Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1156,2,Mod(829,1156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1156, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1156.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1156 = 2^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1156.e (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: | \(9.23070647366\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 68) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 905.2 | ||
Root | \(-2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1156.905 |
Dual form | 1156.2.e.c.829.2 |
$q$-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 \(\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times\).
\(n\) | \(579\) | \(581\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 2.30278 | − | 2.30278i | 1.32951 | − | 1.32951i | 0.423710 | − | 0.905798i | \(-0.360727\pi\) |
0.905798 | − | 0.423710i | \(-0.139273\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 1.00000i | 0.447214 | − | 0.447214i | −0.447214 | − | 0.894427i | \(-0.647584\pi\) |
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.30278 | − | 2.30278i | −0.870367 | − | 0.870367i | 0.122145 | − | 0.992512i | \(-0.461023\pi\) |
−0.992512 | + | 0.122145i | \(0.961023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 7.60555i | − | 2.53518i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.302776 | + | 0.302776i | 0.0912903 | + | 0.0912903i | 0.751277 | − | 0.659987i | \(-0.229438\pi\) |
−0.659987 | + | 0.751277i | \(0.729438\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60555 | 0.722650 | 0.361325 | − | 0.932440i | \(-0.382325\pi\) | ||||
0.361325 | + | 0.932440i | \(0.382325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 4.60555i | − | 1.18915i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.605551i | 0.138923i | 0.997585 | + | 0.0694615i | \(0.0221281\pi\) | ||||
−0.997585 | + | 0.0694615i | \(0.977872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.6056 | −2.31432 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.30278 | + | 4.30278i | 0.897191 | + | 0.897191i | 0.995187 | − | 0.0979961i | \(-0.0312433\pi\) |
−0.0979961 | + | 0.995187i | \(0.531243\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.6056 | − | 10.6056i | −2.04104 | − | 2.04104i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.60555 | − | 1.60555i | 0.298143 | − | 0.298143i | −0.542143 | − | 0.840286i | \(-0.682387\pi\) |
0.840286 | + | 0.542143i | \(0.182387\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.30278 | + | 4.30278i | −0.772801 | + | 0.772801i | −0.978595 | − | 0.205794i | \(-0.934022\pi\) |
0.205794 | + | 0.978595i | \(0.434022\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.39445 | 0.242742 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.60555 | −0.778480 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 3.00000i | −0.493197 | + | 0.493197i | −0.909312 | − | 0.416115i | \(-0.863391\pi\) |
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.00000 | − | 6.00000i | 0.960769 | − | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | − | 1.00000i | −0.156174 | − | 0.156174i | 0.624695 | − | 0.780869i | \(-0.285223\pi\) |
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.39445i | − | 0.517649i | −0.965924 | − | 0.258824i | \(-0.916665\pi\) | ||
0.965924 | − | 0.258824i | \(-0.0833351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.60555 | − | 7.60555i | −1.13377 | − | 1.13377i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.60555i | 0.515079i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.21110i | − | 0.715800i | −0.933760 | − | 0.357900i | \(-0.883493\pi\) | ||
0.933760 | − | 0.357900i | \(-0.116507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.605551 | 0.0816525 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.39445 | + | 1.39445i | 0.184699 | + | 0.184699i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.60555i | − | 1.12035i | −0.828375 | − | 0.560174i | \(-0.810734\pi\) | ||
0.828375 | − | 0.560174i | \(-0.189266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.21110 | + | 6.21110i | 0.795250 | + | 0.795250i | 0.982342 | − | 0.187092i | \(-0.0599063\pi\) |
−0.187092 | + | 0.982342i | \(0.559906\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −17.5139 | + | 17.5139i | −2.20654 | + | 2.20654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.60555 | − | 2.60555i | 0.323179 | − | 0.323179i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.21110 | 1.12532 | 0.562658 | − | 0.826690i | \(-0.309779\pi\) | ||||
0.562658 | + | 0.826690i | \(0.309779\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.8167 | 2.38564 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.90833 | + | 2.90833i | −0.345155 | + | 0.345155i | −0.858301 | − | 0.513146i | \(-0.828480\pi\) |
0.513146 | + | 0.858301i | \(0.328480\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | − | 7.00000i | 0.819288 | − | 0.819288i | −0.166717 | − | 0.986005i | \(-0.553317\pi\) |
0.986005 | + | 0.166717i | \(0.0533166\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.90833 | + | 6.90833i | 0.797705 | + | 0.797705i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.39445i | − | 0.158912i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.302776 | + | 0.302776i | 0.0340649 | + | 0.0340649i | 0.723934 | − | 0.689869i | \(-0.242332\pi\) |
−0.689869 | + | 0.723934i | \(0.742332\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −26.0278 | −2.89197 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.8167i | 1.95563i | 0.209466 | + | 0.977816i | \(0.432827\pi\) | ||||
−0.209466 | + | 0.977816i | \(0.567173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.39445i | − | 0.792768i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.81665 | 0.828564 | 0.414282 | − | 0.910149i | \(-0.364033\pi\) | ||||
0.414282 | + | 0.910149i | \(0.364033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | − | 6.00000i | −0.628971 | − | 0.628971i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.8167i | 2.05489i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.605551 | + | 0.605551i | 0.0621282 | + | 0.0621282i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.60555 | − | 7.60555i | 0.772227 | − | 0.772227i | −0.206269 | − | 0.978495i | \(-0.566132\pi\) |
0.978495 | + | 0.206269i | \(0.0661321\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.30278 | − | 2.30278i | 0.231438 | − | 0.231438i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.6056 | 1.05529 | 0.527646 | − | 0.849464i | \(-0.323075\pi\) | ||||
0.527646 | + | 0.849464i | \(0.323075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2111 | −1.30173 | −0.650864 | − | 0.759194i | \(-0.725593\pi\) | ||||
−0.650864 | + | 0.759194i | \(0.725593\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.6056 | + | 10.6056i | −1.03500 | + | 1.03500i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.69722 | + | 5.69722i | −0.550771 | + | 0.550771i | −0.926663 | − | 0.375892i | \(-0.877336\pi\) |
