LMFDB - Embedded newform 819.2.fm.f.622.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			622.1
Character	$\chi$	$=$	819.622
Dual form			819.2.fm.f.370.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687394 + 2.56539i) q^{2} +(-4.37666 - 2.52687i) q^{4} +(-1.17771 + 1.17771i) q^{5} +(2.40809 + 1.09594i) q^{7} +(5.73490 - 5.73490i) q^{8} +O(q^{10})$	\(q+(-0.687394 + 2.56539i) q^{2} +(-4.37666 - 2.52687i) q^{4} +(-1.17771 + 1.17771i) q^{5} +(2.40809 + 1.09594i) q^{7} +(5.73490 - 5.73490i) q^{8} +(-2.21174 - 3.83085i) q^{10} +(4.50301 + 1.20658i) q^{11} +(3.59585 - 0.264293i) q^{13} +(-4.46682 + 5.42436i) q^{14} +(5.71638 + 9.90107i) q^{16} +(3.15625 - 5.46679i) q^{17} +(1.09384 + 4.08225i) q^{19} +(8.13039 - 2.17853i) q^{20} +(-6.19069 + 10.7226i) q^{22} +(-3.67599 + 2.12233i) q^{23} +2.22598i q^{25} +(-1.79375 + 9.40643i) q^{26} +(-7.77012 - 10.8815i) q^{28} +(0.526889 + 0.912598i) q^{29} +(5.61834 - 5.61834i) q^{31} +(-13.6615 + 3.66058i) q^{32} +(11.8549 + 11.8549i) q^{34} +(-4.12675 + 1.54534i) q^{35} +(0.572076 + 0.153287i) q^{37} -11.2245 q^{38} +13.5081i q^{40} +(1.24468 + 0.333510i) q^{41} +(-9.27990 - 5.35775i) q^{43} +(-16.6593 - 16.6593i) q^{44} +(-2.91776 - 10.8892i) q^{46} +(2.85718 + 2.85718i) q^{47} +(4.59783 + 5.27825i) q^{49} +(-5.71050 - 1.53012i) q^{50} +(-16.4057 - 7.92952i) q^{52} +0.398831 q^{53} +(-6.72427 + 3.88226i) q^{55} +(20.0953 - 7.52507i) q^{56} +(-2.70335 + 0.724361i) q^{58} +(-8.26243 + 2.21391i) q^{59} +(-4.22976 - 2.44205i) q^{61} +(10.5512 + 18.2752i) q^{62} -14.6977i q^{64} +(-3.92362 + 4.54615i) q^{65} +(-2.76762 + 10.3289i) q^{67} +(-27.6277 + 15.9509i) q^{68} +(-1.12770 - 11.6490i) q^{70} +(-4.31760 + 1.15690i) q^{71} +(0.935407 + 0.935407i) q^{73} +(-0.786484 + 1.36223i) q^{74} +(5.52795 - 20.6306i) q^{76} +(9.52134 + 7.84059i) q^{77} -0.927988 q^{79} +(-18.3929 - 4.92836i) q^{80} +(-1.71117 + 2.96383i) q^{82} +(7.79378 - 7.79378i) q^{83} +(2.72115 + 10.1555i) q^{85} +(20.1237 - 20.1237i) q^{86} +(32.7439 - 18.9047i) q^{88} +(1.28296 - 4.78807i) q^{89} +(8.94880 + 3.30440i) q^{91} +21.4514 q^{92} +(-9.29378 + 5.36577i) q^{94} +(-6.09595 - 3.51950i) q^{95} +(1.65635 + 6.18160i) q^{97} +(-16.7013 + 8.16698i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$

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 $

$2$	−0.687394	+	2.56539i	−0.486061	+	1.81400i	0.0891737	+	0.996016i	$0.471577\pi$
$2$	−0.687394	+	2.56539i	−0.486061	+	1.81400i	−0.575235	+	0.817988i	$0.695089\pi$
$3$		0			0
$3$		0			0
$4$	−4.37666	−	2.52687i	−2.18833	−	1.26343i
$5$	−1.17771	+	1.17771i	−0.526690	+	0.526690i	−0.919584	−	0.392894i	$-0.871474\pi$
$5$	−1.17771	+	1.17771i	−0.526690	+	0.526690i	0.392894	+	0.919584i	$0.371474\pi$
$6$		0			0
$7$	2.40809	+	1.09594i	0.910174	+	0.414227i
$7$	2.40809	+	1.09594i	0.910174	+	0.414227i
$8$	5.73490	−	5.73490i	2.02759	−	2.02759i
$9$		0			0
$10$	−2.21174	−	3.83085i	−0.699414	−	1.21142i
$11$	4.50301	+	1.20658i	1.35771	+	0.363797i	0.862975	−	0.505247i	$-0.168599\pi$
$11$	4.50301	+	1.20658i	1.35771	+	0.363797i	0.494734	+	0.869044i	$0.335265\pi$
$12$		0			0
$13$	3.59585	−	0.264293i	0.997310	−	0.0733017i
$13$	3.59585	−	0.264293i	0.997310	−	0.0733017i
$14$	−4.46682	+	5.42436i	−1.19381	+	1.44972i
$15$		0			0
$16$	5.71638	+	9.90107i	1.42910	+	2.47527i
$17$	3.15625	−	5.46679i	0.765503	−	1.32589i	−0.174476	−	0.984661i	$-0.555823\pi$
$17$	3.15625	−	5.46679i	0.765503	−	1.32589i	0.939980	−	0.341230i	$-0.110843\pi$
$18$		0			0
$19$	1.09384	+	4.08225i	0.250943	+	0.936532i	0.970303	+	0.241894i	$0.0777687\pi$
$19$	1.09384	+	4.08225i	0.250943	+	0.936532i	−0.719360	+	0.694638i	$0.755565\pi$
$20$	8.13039	−	2.17853i	1.81801	−	0.487134i
$21$		0			0
$22$	−6.19069	+	10.7226i	−1.31986	+	2.28606i
$23$	−3.67599	+	2.12233i	−0.766496	+	0.442537i	−0.831623	−	0.555340i	$-0.812588\pi$
$23$	−3.67599	+	2.12233i	−0.766496	+	0.442537i	0.0651270	+	0.997877i	$0.479255\pi$
$24$		0			0
$25$			2.22598i			0.445196i
$26$	−1.79375	+	9.40643i	−0.351784	+	1.84475i
$27$		0			0
$28$	−7.77012	−	10.8815i	−1.46841	−	2.05641i
$29$	0.526889	+	0.912598i	0.0978408	+	0.169465i	0.910791	−	0.412868i	$-0.135473\pi$
$29$	0.526889	+	0.912598i	0.0978408	+	0.169465i	−0.812950	+	0.582334i	$0.802140\pi$
$30$		0			0
$31$	5.61834	−	5.61834i	1.00908	−	1.00908i	0.00912491	−	0.999958i	$-0.497095\pi$
$31$	5.61834	−	5.61834i	1.00908	−	1.00908i	0.999958	−	0.00912491i	$-0.00290459\pi$
$32$	−13.6615	+	3.66058i	−2.41503	+	0.647105i
$33$		0			0
$34$	11.8549	+	11.8549i	2.03309	+	2.03309i
$35$	−4.12675	+	1.54534i	−0.697548	+	0.261210i
$36$		0			0
$37$	0.572076	+	0.153287i	0.0940488	+	0.0252003i	0.305537	−	0.952180i	$-0.401164\pi$
$37$	0.572076	+	0.153287i	0.0940488	+	0.0252003i	−0.211488	+	0.977381i	$0.567831\pi$
$38$	−11.2245			−1.82085
$39$		0			0
$40$			13.5081i			2.13583i
$41$	1.24468	+	0.333510i	0.194386	+	0.0520856i	0.354698	−	0.934981i	$-0.384584\pi$
$41$	1.24468	+	0.333510i	0.194386	+	0.0520856i	−0.160312	+	0.987066i	$0.551250\pi$
$42$		0			0
$43$	−9.27990	−	5.35775i	−1.41517	−	0.817050i	−0.419302	−	0.907847i	$-0.637725\pi$
$43$	−9.27990	−	5.35775i	−1.41517	−	0.817050i	−0.995869	+	0.0907973i	$0.971058\pi$
$44$	−16.6593	−	16.6593i	−2.51148	−	2.51148i
$45$		0			0
$46$	−2.91776	−	10.8892i	−0.430200	−	1.60553i
$47$	2.85718	+	2.85718i	0.416762	+	0.416762i	0.884086	−	0.467324i	$-0.154782\pi$
$47$	2.85718	+	2.85718i	0.416762	+	0.416762i	−0.467324	+	0.884086i	$0.654782\pi$
$48$		0			0
$49$	4.59783	+	5.27825i	0.656833	+	0.754036i
$50$	−5.71050	−	1.53012i	−0.807587	−	0.216392i
$51$		0			0
$52$	−16.4057	−	7.92952i	−2.27506	−	1.09963i
$53$	0.398831			0.0547836			0.0273918	−	0.999625i	$-0.491280\pi$
$53$	0.398831			0.0547836			0.0273918	+	0.999625i	$0.491280\pi$
$54$		0			0
$55$	−6.72427	+	3.88226i	−0.906700	+	0.523483i
$56$	20.0953	−	7.52507i	2.68535	−	1.00558i
$57$		0			0
$58$	−2.70335	+	0.724361i	−0.354967	+	0.0951132i
$59$	−8.26243	+	2.21391i	−1.07568	+	0.288227i	−0.752824	−	0.658222i	$-0.771309\pi$
$59$	−8.26243	+	2.21391i	−1.07568	+	0.288227i	−0.322854	+	0.946449i	$0.604642\pi$
$60$		0			0
$61$	−4.22976	−	2.44205i	−0.541565	−	0.312673i	0.204148	−	0.978940i	$-0.434558\pi$
$61$	−4.22976	−	2.44205i	−0.541565	−	0.312673i	−0.745713	+	0.666267i	$0.767891\pi$
$62$	10.5512	+	18.2752i	1.34001	+	2.32096i
$63$		0			0
$64$		−	14.6977i		−	1.83721i
$65$	−3.92362	+	4.54615i	−0.486666	+	0.563880i
$66$		0			0
$67$	−2.76762	+	10.3289i	−0.338118	+	1.26188i	0.562330	+	0.826913i	$0.309905\pi$
$67$	−2.76762	+	10.3289i	−0.338118	+	1.26188i	−0.900449	+	0.434962i	$0.856762\pi$
$68$	−27.6277	+	15.9509i	−3.35035	+	1.93433i
$69$		0			0
$70$	−1.12770	−	11.6490i	−0.134786	−	1.39232i
$71$	−4.31760	+	1.15690i	−0.512405	+	0.137298i	−0.505751	−	0.862679i	$-0.668785\pi$
$71$	−4.31760	+	1.15690i	−0.512405	+	0.137298i	−0.00665372	+	0.999978i	$0.502118\pi$
$72$		0			0
$73$	0.935407	+	0.935407i	0.109481	+	0.109481i	0.759725	−	0.650244i	$-0.225333\pi$
$73$	0.935407	+	0.935407i	0.109481	+	0.109481i	−0.650244	+	0.759725i	$0.725333\pi$
$74$	−0.786484	+	1.36223i	−0.0914269	+	0.158356i
$75$		0			0
$76$	5.52795	−	20.6306i	0.634100	−	2.36649i
$77$	9.52134	+	7.84059i	1.08506	+	0.893518i
$78$		0			0
$79$	−0.927988			−0.104407			−0.0522034	−	0.998636i	$-0.516624\pi$
$79$	−0.927988			−0.104407			−0.0522034	+	0.998636i	$0.516624\pi$
$80$	−18.3929	−	4.92836i	−2.05639	−	0.551008i
$81$		0			0
