Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(1025,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.e (of order \(2\), degree \(1\), 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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2441150464.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 77x^{4} - 188x^{2} + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.7 | ||
Root | \(-1.52833 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1025 |
Dual form | 1728.3.e.v.1025.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 7.37942i | 1.47588i | 0.674864 | + | 0.737942i | \(0.264202\pi\) | ||||
−0.674864 | + | 0.737942i | \(0.735798\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.26611 | −0.180873 | −0.0904363 | − | 0.995902i | \(-0.528826\pi\) | ||||
−0.0904363 | + | 0.995902i | \(0.528826\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.82843i | − 0.529857i | −0.964268 | − | 0.264929i | \(-0.914652\pi\) | ||||
0.964268 | − | 0.264929i | \(-0.0853484\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.4853 | 0.806560 | 0.403280 | − | 0.915077i | \(-0.367870\pi\) | ||||
0.403280 | + | 0.915077i | \(0.367870\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 18.3399i | − 1.07882i | −0.842043 | − | 0.539410i | \(-0.818647\pi\) | ||||
0.842043 | − | 0.539410i | \(-0.181353\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.8722 | −1.09853 | −0.549267 | − | 0.835647i | \(-0.685093\pi\) | ||||
−0.549267 | + | 0.835647i | \(0.685093\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 20.4853i | − 0.890664i | −0.895365 | − | 0.445332i | \(-0.853086\pi\) | ||||
0.895365 | − | 0.445332i | \(-0.146914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −29.4558 | −1.17823 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11.1777i | 0.385439i | 0.981254 | + | 0.192720i | \(0.0617308\pi\) | ||||
−0.981254 | + | 0.192720i | \(0.938269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −61.3503 | −1.97904 | −0.989522 | − | 0.144384i | \(-0.953880\pi\) | ||||
−0.989522 | + | 0.144384i | \(0.953880\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 9.34315i | − 0.266947i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.4264 | 1.03855 | 0.519276 | − | 0.854607i | \(-0.326202\pi\) | ||||
0.519276 | + | 0.854607i | \(0.326202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.0988i | 0.807287i | 0.914916 | + | 0.403644i | \(0.132256\pi\) | ||||
−0.914916 | + | 0.403644i | \(0.867744\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −49.3410 | −1.14746 | −0.573732 | − | 0.819043i | \(-0.694505\pi\) | ||||
−0.573732 | + | 0.819043i | \(0.694505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 21.5980i | 0.459531i | 0.973246 | + | 0.229766i | \(0.0737960\pi\) | ||||
−0.973246 | + | 0.229766i | \(0.926204\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −47.3970 | −0.967285 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 77.5925i | − 1.46401i | −0.681299 | − | 0.732005i | \(-0.738585\pi\) | ||||
0.681299 | − | 0.732005i | \(-0.261415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 43.0104 | 0.782008 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 25.7157i | − 0.435860i | −0.975964 | − | 0.217930i | \(-0.930070\pi\) | ||||
0.975964 | − | 0.217930i | \(-0.0699304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 55.8823 | 0.916102 | 0.458051 | − | 0.888926i | \(-0.348548\pi\) | ||||
0.458051 | + | 0.888926i | \(0.348548\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 77.3753i | 1.19039i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 91.0853 | 1.35948 | 0.679741 | − | 0.733452i | \(-0.262092\pi\) | ||||
0.679741 | + | 0.733452i | \(0.262092\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 114.770i | − 1.61647i | −0.588858 | − | 0.808236i | \(-0.700422\pi\) | ||||
0.588858 | − | 0.808236i | \(-0.299578\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −120.338 | −1.64847 | −0.824234 | − | 0.566250i | \(-0.808394\pi\) | ||||
−0.824234 | + | 0.566250i | \(0.808394\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.37942i | 0.0958366i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.21107 | 0.103938 | 0.0519688 | − | 0.998649i | \(-0.483450\pi\) | ||||
0.0519688 | + | 0.998649i | \(0.483450\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 150.338i | − 1.81130i | −0.424024 | − | 0.905651i | \(-0.639383\pi\) | ||||
0.424024 | − | 0.905651i | \(-0.360617\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 135.338 | 1.59221 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 118.505i | − 1.33152i | −0.746166 | − | 0.665759i | \(-0.768108\pi\) | ||||
0.746166 | − | 0.665759i | \(-0.231892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.2755 | −0.145885 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 154.024i | − 1.62131i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −72.8823 | −0.751363 | −0.375682 | − | 0.926749i | \(-0.622591\pi\) | ||||
−0.375682 | + | 0.926749i | \(0.622591\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 113.838i | 1.12711i | 0.826079 | + | 0.563554i | \(0.190566\pi\) | ||||
