Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(34,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.i (of order \(4\), degree \(2\), 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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 35x^{8} + 295x^{4} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 34.4 | ||
Root | \(1.52891 - 1.52891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.34 |
Dual form | 91.2.i.a.83.3 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.403032 | − | 0.403032i | −0.284986 | − | 0.284986i | 0.550107 | − | 0.835094i | \(-0.314587\pi\) |
−0.835094 | + | 0.550107i | \(0.814587\pi\) | |||||||
\(3\) | 1.23240i | 0.711526i | 0.934576 | + | 0.355763i | \(0.115779\pi\) | ||||
−0.934576 | + | 0.355763i | \(0.884221\pi\) | |||||||
\(4\) | − | 1.67513i | − | 0.837565i | ||||||
\(5\) | 1.03221 | − | 1.03221i | 0.461620 | − | 0.461620i | −0.437566 | − | 0.899186i | \(-0.644159\pi\) |
0.899186 | + | 0.437566i | \(0.144159\pi\) | |||||||
\(6\) | 0.496696 | − | 0.496696i | 0.202775 | − | 0.202775i | ||||
\(7\) | 2.60707 | + | 0.450747i | 0.985381 | + | 0.170366i | ||||
\(8\) | −1.48119 | + | 1.48119i | −0.523681 | + | 0.523681i | ||||
\(9\) | 1.48119 | 0.493731 | ||||||||
\(10\) | −0.832030 | −0.263111 | ||||||||
\(11\) | −0.596968 | + | 0.596968i | −0.179993 | + | 0.179993i | −0.791353 | − | 0.611360i | \(-0.790623\pi\) |
0.611360 | + | 0.791353i | \(0.290623\pi\) | |||||||
\(12\) | 2.06443 | 0.595949 | ||||||||
\(13\) | −3.59334 | + | 0.296512i | −0.996613 | + | 0.0822375i | ||||
\(14\) | −0.869067 | − | 1.23240i | −0.232268 | − | 0.329372i | ||||
\(15\) | 1.27210 | + | 1.27210i | 0.328455 | + | 0.328455i | ||||
\(16\) | −2.15633 | −0.539081 | ||||||||
\(17\) | −7.34804 | −1.78216 | −0.891080 | − | 0.453845i | \(-0.850052\pi\) | ||||
−0.891080 | + | 0.453845i | \(0.850052\pi\) | |||||||
\(18\) | −0.596968 | − | 0.596968i | −0.140707 | − | 0.140707i | ||||
\(19\) | 3.59334 | − | 3.59334i | 0.824368 | − | 0.824368i | −0.162363 | − | 0.986731i | \(-0.551911\pi\) |
0.986731 | + | 0.162363i | \(0.0519115\pi\) | |||||||
\(20\) | −1.72909 | − | 1.72909i | −0.386637 | − | 0.386637i | ||||
\(21\) | −0.555500 | + | 3.21295i | −0.121220 | + | 0.701124i | ||||
\(22\) | 0.481194 | 0.102591 | ||||||||
\(23\) | 4.44358i | 0.926551i | 0.886214 | + | 0.463276i | \(0.153326\pi\) | ||||
−0.886214 | + | 0.463276i | \(0.846674\pi\) | |||||||
\(24\) | −1.82542 | − | 1.82542i | −0.372613 | − | 0.372613i | ||||
\(25\) | 2.86907i | 0.573813i | ||||||||
\(26\) | 1.56773 | + | 1.32873i | 0.307458 | + | 0.260585i | ||||
\(27\) | 5.52262i | 1.06283i | ||||||||
\(28\) | 0.755061 | − | 4.36719i | 0.142693 | − | 0.825321i | ||||
\(29\) | −3.54420 | −0.658141 | −0.329071 | − | 0.944305i | \(-0.606735\pi\) | ||||
−0.329071 | + | 0.944305i | \(0.606735\pi\) | |||||||
\(30\) | − | 1.02539i | − | 0.187210i | ||||||
\(31\) | −1.27122 | + | 1.27122i | −0.228318 | + | 0.228318i | −0.811990 | − | 0.583672i | \(-0.801616\pi\) |
0.583672 | + | 0.811990i | \(0.301616\pi\) | |||||||
\(32\) | 3.83146 | + | 3.83146i | 0.677312 | + | 0.677312i | ||||
\(33\) | −0.735703 | − | 0.735703i | −0.128069 | − | 0.128069i | ||||
\(34\) | 2.96149 | + | 2.96149i | 0.507892 | + | 0.507892i | ||||
\(35\) | 3.15633 | − | 2.22579i | 0.533516 | − | 0.376227i | ||||
\(36\) | − | 2.48119i | − | 0.413532i | ||||||
\(37\) | 2.88423 | − | 2.88423i | 0.474164 | − | 0.474164i | −0.429095 | − | 0.903259i | \(-0.641168\pi\) |
0.903259 | + | 0.429095i | \(0.141168\pi\) | |||||||
\(38\) | −2.89646 | −0.469868 | ||||||||
\(39\) | −0.365420 | − | 4.42842i | −0.0585141 | − | 0.709115i | ||||
\(40\) | 3.05782i | 0.483484i | ||||||||
\(41\) | 1.23240 | − | 1.23240i | 0.192468 | − | 0.192468i | −0.604294 | − | 0.796762i | \(-0.706545\pi\) |
0.796762 | + | 0.604294i | \(0.206545\pi\) | |||||||
\(42\) | 1.51881 | − | 1.07104i | 0.234357 | − | 0.165265i | ||||
\(43\) | − | 8.66291i | − | 1.32108i | −0.750790 | − | 0.660541i | \(-0.770327\pi\) | ||
0.750790 | − | 0.660541i | \(-0.229673\pi\) | |||||||
\(44\) | 1.00000 | + | 1.00000i | 0.150756 | + | 0.150756i | ||||
\(45\) | 1.52891 | − | 1.52891i | 0.227916 | − | 0.227916i | ||||
\(46\) | 1.79090 | − | 1.79090i | 0.264055 | − | 0.264055i | ||||
\(47\) | 2.52230 | + | 2.52230i | 0.367915 | + | 0.367915i | 0.866717 | − | 0.498801i | \(-0.166226\pi\) |
−0.498801 | + | 0.866717i | \(0.666226\pi\) | |||||||
\(48\) | − | 2.65745i | − | 0.383570i | ||||||
\(49\) | 6.59365 | + | 2.35026i | 0.941951 | + | 0.335752i | ||||
\(50\) | 1.15633 | − | 1.15633i | 0.163529 | − | 0.163529i | ||||
\(51\) | − | 9.05571i | − | 1.26805i | ||||||
\(52\) | 0.496696 | + | 6.01931i | 0.0688793 | + | 0.834728i | ||||
\(53\) | −9.79384 | −1.34529 | −0.672644 | − | 0.739966i | \(-0.734841\pi\) | ||||
−0.672644 | + | 0.739966i | \(0.734841\pi\) | |||||||
\(54\) | 2.22579 | − | 2.22579i | 0.302892 | − | 0.302892i | ||||
\(55\) | 1.23240i | 0.166177i | ||||||||
\(56\) | −4.52923 | + | 3.19394i | −0.605243 | + | 0.426808i | ||||
\(57\) | 4.42842 | + | 4.42842i | 0.586559 | + | 0.586559i | ||||
\(58\) | 1.42842 | + | 1.42842i | 0.187561 | + | 0.187561i | ||||
\(59\) | −1.08972 | − | 1.08972i | −0.141869 | − | 0.141869i | 0.632605 | − | 0.774474i | \(-0.281986\pi\) |
−0.774474 | + | 0.632605i | \(0.781986\pi\) | |||||||
\(60\) | 2.13093 | − | 2.13093i | 0.275102 | − | 0.275102i | ||||
\(61\) | − | 7.10903i | − | 0.910218i | −0.890436 | − | 0.455109i | \(-0.849600\pi\) | ||
0.890436 | − | 0.455109i | \(-0.150400\pi\) | |||||||
\(62\) | 1.02469 | 0.130135 | ||||||||
\(63\) | 3.86158 | + | 0.667644i | 0.486513 | + | 0.0841153i | ||||
\(64\) | 1.22425i | 0.153032i | ||||||||
\(65\) | −3.40303 | + | 4.01516i | −0.422094 | + | 0.498019i | ||||
\(66\) | 0.593023i | 0.0729961i | ||||||||
\(67\) | 8.76845 | + | 8.76845i | 1.07124 | + | 1.07124i | 0.997260 | + | 0.0739770i | \(0.0235691\pi\) |
0.0739770 | + | 0.997260i | \(0.476431\pi\) | |||||||
\(68\) | 12.3089i | 1.49268i | ||||||||
\(69\) | −5.47626 | −0.659265 | ||||||||
\(70\) | −2.16916 | − | 0.375035i | −0.259265 | − | 0.0448253i | ||||
\(71\) | −1.46604 | − | 1.46604i | −0.173986 | − | 0.173986i | 0.614742 | − | 0.788728i | \(-0.289260\pi\) |
−0.788728 | + | 0.614742i | \(0.789260\pi\) | |||||||
\(72\) | −2.19394 | + | 2.19394i | −0.258558 | + | 0.258558i | ||||
\(73\) | −0.103857 | − | 0.103857i | −0.0121555 | − | 0.0121555i | 0.701003 | − | 0.713158i | \(-0.252736\pi\) |
−0.713158 | + | 0.701003i | \(0.752736\pi\) | |||||||
\(74\) | −2.32487 | −0.270261 | ||||||||
\(75\) | −3.53583 | −0.408283 | ||||||||
\(76\) | −6.01931 | − | 6.01931i | −0.690462 | − | 0.690462i | ||||
\(77\) | −1.82542 | + | 1.28726i | −0.208026 | + | 0.146697i | ||||
\(78\) | −1.63752 | + | 1.93207i | −0.185413 | + | 0.218764i | ||||
\(79\) | −4.79877 | −0.539904 | −0.269952 | − | 0.962874i | \(-0.587008\pi\) | ||||
−0.269952 | + | 0.962874i | \(0.587008\pi\) | |||||||
\(80\) | −2.22579 | + | 2.22579i | −0.248851 | + | 0.248851i | ||||
\(81\) | −2.36248 | −0.262498 | ||||||||
\(82\) | −0.993391 | −0.109702 | ||||||||
\(83\) | 12.3165 | − | 12.3165i | 1.35191 | − | 1.35191i | 0.468379 | − | 0.883528i | \(-0.344838\pi\) |
0.883528 | − | 0.468379i | \(-0.155162\pi\) | |||||||
\(84\) | 5.38211 | + | 0.930536i | 0.587237 | + | 0.101530i | ||||
\(85\) | −7.58475 | + | 7.58475i | −0.822682 | + | 0.822682i | ||||
\(86\) | −3.49143 | + | 3.49143i | −0.376490 | + | 0.376490i | ||||
\(87\) | − | 4.36786i | − | 0.468284i | ||||||
\(88\) | − | 1.76845i | − | 0.188518i | ||||||
\(89\) | −6.89017 | − | 6.89017i | −0.730356 | − | 0.730356i | 0.240334 | − | 0.970690i | \(-0.422743\pi\) |
−0.970690 | + | 0.240334i | \(0.922743\pi\) | |||||||
\(90\) | −1.23240 | −0.129906 | ||||||||
\(91\) | −9.50175 | − | 0.846661i | −0.996054 | − | 0.0887541i | ||||
\(92\) | 7.44358 | 0.776047 | ||||||||
\(93\) | −1.56665 | − | 1.56665i | −0.162454 | − | 0.162454i | ||||
\(94\) | − | 2.03313i | − | 0.209702i | ||||||
\(95\) | − | 7.41819i | − | 0.761090i | ||||||
\(96\) | −4.72188 | + | 4.72188i | −0.481925 | + | 0.481925i | ||||
\(97\) | −6.05814 | + | 6.05814i | −0.615110 | + | 0.615110i | −0.944273 | − | 0.329163i | \(-0.893234\pi\) |
0.329163 | + | 0.944273i | \(0.393234\pi\) | |||||||
\(98\) | −1.71022 | − | 3.60468i | −0.172758 | − | 0.364128i | ||||
\(99\) | −0.884226 | + | 0.884226i | −0.0888681 | + | 0.0888681i | ||||
\(100\) | 4.80606 | 0.480606 | ||||||||
\(101\) | 12.8707 | 1.28068 | 0.640339 | − | 0.768092i | \(-0.278794\pi\) | ||||
0.640339 | + | 0.768092i | \(0.278794\pi\) | |||||||
\(102\) | −3.64974 | + | 3.64974i | −0.361378 | + | 0.361378i | ||||
\(103\) | −6.11564 | −0.602592 | −0.301296 | − | 0.953531i | \(-0.597419\pi\) | ||||
−0.301296 | + | 0.953531i | \(0.597419\pi\) | |||||||
\(104\) | 4.88324 | − | 5.76162i | 0.478841 | − | 0.564974i | ||||
\(105\) | 2.74306 | + | 3.88985i | 0.267695 | + | 0.379610i | ||||
\(106\) | 3.94723 | + | 3.94723i | 0.383389 | + | 0.383389i | ||||
\(107\) | 8.86907 | 0.857405 | 0.428703 | − | 0.903446i | \(-0.358971\pi\) | ||||
0.428703 | + | 0.903446i | \(0.358971\pi\) | |||||||
\(108\) | 9.25111 | 0.890188 | ||||||||
\(109\) | −4.59697 | − | 4.59697i | −0.440310 | − | 0.440310i | 0.451806 | − | 0.892116i | \(-0.350780\pi\) |
−0.892116 | + | 0.451806i | \(0.850780\pi\) | |||||||
\(110\) | 0.496696 | − | 0.496696i | 0.0473581 | − | 0.0473581i | ||||
\(111\) | 3.55452 | + | 3.55452i | 0.337380 | + | 0.337380i | ||||
\(112\) | −5.62170 | − | 0.971958i | −0.531200 | − | 0.0918414i | ||||
\(113\) | 1.60720 | 0.151193 | 0.0755964 | − | 0.997138i | \(-0.475914\pi\) | ||||
