Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(160,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.160");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.h (of order \(2\), degree \(1\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 14x^{10} + 67x^{8} + 141x^{6} + 129x^{4} + 39x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 160.8 | ||
Root | \(0.167898i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.160 |
Dual form | 483.2.h.b.160.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.254102 | 0.179677 | 0.0898385 | − | 0.995956i | \(-0.471365\pi\) | ||||
0.0898385 | + | 0.995956i | \(0.471365\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.93543 | −0.967716 | ||||||||
\(5\) | 0.458377 | 0.204993 | 0.102496 | − | 0.994733i | \(-0.467317\pi\) | ||||
0.102496 | + | 0.994733i | \(0.467317\pi\) | |||||||
\(6\) | 0.254102i | 0.103737i | ||||||||
\(7\) | −1.07291 | + | 2.41844i | −0.405521 | + | 0.914086i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.116474 | 0.0368325 | ||||||||
\(11\) | 1.34554i | 0.405694i | 0.979210 | + | 0.202847i | \(0.0650194\pi\) | ||||
−0.979210 | + | 0.202847i | \(0.934981\pi\) | |||||||
\(12\) | − | 1.93543i | − | 0.558711i | ||||||
\(13\) | − | 4.42723i | − | 1.22789i | −0.789348 | − | 0.613946i | \(-0.789581\pi\) | ||
0.789348 | − | 0.613946i | \(-0.210419\pi\) | |||||||
\(14\) | −0.272628 | + | 0.614531i | −0.0728628 | + | 0.164240i | ||||
\(15\) | 0.458377i | 0.118353i | ||||||||
\(16\) | 3.61676 | 0.904191 | ||||||||
\(17\) | −7.09918 | −1.72180 | −0.860902 | − | 0.508771i | \(-0.830100\pi\) | ||||
−0.860902 | + | 0.508771i | \(0.830100\pi\) | |||||||
\(18\) | −0.254102 | −0.0598923 | ||||||||
\(19\) | −4.40811 | −1.01129 | −0.505644 | − | 0.862742i | \(-0.668745\pi\) | ||||
−0.505644 | + | 0.862742i | \(0.668745\pi\) | |||||||
\(20\) | −0.887158 | −0.198375 | ||||||||
\(21\) | −2.41844 | − | 1.07291i | −0.527748 | − | 0.234128i | ||||
\(22\) | 0.341903i | 0.0728939i | ||||||||
\(23\) | −4.44364 | + | 1.80391i | −0.926562 | + | 0.376142i | ||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −4.78989 | −0.957978 | ||||||||
\(26\) | − | 1.12497i | − | 0.220624i | ||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.07654 | − | 4.68073i | 0.392429 | − | 0.884576i | ||||
\(29\) | 4.18953 | 0.777977 | 0.388988 | − | 0.921243i | \(-0.372825\pi\) | ||||
0.388988 | + | 0.921243i | \(0.372825\pi\) | |||||||
\(30\) | 0.116474i | 0.0212652i | ||||||||
\(31\) | 4.31867i | 0.775656i | 0.921732 | + | 0.387828i | \(0.126775\pi\) | ||||
−0.921732 | + | 0.387828i | \(0.873225\pi\) | |||||||
\(32\) | 2.91903 | 0.516016 | ||||||||
\(33\) | −1.34554 | −0.234228 | ||||||||
\(34\) | −1.80391 | −0.309369 | ||||||||
\(35\) | −0.491797 | + | 1.10856i | −0.0831288 | + | 0.187381i | ||||
\(36\) | 1.93543 | 0.322572 | ||||||||
\(37\) | 8.56119i | 1.40745i | 0.710472 | + | 0.703725i | \(0.248481\pi\) | ||||
−0.710472 | + | 0.703725i | \(0.751519\pi\) | |||||||
\(38\) | −1.12011 | −0.181705 | ||||||||
\(39\) | 4.42723 | 0.708924 | ||||||||
\(40\) | −0.458377 | −0.0724758 | ||||||||
\(41\) | − | 3.81047i | − | 0.595095i | −0.954707 | − | 0.297547i | \(-0.903831\pi\) | ||
0.954707 | − | 0.297547i | \(-0.0961686\pi\) | |||||||
\(42\) | −0.614531 | − | 0.272628i | −0.0948241 | − | 0.0420674i | ||||
\(43\) | 7.18606i | 1.09586i | 0.836523 | + | 0.547932i | \(0.184585\pi\) | ||||
−0.836523 | + | 0.547932i | \(0.815415\pi\) | |||||||
\(44\) | − | 2.60419i | − | 0.392597i | ||||||
\(45\) | −0.458377 | −0.0683309 | ||||||||
\(46\) | −1.12914 | + | 0.458377i | −0.166482 | + | 0.0675840i | ||||
\(47\) | − | 7.23353i | − | 1.05512i | −0.849518 | − | 0.527559i | \(-0.823107\pi\) | ||
0.849518 | − | 0.527559i | \(-0.176893\pi\) | |||||||
\(48\) | 3.61676i | 0.522035i | ||||||||
\(49\) | −4.69774 | − | 5.18953i | −0.671105 | − | 0.741362i | ||||
\(50\) | −1.21712 | −0.172127 | ||||||||
\(51\) | − | 7.09918i | − | 0.994084i | ||||||
\(52\) | 8.56860i | 1.18825i | ||||||||
\(53\) | − | 8.35783i | − | 1.14804i | −0.818842 | − | 0.574018i | \(-0.805384\pi\) | ||
0.818842 | − | 0.574018i | \(-0.194616\pi\) | |||||||
\(54\) | − | 0.254102i | − | 0.0345789i | ||||||
\(55\) | 0.616763i | 0.0831643i | ||||||||
\(56\) | 1.07291 | − | 2.41844i | 0.143373 | − | 0.323178i | ||||
\(57\) | − | 4.40811i | − | 0.583868i | ||||||
\(58\) | 1.06457 | 0.139785 | ||||||||
\(59\) | 8.10856i | 1.05564i | 0.849355 | + | 0.527822i | \(0.176991\pi\) | ||||
−0.849355 | + | 0.527822i | \(0.823009\pi\) | |||||||
\(60\) | − | 0.887158i | − | 0.114532i | ||||||
\(61\) | 10.2486 | 1.31220 | 0.656101 | − | 0.754673i | \(-0.272205\pi\) | ||||
0.656101 | + | 0.754673i | \(0.272205\pi\) | |||||||
\(62\) | 1.09738i | 0.139368i | ||||||||
\(63\) | 1.07291 | − | 2.41844i | 0.135174 | − | 0.304695i | ||||
\(64\) | −6.49180 | −0.811475 | ||||||||
\(65\) | − | 2.02934i | − | 0.251709i | ||||||
\(66\) | −0.341903 | −0.0420853 | ||||||||
\(67\) | 5.84052i | 0.713533i | 0.934194 | + | 0.356767i | \(0.116121\pi\) | ||||
−0.934194 | + | 0.356767i | \(0.883879\pi\) | |||||||
\(68\) | 13.7400 | 1.66622 | ||||||||
\(69\) | −1.80391 | − | 4.44364i | −0.217166 | − | 0.534951i | ||||
\(70\) | −0.124966 | + | 0.281687i | −0.0149363 | + | 0.0336680i | ||||
\(71\) | 8.42723 | 1.00013 | 0.500064 | − | 0.865988i | \(-0.333310\pi\) | ||||
0.500064 | + | 0.865988i | \(0.333310\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 7.04399i | 0.824437i | 0.911085 | + | 0.412218i | \(0.135246\pi\) | ||||
−0.911085 | + | 0.412218i | \(0.864754\pi\) | |||||||
\(74\) | 2.17541i | 0.252887i | ||||||||
\(75\) | − | 4.78989i | − | 0.553089i | ||||||
\(76\) | 8.53159 | 0.978641 | ||||||||
\(77\) | −3.25410 | − | 1.44364i | −0.370839 | − | 0.164518i | ||||
\(78\) | 1.12497 | 0.127377 | ||||||||
\(79\) | 6.86623i | 0.772511i | 0.922392 | + | 0.386256i | \(0.126232\pi\) | ||||
−0.922392 | + | 0.386256i | \(0.873768\pi\) | |||||||
\(80\) | 1.65784 | 0.185352 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 0.968246i | − | 0.106925i | ||||||
\(83\) | 4.95336 | 0.543702 | 0.271851 | − | 0.962339i | \(-0.412364\pi\) | ||||
0.271851 | + | 0.962339i | \(0.412364\pi\) | |||||||
\(84\) | 4.68073 | + | 2.07654i | 0.510710 | + | 0.226569i | ||||
\(85\) | −3.25410 | −0.352957 | ||||||||
\(86\) | 1.82599i | 0.196901i | ||||||||
\(87\) | 4.18953i | 0.449165i | ||||||||
\(88\) | − | 1.34554i | − | 0.143435i | ||||||
\(89\) | −16.0023 | −1.69624 | −0.848118 | − | 0.529807i | \(-0.822264\pi\) | ||||
−0.848118 | + | 0.529807i | \(0.822264\pi\) | |||||||
\(90\) | −0.116474 | −0.0122775 | ||||||||
\(91\) | 10.7070 | + | 4.75001i | 1.12240 | + | 0.497936i | ||||
\(92\) | 8.60036 | − | 3.49135i | 0.896649 | − | 0.363999i | ||||
\(93\) | −4.31867 | −0.447825 | ||||||||
\(94\) | − | 1.83805i | − | 0.189581i | ||||||
\(95\) | −2.02058 | −0.207307 | ||||||||
\(96\) | 2.91903i | 0.297922i | ||||||||
\(97\) | 3.86285 | 0.392213 | 0.196107 | − | 0.980583i | \(-0.437170\pi\) | ||||
0.196107 | + | 0.980583i | \(0.437170\pi\) | |||||||
\(98\) | −1.19370 | − | 1.31867i | −0.120582 | − | 0.133206i | ||||
\(99\) | − | 1.34554i | − | 0.135231i | ||||||
\(100\) | 9.27051 | 0.927051 | ||||||||
\(101\) | 12.6496i | 1.25868i | 0.777130 | + | 0.629340i | \(0.216675\pi\) | ||||
−0.777130 | + | 0.629340i | \(0.783325\pi\) | |||||||
\(102\) | − | 1.80391i | − | 0.178614i | ||||||
\(103\) | 7.52796 | 0.741752 | 0.370876 | − | 0.928682i | \(-0.379058\pi\) | ||||
0.370876 | + | 0.928682i | \(0.379058\pi\) | |||||||
\(104\) | 4.42723i | 0.434126i | ||||||||
\(105\) | −1.10856 | − | 0.491797i | −0.108184 | − | 0.0479944i | ||||
\(106\) | − | 2.12374i | − | 0.206276i | ||||||
\(107\) | − | 20.1553i | − | 1.94849i | −0.225490 | − | 0.974246i | \(-0.572398\pi\) | ||
0.225490 | − | 0.974246i | \(-0.427602\pi\) | |||||||
\(108\) | 1.93543i | 0.186237i | ||||||||
\(109\) | 5.06232i | 0.484882i | 0.970166 | + | 0.242441i | \(0.0779481\pi\) | ||||
−0.970166 | + | 0.242441i | \(0.922052\pi\) | |||||||
\(110\) | 0.156721i | 0.0149427i | ||||||||
\(111\) | −8.56119 | −0.812592 | ||||||||
