Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(289,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.k (of order \(4\), degree \(2\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 - 2.10607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.289 |
Dual form | 1152.2.k.f.865.1 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.68554 | + | 2.68554i | −1.20101 | + | 1.20101i | −0.227153 | + | 0.973859i | \(0.572942\pi\) |
−0.973859 | + | 0.227153i | \(0.927058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.15894i | 0.816003i | 0.912981 | + | 0.408002i | \(0.133774\pi\) | ||||
−0.912981 | + | 0.408002i | \(0.866226\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79793 | + | 1.79793i | −0.542097 | + | 0.542097i | −0.924143 | − | 0.382046i | \(-0.875220\pi\) |
0.382046 | + | 0.924143i | \(0.375220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.38372 | − | 1.38372i | −0.383775 | − | 0.383775i | 0.488685 | − | 0.872460i | \(-0.337477\pi\) |
−0.872460 | + | 0.488685i | \(0.837477\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.224777 | 0.0545165 | 0.0272583 | − | 0.999628i | \(-0.491322\pi\) | ||||
0.0272583 | + | 0.999628i | \(0.491322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.158942 | + | 0.158942i | 0.0364637 | + | 0.0364637i | 0.725104 | − | 0.688640i | \(-0.241792\pi\) |
−0.688640 | + | 0.725104i | \(0.741792\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.82843i | − | 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 9.42429i | − | 1.88486i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.85712 | − | 1.85712i | −0.344858 | − | 0.344858i | 0.513332 | − | 0.858190i | \(-0.328411\pi\) |
−0.858190 | + | 0.513332i | \(0.828411\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.84106 | −0.330664 | −0.165332 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165332 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.79793 | − | 5.79793i | −0.980029 | − | 0.980029i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.66949 | − | 3.66949i | 0.603260 | − | 0.603260i | −0.337916 | − | 0.941176i | \(-0.609722\pi\) |
0.941176 | + | 0.337916i | \(0.109722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.88163i | − | 0.918557i | −0.888292 | − | 0.459278i | \(-0.848108\pi\) | ||
0.888292 | − | 0.459278i | \(-0.151892\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.75481 | + | 7.75481i | −1.18260 | + | 1.18260i | −0.203528 | + | 0.979069i | \(0.565241\pi\) |
−0.979069 | + | 0.203528i | \(0.934759\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.33897 | 0.334139 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.51397 | − | 7.51397i | 1.03212 | − | 1.03212i | 0.0326567 | − | 0.999467i | \(-0.489603\pi\) |
0.999467 | − | 0.0326567i | \(-0.0103968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.65685i | − | 1.30213i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | + | 4.00000i | −0.520756 | + | 0.520756i | −0.917800 | − | 0.397044i | \(-0.870036\pi\) |
0.397044 | + | 0.917800i | \(0.370036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.98737 | − | 5.98737i | −0.766604 | − | 0.766604i | 0.210903 | − | 0.977507i | \(-0.432360\pi\) |
−0.977507 | + | 0.210903i | \(0.932360\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.43208 | 0.921836 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4243 | − | 10.4243i | −1.27353 | − | 1.27353i | −0.944223 | − | 0.329307i | \(-0.893185\pi\) |
−0.329307 | − | 0.944223i | \(-0.606815\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.31788i | 0.512438i | 0.966619 | + | 0.256219i | \(0.0824769\pi\) | ||||
−0.966619 | + | 0.256219i | \(0.917523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.97474i | 0.699290i | 0.936882 | + | 0.349645i | \(0.113698\pi\) | ||||
−0.936882 | + | 0.349645i | \(0.886302\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.88163 | − | 3.88163i | −0.442353 | − | 0.442353i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0075 | −1.68848 | −0.844239 | − | 0.535966i | \(-0.819947\pi\) | ||||
−0.844239 | + | 0.535966i | \(0.819947\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.1158 | + | 10.1158i | 1.11036 | + | 1.11036i | 0.993102 | + | 0.117253i | \(0.0374088\pi\) |
0.117253 | + | 0.993102i | \(0.462591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.603650 | + | 0.603650i | −0.0654750 | + | 0.0654750i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.42847i | − | 0.151417i | −0.997130 | − | 0.0757086i | \(-0.975878\pi\) | ||