$82$	−1.71117	+	2.96383i	−0.188967	+	0.327300i
$83$	7.79378	−	7.79378i	0.855479	−	0.855479i	−0.135323	−	0.990802i	$-0.543207\pi$
$83$	7.79378	−	7.79378i	0.855479	−	0.855479i	0.990802	+	0.135323i	$0.0432072\pi$
$84$		0			0
$85$	2.72115	+	10.1555i	0.295150	+	1.10152i
$86$	20.1237	−	20.1237i	2.16999	−	2.16999i
$87$		0			0
$88$	32.7439	−	18.9047i	3.49052	−	2.01525i
$89$	1.28296	−	4.78807i	0.135993	−	0.507534i	−0.863998	−	0.503495i	$-0.832047\pi$
$89$	1.28296	−	4.78807i	0.135993	−	0.507534i	0.999992	−	0.00403982i	$-0.00128592\pi$
$90$		0			0
$91$	8.94880	+	3.30440i	0.938089	+	0.346395i
$92$	21.4514			2.23646
$93$		0			0
$94$	−9.29378	+	5.36577i	−0.958580	+	0.553436i
$95$	−6.09595	−	3.51950i	−0.625431	−	0.361093i
$96$		0			0
$97$	1.65635	+	6.18160i	0.168177	+	0.627646i	0.997614	+	0.0690447i	$0.0219951\pi$
$97$	1.65635	+	6.18160i	0.168177	+	0.627646i	−0.829436	+	0.558601i	$0.811338\pi$
$98$	−16.7013	+	8.16698i	−1.68709	+	0.824990i
$99$		0			0
$100$	5.62475	−	9.74235i	0.562475	−	0.974235i
$101$	−0.472587	−	0.818544i	−0.0470241	−	0.0814482i	0.841555	−	0.540171i	$-0.181640\pi$
$101$	−0.472587	−	0.818544i	−0.0470241	−	0.0814482i	−0.888579	+	0.458723i	$0.848307\pi$
$102$		0			0
$103$	8.04965			0.793156			0.396578	−	0.918001i	$-0.370198\pi$
$103$	8.04965			0.793156			0.396578	+	0.918001i	$0.370198\pi$
$104$	19.1062	−	22.1375i	1.87351	−	2.17077i
$105$		0			0
$106$	−0.274154	+	1.02316i	−0.0266282	+	0.0993777i
$107$	8.52440	+	14.7647i	0.824085	+	1.42736i	0.902617	+	0.430445i	$0.141643\pi$
$107$	8.52440	+	14.7647i	0.824085	+	1.42736i	−0.0785320	+	0.996912i	$0.525023\pi$
$108$		0			0
$109$	1.56781	+	1.56781i	0.150169	+	0.150169i	0.778193	−	0.628025i	$-0.216136\pi$
$109$	1.56781	+	1.56781i	0.150169	+	0.150169i	−0.628025	+	0.778193i	$0.716136\pi$
$110$	−5.33728	−	19.9190i	−0.508890	−	1.89920i
$111$		0			0
$112$	2.91461	+	30.1075i	0.275405	+	2.84489i
$113$	3.02535	−	5.24006i	0.284601	−	0.492943i	−0.687911	−	0.725795i	$-0.741472\pi$
$113$	3.02535	−	5.24006i	0.284601	−	0.492943i	0.972512	+	0.232852i	$0.0748056\pi$
$114$		0			0
$115$	1.82976	−	6.82876i	0.170626	−	0.636786i
$116$		−	5.32551i		−	0.494462i
$117$		0			0
$118$		−	22.7182i		−	2.09138i
$119$	13.5918	−	9.70547i	1.24596	−	0.889699i
$120$		0			0
$121$	9.29500	+	5.36647i	0.845000	+	0.487861i
$122$	9.17232	−	9.17232i	0.830423	−	0.830423i
$123$		0			0
$124$	−38.7864	+	10.3928i	−3.48312	+	0.933299i
$125$	−8.51014	−	8.51014i	−0.761170	−	0.761170i
$126$		0			0
$127$	−1.60575	+	0.927079i	−0.142487	+	0.0822650i	−0.569549	−	0.821958i	$-0.692882\pi$
$127$	−1.60575	+	0.927079i	−0.142487	+	0.0822650i	0.427062	+	0.904222i	$0.359549\pi$
$128$	10.3824	+	2.78196i	0.917684	+	0.245893i
$129$		0			0
$130$	−8.96556	−	13.1906i	−0.786332	−	1.15689i
$131$			4.94735i			0.432252i	0.976365	+	0.216126i	$0.0693422\pi$
$131$			4.94735i			0.432252i	−0.976365	+	0.216126i	$0.930658\pi$
$132$		0			0
$133$	−1.83984	+	11.0292i	−0.159535	+	0.956354i
$134$	−24.5952	−	14.2000i	−2.12470	−	1.22670i
$135$		0			0
$136$	−13.2507	−	49.4523i	−1.13624	−	4.24050i
$137$	−1.82558	−	6.81316i	−0.155970	−	0.582088i	−0.999020	−	0.0442531i	$-0.985909\pi$
$137$	−1.82558	−	6.81316i	−0.155970	−	0.582088i	0.843050	−	0.537834i	$-0.180757\pi$
$138$		0			0
$139$	−10.4051	−	6.00737i	−0.882547	−	0.509539i	−0.0110494	−	0.999939i	$-0.503517\pi$
$139$	−10.4051	−	6.00737i	−0.882547	−	0.509539i	−0.871497	+	0.490400i	$0.836851\pi$
$140$	21.9663	+	3.66431i	1.85649	+	0.309691i
$141$		0			0
$142$		−	11.8716i		−	0.996240i
$143$	16.5111	+	3.14856i	1.38072	+	0.263296i
$144$		0			0
$145$	−1.69530	−	0.454256i	−0.140787	−	0.0377239i
$146$	−3.04268	+	1.75669i	−0.251814	+	0.145385i
$147$		0			0
$148$	−2.11645	−	2.11645i	−0.173971	−	0.173971i
$149$	4.76731	−	1.27740i	0.390553	−	0.104648i	−0.0581981	−	0.998305i	$-0.518535\pi$
$149$	4.76731	−	1.27740i	0.390553	−	0.104648i	0.448752	+	0.893657i	$0.351869\pi$
$150$		0			0
$151$	−13.7886	+	13.7886i	−1.12210	+	1.12210i	−0.130675	+	0.991425i	$0.541714\pi$
$151$	−13.7886	+	13.7886i	−1.12210	+	1.12210i	−0.991425	+	0.130675i	$0.958286\pi$
$152$	29.6843	+	17.1383i	2.40772	+	1.39010i
$153$		0			0
$154$	−26.6591	+	19.0364i	−2.14825	+	1.53399i
$155$			13.2336i			1.06295i
$156$		0			0
$157$			19.9821i			1.59474i	0.603489	+	0.797371i	$0.293777\pi$
$157$			19.9821i			1.59474i	−0.603489	+	0.797371i	$0.706223\pi$
$158$	0.637894	−	2.38065i	0.0507481	−	0.189394i
$159$		0			0
$160$	11.7782	−	20.4004i	0.931147	−	1.61279i
$161$	−11.1781	+	1.08211i	−0.880955	+	0.0852824i
$162$		0			0
$163$	−1.46606	−	5.47141i	−0.114831	−	0.428554i	0.884444	−	0.466647i	$-0.154538\pi$
$163$	−1.46606	−	5.47141i	−0.114831	−	0.428554i	−0.999274	+	0.0380934i	$0.987872\pi$
$164$	−4.60480	−	4.60480i	−0.359574	−	0.359574i
$165$		0			0
$166$	14.6367	+	25.3515i	1.13603	+	1.96766i
$167$	1.10228	−	4.11377i	0.0852972	−	0.318333i	−0.910073	−	0.414448i	$-0.863975\pi$
$167$	1.10228	−	4.11377i	0.0852972	−	0.318333i	0.995370	+	0.0961143i	$0.0306414\pi$
$168$		0			0
$169$	12.8603	−	1.90072i	0.989254	−	0.146209i
$170$	−27.9233			−2.14162
$171$		0			0
$172$	27.0767	+	46.8982i	2.06458	+	3.57595i
$173$	0.873930	−	1.51369i	0.0664437	−	0.115084i	−0.830890	−	0.556437i	$-0.812168\pi$
$173$	0.873930	−	1.51369i	0.0664437	−	0.115084i	0.897333	+	0.441353i	$0.145501\pi$
$174$		0			0
$175$	−2.43954	+	5.36036i	−0.184412	+	0.405205i
$176$	13.7945	+	51.4819i	1.03980	+	3.88059i
$177$		0			0
$178$	11.4014	+	6.58258i	0.854568	+	0.493385i
$179$	19.7578	−	11.4072i	1.47677	−	0.852613i	0.477113	−	0.878842i	$-0.341683\pi$
$179$	19.7578	−	11.4072i	1.47677	−	0.852613i	0.999656	+	0.0262285i	$0.00834976\pi$
$180$		0			0
$181$	−13.7425			−1.02147			−0.510737	−	0.859737i	$-0.670628\pi$
$181$	−13.7425			−1.02147			−0.510737	+	0.859737i	$0.670628\pi$
$182$	−14.6284	+	20.6857i	−1.08433	+	1.53333i
$183$		0			0
$184$	−8.91006	+	33.2528i	−0.656858	+	2.45143i
$185$	−0.854271	+	0.493214i	−0.0628073	+	0.0362618i
$186$		0			0
$187$	20.8087	−	20.8087i	1.52169	−	1.52169i
$188$	−5.28519	−	19.7246i	−0.385462	−	1.43856i
$189$		0			0
$190$	13.2192	−	13.2192i	0.959021	−	0.959021i
$191$	−6.02586	+	10.4371i	−0.436016	+	0.755201i	−0.997378	−	0.0723688i	$-0.976944\pi$
$191$	−6.02586	+	10.4371i	−0.436016	+	0.755201i	0.561362	+	0.827570i	$0.310277\pi$
$192$		0			0
$193$	−4.42174	−	1.18480i	−0.318284	−	0.0852838i	0.0961404	−	0.995368i	$-0.469350\pi$
$193$	−4.42174	−	1.18480i	−0.318284	−	0.0852838i	−0.414424	+	0.910084i	$0.636017\pi$
$194$	−16.9968			−1.22030
$195$		0			0
$196$	−6.78570	−	34.7192i	−0.484693	−	2.47995i
$197$	−5.05766	+	18.8754i	−0.360343	+	1.34482i	0.513282	+	0.858220i	$0.328430\pi$
$197$	−5.05766	+	18.8754i	−0.360343	+	1.34482i	−0.873625	+	0.486599i	$0.838237\pi$
$198$		0			0
$199$	12.2497	−	21.2170i	0.868355	−	1.50403i	0.00467796	−	0.999989i	$-0.498511\pi$
$199$	12.2497	−	21.2170i	0.868355	−	1.50403i	0.863677	−	0.504046i	$-0.168156\pi$
$200$	12.7658	+	12.7658i	0.902676	+	0.902676i
$201$		0			0
$202$	2.42474	−	0.649707i	0.170604	−	0.0457132i
$203$	0.268644	+	2.77506i	0.0188551	+	0.194771i
$204$		0			0
$205$	−1.85865	+	1.07309i	−0.129814	+	0.0749482i
$206$	−5.53328	+	20.6505i	−0.385522	+	1.43879i
$207$		0			0
$208$	23.1721	+	34.0920i	1.60669	+	2.36385i
$209$			19.7022i			1.36283i
$210$		0			0
$211$	−11.4160	−	19.7731i	−0.785910	−	1.36124i	−0.928454	−	0.371448i	$-0.878862\pi$
