Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [71,2,Mod(5,71)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(71, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("71.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 71.c (of order \(5\), degree \(4\), 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: | \(0.566937854351\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6 x^{19} + 28 x^{18} - 91 x^{17} + 268 x^{16} - 604 x^{15} + 1278 x^{14} - 1990 x^{13} + \cdots + 961 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 57.4 | ||
Root | \(-0.420063 - 1.29282i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 71.57 |
Dual form | 71.2.c.a.5.4 |
$q$-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 \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.420063 | − | 1.29282i | 0.297030 | − | 0.914164i | −0.685502 | − | 0.728070i | \(-0.740417\pi\) |
0.982532 | − | 0.186093i | \(-0.0595826\pi\) | |||||||
\(3\) | 0.672312 | − | 2.06916i | 0.388159 | − | 1.19463i | −0.546003 | − | 0.837783i | \(-0.683851\pi\) |
0.934162 | − | 0.356848i | \(-0.116149\pi\) | |||||||
\(4\) | 0.123097 | + | 0.0894354i | 0.0615487 | + | 0.0447177i | ||||
\(5\) | −2.53185 | + | 1.83950i | −1.13228 | + | 0.822650i | −0.986025 | − | 0.166597i | \(-0.946722\pi\) |
−0.146255 | + | 0.989247i | \(0.546722\pi\) | |||||||
\(6\) | −2.39265 | − | 1.73836i | −0.976794 | − | 0.709682i | ||||
\(7\) | −1.31457 | + | 4.04584i | −0.496862 | + | 1.52918i | 0.317172 | + | 0.948368i | \(0.397267\pi\) |
−0.814035 | + | 0.580817i | \(0.802733\pi\) | |||||||
\(8\) | 2.36681 | − | 1.71959i | 0.836795 | − | 0.607967i | ||||
\(9\) | −1.40238 | − | 1.01889i | −0.467459 | − | 0.339629i | ||||
\(10\) | 1.31461 | + | 4.04595i | 0.415715 | + | 1.27944i | ||||
\(11\) | 0.802829 | − | 2.47085i | 0.242062 | − | 0.744990i | −0.754044 | − | 0.656824i | \(-0.771899\pi\) |
0.996106 | − | 0.0881662i | \(-0.0281007\pi\) | |||||||
\(12\) | 0.267816 | − | 0.194580i | 0.0773119 | − | 0.0561704i | ||||
\(13\) | −1.18431 | − | 3.64494i | −0.328469 | − | 1.01092i | −0.969850 | − | 0.243701i | \(-0.921638\pi\) |
0.641381 | − | 0.767222i | \(-0.278362\pi\) | |||||||
\(14\) | 4.67835 | + | 3.39902i | 1.25034 | + | 0.908427i | ||||
\(15\) | 2.10403 | + | 6.47554i | 0.543258 | + | 1.67198i | ||||
\(16\) | −1.13488 | − | 3.49279i | −0.283719 | − | 0.873197i | ||||
\(17\) | −0.514419 | − | 1.58322i | −0.124765 | − | 0.383987i | 0.869093 | − | 0.494648i | \(-0.164703\pi\) |
−0.993858 | + | 0.110661i | \(0.964703\pi\) | |||||||
\(18\) | −1.90633 | + | 1.38503i | −0.449326 | + | 0.326454i | ||||
\(19\) | −2.14855 | + | 6.61255i | −0.492910 | + | 1.51702i | 0.327278 | + | 0.944928i | \(0.393869\pi\) |
−0.820188 | + | 0.572094i | \(0.806131\pi\) | |||||||
\(20\) | −0.476181 | −0.106477 | ||||||||
\(21\) | 7.48770 | + | 5.44013i | 1.63395 | + | 1.18713i | ||||
\(22\) | −2.85714 | − | 2.07583i | −0.609143 | − | 0.442569i | ||||
\(23\) | −4.87491 | −1.01649 | −0.508244 | − | 0.861213i | \(-0.669705\pi\) | ||||
−0.508244 | + | 0.861213i | \(0.669705\pi\) | |||||||
\(24\) | −1.96688 | − | 6.05342i | −0.401487 | − | 1.23565i | ||||
\(25\) | 1.48144 | − | 4.55941i | 0.296289 | − | 0.911882i | ||||
\(26\) | −5.20974 | −1.02171 | ||||||||
\(27\) | 2.22933 | − | 1.61970i | 0.429034 | − | 0.311711i | ||||
\(28\) | −0.523662 | + | 0.380463i | −0.0989628 | + | 0.0719007i | ||||
\(29\) | 0.829618 | − | 0.602753i | 0.154056 | − | 0.111928i | −0.508087 | − | 0.861306i | \(-0.669647\pi\) |
0.662143 | + | 0.749377i | \(0.269647\pi\) | |||||||
\(30\) | 9.25554 | 1.68982 | ||||||||
\(31\) | −1.21584 | + | 3.74197i | −0.218371 | + | 0.672078i | 0.780526 | + | 0.625124i | \(0.214952\pi\) |
−0.998897 | + | 0.0469544i | \(0.985048\pi\) | |||||||
\(32\) | 0.858810 | 0.151818 | ||||||||
\(33\) | −4.57285 | − | 3.32237i | −0.796030 | − | 0.578350i | ||||
\(34\) | −2.26291 | −0.388086 | ||||||||
\(35\) | −4.11402 | − | 12.6616i | −0.695396 | − | 2.14021i | ||||
\(36\) | −0.0815044 | − | 0.250845i | −0.0135841 | − | 0.0418074i | ||||
\(37\) | 6.90721 | 1.13554 | 0.567769 | − | 0.823188i | \(-0.307807\pi\) | ||||
0.567769 | + | 0.823188i | \(0.307807\pi\) | |||||||
\(38\) | 7.64632 | + | 5.55538i | 1.24040 | + | 0.901201i | ||||
\(39\) | −8.33819 | −1.33518 | ||||||||
\(40\) | −2.82924 | + | 8.70751i | −0.447342 | + | 1.37678i | ||||
\(41\) | −3.25301 | −0.508034 | −0.254017 | − | 0.967200i | \(-0.581752\pi\) | ||||
−0.254017 | + | 0.967200i | \(0.581752\pi\) | |||||||
\(42\) | 10.1784 | − | 7.39507i | 1.57057 | − | 1.14108i | ||||
\(43\) | 5.06571 | − | 3.68045i | 0.772513 | − | 0.561264i | −0.130210 | − | 0.991486i | \(-0.541565\pi\) |
0.902723 | + | 0.430223i | \(0.141565\pi\) | |||||||
\(44\) | 0.319808 | − | 0.232354i | 0.0482129 | − | 0.0350287i | ||||
\(45\) | 5.42486 | 0.808691 | ||||||||
\(46\) | −2.04777 | + | 6.30239i | −0.301927 | + | 0.929237i | ||||
\(47\) | −0.919569 | − | 2.83014i | −0.134133 | − | 0.412818i | 0.861321 | − | 0.508061i | \(-0.169637\pi\) |
−0.995454 | + | 0.0952422i | \(0.969637\pi\) | |||||||
\(48\) | −7.99014 | −1.15328 | ||||||||
\(49\) | −8.97761 | − | 6.52262i | −1.28252 | − | 0.931802i | ||||
\(50\) | −5.27221 | − | 3.83049i | −0.745603 | − | 0.541712i | ||||
\(51\) | −3.62179 | −0.507152 | ||||||||
\(52\) | 0.180201 | − | 0.554601i | 0.0249894 | − | 0.0769094i | ||||
\(53\) | 2.74839 | − | 1.99682i | 0.377520 | − | 0.274285i | −0.382802 | − | 0.923830i | \(-0.625041\pi\) |
0.760322 | + | 0.649546i | \(0.225041\pi\) | |||||||
\(54\) | −1.15753 | − | 3.56250i | −0.157519 | − | 0.484795i | ||||
\(55\) | 2.51249 | + | 7.73265i | 0.338784 | + | 1.04267i | ||||
\(56\) | 3.84584 | + | 11.8363i | 0.513922 | + | 1.58169i | ||||
\(57\) | 12.2379 | + | 8.89138i | 1.62095 | + | 1.17769i | ||||
\(58\) | −0.430760 | − | 1.32574i | −0.0565616 | − | 0.174079i | ||||
\(59\) | 0.332599 | − | 0.241648i | 0.0433008 | − | 0.0314598i | −0.565924 | − | 0.824457i | \(-0.691481\pi\) |
0.609225 | + | 0.792997i | \(0.291481\pi\) | |||||||
\(60\) | −0.320142 | + | 0.985296i | −0.0413302 | + | 0.127201i | ||||
\(61\) | 0.569635 | + | 1.75316i | 0.0729343 | + | 0.224469i | 0.980878 | − | 0.194623i | \(-0.0623485\pi\) |
−0.907944 | + | 0.419092i | \(0.862348\pi\) | |||||||
\(62\) | 4.32698 | + | 3.14373i | 0.549527 | + | 0.399254i | ||||
\(63\) | 5.96579 | − | 4.33440i | 0.751618 | − | 0.546083i | ||||
\(64\) | 2.63051 | − | 8.09587i | 0.328813 | − | 1.01198i | ||||
\(65\) | 9.70337 | + | 7.04991i | 1.20355 | + | 0.874433i | ||||
\(66\) | −6.21612 | + | 4.51627i | −0.765151 | + | 0.555915i | ||||
\(67\) | −7.81299 | − | 5.67647i | −0.954508 | − | 0.693491i | −0.00263931 | − | 0.999997i | \(-0.500840\pi\) |
−0.951869 | + | 0.306506i | \(0.900840\pi\) | |||||||
\(68\) | 0.0782723 | − | 0.240897i | 0.00949191 | − | 0.0292131i | ||||
\(69\) | −3.27746 | + | 10.0870i | −0.394560 | + | 1.21433i | ||||
\(70\) | −18.0974 | −2.16305 | ||||||||
\(71\) | 2.18500 | + | 8.13792i | 0.259312 | + | 0.965794i | ||||
\(72\) | −5.07124 | −0.597651 | ||||||||
\(73\) | 2.11717 | − | 6.51599i | 0.247796 | − | 0.762639i | −0.747368 | − | 0.664411i | \(-0.768683\pi\) |
0.995164 | − | 0.0982279i | \(-0.0313174\pi\) | |||||||
\(74\) | 2.90147 | − | 8.92980i | 0.337289 | − | 1.03807i | ||||
\(75\) | −8.43817 | − | 6.13069i | −0.974356 | − | 0.707911i | ||||
\(76\) | −0.855876 | + | 0.621831i | −0.0981758 | + | 0.0713289i | ||||
\(77\) | 8.94131 | + | 6.49624i | 1.01896 | + | 0.740315i | ||||
\(78\) | −3.50257 | + | 10.7798i | −0.396588 | + | 1.22057i | ||||
\(79\) | −6.72113 | + | 4.88318i | −0.756186 | + | 0.549401i | −0.897738 | − | 0.440530i | \(-0.854791\pi\) |
0.141552 | + | 0.989931i | \(0.454791\pi\) | |||||||
\(80\) | 9.29833 | + | 6.75563i | 1.03958 | + | 0.755302i | ||||
\(81\) | −3.45960 | − | 10.6476i | −0.384400 | − | 1.18306i | ||||
\(82\) | −1.36647 | + | 4.20556i | −0.150901 | + | 0.464427i | ||||
\(83\) | −5.85783 | + | 4.25596i | −0.642980 | + | 0.467153i | −0.860873 | − | 0.508820i | \(-0.830082\pi\) |
0.217892 | + | 0.975973i | \(0.430082\pi\) | |||||||
\(84\) | 0.435175 | + | 1.33933i | 0.0474815 | + | 0.146133i | ||||
\(85\) | 4.21477 | + | 3.06221i | 0.457156 | + | 0.332143i | ||||
\(86\) | −2.63025 | − | 8.09508i | −0.283627 | − | 0.872915i | ||||
\(87\) | −0.689431 | − | 2.12185i | −0.0739148 | − | 0.227486i | ||||
\(88\) | −2.34871 | − | 7.22859i | −0.250373 | − | 0.770570i | ||||
\(89\) | 4.44552 | − | 3.22986i | 0.471225 | − | 0.342365i | −0.326694 | − | 0.945130i | \(-0.605935\pi\) |
0.797918 | + | 0.602766i | \(0.205935\pi\) | |||||||
\(90\) | 2.27879 | − | 7.01338i | 0.240205 | − | 0.739275i | ||||
\(91\) | 16.3037 | 1.70909 | ||||||||
\(92\) | −0.600088 | − | 0.435990i | −0.0625635 | − | 0.0454551i | ||||
\(93\) | 6.92533 | + | 5.03154i | 0.718123 | + | 0.521747i | ||||
\(94\) | −4.04515 | −0.417225 | ||||||||
\(95\) | −6.72397 | − | 20.6943i | −0.689865 | − | 2.12319i | ||||
\(96\) | 0.577388 | − | 1.77702i | 0.0589294 | − | 0.181366i | ||||
\(97\) | 13.7133 | 1.39238 | 0.696190 | − | 0.717858i | \(-0.254877\pi\) | ||||
0.696190 | + | 0.717858i | \(0.254877\pi\) | |||||||
\(98\) | −12.2038 | + | 8.86655i | −1.23277 | + | 0.895656i | ||||
\(99\) | −3.64339 | + | 2.64708i | −0.366175 | + | 0.266041i | ||||
\(100\) | 0.590135 | − | 0.428758i | 0.0590135 | − | 0.0428758i | ||||
\(101\) | 3.75113 | 0.373252 | 0.186626 | − | 0.982431i | \(-0.440245\pi\) | ||||
0.186626 | + | 0.982431i | \(0.440245\pi\) | |||||||
\(102\) | −1.52138 | + | 4.68233i | −0.150639 | + | 0.463619i | ||||
\(103\) | 4.58382 | 0.451657 | 0.225828 | − | 0.974167i | \(-0.427491\pi\) | ||||
0.225828 | + | 0.974167i | \(0.427491\pi\) | |||||||
\(104\) | −9.07084 | − | 6.59035i | −0.889469 | − | 0.646237i | ||||
\(105\) | −28.9649 | −2.82668 | ||||||||
\(106\) | −1.42704 | − | 4.39197i | −0.138606 | − | 0.426586i | ||||
\(107\) | 0.0622978 | + | 0.191733i | 0.00602255 | + | 0.0185355i | 0.954023 | − | 0.299735i | \(-0.0968981\pi\) |
−0.948000 | + | 0.318270i | \(0.896898\pi\) | |||||||
\(108\) | 0.419283 | 0.0403455 | ||||||||
