Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(449,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.g (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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.449 |
Dual form | 1400.2.g.k.449.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 2.56155i | − 1.47891i | −0.673204 | − | 0.739457i | \(-0.735083\pi\) | ||||
0.673204 | − | 0.739457i | \(-0.264917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.56155 | −1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.68466i | 1.57664i | 0.615265 | + | 0.788320i | \(0.289049\pi\) | ||||
−0.615265 | + | 0.788320i | \(0.710951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.43845i | 0.833946i | 0.908919 | + | 0.416973i | \(0.136909\pi\) | ||||
−0.908919 | + | 0.416973i | \(0.863091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.12311 | −0.257658 | −0.128829 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56155 | 0.558977 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.12311i | 1.06824i | 0.845408 | + | 0.534121i | \(0.179357\pi\) | ||||
−0.845408 | + | 0.534121i | \(0.820643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43845i | 0.276829i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.56155 | −0.847059 | −0.423530 | − | 0.905882i | \(-0.639209\pi\) | ||||
−0.423530 | + | 0.905882i | \(0.639209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2462 | −1.84027 | −0.920137 | − | 0.391597i | \(-0.871923\pi\) | ||||
−0.920137 | + | 0.391597i | \(0.871923\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.56155i | 1.14222i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24621i | 1.35567i | 0.735215 | + | 0.677834i | \(0.237081\pi\) | ||||
−0.735215 | + | 0.677834i | \(0.762919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.5616 | 2.33171 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.12311 | 1.11244 | 0.556221 | − | 0.831034i | \(-0.312251\pi\) | ||||
0.556221 | + | 0.831034i | \(0.312251\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.12311i | − 0.171272i | −0.996326 | − | 0.0856360i | \(-0.972708\pi\) | ||||
0.996326 | − | 0.0856360i | \(-0.0272922\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.56155i | 0.957101i | 0.878060 | + | 0.478550i | \(0.158838\pi\) | ||||
−0.878060 | + | 0.478550i | \(0.841162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.80776 | 1.23333 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.87689i | 0.669893i | 0.942237 | + | 0.334946i | \(0.108718\pi\) | ||||
−0.942237 | + | 0.334946i | \(0.891282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.87689i | 0.381054i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.1231 | −1.93632 | −0.968158 | − | 0.250341i | \(-0.919457\pi\) | ||||
−0.968158 | + | 0.250341i | \(0.919457\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3.56155i | − 0.448713i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 14.2462i | − 1.74045i | −0.492653 | − | 0.870226i | \(-0.663973\pi\) | ||||
0.492653 | − | 0.870226i | \(-0.336027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.1231 | 1.57984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 12.2462i | − 1.43331i | −0.697428 | − | 0.716655i | \(-0.745672\pi\) | ||||
0.697428 | − | 0.716655i | \(-0.254328\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.56155i | − 0.291916i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6847 | 1.31463 | 0.657313 | − | 0.753617i | \(-0.271693\pi\) | ||||
0.657313 | + | 0.753617i | \(0.271693\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 12.0000i | − 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.6847i | 1.25273i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.12311 | 0.331049 | 0.165524 | − | 0.986206i | \(-0.447068\pi\) | ||||
0.165524 | + | 0.986206i | \(0.447068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.68466 | −0.595914 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.2462i | 2.72161i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6847i | 1.38947i | 0.719267 | + | 0.694733i | \(0.244478\pi\) | ||||
−0.719267 | + | 0.694733i | \(0.755522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.12311 | 0.916907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 8.80776i | − 0.867855i | −0.900948 | − | 0.433927i | \(-0.857127\pi\) | ||||
0.900948 | − | 0.433927i | \(-0.142873\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.87689i | 0.664814i | 0.943136 | + | 0.332407i | \(0.107861\pi\) | ||||
−0.943136 | + | 0.332407i | \(0.892139\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.56155 | 0.820048 | 0.410024 | − | 0.912075i | \(-0.365520\pi\) | ||||
0.410024 | + | 0.912075i | \(0.365520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.1231 | 2.00492 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.24621i | 0.775738i | 0.921714 | + | 0.387869i | \(0.126789\pi\) | ||||
−0.921714 | + | 0.387869i | \(0.873211\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 20.2462i | − 1.87176i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.43845 | −0.315202 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 18.2462i | − 1.64521i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2462i | 0.909204i | 0.890695 | + | 0.454602i | \(0.150219\pi\) | ||||
