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 | 593.21 | ||
Character | \(\chi\) | \(=\) | 1008.593 |
Dual form | 1008.4.bt.d.17.21 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | −0.260510 | − | 0.965471i | \(-0.583891\pi\) |
0.966378 | − | 0.257127i | \(-0.0827759\pi\) | |||||||
\(6\) | 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 | \(-0.814162\pi\) |
0.0601918 | + | 0.998187i | \(0.480829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 54.3118i | − | 1.15872i | −0.815071 | − | 0.579361i | \(-0.803302\pi\) | ||
0.815071 | − | 0.579361i | \(-0.196698\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.3222 | + | 21.3427i | 0.175798 | + | 0.304491i | 0.940437 | − | 0.339967i | \(-0.110416\pi\) |
−0.764639 | + | 0.644459i | \(0.777083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.2989 | − | 9.41015i | −0.196801 | − | 0.113623i | 0.398362 | − | 0.917228i | \(-0.369579\pi\) |
−0.595162 | + | 0.803606i | \(0.702912\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 46.7289 | + | 26.9789i | 0.423637 | + | 0.244587i | 0.696632 | − | 0.717429i | \(-0.254681\pi\) |
−0.272995 | + | 0.962015i | \(0.588014\pi\) | |||||||
\(24\) | 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 | −0.615233 | − | 0.788345i | \(-0.710938\pi\) |
0.375111 | + | 0.926980i | \(0.377605\pi\) | |||||||
\(32\) | 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 | −0.953010 | − | 0.302940i | \(-0.902032\pi\) |
0.738858 | + | 0.673861i | \(0.235365\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −263.002 | −1.00181 | −0.500903 | − | 0.865503i | \(-0.666999\pi\) | ||||
−0.500903 | + | 0.865503i | \(0.666999\pi\) | |||||||
\(42\) | 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 | \(-0.771101\pi\) |
0.946659 | + | 0.322237i | \(0.104435\pi\) | |||||||
\(48\) | 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 | \(-0.916005\pi\) |
−0.256810 | + | 0.966462i | \(0.582671\pi\) | |||||||
\(54\) | 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 | \(-0.0294334\pi\) |
−0.577829 | + | 0.816158i | \(0.696100\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 587.204 | + | 339.022i | 1.23252 | + | 0.711596i | 0.967555 | − | 0.252662i | \(-0.0813061\pi\) |
0.264966 | + | 0.964258i | \(0.414639\pi\) | |||||||
\(62\) | 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 | 0.987128 | + | 0.159929i | \(0.0511266\pi\) |
−0.355061 | + | 0.934843i | \(0.615540\pi\) | |||||||
\(68\) | 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 | 0.100058 | − | 0.994982i | \(-0.468097\pi\) |
0.911708 | + | 0.410838i | \(0.134764\pi\) | |||||||
\(74\) | 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 | 0.361856 | + | 0.932234i | \(0.382143\pi\) |
−0.988266 | + | 0.152740i | \(0.951190\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1222.11 | −1.61619 | −0.808096 | − | 0.589050i | \(-0.799502\pi\) | ||||
−0.808096 | + | 0.589050i | \(0.799502\pi\) | |||||||
\(84\) | 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 | \(-0.862168\pi\) |
0.817244 | + | 0.576292i | \(0.195501\pi\) | |||||||
\(90\) | 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 | \(-0.686672\pi\) | ||
0.553406 | − | 0.832912i | \(-0.313328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 28.6940 | + | 49.6994i | 0.0282689 | + | 0.0489631i | 0.879814 | − | 0.475319i | \(-0.157667\pi\) |
−0.851545 | + | 0.524282i | \(0.824334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1674.25 | + | 966.626i | 1.60163 | + | 0.924704i | 0.991161 | + | 0.132667i | \(0.0423541\pi\) |
0.610473 | + | 0.792037i | \(0.290979\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1729.67 | + | 998.625i | 1.56274 | + | 0.902249i | 0.996978 | + | 0.0776819i | \(0.0247519\pi\) |
0.565764 | + | 0.824567i | \(0.308581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 698.958 | + | 1210.63i | 0.614202 | + | 1.06383i | 0.990524 | + | 0.137340i | \(0.0438554\pi\) |
