Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1503,2,Mod(1502,1503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1503, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1503.1502");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1503 = 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1503.c (of order \(2\), degree \(1\), 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: | \(12.0015154238\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1502.16 | ||
Character | \(\chi\) | \(=\) | 1503.1502 |
Dual form | 1503.2.c.a.1502.15 |
$q$-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 \(\left(\mathbb{Z}/1503\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(335\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16730i | 1.53251i | 0.642537 | + | 0.766255i | \(0.277882\pi\) | ||||
−0.642537 | + | 0.766255i | \(0.722118\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.69717 | −1.34859 | ||||||||
\(5\) | −1.88079 | −0.841117 | −0.420558 | − | 0.907265i | \(-0.638166\pi\) | ||||
−0.420558 | + | 0.907265i | \(0.638166\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.73517 | −1.41176 | −0.705880 | − | 0.708331i | \(-0.749448\pi\) | ||||
−0.705880 | + | 0.708331i | \(0.749448\pi\) | |||||||
\(8\) | − | 1.51098i | − | 0.534211i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 4.07624i | − | 1.28902i | ||||||
\(11\) | 1.85446i | 0.559139i | 0.960125 | + | 0.279570i | \(0.0901918\pi\) | ||||
−0.960125 | + | 0.279570i | \(0.909808\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.16402i | 1.15489i | 0.816429 | + | 0.577446i | \(0.195950\pi\) | ||||
−0.816429 | + | 0.577446i | \(0.804050\pi\) | |||||||
\(14\) | − | 8.09521i | − | 2.16354i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.11961 | −0.529902 | ||||||||
\(17\) | −2.49228 | −0.604466 | −0.302233 | − | 0.953234i | \(-0.597732\pi\) | ||||
−0.302233 | + | 0.953234i | \(0.597732\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.11128 | −0.484361 | −0.242181 | − | 0.970231i | \(-0.577863\pi\) | ||||
−0.242181 | + | 0.970231i | \(0.577863\pi\) | |||||||
\(20\) | 5.07283 | 1.13432 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.01915 | −0.856886 | ||||||||
\(23\) | 8.93205 | 1.86246 | 0.931230 | − | 0.364431i | \(-0.118736\pi\) | ||||
0.931230 | + | 0.364431i | \(0.118736\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.46261 | −0.292522 | ||||||||
\(26\) | −9.02466 | −1.76988 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.0744 | 1.90388 | ||||||||
\(29\) | − | 6.40845i | − | 1.19002i | −0.803718 | − | 0.595010i | \(-0.797148\pi\) | ||
0.803718 | − | 0.595010i | \(-0.202852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50442 | −0.270201 | −0.135100 | − | 0.990832i | \(-0.543136\pi\) | ||||
−0.135100 | + | 0.990832i | \(0.543136\pi\) | |||||||
\(32\) | − | 7.61577i | − | 1.34629i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.40150i | − | 0.926350i | ||||||
\(35\) | 7.02508 | 1.18746 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.34193i | − | 0.385012i | −0.981296 | − | 0.192506i | \(-0.938339\pi\) | ||
0.981296 | − | 0.192506i | \(-0.0616614\pi\) | |||||||
\(38\) | − | 4.57577i | − | 0.742289i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.84184i | 0.449334i | ||||||||
\(41\) | 8.37955 | 1.30867 | 0.654333 | − | 0.756207i | \(-0.272950\pi\) | ||||
0.654333 | + | 0.756207i | \(0.272950\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.29965i | − | 1.41818i | −0.705116 | − | 0.709092i | \(-0.749105\pi\) | ||
0.705116 | − | 0.709092i | \(-0.250895\pi\) | |||||||
\(44\) | − | 5.00178i | − | 0.754047i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 19.3584i | 2.85424i | ||||||||
\(47\) | − | 2.45945i | − | 0.358748i | −0.983781 | − | 0.179374i | \(-0.942593\pi\) | ||
0.983781 | − | 0.179374i | \(-0.0574071\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.95147 | 0.993068 | ||||||||
\(50\) | − | 3.16991i | − | 0.448293i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 11.2311i | − | 1.55747i | ||||||
\(53\) | −6.33808 | −0.870602 | −0.435301 | − | 0.900285i | \(-0.643358\pi\) | ||||
−0.435301 | + | 0.900285i | \(0.643358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.48785i | − | 0.470301i | ||||||
\(56\) | 5.64376i | 0.754179i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13.8890 | 1.82372 | ||||||||
\(59\) | 9.45469 | 1.23090 | 0.615448 | − | 0.788178i | \(-0.288975\pi\) | ||||
0.615448 | + | 0.788178i | \(0.288975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.660137 | 0.0845219 | 0.0422610 | − | 0.999107i | \(-0.486544\pi\) | ||||
0.0422610 | + | 0.999107i | \(0.486544\pi\) | |||||||
\(62\) | − | 3.26051i | − | 0.414086i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.2664 | 1.53330 | ||||||||
\(65\) | − | 7.83167i | − | 0.971399i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.29499i | 0.524717i | 0.964970 | + | 0.262359i | \(0.0845003\pi\) | ||||
−0.964970 | + | 0.262359i | \(0.915500\pi\) | |||||||
\(68\) | 6.72210 | 0.815174 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.2254i | 1.81979i | ||||||||
\(71\) | −1.12478 | −0.133487 | −0.0667436 | − | 0.997770i | \(-0.521261\pi\) | ||||
−0.0667436 | + | 0.997770i | \(0.521261\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.87565i | 0.804734i | 0.915478 | + | 0.402367i | \(0.131812\pi\) | ||||
−0.915478 | + | 0.402367i | \(0.868188\pi\) | |||||||
\(74\) | 5.07567 | 0.590034 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.69449 | 0.653203 | ||||||||
\(77\) | − | 6.92670i | − | 0.789371i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.70341i | 0.304158i | 0.988368 | + | 0.152079i | \(0.0485968\pi\) | ||||
−0.988368 | + | 0.152079i | \(0.951403\pi\) | |||||||
\(80\) | 3.98655 | 0.445709 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.1610i | 2.00554i | ||||||||
\(83\) | −7.93347 | −0.870811 | −0.435406 | − | 0.900234i | \(-0.643395\pi\) | ||||
−0.435406 | + | 0.900234i | \(0.643395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.68746 | 0.508427 | ||||||||
\(86\) | 20.1551 | 2.17338 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.80204 | 0.298699 | ||||||||
\(89\) | − | 15.3639i | − | 1.62857i | −0.580462 | − | 0.814287i | \(-0.697128\pi\) | ||
0.580462 | − | 0.814287i | \(-0.302872\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15.5533i | − | 1.63043i | ||||||
\(92\) | −24.0913 | −2.51169 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.33036 | 0.549784 | ||||||||
\(95\) | 3.97089 | 0.407405 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9800 | −1.31792 | −0.658961 | − | 0.752177i | \(-0.729004\pi\) | ||||
−0.658961 | + | 0.752177i | \(0.729004\pi\) | |||||||
\(98\) | 15.0659i | 1.52189i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.94492 | 0.394492 | ||||||||
\(101\) | 10.4273 | 1.03755 | 0.518776 | − | 0.854910i | \(-0.326388\pi\) | ||||
