Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), 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: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Character | \(\chi\) | \(=\) | 1008.17 |
Dual form | 1008.4.bt.d.593.4 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.89184 | − | 13.6691i | −0.705867 | − | 1.22260i | −0.966378 | − | 0.257127i | \(-0.917224\pi\) |
0.260510 | − | 0.965471i | \(-0.416109\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.6185 | − | 15.1739i | −0.573343 | − | 0.819316i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.2439 | + | 16.3066i | 0.774167 | + | 0.446966i | 0.834359 | − | 0.551221i | \(-0.185838\pi\) |
−0.0601918 | + | 0.998187i | \(0.519171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.3118i | 1.15872i | 0.815071 | + | 0.579361i | \(0.196698\pi\) | ||||
−0.815071 | + | 0.579361i | \(0.803302\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.3222 | + | 21.3427i | −0.175798 | + | 0.304491i | −0.940437 | − | 0.339967i | \(-0.889584\pi\) |
0.764639 | + | 0.644459i | \(0.222917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.2989 | + | 9.41015i | −0.196801 | + | 0.113623i | −0.595162 | − | 0.803606i | \(-0.702912\pi\) |
0.398362 | + | 0.917228i | \(0.369579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −46.7289 | + | 26.9789i | −0.423637 | + | 0.244587i | −0.696632 | − | 0.717429i | \(-0.745319\pi\) |
0.272995 | + | 0.962015i | \(0.411986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −62.0622 | + | 107.495i | −0.496498 | + | 0.859959i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 157.048i | 1.00562i | 0.864397 | + | 0.502811i | \(0.167701\pi\) | ||||
−0.864397 | + | 0.502811i | \(0.832299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −41.4452 | − | 23.9284i | −0.240122 | − | 0.138634i | 0.375111 | − | 0.926980i | \(-0.377605\pi\) |
−0.615233 | + | 0.788345i | \(0.710938\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −123.614 | + | 264.895i | −0.596990 | + | 1.27930i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −48.1973 | − | 83.4802i | −0.214151 | − | 0.370921i | 0.738858 | − | 0.673861i | \(-0.235365\pi\) |
−0.953010 | + | 0.302940i | \(0.902032\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 263.002 | 1.00181 | 0.500903 | − | 0.865503i | \(-0.333001\pi\) | ||||
0.500903 | + | 0.865503i | \(0.333001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −258.982 | −0.918474 | −0.459237 | − | 0.888314i | \(-0.651877\pi\) | ||||
−0.459237 | + | 0.888314i | \(0.651877\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −62.5951 | − | 108.418i | −0.194264 | − | 0.336476i | 0.752395 | − | 0.658713i | \(-0.228899\pi\) |
−0.946659 | + | 0.322237i | \(0.895565\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −117.497 | + | 322.248i | −0.342557 | + | 0.939497i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 471.579 | + | 272.266i | 1.22220 | + | 0.705635i | 0.965386 | − | 0.260827i | \(-0.0839952\pi\) |
0.256810 | + | 0.966462i | \(0.417329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 514.756i | − | 1.26199i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −189.386 | + | 328.027i | −0.417899 | + | 0.723822i | −0.995728 | − | 0.0923360i | \(-0.970567\pi\) |
0.577829 | + | 0.816158i | \(0.303900\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 587.204 | − | 339.022i | 1.23252 | − | 0.711596i | 0.264966 | − | 0.964258i | \(-0.414639\pi\) |
0.967555 | + | 0.252662i | \(0.0813061\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 742.392 | − | 428.620i | 1.41665 | − | 0.817905i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 346.637 | − | 600.394i | 0.632067 | − | 1.09477i | −0.355061 | − | 0.934843i | \(-0.615540\pi\) |
0.987128 | − | 0.159929i | \(-0.0511266\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 238.831i | − | 0.399212i | −0.979876 | − | 0.199606i | \(-0.936034\pi\) | ||
0.979876 | − | 0.199606i | \(-0.0639662\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 631.051 | + | 364.337i | 1.01177 | + | 0.584143i | 0.911708 | − | 0.410838i | \(-0.134764\pi\) |
0.100058 | + | 0.994982i | \(0.468097\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −52.4707 | − | 601.721i | −0.0776570 | − | 0.890552i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −439.845 | − | 761.833i | −0.626410 | − | 1.08497i | −0.988266 | − | 0.152740i | \(-0.951190\pi\) |
0.361856 | − | 0.932234i | \(-0.382143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1222.11 | 1.61619 | 0.808096 | − | 0.589050i | \(-0.200498\pi\) | ||||
0.808096 | + | 0.589050i | \(0.200498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 388.979 | 0.496361 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 75.9540 | + | 131.556i | 0.0904619 | + | 0.156685i | 0.907706 | − | 0.419608i | \(-0.137832\pi\) |
−0.817244 | + | 0.576292i | \(0.804499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 824.125 | − | 576.708i | 0.949360 | − | 0.664345i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 257.256 | + | 148.527i | 0.277830 | + | 0.160405i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1591.43i | 1.66582i | 0.553406 | + | 0.832912i | \(0.313328\pi\) | ||||
−0.553406 | + | 0.832912i | \(0.686672\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −28.6940 | + | 49.6994i | −0.0282689 | + | 0.0489631i | −0.879814 | − | 0.475319i | \(-0.842333\pi\) |
0.851545 | + | 0.524282i | \(0.175666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1674.25 | − | 966.626i | 1.60163 | − | 0.924704i | 0.610473 | − | 0.792037i | \(-0.290979\pi\) |
0.991161 | − | 0.132667i | \(-0.0423541\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1729.67 | + | 998.625i | −1.56274 | + | 0.902249i | −0.565764 | + | 0.824567i | \(0.691419\pi\) |
−0.996978 | + | 0.0776819i | \(0.975248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 698.958 | − | 1210.63i | 0.614202 | − | 1.06383i | −0.376322 | − | 0.926489i | \(-0.622811\pi\) |
