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.d.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 | 0.894427 | − | 0.447214i | \(-0.147584\pi\) |
0.316228 | + | 0.948683i | \(0.397584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 1.00000i | −0.377964 | − | 0.377964i | 0.492403 | − | 0.870367i | \(-0.336119\pi\) |
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 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 | −0.282464 | − | 0.959278i | \(-0.591152\pi\) |
0.478580 | + | 0.878044i | \(0.341152\pi\) | |||||||
\(14\) | 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 | \(0.579134\pi\) |
−0.969256 | + | 0.246055i | \(0.920866\pi\) | |||||||
\(24\) | 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 | 0.997291 | − | 0.0735609i | \(-0.0234363\pi\) |
−0.757206 | + | 0.653176i | \(0.773436\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 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 | 0.440049 | − | 0.897974i | \(-0.354961\pi\) |
−0.323802 | + | 0.946125i | \(0.604961\pi\) | |||||||
\(38\) | 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 | \(0.00796701\pi\) | ||||
−0.999687 | + | 0.0250265i | \(0.992033\pi\) | |||||||
\(48\) | 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 | −0.888764 | − | 0.458364i | \(-0.848436\pi\) |
0.952564 | + | 0.304339i | \(0.0984356\pi\) | |||||||
\(54\) | 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 | 0.872125 | − | 0.489283i | \(-0.162741\pi\) |
−0.962661 | + | 0.270710i | \(0.912741\pi\) | |||||||
\(62\) | 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 | 0.962607 | − | 0.270900i | \(-0.0873214\pi\) |
−0.270900 | + | 0.962607i | \(0.587321\pi\) | |||||||
\(72\) | 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 | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(80\) | 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 | 0.212791 | − | 0.977098i | \(-0.431745\pi\) |
−0.540446 | + | 0.841379i | \(0.681745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.48528 | − | 9.48528i | −0.934613 | − | 0.934613i | 0.0633771 | − | 0.997990i | \(-0.479813\pi\) |
−0.997990 | + | 0.0633771i | \(0.979813\pi\) | |||||||
\(104\) | 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 | −0.927702 | − | 0.373320i | \(-0.878219\pi\) |
−0.392007 | + | 0.919962i | \(0.628219\pi\) | |||||||
\(110\) | 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 | \(-0.304817\pi\) | ||||
0.575476 | + | 0.817819i | \(0.304817\pi\) | |||||||
\(128\) | 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 | \(-0.631755\pi\) |
0.931792 | − | 0.362992i | \(-0.118245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.48528 | − | 1.48528i | 0.120870 | − | 0.120870i | −0.644084 | − | 0.764955i | \(-0.722761\pi\) |
0.764955 | + | 0.644084i | \(0.222761\pi\) | |||||||
\(152\) | 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 | 0.893148 | − | 0.449763i | \(-0.148491\pi\) |
−0.949581 | + | 0.313521i | \(0.898491\pi\) | |||||||
\(158\) | 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 | \(-0.953776\pi\) |
−0.144707 | − | 0.989475i | \(-0.546224\pi\) | |||||||
\(168\) | 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 | −0.0773656 | − | 0.997003i | \(-0.524651\pi\) |
0.650282 | + | 0.759693i | \(0.274651\pi\) | |||||||
\(174\) | 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 | \(0.350804\pi\) |
−0.950272 | + | 0.311420i | \(0.899196\pi\) | |||||||
\(182\) | 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 | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 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 | 0.743924 | − | 0.668264i | \(-0.232962\pi\) |
0.0535002 | + | 0.998568i | \(0.482962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.9706 | + | 15.9706i | 1.13212 | + | 1.13212i | 0.989824 | + | 0.142300i | \(0.0454496\pi\) |
0.142300 | + | 0.989824i | \(0.454550\pi\) | |||||||
\(200\) | 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 | \(-0.747775\pi\) | ||||
