LMFDB - Embedded newform 270.2.r.a.83.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(23,270)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 27]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("270.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.r (of order $36$, degree $12$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			83.6
Character	$\chi$	$=$	270.83
Dual form			270.2.r.a.257.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.819152 + 0.573576i) q^{2} +(0.618740 + 1.61776i) q^{3} +(0.342020 - 0.939693i) q^{4} +(1.91317 + 1.15748i) q^{5} +(-1.43475 - 0.970300i) q^{6} +(-0.957323 + 2.05299i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.23432 + 2.00195i) q^{9} +(-2.23108 + 0.149199i) q^{10} +(3.39033 - 4.04043i) q^{11} +(1.73182 - 0.0281171i) q^{12} +(-2.24888 + 3.21174i) q^{13} +(-0.393351 - 2.23081i) q^{14} +(-0.688774 + 3.81125i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(0.889884 - 3.32109i) q^{17} +(0.681979 - 2.92146i) q^{18} +(3.09115 + 1.78467i) q^{19} +(1.74202 - 1.40191i) q^{20} +(-3.91358 - 0.278459i) q^{21} +(-0.459695 + 5.25434i) q^{22} +(-4.68275 + 2.18360i) q^{23} +(-1.40250 + 1.01636i) q^{24} +(2.32048 + 4.42893i) q^{25} -3.92081i q^{26} +(-4.62115 - 2.37592i) q^{27} +(1.60175 + 1.60175i) q^{28} +(-0.136517 + 0.774225i) q^{29} +(-1.62183 - 3.51705i) q^{30} +(-10.3110 - 3.75290i) q^{31} +(0.996195 + 0.0871557i) q^{32} +(8.63420 + 2.98477i) q^{33} +(1.17595 + 3.23090i) q^{34} +(-4.20782 + 2.81964i) q^{35} +(1.11703 + 2.78428i) q^{36} +(8.66041 + 2.32055i) q^{37} +(-3.55576 + 0.311089i) q^{38} +(-6.58730 - 1.65093i) q^{39} +(-0.622874 + 2.14756i) q^{40} +(2.74726 - 0.484417i) q^{41} +(3.36554 - 2.01664i) q^{42} +(-0.583752 - 6.67232i) q^{43} +(-2.63721 - 4.56777i) q^{44} +(-6.59187 + 1.24389i) q^{45} +(2.58342 - 4.47461i) q^{46} +(5.28675 + 2.46525i) q^{47} +(0.565897 - 1.63700i) q^{48} +(1.20123 + 1.43157i) q^{49} +(-4.44115 - 2.29699i) q^{50} +(5.92335 - 0.615269i) q^{51} +(2.24888 + 3.21174i) q^{52} +(9.14166 - 9.14166i) q^{53} +(5.14819 - 0.704340i) q^{54} +(11.1630 - 3.80582i) q^{55} +(-2.23081 - 0.393351i) q^{56} +(-0.974567 + 6.10499i) q^{57} +(-0.332249 - 0.712510i) q^{58} +(8.39725 - 7.04613i) q^{59} +(3.34582 + 1.95076i) q^{60} +(1.73115 - 0.630087i) q^{61} +(10.5989 - 2.83996i) q^{62} +(-1.97101 - 6.50355i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-8.02003 + 3.54158i) q^{65} +(-8.78472 + 2.50739i) q^{66} +(-2.63797 - 1.84712i) q^{67} +(-2.81645 - 1.97210i) q^{68} +(-6.42995 - 6.22450i) q^{69} +(1.82957 - 4.72322i) q^{70} +(4.51486 - 2.60666i) q^{71} +(-2.51202 - 1.64005i) q^{72} +(-3.63280 + 0.973406i) q^{73} +(-8.42520 + 3.06652i) q^{74} +(-5.72919 + 6.49434i) q^{75} +(2.73428 - 2.29433i) q^{76} +(5.04932 + 10.8283i) q^{77} +(6.34294 - 2.42596i) q^{78} +(-6.60413 - 1.16449i) q^{79} +(-0.721563 - 2.11645i) q^{80} +(0.984394 - 8.94600i) q^{81} +(-1.97258 + 1.97258i) q^{82} +(-1.91102 - 2.72922i) q^{83} +(-1.60019 + 3.58232i) q^{84} +(5.54661 - 5.32381i) q^{85} +(4.30526 + 5.13081i) q^{86} +(-1.33698 + 0.258192i) q^{87} +(4.78024 + 2.22906i) q^{88} +(1.05755 - 1.83173i) q^{89} +(4.68627 - 4.79988i) q^{90} +(-4.44074 - 7.69159i) q^{91} +(0.450320 + 5.14718i) q^{92} +(-0.308522 - 19.0029i) q^{93} +(-5.74466 + 1.01294i) q^{94} +(3.84818 + 6.99233i) q^{95} +(0.475388 + 1.66553i) q^{96} +(11.4669 - 1.00322i) q^{97} +(-1.80510 - 0.483676i) q^{98} +(0.513663 + 15.8149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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 $

$2$	−0.819152	+	0.573576i	−0.579228	+	0.405580i
$2$	−0.819152	+	0.573576i	−0.579228	+	0.405580i
$3$	0.618740	+	1.61776i	0.357230	+	0.934017i
$3$	0.618740	+	1.61776i	0.357230	+	0.934017i
$4$	0.342020	−	0.939693i	0.171010	−	0.469846i
$5$	1.91317	+	1.15748i	0.855598	+	0.517641i
$5$	1.91317	+	1.15748i	0.855598	+	0.517641i
$6$	−1.43475	−	0.970300i	−0.585736	−	0.396123i
$7$	−0.957323	+	2.05299i	−0.361834	+	0.775956i	0.638148	+	0.769914i	$0.279701\pi$
$7$	−0.957323	+	2.05299i	−0.361834	+	0.775956i	−0.999982	+	0.00604179i	$0.998077\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	−2.23432	+	2.00195i	−0.744774	+	0.667317i
$10$	−2.23108	+	0.149199i	−0.705531	+	0.0471810i
$11$	3.39033	−	4.04043i	1.02222	−	1.21824i	0.0465691	−	0.998915i	$-0.485171\pi$
$11$	3.39033	−	4.04043i	1.02222	−	1.21824i	0.975653	−	0.219321i	$-0.0703843\pi$
$12$	1.73182	−	0.0281171i	0.499934	−	0.00811671i
$13$	−2.24888	+	3.21174i	−0.623728	+	0.890775i	−0.999352	−	0.0359967i	$-0.988539\pi$
$13$	−2.24888	+	3.21174i	−0.623728	+	0.890775i	0.375624	+	0.926772i	$0.377428\pi$
$14$	−0.393351	−	2.23081i	−0.105128	−	0.596208i
$15$	−0.688774	+	3.81125i	−0.177841	+	0.984059i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	0.889884	−	3.32109i	0.215829	−	0.805483i	−0.770045	−	0.637990i	$-0.779766\pi$
$17$	0.889884	−	3.32109i	0.215829	−	0.805483i	0.985873	−	0.167493i	$-0.0535673\pi$
$18$	0.681979	−	2.92146i	0.160744	−	0.688594i
$19$	3.09115	+	1.78467i	0.709157	+	0.409432i	0.810749	−	0.585394i	$-0.199060\pi$
$19$	3.09115	+	1.78467i	0.709157	+	0.409432i	−0.101592	+	0.994826i	$0.532393\pi$
$20$	1.74202	−	1.40191i	0.389528	−	0.313478i
$21$	−3.91358	−	0.278459i	−0.854013	−	0.0607648i
$22$	−0.459695	+	5.25434i	−0.0980073	+	1.12023i
$23$	−4.68275	+	2.18360i	−0.976420	+	0.455312i	−0.844270	−	0.535918i	$-0.819966\pi$
$23$	−4.68275	+	2.18360i	−0.976420	+	0.455312i	−0.132150	+	0.991230i	$0.542188\pi$
$24$	−1.40250	+	1.01636i	−0.286284	+	0.207465i
$25$	2.32048	+	4.42893i	0.464095	+	0.885785i
$26$		−	3.92081i		−	0.768933i
$27$	−4.62115	−	2.37592i	−0.889340	−	0.457246i
$28$	1.60175	+	1.60175i	0.302703	+	0.302703i
$29$	−0.136517	+	0.774225i	−0.0253505	+	0.143770i	−0.994856	−	0.101300i	$-0.967700\pi$
$29$	−0.136517	+	0.774225i	−0.0253505	+	0.143770i	0.969505	+	0.245070i	$0.0788109\pi$
$30$	−1.62183	−	3.51705i	−0.296104	−	0.642123i
$31$	−10.3110	−	3.75290i	−1.85191	−	0.674041i	−0.984222	−	0.176935i	$-0.943382\pi$
$31$	−10.3110	−	3.75290i	−1.85191	−	0.674041i	−0.867690	−	0.497106i	$-0.834396\pi$
$32$	0.996195	+	0.0871557i	0.176104	+	0.0154071i
$33$	8.63420	+	2.98477i	1.50302	+	0.519582i
$34$	1.17595	+	3.23090i	0.201674	+	0.554094i
$35$	−4.20782	+	2.81964i	−0.711251	+	0.476606i
$36$	1.11703	+	2.78428i	0.186172	+	0.464047i
$37$	8.66041	+	2.32055i	1.42376	+	0.381496i	0.886817	−	0.462121i	$-0.152911\pi$
$37$	8.66041	+	2.32055i	1.42376	+	0.381496i	0.536946	+	0.843617i	$0.319578\pi$
$38$	−3.55576	+	0.311089i	−0.576821	+	0.0504653i
$39$	−6.58730	−	1.65093i	−1.05481	−	0.264361i
$40$	−0.622874	+	2.14756i	−0.0984851	+	0.339560i
$41$	2.74726	−	0.484417i	0.429050	−	0.0756532i	0.0450470	−	0.998985i	$-0.485656\pi$
$41$	2.74726	−	0.484417i	0.429050	−	0.0756532i	0.384003	+	0.923332i	$0.374545\pi$
$42$	3.36554	−	2.01664i	0.519313	−	0.311174i
$43$	−0.583752	−	6.67232i	−0.0890213	−	1.01752i	−0.900996	−	0.433826i	$-0.857163\pi$
$43$	−0.583752	−	6.67232i	−0.0890213	−	1.01752i	0.811975	−	0.583692i	$-0.198392\pi$
$44$	−2.63721	−	4.56777i	−0.397574	−	0.688618i
$45$	−6.59187	+	1.24389i	−0.982658	+	0.185429i
$46$	2.58342	−	4.47461i	0.380904	−	0.659746i
$47$	5.28675	+	2.46525i	0.771152	+	0.359594i	0.768041	−	0.640401i	$-0.221232\pi$
$47$	5.28675	+	2.46525i	0.771152	+	0.359594i	0.00311126	+	0.999995i	$0.499010\pi$
$48$	0.565897	−	1.63700i	0.0816802	−	0.236280i
$49$	1.20123	+	1.43157i	0.171604	+	0.204510i
$50$	−4.44115	−	2.29699i	−0.628074	−	0.324844i
$51$	5.92335	−	0.615269i	0.829435	−	0.0861549i
$52$	2.24888	+	3.21174i	0.311864	+	0.445388i
$53$	9.14166	−	9.14166i	1.25570	−	1.25570i	0.302579	−	0.953124i	$-0.402152\pi$
$53$	9.14166	−	9.14166i	1.25570	−	1.25570i	0.953124	−	0.302579i	$-0.0978476\pi$
$54$	5.14819	−	0.704340i	0.700581	−	0.0958486i
$55$	11.1630	−	3.80582i	1.50522	−	0.513176i
$56$	−2.23081	−	0.393351i	−0.298104	−	0.0525638i
$57$	−0.974567	+	6.10499i	−0.129085	+	0.808626i
$58$	−0.332249	−	0.712510i	−0.0436264	−	0.0935572i
$59$	8.39725	−	7.04613i	1.09323	−	0.917328i	0.0962781	−	0.995354i	$-0.469306\pi$
$59$	8.39725	−	7.04613i	1.09323	−	0.917328i	0.996951	+	0.0780261i	$0.0248617\pi$
$60$	3.34582	+	1.95076i	0.431944	+	0.251842i
$61$	1.73115	−	0.630087i	0.221651	−	0.0806744i	−0.228808	−	0.973472i	$-0.573483\pi$
$61$	1.73115	−	0.630087i	0.221651	−	0.0806744i	0.450459	+	0.892797i	$0.351260\pi$
$62$	10.5989	−	2.83996i	1.34606	−	0.360675i
$63$	−1.97101	−	6.50355i	−0.248323	−	0.819370i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	−8.02003	+	3.54158i	−0.994762	+	0.439278i
$66$	−8.78472	+	2.50739i	−1.08132	+	0.308638i
$67$	−2.63797	−	1.84712i	−0.322279	−	0.225662i	0.401230	−	0.915977i	$-0.368583\pi$
$67$	−2.63797	−	1.84712i	−0.322279	−	0.225662i	−0.723509	+	0.690315i	$0.757472\pi$
$68$	−2.81645	−	1.97210i	−0.341545	−	0.239152i
$69$	−6.42995	−	6.22450i	−0.774075	−	0.749342i
$70$	1.82957	−	4.72322i	0.218675	−	0.564533i
$71$	4.51486	−	2.60666i	0.535816	−	0.309353i	−0.207566	−	0.978221i	$-0.566554\pi$
$71$	4.51486	−	2.60666i	0.535816	−	0.309353i	0.743381	+	0.668868i	$0.233221\pi$
$72$	−2.51202	−	1.64005i	−0.296044	−	0.193281i
$73$	−3.63280	+	0.973406i	−0.425187	+	0.113929i	−0.465066	−	0.885276i	$-0.653969\pi$
$73$	−3.63280	+	0.973406i	−0.425187	+	0.113929i	0.0398790	+	0.999205i	$0.487303\pi$
$74$	−8.42520	+	3.06652i	−0.979410	+	0.356476i
$75$	−5.72919	+	6.49434i	−0.661550	+	0.749901i