0.990524 | − | 0.137340i | \(-0.0438554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1636.31i | 1.36222i | 0.732181 | + | 0.681110i | \(0.238502\pi\) | ||||
−0.732181 | + | 0.681110i | \(0.761498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 737.553 | + | 425.827i | 0.598063 | + | 0.345292i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 454.695 | − | 39.6498i | 0.350267 | − | 0.0305436i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −133.690 | − | 231.558i | −0.100443 | − | 0.173973i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.8192 | −0.00988823 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1729.20 | −1.20820 | −0.604101 | − | 0.796908i | \(-0.706468\pi\) | ||||
−0.604101 | + | 0.796908i | \(0.706468\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 89.9310 | + | 155.765i | 0.0599795 | + | 0.103887i | 0.894456 | − | 0.447156i | \(-0.147563\pi\) |
−0.834476 | + | 0.551044i | \(0.814230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 315.858 | + | 147.397i | 0.205927 | + | 0.0960970i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2466.49 | + | 1424.03i | 1.53815 | + | 0.888053i | 0.998947 | + | 0.0458784i | \(0.0146087\pi\) |
0.539205 | + | 0.842174i | \(0.318725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 58.4498i | − | 0.0356665i | −0.999841 | − | 0.0178333i | \(-0.994323\pi\) | ||
0.999841 | − | 0.0178333i | \(-0.00567680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −885.641 | + | 1533.98i | −0.517909 | + | 0.897045i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2146.70 | − | 1239.40i | 1.22947 | − | 0.709836i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 701.675 | − | 405.112i | 0.385795 | − | 0.222739i | −0.294542 | − | 0.955639i | \(-0.595167\pi\) |
0.680337 | + | 0.732900i | \(0.261834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1271.69 | + | 2202.64i | −0.685357 | + | 1.18707i | 0.287968 | + | 0.957640i | \(0.407020\pi\) |
−0.973325 | + | 0.229433i | \(0.926313\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 755.357i | 0.391430i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2181.59 | − | 1259.54i | −1.10898 | − | 0.640271i | −0.170417 | − | 0.985372i | \(-0.554511\pi\) |
−0.938566 | + | 0.345101i | \(0.887845\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 905.565 | + | 422.587i | 0.443283 | + | 0.206860i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1072.18 | − | 1857.07i | −0.515213 | − | 0.892375i | −0.999844 | − | 0.0176561i | \(-0.994380\pi\) |
0.484631 | − | 0.874718i | \(-0.338954\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3381.59 | 1.56692 | 0.783458 | − | 0.621445i | \(-0.213454\pi\) | ||||
0.783458 | + | 0.621445i | \(0.213454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −752.775 | −0.342638 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 98.9912 | + | 171.458i | 0.0435038 | + | 0.0753509i | 0.886957 | − | 0.461851i | \(-0.152815\pi\) |
−0.843454 | + | 0.537202i | \(0.819481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2290.13 | − | 199.701i | 0.989242 | − | 0.0862628i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3007.52 | + | 1736.40i | 1.25583 | + | 0.725052i | 0.972260 | − | 0.233901i | \(-0.0751491\pi\) |
0.283566 | + | 0.958953i | \(0.408482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2872.95i | − | 1.17980i | −0.807475 | − | 0.589902i | \(-0.799166\pi\) | ||
0.807475 | − | 0.589902i | \(-0.200834\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −760.731 | + | 1317.63i | −0.302325 | + | 0.523642i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −696.052 | + | 401.866i | −0.272194 | + | 0.157152i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1075.20 | − | 620.765i | 0.407322 | − | 0.235167i | −0.282317 | − | 0.959321i | \(-0.591103\pi\) |
0.689638 | + | 0.724154i | \(0.257770\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1341.31 | + | 2323.21i | −0.500256 | + | 0.866468i | 0.499744 | + | 0.866173i | \(0.333427\pi\) |
−1.00000 | 0.000295140i | \(0.999906\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3056.57i | 1.10544i | 0.833367 | + | 0.552719i | \(0.186410\pi\) | ||||
−0.833367 | + | 0.552719i | \(0.813590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1864.33 | + | 1076.37i | 0.664115 | + | 0.383427i | 0.793843 | − | 0.608123i | \(-0.208077\pi\) |
−0.129728 | + | 0.991550i | \(0.541411\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2383.03 | − | 1667.60i | 0.823922 | − | 0.576566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2075.57 | − | 3595.00i | −0.707143 | − | 1.22481i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −613.790 | −0.203142 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3912.38 | 1.27649 | 0.638245 | − | 0.769834i | \(-0.279661\pi\) | ||||
0.638245 | + | 0.769834i | \(0.279661\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2043.84 | + | 3540.04i | 0.648321 | + | 1.12292i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 76.9958 | + | 882.970i | 0.0240867 | + | 0.276221i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1159.16 | − | 669.241i | −0.352821 | − | 0.203701i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 885.668i | 0.265958i | 0.991119 | + | 0.132979i | \(0.0424544\pi\) | ||||
−0.991119 | + | 0.132979i | \(0.957546\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2687.02 | − | 4654.05i | 0.785654 | − | 1.36079i | −0.142953 | − | 0.989729i | \(-0.545660\pi\) |
0.928607 | − | 0.371064i | \(-0.121007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5385.90 | − | 3109.55i | 1.55419 | − | 0.897314i | 0.556400 | − | 0.830914i | \(-0.312182\pi\) |
0.997793 | − | 0.0663998i | \(-0.0211513\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5180.55 | + | 2990.99i | −1.45661 | + | 0.840972i | −0.998842 | − | 0.0481015i | \(-0.984683\pi\) |
