Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(449,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 17x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(2.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.449 |
Dual form | 1400.2.g.i.449.2 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.37228i | 1.36964i | 0.728714 | + | 0.684819i | \(0.240119\pi\) | ||||
−0.728714 | + | 0.684819i | \(0.759881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.62772 | −0.875906 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.37228 | 1.92132 | 0.960658 | − | 0.277736i | \(-0.0895839\pi\) | ||||
0.960658 | + | 0.277736i | \(0.0895839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.37228i | 1.21265i | 0.795216 | + | 0.606326i | \(0.207357\pi\) | ||||
−0.795216 | + | 0.606326i | \(0.792643\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.372281i | 0.0902915i | 0.998980 | + | 0.0451457i | \(0.0143752\pi\) | ||||
−0.998980 | + | 0.0451457i | \(0.985625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.74456 | 1.08848 | 0.544239 | − | 0.838930i | \(-0.316819\pi\) | ||||
0.544239 | + | 0.838930i | \(0.316819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.37228 | −0.517674 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4.74456i | − 0.989310i | −0.869090 | − | 0.494655i | \(-0.835294\pi\) | ||||
0.869090 | − | 0.494655i | \(-0.164706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.883156i | 0.169963i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.37228 | 0.811912 | 0.405956 | − | 0.913893i | \(-0.366939\pi\) | ||||
0.405956 | + | 0.913893i | \(0.366939\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.1168i | 2.63150i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.3723 | −1.66089 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.74456 | 1.05332 | 0.526662 | − | 0.850075i | \(-0.323443\pi\) | ||||
0.526662 | + | 0.850075i | \(0.323443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.74456i | − 1.33353i | −0.745267 | − | 0.666767i | \(-0.767678\pi\) | ||||
0.745267 | − | 0.666767i | \(-0.232322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.11684i | 1.03810i | 0.854744 | + | 0.519049i | \(0.173714\pi\) | ||||
−0.854744 | + | 0.519049i | \(0.826286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.883156 | −0.123667 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7446i | 1.47588i | 0.674867 | + | 0.737940i | \(0.264201\pi\) | ||||
−0.674867 | + | 0.737940i | \(0.735799\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.2554i | 1.49082i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.74456 | −0.351405 | −0.175703 | − | 0.984443i | \(-0.556220\pi\) | ||||
−0.175703 | + | 0.984443i | \(0.556220\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 2.62772i | − 0.331061i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.2554 | 1.35500 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.00000i | − 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.37228i | 0.726189i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.1168 | −1.70078 | −0.850389 | − | 0.526155i | \(-0.823633\pi\) | ||||
−0.850389 | + | 0.526155i | \(0.823633\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.97825 | −1.10869 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 9.48913i | − 1.04157i | −0.853689 | − | 0.520783i | \(-0.825640\pi\) | ||||
0.853689 | − | 0.520783i | \(-0.174360\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3723i | 1.11203i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7446 | −1.56292 | −0.781460 | − | 0.623955i | \(-0.785525\pi\) | ||||
−0.781460 | + | 0.623955i | \(0.785525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.37228 | −0.458340 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 18.9783i | − 1.96795i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.86141i | 1.00127i | 0.865657 | + | 0.500637i | \(0.166901\pi\) | ||||
−0.865657 | + | 0.500637i | \(0.833099\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.7446 | −1.68289 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.62772i | − 0.554516i | −0.960796 | − | 0.277258i | \(-0.910574\pi\) | ||||
0.960796 | − | 0.277258i | \(-0.0894256\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.74456i | − 0.845369i | −0.906277 | − | 0.422684i | \(-0.861088\pi\) | ||||
0.906277 | − | 0.422684i | \(-0.138912\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.372281 | −0.0356581 | −0.0178290 | − | 0.999841i | \(-0.505675\pi\) | ||||
−0.0178290 | + | 0.999841i | \(0.505675\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.74456 | −0.450334 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000i | 0.188144i | 0.995565 | + | 0.0940721i | \(0.0299884\pi\) | ||||
−0.995565 | + | 0.0940721i | \(0.970012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 11.4891i | − 1.06217i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.372281 | −0.0341270 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29.6060 | 2.69145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.0000i | 1.44267i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 8.00000i | − 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.7446 | 1.82646 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.74456 | −0.414534 | −0.207267 | − | 0.978284i | \(-0.566457\pi\) | ||||
