Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(199,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.j (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: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 450) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.199 |
Dual form | 1350.2.j.b.1099.1 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 1.00000i | 0.654654 | − | 0.377964i | −0.135583 | − | 0.990766i | \(-0.543291\pi\) |
0.790237 | + | 0.612801i | \(0.209957\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | − | 2.00000i | −0.960769 | − | 0.554700i | −0.0643593 | − | 0.997927i | \(-0.520500\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | −1.00000 | + | 1.73205i | −0.267261 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 6.00000i | 1.45521i | 0.685994 | + | 0.727607i | \(0.259367\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000 | 1.60591 | 0.802955 | − | 0.596040i | \(-0.203260\pi\) | ||||
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | − | 8.66025i | 0.898027 | − | 1.55543i | 0.0680129 | − | 0.997684i | \(-0.478334\pi\) |
0.830014 | − | 0.557743i | \(-0.188333\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | − | 5.19615i | −0.514496 | − | 0.891133i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | −6.06218 | + | 3.50000i | −0.983415 | + | 0.567775i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.866025 | − | 0.500000i | 0.132068 | − | 0.0762493i | −0.432511 | − | 0.901629i | \(-0.642372\pi\) |
0.564578 | + | 0.825380i | \(0.309039\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19615 | + | 3.00000i | −0.757937 | + | 0.437595i | −0.828554 | − | 0.559908i | \(-0.810836\pi\) |
0.0706177 | + | 0.997503i | \(0.477503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.50000 | + | 2.59808i | −0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.46410 | + | 2.00000i | −0.480384 | + | 0.277350i | ||||
\(53\) | − | 12.0000i | − | 1.64833i | −0.566352 | − | 0.824163i | \(-0.691646\pi\) | ||
0.566352 | − | 0.824163i | \(-0.308354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | + | 1.73205i | 0.133631 | + | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.19615 | − | 3.00000i | −0.682288 | − | 0.393919i | ||||
\(59\) | 4.50000 | − | 7.79423i | 0.585850 | − | 1.01472i | −0.408919 | − | 0.912571i | \(-0.634094\pi\) |
0.994769 | − | 0.102151i | \(-0.0325726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | 10.0000i | 1.27000i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2583 | + | 6.50000i | 1.37542 | + | 0.794101i | 0.991605 | − | 0.129307i | \(-0.0412752\pi\) |
0.383819 | + | 0.923408i | \(0.374609\pi\) | |||||||
\(68\) | 5.19615 | + | 3.00000i | 0.630126 | + | 0.363803i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000i | 0.117041i | 0.998286 | + | 0.0585206i | \(0.0186383\pi\) | ||||
−0.998286 | + | 0.0585206i | \(0.981362\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.50000 | − | 6.06218i | 0.401478 | − | 0.695379i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | + | 1.73205i | 0.112509 | + | 0.194871i | 0.916781 | − | 0.399390i | \(-0.130778\pi\) |
−0.804272 | + | 0.594261i | \(0.797445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.00000i | 0.993884i | ||||||||
\(83\) | 7.79423 | − | 4.50000i | 0.855528 | − | 0.493939i | −0.00698436 | − | 0.999976i | \(-0.502223\pi\) |
0.862512 | + | 0.506036i | \(0.168890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.500000 | + | 0.866025i | −0.0539164 | + | 0.0933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0000 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.00000 | − | 5.19615i | 0.309426 | − | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.7224 | − | 8.50000i | 1.49484 | − | 0.863044i | 0.494854 | − | 0.868976i | \(-0.335222\pi\) |
0.999982 | + | 0.00593185i | \(0.00188818\pi\) | |||||||
\(98\) | − | 3.00000i | − | 0.303046i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.73205 | + | 1.00000i | 0.170664 | + | 0.0985329i | 0.582899 | − | 0.812545i | \(-0.301918\pi\) |
−0.412235 | + | 0.911078i | \(0.635252\pi\) | |||||||
\(104\) | 2.00000 | − | 3.46410i | 0.196116 | − | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | + | 10.3923i | 0.582772 | + | 1.00939i | ||||
\(107\) | − | 9.00000i | − | 0.870063i | −0.900415 | − | 0.435031i | \(-0.856737\pi\) | ||
0.900415 | − | 0.435031i | \(-0.143263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.73205 | − | 1.00000i | −0.163663 | − | 0.0944911i | ||||
\(113\) | −2.59808 | − | 1.50000i | −0.244406 | − | 0.141108i | 0.372794 | − | 0.927914i | \(-0.378400\pi\) |
−0.617200 | + | 0.786806i | \(0.711733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.00000i | 0.828517i | ||||||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | −3.46410 | − | 2.00000i | −0.313625 | − | 0.181071i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.00000 | − | 8.66025i | −0.449013 | − | 0.777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000i | 1.77471i | 0.461084 | + | 0.887357i | \(0.347461\pi\) | ||||
−0.461084 | + | 0.887357i | \(0.652539\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.1244 | − | 7.00000i | 1.05131 | − | 0.606977i | ||||
\(134\) | −13.0000 | −1.12303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 2.59808 | − | 1.50000i | 0.221969 | − | 0.128154i | −0.384893 | − | 0.922961i | \(-0.625762\pi\) |
0.606861 | + | 0.794808i | \(0.292428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | + | 3.46410i | −0.169638 | + | 0.293821i | −0.938293 | − | 0.345843i | \(-0.887593\pi\) |
0.768655 | + | 0.639664i | \(0.220926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.19615 | − | 3.00000i | 0.436051 | − | 0.251754i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.500000 | − | 0.866025i | −0.0413803 | − | 0.0716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.73205 | + | 1.00000i | 0.142374 | + | 0.0821995i | ||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | + | 3.46410i | 0.162758 | + | 0.281905i | 0.935857 | − | 0.352381i | \(-0.114628\pi\) |
