Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1749,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1900.1749");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.c (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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 22x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1749.3 | ||
Root | \(0.713538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1749 |
Dual form | 1900.2.c.g.1749.4 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 0.286462i | − 0.165389i | −0.996575 | − | 0.0826945i | \(-0.973647\pi\) | ||||
0.996575 | − | 0.0826945i | \(-0.0263526\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.286462i | 0.108272i | 0.998534 | + | 0.0541362i | \(0.0172405\pi\) | ||||
−0.998534 | + | 0.0541362i | \(0.982759\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.91794 | 0.972646 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.26819 | 1.28691 | 0.643454 | − | 0.765485i | \(-0.277501\pi\) | ||||
0.643454 | + | 0.765485i | \(0.277501\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.20440i | − 0.888741i | −0.895843 | − | 0.444371i | \(-0.853427\pi\) | ||||
0.895843 | − | 0.444371i | \(-0.146573\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.286462i | 0.0694773i | 0.999396 | + | 0.0347386i | \(0.0110599\pi\) | ||||
−0.999396 | + | 0.0347386i | \(0.988940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0820605 | 0.0179071 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 0.936212i | − 0.195214i | −0.995225 | − | 0.0976069i | \(-0.968881\pi\) | ||||
0.995225 | − | 0.0976069i | \(-0.0311188\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.69527i | − 0.326254i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.26819 | −0.421192 | −0.210596 | − | 0.977573i | \(-0.567540\pi\) | ||||
−0.210596 | + | 0.977573i | \(0.567540\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.18613 | −0.751851 | −0.375925 | − | 0.926650i | \(-0.622675\pi\) | ||||
−0.375925 | + | 0.926650i | \(0.622675\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 1.22267i | − 0.212840i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.67699i | 1.42649i | 0.700915 | + | 0.713244i | \(0.252775\pi\) | ||||
−0.700915 | + | 0.713244i | \(0.747225\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.917939 | −0.146988 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.08206 | 0.168989 | 0.0844947 | − | 0.996424i | \(-0.473072\pi\) | ||||
0.0844947 | + | 0.996424i | \(0.473072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.42708i | − 0.675123i | −0.941304 | − | 0.337561i | \(-0.890398\pi\) | ||||
0.941304 | − | 0.337561i | \(-0.109602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 0.759053i | − 0.110719i | −0.998466 | − | 0.0553596i | \(-0.982369\pi\) | ||||
0.998466 | − | 0.0553596i | \(-0.0176305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.91794 | 0.988277 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0820605 | 0.0114908 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.42708i | − 0.608106i | −0.952655 | − | 0.304053i | \(-0.901660\pi\) | ||||
0.952655 | − | 0.304053i | \(-0.0983399\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 0.286462i | − 0.0379428i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.70050 | 0.611953 | 0.305976 | − | 0.952039i | \(-0.401017\pi\) | ||||
0.305976 | + | 0.952039i | \(0.401017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1861 | 1.30420 | 0.652100 | − | 0.758133i | \(-0.273888\pi\) | ||||
0.652100 | + | 0.758133i | \(0.273888\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.835879i | 0.105311i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.82284i | 1.20005i | 0.799981 | + | 0.600025i | \(0.204843\pi\) | ||||
−0.799981 | + | 0.600025i | \(0.795157\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.268189 | −0.0322862 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.83588 | 0.573913 | 0.286957 | − | 0.957944i | \(-0.407356\pi\) | ||||
0.286957 | + | 0.957944i | \(0.407356\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 10.4726i | − 1.22572i | −0.790190 | − | 0.612862i | \(-0.790018\pi\) | ||||
0.790190 | − | 0.612862i | \(-0.209982\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.22267i | 0.139337i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.10407 | −0.574253 | −0.287126 | − | 0.957893i | \(-0.592700\pi\) | ||||
−0.287126 | + | 0.957893i | \(0.592700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.26819 | 0.918688 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 15.7355i | − 1.72720i | −0.504177 | − | 0.863600i | \(-0.668204\pi\) | ||||
0.504177 | − | 0.863600i | \(-0.331796\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.649750i | 0.0696605i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.75382 | 1.03390 | 0.516951 | − | 0.856015i | \(-0.327067\pi\) | ||||
0.516951 | + | 0.856015i | \(0.327067\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.917939 | 0.0962262 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.19917i | 0.124348i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 9.61320i | − 0.976073i | −0.872823 | − | 0.488037i | \(-0.837713\pi\) | ||||
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.4543 | 1.25171 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.731811 | 0.0728179 | 0.0364089 | − | 0.999337i | \(-0.488408\pi\) | ||||
0.0364089 | + | 0.999337i | \(0.488408\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.10407i | 0.305853i | 0.988238 | + | 0.152926i | \(0.0488698\pi\) | ||||
−0.988238 | + | 0.152926i | \(0.951130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1731i | 1.37016i | 0.728466 | + | 0.685082i | \(0.240234\pi\) | ||||
