LMFDB - Embedded newform 819.2.fm.f.496.2

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			496.2
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.f.748.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96303 - 0.525993i) q^{2} +(1.84478 + 1.06508i) q^{4} +(-1.56698 - 1.56698i) q^{5} +(2.02456 - 1.70328i) q^{7} +(-0.187059 - 0.187059i) q^{8} +O(q^{10})$	\(q+(-1.96303 - 0.525993i) q^{2} +(1.84478 + 1.06508i) q^{4} +(-1.56698 - 1.56698i) q^{5} +(2.02456 - 1.70328i) q^{7} +(-0.187059 - 0.187059i) q^{8} +(2.25182 + 3.90026i) q^{10} +(1.16197 - 4.33653i) q^{11} +(-3.51879 + 0.786201i) q^{13} +(-4.87020 + 2.27868i) q^{14} +(-1.86136 - 3.22397i) q^{16} +(-1.31427 + 2.27639i) q^{17} +(6.01372 - 1.61137i) q^{19} +(-1.22177 - 4.55971i) q^{20} +(-4.56197 + 7.90156i) q^{22} +(4.58893 - 2.64942i) q^{23} -0.0891302i q^{25} +(7.32104 + 0.307521i) q^{26} +(5.54901 - 0.985840i) q^{28} +(2.06391 + 3.57480i) q^{29} +(-2.44135 - 2.44135i) q^{31} +(2.09506 + 7.81887i) q^{32} +(3.77733 - 3.77733i) q^{34} +(-5.84146 - 0.503451i) q^{35} +(0.0290943 - 0.108582i) q^{37} -12.6527 q^{38} +0.586237i q^{40} +(-2.03234 + 7.58481i) q^{41} +(-5.47731 - 3.16233i) q^{43} +(6.76235 - 6.76235i) q^{44} +(-10.4018 + 2.78716i) q^{46} +(5.82732 - 5.82732i) q^{47} +(1.19770 - 6.89677i) q^{49} +(-0.0468819 + 0.174966i) q^{50} +(-7.32877 - 2.29744i) q^{52} -9.24486 q^{53} +(-8.61605 + 4.97448i) q^{55} +(-0.697326 - 0.0600996i) q^{56} +(-2.17121 - 8.10305i) q^{58} +(-1.27986 - 4.77649i) q^{59} +(-3.33568 - 1.92586i) q^{61} +(3.50831 + 6.07658i) q^{62} -9.00526i q^{64} +(6.74585 + 4.28192i) q^{65} +(10.1688 + 2.72472i) q^{67} +(-4.84909 + 2.79963i) q^{68} +(11.2022 + 4.06086i) q^{70} +(-3.56722 - 13.3131i) q^{71} +(-11.8088 + 11.8088i) q^{73} +(-0.114226 + 0.197846i) q^{74} +(12.8102 + 3.43249i) q^{76} +(-5.03382 - 10.7587i) q^{77} -13.3186 q^{79} +(-2.13518 + 7.96862i) q^{80} +(7.97912 - 13.8202i) q^{82} +(-5.15552 - 5.15552i) q^{83} +(5.62651 - 1.50762i) q^{85} +(9.08878 + 9.08878i) q^{86} +(-1.02854 + 0.593831i) q^{88} +(-7.93017 - 2.12488i) q^{89} +(-5.78489 + 7.58518i) q^{91} +11.2874 q^{92} +(-14.5044 + 8.37409i) q^{94} +(-11.9484 - 6.89840i) q^{95} +(-1.93349 + 0.518076i) q^{97} +(-5.97879 + 12.9086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.96303	−	0.525993i	−1.38807	−	0.371933i	−0.514027	−	0.857774i	$-0.671847\pi$
$2$	−1.96303	−	0.525993i	−1.38807	−	0.371933i	−0.874047	+	0.485841i	$0.838514\pi$
$3$		0			0
$3$		0			0
$4$	1.84478	+	1.06508i	0.922391	+	0.532542i
$5$	−1.56698	−	1.56698i	−0.700776	−	0.700776i	0.263801	−	0.964577i	$-0.415024\pi$
$5$	−1.56698	−	1.56698i	−0.700776	−	0.700776i	−0.964577	+	0.263801i	$0.915024\pi$
$6$		0			0
$7$	2.02456	−	1.70328i	0.765213	−	0.643778i
$7$	2.02456	−	1.70328i	0.765213	−	0.643778i
$8$	−0.187059	−	0.187059i	−0.0661354	−	0.0661354i
$9$		0			0
$10$	2.25182	+	3.90026i	0.712087	+	1.23337i
$11$	1.16197	−	4.33653i	0.350347	−	1.30751i	−0.535893	−	0.844286i	$-0.680025\pi$
$11$	1.16197	−	4.33653i	0.350347	−	1.30751i	0.886240	−	0.463227i	$-0.153308\pi$
$12$		0			0
$13$	−3.51879	+	0.786201i	−0.975937	+	0.218053i
$13$	−3.51879	+	0.786201i	−0.975937	+	0.218053i
$14$	−4.87020	+	2.27868i	−1.30161	+	0.609003i
$15$		0			0
$16$	−1.86136	−	3.22397i	−0.465340	−	0.805992i
$17$	−1.31427	+	2.27639i	−0.318758	+	0.552105i	−0.980229	−	0.197865i	$-0.936599\pi$
$17$	−1.31427	+	2.27639i	−0.318758	+	0.552105i	0.661471	+	0.749971i	$0.269932\pi$
$18$		0			0
$19$	6.01372	−	1.61137i	1.37964	−	0.369674i	0.508650	−	0.860973i	$-0.330145\pi$
$19$	6.01372	−	1.61137i	1.37964	−	0.369674i	0.870991	+	0.491299i	$0.163478\pi$
$20$	−1.22177	−	4.55971i	−0.273196	−	1.01958i
$21$		0			0
$22$	−4.56197	+	7.90156i	−0.972615	+	1.68462i
$23$	4.58893	−	2.64942i	0.956859	−	0.552443i	0.0616538	−	0.998098i	$-0.480363\pi$
$23$	4.58893	−	2.64942i	0.956859	−	0.552443i	0.895205	+	0.445655i	$0.147029\pi$
$24$		0			0
$25$		−	0.0891302i		−	0.0178260i
$26$	7.32104	+	0.307521i	1.43577	+	0.0603099i
$27$		0			0
$28$	5.54901	−	0.985840i	1.04866	−	0.186306i
$29$	2.06391	+	3.57480i	0.383258	+	0.663823i	0.991526	−	0.129909i	$-0.0414685\pi$
$29$	2.06391	+	3.57480i	0.383258	+	0.663823i	−0.608267	+	0.793732i	$0.708135\pi$
$30$		0			0
$31$	−2.44135	−	2.44135i	−0.438479	−	0.438479i	0.453021	−	0.891500i	$-0.350346\pi$
$31$	−2.44135	−	2.44135i	−0.438479	−	0.438479i	−0.891500	+	0.453021i	$0.850346\pi$
$32$	2.09506	+	7.81887i	0.370358	+	1.38219i
$33$		0			0
$34$	3.77733	−	3.77733i	0.647807	−	0.647807i
$35$	−5.84146	−	0.503451i	−0.987387	−	0.0850987i
$36$		0			0
$37$	0.0290943	−	0.108582i	0.00478308	−	0.0178507i	−0.963493	−	0.267733i	$-0.913725\pi$
$37$	0.0290943	−	0.108582i	0.00478308	−	0.0178507i	0.968276	+	0.249883i	$0.0803920\pi$
$38$	−12.6527			−2.05254
$39$		0			0
$40$			0.586237i			0.0926922i
$41$	−2.03234	+	7.58481i	−0.317399	+	1.18455i	0.604336	+	0.796729i	$0.293438\pi$
$41$	−2.03234	+	7.58481i	−0.317399	+	1.18455i	−0.921735	+	0.387819i	$0.873228\pi$
$42$		0			0
$43$	−5.47731	−	3.16233i	−0.835282	−	0.482250i	0.0203758	−	0.999792i	$-0.493514\pi$
$43$	−5.47731	−	3.16233i	−0.835282	−	0.482250i	−0.855658	+	0.517542i	$0.826847\pi$
$44$	6.76235	−	6.76235i	1.01946	−	1.01946i
$45$		0			0
$46$	−10.4018	+	2.78716i	−1.53366	+	0.410944i
$47$	5.82732	−	5.82732i	0.850002	−	0.850002i	−0.140131	−	0.990133i	$-0.544752\pi$
$47$	5.82732	−	5.82732i	0.850002	−	0.850002i	0.990133	+	0.140131i	$0.0447524\pi$
$48$		0			0
$49$	1.19770	−	6.89677i	0.171101	−	0.985254i
$50$	−0.0468819	+	0.174966i	−0.00663010	+	0.0247439i
$51$		0			0
$52$	−7.32877	−	2.29744i	−1.01632	−	0.318598i
$53$	−9.24486			−1.26988			−0.634940	−	0.772562i	$-0.718975\pi$
$53$	−9.24486			−1.26988			−0.634940	+	0.772562i	$0.718975\pi$
$54$		0			0
$55$	−8.61605	+	4.97448i	−1.16179	+	0.670759i
$56$	−0.697326	−	0.0600996i	−0.0931842	−	0.00803115i
$57$		0			0
$58$	−2.17121	−	8.10305i	−0.285093	−	1.06398i
$59$	−1.27986	−	4.77649i	−0.166623	−	0.621846i	−0.997828	−	0.0658791i	$-0.979015\pi$
$59$	−1.27986	−	4.77649i	−0.166623	−	0.621846i	0.831205	−	0.555967i	$-0.187652\pi$
$60$		0			0
$61$	−3.33568	−	1.92586i	−0.427090	−	0.246581i	0.271016	−	0.962575i	$-0.412640\pi$
$61$	−3.33568	−	1.92586i	−0.427090	−	0.246581i	−0.698106	+	0.715994i	$0.745974\pi$
$62$	3.50831	+	6.07658i	0.445556	+	0.771726i
$63$		0			0
$64$		−	9.00526i		−	1.12566i
$65$	6.74585	+	4.28192i	0.836719	+	0.531107i
$66$		0			0
$67$	10.1688	+	2.72472i	1.24232	+	0.332878i	0.819364	−	0.573273i	$-0.194327\pi$
$67$	10.1688	+	2.72472i	1.24232	+	0.332878i	0.422954	+	0.906151i	$0.360993\pi$
$68$	−4.84909	+	2.79963i	−0.588039	+	0.339505i
$69$		0			0
$70$	11.2022	+	4.06086i	1.33891	+	0.485365i
$71$	−3.56722	−	13.3131i	−0.423352	−	1.57997i	−0.767496	−	0.641053i	$-0.778498\pi$
$71$	−3.56722	−	13.3131i	−0.423352	−	1.57997i	0.344145	−	0.938917i	$-0.388169\pi$
$72$		0			0
$73$	−11.8088	+	11.8088i	−1.38211	+	1.38211i	−0.541259	+	0.840856i	$0.682052\pi$
$73$	−11.8088	+	11.8088i	−1.38211	+	1.38211i	−0.840856	+	0.541259i	$0.817948\pi$
$74$	−0.114226	+	0.197846i	−0.0132785	+	0.0229991i
$75$		0			0
$76$	12.8102	+	3.43249i	1.46944	+	0.393734i
$77$	−5.03382	−	10.7587i	−0.573657	−	1.22607i
$78$		0			0
$79$	−13.3186			−1.49846			−0.749229	−	0.662311i	$-0.769576\pi$
$79$	−13.3186			−1.49846			−0.749229	+	0.662311i	$0.769576\pi$
$80$	−2.13518	+	7.96862i	−0.238721	+	0.890918i
$81$		0			0
$82$	7.97912	−	13.8202i	0.881146	−	1.52619i
