LMFDB - Embedded newform 175.2.s.a.27.1

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			27.1
Character	$\chi$	$=$	175.27
Dual form			175.2.s.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43824 - 0.386179i) q^{2} +(-0.183665 + 0.0935818i) q^{3} +(3.89376 + 1.26516i) q^{4} +(2.22917 - 0.175511i) q^{5} +(0.483957 - 0.157247i) q^{6} +(-2.41722 + 1.07566i) q^{7} +(-4.60620 - 2.34698i) q^{8} +(-1.73838 + 2.39268i) q^{9} +O(q^{10})$	\(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} +(-2.41722 + 1.07566i) 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} +(6.30916 - 1.68924i) 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} +(0.343295 - 0.423769i) 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} +(-10.7730 + 1.13020i) 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} +(-5.19960 + 2.82208i) 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} +(-1.00069 + 0.900676i) 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} +(13.6588 + 0.718439i) 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} +(1.62834 - 7.65353i) 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} +(13.7677 - 4.87293i) 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} +(-5.84181 + 10.1139i) 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} +(1.87284 - 1.21573i) 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} +(-2.73703 - 4.21642i) 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} +(-13.4336 + 10.8698i) 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	−0.506205	−	0.862413i	$-0.668952\pi$
$3$	−0.183665	+	0.0935818i	−0.106039	+	0.0540295i	0.400167	+	0.916442i	$0.368952\pi$
$4$	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
$7$	−2.41722	+	1.07566i	−0.913623	+	0.406562i
$7$	−2.41722	+	1.07566i	−0.913623	+	0.406562i
$8$	−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	$0.0348705\pi$
$13$	0.297223	+	1.87659i	0.0824349	+	0.520473i	−0.911571	+	0.411143i	$0.865130\pi$
$14$	6.30916	−	1.68924i	1.68619	−	0.451469i
$15$	−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	$0.0158991\pi$
$17$	6.70498	+	3.41636i	1.62620	+	0.828589i	0.627445	+	0.778661i	$0.284101\pi$
$18$	5.16259	−	5.16259i	1.21683	−	1.21683i
$19$	1.89087	+	5.81950i	0.433795	+	1.33508i	0.894316	+	0.447435i	$0.147663\pi$
$19$	1.89087	+	5.81950i	0.433795	+	1.33508i	−0.460521	+	0.887649i	$0.652337\pi$
$20$	8.90190	+	2.13686i	1.99052	+	0.477815i
$21$	0.343295	−	0.423769i	0.0749131	−	0.0924739i
$22$	−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
$28$	−10.7730	+	1.13020i	−2.03590	+	0.213588i
$29$	−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	−0.132602	−	0.991169i	$-0.542333\pi$
$31$	1.90816	−	0.619999i	0.342716	−	0.111355i	0.475318	+	0.879814i	$0.342333\pi$
$32$	−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
$35$	−5.19960	+	2.82208i	−0.878893	+	0.477019i
$36$	−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	$0.414418\pi$
$41$	−4.69566	+	6.46303i	−0.733340	+	1.00936i	−0.998974	+	0.0452815i	$0.985582\pi$
$42$	−1.00069	+	0.900676i	−0.154409	+	0.138977i
$43$	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	$-0.925447\pi$
$47$	−4.03603	−	7.92115i	−0.588715	−	1.15542i	0.383982	−	0.923341i	$-0.374553\pi$
$48$	−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
$56$	13.6588	+	0.718439i	1.82523	+	0.0960055i
$57$	−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	0.339121	−	0.940743i	$-0.389870\pi$
$59$	−3.46254	−	2.51568i	−0.450784	−	0.327514i	−0.789905	+	0.613229i	$0.789870\pi$
$60$	−1.83493	+	0.440591i	−0.236889	+	0.0568800i
$61$	−3.15174	−	4.33800i	−0.403539	−	0.555424i	0.558089	−	0.829781i	$-0.311535\pi$
$61$	−3.15174	−	4.33800i	−0.403539	−	0.555424i	−0.961628	+	0.274357i	$0.911535\pi$
$62$	−4.89198	+	0.774813i	−0.621282	+	0.0984014i
$63$	1.62834	−	7.65353i	0.205151	−	0.964255i
$64$	−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
