Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,3,Mod(97,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.b (of order \(2\), degree \(1\), 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: | \(5.34061318146\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2048.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Root | \(1.84776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.97 |
Dual form | 196.3.b.b.97.2 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.317025i | 0.105675i | 0.998603 | + | 0.0528376i | \(0.0168266\pi\) | ||||
−0.998603 | + | 0.0528376i | \(0.983173\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 5.67459i | − 1.13492i | −0.823401 | − | 0.567459i | \(-0.807926\pi\) | ||||
0.823401 | − | 0.567459i | \(-0.192074\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.89949 | 0.988833 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.8995 | −1.44541 | −0.722704 | − | 0.691157i | \(-0.757101\pi\) | ||||
−0.722704 | + | 0.691157i | \(0.757101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 20.1940i | − 1.55339i | −0.629879 | − | 0.776694i | \(-0.716895\pi\) | ||||
0.629879 | − | 0.776694i | \(-0.283105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.79899 | 0.119933 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.951076i | 0.0559456i | 0.999609 | + | 0.0279728i | \(0.00890519\pi\) | ||||
−0.999609 | + | 0.0279728i | \(0.991095\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 31.8602i | − 1.67686i | −0.545013 | − | 0.838428i | \(-0.683475\pi\) | ||||
0.545013 | − | 0.838428i | \(-0.316525\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 26.0000 | 1.13043 | 0.565217 | − | 0.824942i | \(-0.308792\pi\) | ||||
0.565217 | + | 0.824942i | \(0.308792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.20101 | −0.288040 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.67459i | 0.210170i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.7990 | 0.958586 | 0.479293 | − | 0.877655i | \(-0.340893\pi\) | ||||
0.479293 | + | 0.877655i | \(0.340893\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 15.1535i | 0.488822i | 0.969672 | + | 0.244411i | \(0.0785946\pi\) | ||||
−0.969672 | + | 0.244411i | \(0.921405\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 5.04054i | − 0.152744i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.0000 | −0.864865 | −0.432432 | − | 0.901666i | \(-0.642345\pi\) | ||||
−0.432432 | + | 0.901666i | \(0.642345\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.40202 | 0.164154 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 17.3408i | − 0.422946i | −0.977384 | − | 0.211473i | \(-0.932174\pi\) | ||||
0.977384 | − | 0.211473i | \(-0.0678261\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −59.2965 | −1.37899 | −0.689494 | − | 0.724292i | \(-0.742167\pi\) | ||||
−0.689494 | + | 0.724292i | \(0.742167\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 50.5010i | − 1.12224i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 76.3378i | 1.62421i | 0.583513 | + | 0.812104i | \(0.301678\pi\) | ||||
−0.583513 | + | 0.812104i | \(0.698322\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.301515 | −0.00591206 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25.7990 | 0.486773 | 0.243387 | − | 0.969929i | \(-0.421742\pi\) | ||||
0.243387 | + | 0.969929i | \(0.421742\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 90.2232i | 1.64042i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.1005 | 0.177202 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 68.4440i | 1.16007i | 0.814592 | + | 0.580034i | \(0.196961\pi\) | ||||
−0.814592 | + | 0.580034i | \(0.803039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 54.2416i | 0.889206i | 0.895728 | + | 0.444603i | \(0.146655\pi\) | ||||
−0.895728 | + | 0.444603i | \(0.853345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −114.593 | −1.76297 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 87.3970 | 1.30443 | 0.652216 | − | 0.758033i | \(-0.273839\pi\) | ||||
0.652216 | + | 0.758033i | \(0.273839\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.24266i | 0.119459i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.4020 | 0.231014 | 0.115507 | − | 0.993307i | \(-0.463151\pi\) | ||||
0.115507 | + | 0.993307i | \(0.463151\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 70.3462i | − 0.963646i | −0.876269 | − | 0.481823i | \(-0.839975\pi\) | ||||
0.876269 | − | 0.481823i | \(-0.160025\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 2.28290i | − 0.0304387i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 40.2010 | 0.508874 | 0.254437 | − | 0.967089i | \(-0.418110\pi\) | ||||
0.254437 | + | 0.967089i | \(0.418110\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 78.2965 | 0.966623 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 71.5505i | 0.862055i | 0.902339 | + | 0.431027i | \(0.141849\pi\) | ||||
−0.902339 | + | 0.431027i | \(0.858151\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.39697 | 0.0634938 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.81298i | 0.101299i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 77.3207i | 0.868772i | 0.900727 | + | 0.434386i | \(0.143035\pi\) | ||||
−0.900727 | + | 0.434386i | \(0.856965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.80404 | −0.0516563 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −180.794 | −1.90309 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 128.328i | − 1.32297i | −0.749957 | − | 0.661486i | \(-0.769926\pi\) | ||||
0.749957 | − | 0.661486i | \(-0.230074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −141.497 | −1.42927 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 100.272i | 0.992796i | 0.868095 | + | 0.496398i | \(0.165344\pi\) | ||||
−0.868095 | + | 0.496398i | \(0.834656\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 49.2011i | − 0.477680i | −0.971059 | − | 0.238840i | \(-0.923233\pi\) | ||||
0.971059 | − | 0.238840i | \(-0.0767672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 29.5980 | 0.276617 | 0.138308 | − | 0.990389i | \(-0.455834\pi\) | ||||
