Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 9 x^{10} - 15 x^{9} + 29 x^{8} - 26 x^{7} + 43 x^{6} + 24 x^{5} + 16 x^{4} + \cdots + 1 \) |
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 | 313.1 | ||
Root | \(-0.566948 + 1.74489i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.313 |
Dual form | 429.2.n.a.196.1 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.566948 | − | 1.74489i | −0.400893 | − | 1.23382i | −0.924277 | − | 0.381723i | \(-0.875331\pi\) |
0.523384 | − | 0.852097i | \(-0.324669\pi\) | |||||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | −1.10516 | + | 0.802947i | −0.552581 | + | 0.401473i | ||||
\(5\) | −0.477448 | + | 1.46943i | −0.213521 | + | 0.657151i | 0.785734 | + | 0.618564i | \(0.212285\pi\) |
−0.999255 | + | 0.0385862i | \(0.987715\pi\) | |||||||
\(6\) | −0.566948 | + | 1.74489i | −0.231455 | + | 0.712346i | ||||
\(7\) | −0.675271 | + | 0.490613i | −0.255228 | + | 0.185434i | −0.708041 | − | 0.706171i | \(-0.750421\pi\) |
0.452812 | + | 0.891606i | \(0.350421\pi\) | |||||||
\(8\) | −0.940958 | − | 0.683646i | −0.332679 | − | 0.241705i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 2.83468 | 0.896405 | ||||||||
\(11\) | −2.09568 | + | 2.57063i | −0.631872 | + | 0.775073i | ||||
\(12\) | 1.36605 | 0.394346 | ||||||||
\(13\) | 0.309017 | + | 0.951057i | 0.0857059 | + | 0.263776i | ||||
\(14\) | 1.23891 | + | 0.900119i | 0.331112 | + | 0.240567i | ||||
\(15\) | 1.24997 | − | 0.908160i | 0.322742 | − | 0.234486i | ||||
\(16\) | −1.50368 | + | 4.62784i | −0.375919 | + | 1.15696i | ||||
\(17\) | −1.22440 | + | 3.76833i | −0.296961 | + | 0.913953i | 0.685594 | + | 0.727984i | \(0.259542\pi\) |
−0.982556 | + | 0.185969i | \(0.940458\pi\) | |||||||
\(18\) | 1.48429 | − | 1.07840i | 0.349850 | − | 0.254181i | ||||
\(19\) | 1.21176 | + | 0.880396i | 0.277997 | + | 0.201977i | 0.718043 | − | 0.695998i | \(-0.245038\pi\) |
−0.440046 | + | 0.897975i | \(0.645038\pi\) | |||||||
\(20\) | −0.652220 | − | 2.00733i | −0.145841 | − | 0.448852i | ||||
\(21\) | 0.834681 | 0.182142 | ||||||||
\(22\) | 5.67359 | + | 2.19931i | 1.20961 | + | 0.468895i | ||||
\(23\) | 1.75538 | 0.366021 | 0.183011 | − | 0.983111i | \(-0.441416\pi\) | ||||
0.183011 | + | 0.983111i | \(0.441416\pi\) | |||||||
\(24\) | 0.359414 | + | 1.10616i | 0.0733651 | + | 0.225794i | ||||
\(25\) | 2.11381 | + | 1.53577i | 0.422761 | + | 0.307154i | ||||
\(26\) | 1.48429 | − | 1.07840i | 0.291093 | − | 0.211491i | ||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | 0.352347 | − | 1.08441i | 0.0665874 | − | 0.204935i | ||||
\(29\) | −6.88940 | + | 5.00544i | −1.27933 | + | 0.929487i | −0.999533 | − | 0.0305729i | \(-0.990267\pi\) |
−0.279796 | + | 0.960059i | \(0.590267\pi\) | |||||||
\(30\) | −2.29331 | − | 1.66618i | −0.418698 | − | 0.304202i | ||||
\(31\) | −0.487584 | − | 1.50063i | −0.0875728 | − | 0.269521i | 0.897674 | − | 0.440660i | \(-0.145255\pi\) |
−0.985247 | + | 0.171138i | \(0.945255\pi\) | |||||||
\(32\) | 6.60139 | 1.16697 | ||||||||
\(33\) | 3.20642 | − | 0.847870i | 0.558166 | − | 0.147595i | ||||
\(34\) | 7.26947 | 1.24670 | ||||||||
\(35\) | −0.398517 | − | 1.22651i | −0.0673616 | − | 0.207318i | ||||
\(36\) | −1.10516 | − | 0.802947i | −0.184194 | − | 0.133824i | ||||
\(37\) | 4.46927 | − | 3.24711i | 0.734743 | − | 0.533822i | −0.156318 | − | 0.987707i | \(-0.549962\pi\) |
0.891060 | + | 0.453885i | \(0.149962\pi\) | |||||||
\(38\) | 0.849185 | − | 2.61352i | 0.137756 | − | 0.423969i | ||||
\(39\) | 0.309017 | − | 0.951057i | 0.0494823 | − | 0.152291i | ||||
\(40\) | 1.45383 | − | 1.05627i | 0.229871 | − | 0.167011i | ||||
\(41\) | −7.17922 | − | 5.21601i | −1.12121 | − | 0.814604i | −0.136815 | − | 0.990597i | \(-0.543686\pi\) |
−0.984391 | + | 0.175993i | \(0.943686\pi\) | |||||||
\(42\) | −0.473220 | − | 1.45642i | −0.0730195 | − | 0.224731i | ||||
\(43\) | 3.09803 | 0.472445 | 0.236222 | − | 0.971699i | \(-0.424091\pi\) | ||||
0.236222 | + | 0.971699i | \(0.424091\pi\) | |||||||
\(44\) | 0.251990 | − | 4.52368i | 0.0379890 | − | 0.681970i | ||||
\(45\) | −1.54505 | −0.230323 | ||||||||
\(46\) | −0.995206 | − | 3.06293i | −0.146735 | − | 0.451604i | ||||
\(47\) | −1.80257 | − | 1.30964i | −0.262932 | − | 0.191031i | 0.448507 | − | 0.893779i | \(-0.351956\pi\) |
−0.711438 | + | 0.702748i | \(0.751956\pi\) | |||||||
\(48\) | 3.93668 | − | 2.86017i | 0.568211 | − | 0.412829i | ||||
\(49\) | −1.94783 | + | 5.99480i | −0.278261 | + | 0.856400i | ||||
\(50\) | 1.48133 | − | 4.55905i | 0.209491 | − | 0.644747i | ||||
\(51\) | 3.20553 | − | 2.32895i | 0.448864 | − | 0.326119i | ||||
\(52\) | −1.10516 | − | 0.802947i | −0.153258 | − | 0.111349i | ||||
\(53\) | 0.153958 | + | 0.473834i | 0.0211478 | + | 0.0650861i | 0.961073 | − | 0.276293i | \(-0.0891060\pi\) |
−0.939926 | + | 0.341379i | \(0.889106\pi\) | |||||||
\(54\) | −1.83468 | −0.249668 | ||||||||
\(55\) | −2.77679 | − | 4.30680i | −0.374422 | − | 0.580729i | ||||
\(56\) | 0.970807 | 0.129730 | ||||||||
\(57\) | −0.462852 | − | 1.42451i | −0.0613062 | − | 0.188681i | ||||
\(58\) | 12.6398 | + | 9.18338i | 1.65969 | + | 1.20584i | ||||
\(59\) | 4.72692 | − | 3.43430i | 0.615392 | − | 0.447108i | −0.235917 | − | 0.971773i | \(-0.575809\pi\) |
0.851309 | + | 0.524665i | \(0.175809\pi\) | |||||||
\(60\) | −0.652220 | + | 2.00733i | −0.0842012 | + | 0.259145i | ||||
\(61\) | −3.39577 | + | 10.4511i | −0.434784 | + | 1.33813i | 0.458524 | + | 0.888682i | \(0.348378\pi\) |
−0.893308 | + | 0.449445i | \(0.851622\pi\) | |||||||
\(62\) | −2.34199 | + | 1.70156i | −0.297433 | + | 0.216098i | ||||
\(63\) | −0.675271 | − | 0.490613i | −0.0850762 | − | 0.0618115i | ||||
\(64\) | −0.735286 | − | 2.26298i | −0.0919108 | − | 0.282872i | ||||
\(65\) | −1.54505 | −0.191640 | ||||||||
\(66\) | −3.29731 | − | 5.11413i | −0.405870 | − | 0.629506i | ||||
\(67\) | −8.43289 | −1.03024 | −0.515121 | − | 0.857117i | \(-0.672253\pi\) | ||||
−0.515121 | + | 0.857117i | \(0.672253\pi\) | |||||||
\(68\) | −1.67260 | − | 5.14774i | −0.202833 | − | 0.624255i | ||||
\(69\) | −1.42013 | − | 1.03178i | −0.170963 | − | 0.124212i | ||||
\(70\) | −1.91418 | + | 1.39073i | −0.228788 | + | 0.166224i | ||||
\(71\) | −1.46101 | + | 4.49653i | −0.173390 | + | 0.533640i | −0.999556 | − | 0.0297868i | \(-0.990517\pi\) |
0.826166 | + | 0.563426i | \(0.190517\pi\) | |||||||
\(72\) | 0.359414 | − | 1.10616i | 0.0423573 | − | 0.130362i | ||||
\(73\) | −1.33175 | + | 0.967570i | −0.155869 | + | 0.113245i | −0.662986 | − | 0.748632i | \(-0.730711\pi\) |
0.507117 | + | 0.861877i | \(0.330711\pi\) | |||||||
\(74\) | −8.19968 | − | 5.95741i | −0.953193 | − | 0.692535i | ||||
\(75\) | −0.807402 | − | 2.48493i | −0.0932308 | − | 0.286935i | ||||
\(76\) | −2.04610 | −0.234704 | ||||||||
\(77\) | 0.153970 | − | 2.76404i | 0.0175465 | − | 0.314991i | ||||
\(78\) | −1.83468 | −0.207737 | ||||||||
\(79\) | −0.734755 | − | 2.26134i | −0.0826664 | − | 0.254421i | 0.901177 | − | 0.433451i | \(-0.142704\pi\) |
−0.983844 | + | 0.179030i | \(0.942704\pi\) | |||||||
\(80\) | −6.08238 | − | 4.41911i | −0.680031 | − | 0.494071i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | −5.03110 | + | 15.4841i | −0.555592 | + | 1.70994i | ||||
\(83\) | −3.49105 | + | 10.7444i | −0.383193 | + | 1.17935i | 0.554590 | + | 0.832124i | \(0.312875\pi\) |
−0.937783 | + | 0.347222i | \(0.887125\pi\) | |||||||
\(84\) | −0.922457 | + | 0.670204i | −0.100648 | + | 0.0731253i | ||||
\(85\) | −4.95272 | − | 3.59836i | −0.537197 | − | 0.390297i | ||||
\(86\) | −1.75642 | − | 5.40570i | −0.189399 | − | 0.582912i | ||||
\(87\) | 8.51576 | 0.912985 | ||||||||
\(88\) | 3.72935 | − | 0.986147i | 0.397550 | − | 0.105124i | ||||
\(89\) | −6.16923 | −0.653937 | −0.326968 | − | 0.945035i | \(-0.606027\pi\) | ||||
−0.326968 | + | 0.945035i | \(0.606027\pi\) | |||||||
\(90\) | 0.875965 | + | 2.69594i | 0.0923348 | + | 0.284177i | ||||
\(91\) | −0.675271 | − | 0.490613i | −0.0707876 | − | 0.0514302i | ||||
\(92\) | −1.93997 | + | 1.40947i | −0.202256 | + | 0.146948i | ||||
\(93\) | −0.487584 | + | 1.50063i | −0.0505602 | + | 0.155608i | ||||
\(94\) | −1.26321 | + | 3.88777i | −0.130291 | + | 0.400993i | ||||
\(95\) | −1.87224 | + | 1.36026i | −0.192087 | + | 0.139560i | ||||
\(96\) | −5.34064 | − | 3.88020i | −0.545076 | − | 0.396021i | ||||
\(97\) | 3.31764 | + | 10.2106i | 0.336855 | + | 1.03673i | 0.965801 | + | 0.259285i | \(0.0834868\pi\) |
−0.628946 | + | 0.777449i | \(0.716513\pi\) | |||||||
\(98\) | 11.5646 | 1.16820 | ||||||||
\(99\) | −3.09241 | − | 1.19874i | −0.310799 | − | 0.120478i | ||||
\(100\) | −3.56924 | −0.356924 | ||||||||
\(101\) | 2.36659 | + | 7.28361i | 0.235484 | + | 0.724746i | 0.997057 | + | 0.0766663i | \(0.0244276\pi\) |
−0.761573 | + | 0.648080i | \(0.775572\pi\) | |||||||
\(102\) | −5.88112 | − | 4.27289i | −0.582318 | − | 0.423079i | ||||
\(103\) | 5.74057 | − | 4.17077i | 0.565635 | − | 0.410958i | −0.267882 | − | 0.963452i | \(-0.586324\pi\) |
0.833517 | + | 0.552494i | \(0.186324\pi\) | |||||||
\(104\) | 0.359414 | − | 1.10616i | 0.0352434 | − | 0.108468i | ||||
\(105\) | −0.398517 | + | 1.22651i | −0.0388912 | + | 0.119695i | ||||
\(106\) | 0.739500 | − | 0.537278i | 0.0718266 | − | 0.0521851i | ||||
\(107\) | −13.4846 | − | 9.79711i | −1.30360 | − | 0.947123i | −0.303619 | − | 0.952794i | \(-0.598195\pi\) |
−0.999984 | + | 0.00567100i | \(0.998195\pi\) | |||||||
\(108\) | 0.422134 | + | 1.29919i | 0.0406199 | + | 0.125015i | ||||
\(109\) | −19.4175 | −1.85986 | −0.929928 | − | 0.367742i | \(-0.880131\pi\) | ||||
−0.929928 | + | 0.367742i | \(0.880131\pi\) | |||||||
\(110\) | −5.94059 | + | 7.28691i | −0.566413 | + | 0.694779i | ||||
\(111\) | −5.52432 | −0.524345 | ||||||||
\(112\) | −1.25509 | − | 3.86277i | −0.118595 | − | 0.364998i | ||||
\(113\) | 10.4142 | + | 7.56633i | 0.979682 | + | 0.711781i | 0.957638 | − | 0.287976i | \(-0.0929824\pi\) |
0.0220447 | + | 0.999757i | \(0.492982\pi\) | |||||||
\(114\) | −2.22320 | + | 1.61525i | −0.208221 | + | 0.151282i | ||||
