LMFDB - Embedded newform 231.2.ba.a.40.1

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			40.1
Character	$\chi$	$=$	231.40
Dual form			231.2.ba.a.52.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08550 - 2.43806i) q^{2} +(0.207912 + 0.978148i) q^{3} +(-3.42759 + 3.80673i) q^{4} +(-0.234311 + 0.0246271i) q^{5} +(2.15910 - 1.56868i) q^{6} +(-2.20197 + 1.46674i) q^{7} +(7.92533 + 2.57510i) q^{8} +(-0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-1.08550 - 2.43806i) q^{2} +(0.207912 + 0.978148i) q^{3} +(-3.42759 + 3.80673i) q^{4} +(-0.234311 + 0.0246271i) q^{5} +(2.15910 - 1.56868i) q^{6} +(-2.20197 + 1.46674i) q^{7} +(7.92533 + 2.57510i) q^{8} +(-0.913545 + 0.406737i) q^{9} +(0.314386 + 0.544533i) q^{10} +(3.28534 + 0.454496i) q^{11} +(-4.43618 - 2.56123i) q^{12} +(3.01526 + 2.19072i) q^{13} +(5.96624 + 3.77639i) q^{14} +(-0.0728050 - 0.224071i) q^{15} +(-1.25378 - 11.9289i) q^{16} +(3.51221 + 1.56374i) q^{17} +(1.98330 + 1.78577i) q^{18} +(3.20237 + 3.55660i) q^{19} +(0.709375 - 0.976371i) q^{20} +(-1.89251 - 1.84890i) q^{21} +(-2.45813 - 8.50321i) q^{22} +(-2.07688 + 3.59726i) q^{23} +(-0.871055 + 8.28754i) q^{24} +(-4.83644 + 1.02802i) q^{25} +(2.06805 - 9.72941i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(1.96395 - 13.4097i) q^{28} +(-3.14773 + 1.02276i) q^{29} +(-0.467269 + 0.420731i) q^{30} +(-7.43903 - 0.781874i) q^{31} +(-13.2890 + 7.67242i) q^{32} +(0.238496 + 3.30804i) q^{33} -10.2604i q^{34} +(0.479824 - 0.397903i) q^{35} +(1.58293 - 4.87175i) q^{36} +(4.10148 + 0.871796i) q^{37} +(5.19505 - 11.6683i) q^{38} +(-1.51593 + 3.40485i) q^{39} +(-1.92041 - 0.408196i) q^{40} +(1.45611 - 4.48144i) q^{41} +(-2.45342 + 6.62102i) q^{42} +10.6448i q^{43} +(-12.9909 + 10.9486i) q^{44} +(0.204037 - 0.117801i) q^{45} +(11.0248 + 1.15875i) q^{46} +(2.77236 - 2.49624i) q^{47} +(11.4076 - 3.70655i) q^{48} +(2.69732 - 6.45945i) q^{49} +(7.75631 + 10.6756i) q^{50} +(-0.799337 + 3.76058i) q^{51} +(-18.6745 + 3.96940i) q^{52} +(0.665778 - 6.33445i) q^{53} +(-1.33440 + 2.31124i) q^{54} +(-0.780984 - 0.0255852i) q^{55} +(-21.2283 + 5.95415i) q^{56} +(-2.81307 + 3.87185i) q^{57} +(5.91041 + 6.56417i) q^{58} +(-1.90355 - 1.71396i) q^{59} +(1.10252 + 0.490874i) q^{60} +(0.742369 + 7.06317i) q^{61} +(6.16878 + 18.9856i) q^{62} +(1.41502 - 2.23556i) q^{63} +(13.7233 + 9.97055i) q^{64} +(-0.760461 - 0.439052i) q^{65} +(7.80632 - 4.17233i) q^{66} +(5.39141 + 9.33820i) q^{67} +(-17.9912 + 8.01018i) q^{68} +(-3.95046 - 1.28358i) q^{69} +(-1.49096 - 0.737920i) q^{70} +(-2.72196 + 1.97762i) q^{71} +(-8.28754 + 0.871055i) q^{72} +(8.21566 - 9.12441i) q^{73} +(-2.32664 - 10.9460i) q^{74} +(-2.01111 - 4.51702i) q^{75} -24.5154 q^{76} +(-7.90083 + 3.81796i) q^{77} +9.94677 q^{78} +(-4.47134 - 10.0428i) q^{79} +(0.587550 + 2.76421i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-12.5066 + 1.31450i) q^{82} +(12.9336 - 9.39678i) q^{83} +(13.5250 - 0.866994i) q^{84} +(-0.861462 - 0.279906i) q^{85} +(25.9528 - 11.5549i) q^{86} +(-1.65486 - 2.86631i) q^{87} +(24.8670 + 12.0621i) q^{88} +(-7.15365 - 4.13016i) q^{89} +(-0.508688 - 0.369583i) q^{90} +(-9.85272 - 0.401269i) q^{91} +(-6.57510 - 20.2361i) q^{92} +(-0.781874 - 7.43903i) q^{93} +(-9.09538 - 4.04952i) q^{94} +(-0.837941 - 0.754486i) q^{95} +(-10.2677 - 11.4034i) q^{96} +(-1.40251 + 1.93039i) q^{97} +(-18.6765 + 0.435452i) q^{98} +(-3.18616 + 0.921064i) 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 $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.08550	−	2.43806i	−0.767562	−	1.72397i	−0.686346	−	0.727275i	$-0.740787\pi$
$2$	−1.08550	−	2.43806i	−0.767562	−	1.72397i	−0.0812151	−	0.996697i	$-0.525880\pi$
$3$	0.207912	+	0.978148i	0.120038	+	0.564734i
$3$	0.207912	+	0.978148i	0.120038	+	0.564734i
$4$	−3.42759	+	3.80673i	−1.71380	+	1.90336i
$5$	−0.234311	+	0.0246271i	−0.104787	+	0.0110136i	−0.156777	−	0.987634i	$-0.550110\pi$
$5$	−0.234311	+	0.0246271i	−0.104787	+	0.0110136i	0.0519897	+	0.998648i	$0.483444\pi$
$6$	2.15910	−	1.56868i	0.881448	−	0.640410i
$7$	−2.20197	+	1.46674i	−0.832266	+	0.554377i
$7$	−2.20197	+	1.46674i	−0.832266	+	0.554377i
$8$	7.92533	+	2.57510i	2.80203	+	0.910434i
$9$	−0.913545	+	0.406737i	−0.304515	+	0.135579i
$10$	0.314386	+	0.544533i	0.0994177	+	0.172197i
$11$	3.28534	+	0.454496i	0.990566	+	0.137036i
$11$	3.28534	+	0.454496i	0.990566	+	0.137036i
$12$	−4.43618	−	2.56123i	−1.28061	−	0.739363i
$13$	3.01526	+	2.19072i	0.836283	+	0.607595i	0.921330	−	0.388782i	$-0.127104\pi$
$13$	3.01526	+	2.19072i	0.836283	+	0.607595i	−0.0850470	+	0.996377i	$0.527104\pi$
$14$	5.96624	+	3.77639i	1.59455	+	1.00928i
$15$	−0.0728050	−	0.224071i	−0.0187982	−	0.0578548i
$16$	−1.25378	−	11.9289i	−0.313445	−	2.98223i
$17$	3.51221	+	1.56374i	0.851837	+	0.379262i	0.785745	−	0.618551i	$-0.212280\pi$
$17$	3.51221	+	1.56374i	0.851837	+	0.379262i	0.0660927	+	0.997813i	$0.478947\pi$
$18$	1.98330	+	1.78577i	0.467468	+	0.420910i
$19$	3.20237	+	3.55660i	0.734675	+	0.815939i	0.988486	−	0.151315i	$-0.0483506\pi$
$19$	3.20237	+	3.55660i	0.734675	+	0.815939i	−0.253811	+	0.967254i	$0.581684\pi$
$20$	0.709375	−	0.976371i	0.158621	−	0.218323i
$21$	−1.89251	−	1.84890i	−0.412979	−	0.403462i
$22$	−2.45813	−	8.50321i	−0.524075	−	1.81289i
$23$	−2.07688	+	3.59726i	−0.433060	+	0.750081i	−0.997135	−	0.0756420i	$-0.975899\pi$
$23$	−2.07688	+	3.59726i	−0.433060	+	0.750081i	0.564075	+	0.825723i	$0.309233\pi$
$24$	−0.871055	+	8.28754i	−0.177803	+	1.69169i
$25$	−4.83644	+	1.02802i	−0.967289	+	0.205604i
$26$	2.06805	−	9.72941i	0.405578	−	1.90809i
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	1.96395	−	13.4097i	0.371153	−	2.53419i
$29$	−3.14773	+	1.02276i	−0.584520	+	0.189922i	−0.586324	−	0.810076i	$-0.699426\pi$
$29$	−3.14773	+	1.02276i	−0.584520	+	0.189922i	0.00180464	+	0.999998i	$0.499426\pi$
$30$	−0.467269	+	0.420731i	−0.0853113	+	0.0768146i
$31$	−7.43903	−	0.781874i	−1.33609	−	0.140429i	−0.590610	−	0.806957i	$-0.701113\pi$
$31$	−7.43903	−	0.781874i	−1.33609	−	0.140429i	−0.745480	+	0.666528i	$0.767779\pi$
$32$	−13.2890	+	7.67242i	−2.34919	+	1.35631i
$33$	0.238496	+	3.30804i	0.0415168	+	0.575856i
$34$		−	10.2604i		−	1.75965i
$35$	0.479824	−	0.397903i	0.0811051	−	0.0672578i
$36$	1.58293	−	4.87175i	0.263821	−	0.811958i
$37$	4.10148	+	0.871796i	0.674279	+	0.143322i	0.532311	−	0.846549i	$-0.321324\pi$
$37$	4.10148	+	0.871796i	0.674279	+	0.143322i	0.141968	+	0.989871i	$0.454657\pi$
$38$	5.19505	−	11.6683i	0.842748	−	1.89284i
$39$	−1.51593	+	3.40485i	−0.242744	+	0.545212i
$40$	−1.92041	−	0.408196i	−0.303644	−	0.0645415i
$41$	1.45611	−	4.48144i	0.227406	−	0.699883i	−0.770633	−	0.637280i	$-0.780060\pi$
$41$	1.45611	−	4.48144i	0.227406	−	0.699883i	0.998038	−	0.0626037i	$-0.0199404\pi$
$42$	−2.45342	+	6.62102i	−0.378571	+	1.02165i
$43$			10.6448i			1.62332i	0.584129	+	0.811661i	$0.301436\pi$
$43$			10.6448i			1.62332i	−0.584129	+	0.811661i	$0.698564\pi$
$44$	−12.9909	+	10.9486i	−1.95846	+	1.65056i
$45$	0.204037	−	0.117801i	0.0304161	−	0.0175607i
$46$	11.0248	+	1.15875i	1.62552	+	0.170849i
$47$	2.77236	−	2.49624i	0.404390	−	0.364114i	−0.441693	−	0.897166i	$-0.645622\pi$
$47$	2.77236	−	2.49624i	0.404390	−	0.364114i	0.846082	+	0.533052i	$0.178955\pi$
$48$	11.4076	−	3.70655i	1.64654	−	0.534994i
$49$	2.69732	−	6.45945i	0.385332	−	0.922778i
$50$	7.75631	+	10.6756i	1.09691	+	1.50976i
$51$	−0.799337	+	3.76058i	−0.111930	+	0.526587i
$52$	−18.6745	+	3.96940i	−2.58969	+	0.550456i
$53$	0.665778	−	6.33445i	0.0914516	−	0.870104i	−0.848592	−	0.529048i	$-0.822549\pi$
$53$	0.665778	−	6.33445i	0.0914516	−	0.870104i	0.940043	−	0.341055i	$-0.110784\pi$
$54$	−1.33440	+	2.31124i	−0.181588	+	0.314520i
$55$	−0.780984	−	0.0255852i	−0.105308	−	0.00344990i
$56$	−21.2283	+	5.95415i	−2.83676	+	0.795657i
$57$	−2.81307	+	3.87185i	−0.372600	+	0.512840i
$58$	5.91041	+	6.56417i	0.776075	+	0.861918i
$59$	−1.90355	−	1.71396i	−0.247821	−	0.223139i	0.535853	−	0.844311i	$-0.319990\pi$
$59$	−1.90355	−	1.71396i	−0.247821	−	0.223139i	−0.783674	+	0.621172i	$0.786657\pi$
$60$	1.10252	+	0.490874i	0.142335	+	0.0633716i
$61$	0.742369	+	7.06317i	0.0950506	+	0.904346i	0.933309	+	0.359073i	$0.116907\pi$
$61$	0.742369	+	7.06317i	0.0950506	+	0.904346i	−0.838259	+	0.545273i	$0.816426\pi$
$62$	6.16878	+	18.9856i	0.783436	+	2.41117i
$63$	1.41502	−	2.23556i	0.178276	−	0.281654i
$64$	13.7233	+	9.97055i	1.71541	+	1.24632i
$65$	−0.760461	−	0.439052i	−0.0943235	−	0.0544577i
$66$	7.80632	−	4.17233i	0.960892	−	0.513578i
$67$	5.39141	+	9.33820i	0.658666	+	1.14084i	0.980961	+	0.194204i	$0.0622123\pi$
$67$	5.39141	+	9.33820i	0.658666	+	1.14084i	−0.322295	+	0.946639i	$0.604454\pi$
$68$	−17.9912	+	8.01018i	−2.18175	+	0.971377i
$69$	−3.95046	−	1.28358i	−0.475580	−	0.154525i
$70$	−1.49096	−	0.737920i	−0.178204	−	0.0881983i
$71$	−2.72196	+	1.97762i	−0.323037	+	0.234700i	−0.737470	−	0.675380i	$-0.763980\pi$
$71$	−2.72196	+	1.97762i	−0.323037	+	0.234700i	0.414433	+	0.910080i	$0.363980\pi$
$72$	−8.28754	+	0.871055i	−0.976696	+	0.102655i
$73$	8.21566	−	9.12441i	0.961570	−	1.06793i	−0.0360753	−	0.999349i	$-0.511486\pi$
$73$	8.21566	−	9.12441i	0.961570	−	1.06793i	0.997645	−	0.0685827i	$-0.0218477\pi$
$74$	−2.32664	−	10.9460i	−0.270467	−	1.27245i
$75$	−2.01111	−	4.51702i	−0.232223	−	0.521580i
$76$	−24.5154			−2.81211
