LMFDB - Embedded newform 231.2.ba.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(19,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("231.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.ba (of order $30$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	231.19
Dual form			231.2.ba.a.73.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58179 + 0.166253i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(0.518133 - 0.110133i) q^{4} +(1.31309 + 2.94925i) q^{5} +(1.28675 + 0.934876i) q^{6} +(-2.10118 - 1.60780i) q^{7} +(2.22405 - 0.722639i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-1.58179 + 0.166253i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(0.518133 - 0.110133i) q^{4} +(1.31309 + 2.94925i) q^{5} +(1.28675 + 0.934876i) q^{6} +(-2.10118 - 1.60780i) q^{7} +(2.22405 - 0.722639i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-2.56736 - 4.44679i) q^{10} +(-1.47975 - 2.96822i) q^{11} +(-0.458741 - 0.264854i) q^{12} +(-3.35577 + 2.43811i) q^{13} +(3.59094 + 2.19388i) q^{14} +(0.997616 - 3.07035i) q^{15} +(-4.36567 + 1.94372i) q^{16} +(-0.658873 + 6.26876i) q^{17} +(-0.330685 - 1.55575i) q^{18} +(-6.37445 - 1.35493i) q^{19} +(1.00516 + 1.38349i) q^{20} +(0.485653 + 2.60080i) q^{21} +(2.83414 + 4.44909i) q^{22} +(-2.41905 + 4.18991i) q^{23} +(-2.13633 - 0.951157i) q^{24} +(-3.62820 + 4.02952i) q^{25} +(4.90279 - 4.41449i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-1.26576 - 0.601647i) q^{28} +(-2.62883 - 0.854157i) q^{29} +(-1.06757 + 5.02251i) q^{30} +(0.631813 - 1.41908i) q^{31} +(2.53203 - 1.46187i) q^{32} +(-0.886456 + 3.19597i) q^{33} -10.0254i q^{34} +(1.98277 - 8.30810i) q^{35} +(0.163689 + 0.503782i) q^{36} +(-2.66510 - 2.95989i) q^{37} +(10.3083 + 1.08345i) q^{38} +(4.12524 + 0.433580i) q^{39} +(5.05162 + 5.61039i) q^{40} +(-2.87918 - 8.86121i) q^{41} +(-1.20059 - 4.03318i) q^{42} -2.68093i q^{43} +(-1.09361 - 1.37496i) q^{44} +(-2.79584 + 1.61418i) q^{45} +(3.12985 - 7.02975i) q^{46} +(-2.43302 + 11.4465i) q^{47} +(4.54493 + 1.47674i) q^{48} +(1.82994 + 6.75658i) q^{49} +(5.06914 - 6.97707i) q^{50} +(4.68425 - 4.21772i) q^{51} +(-1.47022 + 1.63285i) q^{52} +(4.43106 + 1.97284i) q^{53} +(-0.795253 + 1.37742i) q^{54} +(6.81096 - 8.26170i) q^{55} +(-5.83500 - 2.05744i) q^{56} +(3.83052 + 5.27225i) q^{57} +(4.30026 + 0.914049i) q^{58} +(1.78351 + 8.39076i) q^{59} +(0.178753 - 1.70072i) q^{60} +(10.2185 - 4.54955i) q^{61} +(-0.763472 + 2.34973i) q^{62} +(1.37936 - 2.25773i) q^{63} +(3.97020 - 2.88452i) q^{64} +(-11.5970 - 6.69554i) q^{65} +(0.870850 - 5.20273i) q^{66} +(1.15470 + 2.00000i) q^{67} +(0.349010 + 3.32061i) q^{68} +(4.60130 - 1.49505i) q^{69} +(-1.75508 + 13.4713i) q^{70} +(-1.03618 - 0.752831i) q^{71} +(0.951157 + 2.13633i) q^{72} +(0.478632 - 0.101736i) q^{73} +(4.70772 + 4.23885i) q^{74} +(5.39256 - 0.566780i) q^{75} -3.45204 q^{76} +(-1.66308 + 8.61592i) q^{77} -6.59736 q^{78} +(-6.78913 + 0.713566i) q^{79} +(-11.4650 - 10.3232i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(6.02747 + 13.5379i) q^{82} +(5.01938 + 3.64679i) q^{83} +(0.538065 + 1.29407i) q^{84} +(-19.3533 + 6.28826i) q^{85} +(0.445713 + 4.24068i) q^{86} +(1.38206 + 2.39379i) q^{87} +(-5.43600 - 5.53215i) q^{88} +(-7.03808 - 4.06344i) q^{89} +(4.15407 - 3.01811i) q^{90} +(10.9711 + 0.272505i) q^{91} +(-0.791942 + 2.43735i) q^{92} +(-1.41908 + 0.631813i) q^{93} +(1.94553 - 18.5104i) q^{94} +(-4.37420 - 20.5790i) q^{95} +(-2.85984 - 0.607878i) q^{96} +(0.702405 + 0.966777i) q^{97} +(-4.01788 - 10.3833i) q^{98} +(2.79728 - 1.78191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−1.58179	+	0.166253i	−1.11850	+	0.117559i	−0.645684	−	0.763605i	$-0.723428\pi$
$2$	−1.58179	+	0.166253i	−1.11850	+	0.117559i	−0.472812	+	0.881163i	$0.656761\pi$
$3$	−0.743145	−	0.669131i	−0.429055	−	0.386323i
$3$	−0.743145	−	0.669131i	−0.429055	−	0.386323i
$4$	0.518133	−	0.110133i	0.259066	−	0.0550663i
$5$	1.31309	+	2.94925i	0.587231	+	1.31894i	0.925804	+	0.378003i	$0.123389\pi$
$5$	1.31309	+	2.94925i	0.587231	+	1.31894i	−0.338573	+	0.940940i	$0.609944\pi$
$6$	1.28675	+	0.934876i	0.525312	+	0.381661i
$7$	−2.10118	−	1.60780i	−0.794172	−	0.607693i
$7$	−2.10118	−	1.60780i	−0.794172	−	0.607693i
$8$	2.22405	−	0.722639i	0.786321	−	0.255491i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	−2.56736	−	4.44679i	−0.811869	−	1.40620i
$11$	−1.47975	−	2.96822i	−0.446162	−	0.894952i
$11$	−1.47975	−	2.96822i	−0.446162	−	0.894952i
$12$	−0.458741	−	0.264854i	−0.132427	−	0.0764568i
$13$	−3.35577	+	2.43811i	−0.930724	+	0.676210i	−0.946170	−	0.323670i	$-0.895083\pi$
$13$	−3.35577	+	2.43811i	−0.930724	+	0.676210i	0.0154461	+	0.999881i	$0.495083\pi$
$14$	3.59094	+	2.19388i	0.959718	+	0.586340i
$15$	0.997616	−	3.07035i	0.257583	−	0.792760i
$16$	−4.36567	+	1.94372i	−1.09142	+	0.485931i
$17$	−0.658873	+	6.26876i	−0.159800	+	1.52040i	0.561327	+	0.827594i	$0.310291\pi$
$17$	−0.658873	+	6.26876i	−0.159800	+	1.52040i	−0.721127	+	0.692803i	$0.756376\pi$
$18$	−0.330685	−	1.55575i	−0.0779431	−	0.366694i
$19$	−6.37445	−	1.35493i	−1.46240	−	0.310843i	−0.593101	−	0.805128i	$-0.702096\pi$
$19$	−6.37445	−	1.35493i	−1.46240	−	0.310843i	−0.869300	+	0.494286i	$0.835430\pi$
$20$	1.00516	+	1.38349i	0.224761	+	0.309357i
$21$	0.485653	+	2.60080i	0.105978	+	0.567540i
$22$	2.83414	+	4.44909i	0.604240	+	0.948550i
$23$	−2.41905	+	4.18991i	−0.504406	+	0.873658i	0.495581	+	0.868562i	$0.334955\pi$
$23$	−2.41905	+	4.18991i	−0.504406	+	0.873658i	−0.999987	+	0.00509560i	$0.998378\pi$
$24$	−2.13633	−	0.951157i	−0.436077	−	0.194154i
$25$	−3.62820	+	4.02952i	−0.725640	+	0.805905i
$26$	4.90279	−	4.41449i	0.961517	−	0.865754i
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−1.26576	−	0.601647i	−0.239207	−	0.113701i
$29$	−2.62883	−	0.854157i	−0.488161	−	0.158613i	0.0545866	−	0.998509i	$-0.482616\pi$
$29$	−2.62883	−	0.854157i	−0.488161	−	0.158613i	−0.542747	+	0.839896i	$0.682616\pi$
$30$	−1.06757	+	5.02251i	−0.194910	+	0.916980i
$31$	0.631813	−	1.41908i	0.113477	−	0.254874i	−0.847875	−	0.530197i	$-0.822118\pi$
$31$	0.631813	−	1.41908i	0.113477	−	0.254874i	0.961352	+	0.275323i	$0.0887848\pi$
$32$	2.53203	−	1.46187i	0.447604	−	0.258424i
$33$	−0.886456	+	3.19597i	−0.154312	+	0.556346i
$34$		−	10.0254i		−	1.71934i
$35$	1.98277	−	8.30810i	0.335149	−	1.40432i
$36$	0.163689	+	0.503782i	0.0272815	+	0.0839637i
$37$	−2.66510	−	2.95989i	−0.438139	−	0.486603i	0.483119	−	0.875555i	$-0.339504\pi$
$37$	−2.66510	−	2.95989i	−0.438139	−	0.486603i	−0.921258	+	0.388952i	$0.872837\pi$
$38$	10.3083	+	1.08345i	1.67223	+	0.175759i
$39$	4.12524	+	0.433580i	0.660567	+	0.0694284i
$40$	5.05162	+	5.61039i	0.798731	+	0.887081i
$41$	−2.87918	−	8.86121i	−0.449653	−	1.38389i	−0.877300	−	0.479943i	$-0.840657\pi$
$41$	−2.87918	−	8.86121i	−0.449653	−	1.38389i	0.427647	−	0.903946i	$-0.359343\pi$
$42$	−1.20059	−	4.03318i	−0.185255	−	0.622333i
$43$		−	2.68093i		−	0.408838i	−0.978883	−	0.204419i	$-0.934469\pi$
$43$		−	2.68093i		−	0.408838i	0.978883	−	0.204419i	$-0.0655305\pi$
$44$	−1.09361	−	1.37496i	−0.164867	−	0.207283i
$45$	−2.79584	+	1.61418i	−0.416778	+	0.240627i
$46$	3.12985	−	7.02975i	0.461471	−	1.03648i
$47$	−2.43302	+	11.4465i	−0.354893	+	1.66964i	0.332307	+	0.943171i	$0.392173\pi$
$47$	−2.43302	+	11.4465i	−0.354893	+	1.66964i	−0.687200	+	0.726469i	$0.741160\pi$
$48$	4.54493	+	1.47674i	0.656005	+	0.213149i
$49$	1.82994	+	6.75658i	0.261420	+	0.965225i
$50$	5.06914	−	6.97707i	0.716884	−	0.986707i
$51$	4.68425	−	4.21772i	0.655927	−	0.590599i
$52$	−1.47022	+	1.63285i	−0.203883	+	0.226435i
$53$	4.43106	+	1.97284i	0.608653	+	0.270990i	0.687831	−	0.725871i	$-0.258563\pi$
$53$	4.43106	+	1.97284i	0.608653	+	0.270990i	−0.0791780	+	0.996860i	$0.525230\pi$
$54$	−0.795253	+	1.37742i	−0.108220	+	0.187443i
$55$	6.81096	−	8.26170i	0.918390	−	1.11401i
$56$	−5.83500	−	2.05744i	−0.779735	−	0.274938i
$57$	3.83052	+	5.27225i	0.507364	+	0.698327i
$58$	4.30026	+	0.914049i	0.564652	+	0.120021i
$59$	1.78351	+	8.39076i	0.232193	+	1.09238i	0.927544	+	0.373713i	$0.121916\pi$
$59$	1.78351	+	8.39076i	0.232193	+	1.09238i	−0.695351	+	0.718670i	$0.744751\pi$
$60$	0.178753	−	1.70072i	0.0230768	−	0.219562i
$61$	10.2185	−	4.54955i	1.30834	−	0.582510i	0.370259	−	0.928928i	$-0.379269\pi$
$61$	10.2185	−	4.54955i	1.30834	−	0.582510i	0.938080	+	0.346418i	$0.112602\pi$
$62$	−0.763472	+	2.34973i	−0.0969610	+	0.298415i
$63$	1.37936	−	2.25773i	0.173783	−	0.284448i
$64$	3.97020	−	2.88452i	0.496275	−	0.360565i
$65$	−11.5970	−	6.69554i	−1.43843	−	0.830480i
$66$	0.870850	−	5.20273i	0.107194	−	0.640412i
$67$	1.15470	+	2.00000i	0.141069	+	0.244339i	0.927899	−	0.372830i	$-0.121613\pi$
$67$	1.15470	+	2.00000i	0.141069	+	0.244339i	−0.786830	+	0.617169i	$0.788279\pi$
$68$	0.349010	+	3.32061i	0.0423237	+	0.402683i
$69$	4.60130	−	1.49505i	0.553932	−	0.179983i
$70$	−1.75508	+	13.4713i	−0.209772	+	1.61013i
$71$	−1.03618	−	0.752831i	−0.122972	−	0.0893446i	0.524599	−	0.851349i	$-0.324215\pi$
$71$	−1.03618	−	0.752831i	−0.122972	−	0.0893446i	−0.647571	+	0.762005i	$0.724215\pi$
$72$	0.951157	+	2.13633i	0.112095	+	0.251769i
$73$	0.478632	−	0.101736i	0.0560196	−	0.0119073i	−0.179817	−	0.983700i	$-0.557550\pi$
$73$	0.478632	−	0.101736i	0.0560196	−	0.0119073i	0.235836	+	0.971793i	$0.424217\pi$
$74$	4.70772	+	4.23885i	0.547261	+	0.492756i