0.997130 | − | 0.0757086i | \(-0.0241219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.98737 | − | 2.98737i | 0.313161 | − | 0.313161i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.853690 | −0.0875867 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.3990 | −1.66507 | −0.832535 | − | 0.553973i | \(-0.813111\pi\) | ||||
−0.832535 | + | 0.553973i | \(0.813111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0818942 | − | 0.0818942i | 0.00814878 | − | 0.00814878i | −0.703021 | − | 0.711169i | \(-0.748166\pi\) |
0.711169 | + | 0.703021i | \(0.248166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.3507i | 1.31548i | 0.753245 | + | 0.657740i | \(0.228488\pi\) | ||||
−0.753245 | + | 0.657740i | \(0.771512\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.27798 | − | 7.27798i | 0.703589 | − | 0.703589i | −0.261590 | − | 0.965179i | \(-0.584247\pi\) |
0.965179 | + | 0.261590i | \(0.0842468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.04057 | + | 7.04057i | 0.674365 | + | 0.674365i | 0.958719 | − | 0.284355i | \(-0.0917793\pi\) |
−0.284355 | + | 0.958719i | \(0.591779\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.8486 | −1.77313 | −0.886563 | − | 0.462608i | \(-0.846914\pi\) | ||||
−0.886563 | + | 0.462608i | \(0.846914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.59587 | + | 7.59587i | 0.708318 | + | 0.708318i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.485281i | 0.0444857i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.53488i | 0.412261i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8816 | + | 11.8816i | 1.06273 | + | 1.06273i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.81580 | 0.338597 | 0.169299 | − | 0.985565i | \(-0.445850\pi\) | ||||
0.169299 | + | 0.985565i | \(0.445850\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.767438 | + | 0.767438i | 0.0670514 | + | 0.0670514i | 0.739837 | − | 0.672786i | \(-0.234902\pi\) |
−0.672786 | + | 0.739837i | \(0.734902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.343146 | + | 0.343146i | −0.0297545 | + | 0.0297545i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.31010i | 0.453672i | 0.973933 | + | 0.226836i | \(0.0728382\pi\) | ||||
−0.973933 | + | 0.226836i | \(0.927162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.76744 | − | 8.76744i | 0.743644 | − | 0.743644i | −0.229633 | − | 0.973277i | \(-0.573753\pi\) |
0.973277 | + | 0.229633i | \(0.0737526\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.97567 | 0.416086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.97474 | 0.828357 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.02869 | + | 1.02869i | −0.0842735 | + | 0.0842735i | −0.747987 | − | 0.663713i | \(-0.768979\pi\) |
0.663713 | + | 0.747987i | \(0.268979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.03696i | − | 0.165766i | −0.996559 | − | 0.0828829i | \(-0.973587\pi\) | ||
0.996559 | − | 0.0828829i | \(-0.0264127\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.94424 | − | 4.94424i | 0.397131 | − | 0.397131i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.09378 | − | 6.09378i | −0.486336 | − | 0.486336i | 0.420812 | − | 0.907148i | \(-0.361745\pi\) |
−0.907148 | + | 0.420812i | \(0.861745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.10641 | 0.481252 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.43692 | + | 3.43692i | 0.269201 | + | 0.269201i | 0.828778 | − | 0.559577i | \(-0.189037\pi\) |
−0.559577 | + | 0.828778i | \(0.689037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.7023i | 1.67937i | 0.543072 | + | 0.839686i | \(0.317261\pi\) | ||||
−0.543072 | + | 0.839686i | \(0.682739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.17064i | − | 0.705434i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.74653 | − | 8.74653i | −0.664987 | − | 0.664987i | 0.291565 | − | 0.956551i | \(-0.405824\pi\) |
−0.956551 | + | 0.291565i | \(0.905824\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.3465 | 1.53805 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.23163 | − | 8.23163i | −0.615261 | − | 0.615261i | 0.329051 | − | 0.944312i | \(-0.393271\pi\) |
−0.944312 | + | 0.329051i | \(0.893271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.72269 | + | 6.72269i | −0.499694 | + | 0.499694i | −0.911343 | − | 0.411649i | \(-0.864953\pi\) |
