Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), degree \(2\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.2.e.g.226.2 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.207107 | + | 0.358719i | 0.146447 | + | 0.253653i | 0.929912 | − | 0.367783i | \(-0.119883\pi\) |
−0.783465 | + | 0.621436i | \(0.786550\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.914214 | − | 1.58346i | 0.457107 | − | 0.791732i | ||||
\(5\) | 1.70711 | + | 2.95680i | 0.763441 | + | 1.32232i | 0.941067 | + | 0.338221i | \(0.109825\pi\) |
−0.177625 | + | 0.984098i | \(0.556842\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.707107 | + | 1.22474i | −0.223607 | + | 0.387298i | ||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.58579 | 0.717168 | 0.358584 | − | 0.933497i | \(-0.383260\pi\) | ||||
0.358584 | + | 0.933497i | \(0.383260\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | −1.12132 | + | 1.94218i | −0.271960 | + | 0.471049i | −0.969364 | − | 0.245630i | \(-0.921005\pi\) |
0.697404 | + | 0.716679i | \(0.254339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41421 | + | 2.44949i | 0.324443 | + | 0.561951i | 0.981399 | − | 0.191977i | \(-0.0614899\pi\) |
−0.656957 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(20\) | 6.24264 | 1.39590 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.828427 | −0.176621 | ||||||||
\(23\) | −3.82843 | − | 6.63103i | −0.798282 | − | 1.38267i | −0.920734 | − | 0.390191i | \(-0.872409\pi\) |
0.122452 | − | 0.992474i | \(-0.460924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.32843 | + | 5.76500i | −0.665685 | + | 1.15300i | ||||
\(26\) | 0.535534 | + | 0.927572i | 0.105027 | + | 0.181912i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.82843 | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.585786 | − | 1.01461i | 0.105210 | − | 0.182230i | −0.808614 | − | 0.588340i | \(-0.799782\pi\) |
0.913824 | + | 0.406110i | \(0.133115\pi\) | |||||||
\(32\) | 2.20711 | − | 3.82282i | 0.390165 | − | 0.675786i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.928932 | −0.159311 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | −0.585786 | + | 1.01461i | −0.0950271 | + | 0.164592i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.70711 | + | 4.68885i | 0.428031 | + | 0.741372i | ||||
\(41\) | −6.24264 | −0.974937 | −0.487468 | − | 0.873141i | \(-0.662080\pi\) | ||||
−0.487468 | + | 0.873141i | \(0.662080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | 1.82843 | + | 3.16693i | 0.275646 | + | 0.477432i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.58579 | − | 2.74666i | 0.233811 | − | 0.404973i | ||||
\(47\) | −1.41421 | − | 2.44949i | −0.206284 | − | 0.357295i | 0.744257 | − | 0.667893i | \(-0.232804\pi\) |
−0.950541 | + | 0.310599i | \(0.899470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.75736 | −0.389949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.36396 | − | 4.09450i | 0.327822 | − | 0.567805i | ||||
\(53\) | −1.00000 | + | 1.73205i | −0.137361 | + | 0.237915i | −0.926497 | − | 0.376303i | \(-0.877195\pi\) |
0.789136 | + | 0.614218i | \(0.210529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.82843 | −0.920745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.41421 | + | 2.44949i | 0.185695 | + | 0.321634i | ||||
\(59\) | −0.585786 | + | 1.01461i | −0.0762629 | + | 0.132091i | −0.901635 | − | 0.432498i | \(-0.857632\pi\) |
0.825372 | + | 0.564589i | \(0.190965\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.12132 | − | 10.6024i | −0.783755 | − | 1.35750i | −0.929740 | − | 0.368216i | \(-0.879969\pi\) |
0.145985 | − | 0.989287i | \(-0.453365\pi\) | |||||||
\(62\) | 0.485281 | 0.0616308 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 4.41421 | + | 7.64564i | 0.547516 | + | 0.948325i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.82843 | − | 4.89898i | 0.345547 | − | 0.598506i | −0.639906 | − | 0.768453i | \(-0.721027\pi\) |
0.985453 | + | 0.169948i | \(0.0543599\pi\) | |||||||
\(68\) | 2.05025 | + | 3.55114i | 0.248630 | + | 0.430639i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.31371 | −1.10533 | −0.552667 | − | 0.833402i | \(-0.686390\pi\) | ||||
−0.552667 | + | 0.833402i | \(0.686390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.94975 | + | 12.0373i | −0.813406 | + | 1.40886i | 0.0970601 | + | 0.995279i | \(0.469056\pi\) |
−0.910467 | + | 0.413583i | \(0.864277\pi\) | |||||||
\(74\) | −0.828427 | + | 1.43488i | −0.0963027 | + | 0.166801i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.17157 | 0.593220 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.82843 | − | 11.8272i | −0.768258 | − | 1.33066i | −0.938507 | − | 0.345261i | \(-0.887790\pi\) |
0.170249 | − | 0.985401i | \(-0.445543\pi\) | |||||||
\(80\) | 5.12132 | − | 8.87039i | 0.572581 | − | 0.991739i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.29289 | − | 2.23936i | −0.142776 | − | 0.247296i | ||||
\(83\) | −7.31371 | −0.802784 | −0.401392 | − | 0.915906i | \(-0.631473\pi\) | ||||
−0.401392 | + | 0.915906i | \(0.631473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | 1.17157 | + | 2.02922i | 0.126334 | + | 0.218817i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.58579 | + | 2.74666i | −0.169045 | + | 0.292795i | ||||
\(89\) | −7.12132 | − | 12.3345i | −0.754858 | − | 1.30745i | −0.945445 | − | 0.325783i | \(-0.894372\pi\) |
0.190586 | − | 0.981670i | \(-0.438961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.0000 | −1.45960 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.585786 | − | 1.01461i | 0.0604193 | − | 0.104649i | ||||
\(95\) | −4.82843 | + | 8.36308i | −0.495386 | + | 0.858034i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.58579 | 0.262547 | 0.131273 | − | 0.991346i | \(-0.458093\pi\) | ||||
0.131273 | + | 0.991346i | \(0.458093\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.08579 | + | 10.5409i | 0.608579 | + | 1.05409i | ||||
\(101\) | 1.46447 | − | 2.53653i | 0.145720 | − | 0.252394i | −0.783921 | − | 0.620860i | \(-0.786784\pi\) |
0.929641 | + | 0.368466i | \(0.120117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.24264 | − | 3.88437i | −0.220974 | − | 0.382738i | 0.734130 | − | 0.679009i | \(-0.237590\pi\) |
−0.955104 | + | 0.296271i | \(0.904257\pi\) | |||||||
\(104\) | 4.10051 | 0.402088 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.828427 | −0.0804640 | ||||||||
\(107\) | −0.171573 | − | 0.297173i | −0.0165866 | − | 0.0287288i | 0.857613 | − | 0.514296i | \(-0.171947\pi\) |
−0.874200 | + | 0.485567i | \(0.838613\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.82843 | − | 4.89898i | 0.270914 | − | 0.469237i | −0.698182 | − | 0.715920i | \(-0.746007\pi\) |
0.969096 | + | 0.246683i | \(0.0793407\pi\) | |||||||
\(110\) | −1.41421 | − | 2.44949i | −0.134840 | − | 0.233550i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.31371 | 0.499872 | 0.249936 | − | 0.968262i | \(-0.419590\pi\) | ||||
0.249936 | + | 0.968262i | \(0.419590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.0711 | − | 22.6398i | 1.21888 | − | 2.11117i | ||||
\(116\) | 6.24264 | − | 10.8126i | 0.579615 | − | 1.00392i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.485281 | −0.0446738 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 2.53553 | − | 4.39167i | 0.229556 | − | 0.397603i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.07107 | − | 1.85514i | −0.0961847 | − | 0.166597i | ||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.65685 | −0.147022 | −0.0735110 | − | 0.997294i | \(-0.523420\pi\) | ||||