$77$	−7.90083	+	3.81796i	−0.900384	+	0.435097i
$78$	9.94677			1.12625
$79$	−4.47134	−	10.0428i	−0.503065	−	1.12990i	−0.969443	−	0.245316i	$-0.921108\pi$
$79$	−4.47134	−	10.0428i	−0.503065	−	1.12990i	0.466379	−	0.884585i	$-0.345558\pi$
$80$	0.587550	+	2.76421i	0.0656901	+	0.309048i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	−12.5066	+	1.31450i	−1.38113	+	0.145162i
$83$	12.9336	−	9.39678i	1.41964	−	1.03143i	0.427813	−	0.903867i	$-0.359284\pi$
$83$	12.9336	−	9.39678i	1.41964	−	1.03143i	0.991830	−	0.127564i	$-0.0407157\pi$
$84$	13.5250	−	0.866994i	1.47570	−	0.0945968i
$85$	−0.861462	−	0.279906i	−0.0934387	−	0.0303601i
$86$	25.9528	−	11.5549i	2.79856	−	1.24600i
$87$	−1.65486	−	2.86631i	−0.177420	−	0.307300i
$88$	24.8670	+	12.0621i	2.65083	+	1.28582i
$89$	−7.15365	−	4.13016i	−0.758285	−	0.437796i	0.0703946	−	0.997519i	$-0.477574\pi$
$89$	−7.15365	−	4.13016i	−0.758285	−	0.437796i	−0.828680	+	0.559723i	$0.810907\pi$
$90$	−0.508688	−	0.369583i	−0.0536204	−	0.0389575i
$91$	−9.85272	−	0.401269i	−1.03285	−	0.0420644i
$92$	−6.57510	−	20.2361i	−0.685501	−	2.10976i
$93$	−0.781874	−	7.43903i	−0.0810765	−	0.771392i
$94$	−9.09538	−	4.04952i	−0.938116	−	0.417676i
$95$	−0.837941	−	0.754486i	−0.0859710	−	0.0774086i
$96$	−10.2677	−	11.4034i	−1.04794	−	1.16386i
$97$	−1.40251	+	1.93039i	−0.142404	+	0.196002i	−0.874261	−	0.485456i	$-0.838654\pi$
$97$	−1.40251	+	1.93039i	−0.142404	+	0.196002i	0.731858	+	0.681458i	$0.238654\pi$
$98$	−18.6765	+	0.435452i	−1.88661	+	0.0439873i
$99$	−3.18616	+	0.921064i	−0.320222	+	0.0925704i
$100$	12.6640	−	21.9346i	1.26640	−	2.19346i
$101$	1.78825	−	17.0141i	0.177938	−	1.69296i	−0.433087	−	0.901352i	$-0.642576\pi$
$101$	1.78825	−	17.0141i	0.177938	−	1.69296i	0.611025	−	0.791612i	$-0.290758\pi$
$102$	10.0362	−	2.13326i	0.993734	−	0.211225i
$103$	−1.77607	+	8.35573i	−0.175001	+	0.823315i	0.799805	+	0.600260i	$0.204936\pi$
$103$	−1.77607	+	8.35573i	−0.175001	+	0.823315i	−0.974806	+	0.223055i	$0.928397\pi$
$104$	18.2556	+	25.1267i	1.79011	+	2.46388i
$105$	0.488969	+	0.386610i	0.0477185	+	0.0377293i
$106$	−16.1665	+	5.25281i	−1.57023	+	0.510198i
$107$	−4.14631	+	3.73336i	−0.400839	+	0.360917i	−0.844757	−	0.535150i	$-0.820255\pi$
$107$	−4.14631	+	3.73336i	−0.400839	+	0.360917i	0.443918	+	0.896068i	$0.353588\pi$
$108$	5.09439	+	0.535442i	0.490208	+	0.0515230i
$109$	10.0052	−	5.77649i	0.958322	−	0.553287i	0.0626655	−	0.998035i	$-0.480040\pi$
$109$	10.0052	−	5.77649i	0.958322	−	0.553287i	0.895656	+	0.444747i	$0.146707\pi$
$110$	0.785377	+	1.93186i	0.0748828	+	0.184196i
$111$			4.19311i			0.397992i
$112$	20.2575	+	24.4282i	1.91415	+	2.30824i
$113$	−2.07188	+	6.37658i	−0.194906	+	0.599858i	0.805072	+	0.593177i	$0.202127\pi$
$113$	−2.07188	+	6.37658i	−0.194906	+	0.599858i	−0.999978	+	0.00668105i	$0.997873\pi$
$114$	12.4934	+	2.65555i	1.17011	+	0.248715i
$115$	0.398046	−	0.894027i	0.0371180	−	0.0833684i
$116$	6.89578	−	15.4882i	0.640257	−	1.43804i
$117$	−3.64562	−	0.774901i	−0.337038	−	0.0716396i
$118$	−2.11245	+	6.50146i	−0.194467	+	0.598508i
$119$	−10.0274	+	1.70822i	−0.919209	+	0.156592i
$120$		−	1.96332i		−	0.179225i
$121$	10.5869	+	2.98634i	0.962442	+	0.271486i
$122$	16.4146	−	9.47698i	1.48611	−	0.858006i
$123$	4.68625	+	0.492545i	0.422545	+	0.0444113i
$124$	28.4743	−	25.6384i	2.55707	−	2.30240i
$125$	2.22827	−	0.724009i	0.199303	−	0.0647573i
$126$	−6.98643	−	1.02322i	−0.622401	−	0.0911555i
$127$	3.82996	+	5.27148i	0.339854	+	0.467768i	0.944399	−	0.328803i	$-0.106645\pi$
$127$	3.82996	+	5.27148i	0.339854	+	0.467768i	−0.604545	+	0.796571i	$0.706645\pi$
$128$	3.03153	−	14.2622i	0.267952	−	1.26061i
$129$	−10.4122	+	2.21318i	−0.916744	+	0.194860i
$130$	−0.244960	+	2.33064i	−0.0214844	+	0.204411i
$131$	3.55659	−	6.16019i	0.310740	−	0.538218i	−0.667782	−	0.744357i	$-0.732756\pi$
$131$	3.55659	−	6.16019i	0.310740	−	0.538218i	0.978523	+	0.206138i	$0.0660897\pi$
$132$	−13.4103	−	10.4307i	−1.16721	−	0.907878i
$133$	−12.2681	−	3.13445i	−1.06378	−	0.271791i
$134$	16.9148	−	23.2812i	1.46121	−	2.01119i
$135$	0.157648	+	0.175086i	0.0135682	+	0.0150690i
$136$	23.8087	+	21.4374i	2.04158	+	1.83825i
$137$	0.612715	+	0.272798i	0.0523477	+	0.0233067i	0.432744	−	0.901517i	$-0.357546\pi$
$137$	0.612715	+	0.272798i	0.0523477	+	0.0233067i	−0.380396	+	0.924824i	$0.624212\pi$
$138$	1.15875	+	11.0248i	0.0986396	+	0.938494i
$139$	−0.957979	−	2.94836i	−0.0812548	−	0.250076i	0.902174	−	0.431373i	$-0.141971\pi$
$139$	−0.957979	−	2.94836i	−0.0812548	−	0.250076i	−0.983428	+	0.181296i	$0.941971\pi$
$140$	−0.129935	+	3.19041i	−0.0109815	+	0.269639i
$141$	3.01810	+	2.19278i	0.254170	+	0.184665i
$142$	7.77623	+	4.48961i	0.652567	+	0.376760i
$143$	8.91047	+	8.56766i	0.745131	+	0.716464i
$144$	5.99732	+	10.3877i	0.499777	+	0.865639i
$145$	0.712362	−	0.317164i	0.0591585	−	0.0263390i
$146$	−31.1640	−	10.1258i	−2.57915	−	0.838016i
$147$	6.87910	+	1.29539i	0.567378	+	0.106842i
$148$	−17.3769	+	12.6250i	−1.42837	+	1.03777i
$149$	−16.6200	+	1.74683i	−1.36156	+	0.143106i	−0.756981	−	0.653437i	$-0.773327\pi$
$149$	−16.6200	+	1.74683i	−1.36156	+	0.143106i	−0.604582	+	0.796543i	$0.706660\pi$
$150$	−8.82973	+	9.80641i	−0.720944	+	0.800690i
$151$	0.693843	+	3.26427i	0.0564641	+	0.265643i	0.997320	−	0.0731646i	$-0.0233098\pi$
$151$	0.693843	+	3.26427i	0.0564641	+	0.265643i	−0.940856	+	0.338807i	$0.889977\pi$
$152$	16.2213	+	36.4336i	1.31572	+	2.95516i
$153$	−3.84460			−0.310817
$154$	17.8848	+	15.1184i	1.44119	+	1.21827i
$155$	1.76230			0.141552
$156$	−7.76531	−	17.4412i	−0.621722	−	1.39641i
$157$	−4.06344	−	19.1170i	−0.324298	−	1.52570i	−0.774384	−	0.632716i	$-0.781940\pi$
$157$	−4.06344	−	19.1170i	−0.324298	−	1.52570i	0.450086	−	0.892985i	$-0.351393\pi$
$158$	−19.6313	+	21.8028i	−1.56178	+	1.73454i
$159$	6.33445	−	0.665778i	0.502355	−	0.0527996i
$160$	2.92482	−	2.12500i	0.231227	−	0.167996i
$161$	−0.703039	−	10.9673i	−0.0554072	−	0.864345i
$162$	−2.53817	−	0.824702i	−0.199418	−	0.0647947i
$163$	−11.4944	+	5.11763i	−0.900310	+	0.400844i	−0.804084	−	0.594516i	$-0.797344\pi$
$163$	−11.4944	+	5.11763i	−0.900310	+	0.400844i	−0.0962260	+	0.995360i	$0.530677\pi$
$164$	12.0687	+	20.9036i	0.942405	+	1.63229i
$165$	−0.137350	−	0.769237i	−0.0106927	−	0.0598850i
$166$	−36.9493	−	21.3327i	−2.86782	−	1.65574i
$167$	5.12519	+	3.72367i	0.396599	+	0.288146i	0.768154	−	0.640265i	$-0.221175\pi$
$167$	5.12519	+	3.72367i	0.396599	+	0.288146i	−0.371555	+	0.928411i	$0.621175\pi$
$168$	−10.2377	−	19.5265i	−0.789853	−	1.50650i
$169$	0.275343	+	0.847418i	0.0211802	+	0.0651860i
$170$	0.252685	+	2.40414i	0.0193800	+	0.184389i
$171$	−4.37211	−	1.94659i	−0.334344	−	0.148859i
$172$	−40.5220	−	36.4861i	−3.08977	−	2.78204i
$173$	2.27525	+	2.52692i	0.172984	+	0.192118i	0.823402	−	0.567458i	$-0.192073\pi$
$173$	2.27525	+	2.52692i	0.172984	+	0.192118i	−0.650418	+	0.759576i	$0.725406\pi$
$174$	−5.19189	+	7.14602i	−0.393596	+	0.541739i
$175$	9.14185	−	9.35748i	0.691059	−	0.707359i
$176$	1.30256	−	39.7604i	0.0981839	−	2.99705i
$177$	1.28074	−	2.21830i	0.0962661	−	0.166738i
$178$	−2.30434	+	21.9243i	−0.172718	+	1.64330i
$179$	11.6011	−	2.46589i	0.867107	−	0.184309i	0.247181	−	0.968969i	$-0.420496\pi$
$179$	11.6011	−	2.46589i	0.867107	−	0.184309i	0.619926	+	0.784660i	$0.287162\pi$
$180$	−0.250920	+	1.18049i	−0.0187025	+	0.0879884i
$181$	3.36941	+	4.63759i	0.250446	+	0.344710i	0.915668	−	0.401937i	$-0.131663\pi$
$181$	3.36941	+	4.63759i	0.250446	+	0.344710i	−0.665221	+	0.746646i	$0.731663\pi$
$182$	9.71677	+	24.4571i	0.720255	+	1.81288i
$183$	−6.75447	+	2.19466i	−0.499305	+	0.162234i
$184$	−25.7233	+	23.1613i	−1.89634	+	1.70748i
$185$	−0.982492	−	0.103264i	−0.0722343	−	0.00759213i
$186$	−17.2881	+	9.98130i	−1.26763	+	0.731864i
$187$	10.8281	+	6.73369i	0.791829	+	0.492417i
$188$			19.1097i			1.39372i
$189$	2.48090	+	0.919299i	0.180459	+	0.0668692i
$190$	−0.929902	+	2.86195i	−0.0674622	+	0.207627i
$191$	17.0796	+	3.63038i	1.23584	+	0.262685i	0.779091	−	0.626911i	$-0.215681\pi$
$191$	17.0796	+	3.63038i	1.23584	+	0.262685i	0.456747	+	0.889597i	$0.349015\pi$
$192$	−6.89944	+	15.4964i	−0.497924	+	1.11836i
$193$	5.05420	−	11.3519i	0.363810	−	0.817130i	−0.635188	−	0.772358i	$-0.719077\pi$
$193$	5.05420	−	11.3519i	0.363810	−	0.817130i	0.998997	−	0.0447718i	$-0.0142561\pi$
$194$	6.22884	+	1.32398i	0.447205	+	0.0950563i
$195$	0.271349	−	0.835127i	0.0194317	−	0.0598047i
$196$	15.3440	+	32.4083i	1.09600	+	2.31488i
$197$			9.04921i			0.644729i	0.946616	+	0.322365i	$0.104478\pi$
$197$			9.04921i			0.644729i	−0.946616	+	0.322365i	$0.895522\pi$
$198$	5.70418	+	6.76826i	0.405378	+	0.480999i
$199$	−3.64229	+	2.10288i	−0.258195	+	0.149069i	−0.623511	−	0.781815i	$-0.714294\pi$
$199$	−3.64229	+	2.10288i	−0.258195	+	0.149069i	0.365316	+	0.930884i	$0.380961\pi$
$200$	−40.9777	−	4.30693i	−2.89756	−	0.304546i
$201$	−8.01320	+	7.21512i	−0.565208	+	0.508915i
$202$	−43.4225	+	14.1088i	−3.05520	+	0.992694i
$203$	5.43108	−	6.86901i	0.381187	−	0.482110i
$204$	−11.5757	−	15.9326i	−0.810462	−	1.11551i
$205$	−0.230818	+	1.08591i	−0.0161210	+	0.0758434i
$206$	22.2997	−	4.73995i	1.55370	−	0.330248i
$207$	0.434186	−	4.13101i	0.0301780	−	0.287125i
$208$	22.3524	−	38.7155i	1.54986	−	2.68444i
$209$	8.90442	+	13.1401i	0.615932	+	0.908919i
$210$	0.411807	−	1.61180i	0.0284174	−	0.111225i