$76$	2.73428	−	2.29433i	0.313643	−	0.263178i
$77$	5.04932	+	10.8283i	0.575423	+	1.23400i
$78$	6.34294	−	2.42596i	0.718196	−	0.274686i
$79$	−6.60413	−	1.16449i	−0.743023	−	0.131015i	−0.210693	−	0.977552i	$-0.567572\pi$
$79$	−6.60413	−	1.16449i	−0.743023	−	0.131015i	−0.532329	+	0.846537i	$0.678683\pi$
$80$	−0.721563	−	2.11645i	−0.0806732	−	0.236626i
$81$	0.984394	−	8.94600i	0.109377	−	0.994000i
$82$	−1.97258	+	1.97258i	−0.217835	+	0.217835i
$83$	−1.91102	−	2.72922i	−0.209762	−	0.299571i	0.700460	−	0.713691i	$-0.252978\pi$
$83$	−1.91102	−	2.72922i	−0.209762	−	0.299571i	−0.910222	+	0.414121i	$0.864089\pi$
$84$	−1.60019	+	3.58232i	−0.174595	+	0.390864i
$85$	5.54661	−	5.32381i	0.601614	−	0.577448i
$86$	4.30526	+	5.13081i	0.464249	+	0.553270i
$87$	−1.33698	+	0.258192i	−0.143339	+	0.0276810i
$88$	4.78024	+	2.22906i	0.509575	+	0.237619i
$89$	1.05755	−	1.83173i	0.112100	−	0.194163i	−0.804517	−	0.593930i	$-0.797576\pi$
$89$	1.05755	−	1.83173i	0.112100	−	0.194163i	0.916617	+	0.399767i	$0.130909\pi$
$90$	4.68627	−	4.79988i	0.493977	−	0.505952i
$91$	−4.44074	−	7.69159i	−0.465516	−	0.806298i
$92$	0.450320	+	5.14718i	0.0469491	+	0.536630i
$93$	−0.308522	−	19.0029i	−0.0319923	−	1.97050i
$94$	−5.74466	+	1.01294i	−0.592517	+	0.104477i
$95$	3.84818	+	6.99233i	0.394815	+	0.717398i
$96$	0.475388	+	1.66553i	0.0485191	+	0.169988i
$97$	11.4669	−	1.00322i	1.16429	−	0.101862i	0.511417	−	0.859333i	$-0.329121\pi$
$97$	11.4669	−	1.00322i	1.16429	−	0.101862i	0.652869	+	0.757471i	$0.273565\pi$
$98$	−1.80510	−	0.483676i	−0.182343	−	0.0488586i
$99$	0.513663	+	15.8149i	0.0516251	+	1.58946i
$100$	4.95548	−	0.665753i	0.495548	−	0.0665753i
$101$	1.65735	+	4.55352i	0.164912	+	0.453093i	0.994431	−	0.105386i	$-0.0336077\pi$
$101$	1.65735	+	4.55352i	0.164912	+	0.453093i	−0.829519	+	0.558478i	$0.811385\pi$
$102$	−4.49922	+	3.90149i	−0.445489	+	0.386306i
$103$	0.938146	+	0.0820772i	0.0924383	+	0.00808730i	0.133281	−	0.991078i	$-0.457449\pi$
$103$	0.938146	+	0.0820772i	0.0924383	+	0.00808730i	−0.0408427	+	0.999166i	$0.513004\pi$
$104$	−3.68435	−	1.34099i	−0.361280	−	0.131495i
$105$	−7.16505	−	5.06264i	−0.699238	−	0.494063i
$106$	−2.24497	+	12.7318i	−0.218051	+	1.23663i
$107$	−8.74026	−	8.74026i	−0.844953	−	0.844953i	0.144545	−	0.989498i	$-0.453828\pi$
$107$	−8.74026	−	8.74026i	−0.844953	−	0.844953i	−0.989498	+	0.144545i	$0.953828\pi$
$108$	−3.81316	+	3.52984i	−0.366922	+	0.339659i
$109$			2.48109i			0.237645i	0.992915	+	0.118823i	$0.0379120\pi$
$109$			2.48109i			0.237645i	−0.992915	+	0.118823i	$0.962088\pi$
$110$	−6.96128	+	9.52038i	−0.663732	+	0.907733i
$111$	1.60444	+	15.4463i	0.152286	+	1.46610i
$112$	2.05299	−	0.957323i	0.193989	−	0.0904585i
$113$	−0.466860	+	5.33623i	−0.0439185	+	0.501990i	0.942097	+	0.335339i	$0.108851\pi$
$113$	−0.466860	+	5.33623i	−0.0439185	+	0.501990i	−0.986016	+	0.166651i	$0.946705\pi$
$114$	−2.70336	−	5.55991i	−0.253193	−	0.520733i
$115$	−11.4864	−	1.24258i	−1.07111	−	0.115871i
$116$	0.680842	+	0.393084i	0.0632146	+	0.0364969i
$117$	−1.40501	−	11.6782i	−0.129893	−	1.07965i
$118$	−2.83713	+	10.5883i	−0.261179	+	0.974734i
$119$	5.96625	+	5.00628i	0.546925	+	0.458925i
$120$	−3.85965	+	0.321118i	−0.352336	+	0.0293140i
$121$	−2.92066	−	16.5639i	−0.265515	−	1.50581i
$122$	−1.05667	+	1.50908i	−0.0956666	+	0.136626i
$123$	2.48351	+	4.14470i	0.223931	+	0.373715i
$124$	−7.05315	+	8.40561i	−0.633391	+	0.754846i
$125$	−0.686919	+	11.1592i	−0.0614399	+	0.998111i
$126$	5.34483	+	4.19687i	0.476156	+	0.373887i
$127$	−2.83347	−	10.5746i	−0.251429	−	0.938347i	−0.970042	−	0.242937i	$-0.921889\pi$
$127$	−2.83347	−	10.5746i	−0.251429	−	0.938347i	0.718613	−	0.695411i	$-0.244777\pi$
$128$	0.422618	−	0.906308i	0.0373545	−	0.0801070i
$129$	10.4330	−	5.07280i	0.918578	−	0.446635i
$130$	4.53826	−	7.50119i	0.398031	−	0.657898i
$131$	−0.984549	+	2.70503i	−0.0860204	+	0.236339i	−0.975243	−	0.221135i	$-0.929024\pi$
$131$	−0.984549	+	2.70503i	−0.0860204	+	0.236339i	0.889223	+	0.457475i	$0.151246\pi$
$132$	5.75784	−	7.09264i	0.501155	−	0.617335i
$133$	−6.62314	+	4.63757i	−0.574299	+	0.402128i
$134$	3.22036			0.278197
$135$	−6.09098	−	9.89444i	−0.524228	−	0.851578i
$136$	3.43825			0.294827
$137$	−7.53427	+	5.27556i	−0.643696	+	0.450721i	−0.849297	−	0.527915i	$-0.822974\pi$
$137$	−7.53427	+	5.27556i	−0.643696	+	0.450721i	0.205601	+	0.978636i	$0.434085\pi$
$138$	8.83733	+	1.41074i	0.752284	+	0.120090i
$139$	−4.65056	+	12.7773i	−0.394455	+	1.08376i	0.570490	+	0.821305i	$0.306753\pi$
$139$	−4.65056	+	12.7773i	−0.394455	+	1.08376i	−0.964945	+	0.262452i	$0.915469\pi$
$140$	1.21043	+	4.91843i	0.102300	+	0.415683i
$141$	−0.717075	+	10.0781i	−0.0603886	+	0.848726i
$142$	−2.20324	+	4.72487i	−0.184892	+	0.396502i
$143$	5.35236	+	19.9753i	0.447587	+	1.67042i
$144$	2.99842	−	0.0973877i	0.249868	−	0.00811565i
$145$	−1.15733	+	1.32321i	−0.0961111	+	0.109887i
$146$	2.41749	−	2.88106i	0.200073	−	0.238438i
$147$	−1.57269	+	2.82907i	−0.129714	+	0.233338i
$148$	5.14264	−	7.34445i	0.422722	−	0.603710i
$149$	−0.275686	−	1.56349i	−0.0225851	−	0.128086i	0.971431	−	0.237324i	$-0.0762702\pi$
$149$	−0.275686	−	1.56349i	−0.0225851	−	0.128086i	−0.994016	+	0.109237i	$0.965159\pi$
$150$	0.968078	−	8.60598i	0.0790432	−	0.702675i
$151$	5.05010	+	4.23754i	0.410971	+	0.344846i	0.824716	−	0.565547i	$-0.191335\pi$
$151$	5.05010	+	4.23754i	0.410971	+	0.344846i	−0.413745	+	0.910393i	$0.635779\pi$
$152$	−0.923815	+	3.44772i	−0.0749313	+	0.279647i
$153$	4.66037	+	9.20190i	0.376769	+	0.743929i
$154$	−10.3470	−	5.97385i	−0.833786	−	0.481387i
$155$	−15.3829	−	19.1148i	−1.23558	−	1.53533i
$156$	−3.80436	+	5.62539i	−0.304593	+	0.450392i
$157$	−1.36013	+	15.5463i	−0.108550	+	1.24073i	0.725180	+	0.688559i	$0.241756\pi$
$157$	−1.36013	+	15.5463i	−0.108550	+	1.24073i	−0.833730	+	0.552172i	$0.813799\pi$
$158$	6.07771	−	2.83408i	0.483516	−	0.225467i
$159$	20.4454	+	9.13274i	1.62142	+	0.724273i
$160$	1.80501	+	1.31982i	0.142699	+	0.104341i
$161$		−	11.7040i		−	0.922406i
$162$	4.32485	+	7.89276i	0.339792	+	0.620114i
$163$	4.17945	+	4.17945i	0.327360	+	0.327360i	0.851582	−	0.524222i	$-0.175644\pi$
$163$	4.17945	+	4.17945i	0.327360	+	0.327360i	−0.524222	+	0.851582i	$0.675644\pi$
$164$	0.484417	−	2.74726i	0.0378266	−	0.214525i
$165$	13.0639	+	15.7043i	1.01702	+	1.22258i
$166$	3.13083	+	1.13953i	0.242999	+	0.0884446i
$167$	−16.6458	−	1.45632i	−1.28809	−	0.112693i	−0.577554	−	0.816352i	$-0.695993\pi$
$167$	−16.6458	−	1.45632i	−1.28809	−	0.112693i	−0.710538	+	0.703659i	$0.751548\pi$
$168$	−0.743938	−	3.85230i	−0.0573961	−	0.297211i
$169$	−0.811517	−	2.22962i	−0.0624244	−	0.171510i
$170$	−1.48990	+	7.54241i	−0.114270	+	0.578477i
$171$	−10.4794	+	2.20078i	−0.801383	+	0.168298i
$172$	−6.46958	−	1.73352i	−0.493301	−	0.132180i
$173$	−16.6396	+	1.45577i	−1.26508	+	0.110681i	−0.699874	−	0.714266i	$-0.746760\pi$
$173$	−16.6396	+	1.45577i	−1.26508	+	0.110681i	−0.565210	+	0.824947i	$0.691205\pi$
$174$	0.947098	−	0.978359i	0.0717993	−	0.0741692i
$175$	−11.3140	+	0.523993i	−0.855256	+	0.0396101i
$176$	−5.19428	+	0.915892i	−0.391534	+	0.0690379i
$177$	16.5947	+	9.22506i	1.24733	+	0.693398i
$178$	0.184343	+	2.10705i	0.0138171	+	0.157930i
$179$	−8.82559	−	15.2864i	−0.659655	−	1.14256i	−0.980705	−	0.195494i	$-0.937369\pi$
$179$	−8.82559	−	15.2864i	−0.659655	−	1.14256i	0.321050	−	0.947062i	$-0.395964\pi$
$180$	−1.08567	+	6.61977i	−0.0809213	+	0.493408i
$181$	4.29011	−	7.43069i	0.318881	−	0.552319i	−0.661373	−	0.750057i	$-0.730026\pi$
$181$	4.29011	−	7.43069i	0.318881	−	0.552319i	0.980255	+	0.197738i	$0.0633595\pi$
$182$	8.04936	+	3.75348i	0.596658	+	0.278226i
$183$	2.09046	+	2.41073i	0.154532	+	0.178207i
$184$	−3.32118	−	3.95803i	−0.244841	−	0.291790i
$185$	13.8829	+	14.4639i	1.02069	+	1.06341i
$186$	11.1523	+	15.3893i	0.817728	+	1.12840i
$187$	−10.4017	−	14.8551i	−0.760645	−	1.08631i
$188$	4.12475	−	4.12475i	0.300829	−	0.300829i
$189$	9.30166	−	7.21263i	0.676597	−	0.524641i
$190$	−7.16288	−	3.52056i	−0.519650	−	0.255408i
$191$	−5.29919	−	0.934390i	−0.383436	−	0.0676101i	−0.0213920	−	0.999771i	$-0.506810\pi$
$191$	−5.29919	−	0.934390i	−0.383436	−	0.0676101i	−0.362044	+	0.932161i	$0.617921\pi$
$192$	−1.34473	−	1.09166i	−0.0970473	−	0.0787834i
$193$	−10.0875	−	21.6328i	−0.726117	−	1.55716i	−0.826960	−	0.562260i	$-0.809932\pi$
$193$	−10.0875	−	21.6328i	−0.726117	−	1.55716i	0.100843	−	0.994902i	$-0.467846\pi$
$194$	−8.81770	+	7.39893i	−0.633074	+	0.531212i
$195$	−10.6917	−	10.7832i	−0.765652	−	0.772201i
$196$	1.75608	−	0.639160i	0.125434	−	0.0456543i
$197$	−8.88605	+	2.38101i	−0.633105	+	0.169640i	−0.561078	−	0.827763i	$-0.689613\pi$
$197$	−8.88605	+	2.38101i	−0.633105	+	0.169640i	−0.0720268	+	0.997403i	$0.522947\pi$
$198$	−9.49182	−	12.6602i	−0.674554	−	0.899720i
$199$	17.2165	−	9.93993i	1.22044	−	0.704623i	0.255430	−	0.966827i	$-0.417783\pi$
$199$	17.2165	−	9.93993i	1.22044	−	0.704623i	0.965012	+	0.262204i	$0.0844495\pi$
$200$	−3.67743	+	3.38770i	−0.260034	+	0.239546i
$201$	1.35600	−	5.41049i	0.0956446	−	0.381627i
$202$	−3.96941	−	2.77941i	−0.279287	−	0.195559i
$203$	−1.45878	−	1.02145i	−0.102386	−	0.0716917i
$204$	1.44774	−	5.77657i	0.101362	−	0.404440i
$205$	5.81670	+	2.25313i	0.406256	+	0.157365i
$206$	−0.815562	+	0.470865i	−0.0568229	+	0.0328067i
$207$	6.09131	−	14.2535i	0.423375	−	0.990686i
$208$	3.78721	−	1.01478i	0.262596	−	0.0703623i
