Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(97,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.y (of order \(9\), degree \(6\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 193.9 | ||
Character | \(\chi\) | \(=\) | 864.193 |
Dual form | 864.2.y.c.385.9 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.72098 | + | 0.195544i | 0.993607 | + | 0.112897i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.359864 | − | 2.04089i | 0.160936 | − | 0.912713i | −0.792221 | − | 0.610235i | \(-0.791075\pi\) |
0.953156 | − | 0.302478i | \(-0.0978138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.05212 | + | 1.72193i | −0.775628 | + | 0.650829i | −0.942143 | − | 0.335210i | \(-0.891193\pi\) |
0.166516 | + | 0.986039i | \(0.446748\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.92353 | + | 0.673052i | 0.974508 | + | 0.224351i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.982213 | − | 5.57041i | −0.296148 | − | 1.67954i | −0.662498 | − | 0.749064i | \(-0.730504\pi\) |
0.366350 | − | 0.930477i | \(-0.380607\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.917880 | + | 0.334081i | −0.254574 | + | 0.0926574i | −0.466155 | − | 0.884703i | \(-0.654361\pi\) |
0.211581 | + | 0.977360i | \(0.432139\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.01840 | − | 3.44195i | 0.262950 | − | 0.888708i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.69395 | − | 6.39811i | 0.895915 | − | 1.55177i | 0.0632464 | − | 0.997998i | \(-0.479855\pi\) |
0.832668 | − | 0.553772i | \(-0.186812\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.54122 | − | 4.40152i | −0.582996 | − | 1.00978i | −0.995122 | − | 0.0986515i | \(-0.968547\pi\) |
0.412126 | − | 0.911127i | \(-0.364786\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.86836 | + | 2.56213i | −0.844145 | + | 0.559102i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.43554 | + | 4.56096i | 1.13339 | + | 0.951026i | 0.999202 | − | 0.0399300i | \(-0.0127135\pi\) |
0.134186 | + | 0.990956i | \(0.457158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.662742 | + | 0.241218i | 0.132548 | + | 0.0482437i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.89971 | + | 1.72998i | 0.942950 | + | 0.332936i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.14277 | + | 1.50785i | 0.769294 | + | 0.280000i | 0.696701 | − | 0.717362i | \(-0.254650\pi\) |
0.0725929 | + | 0.997362i | \(0.476873\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.954848 | − | 0.801212i | −0.171496 | − | 0.143902i | 0.553000 | − | 0.833181i | \(-0.313483\pi\) |
−0.724496 | + | 0.689279i | \(0.757927\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.601108 | − | 9.77861i | −0.104640 | − | 1.70224i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.77579 | + | 4.80780i | 0.469193 | + | 0.812667i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.29080 | − | 5.69983i | 0.541004 | − | 0.937046i | −0.457843 | − | 0.889033i | \(-0.651378\pi\) |
0.998847 | − | 0.0480131i | \(-0.0152889\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.64498 | + | 0.395460i | −0.263407 | + | 0.0633243i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.43279 | + | 0.521492i | −0.223764 | + | 0.0814434i | −0.451469 | − | 0.892287i | \(-0.649100\pi\) |
0.227705 | + | 0.973730i | \(0.426878\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.751695 | + | 4.26308i | 0.114632 | + | 0.650113i | 0.986932 | + | 0.161140i | \(0.0515171\pi\) |
−0.872299 | + | 0.488973i | \(0.837372\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.42569 | − | 5.72438i | 0.361601 | − | 0.853340i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.06095 | + | 5.08574i | −0.884081 | + | 0.741832i | −0.967014 | − | 0.254723i | \(-0.918016\pi\) |
0.0829332 | + | 0.996555i | \(0.473571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0306027 | − | 0.173557i | 0.00437182 | − | 0.0247938i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.60832 | − | 10.2887i | 1.06538 | − | 1.44070i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.8675 | −1.63013 | −0.815063 | − | 0.579372i | \(-0.803298\pi\) | ||||
−0.815063 | + | 0.579372i | \(0.803298\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.7220 | −1.58060 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.51269 | − | 8.07184i | −0.465267 | − | 1.06914i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.02912 | + | 5.83641i | −0.133980 | + | 0.759836i | 0.841585 | + | 0.540124i | \(0.181623\pi\) |
−0.975565 | + | 0.219712i | \(0.929488\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5213 | − | 9.66749i | 1.47515 | − | 1.23780i | 0.563961 | − | 0.825802i | \(-0.309277\pi\) |
0.911187 | − | 0.411994i | \(-0.135168\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.15837 | + | 3.65293i | −0.901870 | + | 0.460225i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.351510 | + | 1.99351i | 0.0435995 | + | 0.247265i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.83396 | + | 3.57927i | −1.20141 | + | 0.437277i | −0.863716 | − | 0.503979i | \(-0.831869\pi\) |
−0.337694 | + | 0.941256i | \(0.609647\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.46258 | + | 8.91220i | 1.01877 | + | 1.07290i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.838061 | + | 1.45156i | −0.0994595 | + | 0.172269i | −0.911461 | − | 0.411386i | \(-0.865045\pi\) |
0.812002 | + | 0.583655i | \(0.198378\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.01127 | + | 5.21567i | 0.352442 | + | 0.610448i | 0.986677 | − | 0.162693i | \(-0.0520180\pi\) |
−0.634235 | + | 0.773141i | \(0.718685\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.09340 | + | 0.544726i | 0.126254 | + | 0.0628996i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.6075 | + | 9.73983i | 1.32279 | + | 1.10996i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.31076 | − | 1.56899i | −0.484999 | − | 0.176525i | 0.0879359 | − | 0.996126i | \(-0.471973\pi\) |
−0.572935 | + | 0.819601i | \(0.694195\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.09400 | + | 3.93537i | 0.899333 | + | 0.437264i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.6938 | + | 3.89222i | 1.17380 | + | 0.427227i | 0.854007 | − | 0.520262i | \(-0.174166\pi\) |
0.319789 | + | 0.947489i | \(0.396388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.7285 | − | 9.84139i | −1.27214 | − | 1.06745i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.83477 | + | 3.40506i | 0.732764 | + | 0.365061i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.61064 | − | 4.52176i | −0.276727 | − | 0.479305i | 0.693842 | − | 0.720127i | \(-0.255916\pi\) |
−0.970569 | + | 0.240822i | \(0.922583\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30833 | − | 2.26610i | 0.137151 | − | 0.237552i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.48660 | − | 1.56558i | −0.154153 | − | 0.162343i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.89750 | + | 3.60240i | −1.01546 | + | 0.369598i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.66446 | + | 9.43964i | 0.169001 | + | 0.958450i | 0.944843 | + | 0.327523i | \(0.106214\pi\) |
−0.775843 | + | 0.630927i | \(0.782675\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.877652 | − | 16.9463i | 0.0882073 | − | 1.70317i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.135437 | − | 0.113645i | 0.0134765 | − | 0.0113081i | −0.636025 | − | 0.771669i | \(-0.719422\pi\) |
0.649501 | + | 0.760361i | \(0.274978\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.146984 | + | 0.833588i | −0.0144828 | + | 0.0821359i | −0.991192 | − | 0.132429i | \(-0.957722\pi\) |
0.976710 | + | 0.214565i | \(0.0688334\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.83693 | + | 8.81691i | 0.374446 | + | 0.860442i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.25552 | 0.604744 | 0.302372 | − | 0.953190i | \(-0.402222\pi\) | ||||
0.302372 | + | 0.953190i | \(0.402222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.8229 | −1.32400 | −0.661998 | − | 0.749506i | \(-0.730291\pi\) | ||||
