LMFDB - Embedded newform 819.2.fm.g.496.3

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 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			496.3
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.g.748.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.112775 + 0.0302180i) q^{2} +(-1.72025 - 0.993184i) q^{4} +(-1.24841 - 1.24841i) q^{5} +(-2.63771 - 0.206123i) q^{7} +(-0.329103 - 0.329103i) q^{8} +O(q^{10})$	\(q+(0.112775 + 0.0302180i) q^{2} +(-1.72025 - 0.993184i) q^{4} +(-1.24841 - 1.24841i) q^{5} +(-2.63771 - 0.206123i) q^{7} +(-0.329103 - 0.329103i) q^{8} +(-0.103066 - 0.178515i) q^{10} +(0.506699 - 1.89103i) q^{11} +(1.85749 + 3.09026i) q^{13} +(-0.291240 - 0.102952i) q^{14} +(1.95920 + 3.39343i) q^{16} +(-2.13907 + 3.70498i) q^{17} +(-4.12248 + 1.10462i) q^{19} +(0.907674 + 3.38749i) q^{20} +(0.114286 - 0.197949i) q^{22} +(5.53927 - 3.19810i) q^{23} -1.88292i q^{25} +(0.116097 + 0.404635i) q^{26} +(4.33279 + 2.97431i) q^{28} +(3.57954 + 6.19995i) q^{29} +(3.02628 + 3.02628i) q^{31} +(0.359327 + 1.34103i) q^{32} +(-0.353191 + 0.353191i) q^{34} +(3.03563 + 3.55028i) q^{35} +(-0.732202 + 2.73261i) q^{37} -0.498293 q^{38} +0.821715i q^{40} +(-2.94901 + 11.0059i) q^{41} +(-1.55234 - 0.896243i) q^{43} +(-2.74978 + 2.74978i) q^{44} +(0.721333 - 0.193281i) q^{46} +(-4.68665 + 4.68665i) q^{47} +(6.91503 + 1.08738i) q^{49} +(0.0568982 - 0.212347i) q^{50} +(-0.126138 - 7.16084i) q^{52} -4.27793 q^{53} +(-2.99335 + 1.72821i) q^{55} +(0.800244 + 0.935915i) q^{56} +(0.216333 + 0.807367i) q^{58} +(-0.436704 - 1.62980i) q^{59} +(-2.66960 - 1.54129i) q^{61} +(0.249841 + 0.432737i) q^{62} -7.67470i q^{64} +(1.53901 - 6.17685i) q^{65} +(-0.0190380 - 0.00510122i) q^{67} +(7.35945 - 4.24898i) q^{68} +(0.235061 + 0.492115i) q^{70} +(-1.23109 - 4.59449i) q^{71} +(-0.698492 + 0.698492i) q^{73} +(-0.165148 + 0.286046i) q^{74} +(8.18877 + 2.19417i) q^{76} +(-1.72631 + 4.88353i) q^{77} -5.93719 q^{79} +(1.79052 - 6.68230i) q^{80} +(-0.665151 + 1.15208i) q^{82} +(9.87683 + 9.87683i) q^{83} +(7.29580 - 1.95490i) q^{85} +(-0.147983 - 0.147983i) q^{86} +(-0.789099 + 0.455587i) q^{88} +(-7.76240 - 2.07993i) q^{89} +(-4.26255 - 8.53409i) q^{91} -12.7052 q^{92} +(-0.670159 + 0.386917i) q^{94} +(6.52558 + 3.76755i) q^{95} +(-14.2676 + 3.82300i) q^{97} +(0.746985 + 0.331588i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

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 $

$2$	0.112775	+	0.0302180i	0.0797441	+	0.0213674i	0.298471	−	0.954419i	$-0.403524\pi$
$2$	0.112775	+	0.0302180i	0.0797441	+	0.0213674i	−0.218726	+	0.975786i	$0.570190\pi$
$3$		0			0
$3$		0			0
$4$	−1.72025	−	0.993184i	−0.860123	−	0.496592i
$5$	−1.24841	−	1.24841i	−0.558308	−	0.558308i	0.370518	−	0.928825i	$-0.379180\pi$
$5$	−1.24841	−	1.24841i	−0.558308	−	0.558308i	−0.928825	+	0.370518i	$0.879180\pi$
$6$		0			0
$7$	−2.63771	−	0.206123i	−0.996961	−	0.0779070i
$7$	−2.63771	−	0.206123i	−0.996961	−	0.0779070i
$8$	−0.329103	−	0.329103i	−0.116356	−	0.116356i
$9$		0			0
$10$	−0.103066	−	0.178515i	−0.0325922	−	0.0564514i
$11$	0.506699	−	1.89103i	0.152775	−	0.570166i	−0.846510	−	0.532373i	$-0.821301\pi$
$11$	0.506699	−	1.89103i	0.152775	−	0.570166i	0.999286	−	0.0377930i	$-0.0120328\pi$
$12$		0			0
$13$	1.85749	+	3.09026i	0.515175	+	0.857085i
$13$	1.85749	+	3.09026i	0.515175	+	0.857085i
$14$	−0.291240	−	0.102952i	−0.0778371	−	0.0275151i
$15$		0			0
$16$	1.95920	+	3.39343i	0.489800	+	0.848358i
$17$	−2.13907	+	3.70498i	−0.518801	+	0.898589i	0.480960	+	0.876742i	$0.340288\pi$
$17$	−2.13907	+	3.70498i	−0.518801	+	0.898589i	−0.999761	+	0.0218471i	$0.993045\pi$
$18$		0			0
$19$	−4.12248	+	1.10462i	−0.945762	+	0.253416i	−0.698563	−	0.715549i	$-0.746177\pi$
$19$	−4.12248	+	1.10462i	−0.945762	+	0.253416i	−0.247199	+	0.968965i	$0.579510\pi$
$20$	0.907674	+	3.38749i	0.202962	+	0.757465i
$21$		0			0
$22$	0.114286	−	0.197949i	0.0243659	−	0.0422030i
$23$	5.53927	−	3.19810i	1.15502	−	0.666850i	0.204913	−	0.978780i	$-0.434309\pi$
$23$	5.53927	−	3.19810i	1.15502	−	0.666850i	0.950105	+	0.311930i	$0.100976\pi$
$24$		0			0
$25$		−	1.88292i		−	0.376585i
$26$	0.116097	+	0.404635i	0.0227685	+	0.0793554i
$27$		0			0
$28$	4.33279	+	2.97431i	0.818821	+	0.562092i
$29$	3.57954	+	6.19995i	0.664704	+	1.15130i	0.979365	+	0.202097i	$0.0647758\pi$
$29$	3.57954	+	6.19995i	0.664704	+	1.15130i	−0.314661	+	0.949204i	$0.601891\pi$
$30$		0			0
$31$	3.02628	+	3.02628i	0.543535	+	0.543535i	0.924563	−	0.381028i	$-0.124430\pi$
$31$	3.02628	+	3.02628i	0.543535	+	0.543535i	−0.381028	+	0.924563i	$0.624430\pi$
$32$	0.359327	+	1.34103i	0.0635206	+	0.237062i
$33$		0			0
$34$	−0.353191	+	0.353191i	−0.0605718	+	0.0605718i
$35$	3.03563	+	3.55028i	0.513115	+	0.600107i
$36$		0			0
$37$	−0.732202	+	2.73261i	−0.120373	+	0.449239i	−0.999633	−	0.0271042i	$-0.991371\pi$
$37$	−0.732202	+	2.73261i	−0.120373	+	0.449239i	0.879259	+	0.476343i	$0.158038\pi$
$38$	−0.498293			−0.0808338
$39$		0			0
$40$			0.821715i			0.129925i
$41$	−2.94901	+	11.0059i	−0.460558	+	1.71883i	0.210654	+	0.977561i	$0.432441\pi$
$41$	−2.94901	+	11.0059i	−0.460558	+	1.71883i	−0.671212	+	0.741266i	$0.734226\pi$
$42$		0			0
$43$	−1.55234	−	0.896243i	−0.236730	−	0.136676i	0.376943	−	0.926236i	$-0.376975\pi$
$43$	−1.55234	−	0.896243i	−0.236730	−	0.136676i	−0.613673	+	0.789561i	$0.710309\pi$
$44$	−2.74978	+	2.74978i	−0.414545	+	0.414545i
$45$		0			0
$46$	0.721333	−	0.193281i	0.106355	−	0.0284977i
$47$	−4.68665	+	4.68665i	−0.683618	+	0.683618i	−0.960814	−	0.277196i	$-0.910595\pi$
$47$	−4.68665	+	4.68665i	−0.683618	+	0.683618i	0.277196	+	0.960814i	$0.410595\pi$
$48$		0			0
$49$	6.91503	+	1.08738i	0.987861	+	0.155340i
$50$	0.0568982	−	0.212347i	0.00804663	−	0.0300304i
$51$		0			0
$52$	−0.126138	−	7.16084i	−0.0174922	−	0.993030i
$53$	−4.27793			−0.587619			−0.293809	−	0.955864i	$-0.594923\pi$
$53$	−4.27793			−0.587619			−0.293809	+	0.955864i	$0.594923\pi$
$54$		0			0
$55$	−2.99335	+	1.72821i	−0.403624	+	0.233032i
$56$	0.800244	+	0.935915i	0.106937	+	0.125067i
$57$		0			0
$58$	0.216333	+	0.807367i	0.0284060	+	0.106013i
$59$	−0.436704	−	1.62980i	−0.0568541	−	0.212182i	0.931655	−	0.363344i	$-0.118365\pi$
$59$	−0.436704	−	1.62980i	−0.0568541	−	0.212182i	−0.988509	+	0.151162i	$0.951698\pi$
$60$		0			0
$61$	−2.66960	−	1.54129i	−0.341807	−	0.197342i	0.319264	−	0.947666i	$-0.396564\pi$
$61$	−2.66960	−	1.54129i	−0.341807	−	0.197342i	−0.661071	+	0.750323i	$0.729898\pi$
$62$	0.249841	+	0.432737i	0.0317298	+	0.0549577i
$63$		0			0
$64$		−	7.67470i		−	0.959338i
$65$	1.53901	−	6.17685i	0.190891	−	0.766144i
$66$		0			0
$67$	−0.0190380	−	0.00510122i	−0.00232586	−	0.000623213i	0.257656	−	0.966237i	$-0.417050\pi$
$67$	−0.0190380	−	0.00510122i	−0.00232586	−	0.000623213i	−0.259982	+	0.965614i	$0.583717\pi$
$68$	7.35945	−	4.24898i	0.892465	−	0.515265i
$69$		0			0
$70$	0.235061	+	0.492115i	0.0280952	+	0.0588189i
$71$	−1.23109	−	4.59449i	−0.146104	−	0.545266i	−0.999704	−	0.0243373i	$-0.992252\pi$
$71$	−1.23109	−	4.59449i	−0.146104	−	0.545266i	0.853600	−	0.520929i	$-0.174414\pi$
$72$		0			0
$73$	−0.698492	+	0.698492i	−0.0817523	+	0.0817523i	−0.746800	−	0.665048i	$-0.768411\pi$
$73$	−0.698492	+	0.698492i	−0.0817523	+	0.0817523i	0.665048	+	0.746800i	$0.268411\pi$
$74$	−0.165148	+	0.286046i	−0.0191981	+	0.0332521i
$75$		0			0
$76$	8.18877	+	2.19417i	0.939316	+	0.251689i
$77$	−1.72631	+	4.88353i	−0.196731	+	0.556530i
$78$		0			0
$79$	−5.93719			−0.667987			−0.333993	−	0.942575i	$-0.608396\pi$
$79$	−5.93719			−0.667987			−0.333993	+	0.942575i	$0.608396\pi$
$80$	1.79052	−	6.68230i	0.200186	−	0.747104i