−0.728466 | + | 0.685082i | \(0.759766\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.61844 | 0.921279 | 0.460640 | − | 0.887587i | \(-0.347620\pi\) | ||||
0.460640 | + | 0.887587i | \(0.347620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.48563 | 0.235925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 8.77733i | − 0.825701i | −0.910799 | − | 0.412851i | \(-0.864533\pi\) | ||||
0.910799 | − | 0.412851i | \(-0.135467\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 9.35025i | − 0.864431i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0820605 | −0.00752248 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.21744 | 0.656131 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 0.309969i | − 0.0279490i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.77209i | 0.600926i | 0.953793 | + | 0.300463i | \(0.0971412\pi\) | ||||
−0.953793 | + | 0.300463i | \(0.902859\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.26819 | −0.111658 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.91794 | −0.254942 | −0.127471 | − | 0.991842i | \(-0.540686\pi\) | ||||
−0.127471 | + | 0.991842i | \(0.540686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.286462i | 0.0248394i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 14.4360i | − 1.23335i | −0.787216 | − | 0.616677i | \(-0.788478\pi\) | ||||
0.787216 | − | 0.616677i | \(-0.211522\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.29950 | 0.195041 | 0.0975205 | − | 0.995234i | \(-0.468909\pi\) | ||||
0.0975205 | + | 0.995234i | \(0.468909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.217440 | −0.0183117 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 13.6770i | − 1.14373i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.98173i | − 0.163450i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.75382 | −0.553294 | −0.276647 | − | 0.960972i | \(-0.589223\pi\) | ||||
−0.276647 | + | 0.960972i | \(0.589223\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8866 | −0.967320 | −0.483660 | − | 0.875256i | \(-0.660693\pi\) | ||||
−0.483660 | + | 0.875256i | \(0.660693\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.835879i | 0.0675768i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 14.1731i | − 1.13114i | −0.824702 | − | 0.565568i | \(-0.808657\pi\) | ||||
0.824702 | − | 0.565568i | \(-0.191343\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.26819 | −0.100574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.268189 | 0.0211363 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 7.89443i | − 0.618340i | −0.951007 | − | 0.309170i | \(-0.899949\pi\) | ||||
0.951007 | − | 0.309170i | \(-0.100051\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.4726i | 1.58422i | 0.610381 | + | 0.792108i | \(0.291017\pi\) | ||||
−0.610381 | + | 0.792108i | \(0.708983\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.73181 | 0.210139 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.91794 | 0.223140 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.0492i | 1.82843i | 0.405229 | + | 0.914215i | \(0.367192\pi\) | ||||
−0.405229 | + | 0.914215i | \(0.632808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1.34651i | − 0.101210i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.6718 | −1.39559 | −0.697796 | − | 0.716296i | \(-0.745836\pi\) | ||||
−0.697796 | + | 0.716296i | \(0.745836\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.53638 | −0.262857 | −0.131428 | − | 0.991326i | \(-0.541956\pi\) | ||||
−0.131428 | + | 0.991326i | \(0.541956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2.91794i | − 0.215700i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.22267i | 0.0894108i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.485629 | 0.0353243 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2682 | −1.03241 | −0.516205 | − | 0.856465i | \(-0.672656\pi\) | ||||
−0.516205 | + | 0.856465i | \(0.672656\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.18089i | 0.588874i | 0.955671 | + | 0.294437i | \(0.0951321\pi\) | ||||
−0.955671 | + | 0.294437i | \(0.904868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6404i | 0.900595i | 0.892879 | + | 0.450297i | \(0.148682\pi\) | ||||
−0.892879 | + | 0.450297i | \(0.851318\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.10407 | 0.290930 | 0.145465 | − | 0.989363i | \(-0.453532\pi\) | ||||
0.145465 | + | 0.989363i | \(0.453532\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.81387 | 0.198475 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.649750i | − 0.0456035i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2.73181i | − 0.189874i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.26819 | 0.295237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.53638 | 0.105769 | 0.0528843 | − | 0.998601i | \(-0.483159\pi\) | ||||
0.0528843 | + | 0.998601i | \(0.483159\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.38530i | − 0.0949189i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1.19917i | − 0.0814048i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.00000 | −0.202721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.917939 | 0.0617473 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.40880i | − 0.0943404i | −0.998887 | − | 0.0471702i | \(-0.984980\pi\) | ||||
0.998887 | − | 0.0471702i | \(-0.0150203\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.9179i | 1.52112i | 0.649269 | + | 0.760559i | \(0.275075\pi\) | ||||
−0.649269 | + | 0.760559i | \(0.724925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.78513 | −0.250128 | −0.125064 | − | 0.992149i | \(-0.539914\pi\) | ||||
