Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(246,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("637.246");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.c (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: | \(5.08647060876\) |
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: | \( x^{16} + 10x^{14} + 121x^{12} + 296x^{10} + 3468x^{8} - 1748x^{6} + 40192x^{4} - 65056x^{2} + 228484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 246.14 | ||
Root | \(1.41421 + 1.65552i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.246 |
Dual form | 637.2.c.g.246.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.65552i | 1.17063i | 0.810807 | + | 0.585314i | \(0.199029\pi\) | ||||
−0.810807 | + | 0.585314i | \(0.800971\pi\) | |||||||
\(3\) | 0.494977 | 0.285775 | 0.142888 | − | 0.989739i | \(-0.454361\pi\) | ||||
0.142888 | + | 0.989739i | \(0.454361\pi\) | |||||||
\(4\) | −0.740740 | −0.370370 | ||||||||
\(5\) | 2.87389i | 1.28524i | 0.766183 | + | 0.642622i | \(0.222153\pi\) | ||||
−0.766183 | + | 0.642622i | \(0.777847\pi\) | |||||||
\(6\) | 0.819443i | 0.334536i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.08473i | 0.737063i | ||||||||
\(9\) | −2.75500 | −0.918333 | ||||||||
\(10\) | −4.75778 | −1.50454 | ||||||||
\(11\) | − | 2.58138i | − | 0.778315i | −0.921171 | − | 0.389157i | \(-0.872766\pi\) | ||
0.921171 | − | 0.389157i | \(-0.127234\pi\) | |||||||
\(12\) | −0.366649 | −0.105842 | ||||||||
\(13\) | −3.54562 | + | 0.654682i | −0.983377 | + | 0.181576i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.42251i | 0.367291i | ||||||||
\(16\) | −4.93278 | −1.23320 | ||||||||
\(17\) | −2.27584 | −0.551972 | −0.275986 | − | 0.961162i | \(-0.589004\pi\) | ||||
−0.275986 | + | 0.961162i | \(0.589004\pi\) | |||||||
\(18\) | − | 4.56095i | − | 1.07503i | ||||||
\(19\) | 4.39571i | 1.00844i | 0.863574 | + | 0.504222i | \(0.168221\pi\) | ||||
−0.863574 | + | 0.504222i | \(0.831779\pi\) | |||||||
\(20\) | − | 2.12881i | − | 0.476016i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.27352 | 0.911117 | ||||||||
\(23\) | 7.16926 | 1.49489 | 0.747447 | − | 0.664321i | \(-0.231279\pi\) | ||||
0.747447 | + | 0.664321i | \(0.231279\pi\) | |||||||
\(24\) | 1.03189i | 0.210634i | ||||||||
\(25\) | −3.25926 | −0.651852 | ||||||||
\(26\) | −1.08384 | − | 5.86983i | −0.212558 | − | 1.15117i | ||||
\(27\) | −2.84859 | −0.548212 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.19574 | 1.15052 | 0.575260 | − | 0.817971i | \(-0.304901\pi\) | ||||
0.575260 | + | 0.817971i | \(0.304901\pi\) | |||||||
\(30\) | −2.35499 | −0.429961 | ||||||||
\(31\) | 6.85404i | 1.23102i | 0.788129 | + | 0.615511i | \(0.211050\pi\) | ||||
−0.788129 | + | 0.615511i | \(0.788950\pi\) | |||||||
\(32\) | − | 3.99686i | − | 0.706551i | ||||||
\(33\) | − | 1.27772i | − | 0.222423i | ||||||
\(34\) | − | 3.76769i | − | 0.646154i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.04074 | 0.340123 | ||||||||
\(37\) | − | 5.89241i | − | 0.968707i | −0.874872 | − | 0.484353i | \(-0.839055\pi\) | ||
0.874872 | − | 0.484353i | \(-0.160945\pi\) | |||||||
\(38\) | −7.27717 | −1.18051 | ||||||||
\(39\) | −1.75500 | + | 0.324052i | −0.281025 | + | 0.0518899i | ||||
\(40\) | −5.99128 | −0.947305 | ||||||||
\(41\) | 3.98014i | 0.621594i | 0.950476 | + | 0.310797i | \(0.100596\pi\) | ||||
−0.950476 | + | 0.310797i | \(0.899404\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.31425 | 0.200422 | 0.100211 | − | 0.994966i | \(-0.468048\pi\) | ||||
0.100211 | + | 0.994966i | \(0.468048\pi\) | |||||||
\(44\) | 1.91213i | 0.288264i | ||||||||
\(45\) | − | 7.91757i | − | 1.18028i | ||||||
\(46\) | 11.8688i | 1.74997i | ||||||||
\(47\) | 1.35208i | 0.197221i | 0.995126 | + | 0.0986106i | \(0.0314398\pi\) | ||||
−0.995126 | + | 0.0986106i | \(0.968560\pi\) | |||||||
\(48\) | −2.44161 | −0.352417 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 5.39576i | − | 0.763076i | ||||||
\(51\) | −1.12649 | −0.157740 | ||||||||
\(52\) | 2.62638 | − | 0.484949i | 0.364213 | − | 0.0672503i | ||||
\(53\) | −8.28778 | −1.13841 | −0.569207 | − | 0.822194i | \(-0.692750\pi\) | ||||
−0.569207 | + | 0.822194i | \(0.692750\pi\) | |||||||
\(54\) | − | 4.71589i | − | 0.641752i | ||||||
\(55\) | 7.41860 | 1.00032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.17577i | 0.288188i | ||||||||
\(58\) | 10.2572i | 1.34683i | ||||||||
\(59\) | − | 9.61085i | − | 1.25123i | −0.780133 | − | 0.625613i | \(-0.784849\pi\) | ||
0.780133 | − | 0.625613i | \(-0.215151\pi\) | |||||||
\(60\) | − | 1.05371i | − | 0.136033i | ||||||
\(61\) | 9.55301 | 1.22314 | 0.611569 | − | 0.791191i | \(-0.290539\pi\) | ||||
0.611569 | + | 0.791191i | \(0.290539\pi\) | |||||||
\(62\) | −11.3470 | −1.44107 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.24870 | −0.406087 | ||||||||
\(65\) | −1.88149 | − | 10.1897i | −0.233370 | − | 1.26388i | ||||
\(66\) | 2.11529 | 0.260375 | ||||||||
\(67\) | 15.9095i | 1.94366i | 0.235685 | + | 0.971830i | \(0.424267\pi\) | ||||
−0.235685 | + | 0.971830i | \(0.575733\pi\) | |||||||
\(68\) | 1.68581 | 0.204434 | ||||||||
\(69\) | 3.54862 | 0.427204 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.79396i | 0.568938i | 0.958685 | + | 0.284469i | \(0.0918173\pi\) | ||||
−0.958685 | + | 0.284469i | \(0.908183\pi\) | |||||||
\(72\) | − | 5.74342i | − | 0.676869i | ||||||
\(73\) | 5.70507i | 0.667728i | 0.942621 | + | 0.333864i | \(0.108353\pi\) | ||||
−0.942621 | + | 0.333864i | \(0.891647\pi\) | |||||||
\(74\) | 9.75500 | 1.13400 | ||||||||
\(75\) | −1.61326 | −0.186283 | ||||||||
\(76\) | − | 3.25607i | − | 0.373497i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.536475 | − | 2.90543i | −0.0607438 | − | 0.328975i | ||||
\(79\) | −2.01426 | −0.226622 | −0.113311 | − | 0.993560i | \(-0.536146\pi\) | ||||
−0.113311 | + | 0.993560i | \(0.536146\pi\) | |||||||
\(80\) | − | 14.1763i | − | 1.58496i | ||||||
\(81\) | 6.85501 | 0.761667 | ||||||||
\(82\) | −6.58920 | −0.727655 | ||||||||
\(83\) | − | 3.11798i | − | 0.342243i | −0.985250 | − | 0.171122i | \(-0.945261\pi\) | ||
0.985250 | − | 0.171122i | \(-0.0547391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.54052i | − | 0.709419i | ||||||
\(86\) | 2.17577i | 0.234620i | ||||||||
\(87\) | 3.06675 | 0.328790 | ||||||||
\(88\) | 5.38147 | 0.573667 | ||||||||
\(89\) | − | 13.0584i | − | 1.38418i | −0.721810 | − | 0.692092i | \(-0.756689\pi\) | ||
0.721810 | − | 0.692092i | \(-0.243311\pi\) | |||||||
\(90\) | 13.1077 | 1.38167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.31056 | −0.553664 | ||||||||
\(93\) | 3.39259i | 0.351795i | ||||||||
\(94\) | −2.23839 | −0.230873 | ||||||||
\(95\) | −12.6328 | −1.29610 | ||||||||
\(96\) | − | 1.97835i | − | 0.201915i | ||||||
\(97\) | 14.0382i | 1.42536i | 0.701488 | + | 0.712682i | \(0.252520\pi\) | ||||
−0.701488 | + | 0.712682i | \(0.747480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.11169i | 0.714752i | ||||||||
\(100\) | 2.41426 | 0.241426 | ||||||||
\(101\) | 17.4483 | 1.73617 | 0.868083 | − | 0.496419i | \(-0.165352\pi\) | ||||
0.868083 | + | 0.496419i | \(0.165352\pi\) | |||||||
\(102\) | − | 1.86492i | − | 0.184655i | ||||||
\(103\) | 6.55698 | 0.646078 | 0.323039 | − | 0.946386i | \(-0.395295\pi\) | ||||
0.323039 | + | 0.946386i | \(0.395295\pi\) | |||||||
\(104\) | −1.36483 | − | 7.39164i | −0.133833 | − | 0.724810i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 13.7206i | − | 1.33266i | ||||||
\(107\) | 15.6020 | 1.50831 | 0.754153 | − | 0.656699i | \(-0.228048\pi\) | ||||
0.754153 | + | 0.656699i | \(0.228048\pi\) | |||||||