$211$	11.8736	−	16.3426i	0.817414	−	1.12507i	−0.172723	−	0.984970i	$-0.555256\pi$
$211$	11.8736	−	16.3426i	0.817414	−	1.12507i	0.990137	−	0.140104i	$-0.0447435\pi$
$212$	21.8315	+	24.2463i	1.49939	+	1.66525i
$213$	−2.50033	−	2.25131i	−0.171320	−	0.154257i
$214$	13.6030	+	6.05643i	0.929880	+	0.414009i
$215$	−0.262151	−	2.49420i	−0.0178786	−	0.170103i
$216$	−2.57510	−	7.92533i	−0.175213	−	0.539251i
$217$	17.5273	−	9.18949i	1.18983	−	0.623823i
$218$	−24.9440	−	18.1229i	−1.68942	−	1.22744i
$219$	10.6332	+	6.13905i	0.718522	+	0.414839i
$220$	2.77429	−	2.88530i	0.187043	−	0.194527i
$221$	7.16454	+	12.4093i	0.481939	+	0.834743i
$222$	10.2231	−	4.55160i	0.686127	−	0.305483i
$223$	14.7252	+	4.78452i	0.986075	+	0.320395i	0.757288	−	0.653081i	$-0.226524\pi$
$223$	14.7252	+	4.78452i	0.986075	+	0.320395i	0.228787	+	0.973477i	$0.426524\pi$
$224$	18.0085	−	36.3860i	1.20325	−	2.43114i
$225$	4.00018	−	2.90630i	0.266679	−	0.193753i
$226$	17.7955	−	1.87038i	1.18374	−	0.124416i
$227$	−15.7811	+	17.5267i	−1.04743	+	1.16329i	−0.0611643	+	0.998128i	$0.519481\pi$
$227$	−15.7811	+	17.5267i	−1.04743	+	1.16329i	−0.986266	+	0.165162i	$0.947185\pi$
$228$	−5.09704	−	23.9797i	−0.337560	−	1.58809i
$229$	−5.39042	−	12.1071i	−0.356209	−	0.800058i	−0.999410	−	0.0343603i	$-0.989061\pi$
$229$	−5.39042	−	12.1071i	−0.356209	−	0.800058i	0.643201	−	0.765698i	$-0.277606\pi$
$230$	−2.61177			−0.172215
$231$	−5.37721	−	6.93438i	−0.353794	−	0.456249i
$232$	−27.5806			−1.81075
$233$	−6.96037	−	15.6333i	−0.455989	−	1.02417i	−0.984523	−	0.175256i	$-0.943925\pi$
$233$	−6.96037	−	15.6333i	−0.455989	−	1.02417i	0.528534	−	0.848912i	$-0.322742\pi$
$234$	2.06805	+	9.72941i	0.135193	+	0.636031i
$235$	−0.588119	+	0.653172i	−0.0383647	+	0.0426083i
$236$	13.0492	−	1.37152i	0.849428	−	0.0892784i
$237$	8.89368	−	6.46164i	0.577707	−	0.419729i
$238$	15.0494	+	22.5931i	0.975510	+	1.46450i
$239$	−7.85731	−	2.55299i	−0.508247	−	0.165139i	0.0436578	−	0.999047i	$-0.486099\pi$
$239$	−7.85731	−	2.55299i	−0.508247	−	0.165139i	−0.551905	+	0.833907i	$0.686099\pi$
$240$	−2.58164	+	1.14942i	−0.166644	+	0.0741949i
$241$	12.9495	+	22.4291i	0.834148	+	1.44479i	0.894722	+	0.446623i	$0.147374\pi$
$241$	12.9495	+	22.4291i	0.834148	+	1.44479i	−0.0605740	+	0.998164i	$0.519293\pi$
$242$	−4.21111	−	29.0531i	−0.270700	−	1.86761i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−29.4321	−	21.3837i	−1.88420	−	1.36895i
$245$	−0.472936	+	1.57995i	−0.0302148	+	0.100939i
$246$	−3.88605	−	11.9600i	−0.247766	−	0.762544i
$247$	1.86450	+	17.7396i	0.118635	+	1.12874i
$248$	−56.9434	−	25.3528i	−3.61591	−	1.60991i
$249$	11.8805	+	10.6972i	0.752895	+	0.677910i
$250$	−4.18396	−	4.64675i	−0.264617	−	0.293887i
$251$	−8.94180	+	12.3073i	−0.564402	+	0.776832i	−0.991878	−	0.127194i	$-0.959403\pi$
$251$	−8.94180	+	12.3073i	−0.564402	+	0.776832i	0.427476	+	0.904027i	$0.359403\pi$
$252$	3.66005	+	13.0492i	0.230561	+	0.822021i
$253$	−8.45819	+	10.8743i	−0.531762	+	0.683660i
$254$	8.69481	−	15.0598i	0.545561	−	0.944939i
$255$	0.0946813	−	0.900833i	0.00592917	−	0.0564123i
$256$	−4.87841	+	1.03694i	−0.304900	+	0.0648086i
$257$	4.30476	−	20.2523i	0.268524	−	1.26331i	−0.612590	−	0.790401i	$-0.709872\pi$
$257$	4.30476	−	20.2523i	0.268524	−	1.26331i	0.881114	−	0.472904i	$-0.156794\pi$
$258$	16.6983	+	22.9832i	1.03959	+	1.43087i
$259$	−10.3100	+	4.09615i	−0.640634	+	0.254522i
$260$	4.27790	−	1.38997i	0.265304	−	0.0862025i
$261$	2.45960	−	2.21464i	0.152246	−	0.137083i
$262$	−18.8796	−	1.98433i	−1.16639	−	0.122592i
$263$	−13.0755	+	7.54913i	−0.806269	+	0.465500i	−0.845658	−	0.533724i	$-0.820792\pi$
$263$	−13.0755	+	7.54913i	−0.806269	+	0.465500i	0.0393896	+	0.999224i	$0.487459\pi$
$264$	−6.62836	+	26.8315i	−0.407947	+	1.65136i
$265$			1.50063i			0.0921829i
$266$	5.67503	+	33.3129i	0.347958	+	2.04255i
$267$	2.55258	−	7.85603i	0.156215	−	0.480781i
$268$	−54.0276	−	11.4839i	−3.30026	−	0.701491i
$269$	7.28678	−	16.3664i	0.444283	−	0.997876i	−0.543121	−	0.839655i	$-0.682757\pi$
$269$	7.28678	−	16.3664i	0.444283	−	0.997876i	0.987404	−	0.158221i	$-0.0505760\pi$
$270$	0.255745	−	0.574413i	0.0155641	−	0.0349576i
$271$	−11.8045	−	2.50913i	−0.717075	−	0.152419i	−0.165097	−	0.986277i	$-0.552794\pi$
$271$	−11.8045	−	2.50913i	−0.717075	−	0.152419i	−0.551979	+	0.833858i	$0.686127\pi$
$272$	14.2502	−	43.8576i	0.864045	−	2.65926i
$273$	−1.65600	−	9.72085i	−0.100225	−	0.588332i
$274$		−	1.78996i		−	0.108135i
$275$	−16.3566	+	1.17924i	−0.986338	+	0.0711109i
$276$	18.4268	−	10.6387i	1.10916	−	0.640376i
$277$	0.131626	+	0.0138344i	0.00790864	+	0.000831231i	0.108482	−	0.994098i	$-0.465401\pi$
$277$	0.131626	+	0.0138344i	0.00790864	+	0.000831231i	−0.100573	+	0.994930i	$0.532068\pi$
$278$	−6.14840	+	5.53604i	−0.368757	+	0.332030i
$279$	7.11391	−	2.31145i	0.425899	−	0.138383i
$280$	4.82740	−	1.91792i	0.288493	−	0.114618i
$281$	14.8622	+	20.4561i	0.886607	+	1.22031i	0.974547	+	0.224184i	$0.0719716\pi$
$281$	14.8622	+	20.4561i	0.886607	+	1.22031i	−0.0879401	+	0.996126i	$0.528028\pi$
$282$	2.07000	−	9.73856i	0.123266	−	0.579923i
$283$	15.6452	−	3.32549i	0.930009	−	0.197680i	0.282089	−	0.959388i	$-0.408973\pi$
$283$	15.6452	−	3.32549i	0.930009	−	0.197680i	0.647920	+	0.761709i	$0.275639\pi$
$284$	1.80151	−	17.1402i	0.106900	−	1.01708i
$285$	0.563781	−	0.976497i	0.0333955	−	0.0578427i
$286$	11.2162	−	31.0245i	0.663229	−	1.83451i
$287$	3.36682	+	12.0037i	0.198737	+	0.708558i
$288$	9.01947	−	12.4142i	0.531477	−	0.731516i
$289$	−1.48485	−	1.64909i	−0.0873439	−	0.0970052i
$290$	−1.54653	−	1.39250i	−0.0908155	−	0.0817706i
$291$	−2.17981	−	0.970513i	−0.127783	−	0.0568925i
$292$	6.57422	+	62.5495i	0.384727	+	3.66043i
$293$	−4.87645	−	15.0082i	−0.284885	−	0.876786i	−0.986433	−	0.164164i	$-0.947507\pi$
$293$	−4.87645	−	15.0082i	−0.284885	−	0.876786i	0.701548	−	0.712622i	$-0.252493\pi$
$294$	−4.30899	−	18.1778i	−0.251306	−	1.06015i
$295$	0.488232	+	0.354721i	0.0284260	+	0.0206527i
$296$	30.2606	+	17.4710i	1.75886	+	1.01548i
$297$	−1.56338	−	2.92504i	−0.0907164	−	0.169728i
$298$	22.2998	+	38.6244i	1.29179	+	2.23745i
$299$	−14.1429	+	6.29683i	−0.817906	+	0.364155i
$300$	24.0883	+	7.82676i	1.39074	+	0.451878i
$301$	−15.6132	−	23.4396i	−0.899932	−	1.35103i
$302$	7.20534	−	5.23499i	0.414621	−	0.301240i
$303$	17.0141	−	1.78825i	0.977433	−	0.102732i
$304$	38.4113	−	42.6601i	2.20304	−	2.44673i
$305$	−0.347891	−	1.63670i	−0.0199202	−	0.0937170i
$306$	4.17330	+	9.37337i	0.238571	+	0.535840i
$307$	25.7813			1.47142			0.735709	−	0.677298i	$-0.236849\pi$
$307$	25.7813			1.47142			0.735709	+	0.677298i	$0.236849\pi$
$308$	12.5469	−	43.1627i	0.714926	−	2.45942i
$309$	−8.54241			−0.485961
$310$	−1.91297	−	4.29661i	−0.108650	−	0.244031i
$311$	−3.51651	−	16.5439i	−0.199403	−	0.938117i	−0.958047	−	0.286611i	$-0.907471\pi$
$311$	−3.51651	−	16.5439i	−0.199403	−	0.938117i	0.758644	−	0.651505i	$-0.225862\pi$
$312$	−20.7821	+	23.0809i	−1.17655	+	1.30670i
$313$	1.61596	−	0.169844i	0.0913395	−	0.00960017i	−0.0587484	−	0.998273i	$-0.518711\pi$
$313$	1.61596	−	0.169844i	0.0913395	−	0.00960017i	0.150088	+	0.988673i	$0.452044\pi$
$314$	−42.1976	+	30.6583i	−2.38135	+	1.73015i
$315$	−0.276500	+	0.558664i	−0.0155790	+	0.0314772i
$316$	53.5561	+	17.4014i	3.01276	+	0.978906i
$317$	−26.3223	+	11.7195i	−1.47841	+	0.658230i	−0.978198	−	0.207673i	$-0.933411\pi$
$317$	−26.3223	+	11.7195i	−1.47841	+	0.658230i	−0.500211	+	0.865903i	$0.666744\pi$
$318$	−8.49923	−	14.7211i	−0.476613	−	0.825518i
$319$	−10.8062	+	1.92948i	−0.605031	+	0.108030i
$320$	−3.46107	−	1.99825i	−0.193480	−	0.111705i
$321$	−4.51384	−	3.27950i	−0.251938	−	0.183044i
$322$	−25.9759	+	13.6190i	−1.44758	+	0.758959i
$323$	5.68584	+	17.4992i	0.316369	+	0.973682i
$324$	0.535442	+	5.09439i	0.0297468	+	0.283022i
$325$	−16.8352	−	7.49553i	−0.933850	−	0.415777i
$326$	24.9542	+	22.4689i	1.38209	+	1.24444i
$327$	7.73045	+	8.58553i	0.427495	+	0.474781i
$328$	23.0803	−	31.7673i	1.27440	−	1.75406i
$329$	−2.44329	+	9.56298i	−0.134703	+	0.527224i
$330$	−1.72636	+	1.16987i	−0.0950328	+	0.0643993i
$331$	5.43171	−	9.40800i	0.298554	−	0.517110i	−0.677252	−	0.735752i	$-0.736829\pi$
$331$	5.43171	−	9.40800i	0.298554	−	0.517110i	0.975805	+	0.218641i	$0.0701624\pi$
$332$	−8.55999	+	81.4429i	−0.469791	+	4.46976i
$333$	−4.10148	+	0.871796i	−0.224760	+	0.0477741i
$334$	3.51517	−	16.5376i	0.192342	−	0.904896i
$335$	−1.49324	−	2.05527i	−0.0815845	−	0.112291i
$336$	−19.6826	+	24.8937i	−1.07377	+	1.35806i
$337$	9.81536	−	3.18920i	0.534677	−	0.173727i	−0.0292190	−	0.999573i	$-0.509302\pi$
$337$	9.81536	−	3.18920i	0.534677	−	0.173727i	0.563896	+	0.825846i	$0.309302\pi$
$338$	1.76718	−	1.59117i	0.0961217	−	0.0865484i
$339$	−6.66800	−	0.700836i	−0.362156	−	0.0380642i
$340$	4.01827	−	2.31995i	0.217921	−	0.125817i
$341$	−24.0844	−	5.94973i	−1.30424	−	0.322196i
$342$			12.7725i			0.690658i
$343$	3.53493	+	18.1798i	0.190868	+	0.981616i
$344$	−27.4115	+	84.3638i	−1.47793	+	4.54859i
$345$	0.957249	+	0.203470i	0.0515365	+	0.0109544i
$346$	3.69102	−	8.29017i	0.198431	−	0.445682i
$347$	4.48135	−	10.0653i	0.240572	−	0.540333i	−0.752397	−	0.658710i	$-0.771102\pi$
$347$	4.48135	−	10.0653i	0.240572	−	0.540333i	0.992969	+	0.118377i	$0.0377691\pi$
$348$	16.5834	+	3.52492i	0.888965	+	0.188955i
$349$	0.323865	−	0.996755i	0.0173361	−	0.0533551i	−0.942014	−	0.335573i	$-0.891070\pi$
