Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(481,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 31 x^{14} + 20 x^{13} + 474 x^{12} + 463 x^{11} + 6637 x^{10} + 13567 x^{9} + \cdots + 22848400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 481.2 | ||
Root | \(-0.530826 - 1.63371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.481 |
Dual form | 930.2.n.g.901.2 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.530826 | + | 1.63371i | −0.200633 | + | 0.617486i | 0.799231 | + | 0.601024i | \(0.205240\pi\) |
−0.999864 | + | 0.0164621i | \(0.994760\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | −0.809017 | + | 0.587785i | −0.255834 | + | 0.185874i | ||||
\(11\) | 0.890814 | − | 2.74164i | 0.268591 | − | 0.826637i | −0.722254 | − | 0.691628i | \(-0.756894\pi\) |
0.990844 | − | 0.135009i | \(-0.0431062\pi\) | |||||||
\(12\) | −0.809017 | + | 0.587785i | −0.233543 | + | 0.169679i | ||||
\(13\) | 0.180762 | + | 0.131331i | 0.0501344 | + | 0.0364248i | 0.612570 | − | 0.790416i | \(-0.290136\pi\) |
−0.562436 | + | 0.826841i | \(0.690136\pi\) | |||||||
\(14\) | −0.530826 | − | 1.63371i | −0.141869 | − | 0.436628i | ||||
\(15\) | −0.809017 | − | 0.587785i | −0.208887 | − | 0.151765i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 1.60240 | + | 4.93169i | 0.388640 | + | 1.19611i | 0.933805 | + | 0.357781i | \(0.116467\pi\) |
−0.545166 | + | 0.838328i | \(0.683533\pi\) | |||||||
\(18\) | −0.809017 | − | 0.587785i | −0.190687 | − | 0.138542i | ||||
\(19\) | 0.261465 | − | 0.189965i | 0.0599842 | − | 0.0435811i | −0.557389 | − | 0.830251i | \(-0.688197\pi\) |
0.617373 | + | 0.786670i | \(0.288197\pi\) | |||||||
\(20\) | 0.309017 | − | 0.951057i | 0.0690983 | − | 0.212663i | ||||
\(21\) | 1.38972 | − | 1.00969i | 0.303262 | − | 0.220333i | ||||
\(22\) | 0.890814 | + | 2.74164i | 0.189922 | + | 0.584520i | ||||
\(23\) | 0.871763 | + | 2.68301i | 0.181775 | + | 0.559446i | 0.999878 | − | 0.0156258i | \(-0.00497404\pi\) |
−0.818103 | + | 0.575072i | \(0.804974\pi\) | |||||||
\(24\) | 0.309017 | − | 0.951057i | 0.0630778 | − | 0.194134i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.223434 | −0.0438191 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | 1.38972 | + | 1.00969i | 0.262632 | + | 0.190814i | ||||
\(29\) | −3.51438 | + | 2.55335i | −0.652604 | + | 0.474145i | −0.864157 | − | 0.503222i | \(-0.832148\pi\) |
0.211553 | + | 0.977366i | \(0.432148\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 0.731733 | − | 5.51947i | 0.131423 | − | 0.991326i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.33218 | + | 1.69443i | −0.405981 | + | 0.294962i | ||||
\(34\) | −4.19514 | − | 3.04795i | −0.719461 | − | 0.522719i | ||||
\(35\) | −0.530826 | + | 1.63371i | −0.0897259 | + | 0.276148i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.36659 | 0.389064 | 0.194532 | − | 0.980896i | \(-0.437681\pi\) | ||||
0.194532 | + | 0.980896i | \(0.437681\pi\) | |||||||
\(38\) | −0.0998708 | + | 0.307371i | −0.0162012 | + | 0.0498621i | ||||
\(39\) | −0.0690450 | − | 0.212499i | −0.0110560 | − | 0.0340270i | ||||
\(40\) | 0.309017 | + | 0.951057i | 0.0488599 | + | 0.150375i | ||||
\(41\) | −4.56395 | + | 3.31590i | −0.712769 | + | 0.517857i | −0.884066 | − | 0.467363i | \(-0.845204\pi\) |
0.171297 | + | 0.985219i | \(0.445204\pi\) | |||||||
\(42\) | −0.530826 | + | 1.63371i | −0.0819082 | + | 0.252088i | ||||
\(43\) | 5.84403 | − | 4.24594i | 0.891206 | − | 0.647499i | −0.0449859 | − | 0.998988i | \(-0.514324\pi\) |
0.936192 | + | 0.351488i | \(0.114324\pi\) | |||||||
\(44\) | −2.33218 | − | 1.69443i | −0.351590 | − | 0.255445i | ||||
\(45\) | 0.309017 | + | 0.951057i | 0.0460655 | + | 0.141775i | ||||
\(46\) | −2.28230 | − | 1.65819i | −0.336507 | − | 0.244487i | ||||
\(47\) | 6.83776 | + | 4.96792i | 0.997390 | + | 0.724646i | 0.961527 | − | 0.274711i | \(-0.0885820\pi\) |
0.0358630 | + | 0.999357i | \(0.488582\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | 3.27587 | + | 2.38006i | 0.467982 | + | 0.340009i | ||||
\(50\) | −0.809017 | + | 0.587785i | −0.114412 | + | 0.0831254i | ||||
\(51\) | 1.60240 | − | 4.93169i | 0.224381 | − | 0.690574i | ||||
\(52\) | 0.180762 | − | 0.131331i | 0.0250672 | − | 0.0182124i | ||||
\(53\) | 1.25037 | + | 3.84823i | 0.171751 | + | 0.528596i | 0.999470 | − | 0.0325471i | \(-0.0103619\pi\) |
−0.827719 | + | 0.561143i | \(0.810362\pi\) | |||||||
\(54\) | 0.309017 | + | 0.951057i | 0.0420519 | + | 0.129422i | ||||
\(55\) | 0.890814 | − | 2.74164i | 0.120117 | − | 0.369683i | ||||
\(56\) | −1.71779 | −0.229549 | ||||||||
\(57\) | −0.323189 | −0.0428074 | ||||||||
\(58\) | 1.34237 | − | 4.13140i | 0.176262 | − | 0.542480i | ||||
\(59\) | 4.48514 | + | 3.25864i | 0.583915 | + | 0.424239i | 0.840133 | − | 0.542380i | \(-0.182477\pi\) |
−0.256218 | + | 0.966619i | \(0.582477\pi\) | |||||||
\(60\) | −0.809017 | + | 0.587785i | −0.104444 | + | 0.0758827i | ||||
\(61\) | 12.0647 | 1.54472 | 0.772362 | − | 0.635183i | \(-0.219075\pi\) | ||||
0.772362 | + | 0.635183i | \(0.219075\pi\) | |||||||
\(62\) | 2.65228 | + | 4.89545i | 0.336840 | + | 0.621723i | ||||
\(63\) | −1.71779 | −0.216421 | ||||||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0.180762 | + | 0.131331i | 0.0224208 | + | 0.0162897i | ||||
\(66\) | 0.890814 | − | 2.74164i | 0.109652 | − | 0.337473i | ||||
\(67\) | 10.7024 | 1.30751 | 0.653754 | − | 0.756707i | \(-0.273193\pi\) | ||||
0.653754 | + | 0.756707i | \(0.273193\pi\) | |||||||
\(68\) | 5.18548 | 0.628832 | ||||||||
\(69\) | 0.871763 | − | 2.68301i | 0.104948 | − | 0.322996i | ||||
\(70\) | −0.530826 | − | 1.63371i | −0.0634458 | − | 0.195266i | ||||
\(71\) | 2.26300 | + | 6.96480i | 0.268569 | + | 0.826570i | 0.990850 | + | 0.134970i | \(0.0430938\pi\) |
−0.722281 | + | 0.691600i | \(0.756906\pi\) | |||||||
\(72\) | −0.809017 | + | 0.587785i | −0.0953436 | + | 0.0692712i | ||||
\(73\) | −1.54022 | + | 4.74030i | −0.180269 | + | 0.554810i | −0.999835 | − | 0.0181747i | \(-0.994215\pi\) |
0.819566 | + | 0.572985i | \(0.194215\pi\) | |||||||
\(74\) | −1.91461 | + | 1.39104i | −0.222569 | + | 0.161706i | ||||
\(75\) | −0.809017 | − | 0.587785i | −0.0934172 | − | 0.0678716i | ||||
\(76\) | −0.0998708 | − | 0.307371i | −0.0114560 | − | 0.0352578i | ||||
\(77\) | 4.00619 | + | 2.91067i | 0.456548 | + | 0.331702i | ||||
\(78\) | 0.180762 | + | 0.131331i | 0.0204673 | + | 0.0148703i | ||||
\(79\) | −1.72100 | − | 5.29668i | −0.193627 | − | 0.595923i | −0.999990 | − | 0.00450179i | \(-0.998567\pi\) |
0.806363 | − | 0.591421i | \(-0.201433\pi\) | |||||||
\(80\) | −0.809017 | − | 0.587785i | −0.0904508 | − | 0.0657164i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 1.74327 | − | 5.36524i | 0.192512 | − | 0.592492i | ||||
\(83\) | −2.25271 | + | 1.63669i | −0.247267 | + | 0.179650i | −0.704515 | − | 0.709689i | \(-0.748835\pi\) |
0.457248 | + | 0.889339i | \(0.348835\pi\) | |||||||
\(84\) | −0.530826 | − | 1.63371i | −0.0579178 | − | 0.178253i | ||||
\(85\) | 1.60240 | + | 4.93169i | 0.173805 | + | 0.534916i | ||||
\(86\) | −2.23222 | + | 6.87007i | −0.240707 | + | 0.740819i | ||||
\(87\) | 4.34401 | 0.465727 | ||||||||
\(88\) | 2.88274 | 0.307301 | ||||||||
\(89\) | −1.46075 | + | 4.49572i | −0.154839 | + | 0.476545i | −0.998145 | − | 0.0608891i | \(-0.980606\pi\) |
0.843306 | + | 0.537434i | \(0.180606\pi\) | |||||||
\(90\) | −0.809017 | − | 0.587785i | −0.0852779 | − | 0.0619580i | ||||
\(91\) | −0.310511 | + | 0.225599i | −0.0325504 | + | 0.0236493i | ||||
\(92\) | 2.82108 | 0.294118 | ||||||||
\(93\) | −3.83625 | + | 4.03524i | −0.397800 | + | 0.418435i | ||||
\(94\) | −8.45194 | −0.871751 | ||||||||
\(95\) | 0.261465 | − | 0.189965i | 0.0268257 | − | 0.0194900i | ||||
\(96\) | −0.809017 | − | 0.587785i | −0.0825700 | − | 0.0599906i | ||||
\(97\) | −2.06009 | + | 6.34030i | −0.209170 | + | 0.643760i | 0.790346 | + | 0.612661i | \(0.209901\pi\) |
−0.999516 | + | 0.0310990i | \(0.990099\pi\) | |||||||
\(98\) | −4.04920 | −0.409031 | ||||||||
\(99\) | 2.88274 | 0.289726 | ||||||||
\(100\) | 0.309017 | − | 0.951057i | 0.0309017 | − | 0.0951057i | ||||
\(101\) | −1.34795 | − | 4.14856i | −0.134126 | − | 0.412798i | 0.861327 | − | 0.508051i | \(-0.169634\pi\) |
−0.995453 | + | 0.0952534i | \(0.969634\pi\) | |||||||
\(102\) | 1.60240 | + | 4.93169i | 0.158661 | + | 0.488310i | ||||
\(103\) | 0.0978841 | − | 0.0711170i | 0.00964481 | − | 0.00700736i | −0.582952 | − | 0.812506i | \(-0.698103\pi\) |
0.592597 | + | 0.805499i | \(0.298103\pi\) | |||||||
\(104\) | −0.0690450 | + | 0.212499i | −0.00677042 | + | 0.0208372i | ||||
\(105\) | 1.38972 | − | 1.00969i | 0.135623 | − | 0.0985357i | ||||
\(106\) | −3.27350 | − | 2.37834i | −0.317951 | − | 0.231005i | ||||
\(107\) | 5.37576 | + | 16.5449i | 0.519694 | + | 1.59945i | 0.774575 | + | 0.632482i | \(0.217964\pi\) |
−0.254881 | + | 0.966973i | \(0.582036\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | −2.77497 | − | 2.01613i | −0.265794 | − | 0.193110i | 0.446904 | − | 0.894582i | \(-0.352527\pi\) |
−0.712697 | + | 0.701472i | \(0.752527\pi\) | |||||||
\(110\) | 0.890814 | + | 2.74164i | 0.0849358 | + | 0.261405i | ||||
\(111\) | −1.91461 | − | 1.39104i | −0.181727 | − | 0.132032i | ||||
\(112\) | 1.38972 | − | 1.00969i | 0.131316 | − | 0.0954068i | ||||
\(113\) | −0.730108 | + | 2.24704i | −0.0686828 | + | 0.211384i | −0.979507 | − | 0.201411i | \(-0.935447\pi\) |
0.910824 | + | 0.412795i | \(0.135447\pi\) | |||||||
\(114\) | 0.261465 | − | 0.189965i | 0.0244884 | − | 0.0177919i | ||||
\(115\) | 0.871763 | + | 2.68301i | 0.0812923 | + | 0.250192i | ||||
\(116\) | 1.34237 | + | 4.13140i | 0.124636 | + | 0.383591i | ||||
\(117\) | −0.0690450 | + | 0.212499i | −0.00638321 | + | 0.0196455i | ||||
\(118\) | −5.54393 | −0.510361 | ||||||||
\(119\) | −8.90756 | −0.816555 | ||||||||
\(120\) | 0.309017 | − | 0.951057i | 0.0282093 | − | 0.0868192i | ||||
\(121\) | 2.17613 | + | 1.58105i | 0.197830 | + | 0.143732i | ||||
