LMFDB - Embedded newform 135.2.q.a.122.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,2,Mod(2,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.6
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08817 - 0.761943i) q^{2} +(0.660916 - 1.60100i) q^{3} +(-0.0804885 - 0.221140i) q^{4} +(1.23426 - 1.86457i) q^{5} +(-1.93906 + 1.23857i) q^{6} +(0.827388 + 1.77434i) q^{7} +(-0.768546 + 2.86825i) q^{8} +(-2.12638 - 2.11625i) q^{9} +(-2.76377 + 1.08853i) q^{10} +(-2.76562 - 3.29594i) q^{11} +(-0.407241 - 0.0172933i) q^{12} +(2.90740 + 4.15220i) q^{13} +(0.451609 - 2.56120i) q^{14} +(-2.16943 - 3.20836i) q^{15} +(2.66120 - 2.23301i) q^{16} +(-0.828434 - 3.09176i) q^{17} +(0.701399 + 3.92301i) q^{18} +(-0.776109 + 0.448087i) q^{19} +(-0.511675 - 0.122868i) q^{20} +(3.38755 - 0.151957i) q^{21} +(0.498142 + 5.69379i) q^{22} +(5.07230 + 2.36525i) q^{23} +(4.08412 + 3.12611i) q^{24} +(-1.95322 - 4.60271i) q^{25} -6.73356i q^{26} +(-4.79346 + 2.00567i) q^{27} +(0.325783 - 0.325783i) q^{28} +(1.14702 + 6.50507i) q^{29} +(-0.0838887 + 5.14422i) q^{30} +(2.27652 - 0.828586i) q^{31} +(1.31900 - 0.115398i) q^{32} +(-7.10463 + 2.24941i) q^{33} +(-1.45427 + 3.99557i) q^{34} +(4.32959 + 0.647269i) q^{35} +(-0.296839 + 0.640563i) q^{36} +(6.96604 - 1.86654i) q^{37} +(1.18595 + 0.103757i) q^{38} +(8.56920 - 1.91049i) q^{39} +(4.39947 + 4.97316i) q^{40} +(8.33680 + 1.47000i) q^{41} +(-3.80200 - 2.41576i) q^{42} +(0.112459 - 1.28541i) q^{43} +(-0.506265 + 0.876877i) q^{44} +(-6.57039 + 1.35279i) q^{45} +(-3.71732 - 6.43859i) q^{46} +(-7.46943 + 3.48305i) q^{47} +(-1.81622 - 5.73641i) q^{48} +(2.03580 - 2.42617i) q^{49} +(-1.38157 + 6.49676i) q^{50} +(-5.49742 - 0.717071i) q^{51} +(0.684206 - 0.977148i) q^{52} +(-0.947342 - 0.947342i) q^{53} +(6.74430 + 1.46984i) q^{54} +(-9.55899 + 1.08866i) q^{55} +(-5.72514 + 1.00950i) q^{56} +(0.204443 + 1.53869i) q^{57} +(3.70835 - 7.95258i) q^{58} +(-3.72879 - 3.12883i) q^{59} +(-0.534885 + 0.737984i) q^{60} +(-7.90101 - 2.87573i) q^{61} +(-3.10857 - 0.832940i) q^{62} +(1.99560 - 5.52388i) q^{63} +(-7.54029 - 4.35339i) q^{64} +(11.3305 - 0.296169i) q^{65} +(9.44496 + 2.96559i) q^{66} +(-7.90560 + 5.53556i) q^{67} +(-0.617033 + 0.432051i) q^{68} +(7.13912 - 6.55750i) q^{69} +(-4.21814 - 4.00324i) q^{70} +(4.92123 + 2.84127i) q^{71} +(7.70415 - 4.47256i) q^{72} +(4.93694 + 1.32285i) q^{73} +(-9.00242 - 3.27661i) q^{74} +(-8.65984 + 0.0851040i) q^{75} +(0.161558 + 0.135563i) q^{76} +(3.55988 - 7.63418i) q^{77} +(-10.7804 - 4.45032i) q^{78} +(-0.410612 + 0.0724019i) q^{79} +(-0.879000 - 7.71810i) q^{80} +(0.0429919 + 8.99990i) q^{81} +(-7.95178 - 7.95178i) q^{82} +(-5.31732 + 7.59392i) q^{83} +(-0.306263 - 0.736893i) q^{84} +(-6.78729 - 2.27135i) q^{85} +(-1.10179 + 1.31306i) q^{86} +(11.1727 + 2.46293i) q^{87} +(11.5791 - 5.39942i) q^{88} +(-0.974450 - 1.68780i) q^{89} +(8.18043 + 3.53420i) q^{90} +(-4.96186 + 8.59420i) q^{91} +(0.114791 - 1.31207i) q^{92} +(0.178025 - 4.19233i) q^{93} +(10.7819 + 1.90114i) q^{94} +(-0.122429 + 2.00016i) q^{95} +(0.686998 - 2.18799i) q^{96} +(13.4552 + 1.17718i) q^{97} +(-4.06390 + 1.08892i) q^{98} +(-1.09426 + 12.8612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.08817	−	0.761943i	−0.769451	−	0.538775i	0.121654	−	0.992573i	$-0.461180\pi$
$2$	−1.08817	−	0.761943i	−0.769451	−	0.538775i	−0.891105	+	0.453797i	$0.850069\pi$
$3$	0.660916	−	1.60100i	0.381580	−	0.924336i
$3$	0.660916	−	1.60100i	0.381580	−	0.924336i
$4$	−0.0804885	−	0.221140i	−0.0402443	−	0.110570i
$5$	1.23426	−	1.86457i	0.551976	−	0.833860i
$5$	1.23426	−	1.86457i	0.551976	−	0.833860i
$6$	−1.93906	+	1.23857i	−0.791616	+	0.505645i
$7$	0.827388	+	1.77434i	0.312723	+	0.670638i	0.998356	−	0.0573098i	$-0.0182523\pi$
$7$	0.827388	+	1.77434i	0.312723	+	0.670638i	−0.685633	+	0.727947i	$0.740474\pi$
$8$	−0.768546	+	2.86825i	−0.271722	+	1.01408i
$9$	−2.12638	−	2.11625i	−0.708794	−	0.705416i
$10$	−2.76377	+	1.08853i	−0.873982	+	0.344223i
$11$	−2.76562	−	3.29594i	−0.833867	−	0.993764i	−0.999971	−	0.00765542i	$-0.997563\pi$
$11$	−2.76562	−	3.29594i	−0.833867	−	0.993764i	0.166104	−	0.986108i	$-0.446881\pi$
$12$	−0.407241	−	0.0172933i	−0.117560	−	0.00499215i
$13$	2.90740	+	4.15220i	0.806368	+	1.15161i	0.985814	+	0.167844i	$0.0536806\pi$
$13$	2.90740	+	4.15220i	0.806368	+	1.15161i	−0.179446	+	0.983768i	$0.557431\pi$
$14$	0.451609	−	2.56120i	0.120698	−	0.684510i
$15$	−2.16943	−	3.20836i	−0.560144	−	0.828395i
$16$	2.66120	−	2.23301i	0.665301	−	0.558253i
$17$	−0.828434	−	3.09176i	−0.200925	−	0.749861i	−0.990653	−	0.136405i	$-0.956445\pi$
$17$	−0.828434	−	3.09176i	−0.200925	−	0.749861i	0.789729	−	0.613456i	$-0.210221\pi$
$18$	0.701399	+	3.92301i	0.165321	+	0.924663i
$19$	−0.776109	+	0.448087i	−0.178052	+	0.102798i	−0.586377	−	0.810038i	$-0.699446\pi$
$19$	−0.776109	+	0.448087i	−0.178052	+	0.102798i	0.408325	+	0.912836i	$0.366113\pi$
$20$	−0.511675	−	0.122868i	−0.114414	−	0.0274740i
$21$	3.38755	−	0.151957i	0.739223	−	0.0331597i
$22$	0.498142	+	5.69379i	0.106204	+	1.21392i
$23$	5.07230	+	2.36525i	1.05765	+	0.493189i	0.872040	−	0.489435i	$-0.162797\pi$
$23$	5.07230	+	2.36525i	1.05765	+	0.493189i	0.185607	+	0.982624i	$0.440575\pi$
$24$	4.08412	+	3.12611i	0.833667	+	0.638115i
$25$	−1.95322	−	4.60271i	−0.390645	−	0.920541i
$26$		−	6.73356i		−	1.32056i
$27$	−4.79346	+	2.00567i	−0.922503	+	0.385991i
$28$	0.325783	−	0.325783i	0.0615672	−	0.0615672i
$29$	1.14702	+	6.50507i	0.212996	+	1.20796i	0.884350	+	0.466825i	$0.154602\pi$
$29$	1.14702	+	6.50507i	0.212996	+	1.20796i	−0.671354	+	0.741137i	$0.734287\pi$
$30$	−0.0838887	+	5.14422i	−0.0153159	+	0.939201i
$31$	2.27652	−	0.828586i	0.408875	−	0.148818i	−0.129390	−	0.991594i	$-0.541302\pi$
$31$	2.27652	−	0.828586i	0.408875	−	0.148818i	0.538266	+	0.842775i	$0.319080\pi$
$32$	1.31900	−	0.115398i	0.233169	−	0.0203996i
$33$	−7.10463	+	2.24941i	−1.23676	+	0.391573i
$34$	−1.45427	+	3.99557i	−0.249405	+	0.685235i
$35$	4.32959	+	0.647269i	0.731834	+	0.109408i
$36$	−0.296839	+	0.640563i	−0.0494731	+	0.106760i
$37$	6.96604	−	1.86654i	1.14521	−	0.306858i	0.364166	−	0.931334i	$-0.381354\pi$
$37$	6.96604	−	1.86654i	1.14521	−	0.306858i	0.781044	+	0.624476i	$0.214688\pi$
$38$	1.18595	+	0.103757i	0.192387	+	0.0168317i
$39$	8.56920	−	1.91049i	1.37217	−	0.305922i
$40$	4.39947	+	4.97316i	0.695617	+	0.786326i
$41$	8.33680	+	1.47000i	1.30199	+	0.229576i	0.781292	−	0.624166i	$-0.214561\pi$
$41$	8.33680	+	1.47000i	1.30199	+	0.229576i	0.520697	+	0.853742i	$0.325672\pi$
$42$	−3.80200	−	2.41576i	−0.586662	−	0.372761i
$43$	0.112459	−	1.28541i	0.0171499	−	0.196024i	−0.982787	−	0.184745i	$-0.940854\pi$
$43$	0.112459	−	1.28541i	0.0171499	−	0.196024i	0.999936	−	0.0112790i	$-0.00359030\pi$
$44$	−0.506265	+	0.876877i	−0.0763223	+	0.132194i
$45$	−6.57039	+	1.35279i	−0.979455	+	0.201662i
$46$	−3.71732	−	6.43859i	−0.548090	−	0.949319i
$47$	−7.46943	+	3.48305i	−1.08953	+	0.508055i	−0.882516	−	0.470283i	$-0.844152\pi$
$47$	−7.46943	+	3.48305i	−1.08953	+	0.508055i	−0.207013	+	0.978338i	$0.566374\pi$
$48$	−1.81622	−	5.73641i	−0.262148	−	0.827979i
$49$	2.03580	−	2.42617i	0.290829	−	0.346596i
$50$	−1.38157	+	6.49676i	−0.195383	+	0.918781i
$51$	−5.49742	−	0.717071i	−0.769792	−	0.100410i
$52$	0.684206	−	0.977148i	0.0948823	−	0.135506i
$53$	−0.947342	−	0.947342i	−0.130127	−	0.130127i	0.639043	−	0.769171i	$-0.279330\pi$
$53$	−0.947342	−	0.947342i	−0.130127	−	0.130127i	−0.769171	+	0.639043i	$0.779330\pi$
$54$	6.74430	+	1.46984i	0.917783	+	0.200021i
$55$	−9.55899	+	1.08866i	−1.28893	+	0.146794i
$56$	−5.72514	+	1.00950i	−0.765054	+	0.134900i
$57$	0.204443	+	1.53869i	0.0270791	+	0.203805i
$58$	3.70835	−	7.95258i	0.486930	−	1.04422i
$59$	−3.72879	−	3.12883i	−0.485447	−	0.407339i	0.366944	−	0.930243i	$-0.380404\pi$
$59$	−3.72879	−	3.12883i	−0.485447	−	0.407339i	−0.852391	+	0.522904i	$0.824849\pi$
$60$	−0.534885	+	0.737984i	−0.0690533	+	0.0952734i
$61$	−7.90101	−	2.87573i	−1.01162	−	0.368200i	−0.217566	−	0.976046i	$-0.569812\pi$
$61$	−7.90101	−	2.87573i	−1.01162	−	0.368200i	−0.794055	+	0.607846i	$0.792034\pi$
$62$	−3.10857	−	0.832940i	−0.394789	−	0.105783i
$63$	1.99560	−	5.52388i	0.251422	−	0.695944i
$64$	−7.54029	−	4.35339i	−0.942536	−	0.544173i
$65$	11.3305	−	0.296169i	1.40538	−	0.0367352i
$66$	9.44496	+	2.96559i	1.16259	+	0.365039i
$67$	−7.90560	+	5.53556i	−0.965822	+	0.676276i	−0.946217	−	0.323532i	$-0.895130\pi$
$67$	−7.90560	+	5.53556i	−0.965822	+	0.676276i	−0.0196049	+	0.999808i	$0.506241\pi$
$68$	−0.617033	+	0.432051i	−0.0748262	+	0.0523939i
$69$	7.13912	−	6.55750i	0.859449	−	0.789430i
$70$	−4.21814	−	4.00324i	−0.504164	−	0.478478i
$71$	4.92123	+	2.84127i	0.584043	+	0.337197i	0.762738	−	0.646707i	$-0.223854\pi$
$71$	4.92123	+	2.84127i	0.584043	+	0.337197i	−0.178696	+	0.983904i	$0.557188\pi$
$72$	7.70415	−	4.47256i	0.907943	−	0.527097i
$73$	4.93694	+	1.32285i	0.577825	+	0.154828i	0.535883	−	0.844292i	$-0.319979\pi$
$73$	4.93694	+	1.32285i	0.577825	+	0.154828i	0.0419419	+	0.999120i	$0.486646\pi$
$74$	−9.00242	−	3.27661i	−1.04651	−	0.380898i
$75$	−8.65984	+	0.0851040i	−0.999952	+	0.00982697i
$76$	0.161558	+	0.135563i	0.0185320	+	0.0155502i
$77$	3.55988	−	7.63418i	0.405686	−	0.869996i
$78$	−10.7804	−	4.45032i	−1.22064	−	0.503899i
$79$	−0.410612	+	0.0724019i	−0.0461974	+	0.00814585i	−0.196699	−	0.980464i	$-0.563022\pi$