\(112\) | −3.88045 | + | 8.74694i | −0.366668 | + | 0.826508i | ||||
\(113\) | 3.38240i | 0.318189i | 0.987263 | + | 0.159095i | \(0.0508575\pi\) | ||||
−0.987263 | + | 0.159095i | \(0.949143\pi\) | |||||||
\(114\) | − | 1.12011i | − | 0.104908i | ||||||
\(115\) | −2.03686 | + | 0.826873i | −0.189938 | + | 0.0771063i | ||||
\(116\) | −8.10856 | −0.752861 | ||||||||
\(117\) | 4.42723i | 0.409297i | ||||||||
\(118\) | 2.06040i | 0.189675i | ||||||||
\(119\) | 7.61676 | − | 17.1690i | 0.698228 | − | 1.57388i | ||||
\(120\) | − | 0.458377i | − | 0.0418439i | ||||||
\(121\) | 9.18953 | 0.835412 | ||||||||
\(122\) | 2.60419 | 0.235773 | ||||||||
\(123\) | 3.81047 | 0.343578 | ||||||||
\(124\) | − | 8.35849i | − | 0.750615i | ||||||
\(125\) | −4.48746 | −0.401371 | ||||||||
\(126\) | 0.272628 | − | 0.614531i | 0.0242876 | − | 0.0547467i | ||||
\(127\) | −12.2981 | −1.09128 | −0.545640 | − | 0.838020i | \(-0.683713\pi\) | ||||
−0.545640 | + | 0.838020i | \(0.683713\pi\) | |||||||
\(128\) | −7.48763 | −0.661819 | ||||||||
\(129\) | −7.18606 | −0.632697 | ||||||||
\(130\) | − | 0.515659i | − | 0.0452263i | ||||||
\(131\) | 5.17313i | 0.451978i | 0.974130 | + | 0.225989i | \(0.0725614\pi\) | ||||
−0.974130 | + | 0.225989i | \(0.927439\pi\) | |||||||
\(132\) | 2.60419 | 0.226666 | ||||||||
\(133\) | 4.72949 | − | 10.6608i | 0.410099 | − | 0.924405i | ||||
\(134\) | 1.48409i | 0.128205i | ||||||||
\(135\) | − | 0.458377i | − | 0.0394508i | ||||||
\(136\) | 7.09918 | 0.608749 | ||||||||
\(137\) | − | 9.10644i | − | 0.778016i | −0.921234 | − | 0.389008i | \(-0.872818\pi\) | ||
0.921234 | − | 0.389008i | \(-0.127182\pi\) | |||||||
\(138\) | −0.458377 | − | 1.12914i | −0.0390197 | − | 0.0961184i | ||||
\(139\) | 17.8503i | 1.51404i | 0.653391 | + | 0.757021i | \(0.273346\pi\) | ||||
−0.653391 | + | 0.757021i | \(0.726654\pi\) | |||||||
\(140\) | 0.951839 | − | 2.14554i | 0.0804451 | − | 0.181331i | ||||
\(141\) | 7.23353 | 0.609173 | ||||||||
\(142\) | 2.14137 | 0.179700 | ||||||||
\(143\) | 5.95699 | 0.498149 | ||||||||
\(144\) | −3.61676 | −0.301397 | ||||||||
\(145\) | 1.92039 | 0.159479 | ||||||||
\(146\) | 1.78989i | 0.148132i | ||||||||
\(147\) | 5.18953 | − | 4.69774i | 0.428026 | − | 0.387463i | ||||
\(148\) | − | 16.5696i | − | 1.36201i | ||||||
\(149\) | 20.1849i | 1.65362i | 0.562485 | + | 0.826808i | \(0.309845\pi\) | ||||
−0.562485 | + | 0.826808i | \(0.690155\pi\) | |||||||
\(150\) | − | 1.21712i | − | 0.0993774i | ||||||
\(151\) | −11.5798 | −0.942349 | −0.471175 | − | 0.882040i | \(-0.656170\pi\) | ||||
−0.471175 | + | 0.882040i | \(0.656170\pi\) | |||||||
\(152\) | 4.40811 | 0.357545 | ||||||||
\(153\) | 7.09918 | 0.573934 | ||||||||
\(154\) | −0.826873 | − | 0.366830i | −0.0666313 | − | 0.0295600i | ||||
\(155\) | 1.97958i | 0.159004i | ||||||||
\(156\) | −8.56860 | −0.686037 | ||||||||
\(157\) | −20.2643 | −1.61727 | −0.808634 | − | 0.588312i | \(-0.799793\pi\) | ||||
−0.808634 | + | 0.588312i | \(0.799793\pi\) | |||||||
\(158\) | 1.74472i | 0.138802i | ||||||||
\(159\) | 8.35783 | 0.662819 | ||||||||
\(160\) | 1.33802 | 0.105779 | ||||||||
\(161\) | 0.404950 | − | 12.6821i | 0.0319146 | − | 0.999491i | ||||
\(162\) | 0.254102 | 0.0199641 | ||||||||
\(163\) | 7.97942 | 0.624997 | 0.312498 | − | 0.949918i | \(-0.398834\pi\) | ||||
0.312498 | + | 0.949918i | \(0.398834\pi\) | |||||||
\(164\) | 7.37490i | 0.575883i | ||||||||
\(165\) | −0.616763 | −0.0480149 | ||||||||
\(166\) | 1.25866 | 0.0976908 | ||||||||
\(167\) | 3.04399i | 0.235551i | 0.993040 | + | 0.117776i | \(0.0375763\pi\) | ||||
−0.993040 | + | 0.117776i | \(0.962424\pi\) | |||||||
\(168\) | 2.41844 | + | 1.07291i | 0.186587 | + | 0.0827766i | ||||
\(169\) | −6.60036 | −0.507720 | ||||||||
\(170\) | −0.826873 | −0.0634182 | ||||||||
\(171\) | 4.40811 | 0.337096 | ||||||||
\(172\) | − | 13.9081i | − | 1.06048i | ||||||
\(173\) | − | 13.4231i | − | 1.02054i | −0.860015 | − | 0.510268i | \(-0.829546\pi\) | ||
0.860015 | − | 0.510268i | \(-0.170454\pi\) | |||||||
\(174\) | 1.06457i | 0.0807047i | ||||||||
\(175\) | 5.13911 | − | 11.5841i | 0.388480 | − | 0.875674i | ||||
\(176\) | 4.86648i | 0.366825i | ||||||||
\(177\) | −8.10856 | −0.609477 | ||||||||
\(178\) | −4.06620 | −0.304775 | ||||||||
\(179\) | 14.2294 | 1.06355 | 0.531776 | − | 0.846885i | \(-0.321525\pi\) | ||||
0.531776 | + | 0.846885i | \(0.321525\pi\) | |||||||
\(180\) | 0.887158 | 0.0661249 | ||||||||
\(181\) | −19.6026 | −1.45705 | −0.728524 | − | 0.685020i | \(-0.759793\pi\) | ||||
−0.728524 | + | 0.685020i | \(0.759793\pi\) | |||||||
\(182\) | 2.72067 | + | 1.20699i | 0.201669 | + | 0.0894677i | ||||
\(183\) | 10.2486i | 0.757600i | ||||||||
\(184\) | 4.44364 | − | 1.80391i | 0.327589 | − | 0.132986i | ||||
\(185\) | 3.92425i | 0.288517i | ||||||||
\(186\) | −1.09738 | −0.0804639 | ||||||||
\(187\) | − | 9.55220i | − | 0.698526i | ||||||
\(188\) | 14.0000i | 1.02105i | ||||||||
\(189\) | 2.41844 | + | 1.07291i | 0.175916 | + | 0.0780426i | ||||
\(190\) | −0.513432 | −0.0372483 | ||||||||
\(191\) | − | 21.1811i | − | 1.53261i | −0.642478 | − | 0.766304i | \(-0.722094\pi\) | ||
0.642478 | − | 0.766304i | \(-0.277906\pi\) | |||||||
\(192\) | − | 6.49180i | − | 0.468505i | ||||||
\(193\) | 10.0328 | 0.722178 | 0.361089 | − | 0.932531i | \(-0.382405\pi\) | ||||
0.361089 | + | 0.932531i | \(0.382405\pi\) | |||||||
\(194\) | 0.981557 | 0.0704717 | ||||||||
\(195\) | 2.02934 | 0.145324 | ||||||||
\(196\) | 9.09215 | + | 10.0440i | 0.649439 | + | 0.717428i | ||||
\(197\) | 5.53996 | 0.394706 | 0.197353 | − | 0.980333i | \(-0.436766\pi\) | ||||
0.197353 | + | 0.980333i | \(0.436766\pi\) | |||||||
\(198\) | − | 0.341903i | − | 0.0242980i | ||||||
\(199\) | 6.69808 | 0.474814 | 0.237407 | − | 0.971410i | \(-0.423702\pi\) | ||||
0.237407 | + | 0.971410i | \(0.423702\pi\) | |||||||
\(200\) | 4.78989 | 0.338696 | ||||||||
\(201\) | −5.84052 | −0.411958 | ||||||||
\(202\) | 3.21428i | 0.226156i | ||||||||
\(203\) | −4.49498 | + | 10.1322i | −0.315486 | + | 0.711138i | ||||
\(204\) | 13.7400i | 0.961991i | ||||||||
\(205\) | − | 1.74663i | − | 0.121990i | ||||||
\(206\) | 1.91287 | 0.133276 | ||||||||
\(207\) | 4.44364 | − | 1.80391i | 0.308854 | − | 0.125381i | ||||
\(208\) | − | 16.0122i | − | 1.11025i | ||||||
\(209\) | − | 5.93126i | − | 0.410274i | ||||||
\(210\) | −0.281687 | − | 0.124966i | −0.0194382 | − | 0.00862350i | ||||
\(211\) | −9.33508 | −0.642653 | −0.321327 | − | 0.946968i | \(-0.604129\pi\) | ||||
−0.321327 | + | 0.946968i | \(0.604129\pi\) | |||||||
\(212\) | 16.1760i | 1.11097i | ||||||||
\(213\) | 8.42723i | 0.577424i | ||||||||
\(214\) | − | 5.12151i | − | 0.350099i | ||||||
\(215\) | 3.29392i | 0.224644i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −10.4445 | − | 4.63353i | −0.709016 | − | 0.314545i | ||||
\(218\) | 1.28634i | 0.0871221i | ||||||||
\(219\) | −7.04399 | −0.475989 | ||||||||
\(220\) | − | 1.19370i | − | 0.0804794i | ||||||
\(221\) | 31.4297i | 2.11419i | ||||||||
\(222\) | −2.17541 | −0.146004 | ||||||||
\(223\) | 10.3257i | 0.691459i | 0.938334 | + | 0.345729i | \(0.112368\pi\) | ||||
−0.938334 | + | 0.345729i | \(0.887632\pi\) | |||||||
\(224\) | −3.13185 | + | 7.05950i | −0.209255 | + | 0.471683i | ||||
\(225\) | 4.78989 | 0.319326 | ||||||||
\(226\) | 0.859473i | 0.0571713i | ||||||||
\(227\) | −24.6428 | −1.63560 | −0.817800 | − | 0.575502i | \(-0.804807\pi\) | ||||
−0.817800 | + | 0.575502i | \(0.804807\pi\) | |||||||
\(228\) | 8.53159i | 0.565018i | ||||||||
\(229\) | −8.21928 | −0.543146 | −0.271573 | − | 0.962418i | \(-0.587544\pi\) | ||||
−0.271573 | + | 0.962418i | \(0.587544\pi\) | |||||||
\(230\) | −0.517570 | + | 0.210110i | −0.0341276 | + | 0.0138542i | ||||
\(231\) | 1.44364 | − | 3.25410i | 0.0949843 | − | 0.214104i | ||||
\(232\) | −4.18953 | −0.275056 | ||||||||
\(233\) | −11.3749 | −0.745194 | −0.372597 | − | 0.927993i | \(-0.621533\pi\) | ||||
−0.372597 | + | 0.927993i | \(0.621533\pi\) | |||||||
\(234\) | 1.12497i | 0.0735414i | ||||||||
\(235\) | − | 3.31568i | − | 0.216291i | ||||||
\(236\) | − | 15.6936i | − | 1.02156i | ||||||
\(237\) | −6.86623 | −0.446009 | ||||||||