$83$	−5.15552	−	5.15552i	−0.565892	−	0.565892i	0.365083	−	0.930975i	$-0.381041\pi$
$83$	−5.15552	−	5.15552i	−0.565892	−	0.565892i	−0.930975	+	0.365083i	$0.881041\pi$
$84$		0			0
$85$	5.62651	−	1.50762i	0.610280	−	0.163524i
$86$	9.08878	+	9.08878i	0.980068	+	0.980068i
$87$		0			0
$88$	−1.02854	+	0.593831i	−0.109643	+	0.0633025i
$89$	−7.93017	−	2.12488i	−0.840596	−	0.225237i	−0.187265	−	0.982309i	$-0.559962\pi$
$89$	−7.93017	−	2.12488i	−0.840596	−	0.225237i	−0.653331	+	0.757072i	$0.726629\pi$
$90$		0			0
$91$	−5.78489	+	7.58518i	−0.606422	+	0.795143i
$92$	11.2874			1.17680
$93$		0			0
$94$	−14.5044	+	8.37409i	−1.49601	+	0.863722i
$95$	−11.9484	−	6.89840i	−1.22588	−	0.707761i
$96$		0			0
$97$	−1.93349	+	0.518076i	−0.196316	+	0.0526027i	−0.355637	−	0.934624i	$-0.615736\pi$
$97$	−1.93349	+	0.518076i	−0.196316	+	0.0526027i	0.159321	+	0.987227i	$0.449069\pi$
$98$	−5.97879	+	12.9086i	−0.603949	+	1.30397i
$99$		0			0
$100$	0.0949312	−	0.164426i	0.00949312	−	0.0164426i
$101$	−4.49537	−	7.78621i	−0.447306	−	0.774757i	0.550903	−	0.834569i	$-0.314283\pi$
$101$	−4.49537	−	7.78621i	−0.447306	−	0.774757i	−0.998210	+	0.0598118i	$0.980950\pi$
$102$		0			0
$103$	5.08145			0.500690			0.250345	−	0.968157i	$-0.419456\pi$
$103$	5.08145			0.500690			0.250345	+	0.968157i	$0.419456\pi$
$104$	0.805288	+	0.511156i	0.0789650	+	0.0501230i
$105$		0			0
$106$	18.1480	+	4.86273i	1.76269	+	0.472310i
$107$	−0.521017	−	0.902428i	−0.0503686	−	0.0872410i	0.839742	−	0.542986i	$-0.182706\pi$
$107$	−0.521017	−	0.902428i	−0.0503686	−	0.0872410i	−0.890110	+	0.455745i	$0.849373\pi$
$108$		0			0
$109$	2.86707	−	2.86707i	0.274616	−	0.274616i	−0.556339	−	0.830955i	$-0.687795\pi$
$109$	2.86707	−	2.86707i	0.274616	−	0.274616i	0.830955	+	0.556339i	$0.187795\pi$
$110$	19.5301	−	5.23309i	1.86213	−	0.498955i
$111$		0			0
$112$	−9.25974	−	3.35672i	−0.874963	−	0.317180i
$113$	−4.39010	+	7.60388i	−0.412986	+	0.715313i	−0.995215	−	0.0977122i	$-0.968848\pi$
$113$	−4.39010	+	7.60388i	−0.412986	+	0.715313i	0.582229	+	0.813025i	$0.302181\pi$
$114$		0			0
$115$	−11.3424	−	3.03918i	−1.05768	−	0.283405i
$116$			8.79296i			0.816406i
$117$		0			0
$118$			10.0496i			0.925141i
$119$	1.21649	+	6.84726i	0.111515	+	0.627687i
$120$		0			0
$121$	−7.92903	−	4.57783i	−0.720821	−	0.416166i
$122$	5.53507	+	5.53507i	0.501121	+	0.501121i
$123$		0			0
$124$	−1.90351	−	7.10399i	−0.170940	−	0.637957i
$125$	−7.97458	+	7.97458i	−0.713268	+	0.713268i
$126$		0			0
$127$	−6.20223	+	3.58086i	−0.550359	+	0.317750i	−0.749267	−	0.662268i	$-0.769594\pi$
$127$	−6.20223	+	3.58086i	−0.550359	+	0.317750i	0.198908	+	0.980018i	$0.436261\pi$
$128$	−0.546587	+	2.03989i	−0.0483119	+	0.180303i
$129$		0			0
$130$	−10.9901	−	11.9538i	−0.963892	−	1.04842i
$131$		−	8.06442i		−	0.704591i	−0.935889	−	0.352296i	$-0.885401\pi$
$131$		−	8.06442i		−	0.704591i	0.935889	−	0.352296i	$-0.114599\pi$
$132$		0			0
$133$	9.43054	−	13.5053i	0.817731	−	1.17106i
$134$	−18.5285	−	10.6975i	−1.60062	−	0.924119i
$135$		0			0
$136$	0.671666	−	0.179972i	0.0575949	−	0.0154325i
$137$	4.00328	−	1.07268i	0.342023	−	0.0916449i	−0.0837188	−	0.996489i	$-0.526680\pi$
$137$	4.00328	−	1.07268i	0.342023	−	0.0916449i	0.425742	+	0.904845i	$0.360013\pi$
$138$		0			0
$139$	−14.1275	−	8.15651i	−1.19828	−	0.691826i	−0.238107	−	0.971239i	$-0.576527\pi$
$139$	−14.1275	−	8.15651i	−1.19828	−	0.691826i	−0.960171	+	0.279413i	$0.909860\pi$
$140$	−10.2400	−	7.15040i	−0.865437	−	0.604319i
$141$		0			0
$142$			28.0103i			2.35057i
$143$	−0.679344	+	16.1729i	−0.0568096	+	1.35244i
$144$		0			0
$145$	2.36753	−	8.83576i	0.196613	−	0.733770i
$146$	29.3924	−	16.9697i	2.43253	−	1.40442i
$147$		0			0
$148$	0.169321	−	0.169321i	0.0139181	−	0.0139181i
$149$	1.57172	+	5.86575i	0.128761	+	0.480541i	0.999946	−	0.0104133i	$-0.00331473\pi$
$149$	1.57172	+	5.86575i	0.128761	+	0.480541i	−0.871185	+	0.490955i	$0.836648\pi$
$150$		0			0
$151$	13.6338	+	13.6338i	1.10950	+	1.10950i	0.993216	+	0.116285i	$0.0370987\pi$
$151$	13.6338	+	13.6338i	1.10950	+	1.10950i	0.116285	+	0.993216i	$0.462901\pi$
$152$	−1.42634	−	0.823499i	−0.115692	−	0.0667946i
$153$		0			0
$154$	4.22255	+	23.7675i	0.340263	+	1.91524i
$155$			7.65110i			0.614551i
$156$		0			0
$157$			8.31072i			0.663268i	0.943408	+	0.331634i	$0.107600\pi$
$157$			8.31072i			0.663268i	−0.943408	+	0.331634i	$0.892400\pi$
$158$	26.1448	+	7.00549i	2.07997	+	0.557327i
$159$		0			0
$160$	8.96911	−	15.5350i	0.709071	−	1.22815i
$161$	4.77789	−	13.1801i	0.376550	−	1.03874i
$162$		0			0
$163$	0.385067	−	0.103178i	0.0301607	−	0.00808155i	−0.243707	−	0.969849i	$-0.578364\pi$
$163$	0.385067	−	0.103178i	0.0301607	−	0.00808155i	0.273868	+	0.961767i	$0.411697\pi$
$164$	−11.8277	+	11.8277i	−0.923588	+	0.923588i
$165$		0			0
$166$	7.40869	+	12.8322i	0.575026	+	0.995974i
$167$	19.9784	+	5.35319i	1.54597	+	0.414243i	0.928191	−	0.372105i	$-0.121364\pi$
$167$	19.9784	+	5.35319i	1.54597	+	0.414243i	0.617784	+	0.786348i	$0.288031\pi$
$168$		0			0
$169$	11.7638	−	5.53295i	0.904906	−	0.425612i
$170$	−11.8380			−0.907934
$171$		0			0
$172$	−6.73629	−	11.6676i	−0.513637	−	0.889646i
$173$	9.58243	−	16.5973i	0.728539	−	1.26187i	−0.228962	−	0.973435i	$-0.573533\pi$
$173$	9.58243	−	16.5973i	0.728539	−	1.26187i	0.957501	−	0.288431i	$-0.0931334\pi$
$174$		0			0
$175$	−0.151813	−	0.180450i	−0.0114760	−	0.0136407i
$176$	−16.1437	+	4.32568i	−1.21687	+	0.326061i
$177$		0			0
$178$	14.4495	+	8.34243i	1.08304	+	0.625292i
$179$	5.86324	−	3.38514i	0.438239	−	0.253018i	−0.264611	−	0.964355i	$-0.585244\pi$
$179$	5.86324	−	3.38514i	0.438239	−	0.253018i	0.702850	+	0.711338i	$0.251910\pi$
$180$		0			0
$181$	16.5594			1.23085			0.615424	−	0.788197i	$-0.288985\pi$
$181$	16.5594			1.23085			0.615424	+	0.788197i	$0.288985\pi$
$182$	15.3457	−	11.8472i	1.13750	−	0.878169i
$183$		0			0
$184$	−1.35400	−	0.362803i	−0.0998183	−	0.0267462i
$185$	−0.215736	+	0.124555i	−0.0158612	+	0.00915747i
$186$		0			0
$187$	8.34448	+	8.34448i	0.610209	+	0.610209i
$188$	16.9567	−	4.54354i	1.23670	−	0.331372i
$189$		0			0
$190$	19.8266	+	19.8266i	1.43837	+	1.43837i
$191$	−4.44834	+	7.70475i	−0.321870	+	0.557496i	−0.980874	−	0.194644i	$-0.937645\pi$
$191$	−4.44834	+	7.70475i	−0.321870	+	0.557496i	0.659003	+	0.752140i	$0.270978\pi$
$192$		0			0
$193$	−1.15868	+	4.32426i	−0.0834038	+	0.311267i	−0.995007	−	0.0998038i	$-0.968178\pi$
$193$	−1.15868	+	4.32426i	−0.0834038	+	0.311267i	0.911603	+	0.411071i	$0.134845\pi$
$194$	4.06800			0.292066
$195$		0			0
$196$	9.55515	−	11.4474i	0.682511	−	0.817670i
$197$	−1.57369	−	0.421669i	−0.112121	−	0.0300427i	0.202322	−	0.979319i	$-0.435151\pi$
$197$	−1.57369	−	0.421669i	−0.112121	−	0.0300427i	−0.314443	+	0.949276i	$0.601818\pi$
$198$		0			0
$199$	6.21777	−	10.7695i	0.440766	−	0.763429i	−0.556981	−	0.830526i	$-0.688040\pi$
$199$	6.21777	−	10.7695i	0.440766	−	0.763429i	0.997746	+	0.0670965i	$0.0213736\pi$
$200$	−0.0166726	+	0.0166726i	−0.00117893	+	0.00117893i
$201$		0			0
$202$	4.72907	+	17.6491i	0.332736	+	1.24179i
$203$	10.2674	+	3.72199i	0.720629	+	0.261233i
$204$		0			0
$205$	15.0699	−	8.70062i	1.05253	−	0.607678i
$206$	−9.97506	−	2.67281i	−0.694995	−	0.186223i
$207$		0			0
$208$	9.08442	+	9.88106i	0.629891	+	0.685128i
$209$		−	27.9510i		−	1.93341i
$210$		0			0
$211$	0.111585	+	0.193271i	0.00768182	+	0.0133053i	0.869841	−	0.493333i	$-0.164221\pi$
$211$	0.111585	+	0.193271i	0.00768182	+	0.0133053i	−0.862159	+	0.506638i	$0.830888\pi$