$211$	−11.4160	−	19.7731i	−0.785910	−	1.36124i	0.142544	−	0.989788i	$-0.454472\pi$
$212$	−1.74555	−	1.00779i	−0.119885	−	0.0692154i
$213$		0			0
$214$	−43.7368	+	11.7192i	−2.98979	+	0.801111i
$215$	17.2390	−	4.61917i	1.17569	−	0.315025i
$216$		0			0
$217$	19.6868	−	7.37212i	1.33643	−	0.500452i
$218$	−5.09973	+	2.94433i	−0.345397	+	0.199415i
$219$		0			0
$220$	39.2398			2.64555
$221$	9.90458	−	20.4919i	0.666254	−	1.37844i
$222$		0			0
$223$	12.2434	+	3.28062i	0.819881	+	0.219686i	0.644294	−	0.764778i	$-0.277151\pi$
$223$	12.2434	+	3.28062i	0.819881	+	0.219686i	0.175586	+	0.984464i	$0.443818\pi$
$224$	−36.9099	−	6.15713i	−2.46614	−	0.411391i
$225$		0			0
$226$	11.3632	+	11.3632i	0.755868	+	0.755868i
$227$	−2.99465	−	11.1762i	−0.198762	−	0.741790i	−0.991261	−	0.131917i	$-0.957887\pi$
$227$	−2.99465	−	11.1762i	−0.198762	−	0.741790i	0.792499	−	0.609874i	$-0.208780\pi$
$228$		0			0
$229$	−9.10742	−	9.10742i	−0.601835	−	0.601835i	0.338964	−	0.940799i	$-0.389923\pi$
$229$	−9.10742	−	9.10742i	−0.601835	−	0.601835i	−0.940799	+	0.338964i	$0.889923\pi$
$230$	16.2607	+	9.38810i	1.07220	+	0.619033i
$231$		0			0
$232$	8.25532	+	2.21201i	0.541988	+	0.145225i
$233$		−	1.49633i		−	0.0980277i	−0.998798	−	0.0490139i	$-0.984392\pi$
$233$		−	1.49633i		−	0.0980277i	0.998798	−	0.0490139i	$-0.0156079\pi$
$234$		0			0
$235$	−6.72988			−0.439009
$236$	41.7562	+	11.1885i	2.71809	+	0.728311i
$237$		0			0
$238$	15.5554	+	41.5398i	1.00831	+	2.69263i
$239$	3.19313	+	3.19313i	0.206546	+	0.206546i	0.802798	−	0.596252i	$-0.203344\pi$
$239$	3.19313	+	3.19313i	0.206546	+	0.206546i	−0.596252	+	0.802798i	$0.703344\pi$
$240$		0			0
$241$	−9.27435	+	2.48506i	−0.597414	+	0.160076i	−0.544839	−	0.838541i	$-0.683409\pi$
$241$	−9.27435	+	2.48506i	−0.597414	+	0.160076i	−0.0525744	+	0.998617i	$0.516743\pi$
$242$	−20.1564	+	20.1564i	−1.29570	+	1.29570i
$243$		0			0
$244$	12.3415	+	21.3761i	0.790082	+	1.36846i
$245$	−11.6312	−	0.801346i	−0.743090	−	0.0511961i
$246$		0			0
$247$	5.01218	+	14.3901i	0.318917	+	0.915618i
$248$		−	64.4412i		−	4.09202i
$249$		0			0
$250$	27.6816	−	15.9820i	1.75074	−	1.01079i
$251$	−12.9361	+	22.4061i	−0.816522	+	1.41426i	0.0917077	+	0.995786i	$0.470767\pi$
$251$	−12.9361	+	22.4061i	−0.816522	+	1.41426i	−0.908230	+	0.418472i	$0.862566\pi$
$252$		0			0
$253$	−19.1138	+	5.12152i	−1.20167	+	0.321987i
$254$	−1.27454	−	4.75664i	−0.0799716	−	0.298458i
$255$		0			0
$256$	0.424093	−	0.734550i	0.0265058	−	0.0459094i
$257$	−11.4386	−	19.8122i	−0.713518	−	1.23585i	−0.963528	−	0.267606i	$-0.913767\pi$
$257$	−11.4386	−	19.8122i	−0.713518	−	1.23585i	0.250011	−	0.968243i	$-0.419566\pi$
$258$		0			0
$259$	1.20962	+	0.996092i	0.0751621	+	0.0618941i
$260$	28.6599	−	9.98248i	1.77741	−	0.619087i
$261$		0			0
$262$	−12.6919	−	3.40078i	−0.784107	−	0.210101i
$263$	10.9168	+	18.9085i	0.673160	+	1.16595i	0.977003	+	0.213225i	$0.0683966\pi$
$263$	10.9168	+	18.9085i	0.673160	+	1.16595i	−0.303844	+	0.952722i	$0.598270\pi$
$264$		0			0
$265$	−0.469709	+	0.469709i	−0.0288540	+	0.0288540i
$266$	−27.0295	−	12.3013i	−1.65729	−	0.754243i
$267$		0			0
$268$	38.2127	−	38.2127i	2.33421	−	2.33421i
$269$	5.09171	+	2.93970i	0.310447	+	0.179237i	0.647127	−	0.762383i	$-0.275971\pi$
$269$	5.09171	+	2.93970i	0.310447	+	0.179237i	−0.336679	+	0.941619i	$0.609304\pi$
$270$		0			0
$271$	1.80033	−	6.71891i	0.109362	−	0.408145i	−0.889441	−	0.457049i	$-0.848906\pi$
$271$	1.80033	−	6.71891i	0.109362	−	0.408145i	0.998803	+	0.0489044i	$0.0155730\pi$
$272$	72.1694			4.37591
$273$		0			0
$274$	18.7333			1.13172
$275$	−2.68582	+	10.0236i	−0.161961	+	0.604446i
$276$		0			0
$277$	10.7111	+	6.18406i	0.643568	+	0.371564i	0.785988	−	0.618242i	$-0.212155\pi$
$277$	10.7111	+	6.18406i	0.643568	+	0.371564i	−0.142420	+	0.989806i	$0.545488\pi$
$278$	22.5636	−	22.5636i	1.35328	−	1.35328i
$279$		0			0
$280$	−14.8041	+	32.5289i	−0.884716	+	1.94397i
$281$	15.6520	−	15.6520i	0.933721	−	0.933721i	−0.0642154	−	0.997936i	$-0.520454\pi$
$281$	15.6520	−	15.6520i	0.933721	−	0.933721i	0.997936	+	0.0642154i	$0.0204545\pi$
$282$		0			0
$283$	−14.3579	−	24.8687i	−0.853490	−	1.47829i	−0.878039	−	0.478589i	$-0.841148\pi$
$283$	−14.3579	−	24.8687i	−0.853490	−	1.47829i	0.0245489	−	0.999699i	$-0.492185\pi$
$284$	21.8200	+	5.84665i	1.29478	+	0.346935i
$285$		0			0
$286$	−19.4269	+	40.1930i	−1.14874	+	2.37666i
$287$	2.63179	+	2.16722i	0.155350	+	0.127927i
$288$		0			0
$289$	−11.4238	−	19.7867i	−0.671991	−	1.16392i
$290$	2.33069	−	4.03687i	0.136863	−	0.237053i
$291$		0			0
$292$	−1.73031	−	6.45761i	−0.101259	−	0.377903i
$293$	−22.3231	+	5.98146i	−1.30413	+	0.349441i	−0.843011	−	0.537897i	$-0.819219\pi$
$293$	−22.3231	+	5.98146i	−1.30413	+	0.349441i	−0.461120	+	0.887338i	$0.652552\pi$
$294$		0			0
$295$	7.12343	−	12.3381i	0.414742	−	0.718355i
$296$	4.15989	−	2.40171i	0.241789	−	0.139597i
$297$		0			0
$298$			13.1081i			0.759331i
$299$	−12.6574	+	8.60313i	−0.731996	+	0.497532i
$300$		0			0
$301$	−16.4751	−	23.0722i	−0.949608	−	1.32986i
$302$	−25.8949	−	44.8513i	−1.49009	−	2.58090i
$303$		0			0
$304$	−34.1658	+	34.1658i	−1.95954	+	1.95954i
$305$	7.85749	−	2.10541i	0.449918	−	0.120555i
$306$		0			0
$307$	5.52660	+	5.52660i	0.315419	+	0.315419i	0.847005	−	0.531585i	$-0.178404\pi$
$307$	5.52660	+	5.52660i	0.315419	+	0.315419i	−0.531585	+	0.847005i	$0.678404\pi$
$308$	−21.8596	−	58.3748i	−1.24556	−	3.32621i
$309$		0			0
$310$	−33.9493	−	9.09669i	−1.92819	−	0.516658i
$311$	−10.3208			−0.585239			−0.292620	−	0.956229i	$-0.594527\pi$
$311$	−10.3208			−0.585239			−0.292620	+	0.956229i	$0.594527\pi$
$312$		0			0
$313$		−	20.9365i		−	1.18340i	−0.806157	−	0.591701i	$-0.798457\pi$
$313$		−	20.9365i		−	1.18340i	0.806157	−	0.591701i	$-0.201543\pi$
$314$	−51.2618	−	13.7356i	−2.89287	−	0.775142i
$315$		0			0
$316$	4.06149	+	2.34490i	0.228477	+	0.131911i
$317$	−8.45606	−	8.45606i	−0.474940	−	0.474940i	0.428569	−	0.903509i	$-0.359018\pi$
$317$	−8.45606	−	8.45606i	−0.474940	−	0.474940i	−0.903509	+	0.428569i	$0.859018\pi$
$318$		0			0
$319$	1.27147	+	4.74517i	0.0711884	+	0.265679i
$320$	17.3097	+	17.3097i	0.967641	+	0.967641i
$321$		0			0
$322$	4.90770	−	29.4199i	0.273496	−	1.63951i
$323$	25.7692	+	6.90484i	1.43384	+	0.384195i
$324$		0			0
$325$	0.588311	+	8.00429i	0.0326336	+	0.443998i
$326$	15.0441			0.833213
$327$		0			0
$328$	9.05075	−	5.22545i	0.499744	−	0.288527i
$329$	3.74905	+	10.0116i	0.206692	+	0.551960i
$330$		0			0
$331$	25.0550	−	6.71347i	1.37715	−	0.369006i	0.507064	−	0.861909i	$-0.330731\pi$
$331$	25.0550	−	6.71347i	1.37715	−	0.369006i	0.870084	+	0.492903i	$0.164064\pi$
$332$	−53.8046	+	14.4169i	−2.95291	+	0.791230i
$333$		0			0
$334$	9.79573	+	5.65557i	0.535999	+	0.309459i
$335$	−8.90502	−	15.4240i	−0.486533	−	0.842700i
$336$		0			0
$337$		−	26.1315i		−	1.42348i	−0.702445	−	0.711738i	$-0.747908\pi$
$337$		−	26.1315i		−	1.42348i	0.702445	−	0.711738i	$-0.252092\pi$
$338$	−3.96401	+	34.2982i	−0.215614	+	1.86558i
$339$		0			0
$340$	13.7520	−	51.3231i	0.745806	−	2.78339i
$341$	32.0784	−	18.5205i	1.73714	−	1.00294i
$342$		0			0
$343$	5.28735	+	17.7495i	0.285490	+	0.958382i
$344$	−83.9455	+	22.4931i	−4.52604	+	1.21275i
$345$		0			0
$346$	3.28247	+	3.28247i	0.176467	+	0.176467i
$347$	−3.74039	+	6.47855i	−0.200795	+	0.347787i	−0.948785	−	0.315923i	$-0.897686\pi$
$347$	−3.74039	+	6.47855i	−0.200795	+	0.347787i	0.747990	+	0.663710i	$0.231019\pi$
$348$		0			0
