Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(193,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.t (of order \(3\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.6 | ||
Character | \(\chi\) | \(=\) | 504.193 |
Dual form | 504.2.t.d.457.6 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.371921 | + | 1.69165i | 0.214729 | + | 0.976674i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.68316 | 0.752730 | 0.376365 | − | 0.926471i | \(-0.377174\pi\) | ||||
0.376365 | + | 0.926471i | \(0.377174\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.960133 | + | 2.46539i | 0.362896 | + | 0.931830i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.72335 | + | 1.25832i | −0.907783 | + | 0.419440i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.24498 | 0.375376 | 0.187688 | − | 0.982229i | \(-0.439901\pi\) | ||||
0.187688 | + | 0.982229i | \(0.439901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.96039 | − | 3.39550i | 0.543715 | − | 0.941743i | −0.454971 | − | 0.890506i | \(-0.650350\pi\) |
0.998687 | − | 0.0512366i | \(-0.0163162\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.626001 | + | 2.84731i | 0.161633 | + | 0.735172i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.62691 | + | 2.81788i | −0.394582 | + | 0.683437i | −0.993048 | − | 0.117712i | \(-0.962444\pi\) |
0.598465 | + | 0.801149i | \(0.295777\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.36192 | + | 4.09097i | 0.541863 | + | 0.938534i | 0.998797 | + | 0.0490333i | \(0.0156140\pi\) |
−0.456935 | + | 0.889500i | \(0.651053\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.81348 | + | 2.54114i | −0.832169 | + | 0.554522i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.398135 | −0.0830170 | −0.0415085 | − | 0.999138i | \(-0.513216\pi\) | ||||
−0.0415085 | + | 0.999138i | \(0.513216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.16699 | −0.433397 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.14150 | − | 4.13895i | −0.604583 | − | 0.796542i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.19896 | − | 5.54076i | −0.594032 | − | 1.02889i | −0.993683 | − | 0.112226i | \(-0.964202\pi\) |
0.399651 | − | 0.916667i | \(-0.369131\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.289184 | + | 0.500881i | 0.0519389 | + | 0.0899608i | 0.890826 | − | 0.454345i | \(-0.150127\pi\) |
−0.838887 | + | 0.544306i | \(0.816793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.463034 | + | 2.10607i | 0.0806039 | + | 0.366620i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61605 | + | 4.14963i | 0.273163 | + | 0.701416i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.72146 | + | 4.71371i | 0.447405 | + | 0.774928i | 0.998216 | − | 0.0597015i | \(-0.0190149\pi\) |
−0.550811 | + | 0.834630i | \(0.685682\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.47311 | + | 2.05344i | 1.03653 | + | 0.328813i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.20216 | − | 7.27836i | 0.656267 | − | 1.13669i | −0.325307 | − | 0.945608i | \(-0.605468\pi\) |
0.981574 | − | 0.191080i | \(-0.0611990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.46299 | + | 4.26603i | 0.375603 | + | 0.650563i | 0.990417 | − | 0.138109i | \(-0.0441024\pi\) |
−0.614814 | + | 0.788672i | \(0.710769\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.58382 | + | 2.11795i | −0.683316 | + | 0.315725i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.212595 | − | 0.368225i | 0.0310101 | − | 0.0537112i | −0.850104 | − | 0.526615i | \(-0.823461\pi\) |
0.881114 | + | 0.472904i | \(0.156794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.15629 | + | 4.73420i | −0.736613 | + | 0.676315i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.37195 | − | 1.70412i | −0.752223 | − | 0.238625i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.466315 | + | 0.807681i | −0.0640533 | + | 0.110944i | −0.896274 | − | 0.443501i | \(-0.853736\pi\) |
0.832220 | + | 0.554445i | \(0.187069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.09550 | 0.282557 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.04204 | + | 5.51707i | −0.800288 | + | 0.730753i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.02527 | − | 5.23992i | −0.393856 | − | 0.682179i | 0.599098 | − | 0.800676i | \(-0.295526\pi\) |
−0.992954 | + | 0.118496i | \(0.962193\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.10459 | + | 8.84140i | −0.653575 | + | 1.13203i | 0.328674 | + | 0.944444i | \(0.393398\pi\) |
−0.982249 | + | 0.187582i | \(0.939935\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.71702 | − | 5.50596i | −0.720277 | − | 0.693686i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.29965 | − | 5.71516i | 0.409271 | − | 0.708878i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.70976 | + | 8.15754i | 0.575389 | + | 0.996602i | 0.995999 | + | 0.0893612i | \(0.0284825\pi\) |
−0.420611 | + | 0.907241i | \(0.638184\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.148075 | − | 0.673505i | −0.0178261 | − | 0.0810805i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.46617 | 1.00475 | 0.502375 | − | 0.864650i | \(-0.332460\pi\) | ||||
0.502375 | + | 0.864650i | \(0.332460\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.82340 | − | 11.8185i | 0.798619 | − | 1.38325i | −0.121897 | − | 0.992543i | \(-0.538898\pi\) |
0.920516 | − | 0.390705i | \(-0.127769\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.805948 | − | 3.66578i | −0.0930628 | − | 0.423288i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.19535 | + | 3.06936i | 0.136222 | + | 0.349786i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.76670 | − | 4.79207i | 0.311278 | − | 0.539149i | −0.667361 | − | 0.744734i | \(-0.732576\pi\) |
0.978639 | + | 0.205585i | \(0.0659096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.83327 | − | 6.85369i | 0.648141 | − | 0.761521i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.03669 | − | 13.9199i | −0.882141 | − | 1.52791i | −0.848956 | − | 0.528463i | \(-0.822768\pi\) |
−0.0331848 | − | 0.999449i | \(-0.510565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.73833 | + | 4.74293i | −0.297014 | + | 0.514444i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.18325 | − | 7.47224i | 0.877337 | − | 0.801108i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.03776 | − | 10.4577i | −0.640001 | − | 1.10851i | −0.985432 | − | 0.170070i | \(-0.945601\pi\) |
0.345431 | − | 0.938444i | \(-0.387733\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.2535 | + | 1.57300i | 1.07486 | + | 0.164895i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.739760 | + | 0.675485i | −0.0767096 | + | 0.0700445i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.97549 | + | 6.88575i | 0.407876 | + | 0.706463i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.86046 | − | 10.1506i | −0.595040 | − | 1.03064i | −0.993541 | − | 0.113472i | \(-0.963803\pi\) |
0.398501 | − | 0.917168i | \(-0.369530\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.39052 | + | 1.56658i | −0.340760 | + | 0.157447i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.40605 | 0.537922 | 0.268961 | − | 0.963151i | \(-0.413320\pi\) | ||||
0.268961 | + | 0.963151i | \(0.413320\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.6204 | 1.44059 | 0.720294 | − | 0.693669i | \(-0.244007\pi\) | ||||
0.720294 | + | 0.693669i | \(0.244007\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.41868 | + | 4.27713i | −0.626399 | + | 0.417405i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.40209 | − | 5.89259i | −0.328892 | − | 0.569658i | 0.653400 | − | 0.757013i | \(-0.273342\pi\) |
−0.982292 | + | 0.187354i | \(0.940009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.37636 | − | 14.5083i | 0.802310 | − | 1.38964i | −0.115783 | − | 0.993275i | \(-0.536938\pi\) |
0.918092 | − | 0.396367i | \(-0.129729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.96176 | + | 6.35688i | −0.660781 | + | 0.603368i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.77154 | − | 11.7287i | 0.637013 | − | 1.10334i | −0.349072 | − | 0.937096i | \(-0.613503\pi\) |
