Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,2,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.02208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.81 |
Dual form | 128.2.g.a.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 0.292893i | 0.408248 | + | 0.169102i | 0.577350 | − | 0.816497i | \(-0.304087\pi\) |
−0.169102 | + | 0.985599i | \(0.554087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.12132 | + | 2.70711i | 0.501470 | + | 1.21065i | 0.948683 | + | 0.316228i | \(0.102416\pi\) |
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.00000i | −0.377964 | + | 0.377964i | −0.870367 | − | 0.492403i | \(-0.836119\pi\) |
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.70711 | − | 1.70711i | −0.569036 | − | 0.569036i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.12132 | − | 1.70711i | 1.24262 | − | 0.514712i | 0.338091 | − | 0.941113i | \(-0.390219\pi\) |
0.904534 | + | 0.426401i | \(0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.292893 | − | 0.707107i | 0.0812340 | − | 0.196116i | −0.878044 | − | 0.478580i | \(-0.841152\pi\) |
0.959278 | + | 0.282464i | \(0.0911517\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.24264i | 0.579047i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.82843i | − | 0.685994i | −0.939336 | − | 0.342997i | \(-0.888558\pi\) | ||
0.939336 | − | 0.342997i | \(-0.111442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.53553 | + | 3.70711i | −0.352276 | + | 0.850469i | 0.644063 | + | 0.764973i | \(0.277248\pi\) |
−0.996339 | + | 0.0854961i | \(0.972752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | + | 0.414214i | −0.218218 | + | 0.0903888i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.82843 | − | 5.82843i | −1.21531 | − | 1.21531i | −0.969256 | − | 0.246055i | \(-0.920866\pi\) |
−0.246055 | − | 0.969256i | \(-0.579134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.53553 | + | 2.53553i | −0.507107 | + | 0.507107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.58579 | − | 3.82843i | −0.305185 | − | 0.736781i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.12132 | − | 1.29289i | −0.579615 | − | 0.240084i | 0.0735609 | − | 0.997291i | \(-0.476564\pi\) |
−0.653176 | + | 0.757206i | \(0.726564\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.41421 | 0.594338 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.82843 | − | 1.58579i | −0.647122 | − | 0.268047i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.292893 | + | 0.707107i | 0.0481513 | + | 0.116248i | 0.946125 | − | 0.323802i | \(-0.104961\pi\) |
−0.897974 | + | 0.440049i | \(0.854961\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.414214 | − | 0.414214i | 0.0663273 | − | 0.0663273i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.171573 | − | 0.171573i | −0.0267952 | − | 0.0267952i | 0.693582 | − | 0.720377i | \(-0.256031\pi\) |
−0.720377 | + | 0.693582i | \(0.756031\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.70711 | + | 1.94975i | −0.717827 | + | 0.297334i | −0.711539 | − | 0.702647i | \(-0.752002\pi\) |
−0.00628798 | + | 0.999980i | \(0.502002\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.70711 | − | 6.53553i | 0.403552 | − | 0.974260i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.343146i | 0.0500530i | 0.999687 | + | 0.0250265i | \(0.00796701\pi\) | ||||
−0.999687 | + | 0.0250265i | \(0.992033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.828427 | − | 2.00000i | 0.116003 | − | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.12132 | + | 0.464466i | −0.154025 | + | 0.0637993i | −0.458364 | − | 0.888764i | \(-0.651564\pi\) |
0.304339 | + | 0.952564i | \(0.401564\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.24264 | + | 9.24264i | 1.24628 | + | 1.24628i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.17157 | + | 2.17157i | −0.287632 | + | 0.287632i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.87868 | + | 4.53553i | 0.244583 | + | 0.590476i | 0.997727 | − | 0.0673793i | \(-0.0214638\pi\) |
−0.753144 | + | 0.657855i | \(0.771464\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70711 | + | 0.707107i | 0.218573 | + | 0.0905357i | 0.489283 | − | 0.872125i | \(-0.337259\pi\) |
−0.270710 | + | 0.962661i | \(0.587259\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.41421 | 0.430150 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.24264 | 0.278165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.53553 | + | 2.29289i | 0.676273 | + | 0.280121i | 0.694268 | − | 0.719717i | \(-0.255728\pi\) |
−0.0179949 | + | 0.999838i | \(0.505728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.41421 | − | 5.82843i | −0.290637 | − | 0.701660i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.82843 | − | 5.82843i | 0.691707 | − | 0.691707i | −0.270900 | − | 0.962607i | \(-0.587321\pi\) |
0.962607 | + | 0.270900i | \(0.0873214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | + | 7.00000i | 0.819288 | + | 0.819288i | 0.986005 | − | 0.166717i | \(-0.0533166\pi\) |
−0.166717 | + | 0.986005i | \(0.553317\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.53553 | + | 1.05025i | −0.292778 | + | 0.121273i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.41421 | + | 5.82843i | −0.275125 | + | 0.664211i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.00000i | − | 0.675053i | −0.941316 | − | 0.337526i | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.07107i | 0.452341i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.87868 | + | 4.53553i | −0.206212 | + | 0.497840i | −0.992821 | − | 0.119612i | \(-0.961835\pi\) |
0.786609 | + | 0.617452i | \(0.211835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.65685 | − | 3.17157i | 0.830502 | − | 0.344005i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.82843 | − | 1.82843i | −0.196028 | − | 0.196028i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.65685 | − | 8.65685i | 0.917625 | − | 0.917625i | −0.0792315 | − | 0.996856i | \(-0.525247\pi\) |
0.996856 | + | 0.0792315i | \(0.0252466\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.414214 | + | 1.00000i | 0.0434214 | + | 0.104828i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.82843 | + | 1.17157i | 0.293294 | + | 0.121486i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.7574 | −1.20628 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.4853 | −1.87690 | −0.938448 | − | 0.345421i | \(-0.887736\pi\) | ||||
−0.938448 | + | 0.345421i | \(0.887736\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.94975 | − | 4.12132i | −0.999987 | − | 0.414208i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.36396 | − | 3.29289i | −0.135719 | − | 0.327655i | 0.841379 | − | 0.540446i | \(-0.181745\pi\) |
−0.977098 | + | 0.212791i | \(0.931745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.48528 | + | 9.48528i | −0.934613 | + | 0.934613i | −0.997990 | − | 0.0633771i | \(-0.979813\pi\) |
0.0633771 | + | 0.997990i | \(0.479813\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.24264 | − | 2.24264i | −0.218859 | − | 0.218859i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.12132 | − | 1.70711i | 0.398423 | − | 0.165032i | −0.174470 | − | 0.984663i | \(-0.555821\pi\) |
0.572893 | + | 0.819630i | \(0.305821\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.70711 | + | 13.7782i | −0.546642 | + | 1.31971i | 0.373320 | + | 0.927702i | \(0.378219\pi\) |
−0.919962 | + | 0.392007i | \(0.871781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.585786i | 0.0556004i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.34315i | − | 0.596713i | −0.954455 | − | 0.298356i | \(-0.903562\pi\) | ||