−0.457764 | + | 0.889074i | \(0.651350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −987.981 | + | 1711.23i | −0.274250 | + | 0.475015i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3377.80i | 0.914191i | 0.889418 | + | 0.457095i | \(0.151110\pi\) | ||||
−0.889418 | + | 0.457095i | \(0.848890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1168.80 | − | 674.804i | −0.312401 | − | 0.180365i | 0.335599 | − | 0.942005i | \(-0.391061\pi\) |
−0.648001 | + | 0.761640i | \(0.724395\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5332.09 | − | 937.052i | 1.39043 | − | 0.244351i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −511.082 | − | 885.221i | −0.131657 | − | 0.228037i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 731.129 | 0.183858 | 0.0919292 | − | 0.995766i | \(-0.470697\pi\) | ||||
0.0919292 | + | 0.995766i | \(0.470697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1759.74 | −0.437288 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2891.62 | − | 5008.43i | −0.701845 | − | 1.21563i | −0.967818 | − | 0.251651i | \(-0.919026\pi\) |
0.265972 | − | 0.963981i | \(-0.414307\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −754.943 | + | 1617.77i | −0.181119 | + | 0.388122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1273.79 | − | 735.424i | −0.298651 | − | 0.172426i | 0.343185 | − | 0.939268i | \(-0.388494\pi\) |
−0.641837 | + | 0.766841i | \(0.721827\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8594.73i | − | 1.99234i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2298.35 | + | 3980.86i | −0.520941 | + | 0.902296i | 0.478763 | + | 0.877944i | \(0.341085\pi\) |
−0.999703 | + | 0.0243516i | \(0.992248\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 352.954 | − | 203.778i | 0.0791160 | − | 0.0456777i | −0.459920 | − | 0.887960i | \(-0.652122\pi\) |
0.539036 | + | 0.842283i | \(0.318789\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3505.75 | + | 2024.05i | −0.768745 | + | 0.443835i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −786.099 | + | 1361.56i | −0.170513 | + | 0.295337i | −0.938599 | − | 0.345009i | \(-0.887876\pi\) |
0.768086 | + | 0.640346i | \(0.221209\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 391.409i | − | 0.0830943i | −0.999137 | − | 0.0415471i | \(-0.986771\pi\) | ||
0.999137 | − | 0.0415471i | \(-0.0132287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 994.194 | + | 573.998i | 0.208829 | + | 0.120568i | 0.600767 | − | 0.799424i | \(-0.294862\pi\) |
−0.391938 | + | 0.919992i | \(0.628195\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2792.68 | − | 3990.78i | −0.574378 | − | 0.820796i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2152.83 | + | 3728.81i | 0.438190 | + | 0.758967i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7106.43 | 1.41694 | 0.708468 | − | 0.705743i | \(-0.249387\pi\) | ||||
0.708468 | + | 0.705743i | \(0.249387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5978.43 | 1.17992 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1465.27 | − | 2537.93i | −0.283408 | − | 0.490877i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2749.99 | + | 3929.78i | 0.526600 | + | 0.752520i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9268.23 | − | 5351.02i | −1.73999 | − | 1.00458i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8035.73i | 1.49389i | 0.664887 | + | 0.746944i | \(0.268480\pi\) | ||||
−0.664887 | + | 0.746944i | \(0.731520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2093.96 | − | 3626.85i | 0.381793 | − | 0.661285i | −0.609525 | − | 0.792767i | \(-0.708640\pi\) |
0.991319 | + | 0.131481i | \(0.0419733\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6183.56 | − | 3570.08i | 1.11666 | − | 0.644706i | 0.176117 | − | 0.984369i | \(-0.443646\pi\) |
0.940547 | + | 0.339663i | \(0.110313\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5241.84 | − | 3026.38i | 0.928742 | − | 0.536210i | 0.0423286 | − | 0.999104i | \(-0.486522\pi\) |
0.886414 | + | 0.462894i | \(0.153189\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2560.91 | + | 4435.63i | −0.449478 | + | 0.778519i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 463.814i | − | 0.0798988i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5838.25 | − | 3370.71i | −0.996454 | − | 0.575303i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −980.463 | + | 2101.04i | −0.164300 | + | 0.352080i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5297.71 | − | 9175.90i | −0.879724 | − | 1.52373i | −0.851644 | − | 0.524120i | \(-0.824394\pi\) |
−0.0280795 | − | 0.999606i | \(-0.508939\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10942.4 | −1.78462 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −629.759 | −0.101796 | −0.0508978 | − | 0.998704i | \(-0.516208\pi\) | ||||
−0.0508978 | + | 0.998704i | \(0.516208\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −780.382 | − | 1351.66i | −0.123930 | − | 0.214653i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6137.40 | − | 1638.88i | 0.966147 | − | 0.257992i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 355.046 | + | 204.986i | 0.0549276 | + | 0.0317125i | 0.527212 | − | 0.849734i | \(-0.323237\pi\) |
−0.472285 | + | 0.881446i | \(0.656571\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1777.77i | 0.272670i | 0.990663 | + | 0.136335i | \(0.0435324\pi\) | ||||
−0.990663 | + | 0.136335i | \(0.956468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4076.99 | + | 7061.56i | −0.614721 | + | 1.06473i | 0.375713 | + | 0.926736i | \(0.377398\pi\) |
−0.990433 | + | 0.137991i | \(0.955935\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3264.60 | + | 1884.82i | −0.488076 | + | 0.281791i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2451.26 | − | 1415.24i | 0.360370 | − | 0.208060i | −0.308873 | − | 0.951103i | \(-0.599952\pi\) |
