Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,8,Mod(145,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.145");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.d (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: | \(89.9668873394\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(5.57668 - 0.949035i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.145 |
Dual form | 288.8.d.b.145.6 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | − 338.443i | − 1.21085i | −0.795903 | − | 0.605425i | \(-0.793003\pi\) | ||||
0.795903 | − | 0.605425i | \(-0.206997\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 438.996 | 0.483746 | 0.241873 | − | 0.970308i | \(-0.422238\pi\) | ||||
0.241873 | + | 0.970308i | \(0.422238\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1966.58i | 0.445489i | 0.974877 | + | 0.222744i | \(0.0715015\pi\) | ||||
−0.974877 | + | 0.222744i | \(0.928498\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2210.98i | − 0.279115i | −0.990214 | − | 0.139557i | \(-0.955432\pi\) | ||||
0.990214 | − | 0.139557i | \(-0.0445680\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12114.9 | 0.598064 | 0.299032 | − | 0.954243i | \(-0.403336\pi\) | ||||
0.299032 | + | 0.954243i | \(0.403336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32872.2i | 1.09949i | 0.835333 | + | 0.549744i | \(0.185275\pi\) | ||||
−0.835333 | + | 0.549744i | \(0.814725\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19605.1 | 0.335986 | 0.167993 | − | 0.985788i | \(-0.446271\pi\) | ||||
0.167993 | + | 0.985788i | \(0.446271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −36418.4 | −0.466155 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 160689.i | 1.22347i | 0.791063 | + | 0.611735i | \(0.209528\pi\) | ||||
−0.791063 | + | 0.611735i | \(0.790472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 229270. | 1.38224 | 0.691118 | − | 0.722742i | \(-0.257119\pi\) | ||||
0.691118 | + | 0.722742i | \(0.257119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 148575.i | − 0.585744i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 496284.i | 1.61074i | 0.592775 | + | 0.805368i | \(0.298032\pi\) | ||||
−0.592775 | + | 0.805368i | \(0.701968\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −599971. | −1.35952 | −0.679762 | − | 0.733433i | \(-0.737917\pi\) | ||||
−0.679762 | + | 0.733433i | \(0.737917\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 88346.0i | 0.169452i | 0.996404 | + | 0.0847262i | \(0.0270015\pi\) | ||||
−0.996404 | + | 0.0847262i | \(0.972998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 820344. | 1.15253 | 0.576267 | − | 0.817262i | \(-0.304509\pi\) | ||||
0.576267 | + | 0.817262i | \(0.304509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −630825. | −0.765989 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.53717e6i | − 1.41826i | −0.705077 | − | 0.709131i | \(-0.749087\pi\) | ||||
0.705077 | − | 0.709131i | \(-0.250913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 665574. | 0.539420 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.82480e6i | − 1.15673i | −0.815776 | − | 0.578367i | \(-0.803690\pi\) | ||||
0.815776 | − | 0.578367i | \(-0.196310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 484582.i | 0.273346i | 0.990616 | + | 0.136673i | \(0.0436410\pi\) | ||||
−0.990616 | + | 0.136673i | \(0.956359\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −748290. | −0.337966 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 79878.2i | − 0.0324464i | −0.999868 | − | 0.0162232i | \(-0.994836\pi\) | ||||
0.999868 | − | 0.0162232i | \(-0.00516423\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.27078e6 | 0.421373 | 0.210686 | − | 0.977554i | \(-0.432430\pi\) | ||||
0.210686 | + | 0.977554i | \(0.432430\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.70820e6 | 1.11566 | 0.557832 | − | 0.829954i | \(-0.311633\pi\) | ||||
0.557832 | + | 0.829954i | \(0.311633\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 863321.i | 0.215504i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.55846e6 | 0.583827 | 0.291914 | − | 0.956445i | \(-0.405708\pi\) | ||||
0.291914 | + | 0.956445i | \(0.405708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.53414e6i | − 0.294505i | −0.989099 | − | 0.147252i | \(-0.952957\pi\) | ||||
0.989099 | − | 0.147252i | \(-0.0470430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 4.10019e6i | − 0.724166i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.99492e6 | −0.299958 | −0.149979 | − | 0.988689i | \(-0.547921\pi\) | ||||
−0.149979 | + | 0.988689i | \(0.547921\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 970612.i | − 0.135021i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.11253e7 | 1.33131 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −28917.7 | −0.00321708 | −0.00160854 | − | 0.999999i | \(-0.500512\pi\) | ||||
−0.00160854 | + | 0.999999i | \(0.500512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.68077e7i | 1.62324i | 0.584182 | + | 0.811622i | \(0.301415\pi\) | ||||
−0.584182 | + | 0.811622i | \(0.698585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.27746e7 | 1.15191 | 0.575953 | − | 0.817483i | \(-0.304631\pi\) | ||||