0.954455 | − | 0.298356i | \(-0.0964384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.24264 | − | 22.3137i | 0.861881 | − | 2.08076i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.70711 | + | 0.707107i | −0.157822 | + | 0.0653720i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.82843 | + | 2.82843i | 0.259281 | + | 0.259281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.29289 | − | 6.29289i | 0.572081 | − | 0.572081i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0710678 | − | 0.171573i | −0.00640797 | − | 0.0154702i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.82843 | + | 1.58579i | 0.342425 | + | 0.141837i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9706 | −1.15095 | −0.575476 | − | 0.817819i | \(-0.695183\pi\) | ||||
−0.575476 | + | 0.817819i | \(0.695183\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.89949 | −0.343331 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3640 | + | 6.77817i | 1.42973 | + | 0.592212i | 0.957284 | − | 0.289150i | \(-0.0933726\pi\) |
0.472442 | + | 0.881362i | \(0.343373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17157 | − | 5.24264i | −0.188299 | − | 0.454595i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.58579 | − | 8.58579i | 0.738947 | − | 0.738947i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.65685 | − | 8.65685i | −0.739605 | − | 0.739605i | 0.232897 | − | 0.972502i | \(-0.425180\pi\) |
−0.972502 | + | 0.232897i | \(0.925180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.1924 | + | 5.46447i | −1.11896 | + | 0.463490i | −0.864016 | − | 0.503465i | \(-0.832058\pi\) |
−0.254948 | + | 0.966955i | \(0.582058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.100505 | + | 0.242641i | −0.00846405 | + | 0.0204340i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.41421i | − | 0.285511i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.89949i | − | 0.822108i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.46447 | + | 3.53553i | −0.120787 | + | 0.291606i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.6066 | + | 6.46447i | −1.27854 | + | 0.529590i | −0.915551 | − | 0.402203i | \(-0.868245\pi\) |
−0.362992 | + | 0.931792i | \(0.618245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.48528 | + | 1.48528i | 0.120870 | + | 0.120870i | 0.764955 | − | 0.644084i | \(-0.222761\pi\) |
−0.644084 | + | 0.764955i | \(0.722761\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.82843 | + | 4.82843i | −0.390355 | + | 0.390355i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.48528 | + | 10.8284i | 0.360266 | + | 0.869760i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.70711 | + | 0.707107i | 0.136242 | + | 0.0564333i | 0.449763 | − | 0.893148i | \(-0.351509\pi\) |
−0.313521 | + | 0.949581i | \(0.601509\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.928932 | −0.0736691 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.6569 | 0.918689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.464466 | − | 0.192388i | −0.0363798 | − | 0.0150690i | 0.364419 | − | 0.931235i | \(-0.381267\pi\) |
−0.400799 | + | 0.916166i | \(0.631267\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.82843 | + | 9.24264i | 0.298043 | + | 0.719539i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.6569 | + | 14.6569i | −1.13418 | + | 1.13418i | −0.144707 | + | 0.989475i | \(0.546224\pi\) |
−0.989475 | + | 0.144707i | \(0.953776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.77817 | + | 8.77817i | 0.675244 | + | 0.675244i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.94975 | − | 3.70711i | 0.684404 | − | 0.283490i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.12132 | − | 7.53553i | 0.237310 | − | 0.572916i | −0.759693 | − | 0.650282i | \(-0.774651\pi\) |
0.997003 | + | 0.0773656i | \(0.0246509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.07107i | − | 0.383337i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.75736i | 0.282420i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.63604 | − | 3.94975i | 0.122283 | − | 0.295218i | −0.850870 | − | 0.525377i | \(-0.823924\pi\) |
0.973153 | + | 0.230159i | \(0.0739245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1924 | − | 6.70711i | 1.20357 | − | 0.498535i | 0.311420 | − | 0.950272i | \(-0.399196\pi\) |
0.892151 | + | 0.451737i | \(0.149196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000 | + | 1.00000i | 0.0739221 | + | 0.0739221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.58579 | + | 1.58579i | −0.116589 | + | 0.116589i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.82843 | − | 11.6569i | −0.353090 | − | 0.852434i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.41421 | + | 2.24264i | 0.393826 | + | 0.163128i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.51472 | −0.109032 | −0.0545159 | − | 0.998513i | \(-0.517362\pi\) | ||||
−0.0545159 | + | 0.998513i | \(0.517362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.58579 | + | 0.656854i | 0.113561 | + | 0.0470383i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.63604 | + | 11.1924i | 0.330304 | + | 0.797425i | 0.998568 | + | 0.0535002i | \(0.0170378\pi\) |
−0.668264 | + | 0.743924i | \(0.732962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.9706 | − | 15.9706i | 1.13212 | − | 1.13212i | 0.142300 | − | 0.989824i | \(-0.454550\pi\) |
0.989824 | − | 0.142300i | \(-0.0454496\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.24264 | + | 3.24264i | 0.228718 | + | 0.228718i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.41421 | − | 1.82843i | 0.309817 | − | 0.128330i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.272078 | − | 0.656854i | 0.0190027 | − | 0.0458767i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.8995i | 1.38311i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.8995i | 1.23813i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.53553 | + | 18.1924i | −0.518768 | + | 1.25242i | 0.419893 | + | 0.907574i | \(0.362068\pi\) |
−0.938661 | + | 0.344842i | \(0.887932\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.82843 | − | 2.41421i | 0.399357 | − | 0.165419i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.5563 | − | 10.5563i | −0.719937 | − | 0.719937i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | + | 4.00000i | −0.271538 | + | 0.271538i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.89949 | + | 7.00000i | 0.195930 | + | 0.473016i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | − | 0.828427i | −0.134535 | − | 0.0557260i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9706 | 1.40429 | 0.702146 | − | 0.712033i | \(-0.252225\pi\) | ||||
0.702146 | + | 0.712033i | \(0.252225\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.65685 | 0.577124 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.6066 | − | 7.70711i | −1.23496 | − | 0.511539i | −0.332826 | − | 0.942988i | \(-0.608002\pi\) |
−0.902137 | + | 0.431449i | \(0.858002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.22183 | − | 22.2635i | −0.609395 | − | 1.47121i | −0.863659 | − | 0.504076i | \(-0.831833\pi\) |
0.254264 | − | 0.967135i | \(-0.418167\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.41421 | + | 3.41421i | −0.224639 | + | 0.224639i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.65685 | − | 2.65685i | −0.174056 | − | 0.174056i | 0.614703 | − | 0.788759i | \(-0.289276\pi\) |
−0.788759 | + | 0.614703i | \(0.789276\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.928932 | + | 0.384776i | −0.0605969 | + | 0.0251000i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.75736 | − | 4.24264i | 0.114153 | − | 0.275589i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.31371i | 0.343715i | 0.985122 | + | 0.171858i | \(0.0549769\pi\) | ||||
−0.985122 | + | 0.171858i | \(0.945023\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.48528i | − | 0.546585i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) | ||
0.961931 | − | 0.273293i | \(-0.0881127\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.94975 | + | 14.3640i | −0.381676 | + | 0.921449i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.5355 | + | 5.60660i | −0.864754 | + | 0.358193i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.17157 | + | 2.17157i | 0.138174 | + | 0.138174i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.65685 | + | 2.65685i | −0.168371 | + | 0.168371i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.60660 | − | 15.9497i | −0.417005 | − | 1.00674i | −0.983210 | − | 0.182475i | \(-0.941589\pi\) |