\(115\) | −0.838101 | + | 2.57941i | −0.0781533 | + | 0.240531i | ||||
\(116\) | 3.59479 | − | 11.0636i | 0.333768 | − | 1.02723i | ||||
\(117\) | −0.809017 | + | 0.587785i | −0.0747936 | + | 0.0543408i | ||||
\(118\) | −8.67238 | − | 6.30085i | −0.798357 | − | 0.580041i | ||||
\(119\) | −1.02199 | − | 3.14535i | −0.0936853 | − | 0.288334i | ||||
\(120\) | −1.79703 | −0.164046 | ||||||||
\(121\) | −2.21624 | − | 10.7744i | −0.201476 | − | 0.979493i | ||||
\(122\) | 20.1612 | 1.82531 | ||||||||
\(123\) | 2.74222 | + | 8.43968i | 0.247258 | + | 0.760980i | ||||
\(124\) | 1.74379 | + | 1.26693i | 0.156597 | + | 0.113774i | ||||
\(125\) | −9.51582 | + | 6.91365i | −0.851121 | + | 0.618375i | ||||
\(126\) | −0.473220 | + | 1.45642i | −0.0421578 | + | 0.129748i | ||||
\(127\) | 4.03118 | − | 12.4067i | 0.357710 | − | 1.10092i | −0.596712 | − | 0.802455i | \(-0.703527\pi\) |
0.954422 | − | 0.298462i | \(-0.0964735\pi\) | |||||||
\(128\) | 7.14950 | − | 5.19442i | 0.631933 | − | 0.459126i | ||||
\(129\) | −2.50636 | − | 1.82097i | −0.220672 | − | 0.160328i | ||||
\(130\) | 0.875965 | + | 2.69594i | 0.0768272 | + | 0.236450i | ||||
\(131\) | 18.0732 | 1.57906 | 0.789531 | − | 0.613711i | \(-0.210324\pi\) | ||||
0.789531 | + | 0.613711i | \(0.210324\pi\) | |||||||
\(132\) | −2.86282 | + | 3.51162i | −0.249176 | + | 0.305647i | ||||
\(133\) | −1.25020 | −0.108406 | ||||||||
\(134\) | 4.78101 | + | 14.7144i | 0.413016 | + | 1.27113i | ||||
\(135\) | 1.24997 | + | 0.908160i | 0.107581 | + | 0.0781620i | ||||
\(136\) | 3.72831 | − | 2.70878i | 0.319700 | − | 0.232276i | ||||
\(137\) | 4.02283 | − | 12.3810i | 0.343693 | − | 1.05778i | −0.618586 | − | 0.785717i | \(-0.712294\pi\) |
0.962280 | − | 0.272062i | \(-0.0877057\pi\) | |||||||
\(138\) | −0.995206 | + | 3.06293i | −0.0847176 | + | 0.260734i | ||||
\(139\) | −10.8108 | + | 7.85447i | −0.916956 | + | 0.666208i | −0.942765 | − | 0.333459i | \(-0.891784\pi\) |
0.0258083 | + | 0.999667i | \(0.491784\pi\) | |||||||
\(140\) | 1.42525 | + | 1.03550i | 0.120455 | + | 0.0875159i | ||||
\(141\) | 0.688520 | + | 2.11905i | 0.0579838 | + | 0.178456i | ||||
\(142\) | 8.67424 | 0.727926 | ||||||||
\(143\) | −3.09241 | − | 1.19874i | −0.258600 | − | 0.100244i | ||||
\(144\) | −4.86600 | −0.405500 | ||||||||
\(145\) | −4.06583 | − | 12.5133i | −0.337649 | − | 1.03918i | ||||
\(146\) | 2.44333 | + | 1.77518i | 0.202211 | + | 0.146915i | ||||
\(147\) | 5.09948 | − | 3.70499i | 0.420598 | − | 0.305583i | ||||
\(148\) | −2.33200 | + | 7.17716i | −0.191689 | + | 0.589959i | ||||
\(149\) | −1.37468 | + | 4.23083i | −0.112618 | + | 0.346603i | −0.991443 | − | 0.130542i | \(-0.958328\pi\) |
0.878825 | + | 0.477145i | \(0.158328\pi\) | |||||||
\(150\) | −3.87816 | + | 2.81765i | −0.316650 | + | 0.230060i | ||||
\(151\) | −11.2631 | − | 8.18315i | −0.916581 | − | 0.665935i | 0.0260897 | − | 0.999660i | \(-0.491694\pi\) |
−0.942671 | + | 0.333725i | \(0.891694\pi\) | |||||||
\(152\) | −0.538337 | − | 1.65683i | −0.0436649 | − | 0.134387i | ||||
\(153\) | −3.96225 | −0.320329 | ||||||||
\(154\) | −4.91022 | + | 1.29840i | −0.395677 | + | 0.104628i | ||||
\(155\) | 2.43787 | 0.195815 | ||||||||
\(156\) | 0.422134 | + | 1.29919i | 0.0337978 | + | 0.104019i | ||||
\(157\) | 8.60119 | + | 6.24913i | 0.686450 | + | 0.498735i | 0.875491 | − | 0.483234i | \(-0.160538\pi\) |
−0.189041 | + | 0.981969i | \(0.560538\pi\) | |||||||
\(158\) | −3.52922 | + | 2.56413i | −0.280770 | + | 0.203991i | ||||
\(159\) | 0.153958 | − | 0.473834i | 0.0122097 | − | 0.0375775i | ||||
\(160\) | −3.15182 | + | 9.70030i | −0.249173 | + | 0.766876i | ||||
\(161\) | −1.18536 | + | 0.861211i | −0.0934191 | + | 0.0678729i | ||||
\(162\) | 1.48429 | + | 1.07840i | 0.116617 | + | 0.0847270i | ||||
\(163\) | −0.768082 | − | 2.36391i | −0.0601608 | − | 0.185156i | 0.916460 | − | 0.400127i | \(-0.131034\pi\) |
−0.976620 | + | 0.214971i | \(0.931034\pi\) | |||||||
\(164\) | 12.1224 | 0.946599 | ||||||||
\(165\) | −0.285010 | + | 5.11643i | −0.0221880 | + | 0.398314i | ||||
\(166\) | 20.7269 | 1.60872 | ||||||||
\(167\) | −5.46850 | − | 16.8303i | −0.423165 | − | 1.30237i | −0.904740 | − | 0.425964i | \(-0.859935\pi\) |
0.481575 | − | 0.876405i | \(-0.340065\pi\) | |||||||
\(168\) | −0.785400 | − | 0.570626i | −0.0605949 | − | 0.0440248i | ||||
\(169\) | −0.809017 | + | 0.587785i | −0.0622321 | + | 0.0452143i | ||||
\(170\) | −3.47079 | + | 10.6820i | −0.266198 | + | 0.819272i | ||||
\(171\) | −0.462852 | + | 1.42451i | −0.0353951 | + | 0.108935i | ||||
\(172\) | −3.42382 | + | 2.48755i | −0.261064 | + | 0.189674i | ||||
\(173\) | 10.4033 | + | 7.55847i | 0.790952 | + | 0.574660i | 0.908246 | − | 0.418437i | \(-0.137422\pi\) |
−0.117294 | + | 0.993097i | \(0.537422\pi\) | |||||||
\(174\) | −4.82799 | − | 14.8590i | −0.366009 | − | 1.12646i | ||||
\(175\) | −2.18086 | −0.164858 | ||||||||
\(176\) | −8.74523 | − | 13.5639i | −0.659196 | − | 1.02242i | ||||
\(177\) | −5.84279 | −0.439171 | ||||||||
\(178\) | 3.49763 | + | 10.7646i | 0.262158 | + | 0.806841i | ||||
\(179\) | 8.99073 | + | 6.53215i | 0.671999 | + | 0.488236i | 0.870694 | − | 0.491826i | \(-0.163670\pi\) |
−0.198695 | + | 0.980061i | \(0.563670\pi\) | |||||||
\(180\) | 1.70753 | − | 1.24060i | 0.127272 | − | 0.0924686i | ||||
\(181\) | 0.542673 | − | 1.67018i | 0.0403366 | − | 0.124143i | −0.928860 | − | 0.370430i | \(-0.879210\pi\) |
0.969197 | + | 0.246287i | \(0.0792104\pi\) | |||||||
\(182\) | −0.473220 | + | 1.45642i | −0.0350774 | + | 0.107957i | ||||
\(183\) | 8.89024 | − | 6.45914i | 0.657186 | − | 0.477473i | ||||
\(184\) | −1.65174 | − | 1.20006i | −0.121768 | − | 0.0884693i | ||||
\(185\) | 2.63757 | + | 8.11762i | 0.193918 | + | 0.596819i | ||||
\(186\) | 2.89486 | 0.212262 | ||||||||
\(187\) | −7.12100 | − | 11.0447i | −0.520739 | − | 0.807668i | ||||
\(188\) | 3.04370 | 0.221985 | ||||||||
\(189\) | 0.257931 | + | 0.793829i | 0.0187617 | + | 0.0577426i | ||||
\(190\) | 3.43496 | + | 2.49564i | 0.249198 | + | 0.181053i | ||||
\(191\) | 4.36059 | − | 3.16815i | 0.315521 | − | 0.229240i | −0.418741 | − | 0.908106i | \(-0.637528\pi\) |
0.734262 | + | 0.678866i | \(0.237528\pi\) | |||||||
\(192\) | −0.735286 | + | 2.26298i | −0.0530647 | + | 0.163316i | ||||
\(193\) | 2.96202 | − | 9.11616i | 0.213211 | − | 0.656196i | −0.786065 | − | 0.618144i | \(-0.787885\pi\) |
0.999276 | − | 0.0380516i | \(-0.0121151\pi\) | |||||||
\(194\) | 15.9355 | − | 11.5778i | 1.14410 | − | 0.831238i | ||||
\(195\) | 1.24997 | + | 0.908160i | 0.0895126 | + | 0.0650347i | ||||
\(196\) | −2.66084 | − | 8.18923i | −0.190060 | − | 0.584945i | ||||
\(197\) | 12.7324 | 0.907143 | 0.453572 | − | 0.891220i | \(-0.350150\pi\) | ||||
0.453572 | + | 0.891220i | \(0.350150\pi\) | |||||||
\(198\) | −0.338436 | + | 6.07553i | −0.0240516 | + | 0.431769i | ||||
\(199\) | 2.14932 | 0.152361 | 0.0761807 | − | 0.997094i | \(-0.475727\pi\) | ||||
0.0761807 | + | 0.997094i | \(0.475727\pi\) | |||||||
\(200\) | −0.939080 | − | 2.89019i | −0.0664030 | − | 0.204367i | ||||
\(201\) | 6.82236 | + | 4.95673i | 0.481212 | + | 0.349621i | ||||
\(202\) | 11.3673 | − | 8.25885i | 0.799802 | − | 0.581090i | ||||
\(203\) | 2.19648 | − | 6.76006i | 0.154162 | − | 0.474463i | ||||
\(204\) | −1.67260 | + | 5.14774i | −0.117106 | + | 0.360414i | ||||
\(205\) | 11.0923 | − | 8.05902i | 0.774719 | − | 0.562866i | ||||
\(206\) | −10.5321 | − | 7.65203i | −0.733807 | − | 0.533142i | ||||
\(207\) | 0.542441 | + | 1.66946i | 0.0377023 | + | 0.116036i | ||||
\(208\) | −4.86600 | −0.337397 | ||||||||
\(209\) | −4.80263 | + | 1.26996i | −0.332205 | + | 0.0878446i | ||||
\(210\) | 2.36605 | 0.163273 | ||||||||
\(211\) | −6.28270 | − | 19.3362i | −0.432519 | − | 1.33116i | −0.895608 | − | 0.444844i | \(-0.853259\pi\) |
0.463089 | − | 0.886312i | \(-0.346741\pi\) | |||||||
\(212\) | −0.550612 | − | 0.400043i | −0.0378162 | − | 0.0274751i | ||||
\(213\) | 3.82497 | − | 2.77901i | 0.262083 | − | 0.190414i | ||||
\(214\) | −9.44979 | + | 29.0835i | −0.645975 | + | 1.98811i | ||||
\(215\) | −1.47915 | + | 4.55234i | −0.100877 | + | 0.310467i | ||||
\(216\) | −0.940958 | + | 0.683646i | −0.0640241 | + | 0.0465162i | ||||
\(217\) | 1.06548 | + | 0.774117i | 0.0723296 | + | 0.0525505i | ||||
\(218\) | 11.0087 | + | 33.8812i | 0.745602 | + | 2.29473i | ||||
\(219\) | 1.64613 | 0.111235 | ||||||||
\(220\) | 6.52693 | + | 2.53010i | 0.440046 | + | 0.170580i | ||||
\(221\) | −3.96225 | −0.266530 | ||||||||
\(222\) | 3.13200 | + | 9.63930i | 0.210206 | + | 0.646947i | ||||
\(223\) | 17.5855 | + | 12.7766i | 1.17761 | + | 0.855586i | 0.991900 | − | 0.127018i | \(-0.0405407\pi\) |
0.185712 | + | 0.982604i | \(0.440541\pi\) | |||||||
\(224\) | −4.45773 | + | 3.23873i | −0.297844 | + | 0.216397i | ||||
\(225\) | −0.807402 | + | 2.48493i | −0.0538268 | + | 0.165662i | ||||
\(226\) | 7.29810 | − | 22.4612i | 0.485462 | − | 1.49410i | ||||
\(227\) | 15.8779 | − | 11.5359i | 1.05385 | − | 0.765668i | 0.0809103 | − | 0.996721i | \(-0.474217\pi\) |
0.972941 | + | 0.231054i | \(0.0742173\pi\) | |||||||
\(228\) | 1.65533 | + | 1.20267i | 0.109627 | + | 0.0796487i | ||||
\(229\) | 0.160178 | + | 0.492977i | 0.0105849 | + | 0.0325768i | 0.956209 | − | 0.292683i | \(-0.0945481\pi\) |
−0.945625 | + | 0.325260i | \(0.894548\pi\) | |||||||
\(230\) | 4.97593 | 0.328103 | ||||||||
\(231\) | −1.74923 | + | 2.14565i | −0.115091 | + | 0.141174i | ||||
\(232\) | 9.90458 | 0.650267 | ||||||||
\(233\) | −3.52545 | − | 10.8502i | −0.230960 | − | 0.710821i | −0.997632 | − | 0.0687819i | \(-0.978089\pi\) |
0.766672 | − | 0.642039i | \(-0.221911\pi\) | |||||||
\(234\) | 1.48429 | + | 1.07840i | 0.0970310 | + | 0.0704971i | ||||
\(235\) | 2.78506 | − | 2.02347i | 0.181678 | − | 0.131996i | ||||
\(236\) | −2.46644 | + | 7.59092i | −0.160552 | + | 0.494127i | ||||
\(237\) | −0.734755 | + | 2.26134i | −0.0477275 | + | 0.146890i | ||||
\(238\) | −4.90886 | + | 3.56650i | −0.318194 | + | 0.231182i | ||||
\(239\) | 21.6097 | + | 15.7004i | 1.39782 | + | 1.01557i | 0.994956 | + | 0.100310i | \(0.0319836\pi\) |