−0.773099 | + | 0.634285i | \(0.781294\pi\) | |||||||
\(152\) | 7.00000i | 0.567775i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1244 | − | 7.00000i | −0.967629 | − | 0.558661i | −0.0691164 | − | 0.997609i | \(-0.522018\pi\) |
−0.898513 | + | 0.438948i | \(0.855351\pi\) | |||||||
\(158\) | −1.73205 | − | 1.00000i | −0.137795 | − | 0.0795557i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000i | 0.548282i | 0.961689 | + | 0.274141i | \(0.0883936\pi\) | ||||
−0.961689 | + | 0.274141i | \(0.911606\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | 10.3923 | + | 6.00000i | 0.804181 | + | 0.464294i | 0.844931 | − | 0.534875i | \(-0.179641\pi\) |
−0.0407502 | + | 0.999169i | \(0.512975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.50000 | + | 2.59808i | 0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.00000i | − | 0.0762493i | ||||||
\(173\) | −10.3923 | + | 6.00000i | −0.790112 | + | 0.456172i | −0.840002 | − | 0.542583i | \(-0.817446\pi\) |
0.0498898 | + | 0.998755i | \(0.484113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.9904 | + | 7.50000i | −0.973670 | + | 0.562149i | ||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 6.92820 | − | 4.00000i | 0.513553 | − | 0.296500i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.73205 | + | 1.00000i | 0.124676 | + | 0.0719816i | 0.561041 | − | 0.827788i | \(-0.310401\pi\) |
−0.436365 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(194\) | −8.50000 | + | 14.7224i | −0.610264 | + | 1.05701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.50000 | + | 2.59808i | 0.107143 | + | 0.185577i | ||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.3923 | − | 6.00000i | −0.731200 | − | 0.422159i | ||||
\(203\) | 10.3923 | + | 6.00000i | 0.729397 | + | 0.421117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | −0.139347 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.50000 | + | 4.33013i | −0.172107 | + | 0.298098i | −0.939156 | − | 0.343490i | \(-0.888391\pi\) |
0.767049 | + | 0.641588i | \(0.221724\pi\) | |||||||
\(212\) | −10.3923 | − | 6.00000i | −0.713746 | − | 0.412082i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.50000 | + | 7.79423i | 0.307614 | + | 0.532803i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 20.0000i | − | 1.35769i | ||||||
\(218\) | 1.73205 | − | 1.00000i | 0.117309 | − | 0.0677285i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | − | 20.7846i | 0.807207 | − | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.8564 | − | 8.00000i | 0.927894 | − | 0.535720i | 0.0417488 | − | 0.999128i | \(-0.486707\pi\) |
0.886145 | + | 0.463409i | \(0.153374\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | 0.199557 | ||||||||
\(227\) | 12.9904 | − | 7.50000i | 0.862202 | − | 0.497792i | −0.00254715 | − | 0.999997i | \(-0.500811\pi\) |
0.864749 | + | 0.502204i | \(0.167477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.00000 | + | 8.66025i | −0.330409 | + | 0.572286i | −0.982592 | − | 0.185776i | \(-0.940520\pi\) |
0.652183 | + | 0.758062i | \(0.273853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.19615 | + | 3.00000i | −0.341144 | + | 0.196960i | ||||
\(233\) | 3.00000i | 0.196537i | 0.995160 | + | 0.0982683i | \(0.0313303\pi\) | ||||
−0.995160 | + | 0.0982683i | \(0.968670\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.50000 | − | 7.79423i | −0.292925 | − | 0.507361i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.3923 | − | 6.00000i | −0.673633 | − | 0.388922i | ||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.50000 | + | 16.4545i | 0.611949 | + | 1.05993i | 0.990912 | + | 0.134515i | \(0.0429475\pi\) |
−0.378963 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(242\) | 11.0000i | 0.707107i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.2487 | − | 14.0000i | −1.54291 | − | 0.890799i | ||||
\(248\) | 8.66025 | + | 5.00000i | 0.549927 | + | 0.317500i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.0000 | − | 17.3205i | −0.627456 | − | 1.08679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.59808 | + | 1.50000i | 0.162064 | + | 0.0935674i | 0.578838 | − | 0.815442i | \(-0.303506\pi\) |
−0.416775 | + | 0.909010i | \(0.636840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | + | 3.46410i | 0.124274 | + | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 12.0000i | − | 0.741362i | ||||||
\(263\) | −5.19615 | + | 3.00000i | −0.320408 | + | 0.184988i | −0.651575 | − | 0.758585i | \(-0.725891\pi\) |
0.331166 | + | 0.943572i | \(0.392558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.00000 | + | 12.1244i | −0.429198 | + | 0.743392i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.2583 | − | 6.50000i | 0.687712 | − | 0.397051i | ||||
\(269\) | −30.0000 | −1.82913 | −0.914566 | − | 0.404436i | \(-0.867468\pi\) | ||||
−0.914566 | + | 0.404436i | \(0.867468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 5.19615 | − | 3.00000i | 0.315063 | − | 0.181902i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.50000 | + | 2.59808i | −0.0906183 | + | 0.156956i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.73205 | − | 1.00000i | 0.104069 | − | 0.0600842i | −0.447062 | − | 0.894503i | \(-0.647530\pi\) |
0.551131 | + | 0.834419i | \(0.314196\pi\) | |||||||
\(278\) | − | 4.00000i | − | 0.239904i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.00000 | − | 15.5885i | −0.536895 | − | 0.929929i | −0.999069 | − | 0.0431402i | \(-0.986264\pi\) |
0.462174 | − | 0.886789i | \(-0.347070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.4545 | − | 9.50000i | −0.978117 | − | 0.564716i | −0.0764162 | − | 0.997076i | \(-0.524348\pi\) |