$212$	−17.0547	−	9.84656i	−1.17132	−	0.676264i
$213$		0			0
$214$	0.548103	+	2.04555i	0.0374676	+	0.139831i
$215$	3.62754	+	13.5382i	0.247396	+	0.923295i
$216$		0			0
$217$	−9.10094	−	0.784372i	−0.617812	−	0.0532467i
$218$	−7.13622	+	4.12010i	−0.483326	+	0.279048i
$219$		0			0
$220$	−21.1930			−1.42883
$221$	2.83496	−	9.04342i	0.190700	−	0.608326i
$222$		0			0
$223$	1.45774	−	5.44036i	0.0976174	−	0.364313i	−0.899786	−	0.436332i	$-0.856277\pi$
$223$	1.45774	−	5.44036i	0.0976174	−	0.364313i	0.997403	+	0.0720186i	$0.0229441\pi$
$224$	17.5593	+	12.2613i	1.17323	+	0.819244i
$225$		0			0
$226$	12.6175	−	12.6175i	0.839304	−	0.839304i
$227$	4.17248	−	1.11801i	0.276937	−	0.0742050i	−0.117677	−	0.993052i	$-0.537545\pi$
$227$	4.17248	−	1.11801i	0.276937	−	0.0742050i	0.394614	+	0.918847i	$0.370878\pi$
$228$		0			0
$229$	16.9969	−	16.9969i	1.12319	−	1.12319i	0.131929	−	0.991259i	$-0.457883\pi$
$229$	16.9969	−	16.9969i	1.12319	−	1.12319i	0.991259	−	0.131929i	$-0.0421171\pi$
$230$	20.6669	+	11.9320i	1.36273	+	0.786775i
$231$		0			0
$232$	0.282625	−	1.05477i	0.0185553	−	0.0692492i
$233$			13.6445i			0.893880i	0.894564	+	0.446940i	$0.147486\pi$
$233$			13.6445i			0.893880i	−0.894564	+	0.446940i	$0.852514\pi$
$234$		0			0
$235$	−18.2626			−1.19132
$236$	2.72631	−	10.1747i	0.177468	−	0.662319i
$237$		0			0
$238$	1.21361	−	14.0813i	0.0786664	−	0.912753i
$239$	4.70084	−	4.70084i	0.304072	−	0.304072i	−0.538533	−	0.842605i	$-0.681021\pi$
$239$	4.70084	−	4.70084i	0.304072	−	0.304072i	0.842605	+	0.538533i	$0.181021\pi$
$240$		0			0
$241$	−4.03655	−	15.0646i	−0.260017	−	0.970397i	−0.965230	−	0.261401i	$-0.915815\pi$
$241$	−4.03655	−	15.0646i	−0.260017	−	0.970397i	0.705213	−	0.708995i	$-0.250851\pi$
$242$	13.1570	+	13.1570i	0.845767	+	0.845767i
$243$		0			0
$244$	−4.10240	−	7.10557i	−0.262629	−	0.454887i
$245$	−12.6839	+	8.93034i	−0.810345	+	0.570539i
$246$		0			0
$247$	−19.8941	+	10.3981i	−1.26583	+	0.661613i
$248$			0.913353i			0.0579980i
$249$		0			0
$250$	19.8489	−	11.4598i	1.25536	−	0.724781i
$251$	−2.67179	+	4.62768i	−0.168642	+	0.292096i	−0.937943	−	0.346791i	$-0.887271\pi$
$251$	−2.67179	+	4.62768i	−0.168642	+	0.292096i	0.769301	+	0.638887i	$0.220605\pi$
$252$		0			0
$253$	−6.15709	−	22.9786i	−0.387093	−	1.44465i
$254$	14.0587	−	3.76701i	0.882120	−	0.236363i
$255$		0			0
$256$	−6.85933	+	11.8807i	−0.428708	+	0.742544i
$257$	7.85983	+	13.6136i	0.490283	+	0.849195i	0.999937	−	0.0111844i	$-0.00356018\pi$
$257$	7.85983	+	13.6136i	0.490283	+	0.849195i	−0.509655	+	0.860379i	$0.670227\pi$
$258$		0			0
$259$	−0.126041	−	0.269386i	−0.00783180	−	0.0167388i
$260$	7.88400	+	15.0841i	0.488945	+	0.935477i
$261$		0			0
$262$	−4.24183	+	15.8307i	−0.262061	+	0.978025i
$263$	−3.44067	−	5.95942i	−0.212161	−	0.367473i	0.740230	−	0.672354i	$-0.234717\pi$
$263$	−3.44067	−	5.95942i	−0.212161	−	0.367473i	−0.952391	+	0.304881i	$0.901383\pi$
$264$		0			0
$265$	14.4865	+	14.4865i	0.889901	+	0.889901i
$266$	−25.6162	+	21.5510i	−1.57063	+	1.32138i
$267$		0			0
$268$	15.8572	+	15.8572i	0.968631	+	0.968631i
$269$	−18.7176	−	10.8066i	−1.14123	−	0.658890i	−0.194496	−	0.980903i	$-0.562307\pi$
$269$	−18.7176	−	10.8066i	−1.14123	−	0.658890i	−0.946735	+	0.322013i	$0.895640\pi$
$270$		0			0
$271$	5.82362	+	1.56043i	0.353760	+	0.0947896i	0.431322	−	0.902198i	$-0.358047\pi$
$271$	5.82362	+	1.56043i	0.353760	+	0.0947896i	−0.0775628	+	0.996987i	$0.524714\pi$
$272$	9.78534			0.593323
$273$		0			0
$274$	−8.42279			−0.508840
$275$	−0.386516	−	0.103567i	−0.0233078	−	0.00624530i
$276$		0			0
$277$	−17.1918	−	9.92569i	−1.03295	−	0.596377i	−0.115125	−	0.993351i	$-0.536727\pi$
$277$	−17.1918	−	9.92569i	−1.03295	−	0.596377i	−0.917830	+	0.396974i	$0.870060\pi$
$278$	23.4425	+	23.4425i	1.40599	+	1.40599i
$279$		0			0
$280$	0.998523	+	1.18687i	0.0596732	+	0.0709293i
$281$	15.4156	+	15.4156i	0.919617	+	0.919617i	0.997001	−	0.0773842i	$-0.0246568\pi$
$281$	15.4156	+	15.4156i	0.919617	+	0.919617i	−0.0773842	+	0.997001i	$0.524657\pi$
$282$		0			0
$283$	14.1867	+	24.5721i	0.843314	+	1.46066i	0.887077	+	0.461621i	$0.152732\pi$
$283$	14.1867	+	24.5721i	0.843314	+	1.46066i	−0.0437635	+	0.999042i	$0.513935\pi$
$284$	7.59879	−	28.3591i	0.450905	−	1.68280i
$285$		0			0
$286$	9.84040	−	31.3906i	0.581875	−	1.85616i
$287$	8.80442	+	18.8176i	0.519708	+	1.11077i
$288$		0			0
$289$	5.04537	+	8.73884i	0.296786	+	0.514049i
$290$	−9.29510	+	16.0996i	−0.545827	+	0.945400i
$291$		0			0
$292$	−34.3620	+	9.20727i	−2.01088	+	0.538815i
$293$	2.70937	+	10.1115i	0.158283	+	0.590720i	0.998802	+	0.0489378i	$0.0155836\pi$
$293$	2.70937	+	10.1115i	0.158283	+	0.590720i	−0.840519	+	0.541782i	$0.817750\pi$
$294$		0			0
$295$	−5.47916	+	9.49019i	−0.319009	+	0.552540i
$296$	−0.0257535	+	0.0148688i	−0.00149689	+	0.000864232i
$297$		0			0
$298$		−	12.3414i		−	0.714917i
$299$	−14.0645	+	12.9306i	−0.813372	+	0.747795i
$300$		0			0
$301$	−16.4755	+	2.92704i	−0.949630	+	0.168712i
$302$	−19.5923	−	33.9348i	−1.12741	−	1.95273i
$303$		0			0
$304$	−16.3887	−	16.3887i	−0.939956	−	0.939956i
$305$	2.20917	+	8.24474i	0.126497	+	0.472092i
$306$		0			0
$307$	6.15683	−	6.15683i	0.351389	−	0.351389i	−0.509237	−	0.860626i	$-0.670072\pi$
$307$	6.15683	−	6.15683i	0.351389	−	0.351389i	0.860626	+	0.509237i	$0.170072\pi$
$308$	2.17265	−	25.2089i	0.123798	−	1.43641i
$309$		0			0
$310$	4.02442	−	15.0194i	0.228572	−	0.853042i
$311$	−5.30855			−0.301020			−0.150510	−	0.988608i	$-0.548092\pi$
$311$	−5.30855			−0.301020			−0.150510	+	0.988608i	$0.548092\pi$
$312$		0			0
$313$			18.4802i			1.04456i	0.852774	+	0.522280i	$0.174918\pi$
$313$			18.4802i			1.04456i	−0.852774	+	0.522280i	$0.825082\pi$
$314$	4.37139	−	16.3142i	0.246692	−	0.920665i
$315$		0			0
$316$	−24.5699	−	14.1854i	−1.38216	−	0.797993i
$317$	14.8596	−	14.8596i	0.834598	−	0.834598i	−0.153544	−	0.988142i	$-0.549069\pi$
$317$	14.8596	−	14.8596i	0.834598	−	0.834598i	0.988142	+	0.153544i	$0.0490685\pi$
$318$		0			0
$319$	17.9004	−	4.79640i	1.00223	−	0.268547i
$320$	−14.1111	+	14.1111i	−0.788834	+	0.788834i
$321$		0			0
$322$	−16.3118	+	23.3599i	−0.909022	+	1.30180i
$323$	−4.23556	+	15.8073i	−0.235673	+	0.879544i
$324$		0			0
$325$	0.0700742	+	0.313631i	0.00388702	+	0.0173971i
$326$	−0.810170			−0.0448711
$327$		0			0
$328$	1.79898	−	1.03864i	0.0993319	−	0.0573493i
$329$	1.87224	−	21.7233i	0.103220	−	1.19764i
$330$		0			0
$331$	−7.91671	−	29.5456i	−0.435142	−	1.62397i	−0.740727	−	0.671806i	$-0.765519\pi$
$331$	−7.91671	−	29.5456i	−0.435142	−	1.62397i	0.305586	−	0.952165i	$-0.401148\pi$
$332$	−4.01974	−	15.0019i	−0.220612	−	0.823335i
$333$		0			0
$334$	−36.4025	−	21.0170i	−1.99186	−	1.15000i
$335$	−11.6648	−	20.2039i	−0.637314	−	1.10386i
$336$		0			0
$337$		−	2.64409i		−	0.144033i	−0.997403	−	0.0720163i	$-0.977057\pi$
$337$		−	2.64409i		−	0.144033i	0.997403	−	0.0720163i	$-0.0229434\pi$
$338$	−26.0030	+	4.67370i	−1.41438	+	0.254216i
$339$		0			0
$340$	11.9854	+	3.21148i	0.650000	+	0.174167i
$341$	−13.4237	+	7.75020i	−0.726936	+	0.419697i
$342$		0			0
$343$	−9.32228	−	16.0030i	−0.503356	−	0.864079i
$344$	0.433039	+	1.61612i	0.0233479	+	0.0871355i
$345$		0			0
$346$	−27.5407	+	27.5407i	−1.48060	+	1.48060i
$347$	−1.58944	+	2.75299i	−0.0853255	+	0.147788i	−0.905530	−	0.424283i	$-0.860526\pi$
$347$	−1.58944	+	2.75299i	−0.0853255	+	0.147788i	0.820204	+	0.572071i	$0.193860\pi$
$348$		0			0
$349$	−20.2719	−	5.43184i	−1.08513	−	0.290760i	−0.328434	−	0.944527i	$-0.606521\pi$