0.518776 | + | 0.854910i | \(0.326388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.181534i | − | 0.0178871i | −0.999960 | − | 0.00894354i | \(-0.997153\pi\) | ||
0.999960 | − | 0.00894354i | \(-0.00284686\pi\) | |||||||
\(104\) | 6.29174 | 0.616956 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 13.7365i | − | 1.33421i | ||||||
\(107\) | 3.16099i | 0.305584i | 0.988258 | + | 0.152792i | \(0.0488265\pi\) | ||||
−0.988258 | + | 0.152792i | \(0.951174\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.4737i | − | 1.00320i | −0.865099 | − | 0.501601i | \(-0.832745\pi\) | ||
0.865099 | − | 0.501601i | \(-0.167255\pi\) | |||||||
\(110\) | 7.55920 | 0.720742 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.91709 | 0.748094 | ||||||||
\(113\) | −18.1883 | −1.71102 | −0.855508 | − | 0.517790i | \(-0.826755\pi\) | ||||
−0.855508 | + | 0.517790i | \(0.826755\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.7993 | −1.56655 | ||||||||
\(116\) | 17.2847i | 1.60484i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.4911i | 1.88636i | ||||||||
\(119\) | 9.30907 | 0.853361 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.56100 | 0.687363 | ||||||||
\(122\) | 1.43071i | 0.129531i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.05767 | 0.364389 | ||||||||
\(125\) | 12.1548 | 1.08716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.5671 | −1.91377 | −0.956885 | − | 0.290469i | \(-0.906189\pi\) | ||||
−0.956885 | + | 0.290469i | \(0.906189\pi\) | |||||||
\(128\) | 11.3534i | 1.00351i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 16.9735 | 1.48868 | ||||||||
\(131\) | −17.2904 | −1.51067 | −0.755335 | − | 0.655339i | \(-0.772526\pi\) | ||||
−0.755335 | + | 0.655339i | \(0.772526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.88599 | 0.683802 | ||||||||
\(134\) | −9.30852 | −0.804134 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.76578i | 0.322913i | ||||||||
\(137\) | 9.75406i | 0.833346i | 0.909057 | + | 0.416673i | \(0.136804\pi\) | ||||
−0.909057 | + | 0.416673i | \(0.863196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.50529i | 0.721410i | 0.932680 | + | 0.360705i | \(0.117464\pi\) | ||||
−0.932680 | + | 0.360705i | \(0.882536\pi\) | |||||||
\(140\) | −18.9479 | −1.60139 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 2.43774i | − | 0.204571i | ||||||
\(143\) | −7.72199 | −0.645745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0530i | 1.00095i | ||||||||
\(146\) | −14.9016 | −1.23326 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.31660i | 0.519221i | ||||||||
\(149\) | 3.84755 | 0.315203 | 0.157602 | − | 0.987503i | \(-0.449624\pi\) | ||||
0.157602 | + | 0.987503i | \(0.449624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.0238i | − | 0.897100i | −0.893758 | − | 0.448550i | \(-0.851941\pi\) | ||
0.893758 | − | 0.448550i | \(-0.148059\pi\) | |||||||
\(152\) | 3.19010i | 0.258751i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.0122 | 1.20972 | ||||||||
\(155\) | 2.82950 | 0.227271 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9707 | 0.875559 | 0.437779 | − | 0.899082i | \(-0.355765\pi\) | ||||
0.437779 | + | 0.899082i | \(0.355765\pi\) | |||||||
\(158\) | −5.85910 | −0.466125 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.3237i | 1.13239i | ||||||||
\(161\) | −33.3627 | −2.62935 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.3073i | − | 1.04231i | −0.853463 | − | 0.521154i | \(-0.825502\pi\) | ||
0.853463 | − | 0.521154i | \(-0.174498\pi\) | |||||||
\(164\) | −22.6011 | −1.76485 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 17.1942i | − | 1.33453i | ||||||
\(167\) | −5.93764 | − | 11.4780i | −0.459468 | − | 0.888194i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.33906 | −0.333774 | ||||||||
\(170\) | 10.1591i | 0.779169i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 25.0828i | 1.91254i | ||||||||
\(173\) | 11.8056i | 0.897561i | 0.893642 | + | 0.448781i | \(0.148142\pi\) | ||||
−0.893642 | + | 0.448781i | \(0.851858\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.46310 | 0.412972 | ||||||||
\(176\) | − | 3.93072i | − | 0.296289i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 33.2982 | 2.49581 | ||||||||
\(179\) | 7.65053i | 0.571828i | 0.958255 | + | 0.285914i | \(0.0922971\pi\) | ||||
−0.958255 | + | 0.285914i | \(0.907703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.8712 | −1.77433 | −0.887167 | − | 0.461449i | \(-0.847330\pi\) | ||||
−0.887167 | + | 0.461449i | \(0.847330\pi\) | |||||||
\(182\) | 33.7086 | 2.49865 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 13.4961i | − | 0.994948i | ||||||
\(185\) | 4.40470i | 0.323840i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.62182i | − | 0.337981i | ||||||
\(188\) | 6.63356i | 0.483802i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.60609i | 0.624351i | ||||||||
\(191\) | 9.08004i | 0.657009i | 0.944502 | + | 0.328504i | \(0.106545\pi\) | ||||
−0.944502 | + | 0.328504i | \(0.893455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 26.0841i | − | 1.87757i | −0.344498 | − | 0.938787i | \(-0.611951\pi\) | ||
0.344498 | − | 0.938787i | \(-0.388049\pi\) | |||||||
\(194\) | − | 28.1316i | − | 2.01973i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.7493 | −1.33924 | ||||||||
\(197\) | 16.2096 | 1.15488 | 0.577442 | − | 0.816432i | \(-0.304051\pi\) | ||||
0.577442 | + | 0.816432i | \(0.304051\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.94229 | −0.350350 | −0.175175 | − | 0.984537i | \(-0.556049\pi\) | ||||
−0.175175 | + | 0.984537i | \(0.556049\pi\) | |||||||
\(200\) | 2.20998i | 0.156269i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.5990i | 1.59006i | ||||||||
\(203\) | 23.9366i | 1.68002i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.7602 | −1.10074 | ||||||||
\(206\) | 0.393438 | 0.0274121 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 8.82609i | − | 0.611979i | ||||||
\(209\) | − | 3.91528i | − | 0.270826i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.7402 | −1.56550 | −0.782749 | − | 0.622338i | \(-0.786183\pi\) | ||||
−0.782749 | + | 0.622338i | \(0.786183\pi\) | |||||||
\(212\) | 17.0949 | 1.17408 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.85080 | −0.468311 | ||||||||
\(215\) | 17.4907i | 1.19286i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.61924 | 0.381459 | ||||||||
\(218\) | 22.6997 | 1.53742 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.40733i | 0.634242i | ||||||||
\(221\) | − | 10.3779i | − | 0.698093i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.06331 | −0.472994 | −0.236497 | − | 0.971632i | \(-0.575999\pi\) | ||||
−0.236497 | + | 0.971632i | \(0.575999\pi\) | |||||||
\(224\) | 28.4462i | 1.90064i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 39.4195i | − | 2.62215i | ||||||
\(227\) | −3.92199 | −0.260312 | −0.130156 | − | 0.991494i | \(-0.541548\pi\) | ||||