0.566205 | − | 0.824264i | \(-0.308411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.9706 | − | 14.0711i | −2.13571 | − | 0.884640i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.34315 | 0.397223 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | − | 0.414214i | −0.0621370 | − | 0.0257380i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.12132 | + | 7.53553i | 0.193205 | + | 0.466438i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.82843 | − | 5.82843i | 0.359396 | − | 0.359396i | −0.504194 | − | 0.863590i | \(-0.668210\pi\) |
0.863590 | + | 0.504194i | \(0.168210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.51472 | − | 2.51472i | −0.154478 | − | 0.154478i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.65685 | − | 3.58579i | 0.529791 | − | 0.219447i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.12132 | − | 22.0208i | 0.556137 | − | 1.34263i | −0.356666 | − | 0.934232i | \(-0.616087\pi\) |
0.912803 | − | 0.408401i | \(-0.133913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 18.0000i | − | 1.09342i | −0.837321 | − | 0.546711i | \(-0.815880\pi\) | ||
0.837321 | − | 0.546711i | \(-0.184120\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.828427i | 0.0501387i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.12132 | + | 14.7782i | −0.369130 | + | 0.891157i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.70711 | − | 0.707107i | 0.102570 | − | 0.0424859i | −0.330808 | − | 0.943698i | \(-0.607321\pi\) |
0.433378 | + | 0.901212i | \(0.357321\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.82843 | − | 6.82843i | −0.408807 | − | 0.408807i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.8284 | + | 11.8284i | −0.705625 | + | 0.705625i | −0.965612 | − | 0.259987i | \(-0.916282\pi\) |
0.259987 | + | 0.965612i | \(0.416282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.77817 | − | 13.9497i | −0.343477 | − | 0.829226i | −0.997359 | − | 0.0726300i | \(-0.976861\pi\) |
0.653882 | − | 0.756596i | \(-0.273139\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.31371 | − | 3.44365i | −0.492462 | − | 0.203984i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.343146 | 0.0202553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.0711 | − | 5.41421i | −0.766240 | − | 0.317387i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.60660 | + | 23.1924i | 0.561224 | + | 1.35491i | 0.908788 | + | 0.417258i | \(0.137009\pi\) |
−0.347565 | + | 0.937656i | \(0.612991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1716 | + | 10.1716i | −0.592212 | + | 0.592212i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.0711 | − | 13.0711i | −0.758460 | − | 0.758460i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.82843 | + | 2.41421i | −0.337067 | + | 0.139618i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.75736 | − | 6.65685i | 0.158932 | − | 0.383695i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.72792i | − | 0.156715i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.41421i | 0.310017i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.94975 | − | 16.7782i | 0.396643 | − | 0.957581i | −0.591813 | − | 0.806075i | \(-0.701588\pi\) |
0.988456 | − | 0.151506i | \(-0.0484123\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.48528 | + | 3.92893i | −0.539599 | + | 0.223509i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.65685 | + | 2.65685i | 0.150656 | + | 0.150656i | 0.778411 | − | 0.627755i | \(-0.216026\pi\) |
−0.627755 | + | 0.778411i | \(0.716026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.48528 | + | 7.48528i | −0.423093 | + | 0.423093i | −0.886267 | − | 0.463174i | \(-0.846710\pi\) |
0.463174 | + | 0.886267i | \(0.346710\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.82843 | + | 9.24264i | 0.215707 | + | 0.520764i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3640 | + | 7.19239i | 0.975257 | + | 0.403965i | 0.812667 | − | 0.582729i | \(-0.198015\pi\) |
0.162591 | + | 0.986694i | \(0.448015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0711 | −0.843818 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.41421 | 0.190563 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.4853 | + | 4.34315i | 0.583417 | + | 0.241659i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.05025 | + | 2.53553i | 0.0582575 | + | 0.140646i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.07107 | + | 8.07107i | −0.446331 | + | 0.446331i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.343146 | − | 0.343146i | −0.0189182 | − | 0.0189182i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.29289 | − | 0.535534i | 0.0710638 | − | 0.0294356i | −0.346868 | − | 0.937914i | \(-0.612755\pi\) |
0.417932 | + | 0.908478i | \(0.362755\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.707107 | − | 1.70711i | 0.0387492 | − | 0.0935489i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.5563i | 0.959206i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.9706i | − | 0.924445i | −0.886764 | − | 0.462223i | \(-0.847052\pi\) | ||
0.886764 | − | 0.462223i | \(-0.152948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.85786 | − | 4.48528i | 0.100905 | − | 0.243607i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.4853 | − | 6.82843i | 0.892728 | − | 0.369780i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.0711 | − | 13.0711i | 0.703723 | − | 0.703723i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.63604 | − | 3.94975i | −0.0878272 | − | 0.212034i | 0.873863 | − | 0.486172i | \(-0.161607\pi\) |
−0.961690 | + | 0.274139i | \(0.911607\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.6777 | + | 10.2218i | 1.32097 | + | 0.547162i | 0.928065 | − | 0.372419i | \(-0.121472\pi\) |
0.392901 | + | 0.919581i | \(0.371472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.17157 | −0.169286 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.3137 | + | 9.24264i | 1.18429 | + | 0.490548i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.17157 | + | 2.82843i | 0.0620062 | + | 0.149696i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.8284 | − | 17.8284i | 0.940948 | − | 0.940948i | −0.0574027 | − | 0.998351i | \(-0.518282\pi\) |
0.998351 | + | 0.0574027i | \(0.0182819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.05025 | + | 2.05025i | 0.107908 | + | 0.107908i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.29289 | − | 2.60660i | 0.330291 | − | 0.136811i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.1005 | + | 26.7990i | −0.581027 | + | 1.40272i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.00000i | 0.313197i | 0.987662 | + | 0.156599i | \(0.0500529\pi\) | ||||
−0.987662 | + | 0.156599i | \(0.949947\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.585786i | 0.0304948i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.656854 | − | 1.58579i | 0.0341022 | − | 0.0823299i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.2929 | + | 4.26346i | −0.532946 | + | 0.220753i | −0.632893 | − | 0.774239i | \(-0.718133\pi\) |
0.0999471 | + | 0.994993i | \(0.468133\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.24264 | + | 2.24264i | 0.115809 | + | 0.115809i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.82843 | + | 1.82843i | −0.0941688 | + | 0.0941688i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6777 | + | 33.0208i | 0.702575 | + | 1.69617i | 0.717769 | + | 0.696281i | \(0.245163\pi\) |
−0.0151948 | + | 0.999885i | \(0.504837\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.17157 | − | 3.79899i | −0.469874 | − | 0.194628i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9706 | 0.867155 | 0.433578 | − | 0.901116i | \(-0.357251\pi\) | ||||