−0.0735110 | + | 0.997294i | \(0.523420\pi\) | |||||||
\(128\) | −5.27817 | − | 9.14207i | −0.466529 | − | 0.808052i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.82843 | + | 3.16693i | −0.160364 | + | 0.277758i | ||||
\(131\) | −7.65685 | − | 13.2621i | −0.668982 | − | 1.15871i | −0.978189 | − | 0.207717i | \(-0.933397\pi\) |
0.309207 | − | 0.950995i | \(-0.399937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.34315 | 0.202417 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.77817 | + | 3.07989i | −0.152477 | + | 0.264098i | ||||
\(137\) | 7.07107 | − | 12.2474i | 0.604122 | − | 1.04637i | −0.388067 | − | 0.921631i | \(-0.626857\pi\) |
0.992190 | − | 0.124739i | \(-0.0398094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6569 | −1.49763 | −0.748817 | − | 0.662776i | \(-0.769378\pi\) | ||||
−0.748817 | + | 0.662776i | \(0.769378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.92893 | − | 3.34101i | −0.161872 | − | 0.280371i | ||||
\(143\) | −2.58579 | + | 4.47871i | −0.216234 | + | 0.374529i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.6569 | + | 20.1903i | 0.968049 | + | 1.67671i | ||||
\(146\) | −5.75736 | −0.476482 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.31371 | 0.601183 | ||||||||
\(149\) | 8.65685 | + | 14.9941i | 0.709197 | + | 1.22837i | 0.965155 | + | 0.261678i | \(0.0842757\pi\) |
−0.255958 | + | 0.966688i | \(0.582391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.00000 | + | 10.3923i | −0.488273 | + | 0.845714i | −0.999909 | − | 0.0134886i | \(-0.995706\pi\) |
0.511636 | + | 0.859202i | \(0.329040\pi\) | |||||||
\(152\) | 2.24264 | + | 3.88437i | 0.181902 | + | 0.315064i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.87868 | + | 10.1822i | −0.469170 | + | 0.812626i | −0.999379 | − | 0.0352411i | \(-0.988780\pi\) |
0.530209 | + | 0.847867i | \(0.322113\pi\) | |||||||
\(158\) | 2.82843 | − | 4.89898i | 0.225018 | − | 0.389742i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.0711 | 1.19147 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.65685 | + | 9.79796i | 0.443079 | + | 0.767435i | 0.997916 | − | 0.0645236i | \(-0.0205528\pi\) |
−0.554837 | + | 0.831959i | \(0.687219\pi\) | |||||||
\(164\) | −5.70711 | + | 9.88500i | −0.445650 | + | 0.771889i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.51472 | − | 2.62357i | −0.117565 | − | 0.203628i | ||||
\(167\) | 19.7990 | 1.53209 | 0.766046 | − | 0.642786i | \(-0.222221\pi\) | ||||
0.766046 | + | 0.642786i | \(0.222221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.31371 | −0.485670 | ||||||||
\(170\) | −1.58579 | − | 2.74666i | −0.121624 | − | 0.210659i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.17157 | − | 8.95743i | 0.394329 | − | 0.682997i | ||||
\(173\) | 10.5355 | + | 18.2481i | 0.801002 | + | 1.38738i | 0.918957 | + | 0.394357i | \(0.129033\pi\) |
−0.117956 | + | 0.993019i | \(0.537634\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.00000 | 0.452267 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.94975 | − | 5.10911i | 0.221093 | − | 0.382944i | ||||
\(179\) | −9.82843 | + | 17.0233i | −0.734611 | + | 1.27238i | 0.220283 | + | 0.975436i | \(0.429302\pi\) |
−0.954894 | + | 0.296948i | \(0.904031\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.58579 | −0.192200 | −0.0961000 | − | 0.995372i | \(-0.530637\pi\) | ||||
−0.0961000 | + | 0.995372i | \(0.530637\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.07107 | − | 10.5154i | −0.447565 | − | 0.775205i | ||||
\(185\) | −6.82843 | + | 11.8272i | −0.502036 | + | 0.869552i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.24264 | − | 3.88437i | −0.163998 | − | 0.284053i | ||||
\(188\) | −5.17157 | −0.377176 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | −9.00000 | − | 15.5885i | −0.651217 | − | 1.12794i | −0.982828 | − | 0.184525i | \(-0.940925\pi\) |
0.331611 | − | 0.943416i | \(-0.392408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.65685 | + | 4.60181i | −0.191245 | + | 0.331245i | −0.945663 | − | 0.325149i | \(-0.894586\pi\) |
0.754418 | + | 0.656394i | \(0.227919\pi\) | |||||||
\(194\) | 0.535534 | + | 0.927572i | 0.0384491 | + | 0.0665958i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.8284 | + | 18.7554i | −0.767607 | + | 1.32953i | 0.171250 | + | 0.985228i | \(0.445219\pi\) |
−0.938857 | + | 0.344307i | \(0.888114\pi\) | |||||||
\(200\) | −5.27817 | + | 9.14207i | −0.373223 | + | 0.646442i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.21320 | 0.0853607 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.6569 | − | 18.4582i | −0.744307 | − | 1.28918i | ||||
\(206\) | 0.928932 | − | 1.60896i | 0.0647218 | − | 0.112101i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.87868 | − | 6.71807i | −0.268938 | − | 0.465814i | ||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9706 | 0.892930 | 0.446465 | − | 0.894801i | \(-0.352683\pi\) | ||||
0.446465 | + | 0.894801i | \(0.352683\pi\) | |||||||
\(212\) | 1.82843 | + | 3.16693i | 0.125577 | + | 0.217506i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.0710678 | − | 0.123093i | 0.00485810 | − | 0.00841447i | ||||
\(215\) | 9.65685 | + | 16.7262i | 0.658592 | + | 1.14071i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.34315 | 0.158698 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.24264 | + | 10.8126i | −0.420879 | + | 0.728983i | ||||
\(221\) | −2.89949 | + | 5.02207i | −0.195041 | + | 0.337821i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.9706 | 1.67215 | 0.836076 | − | 0.548613i | \(-0.184844\pi\) | ||||
0.836076 | + | 0.548613i | \(0.184844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.10051 | + | 1.90613i | 0.0732045 | + | 0.126794i | ||||
\(227\) | 11.8995 | − | 20.6105i | 0.789797 | − | 1.36797i | −0.136294 | − | 0.990668i | \(-0.543519\pi\) |
0.926091 | − | 0.377300i | \(-0.123148\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.121320 | + | 0.210133i | 0.00801707 | + | 0.0138860i | 0.870006 | − | 0.493041i | \(-0.164115\pi\) |
−0.861989 | + | 0.506927i | \(0.830781\pi\) | |||||||
\(230\) | 10.8284 | 0.714005 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.8284 | 0.710921 | ||||||||
\(233\) | −3.07107 | − | 5.31925i | −0.201192 | − | 0.348475i | 0.747721 | − | 0.664014i | \(-0.231148\pi\) |
−0.948913 | + | 0.315538i | \(0.897815\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.82843 | − | 8.36308i | 0.314972 | − | 0.545547i | ||||
\(236\) | 1.07107 | + | 1.85514i | 0.0697206 | + | 0.120760i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6569 | 1.01276 | 0.506379 | − | 0.862311i | \(-0.330984\pi\) | ||||
0.506379 | + | 0.862311i | \(0.330984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.12132 | − | 14.0665i | 0.523140 | − | 0.906105i | −0.476497 | − | 0.879176i | \(-0.658094\pi\) |
0.999637 | − | 0.0269294i | \(-0.00857294\pi\) | |||||||
\(242\) | −1.44975 | + | 2.51104i | −0.0931933 | + | 0.161416i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −22.3848 | −1.43304 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.65685 | + | 6.33386i | 0.232680 | + | 0.403014i | ||||
\(248\) | 0.928932 | − | 1.60896i | 0.0589873 | − | 0.102169i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.17157 | − | 2.02922i | −0.0740968 | − | 0.128339i | ||||
\(251\) | 12.4853 | 0.788064 | 0.394032 | − | 0.919097i | \(-0.371080\pi\) | ||||
0.394032 | + | 0.919097i | \(0.371080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3137 | 0.962765 | ||||||||