0.0755964 | + | 0.997138i | \(0.475914\pi\) | |||||||
\(114\) | − | 3.56959i | − | 0.334323i | ||||||
\(115\) | 4.58673 | + | 4.58673i | 0.427715 | + | 0.427715i | ||||
\(116\) | 5.93700i | 0.551236i | ||||||||
\(117\) | −5.32243 | + | 0.439191i | −0.492059 | + | 0.0406032i | ||||
\(118\) | 0.878382i | 0.0808617i | ||||||||
\(119\) | −19.1569 | − | 3.31211i | −1.75611 | − | 0.303620i | ||||
\(120\) | −3.76845 | −0.344011 | ||||||||
\(121\) | 10.2873i | 0.935205i | ||||||||
\(122\) | −2.86516 | + | 2.86516i | −0.259400 | + | 0.259400i | ||||
\(123\) | 1.51881 | + | 1.51881i | 0.136946 | + | 0.136946i | ||||
\(124\) | 2.12946 | + | 2.12946i | 0.191231 | + | 0.191231i | ||||
\(125\) | 8.12256 | + | 8.12256i | 0.726504 | + | 0.726504i | ||||
\(126\) | −1.28726 | − | 1.82542i | −0.114678 | − | 0.162621i | ||||
\(127\) | − | 1.54912i | − | 0.137462i | −0.997635 | − | 0.0687312i | \(-0.978105\pi\) | ||
0.997635 | − | 0.0687312i | \(-0.0218951\pi\) | |||||||
\(128\) | 8.15633 | − | 8.15633i | 0.720924 | − | 0.720924i | ||||
\(129\) | 10.6762 | 0.939983 | ||||||||
\(130\) | 2.98977 | − | 0.246707i | 0.262220 | − | 0.0216376i | ||||
\(131\) | − | 5.31490i | − | 0.464365i | −0.972672 | − | 0.232183i | \(-0.925413\pi\) | ||
0.972672 | − | 0.232183i | \(-0.0745867\pi\) | |||||||
\(132\) | −1.23240 | + | 1.23240i | −0.107267 | + | 0.107267i | ||||
\(133\) | 10.9878 | − | 7.74841i | 0.952761 | − | 0.671872i | ||||
\(134\) | − | 7.06793i | − | 0.610576i | ||||||
\(135\) | 5.70052 | + | 5.70052i | 0.490623 | + | 0.490623i | ||||
\(136\) | 10.8839 | − | 10.8839i | 0.933284 | − | 0.933284i | ||||
\(137\) | 12.7157 | − | 12.7157i | 1.08637 | − | 1.08637i | 0.0904753 | − | 0.995899i | \(-0.471161\pi\) |
0.995899 | − | 0.0904753i | \(-0.0288386\pi\) | |||||||
\(138\) | 2.20711 | + | 2.20711i | 0.187882 | + | 0.187882i | ||||
\(139\) | 6.94767i | 0.589294i | 0.955606 | + | 0.294647i | \(0.0952020\pi\) | ||||
−0.955606 | + | 0.294647i | \(0.904798\pi\) | |||||||
\(140\) | −3.72849 | − | 5.28726i | −0.315115 | − | 0.446855i | ||||
\(141\) | −3.10848 | + | 3.10848i | −0.261781 | + | 0.261781i | ||||
\(142\) | 1.18172i | 0.0991676i | ||||||||
\(143\) | 1.96810 | − | 2.32212i | 0.164581 | − | 0.194185i | ||||
\(144\) | −3.19394 | −0.266161 | ||||||||
\(145\) | −3.65837 | + | 3.65837i | −0.303811 | + | 0.303811i | ||||
\(146\) | 0.0837150i | 0.00692831i | ||||||||
\(147\) | −2.89646 | + | 8.12601i | −0.238896 | + | 0.670222i | ||||
\(148\) | −4.83146 | − | 4.83146i | −0.397143 | − | 0.397143i | ||||
\(149\) | −10.9653 | − | 10.9653i | −0.898315 | − | 0.898315i | 0.0969724 | − | 0.995287i | \(-0.469084\pi\) |
−0.995287 | + | 0.0969724i | \(0.969084\pi\) | |||||||
\(150\) | 1.42505 | + | 1.42505i | 0.116355 | + | 0.116355i | ||||
\(151\) | 6.14117 | − | 6.14117i | 0.499761 | − | 0.499761i | −0.411602 | − | 0.911363i | \(-0.635031\pi\) |
0.911363 | + | 0.411602i | \(0.135031\pi\) | |||||||
\(152\) | 10.6449i | 0.863413i | ||||||||
\(153\) | −10.8839 | −0.879909 | ||||||||
\(154\) | 1.25451 | + | 0.216897i | 0.101091 | + | 0.0174781i | ||||
\(155\) | 2.62435i | 0.210793i | ||||||||
\(156\) | −7.41819 | + | 0.612127i | −0.593931 | + | 0.0490094i | ||||
\(157\) | − | 9.69783i | − | 0.773971i | −0.922086 | − | 0.386985i | \(-0.873516\pi\) | ||
0.922086 | − | 0.386985i | \(-0.126484\pi\) | |||||||
\(158\) | 1.93406 | + | 1.93406i | 0.153865 | + | 0.153865i | ||||
\(159\) | − | 12.0699i | − | 0.957207i | ||||||
\(160\) | 7.90977 | 0.625322 | ||||||||
\(161\) | −2.00293 | + | 11.5847i | −0.157853 | + | 0.913006i | ||||
\(162\) | 0.952155 | + | 0.952155i | 0.0748083 | + | 0.0748083i | ||||
\(163\) | −5.41327 | + | 5.41327i | −0.424000 | + | 0.424000i | −0.886578 | − | 0.462579i | \(-0.846924\pi\) |
0.462579 | + | 0.886578i | \(0.346924\pi\) | |||||||
\(164\) | −2.06443 | − | 2.06443i | −0.161205 | − | 0.161205i | ||||
\(165\) | −1.51881 | −0.118239 | ||||||||
\(166\) | −9.92784 | −0.770550 | ||||||||
\(167\) | 8.90824 | + | 8.90824i | 0.689340 | + | 0.689340i | 0.962086 | − | 0.272746i | \(-0.0879318\pi\) |
−0.272746 | + | 0.962086i | \(0.587932\pi\) | |||||||
\(168\) | −3.93620 | − | 5.58181i | −0.303685 | − | 0.430646i | ||||
\(169\) | 12.8242 | − | 2.13093i | 0.986474 | − | 0.163918i | ||||
\(170\) | 6.11379 | 0.468906 | ||||||||
\(171\) | 5.32243 | − | 5.32243i | 0.407017 | − | 0.407017i | ||||
\(172\) | −14.5115 | −1.10649 | ||||||||
\(173\) | 7.15538 | 0.544014 | 0.272007 | − | 0.962295i | \(-0.412313\pi\) | ||||
0.272007 | + | 0.962295i | \(0.412313\pi\) | |||||||
\(174\) | −1.76039 | + | 1.76039i | −0.133455 | + | 0.133455i | ||||
\(175\) | −1.29322 | + | 7.47987i | −0.0977586 | + | 0.565425i | ||||
\(176\) | 1.28726 | − | 1.28726i | 0.0970307 | − | 0.0970307i | ||||
\(177\) | 1.34297 | − | 1.34297i | 0.100944 | − | 0.100944i | ||||
\(178\) | 5.55391i | 0.416283i | ||||||||
\(179\) | 13.8119i | 1.03235i | 0.856482 | + | 0.516177i | \(0.172645\pi\) | ||||
−0.856482 | + | 0.516177i | \(0.827355\pi\) | |||||||
\(180\) | −2.56112 | − | 2.56112i | −0.190895 | − | 0.190895i | ||||
\(181\) | −4.56052 | −0.338981 | −0.169490 | − | 0.985532i | \(-0.554212\pi\) | ||||
−0.169490 | + | 0.985532i | \(0.554212\pi\) | |||||||
\(182\) | 3.48827 | + | 4.17074i | 0.258568 | + | 0.309156i | ||||
\(183\) | 8.76116 | 0.647643 | ||||||||
\(184\) | −6.58181 | − | 6.58181i | −0.485217 | − | 0.485217i | ||||
\(185\) | − | 5.95428i | − | 0.437767i | ||||||
\(186\) | 1.26282i | 0.0925945i | ||||||||
\(187\) | 4.38655 | − | 4.38655i | 0.320776 | − | 0.320776i | ||||
\(188\) | 4.22518 | − | 4.22518i | 0.308153 | − | 0.308153i | ||||
\(189\) | −2.48930 | + | 14.3979i | −0.181070 | + | 1.04729i | ||||
\(190\) | −2.98977 | + | 2.98977i | −0.216900 | + | 0.216900i | ||||
\(191\) | 3.70545 | 0.268117 | 0.134058 | − | 0.990973i | \(-0.457199\pi\) | ||||
0.134058 | + | 0.990973i | \(0.457199\pi\) | |||||||
\(192\) | −1.50877 | −0.108886 | ||||||||
\(193\) | −17.0508 | + | 17.0508i | −1.22734 | + | 1.22734i | −0.262377 | + | 0.964965i | \(0.584506\pi\) |
−0.964965 | + | 0.262377i | \(0.915494\pi\) | |||||||
\(194\) | 4.88324 | 0.350596 | ||||||||
\(195\) | −4.94827 | − | 4.19389i | −0.354353 | − | 0.300331i | ||||
\(196\) | 3.93700 | − | 11.0452i | 0.281214 | − | 0.788945i | ||||
\(197\) | −8.01810 | − | 8.01810i | −0.571266 | − | 0.571266i | 0.361216 | − | 0.932482i | \(-0.382362\pi\) |
−0.932482 | + | 0.361216i | \(0.882362\pi\) | |||||||
\(198\) | 0.712742 | 0.0506524 | ||||||||
\(199\) | −4.57558 | −0.324354 | −0.162177 | − | 0.986762i | \(-0.551852\pi\) | ||||
−0.162177 | + | 0.986762i | \(0.551852\pi\) | |||||||
\(200\) | −4.24965 | − | 4.24965i | −0.300495 | − | 0.300495i | ||||
\(201\) | −10.8062 | + | 10.8062i | −0.762212 | + | 0.762212i | ||||
\(202\) | −5.18728 | − | 5.18728i | −0.364976 | − | 0.364976i | ||||
\(203\) | −9.23998 | − | 1.59754i | −0.648520 | − | 0.112125i | ||||
\(204\) | −15.1695 | −1.06208 | ||||||||
\(205\) | − | 2.54420i | − | 0.177695i | ||||||
\(206\) | 2.46480 | + | 2.46480i | 0.171731 | + | 0.171731i | ||||
\(207\) | 6.58181i | 0.457467i | ||||||||
\(208\) | 7.74841 | − | 0.639375i | 0.537255 | − | 0.0443327i | ||||
\(209\) | 4.29022i | 0.296761i | ||||||||
\(210\) | 0.462193 | − | 2.67327i | 0.0318943 | − | 0.184473i | ||||
\(211\) | −0.594028 | −0.0408946 | −0.0204473 | − | 0.999791i | \(-0.506509\pi\) | ||||
−0.0204473 | + | 0.999791i | \(0.506509\pi\) | |||||||
\(212\) | 16.4060i | 1.12677i | ||||||||
\(213\) | 1.80674 | − | 1.80674i | 0.123796 | − | 0.123796i | ||||
\(214\) | −3.57452 | − | 3.57452i | −0.244349 | − | 0.244349i | ||||
\(215\) | −8.94198 | − | 8.94198i | −0.609838 | − | 0.609838i | ||||
\(216\) | −8.18007 | − | 8.18007i | −0.556583 | − | 0.556583i | ||||
\(217\) | −3.88717 | + | 2.74117i | −0.263878 | + | 0.186083i | ||||
\(218\) | 3.70545i | 0.250965i | ||||||||
\(219\) | 0.127993 | − | 0.127993i | 0.00864895 | − | 0.00864895i | ||||
\(220\) | 2.06443 | 0.139184 | ||||||||
\(221\) | 26.4040 | − | 2.17878i | 1.77612 | − | 0.146560i | ||||
\(222\) | − | 2.86516i | − | 0.192297i | ||||||
\(223\) | 2.85764 | − | 2.85764i | 0.191361 | − | 0.191361i | −0.604923 | − | 0.796284i | \(-0.706796\pi\) |
0.796284 | + | 0.604923i | \(0.206796\pi\) | |||||||
\(224\) | 8.26187 | + | 11.7159i | 0.552019 | + | 0.782802i | ||||
\(225\) | 4.24965i | 0.283310i | ||||||||
\(226\) | −0.647754 | − | 0.647754i | −0.0430879 | − | 0.0430879i | ||||
\(227\) | −19.6570 | + | 19.6570i | −1.30468 | + | 1.30468i | −0.379477 | + | 0.925201i | \(0.623896\pi\) |
−0.925201 | + | 0.379477i | \(0.876104\pi\) | |||||||
\(228\) | 7.41819 | − | 7.41819i | 0.491282 | − | 0.491282i | ||||
\(229\) | −13.2060 | − | 13.2060i | −0.872676 | − | 0.872676i | 0.120087 | − | 0.992763i | \(-0.461683\pi\) |
−0.992763 | + | 0.120087i | \(0.961683\pi\) | |||||||
\(230\) | − | 3.69720i | − | 0.243786i | ||||||
\(231\) | −1.58641 | − | 2.24965i | −0.104378 | − | 0.148016i | ||||
\(232\) | 5.24965 | − | 5.24965i | 0.344656 | − | 0.344656i | ||||
\(233\) | − | 16.2243i | − | 1.06289i | −0.847094 | − | 0.531443i | \(-0.821650\pi\) | ||
0.847094 | − | 0.531443i | \(-0.178350\pi\) | |||||||
\(234\) | 2.32212 | + | 1.96810i | 0.151802 | + | 0.128659i | ||||
\(235\) | 5.20711 | 0.339674 | ||||||||
\(236\) | −1.82542 | + | 1.82542i | −0.118825 | + | 0.118825i | ||||
\(237\) | − | 5.91400i | − | 0.384155i | ||||||
\(238\) | 6.38594 | + | 9.05571i | 0.413939 | + | 0.586994i | ||||
\(239\) | −0.843675 | − | 0.843675i | −0.0545728 | − | 0.0545728i | 0.679294 | − | 0.733867i | \(-0.262286\pi\) |