−0.901701 | + | 0.432360i | \(0.857681\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 18.0000i | − | 1.06251i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.866025 | + | 0.500000i | 0.0506803 | + | 0.0292603i | ||||
\(293\) | −10.3923 | − | 6.00000i | −0.607125 | − | 0.350524i | 0.164714 | − | 0.986341i | \(-0.447330\pi\) |
−0.771839 | + | 0.635818i | \(0.780663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | − | 1.73205i | 0.0576390 | − | 0.0998337i | ||||
\(302\) | −3.46410 | − | 2.00000i | −0.199337 | − | 0.115087i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | − | 6.06218i | −0.200739 | − | 0.347690i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000i | 0.456584i | 0.973593 | + | 0.228292i | \(0.0733141\pi\) | ||||
−0.973593 | + | 0.228292i | \(0.926686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0000 | + | 25.9808i | −0.850572 | + | 1.47323i | 0.0301210 | + | 0.999546i | \(0.490411\pi\) |
−0.880693 | + | 0.473688i | \(0.842923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4545 | − | 9.50000i | 0.930062 | − | 0.536972i | 0.0432311 | − | 0.999065i | \(-0.486235\pi\) |
0.886831 | + | 0.462093i | \(0.152902\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −25.9808 | + | 15.0000i | −1.45922 | + | 0.842484i | −0.998973 | − | 0.0453045i | \(-0.985574\pi\) |
−0.460252 | + | 0.887788i | \(0.652241\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.0000i | 2.33694i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.50000 | − | 6.06218i | −0.193847 | − | 0.335753i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.79423 | + | 4.50000i | 0.430364 | + | 0.248471i | ||||
\(329\) | −6.00000 | + | 10.3923i | −0.330791 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.50000 | − | 9.52628i | −0.302307 | − | 0.523612i | 0.674351 | − | 0.738411i | \(-0.264424\pi\) |
−0.976658 | + | 0.214799i | \(0.931090\pi\) | |||||||
\(332\) | − | 9.00000i | − | 0.493939i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.1244 | − | 7.00000i | −0.660456 | − | 0.381314i | 0.131995 | − | 0.991250i | \(-0.457862\pi\) |
−0.792451 | + | 0.609936i | \(0.791195\pi\) | |||||||
\(338\) | −2.59808 | − | 1.50000i | −0.141317 | − | 0.0815892i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0.500000 | + | 0.866025i | 0.0269582 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | − | 10.3923i | 0.322562 | − | 0.558694i | ||||
\(347\) | −10.3923 | − | 6.00000i | −0.557888 | − | 0.322097i | 0.194409 | − | 0.980921i | \(-0.437721\pi\) |
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.00000 | − | 8.66025i | −0.267644 | − | 0.463573i | 0.700609 | − | 0.713545i | \(-0.252912\pi\) |
−0.968253 | + | 0.249973i | \(0.919578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9904 | − | 7.50000i | 0.691408 | − | 0.399185i | −0.112731 | − | 0.993626i | \(-0.535960\pi\) |
0.804139 | + | 0.594441i | \(0.202627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.50000 | − | 12.9904i | 0.397499 | − | 0.688489i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.79423 | − | 4.50000i | 0.411938 | − | 0.237832i | ||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 13.8564 | − | 8.00000i | 0.728277 | − | 0.420471i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00000 | + | 6.92820i | −0.209657 | + | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.66025 | + | 5.00000i | −0.452062 | + | 0.260998i | −0.708700 | − | 0.705509i | \(-0.750718\pi\) |
0.256639 | + | 0.966507i | \(0.417385\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 20.7846i | −0.623009 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.46410 | − | 2.00000i | −0.179364 | − | 0.103556i | 0.407630 | − | 0.913147i | \(-0.366355\pi\) |
−0.586994 | + | 0.809591i | \(0.699689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.19615 | − | 3.00000i | −0.265858 | − | 0.153493i | ||||
\(383\) | −20.7846 | − | 12.0000i | −1.06204 | − | 0.613171i | −0.136047 | − | 0.990702i | \(-0.543440\pi\) |
−0.925997 | + | 0.377531i | \(0.876773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 17.0000i | − | 0.863044i | ||||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.59808 | − | 1.50000i | −0.131223 | − | 0.0757614i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.0000i | − | 1.10415i | −0.833795 | − | 0.552074i | \(-0.813837\pi\) | ||
0.833795 | − | 0.552074i | \(-0.186163\pi\) | |||||||
\(398\) | −13.8564 | + | 8.00000i | −0.694559 | + | 0.401004i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | − | 15.5885i | 0.449439 | − | 0.778450i | −0.548911 | − | 0.835881i | \(-0.684957\pi\) |
0.998350 | + | 0.0574304i | \(0.0182907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.6410 | + | 20.0000i | −1.72559 | + | 0.996271i | ||||
\(404\) | 12.0000 | 0.597022 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0000 | −0.595550 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.5000 | + | 26.8468i | −0.766426 | + | 1.32749i | 0.173064 | + | 0.984911i | \(0.444633\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.73205 | − | 1.00000i | 0.0853320 | − | 0.0492665i | ||||
\(413\) | − | 18.0000i | − | 0.885722i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | − | 3.46410i | −0.0980581 | − | 0.169842i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.50000 | + | 2.59808i | −0.0732798 | + | 0.126924i | −0.900337 | − | 0.435194i | \(-0.856680\pi\) |
0.827057 | + | 0.562118i | \(0.190013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | − | 5.00000i | − | 0.243396i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.0000 | 0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.92820 | + | 4.00000i | 0.335279 | + | 0.193574i | ||||
\(428\) | −7.79423 | − | 4.50000i | −0.376748 | − | 0.217516i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | −0.289010 | −0.144505 | − | 0.989504i | \(-0.546159\pi\) | ||||