−0.661998 | + | 0.749506i | \(0.730291\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.77795 | − | 9.16578i | 0.643335 | − | 0.869978i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.746884 | + | 4.23579i | −0.0702610 | + | 0.398470i | 0.929313 | + | 0.369292i | \(0.120400\pi\) |
−0.999574 | + | 0.0291774i | \(0.990711\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.2645 | − | 9.45201i | 1.05042 | − | 0.881404i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.90830 | + | 0.358913i | −0.268872 | + | 0.0331815i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.43668 | + | 19.4904i | 0.315040 | + | 1.78668i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.7281 | + | 7.18043i | −1.79346 | + | 0.652767i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.56777 | + | 0.617304i | −0.231528 | + | 0.0556604i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.91173 | − | 10.2394i | 0.528761 | − | 0.915841i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.13220 | − | 1.96103i | −0.100466 | − | 0.174013i | 0.811411 | − | 0.584477i | \(-0.198700\pi\) |
−0.911877 | + | 0.410464i | \(0.865367\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.460033 | + | 7.48364i | 0.0405036 | + | 0.658898i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0297 | + | 9.25498i | 0.963665 | + | 0.808611i | 0.981545 | − | 0.191229i | \(-0.0612473\pi\) |
−0.0178801 | + | 0.999840i | \(0.505692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.7940 | + | 4.65663i | 1.10938 | + | 0.403781i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.29393 | − | 9.37720i | 0.455629 | − | 0.807061i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.06490 | − | 2.57141i | −0.603595 | − | 0.219691i | 0.0221035 | − | 0.999756i | \(-0.492964\pi\) |
−0.625698 | + | 0.780065i | \(0.715186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.82890 | − | 7.40833i | −0.748857 | − | 0.628366i | 0.186343 | − | 0.982485i | \(-0.440336\pi\) |
−0.935200 | + | 0.354119i | \(0.884781\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.4252 | + | 7.56727i | −0.962179 | + | 0.637279i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.76252 | + | 4.78483i | 0.231014 | + | 0.400127i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.56818 | − | 7.91232i | 0.379367 | − | 0.657082i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0866045 | − | 0.292703i | 0.00714302 | − | 0.0241417i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.0049 | − | 4.73338i | 1.06540 | − | 0.387774i | 0.250945 | − | 0.968001i | \(-0.419259\pi\) |
0.814454 | + | 0.580228i | \(0.197036\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.05788 | − | 5.99956i | −0.0860894 | − | 0.488237i | −0.997116 | − | 0.0758902i | \(-0.975820\pi\) |
0.911027 | − | 0.412347i | \(-0.135291\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.1056 | − | 16.2188i | 1.22122 | − | 1.31121i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.97880 | + | 1.66041i | −0.158941 | + | 0.133367i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.63950 | + | 9.29808i | −0.130847 | + | 0.742068i | 0.846816 | + | 0.531886i | \(0.178517\pi\) |
−0.977662 | + | 0.210181i | \(0.932595\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.4237 | − | 2.32061i | −1.61970 | − | 0.184037i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.0080 | −1.49804 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.8882 | 1.24446 | 0.622231 | − | 0.782834i | \(-0.286227\pi\) | ||||
0.622231 | + | 0.782834i | \(0.286227\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.1734 | − | 2.29217i | −1.57049 | − | 0.178445i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.78221 | − | 15.7787i | 0.215294 | − | 1.22099i | −0.665102 | − | 0.746753i | \(-0.731612\pi\) |
0.880396 | − | 0.474240i | \(-0.157277\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.22768 | + | 7.74295i | −0.709822 | + | 0.595611i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.46686 | − | 14.5783i | −0.341590 | − | 1.11483i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.54316 | + | 20.0943i | 0.269381 | + | 1.52774i | 0.756262 | + | 0.654269i | \(0.227024\pi\) |
−0.486880 | + | 0.873469i | \(0.661865\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.77539 | + | 0.646188i | −0.134207 | + | 0.0488472i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.91236 | + | 9.84309i | −0.218906 | + | 0.739852i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.63944 | + | 8.03574i | −0.346768 | + | 0.600619i | −0.985673 | − | 0.168666i | \(-0.946054\pi\) |
0.638905 | + | 0.769285i | \(0.279387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.873953 | + | 1.51373i | 0.0649604 | + | 0.112515i | 0.896676 | − | 0.442687i | \(-0.145975\pi\) |
−0.831716 | + | 0.555201i | \(0.812641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.7183 | − | 14.3846i | 1.60546 | − | 1.06334i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.4485 | − | 8.76731i | −0.768187 | − | 0.644585i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −39.2683 | − | 14.2925i | −2.87158 | − | 1.04517i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.0337 | + | 4.88683i | −0.948062 | + | 0.355465i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.418346 | + | 0.152266i | 0.0302705 | + | 0.0110176i | 0.357111 | − | 0.934062i | \(-0.383762\pi\) |
−0.326841 | + | 0.945080i | \(0.605984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8417 | + | 11.6145i | 0.996345 | + | 0.836033i | 0.986474 | − | 0.163918i | \(-0.0524134\pi\) |
0.00987134 | + | 0.999951i | \(0.496858\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.215122 | + | 3.49953i | 0.0154052 | + | 0.250606i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.05477 | + | 1.82691i | 0.0751491 | + | 0.130162i | 0.901151 | − | 0.433505i | \(-0.142723\pi\) |
−0.826002 | + | 0.563667i | \(0.809390\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.46578 | + | 12.9311i | −0.529235 | + | 0.916663i | 0.470183 | + | 0.882569i | \(0.344188\pi\) |
−0.999419 | + | 0.0340939i | \(0.989145\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.6239 | + | 4.23687i | −1.24310 | + | 0.298846i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.0979 | + | 4.03929i | −0.778918 | + | 0.283503i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.548699 | + | 3.11183i | 0.0383228 | + | 0.217339i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.8212 | + | 16.9925i | 0.891133 | + | 1.18106i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.0222 | + | 18.4789i | −1.52331 | + | 1.27821i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.219941 | + | 1.24734i | −0.0151413 | + | 0.0858707i | −0.991442 | − | 0.130548i | \(-0.958326\pi\) |
0.976301 | + | 0.216418i | \(0.0694375\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.72613 | + | 2.33423i | −0.118272 | + | 0.159939i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.97097 | 0.611815 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.33909 | 0.226672 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.16243 | + | 9.56488i | 0.281271 | + | 0.646335i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.25312 | + | 7.10678i | −0.0842937 | + | 0.478053i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.84358 | + | 6.58155i | −0.525245 | + | 0.440733i | −0.866456 | − | 0.499254i | \(-0.833608\pi\) |
0.341211 | + | 0.939987i | \(0.389163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.77519 | + | 1.15127i | 0.118346 | + | 0.0767512i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.399676 | − | 2.26667i | −0.0265274 | − | 0.150444i | 0.968667 | − | 0.248363i | \(-0.0798926\pi\) |
−0.995194 | + | 0.0979187i | \(0.968781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.30042 | + | 1.56522i | −0.284180 | + | 0.103433i | −0.480177 | − | 0.877171i | \(-0.659428\pi\) |
0.195998 | + | 0.980604i | \(0.437205\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0716 | + | 19.0318i | 1.18903 | + | 1.25220i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.376054 | − | 0.651345i | 0.0246361 | − | 0.0426710i | −0.853444 | − | 0.521184i | \(-0.825491\pi\) |