−0.826079 | + | 0.563554i | \(0.809434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 158.766 | 1.54142 | 0.770709 | − | 0.637187i | \(-0.219902\pi\) | ||||
0.770709 | + | 0.637187i | \(0.219902\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 77.7452i | − 0.726590i | −0.931674 | − | 0.363295i | \(-0.881652\pi\) | ||||
0.931674 | − | 0.363295i | \(-0.118348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3970 | 0.141257 | 0.0706283 | − | 0.997503i | \(-0.477500\pi\) | ||||
0.0706283 | + | 0.997503i | \(0.477500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 76.9408i | − 0.680892i | −0.940264 | − | 0.340446i | \(-0.889422\pi\) | ||||
0.940264 | − | 0.340446i | \(-0.110578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 151.170 | 1.31452 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.2203i | 0.195129i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 87.0294 | 0.719252 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 32.8815i | − 0.263052i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −72.0936 | −0.567666 | −0.283833 | − | 0.958874i | \(-0.591606\pi\) | ||||
−0.283833 | + | 0.958874i | \(0.591606\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 84.4214i | 0.644438i | 0.946665 | + | 0.322219i | \(0.104429\pi\) | ||||
−0.946665 | + | 0.322219i | \(0.895571\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.4264 | 0.198695 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 29.0832i | − 0.212286i | −0.994351 | − | 0.106143i | \(-0.966150\pi\) | ||||
0.994351 | − | 0.106143i | \(-0.0338502\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −130.297 | −0.937391 | −0.468695 | − | 0.883360i | \(-0.655276\pi\) | ||||
−0.468695 | + | 0.883360i | \(0.655276\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 61.1127i | − 0.427362i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −82.4853 | −0.568864 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 92.3514i | 0.619808i | 0.950768 | + | 0.309904i | \(0.100297\pi\) | ||||
−0.950768 | + | 0.309904i | \(0.899703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 44.9282 | 0.297538 | 0.148769 | − | 0.988872i | \(-0.452469\pi\) | ||||
0.148769 | + | 0.988872i | \(0.452469\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 452.730i | − 2.92084i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 131.029 | 0.834582 | 0.417291 | − | 0.908773i | \(-0.362980\pi\) | ||||
0.417291 | + | 0.908773i | \(0.362980\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.9366i | 0.161097i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 258.677 | 1.58697 | 0.793487 | − | 0.608587i | \(-0.208263\pi\) | ||||
0.793487 | + | 0.608587i | \(0.208263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 304.108i | − 1.82100i | −0.413505 | − | 0.910502i | \(-0.635696\pi\) | ||||
0.413505 | − | 0.910502i | \(-0.364304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −59.0589 | −0.349461 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.651690i | 0.00376699i | 0.999998 | + | 0.00188350i | \(0.000599536\pi\) | ||||
−0.999998 | + | 0.00188350i | \(0.999400\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 37.2943 | 0.213110 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 126.765i | 0.708182i | 0.935211 | + | 0.354091i | \(0.115210\pi\) | ||||
−0.935211 | + | 0.354091i | \(0.884790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −304.735 | −1.68362 | −0.841810 | − | 0.539775i | \(-0.818509\pi\) | ||||
−0.841810 | + | 0.539775i | \(0.818509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 283.565i | 1.53278i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −106.893 | −0.571620 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 134.132i | 0.702262i | 0.936326 | + | 0.351131i | \(0.114203\pi\) | ||||
−0.936326 | + | 0.351131i | \(0.885797\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 182.397 | 0.945062 | 0.472531 | − | 0.881314i | \(-0.343340\pi\) | ||||
0.472531 | + | 0.881314i | \(0.343340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 154.533i | − 0.784433i | −0.919873 | − | 0.392217i | \(-0.871708\pi\) | ||||
0.919873 | − | 0.392217i | \(-0.128292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −36.7171 | −0.184508 | −0.0922541 | − | 0.995735i | \(-0.529407\pi\) | ||||
−0.0922541 | + | 0.995735i | \(0.529407\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 14.1522i | − 0.0697155i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −244.250 | −1.19146 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 121.652i | 0.582066i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −359.891 | −1.70564 | −0.852822 | − | 0.522201i | \(-0.825111\pi\) | ||||
−0.852822 | + | 0.522201i | \(0.825111\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 364.108i | − 1.69352i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 77.6762 | 0.357955 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 192.299i | − 0.870133i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −273.870 | −1.22812 | −0.614059 | − | 0.789260i | \(-0.710464\pi\) | ||||
−0.614059 | + | 0.789260i | \(0.710464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 234.500i | − 1.03304i | −0.856276 | − | 0.516519i | \(-0.827228\pi\) | ||||