$70$	13.7677	−	4.87293i	1.64555	−	0.582427i
$71$	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	0.110341	−	0.993894i	$-0.464806\pi$
$73$	−0.784747	−	0.124292i	−0.0918476	−	0.0145472i	−0.202189	+	0.979347i	$0.564806\pi$
$74$		−	9.86703i		−	1.14702i
$75$	−0.833781	+	0.605859i	−0.0962767	+	0.0699585i
$76$			25.0520i			2.87366i
$77$	−5.84181	+	10.1139i	−0.665737	+	1.15258i
$78$	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	−0.869789	−	0.493424i	$-0.835745\pi$
$83$	0.370328	−	0.726810i	0.0406488	−	0.0797778i	0.910438	+	0.413646i	$0.135745\pi$
$84$	1.87284	−	1.21573i	0.204344	−	0.132647i
$85$	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	−0.806596	−	0.591103i	$-0.798692\pi$
$89$	−4.65732	+	3.38374i	−0.493675	+	0.358676i	0.312921	+	0.949779i	$0.398692\pi$
$90$	10.6022	−	12.4144i	1.11757	−	1.30859i
$91$	−2.73703	−	4.21642i	−0.286919	−	0.442001i
$92$	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	0.810433	−	0.585831i	$-0.199232\pi$
$97$	−1.37761	−	2.70371i	−0.139875	−	0.274520i	−0.950308	+	0.311311i	$0.899232\pi$
$98$	−13.4336	+	10.8698i	−1.35699	+	1.09801i
$99$			13.0560i			1.31218i
$100$	20.2189	+	3.20103i	2.02189	+	0.320103i
$101$		−	9.05231i		−	0.900738i	−0.892842	−	0.450369i	$-0.851292\pi$
$101$		−	9.05231i		−	0.900738i	0.892842	−	0.450369i	$-0.148708\pi$
$102$	3.78214	+	0.599032i	0.374488	+	0.0593130i
$103$	−0.197172	+	0.100464i	−0.0194279	+	0.00989903i	−0.463677	−	0.886004i	$-0.653470\pi$
$103$	−0.197172	+	0.100464i	−0.0194279	+	0.00989903i	0.444250	+	0.895903i	$0.353470\pi$
$104$	3.03525	−	9.34154i	0.297631	−	0.916013i
$105$	0.690887	−	1.00490i	0.0674236	−	0.0980686i
$106$	−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
$112$	−11.8360	−	2.51817i	−1.11839	−	0.237945i
$113$	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
$119$	−19.8823	−	1.04579i	−1.82260	−	0.0958675i
$120$	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	−0.483084	−	0.875574i	$-0.660483\pi$
$131$	−4.11189	+	1.33603i	−0.359257	+	0.116730i	0.123827	+	0.992304i	$0.460483\pi$
$132$	−2.63437	+	2.63437i	−0.229293	+	0.229293i
$133$	−10.8305	−	12.0331i	−0.939120	−	1.04340i
$134$	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	−0.729217	−	0.684282i	$-0.760116\pi$
$139$	−3.58136	+	2.60201i	−0.303767	+	0.220700i	0.425450	+	0.904982i	$0.360116\pi$
$140$	−23.8164	+	4.41019i	−2.01285	+	0.372729i
$141$	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
$147$	−0.373987	+	1.39361i	−0.0308460	+	0.114943i
$148$	−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
$154$	18.1495	−	22.4040i	1.46253	−	1.80537i
$155$	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	−0.850972	−	0.525212i	$-0.823986\pi$
$157$	−4.08176	+	4.08176i	−0.325760	+	0.325760i	0.525212	+	0.850972i	$0.323986\pi$
$158$	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
$161$	3.34142	+	12.4799i	0.263341	+	0.983552i
$162$	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	−0.197858	−	0.980231i	$-0.563399\pi$
$167$	−14.3079	−	7.29025i	−1.10718	−	0.564136i	−0.909321	+	0.416094i	$0.863399\pi$
$168$	−2.57586	+	1.14626i	−0.198732	+	0.0884357i
$169$	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	0.544546	−	0.838731i	$-0.316702\pi$
$173$	10.5652	+	1.67336i	0.803258	+	0.127223i	0.258712	+	0.965955i	$0.416702\pi$
$174$	−0.773848			−0.0586653
$175$	−11.0955	+	7.20349i	−0.838740	+	0.544533i
$176$	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	0.653614	−	0.756828i	$-0.273252\pi$
$181$	21.8924	−	7.11328i	1.62725	−	0.528726i	0.973637	+	0.228102i	$0.0732518\pi$
$182$	5.04525	+	11.3376i	0.373979	+	0.840401i
$183$	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
$189$	0.840320	+	3.13852i	0.0611243	+	0.228293i
$190$	−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
$196$	24.8249	−	14.3200i	1.77321	−	1.02286i
$197$	−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	$-0.390494\pi$
