Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(3649,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, 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("3800.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 760) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.5 | ||
Root | \(1.40680 - 0.144584i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.3649 |
Dual form | 3800.2.d.n.3649.2 |
$q$-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 \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(951\) | \(1901\) | \(1977\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.81361i | 1.04709i | 0.851999 | + | 0.523543i | \(0.175390\pi\) | ||||
−0.851999 | + | 0.523543i | \(0.824610\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.91638i | 1.85822i | 0.369807 | + | 0.929109i | \(0.379424\pi\) | ||||
−0.369807 | + | 0.929109i | \(0.620576\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.289169 | −0.0963895 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.578337 | 0.174375 | 0.0871876 | − | 0.996192i | \(-0.472212\pi\) | ||||
0.0871876 | + | 0.996192i | \(0.472212\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.39194i | − 1.77281i | −0.462914 | − | 0.886403i | \(-0.653196\pi\) | ||||
0.462914 | − | 0.886403i | \(-0.346804\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.710831i | 0.172402i | 0.996278 | + | 0.0862010i | \(0.0274727\pi\) | ||||
−0.996278 | + | 0.0862010i | \(0.972527\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.91638 | −1.94571 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 2.71083i | − 0.565247i | −0.959231 | − | 0.282624i | \(-0.908795\pi\) | ||||
0.959231 | − | 0.282624i | \(-0.0912048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.91638i | 0.946158i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.54359 | −1.21512 | −0.607558 | − | 0.794276i | \(-0.707851\pi\) | ||||
−0.607558 | + | 0.794276i | \(0.707851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.42166 | 0.255338 | 0.127669 | − | 0.991817i | \(-0.459250\pi\) | ||||
0.127669 | + | 0.991817i | \(0.459250\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.04888i | 0.182586i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.10278i | 1.49649i | 0.663424 | + | 0.748243i | \(0.269103\pi\) | ||||
−0.663424 | + | 0.748243i | \(0.730897\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.5925 | 1.85628 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.0489 | −1.72554 | −0.862772 | − | 0.505593i | \(-0.831274\pi\) | ||||
−0.862772 | + | 0.505593i | \(0.831274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.83276i | 0.889488i | 0.895658 | + | 0.444744i | \(0.146705\pi\) | ||||
−0.895658 | + | 0.444744i | \(0.853295\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.15667i | 0.168718i | 0.996435 | + | 0.0843591i | \(0.0268843\pi\) | ||||
−0.996435 | + | 0.0843591i | \(0.973116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.1708 | −2.45297 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.28917 | −0.180520 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.2736i | 1.82327i | 0.411004 | + | 0.911633i | \(0.365178\pi\) | ||||
−0.411004 | + | 0.911633i | \(0.634822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1.81361i | − 0.240218i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.3869 | −1.48245 | −0.741225 | − | 0.671256i | \(-0.765755\pi\) | ||||
−0.741225 | + | 0.671256i | \(0.765755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.04888 | −1.15859 | −0.579295 | − | 0.815118i | \(-0.696672\pi\) | ||||
−0.579295 | + | 0.815118i | \(0.696672\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.42166i | − 0.179113i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.97028i | − 0.362878i | −0.983402 | − | 0.181439i | \(-0.941925\pi\) | ||||
0.983402 | − | 0.181439i | \(-0.0580754\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.91638 | 0.591863 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 9.38692i | − 1.09866i | −0.835607 | − | 0.549328i | \(-0.814884\pi\) | ||||
0.835607 | − | 0.549328i | \(-0.185116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.84333i | 0.324027i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.37279 | −0.491977 | −0.245988 | − | 0.969273i | \(-0.579113\pi\) | ||||
−0.245988 | + | 0.969273i | \(0.579113\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.78389 | −1.08710 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.372787i | − 0.0409187i | −0.999791 | − | 0.0204593i | \(-0.993487\pi\) | ||||
0.999791 | − | 0.0204593i | \(-0.00651287\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 11.8675i | − 1.27233i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.6167 | 1.76136 | 0.880681 | − | 0.473710i | \(-0.157086\pi\) | ||||
0.880681 | + | 0.473710i | \(0.157086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 31.4252 | 3.29426 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.57834i | 0.267361i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 3.94610i | − 0.400666i | −0.979728 | − | 0.200333i | \(-0.935798\pi\) | ||||
0.979728 | − | 0.200333i | \(-0.0642024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.167237 | −0.0168079 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.20555 | −0.617475 | −0.308738 | − | 0.951147i | \(-0.599907\pi\) | ||||
−0.308738 | + | 0.951147i | \(0.599907\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.15165i | 0.803206i | 0.915814 | + | 0.401603i | \(0.131547\pi\) | ||||
−0.915814 | + | 0.401603i | \(0.868453\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.0680i | 1.26333i | 0.775240 | + | 0.631667i | \(0.217629\pi\) | ||||