0.138308 | + | 0.990389i | \(0.455834\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.1960 | −0.102715 | −0.0513576 | − | 0.998680i | \(-0.516355\pi\) | ||||
−0.0513576 | + | 0.998680i | \(0.516355\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 10.1448i | − 0.0913947i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 133.698 | 1.18317 | 0.591586 | − | 0.806242i | \(-0.298502\pi\) | ||||
0.591586 | + | 0.806242i | \(0.298502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 147.539i | − 1.28295i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 179.717i | − 1.53604i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 131.794 | 1.08921 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.49747 | 0.0446949 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 101.002i | − 0.808016i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 120.995 | 0.952716 | 0.476358 | − | 0.879251i | \(-0.341957\pi\) | ||||
0.476358 | + | 0.879251i | \(0.341957\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 18.7985i | − 0.145725i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 127.060i | − 0.969925i | −0.874535 | − | 0.484963i | \(-0.838833\pi\) | ||||
0.874535 | − | 0.484963i | \(-0.161167\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 32.2010 | 0.238526 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −149.899 | −1.09416 | −0.547078 | − | 0.837081i | \(-0.684260\pi\) | ||||
−0.547078 | + | 0.837081i | \(0.684260\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2661i | 0.102634i | 0.998682 | + | 0.0513171i | \(0.0163419\pi\) | ||||
−0.998682 | + | 0.0513171i | \(0.983658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.2010 | −0.171638 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 321.075i | 2.24528i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 157.748i | − 1.08792i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 50.6030 | 0.339618 | 0.169809 | − | 0.985477i | \(-0.445685\pi\) | ||||
0.169809 | + | 0.985477i | \(0.445685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −41.7990 | −0.276815 | −0.138407 | − | 0.990375i | \(-0.544198\pi\) | ||||
−0.138407 | + | 0.990375i | \(0.544198\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.46410i | 0.0553209i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 85.9899 | 0.554774 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 143.260i | − 0.912487i | −0.889855 | − | 0.456243i | \(-0.849195\pi\) | ||||
0.889855 | − | 0.456243i | \(-0.150805\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.17893i | 0.0514398i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 114.291 | 0.701174 | 0.350587 | − | 0.936530i | \(-0.385982\pi\) | ||||
0.350587 | + | 0.936530i | \(0.385982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −28.6030 | −0.173352 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 290.895i | − 1.74189i | −0.491382 | − | 0.870944i | \(-0.663508\pi\) | ||||
0.491382 | − | 0.870944i | \(-0.336492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −238.799 | −1.41301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 283.540i | − 1.65813i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 212.496i | 1.22830i | 0.789189 | + | 0.614151i | \(0.210501\pi\) | ||||
−0.789189 | + | 0.614151i | \(0.789499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.6985 | −0.122590 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.6081 | 0.131889 | 0.0659444 | − | 0.997823i | \(-0.478994\pi\) | ||||
0.0659444 | + | 0.997823i | \(0.478994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 156.384i | 0.864002i | 0.901873 | + | 0.432001i | \(0.142192\pi\) | ||||
−0.901873 | + | 0.432001i | \(0.857808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.1960 | −0.0939670 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 181.587i | 0.981551i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.1216i | − 0.0808643i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −245.588 | −1.28580 | −0.642900 | − | 0.765950i | \(-0.722269\pi\) | ||||
−0.642900 | + | 0.765950i | \(0.722269\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 57.4975 | 0.297914 | 0.148957 | − | 0.988844i | \(-0.452408\pi\) | ||||
0.148957 | + | 0.988844i | \(0.452408\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 36.3289i | − 0.186302i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 174.402 | 0.885289 | 0.442645 | − | 0.896697i | \(-0.354040\pi\) | ||||
0.442645 | + | 0.896697i | \(0.354040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 167.765i | 0.843042i | 0.906819 | + | 0.421521i | \(0.138504\pi\) | ||||
−0.906819 | + | 0.421521i | \(0.861496\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.7071i | 0.137846i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −98.4020 | −0.480010 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 231.387 | 1.11781 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 506.562i | 2.42374i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −81.7889 | −0.387625 | −0.193813 | − | 0.981039i | \(-0.562085\pi\) | ||||
−0.193813 | + | 0.981039i | \(0.562085\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.19986i | 0.0244125i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 336.483i | 1.56504i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.3015 | 0.101833 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.2061 | 0.0869053 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 91.4275i | 0.409989i | 0.978763 | + | 0.204994i | \(0.0657176\pi\) | ||||
−0.978763 | + | 0.204994i | \(0.934282\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −64.0854 | −0.284824 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 367.550i | − 1.61916i | −0.587007 | − | 0.809582i | \(-0.699694\pi\) | ||||
0.587007 | − | 0.809582i | \(-0.300306\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 12.0788i | − 0.0527460i | −0.999652 | − | 0.0263730i | \(-0.991604\pi\) | ||||
0.999652 | − | 0.0263730i | \(-0.00839575\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.69848 | −0.00728963 | −0.00364482 | − | 0.999993i | \(-0.501160\pi\) | ||||