$209$	17.6908	−	6.43894i	1.22370	−	0.445391i
$210$	8.77308	+	0.0373625i	0.605400	+	0.00257826i
$211$	−8.47717	+	7.11319i	−0.583593	+	0.489692i	−0.886125	−	0.463447i	$-0.846613\pi$
$211$	−8.47717	+	7.11319i	−0.583593	+	0.489692i	0.302532	+	0.953139i	$0.402168\pi$
$212$	−5.46372	−	11.7170i	−0.375250	−	0.804725i
$213$	7.01048	+	5.69114i	0.480350	+	0.389951i
$214$	12.1728	+	2.14640i	0.832116	+	0.146725i
$215$	6.60626	−	13.4410i	0.450543	−	0.916668i
$216$	1.09892	−	5.07862i	0.0747722	−	0.345556i
$217$	17.5756	−	17.5756i	1.19311	−	1.19311i
$218$	−1.42310	−	2.03239i	−0.0963842	−	0.137651i
$219$	−3.82250	−	5.27473i	−0.258301	−	0.356433i
$220$	0.241675	−	11.7915i	0.0162937	−	0.794980i
$221$	8.66523	+	10.3268i	0.582886	+	0.694657i
$222$	−10.1739	−	11.7326i	−0.682829	−	0.787442i
$223$	−0.164952	−	0.0769186i	−0.0110460	−	0.00515085i	0.417087	−	0.908866i	$-0.363051\pi$
$223$	−0.164952	−	0.0769186i	−0.0110460	−	0.00515085i	−0.428133	+	0.903716i	$0.640829\pi$
$224$	−1.13261	+	1.96174i	−0.0756757	+	0.131074i
$225$	−14.0512	−	5.25017i	−0.936745	−	0.350011i
$226$	−2.67831	−	4.63896i	−0.178158	−	0.308579i
$227$	0.206645	+	2.36196i	0.0137155	+	0.156769i	0.999964	−	0.00850120i	$-0.00270605\pi$
$227$	0.206645	+	2.36196i	0.0137155	+	0.156769i	−0.986248	+	0.165270i	$0.947150\pi$
$228$	5.40350	+	3.00382i	0.357855	+	0.198933i
$229$	−4.67779	+	0.824820i	−0.309117	+	0.0545056i	−0.326055	−	0.945351i	$-0.605719\pi$
$229$	−4.67779	+	0.824820i	−0.309117	+	0.0545056i	0.0169378	+	0.999857i	$0.494608\pi$
$230$	10.1218	−	5.57046i	0.667412	−	0.367305i
$231$	−14.3934	+	14.8685i	−0.947017	+	0.978275i
$232$	−0.783177	+	0.0685191i	−0.0514181	+	0.00449850i
$233$	−17.2623	−	4.62542i	−1.13089	−	0.303021i	−0.355608	−	0.934635i	$-0.615726\pi$
$233$	−17.2623	−	4.62542i	−1.13089	−	0.303021i	−0.775283	+	0.631614i	$0.782393\pi$
$234$	7.84926	+	8.76034i	0.513122	+	0.572682i
$235$	7.26100	+	10.8358i	0.473655	+	0.706848i
$236$	−3.74917	−	10.3008i	−0.244050	−	0.670522i
$237$	−2.20237	−	11.4044i	−0.143059	−	0.740798i
$238$	−7.75875	−	0.678803i	−0.502925	−	0.0440002i
$239$	8.36515	+	3.04466i	0.541096	+	0.196943i	0.598086	−	0.801432i	$-0.295928\pi$
$239$	8.36515	+	3.04466i	0.541096	+	0.196943i	−0.0569898	+	0.998375i	$0.518150\pi$
$240$	2.97745	−	2.47685i	0.192194	−	0.159880i
$241$	0.820520	−	4.65340i	0.0528544	−	0.299752i	−0.946909	−	0.321501i	$-0.895813\pi$
$241$	0.820520	−	4.65340i	0.0528544	−	0.299752i	0.999763	+	0.0217495i	$0.00692362\pi$
$242$	11.8931	+	11.8931i	0.764519	+	0.764519i
$243$	15.0816	−	3.94273i	0.967486	−	0.252926i
$244$		−	1.84225i		−	0.117938i
$245$	0.641148	+	4.12924i	0.0409614	+	0.263807i
$246$	−4.41167	−	1.97065i	−0.281278	−	0.125644i
$247$	−12.6835	+	5.91442i	−0.807033	+	0.376326i
$248$	0.956338	−	10.9310i	0.0607275	−	0.694119i
$249$	3.23281	−	4.78025i	0.204871	−	0.302936i
$250$	−5.83797	−	9.53510i	−0.369226	−	0.603052i
$251$	19.8423	+	11.4560i	1.25243	+	0.723093i	0.971592	−	0.236661i	$-0.0760530\pi$
$251$	19.8423	+	11.4560i	1.25243	+	0.723093i	0.280842	+	0.959754i	$0.409386\pi$
$252$	−6.78546	−	0.372203i	−0.427444	−	0.0234466i
$253$	−7.05334	+	26.3234i	−0.443440	+	1.65494i
$254$	8.38640	+	7.03703i	0.526210	+	0.441542i
$255$	12.0446	+	5.67905i	0.754260	+	0.355636i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−4.36842	+	6.23875i	−0.272495	+	0.389163i	−0.931953	−	0.362578i	$-0.881897\pi$
$257$	−4.36842	+	6.23875i	−0.272495	+	0.389163i	0.659459	+	0.751741i	$0.270786\pi$
$258$	−5.63661	+	10.1395i	−0.350920	+	0.631260i
$259$	−13.0549	+	15.5582i	−0.811190	+	0.966738i
$260$	0.584982	+	8.74765i	0.0362790	+	0.542506i
$261$	−1.24494	−	2.00317i	−0.0770596	−	0.123993i
$262$	−0.745044	−	2.78054i	−0.0460290	−	0.171782i
$263$	−6.15555	+	13.2006i	−0.379567	+	0.813985i	0.620001	+	0.784601i	$0.287132\pi$
$263$	−6.15555	+	13.2006i	−0.379567	+	0.813985i	−0.999568	+	0.0293837i	$0.990646\pi$
$264$	−0.648374	+	9.11251i	−0.0399046	+	0.560836i
$265$	28.0709	−	6.90830i	1.72438	−	0.424373i
$266$	2.76535	−	7.59775i	0.169555	−	0.465848i
$267$	3.61765	+	0.577501i	0.221396	+	0.0353425i
$268$	−2.63797	+	1.84712i	−0.161139	+	0.112831i
$269$	−16.8551			−1.02767			−0.513836	−	0.857889i	$-0.671776\pi$
$269$	−16.8551			−1.02767			−0.513836	+	0.857889i	$0.671776\pi$
$270$	10.6647	+	4.61141i	0.649030	+	0.280641i
$271$	−28.2552			−1.71638			−0.858189	−	0.513334i	$-0.828410\pi$
$271$	−28.2552			−1.71638			−0.858189	+	0.513334i	$0.828410\pi$
$272$	−2.81645	+	1.97210i	−0.170772	+	0.119576i
$273$	9.69552	−	11.9432i	0.586800	−	0.722833i
$274$	3.14578	−	8.64296i	0.190044	−	0.522141i
$275$	25.7620	+	5.63977i	1.55350	+	0.340091i
$276$	−8.04829	+	3.91327i	−0.484450	+	0.235551i
$277$	7.58337	−	16.2626i	0.455640	−	0.977124i	−0.535529	−	0.844517i	$-0.679888\pi$
$277$	7.58337	−	16.2626i	0.455640	−	0.977124i	0.991169	−	0.132607i	$-0.0423347\pi$
$278$	−3.51925	−	13.1340i	−0.211070	−	0.787725i
$279$	30.5512	−	12.2569i	1.82906	−	0.733804i
$280$	−3.81263	−	3.33466i	−0.227848	−	0.199284i
$281$	19.5894	−	23.3457i	1.16860	−	1.39269i	0.265036	−	0.964238i	$-0.414616\pi$
$281$	19.5894	−	23.3457i	1.16860	−	1.39269i	0.903566	−	0.428448i	$-0.140939\pi$
$282$	−5.19315	−	8.66677i	−0.309247	−	0.516098i
$283$	−10.1611	+	14.5116i	−0.604015	+	0.862623i	−0.998413	−	0.0563170i	$-0.982064\pi$
$283$	−10.1611	+	14.5116i	−0.604015	+	0.862623i	0.394398	+	0.918940i	$0.370953\pi$
$284$	−0.905283	−	5.13411i	−0.0537186	−	0.304654i
$285$	−8.93093	+	10.5519i	−0.529023	+	0.625039i
$286$	−15.8418	−	13.2928i	−0.936743	−	0.786020i
$287$	−1.63552	+	6.10384i	−0.0965416	+	0.360298i
$288$	−2.40030	+	1.79960i	−0.141439	+	0.106042i
$289$	4.48467	+	2.58922i	0.263804	+	0.152307i
$290$	0.189067	−	1.74773i	0.0111024	−	0.102630i
$291$	8.71800	+	17.9300i	0.511058	+	1.05107i
$292$	−0.327789	+	3.74664i	−0.0191824	+	0.219256i
$293$	−6.73139	+	3.13890i	−0.393252	+	0.183376i	−0.609178	−	0.793033i	$-0.708501\pi$
$293$	−6.73139	+	3.13890i	−0.393252	+	0.183376i	0.215926	+	0.976410i	$0.430723\pi$
$294$	−0.334415	−	3.21950i	−0.0195035	−	0.187765i
$295$	24.2212	−	3.76082i	1.41021	−	0.218964i
$296$			8.96591i			0.521133i
$297$	−25.2669	+	10.6163i	−1.46614	+	0.616019i
$298$	1.12261	+	1.12261i	0.0650312	+	0.0650312i
$299$	3.51779	−	19.9504i	0.203439	−	1.15376i
$300$	4.14318	+	7.60487i	0.239207	+	0.439067i
$301$	14.2570	+	5.18913i	0.821760	+	0.299096i
$302$	−6.56735	−	0.574569i	−0.377908	−	0.0330627i
$303$	−6.34106	+	5.49864i	−0.364284	+	0.315889i
$304$	−1.22079	−	3.35409i	−0.0700170	−	0.192370i
$305$	4.04131	+	0.798306i	0.231405	+	0.0457109i
$306$	−9.09555	−	4.86467i	−0.519958	−	0.278095i
$307$	2.71392	+	0.727192i	0.154892	+	0.0415031i	0.335432	−	0.942065i	$-0.391118\pi$
$307$	2.71392	+	0.727192i	0.154892	+	0.0415031i	−0.180540	+	0.983568i	$0.557785\pi$
$308$	11.9022	−	1.04131i	0.678193	−	0.0593342i
$309$	0.447687	+	1.56848i	0.0254680	+	0.0892279i
$310$	23.5647	+	6.83465i	1.33838	+	0.388182i
$311$	21.4586	−	3.78374i	1.21681	−	0.214556i	0.471857	−	0.881675i	$-0.343584\pi$
$311$	21.4586	−	3.78374i	1.21681	−	0.214556i	0.744951	+	0.667119i	$0.232473\pi$
$312$	−0.110242	−	6.79014i	−0.00624121	−	0.384416i
$313$	2.03028	+	23.2062i	0.114758	+	1.31169i	0.807225	+	0.590244i	$0.200969\pi$
$313$	2.03028	+	23.2062i	0.114758	+	1.31169i	−0.692466	+	0.721450i	$0.743476\pi$
$314$	−7.80285	−	13.5149i	−0.440340	−	0.762692i
$315$	3.75685	−	14.7238i	0.211674	−	0.829593i
$316$	−3.35300	+	5.80757i	−0.188621	+	0.326702i
$317$	−21.0704	−	9.82531i	−1.18343	−	0.551844i	−0.271603	−	0.962410i	$-0.587554\pi$
$317$	−21.0704	−	9.82531i	−1.18343	−	0.551844i	−0.911831	+	0.410565i	$0.865331\pi$
$318$	−21.9862	+	4.24587i	−1.23292	+	0.238097i
$319$	2.66537	+	3.17646i	0.149232	+	0.177848i
$320$	−2.23560	−	0.0458203i	−0.124974	−	0.00256143i
$321$	8.73174	−	19.5476i	0.487358	−	1.09104i
$322$	6.71315	+	9.58737i	0.374109	+	0.534283i
$323$	8.67783	−	8.67783i	0.482847	−	0.482847i
$324$	−8.06981	−	3.98474i	−0.448323	−	0.221374i
$325$	−19.4430	−	2.50737i	−1.07850	−	0.139084i
$326$	−5.82084	−	1.02637i	−0.322386	−	0.0568454i
$327$	−4.01382	+	1.53515i	−0.221965	+	0.0848940i
$328$	1.17895	+	2.52828i	0.0650969	+	0.139601i
$329$	−10.1223	+	8.49358i	−0.558058	+	0.468266i
$330$	−19.7090	−	5.37106i	−1.08494	−	0.295667i
$331$	−14.7666	+	5.37459i	−0.811644	+	0.295414i	−0.714303	−	0.699837i	$-0.753256\pi$
$331$	−14.7666	+	5.37459i	−0.811644	+	0.295414i	−0.0973413	+	0.995251i	$0.531034\pi$
$332$	−3.21823	+	0.862323i	−0.176623	+	0.0473261i
$333$	−23.9958	+	12.1528i	−1.31496	+	0.665972i
$334$	14.4708	−	8.35470i	0.791805	−	0.457149i
$335$	−2.90888	−	6.58726i	−0.158929	−	0.359901i
$336$	2.81899	+	2.72891i	0.153788	+	0.148874i
$337$	0.492730	+	0.345013i	0.0268407	+	0.0187941i	0.586920	−	0.809645i	$-0.300340\pi$
$337$	0.492730	+	0.345013i	0.0268407	+	0.0187941i	−0.560079	+	0.828439i	$0.689229\pi$
$338$	1.94362	+	1.36093i	0.105719	+	0.0740251i
$339$	−8.92163	+	2.54647i	−0.484556	+	0.138305i
$340$	−3.10569	−	7.03295i	−0.168430	−	0.381415i
$341$	−50.1210	+	28.9374i	−2.71421	+	1.56705i
$342$	7.32194	−	7.81354i	0.395925	−	0.422508i
$343$	−19.4052	+	5.19961i	−1.04778	+	0.280752i
$344$	6.29388	−	2.29078i	0.339343	−	0.123511i
$345$	−5.09688	−	19.3511i	−0.274407	−	1.04183i
$346$	12.7954	−	10.7366i	0.687882	−	0.577202i
$347$	−7.99597	−	17.1474i	−0.429246	−	0.920521i	−0.995362	−	0.0961959i	$-0.969332\pi$
