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 | 160.7 | ||
Root | \(1.51343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.160 |
Dual form | 483.2.h.b.160.5 |
$q$-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 | \(-0.532683\pi\) | ||||
−0.102496 | + | 0.994733i | \(0.532683\pi\) | |||||||
\(6\) | 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 | \(-0.934981\pi\) | ||
0.979210 | − | 0.202847i | \(-0.0650194\pi\) | |||||||
\(12\) | − | 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 | \(-0.169900\pi\) | ||||
0.860902 | + | 0.508771i | \(0.169900\pi\) | |||||||
\(18\) | −0.254102 | −0.0598923 | ||||||||
\(19\) | 4.40811 | 1.01129 | 0.505644 | − | 0.862742i | \(-0.331255\pi\) | ||||
0.505644 | + | 0.862742i | \(0.331255\pi\) | |||||||
\(20\) | 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 | \(-0.751519\pi\) | ||
0.710472 | − | 0.703725i | \(-0.248481\pi\) | |||||||
\(38\) | 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 | \(-0.815415\pi\) | ||
0.836523 | − | 0.547932i | \(-0.184585\pi\) | |||||||
\(44\) | 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 | \(0.194616\pi\) | ||||
−0.818842 | + | 0.574018i | \(0.805384\pi\) | |||||||
\(54\) | − | 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 | \(-0.727795\pi\) | ||||
−0.656101 | + | 0.754673i | \(0.727795\pi\) | |||||||
\(62\) | 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 | \(-0.883879\pi\) | ||
0.934194 | − | 0.356767i | \(-0.116121\pi\) | |||||||
\(68\) | −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 | \(-0.873768\pi\) | ||
0.922392 | − | 0.386256i | \(-0.126232\pi\) | |||||||
\(80\) | −1.65784 | −0.185352 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 0.968246i | − | 0.106925i | ||||||
\(83\) | −4.95336 | −0.543702 | −0.271851 | − | 0.962339i | \(-0.587636\pi\) | ||||
−0.271851 | + | 0.962339i | \(0.587636\pi\) | |||||||
\(84\) | −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 | \(-0.177736\pi\) | ||||
0.848118 | + | 0.529807i | \(0.177736\pi\) | |||||||
\(90\) | 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 | \(-0.562830\pi\) | ||||
−0.196107 | + | 0.980583i | \(0.562830\pi\) | |||||||
\(98\) | −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 | \(-0.620942\pi\) | ||||
−0.370876 | + | 0.928682i | \(0.620942\pi\) | |||||||
\(104\) | 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 | \(0.427602\pi\) | ||||
−0.225490 | + | 0.974246i | \(0.572398\pi\) | |||||||
\(108\) | 1.93543i | 0.186237i | ||||||||
\(109\) | − | 5.06232i | − | 0.484882i | −0.970166 | − | 0.242441i | \(-0.922052\pi\) | ||
0.970166 | − | 0.242441i | \(-0.0779481\pi\) | |||||||
\(110\) | 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 | \(-0.949143\pi\) | ||
0.987263 | − | 0.159095i | \(-0.0508575\pi\) | |||||||
\(114\) | 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 | \(0.127182\pi\) | ||||
−0.921234 | + | 0.389008i | \(0.872818\pi\) | |||||||
\(138\) | 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 | \(-0.690155\pi\) | ||
0.562485 | − | 0.826808i | \(-0.309845\pi\) | |||||||
\(150\) | − | 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 | \(-0.200207\pi\) | ||||
0.808634 | + | 0.588312i | \(0.200207\pi\) | |||||||
\(158\) | − | 1.74472i | − | 0.138802i | ||||||
\(159\) | −8.35783 | −0.662819 | ||||||||
\(160\) | −1.33802 | −0.105779 | ||||||||
\(161\) | −9.13027 | + | 8.81125i | −0.719566 | + | 0.694424i | ||||
\(162\) | 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 | \(-0.240207\pi\) | ||||
0.728524 | + | 0.685020i | \(0.240207\pi\) | |||||||
\(182\) | −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 | \(0.277906\pi\) | ||||
−0.642478 | + | 0.766304i | \(0.722094\pi\) | |||||||