−0.00364482 | + | 0.999993i | \(0.501160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 433.186 | 1.84334 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.7447i | 0.0537753i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 201.397 | 0.842665 | 0.421333 | − | 0.906906i | \(-0.361563\pi\) | ||||
0.421333 | + | 0.906906i | \(0.361563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 97.4192i | 0.404229i | 0.979362 | + | 0.202114i | \(0.0647813\pi\) | ||||
−0.979362 | + | 0.202114i | \(0.935219\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 75.8933i | 0.312318i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −643.387 | −2.60481 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.6833 | −0.0910977 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 77.2251i | − 0.307670i | −0.988097 | − | 0.153835i | \(-0.950838\pi\) | ||||
0.988097 | − | 0.153835i | \(-0.0491624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −413.387 | −1.63394 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.71098i | 0.00670971i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 363.682i | 1.41511i | 0.706660 | + | 0.707553i | \(0.250201\pi\) | ||||
−0.706660 | + | 0.707553i | \(0.749799\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 247.397 | 0.947881 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −410.593 | −1.56119 | −0.780595 | − | 0.625037i | \(-0.785084\pi\) | ||||
−0.780595 | + | 0.625037i | \(0.785084\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 146.399i | − 0.552448i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.5126 | −0.0918076 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 307.855i | 1.14444i | 0.820099 | + | 0.572222i | \(0.193918\pi\) | ||||
−0.820099 | + | 0.572222i | \(0.806082\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 178.417i | 0.658364i | 0.944266 | + | 0.329182i | \(0.106773\pi\) | ||||
−0.944266 | + | 0.329182i | \(0.893227\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 114.492 | 0.416336 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 96.1909 | 0.347260 | 0.173630 | − | 0.984811i | \(-0.444450\pi\) | ||||
0.173630 | + | 0.984811i | \(0.444450\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 134.858i | 0.483363i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −155.106 | −0.551977 | −0.275989 | − | 0.961161i | \(-0.589005\pi\) | ||||
−0.275989 | + | 0.961161i | \(0.589005\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 313.245i | − 1.10687i | −0.832892 | − | 0.553436i | \(-0.813316\pi\) | ||||
0.832892 | − | 0.553436i | \(-0.186684\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 57.3163i | − 0.201110i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 288.095 | 0.996870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 40.6833 | 0.139805 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 202.543i | 0.691271i | 0.938369 | + | 0.345636i | \(0.112337\pi\) | ||||
−0.938369 | + | 0.345636i | \(0.887663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 388.392 | 1.31658 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 90.2232i | − 0.303782i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 525.045i | − 1.75600i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.7889 | −0.104914 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 307.799 | 1.00918 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 378.772i | − 1.23378i | −0.787047 | − | 0.616892i | \(-0.788391\pi\) | ||||
0.787047 | − | 0.616892i | \(-0.211609\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.5980 | 0.0504789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 205.808i | 0.661763i | 0.943672 | + | 0.330882i | \(0.107346\pi\) | ||||
−0.943672 | + | 0.330882i | \(0.892654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 451.971i | − 1.44400i | −0.691894 | − | 0.721999i | \(-0.743224\pi\) | ||||
0.691894 | − | 0.721999i | \(-0.256776\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −83.3869 | −0.263050 | −0.131525 | − | 0.991313i | \(-0.541987\pi\) | ||||
−0.131525 | + | 0.991313i | \(0.541987\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −441.990 | −1.38555 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.38331i | 0.0292315i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.3015 | 0.0938127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 145.417i | 0.447438i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 3.54940i | − 0.0108544i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 153.487 | 0.463708 | 0.231854 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231854 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −284.784 | −0.855207 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 495.942i | − 1.48042i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 519.377 | 1.54118 | 0.770589 | − | 0.637333i | \(-0.219962\pi\) | ||||
0.770589 | + | 0.637333i | \(0.219962\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 42.3858i | 0.125032i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 240.933i | − 0.706548i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 46.7737 | 0.135576 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 84.4823 | 0.243465 | 0.121732 | − | 0.992563i | \(-0.461155\pi\) | ||||
0.121732 | + | 0.992563i | \(0.461155\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 187.959i | 0.538565i | 0.963061 | + | 0.269283i | \(0.0867866\pi\) | ||||
−0.963061 | + | 0.269283i | \(0.913213\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 114.593 | 0.326476 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 113.270i | − 0.320879i | −0.987046 | − | 0.160440i | \(-0.948709\pi\) | ||||
0.987046 | − | 0.160440i | \(-0.0512912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 93.0748i | − 0.262183i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 661.176 | 1.84172 | 0.920858 | − | 0.389899i | \(-0.127490\pi\) | ||||
0.920858 | + | 0.389899i | \(0.127490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −654.075 | −1.81184 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 41.7820i | 0.115102i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −399.186 | −1.09366 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 87.8781i | − 0.239450i | −0.992807 | − | 0.119725i | \(-0.961799\pi\) | ||||
