Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 6x^{4} + 7x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.6 | ||
Root | \(0.407132i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.g.1084.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45620i | 1.73680i | 0.495866 | + | 0.868399i | \(0.334851\pi\) | ||||
−0.495866 | + | 0.868399i | \(0.665149\pi\) | |||||||
\(3\) | − | 1.56104i | − | 0.901270i | −0.892708 | − | 0.450635i | \(-0.851198\pi\) | ||
0.892708 | − | 0.450635i | \(-0.148802\pi\) | |||||||
\(4\) | −4.03293 | −2.01647 | ||||||||
\(5\) | 2.19869 | − | 0.407132i | 0.983285 | − | 0.182075i | ||||
\(6\) | 3.83424 | 1.56532 | ||||||||
\(7\) | − | 4.50527i | − | 1.70283i | −0.524490 | − | 0.851417i | \(-0.675744\pi\) | ||
0.524490 | − | 0.851417i | \(-0.324256\pi\) | |||||||
\(8\) | − | 4.99330i | − | 1.76540i | ||||||
\(9\) | 0.563139 | 0.187713 | ||||||||
\(10\) | 1.00000 | + | 5.40043i | 0.316228 | + | 1.70777i | ||||
\(11\) | 2.19869 | 0.662930 | 0.331465 | − | 0.943467i | \(-0.392457\pi\) | ||||
0.331465 | + | 0.943467i | \(0.392457\pi\) | |||||||
\(12\) | 6.29559i | 1.81738i | ||||||||
\(13\) | 3.75849i | 1.04242i | 0.853429 | + | 0.521209i | \(0.174519\pi\) | ||||
−0.853429 | + | 0.521209i | \(0.825481\pi\) | |||||||
\(14\) | 11.0659 | 2.95748 | ||||||||
\(15\) | −0.635552 | − | 3.43226i | −0.164099 | − | 0.886205i | ||||
\(16\) | 4.19869 | 1.04967 | ||||||||
\(17\) | − | 0.665886i | − | 0.161501i | −0.996734 | − | 0.0807506i | \(-0.974268\pi\) | ||
0.996734 | − | 0.0807506i | \(-0.0257317\pi\) | |||||||
\(18\) | 1.38318i | 0.326020i | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −8.86718 | + | 1.64194i | −1.98276 | + | 0.367149i | ||||
\(21\) | −7.03293 | −1.53471 | ||||||||
\(22\) | 5.40043i | 1.15138i | ||||||||
\(23\) | − | 0.488026i | − | 0.101760i | −0.998705 | − | 0.0508802i | \(-0.983797\pi\) | ||
0.998705 | − | 0.0508802i | \(-0.0162027\pi\) | |||||||
\(24\) | −7.79476 | −1.59110 | ||||||||
\(25\) | 4.66849 | − | 1.79032i | 0.933697 | − | 0.358063i | ||||
\(26\) | −9.23163 | −1.81047 | ||||||||
\(27\) | − | 5.56222i | − | 1.07045i | ||||||
\(28\) | 18.1695i | 3.43371i | ||||||||
\(29\) | 3.59607 | 0.667774 | 0.333887 | − | 0.942613i | \(-0.391640\pi\) | ||||
0.333887 | + | 0.942613i | \(0.391640\pi\) | |||||||
\(30\) | 8.43032 | − | 1.56104i | 1.53916 | − | 0.285006i | ||||
\(31\) | −6.83424 | −1.22747 | −0.613733 | − | 0.789514i | \(-0.710333\pi\) | ||||
−0.613733 | + | 0.789514i | \(0.710333\pi\) | |||||||
\(32\) | 0.326239i | 0.0576714i | ||||||||
\(33\) | − | 3.43226i | − | 0.597479i | ||||||
\(34\) | 1.63555 | 0.280495 | ||||||||
\(35\) | −1.83424 | − | 9.90571i | −0.310044 | − | 1.67437i | ||||
\(36\) | −2.27110 | −0.378517 | ||||||||
\(37\) | − | 3.01171i | − | 0.495123i | −0.968872 | − | 0.247561i | \(-0.920371\pi\) | ||
0.968872 | − | 0.247561i | \(-0.0796292\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.86718 | 0.939500 | ||||||||
\(40\) | −2.03293 | − | 10.9787i | −0.321435 | − | 1.73589i | ||||
\(41\) | −0.0724126 | −0.0113090 | −0.00565448 | − | 0.999984i | \(-0.501800\pi\) | ||||
−0.00565448 | + | 0.999984i | \(0.501800\pi\) | |||||||
\(42\) | − | 17.2743i | − | 2.66548i | ||||||
\(43\) | 0.420541i | 0.0641319i | 0.999486 | + | 0.0320660i | \(0.0102087\pi\) | ||||
−0.999486 | + | 0.0320660i | \(0.989791\pi\) | |||||||
\(44\) | −8.86718 | −1.33678 | ||||||||
\(45\) | 1.23817 | − | 0.229272i | 0.184575 | − | 0.0341779i | ||||
\(46\) | 1.19869 | 0.176737 | ||||||||
\(47\) | − | 5.02278i | − | 0.732648i | −0.930487 | − | 0.366324i | \(-0.880616\pi\) | ||
0.930487 | − | 0.366324i | \(-0.119384\pi\) | |||||||
\(48\) | − | 6.55434i | − | 0.946038i | ||||||
\(49\) | −13.2975 | −1.89964 | ||||||||
\(50\) | 4.39738 | + | 11.4668i | 0.621884 | + | 1.62164i | ||||
\(51\) | −1.03948 | −0.145556 | ||||||||
\(52\) | − | 15.1578i | − | 2.10200i | ||||||
\(53\) | − | 2.61799i | − | 0.359609i | −0.983702 | − | 0.179804i | \(-0.942454\pi\) | ||
0.983702 | − | 0.179804i | \(-0.0575465\pi\) | |||||||
\(54\) | 13.6619 | 1.85915 | ||||||||
\(55\) | 4.83424 | − | 0.895159i | 0.651849 | − | 0.120703i | ||||
\(56\) | −22.4962 | −3.00618 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.83269i | 1.15979i | ||||||||
\(59\) | 12.5357 | 1.63200 | 0.816002 | − | 0.578049i | \(-0.196186\pi\) | ||||
0.816002 | + | 0.578049i | \(0.196186\pi\) | |||||||
\(60\) | 2.56314 | + | 13.8421i | 0.330900 | + | 1.78700i | ||||
\(61\) | 7.06587 | 0.904692 | 0.452346 | − | 0.891843i | \(-0.350587\pi\) | ||||
0.452346 | + | 0.891843i | \(0.350587\pi\) | |||||||
\(62\) | − | 16.7863i | − | 2.13186i | ||||||
\(63\) | − | 2.53710i | − | 0.319644i | ||||||
\(64\) | 7.59607 | 0.949509 | ||||||||
\(65\) | 1.53020 | + | 8.26377i | 0.189799 | + | 1.02499i | ||||
\(66\) | 8.43032 | 1.03770 | ||||||||
\(67\) | 5.72667i | 0.699624i | 0.936820 | + | 0.349812i | \(0.113755\pi\) | ||||
−0.936820 | + | 0.349812i | \(0.886245\pi\) | |||||||
\(68\) | 2.68548i | 0.325662i | ||||||||
\(69\) | −0.761831 | −0.0917136 | ||||||||
\(70\) | 24.3304 | − | 4.50527i | 2.90804 | − | 0.538483i | ||||
\(71\) | −6.97252 | −0.827486 | −0.413743 | − | 0.910394i | \(-0.635779\pi\) | ||||
−0.413743 | + | 0.910394i | \(0.635779\pi\) | |||||||
\(72\) | − | 2.81192i | − | 0.331388i | ||||||
\(73\) | − | 2.95764i | − | 0.346165i | −0.984907 | − | 0.173083i | \(-0.944627\pi\) | ||
0.984907 | − | 0.173083i | \(-0.0553728\pi\) | |||||||
\(74\) | 7.39738 | 0.859928 | ||||||||
\(75\) | −2.79476 | − | 7.28772i | −0.322712 | − | 0.841513i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 9.90571i | − | 1.12886i | ||||||
\(78\) | 14.4110i | 1.63172i | ||||||||
\(79\) | 11.3370 | 1.27551 | 0.637755 | − | 0.770240i | \(-0.279863\pi\) | ||||
0.637755 | + | 0.770240i | \(0.279863\pi\) | |||||||
\(80\) | 9.23163 | − | 1.70942i | 1.03213 | − | 0.191119i | ||||
\(81\) | −6.99346 | −0.777051 | ||||||||
\(82\) | − | 0.177860i | − | 0.0196414i | ||||||
\(83\) | − | 15.6999i | − | 1.72328i | −0.507517 | − | 0.861642i | \(-0.669436\pi\) | ||
0.507517 | − | 0.861642i | \(-0.330564\pi\) | |||||||
\(84\) | 28.3634 | 3.09470 | ||||||||
\(85\) | −0.271104 | − | 1.46408i | −0.0294053 | − | 0.158802i | ||||
\(86\) | −1.03293 | −0.111384 | ||||||||
\(87\) | − | 5.61363i | − | 0.601845i | ||||||
\(88\) | − | 10.9787i | − | 1.17034i | ||||||
\(89\) | −1.33697 | −0.141719 | −0.0708594 | − | 0.997486i | \(-0.522574\pi\) | ||||
−0.0708594 | + | 0.997486i | \(0.522574\pi\) | |||||||
\(90\) | 0.563139 | + | 3.04120i | 0.0593601 | + | 0.320570i | ||||
\(91\) | 16.9330 | 1.77507 | ||||||||
\(92\) | 1.96818i | 0.205197i | ||||||||
\(93\) | 10.6686i | 1.10628i | ||||||||
\(94\) | 12.3370 | 1.27246 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.509273 | 0.0519775 | ||||||||
\(97\) | 4.38638i | 0.445369i | 0.974891 | + | 0.222685i | \(0.0714820\pi\) | ||||
−0.974891 | + | 0.222685i | \(0.928518\pi\) | |||||||
\(98\) | − | 32.6613i | − | 3.29929i | ||||||
\(99\) | 1.23817 | 0.124441 | ||||||||
\(100\) | −18.8277 | + | 7.22023i | −1.88277 | + | 0.722023i | ||||
\(101\) | −10.5686 | −1.05161 | −0.525807 | − | 0.850604i | \(-0.676237\pi\) | ||||
−0.525807 | + | 0.850604i | \(0.676237\pi\) | |||||||
\(102\) | − | 2.55317i | − | 0.252801i | ||||||
\(103\) | − | 5.75615i | − | 0.567171i | −0.958947 | − | 0.283585i | \(-0.908476\pi\) | ||
0.958947 | − | 0.283585i | \(-0.0915239\pi\) | |||||||
\(104\) | 18.7673 | 1.84028 | ||||||||
\(105\) | −15.4633 | + | 2.86334i | −1.50906 | + | 0.279433i | ||||
\(106\) | 6.43032 | 0.624568 | ||||||||
\(107\) | − | 1.30229i | − | 0.125897i | −0.998017 | − | 0.0629486i | \(-0.979950\pi\) | ||
0.998017 | − | 0.0629486i | \(-0.0200504\pi\) | |||||||
\(108\) | 22.4321i | 2.15853i | ||||||||
\(109\) | −12.0329 | −1.15255 | −0.576273 | − | 0.817257i | \(-0.695494\pi\) | ||||
−0.576273 | + | 0.817257i | \(0.695494\pi\) | |||||||
\(110\) | 2.19869 | + | 11.8739i | 0.209637 | + | 1.13213i | ||||
\(111\) | −4.70142 | −0.446239 | ||||||||
\(112\) | − | 18.9163i | − | 1.78742i | ||||||
\(113\) | − | 7.74626i | − | 0.728707i | −0.931261 | − | 0.364353i | \(-0.881290\pi\) | ||