−0.125064 | + | 0.992149i | \(0.539914\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.350250 | 0.0230447 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 2.26819i | − 0.148594i | −0.997236 | − | 0.0742970i | \(-0.976329\pi\) | ||||
0.997236 | − | 0.0742970i | \(-0.0236713\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.46212i | 0.0949750i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.18613 | 0.141409 | 0.0707045 | − | 0.997497i | \(-0.477475\pi\) | ||||
0.0707045 | + | 0.997497i | \(0.477475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.9907 | 1.28771 | 0.643857 | − | 0.765146i | \(-0.277333\pi\) | ||||
0.643857 | + | 0.765146i | \(0.277333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 7.45432i | − 0.478195i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.20440i | − 0.203891i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.50764 | −0.285660 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.35025 | 0.0852270 | 0.0426135 | − | 0.999092i | \(-0.486432\pi\) | ||||
0.0426135 | + | 0.999092i | \(0.486432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.99593i | − 0.251222i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 11.9582i | − 0.745933i | −0.927845 | − | 0.372967i | \(-0.878341\pi\) | ||||
0.927845 | − | 0.372967i | \(-0.121659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.48563 | −0.154449 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.61844 | −0.409671 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.31370i | 0.512645i | 0.966591 | + | 0.256322i | \(0.0825109\pi\) | ||||
−0.966591 | + | 0.256322i | \(0.917489\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.79410i | − 0.170996i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.02201 | 0.306197 | 0.153099 | − | 0.988211i | \(-0.451075\pi\) | ||||
0.153099 | + | 0.988211i | \(0.451075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.96869 | 0.423318 | 0.211659 | − | 0.977344i | \(-0.432113\pi\) | ||||
0.211659 | + | 0.977344i | \(0.432113\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 0.262955i | − 0.0159148i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 12.7083i | − 0.763568i | −0.924252 | − | 0.381784i | \(-0.875310\pi\) | ||||
0.924252 | − | 0.381784i | \(-0.124690\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.2149 | −0.731285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.5364 | −0.986478 | −0.493239 | − | 0.869894i | \(-0.664187\pi\) | ||||
−0.493239 | + | 0.869894i | \(0.664187\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1548i | 1.55474i | 0.629042 | + | 0.777371i | \(0.283447\pi\) | ||||
−0.629042 | + | 0.777371i | \(0.716553\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.309969i | 0.0182969i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9179 | 0.995173 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.75382 | −0.161432 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.95449i | 0.231023i | 0.993306 | + | 0.115512i | \(0.0368508\pi\) | ||||
−0.993306 | + | 0.115512i | \(0.963149\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 7.23571i | − 0.419859i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | −0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.26819 | 0.0730972 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 0.209636i | − 0.0120433i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 20.7355i | − 1.18344i | −0.806144 | − | 0.591720i | \(-0.798449\pi\) | ||||
0.806144 | − | 0.591720i | \(-0.201551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.889198 | 0.0505847 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.97799 | −0.112162 | −0.0560808 | − | 0.998426i | \(-0.517860\pi\) | ||||
−0.0560808 | + | 0.998426i | \(0.517860\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.67699i | 0.490453i | 0.969466 | + | 0.245226i | \(0.0788623\pi\) | ||||
−0.969466 | + | 0.245226i | \(0.921138\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.34502i | − 0.131709i | −0.997829 | − | 0.0658546i | \(-0.979023\pi\) | ||||
0.997829 | − | 0.0658546i | \(-0.0209773\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.68106 | −0.542035 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.06005 | 0.226610 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.286462i | 0.0159392i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2.75532i | − 0.152369i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.217440 | 0.0119878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.8579 | −1.25638 | −0.628192 | − | 0.778059i | \(-0.716205\pi\) | ||||
−0.628192 | + | 0.778059i | \(0.716205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.3189i | 1.38747i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 0.386795i | − 0.0210701i | −0.999945 | − | 0.0105350i | \(-0.996647\pi\) | ||||
0.999945 | − | 0.0105350i | \(-0.00335347\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.51437 | −0.136562 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.8672 | −0.967563 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.98696i | 0.215276i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.1406i | 0.759108i | 0.925170 | + | 0.379554i | \(0.123923\pi\) | ||||
−0.925170 | + | 0.379554i | \(0.876077\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.81387 | 0.150623 | 0.0753115 | − | 0.997160i | \(-0.476005\pi\) | ||||
0.0753115 | + | 0.997160i | \(0.476005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.43231 | −0.289955 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.3137i | 0.708617i | 0.935129 | + | 0.354308i | \(0.115284\pi\) | ||||
