.153783 | − | 0.266360i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.59273 | − | 7.95485i | 0.157252 | − | 0.272369i | −0.776625 | − | 0.629964i | \(-0.783070\pi\) |
0.933877 | + | 0.357595i | \(0.116403\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.9447 | + | 57.5680i | 0.784694 | + | 1.96878i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.1221 | 0.414084 | 0.207042 | − | 0.978332i | \(-0.433616\pi\) | ||||
0.207042 | + | 0.978332i | \(0.433616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.83252 | 0.233123 | 0.116561 | − | 0.993183i | \(-0.462813\pi\) | ||||
0.116561 | + | 0.993183i | \(0.462813\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.2595 | + | 45.4827i | −0.893882 | + | 1.54825i | −0.0587005 | + | 0.998276i | \(0.518696\pi\) |
−0.835182 | + | 0.549974i | \(0.814638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.6981 | − | 75.6873i | −1.48578 | − | 2.57345i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.2967 | − | 1.97326i | −0.927045 | − | 0.0670155i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.704930 | + | 1.22097i | 0.0239131 | + | 0.0414187i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.40249 | 0.250824 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.5166 | + | 38.9309i | 0.525157 | + | 1.31761i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.1564 | 1.08584 | 0.542922 | − | 0.839783i | \(-0.317318\pi\) | ||||
0.542922 | + | 0.839783i | \(0.317318\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.0828 | − | 29.6235i | 0.677375 | − | 0.999175i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.9101 | 0.569715 | 0.284858 | − | 0.958570i | \(-0.408054\pi\) | ||||
0.284858 | + | 0.958570i | \(0.408054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.9999 | −0.471135 | −0.235567 | − | 0.971858i | \(-0.575695\pi\) | ||||
−0.235567 | + | 0.971858i | \(0.575695\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.7828 | − | 1.93611i | −0.900295 | − | 0.0650818i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.4566 | −1.49270 | −0.746352 | − | 0.665551i | \(-0.768197\pi\) | ||||
−0.746352 | + | 0.665551i | \(0.768197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.27075 | − | 22.0198i | −0.176577 | − | 0.737691i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44.7109 | 1.49619 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.8713 | + | 20.5617i | 0.396814 | + | 0.687303i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.62567 | − | 5.34812i | 0.121058 | − | 0.178569i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.46271 | − | 11.1937i | −0.215543 | − | 0.373332i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.37624 | − | 11.0440i | 0.212423 | − | 0.367928i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −46.8826 | −1.55843 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.4478 | −0.546142 | −0.273071 | − | 0.961994i | \(-0.588039\pi\) | ||||
−0.273071 | + | 0.961994i | \(0.588039\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.0506 | + | 21.6136i | −0.565534 | + | 0.716878i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1577 | + | 43.5745i | −0.833513 | + | 1.44369i | 0.0617228 | + | 0.998093i | \(0.480341\pi\) |
−0.895236 | + | 0.445593i | \(0.852993\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.26987 | − | 16.0559i | 0.306788 | − | 0.531372i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −41.7749 | + | 61.6209i | −1.38104 | + | 2.03712i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.2722 | + | 50.7009i | −0.965600 | + | 1.67247i | −0.257606 | + | 0.966250i | \(0.582934\pi\) |
−0.707994 | + | 0.706219i | \(0.750400\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.00902 | + | 18.5820i | 0.296857 | + | 0.612296i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.44124 | − | 2.49630i | −0.0474391 | − | 0.0821669i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.99370 | − | 8.64933i | 0.164192 | − | 0.284388i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.890160 | + | 1.12838i | −0.0292367 | + | 0.0370608i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.318672 | + | 0.551956i | 0.0104553 | + | 0.0181091i | 0.871206 | − | 0.490918i | \(-0.163339\pi\) |
−0.860750 | + | 0.509027i | \(0.830005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.7771 | + | 1.14052i | 0.516521 | + | 0.0373389i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.79291 | − | 8.30156i | −0.156745 | − | 0.271490i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0780 | −0.623250 | −0.311625 | − | 0.950205i | \(-0.600873\pi\) | ||||
−0.311625 | + | 0.950205i | \(0.600873\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.4510 | − | 19.8412i | 0.438958 | − | 0.647493i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.8153 | − | 25.6609i | 0.482965 | − | 0.836521i | −0.516843 | − | 0.856080i | \(-0.672893\pi\) |
0.999809 | + | 0.0195594i | \(0.00622634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.3436 | − | 59.4848i | −1.11838 | − | 1.93709i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.1681 | − | 29.7360i | −0.557888 | − | 0.966290i | −0.997673 | − | 0.0681867i | \(-0.978279\pi\) |
