Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [229,2,Mod(228,229)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(229, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("229.228");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 229.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.82857420629\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-5}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 228.2 | ||
Root | \(2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 229.228 |
Dual form | 229.2.b.a.228.1 |
$q$-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 \(\left(\mathbb{Z}/229\mathbb{Z}\right)^\times\).
\(n\) | \(6\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23607i | 1.58114i | 0.612372 | + | 0.790569i | \(0.290215\pi\) | ||||
−0.612372 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | −3.00000 | −1.50000 | ||||||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 2.23607i | 0.912871i | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | − | 2.23607i | − | 0.790569i | ||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 6.70820i | 2.12132i | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | −3.00000 | −0.866025 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | − | 4.47214i | − | 1.05409i | ||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | −9.00000 | −2.01246 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.70820i | 1.43019i | ||||||||
\(23\) | − | 4.47214i | − | 0.932505i | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||
0.884652 | − | 0.466252i | \(-0.154396\pi\) | |||||||
\(24\) | − | 2.23607i | − | 0.456435i | ||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.47214i | − | 0.830455i | −0.909718 | − | 0.415227i | \(-0.863702\pi\) | ||
0.909718 | − | 0.415227i | \(-0.136298\pi\) | |||||||
\(30\) | 6.70820i | 1.22474i | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | − | 6.70820i | − | 1.18585i | ||||||
\(33\) | 3.00000 | 0.522233 | ||||||||
\(34\) | − | 6.70820i | − | 1.15045i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | − | 2.23607i | − | 0.362738i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 6.70820i | − | 1.06066i | ||||||
\(41\) | − | 4.47214i | − | 0.698430i | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||
0.937043 | − | 0.349215i | \(-0.113552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | −9.00000 | −1.35680 | ||||||||
\(45\) | −6.00000 | −0.894427 | ||||||||
\(46\) | 10.0000 | 1.47442 | ||||||||
\(47\) | 8.94427i | 1.30466i | 0.757937 | + | 0.652328i | \(0.226208\pi\) | ||||
−0.757937 | + | 0.652328i | \(0.773792\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 8.94427i | 1.26491i | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | − | 11.1803i | − | 1.52145i | ||||||
\(55\) | 9.00000 | 1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 10.0000 | 1.31306 | ||||||||
\(59\) | 8.94427i | 1.16445i | 0.813029 | + | 0.582223i | \(0.197817\pi\) | ||||
−0.813029 | + | 0.582223i | \(0.802183\pi\) | |||||||
\(60\) | −9.00000 | −1.16190 | ||||||||
\(61\) | 5.00000 | 0.640184 | 0.320092 | − | 0.947386i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947386i | \(0.396286\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.70820i | 0.825723i | ||||||||
\(67\) | 13.4164i | 1.63908i | 0.573025 | + | 0.819538i | \(0.305770\pi\) | ||||
−0.573025 | + | 0.819538i | \(0.694230\pi\) | |||||||
\(68\) | 9.00000 | 1.09141 | ||||||||
\(69\) | − | 4.47214i | − | 0.538382i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.0000 | −1.78017 | −0.890086 | − | 0.455792i | \(-0.849356\pi\) | ||||
−0.890086 | + | 0.455792i | \(0.849356\pi\) | |||||||
\(72\) | 4.47214i | 0.527046i | ||||||||
\(73\) | − | 13.4164i | − | 1.57027i | −0.619324 | − | 0.785136i | \(-0.712593\pi\) | ||
0.619324 | − | 0.785136i | \(-0.287407\pi\) | |||||||
\(74\) | 4.47214i | 0.519875i | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | 3.00000 | 0.344124 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.4164i | − | 1.50946i | −0.656033 | − | 0.754732i | \(-0.727767\pi\) | ||
0.656033 | − | 0.754732i | \(-0.272233\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.0000 | 1.10432 | ||||||||
\(83\) | −9.00000 | −0.987878 | −0.493939 | − | 0.869496i | \(-0.664443\pi\) | ||||
−0.493939 | + | 0.869496i | \(0.664443\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | −0.976187 | ||||||||
\(86\) | − | 2.23607i | − | 0.241121i | ||||||
\(87\) | − | 4.47214i | − | 0.479463i | ||||||
\(88\) | − | 6.70820i | − | 0.715097i | ||||||
\(89\) | − | 17.8885i | − | 1.89618i | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||
0.317999 | − | 0.948091i | \(-0.396989\pi\) | |||||||
\(90\) | − | 13.4164i | − | 1.41421i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.4164i | 1.39876i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.0000 | −2.06284 | ||||||||
\(95\) | −3.00000 | −0.307794 | ||||||||
\(96\) | − | 6.70820i | − | 0.684653i | ||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | 15.6525i | 1.58114i | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | −12.0000 | −1.20000 | ||||||||
\(101\) | − | 4.47214i | − | 0.444994i | −0.974933 | − | 0.222497i | \(-0.928579\pi\) | ||
0.974933 | − | 0.222497i | \(-0.0714208\pi\) | |||||||
\(102\) | − | 6.70820i | − | 0.664211i | ||||||
\(103\) | 11.0000 | 1.08386 | 0.541931 | − | 0.840423i | \(-0.317693\pi\) | ||||
0.541931 | + | 0.840423i | \(0.317693\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4164i | 1.30312i | ||||||||
\(107\) | 8.94427i | 0.864675i | 0.901712 | + | 0.432338i | \(0.142311\pi\) | ||||
−0.901712 | + | 0.432338i | \(0.857689\pi\) | |||||||
\(108\) | 15.0000 | 1.44338 | ||||||||
\(109\) | 13.4164i | 1.28506i | 0.766261 | + | 0.642529i | \(0.222115\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | 20.1246i | 1.91881i | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.94427i | 0.841406i | 0.907198 | + | 0.420703i | \(0.138217\pi\) | ||||
−0.907198 | + | 0.420703i | \(0.861783\pi\) | |||||||
\(114\) | − | 2.23607i | − | 0.209427i | ||||||
\(115\) | − | 13.4164i | − | 1.25109i | ||||||
\(116\) | 13.4164i | 1.24568i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20.0000 | −1.84115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 6.70820i | − | 0.612372i | ||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 11.1803i | 1.01222i | ||||||||
