LMFDB - Embedded newform 175.2.s.a.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(13,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("175.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.s (of order $20$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.2
Character	$\chi$	$=$	175.27
Dual form			175.2.s.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43824 - 0.386179i) q^{2} +(0.183665 - 0.0935818i) q^{3} +(3.89376 + 1.26516i) q^{4} +(-2.22917 + 0.175511i) q^{5} +(-0.483957 + 0.157247i) q^{6} +(1.07566 - 2.41722i) q^{7} +(-4.60620 - 2.34698i) q^{8} +(-1.73838 + 2.39268i) q^{9} +O(q^{10})$	\(q+(-2.43824 - 0.386179i) q^{2} +(0.183665 - 0.0935818i) q^{3} +(3.89376 + 1.26516i) q^{4} +(-2.22917 + 0.175511i) q^{5} +(-0.483957 + 0.157247i) q^{6} +(1.07566 - 2.41722i) q^{7} +(-4.60620 - 2.34698i) q^{8} +(-1.73838 + 2.39268i) q^{9} +(5.50302 + 0.432920i) q^{10} +(3.57144 - 2.59480i) q^{11} +(0.833541 - 0.132020i) q^{12} +(-0.297223 - 1.87659i) q^{13} +(-3.55620 + 5.47836i) q^{14} +(-0.392995 + 0.240845i) q^{15} +(3.70020 + 2.68836i) q^{16} +(-6.70498 - 3.41636i) q^{17} +(5.16259 - 5.16259i) q^{18} +(-1.89087 - 5.81950i) q^{19} +(-8.90190 - 2.13686i) q^{20} +(-0.0286466 - 0.544620i) q^{21} +(-9.71007 + 4.94753i) q^{22} +(0.763884 - 4.82298i) q^{23} -1.06563 q^{24} +(4.93839 - 0.782488i) q^{25} +4.69036i q^{26} +(-0.192106 + 1.21291i) q^{27} +(7.24654 - 8.05118i) q^{28} +(-1.44631 - 0.469935i) q^{29} +(1.05122 - 0.435471i) q^{30} +(-1.90816 + 0.619999i) q^{31} +(-0.672788 - 0.672788i) q^{32} +(0.413120 - 0.810794i) q^{33} +(15.0290 + 10.9192i) q^{34} +(-1.97359 + 5.57718i) q^{35} +(-9.79595 + 7.11717i) q^{36} +(0.625263 + 3.94776i) q^{37} +(2.36302 + 14.9195i) q^{38} +(-0.230204 - 0.316849i) q^{39} +(10.6799 + 4.42337i) q^{40} +(4.69566 - 6.46303i) q^{41} +(-0.140474 + 1.33898i) q^{42} +(0.773359 - 0.773359i) q^{43} +(17.1891 - 5.58509i) q^{44} +(3.45520 - 5.63878i) q^{45} +(-3.72506 + 11.4646i) q^{46} +(4.03603 + 7.92115i) q^{47} +(0.931177 + 0.147484i) q^{48} +(-4.68590 - 5.20023i) q^{49} +(-12.3432 + 0.000789122i) q^{50} -1.55118 q^{51} +(1.21687 - 7.68303i) q^{52} +(1.12238 + 2.20280i) q^{53} +(0.936802 - 2.88318i) q^{54} +(-7.50592 + 6.41107i) q^{55} +(-10.6279 + 8.60964i) q^{56} +(-0.891884 - 0.891884i) q^{57} +(3.34497 + 1.70435i) q^{58} +(3.46254 + 2.51568i) q^{59} +(-1.83493 + 0.440591i) q^{60} +(3.15174 + 4.33800i) q^{61} +(4.89198 - 0.774813i) q^{62} +(3.91371 + 6.77576i) q^{63} +(-3.99611 - 5.50017i) q^{64} +(0.991924 + 4.13108i) q^{65} +(-1.32040 + 1.81737i) q^{66} +(-2.45898 + 4.82603i) q^{67} +(-21.7854 - 21.7854i) q^{68} +(-0.311044 - 0.957295i) q^{69} +(6.96586 - 12.8363i) q^{70} +(1.20256 - 3.70109i) q^{71} +(13.6229 - 6.94121i) q^{72} +(0.784747 + 0.124292i) q^{73} -9.86703i q^{74} +(0.833781 - 0.605859i) q^{75} -25.0520i q^{76} +(-2.43054 - 11.4241i) q^{77} +(0.438932 + 0.861453i) q^{78} +(-10.4243 - 3.38705i) q^{79} +(-8.72022 - 5.34337i) q^{80} +(-2.66354 - 8.19753i) q^{81} +(-13.9450 + 13.9450i) q^{82} +(-0.370328 + 0.726810i) q^{83} +(0.577488 - 2.15686i) q^{84} +(15.5462 + 6.43885i) q^{85} +(-2.18429 + 1.58698i) q^{86} +(-0.309613 + 0.0490379i) q^{87} +(-22.5407 + 3.57009i) q^{88} +(4.65732 - 3.38374i) q^{89} +(-10.6022 + 12.4144i) q^{90} +(-4.85585 - 1.30013i) q^{91} +(9.07621 - 17.8131i) q^{92} +(-0.292441 + 0.292441i) q^{93} +(-6.78182 - 20.8723i) q^{94} +(5.23645 + 12.6408i) q^{95} +(-0.186528 - 0.0606066i) q^{96} +(1.37761 + 2.70371i) q^{97} +(9.41712 + 14.4890i) q^{98} +13.0560i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9}+O(q^{10}) $ 144 * q - 16 * q^2 - 20 * q^4 - 14 * q^7 - 12 * q^8 - 20 * q^9	$ 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9} - 12 q^{11} - 10 q^{14} - 20 q^{15} + 12 q^{16} - 28 q^{18} - 6 q^{21} + 16 q^{22} - 8 q^{23} - 20 q^{25} - 70 q^{28} + 40 q^{30} - 20 q^{32} - 40 q^{35} - 28 q^{36} + 4 q^{37} - 60 q^{39} - 30 q^{42} + 72 q^{43} - 20 q^{44} - 12 q^{46} + 140 q^{50} - 32 q^{51} - 104 q^{53} - 22 q^{56} + 120 q^{57} - 32 q^{58} - 120 q^{60} + 48 q^{63} + 40 q^{64} - 20 q^{65} - 16 q^{67} + 90 q^{70} - 12 q^{71} - 64 q^{72} + 74 q^{77} + 60 q^{78} - 20 q^{79} - 8 q^{81} + 190 q^{84} - 12 q^{86} + 92 q^{88} - 6 q^{91} - 20 q^{92} - 160 q^{93} + 80 q^{95} + 162 q^{98}+O(q^{100}) $ 144 * q - 16 * q^2 - 20 * q^4 - 14 * q^7 - 12 * q^8 - 20 * q^9 - 12 * q^11 - 10 * q^14 - 20 * q^15 + 12 * q^16 - 28 * q^18 - 6 * q^21 + 16 * q^22 - 8 * q^23 - 20 * q^25 - 70 * q^28 + 40 * q^30 - 20 * q^32 - 40 * q^35 - 28 * q^36 + 4 * q^37 - 60 * q^39 - 30 * q^42 + 72 * q^43 - 20 * q^44 - 12 * q^46 + 140 * q^50 - 32 * q^51 - 104 * q^53 - 22 * q^56 + 120 * q^57 - 32 * q^58 - 120 * q^60 + 48 * q^63 + 40 * q^64 - 20 * q^65 - 16 * q^67 + 90 * q^70 - 12 * q^71 - 64 * q^72 + 74 * q^77 + 60 * q^78 - 20 * q^79 - 8 * q^81 + 190 * q^84 - 12 * q^86 + 92 * q^88 - 6 * q^91 - 20 * q^92 - 160 * q^93 + 80 * q^95 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−2.43824	−	0.386179i	−1.72409	−	0.273070i	−0.785693	−	0.618616i	$-0.787694\pi$
$2$	−2.43824	−	0.386179i	−1.72409	−	0.273070i	−0.938402	+	0.345547i	$0.887694\pi$
$3$	0.183665	−	0.0935818i	0.106039	−	0.0540295i	−0.400167	−	0.916442i	$-0.631048\pi$
$3$	0.183665	−	0.0935818i	0.106039	−	0.0540295i	0.506205	+	0.862413i	$0.331048\pi$
$4$	3.89376	+	1.26516i	1.94688	+	0.632579i
$5$	−2.22917	+	0.175511i	−0.996915	+	0.0784910i
$5$	−2.22917	+	0.175511i	−0.996915	+	0.0784910i
$6$	−0.483957	+	0.157247i	−0.197575	+	0.0641959i
$7$	1.07566	−	2.41722i	0.406562	−	0.913623i
$7$	1.07566	−	2.41722i	0.406562	−	0.913623i
$8$	−4.60620	−	2.34698i	−1.62854	−	0.829781i
$9$	−1.73838	+	2.39268i	−0.579460	+	0.797559i
$10$	5.50302	+	0.432920i	1.74021	+	0.136901i
$11$	3.57144	−	2.59480i	1.07683	−	0.782362i	0.0997012	−	0.995017i	$-0.468211\pi$
$11$	3.57144	−	2.59480i	1.07683	−	0.782362i	0.977127	+	0.212656i	$0.0682113\pi$
$12$	0.833541	−	0.132020i	0.240623	−	0.0381109i
$13$	−0.297223	−	1.87659i	−0.0824349	−	0.520473i	−0.994006	−	0.109330i	$-0.965130\pi$
$13$	−0.297223	−	1.87659i	−0.0824349	−	0.520473i	0.911571	−	0.411143i	$-0.134870\pi$
$14$	−3.55620	+	5.47836i	−0.950435	+	1.46415i
$15$	−0.392995	+	0.240845i	−0.101471	+	0.0621858i
$16$	3.70020	+	2.68836i	0.925051	+	0.672089i
$17$	−6.70498	−	3.41636i	−1.62620	−	0.828589i	−0.998753	−	0.0499278i	$-0.984101\pi$
$17$	−6.70498	−	3.41636i	−1.62620	−	0.828589i	−0.627445	−	0.778661i	$-0.715899\pi$
$18$	5.16259	−	5.16259i	1.21683	−	1.21683i
$19$	−1.89087	−	5.81950i	−0.433795	−	1.33508i	−0.894316	−	0.447435i	$-0.852337\pi$
$19$	−1.89087	−	5.81950i	−0.433795	−	1.33508i	0.460521	−	0.887649i	$-0.347663\pi$
$20$	−8.90190	−	2.13686i	−1.99052	−	0.477815i
$21$	−0.0286466	−	0.544620i	−0.00625119	−	0.118846i
$22$	−9.71007	+	4.94753i	−2.07019	+	1.05482i
$23$	0.763884	−	4.82298i	0.159281	−	1.00566i	−0.770471	−	0.637475i	$-0.779979\pi$
$23$	0.763884	−	4.82298i	0.159281	−	1.00566i	0.929752	−	0.368186i	$-0.120021\pi$
$24$	−1.06563			−0.217521
$25$	4.93839	−	0.782488i	0.987678	−	0.156498i
$26$			4.69036i			0.919856i
$27$	−0.192106	+	1.21291i	−0.0369709	+	0.233425i
$28$	7.24654	−	8.05118i	1.36947	−	1.52153i
$29$	−1.44631	−	0.469935i	−0.268573	−	0.0872647i	0.171635	−	0.985161i	$-0.445095\pi$
$29$	−1.44631	−	0.469935i	−0.268573	−	0.0872647i	−0.440208	+	0.897896i	$0.645095\pi$
$30$	1.05122	−	0.435471i	0.191926	−	0.0795057i
$31$	−1.90816	+	0.619999i	−0.342716	+	0.111355i	−0.475318	−	0.879814i	$-0.657667\pi$
$31$	−1.90816	+	0.619999i	−0.342716	+	0.111355i	0.132602	+	0.991169i	$0.457667\pi$
$32$	−0.672788	−	0.672788i	−0.118933	−	0.118933i
$33$	0.413120	−	0.810794i	0.0719150	−	0.141141i
$34$	15.0290	+	10.9192i	2.57746	+	1.87263i
$35$	−1.97359	+	5.57718i	−0.333597	+	0.942716i
$36$	−9.79595	+	7.11717i	−1.63266	+	1.18620i
$37$	0.625263	+	3.94776i	0.102793	+	0.649007i	0.984255	+	0.176753i	$0.0565594\pi$
$37$	0.625263	+	3.94776i	0.102793	+	0.649007i	−0.881463	+	0.472254i	$0.843441\pi$
$38$	2.36302	+	14.9195i	0.383333	+	2.42027i
$39$	−0.230204	−	0.316849i	−0.0368622	−	0.0507364i
$40$	10.6799	+	4.42337i	1.68864	+	0.699396i
$41$	4.69566	−	6.46303i	0.733340	−	1.00936i	−0.265635	−	0.964074i	$-0.585582\pi$
$41$	4.69566	−	6.46303i	0.733340	−	1.00936i	0.998974	−	0.0452815i	$-0.0144185\pi$
$42$	−0.140474	+	1.33898i	−0.0216755	+	0.206608i
$43$	0.773359	−	0.773359i	0.117936	−	0.117936i	−0.645676	−	0.763612i	$-0.723424\pi$
$43$	0.773359	−	0.773359i	0.117936	−	0.117936i	0.763612	+	0.645676i	$0.223424\pi$
$44$	17.1891	−	5.58509i	2.59136	−	0.841984i
$45$	3.45520	−	5.63878i	0.515071	−	0.840580i
$46$	−3.72506	+	11.4646i	−0.549231	+	1.69036i
$47$	4.03603	+	7.92115i	0.588715	+	1.15542i	0.972697	+	0.232078i	$0.0745526\pi$
$47$	4.03603	+	7.92115i	0.588715	+	1.15542i	−0.383982	+	0.923341i	$0.625447\pi$
$48$	0.931177	+	0.147484i	0.134404	+	0.0212875i
$49$	−4.68590	−	5.20023i	−0.669414	−	0.742889i
$50$	−12.3432		0.000789122i	−1.74559		0.000111599i
$51$	−1.55118			−0.217208
$52$	1.21687	−	7.68303i	0.168750	−	1.06545i
$53$	1.12238	+	2.20280i	0.154171	+	0.302577i	0.955154	−	0.296110i	$-0.0956894\pi$
$53$	1.12238	+	2.20280i	0.154171	+	0.302577i	−0.800983	+	0.598687i	$0.795689\pi$
$54$	0.936802	−	2.88318i	0.127483	−	0.392351i
$55$	−7.50592	+	6.41107i	−1.01210	+	0.864469i
$56$	−10.6279	+	8.60964i	−1.42021	+	1.15051i
$57$	−0.891884	−	0.891884i	−0.118133	−	0.118133i
$58$	3.34497	+	1.70435i	0.439216	+	0.223792i
$59$	3.46254	+	2.51568i	0.450784	+	0.327514i	0.789905	−	0.613229i	$-0.210130\pi$
$59$	3.46254	+	2.51568i	0.450784	+	0.327514i	−0.339121	+	0.940743i	$0.610130\pi$
$60$	−1.83493	+	0.440591i	−0.236889	+	0.0568800i
$61$	3.15174	+	4.33800i	0.403539	+	0.555424i	0.961628	−	0.274357i	$-0.0884651\pi$