0.856276 | − | 0.516519i | \(-0.172772\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.6468 | −0.111995 | −0.0559973 | − | 0.998431i | \(-0.517834\pi\) | ||||
−0.0559973 | + | 0.998431i | \(0.517834\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.30338i | 0.00559390i | 0.999996 | + | 0.00279695i | \(0.000890298\pi\) | ||||
−0.999996 | + | 0.00279695i | \(0.999110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −159.381 | −0.678215 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 75.1615i | − 0.314483i | −0.987560 | − | 0.157242i | \(-0.949740\pi\) | ||||
0.987560 | − | 0.157242i | \(-0.0502601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 252.558 | 1.04796 | 0.523980 | − | 0.851730i | \(-0.324447\pi\) | ||||
0.523980 | + | 0.851730i | \(0.324447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 349.762i | − 1.42760i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −218.850 | −0.886034 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 246.000i | − 0.980080i | −0.871700 | − | 0.490040i | \(-0.836982\pi\) | ||||
0.871700 | − | 0.490040i | \(-0.163018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −119.397 | −0.471925 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 359.097i | − 1.39726i | −0.715482 | − | 0.698632i | \(-0.753793\pi\) | ||||
0.715482 | − | 0.698632i | \(-0.246207\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −48.6520 | −0.187846 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 215.897i | 0.820899i | 0.911883 | + | 0.410450i | \(0.134628\pi\) | ||||
−0.911883 | + | 0.410450i | \(0.865372\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 572.588 | 2.16071 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 488.885i | 1.81742i | 0.417432 | + | 0.908708i | \(0.362930\pi\) | ||||
−0.417432 | + | 0.908708i | \(0.637070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −161.261 | −0.595059 | −0.297530 | − | 0.954713i | \(-0.596163\pi\) | ||||
−0.297530 | + | 0.954713i | \(0.596163\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 171.681i | 0.624295i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −248.617 | −0.897535 | −0.448768 | − | 0.893648i | \(-0.648137\pi\) | ||||
−0.448768 | + | 0.893648i | \(0.648137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 329.579i | − 1.17288i | −0.809993 | − | 0.586439i | \(-0.800529\pi\) | ||||
0.809993 | − | 0.586439i | \(-0.199471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 262.438 | 0.927343 | 0.463671 | − | 0.886007i | \(-0.346532\pi\) | ||||
0.463671 | + | 0.886007i | \(0.346532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 41.9066i | − 0.146016i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −47.3532 | −0.163852 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 335.872i | 1.14632i | 0.819443 | + | 0.573161i | \(0.194283\pi\) | ||||
−0.819443 | + | 0.573161i | \(0.805717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 189.767 | 0.643279 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 214.794i | − 0.718374i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 62.4710 | 0.207545 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 412.379i | 1.35206i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −580.045 | −1.88940 | −0.944698 | − | 0.327941i | \(-0.893645\pi\) | ||||
−0.944698 | + | 0.327941i | \(0.893645\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 452.132i | − 1.45380i | −0.686743 | − | 0.726900i | \(-0.740960\pi\) | ||||
0.686743 | − | 0.726900i | \(-0.259040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −126.632 | −0.404577 | −0.202288 | − | 0.979326i | \(-0.564838\pi\) | ||||
−0.202288 | + | 0.979326i | \(0.564838\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 237.767i | 0.750055i | 0.927014 | + | 0.375028i | \(0.122367\pi\) | ||||
−0.927014 | + | 0.375028i | \(0.877633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 65.1487 | 0.204228 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 382.794i | 1.18512i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −308.853 | −0.950316 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 27.3454i | − 0.0831167i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 222.611 | 0.672542 | 0.336271 | − | 0.941765i | \(-0.390834\pi\) | ||||
0.336271 | + | 0.941765i | \(0.390834\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 672.156i | 2.00644i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 396.794 | 1.17743 | 0.588715 | − | 0.808341i | \(-0.299634\pi\) | ||||
0.588715 | + | 0.808341i | \(0.299634\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 357.576i | 1.04861i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 122.049 | 0.355828 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 218.387i | 0.629357i | 0.949198 | + | 0.314678i | \(0.101897\pi\) | ||||
−0.949198 | + | 0.314678i | \(0.898103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −499.161 | −1.43026 | −0.715131 | − | 0.698990i | \(-0.753633\pi\) | ||||
−0.715131 | + | 0.698990i | \(0.753633\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 423.991i | − 1.20111i | −0.799585 | − | 0.600554i | \(-0.794947\pi\) | ||||