$347$	−7.99597	−	17.1474i	−0.429246	−	0.920521i	0.566116	−	0.824325i	$-0.308445\pi$
$348$	−0.214654	+	1.34466i	−0.0115066	+	0.0720812i
$349$	−15.8581	−	2.79621i	−0.848865	−	0.149678i	−0.267739	−	0.963491i	$-0.586277\pi$
$349$	−15.8581	−	2.79621i	−0.848865	−	0.149678i	−0.581126	+	0.813814i	$0.697388\pi$
$350$	8.96731	−	6.91866i	0.479323	−	0.369818i
$351$	18.0232	−	9.49874i	0.962010	−	0.507005i
$352$	3.72957	−	3.72957i	0.198787	−	0.198787i
$353$	−7.00086	−	9.99827i	−0.372618	−	0.532154i	0.588425	−	0.808552i	$-0.299748\pi$
$353$	−7.00086	−	9.99827i	−0.372618	−	0.532154i	−0.961043	+	0.276398i	$0.910859\pi$
$354$	−18.8849	+	1.96160i	−1.00372	+	0.104258i
$355$	11.6549	+	0.238876i	0.618577	+	0.0126782i
$356$	−1.35956	−	1.62026i	−0.0720564	−	0.0858734i
$357$	−4.40742	+	12.7496i	−0.233266	+	0.674779i
$358$	15.9974	+	7.45971i	0.845488	+	0.394258i
$359$	−14.9022	+	25.8113i	−0.786507	+	1.36227i	0.141587	+	0.989926i	$0.454780\pi$
$359$	−14.9022	+	25.8113i	−0.786507	+	1.36227i	−0.928094	+	0.372345i	$0.878554\pi$
$360$	−2.90761	−	6.04531i	−0.153245	−	0.318616i
$361$	−3.12988	−	5.42111i	−0.164731	−	0.285322i
$362$	0.747816	+	8.54757i	0.0393043	+	0.449250i
$363$	24.9893	−	14.9737i	1.31160	−	0.785914i
$364$	−8.74656	+	1.54225i	−0.458444	+	0.0808361i
$365$	−8.07688	−	2.34260i	−0.422763	−	0.122617i
$366$	−3.09515	−	0.775716i	−0.161786	−	0.0405473i
$367$	15.4507	−	1.35176i	0.806520	−	0.0705613i	0.323564	−	0.946206i	$-0.395119\pi$
$367$	15.4507	−	1.35176i	0.806520	−	0.0705613i	0.482955	+	0.875645i	$0.339563\pi$
$368$	4.99078	+	1.33728i	0.260163	+	0.0697103i
$369$	−5.16849	+	6.58222i	−0.269061	+	0.342657i
$370$	−19.6683	−	3.88522i	−1.02251	−	0.201983i
$371$	10.0162	+	27.5192i	0.520014	+	1.42873i
$372$	−17.9624	−	6.20944i	−0.931305	−	0.321945i
$373$	28.2904	+	2.47509i	1.46482	+	0.128155i	0.791489	−	0.611184i	$-0.209306\pi$
$373$	28.2904	+	2.47509i	1.46482	+	0.128155i	0.673333	+	0.739339i	$0.264862\pi$
$374$	17.0411	+	6.20245i	0.881173	+	0.320721i
$375$	−18.4780	+	5.79338i	−0.954200	+	0.299169i
$376$	−1.01294	+	5.74466i	−0.0522383	+	0.296258i
$377$	−2.17959	−	2.17959i	−0.112255	−	0.112255i
$378$	−3.48249	+	11.2435i	−0.179120	+	0.578301i
$379$			15.8438i			0.813842i	0.913463	+	0.406921i	$0.133398\pi$
$379$			15.8438i			0.813842i	−0.913463	+	0.406921i	$0.866602\pi$
$380$	7.88680	−	1.22458i	0.404584	−	0.0628198i
$381$	15.3541	−	11.1268i	0.786614	−	0.570045i
$382$	4.87679	−	2.27408i	0.249518	−	0.116352i
$383$	2.52368	−	28.8458i	0.128954	−	1.47395i	−0.605800	−	0.795617i	$-0.707147\pi$
$383$	2.52368	−	28.8458i	0.128954	−	1.47395i	0.734754	−	0.678333i	$-0.237297\pi$
$384$	1.72768	+	0.122928i	0.0881655	+	0.00627315i
$385$	−2.87332	+	26.5609i	−0.146438	+	1.35367i
$386$	20.6713	+	11.9346i	1.05214	+	0.607454i
$387$	14.6619	+	13.7395i	0.745308	+	0.698416i
$388$	2.97919	−	11.1185i	0.151245	−	0.564455i
$389$	2.09544	+	1.75828i	0.106243	+	0.0891485i	0.694362	−	0.719626i	$-0.255687\pi$
$389$	2.09544	+	1.75828i	0.106243	+	0.0891485i	−0.588119	+	0.808775i	$0.700131\pi$
$390$	14.9432	+	2.70055i	0.756676	+	0.136748i
$391$	3.08484	+	17.4950i	0.156007	+	0.884759i
$392$	−1.07189	+	1.53082i	−0.0541385	+	0.0773178i
$393$	−4.98527	+	0.0809387i	−0.251474	+	0.00408282i
$394$	5.91334	−	7.04724i	0.297910	−	0.355035i
$395$	−11.2870	−	9.87202i	−0.567910	−	0.496715i
$396$	15.0368	+	4.92633i	0.755629	+	0.247557i
$397$	8.17298	+	30.5020i	0.410190	+	1.53085i	0.794278	+	0.607554i	$0.207849\pi$
$397$	8.17298	+	30.5020i	0.410190	+	1.53085i	−0.384088	+	0.923296i	$0.625484\pi$
$398$	−8.40159	+	18.0173i	−0.421134	+	0.903124i
$399$	−11.6005	−	7.84522i	−0.580751	−	0.392752i
$400$	1.06927	−	4.88433i	0.0534635	−	0.244216i
$401$	1.65822	−	4.55593i	0.0828077	−	0.227512i	−0.891378	−	0.453261i	$-0.850261\pi$
$401$	1.65822	−	4.55593i	0.0828077	−	0.227512i	0.974186	+	0.225749i	$0.0724828\pi$
$402$	1.99256	+	5.20978i	0.0993801	+	0.259840i
$403$	35.2416	−	24.6764i	1.75551	−	1.22922i
$404$	4.84576			0.241086
$405$	12.2381	−	15.9759i	0.608118	−	0.793846i
$406$	1.78084			0.0883818
$407$	38.7376	−	27.1244i	1.92015	−	1.34451i
$408$	2.12738	+	5.56228i	0.105321	+	0.275374i
$409$	−10.0536	+	27.6221i	−0.497119	+	1.36582i	0.396928	+	0.917850i	$0.370076\pi$
$409$	−10.0536	+	27.6221i	−0.497119	+	1.36582i	−0.894047	+	0.447973i	$0.852146\pi$
$410$	−6.05710	+	1.49066i	−0.299139	+	0.0736187i
$411$	−13.1964	−	8.92448i	−0.650928	−	0.440212i
$412$	0.397992	−	0.853497i	0.0196077	−	0.0420488i
$413$	6.42673	+	23.9849i	0.316239	+	1.18022i
$414$	3.18576	+	15.1696i	0.156572	+	0.745545i
$415$	−0.497096	−	7.43344i	−0.0244015	−	0.364893i
$416$	−2.52025	+	3.00351i	−0.123565	+	0.147259i
$417$	−23.5482	+	0.382318i	−1.15316	+	0.0187222i
$418$	−10.7983	+	15.4215i	−0.528160	+	0.754291i
$419$	−0.681601	−	3.86555i	−0.0332984	−	0.188845i	0.963622	−	0.267270i	$-0.0861217\pi$
$419$	−0.681601	−	3.86555i	−0.0332984	−	0.188845i	−0.996920	+	0.0784259i	$0.975011\pi$
$420$	−7.20792	+	5.00143i	−0.351710	+	0.244045i
$421$	10.2416	+	8.59375i	0.499147	+	0.418834i	0.857291	−	0.514832i	$-0.172146\pi$
$421$	10.2416	+	8.59375i	0.499147	+	0.418834i	−0.358144	+	0.933666i	$0.616590\pi$
$422$	2.86413	−	10.6891i	0.139424	−	0.520337i
$423$	−16.7476	+	5.07564i	−0.814297	+	0.246786i
$424$	11.1962	+	6.46413i	0.543735	+	0.313926i
$425$	16.7738	−	3.76529i	0.813650	−	0.182643i
$426$	−9.00696	−	0.640863i	−0.436388	−	0.0310499i
$427$	−0.363710	+	4.15723i	−0.0176012	+	0.201182i
$428$	−11.2025	+	5.22381i	−0.541494	+	0.252503i
$429$	−29.0036	+	21.0184i	−1.40031	+	1.01478i
$430$	2.29790	+	14.7994i	0.110815	+	0.713691i
$431$			6.91088i			0.332885i	0.986051	+	0.166443i	$0.0532281\pi$
$431$			6.91088i			0.332885i	−0.986051	+	0.166443i	$0.946772\pi$
$432$	2.01279	+	4.79048i	0.0968405	+	0.230482i
$433$	11.4765	+	11.4765i	0.551527	+	0.551527i	0.926881	−	0.375355i	$-0.122479\pi$
$433$	11.4765	+	11.4765i	0.551527	+	0.551527i	−0.375355	+	0.926881i	$0.622479\pi$
$434$	−4.31615	+	24.4781i	−0.207182	+	1.17499i
$435$	−2.85673	−	1.05356i	−0.136970	−	0.0505145i
$436$	2.33146	+	0.848583i	0.111657	+	0.0406398i
$437$	−18.3721	−	1.60735i	−0.878855	−	0.0768898i
$438$	6.15667	+	2.12831i	0.294177	+	0.101695i
$439$	−6.97074	−	19.1520i	−0.332695	−	0.914073i	−0.987408	−	0.158195i	$-0.949433\pi$
$439$	−6.97074	−	19.1520i	−0.332695	−	0.914073i	0.654713	−	0.755878i	$-0.272790\pi$
$440$	6.56534	+	9.79762i	0.312990	+	0.467083i
$441$	−5.54986	−	0.793786i	−0.264279	−	0.0377994i
$442$	−13.0214	−	3.48906i	−0.619363	−	0.165958i
$443$	−21.8255	+	1.90948i	−1.03696	+	0.0907223i	−0.592901	−	0.805275i	$-0.702018\pi$
$443$	−21.8255	+	1.90948i	−1.03696	+	0.0907223i	−0.444059	+	0.895997i	$0.646462\pi$
$444$	15.0635	+	3.77527i	0.714884	+	0.179167i
$445$	4.14346	−	2.28032i	0.196419	−	0.108098i
$446$	0.179240	−	0.0316048i	0.00848725	−	0.00149653i
$447$	2.35879	−	1.41339i	0.111567	−	0.0668511i
$448$	−0.197427	−	2.25660i	−0.00932754	−	0.106614i
$449$	−12.5749	−	21.7804i	−0.593447	−	1.02788i	−0.993764	−	0.111504i	$-0.964433\pi$
$449$	−12.5749	−	21.7804i	−0.593447	−	1.02788i	0.400317	−	0.916377i	$-0.368900\pi$
$450$	14.5214	−	3.75874i	0.684547	−	0.177189i
$451$	7.35686	−	12.7425i	0.346421	−	0.600019i
$452$	4.85474	+	2.26380i	0.228348	+	0.106480i
$453$	−3.73064	+	10.7918i	−0.175281	+	0.507043i
$454$	−1.52404	−	1.81628i	−0.0715266	−	0.0852421i
$455$	0.406952	−	19.8554i	0.0190782	−	0.930837i
$456$	−6.14921	+	0.638729i	−0.287963	+	0.0299112i
$457$	−19.9743	−	28.5262i	−0.934358	−	1.33440i	−0.942419	−	0.334434i	$-0.891455\pi$
$457$	−19.9743	−	28.5262i	−0.934358	−	1.33440i	0.00806106	−	0.999968i	$-0.497434\pi$
$458$	3.35872	−	3.35872i	0.156943	−	0.156943i
$459$	−12.0029	+	13.2330i	−0.560249	+	0.617662i
$460$	−5.09622	+	10.3687i	−0.237612	+	0.483442i
$461$	37.9623	+	6.69377i	1.76808	+	0.311760i	0.960558	−	0.278080i	$-0.0896980\pi$
$461$	37.9623	+	6.69377i	1.76808	+	0.311760i	0.807520	+	0.589840i	$0.200809\pi$
$462$	3.26217	−	20.4353i	0.151770	−	0.950735i
$463$	−6.77038	−	14.5191i	−0.314646	−	0.674761i	0.683848	−	0.729625i	$-0.260305\pi$
$463$	−6.77038	−	14.5191i	−0.314646	−	0.674761i	−0.998494	+	0.0548637i	$0.982528\pi$
$464$	0.602240	−	0.505339i	0.0279583	−	0.0234598i
$465$	21.4052	−	36.7129i	0.992642	−	1.70252i
$466$	16.7935	−	6.11232i	0.777943	−	0.283148i
$467$	36.4655	−	9.77089i	1.68742	−	0.452143i	0.717698	−	0.696355i	$-0.245196\pi$
$467$	36.4655	−	9.77089i	1.68742	−	0.452143i	0.969722	+	0.244212i	$0.0785292\pi$
$468$	−11.4545	−	2.67391i	−0.529483	−	0.123601i
$469$	6.31750	−	3.64741i	0.291715	−	0.168422i
$470$	−12.1630	−	4.71141i	−0.561038	−	0.217321i
$471$	−25.9918	+	7.41876i	−1.19764	+	0.341838i
$472$	8.97941	+	6.28745i	0.413311	+	0.289403i
$473$	−28.9382	−	20.2627i	−1.33058	−	0.931681i
$474$	8.34539	+	8.07874i	0.383317	+	0.371069i
$475$	−0.731258	+	17.8317i	−0.0335524	+	0.818177i
$476$	6.74494	−	3.89419i	0.309154	−	0.178490i
$477$	−2.12427	+	38.7266i	−0.0972637	+	1.77317i
$478$	−8.59867	+	2.30401i	−0.393294	+	0.105383i
$479$	11.1551	−	4.06013i	0.509690	−	0.185512i	−0.0743571	−	0.997232i	$-0.523690\pi$
$479$	11.1551	−	4.06013i	0.509690	−	0.185512i	0.584047	+	0.811720i	$0.301468\pi$
$480$	−1.01832	+	3.73671i	−0.0464800	+	0.170557i
$481$	−26.9292	+	22.5963i	−1.22787	+	1.03030i
$482$	1.99695	+	4.28247i	0.0909586	+	0.195061i
$483$	18.9344	−	7.24174i	0.861543	−	0.329511i
$484$	−16.5639	−	2.92066i	−0.752904	−	0.132757i