−0.890695 | + | 0.454602i | \(0.849781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.87689 | −0.253296 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.87689 | 0.600837 | 0.300419 | − | 0.953807i | \(-0.402874\pi\) | ||||
0.300419 | + | 0.953807i | \(0.402874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.12311i | − 0.0973856i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.3693i | 1.48396i | 0.670422 | + | 0.741980i | \(0.266113\pi\) | ||||
−0.670422 | + | 0.741980i | \(0.733887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.36932 | −0.285782 | −0.142891 | − | 0.989738i | \(-0.545640\pi\) | ||||
−0.142891 | + | 0.989738i | \(0.545640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.8078 | 1.41547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 14.5616i | − 1.21770i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.56155i | 0.211273i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.2462 | −1.33094 | −0.665471 | − | 0.746424i | \(-0.731769\pi\) | ||||
−0.665471 | + | 0.746424i | \(0.731769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.807764 | 0.0657349 | 0.0328675 | − | 0.999460i | \(-0.489536\pi\) | ||||
0.0328675 | + | 0.999460i | \(0.489536\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 12.2462i | − 0.990048i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 12.2462i | − 0.977354i | −0.872465 | − | 0.488677i | \(-0.837480\pi\) | ||||
0.872465 | − | 0.488677i | \(-0.162520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.4924 | 0.990714 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.12311 | −0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.6155i | 1.69306i | 0.532342 | + | 0.846529i | \(0.321312\pi\) | ||||
−0.532342 | + | 0.846529i | \(0.678688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.8078i | 1.91968i | 0.280544 | + | 0.959841i | \(0.409485\pi\) | ||||
−0.280544 | + | 0.959841i | \(0.590515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.3153 | −1.48580 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.1771i | − 1.68609i | −0.537841 | − | 0.843046i | \(-0.680760\pi\) | ||||
0.537841 | − | 0.843046i | \(-0.319240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 10.2462i | − 0.770152i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.12311 | 0.232139 | 0.116069 | − | 0.993241i | \(-0.462971\pi\) | ||||
0.116069 | + | 0.993241i | \(0.462971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 38.7386i | 2.86364i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.80776i | − 0.644087i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.43845 | −0.104632 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6847 | 0.845472 | 0.422736 | − | 0.906253i | \(-0.361070\pi\) | ||||
0.422736 | + | 0.906253i | \(0.361070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4.87689i | − 0.351047i | −0.984475 | − | 0.175523i | \(-0.943838\pi\) | ||||
0.984475 | − | 0.175523i | \(-0.0561617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.87689i | − 0.347464i | −0.984793 | − | 0.173732i | \(-0.944417\pi\) | ||||
0.984793 | − | 0.173732i | \(-0.0555827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24621 | −0.159230 | −0.0796148 | − | 0.996826i | \(-0.525369\pi\) | ||||
−0.0796148 | + | 0.996826i | \(0.525369\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −36.4924 | −2.57398 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.56155i | − 0.320158i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 18.2462i | − 1.26820i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.87689 | 0.198999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4384 | −0.925141 | −0.462570 | − | 0.886583i | \(-0.653073\pi\) | ||||
−0.462570 | + | 0.886583i | \(0.653073\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 10.2462i | − 0.695558i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −31.3693 | −2.11974 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.5464 | −1.31483 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 12.3153i | − 0.824696i | −0.911026 | − | 0.412348i | \(-0.864709\pi\) | ||||
0.911026 | − | 0.412348i | \(-0.135291\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 23.6847i | − 1.57201i | −0.618223 | − | 0.786003i | \(-0.712147\pi\) | ||||
0.618223 | − | 0.786003i | \(-0.287853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.3693 | −0.883469 | −0.441735 | − | 0.897146i | \(-0.645637\pi\) | ||||
−0.441735 | + | 0.897146i | \(0.645637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.56155 | −0.431718 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.1231i | 1.25280i | 0.779503 | + | 0.626398i | \(0.215472\pi\) | ||||
−0.779503 | + | 0.626398i | \(0.784528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 29.9309i | − 1.94422i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.0540 | −1.23250 | −0.616250 | − | 0.787551i | \(-0.711349\pi\) | ||||
−0.616250 | + | 0.787551i | \(0.711349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462i | 1.42710i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.38447i | − 0.406234i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.7386 | −1.94798 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.3693 | −0.717625 | −0.358812 | − | 0.933410i | \(-0.616818\pi\) | ||||
−0.358812 | + | 0.933410i | \(0.616818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 13.1231i | − 0.825043i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.4924i | 0.904012i | 0.892015 | + | 0.452006i | \(0.149292\pi\) | ||||
