LMFDB - Embedded newform 459.2.o.a.208.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [459,2,Mod(64,459)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(459, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("459.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.o (of order $12$, degree $4$, not 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:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			208.2
Character	$\chi$	$=$	459.208
Dual form			459.2.o.a.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.07111 - 1.19576i) q^{2} +(1.85966 + 3.22103i) q^{4} +(0.854845 + 0.229055i) q^{5} +(-2.38596 + 0.639316i) q^{7} -4.11179i q^{8} +O(q^{10})$	\(q+(-2.07111 - 1.19576i) q^{2} +(1.85966 + 3.22103i) q^{4} +(0.854845 + 0.229055i) q^{5} +(-2.38596 + 0.639316i) q^{7} -4.11179i q^{8} +(-1.49658 - 1.49658i) q^{10} +(2.06432 - 0.553133i) q^{11} +(0.147179 + 0.254921i) q^{13} +(5.70605 + 1.52893i) q^{14} +(-1.19737 + 2.07391i) q^{16} +(-3.94406 - 1.20183i) q^{17} +6.94854i q^{19} +(0.851931 + 3.17945i) q^{20} +(-4.93685 - 1.32282i) q^{22} +(-1.67723 + 6.25950i) q^{23} +(-3.65183 - 2.10839i) q^{25} -0.703959i q^{26} +(-6.49634 - 6.49634i) q^{28} +(0.853904 + 3.18681i) q^{29} +(3.61311 + 0.968131i) q^{31} +(-2.16206 + 1.24826i) q^{32} +(6.73149 + 7.20525i) q^{34} -2.18606 q^{35} +(-1.49781 + 1.49781i) q^{37} +(8.30876 - 14.3912i) q^{38} +(0.941827 - 3.51495i) q^{40} +(-1.90726 + 7.11801i) q^{41} +(9.64376 + 5.56783i) q^{43} +(5.62060 + 5.62060i) q^{44} +(10.9586 - 10.9586i) q^{46} +(3.03477 - 5.25638i) q^{47} +(-0.778101 + 0.449237i) q^{49} +(5.04223 + 8.73340i) q^{50} +(-0.547406 + 0.948134i) q^{52} +10.6130i q^{53} +1.89137 q^{55} +(2.62873 + 9.81057i) q^{56} +(2.04212 - 7.62130i) q^{58} +(5.41473 - 3.12619i) q^{59} +(9.22562 - 2.47200i) q^{61} +(-6.32551 - 6.32551i) q^{62} +10.7600 q^{64} +(0.0674240 + 0.251630i) q^{65} +(-0.110338 - 0.191110i) q^{67} +(-3.46350 - 14.9389i) q^{68} +(4.52758 + 2.61400i) q^{70} +(7.53881 - 7.53881i) q^{71} +(-9.37016 + 9.37016i) q^{73} +(4.89316 - 1.31112i) q^{74} +(-22.3815 + 12.9220i) q^{76} +(-4.57176 + 2.63951i) q^{77} +(-10.8493 + 2.90706i) q^{79} +(-1.49861 + 1.49861i) q^{80} +(12.4616 - 12.4616i) q^{82} +(-2.97094 - 1.71527i) q^{83} +(-3.09628 - 1.93078i) q^{85} +(-13.3155 - 23.0632i) q^{86} +(-2.27437 - 8.48806i) q^{88} -7.17123 q^{89} +(-0.514137 - 0.514137i) q^{91} +(-23.2811 + 6.23816i) q^{92} +(-12.5707 + 7.25769i) q^{94} +(-1.59160 + 5.93993i) q^{95} +(2.36860 + 8.83975i) q^{97} +2.14871 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 24 q^{4} + 2 q^{5} - 2 q^{7}+O(q^{10}) $ 64 * q + 24 * q^4 + 2 * q^5 - 2 * q^7	$ 64 q + 24 q^{4} + 2 q^{5} - 2 q^{7} - 16 q^{10} - 4 q^{13} - 16 q^{16} + 8 q^{17} - 18 q^{20} - 4 q^{22} + 8 q^{23} + 10 q^{29} - 2 q^{31} + 20 q^{34} + 128 q^{35} - 8 q^{37} + 24 q^{38} - 20 q^{40} - 32 q^{41} - 20 q^{44} - 40 q^{46} + 64 q^{47} - 48 q^{50} + 36 q^{52} - 16 q^{55} - 12 q^{56} - 10 q^{58} - 2 q^{61} + 28 q^{62} - 8 q^{64} - 8 q^{65} - 4 q^{67} + 60 q^{68} + 84 q^{71} - 44 q^{73} + 14 q^{74} + 10 q^{79} - 204 q^{80} - 52 q^{82} + 22 q^{85} - 32 q^{86} + 16 q^{88} - 128 q^{89} + 44 q^{91} - 136 q^{92} - 4 q^{95} - 44 q^{97} - 208 q^{98}+O(q^{100}) $ 64 * q + 24 * q^4 + 2 * q^5 - 2 * q^7 - 16 * q^10 - 4 * q^13 - 16 * q^16 + 8 * q^17 - 18 * q^20 - 4 * q^22 + 8 * q^23 + 10 * q^29 - 2 * q^31 + 20 * q^34 + 128 * q^35 - 8 * q^37 + 24 * q^38 - 20 * q^40 - 32 * q^41 - 20 * q^44 - 40 * q^46 + 64 * q^47 - 48 * q^50 + 36 * q^52 - 16 * q^55 - 12 * q^56 - 10 * q^58 - 2 * q^61 + 28 * q^62 - 8 * q^64 - 8 * q^65 - 4 * q^67 + 60 * q^68 + 84 * q^71 - 44 * q^73 + 14 * q^74 + 10 * q^79 - 204 * q^80 - 52 * q^82 + 22 * q^85 - 32 * q^86 + 16 * q^88 - 128 * q^89 + 44 * q^91 - 136 * q^92 - 4 * q^95 - 44 * q^97 - 208 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.07111	−	1.19576i	−1.46450	−	0.845527i	−0.465282	−	0.885163i	$-0.654047\pi$
$2$	−2.07111	−	1.19576i	−1.46450	−	0.845527i	−0.999214	+	0.0396357i	$0.987380\pi$
$3$		0			0
$3$		0			0
$4$	1.85966	+	3.22103i	0.929832	+	1.61052i
$5$	0.854845	+	0.229055i	0.382298	+	0.102437i	0.444850	−	0.895605i	$-0.353257\pi$
$5$	0.854845	+	0.229055i	0.382298	+	0.102437i	−0.0625514	+	0.998042i	$0.519924\pi$
$6$		0			0
$7$	−2.38596	+	0.639316i	−0.901808	+	0.241639i	−0.679792	−	0.733405i	$-0.737930\pi$
$7$	−2.38596	+	0.639316i	−0.901808	+	0.241639i	−0.222015	+	0.975043i	$0.571263\pi$
$8$		−	4.11179i		−	1.45374i
$9$		0			0
$10$	−1.49658	−	1.49658i	−0.473261	−	0.473261i
$11$	2.06432	−	0.553133i	0.622416	−	0.166776i	0.0661902	−	0.997807i	$-0.478916\pi$
$11$	2.06432	−	0.553133i	0.622416	−	0.166776i	0.556226	+	0.831031i	$0.312249\pi$
$12$		0			0
$13$	0.147179	+	0.254921i	0.0408200	+	0.0707023i	0.885714	−	0.464232i	$-0.153670\pi$
$13$	0.147179	+	0.254921i	0.0408200	+	0.0707023i	−0.844894	+	0.534934i	$0.820336\pi$
$14$	5.70605	+	1.52893i	1.52501	+	0.408624i
$15$		0			0
$16$	−1.19737	+	2.07391i	−0.299343	+	0.518477i
$17$	−3.94406	−	1.20183i	−0.956575	−	0.291486i
$17$	−3.94406	−	1.20183i	−0.956575	−	0.291486i
$18$		0			0
$19$			6.94854i			1.59410i	0.603910	+	0.797052i	$0.293609\pi$
$19$			6.94854i			1.59410i	−0.603910	+	0.797052i	$0.706391\pi$
$20$	0.851931	+	3.17945i	0.190498	+	0.710946i
$21$		0			0
$22$	−4.93685	−	1.32282i	−1.05254	−	0.282027i
$23$	−1.67723	+	6.25950i	−0.349726	+	1.30520i	0.537267	+	0.843412i	$0.319457\pi$
$23$	−1.67723	+	6.25950i	−0.349726	+	1.30520i	−0.886993	+	0.461783i	$0.847210\pi$
$24$		0			0
$25$	−3.65183	−	2.10839i	−0.730367	−	0.421677i
$26$		−	0.703959i		−	0.138058i
$27$		0			0
$28$	−6.49634	−	6.49634i	−1.22769	−	1.22769i
$29$	0.853904	+	3.18681i	0.158566	+	0.591776i	0.998774	+	0.0495113i	$0.0157664\pi$
$29$	0.853904	+	3.18681i	0.158566	+	0.591776i	−0.840208	+	0.542265i	$0.817567\pi$
$30$		0			0
$31$	3.61311	+	0.968131i	0.648934	+	0.173881i	0.568247	−	0.822858i	$-0.307622\pi$
$31$	3.61311	+	0.968131i	0.648934	+	0.173881i	0.0806873	+	0.996739i	$0.474288\pi$
$32$	−2.16206	+	1.24826i	−0.382201	+	0.220664i
$33$		0			0
$34$	6.73149	+	7.20525i	1.15444	+	1.23569i
$35$	−2.18606			−0.369512
$36$		0			0
$37$	−1.49781	+	1.49781i	−0.246239	+	0.246239i	−0.819425	−	0.573186i	$-0.805707\pi$
$37$	−1.49781	+	1.49781i	−0.246239	+	0.246239i	0.573186	+	0.819425i	$0.305707\pi$
$38$	8.30876	−	14.3912i	1.34786	−	2.33456i
$39$		0			0
$40$	0.941827	−	3.51495i	0.148916	−	0.555762i
$41$	−1.90726	+	7.11801i	−0.297865	+	1.11165i	0.641051	+	0.767498i	$0.278499\pi$
$41$	−1.90726	+	7.11801i	−0.297865	+	1.11165i	−0.938916	+	0.344148i	$0.888168\pi$
$42$		0			0
$43$	9.64376	+	5.56783i	1.47066	+	0.849086i	0.999457	−	0.0329396i	$-0.0104869\pi$
$43$	9.64376	+	5.56783i	1.47066	+	0.849086i	0.471202	+	0.882025i	$0.343820\pi$
$44$	5.62060	+	5.62060i	0.847338	+	0.847338i
$45$		0			0
$46$	10.9586	−	10.9586i	1.61575	−	1.61575i
$47$	3.03477	−	5.25638i	0.442667	−	0.766722i	−0.555219	−	0.831704i	$-0.687366\pi$
$47$	3.03477	−	5.25638i	0.442667	−	0.766722i	0.997886	+	0.0649820i	$0.0206990\pi$
$48$		0			0
$49$	−0.778101	+	0.449237i	−0.111157	+	0.0641767i
$50$	5.04223	+	8.73340i	0.713079	+	1.23509i
$51$		0			0
$52$	−0.547406	+	0.948134i	−0.0759115	+	0.131483i
$53$			10.6130i			1.45781i	0.684617	+	0.728903i	$0.259970\pi$
$53$			10.6130i			1.45781i	−0.684617	+	0.728903i	$0.740030\pi$
$54$		0			0
$55$	1.89137			0.255033
$56$	2.62873	+	9.81057i	0.351279	+	1.31099i
$57$		0			0
$58$	2.04212	−	7.62130i	0.268144	−	1.00073i
$59$	5.41473	−	3.12619i	0.704937	−	0.406996i	−0.104246	−	0.994552i	$-0.533243\pi$
$59$	5.41473	−	3.12619i	0.704937	−	0.406996i	0.809184	+	0.587556i	$0.199910\pi$
$60$		0			0
$61$	9.22562	−	2.47200i	1.18122	−	0.316507i	0.385809	−	0.922579i	$-0.373922\pi$