0.931261 | − | 0.364353i | \(-0.118710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.198691 | − | 1.07302i | −0.0185281 | − | 0.100060i | ||||
\(116\) | −14.5027 | −1.34654 | ||||||||
\(117\) | 2.11656i | 0.195676i | ||||||||
\(118\) | 30.7901i | 2.83446i | ||||||||
\(119\) | −3.00000 | −0.275010 | ||||||||
\(120\) | −17.1383 | + | 3.17350i | −1.56450 | + | 0.289700i | ||||
\(121\) | −6.16576 | −0.560523 | ||||||||
\(122\) | 17.3552i | 1.57127i | ||||||||
\(123\) | 0.113039i | 0.0101924i | ||||||||
\(124\) | 27.5621 | 2.47515 | ||||||||
\(125\) | 9.53566 | − | 5.83705i | 0.852896 | − | 0.522081i | ||||
\(126\) | 6.23163 | 0.555157 | ||||||||
\(127\) | − | 3.93635i | − | 0.349295i | −0.984631 | − | 0.174647i | \(-0.944121\pi\) | ||
0.984631 | − | 0.174647i | \(-0.0558786\pi\) | |||||||
\(128\) | 19.3100i | 1.70678i | ||||||||
\(129\) | 0.656483 | 0.0578001 | ||||||||
\(130\) | −20.2975 | + | 3.75849i | −1.78021 | + | 0.329642i | ||||
\(131\) | −16.3250 | −1.42632 | −0.713160 | − | 0.701002i | \(-0.752737\pi\) | ||||
−0.713160 | + | 0.701002i | \(0.752737\pi\) | |||||||
\(132\) | 13.8421i | 1.20480i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.0659 | −1.21511 | ||||||||
\(135\) | −2.26456 | − | 12.2296i | −0.194902 | − | 1.05256i | ||||
\(136\) | −3.32497 | −0.285114 | ||||||||
\(137\) | 16.4306i | 1.40376i | 0.712296 | + | 0.701879i | \(0.247655\pi\) | ||||
−0.712296 | + | 0.701879i | \(0.752345\pi\) | |||||||
\(138\) | − | 1.87121i | − | 0.159288i | ||||||
\(139\) | 2.66849 | 0.226338 | 0.113169 | − | 0.993576i | \(-0.463900\pi\) | ||||
0.113169 | + | 0.993576i | \(0.463900\pi\) | |||||||
\(140\) | 7.39738 | + | 39.9491i | 0.625193 | + | 3.37631i | ||||
\(141\) | −7.84079 | −0.660313 | ||||||||
\(142\) | − | 17.1259i | − | 1.43718i | ||||||
\(143\) | 8.26377i | 0.691051i | ||||||||
\(144\) | 2.36445 | 0.197037 | ||||||||
\(145\) | 7.90666 | − | 1.46408i | 0.656612 | − | 0.121585i | ||||
\(146\) | 7.26456 | 0.601219 | ||||||||
\(147\) | 20.7580i | 1.71209i | ||||||||
\(148\) | 12.1460i | 0.998399i | ||||||||
\(149\) | 17.9660 | 1.47183 | 0.735915 | − | 0.677074i | \(-0.236752\pi\) | ||||
0.735915 | + | 0.677074i | \(0.236752\pi\) | |||||||
\(150\) | 17.9001 | − | 6.86451i | 1.46154 | − | 0.560485i | ||||
\(151\) | 12.7344 | 1.03631 | 0.518154 | − | 0.855288i | \(-0.326620\pi\) | ||||
0.518154 | + | 0.855288i | \(0.326620\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.374987i | − | 0.0303159i | ||||||
\(154\) | 24.3304 | 1.96060 | ||||||||
\(155\) | −15.0264 | + | 2.78244i | −1.20695 | + | 0.223491i | ||||
\(156\) | −23.6619 | −1.89447 | ||||||||
\(157\) | 20.0541i | 1.60049i | 0.599673 | + | 0.800245i | \(0.295298\pi\) | ||||
−0.599673 | + | 0.800245i | \(0.704702\pi\) | |||||||
\(158\) | 27.8459i | 2.21530i | ||||||||
\(159\) | −4.08680 | −0.324104 | ||||||||
\(160\) | 0.132822 | + | 0.717298i | 0.0105005 | + | 0.0567074i | ||||
\(161\) | −2.19869 | −0.173281 | ||||||||
\(162\) | − | 17.1773i | − | 1.34958i | ||||||
\(163\) | − | 14.2331i | − | 1.11482i | −0.830236 | − | 0.557412i | \(-0.811794\pi\) | ||
0.830236 | − | 0.557412i | \(-0.188206\pi\) | |||||||
\(164\) | 0.292035 | 0.0228041 | ||||||||
\(165\) | −1.39738 | − | 7.54647i | −0.108786 | − | 0.587492i | ||||
\(166\) | 38.5621 | 2.99300 | ||||||||
\(167\) | 5.61630i | 0.434602i | 0.976105 | + | 0.217301i | \(0.0697253\pi\) | ||||
−0.976105 | + | 0.217301i | \(0.930275\pi\) | |||||||
\(168\) | 35.1176i | 2.70938i | ||||||||
\(169\) | −1.12628 | −0.0866368 | ||||||||
\(170\) | 3.59607 | − | 0.665886i | 0.275806 | − | 0.0510711i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.69601i | − | 0.129320i | ||||||
\(173\) | 10.6905i | 0.812783i | 0.913699 | + | 0.406391i | \(0.133213\pi\) | ||||
−0.913699 | + | 0.406391i | \(0.866787\pi\) | |||||||
\(174\) | 13.7882 | 1.04528 | ||||||||
\(175\) | −8.06587 | − | 21.0328i | −0.609722 | − | 1.58993i | ||||
\(176\) | 9.23163 | 0.695860 | ||||||||
\(177\) | − | 19.5687i | − | 1.47088i | ||||||
\(178\) | − | 3.28388i | − | 0.246137i | ||||||
\(179\) | 7.68942 | 0.574734 | 0.287367 | − | 0.957821i | \(-0.407220\pi\) | ||||
0.287367 | + | 0.957821i | \(0.407220\pi\) | |||||||
\(180\) | −4.99346 | + | 0.924640i | −0.372190 | + | 0.0689186i | ||||
\(181\) | 6.12628 | 0.455363 | 0.227681 | − | 0.973736i | \(-0.426886\pi\) | ||||
0.227681 | + | 0.973736i | \(0.426886\pi\) | |||||||
\(182\) | 41.5910i | 3.08293i | ||||||||
\(183\) | − | 11.0301i | − | 0.815371i | ||||||
\(184\) | −2.43686 | −0.179648 | ||||||||
\(185\) | −1.22617 | − | 6.62183i | −0.0901496 | − | 0.486847i | ||||
\(186\) | −26.2042 | −1.92138 | ||||||||
\(187\) | − | 1.46408i | − | 0.107064i | ||||||
\(188\) | 20.2565i | 1.47736i | ||||||||
\(189\) | −25.0593 | −1.82280 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.85517 | 0.423666 | 0.211833 | − | 0.977306i | \(-0.432057\pi\) | ||||
0.211833 | + | 0.977306i | \(0.432057\pi\) | |||||||
\(192\) | − | 11.8578i | − | 0.855764i | ||||||
\(193\) | − | 2.59117i | − | 0.186517i | −0.995642 | − | 0.0932584i | \(-0.970272\pi\) | ||
0.995642 | − | 0.0932584i | \(-0.0297283\pi\) | |||||||
\(194\) | −10.7738 | −0.773516 | ||||||||
\(195\) | 12.9001 | − | 2.38872i | 0.923796 | − | 0.171060i | ||||
\(196\) | 53.6279 | 3.83057 | ||||||||
\(197\) | 19.8628i | 1.41517i | 0.706629 | + | 0.707584i | \(0.250215\pi\) | ||||
−0.706629 | + | 0.707584i | \(0.749785\pi\) | |||||||
\(198\) | 3.04120i | 0.216128i | ||||||||
\(199\) | 12.7618 | 0.904662 | 0.452331 | − | 0.891850i | \(-0.350593\pi\) | ||||
0.452331 | + | 0.891850i | \(0.350593\pi\) | |||||||
\(200\) | −8.93959 | − | 23.3112i | −0.632124 | − | 1.64835i | ||||
\(201\) | 8.93959 | 0.630550 | ||||||||
\(202\) | − | 25.9586i | − | 1.82644i | ||||||
\(203\) | − | 16.2013i | − | 1.13711i | ||||||
\(204\) | 4.19215 | 0.293509 | ||||||||
\(205\) | −0.159213 | + | 0.0294815i | −0.0111199 | + | 0.00205908i | ||||
\(206\) | 14.1383 | 0.985061 | ||||||||
\(207\) | − | 0.274827i | − | 0.0191018i | ||||||
\(208\) | 15.7808i | 1.09420i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −7.03293 | − | 37.9809i | −0.485319 | − | 2.62093i | ||||
\(211\) | −13.8552 | −0.953830 | −0.476915 | − | 0.878950i | \(-0.658245\pi\) | ||||
−0.476915 | + | 0.878950i | \(0.658245\pi\) | |||||||
\(212\) | 10.5582i | 0.725139i | ||||||||
\(213\) | 10.8844i | 0.745788i | ||||||||
\(214\) | 3.19869 | 0.218658 | ||||||||
\(215\) | 0.171216 | + | 0.924640i | 0.0116768 | + | 0.0630599i | ||||
\(216\) | −27.7738 | −1.88977 | ||||||||
\(217\) | 30.7901i | 2.09017i | ||||||||
\(218\) | − | 29.5553i | − | 2.00174i | ||||||
\(219\) | −4.61701 | −0.311988 | ||||||||
\(220\) | −19.4962 | + | 3.61012i | −1.31443 | + | 0.243394i | ||||
\(221\) | 2.50273 | 0.168352 | ||||||||
\(222\) | − | 11.5476i | − | 0.775027i | ||||||
\(223\) | 21.6960i | 1.45287i | 0.687233 | + | 0.726437i | \(0.258825\pi\) | ||||
−0.687233 | + | 0.726437i | \(0.741175\pi\) | |||||||
\(224\) | 1.46980 | 0.0982048 | ||||||||
\(225\) | 2.62901 | − | 1.00820i | 0.175267 | − | 0.0672132i | ||||
\(226\) | 19.0264 | 1.26562 | ||||||||
\(227\) | − | 8.19628i | − | 0.544006i | −0.962296 | − | 0.272003i | \(-0.912314\pi\) | ||
0.962296 | − | 0.272003i | \(-0.0876861\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.6619 | 1.10105 | 0.550526 | − | 0.834818i | \(-0.314427\pi\) | ||||
0.550526 | + | 0.834818i | \(0.314427\pi\) | |||||||
\(230\) | 2.63555 | − | 0.488026i | 0.173783 | − | 0.0321795i | ||||
\(231\) | −15.4633 | −1.01741 | ||||||||
\(232\) | − | 17.9563i | − | 1.17889i | ||||||
\(233\) | − | 12.2135i | − | 0.800135i | −0.916486 | − | 0.400068i | \(-0.868987\pi\) | ||
0.916486 | − | 0.400068i | \(-0.131013\pi\) | |||||||
\(234\) | −5.19869 | −0.339849 | ||||||||
\(235\) | −2.04494 | − | 11.0435i | −0.133397 | − | 0.720402i | ||||
\(236\) | −50.5555 | −3.29088 | ||||||||
\(237\) | − | 17.6975i | − | 1.14958i | ||||||
\(238\) | − | 7.36861i | − | 0.477636i | ||||||
\(239\) | −2.03948 | −0.131923 | −0.0659614 | − | 0.997822i | \(-0.521011\pi\) | ||||
−0.0659614 | + | 0.997822i | \(0.521011\pi\) | |||||||
\(240\) | −2.66849 | − | 14.4110i | −0.172250 | − | 0.930225i | ||||
