Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [936,2,Mod(181,936)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(936, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("936.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 936.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.47399762919\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.3 | ||
Root | \(1.90184 + 0.0324487i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 936.181 |
Dual form | 936.2.m.h.181.2 |
$q$-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 \(\left(\mathbb{Z}/936\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(469\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34500 | + | 0.437016i | −0.951057 | + | 0.309017i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.61803 | − | 1.17557i | 0.809017 | − | 0.587785i | ||||
\(5\) | −1.66251 | −0.743496 | −0.371748 | − | 0.928334i | \(-0.621241\pi\) | ||||
−0.371748 | + | 0.928334i | \(0.621241\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.57266i | − | 1.35034i | −0.737662 | − | 0.675170i | \(-0.764070\pi\) | ||
0.737662 | − | 0.675170i | \(-0.235930\pi\) | |||||||
\(8\) | −1.66251 | + | 2.28825i | −0.587785 | + | 0.809017i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.23607 | − | 0.726543i | 0.707107 | − | 0.229753i | ||||
\(11\) | −1.02749 | −0.309799 | −0.154899 | − | 0.987930i | \(-0.549505\pi\) | ||||
−0.154899 | + | 0.987930i | \(0.549505\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.87826 | + | 3.07768i | −0.520936 | + | 0.853596i | ||||
\(14\) | 1.56131 | + | 4.80522i | 0.417278 | + | 1.28425i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | − | 3.80423i | 0.309017 | − | 0.951057i | ||||
\(17\) | −5.05251 | −1.22541 | −0.612707 | − | 0.790310i | \(-0.709919\pi\) | ||||
−0.612707 | + | 0.790310i | \(0.709919\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.16083 | −0.266312 | −0.133156 | − | 0.991095i | \(-0.542511\pi\) | ||||
−0.133156 | + | 0.991095i | \(0.542511\pi\) | |||||||
\(20\) | −2.68999 | + | 1.95440i | −0.601501 | + | 0.437016i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.38197 | − | 0.449028i | 0.294636 | − | 0.0957331i | ||||
\(23\) | 8.17513 | 1.70463 | 0.852317 | − | 0.523026i | \(-0.175197\pi\) | ||||
0.852317 | + | 0.523026i | \(0.175197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23607 | −0.447214 | ||||||||
\(26\) | 1.18126 | − | 4.96031i | 0.231664 | − | 0.972796i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.19992 | − | 5.78069i | −0.793710 | − | 1.09245i | ||||
\(29\) | 4.29792i | 0.798104i | 0.916928 | + | 0.399052i | \(0.130661\pi\) | ||||
−0.916928 | + | 0.399052i | \(0.869339\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.98872i | 1.43482i | 0.696653 | + | 0.717408i | \(0.254672\pi\) | ||||
−0.696653 | + | 0.717408i | \(0.745328\pi\) | |||||||
\(32\) | 5.65685i | 1.00000i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.79561 | − | 2.20803i | 1.16544 | − | 0.378674i | ||||
\(35\) | 5.93958i | 1.00397i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.83470 | 1.61682 | 0.808408 | − | 0.588623i | \(-0.200330\pi\) | ||||
0.808408 | + | 0.588623i | \(0.200330\pi\) | |||||||
\(38\) | 1.56131 | − | 0.507301i | 0.253278 | − | 0.0822951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.76393 | − | 3.80423i | 0.437016 | − | 0.601501i | ||||
\(41\) | 1.62054i | 0.253087i | 0.991961 | + | 0.126543i | \(0.0403883\pi\) | ||||
−0.991961 | + | 0.126543i | \(0.959612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35114i | 0.358546i | 0.983799 | + | 0.179273i | \(0.0573745\pi\) | ||||
−0.983799 | + | 0.179273i | \(0.942626\pi\) | |||||||
\(44\) | −1.66251 | + | 1.20788i | −0.250632 | + | 0.182095i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.9955 | + | 3.57266i | −1.62120 | + | 0.526761i | ||||
\(47\) | 7.73877i | 1.12882i | 0.825496 | + | 0.564408i | \(0.190895\pi\) | ||||
−0.825496 | + | 0.564408i | \(0.809105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.76393 | −0.823419 | ||||||||
\(50\) | 3.00750 | − | 0.977198i | 0.425325 | − | 0.138197i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.578944 | + | 7.18782i | 0.0802851 | + | 0.996772i | ||||
\(53\) | − | 11.2521i | − | 1.54560i | −0.634652 | − | 0.772798i | \(-0.718857\pi\) | ||
0.634652 | − | 0.772798i | \(-0.281143\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.70820 | 0.230334 | ||||||||
\(56\) | 8.17513 | + | 5.93958i | 1.09245 | + | 0.793710i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.87826 | − | 5.78069i | −0.246628 | − | 0.759042i | ||||
\(59\) | −9.73249 | −1.26706 | −0.633531 | − | 0.773717i | \(-0.718395\pi\) | ||||
−0.633531 | + | 0.773717i | \(0.718395\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4127i | 1.46124i | 0.682782 | + | 0.730622i | \(0.260770\pi\) | ||||
−0.682782 | + | 0.730622i | \(0.739230\pi\) | |||||||
\(62\) | −3.49120 | − | 10.7448i | −0.443383 | − | 1.36459i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.47214 | − | 7.60845i | −0.309017 | − | 0.951057i | ||||
\(65\) | 3.12262 | − | 5.11667i | 0.387314 | − | 0.634645i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.23901 | 0.884386 | 0.442193 | − | 0.896920i | \(-0.354201\pi\) | ||||
0.442193 | + | 0.896920i | \(0.354201\pi\) | |||||||
\(68\) | −8.17513 | + | 5.93958i | −0.991381 | + | 0.720280i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.59569 | − | 7.98872i | −0.310245 | − | 0.954835i | ||||
\(71\) | 10.5672i | 1.25410i | 0.778981 | + | 0.627048i | \(0.215737\pi\) | ||||
−0.778981 | + | 0.627048i | \(0.784263\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.41606i | 0.516860i | 0.966030 | + | 0.258430i | \(0.0832052\pi\) | ||||
−0.966030 | + | 0.258430i | \(0.916795\pi\) | |||||||
\(74\) | −13.2276 | + | 4.29792i | −1.53768 | + | 0.499623i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.87826 | + | 1.36464i | −0.215451 | + | 0.156535i | ||||
\(77\) | 3.67086i | 0.418334i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.94427 | −0.781292 | −0.390646 | − | 0.920541i | \(-0.627748\pi\) | ||||
−0.390646 | + | 0.920541i | \(0.627748\pi\) | |||||||
\(80\) | −2.05497 | + | 6.32456i | −0.229753 | + | 0.707107i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.708204 | − | 2.17963i | −0.0782080 | − | 0.240700i | ||||
\(83\) | −2.29753 | −0.252187 | −0.126093 | − | 0.992018i | \(-0.540244\pi\) | ||||
−0.126093 | + | 0.992018i | \(0.540244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.39984 | 0.911090 | ||||||||
\(86\) | −1.02749 | − | 3.16228i | −0.110797 | − | 0.340997i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.70820 | − | 2.35114i | 0.182095 | − | 0.250632i | ||||
\(89\) | − | 9.02546i | − | 0.956697i | −0.878170 | − | 0.478349i | \(-0.841236\pi\) | ||
0.878170 | − | 0.478349i | \(-0.158764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9955 | + | 6.71040i | 1.15264 | + | 0.703441i | ||||
\(92\) | 13.2276 | − | 9.61045i | 1.37908 | − | 1.00196i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.38197 | − | 10.4086i | −0.348823 | − | 1.07357i | ||||
\(95\) | 1.92989 | 0.198002 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.5614i | 1.17388i | 0.809630 | + | 0.586940i | \(0.199668\pi\) | ||||
−0.809630 | + | 0.586940i | \(0.800332\pi\) | |||||||
\(98\) | 7.75247 | − | 2.51893i | 0.783118 | − | 0.254450i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.61803 | + | 2.62866i | −0.361803 | + | 0.262866i | ||||
\(101\) | 7.96879i | 0.792924i | 0.918051 | + | 0.396462i | \(0.129762\pi\) | ||||
−0.918051 | + | 0.396462i | \(0.870238\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.7082 | −1.15364 | −0.576822 | − | 0.816870i | \(-0.695707\pi\) | ||||
−0.576822 | + | 0.816870i | \(0.695707\pi\) | |||||||
\(104\) | −3.91987 | − | 9.41460i | −0.384375 | − | 0.923177i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.91735 | + | 15.1340i | 0.477615 | + | 1.46995i | ||||
\(107\) | − | 2.65626i | − | 0.256791i | −0.991723 | − | 0.128395i | \(-0.959017\pi\) | ||
0.991723 | − | 0.128395i | \(-0.0409826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.1564 | −1.16437 | −0.582184 | − | 0.813057i | \(-0.697802\pi\) | ||||