0.375892 | + | 0.926663i | \(0.377336\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.21110 | + | 6.21110i | 0.594916 | + | 0.594916i | 0.938955 | − | 0.344039i | \(-0.111795\pi\) |
−0.344039 | + | 0.938955i | \(0.611795\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.8167i | 1.31142i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.60555 | − | 9.60555i | −0.903614 | − | 0.903614i | 0.0921325 | − | 0.995747i | \(-0.470632\pi\) |
−0.995747 | + | 0.0921325i | \(0.970632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.60555 | 0.802472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 19.8167i | − | 1.83205i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.8167i | − | 0.983332i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.60555 | −0.415269 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.00000 | + | 8.00000i | 0.715542 | + | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.605551i | − | 0.0537340i | −0.999639 | − | 0.0268670i | \(-0.991447\pi\) | ||
0.999639 | − | 0.0268670i | \(-0.00855306\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.81665 | − | 7.81665i | −0.688218 | − | 0.688218i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.30278 | − | 6.30278i | 0.550676 | − | 0.550676i | −0.375960 | − | 0.926636i | \(-0.622687\pi\) |
0.926636 | + | 0.375960i | \(0.122687\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.39445 | − | 1.39445i | 0.120914 | − | 0.120914i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.2111 | −1.82556 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.60555 | −0.222607 | −0.111304 | − | 0.993786i | \(-0.535503\pi\) | ||||
−0.111304 | + | 0.993786i | \(0.535503\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.302776 | + | 0.302776i | −0.0256811 | + | 0.0256811i | −0.719831 | − | 0.694150i | \(-0.755781\pi\) |
0.694150 | + | 0.719831i | \(0.255781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.21110 | + | 9.21110i | −0.775715 | + | 0.775715i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.788897 | + | 0.788897i | 0.0659709 | + | 0.0659709i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.21110i | − | 0.266668i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.30278 | + | 8.30278i | 0.684801 | + | 0.684801i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.42221 | 0.689974 | 0.344987 | − | 0.938607i | \(-0.387883\pi\) | ||||
0.344987 | + | 0.938607i | \(0.387883\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.60555i | 0.374794i | 0.982284 | + | 0.187397i | \(0.0600052\pi\) | ||||
−0.982284 | + | 0.187397i | \(0.939995\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.60555i | 0.691215i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.42221 | −0.672165 | −0.336083 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336083 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0000 | − | 12.0000i | −0.951662 | − | 0.951662i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 19.8167i | − | 1.56177i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.30278 | + | 4.30278i | 0.337019 | + | 0.337019i | 0.855244 | − | 0.518225i | \(-0.173407\pi\) |
−0.518225 | + | 0.855244i | \(0.673407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.39445 | − | 1.39445i | 0.108558 | − | 0.108558i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.9083 | + | 14.9083i | −1.15364 | + | 1.15364i | −0.167824 | + | 0.985817i | \(0.553674\pi\) |
−0.985817 | + | 0.167824i | \(0.946326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.21110 | −0.477777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.60555 | 0.352195 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8167 | − | 14.8167i | 1.12649 | − | 1.12649i | 0.135746 | − | 0.990744i | \(-0.456657\pi\) |
0.990744 | − | 0.135746i | \(-0.0433430\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.90833 | − | 6.90833i | 0.522220 | − | 0.522220i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.8167 | − | 19.8167i | −1.48951 | − | 1.48951i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 15.0278i | − | 1.12323i | −0.827400 | − | 0.561614i | \(-0.810181\pi\) | ||
0.827400 | − | 0.561614i | \(-0.189819\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0000 | + | 13.0000i | 0.966282 | + | 0.966282i | 0.999450 | − | 0.0331674i | \(-0.0105595\pi\) |
−0.0331674 | + | 0.999450i | \(0.510559\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.6056 | 2.11458 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000i | 0.441129i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 48.8444i | 3.55291i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.78890 | 0.491227 | 0.245614 | − | 0.969368i | \(-0.421011\pi\) | ||||
0.245614 | + | 0.969368i | \(0.421011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.21110 | + | 8.21110i | 0.591048 | + | 0.591048i | 0.937915 | − | 0.346866i | \(-0.112754\pi\) |
−0.346866 | + | 0.937915i | \(0.612754\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 12.0000i | − | 0.859338i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.6056 | + | 17.6056i | 1.25434 | + | 1.25434i | 0.953753 | + | 0.300590i | \(0.0971836\pi\) |
0.300590 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1194 | − | 10.1194i | 0.717347 | − | 0.717347i | −0.250714 | − | 0.968061i | \(-0.580665\pi\) |
0.968061 | + | 0.250714i | \(0.0806653\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.2111 | − | 21.2111i | 1.49612 | − | 1.49612i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.39445 | −0.518989 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 32.7250 | − | 32.7250i | 2.27454 | − | 2.27454i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.183346 | + | 0.183346i | −0.0126823 | + | 0.0126823i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5139 | − | 15.5139i | −1.06802 | − | 1.06802i | −0.997511 | − | 0.0705082i | \(-0.977538\pi\) |
−0.0705082 | − | 0.997511i | \(-0.522462\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.3944i | 0.917773i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.39445 | − | 3.39445i | −0.231499 | − | 0.231499i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.8167 | 1.34524 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 32.2389i | − | 2.17850i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.8167i | − | 1.19309i | −0.802579 | − | 0.596546i | \(-0.796539\pi\) | ||
0.802579 | − | 0.596546i | \(-0.203461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 22.8167 | 1.52111 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.302776 | + | 0.302776i | 0.0200959 | + | 0.0200959i | 0.717083 | − | 0.696987i | \(-0.245477\pi\) |
−0.696987 | + | 0.717083i | \(0.745477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.60555i | 0.304343i | 0.988354 | + | 0.152172i | \(0.0486267\pi\) | ||||
