Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(65,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, 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("512.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.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: | \(4.08834058349\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 512.449 |
Dual form | 512.2.g.c.65.1 |
$q$-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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.292893 | + | 0.707107i | 0.169102 | + | 0.408248i | 0.985599 | − | 0.169102i | \(-0.0540867\pi\) |
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.70711 | − | 1.12132i | −1.21065 | − | 0.501470i | −0.316228 | − | 0.948683i | \(-0.602416\pi\) |
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.00000i | 0.377964 | + | 0.377964i | 0.870367 | − | 0.492403i | \(-0.163881\pi\) |
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.70711 | − | 1.70711i | 0.569036 | − | 0.569036i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.70711 | − | 4.12132i | 0.514712 | − | 1.24262i | −0.426401 | − | 0.904534i | \(-0.640219\pi\) |
0.941113 | − | 0.338091i | \(-0.109781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.707107 | + | 0.292893i | −0.196116 | + | 0.0812340i | −0.478580 | − | 0.878044i | \(-0.658848\pi\) |
0.282464 | + | 0.959278i | \(0.408848\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.24264i | − | 0.579047i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843i | 0.685994i | 0.939336 | + | 0.342997i | \(0.111442\pi\) | ||||
−0.939336 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.70711 | − | 1.53553i | 0.850469 | − | 0.352276i | 0.0854961 | − | 0.996339i | \(-0.472752\pi\) |
0.764973 | + | 0.644063i | \(0.222752\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.414214 | + | 1.00000i | −0.0903888 | + | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.82843 | − | 5.82843i | 1.21531 | − | 1.21531i | 0.246055 | − | 0.969256i | \(-0.420866\pi\) |
0.969256 | − | 0.246055i | \(-0.0791345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.53553 | + | 2.53553i | 0.507107 | + | 0.507107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.82843 | + | 1.58579i | 0.736781 | + | 0.305185i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.29289 | − | 3.12132i | −0.240084 | − | 0.579615i | 0.757206 | − | 0.653176i | \(-0.226564\pi\) |
−0.997291 | + | 0.0735609i | \(0.976564\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −1.58579 | − | 3.82843i | −0.268047 | − | 0.647122i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.707107 | − | 0.292893i | −0.116248 | − | 0.0481513i | 0.323802 | − | 0.946125i | \(-0.395039\pi\) |
−0.440049 | + | 0.897974i | \(0.645039\pi\) | |||||||
\(38\) | 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 | \(-0.743969\pi\) |
0.720377 | + | 0.693582i | \(0.243969\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.94975 | + | 4.70711i | −0.297334 | + | 0.717827i | 0.702647 | + | 0.711539i | \(0.252002\pi\) |
−0.999980 | + | 0.00628798i | \(0.997998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.53553 | + | 2.70711i | −0.974260 | + | 0.403552i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.343146i | − | 0.0500530i | −0.999687 | − | 0.0250265i | \(-0.992033\pi\) | ||
0.999687 | − | 0.0250265i | \(-0.00796701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 0.828427i | −0.280056 | + | 0.116003i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.464466 | + | 1.12132i | −0.0637993 | + | 0.154025i | −0.952564 | − | 0.304339i | \(-0.901564\pi\) |
0.888764 | + | 0.458364i | \(0.151564\pi\) | |||||||
\(54\) | 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 | ||||||||
\(59\) | −4.53553 | − | 1.87868i | −0.590476 | − | 0.244583i | 0.0673793 | − | 0.997727i | \(-0.478536\pi\) |
−0.657855 | + | 0.753144i | \(0.728536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.707107 | + | 1.70711i | 0.0905357 | + | 0.218573i | 0.962661 | − | 0.270710i | \(-0.0872585\pi\) |
−0.872125 | + | 0.489283i | \(0.837259\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.41421 | 0.430150 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.24264 | 0.278165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.29289 | + | 5.53553i | 0.280121 | + | 0.676273i | 0.999838 | − | 0.0179949i | \(-0.00572826\pi\) |
−0.719717 | + | 0.694268i | \(0.755728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.82843 | + | 2.41421i | 0.701660 | + | 0.290637i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.82843 | − | 5.82843i | −0.691707 | − | 0.691707i | 0.270900 | − | 0.962607i | \(-0.412679\pi\) |
−0.962607 | + | 0.270900i | \(0.912679\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | + | 7.00000i | −0.819288 | + | 0.819288i | −0.986005 | − | 0.166717i | \(-0.946683\pi\) |
0.166717 | + | 0.986005i | \(0.446683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.05025 | + | 2.53553i | −0.121273 | + | 0.292778i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.82843 | − | 2.41421i | 0.664211 | − | 0.275125i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000i | 0.675053i | 0.941316 | + | 0.337526i | \(0.109590\pi\) | ||||
−0.941316 | + | 0.337526i | \(0.890410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 4.07107i | − | 0.452341i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.53553 | − | 1.87868i | 0.497840 | − | 0.206212i | −0.119612 | − | 0.992821i | \(-0.538165\pi\) |
0.617452 | + | 0.786609i | \(0.288165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.17157 | − | 7.65685i | 0.344005 | − | 0.830502i | ||||
\(86\) | 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 | \(-0.474753\pi\) |
−0.996856 | + | 0.0792315i | \(0.974753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | − | 0.414214i | −0.104828 | − | 0.0434214i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.17157 | + | 2.82843i | 0.121486 | + | 0.293294i | ||||
\(94\) | 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 | ||||||||
\(99\) | −4.12132 | − | 9.94975i | −0.414208 | − | 0.999987i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.29289 | + | 1.36396i | 0.327655 | + | 0.135719i | 0.540446 | − | 0.841379i | \(-0.318255\pi\) |
−0.212791 | + | 0.977098i | \(0.568255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.48528 | + | 9.48528i | 0.934613 | + | 0.934613i | 0.997990 | − | 0.0633771i | \(-0.0201871\pi\) |
−0.0633771 | + | 0.997990i | \(0.520187\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.24264 | − | 2.24264i | 0.218859 | − | 0.218859i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.70711 | − | 4.12132i | 0.165032 | − | 0.398423i | −0.819630 | − | 0.572893i | \(-0.805821\pi\) |
0.984663 | + | 0.174470i | \(0.0558211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7782 | − | 5.70711i | 1.31971 | − | 0.546642i | 0.392007 | − | 0.919962i | \(-0.371781\pi\) |
