Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1567,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1764.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1212153856.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 10x^{4} - 16x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 196) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.8 | ||
Root | \(-1.36145 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1567 |
Dual form | 1764.2.b.k.1567.5 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20711 | + | 0.736813i | 0.853553 | + | 0.521005i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.914214 | + | 1.77882i | 0.457107 | + | 0.889412i | ||||
\(5\) | 1.08239i | 0.484061i | 0.970269 | + | 0.242030i | \(0.0778133\pi\) | ||||
−0.970269 | + | 0.242030i | \(0.922187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.207107 | + | 2.82083i | −0.0732233 | + | 0.997316i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.797521 | + | 1.30656i | −0.252198 | + | 0.413171i | ||||
\(11\) | 2.08402i | 0.628356i | 0.949364 | + | 0.314178i | \(0.101729\pi\) | ||||
−0.949364 | + | 0.314178i | \(0.898271\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.61313i | 0.724751i | 0.932032 | + | 0.362375i | \(0.118034\pi\) | ||||
−0.932032 | + | 0.362375i | \(0.881966\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.32843 | + | 3.25245i | −0.582107 | + | 0.813112i | ||||
\(17\) | − | 4.46088i | − | 1.08192i | −0.841047 | − | 0.540962i | \(-0.818060\pi\) | ||
0.841047 | − | 0.540962i | \(-0.181940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.12786 | −0.258750 | −0.129375 | − | 0.991596i | \(-0.541297\pi\) | ||||
−0.129375 | + | 0.991596i | \(0.541297\pi\) | |||||||
\(20\) | −1.92538 | + | 0.989538i | −0.430529 | + | 0.221267i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.53553 | + | 2.51564i | −0.327377 | + | 0.536336i | ||||
\(23\) | 7.11529i | 1.48364i | 0.670598 | + | 0.741821i | \(0.266037\pi\) | ||||
−0.670598 | + | 0.741821i | \(0.733963\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.82843 | 0.765685 | ||||||||
\(26\) | −1.92538 | + | 3.15432i | −0.377599 | + | 0.618613i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.17157 | 0.217556 | 0.108778 | − | 0.994066i | \(-0.465306\pi\) | ||||
0.108778 | + | 0.994066i | \(0.465306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.70154 | −1.38324 | −0.691619 | − | 0.722263i | \(-0.743102\pi\) | ||||
−0.691619 | + | 0.722263i | \(0.743102\pi\) | |||||||
\(32\) | −5.20711 | + | 2.21044i | −0.920495 | + | 0.390754i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.28684 | − | 5.38476i | 0.563688 | − | 0.923479i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | −1.36145 | − | 0.831025i | −0.220857 | − | 0.134810i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.05325 | − | 0.224171i | −0.482761 | − | 0.0354445i | ||||
\(41\) | − | 5.54328i | − | 0.865714i | −0.901462 | − | 0.432857i | \(-0.857505\pi\) | ||
0.901462 | − | 0.432857i | \(-0.142495\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.97852i | 1.21671i | 0.793664 | + | 0.608357i | \(0.208171\pi\) | ||||
−0.793664 | + | 0.608357i | \(0.791829\pi\) | |||||||
\(44\) | −3.70711 | + | 1.90524i | −0.558867 | + | 0.287226i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.24264 | + | 8.58892i | −0.772985 | + | 1.26637i | ||||
\(47\) | 5.44581 | 0.794353 | 0.397177 | − | 0.917742i | \(-0.369990\pi\) | ||||
0.397177 | + | 0.917742i | \(0.369990\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.62132 | + | 2.82083i | 0.653553 | + | 0.398926i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.64829 | + | 2.38896i | −0.644602 | + | 0.331288i | ||||
\(53\) | 6.48528 | 0.890822 | 0.445411 | − | 0.895326i | \(-0.353058\pi\) | ||||
0.445411 | + | 0.895326i | \(0.353058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.25573 | −0.304162 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.41421 | + | 0.863230i | 0.185695 | + | 0.113348i | ||||
\(59\) | −8.82940 | −1.14949 | −0.574745 | − | 0.818332i | \(-0.694899\pi\) | ||||
−0.574745 | + | 0.818332i | \(0.694899\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0656i | 1.67288i | 0.548057 | + | 0.836441i | \(0.315368\pi\) | ||||
−0.548057 | + | 0.836441i | \(0.684632\pi\) | |||||||
\(62\) | −9.29658 | − | 5.67459i | −1.18067 | − | 0.720674i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.91421 | − | 1.16843i | −0.989277 | − | 0.146053i | ||||
\(65\) | −2.82843 | −0.350823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.0625i | − | 1.22934i | −0.788786 | − | 0.614668i | \(-0.789290\pi\) | ||
0.788786 | − | 0.614668i | \(-0.210710\pi\) | |||||||
\(68\) | 7.93513 | − | 4.07820i | 0.962276 | − | 0.494555i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.97069i | − | 0.932899i | −0.884548 | − | 0.466450i | \(-0.845533\pi\) | ||
0.884548 | − | 0.466450i | \(-0.154467\pi\) | |||||||
\(74\) | −4.82843 | − | 2.94725i | −0.561293 | − | 0.342611i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.03111 | − | 2.00627i | −0.118276 | − | 0.230135i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.16804i | 0.468941i | 0.972123 | + | 0.234471i | \(0.0753357\pi\) | ||||
−0.972123 | + | 0.234471i | \(0.924664\pi\) | |||||||
\(80\) | −3.52043 | − | 2.52027i | −0.393596 | − | 0.281775i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.08436 | − | 6.69133i | 0.451042 | − | 0.738934i | ||||
\(83\) | 4.31795 | 0.473956 | 0.236978 | − | 0.971515i | \(-0.423843\pi\) | ||||
0.236978 | + | 0.971515i | \(0.423843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | −5.87868 | + | 9.63093i | −0.633914 | + | 1.03853i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.87868 | − | 0.431615i | −0.626669 | − | 0.0460103i | ||||
\(89\) | 4.01254i | 0.425329i | 0.977125 | + | 0.212664i | \(0.0682141\pi\) | ||||
−0.977125 | + | 0.212664i | \(0.931786\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.6569 | + | 6.50490i | −1.31957 | + | 0.678183i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.57368 | + | 4.01254i | 0.678023 | + | 0.413862i | ||||
\(95\) | − | 1.22079i | − | 0.125251i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82683i | 0.388556i | 0.980946 | + | 0.194278i | \(0.0622364\pi\) | ||||
−0.980946 | + | 0.194278i | \(0.937764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.50000 | + | 6.81010i | 0.350000 | + | 0.681010i | ||||
\(101\) | 0.185709i | 0.0184788i | 0.999957 | + | 0.00923938i | \(0.00294103\pi\) | ||||
−0.999957 | + | 0.00923938i | \(0.997059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4031 | 1.51771 | 0.758855 | − | 0.651259i | \(-0.225759\pi\) | ||||
0.758855 | + | 0.651259i | \(0.225759\pi\) | |||||||
\(104\) | −7.37120 | − | 0.541196i | −0.722805 | − | 0.0530686i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.82843 | + | 4.77844i | 0.760364 | + | 0.464123i | ||||
\(107\) | 7.11529i | 0.687861i | 0.938995 | + | 0.343931i | \(0.111759\pi\) | ||||
−0.938995 | + | 0.343931i | \(0.888241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.65685 | 0.541828 | 0.270914 | − | 0.962604i | \(-0.412674\pi\) | ||||
0.270914 | + | 0.962604i | \(0.412674\pi\) | |||||||
\(110\) | −2.72291 | − | 1.66205i | −0.259619 | − | 0.158470i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24264 | −0.399114 | −0.199557 | − | 0.979886i | \(-0.563950\pi\) | ||||