\(241\) | −17.5237 | −1.12880 | −0.564399 | − | 0.825502i | \(-0.690892\pi\) | ||||
−0.564399 | + | 0.825502i | \(0.690892\pi\) | |||||||
\(242\) | − | 15.1444i | − | 0.973516i | ||||||
\(243\) | − | 5.76956i | − | 0.370118i | ||||||
\(244\) | −28.4962 | −1.82428 | ||||||||
\(245\) | −29.2371 | + | 5.41384i | −1.86789 | + | 0.345878i | ||||
\(246\) | −0.277648 | −0.0177022 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 34.1254i | 2.16697i | ||||||||
\(249\) | −24.5082 | −1.55314 | ||||||||
\(250\) | 14.3370 | + | 23.4215i | 0.906750 | + | 1.48131i | ||||
\(251\) | −3.33806 | −0.210696 | −0.105348 | − | 0.994435i | \(-0.533596\pi\) | ||||
−0.105348 | + | 0.994435i | \(0.533596\pi\) | |||||||
\(252\) | 10.2319i | 0.644552i | ||||||||
\(253\) | − | 1.07302i | − | 0.0674601i | ||||||
\(254\) | 9.66849 | 0.606655 | ||||||||
\(255\) | −2.28549 | + | 0.423205i | −0.143123 | + | 0.0265021i | ||||
\(256\) | −32.2371 | −2.01482 | ||||||||
\(257\) | 27.5845i | 1.72067i | 0.509726 | + | 0.860337i | \(0.329747\pi\) | ||||
−0.509726 | + | 0.860337i | \(0.670253\pi\) | |||||||
\(258\) | 1.61246i | 0.100387i | ||||||||
\(259\) | −13.5686 | −0.843112 | ||||||||
\(260\) | −6.17122 | − | 33.3272i | −0.382723 | − | 2.06687i | ||||
\(261\) | 2.02509 | 0.125350 | ||||||||
\(262\) | − | 40.0974i | − | 2.47723i | ||||||
\(263\) | 13.6262i | 0.840227i | 0.907471 | + | 0.420114i | \(0.138010\pi\) | ||||
−0.907471 | + | 0.420114i | \(0.861990\pi\) | |||||||
\(264\) | −17.1383 | −1.05479 | ||||||||
\(265\) | −1.06587 | − | 5.75615i | −0.0654758 | − | 0.353598i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.08707i | 0.127727i | ||||||||
\(268\) | − | 23.0953i | − | 1.41077i | ||||||
\(269\) | −3.60808 | −0.219988 | −0.109994 | − | 0.993932i | \(-0.535083\pi\) | ||||
−0.109994 | + | 0.993932i | \(0.535083\pi\) | |||||||
\(270\) | 30.0384 | − | 5.56222i | 1.82808 | − | 0.338506i | ||||
\(271\) | 10.5631 | 0.641665 | 0.320833 | − | 0.947136i | \(-0.396037\pi\) | ||||
0.320833 | + | 0.947136i | \(0.396037\pi\) | |||||||
\(272\) | − | 2.79585i | − | 0.169523i | ||||||
\(273\) | − | 26.4332i | − | 1.59981i | ||||||
\(274\) | −40.3568 | −2.43804 | ||||||||
\(275\) | 10.2646 | − | 3.93635i | 0.618976 | − | 0.237371i | ||||
\(276\) | 3.07241 | 0.184938 | ||||||||
\(277\) | − | 6.73487i | − | 0.404659i | −0.979317 | − | 0.202330i | \(-0.935149\pi\) | ||
0.979317 | − | 0.202330i | \(-0.0648512\pi\) | |||||||
\(278\) | 6.55434i | 0.393103i | ||||||||
\(279\) | −3.84863 | −0.230412 | ||||||||
\(280\) | −49.4622 | + | 9.15893i | −2.95593 | + | 0.547351i | ||||
\(281\) | −23.4303 | −1.39774 | −0.698868 | − | 0.715251i | \(-0.746312\pi\) | ||||
−0.698868 | + | 0.715251i | \(0.746312\pi\) | |||||||
\(282\) | − | 19.2586i | − | 1.14683i | ||||||
\(283\) | 14.6831i | 0.872822i | 0.899747 | + | 0.436411i | \(0.143751\pi\) | ||||
−0.899747 | + | 0.436411i | \(0.856249\pi\) | |||||||
\(284\) | 28.1197 | 1.66860 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.2975 | −1.20022 | ||||||||
\(287\) | 0.326239i | 0.0192573i | ||||||||
\(288\) | 0.183718i | 0.0108257i | ||||||||
\(289\) | 16.5566 | 0.973917 | ||||||||
\(290\) | 3.59607 | + | 19.4204i | 0.211169 | + | 1.14040i | ||||
\(291\) | 6.84733 | 0.401398 | ||||||||
\(292\) | 11.9280i | 0.698031i | ||||||||
\(293\) | − | 18.1855i | − | 1.06241i | −0.847243 | − | 0.531206i | \(-0.821739\pi\) | ||
0.847243 | − | 0.531206i | \(-0.178261\pi\) | |||||||
\(294\) | −50.9858 | −2.97355 | ||||||||
\(295\) | 27.5621 | − | 5.10368i | 1.60472 | − | 0.297147i | ||||
\(296\) | −15.0384 | −0.874089 | ||||||||
\(297\) | − | 12.2296i | − | 0.709634i | ||||||
\(298\) | 44.1281i | 2.55627i | ||||||||
\(299\) | 1.83424 | 0.106077 | ||||||||
\(300\) | 11.2711 | + | 29.3909i | 0.650737 | + | 1.69688i | ||||
\(301\) | 1.89465 | 0.109206 | ||||||||
\(302\) | 31.2782i | 1.79986i | ||||||||
\(303\) | 16.4981i | 0.947788i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.5357 | − | 2.87674i | 0.889570 | − | 0.164722i | ||||
\(306\) | 0.921044 | 0.0526526 | ||||||||
\(307\) | − | 29.3801i | − | 1.67681i | −0.545045 | − | 0.838406i | \(-0.683488\pi\) | ||
0.545045 | − | 0.838406i | \(-0.316512\pi\) | |||||||
\(308\) | 39.9491i | 2.27631i | ||||||||
\(309\) | −8.98561 | −0.511174 | ||||||||
\(310\) | −6.83424 | − | 36.9079i | −0.388159 | − | 2.09623i | ||||
\(311\) | −0.193232 | −0.0109572 | −0.00547859 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547859 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(312\) | − | 29.2966i | − | 1.65859i | ||||||
\(313\) | 21.2755i | 1.20256i | 0.799038 | + | 0.601281i | \(0.205343\pi\) | ||||
−0.799038 | + | 0.601281i | \(0.794657\pi\) | |||||||
\(314\) | −49.2569 | −2.77973 | ||||||||
\(315\) | −1.03293 | − | 5.57829i | −0.0581993 | − | 0.314301i | ||||
\(316\) | −45.7213 | −2.57202 | ||||||||
\(317\) | − | 19.1701i | − | 1.07670i | −0.842721 | − | 0.538351i | \(-0.819048\pi\) | ||
0.842721 | − | 0.538351i | \(-0.180952\pi\) | |||||||
\(318\) | − | 10.0380i | − | 0.562904i | ||||||
\(319\) | 7.90666 | 0.442688 | ||||||||
\(320\) | 16.7014 | − | 3.09261i | 0.933638 | − | 0.172882i | ||||
\(321\) | −2.03293 | −0.113467 | ||||||||
\(322\) | − | 5.40043i | − | 0.300954i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 28.2042 | 1.56690 | ||||||||
\(325\) | 6.72890 | + | 17.5465i | 0.373252 | + | 0.973304i | ||||
\(326\) | 34.9594 | 1.93622 | ||||||||
\(327\) | 18.7839i | 1.03875i | ||||||||
\(328\) | 0.361578i | 0.0199648i | ||||||||
\(329\) | −22.6290 | −1.24758 | ||||||||
\(330\) | 18.5357 | − | 3.43226i | 1.02035 | − | 0.188939i | ||||
\(331\) | 20.6070 | 1.13266 | 0.566331 | − | 0.824178i | \(-0.308362\pi\) | ||||
0.566331 | + | 0.824178i | \(0.308362\pi\) | |||||||
\(332\) | 63.3165i | 3.47495i | ||||||||
\(333\) | − | 1.69601i | − | 0.0929410i | ||||||
\(334\) | −13.7948 | −0.754816 | ||||||||
\(335\) | 2.33151 | + | 12.5912i | 0.127384 | + | 0.687930i | ||||
\(336\) | −29.5291 | −1.61095 | ||||||||
\(337\) | 10.2074i | 0.556030i | 0.960577 | + | 0.278015i | \(0.0896765\pi\) | ||||
−0.960577 | + | 0.278015i | \(0.910324\pi\) | |||||||
\(338\) | − | 2.76637i | − | 0.150471i | ||||||
\(339\) | −12.0923 | −0.656761 | ||||||||
\(340\) | 1.09334 | + | 5.90453i | 0.0592949 | + | 0.320218i | ||||
\(341\) | −15.0264 | −0.813725 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 28.3719i | 1.53194i | ||||||||
\(344\) | 2.09989 | 0.113218 | ||||||||
\(345\) | −1.67503 | + | 0.310166i | −0.0901806 | + | 0.0166988i | ||||
\(346\) | −26.2580 | −1.41164 | ||||||||
\(347\) | 5.44110i | 0.292094i | 0.989278 | + | 0.146047i | \(0.0466550\pi\) | ||||
−0.989278 | + | 0.146047i | \(0.953345\pi\) | |||||||
\(348\) | 22.6394i | 1.21360i | ||||||||
\(349\) | 1.55114 | 0.0830304 | 0.0415152 | − | 0.999138i | \(-0.486781\pi\) | ||||
0.0415152 | + | 0.999138i | \(0.486781\pi\) | |||||||
\(350\) | 51.6609 | − | 19.8114i | 2.76139 | − | 1.05896i | ||||
\(351\) | 20.9056 | 1.11586 | ||||||||
\(352\) | 0.717298i | 0.0382321i | ||||||||
\(353\) | 32.9335i | 1.75287i | 0.481517 | + | 0.876437i | \(0.340086\pi\) | ||||
−0.481517 | + | 0.876437i | \(0.659914\pi\) | |||||||
\(354\) | 48.0648 | 2.55461 | ||||||||
\(355\) | −15.3304 | + | 2.83874i | −0.813655 | + | 0.150665i | ||||
\(356\) | 5.39192 | 0.285771 | ||||||||
\(357\) | 4.68313i | 0.247858i | ||||||||
\(358\) | 18.8868i | 0.998197i | ||||||||
\(359\) | 3.49727 | 0.184579 | 0.0922894 | − | 0.995732i | \(-0.470581\pi\) | ||||
0.0922894 | + | 0.995732i | \(0.470581\pi\) | |||||||
\(360\) | −1.14483 | − | 6.18255i | −0.0603376 | − | 0.325849i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 15.0474i | 0.790873i | ||||||||
\(363\) | 9.62502i | 0.505183i | ||||||||
\(364\) | −68.2899 | −3.57936 | ||||||||
\(365\) | −1.20415 | − | 6.50293i | −0.0630281 | − | 0.340379i | ||||
\(366\) | 27.0923 | 1.41614 | ||||||||
\(367\) | 19.5039i | 1.01810i | 0.860738 | + | 0.509048i | \(0.170002\pi\) | ||||
−0.860738 | + | 0.509048i | \(0.829998\pi\) | |||||||
\(368\) | − | 2.04907i | − | 0.106815i | ||||||
\(369\) | −0.0407784 | −0.00212284 | ||||||||
\(370\) | 16.2646 | − | 3.01171i | 0.845554 | − | 0.156572i | ||||