$349$	0.323865	−	0.996755i	0.0173361	−	0.0533551i	0.959350	+	0.282218i	$0.0910701\pi$
$350$	−32.7376	−	12.1309i	−1.74990	−	0.648424i
$351$		−	3.72707i		−	0.198936i
$352$	−47.1460	+	19.1667i	−2.51289	+	1.02159i
$353$	3.64157	−	2.10246i	0.193821	−	0.111903i	−0.399949	−	0.916537i	$-0.630972\pi$
$353$	3.64157	−	2.10246i	0.193821	−	0.111903i	0.593770	+	0.804635i	$0.297639\pi$
$354$	−6.79859	−	0.714561i	−0.361341	−	0.0379785i
$355$	0.589082	−	0.530412i	0.0312652	−	0.0281514i
$356$	40.2422	−	13.0755i	2.13283	−	0.692999i
$357$	−3.75570	−	9.45311i	−0.198773	−	0.500312i
$358$	−18.6050	−	25.6075i	−0.983302	−	1.35340i
$359$	−1.16050	+	5.45973i	−0.0612489	+	0.288153i	−0.998103	−	0.0615673i	$-0.980390\pi$
$359$	−1.16050	+	5.45973i	−0.0612489	+	0.288153i	0.936854	+	0.349721i	$0.113723\pi$
$360$	1.92041	−	0.408196i	0.101215	−	0.0215138i
$361$	−0.408141	+	3.88320i	−0.0214811	+	0.204379i
$362$	7.64927	−	13.2489i	0.402037	−	0.696348i
$363$	−0.719951	+	10.9764i	−0.0377876	+	0.576112i
$364$	35.2986	−	36.1312i	1.85015	−	1.89379i
$365$	−1.70031	+	2.34028i	−0.0889985	+	0.122496i
$366$	12.6827	+	14.0855i	0.662934	+	0.736263i
$367$	4.64830	+	4.18535i	0.242640	+	0.218474i	0.781474	−	0.623938i	$-0.214468\pi$
$367$	4.64830	+	4.18535i	0.242640	+	0.218474i	−0.538834	+	0.842412i	$0.681135\pi$
$368$	45.5155	+	20.2648i	2.37266	+	1.05638i
$369$	0.492545	+	4.68625i	0.0256409	+	0.243957i
$370$	0.814727	+	2.50747i	0.0423556	+	0.130357i
$371$	7.82500	+	14.9248i	0.406254	+	0.774856i
$372$	30.9983	+	22.5216i	1.60719	+	1.16769i
$373$	8.39019	+	4.84408i	0.434427	+	0.250817i	0.701231	−	0.712934i	$-0.252634\pi$
$373$	8.39019	+	4.84408i	0.434427	+	0.250817i	−0.266804	+	0.963751i	$0.585967\pi$
$374$	4.66332	−	33.7090i	0.241135	−	1.74305i
$375$	1.17147	+	2.02905i	0.0604945	+	0.104780i
$376$	28.3999	−	12.6445i	1.46461	−	0.652088i
$377$	−11.7318	−	3.81190i	−0.604219	−	0.196323i
$378$	−0.451703	−	7.04650i	−0.0232331	−	0.362433i
$379$	−6.65607	+	4.83592i	−0.341899	+	0.248404i	−0.745463	−	0.666547i	$-0.767771\pi$
$379$	−6.65607	+	4.83592i	−0.341899	+	0.248404i	0.403564	+	0.914952i	$0.367771\pi$
$380$	5.74424	−	0.603744i	0.294673	−	0.0309714i
$381$	−4.35999	+	4.84226i	−0.223369	+	0.248077i
$382$	−9.68874	−	45.5820i	−0.495719	−	2.33218i
$383$	2.85504	+	6.41253i	0.145886	+	0.327665i	0.971678	−	0.236310i	$-0.0759381\pi$
$383$	2.85504	+	6.41253i	0.145886	+	0.327665i	−0.825792	+	0.563975i	$0.809271\pi$
$384$	14.5808			0.744075
$385$	1.75723	−	1.08917i	0.0895567	−	0.0555090i
$386$	−33.1630			−1.68795
$387$	−4.32964	−	9.72454i	−0.220088	−	0.494326i
$388$	−2.54124	−	11.9556i	−0.129012	−	0.606953i
$389$	−3.54533	+	3.93749i	−0.179755	+	0.199639i	−0.826288	−	0.563248i	$-0.809552\pi$
$389$	−3.54533	+	3.93749i	−0.179755	+	0.199639i	0.646533	+	0.762886i	$0.276218\pi$
$390$	−2.33064	+	0.244960i	−0.118017	+	0.0124040i
$391$	−12.9196	+	9.38666i	−0.653374	+	0.474704i
$392$	38.0109	−	44.2474i	1.91984	−	2.23483i
$393$	6.76503	+	2.19809i	0.341251	+	0.110879i
$394$	22.0625	−	9.82288i	1.11150	−	0.494870i
$395$	1.29501	+	2.24302i	0.0651590	+	0.112859i
$396$	7.41463	−	15.2859i	0.372599	−	0.768145i
$397$	9.21969	+	5.32299i	0.462723	+	0.267153i	0.713189	−	0.700972i	$-0.247250\pi$
$397$	9.21969	+	5.32299i	0.462723	+	0.267153i	−0.250465	+	0.968126i	$0.580584\pi$
$398$	9.08065	+	6.59747i	0.455172	+	0.330702i
$399$	0.515264	−	12.6517i	0.0257955	−	0.633379i
$400$	18.3270	+	56.4047i	0.916350	+	2.82023i
$401$	0.387892	+	3.69055i	0.0193704	+	0.184297i	0.999929	−	0.0119302i	$-0.00379759\pi$
$401$	0.387892	+	3.69055i	0.0193704	+	0.184297i	−0.980558	+	0.196227i	$0.937131\pi$
$402$	26.2892	+	11.7047i	1.31119	+	0.583778i
$403$	−20.7178	−	18.6544i	−1.03203	−	0.929239i
$404$	58.6385	+	65.1247i	2.91738	+	3.24007i
$405$	−0.138483	+	0.190606i	−0.00688129	+	0.00947129i
$406$	−22.6425	−	5.78505i	−1.12373	−	0.287107i
$407$	13.0785	+	4.72825i	0.648277	+	0.234371i
$408$	−16.0189	+	27.7455i	−0.793053	+	1.37361i
$409$	2.49843	−	23.7709i	0.123539	−	1.17540i	−0.740530	−	0.672023i	$-0.765425\pi$
$409$	2.49843	−	23.7709i	0.123539	−	1.17540i	0.864069	−	0.503373i	$-0.167908\pi$
$410$	2.89807	−	0.616005i	0.143126	−	0.0304223i
$411$	−0.139446	+	0.656043i	−0.00687838	+	0.0323602i
$412$	−25.7204	−	35.4010i	−1.26715	−	1.74408i
$413$	6.70549	+	0.982071i	0.329955	+	0.0483246i
$414$	−10.5430	+	3.42562i	−0.518159	+	0.168360i
$415$	−2.79906	+	2.52029i	−0.137401	+	0.123716i
$416$	−56.8780	−	5.97811i	−2.78867	−	0.293101i
$417$	2.68475	−	1.55004i	0.131473	−	0.0759059i
$418$	22.3707	−	35.9730i	1.09418	−	1.75950i
$419$		−	25.9740i		−	1.26891i	−0.772958	−	0.634457i	$-0.781224\pi$
$419$		−	25.9740i		−	1.26891i	0.772958	−	0.634457i	$-0.218776\pi$
$420$	−3.14770	+	0.536228i	−0.153592	+	0.0261652i
$421$	−1.84742	+	5.68577i	−0.0900377	+	0.277108i	−0.985929	−	0.167166i	$-0.946538\pi$
$421$	−1.84742	+	5.68577i	−0.0900377	+	0.277108i	0.895891	+	0.444274i	$0.146538\pi$
$422$	−52.7332	−	11.2088i	−2.56701	−	0.545635i
$423$	−1.51736	+	3.40805i	−0.0737766	+	0.165705i
$424$	21.5883	−	48.4882i	1.04842	−	2.35479i
$425$	−18.5942	−	3.95231i	−0.901950	−	0.191715i
$426$	−2.77473	+	8.53974i	−0.134436	+	0.413752i
$427$	−11.9945	−	14.4640i	−0.580456	−	0.699962i
$428$		−	28.5803i		−	1.38148i
$429$	−6.52784	+	10.4971i	−0.315167	+	0.506804i
$430$	−5.79646	+	3.34659i	−0.279530	+	0.161387i
$431$	10.4764	+	1.10111i	0.504631	+	0.0530388i	0.353424	−	0.935463i	$-0.385017\pi$
$431$	10.4764	+	1.10111i	0.504631	+	0.0530388i	0.151207	+	0.988502i	$0.451684\pi$
$432$	−8.91376	+	8.02598i	−0.428863	+	0.386150i
$433$	8.64573	−	2.80917i	0.415487	−	0.135000i	−0.0938112	−	0.995590i	$-0.529905\pi$
$433$	8.64573	−	2.80917i	0.415487	−	0.135000i	0.509298	+	0.860590i	$0.329905\pi$
$434$	−41.4304	−	32.7576i	−1.98872	−	1.57241i
$435$	0.458342	+	0.630853i	0.0219758	+	0.0302471i
$436$	−12.3041	+	57.8864i	−0.589261	+	2.77226i
$437$	−19.4450	+	4.13316i	−0.930179	+	0.197716i
$438$	3.42516	−	32.5882i	0.163661	−	1.55713i
$439$	−11.2092	+	19.4150i	−0.534988	+	0.926626i	0.464176	+	0.885743i	$0.346350\pi$
$439$	−11.2092	+	19.4150i	−0.534988	+	0.926626i	−0.999164	+	0.0408831i	$0.986983\pi$
$440$	−6.12368	−	2.21388i	−0.291935	−	0.105543i
$441$	0.163164	+	6.99810i	0.00776973	+	0.333243i
$442$	22.4777	−	30.9379i	1.06915	−	1.47157i
$443$	−21.4425	−	23.8143i	−1.01876	−	1.13145i	−0.991273	−	0.131828i	$-0.957915\pi$
$443$	−21.4425	−	23.8143i	−1.01876	−	1.13145i	−0.0274893	−	0.999622i	$-0.508751\pi$
$444$	−15.9620	−	14.3723i	−0.757524	−	0.682077i
$445$	1.77789	+	0.791570i	0.0842803	+	0.0375240i
$446$	−4.31922	−	41.0946i	−0.204521	−	1.94589i
$447$	−5.16415	−	15.8936i	−0.244256	−	0.751743i
$448$	−44.8425	−	1.82629i	−2.11861	−	0.0862840i
$449$	14.8444	+	10.7851i	0.700549	+	0.508979i	0.880111	−	0.474768i	$-0.157468\pi$
$449$	14.8444	+	10.7851i	0.700549	+	0.508979i	−0.179562	+	0.983747i	$0.557468\pi$
$450$	−11.4279	−	6.59791i	−0.538717	−	0.311029i
$451$	6.82060	−	14.0612i	0.321170	−	0.662118i
$452$	−17.1724	−	29.7434i	−0.807719	−	1.39901i
$453$	−3.04868	+	1.35736i	−0.143240	+	0.0637744i
$454$	59.8616	+	19.4502i	2.80945	+	0.912844i
$455$	2.31849	−	0.148622i	0.108692	−	0.00696752i
$456$	−32.2649	+	23.4418i	−1.51094	+	1.09776i
$457$	9.95347	−	1.04615i	0.465604	−	0.0489369i	0.131178	−	0.991359i	$-0.458124\pi$
$457$	9.95347	−	1.04615i	0.465604	−	0.0489369i	0.334426	+	0.942422i	$0.391458\pi$
$458$	−23.6665	+	26.2844i	−1.10586	+	1.22819i
$459$	−0.799337	−	3.76058i	−0.0373098	−	0.175529i
$460$	2.03898	+	4.57961i	0.0950677	+	0.213526i
$461$	6.49015			0.302276			0.151138	−	0.988513i	$-0.451706\pi$
$461$	6.49015			0.302276			0.151138	+	0.988513i	$0.451706\pi$
$462$	−11.0695	+	20.6372i	−0.515001	+	0.960130i
$463$	6.25854			0.290859			0.145429	−	0.989369i	$-0.453544\pi$
$463$	6.25854			0.290859			0.145429	+	0.989369i	$0.453544\pi$
$464$	16.1470	+	36.2668i	0.749607	+	1.68364i
$465$	0.366404	+	1.72379i	0.0169916	+	0.0799390i
$466$	−30.5594	+	33.9397i	−1.41564	+	1.57222i
$467$	23.2958	−	2.44848i	1.07800	−	0.113302i	0.451154	−	0.892446i	$-0.351012\pi$
$467$	23.2958	−	2.44848i	1.07800	−	0.113302i	0.626845	+	0.779144i	$0.284346\pi$
$468$	15.4455	−	11.2218i	0.713970	−	0.518730i
$469$	−25.5685	−	12.6546i	−1.18064	−	0.584335i
$470$	2.23088	+	0.724856i	0.102903	+	0.0334351i
$471$	17.8544	−	7.94929i	0.822687	−	0.366284i
$472$	−10.6726	−	18.4855i	−0.491247	−	0.850865i
$473$	−4.83803	+	34.9718i	−0.222453	+	1.60801i
$474$	−25.4079	−	14.6693i	−1.16703	−	0.673782i
$475$	−19.1443	−	13.9092i	−0.878403	−	0.638197i
$476$	27.8671	−	44.0266i	1.27729	−	2.01796i
$477$	1.96824	+	6.05760i	0.0901193	+	0.277359i
$478$	2.30471	+	21.9279i	0.105415	+	1.00296i
$479$	21.3252	+	9.49458i	0.974372	+	0.433819i	0.831257	−	0.555888i	$-0.187621\pi$
$479$	21.3252	+	9.49458i	0.974372	+	0.433819i	0.143115	+	0.989706i	$0.454288\pi$
$480$	2.68667	+	2.41909i	0.122629	+	0.110416i
$481$	10.4572	+	11.6139i	0.476806	+	0.529546i
$482$	40.6270	−	55.9183i	1.85051	−	2.54701i
$483$	10.5815	−	2.96791i	0.481474	−	0.135044i
$484$	−47.6557	+	30.0653i	−2.16617	+	1.36661i
$485$	0.281085	−	0.486853i	0.0127634	−	0.0221068i
$486$	0.278965	−	2.65417i	0.0126541	−	0.120396i
$487$	−38.1715	+	8.11361i	−1.72972	+	0.367663i	−0.961984	−	0.273107i	$-0.911949\pi$
$487$	−38.1715	+	8.11361i	−1.72972	+	0.367663i	−0.767733	+	0.640769i	$0.778616\pi$