0.402859 | + | 0.915262i | \(0.368016\pi\) | |||||||
\(240\) | 2.32326 | + | 7.15027i | 0.149966 | + | 0.461548i | ||||
\(241\) | 2.56160 | 0.165007 | 0.0825037 | − | 0.996591i | \(-0.473708\pi\) | ||||
0.0825037 | + | 0.996591i | \(0.473708\pi\) | |||||||
\(242\) | −17.5437 | + | 9.97562i | −1.12775 | + | 0.641257i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.63881 | − | 14.2768i | −0.296969 | − | 0.913977i | ||||
\(245\) | −7.87898 | − | 5.72441i | −0.503369 | − | 0.365719i | ||||
\(246\) | 13.1716 | − | 9.56971i | 0.839789 | − | 0.610143i | ||||
\(247\) | −0.462852 | + | 1.42451i | −0.0294505 | + | 0.0906394i | ||||
\(248\) | −0.567104 | + | 1.74537i | −0.0360111 | + | 0.110831i | ||||
\(249\) | 9.13969 | − | 6.64038i | 0.579205 | − | 0.420817i | ||||
\(250\) | 17.4585 | + | 12.6843i | 1.10417 | + | 0.802228i | ||||
\(251\) | 6.72921 | + | 20.7104i | 0.424744 | + | 1.30723i | 0.903239 | + | 0.429138i | \(0.141183\pi\) |
−0.478495 | + | 0.878090i | \(0.658817\pi\) | |||||||
\(252\) | 1.14022 | 0.0718271 | ||||||||
\(253\) | −3.67871 | + | 4.51242i | −0.231279 | + | 0.283693i | ||||
\(254\) | −23.9337 | −1.50174 | ||||||||
\(255\) | 1.89177 | + | 5.82227i | 0.118467 | + | 0.364604i | ||||
\(256\) | −16.9671 | − | 12.3273i | −1.06044 | − | 0.770456i | ||||
\(257\) | −7.15461 | + | 5.19813i | −0.446292 | + | 0.324250i | −0.788130 | − | 0.615509i | \(-0.788951\pi\) |
0.341838 | + | 0.939759i | \(0.388951\pi\) | |||||||
\(258\) | −1.75642 | + | 5.40570i | −0.109350 | + | 0.336544i | ||||
\(259\) | −1.42489 | + | 4.38536i | −0.0885384 | + | 0.272493i | ||||
\(260\) | 1.70753 | − | 1.24060i | 0.105897 | − | 0.0769385i | ||||
\(261\) | −6.88940 | − | 5.00544i | −0.426443 | − | 0.309829i | ||||
\(262\) | −10.2465 | − | 31.5356i | −0.633034 | − | 1.94828i | ||||
\(263\) | 5.45172 | 0.336167 | 0.168084 | − | 0.985773i | \(-0.446242\pi\) | ||||
0.168084 | + | 0.985773i | \(0.446242\pi\) | |||||||
\(264\) | −3.59675 | − | 1.39425i | −0.221364 | − | 0.0858099i | ||||
\(265\) | −0.769775 | −0.0472869 | ||||||||
\(266\) | 0.708799 | + | 2.18146i | 0.0434592 | + | 0.133754i | ||||
\(267\) | 4.99101 | + | 3.62618i | 0.305445 | + | 0.221919i | ||||
\(268\) | 9.31971 | − | 6.77116i | 0.569292 | − | 0.413615i | ||||
\(269\) | 3.74998 | − | 11.5413i | 0.228641 | − | 0.703683i | −0.769261 | − | 0.638935i | \(-0.779375\pi\) |
0.997902 | − | 0.0647486i | \(-0.0206245\pi\) | |||||||
\(270\) | 0.875965 | − | 2.69594i | 0.0533095 | − | 0.164070i | ||||
\(271\) | 18.8568 | − | 13.7003i | 1.14547 | − | 0.832234i | 0.157599 | − | 0.987503i | \(-0.449625\pi\) |
0.987872 | + | 0.155269i | \(0.0496245\pi\) | |||||||
\(272\) | −15.5981 | − | 11.3327i | −0.945775 | − | 0.687146i | ||||
\(273\) | 0.257931 | + | 0.793829i | 0.0156107 | + | 0.0480447i | ||||
\(274\) | −23.8841 | −1.44289 | ||||||||
\(275\) | −8.37776 | + | 2.21532i | −0.505198 | + | 0.133589i | ||||
\(276\) | 2.39794 | 0.144339 | ||||||||
\(277\) | −1.98304 | − | 6.10317i | −0.119149 | − | 0.366704i | 0.873641 | − | 0.486572i | \(-0.161753\pi\) |
−0.992790 | + | 0.119868i | \(0.961753\pi\) | |||||||
\(278\) | 19.8343 | + | 14.4105i | 1.18958 | + | 0.864281i | ||||
\(279\) | 1.27651 | − | 0.927441i | 0.0764228 | − | 0.0555244i | ||||
\(280\) | −0.463510 | + | 1.42654i | −0.0277000 | + | 0.0852519i | ||||
\(281\) | −8.63846 | + | 26.5864i | −0.515327 | + | 1.58601i | 0.267359 | + | 0.963597i | \(0.413849\pi\) |
−0.782686 | + | 0.622417i | \(0.786151\pi\) | |||||||
\(282\) | 3.30714 | − | 2.40278i | 0.196937 | − | 0.143083i | ||||
\(283\) | 9.65527 | + | 7.01497i | 0.573946 | + | 0.416996i | 0.836537 | − | 0.547911i | \(-0.184577\pi\) |
−0.262590 | + | 0.964907i | \(0.584577\pi\) | |||||||
\(284\) | −1.99582 | − | 6.14250i | −0.118430 | − | 0.364490i | ||||
\(285\) | 2.31421 | 0.137082 | ||||||||
\(286\) | −0.338436 | + | 6.07553i | −0.0200121 | + | 0.359254i | ||||
\(287\) | 7.40696 | 0.437219 | ||||||||
\(288\) | 2.03994 | + | 6.27829i | 0.120205 | + | 0.369952i | ||||
\(289\) | 1.05218 | + | 0.764451i | 0.0618927 | + | 0.0449677i | ||||
\(290\) | −19.5292 | + | 14.1888i | −1.14680 | + | 0.833196i | ||||
\(291\) | 3.31764 | − | 10.2106i | 0.194484 | − | 0.598559i | ||||
\(292\) | 0.694886 | − | 2.13864i | 0.0406652 | − | 0.125154i | ||||
\(293\) | −5.85520 | + | 4.25405i | −0.342064 | + | 0.248524i | −0.745532 | − | 0.666470i | \(-0.767805\pi\) |
0.403468 | + | 0.914994i | \(0.367805\pi\) | |||||||
\(294\) | −9.35592 | − | 6.79748i | −0.545649 | − | 0.396437i | ||||
\(295\) | 2.78963 | + | 8.58559i | 0.162418 | + | 0.499872i | ||||
\(296\) | −6.42527 | −0.373461 | ||||||||
\(297\) | 1.79721 | + | 2.78748i | 0.104285 | + | 0.161746i | ||||
\(298\) | 8.16169 | 0.472794 | ||||||||
\(299\) | 0.542441 | + | 1.66946i | 0.0313702 | + | 0.0965475i | ||||
\(300\) | 2.88757 | + | 2.09795i | 0.166714 | + | 0.121125i | ||||
\(301\) | −2.09201 | + | 1.51993i | −0.120581 | + | 0.0876074i | ||||
\(302\) | −7.89305 | + | 24.2923i | −0.454194 | + | 1.39786i | ||||
\(303\) | 2.36659 | − | 7.28361i | 0.135957 | − | 0.418432i | ||||
\(304\) | −5.89643 | + | 4.28401i | −0.338184 | + | 0.245705i | ||||
\(305\) | −13.7359 | − | 9.97972i | −0.786515 | − | 0.571437i | ||||
\(306\) | 2.24639 | + | 6.91368i | 0.128418 | + | 0.395228i | ||||
\(307\) | −14.1729 | −0.808890 | −0.404445 | − | 0.914562i | \(-0.632535\pi\) | ||||
−0.404445 | + | 0.914562i | \(0.632535\pi\) | |||||||
\(308\) | 2.04921 | + | 3.17834i | 0.116765 | + | 0.181103i | ||||
\(309\) | −7.09574 | −0.403662 | ||||||||
\(310\) | −1.38215 | − | 4.25381i | −0.0785006 | − | 0.241600i | ||||
\(311\) | −3.99196 | − | 2.90033i | −0.226363 | − | 0.164463i | 0.468823 | − | 0.883292i | \(-0.344678\pi\) |
−0.695186 | + | 0.718830i | \(0.744678\pi\) | |||||||
\(312\) | −0.940958 | + | 0.683646i | −0.0532712 | + | 0.0387038i | ||||
\(313\) | −7.07497 | + | 21.7745i | −0.399901 | + | 1.23077i | 0.525177 | + | 0.850993i | \(0.323999\pi\) |
−0.925078 | + | 0.379776i | \(0.876001\pi\) | |||||||
\(314\) | 6.02759 | − | 18.5510i | 0.340157 | − | 1.04690i | ||||
\(315\) | 1.04333 | − | 0.758024i | 0.0587850 | − | 0.0427098i | ||||
\(316\) | 2.62776 | + | 1.90918i | 0.147823 | + | 0.107400i | ||||
\(317\) | −4.20091 | − | 12.9291i | −0.235947 | − | 0.726170i | −0.996994 | − | 0.0774736i | \(-0.975315\pi\) |
0.761048 | − | 0.648696i | \(-0.224685\pi\) | |||||||
\(318\) | −0.914072 | −0.0512586 | ||||||||
\(319\) | 1.57087 | − | 28.1999i | 0.0879517 | − | 1.57889i | ||||
\(320\) | 3.67636 | 0.205515 | ||||||||
\(321\) | 5.15065 | + | 15.8521i | 0.287481 | + | 0.884776i | ||||
\(322\) | 2.17475 | + | 1.58005i | 0.121194 | + | 0.0880526i | ||||
\(323\) | −4.80130 | + | 3.48835i | −0.267152 | + | 0.194097i | ||||
\(324\) | 0.422134 | − | 1.29919i | 0.0234519 | − | 0.0721775i | ||||
\(325\) | −0.807402 | + | 2.48493i | −0.0447866 | + | 0.137839i | ||||
\(326\) | −3.68929 | + | 2.68043i | −0.204331 | + | 0.148455i | ||||
\(327\) | 15.7091 | + | 11.4133i | 0.868713 | + | 0.631157i | ||||
\(328\) | 3.18944 | + | 9.81609i | 0.176107 | + | 0.542003i | ||||
\(329\) | 1.85975 | 0.102531 | ||||||||
\(330\) | 9.08917 | − | 2.40344i | 0.500342 | − | 0.132305i | ||||
\(331\) | −9.57063 | −0.526049 | −0.263025 | − | 0.964789i | \(-0.584720\pi\) | ||||
−0.263025 | + | 0.964789i | \(0.584720\pi\) | |||||||
\(332\) | −4.76897 | − | 14.6774i | −0.261731 | − | 0.805525i | ||||
\(333\) | 4.46927 | + | 3.24711i | 0.244914 | + | 0.177941i | ||||
\(334\) | −26.2666 | + | 19.0838i | −1.43725 | + | 1.04422i | ||||
\(335\) | 4.02627 | − | 12.3916i | 0.219979 | − | 0.677024i | ||||
\(336\) | −1.25509 | + | 3.86277i | −0.0684709 | + | 0.210732i | ||||
\(337\) | −16.0925 | + | 11.6919i | −0.876617 | + | 0.636899i | −0.932354 | − | 0.361546i | \(-0.882249\pi\) |
0.0557373 | + | 0.998445i | \(0.482249\pi\) | |||||||
\(338\) | 1.48429 | + | 1.07840i | 0.0807346 | + | 0.0586571i | ||||
\(339\) | −3.97786 | − | 12.2426i | −0.216048 | − | 0.664926i | ||||
\(340\) | 8.36284 | 0.453539 | ||||||||
\(341\) | 4.87938 | + | 1.89145i | 0.264233 | + | 0.102428i | ||||
\(342\) | 2.74802 | 0.148596 | ||||||||
\(343\) | −3.43133 | − | 10.5605i | −0.185274 | − | 0.570216i | ||||
\(344\) | −2.91511 | − | 2.11795i | −0.157172 | − | 0.114192i | ||||
\(345\) | 2.19418 | − | 1.59416i | 0.118130 | − | 0.0858268i | ||||
\(346\) | 7.29052 | − | 22.4379i | 0.391941 | − | 1.20627i | ||||
\(347\) | 1.20933 | − | 3.72192i | 0.0649200 | − | 0.199803i | −0.913335 | − | 0.407209i | \(-0.866502\pi\) |
0.978255 | + | 0.207406i | \(0.0665020\pi\) | |||||||
\(348\) | −9.41129 | + | 6.83770i | −0.504498 | + | 0.366539i | ||||
\(349\) | 13.0260 | + | 9.46395i | 0.697266 | + | 0.506594i | 0.879041 | − | 0.476747i | \(-0.158184\pi\) |
−0.181774 | + | 0.983340i | \(0.558184\pi\) | |||||||
\(350\) | 1.23643 | + | 3.80535i | 0.0660902 | + | 0.203405i | ||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −13.8344 | + | 16.9697i | −0.737377 | + | 0.904488i | ||||
\(353\) | −21.8675 | −1.16389 | −0.581944 | − | 0.813229i | \(-0.697708\pi\) | ||||
−0.581944 | + | 0.813229i | \(0.697708\pi\) | |||||||
\(354\) | 3.31256 | + | 10.1950i | 0.176060 | + | 0.541858i | ||||
\(355\) | −5.90979 | − | 4.29372i | −0.313659 | − | 0.227887i | ||||
\(356\) | 6.81799 | − | 4.95356i | 0.361353 | − | 0.262538i | ||||
\(357\) | −1.02199 | + | 3.14535i | −0.0540892 | + | 0.166470i | ||||
\(358\) | 6.30058 | − | 19.3912i | 0.332996 | − | 1.02486i | ||||
\(359\) | 15.3996 | − | 11.1885i | 0.812760 | − | 0.590505i | −0.101869 | − | 0.994798i | \(-0.532482\pi\) |
0.914630 | + | 0.404293i | \(0.132482\pi\) | |||||||
\(360\) | 1.45383 | + | 1.05627i | 0.0766236 | + | 0.0556703i | ||||
\(361\) | −5.17805 | − | 15.9364i | −0.272529 | − | 0.838759i | ||||
\(362\) | −3.22193 | −0.169341 | ||||||||
\(363\) | −4.54008 | + | 10.0194i | −0.238292 | + | 0.525880i | ||||
\(364\) | 1.14022 | 0.0597638 | ||||||||
\(365\) | −0.785940 | − | 2.41888i | −0.0411380 | − | 0.126610i | ||||