$485$	23.0994	+	11.3534i	1.04889	+	0.515530i
$486$	−10.0927	+	11.8801i	−0.457813	+	0.538895i
$487$	−4.60598	+	4.60598i	−0.208717	+	0.208717i	−0.803722	−	0.595005i	$-0.797150\pi$
$487$	−4.60598	+	4.60598i	−0.208717	+	0.208717i	0.595005	+	0.803722i	$0.297150\pi$
$488$	1.05667	+	1.50908i	0.0478333	+	0.0683130i
$489$	−4.17537	+	9.34735i	−0.188817	+	0.422702i
$490$	−2.89363	−	3.01473i	−0.130721	−	0.136192i
$491$	−14.0210	−	16.7096i	−0.632759	−	0.754093i	0.350449	−	0.936582i	$-0.386029\pi$
$491$	−14.0210	−	16.7096i	−0.632759	−	0.754093i	−0.983208	+	0.182489i	$0.941585\pi$
$492$	4.74415	−	0.916169i	0.213883	−	0.0413041i
$493$	2.44979	+	1.14235i	0.110333	+	0.0514491i
$494$	6.99736	−	12.1198i	0.314826	−	0.545295i
$495$	−17.3227	+	30.8512i	−0.778598	+	1.38666i
$496$	5.48638	+	9.50268i	0.246346	+	0.426683i
$497$	1.02925	+	11.7644i	0.0461681	+	0.527704i
$498$	0.0936795	+	5.77002i	0.00419788	+	0.258561i
$499$	37.8964	−	6.68215i	1.69647	−	0.299134i	0.760014	−	0.649907i	$-0.225192\pi$
$499$	37.8964	−	6.68215i	1.69647	−	0.299134i	0.936461	+	0.350772i	$0.114081\pi$
$500$	10.2513	+	4.46217i	0.458452	+	0.199554i
$501$	−7.94344	−	27.8301i	−0.354887	−	1.24336i
$502$	−22.8247	+	1.99690i	−1.01872	+	0.0891262i
$503$	32.4623	+	8.69825i	1.44742	+	0.387836i	0.895126	−	0.445813i	$-0.147085\pi$
$503$	32.4623	+	8.69825i	1.44742	+	0.387836i	0.552296	+	0.833648i	$0.313752\pi$
$504$	5.77181	−	3.58709i	0.257097	−	0.159782i
$505$	−2.09982	+	10.6300i	−0.0934408	+	0.473030i
$506$	−9.32074	−	25.6085i	−0.414358	−	1.13844i
$507$	3.10489	−	2.69240i	0.137893	−	0.119574i
$508$	−10.9060	−	0.954152i	−0.483876	−	0.0423337i
$509$	−31.2904	−	11.3888i	−1.38692	−	0.504798i	−0.462653	−	0.886540i	$-0.653102\pi$
$509$	−31.2904	−	11.3888i	−1.38692	−	0.504798i	−0.924269	+	0.381741i	$0.875324\pi$
$510$	−13.1237	+	2.25648i	−0.581127	+	0.0999185i
$511$	1.47938	−	8.38995i	0.0654437	−	0.371150i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−10.0444	−	15.5916i	−0.443471	−	0.688384i
$514$		−	7.61611i		−	0.335932i
$515$	1.69984	+	1.24291i	0.0749037	+	0.0547694i
$516$	−1.19856	−	11.5389i	−0.0527637	−	0.507970i
$517$	27.8845	−	13.0028i	1.22636	−	0.571860i
$518$	1.77011	−	20.2325i	0.0777743	−	0.888964i
$519$	−12.6507	−	26.0182i	−0.555303	−	1.14207i
$520$	−5.49663	−	6.83012i	−0.241043	−	0.299521i
$521$	−21.7156	−	12.5375i	−0.951376	−	0.549277i	−0.0578681	−	0.998324i	$-0.518430\pi$
$521$	−21.7156	−	12.5375i	−0.951376	−	0.549277i	−0.893508	+	0.449047i	$0.851764\pi$
$522$	2.16876	+	0.926832i	0.0949241	+	0.0405663i
$523$	−0.121127	+	0.452053i	−0.00529653	+	0.0197669i	−0.968524	−	0.248922i	$-0.919924\pi$
$523$	−0.121127	+	0.452053i	−0.00529653	+	0.0197669i	0.963227	+	0.268689i	$0.0865904\pi$
$524$	2.20516	+	1.85035i	0.0963327	+	0.0808328i
$525$	−7.84810	−	17.9791i	−0.342519	−	0.784673i
$526$	−2.52923	−	14.3440i	−0.110280	−	0.625428i
$527$	−21.6393	+	30.9042i	−0.942625	+	1.34621i
$528$	−4.69560	−	7.83642i	−0.204350	−	0.341037i
$529$	2.37588	−	2.83147i	0.103299	−	0.123107i
$530$	−19.0319	+	21.7597i	−0.826692	+	0.945183i
$531$	−4.65617	+	32.5542i	−0.202061	+	1.41273i
$532$	2.09264	+	7.80985i	0.0907276	+	0.338600i
$533$	−4.62245	+	9.91288i	−0.200221	+	0.429374i
$534$	−3.29464	+	1.60194i	−0.142573	+	0.0693226i
$535$	−6.60497	−	26.8383i	−0.285558	−	1.16032i
$536$	1.10143	−	3.02615i	0.0475745	−	0.130710i
$537$	19.2690	−	23.7360i	0.831518	−	1.02428i
$538$	13.8069	−	9.66766i	0.595256	−	0.416803i
$539$	9.85671			0.424559
$540$	−11.3810	+	2.33955i	−0.489759	+	0.100678i
$541$	−34.4459			−1.48095			−0.740473	−	0.672086i	$-0.765398\pi$
$541$	−34.4459			−1.48095			−0.740473	+	0.672086i	$0.765398\pi$
$542$	23.1453	−	16.2065i	0.994174	−	0.696128i
$543$	14.6756	+	2.34273i	0.629789	+	0.100536i
$544$	1.17595	−	3.23090i	0.0504185	−	0.138524i
$545$	−2.87182	+	4.74676i	−0.123015	+	0.203329i
$546$	−1.09178	+	15.3444i	−0.0467241	+	0.656679i
$547$	−10.3667	+	22.2316i	−0.443250	+	0.950552i	0.550066	+	0.835121i	$0.314603\pi$
$547$	−10.3667	+	22.2316i	−0.443250	+	0.950552i	−0.993315	+	0.115431i	$0.963175\pi$
$548$	2.38053	+	8.88425i	0.101691	+	0.379516i
$549$	−2.60655	+	4.87349i	−0.111245	+	0.207996i
$550$	−24.3378	+	10.1566i	−1.03777	+	0.433080i
$551$	−1.80373	+	2.14960i	−0.0768415	+	0.0915762i
$552$	4.34821	−	7.82187i	0.185072	−	0.332921i
$553$	8.71296	−	12.4434i	0.370513	−	0.529147i
$554$	3.11590	+	17.6712i	0.132382	+	0.750776i
$555$	−14.8092	+	31.4086i	−0.628617	+	1.33322i
$556$	10.4162	+	8.74019i	0.441743	+	0.370667i
$557$	2.17970	−	8.13474i	0.0923567	−	0.344680i	−0.904249	−	0.427006i	$-0.859568\pi$
$557$	2.17970	−	8.13474i	0.0923567	−	0.344680i	0.996605	+	0.0823262i	$0.0262349\pi$
$558$	−17.9958	+	27.5638i	−0.761824	+	1.16687i
$559$	22.7425	+	13.1304i	0.961905	+	0.555356i
$560$	5.03580	+	0.544765i	0.212802	+	0.0230205i
$561$	17.5961	−	26.0189i	0.742910	−	1.09852i
$562$	−2.65613	+	30.3597i	−0.112042	+	1.28064i
$563$	19.1477	−	8.92870i	0.806978	−	0.376300i	0.0250634	−	0.999686i	$-0.492021\pi$
$563$	19.1477	−	8.92870i	0.806978	−	0.376300i	0.781914	+	0.623386i	$0.214243\pi$
$564$	9.22503	+	4.12073i	0.388444	+	0.173514i
$565$	−7.06977	+	9.66876i	−0.297427	+	0.406768i
$566$		−	17.7153i		−	0.744631i
$567$	17.4236	+	10.5852i	0.731724	+	0.444535i
$568$	3.68637	+	3.68637i	0.154677	+	0.154677i
$569$	−4.48927	+	25.4599i	−0.188200	+	1.06733i	0.733575	+	0.679609i	$0.237850\pi$
$569$	−4.48927	+	25.4599i	−0.188200	+	1.06733i	−0.921775	+	0.387726i	$0.873261\pi$
$570$	1.26348	−	13.7662i	0.0529214	−	0.576601i
$571$	34.0373	+	12.3886i	1.42442	+	0.518446i	0.935326	−	0.353787i	$-0.115106\pi$
$571$	34.0373	+	12.3886i	1.42442	+	0.518446i	0.489091	+	0.872233i	$0.337328\pi$
$572$	20.6012	+	1.80238i	0.861381	+	0.0753611i
$573$	−1.76720	−	9.15098i	−0.0738256	−	0.382288i
$574$	−2.16128	−	5.93806i	−0.0902100	−	0.247850i
$575$	−20.5372	−	15.6725i	−0.856461	−	0.653590i
$576$	0.934005	−	2.85090i	0.0389169	−	0.118788i
$577$	4.33109	+	1.16051i	0.180305	+	0.0483127i	0.347842	−	0.937553i	$-0.386915\pi$
$577$	4.33109	+	1.16051i	0.180305	+	0.0483127i	−0.167537	+	0.985866i	$0.553581\pi$
$578$	−5.15874	+	0.451331i	−0.214575	+	0.0187729i
$579$	28.7552	−	29.7043i	1.19503	−	1.23447i
$580$	0.847582	+	1.54010i	0.0351939	+	0.0639492i
$581$	7.43251	−	1.31055i	0.308352	−	0.0543708i
$582$	−17.4256	−	9.68695i	−0.722314	−	0.401537i
$583$	−5.94306	−	67.9295i	−0.246136	−	2.81335i
$584$	−1.88048	−	3.25708i	−0.0778146	−	0.134779i
$585$	10.8293	−	23.9687i	0.447735	−	0.990984i
$586$	3.71363	−	6.43220i	0.153409	−	0.265712i
$587$	−24.3374	−	11.3487i	−1.00451	−	0.468412i	−0.150470	−	0.988615i	$-0.548079\pi$
$587$	−24.3374	−	11.3487i	−1.00451	−	0.468412i	−0.854043	+	0.520203i	$0.825856\pi$
$588$	2.12057	+	2.44545i	0.0874507	+	0.100849i
$589$	−25.1751	−	30.0026i	−1.03732	−	1.23623i
$590$	−17.6837	+	16.9734i	−0.728027	+	0.698783i
$591$	−9.35007	−	12.9023i	−0.384610	−	0.530730i
$592$	−5.14264	−	7.34445i	−0.211361	−	0.301855i
$593$	20.2128	−	20.2128i	0.830041	−	0.830041i	−0.157481	−	0.987522i	$-0.550337\pi$
$593$	20.2128	−	20.2128i	0.830041	−	0.830041i	0.987522	+	0.157481i	$0.0503374\pi$
$594$	14.6082	−	23.1889i	0.599382	−	0.951451i
$595$	5.61981	+	16.4837i	0.230390	+	0.675766i
$596$	−1.56349	−	0.275686i	−0.0640432	−	0.0112925i
$597$	26.7330	+	21.7020i	1.09411	+	0.888202i
$598$	8.56147	+	18.3601i	0.350105	+	0.750802i
$599$	3.67565	−	3.08424i	0.150183	−	0.126019i	−0.564600	−	0.825364i	$-0.690970\pi$
$599$	3.67565	−	3.08424i	0.150183	−	0.126019i	0.714783	+	0.699346i	$0.246525\pi$
$600$	−7.75587	−	3.85311i	−0.316632	−	0.157303i
$601$	1.68112	−	0.611877i	0.0685742	−	0.0249590i	−0.307505	−	0.951546i	$-0.599494\pi$
$601$	1.68112	−	0.611877i	0.0685742	−	0.0249590i	0.376080	+	0.926587i	$0.377272\pi$
$602$	−14.6550	+	3.92680i	−0.597294	+	0.160044i
$603$	9.59191	−	1.15401i	0.390613	−	0.0469947i
$604$	5.70922	−	3.29622i	0.232305	−	0.134121i
$605$	13.5846	−	35.0702i	0.552294	−	1.42581i
$606$	2.04040	−	8.14131i	0.0828857	−	0.330718i
$607$	−4.87081	−	3.41057i	−0.197700	−	0.138431i	0.470535	−	0.882381i	$-0.344061\pi$
$607$	−4.87081	−	3.41057i	−0.197700	−	0.138431i	−0.668235	+	0.743950i	$0.732950\pi$
$608$	2.92384	+	2.04729i	0.118577	+	0.0830287i
$609$	0.749859	−	2.99198i	0.0303858	−	0.121241i
$610$	−3.76833	+	1.66406i	−0.152575	+	0.0673760i
$611$	−19.8070	+	11.4356i	−0.801306	+	0.462634i
$612$	10.2409	−	1.23208i	0.413964	−	0.0498041i
$613$	−6.91743	+	1.85352i	−0.279392	+	0.0748629i	−0.395794	−	0.918339i	$-0.629531\pi$
$613$	−6.91743	+	1.85352i	−0.279392	+	0.0748629i	0.116402	+	0.993202i	$0.462864\pi$
$614$	−2.64021	+	0.960959i	−0.106550	+	0.0387811i
$615$	−0.0460124	+	10.8041i	−0.00185540	+	0.435665i
$616$	−9.15247	+	7.67983i	−0.368763	+	0.309429i
$617$	1.05695	+	2.26664i	0.0425512	+	0.0912513i	0.926434	−	0.376457i	$-0.122858\pi$
$617$	1.05695	+	2.26664i	0.0425512	+	0.0912513i	−0.883883	+	0.467708i	$0.845080\pi$
$618$	−1.26637	−	1.02804i	−0.0509408	−	0.0413540i
$619$	−27.4374	−	4.83795i	−1.10280	−	0.194454i	−0.407523	−	0.913195i	$-0.633608\pi$
$619$	−27.4374	−	4.83795i	−1.10280	−	0.194454i	−0.695278	+	0.718741i	$0.744719\pi$
$620$	−23.2232	+	7.91753i	−0.932668	+	0.317976i
$621$	26.8277	+	1.03510i	1.07656	+	0.0415371i
$622$	−15.4076	+	15.4076i	−0.617790	+	0.617790i
$623$	2.74809	+	3.92468i	0.110100	+	0.157239i
$624$	3.98497	+	5.49892i	0.159526	+	0.220133i
$625$	−14.2308	+	20.5544i	−0.569231	+	0.822178i