$81$		0			0
$82$	−0.665151	+	1.15208i	−0.0734536	+	0.127225i
$83$	9.87683	+	9.87683i	1.08412	+	1.08412i	0.996120	+	0.0880033i	$0.0280486\pi$
$83$	9.87683	+	9.87683i	1.08412	+	1.08412i	0.0880033	+	0.996120i	$0.471951\pi$
$84$		0			0
$85$	7.29580	−	1.95490i	0.791340	−	0.212039i
$86$	−0.147983	−	0.147983i	−0.0159574	−	0.0159574i
$87$		0			0
$88$	−0.789099	+	0.455587i	−0.0841183	+	0.0485657i
$89$	−7.76240	−	2.07993i	−0.822813	−	0.220472i	−0.177237	−	0.984168i	$-0.556716\pi$
$89$	−7.76240	−	2.07993i	−0.822813	−	0.220472i	−0.645576	+	0.763696i	$0.723383\pi$
$90$		0			0
$91$	−4.26255	−	8.53409i	−0.446836	−	0.894616i
$92$	−12.7052			−1.32461
$93$		0			0
$94$	−0.670159	+	0.386917i	−0.0691216	+	0.0399074i
$95$	6.52558	+	3.76755i	0.669511	+	0.386542i
$96$		0			0
$97$	−14.2676	+	3.82300i	−1.44866	+	0.388167i	−0.895557	−	0.444946i	$-0.853223\pi$
$97$	−14.2676	+	3.82300i	−1.44866	+	0.388167i	−0.553102	+	0.833113i	$0.686556\pi$
$98$	0.746985	+	0.331588i	0.0754569	+	0.0334955i
$99$		0			0
$100$	−1.87009	+	3.23909i	−0.187009	+	0.323909i
$101$	−8.00479	−	13.8647i	−0.796506	−	1.37959i	−0.921878	−	0.387480i	$-0.873346\pi$
$101$	−8.00479	−	13.8647i	−0.796506	−	1.37959i	0.125372	−	0.992110i	$-0.459988\pi$
$102$		0			0
$103$	11.8151			1.16418			0.582088	−	0.813126i	$-0.302236\pi$
$103$	11.8151			1.16418			0.582088	+	0.813126i	$0.302236\pi$
$104$	0.405710	−	1.62832i	0.0397831	−	0.159670i
$105$		0			0
$106$	−0.482444	−	0.129271i	−0.0468591	−	0.0125559i
$107$	3.99556	+	6.92051i	0.386265	+	0.669031i	0.991944	−	0.126678i	$-0.0404316\pi$
$107$	3.99556	+	6.92051i	0.386265	+	0.669031i	−0.605679	+	0.795709i	$0.707098\pi$
$108$		0			0
$109$	−8.75647	+	8.75647i	−0.838718	+	0.838718i	−0.988690	−	0.149972i	$-0.952082\pi$
$109$	−8.75647	+	8.75647i	−0.838718	+	0.838718i	0.149972	+	0.988690i	$0.452082\pi$
$110$	−0.389799	+	0.104446i	−0.0371659	+	0.00995857i
$111$		0			0
$112$	−4.46833	−	9.35472i	−0.422218	−	0.883938i
$113$	−4.27217	+	7.39961i	−0.401892	+	0.696097i	−0.993954	−	0.109795i	$-0.964981\pi$
$113$	−4.27217	+	7.39961i	−0.401892	+	0.696097i	0.592063	+	0.805892i	$0.298314\pi$
$114$		0			0
$115$	−10.9079	−	2.92275i	−1.01716	−	0.272548i
$116$		−	14.2206i		−	1.32035i
$117$		0			0
$118$		−	0.196998i		−	0.0181351i
$119$	6.40593	−	9.33175i	0.587230	−	0.855440i
$120$		0			0
$121$	6.20705	+	3.58364i	0.564277	+	0.325785i
$122$	−0.254490	−	0.254490i	−0.0230404	−	0.0230404i
$123$		0			0
$124$	−2.20029	−	8.21159i	−0.197592	−	0.737422i
$125$	−8.59274	+	8.59274i	−0.768558	+	0.768558i
$126$		0			0
$127$	−5.29483	+	3.05697i	−0.469840	+	0.271262i	−0.716173	−	0.697923i	$-0.754108\pi$
$127$	−5.29483	+	3.05697i	−0.469840	+	0.271262i	0.246333	+	0.969185i	$0.420774\pi$
$128$	0.950568	−	3.54757i	0.0840191	−	0.313564i
$129$		0			0
$130$	0.360215	−	0.650090i	0.0315929	−	0.0570166i
$131$		−	5.76435i		−	0.503634i	−0.967775	−	0.251817i	$-0.918972\pi$
$131$		−	5.76435i		−	0.503634i	0.967775	−	0.251817i	$-0.0810280\pi$
$132$		0			0
$133$	11.1016	−	2.06392i	0.962630	−	0.178964i
$134$	−0.00199287	−	0.00115058i	−0.000172157	−	9.93951e-5i
$135$		0			0
$136$	1.92330	−	0.515346i	0.164921	−	0.0441905i
$137$	6.06188	−	1.62427i	0.517901	−	0.138771i	0.00960548	−	0.999954i	$-0.496942\pi$
$137$	6.06188	−	1.62427i	0.517901	−	0.138771i	0.508296	+	0.861183i	$0.330276\pi$
$138$		0			0
$139$	18.1314	+	10.4682i	1.53789	+	0.887900i	0.998962	+	0.0455477i	$0.0145033\pi$
$139$	18.1314	+	10.4682i	1.53789	+	0.887900i	0.538927	+	0.842353i	$0.318830\pi$
$140$	−1.69594	−	9.12229i	−0.143333	−	0.770975i
$141$		0			0
$142$		−	0.555346i		−	0.0466036i
$143$	6.78495	−	1.94673i	0.567386	−	0.162794i
$144$		0			0
$145$	3.27135	−	12.2089i	0.271671	−	1.01389i
$146$	−0.0998797	+	0.0576656i	−0.00826610	+	0.00477244i
$147$		0			0
$148$	3.97356	−	3.97356i	0.326624	−	0.326624i
$149$	−4.00070	−	14.9308i	−0.327750	−	1.22318i	−0.911518	−	0.411260i	$-0.865089\pi$
$149$	−4.00070	−	14.9308i	−0.327750	−	1.22318i	0.583768	−	0.811921i	$-0.301578\pi$
$150$		0			0
$151$	3.12599	+	3.12599i	0.254390	+	0.254390i	0.822768	−	0.568378i	$-0.192429\pi$
$151$	3.12599	+	3.12599i	0.254390	+	0.254390i	−0.568378	+	0.822768i	$0.692429\pi$
$152$	1.72026	+	0.993190i	0.139531	+	0.0805583i
$153$		0			0
$154$	−0.342256	+	0.498576i	−0.0275797	+	0.0401764i
$155$		−	7.55609i		−	0.606920i
$156$		0			0
$157$			6.93064i			0.553125i	0.960996	+	0.276563i	$0.0891953\pi$
$157$			6.93064i			0.553125i	−0.960996	+	0.276563i	$0.910805\pi$
$158$	−0.669569	−	0.179410i	−0.0532680	−	0.0142731i
$159$		0			0
$160$	1.22557	−	2.12274i	0.0968896	−	0.167818i
$161$	−15.2702	+	7.29389i	−1.20346	+	0.574839i
$162$		0			0
$163$	−12.4944	+	3.34785i	−0.978634	+	0.262224i	−0.712469	−	0.701703i	$-0.752423\pi$
$163$	−12.4944	+	3.34785i	−0.978634	+	0.262224i	−0.266165	+	0.963928i	$0.585757\pi$
$164$	16.0039	−	16.0039i	1.24969	−	1.24969i
$165$		0			0
$166$	0.815404	+	1.41232i	0.0632876	+	0.109617i
$167$	−0.900490	−	0.241286i	−0.0696820	−	0.0186712i	0.223810	−	0.974633i	$-0.428151\pi$
$167$	−0.900490	−	0.241286i	−0.0696820	−	0.0186712i	−0.293492	+	0.955962i	$0.594817\pi$
$168$		0			0
$169$	−6.09946	+	11.4803i	−0.469189	+	0.883098i
$170$	0.881858			0.0676355
$171$		0			0
$172$	1.78027	+	3.08352i	0.135744	+	0.235116i
$173$	−0.263780	+	0.456880i	−0.0200548	+	0.0347360i	−0.875879	−	0.482531i	$-0.839717\pi$
$173$	−0.263780	+	0.456880i	−0.0200548	+	0.0347360i	0.855824	+	0.517267i	$0.173051\pi$
$174$		0			0
$175$	−0.388113	+	4.96660i	−0.0293386	+	0.375440i
$176$	7.40979	−	1.98545i	0.558534	−	0.149659i
$177$		0			0
$178$	−0.812555	−	0.469129i	−0.0609036	−	0.0351627i
$179$	−7.16206	+	4.13502i	−0.535317	+	0.309066i	−0.743179	−	0.669093i	$-0.766683\pi$
$179$	−7.16206	+	4.13502i	−0.535317	+	0.309066i	0.207862	+	0.978158i	$0.433350\pi$
$180$		0			0
$181$	−14.9785			−1.11334			−0.556672	−	0.830732i	$-0.687922\pi$
$181$	−14.9785			−1.11334			−0.556672	+	0.830732i	$0.687922\pi$
$182$	−0.222826	−	1.09124i	−0.0165170	−	0.0808881i
$183$		0			0
$184$	−2.87550	−	0.770488i	−0.211985	−	0.0568011i
$185$	4.32553	−	2.49734i	0.318019	−	0.183608i
$186$		0			0
$187$	5.92234	+	5.92234i	0.433085	+	0.433085i
$188$	12.7169	−	3.40748i	0.927475	−	0.248516i
$189$		0			0
$190$	0.622076	+	0.622076i	0.0451301	+	0.0451301i
$191$	−7.26461	+	12.5827i	−0.525649	+	0.910450i	0.473905	+	0.880576i	$0.342844\pi$
$191$	−7.26461	+	12.5827i	−0.525649	+	0.910450i	−0.999554	+	0.0298741i	$0.990489\pi$
$192$		0			0
$193$	5.06711	−	18.9107i	0.364738	−	1.36122i	−0.503037	−	0.864265i	$-0.667784\pi$
$193$	5.06711	−	18.9107i	0.364738	−	1.36122i	0.867775	−	0.496957i	$-0.165549\pi$
$194$	−1.72456			−0.123816
$195$		0			0
$196$	−10.8156	−	8.73846i	−0.772541	−	0.624176i
$197$	21.0175	+	5.63163i	1.49744	+	0.401237i	0.912240	−	0.409655i	$-0.134351\pi$
$197$	21.0175	+	5.63163i	1.49744	+	0.401237i	0.585196	+	0.810892i	$0.301018\pi$
$198$		0			0
$199$	9.64065	−	16.6981i	0.683408	−	1.18370i	−0.290527	−	0.956867i	$-0.593830\pi$
$199$	9.64065	−	16.6981i	0.683408	−	1.18370i	0.973934	−	0.226830i	$-0.0728362\pi$
$200$	−0.619676	+	0.619676i	−0.0438177	+	0.0438177i
$201$		0			0
$202$	−0.483778	−	1.80548i	−0.0340385	−	0.127033i
$203$	−8.16384	−	17.0915i	−0.572989	−	1.19959i
$204$		0			0
$205$	17.4215	−	10.0583i	1.21677	−	0.702501i
$206$	1.33245	+	0.357029i	0.0928363	+	0.0248754i
$207$		0			0
$208$	−6.84741	+	12.3577i	−0.474782	+	0.856853i
$209$			8.35542i			0.577957i
$210$		0			0
$211$	1.51130	+	2.61764i	0.104042	+	0.180206i	0.913346	−	0.407184i	$-0.133489\pi$
$211$	1.51130	+	2.61764i	0.104042	+	0.180206i	−0.809304	+	0.587389i	$0.800156\pi$
