Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.f (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: | \(3.33774680449\) |
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: | \( x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + 7288 x^{12} + 5704 x^{11} + 24392 x^{10} + 10376 x^{9} + 48880 x^{8} + 21224 x^{7} + \cdots + 1936 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 229.2 | ||
Root | \(-0.649220 - 1.99809i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.229 |
Dual form | 418.2.f.h.115.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.951057i | −0.218508 | + | 0.672499i | ||||
\(3\) | −1.69968 | + | 1.23489i | −0.981311 | + | 0.712964i | −0.958001 | − | 0.286764i | \(-0.907420\pi\) |
−0.0233095 | + | 0.999728i | \(0.507420\pi\) | |||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 0.760196 | + | 2.33964i | 0.339970 | + | 1.04632i | 0.964222 | + | 0.265097i | \(0.0854040\pi\) |
−0.624252 | + | 0.781223i | \(0.714596\pi\) | |||||||
\(6\) | −0.649220 | − | 1.99809i | −0.265043 | − | 0.815718i | ||||
\(7\) | 2.50791 | + | 1.82211i | 0.947903 | + | 0.688691i | 0.950310 | − | 0.311306i | \(-0.100766\pi\) |
−0.00240735 | + | 0.999997i | \(0.500766\pi\) | |||||||
\(8\) | 0.809017 | − | 0.587785i | 0.286031 | − | 0.207813i | ||||
\(9\) | 0.436908 | − | 1.34467i | 0.145636 | − | 0.448222i | ||||
\(10\) | −2.46005 | −0.777935 | ||||||||
\(11\) | 3.02483 | + | 1.36030i | 0.912020 | + | 0.410146i | ||||
\(12\) | 2.10092 | 0.606483 | ||||||||
\(13\) | −1.22937 | + | 3.78361i | −0.340966 | + | 1.04938i | 0.622743 | + | 0.782427i | \(0.286018\pi\) |
−0.963708 | + | 0.266958i | \(0.913982\pi\) | |||||||
\(14\) | −2.50791 | + | 1.82211i | −0.670268 | + | 0.486978i | ||||
\(15\) | −4.18129 | − | 3.03789i | −1.07960 | − | 0.784379i | ||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −0.663077 | − | 2.04074i | −0.160820 | − | 0.494953i | 0.837884 | − | 0.545848i | \(-0.183792\pi\) |
−0.998704 | + | 0.0508954i | \(0.983792\pi\) | |||||||
\(18\) | 1.14384 | + | 0.831049i | 0.269606 | + | 0.195880i | ||||
\(19\) | 0.809017 | − | 0.587785i | 0.185601 | − | 0.134847i | ||||
\(20\) | 0.760196 | − | 2.33964i | 0.169985 | − | 0.523160i | ||||
\(21\) | −6.51275 | −1.42120 | ||||||||
\(22\) | −2.22845 | + | 2.45643i | −0.475106 | + | 0.523712i | ||||
\(23\) | −2.55940 | −0.533672 | −0.266836 | − | 0.963742i | \(-0.585978\pi\) | ||||
−0.266836 | + | 0.963742i | \(0.585978\pi\) | |||||||
\(24\) | −0.649220 | + | 1.99809i | −0.132521 | + | 0.407859i | ||||
\(25\) | −0.850949 | + | 0.618250i | −0.170190 | + | 0.123650i | ||||
\(26\) | −3.21853 | − | 2.33840i | −0.631206 | − | 0.458598i | ||||
\(27\) | −1.02975 | − | 3.16925i | −0.198176 | − | 0.609922i | ||||
\(28\) | −0.957938 | − | 2.94823i | −0.181033 | − | 0.557163i | ||||
\(29\) | −5.26156 | − | 3.82275i | −0.977048 | − | 0.709867i | −0.0200009 | − | 0.999800i | \(-0.506367\pi\) |
−0.957047 | + | 0.289933i | \(0.906367\pi\) | |||||||
\(30\) | 4.18129 | − | 3.03789i | 0.763396 | − | 0.554640i | ||||
\(31\) | 0.459307 | − | 1.41360i | 0.0824940 | − | 0.253890i | −0.901299 | − | 0.433197i | \(-0.857385\pi\) |
0.983793 | + | 0.179307i | \(0.0573854\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −6.82106 | + | 1.42325i | −1.18739 | + | 0.247756i | ||||
\(34\) | 2.14576 | 0.367995 | ||||||||
\(35\) | −2.35657 | + | 7.25278i | −0.398333 | + | 1.22594i | ||||
\(36\) | −1.14384 | + | 0.831049i | −0.190640 | + | 0.138508i | ||||
\(37\) | 1.41514 | + | 1.02816i | 0.232648 | + | 0.169029i | 0.698002 | − | 0.716096i | \(-0.254073\pi\) |
−0.465354 | + | 0.885125i | \(0.654073\pi\) | |||||||
\(38\) | 0.309017 | + | 0.951057i | 0.0501292 | + | 0.154282i | ||||
\(39\) | −2.58281 | − | 7.94906i | −0.413580 | − | 1.27287i | ||||
\(40\) | 1.99022 | + | 1.44598i | 0.314681 | + | 0.228629i | ||||
\(41\) | −4.43769 | + | 3.22417i | −0.693051 | + | 0.503531i | −0.877662 | − | 0.479281i | \(-0.840898\pi\) |
0.184610 | + | 0.982812i | \(0.440898\pi\) | |||||||
\(42\) | 2.01255 | − | 6.19400i | 0.310543 | − | 0.955754i | ||||
\(43\) | 4.59472 | 0.700689 | 0.350344 | − | 0.936621i | \(-0.386065\pi\) | ||||
0.350344 | + | 0.936621i | \(0.386065\pi\) | |||||||
\(44\) | −1.64757 | − | 2.87846i | −0.248381 | − | 0.433944i | ||||
\(45\) | 3.47817 | 0.518495 | ||||||||
\(46\) | 0.790899 | − | 2.43414i | 0.116612 | − | 0.358894i | ||||
\(47\) | 2.75579 | − | 2.00220i | 0.401973 | − | 0.292051i | −0.368371 | − | 0.929679i | \(-0.620084\pi\) |
0.770344 | + | 0.637628i | \(0.220084\pi\) | |||||||
\(48\) | −1.69968 | − | 1.23489i | −0.245328 | − | 0.178241i | ||||
\(49\) | 0.806443 | + | 2.48198i | 0.115206 | + | 0.354568i | ||||
\(50\) | −0.325033 | − | 1.00035i | −0.0459667 | − | 0.141471i | ||||
\(51\) | 3.64711 | + | 2.64978i | 0.510698 | + | 0.371044i | ||||
\(52\) | 3.21853 | − | 2.33840i | 0.446330 | − | 0.324278i | ||||
\(53\) | −3.63432 | + | 11.1853i | −0.499212 | + | 1.53642i | 0.311076 | + | 0.950385i | \(0.399311\pi\) |
−0.810288 | + | 0.586032i | \(0.800689\pi\) | |||||||
\(54\) | 3.33234 | 0.453475 | ||||||||
\(55\) | −0.883158 | + | 8.11111i | −0.119085 | + | 1.09370i | ||||
\(56\) | 3.09995 | 0.414249 | ||||||||
\(57\) | −0.649220 | + | 1.99809i | −0.0859913 | + | 0.264654i | ||||
\(58\) | 5.26156 | − | 3.82275i | 0.690877 | − | 0.501952i | ||||
\(59\) | 5.38019 | + | 3.90894i | 0.700441 | + | 0.508900i | 0.880076 | − | 0.474833i | \(-0.157492\pi\) |
−0.179635 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(60\) | 1.59711 | + | 4.91540i | 0.206186 | + | 0.634576i | ||||
\(61\) | −1.95935 | − | 6.03026i | −0.250869 | − | 0.772096i | −0.994616 | − | 0.103634i | \(-0.966953\pi\) |
0.743746 | − | 0.668462i | \(-0.233047\pi\) | |||||||
\(62\) | 1.20248 | + | 0.873654i | 0.152715 | + | 0.110954i | ||||
\(63\) | 3.54585 | − | 2.57621i | 0.446735 | − | 0.324572i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −9.78686 | −1.21391 | ||||||||
\(66\) | 0.754232 | − | 6.92702i | 0.0928395 | − | 0.852658i | ||||
\(67\) | 14.1154 | 1.72447 | 0.862236 | − | 0.506506i | \(-0.169063\pi\) | ||||
0.862236 | + | 0.506506i | \(0.169063\pi\) | |||||||
\(68\) | −0.663077 | + | 2.04074i | −0.0804099 | + | 0.247476i | ||||
\(69\) | 4.35016 | − | 3.16058i | 0.523698 | − | 0.380489i | ||||
\(70\) | −6.16959 | − | 4.48247i | −0.737407 | − | 0.535757i | ||||
\(71\) | −4.93486 | − | 15.1879i | −0.585661 | − | 1.80248i | −0.596602 | − | 0.802538i | \(-0.703483\pi\) |
0.0109410 | − | 0.999940i | \(-0.496517\pi\) | |||||||
\(72\) | −0.436908 | − | 1.34467i | −0.0514901 | − | 0.158470i | ||||
\(73\) | 2.56962 | + | 1.86694i | 0.300752 | + | 0.218509i | 0.727918 | − | 0.685664i | \(-0.240488\pi\) |
−0.427166 | + | 0.904173i | \(0.640488\pi\) | |||||||
\(74\) | −1.41514 | + | 1.02816i | −0.164507 | + | 0.119521i | ||||
\(75\) | 0.682869 | − | 2.10166i | 0.0788509 | − | 0.242678i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 5.10739 | + | 8.92308i | 0.582041 | + | 1.01688i | ||||
\(78\) | 8.35814 | 0.946373 | ||||||||
\(79\) | 2.24244 | − | 6.90153i | 0.252294 | − | 0.776482i | −0.742056 | − | 0.670338i | \(-0.766149\pi\) |
0.994351 | − | 0.106145i | \(-0.0338507\pi\) | |||||||
\(80\) | −1.99022 | + | 1.44598i | −0.222513 | + | 0.161665i | ||||
\(81\) | 9.09544 | + | 6.60822i | 1.01060 | + | 0.734247i | ||||
\(82\) | −1.69505 | − | 5.21682i | −0.187187 | − | 0.576102i | ||||
\(83\) | 3.46611 | + | 10.6676i | 0.380454 | + | 1.17092i | 0.939724 | + | 0.341933i | \(0.111082\pi\) |
−0.559270 | + | 0.828986i | \(0.688918\pi\) | |||||||
\(84\) | 5.26893 | + | 3.82810i | 0.574887 | + | 0.417680i | ||||
\(85\) | 4.27054 | − | 3.10273i | 0.463205 | − | 0.336538i | ||||
\(86\) | −1.41985 | + | 4.36984i | −0.153106 | + | 0.471212i | ||||
\(87\) | 13.6636 | 1.46490 | ||||||||
\(88\) | 3.24670 | − | 0.677442i | 0.346100 | − | 0.0722155i | ||||
\(89\) | −4.63686 | −0.491506 | −0.245753 | − | 0.969332i | \(-0.579035\pi\) | ||||
−0.245753 | + | 0.969332i | \(0.579035\pi\) | |||||||
\(90\) | −1.07481 | + | 3.30794i | −0.113295 | + | 0.348687i | ||||
\(91\) | −9.97729 | + | 7.24893i | −1.04590 | + | 0.759894i | ||||
\(92\) | 2.07060 | + | 1.50438i | 0.215875 | + | 0.156842i | ||||
\(93\) | 0.964967 | + | 2.96986i | 0.100062 | + | 0.307960i | ||||
\(94\) | 1.05262 | + | 3.23963i | 0.108569 | + | 0.334142i | ||||
\(95\) | 1.99022 | + | 1.44598i | 0.204192 | + | 0.148354i | ||||
\(96\) | 1.69968 | − | 1.23489i | 0.173473 | − | 0.126035i | ||||
\(97\) | −1.69057 | + | 5.20305i | −0.171652 | + | 0.528290i | −0.999465 | − | 0.0327144i | \(-0.989585\pi\) |
0.827813 | + | 0.561004i | \(0.189585\pi\) | |||||||
\(98\) | −2.60971 | −0.263620 | ||||||||
\(99\) | 3.15072 | − | 3.47305i | 0.316659 | − | 0.349055i | ||||
\(100\) | 1.05183 | 0.105183 | ||||||||
\(101\) | −1.79382 | + | 5.52081i | −0.178492 | + | 0.549341i | −0.999776 | − | 0.0211787i | \(-0.993258\pi\) |
0.821284 | + | 0.570520i | \(0.193258\pi\) | |||||||
\(102\) | −3.64711 | + | 2.64978i | −0.361118 | + | 0.262367i | ||||
\(103\) | 7.73664 | + | 5.62100i | 0.762313 | + | 0.553853i | 0.899619 | − | 0.436676i | \(-0.143844\pi\) |
−0.137306 | + | 0.990529i | \(0.543844\pi\) | |||||||
\(104\) | 1.22937 | + | 3.78361i | 0.120550 | + | 0.371013i | ||||
\(105\) | −4.95097 | − | 15.2375i | −0.483165 | − | 1.48703i | ||||
\(106\) | −9.51477 | − | 6.91289i | −0.924156 | − | 0.671439i | ||||
\(107\) | 11.7844 | − | 8.56187i | 1.13924 | − | 0.827707i | 0.152228 | − | 0.988345i | \(-0.451355\pi\) |
0.987013 | + | 0.160638i | \(0.0513552\pi\) | |||||||
\(108\) | −1.02975 | + | 3.16925i | −0.0990878 | + | 0.304961i | ||||
\(109\) | −3.38080 | −0.323822 | −0.161911 | − | 0.986805i | \(-0.551766\pi\) | ||||
−0.161911 | + | 0.986805i | \(0.551766\pi\) | |||||||
\(110\) | −7.44122 | − | 3.34641i | −0.709492 | − | 0.319067i | ||||
\(111\) | −3.67496 | −0.348811 | ||||||||
\(112\) | −0.957938 | + | 2.94823i | −0.0905166 | + | 0.278582i | ||||
\(113\) | −9.19594 | + | 6.68124i | −0.865081 | + | 0.628518i | −0.929263 | − | 0.369420i | \(-0.879556\pi\) |