$61$	3.15174	+	4.33800i	0.403539	+	0.555424i	−0.558089	+	0.829781i	$0.688465\pi$
$62$	4.89198	−	0.774813i	0.621282	−	0.0984014i
$63$	3.91371	+	6.77576i	0.493081	+	0.853665i
$64$	−3.99611	−	5.50017i	−0.499514	−	0.687521i
$65$	0.991924	+	4.13108i	0.123033	+	0.512397i
$66$	−1.32040	+	1.81737i	−0.162530	+	0.223703i
$67$	−2.45898	+	4.82603i	−0.300413	+	0.589593i	−0.991032	−	0.133625i	$-0.957338\pi$
$67$	−2.45898	+	4.82603i	−0.300413	+	0.589593i	0.690619	+	0.723219i	$0.257338\pi$
$68$	−21.7854	−	21.7854i	−2.64186	−	2.64186i
$69$	−0.311044	−	0.957295i	−0.0374453	−	0.115245i
$70$	6.96586	−	12.8363i	0.832580	−	1.53424i
$71$	1.20256	−	3.70109i	0.142717	−	0.439239i	−0.853993	−	0.520284i	$-0.825826\pi$
$71$	1.20256	−	3.70109i	0.142717	−	0.439239i	0.996710	+	0.0810457i	$0.0258260\pi$
$72$	13.6229	−	6.94121i	1.60547	−	0.818029i
$73$	0.784747	+	0.124292i	0.0918476	+	0.0145472i	0.202189	−	0.979347i	$-0.435194\pi$
$73$	0.784747	+	0.124292i	0.0918476	+	0.0145472i	−0.110341	+	0.993894i	$0.535194\pi$
$74$		−	9.86703i		−	1.14702i
$75$	0.833781	−	0.605859i	0.0962767	−	0.0699585i
$76$		−	25.0520i		−	2.87366i
$77$	−2.43054	−	11.4241i	−0.276986	−	1.30189i
$78$	0.438932	+	0.861453i	0.0496993	+	0.0975404i
$79$	−10.4243	−	3.38705i	−1.17282	−	0.381073i	−0.343127	−	0.939289i	$-0.611486\pi$
$79$	−10.4243	−	3.38705i	−1.17282	−	0.381073i	−0.829696	+	0.558216i	$0.811486\pi$
$80$	−8.72022	−	5.34337i	−0.974950	−	0.597407i
$81$	−2.66354	−	8.19753i	−0.295949	−	0.910837i
$82$	−13.9450	+	13.9450i	−1.53997	+	1.53997i
$83$	−0.370328	+	0.726810i	−0.0406488	+	0.0797778i	−0.910438	−	0.413646i	$-0.864255\pi$
$83$	−0.370328	+	0.726810i	−0.0406488	+	0.0797778i	0.869789	+	0.493424i	$0.164255\pi$
$84$	0.577488	−	2.15686i	0.0630091	−	0.235333i
$85$	15.5462	+	6.43885i	1.68622	+	0.698391i
$86$	−2.18429	+	1.58698i	−0.235538	+	0.171128i
$87$	−0.309613	+	0.0490379i	−0.0331940	+	0.00525742i
$88$	−22.5407	+	3.57009i	−2.40284	+	0.380573i
$89$	4.65732	−	3.38374i	0.493675	−	0.358676i	−0.312921	−	0.949779i	$-0.601308\pi$
$89$	4.65732	−	3.38374i	0.493675	−	0.358676i	0.806596	+	0.591103i	$0.201308\pi$
$90$	−10.6022	+	12.4144i	−1.11757	+	1.30859i
$91$	−4.85585	−	1.30013i	−0.509031	−	0.136290i
$92$	9.07621	−	17.8131i	0.946261	−	1.85714i
$93$	−0.292441	+	0.292441i	−0.0303247	+	0.0303247i
$94$	−6.78182	−	20.8723i	−0.699491	−	2.15281i
$95$	5.23645	+	12.6408i	0.537249	+	1.29692i
$96$	−0.186528	−	0.0606066i	−0.0190374	−	0.00618564i
$97$	1.37761	+	2.70371i	0.139875	+	0.274520i	0.950308	−	0.311311i	$-0.100768\pi$
$97$	1.37761	+	2.70371i	0.139875	+	0.274520i	−0.810433	+	0.585831i	$0.800768\pi$
$98$	9.41712	+	14.4890i	0.951273	+	1.46361i
$99$			13.0560i			1.31218i
$100$	20.2189	+	3.20103i	2.02189	+	0.320103i
$101$			9.05231i			0.900738i	0.892842	+	0.450369i	$0.148708\pi$
$101$			9.05231i			0.900738i	−0.892842	+	0.450369i	$0.851292\pi$
$102$	3.78214	+	0.599032i	0.374488	+	0.0593130i
$103$	0.197172	−	0.100464i	0.0194279	−	0.00989903i	−0.444250	−	0.895903i	$-0.646530\pi$
$103$	0.197172	−	0.100464i	0.0194279	−	0.00989903i	0.463677	+	0.886004i	$0.346530\pi$
$104$	−3.03525	+	9.34154i	−0.297631	+	0.916013i
$105$	0.159445	+	1.20902i	0.0155602	+	0.117988i
$106$	−1.88596	−	5.80438i	−0.183180	−	0.563771i
$107$	−5.28214	−	5.28214i	−0.510643	−	0.510643i	0.404080	−	0.914724i	$-0.367592\pi$
$107$	−5.28214	−	5.28214i	−0.510643	−	0.510643i	−0.914724	+	0.404080i	$0.867592\pi$
$108$	−2.28254	+	4.47974i	−0.219638	+	0.431063i
$109$	−4.53859	+	6.24684i	−0.434719	+	0.598339i	−0.969028	−	0.246950i	$-0.920572\pi$
$109$	−4.53859	+	6.24684i	−0.434719	+	0.598339i	0.534310	+	0.845289i	$0.320572\pi$
$110$	20.7770	−	12.7331i	1.98101	−	1.21405i
$111$	0.484277	+	0.666550i	0.0459655	+	0.0632661i
$112$	10.4785	−	6.05244i	0.990127	−	0.571902i
$113$	7.97103	−	1.26249i	0.749851	−	0.118765i	0.230200	−	0.973143i	$-0.426062\pi$
$113$	7.97103	−	1.26249i	0.749851	−	0.118765i	0.519651	+	0.854379i	$0.326062\pi$
$114$	1.83020	+	2.51905i	0.171414	+	0.235931i
$115$	−0.856342	+	10.8853i	−0.0798543	+	1.01506i
$116$	−5.03704	−	3.65963i	−0.467678	−	0.339788i
$117$	5.00676	+	2.55107i	0.462876	+	0.235847i
$118$	−7.47099	−	7.47099i	−0.687760	−	0.687760i
$119$	−15.4704	+	12.5326i	−1.41817	+	1.14886i
$120$	2.37547	−	0.187030i	0.216850	−	0.0170734i
$121$	2.62298	−	8.07270i	0.238453	−	0.733882i
$122$	−6.00945	−	11.7942i	−0.544070	−	1.06780i
$123$	0.257606	−	1.62646i	0.0232275	−	0.146653i
$124$	−8.21431			−0.737667
$125$	−10.8712	+	2.61104i	−0.972348	+	0.233539i
$126$	−6.92590	−	18.0323i	−0.617009	−	1.60645i
$127$	11.2355	+	1.77953i	0.996988	+	0.157907i	0.633542	−	0.773708i	$-0.281600\pi$
$127$	11.2355	+	1.77953i	0.996988	+	0.157907i	0.363446	+	0.931615i	$0.381600\pi$
$128$	8.48333	+	16.6495i	0.749827	+	1.47162i
$129$	0.0696663	−	0.214411i	0.00613378	−	0.0188778i
$130$	−0.823211	−	10.4556i	−0.0722004	−	0.917018i
$131$	4.11189	−	1.33603i	0.359257	−	0.116730i	−0.123827	−	0.992304i	$-0.539517\pi$
$131$	4.11189	−	1.33603i	0.359257	−	0.116730i	0.483084	+	0.875574i	$0.339517\pi$
$132$	2.63437	−	2.63437i	0.229293	−	0.229293i
$133$	−16.1009	−	1.68917i	−1.39613	−	0.146470i
$134$	7.85930	−	10.8174i	0.678940	−	0.934481i
$135$	0.215358	−	2.73750i	0.0185351	−	0.235607i
$136$	22.8664	+	31.4729i	1.96078	+	2.69878i
$137$	−2.66715	−	16.8397i	−0.227870	−	1.43871i	−0.790731	−	0.612163i	$-0.790299\pi$
$137$	−2.66715	−	16.8397i	−0.227870	−	1.43871i	0.562861	−	0.826551i	$-0.309701\pi$
$138$	0.388712	+	2.45423i	0.0330894	+	0.208918i
$139$	3.58136	−	2.60201i	0.303767	−	0.220700i	−0.425450	−	0.904982i	$-0.639884\pi$
$139$	3.58136	−	2.60201i	0.303767	−	0.220700i	0.729217	+	0.684282i	$0.239884\pi$
$140$	−14.7407	+	19.2193i	−1.24582	+	1.62433i
$141$	1.48255	+	1.07714i	0.124853	+	0.0907113i
$142$	−4.36140	+	8.55974i	−0.366001	+	0.718317i
$143$	−5.93090	−	5.93090i	−0.495966	−	0.495966i
$144$	−12.8647	+	4.18000i	−1.07206	+	0.348333i
$145$	3.30655	+	0.793721i	0.274594	+	0.0659149i
$146$	−1.86540	−	0.606105i	−0.154382	−	0.0501616i
$147$	−1.34728	−	0.516582i	−0.111122	−	0.0426070i
$148$	−2.55991	+	16.1627i	−0.210424	+	1.32856i
$149$		−	5.31631i		−	0.435529i	−0.976001	−	0.217764i	$-0.930124\pi$
$149$		−	5.31631i		−	0.435529i	0.976001	−	0.217764i	$-0.0698764\pi$
$150$	−2.26693	+	1.15524i	−0.185094	+	0.0943249i
$151$	12.5100			1.01805			0.509023	−	0.860753i	$-0.330007\pi$
$151$	12.5100			1.01805			0.509023	+	0.860753i	$0.330007\pi$
$152$	−4.94850	+	31.2436i	−0.401376	+	2.53419i
$153$	19.8301	−	10.1039i	1.60316	−	0.816853i
$154$	1.51450	+	28.7932i	0.122042	+	2.32023i
$155$	4.14479	−	1.71698i	0.332918	−	0.137912i
$156$	−0.495495	−	1.52498i	−0.0396714	−	0.122096i
$157$	4.08176	−	4.08176i	0.325760	−	0.325760i	−0.525212	−	0.850972i	$-0.676014\pi$
$157$	4.08176	−	4.08176i	0.325760	−	0.325760i	0.850972	+	0.525212i	$0.176014\pi$
$158$	24.1089	+	12.2841i	1.91800	+	0.977268i
$159$	0.412283	+	0.299541i	0.0326962	+	0.0237552i
$160$	1.61784	+	1.38168i	0.127902	+	0.109231i
$161$	−10.8365	−	7.03437i	−0.854037	−	0.554386i
$162$	3.32863	+	21.0161i	0.261522	+	1.65118i
$163$	−16.9850	+	2.69015i	−1.33036	+	0.210709i	−0.780820	−	0.624756i	$-0.785199\pi$
$163$	−16.9850	+	2.69015i	−1.33036	+	0.210709i	−0.549544	+	0.835465i	$0.685199\pi$
$164$	26.4605	−	19.2247i	2.06622	−	1.50120i
$165$	−0.778611	+	1.87990i	−0.0606148	+	0.146350i
$166$	1.18363	−	1.62912i	0.0918673	−	0.126445i
$167$	14.3079	+	7.29025i	1.10718	+	0.564136i	0.909321	−	0.416094i	$-0.136601\pi$
$167$	14.3079	+	7.29025i	1.10718	+	0.564136i	0.197858	+	0.980231i	$0.436601\pi$
$168$	−1.14626	+	2.57586i	−0.0884357	+	0.198732i
$169$	8.93048	−	2.90169i	0.686960	−	0.223207i
$170$	−35.4187	−	21.7030i	−2.71649	−	1.66455i
$171$	17.2112	+	5.59226i	1.31617	+	0.427651i
$172$	3.98969	−	2.03285i	0.304211	−	0.155003i
$173$	−10.5652	−	1.67336i	−0.803258	−	0.127223i	−0.258712	−	0.965955i	$-0.583298\pi$
$173$	−10.5652	−	1.67336i	−0.803258	−	0.127223i	−0.544546	+	0.838731i	$0.683298\pi$
$174$	0.773848			0.0586653
$175$	3.42060	−	12.7789i	0.258573	−	0.965992i
$176$	20.1908			1.52194
$177$	0.871367	+	0.138011i	0.0654959	+	0.0103735i
$178$	−12.6624	+	6.45181i	−0.949086	+	0.483583i
$179$	2.00919	+	0.652825i	0.150174	+	0.0487944i	0.383139	−	0.923691i	$-0.374843\pi$
$179$	2.00919	+	0.652825i	0.150174	+	0.0487944i	−0.232965	+	0.972485i	$0.574843\pi$
$180$	20.5877	−	17.5847i	1.53452	−	1.31068i
$181$	−21.8924	+	7.11328i	−1.62725	+	0.528726i	−0.973637	−	0.228102i	$-0.926748\pi$
$181$	−21.8924	+	7.11328i	−1.62725	+	0.528726i	−0.653614	+	0.756828i	$0.726748\pi$
$182$	11.3376	+	5.04525i	0.840401	+	0.373979i
$183$	0.984821	+	0.501791i	0.0728001	+	0.0370935i
$184$	−14.8380	+	20.4228i	−1.09387	+	1.50559i
$185$	−2.08669	−	8.69048i	−0.153417	−	0.638936i
$186$	0.825974	−	0.600106i	0.0605634	−	0.0440019i
$187$	−32.8112	+	5.19678i	−2.39939	+	0.380026i
$188$	5.69381	+	35.9493i	0.415264	+	2.62187i
$189$	2.72523	+	1.76905i	0.198231	+	0.128679i
$190$	−7.88612	−	32.8434i	−0.572119	−	2.38271i
$191$	10.5993	+	7.70086i	0.766940	+	0.557214i	0.901031	−	0.433755i	$-0.142812\pi$
$191$	10.5993	+	7.70086i	0.766940	+	0.557214i	−0.134091	+	0.990969i	$0.542812\pi$
$192$	−1.24866	−	0.636224i	−0.0901142	−	0.0459155i
$193$	7.06153	−	7.06153i	0.508300	−	0.508300i	−0.405704	−	0.914004i	$-0.632974\pi$
$193$	7.06153	−	7.06153i	0.508300	−	0.508300i	0.914004	+	0.405704i	$0.132974\pi$
$194$	−2.31482	−	7.12429i	−0.166195	−	0.511494i
$195$	0.568775	+	0.665906i	0.0407308	+	0.0476866i
$196$	−11.6667	−	26.1768i	−0.833332	−	1.86977i
$197$	−0.315148	+	0.160576i	−0.0224533	+	0.0114405i	−0.465181	−	0.885216i	$-0.654011\pi$
$197$	−0.315148	+	0.160576i	−0.0224533	+	0.0114405i	0.442728	+	0.896656i	$0.354011\pi$
$198$	5.04197	−	31.8337i	0.358317	−	2.26232i