−0.988354 | + | 0.152172i | \(0.951373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.21110 | − | 3.21110i | −0.211275 | − | 0.211275i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.60555 | + | 5.60555i | −0.367232 | + | 0.367232i | −0.866467 | − | 0.499235i | \(-0.833614\pi\) |
0.499235 | + | 0.866467i | \(0.333614\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 4.00000i | −0.260931 | + | 0.260931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.39445 | 0.0905792 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7889 | −0.956614 | −0.478307 | − | 0.878193i | \(-0.658749\pi\) | ||||
−0.478307 | + | 0.878193i | \(0.658749\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.00000 | + | 9.00000i | −0.579741 | + | 0.579741i | −0.934832 | − | 0.355091i | \(-0.884450\pi\) |
0.355091 | + | 0.934832i | \(0.384450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −28.1194 | + | 28.1194i | −1.80386 | + | 1.80386i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.60555 | + | 3.60555i | 0.230350 | + | 0.230350i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.57779i | 0.100393i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 41.0278 | + | 41.0278i | 2.60003 | + | 2.60003i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.60555i | 0.163810i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3944i | 1.20979i | 0.796304 | + | 0.604896i | \(0.206785\pi\) | ||||
−0.796304 | + | 0.604896i | \(0.793215\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.8167 | 0.858525 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.2111 | − | 12.2111i | −0.755848 | − | 0.755848i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.0278i | 1.41995i | 0.704226 | + | 0.709976i | \(0.251294\pi\) | ||||
−0.704226 | + | 0.709976i | \(0.748706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.21110 | − | 5.21110i | −0.320115 | − | 0.320115i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | − | 18.0000i | 1.10158 | − | 1.10158i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.4222 | + | 17.4222i | −1.06225 | + | 1.06225i | −0.0643214 | + | 0.997929i | \(0.520488\pi\) |
−0.997929 | + | 0.0643214i | \(0.979512\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.21110 | 0.0735692 | 0.0367846 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367846 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.6333 | −1.67244 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.908327 | + | 0.908327i | −0.0547742 | + | 0.0547742i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.60555 | + | 3.60555i | −0.216637 | + | 0.216637i | −0.807079 | − | 0.590443i | \(-0.798953\pi\) |
0.590443 | + | 0.807079i | \(0.298953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 32.7250 | + | 32.7250i | 1.95919 | + | 1.95919i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.4222i | 1.09898i | 0.835501 | + | 0.549488i | \(0.185177\pi\) | ||||
−0.835501 | + | 0.549488i | \(0.814823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.11943 | − | 2.11943i | −0.125987 | − | 0.125987i | 0.641302 | − | 0.767289i | \(-0.278395\pi\) |
−0.767289 | + | 0.641302i | \(0.778395\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.78890 | 0.165200 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.60555i | 0.271857i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 35.0278i | − | 2.05336i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.6333 | −1.26383 | −0.631916 | − | 0.775037i | \(-0.717731\pi\) | ||||
−0.631916 | + | 0.775037i | \(0.717731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.60555 | − | 8.60555i | −0.501035 | − | 0.501035i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 6.42221i | − | 0.372654i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.2111 | + | 11.2111i | 0.648355 | + | 0.648355i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.81665 | + | 7.81665i | −0.450544 | + | 0.450544i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.4222 | − | 24.4222i | 1.40302 | − | 1.40302i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.4222 | 0.711293 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.2111 | 1.21058 | 0.605291 | − | 0.796004i | \(-0.293057\pi\) | ||||
0.605291 | + | 0.796004i | \(0.293057\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −30.4222 | + | 30.4222i | −1.73066 | + | 1.73066i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.9083 | + | 18.9083i | −1.07219 | + | 1.07219i | −0.0750101 | + | 0.997183i | \(0.523899\pi\) |
−0.997183 | + | 0.0750101i | \(0.976101\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.21110 | − | 6.21110i | −0.351072 | − | 0.351072i | 0.509436 | − | 0.860508i | \(-0.329854\pi\) |
−0.860508 | + | 0.509436i | \(0.829854\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 35.0278i | 1.97359i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.6056 | − | 19.6056i | −1.10116 | − | 1.10116i | −0.994271 | − | 0.106886i | \(-0.965912\pi\) |
−0.106886 | − | 0.994271i | \(-0.534088\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.972244 | 0.0544352 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.2389i | 1.46451i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.81665i | 0.433590i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.6056 | 1.58189 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.21110 | + | 9.21110i | 0.507825 | + | 0.507825i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.39445i | − | 0.186576i | −0.995639 | − | 0.0932879i | \(-0.970262\pi\) | ||
0.995639 | − | 0.0932879i | \(-0.0297377\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.8167 | + | 22.8167i | 1.25034 | + | 1.25034i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.21110 | − | 9.21110i | 0.503256 | − | 0.503256i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.2111 | − | 16.2111i | 0.883075 | − | 0.883075i | −0.110771 | − | 0.993846i | \(-0.535332\pi\) |
0.993846 | + | 0.110771i | \(0.0353320\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −44.2389 | −2.40273 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.60555 | −0.141099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.81665 | + | 7.81665i | −0.422060 | + | 0.422060i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.8167 | − | 19.8167i | 1.06689 | − | 1.06689i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.51388 | + | 5.51388i | 0.296000 | + | 0.296000i | 0.839445 | − | 0.543445i | \(-0.182880\pi\) |
−0.543445 | + | 0.839445i | \(0.682880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.6333i | 1.26506i | 0.774535 | + | 0.632531i | \(0.217984\pi\) | ||||
−0.774535 | + | 0.632531i | \(0.782016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.6333 | − | 27.6333i | −1.47496 | − | 1.47496i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.2111 | −1.66120 | −0.830600 | − | 0.556870i | \(-0.812002\pi\) | ||||
−0.830600 | + | 0.556870i | \(0.812002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.81665i | 0.308716i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6056i | 0.876407i | 0.898876 | + | 0.438204i | \(0.144385\pi\) | ||||