\(123\) | − | 4.47214i | − | 0.403239i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 15.6525i | 1.38350i | ||||||||
\(129\) | −1.00000 | −0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.47214i | − | 0.390732i | −0.980730 | − | 0.195366i | \(-0.937410\pi\) | ||
0.980730 | − | 0.195366i | \(-0.0625895\pi\) | |||||||
\(132\) | −9.00000 | −0.783349 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −30.0000 | −2.59161 | ||||||||
\(135\) | −15.0000 | −1.29099 | ||||||||
\(136\) | 6.70820i | 0.575224i | ||||||||
\(137\) | 8.94427i | 0.764161i | 0.924129 | + | 0.382080i | \(0.124792\pi\) | ||||
−0.924129 | + | 0.382080i | \(0.875208\pi\) | |||||||
\(138\) | 10.0000 | 0.851257 | ||||||||
\(139\) | 13.4164i | 1.13796i | 0.822350 | + | 0.568982i | \(0.192663\pi\) | ||||
−0.822350 | + | 0.568982i | \(0.807337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.94427i | 0.753244i | ||||||||
\(142\) | − | 33.5410i | − | 2.81470i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.00000 | 0.166667 | ||||||||
\(145\) | − | 13.4164i | − | 1.11417i | ||||||
\(146\) | 30.0000 | 2.48282 | ||||||||
\(147\) | 7.00000 | 0.577350 | ||||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | −21.0000 | −1.72039 | −0.860194 | − | 0.509968i | \(-0.829657\pi\) | ||||
−0.860194 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(150\) | 8.94427i | 0.730297i | ||||||||
\(151\) | −7.00000 | −0.569652 | −0.284826 | − | 0.958579i | \(-0.591936\pi\) | ||||
−0.284826 | + | 0.958579i | \(0.591936\pi\) | |||||||
\(152\) | 2.23607i | 0.181369i | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4164i | 1.07075i | 0.844616 | + | 0.535373i | \(0.179829\pi\) | ||||
−0.844616 | + | 0.535373i | \(0.820171\pi\) | |||||||
\(158\) | 30.0000 | 2.38667 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | − | 20.1246i | − | 1.59099i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.23607i | 0.175682i | ||||||||
\(163\) | 13.4164i | 1.05085i | 0.850839 | + | 0.525427i | \(0.176094\pi\) | ||||
−0.850839 | + | 0.525427i | \(0.823906\pi\) | |||||||
\(164\) | 13.4164i | 1.04765i | ||||||||
\(165\) | 9.00000 | 0.700649 | ||||||||
\(166\) | − | 20.1246i | − | 1.56197i | ||||||
\(167\) | 3.00000 | 0.232147 | 0.116073 | − | 0.993241i | \(-0.462969\pi\) | ||||
0.116073 | + | 0.993241i | \(0.462969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | − | 20.1246i | − | 1.54349i | ||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 3.00000 | 0.228748 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 10.0000 | 0.758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 8.94427i | 0.672293i | ||||||||
\(178\) | 40.0000 | 2.99813 | ||||||||
\(179\) | − | 17.8885i | − | 1.33705i | −0.743689 | − | 0.668526i | \(-0.766925\pi\) | ||
0.743689 | − | 0.668526i | \(-0.233075\pi\) | |||||||
\(180\) | 18.0000 | 1.34164 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.00000 | 0.369611 | ||||||||
\(184\) | −10.0000 | −0.737210 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | −0.658145 | ||||||||
\(188\) | − | 26.8328i | − | 1.95698i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 6.70820i | − | 0.486664i | ||||||
\(191\) | 8.94427i | 0.647185i | 0.946197 | + | 0.323592i | \(0.104891\pi\) | ||||
−0.946197 | + | 0.323592i | \(0.895109\pi\) | |||||||
\(192\) | 13.0000 | 0.938194 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | − | 15.6525i | − | 1.12378i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.0000 | −1.50000 | ||||||||
\(197\) | − | 17.8885i | − | 1.27451i | −0.770655 | − | 0.637253i | \(-0.780071\pi\) | ||
0.770655 | − | 0.637253i | \(-0.219929\pi\) | |||||||
\(198\) | − | 13.4164i | − | 0.953463i | ||||||
\(199\) | 13.4164i | 0.951064i | 0.879698 | + | 0.475532i | \(0.157744\pi\) | ||||
−0.879698 | + | 0.475532i | \(0.842256\pi\) | |||||||
\(200\) | − | 8.94427i | − | 0.632456i | ||||||
\(201\) | 13.4164i | 0.946320i | ||||||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.00000 | 0.630126 | ||||||||
\(205\) | − | 13.4164i | − | 0.937043i | ||||||
\(206\) | 24.5967i | 1.71374i | ||||||||
\(207\) | 8.94427i | 0.621670i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.4164i | 0.923624i | 0.886978 | + | 0.461812i | \(0.152800\pi\) | ||||
−0.886978 | + | 0.461812i | \(0.847200\pi\) | |||||||
\(212\) | −18.0000 | −1.23625 | ||||||||
\(213\) | −15.0000 | −1.02778 | ||||||||
\(214\) | −20.0000 | −1.36717 | ||||||||
\(215\) | −3.00000 | −0.204598 | ||||||||
\(216\) | 11.1803i | 0.760726i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −30.0000 | −2.03186 | ||||||||
\(219\) | − | 13.4164i | − | 0.906597i | ||||||
\(220\) | −27.0000 | −1.82034 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.47214i | 0.300150i | ||||||||
\(223\) | 13.4164i | 0.898429i | 0.893424 | + | 0.449215i | \(0.148296\pi\) | ||||
−0.893424 | + | 0.449215i | \(0.851704\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.00000 | −0.533333 | ||||||||
\(226\) | −20.0000 | −1.33038 | ||||||||
\(227\) | − | 4.47214i | − | 0.296826i | −0.988925 | − | 0.148413i | \(-0.952583\pi\) | ||
0.988925 | − | 0.148413i | \(-0.0474165\pi\) | |||||||
\(228\) | 3.00000 | 0.198680 | ||||||||
\(229\) | 7.00000 | + | 13.4164i | 0.462573 | + | 0.886581i | ||||
\(230\) | 30.0000 | 1.97814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.0000 | −0.656532 | ||||||||
\(233\) | 9.00000 | 0.589610 | 0.294805 | − | 0.955557i | \(-0.404745\pi\) | ||||
0.294805 | + | 0.955557i | \(0.404745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.8328i | 1.75038i | ||||||||
\(236\) | − | 26.8328i | − | 1.74667i | ||||||
\(237\) | − | 13.4164i | − | 0.871489i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3607i | 1.44639i | 0.690643 | + | 0.723196i | \(0.257328\pi\) | ||||
−0.690643 | + | 0.723196i | \(0.742672\pi\) | |||||||
\(240\) | −3.00000 | −0.193649 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | − | 4.47214i | − | 0.287480i | ||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | −15.0000 | −0.960277 | ||||||||
\(245\) | 21.0000 | 1.34164 | ||||||||
\(246\) | 10.0000 | 0.637577 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.00000 | −0.570352 | ||||||||
\(250\) | − | 6.70820i | − | 0.424264i | ||||||