−0.207267 | + | 0.978284i | \(0.566457\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.74456i | 0.411406i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 14.7446i | − 1.25971i | −0.776712 | − | 0.629857i | \(-0.783114\pi\) | ||||
0.776712 | − | 0.629857i | \(-0.216886\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.74456 | 0.402429 | 0.201214 | − | 0.979547i | \(-0.435511\pi\) | ||||
0.201214 | + | 0.979547i | \(0.435511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.8832 | −1.42182 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 27.8614i | 2.32989i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.37228i | − 0.195662i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.4891 | −1.26892 | −0.634459 | − | 0.772956i | \(-0.718777\pi\) | ||||
−0.634459 | + | 0.772956i | \(0.718777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1168 | 1.23019 | 0.615096 | − | 0.788452i | \(-0.289117\pi\) | ||||
0.615096 | + | 0.788452i | \(0.289117\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 0.978251i | − 0.0790869i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.4891i | 1.23617i | 0.786113 | + | 0.618083i | \(0.212091\pi\) | ||||
−0.786113 | + | 0.618083i | \(0.787909\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25.4891 | −2.02142 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.74456 | 0.373924 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.7446i | − 1.31154i | −0.754963 | − | 0.655768i | \(-0.772345\pi\) | ||||
0.754963 | − | 0.655768i | \(-0.227655\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.62772i | 0.435486i | 0.976006 | + | 0.217743i | \(0.0698695\pi\) | ||||
−0.976006 | + | 0.217743i | \(0.930131\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.11684 | −0.470526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.4674 | −0.953404 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 0.372281i | − 0.0283040i | −0.999900 | − | 0.0141520i | \(-0.995495\pi\) | ||||
0.999900 | − | 0.0141520i | \(-0.00450488\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 18.9783i | − 1.42649i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783 | 1.71748 | 0.858738 | − | 0.512416i | \(-0.171249\pi\) | ||||
0.858738 | + | 0.512416i | \(0.171249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.2337 | 1.20664 | 0.603320 | − | 0.797499i | \(-0.293844\pi\) | ||||
0.603320 | + | 0.797499i | \(0.293844\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 6.51087i | − 0.481298i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.37228i | 0.173478i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.883156 | −0.0642401 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.86141 | 0.279402 | 0.139701 | − | 0.990194i | \(-0.455386\pi\) | ||||
0.139701 | + | 0.990194i | \(0.455386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.74456i | 0.485484i | 0.970091 | + | 0.242742i | \(0.0780469\pi\) | ||||
−0.970091 | + | 0.242742i | \(0.921953\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.23369i | 0.586626i | 0.956016 | + | 0.293313i | \(0.0947578\pi\) | ||||
−0.956016 | + | 0.293313i | \(0.905242\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.48913 | −0.669311 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.37228i | 0.306874i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.4674i | 0.866543i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.2337 | 2.09131 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3723 | −0.989429 | −0.494714 | − | 0.869056i | \(-0.664727\pi\) | ||||
−0.494714 | + | 0.869056i | \(0.664727\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.9783i | 1.30037i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 8.00000i | − 0.543075i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.2337 | 0.961823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.62772 | −0.109492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.62772i | − 0.376860i | −0.982087 | − | 0.188430i | \(-0.939660\pi\) | ||||
0.982087 | − | 0.188430i | \(-0.0603398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 19.8614i | − 1.31825i | −0.752034 | − | 0.659124i | \(-0.770927\pi\) | ||||
0.752034 | − | 0.659124i | \(-0.229073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.2337 | 0.808425 | 0.404212 | − | 0.914665i | \(-0.367546\pi\) | ||||
0.404212 | + | 0.914665i | \(0.367546\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.1168 | −0.994615 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1.25544i | − 0.0822464i | −0.999154 | − | 0.0411232i | \(-0.986906\pi\) | ||||
0.999154 | − | 0.0411232i | \(-0.0130936\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 35.8614i | − 2.32945i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6277 | −0.881504 | −0.440752 | − | 0.897629i | \(-0.645288\pi\) | ||||
−0.440752 | + | 0.897629i | \(0.645288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.0000 | 1.67481 | 0.837404 | − | 0.546585i | \(-0.184072\pi\) | ||||
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 21.0217i | − 1.34855i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.7446i | 1.31994i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.5109 | 1.42657 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.74456 | 0.299474 | 0.149737 | − | 0.988726i | \(-0.452157\pi\) | ||||