−0.376322 | + | 0.926489i | \(0.622811\pi\) | |||||||
\(110\) | 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 | \(-0.852437\pi\) |
0.834476 | + | 0.551044i | \(0.185770\pi\) | |||||||
\(132\) | 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 | −0.539205 | + | 0.842174i | \(0.681275\pi\) |
−0.998947 | + | 0.0458784i | \(0.985391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 58.4498i | 0.0356665i | 0.999841 | + | 0.0178333i | \(0.00567680\pi\) | ||||
−0.999841 | + | 0.0178333i | \(0.994323\pi\) | |||||||
\(140\) | 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 | \(-0.404833\pi\) |
−0.680337 | + | 0.732900i | \(0.738166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1271.69 | − | 2202.64i | −0.685357 | − | 1.18707i | −0.973325 | − | 0.229433i | \(-0.926313\pi\) |
0.287968 | − | 0.957640i | \(-0.407020\pi\) | |||||||
\(152\) | 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 | −0.938566 | − | 0.345101i | \(-0.887845\pi\) |
−0.170417 | + | 0.985372i | \(0.554511\pi\) | |||||||
\(158\) | 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 | 0.484631 | + | 0.874718i | \(0.338954\pi\) |
−0.999844 | + | 0.0176561i | \(0.994380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3381.59 | −1.56692 | −0.783458 | − | 0.621445i | \(-0.786546\pi\) | ||||
−0.783458 | + | 0.621445i | \(0.786546\pi\) | |||||||
\(168\) | 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 | \(-0.847185\pi\) |
0.843454 | + | 0.537202i | \(0.180519\pi\) | |||||||
\(174\) | 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 | \(-0.924851\pi\) |
−0.283566 | + | 0.958953i | \(0.591518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2872.95i | 1.17980i | 0.807475 | + | 0.589902i | \(0.200834\pi\) | ||||
−0.807475 | + | 0.589902i | \(0.799166\pi\) | |||||||
\(182\) | 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 | \(-0.408897\pi\) |
−0.689638 | + | 0.724154i | \(0.742230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1341.31 | − | 2323.21i | −0.500256 | − | 0.866468i | −1.00000 | 0.000295140i | \(-0.999906\pi\) | |
0.499744 | − | 0.866173i | \(-0.333427\pi\) | |||||||
\(194\) | 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 | −0.129728 | − | 0.991550i | \(-0.541411\pi\) |
0.793843 | + | 0.608123i | \(0.208077\pi\) | |||||||
\(200\) | 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 | \(-0.957546\pi\) | ||
0.991119 | − | 0.132979i | \(-0.0424544\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2687.02 | − | 4654.05i | −0.785654 | − | 1.36079i | −0.928607 | − | 0.371064i | \(-0.878993\pi\) |
0.142953 | − | 0.989729i | \(-0.454340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5385.90 | + | 3109.55i | 1.55419 | + | 0.897314i | 0.997793 | + | 0.0663998i | \(0.0211513\pi\) |
0.556400 | + | 0.830914i | \(0.312182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5180.55 | + | 2990.99i | 1.45661 | + | 0.840972i | 0.998842 | − | 0.0481015i | \(-0.0153171\pi\) |
0.457764 | + | 0.889074i | \(0.348650\pi\) | |||||||
\(234\) | 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 | −0.648001 | − | 0.761640i | \(-0.724395\pi\) |
0.335599 | + | 0.942005i | \(0.391061\pi\) | |||||||
\(242\) | 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 | \(-0.529303\pi\) | ||||
−0.0919292 | + | 0.995766i | \(0.529303\pi\) | |||||||
\(252\) | 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 | −0.265972 | − | 0.963981i | \(-0.585693\pi\) |
0.967818 | − | 0.251651i | \(-0.0809736\pi\) | |||||||
\(258\) | 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 | \(-0.611506\pi\) |
0.641837 | + | 0.766841i | \(0.278173\pi\) | |||||||
\(264\) | 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 | 0.999703 | + | 0.0243516i | \(0.00775212\pi\) |
−0.478763 | + | 0.877944i | \(0.658915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 352.954 | + | 203.778i | 0.0791160 | + | 0.0456777i | 0.539036 | − | 0.842283i | \(-0.318789\pi\) |