−0.582184 | + | 0.813057i | \(0.697802\pi\) | |||||||
\(110\) | −2.29753 | + | 0.746512i | −0.219061 | + | 0.0711772i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.5912 | − | 4.41606i | −1.28425 | − | 0.417278i | ||||
\(113\) | −5.05251 | −0.475300 | −0.237650 | − | 0.971351i | \(-0.576377\pi\) | ||||
−0.237650 | + | 0.971351i | \(0.576377\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5912 | −1.26739 | ||||||||
\(116\) | 5.05251 | + | 6.95418i | 0.469114 | + | 0.645680i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.0902 | − | 4.25325i | 1.20505 | − | 0.391544i | ||||
\(119\) | 18.0509i | 1.65473i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.94427 | −0.904025 | ||||||||
\(122\) | −4.98752 | − | 15.3500i | −0.451549 | − | 1.38973i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.39130 | + | 12.9260i | 0.843364 | + | 1.16079i | ||||
\(125\) | 12.0300 | 1.07600 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00000 | −0.532414 | −0.266207 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(128\) | 6.65003 | + | 9.15298i | 0.587785 | + | 0.809017i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.96385 | + | 8.24655i | −0.172241 | + | 0.723270i | ||||
\(131\) | 16.5646i | 1.44726i | 0.690189 | + | 0.723629i | \(0.257527\pi\) | ||||
−0.690189 | + | 0.723629i | \(0.742473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.14725i | 0.359612i | ||||||||
\(134\) | −9.73645 | + | 3.16356i | −0.841101 | + | 0.273290i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.39984 | − | 11.5614i | 0.720280 | − | 0.991381i | ||||
\(137\) | − | 13.6020i | − | 1.16209i | −0.813870 | − | 0.581047i | \(-0.802643\pi\) | ||
0.813870 | − | 0.581047i | \(-0.197357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.3642i | 1.64245i | 0.570607 | + | 0.821223i | \(0.306708\pi\) | ||||
−0.570607 | + | 0.821223i | \(0.693292\pi\) | |||||||
\(140\) | 6.98240 | + | 9.61045i | 0.590120 | + | 0.812231i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.61803 | − | 14.2128i | −0.387537 | − | 1.19272i | ||||
\(143\) | 1.92989 | − | 3.16228i | 0.161385 | − | 0.264443i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.14533i | − | 0.593387i | ||||||
\(146\) | −1.92989 | − | 5.93958i | −0.159719 | − | 0.491563i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.9129 | − | 11.5614i | 1.30803 | − | 0.950340i | ||||
\(149\) | −7.04250 | −0.576944 | −0.288472 | − | 0.957488i | \(-0.593147\pi\) | ||||
−0.288472 | + | 0.957488i | \(0.593147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.57266i | 0.290739i | 0.989377 | + | 0.145370i | \(0.0464371\pi\) | ||||
−0.989377 | + | 0.145370i | \(0.953563\pi\) | |||||||
\(152\) | 1.92989 | − | 2.65626i | 0.156535 | − | 0.215451i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.60423 | − | 4.93730i | −0.129272 | − | 0.397859i | ||||
\(155\) | − | 13.2813i | − | 1.06678i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.555029i | 0.0442961i | 0.999755 | + | 0.0221481i | \(0.00705053\pi\) | ||||
−0.999755 | + | 0.0221481i | \(0.992949\pi\) | |||||||
\(158\) | 9.34003 | − | 3.03476i | 0.743052 | − | 0.241432i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 9.40456i | − | 0.743496i | ||||||
\(161\) | − | 29.2070i | − | 2.30183i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.23901 | 0.567003 | 0.283501 | − | 0.958972i | \(-0.408504\pi\) | ||||
0.283501 | + | 0.958972i | \(0.408504\pi\) | |||||||
\(164\) | 1.90506 | + | 2.62210i | 0.148761 | + | 0.204751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.09017 | − | 1.00406i | 0.239844 | − | 0.0779299i | ||||
\(167\) | 7.32611i | 0.566911i | 0.958985 | + | 0.283456i | \(0.0914809\pi\) | ||||
−0.958985 | + | 0.283456i | \(0.908519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.94427 | − | 11.5614i | −0.457252 | − | 0.889337i | ||||
\(170\) | −11.2978 | + | 3.67086i | −0.866498 | + | 0.281542i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.76393 | + | 3.80423i | 0.210748 | + | 0.290070i | ||||
\(173\) | − | 11.2521i | − | 0.855482i | −0.903901 | − | 0.427741i | \(-0.859310\pi\) | ||
0.903901 | − | 0.427741i | \(-0.140690\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.98872i | 0.603891i | ||||||||
\(176\) | −1.27004 | + | 3.90879i | −0.0957331 | + | 0.294636i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.94427 | + | 12.1392i | 0.295636 | + | 0.909873i | ||||
\(179\) | − | 21.8772i | − | 1.63518i | −0.575804 | − | 0.817588i | \(-0.695311\pi\) | ||
0.575804 | − | 0.817588i | \(-0.304689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.8658i | − | 0.956305i | −0.878277 | − | 0.478152i | \(-0.841307\pi\) | ||
0.878277 | − | 0.478152i | \(-0.158693\pi\) | |||||||
\(182\) | −17.7215 | − | 4.22024i | −1.31361 | − | 0.312825i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.5912 | + | 18.7067i | −1.00196 | + | 1.37908i | ||||
\(185\) | −16.3503 | −1.20210 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.19139 | 0.379632 | ||||||||
\(188\) | 9.09747 | + | 12.5216i | 0.663501 | + | 0.913231i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.59569 | + | 0.843392i | −0.188311 | + | 0.0611861i | ||||
\(191\) | 1.92989 | 0.139642 | 0.0698209 | − | 0.997560i | \(-0.477757\pi\) | ||||
0.0698209 | + | 0.997560i | \(0.477757\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.41606i | 0.317875i | 0.987289 | + | 0.158937i | \(0.0508068\pi\) | ||||
−0.987289 | + | 0.158937i | \(0.949193\pi\) | |||||||
\(194\) | −5.05251 | − | 15.5500i | −0.362749 | − | 1.11643i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.32624 | + | 6.77591i | −0.666160 | + | 0.483993i | ||||
\(197\) | 23.1825 | 1.65168 | 0.825841 | − | 0.563903i | \(-0.190701\pi\) | ||||
0.825841 | + | 0.563903i | \(0.190701\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0000 | 1.27599 | 0.637993 | − | 0.770042i | \(-0.279765\pi\) | ||||
0.637993 | + | 0.770042i | \(0.279765\pi\) | |||||||
\(200\) | 3.71748 | − | 5.11667i | 0.262866 | − | 0.361803i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.48249 | − | 10.7180i | −0.245027 | − | 0.754115i | ||||
\(203\) | 15.3550 | 1.07771 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.69417i | − | 0.188169i | ||||||
\(206\) | 15.7475 | − | 5.11667i | 1.09718 | − | 0.356495i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.38655 | + | 10.9496i | 0.650840 | + | 0.759215i | ||||
\(209\) | 1.19274 | 0.0825033 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5146i | 0.723856i | 0.932206 | + | 0.361928i | \(0.117881\pi\) | ||||
−0.932206 | + | 0.361928i | \(0.882119\pi\) | |||||||
\(212\) | −13.2276 | − | 18.2063i | −0.908478 | − | 1.25041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.16083 | + | 3.57266i | 0.0793526 | + | 0.244222i | ||||
\(215\) | − | 3.90879i | − | 0.266577i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.5410 | 1.93749 | ||||||||
\(218\) | 16.3503 | − | 5.31252i | 1.10738 | − | 0.359810i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.76393 | − | 2.00811i | 0.186344 | − | 0.135387i | ||||
\(221\) | 9.48993 | − | 15.5500i | 0.638362 | − | 1.04601i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.98872i | − | 0.534964i | −0.963563 | − | 0.267482i | \(-0.913808\pi\) | ||
0.963563 | − | 0.267482i | \(-0.0861916\pi\) | |||||||
\(224\) | 20.2100 | 1.35034 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.79561 | − | 2.20803i | 0.452037 | − | 0.146876i | ||||
\(227\) | 4.35250 | 0.288886 | 0.144443 | − | 0.989513i | \(-0.453861\pi\) | ||||
0.144443 | + | 0.989513i | \(0.453861\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.43486 | 0.0948185 | 0.0474092 | − | 0.998876i | \(-0.484904\pi\) | ||||
0.0474092 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(230\) | 18.2802 | − | 5.93958i | 1.20536 | − | 0.391644i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.83470 | − | 7.14533i | −0.645680 | − | 0.469114i | ||||
\(233\) | −16.3503 | −1.07114 | −0.535571 | − | 0.844490i | \(-0.679904\pi\) | ||||
−0.535571 | + | 0.844490i | \(0.679904\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.8658i | − | 0.839270i | ||||||
\(236\) | −15.7475 | + | 11.4412i | −1.02507 | + | 0.744761i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.88854 | − | 24.2784i | −0.511338 | − | 1.57374i | ||||