−0.775240 | + | 0.631667i | \(0.782371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5925 | 1.11036 | 0.555179 | − | 0.831731i | \(-0.312650\pi\) | ||||
0.555179 | + | 0.831731i | \(0.312650\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.5089 | −1.56695 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 14.9355i | − 1.40502i | −0.711675 | − | 0.702509i | \(-0.752063\pi\) | ||||
0.711675 | − | 0.702509i | \(-0.247937\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.84835i | 0.170880i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.49472 | −0.320360 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6655 | −0.969593 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 20.0383i | − 1.80679i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 11.8867i | − 1.05477i | −0.849626 | − | 0.527385i | \(-0.823172\pi\) | ||||
0.849626 | − | 0.527385i | \(-0.176828\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.5783 | −0.931371 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.15667 | −0.800022 | −0.400011 | − | 0.916510i | \(-0.630994\pi\) | ||||
−0.400011 | + | 0.916510i | \(0.630994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.91638i | − 0.426304i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 13.3869i | − 1.14372i | −0.820351 | − | 0.571861i | \(-0.806222\pi\) | ||||
0.820351 | − | 0.571861i | \(-0.193778\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.42166 | −0.290222 | −0.145111 | − | 0.989415i | \(-0.546354\pi\) | ||||
−0.145111 | + | 0.989415i | \(0.546354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.09775 | −0.176663 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 3.69670i | − 0.309133i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 31.1411i | − 2.56847i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.36222 | 0.275444 | 0.137722 | − | 0.990471i | \(-0.456022\pi\) | ||||
0.137722 | + | 0.990471i | \(0.456022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.1950 | 1.72482 | 0.862412 | − | 0.506207i | \(-0.168953\pi\) | ||||
0.862412 | + | 0.506207i | \(0.168953\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 0.205550i | − 0.0166177i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7944i | 0.941300i | 0.882320 | + | 0.470650i | \(0.155980\pi\) | ||||
−0.882320 | + | 0.470650i | \(0.844020\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24.0731 | −1.90912 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.3275 | 1.05035 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.2439i | − 1.11567i | −0.829953 | − | 0.557833i | \(-0.811633\pi\) | ||||
0.829953 | − | 0.557833i | \(-0.188367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.47556i | 0.578476i | 0.957257 | + | 0.289238i | \(0.0934020\pi\) | ||||
−0.957257 | + | 0.289238i | \(0.906598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.8569 | −2.14284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.289169 | 0.0221133 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.05390i | 0.308212i | 0.988054 | + | 0.154106i | \(0.0492498\pi\) | ||||
−0.988054 | + | 0.154106i | \(0.950750\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 20.6514i | − 1.55225i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.95112 | −0.220577 | −0.110289 | − | 0.993900i | \(-0.535178\pi\) | ||||
−0.110289 | + | 0.993900i | \(0.535178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.66553 | 0.718433 | 0.359216 | − | 0.933254i | \(-0.383044\pi\) | ||||
0.359216 | + | 0.933254i | \(0.383044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 16.4111i | − 1.21314i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.411100i | 0.0300626i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −24.1708 | −1.75817 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.9058 | −1.15090 | −0.575452 | − | 0.817835i | \(-0.695174\pi\) | ||||
−0.575452 | + | 0.817835i | \(0.695174\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6116i | 1.12375i | 0.827222 | + | 0.561875i | \(0.189920\pi\) | ||||
−0.827222 | + | 0.561875i | \(0.810080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.6655i | 0.973628i | 0.873506 | + | 0.486814i | \(0.161841\pi\) | ||||
−0.873506 | + | 0.486814i | \(0.838159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.91638 | −0.632066 | −0.316033 | − | 0.948748i | \(-0.602351\pi\) | ||||
−0.316033 | + | 0.948748i | \(0.602351\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.38692 | 0.379964 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 32.1708i | − 2.25795i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.783887i | 0.0544839i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.578337 | −0.0400044 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.7980 | 1.36295 | 0.681476 | − | 0.731840i | \(-0.261338\pi\) | ||||
0.681476 | + | 0.731840i | \(0.261338\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.98944i | 0.474474i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.0242 | 1.15039 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.54359 | 0.305635 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.57331i | − 0.105357i | −0.998612 | − | 0.0526784i | \(-0.983224\pi\) | ||||
0.998612 | − | 0.0526784i | \(-0.0167758\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.0575i | 1.86224i | 0.364713 | + | 0.931120i | \(0.381167\pi\) | ||||
−0.364713 | + | 0.931120i | \(0.618833\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.47054 | −0.163258 | −0.0816289 | − | 0.996663i | \(-0.526012\pi\) | ||||