−0.144505 | + | 0.989504i | \(0.546159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.00000i | − | 0.0961139i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480569i | \(-0.0153029\pi\) | |||||||
\(434\) | 10.0000 | + | 17.3205i | 0.480015 | + | 0.831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.00000 | − | 3.46410i | −0.0954548 | − | 0.165333i | 0.814344 | − | 0.580383i | \(-0.197097\pi\) |
−0.909798 | + | 0.415051i | \(0.863764\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.0000i | 1.14156i | ||||||||
\(443\) | 31.1769 | − | 18.0000i | 1.48126 | − | 0.855206i | 0.481486 | − | 0.876454i | \(-0.340097\pi\) |
0.999774 | + | 0.0212481i | \(0.00676401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.00000 | + | 13.8564i | −0.378811 | + | 0.656120i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.73205 | + | 1.00000i | −0.0818317 | + | 0.0472456i | ||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −2.59808 | + | 1.50000i | −0.122203 | + | 0.0705541i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.50000 | + | 12.9904i | −0.351992 | + | 0.609669i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4545 | + | 9.50000i | −0.769708 | + | 0.444391i | −0.832771 | − | 0.553618i | \(-0.813247\pi\) |
0.0630623 | + | 0.998010i | \(0.479913\pi\) | |||||||
\(458\) | − | 10.0000i | − | 0.467269i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00000 | + | 5.19615i | 0.139724 | + | 0.242009i | 0.927392 | − | 0.374091i | \(-0.122045\pi\) |
−0.787668 | + | 0.616100i | \(0.788712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.5167 | + | 13.0000i | 1.04644 | + | 0.604161i | 0.921650 | − | 0.388022i | \(-0.126842\pi\) |
0.124788 | + | 0.992183i | \(0.460175\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.50000 | − | 2.59808i | −0.0694862 | − | 0.120354i | ||||
\(467\) | 15.0000i | 0.694117i | 0.937843 | + | 0.347059i | \(0.112820\pi\) | ||||
−0.937843 | + | 0.347059i | \(0.887180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.0000 | 1.20057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.79423 | + | 4.50000i | 0.358758 | + | 0.207129i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | 0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0000 | − | 31.1769i | −0.822441 | − | 1.42451i | −0.903859 | − | 0.427830i | \(-0.859278\pi\) |
0.0814184 | − | 0.996680i | \(-0.474055\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | − | 6.92820i | 0.182384 | − | 0.315899i | ||||
\(482\) | −16.4545 | − | 9.50000i | −0.749481 | − | 0.432713i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.50000 | − | 9.52628i | −0.250000 | − | 0.433013i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000i | 0.0906287i | 0.998973 | + | 0.0453143i | \(0.0144289\pi\) | ||||
−0.998973 | + | 0.0453143i | \(0.985571\pi\) | |||||||
\(488\) | −3.46410 | + | 2.00000i | −0.156813 | + | 0.0905357i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.50000 | + | 2.59808i | −0.0676941 | + | 0.117250i | −0.897886 | − | 0.440228i | \(-0.854898\pi\) |
0.830192 | + | 0.557478i | \(0.188231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.1769 | + | 18.0000i | −1.40414 | + | 0.810679i | ||||
\(494\) | 28.0000 | 1.25978 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | −10.3923 | + | 6.00000i | −0.466159 | + | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.50000 | − | 9.52628i | 0.246214 | − | 0.426455i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.962472 | + | 0.271380i | \(0.0874801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.9904 | − | 7.50000i | 0.579789 | − | 0.334741i | ||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.3205 | + | 10.0000i | 0.768473 | + | 0.443678i | ||||
\(509\) | 18.0000 | − | 31.1769i | 0.797836 | − | 1.38189i | −0.123187 | − | 0.992384i | \(-0.539311\pi\) |
0.921023 | − | 0.389509i | \(-0.127355\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | + | 1.73205i | 0.0442374 | + | 0.0766214i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.00000 | −0.132324 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.46410 | − | 2.00000i | −0.152204 | − | 0.0878750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.00000i | 0.0437269i | 0.999761 | + | 0.0218635i | \(0.00695991\pi\) | ||||
−0.999761 | + | 0.0218635i | \(0.993040\pi\) | |||||||
\(524\) | 6.00000 | + | 10.3923i | 0.262111 | + | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.00000 | − | 5.19615i | 0.130806 | − | 0.226563i | ||||
\(527\) | 51.9615 | + | 30.0000i | 2.26348 | + | 1.30682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | − | 19.9186i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 14.0000i | − | 0.606977i | ||||||
\(533\) | −31.1769 | + | 18.0000i | −1.35042 | + | 0.779667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.50000 | + | 11.2583i | −0.280757 | + | 0.486286i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.9808 | − | 15.0000i | 1.12011 | − | 0.646696i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.0000 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258536\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258536\pi\) | |||||||
\(542\) | 24.2487 | − | 14.0000i | 1.04157 | − | 0.601351i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.00000 | + | 5.19615i | −0.128624 | + | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.33013 | − | 2.50000i | 0.185143 | − | 0.106892i | −0.404564 | − | 0.914510i | \(-0.632577\pi\) |
0.589707 | + | 0.807617i | \(0.299243\pi\) | |||||||
\(548\) | − | 3.00000i | − | 0.128154i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.0000 | + | 36.3731i | 0.894630 | + | 1.54954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.46410 | + | 2.00000i | 0.147309 | + | 0.0850487i | ||||