\(122\) | −9.76053 | + | 7.09144i | −0.883677 | + | 0.642029i | ||||
\(123\) | 5.64135 | 0.508663 | ||||||||
\(124\) | −5.02321 | − | 2.40153i | −0.451098 | − | 0.215664i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.38972 | − | 1.00969i | 0.123806 | − | 0.0899504i | ||||
\(127\) | −7.64441 | − | 5.55399i | −0.678331 | − | 0.492837i | 0.194472 | − | 0.980908i | \(-0.437701\pi\) |
−0.872804 | + | 0.488071i | \(0.837701\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | −7.22362 | −0.636004 | ||||||||
\(130\) | −0.223434 | −0.0195965 | ||||||||
\(131\) | 3.86613 | − | 11.8987i | 0.337785 | − | 1.03960i | −0.627549 | − | 0.778577i | \(-0.715942\pi\) |
0.965334 | − | 0.261018i | \(-0.0840582\pi\) | |||||||
\(132\) | 0.890814 | + | 2.74164i | 0.0775354 | + | 0.238629i | ||||
\(133\) | 0.171557 | + | 0.527998i | 0.0148759 | + | 0.0457832i | ||||
\(134\) | −8.65843 | + | 6.29072i | −0.747974 | + | 0.543435i | ||||
\(135\) | 0.309017 | − | 0.951057i | 0.0265959 | − | 0.0818539i | ||||
\(136\) | −4.19514 | + | 3.04795i | −0.359731 | + | 0.261360i | ||||
\(137\) | 4.64471 | + | 3.37458i | 0.396824 | + | 0.288310i | 0.768246 | − | 0.640154i | \(-0.221130\pi\) |
−0.371422 | + | 0.928464i | \(0.621130\pi\) | |||||||
\(138\) | 0.871763 | + | 2.68301i | 0.0742094 | + | 0.228393i | ||||
\(139\) | −0.0826333 | − | 0.0600366i | −0.00700887 | − | 0.00509224i | 0.584275 | − | 0.811556i | \(-0.301379\pi\) |
−0.591284 | + | 0.806463i | \(0.701379\pi\) | |||||||
\(140\) | 1.38972 | + | 1.00969i | 0.117453 | + | 0.0853344i | ||||
\(141\) | −2.61179 | − | 8.03827i | −0.219953 | − | 0.676944i | ||||
\(142\) | −5.92461 | − | 4.30448i | −0.497182 | − | 0.361224i | ||||
\(143\) | 0.521089 | − | 0.378594i | 0.0435757 | − | 0.0316596i | ||||
\(144\) | 0.309017 | − | 0.951057i | 0.0257514 | − | 0.0792547i | ||||
\(145\) | −3.51438 | + | 2.55335i | −0.291853 | + | 0.212044i | ||||
\(146\) | −1.54022 | − | 4.74030i | −0.127469 | − | 0.392310i | ||||
\(147\) | −1.25127 | − | 3.85102i | −0.103203 | − | 0.317627i | ||||
\(148\) | 0.731316 | − | 2.25076i | 0.0601138 | − | 0.185011i | ||||
\(149\) | 6.70517 | 0.549309 | 0.274655 | − | 0.961543i | \(-0.411437\pi\) | ||||
0.274655 | + | 0.961543i | \(0.411437\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 1.17488 | − | 3.61590i | 0.0956100 | − | 0.294257i | −0.891802 | − | 0.452426i | \(-0.850559\pi\) |
0.987412 | + | 0.158168i | \(0.0505588\pi\) | |||||||
\(152\) | 0.261465 | + | 0.189965i | 0.0212076 | + | 0.0154082i | ||||
\(153\) | −4.19514 | + | 3.04795i | −0.339157 | + | 0.246412i | ||||
\(154\) | −4.95193 | −0.399038 | ||||||||
\(155\) | 0.731733 | − | 5.51947i | 0.0587742 | − | 0.443335i | ||||
\(156\) | −0.223434 | −0.0178891 | ||||||||
\(157\) | −6.20238 | + | 4.50629i | −0.495004 | + | 0.359641i | −0.807105 | − | 0.590408i | \(-0.798967\pi\) |
0.312102 | + | 0.950049i | \(0.398967\pi\) | |||||||
\(158\) | 4.50563 | + | 3.27353i | 0.358448 | + | 0.260428i | ||||
\(159\) | 1.25037 | − | 3.84823i | 0.0991605 | − | 0.305185i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −4.84602 | −0.381920 | ||||||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | −5.59974 | − | 17.2342i | −0.438605 | − | 1.34989i | −0.889347 | − | 0.457233i | \(-0.848840\pi\) |
0.450742 | − | 0.892654i | \(-0.351160\pi\) | |||||||
\(164\) | 1.74327 | + | 5.36524i | 0.136127 | + | 0.418955i | ||||
\(165\) | −2.33218 | + | 1.69443i | −0.181560 | + | 0.131911i | ||||
\(166\) | 0.860459 | − | 2.64822i | 0.0667845 | − | 0.205542i | ||||
\(167\) | 8.79403 | − | 6.38924i | 0.680503 | − | 0.494414i | −0.193022 | − | 0.981194i | \(-0.561829\pi\) |
0.873524 | + | 0.486780i | \(0.161829\pi\) | |||||||
\(168\) | 1.38972 | + | 1.00969i | 0.107219 | + | 0.0778993i | ||||
\(169\) | −4.00179 | − | 12.3163i | −0.307830 | − | 0.947404i | ||||
\(170\) | −4.19514 | − | 3.04795i | −0.321753 | − | 0.233767i | ||||
\(171\) | 0.261465 | + | 0.189965i | 0.0199947 | + | 0.0145270i | ||||
\(172\) | −2.23222 | − | 6.87007i | −0.170205 | − | 0.523838i | ||||
\(173\) | −13.8128 | − | 10.0356i | −1.05016 | − | 0.762989i | −0.0779210 | − | 0.996960i | \(-0.524828\pi\) |
−0.972244 | + | 0.233970i | \(0.924828\pi\) | |||||||
\(174\) | −3.51438 | + | 2.55335i | −0.266425 | + | 0.193569i | ||||
\(175\) | −0.530826 | + | 1.63371i | −0.0401267 | + | 0.123497i | ||||
\(176\) | −2.33218 | + | 1.69443i | −0.175795 | + | 0.127722i | ||||
\(177\) | −1.71317 | − | 5.27259i | −0.128770 | − | 0.396312i | ||||
\(178\) | −1.46075 | − | 4.49572i | −0.109488 | − | 0.336968i | ||||
\(179\) | 4.37829 | − | 13.4750i | 0.327248 | − | 1.00717i | −0.643167 | − | 0.765726i | \(-0.722380\pi\) |
0.970415 | − | 0.241441i | \(-0.0776201\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −0.250680 | −0.0186329 | −0.00931643 | − | 0.999957i | \(-0.502966\pi\) | ||||
−0.00931643 | + | 0.999957i | \(0.502966\pi\) | |||||||
\(182\) | 0.118605 | − | 0.365028i | 0.00879156 | − | 0.0270576i | ||||
\(183\) | −9.76053 | − | 7.09144i | −0.721519 | − | 0.524214i | ||||
\(184\) | −2.28230 | + | 1.65819i | −0.168254 | + | 0.122243i | ||||
\(185\) | 2.36659 | 0.173995 | ||||||||
\(186\) | 0.731733 | − | 5.51947i | 0.0536533 | − | 0.404707i | ||||
\(187\) | 14.9484 | 1.09313 | ||||||||
\(188\) | 6.83776 | − | 4.96792i | 0.498695 | − | 0.362323i | ||||
\(189\) | 1.38972 | + | 1.00969i | 0.101087 | + | 0.0734442i | ||||
\(190\) | −0.0998708 | + | 0.307371i | −0.00724539 | + | 0.0222990i | ||||
\(191\) | 9.05636 | 0.655295 | 0.327647 | − | 0.944800i | \(-0.393744\pi\) | ||||
0.327647 | + | 0.944800i | \(0.393744\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −0.983094 | + | 3.02565i | −0.0707646 | + | 0.217791i | −0.980184 | − | 0.198089i | \(-0.936526\pi\) |
0.909419 | + | 0.415880i | \(0.136526\pi\) | |||||||
\(194\) | −2.06009 | − | 6.34030i | −0.147906 | − | 0.455207i | ||||
\(195\) | −0.0690450 | − | 0.212499i | −0.00494441 | − | 0.0152173i | ||||
\(196\) | 3.27587 | − | 2.38006i | 0.233991 | − | 0.170004i | ||||
\(197\) | −2.85989 | + | 8.80184i | −0.203759 | + | 0.627105i | 0.796003 | + | 0.605292i | \(0.206944\pi\) |
−0.999762 | + | 0.0218126i | \(0.993056\pi\) | |||||||
\(198\) | −2.33218 | + | 1.69443i | −0.165741 | + | 0.120418i | ||||
\(199\) | −4.42762 | − | 3.21685i | −0.313866 | − | 0.228037i | 0.419688 | − | 0.907669i | \(-0.362140\pi\) |
−0.733553 | + | 0.679632i | \(0.762140\pi\) | |||||||
\(200\) | 0.309017 | + | 0.951057i | 0.0218508 | + | 0.0672499i | ||||
\(201\) | −8.65843 | − | 6.29072i | −0.610719 | − | 0.443713i | ||||
\(202\) | 3.52898 | + | 2.56395i | 0.248298 | + | 0.180399i | ||||
\(203\) | −2.30591 | − | 7.09687i | −0.161843 | − | 0.498103i | ||||
\(204\) | −4.19514 | − | 3.04795i | −0.293719 | − | 0.213399i | ||||
\(205\) | −4.56395 | + | 3.31590i | −0.318760 | + | 0.231593i | ||||
\(206\) | −0.0373884 | + | 0.115070i | −0.00260497 | + | 0.00801728i | ||||
\(207\) | −2.28230 | + | 1.65819i | −0.158631 | + | 0.115252i | ||||
\(208\) | −0.0690450 | − | 0.212499i | −0.00478741 | − | 0.0147341i | ||||
\(209\) | −0.287901 | − | 0.886068i | −0.0199145 | − | 0.0612906i | ||||
\(210\) | −0.530826 | + | 1.63371i | −0.0366305 | + | 0.112737i | ||||
\(211\) | −19.6781 | −1.35470 | −0.677348 | − | 0.735663i | \(-0.736871\pi\) | ||||
−0.677348 | + | 0.735663i | \(0.736871\pi\) | |||||||
\(212\) | 4.04627 | 0.277899 | ||||||||
\(213\) | 2.26300 | − | 6.96480i | 0.155058 | − | 0.477220i | ||||
\(214\) | −14.0739 | − | 10.2253i | −0.962073 | − | 0.698987i | ||||
\(215\) | 5.84403 | − | 4.24594i | 0.398560 | − | 0.289571i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.62881 | + | 4.12532i | 0.585762 | + | 0.280045i | ||||
\(218\) | 3.43005 | 0.232312 | ||||||||
\(219\) | 4.03234 | − | 2.92967i | 0.272480 | − | 0.197968i | ||||
\(220\) | −2.33218 | − | 1.69443i | −0.157236 | − | 0.114238i | ||||
\(221\) | −0.358032 | + | 1.10191i | −0.0240838 | + | 0.0741223i | ||||
\(222\) | 2.36659 | 0.158835 | ||||||||
\(223\) | 1.96582 | 0.131641 | 0.0658206 | − | 0.997831i | \(-0.479033\pi\) | ||||
0.0658206 | + | 0.997831i | \(0.479033\pi\) | |||||||
\(224\) | −0.530826 | + | 1.63371i | −0.0354673 | + | 0.109157i | ||||
\(225\) | 0.309017 | + | 0.951057i | 0.0206011 | + | 0.0634038i | ||||
\(226\) | −0.730108 | − | 2.24704i | −0.0485661 | − | 0.149471i | ||||
\(227\) | −16.7349 | + | 12.1586i | −1.11074 | + | 0.806996i | −0.982779 | − | 0.184783i | \(-0.940842\pi\) |
−0.127956 | + | 0.991780i | \(0.540842\pi\) | |||||||
\(228\) | −0.0998708 | + | 0.307371i | −0.00661410 | + | 0.0203561i | ||||
\(229\) | 17.2964 | − | 12.5666i | 1.14298 | − | 0.830424i | 0.155448 | − | 0.987844i | \(-0.450318\pi\) |
0.987532 | + | 0.157421i | \(0.0503178\pi\) | |||||||
\(230\) | −2.28230 | − | 1.65819i | −0.150491 | − | 0.109338i | ||||
\(231\) | −1.53023 | − | 4.70956i | −0.100682 | − | 0.309867i | ||||
\(232\) | −3.51438 | − | 2.55335i | −0.230730 | − | 0.167635i | ||||
\(233\) | −20.0389 | − | 14.5591i | −1.31279 | − | 0.953798i | −0.999992 | − | 0.00397881i | \(-0.998734\pi\) |
−0.312799 | − | 0.949819i | \(-0.601266\pi\) | |||||||
\(234\) | −0.0690450 | − | 0.212499i | −0.00451361 | − | 0.0138915i | ||||
\(235\) | 6.83776 | + | 4.96792i | 0.446046 | + | 0.324072i | ||||
\(236\) | 4.48514 | − | 3.25864i | 0.291958 | − | 0.212120i | ||||
\(237\) | −1.72100 | + | 5.29668i | −0.111791 | + | 0.344056i | ||||
\(238\) | 7.20637 | − | 5.23573i | 0.467119 | − | 0.339382i | ||||
\(239\) | −2.69159 | − | 8.28387i | −0.174105 | − | 0.535839i | 0.825487 | − | 0.564421i | \(-0.190901\pi\) |
−0.999591 | + | 0.0285824i | \(0.990901\pi\) | |||||||
\(240\) | 0.309017 | + | 0.951057i | 0.0199470 | + | 0.0613904i | ||||
\(241\) | −9.25619 | + | 28.4876i | −0.596244 | + | 1.83505i | −0.0478078 | + | 0.998857i | \(0.515223\pi\) |
−0.548436 | + | 0.836193i | \(0.684777\pi\) | |||||||
\(242\) | −2.68984 | −0.172909 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.72819 | − | 11.4742i | 0.238673 | − | 0.734560i | ||||