0.927702 | + | 0.373320i | \(0.121781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.585786i | − | 0.0556004i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.34315i | 0.596713i | 0.954455 | + | 0.298356i | \(0.0964384\pi\) | ||||
−0.954455 | + | 0.298356i | \(0.903562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −22.3137 | + | 9.24264i | −2.08076 | + | 0.861881i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.707107 | + | 1.70711i | −0.0653720 | + | 0.157822i | ||||
\(118\) | 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 | ||||||||
\(123\) | 0.171573 | + | 0.0710678i | 0.0154702 | + | 0.00640797i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.58579 | + | 3.82843i | 0.141837 | + | 0.342425i | ||||
\(126\) | 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 | ||||||||
\(131\) | 6.77817 | + | 16.3640i | 0.592212 | + | 1.42973i | 0.881362 | + | 0.472442i | \(0.156627\pi\) |
−0.289150 | + | 0.957284i | \(0.593373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.24264 | + | 2.17157i | 0.454595 | + | 0.188299i | ||||
\(134\) | 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 | \(-0.574820\pi\) |
0.972502 | + | 0.232897i | \(0.0748204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.46447 | + | 13.1924i | −0.463490 | + | 1.11896i | 0.503465 | + | 0.864016i | \(0.332058\pi\) |
−0.966955 | + | 0.254948i | \(0.917942\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.242641 | − | 0.100505i | 0.0204340 | − | 0.00846405i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.41421i | 0.285511i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.89949i | 0.822108i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.53553 | − | 1.46447i | 0.291606 | − | 0.120787i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.46447 | + | 15.6066i | −0.529590 | + | 1.27854i | 0.402203 | + | 0.915551i | \(0.368245\pi\) |
−0.931792 | + | 0.362992i | \(0.881755\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.48528 | + | 1.48528i | −0.120870 | + | 0.120870i | −0.764955 | − | 0.644084i | \(-0.777239\pi\) |
0.644084 | + | 0.764955i | \(0.277239\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.82843 | + | 4.82843i | 0.390355 | + | 0.390355i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.8284 | − | 4.48528i | −0.869760 | − | 0.360266i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.707107 | + | 1.70711i | 0.0564333 | + | 0.136242i | 0.949581 | − | 0.313521i | \(-0.101509\pi\) |
−0.893148 | + | 0.449763i | \(0.851509\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.928932 | −0.0736691 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.6569 | 0.918689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.192388 | − | 0.464466i | −0.0150690 | − | 0.0363798i | 0.916166 | − | 0.400799i | \(-0.131267\pi\) |
−0.931235 | + | 0.364419i | \(0.881267\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.24264 | − | 3.82843i | −0.719539 | − | 0.298043i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.6569 | + | 14.6569i | 1.13418 | + | 1.13418i | 0.989475 | + | 0.144707i | \(0.0462239\pi\) |
0.144707 | + | 0.989475i | \(0.453776\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.77817 | + | 8.77817i | −0.675244 | + | 0.675244i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.70711 | − | 8.94975i | 0.283490 | − | 0.684404i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.53553 | + | 3.12132i | −0.572916 | + | 0.237310i | −0.650282 | − | 0.759693i | \(-0.725349\pi\) |
0.0773656 | + | 0.997003i | \(0.475349\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.07107i | 0.383337i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.75736i | − | 0.282420i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.94975 | + | 1.63604i | −0.295218 | + | 0.122283i | −0.525377 | − | 0.850870i | \(-0.676076\pi\) |
0.230159 | + | 0.973153i | \(0.426076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.70711 | − | 16.1924i | 0.498535 | − | 1.20357i | −0.451737 | − | 0.892151i | \(-0.649196\pi\) |
0.950272 | − | 0.311420i | \(-0.100804\pi\) | |||||||
\(182\) | 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 | ||||||||
\(187\) | 11.6569 | + | 4.82843i | 0.852434 | + | 0.353090i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.24264 | + | 5.41421i | 0.163128 | + | 0.393826i | ||||
\(190\) | 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 | ||||||||
\(195\) | 0.656854 | + | 1.58579i | 0.0470383 | + | 0.113561i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.1924 | − | 4.63604i | −0.797425 | − | 0.330304i | −0.0535002 | − | 0.998568i | \(-0.517038\pi\) |
−0.743924 | + | 0.668264i | \(0.767038\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.9706 | − | 15.9706i | −1.13212 | − | 1.13212i | −0.989824 | − | 0.142300i | \(-0.954550\pi\) |
−0.142300 | − | 0.989824i | \(-0.545450\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.24264 | + | 3.24264i | −0.228718 | + | 0.228718i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.82843 | − | 4.41421i | 0.128330 | − | 0.309817i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.656854 | + | 0.272078i | −0.0458767 | + | 0.0190027i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 19.8995i | − | 1.38311i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 17.8995i | − | 1.23813i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1924 | − | 7.53553i | 1.25242 | − | 0.518768i | 0.344842 | − | 0.938661i | \(-0.387932\pi\) |
0.907574 | + | 0.419893i | \(0.137932\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.41421 | − | 5.82843i | 0.165419 | − | 0.399357i | ||||
\(214\) | 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 | ||||||||
\(219\) | −7.00000 | − | 2.89949i | −0.473016 | − | 0.195930i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.828427 | − | 2.00000i | −0.0557260 | − | 0.134535i | ||||
\(222\) | 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 | ||||||||
\(227\) | −7.70711 | − | 18.6066i | −0.511539 | − | 1.23496i | −0.942988 | − | 0.332826i | \(-0.891998\pi\) |
0.431449 | − | 0.902137i | \(-0.358002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2635 | + | 9.22183i | 1.47121 | + | 0.609395i | 0.967135 | − | 0.254264i | \(-0.0818332\pi\) |
0.504076 | + | 0.863659i | \(0.331833\pi\) | |||||||
\(230\) | 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 | \(-0.710724\pi\) |
0.788759 | + | 0.614703i | \(0.210724\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.384776 | + | 0.928932i | −0.0251000 | + | 0.0605969i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.24264 | + | 1.75736i | −0.275589 | + | 0.114153i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.31371i | − | 0.343715i | −0.985122 | − | 0.171858i | \(-0.945023\pi\) | ||
0.985122 | − | 0.171858i | \(-0.0549769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.48528i | 0.546585i | 0.961931 | + | 0.273293i | \(0.0881127\pi\) | ||||