−0.898876 | + | 0.438204i | \(0.855615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.6333 | 0.980700 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.9083 | − | 24.9083i | −1.30735 | − | 1.30735i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 14.0000i | − | 0.732793i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.90833 | + | 6.90833i | 0.360612 | + | 0.360612i | 0.864038 | − | 0.503426i | \(-0.167927\pi\) |
−0.503426 | + | 0.864038i | \(0.667927\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.60555 | + | 7.60555i | −0.395929 | + | 0.395929i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | + | 12.0000i | −0.623009 | + | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.0278 | 1.08878 | 0.544388 | − | 0.838834i | \(-0.316762\pi\) | ||||
0.544388 | + | 0.838834i | \(0.316762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.8444 | 1.90264 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.18335 | − | 4.18335i | 0.215453 | − | 0.215453i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7250 | − | 20.7250i | 1.06457 | − | 1.06457i | 0.0668047 | − | 0.997766i | \(-0.478720\pi\) |
0.997766 | − | 0.0668047i | \(-0.0212804\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.39445 | − | 1.39445i | −0.0714398 | − | 0.0714398i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 19.3944i | − | 0.991010i | −0.868605 | − | 0.495505i | \(-0.834983\pi\) | ||
0.868605 | − | 0.495505i | \(-0.165017\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.39445 | − | 1.39445i | −0.0710677 | − | 0.0710677i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.8167 | −1.31233 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.1833i | 0.516316i | 0.966103 | + | 0.258158i | \(0.0831155\pi\) | ||||
−0.966103 | + | 0.258158i | \(0.916884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 29.0278i | − | 1.46426i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.605551 | 0.0304686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.00000 | + | 9.00000i | 0.451697 | + | 0.451697i | 0.895918 | − | 0.444220i | \(-0.146519\pi\) |
−0.444220 | + | 0.895918i | \(0.646519\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 6.42221i | − | 0.321512i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.00000 | + | 7.00000i | 0.349563 | + | 0.349563i | 0.859947 | − | 0.510384i | \(-0.170497\pi\) |
−0.510384 | + | 0.859947i | \(0.670497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.2111 | + | 11.2111i | −0.558465 | + | 0.558465i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −26.0278 | + | 26.0278i | −1.29333 | + | 1.29333i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.81665 | −0.0900482 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2111 | 1.14772 | 0.573858 | − | 0.818955i | \(-0.305446\pi\) | ||||
0.573858 | + | 0.818955i | \(0.305446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | + | 6.00000i | −0.295958 | + | 0.295958i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.8167 | + | 19.8167i | −0.975114 | + | 0.975114i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.8167 | + | 17.8167i | 0.874585 | + | 0.874585i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.39445i | 0.0682864i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.30278 | − | 2.30278i | −0.112498 | − | 0.112498i | 0.648617 | − | 0.761115i | \(-0.275348\pi\) |
−0.761115 | + | 0.648617i | \(0.775348\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6056 | 0.906779 | 0.453390 | − | 0.891312i | \(-0.350215\pi\) | ||||
0.453390 | + | 0.891312i | \(0.350215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.4222i | 1.47918i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 28.6056i | − | 1.38432i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.63331 | 0.175418 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.88057 | + | 1.88057i | 0.0905839 | + | 0.0905839i | 0.750947 | − | 0.660363i | \(-0.229597\pi\) |
−0.660363 | + | 0.750947i | \(0.729597\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.0278i | − | 0.722188i | −0.932529 | − | 0.361094i | \(-0.882403\pi\) | ||
0.932529 | − | 0.361094i | \(-0.117597\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.39445 | − | 7.39445i | −0.354537 | − | 0.354537i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.60555 | + | 2.60555i | −0.124640 | + | 0.124640i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.3028 | − | 26.3028i | 1.25536 | − | 1.25536i | 0.302081 | − | 0.953282i | \(-0.402319\pi\) |
0.953282 | − | 0.302081i | \(-0.0976812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 27.4222 | 1.30582 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2111 | −0.817724 | −0.408862 | − | 0.912596i | \(-0.634074\pi\) | ||||
−0.408862 | + | 0.912596i | \(0.634074\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.81665 | − | 7.81665i | 0.370545 | − | 0.370545i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.3944 | − | 19.3944i | 0.917326 | − | 0.917326i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.8167 | + | 16.8167i | 0.793627 | + | 0.793627i | 0.982082 | − | 0.188455i | \(-0.0603479\pi\) |
−0.188455 | + | 0.982082i | \(0.560348\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.605551i | − | 0.0285143i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.6056 | + | 10.6056i | 0.498292 | + | 0.498292i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 36.6056i | − | 1.71234i | −0.516698 | − | 0.856168i | \(-0.672839\pi\) | ||
0.516698 | − | 0.856168i | \(-0.327161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.2111i | 1.36050i | 0.732982 | + | 0.680248i | \(0.238128\pi\) | ||||
−0.732982 | + | 0.680248i | \(0.761872\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.6333 | −1.84192 | −0.920958 | − | 0.389662i | \(-0.872592\pi\) | ||||
−0.920958 | + | 0.389662i | \(0.872592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.8167 | + | 19.8167i | 0.918975 | + | 0.918975i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.2389i | 0.751445i | 0.926732 | + | 0.375722i | \(0.122605\pi\) | ||||
−0.926732 | + | 0.375722i | \(0.877395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.2111 | − | 21.2111i | −0.979438 | − | 0.979438i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.3944 | + | 19.3944i | −0.893649 | + | 0.893649i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.02776 | − | 1.02776i | 0.0472563 | − | 0.0472563i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.81665 | −0.0833538 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −39.6333 | −1.81468 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.3028 | + | 12.3028i | −0.562128 | + | 0.562128i | −0.929912 | − | 0.367783i | \(-0.880117\pi\) |
0.367783 | + | 0.929912i | \(0.380117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.81665 | + | 7.81665i | −0.356409 | + | 0.356409i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −45.6333 | − | 45.6333i | −2.07639 | − | 2.07639i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 15.2111i | − | 0.690701i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3305 | + | 17.3305i | 0.785321 | + | 0.785321i | 0.980723 | − | 0.195402i | \(-0.0626011\pi\) |