\(254\) | −0.343146 | − | 0.594346i | −0.0215309 | − | 0.0372926i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.98528 | + | 3.43861i | −0.124080 | + | 0.214913i | ||||
\(257\) | 11.6066 | + | 20.1032i | 0.724000 | + | 1.25400i | 0.959384 | + | 0.282102i | \(0.0910318\pi\) |
−0.235384 | + | 0.971902i | \(0.575635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.1421 | 1.00109 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.17157 | − | 5.49333i | 0.195940 | − | 0.339379i | ||||
\(263\) | 2.65685 | − | 4.60181i | 0.163829 | − | 0.283760i | −0.772410 | − | 0.635124i | \(-0.780949\pi\) |
0.936239 | + | 0.351365i | \(0.114282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.82843 | −0.419467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.17157 | − | 8.95743i | −0.315904 | − | 0.547162i | ||||
\(269\) | −7.36396 | + | 12.7548i | −0.448989 | + | 0.777671i | −0.998320 | − | 0.0579332i | \(-0.981549\pi\) |
0.549332 | + | 0.835604i | \(0.314882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.07107 | + | 8.78335i | 0.308045 | + | 0.533550i | 0.977935 | − | 0.208911i | \(-0.0669918\pi\) |
−0.669889 | + | 0.742461i | \(0.733658\pi\) | |||||||
\(272\) | 6.72792 | 0.407940 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.85786 | 0.353887 | ||||||||
\(275\) | −6.65685 | − | 11.5300i | −0.401423 | − | 0.695286i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.65685 | − | 8.06591i | 0.279803 | − | 0.484633i | −0.691532 | − | 0.722345i | \(-0.743064\pi\) |
0.971336 | + | 0.237712i | \(0.0763974\pi\) | |||||||
\(278\) | −3.65685 | − | 6.33386i | −0.219324 | − | 0.379880i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.485281 | −0.0289495 | −0.0144747 | − | 0.999895i | \(-0.504608\pi\) | ||||
−0.0144747 | + | 0.999895i | \(0.504608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.24264 | − | 7.34847i | 0.252199 | − | 0.436821i | −0.711932 | − | 0.702248i | \(-0.752180\pi\) |
0.964131 | + | 0.265427i | \(0.0855130\pi\) | |||||||
\(284\) | −8.51472 | + | 14.7479i | −0.505256 | + | 0.875128i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.14214 | −0.126667 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.98528 | + | 10.3668i | 0.352075 | + | 0.609812i | ||||
\(290\) | −4.82843 | + | 8.36308i | −0.283535 | + | 0.491097i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.7071 | + | 22.0094i | 0.743627 | + | 1.28800i | ||||
\(293\) | −16.5858 | −0.968952 | −0.484476 | − | 0.874805i | \(-0.660990\pi\) | ||||
−0.484476 | + | 0.874805i | \(0.660990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 3.17157 | + | 5.49333i | 0.184344 | + | 0.319293i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.58579 | + | 6.21076i | −0.207719 | + | 0.359780i | ||||
\(299\) | −9.89949 | − | 17.1464i | −0.572503 | − | 0.991604i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.97056 | −0.286024 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.24264 | − | 7.34847i | 0.243332 | − | 0.421464i | ||||
\(305\) | 20.8995 | − | 36.1990i | 1.19670 | − | 2.07275i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.1421 | 1.72030 | 0.860151 | − | 0.510039i | \(-0.170369\pi\) | ||||
0.860151 | + | 0.510039i | \(0.170369\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.828427 | + | 1.43488i | 0.0470515 | + | 0.0814956i | ||||
\(311\) | 3.07107 | − | 5.31925i | 0.174144 | − | 0.301627i | −0.765721 | − | 0.643173i | \(-0.777617\pi\) |
0.939865 | + | 0.341547i | \(0.110951\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.949747 | − | 1.64501i | −0.0536829 | − | 0.0929815i | 0.837935 | − | 0.545770i | \(-0.183763\pi\) |
−0.891618 | + | 0.452788i | \(0.850429\pi\) | |||||||
\(314\) | −4.87006 | −0.274833 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.9706 | −1.40470 | ||||||||
\(317\) | 5.00000 | + | 8.66025i | 0.280828 | + | 0.486408i | 0.971589 | − | 0.236675i | \(-0.0760576\pi\) |
−0.690761 | + | 0.723083i | \(0.742724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.82843 | + | 11.8272i | −0.382319 | + | 0.662195i | ||||
\(320\) | −7.12132 | − | 12.3345i | −0.398094 | − | 0.689519i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.34315 | −0.352942 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.60660 | + | 14.9071i | −0.477408 | + | 0.826896i | ||||
\(326\) | −2.34315 | + | 4.05845i | −0.129775 | + | 0.224777i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.89949 | −0.546608 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | −6.68629 | + | 11.5810i | −0.366958 | + | 0.635590i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.10051 | + | 7.10228i | 0.224370 | + | 0.388620i | ||||
\(335\) | 19.3137 | 1.05522 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.6569 | −1.61551 | −0.807756 | − | 0.589517i | \(-0.799318\pi\) | ||||
−0.807756 | + | 0.589517i | \(0.799318\pi\) | |||||||
\(338\) | −1.30761 | − | 2.26485i | −0.0711247 | − | 0.123192i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.00000 | + | 12.1244i | −0.379628 | + | 0.657536i | ||||
\(341\) | 1.17157 | + | 2.02922i | 0.0634442 | + | 0.109889i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.97056 | 0.483660 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.36396 | + | 7.55860i | −0.234608 | + | 0.406353i | ||||
\(347\) | 16.6569 | − | 28.8505i | 0.894187 | − | 1.54878i | 0.0593789 | − | 0.998236i | \(-0.481088\pi\) |
0.834808 | − | 0.550541i | \(-0.185579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.89949 | −0.529908 | −0.264954 | − | 0.964261i | \(-0.585357\pi\) | ||||
−0.264954 | + | 0.964261i | \(0.585357\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.41421 | + | 7.64564i | 0.235278 | + | 0.407514i | ||||
\(353\) | −7.36396 | + | 12.7548i | −0.391944 | + | 0.678867i | −0.992706 | − | 0.120561i | \(-0.961531\pi\) |
0.600762 | + | 0.799428i | \(0.294864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.8995 | − | 27.5387i | −0.843858 | − | 1.46160i | ||||
\(356\) | −26.0416 | −1.38020 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.14214 | −0.430325 | ||||||||
\(359\) | −0.171573 | − | 0.297173i | −0.00905527 | − | 0.0156842i | 0.861462 | − | 0.507822i | \(-0.169549\pi\) |
−0.870518 | + | 0.492137i | \(0.836216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | ||||
\(362\) | −0.535534 | − | 0.927572i | −0.0281470 | − | 0.0487521i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −47.4558 | −2.48395 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.65685 | − | 2.86976i | 0.0864871 | − | 0.149800i | −0.819537 | − | 0.573027i | \(-0.805769\pi\) |
0.906024 | + | 0.423226i | \(0.139103\pi\) | |||||||
\(368\) | −11.4853 | + | 19.8931i | −0.598712 | + | 1.03700i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.65685 | −0.294086 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.34315 | + | 9.25460i | 0.276658 | + | 0.479185i | 0.970552 | − | 0.240892i | \(-0.0774399\pi\) |
−0.693894 | + | 0.720077i | \(0.744107\pi\) | |||||||
\(374\) | 0.928932 | − | 1.60896i | 0.0480339 | − | 0.0831972i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.24264 | − | 3.88437i | −0.115655 | − | 0.200321i | ||||
\(377\) | 17.6569 | 0.909374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.68629 | 0.446185 | 0.223092 | − | 0.974797i | \(-0.428385\pi\) | ||||
0.223092 | + | 0.974797i | \(0.428385\pi\) | |||||||
\(380\) | 8.82843 | + | 15.2913i | 0.452889 | + | 0.784426i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.72792 | − | 6.45695i | 0.190737 | − | 0.330366i | ||||
\(383\) | −9.17157 | − | 15.8856i | −0.468645 | − | 0.811718i | 0.530712 | − | 0.847552i | \(-0.321924\pi\) |