−0.0816289 | + | 0.996663i | \(0.526012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.15667 | −0.339284 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.15667i | 0.206801i | 0.994640 | + | 0.103400i | \(0.0329723\pi\) | ||||
−0.994640 | + | 0.103400i | \(0.967028\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 7.93051i | − 0.515142i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.74914 | 0.177827 | 0.0889137 | − | 0.996039i | \(-0.471660\pi\) | ||||
0.0889137 | + | 0.996039i | \(0.471660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.88164 | 0.572117 | 0.286058 | − | 0.958212i | \(-0.407655\pi\) | ||||
0.286058 | + | 0.958212i | \(0.407655\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.99498i | − 0.192128i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.39194i | 0.406710i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.676089 | 0.0428454 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.31335 | 0.398495 | 0.199248 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199248 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.56777i | − 0.0985651i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 7.83830i | − 0.488940i | −0.969657 | − | 0.244470i | \(-0.921386\pi\) | ||||
0.969657 | − | 0.244470i | \(-0.0786140\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.7527 | −2.78080 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.89220 | 0.117124 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.8711i | 0.855327i | 0.903938 | + | 0.427664i | \(0.140663\pi\) | ||||
−0.903938 | + | 0.427664i | \(0.859337\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.1361i | 1.84430i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.07306 | −0.247421 | −0.123710 | − | 0.992318i | \(-0.539479\pi\) | ||||
−0.123710 | + | 0.992318i | \(0.539479\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 56.9930i | 3.44937i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 16.1361i | − 0.969522i | −0.874647 | − | 0.484761i | \(-0.838907\pi\) | ||||
0.874647 | − | 0.484761i | \(-0.161093\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.411100 | −0.0246119 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.4600 | −0.683645 | −0.341822 | − | 0.939765i | \(-0.611044\pi\) | ||||
−0.341822 | + | 0.939765i | \(0.611044\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 21.7250i | − 1.29142i | −0.763585 | − | 0.645708i | \(-0.776563\pi\) | ||||
0.763585 | − | 0.645708i | \(-0.223437\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 54.3205i | − 3.20644i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4947 | 0.970278 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.15667 | 0.419532 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.91136i | − 0.345345i | −0.984979 | − | 0.172673i | \(-0.944760\pi\) | ||||
0.984979 | − | 0.172673i | \(-0.0552403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.84333i | 0.164986i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.3275 | −1.00207 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.6761 | −1.65286 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 11.2544i | − 0.646550i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.7194i | 1.69618i | 0.529854 | + | 0.848089i | \(0.322247\pi\) | ||||
−0.529854 | + | 0.848089i | \(0.677753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.7839 | −0.841026 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.407530 | −0.0231089 | −0.0115544 | − | 0.999933i | \(-0.503678\pi\) | ||||
−0.0115544 | + | 0.999933i | \(0.503678\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 0.338044i | − 0.0191074i | −0.999954 | − | 0.00955370i | \(-0.996959\pi\) | ||||
0.999954 | − | 0.00955370i | \(-0.00304108\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.75468i | 0.491712i | 0.969306 | + | 0.245856i | \(0.0790690\pi\) | ||||
−0.969306 | + | 0.245856i | \(0.920931\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.78440 | −0.211886 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.7003 | −1.32282 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 0.710831i | − 0.0395517i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.0242i | 1.16264i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.68665 | −0.313515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8675 | 1.31188 | 0.655938 | − | 0.754814i | \(-0.272273\pi\) | ||||
0.655938 | + | 0.754814i | \(0.272273\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.63224i | − 0.144246i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0439i | 0.547124i | 0.961854 | + | 0.273562i | \(0.0882018\pi\) | ||||
−0.961854 | + | 0.273562i | \(0.911798\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.0872 | 1.47117 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.822200 | 0.0445246 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 50.0036i | − 2.69994i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.6272i | 0.838913i | 0.907775 | + | 0.419456i | \(0.137779\pi\) | ||||
−0.907775 | + | 0.419456i | \(0.862221\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2544 | −0.923608 | −0.461804 | − | 0.886982i | \(-0.652798\pi\) | ||||
−0.461804 | + | 0.886982i | \(0.652798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31.4252 | 1.67735 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.2197i | 1.44876i | 0.689402 | + | 0.724379i | \(0.257873\pi\) | ||||
−0.689402 | + | 0.724379i | \(0.742127\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 6.33804i | − 0.335445i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.18137 | 0.379018 | 0.189509 | − | 0.981879i | \(-0.439310\pi\) | ||||