$212$	7.35909	+	4.24877i	0.505424	+	0.291807i
$213$		0			0
$214$	0.241476	+	0.901200i	0.0165070	+	0.0616048i
$215$	0.819079	+	3.05685i	0.0558607	+	0.208475i
$216$		0			0
$217$	−7.35865	−	8.60622i	−0.499538	−	0.584228i
$218$	−1.25212	+	0.722910i	−0.0848040	+	0.0489616i
$219$		0			0
$220$	6.86574			0.462888
$221$	−15.4227	+	0.271670i	−1.03744	+	0.0182745i
$222$		0			0
$223$	−1.13865	+	4.24949i	−0.0762495	+	0.284567i	−0.993514	−	0.113712i	$-0.963726\pi$
$223$	−1.13865	+	4.24949i	−0.0762495	+	0.284567i	0.917264	+	0.398279i	$0.130392\pi$
$224$	−0.671384	−	3.61130i	−0.0448587	−	0.241290i
$225$		0			0
$226$	−0.705396	+	0.705396i	−0.0469223	+	0.0469223i
$227$	−3.95917	+	1.06086i	−0.262780	+	0.0704116i	−0.387803	−	0.921742i	$-0.626766\pi$
$227$	−3.95917	+	1.06086i	−0.262780	+	0.0704116i	0.125024	+	0.992154i	$0.460099\pi$
$228$		0			0
$229$	−9.60039	+	9.60039i	−0.634412	+	0.634412i	−0.949171	−	0.314760i	$-0.898076\pi$
$229$	−9.60039	+	9.60039i	−0.634412	+	0.634412i	0.314760	+	0.949171i	$0.398076\pi$
$230$	−1.14182	−	0.659228i	−0.0752892	−	0.0434682i
$231$		0			0
$232$	0.862385	−	3.21846i	0.0566183	−	0.211303i
$233$		−	16.3500i		−	1.07113i	−0.844495	−	0.535563i	$-0.820100\pi$
$233$		−	16.3500i		−	1.07113i	0.844495	−	0.535563i	$-0.179900\pi$
$234$		0			0
$235$	11.7018			0.763339
$236$	−0.867456	+	3.23739i	−0.0564666	+	0.210736i
$237$		0			0
$238$	1.00442	−	0.858816i	0.0651067	−	0.0556688i
$239$	−6.11495	+	6.11495i	−0.395543	+	0.395543i	−0.876658	−	0.481115i	$-0.840232\pi$
$239$	−6.11495	+	6.11495i	−0.395543	+	0.395543i	0.481115	+	0.876658i	$0.340232\pi$
$240$		0			0
$241$	−3.47625	−	12.9736i	−0.223925	−	0.835700i	−0.982832	−	0.184501i	$-0.940933\pi$
$241$	−3.47625	−	12.9736i	−0.223925	−	0.835700i	0.758907	−	0.651199i	$-0.225734\pi$
$242$	0.591711	+	0.591711i	0.0380366	+	0.0380366i
$243$		0			0
$244$	3.06158	+	5.30281i	0.195997	+	0.339478i
$245$	−7.27531	−	9.99032i	−0.464803	−	0.638258i
$246$		0			0
$247$	−11.0710	−	10.6877i	−0.704432	−	0.680045i
$248$		−	1.99192i		−	0.126487i
$249$		0			0
$250$	−1.22870	+	0.709393i	−0.0777101	+	0.0448659i
$251$	−1.74301	+	3.01899i	−0.110018	+	0.190557i	−0.915777	−	0.401686i	$-0.868424\pi$
$251$	−1.74301	+	3.01899i	−0.110018	+	0.190557i	0.805759	+	0.592243i	$0.201758\pi$
$252$		0			0
$253$	−3.24095	−	12.0954i	−0.203756	−	0.760430i
$254$	−0.689501	+	0.184751i	−0.0432631	+	0.0115923i
$255$		0			0
$256$	−7.46030	+	12.9216i	−0.466269	+	0.807601i
$257$	6.72396	+	11.6462i	0.419429	+	0.726472i	0.995882	−	0.0906578i	$-0.0288970\pi$
$257$	6.72396	+	11.6462i	0.419429	+	0.726472i	−0.576453	+	0.817130i	$0.695564\pi$
$258$		0			0
$259$	2.49459	−	7.05692i	0.155006	−	0.438496i
$260$	−8.78223	+	9.09717i	−0.544651	+	0.564183i
$261$		0			0
$262$	0.174187	−	0.650076i	0.0107613	−	0.0401618i
$263$	10.2679	+	17.7846i	0.633147	+	1.09664i	0.986904	+	0.161306i	$0.0515705\pi$
$263$	10.2679	+	17.7846i	0.633147	+	1.09664i	−0.353757	+	0.935337i	$0.615096\pi$
$264$		0			0
$265$	5.34063	+	5.34063i	0.328072	+	0.328072i
$266$	1.31435	+	0.102709i	0.0805881	+	0.00629752i
$267$		0			0
$268$	0.0276836	+	0.0276836i	0.00169104	+	0.00169104i
$269$	−9.29875	−	5.36864i	−0.566955	−	0.327332i	0.188977	−	0.981981i	$-0.439483\pi$
$269$	−9.29875	−	5.36864i	−0.566955	−	0.327332i	−0.755932	+	0.654650i	$0.772816\pi$
$270$		0			0
$271$	1.44767	+	0.387901i	0.0879396	+	0.0235633i	0.302521	−	0.953143i	$-0.402172\pi$
$271$	1.44767	+	0.387901i	0.0879396	+	0.0235633i	−0.214581	+	0.976706i	$0.568839\pi$
$272$	−16.7635			−1.01643
$273$		0			0
$274$	0.732712			0.0442647
$275$	−3.56065	−	0.954075i	−0.214716	−	0.0575329i
$276$		0			0
$277$	4.07919	+	2.35512i	0.245095	+	0.141506i	0.617516	−	0.786558i	$-0.288139\pi$
$277$	4.07919	+	2.35512i	0.245095	+	0.141506i	−0.372421	+	0.928064i	$0.621472\pi$
$278$	1.72845	+	1.72845i	0.103666	+	0.103666i
$279$		0			0
$280$	0.169374	−	2.16745i	0.0101220	−	0.129530i
$281$	−8.01227	−	8.01227i	−0.477972	−	0.477972i	0.426511	−	0.904483i	$-0.359743\pi$
$281$	−8.01227	−	8.01227i	−0.477972	−	0.477972i	−0.904483	+	0.426511i	$0.859743\pi$
$282$		0			0
$283$	3.93934	+	6.82313i	0.234169	+	0.405593i	0.959031	−	0.283301i	$-0.0914297\pi$
$283$	3.93934	+	6.82313i	0.234169	+	0.405593i	−0.724862	+	0.688894i	$0.758096\pi$
$284$	−2.44540	+	9.12636i	−0.145108	+	0.541550i
$285$		0			0
$286$	0.824001	−	0.0145147i	0.0487242	−	0.000858275i
$287$	10.0472	−	28.4224i	0.593067	−	1.67772i
$288$		0			0
$289$	−0.651246	−	1.12799i	−0.0383086	−	0.0663525i
$290$	0.737855	−	1.27800i	0.0433284	−	0.0750469i
$291$		0			0
$292$	1.89531	−	0.507847i	0.110915	−	0.0297195i
$293$	3.16216	+	11.8013i	0.184735	+	0.689442i	0.994687	+	0.102945i	$0.0328267\pi$
$293$	3.16216	+	11.8013i	0.184735	+	0.689442i	−0.809952	+	0.586497i	$0.800507\pi$
$294$		0			0
$295$	−1.48948	+	2.57986i	−0.0867210	+	0.150205i
$296$	1.14028	−	0.658343i	0.0662776	−	0.0382654i
$297$		0			0
$298$		−	1.80472i		−	0.104545i
$299$	20.1721	+	11.1774i	1.16658	+	0.646404i
$300$		0			0
$301$	3.90988	+	2.68400i	0.225362	+	0.154703i
$302$	0.258073	+	0.446996i	0.0148504	+	0.0257217i
$303$		0			0
$304$	−11.8252	−	11.8252i	−0.678221	−	0.678221i
$305$	1.40859	+	5.25694i	0.0806558	+	0.301011i
$306$		0			0
$307$	7.97207	−	7.97207i	0.454990	−	0.454990i	−0.442017	−	0.897007i	$-0.645737\pi$
$307$	7.97207	−	7.97207i	0.454990	−	0.454990i	0.897007	+	0.442017i	$0.145737\pi$
$308$	7.81992	−	6.68634i	0.445581	−	0.380989i
$309$		0			0
$310$	0.228330	−	0.852140i	0.0129683	−	0.0483983i
$311$	−13.0428			−0.739588			−0.369794	−	0.929114i	$-0.620572\pi$
$311$	−13.0428			−0.739588			−0.369794	+	0.929114i	$0.620572\pi$
$312$		0			0
$313$		−	3.57391i		−	0.202009i	−0.994886	−	0.101005i	$-0.967794\pi$
$313$		−	3.57391i		−	0.202009i	0.994886	−	0.101005i	$-0.0322057\pi$
$314$	−0.209430	+	0.781604i	−0.0118188	+	0.0441085i
$315$		0			0
$316$	10.2134	+	5.89673i	0.574551	+	0.331717i
$317$	−23.4565	+	23.4565i	−1.31745	+	1.31745i	−0.401662	+	0.915788i	$0.631567\pi$
$317$	−23.4565	+	23.4565i	−1.31745	+	1.31745i	−0.915788	+	0.401662i	$0.868433\pi$
$318$		0			0
$319$	13.5380	−	3.62750i	0.757983	−	0.203101i
$320$	−9.58121	+	9.58121i	−0.535606	+	0.535606i
$321$		0			0
$322$	−1.94251	+	0.361135i	−0.108252	+	0.0201253i
$323$	4.72570	−	17.6366i	0.262945	−	0.981324i
$324$		0			0
$325$	5.81873	−	3.49751i	0.322765	−	0.194007i
$326$	−1.51022			−0.0836434
$327$		0			0
$328$	4.59260	−	2.65154i	0.253584	−	0.146407i
$329$	13.3280	−	11.3960i	0.734799	−	0.628282i
$330$		0			0
$331$	−0.245395	−	0.915826i	−0.0134881	−	0.0503383i	0.958854	−	0.283900i	$-0.0916285\pi$
$331$	−0.245395	−	0.915826i	−0.0134881	−	0.0503383i	−0.972342	+	0.233562i	$0.924962\pi$
$332$	−7.18106	−	26.8001i	−0.394112	−	1.47085i
$333$		0			0
$334$	−0.0942618	−	0.0544221i	−0.00515778	−	0.00297784i
$335$	0.0173989	+	0.0301357i	0.000950602	+	0.00164649i
$336$		0			0
$337$			14.1901i			0.772982i	0.922293	+	0.386491i	$0.126313\pi$
$337$			14.1901i			0.772982i	−0.922293	+	0.386491i	$0.873687\pi$
$338$	−1.03478	+	1.11038i	−0.0562846	+	0.0603965i
$339$		0			0
$340$	−14.4921	−	3.88316i	−0.785947	−	0.210594i
$341$	7.25617	−	4.18935i	0.392944	−	0.226866i
$342$		0			0
$343$	−18.0157	−	4.29355i	−0.972756	−	0.231830i
$344$	0.215923	+	0.805837i	0.0116418	+	0.0434478i
$345$		0			0
$346$	−0.0435539	+	0.0435539i	−0.00234147	+	0.00234147i
$347$	6.92103	−	11.9876i	0.371540	−	0.643527i	−0.618262	−	0.785972i	$-0.712163\pi$
$347$	6.92103	−	11.9876i	0.371540	−	0.643527i	0.989803	+	0.142445i	$0.0454965\pi$
$348$		0			0
$349$	−14.7875	−	3.96231i	−0.791559	−	0.212098i	−0.159684	−	0.987168i	$-0.551048\pi$