$199$	−9.51572			−0.674552			−0.337276	−	0.941406i	$-0.609506\pi$
$199$	−9.51572			−0.674552			−0.337276	+	0.941406i	$0.609506\pi$
$200$	−24.5837	−	7.98599i	−1.73833	−	0.564695i
$201$			1.11649i			0.0787509i
$202$	3.49581	−	22.0717i	0.245964	−	1.55296i
$203$	−2.69168	+	2.99056i	−0.188919	+	0.209896i
$204$	−6.03991	−	1.96249i	−0.422878	−	0.137401i
$205$	−9.33310	+	15.2313i	−0.651852	+	1.06380i
$206$	−0.519550	+	0.168812i	−0.0361987	+	0.0117617i
$207$	10.2119	+	10.2119i	0.709776	+	0.709776i
$208$	3.94516	−	7.74282i	0.273548	−	0.536868i
$209$	−21.8535	−	15.8775i	−1.51164	−	1.09827i
$210$	0.0781343	−	3.00946i	0.00539178	−	0.207672i
$211$	12.8006	−	9.30020i	0.881232	−	0.640252i	−0.0523453	−	0.998629i	$-0.516670\pi$
$211$	12.8006	−	9.30020i	0.881232	−	0.640252i	0.933577	+	0.358377i	$0.116670\pi$
$212$	1.58339	+	9.99714i	0.108748	+	0.686607i
$213$	−0.125487	−	0.792296i	−0.00859826	−	0.0542873i
$214$	10.8393	+	14.9190i	0.740956	+	1.01984i
$215$	−1.58821	+	1.85968i	−0.108315	+	0.126829i
$216$	3.73155	−	5.13604i	0.253900	−	0.349464i
$217$	−0.553863	+	5.27935i	−0.0375987	+	0.358386i
$218$	13.4786	−	13.4786i	0.912884	−	0.912884i
$219$	0.155762	−	0.0506100i	0.0105254	−	0.00341991i
$220$	−37.3373	+	15.4670i	−2.51728	+	1.04278i
$221$	−4.41824	+	13.5979i	−0.297203	+	0.914697i
$222$	−0.923374	−	1.81222i	−0.0619728	−	0.121629i
$223$	14.0460	+	2.22468i	0.940593	+	0.148975i	0.607859	−	0.794045i	$-0.292029\pi$
$223$	14.0460	+	2.22468i	0.940593	+	0.148975i	0.332734	+	0.943021i	$0.392029\pi$
$224$	−2.34997	+	0.902584i	−0.157014	+	0.0603064i
$225$	−6.71256	+	13.1762i	−0.447504	+	0.878415i
$226$	−19.9228			−1.32525
$227$	−0.806723	+	5.09345i	−0.0535441	+	0.338064i	0.946345	+	0.323159i	$0.104745\pi$
$227$	−0.806723	+	5.09345i	−0.0535441	+	0.338064i	−0.999889	+	0.0149055i	$0.995255\pi$
$228$	−2.34441	−	4.60116i	−0.155262	−	0.304719i
$229$	1.33232	−	4.10046i	0.0880421	−	0.270966i	−0.897336	−	0.441348i	$-0.854500\pi$
$229$	1.33232	−	4.10046i	0.0880421	−	0.270966i	0.985378	+	0.170383i	$0.0545003\pi$
$230$	6.29164	−	26.2103i	0.414858	−	1.72825i
$231$	−1.51549	−	1.87074i	−0.0997119	−	0.123086i
$232$	5.55907	+	5.55907i	0.364971	+	0.364971i
$233$	10.7294	+	5.46689i	0.702904	+	0.358148i	0.768633	−	0.639690i	$-0.220937\pi$
$233$	10.7294	+	5.46689i	0.702904	+	0.358148i	−0.0657289	+	0.997838i	$0.520937\pi$
$234$	−11.2225	−	8.15363i	−0.733639	−	0.533020i
$235$	−10.3872	−	16.9492i	−0.677589	−	1.10565i
$236$	10.2995	+	14.1761i	0.670443	+	0.922786i
$237$	−2.23154	+	0.353440i	−0.144954	+	0.0229584i
$238$	42.5603	−	24.5830i	2.75878	−	1.59348i
$239$	−7.68632	−	10.5793i	−0.497186	−	0.684318i	0.484507	−	0.874788i	$-0.338999\pi$
$239$	−7.68632	−	10.5793i	−0.497186	−	0.684318i	−0.981693	+	0.190469i	$0.938999\pi$
$240$	−2.10164	−	0.165335i	−0.135660	−	0.0106723i
$241$	14.5206	−	19.9860i	0.935357	−	1.28741i	−0.0223759	−	0.999750i	$-0.507123\pi$
$241$	14.5206	−	19.9860i	0.935357	−	1.28741i	0.957733	−	0.287659i	$-0.0928769\pi$
$242$	−9.51295	+	18.6702i	−0.611516	+	1.20017i
$243$	−3.86138	−	3.86138i	−0.247708	−	0.247708i
$244$	6.78386	+	20.8786i	0.434292	+	1.33661i
$245$	11.3584	+	10.7698i	0.725659	+	0.688054i
$246$	−1.25621	+	3.86621i	−0.0800929	+	0.246500i
$247$	−10.3588	+	5.27808i	−0.659116	+	0.335836i
$248$	10.2445	+	1.62257i	0.650526	+	0.103033i
$249$			0.168145i			0.0106558i
$250$	27.5148	−	2.16812i	1.74019	−	0.137124i
$251$			24.7925i			1.56489i	0.622722	+	0.782443i	$0.286027\pi$
$251$			24.7925i			1.56489i	−0.622722	+	0.782443i	$0.713973\pi$
$252$	6.66663	+	31.3346i	0.419959	+	1.97390i
$253$	−9.78649	−	19.2071i	−0.615272	−	1.20754i
$254$	−26.7076	−	8.67782i	−1.67578	−	0.544495i
$255$	3.45784	−	0.272249i	0.216538	−	0.0170489i
$256$	−10.0529	−	30.9398i	−0.628309	−	1.93374i
$257$	13.3266	−	13.3266i	0.831290	−	0.831290i	−0.156403	−	0.987693i	$-0.549990\pi$
$257$	13.3266	−	13.3266i	0.831290	−	0.831290i	0.987693	+	0.156403i	$0.0499899\pi$
$258$	−0.252664	+	0.495881i	−0.0157302	+	0.0308722i
$259$	10.2152	+	2.73506i	0.634739	+	0.169948i
$260$	−1.36416	+	17.3404i	−0.0846015	+	1.07540i
$261$	3.63864	−	2.64363i	0.225226	−	0.163636i
$262$	−10.5417	+	1.66964i	−0.651269	+	0.103151i
$263$	−18.9224	+	2.99702i	−1.16681	+	0.184804i	−0.709632	−	0.704572i	$-0.751139\pi$
$263$	−18.9224	+	2.99702i	−1.16681	+	0.184804i	−0.457175	+	0.889377i	$0.651139\pi$
$264$	−3.80583	+	2.76510i	−0.234233	+	0.170180i
$265$	−2.88859	−	4.71341i	−0.177445	−	0.289543i
$266$	38.6056	+	10.3364i	2.36706	+	0.633768i
$267$	0.538728	−	1.05731i	0.0329696	−	0.0647065i
$268$	−15.6804	+	15.6804i	−0.957832	+	0.957832i
$269$	8.47322	+	26.0779i	0.516621	+	1.59000i	0.780313	+	0.625389i	$0.215060\pi$
$269$	8.47322	+	26.0779i	0.516621	+	1.59000i	−0.263692	+	0.964607i	$0.584940\pi$
$270$	−1.58226	+	6.59152i	−0.0962933	+	0.401147i
$271$	10.0270	+	3.25796i	0.609096	+	0.197907i	0.597293	−	0.802023i	$-0.296243\pi$
$271$	10.0270	+	3.25796i	0.609096	+	0.197907i	0.0118027	+	0.999930i	$0.496243\pi$
$272$	−15.6254	−	30.6666i	−0.947430	−	1.85944i
$273$	−1.01352	+	0.215632i	−0.0613407	+	0.0130506i
$274$			42.0893i			2.54271i
$275$	15.6067	−	15.6087i	0.941122	−	0.941243i
$276$		−	4.12100i		−	0.248055i
$277$	−11.5613	−	1.83113i	−0.694650	−	0.110022i	−0.200882	−	0.979615i	$-0.564381\pi$
$277$	−11.5613	−	1.83113i	−0.694650	−	0.110022i	−0.493768	+	0.869594i	$0.664381\pi$
$278$	−9.73705	+	4.96127i	−0.583989	+	0.297557i
$279$	1.83365	−	5.64340i	0.109778	−	0.337862i
$280$	22.1802	−	21.0577i	1.32552	−	1.25844i
$281$	5.89743	+	18.1504i	0.351811	+	1.08276i	0.957835	+	0.287318i	$0.0927636\pi$
$281$	5.89743	+	18.1504i	0.351811	+	1.08276i	−0.606024	+	0.795446i	$0.707236\pi$
$282$	−3.19885	−	3.19885i	−0.190488	−	0.190488i
$283$	−4.75665	+	9.33546i	−0.282754	+	0.554936i	−0.988079	−	0.153948i	$-0.950801\pi$
$283$	−4.75665	+	9.33546i	−0.282754	+	0.554936i	0.705325	+	0.708884i	$0.250801\pi$
$284$	9.36493	−	12.8897i	0.555707	−	0.764865i
$285$	2.14470	+	1.83163i	0.127041	+	0.108496i
$286$	12.1705	+	16.7513i	0.719660	+	0.990527i
$287$	−10.5716	−	18.3025i	−0.624022	−	1.08036i
$288$	2.77933	−	0.440202i	0.163773	−	0.0259392i
$289$	23.2929	+	32.0600i	1.37017	+	1.88588i
$290$	−7.75564	−	3.21220i	−0.455427	−	0.188627i
$291$	0.506036	+	0.367657i	0.0296644	+	0.0215524i
$292$	2.89836	+	1.47679i	0.169614	+	0.0864226i
$293$	13.9898	+	13.9898i	0.817291	+	0.817291i	0.985715	−	0.168423i	$-0.0538676\pi$
$293$	13.9898	+	13.9898i	0.817291	+	0.817291i	−0.168423	+	0.985715i	$0.553868\pi$
$294$	3.08550	+	1.77984i	0.179950	+	0.103802i
$295$	−8.16011	−	5.00016i	−0.475100	−	0.291121i
$296$	6.38520	−	19.6516i	0.371132	−	1.14223i
$297$	2.46117	+	4.83031i	0.142811	+	0.280283i
$298$	−2.05305	+	12.9624i	−0.118930	+	0.750893i
$299$	−9.27781			−0.536549
$300$	4.01305	−	1.30420i	0.231693	−	0.0752982i
$301$	−1.03750	−	2.70125i	−0.0598008	−	0.155698i
$302$	−30.5022	−	4.83108i	−1.75521	−	0.277997i
$303$	0.847131	+	1.66259i	0.0486664	+	0.0955132i
$304$	8.64827	−	26.6167i	0.496013	−	1.52657i
$305$	−7.78714	−	9.11697i	−0.445890	−	0.522036i
$306$	−52.2523	+	16.9778i	−2.98707	+	0.970557i
$307$	21.2978	−	21.2978i	1.21553	−	1.21553i	0.246347	−	0.969182i	$-0.420770\pi$
$307$	21.2978	−	21.2978i	1.21553	−	1.21553i	0.969182	−	0.246347i	$-0.0792303\pi$
$308$	4.98933	−	47.5576i	0.284293	−	2.70985i
$309$	0.0268119	−	0.0369034i	0.00152528	−	0.00209936i
$310$	−10.7691	+	2.58579i	−0.611641	+	0.146863i
$311$	−15.1640	−	20.8715i	−0.859873	−	1.18351i	−0.981600	−	0.190951i	$-0.938843\pi$
$311$	−15.1640	−	20.8715i	−0.859873	−	1.18351i	0.121726	−	0.992564i	$-0.461157\pi$
$312$	0.316730	+	1.99975i	0.0179313	+	0.113214i
$313$	−2.56622	−	16.2025i	−0.145052	−	0.915820i	−0.947653	−	0.319303i	$-0.896551\pi$
$313$	−2.56622	−	16.2025i	−0.145052	−	0.915820i	0.802601	−	0.596516i	$-0.203449\pi$
$314$	−11.5286	+	8.37602i	−0.650596	+	0.472686i
$315$	−9.91355	−	14.4174i	−0.558565	−	0.812329i
$316$	−36.3044	−	26.3767i	−2.04228	−	1.48381i
$317$	12.5927	−	24.7147i	0.707279	−	1.38811i	−0.205089	−	0.978743i	$-0.565748\pi$
$317$	12.5927	−	24.7147i	0.707279	−	1.38811i	0.912368	−	0.409370i	$-0.134252\pi$
$318$	−0.889568	−	0.889568i	−0.0498845	−	0.0498845i
$319$	−6.38479	+	2.07454i	−0.357480	+	0.116152i
$320$	9.87334	+	11.5595i	0.551937	+	0.646193i
$321$	−1.46445	−	0.475830i	−0.0817378	−	0.0265582i
$322$	23.7055	+	21.3363i	1.32105	+	1.18903i
$323$	−7.20325	+	45.4795i	−0.400800	+	2.53055i
$324$		−	35.2890i		−	1.96050i
$325$	−2.93622	−	9.03478i	−0.162872	−	0.501159i
$326$	42.4523			2.35121
$327$	−0.248989	+	1.57205i	−0.0137691	+	0.0869347i
$328$	−36.7977	+	18.7494i	−2.03182	+	1.03526i
$329$	23.4886	−	1.23548i	1.29497	−	0.0681142i
$330$	2.62442	−	4.28297i	0.144470	−	0.235770i
$331$	1.21725	+	3.74631i	0.0669062	+	0.205916i	0.978920	−	0.204243i	$-0.0654732\pi$
$331$	1.21725	+	3.74631i	0.0669062	+	0.205916i	−0.912014	+	0.410159i	$0.865473\pi$
$332$	−2.36150	+	2.36150i	−0.129604	+	0.129604i
$333$	−10.5326	−	5.36665i	−0.577185	−	0.294091i
$334$	−32.0708	−	23.3008i	−1.75483	−	1.27496i
$335$	4.63447	−	11.1896i	0.253208	−	0.611354i
$336$	1.35813	−	2.09222i	0.0740923	−	0.114140i
$337$	−3.60639	−	22.7699i	−0.196453	−	1.24035i	−0.866933	−	0.498425i	$-0.833912\pi$
$337$	−3.60639	−	22.7699i	−0.196453	−	1.24035i	0.670480	−	0.741928i	$-0.266088\pi$
$338$	−22.8952	+	3.62624i	−1.24533	+	0.197242i
$339$	1.34585	−	0.977817i	0.0730965	−	0.0531077i
$340$	52.3868	+	44.7397i	2.84107	+	2.42635i
$341$	−5.20610	+	7.16558i	−0.281926	+	0.388038i
$342$	−39.8054	−	20.2819i	−2.15243	−	1.09672i
$343$	−17.6105	+	5.73316i	−0.950879	+	0.309562i
$344$	−5.37730	+	1.74719i	−0.289925	+	0.0942022i
$345$	0.861386	+	2.07938i	0.0463755	+	0.111950i
$346$	25.1143	+	8.16012i	1.35015	+	0.438691i