−0.733867 | + | 0.679294i | \(0.762286\pi\) | |||||||
\(240\) | −2.74306 | − | 2.74306i | −0.177064 | − | 0.177064i | ||||
\(241\) | 15.2966 | + | 15.2966i | 0.985342 | + | 0.985342i | 0.999894 | − | 0.0145517i | \(-0.00463211\pi\) |
−0.0145517 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(242\) | 4.14609 | − | 4.14609i | 0.266521 | − | 0.266521i | ||||
\(243\) | 13.6563i | 0.876054i | ||||||||
\(244\) | −11.9086 | −0.762367 | ||||||||
\(245\) | 9.23204 | − | 4.38009i | 0.589813 | − | 0.279834i | ||||
\(246\) | − | 1.22425i | − | 0.0780556i | ||||||
\(247\) | −11.8466 | + | 13.9775i | −0.753782 | + | 0.889370i | ||||
\(248\) | − | 3.76585i | − | 0.239132i | ||||||
\(249\) | 15.1788 | + | 15.1788i | 0.961916 | + | 0.961916i | ||||
\(250\) | − | 6.54730i | − | 0.414088i | ||||||
\(251\) | 27.4367 | 1.73179 | 0.865893 | − | 0.500229i | \(-0.166751\pi\) | ||||
0.865893 | + | 0.500229i | \(0.166751\pi\) | |||||||
\(252\) | 1.11839 | − | 6.46865i | 0.0704521 | − | 0.407487i | ||||
\(253\) | −2.65268 | − | 2.65268i | −0.166772 | − | 0.166772i | ||||
\(254\) | −0.624346 | + | 0.624346i | −0.0391749 | + | 0.0391749i | ||||
\(255\) | −9.34743 | − | 9.34743i | −0.585359 | − | 0.585359i | ||||
\(256\) | −4.12601 | −0.257876 | ||||||||
\(257\) | 20.5727 | 1.28329 | 0.641645 | − | 0.767002i | \(-0.278252\pi\) | ||||
0.641645 | + | 0.767002i | \(0.278252\pi\) | |||||||
\(258\) | −4.30283 | − | 4.30283i | −0.267883 | − | 0.267883i | ||||
\(259\) | 8.81944 | − | 6.21933i | 0.548014 | − | 0.386450i | ||||
\(260\) | 6.72592 | + | 5.70052i | 0.417124 | + | 0.353531i | ||||
\(261\) | −5.24965 | −0.324945 | ||||||||
\(262\) | −2.14207 | + | 2.14207i | −0.132338 | + | 0.132338i | ||||
\(263\) | −23.8568 | −1.47108 | −0.735538 | − | 0.677483i | \(-0.763071\pi\) | ||||
−0.735538 | + | 0.677483i | \(0.763071\pi\) | |||||||
\(264\) | 2.17944 | 0.134135 | ||||||||
\(265\) | −10.1093 | + | 10.1093i | −0.621012 | + | 0.621012i | ||||
\(266\) | −7.55128 | − | 1.30557i | −0.462999 | − | 0.0800497i | ||||
\(267\) | 8.49143 | − | 8.49143i | 0.519667 | − | 0.519667i | ||||
\(268\) | 14.6883 | − | 14.6883i | 0.897231 | − | 0.897231i | ||||
\(269\) | − | 1.10840i | − | 0.0675803i | −0.999429 | − | 0.0337902i | \(-0.989242\pi\) | ||
0.999429 | − | 0.0337902i | \(-0.0107578\pi\) | |||||||
\(270\) | − | 4.59498i | − | 0.279642i | ||||||
\(271\) | 20.8894 | + | 20.8894i | 1.26894 | + | 1.26894i | 0.946637 | + | 0.322301i | \(0.104456\pi\) |
0.322301 | + | 0.946637i | \(0.395544\pi\) | |||||||
\(272\) | 15.8448 | 0.960730 | ||||||||
\(273\) | 1.04342 | − | 11.7099i | 0.0631508 | − | 0.708718i | ||||
\(274\) | −10.2496 | −0.619204 | ||||||||
\(275\) | −1.71274 | − | 1.71274i | −0.103282 | − | 0.103282i | ||||
\(276\) | 9.17346i | 0.552177i | ||||||||
\(277\) | − | 25.8265i | − | 1.55177i | −0.630877 | − | 0.775883i | \(-0.717305\pi\) | ||
0.630877 | − | 0.775883i | \(-0.282695\pi\) | |||||||
\(278\) | 2.80013 | − | 2.80013i | 0.167941 | − | 0.167941i | ||||
\(279\) | −1.88293 | + | 1.88293i | −0.112728 | + | 0.112728i | ||||
\(280\) | −1.37830 | + | 7.97196i | −0.0823694 | + | 0.476416i | ||||
\(281\) | 12.0782 | − | 12.0782i | 0.720523 | − | 0.720523i | −0.248189 | − | 0.968712i | \(-0.579835\pi\) |
0.968712 | + | 0.248189i | \(0.0798354\pi\) | |||||||
\(282\) | 2.50563 | 0.149208 | ||||||||
\(283\) | −15.3667 | −0.913458 | −0.456729 | − | 0.889606i | \(-0.650979\pi\) | ||||
−0.456729 | + | 0.889606i | \(0.650979\pi\) | |||||||
\(284\) | −2.45580 | + | 2.45580i | −0.145725 | + | 0.145725i | ||||
\(285\) | 9.14217 | 0.541535 | ||||||||
\(286\) | −1.72909 | + | 0.142680i | −0.102243 | + | 0.00843683i | ||||
\(287\) | 3.76845 | − | 2.65745i | 0.222445 | − | 0.156864i | ||||
\(288\) | 5.67513 | + | 5.67513i | 0.334410 | + | 0.334410i | ||||
\(289\) | 36.9937 | 2.17610 | ||||||||
\(290\) | 2.94888 | 0.173164 | ||||||||
\(291\) | −7.46604 | − | 7.46604i | −0.437667 | − | 0.437667i | ||||
\(292\) | −0.173973 | + | 0.173973i | −0.0101810 | + | 0.0101810i | ||||
\(293\) | −9.78662 | − | 9.78662i | −0.571741 | − | 0.571741i | 0.360874 | − | 0.932615i | \(-0.382478\pi\) |
−0.932615 | + | 0.360874i | \(0.882478\pi\) | |||||||
\(294\) | 4.44240 | − | 2.10767i | 0.259086 | − | 0.122922i | ||||
\(295\) | −2.24965 | −0.130979 | ||||||||
\(296\) | 8.54420i | 0.496621i | ||||||||
\(297\) | −3.29683 | − | 3.29683i | −0.191301 | − | 0.191301i | ||||
\(298\) | 8.83875i | 0.512015i | ||||||||
\(299\) | −1.31757 | − | 15.9673i | −0.0761972 | − | 0.923413i | ||||
\(300\) | 5.92298i | 0.341964i | ||||||||
\(301\) | 3.90478 | − | 22.5848i | 0.225068 | − | 1.30177i | ||||
\(302\) | −4.95017 | −0.284850 | ||||||||
\(303\) | 15.8618i | 0.911235i | ||||||||
\(304\) | −7.74841 | + | 7.74841i | −0.444402 | + | 0.444402i | ||||
\(305\) | −7.33804 | − | 7.33804i | −0.420175 | − | 0.420175i | ||||
\(306\) | 4.38655 | + | 4.38655i | 0.250762 | + | 0.250762i | ||||
\(307\) | −8.14125 | − | 8.14125i | −0.464645 | − | 0.464645i | 0.435529 | − | 0.900175i | \(-0.356561\pi\) |
−0.900175 | + | 0.435529i | \(0.856561\pi\) | |||||||
\(308\) | 2.15633 | + | 3.05782i | 0.122868 | + | 0.174235i | ||||
\(309\) | − | 7.53690i | − | 0.428759i | ||||||
\(310\) | 1.05769 | − | 1.05769i | 0.0600730 | − | 0.0600730i | ||||
\(311\) | −32.4813 | −1.84184 | −0.920922 | − | 0.389747i | \(-0.872562\pi\) | ||||
−0.920922 | + | 0.389747i | \(0.872562\pi\) | |||||||
\(312\) | 7.10062 | + | 6.01810i | 0.401993 | + | 0.340708i | ||||
\(313\) | 19.7346i | 1.11547i | 0.830020 | + | 0.557733i | \(0.188329\pi\) | ||||
−0.830020 | + | 0.557733i | \(0.811671\pi\) | |||||||
\(314\) | −3.90853 | + | 3.90853i | −0.220571 | + | 0.220571i | ||||
\(315\) | 4.67513 | − | 3.29683i | 0.263414 | − | 0.185755i | ||||
\(316\) | 8.03857i | 0.452205i | ||||||||
\(317\) | −8.11871 | − | 8.11871i | −0.455992 | − | 0.455992i | 0.441345 | − | 0.897337i | \(-0.354501\pi\) |
−0.897337 | + | 0.441345i | \(0.854501\pi\) | |||||||
\(318\) | −4.86456 | + | 4.86456i | −0.272791 | + | 0.272791i | ||||
\(319\) | 2.11577 | − | 2.11577i | 0.118461 | − | 0.118461i | ||||
\(320\) | 1.26369 | + | 1.26369i | 0.0706425 | + | 0.0706425i | ||||
\(321\) | 10.9302i | 0.610066i | ||||||||
\(322\) | 5.47626 | − | 3.86177i | 0.305180 | − | 0.215208i | ||||
\(323\) | −26.4040 | + | 26.4040i | −1.46916 | + | 1.46916i | ||||
\(324\) | 3.95746i | 0.219859i | ||||||||
\(325\) | −0.850712 | − | 10.3095i | −0.0471890 | − | 0.571870i | ||||
\(326\) | 4.36344 | 0.241668 | ||||||||
\(327\) | 5.66530 | − | 5.66530i | 0.313292 | − | 0.313292i | ||||
\(328\) | 3.65084i | 0.201584i | ||||||||
\(329\) | 5.43890 | + | 7.71274i | 0.299856 | + | 0.425217i | ||||
\(330\) | 0.612127 | + | 0.612127i | 0.0336965 | + | 0.0336965i | ||||
\(331\) | −0.806063 | − | 0.806063i | −0.0443053 | − | 0.0443053i | 0.684607 | − | 0.728912i | \(-0.259974\pi\) |
−0.728912 | + | 0.684607i | \(0.759974\pi\) | |||||||
\(332\) | −20.6317 | − | 20.6317i | −1.13231 | − | 1.13231i | ||||
\(333\) | 4.27210 | − | 4.27210i | 0.234110 | − | 0.234110i | ||||
\(334\) | − | 7.18061i | − | 0.392905i | ||||||
\(335\) | 18.1018 | 0.989009 | ||||||||
\(336\) | 1.19784 | − | 6.92817i | 0.0653475 | − | 0.377963i | ||||
\(337\) | 26.6058i | 1.44931i | 0.689112 | + | 0.724655i | \(0.258001\pi\) | ||||
−0.689112 | + | 0.724655i | \(0.741999\pi\) | |||||||
\(338\) | −6.02738 | − | 4.30971i | −0.327846 | − | 0.234417i | ||||
\(339\) | 1.98071i | 0.107578i | ||||||||
\(340\) | 12.7054 | + | 12.7054i | 0.689050 | + | 0.689050i | ||||
\(341\) | − | 1.51776i | − | 0.0821912i | ||||||
\(342\) | −4.29022 | −0.231988 | ||||||||
\(343\) | 16.1308 | + | 9.09937i | 0.870979 | + | 0.491320i | ||||
\(344\) | 12.8315 | + | 12.8315i | 0.691826 | + | 0.691826i | ||||
\(345\) | −5.65268 | + | 5.65268i | −0.304330 | + | 0.304330i | ||||
\(346\) | −2.88385 | − | 2.88385i | −0.155037 | − | 0.155037i | ||||
\(347\) | −20.2071 | −1.08477 | −0.542387 | − | 0.840129i | \(-0.682479\pi\) | ||||
−0.542387 | + | 0.840129i | \(0.682479\pi\) | |||||||
\(348\) | −7.31674 | −0.392219 | ||||||||
\(349\) | −2.31459 | − | 2.31459i | −0.123897 | − | 0.123897i | 0.642439 | − | 0.766336i | \(-0.277922\pi\) |
−0.766336 | + | 0.642439i | \(0.777922\pi\) | |||||||
\(350\) | 3.53583 | − | 2.49341i | 0.188998 | − | 0.133279i | ||||
\(351\) | −1.63752 | − | 19.8446i | −0.0874043 | − | 1.05923i | ||||
\(352\) | −4.57452 | −0.243822 | ||||||||
\(353\) | −10.7412 | + | 10.7412i | −0.571696 | + | 0.571696i | −0.932602 | − | 0.360906i | \(-0.882467\pi\) |
0.360906 | + | 0.932602i | \(0.382467\pi\) | |||||||
\(354\) | −1.08252 | −0.0575351 | ||||||||
\(355\) | −3.02653 | −0.160631 | ||||||||
\(356\) | −11.5419 | + | 11.5419i | −0.611721 | + | 0.611721i | ||||
\(357\) | 4.08184 | − | 23.6089i | 0.216034 | − | 1.24952i | ||||
\(358\) | 5.56665 | − | 5.56665i | 0.294207 | − | 0.294207i | ||||
\(359\) | −16.9726 | + | 16.9726i | −0.895781 | + | 0.895781i | −0.995060 | − | 0.0992789i | \(-0.968346\pi\) |
0.0992789 | + | 0.995060i | \(0.468346\pi\) | |||||||
\(360\) | 4.52923i | 0.238711i | ||||||||
\(361\) | − | 6.82416i | − | 0.359166i | ||||||
\(362\) | 1.83803 | + | 1.83803i | 0.0966049 | + | 0.0966049i | ||||
\(363\) | −12.6780 | −0.665422 | ||||||||
\(364\) | −1.41827 | + | 15.9167i | −0.0743374 | + | 0.834260i | ||||
\(365\) | −0.214405 | −0.0112225 | ||||||||
\(366\) | −3.53102 | − | 3.53102i | −0.184570 | − | 0.184570i | ||||
\(367\) | − | 9.79778i | − | 0.511440i | −0.966751 | − | 0.255720i | \(-0.917688\pi\) | ||
0.966751 | − | 0.255720i | \(-0.0823125\pi\) | |||||||