$349$	−14.7875	−	3.96231i	−0.791559	−	0.212098i	−0.631875	+	0.775071i	$0.717714\pi$
$350$	−0.193851	+	0.548382i	−0.0103617	+	0.0293123i
$351$		0			0
$352$	2.71798			0.144869
$353$	−4.07649	+	15.2137i	−0.216970	+	0.809742i	0.768494	+	0.639857i	$0.221006\pi$
$353$	−4.07649	+	15.2137i	−0.216970	+	0.809742i	−0.985464	+	0.169885i	$0.945660\pi$
$354$		0			0
$355$	−4.19892	+	7.27274i	−0.222856	+	0.385997i
$356$	11.2875	+	11.2875i	0.598235	+	0.598235i
$357$		0			0
$358$	−0.932655	+	0.249904i	−0.0492924	+	0.0132078i
$359$	4.68787	+	4.68787i	0.247416	+	0.247416i	0.819910	−	0.572493i	$-0.194024\pi$
$359$	4.68787	+	4.68787i	0.247416	+	0.247416i	−0.572493	+	0.819910i	$0.694024\pi$
$360$		0			0
$361$	−0.679814	+	0.392491i	−0.0357797	+	0.0206574i
$362$	−1.68920	−	0.452621i	−0.0887826	−	0.0237892i
$363$		0			0
$364$	−1.14330	+	18.9142i	−0.0599250	+	0.991375i
$365$	1.74402			0.0912859
$366$		0			0
$367$	−28.4547	+	16.4284i	−1.48533	+	0.857553i	−0.999860	−	0.0167033i	$-0.994683\pi$
$367$	−28.4547	+	16.4284i	−1.48533	+	0.857553i	−0.485465	+	0.874256i	$0.661350\pi$
$368$	21.7051	+	12.5314i	1.13145	+	0.653246i
$369$		0			0
$370$	0.563277	−	0.150930i	0.0292834	−	0.00784646i
$371$	11.2839	+	0.881778i	0.585833	+	0.0457796i
$372$		0			0
$373$	−3.93986	+	6.82405i	−0.203998	+	0.353336i	−0.949813	−	0.312818i	$-0.898727\pi$
$373$	−3.93986	+	6.82405i	−0.203998	+	0.353336i	0.745815	+	0.666153i	$0.232060\pi$
$374$	0.488932	+	0.846855i	0.0252821	+	0.0437899i
$375$		0			0
$376$	3.08478			0.159086
$377$	−12.5105	+	22.5781i	−0.644324	+	1.16283i
$378$		0			0
$379$	10.8095	+	2.89639i	0.555245	+	0.148778i	0.525521	−	0.850781i	$-0.323870\pi$
$379$	10.8095	+	2.89639i	0.555245	+	0.148778i	0.0297243	+	0.999558i	$0.490537\pi$
$380$	−7.48374	−	12.9622i	−0.383908	−	0.664947i
$381$		0			0
$382$	−1.19949	+	1.19949i	−0.0613713	+	0.0613713i
$383$	2.32841	−	0.623897i	0.118976	−	0.0318796i	−0.198840	−	0.980032i	$-0.563717\pi$
$383$	2.32841	−	0.623897i	0.118976	−	0.0318796i	0.317816	+	0.948152i	$0.397051\pi$
$384$		0			0
$385$	8.25182	−	3.94153i	0.420552	−	0.200879i
$386$	1.14289	−	1.97954i	0.0581715	−	0.100756i
$387$		0			0
$388$	28.3408	+	7.59389i	1.43879	+	0.385522i
$389$		−	16.8210i		−	0.852858i	−0.904521	−	0.426429i	$-0.859771\pi$
$389$		−	16.8210i		−	0.852858i	0.904521	−	0.426429i	$-0.140229\pi$
$390$		0			0
$391$			27.3638i			1.38385i
$392$	−1.91790	−	2.63362i	−0.0968685	−	0.133018i
$393$		0			0
$394$	2.20008	+	1.27022i	0.110838	+	0.0639926i
$395$	7.41208	+	7.41208i	0.372942	+	0.372942i
$396$		0			0
$397$	6.08873	+	22.7234i	0.305585	+	1.14046i	0.932441	+	0.361322i	$0.117675\pi$
$397$	6.08873	+	22.7234i	0.305585	+	1.14046i	−0.626856	+	0.779135i	$0.715659\pi$
$398$	1.59181	−	1.59181i	0.0797903	−	0.0797903i
$399$		0			0
$400$	6.38957	−	3.68902i	0.319479	−	0.184451i
$401$	−2.23318	+	8.33434i	−0.111520	+	0.416197i	−0.999003	−	0.0446427i	$-0.985785\pi$
$401$	−2.23318	+	8.33434i	−0.111520	+	0.416197i	0.887483	+	0.460840i	$0.152452\pi$
$402$		0			0
$403$	−3.73071	+	14.9733i	−0.185840	+	0.745872i
$404$			31.8009i			1.58216i
$405$		0			0
$406$	−0.404208	−	2.17419i	−0.0200605	−	0.107903i
$407$	4.79644	+	2.76922i	0.237751	+	0.137265i
$408$		0			0
$409$	12.9780	−	3.47744i	0.641720	−	0.171948i	0.0767375	−	0.997051i	$-0.475550\pi$
$409$	12.9780	−	3.47744i	0.641720	−	0.171948i	0.564982	+	0.825103i	$0.308883\pi$
$410$	2.26865	−	0.607883i	0.112041	−	0.0300212i
$411$		0			0
$412$	−20.3249	−	11.7346i	−1.00133	−	0.578121i
$413$	0.815960	+	4.38896i	0.0401508	+	0.215967i
$414$		0			0
$415$		−	24.6608i		−	1.21055i
$416$	−3.47668	+	3.60136i	−0.170458	+	0.176571i
$417$		0			0
$418$	−0.252484	+	0.942285i	−0.0123494	+	0.0460886i
$419$	−15.0514	+	8.68991i	−0.735308	+	0.424530i	−0.820361	−	0.571846i	$-0.806227\pi$
$419$	−15.0514	+	8.68991i	−0.735308	+	0.424530i	0.0850532	+	0.996376i	$0.472894\pi$
$420$		0			0
$421$	−21.2490	+	21.2490i	−1.03561	+	1.03561i	−0.0362722	+	0.999342i	$0.511548\pi$
$421$	−21.2490	+	21.2490i	−1.03561	+	1.03561i	−0.999342	+	0.0362722i	$0.988452\pi$
$422$	0.0913368	+	0.340874i	0.00444621	+	0.0165935i
$423$		0			0
$424$	1.40788	+	1.40788i	0.0683727	+	0.0683727i
$425$	6.97619	+	4.02771i	0.338395	+	0.195372i
$426$		0			0
$427$	6.72393	+	4.61575i	0.325394	+	0.223372i
$428$		−	15.8733i		−	0.767265i
$429$		0			0
$430$			0.369487i			0.0178183i
$431$	−23.3087	−	6.24554i	−1.12274	−	0.300837i	−0.350748	−	0.936470i	$-0.614073\pi$
$431$	−23.3087	−	6.24554i	−1.12274	−	0.300837i	−0.771991	+	0.635633i	$0.780739\pi$
$432$		0			0
$433$	2.27124	−	3.93391i	0.109149	−	0.189051i	−0.806277	−	0.591538i	$-0.798521\pi$
$433$	2.27124	−	3.93391i	0.109149	−	0.189051i	0.915426	+	0.402487i	$0.131854\pi$
$434$	−0.569811	−	1.19293i	−0.0273518	−	0.0572626i
$435$		0			0
$436$	23.7601	−	6.36649i	1.13790	−	0.304900i
$437$	−19.3029	+	19.3029i	−0.923381	+	0.923381i
$438$		0			0
$439$	−8.50036	−	14.7231i	−0.405700	−	0.702693i	0.588703	−	0.808350i	$-0.299639\pi$
$439$	−8.50036	−	14.7231i	−0.405700	−	0.702693i	−0.994403	+	0.105657i	$0.966306\pi$
$440$	1.55388	+	0.416362i	0.0740785	+	0.0198493i
$441$		0			0
$442$	−1.74750	−	0.435405i	−0.0831203	−	0.0207101i
$443$	36.6165			1.73970			0.869851	−	0.493315i	$-0.164215\pi$
$443$	36.6165			1.73970			0.869851	+	0.493315i	$0.164215\pi$
$444$		0			0
$445$	7.09408	+	12.2873i	0.336292	+	0.582474i
$446$	−0.256823	+	0.444830i	−0.0121609	+	0.0210633i
$447$		0			0
$448$	−1.58193	+	20.2436i	−0.0747392	+	0.956422i
$449$	32.7480	−	8.77481i	1.54547	−	0.414109i	0.617445	−	0.786614i	$-0.288168\pi$
$449$	32.7480	−	8.77481i	1.54547	−	0.414109i	0.928030	+	0.372505i	$0.121501\pi$
$450$		0			0
$451$	19.3181	+	11.1533i	0.909654	+	0.525189i
$452$	14.6984	−	8.48610i	0.691353	−	0.399153i
$453$		0			0
$454$	−0.478554			−0.0224596
$455$	−5.33266	+	15.9755i	−0.249999	+	0.748943i
$456$		0			0
$457$	−2.18565	−	0.585644i	−0.102241	−	0.0273953i	0.207336	−	0.978270i	$-0.433521\pi$
$457$	−2.18565	−	0.585644i	−0.102241	−	0.0273953i	−0.309577	+	0.950874i	$0.600187\pi$
$458$	−1.37279	+	0.792582i	−0.0641463	+	0.0370349i
$459$		0			0
$460$	15.8614	+	15.8614i	0.739540	+	0.739540i
$461$	−24.5455	+	6.57694i	−1.14320	+	0.306319i	−0.780235	−	0.625486i	$-0.784901\pi$
$461$	−24.5455	+	6.57694i	−1.14320	+	0.306319i	−0.362961	+	0.931804i	$0.618234\pi$
$462$		0			0
$463$	−22.6265	−	22.6265i	−1.05154	−	1.05154i	−0.998597	−	0.0529442i	$-0.983139\pi$
$463$	−22.6265	−	22.6265i	−1.05154	−	1.05154i	−0.0529442	−	0.998597i	$-0.516861\pi$
$464$	−14.0261	+	24.2939i	−0.651144	+	1.12781i
$465$		0			0
$466$	0.494066	−	1.84388i	0.0228871	−	0.0854160i
$467$	−11.2941			−0.522627			−0.261314	−	0.965254i	$-0.584156\pi$
$467$	−11.2941			−0.522627			−0.261314	+	0.965254i	$0.584156\pi$
$468$		0			0
$469$	0.0491652	+	0.0173797i	0.00227024	+	0.000802520i
$470$	1.31967	+	0.353604i	0.0608718	+	0.0163105i
$471$		0			0
$472$	−0.392653	+	0.680095i	−0.0180733	+	0.0313039i
$473$	−2.48139	+	2.48139i	−0.114094	+	0.114094i
$474$		0			0
$475$	2.07991	+	7.76231i	0.0954326	+	0.356159i
$476$	−20.2879	+	9.69063i	−0.929895	+	0.444169i
$477$		0			0
$478$	−0.874396	+	0.504833i	−0.0399939	+	0.0230905i
$479$	19.3716	+	5.19059i	0.885109	+	0.237164i	0.672610	−	0.739997i	$-0.265173\pi$
$479$	19.3716	+	5.19059i	0.885109	+	0.237164i	0.212499	+	0.977161i	$0.431840\pi$
$480$		0			0
$481$	−9.80456	+	2.81311i	−0.447049	+	0.128267i
$482$		−	1.56814i		−	0.0714269i
$483$		0			0
$484$	−7.11843	−	12.3295i	−0.323565	−	0.560431i
$485$	22.5846	+	13.0392i	1.02551	+	0.592081i
$486$		0			0
$487$	−8.13109	−	30.3456i	−0.368455	−	1.37509i	−0.862676	−	0.505756i	$-0.831213\pi$