−0.999358 | + | 0.0358343i | \(0.988591\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.20101 | −0.112028 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.36396 | − | 4.09450i | 0.120012 | − | 0.207867i | ||||
\(389\) | −9.07107 | + | 15.7116i | −0.459921 | + | 0.796607i | −0.998956 | − | 0.0456762i | \(-0.985456\pi\) |
0.539035 | + | 0.842283i | \(0.318789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.1716 | 0.868404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.414214 | − | 0.717439i | −0.0208678 | − | 0.0361441i | ||||
\(395\) | 23.3137 | − | 40.3805i | 1.17304 | − | 2.03176i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.19239 | + | 2.06528i | 0.0598442 | + | 0.103653i | 0.894395 | − | 0.447277i | \(-0.147606\pi\) |
−0.834551 | + | 0.550931i | \(0.814273\pi\) | |||||||
\(398\) | −8.97056 | −0.449654 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.9706 | 0.998528 | ||||||||
\(401\) | −3.07107 | − | 5.31925i | −0.153362 | − | 0.265630i | 0.779100 | − | 0.626900i | \(-0.215677\pi\) |
−0.932461 | + | 0.361270i | \(0.882343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.51472 | − | 2.62357i | 0.0754535 | − | 0.130689i | ||||
\(404\) | −2.67767 | − | 4.63786i | −0.133219 | − | 0.230742i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7071 | − | 18.5453i | 0.529432 | − | 0.917004i | −0.469978 | − | 0.882678i | \(-0.655738\pi\) |
0.999411 | − | 0.0343258i | \(-0.0109284\pi\) | |||||||
\(410\) | 4.41421 | − | 7.64564i | 0.218002 | − | 0.377591i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.20101 | −0.404035 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.4853 | − | 21.6251i | −0.612878 | − | 1.06154i | ||||
\(416\) | 5.70711 | − | 9.88500i | 0.279814 | − | 0.484652i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.17157 | − | 2.02922i | −0.0573035 | − | 0.0992526i | ||||
\(419\) | −33.1716 | −1.62054 | −0.810269 | − | 0.586059i | \(-0.800679\pi\) | ||||
−0.810269 | + | 0.586059i | \(0.800679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6274 | 0.810371 | 0.405185 | − | 0.914235i | \(-0.367207\pi\) | ||||
0.405185 | + | 0.914235i | \(0.367207\pi\) | |||||||
\(422\) | 2.68629 | + | 4.65279i | 0.130767 | + | 0.226494i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.58579 | + | 2.74666i | −0.0770126 | + | 0.133390i | ||||
\(425\) | −7.46447 | − | 12.9288i | −0.362080 | − | 0.627141i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.627417 | −0.0303273 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.00000 | + | 6.92820i | −0.192897 | + | 0.334108i | ||||
\(431\) | −13.4853 | + | 23.3572i | −0.649563 | + | 1.12508i | 0.333664 | + | 0.942692i | \(0.391715\pi\) |
−0.983227 | + | 0.182384i | \(0.941618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.2426 | −0.972799 | −0.486400 | − | 0.873736i | \(-0.661690\pi\) | ||||
−0.486400 | + | 0.873736i | \(0.661690\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.17157 | − | 8.95743i | −0.247673 | − | 0.428983i | ||||
\(437\) | 10.8284 | − | 18.7554i | 0.517994 | − | 0.897192i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.34315 | − | 10.9867i | −0.302742 | − | 0.524364i | 0.674014 | − | 0.738718i | \(-0.264569\pi\) |
−0.976756 | + | 0.214354i | \(0.931235\pi\) | |||||||
\(440\) | −10.8284 | −0.516225 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.40202 | −0.114252 | ||||||||
\(443\) | 17.4853 | + | 30.2854i | 0.830751 | + | 1.43890i | 0.897444 | + | 0.441129i | \(0.145422\pi\) |
−0.0666929 | + | 0.997774i | \(0.521245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.3137 | − | 42.1126i | 1.15258 | − | 1.99633i | ||||
\(446\) | 5.17157 | + | 8.95743i | 0.244881 | + | 0.424146i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.31371 | 0.250769 | 0.125385 | − | 0.992108i | \(-0.459983\pi\) | ||||
0.125385 | + | 0.992108i | \(0.459983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.24264 | − | 10.8126i | 0.293954 | − | 0.509144i | ||||
\(452\) | 4.85786 | − | 8.41407i | 0.228495 | − | 0.395764i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.85786 | 0.462652 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.00000 | + | 15.5885i | 0.421002 | + | 0.729197i | 0.996038 | − | 0.0889312i | \(-0.0283451\pi\) |
−0.575036 | + | 0.818128i | \(0.695012\pi\) | |||||||
\(458\) | −0.0502525 | + | 0.0870399i | −0.00234815 | + | 0.00406711i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −23.8995 | − | 41.3951i | −1.11432 | − | 1.93006i | ||||
\(461\) | 16.5858 | 0.772477 | 0.386239 | − | 0.922399i | \(-0.373774\pi\) | ||||
0.386239 | + | 0.922399i | \(0.373774\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6274 | −1.23748 | −0.618741 | − | 0.785595i | \(-0.712357\pi\) | ||||
−0.618741 | + | 0.785595i | \(0.712357\pi\) | |||||||
\(464\) | −10.2426 | − | 17.7408i | −0.475503 | − | 0.823595i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.27208 | − | 2.20330i | 0.0589279 | − | 0.102066i | ||||
\(467\) | 0.100505 | + | 0.174080i | 0.00465082 | + | 0.00805546i | 0.868341 | − | 0.495967i | \(-0.165186\pi\) |
−0.863691 | + | 0.504022i | \(0.831853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.00000 | 0.184506 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.928932 | + | 1.60896i | −0.0427576 | + | 0.0740583i | ||||
\(473\) | −5.65685 | + | 9.79796i | −0.260102 | + | 0.450511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.8284 | −0.863907 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.24264 | + | 5.61642i | 0.148315 | + | 0.256889i | ||||
\(479\) | 0.928932 | − | 1.60896i | 0.0424440 | − | 0.0735152i | −0.844023 | − | 0.536307i | \(-0.819819\pi\) |
0.886467 | + | 0.462792i | \(0.153152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.17157 | + | 8.95743i | 0.235803 | + | 0.408424i | ||||
\(482\) | 6.72792 | 0.306448 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.7990 | 0.581772 | ||||||||
\(485\) | 4.41421 | + | 7.64564i | 0.200439 | + | 0.347171i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.3137 | + | 23.0600i | −0.603302 | + | 1.04495i | 0.389016 | + | 0.921231i | \(0.372815\pi\) |
−0.992317 | + | 0.123718i | \(0.960518\pi\) | |||||||
\(488\) | −9.70711 | − | 16.8132i | −0.439420 | − | 0.761098i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.02944 | −0.226975 | −0.113488 | − | 0.993539i | \(-0.536202\pi\) | ||||
−0.113488 | + | 0.993539i | \(0.536202\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.65685 | + | 13.2621i | −0.344847 | + | 0.597293i | ||||
\(494\) | −1.51472 | + | 2.62357i | −0.0681504 | + | 0.118040i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.51472 | −0.157816 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.65685 | − | 2.86976i | −0.0741710 | − | 0.128468i | 0.826554 | − | 0.562857i | \(-0.190298\pi\) |
−0.900725 | + | 0.434389i | \(0.856964\pi\) | |||||||
\(500\) | −5.17157 | + | 8.95743i | −0.231280 | + | 0.400588i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.58579 | + | 4.47871i | 0.115409 | + | 0.199895i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 3.17157 | + | 5.49333i | 0.140994 | + | 0.244208i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.51472 | + | 2.62357i | −0.0672048 | + | 0.116402i | ||||
\(509\) | 2.77817 | + | 4.81194i | 0.123140 | + | 0.213285i | 0.921005 | − | 0.389552i | \(-0.127370\pi\) |
−0.797864 | + | 0.602837i | \(0.794037\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.80761 | + | 8.32703i | −0.212055 | + | 0.367289i | ||||