\(371\) | −11.7948 | −0.612354 | ||||||||
\(372\) | − | 43.0256i | − | 2.23077i | ||||||
\(373\) | 23.5158i | 1.21760i | 0.793322 | + | 0.608802i | \(0.208350\pi\) | ||||
−0.793322 | + | 0.608802i | \(0.791650\pi\) | |||||||
\(374\) | 3.59607 | 0.185949 | ||||||||
\(375\) | −9.11189 | − | 14.8856i | −0.470536 | − | 0.768689i | ||||
\(376\) | −25.0803 | −1.29342 | ||||||||
\(377\) | 13.5158i | 0.696100i | ||||||||
\(378\) | − | 61.5508i | − | 3.16583i | ||||||
\(379\) | −7.05148 | −0.362210 | −0.181105 | − | 0.983464i | \(-0.557967\pi\) | ||||
−0.181105 | + | 0.983464i | \(0.557967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.14483 | −0.314809 | ||||||||
\(382\) | 14.3815i | 0.735822i | ||||||||
\(383\) | 3.08409i | 0.157589i | 0.996891 | + | 0.0787947i | \(0.0251072\pi\) | ||||
−0.996891 | + | 0.0787947i | \(0.974893\pi\) | |||||||
\(384\) | 30.1437 | 1.53827 | ||||||||
\(385\) | −4.03293 | − | 21.7796i | −0.205537 | − | 1.10999i | ||||
\(386\) | 6.36445 | 0.323942 | ||||||||
\(387\) | 0.236823i | 0.0120384i | ||||||||
\(388\) | − | 17.6900i | − | 0.898072i | ||||||
\(389\) | −9.39084 | −0.476134 | −0.238067 | − | 0.971249i | \(-0.576514\pi\) | ||||
−0.238067 | + | 0.971249i | \(0.576514\pi\) | |||||||
\(390\) | 5.86718 | + | 31.6853i | 0.297096 | + | 1.60445i | ||||
\(391\) | −0.324970 | −0.0164344 | ||||||||
\(392\) | 66.3984i | 3.35362i | ||||||||
\(393\) | 25.4840i | 1.28550i | ||||||||
\(394\) | −48.7871 | −2.45786 | ||||||||
\(395\) | 24.9265 | − | 4.61565i | 1.25419 | − | 0.232239i | ||||
\(396\) | −4.99346 | −0.250931 | ||||||||
\(397\) | − | 26.7595i | − | 1.34302i | −0.740996 | − | 0.671510i | \(-0.765646\pi\) | ||
0.740996 | − | 0.671510i | \(-0.234354\pi\) | |||||||
\(398\) | 31.3456i | 1.57122i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.6015 | − | 7.51699i | 0.980077 | − | 0.375849i | ||||
\(401\) | 25.1701 | 1.25694 | 0.628468 | − | 0.777835i | \(-0.283682\pi\) | ||||
0.628468 | + | 0.777835i | \(0.283682\pi\) | |||||||
\(402\) | 21.9575i | 1.09514i | ||||||||
\(403\) | − | 25.6865i | − | 1.27953i | ||||||
\(404\) | 42.6225 | 2.12055 | ||||||||
\(405\) | −15.3765 | + | 2.84726i | −0.764062 | + | 0.141482i | ||||
\(406\) | 39.7937 | 1.97493 | ||||||||
\(407\) | − | 6.62183i | − | 0.328232i | ||||||
\(408\) | 5.19043i | 0.256964i | ||||||||
\(409\) | −28.3215 | −1.40041 | −0.700204 | − | 0.713943i | \(-0.746908\pi\) | ||||
−0.700204 | + | 0.713943i | \(0.746908\pi\) | |||||||
\(410\) | −0.0724126 | − | 0.391060i | −0.00357621 | − | 0.0193131i | ||||
\(411\) | 25.6489 | 1.26516 | ||||||||
\(412\) | 23.2142i | 1.14368i | ||||||||
\(413\) | − | 56.4766i | − | 2.77903i | ||||||
\(414\) | 0.675030 | 0.0331759 | ||||||||
\(415\) | −6.39192 | − | 34.5192i | −0.313767 | − | 1.69448i | ||||
\(416\) | −1.22617 | −0.0601178 | ||||||||
\(417\) | − | 4.16563i | − | 0.203992i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.0449 | −0.637287 | −0.318643 | − | 0.947875i | \(-0.603227\pi\) | ||||
−0.318643 | + | 0.947875i | \(0.603227\pi\) | |||||||
\(420\) | 62.3623 | − | 11.5476i | 3.04297 | − | 0.563467i | ||||
\(421\) | −3.32497 | −0.162049 | −0.0810246 | − | 0.996712i | \(-0.525819\pi\) | ||||
−0.0810246 | + | 0.996712i | \(0.525819\pi\) | |||||||
\(422\) | − | 34.0311i | − | 1.65661i | ||||||
\(423\) | − | 2.82853i | − | 0.137528i | ||||||
\(424\) | −13.0724 | −0.634852 | ||||||||
\(425\) | −1.19215 | − | 3.10868i | −0.0578276 | − | 0.150793i | ||||
\(426\) | −26.7344 | −1.29528 | ||||||||
\(427\) | − | 31.8337i | − | 1.54054i | ||||||
\(428\) | 5.25205i | 0.253868i | ||||||||
\(429\) | 12.9001 | 0.622823 | ||||||||
\(430\) | −2.27110 | + | 0.420541i | −0.109522 | + | 0.0202803i | ||||
\(431\) | −0.0484069 | −0.00233168 | −0.00116584 | − | 0.999999i | \(-0.500371\pi\) | ||||
−0.00116584 | + | 0.999999i | \(0.500371\pi\) | |||||||
\(432\) | − | 23.3540i | − | 1.12362i | ||||||
\(433\) | − | 9.56872i | − | 0.459844i | −0.973209 | − | 0.229922i | \(-0.926153\pi\) | ||
0.973209 | − | 0.229922i | \(-0.0738470\pi\) | |||||||
\(434\) | −75.6268 | −3.63020 | ||||||||
\(435\) | −2.28549 | − | 12.3426i | −0.109581 | − | 0.591784i | ||||
\(436\) | 48.5280 | 2.32407 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | − | 11.3403i | − | 0.541861i | ||||||
\(439\) | −22.2515 | −1.06200 | −0.531002 | − | 0.847370i | \(-0.678184\pi\) | ||||
−0.531002 | + | 0.847370i | \(0.678184\pi\) | |||||||
\(440\) | −4.46980 | − | 24.1388i | −0.213089 | − | 1.15077i | ||||
\(441\) | −7.48834 | −0.356588 | ||||||||
\(442\) | 6.14721i | 0.292393i | ||||||||
\(443\) | − | 20.1157i | − | 0.955727i | −0.878434 | − | 0.477863i | \(-0.841411\pi\) | ||
0.878434 | − | 0.477863i | \(-0.158589\pi\) | |||||||
\(444\) | 18.9605 | 0.899827 | ||||||||
\(445\) | −2.93959 | + | 0.544325i | −0.139350 | + | 0.0258035i | ||||
\(446\) | −53.2899 | −2.52335 | ||||||||
\(447\) | − | 28.0457i | − | 1.32652i | ||||||
\(448\) | − | 34.2224i | − | 1.61686i | ||||||
\(449\) | −12.4973 | −0.589783 | −0.294891 | − | 0.955531i | \(-0.595283\pi\) | ||||
−0.294891 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(450\) | 2.47634 | + | 6.45738i | 0.116736 | + | 0.304404i | ||||
\(451\) | −0.159213 | −0.00749705 | ||||||||
\(452\) | 31.2402i | 1.46941i | ||||||||
\(453\) | − | 19.8789i | − | 0.933992i | ||||||
\(454\) | 20.1317 | 0.944829 | ||||||||
\(455\) | 37.2305 | − | 6.89399i | 1.74539 | − | 0.323195i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 28.3179i | − | 1.32465i | −0.749215 | − | 0.662327i | \(-0.769569\pi\) | ||
0.749215 | − | 0.662327i | \(-0.230431\pi\) | |||||||
\(458\) | 40.9251i | 1.91231i | ||||||||
\(459\) | −3.70381 | −0.172879 | ||||||||
\(460\) | 0.801309 | + | 4.32741i | 0.0373612 | + | 0.201767i | ||||
\(461\) | 5.31951 | 0.247754 | 0.123877 | − | 0.992298i | \(-0.460467\pi\) | ||||
0.123877 | + | 0.992298i | \(0.460467\pi\) | |||||||
\(462\) | − | 37.9809i | − | 1.76703i | ||||||
\(463\) | 17.9327i | 0.833401i | 0.909044 | + | 0.416701i | \(0.136814\pi\) | ||||
−0.909044 | + | 0.416701i | \(0.863186\pi\) | |||||||
\(464\) | 15.0988 | 0.700944 | ||||||||
\(465\) | 4.34352 | + | 23.4569i | 0.201426 | + | 1.08779i | ||||
\(466\) | 29.9989 | 1.38967 | ||||||||
\(467\) | 28.7791i | 1.33174i | 0.746069 | + | 0.665868i | \(0.231939\pi\) | ||||
−0.746069 | + | 0.665868i | \(0.768061\pi\) | |||||||
\(468\) | − | 8.53593i | − | 0.394574i | ||||||
\(469\) | 25.8002 | 1.19134 | ||||||||
\(470\) | 27.1252 | − | 5.02278i | 1.25119 | − | 0.231684i | ||||
\(471\) | 31.3053 | 1.44247 | ||||||||
\(472\) | − | 62.5943i | − | 2.88114i | ||||||
\(473\) | 0.924640i | 0.0425150i | ||||||||
\(474\) | 43.4687 | 1.99658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0988 | 0.554548 | ||||||||
\(477\) | − | 1.47429i | − | 0.0675033i | ||||||
\(478\) | − | 5.00937i | − | 0.229123i | ||||||
\(479\) | 8.05148 | 0.367882 | 0.183941 | − | 0.982937i | \(-0.441115\pi\) | ||||
0.183941 | + | 0.982937i | \(0.441115\pi\) | |||||||
\(480\) | 1.11973 | − | 0.207342i | 0.0511087 | − | 0.00946381i | ||||
\(481\) | 11.3195 | 0.516125 | ||||||||
\(482\) | − | 43.0417i | − | 1.96049i | ||||||
\(483\) | 3.43226i | 0.156173i | ||||||||
\(484\) | 24.8661 | 1.13028 | ||||||||
\(485\) | 1.78584 | + | 9.64429i | 0.0810907 | + | 0.437925i | ||||
\(486\) | 14.1712 | 0.642819 | ||||||||
\(487\) | − | 1.09761i | − | 0.0497376i | −0.999691 | − | 0.0248688i | \(-0.992083\pi\) | ||
0.999691 | − | 0.0248688i | \(-0.00791680\pi\) | |||||||
\(488\) | − | 35.2820i | − | 1.59714i | ||||||
\(489\) | −22.2185 | −1.00476 | ||||||||
\(490\) | −13.2975 | − | 71.8122i | −0.600720 | − | 3.24415i | ||||
\(491\) | 13.1053 | 0.591436 | 0.295718 | − | 0.955275i | \(-0.404441\pi\) | ||||
0.295718 | + | 0.955275i | \(0.404441\pi\) | |||||||
\(492\) | − | 0.455880i | − | 0.0205527i | ||||||
\(493\) | − | 2.39458i | − | 0.107846i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.72235 | − | 0.504099i | 0.122361 | − | 0.0226576i | ||||
\(496\) | −28.6949 | −1.28844 | ||||||||
\(497\) | 31.4131i | 1.40907i | ||||||||
\(498\) | − | 60.1971i | − | 2.69750i | ||||||
\(499\) | −24.1407 | −1.08068 | −0.540342 | − | 0.841445i | \(-0.681705\pi\) | ||||