\(368\) | − | 9.58181i | − | 0.499486i | ||||||
\(369\) | 1.82542 | − | 1.82542i | 0.0950276 | − | 0.0950276i | ||||
\(370\) | −2.39976 | + | 2.39976i | −0.124758 | + | 0.124758i | ||||
\(371\) | −25.5333 | − | 4.41455i | −1.32562 | − | 0.229192i | ||||
\(372\) | −2.62435 | + | 2.62435i | −0.136066 | + | 0.136066i | ||||
\(373\) | −5.96731 | −0.308976 | −0.154488 | − | 0.987995i | \(-0.549373\pi\) | ||||
−0.154488 | + | 0.987995i | \(0.549373\pi\) | |||||||
\(374\) | −3.53583 | −0.182834 | ||||||||
\(375\) | −10.0102 | + | 10.0102i | −0.516926 | + | 0.516926i | ||||
\(376\) | −7.47204 | −0.385341 | ||||||||
\(377\) | 12.7355 | − | 1.05090i | 0.655912 | − | 0.0541239i | ||||
\(378\) | 6.80606 | − | 4.79953i | 0.350066 | − | 0.246861i | ||||
\(379\) | 2.14117 | + | 2.14117i | 0.109984 | + | 0.109984i | 0.759957 | − | 0.649973i | \(-0.225220\pi\) |
−0.649973 | + | 0.759957i | \(0.725220\pi\) | |||||||
\(380\) | −12.4264 | −0.637463 | ||||||||
\(381\) | 1.90914 | 0.0978080 | ||||||||
\(382\) | −1.49341 | − | 1.49341i | −0.0764097 | − | 0.0764097i | ||||
\(383\) | 2.91152 | − | 2.91152i | 0.148772 | − | 0.148772i | −0.628798 | − | 0.777569i | \(-0.716453\pi\) |
0.777569 | + | 0.628798i | \(0.216453\pi\) | |||||||
\(384\) | 10.0518 | + | 10.0518i | 0.512956 | + | 0.512956i | ||||
\(385\) | −0.555500 | + | 3.21295i | −0.0283109 | + | 0.163747i | ||||
\(386\) | 13.7440 | 0.699552 | ||||||||
\(387\) | − | 12.8315i | − | 0.652260i | ||||||
\(388\) | 10.1482 | + | 10.1482i | 0.515195 | + | 0.515195i | ||||
\(389\) | 17.4436i | 0.884425i | 0.896910 | + | 0.442212i | \(0.145806\pi\) | ||||
−0.896910 | + | 0.442212i | \(0.854194\pi\) | |||||||
\(390\) | 0.304041 | + | 3.68458i | 0.0153957 | + | 0.186576i | ||||
\(391\) | − | 32.6516i | − | 1.65126i | ||||||
\(392\) | −13.2477 | + | 6.28529i | −0.669109 | + | 0.317455i | ||||
\(393\) | 6.55008 | 0.330408 | ||||||||
\(394\) | 6.46310i | 0.325606i | ||||||||
\(395\) | −4.95336 | + | 4.95336i | −0.249230 | + | 0.249230i | ||||
\(396\) | 1.48119 | + | 1.48119i | 0.0744328 | + | 0.0744328i | ||||
\(397\) | 10.1870 | + | 10.1870i | 0.511270 | + | 0.511270i | 0.914916 | − | 0.403645i | \(-0.132257\pi\) |
−0.403645 | + | 0.914916i | \(0.632257\pi\) | |||||||
\(398\) | 1.84410 | + | 1.84410i | 0.0924365 | + | 0.0924365i | ||||
\(399\) | 9.54912 | + | 13.5413i | 0.478054 | + | 0.677914i | ||||
\(400\) | − | 6.18664i | − | 0.309332i | ||||||
\(401\) | 15.5950 | − | 15.5950i | 0.778776 | − | 0.778776i | −0.200846 | − | 0.979623i | \(-0.564369\pi\) |
0.979623 | + | 0.200846i | \(0.0643692\pi\) | |||||||
\(402\) | 8.71050 | 0.434440 | ||||||||
\(403\) | 4.19100 | − | 4.94486i | 0.208768 | − | 0.246321i | ||||
\(404\) | − | 21.5600i | − | 1.07265i | ||||||
\(405\) | −2.43859 | + | 2.43859i | −0.121174 | + | 0.121174i | ||||
\(406\) | 3.08015 | + | 4.36786i | 0.152865 | + | 0.216773i | ||||
\(407\) | 3.44358i | 0.170692i | ||||||||
\(408\) | 13.4133 | + | 13.4133i | 0.664056 | + | 0.664056i | ||||
\(409\) | 1.79921 | − | 1.79921i | 0.0889652 | − | 0.0889652i | −0.661224 | − | 0.750189i | \(-0.729963\pi\) |
0.750189 | + | 0.661224i | \(0.229963\pi\) | |||||||
\(410\) | −1.02539 | + | 1.02539i | −0.0506405 | + | 0.0506405i | ||||
\(411\) | 15.6708 | + | 15.6708i | 0.772983 | + | 0.772983i | ||||
\(412\) | 10.2445i | 0.504710i | ||||||||
\(413\) | −2.34979 | − | 3.33216i | −0.115626 | − | 0.163965i | ||||
\(414\) | 2.65268 | − | 2.65268i | 0.130372 | − | 0.130372i | ||||
\(415\) | − | 25.4264i | − | 1.24813i | ||||||
\(416\) | −14.9038 | − | 12.6316i | −0.730718 | − | 0.619317i | ||||
\(417\) | −8.56230 | −0.419297 | ||||||||
\(418\) | 1.72909 | − | 1.72909i | 0.0845728 | − | 0.0845728i | ||||
\(419\) | 16.5064i | 0.806392i | 0.915114 | + | 0.403196i | \(0.132101\pi\) | ||||
−0.915114 | + | 0.403196i | \(0.867899\pi\) | |||||||
\(420\) | 6.51601 | − | 4.59498i | 0.317949 | − | 0.224212i | ||||
\(421\) | −8.53492 | − | 8.53492i | −0.415967 | − | 0.415967i | 0.467844 | − | 0.883811i | \(-0.345031\pi\) |
−0.883811 | + | 0.467844i | \(0.845031\pi\) | |||||||
\(422\) | 0.239412 | + | 0.239412i | 0.0116544 | + | 0.0116544i | ||||
\(423\) | 3.73602 | + | 3.73602i | 0.181651 | + | 0.181651i | ||||
\(424\) | 14.5066 | − | 14.5066i | 0.704502 | − | 0.704502i | ||||
\(425\) | − | 21.0820i | − | 1.02263i | ||||||
\(426\) | −1.45635 | −0.0705602 | ||||||||
\(427\) | 3.20438 | − | 18.5338i | 0.155071 | − | 0.896911i | ||||
\(428\) | − | 14.8568i | − | 0.718133i | ||||||
\(429\) | 2.86177 | + | 2.42548i | 0.138168 | + | 0.117103i | ||||
\(430\) | 7.20780i | 0.347591i | ||||||||
\(431\) | 24.2071 | + | 24.2071i | 1.16602 | + | 1.16602i | 0.983135 | + | 0.182880i | \(0.0585421\pi\) |
0.182880 | + | 0.983135i | \(0.441458\pi\) | |||||||
\(432\) | − | 11.9086i | − | 0.572951i | ||||||
\(433\) | −35.8708 | −1.72384 | −0.861920 | − | 0.507044i | \(-0.830738\pi\) | ||||
−0.861920 | + | 0.507044i | \(0.830738\pi\) | |||||||
\(434\) | 2.67143 | + | 0.461874i | 0.128233 | + | 0.0221707i | ||||
\(435\) | −4.50857 | − | 4.50857i | −0.216169 | − | 0.216169i | ||||
\(436\) | −7.70052 | + | 7.70052i | −0.368788 | + | 0.368788i | ||||
\(437\) | 15.9673 | + | 15.9673i | 0.763819 | + | 0.763819i | ||||
\(438\) | −0.103170 | −0.00492967 | ||||||||
\(439\) | 10.5299 | 0.502563 | 0.251281 | − | 0.967914i | \(-0.419148\pi\) | ||||
0.251281 | + | 0.967914i | \(0.419148\pi\) | |||||||
\(440\) | −1.82542 | − | 1.82542i | −0.0870236 | − | 0.0870236i | ||||
\(441\) | 9.76648 | + | 3.48119i | 0.465071 | + | 0.165771i | ||||
\(442\) | −11.5198 | − | 9.76353i | −0.547939 | − | 0.464404i | ||||
\(443\) | 12.8618 | 0.611081 | 0.305541 | − | 0.952179i | \(-0.401163\pi\) | ||||
0.305541 | + | 0.952179i | \(0.401163\pi\) | |||||||
\(444\) | 5.95428 | − | 5.95428i | 0.282578 | − | 0.282578i | ||||
\(445\) | −14.2243 | −0.674294 | ||||||||
\(446\) | −2.30344 | −0.109071 | ||||||||
\(447\) | 13.5137 | − | 13.5137i | 0.639174 | − | 0.639174i | ||||
\(448\) | −0.551829 | + | 3.19172i | −0.0260715 | + | 0.150795i | ||||
\(449\) | 9.65069 | − | 9.65069i | 0.455444 | − | 0.455444i | −0.441712 | − | 0.897157i | \(-0.645629\pi\) |
0.897157 | + | 0.441712i | \(0.145629\pi\) | |||||||
\(450\) | 1.71274 | − | 1.71274i | 0.0807394 | − | 0.0807394i | ||||
\(451\) | 1.47141i | 0.0692858i | ||||||||
\(452\) | − | 2.69227i | − | 0.126634i | ||||||
\(453\) | 7.56836 | + | 7.56836i | 0.355593 | + | 0.355593i | ||||
\(454\) | 15.8448 | 0.743631 | ||||||||
\(455\) | −10.6818 | + | 8.93390i | −0.500769 | + | 0.418828i | ||||
\(456\) | −13.1187 | −0.614340 | ||||||||
\(457\) | −22.1217 | − | 22.1217i | −1.03481 | − | 1.03481i | −0.999372 | − | 0.0354353i | \(-0.988718\pi\) |
−0.0354353 | − | 0.999372i | \(-0.511282\pi\) | |||||||
\(458\) | 10.6449i | 0.497402i | ||||||||
\(459\) | − | 40.5804i | − | 1.89413i | ||||||
\(460\) | 7.68337 | − | 7.68337i | 0.358239 | − | 0.358239i | ||||
\(461\) | 0.593023 | − | 0.593023i | 0.0276198 | − | 0.0276198i | −0.693162 | − | 0.720782i | \(-0.743783\pi\) |
0.720782 | + | 0.693162i | \(0.243783\pi\) | |||||||
\(462\) | −0.267304 | + | 1.54605i | −0.0124361 | + | 0.0719289i | ||||
\(463\) | 2.47096 | − | 2.47096i | 0.114835 | − | 0.114835i | −0.647354 | − | 0.762189i | \(-0.724124\pi\) |
0.762189 | + | 0.647354i | \(0.224124\pi\) | |||||||
\(464\) | 7.64244 | 0.354792 | ||||||||
\(465\) | −3.23424 | −0.149984 | ||||||||
\(466\) | −6.53889 | + | 6.53889i | −0.302908 | + | 0.302908i | ||||
\(467\) | −13.3860 | −0.619432 | −0.309716 | − | 0.950829i | \(-0.600234\pi\) | ||||
−0.309716 | + | 0.950829i | \(0.600234\pi\) | |||||||
\(468\) | 0.735703 | + | 8.91577i | 0.0340079 | + | 0.412132i | ||||
\(469\) | 18.9076 | + | 26.8123i | 0.873073 | + | 1.23808i | ||||
\(470\) | −2.09863 | − | 2.09863i | −0.0968026 | − | 0.0968026i | ||||
\(471\) | 11.9516 | 0.550700 | ||||||||
\(472\) | 3.22817 | 0.148589 | ||||||||
\(473\) | 5.17148 | + | 5.17148i | 0.237785 | + | 0.237785i | ||||
\(474\) | −2.38353 | + | 2.38353i | −0.109479 | + | 0.109479i | ||||
\(475\) | 10.3095 | + | 10.3095i | 0.473034 | + | 0.473034i | ||||
\(476\) | −5.54821 | + | 32.0903i | −0.254302 | + | 1.47085i | ||||
\(477\) | −14.5066 | −0.664211 | ||||||||
\(478\) | 0.680055i | 0.0311050i | ||||||||
\(479\) | −8.85827 | − | 8.85827i | −0.404745 | − | 0.404745i | 0.475157 | − | 0.879901i | \(-0.342391\pi\) |
−0.879901 | + | 0.475157i | \(0.842391\pi\) | |||||||
\(480\) | 9.74798i | 0.444933i | ||||||||
\(481\) | −9.50879 | + | 11.2192i | −0.433564 | + | 0.511552i | ||||
\(482\) | − | 12.3301i | − | 0.561619i | ||||||
\(483\) | −14.2770 | − | 2.46841i | −0.649627 | − | 0.112317i | ||||
\(484\) | 17.2325 | 0.783296 | ||||||||
\(485\) | 12.5066i | 0.567895i | ||||||||
\(486\) | 5.50394 | − | 5.50394i | 0.249664 | − | 0.249664i | ||||
\(487\) | 17.9805 | + | 17.9805i | 0.814774 | + | 0.814774i | 0.985345 | − | 0.170572i | \(-0.0545614\pi\) |
−0.170572 | + | 0.985345i | \(0.554561\pi\) | |||||||
\(488\) | 10.5299 | + | 10.5299i | 0.476664 | + | 0.476664i | ||||
\(489\) | −6.67130 | − | 6.67130i | −0.301687 | − | 0.301687i | ||||
\(490\) | −5.48612 | − | 1.95549i | −0.247838 | − | 0.0883400i | ||||
\(491\) | 19.4944i | 0.879769i | 0.898054 | + | 0.439884i | \(0.144981\pi\) | ||||
−0.898054 | + | 0.439884i | \(0.855019\pi\) | |||||||
\(492\) | 2.54420 | − | 2.54420i | 0.114701 | − | 0.114701i | ||||
\(493\) | 26.0429 | 1.17291 | ||||||||
\(494\) | 10.4080 | − | 0.858833i | 0.468276 | − | 0.0386407i | ||||
\(495\) | 1.82542i | 0.0820466i | ||||||||
\(496\) | 2.74117 | − | 2.74117i | 0.123082 | − | 0.123082i | ||||