0.149737 | + | 0.988726i | \(0.452157\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 30.2337i | − 1.90078i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4891i | 1.46521i | 0.680653 | + | 0.732606i | \(0.261696\pi\) | ||||
−0.680653 | + | 0.732606i | \(0.738304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.4891 | −0.711159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.2337i | 1.37099i | 0.728078 | + | 0.685494i | \(0.240414\pi\) | ||||
−0.728078 | + | 0.685494i | \(0.759586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 34.9783i | − 2.14063i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.48913 | 0.576423 | 0.288212 | − | 0.957567i | \(-0.406939\pi\) | ||||
0.288212 | + | 0.957567i | \(0.406939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 10.3723i | − 0.627759i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 24.9783i | − 1.50080i | −0.660985 | − | 0.750399i | \(-0.729861\pi\) | ||||
0.660985 | − | 0.750399i | \(-0.270139\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.0217 | 1.25854 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.6060 | 1.10994 | 0.554970 | − | 0.831871i | \(-0.312730\pi\) | ||||
0.554970 | + | 0.831871i | \(0.312730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8.88316i | − 0.528049i | −0.964516 | − | 0.264024i | \(-0.914950\pi\) | ||||
0.964516 | − | 0.264024i | \(-0.0850500\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.74456i | 0.398119i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8614 | 0.991847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.3940 | −1.37138 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.1168i | 1.46734i | 0.679505 | + | 0.733671i | \(0.262195\pi\) | ||||
−0.679505 | + | 0.733671i | \(0.737805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.62772i | 0.326553i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.7446 | 1.19969 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.74456 | 0.504028 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 14.2337i | − 0.817704i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 31.1168i | − 1.77593i | −0.459909 | − | 0.887966i | \(-0.652118\pi\) | ||||
0.459909 | − | 0.887966i | \(-0.347882\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.3505 | 0.759485 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7446 | −0.722678 | −0.361339 | − | 0.932435i | \(-0.617680\pi\) | ||||
−0.361339 | + | 0.932435i | \(0.617680\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.88316i | 0.162966i | 0.996675 | + | 0.0814828i | \(0.0259656\pi\) | ||||
−0.996675 | + | 0.0814828i | \(0.974034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 14.0000i | − 0.786318i | −0.919470 | − | 0.393159i | \(-0.871382\pi\) | ||||
0.919470 | − | 0.393159i | \(-0.128618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.8614 | 1.55994 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.7446 | 1.15785 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.76631i | 0.0982802i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 0.883156i | − 0.0488386i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.11684 | −0.392364 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 5.25544i | − 0.287996i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.48913i | 0.407959i | 0.978975 | + | 0.203979i | \(0.0653875\pi\) | ||||
−0.978975 | + | 0.203979i | \(0.934612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.74456 | −0.257689 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −50.9783 | −2.76063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.7446i | 1.32836i | 0.747574 | + | 0.664179i | \(0.231219\pi\) | ||||
−0.747574 | + | 0.664179i | \(0.768781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.4891 | −1.04323 | −0.521614 | − | 0.853181i | \(-0.674670\pi\) | ||||
−0.521614 | + | 0.853181i | \(0.674670\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.86141 | −0.206107 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.86141i | − 0.0990727i | −0.998772 | − | 0.0495363i | \(-0.984226\pi\) | ||||
0.998772 | − | 0.0495363i | \(-0.0157744\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 0.883156i | − 0.0467416i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.51087 | 0.184783 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 70.2337i | 3.68631i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 19.8614i | − 1.03676i | −0.855151 | − | 0.518378i | \(-0.826536\pi\) | ||||
0.855151 | − | 0.518378i | \(-0.173464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.7228 | −0.922613 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.7446 | −0.557830 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 30.7446i | − 1.59189i | −0.605367 | − | 0.795947i | \(-0.706974\pi\) | ||||
0.605367 | − | 0.795947i | \(-0.293026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.1168i | 0.984568i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.9783 | 0.972285 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 17.4891i | − 0.893653i | −0.894621 | − | 0.446826i | \(-0.852554\pi\) | ||||
0.894621 | − | 0.446826i | \(-0.147446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.9783i | 1.16805i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.8614 | −0.905609 | −0.452805 | − | 0.891610i | \(-0.649576\pi\) | ||||