$199$	9.51572			0.674552			0.337276	+	0.941406i	$0.390494\pi$
$200$	−24.5837	−	7.98599i	−1.73833	−	0.564695i
$201$		−	1.11649i		−	0.0787509i
$202$	−3.49581	+	22.0717i	−0.245964	+	1.55296i
$203$	4.00154	−	0.419807i	0.280853	−	0.0294647i
$204$	−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
$210$	−2.07262	+	2.18339i	−0.143024	+	0.150668i
$211$	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
$217$	−3.94553	+	3.55121i	−0.267840	+	0.241072i
$218$	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	−0.332734	−	0.943021i	$-0.607971\pi$
$223$	−14.0460	−	2.22468i	−0.940593	−	0.148975i	−0.607859	+	0.794045i	$0.707971\pi$
$224$	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	$-0.895255\pi$
$227$	0.806723	−	5.09345i	0.0535441	−	0.338064i	0.999889	−	0.0149055i	$-0.00474474\pi$
$228$	−2.34441	−	4.60116i	−0.155262	−	0.304719i
$229$	−1.33232	+	4.10046i	−0.0880421	+	0.270966i	−0.985378	−	0.170383i	$-0.945500\pi$
$229$	−1.33232	+	4.10046i	−0.0880421	+	0.270966i	0.897336	+	0.441348i	$0.145500\pi$
$230$	−6.29164	+	26.2103i	−0.414858	+	1.72825i
$231$	0.126461	−	2.40424i	0.00832055	−	0.158188i
$232$	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
$238$	48.0738	+	10.2280i	3.11616	+	0.662983i
$239$	−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	$0.492877\pi$
$241$	−14.5206	+	19.9860i	−0.935357	+	1.28741i	−0.957733	+	0.287659i	$0.907123\pi$
$242$	−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
$245$	9.53297	−	12.4146i	0.609039	−	0.793140i
$246$	−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	$-0.713973\pi$
$251$		−	24.7925i		−	1.56489i	0.622722	−	0.782443i	$-0.286027\pi$
$252$	16.0233	−	27.7409i	1.00937	−	1.74751i
$253$	−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	−0.987693	−	0.156403i	$-0.950010\pi$
$257$	−13.3266	+	13.3266i	−0.831290	+	0.831290i	0.156403	+	0.987693i	$0.450010\pi$
$258$	0.252664	−	0.495881i	0.0157302	−	0.0308722i
$259$	−5.75785	−	8.87002i	−0.357775	−	0.551156i
$260$	−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
$266$	21.7603	+	33.5220i	1.33421	+	2.05536i
$267$	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	$-0.784940\pi$
$269$	−8.47322	−	26.0779i	−0.516621	−	1.59000i	0.263692	−	0.964607i	$-0.415060\pi$
$270$	−1.58226	+	6.59152i	−0.0962933	+	0.401147i
$271$	−10.0270	−	3.25796i	−0.609096	−	0.197907i	−0.0118027	−	0.999930i	$-0.503757\pi$
$271$	−10.0270	−	3.25796i	−0.609096	−	0.197907i	−0.597293	+	0.802023i	$0.703757\pi$
$272$	15.6254	+	30.6666i	0.947430	+	1.85944i
$273$	0.897277	+	0.518271i	0.0543056	+	0.0313672i
$274$			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
$280$	30.5738	−	0.795740i	1.82713	−	0.0475546i
$281$	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	−0.705325	−	0.708884i	$-0.749199\pi$
$283$	4.75665	−	9.33546i	0.282754	−	0.554936i	0.988079	+	0.153948i	$0.0491990\pi$
$284$	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
$287$	4.39841	−	20.6735i	0.259630	−	1.22032i
$288$	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	0.168423	−	0.985715i	$-0.446132\pi$
$293$	−13.9898	−	13.9898i	−0.817291	−	0.817291i	−0.985715	+	0.168423i	$0.946132\pi$
$294$	1.45005	−	3.25353i	0.0845689	−	0.189750i
$295$	−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	$0.579230\pi$
$307$	−21.2978	+	21.2978i	−1.21553	+	1.21553i	−0.969182	+	0.246347i	$0.920770\pi$
$308$	−35.5423	+	31.9901i	−2.02521	+	1.82281i
$309$	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	$0.0611570\pi$
$311$	15.1640	+	20.8715i	0.859873	+	1.18351i	−0.121726	+	0.992564i	$0.538843\pi$
$312$	0.316730	+	1.99975i	0.0179313	+	0.113214i
$313$	2.56622	+	16.2025i	0.145052	+	0.915820i	0.947653	+	0.319303i	$0.103449\pi$
$313$	2.56622	+	16.2025i	0.145052	+	0.915820i	−0.802601	+	0.596516i	$0.796551\pi$
$314$	11.5286	−	8.37602i	0.650596	−	0.472686i
$315$	2.28656	−	17.3468i	0.128833	−	0.977382i
$316$	−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