−0.195402 | + | 0.980723i | \(0.562601\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8167 | 0.896140 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.81665i | − | 0.443019i | −0.975158 | − | 0.221510i | \(-0.928902\pi\) | ||
0.975158 | − | 0.221510i | \(-0.0710984\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 4.60555i | − | 0.207004i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.3944 | 0.600823 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.3028 | − | 10.3028i | −0.461216 | − | 0.461216i | 0.437838 | − | 0.899054i | \(-0.355744\pi\) |
−0.899054 | + | 0.437838i | \(0.855744\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 68.6611i | 3.06755i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.5139 | − | 27.5139i | −1.22678 | − | 1.22678i | −0.965174 | − | 0.261609i | \(-0.915747\pi\) |
−0.261609 | − | 0.965174i | \(-0.584253\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.6056 | − | 10.6056i | 0.471941 | − | 0.471941i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.3028 | + | 14.3028i | −0.635209 | + | 0.635209i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.21110 | −0.142330 | −0.0711648 | − | 0.997465i | \(-0.522672\pi\) | ||||
−0.0711648 | + | 0.997465i | \(0.522672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.2389 | −1.42616 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.42221 | − | 6.42221i | 0.283547 | − | 0.283547i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.2111 | + | 13.2111i | −0.582151 | + | 0.582151i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.21110 | − | 1.21110i | −0.0532642 | − | 0.0532642i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 68.2389i | − | 2.99535i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0000 | − | 13.0000i | −0.569540 | − | 0.569540i | 0.362459 | − | 0.932000i | \(-0.381937\pi\) |
−0.932000 | + | 0.362459i | \(0.881937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0000 | −0.524723 | −0.262362 | − | 0.964970i | \(-0.584501\pi\) | ||||
−0.262362 | + | 0.964970i | \(0.584501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 31.8167i | − | 1.38859i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0278i | 0.609902i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −65.4500 | −2.84029 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.60555 | − | 2.60555i | −0.112859 | − | 0.112859i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.3944i | 0.492625i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.6056 | − | 34.6056i | −1.49334 | − | 1.49334i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.09167 | + | 1.09167i | −0.0470217 | + | 0.0470217i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.00000 | + | 3.00000i | −0.128980 | + | 0.128980i | −0.768650 | − | 0.639670i | \(-0.779071\pi\) |
0.639670 | + | 0.768650i | \(0.279071\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 59.8722 | 2.56936 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.4222 | 0.532109 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.5139 | − | 11.5139i | 0.492298 | − | 0.492298i | −0.416732 | − | 0.909030i | \(-0.636825\pi\) |
0.909030 | + | 0.416732i | \(0.136825\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 47.2389 | − | 47.2389i | 2.01611 | − | 2.01611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.972244 | + | 0.972244i | 0.0414190 | + | 0.0414190i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.39445i | − | 0.0592980i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.8167 | + | 13.8167i | 0.586484 | + | 0.586484i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.3944 | −0.906512 | −0.453256 | − | 0.891380i | \(-0.649738\pi\) | ||||
−0.453256 | + | 0.891380i | \(0.649738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.84441i | − | 0.374079i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.6056i | 0.868420i | 0.900812 | + | 0.434210i | \(0.142972\pi\) | ||||
−0.900812 | + | 0.434210i | \(0.857028\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.2111 | −0.808217 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 59.9361 | + | 59.9361i | 2.51708 | + | 2.51708i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 30.4222i | − | 1.27537i | −0.770299 | − | 0.637683i | \(-0.779893\pi\) | ||
0.770299 | − | 0.637683i | \(-0.220107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.30278 | − | 2.30278i | −0.0963682 | − | 0.0963682i | 0.657279 | − | 0.753647i | \(-0.271707\pi\) |
−0.753647 | + | 0.657279i | \(0.771707\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.6333 | − | 15.6333i | 0.653091 | − | 0.653091i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.9083 | + | 12.9083i | −0.538314 | + | 0.538314i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.4500 | −1.30928 | −0.654640 | − | 0.755941i | \(-0.727180\pi\) | ||||
−0.654640 | + | 0.755941i | \(0.727180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 37.8167 | 1.57161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.0278 | − | 41.0278i | 1.70212 | − | 1.70212i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.57779 | − | 1.57779i | 0.0653456 | − | 0.0653456i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.8167 | − | 19.8167i | −0.819318 | − | 0.819318i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.60555i | − | 0.190091i | −0.995473 | − | 0.0950457i | \(-0.969700\pi\) | ||
0.995473 | − | 0.0950457i | \(-0.0302997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.60555 | − | 2.60555i | −0.107360 | − | 0.107360i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 81.0833 | 3.33532 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.57779i | 0.0647923i | 0.999475 | + | 0.0323961i | \(0.0103138\pi\) | ||||
−0.999475 | + | 0.0323961i | \(0.989686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 46.6056i | − | 1.90744i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.0555 | 1.06460 | 0.532300 | − | 0.846556i | \(-0.321328\pi\) | ||||
0.532300 | + | 0.846556i | \(0.321328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.21110 | + | 4.21110i | 0.171774 | + | 0.171774i | 0.787759 | − | 0.615984i | \(-0.211241\pi\) |
−0.615984 | + | 0.787759i | \(0.711241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 70.0555i | − | 2.85288i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.8167 | − | 10.8167i | −0.439760 | − | 0.439760i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.51388 | + | 9.51388i | −0.386156 | + | 0.386156i | −0.873314 | − | 0.487158i | \(-0.838034\pi\) |
0.487158 | + | 0.873314i | \(0.338034\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.0278 | + | 17.0278i | −0.690000 | + | 0.690000i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.4222 | −0.421637 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.4222 | 1.63264 | 0.816319 | − | 0.577602i | \(-0.196011\pi\) | ||||