0.986085 | − | 0.166243i | \(-0.0531636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.670124 | −0.0624894 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.06621 | + | 11.7139i | −0.0985714 | + | 1.08295i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.50922 | − | 1.30541i | −0.780039 | − | 0.119667i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.45002 | −0.859093 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.8753 | + | 4.40161i | 1.25109 | + | 0.396880i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0632 | −1.07896 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5904 | 0.939748 | 0.469874 | − | 0.882734i | \(-0.344299\pi\) | ||||
0.469874 | + | 0.882734i | \(0.344299\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.30058 | + | 5.75314i | −0.554735 | + | 0.506536i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.3638 | −1.95394 | −0.976968 | − | 0.213387i | \(-0.931551\pi\) | ||||
−0.976968 | + | 0.213387i | \(0.931551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.81808 | + | 9.75094i | −0.677914 | + | 0.845514i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.28764 | − | 6.96651i | −0.455088 | − | 0.599581i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.9540 | 1.53391 | 0.766957 | − | 0.641699i | \(-0.221770\pi\) | ||||
0.766957 | + | 0.641699i | \(0.221770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.570825 | − | 0.988699i | 0.0484168 | − | 0.0838603i | −0.840801 | − | 0.541344i | \(-0.817916\pi\) |
0.889218 | + | 0.457483i | \(0.151249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.701976 | + | 0.222685i | 0.0591170 | + | 0.0187535i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.44065 | − | 4.22733i | 0.204098 | − | 0.353507i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.38434 | − | 9.32596i | −0.447145 | − | 0.774479i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.92634 | − | 6.96188i | −0.818711 | − | 0.574206i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6583 | 1.44663 | 0.723313 | − | 0.690521i | \(-0.242619\pi\) | ||||
0.723313 | + | 0.690521i | \(0.242619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2354 | −1.23984 | −0.619919 | − | 0.784666i | \(-0.712834\pi\) | ||||
−0.619919 | + | 0.784666i | \(0.712834\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.884835 | − | 9.72124i | 0.0715347 | − | 0.785916i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.486741 | + | 0.843060i | 0.0390960 | + | 0.0677162i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.81439 | + | 11.8029i | 0.543847 | + | 0.941971i | 0.998678 | + | 0.0513933i | \(0.0163662\pi\) |
−0.454831 | + | 0.890578i | \(0.650300\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.53974 | − | 0.488447i | −0.122110 | − | 0.0387364i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.382263 | − | 0.981559i | −0.0301265 | − | 0.0773577i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.04726 | − | 7.01005i | −0.317006 | − | 0.549070i | 0.662856 | − | 0.748747i | \(-0.269344\pi\) |
−0.979862 | + | 0.199677i | \(0.936011\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.779359 | + | 3.54484i | 0.0606730 | + | 0.275966i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.07739 | + | 3.59814i | −0.160753 | + | 0.278433i | −0.935139 | − | 0.354281i | \(-0.884726\pi\) |
0.774386 | + | 0.632714i | \(0.218059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.18629 | − | 2.05471i | −0.0912529 | − | 0.158055i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.5801 | − | 8.16909i | −0.885552 | − | 0.624706i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.91730 | + | 11.9811i | −0.525913 | + | 0.910907i | 0.473632 | + | 0.880723i | \(0.342943\pi\) |
−0.999544 | + | 0.0301845i | \(0.990391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.08059 | − | 5.34247i | −0.157278 | − | 0.403852i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.73894 | − | 7.06653i | 0.581694 | − | 0.531153i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.71167 | + | 8.16084i | −0.352166 | + | 0.609970i | −0.986629 | − | 0.162984i | \(-0.947888\pi\) |
0.634462 | + | 0.772954i | \(0.281222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.32133 | 0.0982136 | 0.0491068 | − | 0.998794i | \(-0.484363\pi\) | ||||
0.0491068 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.8550 | − | 5.34686i | −1.24596 | − | 0.395251i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.58064 | + | 7.93390i | 0.336775 | + | 0.583312i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.02546 | + | 3.50821i | −0.148117 | + | 0.256546i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.18787 | − | 11.7190i | 0.522841 | − | 0.852430i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.14271 | + | 14.1036i | −0.589186 | + | 1.02050i | 0.405153 | + | 0.914249i | \(0.367218\pi\) |
−0.994339 | + | 0.106251i | \(0.966115\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.28077 | − | 2.21837i | −0.0921921 | − | 0.159681i | 0.816241 | − | 0.577711i | \(-0.196054\pi\) |
−0.908433 | + | 0.418030i | \(0.862721\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.8952 | + | 3.45626i | 0.780225 | + | 0.247508i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.6916 | 1.54546 | 0.772730 | − | 0.634735i | \(-0.218891\pi\) | ||||
0.772730 | + | 0.634735i | \(0.218891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.59684 | + | 9.69402i | −0.396750 | + | 0.687191i | −0.993323 | − | 0.115368i | \(-0.963195\pi\) |
0.596573 | + | 0.802559i | \(0.296529\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0480 | + | 11.0012i | −0.849803 | + | 0.775966i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.5887 | − | 13.2065i | 0.743181 | − | 0.926917i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.07289 | − | 12.2506i | 0.493992 | − | 0.855620i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.08426 | − | 0.500981i | 0.0753614 | − | 0.0348206i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.94055 | + | 5.09318i | 0.203402 | + | 0.352303i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.1807 | + | 24.5616i | −0.976237 | + | 1.69089i | −0.300444 | + | 0.953799i | \(0.597135\pi\) |
−0.675793 | + | 0.737092i | \(0.736199\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.14875 | + | 14.3218i | 0.215749 | + | 0.981313i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.14560 | + | 7.18039i | 0.282728 | + | 0.489699i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.957211 | + | 1.19386i | −0.0649797 | + | 0.0810446i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.5305 | + | 7.14726i | 1.52247 | + | 0.482967i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.37875 | + | 11.0483i | 0.429081 | + | 0.743190i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6962 | − | 21.9905i | −0.850202 | − | 1.47259i | −0.881026 | − | 0.473068i | \(-0.843147\pi\) |
0.0308242 | − | 0.999525i | \(-0.490187\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.90146 | − | 2.72676i | 0.393431 | − | 0.181784i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.62860 | 0.307211 | 0.153606 | − | 0.988132i | \(-0.450911\pi\) | ||||
0.153606 | + | 0.988132i | \(0.450911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.32592 | 0.153701 | 0.0768506 | − | 0.997043i | \(-0.475514\pi\) | ||||
0.0768506 | + | 0.997043i | \(0.475514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.74771 | + | 3.16367i | −0.312376 | + | 0.208154i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.37989 | − | 11.0503i | −0.417960 | − | 0.723929i | 0.577774 | − | 0.816197i | \(-0.303922\pi\) |
−0.995734 | + | 0.0922683i | \(0.970588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.357830 | − | 0.619780i | 0.0233423 | − | 0.0404300i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.13548 | + | 2.89801i | 0.593413 | + | 0.188246i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0492 | + | 19.1378i | −0.714714 | + | 1.23792i | 0.248355 | + | 0.968669i | \(0.420110\pi\) |