\(108\) | 2.11006 | 0.203041 | ||||||||
\(109\) | − | 10.0171i | − | 0.959466i | −0.877414 | − | 0.479733i | \(-0.840733\pi\) | ||
0.877414 | − | 0.479733i | \(-0.159267\pi\) | |||||||
\(110\) | 12.2816i | 1.17101i | ||||||||
\(111\) | − | 2.91661i | − | 0.276832i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.95074 | −0.371654 | −0.185827 | − | 0.982582i | \(-0.559496\pi\) | ||||
−0.185827 | + | 0.982582i | \(0.559496\pi\) | |||||||
\(114\) | −3.60203 | −0.337361 | ||||||||
\(115\) | 20.6037i | 1.92130i | ||||||||
\(116\) | −4.58943 | −0.426118 | ||||||||
\(117\) | 9.76816 | − | 1.80365i | 0.903067 | − | 0.166747i | ||||
\(118\) | 15.9109 | 1.46472 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.96555 | −0.270716 | ||||||||
\(121\) | 4.33649 | 0.394226 | ||||||||
\(122\) | 15.8152i | 1.43184i | ||||||||
\(123\) | 1.97008i | 0.177636i | ||||||||
\(124\) | − | 5.07706i | − | 0.455933i | ||||||
\(125\) | 5.00270i | 0.447455i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.37353 | −0.210616 | −0.105308 | − | 0.994440i | \(-0.533583\pi\) | ||||
−0.105308 | + | 0.994440i | \(0.533583\pi\) | |||||||
\(128\) | − | 13.3720i | − | 1.18193i | ||||||
\(129\) | 0.650526 | 0.0572756 | ||||||||
\(130\) | 16.8693 | − | 3.11483i | 1.47953 | − | 0.273189i | ||||
\(131\) | 2.13546 | 0.186576 | 0.0932878 | − | 0.995639i | \(-0.470262\pi\) | ||||
0.0932878 | + | 0.995639i | \(0.470262\pi\) | |||||||
\(132\) | 0.946460i | 0.0823788i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −26.3385 | −2.27530 | ||||||||
\(135\) | − | 8.18655i | − | 0.704586i | ||||||
\(136\) | − | 4.74451i | − | 0.406838i | ||||||
\(137\) | − | 0.429210i | − | 0.0366699i | −0.999832 | − | 0.0183349i | \(-0.994163\pi\) | ||
0.999832 | − | 0.0183349i | \(-0.00583652\pi\) | |||||||
\(138\) | 5.87480i | 0.500096i | ||||||||
\(139\) | −19.4858 | −1.65276 | −0.826381 | − | 0.563112i | \(-0.809604\pi\) | ||||
−0.826381 | + | 0.563112i | \(0.809604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.669248i | 0.0563609i | ||||||||
\(142\) | −7.93648 | −0.666015 | ||||||||
\(143\) | 1.68998 | + | 9.15258i | 0.141323 | + | 0.765377i | ||||
\(144\) | 13.5898 | 1.13248 | ||||||||
\(145\) | 17.8059i | 1.47870i | ||||||||
\(146\) | −9.44485 | −0.781661 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.36475i | 0.358780i | ||||||||
\(149\) | 22.9004i | 1.87607i | 0.346534 | + | 0.938037i | \(0.387358\pi\) | ||||
−0.346534 | + | 0.938037i | \(0.612642\pi\) | |||||||
\(150\) | − | 2.67078i | − | 0.218068i | ||||||
\(151\) | − | 11.2207i | − | 0.913131i | −0.889690 | − | 0.456565i | \(-0.849079\pi\) | ||
0.889690 | − | 0.456565i | \(-0.150921\pi\) | |||||||
\(152\) | −9.16385 | −0.743286 | ||||||||
\(153\) | 6.26993 | 0.506894 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.6978 | −1.58216 | ||||||||
\(156\) | 1.30000 | − | 0.240039i | 0.104083 | − | 0.0192185i | ||||
\(157\) | −3.78799 | −0.302315 | −0.151157 | − | 0.988510i | \(-0.548300\pi\) | ||||
−0.151157 | + | 0.988510i | \(0.548300\pi\) | |||||||
\(158\) | − | 3.33464i | − | 0.265290i | ||||||
\(159\) | −4.10226 | −0.325330 | ||||||||
\(160\) | 11.4865 | 0.908091 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.3486i | 0.891629i | ||||||||
\(163\) | 19.6130i | 1.53621i | 0.640326 | + | 0.768103i | \(0.278799\pi\) | ||||
−0.640326 | + | 0.768103i | \(0.721201\pi\) | |||||||
\(164\) | − | 2.94825i | − | 0.230220i | ||||||
\(165\) | 3.67204 | 0.285868 | ||||||||
\(166\) | 5.16188 | 0.400639 | ||||||||
\(167\) | − | 10.2922i | − | 0.796435i | −0.917291 | − | 0.398217i | \(-0.869629\pi\) | ||
0.917291 | − | 0.398217i | \(-0.130371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1428 | − | 4.64250i | 0.934060 | − | 0.357116i | ||||
\(170\) | 10.8279 | 0.830466 | ||||||||
\(171\) | − | 12.1102i | − | 0.926087i | ||||||
\(172\) | −0.973521 | −0.0742303 | ||||||||
\(173\) | −6.00439 | −0.456505 | −0.228253 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228253 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(174\) | 5.07706i | 0.384891i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.7334i | 0.959815i | ||||||||
\(177\) | − | 4.75715i | − | 0.357569i | ||||||
\(178\) | 21.6184 | 1.62036 | ||||||||
\(179\) | 7.75130 | 0.579359 | 0.289680 | − | 0.957124i | \(-0.406451\pi\) | ||||
0.289680 | + | 0.957124i | \(0.406451\pi\) | |||||||
\(180\) | 5.86486i | 0.437141i | ||||||||
\(181\) | 19.9999 | 1.48658 | 0.743289 | − | 0.668970i | \(-0.233265\pi\) | ||||
0.743289 | + | 0.668970i | \(0.233265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.72852 | 0.349542 | ||||||||
\(184\) | 14.9460i | 1.10183i | ||||||||
\(185\) | 16.9342 | 1.24502 | ||||||||
\(186\) | −5.61649 | −0.411821 | ||||||||
\(187\) | 5.87480i | 0.429608i | ||||||||
\(188\) | − | 1.00154i | − | 0.0730448i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 20.9138i | − | 1.51725i | ||||||
\(191\) | 20.4835 | 1.48214 | 0.741068 | − | 0.671430i | \(-0.234320\pi\) | ||||
0.741068 | + | 0.671430i | \(0.234320\pi\) | |||||||
\(192\) | −1.60803 | −0.116050 | ||||||||
\(193\) | − | 12.4329i | − | 0.894942i | −0.894298 | − | 0.447471i | \(-0.852325\pi\) | ||
0.894298 | − | 0.447471i | \(-0.147675\pi\) | |||||||
\(194\) | −23.2405 | −1.66857 | ||||||||
\(195\) | −0.931292 | − | 5.04368i | −0.0666912 | − | 0.361185i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.9805i | 1.35231i | 0.736761 | + | 0.676154i | \(0.236354\pi\) | ||||
−0.736761 | + | 0.676154i | \(0.763646\pi\) | |||||||
\(198\) | −11.7735 | −0.836709 | ||||||||
\(199\) | −12.8188 | −0.908701 | −0.454350 | − | 0.890823i | \(-0.650129\pi\) | ||||
−0.454350 | + | 0.890823i | \(0.650129\pi\) | |||||||
\(200\) | − | 6.79467i | − | 0.480456i | ||||||
\(201\) | 7.87485i | 0.555449i | ||||||||
\(202\) | 28.8859i | 2.03241i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.834435 | 0.0584221 | ||||||||
\(205\) | −11.4385 | −0.798900 | ||||||||
\(206\) | 10.8552i | 0.756317i | ||||||||
\(207\) | −19.7513 | −1.37281 | ||||||||
\(208\) | 17.4898 | − | 3.22940i | 1.21270 | − | 0.223919i | ||||
\(209\) | 11.3470 | 0.784887 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.86926 | −0.541743 | −0.270871 | − | 0.962616i | \(-0.587312\pi\) | ||||
−0.270871 | + | 0.962616i | \(0.587312\pi\) | |||||||
\(212\) | 6.13909 | 0.421634 | ||||||||
\(213\) | 2.37290i | 0.162588i | ||||||||
\(214\) | 25.8294i | 1.76566i | ||||||||
\(215\) | 3.77703i | 0.257591i | ||||||||
\(216\) | − | 5.93854i | − | 0.404066i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.5835 | 1.12318 | ||||||||
\(219\) | 2.82388i | 0.190820i | ||||||||
\(220\) | −5.49526 | −0.370490 | ||||||||
\(221\) | 8.06925 | − | 1.48995i | 0.542797 | − | 0.100225i | ||||
\(222\) | 4.82850 | 0.324068 | ||||||||
\(223\) | 7.77059i | 0.520357i | 0.965560 | + | 0.260179i | \(0.0837815\pi\) | ||||
−0.965560 | + | 0.260179i | \(0.916219\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.97925 | 0.598617 | ||||||||
\(226\) | − | 6.54052i | − | 0.435069i | ||||||
\(227\) | − | 25.5431i | − | 1.69536i | −0.530511 | − | 0.847678i | \(-0.678000\pi\) | ||
0.530511 | − | 0.847678i | \(-0.322000\pi\) | |||||||
\(228\) | − | 1.61168i | − | 0.106736i | ||||||
\(229\) | − | 12.8986i | − | 0.852362i | −0.904638 | − | 0.426181i | \(-0.859859\pi\) | ||
0.904638 | − | 0.426181i | \(-0.140141\pi\) | |||||||
\(230\) | −34.1098 | −2.24913 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.9164i | 0.848005i | ||||||||
\(233\) | −8.14278 | −0.533451 | −0.266726 | − | 0.963772i | \(-0.585942\pi\) | ||||
−0.266726 | + | 0.963772i | \(0.585942\pi\) | |||||||