0.575953 | + | 0.817483i | \(0.304631\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.35610e7i | 1.07016i | 0.844803 | + | 0.535078i | \(0.179718\pi\) | ||||
−0.844803 | + | 0.535078i | \(0.820282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 4.74206e6i | − 0.350731i | −0.984503 | − | 0.175366i | \(-0.943889\pi\) | ||||
0.984503 | − | 0.175366i | \(-0.0561108\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.06832e6 | 0.526028 | 0.263014 | − | 0.964792i | \(-0.415283\pi\) | ||||
0.263014 | + | 0.964792i | \(0.415283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 6.63520e6i | − 0.406828i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.31839e6 | 0.289311 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.56197e7 | 0.801540 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.41153e7i | − 0.646405i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.12410e7 | 0.486960 | 0.243480 | − | 0.969906i | \(-0.421711\pi\) | ||||
0.243480 | + | 0.969906i | \(0.421711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.81527e6i | 0.342599i | 0.985219 | + | 0.171299i | \(0.0547966\pi\) | ||||
−0.985219 | + | 0.171299i | \(0.945203\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.44308e7i | 0.531874i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.33729e7 | 1.10885 | 0.554424 | − | 0.832234i | \(-0.312939\pi\) | ||||
0.554424 | + | 0.832234i | \(0.312939\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.68161e7i | − 1.47857i | −0.673391 | − | 0.739287i | \(-0.735163\pi\) | ||||
0.673391 | − | 0.739287i | \(-0.264837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.34806e6 | 0.124343 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.43840e7 | 1.48144 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.83709e7i | − 0.950277i | −0.879911 | − | 0.475139i | \(-0.842398\pi\) | ||||
0.879911 | − | 0.475139i | \(-0.157602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.17648e7 | 1.69626 | 0.848130 | − | 0.529788i | \(-0.177729\pi\) | ||||
0.848130 | + | 0.529788i | \(0.177729\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 7.75948e7i | − 1.67368i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 4.03778e7i | − 0.832710i | −0.909202 | − | 0.416355i | \(-0.863307\pi\) | ||||
0.909202 | − | 0.416355i | \(-0.136693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.60656e6 | 0.162532 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.84512e7i | 1.78059i | 0.455383 | + | 0.890296i | \(0.349502\pi\) | ||||
−0.455383 | + | 0.890296i | \(0.650498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.24811e7 | −0.705810 | −0.352905 | − | 0.935659i | \(-0.614806\pi\) | ||||
−0.352905 | + | 0.935659i | \(0.614806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.78601e7 | 0.922095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2.65257e7i | − 0.389498i | −0.980853 | − | 0.194749i | \(-0.937611\pi\) | ||||
0.980853 | − | 0.194749i | \(-0.0623893\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.59875e7 | −0.225501 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.42148e7i | 0.315570i | 0.987474 | + | 0.157785i | \(0.0504353\pi\) | ||||
−0.987474 | + | 0.157785i | \(0.949565\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2.78961e7i | − 0.349679i | −0.984597 | − | 0.174839i | \(-0.944059\pi\) | ||||
0.984597 | − | 0.174839i | \(-0.0559406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.67964e8 | 1.95036 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.38249e7i | 0.266431i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.67596e7 | 0.174039 | 0.0870195 | − | 0.996207i | \(-0.472266\pi\) | ||||
0.0870195 | + | 0.996207i | \(0.472266\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.75008e7 | 0.876116 | 0.438058 | − | 0.898947i | \(-0.355667\pi\) | ||||
0.438058 | + | 0.898947i | \(0.355667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.56239e7i | 0.238789i | 0.992847 | + | 0.119394i | \(0.0380953\pi\) | ||||
−0.992847 | + | 0.119394i | \(0.961905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.31884e7 | −0.478444 | −0.239222 | − | 0.970965i | \(-0.576892\pi\) | ||||
−0.239222 | + | 0.970965i | \(0.576892\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.05419e7i | 0.591849i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.03056e8i | 1.64618i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.46457e7 | −0.489810 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.01165e7i | − 0.147423i | −0.997280 | − | 0.0737114i | \(-0.976516\pi\) | ||||
0.997280 | − | 0.0737114i | \(-0.0234844\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.99001e7 | 0.205181 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.00649e8 | 0.668651 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.67858e7i | − 0.166929i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.67012e8 | 1.00851 | 0.504254 | − | 0.863555i | \(-0.331768\pi\) | ||||
0.504254 | + | 0.863555i | \(0.331768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.37308e8i | 0.779122i | 0.921001 | + | 0.389561i | \(0.127373\pi\) | ||||
−0.921001 | + | 0.389561i | \(0.872627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 2.67935e8i | − 1.47436i | −0.675694 | − | 0.737182i | \(-0.736156\pi\) | ||||