−0.459920 | + | 0.887960i | \(0.652122\pi\) | |||||||
\(272\) | 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 | 0.768086 | − | 0.640346i | \(-0.221209\pi\) |
−0.938599 | + | 0.345009i | \(0.887876\pi\) | |||||||
\(278\) | 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 | −0.391938 | − | 0.919992i | \(-0.628195\pi\) |
0.600767 | + | 0.799424i | \(0.294862\pi\) | |||||||
\(284\) | 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 | \(-0.750613\pi\) | ||||
−0.708468 | + | 0.705743i | \(0.750613\pi\) | |||||||
\(294\) | 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 | \(-0.731520\pi\) | ||
0.664887 | − | 0.746944i | \(-0.268480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2093.96 | − | 3626.85i | −0.381793 | − | 0.661285i | 0.609525 | − | 0.792767i | \(-0.291360\pi\) |
−0.991319 | + | 0.131481i | \(0.958027\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6183.56 | + | 3570.08i | 1.11666 | + | 0.644706i | 0.940547 | − | 0.339663i | \(-0.110313\pi\) |
0.176117 | + | 0.984369i | \(0.443646\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5241.84 | − | 3026.38i | −0.928742 | − | 0.536210i | −0.0423286 | − | 0.999104i | \(-0.513478\pi\) |
−0.886414 | + | 0.462894i | \(0.846811\pi\) | |||||||
\(318\) | 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 | −0.0280795 | + | 0.999606i | \(0.508939\pi\) |
−0.851644 | + | 0.524120i | \(0.824394\pi\) | |||||||
\(332\) | 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 | \(-0.676763\pi\) |
0.472285 | + | 0.881446i | \(0.343429\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1777.77i | − | 0.272670i | −0.990663 | − | 0.136335i | \(-0.956468\pi\) | ||
0.990663 | − | 0.136335i | \(-0.0435324\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4076.99 | + | 7061.56i | 0.614721 | + | 1.06473i | 0.990433 | + | 0.137991i | \(0.0440646\pi\) |
−0.375713 | + | 0.926736i | \(0.622602\pi\) | |||||||
\(354\) | 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 | \(-0.400048\pi\) |
−0.669243 | + | 0.743044i | \(0.733381\pi\) | |||||||
\(360\) | 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 | −0.483320 | − | 0.875444i | \(-0.660569\pi\) |
0.516497 | + | 0.856289i | \(0.327236\pi\) | |||||||
\(368\) | 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 | −0.0321693 | − | 0.999482i | \(-0.510242\pi\) |
0.881662 | − | 0.471882i | \(-0.156425\pi\) | |||||||
\(374\) | 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 | 0.404031 | + | 0.914745i | \(0.367609\pi\) |
−0.994208 | + | 0.107472i | \(0.965725\pi\) | |||||||
\(384\) | 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 | \(-0.734455\pi\) |
0.305665 | + | 0.952139i | \(0.401121\pi\) | |||||||
\(390\) | 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 | −0.226173 | − | 0.974087i | \(-0.572621\pi\) |
−0.956671 | + | 0.291172i | \(0.905955\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 595.785 | + | 343.976i | 0.0741947 | + | 0.0428363i | 0.536638 | − | 0.843812i | \(-0.319694\pi\) |
−0.462444 | + | 0.886649i | \(0.653027\pi\) | |||||||
\(402\) | 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 | 0.0149935 | − | 0.999888i | \(-0.495227\pi\) |
0.873425 | + | 0.486959i | \(0.161894\pi\) | |||||||
\(410\) | 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 | \(-0.722201\pi\) | ||||
−0.642736 | + | 0.766088i | \(0.722201\pi\) | |||||||
\(420\) | 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 | \(-0.569359\pi\) |
0.737459 | + | 0.675391i | \(0.236025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4428.30i | − | 0.491480i | −0.969336 | − | 0.245740i | \(-0.920969\pi\) | ||
0.969336 | − | 0.245740i | \(-0.0790309\pi\) | |||||||
\(434\) | 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 | −0.992342 | − | 0.123523i | \(-0.960581\pi\) |