−0.935129 | + | 0.354308i | \(0.884716\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0235072i | 0.00124413i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.1861 | −0.748715 | −0.374358 | − | 0.927284i | \(-0.622137\pi\) | ||||
−0.374358 | + | 0.927284i | \(0.622137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.06752i | − 0.108517i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 28.0272i | − 1.46301i | −0.681836 | − | 0.731505i | \(-0.738818\pi\) | ||||
0.681836 | − | 0.731505i | \(-0.261182\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.15739 | 0.164367 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.26819 | 0.0658411 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.3502i | 1.26081i | 0.776267 | + | 0.630404i | \(0.217111\pi\) | ||||
−0.776267 | + | 0.630404i | \(0.782889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.26819i | 0.374331i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.8866 | −1.48381 | −0.741903 | − | 0.670507i | \(-0.766077\pi\) | ||||
−0.741903 | + | 0.670507i | \(0.766077\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.93995 | 0.0993865 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3398i | 0.528338i | 0.964476 | + | 0.264169i | \(0.0850977\pi\) | ||||
−0.964476 | + | 0.264169i | \(0.914902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 12.9179i | − 0.656656i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.9086 | −1.71924 | −0.859618 | − | 0.510937i | \(-0.829298\pi\) | ||||
−0.859618 | + | 0.510937i | \(0.829298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.268189 | 0.0135629 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.835879i | 0.0421645i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 33.8866i | − 1.70072i | −0.526200 | − | 0.850361i | \(-0.676384\pi\) | ||||
0.526200 | − | 0.850361i | \(-0.323616\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0820605 | 0.00410816 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5051 | −0.524598 | −0.262299 | − | 0.964987i | \(-0.584481\pi\) | ||||
−0.262299 | + | 0.964987i | \(0.584481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.4140i | 0.668201i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 37.0350i | 1.83576i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.78256 | 0.335376 | 0.167688 | − | 0.985840i | \(-0.446370\pi\) | ||||
0.167688 | + | 0.985840i | \(0.446370\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.13538 | −0.203983 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.34651i | 0.0662577i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 0.658720i | − 0.0322576i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.6498 | −0.911100 | −0.455550 | − | 0.890210i | \(-0.650557\pi\) | ||||
−0.455550 | + | 0.890210i | \(0.650557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.64975 | 0.470300 | 0.235150 | − | 0.971959i | \(-0.424442\pi\) | ||||
0.235150 | + | 0.971959i | \(0.424442\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2.21487i | − 0.107691i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.91794i | 0.141209i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.91794 | −0.189160 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.7758 | −1.62692 | −0.813462 | − | 0.581618i | \(-0.802420\pi\) | ||||
−0.813462 | + | 0.581618i | \(0.802420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1.08986i | − 0.0523755i | −0.999657 | − | 0.0261878i | \(-0.991663\pi\) | ||||
0.999657 | − | 0.0261878i | \(-0.00833678\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 0.936212i | − 0.0447851i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9687 | 0.618962 | 0.309481 | − | 0.950906i | \(-0.399845\pi\) | ||||
0.309481 | + | 0.950906i | \(0.399845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.1861 | 0.961244 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.9437i | 1.51769i | 0.651271 | + | 0.758845i | \(0.274236\pi\) | ||||
−0.651271 | + | 0.758845i | \(0.725764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.93471i | 0.0915088i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.05075 | 0.238360 | 0.119180 | − | 0.992873i | \(-0.461974\pi\) | ||||
0.119180 | + | 0.992873i | \(0.461974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.61844 | 0.217474 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.40507i | 0.159984i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.0948i | 1.64166i | 0.571170 | + | 0.820832i | \(0.306490\pi\) | ||||
−0.571170 | + | 0.820832i | \(0.693510\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.485629 | 0.0226672 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.8866 | −1.29881 | −0.649405 | − | 0.760443i | \(-0.724982\pi\) | ||||
−0.649405 | + | 0.760443i | \(0.724982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.0037i | 1.30144i | 0.759316 | + | 0.650722i | \(0.225534\pi\) | ||||
−0.759316 | + | 0.650722i | \(0.774466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.4543i | 0.807690i | 0.914828 | + | 0.403845i | \(0.132326\pi\) | ||||
−0.914828 | + | 0.403845i | \(0.867674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.81387 | −0.129933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.06005 | −0.187077 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 18.8956i | − 0.868821i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 12.9179i | − 0.591472i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.0440 | −1.18998 | −0.594991 | − | 0.803733i | \(-0.702844\pi\) | ||||
−0.594991 | + | 0.803733i | \(0.702844\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.8046 | 1.26778 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 0.0768261i | − 0.00349571i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 21.9907i | − 0.996494i | −0.867035 | − | 0.498247i | \(-0.833977\pi\) | ||||
