Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,7,Mod(161,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.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: | \(37.2687615464\) |
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: | \( x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{42} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.8 | ||
Root | \(-7.20150i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.161 |
Dual form | 162.7.b.c.161.5 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65685i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | − 45.6802i | − 0.365442i | −0.983165 | − | 0.182721i | \(-0.941510\pi\) | ||||
0.983165 | − | 0.182721i | \(-0.0584905\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 490.195 | 1.42914 | 0.714570 | − | 0.699564i | \(-0.246623\pi\) | ||||
0.714570 | + | 0.699564i | \(0.246623\pi\) | |||||||
\(8\) | − 181.019i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 258.406 | 0.258406 | ||||||||
\(11\) | 1008.44i | 0.757657i | 0.925467 | + | 0.378829i | \(0.123673\pi\) | ||||
−0.925467 | + | 0.378829i | \(0.876327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −933.602 | −0.424944 | −0.212472 | − | 0.977167i | \(-0.568151\pi\) | ||||
−0.212472 | + | 0.977167i | \(0.568151\pi\) | |||||||
\(14\) | 2772.96i | 1.01055i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | − 8090.59i | − 1.64677i | −0.567482 | − | 0.823386i | \(-0.692082\pi\) | ||||
0.567482 | − | 0.823386i | \(-0.307918\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7727.36 | −1.12660 | −0.563301 | − | 0.826252i | \(-0.690469\pi\) | ||||
−0.563301 | + | 0.826252i | \(0.690469\pi\) | |||||||
\(20\) | 1461.77i | 0.182721i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5704.61 | −0.535745 | ||||||||
\(23\) | − 13680.9i | − 1.12443i | −0.826992 | − | 0.562213i | \(-0.809950\pi\) | ||||
0.826992 | − | 0.562213i | \(-0.190050\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13538.3 | 0.866452 | ||||||||
\(26\) | − 5281.25i | − 0.300481i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −15686.2 | −0.714570 | ||||||||
\(29\) | 2268.65i | 0.0930192i | 0.998918 | + | 0.0465096i | \(0.0148098\pi\) | ||||
−0.998918 | + | 0.0465096i | \(0.985190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34125.1 | 1.14548 | 0.572742 | − | 0.819735i | \(-0.305880\pi\) | ||||
0.572742 | + | 0.819735i | \(0.305880\pi\) | |||||||
\(32\) | 5792.62i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 45767.3 | 1.16444 | ||||||||
\(35\) | − 22392.2i | − 0.522267i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 92058.0 | 1.81743 | 0.908713 | − | 0.417422i | \(-0.137066\pi\) | ||||
0.908713 | + | 0.417422i | \(0.137066\pi\) | |||||||
\(38\) | − 43712.6i | − 0.796628i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8269.00 | −0.129203 | ||||||||
\(41\) | − 35820.6i | − 0.519734i | −0.965644 | − | 0.259867i | \(-0.916321\pi\) | ||||
0.965644 | − | 0.259867i | \(-0.0836788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −69141.8 | −0.869631 | −0.434816 | − | 0.900520i | \(-0.643186\pi\) | ||||
−0.434816 | + | 0.900520i | \(0.643186\pi\) | |||||||
\(44\) | − 32270.1i | − 0.378829i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 77390.9 | 0.795090 | ||||||||
\(47\) | − 15254.9i | − 0.146932i | −0.997298 | − | 0.0734659i | \(-0.976594\pi\) | ||||
0.997298 | − | 0.0734659i | \(-0.0234060\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 122642. | 1.04244 | ||||||||
\(50\) | 76584.3i | 0.612674i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 29875.3 | 0.212472 | ||||||||
\(53\) | 236591.i | 1.58917i | 0.607153 | + | 0.794585i | \(0.292312\pi\) | ||||
−0.607153 | + | 0.794585i | \(0.707688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46065.9 | 0.276880 | ||||||||
\(56\) | − 88734.7i | − 0.505277i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12833.4 | −0.0657745 | ||||||||
\(59\) | − 256217.i | − 1.24753i | −0.781611 | − | 0.623766i | \(-0.785602\pi\) | ||||
0.781611 | − | 0.623766i | \(-0.214398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39839.2 | 0.175518 | 0.0877589 | − | 0.996142i | \(-0.472029\pi\) | ||||
0.0877589 | + | 0.996142i | \(0.472029\pi\) | |||||||
\(62\) | 193041.i | 0.809980i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | 42647.1i | 0.155292i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 320409. | 1.06532 | 0.532660 | − | 0.846330i | \(-0.321193\pi\) | ||||
0.532660 | + | 0.846330i | \(0.321193\pi\) | |||||||
\(68\) | 258899.i | 0.823386i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 126669. | 0.369299 | ||||||||
\(71\) | − 404593.i | − 1.13043i | −0.824944 | − | 0.565215i | \(-0.808793\pi\) | ||||
0.824944 | − | 0.565215i | \(-0.191207\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 393719. | 1.01209 | 0.506044 | − | 0.862508i | \(-0.331107\pi\) | ||||
0.506044 | + | 0.862508i | \(0.331107\pi\) | |||||||
\(74\) | 520759.i | 1.28511i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 247276. | 0.563301 | ||||||||
\(77\) | 494333.i | 1.08280i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 898368. | 1.82210 | 0.911052 | − | 0.412292i | \(-0.135272\pi\) | ||||
0.911052 | + | 0.412292i | \(0.135272\pi\) | |||||||
\(80\) | − 46776.5i | − 0.0913604i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 202632. | 0.367508 | ||||||||
\(83\) | − 178882.i | − 0.312847i | −0.987690 | − | 0.156424i | \(-0.950003\pi\) | ||||
0.987690 | − | 0.156424i | \(-0.0499965\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −369580. | −0.601799 | ||||||||
\(86\) | − 391125.i | − 0.614922i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 182548. | 0.267872 | ||||||||
\(89\) | − 826458.i | − 1.17233i | −0.810191 | − | 0.586166i | \(-0.800636\pi\) | ||||
0.810191 | − | 0.586166i | \(-0.199364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −457647. | −0.607304 | ||||||||
\(92\) | 437789.i | 0.562213i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 86294.8 | 0.103897 | ||||||||
\(95\) | 352988.i | 0.411707i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 635962. | 0.696813 | 0.348406 | − | 0.937344i | \(-0.386723\pi\) | ||||
0.348406 | + | 0.937344i | \(0.386723\pi\) | |||||||
\(98\) | 693768.i | 0.737116i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −433226. | −0.433226 | ||||||||
\(101\) | 262465.i | 0.254746i | 0.991855 | + | 0.127373i | \(0.0406545\pi\) | ||||
−0.991855 | + | 0.127373i | \(0.959346\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −82476.0 | −0.0754772 | −0.0377386 | − | 0.999288i | \(-0.512015\pi\) | ||||
−0.0377386 | + | 0.999288i | \(0.512015\pi\) | |||||||
\(104\) | 169000.i | 0.150240i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.33836e6 | −1.12371 | ||||||||
\(107\) | 1.03624e6i | 0.845881i | 0.906158 | + | 0.422940i | \(0.139002\pi\) | ||||
−0.906158 | + | 0.422940i | \(0.860998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 420018. | 0.324331 | 0.162165 | − | 0.986764i | \(-0.448152\pi\) | ||||