−0.603145 | − | 0.797632i | \(-0.706086\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15157.8 | + | 8751.39i | 1.62567 | + | 0.938580i | 0.985365 | + | 0.170458i | \(0.0545247\pi\) |
0.640304 | + | 0.768122i | \(0.278809\pi\) | |||||||
\(444\) | 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 | −0.371927 | − | 0.928262i | \(-0.621303\pi\) |
0.989862 | − | 0.142032i | \(-0.0453637\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13447.2 | −1.35856 | −0.679281 | − | 0.733878i | \(-0.737708\pi\) | ||||
−0.679281 | + | 0.733878i | \(0.737708\pi\) | |||||||
\(462\) | 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 | \(-0.854866\pi\) |
0.830248 | + | 0.557395i | \(0.188199\pi\) | |||||||
\(468\) | 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 | \(-0.230194\pi\) |
−0.947963 | + | 0.318381i | \(0.896861\pi\) | |||||||
\(480\) | 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 | −0.995723 | − | 0.0923918i | \(-0.970549\pi\) |
0.417848 | − | 0.908517i | \(-0.362785\pi\) | |||||||
\(488\) | 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 | −0.791498 | − | 0.611172i | \(-0.790698\pi\) |
0.925039 | + | 0.379871i | \(0.124032\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −537.349 | −0.0476327 | −0.0238163 | − | 0.999716i | \(-0.507582\pi\) | ||||
−0.0238163 | + | 0.999716i | \(0.507582\pi\) | |||||||
\(504\) | 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 | \(-0.693828\pi\) |
0.996362 | + | 0.0852256i | \(0.0271611\pi\) | |||||||
\(510\) | 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 | \(-0.0334980\pi\) |
−0.588204 | + | 0.808713i | \(0.700165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5153.64 | − | 2975.46i | −0.430886 | − | 0.248772i | 0.268838 | − | 0.963185i | \(-0.413360\pi\) |
−0.699724 | + | 0.714413i | \(0.746694\pi\) | |||||||
\(524\) | 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 | −0.631473 | − | 0.775398i | \(-0.717549\pi\) |
0.987251 | + | 0.159173i | \(0.0508826\pi\) | |||||||
\(542\) | 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 | \(-0.501631\pi\) |
0.863453 | + | 0.504430i | \(0.168297\pi\) | |||||||
\(558\) | 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 | \(-0.143882\pi\) |
−0.828049 | + | 0.560656i | \(0.810549\pi\) | |||||||
\(564\) | 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 | \(-0.408638\pi\) |
−0.689049 | + | 0.724715i | \(0.741971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3394.59 | + | 5879.61i | 0.248790 | + | 0.430918i | 0.963190 | − | 0.268820i | \(-0.0866336\pi\) |
−0.714400 | + | 0.699737i | \(0.753300\pi\) | |||||||
\(572\) | 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 | −0.263154 | − | 0.964754i | \(-0.584763\pi\) |
0.703924 | + | 0.710275i | \(0.251429\pi\) | |||||||
\(578\) | 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 | \(-0.673431\pi\) | ||||
−0.518290 | + | 0.855205i | \(0.673431\pi\) | |||||||
\(588\) | 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 | \(-0.672276\pi\) |
0.999845 | + | 0.0176216i | \(0.00560944\pi\) | |||||||
\(594\) | 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 | \(-0.669818\pi\) |
0.491402 | + | 0.870933i | \(0.336485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3671.51i | − | 0.249191i | −0.992208 | − | 0.124596i | \(-0.960237\pi\) | ||
0.992208 | − | 0.124596i | \(-0.0397634\pi\) | |||||||
\(602\) | 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 | −0.0580603 | − | 0.998313i | \(-0.518492\pi\) |
−0.893595 | + | 0.448875i | \(0.851825\pi\) | |||||||
\(608\) | 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 | 0.945574 | + | 0.325408i | \(0.105502\pi\) |
−0.190975 | + | 0.981595i | \(0.561165\pi\) | |||||||
\(614\) | 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 | −0.319352 | − | 0.947636i | \(-0.603465\pi\) |
0.661001 | + | 0.750385i | \(0.270132\pi\) | |||||||