−0.892015 | + | 0.452006i | \(0.850708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.24621 | −0.512395 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.2462 | 1.00562 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3693i | 0.947713i | 0.880602 | + | 0.473856i | \(0.157138\pi\) | ||||
−0.880602 | + | 0.473856i | \(0.842862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 8.00000i | − 0.489592i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.2462 | 0.746665 | 0.373332 | − | 0.927698i | \(-0.378215\pi\) | ||||
0.373332 | + | 0.927698i | \(0.378215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2462 | 0.622413 | 0.311207 | − | 0.950342i | \(-0.399267\pi\) | ||||
0.311207 | + | 0.950342i | \(0.399267\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.5616i | 0.881305i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.24621i | 0.495467i | 0.968828 | + | 0.247733i | \(0.0796857\pi\) | ||||
−0.968828 | + | 0.247733i | \(0.920314\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 36.4924 | 2.18474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4384 | −0.920981 | −0.460490 | − | 0.887665i | \(-0.652326\pi\) | ||||
−0.460490 | + | 0.887665i | \(0.652326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7.68466i | − 0.456806i | −0.973567 | − | 0.228403i | \(-0.926650\pi\) | ||||
0.973567 | − | 0.228403i | \(-0.0733503\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.12311i | 0.420464i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.17708 | 0.304534 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 35.0540 | 2.05490 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.05398i | 0.295256i | 0.989043 | + | 0.147628i | \(0.0471639\pi\) | ||||
−0.989043 | + | 0.147628i | \(0.952836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 3.68466i | − 0.213806i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.1231 | −1.68423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.12311 | 0.0647347 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 15.3693i | − 0.882944i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 16.3153i | − 0.931166i | −0.885004 | − | 0.465583i | \(-0.845845\pi\) | ||||
0.885004 | − | 0.465583i | \(-0.154155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.5616 | −1.28348 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.1231 | −1.19778 | −0.598891 | − | 0.800831i | \(-0.704392\pi\) | ||||
−0.598891 | + | 0.800831i | \(0.704392\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 14.3153i | − 0.809151i | −0.914505 | − | 0.404575i | \(-0.867419\pi\) | ||||
0.914505 | − | 0.404575i | \(-0.132581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 10.0000i | − 0.561656i | −0.959758 | − | 0.280828i | \(-0.909391\pi\) | ||||
0.959758 | − | 0.280828i | \(-0.0906090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.6847 | 0.654215 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.6155 | 0.983203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.86174i | − 0.214873i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 21.9309i | − 1.21278i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.56155 | −0.361750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 29.3693i | − 1.60943i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.1231 | 1.14725 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.2462 | 1.42131 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.87689i | 0.369171i | 0.982816 | + | 0.184586i | \(0.0590943\pi\) | ||||
−0.982816 | + | 0.184586i | \(0.940906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.2462 | 1.51199 | 0.755993 | − | 0.654580i | \(-0.227155\pi\) | ||||
0.755993 | + | 0.654580i | \(0.227155\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.17708 | −0.436460 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.8078i | 1.21393i | 0.794727 | + | 0.606967i | \(0.207614\pi\) | ||||
−0.794727 | + | 0.606967i | \(0.792386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.80776i | 0.466156i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.0000 | −1.68890 | −0.844448 | − | 0.535638i | \(-0.820071\pi\) | ||||
−0.844448 | + | 0.535638i | \(0.820071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.3693i | 0.596734i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 13.9309i | − 0.727185i | −0.931558 | − | 0.363593i | \(-0.881550\pi\) | ||||
0.931558 | − | 0.363593i | \(-0.118450\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.3693 | −1.32067 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.87689 | −0.253196 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.36932i | 0.485125i | 0.970136 | + | 0.242562i | \(0.0779879\pi\) | ||||
−0.970136 | + | 0.242562i | \(0.922012\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 25.9309i | − 1.33551i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.492423 | 0.0252940 | 0.0126470 | − | 0.999920i | \(-0.495974\pi\) | ||||
0.0126470 | + | 0.999920i | \(0.495974\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.2462 | 1.34463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.2462i | 1.34112i | 0.741856 | + | 0.670559i | \(0.233946\pi\) | ||||