$75$	5.39256	−	0.566780i	0.622679	−	0.0654462i
$76$	−3.45204			−0.395976
$77$	−1.66308	+	8.61592i	−0.189526	+	0.981876i
$78$	−6.59736			−0.747004
$79$	−6.78913	+	0.713566i	−0.763837	+	0.0802825i	−0.478432	−	0.878125i	$-0.658795\pi$
$79$	−6.78913	+	0.713566i	−0.763837	+	0.0802825i	−0.285405	+	0.958407i	$0.592128\pi$
$80$	−11.4650	−	10.3232i	−1.28183	−	1.15417i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	6.02747	+	13.5379i	0.665623	+	1.49501i
$83$	5.01938	+	3.64679i	0.550949	+	0.400288i	0.828135	−	0.560529i	$-0.189402\pi$
$83$	5.01938	+	3.64679i	0.550949	+	0.400288i	−0.277186	+	0.960816i	$0.589402\pi$
$84$	0.538065	+	1.29407i	0.0587077	+	0.141195i
$85$	−19.3533	+	6.28826i	−2.09916	+	0.682057i
$86$	0.445713	+	4.24068i	0.0480625	+	0.457284i
$87$	1.38206	+	2.39379i	0.148172	+	0.256641i
$88$	−5.43600	−	5.53215i	−0.579480	−	0.589729i
$89$	−7.03808	−	4.06344i	−0.746035	−	0.430723i	0.0782247	−	0.996936i	$-0.475075\pi$
$89$	−7.03808	−	4.06344i	−0.746035	−	0.430723i	−0.824259	+	0.566212i	$0.808408\pi$
$90$	4.15407	−	3.01811i	0.437877	−	0.318137i
$91$	10.9711	+	0.272505i	1.15008	+	0.0285663i
$92$	−0.791942	+	2.43735i	−0.0825657	+	0.254111i
$93$	−1.41908	+	0.631813i	−0.147151	+	0.0655160i
$94$	1.94553	−	18.5104i	0.200666	−	1.90921i
$95$	−4.37420	−	20.5790i	−0.448783	−	2.11136i
$96$	−2.85984	−	0.607878i	−0.291882	−	0.0620413i
$97$	0.702405	+	0.966777i	0.0713184	+	0.0981613i	0.843186	−	0.537622i	$-0.180677\pi$
$97$	0.702405	+	0.966777i	0.0713184	+	0.0981613i	−0.771868	+	0.635783i	$0.780677\pi$
$98$	−4.01788	−	10.3833i	−0.405867	−	1.04887i
$99$	2.79728	−	1.78191i	0.281138	−	0.179089i
$100$	−1.43611	+	2.48741i	−0.143611	+	0.248741i
$101$	12.0092	+	5.34684i	1.19496	+	0.532031i	0.905166	−	0.425058i	$-0.139746\pi$
$101$	12.0092	+	5.34684i	1.19496	+	0.532031i	0.289795	+	0.957089i	$0.406413\pi$
$102$	−6.70831	+	7.45033i	−0.664222	+	0.737693i
$103$	0.374587	−	0.337279i	0.0369091	−	0.0332331i	−0.650470	−	0.759532i	$-0.725428\pi$
$103$	0.374587	−	0.337279i	0.0369091	−	0.0332331i	0.687379	+	0.726299i	$0.258761\pi$
$104$	−5.70154	+	7.84750i	−0.559082	+	0.769511i
$105$	−7.03268	+	4.84739i	−0.686320	+	0.473057i
$106$	−7.33701	−	2.38394i	−0.712634	−	0.231549i
$107$	−0.128129	+	0.602802i	−0.0123867	+	0.0582751i	−0.983907	−	0.178682i	$-0.942817\pi$
$107$	−0.128129	+	0.602802i	−0.0123867	+	0.0582751i	0.971520	+	0.236957i	$0.0761500\pi$
$108$	0.215452	−	0.483912i	0.0207318	−	0.0465645i
$109$	7.91519	−	4.56984i	0.758138	−	0.437711i	−0.0704888	−	0.997513i	$-0.522456\pi$
$109$	7.91519	−	4.56984i	0.758138	−	0.437711i	0.828627	+	0.559801i	$0.189123\pi$
$110$	−9.40000	+	14.2006i	−0.896255	+	1.35398i
$111$			3.98292i			0.378042i
$112$	12.2982	+	2.93503i	1.16207	+	0.277334i
$113$	−3.25545	−	10.0192i	−0.306247	−	0.942531i	−0.979209	−	0.202854i	$-0.934978\pi$
$113$	−3.25545	−	10.0192i	−0.306247	−	0.942531i	0.672962	−	0.739677i	$-0.265022\pi$
$114$	−6.93561	−	7.70278i	−0.649579	−	0.721431i
$115$	−15.5335	−	1.63264i	−1.44851	−	0.152244i
$116$	−1.45615	−	0.153048i	−0.135200	−	0.0142101i
$117$	−2.77553	−	3.08254i	−0.256598	−	0.284981i
$118$	−4.21613	−	12.9759i	−0.388127	−	1.19453i
$119$	11.4633	−	12.1125i	1.05084	−	1.11035i
$120$		−	7.54953i		−	0.689174i
$121$	−6.62066	+	8.78447i	−0.601878	+	0.798588i
$122$	−15.4071	+	8.89530i	−1.39489	+	0.805342i
$123$	−3.78966	+	8.51171i	−0.341702	+	0.767475i
$124$	0.171077	−	0.804853i	0.0153631	−	0.0722779i
$125$	−1.29648	−	0.421252i	−0.115961	−	0.0376779i
$126$	−1.80651	+	3.80059i	−0.160937	+	0.338583i
$127$	−7.63018	+	10.5020i	−0.677069	+	0.931905i	−0.999894	−	0.0145535i	$-0.995367\pi$
$127$	−7.63018	+	10.5020i	−0.677069	+	0.931905i	0.322825	+	0.946459i	$0.395367\pi$
$128$	−10.1460	+	9.13549i	−0.896787	+	0.807471i
$129$	−1.79389	+	1.99232i	−0.157943	+	0.175414i
$130$	19.4572	+	8.66292i	1.70651	+	0.759788i
$131$	−0.429384	+	0.743715i	−0.0375154	+	0.0649786i	−0.884173	−	0.467159i	$-0.845278\pi$
$131$	−0.429384	+	0.743715i	−0.0375154	+	0.0649786i	0.846658	+	0.532137i	$0.178611\pi$
$132$	−0.107322	+	1.75356i	−0.00934118	+	0.152628i
$133$	11.2154	+	13.0958i	0.972501	+	1.13555i
$134$	−2.15900	−	2.97161i	−0.186509	−	0.256708i
$135$	3.15781	+	0.671212i	0.271781	+	0.0577687i
$136$	3.06468	+	14.4182i	0.262794	+	1.23635i
$137$	−0.0413900	+	0.393800i	−0.00353619	+	0.0336446i	−0.996148	−	0.0876912i	$-0.972051\pi$
$137$	−0.0413900	+	0.393800i	−0.00353619	+	0.0336446i	0.992612	+	0.121336i	$0.0387178\pi$
$138$	−7.02975	+	3.12985i	−0.598412	+	0.266430i
$139$	−6.34105	+	19.5158i	−0.537841	+	1.65531i	0.199587	+	0.979880i	$0.436040\pi$
$139$	−6.34105	+	19.5158i	−0.537841	+	1.65531i	−0.737429	+	0.675425i	$0.763960\pi$
$140$	0.112346	−	4.52306i	0.00949495	−	0.382269i
$141$	9.46728	−	6.87838i	0.797288	−	0.579264i
$142$	1.76419	+	1.01855i	0.148047	+	0.0854751i
$143$	12.2026	+	6.35287i	1.02043	+	0.531253i
$144$	−2.38941	−	4.13858i	−0.199118	−	0.344882i
$145$	−0.932762	−	8.87464i	−0.0774617	−	0.736999i
$146$	−0.740183	+	0.240500i	−0.0612579	+	0.0199039i
$147$	3.16112	−	6.24558i	0.260725	−	0.515127i
$148$	−1.70685	−	1.24010i	−0.140303	−	0.101936i
$149$	−2.89641	−	6.50544i	−0.237283	−	0.532946i	0.755176	−	0.655522i	$-0.227551\pi$
$149$	−2.89641	−	6.50544i	−0.237283	−	0.532946i	−0.992459	+	0.122576i	$0.960885\pi$
$150$	−8.43568	+	1.79306i	−0.688770	+	0.146403i
$151$	3.68312	+	3.31630i	0.299728	+	0.269876i	0.805247	−	0.592939i	$-0.202032\pi$
$151$	3.68312	+	3.31630i	0.299728	+	0.269876i	−0.505519	+	0.862815i	$0.668699\pi$
$152$	−15.1562	+	1.59299i	−1.22933	+	0.129208i
$153$	−6.30329			−0.509590
$154$	1.19823	−	13.9051i	0.0965558	−	1.12050i
$155$	5.01483			0.402801
$156$	2.18517	−	0.229671i	0.174954	−	0.0183884i
$157$	−1.37613	−	1.23907i	−0.109827	−	0.0988888i	0.612388	−	0.790558i	$-0.290209\pi$
$157$	−1.37613	−	1.23907i	−0.109827	−	0.0988888i	−0.722215	+	0.691669i	$0.756876\pi$
$158$	10.6204	−	2.25743i	0.844911	−	0.179591i
$159$	−1.97284	−	4.43106i	−0.156456	−	0.351406i
$160$	7.63618	+	5.54801i	0.603693	+	0.438609i
$161$	11.8194	−	4.91442i	0.931501	−	0.387311i
$162$	1.51266	−	0.491493i	0.118846	−	0.0386154i
$163$	−2.50218	−	23.8066i	−0.195986	−	1.86468i	−0.444140	−	0.895957i	$-0.646491\pi$
$163$	−2.50218	−	23.8066i	−0.195986	−	1.86468i	0.248155	−	0.968720i	$-0.420176\pi$
$164$	−2.46771	−	4.27419i	−0.192695	−	0.333758i
$165$	−10.5897	+	1.58221i	−0.824406	+	0.123175i
$166$	−8.54591	−	4.93398i	−0.663291	−	0.382951i
$167$	−11.3908	+	8.27590i	−0.881446	+	0.640408i	−0.933634	−	0.358229i	$-0.883381\pi$
$167$	−11.3908	+	8.27590i	−0.881446	+	0.640408i	0.0521875	+	0.998637i	$0.483381\pi$
$168$	2.95955	+	5.43336i	0.228334	+	0.419193i
$169$	1.29960	−	3.99976i	0.0999693	−	0.307674i
$170$	29.5674	−	13.1643i	2.26772	−	1.00965i
$171$	0.681198	−	6.48116i	0.0520925	−	0.495627i
$172$	−0.295258	−	1.38908i	−0.0225132	−	0.105916i
$173$	8.43142	+	1.79215i	0.641029	+	0.136255i	0.516948	−	0.856017i	$-0.327068\pi$
$173$	8.43142	+	1.79215i	0.641029	+	0.136255i	0.124082	+	0.992272i	$0.460402\pi$
$174$	−2.58410	−	3.55671i	−0.195900	−	0.269633i
$175$	14.1022	−	2.63333i	1.06603	−	0.199061i
$176$	12.2295	+	10.0821i	0.921835	+	0.759963i
$177$	4.28911	−	7.42895i	0.322389	−	0.558394i
$178$	11.8083	+	5.25741i	0.885072	+	0.394060i
$179$	5.62978	−	6.25251i	0.420790	−	0.467334i	−0.495058	−	0.868860i	$-0.664853\pi$
$179$	5.62978	−	6.25251i	0.420790	−	0.467334i	0.915848	+	0.401525i	$0.131520\pi$
$180$	−1.27084	+	1.14427i	−0.0947229	+	0.0852888i
$181$	2.41775	−	3.32774i	0.179710	−	0.247349i	−0.709653	−	0.704551i	$-0.751148\pi$
$181$	2.41775	−	3.32774i	0.179710	−	0.247349i	0.889363	+	0.457202i	$0.151148\pi$
$182$	−17.3993	+	1.39293i	−1.28972	+	0.103251i
$183$	−10.6380	−	3.45651i	−0.786386	−	0.255512i
$184$	−2.35230	+	11.0667i	−0.173414	+	0.815847i
$185$	5.22993	−	11.7466i	0.384512	−	0.863629i
$186$	2.13964	−	1.23532i	0.156886	−	0.0905783i
$187$	19.5820	−	7.32053i	1.43198	−	0.535330i
$188$			6.19875i			0.452090i
$189$	−2.53578	+	0.754849i	−0.184451	+	0.0549072i
$190$	10.3404	+	31.8245i	0.750171	+	2.30879i
$191$	5.81995	+	6.46371i	0.421117	+	0.467698i	0.915951	−	0.401290i	$-0.131438\pi$
$191$	5.81995	+	6.46371i	0.421117	+	0.467698i	−0.494834	+	0.868987i	$0.664771\pi$
$192$	−4.88055	−	0.512967i	−0.352224	−	0.0370202i
$193$	−11.0645	−	1.16293i	−0.796441	−	0.0837093i	−0.302437	−	0.953169i	$-0.597800\pi$
$193$	−11.0645	−	1.16293i	−0.796441	−	0.0837093i	−0.494003	+	0.869460i	$0.664467\pi$
$194$	−1.27179	−	1.41246i	−0.0913091	−	0.101409i
$195$	4.13807	+	12.7357i	0.296334	+	0.912021i
$196$	1.69227	+	3.29927i	0.120876	+	0.235662i
$197$			9.69666i			0.690859i	0.938445	+	0.345429i	$0.112267\pi$
$197$			9.69666i			0.690859i	−0.938445	+	0.345429i	$0.887733\pi$
$198$	−4.12847	+	3.28367i	−0.293398	+	0.233360i
$199$	2.06014	−	1.18942i	0.146039	−	0.0843159i	−0.425200	−	0.905100i	$-0.639796\pi$
$199$	2.06014	−	1.18942i	0.146039	−	0.0843159i	0.571239	+	0.820784i	$0.306463\pi$
$200$	−5.15742	+	11.5838i	−0.364685	+	0.819095i
$201$	0.480151	−	2.25893i	0.0338673	−	0.159333i
$202$	−19.8850	−	6.46103i	−1.39910	−	0.454596i
$203$	4.15033	+	6.02138i	0.291296	+	0.422618i
$204$	1.96256	−	2.70123i	0.137406	−	0.189124i
$205$	22.3533	−	20.1270i	1.56122	−	1.40573i
$206$	−0.536445	+	0.595782i	−0.0373759	+	0.0415101i
$207$	−4.41982	−	1.96783i	−0.307199	−	0.136774i
$208$	9.91120	−	17.1667i	0.687218	−	1.19030i
$209$	5.41088	+	20.9257i	0.374279	+	1.44746i