\(251\) | − | 17.8885i | − | 1.12911i | −0.825394 | − | 0.564557i | \(-0.809047\pi\) | ||
0.825394 | − | 0.564557i | \(-0.190953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.4164i | − | 0.843482i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.00000 | −0.563602 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | − | 17.8885i | − | 1.11586i | −0.829889 | − | 0.557928i | \(-0.811596\pi\) | ||
0.829889 | − | 0.557928i | \(-0.188404\pi\) | |||||||
\(258\) | − | 2.23607i | − | 0.139212i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.94427i | 0.553637i | ||||||||
\(262\) | 10.0000 | 0.617802 | ||||||||
\(263\) | − | 4.47214i | − | 0.275764i | −0.990449 | − | 0.137882i | \(-0.955971\pi\) | ||
0.990449 | − | 0.137882i | \(-0.0440294\pi\) | |||||||
\(264\) | − | 6.70820i | − | 0.412861i | ||||||
\(265\) | 18.0000 | 1.10573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 17.8885i | − | 1.09476i | ||||||
\(268\) | − | 40.2492i | − | 2.45861i | ||||||
\(269\) | 22.3607i | 1.36335i | 0.731653 | + | 0.681677i | \(0.238749\pi\) | ||||
−0.731653 | + | 0.681677i | \(0.761251\pi\) | |||||||
\(270\) | − | 33.5410i | − | 2.04124i | ||||||
\(271\) | −25.0000 | −1.51864 | −0.759321 | − | 0.650716i | \(-0.774469\pi\) | ||||
−0.759321 | + | 0.650716i | \(0.774469\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.0000 | −1.20824 | ||||||||
\(275\) | 12.0000 | 0.723627 | ||||||||
\(276\) | 13.4164i | 0.807573i | ||||||||
\(277\) | 17.0000 | 1.02143 | 0.510716 | − | 0.859750i | \(-0.329381\pi\) | ||||
0.510716 | + | 0.859750i | \(0.329381\pi\) | |||||||
\(278\) | −30.0000 | −1.79928 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 31.3050i | − | 1.86750i | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||
0.357930 | − | 0.933748i | \(-0.383483\pi\) | |||||||
\(282\) | −20.0000 | −1.19098 | ||||||||
\(283\) | 13.4164i | 0.797523i | 0.917055 | + | 0.398761i | \(0.130560\pi\) | ||||
−0.917055 | + | 0.398761i | \(0.869440\pi\) | |||||||
\(284\) | 45.0000 | 2.67026 | ||||||||
\(285\) | −3.00000 | −0.177705 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 13.4164i | 0.790569i | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 30.0000 | 1.76166 | ||||||||
\(291\) | −7.00000 | −0.410347 | ||||||||
\(292\) | 40.2492i | 2.35541i | ||||||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 15.6525i | 0.912871i | ||||||||
\(295\) | 26.8328i | 1.56227i | ||||||||
\(296\) | − | 4.47214i | − | 0.259938i | ||||||
\(297\) | −15.0000 | −0.870388 | ||||||||
\(298\) | − | 46.9574i | − | 2.72017i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −12.0000 | −0.692820 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 15.6525i | − | 0.900699i | ||||||
\(303\) | − | 4.47214i | − | 0.256917i | ||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 15.0000 | 0.858898 | ||||||||
\(306\) | 13.4164i | 0.766965i | ||||||||
\(307\) | 17.0000 | 0.970241 | 0.485121 | − | 0.874447i | \(-0.338776\pi\) | ||||
0.485121 | + | 0.874447i | \(0.338776\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.0000 | 0.625768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0000 | 0.850572 | 0.425286 | − | 0.905059i | \(-0.360174\pi\) | ||||
0.425286 | + | 0.905059i | \(0.360174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.4164i | − | 0.758340i | −0.925327 | − | 0.379170i | \(-0.876210\pi\) | ||
0.925327 | − | 0.379170i | \(-0.123790\pi\) | |||||||
\(314\) | −30.0000 | −1.69300 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 40.2492i | 2.26420i | ||||||||
\(317\) | 8.94427i | 0.502360i | 0.967940 | + | 0.251180i | \(0.0808187\pi\) | ||||
−0.967940 | + | 0.251180i | \(0.919181\pi\) | |||||||
\(318\) | 13.4164i | 0.752355i | ||||||||
\(319\) | − | 13.4164i | − | 0.751175i | ||||||
\(320\) | 39.0000 | 2.18017 | ||||||||
\(321\) | 8.94427i | 0.499221i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | −3.00000 | −0.166667 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.0000 | −1.66155 | ||||||||
\(327\) | 13.4164i | 0.741929i | ||||||||
\(328\) | −10.0000 | −0.552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 20.1246i | 1.10782i | ||||||||
\(331\) | − | 13.4164i | − | 0.737432i | −0.929542 | − | 0.368716i | \(-0.879797\pi\) | ||
0.929542 | − | 0.368716i | \(-0.120203\pi\) | |||||||
\(332\) | 27.0000 | 1.48182 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | 6.70820i | 0.367057i | ||||||||
\(335\) | 40.2492i | 2.19905i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.0000 | −0.708155 | −0.354078 | − | 0.935216i | \(-0.615205\pi\) | ||||
−0.354078 | + | 0.935216i | \(0.615205\pi\) | |||||||
\(338\) | 29.0689i | 1.58114i | ||||||||
\(339\) | 8.94427i | 0.485786i | ||||||||
\(340\) | 27.0000 | 1.46428 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.47214i | 0.241825i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.23607i | 0.120561i | ||||||||
\(345\) | − | 13.4164i | − | 0.722315i | ||||||
\(346\) | 13.4164i | 0.721271i | ||||||||
\(347\) | −12.0000 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(348\) | 13.4164i | 0.719195i | ||||||||
\(349\) | 13.4164i | 0.718164i | 0.933306 | + | 0.359082i | \(0.116910\pi\) | ||||
−0.933306 | + | 0.359082i | \(0.883090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 20.1246i | − | 1.07265i | ||||||
\(353\) | 8.94427i | 0.476056i | 0.971258 | + | 0.238028i | \(0.0765009\pi\) | ||||
−0.971258 | + | 0.238028i | \(0.923499\pi\) | |||||||
\(354\) | −20.0000 | −1.06299 | ||||||||
\(355\) | −45.0000 | −2.38835 | ||||||||
\(356\) | 53.6656i | 2.84427i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 40.0000 | 2.11407 | ||||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 13.4164i | 0.707107i | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | − | 15.6525i | − | 0.822676i | ||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 40.2492i | − | 2.10674i | ||||||
\(366\) | 11.1803i | 0.584406i | ||||||||
\(367\) | 17.0000 | 0.887393 | 0.443696 | − | 0.896177i | \(-0.353667\pi\) | ||||
0.443696 | + | 0.896177i | \(0.353667\pi\) | |||||||
\(368\) | 4.47214i | 0.233126i | ||||||||
\(369\) | 8.94427i | 0.465620i | ||||||||
\(370\) | 13.4164i | 0.697486i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0000 | −0.983783 | −0.491891 | − | 0.870657i | \(-0.663694\pi\) | ||||
−0.491891 | + | 0.870657i | \(0.663694\pi\) | |||||||