$349$	−20.2719	−	5.43184i	−1.08513	−	0.290760i	−0.756696	+	0.653767i	$0.773188\pi$
$350$	0.203099	+	0.434081i	0.0108561	+	0.0232026i
$351$		0			0
$352$	36.3412			1.93699
$353$	−5.34444	+	19.9457i	−0.284456	+	1.06160i	0.664780	+	0.747039i	$0.268525\pi$
$353$	−5.34444	+	19.9457i	−0.284456	+	1.06160i	−0.949236	+	0.314565i	$0.898141\pi$
$354$		0			0
$355$	−15.2716	+	26.4511i	−0.810530	+	1.40388i
$356$	−12.3662	−	12.3662i	−0.655410	−	0.655410i
$357$		0			0
$358$	−13.2903	+	3.56113i	−0.702414	+	0.188211i
$359$	−18.9082	−	18.9082i	−0.997935	−	0.997935i	0.00206292	−	0.999998i	$-0.499343\pi$
$359$	−18.9082	−	18.9082i	−0.997935	−	0.997935i	−0.999998	+	0.00206292i	$0.999343\pi$
$360$		0			0
$361$	17.1138	−	9.88065i	0.900726	−	0.520034i
$362$	−32.5066	−	8.71011i	−1.70851	−	0.457793i
$363$		0			0
$364$	−18.7507	+	7.83160i	−0.982805	+	0.410487i
$365$	37.0084			1.93711
$366$		0			0
$367$	20.8759	−	12.0527i	1.08971	−	0.629146i	0.156212	−	0.987724i	$-0.450072\pi$
$367$	20.8759	−	12.0527i	1.08971	−	0.629146i	0.933500	+	0.358578i	$0.116738\pi$
$368$	−17.0833	−	9.86304i	−0.890528	−	0.514147i
$369$		0			0
$370$	0.489012	−	0.131030i	0.0254225	−	0.00681194i
$371$	−18.7168	+	15.7465i	−0.971727	+	0.817520i
$372$		0			0
$373$	−15.4025	+	26.6780i	−0.797514	+	1.38133i	0.123717	+	0.992318i	$0.460518\pi$
$373$	−15.4025	+	26.6780i	−0.797514	+	1.38133i	−0.921231	+	0.389017i	$0.872815\pi$
$374$	−11.9914	−	20.7696i	−0.620058	−	1.07397i
$375$		0			0
$376$	−2.18011			−0.112430
$377$	−10.0730	−	10.9563i	−0.518785	−	0.564279i
$378$		0			0
$379$	16.9707	+	4.54729i	0.871728	+	0.233579i	0.666835	−	0.745206i	$-0.267649\pi$
$379$	16.9707	+	4.54729i	0.871728	+	0.233579i	0.204893	+	0.978784i	$0.434315\pi$
$380$	−14.6948	−	25.4521i	−0.753826	−	1.30566i
$381$		0			0
$382$	12.7849	−	12.7849i	0.654132	−	0.654132i
$383$	−7.61566	+	2.04061i	−0.389142	+	0.104270i	−0.448085	−	0.893991i	$-0.647894\pi$
$383$	−7.61566	+	2.04061i	−0.389142	+	0.104270i	0.0589428	+	0.998261i	$0.481227\pi$
$384$		0			0
$385$	−8.97082	+	24.7467i	−0.457195	+	1.26121i
$386$	4.54907	−	7.87921i	0.231541	−	0.401041i
$387$		0			0
$388$	−4.11866	−	1.10359i	−0.209093	−	0.0560263i
$389$		−	4.32264i		−	0.219166i	−0.993978	−	0.109583i	$-0.965048\pi$
$389$		−	4.32264i		−	0.219166i	0.993978	−	0.109583i	$-0.0349516\pi$
$390$		0			0
$391$			13.9283i			0.704382i
$392$	−1.51415	+	1.06606i	−0.0764760	+	0.0538443i
$393$		0			0
$394$	2.86741	+	1.65550i	0.144458	+	0.0834029i
$395$	20.8700	+	20.8700i	1.05008	+	1.05008i
$396$		0			0
$397$	−8.67254	−	32.3664i	−0.435262	−	1.62442i	−0.740437	−	0.672125i	$-0.765382\pi$
$397$	−8.67254	−	32.3664i	−0.435262	−	1.62442i	0.305175	−	0.952296i	$-0.401285\pi$
$398$	−17.8704	+	17.8704i	−0.895761	+	0.895761i
$399$		0			0
$400$	−0.287353	+	0.165903i	−0.0143676	+	0.00829516i
$401$	−0.964760	+	3.60053i	−0.0481778	+	0.179802i	−0.985822	−	0.167795i	$-0.946335\pi$
$401$	−0.964760	+	3.60053i	−0.0481778	+	0.179802i	0.937644	+	0.347597i	$0.113002\pi$
$402$		0			0
$403$	10.5100	+	6.67120i	0.523539	+	0.332316i
$404$		−	19.1518i		−	0.952838i
$405$		0			0
$406$	−18.1975	−	12.7070i	−0.903125	−	0.630636i
$407$	−0.437060	−	0.252337i	−0.0216643	−	0.0125079i
$408$		0			0
$409$	16.1066	−	4.31575i	0.796421	−	0.213400i	0.162409	−	0.986724i	$-0.448074\pi$
$409$	16.1066	−	4.31575i	0.796421	−	0.213400i	0.634012	+	0.773323i	$0.281407\pi$
$410$	−34.1592	+	9.15294i	−1.68700	+	0.452031i
$411$		0			0
$412$	9.37417	+	5.41218i	0.461832	+	0.266639i
$413$	−10.7268	−	7.49035i	−0.527833	−	0.368576i
$414$		0			0
$415$			16.1572i			0.793127i
$416$	−13.5193	−	25.8658i	−0.662837	−	1.26818i
$417$		0			0
$418$	−14.7020	+	54.8688i	−0.719101	+	2.68372i
$419$	14.2653	−	8.23605i	0.696904	−	0.402357i	−0.109290	−	0.994010i	$-0.534858\pi$
$419$	14.2653	−	8.23605i	0.696904	−	0.402357i	0.806193	+	0.591652i	$0.201524\pi$
$420$		0			0
$421$	2.29534	−	2.29534i	0.111868	−	0.111868i	−0.648957	−	0.760825i	$-0.724795\pi$
$421$	2.29534	−	2.29534i	0.111868	−	0.111868i	0.760825	+	0.648957i	$0.224795\pi$
$422$	−0.117386	−	0.438090i	−0.00571425	−	0.0213259i
$423$		0			0
$424$	1.72934	+	1.72934i	0.0839840	+	0.0839840i
$425$	0.202895	+	0.117141i	0.00984185	+	0.00568220i
$426$		0			0
$427$	−10.0336	+	1.78257i	−0.485558	+	0.0862645i
$428$		−	2.21971i		−	0.107294i
$429$		0			0
$430$		−	28.4839i		−	1.37362i
$431$	−30.8568	−	8.26807i	−1.48632	−	0.398259i	−0.577828	−	0.816158i	$-0.696100\pi$
$431$	−30.8568	−	8.26807i	−1.48632	−	0.398259i	−0.908493	+	0.417900i	$0.862766\pi$
$432$		0			0
$433$	2.29443	−	3.97407i	0.110263	−	0.190982i	−0.805613	−	0.592442i	$-0.798164\pi$
$433$	2.29443	−	3.97407i	0.110263	−	0.190982i	0.915876	+	0.401460i	$0.131497\pi$
$434$	17.4529	+	6.32678i	0.837765	+	0.303695i
$435$		0			0
$436$	8.34280	−	2.23545i	0.399548	−	0.107058i
$437$	23.3273	−	23.3273i	1.11590	−	1.11590i
$438$		0			0
$439$	8.62001	+	14.9303i	0.411411	+	0.712584i	0.995044	−	0.0994331i	$-0.0317029\pi$
$439$	8.62001	+	14.9303i	0.411411	+	0.712584i	−0.583634	+	0.812017i	$0.698370\pi$
$440$	2.54223	+	0.681190i	0.121196	+	0.0324744i
$441$		0			0
$442$	−10.3219	+	16.2614i	−0.490962	+	0.773474i
$443$	−10.7110			−0.508893			−0.254447	−	0.967087i	$-0.581893\pi$
$443$	−10.7110			−0.508893			−0.254447	+	0.967087i	$0.581893\pi$
$444$		0			0
$445$	9.09678	+	15.7561i	0.431229	+	0.746910i
$446$	−5.72318	+	9.91284i	−0.271000	+	0.469387i
$447$		0			0
$448$	−15.3384	−	18.2317i	−0.724673	−	0.861368i
$449$	4.72490	−	1.26603i	0.222982	−	0.0597478i	−0.145598	−	0.989344i	$-0.546511\pi$
$449$	4.72490	−	1.26603i	0.222982	−	0.0597478i	0.368580	+	0.929596i	$0.379844\pi$
$450$		0			0
$451$	30.5302	+	17.6266i	1.43761	+	0.830006i
$452$	−16.1976	+	9.35166i	−0.761869	+	0.439865i
$453$		0			0
$454$	−8.77878			−0.412008
$455$	20.9507	−	2.82102i	0.982183	−	0.132252i
$456$		0			0
$457$	5.77841	+	1.54832i	0.270303	+	0.0724274i	0.391424	−	0.920210i	$-0.371982\pi$
$457$	5.77841	+	1.54832i	0.270303	+	0.0724274i	−0.121122	+	0.992638i	$0.538649\pi$
$458$	−42.3058	+	24.4253i	−1.97682	+	1.14132i
$459$		0			0
$460$	−17.6872	−	17.6872i	−0.824671	−	0.824671i
$461$	18.4425	−	4.94165i	0.858953	−	0.230156i	0.197648	−	0.980273i	$-0.436670\pi$
$461$	18.4425	−	4.94165i	0.858953	−	0.230156i	0.661305	+	0.750117i	$0.270003\pi$
$462$		0			0
$463$	−19.3096	−	19.3096i	−0.897393	−	0.897393i	0.0978122	−	0.995205i	$-0.468816\pi$
$463$	−19.3096	−	19.3096i	−0.897393	−	0.897393i	−0.995205	+	0.0978122i	$0.968816\pi$
$464$	7.68335	−	13.3080i	0.356691	−	0.617806i
$465$		0			0
$466$	7.17691	−	26.7846i	0.332464	−	1.24077i
$467$	−1.06678			−0.0493647			−0.0246824	−	0.999695i	$-0.507857\pi$
$467$	−1.06678			−0.0493647			−0.0246824	+	0.999695i	$0.507857\pi$
$468$		0			0
$469$	25.2283	−	11.8039i	1.16494	−	0.545054i
$470$	35.8501	+	9.60601i	1.65364	+	0.443092i
$471$		0			0
$472$	−0.654077	+	1.13290i	−0.0301063	+	0.0521457i
$473$	−20.0780	+	20.0780i	−0.923187	+	0.923187i
$474$		0			0
$475$	−0.143622	−	0.536004i	−0.00658982	−	0.0245935i
$476$	−5.04876	+	13.9274i	−0.231410	+	0.638360i
$477$		0			0
$478$	−11.7005	+	6.75529i	−0.535169	+	0.308980i
$479$	37.0845	+	9.93677i	1.69444	+	0.454023i	0.971529	−	0.236922i	$-0.0761387\pi$
$479$	37.0845	+	9.93677i	1.69444	+	0.454023i	0.722907	+	0.690945i	$0.242805\pi$
$480$		0			0
$481$	−0.0170100	+	0.404950i	−0.000775588	+	0.0184641i
$482$			31.6955i			1.44369i
$483$		0			0
$484$	−9.75155	−	16.8902i	−0.443252	−	0.767735i