\(554\) | −1.00000 | + | 1.73205i | −0.0424859 | + | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | 12.0000i | 0.508456i | 0.967144 | + | 0.254228i | \(0.0818214\pi\) | ||||
−0.967144 | + | 0.254228i | \(0.918179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.5885 | + | 9.00000i | 0.657559 | + | 0.379642i | ||||
\(563\) | −7.79423 | − | 4.50000i | −0.328488 | − | 0.189652i | 0.326682 | − | 0.945134i | \(-0.394069\pi\) |
−0.655169 | + | 0.755482i | \(0.727403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.0000 | 0.798630 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 21.0000 | + | 36.3731i | 0.880366 | + | 1.52484i | 0.850935 | + | 0.525271i | \(0.176036\pi\) |
0.0294311 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5000 | + | 30.3109i | −0.732352 | + | 1.26847i | 0.223523 | + | 0.974699i | \(0.428244\pi\) |
−0.955875 | + | 0.293773i | \(0.905089\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.00000 | + | 15.5885i | 0.375653 | + | 0.650650i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.0000i | 1.45707i | 0.685009 | + | 0.728535i | \(0.259798\pi\) | ||||
−0.685009 | + | 0.728535i | \(0.740202\pi\) | |||||||
\(578\) | 16.4545 | − | 9.50000i | 0.684416 | − | 0.395148i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.00000 | − | 15.5885i | 0.373383 | − | 0.646718i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | −31.1769 | + | 18.0000i | −1.28681 | + | 0.742940i | −0.978084 | − | 0.208212i | \(-0.933236\pi\) |
−0.308725 | + | 0.951151i | \(0.599902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.0000 | − | 60.6218i | 1.44215 | − | 2.49788i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.73205 | − | 1.00000i | 0.0711868 | − | 0.0410997i | ||||
\(593\) | − | 9.00000i | − | 0.369586i | −0.982777 | − | 0.184793i | \(-0.940839\pi\) | ||
0.982777 | − | 0.184793i | \(-0.0591614\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.0000 | + | 25.9808i | −0.612883 | + | 1.06155i | 0.377869 | + | 0.925859i | \(0.376657\pi\) |
−0.990752 | + | 0.135686i | \(0.956676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.00000 | + | 8.66025i | 0.203954 | + | 0.353259i | 0.949799 | − | 0.312861i | \(-0.101287\pi\) |
−0.745845 | + | 0.666120i | \(0.767954\pi\) | |||||||
\(602\) | 2.00000i | 0.0815139i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.6410 | + | 20.0000i | 1.40604 | + | 0.811775i | 0.995003 | − | 0.0998457i | \(-0.0318349\pi\) |
0.411033 | + | 0.911621i | \(0.365168\pi\) | |||||||
\(608\) | 6.06218 | + | 3.50000i | 0.245854 | + | 0.141944i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 44.0000i | − | 1.77714i | −0.458738 | − | 0.888572i | \(-0.651698\pi\) | ||
0.458738 | − | 0.888572i | \(-0.348302\pi\) | |||||||
\(614\) | −4.00000 | − | 6.92820i | −0.161427 | − | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.79423 | − | 4.50000i | −0.313784 | − | 0.181163i | 0.334835 | − | 0.942277i | \(-0.391320\pi\) |
−0.648618 | + | 0.761114i | \(0.724653\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5000 | + | 19.9186i | 0.462224 | + | 0.800595i | 0.999071 | − | 0.0430838i | \(-0.0137183\pi\) |
−0.536847 | + | 0.843679i | \(0.680385\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 30.0000i | − | 1.20289i | ||||||
\(623\) | 25.9808 | − | 15.0000i | 1.04090 | − | 0.600962i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.50000 | + | 16.4545i | −0.379696 | + | 0.657653i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.1244 | + | 7.00000i | −0.483814 | + | 0.279330i | ||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | −1.73205 | + | 1.00000i | −0.0688973 | + | 0.0397779i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.0000 | − | 25.9808i | 0.595726 | − | 1.03183i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.3923 | − | 6.00000i | 0.411758 | − | 0.237729i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.2583 | − | 6.50000i | −0.443985 | − | 0.256335i | 0.261301 | − | 0.965257i | \(-0.415848\pi\) |
−0.705287 | + | 0.708922i | \(0.749182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.0000 | − | 36.3731i | −0.826234 | − | 1.43108i | ||||
\(647\) | 48.0000i | 1.88707i | 0.331266 | + | 0.943537i | \(0.392524\pi\) | ||||
−0.331266 | + | 0.943537i | \(0.607476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.06218 | + | 3.50000i | 0.237413 | + | 0.137071i | ||||
\(653\) | 31.1769 | + | 18.0000i | 1.22005 | + | 0.704394i | 0.964928 | − | 0.262515i | \(-0.0845520\pi\) |
0.255119 | + | 0.966910i | \(0.417885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.00000 | −0.351391 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 12.0000i | − | 0.467809i | ||||||
\(659\) | −16.5000 | − | 28.5788i | −0.642749 | − | 1.11327i | −0.984817 | − | 0.173598i | \(-0.944461\pi\) |
0.342068 | − | 0.939675i | \(-0.388873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.00000 | + | 1.73205i | −0.0388955 | + | 0.0673690i | −0.884818 | − | 0.465937i | \(-0.845717\pi\) |
0.845922 | + | 0.533306i | \(0.179051\pi\) | |||||||
\(662\) | 9.52628 | + | 5.50000i | 0.370249 | + | 0.213764i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.50000 | + | 7.79423i | 0.174634 | + | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 10.3923 | − | 6.00000i | 0.402090 | − | 0.232147i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.73205 | + | 1.00000i | −0.0667657 | + | 0.0385472i | −0.533011 | − | 0.846108i | \(-0.678940\pi\) |
0.466246 | + | 0.884655i | \(0.345606\pi\) | |||||||
\(674\) | 14.0000 | 0.539260 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 10.3923 | − | 6.00000i | 0.399409 | − | 0.230599i | −0.286820 | − | 0.957984i | \(-0.592598\pi\) |
0.686229 | + | 0.727386i | \(0.259265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.0000 | − | 29.4449i | 0.652400 | − | 1.12999i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.00000i | − | 0.114792i | −0.998351 | − | 0.0573959i | \(-0.981720\pi\) | ||