0.433578 | + | 0.901116i | \(0.357251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.4853 | −0.942097 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.3640 | + | 4.70711i | 0.577663 | + | 0.239276i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.39340 | − | 20.2635i | −0.425562 | − | 1.02740i | −0.980679 | − | 0.195625i | \(-0.937326\pi\) |
0.555117 | − | 0.831773i | \(-0.312674\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.4853 | + | 16.4853i | −0.833697 | + | 0.833697i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.58579 | + | 9.58579i | 0.483539 | + | 0.483539i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.2426 | − | 6.72792i | 0.817256 | − | 0.338518i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.22183 | + | 22.2635i | −0.462830 | + | 1.11737i | 0.504400 | + | 0.863470i | \(0.331714\pi\) |
−0.967230 | + | 0.253901i | \(0.918286\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 4.34315i | − | 0.217429i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.82843i | − | 0.141245i | −0.997503 | − | 0.0706225i | \(-0.977501\pi\) | ||
0.997503 | − | 0.0706225i | \(-0.0224986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.17157 | − | 2.82843i | 0.0583602 | − | 0.140894i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.0208 | + | 4.56497i | −0.547629 | + | 0.226835i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.41421 | + | 2.41421i | 0.119668 | + | 0.119668i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.4853 | − | 21.4853i | 1.06238 | − | 1.06238i | 0.0644584 | − | 0.997920i | \(-0.479468\pi\) |
0.997920 | − | 0.0644584i | \(-0.0205320\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.58579 | − | 8.65685i | −0.176874 | − | 0.427011i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.41421 | − | 2.65685i | −0.315623 | − | 0.130735i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.3848 | −0.706121 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.9289 | −0.535192 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6066 | − | 5.22183i | −0.615873 | − | 0.255103i | 0.0528644 | − | 0.998602i | \(-0.483165\pi\) |
−0.668737 | + | 0.743499i | \(0.733165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.29289 | + | 15.1924i | 0.306697 | + | 0.740432i | 0.999808 | + | 0.0196009i | \(0.00623955\pi\) |
−0.693111 | + | 0.720831i | \(0.743760\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.585786 | − | 0.585786i | 0.0284819 | − | 0.0284819i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.17157 | + | 7.17157i | 0.347872 | + | 0.347872i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.41421 | + | 1.00000i | −0.116832 | + | 0.0483934i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | − | 2.41421i | 0.0482805 | − | 0.116559i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.3431i | 0.594548i | 0.954792 | + | 0.297274i | \(0.0960775\pi\) | ||||
−0.954792 | + | 0.297274i | \(0.903922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.5147i | − | 0.745590i | −0.927914 | − | 0.372795i | \(-0.878400\pi\) | ||
0.927914 | − | 0.372795i | \(-0.121600\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.89949 | − | 7.00000i | 0.139020 | − | 0.335624i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.5563 | − | 12.6569i | 1.46171 | − | 0.605459i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0000 | + | 17.0000i | 0.811366 | + | 0.811366i | 0.984839 | − | 0.173473i | \(-0.0554989\pi\) |
−0.173473 | + | 0.984839i | \(0.555499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.53553 | − | 8.53553i | 0.406454 | − | 0.406454i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.606602 | − | 1.46447i | −0.0288205 | − | 0.0695789i | 0.908814 | − | 0.417201i | \(-0.136989\pi\) |
−0.937635 | + | 0.347623i | \(0.886989\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.1421 | + | 13.7279i | 1.57109 | + | 0.650766i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.9289 | −0.611518 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.4558 | −0.918178 | −0.459089 | − | 0.888390i | \(-0.651824\pi\) | ||||
−0.459089 | + | 0.888390i | \(0.651824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.00000 | − | 0.414214i | −0.0470882 | − | 0.0195046i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.615224 | + | 1.48528i | 0.0289057 | + | 0.0697846i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.24264 | + | 2.24264i | −0.105137 | + | 0.105137i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.48528 | − | 7.48528i | −0.350147 | − | 0.350147i | 0.510017 | − | 0.860164i | \(-0.329639\pi\) |
−0.860164 | + | 0.510017i | \(0.829639\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.8284 | + | 4.48528i | −0.505428 | + | 0.209355i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.636039 | − | 1.53553i | 0.0296233 | − | 0.0715169i | −0.908376 | − | 0.418155i | \(-0.862677\pi\) |
0.937999 | + | 0.346638i | \(0.112677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.9706i | − | 1.06753i | −0.845632 | − | 0.533766i | \(-0.820776\pi\) | ||
0.845632 | − | 0.533766i | \(-0.179224\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.97056i | 0.416000i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.09188 | − | 21.9497i | 0.420722 | − | 1.01571i | −0.561413 | − | 0.827536i | \(-0.689742\pi\) |
0.982135 | − | 0.188177i | \(-0.0602580\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.82843 | + | 3.24264i | −0.361483 | + | 0.149731i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.00000 | + | 1.00000i | 0.0460776 | + | 0.0460776i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.0711 | + | 16.0711i | −0.738948 | + | 0.738948i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.50610 | − | 13.2929i | −0.252637 | − | 0.609920i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.70711 | + | 1.12132i | 0.123950 | + | 0.0513417i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.9706 | −1.32370 | −0.661849 | − | 0.749637i | \(-0.730228\pi\) | ||||
−0.661849 | + | 0.749637i | \(0.730228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.585786 | 0.0267096 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.24264 | + | 3.41421i | 0.375053 | + | 0.155352i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.7279 | − | 50.0416i | −0.941206 | − | 2.27227i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0000 | − | 11.0000i | 0.498458 | − | 0.498458i | −0.412500 | − | 0.910958i | \(-0.635344\pi\) |
0.910958 | + | 0.412500i | \(0.135344\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.272078 | − | 0.272078i | −0.0123038 | − | 0.0123038i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.3345 | + | 16.2929i | −1.77514 | + | 0.735288i | −0.781343 | + | 0.624102i | \(0.785465\pi\) |
−0.993800 | + | 0.111186i | \(0.964535\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.65685 | + | 8.82843i | −0.164696 | + | 0.397612i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 31.5563i | − | 1.41835i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.6569i | 0.522881i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.949747 | − | 2.29289i | 0.0425165 | − | 0.102644i | −0.901195 | − | 0.433415i | \(-0.857309\pi\) |
0.943711 | + | 0.330771i | \(0.107309\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.6569 | + | 6.07107i | −0.654820 | + | 0.271235i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.1421 | + | 11.1421i | 0.496803 | + | 0.496803i | 0.910441 | − | 0.413638i | \(-0.135742\pi\) |
−0.413638 | + | 0.910441i | \(0.635742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.38478 | − | 7.38478i | 0.328618 | − | 0.328618i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.63604 | + | 8.77817i | 0.161482 | + | 0.389852i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.0919 | − | 10.8076i | −1.15650 | − | 0.479039i | −0.279793 | − | 0.960060i | \(-0.590266\pi\) |