0.189509 | + | 0.981879i | \(0.439310\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 19.3431i | − 1.01525i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 9.15667i | − 0.477975i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) | ||||
0.971023 | − | 0.238987i | \(-0.0768154\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.19499 | 0.166324 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −65.2580 | −3.38803 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8.75468i | − 0.453300i | −0.973976 | − | 0.226650i | \(-0.927223\pi\) | ||||
0.973976 | − | 0.226650i | \(-0.0727774\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.8263i | 2.15416i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9164 | 0.663470 | 0.331735 | − | 0.943373i | \(-0.392366\pi\) | ||||
0.331735 | + | 0.943373i | \(0.392366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.5577 | 1.10444 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.64280i | − 0.0839431i | −0.999119 | − | 0.0419716i | \(-0.986636\pi\) | ||||
0.999119 | − | 0.0419716i | \(-0.0133639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.68665i | − 0.0857373i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8328 | 0.599945 | 0.299972 | − | 0.953948i | \(-0.403023\pi\) | ||||
0.299972 | + | 0.953948i | \(0.403023\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.92694 | 0.0974498 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 16.6066i | − 0.837692i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.1361i | 1.21135i | 0.795710 | + | 0.605677i | \(0.207098\pi\) | ||||
−0.795710 | + | 0.605677i | \(0.792902\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.91638 | 0.446377 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9789 | 0.997697 | 0.498849 | − | 0.866689i | \(-0.333756\pi\) | ||||
0.498849 | + | 0.866689i | \(0.333756\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.08719i | − 0.452665i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.26447i | 0.260950i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.66553 | −0.280142 | −0.140071 | − | 0.990141i | \(-0.544733\pi\) | ||||
−0.140071 | + | 0.990141i | \(0.544733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.2786 | 1.19758 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 55.9824i | − 2.75472i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 6.20555i | − 0.303887i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.6550 | −1.10677 | −0.553384 | − | 0.832926i | \(-0.686664\pi\) | ||||
−0.553384 | + | 0.832926i | \(0.686664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.5330 | −1.24440 | −0.622202 | − | 0.782857i | \(-0.713762\pi\) | ||||
−0.622202 | + | 0.782857i | \(0.713762\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 0.334474i | − 0.0162627i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 44.4877i | − 2.15291i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.70436 | 0.323689 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.7944 | −0.664455 | −0.332228 | − | 0.943199i | \(-0.607800\pi\) | ||||
−0.332228 | + | 0.943199i | \(0.607800\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 29.4444i | − 1.41501i | −0.706710 | − | 0.707504i | \(-0.749821\pi\) | ||||
0.706710 | − | 0.707504i | \(-0.250179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.71083i | 0.129677i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.5472 | 1.64885 | 0.824423 | − | 0.565974i | \(-0.191500\pi\) | ||||
0.824423 | + | 0.565974i | \(0.191500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.96526 | 0.236441 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 23.5577i | − 1.11926i | −0.828742 | − | 0.559631i | \(-0.810943\pi\) | ||||
0.828742 | − | 0.559631i | \(-0.189057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.09775i | 0.288414i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.49115 | 0.353529 | 0.176765 | − | 0.984253i | \(-0.443437\pi\) | ||||
0.176765 | + | 0.984253i | \(0.443437\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.38997 | −0.300892 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 38.4394i | 1.80604i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 38.5819i | − 1.80479i | −0.430914 | − | 0.902393i | \(-0.641809\pi\) | ||||
0.430914 | − | 0.902393i | \(-0.358191\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.49472 | −0.163119 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.9789 | −1.48940 | −0.744702 | − | 0.667397i | \(-0.767409\pi\) | ||||
−0.744702 | + | 0.667397i | \(0.767409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.8122i | 1.43196i | 0.698120 | + | 0.715981i | \(0.254020\pi\) | ||||
−0.698120 | + | 0.715981i | \(0.745980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 41.4600i | − 1.91854i | −0.282493 | − | 0.959269i | \(-0.591161\pi\) | ||||
0.282493 | − | 0.959269i | \(-0.408839\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.6030 | 0.674305 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.3905 | −0.985622 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.37330i | 0.155105i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.83830i | − 0.175744i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.93051 | 0.453737 | 0.226868 | − | 0.973925i | \(-0.427151\pi\) | ||||
0.226868 | + | 0.973925i | \(0.427151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 58.1844 | 2.65298 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.1708i | 1.09981i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.7789i | 0.896266i | 0.893967 | + | 0.448133i | \(0.147911\pi\) | ||||