0.998351 | − | 0.0573959i | \(-0.0182797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.866025 | − | 0.500000i | −0.0330169 | − | 0.0190623i | ||||
\(689\) | −24.0000 | + | 41.5692i | −0.914327 | + | 1.58366i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.5000 | − | 30.3109i | −0.665731 | − | 1.15308i | −0.979086 | − | 0.203445i | \(-0.934786\pi\) |
0.313355 | − | 0.949636i | \(-0.398547\pi\) | |||||||
\(692\) | 12.0000i | 0.456172i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.7654 | + | 27.0000i | 1.77136 | + | 1.02270i | ||||
\(698\) | 8.66025 | + | 5.00000i | 0.327795 | + | 0.189253i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.0000 | 1.81293 | 0.906467 | − | 0.422276i | \(-0.138769\pi\) | ||||
0.906467 | + | 0.422276i | \(0.138769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0000i | 0.528020i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.50000 | + | 12.9904i | −0.282266 | + | 0.488899i | ||||
\(707\) | 20.7846 | + | 12.0000i | 0.781686 | + | 0.451306i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0000 | − | 24.2487i | −0.525781 | − | 0.910679i | −0.999549 | − | 0.0300298i | \(-0.990440\pi\) |
0.473768 | − | 0.880650i | \(-0.342894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.0000i | 0.562149i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.50000 | + | 7.79423i | −0.168173 | + | 0.291284i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.3923 | + | 6.00000i | −0.387837 | + | 0.223918i | ||||
\(719\) | 18.0000 | 0.671287 | 0.335643 | − | 0.941989i | \(-0.391046\pi\) | ||||
0.335643 | + | 0.941989i | \(0.391046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | −25.9808 | + | 15.0000i | −0.966904 | + | 0.558242i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.00000 | + | 13.8564i | −0.297318 | + | 0.514969i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.6410 | + | 20.0000i | −1.28476 | + | 0.741759i | −0.977715 | − | 0.209935i | \(-0.932675\pi\) |
−0.307049 | + | 0.951694i | \(0.599341\pi\) | |||||||
\(728\) | − | 8.00000i | − | 0.296500i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | + | 5.19615i | 0.110959 | + | 0.192187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.0526 | − | 11.0000i | −0.703722 | − | 0.406294i | 0.105010 | − | 0.994471i | \(-0.466513\pi\) |
−0.808732 | + | 0.588177i | \(0.799846\pi\) | |||||||
\(734\) | 5.00000 | − | 8.66025i | 0.184553 | − | 0.319656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.0000 | 0.919640 | 0.459820 | − | 0.888012i | \(-0.347914\pi\) | ||||
0.459820 | + | 0.888012i | \(0.347914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.7846 | + | 12.0000i | 0.763027 | + | 0.440534i | ||||
\(743\) | −5.19615 | − | 3.00000i | −0.190628 | − | 0.110059i | 0.401648 | − | 0.915794i | \(-0.368437\pi\) |
−0.592277 | + | 0.805735i | \(0.701771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.00000 | 0.146450 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.00000 | − | 15.5885i | −0.328853 | − | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | − | 3.46410i | 0.0729810 | − | 0.126407i | −0.827225 | − | 0.561870i | \(-0.810082\pi\) |
0.900207 | + | 0.435463i | \(0.143415\pi\) | |||||||
\(752\) | 5.19615 | + | 3.00000i | 0.189484 | + | 0.109399i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0000 | + | 20.7846i | 0.437014 | + | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 10.0000i | − | 0.363456i | −0.983349 | − | 0.181728i | \(-0.941831\pi\) | ||
0.983349 | − | 0.181728i | \(-0.0581691\pi\) | |||||||
\(758\) | 17.3205 | − | 10.0000i | 0.629109 | − | 0.363216i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5000 | − | 18.1865i | 0.380625 | − | 0.659261i | −0.610527 | − | 0.791995i | \(-0.709042\pi\) |
0.991152 | + | 0.132734i | \(0.0423756\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.46410 | + | 2.00000i | −0.125409 | + | 0.0724049i | ||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | −31.1769 | + | 18.0000i | −1.12573 | + | 0.649942i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.50000 | − | 4.33013i | 0.0901523 | − | 0.156148i | −0.817423 | − | 0.576038i | \(-0.804598\pi\) |
0.907575 | + | 0.419890i | \(0.137931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.73205 | − | 1.00000i | 0.0623379 | − | 0.0359908i | ||||
\(773\) | 6.00000i | 0.215805i | 0.994161 | + | 0.107903i | \(0.0344134\pi\) | ||||
−0.994161 | + | 0.107903i | \(0.965587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.50000 | + | 14.7224i | 0.305132 | + | 0.528505i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.19615 | + | 3.00000i | 0.186291 | + | 0.107555i | ||||
\(779\) | 31.5000 | − | 54.5596i | 1.12860 | − | 1.95480i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3205 | − | 10.0000i | −0.617409 | − | 0.356462i | 0.158450 | − | 0.987367i | \(-0.449350\pi\) |
−0.775860 | + | 0.630905i | \(0.782684\pi\) | |||||||
\(788\) | −15.5885 | − | 9.00000i | −0.555316 | − | 0.320612i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.0000i | − | 0.568177i | ||||||
\(794\) | 11.0000 | + | 19.0526i | 0.390375 | + | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | − | 13.8564i | 0.283552 | − | 0.491127i | ||||
\(797\) | −31.1769 | − | 18.0000i | −1.10434 | − | 0.637593i | −0.166985 | − | 0.985959i | \(-0.553403\pi\) |
−0.937358 | + | 0.348367i | \(0.886736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | − | 31.1769i | −0.636794 | − | 1.10296i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0000i | 0.635602i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.0000 | − | 34.6410i | 0.704470 | − | 1.22018i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.3923 | + | 6.00000i | −0.365600 | + | 0.211079i | ||||