0.992807 | − | 0.119725i | \(-0.0382013\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 154.324i | − 0.418223i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 426.201 | 1.14263 | 0.571315 | − | 0.820731i | \(-0.306433\pi\) | ||||
0.571315 | + | 0.820731i | \(0.306433\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 32.0202 | 0.0853872 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 561.374i | − 1.48905i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −719.879 | −1.89942 | −0.949709 | − | 0.313134i | \(-0.898621\pi\) | ||||
−0.949709 | + | 0.313134i | \(0.898621\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.3585i | 0.100678i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 241.503i | − 0.630557i | −0.948999 | − | 0.315278i | \(-0.897902\pi\) | ||||
0.948999 | − | 0.315278i | \(-0.102098\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −527.709 | −1.36359 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −265.407 | −0.682280 | −0.341140 | − | 0.940012i | \(-0.610813\pi\) | ||||
−0.341140 | + | 0.940012i | \(0.610813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.7280i | 0.0632429i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 40.2813 | 0.102497 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 228.124i | − 0.577530i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 181.112i | 0.456202i | 0.973637 | + | 0.228101i | \(0.0732517\pi\) | ||||
−0.973637 | + | 0.228101i | \(0.926748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −420.593 | −1.04886 | −0.524430 | − | 0.851454i | \(-0.675722\pi\) | ||||
−0.524430 | + | 0.851454i | \(0.675722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 306.010 | 0.759330 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 444.301i | − 1.09704i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 508.784 | 1.25008 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 146.145i | 0.357324i | 0.983911 | + | 0.178662i | \(0.0571768\pi\) | ||||
−0.983911 | + | 0.178662i | \(0.942823\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 47.5219i | − 0.115625i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 406.020 | 0.978362 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.52273 | −0.0108459 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 521.905i | 1.24560i | 0.782383 | + | 0.622798i | \(0.214004\pi\) | ||||
−0.782383 | + | 0.622798i | \(0.785996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 746.181 | 1.77240 | 0.886200 | − | 0.463302i | \(-0.153335\pi\) | ||||
0.886200 | + | 0.463302i | \(0.153335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 679.368i | 1.60607i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 6.84871i | − 0.0161146i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −101.789 | −0.237270 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 248.593 | 0.576782 | 0.288391 | − | 0.957513i | \(-0.406880\pi\) | ||||
0.288391 | + | 0.957513i | \(0.406880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 494.357i | 1.14170i | 0.821054 | + | 0.570851i | \(0.193387\pi\) | ||||
−0.821054 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 50.0101 | 0.114966 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 828.366i | − 1.89558i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 655.274i | 1.49265i | 0.665581 | + | 0.746325i | \(0.268184\pi\) | ||||
−0.665581 | + | 0.746325i | \(0.731816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39.3970 | −0.0889322 | −0.0444661 | − | 0.999011i | \(-0.514159\pi\) | ||||
−0.0444661 | + | 0.999011i | \(0.514159\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 438.764 | 0.985986 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.0424i | 0.0358891i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −700.362 | −1.55983 | −0.779913 | − | 0.625888i | \(-0.784737\pi\) | ||||
−0.779913 | + | 0.625888i | \(0.784737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 275.710i | 0.611330i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 13.2513i | − 0.0292524i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −353.477 | −0.773473 | −0.386737 | − | 0.922190i | \(-0.626398\pi\) | ||||
−0.386737 | + | 0.922190i | \(0.626398\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.39697 | −0.0117581 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 382.482i | 0.829680i | 0.909894 | + | 0.414840i | \(0.136162\pi\) | ||||
−0.909894 | + | 0.414840i | \(0.863838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −309.005 | −0.667398 | −0.333699 | − | 0.942680i | \(-0.608297\pi\) | ||||
−0.333699 | + | 0.942680i | \(0.608297\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.2610i | 0.0586258i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 460.278i | − 0.985605i | −0.870141 | − | 0.492803i | \(-0.835972\pi\) | ||||
0.870141 | − | 0.492803i | \(-0.164028\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 45.4172 | 0.0964271 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 942.784 | 1.99320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 229.426i | 0.483002i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 229.598 | 0.481337 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 14.9623i | − 0.0312366i | −0.999878 | − | 0.0156183i | \(-0.995028\pi\) | ||||
0.999878 | − | 0.0156183i | \(-0.00497166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 646.209i | 1.34347i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −728.211 | −1.50147 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −437.377 | −0.898104 | −0.449052 | − | 0.893506i | \(-0.648238\pi\) | ||||
−0.449052 | + | 0.893506i | \(0.648238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.2333i | 0.0740967i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −816.583 | −1.66310 | −0.831551 | − | 0.555449i | \(-0.812546\pi\) | ||||
−0.831551 | + | 0.555449i | \(0.812546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.4390i | 0.0536287i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 802.941i | 1.62210i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −249.005 | −0.499008 | −0.249504 | − | 0.968374i | \(-0.580268\pi\) | ||||