−0.702146 | + | 0.712033i | \(0.747775\pi\) | |||||||
\(224\) | 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 | −0.504076 | − | 0.863659i | \(-0.668167\pi\) |
−0.967135 | + | 0.254264i | \(0.918167\pi\) | |||||||
\(230\) | 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 | \(0.0549769\pi\) | ||||
−0.985122 | + | 0.171858i | \(0.945023\pi\) | |||||||
\(240\) | 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 | 0.863590 | − | 0.504194i | \(-0.168210\pi\) |
−0.504194 | + | 0.863590i | \(0.668210\pi\) | |||||||
\(264\) | 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 | 0.408401 | − | 0.912803i | \(-0.366087\pi\) |
0.934232 | + | 0.356666i | \(0.116087\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 14.7782 | − | 6.12132i | 0.891157 | − | 0.369130i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.707107 | + | 1.70711i | −0.0424859 | + | 0.102570i | −0.943698 | − | 0.330808i | \(-0.892679\pi\) |
0.901212 | + | 0.433378i | \(0.142679\pi\) | |||||||
\(278\) | 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 | 0.937656 | − | 0.347565i | \(-0.112991\pi\) |
0.417258 | + | 0.908788i | \(0.362991\pi\) | |||||||
\(294\) | 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 | −0.627755 | − | 0.778411i | \(-0.716026\pi\) |
0.778411 | + | 0.627755i | \(0.216026\pi\) | |||||||
\(312\) | 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 | \(-0.948015\pi\) |
0.582729 | − | 0.812667i | \(-0.301985\pi\) | |||||||
\(318\) | 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 | \(-0.871472\pi\) |
0.372419 | − | 0.928065i | \(-0.378528\pi\) | |||||||
\(350\) | 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 | 0.998351 | − | 0.0574027i | \(-0.0182819\pi\) |
−0.0574027 | + | 0.998351i | \(0.518282\pi\) | |||||||
\(360\) | 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 | \(0.0500529\pi\) | ||||
−0.987662 | + | 0.156599i | \(0.949947\pi\) | |||||||
\(368\) | 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 | −0.774239 | − | 0.632893i | \(-0.781867\pi\) |
0.994993 | + | 0.0999471i | \(0.0318673\pi\) | |||||||
\(374\) | 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 | \(-0.642749\pi\) | ||||
−0.433578 | + | 0.901116i | \(0.642749\pi\) | |||||||
\(384\) | 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 | −0.195625 | − | 0.980679i | \(-0.562674\pi\) |
−0.831773 | + | 0.555117i | \(0.812674\pi\) | |||||||
\(390\) | 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 | −0.863470 | − | 0.504400i | \(-0.831714\pi\) |
−0.253901 | + | 0.967230i | \(0.581714\pi\) | |||||||
\(398\) | 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 | 0.720831 | − | 0.693111i | \(-0.243760\pi\) |
0.0196009 | + | 0.999808i | \(0.493760\pi\) | |||||||
\(422\) | 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 | \(0.0960775\pi\) | ||||
−0.954792 | + | 0.297274i | \(0.903922\pi\) | |||||||
\(432\) | 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 | −0.173473 | − | 0.984839i | \(-0.555499\pi\) |
0.984839 | + | 0.173473i | \(0.0554989\pi\) | |||||||
\(440\) | 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 | −0.346638 | − | 0.937999i | \(-0.612677\pi\) |
0.418155 | + | 0.908376i | \(0.362677\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | −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 | \(-0.269772\pi\) | ||||
0.661849 | + | 0.749637i | \(0.269772\pi\) | |||||||
\(480\) | 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 | 0.910958 | − | 0.412500i | \(-0.135344\pi\) |
−0.412500 | + | 0.910958i | \(0.635344\pi\) | |||||||
\(488\) | 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 | −0.413638 | − | 0.910441i | \(-0.635742\pi\) |
0.910441 | + | 0.413638i | \(0.135742\pi\) | |||||||
\(504\) | 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 | \(0.0902660\pi\) |
−0.481021 | + | 0.876709i | \(0.659734\pi\) | |||||||
\(510\) | 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 | \(0.0937370\pi\) |
−0.471433 | + | 0.881902i | \(0.656263\pi\) | |||||||
