LMFDB - Embedded newform 567.2.be.a.503.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(62,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.62"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.be (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			503.21
Character	$\chi$	$=$	567.503
Dual form			567.2.be.a.62.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.878867 - 2.41467i) q^{2} +(-3.52612 - 2.95877i) q^{4} +(-0.588152 + 3.33557i) q^{5} +(-2.64351 + 0.108907i) q^{7} +(-5.79269 + 3.34441i) q^{8} +(7.53740 + 4.35172i) q^{10} +(-4.55474 + 0.803123i) q^{11} +(0.619664 + 1.70251i) q^{13} +(-2.06032 + 6.47891i) q^{14} +(1.38602 + 7.86054i) q^{16} +(-1.40471 + 2.43302i) q^{17} +(-0.586660 + 0.338709i) q^{19} +(11.9431 - 10.0214i) q^{20} +(-2.06373 + 11.7040i) q^{22} +(2.29937 - 2.74028i) q^{23} +(-6.08167 - 2.21355i) q^{25} +4.65561 q^{26} +(9.64357 + 7.43751i) q^{28} +(0.546385 - 1.50118i) q^{29} +(-1.99247 + 2.37454i) q^{31} +(7.02429 + 1.23857i) q^{32} +(4.64039 + 5.53021i) q^{34} +(1.19152 - 8.88167i) q^{35} +(-0.898066 + 1.55550i) q^{37} +(0.302272 + 1.71427i) q^{38} +(-7.74856 - 21.2890i) q^{40} +(-11.6140 + 4.22715i) q^{41} +(-0.0534327 - 0.303032i) q^{43} +(18.4368 + 10.6445i) q^{44} +(-4.59602 - 7.96055i) q^{46} +(2.22186 - 1.86436i) q^{47} +(6.97628 - 0.575794i) q^{49} +(-10.6900 + 12.7398i) q^{50} +(2.85233 - 7.83672i) q^{52} -4.31910i q^{53} -15.6650i q^{55} +(14.9488 - 9.47185i) q^{56} +(-3.14465 - 2.63868i) q^{58} +(1.34243 - 7.61331i) q^{59} +(0.783123 + 0.933289i) q^{61} +(3.98260 + 6.89806i) q^{62} +(1.18236 - 2.04791i) q^{64} +(-6.04332 + 1.06560i) q^{65} +(0.826896 - 0.300966i) q^{67} +(12.1519 - 4.42294i) q^{68} +(-20.3991 - 10.6829i) q^{70} +(-11.6410 - 6.72094i) q^{71} +(-11.2992 + 6.52362i) q^{73} +(2.96672 + 3.53560i) q^{74} +(3.07080 + 0.541464i) q^{76} +(11.9530 - 2.61911i) q^{77} +(13.7757 + 5.01396i) q^{79} -27.0346 q^{80} +31.7590i q^{82} +(-6.55767 - 2.38680i) q^{83} +(-7.28935 - 6.11649i) q^{85} +(-0.778681 - 0.137302i) q^{86} +(23.6982 - 19.8852i) q^{88} +(8.53240 + 14.7785i) q^{89} +(-1.82350 - 4.43313i) q^{91} +(-16.2157 + 2.85927i) q^{92} +(-2.54910 - 7.00358i) q^{94} +(-0.784742 - 2.15606i) q^{95} +(5.81042 - 1.02453i) q^{97} +(4.74087 - 17.3514i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.878867	−	2.41467i	0.621453	−	1.70743i	−0.0819501	−	0.996636i	$-0.526115\pi$
$2$	0.878867	−	2.41467i	0.621453	−	1.70743i	0.703403	−	0.710791i	$-0.251663\pi$
$3$		0			0
$3$		0			0
$4$	−3.52612	−	2.95877i	−1.76306	−	1.47938i
$5$	−0.588152	+	3.33557i	−0.263029	+	1.49171i	0.511559	+	0.859248i	$0.329068\pi$
$5$	−0.588152	+	3.33557i	−0.263029	+	1.49171i	−0.774588	+	0.632466i	$0.782043\pi$
$6$		0			0
$7$	−2.64351	+	0.108907i	−0.999152	+	0.0411630i
$7$	−2.64351	+	0.108907i	−0.999152	+	0.0411630i
$8$	−5.79269	+	3.34441i	−2.04803	+	1.18243i
$9$		0			0
$10$	7.53740	+	4.35172i	2.38353	+	1.37613i
$11$	−4.55474	+	0.803123i	−1.37330	+	0.242151i	−0.811129	−	0.584867i	$-0.801147\pi$
$11$	−4.55474	+	0.803123i	−1.37330	+	0.242151i	−0.562176	+	0.827018i	$0.690035\pi$
$12$		0			0
$13$	0.619664	+	1.70251i	0.171864	+	0.472192i	0.995482	−	0.0949528i	$-0.0302700\pi$
$13$	0.619664	+	1.70251i	0.171864	+	0.472192i	−0.823618	+	0.567145i	$0.808048\pi$
$14$	−2.06032	+	6.47891i	−0.550643	+	1.73156i
$15$		0			0
$16$	1.38602	+	7.86054i	0.346506	+	1.96513i
$17$	−1.40471	+	2.43302i	−0.340692	+	0.590095i	−0.984561	−	0.175040i	$-0.943995\pi$
$17$	−1.40471	+	2.43302i	−0.340692	+	0.590095i	0.643870	+	0.765135i	$0.277328\pi$
$18$		0			0
$19$	−0.586660	+	0.338709i	−0.134589	+	0.0777051i	−0.565783	−	0.824554i	$-0.691426\pi$
$19$	−0.586660	+	0.338709i	−0.134589	+	0.0777051i	0.431194	+	0.902259i	$0.358093\pi$
$20$	11.9431	−	10.0214i	2.67056	−	2.24086i
$21$		0			0
$22$	−2.06373	+	11.7040i	−0.439989	+	2.49530i
$23$	2.29937	−	2.74028i	0.479451	−	0.571388i	−0.471051	−	0.882106i	$-0.656125\pi$
$23$	2.29937	−	2.74028i	0.479451	−	0.571388i	0.950502	+	0.310718i	$0.100570\pi$
$24$		0			0
$25$	−6.08167	−	2.21355i	−1.21633	−	0.442709i
$26$	4.65561			0.913040
$27$		0			0
$28$	9.64357	+	7.43751i	1.82246	+	1.40556i
$29$	0.546385	−	1.50118i	0.101461	−	0.278762i	−0.878568	−	0.477618i	$-0.841500\pi$
$29$	0.546385	−	1.50118i	0.101461	−	0.278762i	0.980029	+	0.198856i	$0.0637225\pi$
$30$		0			0
$31$	−1.99247	+	2.37454i	−0.357859	+	0.426479i	−0.914696	−	0.404142i	$-0.867570\pi$
$31$	−1.99247	+	2.37454i	−0.357859	+	0.426479i	0.556838	+	0.830621i	$0.312015\pi$
$32$	7.02429	+	1.23857i	1.24173	+	0.218951i
$33$		0			0
$34$	4.64039	+	5.53021i	0.795821	+	0.948423i
$35$	1.19152	−	8.88167i	0.201403	−	1.50128i
$36$		0			0
$37$	−0.898066	+	1.55550i	−0.147641	+	0.255722i	−0.930355	−	0.366660i	$-0.880501\pi$
$37$	−0.898066	+	1.55550i	−0.147641	+	0.255722i	0.782714	+	0.622381i	$0.213835\pi$
$38$	0.302272	+	1.71427i	0.0490350	+	0.278091i
$39$		0			0
$40$	−7.74856	−	21.2890i	−1.22515	−	3.36608i
$41$	−11.6140	+	4.22715i	−1.81380	+	0.660169i	−0.817335	+	0.576163i	$0.804549\pi$
$41$	−11.6140	+	4.22715i	−1.81380	+	0.660169i	−0.996465	+	0.0840066i	$0.973228\pi$
$42$		0			0
$43$	−0.0534327	−	0.303032i	−0.00814840	−	0.0462119i	0.980462	−	0.196706i	$-0.0630246\pi$
$43$	−0.0534327	−	0.303032i	−0.00814840	−	0.0462119i	−0.988611	+	0.150494i	$0.951913\pi$
$44$	18.4368	+	10.6445i	2.77945	+	1.60472i
$45$		0			0
$46$	−4.59602	−	7.96055i	−0.677647	−	1.17372i
$47$	2.22186	−	1.86436i	0.324092	−	0.271945i	−0.466196	−	0.884682i	$-0.654376\pi$
$47$	2.22186	−	1.86436i	0.324092	−	0.271945i	0.790287	+	0.612736i	$0.209931\pi$
$48$		0			0
$49$	6.97628	−	0.575794i	0.996611	−	0.0822563i
$50$	−10.6900	+	12.7398i	−1.51179	+	1.80168i
$51$		0			0
$52$	2.85233	−	7.83672i	0.395547	−	1.08676i
$53$		−	4.31910i		−	0.593273i	−0.954990	−	0.296637i	$-0.904135\pi$
$53$		−	4.31910i		−	0.593273i	0.954990	−	0.296637i	$-0.0958650\pi$
$54$		0			0
$55$		−	15.6650i		−	2.11227i
$56$	14.9488	−	9.47185i	1.99762	−	1.26573i
$57$		0			0
$58$	−3.14465	−	2.63868i	−0.412913	−	0.346475i
$59$	1.34243	−	7.61331i	0.174770	−	0.991168i	−0.763640	−	0.645643i	$-0.776590\pi$
$59$	1.34243	−	7.61331i	0.174770	−	0.991168i	0.938409	−	0.345525i	$-0.112299\pi$
$60$		0			0
$61$	0.783123	+	0.933289i	0.100269	+	0.119495i	0.813845	−	0.581082i	$-0.197370\pi$
$61$	0.783123	+	0.933289i	0.100269	+	0.119495i	−0.713577	+	0.700577i	$0.752926\pi$
$62$	3.98260	+	6.89806i	0.505790	+	0.876055i
$63$		0			0
$64$	1.18236	−	2.04791i	0.147795	−	0.255988i
$65$	−6.04332	+	1.06560i	−0.749582	+	0.132171i
$66$		0			0
$67$	0.826896	−	0.300966i	0.101021	−	0.0367688i	−0.291015	−	0.956719i	$-0.593993\pi$
$67$	0.826896	−	0.300966i	0.101021	−	0.0367688i	0.392036	+	0.919950i	$0.371771\pi$
$68$	12.1519	−	4.42294i	1.47364	−	0.536360i
$69$		0			0
$70$	−20.3991	−	10.6829i	−2.43816	−	1.27685i
$71$	−11.6410	−	6.72094i	−1.38153	−	0.797629i	−0.389193	−	0.921156i	$-0.627246\pi$
$71$	−11.6410	−	6.72094i	−1.38153	−	0.797629i	−0.992341	+	0.123527i	$0.960579\pi$
$72$		0			0
$73$	−11.2992	+	6.52362i	−1.32248	+	0.763532i	−0.984123	−	0.177487i	$-0.943203\pi$
$73$	−11.2992	+	6.52362i	−1.32248	+	0.763532i	−0.338354	+	0.941019i	$0.609870\pi$
$74$	2.96672	+	3.53560i	0.344875	+	0.411006i
$75$		0			0
$76$	3.07080	+	0.541464i	0.352244	+	0.0621102i
$77$	11.9530	−	2.61911i	1.36217	−	0.298475i
$78$		0			0
$79$	13.7757	+	5.01396i	1.54989	+	0.564115i	0.968392	−	0.249432i	$-0.0802438\pi$
$79$	13.7757	+	5.01396i	1.54989	+	0.564115i	0.581500	+	0.813546i	$0.302466\pi$