0.0641814 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(114\) | −1.69968 | − | 1.23489i | −0.159190 | − | 0.115658i | ||||
\(115\) | −1.94565 | − | 5.98809i | −0.181433 | − | 0.558392i | ||||
\(116\) | 2.00974 | + | 6.18534i | 0.186600 | + | 0.574294i | ||||
\(117\) | 4.55057 | + | 3.30618i | 0.420700 | + | 0.305656i | ||||
\(118\) | −5.38019 | + | 3.90894i | −0.495287 | + | 0.359847i | ||||
\(119\) | 2.05551 | − | 6.32620i | 0.188428 | − | 0.579922i | ||||
\(120\) | −5.16836 | −0.471805 | ||||||||
\(121\) | 7.29916 | + | 8.22935i | 0.663560 | + | 0.748123i | ||||
\(122\) | 6.34059 | 0.574050 | ||||||||
\(123\) | 3.56116 | − | 10.9601i | 0.321099 | − | 0.988241i | ||||
\(124\) | −1.20248 | + | 0.873654i | −0.107986 | + | 0.0784564i | ||||
\(125\) | 7.85772 | + | 5.70897i | 0.702816 | + | 0.510626i | ||||
\(126\) | 1.35439 | + | 4.16840i | 0.120659 | + | 0.371350i | ||||
\(127\) | −4.12433 | − | 12.6934i | −0.365975 | − | 1.12636i | −0.949368 | − | 0.314166i | \(-0.898275\pi\) |
0.583393 | − | 0.812190i | \(-0.301725\pi\) | |||||||
\(128\) | 0.809017 | + | 0.587785i | 0.0715077 | + | 0.0519534i | ||||
\(129\) | −7.80956 | + | 5.67398i | −0.687593 | + | 0.499566i | ||||
\(130\) | 3.02431 | − | 9.30786i | 0.265249 | − | 0.816353i | ||||
\(131\) | −4.58757 | −0.400818 | −0.200409 | − | 0.979712i | \(-0.564227\pi\) | ||||
−0.200409 | + | 0.979712i | \(0.564227\pi\) | |||||||
\(132\) | 6.35492 | + | 2.85788i | 0.553125 | + | 0.248747i | ||||
\(133\) | 3.09995 | 0.268800 | ||||||||
\(134\) | −4.36190 | + | 13.4246i | −0.376811 | + | 1.15971i | ||||
\(135\) | 6.63210 | − | 4.81850i | 0.570800 | − | 0.414710i | ||||
\(136\) | −1.73596 | − | 1.26125i | −0.148857 | − | 0.108151i | ||||
\(137\) | −4.21408 | − | 12.9696i | −0.360033 | − | 1.10807i | −0.953033 | − | 0.302866i | \(-0.902057\pi\) |
0.593000 | − | 0.805203i | \(-0.297943\pi\) | |||||||
\(138\) | 1.66161 | + | 5.11392i | 0.141446 | + | 0.435326i | ||||
\(139\) | 4.68407 | + | 3.40317i | 0.397297 | + | 0.288653i | 0.768439 | − | 0.639923i | \(-0.221034\pi\) |
−0.371142 | + | 0.928576i | \(0.621034\pi\) | |||||||
\(140\) | 6.16959 | − | 4.48247i | 0.521425 | − | 0.378838i | ||||
\(141\) | −2.21147 | + | 6.80619i | −0.186239 | + | 0.573185i | ||||
\(142\) | 15.9696 | 1.34014 | ||||||||
\(143\) | −8.86548 | + | 9.77245i | −0.741369 | + | 0.817213i | ||||
\(144\) | 1.41386 | 0.117822 | ||||||||
\(145\) | 4.94405 | − | 15.2162i | 0.410581 | − | 1.26364i | ||||
\(146\) | −2.56962 | + | 1.86694i | −0.212663 | + | 0.154509i | ||||
\(147\) | −4.43566 | − | 3.22270i | −0.365847 | − | 0.265804i | ||||
\(148\) | −0.540537 | − | 1.66360i | −0.0444318 | − | 0.136747i | ||||
\(149\) | −3.19841 | − | 9.84368i | −0.262024 | − | 0.806426i | −0.992364 | − | 0.123343i | \(-0.960639\pi\) |
0.730340 | − | 0.683083i | \(-0.239361\pi\) | |||||||
\(150\) | 1.78777 | + | 1.29889i | 0.145971 | + | 0.106054i | ||||
\(151\) | 9.84824 | − | 7.15517i | 0.801438 | − | 0.582279i | −0.109897 | − | 0.993943i | \(-0.535052\pi\) |
0.911336 | + | 0.411664i | \(0.135052\pi\) | |||||||
\(152\) | 0.309017 | − | 0.951057i | 0.0250646 | − | 0.0771409i | ||||
\(153\) | −3.03382 | −0.245270 | ||||||||
\(154\) | −10.0646 | + | 2.10004i | −0.811030 | + | 0.169226i | ||||
\(155\) | 3.65649 | 0.293696 | ||||||||
\(156\) | −2.58281 | + | 7.94906i | −0.206790 | + | 0.636434i | ||||
\(157\) | −3.01269 | + | 2.18885i | −0.240439 | + | 0.174689i | −0.701479 | − | 0.712690i | \(-0.747476\pi\) |
0.461040 | + | 0.887379i | \(0.347476\pi\) | |||||||
\(158\) | 5.87079 | + | 4.26538i | 0.467055 | + | 0.339335i | ||||
\(159\) | −7.63541 | − | 23.4994i | −0.605528 | − | 1.86362i | ||||
\(160\) | −0.760196 | − | 2.33964i | −0.0600988 | − | 0.184965i | ||||
\(161\) | −6.41876 | − | 4.66350i | −0.505869 | − | 0.367535i | ||||
\(162\) | −9.09544 | + | 6.60822i | −0.714605 | + | 0.519191i | ||||
\(163\) | −6.14697 | + | 18.9184i | −0.481468 | + | 1.48181i | 0.355563 | + | 0.934652i | \(0.384289\pi\) |
−0.837032 | + | 0.547155i | \(0.815711\pi\) | |||||||
\(164\) | 5.48529 | 0.428329 | ||||||||
\(165\) | −8.51524 | − | 14.8769i | −0.662911 | − | 1.15817i | ||||
\(166\) | −11.2166 | −0.870573 | ||||||||
\(167\) | −6.79426 | + | 20.9106i | −0.525755 | + | 1.61811i | 0.237062 | + | 0.971495i | \(0.423816\pi\) |
−0.762817 | + | 0.646614i | \(0.776184\pi\) | |||||||
\(168\) | −5.26893 | + | 3.82810i | −0.406507 | + | 0.295344i | ||||
\(169\) | −2.28713 | − | 1.66170i | −0.175933 | − | 0.127823i | ||||
\(170\) | 1.63120 | + | 5.02032i | 0.125107 | + | 0.385041i | ||||
\(171\) | −0.436908 | − | 1.34467i | −0.0334112 | − | 0.102829i | ||||
\(172\) | −3.71721 | − | 2.70071i | −0.283434 | − | 0.205927i | ||||
\(173\) | 20.6153 | − | 14.9779i | 1.56735 | − | 1.13875i | 0.637708 | − | 0.770278i | \(-0.279883\pi\) |
0.929641 | − | 0.368467i | \(-0.120117\pi\) | |||||||
\(174\) | −4.22230 | + | 12.9949i | −0.320092 | + | 0.985141i | ||||
\(175\) | −3.26062 | −0.246480 | ||||||||
\(176\) | −0.359001 | + | 3.29714i | −0.0270607 | + | 0.248531i | ||||
\(177\) | −13.9717 | −1.05018 | ||||||||
\(178\) | 1.43287 | − | 4.40992i | 0.107398 | − | 0.330537i | ||||
\(179\) | −18.4362 | + | 13.3947i | −1.37799 | + | 1.00117i | −0.380922 | + | 0.924607i | \(0.624393\pi\) |
−0.997065 | + | 0.0765594i | \(0.975607\pi\) | |||||||
\(180\) | −2.81390 | − | 2.04442i | −0.209736 | − | 0.152382i | ||||
\(181\) | −0.477575 | − | 1.46983i | −0.0354979 | − | 0.109251i | 0.931738 | − | 0.363132i | \(-0.118293\pi\) |
−0.967235 | + | 0.253881i | \(0.918293\pi\) | |||||||
\(182\) | −3.81099 | − | 11.7290i | −0.282489 | − | 0.869412i | ||||
\(183\) | 10.7770 | + | 7.82993i | 0.796657 | + | 0.578805i | ||||
\(184\) | −2.07060 | + | 1.50438i | −0.152647 | + | 0.110904i | ||||
\(185\) | −1.32975 | + | 4.09254i | −0.0977648 | + | 0.300889i | ||||
\(186\) | −3.12270 | −0.228967 | ||||||||
\(187\) | 0.770330 | − | 7.07488i | 0.0563321 | − | 0.517366i | ||||
\(188\) | −3.40634 | −0.248433 | ||||||||
\(189\) | 3.19218 | − | 9.82452i | 0.232197 | − | 0.714628i | ||||
\(190\) | −1.99022 | + | 1.44598i | −0.144386 | + | 0.104902i | ||||
\(191\) | −5.77965 | − | 4.19916i | −0.418201 | − | 0.303841i | 0.358713 | − | 0.933448i | \(-0.383216\pi\) |
−0.776914 | + | 0.629607i | \(0.783216\pi\) | |||||||
\(192\) | 0.649220 | + | 1.99809i | 0.0468534 | + | 0.144200i | ||||
\(193\) | −3.73849 | − | 11.5059i | −0.269102 | − | 0.828211i | −0.990720 | − | 0.135920i | \(-0.956601\pi\) |
0.721618 | − | 0.692292i | \(-0.243399\pi\) | |||||||
\(194\) | −4.42598 | − | 3.21566i | −0.317767 | − | 0.230871i | ||||
\(195\) | 16.6345 | − | 12.0857i | 1.19122 | − | 0.865474i | ||||
\(196\) | 0.806443 | − | 2.48198i | 0.0576031 | − | 0.177284i | ||||
\(197\) | 18.2516 | 1.30037 | 0.650186 | − | 0.759775i | \(-0.274691\pi\) | ||||
0.650186 | + | 0.759775i | \(0.274691\pi\) | |||||||
\(198\) | 2.32944 | + | 4.06975i | 0.165546 | + | 0.289224i | ||||
\(199\) | 23.9705 | 1.69923 | 0.849613 | − | 0.527406i | \(-0.176835\pi\) | ||||
0.849613 | + | 0.527406i | \(0.176835\pi\) | |||||||
\(200\) | −0.325033 | + | 1.00035i | −0.0229833 | + | 0.0707354i | ||||
\(201\) | −23.9917 | + | 17.4310i | −1.69224 | + | 1.22949i | ||||
\(202\) | −4.69628 | − | 3.41205i | −0.330429 | − | 0.240071i | ||||
\(203\) | −6.23009 | − | 19.1743i | −0.437267 | − | 1.34577i | ||||
\(204\) | −1.39307 | − | 4.28744i | −0.0975346 | − | 0.300181i | ||||
\(205\) | −10.9169 | − | 7.93162i | −0.762472 | − | 0.553968i | ||||
\(206\) | −7.73664 | + | 5.62100i | −0.539037 | + | 0.391633i | ||||
\(207\) | −1.11822 | + | 3.44154i | −0.0777219 | + | 0.239203i | ||||
\(208\) | −3.97832 | −0.275847 | ||||||||
\(209\) | 3.24670 | − | 0.677442i | 0.224579 | − | 0.0468596i | ||||
\(210\) | 16.0217 | 1.10560 | ||||||||
\(211\) | 6.41106 | − | 19.7312i | 0.441356 | − | 1.35835i | −0.445076 | − | 0.895493i | \(-0.646823\pi\) |
0.886431 | − | 0.462860i | \(-0.153177\pi\) | |||||||
\(212\) | 9.51477 | − | 6.91289i | 0.653477 | − | 0.474779i | ||||
\(213\) | 27.1431 | + | 19.7206i | 1.85982 | + | 1.35124i | ||||
\(214\) | 4.50124 | + | 13.8534i | 0.307699 | + | 0.946999i | ||||
\(215\) | 3.49289 | + | 10.7500i | 0.238213 | + | 0.733145i | ||||
\(216\) | −2.69592 | − | 1.95870i | −0.183434 | − | 0.133273i | ||||
\(217\) | 3.72763 | − | 2.70828i | 0.253048 | − | 0.183850i | ||||
\(218\) | 1.04472 | − | 3.21533i | 0.0707577 | − | 0.217770i | ||||
\(219\) | −6.67300 | −0.450920 | ||||||||
\(220\) | 5.48208 | − | 6.04292i | 0.369602 | − | 0.407414i | ||||
\(221\) | 8.53654 | 0.574230 | ||||||||
\(222\) | 1.13562 | − | 3.49509i | 0.0762181 | − | 0.234575i | ||||
\(223\) | −22.9636 | + | 16.6840i | −1.53775 | + | 1.11724i | −0.586028 | + | 0.810290i | \(0.699309\pi\) |
−0.951725 | + | 0.306953i | \(0.900691\pi\) | |||||||
\(224\) | −2.50791 | − | 1.82211i | −0.167567 | − | 0.121745i | ||||
\(225\) | 0.459553 | + | 1.41436i | 0.0306369 | + | 0.0942906i | ||||
\(226\) | −3.51254 | − | 10.8105i | −0.233650 | − | 0.719102i | ||||
\(227\) | 6.88177 | + | 4.99990i | 0.456759 | + | 0.331855i | 0.792259 | − | 0.610185i | \(-0.208905\pi\) |
−0.335499 | + | 0.942040i | \(0.608905\pi\) | |||||||
\(228\) | 1.69968 | − | 1.23489i | 0.112564 | − | 0.0817826i | ||||
\(229\) | −0.527586 | + | 1.62374i | −0.0348638 | + | 0.107300i | −0.966974 | − | 0.254875i | \(-0.917966\pi\) |
0.932110 | + | 0.362175i | \(0.117966\pi\) | |||||||
\(230\) | 6.29625 | 0.415162 | ||||||||
\(231\) | −19.6999 | − | 8.85931i | −1.29616 | − | 0.582900i | ||||
\(232\) | −6.50365 | −0.426986 | ||||||||
\(233\) | 3.07667 | − | 9.46902i | 0.201559 | − | 0.620336i | −0.798278 | − | 0.602289i | \(-0.794255\pi\) |
0.999837 | − | 0.0180465i | \(-0.00574470\pi\) | |||||||
\(234\) | −4.55057 | + | 3.30618i | −0.297480 | + | 0.216132i | ||||
\(235\) | 6.77937 | + | 4.92550i | 0.442237 | + | 0.321304i | ||||
\(236\) | −2.05505 | − | 6.32479i | −0.133772 | − | 0.411709i | ||||
\(237\) | 4.71119 | + | 14.4996i | 0.306025 | + | 0.941847i | ||||