\(515\) | 7.65685 | − | 13.2621i | 0.337401 | − | 0.584396i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.65685 | 0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.00000 | + | 12.1244i | 0.306970 | + | 0.531688i | ||||
\(521\) | −17.7071 | + | 30.6696i | −0.775762 | + | 1.34366i | 0.158603 | + | 0.987343i | \(0.449301\pi\) |
−0.934365 | + | 0.356317i | \(0.884032\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8284 | + | 22.2195i | 0.560948 | + | 0.971590i | 0.997414 | + | 0.0718696i | \(0.0228966\pi\) |
−0.436466 | + | 0.899721i | \(0.643770\pi\) | |||||||
\(524\) | −28.0000 | −1.22319 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.20101 | 0.0959686 | ||||||||
\(527\) | 1.31371 | + | 2.27541i | 0.0572260 | + | 0.0991184i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.8137 | + | 30.8542i | −0.774509 | + | 1.34149i | ||||
\(530\) | −1.41421 | − | 2.44949i | −0.0614295 | − | 0.106399i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.1421 | −0.699194 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.585786 | − | 1.01461i | 0.0253258 | − | 0.0438655i | ||||
\(536\) | 4.48528 | − | 7.76874i | 0.193735 | − | 0.335558i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.10051 | −0.263011 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.65685 | − | 14.9941i | −0.372187 | − | 0.644647i | 0.617715 | − | 0.786402i | \(-0.288059\pi\) |
−0.989902 | + | 0.141755i | \(0.954725\pi\) | |||||||
\(542\) | −2.10051 | + | 3.63818i | −0.0902244 | + | 0.156273i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.94975 | + | 8.57321i | 0.212219 | + | 0.367574i | ||||
\(545\) | 19.3137 | 0.827308 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9706 | −1.58075 | −0.790374 | − | 0.612625i | \(-0.790114\pi\) | ||||
−0.790374 | + | 0.612625i | \(0.790114\pi\) | |||||||
\(548\) | −12.9289 | − | 22.3936i | −0.552297 | − | 0.956606i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.75736 | − | 4.77589i | 0.117574 | − | 0.203644i | ||||
\(551\) | 9.65685 | + | 16.7262i | 0.411396 | + | 0.712558i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.85786 | 0.163905 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.1421 | + | 27.9590i | −0.684579 | + | 1.18573i | ||||
\(557\) | 13.0000 | − | 22.5167i | 0.550828 | − | 0.954062i | −0.447387 | − | 0.894340i | \(-0.647645\pi\) |
0.998215 | − | 0.0597213i | \(-0.0190212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6274 | 0.618674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.100505 | − | 0.174080i | −0.00423955 | − | 0.00734312i | ||||
\(563\) | −0.585786 | + | 1.01461i | −0.0246880 | + | 0.0427608i | −0.878105 | − | 0.478467i | \(-0.841193\pi\) |
0.853417 | + | 0.521228i | \(0.174526\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.07107 | + | 15.7116i | 0.381623 | + | 0.660990i | ||||
\(566\) | 3.51472 | 0.147735 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.7696 | −0.619717 | ||||||||
\(569\) | −8.24264 | − | 14.2767i | −0.345549 | − | 0.598509i | 0.639904 | − | 0.768455i | \(-0.278974\pi\) |
−0.985453 | + | 0.169946i | \(0.945641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.1716 | + | 19.3497i | −0.467516 | + | 0.809761i | −0.999311 | − | 0.0371118i | \(-0.988184\pi\) |
0.531795 | + | 0.846873i | \(0.321518\pi\) | |||||||
\(572\) | 4.72792 | + | 8.18900i | 0.197684 | + | 0.342399i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 50.9706 | 2.12562 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.9497 | − | 29.3578i | 0.705627 | − | 1.22218i | −0.260837 | − | 0.965383i | \(-0.583999\pi\) |
0.966465 | − | 0.256799i | \(-0.0826680\pi\) | |||||||
\(578\) | −2.47918 | + | 4.29407i | −0.103120 | + | 0.178610i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 42.6274 | 1.77001 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | − | 3.46410i | −0.0828315 | − | 0.143468i | ||||
\(584\) | −11.0208 | + | 19.0886i | −0.456045 | + | 0.789892i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.43503 | − | 5.94964i | −0.141900 | − | 0.245778i | ||||
\(587\) | 22.8284 | 0.942230 | 0.471115 | − | 0.882072i | \(-0.343852\pi\) | ||||
0.471115 | + | 0.882072i | \(0.343852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.31371 | 0.136539 | ||||||||
\(590\) | −0.828427 | − | 1.43488i | −0.0341058 | − | 0.0590730i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | − | 10.3923i | 0.246598 | − | 0.427121i | ||||
\(593\) | −3.46447 | − | 6.00063i | −0.142269 | − | 0.246416i | 0.786082 | − | 0.618122i | \(-0.212106\pi\) |
−0.928351 | + | 0.371706i | \(0.878773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 31.6569 | 1.29672 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.10051 | − | 7.10228i | 0.167682 | − | 0.290434i | ||||
\(599\) | −1.00000 | + | 1.73205i | −0.0408589 | + | 0.0707697i | −0.885732 | − | 0.464198i | \(-0.846343\pi\) |
0.844873 | + | 0.534967i | \(0.179676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0711 | −0.614762 | −0.307381 | − | 0.951587i | \(-0.599453\pi\) | ||||
−0.307381 | + | 0.951587i | \(0.599453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.9706 | + | 19.0016i | 0.446386 | + | 0.773163i | ||||
\(605\) | −11.9497 | + | 20.6976i | −0.485826 | + | 0.841476i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.17157 | + | 15.8856i | 0.372263 | + | 0.644778i | 0.989913 | − | 0.141675i | \(-0.0452487\pi\) |
−0.617651 | + | 0.786453i | \(0.711915\pi\) | |||||||
\(608\) | 12.4853 | 0.506345 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.3137 | 0.701012 | ||||||||
\(611\) | −3.65685 | − | 6.33386i | −0.147940 | − | 0.256240i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.34315 | + | 4.05845i | −0.0946388 | + | 0.163919i | −0.909458 | − | 0.415796i | \(-0.863503\pi\) |
0.814819 | + | 0.579715i | \(0.196836\pi\) | |||||||
\(614\) | 6.24264 | + | 10.8126i | 0.251932 | + | 0.436360i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4853 | 0.985740 | 0.492870 | − | 0.870103i | \(-0.335948\pi\) | ||||
0.492870 | + | 0.870103i | \(0.335948\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4853 | + | 25.0892i | −0.582213 | + | 1.00842i | 0.413004 | + | 0.910729i | \(0.364480\pi\) |
−0.995217 | + | 0.0976926i | \(0.968854\pi\) | |||||||
\(620\) | 3.65685 | − | 6.33386i | 0.146863 | − | 0.254374i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.54416 | 0.102011 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.98528 | + | 12.0989i | 0.279411 | + | 0.483954i | ||||
\(626\) | 0.393398 | − | 0.681386i | 0.0157234 | − | 0.0272337i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.7487 | + | 18.6174i | 0.428921 | + | 0.742914i | ||||
\(629\) | −8.97056 | −0.357680 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3137 | 0.928104 | 0.464052 | − | 0.885808i | \(-0.346395\pi\) | ||||
0.464052 | + | 0.885808i | \(0.346395\pi\) | |||||||
\(632\) | −10.8284 | − | 18.7554i | −0.430732 | − | 0.746049i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.07107 | + | 3.58719i | −0.0822526 | + | 0.142466i | ||||
\(635\) | −2.82843 | − | 4.89898i | −0.112243 | − | 0.194410i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.65685 | −0.223957 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.0208 | − | 31.2130i | 0.712335 | − | 1.23380i | ||||
\(641\) | −5.41421 | + | 9.37769i | −0.213849 | + | 0.370397i | −0.952916 | − | 0.303235i | \(-0.901933\pi\) |
0.739067 | + | 0.673632i | \(0.235267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.4264 | −1.35764 | −0.678822 | − | 0.734302i | \(-0.737509\pi\) | ||||
−0.678822 | + | 0.734302i | \(0.737509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.31371 | − | 2.27541i | −0.0516872 | − | 0.0895248i | ||||
