Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,3,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (of order \(6\), degree \(2\), not 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: | \(4.41418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.107 |
Dual form | 162.3.d.a.53.2 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 0.707107i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | −7.34847 | + | 4.24264i | −1.46969 | + | 0.848528i | −0.999422 | − | 0.0339935i | \(-0.989177\pi\) |
−0.470272 | + | 0.882522i | \(0.655844\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 4.33013i | −0.357143 | + | 0.618590i | −0.987482 | − | 0.157730i | \(-0.949582\pi\) |
0.630339 | + | 0.776320i | \(0.282916\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −12.0000 | −1.20000 | ||||||||
\(11\) | −7.34847 | − | 4.24264i | −0.668043 | − | 0.385695i | 0.127292 | − | 0.991865i | \(-0.459371\pi\) |
−0.795335 | + | 0.606171i | \(0.792705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.0384615 | + | 0.0666173i | 0.884615 | − | 0.466321i | \(-0.154421\pi\) |
−0.846154 | + | 0.532939i | \(0.821088\pi\) | |||||||
\(14\) | −6.12372 | + | 3.53553i | −0.437409 | + | 0.252538i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 25.4558i | 1.49740i | 0.662908 | + | 0.748701i | \(0.269322\pi\) | ||||
−0.662908 | + | 0.748701i | \(0.730678\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.0000 | 1.52632 | 0.763158 | − | 0.646212i | \(-0.223648\pi\) | ||||
0.763158 | + | 0.646212i | \(0.223648\pi\) | |||||||
\(20\) | −14.6969 | − | 8.48528i | −0.734847 | − | 0.424264i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | − | 10.3923i | −0.272727 | − | 0.472377i | ||||
\(23\) | −7.34847 | + | 4.24264i | −0.319499 | + | 0.184463i | −0.651169 | − | 0.758933i | \(-0.725721\pi\) |
0.331670 | + | 0.943395i | \(0.392388\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.5000 | − | 40.7032i | 0.940000 | − | 1.62813i | ||||
\(26\) | 1.41421i | 0.0543928i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.0000 | −0.357143 | ||||||||
\(29\) | 14.6969 | + | 8.48528i | 0.506791 | + | 0.292596i | 0.731514 | − | 0.681827i | \(-0.238814\pi\) |
−0.224723 | + | 0.974423i | \(0.572148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | + | 8.66025i | 0.161290 | + | 0.279363i | 0.935332 | − | 0.353772i | \(-0.115101\pi\) |
−0.774041 | + | 0.633135i | \(0.781768\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.0000 | + | 31.1769i | −0.529412 | + | 0.916968i | ||||
\(35\) | − | 42.4264i | − | 1.21218i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −25.0000 | −0.675676 | −0.337838 | − | 0.941204i | \(-0.609696\pi\) | ||||
−0.337838 | + | 0.941204i | \(0.609696\pi\) | |||||||
\(38\) | 35.5176 | + | 20.5061i | 0.934674 | + | 0.539634i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.0000 | − | 20.7846i | −0.300000 | − | 0.519615i | ||||
\(41\) | 14.6969 | − | 8.48528i | 0.358462 | − | 0.206958i | −0.309944 | − | 0.950755i | \(-0.600310\pi\) |
0.668406 | + | 0.743797i | \(0.266977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.00000 | + | 12.1244i | −0.162791 | + | 0.281962i | −0.935869 | − | 0.352349i | \(-0.885383\pi\) |
0.773078 | + | 0.634311i | \(0.218716\pi\) | |||||||
\(44\) | − | 16.9706i | − | 0.385695i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | −0.260870 | ||||||||
\(47\) | −7.34847 | − | 4.24264i | −0.156350 | − | 0.0902690i | 0.419784 | − | 0.907624i | \(-0.362106\pi\) |
−0.576134 | + | 0.817355i | \(0.695439\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.0000 | + | 20.7846i | 0.244898 | + | 0.424176i | ||||
\(50\) | 57.5630 | − | 33.2340i | 1.15126 | − | 0.664680i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | + | 1.73205i | −0.0192308 | + | 0.0333087i | ||||
\(53\) | − | 50.9117i | − | 0.960598i | −0.877105 | − | 0.480299i | \(-0.840528\pi\) | ||
0.877105 | − | 0.480299i | \(-0.159472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 72.0000 | 1.30909 | ||||||||
\(56\) | −12.2474 | − | 7.07107i | −0.218704 | − | 0.126269i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.0000 | + | 20.7846i | 0.206897 | + | 0.358355i | ||||
\(59\) | 80.8332 | − | 46.6690i | 1.37005 | − | 0.791001i | 0.379119 | − | 0.925348i | \(-0.376227\pi\) |
0.990934 | + | 0.134347i | \(0.0428937\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.5000 | + | 19.9186i | −0.188525 | + | 0.326534i | −0.944759 | − | 0.327767i | \(-0.893704\pi\) |
0.756234 | + | 0.654301i | \(0.227037\pi\) | |||||||
\(62\) | 14.1421i | 0.228099i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −7.34847 | − | 4.24264i | −0.113053 | − | 0.0652714i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.50000 | + | 16.4545i | 0.141791 | + | 0.245589i | 0.928171 | − | 0.372154i | \(-0.121381\pi\) |
−0.786380 | + | 0.617743i | \(0.788047\pi\) | |||||||
\(68\) | −44.0908 | + | 25.4558i | −0.648394 | + | 0.374351i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 30.0000 | − | 51.9615i | 0.428571 | − | 0.742307i | ||||
\(71\) | 101.823i | 1.43413i | 0.697005 | + | 0.717066i | \(0.254515\pi\) | ||||
−0.697005 | + | 0.717066i | \(0.745485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −97.0000 | −1.32877 | −0.664384 | − | 0.747392i | \(-0.731306\pi\) | ||||
−0.664384 | + | 0.747392i | \(0.731306\pi\) | |||||||
\(74\) | −30.6186 | − | 17.6777i | −0.413765 | − | 0.238887i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 29.0000 | + | 50.2295i | 0.381579 | + | 0.660914i | ||||
\(77\) | 36.7423 | − | 21.2132i | 0.477173 | − | 0.275496i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −38.5000 | + | 66.6840i | −0.487342 | + | 0.844101i | −0.999894 | − | 0.0145553i | \(-0.995367\pi\) |
0.512552 | + | 0.858656i | \(0.328700\pi\) | |||||||
\(80\) | − | 33.9411i | − | 0.424264i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 24.0000 | 0.292683 | ||||||||
\(83\) | 102.879 | + | 59.3970i | 1.23950 | + | 0.715626i | 0.968992 | − | 0.247091i | \(-0.0794748\pi\) |
0.270509 | + | 0.962718i | \(0.412808\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −108.000 | − | 187.061i | −1.27059 | − | 2.20072i | ||||
\(86\) | −17.1464 | + | 9.89949i | −0.199377 | + | 0.115110i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.0000 | − | 20.7846i | 0.136364 | − | 0.236189i | ||||
\(89\) | − | 76.3675i | − | 0.858062i | −0.903290 | − | 0.429031i | \(-0.858855\pi\) | ||
0.903290 | − | 0.429031i | \(-0.141145\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00000 | −0.0549451 | ||||||||
\(92\) | −14.6969 | − | 8.48528i | −0.159749 | − | 0.0922313i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | − | 10.3923i | −0.0638298 | − | 0.110556i | ||||
\(95\) | −213.106 | + | 123.037i | −2.24322 | + | 1.29512i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 24.5000 | − | 42.4352i | 0.252577 | − | 0.437477i | −0.711657 | − | 0.702527i | \(-0.752055\pi\) |
0.964235 | + | 0.265050i | \(0.0853885\pi\) | |||||||
\(98\) | 33.9411i | 0.346338i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 94.0000 | 0.940000 | ||||||||
\(101\) | −117.576 | − | 67.8823i | −1.16411 | − | 0.672101i | −0.211827 | − | 0.977307i | \(-0.567941\pi\) |
−0.952286 | + | 0.305206i | \(0.901275\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 81.5000 | + | 141.162i | 0.791262 | + | 1.37051i | 0.925186 | + | 0.379515i | \(0.123909\pi\) |
−0.133924 | + | 0.990992i | \(0.542758\pi\) | |||||||
\(104\) | −2.44949 | + | 1.41421i | −0.0235528 | + | 0.0135982i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 36.0000 | − | 62.3538i | 0.339623 | − | 0.588244i | ||||
\(107\) | 25.4558i | 0.237905i | 0.992900 | + | 0.118953i | \(0.0379536\pi\) | ||||
−0.992900 | + | 0.118953i | \(0.962046\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.0183486 | 0.00917431 | − | 0.999958i | \(-0.497080\pi\) | ||||
0.00917431 | + | 0.999958i | \(0.497080\pi\) | |||||||
\(110\) | 88.1816 | + | 50.9117i | 0.801651 | + | 0.462834i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.0000 | − | 17.3205i | −0.0892857 | − | 0.154647i | ||||
\(113\) | −95.5301 | + | 55.1543i | −0.845399 | + | 0.488091i | −0.859096 | − | 0.511815i | \(-0.828973\pi\) |
0.0136967 | + | 0.999906i | \(0.495640\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 36.0000 | − | 62.3538i | 0.313043 | − | 0.542207i | ||||
\(116\) | 33.9411i | 0.292596i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 132.000 | 1.11864 | ||||||||
\(119\) | −110.227 | − | 63.6396i | −0.926278 | − | 0.534787i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.5000 | − | 42.4352i | −0.202479 | − | 0.350705i | ||||