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.70154 | −0.718172 | ||||||||
\(116\) | 1.07107 | + | 2.08402i | 0.0994461 | + | 0.193497i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.6580 | − | 6.50562i | −0.981151 | − | 0.598891i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.65685 | 0.605169 | ||||||||
\(122\) | −9.62692 | + | 15.7716i | −0.871581 | + | 1.42789i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.04085 | − | 13.6997i | −0.632287 | − | 1.23027i | ||||
\(125\) | 9.55582i | 0.854699i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.2833i | − | 1.00123i | −0.865669 | − | 0.500617i | \(-0.833106\pi\) | ||
0.865669 | − | 0.500617i | \(-0.166894\pi\) | |||||||
\(128\) | −8.69239 | − | 7.24171i | −0.768306 | − | 0.640083i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.41421 | − | 2.08402i | −0.299446 | − | 0.182781i | ||||
\(131\) | 15.8703 | 1.38659 | 0.693295 | − | 0.720654i | \(-0.256158\pi\) | ||||
0.693295 | + | 0.720654i | \(0.256158\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.41421 | − | 12.1466i | 0.640490 | − | 1.04930i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.5834 | + | 0.923880i | 1.07902 | + | 0.0792220i | ||||
\(137\) | −0.242641 | −0.0207302 | −0.0103651 | − | 0.999946i | \(-0.503299\pi\) | ||||
−0.0103651 | + | 0.999946i | \(0.503299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.78855 | −0.151703 | −0.0758515 | − | 0.997119i | \(-0.524167\pi\) | ||||
−0.0758515 | + | 0.997119i | \(0.524167\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.44581 | −0.455402 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.26810i | 0.105310i | ||||||||
\(146\) | 5.87291 | − | 9.62148i | 0.486045 | − | 0.796279i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.65685 | − | 7.11529i | −0.300592 | − | 0.584874i | ||||
\(149\) | 0.828427 | 0.0678674 | 0.0339337 | − | 0.999424i | \(-0.489196\pi\) | ||||
0.0339337 | + | 0.999424i | \(0.489196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.38883i | − | 0.438537i | −0.975665 | − | 0.219269i | \(-0.929633\pi\) | ||
0.975665 | − | 0.219269i | \(-0.0703671\pi\) | |||||||
\(152\) | 0.233588 | − | 3.18152i | 0.0189465 | − | 0.258055i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.33609i | − | 0.669571i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.1940i | − | 1.61166i | −0.592147 | − | 0.805830i | \(-0.701720\pi\) | ||
0.592147 | − | 0.805830i | \(-0.298280\pi\) | |||||||
\(158\) | −3.07107 | + | 5.03127i | −0.244321 | + | 0.400267i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.39256 | − | 5.63613i | −0.189149 | − | 0.445575i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.81048i | − | 0.298460i | −0.988803 | − | 0.149230i | \(-0.952321\pi\) | ||
0.988803 | − | 0.149230i | \(-0.0476795\pi\) | |||||||
\(164\) | 9.86051 | − | 5.06774i | 0.769977 | − | 0.395724i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.21222 | + | 3.18152i | 0.404547 | + | 0.246934i | ||||
\(167\) | −20.8489 | −1.61334 | −0.806668 | − | 0.591005i | \(-0.798731\pi\) | ||||
−0.806668 | + | 0.591005i | \(0.798731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.17157 | 0.474736 | ||||||||
\(170\) | 5.82843 | + | 3.55765i | 0.447020 | + | 0.272859i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.1924 | + | 7.29408i | −1.08216 | + | 0.556168i | ||||
\(173\) | 21.0907i | 1.60350i | 0.597661 | + | 0.801749i | \(0.296097\pi\) | ||||
−0.597661 | + | 0.801749i | \(0.703903\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.77817 | − | 4.85249i | −0.510924 | − | 0.365770i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.95649 | + | 4.84357i | −0.221599 | + | 0.363041i | ||||
\(179\) | − | 1.22079i | − | 0.0912462i | −0.998959 | − | 0.0456231i | \(-0.985473\pi\) | ||
0.998959 | − | 0.0456231i | \(-0.0145273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.04601i | 0.449397i | 0.974428 | + | 0.224698i | \(0.0721396\pi\) | ||||
−0.974428 | + | 0.224698i | \(0.927860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −20.0711 | − | 1.47363i | −1.47966 | − | 0.108637i | ||||
\(185\) | − | 4.32957i | − | 0.318316i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.29658 | 0.679833 | ||||||||
\(188\) | 4.97863 | + | 9.68714i | 0.363104 | + | 0.706507i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.899495 | − | 1.47363i | 0.0652562 | − | 0.106908i | ||||
\(191\) | − | 20.1251i | − | 1.45620i | −0.685471 | − | 0.728100i | \(-0.740404\pi\) | ||
0.685471 | − | 0.728100i | \(-0.259596\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4142 | 1.25350 | 0.626751 | − | 0.779219i | \(-0.284384\pi\) | ||||
0.626751 | + | 0.779219i | \(0.284384\pi\) | |||||||
\(194\) | −2.81966 | + | 4.61940i | −0.202440 | + | 0.331653i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.7832 | 1.54417 | 0.772087 | − | 0.635517i | \(-0.219213\pi\) | ||||
0.772087 | + | 0.635517i | \(0.219213\pi\) | |||||||
\(200\) | −0.792893 | + | 10.7994i | −0.0560660 | + | 0.763630i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.136833 | + | 0.224171i | −0.00962753 | + | 0.0157726i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | 18.5932 | + | 11.3492i | 1.29545 | + | 0.790735i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.49906 | − | 6.08447i | −0.589304 | − | 0.421882i | ||||
\(209\) | − | 2.35049i | − | 0.162587i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.9570i | − | 1.09853i | −0.835649 | − | 0.549264i | \(-0.814908\pi\) | ||
0.835649 | − | 0.549264i | \(-0.185092\pi\) | |||||||
\(212\) | 5.92893 | + | 11.5362i | 0.407201 | + | 0.792308i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.24264 | + | 8.58892i | −0.358380 | + | 0.587127i | ||||
\(215\) | −8.63589 | −0.588963 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.82843 | + | 4.16804i | 0.462479 | + | 0.282295i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.06222 | − | 4.01254i | −0.139035 | − | 0.270526i | ||||
\(221\) | 11.6569 | 0.784125 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.8489 | 1.39614 | 0.698072 | − | 0.716027i | \(-0.254041\pi\) | ||||
0.698072 | + | 0.716027i | \(0.254041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.12132 | − | 3.12603i | −0.340665 | − | 0.207941i | ||||
\(227\) | 18.1260 | 1.20306 | 0.601532 | − | 0.798849i | \(-0.294557\pi\) | ||||
0.601532 | + | 0.798849i | \(0.294557\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.9259i | 1.25066i | 0.780360 | + | 0.625330i | \(0.215036\pi\) | ||||
−0.780360 | + | 0.625330i | \(0.784964\pi\) | |||||||
\(230\) | −9.29658 | − | 5.67459i | −0.612998 | − | 0.374172i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.242641 | + | 3.30481i | −0.0159301 | + | 0.216972i | ||||
\(233\) | −7.75736 | −0.508202 | −0.254101 | − | 0.967178i | \(-0.581779\pi\) | ||||
−0.254101 | + | 0.967178i | \(0.581779\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.89450i | 0.384515i | ||||||||
\(236\) | −8.07196 | − | 15.7060i | −0.525440 | − | 1.02237i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.2833i | 0.729858i | 0.931035 | + | 0.364929i | \(0.118907\pi\) | ||||
−0.931035 | + | 0.364929i | \(0.881093\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.60474i | 0.554280i | 0.960830 | + | 0.277140i | \(0.0893866\pi\) | ||||
−0.960830 | + | 0.277140i | \(0.910613\pi\) | |||||||