0.867035 | − | 0.498247i | \(-0.166023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.26146 | −0.102267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.9907 | −1.53398 | −0.766989 | − | 0.641660i | \(-0.778246\pi\) | ||||
−0.766989 | + | 0.641660i | \(0.778246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 0.649750i | − 0.0292633i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.38530i | 0.0621390i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.83331 | −0.305901 | −0.152950 | − | 0.988234i | \(-0.548877\pi\) | ||||
−0.152950 | + | 0.988234i | \(0.548877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.86462 | 0.262012 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 34.4685i | − 1.53688i | −0.639925 | − | 0.768438i | \(-0.721034\pi\) | ||||
0.639925 | − | 0.768438i | \(-0.278966\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 0.782560i | − 0.0347547i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.9179 | −0.838523 | −0.419261 | − | 0.907866i | \(-0.637711\pi\) | ||||
−0.419261 | + | 0.907866i | \(0.637711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | 0.132712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 1.69527i | − 0.0748478i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3.23978i | − 0.142485i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.88920 | 0.302402 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.62774 | −0.0713127 | −0.0356563 | − | 0.999364i | \(-0.511352\pi\) | ||||
−0.0356563 | + | 0.999364i | \(0.511352\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.16669i | 0.0510158i | 0.999675 | + | 0.0255079i | \(0.00812030\pi\) | ||||
−0.999675 | + | 0.0255079i | \(0.991880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.19917i | − 0.0522365i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.1235 | 0.961892 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.7158 | 0.595214 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.46736i | − 0.150188i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.34875i | 0.230816i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.5271 | 1.27182 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9399 | −1.02926 | −0.514629 | − | 0.857413i | \(-0.672070\pi\) | ||||
−0.514629 | + | 0.857413i | \(0.672070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.01304i | 0.0434736i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8139i | 0.633395i | 0.948527 | + | 0.316698i | \(0.102574\pi\) | ||||
−0.948527 | + | 0.316698i | \(0.897426\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.7225 | 1.26853 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.26819 | −0.0966281 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.46212i | − 0.0621757i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 39.3592i | − 1.66770i | −0.551988 | − | 0.833852i | \(-0.686131\pi\) | ||||
0.551988 | − | 0.833852i | \(-0.313869\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.1861 | −0.600009 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.350250 | 0.0147876 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 9.55722i | − 0.402789i | −0.979510 | − | 0.201394i | \(-0.935453\pi\) | ||||
0.979510 | − | 0.201394i | \(-0.0645473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.36852i | 0.0994686i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.2995 | −0.892922 | −0.446461 | − | 0.894803i | \(-0.647316\pi\) | ||||
−0.446461 | + | 0.894803i | \(0.647316\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.4543 | −0.730440 | −0.365220 | − | 0.930921i | \(-0.619006\pi\) | ||||
−0.365220 | + | 0.930921i | \(0.619006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.08729i | 0.170749i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 37.2861i | − 1.55224i | −0.630584 | − | 0.776121i | \(-0.717185\pi\) | ||||
0.630584 | − | 0.776121i | \(-0.282815\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.34352 | 0.0973932 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.50764 | 0.187008 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 18.8956i | − 0.782576i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7.73181i | − 0.319126i | −0.987188 | − | 0.159563i | \(-0.948991\pi\) | ||||
0.987188 | − | 0.159563i | \(-0.0510085\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.18613 | −0.172486 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.62101 | 0.148948 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.74858i | 0.277131i | 0.990353 | + | 0.138566i | \(0.0442492\pi\) | ||||
−0.990353 | + | 0.138566i | \(0.955751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.17566i | − 0.0481166i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.9687 | 0.693322 | 0.346661 | − | 0.937991i | \(-0.387315\pi\) | ||||
0.346661 | + | 0.937991i | \(0.387315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.7251 | 1.29409 | 0.647046 | − | 0.762451i | \(-0.276004\pi\) | ||||
0.647046 | + | 0.762451i | \(0.276004\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.6625i | 1.16723i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.84518i | 0.156071i | 0.996951 | + | 0.0780356i | \(0.0248648\pi\) | ||||
−0.996951 | + | 0.0780356i | \(0.975135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.186129 | −0.00754232 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.43231 | −0.0984007 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.1208i | 1.29735i | 0.761066 | + | 0.648674i | \(0.224676\pi\) | ||||
−0.761066 | + | 0.648674i | \(0.775324\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.2630i | 1.41963i | 0.704387 | + | 0.709817i | \(0.251222\pi\) | ||||