$210$	10.3184	−	8.83677i	0.712034	−	0.609795i
$211$	−14.1987	−	19.5428i	−0.977476	−	1.34538i	−0.938178	−	0.346152i	$-0.887488\pi$
$211$	−14.1987	−	19.5428i	−0.977476	−	1.34538i	−0.0392974	−	0.999228i	$-0.512512\pi$
$212$	2.51315	+	0.534187i	0.172604	+	0.0366881i
$213$	0.266292	+	1.25280i	0.0182460	+	0.0858407i
$214$	0.102457	−	0.974809i	0.00700379	−	0.0666366i
$215$	7.90673	−	3.52030i	0.539234	−	0.240083i
$216$	0.722639	−	2.22405i	0.0491693	−	0.151328i
$217$	−3.60915	+	1.96591i	−0.245005	+	0.133454i
$218$	−11.7604	+	8.54446i	−0.796518	+	0.578704i
$219$	−0.423768	−	0.244662i	−0.0286356	−	0.0165328i
$220$	2.61910	−	5.03076i	0.176580	−	0.339174i
$221$	−13.0729	−	22.6429i	−0.879378	−	1.52313i
$222$	−0.662174	−	6.30016i	−0.0444422	−	0.422839i
$223$	10.3192	−	3.35290i	0.691022	−	0.224527i	0.0576075	−	0.998339i	$-0.481653\pi$
$223$	10.3192	−	3.35290i	0.691022	−	0.224527i	0.633415	+	0.773813i	$0.281653\pi$
$224$	−7.67065	−	0.999353i	−0.512517	−	0.0667721i
$225$	−4.38670	−	3.18712i	−0.292447	−	0.212475i
$226$	6.81517	+	15.3071i	0.453339	+	1.01822i
$227$	9.32048	−	1.98113i	0.618622	−	0.131492i	0.112068	−	0.993701i	$-0.464253\pi$
$227$	9.32048	−	1.98113i	0.618622	−	0.131492i	0.506554	+	0.862208i	$0.330919\pi$
$228$	2.56536	+	2.30986i	0.169895	+	0.152974i
$229$	−2.57100	+	0.270223i	−0.169897	+	0.0178568i	−0.189095	−	0.981959i	$-0.560555\pi$
$229$	−2.57100	+	0.270223i	−0.169897	+	0.0178568i	0.0191982	+	0.999816i	$0.493889\pi$
$230$	24.8422			1.63805
$231$	7.00109	−	5.29006i	0.460638	−	0.348060i
$232$	−6.46390			−0.424376
$233$	−20.1841	+	2.12143i	−1.32230	+	0.138980i	−0.739237	−	0.673445i	$-0.764814\pi$
$233$	−20.1841	+	2.12143i	−1.32230	+	0.138980i	−0.583066	+	0.812425i	$0.698147\pi$
$234$	4.90279	+	4.41449i	0.320506	+	0.288585i
$235$	−36.9533	+	7.85466i	−2.41056	+	0.512381i
$236$	1.84819	+	4.15110i	0.120307	+	0.270214i
$237$	5.52278	+	4.01253i	0.358743	+	0.260642i
$238$	−16.1189	+	21.0652i	−1.04483	+	1.36546i
$239$	17.1542	−	5.57373i	1.10961	−	0.360534i	0.303817	−	0.952731i	$-0.401739\pi$
$239$	17.1542	−	5.57373i	1.10961	−	0.360534i	0.805794	+	0.592196i	$0.201739\pi$
$240$	1.61264	+	15.3432i	0.104095	+	0.990400i
$241$	−3.45311	−	5.98097i	−0.222435	−	0.385268i	0.733112	−	0.680108i	$-0.238067\pi$
$241$	−3.45311	−	5.98097i	−0.222435	−	0.385268i	−0.955547	+	0.294840i	$0.904734\pi$
$242$	9.01207	−	14.9959i	0.579317	−	0.963974i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.79346	−	3.48266i	0.306870	−	0.222954i
$245$	−17.5239	+	14.2689i	−1.11956	+	0.911608i
$246$	4.57936	−	14.0938i	0.291969	−	0.898588i
$247$	24.6947	−	10.9948i	1.57129	−	0.699581i
$248$	0.379707	−	3.61267i	0.0241114	−	0.229405i
$249$	−1.28995	−	6.06872i	−0.0817470	−	0.384589i
$250$	2.12080	+	0.450790i	0.134131	+	0.0285104i
$251$	5.04616	+	6.94545i	0.318511	+	0.438393i	0.938012	−	0.346603i	$-0.112665\pi$
$251$	5.04616	+	6.94545i	0.318511	+	0.438393i	−0.619501	+	0.784996i	$0.712665\pi$
$252$	0.466043	−	1.32172i	0.0293579	−	0.0832604i
$253$	16.0162	+	0.980227i	1.00693	+	0.0616263i
$254$	10.3234	−	17.8806i	0.647745	−	1.12193i
$255$	18.5899	+	8.27678i	1.16415	+	0.518312i
$256$	7.96261	−	8.84338i	0.497663	−	0.552711i
$257$	−15.7583	+	14.1888i	−0.982977	+	0.885076i	−0.993381	−	0.114870i	$-0.963355\pi$
$257$	−15.7583	+	14.1888i	−0.982977	+	0.885076i	0.0104040	+	0.999946i	$0.496688\pi$
$258$	2.50634	−	3.44968i	0.156038	−	0.214767i
$259$	0.840934	+	10.5042i	0.0522531	+	0.652700i
$260$	−6.74619	−	2.19197i	−0.418381	−	0.135940i
$261$	0.574691	−	2.70371i	0.0355725	−	0.167355i
$262$	0.555551	−	1.24779i	0.0343221	−	0.0770886i
$263$	−7.94416	+	4.58656i	−0.489858	+	0.282820i	−0.724516	−	0.689258i	$-0.757936\pi$
$263$	−7.94416	+	4.58656i	−0.489858	+	0.282820i	0.234657	+	0.972078i	$0.424603\pi$
$264$	0.338004	+	7.74858i	0.0208027	+	0.476892i
$265$			15.6588i			0.961913i
$266$	−19.9177	−	18.8503i	−1.22123	−	1.15579i
$267$	2.51134	+	7.72911i	0.153692	+	0.473014i
$268$	0.818553	+	0.909095i	0.0500011	+	0.0555318i
$269$	0.408283	+	0.0429122i	0.0248934	+	0.00261640i	0.116967	−	0.993136i	$-0.462683\pi$
$269$	0.408283	+	0.0429122i	0.0248934	+	0.00261640i	−0.0920736	+	0.995752i	$0.529349\pi$
$270$	−5.10658	−	0.536724i	−0.310777	−	0.0326640i
$271$	−6.51708	−	7.23795i	−0.395884	−	0.439674i	0.511942	−	0.859020i	$-0.328926\pi$
$271$	−6.51708	−	7.23795i	−0.395884	−	0.439674i	−0.907827	+	0.419346i	$0.862260\pi$
$272$	−9.30830	−	28.6480i	−0.564399	−	1.73704i
$273$	−7.97077	−	7.54361i	−0.482413	−	0.456560i
$274$		−	0.629791i		−	0.0380471i
$275$	17.3294	+	4.80659i	1.04500	+	0.289848i
$276$	2.21943	−	1.28139i	0.133594	−	0.0771306i
$277$	−6.83291	+	15.3470i	−0.410550	+	0.922110i	0.583391	+	0.812192i	$0.301726\pi$
$277$	−6.83291	+	15.3470i	−0.410550	+	0.922110i	−0.993941	+	0.109919i	$0.964941\pi$
$278$	6.78568	−	31.9241i	0.406978	−	1.91468i
$279$	1.47734	+	0.480018i	0.0884463	+	0.0287380i
$280$	−1.59397	−	19.9105i	−0.0952578	−	1.18988i
$281$	−16.3397	+	22.4897i	−0.974745	+	1.34162i	−0.0351323	+	0.999383i	$0.511185\pi$
$281$	−16.3397	+	22.4897i	−0.974745	+	1.34162i	−0.939613	+	0.342239i	$0.888815\pi$
$282$	−13.8317	+	12.4541i	−0.823667	+	0.741633i
$283$	−10.8794	+	12.0829i	−0.646716	+	0.718251i	−0.973968	−	0.226686i	$-0.927211\pi$
$283$	−10.8794	+	12.0829i	−0.646716	+	0.718251i	0.327252	+	0.944937i	$0.393877\pi$
$284$	−0.619791	−	0.275949i	−0.0367778	−	0.0163745i
$285$	−10.5194	+	18.2201i	−0.623113	+	1.07926i
$286$	−20.3581	−	8.02020i	−1.20380	−	0.474245i
$287$	−8.19740	+	23.2482i	−0.483877	+	1.37230i
$288$	1.71853	+	2.36535i	0.101265	+	0.139380i
$289$	−22.2347	−	4.72613i	−1.30792	−	0.278007i
$290$	2.95087	+	13.8828i	0.173281	+	0.815224i
$291$	0.124912	−	1.18846i	0.00732246	−	0.0696685i
$292$	0.236790	−	0.105426i	0.0138571	−	0.00616958i
$293$	3.21502	−	9.89483i	0.187824	−	0.578062i	−0.812162	−	0.583432i	$-0.801709\pi$
$293$	3.21502	−	9.89483i	0.187824	−	0.578062i	0.999986	+	0.00537017i	$0.00170938\pi$
$294$	−3.96190	+	10.4048i	−0.231062	+	0.606818i
$295$	−22.4045	+	16.2778i	−1.30444	+	0.947732i
$296$	−8.06625	−	4.65705i	−0.468841	−	0.270685i
$297$	−3.27112	−	0.547530i	−0.189809	−	0.0317709i
$298$	5.66306	+	9.80872i	0.328053	+	0.568204i
$299$	−2.09770	−	19.9583i	−0.121313	−	1.15422i
$300$	2.73164	−	0.887563i	0.157711	−	0.0512435i
$301$	−4.31041	+	5.63312i	−0.248448	+	0.324688i
$302$	−6.37728	−	4.63336i	−0.366971	−	0.266620i
$303$	−5.34684	−	12.0092i	−0.307168	−	0.689911i
$304$	30.4624	−	6.47498i	1.74714	−	0.371366i
$305$	26.8355	+	24.1628i	1.53660	+	1.38356i
$306$	9.97049	−	1.04794i	0.569975	−	0.0599068i
$307$	−8.83415			−0.504192			−0.252096	−	0.967702i	$-0.581120\pi$
$307$	−8.83415			−0.504192			−0.252096	+	0.967702i	$0.581120\pi$
$308$	0.0871964	+	4.64735i	0.00496848	+	0.264807i
$309$	−0.504056			−0.0286748
$310$	−7.93243	+	0.833732i	−0.450532	+	0.0473528i
$311$	−16.5824	−	14.9308i	−0.940301	−	0.846650i	0.0480500	−	0.998845i	$-0.484699\pi$
$311$	−16.5824	−	14.9308i	−0.940301	−	0.846650i	−0.988351	+	0.152194i	$0.951366\pi$
$312$	9.48807	−	2.01675i	0.537156	−	0.114176i
$313$	3.48573	+	7.82909i	0.197025	+	0.442526i	0.984858	−	0.173363i	$-0.0554635\pi$
$313$	3.48573	+	7.82909i	0.197025	+	0.442526i	−0.787833	+	0.615889i	$0.788797\pi$
$314$	2.38275	+	1.73117i	0.134467	+	0.0976957i
$315$	8.46984	+	1.10347i	0.477221	+	0.0621737i
$316$	−3.43908	+	1.11743i	−0.193464	+	0.0628601i
$317$	1.81150	+	17.2353i	0.101744	+	0.968030i	0.919666	+	0.392701i	$0.128459\pi$
$317$	1.81150	+	17.2353i	0.101744	+	0.968030i	−0.817922	+	0.575329i	$0.804874\pi$
$318$	3.85730	+	6.68103i	0.216306	+	0.374654i
$319$	1.35469	+	9.06688i	0.0758480	+	0.507648i
$320$	13.7204	+	7.92147i	0.766993	+	0.442823i
$321$	0.498572	−	0.362234i	0.0278276	−	0.0202179i
$322$	−17.8788	+	9.73861i	−0.996349	+	0.542712i
$323$	12.6937	−	39.0672i	0.706296	−	2.17376i
$324$	−0.483912	+	0.215452i	−0.0268840	+	0.0119695i
$325$	2.35098	−	22.3681i	0.130409	−	1.24076i
$326$	7.91585	+	37.2411i	0.438418	+	2.06260i
$327$	−8.93995	−	1.90025i	−0.494381	−	0.105084i
$328$	−12.8069	−	17.6272i	−0.707143	−	0.973299i
$329$	23.5159	−	20.1393i	1.29647	−	1.11032i
$330$	16.4876	−	4.26330i	0.907615	−	0.234687i
$331$	5.29949	−	9.17899i	0.291286	−	0.504523i	−0.682828	−	0.730579i	$-0.739250\pi$
$331$	5.29949	−	9.17899i	0.291286	−	0.504523i	0.974114	+	0.226056i	$0.0725834\pi$
$332$	3.00234	+	1.33673i	0.164775	+	0.0733624i
$333$	2.66510	−	2.95989i	0.146046	−	0.162201i
$334$	16.6420	−	14.9845i	0.910609	−	0.819916i
$335$	−4.38227	+	6.03167i	−0.239429	+	0.329546i
$336$	−7.17543	−	10.4103i	−0.391452	−	0.567926i
$337$	15.0528	+	4.89095i	0.819977	+	0.266427i	0.688818	−	0.724934i	$-0.258130\pi$
$337$	15.0528	+	4.89095i	0.819977	+	0.266427i	0.131160	+	0.991361i	$0.458130\pi$
$338$	−1.39073	+	6.54286i	−0.0756456	+	0.355884i
$339$	−4.28491	+	9.62407i	−0.232724	+	0.522708i
$340$	−9.33502	+	5.38958i	−0.506262	+	0.292291i
$341$	−5.14706	+	0.224522i	−0.278729	+	0.0121585i
$342$			10.3651i			0.560481i
$343$	7.01822	−	17.1390i	0.378948	−	0.925418i
$344$	−1.93734	−	5.96253i	−0.104455	−	0.321478i
$345$	10.4512	+	11.6072i	0.562674	+	0.624913i
$346$	−13.6347	−	1.43307i	−0.733007	−	0.0770421i
$347$	−0.572423	−	0.0601641i	−0.0307293	−	0.00322978i	0.0891514	−	0.996018i	$-0.471585\pi$
$347$	−0.572423	−	0.0601641i	−0.0307293	−	0.00322978i	−0.119881	+	0.992788i	$0.538251\pi$
$348$	0.979723	+	1.08809i	0.0525186	+	0.0583279i