\(234\) | 2.98597 | + | 16.1714i | 0.195199 | + | 1.05716i | ||||
\(235\) | −3.88573 | −0.253477 | ||||||||
\(236\) | 7.11914i | 0.463417i | ||||||||
\(237\) | −0.997011 | −0.0647628 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.8122i | − | 1.54028i | −0.637875 | − | 0.770140i | \(-0.720186\pi\) | ||
0.637875 | − | 0.770140i | \(-0.279814\pi\) | |||||||
\(240\) | − | 7.01694i | − | 0.452941i | ||||||
\(241\) | 0.288546i | 0.0185869i | 0.999957 | + | 0.00929346i | \(0.00295824\pi\) | ||||
−0.999957 | + | 0.00929346i | \(0.997042\pi\) | |||||||
\(242\) | 7.17913i | 0.461492i | ||||||||
\(243\) | 11.9388 | 0.765877 | ||||||||
\(244\) | −7.07630 | −0.453013 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.26150 | −0.207946 | ||||||||
\(247\) | −2.87779 | − | 15.5855i | −0.183109 | − | 0.991681i | ||||
\(248\) | −14.2888 | −0.907340 | ||||||||
\(249\) | − | 1.54333i | − | 0.0978045i | ||||||
\(250\) | −8.28206 | −0.523803 | ||||||||
\(251\) | 7.61843 | 0.480871 | 0.240435 | − | 0.970665i | \(-0.422710\pi\) | ||||
0.240435 | + | 0.970665i | \(0.422710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.5066i | − | 1.16350i | ||||||
\(254\) | − | 3.92942i | − | 0.246554i | ||||||
\(255\) | − | 3.23741i | − | 0.202734i | ||||||
\(256\) | 15.6402 | 0.977511 | ||||||||
\(257\) | 11.6560 | 0.727082 | 0.363541 | − | 0.931578i | \(-0.381568\pi\) | ||||
0.363541 | + | 0.931578i | \(0.381568\pi\) | |||||||
\(258\) | 1.07696i | 0.0670484i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.39369 | + | 7.54793i | 0.0864331 | + | 0.468103i | ||||
\(261\) | −17.0693 | −1.05656 | ||||||||
\(262\) | 3.53529i | 0.218411i | ||||||||
\(263\) | −13.5528 | −0.835700 | −0.417850 | − | 0.908516i | \(-0.637216\pi\) | ||||
−0.417850 | + | 0.908516i | \(0.637216\pi\) | |||||||
\(264\) | 2.66370 | 0.163940 | ||||||||
\(265\) | − | 23.8182i | − | 1.46314i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.46359i | − | 0.395565i | ||||||
\(268\) | − | 11.7848i | − | 0.719873i | ||||||
\(269\) | −17.8332 | −1.08731 | −0.543656 | − | 0.839308i | \(-0.682960\pi\) | ||||
−0.543656 | + | 0.839308i | \(0.682960\pi\) | |||||||
\(270\) | 13.5530 | 0.824808 | ||||||||
\(271\) | − | 30.3743i | − | 1.84511i | −0.385866 | − | 0.922555i | \(-0.626097\pi\) | ||
0.385866 | − | 0.922555i | \(-0.373903\pi\) | |||||||
\(272\) | 11.2262 | 0.680690 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.710564 | 0.0429268 | ||||||||
\(275\) | 8.41338i | 0.507346i | ||||||||
\(276\) | −2.62860 | −0.158223 | ||||||||
\(277\) | −5.21425 | −0.313294 | −0.156647 | − | 0.987655i | \(-0.550068\pi\) | ||||
−0.156647 | + | 0.987655i | \(0.550068\pi\) | |||||||
\(278\) | − | 32.2591i | − | 1.93477i | ||||||
\(279\) | − | 18.8829i | − | 1.13049i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.66255i | 0.0991794i | 0.998770 | + | 0.0495897i | \(0.0157914\pi\) | ||||
−0.998770 | + | 0.0495897i | \(0.984209\pi\) | |||||||
\(282\) | −1.10795 | −0.0659776 | ||||||||
\(283\) | 13.7957 | 0.820066 | 0.410033 | − | 0.912071i | \(-0.365517\pi\) | ||||
0.410033 | + | 0.912071i | \(0.365517\pi\) | |||||||
\(284\) | − | 3.55107i | − | 0.210718i | ||||||
\(285\) | −6.25294 | −0.370392 | ||||||||
\(286\) | −15.1523 | + | 2.79780i | −0.895972 | + | 0.165437i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 11.0113i | 0.648849i | ||||||||
\(289\) | −11.8206 | −0.695327 | ||||||||
\(290\) | −29.4780 | −1.73101 | ||||||||
\(291\) | 6.94859i | 0.407333i | ||||||||
\(292\) | − | 4.22597i | − | 0.247306i | ||||||
\(293\) | − | 12.8576i | − | 0.751149i | −0.926792 | − | 0.375574i | \(-0.877445\pi\) | ||
0.926792 | − | 0.375574i | \(-0.122555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.6206 | 1.60813 | ||||||||
\(296\) | 12.2841 | 0.713998 | ||||||||
\(297\) | 7.35329i | 0.426681i | ||||||||
\(298\) | −37.9120 | −2.19619 | ||||||||
\(299\) | −25.4194 | + | 4.69359i | −1.47004 | + | 0.271437i | ||||
\(300\) | 1.19500 | 0.0689936 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.5761 | 1.06894 | ||||||||
\(303\) | 8.63648 | 0.496153 | ||||||||
\(304\) | − | 21.6831i | − | 1.24361i | ||||||
\(305\) | 27.4543i | 1.57203i | ||||||||
\(306\) | 10.3800i | 0.593384i | ||||||||
\(307\) | 20.9016i | 1.19292i | 0.802644 | + | 0.596458i | \(0.203426\pi\) | ||||
−0.802644 | + | 0.596458i | \(0.796574\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.24555 | 0.184633 | ||||||||
\(310\) | − | 32.6100i | − | 1.85212i | ||||||
\(311\) | −17.1392 | −0.971876 | −0.485938 | − | 0.873993i | \(-0.661522\pi\) | ||||
−0.485938 | + | 0.873993i | \(0.661522\pi\) | |||||||
\(312\) | −0.675561 | − | 3.65869i | −0.0382461 | − | 0.207133i | ||||
\(313\) | −2.55266 | −0.144285 | −0.0721424 | − | 0.997394i | \(-0.522984\pi\) | ||||
−0.0721424 | + | 0.997394i | \(0.522984\pi\) | |||||||
\(314\) | − | 6.27109i | − | 0.353898i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.49204 | 0.0839339 | ||||||||
\(317\) | − | 27.2888i | − | 1.53269i | −0.642430 | − | 0.766345i | \(-0.722073\pi\) | ||
0.642430 | − | 0.766345i | \(-0.277927\pi\) | |||||||
\(318\) | − | 6.79136i | − | 0.380841i | ||||||
\(319\) | − | 15.9936i | − | 0.895467i | ||||||
\(320\) | − | 9.33641i | − | 0.521921i | ||||||
\(321\) | 7.72264 | 0.431036 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.0039i | − | 0.556633i | ||||||
\(324\) | −5.07778 | −0.282099 | ||||||||
\(325\) | 11.5561 | − | 2.13378i | 0.641016 | − | 0.118361i | ||||
\(326\) | −32.4696 | −1.79833 | ||||||||
\(327\) | − | 4.95824i | − | 0.274192i | ||||||
\(328\) | −8.29751 | −0.458154 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.07912i | 0.334645i | ||||||||
\(331\) | 9.69307i | 0.532779i | 0.963865 | + | 0.266390i | \(0.0858308\pi\) | ||||
−0.963865 | + | 0.266390i | \(0.914169\pi\) | |||||||
\(332\) | 2.30961i | 0.126757i | ||||||||
\(333\) | 16.2336i | 0.889595i | ||||||||
\(334\) | 17.0389 | 0.932329 | ||||||||
\(335\) | −45.7223 | −2.49808 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.31370 | 0.343929 | 0.171965 | − | 0.985103i | \(-0.444988\pi\) | ||||
0.171965 | + | 0.985103i | \(0.444988\pi\) | |||||||
\(338\) | 7.68575 | + | 20.1026i | 0.418049 | + | 1.09344i | ||||
\(339\) | −1.95552 | −0.106210 | ||||||||
\(340\) | 4.84482i | 0.262747i | ||||||||
\(341\) | 17.6929 | 0.958122 | ||||||||
\(342\) | 20.0486 | 1.08410 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.73986i | 0.147724i | ||||||||
\(345\) | 10.1984i | 0.549061i | ||||||||
\(346\) | − | 9.94038i | − | 0.534398i | ||||||
\(347\) | 29.1200 | 1.56324 | 0.781622 | − | 0.623753i | \(-0.214393\pi\) | ||||
0.781622 | + | 0.623753i | \(0.214393\pi\) | |||||||
\(348\) | −2.27166 | −0.121774 | ||||||||
\(349\) | − | 20.3297i | − | 1.08822i | −0.839013 | − | 0.544112i | \(-0.816867\pi\) | ||
0.839013 | − | 0.544112i | \(-0.183133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.1000 | − | 1.86492i | 0.539099 | − | 0.0995421i | ||||
\(352\) | −10.3174 | −0.549919 | ||||||||
\(353\) | − | 14.1980i | − | 0.755683i | −0.925870 | − | 0.377841i | \(-0.876666\pi\) | ||
0.925870 | − | 0.377841i | \(-0.123334\pi\) | |||||||
\(354\) | 7.87555 | 0.418581 | ||||||||
\(355\) | −13.7773 | −0.731224 | ||||||||
\(356\) | 9.67285i | 0.512660i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.8324i | 0.678214i | ||||||||
\(359\) | 7.50164i | 0.395921i | 0.980210 | + | 0.197961i | \(0.0634318\pi\) | ||||
−0.980210 | + | 0.197961i | \(0.936568\pi\) | |||||||
\(360\) | 16.5060 | 0.869941 | ||||||||
\(361\) | −0.322229 | −0.0169594 | ||||||||
\(362\) | 33.1101i | 1.74023i | ||||||||