$61$	9.22562	−	2.47200i	1.18122	−	0.316507i	0.795410	+	0.606072i	$0.207256\pi$
$62$	−6.32551	−	6.32551i	−0.803340	−	0.803340i
$63$		0			0
$64$	10.7600			1.34500
$65$	0.0674240	+	0.251630i	0.00836292	+	0.0312108i
$66$		0			0
$67$	−0.110338	−	0.191110i	−0.0134799	−	0.0233478i	0.859207	−	0.511628i	$-0.170958\pi$
$67$	−0.110338	−	0.191110i	−0.0134799	−	0.0233478i	−0.872687	+	0.488281i	$0.837624\pi$
$68$	−3.46350	−	14.9389i	−0.420011	−	1.81161i
$69$		0			0
$70$	4.52758	+	2.61400i	0.541149	+	0.312433i
$71$	7.53881	−	7.53881i	0.894693	−	0.894693i	−0.100268	−	0.994960i	$-0.531970\pi$
$71$	7.53881	−	7.53881i	0.894693	−	0.894693i	0.994960	+	0.100268i	$0.0319699\pi$
$72$		0			0
$73$	−9.37016	+	9.37016i	−1.09669	+	1.09669i	−0.101899	+	0.994795i	$0.532492\pi$
$73$	−9.37016	+	9.37016i	−1.09669	+	1.09669i	−0.994795	+	0.101899i	$0.967508\pi$
$74$	4.89316	−	1.31112i	0.568818	−	0.152414i
$75$		0			0
$76$	−22.3815	+	12.9220i	−2.56733	+	1.48225i
$77$	−4.57176	+	2.63951i	−0.521000	+	0.300800i
$78$		0			0
$79$	−10.8493	+	2.90706i	−1.22064	+	0.327070i	−0.810929	−	0.585145i	$-0.801038\pi$
$79$	−10.8493	+	2.90706i	−1.22064	+	0.327070i	−0.409712	+	0.912215i	$0.634371\pi$
$80$	−1.49861	+	1.49861i	−0.167549	+	0.167549i
$81$		0			0
$82$	12.4616	−	12.4616i	1.37615	−	1.37615i
$83$	−2.97094	−	1.71527i	−0.326103	−	0.188276i	0.328007	−	0.944675i	$-0.393623\pi$
$83$	−2.97094	−	1.71527i	−0.326103	−	0.188276i	−0.654110	+	0.756400i	$0.726956\pi$
$84$		0			0
$85$	−3.09628	−	1.93078i	−0.335838	−	0.209423i
$86$	−13.3155	−	23.0632i	−1.43585	−	2.48696i
$87$		0			0
$88$	−2.27437	−	8.48806i	−0.242448	−	0.904830i
$89$	−7.17123			−0.760149			−0.380074	−	0.924956i	$-0.624102\pi$
$89$	−7.17123			−0.760149			−0.380074	+	0.924956i	$0.624102\pi$
$90$		0			0
$91$	−0.514137	−	0.514137i	−0.0538962	−	0.0538962i
$92$	−23.2811	+	6.23816i	−2.42722	+	0.650373i
$93$		0			0
$94$	−12.5707	+	7.25769i	−1.29657	+	0.748574i
$95$	−1.59160	+	5.93993i	−0.163295	+	0.609424i
$96$		0			0
$97$	2.36860	+	8.83975i	0.240495	+	0.897541i	0.975594	+	0.219581i	$0.0704690\pi$
$97$	2.36860	+	8.83975i	0.240495	+	0.897541i	−0.735099	+	0.677960i	$0.762864\pi$
$98$	2.14871			0.217053
$99$		0			0
$100$		−	15.6836i		−	1.56836i
$101$	−7.72862	+	13.3864i	−0.769026	+	1.33199i	0.169065	+	0.985605i	$0.445925\pi$
$101$	−7.72862	+	13.3864i	−0.769026	+	1.33199i	−0.938091	+	0.346388i	$0.887408\pi$
$102$		0			0
$103$	−3.90560	−	6.76471i	−0.384831	−	0.666546i	0.606915	−	0.794767i	$-0.292407\pi$
$103$	−3.90560	−	6.76471i	−0.384831	−	0.666546i	−0.991746	+	0.128220i	$0.959073\pi$
$104$	1.04818	−	0.605168i	0.102783	−	0.0593416i
$105$		0			0
$106$	12.6905	−	21.9807i	1.23261	−	2.13495i
$107$	−1.03432	+	1.03432i	−0.0999914	+	0.0999914i	−0.755333	−	0.655341i	$-0.772525\pi$
$107$	−1.03432	+	1.03432i	−0.0999914	+	0.0999914i	0.655341	+	0.755333i	$0.272525\pi$
$108$		0			0
$109$	−3.52238	−	3.52238i	−0.337383	−	0.337383i	0.517998	−	0.855382i	$-0.326677\pi$
$109$	−3.52238	−	3.52238i	−0.337383	−	0.337383i	−0.855382	+	0.517998i	$0.826677\pi$
$110$	−3.91724	−	2.26162i	−0.373494	−	0.215637i
$111$		0			0
$112$	1.53100	−	5.71376i	0.144666	−	0.539900i
$113$	2.47345	−	9.23103i	0.232682	−	0.868382i	−0.746498	−	0.665388i	$-0.768266\pi$
$113$	2.47345	−	9.23103i	0.232682	−	0.868382i	0.979180	−	0.202994i	$-0.0650672\pi$
$114$		0			0
$115$	−2.86754	+	4.96672i	−0.267399	+	0.463149i
$116$	−8.67685	+	8.67685i	−0.805625	+	0.805625i
$117$		0			0
$118$	−14.9527			−1.37650
$119$	10.1787	+	0.346012i	0.933081	+	0.0317189i
$120$		0			0
$121$	−5.57082	+	3.21631i	−0.506438	+	0.292392i
$122$	−22.0632	−	5.91181i	−1.99751	−	0.535230i
$123$		0			0
$124$	3.60080	+	13.4384i	0.323361	+	1.20680i
$125$	−5.76777	−	5.76777i	−0.515885	−	0.515885i
$126$		0			0
$127$		−	9.07047i		−	0.804875i	−0.915448	−	0.402437i	$-0.868163\pi$
$127$		−	9.07047i		−	0.804875i	0.915448	−	0.402437i	$-0.131837\pi$
$128$	−17.9610	−	10.3698i	−1.58754	−	0.916566i
$129$		0			0
$130$	0.161245	−	0.601776i	0.0141421	−	0.0527792i
$131$	12.3044	+	3.29694i	1.07504	+	0.288055i	0.752561	−	0.658522i	$-0.228818\pi$
$131$	12.3044	+	3.29694i	1.07504	+	0.288055i	0.322476	+	0.946578i	$0.395485\pi$
$132$		0			0
$133$	−4.44231	−	16.5789i	−0.385197	−	1.43758i
$134$			0.527747i			0.0455904i
$135$		0			0
$136$	−4.94167	+	16.2172i	−0.423744	+	1.39061i
$137$	−2.76675	+	4.79216i	−0.236380	+	0.409422i	−0.959673	−	0.281119i	$-0.909294\pi$
$137$	−2.76675	+	4.79216i	−0.236380	+	0.409422i	0.723293	+	0.690541i	$0.242628\pi$
$138$		0			0
$139$	14.5419	+	3.89650i	1.23343	+	0.330497i	0.815914	−	0.578173i	$-0.196234\pi$
$139$	14.5419	+	3.89650i	1.23343	+	0.330497i	0.417516	+	0.908669i	$0.362901\pi$
$140$	−4.06534	−	7.04138i	−0.343584	−	0.595105i
$141$		0			0
$142$	−24.6283	+	6.59913i	−2.06676	+	0.553787i
$143$	0.444829	+	0.444829i	0.0371985	+	0.0371985i
$144$		0			0
$145$			2.91982i			0.242478i
$146$	30.6110	−	8.20221i	2.53339	−	0.678819i
$147$		0			0
$148$	−7.60994	−	2.03908i	−0.625533	−	0.167611i
$149$	5.37799	+	9.31495i	0.440582	+	0.763110i	0.997733	−	0.0673010i	$-0.0214388\pi$
$149$	5.37799	+	9.31495i	0.440582	+	0.763110i	−0.557151	+	0.830411i	$0.688105\pi$
$150$		0			0
$151$	−12.8919	−	7.44316i	−1.04913	−	0.605716i	−0.126725	−	0.991938i	$-0.540447\pi$
$151$	−12.8919	−	7.44316i	−1.04913	−	0.605716i	−0.922406	+	0.386222i	$0.873780\pi$
$152$	28.5710			2.31741
$153$		0			0
$154$	12.6248			1.01734
$155$	2.86690	+	1.65520i	0.230275	+	0.132949i
$156$		0			0
$157$	−2.16855	−	3.75605i	−0.173069	−	0.299765i	0.766422	−	0.642337i	$-0.222035\pi$
$157$	−2.16855	−	3.75605i	−0.173069	−	0.299765i	−0.939491	+	0.342572i	$0.888702\pi$
$158$	25.9462	+	6.95227i	2.06417	+	0.553093i
$159$		0			0
$160$	−2.13414	+	0.571842i	−0.168719	+	0.0452081i
$161$		−	16.0072i		−	1.26154i
$162$		0			0
$163$	−2.07729	−	2.07729i	−0.162706	−	0.162706i	0.621059	−	0.783764i	$-0.286703\pi$
$163$	−2.07729	−	2.07729i	−0.162706	−	0.162706i	−0.783764	+	0.621059i	$0.786703\pi$
$164$	−26.4742	+	7.09374i	−2.06729	+	0.553928i
$165$		0			0
$166$	4.10209	+	7.10504i	0.318384	+	0.551458i
$167$	1.70278	+	0.456259i	0.131765	+	0.0353064i	0.324099	−	0.946023i	$-0.394939\pi$
$167$	1.70278	+	0.456259i	0.131765	+	0.0353064i	−0.192334	+	0.981330i	$0.561606\pi$
$168$		0			0
$169$	6.45668	−	11.1833i	0.496667	−	0.860253i
$170$	4.10398	+	7.70125i	0.314761	+	0.590659i
$171$		0			0
$172$			41.4171i			3.15803i
$173$	−2.25023	−	8.39796i	−0.171082	−	0.638485i	−0.997186	−	0.0749680i	$-0.976115\pi$
$173$	−2.25023	−	8.39796i	−0.171082	−	0.638485i	0.826104	−	0.563517i	$-0.190552\pi$
$174$		0			0
$175$	10.0610	+	2.69585i	0.760544	+	0.203787i
$176$	−1.32461	+	4.94352i	−0.0998464	+	0.372632i
$177$		0			0
$178$	14.8524	+	8.57504i	1.11323	+	0.642726i
$179$			9.76156i			0.729613i	0.931083	+	0.364807i	$0.118865\pi$
$179$			9.76156i			0.729613i	−0.931083	+	0.364807i	$0.881135\pi$
$180$		0			0
$181$	−3.58567	−	3.58567i	−0.266521	−	0.266521i	0.561176	−	0.827697i	$-0.310349\pi$
$181$	−3.58567	−	3.58567i	−0.266521	−	0.266521i	−0.827697	+	0.561176i	$0.810349\pi$
$182$	0.450052	+	1.67962i	0.0333601	+	0.124501i
$183$		0			0
$184$	25.7378	+	6.89641i	1.89741	+	0.508410i
$185$	−1.62348	+	0.937318i	−0.119361	+	0.0689130i
$186$		0			0
$187$	−8.80657	−	0.299368i	−0.644001	−	0.0218920i
$188$	22.5746			1.64642
$189$		0			0
$190$	10.3991	−	10.3991i	0.754428	−	0.754428i
$191$	9.84003	−	17.0434i	0.712000	−	1.23322i	−0.252106	−	0.967700i	$-0.581123\pi$
$191$	9.84003	−	17.0434i	0.712000	−	1.23322i	0.964105	−	0.265520i	$-0.0855435\pi$
$192$		0			0
$193$	3.74323	−	13.9699i	0.269443	−	1.00558i	−0.690031	−	0.723780i	$-0.742403\pi$
$193$	3.74323	−	13.9699i	0.269443	−	1.00558i	0.959474	−	0.281797i	$-0.0909303\pi$
$194$	5.66454	−	21.1404i	0.406691	−	1.51779i
$195$		0			0