$349$	−0.528661	+	1.97299i	−0.0282986	+	0.105612i	−0.978631	−	0.205626i	$-0.934077\pi$
$349$	−0.528661	+	1.97299i	−0.0282986	+	0.105612i	0.950332	+	0.311238i	$0.100744\pi$
$350$	−12.0745	−	9.94305i	−0.645409	−	0.531478i
$351$		0			0
$352$	−65.9345			−3.51432
$353$	−12.1175	−	3.24687i	−0.644949	−	0.172813i	−0.0785047	−	0.996914i	$-0.525015\pi$
$353$	−12.1175	−	3.24687i	−0.644949	−	0.172813i	−0.566444	+	0.824100i	$0.691681\pi$
$354$		0			0
$355$	3.72241	−	6.44740i	0.197565	−	0.342192i
$356$	−17.7139	+	17.7139i	−0.938835	+	0.938835i
$357$		0			0
$358$	15.6825	+	58.5278i	0.828844	+	3.09329i
$359$	6.92976	−	6.92976i	0.365739	−	0.365739i	−0.500182	−	0.865920i	$-0.666733\pi$
$359$	6.92976	−	6.92976i	0.365739	−	0.365739i	0.865920	+	0.500182i	$0.166733\pi$
$360$		0			0
$361$	0.986209	−	0.569388i	0.0519057	−	0.0299678i
$362$	9.44654	−	35.2550i	0.496499	−	1.85296i
$363$		0			0
$364$	−30.8161	−	37.0747i	−1.61520	−	1.94324i
$365$	−2.20328			−0.115325
$366$		0			0
$367$	−21.7912	+	12.5811i	−1.13749	+	0.656730i	−0.945808	−	0.324727i	$-0.894728\pi$
$367$	−21.7912	+	12.5811i	−1.13749	+	0.656730i	−0.191682	+	0.981457i	$0.561394\pi$
$368$	−42.0267	−	24.2641i	−2.19079	−	1.26486i
$369$		0			0
$370$	−0.678064	−	2.53057i	−0.0352509	−	0.131558i
$371$	0.960421	+	0.437095i	0.0498626	+	0.0226928i
$372$		0			0
$373$	5.81848	−	10.0779i	0.301270	−	0.521814i	−0.675154	−	0.737677i	$-0.735923\pi$
$373$	5.81848	−	10.0779i	0.301270	−	0.521814i	0.976424	+	0.215862i	$0.0692562\pi$
$374$	39.0787	+	67.6864i	2.02071	+	3.49998i
$375$		0			0
$376$	32.7713			1.69005
$377$	2.13581	+	3.14232i	0.110000	+	0.161837i
$378$		0			0
$379$	−6.70131	+	25.0096i	−0.344223	+	1.28466i	0.549294	+	0.835629i	$0.314897\pi$
$379$	−6.70131	+	25.0096i	−0.344223	+	1.28466i	−0.893517	+	0.449029i	$0.851770\pi$
$380$	17.7866	+	30.8073i	0.912434	+	1.58038i
$381$		0			0
$382$	−22.6331	−	22.6331i	−1.15801	−	1.15801i
$383$	2.62259	+	9.78763i	0.134008	+	0.500125i	1.00000		6.67944e-5i	$2.12613e-5\pi$
$383$	2.62259	+	9.78763i	0.134008	+	0.500125i	−0.865992	+	0.500058i	$0.833312\pi$
$384$		0			0
$385$	−20.4474	+	1.97944i	−1.04210	+	0.100882i
$386$	6.07895	−	10.5291i	0.309410	−	0.535915i
$387$		0			0
$388$	8.37077	−	31.2401i	0.424962	−	1.58598i
$389$		−	25.4046i		−	1.28806i	−0.764999	−	0.644032i	$-0.777260\pi$
$389$		−	25.4046i		−	1.28806i	0.764999	−	0.644032i	$-0.222740\pi$
$390$		0			0
$391$			26.7945i			1.35505i
$392$	56.6384	+	3.90217i	2.86067	+	0.197089i
$393$		0			0
$394$	−44.9463	−	25.9497i	−2.26436	−	1.30733i
$395$	1.09291	−	1.09291i	0.0549900	−	0.0549900i
$396$		0			0
$397$	23.6455	−	6.33580i	1.18673	−	0.317984i	0.389140	−	0.921179i	$-0.372772\pi$
$397$	23.6455	−	6.33580i	1.18673	−	0.317984i	0.797594	+	0.603194i	$0.206106\pi$
$398$	46.0096	+	46.0096i	2.30625	+	2.30625i
$399$		0			0
$400$	−22.0396	+	12.7245i	−1.10198	+	0.636227i
$401$	−19.0591	−	5.10686i	−0.951765	−	0.255025i	−0.250654	−	0.968077i	$-0.580646\pi$
$401$	−19.0591	−	5.10686i	−0.951765	−	0.255025i	−0.701111	+	0.713052i	$0.747312\pi$
$402$		0			0
$403$	18.7178	−	21.6876i	0.932401	−	1.08034i
$404$			4.77666i			0.237647i
$405$		0			0
$406$	−7.30378	−	1.21838i	−0.362480	−	0.0604673i
$407$	2.39111	+	1.38051i	0.118523	+	0.0684293i
$408$		0			0
$409$	−6.62979	−	24.7427i	−0.327822	−	1.22345i	−0.911444	−	0.411423i	$-0.865032\pi$
$409$	−6.62979	−	24.7427i	−0.327822	−	1.22345i	0.583622	−	0.812025i	$-0.301635\pi$
$410$	−1.47528	−	5.50581i	−0.0728588	−	0.271913i
$411$		0			0
$412$	−35.2306	−	20.3404i	−1.73569	−	1.00210i
$413$	−22.3230	−	3.72383i	−1.09844	−	0.183238i
$414$		0			0
$415$			18.3577i			0.901144i
$416$	−48.1571	+	16.7735i	−2.36110	+	0.822390i
$417$		0			0
$418$	−50.5438	−	13.5432i	−2.47218	−	0.662419i
$419$	2.48993	−	1.43756i	0.121641	−	0.0702295i	−0.437945	−	0.899002i	$-0.644294\pi$
$419$	2.48993	−	1.43756i	0.121641	−	0.0702295i	0.559586	+	0.828772i	$0.310960\pi$
$420$		0			0
$421$	−13.5970	−	13.5970i	−0.662676	−	0.662676i	0.293334	−	0.956010i	$-0.405235\pi$
$421$	−13.5970	−	13.5970i	−0.662676	−	0.662676i	−0.956010	+	0.293334i	$0.905235\pi$
$422$	58.5730	−	15.6946i	2.85129	−	0.764000i
$423$		0			0
$424$	2.28725	−	2.28725i	0.111079	−	0.111079i
$425$	12.1689	+	7.02575i	0.590281	+	0.340799i
$426$		0			0
$427$	−7.50931	−	10.5163i	−0.363401	−	0.508917i
$428$		−	86.1601i		−	4.16471i
$429$		0			0
$430$			47.3999i			2.28582i
$431$	−9.48793	+	35.4094i	−0.457017	+	1.70561i	0.225071	+	0.974342i	$0.427738\pi$
$431$	−9.48793	+	35.4094i	−0.457017	+	1.70561i	−0.682089	+	0.731269i	$0.738928\pi$
$432$		0			0
$433$	0.0741930	−	0.128506i	0.00356549	−	0.00617561i	−0.864237	−	0.503085i	$-0.832198\pi$
$433$	0.0741930	−	0.128506i	0.00356549	−	0.00617561i	0.867803	+	0.496909i	$0.165532\pi$
$434$	5.37974	+	55.5720i	0.258236	+	2.66754i
$435$		0			0
$436$	−2.90012	−	10.8234i	−0.138891	−	0.518346i
$437$	−12.6848	−	12.6848i	−0.606797	−	0.606797i
$438$		0			0
$439$	−4.05749	−	7.02778i	−0.193654	−	0.335418i	0.752805	−	0.658244i	$-0.228700\pi$
$439$	−4.05749	−	7.02778i	−0.193654	−	0.335418i	−0.946458	+	0.322826i	$0.895367\pi$
$440$	−16.2986	+	60.8274i	−0.777007	+	2.89983i
$441$		0			0
$442$	45.7615	+	39.4951i	2.17665	+	1.87859i
$443$	26.1952			1.24457			0.622285	−	0.782790i	$-0.286204\pi$
$443$	26.1952			1.24457			0.622285	+	0.782790i	$0.286204\pi$
$444$		0			0
$445$	4.12802	+	7.14994i	0.195687	+	0.338940i
$446$	−16.8321	+	29.1541i	−0.797024	+	1.38049i
$447$		0			0
$448$	16.1078	−	35.3934i	0.761022	−	1.67218i
$449$	−0.953576	−	3.55879i	−0.0450020	−	0.167950i	0.939768	−	0.341814i	$-0.111041\pi$
$449$	−0.953576	−	3.55879i	−0.0450020	−	0.167950i	−0.984770	+	0.173864i	$0.944375\pi$
$450$		0			0
$451$	5.20239	+	3.00360i	0.244971	+	0.141434i
$452$	−26.4819	+	15.2893i	−1.24560	+	0.719148i
$453$		0			0
$454$	30.7298			1.44222
$455$	−14.4308	+	6.64749i	−0.676525	+	0.311639i
$456$		0			0
$457$	2.49719	−	9.31962i	0.116813	−	0.435954i	−0.882603	−	0.470119i	$-0.844211\pi$
$457$	2.49719	−	9.31962i	0.116813	−	0.435954i	0.999416	+	0.0341660i	$0.0108775\pi$
$458$	29.6245	−	17.1037i	1.38426	−	0.799203i
$459$		0			0
$460$	−25.2636	+	25.2636i	−1.17792	+	1.17792i
$461$	−1.90787	−	7.12028i	−0.0888585	−	0.331624i	0.907158	−	0.420789i	$-0.138247\pi$
$461$	−1.90787	−	7.12028i	−0.0888585	−	0.331624i	−0.996017	+	0.0891650i	$0.971580\pi$
$462$		0			0
$463$	10.2671	−	10.2671i	0.477153	−	0.477153i	−0.427067	−	0.904220i	$-0.640453\pi$
$463$	10.2671	−	10.2671i	0.477153	−	0.477153i	0.904220	+	0.427067i	$0.140453\pi$
$464$	−6.02380	+	10.4335i	−0.279648	+	0.484364i
$465$		0			0
$466$	3.83867	+	1.02857i	0.177823	+	0.0476475i
$467$	34.1823			1.58177			0.790883	−	0.611967i	$-0.209621\pi$
$467$	34.1823			1.58177			0.790883	+	0.611967i	$0.209621\pi$
$468$		0			0
$469$	−17.9845	+	21.8398i	−0.830449	+	1.00847i
$470$	4.62608	−	17.2648i	0.213385	−	0.796364i
$471$		0			0
$472$	−34.6877	+	60.0808i	−1.59663	+	2.76544i
$473$	−35.3229	−	35.3229i	−1.62415	−	1.62415i
$474$		0			0
$475$	−9.08699	+	2.43485i	−0.416940	+	0.111719i
$476$	−84.0113	+	8.13285i	−3.85065	+	0.372769i
$477$		0			0
$478$	−10.3865	+	5.99668i	−0.475070	+	0.274282i
$479$	9.19517	−	34.3169i	0.420138	−	1.56798i	−0.354178	−	0.935178i	$-0.615239\pi$
$479$	9.19517	−	34.3169i	0.420138	−	1.56798i	0.774316	−	0.632799i	$-0.218094\pi$
$480$		0			0
$481$	2.09761	+	0.400003i	0.0956430	+	0.0182386i
$482$		−	25.5005i		−	1.16152i
$483$		0			0
$484$	−27.1207	−	46.9745i	−1.23276	−	2.13520i