−0.876709 | + | 0.481021i | \(0.840266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | −0.619324 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.6274 | 0.734118 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.3137 | − | 15.0416i | −1.60017 | − | 0.662813i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.585786 | + | 1.41421i | 0.0257629 | + | 0.0621970i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.41421 | − | 4.41421i | 0.193762 | − | 0.193762i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.34315 | + | 3.34315i | 0.146466 | + | 0.146466i | 0.776537 | − | 0.630071i | \(-0.216974\pi\) |
−0.630071 | + | 0.776537i | \(0.716974\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.1924 | + | 7.94975i | −0.839225 | + | 0.347618i | −0.760548 | − | 0.649282i | \(-0.775070\pi\) |
−0.0786768 | + | 0.996900i | \(0.525070\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.48528 | − | 3.58579i | 0.0648230 | − | 0.156497i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 11.3137i | − | 0.492833i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.9411i | 1.95396i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.53553 | − | 10.9497i | 0.196825 | − | 0.475179i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.171573 | + | 0.0710678i | −0.00743165 | + | 0.00307829i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.24264 | + | 9.24264i | 0.399594 | + | 0.399594i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.31371 | − | 2.31371i | 0.0998439 | − | 0.0998439i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.53553 | + | 20.6066i | 0.367651 | + | 0.887589i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.2635 | − | 11.2929i | −1.17215 | − | 0.485519i | −0.290246 | − | 0.956952i | \(-0.593737\pi\) |
−0.881902 | + | 0.471433i | \(0.843737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.4142 | 0.575659 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −43.6985 | −1.87184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.5355 | + | 7.26346i | 0.749765 | + | 0.310563i | 0.724646 | − | 0.689122i | \(-0.242003\pi\) |
0.0251195 | + | 0.999684i | \(0.492003\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.70711 | − | 4.12132i | −0.0728575 | − | 0.175894i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.58579 | − | 9.58579i | 0.408368 | − | 0.408368i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | + | 6.00000i | 0.255146 | + | 0.255146i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.58579 | + | 0.656854i | −0.0673129 | + | 0.0278819i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.1213 | − | 36.5061i | 0.640711 | − | 1.54681i | −0.185012 | − | 0.982736i | \(-0.559232\pi\) |
0.825722 | − | 0.564077i | \(-0.190768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.89949i | 0.164931i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 9.65685i | − | 0.407713i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.87868 | + | 19.0208i | −0.332047 | + | 0.801632i | 0.666383 | + | 0.745610i | \(0.267842\pi\) |
−0.998430 | + | 0.0560220i | \(0.982158\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.1716 | − | 7.11270i | 0.722414 | − | 0.299233i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.07107 | − | 4.07107i | −0.170969 | − | 0.170969i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.6569 | − | 14.6569i | 0.614447 | − | 0.614447i | −0.329654 | − | 0.944102i | \(-0.606932\pi\) |
0.944102 | + | 0.329654i | \(0.106932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.70711 | + | 6.53553i | 0.113289 | + | 0.273504i | 0.970347 | − | 0.241716i | \(-0.0777103\pi\) |
−0.857058 | + | 0.515220i | \(0.827710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.48528 | + | 3.51472i | 0.354478 | + | 0.146829i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 29.5563 | 1.23258 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9706 | 0.789755 | 0.394877 | − | 0.918734i | \(-0.370787\pi\) | ||||
0.394877 | + | 0.918734i | \(0.370787\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.07107 | − | 0.443651i | −0.0445121 | − | 0.0184375i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.65685 | − | 6.41421i | −0.110225 | − | 0.266106i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.82843 | + | 3.82843i | −0.158557 | + | 0.158557i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.82843 | − | 3.82843i | −0.158286 | − | 0.158286i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.6066 | − | 5.22183i | 0.520330 | − | 0.215528i | −0.107032 | − | 0.994256i | \(-0.534135\pi\) |
0.627362 | + | 0.778728i | \(0.284135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.14214 | + | 14.8284i | −0.253082 | + | 0.610995i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.27208i | 0.381402i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.2843i | − | 1.16150i | −0.814083 | − | 0.580748i | \(-0.802760\pi\) | ||
0.814083 | − | 0.580748i | \(-0.197240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.48528 | + | 10.8284i | −0.183879 | + | 0.443922i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.9706 | − | 6.61522i | 0.653632 | − | 0.270743i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.6569 | + | 26.6569i | 1.08917 | + | 1.08917i | 0.995614 | + | 0.0935555i | \(0.0298232\pi\) |
0.0935555 | + | 0.995614i | \(0.470177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.9706 | + | 21.9706i | −0.896198 | + | 0.896198i | −0.995097 | − | 0.0988995i | \(-0.968468\pi\) |
0.0988995 | + | 0.995097i | \(0.468468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.53553 | − | 13.3640i | −0.225424 | − | 0.544223i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.0919 | + | 9.97918i | 0.979474 | + | 0.405712i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9706 | 1.33823 | 0.669117 | − | 0.743157i | \(-0.266673\pi\) | ||||
0.669117 | + | 0.743157i | \(0.266673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.65685 | 0.148183 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.242641 | + | 0.100505i | 0.00981619 | + | 0.00406600i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.32233 | + | 3.19239i | 0.0534084 | + | 0.128939i | 0.948332 | − | 0.317281i | \(-0.102770\pi\) |
−0.894923 | + | 0.446220i | \(0.852770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.384776 | − | 0.384776i | 0.0155157 | − | 0.0155157i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.7990 | + | 22.7990i | 0.917853 | + | 0.917853i | 0.996873 | − | 0.0790202i | \(-0.0251792\pi\) |
−0.0790202 | + | 0.996873i | \(0.525179\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.7782 | − | 9.02082i | 0.875339 | − | 0.362577i | 0.100651 | − | 0.994922i | \(-0.467907\pi\) |
0.774687 | + | 0.632345i | \(0.217907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.0711 | + | 31.5563i | −0.524524 | + | 1.26631i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.3137i | 0.693659i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.0711i | 1.20284i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.24264 | + | 12.6569i | −0.209371 | + | 0.505466i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.00000 | − | 0.828427i | 0.0797452 | − | 0.0330316i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.4558 | − | 32.4558i | −1.29205 | − | 1.29205i | −0.933519 | − | 0.358528i | \(-0.883279\pi\) |
−0.358528 | − | 0.933519i | \(-0.616721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.6569 | + | 10.6569i | −0.423572 | + | 0.423572i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.5442 | − | 35.1127i | −0.577167 | − | 1.39340i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.53553 | + | 1.46447i | 0.140083 | + | 0.0580243i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.8995 | −0.787212 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.45584 | 0.294488 | 0.147244 | − | 0.989100i | \(-0.452960\pi\) | ||||
0.147244 | + | 0.989100i | \(0.452960\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.4350 | − | 4.73654i | −0.450954 | − | 0.186791i | 0.145635 | − | 0.989338i | \(-0.453478\pi\) |