−0.741856 | + | 0.670559i | \(0.766054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.3002 | 1.58698 | 0.793491 | − | 0.608582i | \(-0.208261\pi\) | ||||
0.793491 | + | 0.608582i | \(0.208261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.6155 | −0.890856 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 17.6155i | − 0.888586i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.1771i | 1.11304i | 0.830836 | + | 0.556518i | \(0.187863\pi\) | ||||
−0.830836 | + | 0.556518i | \(0.812137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.87689 | −0.144025 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.9309 | 0.795550 | 0.397775 | − | 0.917483i | \(-0.369783\pi\) | ||||
0.397775 | + | 0.917483i | \(0.369783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 58.2462i | − 2.90145i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 21.1231i | − 1.04703i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4924 | −0.716604 | −0.358302 | − | 0.933606i | \(-0.616644\pi\) | ||||
−0.358302 | + | 0.933606i | \(0.616644\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 44.4924 | 2.19465 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.63068i | 0.422646i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.75379 | 0.0856782 | 0.0428391 | − | 0.999082i | \(-0.486360\pi\) | ||||
0.0428391 | + | 0.999082i | \(0.486360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.561553 | −0.0273684 | −0.0136842 | − | 0.999906i | \(-0.504356\pi\) | ||||
−0.0136842 | + | 0.999906i | \(0.504356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 23.3693i | − 1.13626i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 15.1231i | − 0.731858i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −37.3002 | −1.80087 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.93087 | 0.285680 | 0.142840 | − | 0.989746i | \(-0.454377\pi\) | ||||
0.142840 | + | 0.989746i | \(0.454377\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 36.2462i | − 1.74188i | −0.491388 | − | 0.870941i | \(-0.663510\pi\) | ||||
0.491388 | − | 0.870941i | \(-0.336490\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5.75379i | − 0.275241i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.8769 | −0.519126 | −0.259563 | − | 0.965726i | \(-0.583578\pi\) | ||||
−0.259563 | + | 0.965726i | \(0.583578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.56155 | 0.169598 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 21.6155i | − 1.02698i | −0.858094 | − | 0.513492i | \(-0.828351\pi\) | ||||
0.858094 | − | 0.513492i | \(-0.171649\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41.6155i | 1.96835i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.6847 | 1.58968 | 0.794839 | − | 0.606821i | \(-0.207555\pi\) | ||||
0.794839 | + | 0.606821i | \(0.207555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.2462 | −0.859181 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 2.06913i | − 0.0972162i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.3693i | 1.56095i | 0.625186 | + | 0.780475i | \(0.285023\pi\) | ||||
−0.625186 | + | 0.780475i | \(0.714977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.94602 | −0.230861 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.1231 | 1.26325 | 0.631624 | − | 0.775274i | \(-0.282388\pi\) | ||||
0.631624 | + | 0.775274i | \(0.282388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 10.2462i | − 0.476182i | −0.971243 | − | 0.238091i | \(-0.923478\pi\) | ||||
0.971243 | − | 0.238091i | \(-0.0765216\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.4384i | 0.992053i | 0.868307 | + | 0.496027i | \(0.165208\pi\) | ||||
−0.868307 | + | 0.496027i | \(0.834792\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2462 | 0.657829 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.3693 | −1.44542 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.87689i | 0.132280i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 17.3693i | − 0.795286i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.36932 | 0.336713 | 0.168356 | − | 0.985726i | \(-0.446154\pi\) | ||||
0.168356 | + | 0.985726i | \(0.446154\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.8769 | −2.13740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.1231i | 0.597122i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.12311i | − 0.232150i | −0.993240 | − | 0.116075i | \(-0.962969\pi\) | ||||
0.993240 | − | 0.116075i | \(-0.0370313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 55.3693 | 2.50389 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6847 | −0.707839 | −0.353919 | − | 0.935276i | \(-0.615151\pi\) | ||||
−0.353919 | + | 0.935276i | \(0.615151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 15.6847i | − 0.706401i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8078 | 0.931483 | 0.465742 | − | 0.884921i | \(-0.345788\pi\) | ||||
0.465742 | + | 0.884921i | \(0.345788\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 63.5464 | 2.83904 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 16.1771i | − 0.721300i | −0.932701 | − | 0.360650i | \(-0.882555\pi\) | ||||
0.932701 | − | 0.360650i | \(-0.117445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 49.4773i | 2.19736i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.7386 | 0.741927 | 0.370963 | − | 0.928647i | \(-0.379028\pi\) | ||||