$487$	−8.13109	−	30.3456i	−0.368455	−	1.37509i	0.494221	−	0.869336i	$-0.335453\pi$
$488$	0.371329	+	1.38582i	0.0168093	+	0.0627331i
$489$		0			0
$490$	−0.518587	−	1.34651i	−0.0234274	−	0.0608290i
$491$	16.8341	−	9.71919i	0.759714	−	0.438621i	−0.0694792	−	0.997583i	$-0.522134\pi$
$491$	16.8341	−	9.71919i	0.759714	−	0.438621i	0.829193	+	0.558962i	$0.188800\pi$
$492$		0			0
$493$	−30.6276			−1.37940
$494$	−0.925574	−	1.53986i	−0.0416436	−	0.0692814i
$495$		0			0
$496$	−4.34038	+	16.1985i	−0.194889	+	0.727336i
$497$	2.30023	+	12.3727i	0.103179	+	0.554991i
$498$		0			0
$499$	11.8051	−	11.8051i	0.528471	−	0.528471i	−0.391645	−	0.920116i	$-0.628094\pi$
$499$	11.8051	−	11.8051i	0.528471	−	0.528471i	0.920116	+	0.391645i	$0.128094\pi$
$500$	23.3158	−	6.24745i	1.04271	−	0.279394i
$501$		0			0
$502$	−0.287797	+	0.287797i	−0.0128450	+	0.0128450i
$503$	25.9585	+	14.9871i	1.15743	+	0.668243i	0.950687	−	0.310153i	$-0.100380\pi$
$503$	25.9585	+	14.9871i	1.15743	+	0.668243i	0.206743	+	0.978395i	$0.433713\pi$
$504$		0			0
$505$	−7.31560	+	27.3022i	−0.325540	+	1.21493i
$506$		−	1.46199i		−	0.0649935i
$507$		0			0
$508$	12.1445			0.538827
$509$	−3.62928	+	13.5446i	−0.160865	+	0.600356i	0.837667	+	0.546182i	$0.183919\pi$
$509$	−3.62928	+	13.5446i	−0.160865	+	0.600356i	−0.998532	+	0.0541739i	$0.982747\pi$
$510$		0			0
$511$	1.98639	−	1.69844i	0.0878729	−	0.0751348i
$512$	−6.42580	+	6.42580i	−0.283983	+	0.283983i
$513$		0			0
$514$	0.406370	+	1.51659i	0.0179242	+	0.0668940i
$515$	−14.7501	−	14.7501i	−0.649969	−	0.649969i
$516$		0			0
$517$	6.48785	+	11.2373i	0.285335	+	0.494215i
$518$	0.494574	−	0.720464i	0.0217303	−	0.0316554i
$519$		0			0
$520$	−2.53932	+	1.52633i	−0.111356	+	0.0669339i
$521$		−	0.875247i		−	0.0383452i	−0.999816	−	0.0191726i	$-0.993897\pi$
$521$		−	0.875247i		−	0.0383452i	0.999816	−	0.0191726i	$-0.00610321\pi$
$522$		0			0
$523$	11.7198	−	6.76640i	0.512469	−	0.295874i	−0.221379	−	0.975188i	$-0.571056\pi$
$523$	11.7198	−	6.76640i	0.512469	−	0.295874i	0.733848	+	0.679314i	$0.237722\pi$
$524$	−5.72506	+	9.91610i	−0.250100	+	0.433187i
$525$		0			0
$526$	0.620553	+	2.31593i	0.0270574	+	0.100980i
$527$	−17.6857	+	4.73887i	−0.770401	+	0.206428i
$528$		0			0
$529$	8.95568	−	15.5117i	0.389377	−	0.674421i
$530$	0.440907	+	0.763674i	0.0191518	+	0.0331719i
$531$		0			0
$532$	−21.1473	−	7.47548i	−0.916853	−	0.324103i
$533$	−39.4888	+	11.3301i	−1.71045	+	0.490759i
$534$		0			0
$535$	3.65155	−	13.6278i	0.157870	−	0.589180i
$536$	0.00458664	+	0.00794430i	0.000198113	+	0.000343141i
$537$		0			0
$538$	−0.886440	−	0.886440i	−0.0382171	−	0.0382171i
$539$	5.56010	−	12.5255i	0.239491	−	0.539512i
$540$		0			0
$541$	8.68791	+	8.68791i	0.373522	+	0.373522i	0.868758	−	0.495236i	$-0.164918\pi$
$541$	8.68791	+	8.68791i	0.373522	+	0.373522i	−0.495236	+	0.868758i	$0.664918\pi$
$542$	0.151539	+	0.0874914i	0.00650918	+	0.00375808i
$543$		0			0
$544$	−5.73710	−	1.53725i	−0.245976	−	0.0659091i
$545$	21.8634			0.936526
$546$		0			0
$547$	16.2786			0.696022			0.348011	−	0.937490i	$-0.386857\pi$
$547$	16.2786			0.696022			0.348011	+	0.937490i	$0.386857\pi$
$548$	−12.0411	−	3.22641i	−0.514371	−	0.137825i
$549$		0			0
$550$	−0.372723	−	0.215192i	−0.0158930	−	0.00917582i
$551$	−21.6051	−	21.6051i	−0.920410	−	0.920410i
$552$		0			0
$553$	15.6606	+	1.22379i	0.665956	+	0.0520408i
$554$	0.388865	+	0.388865i	0.0165213	+	0.0165213i
$555$		0			0
$556$	−20.7937	−	36.0157i	−0.881849	−	1.52741i
$557$	−2.13873	+	7.98185i	−0.0906210	+	0.338202i	−0.996319	−	0.0857210i	$-0.972681\pi$
$557$	−2.13873	+	7.98185i	−0.0906210	+	0.338202i	0.905698	+	0.423923i	$0.139347\pi$
$558$		0			0
$559$	−0.113826	−	6.46190i	−0.00481433	−	0.273309i
$560$	−6.10024	+	17.2569i	−0.257782	+	0.729237i
$561$		0			0
$562$	−0.661470	−	1.14570i	−0.0279024	−	0.0483285i
$563$	14.0767	−	24.3815i	0.593261	−	1.02756i	−0.400528	−	0.916284i	$-0.631173\pi$
$563$	14.0767	−	24.3815i	0.593261	−	1.02756i	0.993790	−	0.111274i	$-0.0354932\pi$
$564$		0			0
$565$	14.5712	−	3.90435i	0.613016	−	0.164257i
$566$	0.238078	+	0.888519i	0.0100072	+	0.0373472i
$567$		0			0
$568$	−1.10691	+	1.91722i	−0.0464448	+	0.0804447i
$569$	8.62645	−	4.98048i	0.361640	−	0.208793i	−0.308160	−	0.951335i	$-0.599713\pi$
$569$	8.62645	−	4.98048i	0.361640	−	0.208793i	0.669800	+	0.742542i	$0.266380\pi$
$570$		0			0
$571$			5.15214i			0.215610i	0.994172	+	0.107805i	$0.0343823\pi$
$571$			5.15214i			0.215610i	−0.994172	+	0.107805i	$0.965618\pi$
$572$	−13.6052	−	3.38986i	−0.568864	−	0.141737i
$573$		0			0
$574$	1.99194	−	2.90174i	0.0831421	−	0.121116i
$575$	−6.02177	−	10.4300i	−0.251125	−	0.434962i
$576$		0			0
$577$	9.50342	+	9.50342i	0.395633	+	0.395633i	0.876689	−	0.481057i	$-0.159747\pi$
$577$	9.50342	+	9.50342i	0.395633	+	0.395633i	−0.481057	+	0.876689i	$0.659747\pi$
$578$	−0.0393588	−	0.146889i	−0.00163711	−	0.00610978i
$579$		0			0
$580$	−17.7532	+	17.7532i	−0.737161	+	0.737161i
$581$	−24.0164	−	28.0881i	−0.996368	−	1.16529i
$582$		0			0
$583$	−2.16762	+	8.08967i	−0.0897737	+	0.335040i
$584$	0.459752			0.0190247
$585$		0			0
$586$			1.42645i			0.0589263i
$587$	9.73498	−	36.3314i	0.401806	−	1.49956i	−0.408066	−	0.912952i	$-0.633797\pi$
$587$	9.73498	−	36.3314i	0.401806	−	1.49956i	0.809872	−	0.586607i	$-0.199537\pi$
$588$		0			0
$589$	−15.8186	−	9.13289i	−0.651795	−	0.376314i
$590$	−0.245935	+	0.245935i	−0.0101250	+	0.0101250i
$591$		0			0
$592$	−10.7075	+	2.86906i	−0.440074	+	0.117918i
$593$	25.8396	−	25.8396i	1.06110	−	1.06110i	0.0630974	−	0.998007i	$-0.479902\pi$
$593$	25.8396	−	25.8396i	1.06110	−	1.06110i	0.998007	−	0.0630974i	$-0.0200979\pi$
$594$		0			0
$595$	−19.6471	+	3.65264i	−0.805454	+	0.149744i
$596$	−7.94687	+	29.6581i	−0.325517	+	1.21484i
$597$		0			0
$598$	1.93716	+	1.87009i	0.0792162	+	0.0764738i
$599$	−5.32027			−0.217381			−0.108690	−	0.994076i	$-0.534666\pi$
$599$	−5.32027			−0.217381			−0.108690	+	0.994076i	$0.534666\pi$
$600$		0			0
$601$	21.4564	−	12.3879i	0.875225	−	0.505312i	0.00614424	−	0.999981i	$-0.498044\pi$
$601$	21.4564	−	12.3879i	0.875225	−	0.505312i	0.869081	+	0.494669i	$0.164711\pi$
$602$	0.359833	+	0.420838i	0.0146657	+	0.0171521i
$603$		0			0
$604$	−2.27279	−	8.48216i	−0.0924785	−	0.345134i
$605$	−3.27510	−	12.2228i	−0.133152	−	0.496929i
$606$		0			0
$607$	−19.5367	−	11.2795i	−0.792971	−	0.457822i	0.0480365	−	0.998846i	$-0.484704\pi$
$607$	−19.5367	−	11.2795i	−0.792971	−	0.457822i	−0.841007	+	0.541024i	$0.818037\pi$
$608$	−2.96263	−	5.13143i	−0.120151	−	0.208107i
$609$		0			0
$610$			0.635418i			0.0257273i
$611$	−23.1884	−	5.77758i	−0.938102	−	0.233736i
$612$		0			0
$613$	−22.2201	−	5.95385i	−0.897459	−	0.240474i	−0.219535	−	0.975605i	$-0.570454\pi$
$613$	−22.2201	−	5.95385i	−0.897459	−	0.240474i	−0.677925	+	0.735131i	$0.737121\pi$
$614$	1.13995	−	0.658151i	0.0460047	−	0.0265608i
$615$		0			0
$616$	2.17532	−	1.03905i	0.0876462	−	0.0418647i
$617$	−7.79350	−	29.0858i	−0.313755	−	1.17095i	−0.925143	−	0.379618i	$-0.876055\pi$
$617$	−7.79350	−	29.0858i	−0.313755	−	1.17095i	0.611389	−	0.791330i	$-0.290611\pi$
$618$		0			0
$619$	−7.55579	+	7.55579i	−0.303693	+	0.303693i	−0.842457	−	0.538764i	$-0.818891\pi$
$619$	−7.55579	+	7.55579i	−0.303693	+	0.303693i	0.538764	+	0.842457i	$0.318891\pi$
$620$	−7.50459	+	12.9983i	−0.301392	+	0.522026i
$621$		0			0
$622$	−1.47090	−	0.394127i	−0.0589778	−	0.0158031i
$623$	20.0462	+	7.08625i	0.803135	+	0.283905i
$624$		0			0
$625$	12.0400			0.481599
$626$	0.107997	−	0.403049i	0.00431641	−	0.0161091i
$627$		0			0
$628$	6.88340	−	11.9224i	0.274678	−	0.475755i
$629$	−8.55805	−	8.55805i	−0.341232	−	0.341232i
$630$		0			0