\(366\) | −16.3108 | − | 11.8505i | −0.852577 | − | 0.619433i | ||||
\(367\) | −0.465136 | + | 0.337941i | −0.0242799 | + | 0.0176404i | −0.599859 | − | 0.800106i | \(-0.704777\pi\) |
0.575579 | + | 0.817746i | \(0.304777\pi\) | |||||||
\(368\) | −2.63952 | + | 8.12361i | −0.137595 | + | 0.423472i | ||||
\(369\) | 2.74222 | − | 8.43968i | 0.142754 | − | 0.439352i | ||||
\(370\) | 12.6689 | − | 9.20453i | 0.658627 | − | 0.478521i | ||||
\(371\) | −0.336433 | − | 0.244433i | −0.0174667 | − | 0.0126903i | ||||
\(372\) | −0.666067 | − | 2.04994i | −0.0345340 | − | 0.106285i | ||||
\(373\) | 4.60635 | 0.238508 | 0.119254 | − | 0.992864i | \(-0.461950\pi\) | ||||
0.119254 | + | 0.992864i | \(0.461950\pi\) | |||||||
\(374\) | −15.2345 | + | 18.6871i | −0.787757 | + | 0.966286i | ||||
\(375\) | 11.7622 | 0.607397 | ||||||||
\(376\) | 0.800809 | + | 2.46464i | 0.0412986 | + | 0.127104i | ||||
\(377\) | −6.88940 | − | 5.00544i | −0.354822 | − | 0.257793i | ||||
\(378\) | 1.23891 | − | 0.900119i | 0.0637225 | − | 0.0462971i | ||||
\(379\) | −11.2329 | + | 34.5714i | −0.576997 | + | 1.77581i | 0.0522807 | + | 0.998632i | \(0.483351\pi\) |
−0.629277 | + | 0.777181i | \(0.716649\pi\) | |||||||
\(380\) | 0.976907 | − | 3.00661i | 0.0501143 | − | 0.154236i | ||||
\(381\) | −10.5538 | + | 7.66777i | −0.540686 | + | 0.392832i | ||||
\(382\) | −8.00029 | − | 5.81255i | −0.409331 | − | 0.297396i | ||||
\(383\) | −6.06664 | − | 18.6712i | −0.309991 | − | 0.954054i | −0.977768 | − | 0.209692i | \(-0.932754\pi\) |
0.667777 | − | 0.744362i | \(-0.267246\pi\) | |||||||
\(384\) | −8.83727 | −0.450975 | ||||||||
\(385\) | 3.98806 | + | 1.54593i | 0.203250 | + | 0.0787881i | ||||
\(386\) | −17.5860 | −0.895102 | ||||||||
\(387\) | 0.957343 | + | 2.94640i | 0.0486645 | + | 0.149774i | ||||
\(388\) | −11.8651 | − | 8.62052i | −0.602361 | − | 0.437641i | ||||
\(389\) | −14.9467 | + | 10.8594i | −0.757829 | + | 0.550595i | −0.898244 | − | 0.439498i | \(-0.855156\pi\) |
0.140415 | + | 0.990093i | \(0.455156\pi\) | |||||||
\(390\) | 0.875965 | − | 2.69594i | 0.0443562 | − | 0.136514i | ||||
\(391\) | −2.14929 | + | 6.61483i | −0.108694 | + | 0.334526i | ||||
\(392\) | 5.93115 | − | 4.30923i | 0.299568 | − | 0.217649i | ||||
\(393\) | −14.6215 | − | 10.6231i | −0.737558 | − | 0.535867i | ||||
\(394\) | −7.21858 | − | 22.2165i | −0.363667 | − | 1.11925i | ||||
\(395\) | 3.67370 | 0.184844 | ||||||||
\(396\) | 4.38014 | − | 1.15824i | 0.220110 | − | 0.0582035i | ||||
\(397\) | 22.7651 | 1.14255 | 0.571273 | − | 0.820760i | \(-0.306450\pi\) | ||||
0.571273 | + | 0.820760i | \(0.306450\pi\) | |||||||
\(398\) | −1.21855 | − | 3.75032i | −0.0610805 | − | 0.187986i | ||||
\(399\) | 1.01143 | + | 0.734850i | 0.0506350 | + | 0.0367885i | ||||
\(400\) | −10.2858 | + | 7.47306i | −0.514290 | + | 0.373653i | ||||
\(401\) | 9.43111 | − | 29.0260i | 0.470967 | − | 1.44949i | −0.380353 | − | 0.924842i | \(-0.624197\pi\) |
0.851320 | − | 0.524647i | \(-0.175803\pi\) | |||||||
\(402\) | 4.78101 | − | 14.7144i | 0.238455 | − | 0.733889i | ||||
\(403\) | 1.27651 | − | 0.927441i | 0.0635876 | − | 0.0461991i | ||||
\(404\) | −8.46381 | − | 6.14932i | −0.421090 | − | 0.305940i | ||||
\(405\) | −0.477448 | − | 1.46943i | −0.0237246 | − | 0.0730167i | ||||
\(406\) | −13.0408 | −0.647205 | ||||||||
\(407\) | −1.01905 | + | 18.2937i | −0.0505123 | + | 0.906786i | ||||
\(408\) | −4.60845 | −0.228152 | ||||||||
\(409\) | −5.16397 | − | 15.8931i | −0.255342 | − | 0.785861i | −0.993762 | − | 0.111520i | \(-0.964428\pi\) |
0.738420 | − | 0.674341i | \(-0.235572\pi\) | |||||||
\(410\) | −20.3508 | − | 14.7857i | −1.00505 | − | 0.730215i | ||||
\(411\) | −10.5319 | + | 7.65187i | −0.519500 | + | 0.377439i | ||||
\(412\) | −2.99535 | + | 9.21875i | −0.147570 | + | 0.454175i | ||||
\(413\) | −1.50703 | + | 4.63817i | −0.0741563 | + | 0.228230i | ||||
\(414\) | 2.60548 | − | 1.89300i | 0.128053 | − | 0.0930356i | ||||
\(415\) | −14.1213 | − | 10.2597i | −0.693188 | − | 0.503631i | ||||
\(416\) | 2.03994 | + | 6.27829i | 0.100016 | + | 0.307819i | ||||
\(417\) | 13.3628 | 0.654380 | ||||||||
\(418\) | 4.93877 | + | 7.66005i | 0.241563 | + | 0.374665i | ||||
\(419\) | 33.3642 | 1.62995 | 0.814974 | − | 0.579498i | \(-0.196751\pi\) | ||||
0.814974 | + | 0.579498i | \(0.196751\pi\) | |||||||
\(420\) | −0.544396 | − | 1.67548i | −0.0265638 | − | 0.0817549i | ||||
\(421\) | 15.4063 | + | 11.1933i | 0.750855 | + | 0.545528i | 0.896092 | − | 0.443869i | \(-0.146394\pi\) |
−0.145237 | + | 0.989397i | \(0.546394\pi\) | |||||||
\(422\) | −30.1774 | + | 21.9252i | −1.46901 | + | 1.06730i | ||||
\(423\) | 0.688520 | − | 2.11905i | 0.0334770 | − | 0.103032i | ||||
\(424\) | 0.179067 | − | 0.551111i | 0.00869625 | − | 0.0267643i | ||||
\(425\) | −8.37543 | + | 6.08511i | −0.406268 | + | 0.295171i | ||||
\(426\) | −7.01761 | − | 5.09859i | −0.340004 | − | 0.247028i | ||||
\(427\) | −2.83438 | − | 8.72334i | −0.137165 | − | 0.422152i | ||||
\(428\) | 22.7692 | 1.10059 | ||||||||
\(429\) | 1.79721 | + | 2.78748i | 0.0867701 | + | 0.134581i | ||||
\(430\) | 8.78192 | 0.423502 | ||||||||
\(431\) | 1.95061 | + | 6.00335i | 0.0939575 | + | 0.289171i | 0.986981 | − | 0.160839i | \(-0.0514201\pi\) |
−0.893023 | + | 0.450011i | \(0.851420\pi\) | |||||||
\(432\) | 3.93668 | + | 2.86017i | 0.189404 | + | 0.137610i | ||||
\(433\) | 8.82377 | − | 6.41085i | 0.424043 | − | 0.308086i | −0.355219 | − | 0.934783i | \(-0.615594\pi\) |
0.779263 | + | 0.626697i | \(0.215594\pi\) | |||||||
\(434\) | 0.746674 | − | 2.29803i | 0.0358415 | − | 0.110309i | ||||
\(435\) | −4.06583 | + | 12.5133i | −0.194942 | + | 0.599969i | ||||
\(436\) | 21.4594 | − | 15.5912i | 1.02772 | − | 0.746682i | ||||
\(437\) | 2.12710 | + | 1.54543i | 0.101753 | + | 0.0739278i | ||||
\(438\) | −0.933268 | − | 2.87230i | −0.0445933 | − | 0.137244i | ||||
\(439\) | −11.6936 | −0.558104 | −0.279052 | − | 0.960276i | \(-0.590020\pi\) | ||||
−0.279052 | + | 0.960276i | \(0.590020\pi\) | |||||||
\(440\) | −0.331491 | + | 5.95086i | −0.0158032 | + | 0.283696i | ||||
\(441\) | −6.30331 | −0.300158 | ||||||||
\(442\) | 2.24639 | + | 6.91368i | 0.106850 | + | 0.328850i | ||||
\(443\) | 27.5167 | + | 19.9921i | 1.30736 | + | 0.949852i | 0.999998 | − | 0.00174158i | \(-0.000554362\pi\) |
0.307360 | + | 0.951593i | \(0.400554\pi\) | |||||||
\(444\) | 6.10526 | − | 4.43573i | 0.289743 | − | 0.210510i | ||||
\(445\) | 2.94548 | − | 9.06527i | 0.139629 | − | 0.429735i | ||||
\(446\) | 12.3237 | − | 37.9284i | 0.583543 | − | 1.79596i | ||||
\(447\) | 3.59896 | − | 2.61480i | 0.170225 | − | 0.123676i | ||||
\(448\) | 1.60676 | + | 1.16738i | 0.0759125 | + | 0.0551537i | ||||
\(449\) | 5.59627 | + | 17.2236i | 0.264104 | + | 0.812830i | 0.991898 | + | 0.127034i | \(0.0405458\pi\) |
−0.727794 | + | 0.685796i | \(0.759454\pi\) | |||||||
\(450\) | 4.79367 | 0.225976 | ||||||||
\(451\) | 28.4538 | − | 7.52400i | 1.33984 | − | 0.354291i | ||||
\(452\) | −17.5847 | −0.827115 | ||||||||
\(453\) | 4.30213 | + | 13.2406i | 0.202132 | + | 0.622098i | ||||
\(454\) | −29.1308 | − | 21.1648i | −1.36718 | − | 0.993313i | ||||
\(455\) | 1.04333 | − | 0.758024i | 0.0489121 | − | 0.0355367i | ||||
\(456\) | −0.538337 | + | 1.65683i | −0.0252099 | + | 0.0775882i | ||||
\(457\) | −6.09735 | + | 18.7657i | −0.285222 | + | 0.877823i | 0.701110 | + | 0.713053i | \(0.252688\pi\) |
−0.986332 | + | 0.164770i | \(0.947312\pi\) | |||||||
\(458\) | 0.769376 | − | 0.558984i | 0.0359506 | − | 0.0261196i | ||||
\(459\) | 3.20553 | + | 2.32895i | 0.149621 | + | 0.108706i | ||||
\(460\) | −1.14489 | − | 3.52361i | −0.0533808 | − | 0.164289i | ||||
\(461\) | −23.9263 | −1.11436 | −0.557180 | − | 0.830392i | \(-0.688117\pi\) | ||||
−0.557180 | + | 0.830392i | \(0.688117\pi\) | |||||||
\(462\) | 4.73564 | + | 1.83573i | 0.220322 | + | 0.0854057i | ||||
\(463\) | 3.65825 | 0.170013 | 0.0850067 | − | 0.996380i | \(-0.472909\pi\) | ||||
0.0850067 | + | 0.996380i | \(0.472909\pi\) | |||||||
\(464\) | −12.8050 | − | 39.4096i | −0.594455 | − | 1.82955i | ||||
\(465\) | −1.97228 | − | 1.43295i | −0.0914623 | − | 0.0664513i | ||||
\(466\) | −16.9336 | + | 12.3030i | −0.784435 | + | 0.569926i | ||||
\(467\) | 3.38297 | − | 10.4117i | 0.156545 | − | 0.481797i | −0.841769 | − | 0.539838i | \(-0.818485\pi\) |
0.998314 | + | 0.0580412i | \(0.0184855\pi\) | |||||||
\(468\) | 0.422134 | − | 1.29919i | 0.0195132 | − | 0.0600553i | ||||
\(469\) | 5.69449 | − | 4.13729i | 0.262947 | − | 0.191042i | ||||
\(470\) | −5.10970 | − | 3.71242i | −0.235693 | − | 0.171241i | ||||
\(471\) | −3.28536 | − | 10.1113i | −0.151382 | − | 0.465905i | ||||
\(472\) | −6.79568 | −0.312796 | ||||||||
\(473\) | −6.49248 | + | 7.96387i | −0.298524 | + | 0.366179i | ||||
\(474\) | 4.36236 | 0.200370 | ||||||||
\(475\) | 1.20934 | + | 3.72197i | 0.0554884 | + | 0.170776i | ||||
\(476\) | 3.65501 | + | 2.65552i | 0.167527 | + | 0.121715i | ||||
\(477\) | −0.403067 | + | 0.292846i | −0.0184552 | + | 0.0134085i | ||||
\(478\) | 15.1438 | − | 46.6077i | 0.692660 | − | 2.13179i | ||||
\(479\) | 5.63826 | − | 17.3528i | 0.257619 | − | 0.792868i | −0.735684 | − | 0.677325i | \(-0.763139\pi\) |
0.993302 | − | 0.115543i | \(-0.0368609\pi\) | |||||||
\(480\) | 8.25157 | − | 5.99512i | 0.376631 | − | 0.273638i | ||||
\(481\) | 4.46927 | + | 3.24711i | 0.203781 | + | 0.148056i | ||||
\(482\) | −1.45229 | − | 4.46970i | −0.0661502 | − | 0.203589i | ||||
\(483\) | 1.46518 | 0.0666680 | ||||||||
\(484\) | 11.1006 | + | 10.1280i | 0.504572 | + | 0.460362i | ||||
\(485\) | −16.5879 | −0.753216 | ||||||||
\(486\) | −0.566948 | − | 1.74489i | −0.0257173 | − | 0.0791496i | ||||
\(487\) | 7.13632 | + | 5.18484i | 0.323378 | + | 0.234948i | 0.737615 | − | 0.675221i | \(-0.235952\pi\) |
−0.414238 | + | 0.910169i | \(0.635952\pi\) | |||||||
\(488\) | 10.3401 | − | 7.51255i | 0.468076 | − | 0.340077i | ||||
\(489\) | −0.768082 | + | 2.36391i | −0.0347339 | + | 0.106900i | ||||
\(490\) | −5.52147 | + | 16.9934i | −0.249435 | + | 0.767681i | ||||