−0.961931 | + | 0.273293i | \(0.911887\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3640 | − | 5.94975i | 0.921449 | − | 0.381676i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.60660 | + | 13.5355i | −0.358193 | + | 0.864754i | ||||
\(246\) | 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 | ||||||||
\(251\) | 15.9497 | + | 6.60660i | 1.00674 | + | 0.417005i | 0.824264 | − | 0.566205i | \(-0.191589\pi\) |
0.182475 | + | 0.983210i | \(0.441589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.0711 | − | 33.9706i | −0.884640 | − | 2.13571i | ||||
\(254\) | 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 | ||||||||
\(259\) | −0.414214 | − | 1.00000i | −0.0257380 | − | 0.0621370i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.53553 | − | 3.12132i | −0.466438 | − | 0.193205i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.82843 | − | 5.82843i | −0.359396 | − | 0.359396i | 0.504194 | − | 0.863590i | \(-0.331790\pi\) |
−0.863590 | + | 0.504194i | \(0.831790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.51472 | − | 2.51472i | 0.154478 | − | 0.154478i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.58579 | − | 8.65685i | 0.219447 | − | 0.529791i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.0208 | + | 9.12132i | −1.34263 | + | 0.556137i | −0.934232 | − | 0.356666i | \(-0.883913\pi\) |
−0.408401 | + | 0.912803i | \(0.633913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0000i | 1.09342i | 0.837321 | + | 0.546711i | \(0.184120\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 0.828427i | − | 0.0501387i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.7782 | − | 6.12132i | 0.891157 | − | 0.369130i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.707107 | − | 1.70711i | 0.0424859 | − | 0.102570i | −0.901212 | − | 0.433378i | \(-0.857321\pi\) |
0.943698 | + | 0.330808i | \(0.107321\pi\) | |||||||
\(278\) | 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 | \(-0.0837184\pi\) |
−0.259987 | + | 0.965612i | \(0.583718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.9497 | + | 5.77817i | 0.829226 | + | 0.343477i | 0.756596 | − | 0.653882i | \(-0.226861\pi\) |
0.0726300 | + | 0.997359i | \(0.476861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.44365 | − | 8.31371i | −0.203984 | − | 0.492462i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.343146 | 0.0202553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.41421 | − | 13.0711i | −0.317387 | − | 0.766240i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.1924 | − | 9.60660i | −1.35491 | − | 0.561224i | −0.417258 | − | 0.908788i | \(-0.637009\pi\) |
−0.937656 | + | 0.347565i | \(0.887009\pi\) | |||||||
\(294\) | 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 | ||||||||
\(299\) | −2.41421 | + | 5.82843i | −0.139618 | + | 0.337067i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.65685 | + | 2.75736i | −0.383695 | + | 0.158932i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.72792i | 0.156715i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.41421i | − | 0.310017i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.7782 | + | 6.94975i | −0.957581 | + | 0.396643i | −0.806075 | − | 0.591813i | \(-0.798412\pi\) |
−0.151506 | + | 0.988456i | \(0.548412\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.92893 | + | 9.48528i | −0.223509 | + | 0.539599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.65685 | + | 2.65685i | −0.150656 | + | 0.150656i | −0.778411 | − | 0.627755i | \(-0.783974\pi\) |
0.627755 | + | 0.778411i | \(0.283974\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.48528 | + | 7.48528i | 0.423093 | + | 0.423093i | 0.886267 | − | 0.463174i | \(-0.153290\pi\) |
−0.463174 | + | 0.886267i | \(0.653290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.24264 | − | 3.82843i | −0.520764 | − | 0.215707i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.19239 | + | 17.3640i | 0.403965 | + | 0.975257i | 0.986694 | + | 0.162591i | \(0.0519850\pi\) |
−0.582729 | + | 0.812667i | \(0.698015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0711 | −0.843818 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.41421 | 0.190563 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.34315 | + | 10.4853i | 0.241659 | + | 0.583417i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.53553 | − | 1.05025i | −0.140646 | − | 0.0582575i | ||||
\(326\) | 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 | ||||||||
\(331\) | 0.535534 | − | 1.29289i | 0.0294356 | − | 0.0710638i | −0.908478 | − | 0.417932i | \(-0.862755\pi\) |
0.937914 | + | 0.346868i | \(0.112755\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.70711 | + | 0.707107i | −0.0935489 | + | 0.0387492i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 17.5563i | − | 0.959206i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9706i | 0.924445i | 0.886764 | + | 0.462223i | \(0.152948\pi\) | ||||
−0.886764 | + | 0.462223i | \(0.847052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.48528 | + | 1.85786i | −0.243607 | + | 0.100905i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.82843 | − | 16.4853i | 0.369780 | − | 0.892728i | ||||
\(342\) | 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 | ||||||||
\(347\) | 3.94975 | + | 1.63604i | 0.212034 | + | 0.0878272i | 0.486172 | − | 0.873863i | \(-0.338393\pi\) |
−0.274139 | + | 0.961690i | \(0.588393\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.2218 | + | 24.6777i | 0.547162 | + | 1.32097i | 0.919581 | + | 0.392901i | \(0.128528\pi\) |
−0.372419 | + | 0.928065i | \(0.621472\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 9.24264 | + | 22.3137i | 0.490548 | + | 1.18429i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.82843 | − | 1.17157i | −0.149696 | − | 0.0620062i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.8284 | − | 17.8284i | −0.940948 | − | 0.940948i | 0.0574027 | − | 0.998351i | \(-0.481718\pi\) |
−0.998351 | + | 0.0574027i | \(0.981718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.05025 | + | 2.05025i | −0.107908 | + | 0.107908i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.60660 | − | 6.29289i | 0.136811 | − | 0.330291i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.7990 | − | 11.1005i | 1.40272 | − | 0.581027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.00000i | − | 0.313197i | −0.987662 | − | 0.156599i | \(-0.949947\pi\) | ||
0.987662 | − | 0.156599i | \(-0.0500529\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.585786i | − | 0.0304948i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.58579 | + | 0.656854i | −0.0823299 | + | 0.0341022i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.26346 | + | 10.2929i | −0.220753 | + | 0.532946i | −0.994993 | − | 0.0999471i | \(-0.968133\pi\) |
0.774239 | + | 0.632893i | \(0.218133\pi\) | |||||||
\(374\) | 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 | ||||||||
\(379\) | −33.0208 | − | 13.6777i | −1.69617 | − | 0.702575i | −0.696281 | − | 0.717769i | \(-0.745163\pi\) |
