Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(116,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 9, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.y (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 116.7 | ||
Character | \(\chi\) | \(=\) | 429.116 |
Dual form | 429.2.y.a.233.7 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.06579 | − | 0.671217i | 1.46074 | − | 0.474622i | 0.532441 | − | 0.846467i | \(-0.321275\pi\) |
0.928295 | + | 0.371845i | \(0.121275\pi\) | |||||||
\(3\) | 1.40126 | + | 1.01807i | 0.809017 | + | 0.587785i | ||||
\(4\) | 2.19893 | − | 1.59762i | 1.09947 | − | 0.798809i | ||||
\(5\) | 0.710253 | − | 2.18593i | 0.317635 | − | 0.977579i | −0.657022 | − | 0.753872i | \(-0.728184\pi\) |
0.974656 | − | 0.223708i | \(-0.0718161\pi\) | |||||||
\(6\) | 3.57806 | + | 1.16258i | 1.46074 | + | 0.474622i | ||||
\(7\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(8\) | 0.916732 | − | 1.26177i | 0.324114 | − | 0.446104i | ||||
\(9\) | 0.927051 | + | 2.85317i | 0.309017 | + | 0.951057i | ||||
\(10\) | − | 4.99242i | − | 1.57874i | ||||||
\(11\) | −2.94009 | − | 1.53488i | −0.886471 | − | 0.462785i | ||||
\(12\) | 4.70777 | 1.35902 | ||||||||
\(13\) | −3.42908 | + | 1.11418i | −0.951057 | + | 0.309017i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.22069 | − | 2.33997i | 0.831579 | − | 0.604177i | ||||
\(16\) | −0.632981 | + | 1.94811i | −0.158245 | + | 0.487029i | ||||
\(17\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(18\) | 3.83019 | + | 5.27180i | 0.902785 | + | 1.24258i | ||||
\(19\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(20\) | −1.93049 | − | 5.94144i | −0.431671 | − | 1.32855i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.10386 | − | 1.19731i | −1.51455 | − | 0.255268i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 2.56916 | − | 0.834770i | 0.524427 | − | 0.170397i | ||||
\(25\) | −0.228763 | − | 0.166206i | −0.0457526 | − | 0.0332412i | ||||
\(26\) | −6.33592 | + | 4.60332i | −1.24258 | + | 0.902785i | ||||
\(27\) | −1.60570 | + | 4.94183i | −0.309017 | + | 0.951057i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(30\) | 5.08265 | − | 6.99567i | 0.927961 | − | 1.27723i | ||||
\(31\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(32\) | 7.56854i | 1.33794i | ||||||||
\(33\) | −2.55720 | − | 5.14400i | −0.445152 | − | 0.895455i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.59680 | + | 4.79286i | 1.09947 | + | 0.798809i | ||||
\(37\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.93935 | − | 1.92981i | −0.951057 | − | 0.309017i | ||||
\(40\) | −2.10704 | − | 2.90009i | −0.333153 | − | 0.458545i | ||||
\(41\) | 4.59885 | − | 6.32977i | 0.718219 | − | 0.988544i | −0.281362 | − | 0.959602i | \(-0.590786\pi\) |
0.999581 | − | 0.0289423i | \(-0.00921390\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.75348i | − | 1.18239i | −0.806527 | − | 0.591197i | \(-0.798656\pi\) | ||
0.806527 | − | 0.591197i | \(-0.201344\pi\) | |||||||
\(44\) | −8.91722 | + | 1.32204i | −1.34432 | + | 0.199304i | ||||
\(45\) | 6.89528 | 1.02789 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.39703 | + | 3.92117i | 0.787238 | + | 0.571962i | 0.907142 | − | 0.420824i | \(-0.138259\pi\) |
−0.119905 | + | 0.992785i | \(0.538259\pi\) | |||||||
\(48\) | −2.87029 | + | 2.08539i | −0.414291 | + | 0.301000i | ||||
\(49\) | −2.16312 | + | 6.65740i | −0.309017 | + | 0.951057i | ||||
\(50\) | −0.584137 | − | 0.189798i | −0.0826094 | − | 0.0268414i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.76030 | + | 7.92837i | −0.798809 | + | 1.09947i | ||||
\(53\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(54\) | 11.2866i | 1.53591i | ||||||||
\(55\) | −5.44336 | + | 5.33669i | −0.733983 | + | 0.719599i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.20012 | − | 3.05156i | 0.546808 | − | 0.397280i | −0.279799 | − | 0.960059i | \(-0.590268\pi\) |
0.826607 | + | 0.562779i | \(0.190268\pi\) | |||||||
\(60\) | 3.34371 | − | 10.2909i | 0.431671 | − | 1.32855i | ||||
\(61\) | −10.4139 | − | 3.38370i | −1.33337 | − | 0.433238i | −0.446304 | − | 0.894881i | \(-0.647260\pi\) |
−0.887066 | + | 0.461644i | \(0.847260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.81417 | + | 11.7388i | 0.476771 | + | 1.46735i | ||||
\(65\) | 8.28710i | 1.02789i | ||||||||
\(66\) | −8.73539 | − | 8.91000i | −1.07525 | − | 1.09675i | ||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.52081 | − | 4.68057i | 0.180487 | − | 0.555481i | −0.819355 | − | 0.573287i | \(-0.805668\pi\) |
0.999841 | + | 0.0178059i | \(0.00566810\pi\) | |||||||
\(72\) | 4.44991 | + | 1.44586i | 0.524427 | + | 0.170397i | ||||
\(73\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.151346 | − | 0.465795i | −0.0174759 | − | 0.0537854i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.5648 | −1.53591 | ||||||||
\(79\) | 13.6385 | − | 4.43142i | 1.53445 | − | 0.498574i | 0.584613 | − | 0.811312i | \(-0.301246\pi\) |
0.949839 | + | 0.312739i | \(0.101246\pi\) | |||||||
\(80\) | 3.80887 | + | 2.76731i | 0.425845 | + | 0.309394i | ||||
\(81\) | −7.28115 | + | 5.29007i | −0.809017 | + | 0.587785i | ||||
\(82\) | 5.25162 | − | 16.1628i | 0.579944 | − | 1.78488i | ||||
\(83\) | −17.0554 | − | 5.54164i | −1.87207 | − | 0.608274i | −0.990738 | − | 0.135785i | \(-0.956644\pi\) |
−0.881336 | − | 0.472489i | \(-0.843356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.20426 | − | 16.0171i | −0.561190 | − | 1.72717i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.63195 | + | 2.30265i | −0.493768 | + | 0.245463i | ||||
\(89\) | −18.3671 | −1.94690 | −0.973452 | − | 0.228892i | \(-0.926490\pi\) | ||||
−0.973452 | + | 0.228892i | \(0.926490\pi\) | |||||||
\(90\) | 14.2442 | − | 4.62823i | 1.50147 | − | 0.487858i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.7811 | + | 4.47775i | 1.42141 | + | 0.461845i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.70534 | + | 10.6055i | −0.786423 | + | 1.08242i | ||||