0.878081 | + | 0.478513i | \(0.158824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.19831 | + | 14.1999i | 0.534799 | + | 0.926299i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.11192 | − | 3.54314i | −0.461969 | − | 0.230152i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.67746 | − | 3.08576i | −0.237875 | − | 0.199601i | 0.516055 | − | 0.856555i | \(-0.327400\pi\) |
−0.753930 | + | 0.656954i | \(0.771844\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.9150 | + | 7.24845i | 1.28284 | + | 0.466914i | 0.891369 | − | 0.453278i | \(-0.149746\pi\) |
0.391467 | + | 0.920192i | \(0.371968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.1601 | + | 8.35542i | 0.844218 | + | 0.536000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.343197 | − | 0.124913i | −0.0219260 | − | 0.00798042i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.80300 | + | 3.19109i | 0.241979 | + | 0.203044i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.6427 | + | 8.78953i | 1.11806 | + | 0.557014i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.91693 | − | 6.78433i | −0.247235 | − | 0.428223i | 0.715523 | − | 0.698589i | \(-0.246189\pi\) |
−0.962758 | + | 0.270366i | \(0.912855\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.0675 | − | 34.7580i | 1.26164 | − | 2.18522i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.2601 | − | 19.2302i | −1.14349 | − | 1.20424i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.4314 | − | 9.25629i | 1.58637 | − | 0.577391i | 0.609793 | − | 0.792561i | \(-0.291253\pi\) |
0.976577 | + | 0.215170i | \(0.0690304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.06161 | + | 17.3632i | 0.190239 | + | 1.07890i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.0966 | + | 7.19653i | 0.686865 | + | 0.445454i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5941 | − | 8.88949i | 0.653259 | − | 0.548150i | −0.254799 | − | 0.966994i | \(-0.582009\pi\) |
0.908058 | + | 0.418845i | \(0.137565\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.27068 | + | 24.2202i | −0.262346 | + | 1.48784i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.60865 | − | 8.29233i | −0.220846 | − | 0.507483i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.6670 | 1.07717 | 0.538587 | − | 0.842570i | \(-0.318958\pi\) | ||||
0.538587 | + | 0.842570i | \(0.318958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.6064 | −0.948022 | −0.474011 | − | 0.880519i | \(-0.657194\pi\) | ||||
−0.474011 | + | 0.880519i | \(0.657194\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.69473 | − | 3.64407i | 0.163093 | − | 0.220549i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.692731 | − | 3.92867i | 0.0417732 | − | 0.236908i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.8550 | + | 20.0167i | −1.43331 | + | 1.20269i | −0.489585 | + | 0.871956i | \(0.662852\pi\) |
−0.943724 | + | 0.330734i | \(0.892704\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.25226 | − | 2.98503i | −0.134839 | − | 0.178709i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.44891 | + | 13.8884i | 0.146089 | + | 0.828514i | 0.966486 | + | 0.256719i | \(0.0826416\pi\) |
−0.820397 | + | 0.571795i | \(0.806247\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.543578 | + | 0.197846i | −0.0323124 | + | 0.0117607i | −0.358126 | − | 0.933673i | \(-0.616584\pi\) |
0.325813 | + | 0.945434i | \(0.394362\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.7378 | + | 4.26425i | −1.05070 | + | 0.252592i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.04228 | − | 3.53733i | 0.120552 | − | 0.208802i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.7906 | − | 32.5462i | −1.10533 | − | 1.91448i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.01864 | + | 16.5709i | 0.0597138 | + | 0.971402i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4645 | + | 8.78073i | 0.611341 | + | 0.512976i | 0.895068 | − | 0.445929i | \(-0.147127\pi\) |
−0.283728 | + | 0.958905i | \(0.591571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5411 | + | 4.20062i | 0.671950 | + | 0.244570i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.82416 | − | 28.9926i | 0.279926 | − | 1.68232i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.51290 | − | 2.37050i | −0.376651 | − | 0.137090i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.88329 | − | 7.45396i | −0.512024 | − | 0.429639i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.255306 | − | 0.169097i | 0.0146670 | − | 0.00971435i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.5842 | − | 26.9926i | −0.892348 | − | 1.54559i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.31710 | + | 4.01334i | −0.132244 | + | 0.229053i | −0.924541 | − | 0.381082i | \(-0.875552\pi\) |
0.792297 | + | 0.610135i | \(0.208885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.415959 | + | 1.40584i | −0.0236631 | + | 0.0799757i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.79469 | − | 2.83704i | 0.441996 | − | 0.160874i | −0.111429 | − | 0.993772i | \(-0.535543\pi\) |
0.553425 | + | 0.832899i | \(0.313320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.55347 | + | 14.4815i | 0.144331 | + | 0.818540i | 0.967902 | + | 0.251328i | \(0.0808672\pi\) |
−0.823571 | + | 0.567213i | \(0.808022\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.87918 | + | 15.9240i | 0.274910 | + | 0.897215i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.4637 | + | 17.1711i | −1.14935 | + | 0.964422i | −0.999704 | − | 0.0243167i | \(-0.992259\pi\) |
−0.149650 | + | 0.988739i | \(0.547815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.33023 | − | 24.5580i | 0.242446 | − | 1.37498i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.7656 | + | 1.22323i | 0.600877 | + | 0.0682739i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −37.5486 | −2.08926 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.688904 | −0.0382135 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.7889 | − | 2.70298i | −1.31553 | − | 0.149475i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.68049 | − | 20.8731i | 0.202912 | − | 1.15077i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6199 | − | 8.91116i | 0.583723 | − | 0.489802i | −0.302445 | − | 0.953167i | \(-0.597803\pi\) |
0.886167 | + | 0.463365i | \(0.153358\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.4570 | − | 14.4487i | 0.737440 | − | 0.791785i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.76600 | + | 21.3581i | 0.205759 | + | 1.16692i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.94733 | + | 2.16465i | −0.323972 | + | 0.117916i | −0.498886 | − | 0.866668i | \(-0.666257\pi\) |
0.174914 | + | 0.984584i | \(0.444035\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.11365 | + | 7.14365i | −0.114798 | + | 0.387990i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.52521 | + | 6.10585i | −0.190901 | + | 0.330650i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.13992 | − | 15.8308i | −0.493509 | − | 0.854783i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.2342 | − | 14.0640i | 1.14321 | − | 0.757180i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.7910 | + | 9.05469i | 0.579289 | + | 0.486081i | 0.884714 | − | 0.466135i | \(-0.154354\pi\) |
−0.305424 | + | 0.952216i | \(0.598798\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.38621 | − | 0.868508i | −0.127731 | − | 0.0464902i | 0.277364 | − | 0.960765i | \(-0.410539\pi\) |
−0.405095 | + | 0.914275i | \(0.632761\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.07530 | + | 0.0489812i | −0.270899 | + | 0.00261442i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.55203 | − | 3.47665i | −0.508403 | − | 0.185044i | 0.0750666 | − | 0.997179i | \(-0.476083\pi\) |
−0.583470 | + | 0.812135i | \(0.698305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.66089 | + | 2.23275i | 0.141225 | + | 0.118502i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.10323 | + | 34.2146i | 0.111315 | + | 1.81083i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.171055 | + | 0.296276i | 0.00902793 | + | 0.0156368i | 0.870504 | − | 0.492161i | \(-0.163793\pi\) |