\(363\) | 2.14646 | 0.112660 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.3958 | −0.858193 | ||||||||
\(366\) | 7.82815i | 0.409184i | ||||||||
\(367\) | −28.5883 | −1.49230 | −0.746149 | − | 0.665779i | \(-0.768099\pi\) | ||||
−0.746149 | + | 0.665779i | \(0.768099\pi\) | |||||||
\(368\) | −35.3644 | −1.84350 | ||||||||
\(369\) | − | 10.9653i | − | 0.570830i | ||||||
\(370\) | 28.0348i | 1.45746i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 2.51303i | − | 0.130294i | ||||||
\(373\) | −7.91204 | −0.409670 | −0.204835 | − | 0.978797i | \(-0.565666\pi\) | ||||
−0.204835 | + | 0.978797i | \(0.565666\pi\) | |||||||
\(374\) | −9.72584 | −0.502911 | ||||||||
\(375\) | 2.47622i | 0.127871i | ||||||||
\(376\) | −2.81872 | −0.145364 | ||||||||
\(377\) | −21.9677 | + | 4.05624i | −1.13139 | + | 0.208907i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.78091i | 0.0914791i | 0.998953 | + | 0.0457395i | \(0.0145644\pi\) | ||||
−0.998953 | + | 0.0457395i | \(0.985436\pi\) | |||||||
\(380\) | 9.35761 | 0.480035 | ||||||||
\(381\) | −1.17484 | −0.0601889 | ||||||||
\(382\) | 33.9108i | 1.73503i | ||||||||
\(383\) | − | 14.1997i | − | 0.725572i | −0.931872 | − | 0.362786i | \(-0.881826\pi\) | ||
0.931872 | − | 0.362786i | \(-0.118174\pi\) | |||||||
\(384\) | − | 6.61883i | − | 0.337766i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.5829 | 1.04764 | ||||||||
\(387\) | −3.62077 | −0.184054 | ||||||||
\(388\) | − | 10.3987i | − | 0.527912i | ||||||
\(389\) | 6.77499 | 0.343506 | 0.171753 | − | 0.985140i | \(-0.445057\pi\) | ||||
0.171753 | + | 0.985140i | \(0.445057\pi\) | |||||||
\(390\) | 8.34990 | − | 1.54177i | 0.422813 | − | 0.0780706i | ||||
\(391\) | −16.3161 | −0.825140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.05700 | 0.0533187 | ||||||||
\(394\) | −31.4226 | −1.58305 | ||||||||
\(395\) | − | 5.78876i | − | 0.291264i | ||||||
\(396\) | − | 5.26791i | − | 0.264723i | ||||||
\(397\) | 29.0023i | 1.45558i | 0.685798 | + | 0.727792i | \(0.259453\pi\) | ||||
−0.685798 | + | 0.727792i | \(0.740547\pi\) | |||||||
\(398\) | − | 21.2218i | − | 1.06375i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0772 | 0.803861 | ||||||||
\(401\) | 21.9604i | 1.09665i | 0.836265 | + | 0.548326i | \(0.184735\pi\) | ||||
−0.836265 | + | 0.548326i | \(0.815265\pi\) | |||||||
\(402\) | −13.0370 | −0.650224 | ||||||||
\(403\) | −4.48721 | − | 24.3018i | −0.223524 | − | 1.21056i | ||||
\(404\) | −12.9246 | −0.643024 | ||||||||
\(405\) | 19.7006i | 0.978928i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.2105 | −0.753959 | ||||||||
\(408\) | − | 2.34842i | − | 0.116264i | ||||||
\(409\) | 4.00290i | 0.197931i | 0.995091 | + | 0.0989653i | \(0.0315533\pi\) | ||||
−0.995091 | + | 0.0989653i | \(0.968447\pi\) | |||||||
\(410\) | − | 18.9366i | − | 0.935214i | ||||||
\(411\) | − | 0.212449i | − | 0.0104793i | ||||||
\(412\) | −4.85702 | −0.239288 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 32.6986i | − | 1.60705i | ||||||
\(415\) | 8.96075 | 0.439866 | ||||||||
\(416\) | 2.61667 | + | 14.1713i | 0.128293 | + | 0.694806i | ||||
\(417\) | −9.64501 | −0.472318 | ||||||||
\(418\) | 18.7851i | 0.918811i | ||||||||
\(419\) | 1.75047 | 0.0855162 | 0.0427581 | − | 0.999085i | \(-0.486386\pi\) | ||||
0.0427581 | + | 0.999085i | \(0.486386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2204i | 0.790533i | 0.918566 | + | 0.395267i | \(0.129348\pi\) | ||||
−0.918566 | + | 0.395267i | \(0.870652\pi\) | |||||||
\(422\) | − | 13.0277i | − | 0.634179i | ||||||
\(423\) | − | 3.72498i | − | 0.181115i | ||||||
\(424\) | − | 17.2778i | − | 0.839082i | ||||||
\(425\) | 7.41755 | 0.359804 | ||||||||
\(426\) | −3.92837 | −0.190330 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.5570 | −0.558631 | ||||||||
\(429\) | 0.836502 | + | 4.53031i | 0.0403867 | + | 0.218726i | ||||
\(430\) | −6.25294 | −0.301543 | ||||||||
\(431\) | − | 11.6797i | − | 0.562590i | −0.959621 | − | 0.281295i | \(-0.909236\pi\) | ||
0.959621 | − | 0.281295i | \(-0.0907639\pi\) | |||||||
\(432\) | 14.0515 | 0.676052 | ||||||||
\(433\) | 31.6289 | 1.51999 | 0.759994 | − | 0.649930i | \(-0.225202\pi\) | ||||
0.759994 | + | 0.649930i | \(0.225202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.81351i | 0.422575i | ||||||||
\(436\) | 7.42008i | 0.355357i | ||||||||
\(437\) | 31.5140i | 1.50752i | ||||||||
\(438\) | −4.67498 | −0.223379 | ||||||||
\(439\) | −9.71539 | −0.463690 | −0.231845 | − | 0.972753i | \(-0.574476\pi\) | ||||
−0.231845 | + | 0.972753i | \(0.574476\pi\) | |||||||
\(440\) | 15.4658i | 0.737302i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.46664 | + | 13.3588i | 0.117326 | + | 0.635413i | ||||
\(443\) | 21.1163 | 1.00327 | 0.501633 | − | 0.865081i | \(-0.332733\pi\) | ||||
0.501633 | + | 0.865081i | \(0.332733\pi\) | |||||||
\(444\) | 2.16045i | 0.102530i | ||||||||
\(445\) | 37.5283 | 1.77901 | ||||||||
\(446\) | −12.8644 | −0.609145 | ||||||||
\(447\) | 11.3352i | 0.536135i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13.4710i | − | 0.635735i | −0.948135 | − | 0.317867i | \(-0.897033\pi\) | ||
0.948135 | − | 0.317867i | \(-0.102967\pi\) | |||||||
\(450\) | 14.8653i | 0.700758i | ||||||||
\(451\) | 10.2743 | 0.483796 | ||||||||
\(452\) | 2.92647 | 0.137650 | ||||||||
\(453\) | − | 5.55401i | − | 0.260950i | ||||||
\(454\) | 42.2871 | 1.98463 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.53589 | −0.212413 | ||||||||
\(457\) | − | 9.35582i | − | 0.437647i | −0.975764 | − | 0.218823i | \(-0.929778\pi\) | ||
0.975764 | − | 0.218823i | \(-0.0702218\pi\) | |||||||
\(458\) | 21.3538 | 0.997798 | ||||||||
\(459\) | 6.48294 | 0.302598 | ||||||||
\(460\) | − | 15.2620i | − | 0.711593i | ||||||
\(461\) | − | 8.14109i | − | 0.379168i | −0.981864 | − | 0.189584i | \(-0.939286\pi\) | ||
0.981864 | − | 0.189584i | \(-0.0607140\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3018i | 1.12940i | 0.825296 | + | 0.564700i | \(0.191008\pi\) | ||||
−0.825296 | + | 0.564700i | \(0.808992\pi\) | |||||||
\(464\) | −30.5623 | −1.41882 | ||||||||
\(465\) | −9.74994 | −0.452143 | ||||||||
\(466\) | − | 13.4805i | − | 0.624473i | ||||||
\(467\) | −32.7935 | −1.51750 | −0.758751 | − | 0.651381i | \(-0.774190\pi\) | ||||
−0.758751 | + | 0.651381i | \(0.774190\pi\) | |||||||
\(468\) | −7.23567 | + | 1.33603i | −0.334469 | + | 0.0617582i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 6.43290i | − | 0.296728i | ||||||
\(471\) | −1.87497 | −0.0863940 | ||||||||
\(472\) | 20.0360 | 0.922232 | ||||||||
\(473\) | − | 3.39259i | − | 0.155991i | ||||||
\(474\) | − | 1.65057i | − | 0.0758132i | ||||||
\(475\) | − | 14.3267i | − | 0.657356i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.8328 | 1.04544 | ||||||||
\(478\) | 39.4215 | 1.80310 | ||||||||
\(479\) | 2.48109i | 0.113364i | 0.998392 | + | 0.0566819i | \(0.0180521\pi\) | ||||
−0.998392 | + | 0.0566819i | \(0.981948\pi\) | |||||||
\(480\) | 5.68557 | 0.259510 | ||||||||
\(481\) | 3.85766 | + | 20.8922i | 0.175894 | + | 0.952604i | ||||
\(482\) | −0.477694 | −0.0217584 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.21221 | −0.146009 | ||||||||
\(485\) | −40.3443 | −1.83194 | ||||||||
\(486\) | 19.7650i | 0.896557i | ||||||||
\(487\) | − | 22.9216i | − | 1.03867i | −0.854569 | − | 0.519337i | \(-0.826179\pi\) | ||
0.854569 | − | 0.519337i | \(-0.173821\pi\) | |||||||
\(488\) | 19.9154i | 0.901529i | ||||||||
\(489\) | 9.70797i | 0.439010i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.8735 | −1.03227 | −0.516134 | − | 0.856508i | \(-0.672629\pi\) | ||||
−0.516134 | + | 0.856508i | \(0.672629\pi\) | |||||||
\(492\) | − | 1.45932i | − | 0.0657910i | ||||||