\(245\) | 3.27587 | + | 2.38006i | 0.209288 | + | 0.152057i | ||||
\(246\) | −4.56395 | + | 3.31590i | −0.290987 | + | 0.211414i | ||||
\(247\) | 0.0722114 | 0.00459470 | ||||||||
\(248\) | 5.47545 | − | 1.00969i | 0.347691 | − | 0.0641154i | ||||
\(249\) | 2.78450 | 0.176461 | ||||||||
\(250\) | −0.809017 | + | 0.587785i | −0.0511667 | + | 0.0371748i | ||||
\(251\) | −14.2036 | − | 10.3195i | −0.896523 | − | 0.651362i | 0.0410478 | − | 0.999157i | \(-0.486930\pi\) |
−0.937570 | + | 0.347795i | \(0.886930\pi\) | |||||||
\(252\) | −0.530826 | + | 1.63371i | −0.0334389 | + | 0.102914i | ||||
\(253\) | 8.13244 | 0.511282 | ||||||||
\(254\) | 9.44901 | 0.592883 | ||||||||
\(255\) | 1.60240 | − | 4.93169i | 0.100346 | − | 0.308834i | ||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 6.09771 | + | 18.7668i | 0.380365 | + | 1.17064i | 0.939787 | + | 0.341760i | \(0.111023\pi\) |
−0.559422 | + | 0.828883i | \(0.688977\pi\) | |||||||
\(258\) | 5.84403 | − | 4.24594i | 0.363833 | − | 0.264341i | ||||
\(259\) | −1.25625 | + | 3.86633i | −0.0780593 | + | 0.240242i | ||||
\(260\) | 0.180762 | − | 0.131331i | 0.0112104 | − | 0.00814483i | ||||
\(261\) | −3.51438 | − | 2.55335i | −0.217535 | − | 0.158048i | ||||
\(262\) | 3.86613 | + | 11.8987i | 0.238850 | + | 0.735105i | ||||
\(263\) | −12.1942 | − | 8.85958i | −0.751924 | − | 0.546305i | 0.144499 | − | 0.989505i | \(-0.453843\pi\) |
−0.896423 | + | 0.443200i | \(0.853843\pi\) | |||||||
\(264\) | −2.33218 | − | 1.69443i | −0.143536 | − | 0.104285i | ||||
\(265\) | 1.25037 | + | 3.84823i | 0.0768094 | + | 0.236395i | ||||
\(266\) | −0.449142 | − | 0.326320i | −0.0275386 | − | 0.0200080i | ||||
\(267\) | 3.82429 | − | 2.77851i | 0.234042 | − | 0.170042i | ||||
\(268\) | 3.30723 | − | 10.1786i | 0.202021 | − | 0.621757i | ||||
\(269\) | 5.74835 | − | 4.17642i | 0.350483 | − | 0.254641i | −0.398589 | − | 0.917130i | \(-0.630500\pi\) |
0.749072 | + | 0.662489i | \(0.230500\pi\) | |||||||
\(270\) | 0.309017 | + | 0.951057i | 0.0188062 | + | 0.0578795i | ||||
\(271\) | −0.863951 | − | 2.65897i | −0.0524813 | − | 0.161521i | 0.921381 | − | 0.388661i | \(-0.127062\pi\) |
−0.973862 | + | 0.227140i | \(0.927062\pi\) | |||||||
\(272\) | 1.60240 | − | 4.93169i | 0.0971599 | − | 0.299027i | ||||
\(273\) | 0.383813 | 0.0232294 | ||||||||
\(274\) | −5.74118 | −0.346837 | ||||||||
\(275\) | 0.890814 | − | 2.74164i | 0.0537181 | − | 0.165327i | ||||
\(276\) | −2.28230 | − | 1.65819i | −0.137379 | − | 0.0998114i | ||||
\(277\) | 19.3237 | − | 14.0395i | 1.16105 | − | 0.843552i | 0.171139 | − | 0.985247i | \(-0.445255\pi\) |
0.989910 | + | 0.141695i | \(0.0452553\pi\) | |||||||
\(278\) | 0.102140 | 0.00612597 | ||||||||
\(279\) | 5.47545 | − | 1.00969i | 0.327806 | − | 0.0604486i | ||||
\(280\) | −1.71779 | −0.102657 | ||||||||
\(281\) | −12.3433 | + | 8.96795i | −0.736341 | + | 0.534983i | −0.891563 | − | 0.452897i | \(-0.850391\pi\) |
0.155222 | + | 0.987880i | \(0.450391\pi\) | |||||||
\(282\) | 6.83776 | + | 4.96792i | 0.407183 | + | 0.295836i | ||||
\(283\) | −5.98758 | + | 18.4279i | −0.355925 | + | 1.09542i | 0.599547 | + | 0.800340i | \(0.295348\pi\) |
−0.955471 | + | 0.295084i | \(0.904652\pi\) | |||||||
\(284\) | 7.32322 | 0.434553 | ||||||||
\(285\) | −0.323189 | −0.0191440 | ||||||||
\(286\) | −0.199038 | + | 0.612577i | −0.0117694 | + | 0.0362224i | ||||
\(287\) | −2.99457 | − | 9.21635i | −0.176764 | − | 0.544024i | ||||
\(288\) | 0.309017 | + | 0.951057i | 0.0182090 | + | 0.0560415i | ||||
\(289\) | −8.00055 | + | 5.81274i | −0.470621 | + | 0.341926i | ||||
\(290\) | 1.34237 | − | 4.13140i | 0.0788269 | − | 0.242604i | ||||
\(291\) | 5.39338 | − | 3.91852i | 0.316165 | − | 0.229708i | ||||
\(292\) | 4.03234 | + | 2.92967i | 0.235975 | + | 0.171446i | ||||
\(293\) | −3.03319 | − | 9.33519i | −0.177201 | − | 0.545368i | 0.822526 | − | 0.568727i | \(-0.192564\pi\) |
−0.999727 | + | 0.0233591i | \(0.992564\pi\) | |||||||
\(294\) | 3.27587 | + | 2.38006i | 0.191053 | + | 0.138808i | ||||
\(295\) | 4.48514 | + | 3.25864i | 0.261135 | + | 0.189726i | ||||
\(296\) | 0.731316 | + | 2.25076i | 0.0425069 | + | 0.130823i | ||||
\(297\) | −2.33218 | − | 1.69443i | −0.135327 | − | 0.0983208i | ||||
\(298\) | −5.42460 | + | 3.94120i | −0.314238 | + | 0.228308i | ||||
\(299\) | −0.194782 | + | 0.599476i | −0.0112645 | + | 0.0346686i | ||||
\(300\) | −0.809017 | + | 0.587785i | −0.0467086 | + | 0.0339358i | ||||
\(301\) | 3.83448 | + | 11.8013i | 0.221016 | + | 0.680217i | ||||
\(302\) | 1.17488 | + | 3.61590i | 0.0676065 | + | 0.208071i | ||||
\(303\) | −1.34795 | + | 4.14856i | −0.0774377 | + | 0.238329i | ||||
\(304\) | −0.323189 | −0.0185361 | ||||||||
\(305\) | 12.0647 | 0.690821 | ||||||||
\(306\) | 1.60240 | − | 4.93169i | 0.0916032 | − | 0.281926i | ||||
\(307\) | −26.2594 | − | 19.0786i | −1.49870 | − | 1.08887i | −0.970894 | − | 0.239509i | \(-0.923014\pi\) |
−0.527809 | − | 0.849363i | \(-0.676986\pi\) | |||||||
\(308\) | 4.00619 | − | 2.91067i | 0.228274 | − | 0.165851i | ||||
\(309\) | −0.120991 | −0.00688296 | ||||||||
\(310\) | 2.65228 | + | 4.89545i | 0.150639 | + | 0.278043i | ||||
\(311\) | −2.01199 | −0.114089 | −0.0570447 | − | 0.998372i | \(-0.518168\pi\) | ||||
−0.0570447 | + | 0.998372i | \(0.518168\pi\) | |||||||
\(312\) | 0.180762 | − | 0.131331i | 0.0102336 | − | 0.00743517i | ||||
\(313\) | −10.4051 | − | 7.55973i | −0.588130 | − | 0.427301i | 0.253516 | − | 0.967331i | \(-0.418413\pi\) |
−0.841646 | + | 0.540030i | \(0.818413\pi\) | |||||||
\(314\) | 2.36910 | − | 7.29133i | 0.133696 | − | 0.411474i | ||||
\(315\) | −1.71779 | −0.0967864 | ||||||||
\(316\) | −5.56926 | −0.313295 | ||||||||
\(317\) | −8.20440 | + | 25.2505i | −0.460805 | + | 1.41821i | 0.403378 | + | 0.915033i | \(0.367836\pi\) |
−0.864183 | + | 0.503178i | \(0.832164\pi\) | |||||||
\(318\) | 1.25037 | + | 3.84823i | 0.0701171 | + | 0.215798i | ||||
\(319\) | 3.86971 | + | 11.9097i | 0.216662 | + | 0.666817i | ||||
\(320\) | −0.809017 | + | 0.587785i | −0.0452254 | + | 0.0328582i | ||||
\(321\) | 5.37576 | − | 16.5449i | 0.300046 | − | 0.923446i | ||||
\(322\) | 3.92052 | − | 2.84842i | 0.218482 | − | 0.158736i | ||||
\(323\) | 1.35582 | + | 0.985063i | 0.0754400 | + | 0.0548103i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | 0.180762 | + | 0.131331i | 0.0100269 | + | 0.00728495i | ||||
\(326\) | 14.6603 | + | 10.6513i | 0.811959 | + | 0.589923i | ||||
\(327\) | 1.05994 | + | 3.26217i | 0.0586150 | + | 0.180398i | ||||
\(328\) | −4.56395 | − | 3.31590i | −0.252002 | − | 0.183090i | ||||
\(329\) | −11.7458 | + | 8.53384i | −0.647568 | + | 0.470486i | ||||
\(330\) | 0.890814 | − | 2.74164i | 0.0490377 | − | 0.150923i | ||||
\(331\) | 10.2079 | − | 7.41647i | 0.561077 | − | 0.407646i | −0.270776 | − | 0.962642i | \(-0.587280\pi\) |
0.831853 | + | 0.554996i | \(0.187280\pi\) | |||||||
\(332\) | 0.860459 | + | 2.64822i | 0.0472238 | + | 0.145340i | ||||
\(333\) | 0.731316 | + | 2.25076i | 0.0400758 | + | 0.123341i | ||||
\(334\) | −3.35902 | + | 10.3380i | −0.183797 | + | 0.565670i | ||||
\(335\) | 10.7024 | 0.584735 | ||||||||
\(336\) | −1.71779 | −0.0937130 | ||||||||
\(337\) | 1.98791 | − | 6.11815i | 0.108288 | − | 0.333277i | −0.882200 | − | 0.470875i | \(-0.843938\pi\) |
0.990488 | + | 0.137598i | \(0.0439383\pi\) | |||||||
\(338\) | 10.4768 | + | 7.61186i | 0.569865 | + | 0.414031i | ||||
\(339\) | 1.91145 | − | 1.38875i | 0.103816 | − | 0.0754264i | ||||
\(340\) | 5.18548 | 0.281222 | ||||||||
\(341\) | −14.4806 | − | 6.92298i | −0.784168 | − | 0.374900i | ||||
\(342\) | −0.323189 | −0.0174760 | ||||||||
\(343\) | −15.3553 | + | 11.1563i | −0.829108 | + | 0.602382i | ||||
\(344\) | 5.84403 | + | 4.24594i | 0.315089 | + | 0.228926i | ||||
\(345\) | 0.871763 | − | 2.68301i | 0.0469341 | − | 0.144448i | ||||
\(346\) | 17.0735 | 0.917878 | ||||||||
\(347\) | 6.15717 | 0.330534 | 0.165267 | − | 0.986249i | \(-0.447151\pi\) | ||||
0.165267 | + | 0.986249i | \(0.447151\pi\) | |||||||
\(348\) | 1.34237 | − | 4.13140i | 0.0719588 | − | 0.221466i | ||||
\(349\) | −5.24895 | − | 16.1546i | −0.280970 | − | 0.864737i | −0.987578 | − | 0.157131i | \(-0.949775\pi\) |
0.706608 | − | 0.707606i | \(-0.250225\pi\) | |||||||
\(350\) | −0.530826 | − | 1.63371i | −0.0283738 | − | 0.0873257i | ||||
\(351\) | 0.180762 | − | 0.131331i | 0.00964837 | − | 0.00700995i | ||||
\(352\) | 0.890814 | − | 2.74164i | 0.0474806 | − | 0.146130i | ||||
\(353\) | 11.1730 | − | 8.11768i | 0.594680 | − | 0.432061i | −0.249306 | − | 0.968425i | \(-0.580203\pi\) |
0.843987 | + | 0.536364i | \(0.180203\pi\) | |||||||
\(354\) | 4.48514 | + | 3.25864i | 0.238382 | + | 0.173195i | ||||
\(355\) | 2.26300 | + | 6.96480i | 0.120108 | + | 0.369653i | ||||
\(356\) | 3.82429 | + | 2.77851i | 0.202687 | + | 0.147261i | ||||
\(357\) | 7.20637 | + | 5.23573i | 0.381401 | + | 0.277104i | ||||
\(358\) | 4.37829 | + | 13.4750i | 0.231400 | + | 0.712175i | ||||
\(359\) | −14.0906 | − | 10.2374i | −0.743672 | − | 0.540309i | 0.150187 | − | 0.988658i | \(-0.452012\pi\) |
−0.893859 | + | 0.448348i | \(0.852012\pi\) | |||||||
\(360\) | −0.809017 | + | 0.587785i | −0.0426389 | + | 0.0309790i | ||||
\(361\) | −5.83905 | + | 17.9707i | −0.307318 | + | 0.945828i | ||||
\(362\) | 0.202804 | − | 0.147346i | 0.0106591 | − | 0.00774432i | ||||
\(363\) | −0.831206 | − | 2.55819i | −0.0436270 | − | 0.134270i | ||||
\(364\) | 0.118605 | + | 0.365028i | 0.00621657 | + | 0.0191326i | ||||
\(365\) | −1.54022 | + | 4.74030i | −0.0806186 | + | 0.248119i | ||||
\(366\) | 12.0647 | 0.630631 | ||||||||
\(367\) | 6.65365 | 0.347318 | 0.173659 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173659 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(368\) | 0.871763 | − | 2.68301i | 0.0454438 | − | 0.139862i | ||||
\(369\) | −4.56395 | − | 3.31590i | −0.237590 | − | 0.172619i | ||||