$485$	−9.23087	−	5.32944i	−0.419152	−	0.241998i
$486$		0			0
$487$	22.0147	−	5.89883i	0.997583	−	0.267302i	0.277150	−	0.960827i	$-0.410610\pi$
$487$	22.0147	−	5.89883i	0.997583	−	0.267302i	0.720433	+	0.693525i	$0.243943\pi$
$488$	−38.2622	+	10.2523i	−1.73205	+	0.464101i
$489$		0			0
$490$	10.0510	−	29.2877i	0.454057	−	1.32308i
$491$	−12.8664	+	7.42840i	−0.580651	+	0.335239i	−0.761392	−	0.648292i	$-0.775484\pi$
$491$	−12.8664	+	7.42840i	−0.580651	+	0.335239i	0.180741	+	0.983531i	$0.442150\pi$
$492$		0			0
$493$	6.65198			0.299590
$494$	−40.3615	+	2.96655i	−1.81595	+	0.133471i
$495$		0			0
$496$	87.7441	+	23.5110i	3.93983	+	1.05567i
$497$	−11.6651	−	1.94592i	−0.523250	−	0.0872862i
$498$		0			0
$499$	−11.2290	−	11.2290i	−0.502679	−	0.502679i	0.409590	−	0.912270i	$-0.365672\pi$
$499$	−11.2290	−	11.2290i	−0.502679	−	0.502679i	−0.912270	+	0.409590i	$0.865672\pi$
$500$	15.7420	+	58.7500i	0.704004	+	2.62738i
$501$		0			0
$502$	−48.5880	−	48.5880i	−2.16859	−	2.16859i
$503$	13.8096	+	7.97299i	0.615741	+	0.355498i	0.775209	−	0.631705i	$-0.217645\pi$
$503$	13.8096	+	7.97299i	0.615741	+	0.355498i	−0.159468	+	0.987203i	$0.550978\pi$
$504$		0			0
$505$	1.52058	+	0.407439i	0.0676651	+	0.0181308i
$506$		−	52.5548i		−	2.33635i
$507$		0			0
$508$	9.37043			0.415745
$509$	−21.2058	−	5.68207i	−0.939930	−	0.251853i	−0.243846	−	0.969814i	$-0.578409\pi$
$509$	−21.2058	−	5.68207i	−0.939930	−	0.251853i	−0.696084	+	0.717961i	$0.745076\pi$
$510$		0			0
$511$	1.22740	+	3.27770i	0.0542968	+	0.144997i
$512$	16.7938	+	16.7938i	0.742187	+	0.742187i
$513$		0			0
$514$	58.6887	−	15.7256i	2.58865	−	0.693626i
$515$	−9.48019	+	9.48019i	−0.417747	+	0.417747i
$516$		0			0
$517$	9.41849	+	16.3133i	0.414225	+	0.717458i
$518$	−3.38685	+	2.41844i	−0.148810	+	0.106260i
$519$		0			0
$520$	3.57011	+	48.5733i	0.156560	+	2.13008i
$521$		−	27.9103i		−	1.22277i	−0.791332	−	0.611387i	$-0.790612\pi$
$521$		−	27.9103i		−	1.22277i	0.791332	−	0.611387i	$-0.209388\pi$
$522$		0			0
$523$	−14.4506	+	8.34306i	−0.631881	+	0.364817i	−0.781480	−	0.623930i	$-0.785535\pi$
$523$	−14.4506	+	8.34306i	−0.631881	+	0.364817i	0.149599	+	0.988747i	$0.452202\pi$
$524$	12.5013	−	21.6529i	0.546122	−	0.945911i
$525$		0			0
$526$	−56.0118	+	15.0083i	−2.44223	+	0.654393i
$527$	−12.9814	−	48.4472i	−0.565478	−	2.11039i
$528$		0			0
$529$	−2.49141	+	4.31525i	−0.108322	+	0.187620i
$530$	−0.882111	−	1.52786i	−0.0383164	−	0.0663660i
$531$		0			0
$532$	35.9217	−	43.6221i	1.55740	−	1.89126i
$533$	4.56382	+	0.870294i	0.197681	+	0.0376966i
$534$		0			0
$535$	−27.4279	−	7.34928i	−1.18581	−	0.317737i
$536$	43.3632	+	75.1072i	1.87300	+	3.24414i
$537$		0			0
$538$	−11.0415	+	11.0415i	−0.476032	+	0.476032i
$539$	14.3355	+	29.3157i	0.617472	+	1.26272i
$540$		0			0
$541$	−14.9557	+	14.9557i	−0.642996	+	0.642996i	−0.951291	−	0.308295i	$-0.900242\pi$
$541$	−14.9557	+	14.9557i	−0.642996	+	0.642996i	0.308295	+	0.951291i	$0.400242\pi$
$542$	15.9991	+	9.23708i	0.687220	+	0.396767i
$543$		0			0
$544$	−23.1074	+	86.2380i	−0.990722	+	3.69743i
$545$	−3.69285			−0.158184
$546$		0			0
$547$	39.1844			1.67540			0.837702	−	0.546127i	$-0.183898\pi$
$547$	39.1844			1.67540			0.837702	+	0.546127i	$0.183898\pi$
$548$	−9.22600	+	34.4319i	−0.394115	+	1.47086i
$549$		0			0
$550$	−23.8682	−	13.7803i	−1.01775	−	0.587595i
$551$	−3.14912	+	3.14912i	−0.134157	+	0.134157i
$552$		0			0
$553$	−2.23468	−	1.01702i	−0.0950284	−	0.0432481i
$554$	−23.2273	+	23.2273i	−0.986833	+	0.986833i
$555$		0			0
$556$	30.3597	+	52.5845i	1.28754	+	2.23008i
$557$	1.74793	+	0.468357i	0.0740623	+	0.0198449i	0.295660	−	0.955293i	$-0.404460\pi$
$557$	1.74793	+	0.468357i	0.0740623	+	0.0198449i	−0.221598	+	0.975138i	$0.571127\pi$
$558$		0			0
$559$	−34.7852	−	16.8131i	−1.47126	−	0.711117i
$560$	−38.8906	−	32.0255i	−1.64343	−	1.35332i
$561$		0			0
$562$	29.3944	+	50.9126i	1.23993	+	2.14762i
$563$	−3.27798	+	5.67763i	−0.138150	+	0.239284i	−0.926797	−	0.375564i	$-0.877449\pi$
$563$	−3.27798	+	5.67763i	−0.138150	+	0.239284i	0.788646	+	0.614847i	$0.210782\pi$
$564$		0			0
$565$	2.60829	+	9.73429i	0.109732	+	0.409524i
$566$	73.6673	−	19.7391i	3.09647	−	0.829696i
$567$		0			0
$568$	−18.1263	+	31.3957i	−0.760563	+	1.31733i
$569$	7.73692	−	4.46691i	0.324349	−	0.187263i	−0.328981	−	0.944337i	$-0.606705\pi$
$569$	7.73692	−	4.46691i	0.324349	−	0.187263i	0.653329	+	0.757074i	$0.273372\pi$
$570$		0			0
$571$			21.0842i			0.882348i	0.897422	+	0.441174i	$0.145438\pi$
$571$			21.0842i			0.882348i	−0.897422	+	0.441174i	$0.854562\pi$
$572$	−64.3073	−	55.5014i	−2.68882	−	2.32063i
$573$		0			0
$574$	−7.36884	+	5.26184i	−0.307569	+	0.219625i
$575$	−4.72426	−	8.18267i	−0.197015	−	0.341241i
$576$		0			0
$577$	4.76619	−	4.76619i	0.198419	−	0.198419i	−0.600903	−	0.799322i	$-0.705192\pi$
$577$	4.76619	−	4.76619i	0.198419	−	0.198419i	0.799322	+	0.600903i	$0.205192\pi$
$578$	58.6133	−	15.7054i	2.43799	−	0.653257i
$579$		0			0
$580$	6.27193	+	6.27193i	0.260428	+	0.260428i
$581$	27.3097	−	10.2266i	1.13300	−	0.424272i
$582$		0			0
$583$	1.79594	+	0.481220i	0.0743802	+	0.0199301i
$584$	10.7289			0.443966
$585$		0			0
$586$		−	61.3791i		−	2.53555i
$587$	13.3468	+	3.57628i	0.550883	+	0.147609i	0.523515	−	0.852017i	$-0.324621\pi$
$587$	13.3468	+	3.57628i	0.550883	+	0.147609i	0.0273686	+	0.999625i	$0.491287\pi$
$588$		0			0
$589$	29.0810	+	16.7899i	1.19826	+	0.691816i
$590$	26.7555	+	26.7555i	1.10151	+	1.10151i
$591$		0			0
$592$	1.75250	+	6.54042i	0.0720273	+	0.268809i
$593$	−17.2336	−	17.2336i	−0.707698	−	0.707698i	0.258353	−	0.966051i	$-0.416820\pi$
$593$	−17.2336	−	17.2336i	−0.707698	−	0.707698i	−0.966051	+	0.258353i	$0.916820\pi$
$594$		0			0
$595$	−4.57701	+	27.4376i	−0.187639	+	1.12483i
$596$	−24.0927	−	6.45563i	−0.986877	−	0.264433i
$597$		0			0
$598$	−13.3698	−	38.3849i	−0.546730	−	1.56967i
$599$	−35.8803			−1.46603			−0.733015	−	0.680212i	$-0.761888\pi$
$599$	−35.8803			−1.46603			−0.733015	+	0.680212i	$0.761888\pi$
$600$		0			0
$601$	−1.74937	+	1.01000i	−0.0713582	+	0.0411987i	−0.535255	−	0.844691i	$-0.679784\pi$
$601$	−1.74937	+	1.01000i	−0.0713582	+	0.0411987i	0.463896	+	0.885889i	$0.346451\pi$
$602$	70.5140	−	26.4053i	2.87394	−	1.07620i
$603$		0			0
$604$	95.1900	−	25.5061i	3.87323	−	1.03783i
$605$	−17.2670	+	4.62669i	−0.702005	+	0.188102i
$606$		0			0
$607$	26.9378	+	15.5526i	1.09337	+	0.631259i	0.934473	−	0.356035i	$-0.115872\pi$
$607$	26.9378	+	15.5526i	1.09337	+	0.631259i	0.158901	+	0.987295i	$0.449205\pi$
$608$	−29.8868	−	51.7654i	−1.21207	−	2.09936i
$609$		0			0
$610$			21.6048i			0.874751i
$611$	11.0291	+	9.51885i	0.446190	+	0.385092i
$612$		0			0
$613$	2.49860	−	9.32490i	0.100917	−	0.376629i	−0.896933	−	0.442167i	$-0.854210\pi$
$613$	2.49860	−	9.32490i	0.100917	−	0.376629i	0.997850	+	0.0655381i	$0.0208764\pi$
$614$	−17.9768	+	10.3789i	−0.725485	+	0.418859i
$615$		0			0
$616$	99.5689	−	9.63893i	4.01175	−	0.388364i
$617$	7.40462	−	1.98406i	0.298099	−	0.0798753i	−0.106670	−	0.994294i	$-0.534019\pi$
$617$	7.40462	−	1.98406i	0.298099	−	0.0798753i	0.404768	+	0.914419i	$0.367352\pi$
$618$		0			0
$619$	23.5040	+	23.5040i	0.944707	+	0.944707i	0.998549	−	0.0538424i	$-0.0171469\pi$
$619$	23.5040	+	23.5040i	0.944707	+	0.944707i	−0.0538424	+	0.998549i	$0.517147\pi$
$620$	33.4395	−	57.9190i	1.34296	−	2.32608i
$621$		0			0
$622$	7.09446	−	26.4769i	0.284462	−	1.06163i
$623$	8.33692	−	10.1241i	0.334012	−	0.405612i