\(97\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(98\) | 15.2047i | 1.53591i | ||||||||
\(99\) | 1.65367 | − | 9.81149i | 0.166200 | − | 0.986092i | ||||
\(100\) | −0.768568 | −0.0768568 | ||||||||
\(101\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4115 | − | 11.9236i | 1.61707 | − | 1.17487i | 0.788263 | − | 0.615338i | \(-0.210980\pi\) |
0.828808 | − | 0.559533i | \(-0.189020\pi\) | |||||||
\(104\) | −1.73771 | + | 5.34813i | −0.170397 | + | 0.524427i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(108\) | 4.36434 | + | 13.4321i | 0.419959 | + | 1.29250i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | −7.66279 | + | 14.6782i | −0.730618 | + | 1.39951i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.35787 | − | 8.75086i | −0.587785 | − | 0.809017i | ||||
\(118\) | 6.62831 | − | 9.12308i | 0.610185 | − | 0.839848i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 6.20891i | − | 0.566793i | ||||||
\(121\) | 6.28826 | + | 9.02540i | 0.571660 | + | 0.820491i | ||||
\(122\) | −23.7843 | −2.15332 | ||||||||
\(123\) | 12.8883 | − | 4.18768i | 1.16210 | − | 0.377590i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.77154 | − | 6.37290i | 0.784550 | − | 0.570009i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.41429 | − | 0.459530i | −0.125498 | − | 0.0407767i | 0.245595 | − | 0.969373i | \(-0.421017\pi\) |
−0.371093 | + | 0.928596i | \(0.621017\pi\) | |||||||
\(128\) | 6.86122 | + | 9.44366i | 0.606452 | + | 0.834709i | ||||
\(129\) | 7.89361 | − | 10.8646i | 0.694994 | − | 0.956577i | ||||
\(130\) | 5.56244 | + | 17.1194i | 0.487858 | + | 1.50147i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −13.8413 | − | 7.22588i | −1.20473 | − | 0.628932i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.66207 | + | 7.01991i | 0.831579 | + | 0.604177i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.77919 | + | 20.8642i | −0.579186 | + | 1.78255i | 0.0422769 | + | 0.999106i | \(0.486539\pi\) |
−0.621463 | + | 0.783444i | \(0.713461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4490 | + | 18.5109i | 1.14073 | + | 1.57008i | 0.765874 | + | 0.642991i | \(0.222307\pi\) |
0.374853 | + | 0.927084i | \(0.377693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.57059 | + | 10.9891i | 0.300698 | + | 0.925453i | ||||
\(142\) | − | 10.6899i | − | 0.897074i | ||||||
\(143\) | 11.7919 | + | 1.98747i | 0.986092 | + | 0.166200i | ||||
\(144\) | −6.14511 | −0.512092 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.80881 | + | 7.12652i | −0.809017 | + | 0.587785i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.9477 | − | 6.15649i | −1.55226 | − | 0.504359i | −0.597531 | − | 0.801846i | \(-0.703852\pi\) |
−0.954726 | + | 0.297487i | \(0.903852\pi\) | |||||||
\(150\) | −0.625299 | − | 0.860650i | −0.0510554 | − | 0.0702718i | ||||
\(151\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −16.1433 | + | 5.24529i | −1.29250 | + | 0.419959i | ||||
\(157\) | 18.7201 | + | 13.6010i | 1.49403 | + | 1.08548i | 0.972685 | + | 0.232129i | \(0.0745691\pi\) |
0.521344 | + | 0.853347i | \(0.325431\pi\) | |||||||
\(158\) | 25.1999 | − | 18.3088i | 2.00480 | − | 1.45657i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.5443 | + | 5.37558i | 1.30794 | + | 0.424977i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.4906 | + | 15.8154i | −0.902785 | + | 1.24258i | ||||
\(163\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(164\) | − | 21.2659i | − | 1.66059i | ||||||
\(165\) | −13.0607 | + | 1.93633i | −1.01677 | + | 0.150743i | ||||
\(166\) | −38.9526 | −3.02331 | ||||||||
\(167\) | 24.2443 | − | 7.87744i | 1.87608 | − | 0.609575i | 0.887087 | − | 0.461602i | \(-0.152725\pi\) |
0.988991 | − | 0.147973i | \(-0.0472749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5172 | − | 7.64121i | 0.809017 | − | 0.587785i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.3871 | − | 17.0494i | −0.944508 | − | 1.30000i | ||||
\(173\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.85115 | − | 4.75608i | 0.365669 | − | 0.358503i | ||||
\(177\) | 8.99216 | 0.675892 | ||||||||
\(178\) | −37.9425 | + | 12.3283i | −2.84391 | + | 0.924043i | ||||
\(179\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(180\) | 15.1623 | − | 11.0160i | 1.13013 | − | 0.821086i | ||||
\(181\) | 7.03726 | − | 21.6584i | 0.523075 | − | 1.60986i | −0.245016 | − | 0.969519i | \(-0.578793\pi\) |
0.768091 | − | 0.640341i | \(-0.221207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.1478 | − | 15.3436i | −0.824068 | − | 1.13423i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 18.1322 | 1.32243 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(192\) | −6.60634 | + | 20.3322i | −0.476771 | + | 1.46735i | ||||
\(193\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.43688 | + | 11.6124i | −0.604177 | + | 0.831579i | ||||
\(196\) | 5.87943 | + | 18.0950i | 0.419959 | + | 1.29250i | ||||
\(197\) | 18.9032i | 1.34680i | 0.739278 | + | 0.673400i | \(0.235167\pi\) | ||||
−0.739278 | + | 0.673400i | \(0.764833\pi\) | |||||||
\(198\) | −3.16950 | − | 21.3785i | −0.225246 | − | 1.51930i | ||||
\(199\) | 21.2096 | 1.50351 | 0.751754 | − | 0.659443i | \(-0.229208\pi\) | ||||
0.751754 | + | 0.659443i | \(0.229208\pi\) | |||||||
\(200\) | −0.419429 | + | 0.136281i | −0.0296581 | + | 0.00963649i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.5701 | − | 14.5485i | −0.738249 | − | 1.01611i | ||||
\(206\) | 25.8994 | − | 35.6474i | 1.80449 | − | 2.48367i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 7.38550i | − | 0.512092i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.1300 | + | 7.84031i | −1.66118 | + | 0.539749i | −0.981118 | − | 0.193409i | \(-0.938046\pi\) |