0.162165 | + | 0.986764i | \(0.448152\pi\) | |||||||
\(110\) | 260588.i | 0.195784i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 501959. | 0.357285 | ||||||||
\(113\) | − 1.52972e6i | − 1.06017i | −0.847944 | − | 0.530086i | \(-0.822160\pi\) | ||||
0.847944 | − | 0.530086i | \(-0.177840\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −624947. | −0.410913 | ||||||||
\(116\) | − 72596.7i | − 0.0465096i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.44938e6 | 0.882139 | ||||||||
\(119\) | − 3.96596e6i | − 2.35347i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 754606. | 0.425955 | ||||||||
\(122\) | 225365.i | 0.124110i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.09200e6 | −0.572742 | ||||||||
\(125\) | − 1.33219e6i | − 0.682080i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −949267. | −0.463422 | −0.231711 | − | 0.972785i | \(-0.574432\pi\) | ||||
−0.231711 | + | 0.972785i | \(0.574432\pi\) | |||||||
\(128\) | − 185364.i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −241249. | −0.109808 | ||||||||
\(131\) | − 917060.i | − 0.407928i | −0.978978 | − | 0.203964i | \(-0.934617\pi\) | ||||
0.978978 | − | 0.203964i | \(-0.0653826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.78791e6 | −1.61007 | ||||||||
\(134\) | 1.81250e6i | 0.753294i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.46455e6 | −0.582222 | ||||||||
\(137\) | 477205.i | 0.185585i | 0.995685 | + | 0.0927926i | \(0.0295794\pi\) | ||||
−0.995685 | + | 0.0927926i | \(0.970421\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.08452e6 | −1.52089 | −0.760443 | − | 0.649405i | \(-0.775018\pi\) | ||||
−0.760443 | + | 0.649405i | \(0.775018\pi\) | |||||||
\(140\) | 716551.i | 0.261134i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.28872e6 | 0.799334 | ||||||||
\(143\) | − 941484.i | − 0.321962i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 103632. | 0.0339931 | ||||||||
\(146\) | 2.22721e6i | 0.715654i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.94586e6 | −0.908713 | ||||||||
\(149\) | − 3.68008e6i | − 1.11250i | −0.831017 | − | 0.556248i | \(-0.812241\pi\) | ||||
0.831017 | − | 0.556248i | \(-0.187759\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −667485. | −0.193870 | −0.0969350 | − | 0.995291i | \(-0.530904\pi\) | ||||
−0.0969350 | + | 0.995291i | \(0.530904\pi\) | |||||||
\(152\) | 1.39880e6i | 0.398314i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.79637e6 | −0.765654 | ||||||||
\(155\) | − 1.55884e6i | − 0.418608i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50716e6 | −0.389458 | −0.194729 | − | 0.980857i | \(-0.562383\pi\) | ||||
−0.194729 | + | 0.980857i | \(0.562383\pi\) | |||||||
\(158\) | 5.08194e6i | 1.28842i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 264608. | 0.0646016 | ||||||||
\(161\) | − 6.70631e6i | − 1.60696i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.90805e6 | −1.36421 | −0.682105 | − | 0.731254i | \(-0.738935\pi\) | ||||
−0.682105 | + | 0.731254i | \(0.738935\pi\) | |||||||
\(164\) | 1.14626e6i | 0.259867i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.01191e6 | 0.221216 | ||||||||
\(167\) | 2.69176e6i | 0.577945i | 0.957337 | + | 0.288972i | \(0.0933136\pi\) | ||||
−0.957337 | + | 0.288972i | \(0.906686\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.95520e6 | −0.819423 | ||||||||
\(170\) | − 2.09066e6i | − 0.425536i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.21254e6 | 0.434816 | ||||||||
\(173\) | 6.34579e6i | 1.22560i | 0.790239 | + | 0.612798i | \(0.209956\pi\) | ||||
−0.790239 | + | 0.612798i | \(0.790044\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.63641e6 | 1.23828 | ||||||||
\(176\) | 1.03264e6i | 0.189414i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.67515e6 | 0.828964 | ||||||||
\(179\) | 9.31786e6i | 1.62464i | 0.583212 | + | 0.812320i | \(0.301796\pi\) | ||||
−0.583212 | + | 0.812320i | \(0.698204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.28997e6 | 0.217542 | 0.108771 | − | 0.994067i | \(-0.465308\pi\) | ||||
0.108771 | + | 0.994067i | \(0.465308\pi\) | |||||||
\(182\) | − 2.58884e6i | − 0.429429i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.47651e6 | −0.397545 | ||||||||
\(185\) | − 4.20523e6i | − 0.664163i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.15889e6 | 1.24769 | ||||||||
\(188\) | 488157.i | 0.0734659i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.99680e6 | −0.291121 | ||||||||
\(191\) | 7.23490e6i | 1.03832i | 0.854676 | + | 0.519161i | \(0.173756\pi\) | ||||
−0.854676 | + | 0.519161i | \(0.826244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.67637e6 | −0.650485 | −0.325243 | − | 0.945631i | \(-0.605446\pi\) | ||||
−0.325243 | + | 0.945631i | \(0.605446\pi\) | |||||||
\(194\) | 3.59755e6i | 0.492721i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.92454e6 | −0.521220 | ||||||||
\(197\) | − 2.50022e6i | − 0.327024i | −0.986541 | − | 0.163512i | \(-0.947718\pi\) | ||||
0.986541 | − | 0.163512i | \(-0.0522822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.28474e6 | −0.416814 | −0.208407 | − | 0.978042i | \(-0.566828\pi\) | ||||
−0.208407 | + | 0.978042i | \(0.566828\pi\) | |||||||
\(200\) | − 2.45070e6i | − 0.306337i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.48472e6 | −0.180132 | ||||||||
\(203\) | 1.11208e6i | 0.132937i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.63629e6 | −0.189933 | ||||||||
\(206\) | − 466555.i | − 0.0533704i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −956008. | −0.106236 | ||||||||
\(209\) | − 7.79260e6i | − 0.853578i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.66888e6 | 0.177655 | 0.0888276 | − | 0.996047i | \(-0.471688\pi\) | ||||
0.0888276 | + | 0.996047i | \(0.471688\pi\) | |||||||
\(212\) | − 7.57091e6i | − 0.794585i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.86186e6 | −0.598128 | ||||||||
\(215\) | 3.15841e6i | 0.317800i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.67280e7 | 1.63706 | ||||||||
\(218\) | 2.37598e6i | 0.229337i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.47411e6 | −0.138440 | ||||||||
\(221\) | 7.55339e6i | 0.699786i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.13073e7 | −1.01963 | −0.509815 | − | 0.860284i | \(-0.670286\pi\) | ||||
−0.509815 | + | 0.860284i | \(0.670286\pi\) | |||||||
\(224\) | 2.83951e6i | 0.252639i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.65340e6 | 0.749655 | ||||||||
\(227\) | − 1.53264e7i | − 1.31028i | −0.755508 | − | 0.655139i | \(-0.772610\pi\) | ||||
0.755508 | − | 0.655139i | \(-0.227390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.27105e6 | 0.105842 | 0.0529208 | − | 0.998599i | \(-0.483147\pi\) | ||||
0.0529208 | + | 0.998599i | \(0.483147\pi\) | |||||||
\(230\) | − 3.53523e6i | − 0.290559i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 410669. | 0.0328873 | ||||||||
\(233\) | 1.45867e6i | 0.115316i | 0.998336 | + | 0.0576578i | \(0.0183632\pi\) | ||||
−0.998336 | + | 0.0576578i | \(0.981637\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −696848. | −0.0536951 | ||||||||