\(238\) | 1.93543 | − | 4.36266i | 0.125455 | − | 0.282789i | ||||
\(239\) | −26.9547 | −1.74355 | −0.871777 | − | 0.489904i | \(-0.837032\pi\) | ||||
−0.871777 | + | 0.489904i | \(0.837032\pi\) | |||||||
\(240\) | 1.65784i | 0.107013i | ||||||||
\(241\) | 5.40422 | 0.348116 | 0.174058 | − | 0.984735i | \(-0.444312\pi\) | ||||
0.174058 | + | 0.984735i | \(0.444312\pi\) | |||||||
\(242\) | 2.33508 | 0.150104 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −19.8355 | −1.26984 | ||||||||
\(245\) | −2.15334 | − | 2.37876i | −0.137572 | − | 0.151974i | ||||
\(246\) | 0.968246 | 0.0617331 | ||||||||
\(247\) | 19.5157i | 1.24175i | ||||||||
\(248\) | − | 4.31867i | − | 0.274236i | ||||||
\(249\) | 4.95336i | 0.313907i | ||||||||
\(250\) | −1.14027 | −0.0721171 | ||||||||
\(251\) | 19.4067 | 1.22494 | 0.612471 | − | 0.790493i | \(-0.290176\pi\) | ||||
0.612471 | + | 0.790493i | \(0.290176\pi\) | |||||||
\(252\) | −2.07654 | + | 4.68073i | −0.130810 | + | 0.294859i | ||||
\(253\) | −2.42723 | − | 5.97907i | −0.152599 | − | 0.375901i | ||||
\(254\) | −3.12497 | −0.196078 | ||||||||
\(255\) | − | 3.25410i | − | 0.203780i | ||||||
\(256\) | 11.0810 | 0.692561 | ||||||||
\(257\) | − | 4.34625i | − | 0.271112i | −0.990770 | − | 0.135556i | \(-0.956718\pi\) | ||
0.990770 | − | 0.135556i | \(-0.0432821\pi\) | |||||||
\(258\) | −1.82599 | −0.113681 | ||||||||
\(259\) | −20.7047 | − | 9.18537i | −1.28653 | − | 0.570751i | ||||
\(260\) | 3.92765i | 0.243583i | ||||||||
\(261\) | −4.18953 | −0.259326 | ||||||||
\(262\) | 1.31450i | 0.0812101i | ||||||||
\(263\) | 1.57848i | 0.0973335i | 0.998815 | + | 0.0486668i | \(0.0154972\pi\) | ||||
−0.998815 | + | 0.0486668i | \(0.984503\pi\) | |||||||
\(264\) | 1.34554 | 0.0828120 | ||||||||
\(265\) | − | 3.83104i | − | 0.235339i | ||||||
\(266\) | 1.20177 | − | 2.70892i | 0.0736854 | − | 0.166094i | ||||
\(267\) | − | 16.0023i | − | 0.979323i | ||||||
\(268\) | − | 11.3039i | − | 0.690497i | ||||||
\(269\) | − | 21.4025i | − | 1.30493i | −0.757818 | − | 0.652466i | \(-0.773734\pi\) | ||
0.757818 | − | 0.652466i | \(-0.226266\pi\) | |||||||
\(270\) | − | 0.116474i | − | 0.00708841i | ||||||
\(271\) | 15.3267i | 0.931033i | 0.885039 | + | 0.465517i | \(0.154131\pi\) | ||||
−0.885039 | + | 0.465517i | \(0.845869\pi\) | |||||||
\(272\) | −25.6760 | −1.55684 | ||||||||
\(273\) | −4.75001 | + | 10.7070i | −0.287484 | + | 0.648017i | ||||
\(274\) | − | 2.31396i | − | 0.139792i | ||||||
\(275\) | − | 6.44497i | − | 0.388646i | ||||||
\(276\) | 3.49135 | + | 8.60036i | 0.210155 | + | 0.517681i | ||||
\(277\) | 10.5152 | 0.631798 | 0.315899 | − | 0.948793i | \(-0.397694\pi\) | ||||
0.315899 | + | 0.948793i | \(0.397694\pi\) | |||||||
\(278\) | 4.53579i | 0.272039i | ||||||||
\(279\) | − | 4.31867i | − | 0.258552i | ||||||
\(280\) | 0.491797 | − | 1.10856i | 0.0293905 | − | 0.0662491i | ||||
\(281\) | − | 5.30278i | − | 0.316338i | −0.987412 | − | 0.158169i | \(-0.949441\pi\) | ||
0.987412 | − | 0.158169i | \(-0.0505590\pi\) | |||||||
\(282\) | 1.83805 | 0.109454 | ||||||||
\(283\) | −2.05894 | −0.122391 | −0.0611956 | − | 0.998126i | \(-0.519491\pi\) | ||||
−0.0611956 | + | 0.998126i | \(0.519491\pi\) | |||||||
\(284\) | −16.3103 | −0.967840 | ||||||||
\(285\) | − | 2.02058i | − | 0.119689i | ||||||
\(286\) | 1.51368 | 0.0895059 | ||||||||
\(287\) | 9.21540 | + | 4.08828i | 0.543968 | + | 0.241323i | ||||
\(288\) | −2.91903 | −0.172005 | ||||||||
\(289\) | 33.3983 | 1.96461 | ||||||||
\(290\) | 0.487974 | 0.0286548 | ||||||||
\(291\) | 3.86285i | 0.226444i | ||||||||
\(292\) | − | 13.6332i | − | 0.797821i | ||||||
\(293\) | −17.4939 | −1.02200 | −0.511001 | − | 0.859580i | \(-0.670725\pi\) | ||||
−0.511001 | + | 0.859580i | \(0.670725\pi\) | |||||||
\(294\) | 1.31867 | − | 1.19370i | 0.0769064 | − | 0.0696182i | ||||
\(295\) | 3.71678i | 0.216399i | ||||||||
\(296\) | − | 8.56119i | − | 0.497609i | ||||||
\(297\) | 1.34554 | 0.0780759 | ||||||||
\(298\) | 5.12903i | 0.297117i | ||||||||
\(299\) | 7.98634 | + | 19.6730i | 0.461862 | + | 1.13772i | ||||
\(300\) | 9.27051i | 0.535233i | ||||||||
\(301\) | −17.3791 | − | 7.70998i | −1.00171 | − | 0.444396i | ||||
\(302\) | −2.94244 | −0.169318 | ||||||||
\(303\) | −12.6496 | −0.726699 | ||||||||
\(304\) | −15.9431 | −0.914398 | ||||||||
\(305\) | 4.69774 | 0.268992 | ||||||||
\(306\) | 1.80391 | 0.103123 | ||||||||
\(307\) | − | 31.8573i | − | 1.81819i | −0.416587 | − | 0.909096i | \(-0.636774\pi\) | ||
0.416587 | − | 0.909096i | \(-0.363226\pi\) | |||||||
\(308\) | 6.29809 | + | 2.79406i | 0.358867 | + | 0.159206i | ||||
\(309\) | 7.52796i | 0.428251i | ||||||||
\(310\) | 0.503015i | 0.0285693i | ||||||||
\(311\) | 2.71831i | 0.154141i | 0.997026 | + | 0.0770707i | \(0.0245567\pi\) | ||||
−0.997026 | + | 0.0770707i | \(0.975443\pi\) | |||||||
\(312\) | −4.42723 | −0.250642 | ||||||||
\(313\) | −21.1811 | −1.19722 | −0.598612 | − | 0.801039i | \(-0.704281\pi\) | ||||
−0.598612 | + | 0.801039i | \(0.704281\pi\) | |||||||
\(314\) | −5.14919 | −0.290586 | ||||||||
\(315\) | 0.491797 | − | 1.10856i | 0.0277096 | − | 0.0624603i | ||||
\(316\) | − | 13.2891i | − | 0.747571i | ||||||
\(317\) | −11.2541 | −0.632093 | −0.316047 | − | 0.948744i | \(-0.602356\pi\) | ||||
−0.316047 | + | 0.948744i | \(0.602356\pi\) | |||||||
\(318\) | 2.12374 | 0.119093 | ||||||||
\(319\) | 5.63717i | 0.315621i | ||||||||
\(320\) | −2.97569 | −0.166346 | ||||||||
\(321\) | 20.1553 | 1.12496 | ||||||||
\(322\) | 0.102899 | − | 3.22255i | 0.00573431 | − | 0.179585i | ||||
\(323\) | 31.2939 | 1.74124 | ||||||||
\(324\) | −1.93543 | −0.107524 | ||||||||
\(325\) | 21.2059i | 1.17629i | ||||||||
\(326\) | 2.02759 | 0.112298 | ||||||||
\(327\) | −5.06232 | −0.279947 | ||||||||
\(328\) | 3.81047i | 0.210398i | ||||||||
\(329\) | 17.4939 | + | 7.76091i | 0.964468 | + | 0.427873i | ||||
\(330\) | −0.156721 | −0.00862718 | ||||||||
\(331\) | 8.54102 | 0.469457 | 0.234728 | − | 0.972061i | \(-0.424580\pi\) | ||||
0.234728 | + | 0.972061i | \(0.424580\pi\) | |||||||
\(332\) | −9.58690 | −0.526149 | ||||||||
\(333\) | − | 8.56119i | − | 0.469150i | ||||||
\(334\) | 0.773483i | 0.0423231i | ||||||||
\(335\) | 2.67716i | 0.146269i | ||||||||
\(336\) | −8.74694 | − | 3.88045i | −0.477185 | − | 0.211696i | ||||
\(337\) | 8.24136i | 0.448935i | 0.974482 | + | 0.224468i | \(0.0720643\pi\) | ||||
−0.974482 | + | 0.224468i | \(0.927936\pi\) | |||||||
\(338\) | −1.67716 | −0.0912256 | ||||||||
\(339\) | −3.38240 | −0.183707 | ||||||||
\(340\) | 6.29809 | 0.341562 | ||||||||
\(341\) | −5.81092 | −0.314679 | ||||||||
\(342\) | 1.12011 | 0.0605685 | ||||||||
\(343\) | 17.5908 | − | 5.79332i | 0.949816 | − | 0.312810i | ||||
\(344\) | − | 7.18606i | − | 0.387446i | ||||||
\(345\) | −0.826873 | − | 2.03686i | −0.0445173 | − | 0.109661i | ||||
\(346\) | − | 3.41082i | − | 0.183367i | ||||||
\(347\) | −10.6649 | −0.572523 | −0.286262 | − | 0.958152i | \(-0.592413\pi\) | ||||
−0.286262 | + | 0.958152i | \(0.592413\pi\) | |||||||
\(348\) | − | 8.10856i | − | 0.434664i | ||||||
\(349\) | 1.00417i | 0.0537519i | 0.999639 | + | 0.0268760i | \(0.00855592\pi\) | ||||
−0.999639 | + | 0.0268760i | \(0.991444\pi\) | |||||||
\(350\) | 1.30586 | − | 2.94353i | 0.0698010 | − | 0.157339i | ||||
\(351\) | −4.42723 | −0.236308 | ||||||||
\(352\) | 3.92765i | 0.209345i | ||||||||
\(353\) | 35.7693i | 1.90381i | 0.306396 | + | 0.951904i | \(0.400877\pi\) | ||||
−0.306396 | + | 0.951904i | \(0.599123\pi\) | |||||||
\(354\) | −2.06040 | −0.109509 | ||||||||
\(355\) | 3.86285 | 0.205019 | ||||||||
\(356\) | 30.9713 | 1.64148 | ||||||||
\(357\) | 17.1690 | + | 7.61676i | 0.908678 | + | 0.403122i | ||||
\(358\) | 3.61570 | 0.191096 | ||||||||
\(359\) | 20.6433i | 1.08951i | 0.838594 | + | 0.544756i | \(0.183378\pi\) | ||||
−0.838594 | + | 0.544756i | \(0.816622\pi\) | |||||||
\(360\) | 0.458377 | 0.0241586 | ||||||||
\(361\) | 0.431398 | 0.0227052 | ||||||||
\(362\) | −4.98105 | −0.261798 | ||||||||
\(363\) | 9.18953i | 0.482325i | ||||||||
\(364\) | −20.7227 | − | 9.19332i | −1.08616 | − | 0.481861i | ||||
\(365\) | 3.22881i | 0.169003i | ||||||||