0.439785 | − | 0.898103i | \(-0.355055\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.54461 | + | 4.40740i | −0.0826017 | + | 0.143070i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.78015 | + | 2.62584i | −0.0577252 | + | 0.0851488i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.6361 | 1.73744 | 0.868722 | − | 0.495301i | \(-0.164942\pi\) | ||||
0.868722 | + | 0.495301i | \(0.164942\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.7163 | + | 42.8099i | 0.799800 | + | 1.38529i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.98230 | − | 0.577036i | −0.258031 | − | 0.0186529i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.26272 | − | 16.0435i | −0.298798 | − | 0.517533i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.95090 | + | 14.9307i | 0.191765 | + | 0.481136i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.8049 | + | 20.4467i | −0.380014 | + | 0.658204i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.5629 | + | 25.2236i | 0.468310 | + | 0.811136i | 0.999344 | − | 0.0362139i | \(-0.0115298\pi\) |
−0.531034 | + | 0.847350i | \(0.678196\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.91220 | + | 10.1319i | 0.157803 | + | 0.325483i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.9191 | + | 20.6446i | −0.382503 | + | 0.662515i | −0.991419 | − | 0.130719i | \(-0.958271\pi\) |
0.608916 | + | 0.793235i | \(0.291605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.03587 | − | 5.95318i | 0.129251 | − | 0.190654i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.0842 | + | 33.0547i | −0.610556 | + | 1.05751i | 0.380591 | + | 0.924744i | \(0.375721\pi\) |
−0.991147 | + | 0.132771i | \(0.957613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.2771 | − | 26.4607i | 0.488258 | − | 0.845688i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −46.7608 | − | 6.79613i | −1.49296 | − | 0.216984i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.57537 | −0.241617 | −0.120808 | − | 0.992676i | \(-0.538549\pi\) | ||||
−0.120808 | + | 0.992676i | \(0.538549\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −64.4726 | −2.05427 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.2607 | + | 62.8054i | −1.15302 | + | 1.99709i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.68952 | + | 8.12248i | 0.148967 | + | 0.258019i | 0.930846 | − | 0.365411i | \(-0.119072\pi\) |
−0.781879 | + | 0.623431i | \(0.785738\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.200473 | − | 0.295711i | 0.00636181 | − | 0.00938411i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.2219 | + | 50.6138i | 0.926397 | + | 1.60457i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.43658 | 0.267189 | 0.133595 | − | 0.991036i | \(-0.457348\pi\) | ||||
0.133595 | + | 0.991036i | \(0.457348\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.92372 | − | 5.39140i | 0.155780 | − | 0.170576i |
(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 | 1764.2.l.j.961.4 | 24 | ||
3.2 | odd | 2 | 5292.2.l.j.3313.11 | 24 | |||
7.2 | even | 3 | 1764.2.j.i.1177.12 | yes | 24 | ||
7.3 | odd | 6 | 1764.2.i.j.1537.9 | 24 | |||
7.4 | even | 3 | 1764.2.i.j.1537.4 | 24 | |||
7.5 | odd | 6 | 1764.2.j.i.1177.1 | yes | 24 | ||
7.6 | odd | 2 | inner | 1764.2.l.j.961.9 | 24 | ||
9.4 | even | 3 | 1764.2.i.j.373.4 | 24 | |||
9.5 | odd | 6 | 5292.2.i.j.1549.2 | 24 | |||
21.2 | odd | 6 | 5292.2.j.i.3529.2 | 24 | |||
21.5 | even | 6 | 5292.2.j.i.3529.11 | 24 | |||
21.11 | odd | 6 | 5292.2.i.j.2125.2 | 24 | |||
21.17 | even | 6 | 5292.2.i.j.2125.11 | 24 | |||
21.20 | even | 2 | 5292.2.l.j.3313.2 | 24 | |||
63.4 | even | 3 | inner | 1764.2.l.j.949.4 | 24 | ||
63.5 | even | 6 | 5292.2.j.i.1765.11 | 24 | |||
63.13 | odd | 6 | 1764.2.i.j.373.9 | 24 | |||
63.23 | odd | 6 | 5292.2.j.i.1765.2 | 24 | |||
63.31 | odd | 6 | inner | 1764.2.l.j.949.9 | 24 | ||
63.32 | odd | 6 | 5292.2.l.j.361.11 | 24 | |||
63.40 | odd | 6 | 1764.2.j.i.589.1 | ✓ | 24 | ||
63.41 | even | 6 | 5292.2.i.j.1549.11 | 24 | |||
63.58 | even | 3 | 1764.2.j.i.589.12 | yes | 24 | ||
63.59 | even | 6 | 5292.2.l.j.361.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.i.j.373.4 | 24 | 9.4 | even | 3 | |||
1764.2.i.j.373.9 | 24 | 63.13 | odd | 6 | |||
1764.2.i.j.1537.4 | 24 | 7.4 | even | 3 | |||
1764.2.i.j.1537.9 | 24 | 7.3 | odd | 6 | |||
1764.2.j.i.589.1 | ✓ | 24 | 63.40 | odd | 6 | ||
1764.2.j.i.589.12 | yes | 24 | 63.58 | even | 3 | ||
1764.2.j.i.1177.1 | yes | 24 | 7.5 | odd | 6 | ||
1764.2.j.i.1177.12 | yes | 24 | 7.2 | even | 3 | ||
1764.2.l.j.949.4 | 24 | 63.4 | even | 3 | inner | ||
1764.2.l.j.949.9 | 24 | 63.31 | odd | 6 | inner | ||
1764.2.l.j.961.4 | 24 | 1.1 | even | 1 | trivial | ||
1764.2.l.j.961.9 | 24 | 7.6 | odd | 2 | inner | ||
5292.2.i.j.1549.2 | 24 | 9.5 | odd | 6 | |||
5292.2.i.j.1549.11 | 24 | 63.41 | even | 6 | |||
5292.2.i.j.2125.2 | 24 | 21.11 | odd | 6 | |||
5292.2.i.j.2125.11 | 24 | 21.17 | even | 6 | |||
5292.2.j.i.1765.2 | 24 | 63.23 | odd | 6 | |||
5292.2.j.i.1765.11 | 24 | 63.5 | even | 6 | |||
5292.2.j.i.3529.2 | 24 | 21.2 | odd | 6 | |||
5292.2.j.i.3529.11 | 24 | 21.5 | even | 6 | |||
5292.2.l.j.361.2 | 24 | 63.59 | even | 6 | |||
5292.2.l.j.361.11 | 24 | 63.32 | odd | 6 | |||
5292.2.l.j.3313.2 | 24 | 21.20 | even | 2 | |||
5292.2.l.j.3313.11 | 24 | 3.2 | odd | 2 |