$626$	−14.9737	−	17.8449i	−0.598468	−	0.713227i
$627$	21.3627	+	24.6356i	0.853145	+	0.983851i
$628$	14.1436	+	6.59525i	0.564390	+	0.263179i
$629$	15.4135	−	26.6970i	0.614577	−	1.06448i
$630$	5.36781	+	14.2159i	0.213859	+	0.566375i
$631$	2.60673	+	4.51500i	0.103772	+	0.179739i	0.913236	−	0.407431i	$-0.133575\pi$
$631$	2.60673	+	4.51500i	0.103772	+	0.179739i	−0.809464	+	0.587170i	$0.800242\pi$
$632$	−0.584467	−	6.68049i	−0.0232489	−	0.265736i
$633$	−16.7526	−	9.31285i	−0.665857	−	0.370153i
$634$	22.8955	−	4.03709i	0.909295	−	0.160333i
$635$	6.81902	−	23.5108i	0.270605	−	0.932998i
$636$	15.5747	−	16.0888i	0.617577	−	0.637961i
$637$	−7.29924	+	0.638601i	−0.289206	+	0.0253023i
$638$	−4.00528	−	1.07321i	−0.158571	−	0.0424889i
$639$	−4.86926	+	14.8626i	−0.192625	+	0.587957i
$640$	1.85758	−	1.24475i	0.0734272	−	0.0492032i
$641$	0.875297	+	2.40486i	0.0345722	+	0.0949862i	0.955778	−	0.294090i	$-0.0950165\pi$
$641$	0.875297	+	2.40486i	0.0345722	+	0.0949862i	−0.921206	+	0.389076i	$0.872794\pi$
$642$	4.05944	+	21.0208i	0.160213	+	0.829625i
$643$	−36.3704	−	3.18199i	−1.43431	−	0.125486i	−0.656660	−	0.754187i	$-0.728031\pi$
$643$	−36.3704	−	3.18199i	−1.43431	−	0.125486i	−0.777647	+	0.628701i	$0.783587\pi$
$644$	−10.9982	−	4.00301i	−0.433389	−	0.157741i
$645$	25.8319	+	2.37089i	1.01713	+	0.0933539i
$646$	−2.13106	+	12.0859i	−0.0838456	+	0.475512i
$647$	2.18876	+	2.18876i	0.0860490	+	0.0860490i	0.748821	−	0.662772i	$-0.230620\pi$
$647$	2.18876	+	2.18876i	0.0860490	+	0.0860490i	−0.662772	+	0.748821i	$0.730620\pi$
$648$	8.89596	−	1.36454i	0.349466	−	0.0536044i
$649$		−	57.8172i		−	2.26952i
$650$	17.3650	−	9.09814i	0.681110	−	0.356858i
$651$	39.3080	+	17.5585i	1.54060	+	0.688171i
$652$	5.35685	−	2.49794i	0.209791	−	0.0978269i
$653$	0.607544	−	6.94426i	0.0237750	−	0.271750i	−0.974997	−	0.222216i	$-0.928671\pi$
$653$	0.607544	−	6.94426i	0.0237750	−	0.271750i	0.998772	−	0.0495336i	$-0.0157735\pi$
$654$	2.40740	−	3.55975i	0.0941370	−	0.139197i
$655$	−5.01463	+	4.03559i	−0.195938	+	0.157684i
$656$	−2.41590	−	1.39482i	−0.0943251	−	0.0544586i
$657$	6.16814	−	9.44759i	0.240642	−	0.368585i
$658$	3.41995	−	12.7634i	0.133324	−	0.497570i
$659$	−3.29307	−	2.76322i	−0.128280	−	0.107640i	0.576391	−	0.817174i	$-0.304461\pi$
$659$	−3.29307	−	2.76322i	−0.128280	−	0.107640i	−0.704670	+	0.709535i	$0.748905\pi$
$660$	19.2253	−	6.90487i	0.748346	−	0.268772i
$661$	2.43780	+	13.8255i	0.0948196	+	0.537748i	0.994802	+	0.101823i	$0.0324676\pi$
$661$	2.43780	+	13.8255i	0.0948196	+	0.537748i	−0.899983	+	0.435925i	$0.856421\pi$
$662$	9.01333	−	12.8724i	0.350313	−	0.500299i
$663$	−11.3448	+	20.4079i	−0.440597	+	0.792578i
$664$	2.14161	−	2.55228i	0.0831107	−	0.0990475i
$665$	−18.0391	+	1.20633i	−0.699527	+	0.0467795i
$666$	12.6856	−	23.7184i	0.491557	−	0.919071i
$667$	−1.05132	−	3.92359i	−0.0407074	−	0.151922i
$668$	−7.06170	+	15.1439i	−0.273225	+	0.585933i
$669$	0.0223735	−	0.314447i	0.000865010	−	0.0121572i
$670$	6.16111	+	3.72751i	0.238025	+	0.144006i
$671$	3.32334	−	9.13080i	0.128296	−	0.352491i
$672$	−3.87442	−	0.618491i	−0.149459	−	0.0238588i
$673$	16.5854	−	11.6132i	0.639321	−	0.447657i	−0.208441	−	0.978035i	$-0.566839\pi$
$673$	16.5854	−	11.6132i	0.639321	−	0.447657i	0.847761	+	0.530378i	$0.177950\pi$
$674$	−0.601512			−0.0231694
$675$	−0.200483	−	25.9800i	−0.00771658	−	0.999970i
$676$	−2.37272			−0.0912583
$677$	6.24019	−	4.36943i	0.239830	−	0.167931i	−0.447482	−	0.894293i	$-0.647679\pi$
$677$	6.24019	−	4.36943i	0.239830	−	0.167931i	0.687312	+	0.726362i	$0.258790\pi$
$678$	5.84757	−	7.20318i	0.224575	−	0.276636i
$679$	−8.91792	+	24.5018i	−0.342238	+	0.940292i
$680$	6.57797	+	3.97971i	0.252254	+	0.152615i
$681$	−3.69323	+	1.79574i	−0.141525	+	0.0688129i
$682$	24.4589	−	52.4524i	0.936581	−	2.00851i
$683$	7.31689	+	27.3070i	0.279973	+	1.04487i	0.952435	+	0.304742i	$0.0985703\pi$
$683$	7.31689	+	27.3070i	0.279973	+	1.04487i	−0.672462	+	0.740132i	$0.734763\pi$
$684$	−1.51612	+	10.6002i	−0.0579704	+	0.405307i
$685$	−20.5207	+	1.37228i	−0.784057	+	0.0524322i
$686$	12.9134	−	15.3896i	0.493037	−	0.587579i
$687$	−4.22870	−	7.05721i	−0.161335	−	0.269249i
$688$	−3.84170	+	5.48652i	−0.146463	+	0.209172i
$689$	8.80208	+	49.9191i	0.335333	+	1.90177i
$690$	15.2745	+	12.9280i	0.581489	+	0.492162i
$691$	−23.0914	−	19.3760i	−0.878438	−	0.737097i	0.0874193	−	0.996172i	$-0.472138\pi$
$691$	−23.0914	−	19.3760i	−0.878438	−	0.737097i	−0.965857	+	0.259075i	$0.916582\pi$
$692$	−4.32309	+	16.1340i	−0.164339	+	0.613323i
$693$	−32.9595	−	14.0854i	−1.25203	−	0.535061i
$694$	16.3853	+	9.46004i	0.621976	+	0.359098i
$695$	−23.6868	+	19.0623i	−0.898492	+	0.723074i
$696$	−0.595430	−	1.22460i	−0.0225697	−	0.0464183i
$697$	0.835953	−	9.55499i	0.0316640	−	0.361921i
$698$	14.5940	−	6.80532i	0.552393	−	0.257585i
$699$	−3.19803	−	30.7882i	−0.120961	−	1.16452i
$700$	−3.37721	+	10.8109i	−0.127647	+	0.408612i
$701$			24.3339i			0.919079i	0.888157	+	0.459539i	$0.151986\pi$
$701$			24.3339i			0.919079i	−0.888157	+	0.459539i	$0.848014\pi$
$702$	−9.31553	+	18.1186i	−0.351592	+	0.683843i
$703$	22.6292	+	22.6292i	0.853475	+	0.853475i
$704$	−0.915892	+	5.19428i	−0.0345190	+	0.195767i
$705$	−13.0371	+	18.4511i	−0.491004	+	0.694909i
$706$	11.4695	+	4.17457i	0.431662	+	0.157112i
$707$	−10.9349	−	0.956683i	−0.411251	−	0.0359798i
$708$	14.3444	−	12.4388i	0.539097	−	0.467477i
$709$	5.51749	+	15.1592i	0.207214	+	0.569315i	0.999147	−	0.0412927i	$-0.0131476\pi$
$709$	5.51749	+	15.1592i	0.207214	+	0.569315i	−0.791934	+	0.610607i	$0.790925\pi$
$710$	−9.68413	+	6.48929i	−0.363439	+	0.243539i
$711$	17.0870	−	10.6193i	0.640812	−	0.398255i
$712$	2.04302	+	0.547427i	0.0765656	+	0.0205157i
$713$	56.4787	−	4.94124i	2.11514	−	0.185051i
$714$	−3.70250	−	12.9718i	−0.138563	−	0.485459i
$715$	−12.8810	+	44.4115i	−0.481722	+	1.66090i
$716$	−17.3830	+	3.06509i	−0.649634	+	0.114548i
$717$	0.250299	+	15.4167i	0.00934758	+	0.575747i
$718$	−2.59762	−	29.6910i	−0.0969424	−	1.10806i
$719$	20.0698	+	34.7619i	0.748478	+	1.29640i	0.948552	+	0.316621i	$0.102548\pi$
$719$	20.0698	+	34.7619i	0.748478	+	1.29640i	−0.200074	+	0.979781i	$0.564118\pi$
$720$	5.84922	+	3.28429i	0.217988	+	0.122398i
$721$	−1.06661	+	1.84743i	−0.0397227	+	0.0688018i
$722$	5.67327	+	2.64549i	0.211137	+	0.0984549i
$723$	8.03580	−	1.55184i	0.298854	−	0.0577134i
$724$	−5.51526	−	6.57283i	−0.204973	−	0.244277i
$725$	−3.74577	+	1.19195i	−0.139114	+	0.0442678i
$726$	−11.8815	+	26.5990i	−0.440965	+	0.987182i
$727$	−1.85205	−	2.64500i	−0.0686887	−	0.0980977i	0.783338	−	0.621596i	$-0.213515\pi$
$727$	−1.85205	−	2.64500i	−0.0686887	−	0.0980977i	−0.852027	+	0.523498i	$0.824627\pi$
$728$	6.28016	−	6.28016i	0.232758	−	0.232758i
$729$	15.7100	+	21.9590i	0.581852	+	0.813295i
$730$	7.95985	−	2.71376i	0.294607	−	0.100441i
$731$	−22.6789	−	3.99889i	−0.838808	−	0.147904i
$732$	2.98033	−	1.13987i	0.110156	−	0.0421310i
$733$	−2.74347	−	5.88338i	−0.101332	−	0.217308i	0.849105	−	0.528224i	$-0.177142\pi$
$733$	−2.74347	−	5.88338i	−0.101332	−	0.217308i	−0.950437	+	0.310916i	$0.899364\pi$
$734$	−11.8811	+	9.96945i	−0.438541	+	0.367979i
$735$	−6.28343	+	3.59215i	−0.231768	+	0.132498i
$736$	−4.85524	+	1.76716i	−0.178967	+	0.0651385i
$737$	−16.4067	+	4.39617i	−0.604350	+	0.161935i
$738$	0.458373	−	8.35637i	0.0168729	−	0.307602i
$739$	−33.8397	+	19.5374i	−1.24481	+	0.718693i	−0.970070	−	0.242825i	$-0.921926\pi$
$739$	−33.8397	+	19.5374i	−1.24481	+	0.718693i	−0.274743	+	0.961518i	$0.588593\pi$
$740$	18.3398	−	8.09871i	0.674185	−	0.297714i
$741$	−17.4159	−	16.8595i	−0.639791	−	0.619348i
$742$	−23.9891	−	16.7974i	−0.880669	−	0.616651i
$743$	−5.05580	−	3.54011i	−0.185479	−	0.129874i	0.477149	−	0.878822i	$-0.341670\pi$
$743$	−5.05580	−	3.54011i	−0.185479	−	0.129874i	−0.662628	+	0.748948i	$0.730559\pi$
$744$	18.2755	−	5.21631i	0.670012	−	0.191239i
$745$	1.28228	−	3.31034i	0.0469790	−	0.121281i
$746$	−24.5938	+	14.1992i	−0.900443	+	0.519871i
$747$	9.73359	+	2.27219i	0.356133	+	0.0831350i
$748$	−17.5168	+	4.69362i	−0.640478	+	0.171616i
$749$	26.3109	−	9.57638i	0.961379	−	0.349913i
$750$	11.8134	−	15.3442i	0.431363	−	0.560291i
$751$	0.718971	−	0.603288i	0.0262356	−	0.0220143i	−0.629576	−	0.776939i	$-0.716771\pi$
$751$	0.718971	−	0.603288i	0.0262356	−	0.0220143i	0.655811	+	0.754925i	$0.272327\pi$
$752$	−2.46525	−	5.28675i	−0.0898985	−	0.192788i
$753$	−6.25582	+	39.1884i	−0.227975	+	1.42810i
$754$	3.03558	+	0.535255i	0.110549	+	0.0194929i
$755$	4.75686	+	13.9525i	0.173120	+	0.507785i
$756$	−3.59629	−	11.2076i	−0.130796	−	0.407615i
$757$	−3.26714	+	3.26714i	−0.118746	+	0.118746i	−0.763983	−	0.645237i	$-0.776759\pi$
$757$	−3.26714	+	3.26714i	−0.118746	+	0.118746i	0.645237	+	0.763983i	$0.276759\pi$
$758$	−9.08764	−	12.9785i	−0.330078	−	0.471400i
$759$	−46.9493	+	4.87671i	−1.70415	+	0.177013i
$760$	−5.75809	+	5.52680i	−0.208868	+	0.200478i
$761$	9.10126	+	10.8465i	0.329920	+	0.393184i	0.905349	−	0.424668i	$-0.139609\pi$
$761$	9.10126	+	10.8465i	0.329920	+	0.393184i	−0.575429	+	0.817852i	$0.695165\pi$
$762$	−6.19525	+	17.9213i	−0.224430	+	0.649221i
$763$	−5.09365	−	2.37521i	−0.184402	−	0.0859883i
$764$	−2.69047	+	4.66003i	−0.0973377	+	0.168594i
$765$	−1.73491	+	22.9991i	−0.0627258	+	0.831535i
$766$	14.4780	+	25.0766i	0.523111	+	0.906054i
$767$	3.74589	+	42.8157i	0.135256	+	1.54598i
$768$	−1.48574	+	0.890261i	−0.0536122	+	0.0321245i