$347$	21.0525	−	10.7268i	1.13016	−	0.575844i	0.214069	−	0.976819i	$-0.431328\pi$
$347$	21.0525	−	10.7268i	1.13016	−	0.575844i	0.916089	+	0.400974i	$0.131328\pi$
$348$	−1.26760	−	0.200768i	−0.0679505	−	0.0107623i
$349$	−9.96173			−0.533239			−0.266620	−	0.963802i	$-0.585907\pi$
$349$	−9.96173			−0.533239			−0.266620	+	0.963802i	$0.585907\pi$
$350$	−13.2752	+	29.8370i	−0.709587	+	1.59485i
$351$	2.33324			0.124539
$352$	−4.14857	−	0.657069i	−0.221120	−	0.0350219i
$353$	−17.1476	+	8.73712i	−0.912672	+	0.465030i	−0.846265	−	0.532763i	$-0.821154\pi$
$353$	−17.1476	+	8.73712i	−0.912672	+	0.465030i	−0.0664077	+	0.997793i	$0.521154\pi$
$354$	−2.07130	−	0.673007i	−0.110089	−	0.0357699i
$355$	−2.03112	+	8.46142i	−0.107801	+	0.449085i
$356$	22.4154	−	7.28322i	1.18802	−	0.386010i
$357$	−1.66854	+	3.74953i	−0.0883087	+	0.198446i
$358$	−4.64677	−	2.36765i	−0.245590	−	0.125134i
$359$	1.39337	−	1.91781i	0.0735394	−	0.101218i	−0.770663	−	0.637243i	$-0.780075\pi$
$359$	1.39337	−	1.91781i	0.0735394	−	0.101218i	0.844202	+	0.536025i	$0.180075\pi$
$360$	−29.1495	+	17.8641i	−1.53631	+	0.941520i
$361$	−14.9198	+	10.8399i	−0.785255	+	0.570521i
$362$	56.1260	−	8.88948i	2.94992	−	0.467221i
$363$	−0.273709	−	1.72813i	−0.0143660	−	0.0907034i
$364$	−17.2626	−	11.2058i	−0.904808	−	0.587344i
$365$	−1.77115	−	0.139335i	−0.0927061	−	0.00729315i
$366$	−2.20745	−	1.60380i	−0.115385	−	0.0838322i
$367$	−0.381987	−	0.194632i	−0.0199396	−	0.0101597i	0.443992	−	0.896031i	$-0.353562\pi$
$367$	−0.381987	−	0.194632i	−0.0199396	−	0.0101597i	−0.463932	+	0.885871i	$0.653562\pi$
$368$	15.7924	−	15.7924i	0.823236	−	0.823236i
$369$	7.30108	+	22.4704i	0.380079	+	1.16976i
$370$	1.73177	+	21.9953i	0.0900306	+	1.14348i
$371$	6.53194	−	0.343575i	0.339122	−	0.0178375i
$372$	−1.50868	+	0.768709i	−0.0782213	+	0.0398557i
$373$	3.82756	−	24.1662i	0.198183	−	1.25128i	−0.665174	−	0.746688i	$-0.731643\pi$
$373$	3.82756	−	24.1662i	0.198183	−	1.25128i	0.863358	−	0.504592i	$-0.168357\pi$
$374$	82.0084			4.24055
$375$	−1.75230	+	1.49690i	−0.0904886	+	0.0772996i
$376$		−	45.9589i		−	2.37015i
$377$	−0.451999	+	2.85381i	−0.0232792	+	0.146979i
$378$	−5.96160	−	5.36578i	−0.306631	−	0.275986i
$379$	16.6292	+	5.40314i	0.854182	+	0.277541i	0.703197	−	0.710995i	$-0.251755\pi$
$379$	16.6292	+	5.40314i	0.854182	+	0.277541i	0.150986	+	0.988536i	$0.451755\pi$
$380$	4.39690	+	55.8451i	0.225556	+	2.86479i
$381$	2.23009	−	0.724601i	0.114251	−	0.0371224i
$382$	−22.8698	−	22.8698i	−1.17012	−	1.17012i
$383$	15.1563	−	29.7460i	0.774453	−	1.51995i	−0.0778868	−	0.996962i	$-0.524817\pi$
$383$	15.1563	−	29.7460i	0.774453	−	1.51995i	0.852340	−	0.522988i	$-0.175183\pi$
$384$	3.11617	+	2.26403i	0.159022	+	0.115536i
$385$	7.42314	+	25.0396i	0.378318	+	1.27614i
$386$	−19.9447	+	14.4907i	−1.01516	+	0.737556i
$387$	0.506005	+	3.19479i	0.0257217	+	0.162400i
$388$	1.94345	+	12.2705i	0.0986640	+	0.622940i
$389$	−8.93652	−	12.3001i	−0.453099	−	0.623638i	0.519961	−	0.854190i	$-0.325947\pi$
$389$	−8.93652	−	12.3001i	−0.453099	−	0.623638i	−0.973060	+	0.230553i	$0.925947\pi$
$390$	−1.12965	−	1.84329i	−0.0572020	−	0.0933385i
$391$	−21.5989	+	29.7283i	−1.09230	+	1.50342i
$392$	9.37939	+	34.9510i	0.473731	+	1.76529i
$393$	0.630179	−	0.630179i	0.0317883	−	0.0317883i
$394$	0.830416	−	0.269818i	0.0418357	−	0.0135933i
$395$	23.8319	+	5.72074i	1.19911	+	0.287841i
$396$	−16.5180	+	50.8371i	−0.830059	+	2.55466i
$397$	10.9935	+	21.5760i	0.551748	+	1.08287i	0.983506	+	0.180877i	$0.0578936\pi$
$397$	10.9935	+	21.5760i	0.551748	+	1.08287i	−0.431758	+	0.901990i	$0.642106\pi$
$398$	23.2016	+	3.67477i	1.16299	+	0.184200i
$399$	−3.11525	+	1.19651i	−0.155957	+	0.0599006i
$400$	20.3767	+	10.3808i	1.01883	+	0.519039i
$401$	−31.4063			−1.56835			−0.784177	−	0.620537i	$-0.786915\pi$
$401$	−31.4063			−1.56835			−0.784177	+	0.620537i	$0.786915\pi$
$402$	0.431164	−	2.72226i	0.0215045	−	0.135774i
$403$	1.73063	+	3.39656i	0.0862090	+	0.169195i
$404$	−11.4526	+	35.2475i	−0.569788	+	1.75363i
$405$	7.37624	+	17.8062i	0.366528	+	0.884797i
$406$	7.71784	−	6.25223i	0.383030	−	0.310293i
$407$	12.4767	+	12.4767i	0.618448	+	0.618448i
$408$	7.14503	+	3.64058i	0.353732	+	0.180235i
$409$	17.6612	+	12.8316i	0.873291	+	0.634483i	0.931468	−	0.363823i	$-0.118529\pi$
$409$	17.6612	+	12.8316i	0.873291	+	0.634483i	−0.0581767	+	0.998306i	$0.518529\pi$
$410$	28.6383	−	33.5333i	1.41435	−	1.65609i
$411$	−2.06575	−	2.84326i	−0.101896	−	0.140248i
$412$	0.894843	−	0.141729i	0.0440858	−	0.00698250i
$413$	9.80547	−	5.66369i	0.482496	−	0.278692i
$414$	−20.9554	−	28.8427i	−1.02990	−	1.41754i
$415$	0.697961	−	1.68518i	0.0342616	−	0.0827223i
$416$	−1.06258	+	1.46252i	−0.0520973	+	0.0717058i
$417$	0.414268	−	0.813047i	0.0202868	−	0.0398151i
$418$	47.1526	+	47.1526i	2.30631	+	2.30631i
$419$	−10.8766	−	33.4748i	−0.531358	−	1.63535i	−0.751390	−	0.659858i	$-0.770616\pi$
$419$	−10.8766	−	33.4748i	−0.531358	−	1.63535i	0.220033	−	0.975493i	$-0.429384\pi$
$420$	−0.908765	+	4.90936i	−0.0443432	+	0.239552i
$421$	−3.38146	+	10.4071i	−0.164802	+	0.507210i	−0.999022	−	0.0442233i	$-0.985919\pi$
$421$	−3.38146	+	10.4071i	−0.164802	+	0.507210i	0.834219	+	0.551433i	$0.185919\pi$
$422$	−34.8025	+	17.7328i	−1.69416	+	0.863218i
$423$	−25.9689	−	4.11307i	−1.26265	−	0.199984i
$424$		−	12.7807i		−	0.620686i
$425$	−35.7851	−	11.6248i	−1.73583	−	0.563883i
$426$			1.98027i			0.0959443i
$427$	13.8761	−	2.95223i	0.671512	−	0.142868i
$428$	−13.8846	−	27.2501i	−0.671139	−	1.31718i
$429$	−1.64432	−	0.534272i	−0.0793885	−	0.0257949i
$430$	4.59062	−	3.92101i	0.221379	−	0.189088i
$431$	−4.21755	−	12.9803i	−0.203152	−	0.625239i	−0.999784	−	0.0207739i	$-0.993387\pi$
$431$	−4.21755	−	12.9803i	−0.203152	−	0.625239i	0.796632	−	0.604465i	$-0.206613\pi$
$432$	−3.97157	+	3.97157i	−0.191082	+	0.191082i
$433$	5.88887	−	11.5575i	0.283001	−	0.555420i	−0.705122	−	0.709086i	$-0.749108\pi$
$433$	5.88887	−	11.5575i	0.283001	−	0.555420i	0.988123	+	0.153666i	$0.0491078\pi$
$434$	3.38922	−	12.6584i	0.162688	−	0.607624i
$435$	0.681574	−	0.163654i	0.0326790	−	0.00784663i
$436$	−25.5754	+	18.5816i	−1.22484	+	0.889899i
$437$	−29.5117	+	4.67419i	−1.41174	+	0.223597i
$438$	−0.399328	+	0.0632474i	−0.0190806	+	0.00302208i
$439$	0.917813	−	0.666831i	0.0438048	−	0.0318261i	−0.565667	−	0.824634i	$-0.691381\pi$
$439$	0.917813	−	0.666831i	0.0438048	−	0.0318261i	0.609472	+	0.792807i	$0.291381\pi$
$440$	49.6204	−	11.9145i	2.36556	−	0.568001i
$441$	20.5883	−	2.17187i	0.980397	−	0.103422i
$442$	16.0240	−	31.4488i	0.762182	−	1.49587i
$443$	−13.9503	+	13.9503i	−0.662797	+	0.662797i	−0.956038	−	0.293242i	$-0.905266\pi$
$443$	−13.9503	+	13.9503i	−0.662797	+	0.662797i	0.293242	+	0.956038i	$0.405266\pi$
$444$	1.04237	+	3.20807i	0.0494685	+	0.152248i
$445$	−9.78807	+	8.36034i	−0.463999	+	0.396318i
$446$	−33.3885	−	10.8486i	−1.58099	−	0.513695i
$447$	−0.497509	−	0.976417i	−0.0235314	−	0.0461829i
$448$	−17.5936	+	3.74314i	−0.831219	+	0.176847i
$449$		−	14.4907i		−	0.683860i	−0.939725	−	0.341930i	$-0.888919\pi$
$449$		−	14.4907i		−	0.683860i	0.939725	−	0.341930i	$-0.111081\pi$
$450$	21.4552	−	29.5345i	1.01141	−	1.39227i
$451$		−	35.2666i		−	1.66064i
$452$	32.6345	+	5.16880i	1.53500	+	0.243120i
$453$	2.29763	−	1.17070i	0.107952	−	0.0550044i
$454$	3.93397	−	12.1075i	0.184630	−	0.568233i
$455$	11.0527	+	2.04595i	0.518158	+	0.0959155i
$456$	2.01497	+	6.20143i	0.0943595	+	0.290409i
$457$	4.42308	+	4.42308i	0.206903	+	0.206903i	0.802950	−	0.596047i	$-0.203263\pi$
$457$	4.42308	+	4.42308i	0.206903	+	0.206903i	−0.596047	+	0.802950i	$0.703263\pi$
$458$	−4.83202	+	9.48338i	−0.225786	+	0.443129i
$459$	5.43181	−	7.47625i	0.253535	−	0.348961i
$460$	−17.1060	+	41.3013i	−0.797572	+	1.92568i
$461$	−3.16235	−	4.35260i	−0.147285	−	0.202721i	0.729000	−	0.684514i	$-0.239986\pi$
$461$	−3.16235	−	4.35260i	−0.147285	−	0.202721i	−0.876285	+	0.481793i	$0.839986\pi$
$462$	2.97268	+	5.14657i	0.138302	+	0.239440i
$463$	24.3710	−	3.85998i	1.13261	−	0.179389i	0.438141	−	0.898906i	$-0.355637\pi$
$463$	24.3710	−	3.85998i	1.13261	−	0.179389i	0.694474	+	0.719518i	$0.255637\pi$
$464$	−4.08829	−	5.62705i	−0.189794	−	0.261229i
$465$	0.600573	−	0.703226i	0.0278509	−	0.0326113i
$466$	−24.0496	−	17.4730i	−1.11407	−	0.809422i
$467$	7.93600	+	4.04359i	0.367234	+	0.187115i	0.627863	−	0.778324i	$-0.283930\pi$
$467$	7.93600	+	4.04359i	0.367234	+	0.187115i	−0.260629	+	0.965439i	$0.583930\pi$
$468$	16.2676	+	16.2676i	0.751971	+	0.751971i
$469$	9.02053	+	11.1351i	0.416530	+	0.514170i
$470$	18.7811	+	45.3376i	0.866310	+	2.09127i
$471$	0.367696	−	1.13165i	0.0169426	−	0.0521438i
$472$	−10.0449	−	19.7142i	−0.462354	−	0.907420i
$473$	0.755290	−	4.76871i	0.0347283	−	0.219266i
$474$	5.57751			0.256183
$475$	−13.8915	−	27.2594i	−0.637388	−	1.25075i
$476$	−76.0937	+	29.2263i	−3.48775	+	1.33958i
$477$	−7.22170	−	1.14380i	−0.330659	−	0.0523712i
$478$	14.6556	+	28.7632i	0.670330	+	1.31560i
$479$	4.09301	−	12.5970i	0.187014	−	0.575571i	−0.812963	−	0.582316i	$-0.802147\pi$
$479$	4.09301	−	12.5970i	0.187014	−	0.575571i	0.999977	+	0.00674428i	$0.00214679\pi$
$480$	0.426440	+	0.102365i	0.0194642	+	0.00467229i
$481$	7.22249	−	2.34673i	0.329317	−	0.107002i
$482$	−43.1229	+	43.1229i	−1.96420	+	1.96420i
$483$	−2.64857	−	0.277865i	−0.120514	−	0.0126433i
$484$	20.4265	−	28.1147i	0.928477	−	1.27794i
$485$	−3.54546	−	5.78524i	−0.160991	−	0.262694i
$486$	7.92379	+	10.9062i	0.359430	+	0.494713i
$487$	2.71331	+	17.1311i	0.122952	+	0.776286i	0.969701	+	0.244294i	$0.0785563\pi$
$487$	2.71331	+	17.1311i	0.122952	+	0.776286i	−0.846749	+	0.531992i	$0.821444\pi$
$488$	−4.33637	−	27.3788i	−0.196298	−	1.23938i
$489$	−2.86779	+	2.08357i	−0.129686	+	0.0942222i
$490$	−23.5353	−	30.6456i	−1.06322	−	1.38443i