\(497\) | −3.16125 | − | 4.48287i | −0.141801 | − | 0.201084i | ||||
\(498\) | − | 12.2351i | − | 0.548266i | ||||||
\(499\) | 10.2150 | + | 10.2150i | 0.457285 | + | 0.457285i | 0.897763 | − | 0.440478i | \(-0.145191\pi\) |
−0.440478 | + | 0.897763i | \(0.645191\pi\) | |||||||
\(500\) | 13.6064 | − | 13.6064i | 0.608495 | − | 0.608495i | ||||
\(501\) | −10.9785 | + | 10.9785i | −0.490483 | + | 0.490483i | ||||
\(502\) | −11.0578 | − | 11.0578i | −0.493536 | − | 0.493536i | ||||
\(503\) | − | 31.8196i | − | 1.41877i | −0.704824 | − | 0.709383i | \(-0.748974\pi\) | ||
0.704824 | − | 0.709383i | \(-0.251026\pi\) | |||||||
\(504\) | −6.70866 | + | 4.73084i | −0.298828 | + | 0.210728i | ||||
\(505\) | 13.2853 | − | 13.2853i | 0.591187 | − | 0.591187i | ||||
\(506\) | 2.13823i | 0.0950558i | ||||||||
\(507\) | 2.62616 | + | 15.8045i | 0.116632 | + | 0.701901i | ||||
\(508\) | −2.59498 | −0.115134 | ||||||||
\(509\) | −13.6139 | + | 13.6139i | −0.603425 | + | 0.603425i | −0.941220 | − | 0.337795i | \(-0.890319\pi\) |
0.337795 | + | 0.941220i | \(0.390319\pi\) | |||||||
\(510\) | 7.53462i | 0.333639i | ||||||||
\(511\) | −0.223949 | − | 0.317575i | −0.00990691 | − | 0.0140487i | ||||
\(512\) | −14.6497 | − | 14.6497i | −0.647433 | − | 0.647433i | ||||
\(513\) | 19.8446 | + | 19.8446i | 0.876162 | + | 0.876162i | ||||
\(514\) | −8.29145 | − | 8.29145i | −0.365720 | − | 0.365720i | ||||
\(515\) | −6.31265 | + | 6.31265i | −0.278169 | + | 0.278169i | ||||
\(516\) | − | 17.8840i | − | 0.787298i | ||||||
\(517\) | −3.01147 | −0.132444 | ||||||||
\(518\) | −6.06110 | − | 1.04793i | −0.266310 | − | 0.0460433i | ||||
\(519\) | 8.81828i | 0.387080i | ||||||||
\(520\) | −0.906679 | − | 10.9878i | −0.0397605 | − | 0.481846i | ||||
\(521\) | 21.6750i | 0.949601i | 0.880094 | + | 0.474800i | \(0.157480\pi\) | ||||
−0.880094 | + | 0.474800i | \(0.842520\pi\) | |||||||
\(522\) | 2.11577 | + | 2.11577i | 0.0926049 | + | 0.0926049i | ||||
\(523\) | 8.77309i | 0.383620i | 0.981432 | + | 0.191810i | \(0.0614358\pi\) | ||||
−0.981432 | + | 0.191810i | \(0.938564\pi\) | |||||||
\(524\) | −8.90316 | −0.388936 | ||||||||
\(525\) | −9.21818 | − | 1.59377i | −0.402314 | − | 0.0695577i | ||||
\(526\) | 9.61507 | + | 9.61507i | 0.419237 | + | 0.419237i | ||||
\(527\) | 9.34098 | − | 9.34098i | 0.406900 | − | 0.406900i | ||||
\(528\) | 1.58641 | + | 1.58641i | 0.0690398 | + | 0.0690398i | ||||
\(529\) | 3.25457 | 0.141503 | ||||||||
\(530\) | 8.14877 | 0.353960 | ||||||||
\(531\) | −1.61409 | − | 1.61409i | −0.0700453 | − | 0.0700453i | ||||
\(532\) | −12.9796 | − | 18.4060i | −0.562737 | − | 0.798000i | ||||
\(533\) | −4.06300 | + | 4.79384i | −0.175988 | + | 0.207644i | ||||
\(534\) | −6.84463 | −0.296196 | ||||||||
\(535\) | 9.15478 | − | 9.15478i | 0.395796 | − | 0.395796i | ||||
\(536\) | −25.9756 | −1.12197 | ||||||||
\(537\) | −17.0218 | −0.734546 | ||||||||
\(538\) | −0.446720 | + | 0.446720i | −0.0192595 | + | 0.0192595i | ||||
\(539\) | −5.33923 | + | 2.53317i | −0.229977 | + | 0.109111i | ||||
\(540\) | 9.54912 | − | 9.54912i | 0.410929 | − | 0.410929i | ||||
\(541\) | −23.2853 | + | 23.2853i | −1.00111 | + | 1.00111i | −0.00111270 | + | 0.999999i | \(0.500354\pi\) |
−0.999999 | + | 0.00111270i | \(0.999646\pi\) | |||||||
\(542\) | − | 16.8382i | − | 0.723260i | ||||||
\(543\) | − | 5.62038i | − | 0.241193i | ||||||
\(544\) | −28.1537 | − | 28.1537i | −1.20708 | − | 1.20708i | ||||
\(545\) | −9.49011 | −0.406512 | ||||||||
\(546\) | −5.14001 | + | 4.29894i | −0.219972 | + | 0.183978i | ||||
\(547\) | −15.1744 | −0.648812 | −0.324406 | − | 0.945918i | \(-0.605164\pi\) | ||||
−0.324406 | + | 0.945918i | \(0.605164\pi\) | |||||||
\(548\) | −21.3004 | − | 21.3004i | −0.909909 | − | 0.909909i | ||||
\(549\) | − | 10.5299i | − | 0.449403i | ||||||
\(550\) | 1.38058i | 0.0588681i | ||||||||
\(551\) | −12.7355 | + | 12.7355i | −0.542551 | + | 0.542551i | ||||
\(552\) | 8.11141 | − | 8.11141i | 0.345245 | − | 0.345245i | ||||
\(553\) | −12.5107 | − | 2.16303i | −0.532011 | − | 0.0919815i | ||||
\(554\) | −10.4089 | + | 10.4089i | −0.442232 | + | 0.442232i | ||||
\(555\) | 7.33804 | 0.311483 | ||||||||
\(556\) | 11.6383 | 0.493572 | ||||||||
\(557\) | 8.45676 | − | 8.45676i | 0.358324 | − | 0.358324i | −0.504871 | − | 0.863195i | \(-0.668460\pi\) |
0.863195 | + | 0.504871i | \(0.168460\pi\) | |||||||
\(558\) | 1.51776 | 0.0642518 | ||||||||
\(559\) | 2.56865 | + | 31.1288i | 0.108642 | + | 1.31661i | ||||
\(560\) | −6.80606 | + | 4.79953i | −0.287609 | + | 0.202817i | ||||
\(561\) | 5.40597 | + | 5.40597i | 0.228240 | + | 0.228240i | ||||
\(562\) | −9.73577 | −0.410678 | ||||||||
\(563\) | 6.34858 | 0.267561 | 0.133780 | − | 0.991011i | \(-0.457288\pi\) | ||||
0.133780 | + | 0.991011i | \(0.457288\pi\) | |||||||
\(564\) | 5.20711 | + | 5.20711i | 0.219259 | + | 0.219259i | ||||
\(565\) | 1.65898 | − | 1.65898i | 0.0697937 | − | 0.0697937i | ||||
\(566\) | 6.19329 | + | 6.19329i | 0.260323 | + | 0.260323i | ||||
\(567\) | −6.15916 | − | 1.06488i | −0.258660 | − | 0.0447208i | ||||
\(568\) | 4.34297 | 0.182227 | ||||||||
\(569\) | 36.6140i | 1.53494i | 0.641085 | + | 0.767470i | \(0.278485\pi\) | ||||
−0.641085 | + | 0.767470i | \(0.721515\pi\) | |||||||
\(570\) | −3.68458 | − | 3.68458i | −0.154330 | − | 0.154330i | ||||
\(571\) | − | 18.8070i | − | 0.787049i | −0.919314 | − | 0.393525i | \(-0.871256\pi\) | ||
0.919314 | − | 0.393525i | \(-0.128744\pi\) | |||||||
\(572\) | −3.88985 | − | 3.29683i | −0.162643 | − | 0.137847i | ||||
\(573\) | 4.56659i | 0.190772i | ||||||||
\(574\) | −2.58984 | − | 0.447768i | −0.108098 | − | 0.0186895i | ||||
\(575\) | −12.7489 | −0.531668 | ||||||||
\(576\) | 1.81336i | 0.0755566i | ||||||||
\(577\) | 31.3416 | − | 31.3416i | 1.30477 | − | 1.30477i | 0.379627 | − | 0.925140i | \(-0.376052\pi\) |
0.925140 | − | 0.379627i | \(-0.123948\pi\) | |||||||
\(578\) | −14.9096 | − | 14.9096i | −0.620158 | − | 0.620158i | ||||
\(579\) | −21.0134 | − | 21.0134i | −0.873285 | − | 0.873285i | ||||
\(580\) | 6.12825 | + | 6.12825i | 0.254462 | + | 0.254462i | ||||
\(581\) | 37.6615 | − | 26.5583i | 1.56246 | − | 1.10182i | ||||
\(582\) | 6.01810i | 0.249458i | ||||||||
\(583\) | 5.84661 | − | 5.84661i | 0.242142 | − | 0.242142i | ||||
\(584\) | 0.307664 | 0.0127312 | ||||||||
\(585\) | −5.04055 | + | 5.94723i | −0.208401 | + | 0.245888i | ||||
\(586\) | 7.88864i | 0.325877i | ||||||||
\(587\) | 3.36694 | − | 3.36694i | 0.138969 | − | 0.138969i | −0.634200 | − | 0.773169i | \(-0.718671\pi\) |
0.773169 | + | 0.634200i | \(0.218671\pi\) | |||||||
\(588\) | 13.6121 | + | 4.85195i | 0.561355 | + | 0.200091i | ||||
\(589\) | 9.13586i | 0.376436i | ||||||||
\(590\) | 0.906679 | + | 0.906679i | 0.0373274 | + | 0.0373274i | ||||
\(591\) | 9.88149 | − | 9.88149i | 0.406470 | − | 0.406470i | ||||
\(592\) | −6.21933 | + | 6.21933i | −0.255613 | + | 0.255613i | ||||
\(593\) | 10.6837 | + | 10.6837i | 0.438726 | + | 0.438726i | 0.891583 | − | 0.452857i | \(-0.149595\pi\) |
−0.452857 | + | 0.891583i | \(0.649595\pi\) | |||||||
\(594\) | 2.65745i | 0.109037i | ||||||||
\(595\) | −23.1928 | + | 16.3552i | −0.950812 | + | 0.670497i | ||||
\(596\) | −18.3684 | + | 18.3684i | −0.752397 | + | 0.752397i | ||||
\(597\) | − | 5.63893i | − | 0.230786i | ||||||
\(598\) | −5.90430 | + | 6.96635i | −0.241445 | + | 0.284875i | ||||
\(599\) | −12.8437 | −0.524778 | −0.262389 | − | 0.964962i | \(-0.584510\pi\) | ||||
−0.262389 | + | 0.964962i | \(0.584510\pi\) | |||||||
\(600\) | 5.23726 | − | 5.23726i | 0.213810 | − | 0.213810i | ||||
\(601\) | − | 19.5732i | − | 0.798409i | −0.916862 | − | 0.399205i | \(-0.869286\pi\) | ||
0.916862 | − | 0.399205i | \(-0.130714\pi\) | |||||||
\(602\) | −10.6762 | + | 7.52865i | −0.435128 | + | 0.306845i | ||||
\(603\) | 12.9878 | + | 12.9878i | 0.528903 | + | 0.528903i | ||||
\(604\) | −10.2873 | − | 10.2873i | −0.418583 | − | 0.418583i | ||||
\(605\) | 10.6187 | + | 10.6187i | 0.431710 | + | 0.431710i | ||||
\(606\) | 6.39280 | − | 6.39280i | 0.259690 | − | 0.259690i | ||||
\(607\) | 41.9804i | 1.70393i | 0.523598 | + | 0.851965i | \(0.324589\pi\) | ||||
−0.523598 | + | 0.851965i | \(0.675411\pi\) | |||||||
\(608\) | 27.5354 | 1.11671 | ||||||||
\(609\) | 1.96880 | − | 11.3873i | 0.0797799 | − | 0.461438i | ||||
\(610\) | 5.91493i | 0.239488i | ||||||||
\(611\) | −9.81137 | − | 8.31559i | −0.396926 | − | 0.336413i | ||||
\(612\) | 18.2319i | 0.736981i | ||||||||
\(613\) | 20.4993 | + | 20.4993i | 0.827959 | + | 0.827959i | 0.987234 | − | 0.159276i | \(-0.0509158\pi\) |
−0.159276 | + | 0.987234i | \(0.550916\pi\) | |||||||
\(614\) | 6.56236i | 0.264835i | ||||||||
\(615\) | 3.13547 | 0.126434 | ||||||||
\(616\) | 0.797125 | − | 4.61048i | 0.0321171 | − | 0.185762i | ||||
\(617\) | 8.21440 | + | 8.21440i | 0.330699 | + | 0.330699i | 0.852852 | − | 0.522153i | \(-0.174871\pi\) |
−0.522153 | + | 0.852852i | \(0.674871\pi\) | |||||||
\(618\) | −3.03761 | + | 3.03761i | −0.122191 | + | 0.122191i | ||||
\(619\) | 26.6973 | + | 26.6973i | 1.07306 | + | 1.07306i | 0.997112 | + | 0.0759445i | \(0.0241972\pi\) |
0.0759445 | + | 0.997112i | \(0.475803\pi\) | |||||||
\(620\) | 4.39612 | 0.176553 | ||||||||
\(621\) | −24.5402 | −0.984764 | ||||||||
\(622\) | 13.0910 | + | 13.0910i | 0.524900 | + | 0.524900i | ||||
\(623\) | −14.8574 | − | 21.0689i | −0.595251 | − | 0.844107i | ||||
\(624\) | 0.787965 | + | 9.54912i | 0.0315438 | + | 0.382271i | ||||
\(625\) | 2.42311 | 0.0969246 | ||||||||
\(626\) | 7.95367 | − | 7.95367i | 0.317893 | − | 0.317893i | ||||
\(627\) | −5.28726 | −0.211153 | ||||||||