\(238\) | 5.38139 | + | 3.90981i | 0.348824 | + | 0.253435i | ||||
\(239\) | −13.1696 | + | 9.56830i | −0.851873 | + | 0.618922i | −0.925662 | − | 0.378352i | \(-0.876491\pi\) |
0.0737888 | + | 0.997274i | \(0.476491\pi\) | |||||||
\(240\) | 1.59711 | − | 4.91540i | 0.103093 | − | 0.317288i | ||||
\(241\) | −5.95144 | −0.383366 | −0.191683 | − | 0.981457i | \(-0.561395\pi\) | ||||
−0.191683 | + | 0.981457i | \(0.561395\pi\) | |||||||
\(242\) | −10.0821 | + | 4.39890i | −0.648105 | + | 0.282772i | ||||
\(243\) | −13.6227 | −0.873899 | ||||||||
\(244\) | −1.95935 | + | 6.03026i | −0.125435 | + | 0.386048i | ||||
\(245\) | −5.19389 | + | 3.77358i | −0.331825 | + | 0.241085i | ||||
\(246\) | 9.32324 | + | 6.77373i | 0.594428 | + | 0.431877i | ||||
\(247\) | 1.22937 | + | 3.78361i | 0.0782229 | + | 0.240745i | ||||
\(248\) | −0.459307 | − | 1.41360i | −0.0291660 | − | 0.0897638i | ||||
\(249\) | −19.0645 | − | 13.8512i | −1.20817 | − | 0.877784i | ||||
\(250\) | −7.85772 | + | 5.70897i | −0.496966 | + | 0.361067i | ||||
\(251\) | −6.50772 | + | 20.0287i | −0.410764 | + | 1.26420i | 0.505222 | + | 0.862989i | \(0.331411\pi\) |
−0.915986 | + | 0.401211i | \(0.868589\pi\) | |||||||
\(252\) | −4.38291 | −0.276098 | ||||||||
\(253\) | −7.74175 | − | 3.48156i | −0.486719 | − | 0.218884i | ||||
\(254\) | 13.3466 | 0.837441 | ||||||||
\(255\) | −3.42702 | + | 10.5473i | −0.214609 | + | 0.660497i | ||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | −1.03343 | − | 0.750828i | −0.0644633 | − | 0.0468353i | 0.555087 | − | 0.831792i | \(-0.312685\pi\) |
−0.619550 | + | 0.784957i | \(0.712685\pi\) | |||||||
\(258\) | −2.98299 | − | 9.18068i | −0.185713 | − | 0.571564i | ||||
\(259\) | 1.67564 | + | 5.15708i | 0.104119 | + | 0.320446i | ||||
\(260\) | 7.91773 | + | 5.75257i | 0.491037 | + | 0.356759i | ||||
\(261\) | −7.43914 | + | 5.40485i | −0.460471 | + | 0.334552i | ||||
\(262\) | 1.41764 | − | 4.36304i | 0.0875820 | − | 0.269550i | ||||
\(263\) | 8.85896 | 0.546267 | 0.273134 | − | 0.961976i | \(-0.411940\pi\) | ||||
0.273134 | + | 0.961976i | \(0.411940\pi\) | |||||||
\(264\) | −4.68179 | + | 5.16075i | −0.288144 | + | 0.317622i | ||||
\(265\) | −28.9324 | −1.77730 | ||||||||
\(266\) | −0.957938 | + | 2.94823i | −0.0587349 | + | 0.180768i | ||||
\(267\) | 7.88118 | − | 5.72601i | 0.482320 | − | 0.350426i | ||||
\(268\) | −11.4196 | − | 8.29684i | −0.697564 | − | 0.506810i | ||||
\(269\) | 8.04167 | + | 24.7497i | 0.490309 | + | 1.50902i | 0.824141 | + | 0.566384i | \(0.191658\pi\) |
−0.333832 | + | 0.942633i | \(0.608342\pi\) | |||||||
\(270\) | 2.53324 | + | 7.79650i | 0.154168 | + | 0.474480i | ||||
\(271\) | −13.8201 | − | 10.0409i | −0.839514 | − | 0.609942i | 0.0827211 | − | 0.996573i | \(-0.473639\pi\) |
−0.922235 | + | 0.386630i | \(0.873639\pi\) | |||||||
\(272\) | 1.73596 | − | 1.26125i | 0.105258 | − | 0.0764744i | ||||
\(273\) | 8.00658 | − | 24.6417i | 0.484580 | − | 1.49138i | ||||
\(274\) | 13.6371 | 0.823845 | ||||||||
\(275\) | −3.41498 | + | 0.712554i | −0.205931 | + | 0.0429686i | ||||
\(276\) | −5.37710 | −0.323663 | ||||||||
\(277\) | 2.62481 | − | 8.07834i | 0.157710 | − | 0.485380i | −0.840716 | − | 0.541477i | \(-0.817865\pi\) |
0.998425 | + | 0.0560965i | \(0.0178655\pi\) | |||||||
\(278\) | −4.68407 | + | 3.40317i | −0.280932 | + | 0.204109i | ||||
\(279\) | −1.70015 | − | 1.23523i | −0.101785 | − | 0.0739512i | ||||
\(280\) | 2.35657 | + | 7.25278i | 0.140832 | + | 0.433437i | ||||
\(281\) | 9.09244 | + | 27.9837i | 0.542410 | + | 1.66937i | 0.727070 | + | 0.686563i | \(0.240881\pi\) |
−0.184660 | + | 0.982802i | \(0.559119\pi\) | |||||||
\(282\) | −5.78969 | − | 4.20646i | −0.344771 | − | 0.250491i | ||||
\(283\) | 13.8010 | − | 10.0270i | 0.820382 | − | 0.596043i | −0.0964396 | − | 0.995339i | \(-0.530745\pi\) |
0.916822 | + | 0.399296i | \(0.130745\pi\) | |||||||
\(284\) | −4.93486 | + | 15.1879i | −0.292830 | + | 0.901239i | ||||
\(285\) | −5.16836 | −0.306147 | ||||||||
\(286\) | −6.55457 | − | 11.4514i | −0.387580 | − | 0.677137i | ||||
\(287\) | −17.0041 | −1.00372 | ||||||||
\(288\) | −0.436908 | + | 1.34467i | −0.0257451 | + | 0.0792351i | ||||
\(289\) | 10.0283 | − | 7.28601i | 0.589902 | − | 0.428589i | ||||
\(290\) | 12.9437 | + | 9.40414i | 0.760080 | + | 0.552230i | ||||
\(291\) | −3.55176 | − | 10.9312i | −0.208208 | − | 0.640798i | ||||
\(292\) | −0.981508 | − | 3.02077i | −0.0574384 | − | 0.176777i | ||||
\(293\) | −16.5964 | − | 12.0580i | −0.969569 | − | 0.704433i | −0.0142160 | − | 0.999899i | \(-0.504525\pi\) |
−0.955353 | + | 0.295466i | \(0.904525\pi\) | |||||||
\(294\) | 4.43566 | − | 3.22270i | 0.258693 | − | 0.187952i | ||||
\(295\) | −5.05552 | + | 15.5593i | −0.294344 | + | 0.905897i | ||||
\(296\) | 1.74921 | 0.101671 | ||||||||
\(297\) | 1.19631 | − | 10.9872i | 0.0694171 | − | 0.637542i | ||||
\(298\) | 10.3503 | 0.599575 | ||||||||
\(299\) | 3.14645 | − | 9.68377i | 0.181964 | − | 0.560027i | ||||
\(300\) | −1.78777 | + | 1.29889i | −0.103217 | + | 0.0749917i | ||||
\(301\) | 11.5232 | + | 8.37207i | 0.664184 | + | 0.482558i | ||||
\(302\) | 3.76169 | + | 11.5773i | 0.216461 | + | 0.666199i | ||||
\(303\) | −3.76867 | − | 11.5988i | −0.216504 | − | 0.666332i | ||||
\(304\) | 0.809017 | + | 0.587785i | 0.0464003 | + | 0.0337118i | ||||
\(305\) | 12.6192 | − | 9.16836i | 0.722571 | − | 0.524979i | ||||
\(306\) | 0.937502 | − | 2.88533i | 0.0535934 | − | 0.164944i | ||||
\(307\) | 5.64603 | 0.322236 | 0.161118 | − | 0.986935i | \(-0.448490\pi\) | ||||
0.161118 | + | 0.986935i | \(0.448490\pi\) | |||||||
\(308\) | 1.11288 | − | 10.2210i | 0.0634125 | − | 0.582394i | ||||
\(309\) | −20.0911 | −1.14294 | ||||||||
\(310\) | −1.12992 | + | 3.47753i | −0.0641749 | + | 0.197510i | ||||
\(311\) | −6.80879 | + | 4.94688i | −0.386091 | + | 0.280512i | −0.763852 | − | 0.645392i | \(-0.776694\pi\) |
0.377761 | + | 0.925903i | \(0.376694\pi\) | |||||||
\(312\) | −6.76187 | − | 4.91279i | −0.382816 | − | 0.278132i | ||||
\(313\) | 9.69591 | + | 29.8409i | 0.548045 | + | 1.68671i | 0.713638 | + | 0.700515i | \(0.247046\pi\) |
−0.165593 | + | 0.986194i | \(0.552954\pi\) | |||||||
\(314\) | −1.15074 | − | 3.54163i | −0.0649403 | − | 0.199866i | ||||
\(315\) | 8.72296 | + | 6.33760i | 0.491483 | + | 0.357083i | ||||
\(316\) | −5.87079 | + | 4.26538i | −0.330258 | + | 0.239946i | ||||
\(317\) | 2.22582 | − | 6.85036i | 0.125014 | − | 0.384755i | −0.868889 | − | 0.495006i | \(-0.835166\pi\) |
0.993904 | + | 0.110252i | \(0.0351657\pi\) | |||||||
\(318\) | 24.7087 | 1.38560 | ||||||||
\(319\) | −10.7152 | − | 18.7205i | −0.599938 | − | 1.04815i | ||||
\(320\) | 2.46005 | 0.137521 | ||||||||
\(321\) | −9.45675 | + | 29.1049i | −0.527824 | + | 1.62448i | ||||
\(322\) | 6.41876 | − | 4.66350i | 0.357703 | − | 0.259887i | ||||
\(323\) | −1.73596 | − | 1.26125i | −0.0965914 | − | 0.0701777i | ||||
\(324\) | −3.47415 | − | 10.6923i | −0.193008 | − | 0.594018i | ||||
\(325\) | −1.29309 | − | 3.97971i | −0.0717276 | − | 0.220755i | ||||
\(326\) | −16.0930 | − | 11.6922i | −0.891308 | − | 0.647573i | ||||
\(327\) | 5.74628 | − | 4.17492i | 0.317770 | − | 0.230873i | ||||
\(328\) | −1.69505 | + | 5.21682i | −0.0935934 | + | 0.288051i | ||||
\(329\) | 10.5595 | 0.582164 | ||||||||
\(330\) | 16.7801 | − | 3.50126i | 0.923716 | − | 0.192738i | ||||
\(331\) | 20.4083 | 1.12174 | 0.560870 | − | 0.827904i | \(-0.310467\pi\) | ||||
0.560870 | + | 0.827904i | \(0.310467\pi\) | |||||||
\(332\) | 3.46611 | − | 10.6676i | 0.190227 | − | 0.585459i | ||||
\(333\) | 2.00082 | − | 1.45368i | 0.109644 | − | 0.0796612i | ||||
\(334\) | −17.7876 | − | 12.9234i | −0.973294 | − | 0.707139i | ||||
\(335\) | 10.7305 | + | 33.0250i | 0.586269 | + | 1.80435i | ||||
\(336\) | −2.01255 | − | 6.19400i | −0.109794 | − | 0.337910i | ||||
\(337\) | 25.9791 | + | 18.8749i | 1.41517 | + | 1.02818i | 0.992545 | + | 0.121877i | \(0.0388912\pi\) |
0.422625 | + | 0.906305i | \(0.361109\pi\) | |||||||
\(338\) | 2.28713 | − | 1.66170i | 0.124403 | − | 0.0903843i | ||||
\(339\) | 7.37956 | − | 22.7119i | 0.400803 | − | 1.23354i | ||||
\(340\) | −5.27868 | −0.286277 | ||||||||
\(341\) | 3.31225 | − | 3.65110i | 0.179368 | − | 0.197718i | ||||
\(342\) | 1.41386 | 0.0764530 | ||||||||
\(343\) | 4.20563 | − | 12.9436i | 0.227083 | − | 0.698889i | ||||
\(344\) | 3.71721 | − | 2.70071i | 0.200418 | − | 0.145613i | ||||
\(345\) | 10.7016 | + | 7.77517i | 0.576155 | + | 0.418601i | ||||
\(346\) | 7.87433 | + | 24.2347i | 0.423326 | + | 1.30286i | ||||
\(347\) | 0.349090 | + | 1.07439i | 0.0187401 | + | 0.0576762i | 0.959989 | − | 0.280037i | \(-0.0903467\pi\) |
−0.941249 | + | 0.337713i | \(0.890347\pi\) | |||||||
\(348\) | −11.0541 | − | 8.03129i | −0.592563 | − | 0.430522i | ||||
\(349\) | 17.1155 | − | 12.4351i | 0.916171 | − | 0.665637i | −0.0263972 | − | 0.999652i | \(-0.508403\pi\) |
0.942568 | + | 0.334015i | \(0.108403\pi\) | |||||||
\(350\) | 1.00759 | − | 3.10104i | 0.0538579 | − | 0.165757i | ||||
\(351\) | 13.2571 | 0.707614 | ||||||||
\(352\) | −3.02483 | − | 1.36030i | −0.161224 | − | 0.0725043i | ||||
\(353\) | −0.0272714 | −0.00145151 | −0.000725755 | − | 1.00000i | \(-0.500231\pi\) | ||||
−0.000725755 | 1.00000i | \(0.500231\pi\) | ||||||||
\(354\) | 4.31749 | − | 13.2879i | 0.229472 | − | 0.706243i | ||||
\(355\) | 31.7829 | − | 23.0916i | 1.68686 | − | 1.22558i | ||||
\(356\) | 3.75130 | + | 2.72548i | 0.198818 | + | 0.144450i | ||||
\(357\) | 4.31846 | + | 13.2908i | 0.228557 | + | 0.703426i | ||||
\(358\) | −7.04201 | − | 21.6731i | −0.372182 | − | 1.14546i | ||||
\(359\) | −12.2286 | − | 8.88459i | −0.645400 | − | 0.468911i | 0.216301 | − | 0.976327i | \(-0.430601\pi\) |
−0.861701 | + | 0.507416i | \(0.830601\pi\) | |||||||
\(360\) | 2.81390 | − | 2.04442i | 0.148306 | − | 0.107750i | ||||
\(361\) | 0.309017 | − | 0.951057i | 0.0162641 | − | 0.0500556i | ||||
\(362\) | 1.54547 | 0.0812279 | ||||||||
\(363\) | −22.5686 | − | 4.97361i | −1.18454 | − | 0.261047i | ||||
\(364\) | 12.3326 | 0.646404 | ||||||||