−0.596588 | + | 0.802547i | \(0.703478\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.37258 | − | 10.5563i | −0.172170 | − | 0.415656i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.17157 | + | 6.17157i | −0.242630 | + | 0.242630i | −0.817937 | − | 0.575308i | \(-0.804882\pi\) |
0.575308 | + | 0.817937i | \(0.304882\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4853 | + | 15.4853i | 0.607850 | + | 0.607850i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | + | 1.65685i | −0.156772 | + | 0.0649372i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.09188 | − | 5.05025i | 0.0818617 | − | 0.197632i | −0.877649 | − | 0.479304i | \(-0.840889\pi\) |
0.959511 | + | 0.281672i | \(0.0908891\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 51.8995i | 2.02788i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 23.8995i | − | 0.932408i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1213 | − | 24.4350i | 0.394271 | − | 0.951854i | −0.594728 | − | 0.803927i | \(-0.702740\pi\) |
0.988998 | − | 0.147926i | \(-0.0472599\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.7487 | + | 17.2929i | −1.62384 | + | 0.672616i | −0.994521 | − | 0.104534i | \(-0.966665\pi\) |
−0.629316 | + | 0.777149i | \(0.716665\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.17157 | − | 1.17157i | −0.0455001 | − | 0.0455001i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.7574 | − | 11.7574i | 0.455931 | − | 0.455931i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.6569 | + | 25.7279i | 0.412635 | + | 0.996189i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.8284 | + | 6.14214i | 0.573300 | + | 0.237469i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.24264 | 0.318204 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.4853 | 0.866744 | 0.433372 | − | 0.901215i | \(-0.357324\pi\) | ||||
0.433372 | + | 0.901215i | \(0.357324\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.7279 | + | 5.68629i | 0.528388 | + | 0.218865i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6066 | + | 37.6777i | 0.599810 | + | 1.44807i | 0.873775 | + | 0.486331i | \(0.161665\pi\) |
−0.273964 | + | 0.961740i | \(0.588335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4853 | − | 18.4853i | 0.709400 | − | 0.709400i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.8995 | − | 10.8995i | −0.417670 | − | 0.417670i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.1213 | − | 4.19239i | 0.387282 | − | 0.160417i | −0.180543 | − | 0.983567i | \(-0.557785\pi\) |
0.567824 | + | 0.823150i | \(0.307785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.7279 | − | 33.1421i | 0.524517 | − | 1.26630i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 18.4437i | − | 0.703669i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.928932i | 0.0353895i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.5061 | + | 30.1924i | −0.475754 | + | 1.14857i | 0.485828 | + | 0.874055i | \(0.338518\pi\) |
−0.961582 | + | 0.274518i | \(0.911482\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.0711 | − | 5.82843i | 0.534516 | − | 0.221404i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.5858 | − | 29.5858i | −1.12225 | − | 1.12225i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.485281 | + | 0.485281i | −0.0183813 | + | 0.0183813i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.10051 | − | 2.65685i | −0.0416249 | − | 0.100491i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.87868 | + | 1.19239i | 0.108726 | + | 0.0450359i | 0.436383 | − | 0.899761i | \(-0.356259\pi\) |
−0.327657 | + | 0.944797i | \(0.606259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.07107 | −0.115828 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.769553 | −0.0289830 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.65685 | + | 1.92893i | 0.175139 | + | 0.0725450i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.77817 | + | 21.1924i | 0.329671 | + | 0.795897i | 0.998616 | + | 0.0525851i | \(0.0167461\pi\) |
−0.668945 | + | 0.743312i | \(0.733254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.2426 | + | 10.2426i | −0.384129 | + | 0.384129i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.3137 | − | 23.3137i | −0.873105 | − | 0.873105i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.24264 | − | 3.82843i | 0.345655 | − | 0.143175i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.55635 | + | 3.75736i | −0.0581229 | + | 0.140321i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 35.6569i | − | 1.32978i | −0.746943 | − | 0.664888i | \(-0.768479\pi\) | ||
0.746943 | − | 0.664888i | \(-0.231521\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 18.9706i | − | 0.706501i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.48528 | − | 6.00000i | 0.0924286 | − | 0.223142i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.1924 | − | 4.63604i | 0.415675 | − | 0.172178i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.97056 | + | 9.97056i | 0.369788 | + | 0.369788i | 0.867400 | − | 0.497612i | \(-0.165790\pi\) |
−0.497612 | + | 0.867400i | \(0.665790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.221825 | − | 0.221825i | 0.00821576 | − | 0.00821576i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.51472 | + | 13.3137i | 0.203969 | + | 0.492425i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.2635 | − | 13.7782i | −1.22861 | − | 0.508908i | −0.328475 | − | 0.944513i | \(-0.606535\pi\) |
−0.900138 | + | 0.435604i | \(0.856535\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.2132 | −0.413605 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.7279 | 0.984536 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.464466 | − | 0.192388i | −0.0170857 | − | 0.00707711i | 0.374124 | − | 0.927379i | \(-0.377943\pi\) |
−0.391210 | + | 0.920301i | \(0.627943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.899495 | + | 2.17157i | 0.0330438 | + | 0.0797747i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.6274 | + | 31.6274i | −1.16030 | + | 1.16030i | −0.175887 | + | 0.984410i | \(0.556279\pi\) |
−0.984410 | + | 0.175887i | \(0.943721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.0000 | − | 35.0000i | −1.28230 | − | 1.28230i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.9497 | − | 4.53553i | 0.400630 | − | 0.165947i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.41421 | + | 5.82843i | −0.0882134 | + | 0.212966i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9706i | 0.400322i | 0.979763 | + | 0.200161i | \(0.0641464\pi\) | ||||
−0.979763 | + | 0.200161i | \(0.935854\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 13.2132i | − | 0.481516i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.35534 | + | 5.68629i | −0.0857196 | + | 0.206945i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.2635 | + | 13.7782i | −1.20898 | + | 0.500776i | −0.893890 | − | 0.448285i | \(-0.852035\pi\) |
−0.315090 | + | 0.949062i | \(0.602035\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.8995 | − | 19.8995i | −0.722306 | − | 0.722306i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8284 | + | 29.8284i | −1.08128 | + | 1.08128i | −0.0848892 | + | 0.996390i | \(0.527054\pi\) |
−0.996390 | + | 0.0848892i | \(0.972946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.07107 | − | 19.4853i | −0.292192 | − | 0.705415i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.4853 | − | 7.65685i | −0.668337 | − | 0.276834i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.75736 | 0.135670 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.51472 | 0.198866 | 0.0994329 | − | 0.995044i | \(-0.468297\pi\) | ||||
0.0994329 | + | 0.995044i | \(0.468297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.24264 | + | 1.75736i | 0.152795 | + | 0.0632897i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0919 | + | 29.1924i | 0.434915 | + | 1.04998i | 0.977681 | + | 0.210094i | \(0.0673769\pi\) |