\(628\) | −16.2451 | −0.648251 | ||||||||
\(629\) | −21.1934 | + | 21.1934i | −0.845036 | + | 0.845036i | ||||
\(630\) | −3.21295 | − | 0.555500i | −0.128007 | − | 0.0221317i | ||||
\(631\) | 5.13093 | − | 5.13093i | 0.204259 | − | 0.204259i | −0.597563 | − | 0.801822i | \(-0.703864\pi\) |
0.801822 | + | 0.597563i | \(0.203864\pi\) | |||||||
\(632\) | 7.10791 | − | 7.10791i | 0.282737 | − | 0.282737i | ||||
\(633\) | − | 0.732080i | − | 0.0290976i | ||||||
\(634\) | 6.54420i | 0.259903i | ||||||||
\(635\) | −1.59903 | − | 1.59903i | −0.0634554 | − | 0.0634554i | ||||
\(636\) | −20.2187 | −0.801723 | ||||||||
\(637\) | −24.3901 | − | 6.49019i | −0.966371 | − | 0.257151i | ||||
\(638\) | −1.70545 | −0.0675193 | ||||||||
\(639\) | −2.17148 | − | 2.17148i | −0.0859026 | − | 0.0859026i | ||||
\(640\) | − | 16.8382i | − | 0.665586i | ||||||
\(641\) | − | 16.3357i | − | 0.645220i | −0.946532 | − | 0.322610i | \(-0.895440\pi\) | ||
0.946532 | − | 0.322610i | \(-0.104560\pi\) | |||||||
\(642\) | 4.40523 | − | 4.40523i | 0.173860 | − | 0.173860i | ||||
\(643\) | 28.1910 | − | 28.1910i | 1.11175 | − | 1.11175i | 0.118832 | − | 0.992914i | \(-0.462085\pi\) |
0.992914 | − | 0.118832i | \(-0.0379150\pi\) | |||||||
\(644\) | 19.4060 | + | 3.35517i | 0.764702 | + | 0.132212i | ||||
\(645\) | 11.0201 | − | 11.0201i | 0.433915 | − | 0.433915i | ||||
\(646\) | 21.2833 | 0.837380 | ||||||||
\(647\) | 11.1139 | 0.436932 | 0.218466 | − | 0.975845i | \(-0.429895\pi\) | ||||
0.218466 | + | 0.975845i | \(0.429895\pi\) | |||||||
\(648\) | 3.49929 | − | 3.49929i | 0.137465 | − | 0.137465i | ||||
\(649\) | 1.30105 | 0.0510709 | ||||||||
\(650\) | −3.81220 | + | 4.49793i | −0.149527 | + | 0.176423i | ||||
\(651\) | −3.37821 | − | 4.79054i | −0.132402 | − | 0.187756i | ||||
\(652\) | 9.06793 | + | 9.06793i | 0.355127 | + | 0.355127i | ||||
\(653\) | 4.95651 | 0.193963 | 0.0969816 | − | 0.995286i | \(-0.469081\pi\) | ||||
0.0969816 | + | 0.995286i | \(0.469081\pi\) | |||||||
\(654\) | −4.56659 | −0.178568 | ||||||||
\(655\) | −5.48612 | − | 5.48612i | −0.214360 | − | 0.214360i | ||||
\(656\) | −2.65745 | + | 2.65745i | −0.103756 | + | 0.103756i | ||||
\(657\) | −0.153832 | − | 0.153832i | −0.00600155 | − | 0.00600155i | ||||
\(658\) | 0.916430 | − | 5.30053i | 0.0357262 | − | 0.206636i | ||||
\(659\) | 26.1514 | 1.01871 | 0.509357 | − | 0.860555i | \(-0.329883\pi\) | ||||
0.509357 | + | 0.860555i | \(0.329883\pi\) | |||||||
\(660\) | 2.54420i | 0.0990328i | ||||||||
\(661\) | −22.2906 | − | 22.2906i | −0.867006 | − | 0.867006i | 0.125134 | − | 0.992140i | \(-0.460064\pi\) |
−0.992140 | + | 0.125134i | \(0.960064\pi\) | |||||||
\(662\) | 0.649738i | 0.0252528i | ||||||||
\(663\) | 2.68512 | + | 32.5402i | 0.104282 | + | 1.26376i | ||||
\(664\) | 36.4861i | 1.41594i | ||||||||
\(665\) | 3.34373 | − | 19.3398i | 0.129664 | − | 0.749964i | ||||
\(666\) | −3.44358 | −0.133436 | ||||||||
\(667\) | − | 15.7489i | − | 0.609801i | ||||||
\(668\) | 14.9225 | − | 14.9225i | 0.577368 | − | 0.577368i | ||||
\(669\) | 3.52175 | + | 3.52175i | 0.136159 | + | 0.136159i | ||||
\(670\) | −7.29562 | − | 7.29562i | −0.281854 | − | 0.281854i | ||||
\(671\) | 4.24387 | + | 4.24387i | 0.163833 | + | 0.163833i | ||||
\(672\) | −14.4387 | + | 10.1819i | −0.556983 | + | 0.392776i | ||||
\(673\) | 1.38550i | 0.0534072i | 0.999643 | + | 0.0267036i | \(0.00850104\pi\) | ||||
−0.999643 | + | 0.0267036i | \(0.991499\pi\) | |||||||
\(674\) | 10.7230 | − | 10.7230i | 0.413034 | − | 0.413034i | ||||
\(675\) | −15.8448 | −0.609865 | ||||||||
\(676\) | −3.56959 | − | 21.4821i | −0.137292 | − | 0.826237i | ||||
\(677\) | 14.1868i | 0.545242i | 0.962122 | + | 0.272621i | \(0.0878905\pi\) | ||||
−0.962122 | + | 0.272621i | \(0.912110\pi\) | |||||||
\(678\) | 0.798290 | − | 0.798290i | 0.0306582 | − | 0.0306582i | ||||
\(679\) | −18.5247 | + | 13.0633i | −0.710912 | + | 0.501324i | ||||
\(680\) | − | 22.4690i | − | 0.861646i | ||||||
\(681\) | −24.2252 | − | 24.2252i | −0.928312 | − | 0.928312i | ||||
\(682\) | −0.611704 | + | 0.611704i | −0.0234234 | + | 0.0234234i | ||||
\(683\) | 27.2882 | − | 27.2882i | 1.04415 | − | 1.04415i | 0.0451754 | − | 0.998979i | \(-0.485615\pi\) |
0.998979 | − | 0.0451754i | \(-0.0143847\pi\) | |||||||
\(684\) | −8.91577 | − | 8.91577i | −0.340903 | − | 0.340903i | ||||
\(685\) | − | 26.2506i | − | 1.00298i | ||||||
\(686\) | −2.83387 | − | 10.1685i | −0.108198 | − | 0.388237i | ||||
\(687\) | 16.2750 | − | 16.2750i | 0.620931 | − | 0.620931i | ||||
\(688\) | 18.6801i | 0.712170i | ||||||||
\(689\) | 35.1926 | − | 2.90399i | 1.34073 | − | 0.110633i | ||||
\(690\) | 4.55642 | 0.173460 | ||||||||
\(691\) | 16.1937 | − | 16.1937i | 0.616037 | − | 0.616037i | −0.328475 | − | 0.944513i | \(-0.606535\pi\) |
0.944513 | + | 0.328475i | \(0.106535\pi\) | |||||||
\(692\) | − | 11.9862i | − | 0.455647i | ||||||
\(693\) | −2.70380 | + | 1.90668i | −0.102709 | + | 0.0724287i | ||||
\(694\) | 8.14411 | + | 8.14411i | 0.309146 | + | 0.309146i | ||||
\(695\) | 7.17148 | + | 7.17148i | 0.272030 | + | 0.272030i | ||||
\(696\) | 6.46966 | + | 6.46966i | 0.245232 | + | 0.245232i | ||||
\(697\) | −9.05571 | + | 9.05571i | −0.343009 | + | 0.343009i | ||||
\(698\) | 1.86570i | 0.0706180i | ||||||||
\(699\) | 19.9947 | 0.756271 | ||||||||
\(700\) | 12.5298 | + | 2.16632i | 0.473580 | + | 0.0818792i | ||||
\(701\) | − | 15.2981i | − | 0.577800i | −0.957359 | − | 0.288900i | \(-0.906711\pi\) | ||
0.957359 | − | 0.288900i | \(-0.0932895\pi\) | |||||||
\(702\) | −7.33804 | + | 8.65799i | −0.276957 | + | 0.326775i | ||||
\(703\) | − | 20.7280i | − | 0.781771i | ||||||
\(704\) | −0.730841 | − | 0.730841i | −0.0275446 | − | 0.0275446i | ||||
\(705\) | 6.41723i | 0.241687i | ||||||||
\(706\) | 8.65808 | 0.325851 | ||||||||
\(707\) | 33.5547 | + | 5.80141i | 1.26196 | + | 0.218185i | ||||
\(708\) | −2.24965 | − | 2.24965i | −0.0845469 | − | 0.0845469i | ||||
\(709\) | −2.74107 | + | 2.74107i | −0.102943 | + | 0.102943i | −0.756703 | − | 0.653759i | \(-0.773191\pi\) |
0.653759 | + | 0.756703i | \(0.273191\pi\) | |||||||
\(710\) | 1.21979 | + | 1.21979i | 0.0457778 | + | 0.0457778i | ||||
\(711\) | −7.10791 | −0.266567 | ||||||||
\(712\) | 20.4113 | 0.764948 | ||||||||
\(713\) | −5.64878 | − | 5.64878i | −0.211548 | − | 0.211548i | ||||
\(714\) | −11.1602 | + | 7.87002i | −0.417662 | + | 0.294528i | ||||
\(715\) | −0.365420 | − | 4.42842i | −0.0136659 | − | 0.165614i | ||||
\(716\) | 23.1368 | 0.864663 | ||||||||
\(717\) | 1.03974 | − | 1.03974i | 0.0388299 | − | 0.0388299i | ||||
\(718\) | 13.6810 | 0.510571 | ||||||||
\(719\) | −5.99456 | −0.223559 | −0.111780 | − | 0.993733i | \(-0.535655\pi\) | ||||
−0.111780 | + | 0.993733i | \(0.535655\pi\) | |||||||
\(720\) | −3.29683 | + | 3.29683i | −0.122865 | + | 0.122865i | ||||
\(721\) | −15.9439 | − | 2.75661i | −0.593782 | − | 0.102661i | ||||
\(722\) | −2.75035 | + | 2.75035i | −0.102358 | + | 0.102358i | ||||
\(723\) | −18.8515 | + | 18.8515i | −0.701096 | + | 0.701096i | ||||
\(724\) | 7.63947i | 0.283919i | ||||||||
\(725\) | − | 10.1685i | − | 0.377650i | ||||||
\(726\) | 5.10964 | + | 5.10964i | 0.189636 | + | 0.189636i | ||||
\(727\) | 14.6184 | 0.542168 | 0.271084 | − | 0.962556i | \(-0.412618\pi\) | ||||
0.271084 | + | 0.962556i | \(0.412618\pi\) | |||||||
\(728\) | 15.3280 | − | 12.8199i | 0.568093 | − | 0.475136i | ||||
\(729\) | −23.9175 | −0.885833 | ||||||||
\(730\) | 0.0864119 | + | 0.0864119i | 0.00319825 | + | 0.00319825i | ||||
\(731\) | 63.6554i | 2.35438i | ||||||||
\(732\) | − | 14.6761i | − | 0.542444i | ||||||
\(733\) | −28.0685 | + | 28.0685i | −1.03673 | + | 1.03673i | −0.0374350 | + | 0.999299i | \(0.511919\pi\) |
−0.999299 | + | 0.0374350i | \(0.988081\pi\) | |||||||
\(734\) | −3.94881 | + | 3.94881i | −0.145753 | + | 0.145753i | ||||
\(735\) | 5.39802 | + | 11.3775i | 0.199109 | + | 0.419667i | ||||
\(736\) | −17.0254 | + | 17.0254i | −0.627564 | + | 0.627564i | ||||
\(737\) | −10.4690 | −0.385630 | ||||||||
\(738\) | −1.47141 | −0.0541632 | ||||||||
\(739\) | −16.6028 | + | 16.6028i | −0.610746 | + | 0.610746i | −0.943140 | − | 0.332395i | \(-0.892143\pi\) |
0.332395 | + | 0.943140i | \(0.392143\pi\) | |||||||
\(740\) | −9.97420 | −0.366659 | ||||||||
\(741\) | −17.2259 | − | 14.5997i | −0.632809 | − | 0.536335i | ||||
\(742\) | 8.51151 | + | 12.0699i | 0.312467 | + | 0.443101i | ||||
\(743\) | −2.87636 | − | 2.87636i | −0.105523 | − | 0.105523i | 0.652374 | − | 0.757897i | \(-0.273773\pi\) |
−0.757897 | + | 0.652374i | \(0.773773\pi\) | |||||||
\(744\) | 4.64103 | 0.170148 | ||||||||
\(745\) | −22.6371 | −0.829361 | ||||||||
\(746\) | 2.40502 | + | 2.40502i | 0.0880539 | + | 0.0880539i | ||||
\(747\) | 18.2431 | − | 18.2431i | 0.667479 | − | 0.667479i | ||||
\(748\) | −7.34804 | − | 7.34804i | −0.268671 | − | 0.268671i | ||||
\(749\) | 23.1223 | + | 3.99771i | 0.844871 | + | 0.146073i | ||||
\(750\) | 8.06888 | 0.294634 | ||||||||
\(751\) | − | 45.9438i | − | 1.67651i | −0.545275 | − | 0.838257i | \(-0.683575\pi\) | ||
0.545275 | − | 0.838257i | \(-0.316425\pi\) | |||||||
\(752\) | −5.43890 | − | 5.43890i | −0.198336 | − | 0.198336i | ||||
\(753\) | 33.8129i | 1.23221i | ||||||||
\(754\) | −5.55636 | − | 4.70927i | −0.202351 | − | 0.171501i | ||||
\(755\) | − | 12.6780i | − | 0.461400i | ||||||
\(756\) | 24.1183 | + | 4.16991i | 0.877174 | + | 0.151658i | ||||
\(757\) | −24.7889 | −0.900969 | −0.450484 | − | 0.892784i | \(-0.648749\pi\) | ||||
−0.450484 | + | 0.892784i | \(0.648749\pi\) | |||||||