−0.680058 | + | 0.733158i | \(0.738046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.89621 | − | 5.01039i | 0.472520 | − | 0.343306i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.9486 | − | 5.50693i | −1.15588 | − | 0.375570i | ||||
\(216\) | 4.76348 | + | 6.55637i | 0.324114 | + | 0.446104i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.44360 | + | 20.4314i | −0.232168 | + | 1.37749i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.262139 | − | 0.806781i | 0.0174759 | − | 0.0537854i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5338 | − | 21.3804i | −1.03101 | − | 1.41907i | −0.904184 | − | 0.427143i | \(-0.859520\pi\) |
−0.126828 | − | 0.991925i | \(-0.540480\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(234\) | −19.0078 | − | 13.8099i | −1.24258 | − | 0.902785i | ||||
\(235\) | 12.4047 | − | 9.01252i | 0.809192 | − | 0.587912i | ||||
\(236\) | 4.36054 | − | 13.4204i | 0.283847 | − | 0.873591i | ||||
\(237\) | 23.6226 | + | 7.67544i | 1.53445 | + | 0.498574i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.798759 | − | 1.09940i | 0.0516674 | − | 0.0711141i | −0.782402 | − | 0.622774i | \(-0.786005\pi\) |
0.834069 | + | 0.551660i | \(0.186005\pi\) | |||||||
\(240\) | 2.51989 | + | 7.75543i | 0.162658 | + | 0.500611i | ||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 19.0482 | + | 14.4238i | 1.22447 | + | 0.927198i | ||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | −28.3054 | + | 9.19699i | −1.81207 | + | 0.588777i | ||||
\(245\) | 13.0163 | + | 9.45687i | 0.831579 | + | 0.604177i | ||||
\(246\) | 23.8138 | − | 17.3018i | 1.51831 | − | 1.10312i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.2572 | − | 25.1289i | −1.15701 | − | 1.59248i | ||||
\(250\) | 13.8426 | − | 19.0527i | 0.875482 | − | 1.20500i | ||||
\(251\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.23007 | −0.202673 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.541336 | + | 0.393304i | 0.0338335 | + | 0.0245815i | ||||
\(257\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(258\) | 9.01405 | − | 27.7424i | 0.561190 | − | 1.72717i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.2396 | + | 18.2228i | 0.821086 | + | 1.13013i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | −8.83483 | − | 1.48906i | −0.543746 | − | 0.0916453i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.7370 | − | 18.6990i | −1.57508 | − | 1.14436i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(270\) | 24.6717 | + | 8.01633i | 1.50147 | + | 0.487858i | ||||
\(271\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 47.6514i | 2.87873i | ||||||||
\(275\) | 0.417477 | + | 0.839785i | 0.0251748 | + | 0.0506409i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.7574 | + | 7.71924i | −1.42744 | + | 0.463804i | −0.917959 | − | 0.396676i | \(-0.870164\pi\) |
−0.509484 | + | 0.860480i | \(0.670164\pi\) | |||||||
\(278\) | 40.2076 | + | 29.2125i | 2.41149 | + | 1.75205i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.66582 | − | 1.19110i | −0.218685 | − | 0.0710550i | 0.197626 | − | 0.980278i | \(-0.436677\pi\) |
−0.416310 | + | 0.909223i | \(0.636677\pi\) | |||||||
\(282\) | 14.7522 | + | 20.3047i | 0.878481 | + | 1.20912i | ||||
\(283\) | −4.44329 | + | 6.11566i | −0.264126 | + | 0.363538i | −0.920396 | − | 0.390988i | \(-0.872133\pi\) |
0.656270 | + | 0.754526i | \(0.272133\pi\) | |||||||
\(284\) | −4.13360 | − | 12.7219i | −0.245284 | − | 0.754907i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 25.6937 | − | 3.80926i | 1.51930 | − | 0.225246i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −21.5943 | + | 7.01643i | −1.27246 | + | 0.413447i | ||||
\(289\) | 13.7533 | + | 9.99235i | 0.809017 | + | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.2106 | + | 22.3120i | 0.947034 | + | 1.30348i | 0.952832 | + | 0.303498i | \(0.0981545\pi\) |
−0.00579779 | + | 0.999983i | \(0.501846\pi\) | |||||||
\(294\) | −15.4795 | + | 21.3057i | −0.902785 | + | 1.24258i | ||||
\(295\) | −3.68737 | − | 11.3486i | −0.214687 | − | 0.660738i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.3060 | − | 12.0649i | 0.714069 | − | 0.700075i | ||||
\(298\) | −43.2744 | −2.50682 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.07696 | − | 0.782459i | −0.0621785 | − | 0.0451753i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.7931 | + | 20.3609i | −0.847049 | + | 1.16586i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.1359 | 1.99881 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(312\) | −7.87977 | + | 5.72499i | −0.446104 | + | 0.324114i | ||||
\(313\) | 9.97005 | − | 30.6847i | 0.563540 | − | 1.73440i | −0.108708 | − | 0.994074i | \(-0.534671\pi\) |
0.672249 | − | 0.740325i | \(-0.265329\pi\) | |||||||
\(314\) | 47.8011 | + | 15.5315i | 2.69757 | + | 0.876494i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.9105 | − | 31.5335i | 1.28881 | − | 1.77390i | ||||
\(317\) | 9.89558 | + | 30.4555i | 0.555791 | + | 1.71055i | 0.693844 | + | 0.720125i | \(0.255916\pi\) |
−0.138053 | + | 0.990425i | \(0.544084\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 28.3693 | 1.58589 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.55926 | + | 23.2650i | −0.419959 | + | 1.29250i | ||||
\(325\) | 0.969630 | + | 0.315052i | 0.0537854 | + | 0.0174759i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.77083 | − | 11.6054i | −0.208209 | − | 0.640801i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −25.6810 | + | 12.7666i | −1.41369 | + | 0.702779i | ||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | −46.3571 | + | 15.0624i | −2.54418 | + | 0.826654i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 44.7962 | − | 32.5463i | 2.45114 | − | 1.78086i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4219 | − | 14.3446i | −0.567720 | − | 0.781399i | 0.424563 | − | 0.905399i | \(-0.360428\pi\) |