\(365\) | −2.41456 | + | 7.43124i | −0.126384 | + | 0.388969i | ||||
\(366\) | −10.7770 | + | 7.82993i | −0.563322 | + | 0.409277i | ||||
\(367\) | −17.3707 | − | 12.6206i | −0.906744 | − | 0.658788i | 0.0334451 | − | 0.999441i | \(-0.489352\pi\) |
−0.940189 | + | 0.340652i | \(0.889352\pi\) | |||||||
\(368\) | −0.790899 | − | 2.43414i | −0.0412284 | − | 0.126888i | ||||
\(369\) | 2.39657 | + | 7.37588i | 0.124760 | + | 0.383973i | ||||
\(370\) | −3.48132 | − | 2.52933i | −0.180985 | − | 0.131493i | ||||
\(371\) | −29.4953 | + | 21.4296i | −1.53132 | + | 1.11257i | ||||
\(372\) | 0.964967 | − | 2.96986i | 0.0500312 | − | 0.153980i | ||||
\(373\) | −18.3417 | −0.949697 | −0.474848 | − | 0.880068i | \(-0.657497\pi\) | ||||
−0.474848 | + | 0.880068i | \(0.657497\pi\) | |||||||
\(374\) | 6.49056 | + | 2.91889i | 0.335619 | + | 0.150932i | ||||
\(375\) | −20.4056 | −1.05374 | ||||||||
\(376\) | 1.05262 | − | 3.23963i | 0.0542846 | − | 0.167071i | ||||
\(377\) | 20.9322 | − | 15.2081i | 1.07806 | − | 0.783258i | ||||
\(378\) | 8.35723 | + | 6.07188i | 0.429850 | + | 0.312304i | ||||
\(379\) | 3.80809 | + | 11.7201i | 0.195609 | + | 0.602021i | 0.999969 | + | 0.00787967i | \(0.00250820\pi\) |
−0.804360 | + | 0.594142i | \(0.797492\pi\) | |||||||
\(380\) | −0.760196 | − | 2.33964i | −0.0389972 | − | 0.120021i | ||||
\(381\) | 22.6850 | + | 16.4816i | 1.16219 | + | 0.844378i | ||||
\(382\) | 5.77965 | − | 4.19916i | 0.295713 | − | 0.214848i | ||||
\(383\) | 8.88446 | − | 27.3436i | 0.453975 | − | 1.39719i | −0.418360 | − | 0.908281i | \(-0.637395\pi\) |
0.872335 | − | 0.488909i | \(-0.162605\pi\) | |||||||
\(384\) | −2.10092 | −0.107212 | ||||||||
\(385\) | −16.9942 | + | 18.7328i | −0.866104 | + | 0.954710i | ||||
\(386\) | 12.0980 | 0.615772 | ||||||||
\(387\) | 2.00747 | − | 6.17836i | 0.102046 | − | 0.314064i | ||||
\(388\) | 4.42598 | − | 3.21566i | 0.224695 | − | 0.163251i | ||||
\(389\) | −2.20852 | − | 1.60458i | −0.111976 | − | 0.0813556i | 0.530388 | − | 0.847755i | \(-0.322046\pi\) |
−0.642364 | + | 0.766400i | \(0.722046\pi\) | |||||||
\(390\) | 6.35382 | + | 19.5551i | 0.321738 | + | 0.990209i | ||||
\(391\) | 1.69708 | + | 5.22308i | 0.0858251 | + | 0.264142i | ||||
\(392\) | 2.11130 | + | 1.53395i | 0.106637 | + | 0.0774760i | ||||
\(393\) | 7.79741 | − | 5.66515i | 0.393327 | − | 0.285769i | ||||
\(394\) | −5.64005 | + | 17.3583i | −0.284142 | + | 0.874498i | ||||
\(395\) | 17.8518 | 0.898222 | ||||||||
\(396\) | −4.59040 | + | 0.957811i | −0.230676 | + | 0.0481318i | ||||
\(397\) | 7.21330 | 0.362025 | 0.181013 | − | 0.983481i | \(-0.442062\pi\) | ||||
0.181013 | + | 0.983481i | \(0.442062\pi\) | |||||||
\(398\) | −7.40730 | + | 22.7973i | −0.371295 | + | 1.14273i | ||||
\(399\) | −5.26893 | + | 3.82810i | −0.263776 | + | 0.191645i | ||||
\(400\) | −0.850949 | − | 0.618250i | −0.0425474 | − | 0.0309125i | ||||
\(401\) | −0.367672 | − | 1.13158i | −0.0183607 | − | 0.0565083i | 0.941456 | − | 0.337135i | \(-0.109458\pi\) |
−0.959817 | + | 0.280626i | \(0.909458\pi\) | |||||||
\(402\) | −9.16401 | − | 28.2039i | −0.457059 | − | 1.40668i | ||||
\(403\) | 4.78386 | + | 3.47568i | 0.238301 | + | 0.173136i | ||||
\(404\) | 4.69628 | − | 3.41205i | 0.233649 | − | 0.169756i | ||||
\(405\) | −8.54657 | + | 26.3036i | −0.424682 | + | 1.30704i | ||||
\(406\) | 20.1610 | 1.00057 | ||||||||
\(407\) | 2.88195 | + | 5.03503i | 0.142853 | + | 0.249577i | ||||
\(408\) | 4.50808 | 0.223183 | ||||||||
\(409\) | 3.63996 | − | 11.2026i | 0.179984 | − | 0.553935i | −0.819842 | − | 0.572591i | \(-0.805939\pi\) |
0.999826 | + | 0.0186553i | \(0.00593851\pi\) | |||||||
\(410\) | 10.9169 | − | 7.93162i | 0.539149 | − | 0.391715i | ||||
\(411\) | 23.1786 | + | 16.8403i | 1.14332 | + | 0.830669i | ||||
\(412\) | −2.95513 | − | 9.09496i | −0.145589 | − | 0.448077i | ||||
\(413\) | 6.37056 | + | 19.6066i | 0.313475 | + | 0.964776i | ||||
\(414\) | −2.92755 | − | 2.12699i | −0.143881 | − | 0.104536i | ||||
\(415\) | −22.3234 | + | 16.2189i | −1.09581 | + | 0.796155i | ||||
\(416\) | 1.22937 | − | 3.78361i | 0.0602748 | − | 0.185507i | ||||
\(417\) | −12.1640 | −0.595672 | ||||||||
\(418\) | −0.359001 | + | 3.29714i | −0.0175593 | + | 0.161268i | ||||
\(419\) | 20.0798 | 0.980963 | 0.490482 | − | 0.871452i | \(-0.336821\pi\) | ||||
0.490482 | + | 0.871452i | \(0.336821\pi\) | |||||||
\(420\) | −4.95097 | + | 15.2375i | −0.241583 | + | 0.743515i | ||||
\(421\) | −0.716128 | + | 0.520297i | −0.0349019 | + | 0.0253577i | −0.605099 | − | 0.796150i | \(-0.706867\pi\) |
0.570198 | + | 0.821508i | \(0.306867\pi\) | |||||||
\(422\) | 16.7844 | + | 12.1946i | 0.817051 | + | 0.593622i | ||||
\(423\) | −1.48826 | − | 4.58039i | −0.0723616 | − | 0.222706i | ||||
\(424\) | 3.63432 | + | 11.1853i | 0.176498 | + | 0.543206i | ||||
\(425\) | 1.82593 | + | 1.32662i | 0.0885708 | + | 0.0643505i | ||||
\(426\) | −27.1431 | + | 19.7206i | −1.31509 | + | 0.955468i | ||||
\(427\) | 6.07389 | − | 18.6935i | 0.293936 | − | 0.904643i | ||||
\(428\) | −14.5663 | −0.704090 | ||||||||
\(429\) | 3.00058 | − | 27.5579i | 0.144869 | − | 1.33051i | ||||
\(430\) | −11.3032 | −0.545090 | ||||||||
\(431\) | −6.27447 | + | 19.3108i | −0.302230 | + | 0.930169i | 0.678466 | + | 0.734632i | \(0.262645\pi\) |
−0.980696 | + | 0.195538i | \(0.937355\pi\) | |||||||
\(432\) | 2.69592 | − | 1.95870i | 0.129708 | − | 0.0942381i | ||||
\(433\) | 29.2632 | + | 21.2609i | 1.40630 | + | 1.02174i | 0.993848 | + | 0.110756i | \(0.0353271\pi\) |
0.412451 | + | 0.910980i | \(0.364673\pi\) | |||||||
\(434\) | 1.42383 | + | 4.38210i | 0.0683460 | + | 0.210347i | ||||
\(435\) | 10.3871 | + | 31.9681i | 0.498021 | + | 1.53275i | ||||
\(436\) | 2.73512 | + | 1.98718i | 0.130989 | + | 0.0951689i | ||||
\(437\) | −2.07060 | + | 1.50438i | −0.0990502 | + | 0.0719642i | ||||
\(438\) | 2.06207 | − | 6.34640i | 0.0985295 | − | 0.303243i | ||||
\(439\) | 21.4914 | 1.02573 | 0.512864 | − | 0.858470i | \(-0.328584\pi\) | ||||
0.512864 | + | 0.858470i | \(0.328584\pi\) | |||||||
\(440\) | 4.05310 | + | 7.08114i | 0.193224 | + | 0.337580i | ||||
\(441\) | 3.68977 | 0.175703 | ||||||||
\(442\) | −2.63794 | + | 8.11873i | −0.125474 | + | 0.386169i | ||||
\(443\) | 19.9014 | − | 14.4592i | 0.945546 | − | 0.686979i | −0.00420349 | − | 0.999991i | \(-0.501338\pi\) |
0.949749 | + | 0.313012i | \(0.101338\pi\) | |||||||
\(444\) | 2.97310 | + | 2.16009i | 0.141097 | + | 0.102513i | ||||
\(445\) | −3.52492 | − | 10.8486i | −0.167097 | − | 0.514273i | ||||
\(446\) | −8.77130 | − | 26.9953i | −0.415333 | − | 1.27826i | ||||
\(447\) | 17.5921 | + | 12.7814i | 0.832079 | + | 0.604541i | ||||
\(448\) | 2.50791 | − | 1.82211i | 0.118488 | − | 0.0860864i | ||||
\(449\) | 10.8991 | − | 33.5439i | 0.514359 | − | 1.58303i | −0.270086 | − | 0.962836i | \(-0.587052\pi\) |
0.784445 | − | 0.620198i | \(-0.212948\pi\) | |||||||
\(450\) | −1.48715 | −0.0701047 | ||||||||
\(451\) | −17.8091 | + | 3.71597i | −0.838598 | + | 0.174978i | ||||
\(452\) | 11.3668 | 0.534650 | ||||||||
\(453\) | −7.90302 | + | 24.3230i | −0.371316 | + | 1.14279i | ||||
\(454\) | −6.88177 | + | 4.99990i | −0.322977 | + | 0.234657i | ||||
\(455\) | −24.5446 | − | 17.8327i | −1.15067 | − | 0.836010i | ||||
\(456\) | 0.649220 | + | 1.99809i | 0.0304025 | + | 0.0935693i | ||||
\(457\) | −2.27762 | − | 7.00981i | −0.106543 | − | 0.327905i | 0.883547 | − | 0.468343i | \(-0.155149\pi\) |
−0.990089 | + | 0.140438i | \(0.955149\pi\) | |||||||
\(458\) | −1.38124 | − | 1.00353i | −0.0645410 | − | 0.0468918i | ||||
\(459\) | −5.78481 | + | 4.20291i | −0.270012 | + | 0.196175i | ||||
\(460\) | −1.94565 | + | 5.98809i | −0.0907163 | + | 0.279196i | ||||
\(461\) | −36.4875 | −1.69939 | −0.849696 | − | 0.527272i | \(-0.823215\pi\) | ||||
−0.849696 | + | 0.527272i | \(0.823215\pi\) | |||||||
\(462\) | 14.5133 | − | 15.9981i | 0.675221 | − | 0.744298i | ||||
\(463\) | −16.2208 | −0.753844 | −0.376922 | − | 0.926245i | \(-0.623018\pi\) | ||||
−0.376922 | + | 0.926245i | \(0.623018\pi\) | |||||||
\(464\) | 2.00974 | − | 6.18534i | 0.0932998 | − | 0.287147i | ||||
\(465\) | −6.21486 | + | 4.51536i | −0.288207 | + | 0.209395i | ||||
\(466\) | 8.05483 | + | 5.85218i | 0.373133 | + | 0.271097i | ||||
\(467\) | 1.32060 | + | 4.06438i | 0.0611099 | + | 0.188077i | 0.976951 | − | 0.213464i | \(-0.0684747\pi\) |
−0.915841 | + | 0.401541i | \(0.868475\pi\) | |||||||
\(468\) | −1.73816 | − | 5.34951i | −0.0803465 | − | 0.247281i | ||||
\(469\) | 35.4003 | + | 25.7198i | 1.63463 | + | 1.18763i | ||||
\(470\) | −6.77937 | + | 4.92550i | −0.312709 | + | 0.227196i | ||||
\(471\) | 2.41762 | − | 7.44068i | 0.111398 | − | 0.342848i | ||||
\(472\) | 6.65028 | 0.306104 | ||||||||
\(473\) | 13.8982 | + | 6.25021i | 0.639042 | + | 0.287385i | ||||
\(474\) | −15.2457 | −0.700260 | ||||||||
\(475\) | −0.325033 | + | 1.00035i | −0.0149136 | + | 0.0458992i | ||||
\(476\) | −5.38139 | + | 3.90981i | −0.246656 | + | 0.179206i | ||||
\(477\) | 13.4526 | + | 9.77389i | 0.615952 | + | 0.447515i | ||||
\(478\) | −5.03035 | − | 15.4818i | −0.230083 | − | 0.708123i | ||||
\(479\) | −12.1115 | − | 37.2754i | −0.553389 | − | 1.70315i | −0.700161 | − | 0.713985i | \(-0.746889\pi\) |
0.146773 | − | 0.989170i | \(-0.453111\pi\) | |||||||
\(480\) | 4.18129 | + | 3.03789i | 0.190849 | + | 0.138660i | ||||
\(481\) | −5.62990 | + | 4.09036i | −0.256701 | + | 0.186504i | ||||
\(482\) | 1.83910 | − | 5.66016i | 0.0837686 | − | 0.257813i | ||||
\(483\) | 16.6687 | 0.758454 | ||||||||
\(484\) | −1.06805 | − | 10.9480i | −0.0485478 | − | 0.497638i | ||||
\(485\) | −13.4585 | −0.611117 | ||||||||
\(486\) | 4.20966 | − | 12.9560i | 0.190954 | − | 0.587696i | ||||
\(487\) | −2.64903 | + | 1.92463i | −0.120039 | + | 0.0872134i | −0.646185 | − | 0.763181i | \(-0.723637\pi\) |
0.526146 | + | 0.850394i | \(0.323637\pi\) | |||||||
\(488\) | −5.12965 | − | 3.72691i | −0.232208 | − | 0.168709i | ||||
\(489\) | −12.9143 | − | 39.7461i | −0.584005 | − | 1.79738i | ||||
\(490\) | −1.98389 | − | 6.10578i | −0.0896229 | − | 0.275831i | ||||