−0.704387 | + | 0.709817i | \(0.748778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.29020 | −0.373405 | −0.186702 | − | 0.982417i | \(-0.559780\pi\) | ||||
−0.186702 | + | 0.982417i | \(0.559780\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.58713 | −0.0636893 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.79410i | 0.111943i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.22267i | − 0.0488289i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.48563 | −0.0991085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.5271 | −1.05603 | −0.528013 | − | 0.849236i | \(-0.677063\pi\) | ||||
−0.528013 | + | 0.849236i | \(0.677063\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 0.440114i | − 0.0174930i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 22.1679i | − 0.878322i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.1108 | 0.558215 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.86462 | −0.310634 | −0.155317 | − | 0.987865i | \(-0.549640\pi\) | ||||
−0.155317 | + | 0.987865i | \(0.549640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.67176i | 0.0659277i | 0.999457 | + | 0.0329638i | \(0.0104946\pi\) | ||||
−0.999457 | + | 0.0329638i | \(0.989505\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.4909i | 1.51323i | 0.653859 | + | 0.756616i | \(0.273149\pi\) | ||||
−0.653859 | + | 0.756616i | \(0.726851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.0626 | 0.787527 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.343516 | −0.0134634 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9985i | 1.01740i | 0.860944 | + | 0.508700i | \(0.169874\pi\) | ||||
−0.860944 | + | 0.508700i | \(0.830126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 30.5584i | − 1.19220i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.9594 | −1.82928 | −0.914639 | − | 0.404272i | \(-0.867525\pi\) | ||||
−0.914639 | + | 0.404272i | \(0.867525\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7225 | −1.38944 | −0.694722 | − | 0.719278i | \(-0.744473\pi\) | ||||
−0.694722 | + | 0.719278i | \(0.744473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 0.262955i | − 0.0102123i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.12351i | 0.0822225i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.403569 | −0.0156029 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.4763 | 1.67838 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 27.3450i | − 1.05407i | −0.849843 | − | 0.527036i | \(-0.823303\pi\) | ||||
0.849843 | − | 0.527036i | \(-0.176697\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 39.9944i | − 1.53711i | −0.639783 | − | 0.768555i | \(-0.720976\pi\) | ||||
0.639783 | − | 0.768555i | \(-0.279024\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.75382 | 0.105682 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.56512 | 0.251576 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 21.0130i | − 0.804042i | −0.915631 | − | 0.402021i | \(-0.868308\pi\) | ||||
0.915631 | − | 0.402021i | \(-0.131692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.08430i | 0.0413685i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.1861 | −0.540448 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.7445 | −0.408741 | −0.204370 | − | 0.978894i | \(-0.565515\pi\) | ||||
−0.204370 | + | 0.978894i | \(0.565515\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.56769i | 0.135525i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.309969i | 0.0117409i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.649750 | −0.0245758 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.3029 | 1.59776 | 0.798879 | − | 0.601491i | \(-0.205427\pi\) | ||||
0.798879 | + | 0.601491i | \(0.205427\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.67699i | 0.327259i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.209636i | 0.00788417i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.5584 | 1.52320 | 0.761601 | − | 0.648046i | \(-0.224414\pi\) | ||||
0.761601 | + | 0.648046i | \(0.224414\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.8934 | −0.558545 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.91911i | 0.146772i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 0.626243i | − 0.0233875i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.8866 | −0.629765 | −0.314882 | − | 0.949131i | \(-0.601965\pi\) | ||||
−0.314882 | + | 0.949131i | \(0.601965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.889198 | −0.0331155 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 5.72658i | − 0.212974i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.4398i | 1.01769i | 0.860860 | + | 0.508843i | \(0.169926\pi\) | ||||
−0.860860 | + | 0.508843i | \(0.830074\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.6692 | 0.839600 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.26819 | 0.0469057 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0078i | 0.517390i | 0.965959 | + | 0.258695i | \(0.0832925\pi\) | ||||
−0.965959 | + | 0.258695i | \(0.916708\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.9257i | 1.54435i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.7851 | 0.727808 | 0.363904 | − | 0.931437i | \(-0.381444\pi\) | ||||
0.363904 | + | 0.931437i | \(0.381444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.917939 | −0.0337213 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 41.8344i | − 1.53475i | −0.641196 | − | 0.767377i | \(-0.721561\pi\) | ||||