0.669243 | + | 0.743044i | \(0.266619\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3252.40 | + | 5633.32i | −0.474180 | + | 0.821303i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 11501.2i | − | 1.64931i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 233.258 | + | 134.671i | 0.0331770 | + | 0.0191547i | 0.516497 | − | 0.856289i | \(-0.327236\pi\) |
−0.483320 | + | 0.875444i | \(0.660569\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −876.087 | − | 10046.8i | −0.122599 | − | 1.40593i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6119.60 | + | 10599.5i | 0.849493 | + | 1.47136i | 0.881662 | + | 0.471882i | \(0.156425\pi\) |
−0.0321693 | + | 0.999482i | \(0.510242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8529.55 | −1.16524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −690.914 | −0.0936409 | −0.0468204 | − | 0.998903i | \(-0.514909\pi\) | ||||
−0.0468204 | + | 0.998903i | \(0.514909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4423.65 | + | 7661.98i | 0.590177 | + | 1.02222i | 0.994208 | + | 0.107472i | \(0.0342755\pi\) |
−0.404031 | + | 0.914745i | \(0.632391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7810.88 | + | 5465.91i | −1.03397 | + | 0.723555i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2808.67 | + | 1621.58i | 0.366080 | + | 0.211356i | 0.671744 | − | 0.740783i | \(-0.265545\pi\) |
−0.305665 | + | 0.952139i | \(0.598879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1329.76i | − | 0.171992i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6942.37 | + | 12024.5i | −0.884325 | + | 1.53170i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9356.49 | + | 5401.97i | −1.18284 | + | 0.682915i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
−0.226173 | + | 0.974087i | \(0.572621\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −595.785 | + | 343.976i | −0.0741947 | + | 0.0428363i | −0.536638 | − | 0.843812i | \(-0.680306\pi\) |
0.462444 | + | 0.886649i | \(0.346973\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1299.60 | − | 2250.97i | 0.160639 | − | 0.278235i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3143.74i | − | 0.382873i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7348.56 | + | 4242.70i | 0.888418 | + | 0.512929i | 0.873425 | − | 0.486959i | \(-0.161894\pi\) |
0.0149935 | + | 0.999888i | \(0.495227\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6988.45 | − | 609.400i | 0.832638 | − | 0.0726068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9644.69 | − | 16705.1i | −1.14082 | − | 1.97595i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11025.1 | 1.28547 | 0.642736 | − | 0.766088i | \(-0.277799\pi\) | ||||
0.642736 | + | 0.766088i | \(0.277799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9636.91 | −1.11562 | −0.557808 | − | 0.829970i | \(-0.688357\pi\) | ||||
−0.557808 | + | 0.829970i | \(0.688357\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1529.48 | − | 2649.15i | −0.174567 | − | 0.302359i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11379.5 | − | 5310.30i | −1.28968 | − | 0.601835i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4664.33 | − | 2692.95i | −0.521283 | − | 0.300963i | 0.216176 | − | 0.976354i | \(-0.430641\pi\) |
−0.737459 | + | 0.675391i | \(0.763975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4428.30i | 0.491480i | 0.969336 | + | 0.245740i | \(0.0790309\pi\) | ||||
−0.969336 | + | 0.245740i | \(0.920969\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 507.751 | − | 879.451i | 0.0555813 | − | 0.0962697i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14675.4 | + | 8472.85i | −1.59549 | + | 0.921155i | −0.603145 | + | 0.797632i | \(0.706086\pi\) |
−0.992342 | + | 0.123523i | \(0.960581\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15157.8 | + | 8751.39i | −1.62567 | + | 0.938580i | −0.640304 | + | 0.768122i | \(0.721191\pi\) |
−0.985365 | + | 0.170458i | \(0.945475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1198.83 | − | 2076.44i | 0.127708 | − | 0.221197i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1975.26i | − | 0.207614i | −0.994597 | − | 0.103807i | \(-0.966898\pi\) | ||
0.994597 | − | 0.103807i | \(-0.0331024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7428.20 | + | 4288.67i | 0.775566 | + | 0.447773i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14386.9 | − | 6713.73i | −1.48235 | − | 0.691746i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6036.94 | + | 10456.3i | 0.617935 | + | 1.07029i | 0.989862 | + | 0.142032i | \(0.0453637\pi\) |
−0.371927 | + | 0.928262i | \(0.621303\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13447.2 | 1.35856 | 0.679281 | − | 0.733878i | \(-0.262292\pi\) | ||||
0.679281 | + | 0.733878i | \(0.262292\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15720.4 | −1.57795 | −0.788973 | − | 0.614428i | \(-0.789387\pi\) | ||||
−0.788973 | + | 0.614428i | \(0.789387\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 682.156 | + | 1181.53i | 0.0675940 | + | 0.117076i | 0.897842 | − | 0.440318i | \(-0.145134\pi\) |
−0.830248 | + | 0.557395i | \(0.811801\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12791.1 | + | 1115.40i | −1.25936 | + | 0.109817i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7314.65 | − | 4223.11i | −0.711052 | − | 0.410526i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2336.06i | − | 0.225654i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2078.39 | − | 3599.88i | 0.198255 | − | 0.343388i | −0.749708 | − | 0.661769i | \(-0.769806\pi\) |
0.947963 | + | 0.318381i | \(0.103139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4533.96 | − | 2617.69i | 0.429794 | − | 0.248142i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21753.3 | − | 12559.3i | 2.03663 | − | 1.17585i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6210.51 | + | 10756.9i | −0.577875 | + | 1.00091i | 0.417848 | + | 0.908517i | \(0.362785\pi\) |