$80$	−27.0346			−3.02256
$81$		0			0
$82$			31.7590i			3.50720i
$83$	−6.55767	−	2.38680i	−0.719798	−	0.261985i	−0.0439581	−	0.999033i	$-0.513997\pi$
$83$	−6.55767	−	2.38680i	−0.719798	−	0.261985i	−0.675840	+	0.737048i	$0.736219\pi$
$84$		0			0
$85$	−7.28935	−	6.11649i	−0.790642	−	0.663427i
$86$	−0.778681	−	0.137302i	−0.0839673	−	0.0148057i
$87$		0			0
$88$	23.6982	−	19.8852i	2.52624	−	2.11977i
$89$	8.53240	+	14.7785i	0.904432	+	1.56652i	0.821678	+	0.569952i	$0.193038\pi$
$89$	8.53240	+	14.7785i	0.904432	+	1.56652i	0.0827545	+	0.996570i	$0.473628\pi$
$90$		0			0
$91$	−1.82350	−	4.43313i	−0.191155	−	0.464718i
$92$	−16.2157	+	2.85927i	−1.69060	+	0.298099i
$93$		0			0
$94$	−2.54910	−	7.00358i	−0.262919	−	0.722364i
$95$	−0.784742	−	2.15606i	−0.0805128	−	0.221207i
$96$		0			0
$97$	5.81042	−	1.02453i	0.589959	−	0.104026i	0.129304	−	0.991605i	$-0.458726\pi$
$97$	5.81042	−	1.02453i	0.589959	−	0.104026i	0.460655	+	0.887579i	$0.347615\pi$
$98$	4.74087	−	17.3514i	0.478900	−	1.75276i
$99$		0			0
$100$	14.8953	+	25.7995i	1.48953	+	2.57995i
$101$	−4.44425	+	3.72917i	−0.442219	+	0.371066i	−0.836539	−	0.547907i	$-0.815425\pi$
$101$	−4.44425	+	3.72917i	−0.442219	+	0.371066i	0.394320	+	0.918973i	$0.370980\pi$
$102$		0			0
$103$	−1.31146	−	0.231246i	−0.129222	−	0.0227853i	0.108663	−	0.994079i	$-0.465343\pi$
$103$	−1.31146	−	0.231246i	−0.129222	−	0.0227853i	−0.237885	+	0.971293i	$0.576454\pi$
$104$	−9.28344	−	7.78973i	−0.910316	−	0.763846i
$105$		0			0
$106$	−10.4292	−	3.79591i	−1.01297	−	0.368691i
$107$		−	5.37579i		−	0.519697i	−0.965649	−	0.259848i	$-0.916327\pi$
$107$		−	5.37579i		−	0.519697i	0.965649	−	0.259848i	$-0.0836726\pi$
$108$		0			0
$109$	−8.37864			−0.802529			−0.401264	−	0.915962i	$-0.631429\pi$
$109$	−8.37864			−0.802529			−0.401264	+	0.915962i	$0.631429\pi$
$110$	−37.8258	−	13.7675i	−3.60655	−	1.31268i
$111$		0			0
$112$	−4.52004	−	20.6284i	−0.427103	−	1.94920i
$113$	11.4667	+	2.02188i	1.07869	+	0.190203i	0.684638	−	0.728883i	$-0.259960\pi$
$113$	11.4667	+	2.02188i	1.07869	+	0.190203i	0.394056	+	0.919086i	$0.371071\pi$
$114$		0			0
$115$	7.78803	+	9.28141i	0.726237	+	0.865496i
$116$	−6.36827	+	3.67672i	−0.591279	+	0.341375i
$117$		0			0
$118$	−17.2038	−	9.93261i	−1.58374	−	0.914371i
$119$	3.44838	−	6.58471i	0.316113	−	0.603619i
$120$		0			0
$121$	9.76399	−	3.55380i	0.887636	−	0.323073i
$122$	2.94184	−	1.07074i	0.266342	−	0.0969406i
$123$		0			0
$124$	14.0514	−	2.47764i	1.26185	−	0.222499i
$125$	2.49282	−	4.31769i	0.222964	−	0.386186i
$126$		0			0
$127$	6.11354	+	10.5890i	0.542489	+	0.939618i	0.998760	+	0.0497777i	$0.0158513\pi$
$127$	6.11354	+	10.5890i	0.542489	+	0.939618i	−0.456271	+	0.889841i	$0.650815\pi$
$128$	5.26368	+	6.27301i	0.465248	+	0.554461i
$129$		0			0
$130$	−2.73820	+	15.5291i	−0.240156	+	1.36199i
$131$	9.11926	+	7.65197i	0.796753	+	0.668556i	0.947407	−	0.320031i	$-0.103693\pi$
$131$	9.11926	+	7.65197i	0.796753	+	0.668556i	−0.150654	+	0.988587i	$0.548138\pi$
$132$		0			0
$133$	1.51395	−	0.959270i	0.131276	−	0.0831793i
$134$		−	2.26119i		−	0.195337i
$135$		0			0
$136$		−	18.7917i		−	1.61137i
$137$	−2.07270	+	5.69469i	−0.177082	+	0.486530i	−0.996200	−	0.0870958i	$-0.972241\pi$
$137$	−2.07270	+	5.69469i	−0.177082	+	0.486530i	0.819118	+	0.573626i	$0.194464\pi$
$138$		0			0
$139$	−3.77560	+	4.49958i	−0.320242	+	0.381650i	−0.902017	−	0.431700i	$-0.857914\pi$
$139$	−3.77560	+	4.49958i	−0.320242	+	0.381650i	0.581775	+	0.813350i	$0.302358\pi$
$140$	−30.4802	+	27.7925i	−2.57605	+	2.34889i
$141$		0			0
$142$	−26.4597	+	22.2024i	−2.22045	+	1.86318i
$143$	−4.18974	−	7.25684i	−0.350363	−	0.606847i
$144$		0			0
$145$	4.68594	+	2.70543i	0.389147	+	0.224674i
$146$	5.82184	+	33.0173i	0.481819	+	2.73253i
$147$		0			0
$148$	7.76904	−	2.82770i	0.638611	−	0.232435i
$149$	3.41781	+	9.39037i	0.279998	+	0.769289i	0.997362	+	0.0725900i	$0.0231264\pi$
$149$	3.41781	+	9.39037i	0.279998	+	0.769289i	−0.717364	+	0.696699i	$0.754651\pi$
$150$		0			0
$151$	1.48657	+	8.43073i	0.120975	+	0.686083i	0.983617	+	0.180269i	$0.0576968\pi$
$151$	1.48657	+	8.43073i	0.120975	+	0.686083i	−0.862642	+	0.505814i	$0.831192\pi$
$152$	2.26556	−	3.92407i	0.183761	−	0.318284i
$153$		0			0
$154$	4.18085	−	31.1644i	0.336902	−	2.51130i
$155$	−6.74857	−	8.04263i	−0.542058	−	0.645999i
$156$		0			0
$157$	−0.122753	−	0.0216446i	−0.00979672	−	0.00172743i	0.168748	−	0.985659i	$-0.446028\pi$
$157$	−0.122753	−	0.0216446i	−0.00979672	−	0.00172743i	−0.178544	+	0.983932i	$0.557139\pi$
$158$	24.2141	−	28.8572i	1.92637	−	2.29576i
$159$		0			0
$160$	−8.26270	+	22.7016i	−0.653224	+	1.79472i
$161$	−5.77996	+	7.49437i	−0.455525	+	0.590639i
$162$		0			0
$163$	−11.4176			−0.894293			−0.447146	−	0.894461i	$-0.647560\pi$
$163$	−11.4176			−0.894293			−0.447146	+	0.894461i	$0.647560\pi$
$164$	53.4595	+	19.4577i	4.17448	+	1.51939i
$165$		0			0
$166$	−11.5266	+	13.7369i	−0.894641	+	1.06619i
$167$	−1.76953	+	10.0355i	−0.136930	+	0.776570i	0.836566	+	0.547866i	$0.184560\pi$
$167$	−1.76953	+	10.0355i	−0.136930	+	0.776570i	−0.973496	+	0.228703i	$0.926551\pi$
$168$		0			0
$169$	7.44401	−	6.24626i	0.572616	−	0.480482i
$170$	−21.1757	+	12.2258i	−1.62410	+	0.937675i
$171$		0			0
$172$	−0.708190	+	1.22662i	−0.0539990	+	0.0935290i
$173$	−3.27964	−	18.5997i	−0.249346	−	1.41411i	−0.810179	−	0.586183i	$-0.800630\pi$
$173$	−3.27964	−	18.5997i	−0.249346	−	1.41411i	0.560832	−	0.827929i	$-0.310481\pi$
$174$		0			0
$175$	16.3180	+	5.18919i	1.23353	+	0.392266i
$176$	−12.6260	−	34.6895i	−0.951717	−	2.61482i
$177$		0			0
$178$	43.1841	−	7.61452i	3.23679	−	0.570733i
$179$	4.68484	+	2.70479i	0.350161	+	0.202166i	0.664756	−	0.747060i	$-0.268535\pi$
$179$	4.68484	+	2.70479i	0.350161	+	0.202166i	−0.314595	+	0.949226i	$0.601869\pi$
$180$		0			0
$181$	−1.56807	+	0.905328i	−0.116554	+	0.0672925i	−0.557144	−	0.830416i	$-0.688103\pi$
$181$	−1.56807	+	0.905328i	−0.116554	+	0.0672925i	0.440590	+	0.897709i	$0.354769\pi$
$182$	−12.3071	+	0.507029i	−0.912266	+	0.0375835i
$183$		0			0
$184$	−4.15490	+	23.5636i	−0.306304	+	1.73713i
$185$	−4.66027	−	3.91043i	−0.342630	−	0.287501i
$186$		0			0
$187$	4.44405	−	12.2099i	0.324981	−	0.892879i
$188$	−13.3508			−0.973705
$189$		0			0
$190$	−5.89585			−0.427730
$191$	4.04999	−	11.1272i	0.293047	−	0.805139i	−0.702570	−	0.711614i	$-0.747964\pi$
$191$	4.04999	−	11.1272i	0.293047	−	0.805139i	0.995617	−	0.0935249i	$-0.0298135\pi$
$192$		0			0
$193$	13.2951	+	11.1559i	0.957000	+	0.803018i	0.980462	−	0.196707i	$-0.0630247\pi$
$193$	13.2951	+	11.1559i	0.957000	+	0.803018i	−0.0234627	+	0.999725i	$0.507469\pi$
$194$	2.63268	−	14.9307i	0.189015	−	1.07196i
$195$		0			0
$196$	−26.3029	−	18.6109i	−1.87878	−	1.32935i
$197$	−14.3984	+	8.31290i	−1.02584	+	0.592270i	−0.915791	−	0.401656i	$-0.868435\pi$
$197$	−14.3984	+	8.31290i	−1.02584	+	0.592270i	−0.110051	+	0.993926i	$0.535101\pi$
$198$		0			0
$199$	−19.4018	−	11.2016i	−1.37536	−	0.794062i	−0.383760	−	0.923433i	$-0.625371\pi$
$199$	−19.4018	−	11.2016i	−1.37536	−	0.794062i	−0.991596	+	0.129371i	$0.958704\pi$
$200$	42.6323	−	7.51722i	3.01456	−	0.531548i
$201$		0			0
$202$	5.09879	+	14.0088i	0.358750	+	0.985657i
$203$	−1.28089	+	4.02789i	−0.0899005	+	0.282703i
$204$		0			0
$205$	−7.26917	−	41.2255i	−0.507701	−	2.87932i
$206$	−1.71098	+	2.96350i	−0.119210	+	0.206477i
$207$		0			0
$208$	−12.5238	+	7.23062i	−0.868369	+	0.501353i
$209$	2.40006	−	2.01389i	0.166016	−	0.139304i
$210$		0			0
$211$	1.47800	−	8.38217i	0.101750	−	0.577052i	−0.890719	−	0.454554i	$-0.849798\pi$