−0.130156 | + | 0.991494i | \(0.541548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9412 | 0.789094 | 0.394547 | − | 0.918876i | \(-0.370902\pi\) | ||||
0.394547 | + | 0.918876i | \(0.370902\pi\) | |||||||
\(230\) | − | 36.4092i | − | 2.40075i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.68303 | −0.635722 | ||||||||
\(233\) | 17.0336i | 1.11591i | 0.829873 | + | 0.557953i | \(0.188413\pi\) | ||||
−0.829873 | + | 0.557953i | \(0.811587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.62572i | 0.301749i | ||||||||
\(236\) | −25.5009 | −1.65997 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 20.1755i | 1.30778i | ||||||||
\(239\) | 11.9142i | 0.770668i | 0.922777 | + | 0.385334i | \(0.125914\pi\) | ||||
−0.922777 | + | 0.385334i | \(0.874086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.49274i | − | 0.418234i | −0.977891 | − | 0.209117i | \(-0.932941\pi\) | ||
0.977891 | − | 0.209117i | \(-0.0670589\pi\) | |||||||
\(242\) | 16.3869i | 1.05339i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.78050 | −0.113985 | ||||||||
\(245\) | −13.0743 | −0.835286 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.79142i | − | 0.559385i | ||||||
\(248\) | 2.27314i | 0.144344i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 26.3431i | 1.66609i | ||||||||
\(251\) | 0.0745657i | 0.00470655i | 0.999997 | + | 0.00235327i | \(0.000749071\pi\) | ||||
−0.999997 | + | 0.00235327i | \(0.999251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.5641i | 1.04138i | ||||||||
\(254\) | − | 46.7423i | − | 2.93287i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.0733770 | −0.00458606 | ||||||||
\(257\) | 13.8692 | 0.865140 | 0.432570 | − | 0.901600i | \(-0.357607\pi\) | ||||
0.432570 | + | 0.901600i | \(0.357607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.74752i | 0.543544i | ||||||||
\(260\) | 21.1234i | 1.31001i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 37.4734i | − | 2.31512i | ||||||
\(263\) | 5.00657i | 0.308719i | 0.988015 | + | 0.154359i | \(0.0493313\pi\) | ||||
−0.988015 | + | 0.154359i | \(0.950669\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.9206 | 0.732278 | ||||||||
\(266\) | 17.0913i | 1.04793i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 11.5843i | − | 0.707626i | ||||||
\(269\) | 26.1035 | 1.59156 | 0.795778 | − | 0.605588i | \(-0.207062\pi\) | ||||
0.795778 | + | 0.605588i | \(0.207062\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2610i | 0.805550i | 0.915299 | + | 0.402775i | \(0.131954\pi\) | ||||
−0.915299 | + | 0.402775i | \(0.868046\pi\) | |||||||
\(272\) | 5.28265 | 0.320308 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.1399 | −1.27711 | ||||||||
\(275\) | − | 2.71235i | − | 0.163561i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0561i | 1.08489i | 0.840092 | + | 0.542443i | \(0.182501\pi\) | ||||
−0.840092 | + | 0.542443i | \(0.817499\pi\) | |||||||
\(278\) | −18.4335 | −1.10557 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 10.6147i | − | 0.634352i | ||||||
\(281\) | − | 21.4639i | − | 1.28043i | −0.768195 | − | 0.640215i | \(-0.778845\pi\) | ||
0.768195 | − | 0.640215i | \(-0.221155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.1803 | −1.31848 | −0.659242 | − | 0.751930i | \(-0.729123\pi\) | ||||
−0.659242 | + | 0.751930i | \(0.729123\pi\) | |||||||
\(284\) | 3.03374 | 0.180019 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 16.7358i | − | 0.989611i | ||||||
\(287\) | −31.2990 | −1.84752 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7886 | −0.634621 | ||||||||
\(290\) | −26.1224 | −1.53396 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 18.5448i | − | 1.08525i | ||||||
\(293\) | − | 20.2245i | − | 1.18153i | −0.806845 | − | 0.590763i | \(-0.798827\pi\) | ||
0.806845 | − | 0.590763i | \(-0.201173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.7823 | −1.03533 | ||||||||
\(296\) | −3.53861 | −0.205678 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.33877i | 0.483052i | ||||||||
\(299\) | 37.1932i | 2.15094i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.7357i | 2.00214i | ||||||||
\(302\) | 23.8917 | 1.37481 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.47509 | 0.256664 | ||||||||
\(305\) | −1.24158 | −0.0710928 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.32662i | 0.246933i | 0.992349 | + | 0.123467i | \(0.0394012\pi\) | ||||
−0.992349 | + | 0.123467i | \(0.960599\pi\) | |||||||
\(308\) | 18.6825i | 1.06453i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.13235i | 0.348294i | ||||||||
\(311\) | − | 15.5067i | − | 0.879303i | −0.898169 | − | 0.439651i | \(-0.855102\pi\) | ||
0.898169 | − | 0.439651i | \(-0.144898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.663701i | 0.0375146i | 0.999824 | + | 0.0187573i | \(0.00597098\pi\) | ||||
−0.999824 | + | 0.0187573i | \(0.994029\pi\) | |||||||
\(314\) | 23.7768i | 1.34180i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 7.29157i | − | 0.410183i | ||||||
\(317\) | 2.78217i | 0.156262i | 0.996943 | + | 0.0781310i | \(0.0248952\pi\) | ||||
−0.996943 | + | 0.0781310i | \(0.975105\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.8842 | 0.665387 | ||||||||
\(320\) | −23.0706 | −1.28969 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 72.3068i | − | 4.02950i | ||||||
\(323\) | 5.26190 | 0.292780 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.09035i | − | 0.337832i | ||||||
\(326\) | 28.8409 | 1.59735 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 12.6613i | − | 0.699104i | ||||||
\(329\) | 9.18645i | 0.506466i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 34.2735i | − | 1.88384i | −0.335838 | − | 0.941920i | \(-0.609019\pi\) | ||
0.335838 | − | 0.941920i | \(-0.390981\pi\) | |||||||
\(332\) | 21.3979 | 1.17436 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.8762 | − | 12.8686i | 1.36117 | − | 0.704140i | ||||
\(335\) | − | 8.07800i | − | 0.441348i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.64893 | 0.525611 | 0.262805 | − | 0.964849i | \(-0.415352\pi\) | ||||
0.262805 | + | 0.964849i | \(0.415352\pi\) | |||||||
\(338\) | − | 9.40404i | − | 0.511512i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.6429 | −0.685657 | ||||||||
\(341\) | − | 2.78987i | − | 0.151080i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.181258 | 0.00978701 | ||||||||
\(344\) | −14.0516 | −0.757610 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.5862 | −1.37552 | ||||||||
\(347\) | −16.0340 | −0.860750 | −0.430375 | − | 0.902650i | \(-0.641619\pi\) | ||||
−0.430375 | + | 0.902650i | \(0.641619\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.5841i | − | 1.10184i | −0.834558 | − | 0.550921i | \(-0.814277\pi\) | ||
0.834558 | − | 0.550921i | \(-0.185723\pi\) | |||||||
\(350\) | 11.8402i | 0.632883i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.1231 | 0.752764 | ||||||||
\(353\) | 9.22419i | 0.490954i | 0.969402 | + | 0.245477i | \(0.0789446\pi\) | ||||