\(109\) | 3.58093 | + | 2.60170i | 0.342991 | + | 0.249198i | 0.745923 | − | 0.666032i | \(-0.232009\pi\) |
−0.402932 | + | 0.915230i | \(0.632009\pi\) | |||||||
\(110\) | 11.0523 | 1.05380 | ||||||||
\(111\) | 4.64380 | − | 14.2921i | 0.440770 | − | 1.35655i | ||||
\(112\) | 15.6231 | 1.47625 | ||||||||
\(113\) | −10.2559 | + | 7.45138i | −0.964798 | + | 0.700967i | −0.954260 | − | 0.298978i | \(-0.903354\pi\) |
−0.0105379 | + | 0.999944i | \(0.503354\pi\) | |||||||
\(114\) | 16.6357 | − | 12.0865i | 1.55808 | − | 1.13201i | ||||
\(115\) | 12.3426 | − | 8.96740i | 1.15095 | − | 0.836214i | ||||
\(116\) | 0.156031 | 0.0144871 | ||||||||
\(117\) | −2.05293 | + | 6.31826i | −0.189793 | + | 0.584123i | ||||
\(118\) | −0.172695 | − | 0.531499i | −0.0158978 | − | 0.0489285i | ||||
\(119\) | 7.08170 | 0.649178 | ||||||||
\(120\) | 16.1151 | + | 11.7083i | 1.47110 | + | 1.06882i | ||||
\(121\) | 3.43860 | + | 2.49829i | 0.312600 | + | 0.227117i | ||||
\(122\) | 2.50580 | 0.226865 | ||||||||
\(123\) | −2.18703 | + | 6.73100i | −0.197198 | + | 0.606914i | ||||
\(124\) | −0.484332 | + | 0.351888i | −0.0434943 | + | 0.0316004i | ||||
\(125\) | −0.199171 | − | 0.612985i | −0.0178144 | − | 0.0548270i | ||||
\(126\) | −3.09760 | − | 9.53342i | −0.275956 | − | 0.849305i | ||||
\(127\) | −0.431074 | − | 1.32671i | −0.0382516 | − | 0.117726i | 0.930107 | − | 0.367288i | \(-0.119714\pi\) |
−0.968359 | + | 0.249561i | \(0.919714\pi\) | |||||||
\(128\) | −7.97195 | − | 5.79196i | −0.704628 | − | 0.511942i | ||||
\(129\) | −4.20972 | − | 12.9562i | −0.370645 | − | 1.14073i | ||||
\(130\) | 13.1903 | − | 9.58332i | 1.15687 | − | 0.840513i | ||||
\(131\) | −5.92233 | + | 18.2271i | −0.517436 | + | 1.59250i | 0.261369 | + | 0.965239i | \(0.415826\pi\) |
−0.778805 | + | 0.627266i | \(0.784174\pi\) | |||||||
\(132\) | −0.265768 | − | 0.817949i | −0.0231321 | − | 0.0711933i | ||||
\(133\) | −23.9289 | − | 17.3854i | −2.07490 | − | 1.50750i | ||||
\(134\) | −10.6206 | + | 7.71633i | −0.917481 | + | 0.666589i | ||||
\(135\) | −2.66489 | + | 8.20169i | −0.229357 | + | 0.705889i | ||||
\(136\) | −3.94002 | − | 2.86259i | −0.337854 | − | 0.245465i | ||||
\(137\) | −15.8872 | + | 11.5427i | −1.35734 | + | 0.986163i | −0.358727 | + | 0.933442i | \(0.616789\pi\) |
−0.998609 | + | 0.0527202i | \(0.983211\pi\) | |||||||
\(138\) | 11.6639 | + | 8.47434i | 0.992900 | + | 0.721384i | ||||
\(139\) | −4.80264 | + | 14.7810i | −0.407355 | + | 1.25371i | 0.511558 | + | 0.859249i | \(0.329069\pi\) |
−0.918913 | + | 0.394461i | \(0.870931\pi\) | |||||||
\(140\) | 0.625975 | − | 1.92655i | 0.0529046 | − | 0.162823i | ||||
\(141\) | −6.47426 | −0.545231 | ||||||||
\(142\) | 11.4387 | + | 0.593622i | 0.959917 | + | 0.0498157i | ||||
\(143\) | −9.95690 | −0.832638 | ||||||||
\(144\) | −1.96723 | + | 6.05452i | −0.163936 | + | 0.504543i | ||||
\(145\) | −0.991708 | + | 3.05216i | −0.0823569 | + | 0.253468i | ||||
\(146\) | −7.53467 | − | 5.47426i | −0.623573 | − | 0.453053i | ||||
\(147\) | −19.5321 | + | 14.1909i | −1.61098 | + | 1.17045i | ||||
\(148\) | 0.850259 | + | 0.617750i | 0.0698909 | + | 0.0507787i | ||||
\(149\) | 2.07646 | − | 6.39069i | 0.170110 | − | 0.523545i | −0.829266 | − | 0.558854i | \(-0.811241\pi\) |
0.999376 | + | 0.0353083i | \(0.0112413\pi\) | |||||||
\(150\) | −11.4705 | + | 8.33378i | −0.936559 | + | 0.680450i | ||||
\(151\) | 8.10050 | + | 5.88536i | 0.659210 | + | 0.478944i | 0.866396 | − | 0.499358i | \(-0.166431\pi\) |
−0.207186 | + | 0.978302i | \(0.566431\pi\) | |||||||
\(152\) | 6.28566 | + | 19.3453i | 0.509835 | + | 1.56911i | ||||
\(153\) | −0.891712 | + | 2.74441i | −0.0720906 | + | 0.221872i | ||||
\(154\) | 12.1544 | − | 8.83069i | 0.979429 | − | 0.711597i | ||||
\(155\) | −3.80503 | − | 11.7107i | −0.305627 | − | 0.940624i | ||||
\(156\) | −1.02641 | − | 0.745730i | −0.0821785 | − | 0.0597062i | ||||
\(157\) | −2.83410 | − | 8.72247i | −0.226186 | − | 0.696129i | −0.998169 | − | 0.0604858i | \(-0.980735\pi\) |
0.771983 | − | 0.635643i | \(-0.219265\pi\) | |||||||
\(158\) | 3.48979 | + | 10.7405i | 0.277633 | + | 0.854466i | ||||
\(159\) | −2.28397 | − | 7.02935i | −0.181131 | − | 0.557464i | ||||
\(160\) | −2.17438 | + | 1.57978i | −0.171900 | + | 0.124893i | ||||
\(161\) | 6.40843 | − | 19.7231i | 0.505055 | − | 1.55440i | ||||
\(162\) | −15.2187 | −1.19569 | ||||||||
\(163\) | 15.8141 | + | 11.4896i | 1.23866 | + | 0.899939i | 0.997508 | − | 0.0705489i | \(-0.0224751\pi\) |
0.241151 | + | 0.970488i | \(0.422475\pi\) | |||||||
\(164\) | −0.400437 | − | 0.290934i | −0.0312688 | − | 0.0227181i | ||||
\(165\) | 17.6893 | 1.37711 | ||||||||
\(166\) | 3.04154 | + | 9.36091i | 0.236070 | + | 0.726547i | ||||
\(167\) | −6.20089 | + | 19.0844i | −0.479840 | + | 1.47679i | 0.359478 | + | 0.933153i | \(0.382955\pi\) |
−0.839318 | + | 0.543641i | \(0.817045\pi\) | |||||||
\(168\) | 27.0768 | 2.08902 | ||||||||
\(169\) | −1.36574 | + | 0.992271i | −0.105057 | + | 0.0763285i | ||||
\(170\) | 5.72936 | − | 4.16262i | 0.439422 | − | 0.319259i | ||||
\(171\) | 9.75051 | − | 7.08416i | 0.745640 | − | 0.541740i | ||||
\(172\) | 0.952738 | 0.0726456 | ||||||||
\(173\) | 3.43572 | − | 10.5741i | 0.261213 | − | 0.803932i | −0.731328 | − | 0.682025i | \(-0.761099\pi\) |
0.992542 | − | 0.121906i | \(-0.0389007\pi\) | |||||||
\(174\) | −3.03278 | −0.229915 | ||||||||
\(175\) | 16.4992 | + | 11.9874i | 1.24722 | + | 0.906160i | ||||
\(176\) | −9.54128 | −0.719201 | ||||||||
\(177\) | −0.276398 | − | 0.850665i | −0.0207753 | − | 0.0639399i | ||||
\(178\) | −2.30824 | − | 7.10402i | −0.173010 | − | 0.532469i | ||||
\(179\) | 22.0389 | 1.64726 | 0.823632 | − | 0.567125i | \(-0.191944\pi\) | ||||
0.823632 | + | 0.567125i | \(0.191944\pi\) | |||||||
\(180\) | 0.667786 | + | 0.485175i | 0.0497738 | + | 0.0361628i | ||||
\(181\) | −11.6108 | −0.863025 | −0.431513 | − | 0.902107i | \(-0.642020\pi\) | ||||
−0.431513 | + | 0.902107i | \(0.642020\pi\) | |||||||
\(182\) | 6.84859 | − | 21.0778i | 0.507651 | − | 1.56239i | ||||
\(183\) | 4.01054 | 0.296467 | ||||||||
\(184\) | −11.5380 | + | 8.38285i | −0.850593 | + | 0.617992i | ||||
\(185\) | −17.4881 | + | 12.7058i | −1.28575 | + | 0.934150i | ||||
\(186\) | 9.41397 | − | 6.83965i | 0.690266 | − | 0.501507i | ||||
\(187\) | −4.32489 | −0.316268 | ||||||||
\(188\) | 0.139918 | − | 0.430625i | 0.0102046 | − | 0.0314065i | ||||
\(189\) | 3.62244 | + | 11.1487i | 0.263493 | + | 0.810949i | ||||
\(190\) | −29.5785 | −2.14585 | ||||||||
\(191\) | −4.51578 | − | 3.28091i | −0.326750 | − | 0.237398i | 0.412300 | − | 0.911048i | \(-0.364726\pi\) |
−0.739051 | + | 0.673650i | \(0.764726\pi\) | |||||||
\(192\) | −14.9831 | − | 10.8859i | −1.08131 | − | 0.785621i | ||||
\(193\) | 9.65947 | 0.695304 | 0.347652 | − | 0.937624i | \(-0.386979\pi\) | ||||
0.347652 | + | 0.937624i | \(0.386979\pi\) | |||||||
\(194\) | 5.76048 | − | 17.7289i | 0.413578 | − | 1.27286i | ||||
\(195\) | 21.1111 | − | 15.3381i | 1.51180 | − | 1.09838i | ||||
\(196\) | −0.521767 | − | 1.60583i | −0.0372691 | − | 0.114702i | ||||
\(197\) | −0.300539 | − | 0.924963i | −0.0214125 | − | 0.0659009i | 0.939779 | − | 0.341782i | \(-0.111030\pi\) |
−0.961192 | + | 0.275881i | \(0.911030\pi\) | |||||||
\(198\) | 1.89175 | + | 5.82220i | 0.134441 | + | 0.413766i | ||||
\(199\) | −12.7620 | − | 9.27215i | −0.904676 | − | 0.657285i | 0.0349871 | − | 0.999388i | \(-0.488861\pi\) |
−0.939663 | + | 0.342103i | \(0.888861\pi\) | |||||||
\(200\) | −4.33402 | − | 13.3388i | −0.306462 | − | 0.943192i | ||||
\(201\) | −16.9983 | + | 12.3500i | −1.19897 | + | 0.871100i | ||||
\(202\) | 1.57571 | − | 4.84955i | 0.110867 | − | 0.341213i | ||||
\(203\) | 1.34805 | + | 4.14887i | 0.0946144 | + | 0.291193i | ||||
\(204\) | −0.445832 | − | 0.323916i | −0.0312145 | − | 0.0226787i | ||||
\(205\) | 8.23614 | − | 5.98391i | 0.575237 | − | 0.417934i | ||||
\(206\) | 1.92549 | − | 5.92606i | 0.134156 | − | 0.412888i | ||||
\(207\) | 6.83647 | + | 4.96698i | 0.475167 | + | 0.345229i | ||||
\(208\) | −11.3869 | + | 8.27310i | −0.789542 | + | 0.573636i | ||||
\(209\) | 14.6137 | + | 10.6175i | 1.01085 | + | 0.734427i | ||||
\(210\) | −12.1671 | + | 37.4465i | −0.839609 | + | 2.58405i | ||||
\(211\) | 5.85429 | − | 18.0176i | 0.403026 | − | 1.24039i | −0.519507 | − | 0.854466i | \(-0.673884\pi\) |
0.922533 | − | 0.385919i | \(-0.126116\pi\) | |||||||
\(212\) | 0.516906 | 0.0355012 | ||||||||
\(213\) | 18.3077 | + | 0.950092i | 1.25442 | + | 0.0650993i | ||||
\(214\) | 0.274046 | 0.0187334 | ||||||||
\(215\) | −6.05544 | + | 18.6367i | −0.412978 | + | 1.27101i | ||||
\(216\) | 2.49118 | − | 7.66705i | 0.169503 | − | 0.521677i | ||||
\(217\) | −13.5411 | − | 9.83820i | −0.919231 | − | 0.667860i | ||||
\(218\) | 4.86776 | − | 3.53663i | 0.329686 | − | 0.239531i | ||||
\(219\) | −12.0592 | − | 8.76155i | −0.814887 | − | 0.592050i | ||||
\(220\) | −0.382292 | + | 1.17657i | −0.0257741 | + | 0.0793246i | ||||
\(221\) | −5.16150 | + | 3.75005i | −0.347200 | + | 0.252256i | ||||
\(222\) | −16.5265 | − | 12.0072i | −1.10919 | − | 0.805871i | ||||
\(223\) | −8.76855 | − | 26.9868i | −0.587186 | − | 1.80717i | −0.590309 | − | 0.807177i | \(-0.700994\pi\) |
0.00312362 | − | 0.999995i | \(-0.499006\pi\) | |||||||
\(224\) | −1.12897 | + | 3.47461i | −0.0754324 | + | 0.232157i | ||||
\(225\) | −6.72307 | + | 4.88460i | −0.448205 | + | 0.325640i | ||||
\(226\) | 5.32516 | + | 16.3892i | 0.354225 | + | 1.09019i | ||||
\(227\) | 2.39001 | + | 1.73644i | 0.158630 | + | 0.115252i | 0.664269 | − | 0.747494i | \(-0.268743\pi\) |
−0.505638 | + | 0.862745i | \(0.668743\pi\) | |||||||
\(228\) | 0.711253 | + | 2.18901i | 0.0471039 | + | 0.144971i | ||||
\(229\) | −5.95231 | − | 18.3193i | −0.393340 | − | 1.21058i | −0.930247 | − | 0.366934i | \(-0.880407\pi\) |
0.536907 | − | 0.843642i | \(-0.319593\pi\) | |||||||
\(230\) | −6.40859 | − | 19.7236i | −0.422570 | − | 1.30054i | ||||
\(231\) | 19.4531 | − | 14.1335i | 1.27992 | − | 0.929917i | ||||
\(232\) | 0.927063 | − | 2.85321i | 0.0608647 | − | 0.187322i | ||||