$322$	−3.32771	−	31.7193i	−0.185446	−	1.76765i
$323$	−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
$329$	18.2765	+	14.8058i	1.00761	+	0.816268i
$330$	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
$336$	2.40950	−	0.645131i	0.131449	−	0.0351948i
$337$	−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
$343$	−5.73316	+	17.6105i	−0.309562	+	0.950879i
$344$	−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	$-0.414093\pi$
$349$	9.96173			0.533239			0.266620	+	0.963802i	$0.414093\pi$
$350$	29.8353	−	13.2790i	1.59476	−	0.709791i
$351$	2.33324			0.124539
$352$	−4.14857	−	0.657069i	−0.221120	−	0.0350219i
$353$	17.1476	−	8.73712i	0.912672	−	0.465030i	0.0664077	−	0.997793i	$-0.478846\pi$
$353$	17.1476	−	8.73712i	0.912672	−	0.465030i	0.846265	+	0.532763i	$0.178846\pi$
$354$	−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
$357$	3.74953	−	1.66854i	0.198446	−	0.0883087i
$358$	−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
$364$	−5.32290	−	19.8805i	−0.278996	−	1.04202i
$365$	−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	0.463932	−	0.885871i	$-0.346438\pi$
$367$	0.381987	+	0.194632i	0.0199396	+	0.0101597i	−0.443992	+	0.896031i	$0.646438\pi$
$368$	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
$371$	−5.08250	−	4.11734i	−0.263870	−	0.213761i
$372$	−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
$378$	−0.836873	−	7.97696i	−0.0430441	−	0.410291i
$379$	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	$0.475183\pi$
$383$	−15.1563	+	29.7460i	−0.774453	+	1.51995i	−0.852340	+	0.522988i	$0.824817\pi$
$384$	−3.11617	−	2.26403i	−0.159022	−	0.115536i
$385$	−11.2473	+	23.5708i	−0.573215	+	1.20128i
$386$	−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
$392$	−33.7890	+	12.9556i	−1.70660	+	0.654356i
$393$	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	$-0.942106\pi$
$397$	−10.9935	−	21.5760i	−0.551748	−	1.08287i	0.431758	−	0.901990i	$-0.357894\pi$
$398$	−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
$406$	−9.91883	−	0.521723i	−0.492263	−	0.0258927i
$407$	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	0.0581767	−	0.998306i	$-0.481471\pi$
$409$	−17.6612	−	12.8316i	−0.873291	−	0.634483i	−0.931468	+	0.363823i	$0.881471\pi$
$410$	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
$413$	11.0757	+	2.35643i	0.545001	+	0.115952i
$414$	−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	$0.229384\pi$
$419$	10.8766	+	33.4748i	0.531358	+	1.63535i	−0.220033	+	0.975493i	$0.570616\pi$
$420$	3.96151	−	3.03877i	0.193302	−	0.148277i
$421$	−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
$427$	12.2847	+	7.09569i	0.594497	+	0.343385i
$428$	−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	−0.988123	−	0.153666i	$-0.950892\pi$
$433$	−5.88887	+	11.5575i	−0.283001	+	0.555420i	0.705122	+	0.709086i	$0.250892\pi$
$434$	10.9915	−	7.13501i	0.527611	−	0.342491i
$435$	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	−0.609472	−	0.792807i	$-0.708619\pi$
$439$	−0.917813	+	0.666831i	−0.0438048	+	0.0318261i	0.565667	+	0.824634i	$0.308619\pi$
$440$	−49.6204	+	11.9145i	−2.36556	+	0.568001i
$441$	4.29657	+	20.2518i	0.204599	+	0.964372i
$442$	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
$448$	15.5758	+	8.99666i	0.735887	+	0.425052i
$449$		−	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
$455$	−6.84134	−	8.91874i	−0.320727	−	0.418117i
$456$	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	0.876285	−	0.481793i	$-0.160014\pi$
$461$	3.16235	+	4.35260i	0.147285	+	0.202721i	−0.729000	+	0.684514i	$0.760014\pi$
$462$	−1.23681	+	5.81329i	−0.0575417	+	0.270459i
$463$	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	0.260629	−	0.965439i	$-0.416070\pi$
$467$	−7.93600	−	4.04359i	−0.367234	−	0.187115i	−0.627863	+	0.778324i	$0.716070\pi$
$468$	−16.2676	−	16.2676i	−0.751971	−	0.751971i
$469$	0.752727	−	14.3106i	0.0347577	−	0.660803i