\(192\) | − | 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 | \(-0.576298\pi\) | ||||
−0.237407 | + | 0.971410i | \(0.576298\pi\) | |||||||
\(200\) | 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 | \(-0.195193\pi\) | ||||
0.817800 | + | 0.575502i | \(0.195193\pi\) | |||||||
\(228\) | − | 8.53159i | − | 0.565018i | ||||||
\(229\) | 8.21928 | 0.543146 | 0.271573 | − | 0.962418i | \(-0.412456\pi\) | ||||
0.271573 | + | 0.962418i | \(0.412456\pi\) | |||||||
\(230\) | 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 | \(-0.555688\pi\) | ||||
−0.174058 | + | 0.984735i | \(0.555688\pi\) | |||||||
\(242\) | 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 | \(-0.709824\pi\) | ||||
−0.612471 | + | 0.790493i | \(0.709824\pi\) | |||||||
\(252\) | 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 | \(-0.984503\pi\) | ||
0.998815 | − | 0.0486668i | \(-0.0154972\pi\) | |||||||
\(264\) | −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 | \(0.0505590\pi\) | ||||
−0.987412 | + | 0.158169i | \(0.949441\pi\) | |||||||
\(282\) | 1.83805 | 0.109454 | ||||||||
\(283\) | 2.05894 | 0.122391 | 0.0611956 | − | 0.998126i | \(-0.480509\pi\) | ||||
0.0611956 | + | 0.998126i | \(0.480509\pi\) | |||||||
\(284\) | −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 | \(-0.329275\pi\) | ||||
0.511001 | + | 0.859580i | \(0.329275\pi\) | |||||||
\(294\) | 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 | \(-0.295719\pi\) | ||||
0.598612 | + | 0.801039i | \(0.295719\pi\) | |||||||
\(314\) | 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 | ||||||||
\(322\) | −2.32002 | + | 2.23895i | −0.129290 | + | 0.124772i | ||||
\(323\) | 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 | \(-0.927936\pi\) | ||
0.974482 | − | 0.224468i | \(-0.0720643\pi\) | |||||||
\(338\) | −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 | \(-0.816622\pi\) | ||
0.838594 | − | 0.544756i | \(-0.183378\pi\) | |||||||
\(360\) | −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 | \(-0.734429\pi\) | ||||
−0.671684 | + | 0.740838i | \(0.734429\pi\) | |||||||
\(368\) | −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 | \(0.142118\pi\) | ||||
−0.901974 | + | 0.431791i | \(0.857882\pi\) | |||||||
\(374\) | − | 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 | \(0.292465\pi\) | ||||
−0.606770 | + | 0.794878i | \(0.707535\pi\) | |||||||
\(380\) | 3.91069 | 0.200614 | ||||||||
\(381\) | − | 12.2981i | − | 0.630050i | ||||||
\(382\) | 5.38214i | 0.275374i | ||||||||
\(383\) | −18.6858 | −0.954801 | −0.477400 | − | 0.878686i | \(-0.658421\pi\) | ||||
−0.477400 | + | 0.878686i | \(0.658421\pi\) | |||||||
\(384\) | − | 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 | \(0.234544\pi\) | ||||
−0.740595 | + | 0.671952i | \(0.765456\pi\) | |||||||
\(390\) | −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 | \(-0.895342\pi\) | ||
0.946433 | − | 0.322901i | \(-0.104658\pi\) | |||||||
\(402\) | 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 | \(-0.546190\pi\) | ||||
−0.144602 | + | 0.989490i | \(0.546190\pi\) | |||||||
\(420\) | 2.14554 | + | 0.951839i | 0.104692 | + | 0.0464450i | ||||
\(421\) | 10.4816i | 0.510841i | 0.966830 | + | 0.255420i | \(0.0822139\pi\) | ||||
−0.966830 | + | 0.255420i | \(0.917786\pi\) | |||||||
\(422\) | −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 | \(0.168905\pi\) | ||||
−0.862488 | + | 0.506078i | \(0.831095\pi\) | |||||||
\(432\) | − | 3.61676i | − | 0.174012i | ||||||
\(433\) | −7.21565 | −0.346762 | −0.173381 | − | 0.984855i | \(-0.555469\pi\) | ||||
−0.173381 | + | 0.984855i | \(0.555469\pi\) | |||||||
\(434\) | 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 | \(-0.870960\pi\) | ||
0.918948 | − | 0.394379i | \(-0.129040\pi\) | |||||||