$79$	−0.410612	+	0.0724019i	−0.0461974	+	0.00814585i	0.150502	+	0.988610i	$0.451911\pi$
$80$	−0.879000	−	7.71810i	−0.0982752	−	0.862910i
$81$	0.0429919	+	8.99990i	0.00477688	+	0.999989i
$82$	−7.95178	−	7.95178i	−0.878127	−	0.878127i
$83$	−5.31732	+	7.59392i	−0.583652	+	0.833541i	−0.997030	−	0.0770185i	$-0.975460\pi$
$83$	−5.31732	+	7.59392i	−0.583652	+	0.833541i	0.413378	+	0.910560i	$0.364349\pi$
$84$	−0.306263	−	0.736893i	−0.0334160	−	0.0804016i
$85$	−6.78729	−	2.27135i	−0.736185	−	0.246362i
$86$	−1.10179	+	1.31306i	−0.118809	+	0.141591i
$87$	11.1727	+	2.46293i	1.19784	+	0.264054i
$88$	11.5791	−	5.39942i	1.23434	−	0.575580i
$89$	−0.974450	−	1.68780i	−0.103292	−	0.178906i	0.809747	−	0.586779i	$-0.199604\pi$
$89$	−0.974450	−	1.68780i	−0.103292	−	0.178906i	−0.913039	+	0.407872i	$0.866271\pi$
$90$	8.18043	+	3.53420i	0.862293	+	0.372537i
$91$	−4.96186	+	8.59420i	−0.520144	+	0.900917i
$92$	0.114791	−	1.31207i	0.0119678	−	0.136792i
$93$	0.178025	−	4.19233i	0.0184604	−	0.434724i
$94$	10.7819	+	1.90114i	1.11207	+	0.196087i
$95$	−0.122429	+	2.00016i	−0.0125610	+	0.205212i
$96$	0.686998	−	2.18799i	0.0701164	−	0.223310i
$97$	13.4552	+	1.17718i	1.36617	+	0.119524i	0.746524	−	0.665359i	$-0.231721\pi$
$97$	13.4552	+	1.17718i	1.36617	+	0.119524i	0.619644	+	0.784883i	$0.287277\pi$
$98$	−4.06390	+	1.08892i	−0.410516	+	0.109997i
$99$	−1.09426	+	12.8612i	−0.109977	+	1.29260i
$100$	−0.860633	+	0.802402i	−0.0860633	+	0.0802402i
$101$	−1.45521	+	3.99814i	−0.144798	+	0.397830i	−0.990797	−	0.135354i	$-0.956783\pi$
$101$	−1.45521	+	3.99814i	−0.144798	+	0.397830i	0.845999	+	0.533185i	$0.179005\pi$
$102$	5.43575	+	4.96901i	0.538219	+	0.492006i
$103$	−13.3028	+	1.16385i	−1.31077	+	0.114677i	−0.721022	−	0.692912i	$-0.756327\pi$
$103$	−13.3028	+	1.16385i	−1.31077	+	0.114677i	−0.589745	+	0.807589i	$0.700772\pi$
$104$	−14.1440	+	5.14800i	−1.38694	+	0.504803i
$105$	3.89777	−	6.50386i	0.380383	−	0.634712i
$106$	0.309046	+	1.75269i	0.0300172	+	0.170236i
$107$	−10.2616	+	10.2616i	−0.992026	+	0.992026i	−0.999968	−	0.00794276i	$-0.997472\pi$
$107$	−10.2616	+	10.2616i	−0.992026	+	0.992026i	0.00794276	+	0.999968i	$0.497472\pi$
$108$	0.829353	+	0.898596i	0.0798045	+	0.0864674i
$109$			14.3459i			1.37409i	0.726615	+	0.687045i	$0.241092\pi$
$109$			14.3459i			1.37409i	−0.726615	+	0.687045i	$0.758908\pi$
$110$	11.2313	+	6.09877i	1.07086	+	0.581495i
$111$	1.61563	−	12.3862i	0.153349	−	1.17565i
$112$	6.16397	+	2.87431i	0.582441	+	0.271597i
$113$	1.18867	+	13.5865i	0.111821	+	1.27811i	0.820116	+	0.572198i	$0.193909\pi$
$113$	1.18867	+	13.5865i	0.111821	+	1.27811i	−0.708295	+	0.705916i	$0.750535\pi$
$114$	0.949930	−	1.83013i	0.0889691	−	0.171408i
$115$	10.6707	−	6.53832i	0.995046	−	0.609701i
$116$	1.34621	−	0.777236i	0.124993	−	0.0721646i
$117$	2.60484	−	14.9819i	0.240817	−	1.38508i
$118$	1.67356	+	6.24582i	0.154064	+	0.574974i
$119$	4.80039	−	4.02801i	0.440051	−	0.369247i
$120$	10.8697	−	3.75669i	0.992263	−	0.342937i
$121$	−1.30443	+	7.39778i	−0.118584	+	0.672525i
$122$	6.40648	+	9.14940i	0.580016	+	0.828348i
$123$	7.86339	−	12.3756i	0.709018	−	1.11587i
$124$	−0.366468	−	0.436739i	−0.0329098	−	0.0392204i
$125$	−10.9928	−	2.03900i	−0.983229	−	0.182374i
$126$	−6.38043	+	4.49038i	−0.568414	+	0.400035i
$127$	0.931838	−	3.47767i	0.0826872	−	0.308593i	−0.912179	−	0.409792i	$-0.865601\pi$
$127$	0.931838	−	3.47767i	0.0826872	−	0.308593i	0.994866	+	0.101199i	$0.0322679\pi$
$128$	3.76894	+	8.08251i	0.333130	+	0.714400i
$129$	−1.98362	−	1.02960i	−0.174648	−	0.0906510i
$130$	−12.5552	−	8.31094i	−1.10116	−	0.728918i
$131$	0.189922	+	0.521807i	0.0165936	+	0.0455905i	0.947713	−	0.319124i	$-0.103389\pi$
$131$	0.189922	+	0.521807i	0.0165936	+	0.0455905i	−0.931119	+	0.364715i	$0.881167\pi$
$132$	1.06928	+	1.39007i	0.0930687	+	0.120990i
$133$	−1.43720	−	1.00634i	−0.124621	−	0.0872607i
$134$	12.8204			1.10751
$135$	−2.17666	+	11.4132i	−0.187337	+	0.982296i
$136$	9.50463			0.815015
$137$	−4.95031	−	3.46624i	−0.422934	−	0.296141i	0.342668	−	0.939457i	$-0.388670\pi$
$137$	−4.95031	−	3.46624i	−0.422934	−	0.296141i	−0.765601	+	0.643315i	$0.777558\pi$
$138$	−12.7650	+	1.69606i	−1.08663	+	0.144378i
$139$	−6.33390	−	17.4022i	−0.537234	−	1.47604i	−0.850295	−	0.526306i	$-0.823577\pi$
$139$	−6.33390	−	17.4022i	−0.537234	−	1.47604i	0.313061	−	0.949733i	$-0.398646\pi$
$140$	−0.205345	−	1.00954i	−0.0173548	−	0.0853221i
$141$	0.639692	+	14.2605i	0.0538718	+	1.20095i
$142$	−3.19024	−	6.84148i	−0.267719	−	0.574125i
$143$	5.64463	−	21.0660i	0.472027	−	1.76163i
$144$	−10.3843	−	0.883525i	−0.865362	−	0.0736271i
$145$	13.5449	+	5.89023i	1.12484	+	0.489157i
$146$	−4.36428	−	5.20115i	−0.361190	−	0.430450i
$147$	−2.53880	−	4.86281i	−0.209397	−	0.401078i
$148$	−0.973455	−	1.39024i	−0.0800175	−	0.114277i
$149$	1.50609	−	8.54145i	0.123384	−	0.699743i	−0.858871	−	0.512192i	$-0.828834\pi$
$149$	1.50609	−	8.54145i	0.123384	−	0.699743i	0.982255	−	0.187551i	$-0.0600551\pi$
$150$	9.48820	+	6.50570i	0.774708	+	0.531188i
$151$	−12.2052	+	10.2414i	−0.993244	+	0.833431i	−0.986034	−	0.166543i	$-0.946740\pi$
$151$	−12.2052	+	10.2414i	−0.993244	+	0.833431i	−0.00721007	+	0.999974i	$0.502295\pi$
$152$	−0.688750	−	2.57045i	−0.0558650	−	0.208491i
$153$	−4.78136	+	8.32742i	−0.386550	+	0.673232i
$154$	−9.69056	+	5.59485i	−0.780887	+	0.450846i
$155$	1.26486	−	5.26742i	0.101596	−	0.423089i
$156$	−1.11221	−	1.74122i	−0.0890479	−	0.139410i
$157$	1.15698	+	13.2243i	0.0923367	+	1.05541i	0.891112	+	0.453784i	$0.149926\pi$
$157$	1.15698	+	13.2243i	0.0923367	+	1.05541i	−0.798775	+	0.601630i	$0.794518\pi$
$158$	0.501981	+	0.234077i	0.0399354	+	0.0186222i
$159$	−2.14280	+	0.890578i	−0.169935	+	0.0706274i
$160$	1.41282	−	2.60180i	0.111693	−	0.205690i
$161$			10.9570i			0.863530i
$162$	6.81063	−	9.82616i	0.535094	−	0.772016i
$163$	5.24760	−	5.24760i	0.411024	−	0.411024i	−0.471071	−	0.882095i	$-0.656133\pi$
$163$	5.24760	−	5.24760i	0.411024	−	0.411024i	0.882095	+	0.471071i	$0.156133\pi$
$164$	−0.345940	−	1.96192i	−0.0270133	−	0.153200i
$165$	−4.57475	+	16.0234i	−0.356144	+	1.24742i
$166$	11.5723	−	4.21196i	0.898183	−	0.326912i
$167$	8.20120	−	0.717512i	0.634628	−	0.0555227i	0.234698	−	0.972068i	$-0.424590\pi$
$167$	8.20120	−	0.717512i	0.634628	−	0.0555227i	0.399930	+	0.916546i	$0.369034\pi$
$168$	−2.16763	+	9.83313i	−0.167237	+	0.758642i
$169$	−4.34150	+	11.9282i	−0.333962	+	0.917553i
$170$	5.65507	+	7.64314i	0.433724	+	0.586202i
$171$	2.59856	+	0.689635i	0.198717	+	0.0527377i
$172$	−0.293309	+	0.0785918i	−0.0223646	+	0.00599257i
$173$	−7.74393	−	0.677506i	−0.588760	−	0.0515098i	−0.211116	−	0.977461i	$-0.567710\pi$
$173$	−7.74393	−	0.677506i	−0.588760	−	0.0515098i	−0.377643	+	0.925951i	$0.623265\pi$
$174$	−10.2811	−	11.1930i	−0.779412	−	0.848542i
$175$	6.55069	−	7.27391i	0.495186	−	0.549856i
$176$	−14.7198	−	2.59549i	−1.10954	−	0.195643i
$177$	−7.47366	+	3.90189i	−0.561755	+	0.293284i
$178$	−0.225641	+	2.57908i	−0.0169125	+	0.193310i
$179$	2.19929	−	3.80928i	0.164382	−	0.284719i	−0.772053	−	0.635558i	$-0.780770\pi$
$179$	2.19929	−	3.80928i	0.164382	−	0.284719i	0.936436	+	0.350839i	$0.114104\pi$
$180$	0.827997	+	1.34409i	0.0617153	+	0.100183i
$181$	−2.85830	−	4.95072i	−0.212456	−	0.367984i	0.740027	−	0.672577i	$-0.234813\pi$
$181$	−2.85830	−	4.95072i	−0.212456	−	0.367984i	−0.952483	+	0.304593i	$0.901479\pi$
$182$	11.9476	−	5.57127i	0.885617	−	0.412970i
$183$	−9.82594	+	10.7489i	−0.726355	+	0.794580i
$184$	−10.6824	+	12.7308i	−0.787519	+	0.938529i
$185$	5.11758	−	15.2924i	0.376252	−	1.12432i
$186$	−3.38804	+	4.42631i	−0.248423	+	0.324553i
$187$	−7.89911	+	11.2811i	−0.577640	+	0.824956i
$188$	1.37145	+	1.37145i	0.100023	+	0.100023i
$189$	−7.52479	−	6.84577i	−0.547348	−	0.497957i
$190$	1.65723	−	2.08323i	0.120228	−	0.151133i
$191$	14.2067	−	2.50503i	1.02796	−	0.181258i	0.365860	−	0.930670i	$-0.380775\pi$
$191$	14.2067	−	2.50503i	1.02796	−	0.181258i	0.662104	+	0.749412i	$0.269664\pi$
$192$	−11.9532	+	9.19475i	−0.862651	+	0.663574i
$193$	7.33254	−	15.7247i	0.527808	−	1.13189i	−0.443981	−	0.896036i	$-0.646434\pi$
$193$	7.33254	−	15.7247i	0.527808	−	1.13189i	0.971789	−	0.235852i	$-0.0757879\pi$
$194$	−13.7446	−	11.5331i	−0.986802	−	0.828025i
$195$	7.01436	−	18.3359i	0.502309	−	1.31306i
$196$	−0.700384	−	0.254919i	−0.0500274	−	0.0182085i
$197$	−13.1476	−	3.52289i	−0.936727	−	0.250995i	−0.242006	−	0.970275i	$-0.577805\pi$
$197$	−13.1476	−	3.52289i	−0.936727	−	0.250995i	−0.694721	+	0.719280i	$0.744472\pi$
$198$	10.9902	−	13.1613i	0.781041	−	0.935336i
$199$	−7.78555	−	4.49499i	−0.551903	−	0.318641i	0.197986	−	0.980205i	$-0.436560\pi$
$199$	−7.78555	−	4.49499i	−0.551903	−	0.318641i	−0.749889	+	0.661564i	$0.769893\pi$
$200$	14.7029	−	2.06495i	1.03965	−	0.146014i
$201$	3.63748	+	16.3154i	0.256568	+	1.15080i
$202$	4.62987	−	3.24187i	0.325756	−	0.228097i
$203$	−10.5932	+	7.41743i	−0.743496	+	0.520601i
$204$	0.283906	+	1.27342i	0.0198774	+	0.0891570i
$205$	13.0307	−	13.7302i	0.910101	−	0.958956i
$206$	15.3625	+	8.86955i	1.07036	+	0.617971i
$207$	−5.78018	−	15.7637i	−0.401750	−	1.09565i
$208$	17.0091	+	4.55757i	1.17937	+	0.316011i
$209$	3.62329	+	1.31877i	0.250628	+	0.0912212i
$210$	−9.19700	+	4.10742i	−0.634653	+	0.283439i
$211$	−14.3607	−	12.0500i	−0.988631	−	0.829559i	−0.00326162	−	0.999995i	$-0.501038\pi$
$211$	−14.3607	−	12.0500i	−0.988631	−	0.829559i	−0.985369	+	0.170435i	$0.945483\pi$