\(239\) | − | 7.07107i | − | 0.457389i | −0.973498 | − | 0.228695i | \(-0.926554\pi\) | ||
0.973498 | − | 0.228695i | \(-0.0734457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.9774i | − | 1.02920i | −0.857431 | − | 0.514599i | \(-0.827941\pi\) | ||
0.857431 | − | 0.514599i | \(-0.172059\pi\) | |||||||
\(242\) | 13.3750 | − | 4.34581i | 0.859779 | − | 0.279359i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.4164 | + | 18.4661i | 0.858898 | + | 1.18217i | ||||
\(245\) | 9.58258 | 0.612209 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.18034 | − | 3.57266i | 0.138732 | − | 0.227323i | ||||
\(248\) | −18.2802 | − | 13.2813i | −1.16079 | − | 0.843364i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16.1803 | + | 5.25731i | −1.02333 | + | 0.332502i | ||||
\(251\) | 22.5042i | 1.42045i | 0.703973 | + | 0.710227i | \(0.251408\pi\) | ||||
−0.703973 | + | 0.710227i | \(0.748592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.39984 | −0.528093 | ||||||||
\(254\) | 8.06998 | − | 2.62210i | 0.506356 | − | 0.164525i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(257\) | −22.5955 | −1.40947 | −0.704735 | − | 0.709471i | \(-0.748934\pi\) | ||||
−0.704735 | + | 0.709471i | \(0.748934\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 35.1361i | − | 2.18325i | ||||||
\(260\) | −0.962499 | − | 11.9498i | −0.0596916 | − | 0.741096i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.23901 | − | 22.2794i | −0.447227 | − | 1.37642i | ||||
\(263\) | 16.3503 | 1.00820 | 0.504100 | − | 0.863645i | \(-0.331824\pi\) | ||||
0.504100 | + | 0.863645i | \(0.331824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.7067i | 1.14914i | ||||||||
\(266\) | −1.81242 | − | 5.57804i | −0.111126 | − | 0.342012i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.7130 | − | 8.50997i | 0.715483 | − | 0.519829i | ||||
\(269\) | − | 7.58124i | − | 0.462237i | −0.972926 | − | 0.231118i | \(-0.925762\pi\) | ||
0.972926 | − | 0.231118i | \(-0.0742384\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.98872i | − | 0.485280i | −0.970116 | − | 0.242640i | \(-0.921987\pi\) | ||
0.970116 | − | 0.242640i | \(-0.0780134\pi\) | |||||||
\(272\) | −6.24525 | + | 19.2209i | −0.378674 | + | 1.16544i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.94427 | + | 18.2946i | 0.359107 | + | 1.10522i | ||||
\(275\) | 2.29753 | 0.138546 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.1231i | − | 1.08891i | −0.838790 | − | 0.544455i | \(-0.816737\pi\) | ||
0.838790 | − | 0.544455i | \(-0.183263\pi\) | |||||||
\(278\) | −8.46245 | − | 26.0447i | −0.507544 | − | 1.56206i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.5912 | − | 9.87460i | −0.812231 | − | 0.590120i | ||||
\(281\) | 6.19704i | 0.369684i | 0.982768 | + | 0.184842i | \(0.0591774\pi\) | ||||
−0.982768 | + | 0.184842i | \(0.940823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.90617i | 0.172754i | 0.996263 | + | 0.0863769i | \(0.0275289\pi\) | ||||
−0.996263 | + | 0.0863769i | \(0.972471\pi\) | |||||||
\(284\) | 12.4225 | + | 17.0981i | 0.737139 | + | 1.01458i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.21373 | + | 5.09665i | −0.0717692 | + | 0.301371i | ||||
\(287\) | 5.78966 | 0.341753 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.52786 | 0.501639 | ||||||||
\(290\) | 3.12262 | + | 9.61045i | 0.183367 | + | 0.564345i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.19139 | + | 7.14533i | 0.303803 | + | 0.418149i | ||||
\(293\) | −0.877578 | −0.0512687 | −0.0256343 | − | 0.999671i | \(-0.508161\pi\) | ||||
−0.0256343 | + | 0.999671i | \(0.508161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.1803 | 0.942056 | ||||||||
\(296\) | −16.3503 | + | 22.5042i | −0.950340 | + | 1.30803i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.47214 | − | 3.07768i | 0.548706 | − | 0.178285i | ||||
\(299\) | −15.3550 | + | 25.1605i | −0.888005 | + | 1.45507i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.39984 | 0.484159 | ||||||||
\(302\) | −1.56131 | − | 4.80522i | −0.0898434 | − | 0.276510i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.43486 | + | 4.41606i | −0.0822951 | + | 0.253278i | ||||
\(305\) | − | 18.9737i | − | 1.08643i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7521 | −0.841944 | −0.420972 | − | 0.907074i | \(-0.638311\pi\) | ||||
−0.420972 | + | 0.907074i | \(0.638311\pi\) | |||||||
\(308\) | 4.31536 | + | 5.93958i | 0.245890 | + | 0.338439i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.80415 | + | 17.8633i | 0.329653 | + | 1.01457i | ||||
\(311\) | 24.5254 | 1.39071 | 0.695354 | − | 0.718667i | \(-0.255248\pi\) | ||||
0.695354 | + | 0.718667i | \(0.255248\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.47214 | 0.365827 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(314\) | −0.242557 | − | 0.746512i | −0.0136883 | − | 0.0421281i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.2361 | + | 8.16348i | −0.632078 | + | 0.459232i | ||||
\(317\) | −31.1025 | −1.74689 | −0.873446 | − | 0.486921i | \(-0.838120\pi\) | ||||
−0.873446 | + | 0.486921i | \(0.838120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.41606i | − | 0.247252i | ||||||
\(320\) | 4.10995 | + | 12.6491i | 0.229753 | + | 0.707107i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.7639 | + | 39.2833i | 0.711306 | + | 2.18918i | ||||
\(323\) | 5.86510 | 0.326343 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.19992 | − | 6.88191i | 0.232970 | − | 0.381740i | ||||
\(326\) | −9.73645 | + | 3.16356i | −0.539252 | + | 0.175214i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.70820 | − | 2.69417i | −0.204751 | − | 0.148761i | ||||
\(329\) | 27.6480 | 1.52428 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9955 | −0.604369 | −0.302185 | − | 0.953249i | \(-0.597716\pi\) | ||||
−0.302185 | + | 0.953249i | \(0.597716\pi\) | |||||||
\(332\) | −3.71748 | + | 2.70091i | −0.204023 | + | 0.148232i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.20163 | − | 9.85359i | −0.175185 | − | 0.539165i | ||||
\(335\) | −12.0349 | −0.657537 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.52786 | 0.301122 | 0.150561 | − | 0.988601i | \(-0.451892\pi\) | ||||
0.150561 | + | 0.988601i | \(0.451892\pi\) | |||||||
\(338\) | 13.0475 | + | 12.9523i | 0.709693 | + | 0.704512i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.5912 | − | 9.87460i | 0.737088 | − | 0.535525i | ||||
\(341\) | − | 8.20830i | − | 0.444504i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4.41606i | − | 0.238445i | ||||||
\(344\) | −5.37999 | − | 3.90879i | −0.290070 | − | 0.210748i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.91735 | + | 15.1340i | 0.264358 | + | 0.813612i | ||||
\(347\) | − | 20.4750i | − | 1.09916i | −0.835442 | − | 0.549578i | \(-0.814788\pi\) | ||
0.835442 | − | 0.549578i | \(-0.185212\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.5912 | −0.727522 | −0.363761 | − | 0.931492i | \(-0.618507\pi\) | ||||
−0.363761 | + | 0.931492i | \(0.618507\pi\) | |||||||
\(350\) | −3.49120 | − | 10.7448i | −0.186612 | − | 0.574334i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 5.81234i | − | 0.309799i | ||||||
\(353\) | 20.5942i | 1.09612i | 0.836439 | + | 0.548060i | \(0.184633\pi\) | ||||
−0.836439 | + | 0.548060i | \(0.815367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 17.5680i | − | 0.932415i | ||||||
\(356\) | −10.6101 | − | 14.6035i | −0.562332 | − | 0.773984i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.56067 | + | 29.4247i | 0.505297 | + | 1.55514i | ||||
\(359\) | 32.1142i | 1.69493i | 0.530855 | + | 0.847463i | \(0.321871\pi\) | ||||
−0.530855 | + | 0.847463i | \(0.678129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6525 | −0.929078 | ||||||||
\(362\) | 5.62254 | + | 17.3044i | 0.295514 | + | 0.909500i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 25.6797 | − | 2.06837i | 1.34598 | − | 0.108412i | ||||
\(365\) | − | 7.34173i | − | 0.384284i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.1246 | 1.62469 | 0.812346 | − | 0.583176i | \(-0.198190\pi\) | ||||
0.812346 | + | 0.583176i | \(0.198190\pi\) | |||||||