\(491\) | −16.2029 | + | 11.7721i | −0.731227 | + | 0.531268i | −0.889951 | − | 0.456055i | \(-0.849262\pi\) |
0.158724 | + | 0.987323i | \(0.449262\pi\) | |||||||
\(492\) | −9.80721 | − | 7.12535i | −0.442143 | − | 0.321236i | ||||
\(493\) | −10.4267 | − | 32.0902i | −0.469596 | − | 1.44527i | ||||
\(494\) | 2.74802 | 0.123639 | ||||||||
\(495\) | 3.23794 | − | 3.97176i | 0.145535 | − | 0.178517i | ||||
\(496\) | 7.67786 | 0.344746 | ||||||||
\(497\) | −1.21948 | − | 3.75317i | −0.0547010 | − | 0.168353i | ||||
\(498\) | −16.7684 | − | 12.1830i | −0.751411 | − | 0.545932i | ||||
\(499\) | −21.8250 | + | 15.8568i | −0.977021 | + | 0.709847i | −0.957041 | − | 0.289953i | \(-0.906360\pi\) |
−0.0199803 | + | 0.999800i | \(0.506360\pi\) | |||||||
\(500\) | 4.96522 | − | 15.2814i | 0.222052 | − | 0.683405i | ||||
\(501\) | −5.46850 | + | 16.8303i | −0.244315 | + | 0.751923i | ||||
\(502\) | 32.3221 | − | 23.4834i | 1.44261 | − | 1.04812i | ||||
\(503\) | 32.7835 | + | 23.8186i | 1.46174 | + | 1.06202i | 0.982905 | + | 0.184115i | \(0.0589419\pi\) |
0.478838 | + | 0.877903i | \(0.341058\pi\) | |||||||
\(504\) | 0.299996 | + | 0.923293i | 0.0133629 | + | 0.0411267i | ||||
\(505\) | −11.8327 | −0.526548 | ||||||||
\(506\) | 9.95929 | + | 3.86062i | 0.442744 | + | 0.171626i | ||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 5.50682 | + | 16.9482i | 0.244325 | + | 0.751956i | ||||
\(509\) | 25.5683 | + | 18.5764i | 1.13329 | + | 0.823386i | 0.986171 | − | 0.165732i | \(-0.0529988\pi\) |
0.147123 | + | 0.989118i | \(0.452999\pi\) | |||||||
\(510\) | 9.08665 | − | 6.60184i | 0.402364 | − | 0.292334i | ||||
\(511\) | 0.424587 | − | 1.30674i | 0.0187826 | − | 0.0578069i | ||||
\(512\) | −6.42855 | + | 19.7850i | −0.284104 | + | 0.874383i | ||||
\(513\) | 1.21176 | − | 0.880396i | 0.0535006 | − | 0.0388704i | ||||
\(514\) | 13.1264 | + | 9.53691i | 0.578982 | + | 0.420655i | ||||
\(515\) | 3.38784 | + | 10.4267i | 0.149286 | + | 0.459456i | ||||
\(516\) | 4.23207 | 0.186307 | ||||||||
\(517\) | 7.14421 | − | 1.88913i | 0.314202 | − | 0.0830841i | ||||
\(518\) | 8.45979 | 0.371702 | ||||||||
\(519\) | −3.97372 | − | 12.2299i | −0.174427 | − | 0.536831i | ||||
\(520\) | 1.45383 | + | 1.05627i | 0.0637547 | + | 0.0463205i | ||||
\(521\) | 28.1358 | − | 20.4418i | 1.23265 | − | 0.895573i | 0.235565 | − | 0.971859i | \(-0.424306\pi\) |
0.997086 | + | 0.0762855i | \(0.0243060\pi\) | |||||||
\(522\) | −4.82799 | + | 14.8590i | −0.211315 | + | 0.650362i | ||||
\(523\) | −3.65723 | + | 11.2558i | −0.159919 | + | 0.492181i | −0.998626 | − | 0.0524022i | \(-0.983312\pi\) |
0.838707 | + | 0.544583i | \(0.183312\pi\) | |||||||
\(524\) | −19.9738 | + | 14.5118i | −0.872559 | + | 0.633951i | ||||
\(525\) | 1.76435 | + | 1.28188i | 0.0770027 | + | 0.0559458i | ||||
\(526\) | −3.09084 | − | 9.51262i | −0.134767 | − | 0.414770i | ||||
\(527\) | 6.25186 | 0.272336 | ||||||||
\(528\) | −0.897612 | + | 16.1137i | −0.0390635 | + | 0.701260i | ||||
\(529\) | −19.9187 | −0.866028 | ||||||||
\(530\) | 0.436422 | + | 1.34317i | 0.0189570 | + | 0.0583435i | ||||
\(531\) | 4.72692 | + | 3.43430i | 0.205131 | + | 0.149036i | ||||
\(532\) | 1.38167 | − | 1.00384i | 0.0599032 | − | 0.0435222i | ||||
\(533\) | 2.74222 | − | 8.43968i | 0.118779 | − | 0.365563i | ||||
\(534\) | 3.49763 | − | 10.7646i | 0.151357 | − | 0.465830i | ||||
\(535\) | 20.8344 | − | 15.1371i | 0.900749 | − | 0.654432i | ||||
\(536\) | 7.93500 | + | 5.76511i | 0.342740 | + | 0.249015i | ||||
\(537\) | −3.43415 | − | 10.5692i | −0.148195 | − | 0.456096i | ||||
\(538\) | −22.2642 | −0.959879 | ||||||||
\(539\) | −11.3284 | − | 17.5703i | −0.487947 | − | 0.756808i | ||||
\(540\) | −2.11063 | −0.0908270 | ||||||||
\(541\) | 5.24782 | + | 16.1511i | 0.225621 | + | 0.694391i | 0.998228 | + | 0.0595062i | \(0.0189526\pi\) |
−0.772607 | + | 0.634885i | \(0.781047\pi\) | |||||||
\(542\) | −34.5963 | − | 25.1357i | −1.48604 | − | 1.07967i | ||||
\(543\) | −1.42074 | + | 1.03223i | −0.0609697 | + | 0.0442971i | ||||
\(544\) | −8.08276 | + | 24.8762i | −0.346546 | + | 1.06656i | ||||
\(545\) | 9.27083 | − | 28.5327i | 0.397119 | − | 1.22221i | ||||
\(546\) | 1.23891 | − | 0.900119i | 0.0530203 | − | 0.0385215i | ||||
\(547\) | −25.1290 | − | 18.2573i | −1.07444 | − | 0.780626i | −0.0977350 | − | 0.995212i | \(-0.531160\pi\) |
−0.976705 | + | 0.214586i | \(0.931160\pi\) | |||||||
\(548\) | 5.49540 | + | 16.9131i | 0.234752 | + | 0.722492i | ||||
\(549\) | −10.9889 | −0.468997 | ||||||||
\(550\) | 8.61523 | + | 13.3623i | 0.367355 | + | 0.569768i | ||||
\(551\) | −12.7551 | −0.543384 | ||||||||
\(552\) | 0.630907 | + | 1.94173i | 0.0268532 | + | 0.0826456i | ||||
\(553\) | 1.60560 | + | 1.16654i | 0.0682773 | + | 0.0496063i | ||||
\(554\) | −9.52505 | + | 6.92035i | −0.404681 | + | 0.294018i | ||||
\(555\) | 2.63757 | − | 8.11762i | 0.111959 | − | 0.344574i | ||||
\(556\) | 5.64090 | − | 17.3609i | 0.239228 | − | 0.736267i | ||||
\(557\) | 15.6295 | − | 11.3555i | 0.662242 | − | 0.481147i | −0.205177 | − | 0.978725i | \(-0.565777\pi\) |
0.867419 | + | 0.497578i | \(0.165777\pi\) | |||||||
\(558\) | −2.34199 | − | 1.70156i | −0.0991445 | − | 0.0720327i | ||||
\(559\) | 0.957343 | + | 2.94640i | 0.0404913 | + | 0.124619i | ||||
\(560\) | 6.27533 | 0.265181 | ||||||||
\(561\) | −0.730900 | + | 13.1210i | −0.0308586 | + | 0.553967i | ||||
\(562\) | 51.2878 | 2.16345 | ||||||||
\(563\) | 11.1542 | + | 34.3291i | 0.470094 | + | 1.44680i | 0.852462 | + | 0.522790i | \(0.175109\pi\) |
−0.382368 | + | 0.924010i | \(0.624891\pi\) | |||||||
\(564\) | −2.46241 | − | 1.78904i | −0.103686 | − | 0.0753323i | ||||
\(565\) | −16.0904 | + | 11.6904i | −0.676930 | + | 0.491819i | ||||
\(566\) | 6.76628 | − | 20.8245i | 0.284408 | − | 0.875317i | ||||
\(567\) | 0.257931 | − | 0.793829i | 0.0108321 | − | 0.0333377i | ||||
\(568\) | 4.44878 | − | 3.23223i | 0.186667 | − | 0.135621i | ||||
\(569\) | 27.3632 | + | 19.8805i | 1.14712 | + | 0.833434i | 0.988096 | − | 0.153840i | \(-0.0491641\pi\) |
0.159028 | + | 0.987274i | \(0.449164\pi\) | |||||||
\(570\) | −1.31204 | − | 4.03803i | −0.0549552 | − | 0.169135i | ||||
\(571\) | −32.5069 | −1.36037 | −0.680185 | − | 0.733041i | \(-0.738100\pi\) | ||||
−0.680185 | + | 0.733041i | \(0.738100\pi\) | |||||||
\(572\) | 4.38014 | − | 1.15824i | 0.183143 | − | 0.0484283i | ||||
\(573\) | −5.38999 | −0.225170 | ||||||||
\(574\) | −4.19936 | − | 12.9243i | −0.175278 | − | 0.539450i | ||||
\(575\) | 3.71053 | + | 2.69585i | 0.154740 | + | 0.112425i | ||||
\(576\) | 1.92500 | − | 1.39860i | 0.0802085 | − | 0.0582749i | ||||
\(577\) | 1.53716 | − | 4.73090i | 0.0639929 | − | 0.196950i | −0.913948 | − | 0.405831i | \(-0.866982\pi\) |
0.977941 | + | 0.208881i | \(0.0669822\pi\) | |||||||
\(578\) | 0.737350 | − | 2.26933i | 0.0306697 | − | 0.0943917i | ||||
\(579\) | −7.75467 | + | 5.63410i | −0.322273 | + | 0.234145i | ||||
\(580\) | 14.5409 | + | 10.5646i | 0.603780 | + | 0.438672i | ||||
\(581\) | −2.91391 | − | 8.96811i | −0.120890 | − | 0.372060i | ||||
\(582\) | −19.6973 | −0.816481 | ||||||||
\(583\) | −1.54070 | − | 0.597237i | −0.0638092 | − | 0.0247350i | ||||
\(584\) | 1.91459 | 0.0792263 | ||||||||
\(585\) | −0.477448 | − | 1.46943i | −0.0197400 | − | 0.0607536i | ||||
\(586\) | 10.7424 | + | 7.80482i | 0.443765 | + | 0.322414i | ||||
\(587\) | −13.6095 | + | 9.88786i | −0.561723 | + | 0.408116i | −0.832089 | − | 0.554642i | \(-0.812855\pi\) |
0.270366 | + | 0.962758i | \(0.412855\pi\) | |||||||
\(588\) | −2.66084 | + | 8.18923i | −0.109731 | + | 0.337718i | ||||
\(589\) | 0.730313 | − | 2.24767i | 0.0300920 | − | 0.0926138i | ||||
\(590\) | 13.3993 | − | 9.73516i | 0.551640 | − | 0.400790i | ||||
\(591\) | −10.3007 | − | 7.48390i | −0.423714 | − | 0.307846i | ||||
\(592\) | 8.30679 | + | 25.5657i | 0.341407 | + | 1.05074i | ||||
\(593\) | 2.27552 | 0.0934445 | 0.0467222 | − | 0.998908i | \(-0.485122\pi\) | ||||
0.0467222 | + | 0.998908i | \(0.485122\pi\) | |||||||
\(594\) | 3.84491 | − | 4.71628i | 0.157758 | − | 0.193511i | ||||
\(595\) | 5.10983 | 0.209483 | ||||||||
\(596\) | −1.87789 | − | 5.77955i | −0.0769213 | − | 0.236739i | ||||
\(597\) | −1.73884 | − | 1.26334i | −0.0711659 | − | 0.0517050i | ||||
\(598\) | 2.60548 | − | 1.89300i | 0.106546 | − | 0.0774103i | ||||
\(599\) | 6.79506 | − | 20.9130i | 0.277638 | − | 0.854483i | −0.710871 | − | 0.703323i | \(-0.751699\pi\) |
0.988509 | − | 0.151161i | \(-0.0483011\pi\) | |||||||
\(600\) | −0.939080 | + | 2.89019i | −0.0383378 | + | 0.117992i | ||||
\(601\) | −23.2877 | + | 16.9195i | −0.949925 | + | 0.690161i | −0.950789 | − | 0.309839i | \(-0.899725\pi\) |
0.000864048 | 1.00000i | \(0.499725\pi\) | ||||||||
\(602\) | 3.83817 | + | 2.78859i | 0.156432 | + | 0.113654i | ||||
\(603\) | −2.60591 | − | 8.02016i | −0.106121 | − | 0.326606i | ||||
\(604\) | 19.0182 | 0.773840 | ||||||||
\(605\) | 16.8904 | + | 1.88761i | 0.686694 | + | 0.0767424i | ||||
\(606\) | −14.0508 | −0.570774 | ||||||||
\(607\) | 8.93501 | + | 27.4991i | 0.362661 | + | 1.11616i | 0.951433 | + | 0.307856i | \(0.0996116\pi\) |
−0.588772 | + | 0.808299i | \(0.700388\pi\) | |||||||
\(608\) | 7.99931 | + | 5.81184i | 0.324415 | + | 0.235701i | ||||
\(609\) | −5.75045 | + | 4.17794i | −0.233020 | + | 0.169299i | ||||
\(610\) | −9.62592 | + | 29.6255i | −0.389742 | + | 1.19950i | ||||
\(611\) | 0.688520 | − | 2.11905i | 0.0278545 | − | 0.0857274i | ||||
\(612\) | 4.37893 | − | 3.18148i | 0.177008 | − | 0.128604i | ||||
\(613\) | 25.8923 | + | 18.8119i | 1.04578 | + | 0.759805i | 0.971406 | − | 0.237426i | \(-0.0763036\pi\) |
0.0743755 | + | 0.997230i | \(0.476304\pi\) | |||||||
\(614\) | 8.03529 | + | 24.7301i | 0.324278 | + | 0.998024i | ||||
\(615\) | −13.7108 | −0.552874 | ||||||||
\(616\) | −2.03450 | + | 2.49558i | −0.0819725 | + | 0.100550i | ||||
\(617\) | −20.8138 | −0.837932 | −0.418966 | − | 0.908002i | \(-0.637607\pi\) | ||||
−0.418966 | + | 0.908002i | \(0.637607\pi\) | |||||||
\(618\) | 4.02291 | + | 12.3812i | 0.161825 | + | 0.498047i | ||||