\(491\) | −32.8868 | − | 23.8936i | −1.48416 | − | 1.07830i | −0.976187 | − | 0.216930i | \(-0.930396\pi\) |
−0.507971 | − | 0.861374i | \(-0.669604\pi\) | |||||||
\(492\) | −9.32324 | + | 6.77373i | −0.420324 | + | 0.305383i | ||||
\(493\) | −4.31242 | + | 13.2723i | −0.194222 | + | 0.597753i | ||||
\(494\) | −3.97832 | −0.178993 | ||||||||
\(495\) | 10.5209 | + | 4.73136i | 0.472878 | + | 0.212659i | ||||
\(496\) | 1.48635 | 0.0667390 | ||||||||
\(497\) | 15.2978 | − | 47.0819i | 0.686202 | − | 2.11191i | ||||
\(498\) | 19.0645 | − | 13.8512i | 0.854303 | − | 0.620687i | ||||
\(499\) | 11.4431 | + | 8.31393i | 0.512266 | + | 0.372183i | 0.813682 | − | 0.581310i | \(-0.197460\pi\) |
−0.301417 | + | 0.953492i | \(0.597460\pi\) | |||||||
\(500\) | −3.00138 | − | 9.23731i | −0.134226 | − | 0.413105i | ||||
\(501\) | −14.2742 | − | 43.9314i | −0.637724 | − | 1.96271i | ||||
\(502\) | −17.0374 | − | 12.3784i | −0.760418 | − | 0.552476i | ||||
\(503\) | 22.4423 | − | 16.3053i | 1.00065 | − | 0.727017i | 0.0384254 | − | 0.999261i | \(-0.487766\pi\) |
0.962228 | + | 0.272244i | \(0.0877658\pi\) | |||||||
\(504\) | 1.35439 | − | 4.16840i | 0.0603295 | − | 0.185675i | ||||
\(505\) | −14.2804 | −0.635468 | ||||||||
\(506\) | 5.70349 | − | 6.28698i | 0.253551 | − | 0.279490i | ||||
\(507\) | 5.93940 | 0.263778 | ||||||||
\(508\) | −4.12433 | + | 12.6934i | −0.182988 | + | 0.563178i | ||||
\(509\) | −3.93843 | + | 2.86144i | −0.174568 | + | 0.126831i | −0.671638 | − | 0.740879i | \(-0.734409\pi\) |
0.497070 | + | 0.867710i | \(0.334409\pi\) | |||||||
\(510\) | −8.97206 | − | 6.51859i | −0.397290 | − | 0.288648i | ||||
\(511\) | 3.04263 | + | 9.36425i | 0.134598 | + | 0.414250i | ||||
\(512\) | −0.309017 | − | 0.951057i | −0.0136568 | − | 0.0420312i | ||||
\(513\) | −2.69592 | − | 1.95870i | −0.119028 | − | 0.0864788i | ||||
\(514\) | 1.03343 | − | 0.750828i | 0.0455825 | − | 0.0331176i | ||||
\(515\) | −7.26976 | + | 22.3740i | −0.320344 | + | 0.985918i | ||||
\(516\) | 9.65314 | 0.424956 | ||||||||
\(517\) | 11.0594 | − | 2.30760i | 0.486391 | − | 0.101488i | ||||
\(518\) | −5.42248 | −0.238250 | ||||||||
\(519\) | −16.5433 | + | 50.9151i | −0.726171 | + | 2.23493i | ||||
\(520\) | −7.91773 | + | 5.75257i | −0.347216 | + | 0.252267i | ||||
\(521\) | −15.0920 | − | 10.9650i | −0.661195 | − | 0.480386i | 0.205872 | − | 0.978579i | \(-0.433997\pi\) |
−0.867066 | + | 0.498193i | \(0.833997\pi\) | |||||||
\(522\) | −2.84150 | − | 8.74523i | −0.124369 | − | 0.382768i | ||||
\(523\) | −2.59339 | − | 7.98164i | −0.113401 | − | 0.349013i | 0.878209 | − | 0.478277i | \(-0.158738\pi\) |
−0.991610 | + | 0.129264i | \(0.958738\pi\) | |||||||
\(524\) | 3.71142 | + | 2.69651i | 0.162134 | + | 0.117798i | ||||
\(525\) | 5.54202 | − | 4.02651i | 0.241873 | − | 0.175731i | ||||
\(526\) | −2.73757 | + | 8.42537i | −0.119364 | + | 0.367364i | ||||
\(527\) | −3.18935 | −0.138930 | ||||||||
\(528\) | −3.46142 | − | 6.04741i | −0.150639 | − | 0.263180i | ||||
\(529\) | −16.4495 | −0.715194 | ||||||||
\(530\) | 8.94060 | − | 27.5163i | 0.388355 | − | 1.19523i | ||||
\(531\) | 7.60686 | − | 5.52671i | 0.330110 | − | 0.239839i | ||||
\(532\) | −2.50791 | − | 1.82211i | −0.108732 | − | 0.0789983i | ||||
\(533\) | −6.74345 | − | 20.7542i | −0.292091 | − | 0.898964i | ||||
\(534\) | 3.01034 | + | 9.26488i | 0.130270 | + | 0.400931i | ||||
\(535\) | 28.9902 | + | 21.0626i | 1.25336 | + | 0.910616i | ||||
\(536\) | 11.4196 | − | 8.29684i | 0.493252 | − | 0.358369i | ||||
\(537\) | 14.7947 | − | 45.5334i | 0.638438 | − | 1.96491i | ||||
\(538\) | −26.0234 | −1.12195 | ||||||||
\(539\) | −0.936886 | + | 8.60456i | −0.0403545 | + | 0.370625i | ||||
\(540\) | −8.19772 | −0.352774 | ||||||||
\(541\) | −9.89470 | + | 30.4528i | −0.425407 | + | 1.30927i | 0.477198 | + | 0.878796i | \(0.341653\pi\) |
−0.902604 | + | 0.430471i | \(0.858347\pi\) | |||||||
\(542\) | 13.8201 | − | 10.0409i | 0.593626 | − | 0.431294i | ||||
\(543\) | 2.62680 | + | 1.90848i | 0.112727 | + | 0.0819007i | ||||
\(544\) | 0.663077 | + | 2.04074i | 0.0284292 | + | 0.0874961i | ||||
\(545\) | −2.57007 | − | 7.90987i | −0.110090 | − | 0.338821i | ||||
\(546\) | 20.9615 | + | 15.2294i | 0.897069 | + | 0.651759i | ||||
\(547\) | −20.8060 | + | 15.1164i | −0.889599 | + | 0.646332i | −0.935773 | − | 0.352602i | \(-0.885297\pi\) |
0.0461743 | + | 0.998933i | \(0.485297\pi\) | |||||||
\(548\) | −4.21408 | + | 12.9696i | −0.180017 | + | 0.554034i | ||||
\(549\) | −8.96474 | −0.382606 | ||||||||
\(550\) | 0.377608 | − | 3.46803i | 0.0161012 | − | 0.147877i | ||||
\(551\) | −6.50365 | −0.277065 | ||||||||
\(552\) | 1.66161 | − | 5.11392i | 0.0707230 | − | 0.217663i | ||||
\(553\) | 18.1992 | − | 13.2225i | 0.773907 | − | 0.562277i | ||||
\(554\) | 6.87184 | + | 4.99269i | 0.291957 | + | 0.212119i | ||||
\(555\) | −2.79369 | − | 8.59809i | −0.118585 | − | 0.364969i | ||||
\(556\) | −1.78915 | − | 5.50645i | −0.0758770 | − | 0.233525i | ||||
\(557\) | −30.1853 | − | 21.9309i | −1.27899 | − | 0.929243i | −0.279471 | − | 0.960154i | \(-0.590159\pi\) |
−0.999522 | + | 0.0309112i | \(0.990159\pi\) | |||||||
\(558\) | 1.70015 | − | 1.23523i | 0.0719729 | − | 0.0522914i | ||||
\(559\) | −5.64861 | + | 17.3846i | −0.238911 | + | 0.735292i | ||||
\(560\) | −7.62603 | −0.322259 | ||||||||
\(561\) | 7.42738 | + | 12.9763i | 0.313584 | + | 0.547860i | ||||
\(562\) | −29.4238 | −1.24117 | ||||||||
\(563\) | 0.234541 | − | 0.721842i | 0.00988472 | − | 0.0304220i | −0.945993 | − | 0.324188i | \(-0.894909\pi\) |
0.955877 | + | 0.293766i | \(0.0949088\pi\) | |||||||
\(564\) | 5.78969 | − | 4.20646i | 0.243790 | − | 0.177124i | ||||
\(565\) | −22.6224 | − | 16.4362i | −0.951733 | − | 0.691475i | ||||
\(566\) | 5.27150 | + | 16.2240i | 0.221578 | + | 0.681946i | ||||
\(567\) | 10.7697 | + | 33.1457i | 0.452285 | + | 1.39199i | ||||
\(568\) | −12.9196 | − | 9.38667i | −0.542096 | − | 0.393856i | ||||
\(569\) | 25.2807 | − | 18.3675i | 1.05982 | − | 0.770007i | 0.0857675 | − | 0.996315i | \(-0.472666\pi\) |
0.974056 | + | 0.226309i | \(0.0726658\pi\) | |||||||
\(570\) | 1.59711 | − | 4.91540i | 0.0668956 | − | 0.205884i | ||||
\(571\) | −20.5848 | −0.861445 | −0.430723 | − | 0.902484i | \(-0.641741\pi\) | ||||
−0.430723 | + | 0.902484i | \(0.641741\pi\) | |||||||
\(572\) | 12.9164 | − | 2.69508i | 0.540063 | − | 0.112687i | ||||
\(573\) | 15.0091 | 0.627012 | ||||||||
\(574\) | 5.25457 | − | 16.1719i | 0.219321 | − | 0.675002i | ||||
\(575\) | 2.17792 | − | 1.58235i | 0.0908255 | − | 0.0659886i | ||||
\(576\) | −1.14384 | − | 0.831049i | −0.0476600 | − | 0.0346270i | ||||
\(577\) | 3.86681 | + | 11.9008i | 0.160977 | + | 0.495437i | 0.998717 | − | 0.0506319i | \(-0.0161235\pi\) |
−0.837740 | + | 0.546069i | \(0.816124\pi\) | |||||||
\(578\) | 3.83048 | + | 11.7890i | 0.159327 | + | 0.490358i | ||||
\(579\) | 20.5627 | + | 14.9397i | 0.854558 | + | 0.620873i | ||||
\(580\) | −12.9437 | + | 9.40414i | −0.537458 | + | 0.390486i | ||||
\(581\) | −10.7448 | + | 33.0690i | −0.445768 | + | 1.37193i | ||||
\(582\) | 11.4937 | 0.476431 | ||||||||
\(583\) | −26.2086 | + | 28.8898i | −1.08545 | + | 1.19649i | ||||
\(584\) | 3.17623 | 0.131433 | ||||||||
\(585\) | −4.27596 | + | 13.1600i | −0.176789 | + | 0.544101i | ||||
\(586\) | 16.5964 | − | 12.0580i | 0.685589 | − | 0.498110i | ||||
\(587\) | −9.72555 | − | 7.06602i | −0.401416 | − | 0.291646i | 0.368701 | − | 0.929548i | \(-0.379803\pi\) |
−0.770118 | + | 0.637902i | \(0.779803\pi\) | |||||||
\(588\) | 1.69427 | + | 5.21444i | 0.0698706 | + | 0.215040i | ||||
\(589\) | −0.459307 | − | 1.41360i | −0.0189254 | − | 0.0582464i | ||||
\(590\) | −13.2355 | − | 9.61617i | −0.544898 | − | 0.395891i | ||||
\(591\) | −31.0219 | + | 22.5387i | −1.27607 | + | 0.927118i | ||||
\(592\) | −0.540537 | + | 1.66360i | −0.0222159 | + | 0.0683736i | ||||
\(593\) | −33.2839 | −1.36680 | −0.683402 | − | 0.730042i | \(-0.739500\pi\) | ||||
−0.683402 | + | 0.730042i | \(0.739500\pi\) | |||||||
\(594\) | 10.0798 | + | 4.53299i | 0.413578 | + | 0.185991i | ||||
\(595\) | 16.3637 | 0.670844 | ||||||||
\(596\) | −3.19841 | + | 9.84368i | −0.131012 | + | 0.403213i | ||||
\(597\) | −40.7422 | + | 29.6010i | −1.66747 | + | 1.21149i | ||||
\(598\) | 8.23751 | + | 5.98490i | 0.336857 | + | 0.244741i | ||||
\(599\) | −4.59137 | − | 14.1308i | −0.187598 | − | 0.577368i | 0.812385 | − | 0.583121i | \(-0.198169\pi\) |
−0.999983 | + | 0.00575289i | \(0.998169\pi\) | |||||||
\(600\) | −0.682869 | − | 2.10166i | −0.0278780 | − | 0.0857997i | ||||
\(601\) | −25.0415 | − | 18.1937i | −1.02147 | − | 0.742138i | −0.0548831 | − | 0.998493i | \(-0.517479\pi\) |
−0.966583 | + | 0.256354i | \(0.917479\pi\) | |||||||
\(602\) | −11.5232 | + | 8.37207i | −0.469649 | + | 0.341220i | ||||
\(603\) | 6.16714 | − | 18.9805i | 0.251145 | − | 0.772946i | ||||
\(604\) | −12.1731 | −0.495316 | ||||||||
\(605\) | −13.7050 | + | 23.3334i | −0.557186 | + | 0.948636i | ||||
\(606\) | 12.1957 | 0.495415 | ||||||||
\(607\) | 9.09384 | − | 27.9880i | 0.369108 | − | 1.13600i | −0.578261 | − | 0.815852i | \(-0.696268\pi\) |
0.947369 | − | 0.320145i | \(-0.103732\pi\) | |||||||
\(608\) | −0.809017 | + | 0.587785i | −0.0328100 | + | 0.0238378i | ||||
\(609\) | 34.2673 | + | 24.8966i | 1.38858 | + | 1.00886i | ||||
\(610\) | 4.82009 | + | 14.8347i | 0.195160 | + | 0.600640i | ||||
\(611\) | 4.18765 | + | 12.8883i | 0.169414 | + | 0.521404i | ||||
\(612\) | 2.45441 | + | 1.78323i | 0.0992137 | + | 0.0720830i | ||||
\(613\) | −17.4575 | + | 12.6836i | −0.705102 | + | 0.512287i | −0.881590 | − | 0.472016i | \(-0.843526\pi\) |
0.176488 | + | 0.984303i | \(0.443526\pi\) | |||||||
\(614\) | −1.74472 | + | 5.36969i | −0.0704111 | + | 0.216703i | ||||
\(615\) | 28.3500 | 1.14318 | ||||||||
\(616\) | 9.37682 | + | 4.21687i | 0.377803 | + | 0.169903i | ||||
\(617\) | −21.8270 | −0.878721 | −0.439360 | − | 0.898311i | \(-0.644795\pi\) | ||||
−0.439360 | + | 0.898311i | \(0.644795\pi\) | |||||||