\(809\) | −39.0000 | −1.37117 | −0.685583 | − | 0.727994i | \(-0.740453\pi\) | ||||
−0.685583 | + | 0.727994i | \(0.740453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.00000 | 0.175574 | 0.0877869 | − | 0.996139i | \(-0.472021\pi\) | ||||
0.0877869 | + | 0.996139i | \(0.472021\pi\) | |||||||
\(812\) | 10.3923 | − | 6.00000i | 0.364698 | − | 0.210559i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.06218 | − | 3.50000i | 0.212089 | − | 0.122449i | ||||
\(818\) | − | 31.0000i | − | 1.08389i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0000 | − | 20.7846i | −0.418803 | − | 0.725388i | 0.577016 | − | 0.816733i | \(-0.304217\pi\) |
−0.995819 | + | 0.0913446i | \(0.970884\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.1244 | + | 7.00000i | 0.422628 | + | 0.244005i | 0.696201 | − | 0.717847i | \(-0.254872\pi\) |
−0.273573 | + | 0.961851i | \(0.588205\pi\) | |||||||
\(824\) | −1.00000 | + | 1.73205i | −0.0348367 | + | 0.0603388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.00000 | + | 15.5885i | 0.313150 | + | 0.542392i | ||||
\(827\) | 27.0000i | 0.938882i | 0.882964 | + | 0.469441i | \(0.155545\pi\) | ||||
−0.882964 | + | 0.469441i | \(0.844455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.0000 | −1.11141 | −0.555703 | − | 0.831381i | \(-0.687551\pi\) | ||||
−0.555703 | + | 0.831381i | \(0.687551\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.46410 | + | 2.00000i | 0.120096 | + | 0.0693375i | ||||
\(833\) | −15.5885 | − | 9.00000i | −0.540108 | − | 0.311832i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 3.00000i | − | 0.103633i | ||||||
\(839\) | 21.0000 | + | 36.3731i | 0.725001 | + | 1.25574i | 0.958974 | + | 0.283495i | \(0.0914938\pi\) |
−0.233973 | + | 0.972243i | \(0.575173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −8.66025 | − | 5.00000i | −0.298452 | − | 0.172311i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.50000 | + | 4.33013i | 0.0860535 | + | 0.149049i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.0000i | − | 0.755929i | ||||||
\(848\) | −10.3923 | + | 6.00000i | −0.356873 | + | 0.206041i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.66025 | − | 5.00000i | 0.296521 | − | 0.171197i | −0.344358 | − | 0.938839i | \(-0.611903\pi\) |
0.640879 | + | 0.767642i | \(0.278570\pi\) | |||||||
\(854\) | −8.00000 | −0.273754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | 0.307614 | ||||||||
\(857\) | 33.7750 | − | 19.5000i | 1.15373 | − | 0.666107i | 0.203938 | − | 0.978984i | \(-0.434626\pi\) |
0.949794 | + | 0.312877i | \(0.101293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.5000 | + | 26.8468i | −0.528853 | + | 0.916001i | 0.470581 | + | 0.882357i | \(0.344044\pi\) |
−0.999434 | + | 0.0336436i | \(0.989289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.19615 | − | 3.00000i | 0.176982 | − | 0.102180i | ||||
\(863\) | 12.0000i | 0.408485i | 0.978920 | + | 0.204242i | \(0.0654731\pi\) | ||||
−0.978920 | + | 0.204242i | \(0.934527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.00000 | + | 1.73205i | 0.0339814 | + | 0.0588575i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −17.3205 | − | 10.0000i | −0.587896 | − | 0.339422i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.0000 | − | 45.0333i | −0.880976 | − | 1.52590i | ||||
\(872\) | − | 2.00000i | − | 0.0677285i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.66025 | + | 5.00000i | 0.292436 | + | 0.168838i | 0.639040 | − | 0.769174i | \(-0.279332\pi\) |
−0.346604 | + | 0.938012i | \(0.612665\pi\) | |||||||
\(878\) | 3.46410 | + | 2.00000i | 0.116908 | + | 0.0674967i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.0000i | − | 0.673054i | −0.941674 | − | 0.336527i | \(-0.890748\pi\) | ||
0.941674 | − | 0.336527i | \(-0.109252\pi\) | |||||||
\(884\) | −12.0000 | − | 20.7846i | −0.403604 | − | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.0000 | + | 31.1769i | −0.604722 | + | 1.04741i | ||||
\(887\) | 5.19615 | + | 3.00000i | 0.174470 | + | 0.100730i | 0.584692 | − | 0.811256i | \(-0.301215\pi\) |
−0.410222 | + | 0.911986i | \(0.634549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | + | 34.6410i | 0.670778 | + | 1.16182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 16.0000i | − | 0.535720i | ||||||
\(893\) | −36.3731 | + | 21.0000i | −1.21718 | + | 0.702738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | − | 1.73205i | 0.0334077 | − | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.9904 | − | 7.50000i | 0.433495 | − | 0.250278i | ||||
\(899\) | 60.0000 | 2.00111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 72.0000 | 2.39867 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.50000 | − | 2.59808i | 0.0498893 | − | 0.0864107i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.06218 | + | 3.50000i | −0.201291 | + | 0.116216i | −0.597258 | − | 0.802049i | \(-0.703743\pi\) |
0.395966 | + | 0.918265i | \(0.370410\pi\) | |||||||
\(908\) | − | 15.0000i | − | 0.497792i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000 | + | 10.3923i | 0.198789 | + | 0.344312i | 0.948136 | − | 0.317865i | \(-0.102966\pi\) |
−0.749347 | + | 0.662177i | \(0.769633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.50000 | − | 16.4545i | 0.314232 | − | 0.544266i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.00000 | + | 8.66025i | 0.165205 | + | 0.286143i | ||||
\(917\) | 24.0000i | 0.792550i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.19615 | − | 3.00000i | −0.171126 | − | 0.0987997i | ||||
\(923\) | 20.7846 | + | 12.0000i | 0.684134 | + | 0.394985i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −26.0000 | −0.854413 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | 27.0000 | + | 46.7654i | 0.885841 | + | 1.53432i | 0.844746 | + | 0.535167i | \(0.179751\pi\) |