−0.542766 | + | 0.839884i | \(0.682623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.1421 | + | 10.1421i | −0.364316 | + | 0.364316i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.585786 | − | 0.585786i | −0.0210150 | − | 0.0210150i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.899495 | − | 0.372583i | 0.0322278 | − | 0.0133492i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0711 | − | 33.9706i | 0.503502 | − | 1.21556i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.0000i | 0.500319i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.41421i | 0.193242i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.949747 | − | 2.29289i | 0.0338548 | − | 0.0817328i | −0.906048 | − | 0.423175i | \(-0.860915\pi\) |
0.939903 | + | 0.341442i | \(0.110915\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.82843 | − | 2.41421i | 0.207498 | − | 0.0859483i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.34315 | + | 6.34315i | 0.225536 | + | 0.225536i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | − | 1.00000i | 0.0355110 | − | 0.0355110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.04163 | − | 2.51472i | −0.0369428 | − | 0.0891879i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.0919 | − | 10.8076i | −0.924222 | − | 0.382825i | −0.130738 | − | 0.991417i | \(-0.541735\pi\) |
−0.793484 | + | 0.608592i | \(0.791735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.970563 | 0.0343360 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.5563 | −1.04432 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40.7990 | + | 16.8995i | 1.43977 | + | 0.596370i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.0711 | + | 31.5563i | 0.460695 | + | 1.11222i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.8995 | − | 12.8995i | 0.454084 | − | 0.454084i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.1421 | − | 29.1421i | −1.02458 | − | 1.02458i | −0.999690 | − | 0.0248928i | \(-0.992076\pi\) |
−0.0248928 | − | 0.999690i | \(-0.507924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.2635 | − | 17.5061i | 1.48407 | − | 0.614722i | 0.514053 | − | 0.857758i | \(-0.328143\pi\) |
0.970017 | + | 0.243036i | \(0.0781433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.27208 | − | 12.7279i | 0.184900 | − | 0.446388i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.47309i | − | 0.0516000i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 20.4437i | − | 0.715233i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.00000 | − | 2.41421i | 0.0349428 | − | 0.0843594i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.6066 | + | 8.94975i | −0.754076 | + | 0.312348i | −0.726403 | − | 0.687269i | \(-0.758809\pi\) |
−0.0276723 | + | 0.999617i | \(0.508809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.9706 | − | 35.9706i | −1.25385 | − | 1.25385i | −0.953978 | − | 0.299877i | \(-0.903054\pi\) |
−0.299877 | − | 0.953978i | \(-0.596946\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.65685 | + | 8.65685i | −0.301393 | + | 0.301393i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.1213 | − | 38.9203i | −0.560593 | − | 1.35339i | −0.909293 | − | 0.416157i | \(-0.863377\pi\) |
0.348699 | − | 0.937235i | \(-0.386623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.1924 | + | 14.1630i | 1.18755 | + | 0.491900i | 0.886957 | − | 0.461853i | \(-0.152815\pi\) |
0.300594 | + | 0.953752i | \(0.402815\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41421 | 0.0490585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.1421 | 0.489996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −56.1127 | − | 23.2426i | −1.94186 | − | 0.804345i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.34315 | − | 15.3137i | −0.219251 | − | 0.529319i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.68629 | + | 9.68629i | −0.334408 | + | 0.334408i | −0.854258 | − | 0.519850i | \(-0.825988\pi\) |
0.519850 | + | 0.854258i | \(0.325988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.4350 | − | 12.4350i | −0.428794 | − | 0.428794i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.8284 | + | 4.89949i | −0.407393 | + | 0.168748i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.9203 | + | 33.6066i | −0.478873 | + | 1.15610i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.5858i | 0.432453i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 11.5563i | − | 0.396613i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.41421 | − | 5.82843i | 0.0827582 | − | 0.199796i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.1630 | − | 21.1924i | 1.75179 | − | 0.725614i | 0.754164 | − | 0.656686i | \(-0.228042\pi\) |
0.997622 | − | 0.0689279i | \(-0.0219579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20.0711 | + | 20.0711i | 0.686416 | + | 0.686416i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.68629 | − | 9.68629i | 0.330877 | − | 0.330877i | −0.522042 | − | 0.852920i | \(-0.674830\pi\) |
0.852920 | + | 0.522042i | \(0.174830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.67767 | + | 4.05025i | 0.0572413 | + | 0.138193i | 0.949913 | − | 0.312515i | \(-0.101172\pi\) |
−0.892671 | + | 0.450708i | \(0.851172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.242641 | + | 0.100505i | 0.00826917 | + | 0.00342520i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.9411 | −0.746885 | −0.373442 | − | 0.927653i | \(-0.621823\pi\) | ||||
−0.373442 | + | 0.927653i | \(0.621823\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.8995 | 0.812607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.36396 | + | 2.63604i | 0.216131 | + | 0.0895246i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.2426 | − | 24.7279i | −0.347458 | − | 0.838837i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.24264 | − | 3.24264i | 0.109873 | − | 0.109873i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.5563 | + | 31.5563i | 1.06802 | + | 1.06802i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.41421 | + | 2.24264i | −0.183034 | + | 0.0758151i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.736544 | + | 1.77817i | −0.0248713 | + | 0.0600447i | −0.935827 | − | 0.352459i | \(-0.885346\pi\) |
0.910956 | + | 0.412504i | \(0.135346\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.2132i | 0.648045i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.6274i | 0.762337i | 0.924506 | + | 0.381169i | \(0.124478\pi\) | ||||
−0.924506 | + | 0.381169i | \(0.875522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.5650 | + | 49.6482i | −0.692066 | + | 1.67080i | 0.0485090 | + | 0.998823i | \(0.484553\pi\) |
−0.740575 | + | 0.671973i | \(0.765447\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.1716 | + | 4.21320i | −0.341914 | + | 0.141625i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.31371 | − | 2.31371i | −0.0776867 | − | 0.0776867i | 0.667196 | − | 0.744882i | \(-0.267494\pi\) |
−0.744882 | + | 0.667196i | \(0.767494\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.9706 | − | 12.9706i | 0.435019 | − | 0.435019i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.94975 | + | 16.7782i | 0.232825 | + | 0.562090i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.27208 | − | 0.526912i | −0.0425685 | − | 0.0176324i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.5269 | 0.418728 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.82843 | −0.161216 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.4853 | − | 5.17157i | −0.416407 | − | 0.172482i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.31371 | + | 3.17157i | 0.0437660 | + | 0.105660i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.89949 | − | 3.89949i | 0.129767 | − | 0.129767i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.3137 | + | 36.3137i | 1.20711 | + | 1.20711i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.7782 | − | 6.53553i | 0.523906 | − | 0.217009i | −0.105026 | − | 0.994469i | \(-0.533493\pi\) |