$349$	−1.97096	−	6.06599i	−0.105503	−	0.324705i	0.884345	−	0.466834i	$-0.154605\pi$
$349$	−1.97096	−	6.06599i	−0.105503	−	0.324705i	−0.989848	+	0.142129i	$0.954605\pi$
$350$	−21.8689	+	6.50992i	−1.16894	+	0.347970i
$351$			4.14796i			0.221402i
$352$	−8.08592	−	5.35241i	−0.430981	−	0.285285i
$353$	3.52086	−	2.03277i	0.187396	−	0.108193i	−0.403367	−	0.915038i	$-0.632160\pi$
$353$	3.52086	−	2.03277i	0.187396	−	0.108193i	0.590763	+	0.806845i	$0.298827\pi$
$354$	−5.54939	+	12.4641i	−0.294947	+	0.662461i
$355$	0.859683	−	4.04449i	0.0456272	−	0.214659i
$356$	−4.09417	−	1.33028i	−0.216991	−	0.0705046i
$357$	−16.6237	+	1.33084i	−0.879822	+	0.0704357i
$358$	−7.86565	+	10.8261i	−0.415713	+	0.572179i
$359$	−14.3018	+	12.8774i	−0.754822	+	0.679645i	−0.953828	−	0.300353i	$-0.902895\pi$
$359$	−14.3018	+	12.8774i	−0.754822	+	0.679645i	0.199006	+	0.979998i	$0.436229\pi$
$360$	−5.05162	+	5.61039i	−0.266244	+	0.295694i
$361$	21.4405	+	9.54591i	1.12845	+	0.502416i
$362$	−3.27113	+	5.66576i	−0.171927	+	0.297786i
$363$	10.7981	−	2.09805i	0.566751	−	0.110119i
$364$	5.71450	−	1.06708i	0.299521	−	0.0559302i
$365$	0.928532	+	1.27801i	0.0486016	+	0.0668944i
$366$	17.4018	+	3.69887i	0.909608	+	0.193343i
$367$	−1.24010	−	5.83422i	−0.0647328	−	0.304544i	0.933856	−	0.357649i	$-0.116422\pi$
$367$	−1.24010	−	5.83422i	−0.0647328	−	0.304544i	−0.998589	+	0.0531050i	$0.983088\pi$
$368$	2.41674	−	22.9938i	0.125981	−	1.19863i
$369$	8.51171	−	3.78966i	0.443102	−	0.197282i
$370$	−6.31976	+	19.4502i	−0.328549	+	1.01117i
$371$	−6.13854	−	11.2696i	−0.318697	−	0.585087i
$372$	−0.665687	+	0.483650i	−0.0345142	+	0.0250761i
$373$	24.6005	+	14.2031i	1.27376	+	0.735407i	0.975694	−	0.219137i	$-0.0703241\pi$
$373$	24.6005	+	14.2031i	1.27376	+	0.735407i	0.298069	+	0.954544i	$0.403657\pi$
$374$	−29.7576	+	14.8351i	−1.53873	+	0.767107i
$375$	0.681600	+	1.18057i	0.0351977	+	0.0609642i
$376$	2.86049	+	27.2158i	0.147519	+	1.40355i
$377$	10.9043	−	3.54301i	0.561599	−	0.182474i
$378$	3.88559	−	1.61560i	0.199853	−	0.0830974i
$379$	9.46318	+	6.87541i	0.486091	+	0.353166i	0.803679	−	0.595063i	$-0.202873\pi$
$379$	9.46318	+	6.87541i	0.486091	+	0.353166i	−0.317588	+	0.948229i	$0.602873\pi$
$380$	−4.53283	−	10.1809i	−0.232529	−	0.522269i
$381$	12.6976	−	2.69895i	0.650516	−	0.138271i
$382$	−10.2806	−	9.25667i	−0.526000	−	0.473612i
$383$	14.5543	−	1.52972i	0.743691	−	0.0781651i	0.274898	−	0.961473i	$-0.411356\pi$
$383$	14.5543	−	1.52972i	0.743691	−	0.0781651i	0.468793	+	0.883308i	$0.344689\pi$
$384$	13.6528			0.696715
$385$	−27.5943	+	6.40864i	−1.40633	+	0.326615i
$386$	17.6951			0.900657
$387$	2.66624	−	0.280234i	0.135533	−	0.0142451i
$388$	0.470412	+	0.423561i	0.0238816	+	0.0215031i
$389$	−33.7240	+	7.16825i	−1.70987	+	0.363445i	−0.955953	−	0.293521i	$-0.905173\pi$
$389$	−33.7240	+	7.16825i	−1.70987	+	0.363445i	−0.753920	+	0.656966i	$0.771840\pi$
$390$	−8.66292	−	19.4572i	−0.438664	−	0.985256i
$391$	−24.6717	−	17.9250i	−1.24770	−	0.906508i
$392$	8.95244	+	13.7046i	0.452166	+	0.692187i
$393$	0.816737	−	0.265374i	0.0411989	−	0.0133863i
$394$	−1.61210	−	15.3381i	−0.0812164	−	0.772723i
$395$	−11.0192	−	19.0858i	−0.554437	−	0.960313i
$396$	1.25312	−	1.23134i	0.0629715	−	0.0618771i
$397$	−3.19665	−	1.84558i	−0.160435	−	0.0926272i	0.417633	−	0.908616i	$-0.362860\pi$
$397$	−3.19665	−	1.84558i	−0.160435	−	0.0926272i	−0.578068	+	0.815989i	$0.696193\pi$
$398$	−3.06097	+	2.22392i	−0.153433	+	0.111475i
$399$	0.428132	−	17.2367i	0.0214334	−	0.862913i
$400$	8.00726	−	24.6438i	0.400363	−	1.23219i
$401$	6.60470	−	2.94060i	0.329823	−	0.146847i	−0.235143	−	0.971961i	$-0.575556\pi$
$401$	6.60470	−	2.94060i	0.329823	−	0.146847i	0.564966	+	0.825114i	$0.308889\pi$
$402$	−0.383945	+	3.65299i	−0.0191494	+	0.182195i
$403$	1.33964	+	6.30253i	0.0667324	+	0.313951i
$404$	6.81122	+	1.44777i	0.338871	+	0.0720293i
$405$	−1.89758	−	2.61179i	−0.0942914	−	0.129781i
$406$	−7.56603	−	8.83456i	−0.375496	−	0.438452i
$407$	−4.84192	+	12.2905i	−0.240005	+	0.609217i
$408$	7.37014	−	12.7655i	0.364876	−	0.631984i
$409$	11.0305	+	4.91109i	0.545422	+	0.242838i	0.660902	−	0.750472i	$-0.270174\pi$
$409$	11.0305	+	4.91109i	0.545422	+	0.242838i	−0.115480	+	0.993310i	$0.536841\pi$
$410$	−32.0121	+	35.5530i	−1.58096	+	1.75584i
$411$	0.294262	−	0.264955i	0.0145149	−	0.0130693i
$412$	0.156940	−	0.216010i	0.00773189	−	0.0106420i
$413$	9.74321	−	20.4980i	0.479432	−	1.00864i
$414$	7.31840	+	2.37789i	0.359680	+	0.116867i
$415$	−4.16440	+	19.5920i	−0.204422	+	0.961731i
$416$	−4.93272	+	11.0791i	−0.241846	+	0.543196i
$417$	17.7709	−	10.2600i	0.870245	−	0.502436i
$418$	−12.0379	−	32.2006i	−0.588791	−	1.57498i
$419$		−	0.0456299i		−	0.00222916i	−0.999999	−	0.00111458i	$-0.999645\pi$
$419$		−	0.0456299i		−	0.00222916i	0.999999	−	0.00111458i	$-0.000354783\pi$
$420$	−3.11001	+	3.28612i	−0.151753	+	0.160346i
$421$	−6.04185	−	18.5949i	−0.294462	−	0.906261i	−0.983402	−	0.181442i	$-0.941924\pi$
$421$	−6.04185	−	18.5949i	−0.294462	−	0.906261i	0.688940	−	0.724819i	$-0.258076\pi$
$422$	25.7084	+	28.5520i	1.25146	+	1.38989i
$423$	−11.6381	−	1.22321i	−0.565863	−	0.0594746i
$424$	11.2806	+	1.18564i	0.547833	+	0.0575795i
$425$	−22.8696	−	25.3992i	−1.10934	−	1.23204i
$426$	−0.629501	−	1.93740i	−0.0304994	−	0.0938675i
$427$	−28.7856	−	6.86983i	−1.39303	−	0.332455i
$428$			0.326443i			0.0157792i
$429$	−4.81738	−	12.8862i	−0.232585	−	0.622152i
$430$	−11.9215	+	6.88290i	−0.574908	+	0.331923i
$431$	−6.29264	+	14.1335i	−0.303106	+	0.680787i	−0.999313	−	0.0370539i	$-0.988203\pi$
$431$	−6.29264	+	14.1335i	−0.303106	+	0.680787i	0.696208	+	0.717841i	$0.254869\pi$
$432$	−0.993574	+	4.67440i	−0.0478033	+	0.224897i
$433$	−23.2485	−	7.55391i	−1.11725	−	0.363018i	−0.308535	−	0.951213i	$-0.599839\pi$
$433$	−23.2485	−	7.55391i	−1.11725	−	0.363018i	−0.808719	+	0.588195i	$0.799839\pi$
$434$	5.38209	−	3.70969i	0.258349	−	0.178071i
$435$	−5.24512	+	7.21928i	−0.251484	+	0.346138i
$436$	3.59783	−	3.23950i	0.172305	−	0.155144i
$437$	21.0972	−	23.4308i	1.00921	−	1.12085i
$438$	0.710989	+	0.316553i	0.0339724	+	0.0151255i
$439$	−9.88210	+	17.1163i	−0.471647	+	0.816916i	−0.999474	−	0.0324358i	$-0.989674\pi$
$439$	−9.88210	+	17.1163i	−0.471647	+	0.816916i	0.527827	+	0.849352i	$0.323007\pi$
$440$	9.17772	−	23.2963i	0.437531	−	1.11061i
$441$	−6.52828	+	2.52617i	−0.310871	+	0.120294i
$442$	24.4431	+	33.6430i	1.16264	+	1.60023i
$443$	29.6737	+	6.30734i	1.40984	+	0.299671i	0.849061	−	0.528295i	$-0.177169\pi$
$443$	29.6737	+	6.30734i	1.40984	+	0.299671i	0.560778	+	0.827966i	$0.310502\pi$
$444$	0.438649	+	2.06368i	0.0208174	+	0.0979381i
$445$	2.74245	−	26.0927i	0.130005	−	1.23691i
$446$	−15.7653	+	7.01918i	−0.746511	+	0.332368i
$447$	−2.20054	+	6.77256i	−0.104082	+	0.320331i
$448$	−12.9799	−	0.322399i	−0.613240	−	0.0152319i
$449$	−22.4279	+	16.2948i	−1.05844	+	0.768999i	−0.973798	−	0.227413i	$-0.926973\pi$
$449$	−22.4279	+	16.2948i	−1.05844	+	0.768999i	−0.0846376	+	0.996412i	$0.526973\pi$
$450$	7.46872	+	4.31207i	0.352079	+	0.203273i
$451$	−22.0415	+	21.6585i	−1.03790	+	1.01986i
$452$	−2.79020	−	4.83277i	−0.131240	−	0.227314i
$453$	−0.518056	−	4.92898i	−0.0243404	−	0.231584i
$454$	−14.4137	+	4.68329i	−0.676468	+	0.219798i
$455$	13.6023	+	32.7143i	0.637688	+	1.53367i
$456$	12.3292	+	8.95769i	0.577368	+	0.419482i
$457$	11.8102	+	26.5263i	0.552460	+	1.24085i	0.946783	+	0.321874i	$0.104313\pi$
$457$	11.8102	+	26.5263i	0.552460	+	1.24085i	−0.394323	+	0.918972i	$0.629021\pi$
$458$	4.02187	−	0.854874i	0.187929	−	0.0399456i
$459$	4.68425	+	4.21772i	0.218642	+	0.196866i
$460$	−8.22823	+	0.864822i	−0.383643	+	0.0403225i
$461$	5.00753			0.233224			0.116612	−	0.993178i	$-0.462797\pi$
$461$	5.00753			0.233224			0.116612	+	0.993178i	$0.462797\pi$
$462$	−10.1948	+	9.53173i	−0.474304	+	0.443456i
$463$	−3.70973			−0.172406			−0.0862030	−	0.996278i	$-0.527473\pi$
$463$	−3.70973			−0.172406			−0.0862030	+	0.996278i	$0.527473\pi$
$464$	13.1368	−	1.38074i	0.609863	−	0.0640992i
$465$	−3.72675	−	3.35558i	−0.172824	−	0.155611i
$466$	31.5743	−	6.71133i	1.46265	−	0.310896i
$467$	−9.00215	−	20.2192i	−0.416570	−	0.935632i	−0.992959	−	0.118456i	$-0.962205\pi$
$467$	−9.00215	−	20.2192i	−0.416570	−	0.935632i	0.576389	−	0.817175i	$-0.304461\pi$
$468$	−1.77758	−	1.29149i	−0.0821687	−	0.0596990i
$469$	0.789370	−	6.05890i	0.0364497	−	0.279774i
$470$	57.1465	−	18.5680i	2.63597	−	0.856479i
$471$	0.193562	+	1.84162i	0.00891888	+	0.0848575i
$472$	10.0301	+	17.3727i	0.461673	+	0.799641i
$473$	−7.95759	+	3.96712i	−0.365890	+	0.182408i
$474$	−9.40298	−	5.42882i	−0.431893	−	0.249354i
$475$	28.5875	−	20.7700i	1.31169	−	0.952995i
$476$	4.60556	−	7.53835i	0.211095	−	0.345520i
$477$	−1.49886	+	4.61301i	−0.0686279	+	0.211215i
$478$	−26.2077	+	11.6684i	−1.19871	+	0.533701i
$479$	−1.16228	+	11.0583i	−0.0531059	+	0.505269i	0.935346	+	0.353734i	$0.115088\pi$
$479$	−1.16228	+	11.0583i	−0.0531059	+	0.505269i	−0.988452	+	0.151535i	$0.951578\pi$
$480$	−1.96245	−	9.23258i	−0.0895730	−	0.421408i
$481$	16.1600	+	3.43491i	0.736833	+	0.156619i
$482$	6.45646	+	8.88656i	0.294084	+	0.404772i
$483$	−12.0719	−	4.25661i	−0.549292	−	0.193682i
$484$	−2.46292	+	5.28067i	−0.111951	+	0.240030i
$485$	−1.92894	+	3.34103i	−0.0875888	+	0.151708i
$486$	−1.45300	−	0.646917i	−0.0659094	−	0.0293447i
$487$	25.6664	−	28.5054i	1.16305	−	1.29170i	0.213912	−	0.976853i	$-0.431380\pi$