\(236\) | 8.19894e6i | 0.623766i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.24349e7 | 1.66415 | ||||||||
\(239\) | 5.02512e6i | 0.368089i | 0.982918 | + | 0.184044i | \(0.0589190\pi\) | ||||
−0.982918 | + | 0.184044i | \(0.941081\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.13489e6 | 0.366843 | 0.183421 | − | 0.983034i | \(-0.441283\pi\) | ||||
0.183421 | + | 0.983034i | \(0.441283\pi\) | |||||||
\(242\) | 4.26869e6i | 0.301196i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.27485e6 | −0.0877589 | ||||||||
\(245\) | − 5.60231e6i | − 0.380951i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.21428e6 | 0.478743 | ||||||||
\(248\) | − 6.17731e6i | − 0.404990i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.53599e6 | 0.482303 | ||||||||
\(251\) | − 1.72705e6i | − 0.109216i | −0.998508 | − | 0.0546078i | \(-0.982609\pi\) | ||||
0.998508 | − | 0.0546078i | \(-0.0173909\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.37964e7 | 0.851930 | ||||||||
\(254\) | − 5.36986e6i | − 0.327689i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | − 1.32178e7i | − 0.778682i | −0.921094 | − | 0.389341i | \(-0.872703\pi\) | ||||
0.921094 | − | 0.389341i | \(-0.127297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.51264e7 | 2.59735 | ||||||||
\(260\) | − 1.36471e6i | − 0.0776462i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.18767e6 | 0.288449 | ||||||||
\(263\) | 1.19615e7i | 0.657537i | 0.944411 | + | 0.328768i | \(0.106634\pi\) | ||||
−0.944411 | + | 0.328768i | \(0.893366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.08075e7 | 0.580749 | ||||||||
\(266\) | − 2.14277e7i | − 1.13849i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.02531e7 | −0.532660 | ||||||||
\(269\) | − 210238.i | − 0.0108007i | −0.999985 | − | 0.00540037i | \(-0.998281\pi\) | ||||
0.999985 | − | 0.00540037i | \(-0.00171900\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.71422e6 | −0.0861309 | −0.0430654 | − | 0.999072i | \(-0.513712\pi\) | ||||
−0.0430654 | + | 0.999072i | \(0.513712\pi\) | |||||||
\(272\) | − 8.28476e6i | − 0.411693i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.69948e6 | −0.131229 | ||||||||
\(275\) | 1.36526e7i | 0.656474i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.46890e7 | 0.691118 | 0.345559 | − | 0.938397i | \(-0.387689\pi\) | ||||
0.345559 | + | 0.938397i | \(0.387689\pi\) | |||||||
\(278\) | − 2.31055e7i | − 1.07543i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.05342e6 | −0.184649 | ||||||||
\(281\) | 1.30860e7i | 0.589776i | 0.955532 | + | 0.294888i | \(0.0952824\pi\) | ||||
−0.955532 | + | 0.294888i | \(0.904718\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.05680e6 | 0.134868 | 0.0674338 | − | 0.997724i | \(-0.478519\pi\) | ||||
0.0674338 | + | 0.997724i | \(0.478519\pi\) | |||||||
\(284\) | 1.29470e7i | 0.565215i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.32584e6 | 0.227662 | ||||||||
\(287\) | − 1.75591e7i | − 0.742773i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.13200e7 | −1.71186 | ||||||||
\(290\) | 586232.i | 0.0240368i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.25990e7 | −0.506044 | ||||||||
\(293\) | 2.94163e7i | 1.16946i | 0.811228 | + | 0.584729i | \(0.198799\pi\) | ||||
−0.811228 | + | 0.584729i | \(0.801201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17040e7 | −0.455901 | ||||||||
\(296\) | − 1.66643e7i | − 0.642557i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.08177e7 | 0.786653 | ||||||||
\(299\) | 1.27725e7i | 0.477818i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.38929e7 | −1.24282 | ||||||||
\(302\) | − 3.77587e6i | − 0.137087i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.91282e6 | −0.281650 | ||||||||
\(305\) | − 1.81986e6i | − 0.0641415i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.82307e7 | 1.32129 | 0.660643 | − | 0.750700i | \(-0.270284\pi\) | ||||
0.660643 | + | 0.750700i | \(0.270284\pi\) | |||||||
\(308\) | − 1.58187e7i | − 0.541399i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.81815e6 | 0.296001 | ||||||||
\(311\) | − 736808.i | − 0.0244948i | −0.999925 | − | 0.0122474i | \(-0.996101\pi\) | ||||
0.999925 | − | 0.0122474i | \(-0.00389856\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.42553e7 | −0.464883 | −0.232442 | − | 0.972610i | \(-0.574671\pi\) | ||||
−0.232442 | + | 0.972610i | \(0.574671\pi\) | |||||||
\(314\) | − 8.52579e6i | − 0.275388i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.87478e7 | −0.911052 | ||||||||
\(317\) | 5.31100e7i | 1.66724i | 0.552337 | + | 0.833621i | \(0.313736\pi\) | ||||
−0.552337 | + | 0.833621i | \(0.686264\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.28780e6 | −0.0704767 | ||||||||
\(320\) | 1.49685e6i | 0.0456802i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.79366e7 | 1.13629 | ||||||||
\(323\) | 6.25189e7i | 1.85526i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.26394e7 | −0.368194 | ||||||||
\(326\) | − 3.34210e7i | − 0.964643i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.48422e6 | −0.183754 | ||||||||
\(329\) | − 7.47788e6i | − 0.209986i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.09562e7 | −1.40512 | −0.702559 | − | 0.711625i | \(-0.747959\pi\) | ||||
−0.702559 | + | 0.711625i | \(0.747959\pi\) | |||||||
\(332\) | 5.72422e6i | 0.156424i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.52269e7 | −0.408669 | ||||||||
\(335\) | − 1.46363e7i | − 0.389312i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.42292e7 | 1.41691 | 0.708457 | − | 0.705754i | \(-0.249392\pi\) | ||||
0.708457 | + | 0.705754i | \(0.249392\pi\) | |||||||
\(338\) | − 2.23740e7i | − 0.579419i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.18266e7 | 0.300900 | ||||||||
\(341\) | 3.44132e7i | 0.867885i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.44751e6 | 0.0606517 | ||||||||
\(344\) | 1.25160e7i | 0.307461i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.58972e7 | −0.866628 | ||||||||
\(347\) | − 2.06891e7i | − 0.495169i | −0.968866 | − | 0.247584i | \(-0.920363\pi\) | ||||
0.968866 | − | 0.247584i | \(-0.0796368\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.45539e7 | −0.812871 | −0.406435 | − | 0.913680i | \(-0.633228\pi\) | ||||
−0.406435 | + | 0.913680i | \(0.633228\pi\) | |||||||
\(350\) | 3.75412e7i | 0.875597i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.84152e6 | −0.133936 | ||||||||
\(353\) | − 8.06874e7i | − 1.83435i | −0.398487 | − | 0.917174i | \(-0.630464\pi\) | ||||
0.398487 | − | 0.917174i | \(-0.369536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.84819e7 | −0.413106 | ||||||||
\(356\) | 2.64467e7i | 0.586166i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.27098e7 | −1.14879 | ||||||||
\(359\) | 1.64156e7i | 0.354792i | 0.984140 | + | 0.177396i | \(0.0567674\pi\) | ||||
−0.984140 | + | 0.177396i | \(0.943233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.26662e7 | 0.269231 | ||||||||