0.411649 | + | 0.911343i | \(0.364953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.7091i | 1.44904i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.404135 | + | 0.404135i | −0.0295533 | + | 0.0295533i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.8032 | −1.50526 | −0.752632 | − | 0.658441i | \(-0.771216\pi\) | ||||
−0.752632 | + | 0.658441i | \(0.771216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1454 | 1.01821 | 0.509103 | − | 0.860705i | \(-0.329977\pi\) | ||||
0.509103 | + | 0.860705i | \(0.329977\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.42865 | + | 2.42865i | −0.173034 | + | 0.173034i | −0.788311 | − | 0.615277i | \(-0.789044\pi\) |
0.615277 | + | 0.788311i | \(0.289044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.306182i | 0.0217047i | 0.999941 | + | 0.0108523i | \(0.00345447\pi\) | ||||
−0.999941 | + | 0.0108523i | \(0.996546\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00941 | − | 4.00941i | 0.281405 | − | 0.281405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.7954 | + | 15.7954i | 1.10320 | + | 1.10320i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.571533 | −0.0395337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.23256 | + | 7.23256i | 0.497910 | + | 0.497910i | 0.910787 | − | 0.412877i | \(-0.135476\pi\) |
−0.412877 | + | 0.910787i | \(0.635476\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 41.6517i | − | 2.84063i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.97474i | − | 0.269823i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.311029 | − | 0.311029i | −0.0209221 | − | 0.0209221i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.71908 | 0.115118 | 0.0575591 | − | 0.998342i | \(-0.481668\pi\) | ||||
0.0575591 | + | 0.998342i | \(0.481668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.1158 | − | 10.1158i | −0.671410 | − | 0.671410i | 0.286631 | − | 0.958041i | \(-0.407465\pi\) |
−0.958041 | + | 0.286631i | \(0.907465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0195 | − | 12.0195i | 0.794270 | − | 0.794270i | −0.187915 | − | 0.982185i | \(-0.560173\pi\) |
0.982185 | + | 0.187915i | \(0.0601730\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.3779i | − | 0.876418i | −0.898873 | − | 0.438209i | \(-0.855613\pi\) | ||
0.898873 | − | 0.438209i | \(-0.144387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.59587 | − | 7.59587i | 0.495500 | − | 0.495500i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3675 | 0.864670 | 0.432335 | − | 0.901713i | \(-0.357690\pi\) | ||||
0.432335 | + | 0.901713i | \(0.357690\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.211474 | 0.0136222 | 0.00681112 | − | 0.999977i | \(-0.497832\pi\) | ||||
0.00681112 | + | 0.999977i | \(0.497832\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.28141 | + | 6.28141i | −0.401305 | + | 0.401305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.439861i | − | 0.0279877i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.4337 | + | 10.4337i | −0.658569 | + | 0.658569i | −0.955041 | − | 0.296472i | \(-0.904190\pi\) |
0.296472 | + | 0.955041i | \(0.404190\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.08532 | + | 5.08532i | 0.319711 | + | 0.319711i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.742176 | 0.0462957 | 0.0231478 | − | 0.999732i | \(-0.492631\pi\) | ||||
0.0231478 | + | 0.999732i | \(0.492631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.92221 | + | 7.92221i | 0.492262 | + | 0.492262i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5.48435i | − | 0.338180i | −0.985601 | − | 0.169090i | \(-0.945917\pi\) | ||
0.985601 | − | 0.169090i | \(-0.0540828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.3582i | 2.47918i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.4741 | + | 14.4741i | 0.882500 | + | 0.882500i | 0.993788 | − | 0.111289i | \(-0.0354978\pi\) |
−0.111289 | + | 0.993788i | \(0.535498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0370 | 0.852685 | 0.426342 | − | 0.904562i | \(-0.359802\pi\) | ||||
0.426342 | + | 0.904562i | \(0.359802\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.9442 | + | 16.9442i | 1.02178 | + | 1.02178i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.49013 | + | 9.49013i | −0.570207 | + | 0.570207i | −0.932186 | − | 0.361980i | \(-0.882101\pi\) |
0.361980 | + | 0.932186i | \(0.382101\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.89359i | 0.232272i | 0.993233 | + | 0.116136i | \(0.0370509\pi\) | ||||