\(233\) | −24.2031 | −1.58559 | −0.792797 | − | 0.609485i | \(-0.791376\pi\) | ||||
−0.792797 | + | 0.609485i | \(0.791376\pi\) | |||||||
\(234\) | 7.30603 | + | 5.30814i | 0.477610 | + | 0.347004i | ||||
\(235\) | 7.53426 | + | 5.47396i | 0.491481 | + | 0.357082i | ||||
\(236\) | 0.0625540 | 0.00407192 | ||||||||
\(237\) | 5.58541 | + | 17.1901i | 0.362811 | + | 1.11662i | ||||
\(238\) | 2.97476 | − | 9.15537i | 0.192825 | − | 0.593455i | ||||
\(239\) | −21.3521 | −1.38115 | −0.690576 | − | 0.723260i | \(-0.742643\pi\) | ||||
−0.690576 | + | 0.723260i | \(0.742643\pi\) | |||||||
\(240\) | 20.2299 | − | 14.6979i | 1.30583 | − | 0.948743i | ||||
\(241\) | −2.79962 | + | 2.03404i | −0.180339 | + | 0.131024i | −0.674293 | − | 0.738464i | \(-0.735551\pi\) |
0.493953 | + | 0.869488i | \(0.335551\pi\) | |||||||
\(242\) | 4.67428 | − | 3.39606i | 0.300474 | − | 0.218307i | ||||
\(243\) | −16.0907 | −1.03222 | ||||||||
\(244\) | −0.0866738 | + | 0.266754i | −0.00554872 | + | 0.0170772i | ||||
\(245\) | 34.7284 | 2.21871 | ||||||||
\(246\) | 7.78330 | + | 5.65490i | 0.496245 | + | 0.360543i | ||||
\(247\) | 26.6469 | 1.69550 | ||||||||
\(248\) | 3.55699 | + | 10.9473i | 0.225869 | + | 0.695154i | ||||
\(249\) | 4.86799 | + | 14.9821i | 0.308496 | + | 0.949454i | ||||
\(250\) | −0.876145 | −0.0554123 | ||||||||
\(251\) | 4.82004 | + | 3.50197i | 0.304238 | + | 0.221042i | 0.729420 | − | 0.684066i | \(-0.239790\pi\) |
−0.425182 | + | 0.905108i | \(0.639790\pi\) | |||||||
\(252\) | 1.12202 | 0.0706807 | ||||||||
\(253\) | −3.91372 | + | 12.0452i | −0.246053 | + | 0.757274i | ||||
\(254\) | −1.89628 | −0.118983 | ||||||||
\(255\) | 9.16984 | − | 6.66228i | 0.574238 | − | 0.417208i | ||||
\(256\) | 2.93680 | − | 2.13371i | 0.183550 | − | 0.133357i | ||||
\(257\) | 16.6089 | − | 12.0671i | 1.03603 | − | 0.752723i | 0.0665270 | − | 0.997785i | \(-0.478808\pi\) |
0.969508 | + | 0.245062i | \(0.0788082\pi\) | |||||||
\(258\) | −18.5184 | −1.15290 | ||||||||
\(259\) | −9.08004 | + | 27.9455i | −0.564206 | + | 1.73645i | ||||
\(260\) | 0.563947 | + | 1.73565i | 0.0349745 | + | 0.107640i | ||||
\(261\) | −1.77758 | −0.110029 | ||||||||
\(262\) | 21.0766 | + | 15.3130i | 1.30212 | + | 0.946043i | ||||
\(263\) | 11.8633 | + | 8.61917i | 0.731521 | + | 0.531481i | 0.890044 | − | 0.455874i | \(-0.150673\pi\) |
−0.158523 | + | 0.987355i | \(0.550673\pi\) | |||||||
\(264\) | −16.5362 | −1.01773 | ||||||||
\(265\) | −3.28537 | + | 10.1113i | −0.201819 | + | 0.621134i | ||||
\(266\) | −32.5278 | + | 23.6329i | −1.99441 | + | 1.44902i | ||||
\(267\) | −3.69433 | − | 11.3700i | −0.226089 | − | 0.695832i | ||||
\(268\) | −0.454080 | − | 1.39752i | −0.0277374 | − | 0.0853669i | ||||
\(269\) | −3.91608 | − | 12.0525i | −0.238768 | − | 0.734851i | −0.996599 | − | 0.0824012i | \(-0.973741\pi\) |
0.757832 | − | 0.652450i | \(-0.226259\pi\) | |||||||
\(270\) | 9.48390 | + | 6.89046i | 0.577172 | + | 0.419340i | ||||
\(271\) | 0.481126 | + | 1.48075i | 0.0292263 | + | 0.0899494i | 0.964606 | − | 0.263697i | \(-0.0849418\pi\) |
−0.935379 | + | 0.353646i | \(0.884942\pi\) | |||||||
\(272\) | −4.94605 | + | 3.59351i | −0.299898 | + | 0.217889i | ||||
\(273\) | 10.9612 | − | 33.7350i | 0.663400 | − | 2.04173i | ||||
\(274\) | 8.24907 | + | 25.3880i | 0.498345 | + | 1.53375i | ||||
\(275\) | −10.0763 | − | 7.32086i | −0.607624 | − | 0.441464i | ||||
\(276\) | −1.30558 | + | 0.948559i | −0.0785867 | + | 0.0570965i | ||||
\(277\) | −4.29289 | + | 13.2122i | −0.257935 | + | 0.793842i | 0.735302 | + | 0.677739i | \(0.237040\pi\) |
−0.993237 | + | 0.116102i | \(0.962960\pi\) | |||||||
\(278\) | 17.0918 | + | 12.4179i | 1.02510 | + | 0.744778i | ||||
\(279\) | 5.51772 | − | 4.00886i | 0.330337 | − | 0.240004i | ||||
\(280\) | −31.5100 | − | 22.8933i | −1.88308 | − | 1.36814i | ||||
\(281\) | −0.739039 | + | 2.27453i | −0.0440874 | + | 0.135687i | −0.970677 | − | 0.240386i | \(-0.922726\pi\) |
0.926590 | + | 0.376073i | \(0.122726\pi\) | |||||||
\(282\) | −2.71960 | + | 8.37007i | −0.161950 | + | 0.498430i | ||||
\(283\) | −0.510962 | −0.0303735 | −0.0151868 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151868 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(284\) | −0.458851 | + | 1.19717i | −0.0272278 | + | 0.0710392i | ||||
\(285\) | −47.3404 | −2.80420 | ||||||||
\(286\) | −4.18253 | + | 12.8725i | −0.247318 | + | 0.761167i | ||||
\(287\) | 4.27632 | − | 13.1612i | 0.252423 | − | 0.776878i | ||||
\(288\) | −1.20438 | − | 0.875031i | −0.0709686 | − | 0.0515617i | ||||
\(289\) | 11.5113 | − | 8.36347i | 0.677137 | − | 0.491969i | ||||
\(290\) | 3.52933 | + | 2.56421i | 0.207249 | + | 0.150575i | ||||
\(291\) | 9.21964 | − | 28.3751i | 0.540465 | − | 1.66338i | ||||
\(292\) | 0.843378 | − | 0.612750i | 0.0493550 | − | 0.0358585i | ||||
\(293\) | −5.20136 | − | 3.77901i | −0.303867 | − | 0.220772i | 0.425393 | − | 0.905009i | \(-0.360136\pi\) |
−0.729260 | + | 0.684236i | \(0.760136\pi\) | |||||||
\(294\) | 10.1416 | + | 31.2126i | 0.591470 | + | 1.82036i | ||||
\(295\) | −0.397583 | + | 1.22363i | −0.0231482 | + | 0.0712427i | ||||
\(296\) | 16.3481 | − | 11.8776i | 0.950213 | − | 0.690370i | ||||
\(297\) | −2.21227 | − | 6.80868i | −0.128369 | − | 0.395080i | ||||
\(298\) | −7.38978 | − | 5.36899i | −0.428078 | − | 0.311017i | ||||
\(299\) | 5.77341 | + | 17.7687i | 0.333885 | + | 1.02759i | ||||
\(300\) | −0.490415 | − | 1.50934i | −0.0283141 | − | 0.0871420i | ||||
\(301\) | 8.23128 | + | 25.3333i | 0.474443 | + | 1.46019i | ||||
\(302\) | 11.0115 | − | 8.00029i | 0.633638 | − | 0.460365i | ||||
\(303\) | 2.52193 | − | 7.76171i | 0.144881 | − | 0.445898i | ||||
\(304\) | 25.5346 | 1.46451 | ||||||||
\(305\) | −4.66716 | − | 3.39089i | −0.267241 | − | 0.194162i | ||||
\(306\) | 3.17346 | + | 2.30565i | 0.181414 | + | 0.131805i | ||||
\(307\) | −18.0716 | −1.03140 | −0.515699 | − | 0.856770i | \(-0.672468\pi\) | ||||
−0.515699 | + | 0.856770i | \(0.672468\pi\) | |||||||
\(308\) | 0.519657 | + | 1.59934i | 0.0296102 | + | 0.0911308i | ||||
\(309\) | 3.08175 | − | 9.48466i | 0.175315 | − | 0.539563i | ||||
\(310\) | −16.7382 | −0.950664 | ||||||||
\(311\) | −10.4703 | + | 7.60715i | −0.593718 | + | 0.431362i | −0.843644 | − | 0.536903i | \(-0.819594\pi\) |
0.249925 | + | 0.968265i | \(0.419594\pi\) | |||||||
\(312\) | −19.7349 | + | 14.3383i | −1.11727 | + | 0.811745i | ||||
\(313\) | 3.02261 | − | 2.19605i | 0.170848 | − | 0.124128i | −0.499075 | − | 0.866559i | \(-0.666327\pi\) |
0.669923 | + | 0.742430i | \(0.266327\pi\) | |||||||
\(314\) | −12.4671 | −0.703560 | ||||||||
\(315\) | −7.13138 | + | 21.9481i | −0.401808 | + | 1.23664i | ||||
\(316\) | −1.26408 | −0.0711102 | ||||||||
\(317\) | −17.3756 | − | 12.6241i | −0.975909 | − | 0.709039i | −0.0191184 | − | 0.999817i | \(-0.506086\pi\) |
−0.956791 | + | 0.290778i | \(0.906086\pi\) | |||||||
\(318\) | −10.0471 | −0.563414 | ||||||||
\(319\) | −0.823272 | − | 2.53377i | −0.0460944 | − | 0.141864i | ||||
\(320\) | 8.23229 | + | 25.3364i | 0.460199 | + | 1.41635i | ||||
\(321\) | 0.438610 | 0.0244808 | ||||||||
\(322\) | −22.8065 | − | 16.5699i | −1.27096 | − | 0.923405i | ||||
\(323\) | 11.5744 | 0.644015 | ||||||||
\(324\) | 0.526402 | − | 1.62010i | 0.0292445 | − | 0.0900054i | ||||
\(325\) | −18.3733 | −1.01916 | ||||||||
\(326\) | 21.4970 | − | 15.6185i | 1.19061 | − | 0.865029i | ||||
\(327\) | 7.79084 | − | 5.66038i | 0.430835 | − | 0.313020i | ||||
\(328\) | −7.69926 | + | 5.59384i | −0.425121 | + | 0.308868i | ||||
\(329\) | 12.6591 | 0.697921 | ||||||||
\(330\) | 7.43062 | − | 22.8691i | 0.409042 | − | 1.25890i | ||||
\(331\) | 3.49059 | + | 10.7429i | 0.191860 | + | 0.590485i | 0.999999 | + | 0.00149289i | \(0.000475203\pi\) |
−0.808139 | + | 0.588992i | \(0.799525\pi\) | |||||||
\(332\) | −1.10172 | −0.0604646 | ||||||||
\(333\) | −9.68652 | − | 7.03767i | −0.530818 | − | 0.385662i | ||||
\(334\) | 22.0680 | + | 16.0333i | 1.20750 | + | 0.877304i | ||||
\(335\) | 30.2232 | 1.65127 | ||||||||
\(336\) | 10.5036 | − | 32.3268i | 0.573020 | − | 1.76357i | ||||
\(337\) | −18.4497 | + | 13.4045i | −1.00502 | + | 0.730191i | −0.963159 | − | 0.268933i | \(-0.913329\pi\) |
−0.0418624 | + | 0.999123i | \(0.513329\pi\) | |||||||
\(338\) | 0.709131 | + | 2.18248i | 0.0385716 | + | 0.118711i | ||||
\(339\) | 8.52292 | + | 26.2309i | 0.462902 | + | 1.42466i | ||||
\(340\) | 0.244957 | + | 0.753899i | 0.0132846 | + | 0.0408859i | ||||
\(341\) | 8.26976 | + | 6.00833i | 0.447832 | + | 0.325369i | ||||
\(342\) | −5.06273 | − | 15.5815i | −0.273761 | − | 0.842550i | ||||
\(343\) | 14.1000 | − | 10.2443i | 0.761329 | − | 0.553138i | ||||
\(344\) | 5.66071 | − | 17.4219i | 0.305205 | − | 0.939325i | ||||
\(345\) | −10.2569 | − | 31.5676i | −0.552216 | − | 1.69954i | ||||
\(346\) | −12.2272 | − | 8.88356i | −0.657337 | − | 0.477583i | ||||
\(347\) | 7.49897 | − | 5.44832i | 0.402566 | − | 0.292481i | −0.368019 | − | 0.929818i | \(-0.619964\pi\) |
0.770585 | + | 0.637337i | \(0.219964\pi\) | |||||||
\(348\) | 0.104902 | − | 0.322854i | 0.00562331 | − | 0.0173068i | ||||
\(349\) | 21.0774 | + | 15.3136i | 1.12825 | + | 0.819719i | 0.985439 | − | 0.170031i | \(-0.0543869\pi\) |
0.142808 | + | 0.989750i | \(0.454387\pi\) | |||||||
\(350\) | 22.4282 | − | 16.2951i | 1.19884 | − | 0.871008i | ||||
\(351\) | −8.54392 | − | 6.20752i | −0.456041 | − | 0.331333i | ||||
\(352\) | 0.689478 | − | 2.12199i | 0.0367493 | − | 0.113103i | ||||
\(353\) | −4.20751 | + | 12.9494i | −0.223943 | + | 0.689226i | 0.774454 | + | 0.632630i | \(0.218025\pi\) |
−0.998397 | + | 0.0565959i | \(0.981975\pi\) | |||||||
\(354\) | −1.21586 | −0.0646224 | ||||||||
\(355\) | −20.5018 | − | 16.5847i | −1.08812 | − | 0.880226i | ||||
\(356\) | 0.836096 | 0.0443130 | ||||||||
\(357\) | 4.76111 | − | 14.6532i | 0.251984 | − | 0.775528i | ||||
\(358\) | 9.25773 | − | 28.4924i | 0.489286 | − | 1.50587i | ||||
\(359\) | −10.8917 | − | 7.91328i | −0.574842 | − | 0.417647i | 0.262019 | − | 0.965063i | \(-0.415612\pi\) |
−0.836861 | + | 0.547416i | \(0.815612\pi\) | |||||||