\(122\) | −28.1691 | + | 16.2635i | −0.230895 | + | 0.133307i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.0000 | + | 17.3205i | −0.0806452 | + | 0.139682i | ||||
\(125\) | 186.676i | 1.49341i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −178.000 | −1.40157 | −0.700787 | − | 0.713370i | \(-0.747168\pi\) | ||||
−0.700787 | + | 0.713370i | \(0.747168\pi\) | |||||||
\(128\) | −9.79796 | − | 5.65685i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.00000 | − | 10.3923i | −0.0461538 | − | 0.0799408i | ||||
\(131\) | 102.879 | − | 59.3970i | 0.785333 | − | 0.453412i | −0.0529842 | − | 0.998595i | \(-0.516873\pi\) |
0.838317 | + | 0.545183i | \(0.183540\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −72.5000 | + | 125.574i | −0.545113 | + | 0.944163i | ||||
\(134\) | 26.8701i | 0.200523i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −72.0000 | −0.529412 | ||||||||
\(137\) | 80.8332 | + | 46.6690i | 0.590023 | + | 0.340650i | 0.765107 | − | 0.643904i | \(-0.222686\pi\) |
−0.175084 | + | 0.984554i | \(0.556020\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 81.5000 | + | 141.162i | 0.586331 | + | 1.01555i | 0.994708 | + | 0.102742i | \(0.0327615\pi\) |
−0.408377 | + | 0.912813i | \(0.633905\pi\) | |||||||
\(140\) | 73.4847 | − | 42.4264i | 0.524891 | − | 0.303046i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −72.0000 | + | 124.708i | −0.507042 | + | 0.878223i | ||||
\(143\) | − | 8.48528i | − | 0.0593376i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −144.000 | −0.993103 | ||||||||
\(146\) | −118.800 | − | 68.5894i | −0.813700 | − | 0.469790i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −25.0000 | − | 43.3013i | −0.168919 | − | 0.292576i | ||||
\(149\) | −29.3939 | + | 16.9706i | −0.197274 | + | 0.113896i | −0.595383 | − | 0.803442i | \(-0.703000\pi\) |
0.398109 | + | 0.917338i | \(0.369667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −74.5000 | + | 129.038i | −0.493377 | + | 0.854555i | −0.999971 | − | 0.00763022i | \(-0.997571\pi\) |
0.506593 | + | 0.862185i | \(0.330905\pi\) | |||||||
\(152\) | 82.0244i | 0.539634i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 60.0000 | 0.389610 | ||||||||
\(155\) | −73.4847 | − | 42.4264i | −0.474095 | − | 0.273719i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −121.000 | − | 209.578i | −0.770701 | − | 1.33489i | −0.937179 | − | 0.348848i | \(-0.886573\pi\) |
0.166479 | − | 0.986045i | \(-0.446760\pi\) | |||||||
\(158\) | −94.3054 | + | 54.4472i | −0.596869 | + | 0.344603i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 24.0000 | − | 41.5692i | 0.150000 | − | 0.259808i | ||||
\(161\) | − | 42.4264i | − | 0.263518i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 173.000 | 1.06135 | 0.530675 | − | 0.847575i | \(-0.321939\pi\) | ||||
0.530675 | + | 0.847575i | \(0.321939\pi\) | |||||||
\(164\) | 29.3939 | + | 16.9706i | 0.179231 | + | 0.103479i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 84.0000 | + | 145.492i | 0.506024 | + | 0.876459i | ||||
\(167\) | 169.015 | − | 97.5807i | 1.01206 | − | 0.584316i | 0.100269 | − | 0.994960i | \(-0.468030\pi\) |
0.911796 | + | 0.410645i | \(0.134696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 84.0000 | − | 145.492i | 0.497041 | − | 0.860901i | ||||
\(170\) | − | 305.470i | − | 1.79688i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −28.0000 | −0.162791 | ||||||||
\(173\) | 279.242 | + | 161.220i | 1.61411 | + | 0.931910i | 0.988403 | + | 0.151855i | \(0.0485248\pi\) |
0.625712 | + | 0.780054i | \(0.284809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 117.500 | + | 203.516i | 0.671429 | + | 1.16295i | ||||
\(176\) | 29.3939 | − | 16.9706i | 0.167011 | − | 0.0964237i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 54.0000 | − | 93.5307i | 0.303371 | − | 0.525454i | ||||
\(179\) | − | 305.470i | − | 1.70654i | −0.521472 | − | 0.853269i | \(-0.674617\pi\) | ||
0.521472 | − | 0.853269i | \(-0.325383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 263.000 | 1.45304 | 0.726519 | − | 0.687146i | \(-0.241137\pi\) | ||||
0.726519 | + | 0.687146i | \(0.241137\pi\) | |||||||
\(182\) | −6.12372 | − | 3.53553i | −0.0336468 | − | 0.0194260i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.0000 | − | 20.7846i | −0.0652174 | − | 0.112960i | ||||
\(185\) | 183.712 | − | 106.066i | 0.993036 | − | 0.573330i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 108.000 | − | 187.061i | 0.577540 | − | 1.00033i | ||||
\(188\) | − | 16.9706i | − | 0.0902690i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −348.000 | −1.83158 | ||||||||
\(191\) | 124.924 | + | 72.1249i | 0.654052 | + | 0.377617i | 0.790007 | − | 0.613098i | \(-0.210077\pi\) |
−0.135955 | + | 0.990715i | \(0.543410\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −35.5000 | − | 61.4878i | −0.183938 | − | 0.318590i | 0.759280 | − | 0.650764i | \(-0.225551\pi\) |
−0.943218 | + | 0.332174i | \(0.892218\pi\) | |||||||
\(194\) | 60.0125 | − | 34.6482i | 0.309343 | − | 0.178599i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.0000 | + | 41.5692i | −0.122449 | + | 0.212088i | ||||
\(197\) | − | 76.3675i | − | 0.387652i | −0.981036 | − | 0.193826i | \(-0.937910\pi\) | ||
0.981036 | − | 0.193826i | \(-0.0620898\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 173.000 | 0.869347 | 0.434673 | − | 0.900588i | \(-0.356864\pi\) | ||||
0.434673 | + | 0.900588i | \(0.356864\pi\) | |||||||
\(200\) | 115.126 | + | 66.4680i | 0.575630 | + | 0.332340i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −96.0000 | − | 166.277i | −0.475248 | − | 0.823153i | ||||
\(203\) | −73.4847 | + | 42.4264i | −0.361994 | + | 0.208997i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −72.0000 | + | 124.708i | −0.351220 | + | 0.608330i | ||||
\(206\) | 230.517i | 1.11901i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | −0.0192308 | ||||||||
\(209\) | −213.106 | − | 123.037i | −1.01964 | − | 0.588692i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −170.500 | − | 295.315i | −0.808057 | − | 1.39960i | −0.914208 | − | 0.405246i | \(-0.867186\pi\) |
0.106151 | − | 0.994350i | \(-0.466147\pi\) | |||||||
\(212\) | 88.1816 | − | 50.9117i | 0.415951 | − | 0.240149i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.0000 | + | 31.1769i | −0.0841121 | + | 0.145687i | ||||
\(215\) | − | 118.794i | − | 0.552530i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −50.0000 | −0.230415 | ||||||||
\(218\) | 2.44949 | + | 1.41421i | 0.0112362 | + | 0.00648722i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 72.0000 | + | 124.708i | 0.327273 | + | 0.566853i | ||||
\(221\) | −22.0454 | + | 12.7279i | −0.0997530 | + | 0.0575924i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.0000 | − | 50.2295i | 0.130045 | − | 0.225244i | −0.793649 | − | 0.608376i | \(-0.791821\pi\) |
0.923694 | + | 0.383132i | \(0.125155\pi\) | |||||||
\(224\) | − | 28.2843i | − | 0.126269i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −156.000 | −0.690265 | ||||||||
\(227\) | −117.576 | − | 67.8823i | −0.517954 | − | 0.299041i | 0.218143 | − | 0.975917i | \(-0.430000\pi\) |
−0.736097 | + | 0.676876i | \(0.763333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 131.000 | + | 226.899i | 0.572052 | + | 0.990824i | 0.996355 | + | 0.0853034i | \(0.0271859\pi\) |
−0.424303 | + | 0.905520i | \(0.639481\pi\) | |||||||
\(230\) | 88.1816 | − | 50.9117i | 0.383398 | − | 0.221355i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.0000 | + | 41.5692i | −0.103448 | + | 0.179178i | ||||
\(233\) | 305.470i | 1.31103i | 0.755182 | + | 0.655515i | \(0.227549\pi\) | ||||
−0.755182 | + | 0.655515i | \(0.772451\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 72.0000 | 0.306383 | ||||||||
\(236\) | 161.666 | + | 93.3381i | 0.685027 | + | 0.395500i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −90.0000 | − | 155.885i | −0.378151 | − | 0.654977i | ||||
\(239\) | 146.969 | − | 84.8528i | 0.614935 | − | 0.355033i | −0.159960 | − | 0.987124i | \(-0.551136\pi\) |
0.774894 | + | 0.632091i | \(0.217803\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 60.5000 | − | 104.789i | 0.251037 | − | 0.434809i | −0.712774 | − | 0.701393i | \(-0.752562\pi\) |
0.963812 | + | 0.266584i | \(0.0858950\pi\) | |||||||
\(242\) | − | 69.2965i | − | 0.286349i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −46.0000 | −0.188525 | ||||||||