$487$	25.6664	−	28.5054i	1.16305	−	1.29170i	0.949142	−	0.314849i	$-0.101954\pi$
$488$	19.4387	−	17.5027i	0.879949	−	0.792310i
$489$	−14.0703	+	19.3660i	−0.636279	+	0.875763i
$490$	25.3470	−	25.4839i	1.14506	−	1.15124i
$491$	6.59604	+	2.14318i	0.297675	+	0.0967205i	0.454047	−	0.890978i	$-0.349980\pi$
$491$	6.59604	+	2.14318i	0.297675	+	0.0967205i	−0.156372	+	0.987698i	$0.549980\pi$
$492$	−1.02613	+	4.82756i	−0.0462615	+	0.217643i
$493$	7.08657	−	15.9167i	0.319163	−	0.716852i
$494$	−37.2340	+	21.4970i	−1.67524	+	0.967198i
$495$	8.92838	+	5.91007i	0.401301	+	0.265638i
$496$			7.42330i			0.333316i
$497$	0.966805	+	3.24781i	0.0433671	+	0.145684i
$498$	3.04937	+	9.38500i	0.136646	+	0.420552i
$499$	−9.43807	−	10.4820i	−0.422506	−	0.469241i	0.493883	−	0.869528i	$-0.335577\pi$
$499$	−9.43807	−	10.4820i	−0.422506	−	0.469241i	−0.916390	+	0.400287i	$0.868910\pi$
$500$	−0.718143	−	0.0754799i	−0.0321163	−	0.00337556i
$501$	14.0027	+	1.47174i	0.625593	+	0.0657525i
$502$	−9.13669	−	10.1473i	−0.407790	−	0.452897i
$503$	−0.900931	−	2.77278i	−0.0401705	−	0.123632i	0.928960	−	0.370180i	$-0.120704\pi$
$503$	−0.900931	−	2.77278i	−0.0401705	−	0.123632i	−0.969131	+	0.246547i	$0.920704\pi$
$504$	1.43625	−	6.01810i	0.0639756	−	0.268067i
$505$			42.4390i			1.88851i
$506$	−25.4972	+	1.11222i	−1.13349	+	0.0494444i
$507$	−3.64215	+	2.10280i	−0.161754	+	0.0933886i
$508$	−2.79683	+	6.28178i	−0.124089	+	0.278709i
$509$	0.124701	−	0.586673i	0.00552729	−	0.0260038i	−0.975298	−	0.220895i	$-0.929102\pi$
$509$	0.124701	−	0.586673i	0.00552729	−	0.0260038i	0.980825	+	0.194891i	$0.0624354\pi$
$510$	−30.7815	−	10.0015i	−1.36303	−	0.442874i
$511$	−1.16927	−	0.555779i	−0.0517253	−	0.0245862i
$512$	4.92483	−	6.77845i	0.217649	−	0.299568i
$513$	−4.84297	+	4.36063i	−0.213822	+	0.192527i
$514$	22.5674	−	25.0637i	0.995407	−	1.10551i
$515$	1.48659	+	0.661871i	0.0655068	+	0.0291655i
$516$	−0.710055	+	1.22985i	−0.0312584	+	0.0541412i
$517$	37.5759	−	9.71621i	1.65259	−	0.427319i
$518$	−3.07654	−	16.4757i	−0.135176	−	0.723900i
$519$	−5.06658	−	6.97355i	−0.222398	−	0.306105i
$520$	−30.6308	−	6.51079i	−1.34325	−	0.285517i
$521$	5.56852	+	26.1978i	0.243961	+	1.14775i	0.914093	+	0.405506i	$0.132905\pi$
$521$	5.56852	+	26.1978i	0.243961	+	1.14775i	−0.670131	+	0.742243i	$0.733762\pi$
$522$	−0.459542	+	4.37225i	−0.0201136	+	0.191368i
$523$	−19.0499	+	8.48157i	−0.832995	+	0.370873i	−0.778503	−	0.627641i	$-0.784021\pi$
$523$	−19.0499	+	8.48157i	−0.832995	+	0.370873i	−0.0544920	+	0.998514i	$0.517354\pi$
$524$	−0.140571	+	0.432632i	−0.00614086	+	0.0188996i
$525$	−12.2420	−	7.47926i	−0.534285	−	0.326422i
$526$	11.8035	−	8.57574i	0.514657	−	0.373920i
$527$	8.47956	+	4.89568i	0.369375	+	0.213259i
$528$	−2.34210	−	15.6756i	−0.101927	−	0.682192i
$529$	−0.203589	−	0.352627i	−0.00885170	−	0.0153316i
$530$	−2.60333	−	24.7690i	−0.113081	−	1.07590i
$531$	−8.15836	+	2.65081i	−0.354043	+	0.115035i
$532$	7.25336	+	5.55019i	0.314473	+	0.240631i
$533$	31.2665	+	22.7164i	1.35430	+	0.983959i
$534$	−5.25741	−	11.8083i	−0.227510	−	0.510997i
$535$	−1.94606	+	0.413647i	−0.0841354	+	0.0178835i
$536$	4.01339	+	3.61367i	0.173352	+	0.156087i
$537$	−8.36749	+	0.879459i	−0.361084	+	0.0379514i
$538$	−0.652953			−0.0281508
$539$	17.3472	−	15.4297i	0.747195	−	0.664605i
$540$	1.71008			0.0735903
$541$	−6.10309	+	0.641461i	−0.262392	+	0.0275786i	−0.234811	−	0.972041i	$-0.575447\pi$
$541$	−6.10309	+	0.641461i	−0.262392	+	0.0275786i	−0.0275813	+	0.999620i	$0.508781\pi$
$542$	11.5120	+	10.3655i	0.494483	+	0.445234i
$543$	−4.02343	+	0.855207i	−0.172662	+	0.0367004i
$544$	7.49580	+	16.8358i	0.321380	+	0.721831i
$545$	23.8709	+	17.3433i	1.02252	+	0.742903i
$546$	13.8623	+	10.6073i	0.593250	+	0.453949i
$547$	26.8033	−	8.70891i	1.14602	−	0.372366i	0.326380	−	0.945239i	$-0.394171\pi$
$547$	26.8033	−	8.70891i	1.14602	−	0.372366i	0.819644	+	0.572873i	$0.194171\pi$
$548$	0.0219246	+	0.208599i	0.000936574	+	0.00891091i
$549$	5.59275	+	9.68692i	0.238693	+	0.413428i
$550$	−28.2106	−	4.72197i	−1.20290	−	0.201346i
$551$	15.6000	+	9.00667i	0.664583	+	0.383697i
$552$	9.15316	−	6.65016i	0.389584	−	0.283050i
$553$	15.4125	+	9.41625i	0.655405	+	0.400420i
$554$	8.25677	−	25.4117i	0.350796	−	1.07964i
$555$	−11.7466	+	5.22993i	−0.498617	+	0.221998i
$556$	−1.13619	+	10.8101i	−0.0481851	+	0.458451i
$557$	−4.54012	−	21.3596i	−0.192371	−	0.905034i	−0.963365	−	0.268192i	$-0.913574\pi$
$557$	−4.54012	−	21.3596i	−0.192371	−	0.905034i	0.770994	−	0.636842i	$-0.219760\pi$
$558$	−2.41666	−	0.513676i	−0.102305	−	0.0217457i
$559$	6.53641	+	8.99659i	0.276461	+	0.380515i
$560$	7.49252	+	40.1244i	0.316617	+	1.69556i
$561$	−19.4507	−	7.66271i	−0.821208	−	0.323520i
$562$	22.1070	−	38.2905i	0.932530	−	1.61519i
$563$	7.79499	+	3.47055i	0.328520	+	0.146266i	0.564368	−	0.825524i	$-0.309120\pi$
$563$	7.79499	+	3.47055i	0.328520	+	0.146266i	−0.235848	+	0.971790i	$0.575787\pi$
$564$	4.14777	−	4.60657i	0.174653	−	0.193972i
$565$	25.2745	−	22.7573i	1.06331	−	0.957406i
$566$	15.2002	−	20.9213i	0.638913	−	0.879388i
$567$	2.38955	+	1.13581i	0.100352	+	0.0476995i
$568$	−2.84855	−	0.925550i	−0.119522	−	0.0388352i
$569$	3.82735	−	18.0062i	0.160451	−	0.754861i	−0.822171	−	0.569241i	$-0.807237\pi$
$569$	3.82735	−	18.0062i	0.160451	−	0.754861i	0.982622	−	0.185620i	$-0.0594294\pi$
$570$	13.6103	−	30.5693i	0.570073	−	1.28041i
$571$	−31.2982	+	18.0700i	−1.30979	+	0.756206i	−0.982061	−	0.188566i	$-0.939616\pi$
$571$	−31.2982	+	18.0700i	−1.30979	+	0.756206i	−0.327727	+	0.944772i	$0.606283\pi$
$572$	7.02221	+	1.94773i	0.293613	+	0.0814386i
$573$		−	8.69778i		−	0.363355i
$574$	9.10150	−	38.1367i	0.379889	−	1.59179i
$575$	−8.10657	−	24.9495i	−0.338067	−	1.04046i
$576$	3.28372	+	3.64694i	0.136821	+	0.151956i
$577$	−45.5196	−	4.78431i	−1.89501	−	0.199173i	−0.915743	−	0.401764i	$-0.868397\pi$
$577$	−45.5196	−	4.78431i	−1.89501	−	0.199173i	−0.979263	+	0.202591i	$0.935064\pi$
$578$	35.9564	+	3.77917i	1.49559	+	0.157193i
$579$	7.44438	+	8.26782i	0.309378	+	0.343599i
$580$	−1.46068	−	4.49552i	−0.0606515	−	0.186666i
$581$	−4.68331	−	15.7328i	−0.194296	−	0.652705i
$582$			1.90066i			0.0787848i
$583$	−0.701069	−	16.0717i	−0.0290353	−	0.665621i
$584$	0.990984	−	0.572145i	0.0410072	−	0.0236755i
$585$	5.44665	−	12.2334i	0.225191	−	0.505787i
$586$	−3.44046	+	16.1861i	−0.142124	+	0.668641i
$587$	−25.7656	−	8.37176i	−1.06346	−	0.345540i	−0.275524	−	0.961294i	$-0.588851\pi$
$587$	−25.7656	−	8.37176i	−1.06346	−	0.345540i	−0.787938	+	0.615755i	$0.788851\pi$
$588$	0.950040	−	3.58418i	0.0391790	−	0.147809i
$589$	−5.95022	+	8.18977i	−0.245174	+	0.337454i
$590$	32.7330	−	29.4730i	1.34760	−	1.21338i
$591$	6.48833	−	7.20602i	0.266894	−	0.296416i
$592$	17.3882	+	7.74170i	0.714649	+	0.318182i
$593$	−15.1983	+	26.3242i	−0.624120	+	1.08101i	0.364591	+	0.931168i	$0.381209\pi$
$593$	−15.1983	+	26.3242i	−0.624120	+	1.08101i	−0.988710	+	0.149839i	$0.952124\pi$
$594$	5.26526	+	0.322246i	0.216036	+	0.0132219i
$595$	50.7750	+	17.9035i	2.08157	+	0.733971i
$596$	−2.21718	−	3.05169i	−0.0908194	−	0.125002i
$597$	−2.32686	−	0.494590i	−0.0952321	−	0.0202422i
$598$	6.63626	+	31.2212i	0.271377	+	1.27673i
$599$	−3.34317	+	31.8082i	−0.136598	+	1.29965i	0.684565	+	0.728952i	$0.259992\pi$
$599$	−3.34317	+	31.8082i	−0.136598	+	1.29965i	−0.821163	+	0.570694i	$0.806674\pi$
$600$	11.5838	−	5.15742i	0.472905	−	0.210551i
$601$	1.26505	−	3.89343i	0.0516025	−	0.158816i	−0.921934	−	0.387346i	$-0.873392\pi$
$601$	1.26505	−	3.89343i	0.0516025	−	0.158816i	0.973537	+	0.228530i	$0.0733919\pi$
$602$	5.88165	−	9.62705i	0.239718	−	0.392369i
$603$	−1.86834	+	1.35743i	−0.0760849	+	0.0552789i
$604$	2.27358	+	1.31265i	0.0925105	+	0.0534110i
$605$	−34.6011	−	7.99117i	−1.40673	−	0.324887i
$606$	10.4542	+	18.1071i	0.424671	+	0.735553i
$607$	3.03995	+	28.9232i	0.123388	+	1.17396i	0.864520	+	0.502598i	$0.167622\pi$
$607$	3.03995	+	28.9232i	0.123388	+	1.17396i	−0.741133	+	0.671359i	$0.765711\pi$
$608$	−18.1210	+	5.88788i	−0.734905	+	0.238785i
$609$	0.944793	−	7.25187i	0.0382850	−	0.293860i
$610$	−46.4653	−	33.7590i	−1.88133	−	1.36686i
$611$	−19.7431	−	44.3438i	−0.798721	−	1.79396i
$612$	−3.26594	+	0.694197i	−0.132018	+	0.0280612i
$613$	12.7915	+	11.5175i	0.516645	+	0.465189i	0.885726	−	0.464208i	$-0.153661\pi$
$613$	12.7915	+	11.5175i	0.516645	+	0.465189i	−0.369081	+	0.929397i	$0.620328\pi$
$614$	13.9738	−	1.46871i	0.563937	−	0.0592721i
$615$	−30.0793			−1.21291
$616$	2.52742	+	20.3641i	0.101833	+	0.820492i
$617$	−38.7207			−1.55884			−0.779418	−	0.626504i	$-0.784485\pi$
$617$	−38.7207			−1.55884			−0.779418	+	0.626504i	$0.784485\pi$
$618$	0.797312	−	0.0838009i	0.0320726	−	0.00337097i
$619$	32.0637	+	28.8703i	1.28875	+	1.16040i	0.977701	+	0.210002i	$0.0673470\pi$
$619$	32.0637	+	28.8703i	1.28875	+	1.16040i	0.311049	+	0.950394i	$0.399320\pi$
$620$	2.59835	−	0.552296i	0.104352	−	0.0221807i
$621$	1.96783	+	4.41982i	0.0789663	+	0.177361i
$622$	28.7122	+	20.8606i	1.15125	+	0.836435i
$623$	8.25508	+	19.8539i	0.330733	+	0.795428i
$624$	−18.8522	+	6.12546i	−0.754693	+	0.245214i
$625$	2.37388	+	22.5860i	0.0949553	+	0.903440i
$626$	−6.81532	−	11.8045i	−0.272395	−	0.471802i
$627$	9.98099	−	19.1714i	0.398602	−	0.765634i
$628$	−0.849481	−	0.490448i	−0.0338980	−	0.0195710i
$629$	20.3108	−	14.7566i	0.809844	−	0.588386i