0.370963 | + | 0.928647i | \(0.379028\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.2462 | 0.541740 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 1.61553i | − 0.0713273i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.8078i | − 0.739205i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −56.8078 | −2.49358 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.24621 | 0.186030 | 0.0930149 | − | 0.995665i | \(-0.470350\pi\) | ||||
0.0930149 | + | 0.995665i | \(0.470350\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0000i | 0.524723i | 0.964970 | + | 0.262362i | \(0.0845013\pi\) | ||||
−0.964970 | + | 0.262362i | \(0.915499\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 35.2311i | − 1.53469i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.24621 | −0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.2462 | −0.618233 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.4924i | 1.75392i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 10.2462i | − 0.442157i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.56155 | 0.110334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.4233 | −0.878066 | −0.439033 | − | 0.898471i | \(-0.644679\pi\) | ||||
−0.439033 | + | 0.898471i | \(0.644679\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 8.00000i | − 0.343313i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 53.8617 | 2.29876 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.12311 | 0.218252 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6847i | 0.496882i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.6155i | 1.00062i | 0.865846 | + | 0.500311i | \(0.166781\pi\) | ||||
−0.865846 | + | 0.500311i | \(0.833219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.38447 | 0.270034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5616 | −0.952550 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.4924i | 1.70655i | 0.521459 | + | 0.853276i | \(0.325388\pi\) | ||||
−0.521459 | + | 0.853276i | \(0.674612\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 7.00000i | − 0.293972i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.9848 | 1.96971 | 0.984854 | − | 0.173388i | \(-0.0554715\pi\) | ||||
0.984854 | + | 0.173388i | \(0.0554715\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 29.9309i | − 1.25038i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.561553i | 0.0233777i | 0.999932 | + | 0.0116889i | \(0.00372077\pi\) | ||||
−0.999932 | + | 0.0116889i | \(0.996279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.4924 | −0.519167 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 12.4924i | − 0.517383i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 6.24621i | − 0.257809i | −0.991657 | − | 0.128904i | \(-0.958854\pi\) | ||||
0.991657 | − | 0.128904i | \(-0.0411460\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.5076 | 0.474161 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4924 | −0.513870 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.4233i | 1.00294i | 0.865174 | + | 0.501472i | \(0.167208\pi\) | ||||
−0.865174 | + | 0.501472i | \(0.832792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.75379i | 0.235487i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.0691 | 0.738285 | 0.369142 | − | 0.929373i | \(-0.379651\pi\) | ||||
0.369142 | + | 0.929373i | \(0.379651\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 50.7386i | 2.06624i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.68466i | 0.149556i | 0.997200 | + | 0.0747778i | \(0.0238248\pi\) | ||||
−0.997200 | + | 0.0747778i | \(0.976175\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.6847 | −0.473486 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.3002 | −1.50900 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.7386i | 1.32230i | 0.750253 | + | 0.661150i | \(0.229932\pi\) | ||||
−0.750253 | + | 0.661150i | \(0.770068\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 32.2462i | − 1.29818i | −0.760710 | − | 0.649092i | \(-0.775149\pi\) | ||||
0.760710 | − | 0.649092i | \(-0.224851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.3693 | −1.42161 | −0.710806 | − | 0.703388i | \(-0.751670\pi\) | ||||
−0.710806 | + | 0.703388i | \(0.751670\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.36932 | −0.295720 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.12311i | 0.125125i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7.36932i | − 0.294302i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.3542 | −1.13055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.4233 | 1.37037 | 0.685185 | − | 0.728369i | \(-0.259721\pi\) | ||||
0.685185 | + | 0.728369i | \(0.259721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.4233i | 1.36820i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5.68466i | − 0.225234i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.9848 | 1.69780 | 0.848900 | − | 0.528554i | \(-0.177266\pi\) | ||||
0.848900 | + | 0.528554i | \(0.177266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 7.05398i | − 0.278182i | −0.990280 | − | 0.139091i | \(-0.955582\pi\) | ||||
0.990280 | − | 0.139091i | \(-0.0444180\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.00000i | 0.314512i | 0.987558 | + | 0.157256i | \(0.0502649\pi\) | ||||