0.799585 | − | 0.600554i | \(-0.205053\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 846.933 | 2.38573 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.2254i | 0.0897643i | 0.998992 | + | 0.0448822i | \(0.0142912\pi\) | ||||
−0.998992 | + | 0.0448822i | \(0.985709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 74.6468 | 0.206778 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 888.025i | − 2.43295i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 449.710 | 1.22537 | 0.612684 | − | 0.790328i | \(-0.290090\pi\) | ||||
0.612684 | + | 0.790328i | \(0.290090\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 98.2405i | 0.264799i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 386.368 | 1.03584 | 0.517919 | − | 0.855430i | \(-0.326707\pi\) | ||||
0.517919 | + | 0.855430i | \(0.326707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 117.202i | 0.310880i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 508.603 | 1.34196 | 0.670980 | − | 0.741475i | \(-0.265874\pi\) | ||||
0.670980 | + | 0.741475i | \(0.265874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 308.142i | 0.804549i | 0.915519 | + | 0.402274i | \(0.131780\pi\) | ||||
−0.915519 | + | 0.402274i | \(0.868220\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −54.4558 | −0.141444 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 356.707i | − 0.916985i | −0.888698 | − | 0.458492i | \(-0.848390\pi\) | ||||
0.888698 | − | 0.458492i | \(-0.151610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −375.699 | −0.960866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 60.5929i | 0.153400i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −524.191 | −1.32038 | −0.660190 | − | 0.751099i | \(-0.729524\pi\) | ||||
−0.660190 | + | 0.751099i | \(0.729524\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 236.141i | − 0.588881i | −0.955670 | − | 0.294441i | \(-0.904867\pi\) | ||||
0.955670 | − | 0.294441i | \(-0.0951333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −643.276 | −1.59622 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 223.966i | − 0.550284i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 261.235 | 0.638718 | 0.319359 | − | 0.947634i | \(-0.396532\pi\) | ||||
0.319359 | + | 0.947634i | \(0.396532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 32.5589i | 0.0788351i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1109.41 | 2.67327 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 392.745i | 0.937339i | 0.883374 | + | 0.468670i | \(0.155267\pi\) | ||||
−0.883374 | + | 0.468670i | \(0.844733\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 266.794 | 0.633715 | 0.316857 | − | 0.948473i | \(-0.397372\pi\) | ||||
0.316857 | + | 0.948473i | \(0.397372\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 540.218i | 1.27110i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −70.7530 | −0.165698 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 601.029i | 1.39450i | 0.716828 | + | 0.697250i | \(0.245593\pi\) | ||||
−0.716828 | + | 0.697250i | \(0.754407\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −605.500 | −1.39838 | −0.699191 | − | 0.714935i | \(-0.746456\pi\) | ||||
−0.699191 | + | 0.714935i | \(0.746456\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 427.572i | 0.978425i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −333.992 | −0.760801 | −0.380401 | − | 0.924822i | \(-0.624214\pi\) | ||||
−0.380401 | + | 0.924822i | \(0.624214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 203.823i | − 0.460098i | −0.973179 | − | 0.230049i | \(-0.926111\pi\) | ||||
0.973179 | − | 0.230049i | \(-0.0738886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 874.500 | 1.96517 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 733.492i | 1.63361i | 0.576912 | + | 0.816806i | \(0.304258\pi\) | ||||
−0.576912 | + | 0.816806i | \(0.695742\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 192.914 | 0.427747 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 97.9655i | − 0.215309i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −514.765 | −1.12640 | −0.563200 | − | 0.826321i | \(-0.690430\pi\) | ||||
−0.563200 | + | 0.826321i | \(0.690430\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 232.778i | − 0.504941i | −0.967605 | − | 0.252470i | \(-0.918757\pi\) | ||||
0.967605 | − | 0.252470i | \(-0.0812430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 72.7826 | 0.157198 | 0.0785989 | − | 0.996906i | \(-0.474955\pi\) | ||||
0.0785989 | + | 0.996906i | \(0.474955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 304.643i | 0.652340i | 0.945311 | + | 0.326170i | \(0.105758\pi\) | ||||
−0.945311 | + | 0.326170i | \(0.894242\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −115.324 | −0.245893 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 287.580i | 0.607992i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 614.807 | 1.29433 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 310.118i | 0.647427i | 0.946155 | + | 0.323714i | \(0.104931\pi\) | ||||