$624$		0			0
$625$	8.91513			0.356605
$626$	53.7104	+	14.3916i	2.14670	+	0.575206i
$627$		0			0
$628$	50.4920	−	87.4548i	2.01485	−	3.48983i
$629$	2.64361	−	2.64361i	0.105408	−	0.105408i
$630$		0			0
$631$	−6.11577	−	22.8244i	−0.243465	−	0.908623i	−0.974149	−	0.225907i	$-0.927465\pi$
$631$	−6.11577	−	22.8244i	−0.243465	−	0.908623i	0.730684	−	0.682716i	$-0.239201\pi$
$632$	−5.32192	+	5.32192i	−0.211695	+	0.211695i
$633$		0			0
$634$	27.5057	−	15.8804i	1.09239	−	0.630693i
$635$	0.799278	−	2.98295i	0.0317184	−	0.118375i
$636$		0			0
$637$	17.9281	+	17.7646i	0.710338	+	0.703861i
$638$	−13.0472			−0.516544
$639$		0			0
$640$	−15.5039	+	8.95116i	−0.612844	+	0.353826i
$641$	1.08956	+	0.629057i	0.0430350	+	0.0248463i	0.521363	−	0.853335i	$-0.325424\pi$
$641$	1.08956	+	0.629057i	0.0430350	+	0.0248463i	−0.478328	+	0.878181i	$0.658757\pi$
$642$		0			0
$643$	8.43652	+	31.4855i	0.332704	+	1.24167i	0.906337	+	0.422556i	$0.138867\pi$
$643$	8.43652	+	31.4855i	0.332704	+	1.24167i	−0.573633	+	0.819113i	$0.694466\pi$
$644$	51.6570	+	23.5095i	2.03557	+	0.926403i
$645$		0			0
$646$	−35.4272	+	61.3617i	−1.39386	+	2.41424i
$647$	−4.65030	−	8.05456i	−0.182822	−	0.316657i	0.760018	−	0.649902i	$-0.225190\pi$
$647$	−4.65030	−	8.05456i	−0.182822	−	0.316657i	−0.942841	+	0.333244i	$0.891857\pi$
$648$		0			0
$649$	−39.8771			−1.56531
$650$	−20.9385	−	3.99285i	−0.821276	−	0.156613i
$651$		0			0
$652$	−7.40908	+	27.6510i	−0.290162	+	1.08290i
$653$	13.4181	+	23.2408i	0.525090	+	0.909482i	0.999573	+	0.0292175i	$0.00930153\pi$
$653$	13.4181	+	23.2408i	0.525090	+	0.909482i	−0.474483	+	0.880264i	$0.657365\pi$
$654$		0			0
$655$	−5.82657	−	5.82657i	−0.227663	−	0.227663i
$656$	3.81295	+	14.2301i	0.148871	+	0.555593i
$657$		0			0
$658$	−28.2608	+	2.73584i	−1.10172	+	0.106654i
$659$	7.95731	−	13.7825i	0.309973	−	0.536889i	−0.668383	−	0.743817i	$-0.733013\pi$
$659$	7.95731	−	13.7825i	0.309973	−	0.536889i	0.978356	+	0.206928i	$0.0663467\pi$
$660$		0			0
$661$	−0.555848	+	2.07445i	−0.0216200	+	0.0806868i	−0.975893	−	0.218250i	$-0.929965\pi$
$661$	−0.555848	+	2.07445i	−0.0216200	+	0.0806868i	0.954273	+	0.298937i	$0.0966319\pi$
$662$			68.8907i			2.67751i
$663$		0			0
$664$		−	89.3931i		−	3.46913i
$665$	−10.8225	−	15.1561i	−0.419677	−	0.587727i
$666$		0			0
$667$	−3.87367	−	2.23647i	−0.149989	−	0.0865963i
$668$	−15.2193	+	15.2193i	−0.588852	+	0.588852i
$669$		0			0
$670$	45.6897	−	12.2425i	1.76515	−	0.472970i
$671$	−16.1001	−	16.1001i	−0.621538	−	0.621538i
$672$		0			0
$673$	−33.3114	+	19.2323i	−1.28406	+	0.741352i	−0.977588	−	0.210528i	$-0.932482\pi$
$673$	−33.3114	+	19.2323i	−1.28406	+	0.741352i	−0.306472	+	0.951880i	$0.599148\pi$
$674$	67.0376	+	17.9627i	2.58219	+	0.691896i
$675$		0			0
$676$	−61.0881	−	24.1775i	−2.34954	−	0.929903i
$677$			18.0903i			0.695268i	0.937630	+	0.347634i	$0.113015\pi$
$677$			18.0903i			0.695268i	−0.937630	+	0.347634i	$0.886985\pi$
$678$		0			0
$679$	−2.78601	+	16.7011i	−0.106917	+	0.640930i
$680$	73.8462	+	42.6351i	2.83187	+	1.63498i
$681$		0			0
$682$	25.4617	+	95.0245i	0.974980	+	3.63868i
$683$	9.14504	+	34.1297i	0.349925	+	1.30594i	0.886752	+	0.462246i	$0.152956\pi$
$683$	9.14504	+	34.1297i	0.349925	+	1.30594i	−0.536827	+	0.843693i	$0.680377\pi$
$684$		0			0
$685$	10.1740	+	5.87394i	0.388727	+	0.224432i
$686$	−49.1688	+	1.36323i	−1.87727	+	0.0520485i
$687$		0			0
$688$		−	122.508i		−	4.67057i
$689$	1.43414	−	0.105408i	0.0546362	−	0.00401573i
$690$		0			0
$691$	18.6167	+	4.98833i	0.708213	+	0.189765i	0.594906	−	0.803795i	$-0.297189\pi$
$691$	18.6167	+	4.98833i	0.708213	+	0.189765i	0.113306	+	0.993560i	$0.463856\pi$
$692$	−7.64980	+	4.41661i	−0.290802	+	0.167894i
$693$		0			0
$694$	−14.0489	−	14.0489i	−0.533289	−	0.533289i
$695$	19.3292	−	5.17924i	0.733197	−	0.196460i
$696$		0			0
$697$	5.75175	−	5.75175i	0.217863	−	0.217863i
$698$	−4.69809	−	2.71244i	−0.177825	−	0.102668i
$699$		0			0
$700$	24.2220	−	17.2961i	0.915504	−	0.653732i
$701$			30.2993i			1.14439i	0.820118	+	0.572194i	$0.193908\pi$
$701$			30.2993i			1.14439i	−0.820118	+	0.572194i	$0.806092\pi$
$702$		0			0
$703$			2.50303i			0.0944035i
$704$	17.7339	−	66.1839i	0.668373	−	2.49440i
$705$		0			0
$706$	16.6590	−	28.8542i	0.626969	−	1.08594i
$707$	−0.240957	−	2.48906i	−0.00906214	−	0.0936106i
$708$		0			0
$709$	−4.09223	−	15.2724i	−0.153687	−	0.573567i	−0.999214	−	0.0396350i	$-0.987380\pi$
$709$	−4.09223	−	15.2724i	−0.153687	−	0.573567i	0.845527	−	0.533932i	$-0.179286\pi$
$710$	13.9813	+	13.9813i	0.524710	+	0.524710i
$711$		0			0
$712$	−20.1015	−	34.8167i	−0.753334	−	1.30481i
$713$	−8.72896	+	32.5769i	−0.326902	+	1.22002i
$714$		0			0
$715$	−23.1534	+	15.7372i	−0.865888	+	0.588538i
$716$	−115.298			−4.30888
$717$		0			0
$718$	13.0141	+	22.5410i	0.485680	+	0.841223i
$719$	4.93530	−	8.54819i	0.184056	−	0.318794i	−0.759202	−	0.650855i	$-0.774411\pi$
$719$	4.93530	−	8.54819i	0.184056	−	0.318794i	0.943258	+	0.332061i	$0.107744\pi$
$720$		0			0
$721$	19.3843	+	8.82194i	0.721909	+	0.328546i
$722$	0.782788	+	2.92140i	0.0291324	+	0.108723i
$723$		0			0
$724$	60.1465	+	34.7256i	2.23533	+	1.29057i
$725$	−2.03142	+	1.17284i	−0.0754452	+	0.0435583i
$726$		0			0
$727$	−24.0371			−0.891486			−0.445743	−	0.895161i	$-0.647061\pi$
$727$	−24.0371			−0.891486			−0.445743	+	0.895161i	$0.647061\pi$
$728$	70.2708	−	32.3701i	2.60441	−	1.19971i
$729$		0			0
$730$	1.51452	−	5.65228i	0.0560551	−	0.209200i
$731$	−58.5794	+	33.8208i	−2.16664	+	1.25091i
$732$		0			0
$733$	12.9796	−	12.9796i	0.479413	−	0.479413i	−0.425531	−	0.904944i	$-0.639913\pi$
$733$	12.9796	−	12.9796i	0.479413	−	0.479413i	0.904944	+	0.425531i	$0.139913\pi$
$734$	−17.2964	−	64.5510i	−0.638422	−	2.38262i
$735$		0			0
$736$	42.4504	−	42.4504i	1.56474	−	1.56474i
$737$	−24.9252	+	43.1718i	−0.918133	+	1.59025i
$738$		0			0
$739$	−27.1236	−	7.26773i	−0.997756	−	0.267348i	−0.277251	−	0.960798i	$-0.589423\pi$
$739$	−27.1236	−	7.26773i	−0.997756	−	0.267348i	−0.720505	+	0.693450i	$0.756090\pi$
$740$	4.98514			0.183258
$741$		0			0
$742$	−1.78151	+	2.16340i	−0.0654011	+	0.0794209i
$743$	5.26385	−	19.6449i	0.193112	−	0.720703i	−0.799636	−	0.600485i	$-0.794974\pi$
$743$	5.26385	−	19.6449i	0.193112	−	0.720703i	0.992748	−	0.120218i	$-0.0383592\pi$
$744$		0			0
$745$	−4.11012	+	7.11894i	−0.150583	+	0.260818i
$746$	21.8542	+	21.8542i	0.800138	+	0.800138i
$747$		0			0
$748$	−143.654	+	38.4919i	−5.25250	+	1.40740i
$749$	4.34633	+	44.8970i	0.158811	+	1.64050i
$750$		0			0
$751$	−29.4512	+	17.0036i	−1.07469	+	0.620472i	−0.929459	−	0.368926i	$-0.879725\pi$
$751$	−29.4512	+	17.0036i	−1.07469	+	0.620472i	−0.145230	+	0.989398i	$0.546392\pi$
$752$	−11.9564	+	44.6218i	−0.436004	+	1.62719i
$753$		0			0
$754$	−9.52941	+	3.31917i	−0.347040	+	0.120877i
$755$		−	32.4781i		−	1.18200i
$756$		0			0
$757$	−12.1464	−	21.0382i	−0.441469	−	0.764646i	0.556330	−	0.830961i	$-0.312209\pi$
$757$	−12.1464	−	21.0382i	−0.441469	−	0.764646i	−0.997799	+	0.0663153i	$0.978876\pi$
$758$	−59.5530	−	34.3830i	−2.16306	−	1.24885i
$759$		0			0
$760$	−55.1436	+	14.7757i	−2.00027	+	0.535971i
$761$	−16.6934	+	4.47299i	−0.605136	+	0.162146i	−0.548362	−	0.836241i	$-0.684748\pi$
$761$	−16.6934	+	4.47299i	−0.605136	+	0.162146i	−0.0567745	+	0.998387i	$0.518082\pi$
$762$		0			0
$763$	2.05720	+	5.49364i	0.0744757	+	0.198883i
$764$	52.7463	−	30.4531i	1.90829	−	1.10175i
$765$		0			0