\(242\) | 8.03553 | + | 4.90486i | 0.516544 | + | 0.315296i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −23.2415 | + | 11.9448i | −1.48788 | + | 0.764686i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.94725i | − | 0.187529i | ||||||
\(248\) | 1.59504 | − | 21.7248i | 0.101285 | − | 1.37952i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.04085 | + | 11.5349i | −0.445303 | + | 0.729531i | ||||
\(251\) | 10.4244 | 0.657985 | 0.328993 | − | 0.944333i | \(-0.393291\pi\) | ||||
0.328993 | + | 0.944333i | \(0.393291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.8284 | −0.932255 | ||||||||
\(254\) | 8.31371 | − | 13.6202i | 0.521648 | − | 0.854607i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.15685 | − | 15.1462i | −0.322303 | − | 0.946636i | ||||
\(257\) | − | 9.42450i | − | 0.587884i | −0.955823 | − | 0.293942i | \(-0.905033\pi\) | ||
0.955823 | − | 0.293942i | \(-0.0949673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.58579 | − | 5.03127i | −0.160364 | − | 0.312026i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.1571 | + | 11.6934i | 1.18353 | + | 0.722421i | ||||
\(263\) | − | 21.8516i | − | 1.34742i | −0.738994 | − | 0.673712i | \(-0.764699\pi\) | ||
0.738994 | − | 0.673712i | \(-0.235301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.01962i | 0.431212i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.8995 | − | 9.19932i | 1.09339 | − | 0.561938i | ||||
\(269\) | − | 17.3952i | − | 1.06060i | −0.847809 | − | 0.530302i | \(-0.822079\pi\) | ||
0.847809 | − | 0.530302i | \(-0.177921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.44581 | −0.330809 | −0.165405 | − | 0.986226i | \(-0.552893\pi\) | ||||
−0.165405 | + | 0.986226i | \(0.552893\pi\) | |||||||
\(272\) | 14.5088 | + | 10.3868i | 0.879725 | + | 0.629795i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.292893 | − | 0.178781i | −0.0176943 | − | 0.0108005i | ||||
\(275\) | 7.97852i | 0.481123i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.1421 | 1.45056 | 0.725280 | − | 0.688454i | \(-0.241710\pi\) | ||||
0.725280 | + | 0.688454i | \(0.241710\pi\) | |||||||
\(278\) | −2.15897 | − | 1.31783i | −0.129487 | − | 0.0790381i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.3848 | 1.57398 | 0.786992 | − | 0.616963i | \(-0.211637\pi\) | ||||
0.786992 | + | 0.616963i | \(0.211637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0195 | −0.714484 | −0.357242 | − | 0.934012i | \(-0.616283\pi\) | ||||
−0.357242 | + | 0.934012i | \(0.616283\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.57368 | − | 4.01254i | −0.388710 | − | 0.237267i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.89949 | −0.170559 | ||||||||
\(290\) | −0.934353 | + | 1.53073i | −0.0548671 | + | 0.0898878i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.1785 | − | 7.28692i | 0.829732 | − | 0.426435i | ||||
\(293\) | 23.2555i | 1.35860i | 0.733860 | + | 0.679300i | \(0.237717\pi\) | ||||
−0.733860 | + | 0.679300i | \(0.762283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.55688i | − | 0.556423i | ||||||
\(296\) | 0.828427 | − | 11.2833i | 0.0481513 | − | 0.655831i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | + | 0.610396i | 0.0579284 | + | 0.0353593i | ||||
\(299\) | −18.5932 | −1.07527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.97056 | − | 6.50490i | 0.228480 | − | 0.374315i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.62615 | − | 3.66832i | 0.150620 | − | 0.210393i | ||||
\(305\) | −14.1421 | −0.809776 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.4244 | −0.594954 | −0.297477 | − | 0.954729i | \(-0.596145\pi\) | ||||
−0.297477 | + | 0.954729i | \(0.596145\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.14214 | − | 10.0625i | 0.348850 | − | 0.571514i | ||||
\(311\) | −4.51146 | −0.255821 | −0.127911 | − | 0.991786i | \(-0.540827\pi\) | ||||
−0.127911 | + | 0.991786i | \(0.540827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.87285i | − | 0.558046i | −0.960284 | − | 0.279023i | \(-0.909989\pi\) | ||
0.960284 | − | 0.279023i | \(-0.0900106\pi\) | |||||||
\(314\) | 14.8792 | − | 24.3764i | 0.839683 | − | 1.37564i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.41421 | + | 3.81048i | −0.417082 | + | 0.214356i | ||||
\(317\) | 22.4853 | 1.26290 | 0.631450 | − | 0.775417i | \(-0.282460\pi\) | ||||
0.631450 | + | 0.775417i | \(0.282460\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.44158i | 0.136702i | ||||||||
\(320\) | 1.26470 | − | 8.56628i | 0.0706987 | − | 0.478870i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.03127i | 0.279948i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0042i | 0.554931i | ||||||||
\(326\) | 2.80761 | − | 4.59966i | 0.155499 | − | 0.254751i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.6367 | + | 1.14805i | 0.863391 | + | 0.0633905i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.81048i | − | 0.209443i | −0.994502 | − | 0.104722i | \(-0.966605\pi\) | ||
0.994502 | − | 0.104722i | \(-0.0333951\pi\) | |||||||
\(332\) | 3.94753 | + | 7.68087i | 0.216649 | + | 0.421542i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.1668 | − | 15.3617i | −1.37707 | − | 0.840556i | ||||
\(335\) | 10.8916 | 0.595073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.17157 | 0.281714 | 0.140857 | − | 0.990030i | \(-0.455014\pi\) | ||||
0.140857 | + | 0.990030i | \(0.455014\pi\) | |||||||
\(338\) | 7.44975 | + | 4.54729i | 0.405213 | + | 0.247340i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.41421 | + | 8.58892i | 0.239394 | + | 0.465800i | ||||
\(341\) | − | 16.0502i | − | 0.869166i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −22.5061 | − | 1.65241i | −1.21345 | − | 0.0890918i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.5399 | + | 25.4587i | −0.835431 | + | 1.36867i | ||||
\(347\) | 2.08402i | 0.111876i | 0.998434 | + | 0.0559381i | \(0.0178149\pi\) | ||||
−0.998434 | + | 0.0559381i | \(0.982185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.67459i | − | 0.303754i | −0.988399 | − | 0.151877i | \(-0.951468\pi\) | ||
0.988399 | − | 0.151877i | \(-0.0485318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.60660 | − | 10.8517i | −0.245533 | − | 0.578399i | ||||
\(353\) | 27.9790i | 1.48917i | 0.667526 | + | 0.744586i | \(0.267353\pi\) | ||||
−0.667526 | + | 0.744586i | \(0.732647\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.13761 | + | 3.66832i | −0.378292 | + | 0.194421i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.899495 | − | 1.47363i | 0.0475398 | − | 0.0778835i | ||||
\(359\) | − | 24.7988i | − | 1.30883i | −0.756135 | − | 0.654415i | \(-0.772915\pi\) | ||
0.756135 | − | 0.654415i | \(-0.227085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7279 | −0.933049 | ||||||||
\(362\) | −4.45478 | + | 7.29818i | −0.234138 | + | 0.383584i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.62742 | 0.451580 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3374 | −0.852807 | −0.426404 | − | 0.904533i | \(-0.640220\pi\) | ||||
−0.426404 | + | 0.904533i | \(0.640220\pi\) | |||||||
\(368\) | −23.1421 | − | 16.5674i | −1.20637 | − | 0.863638i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.19008 | − | 5.22625i | 0.165844 | − | 0.271700i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.14214 | 0.421584 | 0.210792 | − | 0.977531i | \(-0.432396\pi\) | ||||
0.210792 | + | 0.977531i | \(0.432396\pi\) | |||||||