−0.946155 | + | 0.323714i | \(0.895069\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 402.912 | 0.837654 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 537.829i | − 1.10893i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −744.415 | −1.52857 | −0.764287 | − | 0.644877i | \(-0.776909\pi\) | ||||
−0.764287 | + | 0.644877i | \(0.776909\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 480.754i | − 0.979133i | −0.871966 | − | 0.489567i | \(-0.837155\pi\) | ||||
0.871966 | − | 0.489567i | \(-0.162845\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 204.999 | 0.415820 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 145.311i | 0.292376i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −694.534 | −1.39185 | −0.695926 | − | 0.718113i | \(-0.745006\pi\) | ||||
−0.695926 | + | 0.718113i | \(0.745006\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 266.309i | − 0.529441i | −0.964325 | − | 0.264720i | \(-0.914720\pi\) | ||||
0.964325 | − | 0.264720i | \(-0.0852796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −840.058 | −1.66348 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 205.538i | 0.403807i | 0.979405 | + | 0.201903i | \(0.0647127\pi\) | ||||
−0.979405 | + | 0.201903i | \(0.935287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 152.361 | 0.298163 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1171.60i | 2.27496i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 125.882 | 0.243486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 940.550i | − 1.80528i | −0.430398 | − | 0.902639i | \(-0.641627\pi\) | ||||
0.430398 | − | 0.902639i | \(-0.358373\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −94.3064 | −0.180318 | −0.0901591 | − | 0.995927i | \(-0.528738\pi\) | ||||
−0.0901591 | + | 0.995927i | \(0.528738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1125.16i | 2.13503i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 109.353 | 0.206717 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 347.050i | 0.651126i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 573.714 | 1.07236 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 276.250i | 0.512523i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.7645 | 0.0661081 | 0.0330541 | − | 0.999454i | \(-0.489477\pi\) | ||||
0.0330541 | + | 0.999454i | \(0.489477\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 113.621i | 0.208478i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 443.305 | 0.810430 | 0.405215 | − | 0.914221i | \(-0.367197\pi\) | ||||
0.405215 | + | 0.914221i | \(0.367197\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 233.304i | − 0.423419i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.3961 | −0.0187995 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 438.098i | 0.786531i | 0.919425 | + | 0.393266i | \(0.128655\pi\) | ||||
−0.919425 | + | 0.393266i | \(0.871345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −517.354 | −0.925499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1065.07i | 1.89178i | 0.324485 | + | 0.945891i | \(0.394809\pi\) | ||||
−0.324485 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 567.779 | 1.00492 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 939.141i | − 1.65051i | −0.564759 | − | 0.825256i | \(-0.691031\pi\) | ||||
0.564759 | − | 0.825256i | \(-0.308969\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −294.128 | −0.515110 | −0.257555 | − | 0.966264i | \(-0.582917\pi\) | ||||
−0.257555 | + | 0.966264i | \(0.582917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 603.411i | 1.04941i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −546.500 | −0.947140 | −0.473570 | − | 0.880756i | \(-0.657035\pi\) | ||||
−0.473570 | + | 0.880756i | \(0.657035\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 190.344i | 0.327615i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −452.242 | −0.775716 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.7939i | 0.0746064i | 0.999304 | + | 0.0373032i | \(0.0118767\pi\) | ||||
−0.999304 | + | 0.0373032i | \(0.988123\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1280.51 | 2.17405 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 823.454i | − 1.38862i | −0.719674 | − | 0.694312i | \(-0.755709\pi\) | ||||
0.719674 | − | 0.694312i | \(-0.244291\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −171.353 | −0.287988 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 826.244i | 1.37937i | 0.724109 | + | 0.689686i | \(0.242251\pi\) | ||||
−0.724109 | + | 0.689686i | \(0.757749\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −378.632 | −0.630004 | −0.315002 | − | 0.949091i | \(-0.602005\pi\) | ||||
−0.315002 | + | 0.949091i | \(0.602005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 642.227i | 1.06153i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 139.737 | 0.230210 | 0.115105 | − | 0.993353i | \(-0.463280\pi\) | ||||
0.115105 | + | 0.993353i | \(0.463280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 226.461i | 0.370640i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 508.587 | 0.829669 | 0.414834 | − | 0.909897i | \(-0.363839\pi\) | ||||
0.414834 | + | 0.909897i | \(0.363839\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 429.415i | 0.695973i | 0.937500 | + | 0.347986i | \(0.113134\pi\) | ||||