$631$	13.6759	−	3.66444i	0.544428	−	0.145879i	0.0238855	−	0.999715i	$-0.492396\pi$
$631$	13.6759	−	3.66444i	0.544428	−	0.145879i	0.520543	+	0.853836i	$0.325730\pi$
$632$	1.95395	+	1.95395i	0.0777240	+	0.0777240i
$633$		0			0
$634$	−3.35413	+	1.93651i	−0.133209	+	0.0769085i
$635$	10.4265	+	2.79377i	0.413763	+	0.110867i
$636$		0			0
$637$	9.48429	+	23.3891i	0.375781	+	0.926708i
$638$	1.63637			0.0647844
$639$		0			0
$640$	−5.61554	+	3.24213i	−0.221974	+	0.128157i
$641$	32.0667	+	18.5137i	1.26656	+	0.731248i	0.974335	−	0.225102i	$-0.0722714\pi$
$641$	32.0667	+	18.5137i	1.26656	+	0.731248i	0.292224	+	0.956350i	$0.405605\pi$
$642$		0			0
$643$	33.2886	−	8.91965i	1.31277	−	0.351757i	0.466507	−	0.884517i	$-0.345512\pi$
$643$	33.2886	−	8.91965i	1.31277	−	0.351757i	0.846266	+	0.532761i	$0.178845\pi$
$644$	33.5127	+	2.61883i	1.32058	+	0.103196i
$645$		0			0
$646$	1.06588	−	1.84617i	0.0419366	−	0.0726364i
$647$	3.03363	+	5.25440i	0.119264	+	0.206572i	0.919476	−	0.393145i	$-0.128613\pi$
$647$	3.03363	+	5.25440i	0.119264	+	0.206572i	−0.800212	+	0.599717i	$0.795280\pi$
$648$		0			0
$649$	−3.30328			−0.129665
$650$	0.761896	−	0.218602i	0.0298840	−	0.00857428i
$651$		0			0
$652$	24.8184	+	6.65007i	0.971964	+	0.260437i
$653$	15.1009	+	26.1555i	0.590943	+	1.02354i	0.994106	+	0.108416i	$0.0345777\pi$
$653$	15.1009	+	26.1555i	0.590943	+	1.02354i	−0.403162	+	0.915129i	$0.632089\pi$
$654$		0			0
$655$	−7.19630	+	7.19630i	−0.281183	+	0.281183i
$656$	−43.1253	+	11.5554i	−1.68376	+	0.451162i
$657$		0			0
$658$	1.84744	−	0.882439i	0.0720206	−	0.0344010i
$659$	−4.37179	+	7.57216i	−0.170301	+	0.294969i	−0.938525	−	0.345211i	$-0.887807\pi$
$659$	−4.37179	+	7.57216i	−0.170301	+	0.294969i	0.768224	+	0.640181i	$0.221141\pi$
$660$		0			0
$661$	−17.3494	−	4.64874i	−0.674812	−	0.180815i	−0.0948903	−	0.995488i	$-0.530250\pi$
$661$	−17.3494	−	4.64874i	−0.674812	−	0.180815i	−0.579921	+	0.814673i	$0.696917\pi$
$662$		−	0.110698i		−	0.00430239i
$663$		0			0
$664$		−	6.50100i		−	0.252288i
$665$	−16.4360	−	11.2828i	−0.637361	−	0.437527i
$666$		0			0
$667$	39.6561	+	22.8955i	1.53549	+	0.886516i
$668$	1.30942	+	1.30942i	0.0506631	+	0.0506631i
$669$		0			0
$670$	0.00105152	+	0.00392433i	4.06238e−5	+	0.000151610i
$671$	−4.26731	+	4.26731i	−0.164738	+	0.164738i
$672$		0			0
$673$	22.0524	−	12.7319i	0.850057	−	0.490780i	−0.0106133	−	0.999944i	$-0.503378\pi$
$673$	22.0524	−	12.7319i	0.850057	−	0.490780i	0.860670	+	0.509163i	$0.170045\pi$
$674$	−0.428796	+	1.60029i	−0.0165166	+	0.0616408i
$675$		0			0
$676$	21.8946	−	13.6910i	0.842100	−	0.526577i
$677$		−	21.8547i		−	0.839946i	−0.907537	−	0.419973i	$-0.862039\pi$
$677$		−	21.8547i		−	0.839946i	0.907537	−	0.419973i	$-0.137961\pi$
$678$		0			0
$679$	38.4219	−	7.14309i	1.47450	−	0.274127i
$680$	−3.04444	−	1.75771i	−0.116749	−	0.0674050i
$681$		0			0
$682$	0.944911	−	0.253188i	0.0361825	−	0.00969507i
$683$	−30.9579	+	8.29515i	−1.18457	+	0.317405i	−0.796738	−	0.604324i	$-0.793443\pi$
$683$	−30.9579	+	8.29515i	−1.18457	+	0.317405i	−0.387833	+	0.921729i	$0.626776\pi$
$684$		0			0
$685$	−9.59550	−	5.53997i	−0.366625	−	0.211671i
$686$	−1.90198	−	1.02860i	−0.0726180	−	0.0392723i
$687$		0			0
$688$		−	7.02368i		−	0.267775i
$689$	−7.94621	−	13.2199i	−0.302726	−	0.503639i
$690$		0			0
$691$	7.27863	−	27.1642i	0.276892	−	1.03337i	−0.677671	−	0.735365i	$-0.737011\pi$
$691$	7.27863	−	27.1642i	0.276892	−	1.03337i	0.954563	−	0.298010i	$-0.0963227\pi$
$692$	0.907533	−	0.523964i	0.0344992	−	0.0199181i
$693$		0			0
$694$	1.14276	−	1.14276i	0.0433786	−	0.0433786i
$695$	−9.56691	−	35.7042i	−0.362894	−	1.35434i
$696$		0			0
$697$	−34.4683	−	34.4683i	−1.30558	−	1.30558i
$698$	−1.54794	−	0.893701i	−0.0585902	−	0.0338271i
$699$		0			0
$700$	5.60040	−	8.15831i	0.211675	−	0.308355i
$701$			41.8411i			1.58032i	0.612904	+	0.790158i	$0.290001\pi$
$701$			41.8411i			1.58032i	−0.612904	+	0.790158i	$0.709999\pi$
$702$		0			0
$703$		−	12.0740i		−	0.455378i
$704$	−14.5131	−	3.88876i	−0.546981	−	0.146563i
$705$		0			0
$706$	−0.919455	+	1.59254i	−0.0346041	+	0.0599361i
$707$	18.2565	+	38.2210i	0.686606	+	1.43745i
$708$		0			0
$709$	−36.1012	+	9.67328i	−1.35581	+	0.363288i	−0.862275	−	0.506440i	$-0.830961\pi$
$709$	−36.1012	+	9.67328i	−1.35581	+	0.363288i	−0.493532	+	0.869727i	$0.664295\pi$
$710$	−0.693302	+	0.693302i	−0.0260192	+	0.0260192i
$711$		0			0
$712$	1.87012	+	3.23914i	0.0700857	+	0.121392i
$713$	26.4417	+	7.08503i	0.990249	+	0.265336i
$714$		0			0
$715$	−10.9008	−	6.04011i	−0.407665	−	0.225887i
$716$	16.4273			0.613918
$717$		0			0
$718$	0.387018	+	0.670334i	0.0144434	+	0.0250166i
$719$	14.7469	−	25.5425i	0.549968	−	0.952573i	−0.448308	−	0.893879i	$-0.647973\pi$
$719$	14.7469	−	25.5425i	0.549968	−	0.952573i	0.998276	−	0.0586936i	$-0.0186935\pi$
$720$		0			0
$721$	−31.1648	−	2.43536i	−1.16064	−	0.0906975i
$722$	−0.0885265	+	0.0237206i	−0.00329461	+	0.000882789i
$723$		0			0
$724$	25.7667	+	14.8764i	0.957612	+	0.552878i
$725$	11.6740	−	6.74000i	0.433562	−	0.250317i
$726$		0			0
$727$	3.04387			0.112891			0.0564455	−	0.998406i	$-0.482023\pi$
$727$	3.04387			0.112891			0.0564455	+	0.998406i	$0.482023\pi$
$728$	−1.40578	+	4.21142i	−0.0521017	+	0.156086i
$729$		0			0
$730$	0.196682	+	0.0527007i	0.00727952	+	0.00195054i
$731$	6.64113	−	3.83426i	0.245631	−	0.141815i
$732$		0			0
$733$	−0.928339	−	0.928339i	−0.0342890	−	0.0342890i	0.689754	−	0.724043i	$-0.257718\pi$
$733$	−0.928339	−	0.928339i	−0.0342890	−	0.0342890i	−0.724043	+	0.689754i	$0.757718\pi$
$734$	−3.70542	+	0.992865i	−0.136770	+	0.0366473i
$735$		0			0
$736$	6.27914	+	6.27914i	0.231452	+	0.231452i
$737$	−0.0192931	+	0.0334166i	−0.000710669	+	0.00123091i
$738$		0			0
$739$	−7.76649	+	28.9849i	−0.285695	+	1.06623i	0.662635	+	0.748942i	$0.269438\pi$
$739$	−7.76649	+	28.9849i	−0.285695	+	1.06623i	−0.948330	+	0.317285i	$0.897229\pi$
$740$	−9.92129			−0.364714
$741$		0			0
$742$	1.24590	+	0.440421i	0.0457385	+	0.0161684i
$743$	39.4397	+	10.5678i	1.44690	+	0.387697i	0.894946	−	0.446175i	$-0.147214\pi$
$743$	39.4397	+	10.5678i	1.44690	+	0.387697i	0.551958	+	0.833872i	$0.313881\pi$
$744$		0			0
$745$	−13.6453	+	23.6344i	−0.499926	+	0.865897i
$746$	−0.650528	+	0.650528i	−0.0238175	+	0.0238175i
$747$		0			0
$748$	−4.30591	−	16.0699i	−0.157440	−	0.587573i
$749$	−9.11265	−	19.0779i	−0.332969	−	0.697090i
$750$		0			0
$751$	−31.0690	+	17.9377i	−1.13372	+	0.654556i	−0.944869	−	0.327448i	$-0.893811\pi$
$751$	−31.0690	+	17.9377i	−1.13372	+	0.654556i	−0.188856	+	0.982005i	$0.560478\pi$
$752$	−25.0859	−	6.72175i	−0.914789	−	0.245117i
$753$		0			0
$754$	−2.09314	+	2.16820i	−0.0762277	+	0.0789614i
$755$		−	7.80507i		−	0.284056i
$756$		0			0
$757$	−0.439138	−	0.760610i	−0.0159607	−	0.0276448i	0.857935	−	0.513759i	$-0.171747\pi$
$757$	−0.439138	−	0.760610i	−0.0159607	−	0.0276448i	−0.873895	+	0.486114i	$0.838414\pi$
$758$	1.13152	+	0.653282i	0.0410986	+	0.0237283i
$759$		0			0
$760$	−0.907679	−	3.38750i	−0.0329250	−	0.122878i
$761$	−9.46773	−	35.3341i	−0.343205	−	1.28086i	−0.894695	−	0.446677i	$-0.852607\pi$
$761$	−9.46773	−	35.3341i	−0.343205	−	1.28086i	0.551490	−	0.834181i	$-0.314059\pi$
$762$		0			0
$763$	24.9019	−	21.2921i	0.901511	−	0.770827i
$764$	24.9938	−	14.4302i	0.904245	−	0.522066i
$765$		0			0
$766$	0.281440			0.0101689
$767$	4.22535	−	4.37687i	0.152568	−	0.158040i
$768$		0			0
$769$	−7.85943	+	29.3318i	−0.283418	+	1.05773i	0.666569	+	0.745443i	$0.267762\pi$
$769$	−7.85943	+	29.3318i	−0.283418	+	1.05773i	−0.949987	+	0.312288i	$0.898904\pi$
$770$	1.04971	−	0.195153i	0.0378288	−	0.00703282i
$771$		0			0