\(362\) | 7.29717e6i | 0.153826i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.46447e7 | 0.303652 | ||||||||
\(365\) | − 1.79852e7i | − 0.369859i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.05783e7 | −1.02321 | −0.511606 | − | 0.859220i | \(-0.670949\pi\) | ||||
−0.511606 | + | 0.859220i | \(0.670949\pi\) | |||||||
\(368\) | − 1.40092e7i | − 0.281107i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.37884e7 | 0.469634 | ||||||||
\(371\) | 1.15976e8i | 2.27115i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.40213e7 | 0.270185 | 0.135092 | − | 0.990833i | \(-0.456867\pi\) | ||||
0.135092 | + | 0.990833i | \(0.456867\pi\) | |||||||
\(374\) | 4.61536e7i | 0.882249i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.76143e6 | −0.0519483 | ||||||||
\(377\) | − 2.11801e6i | − 0.0395280i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.76705e7 | −0.324587 | −0.162294 | − | 0.986743i | \(-0.551889\pi\) | ||||
−0.162294 | + | 0.986743i | \(0.551889\pi\) | |||||||
\(380\) | − 1.12956e7i | − 0.205854i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.09268e7 | −0.734205 | ||||||||
\(383\) | 9.08579e7i | 1.61721i | 0.588352 | + | 0.808605i | \(0.299777\pi\) | ||||
−0.588352 | + | 0.808605i | \(0.700223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.25812e7 | 0.395700 | ||||||||
\(386\) | − 2.64536e7i | − 0.459962i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.03508e7 | −0.348406 | ||||||||
\(389\) | − 8.10099e7i | − 1.37622i | −0.725604 | − | 0.688112i | \(-0.758440\pi\) | ||||
0.725604 | − | 0.688112i | \(-0.241560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.10687e8 | −1.85167 | ||||||||
\(392\) | − 2.22006e7i | − 0.368558i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.41434e7 | 0.231241 | ||||||||
\(395\) | − 4.10377e7i | − 0.665873i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.78058e7 | −0.923846 | −0.461923 | − | 0.886920i | \(-0.652840\pi\) | ||||
−0.461923 | + | 0.886920i | \(0.652840\pi\) | |||||||
\(398\) | − 1.85813e7i | − 0.294732i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.38632e7 | 0.216613 | ||||||||
\(401\) | − 1.22792e8i | − 1.90431i | −0.305622 | − | 0.952153i | \(-0.598864\pi\) | ||||
0.305622 | − | 0.952153i | \(-0.401136\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.18593e7 | −0.486767 | ||||||||
\(404\) | − 8.39887e6i | − 0.127373i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.29086e6 | −0.0940009 | ||||||||
\(407\) | 9.28352e7i | 1.37699i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.80741e7 | −0.264172 | −0.132086 | − | 0.991238i | \(-0.542168\pi\) | ||||
−0.132086 | + | 0.991238i | \(0.542168\pi\) | |||||||
\(410\) | − 9.25627e6i | − 0.134303i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.63923e6 | 0.0377386 | ||||||||
\(413\) | − 1.25596e8i | − 1.78290i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.17137e6 | −0.114327 | ||||||||
\(416\) | − 5.40800e6i | − 0.0751202i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.40816e7 | 0.603571 | ||||||||
\(419\) | − 1.00741e7i | − 0.136950i | −0.997653 | − | 0.0684751i | \(-0.978187\pi\) | ||||
0.997653 | − | 0.0684751i | \(-0.0218134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.40856e8 | 1.88768 | 0.943839 | − | 0.330406i | \(-0.107186\pi\) | ||||
0.943839 | + | 0.330406i | \(0.107186\pi\) | |||||||
\(422\) | 9.44061e6i | 0.125621i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.28275e7 | 0.561857 | ||||||||
\(425\) | − 1.09533e8i | − 1.42685i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.95290e7 | 0.250839 | ||||||||
\(428\) | − 3.31597e7i | − 0.422940i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.78667e7 | −0.224718 | ||||||||
\(431\) | 6.81157e6i | 0.0850777i | 0.999095 | + | 0.0425388i | \(0.0135446\pi\) | ||||
−0.999095 | + | 0.0425388i | \(0.986455\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.17807e8 | −1.45113 | −0.725566 | − | 0.688153i | \(-0.758422\pi\) | ||||
−0.725566 | + | 0.688153i | \(0.758422\pi\) | |||||||
\(434\) | 9.46277e7i | 1.15757i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.34406e7 | −0.162165 | ||||||||
\(437\) | 1.05717e8i | 1.26678i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.10305e7 | 0.839559 | 0.419780 | − | 0.907626i | \(-0.362107\pi\) | ||||
0.419780 | + | 0.907626i | \(0.362107\pi\) | |||||||
\(440\) | − 8.33881e6i | − 0.0978918i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.27284e7 | −0.494823 | ||||||||
\(443\) | − 2.11414e7i | − 0.243177i | −0.992581 | − | 0.121588i | \(-0.961201\pi\) | ||||
0.992581 | − | 0.121588i | \(-0.0387988\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.77528e7 | −0.428419 | ||||||||
\(446\) | − 6.39635e7i | − 0.720987i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.60627e7 | −0.178642 | ||||||||
\(449\) | 5.48751e7i | 0.606228i | 0.952954 | + | 0.303114i | \(0.0980263\pi\) | ||||
−0.952954 | + | 0.303114i | \(0.901974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.61230e7 | 0.393780 | ||||||||
\(452\) | 4.89510e7i | 0.530086i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.66994e7 | 0.926507 | ||||||||
\(455\) | 2.09054e7i | 0.221934i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.96565e7 | −0.205948 | −0.102974 | − | 0.994684i | \(-0.532836\pi\) | ||||
−0.102974 | + | 0.994684i | \(0.532836\pi\) | |||||||
\(458\) | 7.19015e6i | 0.0748413i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.99983e7 | 0.205456 | ||||||||
\(461\) | − 5.73967e7i | − 0.585847i | −0.956136 | − | 0.292923i | \(-0.905372\pi\) | ||||
0.956136 | − | 0.292923i | \(-0.0946281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.01215e8 | 1.01977 | 0.509885 | − | 0.860242i | \(-0.329688\pi\) | ||||
0.509885 | + | 0.860242i | \(0.329688\pi\) | |||||||
\(464\) | 2.32309e6i | 0.0232548i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.25146e6 | −0.0815404 | ||||||||
\(467\) | − 1.26426e8i | − 1.24133i | −0.784077 | − | 0.620663i | \(-0.786863\pi\) | ||||
0.784077 | − | 0.620663i | \(-0.213137\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.57063e8 | 1.52249 | ||||||||
\(470\) | − 3.94197e6i | − 0.0379681i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.63802e7 | −0.441069 | ||||||||
\(473\) | − 6.97255e7i | − 0.658882i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.04615e8 | −0.976147 | ||||||||
\(476\) | 1.26911e8i | 1.17673i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.84264e7 | −0.260278 | ||||||||
\(479\) | 6.67030e7i | 0.606931i | 0.952843 | + | 0.303465i | \(0.0981436\pi\) | ||||
−0.952843 | + | 0.303465i | \(0.901856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.59456e7 | −0.772304 | ||||||||
\(482\) | 2.90473e7i | 0.259397i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.41474e7 | −0.212978 | ||||||||
\(485\) | − 2.90509e7i | − 0.254645i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.97650e7 | 0.604019 | 0.302009 | − | 0.953305i | \(-0.402343\pi\) | ||||
0.302009 | + | 0.953305i | \(0.402343\pi\) | |||||||
\(488\) | − 7.21167e6i | − 0.0620549i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.16915e7 | 0.269373 | ||||||||