−0.969402 | + | 0.245477i | \(0.921055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.11549 | 0.112278 | ||||||||
\(356\) | 41.4392i | 2.19627i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.5810 | −0.876331 | ||||||||
\(359\) | − | 30.5458i | − | 1.61215i | −0.591816 | − | 0.806073i | \(-0.701589\pi\) | ||
0.591816 | − | 0.806073i | \(-0.298411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5425 | −0.765394 | ||||||||
\(362\) | − | 51.7360i | − | 2.71918i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 41.9500i | 2.19878i | ||||||||
\(365\) | − | 12.9317i | − | 0.676875i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.54381 | 0.237185 | 0.118592 | − | 0.992943i | \(-0.462162\pi\) | ||||
0.118592 | + | 0.992943i | \(0.462162\pi\) | |||||||
\(368\) | −18.9324 | −0.986921 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.54628 | −0.496288 | ||||||||
\(371\) | 23.6738 | 1.22908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.6283i | − | 0.964538i | −0.876023 | − | 0.482269i | \(-0.839813\pi\) | ||
0.876023 | − | 0.482269i | \(-0.160187\pi\) | |||||||
\(374\) | 10.0168 | 0.517959 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.71617 | −0.191647 | ||||||||
\(377\) | 26.6849 | 1.37434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 18.1414i | − | 0.931861i | −0.884821 | − | 0.465931i | \(-0.845720\pi\) | ||
0.884821 | − | 0.465931i | \(-0.154280\pi\) | |||||||
\(380\) | −10.7102 | −0.549420 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.6791 | −1.00687 | ||||||||
\(383\) | − | 25.6015i | − | 1.30817i | −0.756419 | − | 0.654087i | \(-0.773053\pi\) | ||
0.756419 | − | 0.654087i | \(-0.226947\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.0277i | 0.663953i | ||||||||
\(386\) | 56.5320 | 2.87740 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 35.0094 | 1.77733 | ||||||||
\(389\) | −8.60355 | −0.436217 | −0.218109 | − | 0.975924i | \(-0.569989\pi\) | ||||
−0.218109 | + | 0.975924i | \(0.569989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.2611 | −1.12579 | ||||||||
\(392\) | − | 10.5035i | − | 0.530508i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 35.1309i | 1.76987i | ||||||||
\(395\) | − | 5.08457i | − | 0.255832i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.94816 | −0.198152 | −0.0990761 | − | 0.995080i | \(-0.531589\pi\) | ||||
−0.0990761 | + | 0.995080i | \(0.531589\pi\) | |||||||
\(398\) | − | 10.7114i | − | 0.536914i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.10016 | 0.155008 | ||||||||
\(401\) | −3.37506 | −0.168542 | −0.0842712 | − | 0.996443i | \(-0.526856\pi\) | ||||
−0.0842712 | + | 0.996443i | \(0.526856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.26441i | − | 0.312053i | ||||||
\(404\) | −28.1241 | −1.39923 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −51.8778 | −2.57465 | ||||||||
\(407\) | 4.34301 | 0.215275 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.65075 | 0.131071 | 0.0655356 | − | 0.997850i | \(-0.479124\pi\) | ||||
0.0655356 | + | 0.997850i | \(0.479124\pi\) | |||||||
\(410\) | − | 34.1570i | − | 1.68690i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.489629i | 0.0241223i | ||||||||
\(413\) | −35.3148 | −1.73773 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.9212 | 0.732454 | ||||||||
\(416\) | 31.7122 | 1.55482 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.48557 | 0.415043 | ||||||||
\(419\) | − | 23.3304i | − | 1.13977i | −0.821726 | − | 0.569883i | \(-0.806988\pi\) | ||
0.821726 | − | 0.569883i | \(-0.193012\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.5887 | −1.44207 | −0.721034 | − | 0.692900i | \(-0.756333\pi\) | ||||
−0.721034 | + | 0.692900i | \(0.756333\pi\) | |||||||
\(422\) | − | 49.2847i | − | 2.39914i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.57670i | 0.465085i | ||||||||
\(425\) | 3.64524 | 0.176820 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.46572 | −0.119325 | ||||||||
\(428\) | − | 8.52573i | − | 0.412107i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −37.9076 | −1.82807 | ||||||||
\(431\) | − | 25.5345i | − | 1.22995i | −0.788546 | − | 0.614976i | \(-0.789166\pi\) | ||
0.788546 | − | 0.614976i | \(-0.210834\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.62340 | 0.318300 | 0.159150 | − | 0.987254i | \(-0.449125\pi\) | ||||
0.159150 | + | 0.987254i | \(0.449125\pi\) | |||||||
\(434\) | 12.1786i | 0.584590i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28.2495i | 1.35290i | ||||||||
\(437\) | −18.8581 | −0.902104 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.5668i | 1.02933i | 0.857392 | + | 0.514664i | \(0.172083\pi\) | ||||
−0.857392 | + | 0.514664i | \(0.827917\pi\) | |||||||
\(440\) | −5.27006 | −0.251240 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.4920 | 1.06983 | ||||||||
\(443\) | −0.831700 | −0.0395153 | −0.0197576 | − | 0.999805i | \(-0.506289\pi\) | ||||
−0.0197576 | + | 0.999805i | \(0.506289\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.8964i | 1.36982i | ||||||||
\(446\) | − | 15.3083i | − | 0.724868i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −45.8171 | −2.16466 | ||||||||
\(449\) | − | 29.3604i | − | 1.38560i | −0.721127 | − | 0.692802i | \(-0.756376\pi\) | ||
0.721127 | − | 0.692802i | \(-0.243624\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.5395i | 0.731727i | ||||||||
\(452\) | 49.0571 | 2.30745 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 8.50012i | − | 0.398930i | ||||||
\(455\) | 29.2526i | 1.37138i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.8560i | − | 0.507822i | −0.967228 | − | 0.253911i | \(-0.918283\pi\) | ||
0.967228 | − | 0.253911i | \(-0.0817171\pi\) | |||||||
\(458\) | 25.8800i | 1.20929i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 45.3107 | 2.11262 | ||||||||
\(461\) | − | 0.0680390i | − | 0.00316889i | −0.999999 | − | 0.00158445i | \(-0.999496\pi\) | ||
0.999999 | − | 0.00158445i | \(-0.000504345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.2704i | − | 0.570254i | −0.958490 | − | 0.285127i | \(-0.907964\pi\) | ||
0.958490 | − | 0.285127i | \(-0.0920358\pi\) | |||||||
\(464\) | 13.5834i | 0.630594i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −36.9168 | −1.71014 | ||||||||
\(467\) | 9.30810i | 0.430727i | 0.976534 | + | 0.215364i | \(0.0690937\pi\) | ||||
−0.976534 | + | 0.215364i | \(0.930906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 16.0425i | − | 0.740775i | ||||||
\(470\) | −10.0253 | −0.462433 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 14.2858i | − | 0.657559i | ||||||
\(473\) | 17.2458 | 0.792962 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.08799 | 0.141687 | ||||||||
\(476\) | −25.1082 | −1.15083 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −25.8217 | −1.18106 | ||||||||
\(479\) | 2.11731 | 0.0967423 | 0.0483711 | − | 0.998829i | \(-0.484597\pi\) | ||||
0.0483711 | + | 0.998829i | \(0.484597\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.75186 | 0.444647 | ||||||||