$485$	3.84156	+	2.21792i	0.174436	+	0.100711i
$486$		0			0
$487$	6.88259	+	25.6862i	0.311880	+	1.16395i	0.926860	+	0.375408i	$0.122498\pi$
$487$	6.88259	+	25.6862i	0.311880	+	1.16395i	−0.614980	+	0.788543i	$0.710836\pi$
$488$	0.263721	+	0.984219i	0.0119381	+	0.0445535i
$489$		0			0
$490$	29.5962	−	10.8589i	1.33702	−	0.490556i
$491$	14.4502	−	8.34283i	0.652129	−	0.376507i	−0.137142	−	0.990551i	$-0.543792\pi$
$491$	14.4502	−	8.34283i	0.652129	−	0.376507i	0.789271	+	0.614044i	$0.210458\pi$
$492$		0			0
$493$	−10.8502			−0.488667
$494$	44.5222	−	9.94756i	2.00315	−	0.447562i
$495$		0			0
$496$	−3.32660	+	12.4150i	−0.149369	+	0.557452i
$497$	−29.8979	−	20.8772i	−1.34110	−	0.936468i
$498$		0			0
$499$	24.5083	−	24.5083i	1.09714	−	1.09714i	0.102400	−	0.994743i	$-0.467348\pi$
$499$	24.5083	−	24.5083i	1.09714	−	1.09714i	0.994743	−	0.102400i	$-0.0326523\pi$
$500$	−23.2050	+	6.21775i	−1.03776	+	0.278066i
$501$		0			0
$502$	7.67894	−	7.67894i	0.342728	−	0.342728i
$503$	35.6704	+	20.5943i	1.59046	+	0.918254i	0.993227	+	0.116188i	$0.0370675\pi$
$503$	35.6704	+	20.5943i	1.59046	+	0.918254i	0.597235	+	0.802066i	$0.296266\pi$
$504$		0			0
$505$	−5.15669	+	19.2450i	−0.229470	+	0.856393i
$506$			48.3463i			2.14926i
$507$		0			0
$508$	−15.2557			−0.676861
$509$	8.60918	−	32.1299i	0.381595	−	1.42413i	−0.461869	−	0.886948i	$-0.652821\pi$
$509$	8.60918	−	32.1299i	0.381595	−	1.42413i	0.843464	−	0.537185i	$-0.180512\pi$
$510$		0			0
$511$	−3.79401	+	44.0213i	−0.167837	+	1.94739i
$512$	22.7009	−	22.7009i	1.00325	−	1.00325i
$513$		0			0
$514$	−8.26844	−	30.8582i	−0.364705	−	1.36110i
$515$	−7.96255	−	7.96255i	−0.350872	−	0.350872i
$516$		0			0
$517$	−18.4992	−	32.0415i	−0.813592	−	1.40918i
$518$	0.105728	+	0.595110i	0.00464540	+	0.0261476i
$519$		0			0
$520$	−0.460900	−	2.06285i	−0.0202118	−	0.0904618i
$521$			7.74380i			0.339262i	0.985508	+	0.169631i	$0.0542576\pi$
$521$			7.74380i			0.339262i	−0.985508	+	0.169631i	$0.945742\pi$
$522$		0			0
$523$	25.4357	−	14.6853i	1.11223	−	0.642144i	0.172821	−	0.984953i	$-0.444712\pi$
$523$	25.4357	−	14.6853i	1.11223	−	0.642144i	0.939405	+	0.342809i	$0.111378\pi$
$524$	8.58929	−	14.8771i	0.375225	−	0.649908i
$525$		0			0
$526$	3.61954	+	13.5083i	0.157819	+	0.588990i
$527$	8.76605	−	2.34886i	0.381855	−	0.102318i
$528$		0			0
$529$	2.53887	−	4.39745i	0.110386	−	0.191194i
$530$	−20.8177	−	36.0574i	−0.904265	−	1.56623i
$531$		0			0
$532$	31.7816	−	14.8701i	1.37791	−	0.644699i
$533$	1.18821	−	28.2872i	0.0514670	−	1.22525i
$534$		0			0
$535$	−0.597665	+	2.23051i	−0.0258393	+	0.0964336i
$536$	−1.39248	−	2.41185i	−0.0601462	−	0.104176i
$537$		0			0
$538$	31.0590	+	31.0590i	1.33905	+	1.33905i
$539$	−28.5164	−	13.2077i	−1.22829	−	0.568897i
$540$		0			0
$541$	−22.3031	−	22.3031i	−0.958885	−	0.958885i	0.0403026	−	0.999188i	$-0.487168\pi$
$541$	−22.3031	−	22.3031i	−0.958885	−	0.958885i	−0.999188	+	0.0403026i	$0.987168\pi$
$542$	−10.6112	−	6.12637i	−0.455789	−	0.263150i
$543$		0			0
$544$	−20.5523	−	5.50697i	−0.881172	−	0.236109i
$545$	−8.98531			−0.384888
$546$		0			0
$547$	−24.0410			−1.02792			−0.513959	−	0.857815i	$-0.671822\pi$
$547$	−24.0410			−1.02792			−0.513959	+	0.857815i	$0.671822\pi$
$548$	8.52767	+	2.28498i	0.364284	+	0.0976096i
$549$		0			0
$550$	0.704268	+	0.406609i	0.0300301	+	0.0173379i
$551$	18.1721	+	18.1721i	0.774157	+	0.774157i
$552$		0			0
$553$	−26.9643	+	22.6852i	−1.14664	+	0.964674i
$554$	28.5272	+	28.5272i	1.21201	+	1.21201i
$555$		0			0
$556$	−17.3748	−	30.0940i	−0.736854	−	1.27627i
$557$	−6.46251	+	24.1184i	−0.273825	+	1.02193i	0.682799	+	0.730606i	$0.260762\pi$
$557$	−6.46251	+	24.1184i	−0.273825	+	1.02193i	−0.956624	+	0.291324i	$0.905904\pi$
$558$		0			0
$559$	21.7597	+	6.82130i	0.920338	+	0.288510i
$560$	9.24994	+	19.7698i	0.390881	+	0.835425i
$561$		0			0
$562$	−22.1528	−	38.3698i	−0.934461	−	1.61853i
$563$	10.6879	−	18.5120i	0.450442	−	0.780189i	−0.547971	−	0.836497i	$-0.684600\pi$
$563$	10.6879	−	18.5120i	0.450442	−	0.780189i	0.998413	+	0.0563081i	$0.0179329\pi$
$564$		0			0
$565$	18.7944	−	5.03594i	0.790685	−	0.211863i
$566$	−14.9243	−	55.6981i	−0.627313	−	2.34116i
$567$		0			0
$568$	−1.82305	+	3.15761i	−0.0764934	+	0.132490i
$569$	−6.81979	+	3.93741i	−0.285901	+	0.165065i	−0.636092	−	0.771614i	$-0.719450\pi$
$569$	−6.81979	+	3.93741i	−0.285901	+	0.165065i	0.350191	+	0.936678i	$0.386117\pi$
$570$		0			0
$571$			30.5555i			1.27871i	0.768912	+	0.639355i	$0.220798\pi$
$571$			30.5555i			1.27871i	−0.768912	+	0.639355i	$0.779202\pi$
$572$	−18.4787	+	29.1119i	−0.772634	+	1.21723i
$573$		0			0
$574$	−7.38545	−	41.5706i	−0.308263	−	1.73512i
$575$	−0.236143	−	0.409012i	−0.00984786	−	0.0170570i
$576$		0			0
$577$	10.2122	+	10.2122i	0.425140	+	0.425140i	0.886969	−	0.461829i	$-0.152807\pi$
$577$	10.2122	+	10.2122i	0.425140	+	0.425140i	−0.461829	+	0.886969i	$0.652807\pi$
$578$	−5.30766	−	19.8085i	−0.220770	−	0.823923i
$579$		0			0
$580$	13.7784	−	13.7784i	0.572117	−	0.572117i
$581$	−19.2189	−	1.65640i	−0.797336	−	0.0687190i
$582$		0			0
$583$	−10.7422	+	40.0906i	−0.444898	+	1.66038i
$584$	4.41789			0.182813
$585$		0			0
$586$		−	21.2743i		−	0.878834i
$587$	−6.93252	+	25.8725i	−0.286136	+	1.06787i	0.661870	+	0.749619i	$0.269763\pi$
$587$	−6.93252	+	25.8725i	−0.286136	+	1.06787i	−0.948005	+	0.318254i	$0.896903\pi$
$588$		0			0
$589$	−18.6155	−	10.7477i	−0.767037	−	0.442849i
$590$	15.7476	−	15.7476i	0.648317	−	0.648317i
$591$		0			0
$592$	−0.404218	+	0.108310i	−0.0166133	+	0.00445151i
$593$	−4.55865	+	4.55865i	−0.187201	+	0.187201i	−0.794485	−	0.607284i	$-0.792259\pi$
$593$	−4.55865	+	4.55865i	−0.187201	+	0.187201i	0.607284	+	0.794485i	$0.292259\pi$
$594$		0			0
$595$	8.82332	−	12.6358i	0.361721	−	0.518016i
$596$	−3.34804	+	12.4951i	−0.137141	+	0.511817i
$597$		0			0
$598$	34.4105	−	17.9853i	1.40715	−	0.735475i
$599$	11.7896			0.481711			0.240855	−	0.970561i	$-0.422572\pi$
$599$	11.7896			0.481711			0.240855	+	0.970561i	$0.422572\pi$
$600$		0			0
$601$	−12.6934	+	7.32853i	−0.517774	+	0.298937i	−0.736023	−	0.676956i	$-0.763299\pi$
$601$	−12.6934	+	7.32853i	−0.517774	+	0.298937i	0.218250	+	0.975893i	$0.429965\pi$
$602$	33.8815	+	2.92010i	1.38091	+	0.119015i
$603$		0			0
$604$	10.6302	+	39.6725i	0.432537	+	1.61425i
$605$	5.25127	+	19.5980i	0.213495	+	0.796773i
$606$		0			0
$607$	−8.67196	−	5.00676i	−0.351984	−	0.203218i	0.313575	−	0.949564i	$-0.398473\pi$
$607$	−8.67196	−	5.00676i	−0.351984	−	0.203218i	−0.665559	+	0.746345i	$0.731807\pi$
$608$	25.1982	+	43.6446i	1.02192	+	1.77002i
$609$		0			0
$610$		−	17.3467i		−	0.702348i
$611$	−15.9237	+	25.0866i	−0.644203	+	1.01489i
$612$		0			0
$613$	5.30907	+	1.42256i	0.214431	+	0.0574567i	0.364435	−	0.931229i	$-0.381262\pi$
$613$	5.30907	+	1.42256i	0.214431	+	0.0574567i	−0.150004	+	0.988685i	$0.547929\pi$
$614$	−15.3245	+	8.84762i	−0.618447	+	0.357061i
$615$		0			0
$616$	−1.07090	+	2.95414i	−0.0431476	+	0.119026i
$617$	−1.17910	−	4.40045i	−0.0474687	−	0.177156i	0.938122	−	0.346306i	$-0.112564\pi$
$617$	−1.17910	−	4.40045i	−0.0474687	−	0.177156i	−0.985590	+	0.169151i	$0.945898\pi$
$618$		0			0
$619$	24.3594	−	24.3594i	0.979088	−	0.979088i	−0.0206980	−	0.999786i	$-0.506589\pi$
$619$	24.3594	−	24.3594i	0.979088	−	0.979088i	0.999786	+	0.0206980i	$0.00658886\pi$
$620$	−8.14907	+	14.1146i	−0.327274	+	0.566856i
$621$		0			0
$622$	10.4209	+	2.79226i	0.417839	+	0.111960i
$623$	−19.6744	+	9.20531i	−0.788237	+	0.368803i