\(374\) | 11.2220 | + | 6.84984i | 0.580274 | + | 0.354197i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.12786 | + | 15.3617i | −0.0581652 | + | 0.792221i | ||||
\(377\) | 3.06147i | 0.157674i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.9356i | 1.22949i | 0.788727 | + | 0.614744i | \(0.210741\pi\) | ||||
−0.788727 | + | 0.614744i | \(0.789259\pi\) | |||||||
\(380\) | 2.17157 | − | 1.11606i | 0.111399 | − | 0.0572529i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.8284 | − | 24.2931i | 0.758688 | − | 1.24294i | ||||
\(383\) | −6.76719 | −0.345787 | −0.172894 | − | 0.984941i | \(-0.555312\pi\) | ||||
−0.172894 | + | 0.984941i | \(0.555312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.0208 | + | 12.8310i | 1.06993 | + | 0.653082i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.80726 | + | 3.49854i | −0.345586 | + | 0.177612i | ||||
\(389\) | 14.1421 | 0.717035 | 0.358517 | − | 0.933523i | \(-0.383282\pi\) | ||||
0.358517 | + | 0.933523i | \(0.383282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.7405 | 1.60519 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.41421 | − | 1.47363i | −0.121626 | − | 0.0742402i | ||||
\(395\) | −4.51146 | −0.226996 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.8030i | − | 0.642564i | −0.946984 | − | 0.321282i | \(-0.895886\pi\) | ||
0.946984 | − | 0.321282i | \(-0.104114\pi\) | |||||||
\(398\) | 26.2947 | + | 16.0502i | 1.31803 | + | 0.804523i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.91421 | + | 12.4518i | −0.445711 | + | 0.622588i | ||||
\(401\) | 7.17157 | 0.358131 | 0.179066 | − | 0.983837i | \(-0.442693\pi\) | ||||
0.179066 | + | 0.983837i | \(0.442693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.1251i | − | 1.00250i | ||||||
\(404\) | −0.330344 | + | 0.169778i | −0.0164352 | + | 0.00844676i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.33609i | − | 0.413204i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.25972i | − | 0.358970i | −0.983761 | − | 0.179485i | \(-0.942557\pi\) | ||
0.983761 | − | 0.179485i | \(-0.0574431\pi\) | |||||||
\(410\) | 7.24264 | + | 4.42088i | 0.357689 | + | 0.218332i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.0817 | + | 27.3994i | 0.693756 | + | 1.34987i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.67371i | 0.229423i | ||||||||
\(416\) | −5.77615 | − | 13.6068i | −0.283199 | − | 0.667130i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.73187 | − | 2.83730i | 0.0847087 | − | 0.138777i | ||||
\(419\) | 16.5309 | 0.807589 | 0.403795 | − | 0.914850i | \(-0.367691\pi\) | ||||
0.403795 | + | 0.914850i | \(0.367691\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.48528 | 0.316073 | 0.158037 | − | 0.987433i | \(-0.449484\pi\) | ||||
0.158037 | + | 0.987433i | \(0.449484\pi\) | |||||||
\(422\) | 11.7574 | − | 19.2619i | 0.572339 | − | 0.937653i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.34315 | + | 18.2939i | −0.0652289 | + | 0.888431i | ||||
\(425\) | − | 17.0782i | − | 0.828413i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.6569 | + | 6.50490i | −0.611792 | + | 0.314426i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.4244 | − | 6.36304i | −0.502711 | − | 0.306853i | ||||
\(431\) | − | 17.1778i | − | 0.827427i | −0.910407 | − | 0.413714i | \(-0.864231\pi\) | ||
0.910407 | − | 0.413714i | \(-0.135769\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.1760i | − | 0.729313i | −0.931142 | − | 0.364657i | \(-0.881186\pi\) | ||
0.931142 | − | 0.364657i | \(-0.118814\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.17157 | + | 10.0625i | 0.247673 | + | 0.481909i | ||||
\(437\) | − | 8.02509i | − | 0.383892i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.6588 | −0.842809 | −0.421404 | − | 0.906873i | \(-0.638463\pi\) | ||||
−0.421404 | + | 0.906873i | \(0.638463\pi\) | |||||||
\(440\) | 0.467177 | − | 6.36304i | 0.0222718 | − | 0.303346i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.0711 | + | 8.58892i | 0.669292 | + | 0.408533i | ||||
\(443\) | − | 26.7347i | − | 1.27020i | −0.772428 | − | 0.635102i | \(-0.780958\pi\) | ||
0.772428 | − | 0.635102i | \(-0.219042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.34315 | −0.205885 | ||||||||
\(446\) | 25.1668 | + | 15.3617i | 1.19168 | + | 0.727399i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.2843 | −1.90113 | −0.950566 | − | 0.310522i | \(-0.899496\pi\) | ||||
−0.950566 | + | 0.310522i | \(0.899496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.5523 | 0.543977 | ||||||||
\(452\) | −3.87868 | − | 7.54691i | −0.182438 | − | 0.354977i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.8800 | + | 13.3555i | 1.02688 | + | 0.626803i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.7279 | −1.15672 | −0.578362 | − | 0.815780i | \(-0.696308\pi\) | ||||
−0.578362 | + | 0.815780i | \(0.696308\pi\) | |||||||
\(458\) | −13.9449 | + | 22.8456i | −0.651601 | + | 1.06751i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.04085 | − | 13.6997i | −0.328281 | − | 0.638751i | ||||
\(461\) | − | 27.4763i | − | 1.27970i | −0.768501 | − | 0.639849i | \(-0.778997\pi\) | ||
0.768501 | − | 0.639849i | \(-0.221003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.60963i | 0.307175i | 0.988135 | + | 0.153588i | \(0.0490828\pi\) | ||||
−0.988135 | + | 0.153588i | \(0.950917\pi\) | |||||||
\(464\) | −2.72792 | + | 3.81048i | −0.126641 | + | 0.176897i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.36396 | − | 5.71572i | −0.433777 | − | 0.264776i | ||||
\(467\) | −7.50803 | −0.347430 | −0.173715 | − | 0.984796i | \(-0.555577\pi\) | ||||
−0.173715 | + | 0.984796i | \(0.555577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.34315 | + | 7.11529i | −0.200334 | + | 0.328204i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.82863 | − | 24.9063i | 0.0841695 | − | 1.14640i | ||||
\(473\) | −16.6274 | −0.764529 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.31795 | −0.198121 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.31371 | + | 13.6202i | −0.380260 | + | 0.622973i | ||||
\(479\) | 19.9145 | 0.909918 | 0.454959 | − | 0.890512i | \(-0.349654\pi\) | ||||
0.454959 | + | 0.890512i | \(0.349654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 10.4525i | − | 0.476593i | ||||||
\(482\) | −6.34009 | + | 10.3868i | −0.288783 | + | 0.473108i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.08579 | + | 11.8414i | 0.276627 | + | 0.538244i | ||||
\(485\) | −4.14214 | −0.188085 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.7445i | 1.80100i | 0.434860 | + | 0.900498i | \(0.356798\pi\) | ||||
−0.434860 | + | 0.900498i | \(0.643202\pi\) | |||||||
\(488\) | −36.8560 | − | 2.70598i | −1.66839 | − | 0.122494i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.9570i | − | 0.720132i | −0.932927 | − | 0.360066i | \(-0.882754\pi\) | ||
0.932927 | − | 0.360066i | \(-0.117246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.22625i | − | 0.235379i | ||||||
\(494\) | 2.17157 | − | 3.55765i | 0.0977037 | − | 0.160066i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.9325 | − | 25.0489i | 0.805192 | − | 1.12473i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.3986i | − | 0.823636i | −0.911266 | − | 0.411818i | \(-0.864894\pi\) | ||
0.911266 | − | 0.411818i | \(-0.135106\pi\) | |||||||
\(500\) | −16.9981 | + | 8.73606i | −0.760179 | + | 0.390689i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.5834 | + | 7.68087i | 0.561625 | + | 0.342814i | ||||