−0.999885 | + | 0.0151948i | \(0.995163\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.79899 | − | 9.17157i | −0.194628 | − | 0.469874i | ||||
\(382\) | 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 | ||||||||
\(387\) | 4.70711 | + | 11.3640i | 0.239276 | + | 0.577663i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.2635 | + | 8.39340i | 1.02740 | + | 0.425562i | 0.831773 | − | 0.555117i | \(-0.187326\pi\) |
0.195625 | + | 0.980679i | \(0.437326\pi\) | |||||||
\(390\) | 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 | ||||||||
\(395\) | 6.72792 | − | 16.2426i | 0.338518 | − | 0.817256i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2635 | − | 9.22183i | 1.11737 | − | 0.462830i | 0.253901 | − | 0.967230i | \(-0.418286\pi\) |
0.863470 | + | 0.504400i | \(0.168286\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.34315i | 0.217429i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.82843i | 0.141245i | 0.997503 | + | 0.0706225i | \(0.0224986\pi\) | ||||
−0.997503 | + | 0.0706225i | \(0.977501\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.82843 | + | 1.17157i | −0.140894 | + | 0.0583602i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.56497 | + | 11.0208i | −0.226835 | + | 0.547629i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.41421 | + | 2.41421i | −0.119668 | + | 0.119668i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.4853 | − | 21.4853i | −1.06238 | − | 1.06238i | −0.997920 | − | 0.0644584i | \(-0.979468\pi\) |
−0.0644584 | − | 0.997920i | \(-0.520532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.65685 | + | 3.58579i | 0.427011 | + | 0.176874i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.65685 | − | 6.41421i | −0.130735 | − | 0.315623i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.3848 | −0.706121 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.9289 | −0.535192 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.22183 | − | 12.6066i | −0.255103 | − | 0.615873i | 0.743499 | − | 0.668737i | \(-0.233165\pi\) |
−0.998602 | + | 0.0528644i | \(0.983165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1924 | − | 6.29289i | −0.740432 | − | 0.306697i | −0.0196009 | − | 0.999808i | \(-0.506240\pi\) |
−0.720831 | + | 0.693111i | \(0.756240\pi\) | |||||||
\(422\) | 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 | ||||||||
\(427\) | −1.00000 | + | 2.41421i | −0.0483934 | + | 0.116832i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.41421 | + | 1.00000i | −0.116559 | + | 0.0482805i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.3431i | − | 0.594548i | −0.954792 | − | 0.297274i | \(-0.903922\pi\) | ||
0.954792 | − | 0.297274i | \(-0.0960775\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5147i | 0.745590i | 0.927914 | + | 0.372795i | \(0.121600\pi\) | ||||
−0.927914 | + | 0.372795i | \(0.878400\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.00000 | + | 2.89949i | −0.335624 | + | 0.139020i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.6569 | − | 30.5563i | 0.605459 | − | 1.46171i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.0000 | + | 17.0000i | −0.811366 | + | 0.811366i | −0.984839 | − | 0.173473i | \(-0.944501\pi\) |
0.173473 | + | 0.984839i | \(0.444501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.53553 | − | 8.53553i | −0.406454 | − | 0.406454i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.46447 | + | 0.606602i | 0.0695789 | + | 0.0288205i | 0.417201 | − | 0.908814i | \(-0.363011\pi\) |
−0.347623 | + | 0.937635i | \(0.613011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.7279 | + | 33.1421i | 0.650766 | + | 1.57109i | ||||
\(446\) | 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 | ||||||||
\(451\) | −0.414214 | − | 1.00000i | −0.0195046 | − | 0.0470882i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.48528 | − | 0.615224i | −0.0697846 | − | 0.0289057i | ||||
\(454\) | 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 | \(-0.670361\pi\) |
0.860164 | + | 0.510017i | \(0.170361\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.48528 | + | 10.8284i | −0.209355 | + | 0.505428i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.53553 | + | 0.636039i | −0.0715169 | + | 0.0296233i | −0.418155 | − | 0.908376i | \(-0.637323\pi\) |
0.346638 | + | 0.937999i | \(0.387323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.9706i | 1.06753i | 0.845632 | + | 0.533766i | \(0.179224\pi\) | ||||
−0.845632 | + | 0.533766i | \(0.820776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 8.97056i | − | 0.416000i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.9497 | + | 9.09188i | −1.01571 | + | 0.420722i | −0.827536 | − | 0.561413i | \(-0.810258\pi\) |
−0.188177 | + | 0.982135i | \(0.560258\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.24264 | + | 7.82843i | −0.149731 | + | 0.361483i | ||||
\(470\) | 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 | ||||||||
\(475\) | 13.2929 | + | 5.50610i | 0.609920 | + | 0.252637i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.12132 | + | 2.70711i | 0.0513417 | + | 0.123950i | ||||
\(478\) | 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 | ||||||||
\(483\) | 3.41421 | + | 8.24264i | 0.155352 | + | 0.375053i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 50.0416 | + | 20.7279i | 2.27227 | + | 0.941206i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0000 | − | 11.0000i | −0.498458 | − | 0.498458i | 0.412500 | − | 0.910958i | \(-0.364656\pi\) |
−0.910958 | + | 0.412500i | \(0.864656\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.272078 | − | 0.272078i | 0.0123038 | − | 0.0123038i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.2929 | + | 39.3345i | −0.735288 | + | 1.77514i | −0.111186 | + | 0.993800i | \(0.535465\pi\) |
−0.624102 | + | 0.781343i | \(0.714535\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.82843 | − | 3.65685i | 0.397612 | − | 0.164696i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 31.5563i | 1.41835i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 11.6569i | − | 0.522881i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.29289 | + | 0.949747i | −0.102644 | + | 0.0425165i | −0.433415 | − | 0.901195i | \(-0.642691\pi\) |
0.330771 | + | 0.943711i | \(0.392691\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.07107 | + | 14.6569i | −0.271235 | + | 0.654820i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.1421 | + | 11.1421i | −0.496803 | + | 0.496803i | −0.910441 | − | 0.413638i | \(-0.864258\pi\) |
0.413638 | + | 0.910441i | \(0.364258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.38478 | − | 7.38478i | −0.328618 | − | 0.328618i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.77817 | − | 3.63604i | −0.389852 | − | 0.161482i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.8076 | − | 26.0919i | −0.479039 | − | 1.15650i | −0.960060 | − | 0.279793i | \(-0.909734\pi\) |