−0.893967 | + | 0.448133i | \(0.852089\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.8328 | 1.16820 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1461 | −0.728664 | −0.364332 | − | 0.931269i | \(-0.618703\pi\) | ||||
−0.364332 | + | 0.931269i | \(0.618703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.65139i | − 0.209488i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.8222 | 1.73792 | 0.868960 | − | 0.494882i | \(-0.164789\pi\) | ||||
0.868960 | + | 0.494882i | \(0.164789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5577 | −0.605715 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.5436i | 0.559291i | 0.960103 | + | 0.279646i | \(0.0902170\pi\) | ||||
−0.960103 | + | 0.279646i | \(0.909783\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 50.5215i | − 2.24374i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.0278 | −1.10934 | −0.554668 | − | 0.832072i | \(-0.687155\pi\) | ||||
−0.554668 | + | 0.832072i | \(0.687155\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 46.1497 | 2.04154 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 4.91638i | − 0.217064i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.668948i | 0.0294203i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.35218 | −0.322725 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.6550 | −0.729667 | −0.364834 | − | 0.931073i | \(-0.618874\pi\) | ||||
−0.364834 | + | 0.931073i | \(0.618874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3608i | 1.06522i | 0.846360 | + | 0.532611i | \(0.178789\pi\) | ||||
−0.846360 | + | 0.532611i | \(0.821211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.01056i | 0.0440208i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.6514 | 0.680495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.29274 | 0.142893 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 70.6238i | 3.05906i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 5.35218i | − 0.230964i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.93051 | −0.427738 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.3622 | 0.660474 | 0.330237 | − | 0.943898i | \(-0.392871\pi\) | ||||
0.330237 | + | 0.943898i | \(0.392871\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.5295i | 0.752261i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.5527i | 1.13531i | 0.823266 | + | 0.567656i | \(0.192150\pi\) | ||||
−0.823266 | + | 0.567656i | \(0.807850\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.61665 | 0.111676 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.54359 | 0.278767 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 21.4983i | − 0.914200i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.9583i | 1.22700i | 0.789694 | + | 0.613501i | \(0.210239\pi\) | ||||
−0.789694 | + | 0.613501i | \(0.789761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.2827 | 1.57689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.745574 | −0.0314782 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.64280i | − 0.0692357i | −0.999401 | − | 0.0346179i | \(-0.988979\pi\) | ||||
0.999401 | − | 0.0346179i | \(-0.0110214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 48.1013i | − 2.02007i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.3416 | −0.601232 | −0.300616 | − | 0.953745i | \(-0.597192\pi\) | ||||
−0.300616 | + | 0.953745i | \(0.597192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.0177 | −1.63284 | −0.816420 | − | 0.577458i | \(-0.804045\pi\) | ||||
−0.816420 | + | 0.577458i | \(0.804045\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 28.8469i | − 1.20510i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 25.4947i | − 1.06136i | −0.847573 | − | 0.530680i | \(-0.821937\pi\) | ||||
0.847573 | − | 0.530680i | \(-0.178063\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.3133 | −1.17666 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.83276 | 0.0760358 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.67661i | 0.317933i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.72496i | 0.401392i | 0.979654 | + | 0.200696i | \(0.0643204\pi\) | ||||
−0.979654 | + | 0.200696i | \(0.935680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.42166 | −0.0585786 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.7839 | −1.01947 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 13.0388i | − 0.535441i | −0.963497 | − | 0.267720i | \(-0.913730\pi\) | ||||
0.963497 | − | 0.267720i | \(-0.0862703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 16.1708i | − 0.661827i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.6861 | 0.763495 | 0.381747 | − | 0.924267i | \(-0.375322\pi\) | ||||
0.381747 | + | 0.924267i | \(0.375322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7355 | 0.519493 | 0.259747 | − | 0.965677i | \(-0.416361\pi\) | ||||
0.259747 | + | 0.965677i | \(0.416361\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.858912i | 0.0349776i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 23.0645i | − 0.936158i | −0.883687 | − | 0.468079i | \(-0.844946\pi\) | ||||
0.883687 | − | 0.468079i | \(-0.155054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 58.3452 | 2.36427 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.39340 | 0.299105 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.7038i | 1.03817i | 0.854723 | + | 0.519084i | \(0.173727\pi\) | ||||
−0.854723 | + | 0.519084i | \(0.826273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.205550i | 0.00827514i | 0.999991 | + | 0.00413757i | \(0.00131703\pi\) | ||||
−0.999991 | + | 0.00413757i | \(0.998683\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.0872 | 0.445632 | 0.222816 | − | 0.974861i | \(-0.428475\pi\) | ||||