−0.452805 | + | 0.891610i | \(0.649576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.76631 | 0.0893262 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 11.2554i | − 0.567762i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 31.6277i | − 1.58735i | −0.608342 | − | 0.793675i | \(-0.708165\pi\) | ||||
0.608342 | − | 0.793675i | \(-0.291835\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.2554 | −0.563477 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.6060 | −1.92789 | −0.963945 | − | 0.266101i | \(-0.914264\pi\) | ||||
−0.963945 | + | 0.266101i | \(0.914264\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 34.9783i | − 1.74239i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.7446i | 0.631725i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.4891 | −0.568101 | −0.284050 | − | 0.958809i | \(-0.591678\pi\) | ||||
−0.284050 | + | 0.958809i | \(0.591678\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.9783 | 1.72535 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8.00000i | − 0.393654i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.2554i | 0.551181i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.5109 | 0.708903 | 0.354451 | − | 0.935074i | \(-0.384668\pi\) | ||||
0.354451 | + | 0.935074i | \(0.384668\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.6060 | −0.906799 | −0.453400 | − | 0.891307i | \(-0.649789\pi\) | ||||
−0.453400 | + | 0.891307i | \(0.649789\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 18.7011i | − 0.909277i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.74456i | − 0.132819i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −66.0951 | −3.19110 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3723 | 0.884962 | 0.442481 | − | 0.896778i | \(-0.354098\pi\) | ||||
0.442481 | + | 0.896778i | \(0.354098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.9783i | 1.39261i | 0.717748 | + | 0.696303i | \(0.245173\pi\) | ||||
−0.717748 | + | 0.696303i | \(0.754827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 22.5109i | − 1.07684i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.23369 | 0.297518 | 0.148759 | − | 0.988874i | \(-0.452472\pi\) | ||||
0.148759 | + | 0.988874i | \(0.452472\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.62772 | 0.125129 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 16.7446i | − 0.795558i | −0.917481 | − | 0.397779i | \(-0.869781\pi\) | ||||
0.917481 | − | 0.397779i | \(-0.130219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 36.7446i | − 1.73796i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.1168 | −0.807794 | −0.403897 | − | 0.914805i | \(-0.632345\pi\) | ||||
−0.403897 | + | 0.914805i | \(0.632345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.9783 | 2.02377 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.8614i | 1.68492i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 5.25544i | − 0.245839i | −0.992417 | − | 0.122919i | \(-0.960774\pi\) | ||||
0.992417 | − | 0.122919i | \(-0.0392257\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.328782 | −0.0153463 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.25544 | −0.0584715 | −0.0292358 | − | 0.999573i | \(-0.509307\pi\) | ||||
−0.0292358 | + | 0.999573i | \(0.509307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6.51087i | − 0.302586i | −0.988489 | − | 0.151293i | \(-0.951656\pi\) | ||||
0.988489 | − | 0.151293i | \(-0.0483437\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.60597i | − 0.398237i | −0.979975 | − | 0.199118i | \(-0.936192\pi\) | ||||
0.979975 | − | 0.199118i | \(-0.0638078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.7446 | −1.69310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 55.7228i | − 2.56214i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 28.2337i | − 1.29273i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.2337 | −1.01588 | −0.507942 | − | 0.861392i | \(-0.669593\pi\) | ||||
−0.507942 | + | 0.861392i | \(0.669593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.74456 | −0.398718 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.2554i | 0.512140i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 30.2337i | − 1.37002i | −0.728534 | − | 0.685010i | \(-0.759798\pi\) | ||||
0.728534 | − | 0.685010i | \(-0.240202\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 39.7228 | 1.79633 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.1168 | 1.58480 | 0.792400 | − | 0.610001i | \(-0.208831\pi\) | ||||
0.792400 | + | 0.610001i | \(0.208831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.62772i | 0.0733088i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.8614 | −1.42631 | −0.713156 | − | 0.701005i | \(-0.752735\pi\) | ||||
−0.713156 | + | 0.701005i | \(0.752735\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.3505 | −0.596458 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 18.3723i | − 0.819180i | −0.912270 | − | 0.409590i | \(-0.865672\pi\) | ||||
0.912270 | − | 0.409590i | \(-0.134328\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 14.5109i | − 0.644451i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.9783 | 1.81633 | 0.908165 | − | 0.418613i | \(-0.137484\pi\) | ||||
0.908165 | + | 0.418613i | \(0.137484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | 0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.19019i | 0.185001i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.3505i | 1.99451i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.883156 | 0.0387662 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 36.4674i | − 1.59461i | −0.603579 | − | 0.797304i | \(-0.706259\pi\) | ||||