$196$	−2.89401	−	1.67086i	−0.206715	−	0.119347i
$197$	−7.71773	−	7.71773i	−0.549866	−	0.549866i	0.376536	−	0.926402i	$-0.377115\pi$
$197$	−7.71773	−	7.71773i	−0.549866	−	0.549866i	−0.926402	+	0.376536i	$0.877115\pi$
$198$		0			0
$199$	−2.39618	+	2.39618i	−0.169860	+	0.169860i	−0.786918	−	0.617058i	$-0.788325\pi$
$199$	−2.39618	+	2.39618i	−0.169860	+	0.169860i	0.617058	+	0.786918i	$0.288325\pi$
$200$	−8.66925	+	15.0156i	−0.613008	+	1.06176i
$201$		0			0
$202$	32.0136	−	18.4831i	2.25247	−	1.30047i
$203$	−4.07476	−	7.05769i	−0.285992	−	0.495353i
$204$		0			0
$205$	−3.26083	+	5.64792i	−0.227746	+	0.394468i
$206$			18.6806i			1.30154i
$207$		0			0
$208$	−0.704910			−0.0488767
$209$	3.84347	+	14.3440i	0.265858	+	0.992196i
$210$		0			0
$211$	−1.43904	+	5.37056i	−0.0990674	+	0.369725i	−0.997605	−	0.0691725i	$-0.977964\pi$
$211$	−1.43904	+	5.37056i	−0.0990674	+	0.369725i	0.898537	+	0.438897i	$0.144631\pi$
$212$	−34.1848	+	19.7366i	−2.34782	+	1.35551i
$213$		0			0
$214$	3.37898	−	0.905396i	0.230982	−	0.0618916i
$215$	6.96858	+	6.96858i	0.475253	+	0.475253i
$216$		0			0
$217$	−9.23968			−0.627230
$218$	3.08333	+	11.5072i	0.208830	+	0.779363i
$219$		0			0
$220$	3.51732	+	6.09217i	0.237137	+	0.410734i
$221$	−0.274110	−	1.18231i	−0.0184387	−	0.0795305i
$222$		0			0
$223$	3.07915	+	1.77775i	0.206195	+	0.119047i	0.599542	−	0.800343i	$-0.295349\pi$
$223$	3.07915	+	1.77775i	0.206195	+	0.119047i	−0.393347	+	0.919390i	$0.628683\pi$
$224$	4.36054	−	4.36054i	0.291351	−	0.291351i
$225$		0			0
$226$	−16.1608	+	16.1608i	−1.07500	+	1.07500i
$227$	9.07233	−	2.43092i	0.602151	−	0.161346i	0.0551506	−	0.998478i	$-0.482436\pi$
$227$	9.07233	−	2.43092i	0.602151	−	0.161346i	0.547001	+	0.837132i	$0.315769\pi$
$228$		0			0
$229$	20.9097	−	12.0722i	1.38175	−	0.797754i	0.389383	−	0.921076i	$-0.372688\pi$
$229$	20.9097	−	12.0722i	1.38175	−	0.797754i	0.992367	+	0.123322i	$0.0393549\pi$
$230$	11.8780	−	6.85775i	0.783211	−	0.452187i
$231$		0			0
$232$	13.1035	−	3.51107i	0.860288	−	0.230513i
$233$	−6.96007	+	6.96007i	−0.455969	+	0.455969i	−0.897330	−	0.441361i	$-0.854496\pi$
$233$	−6.96007	+	6.96007i	−0.455969	+	0.455969i	0.441361	+	0.897330i	$0.354496\pi$
$234$		0			0
$235$	3.79826	−	3.79826i	0.247771	−	0.247771i
$236$	20.1391	+	11.6273i	1.31095	+	0.756875i
$237$		0			0
$238$	−20.6675	−	12.8879i	−1.33967	−	0.835398i
$239$	2.85777	+	4.94980i	0.184854	+	0.320176i	0.943527	−	0.331295i	$-0.107486\pi$
$239$	2.85777	+	4.94980i	0.184854	+	0.320176i	−0.758673	+	0.651471i	$0.774152\pi$
$240$		0			0
$241$	−0.926361	−	3.45723i	−0.0596721	−	0.222699i	0.929650	−	0.368443i	$-0.120109\pi$
$241$	−0.926361	−	3.45723i	−0.0596721	−	0.222699i	−0.989322	+	0.145744i	$0.953442\pi$
$242$	15.3837			0.988902
$243$		0			0
$244$	25.1189	+	25.1189i	1.60807	+	1.60807i
$245$	−0.768056	+	0.205800i	−0.0490693	+	0.0131481i
$246$		0			0
$247$	−1.77133	+	1.02268i	−0.112707	+	0.0650714i
$248$	3.98075	−	14.8564i	0.252778	−	0.943381i
$249$		0			0
$250$	5.04884	+	18.8425i	0.319316	+	1.19171i
$251$	−4.30640			−0.271818			−0.135909	−	0.990721i	$-0.543395\pi$
$251$	−4.30640			−0.271818			−0.135909	+	0.990721i	$0.543395\pi$
$252$		0			0
$253$			13.8493i			0.870700i
$254$	−10.8461	+	18.7859i	−0.680543	+	1.17874i
$255$		0			0
$256$	14.0394	+	24.3170i	0.877465	+	1.51981i
$257$	19.5623	−	11.2943i	1.22026	−	0.704518i	0.255287	−	0.966865i	$-0.417830\pi$
$257$	19.5623	−	11.2943i	1.22026	−	0.704518i	0.964973	+	0.262348i	$0.0844968\pi$
$258$		0			0
$259$	2.61615	−	4.53130i	0.162560	−	0.281561i
$260$	−0.685122	+	0.685122i	−0.0424895	+	0.0424895i
$261$		0			0
$262$	−21.5413	−	21.5413i	−1.33083	−	1.33083i
$263$	−19.8359	−	11.4522i	−1.22313	−	0.706175i	−0.257547	−	0.966266i	$-0.582914\pi$
$263$	−19.8359	−	11.4522i	−1.22313	−	0.706175i	−0.965584	+	0.260091i	$0.916248\pi$
$264$		0			0
$265$	−2.43096	+	9.07246i	−0.149333	+	0.557317i
$266$	−10.6238	+	39.6487i	−0.651390	+	2.43102i
$267$		0			0
$268$	0.410382	−	0.710802i	0.0250680	−	0.0434191i
$269$	−14.2952	+	14.2952i	−0.871592	+	0.871592i	−0.992646	−	0.121054i	$-0.961373\pi$
$269$	−14.2952	+	14.2952i	−0.871592	+	0.871592i	0.121054	+	0.992646i	$0.461373\pi$
$270$		0			0
$271$	−21.2643			−1.29172			−0.645858	−	0.763458i	$-0.723500\pi$
$271$	−21.2643			−1.29172			−0.645858	+	0.763458i	$0.723500\pi$
$272$	7.21499	−	6.74059i	0.437473	−	0.408708i
$273$		0			0
$274$	11.4605	−	6.61672i	0.692354	−	0.399731i
$275$	−8.70477	−	2.33244i	−0.524918	−	0.140651i
$276$		0			0
$277$	0.737115	+	2.75095i	0.0442889	+	0.165289i	0.984528	−	0.175226i	$-0.0560655\pi$
$277$	0.737115	+	2.75095i	0.0442889	+	0.165289i	−0.940239	+	0.340514i	$0.889399\pi$
$278$	−25.4587	−	25.4587i	−1.52691	−	1.52691i
$279$		0			0
$280$			8.98864i			0.537174i
$281$	−2.53095	−	1.46124i	−0.150984	−	0.0871705i	0.422605	−	0.906314i	$-0.361116\pi$
$281$	−2.53095	−	1.46124i	−0.150984	−	0.0871705i	−0.573589	+	0.819144i	$0.694449\pi$
$282$		0			0
$283$	−6.80630	+	25.4014i	−0.404592	+	1.50996i	0.400214	+	0.916422i	$0.368936\pi$
$283$	−6.80630	+	25.4014i	−0.404592	+	1.50996i	−0.804806	+	0.593538i	$0.797731\pi$
$284$	38.3024	+	10.2631i	2.27283	+	0.609003i
$285$		0			0
$286$	−0.389383	−	1.45320i	−0.0230247	−	0.0859293i
$287$		−	18.2026i		−	1.07447i
$288$		0			0
$289$	14.1112	+	9.48016i	0.830072	+	0.557657i
$290$	3.49139	−	6.04727i	0.205022	−	0.355108i
$291$		0			0
$292$	−47.6069	−	12.7562i	−2.78598	−	0.746502i
$293$	−8.31563	−	14.4031i	−0.485804	−	0.841438i	0.514063	−	0.857753i	$-0.328140\pi$
$293$	−8.31563	−	14.4031i	−0.485804	−	0.841438i	−0.999867	+	0.0163148i	$0.994807\pi$
$294$		0			0
$295$	5.34482	−	1.43214i	0.311188	−	0.0833825i
$296$	6.15870	+	6.15870i	0.357967	+	0.357967i
$297$		0			0
$298$		−	25.7230i		−	1.49010i
$299$	−1.84253	+	0.493704i	−0.106556	+	0.0285516i
$300$		0			0
$301$	−26.5692	−	7.11920i	−1.53142	−	0.410344i
$302$	17.8004	+	30.8312i	1.02430	+	1.77414i
$303$		0			0
$304$	−14.4106	−	8.31999i	−0.826507	−	0.477184i
$305$	8.45270			0.484000
$306$		0			0
$307$	32.6602			1.86402			0.932008	−	0.362439i	$-0.118056\pi$
$307$	32.6602			1.86402			0.932008	+	0.362439i	$0.118056\pi$
$308$	−17.0039	−	9.81719i	−0.968885	−	0.559386i
$309$		0			0
$310$	−3.95844	−	6.85622i	−0.224824	−	0.389407i
$311$	−10.2785	−	2.75411i	−0.582838	−	0.156171i	−0.0446601	−	0.999002i	$-0.514220\pi$
$311$	−10.2785	−	2.75411i	−0.582838	−	0.156171i	−0.538178	+	0.842831i	$0.680887\pi$
$312$		0			0
$313$	−15.1230	+	4.05219i	−0.854801	+	0.229043i	−0.659504	−	0.751701i	$-0.729234\pi$
$313$	−15.1230	+	4.05219i	−0.854801	+	0.229043i	−0.195297	+	0.980744i	$0.562567\pi$
$314$			10.3722i			0.585340i
$315$		0			0
$316$	−29.5398	−	29.5398i	−1.66174	−	1.66174i
$317$	27.7714	−	7.44133i	1.55980	−	0.417947i	0.627199	−	0.778859i	$-0.284201\pi$
$317$	27.7714	−	7.44133i	1.55980	−	0.417947i	0.932600	+	0.360912i	$0.117534\pi$
$318$		0			0
$319$	3.52546	+	6.10628i	0.197388	+	0.341886i
$320$	9.19810	+	2.46462i	0.514189	+	0.137777i
$321$		0			0
$322$	−19.1407	+	33.1526i	−1.06667	+	1.84752i
$323$	8.35095	−	27.4055i	0.464659	−	1.52488i
$324$		0			0
$325$		−	1.24124i		−	0.0688515i
$326$	1.81836	+	6.78621i	0.100710	+	0.375854i
$327$		0			0
$328$	29.2678	+	7.84227i	1.61604	+	0.433017i
$329$	−3.88036	+	14.4817i	−0.213931	+	0.798401i
$330$		0			0
$331$	3.11889	+	1.80069i	0.171430	+	0.0989751i	0.583260	−	0.812286i	$-0.301777\pi$
$331$	3.11889	+	1.80069i	0.171430	+	0.0989751i	−0.411830	+	0.911261i	$0.635110\pi$
$332$		−	12.7593i		−	0.700259i
$333$		0			0
$334$	−2.98107	−	2.98107i	−0.163117	−	0.163117i
$335$	−0.0505467	−	0.188643i	−0.00276166	−	0.0103067i
$336$		0			0
$337$	31.9449	+	8.55961i	1.74015	+	0.466271i	0.982480	−	0.186368i	$-0.0596717\pi$
$337$	31.9449	+	8.55961i	1.74015	+	0.466271i	0.757669	+	0.652639i	$0.226338\pi$