−0.995723 | + | 0.0923918i | \(0.970549\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8234.71i | − | 0.756879i | −0.925626 | − | 0.378439i | \(-0.876461\pi\) | ||
0.925626 | − | 0.378439i | \(-0.123539\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3351.81 | − | 1935.17i | −0.306203 | − | 0.176786i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3624.01 | + | 2536.02i | −0.327081 | + | 0.228885i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1488.56 | + | 2578.26i | 0.133541 | + | 0.231300i | 0.925039 | − | 0.379871i | \(-0.124032\pi\) |
−0.791498 | + | 0.611172i | \(0.790698\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 537.349 | 0.0476327 | 0.0238163 | − | 0.999716i | \(-0.492418\pi\) | ||||
0.0238163 | + | 0.999716i | \(0.492418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 905.792 | 0.0798163 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4873.32 | − | 8440.83i | −0.424373 | − | 0.735036i | 0.571988 | − | 0.820262i | \(-0.306172\pi\) |
−0.996362 | + | 0.0852256i | \(0.972839\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1172.35 | − | 13444.2i | −0.101491 | − | 1.16387i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26425.8 | − | 15256.9i | −2.26108 | − | 1.30544i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4082.85i | − | 0.347318i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4831.31 | + | 8368.07i | −0.406264 | + | 0.703670i | −0.994468 | − | 0.105043i | \(-0.966502\pi\) |
0.588204 | + | 0.808713i | \(0.299835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5153.64 | + | 2975.46i | −0.430886 | + | 0.248772i | −0.699724 | − | 0.714413i | \(-0.746694\pi\) |
0.268838 | + | 0.963185i | \(0.413360\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1021.39 | − | 589.701i | 0.0844260 | − | 0.0487434i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4627.78 | + | 8015.54i | −0.380355 | + | 0.658794i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14284.1i | 1.16082i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27300.5 | + | 15762.0i | 2.20618 | + | 1.27374i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8573.33 | + | 7185.54i | −0.685119 | + | 0.574217i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4476.87 | + | 7754.17i | 0.355778 | + | 0.616225i | 0.987251 | − | 0.159173i | \(-0.0508826\pi\) |
−0.631473 | + | 0.775398i | \(0.717549\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22064.3 | −1.73418 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20723.2 | 1.61985 | 0.809926 | − | 0.586532i | \(-0.199507\pi\) | ||||
0.809926 | + | 0.586532i | \(0.199507\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1477.84 | − | 2559.70i | −0.114262 | − | 0.197907i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6889.54 | + | 14763.7i | −0.529789 | + | 1.13529i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11283.3 | − | 6514.43i | −0.858330 | − | 0.495557i | 0.00512296 | − | 0.999987i | \(-0.498369\pi\) |
−0.863453 | + | 0.504430i | \(0.831703\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14065.8i | − | 1.06426i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −955.378 | + | 1654.76i | −0.0715176 | + | 0.123872i | −0.899567 | − | 0.436784i | \(-0.856118\pi\) |
0.828049 | + | 0.560656i | \(0.189451\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22366.8 | − | 12913.5i | 1.66545 | − | 0.961546i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5509.88 | − | 3181.13i | 0.405951 | − | 0.234376i | −0.283098 | − | 0.959091i | \(-0.591362\pi\) |
0.689049 | + | 0.724715i | \(0.258029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3394.59 | − | 5879.61i | 0.248790 | − | 0.430918i | −0.714400 | − | 0.699737i | \(-0.753300\pi\) |
0.963190 | + | 0.268820i | \(0.0866336\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6697.49i | − | 0.485747i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6109.08 | + | 3527.08i | 0.440770 | + | 0.254479i | 0.703924 | − | 0.710275i | \(-0.251429\pi\) |
−0.263154 | + | 0.964754i | \(0.584763\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12976.9 | − | 18544.2i | −0.926632 | − | 1.32417i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8879.47 | + | 15379.7i | 0.630789 | + | 1.09256i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14742.1 | 1.03658 | 0.518290 | − | 0.855205i | \(-0.326569\pi\) | ||||
0.518290 | + | 0.855205i | \(0.326569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 900.679 | 0.0630082 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6998.75 | − | 12122.2i | −0.484662 | − | 0.839458i | 0.515183 | − | 0.857080i | \(-0.327724\pi\) |
−0.999845 | + | 0.0176216i | \(0.994391\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4130.35 | − | 5902.34i | −0.284585 | − | 0.406676i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 251.377 | + | 145.133i | 0.0171469 | + | 0.00989977i | 0.508549 | − | 0.861033i | \(-0.330182\pi\) |
−0.491402 | + | 0.870933i | \(0.663515\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3671.51i | 0.249191i | 0.992208 | + | 0.124596i | \(0.0397634\pi\) | ||||
−0.992208 | + | 0.124596i | \(0.960237\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2110.12 | + | 3654.83i | −0.141799 | + | 0.245603i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14231.9 | + | 8216.78i | −0.951655 | + | 0.549438i | −0.893595 | − | 0.448875i | \(-0.851825\pi\) |
−0.0580603 | + | 0.998313i | \(0.518492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5888.37 | − | 3399.65i | 0.389882 | − | 0.225099i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11452.7 | − | 19836.6i | 0.754599 | − | 1.30700i | −0.190975 | − | 0.981595i | \(-0.561165\pi\) |
0.945574 | − | 0.325408i | \(-0.105502\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10613.9i | 0.692541i | 0.938135 | + | 0.346271i | \(0.112552\pi\) | ||||
−0.938135 | + | 0.346271i | \(0.887448\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5261.57 | + | 3037.77i | 0.341648 | + | 0.197251i | 0.661001 | − | 0.750385i | \(-0.270132\pi\) |