\(366\) | 2.60419i | 0.136123i | ||||||||
\(367\) | 25.7352 | 1.34337 | 0.671684 | − | 0.740838i | \(-0.265571\pi\) | ||||
0.671684 | + | 0.740838i | \(0.265571\pi\) | |||||||
\(368\) | −16.0716 | + | 6.52433i | −0.837789 | + | 0.340104i | ||||
\(369\) | 3.81047i | 0.198365i | ||||||||
\(370\) | 0.997160i | 0.0518399i | ||||||||
\(371\) | 20.2130 | + | 8.96719i | 1.04940 | + | 0.465553i | ||||
\(372\) | 8.35849 | 0.433368 | ||||||||
\(373\) | − | 16.6786i | − | 0.863583i | −0.901974 | − | 0.431791i | \(-0.857882\pi\) | ||
0.901974 | − | 0.431791i | \(-0.142118\pi\) | |||||||
\(374\) | − | 2.42723i | − | 0.125509i | ||||||
\(375\) | − | 4.48746i | − | 0.231732i | ||||||
\(376\) | 7.23353i | 0.373041i | ||||||||
\(377\) | − | 18.5480i | − | 0.955272i | ||||||
\(378\) | 0.614531 | + | 0.272628i | 0.0316080 | + | 0.0140225i | ||||
\(379\) | − | 30.9492i | − | 1.58976i | −0.606770 | − | 0.794878i | \(-0.707535\pi\) | ||
0.606770 | − | 0.794878i | \(-0.292465\pi\) | |||||||
\(380\) | 3.91069 | 0.200614 | ||||||||
\(381\) | − | 12.2981i | − | 0.630050i | ||||||
\(382\) | − | 5.38214i | − | 0.275374i | ||||||
\(383\) | 18.6858 | 0.954801 | 0.477400 | − | 0.878686i | \(-0.341579\pi\) | ||||
0.477400 | + | 0.878686i | \(0.341579\pi\) | |||||||
\(384\) | − | 7.48763i | − | 0.382101i | ||||||
\(385\) | −1.49161 | − | 0.661730i | −0.0760193 | − | 0.0337249i | ||||
\(386\) | 2.54935 | 0.129759 | ||||||||
\(387\) | − | 7.18606i | − | 0.365288i | ||||||
\(388\) | −7.47629 | −0.379551 | ||||||||
\(389\) | − | 26.5059i | − | 1.34390i | −0.740595 | − | 0.671952i | \(-0.765456\pi\) | ||
0.740595 | − | 0.671952i | \(-0.234544\pi\) | |||||||
\(390\) | 0.515659 | 0.0261114 | ||||||||
\(391\) | 31.5462 | − | 12.8063i | 1.59536 | − | 0.647642i | ||||
\(392\) | 4.69774 | + | 5.18953i | 0.237272 | + | 0.262111i | ||||
\(393\) | −5.17313 | −0.260950 | ||||||||
\(394\) | 1.40771 | 0.0709195 | ||||||||
\(395\) | 3.14732i | 0.158359i | ||||||||
\(396\) | 2.60419i | 0.130866i | ||||||||
\(397\) | − | 8.63734i | − | 0.433496i | −0.976228 | − | 0.216748i | \(-0.930455\pi\) | ||
0.976228 | − | 0.216748i | \(-0.0695449\pi\) | |||||||
\(398\) | 1.70199 | 0.0853132 | ||||||||
\(399\) | 10.6608 | + | 4.72949i | 0.533705 | + | 0.236771i | ||||
\(400\) | −17.3239 | −0.866195 | ||||||||
\(401\) | 12.9322i | 0.645802i | 0.946433 | + | 0.322901i | \(0.104658\pi\) | ||||
−0.946433 | + | 0.322901i | \(0.895342\pi\) | |||||||
\(402\) | −1.48409 | −0.0740195 | ||||||||
\(403\) | 19.1197 | 0.952422 | ||||||||
\(404\) | − | 24.4824i | − | 1.21804i | ||||||
\(405\) | 0.458377 | 0.0227770 | ||||||||
\(406\) | −1.14218 | + | 2.57460i | −0.0566856 | + | 0.127775i | ||||
\(407\) | −11.5194 | −0.570995 | ||||||||
\(408\) | 7.09918i | 0.351462i | ||||||||
\(409\) | 4.40665i | 0.217895i | 0.994048 | + | 0.108947i | \(0.0347480\pi\) | ||||
−0.994048 | + | 0.108947i | \(0.965252\pi\) | |||||||
\(410\) | − | 0.443822i | − | 0.0219188i | ||||||
\(411\) | 9.10644 | 0.449188 | ||||||||
\(412\) | −14.5699 | −0.717805 | ||||||||
\(413\) | −19.6101 | − | 8.69974i | −0.964950 | − | 0.428086i | ||||
\(414\) | 1.12914 | − | 0.458377i | 0.0554940 | − | 0.0225280i | ||||
\(415\) | 2.27051 | 0.111455 | ||||||||
\(416\) | − | 12.9232i | − | 0.633612i | ||||||
\(417\) | −17.8503 | −0.874132 | ||||||||
\(418\) | − | 1.50714i | − | 0.0737168i | ||||||
\(419\) | 5.91988 | 0.289205 | 0.144602 | − | 0.989490i | \(-0.453810\pi\) | ||||
0.144602 | + | 0.989490i | \(0.453810\pi\) | |||||||
\(420\) | 2.14554 | + | 0.951839i | 0.104692 | + | 0.0464450i | ||||
\(421\) | − | 10.4816i | − | 0.510841i | −0.966830 | − | 0.255420i | \(-0.917786\pi\) | ||
0.966830 | − | 0.255420i | \(-0.0822139\pi\) | |||||||
\(422\) | −2.37206 | −0.115470 | ||||||||
\(423\) | 7.23353i | 0.351706i | ||||||||
\(424\) | 8.35783i | 0.405892i | ||||||||
\(425\) | 34.0043 | 1.64945 | ||||||||
\(426\) | 2.14137i | 0.103750i | ||||||||
\(427\) | −10.9958 | + | 24.7857i | −0.532126 | + | 1.19947i | ||||
\(428\) | 39.0093i | 1.88559i | ||||||||
\(429\) | 5.95699i | 0.287606i | ||||||||
\(430\) | 0.836992i | 0.0403633i | ||||||||
\(431\) | − | 21.0129i | − | 1.01216i | −0.862488 | − | 0.506078i | \(-0.831095\pi\) | ||
0.862488 | − | 0.506078i | \(-0.168905\pi\) | |||||||
\(432\) | − | 3.61676i | − | 0.174012i | ||||||
\(433\) | 7.21565 | 0.346762 | 0.173381 | − | 0.984855i | \(-0.444531\pi\) | ||||
0.173381 | + | 0.984855i | \(0.444531\pi\) | |||||||
\(434\) | −2.65395 | − | 1.17739i | −0.127394 | − | 0.0565165i | ||||
\(435\) | 1.92039i | 0.0920755i | ||||||||
\(436\) | − | 9.79777i | − | 0.469228i | ||||||
\(437\) | 19.5880 | − | 7.95184i | 0.937022 | − | 0.380388i | ||||
\(438\) | −1.78989 | −0.0855243 | ||||||||
\(439\) | 37.1565i | 1.77338i | 0.462364 | + | 0.886690i | \(0.347001\pi\) | ||||
−0.462364 | + | 0.886690i | \(0.652999\pi\) | |||||||
\(440\) | − | 0.616763i | − | 0.0294030i | ||||||
\(441\) | 4.69774 | + | 5.18953i | 0.223702 | + | 0.247121i | ||||
\(442\) | 7.98634i | 0.379871i | ||||||||
\(443\) | −16.8461 | −0.800383 | −0.400192 | − | 0.916431i | \(-0.631056\pi\) | ||||
−0.400192 | + | 0.916431i | \(0.631056\pi\) | |||||||
\(444\) | 16.5696 | 0.786358 | ||||||||
\(445\) | −7.33508 | −0.347716 | ||||||||
\(446\) | 2.62377i | 0.124239i | ||||||||
\(447\) | −20.1849 | −0.954715 | ||||||||
\(448\) | 6.96510 | − | 15.7000i | 0.329070 | − | 0.741757i | ||||
\(449\) | 0.583949 | 0.0275583 | 0.0137791 | − | 0.999905i | \(-0.495614\pi\) | ||||
0.0137791 | + | 0.999905i | \(0.495614\pi\) | |||||||
\(450\) | 1.21712 | 0.0573755 | ||||||||
\(451\) | 5.12712 | 0.241427 | ||||||||
\(452\) | − | 6.54640i | − | 0.307917i | ||||||
\(453\) | − | 11.5798i | − | 0.544066i | ||||||
\(454\) | −6.26178 | −0.293880 | ||||||||
\(455\) | 4.90785 | + | 2.17730i | 0.230083 | + | 0.102073i | ||||
\(456\) | 4.40811i | 0.206428i | ||||||||
\(457\) | 16.8617i | 0.788759i | 0.918948 | + | 0.394379i | \(0.129040\pi\) | ||||
−0.918948 | + | 0.394379i | \(0.870960\pi\) | |||||||
\(458\) | −2.08853 | −0.0975908 | ||||||||
\(459\) | 7.09918i | 0.331361i | ||||||||
\(460\) | 3.94221 | − | 1.60036i | 0.183806 | − | 0.0746170i | ||||
\(461\) | 5.50403i | 0.256348i | 0.991752 | + | 0.128174i | \(0.0409117\pi\) | ||||
−0.991752 | + | 0.128174i | \(0.959088\pi\) | |||||||
\(462\) | 0.366830 | − | 0.826873i | 0.0170665 | − | 0.0384696i | ||||
\(463\) | 14.3103 | 0.665058 | 0.332529 | − | 0.943093i | \(-0.392098\pi\) | ||||
0.332529 | + | 0.943093i | \(0.392098\pi\) | |||||||
\(464\) | 15.1526 | 0.703440 | ||||||||
\(465\) | −1.97958 | −0.0918008 | ||||||||
\(466\) | −2.89038 | −0.133894 | ||||||||
\(467\) | −9.88465 | −0.457407 | −0.228703 | − | 0.973496i | \(-0.573449\pi\) | ||||
−0.228703 | + | 0.973496i | \(0.573449\pi\) | |||||||
\(468\) | − | 8.56860i | − | 0.396084i | ||||||
\(469\) | −14.1250 | − | 6.26634i | −0.652230 | − | 0.289353i | ||||
\(470\) | − | 0.842521i | − | 0.0388626i | ||||||
\(471\) | − | 20.2643i | − | 0.933730i | ||||||
\(472\) | − | 8.10856i | − | 0.373227i | ||||||
\(473\) | −9.66909 | −0.444585 | ||||||||
\(474\) | −1.74472 | −0.0801377 | ||||||||
\(475\) | 21.1143 | 0.968793 | ||||||||
\(476\) | −14.7417 | + | 33.2294i | −0.675686 | + | 1.52307i | ||||
\(477\) | 8.35783i | 0.382679i | ||||||||
\(478\) | −6.84923 | −0.313276 | ||||||||
\(479\) | −0.894679 | −0.0408789 | −0.0204395 | − | 0.999791i | \(-0.506507\pi\) | ||||
−0.0204395 | + | 0.999791i | \(0.506507\pi\) | |||||||
\(480\) | 1.33802i | 0.0610718i | ||||||||
\(481\) | 37.9023 | 1.72820 | ||||||||
\(482\) | 1.37322 | 0.0625485 | ||||||||
\(483\) | 12.6821 | + | 0.404950i | 0.577056 | + | 0.0184259i | ||||
\(484\) | −17.7857 | −0.808442 | ||||||||
\(485\) | 1.77064 | 0.0804008 | ||||||||
\(486\) | 0.254102i | 0.0115263i | ||||||||
\(487\) | 4.41499 | 0.200062 | 0.100031 | − | 0.994984i | \(-0.468106\pi\) | ||||
0.100031 | + | 0.994984i | \(0.468106\pi\) | |||||||
\(488\) | −10.2486 | −0.463933 | ||||||||
\(489\) | 7.97942i | 0.360842i | ||||||||
\(490\) | −0.547166 | − | 0.604448i | −0.0247185 | − | 0.0273062i | ||||
\(491\) | 26.5480 | 1.19810 | 0.599048 | − | 0.800713i | \(-0.295546\pi\) | ||||