\(491\) | 1.06576e8i | 0.900356i | 0.892939 | + | 0.450178i | \(0.148640\pi\) | ||||
−0.892939 | + | 0.450178i | \(0.851360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.83547e7 | 0.153181 | ||||||||
\(494\) | 4.08101e7i | 0.338522i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.49441e7 | 0.286371 | ||||||||
\(497\) | − 1.98329e8i | − 1.61554i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.35114e8 | 1.08743 | 0.543713 | − | 0.839271i | \(-0.317018\pi\) | ||||
0.543713 | + | 0.839271i | \(0.317018\pi\) | |||||||
\(500\) | 4.26300e7i | 0.341040i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.76969e6 | 0.0772271 | ||||||||
\(503\) | 2.31473e8i | 1.81885i | 0.415869 | + | 0.909425i | \(0.363477\pi\) | ||||
−0.415869 | + | 0.909425i | \(0.636523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.19894e7 | 0.0930947 | ||||||||
\(506\) | 7.80442e7i | 0.602406i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.03765e7 | 0.231711 | ||||||||
\(509\) | − 1.31287e8i | − 0.995559i | −0.867304 | − | 0.497780i | \(-0.834149\pi\) | ||||
0.867304 | − | 0.497780i | \(-0.165851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.92999e8 | 1.44641 | ||||||||
\(512\) | 5.93164e6i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.47712e7 | 0.550611 | ||||||||
\(515\) | 3.76752e6i | 0.0275825i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.53837e7 | 0.111324 | ||||||||
\(518\) | 2.55273e8i | 1.83661i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.71996e6 | 0.0549041 | ||||||||
\(521\) | − 1.14057e8i | − 0.806509i | −0.915088 | − | 0.403255i | \(-0.867879\pi\) | ||||
0.915088 | − | 0.403255i | \(-0.132121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.52785e7 | 0.456315 | 0.228158 | − | 0.973624i | \(-0.426730\pi\) | ||||
0.228158 | + | 0.973624i | \(0.426730\pi\) | |||||||
\(524\) | 2.93459e7i | 0.203964i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.76647e7 | −0.464949 | ||||||||
\(527\) | − 2.76092e8i | − 1.88635i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.91312e7 | −0.264336 | ||||||||
\(530\) | 6.11366e7i | 0.410652i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.21213e8 | 0.805035 | ||||||||
\(533\) | 3.34422e7i | 0.220858i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.73357e7 | 0.309120 | ||||||||
\(536\) | − 5.80001e7i | − 0.376647i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.18928e6 | 0.00763728 | ||||||||
\(539\) | 1.23677e8i | 0.789812i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.71142e8 | 1.08085 | 0.540423 | − | 0.841394i | \(-0.318264\pi\) | ||||
0.540423 | + | 0.841394i | \(0.318264\pi\) | |||||||
\(542\) | − 9.69710e6i | − 0.0609037i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.68657e7 | 0.291111 | ||||||||
\(545\) | − 1.91865e7i | − 0.118524i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.80956e7 | 0.354961 | 0.177481 | − | 0.984124i | \(-0.443205\pi\) | ||||
0.177481 | + | 0.984124i | \(0.443205\pi\) | |||||||
\(548\) | − 1.52706e7i | − 0.0927926i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.72308e7 | −0.464197 | ||||||||
\(551\) | − 1.75306e7i | − 0.104796i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.40375e8 | 2.60404 | ||||||||
\(554\) | 8.30934e7i | 0.488694i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.30705e8 | 0.760443 | ||||||||
\(557\) | − 1.36639e8i | − 0.790696i | −0.918532 | − | 0.395348i | \(-0.870624\pi\) | ||||
0.918532 | − | 0.395348i | \(-0.129376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.45509e7 | 0.369544 | ||||||||
\(560\) | − 2.29296e7i | − 0.130567i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.40255e7 | −0.417035 | ||||||||
\(563\) | 2.77071e8i | 1.55262i | 0.630350 | + | 0.776311i | \(0.282912\pi\) | ||||
−0.630350 | + | 0.776311i | \(0.717088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.98779e7 | −0.387431 | ||||||||
\(566\) | 1.72919e7i | 0.0953657i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.32392e7 | −0.399667 | ||||||||
\(569\) | 2.43372e8i | 1.32109i | 0.750785 | + | 0.660546i | \(0.229675\pi\) | ||||
−0.750785 | + | 0.660546i | \(0.770325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.39062e8 | −0.746965 | −0.373483 | − | 0.927637i | \(-0.621836\pi\) | ||||
−0.373483 | + | 0.927637i | \(0.621836\pi\) | |||||||
\(572\) | 3.01275e7i | 0.160981i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.93291e7 | 0.525220 | ||||||||
\(575\) | − 1.85216e8i | − 0.974262i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.45574e8 | −1.79893 | −0.899464 | − | 0.436994i | \(-0.856043\pi\) | ||||
−0.899464 | + | 0.436994i | \(0.856043\pi\) | |||||||
\(578\) | − 2.33741e8i | − 1.21046i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.31623e6 | −0.0169966 | ||||||||
\(581\) | − 8.76870e7i | − 0.447102i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.38588e8 | −1.20405 | ||||||||
\(584\) | − 7.12708e7i | − 0.357827i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.66404e8 | −0.826932 | ||||||||
\(587\) | 1.65925e8i | 0.820349i | 0.912007 | + | 0.410174i | \(0.134532\pi\) | ||||
−0.912007 | + | 0.410174i | \(0.865468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.63697e8 | −1.29051 | ||||||||
\(590\) | − 6.62081e7i | − 0.322370i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.42674e7 | 0.454356 | ||||||||
\(593\) | 2.87880e8i | 1.38054i | 0.723553 | + | 0.690268i | \(0.242508\pi\) | ||||
−0.723553 | + | 0.690268i | \(0.757492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.81166e8 | −0.860055 | ||||||||
\(596\) | 1.17762e8i | 0.556248i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.22523e7 | −0.337869 | ||||||||
\(599\) | 4.24365e7i | 0.197451i | 0.995115 | + | 0.0987254i | \(0.0314765\pi\) | ||||
−0.995115 | + | 0.0987254i | \(0.968523\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.78000e7 | −0.0819968 | −0.0409984 | − | 0.999159i | \(-0.513054\pi\) | ||||
−0.0409984 | + | 0.999159i | \(0.513054\pi\) | |||||||
\(602\) | − 1.91727e8i | − 0.878809i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.13595e7 | 0.0969350 | ||||||||
\(605\) | − 3.44706e7i | − 0.155662i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.44970e8 | −1.54246 | −0.771232 | − | 0.636554i | \(-0.780359\pi\) | ||||
−0.771232 | + | 0.636554i | \(0.780359\pi\) | |||||||
\(608\) | − 4.47617e7i | − 0.199157i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.02947e7 | 0.0453549 | ||||||||
\(611\) | 1.42420e7i | 0.0624378i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.15533e8 | 0.501562 | 0.250781 | − | 0.968044i | \(-0.419313\pi\) | ||||
0.250781 | + | 0.968044i | \(0.419313\pi\) | |||||||
\(614\) | 2.16265e8i | 0.934291i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.94838e7 | 0.382827 | ||||||||
\(617\) | − 2.30584e8i | − 0.981689i | −0.871247 | − | 0.490845i | \(-0.836688\pi\) | ||||
0.871247 | − | 0.490845i | \(-0.163312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.86629e8 | 1.20851 | 0.604253 | − | 0.796792i | \(-0.293472\pi\) | ||||