\(503\) | 20.8489 | 0.929606 | 0.464803 | − | 0.885414i | \(-0.346125\pi\) | ||||
0.464803 | + | 0.885414i | \(0.346125\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.201010 | −0.00894483 | ||||||||
\(506\) | −17.8995 | − | 10.9258i | −0.795730 | − | 0.485710i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.0711 | − | 10.3154i | 0.890510 | − | 0.457671i | ||||
\(509\) | 21.0907i | 0.934830i | 0.884038 | + | 0.467415i | \(0.154815\pi\) | ||||
−0.884038 | + | 0.467415i | \(0.845185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4.93503 | − | 22.0827i | 0.218100 | − | 0.975927i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.94410 | − | 11.3764i | 0.306291 | − | 0.501791i | ||||
\(515\) | 16.6722i | 0.734664i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3492i | 0.499137i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.585786 | − | 7.97852i | 0.0256884 | − | 0.349881i | ||||
\(521\) | 17.9749i | 0.787493i | 0.919219 | + | 0.393746i | \(0.128821\pi\) | ||||
−0.919219 | + | 0.393746i | \(0.871179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.7191 | −1.60562 | −0.802808 | − | 0.596238i | \(-0.796662\pi\) | ||||
−0.802808 | + | 0.596238i | \(0.796662\pi\) | |||||||
\(524\) | 14.5088 | + | 28.2304i | 0.633820 | + | 1.23325i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.1005 | − | 26.3772i | 0.702015 | − | 1.15010i | ||||
\(527\) | 34.3557i | 1.49656i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.6274 | −1.20119 | ||||||||
\(530\) | −5.17214 | + | 8.47343i | −0.224664 | + | 0.368062i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.4853 | 0.627427 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.70154 | −0.332967 | ||||||||
\(536\) | 28.3848 | + | 2.08402i | 1.22604 | + | 0.0900160i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.8170 | − | 20.9979i | 0.552580 | − | 0.905282i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.6863 | 0.975360 | 0.487680 | − | 0.873023i | \(-0.337843\pi\) | ||||
0.487680 | + | 0.873023i | \(0.337843\pi\) | |||||||
\(542\) | −6.57368 | − | 4.01254i | −0.282364 | − | 0.172353i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.86051 | + | 23.2283i | 0.422766 | + | 0.995905i | ||||
\(545\) | 6.12293i | 0.262278i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5882i | 0.623744i | 0.950124 | + | 0.311872i | \(0.100956\pi\) | ||||
−0.950124 | + | 0.311872i | \(0.899044\pi\) | |||||||
\(548\) | −0.221825 | − | 0.431615i | −0.00947591 | − | 0.0184377i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.87868 | + | 9.63093i | −0.250668 | + | 0.410664i | ||||
\(551\) | −1.32138 | −0.0562925 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 29.1421 | + | 17.7882i | 1.23813 | + | 0.755750i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.63512 | − | 3.18152i | −0.0693445 | − | 0.134926i | ||||
\(557\) | 8.34315 | 0.353510 | 0.176755 | − | 0.984255i | \(-0.443440\pi\) | ||||
0.176755 | + | 0.984255i | \(0.443440\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.8489 | −0.881814 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.8492 | + | 19.4406i | 1.34348 | + | 0.820054i | ||||
\(563\) | −11.3588 | −0.478716 | −0.239358 | − | 0.970931i | \(-0.576937\pi\) | ||||
−0.239358 | + | 0.970931i | \(0.576937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 4.59220i | − | 0.193195i | ||||||
\(566\) | −14.5088 | − | 8.85611i | −0.609850 | − | 0.372250i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.1716 | −0.552181 | −0.276091 | − | 0.961132i | \(-0.589039\pi\) | ||||
−0.276091 | + | 0.961132i | \(0.589039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 40.6077i | − | 1.69938i | −0.527282 | − | 0.849691i | \(-0.676789\pi\) | ||
0.527282 | − | 0.849691i | \(-0.323211\pi\) | |||||||
\(572\) | −4.97863 | − | 9.68714i | −0.208167 | − | 0.405040i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.2404i | 1.13600i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.6172i | 1.60766i | 0.594862 | + | 0.803828i | \(0.297207\pi\) | ||||
−0.594862 | + | 0.803828i | \(0.702793\pi\) | |||||||
\(578\) | −3.50000 | − | 2.13639i | −0.145581 | − | 0.0888619i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.25573 | + | 1.15932i | −0.0936640 | + | 0.0481380i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5155i | 0.559753i | ||||||||
\(584\) | 22.4840 | + | 1.65078i | 0.930395 | + | 0.0683100i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.1350 | + | 28.0719i | −0.707838 | + | 1.15964i | ||||
\(587\) | −1.78855 | −0.0738214 | −0.0369107 | − | 0.999319i | \(-0.511752\pi\) | ||||
−0.0369107 | + | 0.999319i | \(0.511752\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.68629 | 0.357912 | ||||||||
\(590\) | 7.04163 | − | 11.5362i | 0.289899 | − | 0.474937i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.31371 | − | 13.0098i | 0.382791 | − | 0.534699i | ||||
\(593\) | − | 34.9986i | − | 1.43722i | −0.695412 | − | 0.718611i | \(-0.744778\pi\) | ||
0.695412 | − | 0.718611i | \(-0.255222\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.757359 | + | 1.47363i | 0.0310226 | + | 0.0603621i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.4439 | − | 13.6997i | −0.917801 | − | 0.560222i | ||||
\(599\) | 41.9766i | 1.71512i | 0.514385 | + | 0.857560i | \(0.328020\pi\) | ||||
−0.514385 | + | 0.857560i | \(0.671980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.25425i | 0.255116i | 0.991831 | + | 0.127558i | \(0.0407139\pi\) | ||||
−0.991831 | + | 0.127558i | \(0.959286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.58579 | − | 4.92655i | 0.390040 | − | 0.200458i | ||||
\(605\) | 7.20533i | 0.292938i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.4031 | 0.625192 | 0.312596 | − | 0.949886i | \(-0.398801\pi\) | ||||
0.312596 | + | 0.949886i | \(0.398801\pi\) | |||||||
\(608\) | 5.87291 | − | 2.49307i | 0.238178 | − | 0.101108i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.0711 | − | 10.4201i | −0.691187 | − | 0.421898i | ||||
\(611\) | 14.2306i | 0.575708i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.3137 | −1.26475 | −0.632374 | − | 0.774663i | \(-0.717920\pi\) | ||||
−0.632374 | + | 0.774663i | \(0.717920\pi\) | |||||||
\(614\) | −12.5834 | − | 7.68087i | −0.507825 | − | 0.309974i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.4558 | −0.622229 | −0.311114 | − | 0.950372i | \(-0.600702\pi\) | ||||
−0.311114 | + | 0.950372i | \(0.600702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.4207 | 1.78542 | 0.892709 | − | 0.450634i | \(-0.148802\pi\) | ||||
0.892709 | + | 0.450634i | \(0.148802\pi\) | |||||||
\(620\) | 14.8284 | − | 7.62096i | 0.595524 | − | 0.306065i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.44581 | − | 3.32410i | −0.218357 | − | 0.133284i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.79899 | 0.351960 | ||||||||
\(626\) | 7.27444 | − | 11.9176i | 0.290745 | − | 0.476322i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 35.9216 | − | 18.4617i | 1.43343 | − | 0.736700i | ||||
\(629\) | 17.8435i | 0.711469i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5667i | 0.898365i | 0.893440 | + | 0.449183i | \(0.148285\pi\) | ||||
−0.893440 | + | 0.449183i | \(0.851715\pi\) | |||||||
\(632\) | −11.7574 | − | 0.863230i | −0.467683 | − | 0.0343374i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.1421 | + | 16.5674i | 1.07795 | + | 0.657977i | ||||