$470$	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	−0.999977	−	0.00674428i	$-0.997853\pi$
$479$	−4.09301	+	12.5970i	−0.187014	+	0.575571i	0.812963	+	0.582316i	$0.197853\pi$
$480$	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
$483$	−1.78159	−	1.97941i	−0.0810651	−	0.0900665i
$484$	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
$490$	−28.0379	+	26.5883i	−1.26662	+	1.20114i
$491$	−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
$497$	1.07428	+	10.2399i	0.0481880	+	0.459322i
$498$	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	0.251507	−	0.967856i	$-0.419074\pi$
$503$	26.5174	−	13.5113i	1.18235	−	0.602438i	0.930844	+	0.365418i	$0.119074\pi$
$504$	−25.4631	+	31.4320i	−1.13422	+	1.40009i
$505$	−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	0.283763	−	0.958894i	$-0.408417\pi$
$509$	−12.1945	−	8.85982i	−0.540512	−	0.392705i	−0.824275	+	0.566190i	$0.808417\pi$
$510$	8.53616	+	0.671536i	0.377988	+	0.0297361i
$511$	2.03060	−	0.543682i	0.0898285	−	0.0240511i
$512$	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
$518$	10.6136	+	23.8508i	0.466335	+	1.04794i
$519$	−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	0.865952	−	0.500127i	$-0.166713\pi$
$521$	29.0466	+	9.43781i	1.27255	+	0.413478i	0.406603	+	0.913605i	$0.366713\pi$
$522$	−9.89278	+	5.04063i	−0.432995	+	0.220622i
$523$	−31.3337	−	4.96277i	−1.37013	−	0.217007i	−0.572375	−	0.819992i	$-0.693978\pi$
$523$	−31.3337	−	4.96277i	−1.37013	−	0.217007i	−0.797752	+	0.602986i	$0.793978\pi$
$524$	−17.7010			−0.773271
$525$	1.36373	−	2.36136i	0.0595181	−	0.103058i
$526$	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
$532$	−26.9475	−	60.5561i	−1.16832	−	2.62544i
$533$	−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
$539$	3.24185	−	30.7312i	0.139636	−	1.32369i
$540$	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
$546$	−1.98763	−	1.61018i	−0.0850627	−	0.0689093i
$547$	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
$553$	28.8411	−	3.02575i	1.22645	−	0.128668i
$554$	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
$560$	−26.8263	−	3.53609i	−1.13362	−	0.149427i
$561$	−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	0.960127	−	0.279565i	$-0.0901904\pi$
$563$	−0.934834	−	5.90231i	−0.0393985	−	0.248753i	−0.999525	+	0.0308129i	$0.990190\pi$
$564$	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
$567$	15.2561	+	16.9502i	0.640697	+	0.711840i
$568$	−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	$0.392756\pi$
$577$	−6.61687	+	41.7773i	−0.275464	+	1.73921i	−0.606043	+	0.795432i	$0.707244\pi$
$578$	−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
$581$	−0.113362	+	2.15521i	−0.00470306	+	0.0894131i
$582$	−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	−0.0843542	−	0.996436i	$-0.526883\pi$
$587$	3.47275	−	0.550030i	0.143336	−	0.0227022i	0.227690	+	0.973734i	$0.426883\pi$
$588$	−3.21936	+	4.95323i	−0.132764	+	0.204268i
$589$	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	0.554570	−	0.832137i	$-0.312883\pi$
$593$	−6.75921	−	6.75921i	−0.277567	−	0.277567i	−0.832137	+	0.554570i	$0.812883\pi$
$594$	4.13555	+	12.7279i	0.169684	+	0.522232i
$595$	−44.5045	+	1.15831i	−1.82451	+	0.0474862i
$596$	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	$-0.793253\pi$
$601$		−	29.6537i		−	1.20960i	0.796378	−	0.604800i	$-0.206747\pi$
$602$	3.57285	−	6.18563i	0.145619	−	0.252108i
$603$	−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	−0.394864	−	0.918740i	$-0.629208\pi$
$607$	12.9069	−	12.9069i	0.523876	−	0.523876i	0.918740	+	0.394864i	$0.129208\pi$
$608$	2.64313	−	5.18744i	0.107193	−	0.210379i
$609$	−0.695655	+	0.451575i	−0.0281894	+	0.0182987i
$610$	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
$616$	50.6456	−	32.8759i	2.04057	−	1.32461i
$617$	−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	0.856089	−	0.516829i	$-0.172888\pi$