−0.963070 | + | 0.269252i | \(0.913223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0177 | 1.28945 | 0.644726 | − | 0.764414i | \(-0.276972\pi\) | ||||
0.644726 | + | 0.764414i | \(0.276972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.7635 | + | 7.31880i | 0.882932 | + | 0.469502i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.67884 | + | 7.96840i | −0.554471 | + | 0.509082i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.5212 | 1.17848 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.5586 | − | 18.7724i | 1.30285 | − | 1.18965i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.12390 | −0.134059 | −0.0670297 | − | 0.997751i | \(-0.521352\pi\) | ||||
−0.0670297 | + | 0.997751i | \(0.521352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.495671 | −0.0311625 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.04182 | − | 2.86830i | −0.566221 | − | 0.179620i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.7630 | −0.796134 | −0.398067 | − | 0.917356i | \(-0.630319\pi\) | ||||
−0.398067 | + | 0.917356i | \(0.630319\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.00816 | + | 11.2352i | −0.559740 | + | 0.698124i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.6839 | + | 11.0641i | 0.970810 | + | 0.684851i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.0686 | −0.682522 | −0.341261 | − | 0.939969i | \(-0.610854\pi\) | ||||
−0.341261 | + | 0.939969i | \(0.610854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.784881 | + | 1.35945i | −0.0482148 | + | 0.0835105i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.4452 | − | 14.1032i | 0.945230 | − | 0.863102i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.77479 | + | 3.07403i | −0.108211 | + | 0.187427i | −0.915046 | − | 0.403351i | \(-0.867846\pi\) |
0.806835 | + | 0.590777i | \(0.201179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.687666 | − | 1.19107i | −0.0417727 | − | 0.0723525i | 0.844383 | − | 0.535740i | \(-0.179967\pi\) |
−0.886156 | + | 0.463387i | \(0.846634\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.15252 | + | 17.9303i | 0.0697534 | + | 1.08519i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.69786 | −0.162687 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.1617 | −1.75216 | −0.876079 | − | 0.482168i | \(-0.839849\pi\) | ||||
−0.876079 | + | 0.482168i | \(0.839849\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.41782 | − | 1.00019i | −0.0848824 | − | 0.0598797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.29603 | + | 10.9050i | 0.375590 | + | 0.650540i | 0.990415 | − | 0.138123i | \(-0.0441069\pi\) |
−0.614826 | + | 0.788663i | \(0.710774\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.73028 | + | 8.19309i | 0.281186 | + | 0.487029i | 0.971677 | − | 0.236312i | \(-0.0759389\pi\) |
−0.690491 | + | 0.723341i | \(0.742606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.1697 | + | 9.28608i | −0.602401 | + | 0.550060i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.9786 | + | 3.37178i | 1.29736 | + | 0.199030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.20636 | + | 5.55358i | 0.188609 | + | 0.326681i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.9917 | − | 13.6891i | 0.878826 | − | 0.802468i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.32726 | + | 14.4232i | −0.486484 | + | 0.842614i | −0.999879 | − | 0.0155376i | \(-0.995054\pi\) |
0.513396 | + | 0.858152i | \(0.328387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.09200 | − | 8.81960i | −0.296468 | − | 0.513497i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.91111 | − | 5.15292i | −0.226946 | − | 0.299003i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.780502 | + | 1.35187i | −0.0451376 | + | 0.0781806i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.15262 | + | 10.1682i | −0.469909 | + | 0.586085i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.01062 | + | 9.14513i | 0.115507 | + | 0.525374i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.59181 | + | 14.8815i | −0.491966 | + | 0.852110i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.55966 | −0.545599 | −0.272799 | − | 0.962071i | \(-0.587949\pi\) | ||||
−0.272799 | + | 0.962071i | \(0.587949\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.43762 | + | 24.7325i | 0.309335 | + | 1.40698i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.1851 | − | 22.8373i | −0.747658 | − | 1.29498i | −0.948943 | − | 0.315449i | \(-0.897845\pi\) |
0.201284 | − | 0.979533i | \(-0.435488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.35091 | − | 11.0001i | 0.358975 | − | 0.621762i | −0.628815 | − | 0.777555i | \(-0.716460\pi\) |
0.987790 | + | 0.155792i | \(0.0497931\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.62264 | − | 9.26739i | −0.542174 | − | 0.522159i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.0165768 | + | 0.0287119i | −0.000931047 | + | 0.00161262i | −0.866491 | − | 0.499193i | \(-0.833630\pi\) |
0.865560 | + | 0.500806i | \(0.166963\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.98264 | − | 6.89813i | −0.222985 | − | 0.386221i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.70289 | − | 7.94672i | 0.485748 | − | 0.443543i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.3705 | −0.855238 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.24815 | + | 7.35801i | −0.235645 | + | 0.408149i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.6583 | + | 8.77392i | 1.52951 | + | 0.485199i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.11194 | + | 0.170584i | 0.0613031 | + | 0.00940461i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.42694 | − | 4.20358i | 0.133397 | − | 0.231050i | −0.791587 | − | 0.611056i | \(-0.790745\pi\) |
0.924984 | + | 0.380006i | \(0.124078\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.3428 | − | 9.41260i | −0.731183 | − | 0.515807i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.92726 | + | 13.7304i | 0.433112 | + | 0.750173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.32200 | + | 7.48592i | −0.235434 | + | 0.407784i | −0.959399 | − | 0.282053i | \(-0.908985\pi\) |
0.723965 | + | 0.689837i | \(0.242318\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.3592 | + | 7.09293i | 1.21439 | + | 0.385235i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.360028 | + | 0.623586i | 0.0194966 | + | 0.0337691i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.6224 | − | 8.16680i | −0.897524 | − | 0.440966i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.249233 | − | 1.13361i | −0.0134183 | − | 0.0610317i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6116 | + | 20.1119i | 0.623344 | + | 1.07966i | 0.988859 | + | 0.148858i | \(0.0475596\pi\) |
−0.365515 | + | 0.930806i | \(0.619107\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.76025 | − | 6.51295i | −0.201282 | − | 0.348630i | 0.747660 | − | 0.664082i | \(-0.231177\pi\) |
−0.948942 | + | 0.315452i | \(0.897844\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.2124 | + | 2.55300i | −1.07886 | + | 0.136269i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.919056 | −0.0489164 | −0.0244582 | − | 0.999701i | \(-0.507786\pi\) | ||||
−0.0244582 | + | 0.999701i | \(0.507786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.2499 | 0.756306 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.956458 | − | 14.8801i | −0.0506211 | − | 0.787540i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.24300 | + | 14.2773i | 0.435049 | + | 0.753527i | 0.997300 | − | 0.0734398i | \(-0.0233977\pi\) |
−0.562251 | + | 0.826967i | \(0.690064\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.65737 | + | 2.87066i | −0.0872302 | + | 0.151087i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.51466 | − | 15.9861i | −0.184472 | − | 0.839054i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.4848 | − | 19.8923i | 0.601144 | − | 1.04121i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.6784 | −0.661808 | −0.330904 | − | 0.943664i | \(-0.607354\pi\) | ||||