−0.319352 | + | 0.947636i | \(0.603465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1189.71 | − | 2549.44i | 0.0765085 | − | 0.163951i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7866.84 | + | 13625.8i | 0.503478 | + | 0.872049i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2375.59 | 0.150590 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16951.1 | −1.06944 | −0.534718 | − | 0.845031i | \(-0.679582\pi\) | ||||
−0.534718 | + | 0.845031i | \(0.679582\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13646.6 | + | 23636.5i | 0.852830 | + | 1.47715i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17501.9 | − | 6381.47i | −1.08862 | − | 0.396928i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10591.3 | − | 6114.91i | −0.652625 | − | 0.376793i | 0.136836 | − | 0.990594i | \(-0.456307\pi\) |
−0.789461 | + | 0.613800i | \(0.789640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11251.9i | 0.690095i | 0.938585 | + | 0.345048i | \(0.112137\pi\) | ||||
−0.938585 | + | 0.345048i | \(0.887863\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3237.83 | − | 5608.08i | 0.196742 | − | 0.340767i | −0.750728 | − | 0.660611i | \(-0.770297\pi\) |
0.947470 | + | 0.319844i | \(0.103630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10698.0 | + | 6176.50i | −0.647047 | + | 0.373573i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16416.0 | − | 9477.77i | 0.983778 | − | 0.567984i | 0.0803694 | − | 0.996765i | \(-0.474390\pi\) |
0.903409 | + | 0.428781i | \(0.141057\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1419.44 | − | 2458.55i | 0.0846751 | − | 0.146662i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22148.1i | − | 1.30921i | −0.755973 | − | 0.654603i | \(-0.772836\pi\) | ||
0.755973 | − | 0.654603i | \(-0.227164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14010.5 | − | 8088.96i | −0.824425 | − | 0.475982i | 0.0275153 | − | 0.999621i | \(-0.491240\pi\) |
−0.851940 | + | 0.523640i | \(0.824574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −477.923 | − | 5480.71i | −0.0278693 | − | 0.319598i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4236.98 | − | 7338.66i | −0.245962 | − | 0.426018i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22113.2 | 1.27224 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16420.1 | 0.940488 | 0.470244 | − | 0.882537i | \(-0.344166\pi\) | ||||
0.470244 | + | 0.882537i | \(0.344166\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11989.3 | + | 20766.0i | 0.680627 | + | 1.17888i | 0.974790 | + | 0.223125i | \(0.0716258\pi\) |
−0.294163 | + | 0.955755i | \(0.595041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24148.2 | − | 16898.5i | 1.36484 | − | 0.955088i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1924.00 | − | 1110.82i | −0.107789 | − | 0.0622319i | 0.445136 | − | 0.895463i | \(-0.353155\pi\) |
−0.552925 | + | 0.833231i | \(0.686488\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 44952.9i | − | 2.50739i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14787.3 | + | 25612.3i | −0.817635 | + | 1.41619i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20155.6 | + | 11636.9i | −1.10963 | + | 0.640647i | −0.938734 | − | 0.344642i | \(-0.888000\pi\) |
−0.170899 | + | 0.985289i | \(0.554667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −798.954 | + | 461.276i | −0.0436058 | + | 0.0251758i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3240.77 | + | 5613.17i | −0.176116 | + | 0.305042i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5003.94i | 0.269610i | 0.990872 | + | 0.134805i | \(0.0430407\pi\) | ||||
−0.990872 | + | 0.134805i | \(0.956959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1571.12 | + | 907.088i | 0.0842902 | + | 0.0486650i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1058.82 | − | 92.3302i | 0.0563240 | − | 0.00491151i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15002.2 | − | 25984.6i | −0.794669 | − | 1.37641i | −0.923049 | − | 0.384682i | \(-0.874311\pi\) |
0.128381 | − | 0.991725i | \(-0.459022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2582.25 | 0.135633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27957.3 | 1.46230 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7195.48 | + | 12462.9i | 0.373221 | + | 0.646438i | 0.990059 | − | 0.140652i | \(-0.0449198\pi\) |
−0.616838 | + | 0.787090i | \(0.711587\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32445.4 | − | 15140.8i | −1.67591 | − | 0.782072i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16881.8 | − | 9746.73i | −0.864794 | − | 0.499289i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4931.70i | − | 0.251591i | −0.992056 | − | 0.125795i | \(-0.959852\pi\) | ||
0.992056 | − | 0.125795i | \(-0.0401483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3191.22 | − | 5527.36i | 0.161466 | − | 0.279667i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17813.2 | − | 10284.4i | 0.897604 | − | 0.518232i | 0.0211822 | − | 0.999776i | \(-0.493257\pi\) |
0.876422 | + | 0.481543i | \(0.159924\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19580.7 | − | 11305.0i | 0.978652 | − | 0.565025i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15864.0 | + | 27477.2i | −0.789669 | + | 1.36775i | 0.136501 | + | 0.990640i | \(0.456414\pi\) |
−0.926170 | + | 0.377106i | \(0.876919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30966.4i | 1.52900i | 0.644623 | + | 0.764501i | \(0.277014\pi\) | ||||
−0.644623 | + | 0.764501i | \(0.722986\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11075.0 | − | 6394.16i | −0.544640 | − | 0.314448i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33519.5 | + | 15642.0i | 1.63521 | + | 0.763081i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17017.6 | + | 29475.4i | 0.826873 | + | 1.43219i | 0.900480 | + | 0.434898i | \(0.143216\pi\) |