−0.861476 | + | 0.507798i | \(0.830460\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.41559 | + | 5.91598i | −0.179768 | + | 0.311367i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −35.3557 | + | 8.49966i | −1.85569 | + | 0.446116i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.7282 | − | 4.26873i | 0.613884 | − | 0.223435i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.97632 | + | 33.8934i | 0.311962 | + | 1.76922i | 0.588774 | + | 0.808298i | \(0.299611\pi\) |
−0.276812 | + | 0.960924i | \(0.589278\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.53978 | + | 0.560254i | −0.236332 | + | 0.0291657i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.3535 | − | 20.4350i | 1.26437 | − | 1.06093i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.40368 | − | 19.3032i | 0.176236 | − | 0.999482i | −0.760472 | − | 0.649370i | \(-0.775032\pi\) |
0.936708 | − | 0.350112i | \(-0.113856\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.1762 | − | 16.4658i | 0.628776 | − | 0.850290i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.30631 | −0.221786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7651 | −0.809798 | −0.404899 | − | 0.914361i | \(-0.632693\pi\) | ||||
−0.404899 | + | 0.914361i | \(0.632693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.56502 | − | 3.59628i | −0.0801785 | − | 0.184243i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.71505 | − | 26.7404i | 0.240928 | − | 1.36637i | −0.588836 | − | 0.808253i | \(-0.700414\pi\) |
0.829763 | − | 0.558115i | \(-0.188475\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.0550 | − | 20.1845i | 1.22596 | − | 1.02870i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.671673 | + | 12.9691i | −0.0341431 | + | 0.659258i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.08450 | − | 11.8218i | −0.105688 | − | 0.599389i | −0.990943 | − | 0.134282i | \(-0.957127\pi\) |
0.885255 | − | 0.465106i | \(-0.153984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49.2602 | − | 17.9292i | 2.49119 | − | 0.906720i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.1720 | + | 18.0844i | 0.866214 | + | 0.912237i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.75342 | + | 8.23316i | −0.239170 | + | 0.414255i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.40851 | − | 11.0999i | −0.321634 | − | 0.557086i | 0.659192 | − | 0.751975i | \(-0.270899\pi\) |
−0.980825 | + | 0.194889i | \(0.937565\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.1076 | + | 10.5157i | 1.05670 | + | 0.526446i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.7646 | + | 14.0672i | 0.837187 | + | 0.702483i | 0.956929 | − | 0.290322i | \(-0.0937624\pi\) |
−0.119742 | + | 0.992805i | \(0.538207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.14410 | + | 0.416420i | 0.0569919 | + | 0.0207434i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.9444 | − | 15.1027i | 0.543831 | − | 0.750462i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.9826 | − | 12.7326i | −1.73402 | − | 0.631133i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.9289 | − | 20.9179i | −1.23266 | − | 1.03432i | −0.998062 | − | 0.0622284i | \(-0.980179\pi\) |
−0.234595 | − | 0.972093i | \(-0.575376\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.6557 | − | 5.80684i | −0.574933 | − | 0.286430i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.93803 | − | 13.7491i | −0.390605 | − | 0.676548i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.7919 | − | 20.4242i | 0.578841 | − | 1.00258i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.7457 | − | 14.4760i | −0.673129 | − | 0.708893i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.60955 | − | 1.31377i | 0.176338 | − | 0.0641817i | −0.252342 | − | 0.967638i | \(-0.581201\pi\) |
0.428680 | + | 0.903456i | \(0.358979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.432258 | + | 2.45146i | 0.0210670 | + | 0.119477i | 0.993528 | − | 0.113590i | \(-0.0362351\pi\) |
−0.972461 | + | 0.233067i | \(0.925124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.1423 | + | 10.7890i | −1.02797 | + | 0.524577i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.99148 | − | 3.34925i | 0.193615 | − | 0.162462i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.99624 | + | 39.6777i | −0.338572 | + | 1.92014i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.81859 | + | 8.77477i | 0.184363 | + | 0.423650i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.82650 | 0.376989 | 0.188495 | − | 0.982074i | \(-0.439639\pi\) | ||||
0.188495 | + | 0.982074i | \(0.439639\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.715996 | 0.0344086 | 0.0172043 | − | 0.999852i | \(-0.494523\pi\) | ||||
0.0172043 | + | 0.999852i | \(0.494523\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.40894 | − | 12.7236i | 0.451124 | − | 0.610052i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.26226 | − | 35.5151i | 0.299565 | − | 1.69892i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.0678 | − | 22.7126i | 1.29188 | − | 1.08401i | 0.300388 | − | 0.953817i | \(-0.402884\pi\) |
0.991488 | − | 0.130196i | \(-0.0415607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.206280 | − | 0.486800i | 0.00982288 | − | 0.0231809i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.65518 | − | 32.0721i | −0.268686 | − | 1.52379i | −0.758331 | − | 0.651870i | \(-0.773985\pi\) |
0.489645 | − | 0.871922i | \(-0.337126\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1679 | + | 3.70080i | −0.482003 | + | 0.175435i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.3067 | − | 5.60302i | 1.10237 | − | 0.265014i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.5847 | + | 20.0653i | −0.546717 | + | 0.946942i | 0.451779 | + | 0.892130i | \(0.350789\pi\) |
−0.998497 | + | 0.0548124i | \(0.982544\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.31223 | + | 7.46900i | 0.203055 | + | 0.351701i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.647419 | − | 10.5320i | −0.0304184 | − | 0.494835i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.15403 | − | 3.48565i | −0.194744 | − | 0.163410i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.6611 | + | 9.70386i | 1.24715 | + | 0.453927i | 0.879439 | − | 0.476011i | \(-0.157918\pi\) |
0.367716 | + | 0.929938i | \(0.380140\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 29.1679 | − | 24.9584i | 1.36144 | − | 1.16496i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.0555796 | + | 0.0202293i | 0.00258860 | + | 0.000942173i | 0.343314 | − | 0.939221i | \(-0.388450\pi\) |
−0.340726 | + | 0.940163i | \(0.610673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.86124 | + | 7.43546i | 0.411817 | + | 0.345555i | 0.825040 | − | 0.565075i | \(-0.191153\pi\) |
−0.413223 | + | 0.910630i | \(0.635597\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.73015 | + | 2.47059i | −0.172982 | + | 0.114571i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.03520 | − | 5.25712i | −0.140452 | − | 0.243271i | 0.787215 | − | 0.616679i | \(-0.211522\pi\) |
−0.927667 | + | 0.373408i | \(0.878189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0172 | − | 24.2785i | 0.647254 | − | 1.12108i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.63973 | + | 15.6812i | −0.213787 | + | 0.722551i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.0087 | − | 8.37450i | 1.05794 | − | 0.385060i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.622445 | − | 3.53006i | −0.0285597 | − | 0.161970i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.6949 | − | 7.98745i | −1.58857 | − | 0.365720i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.21611 | + | 4.37684i | −0.238330 | + | 0.199983i | −0.754128 | − | 0.656728i | \(-0.771940\pi\) |
0.515798 | + | 0.856710i | \(0.327496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.11635 | + | 6.33115i | −0.0509013 | + | 0.288676i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −32.7124 | − | 3.71690i | −1.48847 | − | 0.169125i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.8642 | 0.901988 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.4345 | 1.87758 | 0.938788 | − | 0.344496i | \(-0.111950\pi\) | ||||