\(368\) | 10.1050 | − | 31.1001i | 0.526761 | − | 1.62120i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.9911 | − | 7.14533i | 1.14326 | − | 0.371468i | ||||
\(371\) | −40.2000 | −2.08708 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.0746i | 1.35009i | 0.737777 | + | 0.675045i | \(0.235876\pi\) | ||||
−0.737777 | + | 0.675045i | \(0.764124\pi\) | |||||||
\(374\) | −6.98240 | + | 2.26872i | −0.361051 | + | 0.117313i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.7082 | − | 12.8658i | −0.913231 | − | 0.663501i | ||||
\(377\) | −13.2276 | − | 8.07262i | −0.681258 | − | 0.415761i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3954 | −0.996273 | −0.498137 | − | 0.867099i | \(-0.665982\pi\) | ||||
−0.498137 | + | 0.867099i | \(0.665982\pi\) | |||||||
\(380\) | 3.12262 | − | 2.26872i | 0.160187 | − | 0.116383i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.59569 | + | 0.843392i | −0.132807 | + | 0.0431517i | ||||
\(383\) | − | 3.57494i | − | 0.182671i | −0.995820 | − | 0.0913354i | \(-0.970886\pi\) | ||
0.995820 | − | 0.0913354i | \(-0.0291135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6.10284i | − | 0.311030i | ||||||
\(386\) | −1.92989 | − | 5.93958i | −0.0982287 | − | 0.302317i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.5912 | + | 18.7067i | 0.689990 | + | 0.949690i | ||||
\(389\) | 35.3980i | 1.79475i | 0.441270 | + | 0.897374i | \(0.354528\pi\) | ||||
−0.441270 | + | 0.897374i | \(0.645472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.3050 | −2.08888 | ||||||||
\(392\) | 9.58258 | − | 13.1893i | 0.483993 | − | 0.666160i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −31.1803 | + | 10.1311i | −1.57084 | + | 0.510398i | ||||
\(395\) | 11.5449 | 0.580887 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.5562 | −1.03169 | −0.515843 | − | 0.856683i | \(-0.672521\pi\) | ||||
−0.515843 | + | 0.856683i | \(0.672521\pi\) | |||||||
\(398\) | −24.2099 | + | 7.86629i | −1.21353 | + | 0.394301i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.76393 | + | 8.50651i | −0.138197 | + | 0.425325i | ||||
\(401\) | 30.4149i | 1.51885i | 0.650596 | + | 0.759424i | \(0.274519\pi\) | ||||
−0.650596 | + | 0.759424i | \(0.725481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.5868 | − | 15.0049i | −1.22475 | − | 0.747447i | ||||
\(404\) | 9.36787 | + | 12.8938i | 0.466069 | + | 0.641489i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.6525 | + | 6.71040i | −1.02497 | + | 0.333031i | ||||
\(407\) | −10.1050 | −0.500887 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 34.6842i | − | 1.71502i | −0.514466 | − | 0.857511i | \(-0.672010\pi\) | ||
0.514466 | − | 0.857511i | \(-0.327990\pi\) | |||||||
\(410\) | 1.17739 | + | 3.62365i | 0.0581474 | + | 0.178959i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.9443 | + | 13.7638i | −0.933317 | + | 0.678095i | ||||
\(413\) | 34.7709i | 1.71097i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.81966 | 0.187500 | ||||||||
\(416\) | −17.4100 | − | 10.6250i | −0.853596 | − | 0.520936i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.60423 | + | 0.521245i | −0.0784653 | + | 0.0254949i | ||||
\(419\) | − | 7.96879i | − | 0.389301i | −0.980873 | − | 0.194650i | \(-0.937643\pi\) | ||
0.980873 | − | 0.194650i | \(-0.0623572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.39984 | 0.409383 | 0.204692 | − | 0.978827i | \(-0.434381\pi\) | ||||
0.204692 | + | 0.978827i | \(0.434381\pi\) | |||||||
\(422\) | −4.59506 | − | 14.1421i | −0.223684 | − | 0.688428i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.7476 | + | 18.7067i | 1.25041 | + | 0.908478i | ||||
\(425\) | 11.2978 | 0.548022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 40.7737 | 1.97318 | ||||||||
\(428\) | −3.12262 | − | 4.29792i | −0.150938 | − | 0.207748i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.70820 | + | 5.25731i | 0.0823769 | + | 0.253530i | ||||
\(431\) | − | 1.82688i | − | 0.0879975i | −0.999032 | − | 0.0439987i | \(-0.985990\pi\) | ||
0.999032 | − | 0.0439987i | \(-0.0140098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.18034 | −0.393122 | −0.196561 | − | 0.980492i | \(-0.562977\pi\) | ||||
−0.196561 | + | 0.980492i | \(0.562977\pi\) | |||||||
\(434\) | −38.3876 | + | 12.4729i | −1.84266 | + | 0.598718i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.6694 | + | 14.2907i | −0.941994 | + | 0.684398i | ||||
\(437\) | −9.48993 | −0.453965 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.81966 | 0.0868476 | 0.0434238 | − | 0.999057i | \(-0.486173\pi\) | ||||
0.0434238 | + | 0.999057i | \(0.486173\pi\) | |||||||
\(440\) | −2.83990 | + | 3.90879i | −0.135387 | + | 0.186344i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.96832 | + | 25.0620i | −0.283884 | + | 1.19208i | ||||
\(443\) | 11.2521i | 0.534604i | 0.963613 | + | 0.267302i | \(0.0861321\pi\) | ||||
−0.963613 | + | 0.267302i | \(0.913868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0049i | 0.711301i | ||||||||
\(446\) | 3.49120 | + | 10.7448i | 0.165313 | + | 0.508781i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −27.1824 | + | 8.83211i | −1.28425 | + | 0.417278i | ||||
\(449\) | − | 4.86163i | − | 0.229435i | −0.993398 | − | 0.114717i | \(-0.963404\pi\) | ||
0.993398 | − | 0.114717i | \(-0.0365962\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.66509i | − | 0.0784059i | ||||||
\(452\) | −8.17513 | + | 5.93958i | −0.384526 | + | 0.279374i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.85410 | + | 1.90211i | −0.274747 | + | 0.0892706i | ||||
\(455\) | −18.2802 | − | 11.1561i | −0.856987 | − | 0.523005i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0199i | 0.796159i | 0.917351 | + | 0.398079i | \(0.130323\pi\) | ||||
−0.917351 | + | 0.398079i | \(0.869677\pi\) | |||||||
\(458\) | −1.92989 | + | 0.627058i | −0.0901777 | + | 0.0293005i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.9911 | + | 15.9774i | −1.02534 | + | 0.744952i | ||||
\(461\) | −21.9124 | −1.02056 | −0.510282 | − | 0.860007i | \(-0.670459\pi\) | ||||
−0.510282 | + | 0.860007i | \(0.670459\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.57266i | − | 0.166036i | −0.996548 | − | 0.0830179i | \(-0.973544\pi\) | ||
0.996548 | − | 0.0830179i | \(-0.0264559\pi\) | |||||||
\(464\) | 16.3503 | + | 5.31252i | 0.759042 | + | 0.246628i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.9911 | − | 7.14533i | 1.01872 | − | 0.331001i | ||||
\(467\) | − | 8.59584i | − | 0.397768i | −0.980023 | − | 0.198884i | \(-0.936268\pi\) | ||
0.980023 | − | 0.198884i | \(-0.0637317\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 25.8626i | − | 1.19422i | ||||||
\(470\) | 5.62254 | + | 17.3044i | 0.259349 | + | 0.798193i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.1803 | − | 22.2703i | 0.744761 | − | 1.02507i | ||||
\(473\) | − | 2.41577i | − | 0.111077i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.59569 | 0.119099 | ||||||||
\(476\) | 21.2201 | + | 29.2070i | 0.972623 | + | 1.33870i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.09017 | + | 9.51057i | 0.141341 | + | 0.435003i | ||||
\(479\) | 29.2858i | 1.33810i | 0.743216 | + | 0.669052i | \(0.233300\pi\) | ||||
−0.743216 | + | 0.669052i | \(0.766700\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.4721 | + | 30.2681i | −0.842257 | + | 1.38011i | ||||
\(482\) | 6.98240 | + | 21.4896i | 0.318040 | + | 0.978825i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.0902 | + | 11.6902i | −0.731371 | + | 0.531372i | ||||
\(485\) | − | 19.2209i | − | 0.872776i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.843392i | − | 0.0382177i | −0.999817 | − | 0.0191089i | \(-0.993917\pi\) | ||
0.999817 | − | 0.0191089i | \(-0.00608291\pi\) | |||||||
\(488\) | −26.1150 | − | 18.9737i | −1.18217 | − | 0.858898i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.8885 | + | 4.18774i | −0.582245 | + | 0.189183i | ||||
\(491\) | − | 2.02920i | − | 0.0915767i | −0.998951 | − | 0.0457883i | \(-0.985420\pi\) | ||
0.998951 | − | 0.0457883i | \(-0.0145800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 21.7153i | − | 0.978008i | ||||||
\(494\) | −1.37124 | + | 5.75807i | −0.0616950 | + | 0.259068i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.3909 | + | 9.87460i | 1.36459 | + | 0.443383i | ||||