\(370\) | −1.91461 | + | 1.39104i | −0.0995358 | + | 0.0723170i | ||||
\(371\) | −6.95064 | −0.360859 | ||||||||
\(372\) | 2.65228 | + | 4.89545i | 0.137514 | + | 0.253817i | ||||
\(373\) | −24.2905 | −1.25771 | −0.628856 | − | 0.777521i | \(-0.716477\pi\) | ||||
−0.628856 | + | 0.777521i | \(0.716477\pi\) | |||||||
\(374\) | −12.0935 | + | 8.78643i | −0.625339 | + | 0.454336i | ||||
\(375\) | −0.809017 | − | 0.587785i | −0.0417775 | − | 0.0303531i | ||||
\(376\) | −2.61179 | + | 8.03827i | −0.134693 | + | 0.414542i | ||||
\(377\) | −0.970601 | −0.0499885 | ||||||||
\(378\) | −1.71779 | −0.0883535 | ||||||||
\(379\) | −3.44040 | + | 10.5884i | −0.176721 | + | 0.543892i | −0.999708 | − | 0.0241686i | \(-0.992306\pi\) |
0.822987 | + | 0.568061i | \(0.192306\pi\) | |||||||
\(380\) | −0.0998708 | − | 0.307371i | −0.00512326 | − | 0.0157678i | ||||
\(381\) | 2.91990 | + | 8.98654i | 0.149591 | + | 0.460394i | ||||
\(382\) | −7.32675 | + | 5.32319i | −0.374869 | + | 0.272358i | ||||
\(383\) | 5.12924 | − | 15.7862i | 0.262092 | − | 0.806637i | −0.730257 | − | 0.683173i | \(-0.760600\pi\) |
0.992349 | − | 0.123464i | \(-0.0394004\pi\) | |||||||
\(384\) | −0.809017 | + | 0.587785i | −0.0412850 | + | 0.0299953i | ||||
\(385\) | 4.00619 | + | 2.91067i | 0.204175 | + | 0.148342i | ||||
\(386\) | −0.983094 | − | 3.02565i | −0.0500382 | − | 0.154002i | ||||
\(387\) | 5.84403 | + | 4.24594i | 0.297069 | + | 0.215833i | ||||
\(388\) | 5.39338 | + | 3.91852i | 0.273807 | + | 0.198933i | ||||
\(389\) | −0.257381 | − | 0.792137i | −0.0130497 | − | 0.0401629i | 0.944320 | − | 0.329030i | \(-0.106722\pi\) |
−0.957369 | + | 0.288867i | \(0.906722\pi\) | |||||||
\(390\) | 0.180762 | + | 0.131331i | 0.00915325 | + | 0.00665022i | ||||
\(391\) | −11.8348 | + | 8.59852i | −0.598514 | + | 0.434846i | ||||
\(392\) | −1.25127 | + | 3.85102i | −0.0631988 | + | 0.194506i | ||||
\(393\) | −10.1216 | + | 7.35381i | −0.510570 | + | 0.370951i | ||||
\(394\) | −2.85989 | − | 8.80184i | −0.144079 | − | 0.443430i | ||||
\(395\) | −1.72100 | − | 5.29668i | −0.0865927 | − | 0.266505i | ||||
\(396\) | 0.890814 | − | 2.74164i | 0.0447651 | − | 0.137773i | ||||
\(397\) | 2.61800 | 0.131393 | 0.0656967 | − | 0.997840i | \(-0.479073\pi\) | ||||
0.0656967 | + | 0.997840i | \(0.479073\pi\) | |||||||
\(398\) | 5.47284 | 0.274329 | ||||||||
\(399\) | 0.171557 | − | 0.527998i | 0.00858858 | − | 0.0264329i | ||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | 14.2264 | − | 10.3361i | 0.710434 | − | 0.516160i | −0.172880 | − | 0.984943i | \(-0.555307\pi\) |
0.883314 | + | 0.468783i | \(0.155307\pi\) | |||||||
\(402\) | 10.7024 | 0.533788 | ||||||||
\(403\) | 0.857149 | − | 0.901612i | 0.0426977 | − | 0.0449125i | ||||
\(404\) | −4.36206 | −0.217021 | ||||||||
\(405\) | −0.809017 | + | 0.587785i | −0.0402004 | + | 0.0292073i | ||||
\(406\) | 6.03696 | + | 4.38611i | 0.299609 | + | 0.217679i | ||||
\(407\) | 2.10819 | − | 6.48834i | 0.104499 | − | 0.321615i | ||||
\(408\) | 5.18548 | 0.256720 | ||||||||
\(409\) | 12.7199 | 0.628959 | 0.314479 | − | 0.949264i | \(-0.398170\pi\) | ||||
0.314479 | + | 0.949264i | \(0.398170\pi\) | |||||||
\(410\) | 1.74327 | − | 5.36524i | 0.0860941 | − | 0.264970i | ||||
\(411\) | −1.77412 | − | 5.46019i | −0.0875110 | − | 0.269331i | ||||
\(412\) | −0.0373884 | − | 0.115070i | −0.00184199 | − | 0.00566908i | ||||
\(413\) | −7.70452 | + | 5.59766i | −0.379114 | + | 0.275443i | ||||
\(414\) | 0.871763 | − | 2.68301i | 0.0428448 | − | 0.131863i | ||||
\(415\) | −2.25271 | + | 1.63669i | −0.110581 | + | 0.0803419i | ||||
\(416\) | 0.180762 | + | 0.131331i | 0.00886259 | + | 0.00643905i | ||||
\(417\) | 0.0315631 | + | 0.0971413i | 0.00154565 | + | 0.00475703i | ||||
\(418\) | 0.753734 | + | 0.547620i | 0.0368664 | + | 0.0267850i | ||||
\(419\) | 8.81298 | + | 6.40301i | 0.430542 | + | 0.312807i | 0.781866 | − | 0.623447i | \(-0.214268\pi\) |
−0.351323 | + | 0.936254i | \(0.614268\pi\) | |||||||
\(420\) | −0.530826 | − | 1.63371i | −0.0259016 | − | 0.0797171i | ||||
\(421\) | 30.7604 | + | 22.3487i | 1.49917 | + | 1.08921i | 0.970711 | + | 0.240250i | \(0.0772295\pi\) |
0.528458 | + | 0.848960i | \(0.322770\pi\) | |||||||
\(422\) | 15.9199 | − | 11.5665i | 0.774969 | − | 0.563048i | ||||
\(423\) | −2.61179 | + | 8.03827i | −0.126990 | + | 0.390834i | ||||
\(424\) | −3.27350 | + | 2.37834i | −0.158975 | + | 0.115502i | ||||
\(425\) | 1.60240 | + | 4.93169i | 0.0777279 | + | 0.239222i | ||||
\(426\) | 2.26300 | + | 6.96480i | 0.109643 | + | 0.337446i | ||||
\(427\) | −6.40424 | + | 19.7102i | −0.309923 | + | 0.953845i | ||||
\(428\) | 17.3963 | 0.840883 | ||||||||
\(429\) | −0.644102 | −0.0310975 | ||||||||
\(430\) | −2.23222 | + | 6.87007i | −0.107647 | + | 0.331304i | ||||
\(431\) | −25.7012 | − | 18.6730i | −1.23798 | − | 0.899448i | −0.240521 | − | 0.970644i | \(-0.577318\pi\) |
−0.997462 | + | 0.0711964i | \(0.977318\pi\) | |||||||
\(432\) | −0.809017 | + | 0.587785i | −0.0389238 | + | 0.0282798i | ||||
\(433\) | −11.1758 | −0.537074 | −0.268537 | − | 0.963269i | \(-0.586540\pi\) | ||||
−0.268537 | + | 0.963269i | \(0.586540\pi\) | |||||||
\(434\) | −9.40566 | + | 1.73443i | −0.451486 | + | 0.0832555i | ||||
\(435\) | 4.34401 | 0.208280 | ||||||||
\(436\) | −2.77497 | + | 2.01613i | −0.132897 | + | 0.0965552i | ||||
\(437\) | 0.737615 | + | 0.535908i | 0.0352849 | + | 0.0256360i | ||||
\(438\) | −1.54022 | + | 4.74030i | −0.0735944 | + | 0.226500i | ||||
\(439\) | 27.2132 | 1.29882 | 0.649408 | − | 0.760440i | \(-0.275017\pi\) | ||||
0.649408 | + | 0.760440i | \(0.275017\pi\) | |||||||
\(440\) | 2.88274 | 0.137429 | ||||||||
\(441\) | −1.25127 | + | 3.85102i | −0.0595844 | + | 0.183382i | ||||
\(442\) | −0.358032 | − | 1.10191i | −0.0170298 | − | 0.0524124i | ||||
\(443\) | 6.30304 | + | 19.3988i | 0.299466 | + | 0.921663i | 0.981684 | + | 0.190514i | \(0.0610154\pi\) |
−0.682218 | + | 0.731149i | \(0.738985\pi\) | |||||||
\(444\) | −1.91461 | + | 1.39104i | −0.0908633 | + | 0.0660161i | ||||
\(445\) | −1.46075 | + | 4.49572i | −0.0692461 | + | 0.213117i | ||||
\(446\) | −1.59038 | + | 1.15548i | −0.0753069 | + | 0.0547137i | ||||
\(447\) | −5.42460 | − | 3.94120i | −0.256575 | − | 0.186412i | ||||
\(448\) | −0.530826 | − | 1.63371i | −0.0250792 | − | 0.0771857i | ||||
\(449\) | −13.2127 | − | 9.59957i | −0.623545 | − | 0.453032i | 0.230613 | − | 0.973045i | \(-0.425927\pi\) |
−0.854158 | + | 0.520014i | \(0.825927\pi\) | |||||||
\(450\) | −0.809017 | − | 0.587785i | −0.0381374 | − | 0.0277085i | ||||
\(451\) | 5.02539 | + | 15.4666i | 0.236637 | + | 0.728292i | ||||
\(452\) | 1.91145 | + | 1.38875i | 0.0899069 | + | 0.0653212i | ||||
\(453\) | −3.07586 | + | 2.23475i | −0.144517 | + | 0.104998i | ||||
\(454\) | 6.39217 | − | 19.6731i | 0.299999 | − | 0.923303i | ||||
\(455\) | −0.310511 | + | 0.225599i | −0.0145570 | + | 0.0105763i | ||||
\(456\) | −0.0998708 | − | 0.307371i | −0.00467688 | − | 0.0143939i | ||||
\(457\) | −3.06118 | − | 9.42133i | −0.143196 | − | 0.440711i | 0.853579 | − | 0.520964i | \(-0.174427\pi\) |
−0.996775 | + | 0.0802526i | \(0.974427\pi\) | |||||||
\(458\) | −6.60665 | + | 20.3332i | −0.308708 | + | 0.950106i | ||||
\(459\) | 5.18548 | 0.242038 | ||||||||
\(460\) | 2.82108 | 0.131534 | ||||||||
\(461\) | −5.25816 | + | 16.1830i | −0.244897 | + | 0.753715i | 0.750756 | + | 0.660579i | \(0.229689\pi\) |
−0.995653 | + | 0.0931362i | \(0.970311\pi\) | |||||||
\(462\) | 4.00619 | + | 2.91067i | 0.186385 | + | 0.135417i | ||||
\(463\) | 4.56597 | − | 3.31737i | 0.212199 | − | 0.154171i | −0.476609 | − | 0.879115i | \(-0.658134\pi\) |
0.688808 | + | 0.724944i | \(0.258134\pi\) | |||||||
\(464\) | 4.34401 | 0.201666 | ||||||||
\(465\) | −3.83625 | + | 4.03524i | −0.177902 | + | 0.187130i | ||||
\(466\) | 24.7694 | 1.14742 | ||||||||
\(467\) | −28.0908 | + | 20.4092i | −1.29989 | + | 0.944424i | −0.999955 | − | 0.00953589i | \(-0.996965\pi\) |
−0.299934 | + | 0.953960i | \(0.596965\pi\) | |||||||
\(468\) | 0.180762 | + | 0.131331i | 0.00835573 | + | 0.00607079i | ||||
\(469\) | −5.68111 | + | 17.4847i | −0.262329 | + | 0.807367i | ||||
\(470\) | −8.45194 | −0.389859 | ||||||||
\(471\) | 7.66656 | 0.353256 | ||||||||
\(472\) | −1.71317 | + | 5.27259i | −0.0788550 | + | 0.242691i | ||||
\(473\) | −6.43490 | − | 19.8046i | −0.295877 | − | 0.910616i | ||||
\(474\) | −1.72100 | − | 5.29668i | −0.0790480 | − | 0.243285i | ||||
\(475\) | 0.261465 | − | 0.189965i | 0.0119968 | − | 0.00871621i | ||||
\(476\) | −2.75259 | + | 8.47159i | −0.126165 | + | 0.388295i | ||||
\(477\) | −3.27350 | + | 2.37834i | −0.149883 | + | 0.108897i | ||||
\(478\) | 7.04668 | + | 5.11971i | 0.322308 | + | 0.234170i | ||||
\(479\) | 3.41731 | + | 10.5174i | 0.156141 | + | 0.480553i | 0.998275 | − | 0.0587161i | \(-0.0187007\pi\) |
−0.842134 | + | 0.539269i | \(0.818701\pi\) | |||||||
\(480\) | −0.809017 | − | 0.587785i | −0.0369264 | − | 0.0268286i | ||||
\(481\) | 0.427789 | + | 0.310807i | 0.0195055 | + | 0.0141716i | ||||
\(482\) | −9.25619 | − | 28.4876i | −0.421608 | − | 1.29758i | ||||
\(483\) | 3.92052 | + | 2.84842i | 0.178390 | + | 0.129608i | ||||
\(484\) | 2.17613 | − | 1.58105i | 0.0989148 | − | 0.0718658i | ||||
\(485\) | −2.06009 | + | 6.34030i | −0.0935437 | + | 0.287898i | ||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | 0.974386 | + | 2.99885i | 0.0441536 | + | 0.135891i | 0.970703 | − | 0.240282i | \(-0.0772399\pi\) |
−0.926550 | + | 0.376173i | \(0.877240\pi\) | |||||||
\(488\) | 3.72819 | + | 11.4742i | 0.168767 | + | 0.519412i | ||||
\(489\) | −5.59974 | + | 17.2342i | −0.253229 | + | 0.779358i | ||||
\(490\) | −4.04920 | −0.182924 | ||||||||
\(491\) | 21.5318 | 0.971715 | 0.485858 | − | 0.874038i | \(-0.338507\pi\) | ||||
0.485858 | + | 0.874038i | \(0.338507\pi\) | |||||||
\(492\) | 1.74327 | − | 5.36524i | 0.0785928 | − | 0.241884i | ||||
\(493\) | −18.2238 | − | 13.2403i | −0.820757 | − | 0.596315i | ||||