$338$	−26.7450	+	15.4412i	−1.45473	+	0.839892i
$339$		0			0
$340$	0.461084	−	13.5638i	0.0250058	−	0.735601i
$341$	7.99413			0.432906
$342$		0			0
$343$	13.7958	−	13.7958i	0.744904	−	0.744904i
$344$	22.8937	−	39.6531i	1.23435	−	2.13795i
$345$		0			0
$346$	−5.38144	+	20.0838i	−0.289308	+	1.07971i
$347$	2.56558	−	9.57489i	0.137728	−	0.514007i	−0.862244	−	0.506493i	$-0.830942\pi$
$347$	2.56558	−	9.57489i	0.137728	−	0.514007i	0.999972	−	0.00751398i	$-0.00239180\pi$
$348$		0			0
$349$	−20.2913	−	11.7152i	−1.08617	−	0.627101i	−0.153616	−	0.988131i	$-0.549092\pi$
$349$	−20.2913	−	11.7152i	−1.08617	−	0.627101i	−0.932554	+	0.361030i	$0.882425\pi$
$350$	−17.6140	−	17.6140i	−0.941506	−	0.941506i
$351$		0			0
$352$	−3.77272	+	3.77272i	−0.201087	+	0.201087i
$353$	7.93811	−	13.7492i	0.422503	−	0.731797i	−0.573681	−	0.819079i	$-0.694485\pi$
$353$	7.93811	−	13.7492i	0.422503	−	0.731797i	0.996184	+	0.0872823i	$0.0278182\pi$
$354$		0			0
$355$	8.17132	−	4.71772i	0.433689	−	0.250390i
$356$	−13.3361	−	23.0988i	−0.706810	−	1.22423i
$357$		0			0
$358$	11.6724	−	20.2173i	0.616908	−	1.06852i
$359$		−	7.53863i		−	0.397873i	−0.980012	−	0.198937i	$-0.936251\pi$
$359$		−	7.53863i		−	0.397873i	0.980012	−	0.198937i	$-0.0637488\pi$
$360$		0			0
$361$	−29.2822			−1.54117
$362$	3.13873	+	11.7139i	0.164968	+	0.615669i
$363$		0			0
$364$	0.699930	−	2.61217i	0.0366863	−	0.136915i
$365$	−10.1563	+	5.86375i	−0.531606	+	0.306923i
$366$		0			0
$367$	7.90713	−	2.11871i	0.412749	−	0.110596i	−0.0464683	−	0.998920i	$-0.514797\pi$
$367$	7.90713	−	2.11871i	0.412749	−	0.110596i	0.459217	+	0.888324i	$0.348130\pi$
$368$	−10.9734	−	10.9734i	−0.572026	−	0.572026i
$369$		0			0
$370$	4.48321			0.233071
$371$	−6.78505	−	25.3222i	−0.352262	−	1.31466i
$372$		0			0
$373$	−4.65772	−	8.06741i	−0.241168	−	0.417715i	0.719880	−	0.694099i	$-0.244197\pi$
$373$	−4.65772	−	8.06741i	−0.241168	−	0.417715i	−0.961047	+	0.276384i	$0.910864\pi$
$374$	17.8814	+	11.1505i	0.924626	+	0.576581i
$375$		0			0
$376$	−21.6131	−	12.4784i	−1.11461	−	0.643522i
$377$	−0.686708	+	0.686708i	−0.0353673	+	0.0353673i
$378$		0			0
$379$	16.6013	−	16.6013i	0.852752	−	0.852752i	−0.137719	−	0.990471i	$-0.543977\pi$
$379$	16.6013	−	16.6013i	0.852752	−	0.852752i	0.990471	+	0.137719i	$0.0439772\pi$
$380$	−22.0925	+	5.91968i	−1.13332	+	0.303673i
$381$		0			0
$382$	−40.7596	+	23.5325i	−2.08544	+	1.20403i
$383$	3.83516	−	2.21423i	0.195967	−	0.113142i	−0.398806	−	0.917035i	$-0.630575\pi$
$383$	3.83516	−	2.21423i	0.195967	−	0.113142i	0.594773	+	0.803894i	$0.297242\pi$
$384$		0			0
$385$	−4.51274	+	1.20918i	−0.229990	+	0.0616257i
$386$	−24.4572	+	24.4572i	−1.24484	+	1.24484i
$387$		0			0
$388$	−24.0683	+	24.0683i	−1.22188	+	1.22188i
$389$	−16.4564	−	9.50112i	−0.834374	−	0.481726i	0.0209741	−	0.999780i	$-0.493323\pi$
$389$	−16.4564	−	9.50112i	−0.834374	−	0.481726i	−0.855348	+	0.518054i	$0.826657\pi$
$390$		0			0
$391$	14.1379	−	22.6721i	0.714986	−	1.14658i
$392$	1.84717	+	3.19939i	0.0932961	+	0.161594i
$393$		0			0
$394$	6.75575	+	25.2128i	0.340350	+	1.27020i
$395$	−9.94034			−0.500153
$396$		0			0
$397$	16.3196	+	16.3196i	0.819059	+	0.819059i	0.985972	−	0.166913i	$-0.0533798\pi$
$397$	16.3196	+	16.3196i	0.819059	+	0.819059i	−0.166913	+	0.985972i	$0.553380\pi$
$398$	7.82798	−	2.09750i	0.392381	−	0.105138i
$399$		0			0
$400$	8.74520	−	5.04905i	0.437260	−	0.252452i
$401$	0.604920	−	2.25759i	0.0302083	−	0.112739i	−0.949175	−	0.314747i	$-0.898080\pi$
$401$	0.604920	−	2.25759i	0.0302083	−	0.112739i	0.979384	+	0.202009i	$0.0647469\pi$
$402$		0			0
$403$	0.284976	+	1.06355i	0.0141957	+	0.0529790i
$404$	−57.4905			−2.86026
$405$		0			0
$406$			19.4897i			0.967256i
$407$	−2.26348	+	3.92046i	−0.112196	+	0.194330i
$408$		0			0
$409$	−1.30201	−	2.25516i	−0.0643805	−	0.111510i	0.832039	−	0.554718i	$-0.187174\pi$
$409$	−1.30201	−	2.25516i	−0.0643805	−	0.111510i	−0.896419	+	0.443208i	$0.853840\pi$
$410$	13.5071	−	7.79832i	0.667067	−	0.385131i
$411$		0			0
$412$	14.5262	−	25.1602i	0.715656	−	1.23955i
$413$	−10.9207	+	10.9207i	−0.537372	+	0.537372i
$414$		0			0
$415$	−2.14680	−	2.14680i	−0.105382	−	0.105382i
$416$	−0.636417	−	0.367435i	−0.0312029	−	0.0180150i
$417$		0			0
$418$	9.19170	−	34.3039i	0.449581	−	1.67786i
$419$	−5.45539	+	20.3598i	−0.266513	+	0.994641i	0.694805	+	0.719199i	$0.255491\pi$
$419$	−5.45539	+	20.3598i	−0.266513	+	0.994641i	−0.961318	+	0.275442i	$0.911176\pi$
$420$		0			0
$421$	10.6721	−	18.4846i	0.520125	−	0.900884i	−0.479601	−	0.877487i	$-0.659219\pi$
$421$	10.6721	−	18.4846i	0.520125	−	0.900884i	0.999726	−	0.0233969i	$-0.00744814\pi$
$422$	9.40228	−	9.40228i	0.457696	−	0.457696i
$423$		0			0
$424$	43.6384			2.11927
$425$	11.8691	+	12.7045i	0.575737	+	0.616258i
$426$		0			0
$427$	−20.4316	+	11.7962i	−0.988752	+	0.570856i
$428$	−5.25506	−	1.40809i	−0.254013	−	0.0680626i
$429$		0			0
$430$	−6.09998	−	22.7654i	−0.294167	−	1.09785i
$431$	20.5378	+	20.5378i	0.989272	+	0.989272i	0.999943	−	0.0106709i	$-0.00339672\pi$
$431$	20.5378	+	20.5378i	0.989272	+	0.989272i	−0.0106709	+	0.999943i	$0.503397\pi$
$432$		0			0
$433$			11.1591i			0.536270i	0.963381	+	0.268135i	$0.0864073\pi$
$433$			11.1591i			0.536270i	−0.963381	+	0.268135i	$0.913593\pi$
$434$	19.1364	+	11.0484i	0.918576	+	0.530340i
$435$		0			0
$436$	4.79526	−	17.8962i	0.229651	−	0.857071i
$437$	−43.4944	−	11.6543i	−2.08062	−	0.557500i
$438$		0			0
$439$	5.54170	+	20.6819i	0.264491	+	0.987094i	0.962561	+	0.271065i	$0.0873758\pi$
$439$	5.54170	+	20.6819i	0.264491	+	0.987094i	−0.698070	+	0.716030i	$0.745958\pi$
$440$		−	7.77693i		−	0.370751i
$441$		0			0
$442$	−0.846037	+	2.77646i	−0.0402419	+	0.132063i
$443$	−14.3605	+	24.8732i	−0.682290	+	1.18176i	0.291990	+	0.956421i	$0.405683\pi$
$443$	−14.3605	+	24.8732i	−0.682290	+	1.18176i	−0.974280	+	0.225340i	$0.927651\pi$
$444$		0			0
$445$	−6.13029	−	1.64261i	−0.290604	−	0.0778670i
$446$	−4.25150	−	7.36382i	−0.201314	−	0.348687i
$447$		0			0
$448$	−25.6728	+	6.87901i	−1.21293	+	0.325003i
$449$	9.98949	+	9.98949i	0.471433	+	0.471433i	0.902378	−	0.430945i	$-0.141820\pi$
$449$	9.98949	+	9.98949i	0.471433	+	0.471433i	−0.430945	+	0.902378i	$0.641820\pi$
$450$		0			0
$451$			15.7488i			0.741583i
$452$	34.3332	−	9.19956i	1.61490	−	0.432711i
$453$		0			0
$454$	−21.6966	−	5.81358i	−1.01827	−	0.272845i
$455$	−0.321742	−	0.557273i	−0.0150835	−	0.0261254i
$456$		0			0
$457$	−4.86756	−	2.81029i	−0.227695	−	0.131460i	0.381813	−	0.924239i	$-0.375300\pi$
$457$	−4.86756	−	2.81029i	−0.227695	−	0.131460i	−0.609508	+	0.792780i	$0.708633\pi$
$458$	−57.7416			−2.69809
$459$		0			0
$460$	−21.3306			−0.994546
$461$	7.07343	+	4.08384i	0.329442	+	0.190204i	0.655593	−	0.755114i	$-0.272419\pi$
$461$	7.07343	+	4.08384i	0.329442	+	0.190204i	−0.326151	+	0.945318i	$0.605752\pi$
$462$		0			0
$463$	9.42462	+	16.3239i	0.437999	+	0.758637i	0.997535	−	0.0701693i	$-0.0223540\pi$
$463$	9.42462	+	16.3239i	0.437999	+	0.758637i	−0.559536	+	0.828806i	$0.689021\pi$
$464$	−7.63160	−	2.04488i	−0.354288	−	0.0949312i
$465$		0			0
$466$	22.7376	−	6.09252i	1.05330	−	0.282231i
$467$			4.58082i			0.211975i	0.994367	+	0.105988i	$0.0338004\pi$
$467$			4.58082i			0.211975i	−0.994367	+	0.105988i	$0.966200\pi$
$468$		0			0
$469$	0.385441	+	0.385441i	0.0177980	+	0.0177980i
$470$	−12.4084	+	3.32482i	−0.572357	+	0.153363i
$471$		0			0
$472$	−12.8543	−	22.2642i	−0.591665	−	1.02479i
$473$	22.9876	+	6.15950i	1.05697	+	0.283214i
$474$		0			0
$475$	14.6502	−	25.3749i	0.672198	−	1.16428i
$476$	17.8145	+	33.4294i	0.816525	+	1.53224i
$477$		0			0
$478$		−	13.6688i		−	0.625196i
$479$	0.668736	+	2.49576i	0.0305553	+	0.114034i	0.979519	−	0.201351i	$-0.0645331\pi$