$488$	−12.3048	+	57.8896i	−0.557013	+	2.62054i
$489$	−7.39562	−	10.1792i	−0.334441	−	0.460319i
$490$	4.36538	−	0.561979i	0.197208	−	0.0253876i
$491$	3.59074	−	1.16670i	0.162048	−	0.0526525i	−0.226870	−	0.973925i	$-0.572849\pi$
$491$	3.59074	−	1.16670i	0.162048	−	0.0526525i	0.388917	+	0.921273i	$0.372849\pi$
$492$	−17.9375	+	16.1510i	−0.808687	+	0.728145i
$493$	−12.6549	−	1.33008i	−0.569946	−	0.0599037i
$494$	41.2263	−	23.8020i	1.85486	−	1.07090i
$495$	0.723871	−	0.294282i	0.0325356	−	0.0132270i
$496$			89.7200i			4.02855i
$497$	3.09300	−	8.34707i	0.138740	−	0.374417i
$498$	13.1843	−	40.5772i	0.590804	−	1.81831i
$499$	−24.2468	−	5.15381i	−1.08543	−	0.230716i	−0.369744	−	0.929134i	$-0.620555\pi$
$499$	−24.2468	−	5.15381i	−1.08543	−	0.230716i	−0.715691	+	0.698417i	$0.753888\pi$
$500$	−4.88150	+	10.9640i	−0.218307	+	0.490326i
$501$	−2.57671	+	5.78739i	−0.115119	+	0.258562i
$502$	39.7124	+	8.44112i	1.77245	+	0.376746i
$503$	13.6237	−	41.9294i	0.607450	−	1.86954i	0.128469	−	0.991714i	$-0.458994\pi$
$503$	13.6237	−	41.9294i	0.607450	−	1.86954i	0.478981	−	0.877825i	$-0.341006\pi$
$504$	16.9713	−	14.0737i	0.755961	−	0.626894i
$505$			4.03063i			0.179361i
$506$	35.6935	+	8.81762i	1.58677	+	0.391991i
$507$	−0.771653	+	0.445514i	−0.0342703	+	0.0197860i
$508$	−33.1946	−	3.48889i	−1.47277	−	0.154795i
$509$	15.8041	−	14.2301i	0.700504	−	0.630736i	−0.239900	−	0.970798i	$-0.577115\pi$
$509$	15.8041	−	14.2301i	0.700504	−	0.630736i	0.940403	+	0.340061i	$0.110448\pi$
$510$	−2.29906	+	0.747011i	−0.101804	+	0.0330782i
$511$	−4.70744	+	32.1419i	−0.208245	+	1.42188i
$512$	−9.31719	−	12.8240i	−0.411765	−	0.566747i
$513$	0.995039	−	4.68129i	0.0439321	−	0.206684i
$514$	−54.0493	+	11.4885i	−2.38401	+	0.506737i
$515$	0.210375	−	2.00158i	0.00927022	−	0.0882003i
$516$	27.2638	−	47.2223i	1.20022	−	2.07885i
$517$	10.2427	−	6.94097i	0.450471	−	0.305263i
$518$	21.1782	+	20.6901i	0.930515	+	0.909073i
$519$	−1.99865	+	2.75091i	−0.0877311	+	0.120751i
$520$	−4.89630	−	5.43789i	−0.214717	−	0.238467i
$521$	30.6505	+	27.5978i	1.34282	+	1.20908i	0.958231	+	0.285995i	$0.0923242\pi$
$521$	30.6505	+	27.5978i	1.34282	+	1.20908i	0.384591	+	0.923087i	$0.374342\pi$
$522$	−8.06932	−	3.59269i	−0.353184	−	0.157248i
$523$	0.650691	+	6.19091i	0.0284527	+	0.270710i	0.999494	+	0.0317990i	$0.0101236\pi$
$523$	0.650691	+	6.19091i	0.0284527	+	0.270710i	−0.971042	+	0.238911i	$0.923210\pi$
$524$	11.2596	+	34.6536i	0.491879	+	1.51385i
$525$	11.0537	+	6.99655i	0.482423	+	0.305355i
$526$	32.5987	+	23.6843i	1.42137	+	1.03268i
$527$	−24.9048	−	14.3788i	−1.08487	−	0.626351i
$528$	39.1624	−	6.99256i	1.70432	−	0.304312i
$529$	2.87313	+	4.97641i	0.124919	+	0.216366i
$530$	3.65863	−	1.62893i	0.158921	−	0.0707561i
$531$	2.43611	+	0.791539i	0.105718	+	0.0343499i
$532$	53.9822	−	35.9579i	2.34042	−	1.55897i
$533$	14.2081	−	10.3228i	0.615421	−	0.447130i
$534$	−21.9243	+	2.30434i	−0.948758	+	0.0997185i
$535$	0.879586	−	0.976879i	0.0380278	−	0.0422342i
$536$	18.6820	+	87.8918i	0.806938	+	3.79635i
$537$	4.82401	+	10.8349i	0.208171	+	0.467561i
$538$	−47.8121			−2.06132
$539$	11.7974	−	19.9955i	0.508150	−	0.861268i
$540$	−1.20686			−0.0519350
$541$	1.69575	+	3.80872i	0.0729061	+	0.163750i	0.946322	−	0.323225i	$-0.104767\pi$
$541$	1.69575	+	3.80872i	0.0729061	+	0.163750i	−0.873416	+	0.486975i	$0.838100\pi$
$542$	6.69636	+	31.5039i	0.287633	+	1.35321i
$543$	−3.83571	+	4.25999i	−0.164606	+	0.182814i
$544$	−58.6716	+	6.16663i	−2.51552	+	0.264392i
$545$	−2.20207	+	1.59989i	−0.0943262	+	0.0685320i
$546$	−21.9025	+	14.5894i	−0.937339	+	0.624367i
$547$	−11.5676	−	3.75853i	−0.494593	−	0.160703i	0.0510910	−	0.998694i	$-0.483730\pi$
$547$	−11.5676	−	3.75853i	−0.494593	−	0.160703i	−0.545684	+	0.837991i	$0.683730\pi$
$548$	−3.13860	+	1.39740i	−0.134074	+	0.0596938i
$549$	−3.55104	−	6.15058i	−0.151555	−	0.262500i
$550$	20.6301	+	38.5983i	0.879668	+	1.64584i
$551$	−13.7178	−	7.91996i	−0.584397	−	0.337402i
$552$	−28.0034	−	20.3456i	−1.19190	−	0.865968i
$553$	24.5759	+	15.5556i	1.04507	+	0.661491i
$554$	−0.109150	−	0.335930i	−0.00463735	−	0.0142723i
$555$	−0.103264	−	0.982492i	−0.00438332	−	0.0417045i
$556$	14.5072	+	6.45900i	0.615240	+	0.273923i
$557$	−1.51192	−	1.36134i	−0.0640622	−	0.0576819i	0.636478	−	0.771295i	$-0.280391\pi$
$557$	−1.51192	−	1.36134i	−0.0640622	−	0.0576819i	−0.700540	+	0.713613i	$0.747057\pi$
$558$	−13.3576	−	14.8351i	−0.565472	−	0.628020i
$559$	−23.3198	+	32.0969i	−0.986322	+	1.35756i
$560$	−5.34815	−	5.22491i	−0.226001	−	0.220793i
$561$	−4.33526	+	11.9915i	−0.183035	+	0.506281i
$562$	33.7404	−	58.4401i	1.42325	−	2.46515i
$563$	−4.48886	+	42.7087i	−0.189183	+	1.79996i	0.328627	+	0.944460i	$0.393414\pi$
$563$	−4.48886	+	42.7087i	−0.189183	+	1.79996i	−0.517810	+	0.855496i	$0.673253\pi$
$564$	−18.6921	+	3.97313i	−0.787080	+	0.167299i
$565$	0.328427	−	1.54513i	0.0138170	−	0.0650041i
$566$	−25.0905	−	34.5341i	−1.05463	−	1.45158i
$567$	−0.383401	+	2.61782i	−0.0161013	+	0.109938i
$568$	−26.6650	+	8.66398i	−1.11884	+	0.363532i
$569$	−19.7042	+	17.7418i	−0.826045	+	0.743774i	−0.969292	−	0.245913i	$-0.920912\pi$
$569$	−19.7042	+	17.7418i	−0.826045	+	0.743774i	0.143247	+	0.989687i	$0.454246\pi$
$570$	−2.99274	−	0.314550i	−0.125352	−	0.0131750i
$571$	−7.25913	+	4.19106i	−0.303785	+	0.175391i	−0.644142	−	0.764906i	$-0.722785\pi$
$571$	−7.25913	+	4.19106i	−0.303785	+	0.175391i	0.340357	+	0.940296i	$0.389452\pi$
$572$	−63.1562	+	4.55330i	−2.64069	+	0.190383i
$573$			17.4612i			0.729451i
$574$	25.6112	−	21.2385i	1.06899	−	0.886479i
$575$	6.34667	−	19.5330i	0.264674	−	0.814584i
$576$	−16.5922	−	3.52679i	−0.691343	−	0.146950i
$577$	−4.31103	+	9.68273i	−0.179471	+	0.403097i	−0.980770	−	0.195166i	$-0.937476\pi$
$577$	−4.31103	+	9.68273i	−0.179471	+	0.403097i	0.801300	+	0.598263i	$0.204142\pi$
$578$	−2.40879	+	5.41023i	−0.100192	+	0.225036i
$579$	12.1547	+	2.58356i	0.505132	+	0.107369i
$580$	−1.23433	+	3.79888i	−0.0512528	+	0.157740i
$581$	−14.6966	+	39.6616i	−0.609718	+	1.64544i
$582$			6.36800i			0.263962i
$583$	5.06628	−	20.5082i	0.209824	−	0.849363i
$584$	88.6081	−	51.1579i	3.66663	−	2.11693i
$585$	0.873294	+	0.0917869i	0.0361063	+	0.00379492i
$586$	−31.2975	+	28.1804i	−1.29289	+	1.16412i
$587$	6.17879	−	2.00761i	0.255026	−	0.0828629i	−0.178714	−	0.983901i	$-0.557194\pi$
$587$	6.17879	−	2.00761i	0.255026	−	0.0828629i	0.433740	+	0.901038i	$0.357194\pi$
$588$	−28.5099	+	21.7468i	−1.17573	+	0.896822i
$589$	−21.0418	−	28.9615i	−0.867011	−	1.19334i
$590$	0.334859	−	1.57539i	0.0137859	−	0.0648578i
$591$	−8.85146	+	1.88144i	−0.364101	+	0.0773920i
$592$	5.25724	−	50.0193i	0.216071	−	2.05578i
$593$	−18.9855	+	32.8839i	−0.779641	+	1.35038i	0.152508	+	0.988302i	$0.451265\pi$
$593$	−18.9855	+	32.8839i	−0.779641	+	1.35038i	−0.932149	+	0.362076i	$0.882068\pi$
$594$	−5.43439	+	6.98673i	−0.222976	+	0.286669i
$595$	2.30746	−	0.647200i	0.0945967	−	0.0265326i
$596$	50.3169	−	69.2552i	2.06106	−	2.83680i
$597$	−2.81420	−	3.12549i	−0.115178	−	0.127918i
$598$	30.7042	+	27.6461i	1.25559	+	1.13053i
$599$	−26.3667	−	11.7392i	−1.07731	−	0.479651i	−0.210148	−	0.977670i	$-0.567395\pi$
$599$	−26.3667	−	11.7392i	−1.07731	−	0.479651i	−0.867167	+	0.498018i	$0.834061\pi$
$600$	−4.30693	−	40.9777i	−0.175830	−	1.67291i
$601$	5.87227	+	18.0730i	0.239535	+	0.737213i	0.996487	+	0.0837428i	$0.0266874\pi$
$601$	5.87227	+	18.0730i	0.239535	+	0.737213i	−0.756952	+	0.653470i	$0.773313\pi$
$602$	−40.1991	+	63.5096i	−1.63839	+	2.58846i
$603$	−8.72349	−	6.33799i	−0.355248	−	0.258103i
$604$	−14.8044	−	8.54733i	−0.602383	−	0.347786i
$605$	−2.55417	−	0.439010i	−0.103842	−	0.0178483i
$606$	−22.8286	−	39.5403i	−0.927348	−	1.60621i
$607$	−7.46525	+	3.32374i	−0.303005	+	0.134907i	−0.552607	−	0.833442i	$-0.686367\pi$
$607$	−7.46525	+	3.32374i	−0.303005	+	0.134907i	0.249602	+	0.968349i	$0.419700\pi$
$608$	−69.8441	−	22.6937i	−2.83255	−	0.920353i
$609$	7.84809	+	3.88425i	0.318021	+	0.157398i
$610$	−3.61274	+	2.62481i	−0.146276	+	0.106275i
$611$	13.8279	−	1.45337i	0.559418	−	0.0587972i
$612$	13.1777	−	14.6353i	0.532677	−	0.591598i
$613$	−3.04079	−	14.3058i	−0.122816	−	0.577806i	−0.995918	−	0.0902666i	$-0.971228\pi$
$613$	−3.04079	−	14.3058i	−0.122816	−	0.577806i	0.873101	−	0.487539i	$-0.162105\pi$
$614$	−27.9855	−	62.8565i	−1.12940	−	2.53668i
$615$	−1.11017			−0.0447664
$616$	−72.4484	+	9.91320i	−2.91903	+	0.399414i
$617$	−17.0126			−0.684901			−0.342450	−	0.939536i	$-0.611257\pi$
$617$	−17.0126			−0.684901			−0.342450	+	0.939536i	$0.611257\pi$
$618$	9.27275	+	20.8269i	0.373005	+	0.837782i
$619$	0.191108	+	0.899094i	0.00768129	+	0.0361376i	0.981821	−	0.189807i	$-0.0607864\pi$
$619$	0.191108	+	0.899094i	0.00768129	+	0.0361376i	−0.974140	+	0.225945i	$0.927453\pi$
$620$	−6.04046	+	6.70861i	−0.242591	+	0.269424i
$621$	4.13101	−	0.434186i	0.165772	−	0.0174233i
$622$	−36.5178	+	26.5318i	−1.46423	+	1.06383i
$623$	21.8100	−	1.39809i	0.873799	−	0.0560132i
$624$	42.5168	+	13.8146i	1.70204	+	0.553025i
$625$	22.0808	−	9.83101i	0.883232	−	0.393240i
$626$	−2.16821	−	3.75545i	−0.0866591	−	0.150098i
$627$	−11.0016	+	11.4418i	−0.439362	+	0.456942i
$628$	86.7010	+	50.0568i	3.45974	+	1.99748i
$629$	13.0420	+	9.47558i	0.520019	+	0.377816i
$630$	1.66220	+	0.0676959i	0.0662236	+	0.00269707i