0.675694 | − | 0.737182i | \(-0.263844\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.98032e8 | −1.02563 | −0.512815 | − | 0.858499i | \(-0.671397\pi\) | ||||
−0.512815 | + | 0.858499i | \(0.671397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.77639e8i | − 1.39554i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.22277e7 | 0.389606 | 0.194803 | − | 0.980842i | \(-0.437593\pi\) | ||||
0.194803 | + | 0.980842i | \(0.437593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.70650e8 | −1.24551 | −0.622757 | − | 0.782415i | \(-0.713988\pi\) | ||||
−0.622757 | + | 0.782415i | \(0.713988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.13498e8i | 0.927498i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.26797e7 | 0.306884 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.90747e8i | − 1.16053i | −0.814427 | − | 0.580266i | \(-0.802949\pi\) | ||||
0.814427 | − | 0.580266i | \(-0.197051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.85549e7i | 0.149678i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.36047e7 | −0.160239 | −0.0801193 | − | 0.996785i | \(-0.525530\pi\) | ||||
−0.0801193 | + | 0.996785i | \(0.525530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.17867e8i | 0.779188i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.27678e8 | 1.44968 | 0.724840 | − | 0.688917i | \(-0.241914\pi\) | ||||
0.724840 | + | 0.688917i | \(0.241914\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.20244e8 | −1.71730 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.26134e7i | 0.258772i | 0.991594 | + | 0.129386i | \(0.0413007\pi\) | ||||
−0.991594 | + | 0.129386i | \(0.958699\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.15189e7 | −0.187766 | −0.0938829 | − | 0.995583i | \(-0.529928\pi\) | ||||
−0.0938829 | + | 0.995583i | \(0.529928\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 7.16196e7i | − 0.207667i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.39237e7i | 0.124171i | 0.998071 | + | 0.0620854i | \(0.0197751\pi\) | ||||
−0.998071 | + | 0.0620854i | \(0.980225\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.80931e8 | −1.56190 | −0.780948 | − | 0.624596i | \(-0.785264\pi\) | ||||
−0.780948 | + | 0.624596i | \(0.785264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.03790e8i | − 1.58356i | −0.610810 | − | 0.791778i | \(-0.709156\pi\) | ||||
0.610810 | − | 0.791778i | \(-0.290844\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.63385e8 | −0.657665 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.63568e8 | −0.642319 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.10504e8i | 0.256649i | 0.991732 | + | 0.128325i | \(0.0409600\pi\) | ||||
−0.991732 | + | 0.128325i | \(0.959040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.17591e8 | −1.40063 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.33464e7i | − 0.0937787i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.87836e7i | 0.0819719i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.64003e8 | 0.330981 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.03386e8i | 1.38742i | 0.720252 | + | 0.693712i | \(0.244026\pi\) | ||||
−0.720252 | + | 0.693712i | \(0.755974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.61240e8 | −1.62354 | −0.811769 | − | 0.583978i | \(-0.801495\pi\) | ||||
−0.811769 | + | 0.583978i | \(0.801495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.42056e8 | 0.446181 | 0.223090 | − | 0.974798i | \(-0.428385\pi\) | ||||
0.223090 | + | 0.974798i | \(0.428385\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5.38362e8i | − 0.949221i | −0.880196 | − | 0.474610i | \(-0.842589\pi\) | ||||
0.880196 | − | 0.474610i | \(-0.157411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.16007e8 | −0.545042 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.98242e8i | 0.657565i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.05203e7i | 0.130111i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.60128e8 | 0.557534 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.05054e9i | 1.59226i | 0.605124 | + | 0.796131i | \(0.293123\pi\) | ||||
−0.605124 | + | 0.796131i | \(0.706877\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.70342e7 | −0.0392877 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.04579e8 | −0.291177 | −0.145589 | − | 0.989345i | \(-0.546508\pi\) | ||||
−0.145589 | + | 0.989345i | \(0.546508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.50878e8i | 0.615770i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.38462e8 | −0.854291 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.28852e8i | 0.807970i | 0.914766 | + | 0.403985i | \(0.132375\pi\) | ||||
−0.914766 | + | 0.403985i | \(0.867625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.86717e8i | 1.24252i | 0.783604 | + | 0.621260i | \(0.213379\pi\) | ||||
−0.783604 | + | 0.621260i | \(0.786621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.59732e8 | −0.677281 | −0.338641 | − | 0.940916i | \(-0.609967\pi\) | ||||
−0.338641 | + | 0.940916i | \(0.609967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4.30087e8i | − 0.510219i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.42390e8 | 0.162424 | 0.0812119 | − | 0.996697i | \(-0.474121\pi\) | ||||