$212$	−0.133245	+	0.285746i	−0.00915134	+	0.0196251i
$213$	7.80139	−	6.00103i	0.534542	−	0.411184i
$214$	18.9851	−	3.34758i	1.29779	−	0.228836i
$215$	−2.25794	−	1.79622i	−0.153990	−	0.122501i
$216$	−2.06876	−	15.2903i	−0.140762	−	1.04037i
$217$	3.35376	+	3.35376i	0.227668	+	0.227668i
$218$	10.9308	−	15.6108i	0.740326	−	1.05729i
$219$	5.38077	−	7.02973i	0.363599	−	0.475025i
$220$	1.01014	+	2.02626i	0.0681033	+	0.136610i
$221$	10.4290	−	12.4288i	0.701530	−	0.836051i
$222$	−11.1957	+	12.2473i	−0.751405	+	0.821984i
$223$	−15.0323	+	7.00968i	−1.00664	+	0.469403i	−0.854775	−	0.518999i	$-0.826305\pi$
$223$	−15.0323	+	7.00968i	−1.00664	+	0.469403i	−0.151862	+	0.988402i	$0.548527\pi$
$224$	1.29608	+	2.24488i	0.0865981	+	0.149992i
$225$	−5.58717	+	13.9206i	−0.372478	+	0.928041i
$226$	9.05870	−	15.6901i	0.602576	−	1.04369i
$227$	−1.57696	+	18.0248i	−0.104667	+	1.19634i	0.744281	+	0.667867i	$0.232793\pi$
$227$	−1.57696	+	18.0248i	−0.104667	+	1.19634i	−0.848947	+	0.528478i	$0.822763\pi$
$228$	0.323812	−	0.169058i	0.0214450	−	0.0111961i
$229$	18.7074	+	3.29862i	1.23622	+	0.217979i	0.753294	−	0.657684i	$-0.228464\pi$
$229$	18.7074	+	3.29862i	1.23622	+	0.217979i	0.482924	+	0.875662i	$0.339575\pi$
$230$	−16.5933	−	1.01567i	−1.09413	−	0.0669714i
$231$	−9.86952	−	10.7449i	−0.649367	−	0.706963i
$232$	−19.5397	−	1.70951i	−1.28285	−	0.112235i
$233$	−7.30551	+	1.95750i	−0.478600	+	0.128240i	−0.490050	−	0.871694i	$-0.663022\pi$
$233$	−7.30551	+	1.95750i	−0.478600	+	0.128240i	0.0114509	+	0.999934i	$0.496355\pi$
$234$	−14.2499	+	14.3181i	−0.931544	+	0.936005i
$235$	−2.72480	+	18.2262i	−0.177747	+	1.18895i
$236$	−0.391785	+	1.07642i	−0.0255031	+	0.0700691i
$237$	−0.155464	+	0.705239i	−0.0100985	+	0.0458102i
$238$	−8.29275	+	0.725521i	−0.537539	+	0.0470286i
$239$	11.7518	−	4.27731i	0.760162	−	0.276676i	0.0672867	−	0.997734i	$-0.478566\pi$
$239$	11.7518	−	4.27731i	0.760162	−	0.276676i	0.692875	+	0.721057i	$0.256344\pi$
$240$	−12.9376	−	3.69374i	−0.835119	−	0.238430i
$241$	2.97320	+	16.8619i	0.191521	+	1.08617i	0.917287	+	0.398227i	$0.130374\pi$
$241$	2.97320	+	16.8619i	0.191521	+	1.08617i	−0.725766	+	0.687942i	$0.758514\pi$
$242$	7.05612	−	7.05612i	0.453585	−	0.453585i
$243$	14.4372	+	5.87934i	0.926148	+	0.377160i
$244$			1.97870i			0.126673i
$245$	−2.01106	−	6.79041i	−0.128482	−	0.433823i
$246$	−17.9862	+	7.47531i	−1.14676	+	0.476609i
$247$	−4.11700	−	1.91979i	−0.261958	−	0.122153i
$248$	0.626983	+	7.16645i	0.0398134	+	0.455070i
$249$	8.64354	+	13.5320i	0.547762	+	0.857553i
$250$	10.4085	+	10.5947i	0.658288	+	0.670067i
$251$	4.66370	−	2.69259i	0.294370	−	0.169955i	−0.345541	−	0.938404i	$-0.612304\pi$
$251$	4.66370	−	2.69259i	0.294370	−	0.169955i	0.639911	+	0.768449i	$0.278971\pi$
$252$	−1.38218	+	0.00330126i	−0.0870690	+	0.000207960i
$253$	−6.23233	−	23.2594i	−0.391823	−	1.46231i
$254$	−3.66378	+	3.07428i	−0.229886	+	0.192897i
$255$	−8.12225	+	9.36526i	−0.508635	+	0.586475i
$256$	−0.966651	+	5.48215i	−0.0604157	+	0.342634i
$257$	−7.03325	−	10.0445i	−0.438722	−	0.626560i	0.537518	−	0.843252i	$-0.319362\pi$
$257$	−7.03325	−	10.0445i	−0.438722	−	0.626560i	−0.976240	+	0.216692i	$0.930473\pi$
$258$	1.37401	+	2.63178i	0.0855424	+	0.163847i
$259$	9.07550	+	10.8158i	0.563924	+	0.672059i
$260$	−0.977472	−	2.48180i	−0.0606203	−	0.153915i
$261$	11.3273	−	16.2596i	0.701145	−	1.00645i
$262$	0.190920	−	0.712524i	0.0117951	−	0.0440199i
$263$	−5.75913	−	12.3505i	−0.355123	−	0.761563i	0.644873	−	0.764289i	$-0.276910\pi$
$263$	−5.75913	−	12.3505i	−0.355123	−	0.761563i	−0.999996	+	0.00272594i	$0.999132\pi$
$264$	−0.991650	−	22.1067i	−0.0610318	−	1.36057i
$265$	−2.93565	+	0.597121i	−0.180335	+	0.0366808i
$266$	0.797143	+	2.19013i	0.0488760	+	0.134286i
$267$	−3.34619	+	0.444600i	−0.204783	+	0.0272091i
$268$	1.86045	+	1.30270i	0.113645	+	0.0795749i
$269$	12.3342			0.752028			0.376014	−	0.926614i	$-0.377294\pi$
$269$	12.3342			0.752028			0.376014	+	0.926614i	$0.377294\pi$
$270$	11.0648	−	10.7610i	0.673383	−	0.654896i
$271$	19.7578			1.20020			0.600099	−	0.799926i	$-0.295128\pi$
$271$	19.7578			1.20020			0.600099	+	0.799926i	$0.295128\pi$
$272$	−9.10856	−	6.37789i	−0.552288	−	0.386716i
$273$	10.4799	+	13.6240i	0.634273	+	0.824560i
$274$	2.74569	+	7.54371i	0.165873	+	0.455732i
$275$	−9.76837	+	19.1671i	−0.589055	+	1.15582i
$276$	−2.02475	−	1.05094i	−0.121875	−	0.0632594i
$277$	−0.856962	−	1.83776i	−0.0514898	−	0.110420i	0.878880	−	0.477044i	$-0.158292\pi$
$277$	−0.856962	−	1.83776i	−0.0514898	−	0.110420i	−0.930370	+	0.366623i	$0.880514\pi$
$278$	−6.36718	+	23.7626i	−0.381878	+	1.42519i
$279$	−6.59425	−	3.05579i	−0.394787	−	0.182946i
$280$	−5.18402	+	11.9209i	−0.309804	+	0.712410i
$281$	−16.8041	−	20.0263i	−1.00245	−	1.19467i	−0.980822	−	0.194903i	$-0.937561\pi$
$281$	−16.8041	−	20.0263i	−1.00245	−	1.19467i	−0.0216244	−	0.999766i	$-0.506884\pi$
$282$	10.1696	−	16.0053i	0.605593	−	0.953100i
$283$	1.33019	+	1.89971i	0.0790717	+	0.112926i	0.856740	−	0.515749i	$-0.172486\pi$
$283$	1.33019	+	1.89971i	0.0790717	+	0.112926i	−0.777668	+	0.628675i	$0.783597\pi$
$284$	0.232218	−	1.31697i	0.0137796	−	0.0781480i
$285$	3.12133	+	1.51795i	0.184892	+	0.0899154i
$286$	−22.1934	+	18.6225i	−1.31232	+	1.10117i
$287$	4.28949	+	16.0086i	0.253200	+	0.944956i
$288$	−3.04891	−	2.54596i	−0.179659	−	0.150022i
$289$	5.84978	−	3.37737i	0.344105	−	0.198669i
$290$	−10.2511	−	16.7300i	−0.601963	−	0.982418i
$291$	10.7774	−	20.7637i	0.631783	−	1.21719i
$292$	−0.104832	−	1.19823i	−0.00613480	−	0.0701211i
$293$	−10.9251	−	5.09445i	−0.638250	−	0.297621i	0.0764274	−	0.997075i	$-0.475649\pi$
$293$	−10.9251	−	5.09445i	−0.638250	−	0.297621i	−0.714677	+	0.699454i	$0.753426\pi$
$294$	−0.942540	+	7.22598i	−0.0549701	+	0.421427i
$295$	−10.4362	+	3.09081i	−0.607619	+	0.179954i
$296$			21.4149i			1.24471i
$297$	19.8675	+	10.2521i	1.15283	+	0.594885i
$298$	−8.14698	+	8.14698i	−0.471942	+	0.471942i
$299$	4.92621	+	27.9379i	0.284890	+	1.61569i
$300$	0.715837	+	1.90819i	0.0413289	+	0.110169i
$301$	2.37381	−	0.863996i	0.136824	−	0.0497999i
$302$	21.0846	−	1.84467i	1.21328	−	0.106149i
$303$	5.43925	+	4.97222i	0.312477	+	0.285646i
$304$	−1.06480	+	2.92551i	−0.0610704	+	0.167790i
$305$	−15.1139	+	11.1826i	−0.865418	+	0.640313i
$306$	11.5479	−	5.41851i	0.660152	−	0.309756i
$307$	22.6984	−	6.08202i	1.29547	−	0.347119i	0.455732	−	0.890117i	$-0.349378\pi$
$307$	22.6984	−	6.08202i	1.29547	−	0.347119i	0.839734	+	0.542998i	$0.182711\pi$
$308$	−1.97476	−	0.172769i	−0.112522	−	0.00984441i
$309$	−6.92874	+	22.0670i	−0.394162	+	1.25535i
$310$	−5.38985	+	4.76809i	−0.306123	+	0.270809i
$311$	3.91683	+	0.690642i	0.222103	+	0.0391627i	0.283592	−	0.958945i	$-0.408474\pi$
$311$	3.91683	+	0.690642i	0.222103	+	0.0391627i	−0.0614891	+	0.998108i	$0.519585\pi$
$312$	−1.10607	+	26.0469i	−0.0626189	+	1.47462i
$313$	−0.0797089	+	0.911077i	−0.00450541	+	0.0514971i	−0.998115	−	0.0613781i	$-0.980450\pi$
$313$	−0.0797089	+	0.911077i	−0.00450541	+	0.0514971i	0.993609	+	0.112875i	$0.0360060\pi$
$314$	8.81718	−	15.2718i	0.497582	−	0.861838i
$315$	−7.83657	−	10.5388i	−0.441541	−	0.593795i
$316$	0.0490605	+	0.0849753i	0.00275987	+	0.00478023i
$317$	23.8990	−	11.1443i	1.34230	−	0.625924i	0.387141	−	0.922021i	$-0.373463\pi$
$317$	23.8990	−	11.1443i	1.34230	−	0.625924i	0.955158	+	0.296096i	$0.0956849\pi$
$318$	3.01030	+	0.663597i	0.168809	+	0.0372127i
$319$	18.2681	−	21.7711i	1.02282	−	1.21895i
$320$	−17.4238	+	8.68618i	−0.974021	+	0.485572i
$321$	9.64673	+	23.2108i	0.538428	+	1.29550i
$322$	8.34859	−	11.9230i	0.465249	−	0.664444i
$323$	2.02833	+	2.02833i	0.112859	+	0.112859i
$324$	1.98678	−	0.733896i	0.110377	−	0.0407720i
$325$	13.4325	−	21.4921i	0.745103	−	1.19217i
$326$	−9.70865	+	1.71190i	−0.537712	+	0.0948132i
$327$	22.9678	+	9.48144i	1.27012	+	0.524325i
$328$	−10.6235	+	22.7823i	−0.586587	+	1.25794i
$329$	−12.3602	−	10.3715i	−0.681442	−	0.571798i
$330$	17.1870	−	13.9505i	0.946116	−	0.767948i
$331$	−12.0746	−	4.39481i	−0.663682	−	0.241561i	−0.0118569	−	0.999930i	$-0.503774\pi$
$331$	−12.0746	−	4.39481i	−0.663682	−	0.241561i	−0.651825	+	0.758369i	$0.725996\pi$
$332$	2.10731	+	0.564651i	0.115653	+	0.0309893i
$333$	−18.7625	−	10.7729i	−1.02818	−	0.590350i
$334$	−9.47099	−	5.46808i	−0.518229	−	0.299200i
$335$	0.563892	+	21.5728i	0.0308087	+	1.17865i
$336$	8.67563	−	7.96883i	0.473294	−	0.434735i
$337$	−6.96283	+	4.87543i	−0.379290	+	0.265581i	−0.747638	−	0.664106i	$-0.768812\pi$
$337$	−6.96283	+	4.87543i	−0.379290	+	0.265581i	0.368349	+	0.929688i	$0.379923\pi$
$338$	13.8129	−	9.67189i	0.751322	−	0.526081i
$339$	22.5376	+	7.07650i	1.22408	+	0.384343i
$340$	0.0440119	+	1.68376i	0.00238688	+	0.0913148i
$341$	−9.02697	−	5.21173i	−0.488838	−	0.282231i
$342$	−2.30221	−	2.73040i	−0.124489	−	0.147643i
$343$	19.2267	+	5.15177i	1.03814	+	0.278169i
$344$	3.60046	+	1.31046i	0.194124	+	0.0706553i
$345$	−3.41540	−	21.4050i	−0.183879	−	1.15241i
$346$	7.91047	+	6.63767i	0.425270	+	0.356844i
$347$	−2.22359	+	4.76851i	−0.119369	+	0.255987i	−0.956909	−	0.290389i	$-0.906215\pi$
$347$	−2.22359	+	4.76851i	−0.119369	+	0.255987i	0.837540	+	0.546376i	$0.183993\pi$
$348$	−0.354620	−	2.66897i	−0.0190096	−	0.143072i
$349$	−20.3047	+	3.58026i	−1.08688	+	0.191647i	−0.688258	−	0.725466i	$-0.741624\pi$
$349$	−20.3047	+	3.58026i	−1.08688	+	0.191647i	−0.398627	+	0.917113i	$0.630513\pi$
$350$	−12.6706	+	2.92398i	−0.677270	+	0.156293i