\(497\) | 37.7530 | 1.69346 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.5347 | −1.50122 | −0.750609 | − | 0.660747i | \(-0.770240\pi\) | ||||
−0.750609 | + | 0.660747i | \(0.770240\pi\) | |||||||
\(500\) | 19.4650 | − | 14.1421i | 0.870500 | − | 0.632456i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.83470 | − | 30.2681i | −0.438944 | − | 1.35093i | ||||
\(503\) | 6.24525 | 0.278462 | 0.139231 | − | 0.990260i | \(-0.455537\pi\) | ||||
0.139231 | + | 0.990260i | \(0.455537\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 13.2482i | − | 0.589536i | ||||||
\(506\) | 11.2978 | − | 3.67086i | 0.502247 | − | 0.163190i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.70820 | + | 7.05342i | −0.430732 | + | 0.312945i | ||||
\(509\) | 9.58258 | 0.424740 | 0.212370 | − | 0.977189i | \(-0.431882\pi\) | ||||
0.212370 | + | 0.977189i | \(0.431882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.7771 | 0.697937 | ||||||||
\(512\) | 21.5200 | + | 6.99226i | 0.951057 | + | 0.309017i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.3909 | − | 9.87460i | 1.34049 | − | 0.435550i | ||||
\(515\) | 19.4650 | 0.857729 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7.95148i | − | 0.349706i | ||||||
\(518\) | 15.3550 | + | 47.2579i | 0.674661 | + | 2.07639i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.51682 | + | 15.6518i | 0.285781 | + | 0.686378i | ||||
\(521\) | 1.19274 | 0.0522547 | 0.0261274 | − | 0.999659i | \(-0.491682\pi\) | ||||
0.0261274 | + | 0.999659i | \(0.491682\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.0664i | 1.05235i | 0.850376 | + | 0.526176i | \(0.176375\pi\) | ||||
−0.850376 | + | 0.526176i | \(0.823625\pi\) | |||||||
\(524\) | 19.4729 | + | 26.8021i | 0.850677 | + | 1.17086i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.9911 | + | 7.14533i | −0.958856 | + | 0.311551i | ||||
\(527\) | − | 40.3631i | − | 1.75824i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.8328 | 1.90577 | ||||||||
\(530\) | −8.17513 | − | 25.1605i | −0.355105 | − | 1.09290i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.87539 | + | 6.71040i | 0.211375 | + | 0.290933i | ||||
\(533\) | −4.98752 | − | 3.04381i | −0.216034 | − | 0.131842i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.41606i | 0.190923i | ||||||||
\(536\) | −12.0349 | + | 16.5646i | −0.519829 | + | 0.715483i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.31312 | + | 10.1967i | 0.142839 | + | 0.439613i | ||||
\(539\) | 5.92236 | 0.255094 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.20845 | 0.137942 | 0.0689711 | − | 0.997619i | \(-0.478028\pi\) | ||||
0.0689711 | + | 0.997619i | \(0.478028\pi\) | |||||||
\(542\) | 3.49120 | + | 10.7448i | 0.149960 | + | 0.461529i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 28.5813i | − | 1.22541i | ||||||
\(545\) | 20.2100 | 0.865703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 42.1895i | − | 1.80389i | −0.431847 | − | 0.901947i | \(-0.642138\pi\) | ||
0.431847 | − | 0.901947i | \(-0.357862\pi\) | |||||||
\(548\) | −15.9901 | − | 22.0084i | −0.683061 | − | 0.940153i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.09017 | + | 1.00406i | −0.131765 | + | 0.0428131i | ||||
\(551\) | − | 4.98915i | − | 0.212545i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.8096i | 1.05501i | ||||||||
\(554\) | 7.92007 | + | 24.3755i | 0.336492 | + | 1.03561i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.7639 | + | 31.3319i | 0.965406 | + | 1.32877i | ||||
\(557\) | 24.4525 | 1.03609 | 0.518043 | − | 0.855355i | \(-0.326661\pi\) | ||||
0.518043 | + | 0.855355i | \(0.326661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.23607 | − | 4.41606i | −0.306053 | − | 0.186779i | ||||
\(560\) | 22.5955 | + | 7.34173i | 0.954835 | + | 0.310245i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.70820 | − | 8.33499i | −0.114239 | − | 0.351591i | ||||
\(563\) | − | 0.627058i | − | 0.0264274i | −0.999913 | − | 0.0132137i | \(-0.995794\pi\) | ||
0.999913 | − | 0.0132137i | \(-0.00420617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.39984 | 0.353384 | ||||||||
\(566\) | −1.27004 | − | 3.90879i | −0.0533839 | − | 0.164299i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.1803 | − | 17.5680i | −1.01458 | − | 0.737139i | ||||
\(569\) | 26.4553 | 1.10906 | 0.554532 | − | 0.832163i | \(-0.312897\pi\) | ||||
0.554532 | + | 0.832163i | \(0.312897\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.6215i | 1.03038i | 0.857077 | + | 0.515188i | \(0.172278\pi\) | ||||
−0.857077 | + | 0.515188i | \(0.827722\pi\) | |||||||
\(572\) | −0.594857 | − | 7.38539i | −0.0248722 | − | 0.308799i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.78708 | + | 2.53018i | −0.325026 | + | 0.105607i | ||||
\(575\) | −18.2802 | −0.762335 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 44.5588i | − | 1.85501i | −0.373816 | − | 0.927503i | \(-0.621951\pi\) | ||
0.373816 | − | 0.927503i | \(-0.378049\pi\) | |||||||
\(578\) | −11.4700 | + | 3.72681i | −0.477087 | + | 0.155015i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.39984 | − | 11.5614i | −0.348784 | − | 0.480060i | ||||
\(581\) | 8.20830i | 0.340538i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.5614i | 0.478824i | ||||||||
\(584\) | −10.1050 | − | 7.34173i | −0.418149 | − | 0.303803i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.18034 | − | 0.383516i | 0.0487594 | − | 0.0158429i | ||||
\(587\) | −10.5174 | −0.434100 | −0.217050 | − | 0.976160i | \(-0.569644\pi\) | ||||
−0.217050 | + | 0.976160i | \(0.569644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.27354i | − | 0.382110i | ||||||
\(590\) | −21.7625 | + | 7.07107i | −0.895948 | + | 0.291111i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.1564 | − | 37.4134i | 0.499623 | − | 1.53768i | ||||
\(593\) | 26.6637i | 1.09495i | 0.836823 | + | 0.547474i | \(0.184411\pi\) | ||||
−0.836823 | + | 0.547474i | \(0.815589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 30.0098i | − | 1.23028i | ||||||
\(596\) | −11.3950 | + | 8.27895i | −0.466757 | + | 0.339119i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.65694 | − | 40.5512i | 0.394902 | − | 1.65826i | ||||
\(599\) | −46.6653 | −1.90669 | −0.953347 | − | 0.301877i | \(-0.902387\pi\) | ||||
−0.953347 | + | 0.301877i | \(0.902387\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.4164 | 0.792012 | 0.396006 | − | 0.918248i | \(-0.370396\pi\) | ||||
0.396006 | + | 0.918248i | \(0.370396\pi\) | |||||||
\(602\) | −11.2978 | + | 3.67086i | −0.460462 | + | 0.149613i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.19992 | + | 5.78069i | 0.170892 | + | 0.235213i | ||||
\(605\) | 16.5324 | 0.672139 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.7082 | 0.637576 | 0.318788 | − | 0.947826i | \(-0.396724\pi\) | ||||
0.318788 | + | 0.947826i | \(0.396724\pi\) | |||||||
\(608\) | − | 6.56664i | − | 0.266312i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.29180 | + | 25.5195i | 0.335725 | + | 1.03326i | ||||
\(611\) | −23.8175 | − | 14.5354i | −0.963552 | − | 0.588040i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.96497 | −0.281313 | −0.140656 | − | 0.990058i | \(-0.544921\pi\) | ||||
−0.140656 | + | 0.990058i | \(0.544921\pi\) | |||||||
\(614\) | 19.8415 | − | 6.44688i | 0.800736 | − | 0.260175i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.39984 | − | 6.10284i | −0.338439 | − | 0.245890i | ||||
\(617\) | 3.36861i | 0.135615i | 0.997698 | + | 0.0678075i | \(0.0216004\pi\) | ||||
−0.997698 | + | 0.0678075i | \(0.978400\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.7781 | 1.19688 | 0.598442 | − | 0.801166i | \(-0.295787\pi\) | ||||
0.598442 | + | 0.801166i | \(0.295787\pi\) | |||||||
\(620\) | −15.6131 | − | 21.4896i | −0.627038 | − | 0.863044i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.9866 | + | 10.7180i | −1.32264 | + | 0.429752i | ||||
\(623\) | −32.2450 | −1.29187 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.81966 | −0.352786 | ||||||||
\(626\) | −8.70500 | + | 2.82843i | −0.347922 | + | 0.113047i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.652476 | + | 0.898056i | 0.0260366 | + | 0.0358363i | ||||