−0.992282 | + | 0.123999i | \(0.960428\pi\) | |||||||
\(338\) | 16.5975 | − | 22.8445i | 0.902785 | − | 1.24258i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.78313 | − | 7.10786i | −0.527471 | − | 0.383230i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 18.7350i | − | 1.00000i | ||||||
\(352\) | 11.6168 | − | 22.2522i | 0.619179 | − | 1.18605i | ||||
\(353\) | −24.0608 | −1.28063 | −0.640314 | − | 0.768114i | \(-0.721196\pi\) | ||||
−0.640314 | + | 0.768114i | \(0.721196\pi\) | |||||||
\(354\) | 18.5759 | − | 6.03569i | 0.987300 | − | 0.320793i | ||||
\(355\) | −9.15125 | − | 6.64877i | −0.485698 | − | 0.352880i | ||||
\(356\) | −40.3879 | + | 29.3435i | −2.14056 | + | 1.55521i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.23226 | + | 1.69606i | 0.0650361 | + | 0.0895145i | 0.840296 | − | 0.542128i | \(-0.182381\pi\) |
−0.775260 | + | 0.631642i | \(0.782381\pi\) | |||||||
\(360\) | 6.32113 | − | 8.70028i | 0.333153 | − | 0.458545i | ||||
\(361\) | −5.87132 | − | 18.0701i | −0.309017 | − | 0.951057i | ||||
\(362\) | − | 49.4654i | − | 2.59984i | ||||||
\(363\) | −0.377040 | + | 19.0488i | −0.0197895 | + | 0.999804i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −33.3279 | − | 24.2141i | −1.74208 | − | 1.26569i | ||||
\(367\) | −30.8302 | + | 22.3994i | −1.60932 | + | 1.16924i | −0.743751 | + | 0.668457i | \(0.766955\pi\) |
−0.865572 | + | 0.500785i | \(0.833045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.3233 | + | 7.25327i | 1.16210 | + | 0.377590i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.3141i | 1.93205i | 0.258446 | + | 0.966026i | \(0.416790\pi\) | ||||
−0.258446 | + | 0.966026i | \(0.583210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.7793 | 0.969757 | ||||||||
\(376\) | 9.89526 | − | 3.21516i | 0.510309 | − | 0.165809i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.51395 | − | 2.08377i | −0.0775619 | − | 0.106755i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.74548 | − | 26.9158i | −0.446873 | − | 1.37533i | −0.880416 | − | 0.474202i | \(-0.842737\pi\) |
0.433543 | − | 0.901133i | \(-0.357263\pi\) | |||||||
\(384\) | 20.2182i | 1.03176i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.1220 | − | 7.18787i | 1.12452 | − | 0.365380i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(390\) | −9.63442 | + | 29.6517i | −0.487858 | + | 1.50147i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 6.41713 | + | 8.83242i | 0.324114 | + | 0.446104i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.6882 | + | 39.0502i | 0.639221 | + | 1.96732i | ||||
\(395\) | − | 32.9603i | − | 1.65841i | ||||||
\(396\) | −12.0387 | − | 24.2168i | −0.604968 | − | 1.21694i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 43.8146 | − | 14.2362i | 2.19623 | − | 0.713598i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.468591 | − | 0.340451i | 0.0234295 | − | 0.0170226i | ||||
\(401\) | −12.3560 | + | 38.0278i | −0.617028 | + | 1.89902i | −0.254267 | + | 0.967134i | \(0.581834\pi\) |
−0.362761 | + | 0.931882i | \(0.618166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.39228 | + | 19.6734i | 0.317635 | + | 0.977579i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(410\) | −31.6009 | − | 22.9594i | −1.56066 | − | 1.13388i | ||||
\(411\) | −30.7407 | + | 22.3344i | −1.51633 | + | 1.10168i | ||||
\(412\) | 17.0383 | − | 52.4386i | 0.839418 | − | 2.58346i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.2273 | + | 33.3460i | −1.18927 | + | 1.63689i | ||||
\(416\) | −8.43269 | − | 25.9532i | −0.413447 | − | 1.27246i | ||||
\(417\) | 39.6306i | 1.94072i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(422\) | −44.5850 | + | 32.3929i | −2.17036 | + | 1.57686i | ||||
\(423\) | −6.18444 | + | 19.0338i | −0.300698 | + | 0.925453i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.8831 | − | 14.9793i | 0.527287 | − | 0.725748i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.5002 | + | 14.7900i | 0.700075 | + | 0.714069i | ||||
\(430\) | −38.7086 | −1.86670 | ||||||||
\(431\) | −39.4464 | + | 12.8169i | −1.90007 | + | 0.617369i | −0.935702 | + | 0.352791i | \(0.885233\pi\) |
−0.964364 | + | 0.264578i | \(0.914767\pi\) | |||||||
\(432\) | −8.61088 | − | 6.25617i | −0.414291 | − | 0.301000i | ||||
\(433\) | −30.7491 | + | 22.3405i | −1.47771 | + | 1.07362i | −0.499422 | + | 0.866359i | \(0.666454\pi\) |
−0.978286 | + | 0.207259i | \(0.933546\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.6160i | − | 1.60441i | −0.597052 | − | 0.802203i | \(-0.703661\pi\) | ||
0.597052 | − | 0.802203i | \(-0.296339\pi\) | |||||||
\(440\) | 1.74358 | + | 11.7606i | 0.0831221 | + | 0.560665i | ||||
\(441\) | −21.0000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.0453 | + | 40.1492i | −0.618404 | + | 1.90325i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.2829 | − | 27.9170i | −0.959348 | − | 1.32043i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.0247 | + | 33.9304i | 0.520286 | + | 1.60127i | 0.773454 | + | 0.633853i | \(0.218527\pi\) |
−0.253168 | + | 0.967422i | \(0.581473\pi\) | |||||||
\(450\) | − | 1.84259i | − | 0.0868607i | ||||||
\(451\) | −23.2365 | + | 11.5514i | −1.09416 | + | 0.543934i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −46.4404 | − | 33.7410i | −2.17956 | − | 1.58354i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 34.9272i | − | 1.62672i | −0.581758 | − | 0.813362i | \(-0.697635\pi\) | ||
0.581758 | − | 0.813362i | \(-0.302365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(468\) | −27.9611 | − | 9.08510i | −1.29250 | − | 0.419959i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19.5761 | − | 26.9442i | 0.902980 | − | 1.24284i | ||||
\(471\) | 12.3849 | + | 38.1169i | 0.570668 | + | 1.75634i | ||||
\(472\) | − | 8.09706i | − | 0.372697i | ||||||
\(473\) | −11.9007 | + | 22.7959i | −0.547194 | + | 1.04816i | ||||