\(245\) | −176.363 | − | 101.823i | −0.719850 | − | 0.415606i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.5000 | + | 25.1147i | 0.0587045 | + | 0.101679i | ||||
\(248\) | −24.4949 | + | 14.1421i | −0.0987697 | + | 0.0570247i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −132.000 | + | 228.631i | −0.528000 | + | 0.914523i | ||||
\(251\) | 356.382i | 1.41985i | 0.704278 | + | 0.709924i | \(0.251271\pi\) | ||||
−0.704278 | + | 0.709924i | \(0.748729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 72.0000 | 0.284585 | ||||||||
\(254\) | −218.005 | − | 125.865i | −0.858286 | − | 0.495532i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −73.4847 | + | 42.4264i | −0.285933 | + | 0.165083i | −0.636106 | − | 0.771602i | \(-0.719456\pi\) |
0.350173 | + | 0.936685i | \(0.386123\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 62.5000 | − | 108.253i | 0.241313 | − | 0.417966i | ||||
\(260\) | − | 16.9706i | − | 0.0652714i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 168.000 | 0.641221 | ||||||||
\(263\) | 146.969 | + | 84.8528i | 0.558819 | + | 0.322634i | 0.752671 | − | 0.658396i | \(-0.228765\pi\) |
−0.193852 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 216.000 | + | 374.123i | 0.815094 | + | 1.41178i | ||||
\(266\) | −177.588 | + | 102.530i | −0.667624 | + | 0.385453i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −19.0000 | + | 32.9090i | −0.0708955 | + | 0.122795i | ||||
\(269\) | − | 280.014i | − | 1.04095i | −0.853878 | − | 0.520473i | \(-0.825756\pi\) | ||
0.853878 | − | 0.520473i | \(-0.174244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.0000 | 0.107011 | 0.0535055 | − | 0.998568i | \(-0.482961\pi\) | ||||
0.0535055 | + | 0.998568i | \(0.482961\pi\) | |||||||
\(272\) | −88.1816 | − | 50.9117i | −0.324197 | − | 0.187175i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 66.0000 | + | 114.315i | 0.240876 | + | 0.417209i | ||||
\(275\) | −345.378 | + | 199.404i | −1.25592 | + | 0.725106i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 191.000 | − | 330.822i | 0.689531 | − | 1.19430i | −0.282459 | − | 0.959279i | \(-0.591150\pi\) |
0.971990 | − | 0.235023i | \(-0.0755165\pi\) | |||||||
\(278\) | 230.517i | 0.829197i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 120.000 | 0.428571 | ||||||||
\(281\) | 191.060 | + | 110.309i | 0.679930 | + | 0.392558i | 0.799829 | − | 0.600229i | \(-0.204924\pi\) |
−0.119899 | + | 0.992786i | \(0.538257\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.0000 | − | 53.6936i | −0.109541 | − | 0.189730i | 0.806044 | − | 0.591856i | \(-0.201605\pi\) |
−0.915584 | + | 0.402126i | \(0.868271\pi\) | |||||||
\(284\) | −176.363 | + | 101.823i | −0.620997 | + | 0.358533i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | − | 10.3923i | 0.0209790 | − | 0.0363367i | ||||
\(287\) | 84.8528i | 0.295654i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −359.000 | −1.24221 | ||||||||
\(290\) | −176.363 | − | 101.823i | −0.608149 | − | 0.351115i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −97.0000 | − | 168.009i | −0.332192 | − | 0.575373i | ||||
\(293\) | −271.893 | + | 156.978i | −0.927964 | + | 0.535760i | −0.886167 | − | 0.463366i | \(-0.846642\pi\) |
−0.0417967 | + | 0.999126i | \(0.513308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −396.000 | + | 685.892i | −1.34237 | + | 2.32506i | ||||
\(296\) | − | 70.7107i | − | 0.238887i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −48.0000 | −0.161074 | ||||||||
\(299\) | −7.34847 | − | 4.24264i | −0.0245768 | − | 0.0141894i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.0000 | − | 60.6218i | −0.116279 | − | 0.201401i | ||||
\(302\) | −182.487 | + | 105.359i | −0.604262 | + | 0.348871i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −58.0000 | + | 100.459i | −0.190789 | + | 0.330457i | ||||
\(305\) | − | 195.161i | − | 0.639874i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.0000 | −0.110749 | −0.0553746 | − | 0.998466i | \(-0.517635\pi\) | ||||
−0.0553746 | + | 0.998466i | \(0.517635\pi\) | |||||||
\(308\) | 73.4847 | + | 42.4264i | 0.238587 | + | 0.137748i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −60.0000 | − | 103.923i | −0.193548 | − | 0.335236i | ||||
\(311\) | −51.4393 | + | 29.6985i | −0.165400 | + | 0.0954935i | −0.580415 | − | 0.814321i | \(-0.697110\pi\) |
0.415015 | + | 0.909814i | \(0.363776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −119.500 | + | 206.980i | −0.381789 | + | 0.661278i | −0.991318 | − | 0.131486i | \(-0.958025\pi\) |
0.609529 | + | 0.792764i | \(0.291359\pi\) | |||||||
\(314\) | − | 342.240i | − | 1.08994i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −154.000 | −0.487342 | ||||||||
\(317\) | 14.6969 | + | 8.48528i | 0.0463626 | + | 0.0267674i | 0.523002 | − | 0.852331i | \(-0.324812\pi\) |
−0.476640 | + | 0.879099i | \(0.658145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −72.0000 | − | 124.708i | −0.225705 | − | 0.390933i | ||||
\(320\) | 58.7878 | − | 33.9411i | 0.183712 | − | 0.106066i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 30.0000 | − | 51.9615i | 0.0931677 | − | 0.161371i | ||||
\(323\) | 738.219i | 2.28551i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 47.0000 | 0.144615 | ||||||||
\(326\) | 211.881 | + | 122.329i | 0.649941 | + | 0.375244i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.0000 | + | 41.5692i | 0.0731707 | + | 0.126735i | ||||
\(329\) | 36.7423 | − | 21.2132i | 0.111679 | − | 0.0644778i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 249.500 | − | 432.147i | 0.753776 | − | 1.30558i | −0.192204 | − | 0.981355i | \(-0.561563\pi\) |
0.945980 | − | 0.324224i | \(-0.105103\pi\) | |||||||
\(332\) | 237.588i | 0.715626i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 276.000 | 0.826347 | ||||||||
\(335\) | −139.621 | − | 80.6102i | −0.416779 | − | 0.240627i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 72.5000 | + | 125.574i | 0.215134 | + | 0.372622i | 0.953314 | − | 0.301981i | \(-0.0976480\pi\) |
−0.738180 | + | 0.674603i | \(0.764315\pi\) | |||||||
\(338\) | 205.757 | − | 118.794i | 0.608749 | − | 0.351461i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 216.000 | − | 374.123i | 0.635294 | − | 1.10036i | ||||
\(341\) | − | 84.8528i | − | 0.248835i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −365.000 | −1.06414 | ||||||||
\(344\) | −34.2929 | − | 19.7990i | −0.0996885 | − | 0.0575552i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 228.000 | + | 394.908i | 0.658960 | + | 1.14135i | ||||
\(347\) | −382.120 | + | 220.617i | −1.10121 | + | 0.635785i | −0.936539 | − | 0.350564i | \(-0.885990\pi\) |
−0.164673 | + | 0.986348i | \(0.552657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 60.5000 | − | 104.789i | 0.173352 | − | 0.300255i | −0.766237 | − | 0.642558i | \(-0.777873\pi\) |
0.939590 | + | 0.342302i | \(0.111207\pi\) | |||||||
\(350\) | 332.340i | 0.949543i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 48.0000 | 0.136364 | ||||||||
\(353\) | −382.120 | − | 220.617i | −1.08249 | − | 0.624978i | −0.150926 | − | 0.988545i | \(-0.548225\pi\) |
−0.931568 | + | 0.363567i | \(0.881559\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −432.000 | − | 748.246i | −1.21690 | − | 2.10774i | ||||
\(356\) | 132.272 | − | 76.3675i | 0.371552 | − | 0.214516i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 216.000 | − | 374.123i | 0.603352 | − | 1.04504i | ||||
\(359\) | − | 432.749i | − | 1.20543i | −0.797957 | − | 0.602715i | \(-0.794086\pi\) | ||
0.797957 | − | 0.602715i | \(-0.205914\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 480.000 | 1.32964 | ||||||||
\(362\) | 322.108 | + | 185.969i | 0.889801 | + | 0.513727i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.00000 | − | 8.66025i | −0.0137363 | − | 0.0237919i | ||||
\(365\) | 712.802 | − | 411.536i | 1.95288 | − | 1.12750i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −74.5000 | + | 129.038i | −0.202997 | + | 0.351602i | −0.949493 | − | 0.313789i | \(-0.898402\pi\) |
0.746496 | + | 0.665390i | \(0.231735\pi\) | |||||||
\(368\) | − | 33.9411i | − | 0.0922313i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 300.000 | 0.810811 | ||||||||
\(371\) | 220.454 | + | 127.279i | 0.594216 | + | 0.343071i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 180.500 | + | 312.635i | 0.483914 | + | 0.838164i | 0.999829 | − | 0.0184757i | \(-0.00588134\pi\) |
−0.515915 | + | 0.856640i | \(0.672548\pi\) | |||||||
\(374\) | 264.545 | − | 152.735i | 0.707339 | − | 0.408383i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.0000 | − | 20.7846i | 0.0319149 | − | 0.0552782i | ||||