\(620\) | 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 | \(-0.543693\pi\) |
0.789461 | + | 0.613800i | \(0.210360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11251.9i | − | 0.690095i | −0.938585 | − | 0.345048i | \(-0.887863\pi\) | ||
0.938585 | − | 0.345048i | \(-0.112137\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3237.83 | − | 5608.08i | −0.196742 | − | 0.340767i | 0.750728 | − | 0.660611i | \(-0.229703\pi\) |
−0.947470 | + | 0.319844i | \(0.896370\pi\) | |||||||
\(648\) | 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 | \(-0.525610\pi\) |
−0.903409 | + | 0.428781i | \(0.858943\pi\) | |||||||
\(654\) | 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 | −0.851940 | − | 0.523640i | \(-0.824574\pi\) |
0.0275153 | + | 0.999621i | \(0.491240\pi\) | |||||||
\(662\) | 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 | 0.294163 | + | 0.955755i | \(0.404959\pi\) |
−0.974790 | + | 0.223125i | \(0.928374\pi\) | |||||||
\(678\) | 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 | \(-0.646845\pi\) |
0.552925 | + | 0.833231i | \(0.313512\pi\) | |||||||
\(684\) | 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 | −0.170899 | − | 0.985289i | \(-0.554667\pi\) |
−0.938734 | + | 0.344642i | \(0.888000\pi\) | |||||||
\(692\) | 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 | 0.128381 | + | 0.991725i | \(0.459022\pi\) |
−0.923049 | + | 0.384682i | \(0.874311\pi\) | |||||||
\(710\) | 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 | \(-0.955080\pi\) |
0.616838 | + | 0.787090i | \(0.288413\pi\) | |||||||
\(720\) | 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 | \(0.0401483\pi\) | ||||
−0.992056 | + | 0.125795i | \(0.959852\pi\) | |||||||
\(728\) | 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 | 0.876422 | − | 0.481543i | \(-0.159924\pi\) |
0.0211822 | + | 0.999776i | \(0.493257\pi\) | |||||||
\(734\) | 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 | −0.926170 | − | 0.377106i | \(-0.876919\pi\) |
0.136501 | − | 0.990640i | \(-0.456414\pi\) | |||||||
\(740\) | 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 | −0.0736070 | − | 0.997287i | \(-0.523451\pi\) |
0.900480 | − | 0.434898i | \(-0.143216\pi\) | |||||||
\(752\) | 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 | 0.289742 | + | 0.957105i | \(0.406430\pi\) |
−0.973748 | + | 0.227628i | \(0.926903\pi\) | |||||||
\(762\) | 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 | \(-0.993176\pi\) | ||
0.999770 | − | 0.0214360i | \(-0.00682380\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6138.69 | + | 10632.5i | 0.285632 | + | 0.494729i | 0.972762 | − | 0.231805i | \(-0.0744633\pi\) |
−0.687131 | + | 0.726534i | \(0.741130\pi\) | |||||||
\(774\) | 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 | −0.0647271 | − | 0.997903i | \(-0.520618\pi\) |
0.831846 | + | 0.555007i | \(0.187284\pi\) | |||||||
\(788\) | 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 | \(-0.523503\pi\) | ||||
−0.0737702 | + | 0.997275i | \(0.523503\pi\) | |||||||
\(798\) | 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 | \(-0.421060\pi\) |
0.962261 | + | 0.272126i | \(0.0877269\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17924.1i | − | 0.776081i | −0.921642 | − | 0.388040i | \(-0.873152\pi\) | ||
0.921642 | − | 0.388040i | \(-0.126848\pi\) | |||||||
\(812\) | 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 | \(-0.363374\pi\) |
−0.579385 | + | 0.815054i | \(0.696707\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6029.71 | − | 10443.8i | −0.255386 | − | 0.442341i | 0.709614 | − | 0.704590i | \(-0.248869\pi\) |
−0.965000 | + | 0.262249i | \(0.915536\pi\) | |||||||
\(824\) | 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 | −0.417034 | − | 0.908891i | \(-0.636930\pi\) |
0.578605 | + | 0.815608i | \(0.303597\pi\) | |||||||
\(830\) | 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 | \(-0.345258\pi\) | ||||