$351$	−22.2644	−	14.0721i	−1.18839	−	0.751115i
$352$	−4.02821	−	4.02821i	−0.214704	−	0.214704i
$353$	16.5268	−	23.6027i	0.879631	−	1.25624i	−0.0859911	−	0.996296i	$-0.527406\pi$
$353$	16.5268	−	23.6027i	0.879631	−	1.25624i	0.965623	−	0.259948i	$-0.0837054\pi$
$354$	11.1056	+	1.44859i	0.590257	+	0.0769918i
$355$	11.3718	−	5.66911i	0.603553	−	0.300885i
$356$	−0.294808	+	0.351339i	−0.0156248	+	0.0186209i
$357$	−3.27617	−	10.3476i	−0.173393	−	0.547652i
$358$	−5.29565	+	2.46940i	−0.279884	+	0.130512i
$359$	8.91393	+	15.4394i	0.470459	+	0.814860i	0.999429	−	0.0337810i	$-0.0107549\pi$
$359$	8.91393	+	15.4394i	0.470459	+	0.814860i	−0.528970	+	0.848641i	$0.677422\pi$
$360$	1.16950	−	19.8852i	0.0616381	−	1.04804i
$361$	−9.09844	+	15.7590i	−0.478865	+	0.829419i
$362$	−0.661859	+	7.56508i	−0.0347865	+	0.397612i
$363$	10.9817	+	6.97769i	0.576390	+	0.366234i
$364$	2.29990	+	0.405534i	0.120547	+	0.0212558i
$365$	8.55998	−	7.57252i	0.448050	−	0.396364i
$366$	18.8823	−	4.20977i	0.986994	−	0.220048i
$367$	−21.8448	−	1.91117i	−1.14029	−	0.0997623i	−0.498674	−	0.866790i	$-0.666179\pi$
$367$	−21.8448	−	1.91117i	−1.14029	−	0.0997623i	−0.641614	+	0.767028i	$0.721735\pi$
$368$	18.7800	−	5.03210i	0.978978	−	0.262316i
$369$	−14.6163	−	20.7685i	−0.760895	−	1.08117i
$370$	−17.2208	+	12.7414i	−0.895264	+	0.662396i
$371$	0.897087	−	2.46473i	0.0465744	−	0.127962i
$372$	−0.941423	+	0.298066i	−0.0488105	+	0.0154540i
$373$	−17.1932	+	1.50421i	−0.890228	+	0.0778848i	−0.523086	−	0.852280i	$-0.675219\pi$
$373$	−17.1932	+	1.50421i	−0.890228	+	0.0778848i	−0.367142	+	0.930165i	$0.619664\pi$
$374$	17.1911	−	6.25706i	0.888932	−	0.323545i
$375$	−10.5298	+	16.2519i	−0.543755	+	0.839244i
$376$	−4.24967	−	24.1011i	−0.219160	−	1.24292i
$377$	−23.6755	+	23.6755i	−1.21935	+	1.21935i
$378$	2.97215	+	13.1828i	0.152871	+	0.678051i
$379$		−	27.1687i		−	1.39556i	−0.716312	−	0.697780i	$-0.754171\pi$
$379$		−	27.1687i		−	1.39556i	0.716312	−	0.697780i	$-0.245829\pi$
$380$	0.452170	−	0.133916i	0.0231959	−	0.00686974i
$381$	−4.95187	−	3.79031i	−0.253692	−	0.194184i
$382$	−17.3680	−	8.09883i	−0.888624	−	0.414372i
$383$	−0.640436	−	7.32022i	−0.0327248	−	0.374046i	−0.994844	−	0.101417i	$-0.967662\pi$
$383$	−0.640436	−	7.32022i	−0.0327248	−	0.374046i	0.962119	−	0.272629i	$-0.0878931\pi$
$384$	15.4310	−	0.692197i	0.787461	−	0.0353235i
$385$	−9.84065	−	16.0602i	−0.501526	−	0.818502i
$386$	−19.9604	+	11.5241i	−1.01596	+	0.586562i
$387$	−2.95939	+	2.49529i	−0.150434	+	0.126843i
$388$	−0.822667	−	3.07024i	−0.0417646	−	0.155868i
$389$	−23.9421	+	20.0898i	−1.21391	+	1.01859i	−0.214792	+	0.976660i	$0.568907\pi$
$389$	−23.9421	+	20.0898i	−1.21391	+	1.01859i	−0.999120	+	0.0419334i	$0.986648\pi$
$390$	−21.6037	+	14.6080i	−1.09395	+	0.739703i
$391$	3.11072	−	17.6418i	0.157316	−	0.892182i
$392$	5.39427	+	7.70382i	0.272452	+	0.389102i
$393$	0.960934	+	0.0408056i	0.0484727	+	0.00205837i
$394$	11.6225	+	13.8512i	0.585535	+	0.697814i
$395$	−0.371802	+	0.854976i	−0.0187074	+	0.0430185i
$396$	2.93220	−	0.793192i	0.147349	−	0.0398594i
$397$	4.26857	−	15.9305i	0.214234	−	0.799531i	−0.772201	−	0.635378i	$-0.780844\pi$
$397$	4.26857	−	15.9305i	0.214234	−	0.799531i	0.986435	−	0.164153i	$-0.0524890\pi$
$398$	5.04706	+	10.8234i	0.252986	+	0.542530i
$399$	−2.56101	+	1.63585i	−0.128211	+	0.0818949i
$400$	−15.4758	−	7.88716i	−0.773792	−	0.394358i
$401$	−0.517022	−	1.42051i	−0.0258188	−	0.0709367i	0.926114	−	0.377245i	$-0.123128\pi$
$401$	−0.517022	−	1.42051i	−0.0258188	−	0.0709367i	−0.951932	+	0.306308i	$0.900906\pi$
$402$	8.47320	−	20.5254i	0.422605	−	1.02371i
$403$	10.0592	+	7.04354i	0.501085	+	0.350864i
$404$	1.00128			0.0498155
$405$	16.8340	+	11.0280i	0.836487	+	0.547987i
$406$	17.1788			0.852571
$407$	−25.4175	−	17.7975i	−1.25990	−	0.882189i
$408$	6.28176	−	15.2169i	0.310993	−	0.753348i
$409$	−8.02778	−	22.0561i	−0.396948	−	1.09061i	−0.963763	−	0.266760i	$-0.914047\pi$
$409$	−8.02778	−	22.0561i	−0.396948	−	1.09061i	0.566815	−	0.823845i	$-0.308175\pi$
$410$	−24.6412	+	5.01210i	−1.21694	+	0.247530i
$411$	−8.82118	+	5.63453i	−0.435117	+	0.277931i
$412$	1.32810	+	2.84812i	0.0654308	+	0.140317i
$413$	2.46645	−	9.20490i	0.121366	−	0.452944i
$414$	−5.72121	+	21.5577i	−0.281182	+	1.05950i
$415$	7.59644	+	19.2873i	0.372895	+	0.946779i
$416$	4.31402	+	5.14125i	0.211512	+	0.252070i
$417$	−32.0471	−	1.36086i	−1.56935	−	0.0666418i
$418$	−2.93792	−	4.19579i	−0.143698	−	0.205223i
$419$	−2.76242	+	15.6665i	−0.134953	+	0.765357i	0.839939	+	0.542680i	$0.182591\pi$
$419$	−2.76242	+	15.6665i	−0.134953	+	0.765357i	−0.974892	+	0.222677i	$0.928521\pi$
$420$	−1.75199	−	0.338467i	−0.0854885	−	0.0165155i
$421$	27.8051	−	23.3312i	1.35514	−	1.13709i	0.377685	−	0.925934i	$-0.376720\pi$
$421$	27.8051	−	23.3312i	1.35514	−	1.13709i	0.977452	−	0.211160i	$-0.0677241\pi$
$422$	6.44539	+	24.0545i	0.313756	+	1.17096i
$423$	23.2539	+	8.40087i	1.13064	+	0.408464i
$424$	3.44529	−	1.98914i	0.167318	−	0.0966012i
$425$	−12.6123	+	9.85193i	−0.611788	+	0.477889i
$426$	−13.0617	+	0.585914i	−0.632840	+	0.0283876i
$427$	−1.43468	−	16.3984i	−0.0694289	−	0.793576i
$428$	3.09519	+	1.44331i	0.149612	+	0.0697652i
$429$	−29.9960	−	22.9599i	−1.44822	−	1.10851i
$430$	1.08840	+	3.67501i	0.0524873	+	0.177225i
$431$		−	10.7570i		−	0.518146i	−0.965858	−	0.259073i	$-0.916583\pi$
$431$		−	10.7570i		−	0.518146i	0.965858	−	0.259073i	$-0.0834169\pi$
$432$	−8.27769	+	16.0414i	−0.398261	+	0.771790i
$433$	−25.8369	+	25.8369i	−1.24164	+	1.24164i	−0.282321	+	0.959320i	$0.591104\pi$
$433$	−25.8369	+	25.8369i	−1.24164	+	1.24164i	−0.959320	+	0.282321i	$0.908896\pi$
$434$	−1.09408	−	6.20483i	−0.0525175	−	0.297842i
$435$	18.3823	−	17.7923i	0.881362	−	0.853077i
$436$	3.17246	−	1.15468i	0.151933	−	0.0552992i
$437$	−4.99649	+	0.437136i	−0.239015	+	0.0209111i
$438$	−11.2114	+	3.54968i	−0.535703	+	0.169610i
$439$	4.76440	−	13.0901i	0.227393	−	0.624756i	−0.772556	−	0.634947i	$-0.781022\pi$
$439$	4.76440	−	13.0901i	0.227393	−	0.624756i	0.999948	+	0.0101913i	$0.00324405\pi$
$440$	4.22398	−	28.2543i	0.201371	−	1.34697i
$441$	−9.46327	+	0.850709i	−0.450632	+	0.0405100i
$442$	−20.8185	+	5.57831i	−0.990237	+	0.265333i
$443$	−11.3601	−	0.993879i	−0.539734	−	0.0472206i	−0.185970	−	0.982555i	$-0.559543\pi$
$443$	−11.3601	−	0.993879i	−0.539734	−	0.0472206i	−0.353764	+	0.935335i	$0.615098\pi$
$444$	−2.86914	+	0.639668i	−0.136163	+	0.0303573i
$445$	−4.34973	−	0.266246i	−0.206197	−	0.0126213i
$446$	21.6986	+	3.82606i	1.02746	+	0.181169i
$447$	−12.6794	−	8.05642i	−0.599717	−	0.381056i
$448$	1.48564	−	16.9810i	0.0701900	−	0.802276i
$449$	0.807925	−	1.39937i	0.0381283	−	0.0660402i	−0.846332	−	0.532657i	$-0.821194\pi$
$449$	0.807925	−	1.39937i	0.0381283	−	0.0660402i	0.884460	+	0.466616i	$0.154527\pi$
$450$	16.6865	−	10.8909i	0.786609	−	0.513400i
$451$	−18.2114	−	31.5431i	−0.857541	−	1.48530i
$452$	2.90886	−	1.35642i	0.136821	−	0.0638008i
$453$	8.32980	+	26.3092i	0.391368	+	1.23611i
$454$	15.4498	−	18.4124i	0.725097	−	0.864137i
$455$	9.90025	+	19.8592i	0.464131	+	0.931012i
$456$	−4.57049	−	0.596164i	−0.214033	−	0.0279180i
$457$	−3.17737	+	4.53775i	−0.148631	+	0.212267i	−0.886563	−	0.462608i	$-0.846914\pi$
$457$	−3.17737	+	4.53775i	−0.148631	+	0.212267i	0.737932	+	0.674875i	$0.235803\pi$
$458$	−17.8434	−	17.8434i	−0.833768	−	0.833768i
$459$	10.1721	+	13.1587i	0.474793	+	0.614194i
$460$	−2.30475	−	1.83346i	−0.107460	−	0.0854855i
$461$	14.9666	−	2.63902i	0.697065	−	0.122911i	0.186123	−	0.982527i	$-0.440408\pi$
$461$	14.9666	−	2.63902i	0.697065	−	0.122911i	0.510942	+	0.859615i	$0.329297\pi$
$462$	2.55269	+	19.2123i	0.118762	+	0.893836i
$463$	−13.9696	+	29.9580i	−0.649224	+	1.39226i	0.255727	+	0.966749i	$0.417685\pi$
$463$	−13.9696	+	29.9580i	−0.649224	+	1.39226i	−0.904951	+	0.425516i	$0.860093\pi$
$464$	17.5784	+	14.7500i	0.816056	+	0.684752i
$465$	−7.59715	−	5.50635i	−0.352310	−	0.255351i
$466$	9.44112	+	3.43629i	0.437352	+	0.159183i
$467$	21.9378	+	5.87822i	1.01516	+	0.272012i	0.727784	−	0.685806i	$-0.240550\pi$
$467$	21.9378	+	5.87822i	1.01516	+	0.272012i	0.287377	+	0.957818i	$0.407217\pi$
$468$	−3.52277	+	0.629839i	−0.162840	+	0.0291143i
$469$	−16.3630	−	9.44716i	−0.755571	−	0.436229i
$470$	16.8524	−	17.7571i	0.777343	−	0.819072i
$471$	21.9367	+	6.88783i	1.01079	+	0.317374i
$472$	11.8400	−	8.29047i	0.544981	−	0.381600i
$473$	−4.54767	+	3.18431i	−0.209102	+	0.146415i
$474$	0.706524	−	0.648964i	0.0324517	−	0.0298079i
$475$	3.57833	+	2.69699i	0.164185	+	0.123746i
$476$	−1.27713	−	0.737352i	−0.0585372	−	0.0337965i
$477$	0.00959972	+	4.01922i	0.000439541	+	0.184027i
$478$	−16.0470	−	4.29979i	−0.733974	−	0.196668i
$479$	21.4594	+	7.81060i	0.980507	+	0.356875i	0.782037	−	0.623232i	$-0.214181\pi$
$479$	21.4594	+	7.81060i	0.980507	+	0.356875i	0.198470	+	0.980107i	$0.436403\pi$
$480$	−3.23172	−	3.98149i	−0.147507	−	0.181729i
$481$	28.0033	+	23.4976i	1.27684	+	1.07140i
$482$	9.61245	−	20.6140i	0.437835	−	0.938941i
$483$	17.5421	+	7.24163i	0.798191	+	0.329506i
$484$	1.74094	−	0.306975i	0.0791336	−	0.0139534i
$485$	18.8021	−	23.6352i	0.853758	−	1.07322i
$486$	−11.2304	−	17.3981i	−0.509421	−	0.789192i
$487$	13.1004	+	13.1004i	0.593634	+	0.593634i	0.938611	−	0.344977i	$-0.112113\pi$
$487$	13.1004	+	13.1004i	0.593634	+	0.593634i	−0.344977	+	0.938611i	$0.612113\pi$
$488$	14.3206	−	20.4520i	0.648264	−	0.925817i