\(494\) | −0.0584203 | + | 0.0424448i | −0.00262845 | + | 0.00190968i | ||||
\(495\) | 2.88274 | 0.129569 | ||||||||
\(496\) | −3.83625 | + | 4.03524i | −0.172253 | + | 0.181188i | ||||
\(497\) | −12.5797 | −0.564279 | ||||||||
\(498\) | −2.25271 | + | 1.63669i | −0.100946 | + | 0.0733418i | ||||
\(499\) | 15.3351 | + | 11.1416i | 0.686495 | + | 0.498768i | 0.875506 | − | 0.483207i | \(-0.160528\pi\) |
−0.189011 | + | 0.981975i | \(0.560528\pi\) | |||||||
\(500\) | 0.309017 | − | 0.951057i | 0.0138197 | − | 0.0425325i | ||||
\(501\) | −10.8700 | −0.485637 | ||||||||
\(502\) | 17.5566 | 0.783590 | ||||||||
\(503\) | 6.84683 | − | 21.0724i | 0.305285 | − | 0.939570i | −0.674286 | − | 0.738470i | \(-0.735548\pi\) |
0.979571 | − | 0.201100i | \(-0.0644515\pi\) | |||||||
\(504\) | −0.530826 | − | 1.63371i | −0.0236449 | − | 0.0727714i | ||||
\(505\) | −1.34795 | − | 4.14856i | −0.0599830 | − | 0.184609i | ||||
\(506\) | −6.57928 | + | 4.78013i | −0.292485 | + | 0.212503i | ||||
\(507\) | −4.00179 | + | 12.3163i | −0.177726 | + | 0.546984i | ||||
\(508\) | −7.64441 | + | 5.55399i | −0.339166 | + | 0.246418i | ||||
\(509\) | 18.5646 | + | 13.4880i | 0.822863 | + | 0.597845i | 0.917531 | − | 0.397664i | \(-0.130179\pi\) |
−0.0946682 | + | 0.995509i | \(0.530179\pi\) | |||||||
\(510\) | 1.60240 | + | 4.93169i | 0.0709556 | + | 0.218379i | ||||
\(511\) | −6.92670 | − | 5.03254i | −0.306419 | − | 0.222627i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | −0.0998708 | − | 0.307371i | −0.00440940 | − | 0.0135707i | ||||
\(514\) | −15.9640 | − | 11.5985i | −0.704143 | − | 0.511590i | ||||
\(515\) | 0.0978841 | − | 0.0711170i | 0.00431329 | − | 0.00313379i | ||||
\(516\) | −2.23222 | + | 6.87007i | −0.0982681 | + | 0.302438i | ||||
\(517\) | 19.7115 | − | 14.3212i | 0.866909 | − | 0.629846i | ||||
\(518\) | −1.25625 | − | 3.86633i | −0.0551962 | − | 0.169877i | ||||
\(519\) | 5.27601 | + | 16.2379i | 0.231591 | + | 0.712764i | ||||
\(520\) | −0.0690450 | + | 0.212499i | −0.00302782 | + | 0.00931868i | ||||
\(521\) | 4.64824 | 0.203643 | 0.101822 | − | 0.994803i | \(-0.467533\pi\) | ||||
0.101822 | + | 0.994803i | \(0.467533\pi\) | |||||||
\(522\) | 4.34401 | 0.190132 | ||||||||
\(523\) | −6.72491 | + | 20.6971i | −0.294060 | + | 0.905023i | 0.689476 | + | 0.724309i | \(0.257841\pi\) |
−0.983536 | + | 0.180714i | \(0.942159\pi\) | |||||||
\(524\) | −10.1216 | − | 7.35381i | −0.442166 | − | 0.321253i | ||||
\(525\) | 1.38972 | − | 1.00969i | 0.0606523 | − | 0.0440665i | ||||
\(526\) | 15.0728 | 0.657206 | ||||||||
\(527\) | 28.3928 | − | 5.23573i | 1.23681 | − | 0.228072i | ||||
\(528\) | 2.88274 | 0.125455 | ||||||||
\(529\) | 12.1688 | − | 8.84116i | 0.529079 | − | 0.384398i | ||||
\(530\) | −3.27350 | − | 2.37834i | −0.142192 | − | 0.103308i | ||||
\(531\) | −1.71317 | + | 5.27259i | −0.0743452 | + | 0.228811i | ||||
\(532\) | 0.555170 | 0.0240697 | ||||||||
\(533\) | −1.26047 | −0.0545971 | ||||||||
\(534\) | −1.46075 | + | 4.49572i | −0.0632127 | + | 0.194549i | ||||
\(535\) | 5.37576 | + | 16.5449i | 0.232414 | + | 0.715298i | ||||
\(536\) | 3.30723 | + | 10.1786i | 0.142850 | + | 0.439648i | ||||
\(537\) | −11.4625 | + | 8.32799i | −0.494643 | + | 0.359379i | ||||
\(538\) | −2.19567 | + | 6.75759i | −0.0946622 | + | 0.291340i | ||||
\(539\) | 9.44348 | − | 6.86109i | 0.406759 | − | 0.295528i | ||||
\(540\) | −0.809017 | − | 0.587785i | −0.0348145 | − | 0.0252942i | ||||
\(541\) | 1.51691 | + | 4.66856i | 0.0652169 | + | 0.200717i | 0.978355 | − | 0.206933i | \(-0.0663483\pi\) |
−0.913138 | + | 0.407650i | \(0.866348\pi\) | |||||||
\(542\) | 2.26185 | + | 1.64333i | 0.0971549 | + | 0.0705872i | ||||
\(543\) | 0.202804 | + | 0.147346i | 0.00870316 | + | 0.00632321i | ||||
\(544\) | 1.60240 | + | 4.93169i | 0.0687024 | + | 0.211444i | ||||
\(545\) | −2.77497 | − | 2.01613i | −0.118867 | − | 0.0863616i | ||||
\(546\) | −0.310511 | + | 0.225599i | −0.0132886 | + | 0.00965477i | ||||
\(547\) | 9.50176 | − | 29.2434i | 0.406266 | − | 1.25036i | −0.513567 | − | 0.858049i | \(-0.671676\pi\) |
0.919833 | − | 0.392309i | \(-0.128324\pi\) | |||||||
\(548\) | 4.64471 | − | 3.37458i | 0.198412 | − | 0.144155i | ||||
\(549\) | 3.72819 | + | 11.4742i | 0.159115 | + | 0.489706i | ||||
\(550\) | 0.890814 | + | 2.74164i | 0.0379844 | + | 0.116904i | ||||
\(551\) | −0.433840 | + | 1.33522i | −0.0184822 | + | 0.0568824i | ||||
\(552\) | 2.82108 | 0.120073 | ||||||||
\(553\) | 9.56681 | 0.406822 | ||||||||
\(554\) | −7.38100 | + | 22.7164i | −0.313589 | + | 0.965127i | ||||
\(555\) | −1.91461 | − | 1.39104i | −0.0812706 | − | 0.0590466i | ||||
\(556\) | −0.0826333 | + | 0.0600366i | −0.00350443 | + | 0.00254612i | ||||
\(557\) | −1.22781 | −0.0520240 | −0.0260120 | − | 0.999662i | \(-0.508281\pi\) | ||||
−0.0260120 | + | 0.999662i | \(0.508281\pi\) | |||||||
\(558\) | −3.83625 | + | 4.03524i | −0.162401 | + | 0.170826i | ||||
\(559\) | 1.61400 | 0.0682651 | ||||||||
\(560\) | 1.38972 | − | 1.00969i | 0.0587264 | − | 0.0426672i | ||||
\(561\) | −12.0935 | − | 8.78643i | −0.510587 | − | 0.370963i | ||||
\(562\) | 4.71473 | − | 14.5104i | 0.198879 | − | 0.612086i | ||||
\(563\) | 45.9900 | 1.93825 | 0.969124 | − | 0.246573i | \(-0.0793045\pi\) | ||||
0.969124 | + | 0.246573i | \(0.0793045\pi\) | |||||||
\(564\) | −8.45194 | −0.355891 | ||||||||
\(565\) | −0.730108 | + | 2.24704i | −0.0307159 | + | 0.0945337i | ||||
\(566\) | −5.98758 | − | 18.4279i | −0.251677 | − | 0.774581i | ||||
\(567\) | −0.530826 | − | 1.63371i | −0.0222926 | − | 0.0686095i | ||||
\(568\) | −5.92461 | + | 4.30448i | −0.248591 | + | 0.180612i | ||||
\(569\) | 12.0958 | − | 37.2269i | 0.507080 | − | 1.56063i | −0.290165 | − | 0.956977i | \(-0.593710\pi\) |
0.797245 | − | 0.603656i | \(-0.206290\pi\) | |||||||
\(570\) | 0.261465 | − | 0.189965i | 0.0109516 | − | 0.00795678i | ||||
\(571\) | 14.5027 | + | 10.5369i | 0.606921 | + | 0.440954i | 0.848329 | − | 0.529470i | \(-0.177609\pi\) |
−0.241408 | + | 0.970424i | \(0.577609\pi\) | |||||||
\(572\) | −0.199038 | − | 0.612577i | −0.00832221 | − | 0.0256131i | ||||
\(573\) | −7.32675 | − | 5.32319i | −0.306079 | − | 0.222380i | ||||
\(574\) | 7.83990 | + | 5.69602i | 0.327231 | + | 0.237747i | ||||
\(575\) | 0.871763 | + | 2.68301i | 0.0363550 | + | 0.111889i | ||||
\(576\) | −0.809017 | − | 0.587785i | −0.0337090 | − | 0.0244911i | ||||
\(577\) | 20.5739 | − | 14.9478i | 0.856501 | − | 0.622284i | −0.0704298 | − | 0.997517i | \(-0.522437\pi\) |
0.926931 | + | 0.375232i | \(0.122437\pi\) | |||||||
\(578\) | 3.05594 | − | 9.40521i | 0.127110 | − | 0.391205i | ||||
\(579\) | 2.57377 | − | 1.86996i | 0.106962 | − | 0.0777127i | ||||
\(580\) | 1.34237 | + | 4.13140i | 0.0557390 | + | 0.171547i | ||||
\(581\) | −1.47809 | − | 4.54908i | −0.0613213 | − | 0.188728i | ||||
\(582\) | −2.06009 | + | 6.34030i | −0.0853934 | + | 0.262814i | ||||
\(583\) | 11.6643 | 0.483087 | ||||||||
\(584\) | −4.98424 | −0.206249 | ||||||||
\(585\) | −0.0690450 | + | 0.212499i | −0.00285466 | + | 0.00878574i | ||||
\(586\) | 7.94099 | + | 5.76947i | 0.328039 | + | 0.238334i | ||||
\(587\) | 23.8910 | − | 17.3579i | 0.986089 | − | 0.716435i | 0.0270277 | − | 0.999635i | \(-0.491396\pi\) |
0.959061 | + | 0.283199i | \(0.0913958\pi\) | |||||||
\(588\) | −4.04920 | −0.166986 | ||||||||
\(589\) | −0.857186 | − | 1.58215i | −0.0353197 | − | 0.0651915i | ||||
\(590\) | −5.54393 | −0.228240 | ||||||||
\(591\) | 7.48729 | − | 5.43983i | 0.307986 | − | 0.223765i | ||||
\(592\) | −1.91461 | − | 1.39104i | −0.0786899 | − | 0.0571716i | ||||
\(593\) | −2.53419 | + | 7.79943i | −0.104067 | + | 0.320284i | −0.989510 | − | 0.144463i | \(-0.953855\pi\) |
0.885444 | + | 0.464747i | \(0.153855\pi\) | |||||||
\(594\) | 2.88274 | 0.118280 | ||||||||
\(595\) | −8.90756 | −0.365174 | ||||||||
\(596\) | 2.07201 | − | 6.37700i | 0.0848729 | − | 0.261212i | ||||
\(597\) | 1.69120 | + | 5.20498i | 0.0692162 | + | 0.213026i | ||||
\(598\) | −0.194782 | − | 0.599476i | −0.00796521 | − | 0.0245144i | ||||
\(599\) | −4.72997 | + | 3.43653i | −0.193261 | + | 0.140413i | −0.680208 | − | 0.733019i | \(-0.738111\pi\) |
0.486947 | + | 0.873432i | \(0.338111\pi\) | |||||||
\(600\) | 0.309017 | − | 0.951057i | 0.0126156 | − | 0.0388267i | ||||
\(601\) | −16.9820 | + | 12.3381i | −0.692709 | + | 0.503283i | −0.877550 | − | 0.479486i | \(-0.840823\pi\) |
0.184840 | + | 0.982769i | \(0.440823\pi\) | |||||||
\(602\) | −10.0388 | − | 7.29362i | −0.409151 | − | 0.297266i | ||||
\(603\) | 3.30723 | + | 10.1786i | 0.134681 | + | 0.414504i | ||||
\(604\) | −3.07586 | − | 2.23475i | −0.125155 | − | 0.0909305i | ||||
\(605\) | 2.17613 | + | 1.58105i | 0.0884721 | + | 0.0642787i | ||||
\(606\) | −1.34795 | − | 4.14856i | −0.0547567 | − | 0.168524i | ||||
\(607\) | −27.1705 | − | 19.7405i | −1.10282 | − | 0.801242i | −0.121298 | − | 0.992616i | \(-0.538706\pi\) |
−0.981517 | + | 0.191374i | \(0.938706\pi\) | |||||||
\(608\) | 0.261465 | − | 0.189965i | 0.0106038 | − | 0.00770412i | ||||
\(609\) | −2.30591 | + | 7.09687i | −0.0934404 | + | 0.287580i | ||||
\(610\) | −9.76053 | + | 7.09144i | −0.395192 | + | 0.287124i | ||||
\(611\) | 0.583564 | + | 1.79603i | 0.0236085 | + | 0.0726594i | ||||
\(612\) | 1.60240 | + | 4.93169i | 0.0647733 | + | 0.199352i | ||||
\(613\) | −6.62349 | + | 20.3850i | −0.267520 | + | 0.823343i | 0.723582 | + | 0.690239i | \(0.242494\pi\) |
−0.991102 | + | 0.133104i | \(0.957506\pi\) | |||||||
\(614\) | 32.4584 | 1.30991 | ||||||||
\(615\) | 5.64135 | 0.227481 | ||||||||
\(616\) | −1.53023 | + | 4.70956i | −0.0616547 | + | 0.189754i | ||||
\(617\) | −14.8926 | − | 10.8201i | −0.599552 | − | 0.435600i | 0.246168 | − | 0.969227i | \(-0.420829\pi\) |
−0.845720 | + | 0.533627i | \(0.820829\pi\) | |||||||
\(618\) | 0.0978841 | − | 0.0711170i | 0.00393748 | − | 0.00286074i | ||||
\(619\) | −5.35806 | −0.215359 | −0.107679 | − | 0.994186i | \(-0.534342\pi\) | ||||