−0.540342 | + | 0.841445i | \(0.681705\pi\) | |||||||
\(500\) | −38.4567 | + | 23.5404i | −1.71984 | + | 1.05276i | ||||
\(501\) | 8.76729 | 0.391694 | ||||||||
\(502\) | − | 8.19895i | − | 0.365937i | ||||||
\(503\) | 18.9618i | 0.845465i | 0.906254 | + | 0.422733i | \(0.138929\pi\) | ||||
−0.906254 | + | 0.422733i | \(0.861071\pi\) | |||||||
\(504\) | −12.6685 | −0.564299 | ||||||||
\(505\) | −23.2371 | + | 4.30282i | −1.03404 | + | 0.191473i | ||||
\(506\) | 2.63555 | 0.117165 | ||||||||
\(507\) | 1.75817i | 0.0780831i | ||||||||
\(508\) | 15.8751i | 0.704342i | ||||||||
\(509\) | 21.9605 | 0.973383 | 0.486692 | − | 0.873574i | \(-0.338204\pi\) | ||||
0.486692 | + | 0.873574i | \(0.338204\pi\) | |||||||
\(510\) | −1.03948 | − | 5.61363i | −0.0460289 | − | 0.248576i | ||||
\(511\) | −13.3250 | −0.589462 | ||||||||
\(512\) | − | 40.5609i | − | 1.79255i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −67.7531 | −2.98846 | ||||||||
\(515\) | −2.34352 | − | 12.6560i | −0.103268 | − | 0.557690i | ||||
\(516\) | −2.64755 | −0.116552 | ||||||||
\(517\) | − | 11.0435i | − | 0.485695i | ||||||
\(518\) | − | 33.3272i | − | 1.46431i | ||||||
\(519\) | 16.6883 | 0.732537 | ||||||||
\(520\) | 41.2635 | − | 7.64077i | 1.80952 | − | 0.335070i | ||||
\(521\) | −6.56968 | −0.287823 | −0.143912 | − | 0.989591i | \(-0.545968\pi\) | ||||
−0.143912 | + | 0.989591i | \(0.545968\pi\) | |||||||
\(522\) | 4.97403i | 0.217708i | ||||||||
\(523\) | 4.19777i | 0.183556i | 0.995780 | + | 0.0917779i | \(0.0292550\pi\) | ||||
−0.995780 | + | 0.0917779i | \(0.970745\pi\) | |||||||
\(524\) | 65.8375 | 2.87613 | ||||||||
\(525\) | −32.8332 | + | 12.5912i | −1.43296 | + | 0.549524i | ||||
\(526\) | −33.4687 | −1.45931 | ||||||||
\(527\) | 4.55083i | 0.198237i | ||||||||
\(528\) | − | 14.4110i | − | 0.627157i | ||||||
\(529\) | 22.7618 | 0.989645 | ||||||||
\(530\) | 14.1383 | − | 2.61799i | 0.614128 | − | 0.113718i | ||||
\(531\) | 7.05933 | 0.306349 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.272162i | − | 0.0117887i | ||||||
\(534\) | −5.12628 | −0.221836 | ||||||||
\(535\) | −0.530205 | − | 2.86334i | −0.0229228 | − | 0.123793i | ||||
\(536\) | 28.5950 | 1.23512 | ||||||||
\(537\) | − | 12.0035i | − | 0.517990i | ||||||
\(538\) | − | 8.86217i | − | 0.382075i | ||||||
\(539\) | −29.2371 | −1.25933 | ||||||||
\(540\) | 9.13282 | + | 49.3212i | 0.393014 | + | 2.12245i | ||||
\(541\) | −4.63009 | −0.199063 | −0.0995316 | − | 0.995034i | \(-0.531734\pi\) | ||||
−0.0995316 | + | 0.995034i | \(0.531734\pi\) | |||||||
\(542\) | 25.9452i | 1.11444i | ||||||||
\(543\) | − | 9.56340i | − | 0.410405i | ||||||
\(544\) | 0.217238 | 0.00931400 | ||||||||
\(545\) | −26.4567 | + | 4.89900i | −1.13328 | + | 0.209850i | ||||
\(546\) | 64.9254 | 2.77855 | ||||||||
\(547\) | 38.0399i | 1.62647i | 0.581938 | + | 0.813233i | \(0.302295\pi\) | ||||
−0.581938 | + | 0.813233i | \(0.697705\pi\) | |||||||
\(548\) | − | 66.2634i | − | 2.83063i | ||||||
\(549\) | 3.97907 | 0.169823 | ||||||||
\(550\) | 9.66849 | + | 25.2118i | 0.412266 | + | 1.07504i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3.80405i | 0.161911i | ||||||||
\(553\) | − | 51.0762i | − | 2.17198i | ||||||
\(554\) | 16.5422 | 0.702811 | ||||||||
\(555\) | −10.3370 | + | 1.91410i | −0.438780 | + | 0.0812491i | ||||
\(556\) | −10.7618 | −0.456403 | ||||||||
\(557\) | 36.4306i | 1.54361i | 0.635857 | + | 0.771807i | \(0.280647\pi\) | ||||
−0.635857 | + | 0.771807i | \(0.719353\pi\) | |||||||
\(558\) | − | 9.45302i | − | 0.400178i | ||||||
\(559\) | −1.58060 | −0.0668523 | ||||||||
\(560\) | −7.70142 | − | 41.5910i | −0.325444 | − | 1.75754i | ||||
\(561\) | −2.28549 | −0.0964935 | ||||||||
\(562\) | − | 57.5496i | − | 2.42758i | ||||||
\(563\) | 20.6856i | 0.871795i | 0.899996 | + | 0.435897i | \(0.143569\pi\) | ||||
−0.899996 | + | 0.435897i | \(0.856431\pi\) | |||||||
\(564\) | 31.6214 | 1.33150 | ||||||||
\(565\) | −3.15375 | − | 17.0316i | −0.132679 | − | 0.716526i | ||||
\(566\) | −36.0648 | −1.51592 | ||||||||
\(567\) | 31.5074i | 1.32319i | ||||||||
\(568\) | 34.8159i | 1.46084i | ||||||||
\(569\) | −27.1132 | −1.13664 | −0.568322 | − | 0.822806i | \(-0.692407\pi\) | ||||
−0.568322 | + | 0.822806i | \(0.692407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.4687 | 1.94466 | 0.972328 | − | 0.233622i | \(-0.0750578\pi\) | ||||
0.972328 | + | 0.233622i | \(0.0750578\pi\) | |||||||
\(572\) | − | 33.3272i | − | 1.39348i | ||||||
\(573\) | − | 9.14019i | − | 0.381837i | ||||||
\(574\) | −0.801309 | −0.0334460 | ||||||||
\(575\) | −0.873721 | − | 2.27834i | −0.0364367 | − | 0.0950135i | ||||
\(576\) | 4.27765 | 0.178235 | ||||||||
\(577\) | 18.0398i | 0.751008i | 0.926821 | + | 0.375504i | \(0.122530\pi\) | ||||
−0.926821 | + | 0.375504i | \(0.877470\pi\) | |||||||
\(578\) | 40.6664i | 1.69150i | ||||||||
\(579\) | −4.04494 | −0.168102 | ||||||||
\(580\) | −31.8870 | + | 5.90453i | −1.32404 | + | 0.245172i | ||||
\(581\) | −70.7322 | −2.93447 | ||||||||
\(582\) | 16.8184i | 0.697147i | ||||||||
\(583\) | − | 5.75615i | − | 0.238395i | ||||||
\(584\) | −14.7684 | −0.611120 | ||||||||
\(585\) | 0.861719 | + | 4.65365i | 0.0356277 | + | 0.192405i | ||||
\(586\) | 44.6674 | 1.84519 | ||||||||
\(587\) | 26.0337i | 1.07452i | 0.843415 | + | 0.537262i | \(0.180541\pi\) | ||||
−0.843415 | + | 0.537262i | \(0.819459\pi\) | |||||||
\(588\) | − | 83.7156i | − | 3.45237i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 12.5357 | + | 67.6980i | 0.516085 | + | 2.78708i | ||||
\(591\) | 31.0068 | 1.27545 | ||||||||
\(592\) | − | 12.6453i | − | 0.519717i | ||||||
\(593\) | 18.1561i | 0.745580i | 0.927916 | + | 0.372790i | \(0.121599\pi\) | ||||
−0.927916 | + | 0.372790i | \(0.878401\pi\) | |||||||
\(594\) | 30.0384 | 1.23249 | ||||||||
\(595\) | −6.59607 | + | 1.22140i | −0.270413 | + | 0.0500724i | ||||
\(596\) | −72.4556 | −2.96790 | ||||||||
\(597\) | − | 19.9218i | − | 0.815345i | ||||||
\(598\) | 4.50527i | 0.184234i | ||||||||
\(599\) | 40.0713 | 1.63727 | 0.818635 | − | 0.574314i | \(-0.194731\pi\) | ||||
0.818635 | + | 0.574314i | \(0.194731\pi\) | |||||||
\(600\) | −36.3898 | + | 13.9551i | −1.48561 | + | 0.569715i | ||||
\(601\) | −15.0473 | −0.613793 | −0.306897 | − | 0.951743i | \(-0.599291\pi\) | ||||
−0.306897 | + | 0.951743i | \(0.599291\pi\) | |||||||
\(602\) | 4.65365i | 0.189669i | ||||||||
\(603\) | 3.22491i | 0.131329i | ||||||||
\(604\) | −51.3568 | −2.08968 | ||||||||
\(605\) | −13.5566 | + | 2.51028i | −0.551154 | + | 0.102057i | ||||
\(606\) | −40.5226 | −1.64612 | ||||||||
\(607\) | 29.3860i | 1.19274i | 0.802709 | + | 0.596370i | \(0.203391\pi\) | ||||
−0.802709 | + | 0.596370i | \(0.796609\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.2910 | −1.02484 | ||||||||
\(610\) | 7.06587 | + | 38.1587i | 0.286089 | + | 1.54500i | ||||
\(611\) | 18.8781 | 0.763726 | ||||||||
\(612\) | 1.51230i | 0.0611310i | ||||||||
\(613\) | 34.7078i | 1.40183i | 0.713243 | + | 0.700917i | \(0.247225\pi\) | ||||
−0.713243 | + | 0.700917i | \(0.752775\pi\) | |||||||
\(614\) | 72.1636 | 2.91229 | ||||||||
\(615\) | 0.0460220 | + | 0.248539i | 0.00185579 | + | 0.0100220i | ||||
\(616\) | −49.4622 | −1.99289 | ||||||||
\(617\) | 10.7275i | 0.431874i | 0.976407 | + | 0.215937i | \(0.0692805\pi\) | ||||
−0.976407 | + | 0.215937i | \(0.930719\pi\) | |||||||
\(618\) | − | 22.0705i | − | 0.887805i | ||||||
\(619\) | 36.1437 | 1.45274 | 0.726370 | − | 0.687304i | \(-0.241206\pi\) | ||||
0.726370 | + | 0.687304i | \(0.241206\pi\) | |||||||
\(620\) | 60.6004 | − | 11.2214i | 2.43377 | − | 0.450663i | ||||
\(621\) | −2.71451 | −0.108929 | ||||||||
\(622\) | − | 0.474617i | − | 0.0190304i | ||||||
\(623\) | 6.02343i | 0.241324i | ||||||||
\(624\) | 24.6345 | 0.986168 | ||||||||
\(625\) | 18.5895 | − | 16.7161i | 0.743581 | − | 0.668646i | ||||
\(626\) | −52.2569 | −2.08861 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 80.8768i | − | 3.22734i | ||||||
\(629\) | −2.00546 | −0.0799629 | ||||||||
\(630\) | 13.7014 | − | 2.53710i | 0.545878 | − | 0.101080i | ||||
\(631\) | −31.5764 | −1.25704 | −0.628519 | − | 0.777794i | \(-0.716339\pi\) | ||||