$631$	−7.15855	−	22.0318i	−0.284977	−	0.877070i	−0.986405	−	0.164330i	$-0.947454\pi$
$631$	−7.15855	−	22.0318i	−0.284977	−	0.877070i	0.701428	−	0.712740i	$-0.252546\pi$
$632$	−9.57568	−	91.1065i	−0.380900	−	3.62402i
$633$	18.4542	+	8.21633i	0.733488	+	0.326570i
$634$	57.1456	+	51.4541i	2.26954	+	2.04350i
$635$	−1.02722	−	1.14085i	−0.0407641	−	0.0452731i
$636$	−19.1775	+	26.3955i	−0.760436	+	1.04665i
$637$	22.2839	−	13.5678i	0.882922	−	0.537577i
$638$	16.4343	+	24.2518i	0.650640	+	0.960137i
$639$	1.68226	−	2.91376i	0.0665493	−	0.115267i
$640$	−0.359084	+	3.41645i	−0.0141940	+	0.135047i
$641$	1.59195	−	0.338379i	0.0628781	−	0.0133652i	−0.176365	−	0.984325i	$-0.556434\pi$
$641$	1.59195	−	0.338379i	0.0628781	−	0.0133652i	0.239243	+	0.970960i	$0.423101\pi$
$642$	−3.09587	+	14.5649i	−0.122184	+	0.574831i
$643$	−4.79592	−	6.60101i	−0.189133	−	0.260319i	0.703912	−	0.710288i	$-0.251435\pi$
$643$	−4.79592	−	6.60101i	−0.189133	−	0.260319i	−0.893044	+	0.449969i	$0.851435\pi$
$644$	44.1593	+	34.9152i	1.74012	+	1.37585i
$645$	2.38520	−	0.774997i	0.0939170	−	0.0305155i
$646$	36.4922	−	32.8578i	1.43577	−	1.29277i
$647$	14.3548	+	1.50875i	0.564347	+	0.0593152i	0.382406	−	0.923994i	$-0.375096\pi$
$647$	14.3548	+	1.50875i	0.564347	+	0.0593152i	0.181940	+	0.983310i	$0.441762\pi$
$648$	7.21675	−	4.16659i	0.283501	−	0.163679i
$649$	−5.47480	−	6.49609i	−0.214905	−	0.254994i
$650$			49.1817i			1.92907i
$651$	12.6328	+	15.2337i	0.495119	+	0.597056i
$652$	19.9166	−	61.2971i	0.779996	−	2.40058i
$653$	27.0529	+	5.75026i	1.05866	+	0.225025i	0.704168	−	0.710034i	$-0.251320\pi$
$653$	27.0529	+	5.75026i	1.05866	+	0.225025i	0.354493	+	0.935059i	$0.384654\pi$
$654$	12.5407	−	28.1669i	0.490381	−	1.10141i
$655$	−0.681641	+	1.53099i	−0.0266339	+	0.0598207i
$656$	−55.2845	−	11.7511i	−2.15850	−	0.458802i
$657$	−3.79414	+	11.6772i	−0.148024	+	0.455570i
$658$	25.9673	−	4.42367i	1.01231	−	0.172453i
$659$		−	41.7753i		−	1.62734i	−0.581330	−	0.813668i	$-0.697467\pi$
$659$		−	41.7753i		−	1.62734i	0.581330	−	0.813668i	$-0.302533\pi$
$660$	3.39905	+	2.11378i	0.132308	+	0.0822787i
$661$	−28.4168	+	16.4065i	−1.10529	+	0.638138i	−0.937605	−	0.347703i	$-0.886962\pi$
$661$	−28.4168	+	16.4065i	−1.10529	+	0.638138i	−0.167682	+	0.985841i	$0.553628\pi$
$662$	−28.8334	−	3.03051i	−1.12064	−	0.117784i
$663$	−10.6486	+	9.58802i	−0.413556	+	0.372368i
$664$	126.700	−	41.1675i	4.91693	−	1.59761i
$665$	2.95176	+	0.432308i	0.114464	+	0.0167642i
$666$	6.57763	+	9.05333i	0.254878	+	0.350810i
$667$	2.85833	−	13.4474i	0.110675	−	0.520685i
$668$	−31.7421	+	6.74698i	−1.22814	+	0.261049i
$669$	−1.61842	+	15.3982i	−0.0625716	+	0.595329i
$670$	−3.38997	+	5.87161i	−0.130966	+	0.226840i
$671$	−0.771249	+	23.5423i	−0.0297737	+	0.908840i
$672$	39.3351	+	10.0499i	1.51738	+	0.387684i
$673$	3.00454	−	4.13540i	0.115817	−	0.159408i	−0.747173	−	0.664630i	$-0.768589\pi$
$673$	3.00454	−	4.13540i	0.115817	−	0.159408i	0.862990	+	0.505222i	$0.168589\pi$
$674$	−18.4300	−	20.4686i	−0.709897	−	0.788421i
$675$	3.67447	+	3.30851i	0.141431	+	0.127345i
$676$	−4.16965	−	1.85645i	−0.160371	−	0.0714019i
$677$	−2.01590	−	19.1800i	−0.0774774	−	0.737148i	−0.962442	−	0.271489i	$-0.912484\pi$
$677$	−2.01590	−	19.1800i	−0.0774774	−	0.737148i	0.884964	−	0.465659i	$-0.154183\pi$
$678$	5.52941	+	17.0178i	0.212356	+	0.653564i
$679$	0.256896	−	6.30779i	0.00985875	−	0.242071i
$680$	−6.10659	−	4.43670i	−0.234177	−	0.170140i
$681$	−20.4248	−	11.7923i	−0.782680	−	0.451881i
$682$	11.6377	+	65.1776i	0.445629	+	2.49578i
$683$	1.48922	+	2.57941i	0.0569835	+	0.0986983i	0.893110	−	0.449838i	$-0.148518\pi$
$683$	1.48922	+	2.57941i	0.0569835	+	0.0986983i	−0.836126	+	0.548537i	$0.815185\pi$
$684$	22.3960	−	9.97132i	0.856331	−	0.381263i
$685$	−0.150284	−	0.0488303i	−0.00574206	−	0.00186571i
$686$	40.4863	−	28.3525i	1.54577	−	1.08250i
$687$	10.7218	−	7.78982i	0.409061	−	0.297200i
$688$	126.981	−	13.3463i	4.84112	−	0.508823i
$689$	15.8845	−	17.6415i	0.605150	−	0.672087i
$690$	−0.543018	−	2.55470i	−0.0206723	−	0.0972557i
$691$	−5.27790	−	11.8544i	−0.200781	−	0.450961i	0.784891	−	0.619633i	$-0.212719\pi$
$691$	−5.27790	−	11.8544i	−0.200781	−	0.450961i	−0.985672	+	0.168672i	$0.946052\pi$
$692$	−17.4179			−0.662130
$693$	5.66487	−	6.70144i	0.215190	−	0.254567i
$694$	−29.4043			−1.11617
$695$	0.297075	+	0.667241i	0.0112687	+	0.0253099i
$696$	−5.73432	−	26.9779i	−0.217359	−	1.02259i
$697$	12.1220	−	13.4628i	0.459152	−	0.509940i
$698$	−2.78171	+	0.292369i	−0.105289	+	0.0110663i
$699$	13.8445	−	10.0586i	0.523646	−	0.380451i
$700$	4.28684	+	66.8742i	0.162027	+	2.52761i
$701$	−29.9894	−	9.74416i	−1.13269	−	0.368032i	−0.318090	−	0.948061i	$-0.603041\pi$
$701$	−29.9894	−	9.74416i	−1.13269	−	0.368032i	−0.814596	+	0.580029i	$0.803041\pi$
$702$	−9.08683	+	4.04572i	−0.342960	+	0.152696i
$703$	10.0338	+	17.3791i	0.378433	+	0.655466i
$704$	40.5540	+	38.9938i	1.52844	+	1.46963i
$705$	−0.761176	−	0.439465i	−0.0286675	−	0.0165512i
$706$	−9.07883	−	6.59616i	−0.341686	−	0.248250i
$707$	21.0176	+	40.0874i	0.790449	+	1.50764i
$708$	4.05462	+	12.4788i	0.152382	+	0.468984i
$709$	4.93307	+	46.9350i	0.185265	+	1.76268i	0.553407	+	0.832911i	$0.313327\pi$
$709$	4.93307	+	46.9350i	0.185265	+	1.76268i	−0.368142	+	0.929770i	$0.620006\pi$
$710$	−1.93262	−	0.860460i	−0.0725301	−	0.0322925i
$711$	8.16954	+	7.35588i	0.306382	+	0.275867i
$712$	−46.0595	−	51.1542i	−1.72615	−	1.91709i
$713$	18.2626	−	25.1363i	0.683939	−	0.941362i
$714$	−18.9705	+	19.4179i	−0.709952	+	0.726698i
$715$	−2.29882	−	1.78806i	−0.0859710	−	0.0668696i
$716$	−30.3769	+	52.6143i	−1.13524	+	1.96629i
$717$	0.863579	−	8.21641i	0.0322510	−	0.306847i
$718$	14.5709	−	3.09714i	0.543780	−	0.115584i
$719$	9.72853	−	45.7691i	0.362813	−	1.70690i	−0.296501	−	0.955033i	$-0.595820\pi$
$719$	9.72853	−	45.7691i	0.362813	−	1.70690i	0.659314	−	0.751868i	$-0.270847\pi$
$720$	−1.66106	−	2.28625i	−0.0619040	−	0.0852035i
$721$	−8.34488	−	21.0041i	−0.310780	−	0.782233i
$722$	9.91052	−	3.22012i	0.368831	−	0.119841i
$723$	−19.2466	+	17.3298i	−0.715791	+	0.644501i
$724$	−29.2030	−	3.06936i	−1.08532	−	0.114072i
$725$	14.1724	−	8.18245i	0.526351	−	0.303889i
$726$	27.5427	−	10.1596i	1.02221	−	0.377057i
$727$			7.14658i			0.265052i	0.991180	+	0.132526i	$0.0423088\pi$
$727$			7.14658i			0.265052i	−0.991180	+	0.132526i	$0.957691\pi$
$728$	−77.0528	−	28.5519i	−2.85577	−	1.05820i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	7.55144	+	1.60511i	0.279491	+	0.0594077i
$731$	−16.6457	+	37.3869i	−0.615665	+	1.38281i
$732$	14.7971	−	33.2348i	0.546917	−	1.22839i
$733$	31.8983	+	6.78019i	1.17819	+	0.250432i	0.755072	−	0.655642i	$-0.227602\pi$
$733$	31.8983	+	6.78019i	1.17819	+	0.250432i	0.423119	+	0.906074i	$0.360935\pi$
$734$	5.15844	−	15.8760i	0.190401	−	0.585996i
$735$	−1.64375	−	0.134112i	−0.0606307	−	0.00494678i
$736$		−	63.7388i		−	2.34944i
$737$	13.4684	+	33.1295i	0.496116	+	1.22034i
$738$	10.8907	−	6.28776i	0.400893	−	0.231456i
$739$	−33.0442	−	3.47309i	−1.21555	−	0.127760i	−0.525038	−	0.851079i	$-0.675949\pi$
$739$	−33.0442	−	3.47309i	−1.21555	−	0.127760i	−0.690514	+	0.723319i	$0.742616\pi$
$740$	3.76068	−	3.38613i	0.138245	−	0.124477i
$741$	−16.9643	+	5.51202i	−0.623197	+	0.202489i
$742$	27.8936	−	35.2786i	1.02401	−	1.29512i
$743$	12.1160	+	16.6763i	0.444494	+	0.611794i	0.971203	−	0.238252i	$-0.0765744\pi$
$743$	12.1160	+	16.6763i	0.444494	+	0.611794i	−0.526709	+	0.850045i	$0.676574\pi$
$744$	12.9596	−	60.9702i	0.475123	−	2.23528i
$745$	3.85123	−	0.818605i	0.141098	−	0.0299914i
$746$	2.70265	−	25.7140i	0.0989512	−	0.941458i
$747$	−7.99338	+	13.8449i	−0.292463	+	0.506560i
$748$	−62.7476	+	18.1392i	−2.29428	+	0.663236i
$749$	3.65417	−	14.3023i	0.133520	−	0.522595i
$750$	3.67532	−	5.05864i	0.134204	−	0.184715i
$751$	−27.6437	−	30.7014i	−1.00873	−	1.12031i	−0.992721	−	0.120439i	$-0.961570\pi$
$751$	−27.6437	−	30.7014i	−1.00873	−	1.12031i	−0.0160112	−	0.999872i	$-0.505097\pi$
$752$	−33.2534	−	29.9415i	−1.21263	−	1.09185i
$753$	−13.8975	−	6.18756i	−0.506453	−	0.225487i
$754$	3.44119	+	32.7407i	0.125321	+	1.19235i
$755$	−0.242965	−	0.747769i	−0.00884239	−	0.0272141i
$756$	−12.0030	+	6.29314i	−0.436547	+	0.228879i
$757$	40.1653	+	29.1818i	1.45983	+	1.06063i	0.983406	+	0.181417i	$0.0580682\pi$
$757$	40.1653	+	29.1818i	1.45983	+	1.06063i	0.476427	+	0.879214i	$0.341932\pi$
$758$	19.0154	+	10.9785i	0.690671	+	0.398759i
$759$	−12.3952	−	6.01247i	−0.449918	−	0.218239i
$760$	−4.69809	−	8.13733i	−0.170418	−	0.295172i
$761$	36.3497	−	16.1839i	1.31767	−	0.586666i	0.377074	−	0.926183i	$-0.376930\pi$
$761$	36.3497	−	16.1839i	1.31767	−	0.586666i	0.940600	+	0.339517i	$0.110264\pi$
$762$	16.5385	+	5.37369i	0.599127	+	0.194668i
$763$	−13.5584	+	27.3947i	−0.490848	+	0.991753i
$764$	−72.3618	+	52.5739i	−2.61796	+	1.90206i
$765$	0.900833	−	0.0946813i	0.0325697	−	0.00342321i
$766$	12.5350	−	13.9215i	0.452909	−	0.503006i
$767$	−1.98489	−	9.33816i	−0.0716701	−	0.337181i
$768$	−2.02856	−	4.55621i	−0.0731992	−	0.164408i
$769$	−6.24486			−0.225195			−0.112598	−	0.993641i	$-0.535917\pi$
$769$	−6.24486			−0.225195			−0.112598	+	0.993641i	$0.535917\pi$
$770$	−4.56292	−	3.10195i	−0.164436	−	0.111787i
$771$	20.7048			0.745664
$772$	25.8899	+	58.1497i	0.931799	+	2.09286i
$773$	1.32973	+	6.25587i	0.0478269	+	0.225008i	0.995570	−	0.0940280i	$-0.0299743\pi$