−0.993233 | + | 0.116136i | \(0.962949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4853 | + | 12.4853i | −0.742173 | + | 0.742173i | −0.972996 | − | 0.230823i | \(-0.925858\pi\) |
0.230823 | + | 0.972996i | \(0.425858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.6981 | 0.749545 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9495 | −0.997028 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1553 | + | 11.1553i | −0.651697 | + | 0.651697i | −0.953402 | − | 0.301704i | \(-0.902444\pi\) |
0.301704 | + | 0.953402i | \(0.402444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 21.4844i | − | 1.25087i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.91375 | + | 3.91375i | −0.226338 | + | 0.226338i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.7422 | − | 16.7422i | −0.965003 | − | 0.965003i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.1587 | 1.84140 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.40320 | − | 5.40320i | −0.308377 | − | 0.308377i | 0.535903 | − | 0.844280i | \(-0.319971\pi\) |
−0.844280 | + | 0.535903i | \(0.819971\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.1623i | 1.37012i | 0.728488 | + | 0.685059i | \(0.240224\pi\) | ||||
−0.728488 | + | 0.685059i | \(0.759776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6105i | 0.938881i | 0.882964 | + | 0.469441i | \(0.155544\pi\) | ||||
−0.882964 | + | 0.469441i | \(0.844456\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.81170 | + | 1.81170i | 0.101755 | + | 0.101755i | 0.756152 | − | 0.654397i | \(-0.227077\pi\) |
−0.654397 | + | 0.756152i | \(0.727077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.67794 | 0.373893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0357265 | + | 0.0357265i | 0.00198788 | + | 0.00198788i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.0406 | + | 13.0406i | −0.723361 | + | 0.723361i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.10641i | − | 0.336657i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5252 | − | 13.5252i | 0.743411 | − | 0.743411i | −0.229822 | − | 0.973233i | \(-0.573814\pi\) |
0.973233 | + | 0.229822i | \(0.0738142\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 55.9898 | 3.05905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.12615 | −0.0613454 | −0.0306727 | − | 0.999529i | \(-0.509765\pi\) | ||||
−0.0306727 | + | 0.999529i | \(0.509765\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.31010 | − | 3.31010i | 0.179252 | − | 0.179252i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1623i | 1.08866i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.7938 | + | 20.7938i | −1.11627 | + | 1.11627i | −0.123983 | + | 0.992284i | \(0.539567\pi\) |
−0.992284 | + | 0.123983i | \(0.960433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.2855 | + | 19.2855i | 1.03233 | + | 1.03233i | 0.999460 | + | 0.0328700i | \(0.0104647\pi\) |
0.0328700 | + | 0.999460i | \(0.489535\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.5908 | −1.36206 | −0.681029 | − | 0.732256i | \(-0.738467\pi\) | ||||
−0.681029 | + | 0.732256i | \(0.738467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.5959 | − | 11.5959i | −0.615445 | − | 0.615445i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 3.77296i | − | 0.199129i | −0.995031 | − | 0.0995645i | \(-0.968255\pi\) | ||
0.995031 | − | 0.0995645i | \(-0.0317450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.9495i | − | 0.997341i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.0454 | − | 16.0454i | −0.839856 | − | 0.839856i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.4474 | 1.43274 | 0.716371 | − | 0.697720i | \(-0.245802\pi\) | ||||
0.716371 | + | 0.697720i | \(0.245802\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.2222 | + | 16.2222i | 0.842216 | + | 0.842216i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6231 | + | 12.6231i | −0.653601 | + | 0.653601i | −0.953858 | − | 0.300257i | \(-0.902928\pi\) |
0.300257 | + | 0.953858i | \(0.402928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.13946i | 0.264695i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6686 | + | 11.6686i | −0.599373 | + | 0.599373i | −0.940146 | − | 0.340772i | \(-0.889311\pi\) |
0.340772 | + | 0.940146i | \(0.389311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.1885 | −0.878291 | −0.439145 | − | 0.898416i | \(-0.644719\pi\) | ||||