0.222816 | + | 0.974861i | \(0.428475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.3275 | 0.534813 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 81.6938i | 3.27299i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.04888i | − 0.0418881i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.47054 | −0.257997 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.4806 | 0.417226 | 0.208613 | − | 0.977998i | \(-0.433105\pi\) | ||||
0.208613 | + | 0.977998i | \(0.433105\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 35.9058i | 1.42713i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 109.755i | 4.34864i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.3694 | 1.47600 | 0.738001 | − | 0.674800i | \(-0.235770\pi\) | ||||
0.738001 | + | 0.674800i | \(0.235770\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.0172i | 1.65700i | 0.559992 | + | 0.828498i | \(0.310804\pi\) | ||||
−0.559992 | + | 0.828498i | \(0.689196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 23.4635i | − 0.922447i | −0.887284 | − | 0.461224i | \(-0.847411\pi\) | ||||
0.887284 | − | 0.461224i | \(-0.152589\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.58548 | −0.258503 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.6761 | −0.496815 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.6272i | 1.31593i | 0.753047 | + | 0.657967i | \(0.228583\pi\) | ||||
−0.753047 | + | 0.657967i | \(0.771417\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.71440i | 0.105899i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.9653 | −0.699827 | −0.349914 | − | 0.936782i | \(-0.613789\pi\) | ||||
−0.349914 | + | 0.936782i | \(0.613789\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5542 | 0.604987 | 0.302493 | − | 0.953152i | \(-0.402181\pi\) | ||||
0.302493 | + | 0.953152i | \(0.402181\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.24029i | 0.320026i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.7386i | 0.686841i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.85337 | 0.110318 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.23330 | −0.202029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2111i | 0.470703i | 0.971910 | + | 0.235351i | \(0.0756241\pi\) | ||||
−0.971910 | + | 0.235351i | \(0.924376\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.0680i | 1.65524i | 0.561290 | + | 0.827619i | \(0.310305\pi\) | ||||
−0.561290 | + | 0.827619i | \(0.689695\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.4005 | 0.744524 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −50.8852 | −1.94993 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 45.3850i | − 1.73661i | −0.496033 | − | 0.868303i | \(-0.665211\pi\) | ||||
0.496033 | − | 0.868303i | \(-0.334789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 4.48059i | − 0.170945i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 84.8440 | 3.23230 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.508852 | −0.0193576 | −0.00967882 | − | 0.999953i | \(-0.503081\pi\) | ||||
−0.00967882 | + | 0.999953i | \(0.503081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 0.822200i | − 0.0312328i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 7.85389i | − 0.297487i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.72496 | −0.216538 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.1844 | −1.51774 | −0.758872 | − | 0.651239i | \(-0.774249\pi\) | ||||
−0.758872 | + | 0.651239i | \(0.774249\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 9.10278i | − 0.343318i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 30.5089i | − 1.14740i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.0978 | −0.754787 | −0.377393 | − | 0.926053i | \(-0.623180\pi\) | ||||
−0.377393 | + | 0.926053i | \(0.623180\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.26447 | 0.0474214 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 3.85389i | − 0.144329i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.98587i | 0.186201i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.5925 | −1.32738 | −0.663688 | − | 0.748010i | \(-0.731010\pi\) | ||||
−0.663688 | + | 0.748010i | \(0.731010\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.0766 | −1.49253 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.1078i | 0.599055i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.1708i | 0.748094i | 0.927410 | + | 0.374047i | \(0.122030\pi\) | ||||
−0.927410 | + | 0.374047i | \(0.877970\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.9200 | −0.885924 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.14611 | −0.153349 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.1461i | 1.11347i | 0.830689 | + | 0.556736i | \(0.187947\pi\) | ||||
−0.830689 | + | 0.556736i | \(0.812053\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.71782i | − 0.0632768i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.0283 | −0.957465 | −0.478733 | − | 0.877961i | \(-0.658904\pi\) | ||||
−0.478733 | + | 0.877961i | \(0.658904\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.5925 | −0.425860 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.221136i | 0.00811269i | 0.999992 | + | 0.00405635i | \(0.00129118\pi\) | ||||
−0.999992 | + | 0.00405635i | \(0.998709\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.107798i | 0.00394413i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −64.2474 | −2.34755 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.9406 | 1.53043 | 0.765216 | − | 0.643773i | \(-0.222632\pi\) | ||||