0.604253 | + | 0.796792i | \(0.293472\pi\) | |||||||
\(620\) | 4.98830e7i | 0.209304i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.16802e6 | 0.0173204 | ||||||||
\(623\) | − 4.05126e8i | − 1.67543i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.50682e8 | 0.617192 | ||||||||
\(626\) | − 8.06402e7i | − 0.328722i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.82291e7 | 0.194729 | ||||||||
\(629\) | − 7.44804e8i | − 2.99288i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.03780e8 | −0.811098 | −0.405549 | − | 0.914073i | \(-0.632920\pi\) | ||||
−0.405549 | + | 0.914073i | \(0.632920\pi\) | |||||||
\(632\) | − 1.62622e8i | − 0.644211i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.00435e8 | −1.17892 | ||||||||
\(635\) | 4.33627e7i | 0.169354i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.14499e8 | −0.442978 | ||||||||
\(638\) | − 1.29417e7i | − 0.0498345i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.46746e6 | −0.0323008 | ||||||||
\(641\) | 4.76661e8i | 1.80982i | 0.425602 | + | 0.904910i | \(0.360062\pi\) | ||||
−0.425602 | + | 0.904910i | \(0.639938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.61187e8 | 0.606315 | 0.303157 | − | 0.952941i | \(-0.401959\pi\) | ||||
0.303157 | + | 0.952941i | \(0.401959\pi\) | |||||||
\(644\) | 2.14602e8i | 0.803481i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.53660e8 | −1.31186 | ||||||||
\(647\) | 3.18171e8i | 1.17476i | 0.809313 | + | 0.587378i | \(0.199840\pi\) | ||||
−0.809313 | + | 0.587378i | \(0.800160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.58380e8 | 0.945202 | ||||||||
\(650\) | − 7.14992e7i | − 0.260352i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.89058e8 | 0.682105 | ||||||||
\(653\) | 1.79024e8i | 0.642943i | 0.946919 | + | 0.321471i | \(0.104177\pi\) | ||||
−0.946919 | + | 0.321471i | \(0.895823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.18915e7 | −0.149074 | ||||||||
\(656\) | − 3.66803e7i | − 0.129934i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.23013e7 | 0.148483 | ||||||||
\(659\) | − 3.16743e8i | − 1.10675i | −0.832932 | − | 0.553376i | \(-0.813339\pi\) | ||||
0.832932 | − | 0.553376i | \(-0.186661\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.76093e8 | −1.30224 | −0.651119 | − | 0.758976i | \(-0.725700\pi\) | ||||
−0.651119 | + | 0.758976i | \(0.725700\pi\) | |||||||
\(662\) | − 2.88252e8i | − 0.993569i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.23811e7 | −0.110608 | ||||||||
\(665\) | 1.73033e8i | 0.588387i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.10371e7 | 0.104593 | ||||||||
\(668\) | − 8.61362e7i | − 0.288972i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.27956e7 | 0.275285 | ||||||||
\(671\) | 4.01755e7i | 0.132982i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.37679e8 | −0.779734 | −0.389867 | − | 0.920871i | \(-0.627479\pi\) | ||||
−0.389867 | + | 0.920871i | \(0.627479\pi\) | |||||||
\(674\) | 3.06767e8i | 1.00191i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.26566e8 | 0.409711 | ||||||||
\(677\) | − 3.89681e8i | − 1.25587i | −0.778267 | − | 0.627933i | \(-0.783901\pi\) | ||||
0.778267 | − | 0.627933i | \(-0.216099\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.11745e8 | 0.995843 | ||||||||
\(680\) | 6.69011e7i | 0.212768i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.94671e8 | −0.613687 | ||||||||
\(683\) | 3.91877e8i | 1.22995i | 0.788546 | + | 0.614975i | \(0.210834\pi\) | ||||
−0.788546 | + | 0.614975i | \(0.789166\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.17988e7 | 0.0678206 | ||||||||
\(686\) | 1.38452e7i | 0.0428872i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.08012e7 | −0.217408 | ||||||||
\(689\) | − 2.20882e8i | − 0.675308i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.52910e8 | −0.766534 | −0.383267 | − | 0.923638i | \(-0.625201\pi\) | ||||
−0.383267 | + | 0.923638i | \(0.625201\pi\) | |||||||
\(692\) | − 2.03065e8i | − 0.612798i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.17035e8 | 0.350137 | ||||||||
\(695\) | 1.86582e8i | 0.555795i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.89810e8 | −0.855883 | ||||||||
\(698\) | − 1.95467e8i | − 0.574786i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.12365e8 | −0.619141 | ||||||||
\(701\) | − 2.15054e8i | − 0.624299i | −0.950033 | − | 0.312150i | \(-0.898951\pi\) | ||||
0.950033 | − | 0.312150i | \(-0.101049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.11366e8 | −2.04751 | ||||||||
\(704\) | − 3.30446e7i | − 0.0947072i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.56437e8 | 1.29708 | ||||||||
\(707\) | 1.28659e8i | 0.364067i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.40902e8 | −0.395346 | −0.197673 | − | 0.980268i | \(-0.563338\pi\) | ||||
−0.197673 | + | 0.980268i | \(0.563338\pi\) | |||||||
\(710\) | − 1.04549e8i | − 0.292110i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.49605e8 | −0.414482 | ||||||||
\(713\) | − 4.66863e8i | − 1.28801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.30072e7 | −0.117658 | ||||||||
\(716\) | − 2.98172e8i | − 0.812320i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.28608e7 | −0.250876 | ||||||||
\(719\) | 4.59075e8i | 1.23508i | 0.786538 | + | 0.617542i | \(0.211872\pi\) | ||||
−0.786538 | + | 0.617542i | \(0.788128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.04293e7 | −0.107867 | ||||||||
\(722\) | 7.16510e7i | 0.190375i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.12790e7 | −0.108771 | ||||||||
\(725\) | 3.07136e7i | 0.0805967i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.52533e8 | 1.17773 | 0.588867 | − | 0.808230i | \(-0.299574\pi\) | ||||
0.588867 | + | 0.808230i | \(0.299574\pi\) | |||||||
\(728\) | 8.28429e7i | 0.214714i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.01740e8 | 0.261530 | ||||||||
\(731\) | 5.59397e8i | 1.43208i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.75576e8 | −1.20756 | −0.603779 | − | 0.797152i | \(-0.706339\pi\) | ||||
−0.603779 | + | 0.797152i | \(0.706339\pi\) | |||||||
\(734\) | − 2.86114e8i | − 0.723520i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.92482e7 | 0.198772 | ||||||||
\(737\) | 3.23113e8i | 0.807147i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.91913e7 | 0.220999 | 0.110499 | − | 0.993876i | \(-0.464755\pi\) | ||||
0.110499 | + | 0.993876i | \(0.464755\pi\) | |||||||
\(740\) | 1.34567e8i | 0.332082i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.56057e8 | −1.60594 | ||||||||
\(743\) | 7.28521e8i | 1.77613i | 0.459715 | + | 0.888066i | \(0.347951\pi\) | ||||
−0.459715 | + | 0.888066i | \(0.652049\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.68107e8 | −0.406552 | ||||||||
\(746\) | 7.93163e7i | 0.191049i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.61084e8 | −0.623844 | ||||||||
\(749\) | 5.07960e8i | 1.20888i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.58845e8 | −0.847201 | −0.423601 | − | 0.905849i | \(-0.639234\pi\) | ||||