$491$	−1.18871	−	0.863649i	−0.0536458	−	0.0389759i	0.560639	−	0.828060i	$-0.310555\pi$
$491$	−1.18871	−	0.863649i	−0.0536458	−	0.0389759i	−0.614285	+	0.789084i	$0.710555\pi$
$492$	3.06078	−	6.00712i	0.137991	−	0.270822i
$493$	8.09202	+	8.09202i	0.364446	+	0.364446i
$494$	27.2955	−	8.86886i	1.22808	−	0.399029i
$495$	−2.29148	−	29.1041i	−0.102994	−	1.30813i
$496$	−8.72735	−	2.83569i	−0.391870	−	0.127326i
$497$	−7.65280	−	6.88797i	−0.343275	−	0.308968i
$498$	0.0649342	−	0.409978i	0.00290977	−	0.0183716i
$499$		−	18.7450i		−	0.839142i	−0.907722	−	0.419571i	$-0.862180\pi$
$499$		−	18.7450i		−	0.839142i	0.907722	−	0.419571i	$-0.137820\pi$
$500$	−45.6331	−	3.58700i	−2.04077	−	0.160416i
$501$	3.31009			0.147884
$502$	9.57433	−	60.4499i	0.427323	−	2.69801i
$503$	−26.5174	+	13.5113i	−1.18235	+	0.602438i	−0.930844	−	0.365418i	$-0.880926\pi$
$503$	−26.5174	+	13.5113i	−1.18235	+	0.602438i	−0.251507	+	0.967856i	$0.580926\pi$
$504$	−2.12479	−	40.3959i	−0.0946457	−	1.79938i
$505$	−1.58878	−	20.1791i	−0.0706998	−	0.897959i
$506$	16.4444	+	50.6108i	0.731044	+	2.24992i
$507$	1.36867	−	1.36867i	0.0607846	−	0.0607846i
$508$	41.4969	+	21.1437i	1.84113	+	0.938101i
$509$	12.1945	+	8.85982i	0.540512	+	0.392705i	0.824275	−	0.566190i	$-0.191583\pi$
$509$	12.1945	+	8.85982i	0.540512	+	0.392705i	−0.283763	+	0.958894i	$0.591583\pi$
$510$	−8.53616	−	0.671536i	−0.377988	−	0.0297361i
$511$	1.14456	−	1.76321i	0.0506325	−	0.0779998i
$512$	6.71687	+	42.4086i	0.296846	+	1.87421i
$513$	7.42178	−	1.17550i	0.327680	−	0.0518994i
$514$	−37.6399	+	27.3470i	−1.66022	+	1.20622i
$515$	−0.421897	+	0.258558i	−0.0185910	+	0.0113934i
$516$	0.542528	−	0.746725i	0.0238834	−	0.0328727i
$517$	34.9682	+	17.8172i	1.53790	+	0.783600i
$518$	−23.8508	−	10.6136i	−1.04794	−	0.466335i
$519$	−2.09705	+	0.681373i	−0.0920503	+	0.0299089i
$520$	5.12654	−	21.3566i	0.224814	−	0.936548i
$521$	−29.0466	−	9.43781i	−1.27255	−	0.413478i	−0.406603	−	0.913605i	$-0.633287\pi$
$521$	−29.0466	−	9.43781i	−1.27255	−	0.413478i	−0.865952	+	0.500127i	$0.833287\pi$
$522$	−9.89278	+	5.04063i	−0.432995	+	0.220622i
$523$	31.3337	+	4.96277i	1.37013	+	0.217007i	0.797752	−	0.602986i	$-0.206022\pi$
$523$	31.3337	+	4.96277i	1.37013	+	0.217007i	0.572375	+	0.819992i	$0.306022\pi$
$524$	17.7010			0.773271
$525$	−0.567627	−	2.66713i	−0.0247733	−	0.116403i
$526$	47.2948			2.06215
$527$	14.9123	+	2.36188i	0.649591	+	0.102885i
$528$	3.70833	−	1.88949i	0.161384	−	0.0822294i
$529$	−0.803278	−	0.261001i	−0.0349251	−	0.0113479i
$530$	5.22285	+	12.6079i	0.226866	+	0.547654i
$531$	−12.0384	+	3.91152i	−0.522423	+	0.169745i
$532$	−60.5561	−	26.9475i	−2.62544	−	1.16832i
$533$	−13.5241	−	6.89089i	−0.585795	−	0.298478i
$534$	−1.72186	+	2.36994i	−0.0745121	+	0.102557i
$535$	12.7018	+	10.8477i	0.549149	+	0.468987i
$536$	22.6532	−	16.4585i	0.978467	−	0.710898i
$537$	0.430109	−	0.0681226i	0.0185606	−	0.00293971i
$538$	−10.5890	−	66.8563i	−0.456524	−	2.88238i
$539$	−30.2289	−	6.41330i	−1.30205	−	0.276240i
$540$	4.30193	−	10.3867i	0.185125	−	0.446973i
$541$	27.4655	+	19.9549i	1.18083	+	0.857926i	0.992266	−	0.124134i	$-0.0396151\pi$
$541$	27.4655	+	19.9549i	1.18083	+	0.857926i	0.188569	+	0.982060i	$0.439615\pi$
$542$	−23.1900	−	11.8159i	−0.996096	−	0.507536i
$543$	−3.35519	+	3.35519i	−0.143985	+	0.143985i
$544$	2.21255	+	6.80952i	0.0948622	+	0.291956i
$545$	9.02091	−	14.7218i	0.386413	−	0.630614i
$546$	2.55446	−	0.134363i	0.109321	−	0.00575020i
$547$	4.65971	−	2.37424i	0.199235	−	0.101515i	−0.351527	−	0.936178i	$-0.614337\pi$
$547$	4.65971	−	2.37424i	0.199235	−	0.101515i	0.550762	+	0.834663i	$0.314337\pi$
$548$	10.9197	−	68.9442i	0.466466	−	2.94515i
$549$	−15.8584			−0.676818
$550$	−44.0807	+	32.0308i	−1.87961	+	1.36580i
$551$			9.30539i			0.396423i
$552$	−0.814018	+	5.13951i	−0.0346469	+	0.218752i
$553$	−19.4002	+	21.5544i	−0.824982	+	0.916588i
$554$	27.4820	+	8.92945i	1.16760	+	0.379376i
$555$	−1.19652	−	1.40086i	−0.0507895	−	0.0594630i
$556$	17.2369	−	5.60061i	0.731008	−	0.237519i
$557$	−20.1686	−	20.1686i	−0.854572	−	0.854572i	0.136120	−	0.990692i	$-0.456537\pi$
$557$	−20.1686	−	20.1686i	−0.854572	−	0.854572i	−0.990692	+	0.136120i	$0.956537\pi$
$558$	−6.65024	+	13.0518i	−0.281527	+	0.552528i
$559$	−1.68114	−	1.22142i	−0.0711046	−	0.0516605i
$560$	−22.2961	+	15.3310i	−0.942183	+	0.647853i
$561$	−5.53993	+	4.02499i	−0.233896	+	0.169935i
$562$	−7.37003	−	46.5326i	−0.310886	−	1.96286i
$563$	0.934834	+	5.90231i	0.0393985	+	0.248753i	0.999525	−	0.0308129i	$-0.00980960\pi$
$563$	0.934834	+	5.90231i	0.0393985	+	0.248753i	−0.960127	+	0.279565i	$0.909810\pi$
$564$	4.40995	+	6.06977i	0.185692	+	0.255584i
$565$	−17.5472	+	4.21330i	−0.738216	+	0.177255i
$566$	15.2030	−	20.9252i	0.639030	−	0.879550i
$567$	−22.6803	−	2.37942i	−0.952483	−	0.0999262i
$568$	−14.2256	+	14.2256i	−0.596892	+	0.596892i
$569$	16.1923	−	5.26120i	0.678817	−	0.220561i	0.0507396	−	0.998712i	$-0.483842\pi$
$569$	16.1923	−	5.26120i	0.678817	−	0.220561i	0.628077	+	0.778151i	$0.283842\pi$
$570$	−4.52195	−	5.29418i	−0.189404	−	0.221749i
$571$	−9.76647	+	30.0581i	−0.408714	+	1.25789i	0.509040	+	0.860743i	$0.330000\pi$
$571$	−9.76647	+	30.0581i	−0.408714	+	1.25789i	−0.917754	+	0.397149i	$0.870000\pi$
$572$	−15.5900	−	30.5970i	−0.651849	−	1.27932i
$573$	2.66738	+	0.422471i	0.111431	+	0.0176490i
$574$	18.7081	+	48.7084i	0.780859	+	2.03305i
$575$	−0.00156093	−	24.4155i	−6.50953e−5	−	1.01820i
$576$	20.1069			0.837787
$577$	6.61687	−	41.7773i	0.275464	−	1.73921i	−0.330579	−	0.943778i	$-0.607244\pi$
$577$	6.61687	−	41.7773i	0.275464	−	1.73921i	0.606043	−	0.795432i	$-0.292756\pi$
$578$	−44.4129	−	87.1651i	−1.84733	−	3.62559i
$579$	0.636122	−	1.95778i	0.0264363	−	0.0813627i
$580$	11.8707	+	7.27387i	0.492905	+	0.302031i
$581$	1.35851	+	1.67697i	0.0563606	+	0.0695724i
$582$	−1.09185	−	1.09185i	−0.0452588	−	0.0452588i
$583$	9.72432	+	4.95479i	0.402740	+	0.205206i
$584$	−3.32299	−	2.41429i	−0.137506	−	0.0999042i
$585$	−11.6087	−	4.80803i	−0.479959	−	0.198788i
$586$	−28.7078	−	39.5130i	−1.18591	−	1.63227i
$587$	−3.47275	+	0.550030i	−0.143336	+	0.0227022i	−0.227690	−	0.973734i	$-0.573117\pi$
$587$	−3.47275	+	0.550030i	−0.143336	+	0.0227022i	0.0843542	+	0.996436i	$0.473117\pi$
$588$	−4.59242	−	3.71597i	−0.189388	−	0.153244i
$589$	7.21616	+	9.93219i	0.297337	+	0.409249i
$590$	17.9653	+	15.3428i	0.739621	+	0.631655i
$591$	−0.0428545	+	0.0589841i	−0.00176280	+	0.00242628i
$592$	−8.29937	+	16.2884i	−0.341102	+	0.669450i
$593$	6.75921	+	6.75921i	0.277567	+	0.277567i	0.832137	−	0.554570i	$-0.187117\pi$
$593$	6.75921	+	6.75921i	0.277567	+	0.277567i	−0.554570	+	0.832137i	$0.687117\pi$
$594$	−4.13555	−	12.7279i	−0.169684	−	0.522232i
$595$	32.2865	−	30.6524i	1.32362	−	1.25663i
$596$	6.72597	−	20.7004i	0.275507	−	0.847922i
$597$	−1.74770	+	0.890498i	−0.0715287	+	0.0364457i
$598$	22.6215	+	3.58289i	0.925062	+	0.146515i
$599$			22.1468i			0.904895i	0.891791	+	0.452448i	$0.149449\pi$
$599$			22.1468i			0.904895i	−0.891791	+	0.452448i	$0.850551\pi$
$600$	−5.26250	+	0.833843i	−0.214841	+	0.0340415i
$601$			29.6537i			1.20960i	0.796378	+	0.604800i	$0.206747\pi$
$601$			29.6537i			1.20960i	−0.796378	+	0.604800i	$0.793253\pi$
$602$	1.48652	+	6.98696i	0.0605859	+	0.284767i
$603$	−7.27247	−	14.2730i	−0.296158	−	0.581243i
$604$	48.7107	+	15.8271i	1.98201	+	0.643995i
$605$	−4.43022	+	18.4558i	−0.180114	+	0.750334i
$606$	−1.42345	−	4.38093i	−0.0578237	−	0.177963i
$607$	−12.9069	+	12.9069i	−0.523876	+	0.523876i	−0.918740	−	0.394864i	$-0.870792\pi$
$607$	−12.9069	+	12.9069i	−0.523876	+	0.523876i	0.394864	+	0.918740i	$0.370792\pi$
$608$	−2.64313	+	5.18744i	−0.107193	+	0.210379i
$609$	−0.214504	+	0.801152i	−0.00869214	+	0.0324643i
$610$	15.4661	+	25.2366i	0.626204	+	1.02180i
$611$	13.6652	−	9.92833i	0.552834	−	0.401657i
$612$	89.9965	−	14.2540i	3.63789	−	0.576186i
$613$	−26.4801	+	4.19404i	−1.06952	+	0.169396i	−0.666283	−	0.745699i	$-0.732116\pi$
$613$	−26.4801	+	4.19404i	−1.06952	+	0.169396i	−0.403239	+	0.915095i	$0.632116\pi$
$614$	−60.1538	+	43.7043i	−2.42761	+	1.76376i
$615$	−0.288785	+	3.67086i	−0.0116449	+	0.148023i
$616$	−15.6165	+	58.3260i	−0.629205	+	2.35002i
$617$	−13.1667	+	25.8411i	−0.530072	+	1.04032i	0.458375	+	0.888759i	$0.348432\pi$
$617$	−13.1667	+	25.8411i	−0.530072	+	1.04032i	−0.988447	+	0.151566i	$0.951568\pi$
$618$	−0.0796251	+	0.0796251i	−0.00320299	+	0.00320299i
$619$	3.49027	+	10.7420i	0.140286	+	0.431756i	0.996375	−	0.0850732i	$-0.0271124\pi$
$619$	3.49027	+	10.7420i	0.140286	+	0.431756i	−0.856089	+	0.516829i	$0.827112\pi$
$620$	18.3111	−	1.44170i	0.735391	−	0.0579002i
$621$	5.70310	+	1.85305i	0.228857	+	0.0743603i
$622$	28.9134	+	56.7457i	1.15932	+	2.27530i
$623$	−3.16954	−	14.8975i	−0.126985	−	0.596857i
$624$		−	1.79128i		−	0.0717084i
$625$	23.7754	−	7.72846i	0.951017	−	0.309139i
$626$			40.4966i			1.61857i
$627$	−5.49957	−	0.871046i	−0.219632	−	0.0347862i
$628$	21.0575	−	10.7293i	0.840285	−	0.428146i
$629$	9.29458	−	28.6058i	0.370599	−	1.14059i
$630$	18.6039	+	38.9815i	0.741196	+	1.55306i
$631$	−4.67999	−	14.4035i	−0.186307	−	0.573395i	0.813661	−	0.581339i	$-0.197471\pi$
$631$	−4.67999	−	14.4035i	−0.186307	−	0.573395i	−0.999968	+	0.00794449i	$0.997471\pi$
$632$	40.0670	+	40.0670i	1.59378	+	1.59378i
$633$	1.48069	−	2.90602i	0.0588522	−	0.115504i
$634$	−40.2484	+	55.3972i	−1.59847	+	2.20010i
$635$	−25.3581	−	1.99491i	−1.00631	−	0.0791657i
$636$	1.22636	+	1.68794i	0.0486285	+	0.0669313i
$637$	−8.36595	+	10.3392i	−0.331471	+	0.409652i
$638$	16.3688	−	2.59256i	0.648047	−	0.102640i
$639$	6.76501	+	9.31123i	0.267620	+	0.368347i
$640$	−21.8329	−	35.6256i	−0.863023	−	1.40822i
$641$	−37.9323	−	27.5594i	−1.49823	−	1.08853i	−0.971078	−	0.238762i	$-0.923258\pi$