\(635\) | 12.2130 | 0.484658 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.79899 | + | 2.94725i | −0.0712227 | + | 0.116683i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.83837 | − | 9.40857i | 0.309839 | − | 0.371907i | ||||
\(641\) | 1.45584 | 0.0575024 | 0.0287512 | − | 0.999587i | \(-0.490847\pi\) | ||||
0.0287512 | + | 0.999587i | \(0.490847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.84734 | −0.270033 | −0.135016 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135016 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.70711 | + | 6.07328i | −0.145854 | + | 0.238950i | ||||
\(647\) | −9.57025 | −0.376245 | −0.188123 | − | 0.982146i | \(-0.560240\pi\) | ||||
−0.188123 | + | 0.982146i | \(0.560240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.4007i | − | 0.722289i | ||||||
\(650\) | −7.37120 | + | 12.0761i | −0.289122 | + | 0.473663i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.77817 | − | 3.48359i | 0.265454 | − | 0.136428i | ||||
\(653\) | −15.7990 | −0.618262 | −0.309131 | − | 0.951019i | \(-0.600038\pi\) | ||||
−0.309131 | + | 0.951019i | \(0.600038\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.1778i | 0.671194i | ||||||||
\(656\) | 18.0292 | + | 12.9071i | 0.703923 | + | 0.503938i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 30.5452i | − | 1.18987i | −0.803773 | − | 0.594936i | \(-0.797177\pi\) | ||
0.803773 | − | 0.594936i | \(-0.202823\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5404i | 0.487764i | 0.969805 | + | 0.243882i | \(0.0784209\pi\) | ||||
−0.969805 | + | 0.243882i | \(0.921579\pi\) | |||||||
\(662\) | 2.80761 | − | 4.59966i | 0.109121 | − | 0.178771i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.894276 | + | 12.1802i | −0.0347046 | + | 0.472684i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.33609i | 0.322775i | ||||||||
\(668\) | −19.0603 | − | 37.0865i | −0.737467 | − | 1.43492i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.1474 | + | 8.02509i | 0.507926 | + | 0.310036i | ||||
\(671\) | −27.2291 | −1.05117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.3848 | −1.01706 | −0.508529 | − | 0.861045i | \(-0.669811\pi\) | ||||
−0.508529 | + | 0.861045i | \(0.669811\pi\) | |||||||
\(674\) | 6.24264 | + | 3.81048i | 0.240458 | + | 0.146774i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.64214 | + | 10.9781i | 0.217005 | + | 0.422236i | ||||
\(677\) | 40.0936i | 1.54092i | 0.637488 | + | 0.770461i | \(0.279974\pi\) | ||||
−0.637488 | + | 0.770461i | \(0.720026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.00000 | + | 13.6202i | −0.0383482 | + | 0.522311i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.8260 | − | 19.3743i | 0.452840 | − | 0.741879i | ||||
\(683\) | 41.9766i | 1.60619i | 0.595850 | + | 0.803096i | \(0.296815\pi\) | ||||
−0.595850 | + | 0.803096i | \(0.703185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.262632i | − | 0.0100347i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25.9497 | − | 18.5774i | −0.989325 | − | 0.708257i | ||||
\(689\) | 16.9469i | 0.645624i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.97863 | 0.189396 | 0.0946981 | − | 0.995506i | \(-0.469811\pi\) | ||||
0.0946981 | + | 0.995506i | \(0.469811\pi\) | |||||||
\(692\) | −37.5167 | + | 19.2814i | −1.42617 | + | 0.732970i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.53553 | + | 2.51564i | −0.0582881 | + | 0.0954923i | ||||
\(695\) | − | 1.93591i | − | 0.0734334i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.7279 | −0.936637 | ||||||||
\(698\) | 4.18111 | − | 6.84984i | 0.158257 | − | 0.259270i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.0000 | −0.604312 | −0.302156 | − | 0.953259i | \(-0.597706\pi\) | ||||
−0.302156 | + | 0.953259i | \(0.597706\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.51146 | 0.170153 | ||||||||
\(704\) | 2.43503 | − | 16.4934i | 0.0917736 | − | 0.621618i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.6153 | + | 33.7737i | −0.775867 | + | 1.27109i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.37258 | −0.0515484 | −0.0257742 | − | 0.999668i | \(-0.508205\pi\) | ||||
−0.0257742 | + | 0.999668i | \(0.508205\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.3187 | − | 0.831025i | −0.424187 | − | 0.0311440i | ||||
\(713\) | − | 54.7987i | − | 2.05223i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.89450i | − | 0.220442i | ||||||
\(716\) | 2.17157 | − | 1.11606i | 0.0811555 | − | 0.0417093i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.2721 | − | 29.9348i | 0.681908 | − | 1.11716i | ||||
\(719\) | −11.8260 | −0.441034 | −0.220517 | − | 0.975383i | \(-0.570775\pi\) | ||||
−0.220517 | + | 0.975383i | \(0.570775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −21.3995 | − | 13.0622i | −0.796407 | − | 0.486123i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.7548 | + | 5.52735i | −0.399699 | + | 0.205422i | ||||
\(725\) | 4.48528 | 0.166579 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.1207 | −1.41382 | −0.706909 | − | 0.707305i | \(-0.749911\pi\) | ||||
−0.706909 | + | 0.707305i | \(0.749911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.4142 | + | 6.35679i | 0.385447 | + | 0.235275i | ||||
\(731\) | 35.5913 | 1.31639 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.35049i | 0.0868175i | 0.999057 | + | 0.0434087i | \(0.0138218\pi\) | ||||
−0.999057 | + | 0.0434087i | \(0.986178\pi\) | |||||||
\(734\) | −19.7210 | − | 12.0376i | −0.727916 | − | 0.444317i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.7279 | − | 37.0501i | −0.579739 | − | 1.36568i | ||||
\(737\) | 20.9706 | 0.772461 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.3968i | 1.92745i | 0.266905 | + | 0.963723i | \(0.413999\pi\) | ||||
−0.266905 | + | 0.963723i | \(0.586001\pi\) | |||||||
\(740\) | 7.70154 | − | 3.95815i | 0.283114 | − | 0.145505i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.8930i | 0.656429i | 0.944603 | + | 0.328215i | \(0.106447\pi\) | ||||
−0.944603 | + | 0.328215i | \(0.893553\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.896683i | 0.0328519i | ||||||||
\(746\) | 9.82843 | + | 5.99923i | 0.359844 | + | 0.219647i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.49906 | + | 16.5370i | 0.310756 | + | 0.604652i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 13.7249i | − | 0.500829i | −0.968139 | − | 0.250415i | \(-0.919433\pi\) | ||
0.968139 | − | 0.250415i | \(-0.0805670\pi\) | |||||||
\(752\) | −12.6802 | + | 17.7122i | −0.462398 | + | 0.645898i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.25573 | + | 3.69552i | −0.0821488 | + | 0.134583i | ||||
\(755\) | 5.83283 | 0.212279 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.2843 | 0.446479 | 0.223240 | − | 0.974764i | \(-0.428337\pi\) | ||||
0.223240 | + | 0.974764i | \(0.428337\pi\) | |||||||
\(758\) | −17.6360 | + | 28.8928i | −0.640570 | + | 1.04943i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.44365 | + | 0.252834i | 0.124914 | + | 0.00917126i | ||||
\(761\) | − | 25.9999i | − | 0.942497i | −0.882000 | − | 0.471249i | \(-0.843803\pi\) | ||
0.882000 | − | 0.471249i | \(-0.156197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 35.7990 | − | 18.3986i | 1.29516 | − | 0.665639i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.16872 | − | 4.98615i | −0.295148 | − | 0.180157i | ||||