$489$	−4.93317	−	11.8696i	−0.223086	−	0.536762i
$490$	−2.98553	+	8.92142i	−0.134873	+	0.403029i
$491$	−5.95862	+	7.10121i	−0.268909	+	0.320473i	−0.883553	−	0.468332i	$-0.844855\pi$
$491$	−5.95862	+	7.10121i	−0.268909	+	0.320473i	0.614644	+	0.788805i	$0.289300\pi$
$492$	−3.36967	−	0.742816i	−0.151916	−	0.0334887i
$493$	19.1619	−	8.93533i	0.863007	−	0.402427i
$494$	3.01722	+	5.22597i	0.135751	+	0.235128i
$495$	22.6299	+	17.9143i	1.01714	+	0.805188i
$496$	4.20804	−	7.28854i	0.188947	−	0.327265i
$497$	−0.969617	+	11.0828i	−0.0434933	+	0.497131i
$498$	0.904958	−	21.3109i	0.0405521	−	0.954965i
$499$	−20.3482	−	3.58794i	−0.910911	−	0.160618i	−0.301494	−	0.953468i	$-0.597485\pi$
$499$	−20.3482	−	3.58794i	−0.910911	−	0.160618i	−0.609417	+	0.792850i	$0.708596\pi$
$500$	0.433892	+	2.59508i	0.0194042	+	0.116055i
$501$	4.27157	−	13.6043i	0.190840	−	0.607796i
$502$	−7.12650	−	0.623488i	−0.318071	−	0.0278276i
$503$	4.53760	−	1.21585i	0.202322	−	0.0542119i	−0.156235	−	0.987720i	$-0.549936\pi$
$503$	4.53760	−	1.21585i	0.202322	−	0.0542119i	0.358557	+	0.933508i	$0.383269\pi$
$504$	14.3102	+	9.96924i	0.637426	+	0.444065i
$505$	5.65871	+	7.64806i	0.251809	+	0.340334i
$506$	−10.9405	+	30.0588i	−0.486365	+	1.33628i
$507$	16.2276	+	14.8343i	0.720694	+	0.658813i
$508$	−0.844055	+	0.0738452i	−0.0374489	+	0.00327635i
$509$	−30.3526	+	11.0475i	−1.34536	+	0.489670i	−0.911496	−	0.411309i	$-0.865072\pi$
$509$	−30.3526	+	11.0475i	−1.34536	+	0.489670i	−0.433862	+	0.900979i	$0.642849\pi$
$510$	15.9742	−	4.00228i	0.707348	−	0.177224i
$511$	1.73758	+	9.85432i	0.0768661	+	0.435929i
$512$	17.8410	−	17.8410i	0.788469	−	0.788469i
$513$	2.82154	−	3.70450i	0.124574	−	0.163558i
$514$			16.2891i			0.718480i
$515$	−14.2490	+	26.2405i	−0.627887	+	1.15630i
$516$	−0.0680271	+	0.521529i	−0.00299472	+	0.0229590i
$517$	32.1376	+	14.9860i	1.41341	+	0.659083i
$518$	−1.63467	−	18.6844i	−0.0718234	−	0.820945i
$519$	−6.20277	+	11.9502i	−0.272271	+	0.524557i
$520$	−7.85854	+	32.7264i	−0.344620	+	1.43515i
$521$	−2.29310	+	1.32392i	−0.100463	+	0.0580021i	−0.549390	−	0.835566i	$-0.685140\pi$
$521$	−2.29310	+	1.32392i	−0.100463	+	0.0580021i	0.448927	+	0.893568i	$0.351806\pi$
$522$	−24.7150	+	9.06243i	−1.08175	+	0.396652i
$523$	3.37351	+	12.5901i	0.147513	+	0.550527i	0.999631	+	0.0271764i	$0.00865159\pi$
$523$	3.37351	+	12.5901i	0.147513	+	0.550527i	−0.852117	+	0.523351i	$0.824682\pi$
$524$	0.100106	−	0.0839990i	0.00437316	−	0.00366951i
$525$	−7.31605	−	15.2951i	−0.319299	−	0.667532i
$526$	−3.14347	+	17.8275i	−0.137062	+	0.777317i
$527$	−4.44773	−	6.35202i	−0.193746	−	0.276698i
$528$	−13.8839	+	21.8509i	−0.604219	+	0.950938i
$529$	5.34967	+	6.37549i	0.232594	+	0.277195i
$530$	3.64945	+	1.58703i	0.158522	+	0.0689361i
$531$	1.30746	+	14.5441i	0.0567388	+	0.631161i
$532$	−0.106864	+	0.398822i	−0.00463314	+	0.0172911i
$533$	18.1347	+	38.8899i	0.785499	+	1.68451i
$534$	3.97997	+	2.06581i	0.172230	+	0.0893962i
$535$	6.46800	+	31.7989i	0.279636	+	1.37478i
$536$	−9.80156	−	26.9296i	−0.423363	−	1.16318i
$537$	−4.64510	−	6.03866i	−0.200451	−	0.260587i
$538$	−13.4217	−	9.39794i	−0.578649	−	0.405174i
$539$	−13.6268			−0.586947
$540$	2.69913	−	0.437288i	0.116152	−	0.0188179i
$541$	−42.0435			−1.80759			−0.903796	−	0.427963i	$-0.859231\pi$
$541$	−42.0435			−1.80759			−0.903796	+	0.427963i	$0.859231\pi$
$542$	−21.4998	−	15.0543i	−0.923494	−	0.646637i
$543$	−9.81518	+	1.30412i	−0.421210	+	0.0559651i
$544$	−1.44949	−	3.98243i	−0.0621463	−	0.170745i
$545$	26.7489	+	17.7065i	1.14580	+	0.758465i
$546$	−1.02321	−	22.8103i	−0.0437894	−	0.976189i
$547$	−9.73975	−	20.8870i	−0.416442	−	0.893062i	−0.996893	−	0.0787671i	$-0.974902\pi$
$547$	−9.73975	−	20.8870i	−0.416442	−	0.893062i	0.580451	−	0.814295i	$-0.302876\pi$
$548$	−0.368084	+	1.37371i	−0.0157238	+	0.0586818i
$549$	10.7148	+	22.8354i	0.457296	+	0.974591i
$550$	25.2338	−	13.4140i	1.07597	−	0.571977i
$551$	−3.80505	−	4.53468i	−0.162101	−	0.193184i
$552$	13.3218	+	25.5165i	0.567014	+	1.08606i
$553$	−0.468201	−	0.668660i	−0.0199099	−	0.0284343i
$554$	−0.467751	+	2.65275i	−0.0198728	+	0.112704i
$555$	−21.1009	−	18.3002i	−0.895682	−	0.776802i
$556$	−3.33853	+	2.80136i	−0.141585	+	0.118804i
$557$	−9.19419	−	34.3132i	−0.389570	−	1.45390i	−0.830835	−	0.556519i	$-0.812137\pi$
$557$	−9.19419	−	34.3132i	−0.389570	−	1.45390i	0.441265	−	0.897377i	$-0.354530\pi$
$558$	4.84731	+	8.34966i	0.205203	+	0.353469i
$559$	5.66426	−	3.27026i	0.239572	−	0.138317i
$560$	12.9673	−	7.94551i	0.547967	−	0.335759i
$561$	12.8404	+	20.1023i	0.542120	+	0.848720i
$562$	3.02674	+	34.5957i	0.127675	+	1.45933i
$563$	−4.24073	−	1.97748i	−0.178725	−	0.0833410i	0.331196	−	0.943562i	$-0.392548\pi$
$563$	−4.24073	−	1.97748i	−0.178725	−	0.0833410i	−0.509922	+	0.860221i	$0.670326\pi$
$564$	3.10209	−	1.28927i	0.130622	−	0.0542881i
$565$	26.8001	+	14.5529i	1.12749	+	0.612246i
$566$		−	3.08073i		−	0.129493i
$567$	−15.9333	+	7.52269i	−0.669136	+	0.315923i
$568$	−11.9317	+	11.9317i	−0.500642	+	0.500642i
$569$	1.37633	+	7.80556i	0.0576988	+	0.327226i	0.999971	−	0.00762185i	$-0.00242613\pi$
$569$	1.37633	+	7.80556i	0.0576988	+	0.327226i	−0.942272	+	0.334848i	$0.891315\pi$
$570$	−2.23995	−	4.03006i	−0.0938211	−	0.168801i
$571$	4.65824	−	1.69546i	0.194941	−	0.0709528i	−0.242705	−	0.970100i	$-0.578035\pi$
$571$	4.65824	−	1.69546i	0.194941	−	0.0709528i	0.437646	+	0.899147i	$0.355812\pi$
$572$	−5.11288	+	0.447319i	−0.213780	+	0.0187033i
$573$	5.37891	−	24.4006i	0.224707	−	1.01935i
$574$	7.52995	−	20.6884i	0.314294	−	0.863516i
$575$	0.979225	−	27.9662i	0.0408365	−	1.16627i
$576$	6.82068	+	25.2141i	0.284195	+	1.05059i
$577$	22.0266	−	5.90200i	0.916977	−	0.245703i	0.230684	−	0.973029i	$-0.425904\pi$
$577$	22.0266	−	5.90200i	0.916977	−	0.245703i	0.686293	+	0.727325i	$0.259237\pi$
$578$	−8.93890	−	0.782053i	−0.371809	−	0.0325291i
$579$	−20.3290	−	22.1321i	−0.844844	−	0.919777i
$580$	0.212362	−	3.46941i	0.00881784	−	0.144060i
$581$	−17.8737	−	3.15161i	−0.741526	−	0.130751i
$582$	−27.5484	+	14.3826i	−1.14192	+	0.596179i
$583$	−0.502393	+	5.74237i	−0.0208070	+	0.237825i
$584$	−7.58853	+	13.1437i	−0.314015	+	0.543891i
$585$	−24.7198	−	23.3484i	−1.02204	−	0.965339i
$586$	8.00664	+	13.8679i	0.330751	+	0.572878i
$587$	33.9155	−	15.8151i	1.39984	−	0.652758i	0.431439	−	0.902142i	$-0.358006\pi$
$587$	33.9155	−	15.8151i	1.39984	−	0.652758i	0.968405	+	0.249384i	$0.0802281\pi$
$588$	−0.871019	+	0.952832i	−0.0359202	+	0.0392941i
$589$	−1.39555	+	1.66315i	−0.0575026	+	0.0685290i
$590$	13.7114	+	4.58847i	0.564488	+	0.188904i
$591$	−14.3296	+	18.7209i	−0.589440	+	0.770075i
$592$	14.3700	−	20.5225i	0.590604	−	0.843470i
$593$	−5.46266	−	5.46266i	−0.224324	−	0.224324i	0.585992	−	0.810317i	$-0.300705\pi$
$593$	−5.46266	−	5.46266i	−0.224324	−	0.224324i	−0.810317	+	0.585992i	$0.800705\pi$
$594$	−13.8077	−	26.2939i	−0.566535	−	1.07885i
$595$	−1.58558	−	13.9222i	−0.0650024	−	0.570756i
$596$	−2.01008	+	0.354432i	−0.0823362	+	0.0145181i
$597$	−12.3421	+	9.49383i	−0.505126	+	0.388556i
$598$	15.9266	−	34.1546i	0.651286	−	1.39669i
$599$	−1.79656	−	1.50749i	−0.0734055	−	0.0615946i	0.605347	−	0.795962i	$-0.293035\pi$
$599$	−1.79656	−	1.50749i	−0.0734055	−	0.0615946i	−0.678752	+	0.734367i	$0.737479\pi$
$600$	6.41138	−	24.9040i	0.261744	−	1.01670i
$601$	38.1639	+	13.8905i	1.55674	+	0.566607i	0.969987	−	0.243159i	$-0.0781836\pi$
$601$	38.1639	+	13.8905i	1.55674	+	0.566607i	0.586753	+	0.809766i	$0.300406\pi$
$602$	−3.24142	−	0.868536i	−0.132110	−	0.0353989i
$603$	28.5249	+	4.95949i	1.16162	+	0.201966i
$604$	3.24716	+	1.87475i	0.132125	+	0.0762824i
$605$	12.1837	+	11.5629i	0.495336	+	0.470101i
$606$	−2.13027	−	9.55500i	−0.0865362	−	0.388146i
$607$	−1.53527	+	1.07501i	−0.0623147	+	0.0436332i	−0.604319	−	0.796743i	$-0.706555\pi$
$607$	−1.53527	+	1.07501i	−0.0623147	+	0.0436332i	0.542004	+	0.840376i	$0.317666\pi$
$608$	−0.971981	+	0.680588i	−0.0394190	+	0.0276015i
$609$	4.87408	+	21.8619i	0.197508	+	0.885891i
$610$	24.9669	−	0.652611i	1.01088	−	0.0264234i
$611$	−36.1789	−	20.8879i	−1.46364	−	0.845035i
$612$	2.22637	+	0.387089i	0.0899958	+	0.0156472i
$613$	−17.5910	−	4.71349i	−0.710494	−	0.190376i	−0.114568	−	0.993415i	$-0.536548\pi$
$613$	−17.5910	−	4.71349i	−0.710494	−	0.190376i	−0.595926	+	0.803039i	$0.703215\pi$
$614$	−29.3338	−	10.6766i	−1.18382	−	0.430874i
$615$	−13.3698	−	29.9365i	−0.539121	−	1.20716i
$616$	19.1608	+	16.0778i	0.772012	+	0.647795i
$617$	−7.87526	+	16.8885i	−0.317046	+	0.679907i	−0.998657	−	0.0518073i	$-0.983502\pi$
$617$	−7.87526	+	16.8885i	−0.317046	+	0.679907i	0.681611	+	0.731715i	$0.261280\pi$
$618$	24.3534	−	18.7333i	0.979639	−	0.753564i
$619$	−28.0130	+	4.93945i	−1.12594	+	0.198533i	−0.705447	−	0.708763i	$-0.749254\pi$
$619$	−28.0130	+	4.93945i	−1.12594	+	0.198533i	−0.420492	+	0.907296i	$0.638142\pi$
$620$	−1.26665	+	0.144256i	−0.0508697	+	0.00579345i
$621$	−29.0578	−	1.16440i	−1.16605	−	0.0467259i
$622$	−3.73594	−	3.73594i	−0.149797	−	0.149797i
$623$	2.18848	−	3.12547i	0.0876795	−	0.125219i
$624$	18.5382	−	24.2193i	0.742123	−	0.969549i
$625$	−17.3698	+	17.9802i	−0.694793	+	0.719210i
$626$	0.780926	−	0.930671i	0.0312121	−	0.0371971i
$627$	4.50604	−	4.92928i	0.179954	−	0.196857i
$628$	2.83130	−	1.32026i	0.112981	−	0.0526840i
$629$	−11.5418	−	19.9910i	−0.460202	−	0.797093i
$630$	0.497522	+	17.4390i	0.0198218	+	0.694787i
$631$	−16.2016	+	28.0619i	−0.644974	+	1.11713i	0.339333	+	0.940666i	$0.389799\pi$