0.599048 | + | 0.800713i | \(0.295546\pi\) | |||||||
\(492\) | −7.37490 | −0.332486 | ||||||||
\(493\) | −29.7422 | −1.33952 | ||||||||
\(494\) | 4.95897i | 0.223115i | ||||||||
\(495\) | − | 0.616763i | − | 0.0277214i | ||||||
\(496\) | 15.6196i | 0.701341i | ||||||||
\(497\) | −9.04164 | + | 20.3808i | −0.405573 | + | 0.914203i | ||||
\(498\) | 1.25866i | 0.0564018i | ||||||||
\(499\) | 20.0206 | 0.896244 | 0.448122 | − | 0.893972i | \(-0.352093\pi\) | ||||
0.448122 | + | 0.893972i | \(0.352093\pi\) | |||||||
\(500\) | 8.68518 | 0.388413 | ||||||||
\(501\) | −3.04399 | −0.135996 | ||||||||
\(502\) | 4.93129 | 0.220094 | ||||||||
\(503\) | −1.17739 | −0.0524972 | −0.0262486 | − | 0.999655i | \(-0.508356\pi\) | ||||
−0.0262486 | + | 0.999655i | \(0.508356\pi\) | |||||||
\(504\) | −1.07291 | + | 2.41844i | −0.0477911 | + | 0.107726i | ||||
\(505\) | 5.79828i | 0.258020i | ||||||||
\(506\) | −0.616763 | − | 1.51929i | −0.0274185 | − | 0.0675408i | ||||
\(507\) | − | 6.60036i | − | 0.293132i | ||||||
\(508\) | 23.8021 | 1.05605 | ||||||||
\(509\) | 8.24993i | 0.365672i | 0.983143 | + | 0.182836i | \(0.0585277\pi\) | ||||
−0.983143 | + | 0.182836i | \(0.941472\pi\) | |||||||
\(510\) | − | 0.826873i | − | 0.0366145i | ||||||
\(511\) | −17.0355 | − | 7.55755i | −0.753606 | − | 0.334327i | ||||
\(512\) | 17.7909 | 0.786256 | ||||||||
\(513\) | 4.40811i | 0.194623i | ||||||||
\(514\) | − | 1.10439i | − | 0.0487126i | ||||||
\(515\) | 3.45065 | 0.152054 | ||||||||
\(516\) | 13.9081 | 0.612271 | ||||||||
\(517\) | 9.73297 | 0.428055 | ||||||||
\(518\) | −5.26111 | − | 2.33402i | −0.231160 | − | 0.102551i | ||||
\(519\) | 13.4231 | 0.589207 | ||||||||
\(520\) | 2.02934i | 0.0889925i | ||||||||
\(521\) | 25.7850 | 1.12966 | 0.564831 | − | 0.825207i | \(-0.308942\pi\) | ||||
0.564831 | + | 0.825207i | \(0.308942\pi\) | |||||||
\(522\) | −1.06457 | −0.0465949 | ||||||||
\(523\) | −26.9939 | −1.18036 | −0.590180 | − | 0.807272i | \(-0.700943\pi\) | ||||
−0.590180 | + | 0.807272i | \(0.700943\pi\) | |||||||
\(524\) | − | 10.0122i | − | 0.437387i | ||||||
\(525\) | 11.5841 | + | 5.13911i | 0.505571 | + | 0.224289i | ||||
\(526\) | 0.401096i | 0.0174886i | ||||||||
\(527\) | − | 30.6590i | − | 1.33553i | ||||||
\(528\) | −4.86648 | −0.211786 | ||||||||
\(529\) | 16.4918 | − | 16.0319i | 0.717035 | − | 0.697038i | ||||
\(530\) | − | 0.973474i | − | 0.0422850i | ||||||
\(531\) | − | 8.10856i | − | 0.351882i | ||||||
\(532\) | −9.15361 | + | 20.6332i | −0.396859 | + | 0.894561i | ||||
\(533\) | −16.8698 | −0.730712 | ||||||||
\(534\) | − | 4.06620i | − | 0.175962i | ||||||
\(535\) | − | 9.23875i | − | 0.399426i | ||||||
\(536\) | − | 5.84052i | − | 0.252272i | ||||||
\(537\) | 14.2294i | 0.614042i | ||||||||
\(538\) | − | 5.43841i | − | 0.234466i | ||||||
\(539\) | 6.98270 | − | 6.32097i | 0.300766 | − | 0.272264i | ||||
\(540\) | 0.887158i | 0.0381772i | ||||||||
\(541\) | −12.6373 | −0.543322 | −0.271661 | − | 0.962393i | \(-0.587573\pi\) | ||||
−0.271661 | + | 0.962393i | \(0.587573\pi\) | |||||||
\(542\) | 3.89455i | 0.167285i | ||||||||
\(543\) | − | 19.6026i | − | 0.841227i | ||||||
\(544\) | −20.7227 | −0.888478 | ||||||||
\(545\) | 2.32045i | 0.0993972i | ||||||||
\(546\) | −1.20699 | + | 2.72067i | −0.0516542 | + | 0.116434i | ||||
\(547\) | 2.52878 | 0.108123 | 0.0540614 | − | 0.998538i | \(-0.482783\pi\) | ||||
0.0540614 | + | 0.998538i | \(0.482783\pi\) | |||||||
\(548\) | 17.6249i | 0.752899i | ||||||||
\(549\) | −10.2486 | −0.437401 | ||||||||
\(550\) | − | 1.63768i | − | 0.0698308i | ||||||
\(551\) | −18.4679 | −0.786759 | ||||||||
\(552\) | 1.80391 | + | 4.44364i | 0.0767796 | + | 0.189134i | ||||
\(553\) | −16.6056 | − | 7.36683i | −0.706141 | − | 0.313269i | ||||
\(554\) | 2.67193 | 0.113520 | ||||||||
\(555\) | −3.92425 | −0.166575 | ||||||||
\(556\) | − | 34.5480i | − | 1.46516i | ||||||
\(557\) | 30.2654i | 1.28239i | 0.767379 | + | 0.641194i | \(0.221560\pi\) | ||||
−0.767379 | + | 0.641194i | \(0.778440\pi\) | |||||||
\(558\) | − | 1.09738i | − | 0.0464558i | ||||||
\(559\) | 31.8143 | 1.34560 | ||||||||
\(560\) | −1.77871 | + | 4.00940i | −0.0751643 | + | 0.169428i | ||||
\(561\) | 9.55220 | 0.403294 | ||||||||
\(562\) | − | 1.34745i | − | 0.0568386i | ||||||
\(563\) | 36.6381 | 1.54411 | 0.772055 | − | 0.635555i | \(-0.219229\pi\) | ||||
0.772055 | + | 0.635555i | \(0.219229\pi\) | |||||||
\(564\) | −14.0000 | −0.589506 | ||||||||
\(565\) | 1.55041i | 0.0652264i | ||||||||
\(566\) | −0.523180 | −0.0219909 | ||||||||
\(567\) | −1.07291 | + | 2.41844i | −0.0450579 | + | 0.101565i | ||||
\(568\) | −8.42723 | −0.353599 | ||||||||
\(569\) | − | 27.1085i | − | 1.13645i | −0.822875 | − | 0.568223i | \(-0.807631\pi\) | ||
0.822875 | − | 0.568223i | \(-0.192369\pi\) | |||||||
\(570\) | − | 0.513432i | − | 0.0215053i | ||||||
\(571\) | 7.95674i | 0.332979i | 0.986043 | + | 0.166490i | \(0.0532432\pi\) | ||||
−0.986043 | + | 0.166490i | \(0.946757\pi\) | |||||||
\(572\) | −11.5294 | −0.482067 | ||||||||
\(573\) | 21.1811 | 0.884851 | ||||||||
\(574\) | 2.34165 | + | 1.03884i | 0.0977385 | + | 0.0433603i | ||||
\(575\) | 21.2845 | − | 8.64054i | 0.887626 | − | 0.360336i | ||||
\(576\) | 6.49180 | 0.270492 | ||||||||
\(577\) | − | 19.9672i | − | 0.831245i | −0.909537 | − | 0.415622i | \(-0.863564\pi\) | ||
0.909537 | − | 0.415622i | \(-0.136436\pi\) | |||||||
\(578\) | 8.48657 | 0.352995 | ||||||||
\(579\) | 10.0328i | 0.416950i | ||||||||
\(580\) | −3.71678 | −0.154331 | ||||||||
\(581\) | −5.31450 | + | 11.9794i | −0.220483 | + | 0.496990i | ||||
\(582\) | 0.981557i | 0.0406868i | ||||||||
\(583\) | 11.2458 | 0.465752 | ||||||||
\(584\) | − | 7.04399i | − | 0.291482i | ||||||
\(585\) | 2.02934i | 0.0839029i | ||||||||
\(586\) | −4.44522 | −0.183630 | ||||||||
\(587\) | 21.8555i | 0.902074i | 0.892505 | + | 0.451037i | \(0.148946\pi\) | ||||
−0.892505 | + | 0.451037i | \(0.851054\pi\) | |||||||
\(588\) | −10.0440 | + | 9.09215i | −0.414207 | + | 0.374954i | ||||
\(589\) | − | 19.0372i | − | 0.784412i | ||||||
\(590\) | 0.944440i | 0.0388820i | ||||||||
\(591\) | 5.53996i | 0.227883i | ||||||||
\(592\) | 30.9638i | 1.27260i | ||||||||
\(593\) | 36.9117i | 1.51578i | 0.652380 | + | 0.757892i | \(0.273771\pi\) | ||||
−0.652380 | + | 0.757892i | \(0.726229\pi\) | |||||||
\(594\) | 0.341903 | 0.0140284 | ||||||||
\(595\) | 3.49135 | − | 7.86986i | 0.143131 | − | 0.322633i | ||||
\(596\) | − | 39.0666i | − | 1.60023i | ||||||
\(597\) | 6.69808i | 0.274134i | ||||||||
\(598\) | 2.02934 | + | 4.99894i | 0.0829859 | + | 0.204422i | ||||
\(599\) | −32.2898 | −1.31932 | −0.659662 | − | 0.751563i | \(-0.729300\pi\) | ||||
−0.659662 | + | 0.751563i | \(0.729300\pi\) | |||||||
\(600\) | 4.78989i | 0.195546i | ||||||||
\(601\) | − | 24.6496i | − | 1.00548i | −0.864438 | − | 0.502739i | \(-0.832326\pi\) | ||
0.864438 | − | 0.502739i | \(-0.167674\pi\) | |||||||
\(602\) | −4.41605 | − | 1.95912i | −0.179985 | − | 0.0798477i | ||||
\(603\) | − | 5.84052i | − | 0.237844i | ||||||
\(604\) | 22.4119 | 0.911927 | ||||||||
\(605\) | 4.21227 | 0.171253 | ||||||||
\(606\) | −3.21428 | −0.130571 | ||||||||
\(607\) | 23.4988i | 0.953787i | 0.878961 | + | 0.476894i | \(0.158237\pi\) | ||||
−0.878961 | + | 0.476894i | \(0.841763\pi\) | |||||||
\(608\) | −12.8674 | −0.521841 | ||||||||
\(609\) | −10.1322 | − | 4.49498i | −0.410575 | − | 0.182146i | ||||
\(610\) | 1.19370 | 0.0483316 | ||||||||
\(611\) | −32.0245 | −1.29557 | ||||||||
\(612\) | −13.7400 | −0.555406 | ||||||||
\(613\) | − | 1.34554i | − | 0.0543457i | −0.999631 | − | 0.0271728i | \(-0.991350\pi\) | ||
0.999631 | − | 0.0271728i | \(-0.00865045\pi\) | |||||||
\(614\) | − | 8.09499i | − | 0.326687i | ||||||
\(615\) | 1.74663 | 0.0704310 | ||||||||
\(616\) | 3.25410 | + | 1.44364i | 0.131111 | + | 0.0581657i | ||||
\(617\) | 20.2347i | 0.814619i | 0.913290 | + | 0.407309i | \(0.133533\pi\) | ||||
−0.913290 | + | 0.407309i | \(0.866467\pi\) | |||||||
\(618\) | 1.91287i | 0.0769468i | ||||||||
\(619\) | 37.2425 | 1.49690 | 0.748452 | − | 0.663189i | \(-0.230798\pi\) | ||||
0.748452 | + | 0.663189i | \(0.230798\pi\) | |||||||