−0.107679 | + | 0.994186i | \(0.534342\pi\) | |||||||
\(620\) | −5.02321 | − | 2.40153i | −0.201737 | − | 0.0964478i | ||||
\(621\) | 2.82108 | 0.113206 | ||||||||
\(622\) | 1.62773 | − | 1.18262i | 0.0652662 | − | 0.0474187i | ||||
\(623\) | −6.56931 | − | 4.77289i | −0.263194 | − | 0.191222i | ||||
\(624\) | −0.0690450 | + | 0.212499i | −0.00276401 | + | 0.00850675i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.8614 | 0.514044 | ||||||||
\(627\) | −0.287901 | + | 0.886068i | −0.0114977 | + | 0.0353861i | ||||
\(628\) | 2.36910 | + | 7.29133i | 0.0945373 | + | 0.290956i | ||||
\(629\) | 3.79222 | + | 11.6713i | 0.151206 | + | 0.465364i | ||||
\(630\) | 1.38972 | − | 1.00969i | 0.0553678 | − | 0.0402270i | ||||
\(631\) | 1.16992 | − | 3.60064i | 0.0465737 | − | 0.143339i | −0.925065 | − | 0.379808i | \(-0.875990\pi\) |
0.971639 | + | 0.236469i | \(0.0759901\pi\) | |||||||
\(632\) | 4.50563 | − | 3.27353i | 0.179224 | − | 0.130214i | ||||
\(633\) | 15.9199 | + | 11.5665i | 0.632760 | + | 0.459727i | ||||
\(634\) | −8.20440 | − | 25.2505i | −0.325838 | − | 1.00283i | ||||
\(635\) | −7.64441 | − | 5.55399i | −0.303359 | − | 0.220403i | ||||
\(636\) | −3.27350 | − | 2.37834i | −0.129803 | − | 0.0943073i | ||||
\(637\) | 0.279577 | + | 0.860450i | 0.0110773 | + | 0.0340923i | ||||
\(638\) | −10.1310 | − | 7.36062i | −0.401091 | − | 0.291410i | ||||
\(639\) | −5.92461 | + | 4.30448i | −0.234374 | + | 0.170283i | ||||
\(640\) | 0.309017 | − | 0.951057i | 0.0122150 | − | 0.0375938i | ||||
\(641\) | −29.8685 | + | 21.7007i | −1.17973 | + | 0.857127i | −0.992142 | − | 0.125120i | \(-0.960068\pi\) |
−0.187593 | + | 0.982247i | \(0.560068\pi\) | |||||||
\(642\) | 5.37576 | + | 16.5449i | 0.212164 | + | 0.652975i | ||||
\(643\) | 0.522563 | + | 1.60828i | 0.0206079 | + | 0.0634245i | 0.960832 | − | 0.277133i | \(-0.0893842\pi\) |
−0.940224 | + | 0.340557i | \(0.889384\pi\) | |||||||
\(644\) | −1.49750 | + | 4.60884i | −0.0590099 | + | 0.181614i | ||||
\(645\) | −7.22362 | −0.284430 | ||||||||
\(646\) | −1.67589 | −0.0659369 | ||||||||
\(647\) | −3.47861 | + | 10.7061i | −0.136758 | + | 0.420898i | −0.995859 | − | 0.0909074i | \(-0.971023\pi\) |
0.859101 | + | 0.511806i | \(0.171023\pi\) | |||||||
\(648\) | −0.809017 | − | 0.587785i | −0.0317812 | − | 0.0230904i | ||||
\(649\) | 12.9295 | − | 9.39380i | 0.507526 | − | 0.368739i | ||||
\(650\) | −0.223434 | −0.00876381 | ||||||||
\(651\) | −4.55605 | − | 8.40934i | −0.178566 | − | 0.329588i | ||||
\(652\) | −18.1211 | −0.709678 | ||||||||
\(653\) | 4.40137 | − | 3.19778i | 0.172239 | − | 0.125139i | −0.498326 | − | 0.866990i | \(-0.666052\pi\) |
0.670565 | + | 0.741851i | \(0.266052\pi\) | |||||||
\(654\) | −2.77497 | − | 2.01613i | −0.108510 | − | 0.0788370i | ||||
\(655\) | 3.86613 | − | 11.8987i | 0.151062 | − | 0.464921i | ||||
\(656\) | 5.64135 | 0.220258 | ||||||||
\(657\) | −4.98424 | −0.194454 | ||||||||
\(658\) | 4.48651 | − | 13.8080i | 0.174902 | − | 0.538294i | ||||
\(659\) | −13.1938 | − | 40.6063i | −0.513957 | − | 1.58180i | −0.785172 | − | 0.619278i | \(-0.787425\pi\) |
0.271214 | − | 0.962519i | \(-0.412575\pi\) | |||||||
\(660\) | 0.890814 | + | 2.74164i | 0.0346749 | + | 0.106718i | ||||
\(661\) | −17.5400 | + | 12.7436i | −0.682228 | + | 0.495668i | −0.874096 | − | 0.485753i | \(-0.838545\pi\) |
0.191868 | + | 0.981421i | \(0.438545\pi\) | |||||||
\(662\) | −3.89907 | + | 12.0001i | −0.151542 | + | 0.466397i | ||||
\(663\) | 0.937339 | − | 0.681016i | 0.0364032 | − | 0.0264485i | ||||
\(664\) | −2.25271 | − | 1.63669i | −0.0874221 | − | 0.0635159i | ||||
\(665\) | 0.171557 | + | 0.527998i | 0.00665269 | + | 0.0204749i | ||||
\(666\) | −1.91461 | − | 1.39104i | −0.0741896 | − | 0.0539019i | ||||
\(667\) | −9.91436 | − | 7.20321i | −0.383886 | − | 0.278909i | ||||
\(668\) | −3.35902 | − | 10.3380i | −0.129964 | − | 0.399989i | ||||
\(669\) | −1.59038 | − | 1.15548i | −0.0614878 | − | 0.0446735i | ||||
\(670\) | −8.65843 | + | 6.29072i | −0.334504 | + | 0.243032i | ||||
\(671\) | 10.7474 | − | 33.0770i | 0.414898 | − | 1.27693i | ||||
\(672\) | 1.38972 | − | 1.00969i | 0.0536096 | − | 0.0389497i | ||||
\(673\) | 8.99547 | + | 27.6852i | 0.346750 | + | 1.06719i | 0.960640 | + | 0.277795i | \(0.0896036\pi\) |
−0.613891 | + | 0.789391i | \(0.710396\pi\) | |||||||
\(674\) | 1.98791 | + | 6.11815i | 0.0765713 | + | 0.235662i | ||||
\(675\) | 0.309017 | − | 0.951057i | 0.0118941 | − | 0.0366062i | ||||
\(676\) | −12.9501 | −0.498080 | ||||||||
\(677\) | 16.4637 | 0.632753 | 0.316376 | − | 0.948634i | \(-0.397534\pi\) | ||||
0.316376 | + | 0.948634i | \(0.397534\pi\) | |||||||
\(678\) | −0.730108 | + | 2.24704i | −0.0280396 | + | 0.0862971i | ||||
\(679\) | −9.26468 | − | 6.73119i | −0.355546 | − | 0.258319i | ||||
\(680\) | −4.19514 | + | 3.04795i | −0.160876 | + | 0.116884i | ||||
\(681\) | 20.6855 | 0.792670 | ||||||||
\(682\) | 15.7843 | − | 2.91067i | 0.604411 | − | 0.111455i | ||||
\(683\) | −26.7204 | −1.02243 | −0.511214 | − | 0.859453i | \(-0.670804\pi\) | ||||
−0.511214 | + | 0.859453i | \(0.670804\pi\) | |||||||
\(684\) | 0.261465 | − | 0.189965i | 0.00999737 | − | 0.00726351i | ||||
\(685\) | 4.64471 | + | 3.37458i | 0.177465 | + | 0.128936i | ||||
\(686\) | 5.86520 | − | 18.0512i | 0.223934 | − | 0.689199i | ||||
\(687\) | −21.3796 | −0.815681 | ||||||||
\(688\) | −7.22362 | −0.275398 | ||||||||
\(689\) | −0.279375 | + | 0.859827i | −0.0106433 | + | 0.0327568i | ||||
\(690\) | 0.871763 | + | 2.68301i | 0.0331874 | + | 0.102140i | ||||
\(691\) | 9.93480 | + | 30.5762i | 0.377937 | + | 1.16317i | 0.941475 | + | 0.337082i | \(0.109440\pi\) |
−0.563538 | + | 0.826090i | \(0.690560\pi\) | |||||||
\(692\) | −13.8128 | + | 10.0356i | −0.525082 | + | 0.381495i | ||||
\(693\) | −1.53023 | + | 4.70956i | −0.0581286 | + | 0.178902i | ||||
\(694\) | −4.98126 | + | 3.61910i | −0.189086 | + | 0.137379i | ||||
\(695\) | −0.0826333 | − | 0.0600366i | −0.00313446 | − | 0.00227732i | ||||
\(696\) | 1.34237 | + | 4.13140i | 0.0508826 | + | 0.156600i | ||||
\(697\) | −23.6663 | − | 17.1946i | −0.896424 | − | 0.651290i | ||||
\(698\) | 13.7419 | + | 9.98410i | 0.520140 | + | 0.377904i | ||||
\(699\) | 7.65417 | + | 23.5571i | 0.289507 | + | 0.891012i | ||||
\(700\) | 1.38972 | + | 1.00969i | 0.0525265 | + | 0.0381627i | ||||
\(701\) | −17.5419 | + | 12.7450i | −0.662549 | + | 0.481370i | −0.867523 | − | 0.497397i | \(-0.834289\pi\) |
0.204974 | + | 0.978768i | \(0.434289\pi\) | |||||||
\(702\) | −0.0690450 | + | 0.212499i | −0.00260594 | + | 0.00802024i | ||||
\(703\) | 0.618780 | − | 0.449570i | 0.0233377 | − | 0.0169558i | ||||
\(704\) | 0.890814 | + | 2.74164i | 0.0335738 | + | 0.103330i | ||||
\(705\) | −2.61179 | − | 8.03827i | −0.0983658 | − | 0.302739i | ||||
\(706\) | −4.26772 | + | 13.1347i | −0.160618 | + | 0.494330i | ||||
\(707\) | 7.49309 | 0.281807 | ||||||||
\(708\) | −5.54393 | −0.208354 | ||||||||
\(709\) | 14.7129 | − | 45.2817i | 0.552555 | − | 1.70059i | −0.149758 | − | 0.988723i | \(-0.547850\pi\) |
0.702314 | − | 0.711868i | \(-0.252150\pi\) | |||||||
\(710\) | −5.92461 | − | 4.30448i | −0.222347 | − | 0.161544i | ||||
\(711\) | 4.50563 | − | 3.27353i | 0.168974 | − | 0.122767i | ||||
\(712\) | −4.72708 | −0.177155 | ||||||||
\(713\) | 15.4467 | − | 2.84842i | 0.578483 | − | 0.106674i | ||||
\(714\) | −8.90756 | −0.333357 | ||||||||
\(715\) | 0.521089 | − | 0.378594i | 0.0194876 | − | 0.0141586i | ||||
\(716\) | −11.4625 | − | 8.32799i | −0.428374 | − | 0.311232i | ||||
\(717\) | −2.69159 | + | 8.28387i | −0.100519 | + | 0.309367i | ||||
\(718\) | 17.4169 | 0.649993 | ||||||||
\(719\) | 41.9163 | 1.56321 | 0.781606 | − | 0.623772i | \(-0.214401\pi\) | ||||
0.781606 | + | 0.623772i | \(0.214401\pi\) | |||||||
\(720\) | 0.309017 | − | 0.951057i | 0.0115164 | − | 0.0354438i | ||||
\(721\) | 0.0642254 | + | 0.197665i | 0.00239188 | + | 0.00736144i | ||||
\(722\) | −5.83905 | − | 17.9707i | −0.217307 | − | 0.668802i | ||||
\(723\) | 24.2330 | − | 17.6063i | 0.901236 | − | 0.654786i | ||||
\(724\) | −0.0774643 | + | 0.238410i | −0.00287894 | + | 0.00886046i | ||||
\(725\) | −3.51438 | + | 2.55335i | −0.130521 | + | 0.0948289i | ||||
\(726\) | 2.17613 | + | 1.58105i | 0.0807636 | + | 0.0586782i | ||||
\(727\) | −13.0808 | − | 40.2585i | −0.485139 | − | 1.49311i | −0.831779 | − | 0.555107i | \(-0.812677\pi\) |
0.346640 | − | 0.937998i | \(-0.387323\pi\) | |||||||
\(728\) | −0.310511 | − | 0.225599i | −0.0115083 | − | 0.00836127i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | −1.54022 | − | 4.74030i | −0.0570060 | − | 0.175446i | ||||
\(731\) | 30.3041 | + | 22.0172i | 1.12084 | + | 0.814337i | ||||
\(732\) | −9.76053 | + | 7.09144i | −0.360759 | + | 0.262107i | ||||
\(733\) | 11.4307 | − | 35.1800i | 0.422202 | − | 1.29940i | −0.483447 | − | 0.875374i | \(-0.660615\pi\) |
0.905648 | − | 0.424029i | \(-0.139385\pi\) | |||||||
\(734\) | −5.38292 | + | 3.91092i | −0.198687 | + | 0.144355i | ||||
\(735\) | −1.25127 | − | 3.85102i | −0.0461539 | − | 0.142047i | ||||
\(736\) | 0.871763 | + | 2.68301i | 0.0321336 | + | 0.0988971i | ||||
\(737\) | 9.53386 | − | 29.3422i | 0.351184 | − | 1.08083i | ||||
\(738\) | 5.64135 | 0.207661 | ||||||||
\(739\) | −14.2737 | −0.525068 | −0.262534 | − | 0.964923i | \(-0.584558\pi\) | ||||
−0.262534 | + | 0.964923i | \(0.584558\pi\) | |||||||
\(740\) | 0.731316 | − | 2.25076i | 0.0268837 | − | 0.0827395i | ||||
\(741\) | −0.0584203 | − | 0.0424448i | −0.00214612 | − | 0.00155925i | ||||
\(742\) | 5.62319 | − | 4.08548i | 0.206434 | − | 0.149983i | ||||
\(743\) | −32.8920 | −1.20669 | −0.603346 | − | 0.797480i | \(-0.706166\pi\) | ||||
−0.603346 | + | 0.797480i | \(0.706166\pi\) | |||||||
\(744\) | −5.02321 | − | 2.40153i | −0.184160 | − | 0.0880444i | ||||
\(745\) | 6.70517 | 0.245658 | ||||||||
\(746\) | 19.6514 | − | 14.2776i | 0.719489 | − | 0.522739i | ||||
\(747\) | −2.25271 | − | 1.63669i | −0.0824223 | − | 0.0598833i | ||||