\(474\) | 53.9513 | 2.47806 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.912137 | − | 2.80727i | 0.0417202 | − | 0.128401i | ||||
\(479\) | 3.05803 | + | 0.993613i | 0.139725 | + | 0.0453993i | 0.378045 | − | 0.925787i | \(-0.376597\pi\) |
−0.238320 | + | 0.971187i | \(0.576597\pi\) | |||||||
\(480\) | 17.7102 | + | 24.3759i | 0.808354 | + | 1.11260i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.2466 | + | 9.80000i | 1.28394 | + | 0.445455i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −32.2025 | + | 10.4632i | −1.46074 | + | 0.474622i | ||||
\(487\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(488\) | −13.8163 | + | 10.0381i | −0.625433 | + | 0.454403i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 33.2365 | + | 10.7992i | 1.50147 | + | 0.487858i | ||||
\(491\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(492\) | 21.6503 | − | 29.7991i | 0.976071 | − | 1.34345i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.2727 | − | 10.5835i | −0.911192 | − | 0.475691i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −54.5826 | − | 39.6566i | −2.44591 | − | 1.77706i | ||||
\(499\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(500\) | 9.10657 | − | 28.0271i | 0.407258 | − | 1.25341i | ||||
\(501\) | 41.9923 | + | 13.6441i | 1.87608 | + | 0.609575i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.5167 | 1.00000 | ||||||||
\(508\) | −3.84408 | + | 1.24902i | −0.170553 | + | 0.0554161i | ||||
\(509\) | 13.0242 | + | 9.46264i | 0.577288 | + | 0.419424i | 0.837745 | − | 0.546061i | \(-0.183873\pi\) |
−0.260457 | + | 0.965485i | \(0.583873\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.8211 | − | 6.76518i | −0.920171 | − | 0.298982i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.4080 | − | 44.3432i | −0.634892 | − | 1.95400i | ||||
\(516\) | − | 36.5016i | − | 1.60689i | ||||||
\(517\) | −9.84921 | − | 19.8124i | −0.433168 | − | 0.871349i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.4564 | + | 7.59705i | 0.458545 | + | 0.333153i | ||||
\(521\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.8787 | − | 3.85962i | −0.519419 | − | 0.168769i | 0.0375627 | − | 0.999294i | \(-0.488041\pi\) |
−0.556982 | + | 0.830525i | \(0.688041\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 11.6398 | − | 1.72567i | 0.506555 | − | 0.0751001i | ||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6003 | + | 9.15469i | 0.546808 | + | 0.397280i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.71735 | + | 26.8292i | −0.377590 | + | 1.16210i | ||||
\(534\) | −65.7184 | − | 21.3532i | −2.84391 | − | 0.924043i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5781 | − | 16.2532i | 0.714069 | − | 0.700075i | ||||
\(540\) | 32.4614 | 1.39692 | ||||||||
\(541\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.9109 | − | 23.1846i | 1.36943 | − | 0.994948i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.84659 | − | 12.1763i | 0.378253 | − | 0.520620i | −0.576868 | − | 0.816838i | \(-0.695725\pi\) |
0.955121 | + | 0.296217i | \(0.0957252\pi\) | |||||||
\(548\) | 18.4261 | + | 56.7096i | 0.787122 | + | 2.42251i | ||||
\(549\) | − | 32.8496i | − | 1.40199i | ||||||
\(550\) | 1.42610 | + | 1.45460i | 0.0608090 | + | 0.0620245i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −43.8965 | + | 31.8927i | −1.86499 | + | 1.35499i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 59.1468 | + | 19.2180i | 2.50838 | + | 0.815023i | ||||
\(557\) | −6.57984 | − | 9.05637i | −0.278797 | − | 0.383731i | 0.646538 | − | 0.762882i | \(-0.276216\pi\) |
−0.925335 | + | 0.379151i | \(0.876216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.63874 | + | 26.5873i | 0.365380 | + | 1.12452i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.37232 | −0.353165 | ||||||||
\(563\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(564\) | 25.4080 | + | 18.4600i | 1.06987 | + | 0.777305i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.07398 | + | 15.6161i | −0.213275 | + | 0.656393i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.51164 | − | 6.20974i | −0.189304 | − | 0.260555i | ||||
\(569\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.8444i | 1.20710i | 0.797325 | + | 0.603550i | \(0.206248\pi\) | ||||
−0.797325 | + | 0.603550i | \(0.793752\pi\) | |||||||
\(572\) | 29.1049 | − | 14.4687i | 1.21694 | − | 0.604968i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −29.9569 | + | 21.7650i | −1.24820 | + | 0.906873i | ||||
\(577\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(578\) | 35.1185 | + | 11.4107i | 1.46074 | + | 0.474622i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −23.6445 | + | 7.68256i | −0.977579 | + | 0.317635i | ||||
\(586\) | 48.4640 | + | 35.2111i | 2.00203 | + | 1.45456i | ||||
\(587\) | 33.7000 | − | 24.4845i | 1.39095 | − | 1.01058i | 0.395189 | − | 0.918600i | \(-0.370679\pi\) |
0.995760 | − | 0.0919844i | \(-0.0293210\pi\) | |||||||
\(588\) | −10.1835 | + | 31.3415i | −0.419959 | + | 1.29250i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −15.2347 | − | 20.9687i | −0.627202 | − | 0.863269i | ||||
\(591\) | −19.2449 | + | 26.4883i | −0.791630 | + | 1.08958i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.3972i | 1.16613i | 0.812425 | + | 0.583066i | \(0.198147\pi\) | ||||
−0.812425 | + | 0.583066i | \(0.801853\pi\) | |||||||
\(594\) | 17.3236 | − | 33.1836i | 0.710795 | − | 1.36154i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −51.5005 | + | 16.7335i | −2.10954 | + | 0.685432i | ||||
\(597\) | 29.7201 | + | 21.5929i | 1.21636 | + | 0.883740i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(600\) | −0.726472 | − | 0.236045i | −0.0296581 | − | 0.00963649i | ||||
\(601\) | −20.1845 | − | 27.7816i | −0.823344 | − | 1.13324i | −0.989126 | − | 0.147074i | \(-0.953015\pi\) |