\(619\) | 18.3855 | + | 13.3579i | 0.738976 | + | 0.536898i | 0.892390 | − | 0.451264i | \(-0.149027\pi\) |
−0.153414 | + | 0.988162i | \(0.549027\pi\) | |||||||
\(620\) | −2.69424 | + | 1.95748i | −0.108203 | + | 0.0786144i | ||||
\(621\) | 0.542441 | − | 1.66946i | 0.0217674 | − | 0.0669932i | ||||
\(622\) | −2.79751 | + | 8.60985i | −0.112170 | + | 0.345223i | ||||
\(623\) | 4.16590 | − | 3.02670i | 0.166903 | − | 0.121262i | ||||
\(624\) | 3.93668 | + | 2.86017i | 0.157593 | + | 0.114498i | ||||
\(625\) | −1.57883 | − | 4.85913i | −0.0631530 | − | 0.194365i | ||||
\(626\) | 42.0052 | 1.67887 | ||||||||
\(627\) | 4.63187 | + | 1.79550i | 0.184979 | + | 0.0717055i | ||||
\(628\) | −14.5234 | −0.579548 | ||||||||
\(629\) | 6.76399 | + | 20.8174i | 0.269698 | + | 0.830045i | ||||
\(630\) | −1.91418 | − | 1.39073i | −0.0762627 | − | 0.0554081i | ||||
\(631\) | 0.516644 | − | 0.375364i | 0.0205673 | − | 0.0149430i | −0.577454 | − | 0.816423i | \(-0.695954\pi\) |
0.598021 | + | 0.801480i | \(0.295954\pi\) | |||||||
\(632\) | −0.854585 | + | 2.63014i | −0.0339936 | + | 0.104621i | ||||
\(633\) | −6.28270 | + | 19.3362i | −0.249715 | + | 0.768543i | ||||
\(634\) | −20.1781 | + | 14.6602i | −0.801374 | + | 0.582232i | ||||
\(635\) | 16.3062 | + | 11.8471i | 0.647090 | + | 0.470138i | ||||
\(636\) | 0.210315 | + | 0.647283i | 0.00833953 | + | 0.0256664i | ||||
\(637\) | −6.30331 | −0.249746 | ||||||||
\(638\) | −50.0961 | + | 13.2469i | −1.98332 | + | 0.524448i | ||||
\(639\) | −4.72793 | −0.187034 | ||||||||
\(640\) | 4.21934 | + | 12.9858i | 0.166784 | + | 0.513308i | ||||
\(641\) | 5.65575 | + | 4.10914i | 0.223389 | + | 0.162301i | 0.693851 | − | 0.720119i | \(-0.255913\pi\) |
−0.470462 | + | 0.882420i | \(0.655913\pi\) | |||||||
\(642\) | 24.7399 | − | 17.9746i | 0.976405 | − | 0.709400i | ||||
\(643\) | −14.4992 | + | 44.6241i | −0.571794 | + | 1.75980i | 0.0750503 | + | 0.997180i | \(0.476088\pi\) |
−0.646845 | + | 0.762622i | \(0.723912\pi\) | |||||||
\(644\) | 0.618502 | − | 1.90355i | 0.0243724 | − | 0.0750105i | ||||
\(645\) | 3.87245 | − | 2.81350i | 0.152478 | − | 0.110782i | ||||
\(646\) | 8.80886 | + | 6.40001i | 0.346580 | + | 0.251805i | ||||
\(647\) | −14.3973 | − | 44.3103i | −0.566016 | − | 1.74202i | −0.664914 | − | 0.746920i | \(-0.731532\pi\) |
0.0988980 | − | 0.995098i | \(-0.468468\pi\) | |||||||
\(648\) | 1.16309 | 0.0456904 | ||||||||
\(649\) | −1.07780 | + | 19.3483i | −0.0423072 | + | 0.759489i | ||||
\(650\) | 4.79367 | 0.188023 | ||||||||
\(651\) | −0.406978 | − | 1.25255i | −0.0159507 | − | 0.0490912i | ||||
\(652\) | 2.74695 | + | 1.99578i | 0.107579 | + | 0.0781606i | ||||
\(653\) | 0.286183 | − | 0.207924i | 0.0111992 | − | 0.00813671i | −0.582172 | − | 0.813066i | \(-0.697797\pi\) |
0.593371 | + | 0.804929i | \(0.297797\pi\) | |||||||
\(654\) | 11.0087 | − | 33.8812i | 0.430474 | − | 1.32486i | ||||
\(655\) | −8.62900 | + | 26.5573i | −0.337163 | + | 1.03768i | ||||
\(656\) | 34.9341 | − | 25.3811i | 1.36395 | − | 0.990966i | ||||
\(657\) | −1.33175 | − | 0.967570i | −0.0519563 | − | 0.0377485i | ||||
\(658\) | −1.05438 | − | 3.24505i | −0.0411040 | − | 0.126505i | ||||
\(659\) | −16.4906 | −0.642383 | −0.321191 | − | 0.947014i | \(-0.604083\pi\) | ||||
−0.321191 | + | 0.947014i | \(0.604083\pi\) | |||||||
\(660\) | −3.79324 | − | 5.88333i | −0.147652 | − | 0.229008i | ||||
\(661\) | 19.9245 | 0.774972 | 0.387486 | − | 0.921876i | \(-0.373344\pi\) | ||||
0.387486 | + | 0.921876i | \(0.373344\pi\) | |||||||
\(662\) | 5.42605 | + | 16.6997i | 0.210889 | + | 0.649051i | ||||
\(663\) | 3.20553 | + | 2.32895i | 0.124492 | + | 0.0904490i | ||||
\(664\) | 10.6303 | − | 7.72334i | 0.412534 | − | 0.299724i | ||||
\(665\) | 0.596906 | − | 1.83709i | 0.0231470 | − | 0.0712392i | ||||
\(666\) | 3.13200 | − | 9.63930i | 0.121362 | − | 0.373515i | ||||
\(667\) | −12.0935 | + | 8.78643i | −0.468261 | + | 0.340212i | ||||
\(668\) | 19.5574 | + | 14.2093i | 0.756700 | + | 0.549774i | ||||
\(669\) | −6.71707 | − | 20.6730i | −0.259697 | − | 0.799265i | ||||
\(670\) | −23.9046 | −0.923514 | ||||||||
\(671\) | −19.7494 | − | 30.6314i | −0.762418 | − | 1.18251i | ||||
\(672\) | 5.51005 | 0.212555 | ||||||||
\(673\) | 3.67564 | + | 11.3125i | 0.141686 | + | 0.436064i | 0.996570 | − | 0.0827551i | \(-0.0263719\pi\) |
−0.854884 | + | 0.518819i | \(0.826372\pi\) | |||||||
\(674\) | 29.5247 | + | 21.4509i | 1.13725 | + | 0.826260i | ||||
\(675\) | 2.11381 | − | 1.53577i | 0.0813605 | − | 0.0591118i | ||||
\(676\) | 0.422134 | − | 1.29919i | 0.0162359 | − | 0.0499690i | ||||
\(677\) | −8.24716 | + | 25.3821i | −0.316964 | + | 0.975515i | 0.657974 | + | 0.753040i | \(0.271414\pi\) |
−0.974938 | + | 0.222475i | \(0.928586\pi\) | |||||||
\(678\) | −19.1067 | + | 13.8818i | −0.733787 | + | 0.533128i | ||||
\(679\) | −7.24979 | − | 5.26728i | −0.278221 | − | 0.202140i | ||||
\(680\) | 2.20029 | + | 6.77181i | 0.0843774 | + | 0.259687i | ||||
\(681\) | −19.6261 | −0.752075 | ||||||||
\(682\) | 0.534004 | − | 9.58631i | 0.0204481 | − | 0.367079i | ||||
\(683\) | −16.2014 | −0.619928 | −0.309964 | − | 0.950748i | \(-0.600317\pi\) | ||||
−0.309964 | + | 0.950748i | \(0.600317\pi\) | |||||||
\(684\) | −0.632280 | − | 1.94596i | −0.0241758 | − | 0.0744056i | ||||
\(685\) | 16.2723 | + | 11.8226i | 0.621734 | + | 0.451716i | ||||
\(686\) | −16.4816 | + | 11.9746i | −0.629269 | + | 0.457191i | ||||
\(687\) | 0.160178 | − | 0.492977i | 0.00611117 | − | 0.0188083i | ||||
\(688\) | −4.65843 | + | 14.3372i | −0.177601 | + | 0.546600i | ||||
\(689\) | −0.403067 | + | 0.292846i | −0.0153556 | + | 0.0111565i | ||||
\(690\) | −4.02561 | − | 2.92478i | −0.153252 | − | 0.111344i | ||||
\(691\) | −7.71714 | − | 23.7509i | −0.293574 | − | 0.903528i | −0.983697 | − | 0.179835i | \(-0.942443\pi\) |
0.690123 | − | 0.723692i | \(-0.257557\pi\) | |||||||
\(692\) | −17.5664 | −0.667775 | ||||||||
\(693\) | 2.67634 | − | 0.707701i | 0.101666 | − | 0.0268833i | ||||
\(694\) | −7.17995 | −0.272547 | ||||||||
\(695\) | −6.38005 | − | 19.6358i | −0.242009 | − | 0.744828i | ||||
\(696\) | −8.01297 | − | 5.82176i | −0.303731 | − | 0.220673i | ||||
\(697\) | 28.4459 | − | 20.6671i | 1.07746 | − | 0.782824i | ||||
\(698\) | 9.12844 | − | 28.0945i | 0.345517 | − | 1.06339i | ||||
\(699\) | −3.52545 | + | 10.8502i | −0.133345 | + | 0.410393i | ||||
\(700\) | 2.41020 | − | 1.75112i | 0.0910971 | − | 0.0661859i | ||||
\(701\) | 10.9205 | + | 7.93419i | 0.412461 | + | 0.299670i | 0.774597 | − | 0.632455i | \(-0.217953\pi\) |
−0.362137 | + | 0.932125i | \(0.617953\pi\) | |||||||
\(702\) | −0.566948 | − | 1.74489i | −0.0213981 | − | 0.0658565i | ||||
\(703\) | 8.27443 | 0.312076 | ||||||||
\(704\) | 7.35820 | + | 2.85234i | 0.277322 | + | 0.107501i | ||||
\(705\) | −3.44253 | −0.129653 | ||||||||
\(706\) | 12.3977 | + | 38.1562i | 0.466594 | + | 1.43603i | ||||
\(707\) | −5.17152 | − | 3.75733i | −0.194495 | − | 0.141309i | ||||
\(708\) | 6.45722 | − | 4.69145i | 0.242677 | − | 0.176315i | ||||
\(709\) | 5.15071 | − | 15.8523i | 0.193439 | − | 0.595344i | −0.806552 | − | 0.591163i | \(-0.798669\pi\) |
0.999991 | − | 0.00418136i | \(-0.00133097\pi\) | |||||||
\(710\) | −4.14150 | + | 12.7462i | −0.155428 | + | 0.478357i | ||||
\(711\) | 1.92361 | − | 1.39759i | 0.0721412 | − | 0.0524136i | ||||
\(712\) | 5.80498 | + | 4.21757i | 0.217551 | + | 0.158060i | ||||
\(713\) | −0.855894 | − | 2.63417i | −0.0320535 | − | 0.0986505i | ||||
\(714\) | 6.06769 | 0.227077 | ||||||||
\(715\) | 3.23794 | − | 3.97176i | 0.121092 | − | 0.148535i | ||||
\(716\) | −15.1812 | −0.567347 | ||||||||
\(717\) | −8.25417 | − | 25.4037i | −0.308258 | − | 0.948720i | ||||
\(718\) | −28.2534 | − | 20.5273i | −1.05441 | − | 0.766071i | ||||
\(719\) | 16.6655 | − | 12.1082i | 0.621518 | − | 0.451559i | −0.231934 | − | 0.972732i | \(-0.574505\pi\) |
0.853451 | + | 0.521173i | \(0.174505\pi\) | |||||||
\(720\) | 2.32326 | − | 7.15027i | 0.0865829 | − | 0.266475i | ||||
\(721\) | −1.83021 | + | 5.63280i | −0.0681605 | + | 0.209776i | ||||
\(722\) | −24.8715 | + | 18.0702i | −0.925622 | + | 0.672504i | ||||
\(723\) | −2.07238 | − | 1.50567i | −0.0770726 | − | 0.0559965i | ||||
\(724\) | 0.741321 | + | 2.28155i | 0.0275510 | + | 0.0847932i | ||||
\(725\) | −22.2501 | −0.826346 | ||||||||
\(726\) | 20.0566 | + | 2.24146i | 0.744371 | + | 0.0831882i | ||||
\(727\) | −19.1211 | −0.709161 | −0.354580 | − | 0.935026i | \(-0.615376\pi\) | ||||
−0.354580 | + | 0.935026i | \(0.615376\pi\) | |||||||
\(728\) | 0.299996 | + | 0.923293i | 0.0111186 | + | 0.0342195i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | −3.77507 | + | 2.74275i | −0.139722 | + | 0.101514i | ||||
\(731\) | −3.79323 | + | 11.6744i | −0.140298 | + | 0.431792i | ||||
\(732\) | −4.63881 | + | 14.2768i | −0.171455 | + | 0.527685i | ||||
\(733\) | −14.4049 | + | 10.4657i | −0.532055 | + | 0.386561i | −0.821126 | − | 0.570747i | \(-0.806654\pi\) |
0.289071 | + | 0.957308i | \(0.406654\pi\) | |||||||
\(734\) | 0.853376 | + | 0.620014i | 0.0314987 | + | 0.0228851i | ||||
\(735\) | 3.00950 | + | 9.26229i | 0.111007 | + | 0.341645i | ||||
\(736\) | 11.5879 | 0.427137 | ||||||||
\(737\) | 17.6727 | − | 21.6778i | 0.650981 | − | 0.798513i | ||||
\(738\) | −16.2810 | −0.599311 | ||||||||
\(739\) | 3.30155 | + | 10.1611i | 0.121449 | + | 0.373783i | 0.993238 | − | 0.116100i | \(-0.0370394\pi\) |
−0.871788 | + | 0.489883i | \(0.837039\pi\) | |||||||
\(740\) | −9.43296 | − | 6.85344i | −0.346762 | − | 0.251938i | ||||
\(741\) | 1.21176 | − | 0.880396i | 0.0445152 | − | 0.0323422i | ||||
\(742\) | −0.235767 | + | 0.725617i | −0.00865529 | + | 0.0266382i | ||||
\(743\) | −1.58783 | + | 4.88684i | −0.0582519 | + | 0.179281i | −0.975949 | − | 0.218001i | \(-0.930046\pi\) |
0.917697 | + | 0.397282i | \(0.130046\pi\) | |||||||
\(744\) | 1.48470 | − | 1.07870i | 0.0544316 | − | 0.0395469i | ||||
\(745\) | −5.56059 | − | 4.04000i | −0.203724 | − | 0.148014i | ||||
\(746\) | −2.61156 | − | 8.03755i | −0.0956159 | − | 0.294275i | ||||