\(482\) | 14.0717 | 0.640948 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.3933 | −0.926968 | ||||||||
\(485\) | 24.4128 | 1.10853 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.68431i | 0.302895i | 0.988465 | + | 0.151447i | \(0.0483934\pi\) | ||||
−0.988465 | + | 0.151447i | \(0.951607\pi\) | |||||||
\(488\) | − | 0.997453i | − | 0.0451526i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 28.3359i | − | 1.28008i | ||||||
\(491\) | 33.2018i | 1.49838i | 0.662357 | + | 0.749188i | \(0.269556\pi\) | ||||
−0.662357 | + | 0.749188i | \(0.730444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.9716i | 0.719327i | ||||||||
\(494\) | 19.0536 | 0.857263 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.18877 | 0.143180 | ||||||||
\(497\) | 4.20126 | 0.188452 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 10.2781i | − | 0.460112i | −0.973177 | − | 0.230056i | \(-0.926109\pi\) | ||
0.973177 | − | 0.230056i | \(-0.0738909\pi\) | |||||||
\(500\) | −32.7837 | −1.46613 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.161606 | −0.00721283 | ||||||||
\(503\) | 10.2410i | 0.456622i | 0.973588 | + | 0.228311i | \(0.0733203\pi\) | ||||
−0.973588 | + | 0.228311i | \(0.926680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.6115 | −0.872703 | ||||||||
\(506\) | −35.8993 | −1.59592 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 58.1701 | 2.58088 | ||||||||
\(509\) | 3.47827i | 0.154171i | 0.997024 | + | 0.0770857i | \(0.0245615\pi\) | ||||
−0.997024 | + | 0.0770857i | \(0.975438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 25.6817i | − | 1.13609i | ||||||
\(512\) | 22.5478i | 0.996482i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.0588i | 1.32584i | ||||||||
\(515\) | 0.341428i | 0.0150451i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.56094 | 0.200590 | ||||||||
\(518\) | −18.9585 | −0.832987 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11.8335 | −0.518932 | ||||||||
\(521\) | −19.8435 | −0.869359 | −0.434679 | − | 0.900585i | \(-0.643138\pi\) | ||||
−0.434679 | + | 0.900585i | \(0.643138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.54400 | 0.373603 | 0.186801 | − | 0.982398i | \(-0.440188\pi\) | ||||
0.186801 | + | 0.982398i | \(0.440188\pi\) | |||||||
\(524\) | 46.6352 | 2.03727 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.8507 | −0.473114 | ||||||||
\(527\) | 3.74942 | 0.163327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.7815 | 2.46876 | ||||||||
\(530\) | 25.8355i | 1.12222i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −21.2699 | −0.922166 | ||||||||
\(533\) | 34.8926i | 1.51137i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 5.94517i | − | 0.257032i | ||||||
\(536\) | 6.48964 | 0.280310 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 56.5739i | 2.43908i | ||||||||
\(539\) | 12.8912i | 0.555263i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.7283i | 1.75105i | 0.483175 | + | 0.875524i | \(0.339484\pi\) | ||||
−0.483175 | + | 0.875524i | \(0.660516\pi\) | |||||||
\(542\) | −28.7406 | −1.23451 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.9806i | 0.813787i | ||||||||
\(545\) | 19.6989i | 0.843810i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.4836i | − | 1.38890i | −0.719543 | − | 0.694448i | \(-0.755648\pi\) | ||
0.719543 | − | 0.694448i | \(-0.244352\pi\) | |||||||
\(548\) | − | 26.3084i | − | 1.12384i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.87846 | 0.250658 | ||||||||
\(551\) | 13.5301i | 0.576400i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 10.0977i | − | 0.429398i | ||||||
\(554\) | −39.1329 | −1.66260 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 22.9402i | − | 0.972883i | ||||||
\(557\) | 20.9341i | 0.887004i | 0.896273 | + | 0.443502i | \(0.146264\pi\) | ||||
−0.896273 | + | 0.443502i | \(0.853736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.7239 | 1.63785 | ||||||||
\(560\) | −14.8904 | −0.629235 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 46.5187 | 1.96227 | ||||||||
\(563\) | 31.1313i | 1.31203i | 0.754749 | + | 0.656014i | \(0.227759\pi\) | ||||
−0.754749 | + | 0.656014i | \(0.772241\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.2085 | 1.43916 | ||||||||
\(566\) | − | 48.0714i | − | 2.02059i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.69952i | 0.0713104i | ||||||||
\(569\) | −20.2604 | −0.849361 | −0.424681 | − | 0.905343i | \(-0.639614\pi\) | ||||
−0.424681 | + | 0.905343i | \(0.639614\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 42.8322i | − | 1.79247i | −0.443580 | − | 0.896235i | \(-0.646292\pi\) | ||
0.443580 | − | 0.896235i | \(-0.353708\pi\) | |||||||
\(572\) | 20.8275 | 0.870843 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 67.8342i | − | 2.83135i | ||||||
\(575\) | −13.0641 | −0.544812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.83395 | 0.284501 | 0.142251 | − | 0.989831i | \(-0.454566\pi\) | ||||
0.142251 | + | 0.989831i | \(0.454566\pi\) | |||||||
\(578\) | − | 23.3820i | − | 0.972563i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 32.5090i | − | 1.34986i | ||||||
\(581\) | 29.6328 | 1.22938 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.7537i | − | 0.486788i | ||||||
\(584\) | 10.3890 | 0.429898 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.8324 | 1.81070 | ||||||||
\(587\) | −13.4295 | −0.554295 | −0.277148 | − | 0.960827i | \(-0.589389\pi\) | ||||
−0.277148 | + | 0.960827i | \(0.589389\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.17625 | 0.130875 | ||||||||
\(590\) | − | 38.5396i | − | 1.58665i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.96398i | 0.204018i | ||||||||
\(593\) | 12.6609 | 0.519922 | 0.259961 | − | 0.965619i | \(-0.416290\pi\) | ||||
0.259961 | + | 0.965619i | \(0.416290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.5085 | −0.717777 | ||||||||
\(596\) | −10.3775 | −0.425079 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −80.6087 | −3.29634 | ||||||||
\(599\) | − | 4.69675i | − | 0.191904i | −0.995386 | − | 0.0959521i | \(-0.969410\pi\) | ||
0.995386 | − | 0.0959521i | \(-0.0305896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.4167 | −1.81180 | −0.905898 | − | 0.423496i | \(-0.860803\pi\) | ||||
−0.905898 | + | 0.423496i | \(0.860803\pi\) | |||||||
\(602\) | −75.2826 | −3.06829 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 29.7330i | 1.20982i | ||||||||
\(605\) | −14.2207 | −0.578153 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.23920i | − | 0.253241i | −0.991951 | − | 0.126621i | \(-0.959587\pi\) | ||
0.991951 | − | 0.126621i | \(-0.0404131\pi\) | |||||||
\(608\) | 16.0790i | 0.652091i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 2.69088i | − | 0.108950i | ||||||
\(611\) | 10.2412 | 0.414314 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.8817 | 0.924184 | 0.462092 | − | 0.886832i | \(-0.347099\pi\) | ||||