\(620\) | − | 3.83134i | − | 0.153870i | ||||||
\(621\) | 1.80391 | + | 4.44364i | 0.0723885 | + | 0.178317i | ||||
\(622\) | 0.690728i | 0.0276957i | ||||||||
\(623\) | 17.1690 | − | 38.7006i | 0.687860 | − | 1.55051i | ||||
\(624\) | 16.0122 | 0.641003 | ||||||||
\(625\) | 21.8925 | 0.875700 | ||||||||
\(626\) | −5.38214 | −0.215114 | ||||||||
\(627\) | 5.93126 | 0.236872 | ||||||||
\(628\) | 39.2202 | 1.56506 | ||||||||
\(629\) | − | 60.7774i | − | 2.42335i | ||||||
\(630\) | 0.124966 | − | 0.281687i | 0.00497878 | − | 0.0112227i | ||||
\(631\) | 39.5546i | 1.57464i | 0.616543 | + | 0.787321i | \(0.288533\pi\) | ||||
−0.616543 | + | 0.787321i | \(0.711467\pi\) | |||||||
\(632\) | − | 6.86623i | − | 0.273124i | ||||||
\(633\) | − | 9.33508i | − | 0.371036i | ||||||
\(634\) | −2.85969 | −0.113573 | ||||||||
\(635\) | −5.63717 | −0.223704 | ||||||||
\(636\) | −16.1760 | −0.641421 | ||||||||
\(637\) | −22.9753 | + | 20.7980i | −0.910313 | + | 0.824045i | ||||
\(638\) | 1.43241i | 0.0567098i | ||||||||
\(639\) | −8.42723 | −0.333376 | ||||||||
\(640\) | −3.43216 | −0.135668 | ||||||||
\(641\) | − | 19.8430i | − | 0.783753i | −0.920018 | − | 0.391877i | \(-0.871826\pi\) | ||
0.920018 | − | 0.391877i | \(-0.128174\pi\) | |||||||
\(642\) | 5.12151 | 0.202130 | ||||||||
\(643\) | −47.0309 | −1.85472 | −0.927358 | − | 0.374176i | \(-0.877926\pi\) | ||||
−0.927358 | + | 0.374176i | \(0.877926\pi\) | |||||||
\(644\) | −0.783754 | + | 24.5454i | −0.0308842 | + | 0.967223i | ||||
\(645\) | −3.29392 | −0.129698 | ||||||||
\(646\) | 7.95184 | 0.312861 | ||||||||
\(647\) | − | 29.5592i | − | 1.16209i | −0.813871 | − | 0.581046i | \(-0.802644\pi\) | ||
0.813871 | − | 0.581046i | \(-0.197356\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −10.9104 | −0.428269 | ||||||||
\(650\) | 5.38847i | 0.211353i | ||||||||
\(651\) | 4.63353 | − | 10.4445i | 0.181603 | − | 0.409351i | ||||
\(652\) | −15.4436 | −0.604819 | ||||||||
\(653\) | 31.9466 | 1.25017 | 0.625084 | − | 0.780558i | \(-0.285065\pi\) | ||||
0.625084 | + | 0.780558i | \(0.285065\pi\) | |||||||
\(654\) | −1.28634 | −0.0503000 | ||||||||
\(655\) | 2.37124i | 0.0926522i | ||||||||
\(656\) | − | 13.7816i | − | 0.538079i | ||||||
\(657\) | − | 7.04399i | − | 0.274812i | ||||||
\(658\) | 4.44522 | + | 1.97206i | 0.173293 | + | 0.0768789i | ||||
\(659\) | − | 32.7104i | − | 1.27422i | −0.770774 | − | 0.637108i | \(-0.780130\pi\) | ||
0.770774 | − | 0.637108i | \(-0.219870\pi\) | |||||||
\(660\) | 1.19370 | 0.0464648 | ||||||||
\(661\) | −11.9361 | −0.464259 | −0.232130 | − | 0.972685i | \(-0.574569\pi\) | ||||
−0.232130 | + | 0.972685i | \(0.574569\pi\) | |||||||
\(662\) | 2.17029 | 0.0843506 | ||||||||
\(663\) | −31.4297 | −1.22063 | ||||||||
\(664\) | −4.95336 | −0.192228 | ||||||||
\(665\) | 2.16789 | − | 4.88665i | 0.0840672 | − | 0.189496i | ||||
\(666\) | − | 2.17541i | − | 0.0842955i | ||||||
\(667\) | −18.6168 | + | 7.55755i | −0.720844 | + | 0.292630i | ||||
\(668\) | − | 5.89144i | − | 0.227947i | ||||||
\(669\) | −10.3257 | −0.399214 | ||||||||
\(670\) | 0.680271i | 0.0262812i | ||||||||
\(671\) | 13.7899i | 0.532353i | ||||||||
\(672\) | −7.05950 | − | 3.13185i | −0.272326 | − | 0.120814i | ||||
\(673\) | −18.0521 | −0.695856 | −0.347928 | − | 0.937521i | \(-0.613115\pi\) | ||||
−0.347928 | + | 0.937521i | \(0.613115\pi\) | |||||||
\(674\) | 2.09414i | 0.0806634i | ||||||||
\(675\) | 4.78989i | 0.184363i | ||||||||
\(676\) | 12.7745 | 0.491329 | ||||||||
\(677\) | −50.0582 | −1.92389 | −0.961947 | − | 0.273237i | \(-0.911906\pi\) | ||||
−0.961947 | + | 0.273237i | \(0.911906\pi\) | |||||||
\(678\) | −0.859473 | −0.0330079 | ||||||||
\(679\) | −4.14448 | + | 9.34209i | −0.159051 | + | 0.358516i | ||||
\(680\) | 3.25410 | 0.124789 | ||||||||
\(681\) | − | 24.6428i | − | 0.944315i | ||||||
\(682\) | −1.47657 | −0.0565406 | ||||||||
\(683\) | 3.61782 | 0.138432 | 0.0692161 | − | 0.997602i | \(-0.477950\pi\) | ||||
0.0692161 | + | 0.997602i | \(0.477950\pi\) | |||||||
\(684\) | −8.53159 | −0.326214 | ||||||||
\(685\) | − | 4.17419i | − | 0.159487i | ||||||
\(686\) | 4.46986 | − | 1.47209i | 0.170660 | − | 0.0562048i | ||||
\(687\) | − | 8.21928i | − | 0.313585i | ||||||
\(688\) | 25.9903i | 0.990869i | ||||||||
\(689\) | −37.0020 | −1.40967 | ||||||||
\(690\) | −0.210110 | − | 0.517570i | −0.00799874 | − | 0.0197036i | ||||
\(691\) | 9.24887i | 0.351844i | 0.984404 | + | 0.175922i | \(0.0562906\pi\) | ||||
−0.984404 | + | 0.175922i | \(0.943709\pi\) | |||||||
\(692\) | 25.9794i | 0.987590i | ||||||||
\(693\) | 3.25410 | + | 1.44364i | 0.123613 | + | 0.0548392i | ||||
\(694\) | −2.70998 | −0.102869 | ||||||||
\(695\) | 8.18217i | 0.310367i | ||||||||
\(696\) | − | 4.18953i | − | 0.158804i | ||||||
\(697\) | 27.0512i | 1.02464i | ||||||||
\(698\) | 0.255161i | 0.00965799i | ||||||||
\(699\) | − | 11.3749i | − | 0.430238i | ||||||
\(700\) | −9.94640 | + | 22.4202i | −0.375939 | + | 0.847404i | ||||
\(701\) | 26.8478i | 1.01403i | 0.861938 | + | 0.507014i | \(0.169251\pi\) | ||||
−0.861938 | + | 0.507014i | \(0.830749\pi\) | |||||||
\(702\) | −1.12497 | −0.0424591 | ||||||||
\(703\) | − | 37.7386i | − | 1.42334i | ||||||
\(704\) | − | 8.73494i | − | 0.329211i | ||||||
\(705\) | 3.31568 | 0.124876 | ||||||||
\(706\) | 9.08904i | 0.342071i | ||||||||
\(707\) | −30.5923 | − | 13.5718i | −1.15054 | − | 0.510421i | ||||
\(708\) | 15.6936 | 0.589800 | ||||||||
\(709\) | 23.7632i | 0.892445i | 0.894922 | + | 0.446222i | \(0.147231\pi\) | ||||
−0.894922 | + | 0.446222i | \(0.852769\pi\) | |||||||
\(710\) | 0.981557 | 0.0368372 | ||||||||
\(711\) | − | 6.86623i | − | 0.257504i | ||||||
\(712\) | 16.0023 | 0.599710 | ||||||||
\(713\) | −7.79050 | − | 19.1906i | −0.291757 | − | 0.718693i | ||||
\(714\) | 4.36266 | + | 1.93543i | 0.163268 | + | 0.0724317i | ||||
\(715\) | 2.73055 | 0.102117 | ||||||||
\(716\) | −27.5400 | −1.02922 | ||||||||
\(717\) | − | 26.9547i | − | 1.00664i | ||||||
\(718\) | 5.24550i | 0.195760i | ||||||||
\(719\) | 43.0768i | 1.60649i | 0.595646 | + | 0.803247i | \(0.296896\pi\) | ||||
−0.595646 | + | 0.803247i | \(0.703104\pi\) | |||||||
\(720\) | −1.65784 | −0.0617841 | ||||||||
\(721\) | −8.07681 | + | 18.2059i | −0.300796 | + | 0.678025i | ||||
\(722\) | 0.109619 | 0.00407959 | ||||||||
\(723\) | 5.40422i | 0.200985i | ||||||||
\(724\) | 37.9395 | 1.41001 | ||||||||
\(725\) | −20.0674 | −0.745285 | ||||||||
\(726\) | 2.33508i | 0.0866628i | ||||||||
\(727\) | −32.3389 | −1.19938 | −0.599692 | − | 0.800231i | \(-0.704710\pi\) | ||||
−0.599692 | + | 0.800231i | \(0.704710\pi\) | |||||||
\(728\) | −10.7070 | − | 4.75001i | −0.396828 | − | 0.176047i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0.820445i | 0.0303660i | ||||||||
\(731\) | − | 51.0151i | − | 1.88686i | ||||||
\(732\) | − | 19.8355i | − | 0.733142i | ||||||
\(733\) | −35.4940 | −1.31100 | −0.655500 | − | 0.755195i | \(-0.727542\pi\) | ||||
−0.655500 | + | 0.755195i | \(0.727542\pi\) | |||||||
\(734\) | 6.53937 | 0.241372 | ||||||||
\(735\) | 2.37876 | − | 2.15334i | 0.0877421 | − | 0.0794270i | ||||
\(736\) | −12.9711 | + | 5.26567i | −0.478121 | + | 0.194095i | ||||
\(737\) | −7.85863 | −0.289476 | ||||||||
\(738\) | 0.968246i | 0.0356416i | ||||||||
\(739\) | −19.9641 | −0.734390 | −0.367195 | − | 0.930144i | \(-0.619682\pi\) | ||||
−0.367195 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(740\) | − | 7.59513i | − | 0.279202i | ||||||
\(741\) | −19.5157 | −0.716927 | ||||||||
\(742\) | 5.13614 | + | 2.27858i | 0.188554 | + | 0.0836492i | ||||
\(743\) | − | 1.29577i | − | 0.0475373i | −0.999717 | − | 0.0237687i | \(-0.992433\pi\) | ||
0.999717 | − | 0.0237687i | \(-0.00756652\pi\) | |||||||
\(744\) | 4.31867 | 0.158330 | ||||||||
\(745\) | 9.25232i | 0.338979i | ||||||||
\(746\) | − | 4.23805i | − | 0.155166i | ||||||
\(747\) | −4.95336 | −0.181234 | ||||||||
\(748\) | 18.4876i | 0.675975i | ||||||||
\(749\) | 48.7446 | + | 21.6248i | 1.78109 | + | 0.790154i | ||||
\(750\) | − | 1.14027i | − | 0.0416368i | ||||||
\(751\) | 45.7445i | 1.66924i | 0.550825 | + | 0.834620i | \(0.314313\pi\) | ||||