\(618\) | 6.20850 | − | 19.1078i | 0.249742 | − | 0.768628i | ||||
\(619\) | −33.6049 | + | 24.4154i | −1.35069 | + | 0.981336i | −0.351717 | + | 0.936106i | \(0.614402\pi\) |
−0.998977 | + | 0.0452299i | \(0.985598\pi\) | |||||||
\(620\) | −2.95816 | − | 2.14923i | −0.118803 | − | 0.0863151i | ||||
\(621\) | 2.63555 | + | 8.11138i | 0.105761 | + | 0.325498i | ||||
\(622\) | −2.60073 | − | 8.00422i | −0.104280 | − | 0.320940i | ||||
\(623\) | −11.6288 | − | 8.44885i | −0.465900 | − | 0.338496i | ||||
\(624\) | 6.76187 | − | 4.91279i | 0.270692 | − | 0.196669i | ||||
\(625\) | −9.00871 | + | 27.7260i | −0.360348 | + | 1.10904i | ||||
\(626\) | −31.3766 | −1.25406 | ||||||||
\(627\) | −4.68179 | + | 5.16075i | −0.186973 | + | 0.206101i | ||||
\(628\) | 3.72389 | 0.148599 | ||||||||
\(629\) | 1.15986 | − | 3.56969i | 0.0462468 | − | 0.142333i | ||||
\(630\) | −8.72296 | + | 6.33760i | −0.347531 | + | 0.252496i | ||||
\(631\) | −1.13636 | − | 0.825616i | −0.0452379 | − | 0.0328672i | 0.564937 | − | 0.825134i | \(-0.308901\pi\) |
−0.610174 | + | 0.792267i | \(0.708901\pi\) | |||||||
\(632\) | −2.24244 | − | 6.90153i | −0.0891996 | − | 0.274528i | ||||
\(633\) | 13.4691 | + | 41.4537i | 0.535350 | + | 1.64764i | ||||
\(634\) | 5.82726 | + | 4.23375i | 0.231430 | + | 0.168144i | ||||
\(635\) | 26.5627 | − | 19.2989i | 1.05411 | − | 0.765855i | ||||
\(636\) | −7.63541 | + | 23.4994i | −0.302764 | + | 0.931811i | ||||
\(637\) | −10.3822 | −0.411360 | ||||||||
\(638\) | 21.1154 | − | 4.40584i | 0.835967 | − | 0.174429i | ||||
\(639\) | −22.5788 | −0.893203 | ||||||||
\(640\) | −0.760196 | + | 2.33964i | −0.0300494 | + | 0.0924825i | ||||
\(641\) | 10.2584 | − | 7.45315i | 0.405182 | − | 0.294382i | −0.366467 | − | 0.930431i | \(-0.619433\pi\) |
0.771648 | + | 0.636049i | \(0.219433\pi\) | |||||||
\(642\) | −24.7581 | − | 17.9878i | −0.977124 | − | 0.709922i | ||||
\(643\) | 1.36681 | + | 4.20660i | 0.0539017 | + | 0.165892i | 0.974383 | − | 0.224893i | \(-0.0722034\pi\) |
−0.920482 | + | 0.390786i | \(0.872203\pi\) | |||||||
\(644\) | 2.45175 | + | 7.54570i | 0.0966124 | + | 0.297342i | ||||
\(645\) | −19.2119 | − | 13.9582i | −0.756467 | − | 0.549605i | ||||
\(646\) | 1.73596 | − | 1.26125i | 0.0683004 | − | 0.0496231i | ||||
\(647\) | −7.59875 | + | 23.3866i | −0.298738 | + | 0.919421i | 0.683202 | + | 0.730229i | \(0.260587\pi\) |
−0.981940 | + | 0.189191i | \(0.939413\pi\) | |||||||
\(648\) | 11.2426 | 0.441650 | ||||||||
\(649\) | 10.9568 | + | 19.1425i | 0.430092 | + | 0.751410i | ||||
\(650\) | 4.18452 | 0.164130 | ||||||||
\(651\) | −2.99135 | + | 9.20643i | −0.117240 | + | 0.360829i | ||||
\(652\) | 16.0930 | − | 11.6922i | 0.630250 | − | 0.457903i | ||||
\(653\) | −15.8056 | − | 11.4834i | −0.618521 | − | 0.449381i | 0.233884 | − | 0.972265i | \(-0.424856\pi\) |
−0.852404 | + | 0.522883i | \(0.824856\pi\) | |||||||
\(654\) | 2.19488 | + | 6.75516i | 0.0858267 | + | 0.264147i | ||||
\(655\) | −3.48746 | − | 10.7333i | −0.136266 | − | 0.419384i | ||||
\(656\) | −4.43769 | − | 3.22417i | −0.173263 | − | 0.125883i | ||||
\(657\) | 3.63310 | − | 2.63960i | 0.141741 | − | 0.102981i | ||||
\(658\) | −3.26307 | + | 10.0427i | −0.127208 | + | 0.391505i | ||||
\(659\) | 35.3980 | 1.37891 | 0.689456 | − | 0.724328i | \(-0.257850\pi\) | ||||
0.689456 | + | 0.724328i | \(0.257850\pi\) | |||||||
\(660\) | −1.85544 | + | 17.0408i | −0.0722231 | + | 0.663312i | ||||
\(661\) | −26.3898 | −1.02644 | −0.513222 | − | 0.858256i | \(-0.671548\pi\) | ||||
−0.513222 | + | 0.858256i | \(0.671548\pi\) | |||||||
\(662\) | −6.30650 | + | 19.4094i | −0.245109 | + | 0.754368i | ||||
\(663\) | −14.5094 | + | 10.5417i | −0.563498 | + | 0.409405i | ||||
\(664\) | 9.07438 | + | 6.59292i | 0.352154 | + | 0.255855i | ||||
\(665\) | 2.35657 | + | 7.25278i | 0.0913840 | + | 0.281251i | ||||
\(666\) | 0.764246 | + | 2.35211i | 0.0296139 | + | 0.0911423i | ||||
\(667\) | 13.4665 | + | 9.78395i | 0.521423 | + | 0.378836i | ||||
\(668\) | 17.7876 | − | 12.9234i | 0.688223 | − | 0.500023i | ||||
\(669\) | 18.4278 | − | 56.7149i | 0.712460 | − | 2.19273i | ||||
\(670\) | −34.7246 | −1.34153 | ||||||||
\(671\) | 2.27628 | − | 20.9058i | 0.0878747 | − | 0.807060i | ||||
\(672\) | 6.51275 | 0.251235 | ||||||||
\(673\) | −1.24471 | + | 3.83081i | −0.0479799 | + | 0.147667i | −0.972176 | − | 0.234251i | \(-0.924736\pi\) |
0.924196 | + | 0.381918i | \(0.124736\pi\) | |||||||
\(674\) | −25.9791 | + | 18.8749i | −1.00068 | + | 0.727034i | ||||
\(675\) | 2.83565 | + | 2.06022i | 0.109144 | + | 0.0792980i | ||||
\(676\) | 0.873605 | + | 2.68868i | 0.0336002 | + | 0.103411i | ||||
\(677\) | 6.67689 | + | 20.5493i | 0.256614 | + | 0.789776i | 0.993507 | + | 0.113767i | \(0.0362918\pi\) |
−0.736894 | + | 0.676009i | \(0.763708\pi\) | |||||||
\(678\) | 19.3199 | + | 14.0368i | 0.741977 | + | 0.539078i | ||||
\(679\) | −13.7203 | + | 9.96840i | −0.526538 | + | 0.382552i | ||||
\(680\) | 1.63120 | − | 5.02032i | 0.0625537 | − | 0.192521i | ||||
\(681\) | −17.8711 | −0.684823 | ||||||||
\(682\) | 2.44887 | + | 4.27839i | 0.0937719 | + | 0.163828i | ||||
\(683\) | 3.73163 | 0.142787 | 0.0713935 | − | 0.997448i | \(-0.477255\pi\) | ||||
0.0713935 | + | 0.997448i | \(0.477255\pi\) | |||||||
\(684\) | −0.436908 | + | 1.34467i | −0.0167056 | + | 0.0514146i | ||||
\(685\) | 27.1407 | − | 19.7189i | 1.03699 | − | 0.753420i | ||||
\(686\) | 11.0105 | + | 7.99958i | 0.420382 | + | 0.305426i | ||||
\(687\) | −1.10842 | − | 3.41135i | −0.0422887 | − | 0.130151i | ||||
\(688\) | 1.41985 | + | 4.36984i | 0.0541312 | + | 0.166599i | ||||
\(689\) | −37.8528 | − | 27.5017i | −1.44208 | − | 1.04773i | ||||
\(690\) | −10.7016 | + | 7.77517i | −0.407403 | + | 0.295996i | ||||
\(691\) | 13.1069 | − | 40.3388i | 0.498608 | − | 1.53456i | −0.312648 | − | 0.949869i | \(-0.601216\pi\) |
0.811257 | − | 0.584690i | \(-0.198784\pi\) | |||||||
\(692\) | −25.4819 | −0.968675 | ||||||||
\(693\) | 14.2300 | − | 2.96917i | 0.540553 | − | 0.112789i | ||||
\(694\) | −1.12968 | −0.0428820 | ||||||||
\(695\) | −4.40140 | + | 13.5461i | −0.166955 | + | 0.513834i | ||||
\(696\) | 11.0541 | − | 8.03129i | 0.419005 | − | 0.304425i | ||||
\(697\) | 9.52224 | + | 6.91831i | 0.360681 | + | 0.262050i | ||||
\(698\) | 6.53753 | + | 20.1205i | 0.247449 | + | 0.761570i | ||||
\(699\) | 6.46384 | + | 19.8936i | 0.244485 | + | 0.752447i | ||||
\(700\) | 2.63790 | + | 1.91655i | 0.0997033 | + | 0.0724387i | ||||
\(701\) | 41.9946 | − | 30.5108i | 1.58611 | − | 1.15238i | 0.676879 | − | 0.736095i | \(-0.263332\pi\) |
0.909235 | − | 0.416284i | \(-0.136668\pi\) | |||||||
\(702\) | −4.09668 | + | 12.6083i | −0.154619 | + | 0.475869i | ||||
\(703\) | 1.74921 | 0.0659728 | ||||||||
\(704\) | 2.22845 | − | 2.45643i | 0.0839877 | − | 0.0925800i | ||||
\(705\) | −17.6052 | −0.663051 | ||||||||
\(706\) | 0.00842732 | − | 0.0259366i | 0.000317166 | − | 0.000976138i | ||||
\(707\) | −14.5582 | + | 10.5772i | −0.547519 | + | 0.397796i | ||||
\(708\) | 11.3033 | + | 8.21236i | 0.424806 | + | 0.308639i | ||||
\(709\) | −13.0146 | − | 40.0548i | −0.488773 | − | 1.50429i | −0.826441 | − | 0.563024i | \(-0.809638\pi\) |
0.337668 | − | 0.941265i | \(-0.390362\pi\) | |||||||
\(710\) | 12.1400 | + | 37.3631i | 0.455606 | + | 1.40221i | ||||
\(711\) | −8.30050 | − | 6.03067i | −0.311293 | − | 0.226168i | ||||
\(712\) | −3.75130 | + | 2.72548i | −0.140586 | + | 0.102142i | ||||
\(713\) | −1.17555 | + | 3.61797i | −0.0440247 | + | 0.135494i | ||||
\(714\) | −13.9748 | −0.522995 | ||||||||
\(715\) | −29.6036 | − | 13.3131i | −1.10711 | − | 0.497881i | ||||
\(716\) | 22.7884 | 0.851643 | ||||||||
\(717\) | 10.5684 | − | 32.5261i | 0.394683 | − | 1.21471i | ||||
\(718\) | 12.2286 | − | 8.88459i | 0.456367 | − | 0.331570i | ||||
\(719\) | 5.15475 | + | 3.74514i | 0.192240 | + | 0.139670i | 0.679742 | − | 0.733452i | \(-0.262092\pi\) |
−0.487502 | + | 0.873122i | \(0.662092\pi\) | |||||||
\(720\) | 1.07481 | + | 3.30794i | 0.0400560 | + | 0.123280i | ||||
\(721\) | 9.16077 | + | 28.1939i | 0.341165 | + | 1.05000i | ||||
\(722\) | 0.809017 | + | 0.587785i | 0.0301085 | + | 0.0218751i | ||||
\(723\) | 10.1155 | − | 7.34938i | 0.376201 | − | 0.273326i | ||||
\(724\) | −0.477575 | + | 1.46983i | −0.0177489 | + | 0.0546256i | ||||
\(725\) | 6.84074 | 0.254059 | ||||||||
\(726\) | 11.7043 | − | 19.9271i | 0.434386 | − | 0.739563i | ||||
\(727\) | −36.8358 | −1.36616 | −0.683082 | − | 0.730342i | \(-0.739361\pi\) | ||||
−0.683082 | + | 0.730342i | \(0.739361\pi\) | |||||||
\(728\) | −3.81099 | + | 11.7290i | −0.141245 | + | 0.434706i | ||||
\(729\) | −4.13203 | + | 3.00210i | −0.153038 | + | 0.111189i | ||||
\(730\) | −6.32139 | − | 4.59276i | −0.233965 | − | 0.169986i | ||||
\(731\) | −3.04666 | − | 9.37664i | −0.112685 | − | 0.346808i | ||||
\(732\) | −4.11644 | − | 12.6691i | −0.152148 | − | 0.468263i | ||||
\(733\) | 5.85493 | + | 4.25386i | 0.216257 | + | 0.157120i | 0.690640 | − | 0.723199i | \(-0.257329\pi\) |
−0.474383 | + | 0.880318i | \(0.657329\pi\) | |||||||
\(734\) | 17.3707 | − | 12.6206i | 0.641165 | − | 0.465834i | ||||
\(735\) | 4.16799 | − | 12.8278i | 0.153739 | − | 0.473159i | ||||
\(736\) | 2.55940 | 0.0943408 | ||||||||
\(737\) | 42.6967 | + | 19.2012i | 1.57275 | + | 0.707286i | ||||
\(738\) | −7.75546 | −0.285482 | ||||||||
\(739\) | 6.07208 | − | 18.6880i | 0.223365 | − | 0.687448i | −0.775088 | − | 0.631853i | \(-0.782295\pi\) |
0.998453 | − | 0.0555945i | \(-0.0177054\pi\) | |||||||
\(740\) | 3.48132 | − | 2.52933i | 0.127976 | − | 0.0929799i | ||||
\(741\) | −6.76187 | − | 4.91279i | −0.248404 | − | 0.180476i | ||||
\(742\) | −11.2662 | − | 34.6739i | −0.413596 | − | 1.27292i | ||||
\(743\) | 2.38663 | + | 7.34530i | 0.0875571 | + | 0.269473i | 0.985243 | − | 0.171164i | \(-0.0547527\pi\) |
−0.897686 | + | 0.440637i | \(0.854753\pi\) | |||||||
\(744\) | 2.52632 | + | 1.83548i | 0.0926193 | + | 0.0672918i | ||||
\(745\) | 20.5993 | − | 14.9663i | 0.754700 | − | 0.548321i | ||||