$631$	−16.2016	+	28.0619i	−0.644974	+	1.11713i	−0.984307	+	0.176462i	$0.943535\pi$
$632$	0.107907	−	1.23338i	0.00429231	−	0.0490613i
$633$	−28.7833	+	15.0273i	−1.14403	+	0.597283i
$634$	−34.4974	−	6.08282i	−1.37007	−	0.241580i
$635$	−5.33422	−	6.02981i	−0.211682	−	0.239286i
$636$	0.369414	+	0.402179i	0.0146482	+	0.0159475i
$637$	15.9928	+	1.39919i	0.633659	+	0.0554380i
$638$	−36.4671	+	9.77134i	−1.44375	+	0.386851i
$639$	−4.45157	−	16.4562i	−0.176102	−	0.650996i
$640$	19.7222	+	2.94845i	0.779589	+	0.116548i
$641$	−7.10695	+	19.5262i	−0.280708	+	0.771238i	0.716571	+	0.697514i	$0.245711\pi$
$641$	−7.10695	+	19.5262i	−0.280708	+	0.771238i	−0.997279	+	0.0737239i	$0.976512\pi$
$642$	7.18807	−	32.6075i	0.283691	−	1.28692i
$643$	39.3334	−	3.44122i	1.55116	−	0.135709i	0.720880	−	0.693060i	$-0.243738\pi$
$643$	39.3334	−	3.44122i	1.55116	−	0.135709i	0.830277	+	0.557351i	$0.188182\pi$
$644$	2.42303	−	0.881910i	0.0954807	−	0.0347521i
$645$	−4.36804	+	2.42780i	−0.171992	+	0.0955946i
$646$	−0.661691	−	3.75263i	−0.0260339	−	0.147645i
$647$	27.7872	−	27.7872i	1.09243	−	1.09243i	0.0971593	−	0.995269i	$-0.469024\pi$
$647$	27.7872	−	27.7872i	1.09243	−	1.09243i	0.995269	−	0.0971593i	$-0.0309756\pi$
$648$	−25.8470	−	6.79352i	−1.01537	−	0.266875i
$649$			20.9430i			0.822086i
$650$	−30.9926	+	13.1522i	−1.21563	+	0.515870i
$651$	7.58592	−	3.15281i	0.297315	−	0.123568i
$652$	−1.58283	−	0.738085i	−0.0619884	−	0.0289056i
$653$	−1.47726	−	16.8852i	−0.0578098	−	0.660770i	−0.968719	−	0.248162i	$-0.920174\pi$
$653$	−1.47726	−	16.8852i	−0.0578098	−	0.660770i	0.910909	−	0.412608i	$-0.135382\pi$
$654$	−17.7685	−	27.8175i	−0.694802	−	1.08775i
$655$	1.20736	+	0.289921i	0.0471754	+	0.0113281i
$656$	25.4684	−	14.7042i	0.994375	−	0.574103i
$657$	−7.69833	−	13.2607i	−0.300341	−	0.517348i
$658$	5.54754	+	20.7037i	0.216266	+	0.807115i
$659$	36.7210	−	30.8125i	1.43045	−	1.20029i	0.484997	−	0.874516i	$-0.338821\pi$
$659$	36.7210	−	30.8125i	1.43045	−	1.20029i	0.945449	−	0.325770i	$-0.105624\pi$
$660$	3.91164	−	0.278039i	0.152260	−	0.0108227i
$661$	−0.726513	+	4.12026i	−0.0282581	+	0.160259i	−0.995671	−	0.0929427i	$-0.970373\pi$
$661$	−0.726513	+	4.12026i	−0.0282581	+	0.160259i	0.967413	+	0.253202i	$0.0814838\pi$
$662$	9.79064	+	13.9825i	0.380524	+	0.543445i
$663$	−13.0058	−	24.9112i	−0.505102	−	0.967470i
$664$	−17.6947	−	21.0877i	−0.686687	−	0.818361i
$665$	−3.65026	+	1.43768i	−0.141551	+	0.0557508i
$666$	12.2084	+	26.0187i	0.473068	+	1.00820i
$667$	−9.56811	+	35.7087i	−0.370479	+	1.38264i
$668$	−0.818774	−	1.75587i	−0.0316793	−	0.0679365i
$669$	1.28739	+	28.6995i	0.0497732	+	1.10959i
$670$	15.8237	−	23.9045i	0.611321	−	0.923511i
$671$	12.3730	+	33.9945i	0.477653	+	1.31234i
$672$	4.45065	−	0.591347i	0.171687	−	0.0228117i
$673$	−19.5570	−	13.6940i	−0.753867	−	0.527863i	0.132311	−	0.991208i	$-0.457760\pi$
$673$	−19.5570	−	13.6940i	−0.753867	−	0.527863i	−0.886178	+	0.463345i	$0.846649\pi$
$674$	11.2915			0.434933
$675$	18.5942	+	18.1454i	0.715692	+	0.698417i
$676$	2.98725			0.114894
$677$	−18.1236	−	12.6903i	−0.696547	−	0.487727i	0.170880	−	0.985292i	$-0.445339\pi$
$677$	−18.1236	−	12.6903i	−0.696547	−	0.487727i	−0.867427	+	0.497565i	$0.834228\pi$
$678$	−19.1328	−	24.8728i	−0.734791	−	0.955235i
$679$	9.04396	+	24.8481i	0.347075	+	0.953581i
$680$	11.7311	−	17.7220i	0.449869	−	0.679608i
$681$	27.8153	+	14.4376i	1.06589	+	0.553248i
$682$	5.85182	+	12.5493i	0.224078	+	0.480537i
$683$	6.53337	−	24.3829i	0.249993	−	0.932985i	−0.720815	−	0.693127i	$-0.756232\pi$
$683$	6.53337	−	24.3829i	0.249993	−	0.932985i	0.970808	−	0.239858i	$-0.0771008\pi$
$684$	−0.0566484	−	0.630155i	−0.00216601	−	0.0240946i
$685$	−12.5730	+	4.95195i	−0.480389	+	0.189204i
$686$	−16.9965	−	20.2556i	−0.648929	−	0.773363i
$687$	17.6451	−	27.7703i	0.673201	−	1.05950i
$688$	−2.57107	−	3.67187i	−0.0980212	−	0.139989i
$689$	1.17925	−	6.68785i	0.0449258	−	0.254787i
$690$	−12.5929	+	25.8946i	−0.479403	+	0.985790i
$691$	25.5999	−	21.4808i	0.973865	−	0.817170i	−0.00928734	−	0.999957i	$-0.502956\pi$
$691$	25.5999	−	21.4808i	0.973865	−	0.817170i	0.983153	+	0.182787i	$0.0585118\pi$
$692$	0.473473	+	1.76703i	0.0179988	+	0.0671723i
$693$	−23.7255	+	8.69959i	−0.901256	+	0.330470i
$694$	6.05298	−	3.49469i	0.229768	−	0.132657i
$695$	−40.2653	−	9.66884i	−1.52735	−	0.366760i
$696$	−15.6510	+	30.1532i	−0.593251	+	1.14295i
$697$	−2.36159	−	26.9931i	−0.0894517	−	1.02244i
$698$	24.8229	+	11.5751i	0.939559	+	0.438124i
$699$	−1.69437	+	12.9898i	−0.0640868	+	0.491321i
$700$	−2.13581	−	0.863157i	−0.0807261	−	0.0326243i
$701$			12.4042i			0.468499i	0.972177	+	0.234249i	$0.0752632\pi$
$701$			12.4042i			0.468499i	−0.972177	+	0.234249i	$0.924737\pi$
$702$	13.5053	+	32.2771i	0.509724	+	1.21822i
$703$	−4.57003	+	4.57003i	−0.172362	+	0.172362i
$704$	6.50508	+	36.8922i	0.245170	+	1.39043i
$705$	27.3793	+	16.4084i	1.03116	+	0.617976i
$706$	−35.9678	+	13.0912i	−1.35367	+	0.492694i
$707$	−8.29809	+	0.725989i	−0.312082	+	0.0273036i
$708$	1.46441	+	1.33867i	0.0550359	+	0.0503103i
$709$	−4.29127	+	11.7902i	−0.161162	+	0.442789i	−0.993821	−	0.110998i	$-0.964595\pi$
$709$	−4.29127	+	11.7902i	−0.161162	+	0.442789i	0.832659	+	0.553786i	$0.186818\pi$
$710$	−16.6940	−	2.49573i	−0.626514	−	0.0936631i
$711$	1.02634	+	0.715002i	0.0384906	+	0.0268147i
$712$	5.58994	−	1.49782i	0.209492	−	0.0561332i
$713$	13.5070	+	1.18171i	0.505842	+	0.0442554i
$714$	−4.31925	+	13.7562i	−0.161644	+	0.514812i
$715$	−32.3121	−	36.5257i	−1.20840	−	1.36598i
$716$	−1.01940	−	0.179748i	−0.0380969	−	0.00671750i
$717$	0.918999	−	21.6416i	0.0343206	−	0.808219i
$718$	2.06408	−	23.5926i	0.0770308	−	0.880466i
$719$	9.10268	−	15.7663i	0.339473	−	0.587984i	−0.644861	−	0.764300i	$-0.723085\pi$
$719$	9.10268	−	15.7663i	0.339473	−	0.587984i	0.984334	+	0.176316i	$0.0564181\pi$
$720$	−14.4643	+	18.2718i	−0.539054	+	0.680950i
$721$	−13.0717	−	22.6408i	−0.486815	−	0.843188i
$722$	21.9081	−	10.2159i	0.815334	−	0.380196i
$723$	28.9608	+	6.38419i	1.07707	+	0.237431i
$724$	−0.864744	+	1.03056i	−0.0321380	+	0.0383005i
$725$	27.7006	−	17.9853i	1.02877	−	0.667956i
$726$	−6.63333	−	15.9603i	−0.246186	−	0.592344i
$727$	−5.64377	+	8.06014i	−0.209316	+	0.298934i	−0.910058	−	0.414480i	$-0.863963\pi$
$727$	−5.64377	+	8.06014i	−0.209316	+	0.298934i	0.700742	+	0.713414i	$0.252852\pi$
$728$	−20.8369	−	20.8369i	−0.772267	−	0.772267i
$729$	18.9546	−	19.2282i	0.702022	−	0.712155i
$730$	−15.0845	+	1.71795i	−0.558304	+	0.0635841i
$731$	−4.06735	+	0.717184i	−0.150436	+	0.0265260i
$732$	3.16789	+	1.30775i	0.117088	+	0.0483359i
$733$	−15.6224	+	33.5024i	−0.577027	+	1.23744i	0.373740	+	0.927533i	$0.378075\pi$
$733$	−15.6224	+	33.5024i	−0.577027	+	1.23744i	−0.950767	+	0.309905i	$0.899703\pi$
$734$	22.3146	+	18.7242i	0.823646	+	0.691121i
$735$	−12.2006	−	1.26818i	−0.450025	−	0.0467775i
$736$	6.96332	+	2.53444i	0.256671	+	0.0934207i
$737$	40.1088	+	10.7471i	1.47743	+	0.395875i
$738$	0.0805779	+	33.7364i	0.00296611	+	1.24186i
$739$	−7.02338	−	4.05495i	−0.258359	−	0.149164i	0.365227	−	0.930919i	$-0.380991\pi$
$739$	−7.02338	−	4.05495i	−0.258359	−	0.149164i	−0.623586	+	0.781755i	$0.714325\pi$
$740$	−3.79368	+	0.0991631i	−0.139459	+	0.00364531i
$741$	−5.79457	+	5.32249i	−0.212869	+	0.195526i
$742$	−2.85416	+	1.99851i	−0.104780	+	0.0733675i
$743$	25.5056	−	17.8592i	0.935709	−	0.655190i	−0.00296531	−	0.999996i	$-0.500944\pi$
$743$	25.5056	−	17.8592i	0.935709	−	0.655190i	0.938674	+	0.344805i	$0.112055\pi$
$744$	11.8878	+	3.73262i	0.435829	+	0.136844i
$745$	−14.0672	−	13.3505i	−0.515383	−	0.489126i
$746$	19.8552	+	11.4634i	0.726949	+	0.419704i
$747$	27.3773	−	4.89480i	1.00168	−	0.179091i
$748$	3.13050	+	0.838814i	0.114462	+	0.0306701i
$749$	−26.6979	−	9.71724i	−0.975519	−	0.355060i
$750$	23.8412	−	9.66169i	0.870557	−	0.352795i
$751$	−13.4156	−	11.2570i	−0.489541	−	0.410774i	0.364321	−	0.931273i	$-0.381301\pi$
$751$	−13.4156	−	11.2570i	−0.489541	−	0.410774i	−0.853862	+	0.520500i	$0.825746\pi$
$752$	−12.1000	+	25.9484i	−0.441240	+	0.946243i
$753$	−1.22851	−	9.24615i	−0.0447695	−	0.336949i
$754$	43.8023	−	7.72353i	1.59519	−	0.281274i
$755$	4.03140	+	35.3979i	0.146718	+	1.28826i
$756$	−0.908217	+	2.21504i	−0.0330315	+	0.0805603i
$757$	−20.1777	−	20.1777i	−0.733371	−	0.733371i	0.237915	−	0.971286i	$-0.423536\pi$
$757$	−20.1777	−	20.1777i	−0.733371	−	0.733371i	−0.971286	+	0.237915i	$0.923536\pi$
$758$	−20.7010	+	29.5641i	−0.751893	+	1.07381i
$759$	−41.3572	−	5.39455i	−1.50117	−	0.195810i
$760$	−5.64287	−	1.88837i	−0.204688	−	0.0684985i
$761$	23.7584	−	28.3141i	0.861240	−	1.02639i	−0.138113	−	0.990416i	$-0.544104\pi$
$761$	23.7584	−	28.3141i	0.861240	−	1.02639i	0.999353	−	0.0359689i	$-0.0114517\pi$
$762$	2.50046	+	7.89754i	0.0905820	+	0.286098i
$763$	−25.4545	+	11.8696i	−0.921516	+	0.429710i
$764$	−1.69744	−	2.94006i	−0.0614113	−	0.106368i
$765$	9.62562	+	19.1933i	0.348015	+	0.693936i
$766$	−4.88069	+	8.45360i	−0.176346	+	0.305441i
$767$	2.15042	−	24.5794i	0.0776472	−	0.887512i
$768$	8.13803	+	5.17084i	0.293656	+	0.186587i
$769$	8.53754	+	1.50540i	0.307872	+	0.0542861i	0.325450	−	0.945559i	$-0.394484\pi$
$769$	8.53754	+	1.50540i	0.307872	+	0.0542861i	−0.0175779	+	0.999845i	$0.505595\pi$
$770$	−1.52866	+	24.9742i	−0.0550891	+	0.900007i
$771$	−20.7296	+	4.62163i	−0.746559	+	0.166444i
$772$	−4.06755	−	0.355865i	−0.146394	−	0.0128078i