\(377\) | 16.9706i | 0.0450148i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 173.000 | 0.456464 | 0.228232 | − | 0.973607i | \(-0.426705\pi\) | ||||
0.228232 | + | 0.973607i | \(0.426705\pi\) | |||||||
\(380\) | −426.211 | − | 246.073i | −1.12161 | − | 0.647561i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 102.000 | + | 176.669i | 0.267016 | + | 0.462485i | ||||
\(383\) | 587.878 | − | 339.411i | 1.53493 | − | 0.886191i | 0.535804 | − | 0.844342i | \(-0.320008\pi\) |
0.999124 | − | 0.0418491i | \(-0.0133249\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −180.000 | + | 311.769i | −0.467532 | + | 0.809790i | ||||
\(386\) | − | 100.409i | − | 0.260127i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 98.0000 | 0.252577 | ||||||||
\(389\) | −360.075 | − | 207.889i | −0.925643 | − | 0.534420i | −0.0402118 | − | 0.999191i | \(-0.512803\pi\) |
−0.885431 | + | 0.464771i | \(0.846137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −108.000 | − | 187.061i | −0.276215 | − | 0.478418i | ||||
\(392\) | −58.7878 | + | 33.9411i | −0.149969 | + | 0.0865845i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 54.0000 | − | 93.5307i | 0.137056 | − | 0.237388i | ||||
\(395\) | − | 653.367i | − | 1.65409i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −286.000 | −0.720403 | −0.360202 | − | 0.932875i | \(-0.617292\pi\) | ||||
−0.360202 | + | 0.932875i | \(0.617292\pi\) | |||||||
\(398\) | 211.881 | + | 122.329i | 0.532364 | + | 0.307360i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 94.0000 | + | 162.813i | 0.235000 | + | 0.407032i | ||||
\(401\) | −293.939 | + | 169.706i | −0.733014 | + | 0.423206i | −0.819524 | − | 0.573045i | \(-0.805762\pi\) |
0.0865095 | + | 0.996251i | \(0.472429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.00000 | + | 8.66025i | −0.0124069 | + | 0.0214895i | ||||
\(404\) | − | 271.529i | − | 0.672101i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −120.000 | −0.295567 | ||||||||
\(407\) | 183.712 | + | 106.066i | 0.451380 | + | 0.260604i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −107.500 | − | 186.195i | −0.262836 | − | 0.455246i | 0.704158 | − | 0.710043i | \(-0.251325\pi\) |
−0.966994 | + | 0.254797i | \(0.917991\pi\) | |||||||
\(410\) | −176.363 | + | 101.823i | −0.430154 | + | 0.248350i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −163.000 | + | 282.324i | −0.395631 | + | 0.685253i | ||||
\(413\) | 466.690i | 1.13000i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1008.00 | −2.42892 | ||||||||
\(416\) | −4.89898 | − | 2.82843i | −0.0117764 | − | 0.00679910i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −174.000 | − | 301.377i | −0.416268 | − | 0.720997i | ||||
\(419\) | 521.741 | − | 301.227i | 1.24521 | − | 0.718920i | 0.275057 | − | 0.961428i | \(-0.411303\pi\) |
0.970149 | + | 0.242508i | \(0.0779701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −227.500 | + | 394.042i | −0.540380 | + | 0.935966i | 0.458502 | + | 0.888693i | \(0.348386\pi\) |
−0.998882 | + | 0.0472723i | \(0.984947\pi\) | |||||||
\(422\) | − | 482.247i | − | 1.14276i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 144.000 | 0.339623 | ||||||||
\(425\) | 1036.13 | + | 598.212i | 2.43796 | + | 1.40756i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −57.5000 | − | 99.5929i | −0.134660 | − | 0.233239i | ||||
\(428\) | −44.0908 | + | 25.4558i | −0.103016 | + | 0.0594763i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 84.0000 | − | 145.492i | 0.195349 | − | 0.338354i | ||||
\(431\) | − | 330.926i | − | 0.767810i | −0.923373 | − | 0.383905i | \(-0.874579\pi\) | ||
0.923373 | − | 0.383905i | \(-0.125421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 218.000 | 0.503464 | 0.251732 | − | 0.967797i | \(-0.419000\pi\) | ||||
0.251732 | + | 0.967797i | \(0.419000\pi\) | |||||||
\(434\) | −61.2372 | − | 35.3553i | −0.141100 | − | 0.0814639i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.00458716 | + | 0.00794519i | ||||
\(437\) | −213.106 | + | 123.037i | −0.487656 | + | 0.281548i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −187.000 | + | 323.894i | −0.425968 | + | 0.737798i | −0.996510 | − | 0.0834699i | \(-0.973400\pi\) |
0.570542 | + | 0.821268i | \(0.306733\pi\) | |||||||
\(440\) | 203.647i | 0.462834i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.0000 | −0.0814480 | ||||||||
\(443\) | 14.6969 | + | 8.48528i | 0.0331759 | + | 0.0191541i | 0.516496 | − | 0.856289i | \(-0.327236\pi\) |
−0.483320 | + | 0.875444i | \(0.660569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 324.000 | + | 561.184i | 0.728090 | + | 1.26109i | ||||
\(446\) | 71.0352 | − | 41.0122i | 0.159272 | − | 0.0919556i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.0000 | − | 34.6410i | 0.0446429 | − | 0.0773237i | ||||
\(449\) | − | 483.661i | − | 1.07720i | −0.842563 | − | 0.538598i | \(-0.818954\pi\) | ||
0.842563 | − | 0.538598i | \(-0.181046\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −144.000 | −0.319290 | ||||||||
\(452\) | −191.060 | − | 110.309i | −0.422700 | − | 0.244046i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −96.0000 | − | 166.277i | −0.211454 | − | 0.366249i | ||||
\(455\) | 36.7423 | − | 21.2132i | 0.0807524 | − | 0.0466224i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0000 | − | 19.0526i | 0.0240700 | − | 0.0416905i | −0.853739 | − | 0.520700i | \(-0.825671\pi\) |
0.877810 | + | 0.479010i | \(0.159004\pi\) | |||||||
\(458\) | 370.524i | 0.809004i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 144.000 | 0.313043 | ||||||||
\(461\) | 345.378 | + | 199.404i | 0.749193 | + | 0.432547i | 0.825402 | − | 0.564545i | \(-0.190948\pi\) |
−0.0762091 | + | 0.997092i | \(0.524282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 441.500 | + | 764.700i | 0.953564 | + | 1.65162i | 0.737621 | + | 0.675215i | \(0.235949\pi\) |
0.215942 | + | 0.976406i | \(0.430718\pi\) | |||||||
\(464\) | −58.7878 | + | 33.9411i | −0.126698 | + | 0.0731490i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −216.000 | + | 374.123i | −0.463519 | + | 0.802839i | ||||
\(467\) | 127.279i | 0.272547i | 0.990671 | + | 0.136273i | \(0.0435125\pi\) | ||||
−0.990671 | + | 0.136273i | \(0.956487\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −95.0000 | −0.202559 | ||||||||
\(470\) | 88.1816 | + | 50.9117i | 0.187620 | + | 0.108323i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 132.000 | + | 228.631i | 0.279661 | + | 0.484387i | ||||
\(473\) | 102.879 | − | 59.3970i | 0.217502 | − | 0.125575i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 681.500 | − | 1180.39i | 1.43474 | − | 2.48504i | ||||
\(476\) | − | 254.558i | − | 0.534787i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 240.000 | 0.502092 | ||||||||
\(479\) | −338.030 | − | 195.161i | −0.705699 | − | 0.407435i | 0.103768 | − | 0.994602i | \(-0.466910\pi\) |
−0.809466 | + | 0.587166i | \(0.800243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5000 | − | 21.6506i | −0.0259875 | − | 0.0450117i | ||||
\(482\) | 148.194 | − | 85.5599i | 0.307457 | − | 0.177510i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 49.0000 | − | 84.8705i | 0.101240 | − | 0.175352i | ||||
\(485\) | 415.779i | 0.857276i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 317.000 | 0.650924 | 0.325462 | − | 0.945555i | \(-0.394480\pi\) | ||||
0.325462 | + | 0.945555i | \(0.394480\pi\) | |||||||
\(488\) | −56.3383 | − | 32.5269i | −0.115447 | − | 0.0666535i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −144.000 | − | 249.415i | −0.293878 | − | 0.509011i | ||||
\(491\) | −315.984 | + | 182.434i | −0.643552 | + | 0.371555i | −0.785982 | − | 0.618250i | \(-0.787842\pi\) |
0.142429 | + | 0.989805i | \(0.454509\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −216.000 | + | 374.123i | −0.438134 | + | 0.758870i | ||||
\(494\) | 41.0122i | 0.0830206i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −40.0000 | −0.0806452 | ||||||||
\(497\) | −440.908 | − | 254.558i | −0.887139 | − | 0.512190i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −355.000 | − | 614.878i | −0.711423 | − | 1.23222i | −0.964323 | − | 0.264728i | \(-0.914718\pi\) |
0.252900 | − | 0.967492i | \(-0.418616\pi\) | |||||||
\(500\) | −323.333 | + | 186.676i | −0.646665 | + | 0.373352i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −252.000 | + | 436.477i | −0.501992 | + | 0.869476i | ||||
\(503\) | 280.014i | 0.556688i | 0.960481 | + | 0.278344i | \(0.0897856\pi\) | ||||