0.165781 | − | 0.986163i | \(-0.446985\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.1952 | − | 7.33541i | 0.983674 | − | 0.298227i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.7187 | − | 15.1798i | 1.89625 | − | 0.616131i | 0.923894 | − | 0.382649i | \(-0.124988\pi\) |
0.972361 | − | 0.233481i | \(-0.0750118\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.8928 | + | 51.9908i | −0.683971 | + | 2.10505i | ||||
\(611\) | −22.8757 | − | 7.43278i | −0.925453 | − | 0.300698i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 31.1474i | − | 1.25598i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.17142 | −0.0471595 | −0.0235798 | − | 0.999722i | \(-0.507506\pi\) | ||||
−0.0235798 | + | 0.999722i | \(0.507506\pi\) | |||||||
\(618\) | 72.5834 | − | 23.5838i | 2.91973 | − | 0.948679i | ||||
\(619\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.51898 | − | 10.3490i | 0.301000 | − | 0.414291i | ||||
\(625\) | −8.13762 | − | 25.0450i | −0.325505 | − | 1.00180i | ||||
\(626\) | − | 70.0802i | − | 2.80097i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 62.8935 | 2.50972 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(632\) | 6.91141 | − | 21.2711i | 0.274921 | − | 0.846120i | ||||
\(633\) | −41.7944 | − | 13.5798i | −1.66118 | − | 0.539749i | ||||
\(634\) | 40.8844 | + | 56.2726i | 1.62373 | + | 2.23487i | ||||
\(635\) | −2.00900 | + | 2.76516i | −0.0797249 | + | 0.109732i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 25.2389i | − | 1.00000i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.7643 | 0.584067 | ||||||||
\(640\) | 25.5164 | − | 8.29079i | 1.00862 | − | 0.327722i | ||||
\(641\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.1429 | − | 24.9716i | −0.714376 | − | 0.983254i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(648\) | 14.0367i | 0.551415i | ||||||||
\(649\) | −17.0325 | + | 2.52518i | −0.668585 | + | 0.0991219i | ||||
\(650\) | 2.21452 | 0.0868607 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.42013 | + | 12.9657i | 0.367794 | + | 0.506226i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | −25.6261 | + | 25.1239i | −0.997494 | + | 0.977946i | ||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.6275 | + | 16.4399i | −0.878119 | + | 0.637991i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 40.7264 | − | 56.0551i | 1.57575 | − | 2.16884i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.4244 | + | 25.9326i | 0.981497 | + | 1.00112i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.3460 | − | 8.88525i | 1.05411 | − | 0.342501i | 0.269830 | − | 0.962908i | \(-0.413032\pi\) |
0.784280 | + | 0.620407i | \(0.213032\pi\) | |||||||
\(674\) | −31.1579 | − | 22.6375i | −1.20016 | − | 0.871966i | ||||
\(675\) | 1.18869 | − | 0.863632i | 0.0457526 | − | 0.0332412i | ||||
\(676\) | 10.9189 | − | 33.6050i | 0.419959 | − | 1.29250i | ||||
\(677\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 45.7740i | − | 1.75406i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −51.3398 | −1.96446 | −0.982231 | − | 0.187674i | \(-0.939905\pi\) | ||||
−0.982231 | + | 0.187674i | \(0.939905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.7928 | + | 29.6377i | 1.55861 | + | 1.13240i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.1047 | + | 4.90780i | 0.575860 | + | 0.187108i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 50.0158 | − | 16.2511i | 1.89721 | − | 0.616440i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(702\) | −12.5752 | − | 38.7026i | −0.474622 | − | 1.46074i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 6.80371 | − | 40.3675i | 0.256424 | − | 1.52141i | ||||
\(705\) | 26.5576 | 1.00022 | ||||||||
\(706\) | −49.7046 | + | 16.1500i | −1.87066 | + | 0.607814i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 19.7732 | − | 14.3660i | 0.743121 | − | 0.539909i | ||||
\(709\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(710\) | −23.3673 | − | 7.59251i | −0.876961 | − | 0.284942i | ||||
\(711\) | 25.2872 | + | 34.8048i | 0.948343 | + | 1.30528i | ||||
\(712\) | −16.8377 | + | 23.1751i | −0.631018 | + | 0.868522i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.7197 | − | 24.3648i | 0.475691 | − | 0.911192i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.23854 | − | 0.727344i | 0.0835997 | − | 0.0271632i | ||||
\(718\) | 3.68401 | + | 2.67659i | 0.137486 | + | 0.0998895i | ||||
\(719\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(720\) | −4.36458 | + | 13.4328i | −0.162658 | + | 0.500611i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.2579 | − | 33.3881i | −0.902785 | − | 1.24258i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.1275 | − | 58.8683i | −0.710867 | − | 2.18782i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.0070 | + | 39.6040i | 0.445622 | + | 1.46984i | ||||
\(727\) | −2.34066 | −0.0868103 | −0.0434052 | − | 0.999058i | \(-0.513821\pi\) | ||||
−0.0434052 | + | 0.999058i | \(0.513821\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.8435 | − | 15.8702i | −0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −49.0265 | − | 15.9297i | −1.81207 | − | 0.588777i | ||||
\(733\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(734\) | −48.6539 | + | 66.9664i | −1.79585 | + | 2.47177i | ||||
\(735\) | 8.61136 | + | 26.5030i | 0.317635 | + | 0.977579i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 50.9838 | 1.87674 | ||||||||
\(739\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.6652 | + | 15.4874i | 1.74867 | + | 0.568177i | 0.995929 | − | 0.0901418i | \(-0.0287320\pi\) |
0.752739 | + | 0.658319i | \(0.228732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.9153 | + | 37.0458i | −0.986102 | + | 1.35725i | ||||
\(746\) | 25.0459 | + | 77.0832i | 0.916994 | + | 2.82222i | ||||
\(747\) | − | 53.7994i | − | 1.96842i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 38.7941 | − | 12.6050i | 1.41656 | − | 0.460268i | ||||