−0.439145 | + | 0.898416i | \(0.644719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.8486 | 1.06254 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.88238 | + | 1.88238i | −0.0954404 | + | 0.0954404i | −0.753215 | − | 0.657774i | \(-0.771498\pi\) |
0.657774 | + | 0.753215i | \(0.271498\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.635767i | − | 0.0321521i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.3034 | − | 40.3034i | 2.02788 | − | 2.02788i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.41166 | − | 8.41166i | −0.422169 | − | 0.422169i | 0.463781 | − | 0.885950i | \(-0.346493\pi\) |
−0.885950 | + | 0.463781i | \(0.846493\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.12389 | −0.0561242 | −0.0280621 | − | 0.999606i | \(-0.508934\pi\) | ||||
−0.0280621 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.54751 | + | 2.54751i | 0.126900 | + | 0.126900i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.1950i | 0.654051i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.7211i | − | 0.678464i | −0.940703 | − | 0.339232i | \(-0.889833\pi\) | ||
0.940703 | − | 0.339232i | \(-0.110167\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.63577 | − | 8.63577i | −0.424938 | − | 0.424938i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −54.3329 | −2.66710 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.30755 | + | 9.30755i | 0.454703 | + | 0.454703i | 0.896912 | − | 0.442209i | \(-0.145805\pi\) |
−0.442209 | + | 0.896912i | \(0.645805\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.44378 | + | 8.44378i | −0.411525 | + | 0.411525i | −0.882269 | − | 0.470745i | \(-0.843985\pi\) |
0.470745 | + | 0.882269i | \(0.343985\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2.11837i | − | 0.102756i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9264 | − | 12.9264i | 0.625551 | − | 0.625551i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.6054 | −1.47421 | −0.737105 | − | 0.675778i | \(-0.763808\pi\) | ||||
−0.737105 | + | 0.675778i | \(0.763808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3137 | −0.735930 | −0.367965 | − | 0.929840i | \(-0.619945\pi\) | ||||
−0.367965 | + | 0.929840i | \(0.619945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.449555 | − | 0.449555i | 0.0215051 | − | 0.0215051i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.3676i | − | 1.59255i | −0.604936 | − | 0.796274i | \(-0.706801\pi\) | ||
0.604936 | − | 0.796274i | \(-0.293199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.28832 | + | 2.28832i | −0.108721 | + | 0.108721i | −0.759375 | − | 0.650653i | \(-0.774495\pi\) |
0.650653 | + | 0.759375i | \(0.274495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.83621 | + | 3.83621i | 0.181854 | + | 0.181854i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.4165 | 1.29387 | 0.646933 | − | 0.762547i | \(-0.276052\pi\) | ||||
0.646933 | + | 0.762547i | \(0.276052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5748 | + | 10.5748i | 0.497947 | + | 0.497947i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.0454i | 0.752221i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.9147i | − | 0.510567i | −0.966866 | − | 0.255284i | \(-0.917831\pi\) | ||
0.966866 | − | 0.255284i | \(-0.0821688\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8319 | + | 17.8319i | 0.830512 | + | 0.830512i | 0.987587 | − | 0.157075i | \(-0.0502063\pi\) |
−0.157075 | + | 0.987587i | \(0.550206\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.4937 | −1.04537 | −0.522686 | − | 0.852525i | \(-0.675070\pi\) | ||||
−0.522686 | + | 0.852525i | \(0.675070\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.2171 | − | 24.2171i | −1.12063 | − | 1.12063i | −0.991646 | − | 0.128989i | \(-0.958827\pi\) |
−0.128989 | − | 0.991646i | \(-0.541173\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.5054 | − | 22.5054i | 1.03920 | − | 1.03920i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 27.8852i | − | 1.28216i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.49791 | − | 1.49791i | 0.0687289 | − | 0.0687289i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.2362 | −1.65568 | −0.827838 | − | 0.560968i | \(-0.810429\pi\) | ||||
−0.827838 | + | 0.560968i | \(0.810429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1551 | −0.463032 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.0403 | − | 44.0403i | 1.99977 | − | 1.99977i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8200i | 0.762186i | 0.924537 | + | 0.381093i | \(0.124452\pi\) | ||||