\(746\) | 5.66789 | − | 17.4440i | 0.207516 | − | 0.638670i | ||||
\(747\) | 15.8587 | 0.580239 | ||||||||
\(748\) | −4.78172 | + | 5.27091i | −0.174837 | + | 0.192723i | ||||
\(749\) | 45.1549 | 1.64992 | ||||||||
\(750\) | 6.30567 | − | 19.4068i | 0.230250 | − | 0.708638i | ||||
\(751\) | 36.7609 | − | 26.7084i | 1.34142 | − | 0.974602i | 0.342034 | − | 0.939688i | \(-0.388884\pi\) |
0.999390 | − | 0.0349139i | \(-0.0111157\pi\) | |||||||
\(752\) | 2.75579 | + | 2.00220i | 0.100493 | + | 0.0730127i | ||||
\(753\) | −13.6722 | − | 42.0787i | −0.498243 | − | 1.53343i | ||||
\(754\) | 7.99539 | + | 24.6073i | 0.291175 | + | 0.896144i | ||||
\(755\) | 24.2271 | + | 17.6020i | 0.881716 | + | 0.640604i | ||||
\(756\) | −8.35723 | + | 6.07188i | −0.303950 | + | 0.220832i | ||||
\(757\) | −0.121953 | + | 0.375334i | −0.00443247 | + | 0.0136417i | −0.953248 | − | 0.302188i | \(-0.902283\pi\) |
0.948816 | + | 0.315830i | \(0.102283\pi\) | |||||||
\(758\) | −12.3232 | −0.447601 | ||||||||
\(759\) | 17.4578 | − | 3.64267i | 0.633679 | − | 0.132221i | ||||
\(760\) | 2.46005 | 0.0892353 | ||||||||
\(761\) | 11.5882 | − | 35.6649i | 0.420072 | − | 1.29285i | −0.487562 | − | 0.873088i | \(-0.662114\pi\) |
0.907634 | − | 0.419762i | \(-0.137886\pi\) | |||||||
\(762\) | −22.6850 | + | 16.4816i | −0.821790 | + | 0.597065i | ||||
\(763\) | −8.47876 | − | 6.16018i | −0.306952 | − | 0.223013i | ||||
\(764\) | 2.20763 | + | 6.79439i | 0.0798692 | + | 0.245812i | ||||
\(765\) | −2.30630 | − | 7.09806i | −0.0833844 | − | 0.256631i | ||||
\(766\) | 23.2598 | + | 16.8992i | 0.840411 | + | 0.610595i | ||||
\(767\) | −21.4041 | + | 15.5510i | −0.772858 | + | 0.561514i | ||||
\(768\) | 0.649220 | − | 1.99809i | 0.0234267 | − | 0.0721000i | ||||
\(769\) | 0.388213 | 0.0139993 | 0.00699965 | − | 0.999976i | \(-0.497772\pi\) | ||||
0.00699965 | + | 0.999976i | \(0.497772\pi\) | |||||||
\(770\) | −12.5644 | − | 21.9512i | −0.452791 | − | 0.791066i | ||||
\(771\) | 2.68368 | 0.0966505 | ||||||||
\(772\) | −3.73849 | + | 11.5059i | −0.134551 | + | 0.414106i | ||||
\(773\) | 26.2976 | − | 19.1063i | 0.945860 | − | 0.687208i | −0.00396401 | − | 0.999992i | \(-0.501262\pi\) |
0.949824 | + | 0.312785i | \(0.101262\pi\) | |||||||
\(774\) | 5.25563 | + | 3.81844i | 0.188910 | + | 0.137251i | ||||
\(775\) | 0.483113 | + | 1.48687i | 0.0173539 | + | 0.0534099i | ||||
\(776\) | 1.69057 | + | 5.20305i | 0.0606881 | + | 0.186779i | ||||
\(777\) | −9.21648 | − | 6.69616i | −0.330639 | − | 0.240223i | ||||
\(778\) | 2.20852 | − | 1.60458i | 0.0791792 | − | 0.0575271i | ||||
\(779\) | −1.69505 | + | 5.21682i | −0.0607314 | + | 0.186912i | ||||
\(780\) | −20.5614 | −0.736216 | ||||||||
\(781\) | 5.73308 | − | 52.6538i | 0.205146 | − | 1.88410i | ||||
\(782\) | −5.49187 | −0.196389 | ||||||||
\(783\) | −6.69714 | + | 20.6117i | −0.239336 | + | 0.736601i | ||||
\(784\) | −2.11130 | + | 1.53395i | −0.0754034 | + | 0.0547838i | ||||
\(785\) | −7.41136 | − | 5.38467i | −0.264523 | − | 0.192187i | ||||
\(786\) | 2.97834 | + | 9.16640i | 0.106234 | + | 0.326955i | ||||
\(787\) | −3.65334 | − | 11.2438i | −0.130228 | − | 0.400799i | 0.864590 | − | 0.502479i | \(-0.167578\pi\) |
−0.994817 | + | 0.101679i | \(0.967578\pi\) | |||||||
\(788\) | −14.7658 | − | 10.7280i | −0.526012 | − | 0.382170i | ||||
\(789\) | −15.0574 | + | 10.9398i | −0.536058 | + | 0.389469i | ||||
\(790\) | −5.51651 | + | 16.9781i | −0.196269 | + | 0.604053i | ||||
\(791\) | −35.2366 | −1.25287 | ||||||||
\(792\) | 0.507578 | − | 4.66171i | 0.0180360 | − | 0.165647i | ||||
\(793\) | 25.2249 | 0.895763 | ||||||||
\(794\) | −2.22903 | + | 6.86026i | −0.0791054 | + | 0.243461i | ||||
\(795\) | 49.1758 | − | 35.7283i | 1.74409 | − | 1.26715i | ||||
\(796\) | −19.3926 | − | 14.0895i | −0.687352 | − | 0.499390i | ||||
\(797\) | 8.46847 | + | 26.0633i | 0.299969 | + | 0.923208i | 0.981507 | + | 0.191426i | \(0.0613112\pi\) |
−0.681538 | + | 0.731782i | \(0.738689\pi\) | |||||||
\(798\) | −2.01255 | − | 6.19400i | −0.0712435 | − | 0.219265i | ||||
\(799\) | −5.91327 | − | 4.29624i | −0.209197 | − | 0.151990i | ||||
\(800\) | 0.850949 | − | 0.618250i | 0.0300856 | − | 0.0218585i | ||||
\(801\) | −2.02588 | + | 6.23502i | −0.0715810 | + | 0.220304i | ||||
\(802\) | 1.18981 | 0.0420137 | ||||||||
\(803\) | 5.23306 | + | 9.14263i | 0.184671 | + | 0.322636i | ||||
\(804\) | 29.6554 | 1.04586 | ||||||||
\(805\) | 6.03141 | − | 18.5628i | 0.212579 | − | 0.654252i | ||||
\(806\) | −4.78386 | + | 3.47568i | −0.168504 | + | 0.122425i | ||||
\(807\) | −44.2314 | − | 32.1360i | −1.55702 | − | 1.13124i | ||||
\(808\) | 1.79382 | + | 5.52081i | 0.0631063 | + | 0.194221i | ||||
\(809\) | 2.85290 | + | 8.78033i | 0.100303 | + | 0.308700i | 0.988599 | − | 0.150570i | \(-0.0481110\pi\) |
−0.888297 | + | 0.459270i | \(0.848111\pi\) | |||||||
\(810\) | −22.3752 | − | 16.2565i | −0.786185 | − | 0.571197i | ||||
\(811\) | 22.9620 | − | 16.6828i | 0.806303 | − | 0.585814i | −0.106453 | − | 0.994318i | \(-0.533949\pi\) |
0.912756 | + | 0.408504i | \(0.133949\pi\) | |||||||
\(812\) | −6.23009 | + | 19.1743i | −0.218633 | + | 0.672884i | ||||
\(813\) | 35.8892 | 1.25869 | ||||||||
\(814\) | −5.67917 | + | 1.18499i | −0.199055 | + | 0.0415339i | ||||
\(815\) | −48.9353 | −1.71413 | ||||||||
\(816\) | −1.39307 | + | 4.28744i | −0.0487673 | + | 0.150090i | ||||
\(817\) | 3.71721 | − | 2.70071i | 0.130049 | − | 0.0944859i | ||||
\(818\) | 9.52954 | + | 6.92362i | 0.333193 | + | 0.242079i | ||||
\(819\) | 5.38822 | + | 16.5832i | 0.188280 | + | 0.579465i | ||||
\(820\) | 4.16990 | + | 12.8336i | 0.145619 | + | 0.448170i | ||||
\(821\) | −23.7179 | − | 17.2321i | −0.827761 | − | 0.601403i | 0.0911641 | − | 0.995836i | \(-0.470941\pi\) |
−0.918925 | + | 0.394432i | \(0.870941\pi\) | |||||||
\(822\) | −23.1786 | + | 16.8403i | −0.808448 | + | 0.587372i | ||||
\(823\) | −5.91914 | + | 18.2172i | −0.206328 | + | 0.635013i | 0.793328 | + | 0.608795i | \(0.208347\pi\) |
−0.999656 | + | 0.0262187i | \(0.991653\pi\) | |||||||
\(824\) | 9.56301 | 0.333143 | ||||||||
\(825\) | 4.92445 | − | 5.42824i | 0.171447 | − | 0.188987i | ||||
\(826\) | −20.6156 | −0.717307 | ||||||||
\(827\) | −5.89089 | + | 18.1303i | −0.204846 | + | 0.630452i | 0.794873 | + | 0.606775i | \(0.207537\pi\) |
−0.999720 | + | 0.0236766i | \(0.992463\pi\) | |||||||
\(828\) | 2.92755 | − | 2.12699i | 0.101739 | − | 0.0739179i | ||||
\(829\) | 2.79451 | + | 2.03033i | 0.0970574 | + | 0.0705163i | 0.635256 | − | 0.772302i | \(-0.280895\pi\) |
−0.538198 | + | 0.842818i | \(0.680895\pi\) | |||||||
\(830\) | −8.52678 | − | 26.2427i | −0.295969 | − | 0.910899i | ||||
\(831\) | 5.51452 | + | 16.9719i | 0.191296 | + | 0.588750i | ||||
\(832\) | 3.21853 | + | 2.33840i | 0.111582 | + | 0.0810694i | ||||
\(833\) | 4.53034 | − | 3.29149i | 0.156967 | − | 0.114043i | ||||
\(834\) | 3.75887 | − | 11.5686i | 0.130159 | − | 0.400588i | ||||
\(835\) | −54.0883 | −1.87180 | ||||||||
\(836\) | −3.02483 | − | 1.36030i | −0.104616 | − | 0.0470470i | ||||
\(837\) | −4.95302 | −0.171202 | ||||||||
\(838\) | −6.20500 | + | 19.0970i | −0.214348 | + | 0.659696i | ||||
\(839\) | −13.5883 | + | 9.87248i | −0.469120 | + | 0.340836i | −0.797098 | − | 0.603849i | \(-0.793633\pi\) |
0.327978 | + | 0.944685i | \(0.393633\pi\) | |||||||
\(840\) | −12.9618 | − | 9.41730i | −0.447225 | − | 0.324928i | ||||
\(841\) | 4.10914 | + | 12.6466i | 0.141695 | + | 0.436091i | ||||
\(842\) | −0.273536 | − | 0.841859i | −0.00942669 | − | 0.0290124i | ||||
\(843\) | −50.0110 | − | 36.3351i | −1.72247 | − | 1.25145i | ||||
\(844\) | −16.7844 | + | 12.1946i | −0.577742 | + | 0.419754i | ||||
\(845\) | 2.14911 | − | 6.61428i | 0.0739316 | − | 0.227538i | ||||
\(846\) | 4.81611 | 0.165581 | ||||||||
\(847\) | 3.31091 | + | 33.9384i | 0.113764 | + | 1.16614i | ||||
\(848\) | −11.7609 | −0.403871 | ||||||||
\(849\) | −11.0750 | + | 34.0853i | −0.380093 | + | 1.16981i | ||||
\(850\) | −1.82593 | + | 1.32662i | −0.0626290 | + | 0.0455027i | ||||
\(851\) | −3.62192 | − | 2.63148i | −0.124158 | − | 0.0902059i | ||||
\(852\) | −10.3678 | − | 31.9087i | −0.355193 | − | 1.09317i | ||||
\(853\) | −1.71110 | − | 5.26623i | −0.0585870 | − | 0.180312i | 0.917480 | − | 0.397782i | \(-0.130220\pi\) |
−0.976067 | + | 0.217469i | \(0.930220\pi\) | |||||||
\(854\) | 15.9017 | + | 11.5532i | 0.544144 | + | 0.395343i | ||||
\(855\) | 2.81390 | − | 2.04442i | 0.0962334 | − | 0.0699176i | ||||
\(856\) | 4.50124 | − | 13.8534i | 0.153849 | − | 0.473499i | ||||
\(857\) | 26.5793 | 0.907932 | 0.453966 | − | 0.891019i | \(-0.350009\pi\) | ||||
0.453966 | + | 0.891019i | \(0.350009\pi\) | |||||||
\(858\) | 25.2819 | + | 11.3696i | 0.863110 | + | 0.388151i | ||||
\(859\) | 19.7426 | 0.673610 | 0.336805 | − | 0.941574i | \(-0.390654\pi\) | ||||
0.336805 | + | 0.941574i | \(0.390654\pi\) | |||||||
\(860\) | 3.49289 | − | 10.7500i | 0.119107 | − | 0.366572i | ||||
\(861\) | 28.9016 | − | 20.9982i | 0.984964 | − | 0.715618i | ||||
\(862\) | −16.4268 | − | 11.9347i | −0.559498 | − | 0.406499i | ||||
\(863\) | −7.05846 | − | 21.7237i | −0.240273 | − | 0.739484i | −0.996378 | − | 0.0850337i | \(-0.972900\pi\) |
0.756105 | − | 0.654450i | \(-0.227100\pi\) | |||||||
\(864\) | 1.02975 | + | 3.16925i | 0.0350328 | + | 0.107820i | ||||
\(865\) | 50.7145 | + | 36.8462i | 1.72434 | + | 1.25281i | ||||
\(866\) | −29.2632 | + | 21.2609i | −0.994403 | + | 0.722476i | ||||
\(867\) | −8.04753 | + | 24.7678i | −0.273309 | + | 0.841157i | ||||
\(868\) | −4.60761 | −0.156392 | ||||||||
\(869\) | 16.1712 | − | 17.8255i | 0.548569 | − | 0.604690i | ||||
\(870\) | −33.6132 | −1.13959 | ||||||||
\(871\) | −17.3531 | + | 53.4072i | −0.587986 | + | 1.80963i | ||||
\(872\) | −2.73512 | + | 1.98718i | −0.0926230 | + | 0.0672946i | ||||
\(873\) | 6.25774 | + | 4.54651i | 0.211792 | + | 0.153876i | ||||
\(874\) | −0.790899 | − | 2.43414i | −0.0267525 | − | 0.0823359i | ||||
\(875\) | 9.30415 | + | 28.6352i | 0.314538 | + | 0.968047i | ||||
\(876\) | 5.39857 | + | 3.92229i | 0.182401 | + | 0.132522i | ||||