\(360\) | 12.8396 | − | 9.32854i | 0.676708 | − | 0.491657i | ||||
\(361\) | −23.7382 | − | 17.2468i | −1.24938 | − | 0.907727i | ||||
\(362\) | −4.87728 | + | 15.0107i | −0.256344 | + | 0.788946i | ||||
\(363\) | 7.48118 | − | 5.43540i | 0.392660 | − | 0.285284i | ||||
\(364\) | 2.00694 | + | 1.45813i | 0.105192 | + | 0.0764267i | ||||
\(365\) | 6.62579 | + | 20.3921i | 0.346809 | + | 1.06737i | ||||
\(366\) | 1.68468 | − | 5.18491i | 0.0880596 | − | 0.271020i | ||||
\(367\) | 4.03067 | − | 2.92845i | 0.210399 | − | 0.152864i | −0.477595 | − | 0.878580i | \(-0.658491\pi\) |
0.687994 | + | 0.725716i | \(0.258491\pi\) | |||||||
\(368\) | 5.53242 | + | 17.0270i | 0.288397 | + | 0.887595i | ||||
\(369\) | 4.56195 | + | 3.31445i | 0.237485 | + | 0.172543i | ||||
\(370\) | 9.08027 | + | 27.9462i | 0.472061 | + | 1.45285i | ||||
\(371\) | 4.46586 | + | 13.7445i | 0.231856 | + | 0.713580i | ||||
\(372\) | 0.402491 | + | 1.23874i | 0.0208682 | + | 0.0642256i | ||||
\(373\) | −16.0917 | + | 11.6913i | −0.833196 | + | 0.605352i | −0.920462 | − | 0.390833i | \(-0.872187\pi\) |
0.0872660 | + | 0.996185i | \(0.472187\pi\) | |||||||
\(374\) | −1.81673 | + | 5.59132i | −0.0939409 | + | 0.289120i | ||||
\(375\) | −1.40227 | −0.0724129 | ||||||||
\(376\) | −7.04313 | − | 5.11714i | −0.363222 | − | 0.263896i | ||||
\(377\) | −3.17952 | − | 2.31006i | −0.163754 | − | 0.118974i | ||||
\(378\) | 15.9350 | 0.819606 | ||||||||
\(379\) | −0.817062 | − | 2.51466i | −0.0419696 | − | 0.129169i | 0.927876 | − | 0.372888i | \(-0.121633\pi\) |
−0.969846 | + | 0.243719i | \(0.921633\pi\) | |||||||
\(380\) | 1.02310 | − | 3.14877i | 0.0524838 | − | 0.161528i | ||||
\(381\) | −3.03499 | −0.155487 | ||||||||
\(382\) | −6.13855 | + | 4.45991i | −0.314075 | + | 0.228189i | ||||
\(383\) | 8.52545 | − | 6.19411i | 0.435630 | − | 0.316504i | −0.348266 | − | 0.937396i | \(-0.613229\pi\) |
0.783896 | + | 0.620892i | \(0.213229\pi\) | |||||||
\(384\) | −17.3441 | + | 12.6013i | −0.885090 | + | 0.643055i | ||||
\(385\) | −34.5879 | −1.76276 | ||||||||
\(386\) | 4.05759 | − | 12.4880i | 0.206526 | − | 0.635622i | ||||
\(387\) | −10.8540 | −0.551740 | ||||||||
\(388\) | 1.68808 | + | 1.22646i | 0.0856991 | + | 0.0622640i | ||||
\(389\) | 25.3752 | 1.28657 | 0.643286 | − | 0.765626i | \(-0.277571\pi\) | ||||
0.643286 | + | 0.765626i | \(0.277571\pi\) | |||||||
\(390\) | −10.9614 | − | 33.7359i | −0.555054 | − | 1.70828i | ||||
\(391\) | 2.50775 | + | 7.71805i | 0.126822 | + | 0.390319i | ||||
\(392\) | −32.4646 | −1.63971 | ||||||||
\(393\) | 33.7331 | + | 24.5085i | 1.70161 | + | 1.23629i | ||||
\(394\) | −1.32206 | −0.0666043 | ||||||||
\(395\) | 8.03430 | − | 24.7270i | 0.404249 | − | 1.24415i | ||||
\(396\) | −0.685234 | −0.0344343 | ||||||||
\(397\) | 9.99217 | − | 7.25974i | 0.501493 | − | 0.364356i | −0.308094 | − | 0.951356i | \(-0.599691\pi\) |
0.809587 | + | 0.587000i | \(0.199691\pi\) | |||||||
\(398\) | −17.3481 | + | 12.6041i | −0.869582 | + | 0.631788i | ||||
\(399\) | −52.0608 | + | 37.8244i | −2.60630 | + | 1.89359i | ||||
\(400\) | −17.6063 | −0.880316 | ||||||||
\(401\) | 3.45851 | − | 10.6442i | 0.172710 | − | 0.531546i | −0.826812 | − | 0.562479i | \(-0.809848\pi\) |
0.999521 | + | 0.0309326i | \(0.00984771\pi\) | |||||||
\(402\) | 8.82597 | + | 27.1635i | 0.440199 | + | 1.35479i | ||||
\(403\) | 15.0792 | 0.751148 | ||||||||
\(404\) | 0.461755 | + | 0.335484i | 0.0229732 | + | 0.0166910i | ||||
\(405\) | 28.3454 | + | 20.5941i | 1.40849 | + | 1.02333i | ||||
\(406\) | 5.93001 | 0.294302 | ||||||||
\(407\) | 5.54531 | − | 17.0667i | 0.274871 | − | 0.845965i | ||||
\(408\) | −8.57210 | + | 6.22799i | −0.424382 | + | 0.308332i | ||||
\(409\) | 1.09279 | + | 3.36327i | 0.0540351 | + | 0.166303i | 0.974432 | − | 0.224682i | \(-0.0721344\pi\) |
−0.920397 | + | 0.390985i | \(0.872134\pi\) | |||||||
\(410\) | −4.27643 | − | 13.1615i | −0.211198 | − | 0.650000i | ||||
\(411\) | 13.2026 | + | 40.6335i | 0.651238 | + | 2.00430i | ||||
\(412\) | 0.564256 | + | 0.409956i | 0.0277989 | + | 0.0201971i | ||||
\(413\) | 0.540442 | + | 1.66331i | 0.0265934 | + | 0.0818461i | ||||
\(414\) | 9.29318 | − | 6.75189i | 0.456735 | − | 0.331837i | ||||
\(415\) | 7.00233 | − | 21.5510i | 0.343731 | − | 1.05789i | ||||
\(416\) | −1.01710 | − | 3.13031i | −0.0498674 | − | 0.153476i | ||||
\(417\) | 27.3554 | + | 19.8749i | 1.33960 | + | 0.973278i | ||||
\(418\) | 19.8652 | − | 14.4329i | 0.971640 | − | 0.705937i | ||||
\(419\) | 6.45206 | − | 19.8574i | 0.315204 | − | 0.970097i | −0.660467 | − | 0.750855i | \(-0.729642\pi\) |
0.975671 | − | 0.219242i | \(-0.0703584\pi\) | |||||||
\(420\) | −3.56550 | − | 2.59049i | −0.173979 | − | 0.126403i | ||||
\(421\) | −23.1026 | + | 16.7850i | −1.12595 | + | 0.818051i | −0.985101 | − | 0.171979i | \(-0.944984\pi\) |
−0.140851 | + | 0.990031i | \(0.544984\pi\) | |||||||
\(422\) | −20.8344 | − | 15.1371i | −1.01420 | − | 0.736863i | ||||
\(423\) | −1.59401 | + | 4.90586i | −0.0775035 | + | 0.238531i | ||||
\(424\) | 3.07121 | − | 9.45221i | 0.149151 | − | 0.459040i | ||||
\(425\) | −7.98063 | −0.387117 | ||||||||
\(426\) | 8.91869 | − | 23.2695i | 0.432112 | − | 1.12741i | ||||
\(427\) | −7.84182 | −0.379492 | ||||||||
\(428\) | −0.00947902 | + | 0.0291734i | −0.000458186 | + | 0.00141015i | ||||
\(429\) | −6.69414 | + | 20.6024i | −0.323196 | + | 0.994696i | ||||
\(430\) | 21.5503 | + | 15.6572i | 1.03925 | + | 0.755058i | ||||
\(431\) | −19.1459 | + | 13.9103i | −0.922225 | + | 0.670036i | −0.944077 | − | 0.329725i | \(-0.893044\pi\) |
0.0218515 | + | 0.999761i | \(0.493044\pi\) | |||||||
\(432\) | −8.18727 | − | 5.94840i | −0.393910 | − | 0.286193i | ||||
\(433\) | 8.50707 | − | 26.1821i | 0.408824 | − | 1.25823i | −0.508836 | − | 0.860863i | \(-0.669924\pi\) |
0.917660 | − | 0.397366i | \(-0.130076\pi\) | |||||||
\(434\) | −18.4072 | + | 13.3736i | −0.883573 | + | 0.641953i | ||||
\(435\) | 5.64869 | + | 4.10401i | 0.270834 | + | 0.196772i | ||||
\(436\) | 0.208119 | + | 0.640525i | 0.00996710 | + | 0.0306756i | ||||
\(437\) | 10.4740 | − | 32.2356i | 0.501038 | − | 1.54204i | ||||
\(438\) | −16.3928 | + | 11.9100i | −0.783277 | + | 0.569084i | ||||
\(439\) | −2.21774 | − | 6.82552i | −0.105847 | − | 0.325764i | 0.884081 | − | 0.467333i | \(-0.154785\pi\) |
−0.989928 | + | 0.141569i | \(0.954785\pi\) | |||||||
\(440\) | 19.2436 | + | 13.9813i | 0.917402 | + | 0.666532i | ||||
\(441\) | 5.94419 | + | 18.2944i | 0.283057 | + | 0.871160i | ||||
\(442\) | 2.67999 | + | 8.24816i | 0.127474 | + | 0.392325i | ||||
\(443\) | −2.88709 | − | 8.88554i | −0.137170 | − | 0.422165i | 0.858751 | − | 0.512392i | \(-0.171241\pi\) |
−0.995921 | + | 0.0902274i | \(0.971241\pi\) | |||||||
\(444\) | 1.84986 | − | 1.34400i | 0.0877906 | − | 0.0637836i | ||||
\(445\) | −5.31409 | + | 16.3551i | −0.251912 | + | 0.775305i | ||||
\(446\) | −38.5725 | −1.82646 | ||||||||
\(447\) | −11.8273 | − | 8.59306i | −0.559414 | − | 0.406438i | ||||
\(448\) | 29.2966 | + | 21.2852i | 1.38413 | + | 1.00563i | ||||
\(449\) | −2.94170 | −0.138827 | −0.0694137 | − | 0.997588i | \(-0.522113\pi\) | ||||
−0.0694137 | + | 0.997588i | \(0.522113\pi\) | |||||||
\(450\) | 3.49080 | + | 10.7436i | 0.164558 | + | 0.506457i | ||||
\(451\) | −2.61161 | + | 8.03771i | −0.122976 | + | 0.378481i | ||||
\(452\) | −1.92890 | −0.0907277 | ||||||||
\(453\) | 17.6238 | − | 12.8045i | 0.828040 | − | 0.601606i | ||||
\(454\) | 3.24887 | − | 2.36044i | 0.152477 | − | 0.110781i | ||||
\(455\) | −41.2786 | + | 29.9907i | −1.93517 | + | 1.40598i | ||||
\(456\) | 44.2545 | 2.07240 | ||||||||
\(457\) | −10.9773 | + | 33.7846i | −0.513495 | + | 1.58038i | 0.272508 | + | 0.962154i | \(0.412147\pi\) |
−0.786003 | + | 0.618222i | \(0.787853\pi\) | |||||||
\(458\) | −26.1840 | −1.22350 | ||||||||
\(459\) | −3.71115 | − | 2.69631i | −0.173221 | − | 0.125853i | ||||
\(460\) | 2.32134 | 0.108233 | ||||||||
\(461\) | 9.60369 | + | 29.5571i | 0.447288 | + | 1.37661i | 0.879955 | + | 0.475058i | \(0.157573\pi\) |
−0.432666 | + | 0.901554i | \(0.642427\pi\) | |||||||
\(462\) | −10.1006 | − | 31.0864i | −0.469922 | − | 1.44627i | ||||
\(463\) | −13.8660 | −0.644407 | −0.322203 | − | 0.946670i | \(-0.604424\pi\) | ||||
−0.322203 | + | 0.946670i | \(0.604424\pi\) | |||||||
\(464\) | −3.04680 | − | 2.21363i | −0.141444 | − | 0.102765i | ||||
\(465\) | −26.7894 | −1.24233 | ||||||||
\(466\) | −10.1668 | + | 31.2903i | −0.470969 | + | 1.44949i | ||||
\(467\) | −14.4287 | −0.667681 | −0.333840 | − | 0.942630i | \(-0.608345\pi\) | ||||
−0.333840 | + | 0.942630i | \(0.608345\pi\) | |||||||
\(468\) | −0.817786 | + | 0.594156i | −0.0378022 | + | 0.0274649i | ||||
\(469\) | 33.2368 | − | 24.1480i | 1.53473 | − | 1.11505i | ||||
\(470\) | 10.2417 | − | 7.44105i | 0.472416 | − | 0.343230i | ||||
\(471\) | −19.9536 | −0.919414 | ||||||||
\(472\) | 0.371666 | − | 1.14387i | 0.0171073 | − | 0.0526509i | ||||
\(473\) | −5.02696 | − | 15.4714i | −0.231140 | − | 0.711375i | ||||
\(474\) | 24.5700 | 1.12854 | ||||||||
\(475\) | 26.9664 | + | 19.5922i | 1.23730 | + | 0.898953i | ||||
\(476\) | 0.871738 | + | 0.633355i | 0.0399560 | + | 0.0290298i | ||||
\(477\) | −5.88882 | −0.269630 | ||||||||
\(478\) | −8.96923 | + | 27.6045i | −0.410243 | + | 1.26260i | ||||
\(479\) | 28.1213 | − | 20.4313i | 1.28489 | − | 0.933530i | 0.285205 | − | 0.958467i | \(-0.407938\pi\) |
0.999689 | + | 0.0249364i | \(0.00793832\pi\) | |||||||
\(480\) | 1.80696 | + | 5.56126i | 0.0824762 | + | 0.253835i | ||||
\(481\) | −8.18029 | − | 25.1763i | −0.372989 | − | 1.14794i | ||||
\(482\) | 1.45364 | + | 4.47383i | 0.0662113 | + | 0.203778i | ||||
\(483\) | −36.5019 | − | 26.5201i | −1.66089 | − | 1.20671i | ||||
\(484\) | 0.199847 | + | 0.615066i | 0.00908396 | + | 0.0279575i | ||||
\(485\) | −34.7202 | + | 25.2257i | −1.57656 | + | 1.14544i | ||||
\(486\) | −6.75910 | + | 20.8024i | −0.306599 | + | 0.943615i | ||||
\(487\) | −0.742357 | − | 2.28474i | −0.0336394 | − | 0.103531i | 0.932827 | − | 0.360325i | \(-0.117334\pi\) |
−0.966466 | + | 0.256793i | \(0.917334\pi\) | |||||||