−0.628519 | + | 0.777794i | \(0.716339\pi\) | |||||||
\(632\) | − | 56.6089i | − | 2.25178i | ||||||
\(633\) | 21.6285i | 0.859658i | ||||||||
\(634\) | 47.0857 | 1.87001 | ||||||||
\(635\) | −1.60262 | − | 8.65483i | −0.0635979 | − | 0.343456i | ||||
\(636\) | 16.4818 | 0.653546 | ||||||||
\(637\) | − | 49.9786i | − | 1.98022i | ||||||
\(638\) | 19.4204i | 0.768859i | ||||||||
\(639\) | −3.92650 | −0.155330 | ||||||||
\(640\) | 7.86172 | + | 42.4567i | 0.310762 | + | 1.67825i | ||||
\(641\) | −19.8266 | −0.783104 | −0.391552 | − | 0.920156i | \(-0.628062\pi\) | ||||
−0.391552 | + | 0.920156i | \(0.628062\pi\) | |||||||
\(642\) | − | 4.99330i | − | 0.197070i | ||||||
\(643\) | − | 13.4569i | − | 0.530687i | −0.964154 | − | 0.265343i | \(-0.914515\pi\) | ||
0.964154 | − | 0.265343i | \(-0.0854853\pi\) | |||||||
\(644\) | 8.86718 | 0.349416 | ||||||||
\(645\) | 1.44340 | − | 0.267276i | 0.0568340 | − | 0.0105240i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.19511i | 0.164927i | 0.996594 | + | 0.0824634i | \(0.0262787\pi\) | ||||
−0.996594 | + | 0.0824634i | \(0.973721\pi\) | |||||||
\(648\) | 34.9204i | 1.37180i | ||||||||
\(649\) | 27.5621 | 1.08191 | ||||||||
\(650\) | −43.0977 | + | 16.5275i | −1.69043 | + | 0.648263i | ||||
\(651\) | 48.0648 | 1.88381 | ||||||||
\(652\) | 57.4012i | 2.24801i | ||||||||
\(653\) | 12.1680i | 0.476170i | 0.971244 | + | 0.238085i | \(0.0765196\pi\) | ||||
−0.971244 | + | 0.238085i | \(0.923480\pi\) | |||||||
\(654\) | −46.1372 | −1.80411 | ||||||||
\(655\) | −35.8936 | + | 6.64642i | −1.40248 | + | 0.259697i | ||||
\(656\) | −0.304038 | −0.0118707 | ||||||||
\(657\) | − | 1.66556i | − | 0.0649798i | ||||||
\(658\) | − | 55.5814i | − | 2.16679i | ||||||
\(659\) | 8.24471 | 0.321168 | 0.160584 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160584 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(660\) | 5.63555 | + | 30.4344i | 0.219364 | + | 1.18466i | ||||
\(661\) | −21.1197 | −0.821462 | −0.410731 | − | 0.911756i | \(-0.634727\pi\) | ||||
−0.410731 | + | 0.911756i | \(0.634727\pi\) | |||||||
\(662\) | 50.6150i | 1.96721i | ||||||||
\(663\) | − | 3.90687i | − | 0.151730i | ||||||
\(664\) | −78.3941 | −3.04228 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.16576 | 0.161420 | ||||||||
\(667\) | − | 1.75498i | − | 0.0679530i | ||||||
\(668\) | − | 22.6502i | − | 0.876361i | ||||||
\(669\) | 33.8685 | 1.30943 | ||||||||
\(670\) | −30.9265 | + | 5.72667i | −1.19480 | + | 0.221241i | ||||
\(671\) | 15.5357 | 0.599748 | ||||||||
\(672\) | − | 2.29442i | − | 0.0885090i | ||||||
\(673\) | − | 30.2802i | − | 1.16722i | −0.812036 | − | 0.583608i | \(-0.801641\pi\) | ||
0.812036 | − | 0.583608i | \(-0.198359\pi\) | |||||||
\(674\) | −25.0713 | −0.965711 | ||||||||
\(675\) | −9.95814 | − | 25.9671i | −0.383289 | − | 0.999476i | ||||
\(676\) | 4.54221 | 0.174700 | ||||||||
\(677\) | − | 49.9003i | − | 1.91783i | −0.283701 | − | 0.958913i | \(-0.591562\pi\) | ||
0.283701 | − | 0.958913i | \(-0.408438\pi\) | |||||||
\(678\) | − | 29.7010i | − | 1.14066i | ||||||
\(679\) | 19.7618 | 0.758389 | ||||||||
\(680\) | −7.31058 | + | 1.35370i | −0.280348 | + | 0.0519121i | ||||
\(681\) | −12.7948 | −0.490296 | ||||||||
\(682\) | − | 36.9079i | − | 1.41328i | ||||||
\(683\) | 3.11357i | 0.119137i | 0.998224 | + | 0.0595687i | \(0.0189725\pi\) | ||||
−0.998224 | + | 0.0595687i | \(0.981027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.68942 | + | 36.1258i | 0.255590 | + | 1.38029i | ||||
\(686\) | −69.6872 | −2.66067 | ||||||||
\(687\) | − | 26.0100i | − | 0.992345i | ||||||
\(688\) | 1.76572i | 0.0673175i | ||||||||
\(689\) | 9.83970 | 0.374863 | ||||||||
\(690\) | −0.761831 | − | 4.11421i | −0.0290024 | − | 0.156625i | ||||
\(691\) | −30.2831 | −1.15202 | −0.576012 | − | 0.817441i | \(-0.695392\pi\) | ||||
−0.576012 | + | 0.817441i | \(0.695392\pi\) | |||||||
\(692\) | − | 43.1140i | − | 1.63895i | ||||||
\(693\) | − | 5.57829i | − | 0.211902i | ||||||
\(694\) | −13.3644 | −0.507308 | ||||||||
\(695\) | 5.86718 | − | 1.08643i | 0.222555 | − | 0.0412105i | ||||
\(696\) | −28.0305 | −1.06250 | ||||||||
\(697\) | 0.0482186i | 0.00182641i | ||||||||
\(698\) | 3.80991i | 0.144207i | ||||||||
\(699\) | −19.0659 | −0.721137 | ||||||||
\(700\) | 32.5291 | + | 84.8239i | 1.22949 | + | 3.20604i | ||||
\(701\) | 44.5699 | 1.68338 | 0.841691 | − | 0.539960i | \(-0.181561\pi\) | ||||
0.841691 | + | 0.539960i | \(0.181561\pi\) | |||||||
\(702\) | 51.3483i | 1.93802i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 16.7014 | 0.629458 | ||||||||
\(705\) | −17.2395 | + | 3.19224i | −0.649276 | + | 0.120227i | ||||
\(706\) | −80.8914 | −3.04439 | ||||||||
\(707\) | 47.6144i | 1.79073i | ||||||||
\(708\) | 78.9194i | 2.96597i | ||||||||
\(709\) | −9.34352 | −0.350903 | −0.175452 | − | 0.984488i | \(-0.556139\pi\) | ||||
−0.175452 | + | 0.984488i | \(0.556139\pi\) | |||||||
\(710\) | −6.97252 | − | 37.6546i | −0.261674 | − | 1.41315i | ||||
\(711\) | 6.38429 | 0.239430 | ||||||||
\(712\) | 6.67591i | 0.250190i | ||||||||
\(713\) | 3.33529i | 0.124908i | ||||||||
\(714\) | −11.5027 | −0.430479 | ||||||||
\(715\) | 3.36445 | + | 18.1695i | 0.125823 | + | 0.679500i | ||||
\(716\) | −31.0109 | −1.15893 | ||||||||
\(717\) | 3.18372i | 0.118898i | ||||||||
\(718\) | 8.59001i | 0.320576i | ||||||||
\(719\) | −25.3974 | −0.947163 | −0.473581 | − | 0.880750i | \(-0.657039\pi\) | ||||
−0.473581 | + | 0.880750i | \(0.657039\pi\) | |||||||
\(720\) | 5.19869 | − | 0.962643i | 0.193744 | − | 0.0358756i | ||||
\(721\) | −25.9330 | −0.965797 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.3552i | 1.01735i | ||||||||
\(724\) | −24.7069 | −0.918224 | ||||||||
\(725\) | 16.7882 | − | 6.43811i | 0.623499 | − | 0.239105i | ||||
\(726\) | −23.6410 | −0.877400 | ||||||||
\(727\) | − | 31.4377i | − | 1.16596i | −0.812486 | − | 0.582980i | \(-0.801886\pi\) | ||
0.812486 | − | 0.582980i | \(-0.198114\pi\) | |||||||
\(728\) | − | 84.5518i | − | 3.13370i | ||||||
\(729\) | −29.9869 | −1.11063 | ||||||||
\(730\) | 15.9725 | − | 2.95764i | 0.591170 | − | 0.109467i | ||||
\(731\) | 0.280033 | 0.0103574 | ||||||||
\(732\) | 44.4838i | 1.64417i | ||||||||
\(733\) | 25.3946i | 0.937971i | 0.883206 | + | 0.468985i | \(0.155380\pi\) | ||||
−0.883206 | + | 0.468985i | \(0.844620\pi\) | |||||||
\(734\) | −47.9056 | −1.76823 | ||||||||
\(735\) | 8.45125 | + | 45.6404i | 0.311729 | + | 1.68347i | ||||
\(736\) | 0.159213 | 0.00586867 | ||||||||
\(737\) | 12.5912i | 0.463802i | ||||||||
\(738\) | − | 0.100160i | − | 0.00368694i | ||||||
\(739\) | −35.5082 | −1.30619 | −0.653095 | − | 0.757276i | \(-0.726530\pi\) | ||||
−0.653095 | + | 0.757276i | \(0.726530\pi\) | |||||||
\(740\) | 4.94505 | + | 26.7054i | 0.181784 | + | 0.981710i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 28.9703i | − | 1.06353i | ||||||
\(743\) | 17.1099i | 0.627700i | 0.949473 | + | 0.313850i | \(0.101619\pi\) | ||||
−0.949473 | + | 0.313850i | \(0.898381\pi\) | |||||||
\(744\) | 53.2713 | 1.95302 | ||||||||
\(745\) | 39.5016 | − | 7.31453i | 1.44723 | − | 0.267984i | ||||
\(746\) | −57.7597 | −2.11473 | ||||||||
\(747\) | − | 8.84121i | − | 0.323483i | ||||||
\(748\) | 5.90453i | 0.215891i | ||||||||
\(749\) | −5.86718 | −0.214382 | ||||||||
\(750\) | 36.5621 | − | 22.3807i | 1.33506 | − | 0.817226i | ||||
\(751\) | 7.45125 | 0.271900 | 0.135950 | − | 0.990716i | \(-0.456591\pi\) | ||||
0.135950 | + | 0.990716i | \(0.456591\pi\) | |||||||
\(752\) | − | 21.0891i | − | 0.769041i | ||||||
\(753\) | 5.21086i | 0.189894i | ||||||||
\(754\) | −33.1976 | −1.20899 | ||||||||
\(755\) | 27.9989 | − | 5.18457i | 1.01898 | − | 0.188686i | ||||
\(756\) | 101.063 | 3.67561 | ||||||||
\(757\) | 53.7675i | 1.95421i | 0.212750 | + | 0.977107i | \(0.431758\pi\) | ||||
−0.212750 | + | 0.977107i | \(0.568242\pi\) | |||||||
\(758\) | − | 17.3199i | − | 0.629086i | ||||||
\(759\) | −1.67503 | −0.0607997 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.3939 | 0.848029 | 0.424014 | − | 0.905655i | \(-0.360621\pi\) | ||||
0.424014 | + | 0.905655i | \(0.360621\pi\) | |||||||