−0.987558 | + | 0.157256i | \(0.949735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2462 | −0.402199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.2462 | −1.02867 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.50758i | 0.215528i | 0.994176 | + | 0.107764i | \(0.0343691\pi\) | ||||
−0.994176 | + | 0.107764i | \(0.965631\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 43.6155i | 1.70160i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.8078 | 0.810555 | 0.405278 | − | 0.914194i | \(-0.367175\pi\) | ||||
0.405278 | + | 0.914194i | \(0.367175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.6155 | 0.918538 | 0.459269 | − | 0.888297i | \(-0.348111\pi\) | ||||
0.459269 | + | 0.888297i | \(0.348111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 50.0691i | 1.94452i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 23.3693i | − 0.904864i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31.5464 | −1.21965 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.7386 | 1.49549 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 0.384472i | − 0.0148203i | −0.999973 | − | 0.00741015i | \(-0.997641\pi\) | ||||
0.999973 | − | 0.00741015i | \(-0.00235875\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 13.6847i | − 0.525944i | −0.964803 | − | 0.262972i | \(-0.915297\pi\) | ||||
0.964803 | − | 0.262972i | \(-0.0847027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.6847 | −0.525169 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −60.6695 | −2.32486 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.9848i | 0.802963i | 0.915867 | + | 0.401481i | \(0.131505\pi\) | ||||
−0.915867 | + | 0.401481i | \(0.868495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.2462i | 1.30657i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.7235 | −1.05618 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4924 | −0.627401 | −0.313701 | − | 0.949522i | \(-0.601569\pi\) | ||||
−0.313701 | + | 0.949522i | \(0.601569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.12311i | 0.346558i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.4924i | 0.927717i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.9848 | 1.85278 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.6847 | −0.819018 | −0.409509 | − | 0.912306i | \(-0.634300\pi\) | ||||
−0.409509 | + | 0.912306i | \(0.634300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 9.26137i | − 0.349299i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000i | 0.225653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.0540 | −1.24137 | −0.620684 | − | 0.784061i | \(-0.713145\pi\) | ||||
−0.620684 | + | 0.784061i | \(0.713145\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.6155 | −1.56070 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 52.4924i | − 1.96586i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 48.8078i | 1.82276i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.6155 | −0.656948 | −0.328474 | − | 0.944513i | \(-0.606534\pi\) | ||||
−0.328474 | + | 0.944513i | \(0.606534\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.80776 | 0.328018 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 5.12311i | − 0.190530i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 16.9848i | − 0.629933i | −0.949103 | − | 0.314967i | \(-0.898007\pi\) | ||||
0.949103 | − | 0.314967i | \(-0.101993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 35.9848 | 1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.86174 | 0.142832 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 20.5616i | − 0.759458i | −0.925098 | − | 0.379729i | \(-0.876017\pi\) | ||||
0.925098 | − | 0.379729i | \(-0.123983\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.4924i | 1.34422i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.5616 | 0.388513 | 0.194257 | − | 0.980951i | \(-0.437771\pi\) | ||||
0.194257 | + | 0.980951i | \(0.437771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.3542 | −0.600785 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.7386i | 1.56372i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.87689 | −0.251276 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.6847 | −1.59408 | −0.797038 | − | 0.603929i | \(-0.793601\pi\) | ||||
−0.797038 | + | 0.603929i | \(0.793601\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.1231i | 1.06130i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9.36932i | − 0.340534i | −0.985398 | − | 0.170267i | \(-0.945537\pi\) | ||||
0.985398 | − | 0.170267i | \(-0.0544630\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33.6155 | −1.22017 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.0000 | 0.942499 | 0.471250 | − | 0.882000i | \(-0.343803\pi\) | ||||
0.471250 | + | 0.882000i | \(0.343803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.56155i | 0.309949i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.7386i | 0.821044i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9848 | 0.828855 | 0.414427 | − | 0.910082i | \(-0.363982\pi\) | ||||
0.414427 | + | 0.910082i | \(0.363982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.1231 | 1.33696 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.19224i | 0.330622i | 0.986242 | + | 0.165311i | \(0.0528627\pi\) | ||||