0.603579 | − | 0.797304i | \(-0.293741\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.97825i | − 0.129735i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.489125 | 0.0212663 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.0217 | 0.912266 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.4891i | 1.27732i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 54.5109i | 2.35232i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.37228 | −0.274474 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.3505 | −1.34786 | −0.673932 | − | 0.738793i | \(-0.735396\pi\) | ||||
−0.673932 | + | 0.738793i | \(0.735396\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 38.5109i | 1.65266i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.9783i | 1.32453i | 0.749268 | + | 0.662267i | \(0.230406\pi\) | ||||
−0.749268 | + | 0.662267i | \(0.769594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.21194 | 0.307798 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.7446 | 0.883748 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 15.1168i | − 0.642834i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.76631i | 0.159584i | 0.996812 | + | 0.0797919i | \(0.0254256\pi\) | ||||
−0.996812 | + | 0.0797919i | \(0.974574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.2337 | 1.61711 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.62772 | −0.237602 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.4891i | 0.737079i | 0.929612 | + | 0.368539i | \(0.120142\pi\) | ||||
−0.929612 | + | 0.368539i | \(0.879858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 9.97825i | − 0.419047i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.9783 | 1.04714 | 0.523571 | − | 0.851982i | \(-0.324599\pi\) | ||||
0.523571 | + | 0.851982i | \(0.324599\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.16034i | 0.382679i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.6060i | 0.941099i | 0.882374 | + | 0.470549i | \(0.155944\pi\) | ||||
−0.882374 | + | 0.470549i | \(0.844056\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.0000 | −0.664937 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.48913 | 0.393675 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 68.4674i | 2.83563i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.9783i | 1.44371i | 0.692046 | + | 0.721853i | \(0.256710\pi\) | ||||
−0.692046 | + | 0.721853i | \(0.743290\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.9565 | −1.56397 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.5326 | −0.803465 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 19.6277i | − 0.806014i | −0.915197 | − | 0.403007i | \(-0.867965\pi\) | ||||
0.915197 | − | 0.403007i | \(-0.132035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.9565i | 1.55346i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.6060 | 1.33224 | 0.666122 | − | 0.745843i | \(-0.267953\pi\) | ||||
0.666122 | + | 0.745843i | \(0.267953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5109 | 0.673493 | 0.336746 | − | 0.941595i | \(-0.390674\pi\) | ||||
0.336746 | + | 0.941595i | \(0.390674\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 10.5109i | − 0.428036i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.6060i | − 0.998725i | −0.866393 | − | 0.499363i | \(-0.833568\pi\) | ||||
0.866393 | − | 0.499363i | \(-0.166432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3723 | −0.420306 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.1168 | −1.25885 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 8.51087i | − 0.343751i | −0.985119 | − | 0.171875i | \(-0.945017\pi\) | ||||
0.985119 | − | 0.171875i | \(-0.0549827\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000i | 0.241551i | 0.992680 | + | 0.120775i | \(0.0385381\pi\) | ||||
−0.992680 | + | 0.120775i | \(0.961462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.7446 | 0.512247 | 0.256124 | − | 0.966644i | \(-0.417555\pi\) | ||||
0.256124 | + | 0.966644i | \(0.417555\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.19019 | 0.168146 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 14.7446i | − 0.590728i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 71.7228i | 2.86433i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.744563 | −0.0296877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.37228 | 0.0944390 | 0.0472195 | − | 0.998885i | \(-0.484964\pi\) | ||||
0.0472195 | + | 0.998885i | \(0.484964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 34.0951i | − 1.35516i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.37228i | − 0.173236i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.0217 | −0.831608 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3723i | 0.724532i | 0.932075 | + | 0.362266i | \(0.117997\pi\) | ||||
−0.932075 | + | 0.362266i | \(0.882003\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.0000i | 0.629025i | 0.949253 | + | 0.314512i | \(0.101841\pi\) | ||||
−0.949253 | + | 0.314512i | \(0.898159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −50.9783 | −2.00107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.9783 | 0.743816 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.00000i | 0.234798i | 0.993085 | + | 0.117399i | \(0.0374557\pi\) | ||||