0.467214 | + | 0.884144i | \(0.345258\pi\) | |||||||
\(840\) | 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 | \(0.0875499\pi\) | ||||
−0.962413 | + | 0.271591i | \(0.912450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7847.69 | + | 13592.6i | 0.312803 | + | 0.541790i | 0.978968 | − | 0.204014i | \(-0.0653988\pi\) |
−0.666165 | + | 0.745804i | \(0.732065\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31542.4 | + | 18211.0i | 1.25287 | + | 0.723342i | 0.971678 | − | 0.236311i | \(-0.0759383\pi\) |
0.281188 | + | 0.959653i | \(0.409272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26424.8 | − | 15256.4i | −1.04231 | − | 0.601777i | −0.121822 | − | 0.992552i | \(-0.538874\pi\) |
−0.920486 | + | 0.390775i | \(0.872207\pi\) | |||||||
\(864\) | 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 | −0.837612 | − | 0.546266i | \(-0.816049\pi\) |
0.891886 | + | 0.452260i | \(0.149382\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18469.6 | −0.706306 | −0.353153 | − | 0.935566i | \(-0.614890\pi\) | ||||
−0.353153 | + | 0.935566i | \(0.614890\pi\) | |||||||
\(882\) | 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 | 0.0948157 | + | 0.995495i | \(0.469774\pi\) |
−0.909532 | + | 0.415635i | \(0.863560\pi\) | |||||||
\(888\) | 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 | 0.963640 | − | 0.267202i | \(-0.0860992\pi\) |
−0.713224 | + | 0.700936i | \(0.752766\pi\) | |||||||
\(908\) | 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 | 0.375694 | + | 0.926744i | \(0.377404\pi\) |
−0.990431 | + | 0.138011i | \(0.955929\pi\) | |||||||
\(920\) | 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 | \(-0.976837\pi\) |
0.561642 | + | 0.827380i | \(0.310170\pi\) | |||||||
\(930\) | 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 | \(0.194325\pi\) | ||||
−0.819367 | + | 0.573269i | \(0.805675\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4016.54 | − | 6956.85i | −0.139145 | − | 0.241006i | 0.788028 | − | 0.615639i | \(-0.211102\pi\) |
−0.927173 | + | 0.374633i | \(0.877769\pi\) | |||||||
\(942\) | 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 | \(-0.236021\pi\) |
−0.216164 | + | 0.976357i | \(0.569354\pi\) | |||||||
\(948\) | 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 | \(-0.913942\pi\) |
0.713134 | + | 0.701027i | \(0.247275\pi\) | |||||||
\(972\) | 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 | \(-0.828727\pi\) |
0.0144714 | + | 0.999895i | \(0.495393\pi\) | |||||||
\(978\) | 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 | 0.999117 | + | 0.0420055i | \(0.0133747\pi\) |
−0.463181 | + | 0.886264i | \(0.653292\pi\) | |||||||
\(984\) | 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 | 0.779756 | − | 0.626084i | \(-0.215343\pi\) |
−0.932082 | + | 0.362246i | \(0.882010\pi\) | |||||||
\(992\) | 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 | −0.232769 | − | 0.972532i | \(-0.574779\pi\) |
0.725853 | + | 0.687850i | \(0.241445\pi\) | |||||||
\(998\) | 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.593.21 | 48 | ||
3.2 | odd | 2 | inner | 1008.4.bt.d.593.4 | 48 | ||
4.3 | odd | 2 | 504.4.bl.a.89.21 | yes | 48 | ||
7.3 | odd | 6 | inner | 1008.4.bt.d.17.4 | 48 | ||
12.11 | even | 2 | 504.4.bl.a.89.4 | yes | 48 | ||
21.17 | even | 6 | inner | 1008.4.bt.d.17.21 | 48 | ||
28.3 | even | 6 | 504.4.bl.a.17.4 | ✓ | 48 | ||
84.59 | odd | 6 | 504.4.bl.a.17.21 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.4.bl.a.17.4 | ✓ | 48 | 28.3 | even | 6 | ||
504.4.bl.a.17.21 | yes | 48 | 84.59 | odd | 6 | ||
504.4.bl.a.89.4 | yes | 48 | 12.11 | even | 2 | ||
504.4.bl.a.89.21 | yes | 48 | 4.3 | odd | 2 | ||
1008.4.bt.d.17.4 | 48 | 7.3 | odd | 6 | inner | ||
1008.4.bt.d.17.21 | 48 | 21.17 | even | 6 | inner | ||
1008.4.bt.d.593.4 | 48 | 3.2 | odd | 2 | inner | ||
1008.4.bt.d.593.21 | 48 | 1.1 | even | 1 | trivial |