0.0812119 | + | 0.996697i | \(0.474121\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.86707e8 | −0.208875 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.25501e9i | − 1.35090i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.13452e8 | −0.753414 | −0.376707 | − | 0.926333i | \(-0.622944\pi\) | ||||
−0.376707 | + | 0.926333i | \(0.622944\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6.74812e8i | − 0.686079i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.14729e8i | − 0.413794i | −0.978363 | − | 0.206897i | \(-0.933664\pi\) | ||||
0.978363 | − | 0.206897i | \(-0.0663364\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.55280e8 | 0.341489 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.23625e8i | − 0.116646i | −0.998298 | − | 0.0583229i | \(-0.981425\pi\) | ||||
0.998298 | − | 0.0583229i | \(-0.0185753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.35784e9 | −1.23496 | −0.617480 | − | 0.786586i | \(-0.711846\pi\) | ||||
−0.617480 | + | 0.786586i | \(0.711846\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.92184e8 | 0.260942 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00573e9i | 0.866281i | 0.901326 | + | 0.433141i | \(0.142595\pi\) | ||||
−0.901326 | + | 0.433141i | \(0.857405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.37513e8 | 0.200941 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 8.65893e8i | − 0.706927i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.30080e8i | 0.184549i | 0.995734 | + | 0.0922747i | \(0.0294138\pi\) | ||||
−0.995734 | + | 0.0922747i | \(0.970586\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.24791e9 | 0.966446 | 0.483223 | − | 0.875497i | \(-0.339466\pi\) | ||||
0.483223 | + | 0.875497i | \(0.339466\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5.06912e8i | − 0.385802i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.75982e8 | −0.717565 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.79923e9 | −1.30033 | −0.650166 | − | 0.759792i | \(-0.725301\pi\) | ||||
−0.650166 | + | 0.759792i | \(0.725301\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8.01081e8i | − 0.559566i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.19219e8 | −0.356601 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.66870e8i | 0.177235i | 0.996066 | + | 0.0886177i | \(0.0282449\pi\) | ||||
−0.996066 | + | 0.0886177i | \(0.971755\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 2.70575e9i | − 1.76726i | −0.468185 | − | 0.883630i | \(-0.655092\pi\) | ||||
0.468185 | − | 0.883630i | \(-0.344908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.41204e8 | −0.278791 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.12730e8i | 0.132230i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.78455e9 | 1.07364 | 0.536820 | − | 0.843697i | \(-0.319626\pi\) | ||||
0.536820 | + | 0.843697i | \(0.319626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.21276e9 | 0.717905 | 0.358953 | − | 0.933356i | \(-0.383134\pi\) | ||||
0.358953 | + | 0.933356i | \(0.383134\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.44461e8i | 0.369413i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.76141e9 | 0.993654 | 0.496827 | − | 0.867850i | \(-0.334498\pi\) | ||||
0.496827 | + | 0.867850i | \(0.334498\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.06208e8i | 0.440590i | 0.975433 | + | 0.220295i | \(0.0707019\pi\) | ||||
−0.975433 | + | 0.220295i | \(0.929298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.75166e8i | 0.363204i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.85913e8 | −0.305472 | −0.152736 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152736 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.17989e9i | − 0.605653i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.28496e8 | −0.163490 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.52640e8 | 0.270854 | 0.135427 | − | 0.990787i | \(-0.456759\pi\) | ||||
0.135427 | + | 0.990787i | \(0.456759\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.74101e9i | 0.827652i | 0.910356 | + | 0.413826i | \(0.135808\pi\) | ||||
−0.910356 | + | 0.413826i | \(0.864192\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.84431e9 | 1.33181 | 0.665906 | − | 0.746035i | \(-0.268045\pi\) | ||||
0.665906 | + | 0.746035i | \(0.268045\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.63130e9i | 0.741183i | 0.928796 | + | 0.370592i | \(0.120845\pi\) | ||||
−0.928796 | + | 0.370592i | \(0.879155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 3.50662e7i | − 0.0156958i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.73739e8 | −0.0754891 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.19715e9i | − 0.512532i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.69345e9 | 1.53553 | 0.767765 | − | 0.640732i | \(-0.221369\pi\) | ||||
0.767765 | + | 0.640732i | \(0.221369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.09727e9 | 0.449580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.78697e6i | 0.00389540i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.57153e9 | −0.616554 | −0.308277 | − | 0.951297i | \(-0.599752\pi\) | ||||