\(374\) | − | 20.1246i | − | 1.04062i | ||||||
\(375\) | −3.00000 | −0.154919 | ||||||||
\(376\) | 20.0000 | 1.03142 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 9.00000 | 0.461690 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.0000 | −1.02329 | ||||||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | 15.6525i | 0.798762i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.3050i | 1.59338i | ||||||||
\(387\) | 2.00000 | 0.101666 | ||||||||
\(388\) | 21.0000 | 1.06611 | ||||||||
\(389\) | − | 31.3050i | − | 1.58722i | −0.608424 | − | 0.793612i | \(-0.708198\pi\) | ||
0.608424 | − | 0.793612i | \(-0.291802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.4164i | 0.678497i | ||||||||
\(392\) | − | 15.6525i | − | 0.790569i | ||||||
\(393\) | − | 4.47214i | − | 0.225589i | ||||||
\(394\) | 40.0000 | 2.01517 | ||||||||
\(395\) | − | 40.2492i | − | 2.02516i | ||||||
\(396\) | 18.0000 | 0.904534 | ||||||||
\(397\) | 23.0000 | 1.15434 | 0.577168 | − | 0.816625i | \(-0.304158\pi\) | ||||
0.577168 | + | 0.816625i | \(0.304158\pi\) | |||||||
\(398\) | −30.0000 | −1.50376 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 27.0000 | 1.34832 | 0.674158 | − | 0.738587i | \(-0.264507\pi\) | ||||
0.674158 | + | 0.738587i | \(0.264507\pi\) | |||||||
\(402\) | −30.0000 | −1.49626 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 13.4164i | 0.667491i | ||||||||
\(405\) | 3.00000 | 0.149071 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 6.70820i | 0.332106i | ||||||||
\(409\) | 35.0000 | 1.73064 | 0.865319 | − | 0.501221i | \(-0.167116\pi\) | ||||
0.865319 | + | 0.501221i | \(0.167116\pi\) | |||||||
\(410\) | 30.0000 | 1.48159 | ||||||||
\(411\) | 8.94427i | 0.441188i | ||||||||
\(412\) | −33.0000 | −1.62579 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −20.0000 | −0.982946 | ||||||||
\(415\) | −27.0000 | −1.32538 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4164i | 0.657004i | ||||||||
\(418\) | − | 6.70820i | − | 0.328109i | ||||||
\(419\) | − | 4.47214i | − | 0.218478i | −0.994016 | − | 0.109239i | \(-0.965159\pi\) | ||
0.994016 | − | 0.109239i | \(-0.0348414\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0000 | 0.828529 | 0.414265 | − | 0.910156i | \(-0.364039\pi\) | ||||
0.414265 | + | 0.910156i | \(0.364039\pi\) | |||||||
\(422\) | −30.0000 | −1.46038 | ||||||||
\(423\) | − | 17.8885i | − | 0.869771i | ||||||
\(424\) | − | 13.4164i | − | 0.651558i | ||||||
\(425\) | −12.0000 | −0.582086 | ||||||||
\(426\) | − | 33.5410i | − | 1.62507i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 26.8328i | − | 1.29701i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 6.70820i | − | 0.323498i | ||||||
\(431\) | 15.0000 | 0.722525 | 0.361262 | − | 0.932464i | \(-0.382346\pi\) | ||||
0.361262 | + | 0.932464i | \(0.382346\pi\) | |||||||
\(432\) | 5.00000 | 0.240563 | ||||||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 13.4164i | − | 0.643268i | ||||||
\(436\) | − | 40.2492i | − | 1.92759i | ||||||
\(437\) | 4.47214i | 0.213931i | ||||||||
\(438\) | 30.0000 | 1.43346 | ||||||||
\(439\) | 20.0000 | 0.954548 | 0.477274 | − | 0.878755i | \(-0.341625\pi\) | ||||
0.477274 | + | 0.878755i | \(0.341625\pi\) | |||||||
\(440\) | − | 20.1246i | − | 0.959403i | ||||||
\(441\) | −14.0000 | −0.666667 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.0000 | 1.71041 | 0.855206 | − | 0.518289i | \(-0.173431\pi\) | ||||
0.855206 | + | 0.518289i | \(0.173431\pi\) | |||||||
\(444\) | −6.00000 | −0.284747 | ||||||||
\(445\) | − | 53.6656i | − | 2.54399i | ||||||
\(446\) | −30.0000 | −1.42054 | ||||||||
\(447\) | −21.0000 | −0.993266 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | − | 17.8885i | − | 0.843274i | ||||||
\(451\) | − | 13.4164i | − | 0.631754i | ||||||
\(452\) | − | 26.8328i | − | 1.26211i | ||||||
\(453\) | −7.00000 | −0.328889 | ||||||||
\(454\) | 10.0000 | 0.469323 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.23607i | 0.104713i | ||||||||
\(457\) | 23.0000 | 1.07589 | 0.537947 | − | 0.842978i | \(-0.319200\pi\) | ||||
0.537947 | + | 0.842978i | \(0.319200\pi\) | |||||||
\(458\) | −30.0000 | + | 15.6525i | −1.40181 | + | 0.731392i | ||||
\(459\) | 15.0000 | 0.700140 | ||||||||
\(460\) | 40.2492i | 1.87663i | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | −0.0464739 | −0.0232370 | − | 0.999730i | \(-0.507397\pi\) | ||||
−0.0232370 | + | 0.999730i | \(0.507397\pi\) | |||||||
\(464\) | 4.47214i | 0.207614i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.1246i | 0.932255i | ||||||||
\(467\) | 27.0000 | 1.24941 | 0.624705 | − | 0.780860i | \(-0.285219\pi\) | ||||
0.624705 | + | 0.780860i | \(0.285219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −60.0000 | −2.76759 | ||||||||
\(471\) | 13.4164i | 0.618195i | ||||||||
\(472\) | 20.0000 | 0.920575 | ||||||||
\(473\) | −3.00000 | −0.137940 | ||||||||
\(474\) | 30.0000 | 1.37795 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | −50.0000 | −2.28695 | ||||||||
\(479\) | 8.94427i | 0.408674i | 0.978901 | + | 0.204337i | \(0.0655039\pi\) | ||||
−0.978901 | + | 0.204337i | \(0.934496\pi\) | |||||||
\(480\) | − | 20.1246i | − | 0.918559i | ||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 22.3607i | − | 1.01850i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.00000 | 0.272727 | ||||||||
\(485\) | −21.0000 | −0.953561 | ||||||||
\(486\) | 35.7771i | 1.62288i | ||||||||
\(487\) | − | 13.4164i | − | 0.607955i | −0.952679 | − | 0.303978i | \(-0.901685\pi\) | ||
0.952679 | − | 0.303978i | \(-0.0983148\pi\) | |||||||
\(488\) | − | 11.1803i | − | 0.506110i | ||||||
\(489\) | 13.4164i | 0.606711i | ||||||||
\(490\) | 46.9574i | 2.12132i | ||||||||
\(491\) | −15.0000 | −0.676941 | −0.338470 | − | 0.940977i | \(-0.609909\pi\) | ||||
−0.338470 | + | 0.940977i | \(0.609909\pi\) | |||||||
\(492\) | 13.4164i | 0.604858i | ||||||||
\(493\) | 13.4164i | 0.604245i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.0000 | −0.809040 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 20.1246i | − | 0.901805i | ||||||
\(499\) | − | 26.8328i | − | 1.20120i | −0.799549 | − | 0.600601i | \(-0.794928\pi\) | ||
0.799549 | − | 0.600601i | \(-0.205072\pi\) | |||||||
\(500\) | 9.00000 | 0.402492 | ||||||||
\(501\) | 3.00000 | 0.134030 | ||||||||