$772$	−27.4985	+	27.4985i	−0.989692	+	0.989692i
$773$	−19.1599	+	5.13389i	−0.689134	+	0.184653i	−0.586359	−	0.810052i	$-0.699439\pi$
$773$	−19.1599	+	5.13389i	−0.689134	+	0.184653i	−0.102776	+	0.994705i	$0.532772\pi$
$774$		0			0
$775$	5.69824	−	5.69824i	0.204687	−	0.204687i
$776$	5.95369	+	3.43737i	0.213725	+	0.123394i
$777$		0			0
$778$	0.508297	−	1.89699i	0.0182233	−	0.0680104i
$779$		−	48.6290i		−	1.74231i
$780$		0			0
$781$	−9.31209			−0.333213
$782$	−0.826882	+	3.08596i	−0.0295692	+	0.110354i
$783$		0			0
$784$	9.85795	+	25.5961i	0.352070	+	0.914145i
$785$	8.65231	−	8.65231i	0.308814	−	0.308814i
$786$		0			0
$787$	−2.27486	−	8.48989i	−0.0810900	−	0.302632i	0.913455	−	0.406940i	$-0.133404\pi$
$787$	−2.27486	−	8.48989i	−0.0810900	−	0.302632i	−0.994545	+	0.104308i	$0.966737\pi$
$788$	−30.5620	−	30.5620i	−1.08873	−	1.08873i
$789$		0			0
$790$	0.611921	+	1.05988i	0.0217712	+	0.0377087i
$791$	12.7940	−	18.6374i	0.454901	−	0.662671i
$792$		0			0
$793$	−0.195750	−	11.1127i	−0.00695128	−	0.394624i
$794$			2.74663i			0.0974743i
$795$		0			0
$796$	−33.1686	+	19.1499i	−1.17563	+	0.678750i
$797$	12.3887	−	21.4579i	0.438832	−	0.760079i	−0.558768	−	0.829324i	$-0.688726\pi$
$797$	12.3887	−	21.4579i	0.438832	−	0.760079i	0.997600	+	0.0692450i	$0.0220590\pi$
$798$		0			0
$799$	−7.33886	−	27.3890i	−0.259630	−	0.968953i
$800$	2.52505	−	0.676585i	0.0892739	−	0.0239209i
$801$		0			0
$802$	−0.503695	+	0.872425i	−0.0177861	+	0.0308064i
$803$	0.966941	+	1.67479i	0.0341226	+	0.0591021i
$804$		0			0
$805$	28.1693	+	9.95773i	0.992838	+	0.350964i
$806$	−0.873195	+	1.57588i	−0.0307570	+	0.0555080i
$807$		0			0
$808$	−1.92852	+	7.19733i	−0.0678450	+	0.253201i
$809$	3.75373	+	6.50166i	0.131974	+	0.228586i	0.924438	−	0.381334i	$-0.124535\pi$
$809$	3.75373	+	6.50166i	0.131974	+	0.228586i	−0.792463	+	0.609920i	$0.791202\pi$
$810$		0			0
$811$	−32.4572	−	32.4572i	−1.13973	−	1.13973i	−0.988499	−	0.151229i	$-0.951677\pi$
$811$	−32.4572	−	32.4572i	−1.13973	−	1.13973i	−0.151229	−	0.988499i	$-0.548323\pi$
$812$	−2.93118	+	37.5098i	−0.102864	+	1.31633i
$813$		0			0
$814$	0.457239	+	0.457239i	0.0160262	+	0.0160262i
$815$	19.7777	+	11.4186i	0.692781	+	0.399977i
$816$		0			0
$817$	7.38949	+	1.98001i	0.258526	+	0.0692717i
$818$	1.56868			0.0548475
$819$		0			0
$820$	−39.9589			−1.39543
$821$	−30.4367	−	8.15549i	−1.06225	−	0.284629i	−0.314944	−	0.949110i	$-0.601986\pi$
$821$	−30.4367	−	8.15549i	−1.06225	−	0.284629i	−0.747305	+	0.664482i	$0.768652\pi$
$822$		0			0
$823$	27.4139	+	15.8274i	0.955590	+	0.551710i	0.894813	−	0.446442i	$-0.147309\pi$
$823$	27.4139	+	15.8274i	0.955590	+	0.551710i	0.0607767	+	0.998151i	$0.480642\pi$
$824$	−3.88839	−	3.88839i	−0.135459	−	0.135459i
$825$		0			0
$826$	−0.0406057	+	0.519623i	−0.00141285	+	0.0180800i
$827$	−25.1824	−	25.1824i	−0.875678	−	0.875678i	0.117406	−	0.993084i	$-0.462542\pi$
$827$	−25.1824	−	25.1824i	−0.875678	−	0.875678i	−0.993084	+	0.117406i	$0.962542\pi$
$828$		0			0
$829$	−1.05432	−	1.82614i	−0.0366182	−	0.0634246i	0.847135	−	0.531377i	$-0.178325\pi$
$829$	−1.05432	−	1.82614i	−0.0366182	−	0.0634246i	−0.883754	+	0.467952i	$0.844992\pi$
$830$	0.745200	−	2.78112i	0.0258663	−	0.0965342i
$831$		0			0
$832$	23.7169	−	14.2557i	0.822234	−	0.494227i
$833$	−18.8205	+	23.2940i	−0.652090	+	0.807091i
$834$		0			0
$835$	0.822960	+	1.42541i	0.0284797	+	0.0493283i
$836$	8.29847	−	14.3734i	0.287009	−	0.497114i
$837$		0			0
$838$	−1.96001	+	0.525184i	−0.0677076	+	0.0181422i
$839$	−6.14897	−	22.9483i	−0.212286	−	0.792262i	−0.987104	−	0.160078i	$-0.948825\pi$
$839$	−6.14897	−	22.9483i	−0.212286	−	0.792262i	0.774818	−	0.632184i	$-0.217841\pi$
$840$		0			0
$841$	−11.1262	+	19.2712i	−0.383663	+	0.664525i
$842$	−3.03847	+	1.75426i	−0.104713	+	0.0604558i
$843$		0			0
$844$		−	6.00398i		−	0.206666i
$845$	21.9468	−	6.71748i	0.754992	−	0.231088i
$846$		0			0
$847$	−15.6337	−	10.7320i	−0.537181	−	0.368756i
$848$	−8.38131	−	14.5169i	−0.287815	−	0.498511i
$849$		0			0
$850$	0.665032	+	0.665032i	0.0228104	+	0.0228104i
$851$	4.68331	+	17.4783i	0.160542	+	0.599150i
$852$		0			0
$853$	4.73993	−	4.73993i	0.162292	−	0.162292i	−0.621289	−	0.783581i	$-0.713391\pi$
$853$	4.73993	−	4.73993i	0.162292	−	0.162292i	0.783581	+	0.621289i	$0.213391\pi$
$854$	0.618814	+	0.723726i	0.0211754	+	0.0247654i
$855$		0			0
$856$	0.962612	−	3.59252i	0.0329014	−	0.122790i
$857$	−11.3220			−0.386751			−0.193376	−	0.981125i	$-0.561944\pi$
$857$	−11.3220			−0.386751			−0.193376	+	0.981125i	$0.561944\pi$
$858$		0			0
$859$		−	48.4452i		−	1.65293i	−0.562988	−	0.826465i	$-0.690348\pi$
$859$		−	48.4452i		−	1.65293i	0.562988	−	0.826465i	$-0.309652\pi$
$860$	1.62699	−	6.07202i	0.0554800	−	0.207054i
$861$		0			0
$862$	−2.43991	−	1.40868i	−0.0831038	−	0.0479800i
$863$	13.2582	−	13.2582i	0.451313	−	0.451313i	−0.444477	−	0.895790i	$-0.646610\pi$
$863$	13.2582	−	13.2582i	0.451313	−	0.451313i	0.895790	+	0.444477i	$0.146610\pi$
$864$		0			0
$865$	0.899682	−	0.241069i	0.0305901	−	0.00819660i
$866$	0.375015	−	0.375015i	0.0127435	−	0.0127435i
$867$		0			0
$868$	4.11113	+	22.1133i	0.139541	+	0.750575i
$869$	−3.00837	+	11.2274i	−0.102052	+	0.380863i
$870$		0			0
$871$	−0.0195988	−	0.0683079i	−0.000664080	−	0.00231452i
$872$	5.76357			0.195179
$873$		0			0
$874$	−2.76018	+	1.59359i	−0.0933645	+	0.0539040i
$875$	24.4363	−	20.8940i	0.826098	−	0.706346i
$876$		0			0
$877$	1.83431	+	6.84575i	0.0619403	+	0.231164i	0.989956	−	0.141377i	$-0.0451530\pi$
$877$	1.83431	+	6.84575i	0.0619403	+	0.231164i	−0.928015	+	0.372542i	$0.878486\pi$
$878$	−0.513728	−	1.91726i	−0.0173375	−	0.0647044i
$879$		0			0
$880$	−11.7291	−	6.77183i	−0.395389	−	0.228278i
$881$	−12.1808	−	21.0977i	−0.410380	−	0.710800i	0.584551	−	0.811357i	$-0.301271\pi$
$881$	−12.1808	−	21.0977i	−0.410380	−	0.710800i	−0.994931	+	0.100557i	$0.967937\pi$
$882$		0			0
$883$		−	4.51673i		−	0.152000i	−0.997108	−	0.0760000i	$-0.975785\pi$
$883$		−	4.51673i		−	0.152000i	0.997108	−	0.0760000i	$-0.0242149\pi$
$884$	26.8006	+	14.8502i	0.901401	+	0.499467i
$885$		0			0
$886$	4.12943	+	1.10648i	0.138731	+	0.0371729i
$887$	38.3035	−	22.1145i	1.28611	−	0.742533i	0.308148	−	0.951338i	$-0.400291\pi$
$887$	38.3035	−	22.1145i	1.28611	−	0.742533i	0.977957	+	0.208805i	$0.0669575\pi$
$888$		0			0
$889$	14.5963	−	6.97202i	0.489545	−	0.233834i
$890$	0.428738	+	1.60007i	0.0143713	+	0.0536346i
$891$		0			0
$892$	6.17928	−	6.17928i	0.206898	−	0.206898i
$893$	14.1437	−	24.4976i	0.473300	−	0.819780i
$894$		0			0
$895$	14.1034	+	3.77900i	0.471426	+	0.126318i
$896$	−3.23856	+	9.16152i	−0.108193	+	0.306065i
$897$		0			0
$898$	3.95832			0.132091
$899$	−7.93007	+	29.5954i	−0.264483	+	0.987063i
$900$		0			0
$901$	9.15079	−	15.8496i	0.304857	−	0.528028i
$902$	1.84157	+	1.84157i	0.0613176	+	0.0613176i
$903$		0			0
$904$	3.84122	−	1.02925i	0.127757	−	0.0342324i
$905$	18.6994	+	18.6994i	0.621589	+	0.621589i
$906$		0			0
$907$	29.3466	−	16.9433i	0.974439	−	0.562593i	0.0738526	−	0.997269i	$-0.476471\pi$
$907$	29.3466	−	16.9433i	0.974439	−	0.562593i	0.900587	+	0.434676i	$0.143137\pi$
$908$	7.86438	+	2.10725i	0.260989	+	0.0699317i
$909$		0			0
$910$	−1.08414	+	1.64050i	−0.0359389	+	0.0543820i
$911$	−4.66390			−0.154522			−0.0772610	−	0.997011i	$-0.524617\pi$
$911$	−4.66390			−0.154522			−0.0772610	+	0.997011i	$0.524617\pi$
$912$		0			0
$913$	23.6819	−	13.6728i	0.783757	−	0.452502i
$914$	−0.228791	−	0.132092i	−0.00756772	−	0.00436923i
$915$		0			0
$916$	26.0500	−	6.98007i	0.860716	−	0.230628i
$917$	−1.18816	+	15.2047i	−0.0392366	+	0.502103i
$918$		0			0
$919$	−12.0900	+	20.9405i	−0.398812	+	0.690763i	−0.993580	−	0.113135i	$-0.963911\pi$