0.641196 | − | 0.767377i | \(-0.278439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 45.9154i | − 1.67996i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.06005 | −0.148351 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.4983 | 1.76973 | 0.884865 | − | 0.465848i | \(-0.154251\pi\) | ||||
0.884865 | + | 0.465848i | \(0.154251\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 0.386795i | − 0.0140956i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2537i | 1.17228i | 0.810210 | + | 0.586139i | \(0.199353\pi\) | ||||
−0.810210 | + | 0.586139i | \(0.800647\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.14468 | −0.0415493 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6184 | −0.928668 | −0.464334 | − | 0.885660i | \(-0.653706\pi\) | ||||
−0.464334 | + | 0.885660i | \(0.653706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.75532i | 0.0997492i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 15.0623i | − 0.543868i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.3096 | −1.52572 | −0.762862 | − | 0.646561i | \(-0.776207\pi\) | ||||
−0.762862 | + | 0.646561i | \(0.776207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.42558 | −0.123369 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.889198i | 0.0319822i | 0.999872 | + | 0.0159911i | \(0.00509035\pi\) | ||||
−0.999872 | + | 0.0159911i | \(0.994910\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.712038i | 0.0255442i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.08206 | 0.0387688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.6404 | 0.738573 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.84518i | 0.137416i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.6650i | 1.80601i | 0.429627 | + | 0.903007i | \(0.358645\pi\) | ||||
−0.429627 | + | 0.903007i | \(0.641355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.38156 | 0.0847858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.51437 | 0.0894007 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 32.6404i | − 1.15910i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.4909i | 1.18631i | 0.805089 | + | 0.593154i | \(0.202117\pi\) | ||||
−0.805089 | + | 0.593154i | \(0.797883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.217440 | 0.00769247 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.4611 | 1.00562 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 44.6990i | − 1.57739i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1.43861i | − 0.0506416i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.35025 | 0.223263 | 0.111631 | − | 0.993750i | \(-0.464392\pi\) | ||||
0.111631 | + | 0.993750i | \(0.464392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.08463 | −0.0380865 | −0.0190433 | − | 0.999819i | \(-0.506062\pi\) | ||||
−0.0190433 | + | 0.999819i | \(0.506062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.99627i | − 0.0700121i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 4.42708i | − 0.154884i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.67849 | 0.0935941 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3630 | −0.431470 | −0.215735 | − | 0.976452i | \(-0.569215\pi\) | ||||
−0.215735 | + | 0.976452i | \(0.569215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 27.0765i | − 0.943827i | −0.881645 | − | 0.471914i | \(-0.843563\pi\) | ||||
0.881645 | − | 0.471914i | \(-0.156437\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 17.0765i | − 0.593808i | −0.954907 | − | 0.296904i | \(-0.904046\pi\) | ||||
0.954907 | − | 0.296904i | \(-0.0959541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.5804 | 0.992638 | 0.496319 | − | 0.868140i | \(-0.334685\pi\) | ||||
0.496319 | + | 0.868140i | \(0.334685\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.64045 | −0.126286 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.98173i | 0.0686628i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.09660i | 0.245294i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 55.9019 | 1.92995 | 0.964974 | − | 0.262346i | \(-0.0844960\pi\) | ||||
0.964974 | + | 0.262346i | \(0.0844960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8553 | −0.822597 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.73705i | 0.163153i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.06752i | 0.0710409i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.49236 | 0.257137 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.12351 | 0.278470 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.93214i | 0.168873i | 0.996429 | + | 0.0844367i | \(0.0269091\pi\) | ||||
−0.996429 | + | 0.0844367i | \(0.973091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.9411i | 1.36436i | 0.731183 | + | 0.682181i | \(0.238968\pi\) | ||||
−0.731183 | + | 0.682181i | \(0.761032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.99070 | −0.0679217 | −0.0339608 | − | 0.999423i | \(-0.510812\pi\) | ||||
−0.0339608 | + | 0.999423i | \(0.510812\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0887944 | 0.00302611 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 31.9817i | − 1.08867i | −0.838868 | − | 0.544335i | \(-0.816782\pi\) | ||||
0.838868 | − | 0.544335i | \(-0.183218\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 4.84635i | − 0.164591i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.7851 | −0.739010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.4763 | 1.06653 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 28.0507i | − 0.949374i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 22.2917i | − 0.752737i | −0.926470 | − | 0.376369i | \(-0.877173\pi\) | ||||
0.926470 | − | 0.376369i | \(-0.122827\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.13281 | 0.0382087 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.6912 | 1.20247 | 0.601233 | − | 0.799073i | \(-0.294676\pi\) | ||||