$773$	11.3983	−	3.05417i	0.409969	−	0.109851i	−0.0479396	−	0.998850i	$-0.515266\pi$
$773$	11.3983	−	3.05417i	0.409969	−	0.109851i	0.457908	+	0.889000i	$0.348599\pi$
$774$	5.12158	−	0.460409i	0.184091	−	0.0165491i
$775$	−8.26030	−	8.85975i	−0.296719	−	0.318252i
$776$	−13.7174	+	37.6882i	−0.492425	+	1.35293i
$777$	23.3141	−	7.38154i	0.836390	−	0.264811i
$778$	41.3603	−	3.61856i	1.48284	−	0.129732i
$779$	−7.12895	+	2.59472i	−0.255421	+	0.0929657i
$780$	−4.61938	−	0.0753300i	−0.165400	−	0.00269725i
$781$	−4.24560	−	24.0780i	−0.151919	−	0.861578i
$782$	−16.8270	+	16.8270i	−0.601733	+	0.601733i
$783$	−18.5452	−	28.8813i	−0.662752	−	1.03213i
$784$		−	11.0025i		−	0.392947i
$785$	26.0856	+	14.1649i	0.931035	+	0.505567i
$786$	−1.01457	−	0.776581i	−0.0361884	−	0.0276997i
$787$	17.0214	+	7.93722i	0.606748	+	0.282931i	0.701612	−	0.712559i	$-0.252464\pi$
$787$	17.0214	+	7.93722i	0.606748	+	0.282931i	−0.0948643	+	0.995490i	$0.530242\pi$
$788$	0.279178	+	3.19101i	0.00994529	+	0.113675i
$789$	−23.5794	+	1.05771i	−0.839448	+	0.0376556i
$790$	1.05603	−	0.647065i	0.0375717	−	0.0230215i
$791$	−23.1237	+	13.3505i	−0.822183	+	0.474687i
$792$	−36.0481	−	13.0230i	−1.28091	−	0.462753i
$793$	−11.0308	−	41.1675i	−0.391715	−	1.46190i
$794$	−16.7831	+	14.0827i	−0.595610	+	0.499776i
$795$	−0.984226	+	5.09461i	−0.0349069	+	0.180687i
$796$	−0.367376	+	2.08349i	−0.0130213	+	0.0738475i
$797$	12.3706	+	17.6670i	0.438188	+	0.625797i	0.976131	−	0.217184i	$-0.0696872\pi$
$797$	12.3706	+	17.6670i	0.438188	+	0.625797i	−0.537943	+	0.842981i	$0.680798\pi$
$798$	4.03324	+	0.171269i	0.142775	+	0.00606287i
$799$	16.9567	+	20.2082i	0.599884	+	0.714914i
$800$	−3.10745	−	5.84558i	−0.109865	−	0.206673i
$801$	−1.49974	+	5.65108i	−0.0529909	+	0.199671i
$802$	−0.519739	+	1.93969i	−0.0183526	+	0.0684929i
$803$	−9.29368	−	19.9304i	−0.327967	−	0.703327i
$804$	3.31521	−	2.11759i	0.116919	−	0.0746818i
$805$	20.4300	+	13.5237i	0.720063	+	0.476648i
$806$	−5.57934	−	15.3291i	−0.196524	−	0.539945i
$807$	8.15185	−	19.7470i	0.286959	−	0.695126i
$808$	−10.3493	−	7.24665i	−0.364087	−	0.254936i
$809$	−4.46938			−0.157135			−0.0785676	−	0.996909i	$-0.525035\pi$
$809$	−4.46938			−0.157135			−0.0785676	+	0.996909i	$0.525035\pi$
$810$	−9.91547	−	24.8269i	−0.348394	−	0.872327i
$811$	37.9099			1.33120			0.665598	−	0.746311i	$-0.268177\pi$
$811$	37.9099			1.33120			0.665598	+	0.746311i	$0.268177\pi$
$812$	2.49292	+	1.74556i	0.0874845	+	0.0612573i
$813$	13.0582	−	31.6321i	0.457971	−	1.10939i
$814$	14.0978	+	38.7333i	0.494127	+	1.35760i
$815$	−3.30762	−	16.2614i	−0.115861	−	0.569612i
$816$	−16.2310	+	10.3675i	−0.568197	+	0.362936i
$817$	0.488696	+	1.04801i	0.0170973	+	0.0366653i
$818$	−8.06996	+	30.1175i	−0.282159	+	1.05303i
$819$	28.7383	−	7.77401i	1.00420	−	0.271646i
$820$	−4.08511	−	1.77649i	−0.142658	−	0.0620376i
$821$	23.1674	+	27.6099i	0.808549	+	0.963591i	0.999839	−	0.0179428i	$-0.00571166\pi$
$821$	23.1674	+	27.6099i	0.808549	+	0.963591i	−0.191290	+	0.981533i	$0.561267\pi$
$822$	13.8921	+	0.589922i	0.484544	+	0.0205759i
$823$	1.52711	+	2.18095i	0.0532319	+	0.0760230i	0.844886	−	0.534947i	$-0.179668\pi$
$823$	1.52711	+	2.18095i	0.0532319	+	0.0760230i	−0.791654	+	0.610970i	$0.790780\pi$
$824$	6.88563	−	39.0504i	0.239872	−	1.36038i
$825$	24.2303	+	28.3069i	0.843592	+	0.985521i
$826$	−9.69752	+	8.13719i	−0.337420	+	0.283129i
$827$	10.6874	+	39.8859i	0.371637	+	1.38697i	0.858197	+	0.513321i	$0.171585\pi$
$827$	10.6874	+	39.8859i	0.371637	+	1.38697i	−0.486560	+	0.873647i	$0.661748\pi$
$828$	−3.02075	+	2.54703i	−0.104978	+	0.0885153i
$829$	19.6326	−	11.3349i	0.681869	−	0.393677i	−0.118690	−	0.992931i	$-0.537869\pi$
$829$	19.6326	−	11.3349i	0.681869	−	0.393677i	0.800559	+	0.599254i	$0.204536\pi$
$830$	6.42966	−	26.7759i	0.223177	−	0.929406i
$831$	−3.50863	+	0.157388i	−0.121713	+	0.00545974i
$832$	−3.84651	−	43.9658i	−0.133354	−	1.52424i
$833$	−9.18766	−	4.28428i	−0.318334	−	0.148441i
$834$	33.8357	+	25.8989i	1.17164	+	0.896806i
$835$	8.78453	−	16.1773i	0.304001	−	0.559838i
$836$		−	0.907402i		−	0.0313832i
$837$	−9.25056	+	8.53774i	−0.319746	+	0.295108i
$838$	14.9429	−	14.9429i	0.516195	−	0.516195i
$839$	−1.44230	−	8.17971i	−0.0497938	−	0.282395i	0.949736	−	0.313052i	$-0.101351\pi$
$839$	−1.44230	−	8.17971i	−0.0497938	−	0.282395i	−0.999530	+	0.0306567i	$0.990240\pi$
$840$	15.6591	+	16.1783i	0.540291	+	0.558204i
$841$	−13.7493	+	5.00432i	−0.474112	+	0.172563i
$842$	−48.0337	+	4.20240i	−1.65535	+	0.144824i
$843$	−43.1681	+	13.6676i	−1.48679	+	0.470736i
$844$	−1.50888	+	4.14562i	−0.0519379	+	0.142698i
$845$	16.8824	+	22.8175i	0.580771	+	0.784945i
$846$	−18.9031	−	26.8597i	−0.649902	−	0.923455i
$847$	−14.2054	+	3.80634i	−0.488105	+	0.130787i
$848$	−4.63650	−	0.405641i	−0.159218	−	0.0139298i
$849$	3.92057	−	0.874084i	0.134554	−	0.0299985i
$850$	21.2310	−	1.11067i	0.728216	−	0.0380957i
$851$	39.7487	+	7.00876i	1.36257	+	0.240257i
$852$	−1.95499	−	1.24219i	−0.0669770	−	0.0425567i
$853$	−0.534954	+	6.11455i	−0.0183165	+	0.209358i	0.981521	+	0.191352i	$0.0612873\pi$
$853$	−0.534954	+	6.11455i	−0.0183165	+	0.209358i	−0.999838	+	0.0180058i	$0.994268\pi$
$854$	−10.9335	+	18.9374i	−0.374137	+	0.648024i
$855$	4.49317	−	3.99401i	0.153663	−	0.136592i
$856$	−21.5463	−	37.3193i	−0.736439	−	1.27555i
$857$	−31.3187	+	14.6042i	−1.06983	+	0.498869i	−0.876072	−	0.482181i	$-0.839845\pi$
$857$	−31.3187	+	14.6042i	−1.06983	+	0.498869i	−0.193756	+	0.981050i	$0.562067\pi$
$858$	15.1466	+	47.8395i	0.517095	+	1.63321i
$859$	−14.4078	+	17.1705i	−0.491587	+	0.585850i	−0.953620	−	0.301012i	$-0.902676\pi$
$859$	−14.4078	+	17.1705i	−0.491587	+	0.585850i	0.462034	+	0.886862i	$0.347120\pi$
$860$	−0.215478	+	0.643896i	−0.00734775	+	0.0219567i
$861$	28.4647	+	3.71287i	0.970073	+	0.126534i
$862$	−8.19621	+	11.7054i	−0.279164	+	0.398688i
$863$	34.4337	+	34.4337i	1.17214	+	1.17214i	0.981700	+	0.190436i	$0.0609900\pi$
$863$	34.4337	+	34.4337i	1.17214	+	1.17214i	0.190436	+	0.981700i	$0.439010\pi$
$864$	−6.09114	+	3.19864i	−0.207225	+	0.108820i
$865$	−10.8212	+	13.6029i	−0.367933	+	0.462511i
$866$	47.8011	−	8.42862i	1.62435	−	0.286416i
$867$	−1.54095	−	11.5976i	−0.0523334	−	0.393876i
$868$	0.471713	−	1.01159i	0.0160110	−	0.0343357i
$869$	1.37423	+	1.15312i	0.0466175	+	0.0391168i
$870$	−33.5597	+	5.35482i	−1.13778	+	0.181545i
$871$	−45.9694	−	16.7315i	−1.55762	−	0.566926i
$872$	−41.1477	−	11.0255i	−1.39344	−	0.373370i
$873$	−26.1197	−	30.9776i	−0.884017	−	1.04843i
$874$	5.77009	+	3.33137i	0.195176	+	0.112685i
$875$	−5.47747	−	21.1921i	−0.185172	−	0.716423i
$876$	−1.98765	−	0.624094i	−0.0671564	−	0.0210862i
$877$	11.3525	−	7.94910i	0.383347	−	0.268422i	−0.365980	−	0.930623i	$-0.619266\pi$
$877$	11.3525	−	7.94910i	0.383347	−	0.268422i	0.749327	+	0.662201i	$0.230377\pi$
$878$	−15.1584	+	10.6140i	−0.511571	+	0.358206i
$879$	−15.3768	+	14.1240i	−0.518645	+	0.476391i
$880$	−23.0074	+	24.2425i	−0.775580	+	0.817214i
$881$	−20.3929	−	11.7738i	−0.687054	−	0.396671i	0.115453	−	0.993313i	$-0.463168\pi$
$881$	−20.3929	−	11.7738i	−0.687054	−	0.396671i	−0.802507	+	0.596642i	$0.796501\pi$
$882$	10.9458	+	6.28476i	0.368565	+	0.211619i
$883$	−15.8795	−	4.25489i	−0.534386	−	0.143188i	−0.0184733	−	0.999829i	$-0.505881\pi$
$883$	−15.8795	−	4.25489i	−0.534386	−	0.143188i	−0.515913	+	0.856641i	$0.672547\pi$
$884$	−3.58792	−	1.30590i	−0.120675	−	0.0439221i
$885$	−1.94907	+	18.7511i	−0.0655172	+	0.630311i
$886$	11.6044	+	9.73725i	0.389857	+	0.327129i
$887$	−4.33234	+	9.29073i	−0.145466	+	0.311952i	−0.965518	−	0.260336i	$-0.916167\pi$
$887$	−4.33234	+	9.29073i	−0.145466	+	0.311952i	0.820052	+	0.572289i	$0.193944\pi$
$888$	34.2851	+	14.1534i	1.15053	+	0.474958i
$889$	6.94156	−	1.22398i	0.232812	−	0.0410511i
$890$	4.53038	+	3.60397i	0.151859	+	0.120805i
$891$	29.5442	−	25.0320i	0.989769	−	0.838604i
$892$	2.76005	+	2.76005i	0.0924133	+	0.0924133i
$893$	4.23638	−	6.05018i	0.141765	−	0.202461i
$894$	7.65882	+	18.4278i	0.256149	+	0.616316i
$895$	−4.38817	−	8.80234i	−0.146680	−	0.294230i
$896$	−11.2227	+	13.3748i	−0.374926	+	0.446819i
$897$	47.9843	+	10.5778i	1.60215	+	0.353181i
$898$	−1.94540	+	0.907153i	−0.0649187	+	0.0302721i
$899$	8.00123	+	13.8585i	0.266856	+	0.462208i
$900$	3.52811	+	0.115099i	0.117604	+	0.00383664i
$901$	−2.14414	+	3.71376i	−0.0714317	+	0.123723i
$902$	−4.21697	+	48.2002i	−0.140410	+	1.60489i
$903$	0.185633	−	4.37149i	0.00617748	−	0.145474i
$904$	−39.8832	−	7.03248i	−1.32649	−	0.233897i
$905$	−12.7588	−	0.780964i	−0.424118	−	0.0259601i
$906$	10.9819	−	34.9756i	0.364848	−	1.16199i
$907$	−13.4551	−	1.17717i	−0.446769	−	0.0390872i	−0.138448	−	0.990370i	$-0.544211\pi$
$907$	−13.4551	−	1.17717i	−0.446769	−	0.0390872i	−0.308321	+	0.951283i	$0.599767\pi$
$908$	4.11293	−	1.10206i	0.136492	−	0.0365730i
$909$	11.5554	−	5.42200i	0.383268	−	0.179836i
$910$	4.35842	−	29.1535i	0.144480	−	0.966430i
$911$	4.95701	−	13.6193i	0.164233	−	0.451227i	−0.830090	−	0.557629i	$-0.811711\pi$
$911$	4.95701	−	13.6193i	0.164233	−	0.451227i	0.994323	+	0.106403i	$0.0339332\pi$
$912$	3.97999	+	3.63825i	0.131791	+	0.120475i
$913$	39.7348	−	3.47635i	1.31503	−	0.115050i
$914$	6.91502	−	2.51686i	0.228729	−	0.0832504i
$915$	7.91428	+	31.5880i	0.261638	+	1.04427i
$916$	−0.776272	−	4.40246i	−0.0256488	−	0.145461i
$917$	−0.768724	+	0.768724i	−0.0253855	+	0.0253855i
$918$	−1.04280	−	22.0694i	−0.0344176	−	0.728399i