0.938788 | + | 0.344496i | \(0.111950\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.3433 | + | 3.10684i | 1.23651 | + | 0.140496i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.04493 | + | 5.92607i | −0.0471568 | + | 0.267440i | −0.999266 | − | 0.0383201i | \(-0.987799\pi\) |
0.952109 | + | 0.305760i | \(0.0989105\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.9506 | − | 20.9360i | 1.12372 | − | 0.942911i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −34.2697 | − | 7.88955i | −1.54031 | − | 0.354609i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.779694 | − | 4.42186i | −0.0349741 | − | 0.198348i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1472 | + | 7.69695i | −0.946679 | + | 0.344563i | −0.768800 | − | 0.639489i | \(-0.779146\pi\) |
−0.177879 | + | 0.984052i | \(0.556924\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.87354 | − | 26.6107i | 0.351764 | − | 1.18888i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6026 | − | 25.2924i | 0.651097 | − | 1.12773i | −0.331759 | − | 0.943364i | \(-0.607642\pi\) |
0.982857 | − | 0.184370i | \(-0.0590244\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.183198 | − | 0.317308i | −0.00815220 | − | 0.0141200i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.3947 | + | 11.5210i | −0.772527 | + | 0.511666i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.4530 | + | 19.6794i | 1.03953 | + | 0.872273i | 0.991955 | − | 0.126594i | \(-0.0404046\pi\) |
0.0475801 | + | 0.998867i | \(0.484849\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.1605 | − | 5.51797i | −0.670661 | − | 0.244101i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.83667 | − | 25.9624i | −0.213544 | − | 1.14627i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.64837 | + | 0.599956i | 0.0726356 | + | 0.0264372i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.2828 | + | 28.7667i | 1.50776 | + | 1.26516i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.16839 | + | 35.2746i | 0.0951819 | + | 1.54838i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.8996 | − | 29.2709i | −0.740384 | − | 1.28238i | −0.952321 | − | 0.305099i | \(-0.901311\pi\) |
0.211937 | − | 0.977283i | \(-0.432023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.0731 | − | 26.1073i | 0.659098 | − | 1.14159i | −0.321751 | − | 0.946824i | \(-0.604271\pi\) |
0.980849 | − | 0.194768i | \(-0.0623953\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.18176 | + | 0.764909i | −0.138863 | + | 0.0333834i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.65341 | + | 3.14958i | −0.376948 | + | 0.137198i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.74884 | + | 26.9320i | 0.206471 | + | 1.17096i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.93686 | + | 16.3702i | −0.301034 | + | 0.710408i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.14091 | − | 0.957334i | 0.0494181 | − | 0.0414667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.25113 | − | 12.7668i | 0.0973249 | − | 0.551957i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.55570 | + | 12.9221i | −0.412359 | + | 0.557630i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.996839 | −0.0429369 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.8374 | 0.938863 | 0.469432 | − | 0.882969i | \(-0.344459\pi\) | ||||
0.469432 | + | 0.882969i | \(0.344459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.20805 | + | 2.77599i | 0.0518425 | + | 0.119129i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.97436 | + | 28.2110i | −0.213078 | + | 1.20843i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.8575 | − | 28.4098i | 1.44764 | − | 1.21472i | 0.513362 | − | 0.858172i | \(-0.328400\pi\) |
0.934279 | − | 0.356543i | \(-0.116045\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 40.1895 | − | 20.5087i | 1.71524 | − | 0.875292i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.89088 | − | 22.0663i | −0.165757 | − | 0.940055i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.5479 | − | 4.20309i | 0.491066 | − | 0.178733i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.2672 | − | 17.1315i | −0.690504 | − | 0.727191i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.672159 | + | 1.16421i | −0.0284803 | + | 0.0493293i | −0.879914 | − | 0.475133i | \(-0.842400\pi\) |
0.851434 | + | 0.524462i | \(0.175733\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.11418 | − | 3.66186i | −0.0894202 | − | 0.154880i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −64.7851 | − | 32.2757i | −2.73523 | − | 1.36268i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.04346 | + | 3.39287i | 0.170411 | + | 0.142992i | 0.724005 | − | 0.689795i | \(-0.242299\pi\) |
−0.553593 | + | 0.832787i | \(0.686744\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.37600 | + | 3.04861i | 0.352381 | + | 0.128256i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.3863 | + | 5.86147i | −0.982132 | + | 0.246158i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.05637 | + | 1.11243i | 0.128129 | + | 0.0466353i | 0.405289 | − | 0.914189i | \(-0.367171\pi\) |
−0.277160 | + | 0.960824i | \(0.589393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.9173 | + | 16.7126i | 0.833515 | + | 0.699402i | 0.956095 | − | 0.293056i | \(-0.0946724\pi\) |
−0.122580 | + | 0.992459i | \(0.539117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.690190 | + | 0.343851i | 0.0288331 | + | 0.0143646i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.50217 | + | 4.33389i | 0.104348 | + | 0.180736i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.57097 | + | 14.8453i | −0.356814 | + | 0.618020i | −0.987427 | − | 0.158078i | \(-0.949470\pi\) |
0.630613 | + | 0.776098i | \(0.282804\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.5500 | + | 22.6950i | 0.895590 | + | 0.943172i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.6471 | + | 10.4267i | −1.18848 | + | 0.432571i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.6564 | + | 66.1068i | 0.482759 | + | 2.73786i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.314090 | + | 6.06467i | −0.0129860 | + | 0.250743i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.9905 | + | 28.5214i | −1.40294 | + | 1.17721i | −0.443161 | + | 0.896442i | \(0.646143\pi\) |
−0.959777 | + | 0.280763i | \(0.909412\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.10008 | + | 6.23884i | −0.0453278 | + | 0.257067i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.45799 | + | 3.35032i | 0.0599737 | + | 0.137814i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.6236 | 1.09330 | 0.546650 | − | 0.837361i | \(-0.315903\pi\) | ||||
0.546650 | + | 0.837361i | \(0.315903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.0145 | 1.68143 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.3770 | + | 20.7943i | −0.629341 | + | 0.851053i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.47258 | + | 36.7078i | −0.264462 | + | 1.49984i | 0.506099 | + | 0.862475i | \(0.331087\pi\) |
−0.770561 | + | 0.637366i | \(0.780024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.4634 | + | 18.0099i | −0.875509 | + | 0.734640i | −0.965251 | − | 0.261325i | \(-0.915840\pi\) |
0.0897413 | + | 0.995965i | \(0.471396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.1589 | + | 3.84531i | −1.26889 | + | 0.156593i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.55504 | + | 42.8468i | 0.307156 | + | 1.74197i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.3766 | + | 7.05251i | −0.786472 | + | 0.286252i | −0.703869 | − | 0.710330i | \(-0.748546\pi\) |
−0.0826034 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.8890 | + | 4.78141i | −0.805945 | + | 0.193753i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.86418 | − | 6.69295i | 0.156328 | − | 0.270768i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6262 | − | 30.5294i | −0.711915 | − | 1.23307i | −0.964138 | − | 0.265403i | \(-0.914495\pi\) |
0.252223 | − | 0.967669i | \(-0.418838\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.335800 | + | 5.46268i | 0.0135408 | + | 0.220276i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.5772 | − | 14.7490i | −0.707630 | − | 0.593772i | 0.216303 | − | 0.976326i | \(-0.430600\pi\) |