0.601233 | + | 0.799073i | \(0.294676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 17.9948i | − 0.605572i | −0.953059 | − | 0.302786i | \(-0.902083\pi\) | ||||
0.953059 | − | 0.302786i | \(-0.0979168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.3566i | 0.817813i | 0.912576 | + | 0.408907i | \(0.134090\pi\) | ||||
−0.912576 | + | 0.408907i | \(0.865910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.93995 | −0.0650637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.2902 | 1.18227 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 0.759053i | − 0.0254007i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.859386i | 0.0286941i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.49493 | 0.316674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26819 | 0.0422495 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 0.363288i | − 0.0120895i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.73821i | 0.190534i | 0.995452 | + | 0.0952671i | \(0.0303705\pi\) | ||||
−0.995452 | + | 0.0952671i | \(0.969629\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.13538 | 0.0708261 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8291 | −1.55152 | −0.775759 | − | 0.631029i | \(-0.782633\pi\) | ||||
−0.775759 | + | 0.631029i | \(0.782633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 67.1623i | − 2.22275i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 0.835879i | − 0.0276032i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.32151 | −0.0765795 | −0.0382897 | − | 0.999267i | \(-0.512191\pi\) | ||||
−0.0382897 | + | 0.999267i | \(0.512191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.93995 | −0.195728 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 15.4961i | − 0.510060i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.05748i | 0.297487i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.5610 | 0.838628 | 0.419314 | − | 0.907841i | \(-0.362271\pi\) | ||||
0.419314 | + | 0.907841i | \(0.362271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.91794 | 0.226726 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.566620i | 0.0185503i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 25.7501i | − 0.841219i | −0.907242 | − | 0.420609i | \(-0.861816\pi\) | ||||
0.907242 | − | 0.420609i | \(-0.138184\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.48563 | 0.0811154 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.1261 | −0.949483 | −0.474741 | − | 0.880125i | \(-0.657458\pi\) | ||||
−0.474741 | + | 0.880125i | \(0.657458\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.01304i | − 0.0329891i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 6.21711i | − 0.202029i | −0.994885 | − | 0.101014i | \(-0.967791\pi\) | ||||
0.994885 | − | 0.101014i | \(-0.0322088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.5584 | −1.08935 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.671758 | −0.0217832 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 47.8266i | − 1.54925i | −0.632418 | − | 0.774627i | \(-0.717937\pi\) | ||||
0.632418 | − | 0.774627i | \(-0.282063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.77326i | 0.0896467i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.13538 | 0.133538 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.4763 | −0.434720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.3562i | 1.33269i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 37.2301i | − 1.19724i | −0.801033 | − | 0.598620i | \(-0.795716\pi\) | ||||
0.801033 | − | 0.598620i | \(-0.204284\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0820605 | 0.00263616 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.8359 | 1.21421 | 0.607106 | − | 0.794621i | \(-0.292331\pi\) | ||||
0.607106 | + | 0.794621i | \(0.292331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.658720i | 0.0211176i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.8684i | 1.78739i | 0.448678 | + | 0.893694i | \(0.351895\pi\) | ||||
−0.448678 | + | 0.893694i | \(0.648105\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.6311 | 1.33054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.0660 | 0.896079 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.93738i | 0.221268i | 0.993861 | + | 0.110634i | \(0.0352881\pi\) | ||||
−0.993861 | + | 0.110634i | \(0.964712\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 0.0622883i | − 0.00198266i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.14468 | −0.131793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.5897 | 1.16231 | 0.581155 | − | 0.813793i | \(-0.302601\pi\) | ||||
0.581155 | + | 0.813793i | \(0.302601\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.54792i | 0.207792i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.7538i | 1.06899i | 0.845170 | + | 0.534497i | \(0.179499\pi\) | ||||
−0.845170 | + | 0.534497i | \(0.820501\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.7098 | 0.465398 |
(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 | 1900.2.c.g.1749.3 | 6 | ||
5.2 | odd | 4 | 1900.2.a.f.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 1900.2.a.h.1.2 | yes | 3 | ||
5.4 | even | 2 | inner | 1900.2.c.g.1749.4 | 6 | ||
20.3 | even | 4 | 7600.2.a.bj.1.2 | 3 | |||
20.7 | even | 4 | 7600.2.a.by.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.f.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
1900.2.a.h.1.2 | yes | 3 | 5.3 | odd | 4 | ||
1900.2.c.g.1749.3 | 6 | 1.1 | even | 1 | trivial | ||
1900.2.c.g.1749.4 | 6 | 5.4 | even | 2 | inner | ||
7600.2.a.bj.1.2 | 3 | 20.3 | even | 4 | |||
7600.2.a.by.1.2 | 3 | 20.7 | even | 4 |