$641$	−37.9323	−	27.5594i	−1.49823	−	1.08853i	−0.527156	−	0.849768i	$-0.676742\pi$
$642$	3.38693	+	1.72573i	0.133671	+	0.0681090i
$643$	−16.5448	−	16.5448i	−0.652463	−	0.652463i	0.301122	−	0.953586i	$-0.402639\pi$
$643$	−16.5448	−	16.5448i	−0.652463	−	0.652463i	−0.953586	+	0.301122i	$0.902639\pi$
$644$	−33.2952	−	41.1000i	−1.31201	−	1.61957i
$645$	−0.117667	+	0.490185i	−0.00463311	+	0.0193010i
$646$	35.1265	−	108.108i	1.38203	−	4.25346i
$647$	3.81842	+	7.49408i	0.150118	+	0.294623i	0.953803	−	0.300431i	$-0.0971307\pi$
$647$	3.81842	+	7.49408i	0.150118	+	0.294623i	−0.803686	+	0.595054i	$0.797131\pi$
$648$	−6.97061	+	44.0107i	−0.273832	+	1.72890i
$649$	18.8939			0.741651
$650$	3.67015	+	23.1628i	0.143955	+	0.908521i
$651$	0.392326	+	1.02146i	0.0153765	+	0.0400342i
$652$	−69.5388	−	11.0139i	−2.72335	−	0.431336i
$653$	12.4766	+	24.4867i	0.488246	+	0.958237i	0.995347	+	0.0963509i	$0.0307171\pi$
$653$	12.4766	+	24.4867i	0.488246	+	0.958237i	−0.507101	+	0.861887i	$0.669283\pi$
$654$	1.21419	−	3.73688i	0.0474785	−	0.146124i
$655$	−8.93160	+	3.69992i	−0.348987	+	0.144568i
$656$	34.7498	−	11.2909i	1.35675	−	0.440836i
$657$	−1.66158	+	1.66158i	−0.0648243	+	0.0648243i
$658$	−57.7479	−	6.05840i	−2.25125	−	0.236181i
$659$	−26.2956	+	36.1928i	−1.02433	+	1.40987i	−0.115211	+	0.993341i	$0.536754\pi$
$659$	−26.2956	+	36.1928i	−1.02433	+	1.40987i	−0.909121	+	0.416531i	$0.863246\pi$
$660$	−5.41010	+	6.33483i	−0.210588	+	0.246583i
$661$	22.4661	+	30.9219i	0.873829	+	1.20272i	0.978092	+	0.208173i	$0.0667517\pi$
$661$	22.4661	+	30.9219i	0.873829	+	1.20272i	−0.104263	+	0.994550i	$0.533248\pi$
$662$	−1.52120	−	9.60448i	−0.0591231	−	0.373289i
$663$	0.461046	+	2.91093i	0.0179055	+	0.113051i
$664$	3.41161	−	2.47868i	0.132396	−	0.0961915i
$665$	36.1882	+	0.939551i	1.40332	+	0.0364342i
$666$	23.6086	+	17.1527i	0.914815	+	0.664652i
$667$	−3.37130	+	6.61655i	−0.130537	+	0.256194i
$668$	46.4883	+	46.4883i	1.79868	+	1.79868i
$669$	2.78795	−	0.905860i	0.107788	−	0.0350226i
$670$	−15.6211	+	25.4932i	−0.603497	+	0.984889i
$671$	22.5125	+	7.31475i	0.869085	+	0.282383i
$672$	−0.347141	+	0.385687i	−0.0133912	+	0.0148782i
$673$	1.58308	−	9.99517i	0.0610232	−	0.385285i	−0.938208	−	0.346073i	$-0.887515\pi$
$673$	1.58308	−	9.99517i	0.0610232	−	0.385285i	0.999231	−	0.0392126i	$-0.0124850\pi$
$674$			56.9110i			2.19213i
$675$	0.000392552		6.14015i	1.51093e−5		0.236335i
$676$	38.4442			1.47862
$677$	−3.02654	+	19.1088i	−0.116319	+	0.734412i	0.858731	+	0.512427i	$0.171254\pi$
$677$	−3.02654	+	19.1088i	−0.116319	+	0.734412i	−0.975050	+	0.221985i	$0.928746\pi$
$678$	−3.65911	+	1.86441i	−0.140527	+	0.0716023i
$679$	8.01730	−	0.421704i	0.307676	−	0.0161835i
$680$	−56.4969	−	66.1451i	−2.16656	−	2.53655i
$681$	0.328488	+	1.01098i	0.0125877	+	0.0387409i
$682$	15.4609	−	15.4609i	0.592028	−	0.592028i
$683$	39.0464	+	19.8951i	1.49407	+	0.761266i	0.994473	−	0.104992i	$-0.0334818\pi$
$683$	39.0464	+	19.8951i	1.49407	+	0.761266i	0.499596	+	0.866258i	$0.333482\pi$
$684$	59.9412	+	43.5499i	2.29191	+	1.66517i
$685$	8.90109	+	37.0705i	0.340093	+	1.41639i
$686$	45.1527	−	7.17799i	1.72394	−	0.274057i
$687$	−0.139028	−	0.877789i	−0.00530425	−	0.0334897i
$688$	4.94065	−	0.782522i	0.188360	−	0.0298334i
$689$	3.80015	−	2.76097i	0.144774	−	0.105185i
$690$	−1.29725	−	5.40268i	−0.0493855	−	0.205676i
$691$	26.4300	−	36.3778i	1.00544	−	1.38388i	0.0835193	−	0.996506i	$-0.473384\pi$
$691$	26.4300	−	36.3778i	1.00544	−	1.38388i	0.921925	−	0.387369i	$-0.126616\pi$
$692$	−39.0213	−	19.8823i	−1.48337	−	0.755813i
$693$	31.5593	+	14.0439i	1.19884	+	0.533483i
$694$	−55.4735	+	18.0244i	−2.10575	+	0.684198i
$695$	−7.52677	+	6.42889i	−0.285507	+	0.243862i
$696$	1.54123	+	0.500777i	0.0584202	+	0.0189819i
$697$	−53.5644	+	27.2924i	−2.02890	+	1.03377i
$698$	24.2891	+	3.84701i	0.919355	+	0.145612i
$699$	2.48220			0.0938856
$700$	29.4863	−	45.4302i	1.11448	−	1.71710i
$701$	−27.9833			−1.05692			−0.528458	−	0.848960i	$-0.677230\pi$
$701$	−27.9833			−1.05692			−0.528458	+	0.848960i	$0.677230\pi$
$702$	−5.68899	−	0.901048i	−0.214717	−	0.0340079i
$703$	21.7917	−	11.1034i	0.821888	−	0.418773i
$704$	−28.5437	−	9.27441i	−1.07578	−	0.349542i
$705$	−3.49391	−	2.14092i	−0.131588	−	0.0806315i
$706$	45.1839	−	14.6811i	1.70052	−	0.552532i
$707$	21.8814	+	9.73723i	0.822935	+	0.366206i
$708$	3.21829	+	1.63980i	0.120951	+	0.0616274i
$709$	19.1433	−	26.3484i	0.718940	−	0.989537i	−0.280618	−	0.959820i	$-0.590539\pi$
$709$	19.1433	−	26.3484i	0.718940	−	0.989537i	0.999558	−	0.0297170i	$-0.00946061\pi$
$710$	8.21998	−	19.8466i	0.308490	−	0.744829i
$711$	26.2255	−	19.0539i	0.983532	−	0.714578i
$712$	−29.3941	+	4.65557i	−1.10159	+	0.174475i
$713$	1.53263	+	9.67661i	0.0573973	+	0.362392i
$714$	5.51630	−	8.49790i	0.206442	−	0.318026i
$715$	14.2619	+	12.1800i	0.533365	+	0.455507i
$716$	6.99737	+	5.08389i	0.261504	+	0.189994i
$717$	−2.40173	−	1.22374i	−0.0896944	−	0.0457016i
$718$	−4.13799	+	4.13799i	−0.154429	+	0.154429i
$719$	13.1048	+	40.3325i	0.488727	+	1.50415i	0.826509	+	0.562923i	$0.190323\pi$
$719$	13.1048	+	40.3325i	0.488727	+	1.50415i	−0.337782	+	0.941224i	$0.609677\pi$
$720$	27.9440	−	11.5758i	1.04141	−	0.431406i
$721$	−0.0307534	−	0.584674i	−0.00114531	−	0.0217744i
$722$	40.5643	−	20.6685i	1.50965	−	0.769203i
$723$	0.796607	−	5.02958i	0.0296261	−	0.187052i
$724$	−94.2433			−3.50252
$725$	−7.51017	−	1.18900i	−0.278921	−	0.0441584i
$726$			4.31930i			0.160304i
$727$	−0.482868	+	3.04871i	−0.0179086	+	0.113070i	−0.995023	−	0.0996428i	$-0.968230\pi$
$727$	−0.482868	+	3.04871i	−0.0179086	+	0.113070i	0.977115	+	0.212713i	$0.0682300\pi$
$728$	19.3156	+	17.3852i	0.715885	+	0.644339i
$729$	23.5220	+	7.64277i	0.871187	+	0.283066i
$730$	4.26467	+	1.02371i	0.157843	+	0.0378893i
$731$	−7.82743	+	2.54329i	−0.289508	+	0.0940668i
$732$	3.19981	+	3.19981i	0.118268	+	0.118268i
$733$	−7.32988	+	14.3857i	−0.270735	+	0.531348i	−0.985844	−	0.167665i	$-0.946377\pi$
$733$	−7.32988	+	14.3857i	−0.270735	+	0.531348i	0.715109	+	0.699013i	$0.246377\pi$
$734$	0.856213	+	0.622075i	0.0316034	+	0.0229612i
$735$	3.09398	+	0.915087i	0.114123	+	0.0337535i
$736$	−3.75877	+	2.73091i	−0.138550	+	0.100663i
$737$	3.74047	+	23.6164i	0.137782	+	0.869922i
$738$	−9.12417	−	57.6077i	−0.335865	−	2.12057i
$739$	−2.80874	−	3.86590i	−0.103321	−	0.142209i	0.754226	−	0.656615i	$-0.228012\pi$
$739$	−2.80874	−	3.86590i	−0.103321	−	0.142209i	−0.857547	+	0.514406i	$0.828012\pi$
$740$	2.86976	−	36.4786i	0.105494	−	1.34098i
$741$	−1.40862	+	1.93879i	−0.0517468	+	0.0712233i
$742$	−16.0591	−	1.68478i	−0.589549	−	0.0618503i
$743$	4.12484	−	4.12484i	0.151326	−	0.151326i	−0.627384	−	0.778710i	$-0.715874\pi$
$743$	4.12484	−	4.12484i	0.151326	−	0.151326i	0.778710	+	0.627384i	$0.215874\pi$
$744$	2.03339	−	0.660689i	0.0745478	−	0.0242220i
$745$	0.933071	+	11.8509i	0.0341851	+	0.434185i
$746$	−18.6650	+	57.4449i	−0.683374	+	2.10321i
$747$	−1.09525	−	2.14955i	−0.0400731	−	0.0786479i
$748$	−134.334	−	21.2764i	−4.91172	−	0.777940i
$749$	−18.4499	+	7.08629i	−0.674144	+	0.258927i
$750$	4.85061	−	2.97309i	0.177119	−	0.108562i
$751$	−9.19974			−0.335703			−0.167852	−	0.985812i	$-0.553683\pi$
$751$	−9.19974			−0.335703			−0.167852	+	0.985812i	$0.553683\pi$
$752$	−6.36075	+	40.1602i	−0.231953	+	1.46449i
$753$	2.32012	+	4.55350i	0.0845500	+	0.165939i
$754$	2.20416	−	6.78372i	0.0802709	−	0.247049i
$755$	−27.8868	+	2.19564i	−1.01490	+	0.0799074i
$756$	8.37327	+	10.3361i	0.304533	+	0.375920i
$757$	9.03988	+	9.03988i	0.328560	+	0.328560i	0.852039	−	0.523479i	$-0.175366\pi$
$757$	9.03988	+	9.03988i	0.328560	+	0.328560i	−0.523479	+	0.852039i	$0.675366\pi$
$758$	−38.4593	−	19.5960i	−1.39690	−	0.711758i
$759$	−3.59486	−	2.61182i	−0.130485	−	0.0948031i
$760$	5.54744	−	70.5158i	0.201227	−	2.55788i
$761$	−23.0673	−	31.7494i	−0.836190	−	1.15092i	−0.986739	−	0.162314i	$-0.948104\pi$
$761$	−23.0673	−	31.7494i	−0.836190	−	1.15092i	0.150550	−	0.988602i	$-0.451896\pi$
$762$	−5.71732	+	0.905535i	−0.207117	+	0.0328041i
$763$	10.2180	+	17.6903i	0.369916	+	0.640431i
$764$	31.5284	+	43.3951i	1.14066	+	1.56998i
$765$	−42.4312	+	26.0037i	−1.53410	+	0.940167i
$766$	−48.4421	+	66.6748i	−1.75028	+	2.40906i
$767$	3.69176	−	7.24549i	0.133302	−	0.261619i
$768$	−4.74177	−	4.74177i	−0.171104	−	0.171104i
$769$	4.04237	+	12.4411i	0.145771	+	0.448639i	0.997109	−	0.0759792i	$-0.0242083\pi$
$769$	4.04237	+	12.4411i	0.145771	+	0.448639i	−0.851338	+	0.524618i	$0.824208\pi$
$770$	−8.42961	−	63.9192i	−0.303782	−	2.30349i
$771$	1.20050	−	3.69475i	0.0432348	−	0.133063i
$772$	36.4299	−	18.5619i	1.31114	−	0.668059i
$773$	12.3295	+	1.95280i	0.443461	+	0.0702372i	0.374172	−	0.927359i	$-0.377927\pi$
$773$	12.3295	+	1.95280i	0.443461	+	0.0702372i	0.0692887	+	0.997597i	$0.477927\pi$
$774$		−	7.98507i		−	0.287017i
$775$	−8.93810	+	4.55491i	−0.321066	+	0.163617i
$776$		−	15.6870i		−	0.563132i
$777$	2.13211	−	0.453620i	0.0764892	−	0.0162735i
$778$	17.0393	+	33.4416i	0.610890	+	1.19894i
$779$	−46.4905	−	15.1057i	−1.66569	−	0.541217i
$780$	1.37219	+	3.31247i	0.0491324	+	0.118605i
$781$	−5.30873	−	16.3386i	−0.189961	−	0.584641i
$782$	64.1436	−	64.1436i	2.29377	−	2.29377i
$783$	0.847835	−	1.66397i	0.0302991	−	0.0594654i
$784$	−3.35873	−	31.8393i	−0.119955	−	1.13712i
$785$	−8.38254	+	9.81533i	−0.299186	+	0.350324i
$786$	−1.77989	+	1.29317i	−0.0634865	+	0.0461257i
$787$	−45.4672	+	7.20130i	−1.62073	+	0.256699i	−0.899798	−	0.436306i	$-0.856286\pi$
$787$	−45.4672	+	7.20130i	−1.62073	+	0.256699i	−0.720933	+	0.693005i	$0.756286\pi$
$788$	−1.43026	+	0.226531i	−0.0509510	+	0.00806984i
$789$	−3.19491	+	2.32124i	−0.113742	+	0.0826384i
$790$	−55.8987	−	23.1519i	−1.98879	−	0.823708i