\(493\) | −14.1005 | −0.635055 | ||||||||
\(494\) | 25.8020 | − | 4.76423i | 1.16089 | − | 0.214353i | ||||
\(495\) | −20.4382 | −0.918631 | ||||||||
\(496\) | − | 33.8095i | − | 1.51809i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.55501 | 0.114493 | ||||||||
\(499\) | 8.48087i | 0.379656i | 0.981817 | + | 0.189828i | \(0.0607930\pi\) | ||||
−0.981817 | + | 0.189828i | \(0.939207\pi\) | |||||||
\(500\) | − | 3.70570i | − | 0.165724i | ||||||
\(501\) | − | 5.09440i | − | 0.227601i | ||||||
\(502\) | 12.6124i | 0.562921i | ||||||||
\(503\) | −9.36890 | −0.417739 | −0.208869 | − | 0.977944i | \(-0.566978\pi\) | ||||
−0.208869 | + | 0.977944i | \(0.566978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50.1444i | 2.23140i | ||||||||
\(506\) | 30.6380 | 1.36202 | ||||||||
\(507\) | 6.01040 | − | 2.29793i | 0.266931 | − | 0.102055i | ||||
\(508\) | 1.75817 | 0.0780060 | ||||||||
\(509\) | − | 21.5402i | − | 0.954753i | −0.878699 | − | 0.477376i | \(-0.841588\pi\) | ||
0.878699 | − | 0.477376i | \(-0.158412\pi\) | |||||||
\(510\) | 5.35958 | 0.237326 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 0.851388i | − | 0.0376264i | ||||||
\(513\) | − | 12.5216i | − | 0.552841i | ||||||
\(514\) | 19.2967i | 0.851143i | ||||||||
\(515\) | 18.8441i | 0.830368i | ||||||||
\(516\) | −0.481870 | −0.0212132 | ||||||||
\(517\) | 3.49023 | 0.153500 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.97203 | −0.130458 | ||||||||
\(520\) | 21.2428 | − | 3.92239i | 0.931558 | − | 0.172008i | ||||
\(521\) | 15.7470 | 0.689889 | 0.344944 | − | 0.938623i | \(-0.387898\pi\) | ||||
0.344944 | + | 0.938623i | \(0.387898\pi\) | |||||||
\(522\) | − | 28.2585i | − | 1.23684i | ||||||
\(523\) | 17.9404 | 0.784477 | 0.392238 | − | 0.919864i | \(-0.371701\pi\) | ||||
0.392238 | + | 0.919864i | \(0.371701\pi\) | |||||||
\(524\) | −1.58182 | −0.0691020 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 22.4369i | − | 0.978293i | ||||||
\(527\) | − | 15.5987i | − | 0.679489i | ||||||
\(528\) | 6.30273i | 0.274291i | ||||||||
\(529\) | 28.3983 | 1.23471 | ||||||||
\(530\) | 39.4314 | 1.71279 | ||||||||
\(531\) | 26.4779i | 1.14904i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.60573 | − | 14.1121i | −0.112867 | − | 0.611261i | ||||
\(534\) | 10.7006 | 0.463060 | ||||||||
\(535\) | 44.8386i | 1.93854i | ||||||||
\(536\) | −33.1671 | −1.43260 | ||||||||
\(537\) | 3.83672 | 0.165566 | ||||||||
\(538\) | − | 29.5232i | − | 1.27284i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.06410i | 0.260957i | ||||||||
\(541\) | − | 9.35582i | − | 0.402238i | −0.979567 | − | 0.201119i | \(-0.935542\pi\) | ||
0.979567 | − | 0.201119i | \(-0.0644578\pi\) | |||||||
\(542\) | 50.2853 | 2.15994 | ||||||||
\(543\) | 9.89947 | 0.424827 | ||||||||
\(544\) | 9.09621i | 0.389997i | ||||||||
\(545\) | 28.7881 | 1.23315 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.1634 | −1.41796 | −0.708981 | − | 0.705227i | \(-0.750845\pi\) | ||||
−0.708981 | + | 0.705227i | \(0.750845\pi\) | |||||||
\(548\) | 0.317933i | 0.0135814i | ||||||||
\(549\) | −26.3185 | −1.12325 | ||||||||
\(550\) | −13.9285 | −0.593914 | ||||||||
\(551\) | 27.2347i | 1.16024i | ||||||||
\(552\) | 7.39790i | 0.314876i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 8.63228i | − | 0.366750i | ||||||
\(555\) | 8.38202 | 0.355797 | ||||||||
\(556\) | 14.4339 | 0.612133 | ||||||||
\(557\) | 11.1532i | 0.472578i | 0.971683 | + | 0.236289i | \(0.0759312\pi\) | ||||
−0.971683 | + | 0.236289i | \(0.924069\pi\) | |||||||
\(558\) | 31.2609 | 1.32338 | ||||||||
\(559\) | −4.65984 | + | 0.860419i | −0.197090 | + | 0.0363918i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.90789i | 0.122771i | ||||||||
\(562\) | −2.75238 | −0.116102 | ||||||||
\(563\) | 19.1778 | 0.808247 | 0.404124 | − | 0.914704i | \(-0.367577\pi\) | ||||
0.404124 | + | 0.914704i | \(0.367577\pi\) | |||||||
\(564\) | − | 0.495739i | − | 0.0208744i | ||||||
\(565\) | − | 11.3540i | − | 0.477666i | ||||||
\(566\) | 22.8389i | 0.959993i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.99409 | −0.419343 | ||||||||
\(569\) | −13.4672 | −0.564575 | −0.282288 | − | 0.959330i | \(-0.591093\pi\) | ||||
−0.282288 | + | 0.959330i | \(0.591093\pi\) | |||||||
\(570\) | − | 10.3519i | − | 0.433591i | ||||||
\(571\) | −25.1608 | −1.05295 | −0.526473 | − | 0.850192i | \(-0.676486\pi\) | ||||
−0.526473 | + | 0.850192i | \(0.676486\pi\) | |||||||
\(572\) | −1.25184 | − | 6.77968i | −0.0523419 | − | 0.283473i | ||||
\(573\) | 10.1389 | 0.423557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.3665 | −0.974450 | ||||||||
\(576\) | 8.95016 | 0.372923 | ||||||||
\(577\) | − | 21.6484i | − | 0.901235i | −0.892717 | − | 0.450617i | \(-0.851204\pi\) | ||
0.892717 | − | 0.450617i | \(-0.148796\pi\) | |||||||
\(578\) | − | 19.5691i | − | 0.813969i | ||||||
\(579\) | − | 6.15401i | − | 0.255752i | ||||||
\(580\) | − | 13.1895i | − | 0.547666i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.5035 | −0.476836 | ||||||||
\(583\) | 21.3939i | 0.886044i | ||||||||
\(584\) | −11.8935 | −0.492157 | ||||||||
\(585\) | 5.18349 | + | 28.0727i | 0.214311 | + | 1.16066i | ||||
\(586\) | 21.2860 | 0.879316 | ||||||||
\(587\) | 34.5576i | 1.42634i | 0.700989 | + | 0.713172i | \(0.252742\pi\) | ||||
−0.700989 | + | 0.713172i | \(0.747258\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.1283 | −1.24142 | ||||||||
\(590\) | 45.7263i | 1.88252i | ||||||||
\(591\) | 9.39493i | 0.386456i | ||||||||
\(592\) | 29.0660i | 1.19461i | ||||||||
\(593\) | 1.26839i | 0.0520865i | 0.999661 | + | 0.0260432i | \(0.00829075\pi\) | ||||
−0.999661 | + | 0.0260432i | \(0.991709\pi\) | |||||||
\(594\) | −12.1735 | −0.499485 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 16.9632i | − | 0.694842i | ||||||
\(597\) | −6.34501 | −0.259684 | ||||||||
\(598\) | −7.77032 | − | 42.0824i | −0.317752 | − | 1.72088i | ||||
\(599\) | 17.5143 | 0.715614 | 0.357807 | − | 0.933796i | \(-0.383525\pi\) | ||||
0.357807 | + | 0.933796i | \(0.383525\pi\) | |||||||
\(600\) | − | 3.36320i | − | 0.137302i | ||||||
\(601\) | −9.02164 | −0.368000 | −0.184000 | − | 0.982926i | \(-0.558905\pi\) | ||||
−0.184000 | + | 0.982926i | \(0.558905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 43.8307i | − | 1.78493i | ||||||
\(604\) | 8.31165i | 0.338196i | ||||||||
\(605\) | 12.4626i | 0.506677i | ||||||||
\(606\) | 14.2979i | 0.580811i | ||||||||
\(607\) | −15.8290 | −0.642479 | −0.321239 | − | 0.946998i | \(-0.604099\pi\) | ||||
−0.321239 | + | 0.946998i | \(0.604099\pi\) | |||||||
\(608\) | 17.5690 | 0.712517 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −45.4511 | −1.84026 | ||||||||
\(611\) | −0.885182 | − | 4.79396i | −0.0358106 | − | 0.193943i | ||||
\(612\) | −4.64439 | −0.187738 | ||||||||
\(613\) | 17.5344i | 0.708209i | 0.935206 | + | 0.354104i | \(0.115214\pi\) | ||||
−0.935206 | + | 0.354104i | \(0.884786\pi\) | |||||||
\(614\) | −34.6029 | −1.39646 | ||||||||
\(615\) | −5.66179 | −0.228306 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.01448i | − | 0.282392i | −0.989982 | − | 0.141196i | \(-0.954905\pi\) | ||
0.989982 | − | 0.141196i | \(-0.0450948\pi\) | |||||||
\(618\) | 5.37307i | 0.216137i | ||||||||
\(619\) | − | 38.8263i | − | 1.56056i | −0.625430 | − | 0.780280i | \(-0.715077\pi\) | ||
0.625430 | − | 0.780280i | \(-0.284923\pi\) | |||||||
\(620\) | 14.5909 | 0.585985 | ||||||||
\(621\) | −20.4223 | −0.819518 | ||||||||
\(622\) | − | 28.3743i | − | 1.13771i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.65703 | − | 1.59848i | 0.346558 | − | 0.0639904i | ||||