−0.249504 | + | 0.968374i | \(0.580268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 92.2212 | 0.184074 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 423.536i | 0.842020i | 0.907056 | + | 0.421010i | \(0.138324\pi\) | ||||
−0.907056 | + | 0.421010i | \(0.861676\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 569.005 | 1.12674 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 75.7053i | − 0.149320i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 775.138i | 1.52286i | 0.648245 | + | 0.761432i | \(0.275503\pi\) | ||||
−0.648245 | + | 0.761432i | \(0.724497\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 180.794 | 0.352425 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −279.196 | −0.542128 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1213.73i | − 2.34764i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −67.3667 | −0.129801 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 509.447i | − 0.977825i | −0.872333 | − | 0.488913i | \(-0.837394\pi\) | ||||
0.872333 | − | 0.488913i | \(-0.162606\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 528.150i | 1.00985i | 0.863164 | + | 0.504923i | \(0.168479\pi\) | ||||
−0.863164 | + | 0.504923i | \(0.831521\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.4121 | −0.0273475 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 147.000 | 0.277883 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 609.117i | 1.14711i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −350.181 | −0.657000 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 167.957i | − 0.313937i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.48436i | 0.0139374i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −529.598 | −0.978924 | −0.489462 | − | 0.872025i | \(-0.662807\pi\) | ||||
−0.489462 | + | 0.872025i | \(0.662807\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −49.5778 | −0.0913035 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 63.5325i | 0.116573i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9045 | 0.0309041 | 0.0154521 | − | 0.999881i | \(-0.495081\pi\) | ||||
0.0154521 | + | 0.999881i | \(0.495081\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 482.723i | 0.879276i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 885.683i | − 1.60741i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −57.5677 | −0.103726 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 893.960 | 1.60495 | 0.802477 | − | 0.596683i | \(-0.203515\pi\) | ||||
0.802477 | + | 0.596683i | \(0.203515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1197.43i | 2.14210i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.79394 | 0.00854535 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 97.1356i | 0.172532i | 0.996272 | + | 0.0862661i | \(0.0274935\pi\) | ||||
−0.996272 | + | 0.0862661i | \(0.972506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 758.685i | − 1.34280i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 760.181 | 1.33599 | 0.667997 | − | 0.744164i | \(-0.267152\pi\) | ||||
0.667997 | + | 0.744164i | \(0.267152\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 338.291 | 0.592454 | 0.296227 | − | 0.955118i | \(-0.404271\pi\) | ||||
0.296227 | + | 0.955118i | \(0.404271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 77.8576i | − 0.135877i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −187.226 | −0.325611 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 241.377i | 0.418332i | 0.977880 | + | 0.209166i | \(0.0670748\pi\) | ||||
−0.977880 | + | 0.209166i | \(0.932925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.2282i | 0.0314821i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −410.191 | −0.703586 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1019.82 | −1.74328 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 405.338i | − 0.690525i | −0.938506 | − | 0.345263i | \(-0.887790\pi\) | ||||
0.938506 | − | 0.345263i | \(-0.112210\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 482.794 | 0.819684 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 55.2899i | 0.0935531i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 148.331i | 0.250137i | 0.992148 | + | 0.125068i | \(0.0399151\pi\) | ||||
−0.992148 | + | 0.125068i | \(0.960085\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −53.1859 | −0.0890885 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 401.789 | 0.670766 | 0.335383 | − | 0.942082i | \(-0.391134\pi\) | ||||
0.335383 | + | 0.942082i | \(0.391134\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 782.716i | − 1.30236i | −0.758925 | − | 0.651178i | \(-0.774275\pi\) | ||||
0.758925 | − | 0.651178i | \(-0.225725\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 777.789 | 1.28987 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 747.877i | − 1.23616i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 131.373i | − 0.216430i | −0.994128 | − | 0.108215i | \(-0.965487\pi\) | ||||
0.994128 | − | 0.108215i | \(-0.0345134\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1541.57 | 2.52302 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1000.76 | −1.63257 | −0.816284 | − | 0.577651i | \(-0.803969\pi\) | ||||
−0.816284 | + | 0.577651i | \(0.803969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 31.1959i | − 0.0507251i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 738.563 | 1.19702 | 0.598511 | − | 0.801115i | \(-0.295759\pi\) | ||||
0.598511 | + | 0.801115i | \(0.295759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 953.904i | 1.54104i | 0.637416 | + | 0.770520i | \(0.280003\pi\) | ||||
−0.637416 | + | 0.770520i | \(0.719997\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 147.539i | 0.237584i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −753.171 | −1.20507 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −160.593 | −0.256129 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 30.4344i | − 0.0483854i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −743.176 | −1.17777 | −0.588887 | − | 0.808215i | \(-0.700434\pi\) | ||||