−0.308277 | + | 0.951297i | \(0.599752\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.63493e9i | 0.623323i | 0.950193 | + | 0.311662i | \(0.100886\pi\) | ||||
−0.950193 | + | 0.311662i | \(0.899114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.94673e9i | 0.731713i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.57868e8 | 0.203838 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 6.86870e8i | − 0.247470i | −0.992315 | − | 0.123735i | \(-0.960513\pi\) | ||||
0.992315 | − | 0.123735i | \(-0.0394873\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.33472e9 | 0.817990 | 0.408995 | − | 0.912537i | \(-0.365879\pi\) | ||||
0.408995 | + | 0.912537i | \(0.365879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.68845e9 | 1.96550 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 6.21342e8i | − 0.208842i | −0.994533 | − | 0.104421i | \(-0.966701\pi\) | ||||
0.994533 | − | 0.104421i | \(-0.0332990\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.62789e9 | 0.539699 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.32347e9i | − 1.39478i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.61327e9i | 0.513441i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.65562e9 | 0.512897 | 0.256448 | − | 0.966558i | \(-0.417448\pi\) | ||||
0.256448 | + | 0.966558i | \(0.417448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.42671e9i | 1.35309i | 0.736403 | + | 0.676543i | \(0.236523\pi\) | ||||
−0.736403 | + | 0.676543i | \(0.763477\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.77758e9 | 0.826665 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.02047e9 | −0.887113 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.32652e9i | 0.379463i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.58961e9 | 1.29580 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.24057e9i | − 0.341240i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.71878e9i | − 1.00974i | −0.863195 | − | 0.504871i | \(-0.831540\pi\) | ||||
0.863195 | − | 0.504871i | \(-0.168460\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.60492e9 | −0.424683 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.20749e9i | − 0.837934i | −0.908002 | − | 0.418967i | \(-0.862392\pi\) | ||||
0.908002 | − | 0.418967i | \(-0.137608\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.28219e9 | −1.34519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.12316e9 | 0.282424 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4.80739e9i | − 1.17873i | −0.807865 | − | 0.589367i | \(-0.799377\pi\) | ||||
0.807865 | − | 0.589367i | \(-0.200623\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.95331e8 | 0.0472967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 3.77127e9i | − 0.890653i | −0.895368 | − | 0.445326i | \(-0.853088\pi\) | ||||
0.895368 | − | 0.445326i | \(-0.146912\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 2.73066e9i | − 0.636940i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.09341e9 | −0.476388 | −0.238194 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238194 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.86085e9i | 1.54224i | 0.636691 | + | 0.771119i | \(0.280303\pi\) | ||||
−0.636691 | + | 0.771119i | \(0.719697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.13986e8 | −0.156622 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.70742e9 | 1.23687 | 0.618435 | − | 0.785836i | \(-0.287767\pi\) | ||||
0.618435 | + | 0.785836i | \(0.287767\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.73483e8i | − 0.142466i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.02297e9 | 0.631820 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.56510e9i | 0.319380i | 0.987167 | + | 0.159690i | \(0.0510495\pi\) | ||||
−0.987167 | + | 0.159690i | \(0.948951\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.53661e9i | 1.51975i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.78410e9 | 0.548268 | 0.274134 | − | 0.961692i | \(-0.411609\pi\) | ||||
0.274134 | + | 0.961692i | \(0.411609\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.79997e9i | − 0.350312i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.18885e9 | 1.17657 | 0.588283 | − | 0.808655i | \(-0.299804\pi\) | ||||
0.588283 | + | 0.808655i | \(0.299804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.42206e9 | −0.455118 | −0.227559 | − | 0.973764i | \(-0.573074\pi\) | ||||
−0.227559 | + | 0.973764i | \(0.573074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 5.28639e9i | − 0.970544i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.62465e9 | 0.839302 | 0.419651 | − | 0.907686i | \(-0.362152\pi\) | ||||
0.419651 | + | 0.907686i | \(0.362152\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.81376e9i | − 0.321689i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.45433e9i | − 0.956378i | −0.878257 | − | 0.478189i | \(-0.841293\pi\) | ||||
0.878257 | − | 0.478189i | \(-0.158707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.32837e9 | 0.399074 | 0.199537 | − | 0.979890i | \(-0.436056\pi\) | ||||
0.199537 | + | 0.979890i | \(0.436056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 9.58626e9i | − 1.62455i | −0.583278 | − | 0.812273i | \(-0.698230\pi\) | ||||