\(625\) | −30.6735 | −1.22694 | ||||||||
\(626\) | − | 4.22597i | − | 0.168904i | ||||||
\(627\) | 5.61649 | 0.224301 | ||||||||
\(628\) | 2.80592 | 0.111968 | ||||||||
\(629\) | 13.4102i | 0.534699i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7484i | 0.507506i | 0.967269 | + | 0.253753i | \(0.0816650\pi\) | ||||
−0.967269 | + | 0.253753i | \(0.918335\pi\) | |||||||
\(632\) | − | 4.19918i | − | 0.167034i | ||||||
\(633\) | −3.89510 | −0.154816 | ||||||||
\(634\) | 45.1770 | 1.79421 | ||||||||
\(635\) | − | 6.82126i | − | 0.270694i | ||||||
\(636\) | 3.03871 | 0.120493 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26.4776 | 1.04826 | ||||||||
\(639\) | − | 13.2073i | − | 0.522474i | ||||||
\(640\) | 38.4297 | 1.51907 | ||||||||
\(641\) | 9.71429 | 0.383691 | 0.191846 | − | 0.981425i | \(-0.438553\pi\) | ||||
0.191846 | + | 0.981425i | \(0.438553\pi\) | |||||||
\(642\) | 12.7850i | 0.504583i | ||||||||
\(643\) | 0.458279i | 0.0180728i | 0.999959 | + | 0.00903639i | \(0.00287641\pi\) | ||||
−0.999959 | + | 0.00903639i | \(0.997124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.86954i | 0.0736131i | ||||||||
\(646\) | 16.5617 | 0.651610 | ||||||||
\(647\) | 6.17722 | 0.242852 | 0.121426 | − | 0.992601i | \(-0.461253\pi\) | ||||
0.121426 | + | 0.992601i | \(0.461253\pi\) | |||||||
\(648\) | 14.2908i | 0.561397i | ||||||||
\(649\) | −24.8093 | −0.973848 | ||||||||
\(650\) | 3.53251 | + | 19.1313i | 0.138556 | + | 0.750392i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 14.5281i | − | 0.568965i | ||||||
\(653\) | 28.4385 | 1.11289 | 0.556443 | − | 0.830886i | \(-0.312166\pi\) | ||||
0.556443 | + | 0.830886i | \(0.312166\pi\) | |||||||
\(654\) | 8.20846 | 0.320976 | ||||||||
\(655\) | 6.13707i | 0.239795i | ||||||||
\(656\) | − | 19.6332i | − | 0.766547i | ||||||
\(657\) | − | 15.7175i | − | 0.613196i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.9818 | −1.01211 | −0.506054 | − | 0.862502i | \(-0.668897\pi\) | ||||
−0.506054 | + | 0.862502i | \(0.668897\pi\) | |||||||
\(660\) | −2.72002 | −0.105877 | ||||||||
\(661\) | − | 37.2752i | − | 1.44984i | −0.688835 | − | 0.724918i | \(-0.741878\pi\) | ||
0.688835 | − | 0.724918i | \(-0.258122\pi\) | |||||||
\(662\) | −16.0471 | −0.623686 | ||||||||
\(663\) | 3.99409 | − | 0.737491i | 0.155118 | − | 0.0286418i | ||||
\(664\) | 6.50015 | 0.252255 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.8750 | −1.04139 | ||||||||
\(667\) | 44.4189 | 1.71991 | ||||||||
\(668\) | 7.62385i | 0.294976i | ||||||||
\(669\) | 3.84626i | 0.148705i | ||||||||
\(670\) | − | 75.6941i | − | 2.92432i | ||||||
\(671\) | − | 24.6599i | − | 0.951986i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.7078 | 1.60772 | 0.803859 | − | 0.594820i | \(-0.202777\pi\) | ||||
0.803859 | + | 0.594820i | \(0.202777\pi\) | |||||||
\(674\) | 10.4525i | 0.402613i | ||||||||
\(675\) | 9.28430 | 0.357353 | ||||||||
\(676\) | −8.99464 | + | 3.43889i | −0.345948 | + | 0.132265i | ||||
\(677\) | 18.2069 | 0.699750 | 0.349875 | − | 0.936796i | \(-0.386224\pi\) | ||||
0.349875 | + | 0.936796i | \(0.386224\pi\) | |||||||
\(678\) | − | 3.23741i | − | 0.124332i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.6352 | 0.522886 | ||||||||
\(681\) | − | 12.6432i | − | 0.484490i | ||||||
\(682\) | 29.2908i | 1.12160i | ||||||||
\(683\) | 27.3360i | 1.04598i | 0.852338 | + | 0.522991i | \(0.175184\pi\) | ||||
−0.852338 | + | 0.522991i | \(0.824816\pi\) | |||||||
\(684\) | 8.97048i | 0.342995i | ||||||||
\(685\) | 1.23350 | 0.0471297 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.38449i | − | 0.243584i | ||||||
\(688\) | −6.48294 | −0.247160 | ||||||||
\(689\) | 29.3853 | − | 5.42586i | 1.11949 | − | 0.206709i | ||||
\(690\) | −16.8836 | −0.642746 | ||||||||
\(691\) | 8.39581i | 0.319392i | 0.987166 | + | 0.159696i | \(0.0510513\pi\) | ||||
−0.987166 | + | 0.159696i | \(0.948949\pi\) | |||||||
\(692\) | 4.44769 | 0.169076 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 48.2087i | 1.82998i | ||||||||
\(695\) | − | 56.0000i | − | 2.12420i | ||||||
\(696\) | 6.39334i | 0.242339i | ||||||||
\(697\) | − | 9.05817i | − | 0.343102i | ||||||
\(698\) | 33.6562 | 1.27391 | ||||||||
\(699\) | −4.03049 | −0.152447 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.4998 | 1.03865 | 0.519327 | − | 0.854576i | \(-0.326183\pi\) | ||||
0.519327 | + | 0.854576i | \(0.326183\pi\) | |||||||
\(702\) | 3.08741 | + | 16.7207i | 0.116527 | + | 0.631084i | ||||
\(703\) | 25.9013 | 0.976887 | ||||||||
\(704\) | 8.38612i | 0.316064i | ||||||||
\(705\) | −1.92335 | −0.0724375 | ||||||||
\(706\) | 23.5050 | 0.884623 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.52381i | 0.132433i | ||||||||
\(709\) | − | 28.9820i | − | 1.08844i | −0.838942 | − | 0.544221i | \(-0.816825\pi\) | ||
0.838942 | − | 0.544221i | \(-0.183175\pi\) | |||||||
\(710\) | − | 22.8086i | − | 0.855991i | ||||||
\(711\) | 5.54928 | 0.208114 | ||||||||
\(712\) | 27.2231 | 1.02023 | ||||||||
\(713\) | 49.1384i | 1.84025i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.3035 | + | 4.85683i | −0.983696 | + | 0.181635i | ||||
\(716\) | −5.74170 | −0.214577 | ||||||||
\(717\) | − | 11.7865i | − | 0.440174i | ||||||
\(718\) | −12.4191 | −0.463476 | ||||||||
\(719\) | 17.5522 | 0.654588 | 0.327294 | − | 0.944923i | \(-0.393863\pi\) | ||||
0.327294 | + | 0.944923i | \(0.393863\pi\) | |||||||
\(720\) | 39.0557i | 1.45552i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 0.533456i | − | 0.0198532i | ||||||
\(723\) | 0.142824i | 0.00531168i | ||||||||
\(724\) | −14.8147 | −0.550584 | ||||||||
\(725\) | −20.1935 | −0.749969 | ||||||||
\(726\) | 3.55350i | 0.131883i | ||||||||
\(727\) | −22.1403 | −0.821139 | −0.410569 | − | 0.911829i | \(-0.634670\pi\) | ||||
−0.410569 | + | 0.911829i | \(0.634670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.6556 | −0.542799 | ||||||||
\(730\) | − | 27.1435i | − | 1.00463i | ||||||
\(731\) | −2.99103 | −0.110627 | ||||||||
\(732\) | −3.50260 | −0.129460 | ||||||||
\(733\) | 51.3414i | 1.89634i | 0.317768 | + | 0.948169i | \(0.397067\pi\) | ||||
−0.317768 | + | 0.948169i | \(0.602933\pi\) | |||||||
\(734\) | − | 47.3285i | − | 1.74693i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 28.6545i | − | 1.05622i | ||||||
\(737\) | 41.0685 | 1.51278 | ||||||||
\(738\) | 18.1532 | 0.668229 | ||||||||
\(739\) | 22.7787i | 0.837929i | 0.908003 | + | 0.418965i | \(0.137607\pi\) | ||||
−0.908003 | + | 0.418965i | \(0.862393\pi\) | |||||||
\(740\) | −12.5438 | −0.461120 | ||||||||
\(741\) | −1.42444 | − | 7.71445i | −0.0523281 | − | 0.283398i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.6199i | − | 1.01328i | −0.862159 | − | 0.506638i | \(-0.830888\pi\) | ||
0.862159 | − | 0.506638i | \(-0.169112\pi\) | |||||||
\(744\) | −7.07262 | −0.259295 | ||||||||
\(745\) | −65.8133 | −2.41121 | ||||||||
\(746\) | − | 13.0985i | − | 0.479571i | ||||||
\(747\) | 8.59004i | 0.314293i | ||||||||
\(748\) | − | 4.35170i | − | 0.159114i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.09943 | −0.149690 | ||||||||
\(751\) | −41.1172 | −1.50039 | −0.750194 | − | 0.661218i | \(-0.770040\pi\) | ||||
−0.750194 | + | 0.661218i | \(0.770040\pi\) | |||||||
\(752\) | − | 6.66952i | − | 0.243212i | ||||||
\(753\) | 3.77095 | 0.137421 | ||||||||
\(754\) | −6.71518 | − | 36.3680i | −0.244552 | − | 1.32444i | ||||
\(755\) | 32.2472 | 1.17360 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0143 | 0.509357 | 0.254678 | − | 0.967026i | \(-0.418030\pi\) | ||||
0.254678 | + | 0.967026i | \(0.418030\pi\) | |||||||