\(762\) | − | 15.0929i | − | 0.546760i | ||||||
\(763\) | 54.2117i | 1.96259i | ||||||||
\(764\) | −23.6135 | −0.854308 | ||||||||
\(765\) | −0.152669 | − | 0.824480i | −0.00551977 | − | 0.0298091i | ||||
\(766\) | −7.57514 | −0.273701 | ||||||||
\(767\) | 47.1152i | 1.70123i | ||||||||
\(768\) | 50.3235i | 1.81589i | ||||||||
\(769\) | 13.2447 | 0.477617 | 0.238808 | − | 0.971067i | \(-0.423243\pi\) | ||||
0.238808 | + | 0.971067i | \(0.423243\pi\) | |||||||
\(770\) | 53.4951 | − | 9.90571i | 1.92783 | − | 0.356977i | ||||
\(771\) | 43.0606 | 1.55079 | ||||||||
\(772\) | 10.4500i | 0.376105i | ||||||||
\(773\) | − | 17.8052i | − | 0.640410i | −0.947348 | − | 0.320205i | \(-0.896248\pi\) | ||
0.947348 | − | 0.320205i | \(-0.103752\pi\) | |||||||
\(774\) | −0.581686 | −0.0209083 | ||||||||
\(775\) | −31.9056 | + | 12.2355i | −1.14608 | + | 0.439511i | ||||
\(776\) | 21.9025 | 0.786254 | ||||||||
\(777\) | 21.1812i | 0.759871i | ||||||||
\(778\) | − | 23.0658i | − | 0.826949i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −52.0253 | + | 9.63354i | −1.86280 | + | 0.344936i | ||||
\(781\) | −15.3304 | −0.548566 | ||||||||
\(782\) | − | 0.798192i | − | 0.0285433i | ||||||
\(783\) | − | 20.0022i | − | 0.714819i | ||||||
\(784\) | −55.8321 | −1.99400 | ||||||||
\(785\) | 8.16467 | + | 44.0928i | 0.291410 | + | 1.57374i | ||||
\(786\) | −62.5939 | −2.23265 | ||||||||
\(787\) | 43.5779i | 1.55339i | 0.629880 | + | 0.776693i | \(0.283104\pi\) | ||||
−0.629880 | + | 0.776693i | \(0.716896\pi\) | |||||||
\(788\) | − | 80.1055i | − | 2.85364i | ||||||
\(789\) | 21.2711 | 0.757271 | ||||||||
\(790\) | 11.3370 | + | 61.2246i | 0.403351 | + | 2.17827i | ||||
\(791\) | −34.8990 | −1.24087 | ||||||||
\(792\) | − | 6.18255i | − | 0.219687i | ||||||
\(793\) | 26.5570i | 0.943068i | ||||||||
\(794\) | 65.7267 | 2.33255 | ||||||||
\(795\) | −8.98561 | + | 1.66387i | −0.318687 | + | 0.0590114i | ||||
\(796\) | −51.4676 | −1.82422 | ||||||||
\(797\) | 16.1311i | 0.571395i | 0.958320 | + | 0.285697i | \(0.0922252\pi\) | ||||
−0.958320 | + | 0.285697i | \(0.907775\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.34460 | −0.118323 | ||||||||
\(800\) | 0.584071 | + | 1.52304i | 0.0206500 | + | 0.0538476i | ||||
\(801\) | −0.752902 | −0.0266025 | ||||||||
\(802\) | 61.8230i | 2.18304i | ||||||||
\(803\) | − | 6.50293i | − | 0.229484i | ||||||
\(804\) | −36.0528 | −1.27148 | ||||||||
\(805\) | −4.83424 | + | 0.895159i | −0.170385 | + | 0.0315502i | ||||
\(806\) | 63.0912 | 2.22229 | ||||||||
\(807\) | 5.63237i | 0.198269i | ||||||||
\(808\) | 52.7722i | 1.85652i | ||||||||
\(809\) | −28.7134 | −1.00951 | −0.504755 | − | 0.863263i | \(-0.668417\pi\) | ||||
−0.504755 | + | 0.863263i | \(0.668417\pi\) | |||||||
\(810\) | −6.99346 | − | 37.7677i | −0.245725 | − | 1.32702i | ||||
\(811\) | −21.5422 | −0.756449 | −0.378225 | − | 0.925714i | \(-0.623465\pi\) | ||||
−0.378225 | + | 0.925714i | \(0.623465\pi\) | |||||||
\(812\) | 65.3388i | 2.29294i | ||||||||
\(813\) | − | 16.4895i | − | 0.578313i | ||||||
\(814\) | 16.2646 | 0.570073 | ||||||||
\(815\) | −5.79476 | − | 31.2942i | −0.202982 | − | 1.09619i | ||||
\(816\) | −4.36445 | −0.152786 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 69.5634i | − | 2.43223i | ||||||
\(819\) | 9.53566 | 0.333203 | ||||||||
\(820\) | 0.642096 | − | 0.118897i | 0.0224230 | − | 0.00415207i | ||||
\(821\) | 33.3204 | 1.16289 | 0.581445 | − | 0.813586i | \(-0.302487\pi\) | ||||
0.581445 | + | 0.813586i | \(0.302487\pi\) | |||||||
\(822\) | 62.9988i | 2.19734i | ||||||||
\(823\) | − | 37.2390i | − | 1.29807i | −0.760759 | − | 0.649035i | \(-0.775173\pi\) | ||
0.760759 | − | 0.649035i | \(-0.224827\pi\) | |||||||
\(824\) | −28.7422 | −1.00128 | ||||||||
\(825\) | −6.14483 | − | 16.0234i | −0.213935 | − | 0.557864i | ||||
\(826\) | 138.718 | 4.82662 | ||||||||
\(827\) | − | 29.0512i | − | 1.01021i | −0.863058 | − | 0.505105i | \(-0.831454\pi\) | ||
0.863058 | − | 0.505105i | \(-0.168546\pi\) | |||||||
\(828\) | 1.10836i | 0.0385181i | ||||||||
\(829\) | 34.5380 | 1.19956 | 0.599778 | − | 0.800166i | \(-0.295256\pi\) | ||||
0.599778 | + | 0.800166i | \(0.295256\pi\) | |||||||
\(830\) | 84.7861 | − | 15.6999i | 2.94297 | − | 0.544950i | ||||
\(831\) | −10.5134 | −0.364707 | ||||||||
\(832\) | 28.5498i | 0.989786i | ||||||||
\(833\) | 8.85462i | 0.306794i | ||||||||
\(834\) | 10.2316 | 0.354292 | ||||||||
\(835\) | 2.28658 | + | 12.3485i | 0.0791302 | + | 0.427338i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.0136i | 1.31394i | ||||||||
\(838\) | − | 32.0410i | − | 1.10684i | ||||||
\(839\) | −44.7243 | −1.54406 | −0.772028 | − | 0.635589i | \(-0.780757\pi\) | ||||
−0.772028 | + | 0.635589i | \(0.780757\pi\) | |||||||
\(840\) | 14.2975 | + | 77.2127i | 0.493310 | + | 2.66409i | ||||
\(841\) | −16.0683 | −0.554078 | ||||||||
\(842\) | − | 8.16680i | − | 0.281447i | ||||||
\(843\) | 36.5758i | 1.25974i | ||||||||
\(844\) | 55.8770 | 1.92337 | ||||||||
\(845\) | −2.47634 | + | 0.458545i | −0.0851886 | + | 0.0157744i | ||||
\(846\) | 6.94743 | 0.238858 | ||||||||
\(847\) | 27.7784i | 0.954478i | ||||||||
\(848\) | − | 10.9921i | − | 0.377471i | ||||||
\(849\) | 22.9210 | 0.786648 | ||||||||
\(850\) | 7.63555 | − | 2.92816i | 0.261897 | − | 0.100435i | ||||
\(851\) | −1.46980 | −0.0503839 | ||||||||
\(852\) | − | 43.8962i | − | 1.50386i | ||||||
\(853\) | − | 16.2603i | − | 0.556741i | −0.960474 | − | 0.278370i | \(-0.910206\pi\) | ||
0.960474 | − | 0.278370i | \(-0.0897943\pi\) | |||||||
\(854\) | 78.1900 | 2.67561 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.50273 | −0.222259 | ||||||||
\(857\) | − | 16.6379i | − | 0.568340i | −0.958774 | − | 0.284170i | \(-0.908282\pi\) | ||
0.958774 | − | 0.284170i | \(-0.0917181\pi\) | |||||||
\(858\) | 31.6853i | 1.08172i | ||||||||
\(859\) | −40.2724 | −1.37408 | −0.687038 | − | 0.726621i | \(-0.741090\pi\) | ||||
−0.687038 | + | 0.726621i | \(0.741090\pi\) | |||||||
\(860\) | −0.690503 | − | 3.72901i | −0.0235459 | − | 0.127158i | ||||
\(861\) | 0.509273 | 0.0173560 | ||||||||
\(862\) | − | 0.118897i | − | 0.00404965i | ||||||
\(863\) | 32.9634i | 1.12209i | 0.827786 | + | 0.561044i | \(0.189600\pi\) | ||||
−0.827786 | + | 0.561044i | \(0.810400\pi\) | |||||||
\(864\) | 1.81461 | 0.0617343 | ||||||||
\(865\) | 4.35245 | + | 23.5051i | 0.147988 | + | 0.799197i | ||||
\(866\) | 23.5027 | 0.798655 | ||||||||
\(867\) | − | 25.8456i | − | 0.877762i | ||||||
\(868\) | − | 124.175i | − | 4.21476i | ||||||
\(869\) | 24.9265 | 0.845574 | ||||||||
\(870\) | 30.3160 | − | 5.61363i | 1.02781 | − | 0.190320i | ||||
\(871\) | −21.5237 | −0.729301 | ||||||||
\(872\) | 60.0841i | 2.03470i | ||||||||
\(873\) | 2.47014i | 0.0836016i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.2975 | − | 42.9608i | −0.889018 | − | 1.45234i | ||||
\(876\) | 18.6201 | 0.629114 | ||||||||
\(877\) | 0.213199i | 0.00719923i | 0.999994 | + | 0.00359962i | \(0.00114580\pi\) | ||||
−0.999994 | + | 0.00359962i | \(0.998854\pi\) | |||||||
\(878\) | − | 54.6541i | − | 1.84449i | ||||||
\(879\) | −28.3885 | −0.957519 | ||||||||
\(880\) | 20.2975 | − | 3.75849i | 0.684228 | − | 0.126699i | ||||
\(881\) | 51.8661 | 1.74741 | 0.873707 | − | 0.486453i | \(-0.161710\pi\) | ||||
0.873707 | + | 0.486453i | \(0.161710\pi\) | |||||||
\(882\) | − | 18.3929i | − | 0.619321i | ||||||
\(883\) | 41.6451i | 1.40147i | 0.713422 | + | 0.700734i | \(0.247144\pi\) | ||||
−0.713422 | + | 0.700734i | \(0.752856\pi\) | |||||||
\(884\) | −10.0933 | −0.339476 | ||||||||
\(885\) | −7.96707 | − | 43.0256i | −0.267810 | − | 1.44629i | ||||
\(886\) | 49.4083 | 1.65990 | ||||||||
\(887\) | 4.09325i | 0.137438i | 0.997636 | + | 0.0687190i | \(0.0218912\pi\) | ||||
−0.997636 | + | 0.0687190i | \(0.978109\pi\) | |||||||
\(888\) | 23.4756i | 0.787790i | ||||||||
\(889\) | −17.7344 | −0.594791 | ||||||||
\(890\) | −1.33697 | − | 7.22023i | −0.0448154 | − | 0.242023i | ||||
\(891\) | −15.3765 | −0.515130 | ||||||||
\(892\) | − | 87.4987i | − | 2.92967i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 68.8859 | 2.30389 | ||||||||
\(895\) | 16.9067 | − | 3.13061i | 0.565127 | − | 0.104645i | ||||