0.765216 | + | 0.643773i | \(0.222632\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.4499i | 0.417259i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.7456i | 0.972084i | 0.873935 | + | 0.486042i | \(0.161560\pi\) | ||||
−0.873935 | + | 0.486042i | \(0.838440\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.84333 | 0.103206 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.6519 | −0.422381 | −0.211191 | − | 0.977445i | \(-0.567734\pi\) | ||||
−0.211191 | + | 0.977445i | \(0.567734\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 56.9930i | 2.06329i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 72.7846i | 2.62810i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.28917 | 0.334976 | 0.167488 | − | 0.985874i | \(-0.446434\pi\) | ||||
0.167488 | + | 0.985874i | \(0.446434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2156 | 0.511962 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 10.3225i | − 0.371273i | −0.982618 | − | 0.185637i | \(-0.940565\pi\) | ||||
0.982618 | − | 0.185637i | \(-0.0594347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 81.1638i | − 2.91174i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.0489 | 0.395867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 32.1708i | − 1.14969i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 49.8902i | − 1.77839i | −0.457524 | − | 0.889197i | \(-0.651264\pi\) | ||||
0.457524 | − | 0.889197i | \(-0.348736\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.1567 | −0.895601 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 73.4288 | 2.61083 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.8399i | 2.05396i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 28.7436i | − 1.01815i | −0.860722 | − | 0.509075i | \(-0.829987\pi\) | ||||
0.860722 | − | 0.509075i | \(-0.170013\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.822200 | −0.0290874 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.80501 | −0.169777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 5.42880i | − 0.191578i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.3905i | 0.893788i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.5124 | −1.35402 | −0.677012 | − | 0.735972i | \(-0.736726\pi\) | ||||
−0.677012 | + | 0.735972i | \(0.736726\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.1013 | −0.986771 | −0.493385 | − | 0.869811i | \(-0.664241\pi\) | ||||
−0.493385 | + | 0.869811i | \(0.664241\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.38692i | − 0.259071i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 5.83276i | − 0.204063i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.08719 | −0.317532 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.2650 | 0.777053 | 0.388527 | − | 0.921437i | \(-0.372984\pi\) | ||||
0.388527 | + | 0.921437i | \(0.372984\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.8363i | 1.38861i | 0.719682 | + | 0.694304i | \(0.244288\pi\) | ||||
−0.719682 | + | 0.694304i | \(0.755712\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.5874i | 1.68955i | 0.535121 | + | 0.844776i | \(0.320266\pi\) | ||||
−0.535121 | + | 0.844776i | \(0.679734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.9058 | 1.59437 | 0.797187 | − | 0.603732i | \(-0.206320\pi\) | ||||
0.797187 | + | 0.603732i | \(0.206320\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.2645 | 1.01517 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 12.2056i | − 0.422897i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.98944i | 0.241590i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.9688 | 0.965591 | 0.482796 | − | 0.875733i | \(-0.339621\pi\) | ||||
0.482796 | + | 0.875733i | \(0.339621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8186 | 0.476504 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 20.7839i | − 0.715835i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 52.4358i | − 1.80172i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 39.4005 | 1.35222 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.6761 | 0.845885 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.56777i | 0.259116i | 0.991572 | + | 0.129558i | \(0.0413558\pi\) | ||||
−0.991572 | + | 0.129558i | \(0.958644\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 21.4756i | − 0.733591i | −0.930302 | − | 0.366796i | \(-0.880455\pi\) | ||||
0.930302 | − | 0.366796i | \(-0.119545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.0177 | 1.12655 | 0.563275 | − | 0.826270i | \(-0.309541\pi\) | ||||
0.563275 | + | 0.826270i | \(0.309541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 98.5160 | 3.35742 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.6605i | 0.635211i | 0.948223 | + | 0.317605i | \(0.102879\pi\) | ||||
−0.948223 | + | 0.317605i | \(0.897121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.9149i | 1.01596i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.52894 | −0.0857886 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.9859 | −0.643312 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.14109i | 0.0386200i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.7925i | 1.95151i | 0.218858 | + | 0.975757i | \(0.429767\pi\) | ||||
−0.218858 | + | 0.975757i | \(0.570233\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.7209 | 0.361606 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.2338 | 1.22075 | 0.610374 | − | 0.792113i | \(-0.291019\pi\) | ||||
0.610374 | + | 0.792113i | \(0.291019\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.98944i | − 0.100603i | −0.998734 | − | 0.0503013i | \(-0.983982\pi\) | ||||