$211$	1.47800	−	8.38217i	0.101750	−	0.577052i	0.992469	−	0.122498i	$-0.0390904\pi$
$212$	−12.7792	+	15.2297i	−0.877679	+	1.04598i
$213$		0			0
$214$	−12.9807	−	4.72460i	−0.887345	−	0.322967i
$215$	1.04221			0.0710782
$216$		0			0
$217$	5.00851	−	6.49410i	0.340000	−	0.440848i
$218$	−7.36371	+	20.2316i	−0.498734	+	1.37026i
$219$		0			0
$220$	−46.3492	+	55.2368i	−3.12486	+	3.72406i
$221$	−5.01271	−	0.883876i	−0.337191	−	0.0594559i
$222$		0			0
$223$	1.93481	+	2.30582i	0.129565	+	0.154409i	0.826926	−	0.562310i	$-0.190087\pi$
$223$	1.93481	+	2.30582i	0.129565	+	0.154409i	−0.697362	+	0.716719i	$0.745643\pi$
$224$	−18.7037	−	2.50918i	−1.24969	−	0.167652i
$225$		0			0
$226$	14.9599	−	25.9112i	0.995115	−	1.72359i
$227$	−1.74616	−	9.90298i	−0.115897	−	0.657284i	−0.986302	−	0.164948i	$-0.947254\pi$
$227$	−1.74616	−	9.90298i	−0.115897	−	0.657284i	0.870405	−	0.492336i	$-0.163857\pi$
$228$		0			0
$229$	−8.78597	−	24.1392i	−0.580593	−	1.59517i	−0.787170	−	0.616736i	$-0.788455\pi$
$229$	−8.78597	−	24.1392i	−0.580593	−	1.59517i	0.206577	−	0.978430i	$-0.433768\pi$
$230$	29.2562	−	10.6484i	1.92909	−	0.702133i
$231$		0			0
$232$	1.85553	+	10.5232i	0.121821	+	0.690884i
$233$	−0.222223	−	0.128301i	−0.0145583	−	0.00840525i	0.492703	−	0.870197i	$-0.336009\pi$
$233$	−0.222223	−	0.128301i	−0.0145583	−	0.00840525i	−0.507261	+	0.861792i	$0.669342\pi$
$234$		0			0
$235$	4.91193	+	8.50771i	0.320419	+	0.554982i
$236$	−27.2596	+	22.8735i	−1.77445	+	1.48894i
$237$		0			0
$238$	−12.8692	−	14.1138i	−0.834187	−	0.914860i
$239$	−8.49409	+	10.1229i	−0.549437	+	0.654794i	−0.967276	−	0.253727i	$-0.918343\pi$
$239$	−8.49409	+	10.1229i	−0.549437	+	0.654794i	0.417838	+	0.908521i	$0.362788\pi$
$240$		0			0
$241$	4.64833	−	12.7712i	0.299425	−	0.822664i	−0.695171	−	0.718844i	$-0.744671\pi$
$241$	4.64833	−	12.7712i	0.299425	−	0.822664i	0.994596	−	0.103820i	$-0.0331064\pi$
$242$		−	26.7001i		−	1.71635i
$243$		0			0
$244$		−	5.60797i		−	0.359014i
$245$	−2.18251	+	23.6085i	−0.139435	+	1.50829i
$246$		0			0
$247$	−0.940189	−	0.788912i	−0.0598228	−	0.0501973i
$248$	3.60035	−	20.4186i	0.228623	−	1.29658i
$249$		0			0
$250$	−8.23493	−	9.81400i	−0.520822	−	0.620692i
$251$	−11.8874	−	20.5896i	−0.750326	−	1.29960i	−0.947665	−	0.319268i	$-0.896563\pi$
$251$	−11.8874	−	20.5896i	−0.750326	−	1.29960i	0.197338	−	0.980335i	$-0.436770\pi$
$252$		0			0
$253$	−8.27223	+	14.3279i	−0.520071	+	0.900789i
$254$	30.9418	−	5.45588i	1.94146	−	0.342332i
$255$		0			0
$256$	24.2175	−	8.81446i	1.51360	−	0.550904i
$257$	−9.29984	+	3.38487i	−0.580108	+	0.211142i	−0.615373	−	0.788236i	$-0.710995\pi$
$257$	−9.29984	+	3.38487i	−0.580108	+	0.211142i	0.0352650	+	0.999378i	$0.488772\pi$
$258$		0			0
$259$	2.20464	−	4.20977i	0.136990	−	0.261583i
$260$	24.4623	+	14.1233i	1.51709	+	0.875893i
$261$		0			0
$262$	26.4916	−	15.2949i	1.63665	−	0.944923i
$263$	−6.43655	−	7.67078i	−0.396895	−	0.473001i	0.530176	−	0.847888i	$-0.322126\pi$
$263$	−6.43655	−	7.67078i	−0.396895	−	0.473001i	−0.927070	+	0.374887i	$0.877681\pi$
$264$		0			0
$265$	14.4067	+	2.54028i	0.884994	+	0.156048i
$266$	−0.985755	−	4.49877i	−0.0604405	−	0.275837i
$267$		0			0
$268$	−3.80623	−	1.38535i	−0.232502	−	0.0846239i
$269$	14.5115			0.884779			0.442389	−	0.896823i	$-0.354131\pi$
$269$	14.5115			0.884779			0.442389	+	0.896823i	$0.354131\pi$
$270$		0			0
$271$		−	0.249134i		−	0.0151338i	−0.999971	−	0.00756690i	$-0.997591\pi$
$271$		−	0.249134i		−	0.0151338i	0.999971	−	0.00756690i	$-0.00240864\pi$
$272$	−21.0718	−	7.66952i	−1.27767	−	0.465033i
$273$		0			0
$274$	11.9292	+	10.0097i	0.720666	+	0.604711i
$275$	29.4782	+	5.19779i	1.77760	+	0.313439i
$276$		0			0
$277$	−11.2035	+	9.40083i	−0.673151	+	0.564841i	−0.913996	−	0.405723i	$-0.867020\pi$
$277$	−11.2035	+	9.40083i	−0.673151	+	0.564841i	0.240845	+	0.970564i	$0.422575\pi$
$278$	7.54675	+	13.0714i	0.452624	+	0.783967i
$279$		0			0
$280$	22.8019	+	55.4338i	1.36267	+	3.31280i
$281$	23.4578	−	4.13624i	1.39937	−	0.246747i	0.577488	−	0.816399i	$-0.304033\pi$
$281$	23.4578	−	4.13624i	1.39937	−	0.246747i	0.821886	+	0.569652i	$0.192922\pi$
$282$		0			0
$283$	6.60507	+	18.1473i	0.392630	+	1.07874i	0.965796	+	0.259303i	$0.0834930\pi$
$283$	6.60507	+	18.1473i	0.392630	+	1.07874i	−0.573166	+	0.819440i	$0.694285\pi$
$284$	21.1619	+	58.1419i	1.25573	+	3.45009i
$285$		0			0
$286$	−21.2051	+	3.73903i	−1.25388	+	0.221093i
$287$	30.2413	−	12.4393i	1.78509	−	0.734271i
$288$		0			0
$289$	4.55359	+	7.88705i	0.267858	+	0.463944i
$290$	10.6510	−	8.93728i	0.625451	−	0.524815i
$291$		0			0
$292$	59.1444	+	10.4288i	3.46117	+	0.610297i
$293$	17.3375	+	14.5479i	1.01287	+	0.849899i	0.988715	−	0.149810i	$-0.0478661\pi$
$293$	17.3375	+	14.5479i	1.01287	+	0.849899i	0.0241549	+	0.999708i	$0.492310\pi$
$294$		0			0
$295$	24.6052	+	8.95556i	1.43257	+	0.521413i
$296$		−	12.0140i		−	0.698301i
$297$		0			0
$298$	25.6784			1.48751
$299$	6.09020	+	2.21665i	0.352205	+	0.128192i
$300$		0			0
$301$	0.174252	+	0.795248i	0.0100437	+	0.0458373i
$302$	21.6639	+	3.81993i	1.24662	+	0.219812i
$303$		0			0
$304$	−3.47556	−	4.14201i	−0.199337	−	0.237560i
$305$	−3.57365	+	2.06325i	−0.204627	+	0.118141i
$306$		0			0
$307$	−3.45170	−	1.99284i	−0.196999	−	0.113737i	0.398256	−	0.917274i	$-0.369616\pi$
$307$	−3.45170	−	1.99284i	−0.196999	−	0.113737i	−0.595255	+	0.803537i	$0.702949\pi$
$308$	−49.8971	−	26.1309i	−2.84315	−	1.48895i
$309$		0			0
$310$	−25.3514	+	9.22714i	−1.43986	+	0.524066i
$311$	−2.45813	+	0.894685i	−0.139388	+	0.0507329i	−0.410772	−	0.911738i	$-0.634741\pi$
$311$	−2.45813	+	0.894685i	−0.139388	+	0.0507329i	0.271384	+	0.962471i	$0.412519\pi$
$312$		0			0
$313$	−25.8005	+	4.54932i	−1.45833	+	0.257143i	−0.845882	−	0.533369i	$-0.820926\pi$
$313$	−25.8005	+	4.54932i	−1.45833	+	0.257143i	−0.612446	+	0.790512i	$0.709814\pi$
$314$	−0.160148	+	0.277384i	−0.00903765	+	0.0156537i
$315$		0			0
$316$	−33.7398	−	58.4391i	−1.89801	−	3.28746i
$317$	3.22194	+	3.83976i	0.180962	+	0.215662i	0.848898	−	0.528556i	$-0.177266\pi$
$317$	3.22194	+	3.83976i	0.180962	+	0.215662i	−0.667936	+	0.744219i	$0.732822\pi$
$318$		0			0
$319$	−1.28301	+	7.27630i	−0.0718347	+	0.407395i
$320$	6.13554	+	5.14833i	0.342987	+	0.287800i
$321$		0			0
$322$	13.0166	+	20.5432i	0.725386	+	1.14483i
$323$		−	1.90315i		−	0.105894i
$324$		0			0
$325$		−	11.7258i		−	0.650430i
$326$	−10.0345	+	27.5696i	−0.555761	+	1.52694i
$327$		0			0
$328$	53.1390	−	63.3286i	2.93411	−	3.49673i
$329$	−5.67047	+	5.17044i	−0.312623	+	0.285055i
$330$		0			0
$331$	5.54912	−	4.65626i	0.305007	−	0.255931i	−0.477418	−	0.878677i	$-0.658427\pi$
$331$	5.54912	−	4.65626i	0.305007	−	0.255931i	0.782425	+	0.622745i	$0.213983\pi$
$332$	16.0612	+	27.8188i	0.881472	+	1.52675i
$333$		0			0
$334$	22.6772	+	13.0927i	1.24084	+	0.716400i
$335$	0.517553	+	2.93519i	0.0282769	+	0.160366i
$336$		0			0
$337$	0.545928	−	0.198702i	0.0297386	−	0.0108240i	−0.327108	−	0.944987i	$-0.606074\pi$
$337$	0.545928	−	0.198702i	0.0297386	−	0.0108240i	0.356847	+	0.934163i	$0.383852\pi$
$338$	−8.54036	−	23.4644i	−0.464534	−	1.27630i
$339$		0			0
$340$	7.60587	+	43.1350i	0.412486	+	2.33932i
$341$	7.16814	−	12.4156i	0.388177	−	0.672342i
$342$		0			0
$343$	−18.3791	+	2.28188i	−0.992381	+	0.123210i
$344$	1.32298	+	1.57667i	0.0713304	+	0.0850083i
$345$		0			0
$346$	−47.7946	−	8.42747i	−2.56945	−	0.453064i
$347$	−2.56214	+	3.05344i	−0.137543	+	0.163917i	−0.830419	−	0.557140i	$-0.811899\pi$