0.816319 | + | 0.577602i | \(0.196011\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.60555 | + | 4.60555i | −0.185714 | + | 0.185714i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.60555 | + | 1.60555i | −0.0646371 | + | 0.0646371i | −0.738686 | − | 0.674049i | \(-0.764554\pi\) |
0.674049 | + | 0.738686i | \(0.264554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4861 | − | 14.4861i | −0.582246 | − | 0.582246i | 0.353274 | − | 0.935520i | \(-0.385068\pi\) |
−0.935520 | + | 0.353274i | \(0.885068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 91.2666i | − | 3.66240i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.0000 | − | 18.0000i | −0.721155 | − | 0.721155i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.844410i | 0.0337225i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.2389i | 0.964934i | 0.875914 | + | 0.482467i | \(0.160259\pi\) | ||||
−0.875914 | + | 0.482467i | \(0.839741\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −71.4500 | −2.83988 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.605551 | − | 0.605551i | −0.0240306 | − | 0.0240306i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.39445i | 0.372222i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.1194 | + | 22.1194i | 0.875031 | + | 0.875031i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.8167 | + | 30.8167i | −1.21718 | + | 1.21718i | −0.248571 | + | 0.968614i | \(0.579961\pi\) |
−0.968614 | + | 0.248571i | \(0.920039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.11943 | + | 4.11943i | −0.162454 | + | 0.162454i | −0.783653 | − | 0.621199i | \(-0.786646\pi\) |
0.621199 | + | 0.783653i | \(0.286646\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.6333 | −0.615561 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2111 | −0.676638 | −0.338319 | − | 0.941031i | \(-0.609858\pi\) | ||||
−0.338319 | + | 0.941031i | \(0.609858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.60555 | − | 2.60555i | 0.102277 | − | 0.102277i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.6333 | − | 45.6333i | 1.78851 | − | 1.78851i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.8167 | − | 24.8167i | −0.971151 | − | 0.971151i | 0.0284447 | − | 0.999595i | \(-0.490945\pi\) |
−0.999595 | + | 0.0284447i | \(0.990945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.6056i | − | 0.492540i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −53.2389 | − | 53.2389i | −2.07705 | − | 2.07705i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.0000 | −1.24654 | −0.623272 | − | 0.782006i | \(-0.714197\pi\) | ||||
−0.623272 | + | 0.782006i | \(0.714197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.21110i | − | 0.0471064i | −0.999723 | − | 0.0235532i | \(-0.992502\pi\) | ||
0.999723 | − | 0.0235532i | \(-0.00749791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.78890i | − | 0.108149i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8167 | 0.534983 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.0278 | − | 41.0278i | −1.58622 | − | 1.58622i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.76114i | 0.145197i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.60555 | − | 5.60555i | −0.216078 | − | 0.216078i | 0.590765 | − | 0.806843i | \(-0.298826\pi\) |
−0.806843 | + | 0.590765i | \(0.798826\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 31.8167 | − | 31.8167i | 1.22462 | − | 1.22462i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.0278 | − | 16.0278i | 0.615997 | − | 0.615997i | −0.328505 | − | 0.944502i | \(-0.606545\pi\) |
0.944502 | + | 0.328505i | \(0.106545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.0278 | −1.34424 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.39445 | 0.0534354 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.724981 | − | 0.724981i | 0.0277406 | − | 0.0277406i | −0.693100 | − | 0.720841i | \(-0.743756\pi\) |
0.720841 | + | 0.693100i | \(0.243756\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.60555 | + | 2.60555i | −0.0995530 | + | 0.0995530i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.6056 | + | 10.6056i | 0.404627 | + | 0.404627i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13.5778i | − | 0.517273i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.51388 | + | 5.51388i | 0.209758 | + | 0.209758i | 0.804165 | − | 0.594407i | \(-0.202613\pi\) |
−0.594407 | + | 0.804165i | \(0.702613\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.6056 | −0.402872 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.605551i | 0.0229699i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.8167i | 0.976476i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.81665 | −0.295231 | −0.147615 | − | 0.989045i | \(-0.547160\pi\) | ||||
−0.147615 | + | 0.989045i | \(0.547160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.81665 | − | 1.81665i | −0.0685164 | − | 0.0685164i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.4222i | 0.693820i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.4222 | − | 24.4222i | −0.918492 | − | 0.918492i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.3944 | + | 14.3944i | −0.540595 | + | 0.540595i | −0.923703 | − | 0.383108i | \(-0.874854\pi\) |
0.383108 | + | 0.923703i | \(0.374854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.30278 | − | 2.30278i | 0.0863608 | − | 0.0863608i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.0278 | −1.38670 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.57779 | 0.0590062 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.0555 | + | 34.0555i | −1.27183 | + | 1.27183i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.72498 | − | 4.72498i | 0.176212 | − | 0.176212i | −0.613490 | − | 0.789702i | \(-0.710235\pi\) |
0.789702 | + | 0.613490i | \(0.210235\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.4222 | + | 30.4222i | 1.13298 | + | 1.13298i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 41.4500i | 1.54154i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.81665 | + | 4.81665i | 0.178886 | + | 0.178886i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.42221 | −0.238186 | −0.119093 | − | 0.992883i | \(-0.537999\pi\) | ||||
−0.119093 | + | 0.992883i | \(0.537999\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 51.4222i | 1.90453i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 46.0555i | − | 1.70110i | −0.525895 | − | 0.850550i | \(-0.676269\pi\) | ||
0.525895 | − | 0.850550i | \(-0.323731\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.6056 | 0.612505 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.78890 | + | 2.78890i | 0.102730 | + | 0.102730i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.6611i | 1.27503i | 0.770439 | + | 0.637514i | \(0.220037\pi\) | ||||
−0.770439 | + | 0.637514i | \(0.779963\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.63331 | + | 3.63331i | 0.133473 | + | 0.133473i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.7250 | + | 14.7250i | −0.540207 | + | 0.540207i | −0.923590 | − | 0.383383i | \(-0.874759\pi\) |