$479$	0.668736	+	2.49576i	0.0305553	+	0.114034i	−0.948964	+	0.315385i	$0.897866\pi$
$480$		0			0
$481$	−0.602271	−	0.161378i	−0.0274612	−	0.00735820i
$482$	−2.21540	+	8.26799i	−0.100909	+	0.376597i
$483$		0			0
$484$	−20.7197	−	11.9625i	−0.941804	−	0.543751i
$485$			8.09916i			0.367764i
$486$		0			0
$487$	26.2558	+	26.2558i	1.18977	+	1.18977i	0.977132	+	0.212633i	$0.0682039\pi$
$487$	26.2558	+	26.2558i	1.18977	+	1.18977i	0.212633	+	0.977132i	$0.431796\pi$
$488$	−10.1643	−	37.9338i	−0.460118	−	1.71718i
$489$		0			0
$490$	1.83682	+	0.492173i	0.0829789	+	0.0222341i
$491$	9.48966	−	5.47886i	0.428262	−	0.247257i	−0.270344	−	0.962764i	$-0.587137\pi$
$491$	9.48966	−	5.47886i	0.428262	−	0.247257i	0.698606	+	0.715507i	$0.253804\pi$
$492$		0			0
$493$	0.462152	−	13.5952i	0.0208143	−	0.612298i
$494$	4.89149			0.220078
$495$		0			0
$496$	−6.33406	+	6.33406i	−0.284407	+	0.284407i
$497$	−13.1676	+	22.8070i	−0.590649	+	1.02303i
$498$		0			0
$499$	6.38029	−	23.8116i	0.285621	−	1.06595i	−0.662763	−	0.748829i	$-0.730616\pi$
$499$	6.38029	−	23.8116i	0.285621	−	1.06595i	0.948384	−	0.317124i	$-0.102717\pi$
$500$	7.85205	−	29.3043i	0.351155	−	1.31053i
$501$		0			0
$502$	8.91903	+	5.14941i	0.398076	+	0.229829i
$503$	19.2077	+	19.2077i	0.856431	+	0.856431i	0.990916	−	0.134485i	$-0.0429380\pi$
$503$	19.2077	+	19.2077i	0.856431	+	0.856431i	−0.134485	+	0.990916i	$0.542938\pi$
$504$		0			0
$505$	−9.67298	+	9.67298i	−0.430442	+	0.430442i
$506$	16.5604	−	28.6835i	0.736201	−	1.27514i
$507$		0			0
$508$	29.2163	−	16.8680i	1.29626	−	0.748398i
$509$	−8.22594	−	14.2478i	−0.364609	−	0.631521i	0.624105	−	0.781341i	$-0.285464\pi$
$509$	−8.22594	−	14.2478i	−0.364609	−	0.631521i	−0.988713	+	0.149820i	$0.952131\pi$
$510$		0			0
$511$	16.3663	−	28.3473i	0.724004	−	1.25401i
$512$		−	25.6719i		−	1.13455i
$513$		0			0
$514$	−54.0208			−2.38275
$515$	−1.78920	−	6.67737i	−0.0788414	−	0.294240i
$516$		0			0
$517$	3.35727	−	12.5295i	0.147652	−	0.551046i
$518$	−10.8367	+	6.25655i	−0.476136	+	0.274897i
$519$		0			0
$520$	1.03465	−	0.277234i	0.0453724	−	0.0121575i
$521$	22.6971	+	22.6971i	0.994378	+	0.994378i	0.999984	−	0.00560632i	$-0.00178456\pi$
$521$	22.6971	+	22.6971i	0.994378	+	0.994378i	−0.00560632	+	0.999984i	$0.501785\pi$
$522$		0			0
$523$	9.78384			0.427817			0.213909	−	0.976854i	$-0.431381\pi$
$523$	9.78384			0.427817			0.213909	+	0.976854i	$0.431381\pi$
$524$	12.2624	+	45.7640i	0.535686	+	1.99921i
$525$		0			0
$526$	27.3882	+	47.4377i	1.19418	+	2.06838i
$527$	−13.0868	−	8.16071i	−0.570070	−	0.355486i
$528$		0			0
$529$	−16.4496	−	9.49720i	−0.715201	−	0.412922i
$530$	15.8832	−	15.8832i	0.689924	−	0.689924i
$531$		0			0
$532$	45.1401	−	45.1401i	1.95707	−	1.95707i
$533$	−2.09524	+	0.561417i	−0.0907548	+	0.0243177i
$534$		0			0
$535$	−1.12110	+	0.647267i	−0.0484693	+	0.0279838i
$536$	−0.785806	+	0.453685i	−0.0339416	+	0.0195962i
$537$		0			0
$538$	46.7004	−	12.5133i	2.01340	−	0.539488i
$539$	−1.35776	+	1.35776i	−0.0584830	+	0.0584830i
$540$		0			0
$541$	6.02025	−	6.02025i	0.258831	−	0.258831i	−0.565748	−	0.824579i	$-0.691412\pi$
$541$	6.02025	−	6.02025i	0.258831	−	0.258831i	0.824579	+	0.565748i	$0.191412\pi$
$542$	44.0407	+	25.4269i	1.89171	+	1.09218i
$543$		0			0
$544$	10.0275	−	2.32481i	0.429925	−	0.0996753i
$545$	−2.20427	−	3.81791i	−0.0944207	−	0.163541i
$546$		0			0
$547$	9.61931	+	35.8998i	0.411292	+	1.53496i	0.792148	+	0.610329i	$0.208963\pi$
$547$	9.61931	+	35.8998i	0.411292	+	1.53496i	−0.380856	+	0.924634i	$0.624371\pi$
$548$	−20.5809			−0.879174
$549$		0			0
$550$	15.2395	+	15.2395i	0.649815	+	0.649815i
$551$	−22.1437	+	5.93339i	−0.943353	+	0.252771i
$552$		0			0
$553$	24.0274	−	13.8723i	1.02175	−	0.589908i
$554$	1.76282	−	6.57893i	0.0748950	−	0.279512i
$555$		0			0
$556$	14.4924	+	54.0862i	0.614613	+	2.29377i
$557$	4.26389			0.180667			0.0903333	−	0.995912i	$-0.471207\pi$
$557$	4.26389			0.180667			0.0903333	+	0.995912i	$0.471207\pi$
$558$		0			0
$559$			3.27786i			0.138639i
$560$	2.61753	−	4.53370i	0.110611	−	0.191584i
$561$		0			0
$562$	3.49458	+	6.05279i	0.147410	+	0.255322i
$563$	−6.27932	+	3.62536i	−0.264642	+	0.152791i	−0.626450	−	0.779462i	$-0.715493\pi$
$563$	−6.27932	+	3.62536i	−0.264642	+	0.152791i	0.361808	+	0.932252i	$0.382159\pi$
$564$		0			0
$565$	4.22883	−	7.32454i	0.177908	−	0.308146i
$566$	44.4705	−	44.4705i	1.86924	−	1.86924i
$567$		0			0
$568$	−30.9980	−	30.9980i	−1.30065	−	1.30065i
$569$	−22.2117	−	12.8239i	−0.931162	−	0.537607i	−0.0439832	−	0.999032i	$-0.514005\pi$
$569$	−22.2117	−	12.8239i	−0.931162	−	0.537607i	−0.887179	+	0.461426i	$0.847338\pi$
$570$		0			0
$571$	−6.78350	+	25.3164i	−0.283881	+	1.05946i	0.665773	+	0.746155i	$0.268102\pi$
$571$	−6.78350	+	25.3164i	−0.283881	+	1.05946i	−0.949653	+	0.313303i	$0.898565\pi$
$572$	−0.605576	+	2.26004i	−0.0253204	+	0.0944971i
$573$		0			0
$574$	−21.7659	+	37.6996i	−0.908491	+	1.57355i
$575$	19.3224	−	19.3224i	0.805800	−	0.805800i
$576$		0			0
$577$	−21.8156			−0.908193			−0.454097	−	0.890952i	$-0.650038\pi$
$577$	−21.8156			−0.908193			−0.454097	+	0.890952i	$0.650038\pi$
$578$	−17.8899	−	36.5080i	−0.744123	−	1.51853i
$579$		0			0
$580$	−9.40484	+	5.42989i	−0.390515	+	0.225464i
$581$	8.18514	+	2.19320i	0.339577	+	0.0909893i
$582$		0			0
$583$	5.87039	+	21.9086i	0.243127	+	0.907362i
$584$	38.5281	+	38.5281i	1.59431	+	1.59431i
$585$		0			0
$586$			39.7739i			1.64304i
$587$	6.33435	+	3.65714i	0.261446	+	0.150946i	0.624994	−	0.780629i	$-0.285101\pi$
$587$	6.33435	+	3.65714i	0.261446	+	0.150946i	−0.363548	+	0.931576i	$0.618435\pi$
$588$		0			0
$589$	−6.72710	+	25.1059i	−0.277185	+	1.03447i
$590$	−12.7822	−	3.42498i	−0.526235	−	0.141004i
$591$		0			0
$592$	−1.31289	−	4.89977i	−0.0539595	−	0.201379i
$593$			9.60461i			0.394414i	0.980362	+	0.197207i	$0.0631871\pi$
$593$			9.60461i			0.394414i	−0.980362	+	0.197207i	$0.936813\pi$
$594$		0			0
$595$	8.62197	+	2.62727i	0.353466	+	0.107708i
$596$	−20.0025	+	34.6453i	−0.819334	+	1.41913i
$597$		0			0
$598$	4.40643	+	1.18070i	0.180192	+	0.0482824i
$599$	18.3657	+	31.8103i	0.750401	+	1.29973i	0.947628	+	0.319375i	$0.103473\pi$
$599$	18.3657	+	31.8103i	0.750401	+	1.29973i	−0.197227	+	0.980358i	$0.563194\pi$
$600$		0			0
$601$	−2.75760	+	0.738898i	−0.112485	+	0.0301403i	−0.314622	−	0.949217i	$-0.601878\pi$
$601$	−2.75760	+	0.738898i	−0.112485	+	0.0301403i	0.202137	+	0.979357i	$0.435211\pi$
$602$	46.5149	+	46.5149i	1.89581	+	1.89581i
$603$		0			0
$604$		−	55.3671i		−	2.25286i
$605$	−5.49890	+	1.47343i	−0.223562	+	0.0599033i
$606$		0			0
$607$	5.13084	+	1.37480i	0.208254	+	0.0558016i	0.361438	−	0.932396i	$-0.382286\pi$
$607$	5.13084	+	1.37480i	0.208254	+	0.0558016i	−0.153184	+	0.988198i	$0.548953\pi$
$608$	−8.67361	−	15.0231i	−0.351761	−	0.609269i
$609$		0			0
$610$	−17.5065	−	10.1074i	−0.708816	−	0.409235i
$611$	1.78661			0.0722787
$612$		0			0
$613$	−31.5380			−1.27381			−0.636904	−	0.770943i	$-0.719785\pi$
$613$	−31.5380			−1.27381			−0.636904	+	0.770943i	$0.719785\pi$
$614$	−67.6428	−	39.0536i	−2.72984	−	1.57608i
$615$		0			0
$616$	10.8531	+	18.7981i	0.437284	+	0.757398i
$617$	−30.2416	−	8.10322i	−1.21748	−	0.326223i	−0.407789	−	0.913076i	$-0.633700\pi$
$617$	−30.2416	−	8.10322i	−1.21748	−	0.326223i	−0.809694	+	0.586853i	$0.800367\pi$
$618$		0			0
$619$	3.23242	−	0.866124i	0.129922	−	0.0348125i	−0.193272	−	0.981145i	$-0.561910\pi$
$619$	3.23242	−	0.866124i	0.129922	−	0.0348125i	0.323194	+	0.946333i	$0.395243\pi$
$620$			12.3125i			0.494482i
$621$		0			0
$622$	17.9946	+	17.9946i	0.721517	+	0.721517i
$623$	17.1103	−	4.58468i	0.685508	−	0.183681i
$624$		0			0
$625$	6.93252	+	12.0075i	0.277301	+	0.480299i
$626$	36.1667	+	9.69085i	1.44551	+	0.387324i
$627$		0			0
$628$	8.06556	−	13.9700i	0.321851	−	0.557462i