\(751\) | −8.36230 | − | 6.07557i | −0.305145 | − | 0.221701i | 0.424666 | − | 0.905350i | \(-0.360392\pi\) |
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | −11.0551 | + | 8.03200i | −0.403138 | + | 0.292897i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5660 | − | 44.8294i | −0.529409 | − | 1.62935i | −0.755429 | − | 0.655230i | \(-0.772572\pi\) |
0.226021 | − | 0.974122i | \(-0.427428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.4810 | + | 3.40548i | −0.379935 | + | 0.123448i | −0.492757 | − | 0.870167i | \(-0.664011\pi\) |
0.112822 | + | 0.993615i | \(0.464011\pi\) | |||||||
\(762\) | −4.52616 | − | 3.28845i | −0.163966 | − | 0.119128i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.1327 | − | 49.7324i | −1.30553 | − | 1.79690i | ||||
\(767\) | −11.0026 | + | 15.1437i | −0.397280 | + | 0.546808i | ||||
\(768\) | 0.358140 | + | 1.10224i | 0.0129233 | + | 0.0397737i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.8442 | + | 32.5813i | 1.61294 | + | 1.17187i | 0.853093 | + | 0.521758i | \(0.174724\pi\) |
0.759842 | + | 0.650108i | \(0.225276\pi\) | |||||||
\(774\) | 40.8748 | − | 29.6973i | 1.46922 | − | 1.06745i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 39.0137i | 1.39692i | ||||||||
\(781\) | −11.6554 | + | 11.4270i | −0.417064 | + | 0.408891i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11.6002 | − | 8.42800i | −0.414291 | − | 0.301000i | ||||
\(785\) | 43.0268 | − | 31.2608i | 1.53569 | − | 1.11575i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(788\) | 30.2002 | + | 41.5670i | 1.07584 | + | 1.48076i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.1235 | − | 68.0892i | −0.787119 | − | 2.42250i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.8639 | − | 11.0811i | −0.386032 | − | 0.393749i | ||||
\(793\) | 39.4803 | 1.40199 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 46.6385 | − | 33.8848i | 1.65306 | − | 1.20102i | ||||
\(797\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.25794 | − | 1.73140i | 0.0444748 | − | 0.0612143i | ||||
\(801\) | −17.0272 | − | 52.4043i | −0.601626 | − | 1.85162i | ||||
\(802\) | 86.8510i | 3.06682i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(810\) | 26.4102 | + | 36.3506i | 0.927961 | + | 1.27723i | ||||
\(811\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −46.4860 | − | 15.1042i | −1.62336 | − | 0.527462i | ||||
\(821\) | −32.0122 | − | 44.0610i | −1.11723 | − | 1.53774i | −0.810306 | − | 0.586007i | \(-0.800699\pi\) |
−0.306928 | − | 0.951733i | \(-0.599301\pi\) | |||||||
\(822\) | −48.5127 | + | 66.7720i | −1.69207 | + | 2.32894i | ||||
\(823\) | −1.67681 | − | 5.16068i | −0.0584498 | − | 0.179890i | 0.917569 | − | 0.397577i | \(-0.130149\pi\) |
−0.976019 | + | 0.217687i | \(0.930149\pi\) | |||||||
\(824\) | − | 31.6384i | − | 1.10217i | ||||||
\(825\) | −0.269971 | + | 1.60178i | −0.00939917 | + | 0.0557668i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.7586 | − | 17.4672i | 1.86937 | − | 0.607395i | 0.877596 | − | 0.479401i | \(-0.159146\pi\) |
0.991775 | − | 0.127995i | \(-0.0408540\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.7668 | + | 33.2515i | −1.58955 | + | 1.15487i | −0.684964 | + | 0.728577i | \(0.740182\pi\) |
−0.904584 | + | 0.426296i | \(0.859818\pi\) | |||||||
\(830\) | −27.6662 | + | 85.1478i | −0.960308 | + | 2.95552i | ||||
\(831\) | −41.1490 | − | 13.3701i | −1.42744 | − | 0.463804i | ||||
\(832\) | −26.1582 | − | 36.0037i | −0.906873 | − | 1.24820i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 26.6007 | + | 81.8687i | 0.921108 | + | 2.83488i | ||||
\(835\) | − | 58.5914i | − | 2.02764i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.6964 | − | 28.8411i | −1.37047 | − | 0.995707i | −0.997700 | − | 0.0677843i | \(-0.978407\pi\) |
−0.372773 | − | 0.927923i | \(-0.621593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96149 | + | 27.5806i | −0.309017 | + | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.92414 | − | 5.40112i | −0.135155 | − | 0.186024i | ||||
\(844\) | −40.5344 | + | 55.7908i | −1.39525 | + | 1.92040i | ||||
\(845\) | −9.23329 | − | 28.4171i | −0.317635 | − | 0.977579i | ||||
\(846\) | 43.4709i | 1.49456i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.4524 | + | 4.04602i | −0.427365 | + | 0.138859i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 7.15961 | − | 22.0350i | 0.245284 | − | 0.754907i | ||||
\(853\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 39.8817 | + | 20.8204i | 1.36154 | + | 0.710795i | ||||
\(859\) | −42.3162 | −1.44381 | −0.721905 | − | 0.691992i | \(-0.756733\pi\) | ||||
−0.721905 | + | 0.691992i | \(0.756733\pi\) | |||||||
\(860\) | −46.0668 | + | 14.9680i | −1.57086 | + | 0.510405i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −72.8852 | + | 52.9542i | −2.48248 | + | 1.80363i | ||||
\(863\) | 5.53688 | − | 17.0408i | 0.188478 | − | 0.580074i | −0.811513 | − | 0.584334i | \(-0.801356\pi\) |
0.999991 | + | 0.00425952i | \(0.00135585\pi\) | |||||||
\(864\) | −37.4025 | − | 12.1528i | −1.27246 | − | 0.413447i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −48.5260 | + | 66.7903i | −1.64898 | + | 2.26963i | ||||
\(867\) | 9.09896 | + | 28.0037i | 0.309017 | + | 0.951057i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −46.9002 | − | 7.90476i | −1.59098 | − | 0.268150i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(878\) | −22.5636 | − | 69.4437i | −0.761486 | − | 2.34361i | ||||
\(879\) | 47.7685i | 1.61119i | ||||||||
\(880\) | −6.95093 | − | 13.9823i | −0.234316 | − | 0.471344i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −43.3816 | + | 14.0956i | −1.46074 | + | 0.474622i | ||||
\(883\) | 20.2929 | + | 14.7437i | 0.682911 | + | 0.496164i | 0.874322 | − | 0.485346i | \(-0.161306\pi\) |