\(647\) | 13.4142 | − | 23.2341i | 0.527367 | − | 0.913427i | −0.472124 | − | 0.881532i | \(-0.656513\pi\) |
0.999491 | − | 0.0318946i | \(-0.0101541\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.17157 | − | 2.02922i | −0.0459883 | − | 0.0796540i | ||||
\(650\) | −7.12994 | −0.279659 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.6863 | 0.810138 | ||||||||
\(653\) | 18.2426 | + | 31.5972i | 0.713890 | + | 1.23649i | 0.963386 | + | 0.268118i | \(0.0864016\pi\) |
−0.249497 | + | 0.968376i | \(0.580265\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.1421 | − | 45.2795i | 1.02146 | − | 1.76922i | ||||
\(656\) | 9.36396 | + | 16.2189i | 0.365601 | + | 0.633240i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.31371 | −0.362811 | −0.181405 | − | 0.983408i | \(-0.558065\pi\) | ||||
−0.181405 | + | 0.983408i | \(0.558065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.7782 | − | 20.4004i | 0.458118 | − | 0.793483i | −0.540744 | − | 0.841187i | \(-0.681857\pi\) |
0.998862 | + | 0.0477040i | \(0.0151904\pi\) | |||||||
\(662\) | −0.828427 | + | 1.43488i | −0.0321977 | + | 0.0557681i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.5980 | −0.450089 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.1421 | − | 45.2795i | −1.01223 | − | 1.75323i | ||||
\(668\) | 18.1005 | − | 31.3510i | 0.700330 | − | 1.21301i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.00000 | + | 6.92820i | 0.154533 | + | 0.267660i | ||||
\(671\) | 24.4853 | 0.945244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3137 | 0.898677 | 0.449339 | − | 0.893361i | \(-0.351660\pi\) | ||||
0.449339 | + | 0.893361i | \(0.351660\pi\) | |||||||
\(674\) | −6.14214 | − | 10.6385i | −0.236586 | − | 0.409779i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.77208 | + | 9.99753i | −0.222003 | + | 0.384520i | ||||
\(677\) | 15.7071 | + | 27.2055i | 0.603673 | + | 1.04559i | 0.992260 | + | 0.124180i | \(0.0396301\pi\) |
−0.388587 | + | 0.921412i | \(0.627037\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.1421 | −0.465630 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.485281 | + | 0.840532i | −0.0185824 | + | 0.0321856i | ||||
\(683\) | −9.82843 | + | 17.0233i | −0.376074 | + | 0.651380i | −0.990487 | − | 0.137605i | \(-0.956060\pi\) |
0.614413 | + | 0.788985i | \(0.289393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.2843 | 1.84485 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.48528 | − | 14.6969i | −0.323498 | − | 0.560316i | ||||
\(689\) | −2.58579 | + | 4.47871i | −0.0985106 | + | 0.170625i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.343146 | + | 0.594346i | 0.0130539 | + | 0.0226100i | 0.872479 | − | 0.488652i | \(-0.162511\pi\) |
−0.859425 | + | 0.511262i | \(0.829178\pi\) | |||||||
\(692\) | 38.5269 | 1.46457 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.7990 | 0.523802 | ||||||||
\(695\) | −30.1421 | − | 52.2077i | −1.14336 | − | 1.98035i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.00000 | − | 12.1244i | 0.265144 | − | 0.459243i | ||||
\(698\) | −2.05025 | − | 3.55114i | −0.0776032 | − | 0.134413i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.1716 | 0.648561 | 0.324281 | − | 0.945961i | \(-0.394878\pi\) | ||||
0.324281 | + | 0.945961i | \(0.394878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.65685 | + | 9.79796i | −0.213352 | + | 0.369537i | ||||
\(704\) | 4.17157 | − | 7.22538i | 0.157222 | − | 0.272317i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.10051 | −0.229596 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.1421 | + | 31.4231i | 0.681342 | + | 1.18012i | 0.974571 | + | 0.224077i | \(0.0719368\pi\) |
−0.293229 | + | 0.956042i | \(0.594730\pi\) | |||||||
\(710\) | 6.58579 | − | 11.4069i | 0.247160 | − | 0.428094i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.2929 | − | 19.5599i | −0.423219 | − | 0.733037i | ||||
\(713\) | −8.97056 | −0.335950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.6569 | −0.660329 | ||||||||
\(716\) | 17.9706 | + | 31.1259i | 0.671591 | + | 1.16323i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.0710678 | − | 0.123093i | 0.00265223 | − | 0.00459379i | ||||
\(719\) | 20.9706 | + | 36.3221i | 0.782070 | + | 1.35459i | 0.930734 | + | 0.365697i | \(0.119169\pi\) |
−0.148664 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.55635 | 0.169570 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.36396 | + | 4.09450i | −0.0878559 | + | 0.152171i | ||||
\(725\) | −22.7279 | + | 39.3659i | −0.844094 | + | 1.46201i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.4853 | 0.463053 | 0.231527 | − | 0.972829i | \(-0.425628\pi\) | ||||
0.231527 | + | 0.972829i | \(0.425628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.82843 | − | 17.0233i | −0.363766 | − | 0.630062i | ||||
\(731\) | −6.34315 | + | 10.9867i | −0.234610 | + | 0.406356i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.8492 | − | 43.0402i | −0.917828 | − | 1.58972i | −0.802708 | − | 0.596373i | \(-0.796608\pi\) |
−0.115120 | − | 0.993352i | \(-0.536725\pi\) | |||||||
\(734\) | 1.37258 | 0.0506630 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.7990 | −1.24585 | ||||||||
\(737\) | 5.65685 | + | 9.79796i | 0.208373 | + | 0.360912i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.34315 | + | 4.05845i | −0.0861940 | + | 0.149292i | −0.905899 | − | 0.423493i | \(-0.860804\pi\) |
0.819705 | + | 0.572785i | \(0.194137\pi\) | |||||||
\(740\) | 12.4853 | + | 21.6251i | 0.458968 | + | 0.794956i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.9706 | 1.86993 | 0.934964 | − | 0.354742i | \(-0.115431\pi\) | ||||
0.934964 | + | 0.354742i | \(0.115431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.5563 | + | 51.1931i | −1.08286 | + | 1.87557i | ||||
\(746\) | −2.21320 | + | 3.83338i | −0.0810311 | + | 0.140350i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.20101 | −0.299859 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.82843 | − | 11.8272i | −0.249173 | − | 0.431580i | 0.714124 | − | 0.700020i | \(-0.246825\pi\) |
−0.963297 | + | 0.268440i | \(0.913492\pi\) | |||||||
\(752\) | −4.24264 | + | 7.34847i | −0.154713 | + | 0.267971i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.65685 | + | 6.33386i | 0.133175 | + | 0.230665i | ||||
\(755\) | −40.9706 | −1.49107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.3431 | 0.957458 | 0.478729 | − | 0.877963i | \(-0.341098\pi\) | ||||
0.478729 | + | 0.877963i | \(0.341098\pi\) | |||||||
\(758\) | 1.79899 | + | 3.11594i | 0.0653423 | + | 0.113176i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.65685 | + | 13.2621i | −0.277743 | + | 0.481065i | ||||
\(761\) | −9.26346 | − | 16.0448i | −0.335800 | − | 0.581623i | 0.647838 | − | 0.761778i | \(-0.275673\pi\) |
−0.983638 | + | 0.180155i | \(0.942340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −32.9117 | −1.19070 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.79899 | − | 6.58004i | 0.137263 | − | 0.237747i | ||||
\(767\) | −1.51472 | + | 2.62357i | −0.0546933 | + | 0.0947316i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.6985 | 1.07095 | 0.535477 | − | 0.844550i | \(-0.320132\pi\) | ||||
0.535477 | + | 0.844550i | \(0.320132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.85786 | + | 8.41407i | 0.174838 | + | 0.302829i | ||||
\(773\) | −4.77817 | + | 8.27604i | −0.171859 | + | 0.297669i | −0.939070 | − | 0.343727i | \(-0.888311\pi\) |
0.767211 | + | 0.641395i | \(0.221644\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.89949 | + | 6.75412i | 0.140074 | + | 0.242615i | ||||