$619$	−3.49027	−	10.7420i	−0.140286	−	0.431756i	−0.996375	+	0.0850732i	$0.972888\pi$
$620$	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
$623$	7.61800	−	13.1889i	0.305209	−	0.528404i
$624$		−	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
$630$	−12.2741	+	41.4126i	−0.489014	+	1.64992i
$631$	−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
$637$	11.1515	+	7.24790i	0.441837	+	0.287172i
$638$	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	0.953586	−	0.301122i	$-0.0973612\pi$
$643$	16.5448	+	16.5448i	0.652463	+	0.652463i	−0.301122	+	0.953586i	$0.597361\pi$
$644$	−2.77834	+	52.8210i	−0.109482	+	2.08144i
$645$	−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	0.803686	−	0.595054i	$-0.202869\pi$
$647$	−3.81842	−	7.49408i	−0.150118	−	0.294623i	−0.953803	+	0.300431i	$0.902869\pi$
$648$	−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
$658$	−38.8447	−	43.1580i	−1.51432	−	1.68247i
$659$	−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	$-0.933248\pi$
$661$	−22.4661	−	30.9219i	−0.873829	−	1.20272i	0.104263	−	0.994550i	$-0.466752\pi$
$662$	−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
$665$	−26.2549	−	24.9229i	−1.01812	−	0.966468i
$666$	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
$672$	−0.516072	+	0.0541417i	−0.0199079	+	0.00208856i
$673$	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	$-0.828746\pi$
$677$	3.02654	−	19.1088i	0.116319	−	0.734412i	0.975050	−	0.221985i	$-0.0712536\pi$
$678$	3.65911	−	1.86441i	0.140527	−	0.0716023i
$679$	6.23826	+	5.05362i	0.239403	+	0.193940i
$680$	−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
$686$	20.7796	−	40.7246i	0.793370	−	1.55487i
$687$	−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	$0.526616\pi$
$691$	−26.4300	+	36.3778i	−1.00544	+	1.38388i	−0.921925	+	0.387369i	$0.873384\pi$
$692$	39.0213	+	19.8823i	1.48337	+	0.755813i
$693$	−14.0439	−	31.5593i	−0.533483	−	1.19884i
$694$	−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
$700$	−52.3167	+	14.0111i	−1.97739	+	0.529570i
$701$	−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
$707$	9.73723	+	21.8814i	0.366206	+	0.822935i
$708$	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
$714$	−9.78662	+	2.62031i	−0.366255	+	0.0980628i
$715$	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	$-0.809677\pi$
$719$	−13.1048	−	40.3325i	−0.488727	−	1.50415i	0.337782	−	0.941224i	$-0.390323\pi$
$720$	−27.9440	+	11.5758i	−1.04141	+	0.431406i
$721$	0.368543	−	0.454934i	0.0137252	−	0.0169426i
$722$	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	−0.977115	−	0.212713i	$-0.931770\pi$
$727$	0.482868	−	3.04871i	0.0179086	−	0.113070i	0.995023	+	0.0996428i	$0.0317700\pi$
$728$	2.71148	+	25.8455i	0.100494	+	0.957896i
$729$	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	−0.715109	−	0.699013i	$-0.753623\pi$
$733$	7.32988	−	14.3857i	0.270735	−	0.531348i	0.985844	+	0.167665i	$0.0536228\pi$
$734$	−0.856213	−	0.622075i	−0.0316034	−	0.0229612i
$735$	−0.589087	+	3.17224i	−0.0217288	+	0.117010i
$736$	−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
$742$	10.8023	+	12.0018i	0.396566	+	0.440600i
$743$	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
$756$	−0.698715	+	13.2838i	−0.0254120	+	0.483126i
$757$	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	$0.0518957\pi$
$761$	23.0673	+	31.7494i	0.836190	+	1.15092i	−0.150550	+	0.988602i	$0.548104\pi$
$762$	5.71732	−	0.905535i	0.207117	−	0.0328041i
$763$	4.25129	−	19.9820i	0.153907	−	0.723396i
$764$	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	0.851338	−	0.524618i	$-0.175792\pi$
$769$	−4.04237	−	12.4411i	−0.145771	−	0.448639i	−0.997109	+	0.0759792i	$0.975792\pi$
$770$	36.5261	−	53.1278i	1.31631	−	1.91459i
$771$	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	−0.0692887	−	0.997597i	$-0.522073\pi$
$773$	−12.3295	−	1.95280i	−0.443461	−	0.0702372i	−0.374172	+	0.927359i	$0.622073\pi$