0.462092 | + | 0.886832i | \(0.347099\pi\) | |||||||
\(614\) | −9.37707 | −0.378428 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.4661 | −0.421691 | ||||||||
\(617\) | − | 7.89901i | − | 0.318002i | −0.987278 | − | 0.159001i | \(-0.949173\pi\) | ||
0.987278 | − | 0.159001i | \(-0.0508274\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.5098i | 1.62823i | 0.580705 | + | 0.814114i | \(0.302777\pi\) | ||||
−0.580705 | + | 0.814114i | \(0.697223\pi\) | |||||||
\(620\) | −7.63164 | −0.306494 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 33.6076 | 1.34754 | ||||||||
\(623\) | 57.3869i | 2.29916i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5477 | −0.621908 | ||||||||
\(626\) | −1.43844 | −0.0574915 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −29.5899 | −1.18077 | ||||||||
\(629\) | 5.83675i | 0.232726i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.2662 | −1.08545 | −0.542725 | − | 0.839910i | \(-0.682607\pi\) | ||||
−0.542725 | + | 0.839910i | \(0.682607\pi\) | |||||||
\(632\) | 4.08480 | 0.162485 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.02978 | −0.239473 | ||||||||
\(635\) | 40.5632 | 1.60970 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.9461i | 1.14689i | ||||||||
\(638\) | 25.7566i | 1.01971i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 21.3534i | − | 0.844069i | ||||||
\(641\) | −36.8500 | −1.45549 | −0.727744 | − | 0.685848i | \(-0.759431\pi\) | ||||
−0.727744 | + | 0.685848i | \(0.759431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.6664i | 1.32767i | 0.747878 | + | 0.663837i | \(0.231073\pi\) | ||||
−0.747878 | + | 0.663837i | \(0.768927\pi\) | |||||||
\(644\) | 89.9849 | 3.54590 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.4041i | 0.448688i | ||||||||
\(647\) | −33.9298 | −1.33392 | −0.666958 | − | 0.745095i | \(-0.732404\pi\) | ||||
−0.666958 | + | 0.745095i | \(0.732404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.5333i | 0.688242i | ||||||||
\(650\) | 13.1996 | 0.517730 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 35.8921i | 1.40564i | ||||||||
\(653\) | − | 19.8232i | − | 0.775743i | −0.921713 | − | 0.387871i | \(-0.873210\pi\) | ||
0.921713 | − | 0.387871i | \(-0.126790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.5197 | 1.27065 | ||||||||
\(656\) | −17.7614 | −0.693464 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.9098 | −0.776164 | ||||||||
\(659\) | −10.4088 | −0.405469 | −0.202734 | − | 0.979234i | \(-0.564983\pi\) | ||||
−0.202734 | + | 0.979234i | \(0.564983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 37.1265i | − | 1.44405i | −0.691865 | − | 0.722027i | \(-0.743211\pi\) | ||
0.691865 | − | 0.722027i | \(-0.256789\pi\) | |||||||
\(662\) | 74.2807 | 2.88700 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.9873i | 0.465197i | ||||||||
\(665\) | −14.8319 | −0.575158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 57.2406i | − | 2.21637i | ||||||
\(668\) | 16.0148 | + | 30.9581i | 0.619633 | + | 1.19781i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.5074 | 0.676371 | ||||||||
\(671\) | 1.22420i | 0.0472595i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.49554i | − | 0.134743i | −0.997728 | − | 0.0673715i | \(-0.978539\pi\) | ||
0.997728 | − | 0.0673715i | \(-0.0214613\pi\) | |||||||
\(674\) | 20.9121i | 0.805504i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.7032 | 0.450123 | ||||||||
\(677\) | 47.1091i | 1.81055i | 0.424828 | + | 0.905274i | \(0.360335\pi\) | ||||
−0.424828 | + | 0.905274i | \(0.639665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.4826 | 1.86059 | ||||||||
\(680\) | − | 7.08265i | − | 0.271607i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.04647 | 0.231531 | ||||||||
\(683\) | −14.0600 | −0.537990 | −0.268995 | − | 0.963142i | \(-0.586692\pi\) | ||||
−0.268995 | + | 0.963142i | \(0.586692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 18.3454i | − | 0.700941i | ||||||
\(686\) | 0.392840i | 0.0149987i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.7116i | 0.751498i | ||||||||
\(689\) | − | 26.3919i | − | 1.00545i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 10.7832i | − | 0.410212i | −0.978740 | − | 0.205106i | \(-0.934246\pi\) | ||
0.978740 | − | 0.205106i | \(-0.0657539\pi\) | |||||||
\(692\) | − | 31.8417i | − | 1.21044i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 34.7504i | − | 1.31911i | ||||||
\(695\) | − | 15.9967i | − | 0.606790i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.8842 | −0.791044 | ||||||||
\(698\) | 44.6118 | 1.68858 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.7349 | −0.556928 | ||||||||
\(701\) | − | 20.4488i | − | 0.772339i | −0.922428 | − | 0.386170i | \(-0.873798\pi\) | ||
0.922428 | − | 0.386170i | \(-0.126202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.94449i | 0.186485i | ||||||||
\(704\) | 22.7475i | 0.857330i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.9915 | −0.752392 | ||||||||
\(707\) | −38.9476 | −1.46477 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.6246i | 0.549237i | 0.961553 | + | 0.274619i | \(0.0885516\pi\) | ||||
−0.961553 | + | 0.274619i | \(0.911448\pi\) | |||||||
\(710\) | 4.58489i | 0.172068i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.2146 | −0.870003 | ||||||||
\(713\) | −13.4375 | −0.503239 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.5235 | 0.543147 | ||||||||
\(716\) | − | 20.6348i | − | 0.771159i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 66.2018 | 2.47063 | ||||||||
\(719\) | 44.1959 | 1.64823 | 0.824115 | − | 0.566422i | \(-0.191673\pi\) | ||||
0.824115 | + | 0.566422i | \(0.191673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.678060i | 0.0252523i | ||||||||
\(722\) | − | 31.5179i | − | 1.17297i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 64.3848 | 2.39284 | ||||||||
\(725\) | 9.37308i | 0.348108i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.6592i | 1.65632i | 0.560493 | + | 0.828159i | \(0.310611\pi\) | ||||
−0.560493 | + | 0.828159i | \(0.689389\pi\) | |||||||
\(728\) | −23.5007 | −0.870994 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 28.0268 | 1.03732 | ||||||||
\(731\) | 23.1773i | 0.857244i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.8148 | 1.65527 | 0.827637 | − | 0.561264i | \(-0.189685\pi\) | ||||
0.827637 | + | 0.561264i | \(0.189685\pi\) | |||||||
\(734\) | 9.84778i | 0.363488i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 68.0244i | − | 2.50741i | ||||||
\(737\) | −7.96487 | −0.293390 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.9767i | 1.50735i | 0.657246 | + | 0.753676i | \(0.271721\pi\) | ||||
−0.657246 | + | 0.753676i | \(0.728279\pi\) | |||||||
\(740\) | − | 11.8802i | − | 0.436726i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 51.3081i | 1.88358i | ||||||||
\(743\) | 9.15050i | 0.335699i | 0.985813 | + | 0.167850i | \(0.0536823\pi\) | ||||