−0.937500 | + | 0.347986i | \(0.886866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −720.471 | −1.16393 | −0.581964 | − | 0.813215i | \(-0.697715\pi\) | ||||
−0.581964 | + | 0.813215i | \(0.697715\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 150.040i | 0.240835i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −493.749 | −0.789999 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 704.738i | − 1.12041i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −479.482 | −0.759877 | −0.379938 | − | 0.925012i | \(-0.624055\pi\) | ||||
−0.379938 | + | 0.925012i | \(0.624055\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 532.009i | − 0.837810i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −496.971 | −0.780174 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 562.679i | 0.877815i | 0.898532 | + | 0.438907i | \(0.144634\pi\) | ||||
−0.898532 | + | 0.438907i | \(0.855366\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −785.471 | −1.22157 | −0.610786 | − | 0.791796i | \(-0.709146\pi\) | ||||
−0.610786 | + | 0.791796i | \(0.709146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 571.529i | 0.883352i | 0.897175 | + | 0.441676i | \(0.145616\pi\) | ||||
−0.897175 | + | 0.441676i | \(0.854384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −149.882 | −0.230943 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 325.346i | 0.498233i | 0.968474 | + | 0.249117i | \(0.0801402\pi\) | ||||
−0.968474 | + | 0.249117i | \(0.919860\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −622.981 | −0.951116 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 902.294i | 1.36919i | 0.728926 | + | 0.684593i | \(0.240020\pi\) | ||||
−0.728926 | + | 0.684593i | \(0.759980\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 59.6325 | 0.0902155 | 0.0451078 | − | 0.998982i | \(-0.485637\pi\) | ||||
0.0451078 | + | 0.998982i | \(0.485637\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 195.012i | 0.293250i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 228.979 | 0.343297 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 325.706i | − 0.485403i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1005.17 | −1.49357 | −0.746787 | − | 0.665064i | \(-0.768404\pi\) | ||||
−0.746787 | + | 0.665064i | \(0.768404\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 175.697i | − 0.259523i | −0.991545 | − | 0.129762i | \(-0.958579\pi\) | ||||
0.991545 | − | 0.129762i | \(-0.0414212\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 92.2768 | 0.135901 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 768.823i | − 1.12566i | −0.826574 | − | 0.562828i | \(-0.809713\pi\) | ||||
0.826574 | − | 0.562828i | \(-0.190287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 214.617 | 0.313310 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 813.579i | − 1.18081i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −590.714 | −0.854868 | −0.427434 | − | 0.904047i | \(-0.640582\pi\) | ||||
−0.427434 | + | 0.904047i | \(0.640582\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 961.519i | − 1.38348i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 607.029 | 0.870917 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 967.139i | − 1.37966i | −0.723974 | − | 0.689828i | \(-0.757686\pi\) | ||||
0.723974 | − | 0.689828i | \(-0.242314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −802.042 | −1.14088 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 144.131i | − 0.203863i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −147.647 | −0.208246 | −0.104123 | − | 0.994564i | \(-0.533204\pi\) | ||||
−0.104123 | + | 0.994564i | \(0.533204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1256.78i | 1.76266i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 450.976 | 0.630736 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 627.098i | 0.872181i | 0.899903 | + | 0.436091i | \(0.143637\pi\) | ||||
−0.899903 | + | 0.436091i | \(0.856363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −201.015 | −0.278800 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 329.250i | − 0.454138i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 150.518 | 0.207040 | 0.103520 | − | 0.994627i | \(-0.466989\pi\) | ||||
0.103520 | + | 0.994627i | \(0.466989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 904.910i | 1.23791i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 430.073 | 0.586730 | 0.293365 | − | 0.956000i | \(-0.405225\pi\) | ||||
0.293365 | + | 0.956000i | \(0.405225\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 530.884i | − 0.720331i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 347.230 | 0.469865 | 0.234932 | − | 0.972012i | \(-0.424513\pi\) | ||||
0.234932 | + | 0.972012i | \(0.424513\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 48.7797i | − 0.0656523i | −0.999461 | − | 0.0328261i | \(-0.989549\pi\) | ||||
0.999461 | − | 0.0328261i | \(-0.0104508\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −681.500 | −0.914765 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 98.4338i | 0.131420i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 323.248 | 0.430424 | 0.215212 | − | 0.976567i | \(-0.430956\pi\) | ||||