$774$		−	7.98507i		−	0.287017i
$775$	8.93810	−	4.55491i	0.321066	−	0.163617i
$776$			15.6870i			0.563132i
$777$	1.88759	+	1.09028i	0.0677167	+	0.0391135i
$778$	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
$784$	31.3188	−	6.64453i	1.11853	−	0.237305i
$785$	−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	0.720933	−	0.693005i	$-0.243714\pi$
$787$	45.4672	−	7.20130i	1.62073	−	0.256699i	0.899798	+	0.436306i	$0.143714\pi$
$788$	−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
$791$	−17.9097	+	11.6258i	−0.636796	+	0.413368i
$792$	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	0.589746	−	0.807589i	$-0.299228\pi$
$797$	−11.5819	−	22.7307i	−0.410251	−	0.805164i	−0.999997	+	0.00242539i	$0.999228\pi$
$798$	−7.13365	−	4.12043i	−0.252528	−	0.145862i
$799$		−	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
$805$	9.63894	+	27.2333i	0.339728	+	0.959848i
$806$	−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	0.795639	−	0.605771i	$-0.207135\pi$
$811$	−0.750387	−	1.03282i	−0.0263497	−	0.0362672i	−0.821989	+	0.569504i	$0.807135\pi$
$812$	16.1122	+	3.42796i	0.565426	+	0.120298i
$813$	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
$819$	14.8465	+	0.780916i	0.518780	+	0.0272874i
$820$	−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	$-0.755084\pi$
$829$	7.82434	−	24.0808i	0.271750	−	0.836362i	0.990061	−	0.140639i	$-0.0449158\pi$
$830$	−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
$833$	49.1847	−	18.8587i	1.70415	−	0.653415i
$834$	−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	$0.731652\pi$
$839$	−45.7909	+	33.2690i	−1.58088	+	1.14857i	−0.915681	+	0.401907i	$0.868348\pi$
$840$	−5.54085	+	3.00730i	−0.191177	+	0.103762i
$841$	−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
$847$	2.34318	+	22.3349i	0.0805128	+	0.767437i
$848$	−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	−0.952666	−	0.304019i	$-0.901671\pi$
$853$	−36.9947	+	18.8497i	−1.26667	+	0.645402i	−0.314007	+	0.949421i	$0.601671\pi$
$854$	−27.2128	−	22.0451i	−0.931202	−	0.754367i
$855$	−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	−0.778623	−	0.627492i	$-0.784082\pi$
$857$	−4.42430	+	4.42430i	−0.151131	+	0.151131i	0.627492	+	0.778623i	$0.284082\pi$
$858$	3.80292	+	1.93768i	0.129829	+	0.0661514i
$859$	−0.0963348	−	0.0699913i	−0.00328690	−	0.00238807i	0.586141	−	0.810209i	$-0.300647\pi$
$859$	−0.0963348	−	0.0699913i	−0.00328690	−	0.00238807i	−0.589427	+	0.807821i	$0.700647\pi$
$860$	8.53692	−	5.23180i	0.291106	−	0.178403i
$861$	1.12683	+	4.20860i	0.0384023	+	0.143429i
$862$	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
$868$	−19.8558	+	8.83582i	−0.673949	+	0.299907i
$869$	−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
$875$	−23.4694	+	18.0052i	−0.793411	+	0.608686i
$876$	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	−0.387922	−	0.921692i	$-0.626807\pi$
$881$	−4.74906	+	1.54306i	−0.160000	+	0.0519871i	0.227922	+	0.973679i	$0.426807\pi$
$882$	−2.65525	−	51.0380i	−0.0894069	−	1.71854i
$883$	−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	−0.450620	−	0.892716i	$-0.648797\pi$
$887$	−17.9684	+	2.84592i	−0.603321	+	0.0955566i	−0.152701	+	0.988272i	$0.548797\pi$
$888$	0.666299	+	4.20685i	0.0223595	+	0.141173i
$889$	−29.0728	+	7.78409i	−0.975071	+	0.261070i
$890$	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
$896$	−38.4153	−	31.1202i	−1.28336	−	1.03965i
$897$	−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
$903$	−0.0622350	−	0.593216i	−0.00207105	−	0.0197410i
$904$	−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
$910$	13.2366	+	24.3880i	0.438789	+	0.808455i
$911$	−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
$917$	8.50221	−	7.65249i	0.280768	−	0.252707i
$918$	−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	−0.862171	−	0.506617i	$-0.830896\pi$
$929$	4.05750	−	12.4877i	0.133122	−	0.409708i	0.995293	+	0.0969092i	$0.0308957\pi$