$347$	−2.56214	+	3.05344i	−0.137543	+	0.163917i	0.692876	+	0.721057i	$0.256343\pi$
$348$		0			0
$349$	−4.94233	+	13.5789i	−0.264557	+	0.726863i	0.734289	+	0.678837i	$0.237516\pi$
$349$	−4.94233	+	13.5789i	−0.264557	+	0.726863i	−0.998846	+	0.0480269i	$0.984707\pi$
$350$	26.8715	−	34.8420i	1.43634	−	1.86238i
$351$		0			0
$352$	−32.9885			−1.75829
$353$	5.93484	+	2.16010i	0.315880	+	0.114971i	0.495094	−	0.868839i	$-0.335133\pi$
$353$	5.93484	+	2.16010i	0.315880	+	0.114971i	−0.179215	+	0.983810i	$0.557356\pi$
$354$		0			0
$355$	29.2649	−	34.8765i	1.55322	−	1.85105i
$356$	13.6400	−	77.3563i	0.722919	−	4.09988i
$357$		0			0
$358$	10.6485	−	8.93517i	0.562792	−	0.472238i
$359$	28.2385	−	16.3035i	1.49037	−	0.860467i	0.490433	−	0.871479i	$-0.336839\pi$
$359$	28.2385	−	16.3035i	1.49037	−	0.860467i	0.999939	+	0.0110119i	$0.00350528\pi$
$360$		0			0
$361$	−9.27055	+	16.0571i	−0.487924	+	0.845109i
$362$	0.807937	+	4.58204i	0.0424642	+	0.240827i
$363$		0			0
$364$	−6.68669	+	21.0271i	−0.350478	+	1.10212i
$365$	−15.1144	−	41.5264i	−0.791122	−	2.17359i
$366$		0			0
$367$	−28.3869	+	5.00537i	−1.48178	+	0.261278i	−0.855290	−	0.518150i	$-0.826621\pi$
$367$	−28.3869	+	5.00537i	−1.48178	+	0.261278i	−0.626492	+	0.779428i	$0.715510\pi$
$368$	24.7270	+	14.2762i	1.28899	+	0.744196i
$369$		0			0
$370$	−13.5382	+	7.81626i	−0.703815	+	0.406348i
$371$	0.470380	+	11.4176i	0.0244209	+	0.592771i
$372$		0			0
$373$	0.466317	−	2.64461i	0.0241450	−	0.136933i	−0.970352	−	0.241694i	$-0.922297\pi$
$373$	0.466317	−	2.64461i	0.0241450	−	0.136933i	0.994497	+	0.104762i	$0.0334079\pi$
$374$	−25.5772	−	21.4618i	−1.32257	−	1.10976i
$375$		0			0
$376$	−6.63536	+	18.2305i	−0.342193	+	0.940167i
$377$	2.89436			0.149067
$378$		0			0
$379$	14.7592			0.758131			0.379066	−	0.925370i	$-0.376245\pi$
$379$	14.7592			0.758131			0.379066	+	0.925370i	$0.376245\pi$
$380$	−3.61219	+	9.92441i	−0.185301	+	0.509111i
$381$		0			0
$382$	−23.3092	−	19.5587i	−1.19260	−	1.00071i
$383$	−5.10475	+	28.9505i	−0.260841	+	1.47930i	0.519783	+	0.854298i	$0.326013\pi$
$383$	−5.10475	+	28.9505i	−0.260841	+	1.47930i	−0.780623	+	0.625002i	$0.785098\pi$
$384$		0			0
$385$	1.70603	+	41.4106i	0.0869475	+	2.11048i
$386$	38.6223	−	22.2986i	1.96583	−	1.13497i
$387$		0			0
$388$	−23.5196	−	13.5791i	−1.19403	−	0.689372i
$389$	−33.7474	+	5.95059i	−1.71106	+	0.301707i	−0.941537	−	0.336909i	$-0.890619\pi$
$389$	−33.7474	+	5.95059i	−1.71106	+	0.301707i	−0.769526	+	0.638615i	$0.779508\pi$
$390$		0			0
$391$	3.43723	+	9.44371i	0.173828	+	0.477589i
$392$	−38.4858	+	26.6670i	−1.94382	+	1.34688i
$393$		0			0
$394$	7.41864	+	42.0732i	0.373746	+	2.11962i
$395$	−24.8267	+	43.0011i	−1.24917	+	2.16362i
$396$		0			0
$397$	−20.6504	+	11.9225i	−1.03642	+	0.598375i	−0.918816	−	0.394686i	$-0.870853\pi$
$397$	−20.6504	+	11.9225i	−1.03642	+	0.598375i	−0.117600	+	0.993061i	$0.537520\pi$
$398$	−44.0998	+	37.0041i	−2.21052	+	1.85485i
$399$		0			0
$400$	8.97032	−	50.8732i	0.448516	−	2.54366i
$401$	−16.1656	+	19.2654i	−0.807269	+	0.962066i	−0.999815	−	0.0192219i	$-0.993881\pi$
$401$	−16.1656	+	19.2654i	−0.807269	+	0.962066i	0.192546	+	0.981288i	$0.438326\pi$
$402$		0			0
$403$	−5.27735	−	1.92080i	−0.262883	−	0.0956817i
$404$	26.7047			1.32861
$405$		0			0
$406$	8.60029	+	6.63289i	0.426825	+	0.329185i
$407$	2.84120	−	7.80613i	0.140833	−	0.386935i
$408$		0			0
$409$	0.228603	−	0.272438i	0.0113037	−	0.0134712i	−0.760363	−	0.649498i	$-0.774979\pi$
$409$	0.228603	−	0.272438i	0.0113037	−	0.0134712i	0.771667	+	0.636027i	$0.219423\pi$
$410$	−105.935	−	18.6791i	−5.23174	−	0.922496i
$411$		0			0
$412$	3.94016	+	4.69570i	0.194118	+	0.231341i
$413$	−2.71959	+	20.2720i	−0.133822	+	0.997522i
$414$		0			0
$415$	11.8182	−	20.4698i	0.580135	−	1.00482i
$416$	2.24402	+	12.7265i	0.110022	+	0.623966i
$417$		0			0
$418$	−2.75354	−	7.56528i	−0.134680	−	0.370030i
$419$	25.0271	−	9.10912i	1.22265	−	0.445010i	0.351578	−	0.936159i	$-0.385645\pi$
$419$	25.0271	−	9.10912i	1.22265	−	0.445010i	0.871076	+	0.491149i	$0.163423\pi$
$420$		0			0
$421$	−4.94818	−	28.0625i	−0.241160	−	1.36768i	−0.829245	−	0.558885i	$-0.811229\pi$
$421$	−4.94818	−	28.0625i	−0.241160	−	1.36768i	0.588085	−	0.808799i	$-0.299882\pi$
$422$	−18.9412	−	10.9357i	−0.922042	−	0.532341i
$423$		0			0
$424$	14.4448	+	25.0192i	0.701504	+	1.21504i
$425$	13.9286	−	11.6875i	0.675636	−	0.566926i
$426$		0			0
$427$	−2.17183	−	2.38187i	−0.105102	−	0.115267i
$428$	−15.9057	+	18.9557i	−0.768831	+	0.916258i
$429$		0			0
$430$	0.915965	−	2.51659i	0.0441718	−	0.121361i
$431$			26.0928i			1.25684i	0.777872	+	0.628422i	$0.216299\pi$
$431$			26.0928i			1.25684i	−0.777872	+	0.628422i	$0.783701\pi$
$432$		0			0
$433$			21.3082i			1.02401i	0.858983	+	0.512004i	$0.171097\pi$
$433$			21.3082i			1.02401i	−0.858983	+	0.512004i	$0.828903\pi$
$434$	−11.2793	−	17.8014i	−0.541423	−	0.854492i
$435$		0			0
$436$	29.5441	+	24.7905i	1.41491	+	1.18725i
$437$	−0.420792	+	2.38643i	−0.0201292	+	0.114158i
$438$		0			0
$439$	−1.15331	−	1.37446i	−0.0550444	−	0.0655994i	0.737820	−	0.674998i	$-0.235855\pi$
$439$	−1.15331	−	1.37446i	−0.0550444	−	0.0655994i	−0.792864	+	0.609398i	$0.791411\pi$
$440$	52.3903	+	90.7427i	2.49761	+	4.32599i
$441$		0			0
$442$	−6.53977	+	11.3272i	−0.311065	+	0.538781i
$443$	−19.7101	+	3.47542i	−0.936454	+	0.165122i	−0.620993	−	0.783816i	$-0.713270\pi$
$443$	−19.7101	+	3.47542i	−0.936454	+	0.165122i	−0.315461	+	0.948938i	$0.602159\pi$
$444$		0			0
$445$	−54.3133	+	19.7684i	−2.57470	+	0.937113i
$446$	7.26823	−	2.64542i	0.344160	−	0.125264i
$447$		0			0
$448$	−2.90255	+	5.54243i	−0.137132	+	0.261855i
$449$	0.145244	+	0.0838569i	0.00685451	+	0.00395745i	0.503423	−	0.864040i	$-0.332074\pi$
$449$	0.145244	+	0.0838569i	0.00685451	+	0.00395745i	−0.496569	+	0.867997i	$0.665407\pi$
$450$		0			0
$451$	49.5037	−	28.5810i	2.33104	−	1.34583i
$452$	−34.4506	−	41.0567i	−1.62042	−	1.93114i
$453$		0			0
$454$	−25.4471	−	4.48700i	−1.19429	−	0.210585i
$455$	15.8595	−	3.47508i	0.743506	−	0.162914i
$456$		0			0
$457$	19.2205	+	6.99570i	0.899099	+	0.327245i	0.749892	−	0.661561i	$-0.230106\pi$
$457$	19.2205	+	6.99570i	0.899099	+	0.327245i	0.149207	+	0.988806i	$0.452328\pi$
$458$	−66.0099			−3.08444
$459$		0			0
$460$		−	55.7704i		−	2.60031i
$461$	1.81793	+	0.661673i	0.0846695	+	0.0308172i	0.384008	−	0.923330i	$-0.374544\pi$
$461$	1.81793	+	0.661673i	0.0846695	+	0.0308172i	−0.299338	+	0.954147i	$0.596766\pi$
$462$		0			0
$463$	−30.6253	−	25.6977i	−1.42328	−	1.19427i	−0.949555	−	0.313599i	$-0.898465\pi$
$463$	−30.6253	−	25.6977i	−1.42328	−	1.19427i	−0.473724	−	0.880674i	$-0.657090\pi$
$464$	12.5574	+	2.21421i	0.582962	+	0.102792i
$465$		0			0
$466$	−0.505108	+	0.423836i	−0.0233987	+	0.0196338i
$467$	0.858878	+	1.48762i	0.0397442	+	0.0688389i	0.885213	−	0.465186i	$-0.154012\pi$
$467$	0.858878	+	1.48762i	0.0397442	+	0.0688389i	−0.845469	+	0.534024i	$0.820679\pi$
$468$		0			0
$469$	−2.15313	+	0.885660i	−0.0994223	+	0.0408960i
$470$	24.8602	−	4.38353i	1.14672	−	0.202197i
$471$		0			0
$472$	17.6858	+	48.5912i	0.814053	+	2.23659i
$473$	0.486743	+	1.33732i	0.0223805	+	0.0614899i
$474$		0			0
$475$	4.31762	−	0.761313i	0.198106	−	0.0349314i
$476$	−31.6420	+	13.0155i	−1.45031	+	0.596565i
$477$		0			0
$478$	16.9782	+	29.4071i	0.776564	+	1.34505i
$479$	22.9906	−	19.2914i	1.05047	−	0.881447i	0.0573246	−	0.998356i	$-0.481743\pi$
$479$	22.9906	−	19.2914i	1.05047	−	0.881447i	0.993143	+	0.116909i	$0.0372985\pi$
$480$		0			0
$481$	−3.20475	−	0.565084i	−0.146124	−	0.0257656i