−0.0736070 | + | 0.997287i | \(0.523451\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40144.0 | 1.93508 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1216.96 | 0.0584293 | 0.0292147 | − | 0.999573i | \(-0.490699\pi\) | ||||
0.0292147 | + | 0.999573i | \(0.490699\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14359.4 | + | 24871.2i | 0.684006 | + | 1.18473i | 0.973748 | + | 0.227628i | \(0.0730971\pi\) |
−0.289742 | + | 0.957105i | \(0.593570\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25791.9 | + | 2249.08i | −1.22376 | + | 0.106713i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17815.7 | − | 10285.9i | −0.838708 | − | 0.484229i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 914.245i | 0.0428719i | 0.999770 | + | 0.0214360i | \(0.00682380\pi\) | ||||
−0.999770 | + | 0.0214360i | \(0.993176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6138.69 | + | 10632.5i | −0.285632 | + | 0.494729i | −0.972762 | − | 0.231805i | \(-0.925537\pi\) |
0.687131 | + | 0.726534i | \(0.258870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5144.37 | − | 2970.10i | 0.238440 | − | 0.137663i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4286.64 | + | 2474.89i | −0.197156 | + | 0.113828i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3894.52 | − | 6745.51i | 0.178434 | − | 0.309057i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39760.5i | 1.80779i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16936.5 | + | 9778.31i | 0.767119 | + | 0.442896i | 0.831846 | − | 0.555007i | \(-0.187284\pi\) |
−0.0647271 | + | 0.997903i | \(0.520618\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24829.2 | − | 17375.0i | 1.11609 | − | 0.781018i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18412.9 | + | 31892.1i | 0.824542 | + | 1.42815i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3319.70 | 0.147540 | 0.0737702 | − | 0.997275i | \(-0.476497\pi\) | ||||
0.0737702 | + | 0.997275i | \(0.476497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3085.23 | 0.136605 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11882.2 | + | 20580.6i | 0.522184 | + | 0.904450i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1370.21 | − | 15713.2i | −0.0599919 | − | 0.687973i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27790.1 | − | 16044.6i | −1.20772 | − | 0.697280i | −0.245462 | − | 0.969406i | \(-0.578940\pi\) |
−0.962261 | + | 0.272126i | \(0.912273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17924.1i | 0.776081i | 0.921642 | + | 0.388040i | \(0.126848\pi\) | ||||
−0.921642 | + | 0.388040i | \(0.873152\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16923.0 | + | 29311.4i | −0.727344 | + | 1.25980i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4221.11 | − | 2437.06i | 0.180756 | − | 0.104360i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3839.60 | − | 2216.79i | 0.163219 | − | 0.0942347i | −0.416165 | − | 0.909289i | \(-0.636626\pi\) |
0.579385 | + | 0.815054i | \(0.303293\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6029.71 | + | 10443.8i | −0.255386 | + | 0.442341i | −0.965000 | − | 0.262249i | \(-0.915536\pi\) |
0.709614 | + | 0.704590i | \(0.248869\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1552.07i | − | 0.0652609i | −0.999467 | − | 0.0326304i | \(-0.989612\pi\) | ||
0.999467 | − | 0.0326304i | \(-0.0103884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3856.52 | + | 2226.56i | 0.161571 | + | 0.0932832i | 0.578605 | − | 0.815608i | \(-0.303597\pi\) |
−0.417034 | + | 0.908891i | \(0.636930\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5429.80 | − | 6478.49i | −0.225848 | − | 0.269467i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26686.9 | − | 46223.1i | −1.10604 | − | 1.91571i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22708.5 | −0.934429 | −0.467214 | − | 0.884144i | \(-0.654742\pi\) | ||||
−0.467214 | + | 0.884144i | \(0.654742\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −274.978 | −0.0112747 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5940.78 | + | 10289.7i | 0.241857 | + | 0.418908i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2094.06 | + | 4487.39i | −0.0849502 | + | 0.182041i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4504.41 | + | 2600.62i | 0.181445 | + | 0.104757i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 13532.2i | − | 0.543183i | −0.962413 | − | 0.271591i | \(-0.912450\pi\) | ||
0.962413 | − | 0.271591i | \(-0.0875499\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7847.69 | + | 13592.6i | −0.312803 | + | 0.541790i | −0.978968 | − | 0.204014i | \(-0.934601\pi\) |
0.666165 | + | 0.745804i | \(0.267935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31542.4 | − | 18211.0i | 1.25287 | − | 0.723342i | 0.281188 | − | 0.959653i | \(-0.409272\pi\) |
0.971678 | + | 0.236311i | \(0.0759383\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26424.8 | − | 15256.4i | 1.04231 | − | 0.601777i | 0.121822 | − | 0.992552i | \(-0.461126\pi\) |
0.920486 | + | 0.390775i | \(0.127793\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1562.45 | − | 2706.24i | 0.0614159 | − | 0.106375i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 28689.5i | − | 1.11994i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32608.5 | + | 18826.5i | 1.26854 | + | 0.732390i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 146.739 | + | 209.692i | 0.00566934 | + | 0.00810158i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1409.59 | + | 2441.48i | 0.0542742 | + | 0.0940057i | 0.891886 | − | 0.452260i | \(-0.149382\pi\) |
−0.837612 | + | 0.546266i | \(0.816049\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18469.6 | 0.706306 | 0.353153 | − | 0.935566i | \(-0.385110\pi\) | ||||
0.353153 | + | 0.935566i | \(0.385110\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2535.09 | 0.0966168 | 0.0483084 | − | 0.998832i | \(-0.484617\pi\) | ||||