0.481021 | − | 0.876709i | \(-0.340266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | −0.619324 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.6274 | 0.734118 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0416 | − | 36.3137i | −0.662813 | − | 1.60017i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.41421 | − | 0.585786i | −0.0621970 | − | 0.0257629i | ||||
\(518\) | 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 | \(-0.783026\pi\) |
0.630071 | + | 0.776537i | \(0.283026\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.94975 | + | 19.1924i | −0.347618 | + | 0.839225i | 0.649282 | + | 0.760548i | \(0.275070\pi\) |
−0.996900 | + | 0.0786768i | \(0.974930\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.58579 | + | 1.48528i | −0.156497 | + | 0.0648230i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.3137i | 0.492833i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 44.9411i | − | 1.95396i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.9497 | + | 4.53553i | −0.475179 | + | 0.196825i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0710678 | + | 0.171573i | −0.00307829 | + | 0.00743165i | ||||
\(534\) | 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 | ||||||||
\(539\) | −20.6066 | − | 8.53553i | −0.887589 | − | 0.367651i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2929 | − | 27.2635i | −0.485519 | − | 1.17215i | −0.956952 | − | 0.290246i | \(-0.906263\pi\) |
0.471433 | − | 0.881902i | \(-0.343737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.4142 | 0.575659 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −43.6985 | −1.87184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.26346 | + | 17.5355i | 0.310563 | + | 0.749765i | 0.999684 | + | 0.0251195i | \(0.00799662\pi\) |
−0.689122 | + | 0.724646i | \(0.742003\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.12132 | + | 1.70711i | 0.175894 | + | 0.0728575i | ||||
\(550\) | 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 | ||||||||
\(555\) | −0.656854 | + | 1.58579i | −0.0278819 | + | 0.0673129i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.5061 | + | 15.1213i | −1.54681 | + | 0.640711i | −0.982736 | − | 0.185012i | \(-0.940768\pi\) |
−0.564077 | + | 0.825722i | \(0.690768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.89949i | − | 0.164931i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.65685i | 0.407713i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.0208 | − | 7.87868i | 0.801632 | − | 0.332047i | 0.0560220 | − | 0.998430i | \(-0.482158\pi\) |
0.745610 | + | 0.666383i | \(0.232158\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.11270 | − | 17.1716i | 0.299233 | − | 0.722414i | ||||
\(566\) | 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 | \(-0.393068\pi\) |
−0.944102 | + | 0.329654i | \(0.893068\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.53553 | − | 2.70711i | −0.273504 | − | 0.113289i | 0.241716 | − | 0.970347i | \(-0.422290\pi\) |
−0.515220 | + | 0.857058i | \(0.672290\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.51472 | + | 8.48528i | 0.146829 | + | 0.354478i | ||||
\(574\) | 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 | ||||||||
\(579\) | −0.443651 | − | 1.07107i | −0.0184375 | − | 0.0445121i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.41421 | + | 2.65685i | 0.266106 | + | 0.110225i | ||||
\(582\) | 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 | ||||||||
\(587\) | 5.22183 | − | 12.6066i | 0.215528 | − | 0.520330i | −0.778728 | − | 0.627362i | \(-0.784135\pi\) |
0.994256 | + | 0.107032i | \(0.0341347\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8284 | − | 6.14214i | 0.610995 | − | 0.253082i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 9.27208i | − | 0.381402i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.2843i | 1.16150i | 0.814083 | + | 0.580748i | \(0.197240\pi\) | ||||
−0.814083 | + | 0.580748i | \(0.802760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.8284 | − | 4.48528i | 0.443922 | − | 0.183879i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.61522 | − | 15.9706i | 0.270743 | − | 0.653632i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6569 | + | 26.6569i | −1.08917 | + | 1.08917i | −0.0935555 | + | 0.995614i | \(0.529823\pi\) |
−0.995614 | + | 0.0935555i | \(0.970177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.9706 | + | 21.9706i | 0.896198 | + | 0.896198i | 0.995097 | − | 0.0988995i | \(-0.0315322\pi\) |
−0.0988995 | + | 0.995097i | \(0.531532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.3640 | + | 5.53553i | 0.544223 | + | 0.225424i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.97918 | + | 24.0919i | 0.405712 | + | 0.979474i | ||||
\(606\) | 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 | ||||||||
\(611\) | 0.100505 | + | 0.242641i | 0.00406600 | + | 0.00981619i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.19239 | − | 1.32233i | −0.128939 | − | 0.0534084i | 0.317281 | − | 0.948332i | \(-0.397230\pi\) |
−0.446220 | + | 0.894923i | \(0.647230\pi\) | |||||||
\(614\) | 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 | \(-0.974821\pi\) |
0.0790202 | + | 0.996873i | \(0.474821\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.02082 | − | 21.7782i | 0.362577 | − | 0.875339i | −0.632345 | − | 0.774687i | \(-0.717907\pi\) |
0.994922 | − | 0.100651i | \(-0.0320927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.5563 | − | 13.0711i | 1.26631 | − | 0.524524i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 17.3137i | − | 0.693659i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 30.0711i | − | 1.20284i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.6569 | − | 5.24264i | 0.505466 | − | 0.209371i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.828427 | − | 2.00000i | 0.0330316 | − | 0.0797452i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4558 | − | 32.4558i | 1.29205 | − | 1.29205i | 0.358528 | − | 0.933519i | \(-0.383279\pi\) |
0.933519 | − | 0.358528i | \(-0.116721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.6569 | + | 10.6569i | 0.423572 | + | 0.423572i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.1127 | + | 14.5442i | 1.39340 | + | 0.577167i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.46447 | + | 3.53553i | 0.0580243 | + | 0.140083i | ||||
\(638\) | 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 | ||||||||
\(643\) | −4.73654 | − | 11.4350i | −0.186791 | − | 0.450954i | 0.802547 | − | 0.596588i | \(-0.203478\pi\) |
−0.989338 | + | 0.145635i | \(0.953478\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.5563 | + | 4.37258i | 0.415656 | + | 0.172170i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.17157 | + | 6.17157i | 0.242630 | + | 0.242630i | 0.817937 | − | 0.575308i | \(-0.195118\pi\) |