\(748\) | 4.61930 | − | 14.2167i | 0.168898 | − | 0.519816i | ||||
\(749\) | −29.8832 | −1.09191 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 3.27727 | − | 10.0864i | 0.119589 | − | 0.368057i | −0.873287 | − | 0.487205i | \(-0.838016\pi\) |
0.992877 | + | 0.119148i | \(0.0380163\pi\) | |||||||
\(752\) | −2.61179 | − | 8.03827i | −0.0952423 | − | 0.293126i | ||||
\(753\) | 5.42529 | + | 16.6973i | 0.197709 | + | 0.608484i | ||||
\(754\) | 0.785233 | − | 0.570505i | 0.0285965 | − | 0.0207766i | ||||
\(755\) | 1.17488 | − | 3.61590i | 0.0427581 | − | 0.131596i | ||||
\(756\) | 1.38972 | − | 1.00969i | 0.0505436 | − | 0.0367221i | ||||
\(757\) | −29.6083 | − | 21.5117i | −1.07613 | − | 0.781855i | −0.0991269 | − | 0.995075i | \(-0.531605\pi\) |
−0.977004 | + | 0.213220i | \(0.931605\pi\) | |||||||
\(758\) | −3.44040 | − | 10.5884i | −0.124961 | − | 0.384590i | ||||
\(759\) | −6.57928 | − | 4.78013i | −0.238813 | − | 0.173508i | ||||
\(760\) | 0.261465 | + | 0.189965i | 0.00948433 | + | 0.00689077i | ||||
\(761\) | −5.04217 | − | 15.5182i | −0.182778 | − | 0.562534i | 0.817125 | − | 0.576461i | \(-0.195567\pi\) |
−0.999903 | + | 0.0139269i | \(0.995567\pi\) | |||||||
\(762\) | −7.64441 | − | 5.55399i | −0.276928 | − | 0.201200i | ||||
\(763\) | 4.76681 | − | 3.46329i | 0.172570 | − | 0.125379i | ||||
\(764\) | 2.79857 | − | 8.61311i | 0.101249 | − | 0.311611i | ||||
\(765\) | −4.19514 | + | 3.04795i | −0.151676 | + | 0.110199i | ||||
\(766\) | 5.12924 | + | 15.7862i | 0.185327 | + | 0.570378i | ||||
\(767\) | 0.382781 | + | 1.17808i | 0.0138214 | + | 0.0425379i | ||||
\(768\) | 0.309017 | − | 0.951057i | 0.0111507 | − | 0.0343183i | ||||
\(769\) | 24.8089 | 0.894633 | 0.447316 | − | 0.894376i | \(-0.352380\pi\) | ||||
0.447316 | + | 0.894376i | \(0.352380\pi\) | |||||||
\(770\) | −4.95193 | −0.178455 | ||||||||
\(771\) | 6.09771 | − | 18.7668i | 0.219604 | − | 0.675871i | ||||
\(772\) | 2.57377 | + | 1.86996i | 0.0926321 | + | 0.0673012i | ||||
\(773\) | 31.0428 | − | 22.5539i | 1.11653 | − | 0.811209i | 0.132853 | − | 0.991136i | \(-0.457586\pi\) |
0.983680 | + | 0.179927i | \(0.0575862\pi\) | |||||||
\(774\) | −7.22362 | −0.259648 | ||||||||
\(775\) | 0.731733 | − | 5.51947i | 0.0262846 | − | 0.198265i | ||||
\(776\) | −6.66658 | −0.239316 | ||||||||
\(777\) | 3.28889 | − | 2.38952i | 0.117988 | − | 0.0857236i | ||||
\(778\) | 0.673832 | + | 0.489568i | 0.0241580 | + | 0.0175519i | ||||
\(779\) | −0.563406 | + | 1.73399i | −0.0201861 | + | 0.0621265i | ||||
\(780\) | −0.223434 | −0.00800023 | ||||||||
\(781\) | 21.1109 | 0.755408 | ||||||||
\(782\) | 4.52051 | − | 13.9127i | 0.161653 | − | 0.497517i | ||||
\(783\) | 1.34237 | + | 4.13140i | 0.0479725 | + | 0.147644i | ||||
\(784\) | −1.25127 | − | 3.85102i | −0.0446883 | − | 0.137536i | ||||
\(785\) | −6.20238 | + | 4.50629i | −0.221372 | + | 0.160836i | ||||
\(786\) | 3.86613 | − | 11.8987i | 0.137900 | − | 0.424413i | ||||
\(787\) | −37.0670 | + | 26.9307i | −1.32129 | + | 0.959977i | −0.321380 | + | 0.946950i | \(0.604147\pi\) |
−0.999915 | + | 0.0130266i | \(0.995853\pi\) | |||||||
\(788\) | 7.48729 | + | 5.43983i | 0.266724 | + | 0.193786i | ||||
\(789\) | 4.65775 | + | 14.3351i | 0.165820 | + | 0.510343i | ||||
\(790\) | 4.50563 | + | 3.27353i | 0.160303 | + | 0.116467i | ||||
\(791\) | −3.28346 | − | 2.38557i | −0.116746 | − | 0.0848213i | ||||
\(792\) | 0.890814 | + | 2.74164i | 0.0316537 | + | 0.0974201i | ||||
\(793\) | 2.18084 | + | 1.58447i | 0.0774438 | + | 0.0562662i | ||||
\(794\) | −2.11800 | + | 1.53882i | −0.0751651 | + | 0.0546106i | ||||
\(795\) | 1.25037 | − | 3.84823i | 0.0443459 | − | 0.136483i | ||||
\(796\) | −4.42762 | + | 3.21685i | −0.156933 | + | 0.114018i | ||||
\(797\) | −0.576362 | − | 1.77386i | −0.0204158 | − | 0.0628333i | 0.940330 | − | 0.340265i | \(-0.110517\pi\) |
−0.960745 | + | 0.277432i | \(0.910517\pi\) | |||||||
\(798\) | 0.171557 | + | 0.527998i | 0.00607305 | + | 0.0186909i | ||||
\(799\) | −13.5434 | + | 41.6823i | −0.479131 | + | 1.47461i | ||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −4.72708 | −0.167023 | ||||||||
\(802\) | −5.43401 | + | 16.7242i | −0.191882 | + | 0.590551i | ||||
\(803\) | 11.6242 | + | 8.44545i | 0.410208 | + | 0.298033i | ||||
\(804\) | −8.65843 | + | 6.29072i | −0.305359 | + | 0.221857i | ||||
\(805\) | −4.84602 | −0.170800 | ||||||||
\(806\) | −0.163494 | + | 1.23324i | −0.00575884 | + | 0.0434390i | ||||
\(807\) | −7.10535 | −0.250120 | ||||||||
\(808\) | 3.52898 | − | 2.56395i | 0.124149 | − | 0.0901996i | ||||
\(809\) | 9.94669 | + | 7.22669i | 0.349707 | + | 0.254077i | 0.748746 | − | 0.662857i | \(-0.230656\pi\) |
−0.399039 | + | 0.916934i | \(0.630656\pi\) | |||||||
\(810\) | 0.309017 | − | 0.951057i | 0.0108578 | − | 0.0334167i | ||||
\(811\) | 6.27472 | 0.220335 | 0.110168 | − | 0.993913i | \(-0.464861\pi\) | ||||
0.110168 | + | 0.993913i | \(0.464861\pi\) | |||||||
\(812\) | −7.46210 | −0.261868 | ||||||||
\(813\) | −0.863951 | + | 2.65897i | −0.0303001 | + | 0.0932541i | ||||
\(814\) | 2.10819 | + | 6.48834i | 0.0738920 | + | 0.227416i | ||||
\(815\) | −5.59974 | − | 17.2342i | −0.196150 | − | 0.603688i | ||||
\(816\) | −4.19514 | + | 3.04795i | −0.146859 | + | 0.106700i | ||||
\(817\) | 0.721428 | − | 2.22033i | 0.0252396 | − | 0.0776795i | ||||
\(818\) | −10.2906 | + | 7.47657i | −0.359803 | + | 0.261412i | ||||
\(819\) | −0.310511 | − | 0.225599i | −0.0108501 | − | 0.00788308i | ||||
\(820\) | 1.74327 | + | 5.36524i | 0.0608777 | + | 0.187362i | ||||
\(821\) | −18.3403 | − | 13.3250i | −0.640080 | − | 0.465045i | 0.219798 | − | 0.975545i | \(-0.429460\pi\) |
−0.859878 | + | 0.510500i | \(0.829460\pi\) | |||||||
\(822\) | 4.64471 | + | 3.37458i | 0.162003 | + | 0.117702i | ||||
\(823\) | −7.84493 | − | 24.1442i | −0.273457 | − | 0.841614i | −0.989624 | − | 0.143685i | \(-0.954105\pi\) |
0.716166 | − | 0.697930i | \(-0.245895\pi\) | |||||||
\(824\) | 0.0978841 | + | 0.0711170i | 0.00340995 | + | 0.00247748i | ||||
\(825\) | −2.33218 | + | 1.69443i | −0.0811961 | + | 0.0589925i | ||||
\(826\) | 2.94286 | − | 9.05720i | 0.102395 | − | 0.315140i | ||||
\(827\) | −4.72503 | + | 3.43293i | −0.164305 | + | 0.119375i | −0.666900 | − | 0.745148i | \(-0.732379\pi\) |
0.502594 | + | 0.864522i | \(0.332379\pi\) | |||||||
\(828\) | 0.871763 | + | 2.68301i | 0.0302958 | + | 0.0932410i | ||||
\(829\) | 10.0578 | + | 30.9546i | 0.349321 | + | 1.07510i | 0.959230 | + | 0.282627i | \(0.0912060\pi\) |
−0.609909 | + | 0.792471i | \(0.708794\pi\) | |||||||
\(830\) | 0.860459 | − | 2.64822i | 0.0298670 | − | 0.0919210i | ||||
\(831\) | −23.8854 | −0.828576 | ||||||||
\(832\) | −0.223434 | −0.00774619 | ||||||||
\(833\) | −6.48845 | + | 19.9694i | −0.224812 | + | 0.691899i | ||||
\(834\) | −0.0826333 | − | 0.0600366i | −0.00286136 | − | 0.00207890i | ||||
\(835\) | 8.79403 | − | 6.38924i | 0.304330 | − | 0.221109i | ||||
\(836\) | −0.931667 | −0.0322224 | ||||||||
\(837\) | −5.02321 | − | 2.40153i | −0.173628 | − | 0.0830090i | ||||
\(838\) | −10.8934 | −0.376308 | ||||||||
\(839\) | −37.4837 | + | 27.2335i | −1.29408 | + | 0.940206i | −0.999879 | − | 0.0155373i | \(-0.995054\pi\) |
−0.294203 | + | 0.955743i | \(0.595054\pi\) | |||||||
\(840\) | 1.38972 | + | 1.00969i | 0.0479499 | + | 0.0348376i | ||||
\(841\) | −3.13020 | + | 9.63377i | −0.107938 | + | 0.332199i | ||||
\(842\) | −38.0219 | −1.31032 | ||||||||
\(843\) | 15.2572 | 0.525485 | ||||||||
\(844\) | −6.08087 | + | 18.7150i | −0.209312 | + | 0.644196i | ||||
\(845\) | −4.00179 | − | 12.3163i | −0.137666 | − | 0.423692i | ||||
\(846\) | −2.61179 | − | 8.03827i | −0.0897953 | − | 0.276361i | ||||
\(847\) | −3.73812 | + | 2.71590i | −0.128443 | + | 0.0933196i | ||||
\(848\) | 1.25037 | − | 3.84823i | 0.0429378 | − | 0.132149i | ||||
\(849\) | 15.6757 | − | 11.3891i | 0.537988 | − | 0.390871i | ||||
\(850\) | −4.19514 | − | 3.04795i | −0.143892 | − | 0.104544i | ||||
\(851\) | 2.06310 | + | 6.34958i | 0.0707222 | + | 0.217661i | ||||
\(852\) | −5.92461 | − | 4.30448i | −0.202974 | − | 0.147469i | ||||
\(853\) | 24.7517 | + | 17.9831i | 0.847481 | + | 0.615731i | 0.924450 | − | 0.381303i | \(-0.124524\pi\) |
−0.0769696 | + | 0.997033i | \(0.524524\pi\) | |||||||
\(854\) | −6.40424 | − | 19.7102i | −0.219149 | − | 0.674470i | ||||
\(855\) | 0.261465 | + | 0.189965i | 0.00894192 | + | 0.00649668i | ||||
\(856\) | −14.0739 | + | 10.2253i | −0.481037 | + | 0.349494i | ||||
\(857\) | 11.0430 | − | 33.9868i | 0.377221 | − | 1.16097i | −0.564748 | − | 0.825264i | \(-0.691026\pi\) |
0.941968 | − | 0.335702i | \(-0.108974\pi\) | |||||||
\(858\) | 0.521089 | − | 0.378594i | 0.0177897 | − | 0.0129250i | ||||
\(859\) | 4.64621 | + | 14.2996i | 0.158527 | + | 0.487895i | 0.998501 | − | 0.0547311i | \(-0.0174301\pi\) |
−0.839974 | + | 0.542626i | \(0.817430\pi\) | |||||||
\(860\) | −2.23222 | − | 6.87007i | −0.0761181 | − | 0.234267i | ||||
\(861\) | −2.99457 | + | 9.21635i | −0.102055 | + | 0.314092i | ||||
\(862\) | 31.7684 | 1.08204 | ||||||||
\(863\) | −54.7870 | −1.86497 | −0.932486 | − | 0.361207i | \(-0.882365\pi\) | ||||
−0.932486 | + | 0.361207i | \(0.882365\pi\) | |||||||
\(864\) | 0.309017 | − | 0.951057i | 0.0105130 | − | 0.0323556i | ||||
\(865\) | −13.8128 | − | 10.0356i | −0.469648 | − | 0.341219i | ||||
\(866\) | 9.04140 | − | 6.56896i | 0.307239 | − | 0.223222i | ||||
\(867\) | 9.88922 | 0.335856 | ||||||||
\(868\) | 6.58986 | − | 6.93170i | 0.223675 | − | 0.235277i | ||||
\(869\) | −16.0547 | −0.544618 | ||||||||
\(870\) | −3.51438 | + | 2.55335i | −0.119149 | + | 0.0865666i | ||||
\(871\) | 1.93459 | + | 1.40556i | 0.0655511 | + | 0.0476257i | ||||
\(872\) | 1.05994 | − | 3.26217i | 0.0358942 | − | 0.110471i | ||||
\(873\) | −6.66658 | −0.225630 | ||||||||
\(874\) | −0.911742 | −0.0308401 | ||||||||
\(875\) | −0.530826 | + | 1.63371i | −0.0179452 | + | 0.0552296i | ||||
\(876\) | −1.54022 | − | 4.74030i | −0.0520391 | − | 0.160160i | ||||