0.998734 | − | 0.0503013i | \(-0.0160182\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.2494i | 1.41860i | 0.704909 | + | 0.709298i | \(0.250988\pi\) | ||||
−0.704909 | + | 0.709298i | \(0.749012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 58.4394 | 1.95999 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.65838 | −0.189563 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.15667i | − 0.0387066i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 31.4252i | − 1.04926i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.30279 | −0.310265 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.43528 | −0.314335 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 52.0071i | − 1.73069i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.97080i | − 0.0654392i | −0.999465 | − | 0.0327196i | \(-0.989583\pi\) | ||||
0.999465 | − | 0.0327196i | \(-0.0104168\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.79445 | 0.0595181 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.98995 | 0.330982 | 0.165491 | − | 0.986211i | \(-0.447079\pi\) | ||||
0.165491 | + | 0.986211i | \(0.447079\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 0.215597i | − 0.00713520i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 45.0177i | − 1.48662i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.24029 | −0.139874 | −0.0699372 | − | 0.997551i | \(-0.522280\pi\) | ||||
−0.0699372 | + | 0.997551i | \(0.522280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −53.8993 | −1.77604 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.35720i | − 0.0774206i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.1531 | 0.431539 | 0.215770 | − | 0.976444i | \(-0.430774\pi\) | ||||
0.215770 | + | 0.976444i | \(0.430774\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.1708 | 0.562750 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 0.739098i | − 0.0241970i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.5436i | 1.25916i | 0.776934 | + | 0.629582i | \(0.216774\pi\) | ||||
−0.776934 | + | 0.629582i | \(0.783226\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.613080 | 0.0200071 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.91638 | −0.0950713 | −0.0475357 | − | 0.998870i | \(-0.515137\pi\) | ||||
−0.0475357 | + | 0.998870i | \(0.515137\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.9516i | 0.975360i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 58.4011i | − 1.89778i | −0.315608 | − | 0.948890i | \(-0.602208\pi\) | ||||
0.315608 | − | 0.948890i | \(-0.397792\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.0007 | −1.94770 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.8776 | −0.514865 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 36.8378i | − 1.19329i | −0.802504 | − | 0.596646i | \(-0.796499\pi\) | ||||
0.802504 | − | 0.596646i | \(-0.203501\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 6.86342i | − 0.221863i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 65.8152 | 2.12528 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9789 | −0.934802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 3.77886i | − 0.121772i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.0278i | 1.38368i | 0.722051 | + | 0.691840i | \(0.243199\pi\) | ||||
−0.722051 | + | 0.691840i | \(0.756801\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.28917 | 0.0414141 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.0177 | −1.57305 | −0.786526 | − | 0.617557i | \(-0.788123\pi\) | ||||
−0.786526 | + | 0.617557i | \(0.788123\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 16.8222i | − 0.539295i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 20.2383i | − 0.647481i | −0.946146 | − | 0.323741i | \(-0.895059\pi\) | ||||
0.946146 | − | 0.323741i | \(-0.104941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.61003 | 0.307138 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.35218 | −0.107027 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.6811i | 0.819100i | 0.912288 | + | 0.409550i | \(0.134314\pi\) | ||||
−0.912288 | + | 0.409550i | \(0.865686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 10.3133i | − 0.328277i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.8116 | 0.502781 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.56829 | 0.272181 | 0.136090 | − | 0.990696i | \(-0.456546\pi\) | ||||
0.136090 | + | 0.990696i | \(0.456546\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.2863i | 1.37365i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29.9688i | − 0.949122i | −0.880223 | − | 0.474561i | \(-0.842607\pi\) | ||||
0.880223 | − | 0.474561i | \(-0.157393\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44.7527 | −1.41591 |
(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 | 3800.2.d.n.3649.5 | 6 | ||
5.2 | odd | 4 | 760.2.a.i.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 3800.2.a.w.1.1 | 3 | |||
5.4 | even | 2 | inner | 3800.2.d.n.3649.2 | 6 | ||
15.2 | even | 4 | 6840.2.a.bm.1.1 | 3 | |||
20.3 | even | 4 | 7600.2.a.bp.1.3 | 3 | |||
20.7 | even | 4 | 1520.2.a.q.1.1 | 3 | |||
40.27 | even | 4 | 6080.2.a.br.1.3 | 3 | |||
40.37 | odd | 4 | 6080.2.a.bx.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.i.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
1520.2.a.q.1.1 | 3 | 20.7 | even | 4 | |||
3800.2.a.w.1.1 | 3 | 5.3 | odd | 4 | |||
3800.2.d.n.3649.2 | 6 | 5.4 | even | 2 | inner | ||
3800.2.d.n.3649.5 | 6 | 1.1 | even | 1 | trivial | ||
6080.2.a.br.1.3 | 3 | 40.27 | even | 4 | |||
6080.2.a.bx.1.1 | 3 | 40.37 | odd | 4 | |||
6840.2.a.bm.1.1 | 3 | 15.2 | even | 4 | |||
7600.2.a.bp.1.3 | 3 | 20.3 | even | 4 |