−0.330904 | + | 0.943664i | \(0.607354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.28546 | + | 25.1092i | −0.118976 | + | 1.30713i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.43897 | − | 0.374167i | −0.126625 | − | 0.0194258i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6821 | 1.17443 | 0.587217 | − | 0.809430i | \(-0.300224\pi\) | ||||
0.587217 | + | 0.809430i | \(0.300224\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.48654 | − | 20.4066i | −0.231684 | − | 1.05379i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.0849 | −1.29194 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0925 | 0.980717 | 0.490358 | − | 0.871521i | \(-0.336866\pi\) | ||||
0.490358 | + | 0.871521i | \(0.336866\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.93880 | + | 17.9153i | 0.201791 | + | 0.917827i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.07925 | −0.310635 | −0.155318 | − | 0.987865i | \(-0.549640\pi\) | ||||
−0.155318 | + | 0.987865i | \(0.549640\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.01195 | + | 5.16621i | 0.102539 | + | 0.263295i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.0756 | − | 8.51865i | −0.613838 | − | 0.433028i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.631562 | −0.0320214 | −0.0160107 | − | 0.999872i | \(-0.505097\pi\) | ||||
−0.0160107 | + | 0.999872i | \(0.505097\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.647728 | − | 1.12190i | 0.0327570 | − | 0.0567368i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.31757 | − | 37.8317i | −0.419566 | − | 1.90836i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.65679 | − | 8.06579i | 0.234308 | − | 0.405834i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.1830 | − | 31.4939i | −0.912578 | − | 1.58063i | −0.810408 | − | 0.585865i | \(-0.800755\pi\) |
−0.102170 | − | 0.994767i | \(-0.532579\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.4029 | − | 9.59887i | −0.971359 | − | 0.480544i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.6137 | −1.57871 | −0.789357 | − | 0.613934i | \(-0.789586\pi\) | ||||
−0.789357 | + | 0.613934i | \(0.789586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.26765 | 0.112960 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.81829 | − | 11.5358i | 0.487875 | − | 0.573220i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.38816 | + | 5.86847i | 0.167945 | + | 0.290889i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0906 | − | 17.4774i | −0.498948 | − | 0.864203i | 0.501051 | − | 0.865418i | \(-0.332947\pi\) |
−0.999999 | + | 0.00121422i | \(0.999614\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.67747 | + | 30.3718i | 0.329375 | + | 1.49813i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.0138 | − | 12.4895i | 0.492746 | − | 0.614567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.5270 | − | 23.4294i | −0.664014 | − | 1.15011i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.88483 | + | 0.597918i | 0.0923006 | + | 0.0292802i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.4159 | + | 21.5049i | −0.606555 | + | 1.05058i | 0.385248 | + | 0.922813i | \(0.374116\pi\) |
−0.991804 | + | 0.127772i | \(0.959217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.71841 | − | 9.90458i | −0.278698 | − | 0.482720i | 0.692363 | − | 0.721549i | \(-0.256570\pi\) |
−0.971062 | + | 0.238829i | \(0.923236\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.115625 | + | 1.27032i | −0.00562190 | + | 0.0617650i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.52548 | − | 6.10631i | 0.171011 | − | 0.296200i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.6986 | − | 4.09587i | −1.29203 | − | 0.198213i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.05889 | + | 2.55649i | 0.389087 | + | 0.123429i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.80157 | − | 4.85246i | 0.134947 | − | 0.233735i | −0.790630 | − | 0.612294i | \(-0.790247\pi\) |
0.925577 | + | 0.378559i | \(0.123580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.22555 | −0.203067 | −0.101534 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101534 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.7737 | − | 12.5769i | 0.660398 | − | 0.603018i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.940366 | − | 1.62876i | −0.0449838 | − | 0.0779142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7316 | − | 30.7120i | 0.846281 | − | 1.46580i | −0.0382233 | − | 0.999269i | \(-0.512170\pi\) |
0.884504 | − | 0.466532i | \(-0.154497\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.08524 | − | 19.3811i | 0.385012 | − | 0.922912i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.4658 | − | 19.8593i | 0.544755 | − | 0.943543i | −0.453867 | − | 0.891069i | \(-0.649956\pi\) |
0.998622 | − | 0.0524740i | \(-0.0167107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1625 | − | 17.6019i | −0.481748 | − | 0.834412i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.56750 | + | 29.8717i | 0.310632 | + | 1.41288i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.4850 | 0.966747 | 0.483373 | − | 0.875414i | \(-0.339411\pi\) | ||||
0.483373 | + | 0.875414i | \(0.339411\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.23161 | − | 9.06141i | 0.246347 | − | 0.426685i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.66636 | − | 25.7729i | −0.266229 | − | 1.21092i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.2582 | + | 2.64761i | 0.809076 | + | 0.124122i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.72677 | + | 13.3832i | −0.361443 | + | 0.626038i | −0.988199 | − | 0.153178i | \(-0.951049\pi\) |
0.626755 | + | 0.779216i | \(0.284383\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.7740 | − | 2.11870i | 0.782944 | − | 0.0988927i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0815 | + | 24.3898i | 0.655839 | + | 1.13595i | 0.981683 | + | 0.190523i | \(0.0610183\pi\) |
−0.325844 | + | 0.945424i | \(0.605648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.3193 | + | 26.5338i | −0.711948 | + | 1.23313i | 0.252177 | + | 0.967681i | \(0.418854\pi\) |
−0.964125 | + | 0.265449i | \(0.914480\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.24513 | + | 1.13695i | −0.0577416 | + | 0.0527246i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.61798 | − | 11.4627i | −0.306244 | − | 0.530429i | 0.671294 | − | 0.741191i | \(-0.265739\pi\) |
−0.977537 | + | 0.210762i | \(0.932406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.5895 | + | 19.4437i | −0.719857 | + | 0.897827i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.4319 | + | 15.9173i | −0.803219 | + | 0.733429i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.06638 | + | 5.31112i | 0.140992 | + | 0.244206i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.11826 | − | 8.86508i | −0.234842 | − | 0.406758i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.253618 | − | 2.78637i | 0.0116124 | − | 0.127579i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0872 | 0.643658 | 0.321829 | − | 0.946798i | \(-0.395702\pi\) | ||||
0.321829 | + | 0.946798i | \(0.395702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.3405 | 0.973044 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.51828 | − | 1.01172i | 0.0690842 | − | 0.0460347i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.86407 | − | 17.0851i | −0.447904 | − | 0.775793i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.45654 | − | 5.98690i | 0.156631 | − | 0.271292i | −0.777021 | − | 0.629475i | \(-0.783270\pi\) |
0.933652 | + | 0.358183i | \(0.116603\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.3533 | − | 9.45372i | 0.468192 | − | 0.427512i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3481 | + | 26.5837i | −0.692651 | + | 1.19971i | 0.278315 | + | 0.960490i | \(0.410224\pi\) |
−0.970966 | + | 0.239217i | \(0.923109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.8176 | 0.937578 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.70677 | + | 2.63680i | −0.256500 | + | 0.118515i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.12865 | + | 20.8724i | 0.364620 | + | 0.936256i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0371 | −0.986518 | −0.493259 | − | 0.869882i | \(-0.664195\pi\) | ||||