\(758\) | −2.94832 | −0.107088 | ||||||||
\(759\) | − | 9.16033i | − | 0.332499i | ||||||
\(760\) | − | 26.3359i | − | 0.955304i | ||||||
\(761\) | − | 34.1648i | − | 1.23847i | −0.785205 | − | 0.619236i | \(-0.787442\pi\) | ||
0.785205 | − | 0.619236i | \(-0.212558\pi\) | |||||||
\(762\) | − | 1.94497i | − | 0.0704588i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.1730 | −0.548938 | ||||||||
\(765\) | 18.0191i | 0.651483i | ||||||||
\(766\) | 23.5079 | 0.849375 | ||||||||
\(767\) | 6.29205 | + | 34.0764i | 0.227193 | + | 1.23043i | ||||
\(768\) | 7.74153 | 0.279348 | ||||||||
\(769\) | − | 52.9061i | − | 1.90784i | −0.300059 | − | 0.953921i | \(-0.597006\pi\) | ||
0.300059 | − | 0.953921i | \(-0.402994\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.76946 | 0.207782 | ||||||||
\(772\) | 9.20957i | 0.331460i | ||||||||
\(773\) | 45.9133i | 1.65139i | 0.564118 | + | 0.825694i | \(0.309216\pi\) | ||||
−0.564118 | + | 0.825694i | \(0.690784\pi\) | |||||||
\(774\) | − | 5.99425i | − | 0.215459i | ||||||
\(775\) | − | 22.3391i | − | 0.802444i | ||||||
\(776\) | −29.2658 | −1.05058 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.2161i | 0.402117i | ||||||||
\(779\) | −17.4955 | −0.626843 | ||||||||
\(780\) | 0.689845 | + | 3.73605i | 0.0247004 | + | 0.133772i | ||||
\(781\) | 12.3750 | 0.442813 | ||||||||
\(782\) | − | 27.0116i | − | 0.965932i | ||||||
\(783\) | −17.6491 | −0.630728 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 10.8863i | − | 0.388548i | ||||||
\(786\) | 1.74989i | 0.0624163i | ||||||||
\(787\) | − | 15.1872i | − | 0.541364i | −0.962669 | − | 0.270682i | \(-0.912751\pi\) | ||
0.962669 | − | 0.270682i | \(-0.0872492\pi\) | |||||||
\(788\) | − | 14.0596i | − | 0.500854i | ||||||
\(789\) | −6.70831 | −0.238822 | ||||||||
\(790\) | 9.58340 | 0.340962 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.8259 | −0.526817 | ||||||||
\(793\) | −33.8713 | + | 6.25418i | −1.20281 | + | 0.222093i | ||||
\(794\) | −48.0138 | −1.70395 | ||||||||
\(795\) | − | 11.7894i | − | 0.418129i | ||||||
\(796\) | 9.49540 | 0.336555 | ||||||||
\(797\) | 16.3006 | 0.577398 | 0.288699 | − | 0.957420i | \(-0.406777\pi\) | ||||
0.288699 | + | 0.957420i | \(0.406777\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.07712i | − | 0.108861i | ||||||
\(800\) | 13.0268i | 0.460567i | ||||||||
\(801\) | 35.9758i | 1.27114i | ||||||||
\(802\) | −36.3559 | −1.28377 | ||||||||
\(803\) | 14.7269 | 0.519703 | ||||||||
\(804\) | − | 5.83322i | − | 0.205722i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 40.2320 | − | 7.42866i | 1.41711 | − | 0.261663i | ||||
\(807\) | −8.82704 | −0.310727 | ||||||||
\(808\) | 36.3749i | 1.27966i | ||||||||
\(809\) | 10.3857 | 0.365142 | 0.182571 | − | 0.983193i | \(-0.441558\pi\) | ||||
0.182571 | + | 0.983193i | \(0.441558\pi\) | |||||||
\(810\) | −32.6146 | −1.14596 | ||||||||
\(811\) | − | 10.9705i | − | 0.385227i | −0.981275 | − | 0.192614i | \(-0.938304\pi\) | ||
0.981275 | − | 0.192614i | \(-0.0616964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 15.0346i | − | 0.527286i | ||||||
\(814\) | − | 25.1813i | − | 0.882605i | ||||||
\(815\) | −56.3656 | −1.97440 | ||||||||
\(816\) | 5.55672 | 0.194524 | ||||||||
\(817\) | 5.77708i | 0.202114i | ||||||||
\(818\) | −6.62687 | −0.231703 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.47296 | 0.295888 | ||||||||
\(821\) | − | 40.2325i | − | 1.40412i | −0.712117 | − | 0.702061i | \(-0.752263\pi\) | ||
0.712117 | − | 0.702061i | \(-0.247737\pi\) | |||||||
\(822\) | 0.351713 | 0.0122674 | ||||||||
\(823\) | 3.26499 | 0.113811 | 0.0569053 | − | 0.998380i | \(-0.481877\pi\) | ||||
0.0569053 | + | 0.998380i | \(0.481877\pi\) | |||||||
\(824\) | 13.6695i | 0.476200i | ||||||||
\(825\) | 4.16443i | 0.144987i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.0118i | 1.59999i | 0.600009 | + | 0.799993i | \(0.295164\pi\) | ||||
−0.600009 | + | 0.799993i | \(0.704836\pi\) | |||||||
\(828\) | 14.6306 | 0.508448 | ||||||||
\(829\) | 30.3865 | 1.05537 | 0.527683 | − | 0.849441i | \(-0.323061\pi\) | ||||
0.527683 | + | 0.849441i | \(0.323061\pi\) | |||||||
\(830\) | 14.8347i | 0.514919i | ||||||||
\(831\) | −2.58093 | −0.0895315 | ||||||||
\(832\) | 11.5186 | − | 2.12686i | 0.399337 | − | 0.0737358i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 15.9675i | − | 0.552909i | ||||||
\(835\) | 29.5787 | 1.02361 | ||||||||
\(836\) | −8.40516 | −0.290699 | ||||||||
\(837\) | − | 19.5243i | − | 0.674860i | ||||||
\(838\) | 2.89794i | 0.100108i | ||||||||
\(839\) | − | 1.52007i | − | 0.0524787i | −0.999656 | − | 0.0262394i | \(-0.991647\pi\) | ||
0.999656 | − | 0.0262394i | \(-0.00835321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.38720 | 0.323697 | ||||||||
\(842\) | −26.8531 | −0.925420 | ||||||||
\(843\) | 0.822923i | 0.0283430i | ||||||||
\(844\) | 5.82908 | 0.200645 | ||||||||
\(845\) | 13.3421 | + | 34.8971i | 0.458981 | + | 1.20050i | ||||
\(846\) | 6.16677 | 0.212018 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 40.8818 | 1.40389 | ||||||||
\(849\) | 6.82853 | 0.234354 | ||||||||
\(850\) | 12.2799i | 0.421197i | ||||||||
\(851\) | − | 42.2443i | − | 1.44811i | ||||||
\(852\) | − | 1.75770i | − | 0.0602178i | ||||||
\(853\) | 43.7939i | 1.49947i | 0.661736 | + | 0.749737i | \(0.269820\pi\) | ||||
−0.661736 | + | 0.749737i | \(0.730180\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 34.8033 | 1.19025 | ||||||||
\(856\) | 32.5260i | 1.11172i | ||||||||
\(857\) | 14.8521 | 0.507338 | 0.253669 | − | 0.967291i | \(-0.418363\pi\) | ||||
0.253669 | + | 0.967291i | \(0.418363\pi\) | |||||||
\(858\) | −7.50002 | + | 1.38484i | −0.256046 | + | 0.0472778i | ||||
\(859\) | −44.3568 | −1.51343 | −0.756717 | − | 0.653742i | \(-0.773198\pi\) | ||||
−0.756717 | + | 0.653742i | \(0.773198\pi\) | |||||||
\(860\) | − | 2.79780i | − | 0.0954040i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.3359 | 0.658584 | ||||||||
\(863\) | 25.8451i | 0.879778i | 0.898052 | + | 0.439889i | \(0.144982\pi\) | ||||
−0.898052 | + | 0.439889i | \(0.855018\pi\) | |||||||
\(864\) | 11.3854i | 0.387340i | ||||||||
\(865\) | − | 17.2560i | − | 0.586721i | ||||||
\(866\) | 52.3622i | 1.77934i | ||||||||
\(867\) | −5.85090 | −0.198707 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.19956i | 0.176383i | ||||||||
\(870\) | −14.5909 | −0.494678 | ||||||||
\(871\) | −10.4157 | − | 56.4091i | −0.352922 | − | 1.91135i | ||||
\(872\) | 20.8830 | 0.707187 | ||||||||
\(873\) | − | 38.6752i | − | 1.30896i | ||||||
\(874\) | −52.1719 | −1.76474 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 2.09176i | − | 0.0706740i | ||||||
\(877\) | − | 1.37284i | − | 0.0463575i | −0.999731 | − | 0.0231788i | \(-0.992621\pi\) | ||
0.999731 | − | 0.0231788i | \(-0.00737869\pi\) | |||||||
\(878\) | − | 16.0840i | − | 0.542809i | ||||||
\(879\) | − | 6.36421i | − | 0.214660i | ||||||
\(880\) | −36.5944 | −1.23360 | ||||||||
\(881\) | 16.2514 | 0.547524 | 0.273762 | − | 0.961797i | \(-0.411732\pi\) | ||||
0.273762 | + | 0.961797i | \(0.411732\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.619110 | 0.0208347 | 0.0104174 | − | 0.999946i | \(-0.496684\pi\) | ||||
0.0104174 | + | 0.999946i | \(0.496684\pi\) | |||||||
\(884\) | −5.97722 | + | 1.10367i | −0.201036 | + | 0.0371203i | ||||
\(885\) | 13.6715 | 0.459564 | ||||||||
\(886\) | 34.9584i | 1.17445i | ||||||||
\(887\) | −31.9379 | −1.07237 | −0.536185 | − | 0.844100i | \(-0.680135\pi\) | ||||
−0.536185 | + | 0.844100i | \(0.680135\pi\) | |||||||
\(888\) | 6.08034 | 0.204043 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 62.1288i | 2.08256i | ||||||||