\(542\) | 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 | 0.564077 | − | 0.825722i | \(-0.309232\pi\) |
0.982736 | + | 0.185012i | \(0.0592323\pi\) | |||||||
\(558\) | 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 | \(-0.470177\pi\) |
0.995614 | − | 0.0935555i | \(-0.0298232\pi\) | |||||||
\(600\) | 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 | \(-0.733327\pi\) | ||||
−0.669117 | + | 0.743157i | \(0.733327\pi\) | |||||||
\(608\) | 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 | 0.446220 | − | 0.894923i | \(-0.352770\pi\) |
−0.317281 | + | 0.948332i | \(0.602770\pi\) | |||||||
\(614\) | 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 | \(0.616721\pi\) |
−0.933519 | + | 0.358528i | \(0.883279\pi\) | |||||||
\(632\) | 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 | 0.575308 | − | 0.817937i | \(-0.304882\pi\) |
−0.817937 | + | 0.575308i | \(0.804882\pi\) | |||||||
\(648\) | 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 | −0.281672 | − | 0.959511i | \(-0.590889\pi\) |
0.479304 | + | 0.877649i | \(0.340889\pi\) | |||||||
\(654\) | 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 | \(-0.533335\pi\) |
0.777149 | − | 0.629316i | \(-0.216665\pi\) | |||||||
\(662\) | 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 | 0.961740 | − | 0.273964i | \(-0.0883351\pi\) |
0.486331 | + | 0.873775i | \(0.338335\pi\) | |||||||
\(678\) | 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 | 0.899761 | − | 0.436383i | \(-0.143741\pi\) |
−0.944797 | + | 0.327657i | \(0.893741\pi\) | |||||||
\(702\) | 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 | 0.743312 | − | 0.668945i | \(-0.233254\pi\) |
0.0525851 | + | 0.998616i | \(0.483254\pi\) | |||||||
\(710\) | 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 | \(-0.768479\pi\) | ||
0.746943 | − | 0.664888i | \(-0.231521\pi\) | |||||||
\(720\) | 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 | −0.497612 | − | 0.867400i | \(-0.665790\pi\) |
0.867400 | + | 0.497612i | \(0.165790\pi\) | |||||||
\(728\) | 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 | \(0.106535\pi\) |
−0.435604 | + | 0.900138i | \(0.643465\pi\) | |||||||
\(734\) | 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 | \(-0.943721\pi\) |
−0.175887 | − | 0.984410i | \(-0.556279\pi\) | |||||||
\(744\) | 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 | \(0.0641464\pi\) | ||||
−0.979763 | + | 0.200161i | \(0.935854\pi\) | |||||||
\(752\) | 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 | \(-0.647965\pi\) |
0.949062 | − | 0.315090i | \(-0.102035\pi\) | |||||||
\(758\) | 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 | 0.839884 | − | 0.542766i | \(-0.182623\pi\) |
0.210094 | + | 0.977681i | \(0.432623\pi\) | |||||||
\(774\) | 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 | \(0.0417348\pi\) |
−0.608592 | + | 0.793484i | \(0.708265\pi\) | |||||||
\(798\) | 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 | \(-0.741191\pi\) |
0.999617 | − | 0.0276723i | \(-0.00880950\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.9706 | + | 35.9706i | −1.25385 | + | 1.25385i | −0.299877 | + | 0.953978i | \(0.596946\pi\) |
−0.953978 | + | 0.299877i | \(0.903054\pi\) | |||||||
\(824\) | 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 | \(-0.902815\pi\) |
0.461853 | − | 0.886957i | \(-0.347185\pi\) | |||||||
\(830\) | 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 | 0.519850 | − | 0.854258i | \(-0.325988\pi\) |
−0.854258 | + | 0.519850i | \(0.825988\pi\) | |||||||
\(840\) | 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 | \(0.521958\pi\) |
−0.656686 | + | 0.754164i | \(0.728042\pi\) | |||||||
\(854\) | 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 | \(-0.378177\pi\) | ||||
0.373442 | + | 0.927653i | \(0.378177\pi\) | |||||||
\(864\) | 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 | −0.412504 | − | 0.910956i | \(-0.635346\pi\) |
0.352459 | + | 0.935827i | \(0.385346\pi\) | |||||||