\(747\) | −11.2973 | −0.413346 | ||||||||
\(748\) | 16.7381 | + | 6.48839i | 0.612007 | + | 0.237239i | ||||
\(749\) | 13.9123 | 0.508346 | ||||||||
\(750\) | −6.66855 | − | 20.5237i | −0.243501 | − | 0.749419i | ||||
\(751\) | −41.6178 | − | 30.2371i | −1.51865 | − | 1.10337i | −0.962149 | − | 0.272523i | \(-0.912142\pi\) |
−0.556505 | − | 0.830844i | \(-0.687858\pi\) | |||||||
\(752\) | 8.77130 | − | 6.37272i | 0.319856 | − | 0.232389i | ||||
\(753\) | 6.72921 | − | 20.7104i | 0.245226 | − | 0.754728i | ||||
\(754\) | −4.82799 | + | 14.8590i | −0.175825 | + | 0.541134i | ||||
\(755\) | 17.4022 | − | 12.6434i | 0.633329 | − | 0.460141i | ||||
\(756\) | −0.922457 | − | 0.670204i | −0.0335494 | − | 0.0243751i | ||||
\(757\) | 9.70112 | + | 29.8570i | 0.352593 | + | 1.08517i | 0.957392 | + | 0.288792i | \(0.0932536\pi\) |
−0.604799 | + | 0.796378i | \(0.706746\pi\) | |||||||
\(758\) | 66.6916 | 2.42235 | ||||||||
\(759\) | 5.62847 | − | 1.48833i | 0.204301 | − | 0.0540230i | ||||
\(760\) | 2.69163 | 0.0976357 | ||||||||
\(761\) | 6.67424 | + | 20.5412i | 0.241941 | + | 0.744618i | 0.996125 | + | 0.0879542i | \(0.0280329\pi\) |
−0.754183 | + | 0.656664i | \(0.771967\pi\) | |||||||
\(762\) | 19.3628 | + | 14.0679i | 0.701441 | + | 0.509626i | ||||
\(763\) | 13.1121 | − | 9.52646i | 0.474688 | − | 0.344881i | ||||
\(764\) | −2.27530 | + | 7.00264i | −0.0823174 | + | 0.253347i | ||||
\(765\) | 1.89177 | − | 5.82227i | 0.0683970 | − | 0.210504i | ||||
\(766\) | −29.1396 | + | 21.1712i | −1.05286 | + | 0.764946i | ||||
\(767\) | 4.72692 | + | 3.43430i | 0.170679 | + | 0.124006i | ||||
\(768\) | 6.48084 | + | 19.9460i | 0.233857 | + | 0.719739i | ||||
\(769\) | 54.0751 | 1.95000 | 0.974998 | − | 0.222213i | \(-0.0713280\pi\) | ||||
0.974998 | + | 0.222213i | \(0.0713280\pi\) | |||||||
\(770\) | 0.436456 | − | 7.83517i | 0.0157288 | − | 0.282360i | ||||
\(771\) | 8.84358 | 0.318494 | ||||||||
\(772\) | 4.04628 | + | 12.4532i | 0.145629 | + | 0.448199i | ||||
\(773\) | −6.63688 | − | 4.82197i | −0.238712 | − | 0.173434i | 0.461997 | − | 0.886881i | \(-0.347133\pi\) |
−0.700709 | + | 0.713447i | \(0.747133\pi\) | |||||||
\(774\) | 4.59836 | − | 3.34091i | 0.165285 | − | 0.120086i | ||||
\(775\) | 1.27396 | − | 3.92086i | 0.0457622 | − | 0.140841i | ||||
\(776\) | 3.85871 | − | 11.8759i | 0.138520 | − | 0.426319i | ||||
\(777\) | 3.73041 | − | 2.71030i | 0.133828 | − | 0.0972316i | ||||
\(778\) | 27.4225 | + | 19.9236i | 0.983143 | + | 0.714295i | ||||
\(779\) | −4.10735 | − | 12.6411i | −0.147161 | − | 0.452915i | ||||
\(780\) | −2.11063 | −0.0755726 | ||||||||
\(781\) | −8.49708 | − | 13.1790i | −0.304049 | − | 0.471582i | ||||
\(782\) | 12.7607 | 0.456320 | ||||||||
\(783\) | 2.63151 | + | 8.09897i | 0.0940427 | + | 0.289434i | ||||
\(784\) | −24.8141 | − | 18.0285i | −0.886218 | − | 0.643875i | ||||
\(785\) | −13.2893 | + | 9.65525i | −0.474316 | + | 0.344611i | ||||
\(786\) | −10.2465 | + | 31.5356i | −0.365482 | + | 1.12484i | ||||
\(787\) | −6.30417 | + | 19.4022i | −0.224719 | + | 0.691615i | 0.773601 | + | 0.633673i | \(0.218454\pi\) |
−0.998320 | + | 0.0579415i | \(0.981546\pi\) | |||||||
\(788\) | −14.0713 | + | 10.2234i | −0.501270 | + | 0.364194i | ||||
\(789\) | −4.41053 | − | 3.20444i | −0.157019 | − | 0.114081i | ||||
\(790\) | −2.08280 | − | 6.41019i | −0.0741026 | − | 0.228064i | ||||
\(791\) | −10.7445 | −0.382031 | ||||||||
\(792\) | 2.09031 | + | 3.24208i | 0.0742760 | + | 0.115202i | ||||
\(793\) | −10.9889 | −0.390229 | ||||||||
\(794\) | −12.9066 | − | 39.7224i | −0.458038 | − | 1.40970i | ||||
\(795\) | 0.622761 | + | 0.452462i | 0.0220870 | + | 0.0160472i | ||||
\(796\) | −2.37535 | + | 1.72579i | −0.0841919 | + | 0.0611690i | ||||
\(797\) | 15.1775 | − | 46.7114i | 0.537613 | − | 1.65460i | −0.200321 | − | 0.979730i | \(-0.564199\pi\) |
0.737934 | − | 0.674873i | \(-0.235801\pi\) | |||||||
\(798\) | 0.708799 | − | 2.18146i | 0.0250912 | − | 0.0772228i | ||||
\(799\) | 7.14223 | − | 5.18913i | 0.252674 | − | 0.183578i | ||||
\(800\) | 13.9541 | + | 10.1382i | 0.493351 | + | 0.358440i | ||||
\(801\) | −1.90640 | − | 5.86728i | −0.0673592 | − | 0.207310i | ||||
\(802\) | −55.9940 | −1.97722 | ||||||||
\(803\) | 0.303654 | − | 5.45114i | 0.0107157 | − | 0.192366i | ||||
\(804\) | −11.5198 | −0.406272 | ||||||||
\(805\) | −0.699547 | − | 2.15298i | −0.0246558 | − | 0.0758827i | ||||
\(806\) | −2.34199 | − | 1.70156i | −0.0824932 | − | 0.0599348i | ||||
\(807\) | −9.81758 | + | 7.13289i | −0.345595 | + | 0.251090i | ||||
\(808\) | 2.75255 | − | 8.47148i | 0.0968343 | − | 0.298025i | ||||
\(809\) | 13.8627 | − | 42.6649i | 0.487385 | − | 1.50002i | −0.341110 | − | 0.940023i | \(-0.610803\pi\) |
0.828496 | − | 0.559995i | \(-0.189197\pi\) | |||||||
\(810\) | −2.29331 | + | 1.66618i | −0.0805785 | + | 0.0585437i | ||||
\(811\) | 17.9764 | + | 13.0606i | 0.631238 | + | 0.458621i | 0.856829 | − | 0.515601i | \(-0.172431\pi\) |
−0.225591 | + | 0.974222i | \(0.572431\pi\) | |||||||
\(812\) | 3.00051 | + | 9.23460i | 0.105297 | + | 0.324071i | ||||
\(813\) | −23.3083 | −0.817459 | ||||||||
\(814\) | 32.4982 | − | 8.59346i | 1.13906 | − | 0.301201i | ||||
\(815\) | 3.84033 | 0.134521 | ||||||||
\(816\) | 5.95795 | + | 18.3367i | 0.208570 | + | 0.641912i | ||||
\(817\) | 3.75407 | + | 2.72749i | 0.131338 | + | 0.0954228i | ||||
\(818\) | −24.8039 | + | 18.0211i | −0.867247 | + | 0.630092i | ||||
\(819\) | 0.257931 | − | 0.793829i | 0.00901283 | − | 0.0277386i | ||||
\(820\) | −5.78780 | + | 17.8130i | −0.202119 | + | 0.622058i | ||||
\(821\) | −20.6955 | + | 15.0362i | −0.722278 | + | 0.524766i | −0.887111 | − | 0.461556i | \(-0.847291\pi\) |
0.164833 | + | 0.986321i | \(0.447291\pi\) | |||||||
\(822\) | 19.3227 | + | 14.0387i | 0.673956 | + | 0.489657i | ||||
\(823\) | −1.03612 | − | 3.18885i | −0.0361169 | − | 0.111156i | 0.931373 | − | 0.364067i | \(-0.118612\pi\) |
−0.967490 | + | 0.252911i | \(0.918612\pi\) | |||||||
\(824\) | −8.25297 | −0.287506 | ||||||||
\(825\) | 8.07988 | + | 3.13209i | 0.281305 | + | 0.109045i | ||||
\(826\) | 8.94749 | 0.311323 | ||||||||
\(827\) | −6.34493 | − | 19.5277i | −0.220635 | − | 0.679044i | −0.998705 | − | 0.0508675i | \(-0.983801\pi\) |
0.778070 | − | 0.628177i | \(-0.216199\pi\) | |||||||
\(828\) | −1.93997 | − | 1.40947i | −0.0674188 | − | 0.0489826i | ||||
\(829\) | 45.6140 | − | 33.1405i | 1.58424 | − | 1.15102i | 0.672619 | − | 0.739989i | \(-0.265169\pi\) |
0.911622 | − | 0.411029i | \(-0.134831\pi\) | |||||||
\(830\) | −9.89602 | + | 30.4568i | −0.343496 | + | 1.05717i | ||||
\(831\) | −1.98304 | + | 6.10317i | −0.0687909 | + | 0.211717i | ||||
\(832\) | 1.92500 | − | 1.39860i | 0.0667375 | − | 0.0484876i | ||||
\(833\) | −20.2054 | − | 14.6801i | −0.700077 | − | 0.508636i | ||||
\(834\) | −7.57602 | − | 23.3166i | −0.262336 | − | 0.807388i | ||||
\(835\) | 27.3420 | 0.946208 | ||||||||
\(836\) | 4.28798 | − | 5.25976i | 0.148303 | − | 0.181913i | ||||
\(837\) | −1.57786 | −0.0545387 | ||||||||
\(838\) | −18.9158 | − | 58.2167i | −0.653434 | − | 2.01106i | ||||
\(839\) | −35.5956 | − | 25.8617i | −1.22890 | − | 0.892846i | −0.232090 | − | 0.972694i | \(-0.574556\pi\) |
−0.996807 | + | 0.0798480i | \(0.974556\pi\) | |||||||
\(840\) | 1.21348 | − | 0.881648i | 0.0418692 | − | 0.0304198i | ||||
\(841\) | 13.4479 | − | 41.3882i | 0.463719 | − | 1.42718i | ||||
\(842\) | 10.7965 | − | 33.2282i | 0.372072 | − | 1.14512i | ||||
\(843\) | 22.6158 | − | 16.4313i | 0.778929 | − | 0.565925i | ||||
\(844\) | 22.4693 | + | 16.3249i | 0.773425 | + | 0.561926i | ||||
\(845\) | −0.477448 | − | 1.46943i | −0.0164247 | − | 0.0505501i | ||||
\(846\) | −4.08785 | −0.140543 | ||||||||
\(847\) | 6.78264 | + | 6.18834i | 0.233054 | + | 0.212634i | ||||
\(848\) | −2.42433 | −0.0832520 | ||||||||
\(849\) | −3.68799 | − | 11.3505i | −0.126571 | − | 0.389547i | ||||
\(850\) | 15.3662 | + | 11.1642i | 0.527058 | + | 0.382930i | ||||
\(851\) | 7.84524 | − | 5.69990i | 0.268931 | − | 0.195390i | ||||
\(852\) | −1.99582 | + | 6.14250i | −0.0683757 | + | 0.210439i | ||||
\(853\) | 5.35849 | − | 16.4918i | 0.183471 | − | 0.564667i | −0.816447 | − | 0.577420i | \(-0.804060\pi\) |
0.999919 | + | 0.0127532i | \(0.00405956\pi\) | |||||||
\(854\) | −13.6143 | + | 9.89135i | −0.465871 | + | 0.338475i | ||||
\(855\) | −1.87224 | − | 1.36026i | −0.0640291 | − | 0.0465199i | ||||
\(856\) | 5.99066 | + | 18.4373i | 0.204756 | + | 0.630175i | ||||
\(857\) | −3.98802 | −0.136228 | −0.0681140 | − | 0.997678i | \(-0.521698\pi\) | ||||
−0.0681140 | + | 0.997678i | \(0.521698\pi\) | |||||||
\(858\) | 3.84491 | − | 4.71628i | 0.131263 | − | 0.161011i | ||||
\(859\) | −4.45502 | −0.152003 | −0.0760017 | − | 0.997108i | \(-0.524215\pi\) | ||||
−0.0760017 | + | 0.997108i | \(0.524215\pi\) | |||||||
\(860\) | −2.02059 | − | 6.21875i | −0.0689017 | − | 0.212058i | ||||
\(861\) | −5.99236 | − | 4.35370i | −0.204219 | − | 0.148374i | ||||
\(862\) | 9.36927 | − | 6.80717i | 0.319119 | − | 0.231853i | ||||
\(863\) | 8.17101 | − | 25.1478i | 0.278144 | − | 0.856040i | −0.710226 | − | 0.703974i | \(-0.751407\pi\) |
0.988370 | − | 0.152066i | \(-0.0485927\pi\) | |||||||
\(864\) | 2.03994 | − | 6.27829i | 0.0694002 | − | 0.213592i | ||||
\(865\) | −16.0737 | + | 11.6782i | −0.546523 | + | 0.397072i | ||||
\(866\) | −16.1888 | − | 11.7619i | −0.550118 | − | 0.399684i | ||||
\(867\) | −0.401895 | − | 1.23691i | −0.0136491 | − | 0.0420076i | ||||
\(868\) | −1.79910 | −0.0610655 | ||||||||
\(869\) | 7.35289 | + | 2.85028i | 0.249430 | + | 0.0966890i | ||||
\(870\) | 24.1395 | 0.818405 | ||||||||
\(871\) | −2.60591 | − | 8.02016i | −0.0882978 | − | 0.271753i | ||||
\(872\) | 18.2710 | + | 13.2747i | 0.618735 | + | 0.449537i | ||||
\(873\) | −8.68570 | + | 6.31053i | −0.293966 | + | 0.213579i | ||||
\(874\) | 1.49064 | − | 4.58772i | 0.0504216 | − | 0.155182i | ||||
\(875\) | 3.03383 | − | 9.33717i | 0.102562 | − | 0.315654i | ||||
\(876\) | −1.81924 | + | 1.32175i | −0.0614663 | + | 0.0446579i | ||||