0.583278 | − | 0.812273i | \(-0.301770\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.75763e8 | −0.145104 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.62240e9 | −1.24885 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.01242e9i | 0.963324i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.18616e10 | −1.87949 | −0.939747 | − | 0.341870i | \(-0.888940\pi\) | ||||
−0.939747 | + | 0.341870i | \(0.888940\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 3.80445e9i | − 0.589635i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.39474e9i | 0.213799i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.06130e8 | 0.0159161 | 0.00795805 | − | 0.999968i | \(-0.497467\pi\) | ||||
0.00795805 | + | 0.999968i | \(0.497467\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.19289e9i | − 0.325296i | −0.986684 | − | 0.162648i | \(-0.947996\pi\) | ||||
0.986684 | − | 0.162648i | \(-0.0520035\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.23914e9 | −0.615337 | −0.307668 | − | 0.951494i | \(-0.599549\pi\) | ||||
−0.307668 | + | 0.951494i | \(0.599549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.58862e9 | 0.515312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.93257e9i | 1.39594i | 0.716129 | + | 0.697968i | \(0.245912\pi\) | ||||
−0.716129 | + | 0.697968i | \(0.754088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.98346e9 | 0.414836 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.36634e10i | 1.85977i | 0.367852 | + | 0.929884i | \(0.380093\pi\) | ||||
−0.367852 | + | 0.929884i | \(0.619907\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.03765e10i | 1.39747i | 0.715378 | + | 0.698737i | \(0.246254\pi\) | ||||
−0.715378 | + | 0.698737i | \(0.753746\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.88398e9 | 0.644019 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.15032e9i | 0.411069i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.52968e8 | −0.121773 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.70776e9 | 0.595336 | 0.297668 | − | 0.954669i | \(-0.403791\pi\) | ||||
0.297668 | + | 0.954669i | \(0.403791\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 9.55050e9i | − 1.18295i | −0.806324 | − | 0.591474i | \(-0.798546\pi\) | ||||
0.806324 | − | 0.591474i | \(-0.201454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.26947e7 | −0.00155625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.06442e10i | 1.27832i | 0.769073 | + | 0.639161i | \(0.220718\pi\) | ||||
−0.769073 | + | 0.639161i | \(0.779282\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.12948e10i | − 1.34265i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.39865e9 | −0.395858 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.41537e9i | 0.970287i | 0.874435 | + | 0.485143i | \(0.161233\pi\) | ||||
−0.874435 | + | 0.485143i | \(0.838767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.58445e10 | −1.79033 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.26858e9 | −0.813083 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.95355e9i | 0.981707i | 0.871242 | + | 0.490854i | \(0.163315\pi\) | ||||
−0.871242 | + | 0.490854i | \(0.836685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.63139e10 | −1.77099 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.37853e9i | 0.785239i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 8.11796e9i | − 0.855431i | −0.903913 | − | 0.427716i | \(-0.859318\pi\) | ||||
0.903913 | − | 0.427716i | \(-0.140682\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.49486e9 | 0.464412 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.47157e9i | − 0.150560i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.54339e8 | 0.0957528 | 0.0478764 | − | 0.998853i | \(-0.484755\pi\) | ||||
0.0478764 | + | 0.998853i | \(0.484755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.60800e9 | 0.557231 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 5.85203e9i | − 0.570327i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.75084e10 | −1.68996 | −0.844979 | − | 0.534799i | \(-0.820387\pi\) | ||||
−0.844979 | + | 0.534799i | \(0.820387\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.07030e9i | 0.101343i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.16062e10i | − 1.08849i | −0.838925 | − | 0.544247i | \(-0.816815\pi\) | ||||
0.838925 | − | 0.544247i | \(-0.183185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.57087e8 | 0.0144545 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.74800e9i | 0.432768i | 0.976308 | + | 0.216384i | \(0.0694263\pi\) | ||||
−0.976308 | + | 0.216384i | \(0.930574\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.35857e9 | −0.389837 | −0.194918 | − | 0.980819i | \(-0.562444\pi\) | ||||
−0.194918 | + | 0.980819i | \(0.562444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.29864e10 | −1.15064 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.95321e9i | 0.517684i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.10987e9 | 0.526371 | 0.263186 | − | 0.964745i | \(-0.415227\pi\) | ||||
0.263186 | + | 0.964745i | \(0.415227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2.42883e10i | − 2.05391i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.29472e10i | 1.92262i | 0.275460 | + | 0.961312i | \(0.411170\pi\) | ||||