$766$	−26.9118			−0.972364
$767$	−29.1254	+	10.1446i	−1.05166	+	0.366301i
$768$		0			0
$769$	−10.4169	−	2.79121i	−0.375644	−	0.100654i	0.0660568	−	0.997816i	$-0.478958\pi$
$769$	−10.4169	−	2.79121i	−0.375644	−	0.100654i	−0.441701	+	0.897162i	$0.645625\pi$
$770$	8.97737	−	53.8162i	0.323522	−	1.93940i
$771$		0			0
$772$	16.3586	+	16.3586i	0.588759	+	0.588759i
$773$	10.6384	+	39.7032i	0.382638	+	1.42802i	0.841857	+	0.539701i	$0.181463\pi$
$773$	10.6384	+	39.7032i	0.382638	+	1.42802i	−0.459219	+	0.888323i	$0.651871\pi$
$774$		0			0
$775$	12.5063	+	12.5063i	0.449239	+	0.449239i
$776$	44.9499	+	25.9518i	1.61361	+	0.931616i
$777$		0			0
$778$	65.1727	+	17.4630i	2.33655	+	0.626078i
$779$			5.44589i			0.195119i
$780$		0			0
$781$	−20.8381			−0.745646
$782$	−68.7382	−	18.4184i	−2.45807	−	0.658639i
$783$		0			0
$784$	−25.9774	+	75.6959i	−0.927764	+	2.70343i
$785$	−23.5332	−	23.5332i	−0.839935	−	0.839935i
$786$		0			0
$787$	26.7623	−	7.17094i	0.953973	−	0.255616i	0.251926	−	0.967747i	$-0.418936\pi$
$787$	26.7623	−	7.17094i	0.953973	−	0.255616i	0.702047	+	0.712130i	$0.252269\pi$
$788$	69.8314	−	69.8314i	2.48764	−	2.48764i
$789$		0			0
$790$	2.05247	+	3.55498i	0.0730236	+	0.126481i
$791$	13.0281	−	9.30295i	0.463226	−	0.330775i
$792$		0			0
$793$	−15.8550	−	7.66336i	−0.563027	−	0.272134i
$794$			65.0151i			2.30730i
$795$		0			0
$796$	−107.225	+	61.9065i	−3.80050	+	2.19422i
$797$	−26.4182	+	45.7577i	−0.935781	+	1.62082i	−0.162546	+	0.986701i	$0.551971\pi$
$797$	−26.4182	+	45.7577i	−0.935781	+	1.62082i	−0.773235	+	0.634119i	$0.781363\pi$
$798$		0			0
$799$	24.6376	−	6.60161i	0.871614	−	0.233548i
$800$	−8.14837	−	30.4101i	−0.288088	−	1.07516i
$801$		0			0
$802$	26.2022	−	45.3835i	0.925232	−	1.60255i
$803$	3.08351	+	5.34079i	0.108815	+	0.188472i
$804$		0			0
$805$	11.8902	−	14.4390i	0.419073	−	0.508908i
$806$	42.7706	+	62.9264i	1.50653	+	2.21649i
$807$		0			0
$808$	−7.40451	−	1.98403i	−0.260490	−	0.0697980i
$809$	−12.7930	−	22.1581i	−0.449776	−	0.779036i	0.548595	−	0.836088i	$-0.315163\pi$
$809$	−12.7930	−	22.1581i	−0.449776	−	0.779036i	−0.998371	+	0.0570528i	$0.981830\pi$
$810$		0			0
$811$	34.1937	−	34.1937i	1.20070	−	1.20070i	0.226749	−	0.973953i	$-0.427190\pi$
$811$	34.1937	−	34.1937i	1.20070	−	1.20070i	0.973953	−	0.226749i	$-0.0728096\pi$
$812$	5.83645	−	12.8243i	0.204819	−	0.450046i
$813$		0			0
$814$	−5.18518	+	5.18518i	−0.181741	+	0.181741i
$815$	8.17035	+	4.71716i	0.286195	+	0.165235i
$816$		0			0
$817$	11.7210	−	43.7433i	0.410066	−	1.53039i
$818$	68.0320			2.37868
$819$		0			0
$820$	10.8463			0.378768
$821$	5.38960	−	20.1142i	0.188098	−	0.701992i	−0.805848	−	0.592123i	$-0.798290\pi$
$821$	5.38960	−	20.1142i	0.188098	−	0.701992i	0.993946	−	0.109869i	$-0.0350432\pi$
$822$		0			0
$823$	−1.66588	−	0.961795i	−0.0580689	−	0.0335261i	0.470684	−	0.882302i	$-0.344007\pi$
$823$	−1.66588	−	0.961795i	−0.0580689	−	0.0335261i	−0.528753	+	0.848776i	$0.677340\pi$
$824$	46.1639	−	46.1639i	1.60820	−	1.60820i
$825$		0			0
$826$	24.8978	−	54.7075i	0.866305	−	1.90352i
$827$	−22.0447	+	22.0447i	−0.766570	+	0.766570i	−0.977501	−	0.210931i	$-0.932351\pi$
$827$	−22.0447	+	22.0447i	−0.766570	+	0.766570i	0.210931	+	0.977501i	$0.432351\pi$
$828$		0			0
$829$	1.67430	+	2.89997i	0.0581508	+	0.100720i	0.893635	−	0.448794i	$-0.148146\pi$
$829$	1.67430	+	2.89997i	0.0581508	+	0.100720i	−0.835485	+	0.549514i	$0.814813\pi$
$830$	−47.0946	−	12.6190i	−1.63468	−	0.438011i
$831$		0			0
$832$	−3.88450	−	52.8508i	−0.134671	−	1.83227i
$833$	43.3670	−	8.47586i	1.50258	−	0.293671i
$834$		0			0
$835$	3.54668	+	6.14303i	0.122738	+	0.212588i
$836$	49.7849	−	86.2299i	1.72185	−	2.98232i
$837$		0			0
$838$	1.97634	+	7.37582i	0.0682717	+	0.254793i
$839$	52.8531	−	14.1619i	1.82469	−	0.488925i	0.827343	−	0.561696i	$-0.189851\pi$
$839$	52.8531	−	14.1619i	1.82469	−	0.488925i	0.997349	+	0.0727716i	$0.0231844\pi$
$840$		0			0
$841$	13.9448	−	24.1531i	0.480854	−	0.832864i
$842$	44.2280	−	25.5351i	1.52420	−	0.879996i
$843$		0			0
$844$			115.387i			3.97178i
$845$	−12.9073	+	17.3843i	−0.444023	+	0.598037i
$846$		0			0
$847$	16.5019	+	23.1097i	0.567012	+	0.794060i
$848$	2.27987	+	3.94885i	0.0782910	+	0.135604i
$849$		0			0
$850$	−26.3886	+	26.3886i	−0.905123	+	0.905123i
$851$	−2.42827	+	0.650654i	−0.0832401	+	0.0223041i
$852$		0			0
$853$	−21.1183	−	21.1183i	−0.723077	−	0.723077i	0.246154	−	0.969231i	$-0.420833\pi$
$853$	−21.1183	−	21.1183i	−0.723077	−	0.723077i	−0.969231	+	0.246154i	$0.920833\pi$
$854$	32.1401	−	12.0355i	1.09981	−	0.411846i
$855$		0			0
$856$	133.561	+	35.7875i	4.56501	+	1.22319i
$857$	−30.2671			−1.03390			−0.516951	−	0.856015i	$-0.672933\pi$
$857$	−30.2671			−1.03390			−0.516951	+	0.856015i	$0.672933\pi$
$858$		0			0
$859$		−	2.18372i		−	0.0745075i	−0.999306	−	0.0372537i	$-0.988139\pi$
$859$		−	2.18372i		−	0.0745075i	0.999306	−	0.0372537i	$-0.0118610\pi$
$860$	−87.1212	−	23.3441i	−2.97081	−	0.796026i
$861$		0			0
$862$	−84.3170	−	48.6805i	−2.87185	−	1.65806i
$863$	−22.7673	−	22.7673i	−0.775006	−	0.775006i	0.203971	−	0.978977i	$-0.434615\pi$
$863$	−22.7673	−	22.7673i	−0.775006	−	0.775006i	−0.978977	+	0.203971i	$0.934615\pi$
$864$		0			0
$865$	0.753456	+	2.81194i	0.0256183	+	0.0956087i
$866$	0.278668	+	0.278668i	0.00946954	+	0.00946954i
$867$		0			0
$868$	−104.791	−	17.4808i	−3.55684	−	0.593336i
$869$	−4.17874	−	1.11969i	−0.141754	−	0.0379829i
$870$		0			0
$871$	−7.22209	+	37.8726i	−0.244711	+	1.28327i
$872$	17.9824			0.608961
$873$		0			0
$874$	41.2609	−	23.8220i	1.39567	−	0.805792i
$875$	−11.1666	−	29.8198i	−0.377500	−	1.00809i
$876$		0			0
$877$	−4.78095	+	1.28105i	−0.161441	+	0.0432580i	−0.338634	−	0.940918i	$-0.609965\pi$
$877$	−4.78095	+	1.28105i	−0.161441	+	0.0432580i	0.177193	+	0.984176i	$0.443298\pi$
$878$	20.8181	−	5.57819i	0.702577	−	0.188255i
$879$		0			0
$880$	−76.8770	−	44.3849i	−2.59152	−	1.49622i
$881$	17.8019	+	30.8338i	0.599762	+	1.03882i	0.992856	+	0.119320i	$0.0380714\pi$
$881$	17.8019	+	30.8338i	0.599762	+	1.03882i	−0.393094	+	0.919498i	$0.628595\pi$
$882$		0			0
$883$		−	16.6669i		−	0.560886i	−0.959871	−	0.280443i	$-0.909519\pi$
$883$		−	16.6669i		−	0.560886i	0.959871	−	0.280443i	$-0.0904814\pi$
$884$	−95.1294	+	64.6587i	−3.19955	+	2.17471i
$885$		0			0
$886$	−18.0064	+	67.2009i	−0.604937	+	2.25766i
$887$	24.7682	−	14.2999i	0.831635	−	0.480145i	−0.0227770	−	0.999741i	$-0.507251\pi$
$887$	24.7682	−	14.2999i	0.831635	−	0.480145i	0.854412	+	0.519596i	$0.173917\pi$
$888$		0			0
$889$	−4.88282	+	0.472689i	−0.163764	+	0.0158535i
$890$	−21.1800	+	5.67515i	−0.709954	+	0.190231i
$891$		0			0
$892$	−45.2957	−	45.2957i	−1.51661	−	1.51661i
$893$	−8.53842	+	14.7890i	−0.285727	+	0.494894i
$894$		0			0
$895$	−9.83467	+	36.7035i	−0.328737	+	1.22686i
$896$	21.9529	+	18.0777i	0.733396	+	0.603934i
$897$		0			0
$898$	9.78518			0.326536
$899$	8.08753	+	2.16705i	0.269734	+	0.0722750i
$900$		0			0
$901$	1.25881	−	2.18032i	0.0419370	−	0.0726371i
$902$	−11.2815	+	11.2815i	−0.375633	+	0.375633i
$903$		0			0
$904$	−12.7011	−	47.4013i	−0.422433	−	1.57654i
$905$	16.1848	−	16.1848i	0.538000	−	0.538000i
$906$		0			0
$907$	31.1299	−	17.9728i	1.03365	−	0.596778i	0.115622	−	0.993293i	$-0.463114\pi$
$907$	31.1299	−	17.9728i	1.03365	−	0.596778i	0.918028	+	0.396515i	$0.129780\pi$
$908$	−15.1342	+	56.4815i	−0.502245	+	1.87441i
$909$		0			0
$910$	−7.13379	−	41.5900i	−0.236483	−	1.37869i