\(629\) | −49.6899 | −1.98127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2794i | 0.886928i | 0.896292 | + | 0.443464i | \(0.146251\pi\) | ||||
−0.896292 | + | 0.443464i | \(0.853749\pi\) | |||||||
\(632\) | 11.5449 | − | 15.8902i | 0.459232 | − | 0.632078i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 41.8328 | − | 13.5923i | 1.66139 | − | 0.539819i | ||||
\(635\) | 9.97505 | 0.395848 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.8262 | − | 17.7396i | 0.428948 | − | 0.702867i | ||||
\(638\) | 1.92989 | + | 5.93958i | 0.0764050 | + | 0.235150i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.0557 | − | 15.2169i | −0.437016 | − | 0.601501i | ||||
\(641\) | −43.9983 | −1.73783 | −0.868914 | − | 0.494963i | \(-0.835182\pi\) | ||||
−0.868914 | + | 0.494963i | \(0.835182\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.8734 | 1.33584 | 0.667918 | − | 0.744235i | \(-0.267186\pi\) | ||||
0.667918 | + | 0.744235i | \(0.267186\pi\) | |||||||
\(644\) | −34.3349 | − | 47.2579i | −1.35298 | − | 1.86222i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.88854 | + | 2.56314i | −0.310371 | + | 0.100846i | ||||
\(647\) | 36.5603 | 1.43733 | 0.718667 | − | 0.695354i | \(-0.244753\pi\) | ||||
0.718667 | + | 0.695354i | \(0.244753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | 0.392534 | ||||||||
\(650\) | −2.64137 | + | 11.0916i | −0.103603 | + | 0.435048i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.7130 | − | 8.50997i | 0.458715 | − | 0.333276i | ||||
\(653\) | 33.3688i | 1.30582i | 0.757435 | + | 0.652911i | \(0.226452\pi\) | ||||
−0.757435 | + | 0.652911i | \(0.773548\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 27.5388i | − | 1.07603i | ||||||
\(656\) | 6.16492 | + | 2.00310i | 0.240700 | + | 0.0782080i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −37.1865 | + | 12.0826i | −1.44968 | + | 0.471030i | ||||
\(659\) | 36.4126i | 1.41843i | 0.704991 | + | 0.709216i | \(0.250951\pi\) | ||||
−0.704991 | + | 0.709216i | \(0.749049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.3038 | −1.80101 | −0.900504 | − | 0.434847i | \(-0.856802\pi\) | ||||
−0.900504 | + | 0.434847i | \(0.856802\pi\) | |||||||
\(662\) | 14.7890 | − | 4.80522i | 0.574789 | − | 0.186760i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.81966 | − | 5.25731i | 0.148232 | − | 0.204023i | ||||
\(665\) | − | 6.89484i | − | 0.267370i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.1361i | 1.36047i | ||||||||
\(668\) | 8.61236 | + | 11.8539i | 0.333222 | + | 0.458641i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.1869 | − | 5.25945i | 0.625355 | − | 0.203190i | ||||
\(671\) | − | 11.7264i | − | 0.452692i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.6525 | −0.487717 | −0.243859 | − | 0.969811i | \(-0.578413\pi\) | ||||
−0.243859 | + | 0.969811i | \(0.578413\pi\) | |||||||
\(674\) | −7.43496 | + | 2.41577i | −0.286384 | + | 0.0930518i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.2093 | − | 11.7188i | −0.892664 | − | 0.450723i | ||||
\(677\) | − | 17.8187i | − | 0.684830i | −0.939549 | − | 0.342415i | \(-0.888755\pi\) | ||
0.939549 | − | 0.342415i | \(-0.111245\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.3050 | 1.58514 | ||||||||
\(680\) | −13.9648 | + | 19.2209i | −0.535525 | + | 0.737088i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.58716 | + | 11.0401i | 0.137359 | + | 0.422749i | ||||
\(683\) | −10.5174 | −0.402438 | −0.201219 | − | 0.979546i | \(-0.564490\pi\) | ||||
−0.201219 | + | 0.979546i | \(0.564490\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.6134i | 0.864012i | ||||||||
\(686\) | 1.92989 | + | 5.93958i | 0.0736834 | + | 0.226774i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.94427 | + | 2.90617i | 0.340997 | + | 0.110797i | ||||
\(689\) | 34.6304 | + | 21.1344i | 1.31931 | + | 0.805156i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.91735 | −0.187065 | −0.0935324 | − | 0.995616i | \(-0.529816\pi\) | ||||
−0.0935324 | + | 0.995616i | \(0.529816\pi\) | |||||||
\(692\) | −13.2276 | − | 18.2063i | −0.502840 | − | 0.692099i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.94791 | + | 27.5388i | 0.339658 | + | 1.04536i | ||||
\(695\) | − | 32.1931i | − | 1.22115i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.18782i | − | 0.310136i | ||||||
\(698\) | 18.2802 | − | 5.93958i | 0.691914 | − | 0.224817i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.39130 | + | 12.9260i | 0.354958 | + | 0.488558i | ||||
\(701\) | − | 26.8021i | − | 1.01230i | −0.862445 | − | 0.506151i | \(-0.831068\pi\) | ||
0.862445 | − | 0.506151i | \(-0.168932\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4164 | −0.430578 | ||||||||
\(704\) | 2.54009 | + | 7.81758i | 0.0957331 | + | 0.294636i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | − | 27.6992i | −0.338719 | − | 1.04247i | ||||
\(707\) | 28.4698 | 1.07072 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.39984 | −0.315463 | −0.157731 | − | 0.987482i | \(-0.550418\pi\) | ||||
−0.157731 | + | 0.987482i | \(0.550418\pi\) | |||||||
\(710\) | 7.67752 | + | 23.6290i | 0.288132 | + | 0.886779i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.6525 | + | 15.0049i | 0.773984 | + | 0.562332i | ||||
\(713\) | 65.3089i | 2.44584i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.20845 | + | 5.25731i | −0.119989 | + | 0.196612i | ||||
\(716\) | −25.7181 | − | 35.3980i | −0.961132 | − | 1.32288i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.0344 | − | 43.1936i | −0.523761 | − | 1.61197i | ||||
\(719\) | 12.0349 | 0.448826 | 0.224413 | − | 0.974494i | \(-0.427953\pi\) | ||||
0.224413 | + | 0.974494i | \(0.427953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.8295i | 1.55781i | ||||||||
\(722\) | 23.7425 | − | 7.71441i | 0.883605 | − | 0.287101i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.1246 | − | 20.8172i | −0.562102 | − | 0.773667i | ||||
\(725\) | − | 9.61045i | − | 0.356923i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.3607 | −0.829312 | −0.414656 | − | 0.909978i | \(-0.636098\pi\) | ||||
−0.414656 | + | 0.909978i | \(0.636098\pi\) | |||||||
\(728\) | −33.6352 | + | 14.0044i | −1.24660 | + | 0.519037i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.20845 | + | 9.87460i | 0.118750 | + | 0.365475i | ||||
\(731\) | − | 11.8792i | − | 0.439367i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.8519 | 1.73051 | 0.865256 | − | 0.501330i | \(-0.167156\pi\) | ||||
0.865256 | + | 0.501330i | \(0.167156\pi\) | |||||||
\(734\) | −41.8625 | + | 13.6020i | −1.54517 | + | 0.502057i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 46.2455i | 1.70463i | ||||||||
\(737\) | −7.43798 | −0.273982 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.9434 | −0.733631 | −0.366816 | − | 0.930294i | \(-0.619552\pi\) | ||||
−0.366816 | + | 0.930294i | \(0.619552\pi\) | |||||||
\(740\) | −26.4553 | + | 19.2209i | −0.972516 | + | 0.706574i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 54.0689 | − | 17.5680i | 1.98493 | − | 0.644943i | ||||
\(743\) | − | 47.5918i | − | 1.74597i | −0.487744 | − | 0.872987i | \(-0.662180\pi\) | ||
0.487744 | − | 0.872987i | \(-0.337820\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7082 | 0.428955 | ||||||||
\(746\) | −11.3950 | − | 35.0702i | −0.417201 | − | 1.28401i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.39984 | − | 6.10284i | 0.307129 | − | 0.223142i | ||||
\(749\) | −9.48993 | −0.346755 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −54.5410 | −1.99023 | −0.995115 | − | 0.0987222i | \(-0.968524\pi\) | ||||
−0.995115 | + | 0.0987222i | \(0.968524\pi\) | |||||||
\(752\) | 29.4400 | + | 9.56564i | 1.07357 | + | 0.348823i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.3190 | + | 5.07696i | 0.776392 | + | 0.184892i | ||||
\(755\) | − | 5.93958i | − | 0.216164i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.50651i | 0.309174i | 0.987979 | + | 0.154587i | \(0.0494047\pi\) | ||||
−0.987979 | + | 0.154587i | \(0.950595\pi\) | |||||||
\(758\) | 26.0867 | − | 8.47609i | 0.947512 | − | 0.307865i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.20845 | + | 4.41606i | −0.116383 | + | 0.160187i | ||||