−0.575308 | + | 0.817937i | \(0.695118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.4853 | + | 15.4853i | −0.607850 | + | 0.607850i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.65685 | + | 4.00000i | −0.0649372 | + | 0.156772i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.05025 | + | 2.09188i | −0.197632 | + | 0.0818617i | −0.479304 | − | 0.877649i | \(-0.659111\pi\) |
0.281672 | + | 0.959511i | \(0.409111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 51.8995i | − | 2.02788i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.8995i | 0.932408i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.4350 | + | 10.1213i | −0.951854 | + | 0.394271i | −0.803927 | − | 0.594728i | \(-0.797260\pi\) |
−0.147926 | + | 0.988998i | \(0.547260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.2929 | + | 41.7487i | −0.672616 | + | 1.62384i | 0.104534 | + | 0.994521i | \(0.466665\pi\) |
−0.777149 | + | 0.629316i | \(0.783335\pi\) | |||||||
\(662\) | 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 | ||||||||
\(667\) | −25.7279 | − | 10.6569i | −0.996189 | − | 0.412635i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.14214 | + | 14.8284i | 0.237469 | + | 0.573300i | ||||
\(670\) | 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 | ||||||||
\(675\) | 5.68629 | + | 13.7279i | 0.218865 | + | 0.528388i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.6777 | − | 15.6066i | −1.44807 | − | 0.599810i | −0.486331 | − | 0.873775i | \(-0.661665\pi\) |
−0.961740 | + | 0.273964i | \(0.911665\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 4.19239 | − | 10.1213i | 0.160417 | − | 0.387282i | −0.823150 | − | 0.567824i | \(-0.807785\pi\) |
0.983567 | + | 0.180543i | \(0.0577854\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.1421 | + | 13.7279i | −1.26630 | + | 0.524517i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.4437i | 0.703669i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.928932i | − | 0.0353895i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.1924 | − | 12.5061i | 1.14857 | − | 0.475754i | 0.274518 | − | 0.961582i | \(-0.411482\pi\) |
0.874055 | + | 0.485828i | \(0.161482\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.82843 | − | 14.0711i | 0.221404 | − | 0.534516i | ||||
\(694\) | 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 | ||||||||
\(699\) | 2.65685 | + | 1.10051i | 0.100491 | + | 0.0416249i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.19239 | + | 2.87868i | 0.0450359 | + | 0.108726i | 0.944797 | − | 0.327657i | \(-0.106259\pi\) |
−0.899761 | + | 0.436383i | \(0.856259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.07107 | −0.115828 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.769553 | −0.0289830 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.92893 | + | 4.65685i | 0.0725450 | + | 0.175139i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.1924 | − | 8.77817i | −0.795897 | − | 0.329671i | −0.0525851 | − | 0.998616i | \(-0.516746\pi\) |
−0.743312 | + | 0.668945i | \(0.766746\pi\) | |||||||
\(710\) | 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 | ||||||||
\(715\) | 3.82843 | − | 9.24264i | 0.143175 | − | 0.345655i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.75736 | − | 1.55635i | 0.140321 | − | 0.0581229i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.6569i | 1.32978i | 0.746943 | + | 0.664888i | \(0.231521\pi\) | ||||
−0.746943 | + | 0.664888i | \(0.768479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9706i | 0.706501i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.00000 | + | 2.48528i | −0.223142 | + | 0.0924286i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.63604 | − | 11.1924i | 0.172178 | − | 0.415675i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.97056 | + | 9.97056i | −0.369788 | + | 0.369788i | −0.867400 | − | 0.497612i | \(-0.834210\pi\) |
0.497612 | + | 0.867400i | \(0.334210\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.221825 | − | 0.221825i | −0.00821576 | − | 0.00821576i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.3137 | − | 5.51472i | −0.492425 | − | 0.203969i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.7782 | − | 33.2635i | −0.508908 | − | 1.22861i | −0.944513 | − | 0.328475i | \(-0.893465\pi\) |
0.435604 | − | 0.900138i | \(-0.356535\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.2132 | −0.413605 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.7279 | 0.984536 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.192388 | − | 0.464466i | −0.00707711 | − | 0.0170857i | 0.920301 | − | 0.391210i | \(-0.127943\pi\) |
−0.927379 | + | 0.374124i | \(0.877943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.17157 | − | 0.899495i | −0.0797747 | − | 0.0330438i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.6274 | + | 31.6274i | 1.16030 | + | 1.16030i | 0.984410 | + | 0.175887i | \(0.0562793\pi\) |
0.175887 | + | 0.984410i | \(0.443721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.0000 | − | 35.0000i | 1.28230 | − | 1.28230i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.53553 | − | 10.9497i | 0.165947 | − | 0.400630i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.82843 | − | 2.41421i | 0.212966 | − | 0.0882134i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 10.9706i | − | 0.400322i | −0.979763 | − | 0.200161i | \(-0.935854\pi\) | ||
0.979763 | − | 0.200161i | \(-0.0641464\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.2132i | 0.481516i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.68629 | − | 2.35534i | 0.206945 | − | 0.0857196i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.7782 | + | 33.2635i | −0.500776 | + | 1.20898i | 0.448285 | + | 0.893890i | \(0.352035\pi\) |
−0.949062 | + | 0.315090i | \(0.897965\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.8995 | − | 19.8995i | 0.722306 | − | 0.722306i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.8284 | + | 29.8284i | 1.08128 | + | 1.08128i | 0.996390 | + | 0.0848892i | \(0.0270536\pi\) |
0.0848892 | + | 0.996390i | \(0.472946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.4853 | + | 8.07107i | 0.705415 | + | 0.292192i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.65685 | − | 18.4853i | −0.276834 | − | 0.668337i | ||||
\(766\) | 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 | ||||||||
\(771\) | 1.75736 | + | 4.24264i | 0.0632897 | + | 0.152795i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.1924 | − | 12.0919i | −1.04998 | − | 0.434915i | −0.210094 | − | 0.977681i | \(-0.567377\pi\) |
−0.839884 | + | 0.542766i | \(0.817377\pi\) | |||||||
\(774\) | 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 | ||||||||
\(779\) | 0.372583 | − | 0.899495i | 0.0133492 | − | 0.0322278i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.9706 | + | 14.0711i | −1.21556 | + | 0.503502i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 14.0000i | − | 0.500319i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.41421i | − | 0.193242i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.29289 | + | 0.949747i | −0.0817328 | + | 0.0338548i | −0.423175 | − | 0.906048i | \(-0.639085\pi\) |