$629$	7.70759	−	4.10736i	0.307322	−	0.163771i
$630$		0			0
$631$		−	29.7591i		−	1.18469i	−0.805684	−	0.592346i	$-0.798202\pi$
$631$		−	29.7591i		−	1.18469i	0.805684	−	0.592346i	$-0.201798\pi$
$632$	11.9532	+	44.6100i	0.475474	+	1.77449i
$633$		0			0
$634$	−66.4157	−	17.7960i	−2.63770	−	0.706771i
$635$	2.07764	−	7.75385i	0.0824486	−	0.307702i
$636$		0			0
$637$	−0.229040	−	0.132236i	−0.00907489	−	0.00523939i
$638$		−	16.8624i		−	0.667587i
$639$		0			0
$640$	−12.9786	−	12.9786i	−0.513024	−	0.513024i
$641$	−4.76788	−	17.7940i	−0.188320	−	0.702819i	−0.993895	−	0.110326i	$-0.964810\pi$
$641$	−4.76788	−	17.7940i	−0.188320	−	0.702819i	0.805576	−	0.592493i	$-0.201856\pi$
$642$		0			0
$643$	−24.3656	−	6.52875i	−0.960887	−	0.257469i	−0.255911	−	0.966700i	$-0.582375\pi$
$643$	−24.3656	−	6.52875i	−0.960887	−	0.257469i	−0.704976	+	0.709231i	$0.749042\pi$
$644$	51.5597	−	29.7680i	2.03173	−	1.17302i
$645$		0			0
$646$	−50.0660	+	46.7740i	−1.96982	+	1.84030i
$647$	−8.13256			−0.319724			−0.159862	−	0.987139i	$-0.551105\pi$
$647$	−8.13256			−0.319724			−0.159862	+	0.987139i	$0.551105\pi$
$648$		0			0
$649$	9.44853	−	9.44853i	0.370887	−	0.370887i
$650$	−1.48422	+	2.57074i	−0.0582158	+	0.100833i
$651$		0			0
$652$	2.82795	−	10.5541i	0.110751	−	0.413329i
$653$	1.75792	−	6.56065i	0.0687928	−	0.256738i	−0.922961	−	0.384892i	$-0.874239\pi$
$653$	1.75792	−	6.56065i	0.0687928	−	0.256738i	0.991754	+	0.128154i	$0.0409053\pi$
$654$		0			0
$655$	9.76314	+	5.63675i	0.381478	+	0.220246i
$656$	−12.4784	−	12.4784i	−0.487199	−	0.487199i
$657$		0			0
$658$	25.3532	−	25.3532i	0.988371	−	0.988371i
$659$	−14.2163	+	24.6234i	−0.553789	+	0.959191i	0.444208	+	0.895924i	$0.353485\pi$
$659$	−14.2163	+	24.6234i	−0.553789	+	0.959191i	−0.997997	+	0.0632668i	$0.979848\pi$
$660$		0			0
$661$	−32.7333	+	18.8986i	−1.27318	+	0.735069i	−0.975584	−	0.219625i	$-0.929517\pi$
$661$	−32.7333	+	18.8986i	−1.27318	+	0.735069i	−0.297592	+	0.954693i	$0.596183\pi$
$662$	−4.30638	−	7.45887i	−0.167372	−	0.289897i
$663$		0			0
$664$	−7.05284	+	12.2159i	−0.273703	+	0.474068i
$665$		−	15.1900i		−	0.589041i
$666$		0			0
$667$	−21.3800			−0.827838
$668$	1.69698	+	6.33320i	0.0656580	+	0.245039i
$669$		0			0
$670$	−0.120883	+	0.451142i	−0.00467012	+	0.0174291i
$671$	17.6773	−	10.2060i	0.682424	−	0.393998i
$672$		0			0
$673$	−13.9567	+	3.73968i	−0.537990	+	0.144154i	−0.517575	−	0.855638i	$-0.673165\pi$
$673$	−13.9567	+	3.73968i	−0.537990	+	0.144154i	−0.0204146	+	0.999792i	$0.506499\pi$
$674$	−55.9262	−	55.9262i	−2.15420	−	2.15420i
$675$		0			0
$676$	48.0290			1.84727
$677$	3.71076	+	13.8487i	0.142616	+	0.532251i	0.999850	+	0.0173233i	$0.00551445\pi$
$677$	3.71076	+	13.8487i	0.142616	+	0.532251i	−0.857234	+	0.514927i	$0.827819\pi$
$678$		0			0
$679$	−11.3028	−	19.5770i	−0.433761	−	0.751296i
$680$	−7.93898	+	12.7312i	−0.304446	+	0.488221i
$681$		0			0
$682$	−16.5567	−	9.55903i	−0.633990	−	0.366034i
$683$	26.4821	−	26.4821i	1.01331	−	1.01331i	0.0133997	−	0.999910i	$-0.495735\pi$
$683$	26.4821	−	26.4821i	1.01331	−	1.01331i	0.999910	−	0.0133997i	$-0.00426539\pi$
$684$		0			0
$685$	−3.46281	+	3.46281i	−0.132307	+	0.132307i
$686$	−45.0691	+	12.0762i	−1.72075	+	0.461072i
$687$		0			0
$688$	−23.0943	+	13.3335i	−0.880463	+	0.508336i
$689$	−2.70547	+	1.56201i	−0.103070	+	0.0595077i
$690$		0			0
$691$	16.7597	−	4.49074i	0.637568	−	0.170836i	0.0744663	−	0.997224i	$-0.476275\pi$
$691$	16.7597	−	4.49074i	0.637568	−	0.170836i	0.563101	+	0.826388i	$0.309608\pi$
$692$	22.8654	−	22.8654i	0.869213	−	0.869213i
$693$		0			0
$694$	−16.7628	+	16.7628i	−0.636309	+	0.636309i
$695$	11.5386	+	6.66181i	0.437684	+	0.252697i
$696$		0			0
$697$	16.0770	−	25.7816i	0.608959	−	0.976549i
$698$	28.0171	+	48.5270i	1.06046	+	1.83677i
$699$		0			0
$700$	10.0268	+	37.4203i	0.378976	+	1.41436i
$701$	−17.0381			−0.643521			−0.321760	−	0.946821i	$-0.604275\pi$
$701$	−17.0381			−0.643521			−0.321760	+	0.946821i	$0.604275\pi$
$702$		0			0
$703$	−10.4076	−	10.4076i	−0.392531	−	0.392531i
$704$	22.2120	−	5.95169i	0.837147	−	0.224313i
$705$		0			0
$706$	−32.8814	+	18.9841i	−1.23751	+	0.714476i
$707$	9.88206	−	36.8803i	0.371653	−	1.38703i
$708$		0			0
$709$	0.127385	+	0.475408i	0.00478405	+	0.0178543i	0.968277	−	0.249881i	$-0.0803914\pi$
$709$	0.127385	+	0.475408i	0.00478405	+	0.0178543i	−0.963493	+	0.267735i	$0.913725\pi$
$710$	−22.5649			−0.846847
$711$		0			0
$712$			29.4866i			1.10506i
$713$	−12.1200	+	20.9925i	−0.453898	+	0.786175i
$714$		0			0
$715$	0.278370	+	0.482150i	0.0104104	+	0.0180314i
$716$	−31.4423	+	18.1532i	−1.17505	+	0.678418i
$717$		0			0
$718$	−9.01436	+	15.6133i	−0.336413	+	0.582684i
$719$	−27.0368	+	27.0368i	−1.00830	+	1.00830i	−0.00833737	+	0.999965i	$0.502654\pi$
$719$	−27.0368	+	27.0368i	−1.00830	+	1.00830i	−0.999965	+	0.00833737i	$0.997346\pi$
$720$		0			0
$721$	13.6434	+	13.6434i	0.508107	+	0.508107i
$722$	60.6467	+	35.0144i	2.25704	+	1.30310i
$723$		0			0
$724$	4.88142	−	18.2177i	0.181417	−	0.677056i
$725$	3.60072	−	13.4381i	0.133727	−	0.499077i
$726$		0			0
$727$	−7.70623	+	13.3476i	−0.285808	+	0.495034i	−0.972805	−	0.231626i	$-0.925595\pi$
$727$	−7.70623	+	13.3476i	−0.285808	+	0.495034i	0.686997	+	0.726661i	$0.258929\pi$
$728$	−2.11403	+	2.11403i	−0.0783510	+	0.0783510i
$729$		0			0
$730$	28.0465			1.03805
$731$	−31.3440	−	33.5500i	−1.15930	−	1.24089i
$732$		0			0
$733$	−2.33527	+	1.34827i	−0.0862552	+	0.0497994i	−0.542507	−	0.840051i	$-0.682525\pi$
$733$	−2.33527	+	1.34827i	−0.0862552	+	0.0497994i	0.456252	+	0.889851i	$0.349192\pi$
$734$	−18.9100	−	5.06692i	−0.697981	−	0.187023i
$735$		0			0
$736$	−4.18724	−	15.6270i	−0.154344	−	0.576019i
$737$	−0.333481	−	0.333481i	−0.0122839	−	0.0122839i
$738$		0			0
$739$		−	47.1358i		−	1.73392i	−0.498378	−	0.866960i	$-0.666071\pi$
$739$		−	47.1358i		−	1.73392i	0.498378	−	0.866960i	$-0.333929\pi$
$740$	−6.03826	−	3.48619i	−0.221971	−	0.128155i
$741$		0			0
$742$	−16.2265	+	60.5582i	−0.595695	+	2.22316i
$743$	9.08629	+	2.43466i	0.333344	+	0.0893192i	0.421609	−	0.906778i	$-0.361466\pi$
$743$	9.08629	+	2.43466i	0.333344	+	0.0893192i	−0.0882651	+	0.996097i	$0.528132\pi$
$744$		0			0
$745$	2.46371	+	9.19469i	0.0902634	+	0.336868i
$746$			22.2780i			0.815655i
$747$		0			0
$748$	−15.4130	−	28.9230i	−0.563555	−	1.05753i
$749$	1.80659	−	3.12910i	0.0660113	−	0.114335i
$750$		0			0
$751$	−30.5556	−	8.18734i	−1.11499	−	0.298760i	−0.346135	−	0.938185i	$-0.612506\pi$
$751$	−30.5556	−	8.18734i	−1.11499	−	0.298760i	−0.768854	+	0.639425i	$0.779173\pi$
$752$	7.26750	+	12.5877i	0.265019	+	0.459026i
$753$		0			0
$754$	2.24338	−	0.601113i	0.0816992	−	0.0218912i
$755$	−9.31571	−	9.31571i	−0.339034	−	0.339034i
$756$		0			0
$757$			25.3772i			0.922351i	0.887309	+	0.461176i	$0.152572\pi$
$757$			25.3772i			0.922351i	−0.887309	+	0.461176i	$0.847428\pi$
$758$	−54.2342	+	14.5320i	−1.96988	+	0.527827i
$759$		0			0
$760$	24.4237	+	6.54432i	0.885942	+	0.237388i
$761$	14.4027	+	24.9463i	0.522099	+	0.904301i	0.999669	+	0.0257082i	$0.00818407\pi$
$761$	14.4027	+	24.9463i	0.522099	+	0.904301i	−0.477571	+	0.878593i	$0.658483\pi$
$762$		0			0
$763$	10.6562	+	6.15235i	0.385780	+	0.222730i
$764$	73.1966			2.64816
$765$		0			0
$766$	−10.5907			−0.382658
$767$	1.59386	+	0.920218i	0.0575511	+	0.0332271i
$768$		0			0
$769$	8.80614	+	15.2527i	0.317558	+	0.550026i	0.979978	−	0.199106i	$-0.0638040\pi$
$769$	8.80614	+	15.2527i	0.317558	+	0.550026i	−0.662420	+	0.749132i	$0.730471\pi$
$770$	10.7923	+	2.89178i	0.388926	+	0.104212i
$771$		0			0
$772$	51.9587	−	13.9223i	1.87003	−	0.501074i
$773$		−	50.3558i		−	1.81117i	−0.424163	−	0.905586i	$-0.639431\pi$
$773$		−	50.3558i		−	1.81117i	0.424163	−	0.905586i	$-0.360569\pi$
$774$		0			0
$775$	−11.1533	−	11.1533i	−0.400638	−	0.400638i