−0.275460 | + | 0.961312i | \(0.588830\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.15151e9 | −0.588236 | −0.294118 | − | 0.955769i | \(-0.595026\pi\) | ||||
−0.294118 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.08175e9i | − 0.169665i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.03460e9 | −0.322862 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.85381e10 | −1.47002 | −0.735011 | − | 0.678055i | \(-0.762823\pi\) | ||||
−0.735011 | + | 0.678055i | \(0.762823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 8.25535e9i | − 0.642846i | −0.946936 | − | 0.321423i | \(-0.895839\pi\) | ||||
0.946936 | − | 0.321423i | \(-0.104161\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.34966e9 | −0.644336 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.97223e10i | − 1.49478i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.49909e9i | 0.187717i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.36656e10 | −1.00829 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.53185e9i | 0.112023i | 0.998430 | + | 0.0560113i | \(0.0178383\pi\) | ||||
−0.998430 | + | 0.0560113i | \(0.982162\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.54196e9 | 0.254464 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.07140e9 | 0.0762950 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.78553e9i | − 0.194896i | −0.995241 | − | 0.0974480i | \(-0.968932\pi\) | ||||
0.995241 | − | 0.0974480i | \(-0.0310680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.93837e9 | 0.689289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.29247e9i | 0.497016i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.91283e9i | − 0.196802i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.17657e10 | −0.781267 | −0.390634 | − | 0.920546i | \(-0.627744\pi\) | ||||
−0.390634 | + | 0.920546i | \(0.627744\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 6.29491e9i | − 0.414397i | −0.978299 | − | 0.207198i | \(-0.933565\pi\) | ||||
0.978299 | − | 0.207198i | \(-0.0664346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.33201e10 | 2.15603 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.90413e9 | −0.186311 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.27400e9i | 0.269546i | 0.990876 | + | 0.134773i | \(0.0430306\pi\) | ||||
−0.990876 | + | 0.134773i | \(0.956969\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.16411e9 | 0.197858 | 0.0989288 | − | 0.995095i | \(-0.468458\pi\) | ||||
0.0989288 | + | 0.995095i | \(0.468458\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.47251e9i | − 0.213488i | −0.994287 | − | 0.106744i | \(-0.965957\pi\) | ||||
0.994287 | − | 0.106744i | \(-0.0340426\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.21388e9i | 0.317848i | 0.987291 | + | 0.158924i | \(0.0508026\pi\) | ||||
−0.987291 | + | 0.158924i | \(0.949197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.64237e9 | −0.458111 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.43774e10i | 0.854629i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.48652e10 | −1.45353 | −0.726766 | − | 0.686885i | \(-0.758977\pi\) | ||||
−0.726766 | + | 0.686885i | \(0.758977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.57107e9 | −0.496877 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.95823e10i | − 1.11652i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.85701e9 | 0.387742 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.72969e9i | 0.541185i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.01930e10i | 1.66565i | 0.553536 | + | 0.832826i | \(0.313278\pi\) | ||||
−0.553536 | + | 0.832826i | \(0.686722\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.57761e10 | −1.39889 | −0.699446 | − | 0.714685i | \(-0.746570\pi\) | ||||
−0.699446 | + | 0.714685i | \(0.746570\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 2.77848e10i | − 1.49565i | −0.663894 | − | 0.747827i | \(-0.731097\pi\) | ||||
0.663894 | − | 0.747827i | \(-0.268903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.02990e10 | 1.60469 | 0.802344 | − | 0.596862i | \(-0.203586\pi\) | ||||
0.802344 | + | 0.596862i | \(0.203586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.97743e9 | −0.471624 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.03142e9i | 0.260089i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.76609e8 | −0.00905627 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.19656e9i | − 0.312696i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.37410e9i | 0.118850i | 0.998233 | + | 0.0594252i | \(0.0189268\pi\) | ||||
−0.998233 | + | 0.0594252i | \(0.981073\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.28058e10 | 1.61635 | 0.808175 | − | 0.588942i | \(-0.200456\pi\) | ||||
0.808175 | + | 0.588942i | \(0.200456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.14967e10i | 1.05078i | 0.850863 | + | 0.525388i | \(0.176080\pi\) | ||||
−0.850863 | + | 0.525388i | \(0.823920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.50080e10 | −0.722089 | −0.361045 | − | 0.932549i | \(-0.617580\pi\) | ||||