−0.588887 | + | 0.808215i | \(0.700434\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 25.9291i | − 0.0409623i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 686.597i | − 1.08126i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 145.970 | 0.228435 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 239.417 | 0.373506 | 0.186753 | − | 0.982407i | \(-0.440204\pi\) | ||||
0.186753 | + | 0.982407i | \(0.440204\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 812.453i | − 1.26353i | −0.775158 | − | 0.631767i | \(-0.782330\pi\) | ||||
0.775158 | − | 0.631767i | \(-0.217670\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −106.674 | −0.165386 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 712.845i | − 1.10177i | −0.834581 | − | 0.550885i | \(-0.814290\pi\) | ||||
0.834581 | − | 0.550885i | \(-0.185710\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 1088.23i | − 1.67677i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 296.583 | 0.454185 | 0.227093 | − | 0.973873i | \(-0.427078\pi\) | ||||
0.227093 | + | 0.973873i | \(0.427078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −721.015 | −1.10079 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 626.045i | − 0.952885i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −617.709 | −0.937342 | −0.468671 | − | 0.883373i | \(-0.655267\pi\) | ||||
−0.468671 | + | 0.883373i | \(0.655267\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 325.099i | 0.491829i | 0.969292 | + | 0.245915i | \(0.0790883\pi\) | ||||
−0.969292 | + | 0.245915i | \(0.920912\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.08881i | 0.00918372i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 722.774 | 1.08362 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.9848 | −0.0433256 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 862.414i | − 1.28527i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −793.899 | −1.17964 | −0.589821 | − | 0.807534i | \(-0.700802\pi\) | ||||
−0.589821 | + | 0.807534i | \(0.700802\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 40.8628i | − 0.0605375i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 342.980i | − 0.506617i | −0.967386 | − | 0.253309i | \(-0.918481\pi\) | ||||
0.967386 | − | 0.253309i | \(-0.0815188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 116.523 | 0.171105 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1192.16 | −1.74548 | −0.872738 | − | 0.488188i | \(-0.837658\pi\) | ||||
−0.872738 | + | 0.488188i | \(0.837658\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 850.619i | 1.24178i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.82929 | 0.00557394 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 520.986i | − 0.756148i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 312.961i | 0.452911i | 0.974022 | + | 0.226455i | \(0.0727137\pi\) | ||||
−0.974022 | + | 0.226455i | \(0.927286\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 80.9545 | 0.116481 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.4924 | 0.0236620 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 0.538463i | 0 0.000770333i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 414.010 | 0.590599 | 0.295300 | − | 0.955405i | \(-0.404581\pi\) | ||||
0.295300 | + | 0.955405i | \(0.404581\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1019.53i | 1.45025i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 137.331i | 0.194796i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1123.96 | 1.58527 | 0.792637 | − | 0.609694i | \(-0.208707\pi\) | ||||
0.792637 | + | 0.609694i | \(0.208707\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 357.769 | 0.503191 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 393.991i | 0.552582i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1821.97 | 2.54821 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 63.8479i | 0.0890487i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1085.72i | − 1.51004i | −0.655700 | − | 0.755021i | \(-0.727626\pi\) | ||||
0.655700 | − | 0.755021i | \(-0.272374\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.8843 | −0.0427169 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −200.181 | −0.276111 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 270.606i | − 0.372223i | −0.982529 | − | 0.186111i | \(-0.940412\pi\) | ||||
0.982529 | − | 0.186111i | \(-0.0595885\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 680.608 | 0.933619 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 56.3954i | − 0.0771484i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 308.298i | − 0.420598i | −0.977637 | − | 0.210299i | \(-0.932556\pi\) | ||||
0.977637 | − | 0.210299i | \(-0.0674437\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1389.57 | −1.88544 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 272.523 | 0.368772 | 0.184386 | − | 0.982854i | \(-0.440970\pi\) | ||||
0.184386 | + | 0.982854i | \(0.440970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 203.970i | − 0.275263i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −225.196 | −0.303090 | −0.151545 | − | 0.988450i | \(-0.548425\pi\) | ||||
−0.151545 | + | 0.988450i | \(0.548425\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 287.152i | − 0.385438i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 636.764i | 0.852428i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −511.387 | −0.680941 | −0.340471 | − | 0.940255i | \(-0.610586\pi\) | ||||
−0.340471 | + | 0.940255i | \(0.610586\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.4823 | 0.0325130 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 237.192i | 0.314162i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −779.598 | −1.02985 | −0.514926 | − | 0.857235i | \(-0.672181\pi\) | ||||
−0.514926 | + | 0.857235i | \(0.672181\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 131.054i | − 0.172667i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 195.028i | − 0.256278i | −0.991756 | − | 0.128139i | \(-0.959100\pi\) | ||||