$630$	−13.5810	−	0.337330i	−0.541079	−	0.0134396i
$631$	1.85773	−	5.71751i	0.0739551	−	0.227610i	−0.907245	−	0.420602i	$-0.861819\pi$
$631$	1.85773	−	5.71751i	0.0739551	−	0.227610i	0.981200	+	0.192991i	$0.0618190\pi$
$632$	−14.5837	+	6.49310i	−0.580110	+	0.258282i
$633$	−2.52501	+	24.0239i	−0.100360	+	0.954863i
$634$	−5.73084	−	26.9615i	−0.227601	−	1.07078i
$635$	−40.9922	−	8.71316i	−1.62673	−	0.345771i
$636$	−1.51020	−	2.07861i	−0.0598831	−	0.0824221i
$637$	−22.6141	−	18.2119i	−0.896005	−	0.721584i
$638$	−3.65023	−	14.1167i	−0.144514	−	0.558885i
$639$	0.640396	−	1.10920i	0.0253337	−	0.0438792i
$640$	−40.2654	−	17.9273i	−1.59163	−	0.708639i
$641$	12.4114	−	13.7843i	0.490221	−	0.544446i	−0.446380	−	0.894844i	$-0.647287\pi$
$641$	12.4114	−	13.7843i	0.490221	−	0.544446i	0.936601	+	0.350398i	$0.113954\pi$
$642$	−0.728415	+	0.655868i	−0.0287482	+	0.0258850i
$643$	−26.1308	+	35.9659i	−1.03050	+	1.41836i	−0.125923	+	0.992040i	$0.540189\pi$
$643$	−26.1308	+	35.9659i	−1.03050	+	1.41836i	−0.904574	+	0.426317i	$0.859811\pi$
$644$	5.58279	−	3.84803i	0.219993	−	0.151633i
$645$	−8.23138	−	2.67454i	−0.324110	−	0.105310i
$646$	−13.5838	+	63.9065i	−0.534446	+	2.51437i
$647$	−4.39561	+	9.87269i	−0.172809	+	0.388136i	−0.979099	−	0.203385i	$-0.934806\pi$
$647$	−4.39561	+	9.87269i	−0.172809	+	0.388136i	0.806290	+	0.591521i	$0.201472\pi$
$648$	−2.02521	+	1.16925i	−0.0795576	+	0.0459326i
$649$	22.2665	−	17.7101i	0.874035	−	0.695182i
$650$			35.7726i			1.40312i
$651$	3.99757	+	0.954040i	0.156677	+	0.0373918i
$652$	−3.91834	−	12.0594i	−0.153454	−	0.472283i
$653$	−5.85263	−	6.50000i	−0.229031	−	0.254365i	0.617665	−	0.786441i	$-0.288079\pi$
$653$	−5.85263	−	6.50000i	−0.229031	−	0.254365i	−0.846696	+	0.532076i	$0.821412\pi$
$654$	14.4571	+	1.51950i	0.565316	+	0.0594171i
$655$	−2.75722	−	0.289795i	−0.107733	−	0.0113232i
$656$	29.7933	+	33.0888i	1.16323	+	1.29190i
$657$	0.151210	+	0.465376i	0.00589925	+	0.0181560i
$658$	−33.8491	+	35.7658i	−1.31957	+	1.39430i
$659$		−	13.1476i		−	0.512158i	−0.966656	−	0.256079i	$-0.917569\pi$
$659$		−	13.1476i		−	0.512158i	0.966656	−	0.256079i	$-0.0824307\pi$
$660$	−5.31261	+	1.98606i	−0.206793	+	0.0773075i
$661$	26.1398	−	15.0918i	1.01672	−	0.587003i	0.103567	−	0.994622i	$-0.466974\pi$
$661$	26.1398	−	15.0918i	1.01672	−	0.587003i	0.913152	+	0.407620i	$0.133641\pi$
$662$	−6.85666	+	15.4003i	−0.266492	+	0.598550i
$663$	−5.43602	+	25.5744i	−0.211117	+	0.993229i
$664$	13.7987	+	4.48346i	0.535493	+	0.173992i
$665$	−23.8960	+	50.2731i	−0.926646	+	1.94951i
$666$	−3.72354	+	5.12501i	−0.144284	+	0.198590i
$667$	9.93810	−	8.94831i	0.384805	−	0.346480i
$668$	−4.99050	+	5.54251i	−0.193088	+	0.214446i
$669$	−9.91216	−	4.41318i	−0.383226	−	0.170623i
$670$	5.92905	−	10.2694i	0.229059	−	0.396742i
$671$	−28.6249	−	23.5984i	−1.10505	−	0.911007i
$672$	5.03170	+	5.87533i	0.194102	+	0.226646i
$673$	−15.1823	−	20.8966i	−0.585234	−	0.805505i	0.409023	−	0.912524i	$-0.365869\pi$
$673$	−15.1823	−	20.8966i	−0.585234	−	0.805505i	−0.994257	+	0.107019i	$0.965869\pi$
$674$	−24.6235	−	5.23389i	−0.948463	−	0.201602i
$675$	1.12735	+	5.30377i	0.0433918	+	0.204142i
$676$	0.232862	−	2.21554i	0.00895624	−	0.0852129i
$677$	−10.3852	+	4.62379i	−0.399136	+	0.177707i	−0.596481	−	0.802627i	$-0.703435\pi$
$677$	−10.3852	+	4.62379i	−0.399136	+	0.177707i	0.197345	+	0.980334i	$0.436768\pi$
$678$	5.17781	−	15.9357i	0.198853	−	0.612005i
$679$	0.0785069	−	3.16070i	0.00301282	−	0.121297i
$680$	−38.4985	+	27.9708i	−1.47635	+	1.07263i
$681$	−8.25210	−	4.76435i	−0.316221	−	0.182570i
$682$	8.10425	−	1.21086i	0.310328	−	0.0463663i
$683$	−0.530326	−	0.918552i	−0.0202924	−	0.0351474i	0.855701	−	0.517471i	$-0.173126\pi$
$683$	−0.530326	−	0.918552i	−0.0202924	−	0.0351474i	−0.875993	+	0.482323i	$0.839793\pi$
$684$	−0.360836	−	3.43312i	−0.0137969	−	0.131269i
$685$	−1.21576	+	0.395025i	−0.0464519	+	0.0150931i
$686$	−8.25195	+	28.2771i	−0.315061	+	1.07963i
$687$	2.09144	+	1.51952i	0.0797934	+	0.0579733i
$688$	5.21099	+	11.7041i	0.198667	+	0.446213i
$689$	−19.6796	+	4.18304i	−0.749734	+	0.159361i
$690$	−18.4614	−	16.6227i	−0.702813	−	0.632815i
$691$	−34.0809	+	3.58205i	−1.29650	+	0.136267i	−0.727521	−	0.686086i	$-0.759328\pi$
$691$	−34.0809	+	3.58205i	−1.29650	+	0.136267i	−0.568977	+	0.822353i	$0.692661\pi$
$692$	4.56597			0.173572
$693$	−8.74257	−	0.753362i	−0.332103	−	0.0286178i
$694$	0.915457			0.0347503
$695$	−65.8832	+	6.92460i	−2.49909	+	0.262665i
$696$	4.80361	+	4.32519i	0.182080	+	0.163946i
$697$	57.4458	−	12.2105i	2.17591	−	0.462505i
$698$	4.12614	+	9.26746i	0.156177	+	0.350779i
$699$	16.4192	+	11.9293i	0.621031	+	0.451206i
$700$	7.01679	−	2.91753i	0.265210	−	0.110272i
$701$	−43.6659	+	14.1879i	−1.64924	+	0.535870i	−0.978575	−	0.205893i	$-0.933990\pi$
$701$	−43.6659	+	14.1879i	−1.64924	+	0.535870i	−0.670663	+	0.741762i	$0.733990\pi$
$702$	−0.689612	−	6.56122i	−0.0260277	−	0.247637i
$703$	12.9781	+	22.4787i	0.489478	+	0.847800i
$704$	−14.4368	−	7.51605i	−0.544107	−	0.283272i
$705$	32.7174	+	18.8894i	1.23221	+	0.711416i
$706$	−5.23132	+	3.80077i	−0.196883	+	0.143044i
$707$	−16.6369	−	30.5431i	−0.625694	−	1.14869i
$708$	1.40416	−	4.32155i	0.0527715	−	0.162414i
$709$	40.8380	−	18.1823i	1.53370	−	0.682849i	0.545800	−	0.837916i	$-0.316226\pi$
$709$	40.8380	−	18.1823i	1.53370	−	0.682849i	0.987904	+	0.155067i	$0.0495593\pi$
$710$	−0.687431	+	6.54047i	−0.0257988	+	0.245460i
$711$	−1.41931	−	6.67735i	−0.0532285	−	0.250420i
$712$	−18.5895	−	3.95131i	−0.696669	−	0.148082i
$713$	4.41742	+	6.08006i	0.165434	+	0.227700i
$714$	26.0741	−	4.86887i	0.975797	−	0.182213i
$715$	−2.71311	+	44.3303i	−0.101465	+	1.65786i
$716$	2.22837	−	3.85965i	0.0832781	−	0.144242i
$717$	−16.4776	−	7.33629i	−0.615366	−	0.273979i
$718$	20.4816	−	22.7472i	0.764368	−	0.848916i
$719$	3.78371	−	3.40687i	0.141109	−	0.127055i	−0.595554	−	0.803315i	$-0.703067\pi$
$719$	3.78371	−	3.40687i	0.141109	−	0.127055i	0.736662	+	0.676261i	$0.236401\pi$
$720$	9.06819	−	12.4813i	0.337952	−	0.465151i
$721$	−1.32935	+	0.106424i	−0.0495077	+	0.00396343i
$722$	−35.5014	−	11.5351i	−1.32123	−	0.429292i
$723$	−1.43588	+	6.75531i	−0.0534011	+	0.251233i
$724$	0.886222	−	1.99049i	0.0329362	−	0.0739758i
$725$	12.9798	−	7.49386i	0.482056	−	0.278315i
$726$	−16.7315	+	5.11389i	−0.620964	+	0.189794i
$727$		−	27.6879i		−	1.02689i	−0.858123	−	0.513443i	$-0.828370\pi$
$727$		−	27.6879i		−	1.02689i	0.858123	−	0.513443i	$-0.171630\pi$
$728$	24.5972	−	7.32207i	0.911634	−	0.271374i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−1.68122	−	1.86718i	−0.0622247	−	0.0691076i
$731$	16.8061	+	1.76639i	0.621596	+	0.0653324i
$732$	−5.89259	−	0.619336i	−0.217796	−	0.0228913i
$733$	−3.22046	−	3.57669i	−0.118951	−	0.132108i	0.680728	−	0.732536i	$-0.261663\pi$
$733$	−3.22046	−	3.57669i	−0.118951	−	0.132108i	−0.799679	+	0.600428i	$0.794997\pi$
$734$	2.93154	+	9.02236i	0.108205	+	0.333021i
$735$	22.5706	+	1.12193i	0.832529	+	0.0413830i
$736$			14.1453i			0.521403i
$737$	4.22777	−	6.38691i	0.155732	−	0.235265i
$738$	−12.8337	+	7.40955i	−0.472416	+	0.272749i
$739$	−17.0550	+	38.3062i	−0.627379	+	1.40912i	0.267828	+	0.963467i	$0.413694\pi$
$739$	−17.0550	+	38.3062i	−0.627379	+	1.40912i	−0.895207	+	0.445650i	$0.852972\pi$
$740$	1.41612	−	6.66230i	0.0520574	−	0.244911i
$741$	−25.7087	−	8.35326i	−0.944432	−	0.306865i
$742$	11.5835	+	16.8056i	0.425244	+	0.616952i
$743$	−0.610147	+	0.839796i	−0.0223841	+	0.0308091i	−0.820062	−	0.572274i	$-0.806061\pi$
$743$	−0.610147	+	0.839796i	−0.0223841	+	0.0308091i	0.797678	+	0.603083i	$0.206061\pi$
$744$	−2.69953	+	2.43067i	−0.0989695	+	0.0891125i
$745$	15.3829	−	17.0844i	0.563586	−	0.625925i
$746$	−41.2741	−	18.3764i	−1.51115	−	0.672809i
$747$	−3.10215	+	5.37308i	−0.113502	+	0.196591i
$748$	9.33985	−	5.94962i	0.341499	−	0.217540i
$749$	1.23841	−	1.06059i	0.0452505	−	0.0387531i
$750$	−1.27442	−	1.75409i	−0.0465354	−	0.0640504i
$751$	22.8852	+	4.86441i	0.835094	+	0.177505i	0.605564	−	0.795797i	$-0.292948\pi$
$751$	22.8852	+	4.86441i	0.835094	+	0.177505i	0.229530	+	0.973301i	$0.426281\pi$
$752$	−11.6270	−	54.7007i	−0.423993	−	1.99473i
$753$	0.897382	−	8.53802i	0.0327024	−	0.311143i
$754$	−16.6593	+	7.41718i	−0.606695	+	0.270118i
$755$	−4.94431	+	15.2170i	−0.179942	+	0.553804i
$756$	−1.23074	+	0.670384i	−0.0447616	+	0.0243816i
$757$	36.5210	−	26.5341i	1.32738	−	0.964396i	0.327569	−	0.944827i	$-0.393770\pi$
$757$	36.5210	−	26.5341i	1.32738	−	0.964396i	0.999809	−	0.0195693i	$-0.00622951\pi$
$758$	−16.1119	−	9.30218i	−0.585209	−	0.337870i
$759$	−11.2464	−	11.4454i	−0.408220	−	0.415441i
$760$	−24.5996	−	42.6078i	−0.892322	−	1.54555i
$761$	0.418719	+	3.98385i	0.0151786	+	0.144414i	0.999486	−	0.0320454i	$-0.0102021\pi$
$761$	0.418719	+	3.98385i	0.0151786	+	0.144414i	−0.984308	+	0.176460i	$0.943535\pi$
$762$	−19.6362	+	6.38019i	−0.711344	+	0.231130i
$763$	−23.9787	−	3.12401i	−0.868086	−	0.113097i
$764$	3.72737	+	2.70810i	0.134852	+	0.0979754i
$765$	−8.27678	−	18.5899i	−0.299248	−	0.672121i
$766$	−22.7676	+	4.83940i	−0.822627	+	0.174855i
$767$	−26.4427	−	23.8091i	−0.954789	−	0.859696i
$768$	−11.8347	+	1.24388i	−0.427050	+	0.0448847i
$769$	41.0994			1.48208			0.741042	−	0.671459i	$-0.234332\pi$
$769$	41.0994			1.48208			0.741042	+	0.671459i	$0.234332\pi$
$770$	42.5829	−	14.7248i	1.53458	−	0.530644i
$771$	21.2049			0.763676
$772$	−5.86096	+	0.616012i	−0.210941	+	0.0221707i