−0.550825 | + | 0.834620i | \(0.685687\pi\) | |||||||
\(752\) | − | 26.1619i | − | 0.954028i | ||||||
\(753\) | 19.4067i | 0.707221i | ||||||||
\(754\) | − | 4.71308i | − | 0.171640i | ||||||
\(755\) | −5.30791 | −0.193175 | ||||||||
\(756\) | −4.68073 | − | 2.07654i | −0.170237 | − | 0.0755231i | ||||
\(757\) | 20.4601i | 0.743636i | 0.928306 | + | 0.371818i | \(0.121265\pi\) | ||||
−0.928306 | + | 0.371818i | \(0.878735\pi\) | |||||||
\(758\) | − | 7.86425i | − | 0.285642i | ||||||
\(759\) | 5.97907 | − | 2.42723i | 0.217026 | − | 0.0881028i | ||||
\(760\) | 2.02058 | 0.0732940 | ||||||||
\(761\) | 41.9177i | 1.51952i | 0.650206 | + | 0.759758i | \(0.274682\pi\) | ||||
−0.650206 | + | 0.759758i | \(0.725318\pi\) | |||||||
\(762\) | − | 3.12497i | − | 0.113206i | ||||||
\(763\) | −12.2429 | − | 5.43140i | −0.443224 | − | 0.196630i | ||||
\(764\) | 40.9945i | 1.48313i | ||||||||
\(765\) | 3.25410 | 0.117652 | ||||||||
\(766\) | 4.74810 | 0.171556 | ||||||||
\(767\) | 35.8984 | 1.29622 | ||||||||
\(768\) | 11.0810i | 0.399850i | ||||||||
\(769\) | 9.95087 | 0.358838 | 0.179419 | − | 0.983773i | \(-0.442578\pi\) | ||||
0.179419 | + | 0.983773i | \(0.442578\pi\) | |||||||
\(770\) | −0.379020 | − | 0.168147i | −0.0136589 | − | 0.00605959i | ||||
\(771\) | 4.34625 | 0.156527 | ||||||||
\(772\) | −19.4178 | −0.698863 | ||||||||
\(773\) | −25.9367 | −0.932877 | −0.466439 | − | 0.884554i | \(-0.654463\pi\) | ||||
−0.466439 | + | 0.884554i | \(0.654463\pi\) | |||||||
\(774\) | − | 1.82599i | − | 0.0656338i | ||||||
\(775\) | − | 20.6860i | − | 0.743061i | ||||||
\(776\) | −3.86285 | −0.138668 | ||||||||
\(777\) | 9.18537 | − | 20.7047i | 0.329523 | − | 0.742779i | ||||
\(778\) | − | 6.73520i | − | 0.241469i | ||||||
\(779\) | 16.7969i | 0.601813i | ||||||||
\(780\) | −3.92765 | −0.140633 | ||||||||
\(781\) | 11.3391i | 0.405746i | ||||||||
\(782\) | 8.01593 | − | 3.25410i | 0.286649 | − | 0.116366i | ||||
\(783\) | − | 4.18953i | − | 0.149722i | ||||||
\(784\) | −16.9906 | − | 18.7693i | −0.606807 | − | 0.670333i | ||||
\(785\) | −9.28870 | −0.331528 | ||||||||
\(786\) | −1.31450 | −0.0468867 | ||||||||
\(787\) | −4.70586 | −0.167746 | −0.0838728 | − | 0.996476i | \(-0.526729\pi\) | ||||
−0.0838728 | + | 0.996476i | \(0.526729\pi\) | |||||||
\(788\) | −10.7222 | −0.381963 | ||||||||
\(789\) | −1.57848 | −0.0561955 | ||||||||
\(790\) | 0.799740i | 0.0284535i | ||||||||
\(791\) | −8.18014 | − | 3.62900i | −0.290852 | − | 0.129032i | ||||
\(792\) | 1.34554i | 0.0478115i | ||||||||
\(793\) | − | 45.3730i | − | 1.61124i | ||||||
\(794\) | − | 2.19476i | − | 0.0778892i | ||||||
\(795\) | 3.83104 | 0.135873 | ||||||||
\(796\) | −12.9637 | −0.459486 | ||||||||
\(797\) | −1.91287 | −0.0677572 | −0.0338786 | − | 0.999426i | \(-0.510786\pi\) | ||||
−0.0338786 | + | 0.999426i | \(0.510786\pi\) | |||||||
\(798\) | 2.70892 | + | 1.20177i | 0.0958946 | + | 0.0425423i | ||||
\(799\) | 51.3521i | 1.81671i | ||||||||
\(800\) | −13.9818 | −0.494332 | ||||||||
\(801\) | 16.0023 | 0.565412 | ||||||||
\(802\) | 3.28609i | 0.116036i | ||||||||
\(803\) | −9.47794 | −0.334469 | ||||||||
\(804\) | 11.3039 | 0.398659 | ||||||||
\(805\) | 0.185620 | − | 5.81319i | 0.00654225 | − | 0.204888i | ||||
\(806\) | 4.85836 | 0.171128 | ||||||||
\(807\) | 21.4025 | 0.753403 | ||||||||
\(808\) | − | 12.6496i | − | 0.445011i | ||||||
\(809\) | −9.22652 | −0.324387 | −0.162194 | − | 0.986759i | \(-0.551857\pi\) | ||||
−0.162194 | + | 0.986759i | \(0.551857\pi\) | |||||||
\(810\) | 0.116474 | 0.00409249 | ||||||||
\(811\) | 24.0192i | 0.843430i | 0.906728 | + | 0.421715i | \(0.138572\pi\) | ||||
−0.906728 | + | 0.421715i | \(0.861428\pi\) | |||||||
\(812\) | 8.69974 | − | 19.6101i | 0.305301 | − | 0.688179i | ||||
\(813\) | −15.3267 | −0.537532 | ||||||||
\(814\) | −2.92709 | −0.102595 | ||||||||
\(815\) | 3.65759 | 0.128120 | ||||||||
\(816\) | − | 25.6760i | − | 0.898841i | ||||||
\(817\) | − | 31.6769i | − | 1.10823i | ||||||
\(818\) | 1.11974i | 0.0391507i | ||||||||
\(819\) | −10.7070 | − | 4.75001i | −0.374133 | − | 0.165979i | ||||
\(820\) | 3.38049i | 0.118052i | ||||||||
\(821\) | 35.7334 | 1.24710 | 0.623552 | − | 0.781782i | \(-0.285689\pi\) | ||||
0.623552 | + | 0.781782i | \(0.285689\pi\) | |||||||
\(822\) | 2.31396 | 0.0807087 | ||||||||
\(823\) | −45.1166 | −1.57267 | −0.786333 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786333 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(824\) | −7.52796 | −0.262249 | ||||||||
\(825\) | 6.44497 | 0.224385 | ||||||||
\(826\) | −4.98296 | − | 2.21062i | −0.173379 | − | 0.0769172i | ||||
\(827\) | − | 12.9618i | − | 0.450725i | −0.974275 | − | 0.225362i | \(-0.927643\pi\) | ||
0.974275 | − | 0.225362i | \(-0.0723566\pi\) | |||||||
\(828\) | −8.60036 | + | 3.49135i | −0.298883 | + | 0.121333i | ||||
\(829\) | − | 4.76125i | − | 0.165365i | −0.996576 | − | 0.0826824i | \(-0.973651\pi\) | ||
0.996576 | − | 0.0826824i | \(-0.0263487\pi\) | |||||||
\(830\) | 0.576940 | 0.0200259 | ||||||||
\(831\) | 10.5152i | 0.364769i | ||||||||
\(832\) | 28.7407i | 0.996403i | ||||||||
\(833\) | 33.3501 | + | 36.8414i | 1.15551 | + | 1.27648i | ||||
\(834\) | −4.53579 | −0.157062 | ||||||||
\(835\) | 1.39530i | 0.0482862i | ||||||||
\(836\) | 11.4796i | 0.397029i | ||||||||
\(837\) | 4.31867 | 0.149275 | ||||||||
\(838\) | 1.50425 | 0.0519635 | ||||||||
\(839\) | −6.23409 | −0.215225 | −0.107612 | − | 0.994193i | \(-0.534321\pi\) | ||||
−0.107612 | + | 0.994193i | \(0.534321\pi\) | |||||||
\(840\) | 1.10856 | + | 0.491797i | 0.0382489 | + | 0.0169686i | ||||
\(841\) | −11.4478 | −0.394752 | ||||||||
\(842\) | − | 2.66339i | − | 0.0917863i | ||||||
\(843\) | 5.30278 | 0.182638 | ||||||||
\(844\) | 18.0674 | 0.621906 | ||||||||
\(845\) | −3.02545 | −0.104079 | ||||||||
\(846\) | 1.83805i | 0.0631935i | ||||||||
\(847\) | −9.85952 | + | 22.2244i | −0.338777 | + | 0.763638i | ||||
\(848\) | − | 30.2283i | − | 1.03804i | ||||||
\(849\) | − | 2.05894i | − | 0.0706626i | ||||||
\(850\) | 8.64054 | 0.296368 | ||||||||
\(851\) | −15.4436 | − | 38.0428i | −0.529401 | − | 1.30409i | ||||
\(852\) | − | 16.3103i | − | 0.558783i | ||||||
\(853\) | − | 2.15361i | − | 0.0737382i | −0.999320 | − | 0.0368691i | \(-0.988262\pi\) | ||
0.999320 | − | 0.0368691i | \(-0.0117385\pi\) | |||||||
\(854\) | −2.79406 | + | 6.29809i | −0.0956107 | + | 0.215516i | ||||
\(855\) | 2.02058 | 0.0691022 | ||||||||
\(856\) | 20.1553i | 0.688896i | ||||||||
\(857\) | − | 48.5222i | − | 1.65749i | −0.559628 | − | 0.828744i | \(-0.689056\pi\) | ||
0.559628 | − | 0.828744i | \(-0.310944\pi\) | |||||||
\(858\) | 1.51368i | 0.0516763i | ||||||||
\(859\) | 27.0081i | 0.921503i | 0.887529 | + | 0.460752i | \(0.152420\pi\) | ||||
−0.887529 | + | 0.460752i | \(0.847580\pi\) | |||||||
\(860\) | − | 6.37517i | − | 0.217391i | ||||||
\(861\) | −4.08828 | + | 9.21540i | −0.139328 | + | 0.314060i | ||||
\(862\) | − | 5.33942i | − | 0.181861i | ||||||
\(863\) | 2.82164 | 0.0960499 | 0.0480249 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480249 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(864\) | − | 2.91903i | − | 0.0993073i | ||||||
\(865\) | − | 6.15283i | − | 0.209202i | ||||||
\(866\) | 1.83351 | 0.0623052 | ||||||||
\(867\) | 33.3983i | 1.13427i | ||||||||
\(868\) | 20.2145 | + | 8.96789i | 0.686126 | + | 0.304390i | ||||
\(869\) | −9.23875 | −0.313403 | ||||||||
\(870\) | 0.487974i | 0.0165439i | ||||||||
\(871\) | 25.8573 | 0.876142 | ||||||||
\(872\) | − | 5.06232i | − | 0.171432i | ||||||
\(873\) | −3.86285 | −0.130738 | ||||||||
\(874\) | 4.97735 | − | 2.02058i | 0.168361 | − | 0.0683470i | ||||
\(875\) | 4.81463 | − | 10.8527i | 0.162764 | − | 0.366887i | ||||
\(876\) | 13.6332 | 0.460622 | ||||||||
\(877\) | 0.194762 | 0.00657666 | 0.00328833 | − | 0.999995i | \(-0.498953\pi\) | ||||
0.00328833 | + | 0.999995i | \(0.498953\pi\) | |||||||
\(878\) | 9.44152i | 0.318636i | ||||||||
\(879\) | − | 17.4939i | − | 0.590054i | ||||||
\(880\) | 2.23069i | 0.0751964i | ||||||||
\(881\) | 11.1799 | 0.376662 | 0.188331 | − | 0.982106i | \(-0.439692\pi\) | ||||