\(488\) | 4.36293 | + | 3.16986i | 0.197501 | + | 0.143493i | ||||
\(489\) | 34.4060 | − | 24.9974i | 1.55589 | − | 1.13042i | ||||
\(490\) | 14.5881 | − | 44.8976i | 0.659024 | − | 2.02827i | ||||
\(491\) | −11.0234 | − | 8.00900i | −0.497481 | − | 0.361441i | 0.310573 | − | 0.950550i | \(-0.399479\pi\) |
−0.808054 | + | 0.589109i | \(0.799479\pi\) | |||||||
\(492\) | −0.871208 | + | 0.632970i | −0.0392771 | + | 0.0285365i | ||||
\(493\) | −1.38106 | − | 1.00340i | −0.0621998 | − | 0.0451908i | ||||
\(494\) | 11.1934 | − | 34.4497i | 0.503614 | − | 1.54996i | ||||
\(495\) | 4.35524 | − | 13.4040i | 0.195753 | − | 0.602467i | ||||
\(496\) | 14.4497 | 0.648813 | ||||||||
\(497\) | −35.7971 | − | 1.85772i | −1.60572 | − | 0.0833301i | ||||
\(498\) | 21.4141 | 0.959589 | ||||||||
\(499\) | 5.35792 | − | 16.4900i | 0.239853 | − | 0.738193i | −0.756587 | − | 0.653893i | \(-0.773135\pi\) |
0.996440 | − | 0.0843000i | \(-0.0268654\pi\) | |||||||
\(500\) | 0.0303052 | − | 0.0932697i | 0.00135529 | − | 0.00417115i | ||||
\(501\) | 35.3198 | + | 25.6613i | 1.57797 | + | 1.14646i | ||||
\(502\) | 6.55214 | − | 4.76041i | 0.292437 | − | 0.212468i | ||||
\(503\) | 7.59835 | + | 5.52053i | 0.338794 | + | 0.246148i | 0.744153 | − | 0.668010i | \(-0.232853\pi\) |
−0.405359 | + | 0.914158i | \(0.632853\pi\) | |||||||
\(504\) | 6.66652 | − | 20.5174i | 0.296950 | − | 0.913919i | ||||
\(505\) | −9.49733 | + | 6.90021i | −0.422626 | + | 0.307055i | ||||
\(506\) | 13.9283 | + | 10.1195i | 0.619188 | + | 0.449866i | ||||
\(507\) | 1.13496 | + | 3.49306i | 0.0504055 | + | 0.155132i | ||||
\(508\) | 0.0655908 | − | 0.201868i | 0.00291012 | − | 0.00895643i | ||||
\(509\) | 22.7231 | − | 16.5093i | 1.00718 | − | 0.731760i | 0.0435656 | − | 0.999051i | \(-0.486128\pi\) |
0.963616 | + | 0.267290i | \(0.0861283\pi\) | |||||||
\(510\) | −4.76123 | − | 14.6536i | −0.210831 | − | 0.648870i | ||||
\(511\) | 23.5795 | + | 17.1315i | 1.04309 | + | 0.757852i | ||||
\(512\) | −7.61490 | − | 23.4362i | −0.336534 | − | 1.03575i | ||||
\(513\) | 5.92053 | + | 18.2215i | 0.261398 | + | 0.804500i | ||||
\(514\) | −8.62379 | − | 26.5413i | −0.380379 | − | 1.17069i | ||||
\(515\) | −11.6056 | + | 8.43193i | −0.511402 | + | 0.371555i | ||||
\(516\) | 0.640537 | − | 1.97137i | 0.0281981 | − | 0.0867847i | ||||
\(517\) | −7.73112 | −0.340014 | ||||||||
\(518\) | 32.3144 | + | 23.4778i | 1.41981 | + | 1.03155i | ||||
\(519\) | −19.5696 | − | 14.2181i | −0.859010 | − | 0.624107i | ||||
\(520\) | 35.0890 | 1.53876 | ||||||||
\(521\) | 0.905965 | + | 2.78827i | 0.0396910 | + | 0.122156i | 0.968939 | − | 0.247301i | \(-0.0795436\pi\) |
−0.929248 | + | 0.369457i | \(0.879544\pi\) | |||||||
\(522\) | −0.746694 | + | 2.29809i | −0.0326819 | + | 0.100585i | ||||
\(523\) | −34.8019 | −1.52178 | −0.760891 | − | 0.648880i | \(-0.775238\pi\) | ||||
−0.760891 | + | 0.648880i | \(0.775238\pi\) | |||||||
\(524\) | −2.35917 | + | 1.71404i | −0.103061 | + | 0.0748780i | ||||
\(525\) | 35.8964 | − | 26.0803i | 1.56665 | − | 1.13824i | ||||
\(526\) | 16.1264 | − | 11.7165i | 0.703144 | − | 0.510864i | ||||
\(527\) | 6.54981 | 0.285314 | ||||||||
\(528\) | −6.41471 | + | 19.7425i | −0.279165 | + | 0.859180i | ||||
\(529\) | 0.764739 | 0.0332495 | ||||||||
\(530\) | 11.6921 | + | 8.49480i | 0.507872 | + | 0.368990i | ||||
\(531\) | −0.712642 | −0.0309260 | ||||||||
\(532\) | −1.39072 | − | 4.28018i | −0.0602952 | − | 0.185569i | ||||
\(533\) | 3.85257 | + | 11.8570i | 0.166874 | + | 0.513584i | ||||
\(534\) | −16.2512 | −0.703259 | ||||||||
\(535\) | −0.510422 | − | 0.370843i | −0.0220675 | − | 0.0160329i | ||||
\(536\) | −28.2531 | −1.22035 | ||||||||
\(537\) | 14.8170 | − | 45.6020i | 0.639401 | − | 1.96787i | ||||
\(538\) | −17.2267 | −0.742696 | ||||||||
\(539\) | −23.3239 | + | 16.9458i | −1.00463 | + | 0.729908i | ||||
\(540\) | −1.06156 | + | 0.771270i | −0.0456824 | + | 0.0331902i | ||||
\(541\) | 20.1847 | − | 14.6650i | 0.867808 | − | 0.630499i | −0.0621900 | − | 0.998064i | \(-0.519808\pi\) |
0.929998 | + | 0.367565i | \(0.119808\pi\) | |||||||
\(542\) | 2.11646 | 0.0909096 | ||||||||
\(543\) | −7.80609 | + | 24.0247i | −0.334991 | + | 1.03100i | ||||
\(544\) | −0.441788 | − | 1.35968i | −0.0189415 | − | 0.0582960i | ||||
\(545\) | −13.8522 | −0.593364 | ||||||||
\(546\) | −39.0090 | − | 28.3417i | −1.66943 | − | 1.21291i | ||||
\(547\) | −22.6668 | − | 16.4684i | −0.969161 | − | 0.704137i | −0.0139006 | − | 0.999903i | \(-0.504425\pi\) |
−0.955260 | + | 0.295767i | \(0.904425\pi\) | |||||||
\(548\) | −2.98800 | −0.127641 | ||||||||
\(549\) | 0.987425 | − | 3.03898i | 0.0421423 | − | 0.129701i | ||||
\(550\) | −13.6973 | + | 9.95164i | −0.584053 | + | 0.424339i | ||||
\(551\) | 2.20326 | + | 6.78093i | 0.0938619 | + | 0.288877i | ||||
\(552\) | 9.58834 | + | 29.5099i | 0.408107 | + | 1.25602i | ||||
\(553\) | −10.9212 | − | 33.6119i | −0.464416 | − | 1.42932i | ||||
\(554\) | 15.2777 | + | 11.0999i | 0.649087 | + | 0.471589i | ||||
\(555\) | 14.5330 | + | 44.7279i | 0.616890 | + | 1.89859i | ||||
\(556\) | −1.91314 | + | 1.38998i | −0.0811352 | + | 0.0589482i | ||||
\(557\) | 4.61095 | − | 14.1910i | 0.195372 | − | 0.601294i | −0.804600 | − | 0.593817i | \(-0.797620\pi\) |
0.999972 | − | 0.00747629i | \(-0.00237980\pi\) | |||||||
\(558\) | −2.86495 | − | 8.81740i | −0.121283 | − | 0.373270i | ||||
\(559\) | −19.4144 | − | 14.1054i | −0.821141 | − | 0.596594i | ||||
\(560\) | −39.5555 | + | 28.7388i | −1.67153 | + | 1.21444i | ||||
\(561\) | −2.90768 | + | 8.94891i | −0.122762 | + | 0.377823i | ||||
\(562\) | 2.63012 | + | 1.91089i | 0.110945 | + | 0.0806062i | ||||
\(563\) | 28.2214 | − | 20.5040i | 1.18939 | − | 0.864142i | 0.196190 | − | 0.980566i | \(-0.437143\pi\) |
0.993200 | + | 0.116424i | \(0.0371432\pi\) | |||||||
\(564\) | −0.796964 | − | 0.579028i | −0.0335582 | − | 0.0243815i | ||||
\(565\) | 12.2597 | − | 37.7316i | 0.515771 | − | 1.58738i | ||||
\(566\) | −0.214636 | + | 0.660583i | −0.00902184 | + | 0.0277664i | ||||
\(567\) | 47.6262 | 2.00011 | ||||||||
\(568\) | 19.1654 | + | 15.5036i | 0.804162 | + | 0.650518i | ||||
\(569\) | 34.1769 | 1.43277 | 0.716386 | − | 0.697704i | \(-0.245795\pi\) | ||||
0.716386 | + | 0.697704i | \(0.245795\pi\) | |||||||
\(570\) | −19.8860 | + | 61.2027i | −0.832931 | + | 2.56350i | ||||
\(571\) | −9.96289 | + | 30.6626i | −0.416934 | + | 1.28319i | 0.493575 | + | 0.869703i | \(0.335690\pi\) |
−0.910510 | + | 0.413488i | \(0.864310\pi\) | |||||||
\(572\) | −1.22567 | − | 0.890500i | −0.0512478 | − | 0.0372337i | ||||
\(573\) | −9.82474 | + | 7.13809i | −0.410434 | + | 0.298198i | ||||
\(574\) | −15.2187 | − | 11.0570i | −0.635217 | − | 0.461512i | ||||
\(575\) | −7.22190 | + | 22.2267i | −0.301174 | + | 0.926918i | ||||
\(576\) | −11.9377 | + | 8.67328i | −0.497406 | + | 0.361387i | ||||
\(577\) | 12.6178 | + | 9.16735i | 0.525285 | + | 0.381642i | 0.818591 | − | 0.574377i | \(-0.194756\pi\) |
−0.293306 | + | 0.956019i | \(0.594756\pi\) | |||||||
\(578\) | −5.97700 | − | 18.3953i | −0.248610 | − | 0.765144i | ||||
\(579\) | 6.49418 | − | 19.9870i | 0.269889 | − | 0.830632i | ||||
\(580\) | −0.395048 | + | 0.287019i | −0.0164035 | + | 0.0119178i | ||||
\(581\) | −9.51840 | − | 29.2946i | −0.394890 | − | 1.21535i | ||||
\(582\) | −32.8112 | − | 23.8387i | −1.36007 | − | 0.988147i | ||||
\(583\) | −2.72737 | − | 8.39397i | −0.112956 | − | 0.347643i | ||||
\(584\) | −6.19388 | − | 19.0628i | −0.256305 | − | 0.788824i | ||||
\(585\) | −6.42473 | − | 19.7733i | −0.265630 | − | 0.817524i | ||||
\(586\) | −7.07050 | + | 5.13702i | −0.292080 | + | 0.212208i | ||||
\(587\) | 12.4939 | − | 38.4522i | 0.515677 | − | 1.58709i | −0.266370 | − | 0.963871i | \(-0.585824\pi\) |
0.782047 | − | 0.623219i | \(-0.214176\pi\) | |||||||
\(588\) | −3.67352 | −0.151493 | ||||||||
\(589\) | −22.1317 | − | 16.0796i | −0.911920 | − | 0.662549i | ||||
\(590\) | 1.41493 | + | 1.02801i | 0.0582518 | + | 0.0423224i | ||||
\(591\) | −2.11595 | −0.0870387 | ||||||||
\(592\) | −7.83883 | − | 24.1254i | −0.322174 | − | 0.991549i | ||||
\(593\) | −11.3245 | + | 34.8533i | −0.465042 | + | 1.43125i | 0.393887 | + | 0.919159i | \(0.371130\pi\) |
−0.858929 | + | 0.512094i | \(0.828870\pi\) | |||||||
\(594\) | −9.73171 | −0.399297 | ||||||||
\(595\) | −17.9298 | + | 13.0268i | −0.735051 | + | 0.534046i | ||||
\(596\) | 0.827161 | − | 0.600967i | 0.0338818 | − | 0.0246166i | ||||
\(597\) | −27.7656 | + | 20.1729i | −1.13637 | + | 0.825622i | ||||
\(598\) | 25.3970 | 1.03856 | ||||||||
\(599\) | −10.9894 | + | 33.8218i | −0.449013 | + | 1.38192i | 0.429009 | + | 0.903300i | \(0.358863\pi\) |
−0.878022 | + | 0.478620i | \(0.841137\pi\) | |||||||
\(600\) | −30.5139 | −1.24572 | ||||||||
\(601\) | 24.4315 | + | 17.7505i | 0.996582 | + | 0.724059i | 0.961353 | − | 0.275320i | \(-0.0887838\pi\) |
0.0352296 | + | 0.999379i | \(0.488784\pi\) | |||||||
\(602\) | 36.2091 | 1.47577 | ||||||||
\(603\) | 5.17308 | + | 15.9211i | 0.210664 | + | 0.648358i | ||||
\(604\) | 0.470791 | + | 1.44894i | 0.0191562 | + | 0.0589567i | ||||
\(605\) | −13.3017 | −0.540789 | ||||||||
\(606\) | −8.97514 | − | 6.52082i | −0.364590 | − | 0.264890i | ||||
\(607\) | 46.6582 | 1.89380 | 0.946898 | − | 0.321533i | \(-0.104198\pi\) | ||||
0.946898 | + | 0.321533i | \(0.104198\pi\) | |||||||
\(608\) | −1.84519 | + | 5.67892i | −0.0748325 | + | 0.230311i | ||||
\(609\) | 9.49098 | 0.384594 | ||||||||
\(610\) | −6.34433 | + | 4.60942i | −0.256874 | + | 0.186630i | ||||
\(611\) | −9.22663 | + | 6.70354i | −0.373269 | + | 0.271196i | ||||
\(612\) | −0.355215 | + | 0.258079i | −0.0143587 | + | 0.0104322i | ||||
\(613\) | 5.57638 | 0.225228 | 0.112614 | − | 0.993639i | \(-0.464078\pi\) | ||||
0.112614 | + | 0.993639i | \(0.464078\pi\) | |||||||
\(614\) | −7.59120 | + | 23.3633i | −0.306356 | + | 0.942867i | ||||
\(615\) | −6.84442 | − | 21.0650i | −0.275994 | − | 0.849421i | ||||
\(616\) | 32.3333 | 1.30274 | ||||||||
\(617\) | 16.5620 | + | 12.0330i | 0.666762 | + | 0.484431i | 0.868940 | − | 0.494918i | \(-0.164802\pi\) |