\(878\) | 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 | −0.744882 | − | 0.667196i | \(-0.767494\pi\) |
0.667196 | + | 0.744882i | \(0.267494\pi\) | |||||||
\(888\) | 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 | \(-0.812115\pi\) | ||
0.830797 | − | 0.556575i | \(-0.187885\pi\) | |||||||
\(912\) | 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 | −0.552583 | − | 0.833458i | \(-0.686358\pi\) |
0.833458 | + | 0.552583i | \(0.186358\pi\) | |||||||
\(920\) | 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 | −0.357514 | − | 0.933908i | \(-0.616376\pi\) |
0.407571 | + | 0.913173i | \(0.366376\pi\) | |||||||
\(942\) | 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 | 0.797376 | − | 0.603483i | \(-0.206221\pi\) |
−0.603483 | + | 0.797376i | \(0.706221\pi\) | |||||||
\(968\) | 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 | −0.321046 | − | 0.947064i | \(-0.604034\pi\) |
0.947064 | + | 0.321046i | \(0.104034\pi\) | |||||||
\(984\) | 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 | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 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 | −0.561690 | − | 0.827348i | \(-0.689849\pi\) |
−0.982198 | + | 0.187848i | \(0.939849\pi\) | |||||||
\(998\) | 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.d.449.1 | 4 | ||
4.3 | odd | 2 | 512.2.g.b.449.1 | 4 | |||
8.3 | odd | 2 | 512.2.g.c.449.1 | 4 | |||
8.5 | even | 2 | 512.2.g.a.449.1 | 4 | |||
16.3 | odd | 4 | 128.2.g.a.49.1 | 4 | |||
16.5 | even | 4 | 256.2.g.b.97.1 | 4 | |||
16.11 | odd | 4 | 256.2.g.a.97.1 | 4 | |||
16.13 | even | 4 | 32.2.g.a.21.1 | ✓ | 4 | ||
32.3 | odd | 8 | 512.2.g.c.65.1 | 4 | |||
32.5 | even | 8 | 32.2.g.a.29.1 | yes | 4 | ||
32.11 | odd | 8 | 256.2.g.a.161.1 | 4 | |||
32.13 | even | 8 | inner | 512.2.g.d.65.1 | 4 | ||
32.19 | odd | 8 | 512.2.g.b.65.1 | 4 | |||
32.21 | even | 8 | 256.2.g.b.161.1 | 4 | |||
32.27 | odd | 8 | 128.2.g.a.81.1 | 4 | |||
32.29 | even | 8 | 512.2.g.a.65.1 | 4 | |||
48.29 | odd | 4 | 288.2.v.a.181.1 | 4 | |||
48.35 | even | 4 | 1152.2.v.a.433.1 | 4 | |||
64.13 | even | 16 | 4096.2.a.e.1.3 | 4 | |||
64.19 | odd | 16 | 4096.2.a.f.1.3 | 4 | |||
64.45 | even | 16 | 4096.2.a.e.1.2 | 4 | |||
64.51 | odd | 16 | 4096.2.a.f.1.2 | 4 | |||
80.13 | odd | 4 | 800.2.ba.a.149.1 | 4 | |||
80.29 | even | 4 | 800.2.y.a.501.1 | 4 | |||
80.77 | odd | 4 | 800.2.ba.b.149.1 | 4 | |||
96.5 | odd | 8 | 288.2.v.a.253.1 | 4 | |||
96.59 | even | 8 | 1152.2.v.a.721.1 | 4 | |||
160.37 | odd | 8 | 800.2.ba.a.349.1 | 4 | |||
160.69 | even | 8 | 800.2.y.a.701.1 | 4 | |||
160.133 | odd | 8 | 800.2.ba.b.349.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.2.g.a.21.1 | ✓ | 4 | 16.13 | even | 4 | ||
32.2.g.a.29.1 | yes | 4 | 32.5 | even | 8 | ||
128.2.g.a.49.1 | 4 | 16.3 | odd | 4 | |||
128.2.g.a.81.1 | 4 | 32.27 | odd | 8 | |||
256.2.g.a.97.1 | 4 | 16.11 | odd | 4 | |||
256.2.g.a.161.1 | 4 | 32.11 | odd | 8 | |||
256.2.g.b.97.1 | 4 | 16.5 | even | 4 | |||
256.2.g.b.161.1 | 4 | 32.21 | even | 8 | |||
288.2.v.a.181.1 | 4 | 48.29 | odd | 4 | |||
288.2.v.a.253.1 | 4 | 96.5 | odd | 8 | |||
512.2.g.a.65.1 | 4 | 32.29 | even | 8 | |||
512.2.g.a.449.1 | 4 | 8.5 | even | 2 | |||
512.2.g.b.65.1 | 4 | 32.19 | odd | 8 | |||
512.2.g.b.449.1 | 4 | 4.3 | odd | 2 | |||
512.2.g.c.65.1 | 4 | 32.3 | odd | 8 | |||
512.2.g.c.449.1 | 4 | 8.3 | odd | 2 | |||
512.2.g.d.65.1 | 4 | 32.13 | even | 8 | inner | ||
512.2.g.d.449.1 | 4 | 1.1 | even | 1 | trivial | ||
800.2.y.a.501.1 | 4 | 80.29 | even | 4 | |||
800.2.y.a.701.1 | 4 | 160.69 | even | 8 | |||
800.2.ba.a.149.1 | 4 | 80.13 | odd | 4 | |||
800.2.ba.a.349.1 | 4 | 160.37 | odd | 8 | |||
800.2.ba.b.149.1 | 4 | 80.77 | odd | 4 | |||
800.2.ba.b.349.1 | 4 | 160.133 | odd | 8 | |||
1152.2.v.a.433.1 | 4 | 48.35 | even | 4 | |||
1152.2.v.a.721.1 | 4 | 96.59 | even | 8 | |||
4096.2.a.e.1.2 | 4 | 64.45 | even | 16 | |||
4096.2.a.e.1.3 | 4 | 64.13 | even | 16 | |||
4096.2.a.f.1.2 | 4 | 64.51 | odd | 16 | |||
4096.2.a.f.1.3 | 4 | 64.19 | odd | 16 |