−0.923933 | + | 0.382554i | \(0.875045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.49929 | − | 2.00158i | −0.221035 | − | 0.0804502i | 0.229129 | − | 0.973396i | \(-0.426412\pi\) |
−0.450164 | + | 0.892946i | \(0.648634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.7422 | + | 31.7508i | 0.752098 | + | 1.27412i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.1435 | + | 4.78384i | 0.526583 | + | 0.191660i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.0687 | − | 13.4832i | −0.642748 | − | 0.539330i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −41.5132 | + | 27.4954i | −1.65788 | + | 1.09806i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.3121 | − | 42.1098i | −0.969387 | − | 1.67903i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.3134 | + | 28.2557i | −0.649427 | + | 1.12484i | 0.333832 | + | 0.942632i | \(0.391658\pi\) |
−0.983260 | + | 0.182209i | \(0.941675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.622423 | + | 2.10364i | −0.0247391 | + | 0.0836123i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.40967 | + | 1.60499i | −0.174992 | + | 0.0636920i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0298923 | + | 0.169528i | 0.00118438 | + | 0.00671694i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.42707 | + | 3.67963i | −0.135573 | + | 0.145564i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.45686 | − | 4.57885i | 0.215533 | − | 0.180854i | −0.528629 | − | 0.848853i | \(-0.677294\pi\) |
0.744162 | + | 0.668000i | \(0.232849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.68965 | − | 9.58246i | 0.0666331 | − | 0.377895i | −0.933195 | − | 0.359370i | \(-0.882992\pi\) |
0.999828 | − | 0.0185255i | \(-0.00589720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.4388 | + | 1.75422i | 0.607903 | + | 0.0690722i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.7867 | 1.95732 | 0.978658 | − | 0.205494i | \(-0.0658801\pi\) | ||||
0.978658 | + | 0.205494i | \(0.0658801\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.5220 | 1.31585 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.74650 | + | 0.652938i | 0.225223 | + | 0.0255907i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.99181 | − | 33.9813i | 0.234478 | − | 1.32979i | −0.609233 | − | 0.792991i | \(-0.708523\pi\) |
0.843711 | − | 0.536798i | \(-0.180366\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.8575 | − | 19.1798i | 0.893118 | − | 0.749415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.29310 | + | 17.2749i | 0.206503 | + | 0.673957i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.19566 | − | 35.1373i | −0.241349 | − | 1.36876i | −0.828822 | − | 0.559512i | \(-0.810988\pi\) |
0.587473 | − | 0.809244i | \(-0.300123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.6551 | + | 15.1612i | −1.62020 | + | 0.589703i | −0.983420 | − | 0.181345i | \(-0.941955\pi\) |
−0.636777 | + | 0.771048i | \(0.719733\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.54627 | + | 11.9856i | −0.137726 | + | 0.465481i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.1078 | − | 24.4354i | 0.547076 | − | 0.947563i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6410 | + | 27.0910i | 0.605622 | + | 1.04897i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.7856 | + | 9.79293i | −0.571645 | + | 0.378617i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −65.1682 | − | 54.6826i | −2.51579 | − | 2.11100i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.7104 | − | 13.7255i | −1.45363 | − | 0.529078i | −0.510027 | − | 0.860158i | \(-0.670365\pi\) |
−0.943603 | + | 0.331080i | \(0.892587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.82994 | + | 2.32843i | 0.108924 | + | 0.0896215i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.1076 | − | 4.40679i | −0.465332 | − | 0.169367i | 0.0987049 | − | 0.995117i | \(-0.468530\pi\) |
−0.564036 | + | 0.825750i | \(0.690752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.6701 | − | 16.5052i | −0.754868 | − | 0.633410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.244599 | − | 3.97905i | −0.00937306 | − | 0.152477i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.7166 | − | 37.6142i | −0.830961 | − | 1.43927i | −0.897277 | − | 0.441469i | \(-0.854458\pi\) |
0.0663153 | − | 0.997799i | \(-0.478876\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.79036 | + | 13.4933i | −0.297654 | + | 0.515553i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.70699 | + | 1.85279i | −0.294040 | + | 0.0706885i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.8929 | − | 3.96471i | 0.414988 | − | 0.151043i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.10611 | − | 17.6156i | −0.118162 | − | 0.670130i | −0.985136 | − | 0.171777i | \(-0.945049\pi\) |
0.866974 | − | 0.498354i | \(-0.166062\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27.3793 | + | 36.2871i | 1.04005 | + | 1.37843i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.2968 | + | 15.3528i | −0.694036 | + | 0.582365i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.95608 | + | 11.0935i | −0.0740920 | + | 0.420196i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.774547 | − | 1.04741i | 0.0292960 | − | 0.0396168i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.3400 | −1.33477 | −0.667386 | − | 0.744712i | \(-0.732587\pi\) | ||||
−0.667386 | + | 0.744712i | \(0.732587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.4506 | −1.26161 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.3324 | + | 26.0408i | 0.426803 | + | 0.980754i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0822434 | + | 0.466426i | −0.00309308 | + | 0.0175417i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.44977 | − | 4.57290i | 0.204670 | − | 0.171739i | −0.534691 | − | 0.845048i | \(-0.679572\pi\) |
0.739361 | + | 0.673309i | \(0.235128\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.5466 | − | 7.48835i | −0.433032 | − | 0.280835i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.53582 | − | 8.71005i | −0.0575168 | − | 0.326194i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7594 | − | 3.91611i | 0.402380 | − | 0.146454i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.72543 | − | 6.02962i | −0.213820 | − | 0.225180i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.9082 | − | 31.0179i | 0.667864 | − | 1.15677i | −0.310637 | − | 0.950529i | \(-0.600542\pi\) |
0.978500 | − | 0.206245i | \(-0.0661244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.13375 | − | 1.96372i | −0.0422231 | − | 0.0731326i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.8558 | + | 16.3687i | 1.22192 | + | 0.608757i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.38187 | + | 1.99863i | 0.0884605 | + | 0.0742271i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.1870 | − | 6.25554i | −0.637429 | − | 0.232005i | 0.00303240 | − | 0.999995i | \(-0.499035\pi\) |
−0.640462 | + | 0.767990i | \(0.721257\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.0143 | + | 16.9528i | 0.778308 | + | 0.627883i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.0524 | + | 10.9382i | 1.11153 | + | 0.404563i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.1799 | − | 11.8983i | −0.523746 | − | 0.439475i | 0.342189 | − | 0.939631i | \(-0.388832\pi\) |
−0.865936 | + | 0.500156i | \(0.833276\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.566208 | − | 0.282083i | −0.0208849 | − | 0.0104048i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.5970 | + | 51.2636i | 1.09022 | + | 1.88832i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.1992 | + | 21.1297i | −0.448755 | + | 0.777267i | −0.998305 | − | 0.0581936i | \(-0.981466\pi\) |
0.549550 | + | 0.835461i | \(0.314799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.92087 | + | 6.23545i | 0.217509 | + | 0.229065i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.07984 | + | 3.30479i | −0.333107 | + | 0.121241i | −0.503159 | − | 0.864194i | \(-0.667829\pi\) |