\(776\) | 4.10051 | 0.147200 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.51472 | −0.269416 | ||||||||
\(779\) | −8.82843 | − | 15.2913i | −0.316311 | − | 0.547867i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.31371 | − | 16.1318i | 0.333271 | − | 0.577242i | ||||
\(782\) | 3.55635 | + | 6.15978i | 0.127175 | + | 0.220273i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −40.1421 | −1.43273 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.3431 | + | 21.3790i | −0.439986 | + | 0.762077i | −0.997688 | − | 0.0679637i | \(-0.978350\pi\) |
0.557702 | + | 0.830041i | \(0.311683\pi\) | |||||||
\(788\) | −1.82843 | + | 3.16693i | −0.0651350 | + | 0.112817i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 19.3137 | 0.687151 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.8284 | − | 27.4156i | −0.562084 | − | 0.973558i | ||||
\(794\) | −0.493903 | + | 0.855466i | −0.0175280 | + | 0.0303593i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.7990 | + | 34.2929i | 0.701757 | + | 1.21548i | ||||
\(797\) | 8.38478 | 0.297004 | 0.148502 | − | 0.988912i | \(-0.452555\pi\) | ||||
0.148502 | + | 0.988912i | \(0.452555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.34315 | 0.224404 | ||||||||
\(800\) | 14.6924 | + | 25.4480i | 0.519454 | + | 0.899721i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.27208 | − | 2.20330i | 0.0449186 | − | 0.0778014i | ||||
\(803\) | −13.8995 | − | 24.0746i | −0.490503 | − | 0.849575i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.25483 | 0.0441996 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.32233 | − | 4.02239i | 0.0816993 | − | 0.141507i | ||||
\(809\) | 9.97056 | − | 17.2695i | 0.350546 | − | 0.607164i | −0.635799 | − | 0.771855i | \(-0.719329\pi\) |
0.986345 | + | 0.164691i | \(0.0526626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.6569 | −0.620016 | −0.310008 | − | 0.950734i | \(-0.600332\pi\) | ||||
−0.310008 | + | 0.950734i | \(0.600332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.65685 | − | 2.86976i | −0.0580727 | − | 0.100585i | ||||
\(815\) | −19.3137 | + | 33.4523i | −0.676530 | + | 1.17178i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | 8.87006 | 0.310134 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −38.9706 | −1.36091 | ||||||||
\(821\) | −5.34315 | − | 9.25460i | −0.186477 | − | 0.322988i | 0.757596 | − | 0.652724i | \(-0.226374\pi\) |
−0.944073 | + | 0.329736i | \(0.893040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.48528 | + | 7.76874i | −0.156347 | + | 0.270801i | −0.933549 | − | 0.358451i | \(-0.883305\pi\) |
0.777202 | + | 0.629252i | \(0.216639\pi\) | |||||||
\(824\) | −3.55635 | − | 6.15978i | −0.123891 | − | 0.214586i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.6569 | −1.65719 | −0.828596 | − | 0.559848i | \(-0.810860\pi\) | ||||
−0.828596 | + | 0.559848i | \(0.810860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.363961 | − | 0.630399i | 0.0126409 | − | 0.0218947i | −0.859636 | − | 0.510907i | \(-0.829310\pi\) |
0.872277 | + | 0.489013i | \(0.162643\pi\) | |||||||
\(830\) | 5.17157 | − | 8.95743i | 0.179508 | − | 0.310917i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.7868 | −0.373965 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.7990 | + | 58.5416i | 1.16966 | + | 2.02591i | ||||
\(836\) | −5.17157 | + | 8.95743i | −0.178863 | + | 0.309799i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.87006 | − | 11.8993i | −0.237322 | − | 0.411054i | ||||
\(839\) | −50.8284 | −1.75479 | −0.877396 | − | 0.479767i | \(-0.840721\pi\) | ||||
−0.877396 | + | 0.479767i | \(0.840721\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | 3.44365 | + | 5.96458i | 0.118676 | + | 0.205553i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.8579 | − | 20.5384i | 0.408165 | − | 0.706962i | ||||
\(845\) | −10.7782 | − | 18.6683i | −0.370780 | − | 0.642211i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.09188 | − | 5.35530i | 0.106051 | − | 0.183685i | ||||
\(851\) | 15.3137 | − | 26.5241i | 0.524947 | − | 0.909235i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.4975 | −1.69476 | −0.847381 | − | 0.530986i | \(-0.821822\pi\) | ||||
−0.847381 | + | 0.530986i | \(0.821822\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.272078 | − | 0.471253i | −0.00929943 | − | 0.0161071i | ||||
\(857\) | 7.70711 | − | 13.3491i | 0.263270 | − | 0.455997i | −0.703839 | − | 0.710359i | \(-0.748532\pi\) |
0.967109 | + | 0.254363i | \(0.0818657\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.7279 | − | 49.7582i | −0.980184 | − | 1.69773i | −0.661642 | − | 0.749820i | \(-0.730140\pi\) |
−0.318542 | − | 0.947909i | \(-0.603193\pi\) | |||||||
\(860\) | 35.3137 | 1.20419 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.1716 | −0.380505 | ||||||||
\(863\) | 8.65685 | + | 14.9941i | 0.294683 | + | 0.510405i | 0.974911 | − | 0.222595i | \(-0.0714527\pi\) |
−0.680228 | + | 0.733000i | \(0.738119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.9706 | + | 62.3028i | −1.22304 | + | 2.11836i | ||||
\(866\) | −4.19239 | − | 7.26143i | −0.142463 | − | 0.246753i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.3137 | 0.926554 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.31371 | − | 12.6677i | 0.247816 | − | 0.429229i | ||||
\(872\) | 4.48528 | − | 7.76874i | 0.151891 | − | 0.263083i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.97056 | 0.303434 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.65685 | + | 9.79796i | 0.191018 | + | 0.330854i | 0.945588 | − | 0.325366i | \(-0.105488\pi\) |
−0.754570 | + | 0.656220i | \(0.772154\pi\) | |||||||
\(878\) | 2.62742 | − | 4.55082i | 0.0886710 | − | 0.153583i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.2426 | + | 17.7408i | 0.345279 | + | 0.598041i | ||||
\(881\) | −21.7574 | −0.733024 | −0.366512 | − | 0.930413i | \(-0.619448\pi\) | ||||
−0.366512 | + | 0.930413i | \(0.619448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.68629 | −0.157706 | −0.0788531 | − | 0.996886i | \(-0.525126\pi\) | ||||
−0.0788531 | + | 0.996886i | \(0.525126\pi\) | |||||||
\(884\) | 5.30152 | + | 9.18249i | 0.178309 | + | 0.308841i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.24264 | + | 12.5446i | −0.243321 | + | 0.421445i | ||||
\(887\) | −1.41421 | − | 2.44949i | −0.0474846 | − | 0.0822458i | 0.841306 | − | 0.540559i | \(-0.181787\pi\) |
−0.888791 | + | 0.458313i | \(0.848454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 20.1421 | 0.675166 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.8284 | − | 39.5400i | 0.764352 | − | 1.32390i | ||||
\(893\) | 4.00000 | − | 6.92820i | 0.133855 | − | 0.231843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −67.1127 | −2.24333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.10051 | + | 1.90613i | 0.0367243 | + | 0.0636084i | ||||
\(899\) | 4.00000 | − | 6.92820i | 0.133407 | − | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.24264 | − | 3.88437i | −0.0747132 | − | 0.129407i | ||||
\(902\) | 5.17157 | 0.172195 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.42641 | 0.280258 | ||||||||
\(905\) | −4.41421 | − | 7.64564i | −0.146733 | − | 0.254150i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000 | − | 13.8564i | 0.265636 | − | 0.460094i | −0.702094 | − | 0.712084i | \(-0.747752\pi\) |
0.967730 | + | 0.251990i | \(0.0810849\pi\) | |||||||
\(908\) | −21.7574 | − | 37.6849i | −0.722043 | − | 1.25062i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.02944 | 0.0341068 | 0.0170534 | − | 0.999855i | \(-0.494571\pi\) | ||||