$776$	36.3472	−	9.73921i	1.30479	−	0.349617i
$777$		0			0
$778$	22.7220	+	39.3557i	0.814625	+	1.41097i
$779$	−49.4598	−	13.2527i	−1.77208	−	0.474827i
$780$		0			0
$781$	11.3926	−	19.7325i	0.407658	−	0.706084i
$782$	−56.3915	+	30.0509i	−2.01656	+	1.07462i
$783$		0			0
$784$		−	2.15162i		−	0.0768434i
$785$	−0.993437	−	3.70756i	−0.0354573	−	0.132328i
$786$		0			0
$787$	15.7202	+	4.21222i	0.560366	+	0.150150i	0.527874	−	0.849322i	$-0.322989\pi$
$787$	15.7202	+	4.21222i	0.560366	+	0.150150i	0.0324914	+	0.999472i	$0.489656\pi$
$788$	10.5067	−	39.2115i	0.374285	−	1.39685i
$789$		0			0
$790$	20.5875	+	11.8862i	0.732472	+	0.422893i
$791$			23.6062i			0.839339i
$792$		0			0
$793$	1.98798	+	1.98798i	0.0705951	+	0.0705951i
$794$	−14.2855	−	53.3141i	−0.506972	−	1.89205i
$795$		0			0
$796$	−12.1742	−	3.26208i	−0.431504	−	0.115621i
$797$	35.6622	−	20.5896i	1.26322	−	0.729320i	0.289524	−	0.957171i	$-0.406503\pi$
$797$	35.6622	−	20.5896i	1.26322	−	0.729320i	0.973696	+	0.227851i	$0.0731698\pi$
$798$		0			0
$799$	−18.2866	+	17.0842i	−0.646933	+	0.604396i
$800$	10.5273			0.372196
$801$		0			0
$802$	−3.95238	+	3.95238i	−0.139564	+	0.139564i
$803$	−14.1601	+	24.5260i	−0.499698	+	0.865502i
$804$		0			0
$805$	3.66653	−	13.6837i	0.129228	−	0.482286i
$806$	0.681524	−	2.54348i	0.0240057	−	0.0895904i
$807$		0			0
$808$	55.0419	+	31.7785i	1.93637	+	1.11796i
$809$	8.74059	+	8.74059i	0.307303	+	0.307303i	0.843862	−	0.536560i	$-0.180276\pi$
$809$	8.74059	+	8.74059i	0.307303	+	0.307303i	−0.536560	+	0.843862i	$0.680276\pi$
$810$		0			0
$811$	32.9521	−	32.9521i	1.15711	−	1.15711i	0.172011	−	0.985095i	$-0.444974\pi$
$811$	32.9521	−	32.9521i	1.15711	−	1.15711i	0.985095	−	0.172011i	$-0.0550265\pi$
$812$	15.1554	−	26.2499i	0.531849	−	0.921189i
$813$		0			0
$814$	9.37583	−	5.41314i	0.328623	−	0.189730i
$815$	−1.29995	−	2.25157i	−0.0455351	−	0.0788691i
$816$		0			0
$817$	−38.6883	+	67.0101i	−1.35353	+	2.34439i
$818$			6.22757i			0.217742i
$819$		0			0
$820$	−24.2562			−0.847063
$821$	3.92565	+	14.6507i	0.137006	+	0.511314i	0.999982	+	0.00606816i	$0.00193157\pi$
$821$	3.92565	+	14.6507i	0.137006	+	0.511314i	−0.862975	+	0.505246i	$0.831402\pi$
$822$		0			0
$823$	−1.47525	+	5.50571i	−0.0514240	+	0.191917i	−0.986860	−	0.161580i	$-0.948341\pi$
$823$	−1.47525	+	5.50571i	−0.0514240	+	0.191917i	0.935436	+	0.353497i	$0.115008\pi$
$824$	−27.8151	+	16.0590i	−0.968984	+	0.559443i
$825$		0			0
$826$	35.6764	−	9.55947i	1.24134	−	0.332617i
$827$	8.60731	+	8.60731i	0.299306	+	0.299306i	0.840742	−	0.541436i	$-0.182119\pi$
$827$	8.60731	+	8.60731i	0.299306	+	0.299306i	−0.541436	+	0.840742i	$0.682119\pi$
$828$		0			0
$829$	−2.24842			−0.0780910			−0.0390455	−	0.999237i	$-0.512432\pi$
$829$	−2.24842			−0.0780910			−0.0390455	+	0.999237i	$0.512432\pi$
$830$	1.87921	+	7.01331i	0.0652284	+	0.243436i
$831$		0			0
$832$	1.58364	+	2.74294i	0.0549027	+	0.0950943i
$833$	3.60878	−	0.836674i	0.125037	−	0.0289890i
$834$		0			0
$835$	1.35111	+	0.780061i	0.0467569	+	0.0269951i
$836$	−39.0550	+	39.0550i	−1.35074	+	1.35074i
$837$		0			0
$838$	35.6440	−	35.6440i	1.23130	−	1.23130i
$839$	−20.0266	+	5.36611i	−0.691395	+	0.185259i	−0.587373	−	0.809316i	$-0.699838\pi$
$839$	−20.0266	+	5.36611i	−0.691395	+	0.185259i	−0.104022	+	0.994575i	$0.533171\pi$
$840$		0			0
$841$	15.6881	−	9.05754i	0.540970	−	0.312329i
$842$	−44.2061	+	25.5224i	−1.52344	+	0.879560i
$843$		0			0
$844$	−19.9749	+	5.35225i	−0.687564	+	0.184232i
$845$	8.08105	−	8.08105i	0.277997	−	0.277997i
$846$		0			0
$847$	11.2355	−	11.2355i	0.386056	−	0.386056i
$848$	−22.0104	−	12.7077i	−0.755839	−	0.436384i
$849$		0			0
$850$	−9.39082	−	40.5050i	−0.322102	−	1.38931i
$851$	−6.86339	−	11.8877i	−0.235274	−	0.407507i
$852$		0			0
$853$	−2.79718	−	10.4392i	−0.0957736	−	0.357432i	0.901362	−	0.433066i	$-0.142568\pi$
$853$	−2.79718	−	10.4392i	−0.0957736	−	0.357432i	−0.997136	+	0.0756344i	$0.975902\pi$
$854$	56.4213			1.93070
$855$		0			0
$856$	4.25291	+	4.25291i	0.145361	+	0.145361i
$857$	8.33591	−	2.23360i	0.284749	−	0.0762983i	−0.113617	−	0.993525i	$-0.536244\pi$
$857$	8.33591	−	2.23360i	0.284749	−	0.0762983i	0.398367	+	0.917226i	$0.369577\pi$
$858$		0			0
$859$	−18.7991	+	10.8537i	−0.641416	+	0.370322i	−0.785160	−	0.619293i	$-0.787419\pi$
$859$	−18.7991	+	10.8537i	−0.641416	+	0.370322i	0.143744	+	0.989615i	$0.454086\pi$
$860$	−9.48681	+	35.4052i	−0.323497	+	1.20731i
$861$		0			0
$862$	−17.9779	−	67.0943i	−0.612329	−	2.28524i
$863$	34.2485			1.16583			0.582916	−	0.812532i	$-0.301912\pi$
$863$	34.2485			1.16583			0.582916	+	0.812532i	$0.301912\pi$
$864$		0			0
$865$		−	7.69438i		−	0.261617i
$866$	13.3435	−	23.1116i	0.453431	−	0.785365i
$867$		0			0
$868$	−17.1827	−	29.7613i	−0.583219	−	1.01016i
$869$	−20.7884	+	12.0022i	−0.705199	+	0.407147i
$870$		0			0
$871$	0.0324787	−	0.0562547i	0.00110050	−	0.00190612i
$872$	−14.4833	+	14.4833i	−0.490467	+	0.490467i
$873$		0			0
$874$	76.1460	+	76.1460i	2.57568	+	2.57568i
$875$	17.4491	+	10.0742i	0.589886	+	0.340571i
$876$		0			0
$877$	3.31755	−	12.3813i	0.112026	−	0.418086i	−0.887021	−	0.461728i	$-0.847230\pi$
$877$	3.31755	−	12.3813i	0.112026	−	0.418086i	0.999047	+	0.0436424i	$0.0138962\pi$
$878$	13.2531	−	49.4611i	0.447269	−	1.66923i
$879$		0			0
$880$	−2.26468	+	3.92253i	−0.0763422	+	0.132229i
$881$	21.0371	−	21.0371i	0.708759	−	0.708759i	−0.257515	−	0.966274i	$-0.582904\pi$
$881$	21.0371	−	21.0371i	0.708759	−	0.708759i	0.966274	+	0.257515i	$0.0829038\pi$
$882$		0			0
$883$	−2.40155			−0.0808187			−0.0404093	−	0.999183i	$-0.512866\pi$
$883$	−2.40155			−0.0808187			−0.0404093	+	0.999183i	$0.512866\pi$
$884$	3.29849	−	3.08161i	0.110940	−	0.103646i
$885$		0			0
$886$	59.4845	−	34.3434i	1.99842	−	1.15379i
$887$	41.6783	+	11.1677i	1.39942	+	0.374973i	0.878136	−	0.478410i	$-0.158787\pi$
$887$	41.6783	+	11.1677i	1.39942	+	0.374973i	0.521283	+	0.853384i	$0.325454\pi$
$888$		0			0
$889$	5.79890	+	21.6418i	0.194489	+	0.725842i
$890$	10.7323	+	10.7323i	0.359749	+	0.359749i
$891$		0			0
$892$			13.2240i			0.442774i
$893$	36.5242	+	21.0872i	1.22224	+	0.705658i
$894$		0			0
$895$	−2.23594	+	8.34462i	−0.0747391	+	0.278930i
$896$	49.4836	+	13.2591i	1.65313	+	0.442956i
$897$		0			0
$898$	−8.74434	−	32.6343i	−0.291802	−	1.08902i
$899$			12.3410i			0.411595i
$900$		0			0
$901$	12.7550	−	41.8583i	0.424930	−	1.39450i
$902$	18.8317	−	32.6175i	0.627028	−	1.08605i
$903$		0			0
$904$	−37.9561	−	10.1703i	−1.26240	−	0.338259i
$905$	−2.24388	−	3.88651i	−0.0745890	−	0.129192i
$906$		0			0
$907$	22.1593	−	5.93756i	0.735787	−	0.197153i	0.128582	−	0.991699i	$-0.458957\pi$
$907$	22.1593	−	5.93756i	0.735787	−	0.197153i	0.607205	+	0.794545i	$0.292291\pi$
$908$	24.7016	+	24.7016i	0.819750	+	0.819750i
$909$		0			0
$910$			1.53890i			0.0510140i
$911$	40.1442	−	10.7566i	1.33004	−	0.356382i	0.477307	−	0.878737i	$-0.341613\pi$
$911$	40.1442	−	10.7566i	1.33004	−	0.356382i	0.852728	+	0.522355i	$0.174946\pi$
$912$		0			0
$913$	−7.08174	−	1.89755i	−0.234372	−	0.0627997i
$914$	6.72084	+	11.6408i	0.222306	+	0.385045i
$915$		0			0
$916$	77.7699	+	44.9005i	2.56959	+	1.48355i
$917$	−31.4655			−1.03908
$918$		0			0
$919$	−55.6614			−1.83610			−0.918051	−	0.396463i	$-0.870238\pi$
$919$	−55.6614			−1.83610			−0.918051	+	0.396463i	$0.870238\pi$
$920$	20.4221	+	11.7907i	0.673298	+	0.388729i
$921$		0			0
$922$	−9.76656	−	16.9162i	−0.321645	−	0.557105i
$923$	3.03135	+	0.812249i	0.0997782	+	0.0267355i
$924$		0			0
$925$	8.62774	−	2.31180i	0.283678	−	0.0760114i
$926$		−	45.0782i		−	1.48136i
$927$		0			0
$928$	−5.82417	−	5.82417i	−0.191188	−	0.191188i
$929$	18.5040	−	4.95812i	0.607096	−	0.162671i	0.0578410	−	0.998326i	$-0.481578\pi$
$929$	18.5040	−	4.95812i	0.607096	−	0.162671i	0.549255	+	0.835655i	$0.314912\pi$