0.170051 | + | 0.985435i | \(0.445607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.98033 | − | 28.2448i | −0.182465 | − | 1.03481i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.6439 | + | 18.5765i | 1.04803 | + | 0.679678i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.8371 | + | 10.7716i | −0.469056 | + | 0.393585i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.04205 | + | 39.9375i | −0.256968 | + | 1.45734i | 0.534002 | + | 0.845483i | \(0.320688\pi\) |
−0.790970 | + | 0.611855i | \(0.790424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.41432 | − | 12.4416i | −0.197309 | − | 0.453397i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.6251 | −0.459475 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.7960 | −1.41007 | −0.705033 | − | 0.709175i | \(-0.749068\pi\) | ||||
−0.705033 | + | 0.709175i | \(0.749068\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 41.3325 | − | 55.8937i | 1.50027 | − | 2.02881i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.49474 | + | 48.1761i | −0.307934 | + | 1.74638i | 0.301429 | + | 0.953489i | \(0.402537\pi\) |
−0.609363 | + | 0.792892i | \(0.708575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.3662 | − | 23.8021i | 1.02693 | − | 0.861694i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.6648 | − | 36.6654i | −1.00022 | − | 1.32564i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.00523 | − | 5.70093i | −0.0362967 | − | 0.205849i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.53774 | + | 3.10748i | −0.307879 | + | 0.112059i | −0.491339 | − | 0.870968i | \(-0.663492\pi\) |
0.183460 | + | 0.983027i | \(0.441270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.5769 | − | 10.9569i | 1.64141 | − | 0.394603i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.67996 | − | 11.5700i | 0.240261 | − | 0.416145i | −0.720527 | − | 0.693427i | \(-0.756100\pi\) |
0.960789 | + | 0.277282i | \(0.0894335\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.439551 | − | 0.761324i | −0.0157891 | − | 0.0273476i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.87369 | + | 30.4804i | 0.0672181 | + | 1.09348i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.93639 | + | 4.98122i | 0.212693 | + | 0.178471i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.90896 | + | 3.24260i | 0.318788 | + | 0.116029i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.6898 | + | 14.5549i | 0.632183 | + | 0.520151i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.3863 | + | 6.69208i | 0.656237 | + | 0.238851i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.0637 | − | 8.44446i | −0.358733 | − | 0.301012i | 0.445553 | − | 0.895256i | \(-0.353007\pi\) |
−0.804285 | + | 0.594243i | \(0.797452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.9705 | − | 13.2270i | 0.710967 | − | 0.470894i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.76105 | − | 9.97843i | −0.204839 | − | 0.354792i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.34541 | + | 12.7226i | −0.260843 | + | 0.451794i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.0859 | + | 40.8474i | −0.428641 | + | 1.44871i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.2577 | + | 14.2886i | −1.39058 | + | 0.506129i | −0.925368 | − | 0.379071i | \(-0.876244\pi\) |
−0.465211 | + | 0.885200i | \(0.654022\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.1503 | + | 57.5651i | 0.359091 | + | 2.03651i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.58889 | − | 14.9766i | −0.162140 | − | 0.529171i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.0957 | − | 21.8969i | 0.920897 | − | 0.772724i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.84030 | + | 38.7933i | −0.241089 | + | 1.36728i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.4044 | + | 3.45466i | 1.07029 | + | 0.121610i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.2120 | −0.991881 | −0.495941 | − | 0.868356i | \(-0.665177\pi\) | ||||
−0.495941 | + | 0.868356i | \(0.665177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.5624 | 0.581584 | 0.290792 | − | 0.956786i | \(-0.406081\pi\) | ||||
0.290792 | + | 0.956786i | \(0.406081\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.8583 | − | 3.05174i | −0.941961 | − | 0.107029i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.71759 | − | 32.4261i | 0.200279 | − | 1.13584i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.8538 | − | 14.1420i | 0.589640 | − | 0.494766i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.35015 | − | 5.74442i | 0.186949 | − | 0.200726i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.57185 | + | 20.2569i | 0.124658 | + | 0.706972i | 0.981510 | + | 0.191410i | \(0.0613059\pi\) |
−0.856852 | + | 0.515563i | \(0.827583\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.8031 | + | 4.29596i | −0.411429 | + | 0.149748i | −0.539438 | − | 0.842025i | \(-0.681363\pi\) |
0.128009 | + | 0.991773i | \(0.459141\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.96040 | − | 6.62569i | 0.0682524 | − | 0.230677i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.60938 | − | 11.4478i | 0.229831 | − | 0.398078i | −0.727927 | − | 0.685654i | \(-0.759516\pi\) |
0.957758 | + | 0.287576i | \(0.0928495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.5508 | + | 28.6668i | 0.574833 | + | 0.995640i | 0.996060 | + | 0.0886844i | \(0.0282663\pi\) |
−0.421227 | + | 0.906955i | \(0.638400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −44.9681 | + | 29.7837i | −1.55993 | + | 1.03318i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.997389 | − | 0.836909i | −0.0345575 | − | 0.0289972i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.2013 | − | 11.3564i | −1.07977 | − | 0.393003i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.29239 | − | 5.57758i | −0.113802 | − | 0.192789i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.7035 | + | 4.98765i | 0.473096 | + | 0.172193i | 0.567554 | − | 0.823336i | \(-0.307890\pi\) |
−0.0944583 | + | 0.995529i | \(0.530112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.32631 | − | 6.14750i | −0.252631 | − | 0.211983i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.49871 | + | 24.3805i | 0.0516185 | + | 0.839710i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4818 | + | 21.6191i | 0.429386 | + | 0.743719i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.1201 | − | 48.7055i | 0.966219 | − | 1.67354i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.974173 | + | 0.234196i | −0.0334335 | + | 0.00803758i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.8840 | − | 15.9725i | 1.50432 | − | 0.547529i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.55426 | + | 42.8423i | 0.258653 | + | 1.46689i | 0.786519 | + | 0.617566i | \(0.211881\pi\) |
−0.527866 | + | 0.849328i | \(0.677008\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −31.3602 | + | 3.87016i | −1.07250 | + | 0.132357i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.8624 | + | 9.95375i | −0.405213 | + | 0.340014i | −0.822504 | − | 0.568759i | \(-0.807424\pi\) |
0.417292 | + | 0.908773i | \(0.362979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.41739 | − | 8.03841i | 0.0483607 | − | 0.274267i | −0.951033 | − | 0.309090i | \(-0.899976\pi\) |
0.999393 | + | 0.0348229i | \(0.0110867\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.20641 | − | 5.68830i | 0.143354 | − | 0.193857i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.4206 | −0.524924 | −0.262462 | − | 0.964942i | \(-0.584534\pi\) | ||||
−0.262462 | + | 0.964942i | \(0.584534\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42.2852 | 1.43774 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.9739 | − | 59.6856i | −0.882120 | − | 2.02703i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.50582 | + | 25.5538i | −0.152850 | + | 0.866853i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.83063 | − | 6.57068i | 0.265331 | − | 0.222639i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.48727 | + | 28.7173i | −0.0503365 | + | 0.971933i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.50000 | + | 31.1921i | 0.185934 | + | 1.05448i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.7748 | − | 5.01362i | 0.465142 | − | 0.169298i | −0.0988084 | − | 0.995106i | \(-0.531503\pi\) |