0.383383 | + | 0.923590i | \(0.374759\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.42221 | − | 8.42221i | 0.308566 | − | 0.308566i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 135.505 | 4.95789 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.2389 | 0.958747 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.69722 | + | 1.69722i | −0.0619326 | + | 0.0619326i | −0.737395 | − | 0.675462i | \(-0.763944\pi\) |
0.675462 | + | 0.737395i | \(0.263944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.6333 | + | 27.6333i | −1.00701 | + | 1.00701i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.60555 | + | 4.60555i | 0.167613 | + | 0.167613i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.0278i | 1.41849i | 0.704963 | + | 0.709244i | \(0.250964\pi\) | ||||
−0.704963 | + | 0.709244i | \(0.749036\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.00000 | + | 6.00000i | 0.217786 | + | 0.217786i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.4500 | −1.14006 | −0.570030 | − | 0.821624i | \(-0.693068\pi\) | ||||
−0.570030 | + | 0.821624i | \(0.693068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 28.6056i | − | 1.03559i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 22.4222i | − | 0.809619i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.6056 | −0.670933 | −0.335467 | − | 0.942052i | \(-0.608894\pi\) | ||||
−0.335467 | + | 0.942052i | \(0.608894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44.6611 | + | 44.6611i | 1.60843 | + | 1.60843i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 28.6056i | − | 1.02887i | −0.857529 | − | 0.514435i | \(-0.828002\pi\) | ||
0.857529 | − | 0.514435i | \(-0.171998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.9083 | − | 12.9083i | −0.463681 | − | 0.463681i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 31.8167 | − | 31.8167i | 1.14142 | − | 1.14142i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.605551 | − | 0.605551i | 0.0216961 | − | 0.0216961i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.76114 | −0.0630186 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −34.0555 | −1.21704 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.42221 | + | 8.42221i | −0.300601 | + | 0.300601i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.7250 | + | 14.7250i | −0.524889 | + | 0.524889i | −0.919044 | − | 0.394155i | \(-0.871037\pi\) |
0.394155 | + | 0.919044i | \(0.371037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 53.0278 | + | 53.0278i | 1.88784 | + | 1.88784i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.2389i | 1.57295i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1833 | + | 16.1833i | 0.574687 | + | 0.574687i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.0000 | −0.851192 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.63331i | 0.128698i | 0.997927 | + | 0.0643492i | \(0.0204971\pi\) | ||||
−0.997927 | + | 0.0643492i | \(0.979503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 59.4500i | − | 2.10056i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.23886 | 0.149586 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.8167 | − | 19.8167i | −0.698445 | − | 0.698445i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 80.2389i | 2.82454i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.8167 | + | 20.8167i | 0.731875 | + | 0.731875i | 0.970991 | − | 0.239116i | \(-0.0768577\pi\) |
−0.239116 | + | 0.970991i | \(0.576858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.7250 | + | 10.7250i | −0.376605 | + | 0.376605i | −0.869876 | − | 0.493271i | \(-0.835801\pi\) |
0.493271 | + | 0.869876i | \(0.335801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.78890 | − | 2.78890i | 0.0978109 | − | 0.0978109i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.60555 | 0.301439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.05551 | 0.0719133 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −45.6333 | + | 45.6333i | −1.59456 | + | 1.59456i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.8167 | + | 12.8167i | −0.447304 | + | 0.447304i | −0.894457 | − | 0.447153i | \(-0.852438\pi\) |
0.447153 | + | 0.894457i | \(0.352438\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.9083 | − | 12.9083i | −0.449956 | − | 0.449956i | 0.445384 | − | 0.895340i | \(-0.353067\pi\) |
−0.895340 | + | 0.445384i | \(0.853067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.18335i | 0.145645i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.30278 | − | 6.30278i | −0.219169 | − | 0.219169i | 0.588979 | − | 0.808148i | \(-0.299530\pi\) |
−0.808148 | + | 0.588979i | \(0.799530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.8444 | −0.654493 | −0.327247 | − | 0.944939i | \(-0.606121\pi\) | ||||
−0.327247 | + | 0.944939i | \(0.606121\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.6056i | 0.576040i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.8167i | 1.03185i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 91.2666 | 3.15464 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.9083 | + | 14.9083i | 0.514693 | + | 0.514693i | 0.915961 | − | 0.401268i | \(-0.131430\pi\) |
−0.401268 | + | 0.915961i | \(0.631430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.8444i | 0.822221i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.4222 | + | 42.4222i | 1.46110 | + | 1.46110i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.21110 | + | 6.21110i | −0.213668 | + | 0.213668i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.9083 | + | 24.9083i | −0.855860 | + | 0.855860i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.76114 | −0.335001 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.8167 | −0.884983 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.4222 | + | 29.4222i | −1.00740 | + | 1.00740i | −0.00742468 | + | 0.999972i | \(0.502363\pi\) |
−0.999972 | + | 0.00742468i | \(0.997637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.60555 | − | 4.60555i | 0.157507 | − | 0.157507i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.6333 | + | 18.6333i | 0.636502 | + | 0.636502i | 0.949691 | − | 0.313189i | \(-0.101397\pi\) |
−0.313189 | + | 0.949691i | \(0.601397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.81665i | 0.0619834i | 0.999520 | + | 0.0309917i | \(0.00986655\pi\) | ||||
−0.999520 | + | 0.0309917i | \(0.990133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.6056 | + | 10.6056i | 0.361436 | + | 0.361436i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.4777 | −1.78636 | −0.893181 | − | 0.449697i | \(-0.851532\pi\) | ||||