−0.960481 | + | 0.278344i | \(0.910214\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1152.00 | 2.28119 | ||||||||
\(506\) | 88.1816 | + | 50.9117i | 0.174272 | + | 0.100616i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −178.000 | − | 308.305i | −0.350394 | − | 0.606900i | ||||
\(509\) | −227.803 | + | 131.522i | −0.447549 | + | 0.258393i | −0.706795 | − | 0.707419i | \(-0.749859\pi\) |
0.259245 | + | 0.965811i | \(0.416526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 242.500 | − | 420.022i | 0.474560 | − | 0.821961i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −120.000 | −0.233463 | ||||||||
\(515\) | −1197.80 | − | 691.550i | −2.32583 | − | 1.34282i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0000 | + | 62.3538i | 0.0696325 | + | 0.120607i | ||||
\(518\) | 153.093 | − | 88.3883i | 0.295547 | − | 0.170634i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.0000 | − | 20.7846i | 0.0230769 | − | 0.0399704i | ||||
\(521\) | 687.308i | 1.31921i | 0.751613 | + | 0.659604i | \(0.229276\pi\) | ||||
−0.751613 | + | 0.659604i | \(0.770724\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −763.000 | −1.45889 | −0.729446 | − | 0.684039i | \(-0.760222\pi\) | ||||
−0.729446 | + | 0.684039i | \(0.760222\pi\) | |||||||
\(524\) | 205.757 | + | 118.794i | 0.392666 | + | 0.226706i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 120.000 | + | 207.846i | 0.228137 | + | 0.395145i | ||||
\(527\) | −220.454 | + | 127.279i | −0.418319 | + | 0.241517i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −228.500 | + | 395.774i | −0.431947 | + | 0.748154i | ||||
\(530\) | 610.940i | 1.15272i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −290.000 | −0.545113 | ||||||||
\(533\) | 14.6969 | + | 8.48528i | 0.0275740 | + | 0.0159199i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −108.000 | − | 187.061i | −0.201869 | − | 0.349648i | ||||
\(536\) | −46.5403 | + | 26.8701i | −0.0868289 | + | 0.0501307i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 198.000 | − | 342.946i | 0.368030 | − | 0.637446i | ||||
\(539\) | − | 203.647i | − | 0.377823i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −313.000 | −0.578558 | −0.289279 | − | 0.957245i | \(-0.593416\pi\) | ||||
−0.289279 | + | 0.957245i | \(0.593416\pi\) | |||||||
\(542\) | 35.5176 | + | 20.5061i | 0.0655306 | + | 0.0378341i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −72.0000 | − | 124.708i | −0.132353 | − | 0.229242i | ||||
\(545\) | −14.6969 | + | 8.48528i | −0.0269669 | + | 0.0155693i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 69.5000 | − | 120.378i | 0.127057 | − | 0.220069i | −0.795478 | − | 0.605982i | \(-0.792780\pi\) |
0.922535 | + | 0.385913i | \(0.126114\pi\) | |||||||
\(548\) | 186.676i | 0.340650i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −564.000 | −1.02545 | ||||||||
\(551\) | 426.211 | + | 246.073i | 0.773523 | + | 0.446594i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −192.500 | − | 333.420i | −0.348101 | − | 0.602929i | ||||
\(554\) | 467.853 | − | 270.115i | 0.844499 | − | 0.487572i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −163.000 | + | 282.324i | −0.293165 | + | 0.507777i | ||||
\(557\) | − | 280.014i | − | 0.502719i | −0.967894 | − | 0.251359i | \(-0.919122\pi\) | ||
0.967894 | − | 0.251359i | \(-0.0808776\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.0000 | −0.0250447 | ||||||||
\(560\) | 146.969 | + | 84.8528i | 0.262445 | + | 0.151523i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 156.000 | + | 270.200i | 0.277580 | + | 0.480783i | ||||
\(563\) | −514.393 | + | 296.985i | −0.913664 | + | 0.527504i | −0.881608 | − | 0.471982i | \(-0.843539\pi\) |
−0.0320558 | + | 0.999486i | \(0.510205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 468.000 | − | 810.600i | 0.828319 | − | 1.43469i | ||||
\(566\) | − | 87.6812i | − | 0.154914i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −288.000 | −0.507042 | ||||||||
\(569\) | −536.438 | − | 309.713i | −0.942774 | − | 0.544311i | −0.0519450 | − | 0.998650i | \(-0.516542\pi\) |
−0.890829 | + | 0.454339i | \(0.849875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 81.5000 | + | 141.162i | 0.142732 | + | 0.247219i | 0.928525 | − | 0.371271i | \(-0.121078\pi\) |
−0.785792 | + | 0.618490i | \(0.787745\pi\) | |||||||
\(572\) | 14.6969 | − | 8.48528i | 0.0256939 | − | 0.0148344i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −60.0000 | + | 103.923i | −0.104530 | + | 0.181051i | ||||
\(575\) | 398.808i | 0.693580i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1127.00 | 1.95321 | 0.976603 | − | 0.215050i | \(-0.0689913\pi\) | ||||
0.976603 | + | 0.215050i | \(0.0689913\pi\) | |||||||
\(578\) | −439.683 | − | 253.851i | −0.760698 | − | 0.439189i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −144.000 | − | 249.415i | −0.248276 | − | 0.430026i | ||||
\(581\) | −514.393 | + | 296.985i | −0.885358 | + | 0.511162i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −216.000 | + | 374.123i | −0.370497 | + | 0.641720i | ||||
\(584\) | − | 274.357i | − | 0.469790i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −444.000 | −0.757679 | ||||||||
\(587\) | 874.468 | + | 504.874i | 1.48972 | + | 0.860092i | 0.999931 | − | 0.0117465i | \(-0.00373911\pi\) |
0.489793 | + | 0.871839i | \(0.337072\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 145.000 | + | 251.147i | 0.246180 | + | 0.426396i | ||||
\(590\) | −969.998 | + | 560.029i | −1.64406 | + | 0.949201i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 50.0000 | − | 86.6025i | 0.0844595 | − | 0.146288i | ||||
\(593\) | 356.382i | 0.600981i | 0.953785 | + | 0.300491i | \(0.0971504\pi\) | ||||
−0.953785 | + | 0.300491i | \(0.902850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1080.00 | 1.81513 | ||||||||
\(596\) | −58.7878 | − | 33.9411i | −0.0986372 | − | 0.0569482i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.00000 | − | 10.3923i | −0.0100334 | − | 0.0173784i | ||||
\(599\) | −778.938 | + | 449.720i | −1.30040 | + | 0.750784i | −0.980472 | − | 0.196658i | \(-0.936991\pi\) |
−0.319925 | + | 0.947443i | \(0.603658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 83.0000 | − | 143.760i | 0.138103 | − | 0.239202i | −0.788675 | − | 0.614810i | \(-0.789233\pi\) |
0.926779 | + | 0.375608i | \(0.122566\pi\) | |||||||
\(602\) | − | 98.9949i | − | 0.164443i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −298.000 | −0.493377 | ||||||||
\(605\) | 360.075 | + | 207.889i | 0.595165 | + | 0.343619i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 261.500 | + | 452.931i | 0.430807 | + | 0.746180i | 0.996943 | − | 0.0781320i | \(-0.0248955\pi\) |
−0.566136 | + | 0.824312i | \(0.691562\pi\) | |||||||
\(608\) | −142.070 | + | 82.0244i | −0.233668 | + | 0.134909i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 138.000 | − | 239.023i | 0.226230 | − | 0.391841i | ||||
\(611\) | − | 8.48528i | − | 0.0138875i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 335.000 | 0.546493 | 0.273246 | − | 0.961944i | \(-0.411903\pi\) | ||||
0.273246 | + | 0.961944i | \(0.411903\pi\) | |||||||
\(614\) | −41.6413 | − | 24.0416i | −0.0678197 | − | 0.0391558i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 60.0000 | + | 103.923i | 0.0974026 | + | 0.168706i | ||||
\(617\) | 433.560 | − | 250.316i | 0.702690 | − | 0.405698i | −0.105659 | − | 0.994402i | \(-0.533695\pi\) |
0.808349 | + | 0.588704i | \(0.200362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.50000 | + | 4.33013i | −0.00403877 | + | 0.00699536i | −0.868038 | − | 0.496498i | \(-0.834619\pi\) |
0.863999 | + | 0.503494i | \(0.167952\pi\) | |||||||
\(620\) | − | 169.706i | − | 0.273719i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −84.0000 | −0.135048 | ||||||||
\(623\) | 330.681 | + | 190.919i | 0.530788 | + | 0.306451i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −204.500 | − | 354.204i | −0.327200 | − | 0.566727i | ||||
\(626\) | −292.714 | + | 168.999i | −0.467594 | + | 0.269966i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 242.000 | − | 419.156i | 0.385350 | − | 0.667446i | ||||
\(629\) | − | 636.396i | − | 1.01176i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 245.000 | 0.388273 | 0.194136 | − | 0.980975i | \(-0.437810\pi\) | ||||
0.194136 | + | 0.980975i | \(0.437810\pi\) | |||||||
\(632\) | −188.611 | − | 108.894i | −0.298435 | − | 0.172301i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.0000 | + | 20.7846i | 0.0189274 | + | 0.0327833i | ||||