0.0483084 | + | 0.998832i | \(0.484617\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21522.4 | + | 37278.0i | 0.814716 | + | 1.41113i | 0.909532 | + | 0.415635i | \(0.136440\pi\) |
−0.0948157 | + | 0.995495i | \(0.530226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18361.4 | + | 26238.8i | 0.692714 | + | 0.989899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2040.46 | + | 1178.06i | 0.0764628 | + | 0.0441458i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 54813.4i | − | 2.04716i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3757.90 | − | 6508.88i | 0.139414 | − | 0.241472i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11621.8 | + | 6709.83i | −0.429720 | + | 0.248099i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39270.5 | + | 22672.8i | −1.44243 | + | 0.832785i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6840.28 | − | 11847.7i | 0.250416 | − | 0.433734i | −0.713224 | − | 0.700936i | \(-0.752766\pi\) |
0.963640 | + | 0.267202i | \(0.0860992\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33621.6i | 1.22276i | 0.791338 | + | 0.611379i | \(0.209385\pi\) | ||||
−0.791338 | + | 0.611379i | \(0.790615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34517.1 | + | 19928.5i | 1.25120 | + | 0.722383i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1408.64 | − | 3018.59i | 0.0507279 | − | 0.108705i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17126.3 | − | 29663.5i | −0.614737 | − | 1.06476i | −0.990431 | − | 0.138011i | \(-0.955929\pi\) |
0.375694 | − | 0.926744i | \(-0.377404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12971.4 | 0.462576 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11964.9 | 0.425302 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12337.4 | + | 21369.0i | 0.435712 | + | 0.754675i | 0.997353 | − | 0.0727058i | \(-0.0231634\pi\) |
−0.561642 | + | 0.827380i | \(0.689830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1117.33 | − | 6357.93i | −0.0393330 | − | 0.223816i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10986.3 | + | 6342.92i | 0.384266 | + | 0.221856i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32885.0i | − | 1.14654i | −0.819367 | − | 0.573269i | \(-0.805675\pi\) | ||
0.819367 | − | 0.573269i | \(-0.194325\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4016.54 | − | 6956.85i | 0.139145 | − | 0.241006i | −0.788028 | − | 0.615639i | \(-0.788898\pi\) |
0.927173 | + | 0.374633i | \(0.122231\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12289.8 | + | 7095.52i | −0.424402 | + | 0.245029i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15192.1 | + | 8771.14i | −0.521305 | + | 0.300975i | −0.737468 | − | 0.675382i | \(-0.763979\pi\) |
0.216164 | + | 0.976357i | \(0.430646\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19787.8 | + | 34273.5i | −0.676860 | + | 1.17236i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40802.9i | − | 1.38692i | −0.720494 | − | 0.693461i | \(-0.756085\pi\) | ||
0.720494 | − | 0.693461i | \(-0.243915\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16970.5 | − | 9797.95i | −0.575030 | − | 0.331994i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4582.19 | − | 52547.5i | −0.154293 | − | 1.76939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13750.4 | − | 23816.3i | −0.461561 | − | 0.799447i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 42341.5 | 1.41246 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57938.1 | 1.92675 | 0.963373 | − | 0.268164i | \(-0.0864169\pi\) | ||||
0.963373 | + | 0.268164i | \(0.0864169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7580.65 | + | 13130.1i | 0.250540 | + | 0.433948i | 0.963675 | − | 0.267079i | \(-0.0860584\pi\) |
−0.713134 | + | 0.701027i | \(0.752725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −886.913 | + | 620.646i | −0.0292221 | + | 0.0204491i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25781.1 | + | 14884.7i | 0.844228 | + | 0.487415i | 0.858699 | − | 0.512480i | \(-0.171273\pi\) |
−0.0144714 | + | 0.999895i | \(0.504607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4954.21i | 0.161733i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16517.5 | + | 28609.1i | −0.535937 | + | 0.928269i | 0.463181 | + | 0.886264i | \(0.346708\pi\) |
−0.999117 | + | 0.0420055i | \(0.986625\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41780.4 | − | 24121.9i | 1.35151 | − | 0.780293i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12101.9 | − | 6987.05i | 0.389099 | − | 0.224646i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4752.11 | + | 8230.89i | −0.152327 | + | 0.263837i | −0.932082 | − | 0.362246i | \(-0.882010\pi\) |
0.779756 | + | 0.626084i | \(0.215343\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 33978.2i | − | 1.08259i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15522.5 | + | 8961.95i | 0.493083 | + | 0.284682i | 0.725853 | − | 0.687850i | \(-0.241445\pi\) |
−0.232769 | + | 0.972532i | \(0.574779\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.4.bt.d.17.4 | 48 | ||
3.2 | odd | 2 | inner | 1008.4.bt.d.17.21 | 48 | ||
4.3 | odd | 2 | 504.4.bl.a.17.4 | ✓ | 48 | ||
7.5 | odd | 6 | inner | 1008.4.bt.d.593.21 | 48 | ||
12.11 | even | 2 | 504.4.bl.a.17.21 | yes | 48 | ||
21.5 | even | 6 | inner | 1008.4.bt.d.593.4 | 48 | ||
28.19 | even | 6 | 504.4.bl.a.89.21 | yes | 48 | ||
84.47 | odd | 6 | 504.4.bl.a.89.4 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.4.bl.a.17.4 | ✓ | 48 | 4.3 | odd | 2 | ||
504.4.bl.a.17.21 | yes | 48 | 12.11 | even | 2 | ||
504.4.bl.a.89.4 | yes | 48 | 84.47 | odd | 6 | ||
504.4.bl.a.89.21 | yes | 48 | 28.19 | even | 6 | ||
1008.4.bt.d.17.4 | 48 | 1.1 | even | 1 | trivial | ||
1008.4.bt.d.17.21 | 48 | 3.2 | odd | 2 | inner | ||
1008.4.bt.d.593.4 | 48 | 21.5 | even | 6 | inner | ||
1008.4.bt.d.593.21 | 48 | 7.5 | odd | 6 | inner |