−0.986242 | + | 0.165311i | \(0.947137\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.1231i | 0.757787i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | −0.286630 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 6.56155i | − 0.234491i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 12.1771i | − 0.434066i | −0.976164 | − | 0.217033i | \(-0.930362\pi\) | ||||
0.976164 | − | 0.217033i | \(-0.0696379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 39.3693 | 1.40158 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.24621 | −0.293202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 85.9697i | − 3.05287i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2.80776i | − 0.0994561i | −0.998763 | − | 0.0497281i | \(-0.984165\pi\) | ||||
0.998763 | − | 0.0497281i | \(-0.0158355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.5616 | −0.798170 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1231 | −0.393016 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.3693i | 1.10700i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 31.3693i | − 1.10425i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.0540 | 1.16212 | 0.581058 | − | 0.813862i | \(-0.302639\pi\) | ||||
0.581058 | + | 0.813862i | \(0.302639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6155 | 0.478106 | 0.239053 | − | 0.971007i | \(-0.423163\pi\) | ||||
0.239053 | + | 0.971007i | \(0.423163\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 26.2462i | − 0.920495i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.26137i | 0.0441296i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.2462 | 0.707460 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.699813 | 0.0244237 | 0.0122118 | − | 0.999925i | \(-0.496113\pi\) | ||||
0.0122118 | + | 0.999925i | \(0.496113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.2462i | 1.19375i | 0.802335 | + | 0.596874i | \(0.203591\pi\) | ||||
−0.802335 | + | 0.596874i | \(0.796409\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.1231i | 1.15180i | 0.817519 | + | 0.575902i | \(0.195349\pi\) | ||||
−0.817519 | + | 0.575902i | \(0.804651\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.6155 | 1.23698 | 0.618489 | − | 0.785793i | \(-0.287745\pi\) | ||||
0.618489 | + | 0.785793i | \(0.287745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1231 | 0.732752 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.43845i | − 0.119135i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 14.7386i | − 0.509442i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.8769 | −0.375512 | −0.187756 | − | 0.982216i | \(-0.560121\pi\) | ||||
−0.187756 | + | 0.982216i | \(0.560121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.19224 | −0.282491 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 39.5464i | 1.36205i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 4.43845i | − 0.152507i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.6847 | −0.675576 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −42.2462 | −1.44818 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 32.2462i | − 1.10409i | −0.833815 | − | 0.552045i | \(-0.813848\pi\) | ||||
0.833815 | − | 0.552045i | \(-0.186152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.26137i | 0.111406i | 0.998447 | + | 0.0557031i | \(0.0177400\pi\) | ||||
−0.998447 | + | 0.0557031i | \(0.982260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.9848 | 0.988950 | 0.494475 | − | 0.869192i | \(-0.335360\pi\) | ||||
0.494475 | + | 0.869192i | \(0.335360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.2462 | 0.621829 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.49242i | 0.152924i | 0.997073 | + | 0.0764619i | \(0.0243624\pi\) | ||||
−0.997073 | + | 0.0764619i | \(0.975638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 13.2614i | − 0.450380i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.9309 | −1.01534 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 80.9848 | 2.74407 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 48.7386i | − 1.64955i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 46.4924i | − 1.56994i | −0.619535 | − | 0.784969i | \(-0.712679\pi\) | ||||
0.619535 | − | 0.784969i | \(-0.287321\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.9460 | 0.436659 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.1080 | −0.677454 | −0.338727 | − | 0.940885i | \(-0.609996\pi\) | ||||
−0.338727 | + | 0.940885i | \(0.609996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 38.2462i | − 1.28709i | −0.765409 | − | 0.643544i | \(-0.777463\pi\) | ||||
0.765409 | − | 0.643544i | \(-0.222537\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 3.50758i | − 0.117773i | −0.998265 | − | 0.0588865i | \(-0.981245\pi\) | ||||
0.998265 | − | 0.0588865i | \(-0.0187550\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2462 | −0.343647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.9309 | 0.600707 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7.36932i | − 0.246605i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 74.6004i | 2.49083i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.7386 | 1.55882 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.7689 | −0.558655 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 2.87689i | − 0.0957371i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.1080i | 0.866900i | 0.901178 | + | 0.433450i | \(0.142704\pi\) | ||||