\(502\) | 40.0000 | 1.78529 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 13.4164i | − | 0.597022i | ||||||
\(506\) | 30.0000 | 1.33366 | ||||||||
\(507\) | 13.0000 | 0.577350 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.00000 | 0.265945 | 0.132973 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132973 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(510\) | − | 20.1246i | − | 0.891133i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.1803i | 0.494106i | ||||||||
\(513\) | 5.00000 | 0.220755 | ||||||||
\(514\) | 40.0000 | 1.76432 | ||||||||
\(515\) | 33.0000 | 1.45415 | ||||||||
\(516\) | 3.00000 | 0.132068 | ||||||||
\(517\) | 26.8328i | 1.18011i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 31.3050i | − | 1.37149i | −0.727840 | − | 0.685747i | \(-0.759475\pi\) | ||
0.727840 | − | 0.685747i | \(-0.240525\pi\) | |||||||
\(522\) | −20.0000 | −0.875376 | ||||||||
\(523\) | − | 26.8328i | − | 1.17332i | −0.809834 | − | 0.586659i | \(-0.800443\pi\) | ||
0.809834 | − | 0.586659i | \(-0.199557\pi\) | |||||||
\(524\) | 13.4164i | 0.586098i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0000 | 0.436021 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −3.00000 | −0.130558 | ||||||||
\(529\) | 3.00000 | 0.130435 | ||||||||
\(530\) | 40.2492i | 1.74831i | ||||||||
\(531\) | − | 17.8885i | − | 0.776297i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 40.0000 | 1.73097 | ||||||||
\(535\) | 26.8328i | 1.16008i | ||||||||
\(536\) | 30.0000 | 1.29580 | ||||||||
\(537\) | − | 17.8885i | − | 0.771948i | ||||||
\(538\) | −50.0000 | −2.15565 | ||||||||
\(539\) | 21.0000 | 0.904534 | ||||||||
\(540\) | 45.0000 | 1.93649 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | − | 55.9017i | − | 2.40118i | ||||||
\(543\) | −7.00000 | −0.300399 | ||||||||
\(544\) | 20.1246i | 0.862836i | ||||||||
\(545\) | 40.2492i | 1.72409i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.4164i | 0.573644i | 0.957984 | + | 0.286822i | \(0.0925989\pi\) | ||||
−0.957984 | + | 0.286822i | \(0.907401\pi\) | |||||||
\(548\) | − | 26.8328i | − | 1.14624i | ||||||
\(549\) | −10.0000 | −0.426790 | ||||||||
\(550\) | 26.8328i | 1.14416i | ||||||||
\(551\) | 4.47214i | 0.190519i | ||||||||
\(552\) | −10.0000 | −0.425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 38.0132i | 1.61502i | ||||||||
\(555\) | 6.00000 | 0.254686 | ||||||||
\(556\) | − | 40.2492i | − | 1.70695i | ||||||
\(557\) | −3.00000 | −0.127114 | −0.0635570 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635570 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | −0.379980 | ||||||||
\(562\) | 70.0000 | 2.95277 | ||||||||
\(563\) | − | 44.7214i | − | 1.88478i | −0.334515 | − | 0.942390i | \(-0.608573\pi\) | ||
0.334515 | − | 0.942390i | \(-0.391427\pi\) | |||||||
\(564\) | − | 26.8328i | − | 1.12987i | ||||||
\(565\) | 26.8328i | 1.12887i | ||||||||
\(566\) | −30.0000 | −1.26099 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 33.5410i | 1.40735i | ||||||||
\(569\) | 45.0000 | 1.88650 | 0.943249 | − | 0.332086i | \(-0.107752\pi\) | ||||
0.943249 | + | 0.332086i | \(0.107752\pi\) | |||||||
\(570\) | − | 6.70820i | − | 0.280976i | ||||||
\(571\) | − | 26.8328i | − | 1.12292i | −0.827504 | − | 0.561459i | \(-0.810240\pi\) | ||
0.827504 | − | 0.561459i | \(-0.189760\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.94427i | 0.373652i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 17.8885i | − | 0.746004i | ||||||
\(576\) | −26.0000 | −1.08333 | ||||||||
\(577\) | 40.2492i | 1.67560i | 0.545979 | + | 0.837799i | \(0.316158\pi\) | ||||
−0.545979 | + | 0.837799i | \(0.683842\pi\) | |||||||
\(578\) | − | 17.8885i | − | 0.744065i | ||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 40.2492i | 1.67126i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 15.6525i | − | 0.648816i | ||||||
\(583\) | 18.0000 | 0.745484 | ||||||||
\(584\) | −30.0000 | −1.24141 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.1246i | 0.831340i | ||||||||
\(587\) | −27.0000 | −1.11441 | −0.557205 | − | 0.830375i | \(-0.688126\pi\) | ||||
−0.557205 | + | 0.830375i | \(0.688126\pi\) | |||||||
\(588\) | −21.0000 | −0.866025 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −60.0000 | −2.47016 | ||||||||
\(591\) | − | 17.8885i | − | 0.735836i | ||||||
\(592\) | −2.00000 | −0.0821995 | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | − | 33.5410i | − | 1.37620i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 63.0000 | 2.58058 | ||||||||
\(597\) | 13.4164i | 0.549097i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.94427i | 0.365453i | 0.983164 | + | 0.182727i | \(0.0584923\pi\) | ||||
−0.983164 | + | 0.182727i | \(0.941508\pi\) | |||||||
\(600\) | − | 8.94427i | − | 0.365148i | ||||||
\(601\) | − | 40.2492i | − | 1.64180i | −0.571072 | − | 0.820900i | \(-0.693472\pi\) | ||
0.571072 | − | 0.820900i | \(-0.306528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 26.8328i | − | 1.09272i | ||||||
\(604\) | 21.0000 | 0.854478 | ||||||||
\(605\) | −6.00000 | −0.243935 | ||||||||
\(606\) | 10.0000 | 0.406222 | ||||||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | 6.70820i | 0.272054i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 33.5410i | 1.35804i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −18.0000 | −0.727607 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 38.0132i | 1.53409i | ||||||||
\(615\) | − | 13.4164i | − | 0.541002i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.0000 | 1.69086 | 0.845428 | − | 0.534089i | \(-0.179345\pi\) | ||||
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(618\) | 24.5967i | 0.989426i | ||||||||
\(619\) | 20.0000 | 0.803868 | 0.401934 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.3607i | 0.897303i | ||||||||
\(622\) | 33.5410i | 1.34487i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 30.0000 | 1.19904 | ||||||||
\(627\) | −3.00000 | −0.119808 | ||||||||
\(628\) | − | 40.2492i | − | 1.60612i | ||||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.0000 | −1.71180 | −0.855901 | − | 0.517139i | \(-0.826997\pi\) | ||||
−0.855901 | + | 0.517139i | \(0.826997\pi\) | |||||||
\(632\) | −30.0000 | −1.19334 | ||||||||
\(633\) | 13.4164i | 0.533254i | ||||||||
\(634\) | −20.0000 | −0.794301 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.0000 | −0.713746 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 30.0000 | 1.18771 | ||||||||