$482$	−26.7529	−	22.4483i	−1.21856	−	1.02249i
$483$		0			0
$484$	−44.9439	−	16.3582i	−2.04291	−	0.743557i
$485$			19.9837i			0.907412i
$486$		0			0
$487$	−37.1109			−1.68165			−0.840827	−	0.541304i	$-0.817931\pi$
$487$	−37.1109			−1.68165			−0.840827	+	0.541304i	$0.817931\pi$
$488$	−7.65770	−	2.78717i	−0.346648	−	0.126169i
$489$		0			0
$490$	55.0887	+	26.0188i	2.48865	+	1.17541i
$491$	33.6615	+	5.93543i	1.51912	+	0.267862i	0.870088	−	0.492897i	$-0.164062\pi$
$491$	33.6615	+	5.93543i	1.51912	+	0.267862i	0.649034	+	0.760759i	$0.275173\pi$
$492$		0			0
$493$	2.88490	+	3.43809i	0.129929	+	0.154844i
$494$	−2.73126	+	1.57689i	−0.122885	+	0.0709478i
$495$		0			0
$496$	−21.4267	−	12.3707i	−0.962089	−	0.555462i
$497$	31.5051	+	16.4991i	1.41320	+	0.740085i
$498$		0			0
$499$	22.0595	−	8.02898i	0.987517	−	0.359427i	0.202759	−	0.979229i	$-0.435009\pi$
$499$	22.0595	−	8.02898i	0.987517	−	0.359427i	0.784758	+	0.619802i	$0.212787\pi$
$500$	−21.5650	+	7.84903i	−0.964417	+	0.351019i
$501$		0			0
$502$	−60.1644	+	10.6086i	−2.68527	+	0.473486i
$503$	−8.06083	+	13.9618i	−0.359415	+	0.622524i	−0.987863	−	0.155327i	$-0.950357\pi$
$503$	−8.06083	+	13.9618i	−0.359415	+	0.622524i	0.628449	+	0.777851i	$0.283690\pi$
$504$		0			0
$505$	−9.82502	−	17.0174i	−0.437208	−	0.757266i
$506$	27.3270	+	32.5670i	1.21483	+	1.44778i
$507$		0			0
$508$	9.77319	−	55.4265i	0.433615	−	2.45915i
$509$	−25.7566	−	21.6124i	−1.14164	−	0.957952i	−0.142151	−	0.989845i	$-0.545402\pi$
$509$	−25.7566	−	21.6124i	−1.14164	−	0.957952i	−0.999491	+	0.0318930i	$0.989846\pi$
$510$		0			0
$511$	29.1592	−	18.4758i	1.28993	−	0.817322i
$512$		−	49.8464i		−	2.20292i
$513$		0			0
$514$			25.4309i			1.12171i
$515$	1.54267	−	4.23846i	0.0679783	−	0.186769i
$516$		0			0
$517$	−8.62268	+	10.2761i	−0.379225	+	0.451943i
$518$	−8.22761	−	9.02330i	−0.361501	−	0.396461i
$519$		0			0
$520$	31.4433	−	26.3841i	1.37888	−	1.15702i
$521$	−5.45369	−	9.44606i	−0.238930	−	0.413839i	0.721477	−	0.692438i	$-0.243463\pi$
$521$	−5.45369	−	9.44606i	−0.238930	−	0.413839i	−0.960408	+	0.278599i	$0.910130\pi$
$522$		0			0
$523$	23.6689	+	13.6653i	1.03497	+	0.597541i	0.918405	−	0.395642i	$-0.129478\pi$
$523$	23.6689	+	13.6653i	1.03497	+	0.597541i	0.116566	+	0.993183i	$0.462811\pi$
$524$	−9.51523	−	53.9636i	−0.415675	−	2.35741i
$525$		0			0
$526$	−24.1793	+	8.80053i	−1.05427	+	0.383721i
$527$	−2.97846	−	8.18326i	−0.129744	−	0.356469i
$528$		0			0
$529$	1.77187	+	10.0488i	0.0770378	+	0.436903i
$530$	18.7955	−	32.5547i	0.816424	−	1.41409i
$531$		0			0
$532$	−8.17665	−	1.09693i	−0.354503	−	0.0475581i
$533$	−14.3936	−	17.1536i	−0.623454	−	0.743004i
$534$		0			0
$535$	17.9313	+	3.16178i	0.775239	+	0.136696i
$536$	−3.78340	+	4.50889i	−0.163418	+	0.194754i
$537$		0			0
$538$	12.7536	−	35.0403i	0.549848	−	1.51070i
$539$	−31.3127	+	8.22540i	−1.34873	+	0.354293i
$540$		0			0
$541$	−27.4497			−1.18015			−0.590076	−	0.807347i	$-0.700902\pi$
$541$	−27.4497			−1.18015			−0.590076	+	0.807347i	$0.700902\pi$
$542$	−0.601575	−	0.218955i	−0.0258399	−	0.00940494i
$543$		0			0
$544$	−12.8806	+	15.3504i	−0.552249	+	0.658145i
$545$	4.92791	−	27.9476i	0.211089	−	1.19714i
$546$		0			0
$547$	−32.0533	+	26.8959i	−1.37050	+	1.14999i	−0.397921	+	0.917420i	$0.630268\pi$
$547$	−32.0533	+	26.8959i	−1.37050	+	1.14999i	−0.972580	+	0.232568i	$0.925287\pi$
$548$	24.1578	−	13.9475i	1.03197	−	0.595809i
$549$		0			0
$550$	38.4583	−	66.6118i	1.63987	−	2.84034i
$551$	0.187920	+	1.06575i	0.00800567	+	0.0454024i
$552$		0			0
$553$	−36.9624	−	11.7542i	−1.57180	−	0.499838i
$554$	12.8535	+	35.3147i	0.546093	+	1.50038i
$555$		0			0
$556$	26.6264	−	4.69496i	1.12921	−	0.199111i
$557$	−27.5246	−	15.8913i	−1.16625	−	0.673337i	−0.213459	−	0.976952i	$-0.568473\pi$
$557$	−27.5246	−	15.8913i	−1.16625	−	0.673337i	−0.952795	+	0.303616i	$0.901806\pi$
$558$		0			0
$559$	0.482805	−	0.278748i	0.0204205	−	0.0117898i
$560$	71.4662	−	2.94426i	3.02000	−	0.124418i
$561$		0			0
$562$	10.6286	−	60.2779i	0.448342	−	2.54267i
$563$	6.98724	+	5.86299i	0.294477	+	0.247095i	0.778041	−	0.628214i	$-0.216214\pi$
$563$	6.98724	+	5.86299i	0.294477	+	0.247095i	−0.483564	+	0.875309i	$0.660658\pi$
$564$		0			0
$565$	−13.4883	+	37.0588i	−0.567457	+	1.55907i
$566$	49.6246			2.08588
$567$		0			0
$568$	89.9105			3.77256
$569$	4.11399	−	11.3031i	0.172468	−	0.473851i	−0.823100	−	0.567896i	$-0.807758\pi$
$569$	4.11399	−	11.3031i	0.172468	−	0.473851i	0.995568	+	0.0940452i	$0.0299798\pi$
$570$		0			0
$571$	22.3766	+	18.7762i	0.936433	+	0.785761i	0.976961	−	0.213417i	$-0.0684594\pi$
$571$	22.3766	+	18.7762i	0.936433	+	0.785761i	−0.0405277	+	0.999178i	$0.512904\pi$
$572$	−6.69777	+	37.9850i	−0.280048	+	1.58823i
$573$		0			0
$574$	−3.45878	−	83.9552i	−0.144367	−	3.50422i
$575$	−20.0497	+	11.5757i	−0.836131	+	0.482741i
$576$		0			0
$577$	12.2130	+	7.05117i	0.508433	+	0.293544i	0.732189	−	0.681101i	$-0.238499\pi$
$577$	12.2130	+	7.05117i	0.508433	+	0.293544i	−0.223756	+	0.974645i	$0.571832\pi$
$578$	23.0466	−	4.06374i	0.958613	−	0.169029i
$579$		0			0
$580$	−8.51847	−	23.4043i	−0.353710	−	0.971811i
$581$	17.5952	+	5.59534i	0.729972	+	0.232134i
$582$		0			0
$583$	3.46876	+	19.6723i	0.143662	+	0.814745i
$584$	43.6354	−	75.5787i	1.80565	−	3.12747i
$585$		0			0
$586$	50.3658	−	29.0787i	2.08059	−	1.20123i
$587$	0.422612	−	0.354614i	0.0174431	−	0.0146365i	−0.634024	−	0.773313i	$-0.718598\pi$
$587$	0.422612	−	0.354614i	0.0174431	−	0.0146365i	0.651467	+	0.758677i	$0.274154\pi$
$588$		0			0
$589$	0.364629	−	2.06791i	0.0150243	−	0.0852069i
$590$	43.2494	−	51.5426i	1.78055	−	2.12198i
$591$		0			0
$592$	−13.4718	−	4.90332i	−0.553686	−	0.201525i
$593$	−24.4959			−1.00593			−0.502964	−	0.864307i	$-0.667757\pi$
$593$	−24.4959			−1.00593			−0.502964	+	0.864307i	$0.667757\pi$
$594$		0			0
$595$	19.9356	+	15.3751i	0.817280	+	0.630320i
$596$	15.7323	−	43.2241i	0.644420	−	1.77053i
$597$		0			0
$598$	10.7050	−	12.7577i	0.437758	−	0.521700i
$599$	−5.18052	−	0.913465i	−0.211670	−	0.0373232i	0.0668074	−	0.997766i	$-0.478719\pi$
$599$	−5.18052	−	0.913465i	−0.211670	−	0.0373232i	−0.278478	+	0.960443i	$0.589830\pi$
$600$		0			0
$601$	17.5340	+	20.8963i	0.715228	+	0.852376i	0.994158	−	0.107936i	$-0.0344240\pi$
$601$	17.5340	+	20.8963i	0.715228	+	0.852376i	−0.278930	+	0.960312i	$0.589980\pi$
$602$	2.07340	+	0.278156i	0.0845056	+	0.0113368i
$603$		0			0
$604$	19.7028	−	34.1262i	0.801694	−	1.38857i
$605$	6.11126	+	34.6587i	0.248458	+	1.40908i
$606$		0			0
$607$	4.85192	+	13.3305i	0.196933	+	0.541069i	0.998374	−	0.0570048i	$-0.0181550\pi$
$607$	4.85192	+	13.3305i	0.196933	+	0.541069i	−0.801441	+	0.598074i	$0.795933\pi$
$608$	−4.54039	+	1.65257i	−0.184137	+	0.0670204i
$609$		0			0
$610$	1.84129	+	10.4425i	0.0745518	+	0.422804i
$611$	4.55091	+	2.62747i	0.184110	+	0.106296i
$612$		0			0
$613$	−2.75943	−	4.77947i	−0.111452	−	0.193041i	0.804904	−	0.593405i	$-0.202217\pi$
$613$	−2.75943	−	4.77947i	−0.111452	−	0.193041i	−0.916356	+	0.400364i	$0.868884\pi$
$614$	−7.84563	+	6.58326i	−0.316624	+	0.265679i
$615$		0			0
$616$	−60.4808	+	55.1475i	−2.43684	+	2.22196i
$617$	−25.0437	+	29.8460i	−1.00822	+	1.20155i	−0.0288310	+	0.999584i	$0.509178\pi$
$617$	−25.0437	+	29.8460i	−1.00822	+	1.20155i	−0.979392	+	0.201969i	$0.935266\pi$
$618$		0			0
$619$	−4.01593	+	11.0337i	−0.161414	+	0.443481i	−0.993863	−	0.110621i	$-0.964716\pi$
$619$	−4.01593	+	11.0337i	−0.161414	+	0.443481i	0.832449	+	0.554102i	$0.186938\pi$
$620$			48.3267i			1.94085i
$621$		0			0