$773$	1.32973	+	6.25587i	0.0478269	+	0.225008i	−0.947743	+	0.319036i	$0.896641\pi$
$774$	−19.0092	+	21.1119i	−0.683273	+	0.758851i
$775$	36.7822	−	3.86597i	1.32126	−	0.138870i
$776$	−16.0863	+	11.6874i	−0.577466	+	0.419553i
$777$	−6.15021	−	9.23309i	−0.220638	−	0.331235i
$778$	13.4483	+	4.36961i	0.482145	+	0.156658i
$779$	20.6017	−	9.17246i	0.738132	−	0.328638i
$780$	2.24902	+	3.89543i	0.0805280	+	0.139479i
$781$	−9.84136	+	5.26002i	−0.352152	+	0.188218i
$782$	36.9095	+	21.3097i	1.31988	+	0.762033i
$783$	2.67762	+	1.94541i	0.0956904	+	0.0695232i
$784$	−80.4362	−	24.0775i	−2.87272	−	0.859910i
$785$	1.42291	+	4.37925i	0.0507857	+	0.156302i
$786$	−1.98433	−	18.8796i	−0.0707785	−	0.673413i
$787$	−11.3909	−	5.07157i	−0.406043	−	0.180782i	0.193544	−	0.981092i	$-0.438002\pi$
$787$	−11.3909	−	5.07157i	−0.406043	−	0.180782i	−0.599587	+	0.800310i	$0.704668\pi$
$788$	−34.4479	−	31.0170i	−1.22715	−	1.10493i
$789$	−10.1027	−	11.2202i	−0.359666	−	0.399450i
$790$	4.06290	−	5.59211i	0.144552	−	0.198958i
$791$	−4.79060	−	17.0799i	−0.170334	−	0.607293i
$792$	−27.6232	−	0.904942i	−0.981549	−	0.0321557i
$793$	−13.2350	+	22.9236i	−0.469987	+	0.814041i
$794$	2.96986	−	28.2563i	0.105396	−	1.00278i
$795$	−1.46784	+	0.311998i	−0.0520588	+	0.0110654i
$796$	4.47921	−	21.0730i	0.158761	−	0.746913i
$797$	3.08834	+	4.25073i	0.109394	+	0.150569i	0.860204	−	0.509950i	$-0.170336\pi$
$797$	3.08834	+	4.25073i	0.109394	+	0.150569i	−0.750809	+	0.660519i	$0.770336\pi$
$798$	−31.4051	+	12.4772i	−1.11173	+	0.441687i
$799$	13.6406	−	4.43209i	0.482569	−	0.156796i
$800$	56.3842	−	50.7686i	1.99348	−	1.79494i
$801$	8.21507	+	0.863439i	0.290265	+	0.0305081i
$802$	8.57674	−	4.95178i	0.302855	−	0.174854i
$803$	31.1382	−	26.2428i	1.09884	−	0.926088i
$804$		−	55.2346i		−	1.94797i
$805$	0.434823	+	2.55245i	0.0153255	+	0.0899621i
$806$	−22.9915	+	70.7604i	−0.809840	+	2.49243i
$807$	17.5238	+	3.72479i	0.616865	+	0.131119i
$808$	57.9854	−	130.237i	2.03992	−	4.58173i
$809$	8.92501	−	20.0459i	0.313787	−	0.704776i	−0.685952	−	0.727647i	$-0.740614\pi$
$809$	8.92501	−	20.0459i	0.313787	−	0.704776i	0.999738	+	0.0228707i	$0.00728061\pi$
$810$	0.615033	+	0.130729i	0.0216100	+	0.00459336i
$811$	−0.0493231	+	0.151801i	−0.00173197	+	0.00533045i	−0.951919	−	0.306351i	$-0.900892\pi$
$811$	−0.0493231	+	0.151801i	−0.00173197	+	0.00533045i	0.950187	+	0.311681i	$0.100892\pi$
$812$	7.53290	+	44.2188i	0.264353	+	1.55178i
$813$		−	12.0683i		−	0.423253i
$814$	−2.66890	−	37.0187i	−0.0935448	−	1.29751i
$815$	2.56723	−	1.48219i	0.0899262	−	0.0519189i
$816$	45.8620	+	4.82029i	1.60549	+	0.168744i
$817$	−37.8594	+	34.0887i	−1.32453	+	1.19261i
$818$	−60.6671	+	19.7119i	−2.12117	+	0.689211i
$819$	9.16412	−	3.64089i	0.320220	−	0.127223i
$820$	−3.34262	−	4.60072i	−0.116729	−	0.160664i
$821$	1.78446	−	8.39521i	0.0622780	−	0.292995i	−0.935976	−	0.352064i	$-0.885480\pi$
$821$	1.78446	−	8.39521i	0.0622780	−	0.292995i	0.998254	+	0.0590692i	$0.0188133\pi$
$822$	1.75084	−	0.372153i	0.0610677	−	0.0129803i
$823$	3.93054	−	37.3966i	0.137010	−	1.30356i	−0.682664	−	0.730732i	$-0.739179\pi$
$823$	3.93054	−	37.3966i	0.137010	−	1.30356i	0.819674	−	0.572830i	$-0.194155\pi$
$824$	−35.5927	+	61.6484i	−1.23993	+	2.14763i
$825$	−4.55419	−	15.7540i	−0.158557	−	0.548483i
$826$	−4.88443	−	17.4144i	−0.169951	−	0.605926i
$827$	−6.66173	+	9.16908i	−0.231651	+	0.318840i	−0.908980	−	0.416840i	$-0.863137\pi$
$827$	−6.66173	+	9.16908i	−0.231651	+	0.318840i	0.677329	+	0.735680i	$0.263137\pi$
$828$	14.2374	+	15.8122i	0.494784	+	0.549513i
$829$	−14.0232	−	12.6265i	−0.487045	−	0.438537i	0.388662	−	0.921380i	$-0.372937\pi$
$829$	−14.0232	−	12.6265i	−0.487045	−	0.438537i	−0.875707	+	0.482843i	$0.839604\pi$
$830$	9.18300	+	4.08853i	0.318746	+	0.141915i
$831$	0.0138344	+	0.131626i	0.000479912	+	0.00456605i
$832$	19.5367	+	60.1276i	0.677312	+	2.08455i
$833$	19.5745	−	18.4690i	0.678215	−	0.639915i
$834$	−6.69339	−	4.86303i	−0.231773	−	0.168393i
$835$	−1.29259	−	0.746279i	−0.0447321	−	0.0258261i
$836$	−80.5414	−	11.1422i	−2.78558	−	0.385360i
$837$	3.74000	+	6.47788i	0.129273	+	0.223908i
$838$	−63.3263	+	28.1947i	−2.18757	+	0.973969i
$839$	−10.8137	−	3.51360i	−0.373332	−	0.121303i	0.116340	−	0.993209i	$-0.462884\pi$
$839$	−10.8137	−	3.51360i	−0.373332	−	0.121303i	−0.489672	+	0.871906i	$0.662884\pi$
$840$	2.87968	+	4.32316i	0.0993584	+	0.149163i
$841$	−14.5993	+	10.6070i	−0.503424	+	0.365759i
$842$	15.8676	−	1.66776i	0.546835	−	0.0574747i
$843$	−16.9191	+	18.7905i	−0.582724	+	0.647180i
$844$	21.5140	+	101.216i	0.740544	+	3.48398i
$845$	−0.0853854	−	0.191779i	−0.00293735	−	0.00659739i
$846$	9.95613			0.342299
$847$	−27.6921	+	8.95239i	−0.951513	+	0.307608i
$848$	−76.3980			−2.62352
$849$	6.50563	+	14.6119i	0.223273	+	0.501479i
$850$	10.5479	+	49.6240i	0.361790	+	1.70209i
$851$	−11.6544	+	12.9435i	−0.399506	+	0.443697i
$852$	17.1402	−	1.80151i	0.587214	−	0.0617187i
$853$	−11.5992	+	8.42735i	−0.397151	+	0.288547i	−0.768379	−	0.639995i	$-0.778937\pi$
$853$	−11.5992	+	8.42735i	−0.397151	+	0.288547i	0.371229	+	0.928541i	$0.378937\pi$
$854$	−22.2441	+	44.9440i	−0.761179	+	1.53795i
$855$	1.07237	+	0.348436i	0.0366744	+	0.0119162i
$856$	−42.4747	+	18.9109i	−1.45175	+	0.646363i
$857$	3.30855	+	5.73059i	0.113018	+	0.195753i	0.916986	−	0.398920i	$-0.130615\pi$
$857$	3.30855	+	5.73059i	0.113018	+	0.195753i	−0.803968	+	0.594673i	$0.797282\pi$
$858$	32.6785	+	4.52077i	1.11563	+	0.154336i
$859$	20.2429	+	11.6873i	0.690679	+	0.398764i	0.803867	−	0.594810i	$-0.202773\pi$
$859$	20.2429	+	11.6873i	0.690679	+	0.398764i	−0.113187	+	0.993574i	$0.536106\pi$
$860$	10.3933	+	7.55117i	0.354409	+	0.257493i
$861$	−11.0414	+	5.78896i	−0.376290	+	0.197287i
$862$	−8.68751	−	26.7374i	−0.295898	−	0.910680i
$863$	−0.942349	−	8.96585i	−0.0320779	−	0.305201i	−0.998784	−	0.0493099i	$-0.984298\pi$
$863$	−0.942349	−	8.96585i	−0.0320779	−	0.305201i	0.966706	−	0.255891i	$-0.0823689\pi$
$864$	14.0182	+	6.24131i	0.476909	+	0.212334i
$865$	−0.595348	−	0.536053i	−0.0202424	−	0.0182264i
$866$	−16.2338	−	18.0295i	−0.551648	−	0.612667i
$867$	1.30433	−	1.79526i	0.0442975	−	0.0609703i
$868$	−25.0946	+	98.2195i	−0.851766	+	3.33379i
$869$	−10.1254	−	35.0261i	−0.343482	−	1.18818i
$870$	1.04053	−	1.80225i	0.0352773	−	0.0611022i
$871$	−4.20082	+	39.9682i	−0.142339	+	1.35427i
$872$	94.1693	−	20.0163i	3.18898	−	0.677838i
$873$	0.496097	−	2.33396i	0.0167904	−	0.0789924i
$874$	31.1843	+	42.9215i	1.05483	+	1.45184i
$875$	−3.84464	+	4.86254i	−0.129973	+	0.164384i
$876$	−59.8158	+	19.4353i	−2.02099	+	0.656659i
$877$	−8.36073	+	7.52804i	−0.282322	+	0.254204i	−0.798109	−	0.602513i	$-0.794166\pi$
$877$	−8.36073	+	7.52804i	−0.282322	+	0.254204i	0.515787	+	0.856717i	$0.327500\pi$
$878$	59.5025	+	6.25397i	2.00811	+	0.211061i
$879$	13.6663	−	7.89026i	0.460954	−	0.266132i
$880$	0.673980	+	9.34839i	0.0227199	+	0.315134i
$881$		−	3.55642i		−	0.119819i	−0.998204	−	0.0599094i	$-0.980919\pi$
$881$		−	3.55642i		−	0.119819i	0.998204	−	0.0599094i	$-0.0190812\pi$
$882$	16.8847	−	7.99421i	0.568537	−	0.269179i
$883$	7.75476	−	23.8667i	0.260968	−	0.803178i	−0.731626	−	0.681706i	$-0.761238\pi$
$883$	7.75476	−	23.8667i	0.260968	−	0.803178i	0.992595	−	0.121472i	$-0.0387616\pi$
$884$	−71.7961	−	15.2607i	−2.41476	−	0.513274i
$885$	−0.245461	+	0.551314i	−0.00825107	+	0.0185322i
$886$	−34.7850	+	78.1284i	−1.16862	+	2.62477i
$887$	−30.1723	−	6.41333i	−1.01309	−	0.215338i	−0.328683	−	0.944440i	$-0.606605\pi$
$887$	−30.1723	−	6.41333i	−1.01309	−	0.215338i	−0.684405	+	0.729102i	$0.739938\pi$
$888$	−10.7977	+	33.2318i	−0.362346	+	1.11519i
$889$	−16.1654	−	5.99007i	−0.542169	−	0.200900i
$890$		−	5.19386i		−	0.174099i
$891$	2.53608	−	2.13736i	0.0849617	−	0.0716044i
$892$	−68.6854	+	39.6556i	−2.29976	+	1.32777i
$893$	17.7562	+	1.86626i	0.594190	+	0.0624519i
$894$	−33.1440	+	29.8430i	−1.10850	+	0.998099i
$895$	−2.65754	+	0.863488i	−0.0888318	+	0.0288632i
$896$	14.2437	+	35.8514i	0.475848	+	1.19771i
$897$	−9.09971	−	12.5247i	−0.303830	−	0.418187i
$898$	10.1812	−	47.8987i	0.339750	−	1.59840i
$899$	24.2158	−	5.14722i	0.807641	−	0.171669i
$900$	−2.64749	+	25.1892i	−0.0882497	+	0.839640i
$901$	12.2438	−	21.2068i	0.407899	−	0.706503i
$902$	−41.6859	−	1.36564i	−1.38799	−	0.0454708i
$903$	19.6812	−	20.1454i	0.654949	−	0.670397i
$904$	−32.8406	+	45.2012i	−1.09226	+	1.50337i
$905$	−0.903701	−	1.00366i	−0.0300400	−	0.0333629i
$906$	6.61867	+	5.95947i	0.219890	+	0.197990i
$907$	−41.7366	−	18.5823i	−1.38584	−	0.617017i	−0.427860	−	0.903845i	$-0.640732\pi$
$907$	−41.7366	−	18.5823i	−1.38584	−	0.617017i	−0.957982	+	0.286828i	$0.907399\pi$
$908$	−12.6282	−	120.149i	−0.419080	−	3.98728i
$909$	5.28660	+	16.2705i	0.175345	+	0.539658i
$910$	−2.87906	−	5.49129i	−0.0954398	−	0.182034i
$911$	−9.33470	−	6.78206i	−0.309272	−	0.224700i	0.422312	−	0.906451i	$-0.361219\pi$
$911$	−9.33470	−	6.78206i	−0.309272	−	0.224700i	−0.731584	+	0.681751i	$0.761219\pi$
$912$	49.7141	+	28.7024i	1.64620	+	0.950432i
$913$	46.7619	−	24.9933i	1.54759	−	0.827159i
$914$	−13.3550	−	23.1316i	−0.441745	−	0.765126i
$915$	1.52860	−	0.680577i	0.0505340	−	0.0224992i
$916$	64.5645	+	20.9783i	2.13327	+	0.693141i
$917$	1.20393	+	18.7811i	0.0397573	+	0.620208i
$918$	−8.30087	+	6.03093i	−0.273969	+	0.199050i
$919$	16.3214	−	1.71545i	0.538395	−	0.0565876i	0.168571	−	0.985690i	$-0.446085\pi$