−0.493259 | + | 0.869882i | \(0.664195\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.85942 | − | 2.17599i | −0.306456 | − | 0.0972159i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.9653 | 1.73737 | 0.868687 | − | 0.495361i | \(-0.164964\pi\) | ||||
0.868687 | + | 0.495361i | \(0.164964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.09922 | 0.404910 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.03464 | − | 2.77097i | 0.134773 | − | 0.123063i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.2941 | −1.25412 | −0.627058 | − | 0.778973i | \(-0.715741\pi\) | ||||
−0.627058 | + | 0.778973i | \(0.715741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.6885 | + | 5.47503i | 1.57877 | + | 0.242201i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.51236 | − | 22.6277i | 0.419981 | − | 0.999038i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.6084 | 1.08437 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.264676 | − | 0.458433i | 0.0116405 | − | 0.0201619i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.8405 | − | 7.24561i | −1.00259 | − | 0.318047i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.98150 | + | 10.3603i | −0.262054 | + | 0.453892i | −0.966788 | − | 0.255581i | \(-0.917733\pi\) |
0.704733 | + | 0.709472i | \(0.251067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.15056 | − | 5.45693i | −0.137764 | − | 0.238615i | 0.788886 | − | 0.614540i | \(-0.210658\pi\) |
−0.926650 | + | 0.375925i | \(0.877325\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.26376 | − | 5.50661i | 0.360660 | − | 0.240328i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.88190 | −0.0819767 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8415 | −0.993108 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.8324 | + | 10.4634i | 0.643669 | + | 0.454072i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.4758 | − | 28.5369i | −0.713645 | − | 1.23607i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.72625 | − | 9.91815i | −0.247567 | − | 0.428799i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.5576 | − | 4.93529i | −0.671362 | − | 0.212974i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.41948 | + | 5.89399i | −0.276507 | + | 0.253872i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.88191 | + | 17.1160i | 0.424857 | + | 0.735873i | 0.996407 | − | 0.0846937i | \(-0.0269912\pi\) |
−0.571550 | + | 0.820567i | \(0.693658\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.491430 | + | 2.23522i | 0.0210893 | + | 0.0959227i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0987 | − | 24.4197i | 0.603923 | − | 1.04602i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.6125 | + | 37.4340i | 0.924085 | + | 1.60056i | 0.793026 | + | 0.609188i | \(0.208504\pi\) |
0.131059 | + | 0.991375i | \(0.458162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.77626 | − | 30.5014i | 0.118488 | − | 1.30177i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.1114 | − | 26.1737i | 0.643767 | − | 1.11504i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4707 | + | 2.21997i | 0.615357 | + | 0.0944029i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.7177 | + | 10.6996i | −0.497390 | + | 0.454173i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0838 | + | 24.3938i | −0.596748 | + | 1.03360i | 0.396550 | + | 0.918013i | \(0.370207\pi\) |
−0.993298 | + | 0.115584i | \(0.963126\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.3137 | 0.816884 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.68797 | − | 2.12160i | −0.282366 | − | 0.0895739i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.8472 | − | 22.2520i | −0.541445 | − | 0.937810i | −0.998821 | − | 0.0485366i | \(-0.984544\pi\) |
0.457377 | − | 0.889273i | \(-0.348789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.3976 | − | 19.7411i | 0.479499 | − | 0.830516i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.4977 | + | 7.80082i | 0.944815 | + | 0.327604i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.7441 | + | 30.7336i | −0.743870 | + | 1.28842i | 0.206851 | + | 0.978373i | \(0.433679\pi\) |
−0.950721 | + | 0.310048i | \(0.899655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.8412 | − | 18.7775i | −0.453689 | − | 0.785813i | 0.544923 | − | 0.838486i | \(-0.316559\pi\) |
−0.998612 | + | 0.0526737i | \(0.983226\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.8868 | − | 8.52919i | −1.12321 | − | 0.356312i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.862754 | 0.0359793 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.60727 | + | 13.1762i | −0.316695 | + | 0.548531i | −0.979796 | − | 0.199998i | \(-0.935906\pi\) |
0.663102 | + | 0.748529i | \(0.269240\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.27635 | − | 2.99168i | 0.136160 | − | 0.124330i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.6018 | − | 33.1786i | 1.10363 | − | 1.37648i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.580553 | + | 1.00555i | −0.0240440 | + | 0.0416455i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.79460 | + | 19.7164i | −0.0741976 | + | 0.815172i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.1924 | − | 33.2423i | −0.792157 | − | 1.37206i | −0.924629 | − | 0.380869i | \(-0.875625\pi\) |
0.132472 | − | 0.991187i | \(-0.457708\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.36606 | + | 2.36608i | −0.0562875 | + | 0.0974928i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.06754 | + | 36.6945i | 0.331854 | + | 1.50941i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.25559 | − | 16.0311i | −0.380081 | − | 0.658320i | 0.610992 | − | 0.791637i | \(-0.290771\pi\) |
−0.991074 | + | 0.133316i | \(0.957437\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.3223 | − | 2.19721i | −0.587159 | − | 0.0900770i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.4805 | − | 5.86248i | −0.756355 | − | 0.239935i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.8413 | + | 18.7776i | 0.442962 | + | 0.767233i | 0.997908 | − | 0.0646536i | \(-0.0205942\pi\) |
−0.554946 | + | 0.831887i | \(0.687261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.95776 | + | 6.85505i | 0.161441 | + | 0.279623i | 0.935386 | − | 0.353630i | \(-0.115053\pi\) |
−0.773945 | + | 0.633253i | \(0.781719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.0911 | − | 16.2895i | −0.940343 | − | 0.663358i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.9059 | −0.646665 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.9247 | 1.45814 | 0.729068 | − | 0.684441i | \(-0.239954\pi\) | ||||
0.729068 | + | 0.684441i | \(0.239954\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.2790 | + | 13.0006i | 1.06488 | + | 0.526810i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.833539 | − | 1.44373i | −0.0337214 | − | 0.0584072i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.60252 | + | 2.77565i | −0.0647253 | + | 0.112108i | −0.896572 | − | 0.442898i | \(-0.853950\pi\) |
0.831847 | + | 0.555005i | \(0.187284\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.3543 | + | 7.40859i | 0.941736 | + | 0.298743i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9357 | − | 27.6015i | 0.641549 | − | 1.11120i | −0.343538 | − | 0.939139i | \(-0.611626\pi\) |
0.985087 | − | 0.172056i | \(-0.0550411\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.9726 | −0.842959 | −0.421480 | − | 0.906838i | \(-0.638489\pi\) | ||||
−0.421480 | + | 0.906838i | \(0.638489\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.25074 | + | 1.64786i | 0.0501906 | + | 0.0661265i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.9853 | − | 24.9262i | 0.800692 | − | 0.998647i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.46924 | −0.378769 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.52222 | + | 6.86864i | −0.300409 | + | 0.274307i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.7102 | −0.706153 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4435 | 1.05270 | 0.526349 | − | 0.850268i | \(-0.323560\pi\) | ||||