−0.893181 | + | 0.449697i | \(0.851532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 29.6333i | − | 1.00756i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.183346i | 0.00621959i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | 0.813209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −57.8444 | − | 57.8444i | −1.95774 | − | 1.95774i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 36.8444i | − | 1.24557i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.78890 | − | 1.78890i | −0.0604068 | − | 0.0604068i | 0.676258 | − | 0.736665i | \(-0.263600\pi\) |
−0.736665 | + | 0.676258i | \(0.763600\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −49.8167 | + | 49.8167i | −1.68027 | + | 1.68027i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.2111 | − | 24.2111i | 0.815693 | − | 0.815693i | −0.169788 | − | 0.985481i | \(-0.554308\pi\) |
0.985481 | + | 0.169788i | \(0.0543083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.5778 | 0.860761 | 0.430381 | − | 0.902647i | \(-0.358379\pi\) | ||||
0.430381 | + | 0.902647i | \(0.358379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39.6333 | −1.33226 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6972 | − | 11.6972i | 0.392754 | − | 0.392754i | −0.482914 | − | 0.875668i | \(-0.660421\pi\) |
0.875668 | + | 0.482914i | \(0.160421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.39445 | + | 1.39445i | −0.0467683 | + | 0.0467683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.88057 | − | 7.88057i | −0.264009 | − | 0.264009i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.42221i | − | 0.0810560i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.0278 | − | 15.0278i | −0.502322 | − | 0.502322i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 51.6333 | 1.72399 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.8167i | 0.460811i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.0000i | 1.19800i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.0000 | 0.864269 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5416 | − | 24.5416i | −0.814892 | − | 0.814892i | 0.170471 | − | 0.985363i | \(-0.445471\pi\) |
−0.985363 | + | 0.170471i | \(0.945471\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 80.6611i | − | 2.67536i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.72498 | − | 4.72498i | −0.156546 | − | 0.156546i | 0.624488 | − | 0.781034i | \(-0.285307\pi\) |
−0.781034 | + | 0.624488i | \(0.785307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.39445 | + | 5.39445i | −0.178530 | + | 0.178530i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28.6056 | − | 28.6056i | 0.945670 | − | 0.945670i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.0278 | −0.958581 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.8444 | 1.34733 | 0.673666 | − | 0.739036i | \(-0.264718\pi\) | ||||
0.673666 | + | 0.739036i | \(0.264718\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.8444 | − | 48.8444i | 1.60948 | − | 1.60948i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.57779 | + | 7.57779i | −0.249426 | + | 0.249426i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.00000 | − | 9.00000i | −0.295918 | − | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 100.478i | 3.30012i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.00000 | − | 1.00000i | −0.0328089 | − | 0.0328089i | 0.690512 | − | 0.723321i | \(-0.257385\pi\) |
−0.723321 | + | 0.690512i | \(0.757385\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.18335 | −0.0715563 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 87.0833i | 2.85098i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.42221i | 0.209804i | 0.994483 | + | 0.104902i | \(0.0334529\pi\) | ||||
−0.994483 | + | 0.104902i | \(0.966547\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.6056 | −0.933507 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.0278 | + | 16.0278i | 0.522490 | + | 0.522490i | 0.918323 | − | 0.395833i | \(-0.129544\pi\) |
−0.395833 | + | 0.918323i | \(0.629544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.60555i | − | 0.280235i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48.8444 | + | 48.8444i | 1.58891 | + | 1.58891i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.27502 | − | 9.27502i | 0.301398 | − | 0.301398i | −0.540163 | − | 0.841560i | \(-0.681637\pi\) |
0.841560 | + | 0.540163i | \(0.181637\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.2389 | − | 18.2389i | 0.592058 | − | 0.592058i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −90.2944 | −2.92800 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.2389 | 1.62740 | 0.813698 | − | 0.581288i | \(-0.197451\pi\) | ||||
0.813698 | + | 0.581288i | \(0.197451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.78890 | − | 6.78890i | 0.219684 | − | 0.219684i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.23886 | − | 2.23886i | 0.0723720 | − | 0.0723720i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | + | 6.00000i | 0.193750 | + | 0.193750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 6.02776i | − | 0.194444i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.3305 | + | 43.3305i | 1.39631 | + | 1.39631i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.4222 | 0.528649 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.8167i | 0.701576i | 0.936455 | + | 0.350788i | \(0.114086\pi\) | ||||
−0.936455 | + | 0.350788i | \(0.885914\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.0278i | 1.76592i | 0.469444 | + | 0.882962i | \(0.344454\pi\) | ||||
−0.469444 | + | 0.882962i | \(0.655546\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.39445 | 0.0447040 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.0000 | + | 18.0000i | 0.576461 | + | 0.576461i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.8444i | 0.538900i | 0.963014 | + | 0.269450i | \(0.0868420\pi\) | ||||
−0.963014 | + | 0.269450i | \(0.913158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.36669 | + | 2.36669i | 0.0756398 | + | 0.0756398i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.2389 | − | 47.2389i | 1.50822 | − | 1.50822i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.11943 | + | 8.11943i | −0.258970 | + | 0.258970i | −0.824635 | − | 0.565665i | \(-0.808619\pi\) |
0.565665 | + | 0.824635i | \(0.308619\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.2111 | 1.12192 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.4222 | 1.35031 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.6056 | − | 14.6056i | 0.464430 | − | 0.464430i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5139 | − | 23.5139i | 0.746943 | − | 0.746943i | −0.226961 | − | 0.973904i | \(-0.572879\pi\) |
0.973904 | + | 0.226961i | \(0.0728790\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.81665 | − | 7.81665i | −0.248054 | − | 0.248054i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 20.2389i | − | 0.641615i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.2389 | − | 39.2389i | −1.24271 | − | 1.24271i | −0.958874 | − | 0.283834i | \(-0.908394\pi\) |
−0.283834 | − | 0.958874i | \(-0.591606\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 63.6333 | 2.01327 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))