$919$		−	11.7599i		−	0.387925i	−0.981009	−	0.193962i	$-0.937866\pi$
$919$		−	11.7599i		−	0.387925i	0.981009	−	0.193962i	$-0.0621340\pi$
$920$	10.5526	+	35.6312i	0.347910	+	1.17473i
$921$	5.26444	−	40.3597i	0.173469	−	1.32990i
$922$	−18.2970	−	8.53202i	−0.602579	−	0.280987i
$923$	2.51046	+	28.6946i	0.0826327	+	0.944496i
$924$	−1.58175	+	3.04739i	−0.0520357	+	0.100252i
$925$	−22.1974	−	28.4169i	−0.729846	−	0.934340i
$926$	38.0276	−	21.9552i	1.24966	−	0.721494i
$927$	30.7499	+	25.6773i	1.00996	+	0.843353i
$928$	2.26359	+	8.44784i	0.0743061	+	0.277314i
$929$	36.0388	−	30.2401i	1.18239	−	0.992146i	0.182433	−	0.983218i	$-0.441603\pi$
$929$	36.0388	−	30.2401i	1.18239	−	0.992146i	0.999960	−	0.00892776i	$-0.00284183\pi$
$930$	4.07145	+	11.7804i	0.133508	+	0.386296i
$931$	−0.492867	+	2.79519i	−0.0161531	+	0.0916086i
$932$	1.02089	+	1.45799i	0.0334405	+	0.0477579i
$933$	3.69441	−	5.81437i	0.120950	−	0.190354i
$934$	−19.3932	−	23.1119i	−0.634563	−	0.756243i
$935$	11.2848	+	28.6522i	0.369054	+	0.937027i
$936$	40.9700	+	18.9856i	1.33915	+	0.620565i
$937$	−9.80740	+	36.6017i	−0.320394	+	1.19573i	0.598468	+	0.801147i	$0.295776\pi$
$937$	−9.80740	+	36.6017i	−0.320394	+	1.19573i	−0.918862	+	0.394580i	$0.870890\pi$
$938$	10.6074	+	22.7477i	0.346346	+	0.742740i
$939$	1.40595	+	0.729759i	0.0458814	+	0.0238148i
$940$	4.24987	−	0.864439i	0.138616	−	0.0281949i
$941$	−3.79401	−	10.4240i	−0.123681	−	0.339811i	0.862364	−	0.506289i	$-0.168983\pi$
$941$	−3.79401	−	10.4240i	−0.123681	−	0.339811i	−0.986045	+	0.166477i	$0.946761\pi$
$942$	−18.6227	−	24.2096i	−0.606760	−	0.788793i
$943$	38.8098	+	27.1749i	1.26382	+	0.884937i
$944$	−16.9098			−0.550367
$945$	−22.0519	+	5.58105i	−0.717349	+	0.181552i
$946$	7.37489			0.239778
$947$	−13.0294	−	9.12331i	−0.423400	−	0.296468i	0.342391	−	0.939558i	$-0.388763\pi$
$947$	−13.0294	−	9.12331i	−0.423400	−	0.296468i	−0.765791	+	0.643090i	$0.777652\pi$
$948$	0.168470	−	0.0223842i	0.00547165	−	0.000727006i
$949$	8.86092	+	24.3452i	0.287638	+	0.790278i
$950$	−1.83887	−	5.66126i	−0.0596607	−	0.183675i
$951$	−2.04674	−	45.6276i	−0.0663701	−	1.47958i
$952$	7.86402	+	16.8644i	0.254874	+	0.546580i
$953$	−9.45180	+	35.2746i	−0.306174	+	1.14266i	0.625756	+	0.780019i	$0.284790\pi$
$953$	−9.45180	+	35.2746i	−0.306174	+	1.14266i	−0.931930	+	0.362638i	$0.881876\pi$
$954$	3.05197	−	4.38090i	0.0988113	−	0.141837i
$955$	12.8639	−	29.5813i	0.416268	−	0.957227i
$956$	−1.89177	−	2.25453i	−0.0611843	−	0.0729167i
$957$	−22.7818	−	43.6361i	−0.736430	−	1.41055i
$958$	−17.4002	−	24.8501i	−0.562176	−	0.802871i
$959$	2.05447	−	11.6515i	0.0663422	−	0.376245i
$960$	2.39087	+	33.6363i	0.0771648	+	1.08561i
$961$	−19.2514	+	16.1538i	−0.621012	+	0.521091i
$962$	−12.5685	−	46.9062i	−0.405224	−	1.51232i
$963$	43.5361	−	0.103984i	1.40293	−	0.00335084i
$964$	3.48953	−	2.01468i	0.112390	−	0.0648886i
$965$	−20.2695	−	33.0803i	−0.652499	−	1.06489i
$966$	−13.5710	−	21.2462i	−0.436640	−	0.683584i
$967$	−0.170714	−	1.95128i	−0.00548981	−	0.0627488i	0.992956	−	0.118487i	$-0.0378044\pi$
$967$	−0.170714	−	1.95128i	−0.00548981	−	0.0627488i	−0.998445	+	0.0557381i	$0.982249\pi$
$968$	−20.2162	−	9.42696i	−0.649773	−	0.302994i
$969$	4.58790	−	1.90679i	0.147385	−	0.0612550i
$970$	−38.4685	+	11.3929i	−1.23515	+	0.365805i
$971$		−	27.5442i		−	0.883934i	−0.897031	−	0.441967i	$-0.854281\pi$
$971$		−	27.5442i		−	0.883934i	0.897031	−	0.441967i	$-0.145719\pi$
$972$	0.138130	−	3.66587i	0.00443052	−	0.117583i
$973$	25.6369	−	25.6369i	0.821881	−	0.821881i
$974$	−4.27366	−	24.2371i	−0.136937	−	0.776607i
$975$	−25.5310	−	35.7099i	−0.817645	−	1.14363i
$976$	−27.4477	+	9.99016i	−0.878581	+	0.319777i
$977$	−32.5167	+	2.84484i	−1.04030	+	0.0910146i	−0.594483	−	0.804108i	$-0.702643\pi$
$977$	−32.5167	+	2.84484i	−1.04030	+	0.0910146i	−0.445819	+	0.895123i	$0.647088\pi$
$978$	−3.67586	+	16.6749i	−0.117541	+	0.533205i
$979$	−2.86792	+	7.87954i	−0.0916591	+	0.251831i
$980$	−1.33977	+	0.991278i	−0.0427973	+	0.0316652i
$981$	30.3595	−	30.5049i	0.969305	−	0.973946i
$982$	11.8947	−	3.18718i	0.379575	−	0.101707i
$983$	−31.9076	−	2.79155i	−1.01769	−	0.0890367i	−0.433919	−	0.900952i	$-0.642870\pi$
$983$	−31.9076	−	2.79155i	−1.01769	−	0.0890367i	−0.583775	+	0.811915i	$0.698425\pi$
$984$	29.4531	+	32.0654i	0.938930	+	1.02221i
$985$	−22.7961	+	20.1664i	−0.726346	+	0.642556i
$986$	−27.6596	−	4.87713i	−0.880860	−	0.155319i
$987$	−24.7738	+	12.9340i	−0.788558	+	0.411695i
$988$	−0.0931716	+	1.06496i	−0.00296418	+	0.0338808i
$989$	3.61075	−	6.25401i	0.114815	−	0.198866i
$990$	−10.9755	−	36.7365i	−0.348824	−	1.16756i
$991$	24.5859	+	42.5840i	0.780995	+	1.35272i	0.931362	+	0.364094i	$0.118621\pi$
$991$	24.5859	+	42.5840i	0.780995	+	1.35272i	−0.150367	+	0.988630i	$0.548046\pi$
$992$	2.90712	−	1.35561i	0.0923012	−	0.0430407i
$993$	−15.0164	+	16.4269i	−0.476531	+	0.521291i
$994$	9.49956	−	11.3211i	0.301308	−	0.359084i
$995$	−17.9906	+	8.96871i	−0.570339	+	0.284327i
$996$	2.29676	−	3.00060i	0.0727755	−	0.0950778i
$997$	−18.0163	+	25.7299i	−0.570581	+	0.814874i	−0.995928	−	0.0901563i	$-0.971263\pi$
$997$	−18.0163	+	25.7299i	−0.570581	+	0.814874i	0.425347	+	0.905031i	$0.360152\pi$
$998$	19.4085	+	19.4085i	0.614364	+	0.614364i
$999$	−29.6478	+	22.9188i	−0.938014	+	0.725118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.6	yes	192
3.2	odd	2		405.2.r.a.152.11		192
5.2	odd	4		675.2.ba.b.68.11		192
5.3	odd	4	inner	135.2.q.a.68.6	yes	192
5.4	even	2		675.2.ba.b.257.11		192
15.8	even	4		405.2.r.a.233.11		192
27.2	odd	18	inner	135.2.q.a.2.6	✓	192
27.25	even	9		405.2.r.a.332.11		192
135.2	even	36		675.2.ba.b.218.11		192
135.29	odd	18		675.2.ba.b.407.11		192
135.83	even	36	inner	135.2.q.a.83.6	yes	192
135.133	odd	36		405.2.r.a.8.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.6	✓	192	27.2	odd	18	inner
135.2.q.a.68.6	yes	192	5.3	odd	4	inner
135.2.q.a.83.6	yes	192	135.83	even	36	inner
135.2.q.a.122.6	yes	192	1.1	even	1	trivial
405.2.r.a.8.11		192	135.133	odd	36
405.2.r.a.152.11		192	3.2	odd	2
405.2.r.a.233.11		192	15.8	even	4
405.2.r.a.332.11		192	27.25	even	9
675.2.ba.b.68.11		192	5.2	odd	4
675.2.ba.b.218.11		192	135.2	even	36
675.2.ba.b.257.11		192	5.4	even	2
675.2.ba.b.407.11		192	135.29	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08817 - 0.761943i) q^{2} +(0.660916 - 1.60100i) q^{3} +(-0.0804885 - 0.221140i) q^{4} +(1.23426 - 1.86457i) q^{5} +(-1.93906 + 1.23857i) q^{6} +(0.827388 + 1.77434i) q^{7} +(-0.768546 + 2.86825i) q^{8} +(-2.12638 - 2.11625i) q^{9} +(-2.76377 + 1.08853i) q^{10} +(-2.76562 - 3.29594i) q^{11} +(-0.407241 - 0.0172933i) q^{12} +(2.90740 + 4.15220i) q^{13} +(0.451609 - 2.56120i) q^{14} +(-2.16943 - 3.20836i) q^{15} +(2.66120 - 2.23301i) q^{16} +(-0.828434 - 3.09176i) q^{17} +(0.701399 + 3.92301i) q^{18} +(-0.776109 + 0.448087i) q^{19} +(-0.511675 - 0.122868i) q^{20} +(3.38755 - 0.151957i) q^{21} +(0.498142 + 5.69379i) q^{22} +(5.07230 + 2.36525i) q^{23} +(4.08412 + 3.12611i) q^{24} +(-1.95322 - 4.60271i) q^{25} -6.73356i q^{26} +(-4.79346 + 2.00567i) q^{27} +(0.325783 - 0.325783i) q^{28} +(1.14702 + 6.50507i) q^{29} +(-0.0838887 + 5.14422i) q^{30} +(2.27652 - 0.828586i) q^{31} +(1.31900 - 0.115398i) q^{32} +(-7.10463 + 2.24941i) q^{33} +(-1.45427 + 3.99557i) q^{34} +(4.32959 + 0.647269i) q^{35} +(-0.296839 + 0.640563i) q^{36} +(6.96604 - 1.86654i) q^{37} +(1.18595 + 0.103757i) q^{38} +(8.56920 - 1.91049i) q^{39} +(4.39947 + 4.97316i) q^{40} +(8.33680 + 1.47000i) q^{41} +(-3.80200 - 2.41576i) q^{42} +(0.112459 - 1.28541i) q^{43} +(-0.506265 + 0.876877i) q^{44} +(-6.57039 + 1.35279i) q^{45} +(-3.71732 - 6.43859i) q^{46} +(-7.46943 + 3.48305i) q^{47} +(-1.81622 - 5.73641i) q^{48} +(2.03580 - 2.42617i) q^{49} +(-1.38157 + 6.49676i) q^{50} +(-5.49742 - 0.717071i) q^{51} +(0.684206 - 0.977148i) q^{52} +(-0.947342 - 0.947342i) q^{53} +(6.74430 + 1.46984i) q^{54} +(-9.55899 + 1.08866i) q^{55} +(-5.72514 + 1.00950i) q^{56} +(0.204443 + 1.53869i) q^{57} +(3.70835 - 7.95258i) q^{58} +(-3.72879 - 3.12883i) q^{59} +(-0.534885 + 0.737984i) q^{60} +(-7.90101 - 2.87573i) q^{61} +(-3.10857 - 0.832940i) q^{62} +(1.99560 - 5.52388i) q^{63} +(-7.54029 - 4.35339i) q^{64} +(11.3305 - 0.296169i) q^{65} +(9.44496 + 2.96559i) q^{66} +(-7.90560 + 5.53556i) q^{67} +(-0.617033 + 0.432051i) q^{68} +(7.13912 - 6.55750i) q^{69} +(-4.21814 - 4.00324i) q^{70} +(4.92123 + 2.84127i) q^{71} +(7.70415 - 4.47256i) q^{72} +(4.93694 + 1.32285i) q^{73} +(-9.00242 - 3.27661i) q^{74} +(-8.65984 + 0.0851040i) q^{75} +(0.161558 + 0.135563i) q^{76} +(3.55988 - 7.63418i) q^{77} +(-10.7804 - 4.45032i) q^{78} +(-0.410612 + 0.0724019i) q^{79} +(-0.879000 - 7.71810i) q^{80} +(0.0429919 + 8.99990i) q^{81} +(-7.95178 - 7.95178i) q^{82} +(-5.31732 + 7.59392i) q^{83} +(-0.306263 - 0.736893i) q^{84} +(-6.78729 - 2.27135i) q^{85} +(-1.10179 + 1.31306i) q^{86} +(11.1727 + 2.46293i) q^{87} +(11.5791 - 5.39942i) q^{88} +(-0.974450 - 1.68780i) q^{89} +(8.18043 + 3.53420i) q^{90} +(-4.96186 + 8.59420i) q^{91} +(0.114791 - 1.31207i) q^{92} +(0.178025 - 4.19233i) q^{93} +(10.7819 + 1.90114i) q^{94} +(-0.122429 + 2.00016i) q^{95} +(0.686998 - 2.18799i) q^{96} +(13.4552 + 1.17718i) q^{97} +(-4.06390 + 1.08892i) q^{98} +(-1.09426 + 12.8612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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