$622$			6.72187i			0.269522i
$623$	−24.1650	−	38.1380i	−0.968148	−	1.52797i
$624$		0			0
$625$	−11.8533	−	9.94610i	−0.474132	−	0.397844i
$626$	−11.6901	+	66.2978i	−0.467230	+	2.64979i
$627$		0			0
$628$	0.368799	+	0.439518i	0.0147167	+	0.0175387i
$629$	−2.52304	−	4.37003i	−0.100600	−	0.174245i
$630$		0			0
$631$	13.6313	−	23.6101i	0.542654	−	0.939904i	−0.456097	−	0.889930i	$-0.650753\pi$
$631$	13.6313	−	23.6101i	0.542654	−	0.939904i	0.998751	−	0.0499740i	$-0.0159138\pi$
$632$	−96.5675	+	17.0274i	−3.84125	+	0.677315i
$633$		0			0
$634$	12.1034	−	4.40528i	0.480688	−	0.174956i
$635$	−38.9160	+	14.1642i	−1.54433	+	0.562091i
$636$		0			0
$637$	5.30325	+	11.5204i	0.210122	+	0.456455i
$638$	16.4422	+	9.49294i	0.650955	+	0.375829i
$639$		0			0
$640$	−24.0199	+	13.8679i	−0.949471	+	0.548178i
$641$	13.0135	+	15.5088i	0.514000	+	0.612562i	0.959151	−	0.282894i	$-0.0912944\pi$
$641$	13.0135	+	15.5088i	0.514000	+	0.612562i	−0.445151	+	0.895456i	$0.646850\pi$
$642$		0			0
$643$	−37.2220	−	6.56324i	−1.46789	−	0.258829i	−0.618164	−	0.786049i	$-0.712123\pi$
$643$	−37.2220	−	6.56324i	−1.46789	−	0.258829i	−0.849729	+	0.527220i	$0.823234\pi$
$644$	42.5550	−	9.32450i	1.67690	−	0.367437i
$645$		0			0
$646$	−4.59546	−	1.67261i	−0.180806	−	0.0658080i
$647$	23.4908			0.923517			0.461759	−	0.887006i	$-0.347219\pi$
$647$	23.4908			0.923517			0.461759	+	0.887006i	$0.347219\pi$
$648$		0			0
$649$			35.7547i			1.40350i
$650$	−28.3139	−	10.3054i	−1.11056	−	0.404211i
$651$		0			0
$652$	40.2597	+	33.7819i	1.57669	+	1.32300i
$653$	4.96907	+	0.876181i	0.194455	+	0.0342876i	0.270027	−	0.962853i	$-0.412967\pi$
$653$	4.96907	+	0.876181i	0.194455	+	0.0342876i	−0.0755724	+	0.997140i	$0.524078\pi$
$654$		0			0
$655$	−30.8872	+	25.9175i	−1.20686	+	1.01268i
$656$	−49.3249	−	85.4332i	−1.92581	−	3.33561i
$657$		0			0
$658$	7.50130	+	18.2364i	0.292431	+	0.710930i
$659$	−28.1030	+	4.95532i	−1.09474	+	0.193032i	−0.691724	−	0.722162i	$-0.743149\pi$
$659$	−28.1030	+	4.95532i	−1.09474	+	0.193032i	−0.403014	+	0.915194i	$0.632038\pi$
$660$		0			0
$661$	−5.93347	−	16.3021i	−0.230785	−	0.634077i	0.769203	−	0.639005i	$-0.220654\pi$
$661$	−5.93347	−	16.3021i	−0.230785	−	0.634077i	−0.999988	+	0.00492766i	$0.998431\pi$
$662$	−6.36639	−	17.4915i	−0.247437	−	0.679827i
$663$		0			0
$664$	45.9690	−	8.10558i	1.78394	−	0.314558i
$665$	2.30928	+	5.61410i	0.0895502	+	0.217706i
$666$		0			0
$667$	−2.85732	−	4.94902i	−0.110636	−	0.191627i
$668$	35.9323	−	30.1508i	1.39026	−	1.16657i
$669$		0			0
$670$	7.54236	+	1.32992i	0.291387	+	0.0513794i
$671$	−4.31646	−	3.62194i	−0.166635	−	0.139824i
$672$		0			0
$673$	−2.93848	−	1.06952i	−0.113270	−	0.0412270i	0.284763	−	0.958598i	$-0.408085\pi$
$673$	−2.93848	−	1.06952i	−0.113270	−	0.0412270i	−0.398034	+	0.917371i	$0.630307\pi$
$674$		−	1.49287i		−	0.0575031i
$675$		0			0
$676$	−44.7297			−1.72037
$677$	32.1288	+	11.6939i	1.23481	+	0.449434i	0.875242	−	0.483685i	$-0.160702\pi$
$677$	32.1288	+	11.6939i	1.23481	+	0.449434i	0.359568	+	0.933119i	$0.382924\pi$
$678$		0			0
$679$	−15.2483	+	3.34116i	−0.585177	+	0.128222i
$680$	62.6811	+	11.0524i	2.40371	+	0.423839i
$681$		0			0
$682$	−23.6797	−	28.2203i	−0.906741	−	1.08061i
$683$	−5.42717	+	3.13338i	−0.207665	+	0.119895i	−0.600226	−	0.799831i	$-0.704923\pi$
$683$	−5.42717	+	3.13338i	−0.207665	+	0.119895i	0.392561	+	0.919726i	$0.371589\pi$
$684$		0			0
$685$	−17.7760	−	10.2630i	−0.679186	−	0.392128i
$686$	−10.6428	+	46.3850i	−0.406345	+	1.77099i
$687$		0			0
$688$	2.30793	−	0.840019i	0.0879891	−	0.0320254i
$689$	7.35332	−	2.67639i	0.280139	−	0.101962i
$690$		0			0
$691$	−22.6829	+	3.99961i	−0.862898	+	0.152152i	−0.587546	−	0.809191i	$-0.699906\pi$
$691$	−22.6829	+	3.99961i	−0.862898	+	0.152152i	−0.275353	+	0.961343i	$0.588795\pi$
$692$	−43.4679	+	75.2887i	−1.65240	+	2.86205i
$693$		0			0
$694$	5.12126	+	8.87027i	0.194400	+	0.336711i
$695$	−12.7881	−	15.2402i	−0.485079	−	0.578095i
$696$		0			0
$697$	6.02951	−	34.1950i	0.228384	−	1.29523i
$698$	28.4450	+	23.8681i	1.07666	+	0.903423i
$699$		0			0
$700$	−42.1857	−	66.5790i	−1.59447	−	2.51645i
$701$		−	12.1725i		−	0.459751i	−0.973220	−	0.229875i	$-0.926168\pi$
$701$		−	12.1725i		−	0.459751i	0.973220	−	0.229875i	$-0.0738319\pi$
$702$		0			0
$703$		−	1.21673i		−	0.0458898i
$704$	−3.74062	+	10.2773i	−0.140980	+	0.387339i
$705$		0			0
$706$	10.4319	−	12.4322i	0.392609	−	0.467893i
$707$	11.3423	−	10.3421i	0.426570	−	0.388955i
$708$		0			0
$709$	10.1824	−	8.54408i	0.382410	−	0.320880i	−0.431238	−	0.902238i	$-0.641923\pi$
$709$	10.1824	−	8.54408i	0.382410	−	0.320880i	0.813648	+	0.581358i	$0.197479\pi$
$710$	−58.4953	−	101.317i	−2.19529	−	3.80235i
$711$		0			0
$712$	−98.8511	−	57.0717i	−3.70460	−	2.13885i
$713$	1.92547	+	10.9199i	0.0721093	+	0.408952i
$714$		0			0
$715$	26.6699	−	9.70706i	0.997398	−	0.363023i
$716$	−8.51645	−	23.3988i	−0.318275	−	0.874453i
$717$		0			0
$718$	−14.5497	−	82.5153i	−0.542989	−	3.07944i
$719$	−5.03392	+	8.71901i	−0.187734	+	0.325164i	−0.944494	−	0.328528i	$-0.893447\pi$
$719$	−5.03392	+	8.71901i	−0.187734	+	0.325164i	0.756761	+	0.653692i	$0.226781\pi$
$720$		0			0
$721$	3.49204	+	0.468472i	0.130050	+	0.0174468i
$722$	30.6249	+	36.4973i	1.13974	+	1.35829i
$723$		0			0
$724$	8.20787	+	1.44727i	0.305043	+	0.0537874i
$725$	−6.64587	+	7.92024i	−0.246821	+	0.294150i
$726$		0			0
$727$	7.35676	−	20.2125i	0.272847	−	0.749641i	−0.725279	−	0.688455i	$-0.758289\pi$
$727$	7.35676	−	20.2125i	0.272847	−	0.749641i	0.998126	−	0.0611864i	$-0.0194884\pi$
$728$	25.3892	+	19.5812i	0.940987	+	0.725727i
$729$		0			0
$730$	−113.556			−4.20289
$731$	0.812341	+	0.295668i	0.0300455	+	0.0109357i
$732$		0			0
$733$	−10.3290	+	12.3096i	−0.381510	+	0.454666i	−0.922290	−	0.386498i	$-0.873685\pi$
$733$	−10.3290	+	12.3096i	−0.381510	+	0.454666i	0.540780	+	0.841164i	$0.318129\pi$
$734$	−12.8620	+	72.9439i	−0.474744	+	2.69241i
$735$		0			0
$736$	19.5455	−	16.4006i	0.720455	−	0.604534i
$737$	−3.52458	+	2.03492i	−0.129830	+	0.0749572i
$738$		0			0
$739$	−14.4202	+	24.9765i	−0.530456	+	0.918777i	0.468912	+	0.883245i	$0.344646\pi$
$739$	−14.4202	+	24.9765i	−0.530456	+	0.918777i	−0.999369	+	0.0355323i	$0.988687\pi$
$740$	4.86263	+	27.5773i	0.178754	+	1.01376i
$741$		0			0
$742$	27.9830	+	8.89871i	1.02729	+	0.326682i
$743$	−14.1355	−	38.8370i	−0.518581	−	1.42479i	−0.872084	−	0.489357i	$-0.837232\pi$
$743$	−14.1355	−	38.8370i	−0.518581	−	1.42479i	0.353502	−	0.935434i	$-0.384991\pi$
$744$		0			0
$745$	−33.3325	+	5.87741i	−1.22121	+	0.215332i
$746$	−5.97603	−	3.45026i	−0.218798	−	0.126323i
$747$		0			0
$748$	−51.7967	+	29.9048i	−1.89387	+	1.09343i
$749$	0.585462	+	14.2109i	0.0213923	+	0.519257i
$750$		0			0
$751$	−4.57803	+	25.9633i	−0.167055	+	0.947415i	0.779866	+	0.625947i	$0.215287\pi$
$751$	−4.57803	+	25.9633i	−0.167055	+	0.947415i	−0.946920	+	0.321468i	$0.895824\pi$
$752$	17.7344	+	14.8810i	0.646709	+	0.542653i
$753$		0			0
$754$	2.54376	−	6.98891i	0.0926381	−	0.254521i
$755$	−28.9957			−1.05526
$756$		0			0
$757$	19.0655			0.692946			0.346473	−	0.938060i	$-0.387379\pi$
$757$	19.0655			0.692946			0.346473	+	0.938060i	$0.387379\pi$
$758$	12.9714	−	35.6387i	0.471143	−	1.29445i
$759$		0			0
$760$	11.7565	+	9.86490i	0.426454	+	0.357838i
$761$	8.16798	−	46.3229i	0.296089	−	1.67920i	−0.366654	−	0.930358i	$-0.619497\pi$
$761$	8.16798	−	46.3229i	0.296089	−	1.67920i	0.662743	−	0.748847i	$-0.269392\pi$
$762$		0			0
$763$	22.1490	−	0.912494i	0.801848	−	0.0330345i
$764$	−47.2037	+	27.2531i	−1.70777	+	0.985981i