\(635\) | 1308.03 | − | 755.190i | 2.05989 | − | 1.18928i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0000 | + | 20.7846i | −0.0188383 | + | 0.0326289i | ||||
\(638\) | − | 203.647i | − | 0.319196i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 96.0000 | 0.150000 | ||||||||
\(641\) | −558.484 | − | 322.441i | −0.871269 | − | 0.503028i | −0.00349951 | − | 0.999994i | \(-0.501114\pi\) |
−0.867770 | + | 0.496966i | \(0.834447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.0000 | + | 71.0141i | 0.0637636 | + | 0.110442i | 0.896145 | − | 0.443762i | \(-0.146356\pi\) |
−0.832381 | + | 0.554203i | \(0.813023\pi\) | |||||||
\(644\) | 73.4847 | − | 42.4264i | 0.114107 | − | 0.0658795i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −522.000 | + | 904.131i | −0.808050 | + | 1.39958i | ||||
\(647\) | 458.205i | 0.708200i | 0.935208 | + | 0.354100i | \(0.115213\pi\) | ||||
−0.935208 | + | 0.354100i | \(0.884787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −792.000 | −1.22034 | ||||||||
\(650\) | 57.5630 | + | 33.2340i | 0.0885585 | + | 0.0511293i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 173.000 | + | 299.645i | 0.265337 | + | 0.459578i | ||||
\(653\) | 279.242 | − | 161.220i | 0.427629 | − | 0.246892i | −0.270707 | − | 0.962662i | \(-0.587257\pi\) |
0.698336 | + | 0.715770i | \(0.253924\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −504.000 | + | 872.954i | −0.769466 | + | 1.33275i | ||||
\(656\) | 67.8823i | 0.103479i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 60.0000 | 0.0911854 | ||||||||
\(659\) | 896.513 | + | 517.602i | 1.36041 | + | 0.785436i | 0.989679 | − | 0.143303i | \(-0.0457722\pi\) |
0.370736 | + | 0.928738i | \(0.379106\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −71.5000 | − | 123.842i | −0.108169 | − | 0.187355i | 0.806859 | − | 0.590744i | \(-0.201166\pi\) |
−0.915029 | + | 0.403389i | \(0.867832\pi\) | |||||||
\(662\) | 611.148 | − | 352.846i | 0.923184 | − | 0.533000i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −168.000 | + | 290.985i | −0.253012 | + | 0.438230i | ||||
\(665\) | − | 1230.37i | − | 1.85017i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −144.000 | −0.215892 | ||||||||
\(668\) | 338.030 | + | 195.161i | 0.506032 | + | 0.292158i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −114.000 | − | 197.454i | −0.170149 | − | 0.294707i | ||||
\(671\) | 169.015 | − | 97.5807i | 0.251885 | − | 0.145426i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −335.500 | + | 581.103i | −0.498514 | + | 0.863452i | −0.999999 | − | 0.00171490i | \(-0.999454\pi\) |
0.501484 | + | 0.865167i | \(0.332787\pi\) | |||||||
\(674\) | 205.061i | 0.304245i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 336.000 | 0.497041 | ||||||||
\(677\) | −7.34847 | − | 4.24264i | −0.0108545 | − | 0.00626683i | 0.494563 | − | 0.869142i | \(-0.335328\pi\) |
−0.505417 | + | 0.862875i | \(0.668661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 122.500 | + | 212.176i | 0.180412 | + | 0.312483i | ||||
\(680\) | 529.090 | − | 305.470i | 0.778073 | − | 0.449221i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 60.0000 | − | 103.923i | 0.0879765 | − | 0.152380i | ||||
\(683\) | 101.823i | 0.149083i | 0.997218 | + | 0.0745413i | \(0.0237493\pi\) | ||||
−0.997218 | + | 0.0745413i | \(0.976251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −792.000 | −1.15620 | ||||||||
\(686\) | −447.032 | − | 258.094i | −0.651650 | − | 0.376230i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.0000 | − | 48.4974i | −0.0406977 | − | 0.0704904i | ||||
\(689\) | 44.0908 | − | 25.4558i | 0.0639925 | − | 0.0369461i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 425.000 | − | 736.122i | 0.615051 | − | 1.06530i | −0.375325 | − | 0.926893i | \(-0.622469\pi\) |
0.990376 | − | 0.138406i | \(-0.0441978\pi\) | |||||||
\(692\) | 644.881i | 0.931910i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −624.000 | −0.899135 | ||||||||
\(695\) | −1197.80 | − | 691.550i | −1.72345 | − | 0.995037i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 216.000 | + | 374.123i | 0.309900 | + | 0.536762i | ||||
\(698\) | 148.194 | − | 85.5599i | 0.212313 | − | 0.122579i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −235.000 | + | 407.032i | −0.335714 | + | 0.581474i | ||||
\(701\) | − | 280.014i | − | 0.399450i | −0.979852 | − | 0.199725i | \(-0.935995\pi\) | ||
0.979852 | − | 0.199725i | \(-0.0640048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −725.000 | −1.03129 | ||||||||
\(704\) | 58.7878 | + | 33.9411i | 0.0835053 | + | 0.0482118i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −312.000 | − | 540.400i | −0.441926 | − | 0.765439i | ||||
\(707\) | 587.878 | − | 339.411i | 0.831510 | − | 0.480072i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 600.500 | − | 1040.10i | 0.846968 | − | 1.46699i | −0.0369339 | − | 0.999318i | \(-0.511759\pi\) |
0.883901 | − | 0.467673i | \(-0.154908\pi\) | |||||||
\(710\) | − | 1221.88i | − | 1.72096i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 216.000 | 0.303371 | ||||||||
\(713\) | −73.4847 | − | 42.4264i | −0.103064 | − | 0.0595041i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | + | 62.3538i | 0.0503497 | + | 0.0872082i | ||||
\(716\) | 529.090 | − | 305.470i | 0.738952 | − | 0.426634i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 306.000 | − | 530.008i | 0.426184 | − | 0.738172i | ||||
\(719\) | 967.322i | 1.34537i | 0.739928 | + | 0.672686i | \(0.234859\pi\) | ||||
−0.739928 | + | 0.672686i | \(0.765141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −815.000 | −1.13037 | ||||||||
\(722\) | 587.878 | + | 339.411i | 0.814235 | + | 0.470099i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 263.000 | + | 455.529i | 0.363260 | + | 0.629184i | ||||
\(725\) | 690.756 | − | 398.808i | 0.952767 | − | 0.550080i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −475.000 | + | 822.724i | −0.653370 | + | 1.13167i | 0.328930 | + | 0.944354i | \(0.393312\pi\) |
−0.982300 | + | 0.187316i | \(0.940021\pi\) | |||||||
\(728\) | − | 14.1421i | − | 0.0194260i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1164.00 | 1.59452 | ||||||||
\(731\) | −308.636 | − | 178.191i | −0.422210 | − | 0.243763i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.0000 | − | 84.8705i | −0.0668486 | − | 0.115785i | 0.830664 | − | 0.556774i | \(-0.187961\pi\) |
−0.897513 | + | 0.440989i | \(0.854628\pi\) | |||||||
\(734\) | −182.487 | + | 105.359i | −0.248620 | + | 0.143541i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.0000 | − | 41.5692i | 0.0326087 | − | 0.0564799i | ||||
\(737\) | − | 161.220i | − | 0.218752i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1262.00 | 1.70771 | 0.853857 | − | 0.520508i | \(-0.174258\pi\) | ||||
0.853857 | + | 0.520508i | \(0.174258\pi\) | |||||||
\(740\) | 367.423 | + | 212.132i | 0.496518 | + | 0.286665i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 180.000 | + | 311.769i | 0.242588 | + | 0.420174i | ||||
\(743\) | −668.711 | + | 386.080i | −0.900014 | + | 0.519624i | −0.877205 | − | 0.480116i | \(-0.840594\pi\) |
−0.0228095 | + | 0.999740i | \(0.507261\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 144.000 | − | 249.415i | 0.193289 | − | 0.334786i | ||||
\(746\) | 510.531i | 0.684358i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 432.000 | 0.577540 | ||||||||
\(749\) | −110.227 | − | 63.6396i | −0.147166 | − | 0.0849661i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −98.5000 | − | 170.607i | −0.131158 | − | 0.227173i | 0.792965 | − | 0.609267i | \(-0.208536\pi\) |
−0.924123 | + | 0.382094i | \(0.875203\pi\) | |||||||
\(752\) | 29.3939 | − | 16.9706i | 0.0390876 | − | 0.0225672i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.0000 | + | 20.7846i | −0.0159151 | + | 0.0275658i | ||||
\(755\) | − | 1264.31i | − | 1.67458i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −241.000 | −0.318362 | −0.159181 | − | 0.987249i | \(-0.550885\pi\) | ||||
−0.159181 | + | 0.987249i | \(0.550885\pi\) | |||||||
\(758\) | 211.881 | + | 122.329i | 0.279526 | + | 0.161385i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −348.000 | − | 602.754i | −0.457895 | − | 0.793097i | ||||
\(761\) | 433.560 | − | 250.316i | 0.569724 | − | 0.328930i | −0.187315 | − | 0.982300i | \(-0.559979\pi\) |
0.757039 | + | 0.653370i | \(0.226645\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.00000 | + | 8.66025i | −0.00655308 | + | 0.0113503i | ||||
\(764\) | 288.500i | 0.377617i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 960.000 | 1.25326 | ||||||||