0.341442 | + | 0.939903i | \(0.389085\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.41421 | − | 5.82843i | 0.0859483 | − | 0.207498i | ||||
\(790\) | 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 | ||||||||
\(795\) | 2.51472 | + | 1.04163i | 0.0891879 | + | 0.0369428i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.8076 | − | 26.0919i | −0.382825 | − | 0.924222i | −0.991417 | − | 0.130738i | \(-0.958265\pi\) |
0.608592 | − | 0.793484i | \(-0.291735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.970563 | 0.0343360 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.5563 | −1.04432 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.8995 | + | 40.7990i | 0.596370 | + | 1.43977i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.5563 | − | 13.0711i | −1.11222 | − | 0.460695i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.8995 | − | 12.8995i | −0.454084 | − | 0.454084i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.1421 | − | 29.1421i | 1.02458 | − | 1.02458i | 0.0248928 | − | 0.999690i | \(-0.492076\pi\) |
0.999690 | − | 0.0248928i | \(-0.00792444\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.5061 | − | 42.2635i | 0.614722 | − | 1.48407i | −0.243036 | − | 0.970017i | \(-0.578143\pi\) |
0.857758 | − | 0.514053i | \(-0.171857\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.7279 | + | 5.27208i | −0.446388 | + | 0.184900i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.47309i | 0.0516000i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.4437i | 0.715233i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.41421 | + | 1.00000i | −0.0843594 | + | 0.0349428i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.94975 | + | 21.6066i | −0.312348 | + | 0.754076i | 0.687269 | + | 0.726403i | \(0.258809\pi\) |
−0.999617 | + | 0.0276723i | \(0.991191\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.9706 | − | 35.9706i | 1.25385 | − | 1.25385i | 0.299877 | − | 0.953978i | \(-0.403054\pi\) |
0.953978 | − | 0.299877i | \(-0.0969457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.65685 | + | 8.65685i | 0.301393 | + | 0.301393i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.9203 | + | 16.1213i | 1.35339 | + | 0.560593i | 0.937235 | − | 0.348699i | \(-0.113377\pi\) |
0.416157 | + | 0.909293i | \(0.363377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.1630 | + | 34.1924i | 0.491900 | + | 1.18755i | 0.953752 | + | 0.300594i | \(0.0971849\pi\) |
−0.461853 | + | 0.886957i | \(0.652815\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41421 | 0.0490585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.1421 | 0.489996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.2426 | − | 56.1127i | −0.804345 | − | 1.94186i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.3137 | + | 6.34315i | 0.529319 | + | 0.219251i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.68629 | + | 9.68629i | 0.334408 | + | 0.334408i | 0.854258 | − | 0.519850i | \(-0.174012\pi\) |
−0.519850 | + | 0.854258i | \(0.674012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4350 | − | 12.4350i | 0.428794 | − | 0.428794i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.89949 | + | 11.8284i | −0.168748 | + | 0.407393i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33.6066 | − | 13.9203i | 1.15610 | − | 0.478873i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.5858i | − | 0.432453i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.5563i | 0.396613i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.82843 | + | 2.41421i | −0.199796 | + | 0.0827582i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.1924 | − | 51.1630i | 0.725614 | − | 1.75179i | 0.0689279 | − | 0.997622i | \(-0.478042\pi\) |
0.656686 | − | 0.754164i | \(-0.271958\pi\) | |||||||
\(854\) | 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 | \(-0.325170\pi\) |
−0.852920 | + | 0.522042i | \(0.825170\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.05025 | − | 1.67767i | −0.138193 | − | 0.0572413i | 0.312515 | − | 0.949913i | \(-0.398828\pi\) |
−0.450708 | + | 0.892671i | \(0.648828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.100505 | + | 0.242641i | 0.00342520 | + | 0.00826917i | ||||
\(862\) | 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 | ||||||||
\(867\) | 2.63604 | + | 6.36396i | 0.0895246 | + | 0.216131i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.7279 | + | 10.2426i | 0.838837 | + | 0.347458i | ||||
\(870\) | 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 | ||||||||
\(875\) | −2.24264 | + | 5.41421i | −0.0758151 | + | 0.183034i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.77817 | − | 0.736544i | 0.0600447 | − | 0.0248713i | −0.352459 | − | 0.935827i | \(-0.614654\pi\) |
0.412504 | + | 0.910956i | \(0.364654\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 19.2132i | − | 0.648045i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22.6274i | − | 0.762337i | −0.924506 | − | 0.381169i | \(-0.875522\pi\) | ||
0.924506 | − | 0.381169i | \(-0.124478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.6482 | − | 20.5650i | 1.67080 | − | 0.692066i | 0.671973 | − | 0.740575i | \(-0.265447\pi\) |
0.998823 | + | 0.0485090i | \(0.0154470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.21320 | + | 10.1716i | −0.141625 | + | 0.341914i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.31371 | − | 2.31371i | 0.0776867 | − | 0.0776867i | −0.667196 | − | 0.744882i | \(-0.732506\pi\) |
0.744882 | + | 0.667196i | \(0.232506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9706 | − | 12.9706i | −0.435019 | − | 0.435019i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.7782 | − | 6.94975i | −0.562090 | − | 0.232825i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.526912 | − | 1.27208i | −0.0176324 | − | 0.0425685i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.5269 | 0.418728 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.82843 | −0.161216 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.17157 | − | 12.4853i | −0.172482 | − | 0.416407i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.17157 | − | 1.31371i | −0.105660 | − | 0.0437660i | ||||
\(902\) | 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 | ||||||||
\(907\) | 6.53553 | − | 15.7782i | 0.217009 | − | 0.523906i | −0.777461 | − | 0.628932i | \(-0.783493\pi\) |
0.994469 | + | 0.105026i | \(0.0334925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.94975 | − | 3.29289i | 0.263676 | − | 0.109218i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.5980i | 1.11315i | 0.830797 | + | 0.556575i | \(0.187885\pi\) | ||||
−0.830797 | + | 0.556575i | \(0.812115\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 21.8995i | − | 0.724767i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.82843 | − | 1.58579i | 0.126564 | − | 0.0524245i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.58579 | + | 23.1421i | −0.316551 | + | 0.764221i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.51472 | + | 8.51472i | −0.280875 | + | 0.280875i | −0.833458 | − | 0.552583i | \(-0.813642\pi\) |