0.563950 | + | 0.825809i | \(0.309281\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.2921 | + | 17.1577i | 0.549519 | + | 0.578715i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.06970 | + | 7.04892i | −0.137112 | + | 0.237484i | −0.926402 | − | 0.376536i | \(-0.877115\pi\) |
0.789291 | + | 0.614020i | \(0.210449\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.63523 | + | 6.29640i | 0.122335 | + | 0.211891i | 0.920688 | − | 0.390299i | \(-0.127628\pi\) |
−0.798353 | + | 0.602190i | \(0.794295\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.0406 | + | 9.48597i | 0.640043 | + | 0.318867i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.00584 | − | 6.71770i | −0.268810 | − | 0.225558i | 0.498412 | − | 0.866941i | \(-0.333917\pi\) |
−0.767221 | + | 0.641382i | \(0.778361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.70016 | + | 2.07469i | 0.191177 | + | 0.0695828i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.9716 | − | 48.9523i | 0.468066 | − | 1.63996i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.7872 | + | 13.7534i | 1.26450 | + | 0.460241i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.7305 | + | 12.3603i | 0.492386 | + | 0.413161i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.7450 | − | 5.35314i | −0.358766 | − | 0.178736i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.74761 | − | 4.75901i | −0.0916380 | − | 0.158722i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.8380 | + | 75.9296i | −1.46045 | + | 2.52958i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.8304 | − | 14.5652i | −0.460246 | − | 0.484699i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.40386 | − | 1.23890i | 0.113148 | − | 0.0411826i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.41097 | − | 30.6871i | −0.179668 | − | 1.01895i | −0.932616 | − | 0.360869i | \(-0.882480\pi\) |
0.752948 | − | 0.658080i | \(-0.228631\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.472442 | − | 0.241088i | 0.0156699 | − | 0.00799638i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0692 | + | 17.6791i | −0.698053 | + | 0.585736i | −0.921219 | − | 0.389045i | \(-0.872805\pi\) |
0.223166 | + | 0.974780i | \(0.428361\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1777 | − | 63.3918i | 0.369927 | − | 2.09796i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.5418 | − | 49.5010i | −0.712150 | − | 1.63645i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.5706 | −1.27371 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.8149 | −1.34636 | −0.673180 | − | 0.739479i | \(-0.735072\pi\) | ||||
−0.673180 | + | 0.739479i | \(0.735072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.77247 | + | 6.45377i | −0.157258 | + | 0.212659i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.284299 | − | 1.61234i | 0.00935783 | − | 0.0530709i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.55585 | − | 2.98372i | 0.116916 | − | 0.0981040i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.990760 | + | 2.33809i | −0.0325408 | + | 0.0767929i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.51042 | + | 14.2373i | 0.0823643 | + | 0.467111i | 0.997894 | + | 0.0648613i | \(0.0206605\pi\) |
−0.915530 | + | 0.402250i | \(0.868228\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.841681 | + | 0.306347i | −0.0275850 | + | 0.0100401i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.9693 | − | 3.35827i | 0.457333 | − | 0.109945i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −43.3006 | + | 74.9989i | −1.41608 | + | 2.45273i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.5105 | − | 30.3290i | −0.572042 | − | 0.990807i | −0.996356 | − | 0.0852912i | \(-0.972818\pi\) |
0.424314 | − | 0.905515i | \(-0.360515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.56271 | + | 25.4216i | 0.0509971 | + | 0.829602i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.40186 | − | 7.05000i | −0.273893 | − | 0.229823i | 0.495486 | − | 0.868616i | \(-0.334990\pi\) |
−0.769379 | + | 0.638792i | \(0.779434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.1665 | − | 3.70030i | −0.331066 | − | 0.120498i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.28312 | + | 28.3589i | 0.171860 | + | 0.922515i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.5935 | − | 11.1351i | −0.994155 | − | 0.361843i | −0.206828 | − | 0.978377i | \(-0.566314\pi\) |
−0.787328 | + | 0.616534i | \(0.788536\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.50643 | − | 3.78135i | −0.146285 | − | 0.122748i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.5752 | + | 25.5495i | −1.25089 | + | 0.828498i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.54773 | − | 6.14484i | −0.114922 | − | 0.199051i | 0.802826 | − | 0.596213i | \(-0.203329\pi\) |
−0.917749 | + | 0.397162i | \(0.869995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.461305 | − | 0.799003i | 0.0149275 | − | 0.0258551i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.2544 | − | 41.4170i | 0.396128 | − | 1.33882i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.9258 | − | 6.88843i | 0.611146 | − | 0.222439i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.11330 | − | 28.9990i | −0.164945 | − | 0.935451i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.2882 | + | 4.21029i | 0.589328 | + | 0.135675i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.6851 | − | 24.0696i | 0.923406 | − | 0.774829i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.05399 | − | 51.3477i | 0.291157 | − | 1.65123i | −0.391268 | − | 0.920277i | \(-0.627964\pi\) |
0.682425 | − | 0.730955i | \(-0.260925\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −64.6202 | − | 7.34238i | −2.07590 | − | 0.235871i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.0048 | −0.802444 | −0.401222 | − | 0.915981i | \(-0.631414\pi\) | ||||
−0.401222 | + | 0.915981i | \(0.631414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.8746 | 0.989793 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.18559 | − | 0.134711i | −0.0379692 | − | 0.00431420i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.94588 | + | 39.3920i | −0.222218 | + | 1.26026i | 0.645714 | + | 0.763580i | \(0.276560\pi\) |
−0.867932 | + | 0.496683i | \(0.834551\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.6238 | + | 18.9836i | −0.723061 | + | 0.606720i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.4116 | − | 9.30355i | −1.29024 | − | 0.297039i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.79966 | − | 10.2064i | −0.0574004 | − | 0.325534i | 0.942564 | − | 0.334027i | \(-0.108408\pi\) |
−0.999964 | + | 0.00849311i | \(0.997297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.10809 | − | 1.49522i | 0.130895 | − | 0.0476418i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.4156 | − | 35.2024i | 0.331533 | − | 1.12051i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.3578 | + | 26.6006i | −0.488351 | + | 0.845849i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.1132 | − | 24.4447i | −0.448319 | − | 0.776512i | 0.549957 | − | 0.835193i | \(-0.314644\pi\) |
−0.998277 | + | 0.0586807i | \(0.981311\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0191 | − | 13.2592i | 0.635288 | − | 0.420769i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.7043 | + | 19.8903i | 0.751477 | + | 0.630564i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.48641 | − | 1.63292i | −0.142086 | − | 0.0517151i | 0.269998 | − | 0.962861i | \(-0.412977\pi\) |
−0.412084 | + | 0.911146i | \(0.635199\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.9846 | − | 22.2345i | 0.822116 | − | 0.703468i |
(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 | 864.2.y.c.193.9 | yes | 54 | |
4.3 | odd | 2 | 864.2.y.b.193.1 | ✓ | 54 | ||
27.7 | even | 9 | inner | 864.2.y.c.385.9 | yes | 54 | |
108.7 | odd | 18 | 864.2.y.b.385.1 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.y.b.193.1 | ✓ | 54 | 4.3 | odd | 2 | ||
864.2.y.b.385.1 | yes | 54 | 108.7 | odd | 18 | ||
864.2.y.c.193.9 | yes | 54 | 1.1 | even | 1 | trivial | |
864.2.y.c.385.9 | yes | 54 | 27.7 | even | 9 | inner |