\(767\) | 80.8332 | + | 46.6690i | 0.105389 | + | 0.0608462i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −215.500 | − | 373.257i | −0.280234 | − | 0.485380i | 0.691208 | − | 0.722656i | \(-0.257079\pi\) |
−0.971442 | + | 0.237276i | \(0.923745\pi\) | |||||||
\(770\) | −440.908 | + | 254.558i | −0.572608 | + | 0.330595i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 71.0000 | − | 122.976i | 0.0919689 | − | 0.159295i | ||||
\(773\) | − | 254.558i | − | 0.329312i | −0.986351 | − | 0.164656i | \(-0.947349\pi\) | ||
0.986351 | − | 0.164656i | \(-0.0526515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 470.000 | 0.606452 | ||||||||
\(776\) | 120.025 | + | 69.2965i | 0.154671 | + | 0.0892996i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −294.000 | − | 509.223i | −0.377892 | − | 0.654528i | ||||
\(779\) | 426.211 | − | 246.073i | 0.547126 | − | 0.315883i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 432.000 | − | 748.246i | 0.553137 | − | 0.958061i | ||||
\(782\) | − | 305.470i | − | 0.390627i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −96.0000 | −0.122449 | ||||||||
\(785\) | 1778.33 | + | 1026.72i | 2.26539 | + | 1.30792i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −62.5000 | − | 108.253i | −0.0794155 | − | 0.137552i | 0.823582 | − | 0.567197i | \(-0.191972\pi\) |
−0.902998 | + | 0.429645i | \(0.858639\pi\) | |||||||
\(788\) | 132.272 | − | 76.3675i | 0.167858 | − | 0.0969131i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 462.000 | − | 800.207i | 0.584810 | − | 1.01292i | ||||
\(791\) | − | 551.543i | − | 0.697273i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.0000 | −0.0290038 | ||||||||
\(794\) | −350.277 | − | 202.233i | −0.441155 | − | 0.254701i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 173.000 | + | 299.645i | 0.217337 | + | 0.376438i | ||||
\(797\) | −734.847 | + | 424.264i | −0.922016 | + | 0.532326i | −0.884278 | − | 0.466961i | \(-0.845349\pi\) |
−0.0377385 | + | 0.999288i | \(0.512015\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 108.000 | − | 187.061i | 0.135169 | − | 0.234120i | ||||
\(800\) | 265.872i | 0.332340i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −480.000 | −0.598504 | ||||||||
\(803\) | 712.802 | + | 411.536i | 0.887673 | + | 0.512498i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 180.000 | + | 311.769i | 0.223602 | + | 0.387291i | ||||
\(806\) | −12.2474 | + | 7.07107i | −0.0151953 | + | 0.00877304i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 192.000 | − | 332.554i | 0.237624 | − | 0.411576i | ||||
\(809\) | 1120.06i | 1.38450i | 0.721660 | + | 0.692248i | \(0.243380\pi\) | ||||
−0.721660 | + | 0.692248i | \(0.756620\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −322.000 | −0.397041 | −0.198520 | − | 0.980097i | \(-0.563614\pi\) | ||||
−0.198520 | + | 0.980097i | \(0.563614\pi\) | |||||||
\(812\) | −146.969 | − | 84.8528i | −0.180997 | − | 0.104499i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 150.000 | + | 259.808i | 0.184275 | + | 0.319174i | ||||
\(815\) | −1271.29 | + | 733.977i | −1.55986 | + | 0.900585i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −203.000 | + | 351.606i | −0.248470 | + | 0.430363i | ||||
\(818\) | − | 304.056i | − | 0.371706i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −288.000 | −0.351220 | ||||||||
\(821\) | −756.892 | − | 436.992i | −0.921915 | − | 0.532268i | −0.0376696 | − | 0.999290i | \(-0.511993\pi\) |
−0.884246 | + | 0.467022i | \(0.845327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −134.500 | − | 232.961i | −0.163426 | − | 0.283063i | 0.772669 | − | 0.634809i | \(-0.218921\pi\) |
−0.936095 | + | 0.351746i | \(0.885588\pi\) | |||||||
\(824\) | −399.267 | + | 230.517i | −0.484547 | + | 0.279753i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −330.000 | + | 571.577i | −0.399516 | + | 0.691982i | ||||
\(827\) | 25.4558i | 0.0307809i | 0.999882 | + | 0.0153905i | \(0.00489913\pi\) | ||||
−0.999882 | + | 0.0153905i | \(0.995101\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1105.00 | −1.33293 | −0.666466 | − | 0.745536i | \(-0.732194\pi\) | ||||
−0.666466 | + | 0.745536i | \(0.732194\pi\) | |||||||
\(830\) | −1234.54 | − | 712.764i | −1.48740 | − | 0.858751i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | − | 6.92820i | −0.00480769 | − | 0.00832717i | ||||
\(833\) | −529.090 | + | 305.470i | −0.635162 | + | 0.366711i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −828.000 | + | 1434.14i | −0.991617 | + | 1.71753i | ||||
\(836\) | − | 492.146i | − | 0.588692i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 852.000 | 1.01671 | ||||||||
\(839\) | 102.879 | + | 59.3970i | 0.122620 | + | 0.0707950i | 0.560056 | − | 0.828455i | \(-0.310780\pi\) |
−0.437435 | + | 0.899250i | \(0.644113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −276.500 | − | 478.912i | −0.328775 | − | 0.569455i | ||||
\(842\) | −557.259 | + | 321.734i | −0.661828 | + | 0.382106i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 341.000 | − | 590.629i | 0.404028 | − | 0.699798i | ||||
\(845\) | 1425.53i | 1.68701i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 245.000 | 0.289256 | ||||||||
\(848\) | 176.363 | + | 101.823i | 0.207976 | + | 0.120075i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 846.000 | + | 1465.31i | 0.995294 | + | 1.72390i | ||||
\(851\) | 183.712 | − | 106.066i | 0.215877 | − | 0.124637i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −695.500 | + | 1204.64i | −0.815358 | + | 1.41224i | 0.0937133 | + | 0.995599i | \(0.470126\pi\) |
−0.909071 | + | 0.416641i | \(0.863207\pi\) | |||||||
\(854\) | − | 162.635i | − | 0.190439i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −72.0000 | −0.0841121 | ||||||||
\(857\) | −470.302 | − | 271.529i | −0.548777 | − | 0.316837i | 0.199851 | − | 0.979826i | \(-0.435954\pi\) |
−0.748629 | + | 0.662990i | \(0.769287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −422.500 | − | 731.791i | −0.491851 | − | 0.851911i | 0.508105 | − | 0.861295i | \(-0.330346\pi\) |
−0.999956 | + | 0.00938424i | \(0.997013\pi\) | |||||||
\(860\) | 205.757 | − | 118.794i | 0.239252 | − | 0.138132i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 234.000 | − | 405.300i | 0.271462 | − | 0.470185i | ||||
\(863\) | − | 1247.34i | − | 1.44535i | −0.691188 | − | 0.722675i | \(-0.742913\pi\) | ||
0.691188 | − | 0.722675i | \(-0.257087\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2736.00 | −3.16301 | ||||||||
\(866\) | 266.994 | + | 154.149i | 0.308308 | + | 0.178001i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −50.0000 | − | 86.6025i | −0.0576037 | − | 0.0997725i | ||||
\(869\) | 565.832 | − | 326.683i | 0.651130 | − | 0.375930i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.50000 | + | 16.4545i | −0.0109070 | + | 0.0188915i | ||||
\(872\) | 5.65685i | 0.00648722i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −348.000 | −0.398169 | ||||||||
\(875\) | −808.332 | − | 466.690i | −0.923808 | − | 0.533361i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −575.500 | − | 996.795i | −0.656214 | − | 1.13660i | −0.981588 | − | 0.191011i | \(-0.938823\pi\) |
0.325374 | − | 0.945586i | \(-0.394510\pi\) | |||||||
\(878\) | −458.055 | + | 264.458i | −0.521702 | + | 0.301205i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −144.000 | + | 249.415i | −0.163636 | + | 0.283426i | ||||
\(881\) | 1298.25i | 1.47361i | 0.676107 | + | 0.736804i | \(0.263666\pi\) | ||||
−0.676107 | + | 0.736804i | \(0.736334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 677.000 | 0.766704 | 0.383352 | − | 0.923602i | \(-0.374770\pi\) | ||||
0.383352 | + | 0.923602i | \(0.374770\pi\) | |||||||
\(884\) | −44.0908 | − | 25.4558i | −0.0498765 | − | 0.0287962i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | + | 20.7846i | 0.0135440 | + | 0.0234589i | ||||
\(887\) | 896.513 | − | 517.602i | 1.01073 | − | 0.583542i | 0.0993213 | − | 0.995055i | \(-0.468333\pi\) |
0.911404 | + | 0.411513i | \(0.135000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 445.000 | − | 770.763i | 0.500562 | − | 0.867000i | ||||
\(890\) | 916.410i | 1.02967i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 116.000 | 0.130045 | ||||||||
\(893\) | −213.106 | − | 123.037i | −0.238640 | − | 0.137779i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1296.00 | + | 2244.74i | 1.44804 | + | 2.50809i | ||||
\(896\) | 48.9898 | − | 28.2843i | 0.0546761 | − | 0.0315673i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 342.000 | − | 592.361i | 0.380846 | − | 0.659645i | ||||