$624$		0			0
$625$	24.5464			0.981856
$626$	9.72044	−	36.2772i	0.388507	−	1.44993i
$627$		0			0
$628$	−8.85163	+	15.3315i	−0.353218	+	0.611792i
$629$	0.208936	+	0.208936i	0.00833082	+	0.00833082i
$630$		0			0
$631$	−29.1395	+	7.80790i	−1.16003	+	0.310828i	−0.786976	−	0.616984i	$-0.788354\pi$
$631$	−29.1395	+	7.80790i	−1.16003	+	0.310828i	−0.373049	+	0.927812i	$0.621688\pi$
$632$	2.49136	+	2.49136i	0.0991012	+	0.0991012i
$633$		0			0
$634$	−36.9859	+	21.3538i	−1.46890	+	0.848070i
$635$	15.3299	+	4.10764i	0.608349	+	0.163007i
$636$		0			0
$637$	1.20778	+	25.2099i	0.0478539	+	0.998854i
$638$	−37.6620			−1.49105
$639$		0			0
$640$	4.05297	−	2.33998i	0.160208	−	0.0924959i
$641$	5.38559	+	3.10937i	0.212718	+	0.122813i	0.602574	−	0.798063i	$-0.294142\pi$
$641$	5.38559	+	3.10937i	0.212718	+	0.122813i	−0.389856	+	0.920876i	$0.627475\pi$
$642$		0			0
$643$	−14.3667	+	3.84955i	−0.566568	+	0.151811i	−0.530722	−	0.847546i	$-0.678079\pi$
$643$	−14.3667	+	3.84955i	−0.566568	+	0.151811i	−0.0358459	+	0.999357i	$0.511413\pi$
$644$	22.8521	−	19.2256i	0.900500	−	0.757595i
$645$		0			0
$646$	16.6291	−	28.8025i	0.654264	−	1.13322i
$647$	3.53916	+	6.13001i	0.139139	+	0.240995i	0.927171	−	0.374639i	$-0.122233\pi$
$647$	3.53916	+	6.13001i	0.139139	+	0.240995i	−0.788032	+	0.615634i	$0.788900\pi$
$648$		0			0
$649$	−22.2005			−0.871447
$650$	0.0274095	−	0.652526i	0.00107509	−	0.0255942i
$651$		0			0
$652$	0.820257	+	0.219787i	0.0321237	+	0.00860753i
$653$	−21.2746	−	36.8487i	−0.832539	−	1.44200i	−0.896019	−	0.444017i	$-0.853553\pi$
$653$	−21.2746	−	36.8487i	−0.832539	−	1.44200i	0.0634796	−	0.997983i	$-0.479780\pi$
$654$		0			0
$655$	−12.6368	+	12.6368i	−0.493761	+	0.493761i
$656$	28.2361	−	7.56584i	1.10243	−	0.295396i
$657$		0			0
$658$	−15.1016	+	41.6588i	−0.588721	+	1.62403i
$659$	−16.5688	+	28.6980i	−0.645429	+	1.11791i	0.338774	+	0.940868i	$0.389988\pi$
$659$	−16.5688	+	28.6980i	−0.645429	+	1.11791i	−0.984202	+	0.177047i	$0.943345\pi$
$660$		0			0
$661$	24.7310	+	6.62666i	0.961925	+	0.257747i	0.705415	−	0.708794i	$-0.250761\pi$
$661$	24.7310	+	6.62666i	0.961925	+	0.257747i	0.256510	+	0.966542i	$0.417427\pi$
$662$			62.1630i			2.41604i
$663$		0			0
$664$			1.92877i			0.0748510i
$665$	−35.9401	+	6.38514i	−1.39370	+	0.247605i
$666$		0			0
$667$	18.9423	+	10.9363i	0.733448	+	0.423457i
$668$	31.1542	+	31.1542i	1.20539	+	1.20539i
$669$		0			0
$670$	12.2712	+	45.7966i	0.474076	+	1.76928i
$671$	−12.2275	+	12.2275i	−0.472037	+	0.472037i
$672$		0			0
$673$	0.329696	−	0.190350i	0.0127088	−	0.00733746i	−0.493632	−	0.869671i	$-0.664331\pi$
$673$	0.329696	−	0.190350i	0.0127088	−	0.00733746i	0.506341	+	0.862333i	$0.330998\pi$
$674$	−1.39077	+	5.19043i	−0.0535705	+	0.199928i
$675$		0			0
$676$	27.5947	+	2.32233i	1.06133	+	0.0893205i
$677$		−	30.7685i		−	1.18253i	−0.806477	−	0.591265i	$-0.798629\pi$
$677$		−	30.7685i		−	1.18253i	0.806477	−	0.591265i	$-0.201371\pi$
$678$		0			0
$679$	−3.03204	+	4.34214i	−0.116359	+	0.166636i
$680$	−1.33450	−	0.770476i	−0.0511759	−	0.0295464i
$681$		0			0
$682$	30.4278	−	8.15310i	1.16514	−	0.312199i
$683$	38.2684	−	10.2540i	1.46430	−	0.392358i	0.563328	−	0.826234i	$-0.309521\pi$
$683$	38.2684	−	10.2540i	1.46430	−	0.392358i	0.900973	+	0.433875i	$0.142854\pi$
$684$		0			0
$685$	−7.95393	−	4.59221i	−0.303904	−	0.175459i
$686$	9.88249	+	36.3178i	0.377315	+	1.38662i
$687$		0			0
$688$			23.5449i			0.897640i
$689$	32.5307	−	7.26832i	1.23932	−	0.276901i
$690$		0			0
$691$	−1.21810	+	4.54600i	−0.0463386	+	0.172938i	−0.985217	−	0.171311i	$-0.945200\pi$
$691$	−1.21810	+	4.54600i	−0.0463386	+	0.172938i	0.938878	+	0.344249i	$0.111866\pi$
$692$	35.3550	−	20.4122i	1.34399	−	0.775955i
$693$		0			0
$694$	4.56817	−	4.56817i	0.173405	−	0.173405i
$695$	9.35642	+	34.9187i	0.354909	+	1.32454i
$696$		0			0
$697$	−14.5949	−	14.5949i	−0.552822	−	0.552822i
$698$	36.9373	+	21.3258i	1.39810	+	0.807192i
$699$		0			0
$700$	−0.0878681	−	0.494584i	−0.00332110	−	0.0186935i
$701$		−	19.5366i		−	0.737886i	−0.929452	−	0.368943i	$-0.879720\pi$
$701$		−	19.5366i		−	0.737886i	0.929452	−	0.368943i	$-0.120280\pi$
$702$		0			0
$703$		−	0.699860i		−	0.0263957i
$704$	−39.0516	−	10.4638i	−1.47181	−	0.394371i
$705$		0			0
$706$	20.9826	−	36.3430i	0.789692	−	1.36779i
$707$	−22.3632	−	8.10682i	−0.841056	−	0.304888i
$708$		0			0
$709$	33.4014	−	8.94988i	1.25442	−	0.336120i	0.430375	−	0.902650i	$-0.358381\pi$
$709$	33.4014	−	8.94988i	1.25442	−	0.336120i	0.824041	+	0.566530i	$0.191715\pi$
$710$	43.8917	−	43.8917i	1.64723	−	1.64723i
$711$		0			0
$712$	1.08593	+	1.88089i	0.0406970	+	0.0704893i
$713$	−17.6713	−	4.73502i	−0.661797	−	0.177328i
$714$		0			0
$715$	26.4071	−	24.2781i	0.987571	−	0.907949i
$716$	14.4219			0.538970
$717$		0			0
$718$	27.1718	+	47.0629i	1.01404	+	1.75637i
$719$	8.27022	−	14.3244i	0.308427	−	0.534211i	−0.669591	−	0.742730i	$-0.733531\pi$
$719$	8.27022	−	14.3244i	0.308427	−	0.534211i	0.978018	+	0.208518i	$0.0668641\pi$
$720$		0			0
$721$	10.2877	−	8.65511i	0.383135	−	0.322333i
$722$	−38.7921	+	10.3943i	−1.44369	+	0.386836i
$723$		0			0
$724$	30.5484	+	17.6371i	1.13532	+	0.655478i
$725$	0.318622	−	0.183957i	0.0118333	−	0.00683198i
$726$		0			0
$727$	−21.0001			−0.778851			−0.389426	−	0.921058i	$-0.627326\pi$
$727$	−21.0001			−0.778851			−0.389426	+	0.921058i	$0.627326\pi$
$728$	2.50100	−	0.336761i	0.0926931	−	0.0124812i
$729$		0			0
$730$	−72.6486	−	19.4661i	−2.68885	−	0.720474i
$731$	14.3974	−	8.31232i	0.532506	−	0.307442i
$732$		0			0
$733$	9.61770	+	9.61770i	0.355238	+	0.355238i	0.862054	−	0.506816i	$-0.169178\pi$
$733$	9.61770	+	9.61770i	0.355238	+	0.355238i	−0.506816	+	0.862054i	$0.669178\pi$
$734$	−47.3197	+	12.6793i	−1.74660	+	0.468001i
$735$		0			0
$736$	30.3296	+	30.3296i	1.11796	+	1.11796i
$737$	23.6317	−	40.9313i	0.870485	−	1.50772i
$738$		0			0
$739$	10.3610	−	38.6677i	0.381135	−	1.42241i	−0.463036	−	0.886339i	$-0.653240\pi$
$739$	10.3610	−	38.6677i	0.381135	−	1.42241i	0.844171	−	0.536074i	$-0.180093\pi$
$740$	−0.530647			−0.0195070
$741$		0			0
$742$	45.0243	−	21.0661i	1.65289	−	0.773360i
$743$	−12.1952	−	3.26770i	−0.447399	−	0.119880i	0.0280832	−	0.999606i	$-0.491060\pi$
$743$	−12.1952	−	3.26770i	−0.447399	−	0.119880i	−0.475482	+	0.879725i	$0.657726\pi$
$744$		0			0
$745$	6.72867	−	11.6544i	0.246519	−	0.426984i
$746$	44.2682	−	44.2682i	1.62077	−	1.62077i
$747$		0			0
$748$	6.50616	+	24.2813i	0.237889	+	0.887813i
$749$	−2.59192	−	0.939586i	−0.0947065	−	0.0343317i
$750$		0			0
$751$	13.0628	−	7.54179i	0.476667	−	0.275204i	−0.242359	−	0.970187i	$-0.577921\pi$
$751$	13.0628	−	7.54179i	0.476667	−	0.275204i	0.719026	+	0.694983i	$0.244588\pi$
$752$	−29.6338	−	7.94035i	−1.08063	−	0.289555i
$753$		0			0
$754$	14.0106	+	26.8059i	0.510237	+	0.976214i
$755$		−	42.7278i		−	1.55502i
$756$		0			0
$757$	6.07461	+	10.5215i	0.220786	+	0.382412i	0.955047	−	0.296455i	$-0.0958046\pi$
$757$	6.07461	+	10.5215i	0.220786	+	0.382412i	−0.734261	+	0.678867i	$0.762471\pi$
$758$	−30.9223	−	17.8530i	−1.12315	−	0.648450i
$759$		0			0
$760$	0.944645	+	3.52546i	0.0342659	+	0.127882i
$761$	−6.05559	−	22.5998i	−0.219515	−	0.819241i	−0.984528	−	0.175226i	$-0.943934\pi$
$761$	−6.05559	−	22.5998i	−0.219515	−	0.819241i	0.765013	−	0.644014i	$-0.222732\pi$
$762$		0			0
$763$	0.921153	−	10.6880i	0.0333480	−	0.386931i
$764$	−16.4124	+	9.47572i	−0.593781	+	0.342819i
$765$		0			0
$766$	16.0231			0.578940