\(891\) | − | 17.6954i | − | 0.592817i | ||||||
\(892\) | − | 5.75599i | − | 0.192725i | ||||||
\(893\) | −5.94335 | −0.198886 | ||||||||
\(894\) | −18.7656 | −0.627615 | ||||||||
\(895\) | 22.2764i | 0.744618i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.5820 | + | 2.32322i | −0.420102 | + | 0.0775700i | ||||
\(898\) | 22.3015 | 0.744209 | ||||||||
\(899\) | 42.4658i | 1.41631i | ||||||||
\(900\) | −6.65129 | −0.221710 | ||||||||
\(901\) | 18.8616 | 0.628373 | ||||||||
\(902\) | 17.0092i | 0.566345i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.23621i | − | 0.273932i | ||||||
\(905\) | 57.4775i | 1.91062i | ||||||||
\(906\) | 9.19476 | 0.305475 | ||||||||
\(907\) | −20.7037 | −0.687455 | −0.343728 | − | 0.939069i | \(-0.611690\pi\) | ||||
−0.343728 | + | 0.939069i | \(0.611690\pi\) | |||||||
\(908\) | 18.9208i | 0.627909i | ||||||||
\(909\) | −48.0699 | −1.59438 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.4143 | 1.30585 | 0.652926 | − | 0.757421i | \(-0.273541\pi\) | ||||
0.652926 | + | 0.757421i | \(0.273541\pi\) | |||||||
\(912\) | − | 10.7326i | − | 0.355392i | ||||||
\(913\) | −8.04869 | −0.266373 | ||||||||
\(914\) | 15.4887 | 0.512321 | ||||||||
\(915\) | 13.5893i | 0.449247i | ||||||||
\(916\) | 9.55449i | 0.315689i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.7326i | 0.354229i | ||||||||
\(919\) | 14.2185 | 0.469025 | 0.234512 | − | 0.972113i | \(-0.424651\pi\) | ||||
0.234512 | + | 0.972113i | \(0.424651\pi\) | |||||||
\(920\) | −42.9531 | −1.41612 | ||||||||
\(921\) | 10.3458i | 0.340906i | ||||||||
\(922\) | 13.4777 | 0.443865 | ||||||||
\(923\) | −3.13852 | − | 16.9975i | −0.103306 | − | 0.559480i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.2049i | 0.631454i | ||||||||
\(926\) | −40.2320 | −1.32211 | ||||||||
\(927\) | −18.0645 | −0.593315 | ||||||||
\(928\) | − | 24.7635i | − | 0.812902i | ||||||
\(929\) | 28.7478i | 0.943185i | 0.881817 | + | 0.471593i | \(0.156321\pi\) | ||||
−0.881817 | + | 0.471593i | \(0.843679\pi\) | |||||||
\(930\) | − | 16.1412i | − | 0.529291i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.03168 | 0.197574 | ||||||||
\(933\) | −8.48352 | −0.277738 | ||||||||
\(934\) | − | 54.2902i | − | 1.77643i | ||||||
\(935\) | −16.8836 | −0.552151 | ||||||||
\(936\) | 3.76011 | + | 20.3640i | 0.122903 | + | 0.665617i | ||||
\(937\) | −19.8495 | −0.648456 | −0.324228 | − | 0.945979i | \(-0.605105\pi\) | ||||
−0.324228 | + | 0.945979i | \(0.605105\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.26351 | −0.0412330 | ||||||||
\(940\) | 2.87832 | 0.0938804 | ||||||||
\(941\) | − | 45.2320i | − | 1.47452i | −0.675609 | − | 0.737260i | \(-0.736119\pi\) | ||
0.675609 | − | 0.737260i | \(-0.263881\pi\) | |||||||
\(942\) | − | 3.10404i | − | 0.101135i | ||||||
\(943\) | 28.5347i | 0.929217i | ||||||||
\(944\) | 47.4083i | 1.54301i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.61649 | 0.182608 | ||||||||
\(947\) | 22.1095i | 0.718462i | 0.933249 | + | 0.359231i | \(0.116961\pi\) | ||||
−0.933249 | + | 0.359231i | \(0.883039\pi\) | |||||||
\(948\) | 0.738526 | 0.0239862 | ||||||||
\(949\) | −3.73501 | − | 20.2280i | −0.121243 | − | 0.656628i | ||||
\(950\) | 23.7182 | 0.769520 | ||||||||
\(951\) | − | 13.5073i | − | 0.438004i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.3502 | −1.11271 | −0.556356 | − | 0.830944i | \(-0.687801\pi\) | ||||
−0.556356 | + | 0.830944i | \(0.687801\pi\) | |||||||
\(954\) | 37.8001i | 1.22382i | ||||||||
\(955\) | 58.8674i | 1.90491i | ||||||||
\(956\) | 17.6386i | 0.570474i | ||||||||
\(957\) | − | 7.91644i | − | 0.255902i | ||||||
\(958\) | −4.10749 | −0.132707 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 4.62131i | − | 0.149152i | ||||||
\(961\) | −15.9778 | −0.515413 | ||||||||
\(962\) | −34.5875 | + | 6.38642i | −1.11514 | + | 0.205906i | ||||
\(963\) | −42.9836 | −1.38513 | ||||||||
\(964\) | − | 0.213738i | − | 0.00688403i | ||||||
\(965\) | 35.7309 | 1.15022 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.8805i | 0.767945i | 0.923344 | + | 0.383973i | \(0.125444\pi\) | ||||
−0.923344 | + | 0.383973i | \(0.874556\pi\) | |||||||
\(968\) | 9.04039i | 0.290569i | ||||||||
\(969\) | − | 4.95171i | − | 0.159072i | ||||||
\(970\) | − | 66.7907i | − | 2.14452i | ||||||
\(971\) | 25.9377 | 0.832381 | 0.416190 | − | 0.909277i | \(-0.363365\pi\) | ||||
0.416190 | + | 0.909277i | \(0.363365\pi\) | |||||||
\(972\) | −8.84358 | −0.283658 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 37.9470 | 1.21590 | ||||||||
\(975\) | 5.71999 | − | 1.05617i | 0.183186 | − | 0.0338245i | ||||
\(976\) | −47.1229 | −1.50837 | ||||||||
\(977\) | − | 45.2971i | − | 1.44918i | −0.689178 | − | 0.724592i | \(-0.742028\pi\) | ||
0.689178 | − | 0.724592i | \(-0.257972\pi\) | |||||||
\(978\) | −16.0717 | −0.513917 | ||||||||
\(979\) | −33.7086 | −1.07733 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.5971i | 0.881109i | ||||||||
\(982\) | − | 37.8675i | − | 1.20840i | ||||||
\(983\) | 2.03101i | 0.0647792i | 0.999475 | + | 0.0323896i | \(0.0103117\pi\) | ||||
−0.999475 | + | 0.0323896i | \(0.989688\pi\) | |||||||
\(984\) | −4.10708 | −0.130929 | ||||||||
\(985\) | −54.5480 | −1.73804 | ||||||||
\(986\) | − | 23.3437i | − | 0.743413i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.13169 | + | 11.5448i | 0.0678182 | + | 0.367289i | ||||
\(989\) | 9.42224 | 0.299610 | ||||||||
\(990\) | − | 33.8359i | − | 1.07537i | ||||||
\(991\) | −26.9665 | −0.856618 | −0.428309 | − | 0.903632i | \(-0.640890\pi\) | ||||
−0.428309 | + | 0.903632i | \(0.640890\pi\) | |||||||
\(992\) | 27.3946 | 0.869780 | ||||||||
\(993\) | 4.79785i | 0.152255i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 36.8399i | − | 1.16790i | ||||||
\(996\) | 1.14321i | 0.0362239i | ||||||||
\(997\) | 6.65574 | 0.210789 | 0.105395 | − | 0.994430i | \(-0.466389\pi\) | ||||
0.105395 | + | 0.994430i | \(0.466389\pi\) | |||||||
\(998\) | −14.0402 | −0.444436 | ||||||||
\(999\) | 16.7851i | 0.531056i |
(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 | 637.2.c.g.246.14 | yes | 16 | |
7.2 | even | 3 | 637.2.r.g.116.13 | 32 | |||
7.3 | odd | 6 | 637.2.r.g.324.4 | 32 | |||
7.4 | even | 3 | 637.2.r.g.324.3 | 32 | |||
7.5 | odd | 6 | 637.2.r.g.116.14 | 32 | |||
7.6 | odd | 2 | inner | 637.2.c.g.246.13 | yes | 16 | |
13.5 | odd | 4 | 8281.2.a.cs.1.14 | 16 | |||
13.8 | odd | 4 | 8281.2.a.cs.1.4 | 16 | |||
13.12 | even | 2 | inner | 637.2.c.g.246.4 | yes | 16 | |
91.12 | odd | 6 | 637.2.r.g.116.4 | 32 | |||
91.25 | even | 6 | 637.2.r.g.324.13 | 32 | |||
91.34 | even | 4 | 8281.2.a.cs.1.3 | 16 | |||
91.38 | odd | 6 | 637.2.r.g.324.14 | 32 | |||
91.51 | even | 6 | 637.2.r.g.116.3 | 32 | |||
91.83 | even | 4 | 8281.2.a.cs.1.13 | 16 | |||
91.90 | odd | 2 | inner | 637.2.c.g.246.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.3 | ✓ | 16 | 91.90 | odd | 2 | inner | |
637.2.c.g.246.4 | yes | 16 | 13.12 | even | 2 | inner | |
637.2.c.g.246.13 | yes | 16 | 7.6 | odd | 2 | inner | |
637.2.c.g.246.14 | yes | 16 | 1.1 | even | 1 | trivial | |
637.2.r.g.116.3 | 32 | 91.51 | even | 6 | |||
637.2.r.g.116.4 | 32 | 91.12 | odd | 6 | |||
637.2.r.g.116.13 | 32 | 7.2 | even | 3 | |||
637.2.r.g.116.14 | 32 | 7.5 | odd | 6 | |||
637.2.r.g.324.3 | 32 | 7.4 | even | 3 | |||
637.2.r.g.324.4 | 32 | 7.3 | odd | 6 | |||
637.2.r.g.324.13 | 32 | 91.25 | even | 6 | |||
637.2.r.g.324.14 | 32 | 91.38 | odd | 6 | |||
8281.2.a.cs.1.3 | 16 | 91.34 | even | 4 | |||
8281.2.a.cs.1.4 | 16 | 13.8 | odd | 4 | |||
8281.2.a.cs.1.13 | 16 | 91.83 | even | 4 | |||
8281.2.a.cs.1.14 | 16 | 13.5 | odd | 4 |