\(899\) | 169.706i | 0.188772i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1296.00 | 1.43840 | ||||||||
\(902\) | −176.363 | − | 101.823i | −0.195525 | − | 0.112886i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −156.000 | − | 270.200i | −0.172566 | − | 0.298894i | ||||
\(905\) | −1932.65 | + | 1115.81i | −2.13552 | + | 1.23294i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.50000 | + | 4.33013i | −0.00275634 | + | 0.00477412i | −0.867400 | − | 0.497611i | \(-0.834211\pi\) |
0.864644 | + | 0.502385i | \(0.167544\pi\) | |||||||
\(908\) | − | 271.529i | − | 0.299041i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 60.0000 | 0.0659341 | ||||||||
\(911\) | −867.119 | − | 500.632i | −0.951832 | − | 0.549541i | −0.0581828 | − | 0.998306i | \(-0.518531\pi\) |
−0.893650 | + | 0.448765i | \(0.851864\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −504.000 | − | 872.954i | −0.552026 | − | 0.956138i | ||||
\(914\) | 26.9444 | − | 15.5563i | 0.0294796 | − | 0.0170201i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −262.000 | + | 453.797i | −0.286026 | + | 0.495412i | ||||
\(917\) | 593.970i | 0.647731i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1190.00 | 1.29489 | 0.647443 | − | 0.762114i | \(-0.275838\pi\) | ||||
0.647443 | + | 0.762114i | \(0.275838\pi\) | |||||||
\(920\) | 176.363 | + | 101.823i | 0.191699 | + | 0.110678i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 282.000 | + | 488.438i | 0.305857 | + | 0.529760i | ||||
\(923\) | −88.1816 | + | 50.9117i | −0.0955381 | + | 0.0551589i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −587.500 | + | 1017.58i | −0.635135 | + | 1.10009i | ||||
\(926\) | 1248.75i | 1.34854i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −96.0000 | −0.103448 | ||||||||
\(929\) | 411.514 | + | 237.588i | 0.442965 | + | 0.255746i | 0.704854 | − | 0.709352i | \(-0.251012\pi\) |
−0.261890 | + | 0.965098i | \(0.584346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 348.000 | + | 602.754i | 0.373792 | + | 0.647426i | ||||
\(932\) | −529.090 | + | 305.470i | −0.567693 | + | 0.327758i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −90.0000 | + | 155.885i | −0.0963597 | + | 0.166900i | ||||
\(935\) | 1832.82i | 1.96024i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1775.00 | 1.89434 | 0.947172 | − | 0.320727i | \(-0.103927\pi\) | ||||
0.947172 | + | 0.320727i | \(0.103927\pi\) | |||||||
\(938\) | −116.351 | − | 67.1751i | −0.124041 | − | 0.0716153i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 72.0000 | + | 124.708i | 0.0765957 | + | 0.132668i | ||||
\(941\) | −139.621 | + | 80.6102i | −0.148375 | + | 0.0856644i | −0.572350 | − | 0.820010i | \(-0.693968\pi\) |
0.423975 | + | 0.905674i | \(0.360635\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −72.0000 | + | 124.708i | −0.0763521 | + | 0.132246i | ||||
\(944\) | 373.352i | 0.395500i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 168.000 | 0.177590 | ||||||||
\(947\) | −492.347 | − | 284.257i | −0.519902 | − | 0.300166i | 0.216992 | − | 0.976173i | \(-0.430375\pi\) |
−0.736895 | + | 0.676008i | \(0.763709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.5000 | − | 84.0045i | −0.0511064 | − | 0.0885189i | ||||
\(950\) | 1669.33 | − | 963.787i | 1.75719 | − | 1.01451i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 180.000 | − | 311.769i | 0.189076 | − | 0.327489i | ||||
\(953\) | − | 1807.36i | − | 1.89650i | −0.317524 | − | 0.948250i | \(-0.602851\pi\) | ||
0.317524 | − | 0.948250i | \(-0.397149\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1224.00 | −1.28168 | ||||||||
\(956\) | 293.939 | + | 169.706i | 0.307467 | + | 0.177516i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −276.000 | − | 478.046i | −0.288100 | − | 0.499004i | ||||
\(959\) | −404.166 | + | 233.345i | −0.421445 | + | 0.243321i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 430.500 | − | 745.648i | 0.447971 | − | 0.775908i | ||||
\(962\) | − | 35.3553i | − | 0.0367519i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 242.000 | 0.251037 | ||||||||
\(965\) | 521.741 | + | 301.227i | 0.540665 | + | 0.312153i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −350.500 | − | 607.084i | −0.362461 | − | 0.627801i | 0.625904 | − | 0.779900i | \(-0.284730\pi\) |
−0.988365 | + | 0.152099i | \(0.951397\pi\) | |||||||
\(968\) | 120.025 | − | 69.2965i | 0.123993 | − | 0.0715873i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −294.000 | + | 509.223i | −0.303093 | + | 0.524972i | ||||
\(971\) | 381.838i | 0.393242i | 0.980480 | + | 0.196621i | \(0.0629968\pi\) | ||||
−0.980480 | + | 0.196621i | \(0.937003\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −815.000 | −0.837616 | ||||||||
\(974\) | 388.244 | + | 224.153i | 0.398608 | + | 0.230136i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.0000 | − | 79.6743i | −0.0471311 | − | 0.0816335i | ||||
\(977\) | 279.242 | − | 161.220i | 0.285816 | − | 0.165016i | −0.350238 | − | 0.936661i | \(-0.613899\pi\) |
0.636053 | + | 0.771645i | \(0.280566\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −324.000 | + | 561.184i | −0.330950 | + | 0.573222i | ||||
\(980\) | − | 407.294i | − | 0.415606i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −516.000 | −0.525458 | ||||||||
\(983\) | 36.7423 | + | 21.2132i | 0.0373778 | + | 0.0215801i | 0.518572 | − | 0.855034i | \(-0.326464\pi\) |
−0.481195 | + | 0.876614i | \(0.659797\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 324.000 | + | 561.184i | 0.328934 | + | 0.569730i | ||||
\(986\) | −529.090 | + | 305.470i | −0.536602 | + | 0.309807i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.0000 | + | 50.2295i | −0.0293522 | + | 0.0508395i | ||||
\(989\) | − | 118.794i | − | 0.120115i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −475.000 | −0.479314 | −0.239657 | − | 0.970858i | \(-0.577035\pi\) | ||||
−0.239657 | + | 0.970858i | \(0.577035\pi\) | |||||||
\(992\) | −48.9898 | − | 28.2843i | −0.0493849 | − | 0.0285124i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −360.000 | − | 623.538i | −0.362173 | − | 0.627302i | ||||
\(995\) | −1271.29 | + | 733.977i | −1.27767 | + | 0.737665i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 767.000 | − | 1328.48i | 0.769308 | − | 1.33248i | −0.168631 | − | 0.985679i | \(-0.553935\pi\) |
0.937939 | − | 0.346801i | \(-0.112732\pi\) | |||||||
\(998\) | − | 1004.09i | − | 1.00610i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.3.d.a.107.2 | 4 | ||
3.2 | odd | 2 | inner | 162.3.d.a.107.1 | 4 | ||
4.3 | odd | 2 | 1296.3.q.i.593.1 | 4 | |||
9.2 | odd | 6 | 54.3.b.a.53.2 | yes | 2 | ||
9.4 | even | 3 | inner | 162.3.d.a.53.1 | 4 | ||
9.5 | odd | 6 | inner | 162.3.d.a.53.2 | 4 | ||
9.7 | even | 3 | 54.3.b.a.53.1 | ✓ | 2 | ||
12.11 | even | 2 | 1296.3.q.i.593.2 | 4 | |||
36.7 | odd | 6 | 432.3.e.d.161.1 | 2 | |||
36.11 | even | 6 | 432.3.e.d.161.2 | 2 | |||
36.23 | even | 6 | 1296.3.q.i.1025.1 | 4 | |||
36.31 | odd | 6 | 1296.3.q.i.1025.2 | 4 | |||
45.2 | even | 12 | 1350.3.b.b.1349.2 | 4 | |||
45.7 | odd | 12 | 1350.3.b.b.1349.4 | 4 | |||
45.29 | odd | 6 | 1350.3.d.d.701.1 | 2 | |||
45.34 | even | 6 | 1350.3.d.d.701.2 | 2 | |||
45.38 | even | 12 | 1350.3.b.b.1349.3 | 4 | |||
45.43 | odd | 12 | 1350.3.b.b.1349.1 | 4 | |||
72.11 | even | 6 | 1728.3.e.f.1025.1 | 2 | |||
72.29 | odd | 6 | 1728.3.e.l.1025.1 | 2 | |||
72.43 | odd | 6 | 1728.3.e.f.1025.2 | 2 | |||
72.61 | even | 6 | 1728.3.e.l.1025.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.3.b.a.53.1 | ✓ | 2 | 9.7 | even | 3 | ||
54.3.b.a.53.2 | yes | 2 | 9.2 | odd | 6 | ||
162.3.d.a.53.1 | 4 | 9.4 | even | 3 | inner | ||
162.3.d.a.53.2 | 4 | 9.5 | odd | 6 | inner | ||
162.3.d.a.107.1 | 4 | 3.2 | odd | 2 | inner | ||
162.3.d.a.107.2 | 4 | 1.1 | even | 1 | trivial | ||
432.3.e.d.161.1 | 2 | 36.7 | odd | 6 | |||
432.3.e.d.161.2 | 2 | 36.11 | even | 6 | |||
1296.3.q.i.593.1 | 4 | 4.3 | odd | 2 | |||
1296.3.q.i.593.2 | 4 | 12.11 | even | 2 | |||
1296.3.q.i.1025.1 | 4 | 36.23 | even | 6 | |||
1296.3.q.i.1025.2 | 4 | 36.31 | odd | 6 | |||
1350.3.b.b.1349.1 | 4 | 45.43 | odd | 12 | |||
1350.3.b.b.1349.2 | 4 | 45.2 | even | 12 | |||
1350.3.b.b.1349.3 | 4 | 45.38 | even | 12 | |||
1350.3.b.b.1349.4 | 4 | 45.7 | odd | 12 | |||
1350.3.d.d.701.1 | 2 | 45.29 | odd | 6 | |||
1350.3.d.d.701.2 | 2 | 45.34 | even | 6 | |||
1728.3.e.f.1025.1 | 2 | 72.11 | even | 6 | |||
1728.3.e.f.1025.2 | 2 | 72.43 | odd | 6 | |||
1728.3.e.l.1025.1 | 2 | 72.29 | odd | 6 | |||
1728.3.e.l.1025.2 | 2 | 72.61 | even | 6 |