\(877\) | −31.6495 | + | 22.9947i | −1.06873 | + | 0.776476i | −0.975683 | − | 0.219186i | \(-0.929660\pi\) |
−0.0930448 | + | 0.995662i | \(0.529660\pi\) | |||||||
\(878\) | −6.64121 | + | 20.4395i | −0.224130 | + | 0.689801i | ||||
\(879\) | 43.0987 | 1.45368 | ||||||||
\(880\) | −7.98704 | + | 1.66654i | −0.269243 | + | 0.0561790i | ||||
\(881\) | 39.7517 | 1.33927 | 0.669635 | − | 0.742691i | \(-0.266451\pi\) | ||||
0.669635 | + | 0.742691i | \(0.266451\pi\) | |||||||
\(882\) | −1.14020 | + | 3.50918i | −0.0383926 | + | 0.118160i | ||||
\(883\) | 19.4987 | − | 14.1667i | 0.656184 | − | 0.476746i | −0.209188 | − | 0.977875i | \(-0.567082\pi\) |
0.865372 | + | 0.501130i | \(0.167082\pi\) | |||||||
\(884\) | −6.90620 | − | 5.01765i | −0.232281 | − | 0.168762i | ||||
\(885\) | −10.6212 | − | 32.6888i | −0.357029 | − | 1.09882i | ||||
\(886\) | 7.60167 | + | 23.3955i | 0.255383 | + | 0.785989i | ||||
\(887\) | 33.1280 | + | 24.0689i | 1.11233 | + | 0.808154i | 0.983029 | − | 0.183452i | \(-0.0587270\pi\) |
0.129300 | + | 0.991606i | \(0.458727\pi\) | |||||||
\(888\) | −2.97310 | + | 2.16009i | −0.0997708 | + | 0.0724877i | ||||
\(889\) | 12.7852 | − | 39.3489i | 0.428803 | − | 1.31972i | ||||
\(890\) | 11.4069 | 0.382360 | ||||||||
\(891\) | 18.5230 | + | 32.3613i | 0.620542 | + | 1.08414i | ||||
\(892\) | 28.3845 | 0.950384 | ||||||||
\(893\) | 1.05262 | − | 3.23963i | 0.0352245 | − | 0.108410i | ||||
\(894\) | −17.5921 | + | 12.7814i | −0.588369 | + | 0.427475i | ||||
\(895\) | −45.3540 | − | 32.9516i | −1.51602 | − | 1.10145i | ||||
\(896\) | 0.957938 | + | 2.94823i | 0.0320025 | + | 0.0984935i | ||||
\(897\) | 6.61044 | + | 20.3448i | 0.220716 | + | 0.679294i | ||||
\(898\) | 28.5341 | + | 20.7313i | 0.952197 | + | 0.691812i | ||||
\(899\) | −7.82052 | + | 5.68194i | −0.260829 | + | 0.189503i | ||||
\(900\) | 0.459553 | − | 1.41436i | 0.0153184 | − | 0.0471453i | ||||
\(901\) | 25.2361 | 0.840737 | ||||||||
\(902\) | 1.96922 | − | 18.0858i | 0.0655679 | − | 0.602190i | ||||
\(903\) | −29.9243 | −0.995818 | ||||||||
\(904\) | −3.51254 | + | 10.8105i | −0.116825 | + | 0.359551i | ||||
\(905\) | 3.07582 | − | 2.23471i | 0.102244 | − | 0.0742843i | ||||
\(906\) | −20.6904 | − | 15.0324i | −0.687391 | − | 0.499419i | ||||
\(907\) | −16.9648 | − | 52.2122i | −0.563306 | − | 1.73368i | −0.672930 | − | 0.739706i | \(-0.734965\pi\) |
0.109624 | − | 0.993973i | \(-0.465035\pi\) | |||||||
\(908\) | −2.62860 | − | 8.09001i | −0.0872332 | − | 0.268476i | ||||
\(909\) | 6.63990 | + | 4.82417i | 0.220232 | + | 0.160008i | ||||
\(910\) | 24.5446 | − | 17.8327i | 0.813646 | − | 0.591148i | ||||
\(911\) | 14.4762 | − | 44.5531i | 0.479617 | − | 1.47611i | −0.360011 | − | 0.932948i | \(-0.617227\pi\) |
0.839628 | − | 0.543162i | \(-0.182773\pi\) | |||||||
\(912\) | −2.10092 | −0.0695684 | ||||||||
\(913\) | −4.02675 | + | 36.9825i | −0.133266 | + | 1.22394i | ||||
\(914\) | 7.37055 | 0.243796 | ||||||||
\(915\) | −10.1266 | + | 31.1666i | −0.334776 | + | 1.03033i | ||||
\(916\) | 1.38124 | − | 1.00353i | 0.0456374 | − | 0.0331575i | ||||
\(917\) | −11.5052 | − | 8.35905i | −0.379937 | − | 0.276040i | ||||
\(918\) | −2.20960 | − | 6.80046i | −0.0729277 | − | 0.224448i | ||||
\(919\) | −0.545464 | − | 1.67876i | −0.0179932 | − | 0.0553773i | 0.941657 | − | 0.336575i | \(-0.109268\pi\) |
−0.959650 | + | 0.281197i | \(0.909268\pi\) | |||||||
\(920\) | −5.09377 | − | 3.70084i | −0.167937 | − | 0.122013i | ||||
\(921\) | −9.59644 | + | 6.97222i | −0.316214 | + | 0.229743i | ||||
\(922\) | 11.2753 | − | 34.7017i | 0.371331 | − | 1.14284i | ||||
\(923\) | 63.5320 | 2.09118 | ||||||||
\(924\) | 10.7302 | + | 18.7467i | 0.352998 | + | 0.616720i | ||||
\(925\) | −1.83988 | −0.0604947 | ||||||||
\(926\) | 5.01250 | − | 15.4269i | 0.164721 | − | 0.506959i | ||||
\(927\) | 10.9386 | − | 7.94733i | 0.359269 | − | 0.261024i | ||||
\(928\) | 5.26156 | + | 3.82275i | 0.172719 | + | 0.125488i | ||||
\(929\) | −8.92707 | − | 27.4747i | −0.292888 | − | 0.901416i | −0.983923 | − | 0.178595i | \(-0.942845\pi\) |
0.691035 | − | 0.722821i | \(-0.257155\pi\) | |||||||
\(930\) | −2.37386 | − | 7.30600i | −0.0778421 | − | 0.239573i | ||||
\(931\) | 2.11130 | + | 1.53395i | 0.0691949 | + | 0.0502731i | ||||
\(932\) | −8.05483 | + | 5.85218i | −0.263845 | + | 0.191694i | ||||
\(933\) | 5.46392 | − | 16.8162i | 0.178881 | − | 0.550538i | ||||
\(934\) | −4.27354 | −0.139835 | ||||||||
\(935\) | 17.1383 | − | 3.57600i | 0.560482 | − | 0.116948i | ||||
\(936\) | 5.62481 | 0.183853 | ||||||||
\(937\) | 7.77009 | − | 23.9139i | 0.253838 | − | 0.781232i | −0.740219 | − | 0.672366i | \(-0.765278\pi\) |
0.994056 | − | 0.108866i | \(-0.0347219\pi\) | |||||||
\(938\) | −35.4003 | + | 25.7198i | −1.15586 | + | 0.839781i | ||||
\(939\) | −53.3302 | − | 38.7467i | −1.74037 | − | 1.26445i | ||||
\(940\) | −2.58949 | − | 7.96963i | −0.0844598 | − | 0.259941i | ||||
\(941\) | −0.230113 | − | 0.708216i | −0.00750148 | − | 0.0230872i | 0.947236 | − | 0.320538i | \(-0.103864\pi\) |
−0.954737 | + | 0.297451i | \(0.903864\pi\) | |||||||
\(942\) | 6.32942 | + | 4.59859i | 0.206224 | + | 0.149830i | ||||
\(943\) | 11.3578 | − | 8.25195i | 0.369862 | − | 0.268721i | ||||
\(944\) | −2.05505 | + | 6.32479i | −0.0668862 | + | 0.205854i | ||||
\(945\) | 25.4125 | 0.826670 | ||||||||
\(946\) | −10.2391 | + | 11.2866i | −0.332902 | + | 0.366959i | ||||
\(947\) | 54.6088 | 1.77455 | 0.887273 | − | 0.461244i | \(-0.152597\pi\) | ||||
0.887273 | + | 0.461244i | \(0.152597\pi\) | |||||||
\(948\) | 4.71119 | − | 14.4996i | 0.153012 | − | 0.470924i | ||||
\(949\) | −10.2228 | + | 7.42729i | −0.331846 | + | 0.241100i | ||||
\(950\) | −0.850949 | − | 0.618250i | −0.0276084 | − | 0.0200587i | ||||
\(951\) | 4.67626 | + | 14.3921i | 0.151638 | + | 0.466694i | ||||
\(952\) | −2.05551 | − | 6.32620i | −0.0666194 | − | 0.205033i | ||||
\(953\) | −23.8404 | − | 17.3211i | −0.772267 | − | 0.561085i | 0.130381 | − | 0.991464i | \(-0.458380\pi\) |
−0.902648 | + | 0.430379i | \(0.858380\pi\) | |||||||
\(954\) | −13.4526 | + | 9.77389i | −0.435544 | + | 0.316441i | ||||
\(955\) | 5.43087 | − | 16.7145i | 0.175739 | − | 0.540869i | ||||
\(956\) | 16.2786 | 0.526487 | ||||||||
\(957\) | 41.3302 | + | 18.5867i | 1.33601 | + | 0.600822i | ||||
\(958\) | 39.1936 | 1.26629 | ||||||||
\(959\) | 13.0635 | − | 40.2052i | 0.421841 | − | 1.29829i | ||||
\(960\) | −4.18129 | + | 3.03789i | −0.134951 | + | 0.0980474i | ||||
\(961\) | 23.2922 | + | 16.9228i | 0.751362 | + | 0.545896i | ||||
\(962\) | −2.15043 | − | 6.61834i | −0.0693326 | − | 0.213384i | ||||
\(963\) | −6.36415 | − | 19.5868i | −0.205082 | − | 0.631177i | ||||
\(964\) | 4.81482 | + | 3.49817i | 0.155075 | + | 0.112668i | ||||
\(965\) | 24.0777 | − | 17.4935i | 0.775088 | − | 0.563134i | ||||
\(966\) | −5.15093 | + | 15.8529i | −0.165728 | + | 0.510059i | ||||
\(967\) | −30.8647 | −0.992541 | −0.496271 | − | 0.868168i | \(-0.665298\pi\) | ||||
−0.496271 | + | 0.868168i | \(0.665298\pi\) | |||||||
\(968\) | 10.7422 | + | 2.36735i | 0.345269 | + | 0.0760895i | ||||
\(969\) | 4.50808 | 0.144820 | ||||||||
\(970\) | 4.15889 | − | 12.7997i | 0.133534 | − | 0.410975i | ||||
\(971\) | 8.76140 | − | 6.36553i | 0.281167 | − | 0.204280i | −0.438259 | − | 0.898849i | \(-0.644405\pi\) |
0.719426 | + | 0.694569i | \(0.244405\pi\) | |||||||
\(972\) | 11.0210 | + | 8.00724i | 0.353499 | + | 0.256832i | ||||
\(973\) | 5.54629 | + | 17.0697i | 0.177806 | + | 0.547231i | ||||
\(974\) | −1.01184 | − | 3.11412i | −0.0324214 | − | 0.0997829i | ||||
\(975\) | 7.11234 | + | 5.16742i | 0.227777 | + | 0.165490i | ||||
\(976\) | 5.12965 | − | 3.72691i | 0.164196 | − | 0.119295i | ||||
\(977\) | 1.70953 | − | 5.26138i | 0.0546926 | − | 0.168327i | −0.919979 | − | 0.391968i | \(-0.871794\pi\) |
0.974672 | + | 0.223641i | \(0.0717944\pi\) | |||||||
\(978\) | 41.7916 | 1.33635 | ||||||||
\(979\) | −14.0257 | − | 6.30753i | −0.448263 | − | 0.201589i | ||||
\(980\) | 6.42000 | 0.205079 | ||||||||
\(981\) | −1.47710 | + | 4.54604i | −0.0471601 | + | 0.145144i | ||||
\(982\) | 32.8868 | − | 23.8936i | 1.04946 | − | 0.762476i | ||||
\(983\) | −17.9985 | − | 13.0767i | −0.574065 | − | 0.417082i | 0.262515 | − | 0.964928i | \(-0.415448\pi\) |
−0.836579 | + | 0.547846i | \(0.815448\pi\) | |||||||
\(984\) | −3.56116 | − | 10.9601i | −0.113526 | − | 0.349396i | ||||
\(985\) | 13.8748 | + | 42.7022i | 0.442088 | + | 1.36061i | ||||
\(986\) | −11.2901 | − | 8.20272i | −0.359549 | − | 0.261228i | ||||
\(987\) | −17.9478 | + | 13.0398i | −0.571284 | + | 0.415062i | ||||
\(988\) | 1.22937 | − | 3.78361i | 0.0391114 | − | 0.120373i | ||||
\(989\) | −11.7597 | −0.373938 | ||||||||
\(990\) | −7.75092 | + | 8.54387i | −0.246340 | + | 0.271542i | ||||
\(991\) | −8.28887 | −0.263305 | −0.131652 | − | 0.991296i | \(-0.542028\pi\) | ||||
−0.131652 | + | 0.991296i | \(0.542028\pi\) | |||||||
\(992\) | −0.459307 | + | 1.41360i | −0.0145830 | + | 0.0448819i | ||||
\(993\) | −34.6875 | + | 25.2020i | −1.10078 | + | 0.799760i | ||||
\(994\) | 40.0503 | + | 29.0982i | 1.27032 | + | 0.922940i | ||||
\(995\) | 18.2223 | + | 56.0825i | 0.577686 | + | 1.77794i | ||||
\(996\) | 7.28201 | + | 22.4117i | 0.230739 | + | 0.710143i | ||||
\(997\) | 22.2912 | + | 16.1955i | 0.705968 | + | 0.512916i | 0.881870 | − | 0.471492i | \(-0.156284\pi\) |
−0.175903 | + | 0.984408i | \(0.556284\pi\) | |||||||
\(998\) | −11.4431 | + | 8.31393i | −0.362226 | + | 0.263173i | ||||
\(999\) | 1.80125 | − | 5.54369i | 0.0569891 | − | 0.175395i |
(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 | 418.2.f.h.229.2 | yes | 20 | |
11.4 | even | 5 | 4598.2.a.cc.1.8 | 10 | |||
11.5 | even | 5 | inner | 418.2.f.h.115.2 | ✓ | 20 | |
11.7 | odd | 10 | 4598.2.a.cd.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.h.115.2 | ✓ | 20 | 11.5 | even | 5 | inner | |
418.2.f.h.229.2 | yes | 20 | 1.1 | even | 1 | trivial | |
4598.2.a.cc.1.8 | 10 | 11.4 | even | 5 | |||
4598.2.a.cd.1.8 | 10 | 11.7 | odd | 10 |