$930$		0			0
$931$	−3.12154	−	5.40667i	−0.102304	−	0.177196i
$932$	−35.3620	−	9.47522i	−1.15832	−	0.310371i
$933$		0			0
$934$	5.47754	−	9.48738i	0.179231	−	0.310437i
$935$	−7.45969	−	2.27310i	−0.243958	−	0.0743384i
$936$		0			0
$937$			47.9982i			1.56803i	0.620740	+	0.784017i	$0.286832\pi$
$937$			47.9982i			1.56803i	−0.620740	+	0.784017i	$0.713168\pi$
$938$	−0.337397	−	1.25918i	−0.0110164	−	0.0411138i
$939$		0			0
$940$	19.2978	+	5.17083i	0.629425	+	0.168654i
$941$	11.6938	−	43.6417i	0.381205	−	1.42268i	−0.462857	−	0.886433i	$-0.653176\pi$
$941$	11.6938	−	43.6417i	0.381205	−	1.42268i	0.844062	−	0.536245i	$-0.180158\pi$
$942$		0			0
$943$	−41.3562	−	23.8770i	−1.34674	−	0.777543i
$944$			14.9729i			0.487325i
$945$		0			0
$946$	−40.2445	−	40.2445i	−1.30846	−	1.30846i
$947$	14.8696	+	55.4941i	0.483197	+	1.80332i	0.588046	+	0.808827i	$0.299897\pi$
$947$	14.8696	+	55.4941i	0.483197	+	1.80332i	−0.104849	+	0.994488i	$0.533436\pi$
$948$		0			0
$949$	−3.76774	−	1.00956i	−0.122306	−	0.0327718i
$950$	−60.6844	+	35.0362i	−1.96886	+	1.13672i
$951$		0			0
$952$	1.42273	−	41.8528i	0.0461110	−	1.35646i
$953$	−8.00149			−0.259194			−0.129597	−	0.991567i	$-0.541368\pi$
$953$	−8.00149			−0.259194			−0.129597	+	0.991567i	$0.541368\pi$
$954$		0			0
$955$	12.3156	−	12.3156i	0.398523	−	0.398523i
$956$	−10.6290	+	18.4099i	−0.343766	+	0.595420i
$957$		0			0
$958$	1.59929	−	5.96863i	0.0516707	−	0.192838i
$959$	3.53766	−	13.2027i	0.114237	−	0.426338i
$960$		0			0
$961$	−14.7295	−	8.50407i	−0.475144	−	0.274325i
$962$	1.05440	+	1.05440i	0.0339952	+	0.0339952i
$963$		0			0
$964$	9.41312	−	9.41312i	0.303176	−	0.303176i
$965$	6.39976	−	11.0847i	0.206016	−	0.356829i
$966$		0			0
$967$	−11.0429	+	6.37562i	−0.355116	+	0.205026i	−0.666936	−	0.745115i	$-0.732395\pi$
$967$	−11.0429	+	6.37562i	−0.355116	+	0.205026i	0.311820	+	0.950141i	$0.399061\pi$
$968$	13.2248	+	22.9060i	0.425061	+	0.736228i
$969$		0			0
$970$	9.68462	−	16.7742i	0.310954	−	0.538589i
$971$		−	4.77766i		−	0.153322i	−0.997057	−	0.0766612i	$-0.975574\pi$
$971$		−	4.77766i		−	0.153322i	0.997057	−	0.0766612i	$-0.0244260\pi$
$972$		0			0
$973$	−37.1876			−1.19218
$974$	−22.9831	−	85.7743i	−0.736427	−	2.74838i
$975$		0			0
$976$	−5.91980	+	22.0930i	−0.189488	+	0.707179i
$977$	20.3125	−	11.7274i	0.649854	−	0.375193i	−0.138547	−	0.990356i	$-0.544243\pi$
$977$	20.3125	−	11.7274i	0.649854	−	0.375193i	0.788400	+	0.615163i	$0.210910\pi$
$978$		0			0
$979$	−14.8037	+	3.96664i	−0.473129	+	0.126774i
$980$	−2.09121	−	2.09121i	−0.0668014	−	0.0668014i
$981$		0			0
$982$	−26.2055			−0.836251
$983$	0.822556	+	3.06982i	0.0262354	+	0.0979120i	0.977802	−	0.209530i	$-0.0671935\pi$
$983$	0.822556	+	3.06982i	0.0262354	+	0.0979120i	−0.951567	+	0.307442i	$0.900527\pi$
$984$		0			0
$985$	−4.82968	−	8.36525i	−0.153886	−	0.266539i
$986$	−17.2137	+	27.6046i	−0.548197	+	0.879109i
$987$		0			0
$988$	−6.58815	−	3.80367i	−0.209597	−	0.121011i
$989$	−51.0266	+	51.0266i	−1.62255	+	1.62255i
$990$		0			0
$991$	−36.5208	+	36.5208i	−1.16012	+	1.16012i	−0.175674	+	0.984448i	$0.556211\pi$
$991$	−36.5208	+	36.5208i	−1.16012	+	1.16012i	−0.984448	+	0.175674i	$0.943789\pi$
$992$	−9.02024	+	2.41696i	−0.286393	+	0.0767387i
$993$		0			0
$994$	54.5432	−	31.4905i	1.73000	−	0.998819i
$995$	−2.59721	+	1.49950i	−0.0823372	+	0.0475374i
$996$		0			0
$997$	18.8632	−	5.05438i	0.597404	−	0.160074i	0.0525690	−	0.998617i	$-0.483259\pi$
$997$	18.8632	−	5.05438i	0.597404	−	0.160074i	0.544835	+	0.838543i	$0.316592\pi$
$998$	−41.6871	+	41.6871i	−1.31958	+	1.31958i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.o.a.208.2		64
3.2	odd	2		153.2.n.a.106.15	yes	64
9.4	even	3	inner	459.2.o.a.361.15		64
9.5	odd	6		153.2.n.a.4.2	✓	64
17.13	even	4	inner	459.2.o.a.370.15		64
51.47	odd	4		153.2.n.a.115.2	yes	64
153.13	even	12	inner	459.2.o.a.64.2		64
153.149	odd	12		153.2.n.a.13.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.n.a.4.2	✓	64	9.5	odd	6
153.2.n.a.13.15	yes	64	153.149	odd	12
153.2.n.a.106.15	yes	64	3.2	odd	2
153.2.n.a.115.2	yes	64	51.47	odd	4
459.2.o.a.64.2		64	153.13	even	12	inner
459.2.o.a.208.2		64	1.1	even	1	trivial
459.2.o.a.361.15		64	9.4	even	3	inner
459.2.o.a.370.15		64	17.13	even	4	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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.07111 - 1.19576i) q^{2} +(1.85966 + 3.22103i) q^{4} +(0.854845 + 0.229055i) q^{5} +(-2.38596 + 0.639316i) q^{7} -4.11179i q^{8} +O(q^{10})\)	\(q+(-2.07111 - 1.19576i) q^{2} +(1.85966 + 3.22103i) q^{4} +(0.854845 + 0.229055i) q^{5} +(-2.38596 + 0.639316i) q^{7} -4.11179i q^{8} +(-1.49658 - 1.49658i) q^{10} +(2.06432 - 0.553133i) q^{11} +(0.147179 + 0.254921i) q^{13} +(5.70605 + 1.52893i) q^{14} +(-1.19737 + 2.07391i) q^{16} +(-3.94406 - 1.20183i) q^{17} +6.94854i q^{19} +(0.851931 + 3.17945i) q^{20} +(-4.93685 - 1.32282i) q^{22} +(-1.67723 + 6.25950i) q^{23} +(-3.65183 - 2.10839i) q^{25} -0.703959i q^{26} +(-6.49634 - 6.49634i) q^{28} +(0.853904 + 3.18681i) q^{29} +(3.61311 + 0.968131i) q^{31} +(-2.16206 + 1.24826i) q^{32} +(6.73149 + 7.20525i) q^{34} -2.18606 q^{35} +(-1.49781 + 1.49781i) q^{37} +(8.30876 - 14.3912i) q^{38} +(0.941827 - 3.51495i) q^{40} +(-1.90726 + 7.11801i) q^{41} +(9.64376 + 5.56783i) q^{43} +(5.62060 + 5.62060i) q^{44} +(10.9586 - 10.9586i) q^{46} +(3.03477 - 5.25638i) q^{47} +(-0.778101 + 0.449237i) q^{49} +(5.04223 + 8.73340i) q^{50} +(-0.547406 + 0.948134i) q^{52} +10.6130i q^{53} +1.89137 q^{55} +(2.62873 + 9.81057i) q^{56} +(2.04212 - 7.62130i) q^{58} +(5.41473 - 3.12619i) q^{59} +(9.22562 - 2.47200i) q^{61} +(-6.32551 - 6.32551i) q^{62} +10.7600 q^{64} +(0.0674240 + 0.251630i) q^{65} +(-0.110338 - 0.191110i) q^{67} +(-3.46350 - 14.9389i) q^{68} +(4.52758 + 2.61400i) q^{70} +(7.53881 - 7.53881i) q^{71} +(-9.37016 + 9.37016i) q^{73} +(4.89316 - 1.31112i) q^{74} +(-22.3815 + 12.9220i) q^{76} +(-4.57176 + 2.63951i) q^{77} +(-10.8493 + 2.90706i) q^{79} +(-1.49861 + 1.49861i) q^{80} +(12.4616 - 12.4616i) q^{82} +(-2.97094 - 1.71527i) q^{83} +(-3.09628 - 1.93078i) q^{85} +(-13.3155 - 23.0632i) q^{86} +(-2.27437 - 8.48806i) q^{88} -7.17123 q^{89} +(-0.514137 - 0.514137i) q^{91} +(-23.2811 + 6.23816i) q^{92} +(-12.5707 + 7.25769i) q^{94} +(-1.59160 + 5.93993i) q^{95} +(2.36860 + 8.83975i) q^{97} +2.14871 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 24 q^{4} + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 64 * q + 24 * q^4 + 2 * q^5 - 2 * q^7	\( 64 q + 24 q^{4} + 2 q^{5} - 2 q^{7} - 16 q^{10} - 4 q^{13} - 16 q^{16} + 8 q^{17} - 18 q^{20} - 4 q^{22} + 8 q^{23} + 10 q^{29} - 2 q^{31} + 20 q^{34} + 128 q^{35} - 8 q^{37} + 24 q^{38} - 20 q^{40} - 32 q^{41} - 20 q^{44} - 40 q^{46} + 64 q^{47} - 48 q^{50} + 36 q^{52} - 16 q^{55} - 12 q^{56} - 10 q^{58} - 2 q^{61} + 28 q^{62} - 8 q^{64} - 8 q^{65} - 4 q^{67} + 60 q^{68} + 84 q^{71} - 44 q^{73} + 14 q^{74} + 10 q^{79} - 204 q^{80} - 52 q^{82} + 22 q^{85} - 32 q^{86} + 16 q^{88} - 128 q^{89} + 44 q^{91} - 136 q^{92} - 4 q^{95} - 44 q^{97} - 208 q^{98}+O(q^{100}) \) 64 * q + 24 * q^4 + 2 * q^5 - 2 * q^7 - 16 * q^10 - 4 * q^13 - 16 * q^16 + 8 * q^17 - 18 * q^20 - 4 * q^22 + 8 * q^23 + 10 * q^29 - 2 * q^31 + 20 * q^34 + 128 * q^35 - 8 * q^37 + 24 * q^38 - 20 * q^40 - 32 * q^41 - 20 * q^44 - 40 * q^46 + 64 * q^47 - 48 * q^50 + 36 * q^52 - 16 * q^55 - 12 * q^56 - 10 * q^58 - 2 * q^61 + 28 * q^62 - 8 * q^64 - 8 * q^65 - 4 * q^67 + 60 * q^68 + 84 * q^71 - 44 * q^73 + 14 * q^74 + 10 * q^79 - 204 * q^80 - 52 * q^82 + 22 * q^85 - 32 * q^86 + 16 * q^88 - 128 * q^89 + 44 * q^91 - 136 * q^92 - 4 * q^95 - 44 * q^97 - 208 * q^98

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