−0.423601 | + | 0.905849i | \(0.639234\pi\) | |||||||
\(752\) | − 1.56210e7i | − 0.0367330i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.19813e7 | 0.0279505 | ||||||||
\(755\) | 3.04909e7i | 0.0708482i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.38232e8 | 0.779700 | 0.389850 | − | 0.920878i | \(-0.372527\pi\) | ||||
0.389850 | + | 0.920878i | \(0.372527\pi\) | |||||||
\(758\) | − 9.99595e7i | − 0.229518i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.38976e7 | 0.145561 | ||||||||
\(761\) | 6.74492e8i | 1.53046i | 0.643755 | + | 0.765232i | \(0.277376\pi\) | ||||
−0.643755 | + | 0.765232i | \(0.722624\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.05891e8 | 0.463514 | ||||||||
\(764\) | − 2.31517e8i | − 0.519161i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.13970e8 | −1.14354 | ||||||||
\(767\) | 2.39205e8i | 0.530132i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.62772e8 | 1.67732 | 0.838660 | − | 0.544656i | \(-0.183340\pi\) | ||||
0.838660 | + | 0.544656i | \(0.183340\pi\) | |||||||
\(770\) | 1.27739e8i | 0.279802i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.49644e8 | 0.325243 | ||||||||
\(773\) | − 6.42100e8i | − 1.39016i | −0.718933 | − | 0.695080i | \(-0.755369\pi\) | ||||
0.718933 | − | 0.695080i | \(-0.244631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.61997e8 | 0.992508 | ||||||||
\(776\) | − 1.15121e8i | − 0.246361i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.58261e8 | 0.973137 | ||||||||
\(779\) | 2.76799e8i | 0.585533i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.08009e8 | 0.856478 | ||||||||
\(782\) | − 6.26138e8i | − 1.30933i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.25585e8 | 0.260610 | ||||||||
\(785\) | 6.88474e7i | 0.142324i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.41525e8 | 0.700646 | 0.350323 | − | 0.936629i | \(-0.386072\pi\) | ||||
0.350323 | + | 0.936629i | \(0.386072\pi\) | |||||||
\(788\) | 8.00070e7i | 0.163512i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.32144e8 | 0.470843 | ||||||||
\(791\) | − 7.49861e8i | − 1.51513i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.71940e7 | −0.0745852 | ||||||||
\(794\) | − 3.26999e8i | − 0.653258i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.05112e8 | 0.208407 | ||||||||
\(797\) | − 5.29044e8i | − 1.04500i | −0.852639 | − | 0.522501i | \(-0.824999\pi\) | ||||
0.852639 | − | 0.522501i | \(-0.175001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.23421e8 | −0.241963 | ||||||||
\(800\) | 7.84223e7i | 0.153169i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.94616e8 | 1.34655 | ||||||||
\(803\) | 3.97043e8i | 0.766816i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.06346e8 | −0.587251 | ||||||||
\(806\) | − 1.80223e8i | − 0.344196i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.75112e7 | 0.0900662 | ||||||||
\(809\) | 7.38055e8i | 1.39394i | 0.717102 | + | 0.696968i | \(0.245468\pi\) | ||||
−0.717102 | + | 0.696968i | \(0.754532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.57151e8 | −0.857031 | −0.428516 | − | 0.903534i | \(-0.640963\pi\) | ||||
−0.428516 | + | 0.903534i | \(0.640963\pi\) | |||||||
\(812\) | − 3.55865e7i | − 0.0664687i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.25155e8 | −0.973676 | ||||||||
\(815\) | 2.69881e8i | 0.498540i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.34283e8 | 0.979728 | ||||||||
\(818\) | − 1.02243e8i | − 0.186798i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.23614e7 | 0.0949663 | ||||||||
\(821\) | 1.40803e8i | 0.254438i | 0.991875 | + | 0.127219i | \(0.0406051\pi\) | ||||
−0.991875 | + | 0.127219i | \(0.959395\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.97363e8 | 0.533443 | 0.266721 | − | 0.963774i | \(-0.414060\pi\) | ||||
0.266721 | + | 0.963774i | \(0.414060\pi\) | |||||||
\(824\) | 1.49297e7i | 0.0266852i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.10480e8 | 1.26070 | ||||||||
\(827\) | 6.71385e8i | 1.18701i | 0.804830 | + | 0.593506i | \(0.202257\pi\) | ||||
−0.804830 | + | 0.593506i | \(0.797743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.09596e8 | −0.718939 | −0.359470 | − | 0.933157i | \(-0.617042\pi\) | ||||
−0.359470 | + | 0.933157i | \(0.617042\pi\) | |||||||
\(830\) | − 4.62242e7i | − 0.0808417i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.05923e7 | 0.0531180 | ||||||||
\(833\) | − 9.92245e8i | − 1.71666i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.22960e8 | 0.211205 | ||||||||
\(836\) | 2.49363e8i | 0.426789i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.69876e7 | 0.0968385 | ||||||||
\(839\) | 3.01060e8i | 0.509761i | 0.966973 | + | 0.254881i | \(0.0820362\pi\) | ||||
−0.966973 | + | 0.254881i | \(0.917964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.89677e8 | 0.991347 | ||||||||
\(842\) | 7.96800e8i | 1.33479i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.34042e7 | −0.0888276 | ||||||||
\(845\) | 1.80674e8i | 0.299451i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.69904e8 | 0.608749 | ||||||||
\(848\) | 2.42269e8i | 0.397293i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.19612e8 | 1.00893 | ||||||||
\(851\) | − 1.25944e9i | − 2.04356i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.30806e8 | −0.532998 | −0.266499 | − | 0.963835i | \(-0.585867\pi\) | ||||
−0.266499 | + | 0.963835i | \(0.585867\pi\) | |||||||
\(854\) | 1.10473e8i | 0.177370i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.87580e8 | 0.299064 | ||||||||
\(857\) | − 7.28944e8i | − 1.15811i | −0.815287 | − | 0.579057i | \(-0.803421\pi\) | ||||
0.815287 | − | 0.579057i | \(-0.196579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.36404e7 | −0.0530739 | −0.0265370 | − | 0.999648i | \(-0.508448\pi\) | ||||
−0.0265370 | + | 0.999648i | \(0.508448\pi\) | |||||||
\(860\) | − 1.01069e8i | − 0.158900i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.85321e7 | −0.0601590 | ||||||||
\(863\) | − 3.65765e8i | − 0.569075i | −0.958665 | − | 0.284537i | \(-0.908160\pi\) | ||||
0.958665 | − | 0.284537i | \(-0.0918400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.89877e8 | 0.447884 | ||||||||
\(866\) | − 6.66416e8i | − 1.02610i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.35295e8 | −0.818529 | ||||||||
\(869\) | 9.05952e8i | 1.38053i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.99134e8 | −0.452701 | ||||||||
\(872\) | − 7.60314e7i | − 0.114668i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.98027e8 | −0.895750 | ||||||||
\(875\) | − 6.53031e8i | − 0.974787i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.33254e8 | 1.08707 | 0.543533 | − | 0.839388i | \(-0.317086\pi\) | ||||
0.543533 | + | 0.839388i | \(0.317086\pi\) | |||||||
\(878\) | 4.01809e8i | 0.593658i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.71714e7 | 0.0692199 | ||||||||
\(881\) | − 1.64762e8i | − 0.240951i | −0.992716 | − | 0.120475i | \(-0.961558\pi\) | ||||
0.992716 | − | 0.120475i | \(-0.0384419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.55533e8 | 0.661665 | 0.330832 | − | 0.943690i | \(-0.392671\pi\) | ||||