−0.202177 | + | 0.979349i | \(0.564802\pi\) | |||||||
\(618\) | −10.9674 | − | 7.96832i | −0.441175 | − | 0.320533i | ||||
\(619\) | 29.0786 | 1.16877 | 0.584383 | − | 0.811478i | \(-0.301337\pi\) | ||||
0.584383 | + | 0.811478i | \(0.301337\pi\) | |||||||
\(620\) | 0.578960 | − | 1.78186i | 0.0232516 | − | 0.0715611i | ||||
\(621\) | −10.8678 | + | 7.89589i | −0.436108 | + | 0.316851i | ||||
\(622\) | 5.43648 | + | 16.7318i | 0.217983 | + | 0.670883i | ||||
\(623\) | 7.22354 | + | 22.2318i | 0.289405 | + | 0.890697i | ||||
\(624\) | 9.46281 | + | 29.1235i | 0.378816 | + | 1.16587i | ||||
\(625\) | 21.0242 | + | 15.2750i | 0.840968 | + | 0.610999i | ||||
\(626\) | −1.56942 | − | 4.83018i | −0.0627266 | − | 0.193053i | ||||
\(627\) | 31.7943 | − | 23.0999i | 1.26974 | − | 0.922521i | ||||
\(628\) | 0.431228 | − | 1.32718i | 0.0172079 | − | 0.0529603i | ||||
\(629\) | −3.55320 | − | 10.9356i | −0.141675 | − | 0.436032i | ||||
\(630\) | 25.3794 | + | 18.4392i | 1.01114 | + | 0.734636i | ||||
\(631\) | −0.233735 | + | 0.169818i | −0.00930483 | + | 0.00676036i | −0.592428 | − | 0.805623i | \(-0.701831\pi\) |
0.583123 | + | 0.812384i | \(0.301831\pi\) | |||||||
\(632\) | −7.51058 | + | 23.1152i | −0.298755 | + | 0.919472i | ||||
\(633\) | −33.3455 | − | 24.2269i | −1.32537 | − | 0.962934i | ||||
\(634\) | −23.6195 | + | 17.1606i | −0.938052 | + | 0.681535i | ||||
\(635\) | 3.53190 | + | 2.56608i | 0.140159 | + | 0.101832i | ||||
\(636\) | 0.347522 | − | 1.06956i | 0.0137801 | − | 0.0424109i | ||||
\(637\) | −13.1422 | + | 40.4476i | −0.520714 | + | 1.60259i | ||||
\(638\) | −3.62154 | −0.143378 | ||||||||
\(639\) | 5.22742 | − | 13.6387i | 0.206794 | − | 0.539539i | ||||
\(640\) | 30.8381 | 1.21898 | ||||||||
\(641\) | 6.06671 | − | 18.6714i | 0.239621 | − | 0.737477i | −0.756854 | − | 0.653584i | \(-0.773265\pi\) |
0.996475 | − | 0.0838929i | \(-0.0267354\pi\) | |||||||
\(642\) | 0.184244 | − | 0.567045i | 0.00727153 | − | 0.0223795i | ||||
\(643\) | 6.53321 | + | 4.74666i | 0.257645 | + | 0.187190i | 0.709108 | − | 0.705100i | \(-0.249098\pi\) |
−0.451463 | + | 0.892290i | \(0.649098\pi\) | |||||||
\(644\) | 2.55281 | − | 1.85472i | 0.100595 | − | 0.0730863i | ||||
\(645\) | 34.4913 | + | 25.0594i | 1.35809 | + | 0.986712i | ||||
\(646\) | 4.86197 | − | 14.9636i | 0.191292 | − | 0.588735i | ||||
\(647\) | 14.3021 | − | 10.3910i | 0.562272 | − | 0.408514i | −0.270018 | − | 0.962855i | \(-0.587030\pi\) |
0.832290 | + | 0.554341i | \(0.187030\pi\) | |||||||
\(648\) | −26.4977 | − | 19.2517i | −1.04093 | − | 0.756278i | ||||
\(649\) | −0.330055 | − | 1.01581i | −0.0129558 | − | 0.0398739i | ||||
\(650\) | −7.71793 | + | 23.7534i | −0.302722 | + | 0.931683i | ||||
\(651\) | −29.4607 | + | 21.4044i | −1.15466 | + | 0.838906i | ||||
\(652\) | 0.919097 | + | 2.82869i | 0.0359946 | + | 0.110780i | ||||
\(653\) | −10.1047 | − | 7.34150i | −0.395428 | − | 0.287295i | 0.372248 | − | 0.928133i | \(-0.378587\pi\) |
−0.767676 | + | 0.640838i | \(0.778587\pi\) | |||||||
\(654\) | −4.04522 | − | 12.4499i | −0.158180 | − | 0.486829i | ||||
\(655\) | −18.5342 | − | 57.0424i | −0.724191 | − | 2.22883i | ||||
\(656\) | 3.69176 | + | 11.3621i | 0.144139 | + | 0.443614i | ||||
\(657\) | −9.60813 | + | 6.98072i | −0.374849 | + | 0.272344i | ||||
\(658\) | 5.31764 | − | 16.3660i | 0.207303 | − | 0.638014i | ||||
\(659\) | 8.95269 | 0.348747 | 0.174374 | − | 0.984680i | \(-0.444210\pi\) | ||||
0.174374 | + | 0.984680i | \(0.444210\pi\) | |||||||
\(660\) | 2.17750 | + | 1.58205i | 0.0847592 | + | 0.0615811i | ||||
\(661\) | −19.4196 | − | 14.1092i | −0.755336 | − | 0.548784i | 0.142140 | − | 0.989847i | \(-0.454602\pi\) |
−0.897476 | + | 0.441063i | \(0.854602\pi\) | |||||||
\(662\) | 15.3550 | 0.596788 | ||||||||
\(663\) | 4.28932 | + | 13.2012i | 0.166584 | + | 0.512691i | ||||
\(664\) | −6.54588 | + | 20.1461i | −0.254029 | + | 0.781822i | ||||
\(665\) | 92.5649 | 3.58951 | ||||||||
\(666\) | −13.1674 | + | 9.56669i | −0.510227 | + | 0.370702i | ||||
\(667\) | −4.04431 | + | 2.93836i | −0.156596 | + | 0.113774i | ||||
\(668\) | −2.47013 | + | 1.79466i | −0.0955724 | + | 0.0694374i | ||||
\(669\) | −61.7353 | −2.38683 | ||||||||
\(670\) | 12.6957 | − | 39.0732i | 0.490476 | − | 1.50953i | ||||
\(671\) | 4.78911 | 0.184882 | ||||||||
\(672\) | 6.43051 | + | 4.67204i | 0.248062 | + | 0.180228i | ||||
\(673\) | −5.51593 | −0.212623 | −0.106312 | − | 0.994333i | \(-0.533904\pi\) | ||||
−0.106312 | + | 0.994333i | \(0.533904\pi\) | |||||||
\(674\) | 9.57960 | + | 29.4830i | 0.368993 | + | 1.13564i | ||||
\(675\) | −4.08226 | − | 12.5639i | −0.157126 | − | 0.483585i | ||||
\(676\) | −0.256864 | −0.00987937 | ||||||||
\(677\) | 16.7555 | + | 12.1736i | 0.643967 | + | 0.467869i | 0.861211 | − | 0.508248i | \(-0.169707\pi\) |
−0.217244 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(678\) | 37.4920 | 1.43987 | ||||||||
\(679\) | −18.0272 | + | 55.4820i | −0.691821 | + | 2.12920i | ||||
\(680\) | 15.2413 | 0.584478 | ||||||||
\(681\) | 5.19981 | − | 3.77788i | 0.199257 | − | 0.144769i | ||||
\(682\) | 11.2415 | − | 8.16745i | 0.430460 | − | 0.312748i | ||||
\(683\) | −6.36427 | + | 4.62391i | −0.243522 | + | 0.176929i | −0.702851 | − | 0.711337i | \(-0.748090\pi\) |
0.459329 | + | 0.888266i | \(0.348090\pi\) | |||||||
\(684\) | 1.83384 | 0.0701185 | ||||||||
\(685\) | 18.9913 | − | 58.4491i | 0.725619 | − | 2.23322i | ||||
\(686\) | −7.32111 | − | 22.5321i | −0.279521 | − | 0.860278i | ||||
\(687\) | −41.9075 | −1.59887 | ||||||||
\(688\) | −18.6040 | − | 13.5166i | −0.709270 | − | 0.515315i | ||||
\(689\) | −10.5332 | − | 7.65284i | −0.401284 | − | 0.291550i | ||||
\(690\) | −45.1199 | −1.71769 | ||||||||
\(691\) | 0.374453 | − | 1.15245i | 0.0142449 | − | 0.0438412i | −0.943681 | − | 0.330855i | \(-0.892663\pi\) |
0.957926 | + | 0.287014i | \(0.0926627\pi\) | |||||||
\(692\) | 1.36862 | − | 0.994364i | 0.0520273 | − | 0.0378001i | ||||
\(693\) | −5.92016 | − | 18.2204i | −0.224888 | − | 0.692134i | ||||
\(694\) | −3.89367 | − | 11.9835i | −0.147802 | − | 0.454887i | ||||
\(695\) | −15.0301 | − | 46.2579i | −0.570124 | − | 1.75466i | ||||
\(696\) | −5.28047 | − | 3.83649i | −0.200156 | − | 0.145422i | ||||
\(697\) | 1.67341 | + | 5.15022i | 0.0633849 | + | 0.195079i | ||||
\(698\) | 28.6516 | − | 20.8166i | 1.08448 | − | 0.787921i | ||||
\(699\) | −16.2720 | + | 50.0800i | −0.615463 | + | 1.89420i | ||||
\(700\) | 0.958911 | + | 2.95123i | 0.0362434 | + | 0.111546i | ||||
\(701\) | −11.7317 | − | 8.52359i | −0.443101 | − | 0.321932i | 0.343765 | − | 0.939056i | \(-0.388298\pi\) |
−0.786866 | + | 0.617124i | \(0.788298\pi\) | |||||||
\(702\) | −11.6142 | + | 8.43822i | −0.438350 | + | 0.318480i | ||||
\(703\) | −14.8405 | + | 45.6743i | −0.559719 | + | 1.72264i | ||||
\(704\) | −17.8919 | − | 12.9992i | −0.674325 | − | 0.489926i | ||||
\(705\) | 16.3919 | − | 11.9094i | 0.617354 | − | 0.448534i | ||||
\(706\) | 14.9738 | + | 10.8791i | 0.563548 | + | 0.409441i | ||||
\(707\) | −4.93114 | + | 15.1765i | −0.185455 | + | 0.570771i | ||||
\(708\) | 0.0420558 | − | 0.129434i | 0.00158055 | − | 0.00486444i | ||||
\(709\) | −14.4150 | −0.541365 | −0.270683 | − | 0.962669i | \(-0.587249\pi\) | ||||
−0.270683 | + | 0.962669i | \(0.587249\pi\) | |||||||
\(710\) | −30.0532 | + | 19.5386i | −1.12788 | + | 0.733270i | ||||
\(711\) | 14.4010 | 0.540079 | ||||||||
\(712\) | 4.96769 | − | 15.2890i | 0.186172 | − | 0.572978i | ||||
\(713\) | 5.92711 | − | 18.2418i | 0.221972 | − | 0.683160i | ||||
\(714\) | −16.9440 | − | 12.3105i | −0.634113 | − | 0.460710i | ||||
\(715\) | 25.2094 | − | 18.3157i | 0.942779 | − | 0.684969i | ||||
\(716\) | 2.71293 | + | 1.97106i | 0.101387 | + | 0.0736619i | ||||
\(717\) | −14.3553 | + | 44.1809i | −0.536107 | + | 1.64997i | ||||
\(718\) | −14.8057 | + | 10.7569i | −0.552543 | + | 0.401446i | ||||
\(719\) | 11.5105 | + | 8.36284i | 0.429268 | + | 0.311881i | 0.781356 | − | 0.624086i | \(-0.214528\pi\) |
−0.352088 | + | 0.935967i | \(0.614528\pi\) | |||||||
\(720\) | −6.15654 | − | 18.9479i | −0.229441 | − | 0.706146i | ||||
\(721\) | −6.02576 | + | 18.5454i | −0.224411 | + | 0.690667i | ||||
\(722\) | −32.2686 | + | 23.4445i | −1.20091 | + | 0.872515i | ||||
\(723\) | 2.32655 | + | 7.16037i | 0.0865252 | + | 0.266297i | ||||
\(724\) | −1.42926 | − | 1.03842i | −0.0531181 | − | 0.0385925i | ||||
\(725\) | −1.51917 | − | 4.67551i | −0.0564204 | − | 0.173644i | ||||
\(726\) | −3.88443 | − | 11.9551i | −0.144165 | − | 0.443694i | ||||
\(727\) | 5.41315 | + | 16.6600i | 0.200763 | + | 0.617884i | 0.999861 | + | 0.0166832i | \(0.00531068\pi\) |
−0.799098 | + | 0.601200i | \(0.794689\pi\) | |||||||
\(728\) | 38.5878 | − | 28.0357i | 1.43016 | − | 1.03907i | ||||
\(729\) | −0.439135 | + | 1.35152i | −0.0162643 | + | 0.0500563i | ||||
\(730\) | 29.1466 | 1.07876 | ||||||||
\(731\) | −8.43286 | − | 6.12683i | −0.311900 | − | 0.226609i | ||||
\(732\) | 0.493686 | + | 0.358684i | 0.0182472 | + | 0.0132573i | ||||
\(733\) | −52.1367 | −1.92571 | −0.962857 | − | 0.270013i | \(-0.912972\pi\) | ||||
−0.962857 | + | 0.270013i | \(0.912972\pi\) | |||||||
\(734\) | −2.09283 | − | 6.44107i | −0.0772478 | − | 0.237744i | ||||
\(735\) | 23.3483 | − | 71.8586i | 0.861214 | − | 2.65055i | ||||
\(736\) | −4.18662 | −0.154321 | ||||||||
\(737\) | −20.2982 | + | 14.7475i | −0.747694 | + | 0.543232i | ||||
\(738\) | 6.20130 | − | 4.50551i | 0.228273 | − | 0.165850i | ||||
\(739\) | 10.3657 | − | 7.53112i | 0.381309 | − | 0.277037i | −0.380576 | − | 0.924750i | \(-0.624274\pi\) |
0.761885 | + | 0.647713i | \(0.224274\pi\) | |||||||
\(740\) | −3.28908 | −0.120909 | ||||||||
\(741\) | 17.9150 | − | 55.1367i | 0.658124 | − | 2.02550i | ||||
\(742\) | 19.6452 | 0.721197 | ||||||||
\(743\) | 11.0213 | + | 8.00746i | 0.404333 | + | 0.293765i | 0.771304 | − | 0.636467i | \(-0.219605\pi\) |
−0.366971 | + | 0.930233i | \(0.619605\pi\) | |||||||
\(744\) | 25.0432 | 0.918127 | ||||||||
\(745\) | 6.49837 | + | 19.9999i | 0.238082 | + | 0.732741i | ||||