0.0170534 | + | 0.999855i | \(0.494571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.31371 | − | 12.6677i | 0.242048 | − | 0.419240i | ||||
\(914\) | −3.72792 | + | 6.45695i | −0.123309 | + | 0.213577i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.443651 | 0.0146586 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.14214 | + | 7.17439i | 0.136636 | + | 0.236661i | 0.926221 | − | 0.376980i | \(-0.123037\pi\) |
−0.789585 | + | 0.613641i | \(0.789704\pi\) | |||||||
\(920\) | 20.7279 | − | 35.9018i | 0.683379 | − | 1.18365i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.43503 | + | 5.94964i | 0.113127 | + | 0.195941i | ||||
\(923\) | −24.0833 | −0.792710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.6274 | −0.875504 | ||||||||
\(926\) | −5.51472 | − | 9.55177i | −0.181225 | − | 0.313891i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.0711 | − | 26.1039i | 0.494732 | − | 0.856901i | ||||
\(929\) | −19.6066 | − | 33.9596i | −0.643272 | − | 1.11418i | −0.984698 | − | 0.174271i | \(-0.944243\pi\) |
0.341426 | − | 0.939909i | \(-0.389090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.2304 | −0.367866 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.0416306 | + | 0.0721062i | −0.00136219 | + | 0.00235939i | ||||
\(935\) | 7.65685 | − | 13.2621i | 0.250406 | − | 0.433716i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.5858 | 0.999194 | 0.499597 | − | 0.866258i | \(-0.333481\pi\) | ||||
0.499597 | + | 0.866258i | \(0.333481\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.82843 | − | 15.2913i | −0.287952 | − | 0.498747i | ||||
\(941\) | 17.6066 | − | 30.4955i | 0.573959 | − | 0.994126i | −0.422195 | − | 0.906505i | \(-0.638740\pi\) |
0.996154 | − | 0.0876208i | \(-0.0279264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.8995 | + | 41.3951i | 0.778275 | + | 1.34801i | ||||
\(944\) | 3.51472 | 0.114394 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.68629 | −0.152364 | ||||||||
\(947\) | 15.3431 | + | 26.5751i | 0.498585 | + | 0.863575i | 0.999999 | − | 0.00163285i | \(-0.000519752\pi\) |
−0.501413 | + | 0.865208i | \(0.667186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9706 | + | 31.1259i | −0.583349 | + | 1.01039i | ||||
\(950\) | −3.89949 | − | 6.75412i | −0.126516 | − | 0.219133i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.00000 | −0.0647864 | −0.0323932 | − | 0.999475i | \(-0.510313\pi\) | ||||
−0.0323932 | + | 0.999475i | \(0.510313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.7279 | − | 53.2223i | 0.994332 | − | 1.72223i | ||||
\(956\) | 14.3137 | − | 24.7921i | 0.462938 | − | 0.801833i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.769553 | 0.0248631 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8137 | + | 25.6581i | 0.477862 | + | 0.827681i | ||||
\(962\) | −2.14214 | + | 3.71029i | −0.0690652 | + | 0.119624i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.8492 | − | 25.7196i | −0.478262 | − | 0.828374i | ||||
\(965\) | −18.1421 | −0.584016 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6569 | 1.08233 | 0.541166 | − | 0.840916i | \(-0.317983\pi\) | ||||
0.541166 | + | 0.840916i | \(0.317983\pi\) | |||||||
\(968\) | 5.55025 | + | 9.61332i | 0.178392 | + | 0.308984i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.82843 | + | 3.16693i | −0.0587073 | + | 0.101684i | ||||
\(971\) | −25.3137 | − | 43.8446i | −0.812356 | − | 1.40704i | −0.911211 | − | 0.411939i | \(-0.864852\pi\) |
0.0988557 | − | 0.995102i | \(-0.468482\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.0294 | −0.353406 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.3640 | + | 31.8073i | −0.587816 | + | 1.01813i | ||||
\(977\) | −10.5858 | + | 18.3351i | −0.338669 | + | 0.586592i | −0.984183 | − | 0.177157i | \(-0.943310\pi\) |
0.645513 | + | 0.763749i | \(0.276643\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.4853 | 0.910394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.04163 | − | 1.80416i | −0.0332398 | − | 0.0575730i | ||||
\(983\) | −26.6274 | + | 46.1200i | −0.849283 | + | 1.47100i | 0.0325667 | + | 0.999470i | \(0.489632\pi\) |
−0.881849 | + | 0.471531i | \(0.843701\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.41421 | − | 5.91359i | −0.108786 | − | 0.188423i | ||||
\(986\) | −6.34315 | −0.202007 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.3726 | 0.425439 | ||||||||
\(989\) | −21.6569 | − | 37.5108i | −0.688648 | − | 1.19277i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.48528 | − | 11.2328i | 0.206012 | − | 0.356823i | −0.744443 | − | 0.667686i | \(-0.767285\pi\) |
0.950455 | + | 0.310863i | \(0.100618\pi\) | |||||||
\(992\) | −2.58579 | − | 4.47871i | −0.0820988 | − | 0.142199i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73.9411 | −2.34409 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1924 | + | 22.8499i | −0.417807 | + | 0.723663i | −0.995719 | − | 0.0924363i | \(-0.970535\pi\) |
0.577911 | + | 0.816099i | \(0.303868\pi\) | |||||||
\(998\) | 0.686292 | − | 1.18869i | 0.0217242 | − | 0.0376274i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.2.e.g.361.2 | 4 | ||
3.2 | odd | 2 | 147.2.e.d.67.1 | 4 | |||
7.2 | even | 3 | inner | 441.2.e.g.226.2 | 4 | ||
7.3 | odd | 6 | 441.2.a.j.1.1 | 2 | |||
7.4 | even | 3 | 441.2.a.i.1.1 | 2 | |||
7.5 | odd | 6 | 441.2.e.f.226.2 | 4 | |||
7.6 | odd | 2 | 441.2.e.f.361.2 | 4 | |||
12.11 | even | 2 | 2352.2.q.bd.1537.1 | 4 | |||
21.2 | odd | 6 | 147.2.e.d.79.1 | 4 | |||
21.5 | even | 6 | 147.2.e.e.79.1 | 4 | |||
21.11 | odd | 6 | 147.2.a.e.1.2 | yes | 2 | ||
21.17 | even | 6 | 147.2.a.d.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 147.2.e.e.67.1 | 4 | |||
28.3 | even | 6 | 7056.2.a.cv.1.2 | 2 | |||
28.11 | odd | 6 | 7056.2.a.cf.1.1 | 2 | |||
84.11 | even | 6 | 2352.2.a.bc.1.2 | 2 | |||
84.23 | even | 6 | 2352.2.q.bd.961.1 | 4 | |||
84.47 | odd | 6 | 2352.2.q.bb.961.2 | 4 | |||
84.59 | odd | 6 | 2352.2.a.be.1.1 | 2 | |||
84.83 | odd | 2 | 2352.2.q.bb.1537.2 | 4 | |||
105.59 | even | 6 | 3675.2.a.bf.1.1 | 2 | |||
105.74 | odd | 6 | 3675.2.a.bd.1.1 | 2 | |||
168.11 | even | 6 | 9408.2.a.dt.1.1 | 2 | |||
168.53 | odd | 6 | 9408.2.a.di.1.1 | 2 | |||
168.59 | odd | 6 | 9408.2.a.dq.1.2 | 2 | |||
168.101 | even | 6 | 9408.2.a.ef.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.2.a.d.1.2 | ✓ | 2 | 21.17 | even | 6 | ||
147.2.a.e.1.2 | yes | 2 | 21.11 | odd | 6 | ||
147.2.e.d.67.1 | 4 | 3.2 | odd | 2 | |||
147.2.e.d.79.1 | 4 | 21.2 | odd | 6 | |||
147.2.e.e.67.1 | 4 | 21.20 | even | 2 | |||
147.2.e.e.79.1 | 4 | 21.5 | even | 6 | |||
441.2.a.i.1.1 | 2 | 7.4 | even | 3 | |||
441.2.a.j.1.1 | 2 | 7.3 | odd | 6 | |||
441.2.e.f.226.2 | 4 | 7.5 | odd | 6 | |||
441.2.e.f.361.2 | 4 | 7.6 | odd | 2 | |||
441.2.e.g.226.2 | 4 | 7.2 | even | 3 | inner | ||
441.2.e.g.361.2 | 4 | 1.1 | even | 1 | trivial | ||
2352.2.a.bc.1.2 | 2 | 84.11 | even | 6 | |||
2352.2.a.be.1.1 | 2 | 84.59 | odd | 6 | |||
2352.2.q.bb.961.2 | 4 | 84.47 | odd | 6 | |||
2352.2.q.bb.1537.2 | 4 | 84.83 | odd | 2 | |||
2352.2.q.bd.961.1 | 4 | 84.23 | even | 6 | |||
2352.2.q.bd.1537.1 | 4 | 12.11 | even | 2 | |||
3675.2.a.bd.1.1 | 2 | 105.74 | odd | 6 | |||
3675.2.a.bf.1.1 | 2 | 105.59 | even | 6 | |||
7056.2.a.cf.1.1 | 2 | 28.11 | odd | 6 | |||
7056.2.a.cv.1.2 | 2 | 28.3 | even | 6 | |||
9408.2.a.di.1.1 | 2 | 168.53 | odd | 6 | |||
9408.2.a.dq.1.2 | 2 | 168.59 | odd | 6 | |||
9408.2.a.dt.1.1 | 2 | 168.11 | even | 6 | |||
9408.2.a.ef.1.2 | 2 | 168.101 | even | 6 |