0.552583 | + | 0.833458i | \(0.313642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.82843 | − | 9.82843i | −0.323858 | − | 0.323858i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.82843 | + | 2.41421i | 0.191845 | + | 0.0794648i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05025 | − | 2.53553i | −0.0345321 | − | 0.0833678i | ||||
\(926\) | 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 | ||||||||
\(931\) | −7.67767 | − | 18.5355i | −0.251625 | − | 0.607478i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.65685 | − | 1.10051i | −0.0869815 | − | 0.0360289i | ||||
\(934\) | 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 | \(-0.894633\pi\) |
0.325008 | + | 0.945711i | \(0.394633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.10051 | + | 7.48528i | −0.101181 | + | 0.244273i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.53553 | + | 0.636039i | −0.0500570 | + | 0.0207343i | −0.407571 | − | 0.913173i | \(-0.633624\pi\) |
0.357514 | + | 0.933908i | \(0.383624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.00000i | − | 0.0651290i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 17.1716i | − | 0.558591i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.5355 | − | 9.33452i | 0.732306 | − | 0.303331i | 0.0148070 | − | 0.999890i | \(-0.495287\pi\) |
0.717499 | + | 0.696559i | \(0.245287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.89949 | − | 7.00000i | 0.0941216 | − | 0.227230i | ||||
\(950\) | 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 | \(-0.358980\pi\) |
−0.903458 | + | 0.428676i | \(0.858980\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.4853 | − | 13.4558i | −1.05120 | − | 0.435421i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.41421 | − | 10.6569i | −0.142691 | − | 0.344487i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.3137 | 0.559089 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.12132 | − | 9.94975i | −0.132808 | − | 0.320626i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.10051 | + | 1.69848i | 0.132000 | + | 0.0546762i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.02944 | − | 6.02944i | −0.193894 | − | 0.193894i | 0.603483 | − | 0.797376i | \(-0.293779\pi\) |
−0.797376 | + | 0.603483i | \(0.793779\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.14214 | + | 6.14214i | −0.197314 | + | 0.197314i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.26346 | + | 22.3640i | −0.297278 | + | 0.717694i | 0.702702 | + | 0.711484i | \(0.251977\pi\) |
−0.999981 | + | 0.00620964i | \(0.998023\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.6569 | + | 7.72792i | −0.598111 | + | 0.247746i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 2.10051i | − | 0.0672700i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 14.1421i | − | 0.452447i | −0.974075 | − | 0.226224i | \(-0.927362\pi\) | ||
0.974075 | − | 0.226224i | \(-0.0726380\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −50.4558 | + | 20.8995i | −1.61258 | + | 0.667951i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.7782 | − | 33.2635i | 0.439903 | − | 1.06202i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.6274 | + | 19.6274i | −0.626017 | + | 0.626017i | −0.947064 | − | 0.321046i | \(-0.895966\pi\) |
0.321046 | + | 0.947064i | \(0.395966\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.1005 | + | 25.1005i | 0.799769 | + | 0.799769i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.343146 | + | 0.142136i | 0.0109224 | + | 0.00452423i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0711 | + | 38.7990i | 0.511030 | + | 1.23374i | ||||
\(990\) | 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 | ||||||||
\(995\) | 25.3259 | + | 61.1421i | 0.802885 | + | 1.93834i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.7487 | + | 20.1924i | 1.54389 | + | 0.639499i | 0.982198 | − | 0.187848i | \(-0.0601514\pi\) |
0.561690 | + | 0.827348i | \(0.310151\pi\) | |||||||
\(998\) | 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 | 512.2.g.c.449.1 | 4 | ||
4.3 | odd | 2 | 512.2.g.a.449.1 | 4 | |||
8.3 | odd | 2 | 512.2.g.d.449.1 | 4 | |||
8.5 | even | 2 | 512.2.g.b.449.1 | 4 | |||
16.3 | odd | 4 | 256.2.g.b.97.1 | 4 | |||
16.5 | even | 4 | 128.2.g.a.49.1 | 4 | |||
16.11 | odd | 4 | 32.2.g.a.21.1 | ✓ | 4 | ||
16.13 | even | 4 | 256.2.g.a.97.1 | 4 | |||
32.3 | odd | 8 | 512.2.g.d.65.1 | 4 | |||
32.5 | even | 8 | 256.2.g.a.161.1 | 4 | |||
32.11 | odd | 8 | 32.2.g.a.29.1 | yes | 4 | ||
32.13 | even | 8 | inner | 512.2.g.c.65.1 | 4 | ||
32.19 | odd | 8 | 512.2.g.a.65.1 | 4 | |||
32.21 | even | 8 | 128.2.g.a.81.1 | 4 | |||
32.27 | odd | 8 | 256.2.g.b.161.1 | 4 | |||
32.29 | even | 8 | 512.2.g.b.65.1 | 4 | |||
48.5 | odd | 4 | 1152.2.v.a.433.1 | 4 | |||
48.11 | even | 4 | 288.2.v.a.181.1 | 4 | |||
64.13 | even | 16 | 4096.2.a.f.1.3 | 4 | |||
64.19 | odd | 16 | 4096.2.a.e.1.3 | 4 | |||
64.45 | even | 16 | 4096.2.a.f.1.2 | 4 | |||
64.51 | odd | 16 | 4096.2.a.e.1.2 | 4 | |||
80.27 | even | 4 | 800.2.ba.b.149.1 | 4 | |||
80.43 | even | 4 | 800.2.ba.a.149.1 | 4 | |||
80.59 | odd | 4 | 800.2.y.a.501.1 | 4 | |||
96.11 | even | 8 | 288.2.v.a.253.1 | 4 | |||
96.53 | odd | 8 | 1152.2.v.a.721.1 | 4 | |||
160.43 | even | 8 | 800.2.ba.b.349.1 | 4 | |||
160.107 | even | 8 | 800.2.ba.a.349.1 | 4 | |||
160.139 | odd | 8 | 800.2.y.a.701.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.2.g.a.21.1 | ✓ | 4 | 16.11 | odd | 4 | ||
32.2.g.a.29.1 | yes | 4 | 32.11 | odd | 8 | ||
128.2.g.a.49.1 | 4 | 16.5 | even | 4 | |||
128.2.g.a.81.1 | 4 | 32.21 | even | 8 | |||
256.2.g.a.97.1 | 4 | 16.13 | even | 4 | |||
256.2.g.a.161.1 | 4 | 32.5 | even | 8 | |||
256.2.g.b.97.1 | 4 | 16.3 | odd | 4 | |||
256.2.g.b.161.1 | 4 | 32.27 | odd | 8 | |||
288.2.v.a.181.1 | 4 | 48.11 | even | 4 | |||
288.2.v.a.253.1 | 4 | 96.11 | even | 8 | |||
512.2.g.a.65.1 | 4 | 32.19 | odd | 8 | |||
512.2.g.a.449.1 | 4 | 4.3 | odd | 2 | |||
512.2.g.b.65.1 | 4 | 32.29 | even | 8 | |||
512.2.g.b.449.1 | 4 | 8.5 | even | 2 | |||
512.2.g.c.65.1 | 4 | 32.13 | even | 8 | inner | ||
512.2.g.c.449.1 | 4 | 1.1 | even | 1 | trivial | ||
512.2.g.d.65.1 | 4 | 32.3 | odd | 8 | |||
512.2.g.d.449.1 | 4 | 8.3 | odd | 2 | |||
800.2.y.a.501.1 | 4 | 80.59 | odd | 4 | |||
800.2.y.a.701.1 | 4 | 160.139 | odd | 8 | |||
800.2.ba.a.149.1 | 4 | 80.43 | even | 4 | |||
800.2.ba.a.349.1 | 4 | 160.107 | even | 8 | |||
800.2.ba.b.149.1 | 4 | 80.27 | even | 4 | |||
800.2.ba.b.349.1 | 4 | 160.43 | even | 8 | |||
1152.2.v.a.433.1 | 4 | 48.5 | odd | 4 | |||
1152.2.v.a.721.1 | 4 | 96.53 | odd | 8 | |||
4096.2.a.e.1.2 | 4 | 64.51 | odd | 16 | |||
4096.2.a.e.1.3 | 4 | 64.19 | odd | 16 | |||
4096.2.a.f.1.2 | 4 | 64.45 | even | 16 | |||
4096.2.a.f.1.3 | 4 | 64.13 | even | 16 |