−0.985813 | + | 0.167850i | \(0.946318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.23644 | −0.265123 | ||||||||
\(746\) | 40.3731 | 1.47816 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.4658i | 0.455796i | ||||||||
\(749\) | − | 11.8068i | − | 0.431412i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.4203i | 0.416733i | 0.978051 | + | 0.208367i | \(0.0668147\pi\) | ||||
−0.978051 | + | 0.208367i | \(0.933185\pi\) | |||||||
\(752\) | 5.21307i | 0.190101i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 57.8341i | 2.10620i | ||||||||
\(755\) | 20.7334i | 0.754566i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.33170 | 0.339166 | 0.169583 | − | 0.985516i | \(-0.445758\pi\) | ||||
0.169583 | + | 0.985516i | \(0.445758\pi\) | |||||||
\(758\) | 39.3178 | 1.42809 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 5.99993i | − | 0.217640i | ||||||
\(761\) | − | 1.08239i | − | 0.0392366i | −0.999808 | − | 0.0196183i | \(-0.993755\pi\) | ||
0.999808 | − | 0.0196183i | \(-0.00624510\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.1212i | 1.41628i | ||||||||
\(764\) | − | 24.4904i | − | 0.886033i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 55.4860 | 2.00479 | ||||||||
\(767\) | 39.3695i | 1.42155i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.5572i | 0.380701i | 0.981716 | + | 0.190351i | \(0.0609625\pi\) | ||||
−0.981716 | + | 0.190351i | \(0.939038\pi\) | |||||||
\(770\) | −28.2349 | −1.01751 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 70.3533i | 2.53207i | ||||||||
\(773\) | 38.0265 | 1.36772 | 0.683859 | − | 0.729614i | \(-0.260300\pi\) | ||||
0.683859 | + | 0.729614i | \(0.260300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.20038 | 0.0790398 | ||||||||
\(776\) | 19.6125i | 0.704049i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 18.6464i | − | 0.668507i | ||||||
\(779\) | −17.6916 | −0.633867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.08586i | − | 0.0746380i | ||||||
\(782\) | − | 48.2465i | − | 1.72529i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14.7344 | −0.526228 | ||||||||
\(785\) | −20.6337 | −0.736447 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.3549i | 1.93754i | 0.247957 | + | 0.968771i | \(0.420241\pi\) | ||||
−0.247957 | + | 0.968771i | \(0.579759\pi\) | |||||||
\(788\) | −43.7200 | −1.55746 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.0198 | 0.392066 | ||||||||
\(791\) | 67.9365 | 2.41554 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.74883i | 0.0976136i | ||||||||
\(794\) | − | 8.55682i | − | 0.303670i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.3302 | 0.472477 | ||||||||
\(797\) | 15.2054 | 0.538605 | 0.269302 | − | 0.963056i | \(-0.413207\pi\) | ||||
0.269302 | + | 0.963056i | \(0.413207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.12963i | 0.216851i | ||||||||
\(800\) | 11.1389i | 0.393820i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 7.31475i | − | 0.258293i | ||||||
\(803\) | −12.7506 | −0.449958 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 62.7484 | 2.21159 | ||||||||
\(806\) | 13.5768 | 0.478224 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 15.7554i | − | 0.554272i | ||||||
\(809\) | 6.44710i | 0.226668i | 0.993557 | + | 0.113334i | \(0.0361530\pi\) | ||||
−0.993557 | + | 0.113334i | \(0.963847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.70976i | 0.305841i | 0.988238 | + | 0.152920i | \(0.0488678\pi\) | ||||
−0.988238 | + | 0.152920i | \(0.951132\pi\) | |||||||
\(812\) | − | 64.5612i | − | 2.26566i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.41259i | 0.329911i | ||||||||
\(815\) | 25.0283i | 0.876703i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.6342i | 0.686913i | ||||||||
\(818\) | 5.74496i | 0.200868i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 42.5080 | 1.48444 | ||||||||
\(821\) | −24.5958 | −0.858401 | −0.429200 | − | 0.903209i | \(-0.641205\pi\) | ||||
−0.429200 | + | 0.903209i | \(0.641205\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.6078i | 0.404624i | 0.979321 | + | 0.202312i | \(0.0648455\pi\) | ||||
−0.979321 | + | 0.202312i | \(0.935155\pi\) | |||||||
\(824\) | −0.274294 | −0.00955549 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 76.5377i | − | 2.66309i | ||||||
\(827\) | −41.5678 | −1.44545 | −0.722727 | − | 0.691134i | \(-0.757112\pi\) | ||||
−0.722727 | + | 0.691134i | \(0.757112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 23.8514i | − | 0.828394i | −0.910187 | − | 0.414197i | \(-0.864062\pi\) | ||
0.910187 | − | 0.414197i | \(-0.135938\pi\) | |||||||
\(830\) | 32.3387i | 1.12249i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 51.0776i | 1.77080i | ||||||||
\(833\) | −17.3250 | −0.600276 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.1675 | + | 21.5878i | 0.386467 | + | 0.747075i | ||||
\(836\) | 10.5602i | 0.365231i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 50.5640 | 1.74670 | ||||||||
\(839\) | − | 28.2628i | − | 0.975741i | −0.872916 | − | 0.487871i | \(-0.837774\pi\) | ||
0.872916 | − | 0.487871i | \(-0.162226\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.0683 | −0.416147 | ||||||||
\(842\) | − | 64.1276i | − | 2.20998i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 61.3341 | 2.11121 | ||||||||
\(845\) | 8.16089 | 0.280743 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.2416 | −0.970392 | ||||||||
\(848\) | 13.4342 | 0.461333 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.90030i | 0.270978i | ||||||||
\(851\) | − | 20.9183i | − | 0.717069i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.65148 | 0.159264 | 0.0796319 | − | 0.996824i | \(-0.474626\pi\) | ||||
0.0796319 | + | 0.996824i | \(0.474626\pi\) | |||||||
\(854\) | − | 5.34395i | − | 0.182866i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.77618 | 0.163247 | ||||||||
\(857\) | 40.0158i | 1.36691i | 0.729992 | + | 0.683456i | \(0.239524\pi\) | ||||
−0.729992 | + | 0.683456i | \(0.760476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.6909 | −0.774203 | −0.387101 | − | 0.922037i | \(-0.626524\pi\) | ||||
−0.387101 | + | 0.922037i | \(0.626524\pi\) | |||||||
\(860\) | − | 47.1755i | − | 1.60867i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 55.3407 | 1.88491 | ||||||||
\(863\) | − | 31.0931i | − | 1.05842i | −0.848490 | − | 0.529212i | \(-0.822488\pi\) | ||
0.848490 | − | 0.529212i | \(-0.177512\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 22.2039i | − | 0.754954i | ||||||
\(866\) | 14.3549i | 0.487798i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.1561 | −0.514430 | ||||||||
\(869\) | −5.01336 | −0.170067 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.8844 | −0.605991 | ||||||||
\(872\) | −15.8256 | −0.535922 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 40.8710i | − | 1.38248i | ||||||
\(875\) | −45.4004 | −1.53481 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.6084 | 1.60762 | 0.803810 | − | 0.594886i | \(-0.202803\pi\) | ||||