−0.361045 | + | 0.932549i | \(0.617580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.93477e9 | 0.235565 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.69665e10i | 1.26720i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.19532e9 | 0.382107 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.68412e10i | 1.69112i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.86226e10i | − 0.848212i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.44124e9 | −0.423408 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.57906e10i | 0.702704i | 0.936243 | + | 0.351352i | \(0.114278\pi\) | ||||
−0.936243 | + | 0.351352i | \(0.885722\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.82128e9 | −0.298917 | −0.149459 | − | 0.988768i | \(-0.547753\pi\) | ||||
−0.149459 | + | 0.988768i | \(0.547753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.01701e9 | 0.131199 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.86987e9i | 0.165731i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.08588e10 | 0.461506 | 0.230753 | − | 0.973012i | \(-0.425881\pi\) | ||||
0.230753 | + | 0.973012i | \(0.425881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.80967e9i | − 0.117611i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1.80739e10i | − 0.750853i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.99248e9 | 0.122455 | 0.0612275 | − | 0.998124i | \(-0.480498\pi\) | ||||
0.0612275 | + | 0.998124i | \(0.480498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.07366e10i | − 0.842197i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.06335e9 | 0.322608 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.39333e10 | 0.950417 | 0.475208 | − | 0.879873i | \(-0.342373\pi\) | ||||
0.475208 | + | 0.879873i | \(0.342373\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.17291e10i | 1.24135i | 0.784068 | + | 0.620675i | \(0.213141\pi\) | ||||
−0.784068 | + | 0.620675i | \(0.786859\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.17625e10 | −0.456781 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.13161e10i | − 1.58086i | −0.612551 | − | 0.790431i | \(-0.709857\pi\) | ||||
0.612551 | − | 0.790431i | \(-0.290143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 8.19876e9i | − 0.311399i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.31993e10 | 1.61678 | 0.808390 | − | 0.588647i | \(-0.200339\pi\) | ||||
0.808390 | + | 0.588647i | \(0.200339\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 5.67216e9i | − 0.210735i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.46506e10 | 0.536401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.50523e10 | 0.910574 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 2.96140e10i | − 1.06084i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.99318e9 | −0.248703 | −0.124352 | − | 0.992238i | \(-0.539685\pi\) | ||||
−0.124352 | + | 0.992238i | \(0.539685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.48357e9i | 0.297380i | 0.988884 | + | 0.148690i | \(0.0475056\pi\) | ||||
−0.988884 | + | 0.148690i | \(0.952494\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.05521e10i | − 0.715255i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.72197e10 | 0.590739 | 0.295370 | − | 0.955383i | \(-0.404557\pi\) | ||||
0.295370 | + | 0.955383i | \(0.404557\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3.92317e9i | − 0.133628i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.76267e10 | −1.26345 | −0.631725 | − | 0.775192i | \(-0.717653\pi\) | ||||
−0.631725 | + | 0.775192i | \(0.717653\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.67222e9 | 0.289137 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.73203e9i | 0.0569336i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.13036e9 | 0.102173 | 0.0510866 | − | 0.998694i | \(-0.483732\pi\) | ||||
0.0510866 | + | 0.998694i | \(0.483732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.80012e10i | 0.579323i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.67605e9i | − 0.0535617i | −0.999641 | − | 0.0267808i | \(-0.991474\pi\) | ||||
0.999641 | − | 0.0267808i | \(-0.00852563\pi\) | |||||||
\(998\) | 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 | 288.8.d.b.145.1 | 6 | ||
3.2 | odd | 2 | 32.8.b.a.17.6 | 6 | |||
4.3 | odd | 2 | 72.8.d.b.37.1 | 6 | |||
8.3 | odd | 2 | 72.8.d.b.37.2 | 6 | |||
8.5 | even | 2 | inner | 288.8.d.b.145.6 | 6 | ||
12.11 | even | 2 | 8.8.b.a.5.6 | yes | 6 | ||
24.5 | odd | 2 | 32.8.b.a.17.1 | 6 | |||
24.11 | even | 2 | 8.8.b.a.5.5 | ✓ | 6 | ||
48.5 | odd | 4 | 256.8.a.q.1.6 | 6 | |||
48.11 | even | 4 | 256.8.a.r.1.1 | 6 | |||
48.29 | odd | 4 | 256.8.a.q.1.1 | 6 | |||
48.35 | even | 4 | 256.8.a.r.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.b.a.5.5 | ✓ | 6 | 24.11 | even | 2 | ||
8.8.b.a.5.6 | yes | 6 | 12.11 | even | 2 | ||
32.8.b.a.17.1 | 6 | 24.5 | odd | 2 | |||
32.8.b.a.17.6 | 6 | 3.2 | odd | 2 | |||
72.8.d.b.37.1 | 6 | 4.3 | odd | 2 | |||
72.8.d.b.37.2 | 6 | 8.3 | odd | 2 | |||
256.8.a.q.1.1 | 6 | 48.29 | odd | 4 | |||
256.8.a.q.1.6 | 6 | 48.5 | odd | 4 | |||
256.8.a.r.1.1 | 6 | 48.11 | even | 4 | |||
256.8.a.r.1.6 | 6 | 48.35 | even | 4 | |||
288.8.d.b.145.1 | 6 | 1.1 | even | 1 | trivial | ||
288.8.d.b.145.6 | 6 | 8.5 | even | 2 | inner |