$769$	28.6310	−	5.04841i	1.03246	−	0.182050i	0.368351	−	0.929687i	$-0.379923\pi$
$769$	28.6310	−	5.04841i	1.03246	−	0.182050i	0.664108	+	0.747636i	$0.268811\pi$
$770$	−12.8810	−	23.4055i	−0.464200	−	0.843475i
$771$	−12.7958	−	3.20691i	−0.460828	−	0.115494i
$772$	−23.7783	+	2.08033i	−0.855800	+	0.0748728i
$773$	13.7334	+	3.67985i	0.493956	+	0.132355i	0.497193	−	0.867640i	$-0.334364\pi$
$773$	13.7334	+	3.67985i	0.493956	+	0.132355i	−0.00323767	+	0.999995i	$0.501031\pi$
$774$	−19.8910	−	2.84497i	−0.714967	−	0.102260i
$775$	−7.30514	−	54.3752i	−0.262408	−	1.95322i
$776$	3.93689	+	10.8165i	0.141326	+	0.388290i
$777$	−33.2470	−	11.4932i	−1.19273	−	0.412317i
$778$	−2.72499	−	0.238406i	−0.0976958	−	0.00854727i
$779$	9.35671	+	3.40557i	0.335239	+	0.122017i
$780$	−13.7897	+	6.35888i	−0.493750	+	0.227684i
$781$	4.77483	−	27.0794i	0.170857	−	0.968978i
$782$	−12.5617	−	12.5617i	−0.449204	−	0.449204i
$783$	2.47036	−	3.25345i	0.0882835	−	0.116269i
$784$		−	1.86878i		−	0.0667421i
$785$	−20.5967	+	28.1685i	−0.735129	+	1.00538i
$786$	4.03727	−	2.92574i	0.144005	−	0.104358i
$787$	−2.85030	+	1.32912i	−0.101602	+	0.0473779i	−0.472755	−	0.881194i	$-0.656740\pi$
$787$	−2.85030	+	1.32912i	−0.101602	+	0.0473779i	0.371153	+	0.928572i	$0.378963\pi$
$788$	−0.801791	+	9.16451i	−0.0285626	+	0.326472i
$789$	−25.1642	−	1.79048i	−0.895868	−	0.0637428i
$790$	14.9081	+	1.61274i	0.530407	+	0.0573786i
$791$	−10.5083	−	6.06695i	−0.373631	−	0.215716i
$792$	−15.1431	+	4.58936i	−0.538085	+	0.163076i
$793$	−1.86948	+	6.97699i	−0.0663871	+	0.247760i
$794$	−24.1901	−	20.2979i	−0.858475	−	0.720346i
$795$	28.5446	+	41.1376i	1.01237	+	1.45900i
$796$	−3.45210	−	19.5778i	−0.122356	−	0.693918i
$797$	4.68030	−	6.68416i	0.165785	−	0.236765i	−0.727660	−	0.685938i	$-0.759392\pi$
$797$	4.68030	−	6.68416i	0.165785	−	0.236765i	0.893445	+	0.449173i	$0.148281\pi$
$798$	14.0024	−	0.227337i	0.495680	−	0.00804764i
$799$	12.8919	−	15.3640i	0.456084	−	0.543539i
$800$	1.92564	+	4.61432i	0.0680817	+	0.163141i
$801$	1.30412	+	6.20982i	0.0460789	+	0.219413i
$802$	1.25484	+	4.68312i	0.0443099	+	0.165367i
$803$	−8.38340	+	17.9783i	−0.295844	+	0.634439i
$804$	−4.62042	−	3.12472i	−0.162950	−	0.110200i
$805$	13.5472	−	22.3918i	0.477475	−	0.789209i
$806$	−14.7144	+	40.4275i	−0.518293	+	1.42400i
$807$	−10.4289	−	27.2675i	−0.367114	−	0.959862i
$808$	−3.96941	+	2.77941i	−0.139643	+	0.0977794i
$809$	−11.1588			−0.392323			−0.196161	−	0.980572i	$-0.562848\pi$
$809$	−11.1588			−0.392323			−0.196161	+	0.980572i	$0.562848\pi$
$810$	−0.861528	+	20.1062i	−0.0302710	+	0.706459i
$811$	40.8224			1.43347			0.716734	−	0.697346i	$-0.245636\pi$
$811$	40.8224			1.43347			0.716734	+	0.697346i	$0.245636\pi$
$812$	−1.45878	+	1.02145i	−0.0511932	+	0.0358459i
$813$	−17.4826	−	45.7102i	−0.613141	−	1.60313i
$814$	−16.1741	+	44.4380i	−0.566902	+	1.55755i
$815$	3.15839	+	12.8336i	0.110633	+	0.449543i
$816$	−4.93304	−	3.33613i	−0.172691	−	0.116788i
$817$	10.1034	−	21.6669i	0.353475	−	0.758029i
$818$	−7.60793	−	28.3932i	−0.266005	−	0.992744i
$819$	25.3202	+	8.29535i	0.884761	+	0.289863i
$820$	4.10668	−	4.69529i	0.143411	−	0.163967i
$821$	−22.2863	+	26.5597i	−0.777796	+	0.926941i	−0.998832	−	0.0483244i	$-0.984612\pi$
$821$	−22.2863	+	26.5597i	−0.777796	+	0.926941i	0.221036	+	0.975266i	$0.429056\pi$
$822$	15.9287	−	0.258611i	0.555577	−	0.00902011i
$823$	13.7385	−	19.6207i	0.478895	−	0.683933i	−0.504911	−	0.863172i	$-0.668475\pi$
$823$	13.7385	−	19.6207i	0.478895	−	0.683933i	0.983806	+	0.179239i	$0.0573634\pi$
$824$	0.163530	+	0.927423i	0.00569683	+	0.0323083i
$825$	6.81612	+	45.1663i	0.237307	+	1.57249i
$826$	−19.0216	−	15.9610i	−0.661847	−	0.555356i
$827$	−5.67676	+	21.1860i	−0.197400	+	0.736708i	0.794232	+	0.607615i	$0.207873\pi$
$827$	−5.67676	+	21.1860i	−0.197400	+	0.736708i	−0.991632	+	0.129094i	$0.958793\pi$
$828$	−11.3105	−	10.5989i	−0.393069	−	0.368338i
$829$	−43.4213	−	25.0693i	−1.50808	−	0.870692i	−0.999956	−	0.00940960i	$-0.997005\pi$
$829$	−43.4213	−	25.0693i	−1.50808	−	0.870692i	−0.508127	−	0.861282i	$-0.669662\pi$
$830$	4.67084	+	5.80399i	0.162127	+	0.201460i
$831$	31.0011	+	2.20579i	1.07542	+	0.0765182i
$832$	0.341721	−	3.90589i	0.0118470	−	0.135412i
$833$	5.82333	−	2.71546i	0.201766	−	0.0940852i
$834$	19.0702	−	13.8198i	0.660348	−	0.478542i
$835$	−30.1607	−	22.0534i	−1.04375	−	0.763190i
$836$		−	18.8262i		−	0.651118i
$837$	38.7321	+	41.8409i	1.33878	+	1.44623i
$838$	2.77552	+	2.77552i	0.0958789	+	0.0958789i
$839$	−7.44054	+	42.1974i	−0.256876	+	1.45682i	0.534335	+	0.845273i	$0.320562\pi$
$839$	−7.44054	+	42.1974i	−0.256876	+	1.45682i	−0.791211	+	0.611543i	$0.790549\pi$
$840$	3.03568	−	8.23122i	0.104741	−	0.284004i
$841$	26.6703	+	9.70720i	0.919665	+	0.334731i
$842$	−13.3186	−	1.16523i	−0.458990	−	0.0401565i
$843$	49.8885	+	17.2461i	1.71825	+	0.593986i
$844$	3.78485	+	10.3988i	0.130280	+	0.357941i
$845$	1.02817	−	5.20498i	0.0353702	−	0.179057i
$846$	10.8076	−	13.7638i	0.371572	−	0.473208i
$847$	36.8014	+	9.86092i	1.26451	+	0.338825i
$848$	−12.8791	+	1.12677i	−0.442269	+	0.0386935i
$849$	−29.7634	−	7.45939i	−1.02148	−	0.256006i
$850$	−11.5806	+	12.7054i	−0.397213	+	0.435792i
$851$	−45.6216	+	8.04433i	−1.56389	+	0.275756i
$852$	7.74565	−	4.64121i	0.265362	−	0.159005i
$853$	3.20547	+	36.6387i	0.109753	+	1.25449i	0.828808	+	0.559533i	$0.189019\pi$
$853$	3.20547	+	36.6387i	0.109753	+	1.25449i	−0.719055	+	0.694953i	$0.755425\pi$
$854$	−2.08655	−	3.61401i	−0.0714004	−	0.123669i
$855$	−22.5964	−	7.91927i	−0.772780	−	0.270833i
$856$	6.18030	−	10.7046i	0.211238	−	0.365875i
$857$	30.3972	+	14.1744i	1.03835	+	0.484189i	0.865579	−	0.500773i	$-0.166951\pi$
$857$	30.3972	+	14.1744i	1.03835	+	0.484189i	0.172769	+	0.984962i	$0.444729\pi$
$858$	11.7027	−	33.8530i	0.399524	−	1.15572i
$859$	−10.7965	−	12.8668i	−0.368372	−	0.439009i	0.549736	−	0.835338i	$-0.314728\pi$
$859$	−10.7965	−	12.8668i	−0.368372	−	0.439009i	−0.918108	+	0.396329i	$0.870284\pi$
$860$	−10.3709	−	10.8049i	−0.353646	−	0.368445i
$861$	−10.8865	+	1.13080i	−0.371012	+	0.0385377i
$862$	−3.96392	−	5.66106i	−0.135012	−	0.192817i
$863$	−11.9401	+	11.9401i	−0.406445	+	0.406445i	−0.880497	−	0.474052i	$-0.842791\pi$
$863$	−11.9401	+	11.9401i	−0.406445	+	0.406445i	0.474052	+	0.880497i	$0.342791\pi$
$864$	−4.39649	−	2.76964i	−0.149572	−	0.0942251i
$865$	−33.5195	−	16.4748i	−1.13970	−	0.560162i
$866$	−15.9837	−	2.81835i	−0.543148	−	0.0957716i
$867$	−1.41391	+	8.85719i	−0.0480190	+	0.300806i
$868$	−10.5045	−	22.5269i	−0.356545	−	0.764613i
$869$	−27.0952	+	22.7356i	−0.919141	+	0.771251i
$870$	2.94440	−	0.775524i	0.0998244	−	0.0262927i
$871$	11.8649	−	4.31849i	0.402028	−	0.146326i
$872$	−2.39655	+	0.642154i	−0.0811574	+	0.0217461i
$873$	−23.6123	+	25.1977i	−0.799156	+	0.852812i
$874$	15.9714	−	9.22112i	0.540242	−	0.311909i
$875$	−22.2521	−	12.0932i	−0.752259	−	0.408825i
$876$	−6.26400	+	1.78791i	−0.211641	+	0.0604079i
$877$	−10.6094	−	7.42880i	−0.358255	−	0.250853i	0.380567	−	0.924753i	$-0.375729\pi$
$877$	−10.6094	−	7.42880i	−0.358255	−	0.250853i	−0.738822	+	0.673901i	$0.764618\pi$
$878$	16.6952	+	11.6901i	0.563436	+	0.394522i
$879$	−9.24297	−	8.94764i	−0.311758	−	0.301796i
$880$	−10.9977	−	4.26002i	−0.370732	−	0.143605i
$881$	40.4376	−	23.3467i	1.36238	−	0.786569i	0.372438	−	0.928057i	$-0.378522\pi$
$881$	40.4376	−	23.3467i	1.36238	−	0.786569i	0.989940	+	0.141488i	$0.0451886\pi$
$882$	5.00148	−	2.53304i	0.168408	−	0.0852918i
$883$	−4.73050	+	1.26753i	−0.159194	+	0.0426559i	−0.337536	−	0.941313i	$-0.609593\pi$
$883$	−4.73050	+	1.26753i	−0.159194	+	0.0426559i	0.178342	+	0.983969i	$0.442927\pi$
$884$	12.6677	−	4.61067i	0.426061	−	0.155074i
$885$	21.0707	+	36.8572i	0.708285	+	1.23894i
$886$	16.7832	−	14.0827i	0.563841	−	0.473119i
$887$	6.11970	+	13.1237i	0.205479	+	0.440652i	0.981859	−	0.189614i	$-0.0607237\pi$
$887$	6.11970	+	13.1237i	0.205479	+	0.440652i	−0.776379	+	0.630266i	$0.782946\pi$
$888$	−14.5047	+	5.54757i	−0.486747	+	0.186164i
$889$	24.4221	+	4.30628i	0.819092	+	0.144428i
$890$	−2.08619	+	4.24452i	−0.0699291	+	0.142277i
$891$	−32.8083	−	34.3072i	−1.09912	−	1.14934i
$892$	−0.128697	+	0.128697i	−0.00430909	+	0.00430909i
$893$	11.9424	+	17.0556i	0.399639	+	0.570743i
$894$	−1.12152	+	2.51073i	−0.0375091	+	0.0839712i
$895$	0.808782	−	39.4609i	0.0270346	−	1.31903i
$896$	1.45606	+	1.73526i	0.0486434	+	0.0579709i
$897$	34.4516	−	6.65314i	1.15031	−	0.222142i
$898$	22.7935	+	10.6288i	0.760629	+	0.354687i
$899$	4.31321	−	7.47071i	0.143854	−	0.249162i
$900$	−9.73933	+	11.4081i	−0.324644	+	0.380271i
$901$	−22.2253	−	38.4953i	−0.740431	−	1.28246i
$902$	1.28239	+	14.6577i	0.0426988	+	0.488049i
$903$	0.426593	+	26.2752i	0.0141961	+	0.874384i
$904$	−5.27523	+	0.930166i	−0.175452	+	0.0309369i
$905$	16.8086	−	9.25049i	0.558737	−	0.307497i
$906$	−3.13396	−	10.9799i	−0.104119	−	0.364784i
$907$	27.9883	−	2.44866i	0.929336	−	0.0813063i	0.387574	−	0.921839i	$-0.373313\pi$
$907$	27.9883	−	2.44866i	0.929336	−	0.0813063i	0.541762	+	0.840532i	$0.317758\pi$
$908$	2.29019	+	0.613655i	0.0760027	+	0.0203649i
$909$	−12.8190	−	6.85612i	−0.425179	−	0.227403i
$910$	11.0553	+	16.4980i	0.366478	+	0.546905i
$911$	−2.71846	−	7.46890i	−0.0900665	−	0.247456i	0.886478	−	0.462770i	$-0.153145\pi$
$911$	−2.71846	−	7.46890i	−0.0900665	−	0.247456i	−0.976545	+	0.215315i	$0.930922\pi$