0.628932 | + | 0.777461i | \(0.283493\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.29289 | + | 7.94975i | −0.109218 | + | 0.263676i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33.5980i | − | 1.11315i | −0.830797 | − | 0.556575i | \(-0.812115\pi\) | ||
0.830797 | − | 0.556575i | \(-0.187885\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.8995i | 0.724767i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.58579 | + | 3.82843i | −0.0524245 | + | 0.126564i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.1421 | + | 9.58579i | −0.764221 | + | 0.316551i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.51472 | + | 8.51472i | 0.280875 | + | 0.280875i | 0.833458 | − | 0.552583i | \(-0.186358\pi\) |
−0.552583 | + | 0.833458i | \(0.686358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.82843 | − | 9.82843i | 0.323858 | − | 0.323858i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.41421 | − | 5.82843i | −0.0794648 | − | 0.191845i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.53553 | − | 1.05025i | −0.0833678 | − | 0.0345321i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.3848 | 1.06366 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.51472 | −0.312168 | −0.156084 | − | 0.987744i | \(-0.549887\pi\) | ||||
−0.156084 | + | 0.987744i | \(0.549887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.5355 | − | 7.67767i | −0.607478 | − | 0.251625i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.10051 | + | 2.65685i | 0.0360289 | + | 0.0869815i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.1421 | − | 26.1421i | 0.854939 | − | 0.854939i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.0000 | + | 19.0000i | 0.620703 | + | 0.620703i | 0.945711 | − | 0.325008i | \(-0.105367\pi\) |
−0.325008 | + | 0.945711i | \(0.605367\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.48528 | + | 3.10051i | −0.244273 | + | 0.101181i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.636039 | − | 1.53553i | 0.0207343 | − | 0.0500570i | −0.913173 | − | 0.407571i | \(-0.866376\pi\) |
0.933908 | + | 0.357514i | \(0.116376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.00000i | 0.0651290i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.1716i | 0.558591i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.33452 | + | 22.5355i | −0.303331 | + | 0.732306i | 0.696559 | + | 0.717499i | \(0.254713\pi\) |
−0.999890 | + | 0.0148070i | \(0.995287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.00000 | − | 2.89949i | 0.227230 | − | 0.0941216i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.1716 | + | 10.1716i | 0.329836 | + | 0.329836i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6569 | − | 14.6569i | 0.474782 | − | 0.474782i | −0.428676 | − | 0.903458i | \(-0.641020\pi\) |
0.903458 | + | 0.428676i | \(0.141020\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.4558 | + | 32.4853i | 0.435421 | + | 1.05120i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.6569 | − | 4.41421i | −0.344487 | − | 0.142691i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.3137 | 0.559089 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.94975 | − | 4.12132i | −0.320626 | − | 0.132808i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.69848 | − | 4.10051i | −0.0546762 | − | 0.132000i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.02944 | − | 6.02944i | 0.193894 | − | 0.193894i | −0.603483 | − | 0.797376i | \(-0.706221\pi\) |
0.797376 | + | 0.603483i | \(0.206221\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.14214 | + | 6.14214i | 0.197314 | + | 0.197314i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.3640 | + | 9.26346i | −0.717694 | + | 0.297278i | −0.711484 | − | 0.702702i | \(-0.751977\pi\) |
−0.00620964 | + | 0.999981i | \(0.501977\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.72792 | − | 18.6569i | 0.247746 | − | 0.598111i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.10051i | 0.0672700i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.1421i | 0.452447i | 0.974075 | + | 0.226224i | \(0.0726380\pi\) | ||||
−0.974075 | + | 0.226224i | \(0.927362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.8995 | − | 50.4558i | 0.667951 | − | 1.61258i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.2635 | − | 13.7782i | 1.06202 | − | 0.439903i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.6274 | + | 19.6274i | 0.626017 | + | 0.626017i | 0.947064 | − | 0.321046i | \(-0.104034\pi\) |
−0.321046 | + | 0.947064i | \(0.604034\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.1005 | + | 25.1005i | −0.799769 | + | 0.799769i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.142136 | − | 0.343146i | −0.00452423 | − | 0.0109224i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.7990 | + | 16.0711i | 1.23374 | + | 0.511030i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.07107 | 0.0339893 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61.1421 | + | 25.3259i | 1.93834 | + | 0.802885i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.1924 | − | 48.7487i | −0.639499 | − | 1.54389i | −0.827348 | − | 0.561690i | \(-0.810151\pi\) |
0.187848 | − | 0.982198i | \(-0.439849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.24264 | − | 2.24264i | 0.0709540 | − | 0.0709540i |
(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 | 128.2.g.a.81.1 | 4 | ||
3.2 | odd | 2 | 1152.2.v.a.721.1 | 4 | |||
4.3 | odd | 2 | 32.2.g.a.29.1 | yes | 4 | ||
8.3 | odd | 2 | 256.2.g.b.161.1 | 4 | |||
8.5 | even | 2 | 256.2.g.a.161.1 | 4 | |||
12.11 | even | 2 | 288.2.v.a.253.1 | 4 | |||
16.3 | odd | 4 | 512.2.g.d.65.1 | 4 | |||
16.5 | even | 4 | 512.2.g.c.65.1 | 4 | |||
16.11 | odd | 4 | 512.2.g.a.65.1 | 4 | |||
16.13 | even | 4 | 512.2.g.b.65.1 | 4 | |||
20.3 | even | 4 | 800.2.ba.b.349.1 | 4 | |||
20.7 | even | 4 | 800.2.ba.a.349.1 | 4 | |||
20.19 | odd | 2 | 800.2.y.a.701.1 | 4 | |||
32.3 | odd | 8 | 512.2.g.a.449.1 | 4 | |||
32.5 | even | 8 | 256.2.g.a.97.1 | 4 | |||
32.11 | odd | 8 | 32.2.g.a.21.1 | ✓ | 4 | ||
32.13 | even | 8 | 512.2.g.b.449.1 | 4 | |||
32.19 | odd | 8 | 512.2.g.d.449.1 | 4 | |||
32.21 | even | 8 | inner | 128.2.g.a.49.1 | 4 | ||
32.27 | odd | 8 | 256.2.g.b.97.1 | 4 | |||
32.29 | even | 8 | 512.2.g.c.449.1 | 4 | |||
64.11 | odd | 16 | 4096.2.a.e.1.2 | 4 | |||
64.21 | even | 16 | 4096.2.a.f.1.2 | 4 | |||
64.43 | odd | 16 | 4096.2.a.e.1.3 | 4 | |||
64.53 | even | 16 | 4096.2.a.f.1.3 | 4 | |||
96.11 | even | 8 | 288.2.v.a.181.1 | 4 | |||
96.53 | odd | 8 | 1152.2.v.a.433.1 | 4 | |||
160.43 | even | 8 | 800.2.ba.a.149.1 | 4 | |||
160.107 | even | 8 | 800.2.ba.b.149.1 | 4 | |||
160.139 | odd | 8 | 800.2.y.a.501.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.2.g.a.21.1 | ✓ | 4 | 32.11 | odd | 8 | ||
32.2.g.a.29.1 | yes | 4 | 4.3 | odd | 2 | ||
128.2.g.a.49.1 | 4 | 32.21 | even | 8 | inner | ||
128.2.g.a.81.1 | 4 | 1.1 | even | 1 | trivial | ||
256.2.g.a.97.1 | 4 | 32.5 | even | 8 | |||
256.2.g.a.161.1 | 4 | 8.5 | even | 2 | |||
256.2.g.b.97.1 | 4 | 32.27 | odd | 8 | |||
256.2.g.b.161.1 | 4 | 8.3 | odd | 2 | |||
288.2.v.a.181.1 | 4 | 96.11 | even | 8 | |||
288.2.v.a.253.1 | 4 | 12.11 | even | 2 | |||
512.2.g.a.65.1 | 4 | 16.11 | odd | 4 | |||
512.2.g.a.449.1 | 4 | 32.3 | odd | 8 | |||
512.2.g.b.65.1 | 4 | 16.13 | even | 4 | |||
512.2.g.b.449.1 | 4 | 32.13 | even | 8 | |||
512.2.g.c.65.1 | 4 | 16.5 | even | 4 | |||
512.2.g.c.449.1 | 4 | 32.29 | even | 8 | |||
512.2.g.d.65.1 | 4 | 16.3 | odd | 4 | |||
512.2.g.d.449.1 | 4 | 32.19 | odd | 8 | |||
800.2.y.a.501.1 | 4 | 160.139 | odd | 8 | |||
800.2.y.a.701.1 | 4 | 20.19 | odd | 2 | |||
800.2.ba.a.149.1 | 4 | 160.43 | even | 8 | |||
800.2.ba.a.349.1 | 4 | 20.7 | even | 4 | |||
800.2.ba.b.149.1 | 4 | 160.107 | even | 8 | |||
800.2.ba.b.349.1 | 4 | 20.3 | even | 4 | |||
1152.2.v.a.433.1 | 4 | 96.53 | odd | 8 | |||
1152.2.v.a.721.1 | 4 | 3.2 | odd | 2 | |||
4096.2.a.e.1.2 | 4 | 64.11 | odd | 16 | |||
4096.2.a.e.1.3 | 4 | 64.43 | odd | 16 | |||
4096.2.a.f.1.2 | 4 | 64.21 | even | 16 | |||
4096.2.a.f.1.3 | 4 | 64.53 | even | 16 |