0.526349 | + | 0.850268i | \(0.323560\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.8237 | − | 14.8537i | −1.86108 | − | 0.590382i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.8253 | 0.707377 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.96663 | + | 26.7891i | 0.236407 | + | 1.06142i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.0564 | + | 10.6532i | −0.912095 | + | 0.421432i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.9618 | −1.10443 | −0.552213 | − | 0.833703i | \(-0.686217\pi\) | ||||
−0.552213 | + | 0.833703i | \(0.686217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.12936 | + | 10.6164i | −0.241718 | + | 0.418669i | −0.961204 | − | 0.275839i | \(-0.911044\pi\) |
0.719485 | + | 0.694508i | \(0.244378\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.6049 | + | 9.68344i | −0.417566 | + | 0.381285i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.49923 | − | 7.79290i | 0.176883 | − | 0.306371i | −0.763928 | − | 0.645301i | \(-0.776732\pi\) |
0.940811 | + | 0.338931i | \(0.110065\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.76640 | − | 6.52360i | −0.147844 | − | 0.256074i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.37560 | − | 1.17524i | −0.0931072 | − | 0.0460614i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.7901 | −0.891844 | −0.445922 | − | 0.895072i | \(-0.647124\pi\) | ||||
−0.445922 | + | 0.895072i | \(0.647124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.6418 | −1.47079 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.71109 | + | 40.7719i | −0.144783 | + | 1.59066i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.3311 | − | 33.4824i | −0.753033 | − | 1.30429i | −0.946347 | − | 0.323154i | \(-0.895257\pi\) |
0.193314 | − | 0.981137i | \(-0.438076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.75399 | + | 9.96621i | 0.223804 | + | 0.387641i | 0.955960 | − | 0.293497i | \(-0.0948190\pi\) |
−0.732156 | + | 0.681137i | \(0.761486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.3175 | + | 14.8997i | −0.633718 | + | 0.578657i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.1590 | + | 16.4124i | −0.510286 | + | 0.636444i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.27362 | + | 2.20597i | 0.0493147 | + | 0.0854156i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 32.4782 | − | 29.6563i | 1.25568 | − | 1.14658i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.35511 | + | 11.0074i | −0.245336 | + | 0.424935i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6642 | − | 18.4709i | −0.411075 | − | 0.712002i | 0.583933 | − | 0.811802i | \(-0.301513\pi\) |
−0.995008 | + | 0.0997997i | \(0.968180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.80760 | + | 8.96906i | 0.262025 | + | 0.345219i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.8799 | + | 24.0407i | −0.533449 | + | 0.923961i | 0.465788 | + | 0.884896i | \(0.345771\pi\) |
−0.999237 | + | 0.0390641i | \(0.987562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.3984 | − | 24.1943i | 0.744443 | − | 0.928491i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.72147 | + | 7.82997i | 0.0659670 | + | 0.300045i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.66854 | + | 15.0143i | −0.331692 | + | 0.574508i | −0.982844 | − | 0.184440i | \(-0.940953\pi\) |
0.651151 | + | 0.758948i | \(0.274286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.2194 | 1.15462 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.865059 | + | 3.93464i | 0.0330041 | + | 0.150116i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.82832 | + | 3.16675i | 0.0696535 | + | 0.120643i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.8023 | + | 34.2986i | −0.753315 | + | 1.30478i | 0.192892 | + | 0.981220i | \(0.438213\pi\) |
−0.946207 | + | 0.323560i | \(0.895120\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.11758 | − | 6.85482i | −0.270375 | − | 0.260393i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.960788 | − | 1.66413i | 0.0364448 | − | 0.0631242i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.6730 | + | 23.6824i | 0.517903 | + | 0.897035i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.3204 | − | 14.9024i | 0.617294 | − | 0.563659i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.28469 | 0.275139 | 0.137570 | − | 0.990492i | \(-0.456071\pi\) | ||||
0.137570 | + | 0.990492i | \(0.456071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.8558 | + | 22.2668i | −0.484864 | + | 0.839809i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.18153 | + | 0.374814i | 0.0444992 | + | 0.0141163i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.19052 | + | 13.3280i | 0.195210 | + | 0.501251i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.00541 | + | 10.4017i | −0.225538 | + | 0.390643i | −0.956481 | − | 0.291796i | \(-0.905747\pi\) |
0.730943 | + | 0.682439i | \(0.239081\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50474 | + | 16.5319i | −0.0564323 | + | 0.619993i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.115134 | − | 0.199418i | −0.00431181 | − | 0.00746827i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.10800 | − | 7.11526i | 0.153630 | − | 0.266096i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −36.4839 | − | 11.5736i | −1.36252 | − | 0.432225i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.15819 | − | 3.73809i | −0.0804868 | − | 0.139407i | 0.822972 | − | 0.568081i | \(-0.192314\pi\) |
−0.903459 | + | 0.428674i | \(0.858981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0375 | + | 36.0449i | 0.522783 | + | 1.34238i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.44499 | + | 33.8629i | 0.276882 | + | 1.25937i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.93210 | + | 12.0067i | 0.257452 | + | 0.445919i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.2483 | + | 17.7506i | 0.380090 | + | 0.658334i | 0.991075 | − | 0.133308i | \(-0.0425598\pi\) |
−0.610985 | + | 0.791642i | \(0.709226\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.26189 | + | 26.0051i | −0.268959 | + | 0.963152i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.0282 | −0.592825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.3322 | 0.935666 | 0.467833 | − | 0.883817i | \(-0.345035\pi\) | ||||
0.467833 | + | 0.883817i | \(0.345035\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.7076 | − | 11.7179i | −0.616268 | − | 0.432222i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.86356 | + | 10.1560i | 0.215987 | + | 0.374100i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.63391 | + | 11.4903i | −0.244032 | + | 0.422676i | −0.961859 | − | 0.273545i | \(-0.911804\pi\) |
0.717827 | + | 0.696222i | \(0.245137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.88843 | + | 31.3314i | 0.253053 | + | 1.15099i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.6116 | − | 39.1644i | 0.829538 | − | 1.43680i | −0.0688624 | − | 0.997626i | \(-0.521937\pi\) |
0.898401 | − | 0.439176i | \(-0.144730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.7217 | 1.08892 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.4024 | + | 27.7962i | 1.44166 | + | 1.01701i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.2611 | − | 14.0451i | 0.411471 | − | 0.513199i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.3797 | −1.03559 | −0.517795 | − | 0.855505i | \(-0.673247\pi\) | ||||
−0.517795 | + | 0.855505i | \(0.673247\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.789924 | − | 3.59289i | −0.0287864 | − | 0.130932i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.6435 | −0.933263 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.08483 | 0.184811 | 0.0924056 | − | 0.995721i | \(-0.470544\pi\) | ||||
0.0924056 | + | 0.995721i | \(0.470544\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.184350 | − | 0.838500i | −0.00669149 | − | 0.0304356i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.7225 | 1.36744 | 0.683720 | − | 0.729745i | \(-0.260361\pi\) | ||||