\(639\) | 30.0000 | 1.18678 | ||||||||
\(640\) | 46.9574i | 1.85616i | ||||||||
\(641\) | −45.0000 | −1.77739 | −0.888697 | − | 0.458496i | \(-0.848388\pi\) | ||||
−0.888697 | + | 0.458496i | \(0.848388\pi\) | |||||||
\(642\) | −20.0000 | −0.789337 | ||||||||
\(643\) | 44.0000 | 1.73519 | 0.867595 | − | 0.497271i | \(-0.165665\pi\) | ||||
0.867595 | + | 0.497271i | \(0.165665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.00000 | −0.118125 | ||||||||
\(646\) | 6.70820i | 0.263931i | ||||||||
\(647\) | − | 17.8885i | − | 0.703271i | −0.936137 | − | 0.351636i | \(-0.885626\pi\) | ||
0.936137 | − | 0.351636i | \(-0.114374\pi\) | |||||||
\(648\) | − | 2.23607i | − | 0.0878410i | ||||||
\(649\) | 26.8328i | 1.05328i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 40.2492i | − | 1.57628i | ||||||
\(653\) | 35.7771i | 1.40007i | 0.714111 | + | 0.700033i | \(0.246831\pi\) | ||||
−0.714111 | + | 0.700033i | \(0.753169\pi\) | |||||||
\(654\) | −30.0000 | −1.17309 | ||||||||
\(655\) | − | 13.4164i | − | 0.524222i | ||||||
\(656\) | 4.47214i | 0.174608i | ||||||||
\(657\) | 26.8328i | 1.04685i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 31.3050i | − | 1.21947i | −0.792606 | − | 0.609734i | \(-0.791276\pi\) | ||
0.792606 | − | 0.609734i | \(-0.208724\pi\) | |||||||
\(660\) | −27.0000 | −1.05097 | ||||||||
\(661\) | −13.0000 | −0.505641 | −0.252821 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(662\) | 30.0000 | 1.16598 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.1246i | 0.780986i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 8.94427i | − | 0.346583i | ||||||
\(667\) | −20.0000 | −0.774403 | ||||||||
\(668\) | −9.00000 | −0.348220 | ||||||||
\(669\) | 13.4164i | 0.518708i | ||||||||
\(670\) | −90.0000 | −3.47700 | ||||||||
\(671\) | 15.0000 | 0.579069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0000 | −0.732396 | −0.366198 | − | 0.930537i | \(-0.619341\pi\) | ||||
−0.366198 | + | 0.930537i | \(0.619341\pi\) | |||||||
\(674\) | − | 29.0689i | − | 1.11969i | ||||||
\(675\) | −20.0000 | −0.769800 | ||||||||
\(676\) | −39.0000 | −1.50000 | ||||||||
\(677\) | 8.94427i | 0.343756i | 0.985118 | + | 0.171878i | \(0.0549835\pi\) | ||||
−0.985118 | + | 0.171878i | \(0.945016\pi\) | |||||||
\(678\) | −20.0000 | −0.768095 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.1246i | 0.771744i | ||||||||
\(681\) | − | 4.47214i | − | 0.171373i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.00000 | 0.344375 | 0.172188 | − | 0.985064i | \(-0.444916\pi\) | ||||
0.172188 | + | 0.985064i | \(0.444916\pi\) | |||||||
\(684\) | −6.00000 | −0.229416 | ||||||||
\(685\) | 26.8328i | 1.02523i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.00000 | + | 13.4164i | 0.267067 | + | 0.511868i | ||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 30.0000 | 1.14208 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 26.8328i | − | 1.01856i | ||||||
\(695\) | 40.2492i | 1.52674i | ||||||||
\(696\) | −10.0000 | −0.379049 | ||||||||
\(697\) | 13.4164i | 0.508183i | ||||||||
\(698\) | −30.0000 | −1.13552 | ||||||||
\(699\) | 9.00000 | 0.340411 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.0000 | 1.24639 | 0.623196 | − | 0.782065i | \(-0.285834\pi\) | ||||
0.623196 | + | 0.782065i | \(0.285834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | −0.0754314 | ||||||||
\(704\) | 39.0000 | 1.46987 | ||||||||
\(705\) | 26.8328i | 1.01058i | ||||||||
\(706\) | −20.0000 | −0.752710 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 26.8328i | − | 1.00844i | ||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | − | 100.623i | − | 3.77632i | ||||||
\(711\) | 26.8328i | 1.00631i | ||||||||
\(712\) | −40.0000 | −1.49906 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 53.6656i | 2.00558i | ||||||||
\(717\) | 22.3607i | 0.835075i | ||||||||
\(718\) | − | 53.6656i | − | 2.00278i | ||||||
\(719\) | − | 4.47214i | − | 0.166783i | −0.996517 | − | 0.0833913i | \(-0.973425\pi\) | ||
0.996517 | − | 0.0833913i | \(-0.0265751\pi\) | |||||||
\(720\) | 6.00000 | 0.223607 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 40.2492i | − | 1.49792i | ||||||
\(723\) | −10.0000 | −0.371904 | ||||||||
\(724\) | 21.0000 | 0.780459 | ||||||||
\(725\) | − | 17.8885i | − | 0.664364i | ||||||
\(726\) | − | 4.47214i | − | 0.165977i | ||||||
\(727\) | 26.8328i | 0.995174i | 0.867414 | + | 0.497587i | \(0.165780\pi\) | ||||
−0.867414 | + | 0.497587i | \(0.834220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 90.0000 | 3.33105 | ||||||||
\(731\) | 3.00000 | 0.110959 | ||||||||
\(732\) | −15.0000 | −0.554416 | ||||||||
\(733\) | 11.0000 | 0.406294 | 0.203147 | − | 0.979148i | \(-0.434883\pi\) | ||||
0.203147 | + | 0.979148i | \(0.434883\pi\) | |||||||
\(734\) | 38.0132i | 1.40309i | ||||||||
\(735\) | 21.0000 | 0.774597 | ||||||||
\(736\) | −30.0000 | −1.10581 | ||||||||
\(737\) | 40.2492i | 1.48260i | ||||||||
\(738\) | −20.0000 | −0.736210 | ||||||||
\(739\) | 13.4164i | 0.493531i | 0.969075 | + | 0.246765i | \(0.0793677\pi\) | ||||
−0.969075 | + | 0.246765i | \(0.920632\pi\) | |||||||
\(740\) | −18.0000 | −0.661693 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.0000 | −1.43077 | −0.715386 | − | 0.698730i | \(-0.753749\pi\) | ||||
−0.715386 | + | 0.698730i | \(0.753749\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −63.0000 | −2.30814 | ||||||||
\(746\) | − | 42.4853i | − | 1.55550i | ||||||
\(747\) | 18.0000 | 0.658586 | ||||||||
\(748\) | 27.0000 | 0.987218 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 6.70820i | − | 0.244949i | ||||||
\(751\) | 5.00000 | 0.182453 | 0.0912263 | − | 0.995830i | \(-0.470921\pi\) | ||||
0.0912263 | + | 0.995830i | \(0.470921\pi\) | |||||||
\(752\) | − | 8.94427i | − | 0.326164i | ||||||
\(753\) | − | 17.8885i | − | 0.651895i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.0000 | −0.764268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.0000 | −0.472493 | −0.236247 | − | 0.971693i | \(-0.575917\pi\) | ||||
−0.236247 | + | 0.971693i | \(0.575917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 13.4164i | − | 0.486985i | ||||||
\(760\) | 6.70820i | 0.243332i | ||||||||
\(761\) | − | 44.7214i | − | 1.62115i | −0.585636 | − | 0.810574i | \(-0.699155\pi\) | ||