$791$	5.52243	−	20.6257i	0.196355	−	0.733367i
$792$	30.6422	−	60.1387i	1.08882	−	2.13694i
$793$	7.20389	−	7.20389i	0.255818	−	0.255818i
$794$	−18.4726	−	56.8528i	−0.655568	−	2.01763i
$795$	−0.971621	−	0.595368i	−0.0344599	−	0.0211155i
$796$	−37.0519	−	12.0389i	−1.31327	−	0.426708i
$797$	11.5819	+	22.7307i	0.410251	+	0.805164i	0.999997	−	0.00242539i	$-0.000772028\pi$
$797$	11.5819	+	22.7307i	0.410251	+	0.805164i	−0.589746	+	0.807589i	$0.700772\pi$
$798$	8.05778	−	1.71434i	0.285242	−	0.0606871i
$799$		−	66.8997i		−	2.36674i
$800$	−3.84894	−	2.79604i	−0.136081	−	0.0988551i
$801$			17.0257i			0.601573i
$802$	76.5760	+	12.1284i	2.70399	+	0.428270i
$803$	3.12518	−	1.59236i	0.110285	−	0.0561932i
$804$	−1.41253	+	4.34733i	−0.0498162	+	0.153318i
$805$	25.3910	+	13.7789i	0.894916	+	0.485642i
$806$	−2.90802	−	8.94996i	−0.102431	−	0.315249i
$807$	3.99664	+	3.99664i	0.140689	+	0.140689i
$808$	21.2456	−	41.6967i	0.747416	−	1.46689i
$809$	19.6228	−	27.0085i	0.689900	−	0.949567i	−0.310099	−	0.950704i	$-0.600362\pi$
$809$	19.6228	−	27.0085i	0.689900	−	0.949567i	0.999999	+	0.00113775i	$0.000362157\pi$
$810$	−11.1086	−	46.2643i	−0.390318	−	1.62556i
$811$	0.750387	+	1.03282i	0.0263497	+	0.0362672i	0.821989	−	0.569504i	$-0.192865\pi$
$811$	0.750387	+	1.03282i	0.0263497	+	0.0362672i	−0.795639	+	0.605771i	$0.792865\pi$
$812$	−14.2643	+	8.23911i	−0.500578	+	0.289136i
$813$	2.14649	−	0.339970i	0.0752806	−	0.0119233i
$814$	−25.6030	−	35.2395i	−0.897384	−	1.23514i
$815$	37.3902	−	8.97786i	1.30972	−	0.314481i
$816$	−5.73967	−	4.17011i	−0.200929	−	0.145983i
$817$	−5.96288	−	3.03824i	−0.208615	−	0.106295i
$818$	−38.1070	−	38.1070i	−1.33238	−	1.33238i
$819$	11.5521	−	9.35835i	0.403663	−	0.327007i
$820$	−55.6109	+	47.4992i	−1.94202	+	1.65875i
$821$	−6.76858	+	20.8315i	−0.236225	+	0.727026i	0.760732	+	0.649067i	$0.224840\pi$
$821$	−6.76858	+	20.8315i	−0.236225	+	0.727026i	−0.996957	+	0.0779591i	$0.975160\pi$
$822$	3.93879	+	7.73030i	0.137381	+	0.269625i
$823$	−4.08930	+	25.8188i	−0.142544	+	0.899987i	0.807951	+	0.589249i	$0.200576\pi$
$823$	−4.08930	+	25.8188i	−0.142544	+	0.899987i	−0.950495	+	0.310738i	$0.899424\pi$
$824$	−1.14400			−0.0398532
$825$	1.40571	−	4.32728i	0.0489406	−	0.150657i
$826$	−26.0953	+	10.0228i	−0.907971	+	0.348736i
$827$	−12.3593	−	1.95753i	−0.429777	−	0.0680699i	−0.0622011	−	0.998064i	$-0.519812\pi$
$827$	−12.3593	−	1.95753i	−0.429777	−	0.0680699i	−0.367575	+	0.929994i	$0.619812\pi$
$828$	26.8430	+	52.6823i	0.932858	+	1.83084i
$829$	−7.82434	+	24.0808i	−0.271750	+	0.836362i	0.718310	+	0.695723i	$0.244916\pi$
$829$	−7.82434	+	24.0808i	−0.271750	+	0.836362i	−0.990061	+	0.140639i	$0.955084\pi$
$830$	−2.35258	+	3.83933i	−0.0816592	+	0.133265i
$831$	−2.29476	+	0.745612i	−0.0796042	+	0.0258650i
$832$	−9.13385	+	9.13385i	−0.316659	+	0.316659i
$833$	13.6530	+	50.8761i	0.473050	+	1.76275i
$834$	−1.32407	+	1.82242i	−0.0458487	+	0.0631053i
$835$	−33.1743	−	13.7400i	−1.14804	−	0.475492i
$836$	−65.0048	−	89.4715i	−2.24824	−	3.09444i
$837$	−0.385434	−	2.43353i	−0.0133225	−	0.0841152i
$838$	13.5925	+	85.8198i	0.469546	+	2.96460i
$839$	45.7909	−	33.2690i	1.58088	−	1.14857i	0.665197	−	0.746668i	$-0.268348\pi$
$839$	45.7909	−	33.2690i	1.58088	−	1.14857i	0.915681	−	0.401907i	$-0.131652\pi$
$840$	2.10311	−	5.94321i	0.0725642	−	0.205060i
$841$	−21.5905	−	15.6864i	−0.744501	−	0.540911i
$842$	12.2638	−	24.0691i	0.422638	−	0.829475i
$843$	2.78170	+	2.78170i	0.0958068	+	0.0958068i
$844$	61.6088	−	20.0179i	2.12066	−	0.689045i
$845$	−19.3983	+	8.03575i	−0.667321	+	0.276438i
$846$	61.7300	+	20.0573i	2.12232	+	0.689584i
$847$	−16.6920	−	15.0238i	−0.573545	−	0.516224i
$848$	−1.76886	+	11.1681i	−0.0607429	+	0.383516i
$849$			2.15973i			0.0741217i
$850$	82.7634	+	42.1634i	2.83876	+	1.44619i
$851$	19.5176			0.669053
$852$	0.513763	−	3.24377i	0.0176012	−	0.111130i
$853$	36.9947	−	18.8497i	1.26667	−	0.645402i	0.314007	−	0.949421i	$-0.398329\pi$
$853$	36.9947	−	18.8497i	1.26667	−	0.645402i	0.952666	+	0.304019i	$0.0983286\pi$
$854$	−34.9734	+	1.83957i	−1.19676	+	0.0629488i
$855$	−39.3482	−	9.44534i	−1.34568	−	0.323024i
$856$	11.9335	+	36.7276i	0.407880	+	1.25532i
$857$	4.42430	−	4.42430i	0.151131	−	0.151131i	−0.627492	−	0.778623i	$-0.715918\pi$
$857$	4.42430	−	4.42430i	0.151131	−	0.151131i	0.778623	+	0.627492i	$0.215918\pi$
$858$	3.80292	+	1.93768i	0.129829	+	0.0661514i
$859$	0.0963348	+	0.0699913i	0.00328690	+	0.00238807i	0.589427	−	0.807821i	$-0.299353\pi$
$859$	0.0963348	+	0.0699913i	0.00328690	+	0.00238807i	−0.586141	+	0.810209i	$0.699353\pi$
$860$	−8.53692	+	5.23180i	−0.291106	+	0.178403i
$861$	−3.65441	−	2.37221i	−0.124542	−	0.0808447i
$862$	5.27068	+	33.2778i	0.179520	+	1.13345i
$863$	31.3863	−	4.97111i	1.06840	−	0.169218i	0.402623	−	0.915366i	$-0.368099\pi$
$863$	31.3863	−	4.97111i	1.06840	−	0.169218i	0.665781	+	0.746147i	$0.268099\pi$
$864$	0.945280	−	0.686786i	0.0321591	−	0.0233649i
$865$	23.8453	+	1.87590i	0.810765	+	0.0637825i
$866$	−18.8217	+	25.9059i	−0.639589	+	0.880318i
$867$	7.27832	+	3.70849i	0.247185	+	0.125947i
$868$	−8.83582	+	19.8558i	−0.299907	+	0.673949i
$869$	−46.0183	+	14.9523i	−1.56107	+	0.507221i
$870$	−1.72504	+	0.135819i	−0.0584843	+	0.00460470i
$871$	9.78736	+	3.18011i	0.331632	+	0.107754i
$872$	35.5669	−	18.1222i	1.20445	−	0.613696i
$873$	−8.86391	−	1.40391i	−0.299998	−	0.0475150i
$874$	73.7616			2.49502
$875$	−5.38226	+	29.0866i	−0.181954	+	0.983307i
$876$	0.670528			0.0226550
$877$	−28.9141	−	4.57954i	−0.976358	−	0.154640i	−0.352189	−	0.935929i	$-0.614563\pi$
$877$	−28.9141	−	4.57954i	−0.976358	−	0.154640i	−0.624169	+	0.781289i	$0.714563\pi$
$878$	−2.49536	+	1.27145i	−0.0842145	+	0.0429094i
$879$	3.87861	+	1.26024i	0.130822	+	0.0425068i
$880$	−45.0087	+	3.54371i	−1.51724	+	0.119458i
$881$	4.74906	−	1.54306i	0.160000	−	0.0519871i	−0.227922	−	0.973679i	$-0.573193\pi$
$881$	4.74906	−	1.54306i	0.160000	−	0.0519871i	0.387922	+	0.921692i	$0.373193\pi$
$882$	−51.0380	−	2.65525i	−1.71854	−	0.0894069i
$883$	−7.05653	−	3.59548i	−0.237471	−	0.120998i	0.331206	−	0.943559i	$-0.392545\pi$
$883$	−7.05653	−	3.59548i	−0.237471	−	0.120998i	−0.568677	+	0.822561i	$0.692545\pi$
$884$	−34.4071	+	47.3573i	−1.15724	+	1.59280i
$885$	−1.96665	−	0.154715i	−0.0661081	−	0.00520069i
$886$	39.4014	−	28.6268i	1.32371	−	0.961735i
$887$	17.9684	−	2.84592i	0.603321	−	0.0955566i	0.152701	−	0.988272i	$-0.451203\pi$
$887$	17.9684	−	2.84592i	0.603321	−	0.0955566i	0.450620	+	0.892716i	$0.351203\pi$
$888$	−0.666299	−	4.20685i	−0.0223595	−	0.141173i
$889$	16.3871	−	25.2445i	0.549606	−	0.846672i
$890$	27.0942	−	16.6046i	0.908201	−	0.556586i
$891$	−30.7836	−	22.3656i	−1.03129	−	0.749276i
$892$	51.8773	+	26.4328i	1.73698	+	0.885037i
$893$	38.4655	−	38.4655i	1.28720	−	1.28720i
$894$	0.835975	+	2.57287i	0.0279592	+	0.0860495i
$895$	−4.59340	−	1.10262i	−0.153540	−	0.0368566i
$896$	49.3706	−	2.59685i	1.64936	−	0.0867548i
$897$	−1.70400	+	0.868233i	−0.0568950	+	0.0289895i
$898$	−5.59602	+	35.3319i	−0.186742	+	1.17904i
$899$	3.05115			0.101762
$900$	−42.8071	+	42.8126i	−1.42690	+	1.42709i
$901$		−	18.6042i		−	0.619794i
$902$	−13.6192	+	85.9884i	−0.453470	+	2.86310i
$903$	−0.443341	−	0.399033i	−0.0147535	−	0.0132790i
$904$	−39.6792	−	12.8925i	−1.31971	−	0.428800i
$905$	47.5535	−	19.6991i	1.58073	−	0.654819i
$906$	−6.05428	+	1.96716i	−0.201140	+	0.0653544i
$907$	24.8734	+	24.8734i	0.825908	+	0.825908i	0.986948	−	0.161040i	$-0.0514849\pi$
$907$	24.8734	+	24.8734i	0.825908	+	0.825908i	−0.161040	+	0.986948i	$0.551485\pi$
$908$	−9.58521	+	18.8120i	−0.318096	+	0.624299i
$909$	−21.6592	−	15.7364i	−0.718392	−	0.521942i
$910$	−26.1590	−	9.25683i	−0.867162	−	0.306861i
$911$	−27.2719	+	19.8142i	−0.903558	+	0.656473i	−0.939377	−	0.342885i	$-0.888596\pi$
$911$	−27.2719	+	19.8142i	−0.903558	+	0.656473i	0.0358197	+	0.999358i	$0.488596\pi$
$912$	−0.902452	−	5.69786i	−0.0298832	−	0.188675i
$913$	0.563324	+	3.55669i	0.0186433	+	0.117709i
$914$	−9.07642	−	12.4926i	−0.300221	−	0.413219i
$915$	−2.28340	−	0.945731i	−0.0754870	−	0.0312649i
$916$	10.3755	−	14.2806i	0.342815	−	0.471844i
$917$	1.19352	−	11.3764i	0.0394134	−	0.375683i
$918$	−16.1312	+	16.1312i	−0.532410	+	0.532410i
$919$	−13.9765	+	4.54122i	−0.461041	+	0.149801i	−0.530323	−	0.847796i	$-0.677929\pi$
$919$	−13.9765	+	4.54122i	−0.461041	+	0.149801i	0.0692820	+	0.997597i	$0.477929\pi$
$920$	29.4920	−	48.1301i	0.972323	−	1.58680i
$921$	1.91856	−	5.90473i	0.0632188	−	0.194568i
$922$	6.02968	+	11.8339i	0.198577	+	0.389729i
$923$	−7.30287	−	1.15666i	−0.240377	−	0.0380719i
$924$	−3.53416	−	9.20156i	−0.116265	−	0.302709i
$925$	6.17687	+	19.0063i	0.203094	+	0.624923i
$926$	−60.9128			−2.00172
$927$	−0.102382	+	0.646414i	−0.00336266	+	0.0212310i
$928$	0.656894	+	1.28923i	0.0215636	+	0.0423210i
$929$	−4.05750	+	12.4877i	−0.133122	+	0.409708i	−0.995293	−	0.0969092i	$-0.969104\pi$
$929$	−4.05750	+	12.4877i	−0.133122	+	0.409708i	0.862171	+	0.506617i	$0.169104\pi$
$930$	−1.73591	+	1.48270i	−0.0569228	+	0.0486198i
$931$	−21.4023	+	37.1025i	−0.701431	+	1.21599i
$932$	34.8611	+	34.8611i	1.14191	+	1.14191i
$933$	−4.73829	−	2.41428i	−0.155125	−	0.0790399i
$934$	−17.7883	−	12.9240i	−0.582051	−	0.422885i
$935$	72.2296	−	17.3432i	2.36216	−	0.567184i
$936$	−17.0749	−	23.5015i	−0.558109	−	0.768171i
$937$	−12.5937	+	1.99465i	−0.411418	+	0.0651622i	−0.358713	−	0.933448i	$-0.616784\pi$
$937$	−12.5937	+	1.99465i	−0.411418	+	0.0651622i	−0.0527051	+	0.998610i	$0.516784\pi$
$938$	−17.6941	−	30.6335i	−0.577732	−	1.00022i
$939$	−1.98758	−	2.73567i	−0.0648623	−	0.0892753i
$940$	−19.0020	−	79.1377i	−0.619776	−	2.58119i
$941$	22.2067	−	30.5649i	0.723917	−	0.996386i	−0.275468	−	0.961310i	$-0.588833\pi$