$919$	16.3214	−	1.71545i	0.538395	−	0.0565876i	0.369824	+	0.929102i	$0.379418\pi$
$920$	5.45686	−	6.06045i	0.179907	−	0.199807i
$921$	5.36024	+	25.2179i	0.176626	+	0.830959i
$922$	−7.04503	−	15.8234i	−0.232016	−	0.521116i
$923$	−12.5398			−0.412753
$924$	44.8282	+	3.29868i	1.47474	+	0.108519i
$925$	−20.7328			−0.681690
$926$	−6.79361	−	15.2587i	−0.223252	−	0.501432i
$927$	−1.77607	−	8.35573i	−0.0583337	−	0.274438i
$928$	33.9833	−	37.7422i	1.11556	−	1.23895i
$929$	26.3599	−	2.77053i	0.864839	−	0.0908983i	0.338289	−	0.941042i	$-0.390152\pi$
$929$	26.3599	−	2.77053i	0.864839	−	0.0908983i	0.526550	+	0.850144i	$0.323485\pi$
$930$	3.80499	−	2.76449i	0.124771	−	0.0906511i
$931$	31.6115	−	11.0923i	1.03602	−	0.363534i
$932$	83.3688	+	27.0882i	2.73084	+	0.887303i
$933$	15.4512	−	6.87933i	0.505850	−	0.225219i
$934$	−31.2570	−	54.1387i	−1.02276	−	1.77147i
$935$	−2.70298	−	1.31112i	−0.0883968	−	0.0428781i
$936$	−26.8973	−	15.5292i	−0.879166	−	0.507587i
$937$	30.3605	+	22.0582i	0.991835	+	0.720611i	0.960322	−	0.278893i	$-0.0899674\pi$
$937$	30.3605	+	22.0582i	0.991835	+	0.720611i	0.0315131	+	0.999503i	$0.489967\pi$
$938$	−3.09825	+	76.0741i	−0.101161	+	2.48391i
$939$	0.502110	+	1.54534i	0.0163857	+	0.0504301i
$940$	−0.470617	−	4.47762i	−0.0153498	−	0.146044i
$941$	−26.9686	−	12.0072i	−0.879152	−	0.391424i	−0.0830207	−	0.996548i	$-0.526457\pi$
$941$	−26.9686	−	12.0072i	−0.879152	−	0.391424i	−0.796131	+	0.605124i	$0.793123\pi$
$942$	−38.7617	−	34.9012i	−1.26293	−	1.13714i
$943$	13.0968	+	14.5454i	0.426489	+	0.473664i
$944$	−18.0591	+	24.8562i	−0.587773	+	0.809000i
$945$	−0.603944	−	0.154305i	−0.0196463	−	0.00501953i
$946$	90.5152	−	26.1664i	2.94290	−	0.850742i
$947$	0.582446	−	1.00883i	0.0189269	−	0.0327824i	−0.856407	−	0.516302i	$-0.827308\pi$
$947$	0.582446	−	1.00883i	0.0189269	−	0.0327824i	0.875334	+	0.483519i	$0.160642\pi$
$948$	−5.88622	+	56.0037i	−0.191176	+	1.81891i
$949$	44.7613	−	9.51432i	1.45301	−	0.308848i
$950$	−13.1304	+	61.7735i	−0.426005	+	2.00420i
$951$	−16.9361	−	23.3105i	−0.549190	−	0.755895i
$952$	−83.8692	−	12.2833i	−2.71822	−	0.398104i
$953$	25.3195	−	8.22679i	0.820178	−	0.266492i	0.131275	−	0.991346i	$-0.458093\pi$
$953$	25.3195	−	8.22679i	0.820178	−	0.266492i	0.688902	+	0.724854i	$0.258093\pi$
$954$	12.6323	−	11.3742i	0.408986	−	0.368253i
$955$	−4.09135	−	0.430018i	−0.132393	−	0.0139151i
$956$	36.6502	−	21.1600i	1.18535	−	0.684363i
$957$	−4.13405	−	10.1689i	−0.133635	−	0.328714i
$958$		−	62.2985i		−	2.01277i
$959$	−1.74930	+	0.298003i	−0.0564879	+	0.00962301i
$960$	1.23499	−	3.80089i	0.0398590	−	0.122673i
$961$	24.4053	+	5.18751i	0.787268	+	0.167339i
$962$	16.9641	−	38.1020i	0.546945	−	1.22846i
$963$	2.26935	−	5.09705i	0.0731289	−	0.164250i
$964$	−129.767	−	27.5828i	−4.17951	−	0.888383i
$965$	−0.904692	+	2.78436i	−0.0291231	+	0.0896316i
$966$	−18.7221	−	22.5767i	−0.602374	−	0.726392i
$967$		−	16.4445i		−	0.528820i	−0.964410	−	0.264410i	$-0.914823\pi$
$967$		−	16.4445i		−	0.528820i	0.964410	−	0.264410i	$-0.0851773\pi$
$968$	76.2143	+	50.9300i	2.44962	+	1.63695i
$969$	−15.9347	+	9.19988i	−0.511895	+	0.295543i
$970$	−1.49209	−	0.156825i	−0.0479083	−	0.00503536i
$971$	−27.6696	+	24.9138i	−0.887960	+	0.799523i	−0.980568	−	0.196180i	$-0.937146\pi$
$971$	−27.6696	+	24.9138i	−0.887960	+	0.799523i	0.0926079	+	0.995703i	$0.470480\pi$
$972$	−4.87175	+	1.58293i	−0.156261	+	0.0507724i
$973$	6.43393	+	5.08708i	0.206262	+	0.163084i
$974$	61.2165	+	84.2573i	1.96150	+	2.69978i
$975$	3.83149	−	18.0257i	0.122706	−	0.577286i
$976$	83.3253	−	17.7113i	2.66718	−	0.566926i
$977$	−3.87325	+	36.8515i	−0.123916	+	1.17898i	0.739024	+	0.673679i	$0.235287\pi$
$977$	−3.87325	+	36.8515i	−0.123916	+	1.17898i	−0.862941	+	0.505305i	$0.831380\pi$
$978$	−16.7896	+	29.0805i	−0.536872	+	0.929890i
$979$	−21.6250	−	16.8203i	−0.691138	−	0.537578i
$980$	−4.39340	−	7.21576i	−0.140342	−	0.230499i
$981$	−6.79067	+	9.34655i	−0.216809	+	0.298413i
$982$	−6.74222	−	7.48800i	−0.215153	−	0.238952i
$983$	−41.9661	−	37.7864i	−1.33851	−	1.20520i	−0.960131	−	0.279550i	$-0.909815\pi$
$983$	−41.9661	−	37.7864i	−1.33851	−	1.20520i	−0.378379	−	0.925651i	$-0.623518\pi$
$984$	35.8718	+	15.9711i	1.14355	+	0.509141i
$985$	−0.222856	−	2.12033i	−0.00710078	−	0.0675594i
$986$	10.4940	+	32.2971i	0.334196	+	1.02855i
$987$	−9.86199	−	0.401647i	−0.313911	−	0.0127846i
$988$	−73.9204	−	53.7063i	−2.35172	−	1.70863i
$989$	−38.2923	−	22.1080i	−1.21762	−	0.702995i
$990$	−1.50324	−	1.44540i	−0.0477760	−	0.0459379i
$991$	−8.47012	−	14.6707i	−0.269062	−	0.466030i	0.699558	−	0.714576i	$-0.253380\pi$
$991$	−8.47012	−	14.6707i	−0.269062	−	0.466030i	−0.968620	+	0.248547i	$0.920047\pi$
$992$	104.856	−	46.6850i	3.32919	−	1.48225i
$993$	10.3317	+	3.35698i	0.327867	+	0.106531i
$994$	−23.7081	+	1.51976i	−0.751976	+	0.0482040i
$995$	0.801642	−	0.582427i	0.0254138	−	0.0184642i
$996$	−81.4429	+	8.55999i	−2.58062	+	0.271234i
$997$	28.2876	−	31.4165i	0.895876	−	0.994971i	−0.104124	−	0.994564i	$-0.533204\pi$
$997$	28.2876	−	31.4165i	0.895876	−	0.994971i	1.00000		0.000407128i	$-0.000129593\pi$
$998$	13.7545	+	64.7096i	0.435390	+	2.04835i
$999$	−1.70549	−	3.83059i	−0.0539593	−	0.121195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.ba.a.40.1	yes	128
3.2	odd	2		693.2.cg.c.271.16		128
7.3	odd	6	inner	231.2.ba.a.73.16	yes	128
11.8	odd	10	inner	231.2.ba.a.19.16	✓	128
21.17	even	6		693.2.cg.c.73.1		128
33.8	even	10		693.2.cg.c.19.1		128
77.52	even	30	inner	231.2.ba.a.52.1	yes	128
231.206	odd	30		693.2.cg.c.514.16		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.16	✓	128	11.8	odd	10	inner
231.2.ba.a.40.1	yes	128	1.1	even	1	trivial
231.2.ba.a.52.1	yes	128	77.52	even	30	inner
231.2.ba.a.73.16	yes	128	7.3	odd	6	inner
693.2.cg.c.19.1		128	33.8	even	10
693.2.cg.c.73.1		128	21.17	even	6
693.2.cg.c.271.16		128	3.2	odd	2
693.2.cg.c.514.16		128	231.206	odd	30

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)

\(f(q)\)	\(=\)	\(q+(-1.08550 - 2.43806i) q^{2} +(0.207912 + 0.978148i) q^{3} +(-3.42759 + 3.80673i) q^{4} +(-0.234311 + 0.0246271i) q^{5} +(2.15910 - 1.56868i) q^{6} +(-2.20197 + 1.46674i) q^{7} +(7.92533 + 2.57510i) q^{8} +(-0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-1.08550 - 2.43806i) q^{2} +(0.207912 + 0.978148i) q^{3} +(-3.42759 + 3.80673i) q^{4} +(-0.234311 + 0.0246271i) q^{5} +(2.15910 - 1.56868i) q^{6} +(-2.20197 + 1.46674i) q^{7} +(7.92533 + 2.57510i) q^{8} +(-0.913545 + 0.406737i) q^{9} +(0.314386 + 0.544533i) q^{10} +(3.28534 + 0.454496i) q^{11} +(-4.43618 - 2.56123i) q^{12} +(3.01526 + 2.19072i) q^{13} +(5.96624 + 3.77639i) q^{14} +(-0.0728050 - 0.224071i) q^{15} +(-1.25378 - 11.9289i) q^{16} +(3.51221 + 1.56374i) q^{17} +(1.98330 + 1.78577i) q^{18} +(3.20237 + 3.55660i) q^{19} +(0.709375 - 0.976371i) q^{20} +(-1.89251 - 1.84890i) q^{21} +(-2.45813 - 8.50321i) q^{22} +(-2.07688 + 3.59726i) q^{23} +(-0.871055 + 8.28754i) q^{24} +(-4.83644 + 1.02802i) q^{25} +(2.06805 - 9.72941i) q^{26} +(-0.587785 - 0.809017i) q^{27} +(1.96395 - 13.4097i) q^{28} +(-3.14773 + 1.02276i) q^{29} +(-0.467269 + 0.420731i) q^{30} +(-7.43903 - 0.781874i) q^{31} +(-13.2890 + 7.67242i) q^{32} +(0.238496 + 3.30804i) q^{33} -10.2604i q^{34} +(0.479824 - 0.397903i) q^{35} +(1.58293 - 4.87175i) q^{36} +(4.10148 + 0.871796i) q^{37} +(5.19505 - 11.6683i) q^{38} +(-1.51593 + 3.40485i) q^{39} +(-1.92041 - 0.408196i) q^{40} +(1.45611 - 4.48144i) q^{41} +(-2.45342 + 6.62102i) q^{42} +10.6448i q^{43} +(-12.9909 + 10.9486i) q^{44} +(0.204037 - 0.117801i) q^{45} +(11.0248 + 1.15875i) q^{46} +(2.77236 - 2.49624i) q^{47} +(11.4076 - 3.70655i) q^{48} +(2.69732 - 6.45945i) q^{49} +(7.75631 + 10.6756i) q^{50} +(-0.799337 + 3.76058i) q^{51} +(-18.6745 + 3.96940i) q^{52} +(0.665778 - 6.33445i) q^{53} +(-1.33440 + 2.31124i) q^{54} +(-0.780984 - 0.0255852i) q^{55} +(-21.2283 + 5.95415i) q^{56} +(-2.81307 + 3.87185i) q^{57} +(5.91041 + 6.56417i) q^{58} +(-1.90355 - 1.71396i) q^{59} +(1.10252 + 0.490874i) q^{60} +(0.742369 + 7.06317i) q^{61} +(6.16878 + 18.9856i) q^{62} +(1.41502 - 2.23556i) q^{63} +(13.7233 + 9.97055i) q^{64} +(-0.760461 - 0.439052i) q^{65} +(7.80632 - 4.17233i) q^{66} +(5.39141 + 9.33820i) q^{67} +(-17.9912 + 8.01018i) q^{68} +(-3.95046 - 1.28358i) q^{69} +(-1.49096 - 0.737920i) q^{70} +(-2.72196 + 1.97762i) q^{71} +(-8.28754 + 0.871055i) q^{72} +(8.21566 - 9.12441i) q^{73} +(-2.32664 - 10.9460i) q^{74} +(-2.01111 - 4.51702i) q^{75} -24.5154 q^{76} +(-7.90083 + 3.81796i) q^{77} +9.94677 q^{78} +(-4.47134 - 10.0428i) q^{79} +(0.587550 + 2.76421i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-12.5066 + 1.31450i) q^{82} +(12.9336 - 9.39678i) q^{83} +(13.5250 - 0.866994i) q^{84} +(-0.861462 - 0.279906i) q^{85} +(25.9528 - 11.5549i) q^{86} +(-1.65486 - 2.86631i) q^{87} +(24.8670 + 12.0621i) q^{88} +(-7.15365 - 4.13016i) q^{89} +(-0.508688 - 0.369583i) q^{90} +(-9.85272 - 0.401269i) q^{91} +(-6.57510 - 20.2361i) q^{92} +(-0.781874 - 7.43903i) q^{93} +(-9.09538 - 4.04952i) q^{94} +(-0.837941 - 0.754486i) q^{95} +(-10.2677 - 11.4034i) q^{96} +(-1.40251 + 1.93039i) q^{97} +(-18.6765 + 0.435452i) q^{98} +(-3.18616 + 0.921064i) 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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