$930$	1.73591	−	1.48270i	0.0569228	−	0.0486198i
$931$	39.1231	+	17.4366i	1.28221	+	0.571463i
$932$	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	0.0527051	−	0.998610i	$-0.483216\pi$
$937$	12.5937	−	1.99465i	0.411418	−	0.0651622i	0.358713	+	0.933448i	$0.383216\pi$
$938$	−7.36178	+	34.6020i	−0.240371	+	1.12979i
$939$	−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	$0.411167\pi$
$941$	−22.2067	+	30.5649i	−0.723917	+	0.996386i	−0.999385	+	0.0350759i	$0.988833\pi$
$942$	−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
$945$	2.42406	+	6.84880i	0.0788547	+	0.222791i
$946$	−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
$952$	89.1273	+	51.4803i	2.88863	+	1.66849i
$953$	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
$959$	24.5610	+	37.8364i	0.793114	+	1.22180i
$960$	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
$966$	3.57953	+	5.51430i	0.115169	+	0.177420i
$967$	−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	−0.161022	−	0.986951i	$-0.551479\pi$
$971$	−27.1538	−	8.82281i	−0.871407	−	0.283137i	−0.710385	+	0.703813i	$0.751479\pi$
$972$	10.1500	+	19.9206i	0.325562	+	0.638952i
$973$	5.85805	−	10.1420i	0.187800	−	0.325136i
$974$		−	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
$980$	52.8255	−	36.2788i	1.68745	−	1.15888i
$981$	−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	$-0.692427\pi$
$983$	13.5238	−	26.5420i	0.431344	−	0.846559i	0.999717	−	0.0237886i	$-0.00757287\pi$
$984$	−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
$987$	−4.74229	−	1.00895i	−0.150949	−	0.0321152i
$988$	−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
$994$	1.33508	−	25.3822i	0.0423462	−	0.805073i
$995$	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	$0.0879834\pi$
$997$	19.4930	+	38.2572i	0.617350	+	1.21162i	−0.344692	+	0.938716i	$0.612017\pi$
$998$	−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.27.1	yes	144
5.2	odd	4		875.2.s.a.468.18		144
5.3	odd	4		875.2.s.b.468.1		144
5.4	even	2		875.2.s.c.657.18		144
7.6	odd	2	inner	175.2.s.a.27.2	yes	144
25.9	even	10		875.2.s.a.832.17		144
25.12	odd	20		875.2.s.c.293.17		144
25.13	odd	20	inner	175.2.s.a.13.2	yes	144
25.16	even	5		875.2.s.b.832.2		144
35.13	even	4		875.2.s.b.468.2		144
35.27	even	4		875.2.s.a.468.17		144
35.34	odd	2		875.2.s.c.657.17		144
175.13	even	20	inner	175.2.s.a.13.1	✓	144
175.34	odd	10		875.2.s.a.832.18		144
175.41	odd	10		875.2.s.b.832.1		144
175.62	even	20		875.2.s.c.293.18		144

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

\(f(q)\)	\(=\)	\(q+(-2.43824 - 0.386179i) q^{2} +(-0.183665 + 0.0935818i) q^{3} +(3.89376 + 1.26516i) q^{4} +(2.22917 - 0.175511i) q^{5} +(0.483957 - 0.157247i) q^{6} +(-2.41722 + 1.07566i) q^{7} +(-4.60620 - 2.34698i) q^{8} +(-1.73838 + 2.39268i) q^{9} +O(q^{10})\)	\(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} +(-2.41722 + 1.07566i) 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} +(6.30916 - 1.68924i) 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} +(0.343295 - 0.423769i) 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} +(-10.7730 + 1.13020i) 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} +(-5.19960 + 2.82208i) 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} +(-1.00069 + 0.900676i) 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} +(13.6588 + 0.718439i) 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} +(1.62834 - 7.65353i) 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} +(13.7677 - 4.87293i) 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} +(-5.84181 + 10.1139i) 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} +(1.87284 - 1.21573i) 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} +(-2.73703 - 4.21642i) 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} +(-13.4336 + 10.8698i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more