−0.924537 | + | 0.381093i | \(0.875548\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.10641 | + | 6.10641i | −0.275578 | + | 0.275578i | −0.831341 | − | 0.555763i | \(-0.812426\pi\) |
0.555763 | + | 0.831341i | \(0.312426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.417438 | − | 0.417438i | −0.0188005 | − | 0.0188005i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.32206 | −0.418151 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.6770 | − | 19.6770i | −0.880864 | − | 0.880864i | 0.112758 | − | 0.993622i | \(-0.464031\pi\) |
−0.993622 | + | 0.112758i | \(0.964031\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 25.7308i | − | 1.14728i | −0.819108 | − | 0.573639i | \(-0.805531\pi\) | ||
0.819108 | − | 0.573639i | \(-0.194469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.439861i | 0.0195736i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.73514 | + | 1.73514i | 0.0769087 | + | 0.0769087i | 0.744515 | − | 0.667606i | \(-0.232681\pi\) |
−0.667606 | + | 0.744515i | \(0.732681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.8991 | −0.570623 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −35.8538 | − | 35.8538i | −1.57991 | − | 1.57991i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.08532 | − | 5.08532i | 0.223652 | − | 0.223652i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.5944i | 1.47180i | 0.677092 | + | 0.735898i | \(0.263240\pi\) | ||||
−0.677092 | + | 0.735898i | \(0.736760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8158 | + | 21.8158i | −0.953938 | + | 0.953938i | −0.998985 | − | 0.0450467i | \(-0.985656\pi\) |
0.0450467 | + | 0.998985i | \(0.485656\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.413828 | −0.0180266 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.13853 | + | 8.13853i | −0.352519 | + | 0.352519i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.0907i | 1.69004i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.20531 | + | 4.20531i | −0.181136 | + | 0.181136i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.2112 | − | 27.2112i | −1.16990 | − | 1.16990i | −0.982232 | − | 0.187669i | \(-0.939907\pi\) |
−0.187669 | − | 0.982232i | \(-0.560093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −37.8155 | −1.61984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.80116 | − | 6.80116i | −0.290796 | − | 0.290796i | 0.546598 | − | 0.837395i | \(-0.315922\pi\) |
−0.837395 | + | 0.546598i | \(0.815922\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.590346i | − | 0.0251496i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 32.4004i | − | 1.37780i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.29337 | − | 4.29337i | −0.181916 | − | 0.181916i | 0.610274 | − | 0.792190i | \(-0.291059\pi\) |
−0.792190 | + | 0.610274i | \(0.791059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.4609 | 0.907701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.0801 | + | 10.0801i | 0.424825 | + | 0.424825i | 0.886861 | − | 0.462036i | \(-0.152881\pi\) |
−0.462036 | + | 0.886861i | \(0.652881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.6187 | − | 50.6187i | 2.12954 | − | 2.12954i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 32.5018i | − | 1.36255i | −0.732029 | − | 0.681274i | \(-0.761426\pi\) | ||
0.732029 | − | 0.681274i | \(-0.238574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.17157 | + | 9.17157i | −0.383818 | + | 0.383818i | −0.872476 | − | 0.488657i | \(-0.837487\pi\) |
0.488657 | + | 0.872476i | \(0.337487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.6559 | −1.11163 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7536 | 0.489308 | 0.244654 | − | 0.969611i | \(-0.421326\pi\) | ||||
0.244654 | + | 0.969611i | \(0.421326\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.8395 | + | 21.8395i | −0.906053 | + | 0.906053i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.0192i | 1.11902i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.46002 | + | 6.46002i | −0.266634 | + | 0.266634i | −0.827742 | − | 0.561109i | \(-0.810375\pi\) |
0.561109 | + | 0.827742i | \(0.310375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.292621 | − | 0.292621i | −0.0120572 | − | 0.0120572i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.49270 | −0.225558 | −0.112779 | − | 0.993620i | \(-0.535975\pi\) | ||||