\(896\) | 86.9967 | 2.90636 | ||||||||
\(897\) | − | 2.86334i | − | 0.0956040i | ||||||
\(898\) | − | 30.6958i | − | 1.02433i | ||||||
\(899\) | −24.5764 | −0.819670 | ||||||||
\(900\) | −10.6026 | + | 4.06600i | −0.353421 | + | 0.135533i | ||||
\(901\) | −1.74328 | −0.0580772 | ||||||||
\(902\) | − | 0.391060i | − | 0.0130209i | ||||||
\(903\) | − | 2.95764i | − | 0.0984240i | ||||||
\(904\) | −38.6794 | −1.28646 | ||||||||
\(905\) | 13.4698 | − | 2.49421i | 0.447751 | − | 0.0829102i | ||||
\(906\) | 48.8266 | 1.62216 | ||||||||
\(907\) | 8.40726i | 0.279158i | 0.990211 | + | 0.139579i | \(0.0445750\pi\) | ||||
−0.990211 | + | 0.139579i | \(0.955425\pi\) | |||||||
\(908\) | 33.0551i | 1.09697i | ||||||||
\(909\) | −5.95159 | −0.197402 | ||||||||
\(910\) | 16.9330 | + | 91.4458i | 0.561325 | + | 3.03140i | ||||
\(911\) | −8.87918 | −0.294180 | −0.147090 | − | 0.989123i | \(-0.546991\pi\) | ||||
−0.147090 | + | 0.989123i | \(0.546991\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 34.5192i | − | 1.14242i | ||||||
\(914\) | 69.5544 | 2.30066 | ||||||||
\(915\) | −4.49073 | − | 24.2519i | −0.148459 | − | 0.801742i | ||||
\(916\) | −67.1965 | −2.22024 | ||||||||
\(917\) | 73.5485i | 2.42878i | ||||||||
\(918\) | − | 9.09730i | − | 0.300256i | ||||||
\(919\) | 45.9834 | 1.51685 | 0.758427 | − | 0.651758i | \(-0.225968\pi\) | ||||
0.758427 | + | 0.651758i | \(0.225968\pi\) | |||||||
\(920\) | −5.35790 | + | 0.992125i | −0.176645 | + | 0.0327094i | ||||
\(921\) | −45.8637 | −1.51126 | ||||||||
\(922\) | 13.0658i | 0.430299i | ||||||||
\(923\) | − | 26.2062i | − | 0.862587i | ||||||
\(924\) | 62.3623 | 2.05157 | ||||||||
\(925\) | −5.39192 | − | 14.0601i | −0.177285 | − | 0.462295i | ||||
\(926\) | −44.0462 | −1.44745 | ||||||||
\(927\) | − | 3.24152i | − | 0.106465i | ||||||
\(928\) | 1.17318i | 0.0385115i | ||||||||
\(929\) | 22.1778 | 0.727629 | 0.363814 | − | 0.931471i | \(-0.381474\pi\) | ||||
0.363814 | + | 0.931471i | \(0.381474\pi\) | |||||||
\(930\) | −57.6148 | + | 10.6686i | −1.88926 | + | 0.349836i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 49.2564i | 1.61345i | ||||||||
\(933\) | 0.301644i | 0.00987538i | ||||||||
\(934\) | −70.6872 | −2.31296 | ||||||||
\(935\) | −0.596074 | − | 3.21906i | −0.0194937 | − | 0.105274i | ||||
\(936\) | 10.5686 | 0.345445 | ||||||||
\(937\) | − | 34.3274i | − | 1.12143i | −0.828009 | − | 0.560714i | \(-0.810527\pi\) | ||
0.828009 | − | 0.560714i | \(-0.189473\pi\) | |||||||
\(938\) | 63.3706i | 2.06912i | ||||||||
\(939\) | 33.2120 | 1.08383 | ||||||||
\(940\) | 8.24710 | + | 44.5379i | 0.268991 | + | 1.45267i | ||||
\(941\) | −33.7213 | −1.09928 | −0.549641 | − | 0.835401i | \(-0.685235\pi\) | ||||
−0.549641 | + | 0.835401i | \(0.685235\pi\) | |||||||
\(942\) | 76.8923i | 2.50529i | ||||||||
\(943\) | 0.0353393i | 0.00115080i | ||||||||
\(944\) | 52.6334 | 1.71307 | ||||||||
\(945\) | −55.0977 | + | 10.2025i | −1.79233 | + | 0.331886i | ||||
\(946\) | −2.27110 | −0.0738400 | ||||||||
\(947\) | 22.1465i | 0.719664i | 0.933017 | + | 0.359832i | \(0.117166\pi\) | ||||
−0.933017 | + | 0.359832i | \(0.882834\pi\) | |||||||
\(948\) | 71.3729i | 2.31809i | ||||||||
\(949\) | 11.1163 | 0.360849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.9254 | −0.970398 | ||||||||
\(952\) | 14.9799i | 0.485501i | ||||||||
\(953\) | 37.2967i | 1.20816i | 0.796924 | + | 0.604079i | \(0.206459\pi\) | ||||
−0.796924 | + | 0.604079i | \(0.793541\pi\) | |||||||
\(954\) | 3.62116 | 0.117240 | ||||||||
\(955\) | 12.8737 | − | 2.38383i | 0.416584 | − | 0.0771390i | ||||
\(956\) | 8.22508 | 0.266018 | ||||||||
\(957\) | − | 12.3426i | − | 0.398981i | ||||||
\(958\) | 19.7761i | 0.638936i | ||||||||
\(959\) | 74.0242 | 2.39037 | ||||||||
\(960\) | −4.82770 | − | 26.0717i | −0.155813 | − | 0.841459i | ||||
\(961\) | 15.7069 | 0.506674 | ||||||||
\(962\) | 27.8030i | 0.896405i | ||||||||
\(963\) | − | 0.733371i | − | 0.0236326i | ||||||
\(964\) | 70.6718 | 2.27618 | ||||||||
\(965\) | −1.05495 | − | 5.69719i | −0.0339601 | − | 0.183399i | ||||
\(966\) | −8.43032 | −0.271241 | ||||||||
\(967\) | 18.6736i | 0.600502i | 0.953860 | + | 0.300251i | \(0.0970704\pi\) | ||||
−0.953860 | + | 0.300251i | \(0.902930\pi\) | |||||||
\(968\) | 30.7875i | 0.989547i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.6883 | + | 4.38638i | −0.760587 | + | 0.140838i | ||||
\(971\) | −28.5806 | −0.917195 | −0.458598 | − | 0.888644i | \(-0.651648\pi\) | ||||
−0.458598 | + | 0.888644i | \(0.651648\pi\) | |||||||
\(972\) | 23.2683i | 0.746330i | ||||||||
\(973\) | − | 12.0223i | − | 0.385416i | ||||||
\(974\) | 2.69596 | 0.0863842 | ||||||||
\(975\) | 27.3908 | − | 10.5041i | 0.877209 | − | 0.336401i | ||||
\(976\) | 29.6674 | 0.949630 | ||||||||
\(977\) | 58.1909i | 1.86169i | 0.365411 | + | 0.930846i | \(0.380928\pi\) | ||||
−0.365411 | + | 0.930846i | \(0.619072\pi\) | |||||||
\(978\) | − | 54.5732i | − | 1.74506i | ||||||
\(979\) | −2.93959 | −0.0939497 | ||||||||
\(980\) | 117.911 | − | 21.8337i | 3.76654 | − | 0.697451i | ||||
\(981\) | −6.77622 | −0.216348 | ||||||||
\(982\) | 32.1894i | 1.02720i | ||||||||
\(983\) | − | 48.0725i | − | 1.53328i | −0.642080 | − | 0.766638i | \(-0.721928\pi\) | ||
0.642080 | − | 0.766638i | \(-0.278072\pi\) | |||||||
\(984\) | 0.564439 | 0.0179937 | ||||||||
\(985\) | 8.08680 | + | 43.6722i | 0.257667 | + | 1.39151i | ||||
\(986\) | 5.88157 | 0.187307 | ||||||||
\(987\) | 35.3249i | 1.12440i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.205235 | 0.00652609 | ||||||||
\(990\) | 1.23817 | + | 6.68665i | 0.0393516 | + | 0.212516i | ||||
\(991\) | −38.3952 | −1.21966 | −0.609832 | − | 0.792531i | \(-0.708763\pi\) | ||||
−0.609832 | + | 0.792531i | \(0.708763\pi\) | |||||||
\(992\) | − | 2.22960i | − | 0.0707897i | ||||||
\(993\) | − | 32.1684i | − | 1.02083i | ||||||
\(994\) | −77.1570 | −2.44727 | ||||||||
\(995\) | 28.0593 | − | 5.19576i | 0.889540 | − | 0.164717i | ||||
\(996\) | 98.8399 | 3.13186 | ||||||||
\(997\) | − | 37.8218i | − | 1.19783i | −0.800814 | − | 0.598914i | \(-0.795599\pi\) | ||
0.800814 | − | 0.598914i | \(-0.204401\pi\) | |||||||
\(998\) | − | 59.2944i | − | 1.87693i | ||||||
\(999\) | −16.7518 | −0.530004 |
(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 | 1805.2.b.g.1084.6 | 6 | ||
5.2 | odd | 4 | 9025.2.a.bt.1.1 | 6 | |||
5.3 | odd | 4 | 9025.2.a.bt.1.6 | 6 | |||
5.4 | even | 2 | inner | 1805.2.b.g.1084.1 | 6 | ||
19.8 | odd | 6 | 95.2.i.b.64.1 | yes | 12 | ||
19.12 | odd | 6 | 95.2.i.b.49.6 | yes | 12 | ||
19.18 | odd | 2 | 1805.2.b.f.1084.1 | 6 | |||
57.8 | even | 6 | 855.2.be.d.64.6 | 12 | |||
57.50 | even | 6 | 855.2.be.d.334.1 | 12 | |||
95.8 | even | 12 | 475.2.e.g.26.6 | 12 | |||
95.12 | even | 12 | 475.2.e.g.201.1 | 12 | |||
95.18 | even | 4 | 9025.2.a.bu.1.1 | 6 | |||
95.27 | even | 12 | 475.2.e.g.26.1 | 12 | |||
95.37 | even | 4 | 9025.2.a.bu.1.6 | 6 | |||
95.69 | odd | 6 | 95.2.i.b.49.1 | ✓ | 12 | ||
95.84 | odd | 6 | 95.2.i.b.64.6 | yes | 12 | ||
95.88 | even | 12 | 475.2.e.g.201.6 | 12 | |||
95.94 | odd | 2 | 1805.2.b.f.1084.6 | 6 | |||
285.164 | even | 6 | 855.2.be.d.334.6 | 12 | |||
285.179 | even | 6 | 855.2.be.d.64.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.1 | ✓ | 12 | 95.69 | odd | 6 | ||
95.2.i.b.49.6 | yes | 12 | 19.12 | odd | 6 | ||
95.2.i.b.64.1 | yes | 12 | 19.8 | odd | 6 | ||
95.2.i.b.64.6 | yes | 12 | 95.84 | odd | 6 | ||
475.2.e.g.26.1 | 12 | 95.27 | even | 12 | |||
475.2.e.g.26.6 | 12 | 95.8 | even | 12 | |||
475.2.e.g.201.1 | 12 | 95.12 | even | 12 | |||
475.2.e.g.201.6 | 12 | 95.88 | even | 12 | |||
855.2.be.d.64.1 | 12 | 285.179 | even | 6 | |||
855.2.be.d.64.6 | 12 | 57.8 | even | 6 | |||
855.2.be.d.334.1 | 12 | 57.50 | even | 6 | |||
855.2.be.d.334.6 | 12 | 285.164 | even | 6 | |||
1805.2.b.f.1084.1 | 6 | 19.18 | odd | 2 | |||
1805.2.b.f.1084.6 | 6 | 95.94 | odd | 2 | |||
1805.2.b.g.1084.1 | 6 | 5.4 | even | 2 | inner | ||
1805.2.b.g.1084.6 | 6 | 1.1 | even | 1 | trivial | ||
9025.2.a.bt.1.1 | 6 | 5.2 | odd | 4 | |||
9025.2.a.bt.1.6 | 6 | 5.3 | odd | 4 | |||
9025.2.a.bu.1.1 | 6 | 95.18 | even | 4 | |||
9025.2.a.bu.1.6 | 6 | 95.37 | even | 4 |