$912$	4.67078	−	4.05026i	0.154665	−	0.134117i
$913$	−17.5062	−	1.53159i	−0.579370	−	0.0506884i
$914$	32.7240	+	11.9106i	1.08241	+	0.393966i
$915$	1.20905	+	7.03183i	0.0399698	+	0.232465i
$916$	−0.824820	+	4.67779i	−0.0272528	+	0.154558i
$917$	−4.61085	−	4.61085i	−0.152264	−	0.152264i
$918$	2.24212	−	17.7244i	0.0740009	−	0.584993i
$919$			45.0659i			1.48659i	0.668965	+	0.743294i	$0.266737\pi$
$919$			45.0659i			1.48659i	−0.668965	+	0.743294i	$0.733263\pi$
$920$	−1.77266	−	11.4166i	−0.0584428	−	0.376394i
$921$	0.502783	+	4.84042i	0.0165673	+	0.159497i
$922$	−34.9362	+	16.2910i	−1.15056	+	0.536517i
$923$	−1.78150	+	20.3626i	−0.0586387	+	0.670244i
$924$	9.04898	+	18.6107i	0.297690	+	0.612247i
$925$	9.81873	+	43.7411i	0.322838	+	1.43820i
$926$	13.8738	+	8.01004i	0.455921	+	0.263226i
$927$	−2.26044	+	1.69474i	−0.0742425	+	0.0556624i
$928$	−0.203475	+	0.759380i	−0.00667940	+	0.0249279i
$929$	−1.75991	−	1.47674i	−0.0577408	−	0.0484503i	0.613461	−	0.789725i	$-0.289777\pi$
$929$	−1.75991	−	1.47674i	−0.0577408	−	0.0484503i	−0.671201	+	0.741275i	$0.734221\pi$
$930$	3.52355	+	42.3510i	0.115542	+	1.38874i
$931$	1.15829	+	6.56899i	0.0379614	+	0.215290i
$932$	−10.2505	+	14.6393i	−0.335767	+	0.479525i
$933$	19.3985	+	32.3739i	0.635079	+	1.05987i
$934$	−24.2664	+	28.9196i	−0.794021	+	0.946277i
$935$	−2.70569	−	40.4601i	−0.0884855	−	1.32319i
$936$	10.9166	−	4.37967i	0.356821	−	0.143154i
$937$	1.77392	+	6.62037i	0.0579515	+	0.216278i	0.988829	−	0.149053i	$-0.0476225\pi$
$937$	1.77392	+	6.62037i	0.0579515	+	0.216278i	−0.930878	+	0.365331i	$0.880956\pi$
$938$	−3.08293	+	6.61136i	−0.100661	+	0.215868i
$939$	−36.2860	+	17.6431i	−1.18415	+	0.575762i
$940$	12.6657	−	3.11705i	0.413110	−	0.101667i
$941$	0.277721	−	0.763032i	0.00905344	−	0.0248741i	−0.935084	−	0.354427i	$-0.884676\pi$
$941$	0.277721	−	0.763032i	0.00905344	−	0.0248741i	0.944137	+	0.329553i	$0.106898\pi$
$942$	17.0360	−	20.9854i	0.555064	−	0.683741i
$943$	−11.8070	+	8.26732i	−0.384488	+	0.269221i
$944$	−10.9618			−0.356777
$945$	26.1442	−	3.03252i	0.850470	−	0.0986478i
$946$	35.3270			1.14858
$947$	−7.48508	+	5.24111i	−0.243232	+	0.170313i	−0.688836	−	0.724917i	$-0.741878\pi$
$947$	−7.48508	+	5.24111i	−0.243232	+	0.170313i	0.445604	+	0.895230i	$0.352989\pi$
$948$	−11.4699	−	1.83099i	−0.372526	−	0.0594679i
$949$	5.04342	−	13.8567i	0.163716	−	0.449807i
$950$	−9.62886	−	15.0263i	−0.312401	−	0.487519i
$951$	2.85791	−	40.1663i	0.0926742	−	1.30248i
$952$	−3.29152	+	7.05868i	−0.106679	+	0.228773i
$953$	5.49003	+	20.4891i	0.177840	+	0.663706i	0.996051	+	0.0887881i	$0.0282994\pi$
$953$	5.49003	+	20.4891i	0.177840	+	0.663706i	−0.818211	+	0.574918i	$0.805034\pi$
$954$	−20.4725	−	32.9414i	−0.662823	−	1.06652i
$955$	−9.05674	−	7.92136i	−0.293069	−	0.256329i
$956$	5.72210	−	6.81933i	0.185066	−	0.220553i
$957$	−3.48960	+	6.27734i	−0.112803	+	0.202917i
$958$	−6.80894	+	9.72417i	−0.219987	+	0.314174i
$959$	−3.61791	−	20.5182i	−0.116828	−	0.662566i
$960$	−1.30913	−	3.64502i	−0.0422519	−	0.117643i
$961$	68.4853	+	57.4660i	2.20920	+	1.85374i
$962$	9.09842	−	33.9558i	0.293345	−	1.09478i
$963$	37.0261	+	2.03100i	1.19315	+	0.0654480i
$964$	−4.09213	−	2.36259i	−0.131799	−	0.0760940i
$965$	5.74032	−	53.0635i	0.184787	−	1.70817i
$966$	−11.3564	+	16.7924i	−0.365387	+	0.540286i
$967$	−1.84703	+	21.1117i	−0.0593966	+	0.678906i	0.906878	+	0.421393i	$0.138459\pi$
$967$	−1.84703	+	21.1117i	−0.0593966	+	0.678906i	−0.966275	+	0.257513i	$0.917097\pi$
$968$	15.2436	−	7.10819i	0.489947	−	0.228466i
$969$	19.4080	+	8.66936i	0.623475	+	0.278500i
$970$	−25.4339	+	3.94913i	−0.816634	+	0.126799i
$971$		−	6.63914i		−	0.213060i	−0.994309	−	0.106530i	$-0.966026\pi$
$971$		−	6.63914i		−	0.213060i	0.994309	−	0.106530i	$-0.0339741\pi$
$972$	1.45326	−	15.5206i	0.0466133	−	0.497822i
$973$	−21.7795	−	21.7795i	−0.698220	−	0.698220i
$974$	1.13112	−	6.41488i	0.0362433	−	0.205546i
$975$	−7.97383	−	33.0056i	−0.255367	−	1.05703i
$976$	−1.73115	−	0.630087i	−0.0554128	−	0.0201686i
$977$	30.5859	+	2.67592i	0.978529	+	0.0856102i	0.565185	−	0.824964i	$-0.308805\pi$
$977$	30.5859	+	2.67592i	0.978529	+	0.0856102i	0.413345	+	0.910575i	$0.364360\pi$
$978$	−1.94116	−	10.0518i	−0.0620714	−	0.321421i
$979$	−3.81554	−	10.4831i	−0.121945	−	0.335041i
$980$	4.09950	+	0.809802i	0.130954	+	0.0258682i
$981$	−4.96702	−	5.54356i	−0.158585	−	0.176992i
$982$	21.0696	+	5.64557i	0.672357	+	0.180157i
$983$	5.80945	−	0.508261i	0.185293	−	0.0162110i	0.00586834	−	0.999983i	$-0.498132\pi$
$983$	5.80945	−	0.508261i	0.185293	−	0.0162110i	0.179424	+	0.983772i	$0.442576\pi$
$984$	−3.36069	+	3.47161i	−0.107135	+	0.110671i
$985$	−19.7566	−	5.73015i	−0.629496	−	0.182578i
$986$	−2.66198	+	0.469378i	−0.0847746	+	0.0149480i
$987$	−20.0037	−	11.1201i	−0.636723	−	0.353957i
$988$	1.21972	+	13.9415i	0.0388045	+	0.443537i
$989$	17.3032	+	29.9701i	0.550211	+	0.952993i
$990$	−3.50560	−	35.2077i	−0.111415	−	1.11898i
$991$	−3.57818	+	6.19759i	−0.113665	+	0.196873i	−0.917245	−	0.398323i	$-0.869592\pi$
$991$	−3.57818	+	6.19759i	−0.113665	+	0.196873i	0.803581	+	0.595196i	$0.202926\pi$
$992$	−9.94469	−	4.63728i	−0.315744	−	0.147234i
$993$	−17.8315	−	20.5634i	−0.565865	−	0.652558i
$994$	−7.59087	−	9.04645i	−0.240768	−	0.286936i
$995$	44.4434	+	0.910901i	1.40895	+	0.0288775i
$996$	−3.38628	−	4.67279i	−0.107298	−	0.148063i
$997$	25.6591	+	36.6449i	0.812631	+	1.16056i	0.984491	+	0.175436i	$0.0561334\pi$
$997$	25.6591	+	36.6449i	0.812631	+	1.16056i	−0.171860	+	0.985121i	$0.554978\pi$
$998$	−27.2102	+	27.2102i	−0.861323	+	0.861323i
$999$	−34.5076	−	31.3000i	−1.09177	−	0.990290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.r.a.83.6	✓	216
3.2	odd	2		810.2.s.a.413.11		216
5.2	odd	4	inner	270.2.r.a.137.9	yes	216
15.2	even	4		810.2.s.a.737.13		216
27.13	even	9		810.2.s.a.233.13		216
27.14	odd	18	inner	270.2.r.a.203.9	yes	216
135.67	odd	36		810.2.s.a.557.11		216
135.122	even	36	inner	270.2.r.a.257.6	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.6	✓	216	1.1	even	1	trivial
270.2.r.a.137.9	yes	216	5.2	odd	4	inner
270.2.r.a.203.9	yes	216	27.14	odd	18	inner
270.2.r.a.257.6	yes	216	135.122	even	36	inner
810.2.s.a.233.13		216	27.13	even	9
810.2.s.a.413.11		216	3.2	odd	2
810.2.s.a.557.11		216	135.67	odd	36
810.2.s.a.737.13		216	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 + 0.573576i) q^{2} +(0.618740 + 1.61776i) q^{3} +(0.342020 - 0.939693i) q^{4} +(1.91317 + 1.15748i) q^{5} +(-1.43475 - 0.970300i) q^{6} +(-0.957323 + 2.05299i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.23432 + 2.00195i) q^{9} +(-2.23108 + 0.149199i) q^{10} +(3.39033 - 4.04043i) q^{11} +(1.73182 - 0.0281171i) q^{12} +(-2.24888 + 3.21174i) q^{13} +(-0.393351 - 2.23081i) q^{14} +(-0.688774 + 3.81125i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(0.889884 - 3.32109i) q^{17} +(0.681979 - 2.92146i) q^{18} +(3.09115 + 1.78467i) q^{19} +(1.74202 - 1.40191i) q^{20} +(-3.91358 - 0.278459i) q^{21} +(-0.459695 + 5.25434i) q^{22} +(-4.68275 + 2.18360i) q^{23} +(-1.40250 + 1.01636i) q^{24} +(2.32048 + 4.42893i) q^{25} -3.92081i q^{26} +(-4.62115 - 2.37592i) q^{27} +(1.60175 + 1.60175i) q^{28} +(-0.136517 + 0.774225i) q^{29} +(-1.62183 - 3.51705i) q^{30} +(-10.3110 - 3.75290i) q^{31} +(0.996195 + 0.0871557i) q^{32} +(8.63420 + 2.98477i) q^{33} +(1.17595 + 3.23090i) q^{34} +(-4.20782 + 2.81964i) q^{35} +(1.11703 + 2.78428i) q^{36} +(8.66041 + 2.32055i) q^{37} +(-3.55576 + 0.311089i) q^{38} +(-6.58730 - 1.65093i) q^{39} +(-0.622874 + 2.14756i) q^{40} +(2.74726 - 0.484417i) q^{41} +(3.36554 - 2.01664i) q^{42} +(-0.583752 - 6.67232i) q^{43} +(-2.63721 - 4.56777i) q^{44} +(-6.59187 + 1.24389i) q^{45} +(2.58342 - 4.47461i) q^{46} +(5.28675 + 2.46525i) q^{47} +(0.565897 - 1.63700i) q^{48} +(1.20123 + 1.43157i) q^{49} +(-4.44115 - 2.29699i) q^{50} +(5.92335 - 0.615269i) q^{51} +(2.24888 + 3.21174i) q^{52} +(9.14166 - 9.14166i) q^{53} +(5.14819 - 0.704340i) q^{54} +(11.1630 - 3.80582i) q^{55} +(-2.23081 - 0.393351i) q^{56} +(-0.974567 + 6.10499i) q^{57} +(-0.332249 - 0.712510i) q^{58} +(8.39725 - 7.04613i) q^{59} +(3.34582 + 1.95076i) q^{60} +(1.73115 - 0.630087i) q^{61} +(10.5989 - 2.83996i) q^{62} +(-1.97101 - 6.50355i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-8.02003 + 3.54158i) q^{65} +(-8.78472 + 2.50739i) q^{66} +(-2.63797 - 1.84712i) q^{67} +(-2.81645 - 1.97210i) q^{68} +(-6.42995 - 6.22450i) q^{69} +(1.82957 - 4.72322i) q^{70} +(4.51486 - 2.60666i) q^{71} +(-2.51202 - 1.64005i) q^{72} +(-3.63280 + 0.973406i) q^{73} +(-8.42520 + 3.06652i) q^{74} +(-5.72919 + 6.49434i) q^{75} +(2.73428 - 2.29433i) q^{76} +(5.04932 + 10.8283i) q^{77} +(6.34294 - 2.42596i) q^{78} +(-6.60413 - 1.16449i) q^{79} +(-0.721563 - 2.11645i) q^{80} +(0.984394 - 8.94600i) q^{81} +(-1.97258 + 1.97258i) q^{82} +(-1.91102 - 2.72922i) q^{83} +(-1.60019 + 3.58232i) q^{84} +(5.54661 - 5.32381i) q^{85} +(4.30526 + 5.13081i) q^{86} +(-1.33698 + 0.258192i) q^{87} +(4.78024 + 2.22906i) q^{88} +(1.05755 - 1.83173i) q^{89} +(4.68627 - 4.79988i) q^{90} +(-4.44074 - 7.69159i) q^{91} +(0.450320 + 5.14718i) q^{92} +(-0.308522 - 19.0029i) q^{93} +(-5.74466 + 1.01294i) q^{94} +(3.84818 + 6.99233i) q^{95} +(0.475388 + 1.66553i) q^{96} +(11.4669 - 1.00322i) q^{97} +(-1.80510 - 0.483676i) q^{98} +(0.513663 + 15.8149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more