\(767\) | − | 23.0723i | − | 0.833094i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 46.1940i | − | 1.66580i | −0.553425 | − | 0.832899i | \(-0.686680\pi\) | ||
0.553425 | − | 0.832899i | \(-0.313320\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.9203 | + | 30.9768i | 0.572985 | + | 1.11488i | ||||
\(773\) | − | 52.9735i | − | 1.90532i | −0.304031 | − | 0.952662i | \(-0.598333\pi\) | ||
0.304031 | − | 0.952662i | \(-0.401667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.4848 | −1.05912 | ||||||||
\(776\) | −10.7949 | − | 0.792563i | −0.387513 | − | 0.0284514i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.0711 | + | 10.4201i | 0.612027 | + | 0.373579i | ||||
\(779\) | 6.25206i | 0.224003i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 38.3142 | + | 23.3868i | 1.37011 | + | 0.836311i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.8579 | 0.780141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.2913 | −1.04412 | −0.522061 | − | 0.852908i | \(-0.674836\pi\) | ||||
−0.522061 | + | 0.852908i | \(0.674836\pi\) | |||||||
\(788\) | −1.82843 | − | 3.55765i | −0.0651350 | − | 0.126736i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.44581 | − | 3.32410i | −0.193753 | − | 0.118266i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.1421 | −1.21242 | ||||||||
\(794\) | 9.43341 | − | 15.4546i | 0.334779 | − | 0.548463i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.9145 | + | 38.7485i | 0.705852 | + | 1.37341i | ||||
\(797\) | − | 19.1886i | − | 0.679694i | −0.940481 | − | 0.339847i | \(-0.889625\pi\) | ||
0.940481 | − | 0.339847i | \(-0.110375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 24.2931i | − | 0.859429i | ||||||
\(800\) | −19.9350 | + | 8.46250i | −0.704810 | + | 0.299195i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.65685 | + | 5.28411i | 0.305684 | + | 0.186588i | ||||
\(803\) | 16.6111 | 0.586193 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.8284 | − | 24.2931i | 0.522309 | − | 0.855689i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.523855 | − | 0.0384616i | −0.0184291 | − | 0.00135308i | ||||
\(809\) | −48.0416 | −1.68905 | −0.844527 | − | 0.535513i | \(-0.820118\pi\) | ||||
−0.844527 | + | 0.535513i | \(0.820118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.4386 | −1.49022 | −0.745111 | − | 0.666941i | \(-0.767603\pi\) | ||||
−0.745111 | + | 0.666941i | \(0.767603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.14214 | − | 10.0625i | 0.215282 | − | 0.352692i | ||||
\(815\) | 4.12444 | 0.144473 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.99869i | − | 0.314824i | ||||||
\(818\) | 5.34906 | − | 8.76326i | 0.187025 | − | 0.306400i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.48528 | + | 10.6729i | 0.191554 | + | 0.372715i | ||||
\(821\) | 18.0000 | 0.628204 | 0.314102 | − | 0.949389i | \(-0.398297\pi\) | ||||
0.314102 | + | 0.949389i | \(0.398297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.6292i | − | 1.13738i | −0.822551 | − | 0.568692i | \(-0.807450\pi\) | ||
0.822551 | − | 0.568692i | \(-0.192550\pi\) | |||||||
\(824\) | −3.19008 | + | 43.4495i | −0.111132 | + | 1.51364i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.8930i | 0.622199i | 0.950377 | + | 0.311100i | \(0.100697\pi\) | ||||
−0.950377 | + | 0.311100i | \(0.899303\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.25265i | 0.147700i | 0.997269 | + | 0.0738502i | \(0.0235287\pi\) | ||||
−0.997269 | + | 0.0738502i | \(0.976471\pi\) | |||||||
\(830\) | −3.44365 | + | 5.64167i | −0.119531 | + | 0.195825i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.05325 | − | 20.6808i | 0.105852 | − | 0.716979i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 22.5667i | − | 0.780952i | ||||||
\(836\) | 4.18111 | − | 2.14885i | 0.144607 | − | 0.0743196i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.9546 | + | 12.1802i | 0.689321 | + | 0.420758i | ||||
\(839\) | −53.9108 | −1.86121 | −0.930603 | − | 0.366029i | \(-0.880717\pi\) | ||||
−0.930603 | + | 0.366029i | \(0.880717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | 7.82843 | + | 4.77844i | 0.269785 | + | 0.164676i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.3848 | − | 14.5882i | 0.977044 | − | 0.502145i | ||||
\(845\) | 6.68006i | 0.229801i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.1005 | + | 21.0930i | −0.518553 | + | 0.724338i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.5834 | − | 20.6152i | 0.431608 | − | 0.707095i | ||||
\(851\) | − | 28.4612i | − | 0.975637i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.61859i | 0.123898i | 0.998079 | + | 0.0619492i | \(0.0197317\pi\) | ||||
−0.998079 | + | 0.0619492i | \(0.980268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.0711 | − | 1.47363i | −0.686015 | − | 0.0503675i | ||||
\(857\) | 39.6996i | 1.35611i | 0.735010 | + | 0.678057i | \(0.237178\pi\) | ||||
−0.735010 | + | 0.678057i | \(0.762822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.7210 | 0.672873 | 0.336436 | − | 0.941706i | \(-0.390778\pi\) | ||||
0.336436 | + | 0.941706i | \(0.390778\pi\) | |||||||
\(860\) | −7.89505 | − | 15.3617i | −0.269219 | − | 0.523831i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.6569 | − | 20.7355i | 0.431094 | − | 0.706254i | ||||
\(863\) | 18.3986i | 0.626297i | 0.949704 | + | 0.313148i | \(0.101384\pi\) | ||||
−0.949704 | + | 0.313148i | \(0.898616\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.8284 | −0.776190 | ||||||||
\(866\) | 11.1819 | − | 18.3191i | 0.379976 | − | 0.622508i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.68629 | −0.294662 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.2947 | 0.890962 | ||||||||
\(872\) | −1.17157 | + | 15.9570i | −0.0396745 | + | 0.540374i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.91299 | − | 9.68714i | 0.200010 | − | 0.327672i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.4264 | −1.83785 | −0.918925 | − | 0.394433i | \(-0.870941\pi\) | ||||
−0.918925 | + | 0.394433i | \(0.870941\pi\) | |||||||
\(878\) | −21.3161 | − | 13.0112i | −0.719382 | − | 0.439108i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.25230 | − | 7.33664i | 0.177055 | − | 0.247318i | ||||
\(881\) | 15.1760i | 0.511293i | 0.966770 | + | 0.255647i | \(0.0822883\pi\) | ||||
−0.966770 | + | 0.255647i | \(0.917712\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.67371i | − | 0.157283i | −0.996903 | − | 0.0786415i | \(-0.974942\pi\) | ||
0.996903 | − | 0.0786415i | \(-0.0250582\pi\) | |||||||
\(884\) | 10.6569 | + | 20.7355i | 0.358429 | + | 0.697410i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.6985 | − | 32.2717i | 0.661784 | − | 1.08419i | ||||
\(887\) | 17.6588 | 0.592925 | 0.296462 | − | 0.955045i | \(-0.404193\pi\) | ||||
0.296462 | + | 0.955045i | \(0.404193\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.24264 | − | 3.20009i | −0.175734 | − | 0.107267i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.0603 | + | 37.0865i | 0.638187 | + | 1.24175i | ||||
\(893\) | −6.14214 | −0.205539 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.32138 | 0.0441687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −48.6274 | − | 29.6820i | −1.62272 | − | 0.990500i | ||||
\(899\) | −9.02291 | −0.300931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 28.9301i | − | 0.963801i | ||||||