0.585636 | − | 0.810574i | \(-0.300845\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 26.8328i | − | 0.970777i | ||||||
\(765\) | 18.0000 | 0.650791 | ||||||||
\(766\) | − | 53.6656i | − | 1.93902i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −9.00000 | −0.324760 | ||||||||
\(769\) | 5.00000 | 0.180305 | 0.0901523 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901523 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 17.8885i | − | 0.644240i | ||||||
\(772\) | −42.0000 | −1.51161 | ||||||||
\(773\) | 35.7771i | 1.28681i | 0.765525 | + | 0.643406i | \(0.222479\pi\) | ||||
−0.765525 | + | 0.643406i | \(0.777521\pi\) | |||||||
\(774\) | 4.47214i | 0.160748i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.6525i | 0.561891i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 70.0000 | 2.50962 | ||||||||
\(779\) | 4.47214i | 0.160231i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45.0000 | −1.61023 | ||||||||
\(782\) | −30.0000 | −1.07280 | ||||||||
\(783\) | 22.3607i | 0.799106i | ||||||||
\(784\) | −7.00000 | −0.250000 | ||||||||
\(785\) | 40.2492i | 1.43656i | ||||||||
\(786\) | 10.0000 | 0.356688 | ||||||||
\(787\) | 23.0000 | 0.819861 | 0.409931 | − | 0.912117i | \(-0.365553\pi\) | ||||
0.409931 | + | 0.912117i | \(0.365553\pi\) | |||||||
\(788\) | 53.6656i | 1.91176i | ||||||||
\(789\) | − | 4.47214i | − | 0.159212i | ||||||
\(790\) | 90.0000 | 3.20206 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 13.4164i | 0.476731i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 51.4296i | 1.82517i | ||||||||
\(795\) | 18.0000 | 0.638394 | ||||||||
\(796\) | − | 40.2492i | − | 1.42660i | ||||||
\(797\) | − | 44.7214i | − | 1.58411i | −0.610449 | − | 0.792056i | \(-0.709011\pi\) | ||
0.610449 | − | 0.792056i | \(-0.290989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 26.8328i | − | 0.949277i | ||||||
\(800\) | − | 26.8328i | − | 0.948683i | ||||||
\(801\) | 35.7771i | 1.26412i | ||||||||
\(802\) | 60.3738i | 2.13187i | ||||||||
\(803\) | − | 40.2492i | − | 1.42036i | ||||||
\(804\) | − | 40.2492i | − | 1.41948i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.3607i | 0.787133i | ||||||||
\(808\) | −10.0000 | −0.351799 | ||||||||
\(809\) | − | 4.47214i | − | 0.157232i | −0.996905 | − | 0.0786160i | \(-0.974950\pi\) | ||
0.996905 | − | 0.0786160i | \(-0.0250501\pi\) | |||||||
\(810\) | 6.70820i | 0.235702i | ||||||||
\(811\) | − | 13.4164i | − | 0.471114i | −0.971861 | − | 0.235557i | \(-0.924309\pi\) | ||
0.971861 | − | 0.235557i | \(-0.0756914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.0000 | −0.876788 | ||||||||
\(814\) | 13.4164i | 0.470245i | ||||||||
\(815\) | 40.2492i | 1.40987i | ||||||||
\(816\) | 3.00000 | 0.105021 | ||||||||
\(817\) | 1.00000 | 0.0349856 | ||||||||
\(818\) | 78.2624i | 2.73638i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40.2492i | 1.40556i | ||||||||
\(821\) | 3.00000 | 0.104701 | 0.0523504 | − | 0.998629i | \(-0.483329\pi\) | ||||
0.0523504 | + | 0.998629i | \(0.483329\pi\) | |||||||
\(822\) | −20.0000 | −0.697580 | ||||||||
\(823\) | − | 26.8328i | − | 0.935333i | −0.883905 | − | 0.467667i | \(-0.845095\pi\) | ||
0.883905 | − | 0.467667i | \(-0.154905\pi\) | |||||||
\(824\) | − | 24.5967i | − | 0.856868i | ||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.8885i | − | 0.622046i | −0.950402 | − | 0.311023i | \(-0.899328\pi\) | ||
0.950402 | − | 0.311023i | \(-0.100672\pi\) | |||||||
\(828\) | − | 26.8328i | − | 0.932505i | ||||||
\(829\) | − | 26.8328i | − | 0.931942i | −0.884800 | − | 0.465971i | \(-0.845705\pi\) | ||
0.884800 | − | 0.465971i | \(-0.154295\pi\) | |||||||
\(830\) | − | 60.3738i | − | 2.09561i | ||||||
\(831\) | 17.0000 | 0.589723 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.0000 | −0.727607 | ||||||||
\(834\) | −30.0000 | −1.03882 | ||||||||
\(835\) | 9.00000 | 0.311458 | ||||||||
\(836\) | 9.00000 | 0.311272 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.0000 | 0.345444 | ||||||||
\(839\) | 22.3607i | 0.771976i | 0.922504 | + | 0.385988i | \(0.126139\pi\) | ||||
−0.922504 | + | 0.385988i | \(0.873861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.00000 | 0.310345 | ||||||||
\(842\) | 38.0132i | 1.31002i | ||||||||
\(843\) | − | 31.3050i | − | 1.07820i | ||||||
\(844\) | − | 40.2492i | − | 1.38544i | ||||||
\(845\) | 39.0000 | 1.34164 | ||||||||
\(846\) | 40.0000 | 1.37523 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 13.4164i | 0.460450i | ||||||||
\(850\) | − | 26.8328i | − | 0.920358i | ||||||
\(851\) | − | 8.94427i | − | 0.306606i | ||||||
\(852\) | 45.0000 | 1.54167 | ||||||||
\(853\) | 26.8328i | 0.918738i | 0.888246 | + | 0.459369i | \(0.151924\pi\) | ||||
−0.888246 | + | 0.459369i | \(0.848076\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | 20.0000 | 0.683586 | ||||||||
\(857\) | − | 4.47214i | − | 0.152765i | −0.997079 | − | 0.0763826i | \(-0.975663\pi\) | ||
0.997079 | − | 0.0763826i | \(-0.0243370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.00000 | 0.170598 | 0.0852989 | − | 0.996355i | \(-0.472815\pi\) | ||||
0.0852989 | + | 0.996355i | \(0.472815\pi\) | |||||||
\(860\) | 9.00000 | 0.306897 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.5410i | 1.14241i | ||||||||
\(863\) | 9.00000 | 0.306364 | 0.153182 | − | 0.988198i | \(-0.451048\pi\) | ||||
0.153182 | + | 0.988198i | \(0.451048\pi\) | |||||||
\(864\) | 33.5410i | 1.14109i | ||||||||
\(865\) | 18.0000 | 0.612018 | ||||||||
\(866\) | − | 42.4853i | − | 1.44371i | ||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 40.2492i | − | 1.36536i | ||||||
\(870\) | 30.0000 | 1.01710 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 30.0000 | 1.01593 | ||||||||
\(873\) | 14.0000 | 0.473828 | ||||||||
\(874\) | −10.0000 | −0.338255 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 40.2492i | 1.35990i | ||||||||
\(877\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(878\) | 44.7214i | 1.50927i | ||||||||
\(879\) | 9.00000 | 0.303562 | ||||||||
\(880\) | −9.00000 | −0.303390 | ||||||||
\(881\) | − | 4.47214i | − | 0.150670i | −0.997158 | − | 0.0753350i | \(-0.975997\pi\) | ||
0.997158 | − | 0.0753350i | \(-0.0240026\pi\) | |||||||
\(882\) | − | 31.3050i | − | 1.05409i | ||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.8328i | 0.901975i | ||||||||