−0.993085 | + | 0.117399i | \(0.962544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.7663i | 0.615102i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.1168 | 0.433051 | 0.216525 | − | 0.976277i | \(-0.430528\pi\) | ||||
0.216525 | + | 0.976277i | \(0.430528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7446 | 0.573497 | 0.286749 | − | 0.958006i | \(-0.407426\pi\) | ||||
0.286749 | + | 0.958006i | \(0.407426\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.86141i | − 0.149965i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 20.7446i | − 0.803233i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.3505 | 0.516161 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.4891 | −0.675160 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.7228i | 0.991542i | 0.868453 | + | 0.495771i | \(0.165114\pi\) | ||||
−0.868453 | + | 0.495771i | \(0.834886\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 15.3505i | − 0.589969i | −0.955502 | − | 0.294984i | \(-0.904686\pi\) | ||||
0.955502 | − | 0.294984i | \(-0.0953145\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.86141 | −0.378446 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 47.1168 | 1.80552 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0000i | 1.37750i | 0.724998 | + | 0.688751i | \(0.241841\pi\) | ||||
−0.724998 | + | 0.688751i | \(0.758159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.0217i | 1.10725i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −46.9783 | −1.78973 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.48913 | −0.360983 | −0.180492 | − | 0.983577i | \(-0.557769\pi\) | ||||
−0.180492 | + | 0.983577i | \(0.557769\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 16.7446i | − 0.636073i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.51087i | 0.0951062i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.97825 | 0.112648 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.13859 | 0.0807736 | 0.0403868 | − | 0.999184i | \(-0.487141\pi\) | ||||
0.0403868 | + | 0.999184i | \(0.487141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.48913i | 0.357889i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 6.00000i | − 0.225653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.60597 | −0.248092 | −0.124046 | − | 0.992276i | \(-0.539587\pi\) | ||||
−0.124046 | + | 0.992276i | \(0.539587\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 39.7228 | 1.48972 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.9565i | 1.42148i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 32.3288i | − 1.20734i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.25544 | −0.121407 | −0.0607037 | − | 0.998156i | \(-0.519334\pi\) | ||||
−0.0607037 | + | 0.998156i | \(0.519334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.62772 | 0.209587 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 61.6793i | 2.29388i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 32.0000i | − 1.18681i | −0.804902 | − | 0.593407i | \(-0.797782\pi\) | ||||
0.804902 | − | 0.593407i | \(-0.202218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.9348 | 0.738324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.25544 | 0.120407 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 10.1386i | − 0.374477i | −0.982314 | − | 0.187239i | \(-0.940046\pi\) | ||||
0.982314 | − | 0.187239i | \(-0.0599538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.4891i | 0.938904i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.6060 | 0.758003 | 0.379001 | − | 0.925396i | \(-0.376268\pi\) | ||||
0.379001 | + | 0.925396i | \(0.376268\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −49.2119 | −1.80785 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 6.51087i | − 0.238861i | −0.992843 | − | 0.119430i | \(-0.961893\pi\) | ||||
0.992843 | − | 0.119430i | \(-0.0381068\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.9348i | 0.912315i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.74456 | 0.319519 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.1386 | 0.734868 | 0.367434 | − | 0.930050i | \(-0.380236\pi\) | ||||
0.367434 | + | 0.930050i | \(0.380236\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.2554i | 0.410171i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.76631i | 0.136889i | 0.997655 | + | 0.0684445i | \(0.0218036\pi\) | ||||
−0.997655 | + | 0.0684445i | \(0.978196\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 71.7228 | 2.60337 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.97825 | 0.180461 | 0.0902307 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902307 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 0.372281i | − 0.0134775i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 34.9783i | − 1.26299i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.48913 | −0.125821 | −0.0629105 | − | 0.998019i | \(-0.520038\pi\) | ||||
−0.0629105 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.7228 | −2.00681 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.37228i | 0.157260i | 0.996904 | + | 0.0786300i | \(0.0250546\pi\) | ||||
−0.996904 | + | 0.0786300i | \(0.974945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 4.74456i | − 0.170210i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.0000 | 1.14652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.9783 | 1.82415 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.86141i | 0.137995i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.1168i | 1.10920i | 0.832119 | + | 0.554598i | \(0.187128\pi\) | ||||