\(761\) | 16.4304i | 0.595601i | 0.954628 | + | 0.297800i | \(0.0962530\pi\) | ||||
−0.954628 | + | 0.297800i | \(0.903747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.4306i | 1.57229i | ||||||||
\(764\) | 3.12262 | − | 2.26872i | 0.112973 | − | 0.0820794i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.56231 | + | 4.80828i | 0.0564484 | + | 0.173730i | ||||
\(767\) | 18.2802 | − | 29.9535i | 0.660058 | − | 1.08156i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 24.1653i | − | 0.871422i | −0.900087 | − | 0.435711i | \(-0.856497\pi\) | ||
0.900087 | − | 0.435711i | \(-0.143503\pi\) | |||||||
\(770\) | 2.66704 | + | 8.20830i | 0.0961134 | + | 0.295807i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.19139 | + | 7.14533i | 0.186842 | + | 0.257166i | ||||
\(773\) | −30.3176 | −1.09045 | −0.545224 | − | 0.838290i | \(-0.683555\pi\) | ||||
−0.545224 | + | 0.838290i | \(0.683555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 17.8633i | − | 0.641669i | ||||||
\(776\) | −26.4553 | − | 19.2209i | −0.949690 | − | 0.689990i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.4695 | − | 47.6102i | −0.554608 | − | 1.70691i | ||||
\(779\) | − | 1.88118i | − | 0.0674001i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 10.8576i | − | 0.388517i | ||||||
\(782\) | 55.5550 | − | 18.0509i | 1.98664 | − | 0.645500i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.12461 | + | 21.9273i | −0.254450 | + | 0.783118i | ||||
\(785\) | − | 0.922740i | − | 0.0329340i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.4996 | −1.44366 | −0.721828 | − | 0.692072i | \(-0.756698\pi\) | ||||
−0.721828 | + | 0.692072i | \(0.756698\pi\) | |||||||
\(788\) | 37.5100 | − | 27.2526i | 1.33624 | − | 0.970834i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.5279 | + | 5.04531i | −0.552457 | + | 0.179504i | ||||
\(791\) | 18.0509i | 0.641817i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.1246 | − | 21.4360i | −1.24731 | − | 0.761214i | ||||
\(794\) | 27.6480 | − | 8.98339i | 0.981192 | − | 0.318809i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 29.1246 | − | 21.1603i | 1.03229 | − | 0.750006i | ||||
\(797\) | 21.4896i | 0.761201i | 0.924740 | + | 0.380601i | \(0.124283\pi\) | ||||
−0.924740 | + | 0.380601i | \(0.875717\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 39.1002i | − | 1.38327i | ||||||
\(800\) | − | 12.6491i | − | 0.447214i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.2918 | − | 40.9079i | −0.469350 | − | 1.44451i | ||||
\(803\) | − | 4.53744i | − | 0.160123i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 48.5569i | 1.71141i | ||||||||
\(806\) | 39.6265 | + | 9.43674i | 1.39578 | + | 0.332395i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.2345 | − | 13.2482i | −0.641489 | − | 0.466069i | ||||
\(809\) | −27.6480 | −0.972053 | −0.486026 | − | 0.873944i | \(-0.661554\pi\) | ||||
−0.486026 | + | 0.873944i | \(0.661554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.7863 | 1.74823 | 0.874116 | − | 0.485717i | \(-0.161441\pi\) | ||||
0.874116 | + | 0.485717i | \(0.161441\pi\) | |||||||
\(812\) | 24.8450 | − | 18.0509i | 0.871887 | − | 0.633463i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.5912 | − | 4.41606i | 0.476372 | − | 0.154783i | ||||
\(815\) | −12.0349 | −0.421564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.72927i | − | 0.0954852i | ||||||
\(818\) | 15.1575 | + | 46.6501i | 0.529971 | + | 1.63108i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.16718 | − | 4.35926i | −0.110603 | − | 0.152232i | ||||
\(821\) | 18.5874 | 0.648705 | 0.324352 | − | 0.945936i | \(-0.394854\pi\) | ||||
0.324352 | + | 0.945936i | \(0.394854\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1803 | 0.494296 | 0.247148 | − | 0.968978i | \(-0.420507\pi\) | ||||
0.247148 | + | 0.968978i | \(0.420507\pi\) | |||||||
\(824\) | 19.4650 | − | 26.7912i | 0.678095 | − | 0.933317i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.1954 | − | 46.7668i | −0.528717 | − | 1.62722i | ||||
\(827\) | 36.3326 | 1.26341 | 0.631704 | − | 0.775209i | \(-0.282356\pi\) | ||||
0.631704 | + | 0.775209i | \(0.282356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 31.3319i | − | 1.08820i | −0.839020 | − | 0.544100i | \(-0.816871\pi\) | ||
0.839020 | − | 0.544100i | \(-0.183129\pi\) | |||||||
\(830\) | −5.13743 | + | 1.66925i | −0.178323 | + | 0.0579406i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.0597 | + | 6.68221i | 0.972796 | + | 0.231664i | ||||
\(833\) | 29.1223 | 1.00903 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 12.1797i | − | 0.421496i | ||||||
\(836\) | 1.92989 | − | 1.40215i | 0.0667465 | − | 0.0484942i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.48249 | + | 10.7180i | 0.120301 | + | 0.370247i | ||||
\(839\) | − | 45.0184i | − | 1.55421i | −0.629372 | − | 0.777104i | \(-0.716688\pi\) | ||
0.629372 | − | 0.777104i | \(-0.283312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5279 | 0.363030 | ||||||||
\(842\) | −11.2978 | + | 3.67086i | −0.389346 | + | 0.126506i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.3607 | + | 17.0130i | 0.425472 | + | 0.585612i | ||||
\(845\) | 9.88240 | + | 19.2209i | 0.339965 | + | 0.661219i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.5275i | 1.22074i | ||||||||
\(848\) | −42.8056 | − | 13.9084i | −1.46995 | − | 0.477615i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15.1954 | + | 4.93730i | −0.521200 | + | 0.169348i | ||||
\(851\) | 80.4000 | 2.75608 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.5041 | −1.01020 | −0.505101 | − | 0.863060i | \(-0.668545\pi\) | ||||
−0.505101 | + | 0.863060i | \(0.668545\pi\) | |||||||
\(854\) | −54.8405 | + | 17.8187i | −1.87660 | + | 0.609745i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.07818 | + | 4.41606i | 0.207748 | + | 0.150938i | ||||
\(857\) | −12.4905 | −0.426667 | −0.213334 | − | 0.976979i | \(-0.568432\pi\) | ||||
−0.213334 | + | 0.976979i | \(0.568432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.5276i | 0.939231i | 0.882871 | + | 0.469615i | \(0.155607\pi\) | ||||
−0.882871 | + | 0.469615i | \(0.844393\pi\) | |||||||
\(860\) | −4.59506 | − | 6.32456i | −0.156690 | − | 0.215666i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.798374 | + | 2.45714i | 0.0271927 | + | 0.0836906i | ||||
\(863\) | − | 12.0602i | − | 0.410535i | −0.978706 | − | 0.205267i | \(-0.934194\pi\) | ||
0.978706 | − | 0.205267i | \(-0.0658064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.7067i | 0.636047i | ||||||||
\(866\) | 11.0025 | − | 3.57494i | 0.373881 | − | 0.121481i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 46.1803 | − | 33.5520i | 1.56746 | − | 1.13883i | ||||
\(869\) | 7.13514 | 0.242043 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.5967 | + | 22.2794i | −0.460708 | + | 0.754908i | ||||
\(872\) | 20.2100 | − | 27.8167i | 0.684398 | − | 0.941994i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.7639 | − | 4.14725i | 0.431746 | − | 0.140283i | ||||
\(875\) | − | 42.9792i | − | 1.45296i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4430 | 0.724078 | 0.362039 | − | 0.932163i | \(-0.382081\pi\) | ||||
0.362039 | + | 0.932163i | \(0.382081\pi\) | |||||||
\(878\) | −2.44744 | + | 0.795221i | −0.0825970 | + | 0.0268374i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.11146 | − | 6.49839i | 0.0711772 | − | 0.219061i | ||||
\(881\) | −10.1050 | −0.340447 | −0.170223 | − | 0.985405i | \(-0.554449\pi\) | ||||
−0.170223 | + | 0.985405i | \(0.554449\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.5146i | 0.353845i | 0.984225 | + | 0.176923i | \(0.0566142\pi\) | ||||
−0.984225 | + | 0.176923i | \(0.943386\pi\) | |||||||
\(884\) | −2.92512 | − | 36.3166i | −0.0983825 | − | 1.22146i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.91735 | − | 15.1340i | −0.165202 | − | 0.508438i | ||||
\(887\) | −30.7706 | −1.03318 | −0.516589 | − | 0.856234i | \(-0.672798\pi\) | ||||
−0.516589 | + | 0.856234i | \(0.672798\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.4360i | 0.718940i | ||||||||