\(877\) | −38.8229 | − | 28.2065i | −1.31096 | − | 0.952466i | −0.999998 | − | 0.00204293i | \(-0.999350\pi\) |
−0.310959 | − | 0.950423i | \(-0.600650\pi\) | |||||||
\(878\) | 6.62964 | + | 20.4039i | 0.223740 | + | 0.688600i | ||||
\(879\) | 7.23742 | 0.244112 | ||||||||
\(880\) | 24.1066 | − | 6.37449i | 0.812634 | − | 0.214884i | ||||
\(881\) | −33.5896 | −1.13166 | −0.565832 | − | 0.824521i | \(-0.691445\pi\) | ||||
−0.565832 | + | 0.824521i | \(0.691445\pi\) | |||||||
\(882\) | 3.57365 | + | 10.9985i | 0.120331 | + | 0.370340i | ||||
\(883\) | −3.21974 | − | 2.33928i | −0.108353 | − | 0.0787231i | 0.532289 | − | 0.846563i | \(-0.321332\pi\) |
−0.640642 | + | 0.767839i | \(0.721332\pi\) | |||||||
\(884\) | 4.37893 | − | 3.18148i | 0.147279 | − | 0.107005i | ||||
\(885\) | 2.78963 | − | 8.58559i | 0.0937723 | − | 0.288601i | ||||
\(886\) | 19.2833 | − | 59.3480i | 0.647836 | − | 1.99383i | ||||
\(887\) | −19.3270 | + | 14.0419i | −0.648936 | + | 0.471479i | −0.862909 | − | 0.505360i | \(-0.831360\pi\) |
0.213973 | + | 0.976840i | \(0.431360\pi\) | |||||||
\(888\) | 5.19815 | + | 3.77668i | 0.174438 | + | 0.126737i | ||||
\(889\) | 3.36475 | + | 10.3556i | 0.112850 | + | 0.347317i | ||||
\(890\) | −17.4878 | −0.586192 | ||||||||
\(891\) | 0.184466 | − | 3.31149i | 0.00617984 | − | 0.110939i | ||||
\(892\) | −29.6938 | −0.994221 | ||||||||
\(893\) | −1.03128 | − | 3.17395i | −0.0345104 | − | 0.106212i | ||||
\(894\) | −6.60294 | − | 4.79732i | −0.220835 | − | 0.160446i | ||||
\(895\) | −13.8912 | + | 10.0925i | −0.464331 | + | 0.337356i | ||||
\(896\) | −2.27940 | + | 7.01528i | −0.0761495 | + | 0.234364i | ||||
\(897\) | 0.542441 | − | 1.66946i | 0.0181116 | − | 0.0557417i | ||||
\(898\) | 26.8803 | − | 19.5297i | 0.897009 | − | 0.651715i | ||||
\(899\) | 10.8705 | + | 7.89786i | 0.362551 | + | 0.263409i | ||||
\(900\) | −1.10296 | − | 3.39455i | −0.0367652 | − | 0.113152i | ||||
\(901\) | −1.97407 | −0.0657657 | ||||||||
\(902\) | −29.2603 | − | 45.3829i | −0.974262 | − | 1.51108i | ||||
\(903\) | 2.58586 | 0.0860521 | ||||||||
\(904\) | −4.62660 | − | 14.2392i | −0.153878 | − | 0.473589i | ||||
\(905\) | 2.19512 | + | 1.59484i | 0.0729681 | + | 0.0530144i | ||||
\(906\) | 20.6643 | − | 15.0135i | 0.686524 | − | 0.498789i | ||||
\(907\) | 12.7122 | − | 39.1240i | 0.422100 | − | 1.29909i | −0.483644 | − | 0.875265i | \(-0.660687\pi\) |
0.905744 | − | 0.423826i | \(-0.139313\pi\) | |||||||
\(908\) | −8.28486 | + | 25.4982i | −0.274943 | + | 0.846186i | ||||
\(909\) | −6.19581 | + | 4.50152i | −0.205502 | + | 0.149306i | ||||
\(910\) | −1.91418 | − | 1.39073i | −0.0634544 | − | 0.0461023i | ||||
\(911\) | 10.7062 | + | 32.9502i | 0.354711 | + | 1.09169i | 0.956177 | + | 0.292790i | \(0.0945838\pi\) |
−0.601465 | + | 0.798899i | \(0.705416\pi\) | |||||||
\(912\) | 7.28839 | 0.241343 | ||||||||
\(913\) | −20.3036 | − | 31.4909i | −0.671951 | − | 1.04220i | ||||
\(914\) | 36.2009 | 1.19742 | ||||||||
\(915\) | 5.24665 | + | 16.1475i | 0.173449 | + | 0.533821i | ||||
\(916\) | −0.572857 | − | 0.416205i | −0.0189277 | − | 0.0137518i | ||||
\(917\) | −12.2043 | + | 8.86694i | −0.403021 | + | 0.292812i | ||||
\(918\) | 2.24639 | − | 6.91368i | 0.0741419 | − | 0.228185i | ||||
\(919\) | 5.17441 | − | 15.9252i | 0.170688 | − | 0.525324i | −0.828722 | − | 0.559660i | \(-0.810932\pi\) |
0.999410 | + | 0.0343364i | \(0.0109318\pi\) | |||||||
\(920\) | 2.55202 | − | 1.85415i | 0.0841376 | − | 0.0611295i | ||||
\(921\) | 11.4661 | + | 8.33062i | 0.377821 | + | 0.274503i | ||||
\(922\) | 13.5650 | + | 41.7487i | 0.446739 | + | 1.37492i | ||||
\(923\) | −4.72793 | −0.155622 | ||||||||
\(924\) | 0.210332 | − | 3.77583i | 0.00691940 | − | 0.124216i | ||||
\(925\) | 14.4340 | 0.474586 | ||||||||
\(926\) | −2.07404 | − | 6.38323i | −0.0681571 | − | 0.209766i | ||||
\(927\) | 5.74057 | + | 4.17077i | 0.188545 | + | 0.136986i | ||||
\(928\) | −45.4796 | + | 33.0429i | −1.49294 | + | 1.08468i | ||||
\(929\) | −8.60400 | + | 26.4804i | −0.282288 | + | 0.868794i | 0.704910 | + | 0.709296i | \(0.250987\pi\) |
−0.987198 | + | 0.159497i | \(0.949013\pi\) | |||||||
\(930\) | −1.38215 | + | 4.25381i | −0.0453224 | + | 0.139488i | ||||
\(931\) | −7.63810 | + | 5.54941i | −0.250329 | + | 0.181874i | ||||
\(932\) | 12.6083 | + | 9.16049i | 0.412999 | + | 0.300062i | ||||
\(933\) | 1.52479 | + | 4.69283i | 0.0499195 | + | 0.153636i | ||||
\(934\) | −20.0852 | −0.657208 | ||||||||
\(935\) | 19.6293 | − | 5.19057i | 0.641948 | − | 0.169750i | ||||
\(936\) | 1.16309 | 0.0380167 | ||||||||
\(937\) | 9.96998 | + | 30.6845i | 0.325705 | + | 1.00242i | 0.971121 | + | 0.238586i | \(0.0766840\pi\) |
−0.645416 | + | 0.763831i | \(0.723316\pi\) | |||||||
\(938\) | −10.4476 | − | 7.59061i | −0.341125 | − | 0.247842i | ||||
\(939\) | 18.5225 | − | 13.4574i | 0.604460 | − | 0.439166i | ||||
\(940\) | −1.45321 | + | 4.47252i | −0.0473984 | + | 0.145877i | ||||
\(941\) | −7.82142 | + | 24.0719i | −0.254971 | + | 0.784720i | 0.738864 | + | 0.673854i | \(0.235362\pi\) |
−0.993835 | + | 0.110866i | \(0.964638\pi\) | |||||||
\(942\) | −15.7804 | + | 11.4652i | −0.514155 | + | 0.373555i | ||||
\(943\) | −12.6022 | − | 9.15606i | −0.410385 | − | 0.298162i | ||||
\(944\) | 8.78567 | + | 27.0395i | 0.285949 | + | 0.880061i | ||||
\(945\) | −1.28963 | −0.0419516 | ||||||||
\(946\) | 17.5769 | + | 6.81353i | 0.571475 | + | 0.221527i | ||||
\(947\) | −45.4202 | −1.47596 | −0.737978 | − | 0.674824i | \(-0.764219\pi\) | ||||
−0.737978 | + | 0.674824i | \(0.764219\pi\) | |||||||
\(948\) | −1.00372 | − | 3.08912i | −0.0325992 | − | 0.100330i | ||||
\(949\) | −1.33175 | − | 0.967570i | −0.0432303 | − | 0.0314086i | ||||
\(950\) | 5.80878 | − | 4.22033i | 0.188462 | − | 0.136926i | ||||
\(951\) | −4.20091 | + | 12.9291i | −0.136224 | + | 0.419254i | ||||
\(952\) | −1.18866 | + | 3.65832i | −0.0385247 | + | 0.118567i | ||||
\(953\) | −25.4686 | + | 18.5040i | −0.825010 | + | 0.599405i | −0.918143 | − | 0.396249i | \(-0.870312\pi\) |
0.0931335 | + | 0.995654i | \(0.470312\pi\) | |||||||
\(954\) | 0.739500 | + | 0.537278i | 0.0239422 | + | 0.0173950i | ||||
\(955\) | 2.57344 | + | 7.92023i | 0.0832745 | + | 0.256293i | ||||
\(956\) | −36.4888 | −1.18013 | ||||||||
\(957\) | −17.8463 | + | 21.8908i | −0.576890 | + | 0.707630i | ||||
\(958\) | −33.4752 | −1.08153 | ||||||||
\(959\) | 3.35778 | + | 10.3342i | 0.108428 | + | 0.333708i | ||||
\(960\) | −2.97424 | − | 2.16091i | −0.0959930 | − | 0.0697430i | ||||
\(961\) | 23.0654 | − | 16.7580i | 0.744044 | − | 0.540580i | ||||
\(962\) | 3.13200 | − | 9.63930i | 0.100980 | − | 0.310783i | ||||
\(963\) | 5.15065 | − | 15.8521i | 0.165977 | − | 0.510826i | ||||
\(964\) | −2.83098 | + | 2.05683i | −0.0911798 | + | 0.0662460i | ||||
\(965\) | 11.9814 | + | 8.70498i | 0.385694 | + | 0.280223i | ||||
\(966\) | −0.830680 | − | 2.55657i | −0.0267267 | − | 0.0822563i | ||||
\(967\) | 20.9984 | 0.675263 | 0.337631 | − | 0.941278i | \(-0.390374\pi\) | ||||
0.337631 | + | 0.941278i | \(0.390374\pi\) | |||||||
\(968\) | −5.28051 | + | 11.6534i | −0.169722 | + | 0.374555i | ||||
\(969\) | 5.93474 | 0.190651 | ||||||||
\(970\) | 9.40445 | + | 28.9439i | 0.301959 | + | 0.929334i | ||||
\(971\) | 1.94634 | + | 1.41410i | 0.0624611 | + | 0.0453806i | 0.618578 | − | 0.785724i | \(-0.287709\pi\) |
−0.556117 | + | 0.831104i | \(0.687709\pi\) | |||||||
\(972\) | −1.10516 | + | 0.802947i | −0.0354481 | + | 0.0257545i | ||||
\(973\) | 3.44668 | − | 10.6078i | 0.110496 | − | 0.340070i | ||||
\(974\) | 5.00103 | − | 15.3916i | 0.160243 | − | 0.493179i | ||||
\(975\) | 2.11381 | − | 1.53577i | 0.0676960 | − | 0.0491840i | ||||
\(976\) | −43.2599 | − | 31.4302i | −1.38472 | − | 1.00606i | ||||
\(977\) | −13.0907 | − | 40.2889i | −0.418808 | − | 1.28896i | −0.908801 | − | 0.417231i | \(-0.863001\pi\) |
0.489993 | − | 0.871726i | \(-0.336999\pi\) | |||||||
\(978\) | 4.56022 | 0.145820 | ||||||||
\(979\) | 12.9287 | − | 15.8588i | 0.413204 | − | 0.506849i | ||||
\(980\) | 13.3039 | 0.424979 | ||||||||
\(981\) | −6.00033 | − | 18.4671i | −0.191576 | − | 0.589609i | ||||
\(982\) | 29.7272 | + | 21.5981i | 0.948632 | + | 0.689222i | ||||
\(983\) | −38.4963 | + | 27.9692i | −1.22784 | + | 0.892078i | −0.996726 | − | 0.0808483i | \(-0.974237\pi\) |
−0.231114 | + | 0.972927i | \(0.574237\pi\) | |||||||
\(984\) | 3.18944 | − | 9.81609i | 0.101676 | − | 0.312926i | ||||
\(985\) | −6.07904 | + | 18.7094i | −0.193694 | + | 0.596130i | ||||
\(986\) | −50.0822 | + | 36.3869i | −1.59494 | + | 1.15879i | ||||
\(987\) | −1.50457 | − | 1.09313i | −0.0478910 | − | 0.0347948i | ||||
\(988\) | −0.632280 | − | 1.94596i | −0.0201155 | − | 0.0619092i | ||||
\(989\) | 5.43820 | 0.172925 | ||||||||
\(990\) | −8.76600 | − | 3.39806i | −0.278602 | − | 0.107997i | ||||
\(991\) | −48.1600 | −1.52985 | −0.764926 | − | 0.644118i | \(-0.777225\pi\) | ||||
−0.764926 | + | 0.644118i | \(0.777225\pi\) | |||||||
\(992\) | −3.21874 | − | 9.90625i | −0.102195 | − | 0.314524i | ||||
\(993\) | 7.74280 | + | 5.62548i | 0.245710 | + | 0.178519i | ||||
\(994\) | −5.85746 | + | 4.25570i | −0.185788 | + | 0.134983i | ||||
\(995\) | −1.02619 | + | 3.15828i | −0.0325324 | + | 0.100124i | ||||
\(996\) | −4.76897 | + | 14.6774i | −0.151111 | + | 0.465070i | ||||
\(997\) | −37.3141 | + | 27.1103i | −1.18175 | + | 0.858592i | −0.992368 | − | 0.123311i | \(-0.960649\pi\) |
−0.189383 | + | 0.981903i | \(0.560649\pi\) | |||||||
\(998\) | 40.0419 | + | 29.0922i | 1.26750 | + | 0.920896i | ||||
\(999\) | −1.70711 | − | 5.25394i | −0.0540105 | − | 0.166227i |
(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 | 429.2.n.a.313.1 | yes | 12 | |
11.3 | even | 5 | 4719.2.a.bg.1.2 | 6 | |||
11.8 | odd | 10 | 4719.2.a.bh.1.5 | 6 | |||
11.9 | even | 5 | inner | 429.2.n.a.196.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.a.196.1 | ✓ | 12 | 11.9 | even | 5 | inner | |
429.2.n.a.313.1 | yes | 12 | 1.1 | even | 1 | trivial | |
4719.2.a.bg.1.2 | 6 | 11.3 | even | 5 | |||
4719.2.a.bh.1.5 | 6 | 11.8 | odd | 10 |