\(458\) | 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 | \(-0.426551\pi\) | ||||
0.228703 | + | 0.973496i | \(0.426551\pi\) | |||||||
\(468\) | − | 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 | \(-0.493493\pi\) | ||||
0.0204395 | + | 0.999791i | \(0.493493\pi\) | |||||||
\(480\) | − | 1.33802i | − | 0.0610718i | ||||||
\(481\) | −37.9023 | −1.72820 | ||||||||
\(482\) | −1.37322 | −0.0625485 | ||||||||
\(483\) | −8.81125 | − | 9.13027i | −0.400926 | − | 0.415442i | ||||
\(484\) | −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 | \(-0.491644\pi\) | ||||
0.0262486 | + | 0.999655i | \(0.491644\pi\) | |||||||
\(504\) | 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 | \(-0.691058\pi\) | ||||
−0.564831 | + | 0.825207i | \(0.691058\pi\) | |||||||
\(522\) | −1.06457 | −0.0465949 | ||||||||
\(523\) | 26.9939 | 1.18036 | 0.590180 | − | 0.807272i | \(-0.299057\pi\) | ||||
0.590180 | + | 0.807272i | \(0.299057\pi\) | |||||||
\(524\) | − | 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 | \(-0.778440\pi\) | ||
0.767379 | − | 0.641194i | \(-0.221560\pi\) | |||||||
\(558\) | − | 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 | \(-0.780771\pi\) | ||||
−0.772055 | + | 0.635555i | \(0.780771\pi\) | |||||||
\(564\) | −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 | \(0.192369\pi\) | ||||
−0.822875 | + | 0.568223i | \(0.807631\pi\) | |||||||
\(570\) | − | 0.513432i | − | 0.0215053i | ||||||
\(571\) | − | 7.95674i | − | 0.332979i | −0.986043 | − | 0.166490i | \(-0.946757\pi\) | ||
0.986043 | − | 0.166490i | \(-0.0532432\pi\) | |||||||
\(572\) | 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 | \(0.00865045\pi\) | ||||
−0.999631 | + | 0.0271728i | \(0.991350\pi\) | |||||||
\(614\) | − | 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 | \(-0.866467\pi\) | ||
0.913290 | − | 0.407309i | \(-0.133533\pi\) | |||||||
\(618\) | − | 1.91287i | − | 0.0769468i | ||||||
\(619\) | −37.2425 | −1.49690 | −0.748452 | − | 0.663189i | \(-0.769202\pi\) | ||||
−0.748452 | + | 0.663189i | \(0.769202\pi\) | |||||||
\(620\) | 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 | \(-0.711467\pi\) | ||
0.616543 | − | 0.787321i | \(-0.288533\pi\) | |||||||
\(632\) | 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 | \(0.128174\pi\) | ||||
−0.920018 | + | 0.391877i | \(0.871826\pi\) | |||||||
\(642\) | −5.12151 | −0.202130 | ||||||||
\(643\) | 47.0309 | 1.85472 | 0.927358 | − | 0.374176i | \(-0.122074\pi\) | ||||
0.927358 | + | 0.374176i | \(0.122074\pi\) | |||||||
\(644\) | 17.6710 | − | 17.0536i | 0.696336 | − | 0.672005i | ||||
\(645\) | −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 | \(0.219870\pi\) | ||||
−0.770774 | + | 0.637108i | \(0.780130\pi\) | |||||||
\(660\) | 1.19370 | 0.0464648 | ||||||||
\(661\) | 11.9361 | 0.464259 | 0.232130 | − | 0.972685i | \(-0.425431\pi\) | ||||
0.232130 | + | 0.972685i | \(0.425431\pi\) | |||||||
\(662\) | 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 | \(-0.0880943\pi\) | ||||
0.961947 | + | 0.273237i | \(0.0880943\pi\) | |||||||
\(678\) | 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 | \(-0.830749\pi\) | ||
0.861938 | − | 0.507014i | \(-0.169251\pi\) | |||||||
\(702\) | −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 | \(-0.852769\pi\) | ||
0.894922 | − | 0.446222i | \(-0.147231\pi\) | |||||||
\(710\) | −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 | \(-0.295290\pi\) | ||||
0.599692 | + | 0.800231i | \(0.295290\pi\) | |||||||
\(728\) | 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 | \(-0.272458\pi\) | ||||
0.655500 | + | 0.755195i | \(0.272458\pi\) | |||||||
\(734\) | −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 | \(0.00756652\pi\) | ||||
−0.999717 | + | 0.0237687i | \(0.992433\pi\) | |||||||