0.188331 | + | 0.982106i | \(0.439692\pi\) | |||||||
\(882\) | 1.19370 | + | 1.31867i | 0.0401941 | + | 0.0444019i | ||||
\(883\) | 17.6279 | 0.593227 | 0.296614 | − | 0.954998i | \(-0.404143\pi\) | ||||
0.296614 | + | 0.954998i | \(0.404143\pi\) | |||||||
\(884\) | − | 60.8300i | − | 2.04594i | ||||||
\(885\) | −3.71678 | −0.124938 | ||||||||
\(886\) | −4.28063 | −0.143810 | ||||||||
\(887\) | − | 13.1442i | − | 0.441339i | −0.975349 | − | 0.220670i | \(-0.929176\pi\) | ||
0.975349 | − | 0.220670i | \(-0.0708243\pi\) | |||||||
\(888\) | 8.56119 | 0.287295 | ||||||||
\(889\) | 13.1947 | − | 29.7422i | 0.442537 | − | 0.997523i | ||||
\(890\) | −1.86386 | −0.0624766 | ||||||||
\(891\) | 1.34554i | 0.0450771i | ||||||||
\(892\) | − | 19.9847i | − | 0.669136i | ||||||
\(893\) | 31.8861i | 1.06703i | ||||||||
\(894\) | −5.12903 | −0.171540 | ||||||||
\(895\) | 6.52241 | 0.218020 | ||||||||
\(896\) | 8.03353 | − | 18.1084i | 0.268382 | − | 0.604959i | ||||
\(897\) | −19.6730 | + | 7.98634i | −0.656862 | + | 0.266656i | ||||
\(898\) | 0.148383 | 0.00495159 | ||||||||
\(899\) | 18.0932i | 0.603442i | ||||||||
\(900\) | −9.27051 | −0.309017 | ||||||||
\(901\) | 59.3337i | 1.97669i | ||||||||
\(902\) | 1.30281 | 0.0433788 | ||||||||
\(903\) | 7.70998 | − | 17.3791i | 0.256572 | − | 0.578339i | ||||
\(904\) | − | 3.38240i | − | 0.112497i | ||||||
\(905\) | −8.98537 | −0.298684 | ||||||||
\(906\) | − | 2.94244i | − | 0.0977561i | ||||||
\(907\) | 30.0048i | 0.996293i | 0.867093 | + | 0.498146i | \(0.165986\pi\) | ||||
−0.867093 | + | 0.498146i | \(0.834014\pi\) | |||||||
\(908\) | 47.6945 | 1.58280 | ||||||||
\(909\) | − | 12.6496i | − | 0.419560i | ||||||
\(910\) | 1.24709 | + | 0.553255i | 0.0413407 | + | 0.0183402i | ||||
\(911\) | 7.15646i | 0.237104i | 0.992948 | + | 0.118552i | \(0.0378252\pi\) | ||||
−0.992948 | + | 0.118552i | \(0.962175\pi\) | |||||||
\(912\) | − | 15.9431i | − | 0.527928i | ||||||
\(913\) | 6.66492i | 0.220577i | ||||||||
\(914\) | 4.28460i | 0.141722i | ||||||||
\(915\) | 4.69774i | 0.155302i | ||||||||
\(916\) | 15.9079 | 0.525611 | ||||||||
\(917\) | −12.5109 | − | 5.55029i | −0.413147 | − | 0.183287i | ||||
\(918\) | 1.80391i | 0.0595380i | ||||||||
\(919\) | 27.3193i | 0.901181i | 0.892731 | + | 0.450591i | \(0.148787\pi\) | ||||
−0.892731 | + | 0.450591i | \(0.851213\pi\) | |||||||
\(920\) | 2.03686 | − | 0.826873i | 0.0671533 | − | 0.0272612i | ||||
\(921\) | 31.8573 | 1.04973 | ||||||||
\(922\) | 1.39858i | 0.0460599i | ||||||||
\(923\) | − | 37.3093i | − | 1.22805i | ||||||
\(924\) | −2.79406 | + | 6.29809i | −0.0919178 | + | 0.207192i | ||||
\(925\) | − | 41.0071i | − | 1.34831i | ||||||
\(926\) | 3.63628 | 0.119496 | ||||||||
\(927\) | −7.52796 | −0.247251 | ||||||||
\(928\) | 12.2294 | 0.401448 | ||||||||
\(929\) | 41.9383i | 1.37595i | 0.725734 | + | 0.687975i | \(0.241500\pi\) | ||||
−0.725734 | + | 0.687975i | \(0.758500\pi\) | |||||||
\(930\) | −0.503015 | −0.0164945 | ||||||||
\(931\) | 20.7081 | + | 22.8760i | 0.678681 | + | 0.749731i | ||||
\(932\) | 22.0153 | 0.721137 | ||||||||
\(933\) | −2.71831 | −0.0889936 | ||||||||
\(934\) | −2.51171 | −0.0821855 | ||||||||
\(935\) | − | 4.37851i | − | 0.143193i | ||||||
\(936\) | − | 4.42723i | − | 0.144709i | ||||||
\(937\) | 16.1835 | 0.528693 | 0.264347 | − | 0.964428i | \(-0.414844\pi\) | ||||
0.264347 | + | 0.964428i | \(0.414844\pi\) | |||||||
\(938\) | −3.58918 | − | 1.59229i | −0.117191 | − | 0.0519900i | ||||
\(939\) | − | 21.1811i | − | 0.691218i | ||||||
\(940\) | 6.41728i | 0.209309i | ||||||||
\(941\) | 16.7358 | 0.545573 | 0.272786 | − | 0.962075i | \(-0.412055\pi\) | ||||
0.272786 | + | 0.962075i | \(0.412055\pi\) | |||||||
\(942\) | − | 5.14919i | − | 0.167770i | ||||||
\(943\) | 6.87375 | + | 16.9323i | 0.223840 | + | 0.551392i | ||||
\(944\) | 29.3267i | 0.954504i | ||||||||
\(945\) | 1.10856 | + | 0.491797i | 0.0360614 | + | 0.0159981i | ||||
\(946\) | −2.45693 | −0.0798818 | ||||||||
\(947\) | −4.16195 | −0.135245 | −0.0676226 | − | 0.997711i | \(-0.521541\pi\) | ||||
−0.0676226 | + | 0.997711i | \(0.521541\pi\) | |||||||
\(948\) | 13.2891 | 0.431611 | ||||||||
\(949\) | 31.1854 | 1.01232 | ||||||||
\(950\) | 5.36519 | 0.174070 | ||||||||
\(951\) | − | 11.2541i | − | 0.364939i | ||||||
\(952\) | −7.61676 | + | 17.1690i | −0.246861 | + | 0.556449i | ||||
\(953\) | − | 8.11785i | − | 0.262963i | −0.991319 | − | 0.131481i | \(-0.958027\pi\) | ||
0.991319 | − | 0.131481i | \(-0.0419734\pi\) | |||||||
\(954\) | 2.12374i | 0.0687586i | ||||||||
\(955\) | − | 9.70892i | − | 0.314173i | ||||||
\(956\) | 52.1690 | 1.68726 | ||||||||
\(957\) | −5.63717 | −0.182224 | ||||||||
\(958\) | −0.227339 | −0.00734500 | ||||||||
\(959\) | 22.0234 | + | 9.77037i | 0.711173 | + | 0.315502i | ||||
\(960\) | − | 2.97569i | − | 0.0960401i | ||||||
\(961\) | 12.3491 | 0.398358 | ||||||||
\(962\) | 9.63105 | 0.310517 | ||||||||
\(963\) | 20.1553i | 0.649497i | ||||||||
\(964\) | −10.4595 | −0.336878 | ||||||||
\(965\) | 4.59881 | 0.148041 | ||||||||
\(966\) | 3.22255 | + | 0.102899i | 0.103684 | + | 0.00331071i | ||||
\(967\) | 7.40381 | 0.238091 | 0.119045 | − | 0.992889i | \(-0.462017\pi\) | ||||
0.119045 | + | 0.992889i | \(0.462017\pi\) | |||||||
\(968\) | −9.18953 | −0.295363 | ||||||||
\(969\) | 31.2939i | 1.00531i | ||||||||
\(970\) | 0.449923 | 0.0144462 | ||||||||
\(971\) | 14.0152 | 0.449768 | 0.224884 | − | 0.974386i | \(-0.427800\pi\) | ||||
0.224884 | + | 0.974386i | \(0.427800\pi\) | |||||||
\(972\) | − | 1.93543i | − | 0.0620790i | ||||||
\(973\) | −43.1699 | − | 19.1517i | −1.38396 | − | 0.613976i | ||||
\(974\) | 1.12186 | 0.0359466 | ||||||||
\(975\) | −21.2059 | −0.679134 | ||||||||
\(976\) | 37.0668 | 1.18648 | ||||||||
\(977\) | 26.5778i | 0.850298i | 0.905123 | + | 0.425149i | \(0.139778\pi\) | ||||
−0.905123 | + | 0.425149i | \(0.860222\pi\) | |||||||
\(978\) | 2.02759i | 0.0648350i | ||||||||
\(979\) | − | 21.5316i | − | 0.688154i | ||||||
\(980\) | 4.16764 | + | 4.60394i | 0.133130 | + | 0.147067i | ||||
\(981\) | − | 5.06232i | − | 0.161627i | ||||||
\(982\) | 6.74590 | 0.215270 | ||||||||
\(983\) | −32.3741 | −1.03257 | −0.516287 | − | 0.856416i | \(-0.672686\pi\) | ||||
−0.516287 | + | 0.856416i | \(0.672686\pi\) | |||||||
\(984\) | −3.81047 | −0.121473 | ||||||||
\(985\) | 2.53939 | 0.0809117 | ||||||||
\(986\) | −7.55755 | −0.240682 | ||||||||
\(987\) | −7.76091 | + | 17.4939i | −0.247032 | + | 0.556836i | ||||
\(988\) | − | 37.7713i | − | 1.20167i | ||||||
\(989\) | −12.9630 | − | 31.9322i | −0.412200 | − | 1.01539i | ||||
\(990\) | − | 0.156721i | − | 0.00498090i | ||||||
\(991\) | −7.50926 | −0.238540 | −0.119270 | − | 0.992862i | \(-0.538055\pi\) | ||||
−0.119270 | + | 0.992862i | \(0.538055\pi\) | |||||||
\(992\) | 12.6063i | 0.400251i | ||||||||
\(993\) | 8.54102i | 0.271041i | ||||||||
\(994\) | −2.29750 | + | 5.17879i | −0.0728722 | + | 0.164261i | ||||
\(995\) | 3.07025 | 0.0973334 | ||||||||
\(996\) | − | 9.58690i | − | 0.303772i | ||||||
\(997\) | 22.3983i | 0.709362i | 0.934987 | + | 0.354681i | \(0.115410\pi\) | ||||
−0.934987 | + | 0.354681i | \(0.884590\pi\) | |||||||
\(998\) | 5.08726 | 0.161034 | ||||||||
\(999\) | 8.56119 | 0.270864 |
(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 | 483.2.h.b.160.8 | yes | 12 | |
3.2 | odd | 2 | 1449.2.h.h.1126.6 | 12 | |||
7.6 | odd | 2 | inner | 483.2.h.b.160.5 | ✓ | 12 | |
21.20 | even | 2 | 1449.2.h.h.1126.8 | 12 | |||
23.22 | odd | 2 | inner | 483.2.h.b.160.7 | yes | 12 | |
69.68 | even | 2 | 1449.2.h.h.1126.7 | 12 | |||
161.160 | even | 2 | inner | 483.2.h.b.160.6 | yes | 12 | |
483.482 | odd | 2 | 1449.2.h.h.1126.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.h.b.160.5 | ✓ | 12 | 7.6 | odd | 2 | inner | |
483.2.h.b.160.6 | yes | 12 | 161.160 | even | 2 | inner | |
483.2.h.b.160.7 | yes | 12 | 23.22 | odd | 2 | inner | |
483.2.h.b.160.8 | yes | 12 | 1.1 | even | 1 | trivial | |
1449.2.h.h.1126.5 | 12 | 483.482 | odd | 2 | |||
1449.2.h.h.1126.6 | 12 | 3.2 | odd | 2 | |||
1449.2.h.h.1126.7 | 12 | 69.68 | even | 2 | |||
1449.2.h.h.1126.8 | 12 | 21.20 | even | 2 |