\(758\) | − | 1.72592i | − | 0.0626881i | ||||||
\(759\) | 3.26916 | − | 3.26916i | 0.118663 | − | 0.118663i | ||||
\(760\) | 10.9878 | + | 10.9878i | 0.398569 | + | 0.398569i | ||||
\(761\) | 10.8450 | + | 10.8450i | 0.393133 | + | 0.393133i | 0.875802 | − | 0.482670i | \(-0.160333\pi\) |
−0.482670 | + | 0.875802i | \(0.660333\pi\) | |||||||
\(762\) | −0.769443 | − | 0.769443i | −0.0278740 | − | 0.0278740i | ||||
\(763\) | −9.91256 | − | 14.0567i | −0.358859 | − | 0.508887i | ||||
\(764\) | − | 6.20711i | − | 0.224565i | ||||||
\(765\) | −11.2345 | + | 11.2345i | −0.406184 | + | 0.406184i | ||||
\(766\) | −2.34687 | −0.0847958 | ||||||||
\(767\) | 4.23884 | + | 3.59261i | 0.153056 | + | 0.129722i | ||||
\(768\) | − | 5.08489i | − | 0.183485i | ||||||
\(769\) | −4.63670 | + | 4.63670i | −0.167204 | + | 0.167204i | −0.785749 | − | 0.618545i | \(-0.787722\pi\) |
0.618545 | + | 0.785749i | \(0.287722\pi\) | |||||||
\(770\) | 1.51881 | − | 1.07104i | 0.0547340 | − | 0.0385975i | ||||
\(771\) | 25.3538i | 0.913094i | ||||||||
\(772\) | 28.5623 | + | 28.5623i | 1.02798 | + | 1.02798i | ||||
\(773\) | −5.68398 | + | 5.68398i | −0.204438 | + | 0.204438i | −0.801899 | − | 0.597460i | \(-0.796177\pi\) |
0.597460 | + | 0.801899i | \(0.296177\pi\) | |||||||
\(774\) | −5.17148 | + | 5.17148i | −0.185885 | + | 0.185885i | ||||
\(775\) | −3.64722 | − | 3.64722i | −0.131012 | − | 0.131012i | ||||
\(776\) | − | 17.9466i | − | 0.644244i | ||||||
\(777\) | 7.66469 | + | 10.8691i | 0.274969 | + | 0.389926i | ||||
\(778\) | 7.03032 | − | 7.03032i | 0.252049 | − | 0.252049i | ||||
\(779\) | − | 8.85685i | − | 0.317330i | ||||||
\(780\) | −7.02532 | + | 8.28901i | −0.251547 | + | 0.296794i | ||||
\(781\) | 1.75035 | 0.0626326 | ||||||||
\(782\) | −13.1596 | + | 13.1596i | −0.470588 | + | 0.470588i | ||||
\(783\) | − | 19.5732i | − | 0.699491i | ||||||
\(784\) | −14.2181 | − | 5.06793i | −0.507788 | − | 0.180997i | ||||
\(785\) | −10.0102 | − | 10.0102i | −0.357281 | − | 0.357281i | ||||
\(786\) | −2.63989 | − | 2.63989i | −0.0941617 | − | 0.0941617i | ||||
\(787\) | −8.65662 | − | 8.65662i | −0.308575 | − | 0.308575i | 0.535781 | − | 0.844357i | \(-0.320017\pi\) |
−0.844357 | + | 0.535781i | \(0.820017\pi\) | |||||||
\(788\) | −13.4314 | + | 13.4314i | −0.478473 | + | 0.478473i | ||||
\(789\) | − | 29.4011i | − | 1.04671i | ||||||
\(790\) | 3.99272 | 0.142055 | ||||||||
\(791\) | 4.19009 | + | 0.724442i | 0.148983 | + | 0.0257582i | ||||
\(792\) | − | 2.61942i | − | 0.0930771i | ||||||
\(793\) | 2.10791 | + | 25.5452i | 0.0748541 | + | 0.907135i | ||||
\(794\) | − | 8.21136i | − | 0.291410i | ||||||
\(795\) | −12.4587 | − | 12.4587i | −0.441866 | − | 0.441866i | ||||
\(796\) | 7.66469i | 0.271668i | ||||||||
\(797\) | −28.1163 | −0.995931 | −0.497966 | − | 0.867197i | \(-0.665919\pi\) | ||||
−0.497966 | + | 0.867197i | \(0.665919\pi\) | |||||||
\(798\) | 1.60898 | − | 9.30618i | 0.0569574 | − | 0.329435i | ||||
\(799\) | −18.5340 | − | 18.5340i | −0.655685 | − | 0.655685i | ||||
\(800\) | −10.9927 | + | 10.9927i | −0.388651 | + | 0.388651i | ||||
\(801\) | −10.2057 | − | 10.2057i | −0.360600 | − | 0.360600i | ||||
\(802\) | −12.5705 | −0.443881 | ||||||||
\(803\) | 0.123998 | 0.00437580 | ||||||||
\(804\) | 18.1018 | + | 18.1018i | 0.638403 | + | 0.638403i | ||||
\(805\) | 9.89048 | + | 14.0254i | 0.348594 | + | 0.494330i | ||||
\(806\) | −3.68204 | + | 0.303831i | −0.129694 | + | 0.0107020i | ||||
\(807\) | 1.36599 | 0.0480851 | ||||||||
\(808\) | −19.0639 | + | 19.0639i | −0.670667 | + | 0.670667i | ||||
\(809\) | 0.687350 | 0.0241659 | 0.0120830 | − | 0.999927i | \(-0.496154\pi\) | ||||
0.0120830 | + | 0.999927i | \(0.496154\pi\) | |||||||
\(810\) | 1.96566 | 0.0690661 | ||||||||
\(811\) | −0.354016 | + | 0.354016i | −0.0124312 | + | 0.0124312i | −0.713295 | − | 0.700864i | \(-0.752798\pi\) |
0.700864 | + | 0.713295i | \(0.252798\pi\) | |||||||
\(812\) | −2.67608 | + | 15.4782i | −0.0939122 | + | 0.543178i | ||||
\(813\) | −25.7440 | + | 25.7440i | −0.902882 | + | 0.902882i | ||||
\(814\) | 1.38787 | − | 1.38787i | 0.0486449 | − | 0.0486449i | ||||
\(815\) | 11.1753i | 0.391454i | ||||||||
\(816\) | 19.5271i | 0.683584i | ||||||||
\(817\) | −31.1288 | − | 31.1288i | −1.08906 | − | 1.08906i | ||||
\(818\) | −1.45028 | −0.0507078 | ||||||||
\(819\) | −14.0739 | − | 1.25407i | −0.491783 | − | 0.0438207i | ||||
\(820\) | −4.26187 | −0.148831 | ||||||||
\(821\) | 20.8773 | + | 20.8773i | 0.728623 | + | 0.728623i | 0.970346 | − | 0.241722i | \(-0.0777122\pi\) |
−0.241722 | + | 0.970346i | \(0.577712\pi\) | |||||||
\(822\) | − | 12.6316i | − | 0.440579i | ||||||
\(823\) | 10.3611i | 0.361164i | 0.983560 | + | 0.180582i | \(0.0577981\pi\) | ||||
−0.983560 | + | 0.180582i | \(0.942202\pi\) | |||||||
\(824\) | 9.05845 | − | 9.05845i | 0.315566 | − | 0.315566i | ||||
\(825\) | 2.11078 | − | 2.11078i | 0.0734880 | − | 0.0734880i | ||||
\(826\) | −0.395928 | + | 2.29001i | −0.0137761 | + | 0.0796795i | ||||
\(827\) | 33.3235 | − | 33.3235i | 1.15877 | − | 1.15877i | 0.174030 | − | 0.984740i | \(-0.444321\pi\) |
0.984740 | − | 0.174030i | \(-0.0556789\pi\) | |||||||
\(828\) | 11.0254 | 0.383159 | ||||||||
\(829\) | −19.8647 | −0.689929 | −0.344964 | − | 0.938616i | \(-0.612109\pi\) | ||||
−0.344964 | + | 0.938616i | \(0.612109\pi\) | |||||||
\(830\) | −10.2477 | + | 10.2477i | −0.355702 | + | 0.355702i | ||||
\(831\) | 31.8286 | 1.10412 | ||||||||
\(832\) | −0.363005 | − | 4.39916i | −0.0125849 | − | 0.152513i | ||||
\(833\) | −48.4504 | − | 17.2698i | −1.67871 | − | 0.598364i | ||||
\(834\) | 3.45088 | + | 3.45088i | 0.119494 | + | 0.119494i | ||||
\(835\) | 18.3904 | 0.636427 | ||||||||
\(836\) | 7.18668 | 0.248556 | ||||||||
\(837\) | −7.02047 | − | 7.02047i | −0.242663 | − | 0.242663i | ||||
\(838\) | 6.65262 | − | 6.65262i | 0.229811 | − | 0.229811i | ||||
\(839\) | −16.2048 | − | 16.2048i | −0.559453 | − | 0.559453i | 0.369698 | − | 0.929152i | \(-0.379461\pi\) |
−0.929152 | + | 0.369698i | \(0.879461\pi\) | |||||||
\(840\) | −9.82463 | − | 1.69862i | −0.338982 | − | 0.0586079i | ||||
\(841\) | −16.4387 | −0.566850 | ||||||||
\(842\) | 6.87969i | 0.237090i | ||||||||
\(843\) | 14.8851 | + | 14.8851i | 0.512670 | + | 0.512670i | ||||
\(844\) | 0.995075i | 0.0342519i | ||||||||
\(845\) | 11.0377 | − | 15.4369i | 0.379709 | − | 0.531044i | ||||
\(846\) | − | 3.01147i | − | 0.103536i | ||||||
\(847\) | −4.63695 | + | 26.8196i | −0.159328 | + | 0.921533i | ||||
\(848\) | 21.1187 | 0.725220 | ||||||||
\(849\) | − | 18.9380i | − | 0.649949i | ||||||
\(850\) | −8.49672 | + | 8.49672i | −0.291435 | + | 0.291435i | ||||
\(851\) | 12.8163 | + | 12.8163i | 0.439337 | + | 0.439337i | ||||
\(852\) | −3.02653 | − | 3.02653i | −0.103687 | − | 0.103687i | ||||
\(853\) | −12.4778 | − | 12.4778i | −0.427232 | − | 0.427232i | 0.460452 | − | 0.887684i | \(-0.347687\pi\) |
−0.887684 | + | 0.460452i | \(0.847687\pi\) | |||||||
\(854\) | −8.76116 | + | 6.17823i | −0.299801 | + | 0.211415i | ||||
\(855\) | − | 10.9878i | − | 0.375774i | ||||||
\(856\) | −13.1368 | + | 13.1368i | −0.449007 | + | 0.449007i | ||||
\(857\) | 27.2501 | 0.930845 | 0.465422 | − | 0.885089i | \(-0.345902\pi\) | ||||
0.465422 | + | 0.885089i | \(0.345902\pi\) | |||||||
\(858\) | −0.175838 | − | 2.13093i | −0.00600302 | − | 0.0727488i | ||||
\(859\) | − | 22.7834i | − | 0.777361i | −0.921373 | − | 0.388680i | \(-0.872931\pi\) | ||
0.921373 | − | 0.388680i | \(-0.127069\pi\) | |||||||
\(860\) | −14.9790 | + | 14.9790i | −0.510779 | + | 0.510779i | ||||
\(861\) | 3.27504 | + | 4.64423i | 0.111613 | + | 0.158275i | ||||
\(862\) | − | 19.5125i | − | 0.664597i | ||||||
\(863\) | −21.1187 | − | 21.1187i | −0.718889 | − | 0.718889i | 0.249488 | − | 0.968378i | \(-0.419738\pi\) |
−0.968378 | + | 0.249488i | \(0.919738\pi\) | |||||||
\(864\) | −21.1597 | + | 21.1597i | −0.719866 | + | 0.719866i | ||||
\(865\) | 7.38589 | − | 7.38589i | 0.251128 | − | 0.251128i | ||||
\(866\) | 14.4571 | + | 14.4571i | 0.491271 | + | 0.491271i | ||||
\(867\) | 45.5909i | 1.54835i | ||||||||
\(868\) | 4.59181 | + | 6.51151i | 0.155856 | + | 0.221015i | ||||
\(869\) | 2.86471 | − | 2.86471i | 0.0971787 | − | 0.0971787i | ||||
\(870\) | 3.63419i | 0.123211i | ||||||||
\(871\) | −34.1080 | − | 28.9081i | −1.15570 | − | 0.979513i | ||||
\(872\) | 13.6180 | 0.461164 | ||||||||
\(873\) | −8.97328 | + | 8.97328i | −0.303699 | + | 0.303699i | ||||
\(874\) | − | 12.8707i | − | 0.435356i | ||||||
\(875\) | 17.5149 | + | 24.8373i | 0.592111 | + | 0.839655i | ||||
\(876\) | −0.214405 | − | 0.214405i | −0.00724406 | − | 0.00724406i | ||||
\(877\) | 14.0455 | + | 14.0455i | 0.474282 | + | 0.474282i | 0.903297 | − | 0.429015i | \(-0.141139\pi\) |
−0.429015 | + | 0.903297i | \(0.641139\pi\) | |||||||
\(878\) | −4.24387 | − | 4.24387i | −0.143224 | − | 0.143224i | ||||
\(879\) | 12.0610 | − | 12.0610i | 0.406808 | − | 0.406808i | ||||
\(880\) | − | 2.65745i | − | 0.0895827i | ||||||
\(881\) | −13.3800 | −0.450782 | −0.225391 | − | 0.974268i | \(-0.572366\pi\) | ||||
−0.225391 | + | 0.974268i | \(0.572366\pi\) | |||||||
\(882\) | −2.53317 | − | 5.33923i | −0.0852963 | − | 0.179781i | ||||
\(883\) | 1.63893i | 0.0551545i | 0.999620 | + | 0.0275773i | \(0.00877923\pi\) | ||||
−0.999620 | + | 0.0275773i | \(0.991221\pi\) | |||||||
\(884\) | −3.64974 | − | 44.2301i | −0.122754 | − | 1.48762i | ||||
\(885\) | − | 2.77246i | − | 0.0931952i | ||||||
\(886\) | −5.18370 | − | 5.18370i | −0.174150 | − | 0.174150i | ||||
\(887\) | 21.4198i | 0.719206i | 0.933105 | + | 0.359603i | \(0.117088\pi\) | ||||