\(744\) | 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 | \(-0.685687\pi\) | ||
0.550825 | − | 0.834620i | \(-0.314313\pi\) | |||||||
\(752\) | − | 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 | \(-0.878735\pi\) | ||
0.928306 | − | 0.371818i | \(-0.121265\pi\) | |||||||
\(758\) | 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 | \(-0.557422\pi\) | ||||
−0.179419 | + | 0.983773i | \(0.557422\pi\) | |||||||
\(770\) | 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 | \(-0.345537\pi\) | ||||
0.466439 | + | 0.884554i | \(0.345537\pi\) | |||||||
\(774\) | 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 | \(-0.473271\pi\) | ||||
0.0838728 | + | 0.996476i | \(0.473271\pi\) | |||||||
\(788\) | −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 | \(-0.489214\pi\) | ||||
0.0338786 | + | 0.999426i | \(0.489214\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 4.18511 | − | 4.03888i | 0.147506 | − | 0.142352i | ||||
\(806\) | 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 | \(0.0723566\pi\) | ||||
−0.974275 | + | 0.225362i | \(0.927643\pi\) | |||||||
\(828\) | −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 | \(-0.465679\pi\) | ||||
0.107612 | + | 0.994193i | \(0.465679\pi\) | |||||||
\(840\) | 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 | \(-0.560308\pi\) | ||||
−0.188331 | + | 0.982106i | \(0.560308\pi\) | |||||||
\(882\) | 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 | \(-0.834014\pi\) | ||
0.867093 | − | 0.498146i | \(-0.165986\pi\) | |||||||
\(908\) | −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 | \(-0.962175\pi\) | ||
0.992948 | − | 0.118552i | \(-0.0378252\pi\) | |||||||
\(912\) | 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 | \(-0.851213\pi\) | ||
0.892731 | − | 0.450591i | \(-0.148787\pi\) | |||||||
\(920\) | −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 | \(-0.585156\pi\) | ||||
−0.264347 | + | 0.964428i | \(0.585156\pi\) | |||||||
\(938\) | −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 | \(-0.587945\pi\) | ||||
−0.272786 | + | 0.962075i | \(0.587945\pi\) | |||||||
\(942\) | 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 | \(0.0419734\pi\) | ||||
−0.991319 | + | 0.131481i | \(0.958027\pi\) | |||||||
\(954\) | − | 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 | ||||||||
\(966\) | −2.23895 | − | 2.32002i | −0.0720371 | − | 0.0746453i | ||||
\(967\) | 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 | \(-0.572200\pi\) | ||||
−0.224884 | + | 0.974386i | \(0.572200\pi\) | |||||||
\(972\) | − | 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 | \(-0.860222\pi\) | ||
0.905123 | − | 0.425149i | \(-0.139778\pi\) | |||||||
\(978\) | 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 | \(-0.327314\pi\) | ||||
0.516287 | + | 0.856416i | \(0.327314\pi\) | |||||||
\(984\) | −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.160.7 | yes | 12 | |
3.2 | odd | 2 | 1449.2.h.h.1126.7 | 12 | |||
7.6 | odd | 2 | inner | 483.2.h.b.160.6 | yes | 12 | |
21.20 | even | 2 | 1449.2.h.h.1126.5 | 12 | |||
23.22 | odd | 2 | inner | 483.2.h.b.160.8 | yes | 12 | |
69.68 | even | 2 | 1449.2.h.h.1126.6 | 12 | |||
161.160 | even | 2 | inner | 483.2.h.b.160.5 | ✓ | 12 | |
483.482 | odd | 2 | 1449.2.h.h.1126.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.h.b.160.5 | ✓ | 12 | 161.160 | even | 2 | inner | |
483.2.h.b.160.6 | yes | 12 | 7.6 | odd | 2 | inner | |
483.2.h.b.160.7 | yes | 12 | 1.1 | even | 1 | trivial | |
483.2.h.b.160.8 | yes | 12 | 23.22 | odd | 2 | inner | |
1449.2.h.h.1126.5 | 12 | 21.20 | even | 2 | |||
1449.2.h.h.1126.6 | 12 | 69.68 | even | 2 | |||
1449.2.h.h.1126.7 | 12 | 3.2 | odd | 2 | |||
1449.2.h.h.1126.8 | 12 | 483.482 | odd | 2 |