0.215212 | + | 0.976567i | \(0.430956\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 331.544i | 0.439131i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −452.912 | −0.598298 | −0.299149 | − | 0.954206i | \(-0.596703\pi\) | ||||
−0.299149 | + | 0.954206i | \(0.596703\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 824.757i | 1.08378i | 0.840449 | + | 0.541890i | \(0.182291\pi\) | ||||
−0.840449 | + | 0.541890i | \(0.817709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.4942 | −0.0255495 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 269.637i | − 0.351547i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 248.955 | 0.323739 | 0.161870 | − | 0.986812i | \(-0.448248\pi\) | ||||
0.161870 | + | 0.986812i | \(0.448248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 351.066i | 0.454160i | 0.973876 | + | 0.227080i | \(0.0729179\pi\) | ||||
−0.973876 | + | 0.227080i | \(0.927082\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1807.13 | 2.33178 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 690.843i | − 0.886833i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −668.926 | −0.856499 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 966.921i | 1.23175i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 342.705 | 0.435458 | 0.217729 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217729 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 97.4154i | 0.123155i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 585.941 | 0.738892 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 485.087i | − 0.608641i | −0.952570 | − | 0.304320i | \(-0.901571\pi\) | ||||
0.952570 | − | 0.304320i | \(-0.0984293\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 396.106 | 0.495752 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 701.382i | 0.873452i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −191.397 | −0.237760 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 179.278i | − 0.221605i | −0.993842 | − | 0.110802i | \(-0.964658\pi\) | ||||
0.993842 | − | 0.110802i | \(-0.0353421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −475.144 | −0.585874 | −0.292937 | − | 0.956132i | \(-0.594633\pi\) | ||||
−0.292937 | + | 0.956132i | \(0.594633\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1908.89i | 2.34219i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1029.85 | 1.26053 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 598.056i | 0.728448i | 0.931311 | + | 0.364224i | \(0.118666\pi\) | ||||
−0.931311 | + | 0.364224i | \(0.881334\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −433.288 | −0.526474 | −0.263237 | − | 0.964731i | \(-0.584790\pi\) | ||||
−0.263237 | + | 0.964731i | \(0.584790\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 62.2153i | 0.0752301i | 0.999292 | + | 0.0376151i | \(0.0119761\pi\) | ||||
−0.999292 | + | 0.0376151i | \(0.988024\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.70563 | −0.00447000 | −0.00223500 | − | 0.999998i | \(-0.500711\pi\) | ||||
−0.00223500 | + | 0.999998i | \(0.500711\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 869.257i | 1.04353i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2244.14 | 2.68759 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1382.59i | − 1.64790i | −0.566660 | − | 0.823952i | \(-0.691765\pi\) | ||||
0.566660 | − | 0.823952i | \(-0.308235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 716.058 | 0.851436 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 435.820i | − 0.515764i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −110.189 | −0.130093 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 787.176i | − 0.925001i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1273.53 | 1.49300 | 0.746500 | − | 0.665385i | \(-0.231733\pi\) | ||||
0.746500 | + | 0.665385i | \(0.231733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1009.57i | − 1.17802i | −0.808125 | − | 0.589011i | \(-0.799517\pi\) | ||||
0.808125 | − | 0.589011i | \(-0.200483\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 719.633 | 0.837757 | 0.418878 | − | 0.908042i | \(-0.362423\pi\) | ||||
0.418878 | + | 0.908042i | \(0.362423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 429.608i | − 0.497808i | −0.968528 | − | 0.248904i | \(-0.919930\pi\) | ||||
0.968528 | − | 0.248904i | \(-0.0800703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.80909 | −0.00555964 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 47.8576i | − 0.0550721i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 955.055 | 1.09650 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.6316i | 0.0475790i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 164.030 | 0.187036 | 0.0935178 | − | 0.995618i | \(-0.470189\pi\) | ||||
0.0935178 | + | 0.995618i | \(0.470189\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 333.265i | 0.378281i | 0.981950 | + | 0.189140i | \(0.0605701\pi\) | ||||
−0.981950 | + | 0.189140i | \(0.939430\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 289.138 | 0.327450 | 0.163725 | − | 0.986506i | \(-0.447649\pi\) | ||||