0.991756 | − | 0.128139i | \(-0.0409004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 48.0303 | 0.0627847 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1382.16 | 1.80203 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 73.8956i | − 0.0960931i | −0.998845 | − | 0.0480465i | \(-0.984700\pi\) | ||||
0.998845 | − | 0.0480465i | \(-0.0152996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −115.296 | −0.149541 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 185.930i | 0.240530i | 0.992742 | + | 0.120265i | \(0.0383744\pi\) | ||||
−0.992742 | + | 0.120265i | \(0.961626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 109.120i | − 0.140801i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −552.482 | −0.709220 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −260.784 | −0.333910 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 157.748i | 0.201466i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −812.944 | −1.03560 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 713.704i | − 0.906866i | −0.891290 | − | 0.453433i | \(-0.850199\pi\) | ||||
0.891290 | − | 0.453433i | \(-0.149801\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 130.168i | − 0.164979i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1095.36 | 1.38128 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 46.4121 | 0.0583800 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 908.540i | 1.13995i | 0.821662 | + | 0.569975i | \(0.193047\pi\) | ||||
−0.821662 | + | 0.569975i | \(0.806953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −72.6030 | −0.0908674 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 688.115i | 0.859070i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1118.47i | 1.39286i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −97.5980 | −0.120939 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −320.111 | −0.395687 | −0.197843 | − | 0.980234i | \(-0.563394\pi\) | ||||
−0.197843 | + | 0.980234i | \(0.563394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 839.749i | 1.03545i | 0.855547 | + | 0.517724i | \(0.173221\pi\) | ||||
−0.855547 | + | 0.517724i | \(0.826779\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −56.5626 | −0.0695727 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 648.557i | − 0.795776i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1889.20i | 2.31236i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 129.960 | 0.158294 | 0.0791471 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791471 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 800.965 | 0.973226 | 0.486613 | − | 0.873618i | \(-0.338232\pi\) | ||||
0.486613 | + | 0.873618i | \(0.338232\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 36.2970i | 0.0439964i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 289.156 | 0.349644 | 0.174822 | − | 0.984600i | \(-0.444065\pi\) | ||||
0.174822 | + | 0.984600i | \(0.444065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 316.541i | 0.381835i | 0.981606 | + | 0.190917i | \(0.0611463\pi\) | ||||
−0.981606 | + | 0.190917i | \(0.938854\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.4950i | 0.0366967i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1650.71 | −1.97690 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −85.9899 | −0.102736 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 802.370i | − 0.956341i | −0.878267 | − | 0.478171i | \(-0.841300\pi\) | ||||
0.878267 | − | 0.478171i | \(-0.158700\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −68.2162 | −0.0811132 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 49.1724i | − 0.0583302i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1355.09i | 1.60365i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 99.3066 | 0.116969 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −832.000 | −0.977673 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 235.386i | − 0.275950i | −0.990436 | − | 0.137975i | \(-0.955941\pi\) | ||||
0.990436 | − | 0.137975i | \(-0.0440594\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1608.97 | −1.88184 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1416.28i | 1.65260i | 0.563232 | + | 0.826299i | \(0.309558\pi\) | ||||
−0.563232 | + | 0.826299i | \(0.690442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1290.10i | 1.50187i | 0.660378 | + | 0.750933i | \(0.270396\pi\) | ||||
−0.660378 | + | 0.750933i | \(0.729604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −372.161 | −0.431241 | −0.215620 | − | 0.976477i | \(-0.569177\pi\) | ||||
−0.215620 | + | 0.976477i | \(0.569177\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1205.83 | 1.39402 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 91.3336i | 0.105344i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −639.176 | −0.735530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1764.90i | − 2.02629i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1142.06i | − 1.30820i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −778.593 | −0.887791 | −0.443896 | − | 0.896078i | \(-0.646404\pi\) | ||||
−0.443896 | + | 0.896078i | \(0.646404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −64.2111 | −0.0730502 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1206.76i | 1.36976i | 0.728657 | + | 0.684879i | \(0.240145\pi\) | ||||
−0.728657 | + | 0.684879i | \(0.759855\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1132.77 | 1.28287 | 0.641435 | − | 0.767178i | \(-0.278340\pi\) | ||||
0.641435 | + | 0.767178i | \(0.278340\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 123.130i | 0.139130i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 728.824i | − 0.821673i | −0.911709 | − | 0.410836i | \(-0.865237\pi\) | ||||
0.911709 | − | 0.410836i | \(-0.134763\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1244.87 | −1.39717 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2432.14 | 2.72356 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 133.966i | − 0.149683i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 166.453 | 0.185566 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 421.252i | 0.468578i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.5368i | 0.0272329i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 887.417 | 0.980571 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.61818 | −0.0106044 | −0.00530220 | − | 0.999986i | \(-0.501688\pi\) | ||||