$765$		0			0
$766$	65.4194	+	37.7699i	2.36370	+	1.36468i
$767$	13.7936	−	2.43219i	0.498059	−	0.0878212i
$768$		0			0
$769$	9.11120	+	25.0328i	0.328558	+	0.902706i	0.988477	+	0.151369i	$0.0483683\pi$
$769$	9.11120	+	25.0328i	0.328558	+	0.902706i	−0.659919	+	0.751337i	$0.729409\pi$
$770$	101.492	+	32.2749i	3.65753	+	1.16311i
$771$		0			0
$772$	−13.8724	−	78.6740i	−0.499277	−	2.83154i
$773$	−3.41916	+	5.92216i	−0.122979	+	0.213005i	−0.920941	−	0.389702i	$-0.872578\pi$
$773$	−3.41916	+	5.92216i	−0.122979	+	0.213005i	0.797962	+	0.602707i	$0.205911\pi$
$774$		0			0
$775$	17.3737	−	10.0307i	0.624082	−	0.360314i
$776$	−30.2315	+	25.3673i	−1.08525	+	0.910632i
$777$		0			0
$778$	−15.2908	+	86.7186i	−0.548203	+	3.10901i
$779$	5.38170	−	6.41366i	0.192819	−	0.229793i
$780$		0			0
$781$	58.4195	+	21.2630i	2.09041	+	0.760848i
$782$	25.8243			0.923474
$783$		0			0
$784$	14.1953	+	54.0392i	0.506976	+	1.92997i
$785$	0.144394	−	0.396720i	0.00515365	−	0.0141595i
$786$		0			0
$787$	23.0217	−	27.4362i	0.820636	−	0.977996i	−0.179347	−	0.983786i	$-0.557399\pi$
$787$	23.0217	−	27.4362i	0.820636	−	0.977996i	0.999983	+	0.00579002i	$0.00184303\pi$
$788$	75.3664	+	13.2891i	2.68482	+	0.473405i
$789$		0			0
$790$	82.0139	+	97.7404i	2.91792	+	3.47745i
$791$	−30.5325	−	4.09607i	−1.08561	−	0.145639i
$792$		0			0
$793$	−1.10366	+	1.91160i	−0.0391923	+	0.0678830i
$794$	10.6400	+	60.3423i	0.377598	+	2.14147i
$795$		0			0
$796$	35.2701	+	96.9037i	1.25011	+	3.43466i
$797$	21.1088	−	7.68297i	0.747712	−	0.272145i	0.0600693	−	0.998194i	$-0.480868\pi$
$797$	21.1088	−	7.68297i	0.747712	−	0.272145i	0.687643	+	0.726049i	$0.258646\pi$
$798$		0			0
$799$	1.41498	+	8.02473i	0.0500583	+	0.283894i
$800$	−39.9778	−	23.0812i	−1.41343	−	0.816043i
$801$		0			0
$802$	32.3121	+	55.9661i	1.14098	+	1.97623i
$803$	46.2258	−	38.7881i	1.63127	−	1.36880i
$804$		0			0
$805$	−21.5985	−	23.6873i	−0.761248	−	0.834868i
$806$	−9.27617	+	11.0549i	−0.326739	+	0.389393i
$807$		0			0
$808$	13.2723	−	36.4653i	0.466918	−	1.28285i
$809$		−	18.6798i		−	0.656746i	−0.944548	−	0.328373i	$-0.893500\pi$
$809$		−	18.6798i		−	0.656746i	0.944548	−	0.328373i	$-0.106500\pi$
$810$		0			0
$811$		−	45.1917i		−	1.58689i	−0.608640	−	0.793447i	$-0.708284\pi$
$811$		−	45.1917i		−	1.58689i	0.608640	−	0.793447i	$-0.291716\pi$
$812$	16.4342	−	10.4130i	0.576726	−	0.365425i
$813$		0			0
$814$	−16.3522	−	13.7211i	−0.573143	−	0.480924i
$815$	6.71526	−	38.0841i	0.235225	−	1.33403i
$816$		0			0
$817$	0.133986	+	0.159679i	0.00468758	+	0.00558645i
$818$	−0.456936	−	0.791436i	−0.0159764	−	0.0276719i
$819$		0			0
$820$	−96.3448	+	166.874i	−3.36451	+	5.82749i
$821$	20.6869	−	3.64765i	0.721976	−	0.127304i	0.199427	−	0.979913i	$-0.436092\pi$
$821$	20.6869	−	3.64765i	0.721976	−	0.127304i	0.522550	+	0.852609i	$0.324981\pi$
$822$		0			0
$823$	−22.7468	+	8.27916i	−0.792904	+	0.288593i	−0.706543	−	0.707671i	$-0.749746\pi$
$823$	−22.7468	+	8.27916i	−0.792904	+	0.288593i	−0.0863611	+	0.996264i	$0.527524\pi$
$824$	8.37026	−	3.04653i	0.291592	−	0.106131i
$825$		0			0
$826$	46.5601	+	24.3833i	1.62003	+	0.848405i
$827$	5.68375	+	3.28152i	0.197644	+	0.114110i	0.595556	−	0.803314i	$-0.296932\pi$
$827$	5.68375	+	3.28152i	0.197644	+	0.114110i	−0.397912	+	0.917423i	$0.630265\pi$
$828$		0			0
$829$	−23.4539	+	13.5411i	−0.814588	+	0.470303i	−0.848547	−	0.529121i	$-0.822522\pi$
$829$	−23.4539	+	13.5411i	−0.814588	+	0.470303i	0.0339585	+	0.999423i	$0.489189\pi$
$830$	−39.0411	−	46.5274i	−1.35514	−	1.61499i
$831$		0			0
$832$	4.21926	+	0.743969i	0.146276	+	0.0257925i
$833$	−8.39871	+	17.7823i	−0.290998	+	0.616120i
$834$		0			0
$835$	−32.4334	−	11.8048i	−1.12240	−	0.408521i
$836$	−14.4215			−0.498779
$837$		0			0
$838$		−	68.4378i		−	2.36415i
$839$	0.0158875	+	0.00578259i	0.000548499	+	0.000199637i	0.342294	−	0.939593i	$-0.388796\pi$
$839$	0.0158875	+	0.00578259i	0.000548499	+	0.000199637i	−0.341746	+	0.939792i	$0.611018\pi$
$840$		0			0
$841$	20.2603	+	17.0004i	0.698630	+	0.586220i
$842$	−72.1105	−	12.7150i	−2.48509	−	0.438189i
$843$		0			0
$844$	−30.0125	+	25.1835i	−1.03307	+	0.866851i
$845$	16.4567	+	28.5038i	0.566127	+	0.980560i
$846$		0			0
$847$	−25.4242	+	10.4579i	−0.873585	+	0.359337i
$848$	33.9504	−	5.98637i	1.16586	−	0.205573i
$849$		0			0
$850$	−15.9800	−	43.9046i	−0.548109	−	1.50592i
$851$	2.19751	+	6.03761i	0.0753296	+	0.206966i
$852$		0			0
$853$	48.3871	−	8.53196i	1.65674	−	0.292129i	0.734463	−	0.678649i	$-0.237434\pi$
$853$	48.3871	−	8.53196i	1.65674	−	0.292129i	0.922281	+	0.386520i	$0.126323\pi$
$854$	−7.66018	+	3.15091i	−0.262126	+	0.107822i
$855$		0			0
$856$	17.9789	+	31.1403i	0.614505	+	1.06435i
$857$	−39.9664	+	33.5358i	−1.36523	+	1.14556i	−0.390897	+	0.920434i	$0.627835\pi$
$857$	−39.9664	+	33.5358i	−1.36523	+	1.14556i	−0.974329	+	0.225127i	$0.927720\pi$
$858$		0			0
$859$	13.3149	+	2.34777i	0.454297	+	0.0801048i	0.396114	−	0.918201i	$-0.370358\pi$
$859$	13.3149	+	2.34777i	0.454297	+	0.0801048i	0.0581825	+	0.998306i	$0.481469\pi$
$860$	−3.67496	−	3.08366i	−0.125315	−	0.105152i
$861$		0			0
$862$	63.0054	+	22.9321i	2.14597	+	0.781070i
$863$		−	4.93737i		−	0.168070i	−0.996463	−	0.0840349i	$-0.973219\pi$
$863$		−	4.93737i		−	0.168070i	0.996463	−	0.0840349i	$-0.0267807\pi$
$864$		0			0
$865$	63.9698			2.17504
$866$	51.4523	+	18.7271i	1.74842	+	0.636373i
$867$		0			0
$868$	−36.8752	+	8.07997i	−1.25163	+	0.274252i
$869$	−66.7717	−	11.7737i	−2.26508	−	0.399394i
$870$		0			0
$871$	1.02480	+	1.22131i	0.0347239	+	0.0413823i
$872$	48.5349	−	28.0217i	1.64360	−	0.948933i
$873$		0			0
$874$	5.39261	+	3.11342i	0.182408	+	0.105313i
$875$	−6.11956	+	11.6853i	−0.206879	+	0.395036i
$876$		0			0
$877$	−28.7212	+	10.4537i	−0.969847	+	0.352995i	−0.777885	−	0.628407i	$-0.783707\pi$
$877$	−28.7212	+	10.4537i	−0.969847	+	0.352995i	−0.191962	+	0.981402i	$0.561485\pi$
$878$	−4.33247	+	1.57689i	−0.146214	+	0.0532174i
$879$		0			0
$880$	123.135	−	21.7121i	4.15089	−	0.731915i
$881$	18.8633	−	32.6722i	0.635521	−	1.10075i	−0.350883	−	0.936419i	$-0.614119\pi$
$881$	18.8633	−	32.6722i	0.635521	−	1.10075i	0.986404	−	0.164336i	$-0.0525481\pi$
$882$		0			0
$883$	−22.0384	−	38.1716i	−0.741651	−	1.28458i	−0.951743	−	0.306896i	$-0.900710\pi$
$883$	−22.0384	−	38.1716i	−0.741651	−	1.28458i	0.210092	−	0.977682i	$-0.432624\pi$
$884$	15.0602	+	17.9481i	0.506531	+	0.603660i
$885$		0			0
$886$	−8.93056	+	50.6477i	−0.300028	+	1.70154i
$887$	22.3368	+	18.7428i	0.749998	+	0.629323i	0.935502	−	0.353321i	$-0.114948\pi$
$887$	22.3368	+	18.7428i	0.749998	+	0.629323i	−0.185505	+	0.982643i	$0.559392\pi$
$888$		0			0
$889$	−17.3144	−	27.3262i	−0.580707	−	0.916491i
$890$			148.522i			4.97848i
$891$		0			0
$892$		−	13.8553i		−	0.463908i
$893$	−0.672002	+	1.84631i	−0.0224877	+	0.0617844i
$894$		0			0
$895$	−11.7774	+	14.0358i	−0.393676	+	0.469165i
$896$	−14.5978	−	16.0095i	−0.487677	−	0.534840i
$897$		0			0
$898$	0.330137	−	0.277018i	0.0110168	−	0.00924421i
$899$	2.47595	+	4.28847i	0.0825776	+	0.143029i
$900$		0			0
$901$	10.5085	+	6.06707i	0.350088	+	0.202123i
$902$	−25.5064	−	144.654i	−0.849270	−	4.81645i
$903$		0			0
$904$	−73.1850	+	26.6372i	−2.43410	+	0.885939i
$905$	−2.09752	−	5.76290i	−0.0697240	−	0.191565i
$906$		0			0
$907$	−6.57304	−	37.2776i	−0.218254	−	1.23778i	−0.875169	−	0.483817i	$-0.839250\pi$
$907$	−6.57304	−	37.2776i	−0.218254	−	1.23778i	0.656915	−	0.753964i	$-0.271861\pi$
$908$	−23.1434	+	40.0856i	−0.768042	+	1.33029i
$909$		0			0