−0.112779 | + | 0.993620i | \(0.535975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.30324 | − | 1.30324i | −0.0534278 | − | 0.0534278i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.4348i | − | 1.48868i | −0.667799 | − | 0.744342i | \(-0.732763\pi\) | ||
0.667799 | − | 0.744342i | \(-0.267237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.97474i | 0.406878i | 0.979088 | + | 0.203439i | \(0.0652119\pi\) | ||||
−0.979088 | + | 0.203439i | \(0.934788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.1786 | − | 12.1786i | −0.495131 | − | 0.495131i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.51900 | −0.183421 | −0.0917103 | − | 0.995786i | \(-0.529233\pi\) | ||||
−0.0917103 | + | 0.995786i | \(0.529233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.91375 | + | 3.91375i | 0.158333 | + | 0.158333i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.43692 | − | 8.43692i | 0.340764 | − | 0.340764i | −0.515890 | − | 0.856655i | \(-0.672539\pi\) |
0.856655 | + | 0.515890i | \(0.172539\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.1201i | 1.29311i | 0.762869 | + | 0.646554i | \(0.223790\pi\) | ||||
−0.762869 | + | 0.646554i | \(0.776210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0412 | − | 15.0412i | 0.604559 | − | 0.604559i | −0.336960 | − | 0.941519i | \(-0.609399\pi\) |
0.941519 | + | 0.336960i | \(0.109399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.08398 | 0.123557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.6958 | −0.667833 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.824818 | − | 0.824818i | 0.0328876 | − | 0.0328876i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 36.4685i | − | 1.45179i | −0.687807 | − | 0.725894i | \(-0.741426\pi\) | ||
0.687807 | − | 0.725894i | \(-0.258574\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.2475 | + | 10.2475i | −0.406659 | + | 0.406659i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.23648 | − | 3.23648i | −0.128234 | − | 0.128234i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.0036 | −0.553109 | −0.276555 | − | 0.960998i | \(-0.589193\pi\) | ||||
−0.276555 | + | 0.960998i | \(0.589193\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.6034 | + | 16.6034i | 0.654774 | + | 0.654774i | 0.954139 | − | 0.299365i | \(-0.0967748\pi\) |
−0.299365 | + | 0.954139i | \(0.596775\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.1908i | 0.479270i | 0.970863 | + | 0.239635i | \(0.0770277\pi\) | ||||
−0.970863 | + | 0.239635i | \(0.922972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.3835i | − | 0.564600i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.983270 | + | 0.983270i | 0.0384783 | + | 0.0384783i | 0.726084 | − | 0.687606i | \(-0.241338\pi\) |
−0.687606 | + | 0.726084i | \(0.741338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.12198 | −0.161059 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0559 | + | 18.0559i | 0.703357 | + | 0.703357i | 0.965130 | − | 0.261772i | \(-0.0843069\pi\) |
−0.261772 | + | 0.965130i | \(0.584307\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.55890 | − | 4.55890i | 0.177321 | − | 0.177321i | −0.612866 | − | 0.790187i | \(-0.709983\pi\) |
0.790187 | + | 0.612866i | \(0.209983\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.84307i | − | 0.0714710i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.25272 | + | 5.25272i | −0.203386 | + | 0.203386i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.5298 | 0.831148 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8569 | −0.418504 | −0.209252 | − | 0.977862i | \(-0.567103\pi\) | ||||
−0.209252 | + | 0.977862i | \(0.567103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.7066 | − | 23.7066i | 0.911120 | − | 0.911120i | −0.0852405 | − | 0.996360i | \(-0.527166\pi\) |
0.996360 | + | 0.0852405i | \(0.0271659\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 35.4045i | − | 1.35870i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8337 | − | 17.8337i | 0.682386 | − | 0.682386i | −0.278151 | − | 0.960537i | \(-0.589722\pi\) |
0.960537 | + | 0.278151i | \(0.0897217\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2605 | − | 14.2605i | −0.544866 | − | 0.544866i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.7945 | −0.792205 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.8557 | + | 10.8557i | 0.412970 | + | 0.412970i | 0.882772 | − | 0.469802i | \(-0.155675\pi\) |