0.683720 | + | 0.729745i | \(0.260361\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.8110 | + | 6.72111i | 1.58606 | + | 0.243321i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.48932 | − | 16.3624i | 0.0538463 | − | 0.591583i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.7229 | −0.856583 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.8729 | − | 20.5644i | 0.428147 | − | 0.741572i | −0.568562 | − | 0.822641i | \(-0.692500\pi\) |
0.996709 | + | 0.0810688i | \(0.0258333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.74683 | − | 21.5905i | −0.170953 | − | 0.777563i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.5347 | − | 33.8351i | 0.702614 | − | 1.21696i | −0.264932 | − | 0.964267i | \(-0.585350\pi\) |
0.967546 | − | 0.252696i | \(-0.0813172\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.626657 | − | 1.08540i | −0.0225102 | − | 0.0389888i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.3564 | − | 11.0600i | −0.802031 | − | 0.396776i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.7008 | 1.42243 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5402 | 0.377159 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.8834 | + | 30.6467i | −0.460415 | + | 1.09522i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.4697 | + | 19.8661i | 0.409370 | + | 0.709050i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.90458 | − | 3.29882i | −0.0678908 | − | 0.117590i | 0.830082 | − | 0.557642i | \(-0.188294\pi\) |
−0.897973 | + | 0.440051i | \(0.854960\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.11666 | − | 18.7242i | −0.146557 | − | 0.666601i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.4173 | + | 5.43342i | 1.25929 | + | 0.193190i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0140 | + | 34.6653i | 0.710718 | + | 1.23100i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.59163 | − | 0.822133i | −0.0919157 | − | 0.0291581i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.8239 | + | 18.7476i | −0.383404 | + | 0.664075i | −0.991546 | − | 0.129753i | \(-0.958582\pi\) |
0.608143 | + | 0.793828i | \(0.291915\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.691743 | + | 1.19813i | 0.0244721 | + | 0.0423870i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.6020 | + | 20.8825i | 1.04594 | + | 0.737848i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.49500 | − | 14.7138i | 0.299782 | − | 0.519238i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.643408 | − | 1.65212i | −0.0226771 | − | 0.0582294i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.86026 | − | 1.85903i | −0.206291 | − | 0.0654408i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.5128 | + | 32.0652i | −0.650877 | + | 1.12735i | 0.332034 | + | 0.943268i | \(0.392265\pi\) |
−0.982910 | + | 0.184084i | \(0.941068\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.37416 | 0.188712 | 0.0943561 | − | 0.995539i | \(-0.469921\pi\) | ||||
0.0943561 | + | 0.995539i | \(0.469921\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.75912 | − | 1.60627i | 0.0616950 | − | 0.0563345i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.81216 | − | 11.7990i | −0.238620 | − | 0.413301i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.6348 | + | 20.1521i | −0.407050 | + | 0.705032i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.9031 | + | 8.61831i | −1.04490 | + | 0.301148i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.11119 | + | 1.92464i | −0.0387809 | + | 0.0671706i | −0.884764 | − | 0.466039i | \(-0.845681\pi\) |
0.845983 | + | 0.533209i | \(0.179014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.5537 | − | 32.1359i | −0.646740 | − | 1.12019i | −0.983897 | − | 0.178738i | \(-0.942799\pi\) |
0.337157 | − | 0.941449i | \(-0.390535\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.00339 | − | 4.56382i | −0.0349335 | − | 0.158892i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4790 | 0.677351 | 0.338676 | − | 0.940903i | \(-0.390021\pi\) | ||||
0.338676 | + | 0.940903i | \(0.390021\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.137129 | − | 0.237514i | 0.00476267 | − | 0.00824919i | −0.863634 | − | 0.504119i | \(-0.831817\pi\) |
0.868397 | + | 0.495870i | \(0.165151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.8459 | − | 49.3314i | −0.376238 | − | 1.71129i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.95163 | − | 22.2319i | −0.171564 | − | 0.770290i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.49657 | + | 6.05623i | −0.121004 | + | 0.209585i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.16465 | − | 2.77044i | 0.0402562 | − | 0.0957603i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.0711 | + | 36.4962i | 0.727455 | + | 1.25999i | 0.957956 | + | 0.286917i | \(0.0926303\pi\) |
−0.230501 | + | 0.973072i | \(0.574036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.96666 | + | 10.3346i | −0.205747 | + | 0.356364i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.1059 | + | 14.7065i | −0.554716 | + | 0.506518i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.99671 | − | 3.45840i | −0.0686888 | − | 0.118973i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.07328 | − | 23.2980i | −0.311762 | − | 0.800528i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.1005 | + | 11.0492i | −0.415289 | + | 0.379206i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.08351 | − | 1.87669i | −0.0371422 | − | 0.0643322i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.3086 | + | 38.6397i | 0.763833 | + | 1.32300i | 0.940862 | + | 0.338791i | \(0.110018\pi\) |
−0.177029 | + | 0.984206i | \(0.556649\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.4911 | − | 13.7499i | −0.666582 | − | 0.470235i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.33227 | −0.250466 | −0.125233 | − | 0.992127i | \(-0.539968\pi\) | ||||
−0.125233 | + | 0.992127i | \(0.539968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.70146 | −0.0921725 | −0.0460863 | − | 0.998937i | \(-0.514675\pi\) | ||||
−0.0460863 | + | 0.998937i | \(0.514675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.47045 | + | 38.4341i | 0.0841928 | + | 1.30983i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.40188 | + | 12.8204i | 0.251963 | + | 0.436413i | 0.964066 | − | 0.265662i | \(-0.0855905\pi\) |
−0.712103 | + | 0.702075i | \(0.752257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.6429 | + | 20.1661i | −0.395870 | + | 0.685668i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.20219 | + | 7.48953i | −0.278561 | + | 0.254358i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.44449 | − | 5.96603i | 0.116846 | − | 0.202384i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.9319 | 1.25139 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.7328 | + | 20.2694i | 0.972458 | + | 0.686014i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.5822 | − | 29.7404i | −0.391551 | − | 1.00541i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0961 | −0.374690 | −0.187345 | − | 0.982294i | \(-0.559988\pi\) | ||||
−0.187345 | + | 0.982294i | \(0.559988\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.4961 | − | 8.72249i | −0.927421 | − | 0.294202i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0536 | 0.507168 | 0.253584 | − | 0.967313i | \(-0.418391\pi\) | ||||
0.253584 | + | 0.967313i | \(0.418391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.39418 | 0.0805704 | 0.0402852 | − | 0.999188i | \(-0.487173\pi\) | ||||
0.0402852 | + | 0.999188i | \(0.487173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.0258 | − | 11.8941i | 0.437859 | − | 0.399815i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.93394 | −0.165666 | −0.0828328 | − | 0.996563i | \(-0.526397\pi\) | ||||