\(890\) | −6.55738 | − | 20.1815i | −0.219804 | − | 0.676487i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.39130 | − | 12.9260i | −0.314444 | − | 0.432795i | ||||
\(893\) | − | 8.98339i | − | 0.300618i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.3709i | 1.21575i | ||||||||
\(896\) | 32.7005 | − | 23.7583i | 1.09245 | − | 0.793710i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.12461 | + | 6.53888i | 0.0708992 | + | 0.218205i | ||||
\(899\) | −34.3349 | −1.14513 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.8514i | 1.89399i | ||||||||
\(902\) | 0.727670 | + | 2.23954i | 0.0242288 | + | 0.0745684i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.39984 | − | 11.5614i | 0.279374 | − | 0.384526i | ||||
\(905\) | 21.3894i | 0.711009i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.81234i | 0.192996i | 0.995333 | + | 0.0964978i | \(0.0307641\pi\) | ||||
−0.995333 | + | 0.0964978i | \(0.969236\pi\) | |||||||
\(908\) | 7.04250 | − | 5.11667i | 0.233713 | − | 0.169803i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 29.4621 | + | 7.01618i | 0.976661 | + | 0.232584i | ||||
\(911\) | 40.8757 | 1.35427 | 0.677136 | − | 0.735858i | \(-0.263221\pi\) | ||||
0.677136 | + | 0.735858i | \(0.263221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.36068 | 0.0781271 | ||||||||
\(914\) | −7.43798 | − | 22.8918i | −0.246027 | − | 0.757192i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.32166 | − | 1.68678i | 0.0767097 | − | 0.0557329i | ||||
\(917\) | 59.1799 | 1.95429 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.41641 | 0.178671 | 0.0893354 | − | 0.996002i | \(-0.471526\pi\) | ||||
0.0893354 | + | 0.996002i | \(0.471526\pi\) | |||||||
\(920\) | 22.5955 | − | 31.1001i | 0.744952 | − | 1.02534i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.4721 | − | 9.57608i | 0.970613 | − | 0.315371i | ||||
\(923\) | −32.5225 | − | 19.8480i | −1.07049 | − | 0.653303i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.9911 | −0.723062 | ||||||||
\(926\) | 1.56131 | + | 4.80522i | 0.0513079 | + | 0.157909i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −24.3127 | −0.798104 | ||||||||
\(929\) | − | 6.86474i | − | 0.225225i | −0.993639 | − | 0.112612i | \(-0.964078\pi\) | ||
0.993639 | − | 0.112612i | \(-0.0359218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.69094 | 0.219287 | ||||||||
\(932\) | −26.4553 | + | 19.2209i | −0.866572 | + | 0.629601i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.75652 | + | 11.5614i | 0.122917 | + | 0.378300i | ||||
\(935\) | −8.63072 | −0.282255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.6525 | −1.00137 | −0.500686 | − | 0.865629i | \(-0.666919\pi\) | ||||
−0.500686 | + | 0.865629i | \(0.666919\pi\) | |||||||
\(938\) | 11.3023 | + | 34.7851i | 0.369035 | + | 1.13577i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.1246 | − | 20.8172i | −0.493310 | − | 0.678984i | ||||
\(941\) | −36.4825 | −1.18930 | −0.594648 | − | 0.803986i | \(-0.702709\pi\) | ||||
−0.594648 | + | 0.803986i | \(0.702709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.2482i | 0.431420i | ||||||||
\(944\) | −12.0300 | + | 37.0246i | −0.391544 | + | 1.20505i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.05573 | + | 3.24920i | 0.0343247 | + | 0.105641i | ||||
\(947\) | 49.9325 | 1.62259 | 0.811294 | − | 0.584638i | \(-0.198764\pi\) | ||||
0.811294 | + | 0.584638i | \(0.198764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.5912 | − | 8.29451i | −0.441190 | − | 0.269251i | ||||
\(950\) | −3.49120 | + | 1.13436i | −0.113269 | + | 0.0368035i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −41.3050 | − | 30.0098i | −1.33870 | − | 0.972623i | ||||
\(953\) | 32.7005 | 1.05927 | 0.529637 | − | 0.848224i | \(-0.322328\pi\) | ||||
0.529637 | + | 0.848224i | \(0.322328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.20845 | −0.103823 | ||||||||
\(956\) | −8.31254 | − | 11.4412i | −0.268847 | − | 0.370036i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.7984 | − | 39.3893i | −0.413497 | − | 1.27261i | ||||
\(959\) | −48.5952 | −1.56922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32.8197 | −1.05870 | ||||||||
\(962\) | 11.6173 | − | 48.7831i | 0.374558 | − | 1.57283i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.7826 | − | 25.8520i | −0.604947 | − | 0.832638i | ||||
\(965\) | − | 7.34173i | − | 0.236339i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.25945i | 0.169132i | 0.996418 | + | 0.0845662i | \(0.0269505\pi\) | ||||
−0.996418 | + | 0.0845662i | \(0.973050\pi\) | |||||||
\(968\) | 16.5324 | − | 22.7549i | 0.531372 | − | 0.731371i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.39984 | + | 25.8520i | 0.269703 | + | 0.830059i | ||||
\(971\) | − | 4.05841i | − | 0.130240i | −0.997877 | − | 0.0651202i | \(-0.979257\pi\) | ||
0.997877 | − | 0.0651202i | \(-0.0207431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 69.1816 | 2.21786 | ||||||||
\(974\) | 0.368576 | + | 1.13436i | 0.0118099 | + | 0.0363472i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 43.4164 | + | 14.1068i | 1.38973 | + | 0.451549i | ||||
\(977\) | 15.1924i | 0.486048i | 0.970020 | + | 0.243024i | \(0.0781393\pi\) | ||||
−0.970020 | + | 0.243024i | \(0.921861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.27354i | 0.296384i | ||||||||
\(980\) | 15.5049 | − | 11.2650i | 0.495287 | − | 0.359847i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.886795 | + | 2.72927i | 0.0282987 | + | 0.0870946i | ||||
\(983\) | − | 24.4543i | − | 0.779971i | −0.920821 | − | 0.389985i | \(-0.872480\pi\) | ||
0.920821 | − | 0.389985i | \(-0.127520\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.5410 | −1.22802 | ||||||||
\(986\) | 9.48993 | + | 29.2070i | 0.302221 | + | 0.930141i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.672055 | − | 8.34384i | −0.0213809 | − | 0.265453i | ||||
\(989\) | 19.2209i | 0.611189i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.1803 | −0.323389 | −0.161695 | − | 0.986841i | \(-0.551696\pi\) | ||||
−0.161695 | + | 0.986841i | \(0.551696\pi\) | |||||||
\(992\) | −45.1910 | −1.43482 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −50.7777 | + | 16.4987i | −1.61057 | + | 0.523307i | ||||
\(995\) | −29.9251 | −0.948691 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.9968i | 0.411612i | 0.978593 | + | 0.205806i | \(0.0659817\pi\) | ||||
−0.978593 | + | 0.205806i | \(0.934018\pi\) | |||||||
\(998\) | 45.1040 | − | 14.6552i | 1.42774 | − | 0.463902i | ||||
\(999\) | 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 | 936.2.m.h.181.3 | yes | 16 | |
3.2 | odd | 2 | inner | 936.2.m.h.181.13 | yes | 16 | |
4.3 | odd | 2 | 3744.2.m.h.1585.7 | 16 | |||
8.3 | odd | 2 | 3744.2.m.h.1585.12 | 16 | |||
8.5 | even | 2 | inner | 936.2.m.h.181.15 | yes | 16 | |
12.11 | even | 2 | 3744.2.m.h.1585.11 | 16 | |||
13.12 | even | 2 | inner | 936.2.m.h.181.14 | yes | 16 | |
24.5 | odd | 2 | inner | 936.2.m.h.181.1 | ✓ | 16 | |
24.11 | even | 2 | 3744.2.m.h.1585.8 | 16 | |||
39.38 | odd | 2 | inner | 936.2.m.h.181.4 | yes | 16 | |
52.51 | odd | 2 | 3744.2.m.h.1585.10 | 16 | |||
104.51 | odd | 2 | 3744.2.m.h.1585.5 | 16 | |||
104.77 | even | 2 | inner | 936.2.m.h.181.2 | yes | 16 | |
156.155 | even | 2 | 3744.2.m.h.1585.6 | 16 | |||
312.77 | odd | 2 | inner | 936.2.m.h.181.16 | yes | 16 | |
312.155 | even | 2 | 3744.2.m.h.1585.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
936.2.m.h.181.1 | ✓ | 16 | 24.5 | odd | 2 | inner | |
936.2.m.h.181.2 | yes | 16 | 104.77 | even | 2 | inner | |
936.2.m.h.181.3 | yes | 16 | 1.1 | even | 1 | trivial | |
936.2.m.h.181.4 | yes | 16 | 39.38 | odd | 2 | inner | |
936.2.m.h.181.13 | yes | 16 | 3.2 | odd | 2 | inner | |
936.2.m.h.181.14 | yes | 16 | 13.12 | even | 2 | inner | |
936.2.m.h.181.15 | yes | 16 | 8.5 | even | 2 | inner | |
936.2.m.h.181.16 | yes | 16 | 312.77 | odd | 2 | inner | |
3744.2.m.h.1585.5 | 16 | 104.51 | odd | 2 | |||
3744.2.m.h.1585.6 | 16 | 156.155 | even | 2 | |||
3744.2.m.h.1585.7 | 16 | 4.3 | odd | 2 | |||
3744.2.m.h.1585.8 | 16 | 24.11 | even | 2 | |||
3744.2.m.h.1585.9 | 16 | 312.155 | even | 2 | |||
3744.2.m.h.1585.10 | 16 | 52.51 | odd | 2 | |||
3744.2.m.h.1585.11 | 16 | 12.11 | even | 2 | |||
3744.2.m.h.1585.12 | 16 | 8.3 | odd | 2 |