\(746\) | 8.35523 | + | 25.7148i | 0.305907 | + | 0.941485i | ||||
\(747\) | 12.5512 | 0.459226 | ||||||||
\(748\) | −0.532383 | − | 0.386799i | −0.0194658 | − | 0.0141428i | ||||
\(749\) | −0.857616 | −0.0313366 | ||||||||
\(750\) | −0.589042 | + | 1.81289i | −0.0215088 | + | 0.0661972i | ||||
\(751\) | −7.07488 | −0.258166 | −0.129083 | − | 0.991634i | \(-0.541203\pi\) | ||||
−0.129083 | + | 0.991634i | \(0.541203\pi\) | |||||||
\(752\) | −8.84149 | + | 6.42372i | −0.322416 | + | 0.234249i | ||||
\(753\) | 10.4867 | − | 7.61904i | 0.382157 | − | 0.277653i | ||||
\(754\) | −4.32209 | + | 3.14019i | −0.157401 | + | 0.114359i | ||||
\(755\) | −31.3354 | −1.14041 | ||||||||
\(756\) | −0.551178 | + | 1.69635i | −0.0200461 | + | 0.0616957i | ||||
\(757\) | −14.1831 | − | 43.6512i | −0.515495 | − | 1.58653i | −0.782379 | − | 0.622803i | \(-0.785994\pi\) |
0.266884 | − | 0.963729i | \(-0.414006\pi\) | |||||||
\(758\) | −3.59422 | −0.130548 | ||||||||
\(759\) | 22.2922 | + | 16.1962i | 0.809156 | + | 0.587886i | ||||
\(760\) | −51.5001 | − | 37.4170i | −1.86810 | − | 1.35726i | ||||
\(761\) | 18.8748 | 0.684211 | 0.342105 | − | 0.939662i | \(-0.388860\pi\) | ||||
0.342105 | + | 0.939662i | \(0.388860\pi\) | |||||||
\(762\) | −1.27489 | + | 3.92371i | −0.0461844 | + | 0.142141i | ||||
\(763\) | −15.2335 | + | 11.0678i | −0.551489 | + | 0.400680i | ||||
\(764\) | −0.262451 | − | 0.807742i | −0.00949515 | − | 0.0292231i | ||||
\(765\) | −2.79065 | − | 8.58874i | −0.100896 | − | 0.310527i | ||||
\(766\) | −4.42665 | − | 13.6238i | −0.159941 | − | 0.492249i | ||||
\(767\) | −1.27469 | − | 0.926118i | −0.0460264 | − | 0.0334402i | ||||
\(768\) | −2.44055 | − | 7.51124i | −0.0880658 | − | 0.271039i | ||||
\(769\) | 25.0734 | − | 18.2169i | 0.904168 | − | 0.656917i | −0.0353649 | − | 0.999374i | \(-0.511259\pi\) |
0.939533 | + | 0.342458i | \(0.111259\pi\) | |||||||
\(770\) | −14.5291 | + | 44.7160i | −0.523593 | + | 1.61145i | ||||
\(771\) | −13.8024 | − | 42.4793i | −0.497080 | − | 1.52986i | ||||
\(772\) | 1.18906 | + | 0.863899i | 0.0427950 | + | 0.0310924i | ||||
\(773\) | −15.4968 | + | 11.2591i | −0.557382 | + | 0.404962i | −0.830500 | − | 0.557019i | \(-0.811945\pi\) |
0.273118 | + | 0.961981i | \(0.411945\pi\) | |||||||
\(774\) | −4.55937 | + | 14.0323i | −0.163883 | + | 0.504381i | ||||
\(775\) | 15.2600 | + | 11.0870i | 0.548155 | + | 0.398258i | ||||
\(776\) | 32.4569 | − | 23.5813i | 1.16514 | − | 0.846521i | ||||
\(777\) | 51.7191 | + | 37.5761i | 1.85541 | + | 1.34804i | ||||
\(778\) | 10.6592 | − | 32.8056i | 0.382150 | − | 1.17614i | ||||
\(779\) | 6.98924 | − | 21.5107i | 0.250415 | − | 0.770700i | ||||
\(780\) | 3.97049 | 0.142166 | ||||||||
\(781\) | 21.8618 | + | 1.13454i | 0.782277 | + | 0.0405969i | ||||
\(782\) | 11.0315 | 0.394485 | ||||||||
\(783\) | 0.873210 | − | 2.68746i | 0.0312060 | − | 0.0960421i | ||||
\(784\) | −12.5936 | + | 38.7593i | −0.449773 | + | 1.38426i | ||||
\(785\) | 23.2205 | + | 16.8707i | 0.828776 | + | 0.602141i | ||||
\(786\) | 45.8552 | − | 33.3157i | 1.63560 | − | 1.18833i | ||||
\(787\) | 20.5087 | + | 14.9005i | 0.731057 | + | 0.531144i | 0.889898 | − | 0.456160i | \(-0.150776\pi\) |
−0.158841 | + | 0.987304i | \(0.550776\pi\) | |||||||
\(788\) | 0.0457289 | − | 0.140739i | 0.00162903 | − | 0.00501363i | ||||
\(789\) | 25.8103 | − | 18.7523i | 0.918870 | − | 0.667598i | ||||
\(790\) | −28.5927 | − | 20.7738i | −1.01728 | − | 0.739100i | ||||
\(791\) | −16.6649 | − | 51.2893i | −0.592536 | − | 1.82364i | ||||
\(792\) | −4.07134 | + | 12.5303i | −0.144669 | + | 0.445244i | ||||
\(793\) | 5.71552 | − | 4.15257i | 0.202964 | − | 0.147462i | ||||
\(794\) | −5.18820 | − | 15.9677i | −0.184122 | − | 0.566671i | ||||
\(795\) | 18.7132 | + | 13.5959i | 0.663688 | + | 0.482198i | ||||
\(796\) | −0.741712 | − | 2.28275i | −0.0262893 | − | 0.0809101i | ||||
\(797\) | 16.7231 | + | 51.4685i | 0.592364 | + | 1.82311i | 0.567433 | + | 0.823420i | \(0.307937\pi\) |
0.0249312 | + | 0.999689i | \(0.492063\pi\) | |||||||
\(798\) | 27.0314 | + | 83.1940i | 0.956900 | + | 2.94504i | ||||
\(799\) | −4.00769 | + | 2.91176i | −0.141782 | + | 0.103011i | ||||
\(800\) | 1.27228 | − | 3.91567i | 0.0449818 | − | 0.138440i | ||||
\(801\) | −9.52517 | −0.336555 | ||||||||
\(802\) | −12.3083 | − | 8.94249i | −0.434620 | − | 0.315770i | ||||
\(803\) | −14.4003 | − | 10.4624i | −0.508176 | − | 0.369212i | ||||
\(804\) | −3.19697 | −0.112748 | ||||||||
\(805\) | 20.0555 | + | 61.7244i | 0.706862 | + | 2.17550i | ||||
\(806\) | 6.33422 | − | 19.4947i | 0.223113 | − | 0.686672i | ||||
\(807\) | −27.5713 | −0.970557 | ||||||||
\(808\) | 8.87824 | − | 6.45042i | 0.312335 | − | 0.226925i | ||||
\(809\) | −24.4217 | + | 17.7434i | −0.858623 | + | 0.623826i | −0.927510 | − | 0.373798i | \(-0.878055\pi\) |
0.0688871 | + | 0.997624i | \(0.478055\pi\) | |||||||
\(810\) | 38.5314 | − | 27.9947i | 1.35386 | − | 0.983634i | ||||
\(811\) | 12.6854 | 0.445444 | 0.222722 | − | 0.974882i | \(-0.428506\pi\) | ||||
0.222722 | + | 0.974882i | \(0.428506\pi\) | |||||||
\(812\) | −0.205114 | + | 0.631278i | −0.00719811 | + | 0.0221535i | ||||
\(813\) | 3.38739 | 0.118801 | ||||||||
\(814\) | −19.7348 | − | 14.3382i | −0.691706 | − | 0.502554i | ||||
\(815\) | −61.1743 | −2.14284 | ||||||||
\(816\) | 4.11028 | + | 12.6501i | 0.143889 | + | 0.442843i | ||||
\(817\) | 13.4532 | + | 41.4048i | 0.470670 | + | 1.44857i | ||||
\(818\) | 4.80715 | 0.168078 | ||||||||
\(819\) | −22.8640 | − | 16.6116i | −0.798931 | − | 0.580457i | ||||
\(820\) | 1.54902 | 0.0540942 | ||||||||
\(821\) | −4.01586 | + | 12.3596i | −0.140155 | + | 0.431351i | −0.996356 | − | 0.0852906i | \(-0.972818\pi\) |
0.856202 | + | 0.516642i | \(0.172818\pi\) | |||||||
\(822\) | 58.0779 | 2.02570 | ||||||||
\(823\) | 7.17127 | − | 5.21024i | 0.249975 | − | 0.181617i | −0.455741 | − | 0.890113i | \(-0.650626\pi\) |
0.705716 | + | 0.708495i | \(0.250626\pi\) | |||||||
\(824\) | 10.8490 | − | 7.88229i | 0.377944 | − | 0.274593i | ||||
\(825\) | −21.9225 | + | 15.9276i | −0.763242 | + | 0.554528i | ||||
\(826\) | 2.37738 | 0.0827197 | ||||||||
\(827\) | 14.4672 | − | 44.5256i | 0.503075 | − | 1.54831i | −0.300907 | − | 0.953653i | \(-0.597290\pi\) |
0.803983 | − | 0.594653i | \(-0.202710\pi\) | |||||||
\(828\) | 0.397326 | + | 1.22284i | 0.0138080 | + | 0.0424968i | ||||
\(829\) | −4.81689 | −0.167298 | −0.0836488 | − | 0.996495i | \(-0.526657\pi\) | ||||
−0.0836488 | + | 0.996495i | \(0.526657\pi\) | |||||||
\(830\) | −24.9201 | − | 18.1055i | −0.864991 | − | 0.628453i | ||||
\(831\) | 24.4519 | + | 17.7654i | 0.848228 | + | 0.616274i | ||||
\(832\) | −32.6243 | −1.13104 | ||||||||
\(833\) | −5.70848 | + | 17.5689i | −0.197787 | + | 0.608726i | ||||
\(834\) | 37.1857 | − | 27.0170i | 1.28764 | − | 0.935523i | ||||
\(835\) | −19.4060 | − | 59.7254i | −0.671571 | − | 2.06688i | ||||
\(836\) | 0.849330 | + | 2.61397i | 0.0293747 | + | 0.0904060i | ||||
\(837\) | 3.35037 | + | 10.3114i | 0.115806 | + | 0.356413i | ||||
\(838\) | −22.9618 | − | 16.6827i | −0.793203 | − | 0.576295i | ||||
\(839\) | −1.45521 | − | 4.47866i | −0.0502393 | − | 0.154621i | 0.922789 | − | 0.385305i | \(-0.125904\pi\) |
−0.973029 | + | 0.230684i | \(0.925904\pi\) | |||||||
\(840\) | −68.5545 | + | 49.8078i | −2.36536 | + | 1.71853i | ||||
\(841\) | −8.63654 | + | 26.5805i | −0.297812 | + | 0.916570i | ||||
\(842\) | 11.9955 | + | 36.9183i | 0.413392 | + | 1.27229i | ||||
\(843\) | 4.20950 | + | 3.05838i | 0.144983 | + | 0.105336i | ||||
\(844\) | 2.33206 | − | 1.69434i | 0.0802729 | − | 0.0583217i | ||||
\(845\) | 1.63258 | − | 5.02457i | 0.0561625 | − | 0.172850i | ||||
\(846\) | 5.67283 | + | 4.12155i | 0.195036 | + | 0.141702i | ||||
\(847\) | −14.6280 | + | 10.6279i | −0.502624 | + | 0.365177i | ||||
\(848\) | −10.0936 | − | 7.33340i | −0.346614 | − | 0.251830i | ||||
\(849\) | −0.343526 | + | 1.05726i | −0.0117898 | + | 0.0362852i | ||||
\(850\) | −3.35237 | + | 10.3175i | −0.114985 | + | 0.353889i | ||||
\(851\) | −33.6720 | −1.15426 | ||||||||
\(852\) | 2.16865 | + | 1.75431i | 0.0742969 | + | 0.0601017i | ||||
\(853\) | −38.7893 | −1.32812 | −0.664060 | − | 0.747679i | \(-0.731168\pi\) | ||||
−0.664060 | + | 0.747679i | \(0.731168\pi\) | |||||||
\(854\) | −3.29406 | + | 10.1381i | −0.112720 | + | 0.346918i | ||||
\(855\) | −11.6556 | + | 35.8721i | −0.398612 | + | 1.22680i | ||||
\(856\) | 0.477149 | + | 0.346669i | 0.0163086 | + | 0.0118489i | ||||
\(857\) | −42.6515 | + | 30.9881i | −1.45695 | + | 1.05853i | −0.472802 | + | 0.881169i | \(0.656758\pi\) |
−0.984145 | + | 0.177366i | \(0.943242\pi\) | |||||||
\(858\) | 23.8233 | + | 17.3087i | 0.813316 | + | 0.590908i | ||||
\(859\) | −3.37561 | + | 10.3891i | −0.115174 | + | 0.354470i | −0.991983 | − | 0.126369i | \(-0.959668\pi\) |
0.876809 | + | 0.480839i | \(0.159668\pi\) | |||||||
\(860\) | −2.41219 | + | 1.75256i | −0.0822551 | + | 0.0597618i | ||||
\(861\) | −24.3575 | − | 17.6968i | −0.830103 | − | 0.603105i | ||||
\(862\) | 9.94107 | + | 30.5955i | 0.338594 | + | 1.04209i | ||||
\(863\) | −9.37471 | + | 28.8524i | −0.319119 | + | 0.982147i | 0.654907 | + | 0.755709i | \(0.272708\pi\) |
−0.974026 | + | 0.226437i | \(0.927292\pi\) | |||||||
\(864\) | 1.91457 | − | 1.39101i | 0.0651349 | − | 0.0473233i | ||||
\(865\) | 10.7522 | + | 33.0920i | 0.365587 | + | 1.12516i | ||||
\(866\) | −30.2753 | − | 21.9963i | −1.02879 | − | 0.747463i | ||||
\(867\) | −9.56618 | − | 29.4417i | −0.324885 | − | 0.999892i | ||||
\(868\) | −0.786992 | − | 2.42211i | −0.0267122 | − | 0.0822118i | ||||
\(869\) | 6.66972 | + | 20.5273i | 0.226255 | + | 0.696340i | ||||
\(870\) | 7.67856 | − | 5.57880i | 0.260328 | − | 0.189139i | ||||
\(871\) | −11.4373 | + | 35.2005i | −0.387540 | + | 1.19272i | ||||
\(872\) | 12.9493 | 0.438517 | ||||||||
\(873\) | −19.2313 | − | 13.9724i | −0.650881 | − | 0.472893i | ||||
\(874\) | −37.2751 | − | 27.0820i | −1.26085 | − | 0.916061i | ||||
\(875\) | 2.74186 | 0.0926919 | ||||||||
\(876\) | −0.700867 | − | 2.15705i | −0.0236801 | − | 0.0728798i | ||||