\(877\) | −17.2967 | − | 53.2338i | −0.584068 | − | 1.79758i | −0.602981 | − | 0.797755i | \(-0.706021\pi\) |
0.0189133 | − | 0.999821i | \(-0.493979\pi\) | |||||||
\(878\) | −22.0159 | + | 15.9955i | −0.743002 | + | 0.539823i | ||||
\(879\) | −3.03319 | + | 9.33519i | −0.102307 | + | 0.314868i | ||||
\(880\) | −2.33218 | + | 1.69443i | −0.0786178 | + | 0.0571192i | ||||
\(881\) | −40.6404 | − | 29.5269i | −1.36921 | − | 0.994788i | −0.997798 | − | 0.0663189i | \(-0.978875\pi\) |
−0.371410 | − | 0.928469i | \(-0.621125\pi\) | |||||||
\(882\) | −1.25127 | − | 3.85102i | −0.0421325 | − | 0.129671i | ||||
\(883\) | 9.53684 | + | 6.92892i | 0.320940 | + | 0.233177i | 0.736577 | − | 0.676354i | \(-0.236441\pi\) |
−0.415636 | + | 0.909531i | \(0.636441\pi\) | |||||||
\(884\) | 0.937339 | + | 0.681016i | 0.0315261 | + | 0.0229051i | ||||
\(885\) | −1.71317 | − | 5.27259i | −0.0575876 | − | 0.177236i | ||||
\(886\) | −16.5016 | − | 11.9891i | −0.554381 | − | 0.402781i | ||||
\(887\) | 7.20354 | − | 5.23368i | 0.241871 | − | 0.175730i | −0.460245 | − | 0.887792i | \(-0.652239\pi\) |
0.702117 | + | 0.712062i | \(0.252239\pi\) | |||||||
\(888\) | 0.731316 | − | 2.25076i | 0.0245413 | − | 0.0755305i | ||||
\(889\) | 13.1315 | − | 9.54057i | 0.440415 | − | 0.319981i | ||||
\(890\) | −1.46075 | − | 4.49572i | −0.0489644 | − | 0.150697i | ||||
\(891\) | 0.890814 | + | 2.74164i | 0.0298434 | + | 0.0918485i | ||||
\(892\) | 0.607473 | − | 1.86961i | 0.0203397 | − | 0.0625991i | ||||
\(893\) | 2.73157 | 0.0914085 | ||||||||
\(894\) | 6.70517 | 0.224254 | ||||||||
\(895\) | 4.37829 | − | 13.4750i | 0.146350 | − | 0.450419i | ||||
\(896\) | 1.38972 | + | 1.00969i | 0.0464273 | + | 0.0337314i | ||||
\(897\) | 0.509945 | − | 0.370497i | 0.0170266 | − | 0.0123705i | ||||
\(898\) | 16.3318 | 0.544998 | ||||||||
\(899\) | 11.5215 | + | 21.2659i | 0.384265 | + | 0.709257i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −16.9747 | + | 12.3328i | −0.565509 | + | 0.410866i | ||||
\(902\) | −13.1567 | − | 9.55887i | −0.438069 | − | 0.318275i | ||||
\(903\) | 3.83448 | − | 11.8013i | 0.127604 | − | 0.392724i | ||||
\(904\) | −2.36268 | −0.0785815 | ||||||||
\(905\) | −0.250680 | −0.00833287 | ||||||||
\(906\) | 1.17488 | − | 3.61590i | 0.0390326 | − | 0.120130i | ||||
\(907\) | −6.79583 | − | 20.9154i | −0.225652 | − | 0.694485i | −0.998225 | − | 0.0595589i | \(-0.981031\pi\) |
0.772573 | − | 0.634926i | \(-0.218969\pi\) | |||||||
\(908\) | 6.39217 | + | 19.6731i | 0.212132 | + | 0.652874i | ||||
\(909\) | 3.52898 | − | 2.56395i | 0.117049 | − | 0.0850410i | ||||
\(910\) | 0.118605 | − | 0.365028i | 0.00393171 | − | 0.0121005i | ||||
\(911\) | 40.1443 | − | 29.1666i | 1.33004 | − | 0.966331i | 0.330293 | − | 0.943879i | \(-0.392852\pi\) |
0.999748 | − | 0.0224527i | \(-0.00714750\pi\) | |||||||
\(912\) | 0.261465 | + | 0.189965i | 0.00865797 | + | 0.00629039i | ||||
\(913\) | 2.48047 | + | 7.63411i | 0.0820917 | + | 0.252652i | ||||
\(914\) | 8.01426 | + | 5.82270i | 0.265088 | + | 0.192598i | ||||
\(915\) | −9.76053 | − | 7.09144i | −0.322673 | − | 0.234436i | ||||
\(916\) | −6.60665 | − | 20.3332i | −0.218290 | − | 0.671827i | ||||
\(917\) | 17.3868 | + | 12.6323i | 0.574164 | + | 0.417155i | ||||
\(918\) | −4.19514 | + | 3.04795i | −0.138460 | + | 0.100597i | ||||
\(919\) | −1.53895 | + | 4.73639i | −0.0507652 | + | 0.156239i | −0.973225 | − | 0.229853i | \(-0.926175\pi\) |
0.922460 | + | 0.386092i | \(0.126175\pi\) | |||||||
\(920\) | −2.28230 | + | 1.65819i | −0.0752454 | + | 0.0546689i | ||||
\(921\) | 10.0302 | + | 30.8698i | 0.330506 | + | 1.01719i | ||||
\(922\) | −5.25816 | − | 16.1830i | −0.173168 | − | 0.532957i | ||||
\(923\) | −0.505632 | + | 1.55617i | −0.0166431 | + | 0.0512221i | ||||
\(924\) | −4.95193 | −0.162906 | ||||||||
\(925\) | 2.36659 | 0.0778129 | ||||||||
\(926\) | −1.74405 | + | 5.36762i | −0.0573129 | + | 0.176391i | ||||
\(927\) | 0.0978841 | + | 0.0711170i | 0.00321494 | + | 0.00233579i | ||||
\(928\) | −3.51438 | + | 2.55335i | −0.115365 | + | 0.0838177i | ||||
\(929\) | −26.9209 | −0.883244 | −0.441622 | − | 0.897201i | \(-0.645597\pi\) | ||||
−0.441622 | + | 0.897201i | \(0.645597\pi\) | |||||||
\(930\) | 0.731733 | − | 5.51947i | 0.0239945 | − | 0.180991i | ||||
\(931\) | 1.30866 | 0.0428895 | ||||||||
\(932\) | −20.0389 | + | 14.5591i | −0.656395 | + | 0.476899i | ||||
\(933\) | 1.62773 | + | 1.18262i | 0.0532896 | + | 0.0387172i | ||||
\(934\) | 10.7297 | − | 33.0227i | 0.351088 | − | 1.08054i | ||||
\(935\) | 14.9484 | 0.488864 | ||||||||
\(936\) | −0.223434 | −0.00730318 | ||||||||
\(937\) | −3.36425 | + | 10.3541i | −0.109905 | + | 0.338254i | −0.990850 | − | 0.134965i | \(-0.956908\pi\) |
0.880945 | + | 0.473218i | \(0.156908\pi\) | |||||||
\(938\) | −5.68111 | − | 17.4847i | −0.185495 | − | 0.570895i | ||||
\(939\) | 3.97438 | + | 12.2319i | 0.129699 | + | 0.399173i | ||||
\(940\) | 6.83776 | − | 4.96792i | 0.223023 | − | 0.162036i | ||||
\(941\) | −12.9130 | + | 39.7421i | −0.420952 | + | 1.29556i | 0.485866 | + | 0.874034i | \(0.338504\pi\) |
−0.906818 | + | 0.421523i | \(0.861496\pi\) | |||||||
\(942\) | −6.20238 | + | 4.50629i | −0.202084 | + | 0.146823i | ||||
\(943\) | −12.8753 | − | 9.35444i | −0.419277 | − | 0.304622i | ||||
\(944\) | −1.71317 | − | 5.27259i | −0.0557589 | − | 0.171608i | ||||
\(945\) | 1.38972 | + | 1.00969i | 0.0452076 | + | 0.0328452i | ||||
\(946\) | 16.8468 | + | 12.2399i | 0.547737 | + | 0.397954i | ||||
\(947\) | 2.66896 | + | 8.21421i | 0.0867295 | + | 0.266926i | 0.985010 | − | 0.172496i | \(-0.0551833\pi\) |
−0.898281 | + | 0.439422i | \(0.855183\pi\) | |||||||
\(948\) | 4.50563 | + | 3.27353i | 0.146336 | + | 0.106319i | ||||
\(949\) | −0.900962 | + | 0.654588i | −0.0292465 | + | 0.0212488i | ||||
\(950\) | −0.0998708 | + | 0.307371i | −0.00324024 | + | 0.00997242i | ||||
\(951\) | 21.4794 | − | 15.6057i | 0.696517 | − | 0.506049i | ||||
\(952\) | −2.75259 | − | 8.47159i | −0.0892119 | − | 0.274566i | ||||
\(953\) | 3.71846 | + | 11.4442i | 0.120453 | + | 0.370715i | 0.993045 | − | 0.117734i | \(-0.0375629\pi\) |
−0.872592 | + | 0.488449i | \(0.837563\pi\) | |||||||
\(954\) | 1.25037 | − | 3.84823i | 0.0404821 | − | 0.124591i | ||||
\(955\) | 9.05636 | 0.293057 | ||||||||
\(956\) | −8.71018 | −0.281707 | ||||||||
\(957\) | 3.86971 | − | 11.9097i | 0.125090 | − | 0.384987i | ||||
\(958\) | −8.94664 | − | 6.50012i | −0.289053 | − | 0.210009i | ||||
\(959\) | −7.97863 | + | 5.79681i | −0.257643 | + | 0.187189i | ||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −29.9291 | − | 8.07756i | −0.965456 | − | 0.260567i | ||||
\(962\) | −0.528777 | −0.0170484 | ||||||||
\(963\) | −14.0739 | + | 10.2253i | −0.453526 | + | 0.329506i | ||||
\(964\) | 24.2330 | + | 17.6063i | 0.780493 | + | 0.567061i | ||||
\(965\) | −0.983094 | + | 3.02565i | −0.0316469 | + | 0.0973992i | ||||
\(966\) | −4.84602 | −0.155918 | ||||||||
\(967\) | −46.4710 | −1.49441 | −0.747203 | − | 0.664596i | \(-0.768604\pi\) | ||||
−0.747203 | + | 0.664596i | \(0.768604\pi\) | |||||||
\(968\) | −0.831206 | + | 2.55819i | −0.0267160 | + | 0.0822233i | ||||
\(969\) | −0.517878 | − | 1.59386i | −0.0166366 | − | 0.0512023i | ||||
\(970\) | −2.06009 | − | 6.34030i | −0.0661454 | − | 0.203575i | ||||
\(971\) | 24.6465 | − | 17.9067i | 0.790943 | − | 0.574654i | −0.117300 | − | 0.993097i | \(-0.537424\pi\) |
0.908243 | + | 0.418443i | \(0.137424\pi\) | |||||||
\(972\) | 0.309017 | − | 0.951057i | 0.00991172 | − | 0.0305052i | ||||
\(973\) | 0.141947 | − | 0.103130i | 0.00455060 | − | 0.00330620i | ||||
\(974\) | −2.55097 | − | 1.85339i | −0.0817385 | − | 0.0593865i | ||||
\(975\) | −0.0690450 | − | 0.212499i | −0.00221121 | − | 0.00680540i | ||||
\(976\) | −9.76053 | − | 7.09144i | −0.312427 | − | 0.226991i | ||||
\(977\) | −27.3604 | − | 19.8785i | −0.875338 | − | 0.635970i | 0.0566763 | − | 0.998393i | \(-0.481950\pi\) |
−0.932014 | + | 0.362423i | \(0.881950\pi\) | |||||||
\(978\) | −5.59974 | − | 17.2342i | −0.179060 | − | 0.551089i | ||||
\(979\) | 11.0244 | + | 8.00970i | 0.352341 | + | 0.255991i | ||||
\(980\) | 3.27587 | − | 2.38006i | 0.104644 | − | 0.0760283i | ||||
\(981\) | 1.05994 | − | 3.26217i | 0.0338414 | − | 0.104153i | ||||
\(982\) | −17.4196 | + | 12.6561i | −0.555881 | + | 0.403871i | ||||
\(983\) | 11.0708 | + | 34.0725i | 0.353105 | + | 1.08675i | 0.957100 | + | 0.289757i | \(0.0935746\pi\) |
−0.603995 | + | 0.796988i | \(0.706425\pi\) | |||||||
\(984\) | 1.74327 | + | 5.36524i | 0.0555735 | + | 0.171038i | ||||
\(985\) | −2.85989 | + | 8.80184i | −0.0911237 | + | 0.280450i | ||||
\(986\) | 22.5258 | 0.717368 | ||||||||
\(987\) | 14.5186 | 0.462133 | ||||||||
\(988\) | 0.0223146 | − | 0.0686771i | 0.000709920 | − | 0.00218491i | ||||
\(989\) | 16.4865 | + | 11.9781i | 0.524240 | + | 0.380883i | ||||
\(990\) | −2.33218 | + | 1.69443i | −0.0741216 | + | 0.0538525i | ||||
\(991\) | 5.35746 | 0.170185 | 0.0850927 | − | 0.996373i | \(-0.472881\pi\) | ||||
0.0850927 | + | 0.996373i | \(0.472881\pi\) | |||||||
\(992\) | 0.731733 | − | 5.51947i | 0.0232326 | − | 0.175243i | ||||
\(993\) | −12.6177 | −0.400409 | ||||||||
\(994\) | 10.1772 | − | 7.39419i | 0.322802 | − | 0.234529i | ||||
\(995\) | −4.42762 | − | 3.21685i | −0.140365 | − | 0.101981i | ||||
\(996\) | 0.860459 | − | 2.64822i | 0.0272647 | − | 0.0839120i | ||||
\(997\) | 27.8556 | 0.882195 | 0.441097 | − | 0.897459i | \(-0.354589\pi\) | ||||
0.441097 | + | 0.897459i | \(0.354589\pi\) | |||||||
\(998\) | −18.9553 | −0.600019 | ||||||||
\(999\) | 0.731316 | − | 2.25076i | 0.0231378 | − | 0.0712108i |
(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 | 930.2.n.g.481.2 | ✓ | 16 | |
31.2 | even | 5 | inner | 930.2.n.g.901.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.n.g.481.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
930.2.n.g.901.2 | yes | 16 | 31.2 | even | 5 | inner |