−0.832119 | + | 0.554598i | \(0.812872\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −52.7446 | −1.87776 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 12.0000i | − 0.426132i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 15.6277i | − 0.553562i | −0.960933 | − | 0.276781i | \(-0.910732\pi\) | ||||
0.960933 | − | 0.276781i | \(-0.0892677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.64947 | −0.0937314 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.7446 | 1.36897 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 38.2337i | − 1.34924i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.2337i | 0.501050i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.3723 | −0.716251 | −0.358126 | − | 0.933673i | \(-0.616584\pi\) | ||||
−0.358126 | + | 0.933673i | \(0.616584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.7446 | 0.447522 | 0.223761 | − | 0.974644i | \(-0.428166\pi\) | ||||
0.223761 | + | 0.974644i | \(0.428166\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.5109i | 0.789491i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 41.4891i | − 1.45152i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.4891 | 0.401463 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.1168 | −0.876584 | −0.438292 | − | 0.898833i | \(-0.644416\pi\) | ||||
−0.438292 | + | 0.898833i | \(0.644416\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 8.00000i | − 0.278862i | −0.990232 | − | 0.139431i | \(-0.955473\pi\) | ||||
0.990232 | − | 0.139431i | \(-0.0445274\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 24.7446i | − 0.860453i | −0.902721 | − | 0.430226i | \(-0.858434\pi\) | ||||
0.902721 | − | 0.430226i | \(-0.141566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2337 | 0.424894 | 0.212447 | − | 0.977173i | \(-0.431857\pi\) | ||||
0.212447 | + | 0.977173i | \(0.431857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 59.2554 | 2.05555 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.372281i | − 0.0128988i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 7.06525i | − 0.244211i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.2554 | 0.388581 | 0.194290 | − | 0.980944i | \(-0.437760\pi\) | ||||
0.194290 | + | 0.980944i | \(0.437760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.88316 | −0.340798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 44.1386i | 1.52021i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.6060i | 1.01727i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.0733 | 0.723235 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.48913 | 0.325283 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 39.4891i | − 1.35208i | −0.736864 | − | 0.676041i | \(-0.763694\pi\) | ||||
0.736864 | − | 0.676041i | \(-0.236306\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 18.0000i | − 0.614868i | −0.951569 | − | 0.307434i | \(-0.900530\pi\) | ||||
0.951569 | − | 0.307434i | \(-0.0994704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.4674 | −1.51721 | −0.758604 | − | 0.651552i | \(-0.774118\pi\) | ||||
−0.758604 | + | 0.651552i | \(0.774118\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | −0.545279 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.4891i | 0.867660i | 0.900995 | + | 0.433830i | \(0.142838\pi\) | ||||
−0.900995 | + | 0.433830i | \(0.857162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.0000i | 1.35847i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −96.3288 | −3.26773 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.4891 | −0.592596 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 25.9130i | − 0.877022i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.02175i | 0.237108i | 0.992948 | + | 0.118554i | \(0.0378258\pi\) | ||||
−0.992948 | + | 0.118554i | \(0.962174\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −59.5842 | −2.00973 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.2554 | −0.850877 | −0.425439 | − | 0.904987i | \(-0.639880\pi\) | ||||
−0.425439 | + | 0.904987i | \(0.639880\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 10.5109i | − 0.353719i | −0.984236 | − | 0.176860i | \(-0.943406\pi\) | ||||
0.984236 | − | 0.176860i | \(-0.0565938\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.0217i | 0.437228i | 0.975811 | + | 0.218614i | \(0.0701535\pi\) | ||||
−0.975811 | + | 0.218614i | \(0.929847\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −63.5842 | −2.13015 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.7663i | 1.12995i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 49.2119i | 1.64314i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.9783 | −1.16659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.7446i | 0.690336i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 11.7228i | − 0.389250i | −0.980878 | − | 0.194625i | \(-0.937651\pi\) | ||||
0.980878 | − | 0.194625i | \(-0.0623489\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.7663 | 0.522936 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.9565 | −1.52261 | −0.761303 | − | 0.648396i | \(-0.775440\pi\) | ||||