\(902\) | 13.9449 | + | 8.51189i | 0.464313 | + | 0.283415i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.878680 | − | 11.9678i | 0.0292245 | − | 0.398043i | ||||
\(905\) | −6.54416 | −0.217535 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.7875i | 0.789850i | 0.918713 | + | 0.394925i | \(0.129229\pi\) | ||||
−0.918713 | + | 0.394925i | \(0.870771\pi\) | |||||||
\(908\) | 16.5710 | + | 32.2429i | 0.549929 | + | 1.07002i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 43.1974i | − | 1.43119i | −0.698513 | − | 0.715597i | \(-0.746155\pi\) | ||
0.698513 | − | 0.715597i | \(-0.253845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.99869i | 0.297813i | ||||||||
\(914\) | −29.8492 | − | 18.2199i | −0.987325 | − | 0.602659i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33.6659 | + | 17.3023i | −1.11235 | + | 0.571686i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.3014i | 1.62630i | 0.582052 | + | 0.813151i | \(0.302250\pi\) | ||||
−0.582052 | + | 0.813151i | \(0.697750\pi\) | |||||||
\(920\) | 1.59504 | − | 21.7248i | 0.0525869 | − | 0.716244i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.2449 | − | 33.1668i | 0.666730 | − | 1.09229i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.3137 | −0.503512 | ||||||||
\(926\) | −4.87006 | + | 7.97852i | −0.160040 | + | 0.262191i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.10051 | + | 2.58969i | −0.200259 | + | 0.0850107i | ||||
\(929\) | − | 16.7068i | − | 0.548131i | −0.961711 | − | 0.274065i | \(-0.911632\pi\) | ||
0.961711 | − | 0.274065i | \(-0.0883685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7.09188 | − | 13.7990i | −0.232302 | − | 0.452000i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.06299 | − | 5.53201i | −0.296550 | − | 0.181013i | ||||
\(935\) | 10.0625i | 0.329080i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 53.4762i | − | 1.74699i | −0.486831 | − | 0.873496i | \(-0.661847\pi\) | ||
0.486831 | − | 0.873496i | \(-0.338153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.4853 | + | 5.38883i | −0.341992 | + | 0.175764i | ||||
\(941\) | − | 8.10201i | − | 0.264118i | −0.991242 | − | 0.132059i | \(-0.957841\pi\) | ||
0.991242 | − | 0.132059i | \(-0.0421588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.4421 | 1.28441 | ||||||||
\(944\) | 20.5586 | − | 28.7172i | 0.669126 | − | 0.934665i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0711 | − | 12.2513i | −0.652567 | − | 0.398324i | ||||
\(947\) | 42.3342i | 1.37568i | 0.725864 | + | 0.687838i | \(0.241440\pi\) | ||||
−0.725864 | + | 0.687838i | \(0.758560\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.8284 | 0.676119 | ||||||||
\(950\) | −5.21222 | − | 3.18152i | −0.169107 | − | 0.103222i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.6569 | −1.21983 | −0.609913 | − | 0.792469i | \(-0.708795\pi\) | ||||
−0.609913 | + | 0.792469i | \(0.708795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.7832 | 0.704889 | ||||||||
\(956\) | −20.0711 | + | 10.3154i | −0.649145 | + | 0.333623i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.0390 | + | 14.6733i | 0.776664 | + | 0.474072i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.3137 | 0.913345 | ||||||||
\(962\) | 7.70154 | − | 12.6173i | 0.248308 | − | 0.406798i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.3063 | + | 7.86657i | −0.492983 | + | 0.253365i | ||||
\(965\) | 18.8490i | 0.606771i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.8930i | − | 0.575399i | −0.957721 | − | 0.287699i | \(-0.907110\pi\) | ||
0.957721 | − | 0.287699i | \(-0.0928904\pi\) | |||||||
\(968\) | −1.37868 | + | 18.7779i | −0.0443124 | + | 0.603544i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.00000 | − | 3.05198i | −0.160540 | − | 0.0979931i | ||||
\(971\) | 21.9768 | 0.705268 | 0.352634 | − | 0.935761i | \(-0.385286\pi\) | ||||
0.352634 | + | 0.935761i | \(0.385286\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.2843 | + | 47.9759i | −0.938329 | + | 1.53725i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.4953 | − | 30.4224i | −1.36024 | − | 0.973796i | ||||
\(977\) | −54.3848 | −1.73992 | −0.869962 | − | 0.493120i | \(-0.835857\pi\) | ||||
−0.869962 | + | 0.493120i | \(0.835857\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.36223 | −0.267258 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.7574 | − | 19.2619i | 0.375192 | − | 0.614671i | ||||
\(983\) | −33.9962 | −1.08431 | −0.542156 | − | 0.840278i | \(-0.682392\pi\) | ||||
−0.542156 | + | 0.840278i | \(0.682392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.16478i | − | 0.0689758i | ||||||
\(986\) | 3.85077 | − | 6.30864i | 0.122633 | − | 0.200908i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.24264 | − | 2.69442i | 0.166791 | − | 0.0857208i | ||||
\(989\) | −56.7696 | −1.80517 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.8516i | 0.694137i | 0.937840 | + | 0.347069i | \(0.112823\pi\) | ||||
−0.937840 | + | 0.347069i | \(0.887177\pi\) | |||||||
\(992\) | 40.1027 | − | 17.0238i | 1.27326 | − | 0.540506i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.5780i | 0.747473i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.68006i | 0.211560i | 0.994390 | + | 0.105780i | \(0.0337339\pi\) | ||||
−0.994390 | + | 0.105780i | \(0.966266\pi\) | |||||||
\(998\) | 13.5563 | − | 22.2091i | 0.429119 | − | 0.703017i | ||||
\(999\) | 0 | 0 |
(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 | 1764.2.b.k.1567.8 | 8 | ||
3.2 | odd | 2 | 196.2.d.c.195.2 | yes | 8 | ||
4.3 | odd | 2 | inner | 1764.2.b.k.1567.6 | 8 | ||
7.6 | odd | 2 | inner | 1764.2.b.k.1567.7 | 8 | ||
12.11 | even | 2 | 196.2.d.c.195.3 | yes | 8 | ||
21.2 | odd | 6 | 196.2.f.d.31.3 | 16 | |||
21.5 | even | 6 | 196.2.f.d.31.4 | 16 | |||
21.11 | odd | 6 | 196.2.f.d.19.7 | 16 | |||
21.17 | even | 6 | 196.2.f.d.19.8 | 16 | |||
21.20 | even | 2 | 196.2.d.c.195.1 | ✓ | 8 | ||
24.5 | odd | 2 | 3136.2.f.i.3135.2 | 8 | |||
24.11 | even | 2 | 3136.2.f.i.3135.8 | 8 | |||
28.27 | even | 2 | inner | 1764.2.b.k.1567.5 | 8 | ||
84.11 | even | 6 | 196.2.f.d.19.4 | 16 | |||
84.23 | even | 6 | 196.2.f.d.31.8 | 16 | |||
84.47 | odd | 6 | 196.2.f.d.31.7 | 16 | |||
84.59 | odd | 6 | 196.2.f.d.19.3 | 16 | |||
84.83 | odd | 2 | 196.2.d.c.195.4 | yes | 8 | ||
168.83 | odd | 2 | 3136.2.f.i.3135.1 | 8 | |||
168.125 | even | 2 | 3136.2.f.i.3135.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.2.d.c.195.1 | ✓ | 8 | 21.20 | even | 2 | ||
196.2.d.c.195.2 | yes | 8 | 3.2 | odd | 2 | ||
196.2.d.c.195.3 | yes | 8 | 12.11 | even | 2 | ||
196.2.d.c.195.4 | yes | 8 | 84.83 | odd | 2 | ||
196.2.f.d.19.3 | 16 | 84.59 | odd | 6 | |||
196.2.f.d.19.4 | 16 | 84.11 | even | 6 | |||
196.2.f.d.19.7 | 16 | 21.11 | odd | 6 | |||
196.2.f.d.19.8 | 16 | 21.17 | even | 6 | |||
196.2.f.d.31.3 | 16 | 21.2 | odd | 6 | |||
196.2.f.d.31.4 | 16 | 21.5 | even | 6 | |||
196.2.f.d.31.7 | 16 | 84.47 | odd | 6 | |||
196.2.f.d.31.8 | 16 | 84.23 | even | 6 | |||
1764.2.b.k.1567.5 | 8 | 28.27 | even | 2 | inner | ||
1764.2.b.k.1567.6 | 8 | 4.3 | odd | 2 | inner | ||
1764.2.b.k.1567.7 | 8 | 7.6 | odd | 2 | inner | ||
1764.2.b.k.1567.8 | 8 | 1.1 | even | 1 | trivial | ||
3136.2.f.i.3135.1 | 8 | 168.83 | odd | 2 | |||
3136.2.f.i.3135.2 | 8 | 24.5 | odd | 2 | |||
3136.2.f.i.3135.7 | 8 | 168.125 | even | 2 | |||
3136.2.f.i.3135.8 | 8 | 24.11 | even | 2 |