$941$	22.2067	−	30.5649i	0.723917	−	0.996386i	0.999385	−	0.0350759i	$-0.0111673\pi$
$942$	−1.33355	+	2.61724i	−0.0434495	+	0.0852744i
$943$	−27.5841	−	27.5841i	−0.898261	−	0.898261i
$944$	6.04905	+	18.6171i	0.196880	+	0.605933i
$945$	−6.38549	−	3.46520i	−0.207720	−	0.112723i
$946$	−3.68315	+	11.3356i	−0.119750	+	0.368552i
$947$	14.2973	−	7.28482i	0.464599	−	0.236725i	−0.205990	−	0.978554i	$-0.566042\pi$
$947$	14.2973	−	7.28482i	0.464599	−	0.236725i	0.670589	+	0.741829i	$0.266042\pi$
$948$	−9.13622	−	1.44703i	−0.296731	−	0.0469975i
$949$		−	1.50959i		−	0.0490034i
$950$	23.3439	+	71.8295i	0.757376	+	2.33046i
$951$		−	5.71766i		−	0.185408i
$952$	100.673	−	21.4189i	3.26284	−	0.694190i
$953$	10.1160	+	19.8538i	0.327691	+	0.643129i	0.994802	−	0.101829i	$-0.0324695\pi$
$953$	10.1160	+	19.8538i	0.327691	+	0.643129i	−0.667111	+	0.744958i	$0.732470\pi$
$954$	17.1665	+	5.57774i	0.555786	+	0.180586i
$955$	−24.9793	−	15.3062i	−0.808310	−	0.495297i
$956$	−16.5442	−	50.9177i	−0.535076	−	1.64680i
$957$	−0.978520	+	0.978520i	−0.0316311	+	0.0316311i
$958$	−14.8444	+	29.1338i	−0.479602	+	0.941272i
$959$	−43.5743	−	11.6668i	−1.40709	−	0.376740i
$960$	2.89514	+	1.19910i	0.0934402	+	0.0387007i
$961$	−21.8229	+	15.8552i	−0.703963	+	0.511459i
$962$	−18.5164	+	2.93271i	−0.596993	+	0.0945544i
$963$	21.8208	−	3.45608i	0.703166	−	0.111370i
$964$	81.8253	−	59.4496i	2.63542	−	1.91474i
$965$	−14.5020	+	16.9807i	−0.466835	+	0.546629i
$966$	6.35054	+	1.70032i	0.204325	+	0.0547070i
$967$	−18.0398	+	35.4051i	−0.580121	+	1.13855i	0.395372	+	0.918521i	$0.370616\pi$
$967$	−18.0398	+	35.4051i	−0.580121	+	1.13855i	−0.975493	+	0.220030i	$0.929384\pi$
$968$	−31.0284	+	31.0284i	−0.997291	+	0.997291i
$969$	2.93307	+	9.02707i	0.0942239	+	0.289991i
$970$	6.41053	+	15.4750i	0.205830	+	0.496872i
$971$	27.1538	+	8.82281i	0.871407	+	0.283137i	0.710385	−	0.703813i	$-0.248521\pi$
$971$	27.1538	+	8.82281i	0.871407	+	0.283137i	0.161022	+	0.986951i	$0.448521\pi$
$972$	−10.1500	−	19.9206i	−0.325562	−	0.638952i
$973$	−2.43729	−	11.4558i	−0.0781361	−	0.367257i
$974$		−	42.8176i		−	1.37197i
$975$	−1.38477	−	1.38459i	−0.0443481	−	0.0443424i
$976$			24.5245i			0.785010i
$977$	48.3318	+	7.65500i	1.54627	+	0.244905i	0.870486	−	0.492194i	$-0.163805\pi$
$977$	48.3318	+	7.65500i	1.54627	+	0.244905i	0.675785	+	0.737099i	$0.263805\pi$
$978$	7.79698	−	3.97276i	0.249320	−	0.127035i
$979$	7.85318	−	24.1696i	0.250989	−	0.772464i
$980$	30.6013	+	56.3050i	0.977522	+	1.79860i
$981$	−7.05686	−	21.7188i	−0.225308	−	0.693427i
$982$	2.56484	+	2.56484i	0.0818472	+	0.0818472i
$983$	−13.5238	+	26.5420i	−0.431344	+	0.846559i	0.568374	+	0.822771i	$0.307573\pi$
$983$	−13.5238	+	26.5420i	−0.431344	+	0.846559i	−0.999717	+	0.0237886i	$0.992427\pi$
$984$	−5.00384	+	6.88719i	−0.159517	+	0.219556i
$985$	0.674334	−	0.413262i	0.0214861	−	0.0131676i
$986$	−16.6053	−	22.8552i	−0.528821	−	0.727859i
$987$	4.19840	−	2.42502i	0.133637	−	0.0771891i
$988$	−47.0123	+	7.44602i	−1.49566	+	0.236890i
$989$	−3.13913	−	4.32065i	−0.0998187	−	0.137389i
$990$	−5.65223	+	71.8477i	−0.179640	+	2.28347i
$991$	29.6993	+	21.5778i	0.943431	+	0.685443i	0.949244	−	0.314540i	$-0.101850\pi$
$991$	29.6993	+	21.5778i	0.943431	+	0.685443i	−0.00581317	+	0.999983i	$0.501850\pi$
$992$	1.70091	+	0.866659i	0.0540041	+	0.0275165i
$993$	0.574152	+	0.574152i	0.0182202	+	0.0182202i
$994$	15.9994	+	19.7499i	0.507469	+	0.626428i
$995$	21.2122	−	1.67012i	0.672471	−	0.0529462i
$996$	−0.212731	+	0.654717i	−0.00674062	+	0.0207455i
$997$	−19.4930	−	38.2572i	−0.617350	−	1.21162i	−0.962042	−	0.272902i	$-0.912017\pi$
$997$	−19.4930	−	38.2572i	−0.617350	−	1.21162i	0.344692	−	0.938716i	$-0.387983\pi$
$998$	−7.23893	+	45.7048i	−0.229144	+	1.44676i
$999$	−4.90840			−0.155295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.s.a.27.2	yes	144
5.2	odd	4		875.2.s.a.468.17		144
5.3	odd	4		875.2.s.b.468.2		144
5.4	even	2		875.2.s.c.657.17		144
7.6	odd	2	inner	175.2.s.a.27.1	yes	144
25.9	even	10		875.2.s.a.832.18		144
25.12	odd	20		875.2.s.c.293.18		144
25.13	odd	20	inner	175.2.s.a.13.1	✓	144
25.16	even	5		875.2.s.b.832.1		144
35.13	even	4		875.2.s.b.468.1		144
35.27	even	4		875.2.s.a.468.18		144
35.34	odd	2		875.2.s.c.657.18		144
175.13	even	20	inner	175.2.s.a.13.2	yes	144
175.34	odd	10		875.2.s.a.832.17		144
175.41	odd	10		875.2.s.b.832.2		144
175.62	even	20		875.2.s.c.293.17		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.s.a.13.1	✓	144	25.13	odd	20	inner
175.2.s.a.13.2	yes	144	175.13	even	20	inner
175.2.s.a.27.1	yes	144	7.6	odd	2	inner
175.2.s.a.27.2	yes	144	1.1	even	1	trivial
875.2.s.a.468.17		144	5.2	odd	4
875.2.s.a.468.18		144	35.27	even	4
875.2.s.a.832.17		144	175.34	odd	10
875.2.s.a.832.18		144	25.9	even	10
875.2.s.b.468.1		144	35.13	even	4
875.2.s.b.468.2		144	5.3	odd	4
875.2.s.b.832.1		144	25.16	even	5
875.2.s.b.832.2		144	175.41	odd	10
875.2.s.c.293.17		144	175.62	even	20
875.2.s.c.293.18		144	25.12	odd	20
875.2.s.c.657.17		144	5.4	even	2
875.2.s.c.657.18		144	35.34	odd	2

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43824 - 0.386179i) q^{2} +(0.183665 - 0.0935818i) q^{3} +(3.89376 + 1.26516i) q^{4} +(-2.22917 + 0.175511i) q^{5} +(-0.483957 + 0.157247i) q^{6} +(1.07566 - 2.41722i) q^{7} +(-4.60620 - 2.34698i) q^{8} +(-1.73838 + 2.39268i) q^{9} +O(q^{10})\)	\(q+(-2.43824 - 0.386179i) q^{2} +(0.183665 - 0.0935818i) q^{3} +(3.89376 + 1.26516i) q^{4} +(-2.22917 + 0.175511i) q^{5} +(-0.483957 + 0.157247i) q^{6} +(1.07566 - 2.41722i) q^{7} +(-4.60620 - 2.34698i) q^{8} +(-1.73838 + 2.39268i) q^{9} +(5.50302 + 0.432920i) q^{10} +(3.57144 - 2.59480i) q^{11} +(0.833541 - 0.132020i) q^{12} +(-0.297223 - 1.87659i) q^{13} +(-3.55620 + 5.47836i) q^{14} +(-0.392995 + 0.240845i) q^{15} +(3.70020 + 2.68836i) q^{16} +(-6.70498 - 3.41636i) q^{17} +(5.16259 - 5.16259i) q^{18} +(-1.89087 - 5.81950i) q^{19} +(-8.90190 - 2.13686i) q^{20} +(-0.0286466 - 0.544620i) q^{21} +(-9.71007 + 4.94753i) q^{22} +(0.763884 - 4.82298i) q^{23} -1.06563 q^{24} +(4.93839 - 0.782488i) q^{25} +4.69036i q^{26} +(-0.192106 + 1.21291i) q^{27} +(7.24654 - 8.05118i) q^{28} +(-1.44631 - 0.469935i) q^{29} +(1.05122 - 0.435471i) q^{30} +(-1.90816 + 0.619999i) q^{31} +(-0.672788 - 0.672788i) q^{32} +(0.413120 - 0.810794i) q^{33} +(15.0290 + 10.9192i) q^{34} +(-1.97359 + 5.57718i) q^{35} +(-9.79595 + 7.11717i) q^{36} +(0.625263 + 3.94776i) q^{37} +(2.36302 + 14.9195i) q^{38} +(-0.230204 - 0.316849i) q^{39} +(10.6799 + 4.42337i) q^{40} +(4.69566 - 6.46303i) q^{41} +(-0.140474 + 1.33898i) q^{42} +(0.773359 - 0.773359i) q^{43} +(17.1891 - 5.58509i) q^{44} +(3.45520 - 5.63878i) q^{45} +(-3.72506 + 11.4646i) q^{46} +(4.03603 + 7.92115i) q^{47} +(0.931177 + 0.147484i) q^{48} +(-4.68590 - 5.20023i) q^{49} +(-12.3432 + 0.000789122i) q^{50} -1.55118 q^{51} +(1.21687 - 7.68303i) q^{52} +(1.12238 + 2.20280i) q^{53} +(0.936802 - 2.88318i) q^{54} +(-7.50592 + 6.41107i) q^{55} +(-10.6279 + 8.60964i) q^{56} +(-0.891884 - 0.891884i) q^{57} +(3.34497 + 1.70435i) q^{58} +(3.46254 + 2.51568i) q^{59} +(-1.83493 + 0.440591i) q^{60} +(3.15174 + 4.33800i) q^{61} +(4.89198 - 0.774813i) q^{62} +(3.91371 + 6.77576i) q^{63} +(-3.99611 - 5.50017i) q^{64} +(0.991924 + 4.13108i) q^{65} +(-1.32040 + 1.81737i) q^{66} +(-2.45898 + 4.82603i) q^{67} +(-21.7854 - 21.7854i) q^{68} +(-0.311044 - 0.957295i) q^{69} +(6.96586 - 12.8363i) q^{70} +(1.20256 - 3.70109i) q^{71} +(13.6229 - 6.94121i) q^{72} +(0.784747 + 0.124292i) q^{73} -9.86703i q^{74} +(0.833781 - 0.605859i) q^{75} -25.0520i q^{76} +(-2.43054 - 11.4241i) q^{77} +(0.438932 + 0.861453i) q^{78} +(-10.4243 - 3.38705i) q^{79} +(-8.72022 - 5.34337i) q^{80} +(-2.66354 - 8.19753i) q^{81} +(-13.9450 + 13.9450i) q^{82} +(-0.370328 + 0.726810i) q^{83} +(0.577488 - 2.15686i) q^{84} +(15.5462 + 6.43885i) q^{85} +(-2.18429 + 1.58698i) q^{86} +(-0.309613 + 0.0490379i) q^{87} +(-22.5407 + 3.57009i) q^{88} +(4.65732 - 3.38374i) q^{89} +(-10.6022 + 12.4144i) q^{90} +(-4.85585 - 1.30013i) q^{91} +(9.07621 - 17.8131i) q^{92} +(-0.292441 + 0.292441i) q^{93} +(-6.78182 - 20.8723i) q^{94} +(5.23645 + 12.6408i) q^{95} +(-0.186528 - 0.0606066i) q^{96} +(1.37761 + 2.70371i) q^{97} +(9.41712 + 14.4890i) q^{98} +13.0560i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9}+O(q^{10}) \) 144 * q - 16 * q^2 - 20 * q^4 - 14 * q^7 - 12 * q^8 - 20 * q^9	\( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9} - 12 q^{11} - 10 q^{14} - 20 q^{15} + 12 q^{16} - 28 q^{18} - 6 q^{21} + 16 q^{22} - 8 q^{23} - 20 q^{25} - 70 q^{28} + 40 q^{30} - 20 q^{32} - 40 q^{35} - 28 q^{36} + 4 q^{37} - 60 q^{39} - 30 q^{42} + 72 q^{43} - 20 q^{44} - 12 q^{46} + 140 q^{50} - 32 q^{51} - 104 q^{53} - 22 q^{56} + 120 q^{57} - 32 q^{58} - 120 q^{60} + 48 q^{63} + 40 q^{64} - 20 q^{65} - 16 q^{67} + 90 q^{70} - 12 q^{71} - 64 q^{72} + 74 q^{77} + 60 q^{78} - 20 q^{79} - 8 q^{81} + 190 q^{84} - 12 q^{86} + 92 q^{88} - 6 q^{91} - 20 q^{92} - 160 q^{93} + 80 q^{95} + 162 q^{98}+O(q^{100}) \) 144 * q - 16 * q^2 - 20 * q^4 - 14 * q^7 - 12 * q^8 - 20 * q^9 - 12 * q^11 - 10 * q^14 - 20 * q^15 + 12 * q^16 - 28 * q^18 - 6 * q^21 + 16 * q^22 - 8 * q^23 - 20 * q^25 - 70 * q^28 + 40 * q^30 - 20 * q^32 - 40 * q^35 - 28 * q^36 + 4 * q^37 - 60 * q^39 - 30 * q^42 + 72 * q^43 - 20 * q^44 - 12 * q^46 + 140 * q^50 - 32 * q^51 - 104 * q^53 - 22 * q^56 + 120 * q^57 - 32 * q^58 - 120 * q^60 + 48 * q^63 + 40 * q^64 - 20 * q^65 - 16 * q^67 + 90 * q^70 - 12 * q^71 - 64 * q^72 + 74 * q^77 + 60 * q^78 - 20 * q^79 - 8 * q^81 + 190 * q^84 - 12 * q^86 + 92 * q^88 - 6 * q^91 - 20 * q^92 - 160 * q^93 + 80 * q^95 + 162 * q^98

Introduction

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