−0.0828328 | + | 0.996563i | \(0.526397\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1682 | + | 26.1095i | 0.341031 | + | 0.875685i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.26230 | − | 8.53270i | 0.243296 | − | 0.285856i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.00853 | 0.0672130 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.93047 | + | 13.7360i | −0.265086 | + | 0.459143i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.57717 | − | 0.817547i | −0.0860493 | − | 0.0272971i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.85017 | − | 3.20459i | 0.0617067 | − | 0.106879i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.51730 | − | 2.62804i | −0.0505486 | − | 0.0875527i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.2331 | − | 10.0096i | −0.673316 | − | 0.333099i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.22400 | 0.0739284 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.39631 | −0.112773 | −0.0563863 | − | 0.998409i | \(-0.517958\pi\) | ||||
−0.0563863 | + | 0.998409i | \(0.517958\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.7226 | + | 6.80253i | −0.488316 | + | 0.225626i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.65142 | + | 8.05649i | 0.154108 | + | 0.266924i | 0.932734 | − | 0.360565i | \(-0.117416\pi\) |
−0.778626 | + | 0.627489i | \(0.784083\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.0055 | − | 17.3301i | −0.331134 | − | 0.573541i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.3697 | − | 8.99960i | −0.937872 | − | 0.297518i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.4722 | − | 55.1355i | −0.709076 | − | 1.82073i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.92656 | + | 15.4613i | 0.294460 | + | 0.510020i | 0.974859 | − | 0.222822i | \(-0.0715268\pi\) |
−0.680399 | + | 0.732842i | \(0.738194\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.55544 | − | 16.1716i | −0.117156 | − | 0.532872i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.5970 | − | 28.7469i | 0.546298 | − | 0.946216i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.89737 | − | 10.2145i | −0.193904 | − | 0.335852i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39.8164 | + | 18.3971i | −1.30774 | + | 0.604240i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.6430 | − | 40.9510i | 0.775703 | − | 1.34356i | −0.158695 | − | 0.987328i | \(-0.550729\pi\) |
0.934398 | − | 0.356230i | \(-0.115938\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.5463 | − | 9.91242i | −1.03389 | − | 0.324866i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.7288 | − | 30.7982i | 1.10423 | − | 1.00829i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.40917 | + | 5.90486i | −0.111492 | + | 0.193110i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.2493 | 0.694183 | 0.347092 | − | 0.937831i | \(-0.387169\pi\) | ||||
0.347092 | + | 0.937831i | \(0.387169\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.9703 | + | 6.65234i | 0.684341 | + | 0.217091i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0405 | + | 52.0316i | 0.979292 | + | 1.69618i | 0.664977 | + | 0.746864i | \(0.268441\pi\) |
0.314315 | + | 0.949319i | \(0.398225\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.67303 | + | 2.89777i | −0.0544813 | + | 0.0943644i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.0983 | − | 19.7249i | 0.393558 | − | 0.641650i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.83468 | + | 3.17775i | −0.0596189 | + | 0.103263i | −0.894294 | − | 0.447479i | \(-0.852322\pi\) |
0.834675 | + | 0.550742i | \(0.185655\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.7531 | − | 46.3377i | −0.868442 | − | 1.50419i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.0547357 | − | 0.0173636i | −0.00177493 | − | 0.000563053i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.837421 | 0.0271267 | 0.0135634 | − | 0.999908i | \(-0.495683\pi\) | ||||
0.0135634 | + | 0.999908i | \(0.495683\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.7055 | + | 23.7385i | −0.443498 | + | 0.768161i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.1880 | − | 9.30279i | 0.329331 | − | 0.300716i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.2382 | + | 44.2636i | 0.556651 | + | 1.42935i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3327 | − | 26.5571i | 0.494605 | − | 0.856680i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.6798 | + | 11.7667i | 0.537500 | + | 0.379176i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.15574 | − | 3.73386i | −0.0693958 | − | 0.120197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.8856 | − | 37.9070i | 0.703795 | − | 1.21901i | −0.263330 | − | 0.964706i | \(-0.584821\pi\) |
0.967125 | − | 0.254302i | \(-0.0818458\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.71661 | − | 26.0015i | −0.183644 | − | 0.835288i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.3059 | − | 35.1709i | −0.651648 | − | 1.12869i | −0.982723 | − | 0.185083i | \(-0.940745\pi\) |
0.331075 | − | 0.943605i | \(-0.392589\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.98560 | + | 0.458025i | 0.0957138 | + | 0.0146836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.0271 | − | 4.44977i | −0.449228 | − | 0.142507i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.7479 | − | 49.7929i | −0.919728 | − | 1.59302i | −0.799827 | − | 0.600230i | \(-0.795076\pi\) |
−0.119901 | − | 0.992786i | \(-0.538258\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.51689 | − | 13.0196i | −0.240241 | − | 0.416109i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.55571 | + | 50.0513i | −0.145452 | + | 1.59801i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.4594 | −0.429289 | −0.214644 | − | 0.976692i | \(-0.568859\pi\) | ||||
−0.214644 | + | 0.976692i | \(0.568859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.5103 | 1.16331 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.124985 | + | 1.94445i | 0.00397830 | + | 0.0618926i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.980604 | − | 1.69846i | −0.0311814 | − | 0.0540078i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7821 | + | 30.7995i | −0.564867 | + | 0.978379i | 0.432195 | + | 0.901780i | \(0.357739\pi\) |
−0.997062 | + | 0.0765983i | \(0.975594\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.01362 | + | 2.54213i | 0.254304 | + | 0.0806720i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.42036 | + | 16.3165i | −0.298645 | + | 0.517269i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.7289 | 1.03653 | 0.518267 | − | 0.855219i | \(-0.326577\pi\) | ||||
0.518267 | + | 0.855219i | \(0.326577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.9603 | − | 26.0721i | 0.346770 | − | 0.824885i |
(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 | 504.2.t.d.193.6 | yes | 22 | |
3.2 | odd | 2 | 1512.2.t.d.361.4 | 22 | |||
4.3 | odd | 2 | 1008.2.t.k.193.6 | 22 | |||
7.2 | even | 3 | 504.2.q.d.121.1 | yes | 22 | ||
9.2 | odd | 6 | 1512.2.q.c.1369.8 | 22 | |||
9.7 | even | 3 | 504.2.q.d.25.1 | ✓ | 22 | ||
12.11 | even | 2 | 3024.2.t.l.1873.4 | 22 | |||
21.2 | odd | 6 | 1512.2.q.c.793.8 | 22 | |||
28.23 | odd | 6 | 1008.2.q.k.625.11 | 22 | |||
36.7 | odd | 6 | 1008.2.q.k.529.11 | 22 | |||
36.11 | even | 6 | 3024.2.q.k.2881.8 | 22 | |||
63.2 | odd | 6 | 1512.2.t.d.289.4 | 22 | |||
63.16 | even | 3 | inner | 504.2.t.d.457.6 | yes | 22 | |
84.23 | even | 6 | 3024.2.q.k.2305.8 | 22 | |||
252.79 | odd | 6 | 1008.2.t.k.961.6 | 22 | |||
252.191 | even | 6 | 3024.2.t.l.289.4 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.1 | ✓ | 22 | 9.7 | even | 3 | ||
504.2.q.d.121.1 | yes | 22 | 7.2 | even | 3 | ||
504.2.t.d.193.6 | yes | 22 | 1.1 | even | 1 | trivial | |
504.2.t.d.457.6 | yes | 22 | 63.16 | even | 3 | inner | |
1008.2.q.k.529.11 | 22 | 36.7 | odd | 6 | |||
1008.2.q.k.625.11 | 22 | 28.23 | odd | 6 | |||
1008.2.t.k.193.6 | 22 | 4.3 | odd | 2 | |||
1008.2.t.k.961.6 | 22 | 252.79 | odd | 6 | |||
1512.2.q.c.793.8 | 22 | 21.2 | odd | 6 | |||
1512.2.q.c.1369.8 | 22 | 9.2 | odd | 6 | |||
1512.2.t.d.289.4 | 22 | 63.2 | odd | 6 | |||
1512.2.t.d.361.4 | 22 | 3.2 | odd | 2 | |||
3024.2.q.k.2305.8 | 22 | 84.23 | even | 6 | |||
3024.2.q.k.2881.8 | 22 | 36.11 | even | 6 | |||
3024.2.t.l.289.4 | 22 | 252.191 | even | 6 | |||
3024.2.t.l.1873.4 | 22 | 12.11 | even | 2 |