0.803810 | + | 0.594886i | \(0.202803\pi\) | |||||||
\(878\) | −46.7417 | −1.57745 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.39287i | 0.249214i | ||||||||
\(881\) | 58.5074 | 1.97116 | 0.985582 | − | 0.169201i | \(-0.0541187\pi\) | ||||
0.985582 | + | 0.169201i | \(0.0541187\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.8561 | −1.61049 | −0.805243 | − | 0.592945i | \(-0.797965\pi\) | ||||
−0.805243 | + | 0.592945i | \(0.797965\pi\) | |||||||
\(884\) | 27.9910i | 0.941438i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 1.80254i | − | 0.0605575i | ||||||
\(887\) | −44.9871 | −1.51052 | −0.755259 | − | 0.655426i | \(-0.772489\pi\) | ||||
−0.755259 | + | 0.655426i | \(0.772489\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 80.5567 | 2.70178 | ||||||||
\(890\) | −62.6271 | −2.09927 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.0510 | 0.637873 | ||||||||
\(893\) | 5.19259i | 0.173763i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 14.3891i | − | 0.480974i | ||||||
\(896\) | − | 42.4069i | − | 1.41672i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 63.6328 | 2.12345 | ||||||||
\(899\) | 9.64097i | 0.321544i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7962 | 0.526249 | ||||||||
\(902\) | −33.6787 | −1.12138 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.4822i | 0.914044i | ||||||||
\(905\) | 44.8969 | 1.49242 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.9092 | −0.760688 | −0.380344 | − | 0.924845i | \(-0.624194\pi\) | ||||
−0.380344 | + | 0.924845i | \(0.624194\pi\) | |||||||
\(908\) | 10.5783 | 0.351053 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −63.3990 | −2.10166 | ||||||||
\(911\) | − | 56.5383i | − | 1.87320i | −0.350403 | − | 0.936599i | \(-0.613955\pi\) | ||
0.350403 | − | 0.936599i | \(-0.386045\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 14.7123i | − | 0.486905i | ||||||
\(914\) | 23.5282 | 0.778243 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −32.2073 | −1.06416 | ||||||||
\(917\) | 64.5825 | 2.13270 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.96335 | −0.196713 | −0.0983564 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983564 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(920\) | 25.3834i | 0.836868i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.147461 | 0.00485636 | ||||||||
\(923\) | − | 4.68362i | − | 0.154163i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.42534i | 0.112625i | ||||||||
\(926\) | 26.5936 | 0.873920 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −48.8053 | −1.60211 | ||||||||
\(929\) | − | 21.0386i | − | 0.690255i | −0.938556 | − | 0.345127i | \(-0.887836\pi\) | ||
0.938556 | − | 0.345127i | \(-0.112164\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.6765 | −0.481004 | ||||||||
\(932\) | − | 45.9425i | − | 1.50490i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.1734 | −0.660094 | ||||||||
\(935\) | 8.69269i | 0.284281i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.7402i | − | 1.26559i | −0.774320 | − | 0.632794i | \(-0.781908\pi\) | ||
0.774320 | − | 0.632794i | \(-0.218092\pi\) | |||||||
\(938\) | 34.7689 | 1.13524 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 12.4764i | − | 0.406934i | ||||||
\(941\) | 40.2288 | 1.31142 | 0.655710 | − | 0.755013i | \(-0.272369\pi\) | ||||
0.655710 | + | 0.755013i | \(0.272369\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.8466 | 2.43734 | ||||||||
\(944\) | −20.0402 | −0.652254 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37.3767i | 1.21522i | ||||||||
\(947\) | − | 2.31151i | − | 0.0751139i | −0.999294 | − | 0.0375570i | \(-0.988042\pi\) | ||
0.999294 | − | 0.0375570i | \(-0.0119576\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.6304 | −0.929381 | ||||||||
\(950\) | 6.69258i | 0.217136i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 14.0658i | − | 0.455875i | ||||||
\(953\) | −50.6620 | −1.64110 | −0.820552 | − | 0.571573i | \(-0.806334\pi\) | ||||
−0.820552 | + | 0.571573i | \(0.806334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 17.0777i | − | 0.552621i | ||||||
\(956\) | − | 32.1347i | − | 1.03931i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.58883i | 0.148258i | ||||||||
\(959\) | − | 36.4330i | − | 1.17648i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7367 | −0.926991 | ||||||||
\(962\) | 21.1352i | 0.681425i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.5120i | 0.564025i | ||||||||
\(965\) | 49.0588i | 1.57926i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8023 | −0.701115 | −0.350557 | − | 0.936541i | \(-0.614008\pi\) | ||||
−0.350557 | + | 0.936541i | \(0.614008\pi\) | |||||||
\(968\) | − | 11.4245i | − | 0.367197i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 52.9097i | 1.69883i | ||||||||
\(971\) | −6.51291 | −0.209009 | −0.104505 | − | 0.994524i | \(-0.533326\pi\) | ||||
−0.104505 | + | 0.994524i | \(0.533326\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 31.7687i | − | 1.01846i | ||||||
\(974\) | −14.4869 | −0.464189 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.39923 | −0.0447883 | ||||||||
\(977\) | 11.9767 | 0.383168 | 0.191584 | − | 0.981476i | \(-0.438638\pi\) | ||||
0.191584 | + | 0.981476i | \(0.438638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.4917 | 0.910600 | ||||||||
\(980\) | 35.2636 | 1.12645 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −71.9581 | −2.29628 | ||||||||
\(983\) | 18.1753 | 0.579700 | 0.289850 | − | 0.957072i | \(-0.406395\pi\) | ||||
0.289850 | + | 0.957072i | \(0.406395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.4869 | −0.971393 | ||||||||
\(986\) | −34.6153 | −1.10238 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.7120i | 0.754379i | ||||||||
\(989\) | − | 83.0649i | − | 2.64131i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.7481i | 0.849682i | 0.905268 | + | 0.424841i | \(0.139670\pi\) | ||||
−0.905268 | + | 0.424841i | \(0.860330\pi\) | |||||||
\(992\) | 11.4573i | 0.363769i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.10536i | 0.288805i | ||||||||
\(995\) | 9.29543 | 0.294685 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.61861 | 0.146273 | 0.0731364 | − | 0.997322i | \(-0.476699\pi\) | ||||
0.0731364 | + | 0.997322i | \(0.476699\pi\) | |||||||
\(998\) | 22.2757 | 0.705126 | ||||||||
\(999\) | 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 | 1503.2.c.a.1502.16 | yes | 56 | |
3.2 | odd | 2 | inner | 1503.2.c.a.1502.41 | yes | 56 | |
167.166 | odd | 2 | inner | 1503.2.c.a.1502.42 | yes | 56 | |
501.500 | even | 2 | inner | 1503.2.c.a.1502.15 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1503.2.c.a.1502.15 | ✓ | 56 | 501.500 | even | 2 | inner | |
1503.2.c.a.1502.16 | yes | 56 | 1.1 | even | 1 | trivial | |
1503.2.c.a.1502.41 | yes | 56 | 3.2 | odd | 2 | inner | |
1503.2.c.a.1502.42 | yes | 56 | 167.166 | odd | 2 | inner |