−0.933105 | + | 0.359603i | \(0.882912\pi\) | |||||||
\(888\) | −10.5299 | −0.353359 | ||||||||
\(889\) | 0.698263 | − | 4.03868i | 0.0234190 | − | 0.135453i | ||||
\(890\) | 5.73283 | + | 5.73283i | 0.192165 | + | 0.192165i | ||||
\(891\) | 1.41033 | − | 1.41033i | 0.0472477 | − | 0.0472477i | ||||
\(892\) | −4.78691 | − | 4.78691i | −0.160278 | − | 0.160278i | ||||
\(893\) | 18.1270 | 0.606596 | ||||||||
\(894\) | −10.8929 | −0.364312 | ||||||||
\(895\) | 14.2569 | + | 14.2569i | 0.476555 | + | 0.476555i | ||||
\(896\) | 24.9406 | − | 17.5877i | 0.833206 | − | 0.587563i | ||||
\(897\) | 19.6781 | − | 1.62378i | 0.657032 | − | 0.0542163i | ||||
\(898\) | −7.77907 | −0.259591 | ||||||||
\(899\) | 4.50546 | − | 4.50546i | 0.150266 | − | 0.150266i | ||||
\(900\) | 7.11871 | 0.237290 | ||||||||
\(901\) | 71.9655 | 2.39752 | ||||||||
\(902\) | 0.593023 | − | 0.593023i | 0.0197455 | − | 0.0197455i | ||||
\(903\) | 27.8335 | + | 4.81225i | 0.926242 | + | 0.160142i | ||||
\(904\) | −2.38058 | + | 2.38058i | −0.0791769 | + | 0.0791769i | ||||
\(905\) | −4.70743 | + | 4.70743i | −0.156480 | + | 0.156480i | ||||
\(906\) | − | 6.10058i | − | 0.202678i | ||||||
\(907\) | − | 2.59991i | − | 0.0863285i | −0.999068 | − | 0.0431643i | \(-0.986256\pi\) | ||
0.999068 | − | 0.0431643i | \(-0.0137439\pi\) | |||||||
\(908\) | 32.9280 | + | 32.9280i | 1.09275 | + | 1.09275i | ||||
\(909\) | 19.0639 | 0.632311 | ||||||||
\(910\) | 7.90574 | + | 0.704447i | 0.262073 | + | 0.0233522i | ||||
\(911\) | 41.2579 | 1.36694 | 0.683468 | − | 0.729981i | \(-0.260471\pi\) | ||||
0.683468 | + | 0.729981i | \(0.260471\pi\) | |||||||
\(912\) | −9.54912 | − | 9.54912i | −0.316203 | − | 0.316203i | ||||
\(913\) | 14.7051i | 0.486667i | ||||||||
\(914\) | 17.8315i | 0.589812i | ||||||||
\(915\) | 9.04339 | − | 9.04339i | 0.298965 | − | 0.298965i | ||||
\(916\) | −22.1218 | + | 22.1218i | −0.730924 | + | 0.730924i | ||||
\(917\) | 2.39568 | − | 13.8563i | 0.0791123 | − | 0.457577i | ||||
\(918\) | −16.3552 | + | 16.3552i | −0.539802 | + | 0.539802i | ||||
\(919\) | −48.3039 | −1.59340 | −0.796700 | − | 0.604375i | \(-0.793423\pi\) | ||||
−0.796700 | + | 0.604375i | \(0.793423\pi\) | |||||||
\(920\) | −13.5877 | −0.447972 | ||||||||
\(921\) | 10.0333 | − | 10.0333i | 0.330607 | − | 0.330607i | ||||
\(922\) | −0.478014 | −0.0157426 | ||||||||
\(923\) | 5.70266 | + | 4.83327i | 0.187705 | + | 0.159089i | ||||
\(924\) | −3.76845 | + | 2.65745i | −0.123973 | + | 0.0874237i | ||||
\(925\) | 8.27504 | + | 8.27504i | 0.272082 | + | 0.272082i | ||||
\(926\) | −1.99175 | −0.0654530 | ||||||||
\(927\) | −9.05845 | −0.297519 | ||||||||
\(928\) | −13.5794 | − | 13.5794i | −0.445767 | − | 0.445767i | ||||
\(929\) | 19.1804 | − | 19.1804i | 0.629289 | − | 0.629289i | −0.318600 | − | 0.947889i | \(-0.603213\pi\) |
0.947889 | + | 0.318600i | \(0.103213\pi\) | |||||||
\(930\) | 1.30350 | + | 1.30350i | 0.0427435 | + | 0.0427435i | ||||
\(931\) | 32.1385 | − | 15.2479i | 1.05330 | − | 0.499731i | ||||
\(932\) | −27.1777 | −0.890237 | ||||||||
\(933\) | − | 40.0299i | − | 1.31052i | ||||||
\(934\) | 5.39500 | + | 5.39500i | 0.176530 | + | 0.176530i | ||||
\(935\) | − | 9.05571i | − | 0.296153i | ||||||
\(936\) | 7.23303 | − | 8.53408i | 0.236419 | − | 0.278945i | ||||
\(937\) | 2.66644i | 0.0871088i | 0.999051 | + | 0.0435544i | \(0.0138682\pi\) | ||||
−0.999051 | + | 0.0435544i | \(0.986132\pi\) | |||||||
\(938\) | 3.18585 | − | 18.4266i | 0.104022 | − | 0.601650i | ||||
\(939\) | −24.3209 | −0.793683 | ||||||||
\(940\) | − | 8.72259i | − | 0.284500i | ||||||
\(941\) | −31.9331 | + | 31.9331i | −1.04099 | + | 1.04099i | −0.0418672 | + | 0.999123i | \(0.513331\pi\) |
−0.999123 | + | 0.0418672i | \(0.986669\pi\) | |||||||
\(942\) | −4.81687 | − | 4.81687i | −0.156942 | − | 0.156942i | ||||
\(943\) | 5.47626 | + | 5.47626i | 0.178332 | + | 0.178332i | ||||
\(944\) | 2.34979 | + | 2.34979i | 0.0764791 | + | 0.0764791i | ||||
\(945\) | 12.2922 | + | 17.4312i | 0.399865 | + | 0.567036i | ||||
\(946\) | − | 4.16854i | − | 0.135531i | ||||||
\(947\) | −8.43041 | + | 8.43041i | −0.273951 | + | 0.273951i | −0.830689 | − | 0.556737i | \(-0.812053\pi\) |
0.556737 | + | 0.830689i | \(0.312053\pi\) | |||||||
\(948\) | −9.90672 | −0.321755 | ||||||||
\(949\) | 0.403987 | + | 0.342397i | 0.0131140 | + | 0.0111147i | ||||
\(950\) | − | 8.31014i | − | 0.269616i | ||||||
\(951\) | 10.0055 | − | 10.0055i | 0.324450 | − | 0.324450i | ||||
\(952\) | 33.2809 | − | 23.4692i | 1.07864 | − | 0.760640i | ||||
\(953\) | − | 20.8846i | − | 0.676519i | −0.941053 | − | 0.338259i | \(-0.890162\pi\) | ||
0.941053 | − | 0.338259i | \(-0.109838\pi\) | |||||||
\(954\) | 5.84661 | + | 5.84661i | 0.189291 | + | 0.189291i | ||||
\(955\) | 3.82482 | − | 3.82482i | 0.123768 | − | 0.123768i | ||||
\(956\) | −1.41327 | + | 1.41327i | −0.0457083 | + | 0.0457083i | ||||
\(957\) | 2.60748 | + | 2.60748i | 0.0842877 | + | 0.0842877i | ||||
\(958\) | 7.14032i | 0.230693i | ||||||||
\(959\) | 38.8823 | − | 27.4191i | 1.25557 | − | 0.885410i | ||||
\(960\) | −1.55737 | + | 1.55737i | −0.0502640 | + | 0.0502640i | ||||
\(961\) | 27.7680i | 0.895742i | ||||||||
\(962\) | 8.35404 | − | 0.689351i | 0.269345 | − | 0.0222256i | ||||
\(963\) | 13.1368 | 0.423328 | ||||||||
\(964\) | 25.6239 | − | 25.6239i | 0.825289 | − | 0.825289i | ||||
\(965\) | 35.2001i | 1.13313i | ||||||||
\(966\) | 4.75924 | + | 6.74894i | 0.153126 | + | 0.217144i | ||||
\(967\) | 20.9628 | + | 20.9628i | 0.674117 | + | 0.674117i | 0.958663 | − | 0.284545i | \(-0.0918426\pi\) |
−0.284545 | + | 0.958663i | \(0.591843\pi\) | |||||||
\(968\) | −15.2374 | − | 15.2374i | −0.489749 | − | 0.489749i | ||||
\(969\) | −32.5402 | − | 32.5402i | −1.04534 | − | 1.04534i | ||||
\(970\) | 5.04055 | − | 5.04055i | 0.161842 | − | 0.161842i | ||||
\(971\) | − | 12.7719i | − | 0.409869i | −0.978776 | − | 0.204935i | \(-0.934302\pi\) | ||
0.978776 | − | 0.204935i | \(-0.0656982\pi\) | |||||||
\(972\) | 22.8761 | 0.733753 | ||||||||
\(973\) | −3.13164 | + | 18.1131i | −0.100396 | + | 0.580679i | ||||
\(974\) | − | 14.4934i | − | 0.464399i | ||||||
\(975\) | 12.7054 | − | 1.04842i | 0.406900 | − | 0.0335762i | ||||
\(976\) | 15.3294i | 0.490682i | ||||||||
\(977\) | −27.8222 | − | 27.8222i | −0.890110 | − | 0.890110i | 0.104423 | − | 0.994533i | \(-0.466701\pi\) |
−0.994533 | + | 0.104423i | \(0.966701\pi\) | |||||||
\(978\) | 5.37749i | 0.171953i | ||||||||
\(979\) | 8.22642 | 0.262918 | ||||||||
\(980\) | −7.33722 | − | 15.4649i | −0.234379 | − | 0.494007i | ||||
\(981\) | −6.80900 | − | 6.80900i | −0.217395 | − | 0.217395i | ||||
\(982\) | 7.85685 | − | 7.85685i | 0.250722 | − | 0.250722i | ||||
\(983\) | −35.8970 | − | 35.8970i | −1.14494 | − | 1.14494i | −0.987535 | − | 0.157402i | \(-0.949688\pi\) |
−0.157402 | − | 0.987535i | \(-0.550312\pi\) | |||||||
\(984\) | −4.49929 | −0.143432 | ||||||||
\(985\) | −16.5528 | −0.527416 | ||||||||
\(986\) | −10.4961 | − | 10.4961i | −0.334264 | − | 0.334264i | ||||
\(987\) | −9.50517 | + | 6.70289i | −0.302553 | + | 0.213355i | ||||
\(988\) | 23.4142 | + | 19.8446i | 0.744906 | + | 0.631342i | ||||
\(989\) | 38.4944 | 1.22405 | ||||||||
\(990\) | 0.735703 | − | 0.735703i | 0.0233822 | − | 0.0233822i | ||||
\(991\) | −8.69418 | −0.276180 | −0.138090 | − | 0.990420i | \(-0.544096\pi\) | ||||
−0.138090 | + | 0.990420i | \(0.544096\pi\) | |||||||
\(992\) | −9.74126 | −0.309285 | ||||||||
\(993\) | 0.993391 | − | 0.993391i | 0.0315243 | − | 0.0315243i | ||||
\(994\) | −0.532656 | + | 3.08082i | −0.0168948 | + | 0.0977178i | ||||
\(995\) | −4.72298 | + | 4.72298i | −0.149728 | + | 0.149728i | ||||
\(996\) | 25.4264 | − | 25.4264i | 0.805668 | − | 0.805668i | ||||
\(997\) | 26.5673i | 0.841394i | 0.907201 | + | 0.420697i | \(0.138214\pi\) | ||||
−0.907201 | + | 0.420697i | \(0.861786\pi\) | |||||||
\(998\) | − | 8.23392i | − | 0.260640i | ||||||
\(999\) | 15.9285 | + | 15.9285i | 0.503955 | + | 0.503955i |
(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 | 91.2.i.a.34.4 | yes | 12 | |
3.2 | odd | 2 | 819.2.y.h.307.3 | 12 | |||
7.2 | even | 3 | 637.2.bc.a.619.3 | 24 | |||
7.3 | odd | 6 | 637.2.bc.a.411.3 | 24 | |||
7.4 | even | 3 | 637.2.bc.a.411.4 | 24 | |||
7.5 | odd | 6 | 637.2.bc.a.619.4 | 24 | |||
7.6 | odd | 2 | inner | 91.2.i.a.34.3 | ✓ | 12 | |
13.5 | odd | 4 | inner | 91.2.i.a.83.4 | yes | 12 | |
21.20 | even | 2 | 819.2.y.h.307.4 | 12 | |||
39.5 | even | 4 | 819.2.y.h.811.4 | 12 | |||
91.5 | even | 12 | 637.2.bc.a.31.4 | 24 | |||
91.18 | odd | 12 | 637.2.bc.a.460.4 | 24 | |||
91.31 | even | 12 | 637.2.bc.a.460.3 | 24 | |||
91.44 | odd | 12 | 637.2.bc.a.31.3 | 24 | |||
91.83 | even | 4 | inner | 91.2.i.a.83.3 | yes | 12 | |
273.83 | odd | 4 | 819.2.y.h.811.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.i.a.34.3 | ✓ | 12 | 7.6 | odd | 2 | inner | |
91.2.i.a.34.4 | yes | 12 | 1.1 | even | 1 | trivial | |
91.2.i.a.83.3 | yes | 12 | 91.83 | even | 4 | inner | |
91.2.i.a.83.4 | yes | 12 | 13.5 | odd | 4 | inner | |
637.2.bc.a.31.3 | 24 | 91.44 | odd | 12 | |||
637.2.bc.a.31.4 | 24 | 91.5 | even | 12 | |||
637.2.bc.a.411.3 | 24 | 7.3 | odd | 6 | |||
637.2.bc.a.411.4 | 24 | 7.4 | even | 3 | |||
637.2.bc.a.460.3 | 24 | 91.31 | even | 12 | |||
637.2.bc.a.460.4 | 24 | 91.18 | odd | 12 | |||
637.2.bc.a.619.3 | 24 | 7.2 | even | 3 | |||
637.2.bc.a.619.4 | 24 | 7.5 | odd | 6 | |||
819.2.y.h.307.3 | 12 | 3.2 | odd | 2 | |||
819.2.y.h.307.4 | 12 | 21.20 | even | 2 | |||
819.2.y.h.811.3 | 12 | 273.83 | odd | 4 | |||
819.2.y.h.811.4 | 12 | 39.5 | even | 4 |