\(877\) | −0.536197 | + | 1.65024i | −0.0181061 | + | 0.0557248i | −0.959701 | − | 0.281022i | \(-0.909327\pi\) |
0.941595 | + | 0.336747i | \(0.109327\pi\) | |||||||
\(878\) | −9.75577 | −0.329241 | ||||||||
\(879\) | −11.3163 | + | 8.22179i | −0.381690 | + | 0.277314i | ||||
\(880\) | 24.1571 | − | 17.5512i | 0.814337 | − | 0.591650i | ||||
\(881\) | 17.0005 | − | 12.3516i | 0.572760 | − | 0.416134i | −0.263347 | − | 0.964701i | \(-0.584826\pi\) |
0.836107 | + | 0.548567i | \(0.184826\pi\) | |||||||
\(882\) | 26.1483 | 0.880459 | ||||||||
\(883\) | 14.5034 | − | 44.6369i | 0.488078 | − | 1.50215i | −0.339394 | − | 0.940644i | \(-0.610222\pi\) |
0.827473 | − | 0.561506i | \(-0.189778\pi\) | |||||||
\(884\) | −0.970754 | −0.0326500 | ||||||||
\(885\) | 2.26460 | + | 1.64533i | 0.0761236 | + | 0.0553070i | ||||
\(886\) | −12.7002 | −0.426671 | ||||||||
\(887\) | 2.05032 | + | 6.31024i | 0.0688431 | + | 0.211877i | 0.979559 | − | 0.201155i | \(-0.0644696\pi\) |
−0.910716 | + | 0.413032i | \(0.864470\pi\) | |||||||
\(888\) | −13.5856 | − | 41.8123i | −0.455904 | − | 1.40313i | ||||
\(889\) | 5.93434 | 0.199031 | ||||||||
\(890\) | 18.9120 | + | 13.7403i | 0.633931 | + | 0.460577i | ||||
\(891\) | −29.0860 | −0.974419 | ||||||||
\(892\) | 1.33419 | − | 4.10623i | 0.0446721 | − | 0.137487i | ||||
\(893\) | 20.6902 | 0.692370 | ||||||||
\(894\) | −16.0775 | + | 11.6810i | −0.537713 | + | 0.390672i | ||||
\(895\) | −55.7993 | + | 40.5405i | −1.86516 | + | 1.35512i | ||||
\(896\) | 33.9131 | − | 24.6393i | 1.13296 | − | 0.823141i | ||||
\(897\) | 40.6479 | 1.35719 | ||||||||
\(898\) | −1.23570 | + | 3.80310i | −0.0412359 | + | 0.126911i | ||||
\(899\) | 1.24680 | + | 3.83726i | 0.0415831 | + | 0.127980i | ||||
\(900\) | −1.26445 | −0.0421483 | ||||||||
\(901\) | −4.57523 | − | 3.32410i | −0.152423 | − | 0.110742i | ||||
\(902\) | 9.29429 | + | 6.75269i | 0.309466 | + | 0.224840i | ||||
\(903\) | 57.9526 | 1.92854 | ||||||||
\(904\) | −11.4606 | + | 35.2721i | −0.381173 | + | 1.17313i | ||||
\(905\) | 29.3969 | − | 21.3581i | 0.977186 | − | 0.709967i | ||||
\(906\) | −9.15077 | − | 28.1632i | −0.304014 | − | 0.935659i | ||||
\(907\) | 12.7624 | + | 39.2786i | 0.423768 | + | 1.30423i | 0.904169 | + | 0.427176i | \(0.140491\pi\) |
−0.480400 | + | 0.877049i | \(0.659509\pi\) | |||||||
\(908\) | 0.138904 | + | 0.427503i | 0.00460969 | + | 0.0141872i | ||||
\(909\) | −5.26051 | − | 3.82198i | −0.174480 | − | 0.126767i | ||||
\(910\) | 21.4330 | + | 65.9639i | 0.710496 | + | 2.18668i | ||||
\(911\) | 22.3677 | − | 16.2511i | 0.741075 | − | 0.538423i | −0.151972 | − | 0.988385i | \(-0.548563\pi\) |
0.893048 | + | 0.449962i | \(0.148563\pi\) | |||||||
\(912\) | 17.1672 | − | 52.8351i | 0.568462 | − | 1.74955i | ||||
\(913\) | 5.81303 | + | 17.8907i | 0.192383 | + | 0.592094i | ||||
\(914\) | 39.0663 | + | 28.3833i | 1.29220 | + | 0.938837i | ||||
\(915\) | −10.1541 | + | 7.37738i | −0.335684 | + | 0.243889i | ||||
\(916\) | 0.905684 | − | 2.78741i | 0.0299247 | − | 0.0920986i | ||||
\(917\) | −65.9584 | − | 47.9216i | −2.17814 | − | 1.58251i | ||||
\(918\) | −5.04476 | + | 3.66523i | −0.166502 | + | 0.120971i | ||||
\(919\) | 28.2965 | + | 20.5586i | 0.933415 | + | 0.678166i | 0.946827 | − | 0.321744i | \(-0.104269\pi\) |
−0.0134112 | + | 0.999910i | \(0.504269\pi\) | |||||||
\(920\) | 13.7923 | − | 42.4483i | 0.454718 | − | 1.39948i | ||||
\(921\) | −12.1497 | + | 37.3930i | −0.400347 | + | 1.23214i | ||||
\(922\) | 42.2463 | 1.39131 | ||||||||
\(923\) | 27.0745 | − | 17.6020i | 0.891167 | − | 0.579378i | ||||
\(924\) | 3.65866 | 0.120361 | ||||||||
\(925\) | 10.2326 | − | 31.4928i | 0.336447 | − | 1.03548i | ||||
\(926\) | −5.82459 | + | 17.9263i | −0.191408 | + | 0.589093i | ||||
\(927\) | −6.42824 | − | 4.67039i | −0.211131 | − | 0.153396i | ||||
\(928\) | 0.712484 | − | 0.517650i | 0.0233884 | − | 0.0169927i | ||||
\(929\) | −24.6643 | − | 17.9196i | −0.809208 | − | 0.587924i | 0.104393 | − | 0.994536i | \(-0.466710\pi\) |
−0.913601 | + | 0.406612i | \(0.866710\pi\) | |||||||
\(930\) | −11.2533 | + | 34.6340i | −0.369009 | + | 1.13569i | ||||
\(931\) | 62.4199 | − | 45.3507i | 2.04573 | − | 1.48631i | ||||
\(932\) | −2.97933 | − | 2.16461i | −0.0975913 | − | 0.0709042i | ||||
\(933\) | 8.70109 | + | 26.7792i | 0.284861 | + | 0.876712i | ||||
\(934\) | −6.06097 | + | 18.6538i | −0.198321 | + | 0.610370i | ||||
\(935\) | 10.9500 | − | 7.95564i | 0.358103 | − | 0.260177i | ||||
\(936\) | 6.00592 | + | 18.4843i | 0.196310 | + | 0.604179i | ||||
\(937\) | −32.0039 | − | 23.2522i | −1.04552 | − | 0.759617i | −0.0741668 | − | 0.997246i | \(-0.523630\pi\) |
−0.971356 | + | 0.237629i | \(0.923630\pi\) | |||||||
\(938\) | −17.2575 | − | 53.1130i | −0.563476 | − | 1.73420i | ||||
\(939\) | −2.51186 | − | 7.73069i | −0.0819713 | − | 0.252282i | ||||
\(940\) | 0.437881 | + | 1.34766i | 0.0142821 | + | 0.0439558i | ||||
\(941\) | 12.3627 | − | 8.98200i | 0.403011 | − | 0.292805i | −0.367755 | − | 0.929923i | \(-0.619874\pi\) |
0.770766 | + | 0.637118i | \(0.219874\pi\) | |||||||
\(942\) | −8.38178 | + | 25.7965i | −0.273093 | + | 0.840494i | ||||
\(943\) | 15.8581 | 0.516411 | ||||||||
\(944\) | −1.22148 | − | 0.887459i | −0.0397559 | − | 0.0288843i | ||||
\(945\) | −29.6795 | − | 21.5634i | −0.965475 | − | 0.701459i | ||||
\(946\) | −22.1134 | −0.718969 | ||||||||
\(947\) | −10.2733 | − | 31.6180i | −0.333838 | − | 1.02745i | −0.967292 | − | 0.253667i | \(-0.918363\pi\) |
0.633454 | − | 0.773781i | \(-0.281637\pi\) | |||||||
\(948\) | −0.849857 | + | 2.61559i | −0.0276021 | + | 0.0849505i | ||||
\(949\) | −26.2577 | −0.852362 | ||||||||
\(950\) | 36.6569 | − | 26.6328i | 1.18931 | − | 0.864081i | ||||
\(951\) | −37.8031 | + | 27.4655i | −1.22585 | + | 0.890631i | ||||
\(952\) | 16.7611 | − | 12.1776i | 0.543229 | − | 0.394679i | ||||
\(953\) | 41.3447 | 1.33929 | 0.669643 | − | 0.742683i | \(-0.266447\pi\) | ||||
0.669643 | + | 0.742683i | \(0.266447\pi\) | |||||||
\(954\) | −2.47368 | + | 7.61319i | −0.0800882 | + | 0.246486i | ||||
\(955\) | 17.4685 | 0.565268 | ||||||||
\(956\) | −2.62839 | − | 1.90963i | −0.0850081 | − | 0.0617620i | ||||
\(957\) | −5.79628 | −0.187367 | ||||||||
\(958\) | −14.6013 | − | 44.9383i | −0.471748 | − | 1.45189i | ||||
\(959\) | −25.8152 | − | 79.4509i | −0.833616 | − | 2.56560i | ||||
\(960\) | 57.9597 | 1.87064 | ||||||||
\(961\) | 12.5554 | + | 9.12206i | 0.405014 | + | 0.294260i | ||||
\(962\) | −35.9848 | −1.16020 | ||||||||
\(963\) | 0.107989 | − | 0.332356i | 0.00347990 | − | 0.0107100i | ||||
\(964\) | −0.526541 | −0.0169587 | ||||||||
\(965\) | −24.4564 | + | 17.7686i | −0.787279 | + | 0.571992i | ||||
\(966\) | −49.6189 | + | 36.0503i | −1.59646 | + | 1.15990i | ||||
\(967\) | −26.2780 | + | 19.0921i | −0.845042 | + | 0.613959i | −0.923775 | − | 0.382937i | \(-0.874913\pi\) |
0.0787323 | + | 0.996896i | \(0.474913\pi\) | |||||||
\(968\) | 12.4346 | 0.399662 | ||||||||
\(969\) | 7.78158 | − | 23.9492i | 0.249980 | − | 0.769360i | ||||
\(970\) | 18.0277 | + | 55.4835i | 0.578834 | + | 1.78147i | ||||
\(971\) | 24.6783 | 0.791965 | 0.395983 | − | 0.918258i | \(-0.370404\pi\) | ||||
0.395983 | + | 0.918258i | \(0.370404\pi\) | |||||||
\(972\) | −1.98072 | − | 1.43908i | −0.0635316 | − | 0.0461584i | ||||
\(973\) | −53.4882 | − | 38.8615i | −1.71475 | − | 1.24584i | ||||
\(974\) | −3.26560 | −0.104637 | ||||||||
\(975\) | −12.3526 | + | 38.0172i | −0.395598 | + | 1.21753i | ||||
\(976\) | 5.47694 | − | 3.97923i | 0.175313 | − | 0.127372i | ||||
\(977\) | 16.9332 | + | 52.1152i | 0.541743 | + | 1.66731i | 0.728611 | + | 0.684927i | \(0.240166\pi\) |
−0.186869 | + | 0.982385i | \(0.559834\pi\) | |||||||
\(978\) | −17.8645 | − | 54.9813i | −0.571244 | − | 1.75811i | ||||
\(979\) | −4.41152 | − | 13.5773i | −0.140993 | − | 0.433931i | ||||
\(980\) | 4.27497 | + | 3.10595i | 0.136559 | + | 0.0992158i | ||||
\(981\) | −2.37098 | − | 7.29714i | −0.0756997 | − | 0.232980i | ||||
\(982\) | −14.9848 | + | 10.8871i | −0.478183 | + | 0.347420i | ||||
\(983\) | −4.75703 | + | 14.6406i | −0.151726 | + | 0.466964i | −0.997814 | − | 0.0660781i | \(-0.978951\pi\) |
0.846089 | + | 0.533042i | \(0.178951\pi\) | |||||||
\(984\) | 6.39826 | + | 19.6918i | 0.203969 | + | 0.627753i | ||||
\(985\) | 2.46239 | + | 1.78903i | 0.0784582 | + | 0.0570032i | ||||
\(986\) | −1.87735 | + | 1.36397i | −0.0597870 | + | 0.0434378i | ||||
\(987\) | 8.51089 | − | 26.1938i | 0.270905 | − | 0.833758i | ||||
\(988\) | 3.28016 | + | 2.38317i | 0.104356 | + | 0.0758188i | ||||
\(989\) | −24.6949 | + | 17.9419i | −0.785251 | + | 0.570518i | ||||
\(990\) | −15.4996 | − | 11.2611i | −0.492609 | − | 0.357901i | ||||
\(991\) | −5.58837 | + | 17.1992i | −0.177520 | + | 0.546351i | −0.999740 | − | 0.0228194i | \(-0.992736\pi\) |
0.822219 | + | 0.569171i | \(0.192736\pi\) | |||||||
\(992\) | −1.04418 | + | 3.21365i | −0.0331526 | + | 0.102033i | ||||
\(993\) | 24.5756 | 0.779885 | ||||||||
\(994\) | −17.4388 | + | 45.4989i | −0.553124 | + | 1.44314i | ||||
\(995\) | 49.3677 | 1.56506 | ||||||||
\(996\) | −0.740697 | + | 2.27963i | −0.0234699 | + | 0.0722329i | ||||
\(997\) | 18.5106 | − | 56.9698i | 0.586237 | − | 1.80425i | −0.00800667 | − | 0.999968i | \(-0.502549\pi\) |
0.594244 | − | 0.804285i | \(-0.297451\pi\) | |||||||
\(998\) | −19.0680 | − | 13.8537i | −0.603586 | − | 0.438531i | ||||
\(999\) | 15.3984 | − | 11.1876i | 0.487184 | − | 0.353960i |
(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 | 71.2.c.a.57.4 | yes | 20 | |
3.2 | odd | 2 | 639.2.f.c.199.2 | 20 | |||
71.5 | even | 5 | inner | 71.2.c.a.5.4 | ✓ | 20 | |
71.17 | odd | 10 | 5041.2.a.j.1.7 | 10 | |||
71.54 | even | 5 | 5041.2.a.i.1.7 | 10 | |||
213.5 | odd | 10 | 639.2.f.c.289.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
71.2.c.a.5.4 | ✓ | 20 | 71.5 | even | 5 | inner | |
71.2.c.a.57.4 | yes | 20 | 1.1 | even | 1 | trivial | |
639.2.f.c.199.2 | 20 | 3.2 | odd | 2 | |||
639.2.f.c.289.2 | 20 | 213.5 | odd | 10 | |||
5041.2.a.i.1.7 | 10 | 71.54 | even | 5 | |||
5041.2.a.j.1.7 | 10 | 71.17 | odd | 10 |