−0.761303 | + | 0.648396i | \(0.775440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 60.4674i | − 2.00118i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.74456i | − 0.156679i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6277 | −0.449537 | −0.224768 | − | 0.974412i | \(-0.572163\pi\) | ||||
−0.224768 | + | 0.974412i | \(0.572163\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 73.8179 | 2.43238 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.9783i | 1.15132i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.7881i | 0.485704i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.76631 | 0.254804 | 0.127402 | − | 0.991851i | \(-0.459336\pi\) | ||||
0.127402 | + | 0.991851i | \(0.459336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.74456 | −0.155497 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 30.2337i | − 0.989807i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 28.0951i | − 0.917827i | −0.888481 | − | 0.458913i | \(-0.848239\pi\) | ||||
0.888481 | − | 0.458913i | \(-0.151761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.83966 | −0.223204 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.2337 | 1.05079 | 0.525394 | − | 0.850859i | \(-0.323918\pi\) | ||||
0.525394 | + | 0.850859i | \(0.323918\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 32.0000i | − 1.04206i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.0000i | 0.909878i | 0.890523 | + | 0.454939i | \(0.150339\pi\) | ||||
−0.890523 | + | 0.454939i | \(0.849661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.2337 | 0.851582 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.2119 | 1.07697 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.2554i | 1.20682i | 0.797430 | + | 0.603411i | \(0.206192\pi\) | ||||
−0.797430 | + | 0.603411i | \(0.793808\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 66.0951i | 2.13655i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.7446 | 0.476127 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.9783i | 0.740464i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.76631i | − 0.0568008i | −0.999597 | − | 0.0284004i | \(-0.990959\pi\) | ||||
0.999597 | − | 0.0284004i | \(-0.00904134\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.19019 | −0.134608 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.4891 | 1.07472 | 0.537359 | − | 0.843354i | \(-0.319422\pi\) | ||||
0.537359 | + | 0.843354i | \(0.319422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.74456i | 0.152104i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 52.9783i | − 1.69492i | −0.530856 | − | 0.847462i | \(-0.678129\pi\) | ||||
0.530856 | − | 0.847462i | \(-0.321871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −93.9565 | −3.00286 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.978251 | 0.0312331 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 10.3723i | − 0.330824i | −0.986225 | − | 0.165412i | \(-0.947105\pi\) | ||||
0.986225 | − | 0.165412i | \(-0.0528954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 16.8832i | − 0.537397i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41.4891 | −1.31928 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.9565 | −1.20573 | −0.602864 | − | 0.797844i | \(-0.705974\pi\) | ||||
−0.602864 | + | 0.797844i | \(0.705974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.4674i | 0.903385i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.88316i | 0.217992i | 0.994042 | + | 0.108996i | \(0.0347635\pi\) | ||||
−0.994042 | + | 0.108996i | \(0.965236\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.76631 | −0.0558836 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1400.2.g.i.449.3 | 4 | ||
4.3 | odd | 2 | 2800.2.g.r.449.2 | 4 | |||
5.2 | odd | 4 | 280.2.a.c.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 1400.2.a.r.1.1 | 2 | |||
5.4 | even | 2 | inner | 1400.2.g.i.449.2 | 4 | ||
15.2 | even | 4 | 2520.2.a.x.1.1 | 2 | |||
20.3 | even | 4 | 2800.2.a.bk.1.2 | 2 | |||
20.7 | even | 4 | 560.2.a.h.1.1 | 2 | |||
20.19 | odd | 2 | 2800.2.g.r.449.3 | 4 | |||
35.2 | odd | 12 | 1960.2.q.t.361.1 | 4 | |||
35.12 | even | 12 | 1960.2.q.r.361.2 | 4 | |||
35.13 | even | 4 | 9800.2.a.bu.1.2 | 2 | |||
35.17 | even | 12 | 1960.2.q.r.961.2 | 4 | |||
35.27 | even | 4 | 1960.2.a.s.1.1 | 2 | |||
35.32 | odd | 12 | 1960.2.q.t.961.1 | 4 | |||
40.27 | even | 4 | 2240.2.a.bg.1.2 | 2 | |||
40.37 | odd | 4 | 2240.2.a.bk.1.1 | 2 | |||
60.47 | odd | 4 | 5040.2.a.by.1.2 | 2 | |||
140.27 | odd | 4 | 3920.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.c.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
560.2.a.h.1.1 | 2 | 20.7 | even | 4 | |||
1400.2.a.r.1.1 | 2 | 5.3 | odd | 4 | |||
1400.2.g.i.449.2 | 4 | 5.4 | even | 2 | inner | ||
1400.2.g.i.449.3 | 4 | 1.1 | even | 1 | trivial | ||
1960.2.a.s.1.1 | 2 | 35.27 | even | 4 | |||
1960.2.q.r.361.2 | 4 | 35.12 | even | 12 | |||
1960.2.q.r.961.2 | 4 | 35.17 | even | 12 | |||
1960.2.q.t.361.1 | 4 | 35.2 | odd | 12 | |||
1960.2.q.t.961.1 | 4 | 35.32 | odd | 12 | |||
2240.2.a.bg.1.2 | 2 | 40.27 | even | 4 | |||
2240.2.a.bk.1.1 | 2 | 40.37 | odd | 4 | |||
2520.2.a.x.1.1 | 2 | 15.2 | even | 4 | |||
2800.2.a.bk.1.2 | 2 | 20.3 | even | 4 | |||
2800.2.g.r.449.2 | 4 | 4.3 | odd | 2 | |||
2800.2.g.r.449.3 | 4 | 20.19 | odd | 2 | |||
3920.2.a.bt.1.2 | 2 | 140.27 | odd | 4 | |||
5040.2.a.by.1.2 | 2 | 60.47 | odd | 4 | |||
9800.2.a.bu.1.2 | 2 | 35.13 | even | 4 |