0.0410949 | + | 0.999155i | \(0.486915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.5000 | + | 18.1865i | −0.344124 | + | 0.596040i | ||||
\(932\) | 2.59808 | + | 1.50000i | 0.0851028 | + | 0.0491341i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.50000 | − | 12.9904i | −0.245407 | − | 0.425058i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0000i | 0.751377i | 0.926746 | + | 0.375689i | \(0.122594\pi\) | ||||
−0.926746 | + | 0.375689i | \(0.877406\pi\) | |||||||
\(938\) | −22.5167 | + | 13.0000i | −0.735195 | + | 0.424465i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0000 | + | 46.7654i | −0.880175 | + | 1.52451i | −0.0290288 | + | 0.999579i | \(0.509241\pi\) |
−0.851146 | + | 0.524929i | \(0.824092\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −9.00000 | −0.292925 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.1865 | − | 10.5000i | 0.590983 | − | 0.341204i | −0.174503 | − | 0.984657i | \(-0.555832\pi\) |
0.765486 | + | 0.643452i | \(0.222499\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.00000 | − | 3.46410i | 0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.3923 | + | 6.00000i | −0.336817 | + | 0.194461i | ||||
\(953\) | − | 30.0000i | − | 0.971795i | −0.874016 | − | 0.485898i | \(-0.838493\pi\) | ||
0.874016 | − | 0.485898i | \(-0.161507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.1769 | + | 18.0000i | 1.00728 | + | 0.581554i | ||||
\(959\) | 3.00000 | − | 5.19615i | 0.0968751 | − | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | − | 59.7558i | −1.11290 | − | 1.92760i | ||||
\(962\) | 8.00000i | 0.257930i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.0000 | 0.611949 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.3205 | − | 10.0000i | −0.556990 | − | 0.321578i | 0.194946 | − | 0.980814i | \(-0.437547\pi\) |
−0.751936 | + | 0.659236i | \(0.770880\pi\) | |||||||
\(968\) | 9.52628 | + | 5.50000i | 0.306186 | + | 0.176777i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0000 | 0.673922 | 0.336961 | − | 0.941519i | \(-0.390601\pi\) | ||||
0.336961 | + | 0.941519i | \(0.390601\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000i | 0.256468i | ||||||||
\(974\) | −1.00000 | − | 1.73205i | −0.0320421 | − | 0.0554985i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | − | 3.46410i | 0.0640184 | − | 0.110883i | ||||
\(977\) | −12.9904 | − | 7.50000i | −0.415599 | − | 0.239946i | 0.277594 | − | 0.960699i | \(-0.410463\pi\) |
−0.693193 | + | 0.720752i | \(0.743796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 3.00000i | − | 0.0957338i | ||||||
\(983\) | −25.9808 | + | 15.0000i | −0.828658 | + | 0.478426i | −0.853393 | − | 0.521268i | \(-0.825459\pi\) |
0.0247352 | + | 0.999694i | \(0.492126\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.0000 | − | 31.1769i | 0.573237 | − | 0.992875i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.2487 | + | 14.0000i | −0.771454 | + | 0.445399i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.0000 | 1.39771 | 0.698853 | − | 0.715265i | \(-0.253694\pi\) | ||||
0.698853 | + | 0.715265i | \(0.253694\pi\) | |||||||
\(992\) | 8.66025 | − | 5.00000i | 0.274963 | − | 0.158750i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | − | 10.3923i | 0.190308 | − | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.2487 | + | 14.0000i | −0.767964 | + | 0.443384i | −0.832148 | − | 0.554554i | \(-0.812889\pi\) |
0.0641836 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(998\) | 11.0000i | 0.348199i | ||||||||
\(999\) | 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 | 1350.2.j.b.199.1 | 4 | ||
3.2 | odd | 2 | 450.2.j.b.49.2 | 4 | |||
5.2 | odd | 4 | 1350.2.e.d.901.1 | 2 | |||
5.3 | odd | 4 | 1350.2.e.h.901.1 | 2 | |||
5.4 | even | 2 | inner | 1350.2.j.b.199.2 | 4 | ||
9.2 | odd | 6 | 450.2.j.b.349.1 | 4 | |||
9.4 | even | 3 | 4050.2.c.m.649.1 | 2 | |||
9.5 | odd | 6 | 4050.2.c.h.649.2 | 2 | |||
9.7 | even | 3 | inner | 1350.2.j.b.1099.2 | 4 | ||
15.2 | even | 4 | 450.2.e.f.301.1 | yes | 2 | ||
15.8 | even | 4 | 450.2.e.c.301.1 | yes | 2 | ||
15.14 | odd | 2 | 450.2.j.b.49.1 | 4 | |||
45.2 | even | 12 | 450.2.e.f.151.1 | yes | 2 | ||
45.4 | even | 6 | 4050.2.c.m.649.2 | 2 | |||
45.7 | odd | 12 | 1350.2.e.d.451.1 | 2 | |||
45.13 | odd | 12 | 4050.2.a.o.1.1 | 1 | |||
45.14 | odd | 6 | 4050.2.c.h.649.1 | 2 | |||
45.22 | odd | 12 | 4050.2.a.u.1.1 | 1 | |||
45.23 | even | 12 | 4050.2.a.bg.1.1 | 1 | |||
45.29 | odd | 6 | 450.2.j.b.349.2 | 4 | |||
45.32 | even | 12 | 4050.2.a.d.1.1 | 1 | |||
45.34 | even | 6 | inner | 1350.2.j.b.1099.1 | 4 | ||
45.38 | even | 12 | 450.2.e.c.151.1 | ✓ | 2 | ||
45.43 | odd | 12 | 1350.2.e.h.451.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.e.c.151.1 | ✓ | 2 | 45.38 | even | 12 | ||
450.2.e.c.301.1 | yes | 2 | 15.8 | even | 4 | ||
450.2.e.f.151.1 | yes | 2 | 45.2 | even | 12 | ||
450.2.e.f.301.1 | yes | 2 | 15.2 | even | 4 | ||
450.2.j.b.49.1 | 4 | 15.14 | odd | 2 | |||
450.2.j.b.49.2 | 4 | 3.2 | odd | 2 | |||
450.2.j.b.349.1 | 4 | 9.2 | odd | 6 | |||
450.2.j.b.349.2 | 4 | 45.29 | odd | 6 | |||
1350.2.e.d.451.1 | 2 | 45.7 | odd | 12 | |||
1350.2.e.d.901.1 | 2 | 5.2 | odd | 4 | |||
1350.2.e.h.451.1 | 2 | 45.43 | odd | 12 | |||
1350.2.e.h.901.1 | 2 | 5.3 | odd | 4 | |||
1350.2.j.b.199.1 | 4 | 1.1 | even | 1 | trivial | ||
1350.2.j.b.199.2 | 4 | 5.4 | even | 2 | inner | ||
1350.2.j.b.1099.1 | 4 | 45.34 | even | 6 | inner | ||
1350.2.j.b.1099.2 | 4 | 9.7 | even | 3 | inner | ||
4050.2.a.d.1.1 | 1 | 45.32 | even | 12 | |||
4050.2.a.o.1.1 | 1 | 45.13 | odd | 12 | |||
4050.2.a.u.1.1 | 1 | 45.22 | odd | 12 | |||
4050.2.a.bg.1.1 | 1 | 45.23 | even | 12 | |||
4050.2.c.h.649.1 | 2 | 45.14 | odd | 6 | |||
4050.2.c.h.649.2 | 2 | 9.5 | odd | 6 | |||
4050.2.c.m.649.1 | 2 | 9.4 | even | 3 | |||
4050.2.c.m.649.2 | 2 | 45.4 | even | 6 |