\(886\) | 80.4984i | 2.70440i | ||||||||
\(887\) | 35.7771i | 1.20128i | 0.799521 | + | 0.600639i | \(0.205087\pi\) | ||||
−0.799521 | + | 0.600639i | \(0.794913\pi\) | |||||||
\(888\) | − | 4.47214i | − | 0.150075i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 120.000 | 4.02241 | ||||||||
\(891\) | 3.00000 | 0.100504 | ||||||||
\(892\) | − | 40.2492i | − | 1.34764i | ||||||
\(893\) | − | 8.94427i | − | 0.299309i | ||||||
\(894\) | − | 46.9574i | − | 1.57049i | ||||||
\(895\) | − | 53.6656i | − | 1.79384i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 67.0820i | − | 2.23856i | ||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 24.0000 | 0.800000 | ||||||||
\(901\) | −18.0000 | −0.599667 | ||||||||
\(902\) | 30.0000 | 0.998891 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.0000 | 0.665190 | ||||||||
\(905\) | −21.0000 | −0.698064 | ||||||||
\(906\) | − | 15.6525i | − | 0.520019i | ||||||
\(907\) | −52.0000 | −1.72663 | −0.863316 | − | 0.504664i | \(-0.831616\pi\) | ||||
−0.863316 | + | 0.504664i | \(0.831616\pi\) | |||||||
\(908\) | 13.4164i | 0.445239i | ||||||||
\(909\) | 8.94427i | 0.296663i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | −0.496972 | −0.248486 | − | 0.968635i | \(-0.579933\pi\) | ||||
−0.248486 | + | 0.968635i | \(0.579933\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −27.0000 | −0.893570 | ||||||||
\(914\) | 51.4296i | 1.70114i | ||||||||
\(915\) | 15.0000 | 0.495885 | ||||||||
\(916\) | −21.0000 | − | 40.2492i | −0.693860 | − | 1.32987i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 33.5410i | 1.10702i | ||||||||
\(919\) | −25.0000 | −0.824674 | −0.412337 | − | 0.911031i | \(-0.635287\pi\) | ||||
−0.412337 | + | 0.911031i | \(0.635287\pi\) | |||||||
\(920\) | −30.0000 | −0.989071 | ||||||||
\(921\) | 17.0000 | 0.560169 | ||||||||
\(922\) | − | 40.2492i | − | 1.32554i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | − | 2.23607i | − | 0.0734818i | ||||||
\(927\) | −22.0000 | −0.722575 | ||||||||
\(928\) | −30.0000 | −0.984798 | ||||||||
\(929\) | − | 4.47214i | − | 0.146726i | −0.997305 | − | 0.0733630i | \(-0.976627\pi\) | ||
0.997305 | − | 0.0733630i | \(-0.0233732\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | −0.229416 | ||||||||
\(932\) | −27.0000 | −0.884414 | ||||||||
\(933\) | 15.0000 | 0.491078 | ||||||||
\(934\) | 60.3738i | 1.97549i | ||||||||
\(935\) | −27.0000 | −0.882994 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.2492i | 1.31488i | 0.753505 | + | 0.657442i | \(0.228362\pi\) | ||||
−0.753505 | + | 0.657442i | \(0.771638\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 13.4164i | − | 0.437828i | ||||||
\(940\) | − | 80.4984i | − | 2.62557i | ||||||
\(941\) | −45.0000 | −1.46696 | −0.733479 | − | 0.679712i | \(-0.762105\pi\) | ||||
−0.733479 | + | 0.679712i | \(0.762105\pi\) | |||||||
\(942\) | −30.0000 | −0.977453 | ||||||||
\(943\) | −20.0000 | −0.651290 | ||||||||
\(944\) | − | 8.94427i | − | 0.291111i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 6.70820i | − | 0.218103i | ||||||
\(947\) | − | 4.47214i | − | 0.145325i | −0.997357 | − | 0.0726624i | \(-0.976850\pi\) | ||
0.997357 | − | 0.0726624i | \(-0.0231496\pi\) | |||||||
\(948\) | 40.2492i | 1.30723i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 8.94427i | − | 0.290191i | ||||||
\(951\) | 8.94427i | 0.290038i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.0000 | −1.26333 | −0.631667 | − | 0.775240i | \(-0.717629\pi\) | ||||
−0.631667 | + | 0.775240i | \(0.717629\pi\) | |||||||
\(954\) | − | 26.8328i | − | 0.868744i | ||||||
\(955\) | 26.8328i | 0.868290i | ||||||||
\(956\) | − | 67.0820i | − | 2.16959i | ||||||
\(957\) | − | 13.4164i | − | 0.433691i | ||||||
\(958\) | −20.0000 | −0.646171 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 39.0000 | 1.25872 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 17.8885i | − | 0.576450i | ||||||
\(964\) | 30.0000 | 0.966235 | ||||||||
\(965\) | 42.0000 | 1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.0000 | −0.900419 | −0.450210 | − | 0.892923i | \(-0.648651\pi\) | ||||
−0.450210 | + | 0.892923i | \(0.648651\pi\) | |||||||
\(968\) | 4.47214i | 0.143740i | ||||||||
\(969\) | 3.00000 | 0.0963739 | ||||||||
\(970\) | − | 46.9574i | − | 1.50771i | ||||||
\(971\) | 33.0000 | 1.05902 | 0.529510 | − | 0.848304i | \(-0.322376\pi\) | ||||
0.529510 | + | 0.848304i | \(0.322376\pi\) | |||||||
\(972\) | −48.0000 | −1.53960 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30.0000 | 0.961262 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.00000 | −0.160046 | ||||||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | −30.0000 | −0.959294 | ||||||||
\(979\) | − | 53.6656i | − | 1.71516i | ||||||
\(980\) | −63.0000 | −2.01246 | ||||||||
\(981\) | − | 26.8328i | − | 0.856706i | ||||||
\(982\) | − | 33.5410i | − | 1.07034i | ||||||
\(983\) | 22.3607i | 0.713195i | 0.934258 | + | 0.356597i | \(0.116063\pi\) | ||||
−0.934258 | + | 0.356597i | \(0.883937\pi\) | |||||||
\(984\) | −10.0000 | −0.318788 | ||||||||
\(985\) | − | 53.6656i | − | 1.70993i | ||||||
\(986\) | −30.0000 | −0.955395 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.47214i | 0.142206i | ||||||||
\(990\) | − | 40.2492i | − | 1.27920i | ||||||
\(991\) | −25.0000 | −0.794151 | −0.397076 | − | 0.917786i | \(-0.629975\pi\) | ||||
−0.397076 | + | 0.917786i | \(0.629975\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.4164i | − | 0.425757i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.2492i | 1.27599i | ||||||||
\(996\) | 27.0000 | 0.855528 | ||||||||
\(997\) | −37.0000 | −1.17180 | −0.585901 | − | 0.810383i | \(-0.699259\pi\) | ||||
−0.585901 | + | 0.810383i | \(0.699259\pi\) | |||||||
\(998\) | 60.0000 | 1.89927 | ||||||||
\(999\) | −10.0000 | −0.316386 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 229.2.b.a.228.2 | yes | 2 | |
3.2 | odd | 2 | 2061.2.c.a.1144.1 | 2 | |||
229.228 | even | 2 | inner | 229.2.b.a.228.1 | ✓ | 2 | |
687.686 | odd | 2 | 2061.2.c.a.1144.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
229.2.b.a.228.1 | ✓ | 2 | 229.228 | even | 2 | inner | |
229.2.b.a.228.2 | yes | 2 | 1.1 | even | 1 | trivial | |
2061.2.c.a.1144.1 | 2 | 3.2 | odd | 2 | |||
2061.2.c.a.1144.2 | 2 | 687.686 | odd | 2 |