−0.901178 | + | 0.433450i | \(0.857296\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.3693 | −0.708776 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.7386i | 1.01730i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.87689i | 0.227095i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.56155 | −0.216446 | −0.108223 | − | 0.994127i | \(-0.534516\pi\) | ||||
−0.108223 | + | 0.994127i | \(0.534516\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.7926 | −1.37711 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.3693i | 1.03030i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1231 | 0.364937 | 0.182469 | − | 0.983212i | \(-0.441591\pi\) | ||||
0.182469 | + | 0.983212i | \(0.441591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.12311 | 0.0368083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.1080i | 1.77141i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.1922i | 0.561646i | 0.959760 | + | 0.280823i | \(0.0906074\pi\) | ||||
−0.959760 | + | 0.280823i | \(0.909393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −36.6695 | −1.19666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.3693 | 1.73979 | 0.869895 | − | 0.493237i | \(-0.164186\pi\) | ||||
0.869895 | + | 0.493237i | \(0.164186\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.4924i | 1.18836i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.2311i | 1.53480i | 0.641167 | + | 0.767402i | \(0.278451\pi\) | ||||
−0.641167 | + | 0.767402i | \(0.721549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 69.6155 | 2.25982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.6155 | −0.830640 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 5.86174i | − 0.189880i | −0.995483 | − | 0.0949402i | \(-0.969734\pi\) | ||||
0.995483 | − | 0.0949402i | \(-0.0302660\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 29.9309i | − 0.967528i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.3693 | −0.560884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9848 | 2.38661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 24.4924i | − 0.789257i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 30.1080i | − 0.968206i | −0.875011 | − | 0.484103i | \(-0.839146\pi\) | ||||
0.875011 | − | 0.484103i | \(-0.160854\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.89205 | −0.317778 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.7386 | 0.858084 | 0.429042 | − | 0.903285i | \(-0.358851\pi\) | ||||
0.429042 | + | 0.903285i | \(0.358851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3.36932i | − 0.108015i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 54.9848i | − 1.75912i | −0.475787 | − | 0.879561i | \(-0.657837\pi\) | ||||
0.475787 | − | 0.879561i | \(-0.342163\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.4924 | −0.973548 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 16.1771i | − 0.515969i | −0.966149 | − | 0.257984i | \(-0.916942\pi\) | ||||
0.966149 | − | 0.257984i | \(-0.0830583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.8078i | 0.534997i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.75379 | 0.182960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4924 | 0.396835 | 0.198417 | − | 0.980118i | \(-0.436420\pi\) | ||||
0.198417 | + | 0.980118i | \(0.436420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.7386i | 0.975461i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 28.0691i | − 0.888958i | −0.895789 | − | 0.444479i | \(-0.853389\pi\) | ||||
0.895789 | − | 0.444479i | \(-0.146611\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.8617 | −0.375289 |
(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 | 1400.2.g.k.449.1 | 4 | ||
4.3 | odd | 2 | 2800.2.g.u.449.4 | 4 | |||
5.2 | odd | 4 | 1400.2.a.p.1.1 | 2 | |||
5.3 | odd | 4 | 280.2.a.d.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1400.2.g.k.449.4 | 4 | ||
15.8 | even | 4 | 2520.2.a.w.1.2 | 2 | |||
20.3 | even | 4 | 560.2.a.g.1.1 | 2 | |||
20.7 | even | 4 | 2800.2.a.bn.1.2 | 2 | |||
20.19 | odd | 2 | 2800.2.g.u.449.1 | 4 | |||
35.3 | even | 12 | 1960.2.q.u.961.2 | 4 | |||
35.13 | even | 4 | 1960.2.a.r.1.1 | 2 | |||
35.18 | odd | 12 | 1960.2.q.s.961.1 | 4 | |||
35.23 | odd | 12 | 1960.2.q.s.361.1 | 4 | |||
35.27 | even | 4 | 9800.2.a.by.1.2 | 2 | |||
35.33 | even | 12 | 1960.2.q.u.361.2 | 4 | |||
40.3 | even | 4 | 2240.2.a.bi.1.2 | 2 | |||
40.13 | odd | 4 | 2240.2.a.be.1.1 | 2 | |||
60.23 | odd | 4 | 5040.2.a.bq.1.1 | 2 | |||
140.83 | odd | 4 | 3920.2.a.bu.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.d.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
560.2.a.g.1.1 | 2 | 20.3 | even | 4 | |||
1400.2.a.p.1.1 | 2 | 5.2 | odd | 4 | |||
1400.2.g.k.449.1 | 4 | 1.1 | even | 1 | trivial | ||
1400.2.g.k.449.4 | 4 | 5.4 | even | 2 | inner | ||
1960.2.a.r.1.1 | 2 | 35.13 | even | 4 | |||
1960.2.q.s.361.1 | 4 | 35.23 | odd | 12 | |||
1960.2.q.s.961.1 | 4 | 35.18 | odd | 12 | |||
1960.2.q.u.361.2 | 4 | 35.33 | even | 12 | |||
1960.2.q.u.961.2 | 4 | 35.3 | even | 12 | |||
2240.2.a.be.1.1 | 2 | 40.13 | odd | 4 | |||
2240.2.a.bi.1.2 | 2 | 40.3 | even | 4 | |||
2520.2.a.w.1.2 | 2 | 15.8 | even | 4 | |||
2800.2.a.bn.1.2 | 2 | 20.7 | even | 4 | |||
2800.2.g.u.449.1 | 4 | 20.19 | odd | 2 | |||
2800.2.g.u.449.4 | 4 | 4.3 | odd | 2 | |||
3920.2.a.bu.1.2 | 2 | 140.83 | odd | 4 | |||
5040.2.a.bq.1.1 | 2 | 60.23 | odd | 4 | |||
9800.2.a.by.1.2 | 2 | 35.27 | even | 4 |