−0.469802 | + | 0.882772i | \(0.655675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 47.0907i | 1.78625i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.32206i | − | 0.0500765i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.08875 | − | 6.08875i | −0.229969 | − | 0.229969i | 0.582711 | − | 0.812680i | \(-0.301992\pi\) |
−0.812680 | + | 0.582711i | \(0.801992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.16647 | 0.0439942 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.176805 | + | 0.176805i | 0.00664943 | + | 0.00664943i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.8836 | + | 22.8836i | −0.859413 | + | 0.859413i | −0.991269 | − | 0.131856i | \(-0.957906\pi\) |
0.131856 | + | 0.991269i | \(0.457906\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.20730i | 0.195015i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.3624 | + | 13.3624i | −0.499724 | + | 0.499724i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.46744 | −0.0547262 | −0.0273631 | − | 0.999626i | \(-0.508711\pi\) | ||||
−0.0273631 | + | 0.999626i | \(0.508711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.8233 | −1.07344 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.5020 | + | 17.5020i | −0.650008 | + | 0.650008i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3928i | 0.570889i | 0.958395 | + | 0.285445i | \(0.0921412\pi\) | ||||
−0.958395 | + | 0.285445i | \(0.907859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.74311 | + | 1.74311i | −0.0644711 | + | 0.0644711i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.4185 | + | 12.4185i | 0.458688 | + | 0.458688i | 0.898225 | − | 0.439536i | \(-0.144857\pi\) |
−0.439536 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.4844 | 1.38075 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.6559 | − | 14.6559i | −0.539127 | − | 0.539127i | 0.384146 | − | 0.923273i | \(-0.374496\pi\) |
−0.923273 | + | 0.384146i | \(0.874496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.7821i | 1.16597i | 0.812482 | + | 0.582986i | \(0.198116\pi\) | ||||
−0.812482 | + | 0.582986i | \(0.801884\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5.52518i | − | 0.202427i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.7127 | + | 15.7127i | 0.574131 | + | 0.574131i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7594 | −1.08594 | −0.542968 | − | 0.839753i | \(-0.682699\pi\) | ||||
−0.542968 | + | 0.839753i | \(0.682699\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.47036 | + | 5.47036i | 0.199087 | + | 0.199087i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6355 | + | 15.6355i | −0.568282 | + | 0.568282i | −0.931647 | − | 0.363365i | \(-0.881628\pi\) |
0.363365 | + | 0.931647i | \(0.381628\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.55957i | − | 0.165284i | −0.996579 | − | 0.0826422i | \(-0.973664\pi\) | ||
0.996579 | − | 0.0826422i | \(-0.0263359\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.2002 | + | 15.2002i | −0.550284 | + | 0.550284i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.0698 | 0.399706 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.5794 | 1.31909 | 0.659543 | − | 0.751667i | \(-0.270750\pi\) | ||||
0.659543 | + | 0.751667i | \(0.270750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7108 | + | 18.7108i | −0.672981 | + | 0.672981i | −0.958402 | − | 0.285421i | \(-0.907867\pi\) |
0.285421 | + | 0.958402i | \(0.407867\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3507i | 0.623255i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.934836 | − | 0.934836i | 0.0334940 | − | 0.0334940i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.76326 | − | 7.76326i | −0.277791 | − | 0.277791i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.7302 | 1.16819 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3759 | + | 13.3759i | 0.476801 | + | 0.476801i | 0.904107 | − | 0.427306i | \(-0.140537\pi\) |
−0.427306 | + | 0.904107i | \(0.640537\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 40.6930i | − | 1.44688i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.5697i | 0.588406i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.8043 | − | 33.8043i | −1.19741 | − | 1.19741i | −0.974939 | − | 0.222471i | \(-0.928588\pi\) |
−0.222471 | − | 0.974939i | \(-0.571412\pi\) | |||||||
\(798\) | 0 | 0 |