$767$	8.25883	+	15.8012i	0.298209	+	0.570550i
$768$		0			0
$769$	9.41454	−	35.1355i	0.339497	−	1.26702i	−0.559414	−	0.828888i	$-0.688974\pi$
$769$	9.41454	−	35.1355i	0.339497	−	1.26702i	0.898911	−	0.438131i	$-0.144360\pi$
$770$	30.6266	−	43.8599i	1.10371	−	1.58060i
$771$		0			0
$772$	−6.74322	+	6.74322i	−0.242694	+	0.242694i
$773$	34.2562	−	9.17892i	1.23211	−	0.330143i	0.416709	−	0.909040i	$-0.363183\pi$
$773$	34.2562	−	9.17892i	1.23211	−	0.330143i	0.815401	+	0.578897i	$0.196517\pi$
$774$		0			0
$775$	−0.217598	+	0.217598i	−0.00781634	+	0.00781634i
$776$	0.458588	+	0.264766i	0.0164623	+	0.00950453i
$777$		0			0
$778$	−2.27368	+	8.48548i	−0.0815153	+	0.304219i
$779$			48.8878i			1.75159i
$780$		0			0
$781$	−61.8775			−2.21415
$782$	7.32617	−	27.3416i	0.261983	−	0.977735i
$783$		0			0
$784$	−24.4643	+	8.97601i	−0.873726	+	0.320572i
$785$	13.0228	−	13.0228i	0.464802	−	0.464802i
$786$		0			0
$787$	−7.98311	−	29.7934i	−0.284567	−	1.06202i	−0.949155	−	0.314809i	$-0.898059\pi$
$787$	−7.98311	−	29.7934i	−0.284567	−	1.06202i	0.664588	−	0.747210i	$-0.268607\pi$
$788$	−2.45400	−	2.45400i	−0.0874201	−	0.0874201i
$789$		0			0
$790$	−29.9910	−	51.9460i	−1.06703	−	1.84815i
$791$	4.06347	+	22.8721i	0.144480	+	0.813238i
$792$		0			0
$793$	13.2517	+	4.15417i	0.470581	+	0.147519i
$794$			68.0980i			2.41671i
$795$		0			0
$796$	22.9408	−	13.2449i	0.813117	−	0.469453i
$797$	−18.5193	+	32.0763i	−0.655986	+	1.13620i	0.325659	+	0.945487i	$0.394414\pi$
$797$	−18.5193	+	32.0763i	−0.655986	+	1.13620i	−0.981646	+	0.190714i	$0.938920\pi$
$798$		0			0
$799$	5.60655	+	20.9239i	0.198346	+	0.740236i
$800$	0.696898	−	0.186733i	0.0246391	−	0.00660201i
$801$		0			0
$802$	3.78771	−	6.56051i	0.133749	−	0.231660i
$803$	37.4877	+	64.9306i	1.32291	+	2.29135i
$804$		0			0
$805$	−28.1399	+	13.1662i	−0.991801	+	0.464047i
$806$	−17.1224	−	18.6240i	−0.603112	−	0.656001i
$807$		0			0
$808$	−0.615582	+	2.29738i	−0.0216561	+	0.0808217i
$809$	19.6518	+	34.0379i	0.690920	+	1.19671i	0.971537	+	0.236888i	$0.0761274\pi$
$809$	19.6518	+	34.0379i	0.690920	+	1.19671i	−0.280617	+	0.959820i	$0.590539\pi$
$810$		0			0
$811$	31.2346	+	31.2346i	1.09680	+	1.09680i	0.994783	+	0.102013i	$0.0325282\pi$
$811$	31.2346	+	31.2346i	1.09680	+	1.09680i	0.102013	+	0.994783i	$0.467472\pi$
$812$	14.9768	+	17.8019i	0.525584	+	0.624724i
$813$		0			0
$814$	0.725236	+	0.725236i	0.0254195	+	0.0254195i
$815$	−0.765071	−	0.441714i	−0.0267993	−	0.0154726i
$816$		0			0
$817$	−38.0347	−	10.1914i	−1.33066	−	0.356550i
$818$	−33.8879			−1.18486
$819$		0			0
$820$	37.0676			1.29446
$821$	13.0783	+	3.50432i	0.456436	+	0.122302i	0.479709	−	0.877427i	$-0.340742\pi$
$821$	13.0783	+	3.50432i	0.456436	+	0.122302i	−0.0232733	+	0.999729i	$0.507409\pi$
$822$		0			0
$823$	−48.1538	−	27.8016i	−1.67853	−	0.969102i	−0.962597	−	0.270939i	$-0.912666\pi$
$823$	−48.1538	−	27.8016i	−1.67853	−	0.969102i	−0.715938	−	0.698164i	$-0.754001\pi$
$824$	−0.950532	−	0.950532i	−0.0331134	−	0.0331134i
$825$		0			0
$826$	17.1172	+	20.3460i	0.595585	+	0.707930i
$827$	12.0154	+	12.0154i	0.417815	+	0.417815i	0.884450	−	0.466635i	$-0.154534\pi$
$827$	12.0154	+	12.0154i	0.417815	+	0.417815i	−0.466635	+	0.884450i	$0.654534\pi$
$828$		0			0
$829$	11.7179	+	20.2959i	0.406978	+	0.704906i	0.994549	−	0.104266i	$-0.0332493\pi$
$829$	11.7179	+	20.2959i	0.406978	+	0.704906i	−0.587572	+	0.809172i	$0.699916\pi$
$830$	8.49859	−	31.7172i	0.294990	−	1.10092i
$831$		0			0
$832$	7.07995	+	31.6876i	0.245453	+	1.09857i
$833$	14.1256	+	11.7907i	0.489424	+	0.408523i
$834$		0			0
$835$	−22.9174	−	39.6942i	−0.793091	−	1.37367i
$836$	29.7702	−	51.5635i	1.02962	−	1.78336i
$837$		0			0
$838$	−32.3353	+	8.66422i	−1.11700	+	0.299300i
$839$	−10.2875	−	38.3937i	−0.355166	−	1.32550i	−0.880276	−	0.474462i	$-0.842643\pi$
$839$	−10.2875	−	38.3937i	−0.355166	−	1.32550i	0.525110	−	0.851034i	$-0.324024\pi$
$840$		0			0
$841$	5.98055	−	10.3586i	0.206226	−	0.357194i
$842$	−5.71316	+	3.29849i	−0.196888	+	0.113674i
$843$		0			0
$844$			0.475390i			0.0163636i
$845$	−27.1037	−	9.76359i	−0.932395	−	0.335878i
$846$		0			0
$847$	−23.8501	+	4.23722i	−0.819499	+	0.145593i
$848$	17.2080	+	29.8051i	0.590925	+	1.02351i
$849$		0			0
$850$	−0.336674	−	0.336674i	−0.0115478	−	0.0115478i
$851$	−0.154166	−	0.575356i	−0.00528475	−	0.0197230i
$852$		0			0
$853$	−1.67153	+	1.67153i	−0.0572322	+	0.0572322i	−0.735144	−	0.677911i	$-0.762885\pi$
$853$	−1.67153	+	1.67153i	−0.0572322	+	0.0572322i	0.677911	+	0.735144i	$0.262885\pi$
$854$	20.6338	+	1.77834i	0.706075	+	0.0608537i
$855$		0			0
$856$	−0.0713465	+	0.266269i	−0.00243857	+	0.00910087i
$857$	32.1656			1.09876			0.549378	−	0.835574i	$-0.314865\pi$
$857$	32.1656			1.09876			0.549378	+	0.835574i	$0.314865\pi$
$858$		0			0
$859$		−	10.9082i		−	0.372182i	−0.982533	−	0.186091i	$-0.940418\pi$
$859$		−	10.9082i		−	0.372182i	0.982533	−	0.186091i	$-0.0595819\pi$
$860$	−7.72727	+	28.8386i	−0.263498	+	0.983387i
$861$		0			0
$862$	56.2241	+	32.4610i	1.91500	+	1.10563i
$863$	29.1191	−	29.1191i	0.991226	−	0.991226i	−0.00873630	−	0.999962i	$-0.502781\pi$
$863$	29.1191	−	29.1191i	0.991226	−	0.991226i	0.999962	+	0.00873630i	$0.00278089\pi$
$864$		0			0
$865$	−41.0231	+	10.9921i	−1.39483	+	0.373743i
$866$	−6.59438	+	6.59438i	−0.224086	+	0.224086i
$867$		0			0
$868$	−15.9538	−	11.1403i	−0.541508	−	0.378125i
$869$	−15.4758	+	57.7564i	−0.524980	+	1.95925i
$870$		0			0
$871$	−37.9241	−	1.59301i	−1.28501	−	0.0539770i
$872$	−1.07263			−0.0363237
$873$		0			0
$874$	−58.0624	+	33.5223i	−1.96399	+	1.13391i
$875$	−2.56213	+	29.7279i	−0.0866157	+	1.00499i
$876$		0			0
$877$	11.3963	+	42.5315i	0.384825	+	1.43619i	0.838442	+	0.544990i	$0.183467\pi$
$877$	11.3963	+	42.5315i	0.384825	+	1.43619i	−0.453617	+	0.891197i	$0.649867\pi$
$878$	−9.06813	−	33.8427i	−0.306035	−	1.14214i
$879$		0			0
$880$	32.0751	+	18.5186i	1.08125	+	0.624261i
$881$	27.3369	+	47.3489i	0.921004	+	1.59522i	0.797866	+	0.602835i	$0.205962\pi$
$881$	27.3369	+	47.3489i	0.921004	+	1.59522i	0.123138	+	0.992390i	$0.460704\pi$
$882$		0			0
$883$			5.53480i			0.186261i	0.995654	+	0.0931304i	$0.0296873\pi$
$883$			5.53480i			0.186261i	−0.995654	+	0.0931304i	$0.970313\pi$
$884$	14.8619	−	13.6637i	0.499859	−	0.459559i
$885$		0			0
$886$	21.0260	+	5.63390i	0.706382	+	0.189274i
$887$	7.88418	−	4.55194i	0.264725	−	0.152839i	−0.361763	−	0.932270i	$-0.617825\pi$
$887$	7.88418	−	4.55194i	0.264725	−	0.152839i	0.626488	+	0.779431i	$0.284492\pi$
$888$		0			0
$889$	−6.45761	+	17.8138i	−0.216581	+	0.597455i
$890$	−9.56969	−	35.7146i	−0.320777	−	1.19716i
$891$		0			0
$892$	8.48365	−	8.48365i	0.284054	−	0.284054i
$893$	25.6539	−	44.4338i	0.858474	−	1.48692i
$894$		0			0
$895$	−14.4921	−	3.88314i	−0.484416	−	0.129799i
$896$	2.36790	+	5.06088i	0.0791059	+	0.169072i
$897$		0			0
$898$	−9.94107			−0.331738
$899$	3.68860	−	13.7660i	0.123022	−	0.459123i
$900$		0			0
$901$	12.1503	−	21.0449i	0.404784	−	0.701107i
$902$	−50.6604	−	50.6604i	−1.68681	−	1.68681i
$903$		0			0
$904$	2.24359	−	0.601167i	0.0746205	−	0.0199945i
$905$	−25.9482	−	25.9482i	−0.862548	−	0.862548i
$906$		0			0
$907$	28.9991	−	16.7426i	0.962899	−	0.555930i	0.0658347	−	0.997831i	$-0.479029\pi$
$907$	28.9991	−	16.7426i	0.962899	−	0.555930i	0.897064	+	0.441901i	$0.145696\pi$
$908$	8.88808	+	2.38155i	0.294961	+	0.0790346i
$909$		0			0
$910$	−42.6107	−	5.48216i	−1.41253	−	0.181732i
$911$	−44.6499			−1.47932			−0.739659	−	0.672982i	$-0.765013\pi$