0.330832 | + | 0.943690i | \(0.392671\pi\) | |||||||
\(884\) | − 2.41708e8i | − 0.349893i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.19594e8 | 0.171952 | ||||||||
\(887\) | − 1.03986e9i | − 1.49005i | −0.667034 | − | 0.745027i | \(-0.732436\pi\) | ||||
0.667034 | − | 0.745027i | \(-0.267564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.65326e8 | −0.662295 | ||||||||
\(890\) | − 2.13562e8i | − 0.302938i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.61832e8 | 0.509815 | ||||||||
\(893\) | 1.17880e8i | 0.165534i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.25642e8 | 0.593712 | ||||||||
\(896\) | − 9.08644e7i | − 0.126319i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.10420e8 | −0.428668 | ||||||||
\(899\) | 7.74178e7i | 0.106552i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.91416e9 | 2.61700 | ||||||||
\(902\) | 2.04343e8i | 0.278445i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.76909e8 | −0.374828 | ||||||||
\(905\) | − 5.89261e7i | − 0.0794991i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.16242e8 | −0.959927 | −0.479963 | − | 0.877289i | \(-0.659350\pi\) | ||||
−0.479963 | + | 0.877289i | \(0.659350\pi\) | |||||||
\(908\) | 4.90446e8i | 0.655139i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.18259e8 | −0.156931 | ||||||||
\(911\) | − 8.69074e8i | − 1.14948i | −0.818336 | − | 0.574740i | \(-0.805103\pi\) | ||||
0.818336 | − | 0.574740i | \(-0.194897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.80392e8 | 0.237031 | ||||||||
\(914\) | − 1.11194e8i | − 0.145627i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.06736e7 | −0.0529208 | ||||||||
\(917\) | − 4.49538e8i | − 0.582986i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.50303e8 | 0.837855 | 0.418928 | − | 0.908020i | \(-0.362406\pi\) | ||||
0.418928 | + | 0.908020i | \(0.362406\pi\) | |||||||
\(920\) | 1.13127e8i | 0.145280i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.24685e8 | 0.414256 | ||||||||
\(923\) | 3.77729e8i | 0.480369i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.24631e9 | 1.57471 | ||||||||
\(926\) | 5.72559e8i | 0.721087i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.31414e7 | −0.0164436 | ||||||||
\(929\) | 3.39542e8i | 0.423493i | 0.977325 | + | 0.211746i | \(0.0679150\pi\) | ||||
−0.977325 | + | 0.211746i | \(0.932085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.47699e8 | −1.17441 | ||||||||
\(932\) | − 4.66773e7i | − 0.0576578i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.15174e8 | 0.877750 | ||||||||
\(935\) | − 3.72700e8i | − 0.455957i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.59228e9 | −1.93554 | −0.967769 | − | 0.251838i | \(-0.918965\pi\) | ||||
−0.967769 | + | 0.251838i | \(0.918965\pi\) | |||||||
\(938\) | 8.88480e8i | 1.07656i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.22991e7 | 0.0268475 | ||||||||
\(941\) | 1.35993e9i | 1.63210i | 0.577981 | + | 0.816051i | \(0.303841\pi\) | ||||
−0.577981 | + | 0.816051i | \(0.696159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.90058e8 | −0.584403 | ||||||||
\(944\) | − 2.62366e8i | − 0.311883i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.94427e8 | 0.465900 | ||||||||
\(947\) | − 3.20462e8i | − 0.377334i | −0.982041 | − | 0.188667i | \(-0.939583\pi\) | ||||
0.982041 | − | 0.188667i | \(-0.0604167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.67577e8 | −0.430081 | ||||||||
\(950\) | − 5.91794e8i | − 0.690240i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.17916e8 | −0.832076 | ||||||||
\(953\) | 6.65905e8i | 0.769367i | 0.923049 | + | 0.384683i | \(0.125689\pi\) | ||||
−0.923049 | + | 0.384683i | \(0.874311\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.30492e8 | 0.379446 | ||||||||
\(956\) | − 1.60804e8i | − 0.184044i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.77329e8 | −0.429165 | ||||||||
\(959\) | 2.33924e8i | 0.265227i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.77021e8 | 0.312135 | ||||||||
\(962\) | − 4.86182e8i | − 0.546101i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.64316e8 | −0.183421 | ||||||||
\(965\) | 2.13618e8i | 0.237714i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.58370e8 | 0.396325 | 0.198163 | − | 0.980169i | \(-0.436503\pi\) | ||||
0.198163 | + | 0.980169i | \(0.436503\pi\) | |||||||
\(968\) | − 1.36598e8i | − 0.150598i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.64337e8 | 0.180061 | ||||||||
\(971\) | − 3.10565e8i | − 0.339230i | −0.985510 | − | 0.169615i | \(-0.945748\pi\) | ||||
0.985510 | − | 0.169615i | \(-0.0542525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.00221e9 | −2.17356 | ||||||||
\(974\) | 3.94650e8i | 0.427106i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.07953e7 | 0.0438794 | ||||||||
\(977\) | − 1.37591e9i | − 1.47539i | −0.675135 | − | 0.737694i | \(-0.735915\pi\) | ||||
0.675135 | − | 0.737694i | \(-0.264085\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.33435e8 | 0.888227 | ||||||||
\(980\) | 1.79274e8i | 0.190475i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.02884e8 | −0.636648 | ||||||||
\(983\) | 5.64536e8i | 0.594335i | 0.954825 | + | 0.297168i | \(0.0960420\pi\) | ||||
−0.954825 | + | 0.297168i | \(0.903958\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.14211e8 | −0.119508 | ||||||||
\(986\) | 1.03830e8i | 0.108316i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.30857e8 | −0.239371 | ||||||||
\(989\) | 9.45922e8i | 0.977836i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.94100e8 | 0.199436 | 0.0997182 | − | 0.995016i | \(-0.468206\pi\) | ||||
0.0997182 | + | 0.995016i | \(0.468206\pi\) | |||||||
\(992\) | 1.97674e8i | 0.202495i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.12192e9 | 1.14236 | ||||||||
\(995\) | 1.50048e8i | 0.152321i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.16571e7 | 0.0420342 | 0.0210171 | − | 0.999779i | \(-0.493310\pi\) | ||||
0.0210171 | + | 0.999779i | \(0.493310\pi\) | |||||||
\(998\) | 7.64322e8i | 0.768926i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.7.b.c.161.8 | 12 | ||
3.2 | odd | 2 | inner | 162.7.b.c.161.5 | 12 | ||
9.2 | odd | 6 | 18.7.d.a.5.2 | ✓ | 12 | ||
9.4 | even | 3 | 18.7.d.a.11.2 | yes | 12 | ||
9.5 | odd | 6 | 54.7.d.a.35.6 | 12 | |||
9.7 | even | 3 | 54.7.d.a.17.6 | 12 | |||
36.7 | odd | 6 | 432.7.q.b.17.5 | 12 | |||
36.11 | even | 6 | 144.7.q.c.113.3 | 12 | |||
36.23 | even | 6 | 432.7.q.b.305.5 | 12 | |||
36.31 | odd | 6 | 144.7.q.c.65.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.7.d.a.5.2 | ✓ | 12 | 9.2 | odd | 6 | ||
18.7.d.a.11.2 | yes | 12 | 9.4 | even | 3 | ||
54.7.d.a.17.6 | 12 | 9.7 | even | 3 | |||
54.7.d.a.35.6 | 12 | 9.5 | odd | 6 | |||
144.7.q.c.65.3 | 12 | 36.31 | odd | 6 | |||
144.7.q.c.113.3 | 12 | 36.11 | even | 6 | |||
162.7.b.c.161.5 | 12 | 3.2 | odd | 2 | inner | ||
162.7.b.c.161.8 | 12 | 1.1 | even | 1 | trivial | ||
432.7.q.b.17.5 | 12 | 36.7 | odd | 6 | |||
432.7.q.b.305.5 | 12 | 36.23 | even | 6 |