$773$	−38.4876	−	34.6544i	−1.38430	−	1.24643i	−0.935744	−	0.352680i	$-0.885270\pi$
$773$	−38.4876	−	34.6544i	−1.38430	−	1.24643i	−0.448560	−	0.893753i	$-0.648063\pi$
$774$	−4.17086	+	0.886543i	−0.149918	+	0.0318661i
$775$	3.42586	+	7.69460i	0.123060	+	0.276398i
$776$	2.26082	+	1.64258i	0.0811585	+	0.0589651i
$777$	6.40376	−	8.36885i	0.229734	−	0.300231i
$778$	52.1526	−	16.9454i	1.86976	−	0.607522i
$779$	6.34688	+	60.3865i	0.227400	+	2.16357i
$780$	3.54668	+	6.14304i	0.126992	+	0.219956i
$781$	−0.701272	+	4.18962i	−0.0250935	+	0.149916i
$782$	42.0056	+	24.2520i	1.50212	+	0.867248i
$783$	−2.23621	+	1.62470i	−0.0799157	+	0.0580622i
$784$	−21.1218	−	25.9401i	−0.754351	−	0.926433i
$785$	1.84735	−	5.68556i	0.0659348	−	0.202926i
$786$	−1.24779	+	0.555551i	−0.0445071	+	0.0198159i
$787$	3.63503	−	34.5850i	0.129575	−	1.23282i	−0.715669	−	0.698440i	$-0.753878\pi$
$787$	3.63503	−	34.5850i	0.129575	−	1.23282i	0.845243	−	0.534381i	$-0.179455\pi$
$788$	1.06792	+	5.02416i	0.0380430	+	0.178978i
$789$	8.97267	+	1.90720i	0.319436	+	0.0678982i
$790$	20.6032	+	28.3579i	0.733029	+	1.00893i
$791$	−9.26868	+	26.2864i	−0.329556	+	0.934636i
$792$	4.93363	−	5.98449i	0.175309	−	0.212650i
$793$	−23.1985	+	40.1810i	−0.823803	+	1.42687i
$794$	5.36327	+	2.38788i	0.190335	+	0.0847427i
$795$	10.4778	−	11.6368i	0.371609	−	0.412713i
$796$	0.936432	−	0.843167i	0.0331910	−	0.0298853i
$797$	1.89226	−	2.60447i	0.0670272	−	0.0922551i	−0.774187	−	0.632957i	$-0.781841\pi$
$797$	1.89226	−	2.60447i	0.0670272	−	0.0922551i	0.841215	+	0.540702i	$0.181841\pi$
$798$	2.18844	+	27.3360i	0.0774698	+	0.967685i
$799$	−70.1521	−	22.7938i	−2.48180	−	0.806387i
$800$	−3.29607	+	15.5068i	−0.116534	+	0.548249i
$801$	3.30550	−	7.42427i	0.116794	−	0.262324i
$802$	−9.95838	+	5.74947i	−0.351643	+	0.203021i
$803$	−1.01023	−	1.27014i	−0.0356504	−	0.0448223i
$804$		−	1.22331i		−	0.0431428i
$805$	30.0138	+	28.4053i	1.05785	+	1.00116i
$806$	−3.16685	−	9.74657i	−0.111548	−	0.343308i
$807$	−0.274699	−	0.305084i	−0.00966987	−	0.0107395i
$808$	30.5729	+	3.21335i	1.07555	+	0.113045i
$809$	21.7507	+	2.28609i	0.764714	+	0.0803747i	0.478851	−	0.877896i	$-0.341053\pi$
$809$	21.7507	+	2.28609i	0.764714	+	0.0803747i	0.285862	+	0.958271i	$0.407720\pi$
$810$	3.43579	+	3.81584i	0.120721	+	0.134075i
$811$	14.8809	+	45.7988i	0.522540	+	1.60821i	0.769130	+	0.639092i	$0.220690\pi$
$811$	14.8809	+	45.7988i	0.522540	+	1.60821i	−0.246590	+	0.969120i	$0.579310\pi$
$812$	2.81357	+	2.66279i	0.0987369	+	0.0934455i
$813$			9.73962i			0.341584i
$814$	5.61558	−	20.2460i	0.196826	−	0.709622i
$815$	66.9260	−	38.6397i	2.34431	−	1.35349i
$816$	−12.2518	+	27.5181i	−0.428900	+	0.963326i
$817$	−3.63248	+	17.0895i	−0.127084	+	0.597885i
$818$	−18.2644	−	5.93447i	−0.638600	−	0.207494i
$819$	0.875780	+	10.9395i	0.0306022	+	0.382256i
$820$	9.36533	−	12.8903i	0.327052	−	0.450148i
$821$	39.4730	−	35.5417i	1.37762	−	1.24041i	0.437653	−	0.899144i	$-0.355810\pi$
$821$	39.4730	−	35.5417i	1.37762	−	1.24041i	0.939966	−	0.341269i	$-0.110857\pi$
$822$	−0.421412	+	0.468026i	−0.0146984	+	0.0163243i
$823$	−2.06370	−	0.918819i	−0.0719361	−	0.0320280i	0.370453	−	0.928851i	$-0.379202\pi$
$823$	−2.06370	−	0.918819i	−0.0719361	−	0.0320280i	−0.442389	+	0.896823i	$0.645869\pi$
$824$	0.589370	−	1.02082i	0.0205317	−	0.0355619i
$825$	−9.66198	−	15.1676i	−0.336387	−	0.528068i
$826$	−12.0039	+	34.0435i	−0.417668	+	1.18452i
$827$	10.7873	+	14.8475i	0.375112	+	0.516298i	0.954281	−	0.298910i	$-0.0966229\pi$
$827$	10.7873	+	14.8475i	0.375112	+	0.516298i	−0.579169	+	0.815207i	$0.696623\pi$
$828$	−2.50678	−	0.532832i	−0.0871165	−	0.0185172i
$829$	1.42202	+	6.69007i	0.0493887	+	0.232356i	0.995918	−	0.0902621i	$-0.0287705\pi$
$829$	1.42202	+	6.69007i	0.0493887	+	0.232356i	−0.946529	+	0.322618i	$0.895437\pi$
$830$	3.32999	−	31.6828i	0.115586	−	1.09972i
$831$	15.3470	−	6.83291i	0.532381	−	0.237031i
$832$	−6.29031	+	19.3596i	−0.218077	+	0.671173i
$833$	−43.5610	+	7.01970i	−1.50930	+	0.243218i
$834$	−26.4041	+	19.1837i	−0.914300	+	0.664278i
$835$	−39.3648	−	22.7273i	−1.36227	−	0.786510i
$836$	5.10816	+	10.2464i	0.176669	+	0.354379i
$837$	−0.776686	−	1.34526i	−0.0268462	−	0.0464990i
$838$	0.00758611	+	0.0721770i	0.000262058	+	0.00249331i
$839$	25.7445	−	8.36490i	0.888799	−	0.288788i	0.171193	−	0.985238i	$-0.445238\pi$
$839$	25.7445	−	8.36490i	0.888799	−	0.288788i	0.717606	+	0.696449i	$0.245238\pi$
$840$	−12.1382	+	15.8629i	−0.418806	+	0.547323i
$841$	−17.2803	−	12.5549i	−0.595874	−	0.432928i
$842$	12.6484	+	28.4088i	0.435893	+	0.979033i
$843$	27.1913	−	5.77969i	0.936518	−	0.199063i
$844$	−9.50908	−	8.56202i	−0.327316	−	0.294717i
$845$	13.5028	−	1.41920i	0.464510	−	0.0488219i
$846$	18.6124			0.639908
$847$	28.0349	−	7.81305i	0.963291	−	0.268460i
$848$	−23.1792			−0.795978
$849$	16.1700	−	1.69954i	0.554953	−	0.0583280i
$850$	40.3976	+	36.3742i	1.38563	+	1.24762i
$851$	18.8487	−	4.00641i	0.646124	−	0.137338i
$852$	0.275949	+	0.619791i	0.00945385	+	0.0212337i
$853$	−27.8758	−	20.2529i	−0.954448	−	0.693447i	−0.00259305	−	0.999997i	$-0.500825\pi$
$853$	−27.8758	−	20.2529i	−0.954448	−	0.693447i	−0.951855	+	0.306550i	$0.900825\pi$
$854$	46.6750	+	6.08095i	1.59719	+	0.208086i
$855$	20.0090	−	6.50133i	0.684294	−	0.222341i
$856$	0.150641	+	1.43325i	0.00514881	+	0.0489876i
$857$	−24.2121	−	41.9366i	−0.827069	−	1.43253i	−0.900328	−	0.435213i	$-0.856673\pi$
$857$	−24.2121	−	41.9366i	−0.827069	−	1.43253i	0.0732587	−	0.997313i	$-0.476660\pi$
$858$	9.76246	+	19.5824i	0.333285	+	0.668533i
$859$	−33.3335	−	19.2451i	−1.13732	−	0.656635i	−0.191558	−	0.981481i	$-0.561354\pi$
$859$	−33.3335	−	19.2451i	−1.13732	−	0.656635i	−0.945767	+	0.324847i	$0.894687\pi$
$860$	3.70903	−	2.69477i	0.126477	−	0.0918909i
$861$	21.6479	−	11.7916i	0.737759	−	0.401858i
$862$	7.60391	−	23.4024i	0.258990	−	0.797090i
$863$	−5.49877	+	2.44821i	−0.187180	+	0.0833380i	−0.498187	−	0.867070i	$-0.666001\pi$
$863$	−5.49877	+	2.44821i	−0.187180	+	0.0833380i	0.311006	+	0.950408i	$0.399334\pi$
$864$	0.305613	−	2.90772i	0.0103972	−	0.0989226i
$865$	5.78570	+	27.2196i	0.196720	+	0.925494i
$866$	38.0302	+	8.08358i	1.29232	+	0.274691i
$867$	13.3612	+	18.3901i	0.453770	+	0.624561i
$868$	−1.65351	+	1.41609i	−0.0561238	+	0.0480651i
$869$	12.1643	+	19.0957i	0.412644	+	0.647778i
$870$	7.09646	−	12.2914i	0.240593	−	0.416718i
$871$	−8.75113	−	3.89626i	−0.296521	−	0.132020i
$872$	14.3015	−	15.8834i	0.484309	−	0.537879i
$873$	−0.888060	+	0.799613i	−0.0300563	+	0.0270628i
$874$	−29.4759	+	40.5701i	−0.997037	+	1.37230i
$875$	2.04685	+	2.96961i	0.0691963	+	0.100391i
$876$	−0.246513	−	0.0800970i	−0.00832891	−	0.00270623i
$877$	9.49204	−	44.6565i	0.320523	−	1.50794i	−0.462874	−	0.886424i	$-0.653182\pi$
$877$	9.49204	−	44.6565i	0.320523	−	1.50794i	0.783398	−	0.621521i	$-0.213485\pi$
$878$	12.7858	−	28.7174i	0.431500	−	0.969164i
$879$	−9.01016	+	5.20202i	−0.303905	+	0.175460i
$880$	−13.6760	+	49.3065i	−0.461018	+	1.66212i
$881$			50.9669i			1.71712i	0.512715	+	0.858559i	$0.328640\pi$
$881$			50.9669i			1.71712i	−0.512715	+	0.858559i	$0.671360\pi$
$882$	9.90641	−	5.08122i	0.333566	−	0.171094i
$883$	−2.29098	−	7.05092i	−0.0770977	−	0.237282i	0.905079	−	0.425244i	$-0.139812\pi$
$883$	−2.29098	−	7.05092i	−0.0770977	−	0.237282i	−0.982176	+	0.187962i	$0.939812\pi$
$884$	−9.26722	−	10.2923i	−0.311690	−	0.346167i
$885$	27.5418	+	2.89476i	0.925807	+	0.0973062i
$886$	−47.9862	−	5.04356i	−1.61213	−	0.169442i
$887$	−5.09313	−	5.65649i	−0.171010	−	0.189926i	0.651547	−	0.758608i	$-0.274120\pi$
$887$	−5.09313	−	5.65649i	−0.171010	−	0.189926i	−0.822558	+	0.568682i	$0.807454\pi$
$888$	2.87821	+	8.85823i	0.0965866	+	0.297263i
$889$	32.9176	−	9.79887i	1.10402	−	0.328644i
$890$			41.7291i			1.39876i
$891$	2.06454	+	2.59570i	0.0691649	+	0.0869592i
$892$	4.97743	−	2.87372i	0.166657	−	0.0962193i
$893$	31.0184	−	69.6684i	1.03799	−	2.33137i
$894$	2.35483	−	11.0786i	0.0787575	−	0.370525i
$895$	25.8326	+	8.39352i	0.863489	+	0.280564i
$896$	36.0066	−	2.88258i	1.20290	−	0.0963001i
$897$	−11.7958	+	16.2356i	−0.393851	+	0.542089i
$898$	32.7672	−	29.5037i	1.09345	−	0.984551i
$899$	−2.87304	+	3.19084i	−0.0958213	+	0.106420i
$900$	−2.62390	−	1.16823i	−0.0874633	−	0.0389412i
$901$	−15.2867	+	26.4774i	−0.509275	+	0.882090i
$902$	31.2644	−	37.9237i	1.04099	−	1.26272i
$903$	6.97255	−	1.30200i	0.232032	−	0.0433279i
$904$	−14.4806	−	19.9308i	−0.481617	−	0.662889i
$905$	12.9891	+	2.76091i	0.431771	+	0.0917757i
$906$	1.63892	+	7.71049i	0.0544493	+	0.256164i
$907$	1.25485	−	11.9391i	0.0416667	−	0.396432i	−0.953735	−	0.300647i	$-0.902797\pi$
$907$	1.25485	−	11.9391i	0.0416667	−	0.396432i	0.995402	−	0.0957848i	$-0.0305360\pi$
$908$	4.61106	−	2.05298i	0.153023	−	0.0681304i
$909$	−4.06225	+	12.5023i	−0.134736	+	0.414676i
$910$	−26.9549	−	49.4858i	−0.893547	−	1.64044i
$911$	39.0336	−	28.3596i	1.29324	−	0.939594i	0.293375	−	0.955997i	$-0.405222\pi$
$911$	39.0336	−	28.3596i	1.29324	−	0.939594i	0.999865	+	0.0164033i	$0.00522156\pi$
$912$	−26.9706	−	15.5715i	−0.893085	−	0.515623i
$913$	3.39704	−	20.2950i	0.112426	−	0.671666i
$914$	−23.0914	−	39.9955i	−0.763797	−	1.32293i
$915$	−3.77460	−	35.9129i	−0.124784	−	1.18724i
$916$	−1.30236	+	0.423162i	−0.0430312	+	0.0139817i
$917$	2.09796	−	0.872315i	0.0692808	−	0.0288064i
$918$	−8.11073	−	5.89279i	−0.267694	−	0.194491i