$911$	−23.0425			−0.763432			−0.381716	−	0.924280i	$-0.624667\pi$
$911$	−23.0425			−0.763432			−0.381716	+	0.924280i	$0.624667\pi$
$912$		0			0
$913$	44.4993	−	25.6917i	1.47271	−	0.850270i
$914$	22.1919	+	12.8125i	0.734043	+	0.423800i
$915$		0			0
$916$	16.8469	+	62.8733i	0.556636	+	2.07739i
$917$	−5.42200	+	11.9137i	−0.179050	+	0.393424i
$918$		0			0
$919$	−19.2005	+	33.2563i	−0.633367	+	1.09702i	0.353492	+	0.935438i	$0.384994\pi$
$919$	−19.2005	+	33.2563i	−0.633367	+	1.09702i	−0.986859	+	0.161586i	$0.948339\pi$
$920$	−28.6688	−	49.6558i	−0.945182	−	1.63710i
$921$		0			0
$922$	19.5777			0.644759
$923$	−15.2197	+	5.30114i	−0.500962	+	0.174489i
$924$		0			0
$925$	−0.341214	+	1.27343i	−0.0112191	+	0.0418701i
$926$	19.2816	+	33.3967i	0.633633	+	1.09748i
$927$		0			0
$928$	−10.5387	−	10.5387i	−0.345950	−	0.345950i
$929$	−0.718418	−	2.68117i	−0.0235705	−	0.0879664i	0.953139	−	0.302534i	$-0.0978325\pi$
$929$	−0.718418	−	2.68117i	−0.0235705	−	0.0879664i	−0.976709	+	0.214567i	$0.931166\pi$
$930$		0			0
$931$	−16.5179	+	24.5430i	−0.541351	+	0.804365i
$932$	−3.78102	+	6.54892i	−0.123852	+	0.214517i
$933$		0			0
$934$	−23.4967	+	87.6908i	−0.768835	+	2.86933i
$935$			49.0135i			1.60291i
$936$		0			0
$937$			34.9632i			1.14220i	0.820881	+	0.571100i	$0.193483\pi$
$937$			34.9632i			1.14220i	−0.820881	+	0.571100i	$0.806517\pi$
$938$	−43.6651	−	61.1499i	−1.42572	−	1.99661i
$939$		0			0
$940$	29.4544	+	17.0055i	0.960697	+	0.554658i
$941$	5.49420	−	5.49420i	0.179106	−	0.179106i	−0.611860	−	0.790966i	$-0.709578\pi$
$941$	5.49420	−	5.49420i	0.179106	−	0.179106i	0.790966	+	0.611860i	$0.209578\pi$
$942$		0			0
$943$	−5.28324	+	1.41564i	−0.172046	+	0.0460996i
$944$	−69.1513	−	69.1513i	−2.25068	−	2.25068i
$945$		0			0
$946$	114.898	−	66.3363i	3.73565	−	2.15678i
$947$	−19.3584	−	5.18706i	−0.629063	−	0.168557i	−0.0698185	−	0.997560i	$-0.522242\pi$
$947$	−19.3584	−	5.18706i	−0.629063	−	0.168557i	−0.559244	+	0.829003i	$0.688909\pi$
$948$		0			0
$949$	3.61081	+	3.11636i	0.117212	+	0.101161i
$950$		−	24.9854i		−	0.810633i
$951$		0			0
$952$	22.2878	−	133.608i	0.722353	−	4.33025i
$953$	10.4017	+	6.00540i	0.336943	+	0.194534i	0.658919	−	0.752214i	$-0.271014\pi$
$953$	10.4017	+	6.00540i	0.336943	+	0.194534i	−0.321977	+	0.946748i	$0.604347\pi$
$954$		0			0
$955$	−5.19517	−	19.3887i	−0.168112	−	0.627402i
$956$	−5.90663	−	22.0438i	−0.191034	−	0.712949i
$957$		0			0
$958$	81.7154	+	47.1784i	2.64010	+	1.52427i
$959$	3.07065	−	18.4075i	0.0991564	−	0.594408i
$960$		0			0
$961$		−	32.1314i		−	1.03650i
$962$	−2.46805	+	5.10624i	−0.0795732	+	0.164632i
$963$		0			0
$964$	46.8701	+	12.5588i	1.50959	+	0.404492i
$965$	6.60290	−	3.81219i	0.212555	−	0.122719i
$966$		0			0
$967$	−2.97257	−	2.97257i	−0.0955913	−	0.0955913i	0.657694	−	0.753285i	$-0.271532\pi$
$967$	−2.97257	−	2.97257i	−0.0955913	−	0.0955913i	−0.753285	+	0.657694i	$0.771532\pi$
$968$	84.0821	−	22.5297i	2.70250	−	0.724133i
$969$		0			0
$970$	20.0173	−	20.0173i	0.642718	−	0.642718i
$971$	−25.0492	−	14.4622i	−0.803867	−	0.464113i	0.0409543	−	0.999161i	$-0.486960\pi$
$971$	−25.0492	−	14.4622i	−0.803867	−	0.464113i	−0.844822	+	0.535048i	$0.820294\pi$
$972$		0			0
$973$	−18.4727	−	25.8696i	−0.592206	−	0.829343i
$974$			60.5312i			1.93954i
$975$		0			0
$976$		−	55.8388i		−	1.78736i
$977$	15.0612	−	56.2091i	0.481850	−	1.79829i	−0.111995	−	0.993709i	$-0.535724\pi$
$977$	15.0612	−	56.2091i	0.481850	−	1.79829i	0.593845	−	0.804579i	$-0.297609\pi$
$978$		0			0
$979$	11.5544	−	20.0127i	0.369279	−	0.639610i
$980$	48.8810	+	32.8977i	1.56145	+	1.05088i
$981$		0			0
$982$	−10.2125	−	38.1135i	−0.325893	−	1.21625i
$983$	−26.9928	−	26.9928i	−0.860937	−	0.860937i	0.130510	−	0.991447i	$-0.458339\pi$
$983$	−26.9928	−	26.9928i	−0.860937	−	0.860937i	−0.991447	+	0.130510i	$0.958339\pi$
$984$		0			0
$985$	−16.2734	−	28.1864i	−0.518514	−	0.898092i
$986$	−4.57253	+	17.0649i	−0.145619	+	0.543458i
$987$		0			0
$988$	14.4252	−	75.6456i	0.458926	−	2.40661i
$989$	45.4837			1.44630
$990$		0			0
$991$	−2.29062	−	3.96747i	−0.0727640	−	0.126031i	0.827348	−	0.561690i	$-0.189849\pi$
$991$	−2.29062	−	3.96747i	−0.0727640	−	0.126031i	−0.900112	+	0.435659i	$0.856515\pi$
$992$	−56.1883	+	97.3211i	−1.78398	+	3.08995i
$993$		0			0
$994$	13.0105	−	28.5879i	0.412669	−	0.906752i
$995$	10.5610	+	39.4142i	0.334806	+	1.24951i
$996$		0			0
$997$	−46.4148	−	26.7976i	−1.46997	−	0.848689i	−0.470540	−	0.882379i	$-0.655941\pi$
$997$	−46.4148	−	26.7976i	−1.46997	−	0.848689i	−0.999432	+	0.0336896i	$0.989274\pi$
$998$	36.5255	−	21.0880i	1.15619	−	0.667529i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.622.1		32
3.2	odd	2		273.2.by.c.76.8	✓	32
7.6	odd	2		819.2.fm.e.622.1		32
13.6	odd	12		819.2.fm.e.370.1		32
21.20	even	2		273.2.by.d.76.8	yes	32
39.32	even	12		273.2.by.d.97.8	yes	32
91.6	even	12	inner	819.2.fm.f.370.1		32
273.188	odd	12		273.2.by.c.97.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.8	✓	32	3.2	odd	2
273.2.by.c.97.8	yes	32	273.188	odd	12
273.2.by.d.76.8	yes	32	21.20	even	2
273.2.by.d.97.8	yes	32	39.32	even	12
819.2.fm.e.370.1		32	13.6	odd	12
819.2.fm.e.622.1		32	7.6	odd	2
819.2.fm.f.370.1		32	91.6	even	12	inner
819.2.fm.f.622.1		32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687394 + 2.56539i) q^{2} +(-4.37666 - 2.52687i) q^{4} +(-1.17771 + 1.17771i) q^{5} +(2.40809 + 1.09594i) q^{7} +(5.73490 - 5.73490i) q^{8} +O(q^{10})\)	\(q+(-0.687394 + 2.56539i) q^{2} +(-4.37666 - 2.52687i) q^{4} +(-1.17771 + 1.17771i) q^{5} +(2.40809 + 1.09594i) q^{7} +(5.73490 - 5.73490i) q^{8} +(-2.21174 - 3.83085i) q^{10} +(4.50301 + 1.20658i) q^{11} +(3.59585 - 0.264293i) q^{13} +(-4.46682 + 5.42436i) q^{14} +(5.71638 + 9.90107i) q^{16} +(3.15625 - 5.46679i) q^{17} +(1.09384 + 4.08225i) q^{19} +(8.13039 - 2.17853i) q^{20} +(-6.19069 + 10.7226i) q^{22} +(-3.67599 + 2.12233i) q^{23} +2.22598i q^{25} +(-1.79375 + 9.40643i) q^{26} +(-7.77012 - 10.8815i) q^{28} +(0.526889 + 0.912598i) q^{29} +(5.61834 - 5.61834i) q^{31} +(-13.6615 + 3.66058i) q^{32} +(11.8549 + 11.8549i) q^{34} +(-4.12675 + 1.54534i) q^{35} +(0.572076 + 0.153287i) q^{37} -11.2245 q^{38} +13.5081i q^{40} +(1.24468 + 0.333510i) q^{41} +(-9.27990 - 5.35775i) q^{43} +(-16.6593 - 16.6593i) q^{44} +(-2.91776 - 10.8892i) q^{46} +(2.85718 + 2.85718i) q^{47} +(4.59783 + 5.27825i) q^{49} +(-5.71050 - 1.53012i) q^{50} +(-16.4057 - 7.92952i) q^{52} +0.398831 q^{53} +(-6.72427 + 3.88226i) q^{55} +(20.0953 - 7.52507i) q^{56} +(-2.70335 + 0.724361i) q^{58} +(-8.26243 + 2.21391i) q^{59} +(-4.22976 - 2.44205i) q^{61} +(10.5512 + 18.2752i) q^{62} -14.6977i q^{64} +(-3.92362 + 4.54615i) q^{65} +(-2.76762 + 10.3289i) q^{67} +(-27.6277 + 15.9509i) q^{68} +(-1.12770 - 11.6490i) q^{70} +(-4.31760 + 1.15690i) q^{71} +(0.935407 + 0.935407i) q^{73} +(-0.786484 + 1.36223i) q^{74} +(5.52795 - 20.6306i) q^{76} +(9.52134 + 7.84059i) q^{77} -0.927988 q^{79} +(-18.3929 - 4.92836i) q^{80} +(-1.71117 + 2.96383i) q^{82} +(7.79378 - 7.79378i) q^{83} +(2.72115 + 10.1555i) q^{85} +(20.1237 - 20.1237i) q^{86} +(32.7439 - 18.9047i) q^{88} +(1.28296 - 4.78807i) q^{89} +(8.94880 + 3.30440i) q^{91} +21.4514 q^{92} +(-9.29378 + 5.36577i) q^{94} +(-6.09595 - 3.51950i) q^{95} +(1.65635 + 6.18160i) q^{97} +(-16.7013 + 8.16698i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Introduction

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