−0.00530220 | + | 0.999986i | \(0.501688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 892.374i | 0.981709i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1015.41 | 1.11461 | 0.557304 | − | 0.830309i | \(-0.311836\pi\) | ||||
0.557304 | + | 0.830309i | \(0.311836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1137.62i | − 1.24602i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 97.5801i | 0.106645i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 483.015 | 0.525588 | 0.262794 | − | 0.964852i | \(-0.415356\pi\) | ||||
0.262794 | + | 0.964852i | \(0.415356\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 120.080 | 0.130380 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 331.223i | − 0.358855i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 230.432 | 0.249116 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 437.865i | − 0.472346i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 942.621i | 1.01466i | 0.861751 | + | 0.507331i | \(0.169368\pi\) | ||||
−0.861751 | + | 0.507331i | \(0.830632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −65.2465 | −0.0699319 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −85.8091 | −0.0917744 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1489.44i | 1.58958i | 0.606882 | + | 0.794792i | \(0.292420\pi\) | ||||
−0.606882 | + | 0.794792i | \(0.707580\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 143.286 | 0.152595 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1098.56i | 1.16744i | 0.811955 | + | 0.583720i | \(0.198403\pi\) | ||||
−0.811955 | + | 0.583720i | \(0.801597\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 450.861i | − 0.478113i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 304.905 | 0.321969 | 0.160984 | − | 0.986957i | \(-0.448533\pi\) | ||||
0.160984 | + | 0.986957i | \(0.448533\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1420.57 | −1.49692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 26.4357i | − 0.0277978i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −803.578 | −0.843209 | −0.421604 | − | 0.906780i | \(-0.638533\pi\) | ||||
−0.421604 | + | 0.906780i | \(0.638533\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1393.61i | 1.45928i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 140.122i | − 0.146418i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 731.372 | 0.761053 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 263.407 | 0.273528 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 326.275i | − 0.338109i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −93.6182 | −0.0968130 | −0.0484065 | − | 0.998828i | \(-0.515414\pi\) | ||||
−0.0484065 | + | 0.998828i | \(0.515414\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.60635i | 0.00991367i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 419.447i | 0.431974i | 0.976396 | + | 0.215987i | \(0.0692969\pi\) | ||||
−0.976396 | + | 0.215987i | \(0.930703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −46.1010 | −0.0472831 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1679.65 | −1.71919 | −0.859595 | − | 0.510977i | \(-0.829284\pi\) | ||||
−0.859595 | + | 0.510977i | \(0.829284\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1229.36i | − 1.25573i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −99.6384 | −0.101568 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 266.359i | − 0.270965i | −0.990780 | − | 0.135483i | \(-0.956742\pi\) | ||||
0.990780 | − | 0.135483i | \(-0.0432585\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 989.661i | − 1.00473i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1541.71 | −1.55886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 894.613 | 0.902738 | 0.451369 | − | 0.892337i | \(-0.350936\pi\) | ||||
0.451369 | + | 0.892337i | \(0.350936\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48.6594i | 0.0490024i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 952.000 | 0.956784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 638.884i | − 0.640806i | −0.947281 | − | 0.320403i | \(-0.896182\pi\) | ||||
0.947281 | − | 0.320403i | \(-0.103818\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 181.587i | − 0.181769i |
(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 | 196.3.b.b.97.3 | yes | 4 | |
3.2 | odd | 2 | 1764.3.d.e.685.3 | 4 | |||
4.3 | odd | 2 | 784.3.c.d.97.2 | 4 | |||
7.2 | even | 3 | 196.3.h.c.129.2 | 8 | |||
7.3 | odd | 6 | 196.3.h.c.117.2 | 8 | |||
7.4 | even | 3 | 196.3.h.c.117.3 | 8 | |||
7.5 | odd | 6 | 196.3.h.c.129.3 | 8 | |||
7.6 | odd | 2 | inner | 196.3.b.b.97.2 | ✓ | 4 | |
21.2 | odd | 6 | 1764.3.z.k.325.3 | 8 | |||
21.5 | even | 6 | 1764.3.z.k.325.2 | 8 | |||
21.11 | odd | 6 | 1764.3.z.k.901.2 | 8 | |||
21.17 | even | 6 | 1764.3.z.k.901.3 | 8 | |||
21.20 | even | 2 | 1764.3.d.e.685.2 | 4 | |||
28.3 | even | 6 | 784.3.s.g.705.3 | 8 | |||
28.11 | odd | 6 | 784.3.s.g.705.2 | 8 | |||
28.19 | even | 6 | 784.3.s.g.129.2 | 8 | |||
28.23 | odd | 6 | 784.3.s.g.129.3 | 8 | |||
28.27 | even | 2 | 784.3.c.d.97.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.3.b.b.97.2 | ✓ | 4 | 7.6 | odd | 2 | inner | |
196.3.b.b.97.3 | yes | 4 | 1.1 | even | 1 | trivial | |
196.3.h.c.117.2 | 8 | 7.3 | odd | 6 | |||
196.3.h.c.117.3 | 8 | 7.4 | even | 3 | |||
196.3.h.c.129.2 | 8 | 7.2 | even | 3 | |||
196.3.h.c.129.3 | 8 | 7.5 | odd | 6 | |||
784.3.c.d.97.2 | 4 | 4.3 | odd | 2 | |||
784.3.c.d.97.3 | 4 | 28.27 | even | 2 | |||
784.3.s.g.129.2 | 8 | 28.19 | even | 6 | |||
784.3.s.g.129.3 | 8 | 28.23 | odd | 6 | |||
784.3.s.g.705.2 | 8 | 28.11 | odd | 6 | |||
784.3.s.g.705.3 | 8 | 28.3 | even | 6 | |||
1764.3.d.e.685.2 | 4 | 21.20 | even | 2 | |||
1764.3.d.e.685.3 | 4 | 3.2 | odd | 2 | |||
1764.3.z.k.325.2 | 8 | 21.5 | even | 6 | |||
1764.3.z.k.325.3 | 8 | 21.2 | odd | 6 | |||
1764.3.z.k.901.2 | 8 | 21.11 | odd | 6 | |||
1764.3.z.k.901.3 | 8 | 21.17 | even | 6 |