$919$	−8.17279	−	18.3564i	−0.269596	−	0.605522i	0.727119	−	0.686511i	$-0.240859\pi$
$919$	−8.17279	−	18.3564i	−0.269596	−	0.605522i	−0.996715	+	0.0809894i	$0.974192\pi$
$920$	−35.7272	+	7.59404i	−1.17789	+	0.250368i
$921$	6.56506	+	5.91120i	0.216326	+	0.194781i
$922$	−7.92088	+	0.832518i	−0.260860	+	0.0274175i
$923$	5.31268			0.174869
$924$	3.04489	−	3.51200i	0.100169	−	0.115536i
$925$	21.5964			0.710087
$926$	5.86803	−	0.616755i	0.192835	−	0.0202678i
$927$	0.374587	+	0.337279i	0.0123030	+	0.0110777i
$928$	−7.90493	+	1.68024i	−0.259492	+	0.0551567i
$929$	−6.64403	−	14.9227i	−0.217984	−	0.489599i	0.771144	−	0.636661i	$-0.219685\pi$
$929$	−6.64403	−	14.9227i	−0.217984	−	0.489599i	−0.989127	+	0.147062i	$0.953018\pi$
$930$	6.45282	+	4.68825i	0.211596	+	0.153734i
$931$	−2.51015	−	45.5489i	−0.0822667	−	1.49281i
$932$	−10.2244	+	3.32211i	−0.334911	+	0.108819i
$933$	2.33243	+	22.1916i	0.0763602	+	0.726519i
$934$	17.6010	+	30.4859i	0.575924	+	0.997529i
$935$	47.3030	+	48.1397i	1.54697	+	1.57434i
$936$	−8.40048	−	4.85002i	−0.274578	−	0.158528i
$937$	24.8240	−	18.0357i	0.810966	−	0.589201i	−0.103145	−	0.994666i	$-0.532890\pi$
$937$	24.8240	−	18.0357i	0.810966	−	0.589201i	0.914111	+	0.405465i	$0.132890\pi$
$938$	−0.241309	+	9.71515i	−0.00787902	+	0.317211i
$939$	2.64828	−	8.15056i	0.0864232	−	0.265983i
$940$	−18.2816	+	8.13951i	−0.596281	+	0.265482i
$941$	−0.803040	+	7.64041i	−0.0261783	+	0.249070i	0.973605	+	0.228241i	$0.0732974\pi$
$941$	−0.803040	+	7.64041i	−0.0261783	+	0.249070i	−0.999783	+	0.0208295i	$0.993369\pi$
$942$	−0.612351	−	2.88088i	−0.0199515	−	0.0938643i
$943$	44.0926	+	9.37217i	1.43585	+	0.305200i
$944$	−24.0955	−	33.1647i	−0.784243	−	1.07942i
$945$	−5.55595	−	6.48747i	−0.180735	−	0.211037i
$946$	11.9277	−	7.59813i	0.387803	−	0.247037i
$947$	−8.96997	+	15.5364i	−0.291485	+	0.504867i	−0.974161	−	0.225854i	$-0.927483\pi$
$947$	−8.96997	+	15.5364i	−0.291485	+	0.504867i	0.682676	+	0.730721i	$0.260816\pi$
$948$	3.30344	+	1.47079i	0.107291	+	0.0477689i
$949$	−1.35814	+	1.50836i	−0.0440869	+	0.0489635i
$950$	−41.7664	+	37.6067i	−1.35508	+	1.22012i
$951$	10.1864	−	14.0204i	0.330318	−	0.454644i
$952$	16.7421	−	35.2226i	0.542616	−	1.14157i
$953$	20.1126	+	6.53499i	0.651512	+	0.211689i	0.616081	−	0.787683i	$-0.288720\pi$
$953$	20.1126	+	6.53499i	0.651512	+	0.211689i	0.0354313	+	0.999372i	$0.488720\pi$
$954$	1.60395	−	7.54601i	0.0519299	−	0.244311i
$955$	−11.4210	+	25.6519i	−0.369574	+	0.830076i
$956$	8.27428	−	4.77716i	0.267609	−	0.154504i
$957$	5.06020	−	7.64447i	0.163573	−	0.247110i
$958$		−	17.6852i		−	0.571384i
$959$	0.720121	−	0.760899i	0.0232539	−	0.0245707i
$960$	−4.89574	−	15.0675i	−0.158009	−	0.486302i
$961$	19.1285	+	21.2443i	0.617047	+	0.685300i
$962$	−26.1328	−	2.74667i	−0.842556	−	0.0885562i
$963$	−0.612893	−	0.0644176i	−0.0197502	−	0.00207583i
$964$	−2.44787	−	2.71863i	−0.0788406	−	0.0875613i
$965$	−11.0989	−	34.1590i	−0.357287	−	1.09962i
$966$	19.8030	+	4.72608i	0.637150	+	0.152059i
$967$			9.04753i			0.290949i	0.989362	+	0.145474i	$0.0464709\pi$
$967$			9.04753i			0.290949i	−0.989362	+	0.145474i	$0.953529\pi$
$968$	−8.37670	+	24.3215i	−0.269237	+	0.781721i
$969$	−35.5743	+	20.5388i	−1.14281	+	0.659802i
$970$	2.49573	−	5.60551i	0.0801332	−	0.179982i
$971$	−12.4286	+	58.4722i	−0.398854	+	1.87646i	0.0771522	+	0.997019i	$0.475417\pi$
$971$	−12.4286	+	58.4722i	−0.398854	+	1.87646i	−0.476006	+	0.879442i	$0.657916\pi$
$972$	0.503782	+	0.163689i	0.0161588	+	0.00525032i
$973$	44.7012	−	30.8110i	1.43306	−	0.987755i
$974$	−35.8597	+	49.3567i	−1.14902	+	1.58149i
$975$	−16.7143	+	15.0496i	−0.535287	+	0.481974i
$976$	−35.7674	+	39.7237i	−1.14489	+	1.27153i
$977$	27.5440	+	12.2634i	0.881210	+	0.392340i	0.796908	−	0.604100i	$-0.206467\pi$
$977$	27.5440	+	12.2634i	0.881210	+	0.392340i	0.0843017	+	0.996440i	$0.473134\pi$
$978$	19.0366	−	32.9723i	0.608722	−	1.05434i
$979$	−1.64655	+	26.9034i	−0.0526240	+	0.859838i
$980$	−7.50826	+	9.32315i	−0.239842	+	0.297817i
$981$	5.37217	+	7.39415i	0.171520	+	0.236077i
$982$	−10.7899	−	2.29346i	−0.344319	−	0.0731872i
$983$	11.8766	+	55.8749i	0.378804	+	1.78213i	0.592855	+	0.805309i	$0.298001\pi$
$983$	11.8766	+	55.8749i	0.378804	+	1.78213i	−0.214051	+	0.976822i	$0.568666\pi$
$984$	−2.27751	+	21.6691i	−0.0726043	+	0.690784i
$985$	−28.5978	+	12.7326i	−0.911203	+	0.405694i
$986$	−8.56328	+	26.3551i	−0.272710	+	0.839316i
$987$	−30.9516	−	0.768788i	−0.985199	−	0.0244708i
$988$	11.5842	−	8.41645i	0.368544	−	0.267763i
$989$	11.2329	+	6.48530i	0.357184	+	0.206221i
$990$	−15.1054	−	7.86414i	−0.480081	−	0.249939i
$991$	−29.4818	−	51.0639i	−0.936519	−	1.62210i	−0.771903	−	0.635741i	$-0.780695\pi$
$991$	−29.4818	−	51.0639i	−0.936519	−	1.62210i	−0.164616	−	0.986358i	$-0.552639\pi$
$992$	−0.474731	−	4.51677i	−0.0150727	−	0.143408i
$993$	−10.0802	+	3.27527i	−0.319887	+	0.103937i
$994$	−2.06924	−	4.97663i	−0.0656324	−	0.157849i
$995$	6.21305	+	4.51404i	0.196967	+	0.143105i
$996$	−1.33673	−	3.00234i	−0.0423558	−	0.0951327i
$997$	−50.4058	+	10.7141i	−1.59637	+	0.339319i	−0.918364	−	0.395738i	$-0.870489\pi$
$997$	−50.4058	+	10.7141i	−1.59637	+	0.339319i	−0.678006	+	0.735057i	$0.737156\pi$
$998$	16.6717	+	15.0113i	0.527735	+	0.475175i
$999$	−3.96111	+	0.416329i	−0.125324	+	0.0131721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.ba.a.19.6	✓	128
3.2	odd	2		693.2.cg.c.19.11		128
7.3	odd	6	inner	231.2.ba.a.52.11	yes	128
11.7	odd	10	inner	231.2.ba.a.40.11	yes	128
21.17	even	6		693.2.cg.c.514.6		128
33.29	even	10		693.2.cg.c.271.6		128
77.73	even	30	inner	231.2.ba.a.73.6	yes	128
231.227	odd	30		693.2.cg.c.73.11		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.6	✓	128	1.1	even	1	trivial
231.2.ba.a.40.11	yes	128	11.7	odd	10	inner
231.2.ba.a.52.11	yes	128	7.3	odd	6	inner
231.2.ba.a.73.6	yes	128	77.73	even	30	inner
693.2.cg.c.19.11		128	3.2	odd	2
693.2.cg.c.73.11		128	231.227	odd	30
693.2.cg.c.271.6		128	33.29	even	10
693.2.cg.c.514.6		128	21.17	even	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58179 + 0.166253i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(0.518133 - 0.110133i) q^{4} +(1.31309 + 2.94925i) q^{5} +(1.28675 + 0.934876i) q^{6} +(-2.10118 - 1.60780i) q^{7} +(2.22405 - 0.722639i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-1.58179 + 0.166253i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(0.518133 - 0.110133i) q^{4} +(1.31309 + 2.94925i) q^{5} +(1.28675 + 0.934876i) q^{6} +(-2.10118 - 1.60780i) q^{7} +(2.22405 - 0.722639i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-2.56736 - 4.44679i) q^{10} +(-1.47975 - 2.96822i) q^{11} +(-0.458741 - 0.264854i) q^{12} +(-3.35577 + 2.43811i) q^{13} +(3.59094 + 2.19388i) q^{14} +(0.997616 - 3.07035i) q^{15} +(-4.36567 + 1.94372i) q^{16} +(-0.658873 + 6.26876i) q^{17} +(-0.330685 - 1.55575i) q^{18} +(-6.37445 - 1.35493i) q^{19} +(1.00516 + 1.38349i) q^{20} +(0.485653 + 2.60080i) q^{21} +(2.83414 + 4.44909i) q^{22} +(-2.41905 + 4.18991i) q^{23} +(-2.13633 - 0.951157i) q^{24} +(-3.62820 + 4.02952i) q^{25} +(4.90279 - 4.41449i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-1.26576 - 0.601647i) q^{28} +(-2.62883 - 0.854157i) q^{29} +(-1.06757 + 5.02251i) q^{30} +(0.631813 - 1.41908i) q^{31} +(2.53203 - 1.46187i) q^{32} +(-0.886456 + 3.19597i) q^{33} -10.0254i q^{34} +(1.98277 - 8.30810i) q^{35} +(0.163689 + 0.503782i) q^{36} +(-2.66510 - 2.95989i) q^{37} +(10.3083 + 1.08345i) q^{38} +(4.12524 + 0.433580i) q^{39} +(5.05162 + 5.61039i) q^{40} +(-2.87918 - 8.86121i) q^{41} +(-1.20059 - 4.03318i) q^{42} -2.68093i q^{43} +(-1.09361 - 1.37496i) q^{44} +(-2.79584 + 1.61418i) q^{45} +(3.12985 - 7.02975i) q^{46} +(-2.43302 + 11.4465i) q^{47} +(4.54493 + 1.47674i) q^{48} +(1.82994 + 6.75658i) q^{49} +(5.06914 - 6.97707i) q^{50} +(4.68425 - 4.21772i) q^{51} +(-1.47022 + 1.63285i) q^{52} +(4.43106 + 1.97284i) q^{53} +(-0.795253 + 1.37742i) q^{54} +(6.81096 - 8.26170i) q^{55} +(-5.83500 - 2.05744i) q^{56} +(3.83052 + 5.27225i) q^{57} +(4.30026 + 0.914049i) q^{58} +(1.78351 + 8.39076i) q^{59} +(0.178753 - 1.70072i) q^{60} +(10.2185 - 4.54955i) q^{61} +(-0.763472 + 2.34973i) q^{62} +(1.37936 - 2.25773i) q^{63} +(3.97020 - 2.88452i) q^{64} +(-11.5970 - 6.69554i) q^{65} +(0.870850 - 5.20273i) q^{66} +(1.15470 + 2.00000i) q^{67} +(0.349010 + 3.32061i) q^{68} +(4.60130 - 1.49505i) q^{69} +(-1.75508 + 13.4713i) q^{70} +(-1.03618 - 0.752831i) q^{71} +(0.951157 + 2.13633i) q^{72} +(0.478632 - 0.101736i) q^{73} +(4.70772 + 4.23885i) q^{74} +(5.39256 - 0.566780i) q^{75} -3.45204 q^{76} +(-1.66308 + 8.61592i) q^{77} -6.59736 q^{78} +(-6.78913 + 0.713566i) q^{79} +(-11.4650 - 10.3232i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(6.02747 + 13.5379i) q^{82} +(5.01938 + 3.64679i) q^{83} +(0.538065 + 1.29407i) q^{84} +(-19.3533 + 6.28826i) q^{85} +(0.445713 + 4.24068i) q^{86} +(1.38206 + 2.39379i) q^{87} +(-5.43600 - 5.53215i) q^{88} +(-7.03808 - 4.06344i) q^{89} +(4.15407 - 3.01811i) q^{90} +(10.9711 + 0.272505i) q^{91} +(-0.791942 + 2.43735i) q^{92} +(-1.41908 + 0.631813i) q^{93} +(1.94553 - 18.5104i) q^{94} +(-4.37420 - 20.5790i) q^{95} +(-2.85984 - 0.607878i) q^{96} +(0.702405 + 0.966777i) q^{97} +(-4.01788 - 10.3833i) q^{98} +(2.79728 - 1.78191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

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