$910$	5.54723	−	41.3496i	0.183889	−	1.37073i
$911$	27.6782	+	32.9856i	0.917021	+	1.09286i	0.995387	+	0.0959383i	$0.0305852\pi$
$911$	27.6782	+	32.9856i	0.917021	+	1.09286i	−0.0783664	+	0.996925i	$0.524970\pi$
$912$		0			0
$913$	31.7854	+	5.60462i	1.05194	+	0.185486i
$914$	33.7846	−	40.2629i	1.11750	−	1.33178i
$915$		0			0
$916$	−40.4420	+	111.114i	−1.33624	+	3.67130i
$917$	−24.9402	−	19.2349i	−0.823598	−	0.635192i
$918$		0			0
$919$	30.6114			1.00978			0.504888	−	0.863185i	$-0.331534\pi$
$919$	30.6114			1.00978			0.504888	+	0.863185i	$0.331534\pi$
$920$	−76.1545	−	27.7180i	−2.51074	−	0.913835i
$921$		0			0
$922$	3.19544	−	3.80818i	0.105236	−	0.125416i
$923$	4.22898	−	23.9837i	0.139198	−	0.789434i
$924$		0			0
$925$	8.90490	−	7.47210i	0.292791	−	0.245681i
$926$	−88.9670	+	51.3651i	−2.92364	+	1.68796i
$927$		0			0
$928$	5.69729	−	9.86800i	0.187023	−	0.323933i
$929$	−0.783935	−	4.44592i	−0.0257201	−	0.145866i	0.969243	−	0.246104i	$-0.0791506\pi$
$929$	−0.783935	−	4.44592i	−0.0257201	−	0.145866i	−0.994963	+	0.100238i	$0.968039\pi$
$930$		0			0
$931$	−3.89768	+	2.70072i	−0.127741	+	0.0885125i
$932$	0.403974	+	1.10991i	0.0132326	+	0.0363563i
$933$		0			0
$934$	4.34695	−	0.766485i	0.142237	−	0.0250801i
$935$	38.1134	+	22.0048i	1.24644	+	0.719633i
$936$		0			0
$937$	−4.61706	+	2.66566i	−0.150833	+	0.0870833i	−0.573517	−	0.819194i	$-0.694421\pi$
$937$	−4.61706	+	2.66566i	−0.150833	+	0.0870833i	0.422684	+	0.906277i	$0.361088\pi$
$938$	0.246260	+	5.97747i	0.00804066	+	0.195171i
$939$		0			0
$940$	7.85228	−	44.5325i	0.256113	−	1.45249i
$941$	9.86127	+	8.27459i	0.321468	+	0.269744i	0.789213	−	0.614120i	$-0.210489\pi$
$941$	9.86127	+	8.27459i	0.321468	+	0.269744i	−0.467745	+	0.883864i	$0.654933\pi$
$942$		0			0
$943$	−15.1213	+	41.5453i	−0.492416	+	1.35290i
$944$	61.7053			2.00834
$945$		0			0
$946$	3.65696			0.118898
$947$	−9.46635	+	26.0086i	−0.307615	+	0.845165i	0.685505	+	0.728068i	$0.259581\pi$
$947$	−9.46635	+	26.0086i	−0.307615	+	0.845165i	−0.993120	+	0.117098i	$0.962641\pi$
$948$		0			0
$949$	−18.1083	−	15.1947i	−0.587820	−	0.493240i
$950$	1.95630	−	11.0947i	0.0634707	−	0.359960i
$951$		0			0
$952$	2.04655	+	49.6760i	0.0663291	+	1.61001i
$953$	39.2760	−	22.6760i	1.27227	−	0.734547i	0.296858	−	0.954922i	$-0.404061\pi$
$953$	39.2760	−	22.6760i	1.27227	−	0.734547i	0.975415	+	0.220374i	$0.0707278\pi$
$954$		0			0
$955$	34.7338	+	20.0535i	1.12396	+	0.648917i
$956$	59.9024	−	10.5624i	1.93738	−	0.341613i
$957$		0			0
$958$	−26.3766	−	72.4692i	−0.852191	−	2.34137i
$959$	4.85900	−	15.2797i	0.156905	−	0.493407i
$960$		0			0
$961$	3.71462	+	21.0666i	0.119826	+	0.679569i
$962$	−4.18104	+	7.24178i	−0.134802	+	0.233484i
$963$		0			0
$964$	−54.1775	+	31.2794i	−1.74494	+	1.00744i
$965$	−45.0308	+	37.7853i	−1.44959	+	1.21635i
$966$		0			0
$967$	−2.82307	+	16.0104i	−0.0907838	+	0.514860i	0.905174	+	0.425041i	$0.139740\pi$
$967$	−2.82307	+	16.0104i	−0.0907838	+	0.514860i	−0.995958	+	0.0898197i	$0.971371\pi$
$968$	−44.6745	+	53.2409i	−1.43589	+	1.71123i
$969$		0			0
$970$	48.2539	+	17.5630i	1.54934	+	0.563914i
$971$	−38.7014			−1.24199			−0.620993	−	0.783816i	$-0.713270\pi$
$971$	−38.7014			−1.24199			−0.620993	+	0.783816i	$0.713270\pi$
$972$		0			0
$973$	9.49079	−	12.3059i	0.304261	−	0.394508i
$974$	−32.6155	+	89.6104i	−1.04507	+	2.87130i
$975$		0			0
$976$	−6.25073	+	7.44932i	−0.200081	+	0.238447i
$977$	30.7656	+	5.42481i	0.984279	+	0.173555i	0.642550	−	0.766244i	$-0.277876\pi$
$977$	30.7656	+	5.42481i	0.984279	+	0.173555i	0.341729	+	0.939799i	$0.388988\pi$
$978$		0			0
$979$	−50.7318	−	60.4598i	−1.62140	−	1.93230i
$980$	77.5480	−	76.7891i	2.47718	−	2.45294i
$981$		0			0
$982$	43.9161	−	76.0649i	1.40142	−	2.42733i
$983$	−2.40791	−	13.6559i	−0.0768003	−	0.435556i	−0.998827	−	0.0484290i	$-0.984579\pi$
$983$	−2.40791	−	13.6559i	−0.0768003	−	0.435556i	0.922026	−	0.387127i	$-0.126533\pi$
$984$		0			0
$985$	−19.2599	−	52.9161i	−0.613671	−	1.68605i
$986$	10.8373	−	3.94445i	0.345130	−	0.125617i
$987$		0			0
$988$	0.981013	+	5.56360i	0.0312102	+	0.177002i
$989$	−0.953253	−	0.550361i	−0.0303117	−	0.0175005i
$990$		0			0
$991$	0.458511	+	0.794164i	0.0145651	+	0.0252275i	0.873216	−	0.487333i	$-0.162030\pi$
$991$	0.458511	+	0.794164i	0.0145651	+	0.0252275i	−0.858651	+	0.512561i	$0.828697\pi$
$992$	−16.9367	+	14.2116i	−0.537742	+	0.451219i
$993$		0			0
$994$	67.5286	−	61.5738i	2.14188	−	1.95300i
$995$	48.7751	−	58.1278i	1.54627	−	1.84278i
$996$		0			0
$997$	5.13116	−	14.0978i	0.162506	−	0.446480i	−0.831537	−	0.555469i	$-0.812539\pi$
$997$	5.13116	−	14.0978i	0.162506	−	0.446480i	0.994043	+	0.108988i	$0.0347611\pi$
$998$		−	60.3227i		−	1.90948i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.503.21		132
3.2	odd	2		189.2.be.a.104.2	yes	132
7.6	odd	2	inner	567.2.be.a.503.22		132
21.20	even	2		189.2.be.a.104.1	yes	132
27.7	even	9		189.2.be.a.20.1	✓	132
27.20	odd	18	inner	567.2.be.a.62.22		132
189.20	even	18	inner	567.2.be.a.62.21		132
189.34	odd	18		189.2.be.a.20.2	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.1	✓	132	27.7	even	9
189.2.be.a.20.2	yes	132	189.34	odd	18
189.2.be.a.104.1	yes	132	21.20	even	2
189.2.be.a.104.2	yes	132	3.2	odd	2
567.2.be.a.62.21		132	189.20	even	18	inner
567.2.be.a.62.22		132	27.20	odd	18	inner
567.2.be.a.503.21		132	1.1	even	1	trivial
567.2.be.a.503.22		132	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.be (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.878867 - 2.41467i) q^{2} +(-3.52612 - 2.95877i) q^{4} +(-0.588152 + 3.33557i) q^{5} +(-2.64351 + 0.108907i) q^{7} +(-5.79269 + 3.34441i) q^{8} +(7.53740 + 4.35172i) q^{10} +(-4.55474 + 0.803123i) q^{11} +(0.619664 + 1.70251i) q^{13} +(-2.06032 + 6.47891i) q^{14} +(1.38602 + 7.86054i) q^{16} +(-1.40471 + 2.43302i) q^{17} +(-0.586660 + 0.338709i) q^{19} +(11.9431 - 10.0214i) q^{20} +(-2.06373 + 11.7040i) q^{22} +(2.29937 - 2.74028i) q^{23} +(-6.08167 - 2.21355i) q^{25} +4.65561 q^{26} +(9.64357 + 7.43751i) q^{28} +(0.546385 - 1.50118i) q^{29} +(-1.99247 + 2.37454i) q^{31} +(7.02429 + 1.23857i) q^{32} +(4.64039 + 5.53021i) q^{34} +(1.19152 - 8.88167i) q^{35} +(-0.898066 + 1.55550i) q^{37} +(0.302272 + 1.71427i) q^{38} +(-7.74856 - 21.2890i) q^{40} +(-11.6140 + 4.22715i) q^{41} +(-0.0534327 - 0.303032i) q^{43} +(18.4368 + 10.6445i) q^{44} +(-4.59602 - 7.96055i) q^{46} +(2.22186 - 1.86436i) q^{47} +(6.97628 - 0.575794i) q^{49} +(-10.6900 + 12.7398i) q^{50} +(2.85233 - 7.83672i) q^{52} -4.31910i q^{53} -15.6650i q^{55} +(14.9488 - 9.47185i) q^{56} +(-3.14465 - 2.63868i) q^{58} +(1.34243 - 7.61331i) q^{59} +(0.783123 + 0.933289i) q^{61} +(3.98260 + 6.89806i) q^{62} +(1.18236 - 2.04791i) q^{64} +(-6.04332 + 1.06560i) q^{65} +(0.826896 - 0.300966i) q^{67} +(12.1519 - 4.42294i) q^{68} +(-20.3991 - 10.6829i) q^{70} +(-11.6410 - 6.72094i) q^{71} +(-11.2992 + 6.52362i) q^{73} +(2.96672 + 3.53560i) q^{74} +(3.07080 + 0.541464i) q^{76} +(11.9530 - 2.61911i) q^{77} +(13.7757 + 5.01396i) q^{79} -27.0346 q^{80} +31.7590i q^{82} +(-6.55767 - 2.38680i) q^{83} +(-7.28935 - 6.11649i) q^{85} +(-0.778681 - 0.137302i) q^{86} +(23.6982 - 19.8852i) q^{88} +(8.53240 + 14.7785i) q^{89} +(-1.82350 - 4.43313i) q^{91} +(-16.2157 + 2.85927i) q^{92} +(-2.54910 - 7.00358i) q^{94} +(-0.784742 - 2.15606i) q^{95} +(5.81042 - 1.02453i) q^{97} +(4.74087 - 17.3514i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Introduction

L-functions

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