0.163725 | + | 0.986506i | \(0.447649\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 483.338i | − 0.544913i | −0.962168 | − | 0.272457i | \(-0.912164\pi\) | ||||
0.962168 | − | 0.272457i | \(-0.0878361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 91.2784 | 0.102675 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 450.796i | − 0.504811i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −935.449 | −1.04519 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 685.759i | − 0.762802i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1423.04 | −1.57940 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 2248.77i | − 2.48483i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −769.663 | −0.848581 | −0.424290 | − | 0.905526i | \(-0.639476\pi\) | ||||
−0.424290 | + | 0.905526i | \(0.639476\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 332.059i | 0.364499i | 0.983252 | + | 0.182250i | \(0.0583379\pi\) | ||||
−0.983252 | + | 0.182250i | \(0.941662\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −876.235 | −0.959731 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 106.887i | − 0.116561i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1339.15 | 1.45718 | 0.728591 | − | 0.684949i | \(-0.240175\pi\) | ||||
0.728591 | + | 0.684949i | \(0.240175\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1203.39i | − 1.30378i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1131.88 | −1.22366 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1194.16i | − 1.28543i | −0.766106 | − | 0.642714i | \(-0.777808\pi\) | ||||
0.766106 | − | 0.642714i | \(-0.222192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 989.277 | 1.06260 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 788.808i | − 0.843645i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 631.705 | 0.674178 | 0.337089 | − | 0.941473i | \(-0.390558\pi\) | ||||
0.337089 | + | 0.941473i | \(0.390558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1616.20i | 1.71753i | 0.512367 | + | 0.858766i | \(0.328769\pi\) | ||||
−0.512367 | + | 0.858766i | \(0.671231\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 678.038 | 0.719022 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1625.50i | 1.71647i | 0.513256 | + | 0.858235i | \(0.328439\pi\) | ||||
−0.513256 | + | 0.858235i | \(0.671561\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1261.78 | −1.32959 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 143.033i | 0.150087i | 0.997180 | + | 0.0750435i | \(0.0239096\pi\) | ||||
−0.997180 | + | 0.0750435i | \(0.976090\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −989.817 | −1.03646 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.8225i | 0.0383968i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2802.87 | 2.91661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1345.98i | 1.39480i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −132.178 | −0.136689 | −0.0683443 | − | 0.997662i | \(-0.521772\pi\) | ||||
−0.0683443 | + | 0.997662i | \(0.521772\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1171.53i | − 1.20652i | −0.797543 | − | 0.603262i | \(-0.793867\pi\) | ||||
0.797543 | − | 0.603262i | \(-0.206133\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 164.971 | 0.169548 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 797.623i | 0.816400i | 0.912893 | + | 0.408200i | \(0.133843\pi\) | ||||
−0.912893 | + | 0.408200i | \(0.866157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −690.699 | −0.705515 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 960.676i | − 0.977290i | −0.872483 | − | 0.488645i | \(-0.837491\pi\) | ||||
0.872483 | − | 0.488645i | \(-0.162509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1140.37 | 1.15773 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1010.76i | 1.02201i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −474.492 | −0.478802 | −0.239401 | − | 0.970921i | \(-0.576951\pi\) | ||||
−0.239401 | + | 0.970921i | \(0.576951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 270.951i | − 0.272313i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −180.219 | −0.180762 | −0.0903809 | − | 0.995907i | \(-0.528808\pi\) | ||||
−0.0903809 | + | 0.995907i | \(0.528808\pi\) | |||||||
\(998\) | 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 | 1728.3.e.v.1025.7 | 8 | ||
3.2 | odd | 2 | inner | 1728.3.e.v.1025.1 | 8 | ||
4.3 | odd | 2 | inner | 1728.3.e.v.1025.8 | 8 | ||
8.3 | odd | 2 | 864.3.e.e.161.2 | yes | 8 | ||
8.5 | even | 2 | 864.3.e.e.161.1 | ✓ | 8 | ||
12.11 | even | 2 | inner | 1728.3.e.v.1025.2 | 8 | ||
24.5 | odd | 2 | 864.3.e.e.161.7 | yes | 8 | ||
24.11 | even | 2 | 864.3.e.e.161.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.e.e.161.1 | ✓ | 8 | 8.5 | even | 2 | ||
864.3.e.e.161.2 | yes | 8 | 8.3 | odd | 2 | ||
864.3.e.e.161.7 | yes | 8 | 24.5 | odd | 2 | ||
864.3.e.e.161.8 | yes | 8 | 24.11 | even | 2 | ||
1728.3.e.v.1025.1 | 8 | 3.2 | odd | 2 | inner | ||
1728.3.e.v.1025.2 | 8 | 12.11 | even | 2 | inner | ||
1728.3.e.v.1025.7 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.e.v.1025.8 | 8 | 4.3 | odd | 2 | inner |