$911$	−44.6499			−1.47932			−0.739659	+	0.672982i	$0.765013\pi$
$912$		0			0
$913$	−28.3476	+	16.3665i	−0.938169	+	0.541652i
$914$	−10.5288	−	6.07881i	−0.348262	−	0.201069i
$915$		0			0
$916$	49.4588	−	13.2524i	1.63416	−	0.437873i
$917$	−13.7359	−	16.3269i	−0.453600	−	0.539162i
$918$		0			0
$919$	28.6298	−	49.5882i	0.944409	−	1.63576i	0.187479	−	0.982269i	$-0.439968\pi$
$919$	28.6298	−	49.5882i	0.944409	−	1.63576i	0.756930	−	0.653496i	$-0.226698\pi$
$920$	1.55319	+	2.69020i	0.0512071	+	0.0886934i
$921$		0			0
$922$	−38.8025			−1.27789
$923$	23.0191	+	44.0413i	0.757681	+	1.44964i
$924$		0			0
$925$	−0.00967789	−	0.00259318i	−0.000318207	−	8.52633e-5i
$926$	27.7487	+	48.0621i	0.911877	+	1.57942i
$927$		0			0
$928$	−23.6269	+	23.6269i	−0.775590	+	0.775590i
$929$	−55.3729	+	14.8371i	−1.81672	+	0.486790i	−0.996375	−	0.0850723i	$-0.972888\pi$
$929$	−55.3729	+	14.8371i	−1.81672	+	0.486790i	−0.820350	+	0.571862i	$0.806221\pi$
$930$		0			0
$931$	−3.91060	−	43.4052i	−0.128165	−	1.42255i
$932$	−14.5325	+	25.1711i	−0.476029	+	0.824506i
$933$		0			0
$934$	2.09413	+	0.561120i	0.0685219	+	0.0183604i
$935$		−	26.1513i		−	0.855239i
$936$		0			0
$937$			33.7193i			1.10156i	0.834650	+	0.550781i	$0.185670\pi$
$937$			33.7193i			1.10156i	−0.834650	+	0.550781i	$0.814330\pi$
$938$	−55.7329	+	9.90153i	−1.81974	+	0.323297i
$939$		0			0
$940$	−33.6905	−	19.4512i	−1.09886	−	0.634429i
$941$	−25.6240	−	25.6240i	−0.835317	−	0.835317i	0.152921	−	0.988238i	$-0.451132\pi$
$941$	−25.6240	−	25.6240i	−0.835317	−	0.835317i	−0.988238	+	0.152921i	$0.951132\pi$
$942$		0			0
$943$	10.7691	+	40.1907i	0.350689	+	1.30879i
$944$	−13.0170	+	13.0170i	−0.423666	+	0.423666i
$945$		0			0
$946$	49.9746	−	28.8529i	1.62482	−	0.938088i
$947$	1.59393	−	5.94864i	0.0517959	−	0.193305i	−0.935180	−	0.354172i	$-0.884763\pi$
$947$	1.59393	−	5.94864i	0.0517959	−	0.193305i	0.986976	+	0.160868i	$0.0514292\pi$
$948$		0			0
$949$	32.2686	−	50.8368i	1.04748	−	1.65023i
$950$			1.12774i			0.0365886i
$951$		0			0
$952$	1.05329	−	1.50840i	0.0341373	−	0.0488875i
$953$	−19.0413	−	10.9935i	−0.616810	−	0.356115i	0.158816	−	0.987308i	$-0.449232\pi$
$953$	−19.0413	−	10.9935i	−0.616810	−	0.356115i	−0.775626	+	0.631193i	$0.782566\pi$
$954$		0			0
$955$	19.0437	−	5.10274i	0.616239	−	0.165121i
$956$	13.6788	−	3.66522i	0.442404	−	0.118542i
$957$		0			0
$958$	−67.5715	−	39.0124i	−2.18314	−	1.26043i
$959$	6.27783	−	8.99039i	0.202722	−	0.290315i
$960$		0			0
$961$		−	19.0797i		−	0.615473i
$962$	0.246392	−	0.785983i	0.00794399	−	0.0253411i
$963$		0			0
$964$	8.59854	−	32.0902i	0.276940	−	1.03356i
$965$	8.59168	−	4.96041i	0.276576	−	0.159681i
$966$		0			0
$967$	17.4299	−	17.4299i	0.560507	−	0.560507i	−0.368944	−	0.929452i	$-0.620281\pi$
$967$	17.4299	−	17.4299i	0.560507	−	0.560507i	0.929452	+	0.368944i	$0.120281\pi$
$968$	0.626873	+	2.33952i	0.0201485	+	0.0751951i
$969$		0			0
$970$	−6.37449	−	6.37449i	−0.204673	−	0.204673i
$971$	−27.7120	−	15.9995i	−0.889319	−	0.513449i	−0.0155992	−	0.999878i	$-0.504966\pi$
$971$	−27.7120	−	15.9995i	−0.889319	−	0.513449i	−0.873720	+	0.486430i	$0.838299\pi$
$972$		0			0
$973$	−42.4948	+	7.54965i	−1.36232	+	0.242031i
$974$		−	54.0430i		−	1.73165i
$975$		0			0
$976$			14.3388i			0.458975i
$977$	50.6623	+	13.5749i	1.62083	+	0.434300i	0.951245	−	0.308435i	$-0.0998053\pi$
$977$	50.6623	+	13.5749i	1.62083	+	0.434300i	0.669585	+	0.742735i	$0.266472\pi$
$978$		0			0
$979$	−18.4292	+	31.9204i	−0.589001	+	1.02018i
$980$	−32.9106	+	2.96509i	−1.05129	+	0.0947163i
$981$		0			0
$982$	−32.7545	+	8.77655i	−1.04524	+	0.280071i
$983$	−14.3239	+	14.3239i	−0.456860	+	0.456860i	−0.897623	−	0.440763i	$-0.854708\pi$
$983$	−14.3239	+	14.3239i	−0.456860	+	0.456860i	0.440763	+	0.897623i	$0.354708\pi$
$984$		0			0
$985$	1.80520	+	3.12669i	0.0575183	+	0.0996247i
$986$	21.2992	+	5.70712i	0.678306	+	0.181752i
$987$		0			0
$988$	−47.7752	−	2.00680i	−1.51993	−	0.0638449i
$989$	−33.5133			−1.06566
$990$		0			0
$991$	26.6097	+	46.0893i	0.845284	+	1.46407i	0.885374	+	0.464879i	$0.153902\pi$
$991$	26.6097	+	46.0893i	0.845284	+	1.46407i	−0.0400904	+	0.999196i	$0.512765\pi$
$992$	13.9738	−	24.2033i	0.443669	−	0.768457i
$993$		0			0
$994$	47.7093	+	56.7086i	1.51325	+	1.79869i
$995$	−26.6187	+	7.13247i	−0.843871	+	0.226115i
$996$		0			0
$997$	4.16686	+	2.40574i	0.131966	+	0.0761904i	0.564529	−	0.825413i	$-0.309058\pi$
$997$	4.16686	+	2.40574i	0.131966	+	0.0761904i	−0.432564	+	0.901603i	$0.642391\pi$
$998$	−61.0019	+	35.2195i	−1.93098	+	1.11485i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.496.2		32
3.2	odd	2		273.2.by.c.223.7	yes	32
7.6	odd	2		819.2.fm.e.496.2		32
13.7	odd	12		819.2.fm.e.748.2		32
21.20	even	2		273.2.by.d.223.7	yes	32
39.20	even	12		273.2.by.d.202.7	yes	32
91.20	even	12	inner	819.2.fm.f.748.2		32
273.20	odd	12		273.2.by.c.202.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.7	✓	32	273.20	odd	12
273.2.by.c.223.7	yes	32	3.2	odd	2
273.2.by.d.202.7	yes	32	39.20	even	12
273.2.by.d.223.7	yes	32	21.20	even	2
819.2.fm.e.496.2		32	7.6	odd	2
819.2.fm.e.748.2		32	13.7	odd	12
819.2.fm.f.496.2		32	1.1	even	1	trivial
819.2.fm.f.748.2		32	91.20	even	12	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.96303 - 0.525993i) q^{2} +(1.84478 + 1.06508i) q^{4} +(-1.56698 - 1.56698i) q^{5} +(2.02456 - 1.70328i) q^{7} +(-0.187059 - 0.187059i) q^{8} +O(q^{10})\)	\(q+(-1.96303 - 0.525993i) q^{2} +(1.84478 + 1.06508i) q^{4} +(-1.56698 - 1.56698i) q^{5} +(2.02456 - 1.70328i) q^{7} +(-0.187059 - 0.187059i) q^{8} +(2.25182 + 3.90026i) q^{10} +(1.16197 - 4.33653i) q^{11} +(-3.51879 + 0.786201i) q^{13} +(-4.87020 + 2.27868i) q^{14} +(-1.86136 - 3.22397i) q^{16} +(-1.31427 + 2.27639i) q^{17} +(6.01372 - 1.61137i) q^{19} +(-1.22177 - 4.55971i) q^{20} +(-4.56197 + 7.90156i) q^{22} +(4.58893 - 2.64942i) q^{23} -0.0891302i q^{25} +(7.32104 + 0.307521i) q^{26} +(5.54901 - 0.985840i) q^{28} +(2.06391 + 3.57480i) q^{29} +(-2.44135 - 2.44135i) q^{31} +(2.09506 + 7.81887i) q^{32} +(3.77733 - 3.77733i) q^{34} +(-5.84146 - 0.503451i) q^{35} +(0.0290943 - 0.108582i) q^{37} -12.6527 q^{38} +0.586237i q^{40} +(-2.03234 + 7.58481i) q^{41} +(-5.47731 - 3.16233i) q^{43} +(6.76235 - 6.76235i) q^{44} +(-10.4018 + 2.78716i) q^{46} +(5.82732 - 5.82732i) q^{47} +(1.19770 - 6.89677i) q^{49} +(-0.0468819 + 0.174966i) q^{50} +(-7.32877 - 2.29744i) q^{52} -9.24486 q^{53} +(-8.61605 + 4.97448i) q^{55} +(-0.697326 - 0.0600996i) q^{56} +(-2.17121 - 8.10305i) q^{58} +(-1.27986 - 4.77649i) q^{59} +(-3.33568 - 1.92586i) q^{61} +(3.50831 + 6.07658i) q^{62} -9.00526i q^{64} +(6.74585 + 4.28192i) q^{65} +(10.1688 + 2.72472i) q^{67} +(-4.84909 + 2.79963i) q^{68} +(11.2022 + 4.06086i) q^{70} +(-3.56722 - 13.3131i) q^{71} +(-11.8088 + 11.8088i) q^{73} +(-0.114226 + 0.197846i) q^{74} +(12.8102 + 3.43249i) q^{76} +(-5.03382 - 10.7587i) q^{77} -13.3186 q^{79} +(-2.13518 + 7.96862i) q^{80} +(7.97912 - 13.8202i) q^{82} +(-5.15552 - 5.15552i) q^{83} +(5.62651 - 1.50762i) q^{85} +(9.08878 + 9.08878i) q^{86} +(-1.02854 + 0.593831i) q^{88} +(-7.93017 - 2.12488i) q^{89} +(-5.78489 + 7.58518i) q^{91} +11.2874 q^{92} +(-14.5044 + 8.37409i) q^{94} +(-11.9484 - 6.89840i) q^{95} +(-1.93349 + 0.518076i) q^{97} +(-5.97879 + 12.9086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 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

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