−0.191411 | + | 0.981510i | \(0.561306\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.38671 | − | 19.6563i | 0.214687 | − | 0.660738i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 91.6960i | 3.07366i | ||||||||
\(891\) | 29.5269 | − | 4.37755i | 0.989188 | − | 0.146653i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −60.6386 | − | 44.0565i | −2.02806 | − | 1.47347i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45.5493 | + | 62.6932i | 1.52000 | + | 2.09210i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.712502 | − | 2.19286i | −0.0237501 | − | 0.0730952i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −40.2483 | + | 39.4595i | −1.34012 | + | 1.31386i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42.3457 | − | 30.7660i | −1.40762 | − | 1.02269i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.3004 | − | 47.0897i | 0.508040 | − | 1.56359i | −0.287559 | − | 0.957763i | \(-0.592844\pi\) |
0.795599 | − | 0.605824i | \(-0.207156\pi\) | |||||||
\(908\) | −68.3155 | − | 22.1970i | −2.26713 | − | 0.736635i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.6387 | + | 42.4710i | 1.37804 | + | 1.40559i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −41.4578 | + | 13.4705i | −1.37055 | + | 0.445320i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.0171 | − | 14.3020i | −1.45199 | − | 0.471780i | −0.526377 | − | 0.850251i | \(-0.676450\pi\) |
−0.925613 | + | 0.378471i | \(0.876450\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.4438 | − | 72.1525i | −0.772079 | − | 2.37621i | ||||
\(923\) | 17.7445i | 0.584067i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 49.2344 | + | 35.7709i | 1.61707 | + | 1.17487i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.2767 | − | 53.1724i | 0.566832 | − | 1.74453i | −0.0956136 | − | 0.995419i | \(-0.530481\pi\) |
0.662445 | − | 0.749110i | \(-0.269519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.8701 | −0.551415 | ||||||||
\(937\) | 58.2035 | − | 18.9115i | 1.90143 | − | 0.617811i | 0.942410 | − | 0.334458i | \(-0.108553\pi\) |
0.959016 | − | 0.283352i | \(-0.0914466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 45.2099 | − | 32.8469i | 1.47537 | − | 1.07192i | ||||
\(940\) | 12.8785 | − | 39.6359i | 0.420050 | − | 1.29278i | ||||
\(941\) | 2.21781 | + | 0.720610i | 0.0722985 | + | 0.0234912i | 0.344943 | − | 0.938624i | \(-0.387898\pi\) |
−0.272644 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(942\) | 51.1695 | + | 70.4287i | 1.66719 | + | 2.29469i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 3.28620 | + | 10.1139i | 0.106957 | + | 0.329179i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.28335 | + | 55.0796i | −0.301828 | + | 1.79079i | ||||
\(947\) | −50.8682 | −1.65300 | −0.826498 | − | 0.562940i | \(-0.809670\pi\) | ||||
−0.826498 | + | 0.562940i | \(0.809670\pi\) | |||||||
\(948\) | 64.2069 | − | 20.8621i | 2.08534 | − | 0.677569i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.1397 | + | 52.7504i | −0.555791 | + | 1.71055i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 3.69361i | − | 0.119460i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.98418 | 0.225649 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 39.7527 | + | 28.8820i | 1.28301 | + | 0.932164i | ||||
\(961\) | −25.0795 | + | 18.2213i | −0.809017 | + | 0.587785i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | 17.1527 | + | 0.339509i | 0.551307 | + | 0.0109122i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(972\) | −34.2780 | + | 24.9044i | −1.09947 | + | 0.798809i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.03796 | + | 1.42862i | 0.0332412 | + | 0.0457526i | ||||
\(976\) | 13.1837 | − | 18.1457i | 0.421998 | − | 0.580831i | ||||
\(977\) | 10.9440 | + | 33.6821i | 0.350128 | + | 1.07758i | 0.958781 | + | 0.284147i | \(0.0917105\pi\) |
−0.608652 | + | 0.793437i | \(0.708289\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.0008 | + | 28.1913i | 1.72587 | + | 0.900998i | ||||
\(980\) | 43.7304 | 1.39692 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.4343 | − | 27.1976i | 1.19397 | − | 0.867470i | 0.200292 | − | 0.979736i | \(-0.435811\pi\) |
0.993678 | + | 0.112267i | \(0.0358110\pi\) | |||||||
\(984\) | 6.53126 | − | 20.1012i | 0.208209 | − | 0.640801i | ||||
\(985\) | 41.3212 | + | 13.4261i | 1.31660 | + | 0.427791i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −48.9831 | − | 8.25582i | −1.55678 | − | 0.262387i | ||||
\(991\) | −30.2350 | −0.960448 | −0.480224 | − | 0.877146i | \(-0.659445\pi\) | ||||
−0.480224 | + | 0.877146i | \(0.659445\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.0642 | − | 46.3628i | 0.477567 | − | 1.46980i | ||||
\(996\) | −80.2929 | − | 26.0888i | −2.54418 | − | 0.826654i | ||||
\(997\) | −31.9172 | − | 43.9303i | −1.01083 | − | 1.39129i | −0.918439 | − | 0.395562i | \(-0.870550\pi\) |
−0.0923886 | − | 0.995723i | \(-0.529450\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 429.2.y.a.116.7 | yes | 32 | |
3.2 | odd | 2 | inner | 429.2.y.a.116.2 | ✓ | 32 | |
11.2 | odd | 10 | inner | 429.2.y.a.233.7 | yes | 32 | |
13.12 | even | 2 | inner | 429.2.y.a.116.2 | ✓ | 32 | |
33.2 | even | 10 | inner | 429.2.y.a.233.2 | yes | 32 | |
39.38 | odd | 2 | CM | 429.2.y.a.116.7 | yes | 32 | |
143.90 | odd | 10 | inner | 429.2.y.a.233.2 | yes | 32 | |
429.233 | even | 10 | inner | 429.2.y.a.233.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.y.a.116.2 | ✓ | 32 | 3.2 | odd | 2 | inner | |
429.2.y.a.116.2 | ✓ | 32 | 13.12 | even | 2 | inner | |
429.2.y.a.116.7 | yes | 32 | 1.1 | even | 1 | trivial | |
429.2.y.a.116.7 | yes | 32 | 39.38 | odd | 2 | CM | |
429.2.y.a.233.2 | yes | 32 | 33.2 | even | 10 | inner | |
429.2.y.a.233.2 | yes | 32 | 143.90 | odd | 10 | inner | |
429.2.y.a.233.7 | yes | 32 | 11.2 | odd | 10 | inner | |
429.2.y.a.233.7 | yes | 32 | 429.233 | even | 10 | inner |