$919$	−12.0900	+	20.9405i	−0.398812	+	0.690763i	0.594767	+	0.803898i	$0.297244\pi$
$920$	2.62793	+	4.55170i	0.0866402	+	0.150065i
$921$		0			0
$922$	−2.96686			−0.0977084
$923$	11.9115	−	12.3386i	0.392070	−	0.406131i
$924$		0			0
$925$	5.14530	+	1.37868i	0.169177	+	0.0453307i
$926$	−1.86798	−	3.23543i	−0.0613856	−	0.106323i
$927$		0			0
$928$	−7.02806	+	7.02806i	−0.230708	+	0.230708i
$929$	−15.0006	+	4.01941i	−0.492155	+	0.131872i	−0.496357	−	0.868119i	$-0.665329\pi$
$929$	−15.0006	+	4.01941i	−0.492155	+	0.131872i	0.00420200	+	0.999991i	$0.498662\pi$
$930$		0			0
$931$	−29.7082	+	3.15573i	−0.973647	+	0.103425i
$932$	−16.2386	+	28.1261i	−0.531913	+	0.921300i
$933$		0			0
$934$	−1.27369	−	0.341285i	−0.0416765	−	0.0111672i
$935$		−	14.7871i		−	0.483589i
$936$		0			0
$937$		−	25.4720i		−	0.832134i	−0.909334	−	0.416067i	$-0.863408\pi$
$937$		−	25.4720i		−	0.832134i	0.909334	−	0.416067i	$-0.136592\pi$
$938$	0.00501944	+	0.00344568i	0.000163891	+	0.000112505i
$939$		0			0
$940$	−20.1299	−	11.6220i	−0.656565	−	0.379068i
$941$	−12.6726	−	12.6726i	−0.413116	−	0.413116i	0.469706	−	0.882823i	$-0.344360\pi$
$941$	−12.6726	−	12.6726i	−0.413116	−	0.413116i	−0.882823	+	0.469706i	$0.844360\pi$
$942$		0			0
$943$	18.8625	+	70.3957i	0.614246	+	2.29240i
$944$	4.67503	−	4.67503i	0.152159	−	0.152159i
$945$		0			0
$946$	−0.354822	+	0.204856i	−0.0115362	+	0.00666046i
$947$	−3.21690	+	12.0056i	−0.104535	+	0.390130i	−0.998292	−	0.0584214i	$-0.981393\pi$
$947$	−3.21690	+	12.0056i	−0.104535	+	0.390130i	0.893757	+	0.448552i	$0.148060\pi$
$948$		0			0
$949$	−3.45597	−	0.861083i	−0.112185	−	0.0279519i
$950$			0.938247i			0.0304408i
$951$		0			0
$952$	−5.17932	+	0.962898i	−0.167863	+	0.0312077i
$953$	−25.0716	−	14.4751i	−0.812147	−	0.468893i	0.0355538	−	0.999368i	$-0.488680\pi$
$953$	−25.0716	−	14.4751i	−0.812147	−	0.468893i	−0.847701	+	0.530474i	$0.822014\pi$
$954$		0			0
$955$	24.7776	−	6.63914i	0.801785	−	0.214838i
$956$	16.5925	−	4.44594i	0.536639	−	0.143792i
$957$		0			0
$958$	2.02778	+	1.17074i	0.0655147	+	0.0378249i
$959$	−16.3243	+	3.03488i	−0.527138	+	0.0980013i
$960$		0			0
$961$		−	12.6833i		−	0.409139i
$962$	−1.19072	+	0.0209745i	−0.0383903	+	0.000676243i
$963$		0			0
$964$	−6.90512	+	25.7703i	−0.222399	+	0.830004i
$965$	−29.9342	+	17.2825i	−0.963617	+	0.556344i
$966$		0			0
$967$	20.8937	−	20.8937i	0.671895	−	0.671895i	−0.286258	−	0.958153i	$-0.592411\pi$
$967$	20.8937	−	20.8937i	0.671895	−	0.671895i	0.958153	+	0.286258i	$0.0924113\pi$
$968$	−0.863372	−	3.22215i	−0.0277498	−	0.103564i
$969$		0			0
$970$	2.15297	+	2.15297i	0.0691276	+	0.0691276i
$971$	−35.5507	−	20.5252i	−1.14088	−	0.658685i	−0.194229	−	0.980956i	$-0.562220\pi$
$971$	−35.5507	−	20.5252i	−1.14088	−	0.658685i	−0.946647	+	0.322271i	$0.895554\pi$
$972$		0			0
$973$	−45.6677	−	31.3494i	−1.46404	−	1.00501i
$974$		−	3.66794i		−	0.117528i
$975$		0			0
$976$		−	12.0788i		−	0.386633i
$977$	22.0546	+	5.90951i	0.705589	+	0.189062i	0.593733	−	0.804662i	$-0.297654\pi$
$977$	22.0546	+	5.90951i	0.705589	+	0.189062i	0.111856	+	0.993724i	$0.464320\pi$
$978$		0			0
$979$	−7.86639	+	13.6250i	−0.251411	+	0.435457i
$980$	2.59309	+	24.4115i	0.0828334	+	0.779798i
$981$		0			0
$982$	2.19217	−	0.587390i	0.0699549	−	0.0187444i
$983$	−21.0430	+	21.0430i	−0.671167	+	0.671167i	−0.957985	−	0.286818i	$-0.907402\pi$
$983$	−21.0430	+	21.0430i	−0.671167	+	0.671167i	0.286818	+	0.957985i	$0.407402\pi$
$984$		0			0
$985$	−19.2080	−	33.2692i	−0.612017	−	1.06004i
$986$	−3.45403	−	0.925505i	−0.109999	−	0.0294741i
$987$		0			0
$988$	8.42998	+	29.3811i	0.268193	+	0.934737i
$989$	−11.4651			−0.364569
$990$		0			0
$991$	1.24883	+	2.16303i	0.0396703	+	0.0687110i	0.885179	−	0.465251i	$-0.154036\pi$
$991$	1.24883	+	2.16303i	0.0396703	+	0.0687110i	−0.845509	+	0.533962i	$0.820703\pi$
$992$	−2.97089	+	5.14574i	−0.0943259	+	0.163377i
$993$		0			0
$994$	−0.114469	+	1.46484i	−0.00363075	+	0.0464620i
$995$	−32.8817	+	8.81062i	−1.04242	+	0.279315i
$996$		0			0
$997$	5.16724	+	2.98331i	0.163648	+	0.0944823i	0.579587	−	0.814910i	$-0.303214\pi$
$997$	5.16724	+	2.98331i	0.163648	+	0.0944823i	−0.415939	+	0.909392i	$0.636547\pi$
$998$	1.68806	−	0.974599i	0.0534345	−	0.0308504i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.g.496.3		32
3.2	odd	2		91.2.bc.a.41.6	yes	32
7.6	odd	2	inner	819.2.fm.g.496.4		32
13.7	odd	12	inner	819.2.fm.g.748.4		32
21.2	odd	6		637.2.x.b.80.4		32
21.5	even	6		637.2.x.b.80.3		32
21.11	odd	6		637.2.bb.b.509.3		32
21.17	even	6		637.2.bb.b.509.4		32
21.20	even	2		91.2.bc.a.41.5	yes	32
39.20	even	12		91.2.bc.a.20.5	✓	32
91.20	even	12	inner	819.2.fm.g.748.3		32
273.20	odd	12		91.2.bc.a.20.6	yes	32
273.59	odd	12		637.2.x.b.215.3		32
273.137	even	12		637.2.x.b.215.4		32
273.215	odd	12		637.2.bb.b.423.3		32
273.254	even	12		637.2.bb.b.423.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.5	✓	32	39.20	even	12
91.2.bc.a.20.6	yes	32	273.20	odd	12
91.2.bc.a.41.5	yes	32	21.20	even	2
91.2.bc.a.41.6	yes	32	3.2	odd	2
637.2.x.b.80.3		32	21.5	even	6
637.2.x.b.80.4		32	21.2	odd	6
637.2.x.b.215.3		32	273.59	odd	12
637.2.x.b.215.4		32	273.137	even	12
637.2.bb.b.423.3		32	273.215	odd	12
637.2.bb.b.423.4		32	273.254	even	12
637.2.bb.b.509.3		32	21.11	odd	6
637.2.bb.b.509.4		32	21.17	even	6
819.2.fm.g.496.3		32	1.1	even	1	trivial
819.2.fm.g.496.4		32	7.6	odd	2	inner
819.2.fm.g.748.3		32	91.20	even	12	inner
819.2.fm.g.748.4		32	13.7	odd	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)

\(f(q)\)	\(=\)	\(q+(0.112775 + 0.0302180i) q^{2} +(-1.72025 - 0.993184i) q^{4} +(-1.24841 - 1.24841i) q^{5} +(-2.63771 - 0.206123i) q^{7} +(-0.329103 - 0.329103i) q^{8} +O(q^{10})\)	\(q+(0.112775 + 0.0302180i) q^{2} +(-1.72025 - 0.993184i) q^{4} +(-1.24841 - 1.24841i) q^{5} +(-2.63771 - 0.206123i) q^{7} +(-0.329103 - 0.329103i) q^{8} +(-0.103066 - 0.178515i) q^{10} +(0.506699 - 1.89103i) q^{11} +(1.85749 + 3.09026i) q^{13} +(-0.291240 - 0.102952i) q^{14} +(1.95920 + 3.39343i) q^{16} +(-2.13907 + 3.70498i) q^{17} +(-4.12248 + 1.10462i) q^{19} +(0.907674 + 3.38749i) q^{20} +(0.114286 - 0.197949i) q^{22} +(5.53927 - 3.19810i) q^{23} -1.88292i q^{25} +(0.116097 + 0.404635i) q^{26} +(4.33279 + 2.97431i) q^{28} +(3.57954 + 6.19995i) q^{29} +(3.02628 + 3.02628i) q^{31} +(0.359327 + 1.34103i) q^{32} +(-0.353191 + 0.353191i) q^{34} +(3.03563 + 3.55028i) q^{35} +(-0.732202 + 2.73261i) q^{37} -0.498293 q^{38} +0.821715i q^{40} +(-2.94901 + 11.0059i) q^{41} +(-1.55234 - 0.896243i) q^{43} +(-2.74978 + 2.74978i) q^{44} +(0.721333 - 0.193281i) q^{46} +(-4.68665 + 4.68665i) q^{47} +(6.91503 + 1.08738i) q^{49} +(0.0568982 - 0.212347i) q^{50} +(-0.126138 - 7.16084i) q^{52} -4.27793 q^{53} +(-2.99335 + 1.72821i) q^{55} +(0.800244 + 0.935915i) q^{56} +(0.216333 + 0.807367i) q^{58} +(-0.436704 - 1.62980i) q^{59} +(-2.66960 - 1.54129i) q^{61} +(0.249841 + 0.432737i) q^{62} -7.67470i q^{64} +(1.53901 - 6.17685i) q^{65} +(-0.0190380 - 0.00510122i) q^{67} +(7.35945 - 4.24898i) q^{68} +(0.235061 + 0.492115i) q^{70} +(-1.23109 - 4.59449i) q^{71} +(-0.698492 + 0.698492i) q^{73} +(-0.165148 + 0.286046i) q^{74} +(8.18877 + 2.19417i) q^{76} +(-1.72631 + 4.88353i) q^{77} -5.93719 q^{79} +(1.79052 - 6.68230i) q^{80} +(-0.665151 + 1.15208i) q^{82} +(9.87683 + 9.87683i) q^{83} +(7.29580 - 1.95490i) q^{85} +(-0.147983 - 0.147983i) q^{86} +(-0.789099 + 0.455587i) q^{88} +(-7.76240 - 2.07993i) q^{89} +(-4.26255 - 8.53409i) q^{91} -12.7052 q^{92} +(-0.670159 + 0.386917i) q^{94} +(6.52558 + 3.76755i) q^{95} +(-14.2676 + 3.82300i) q^{97} +(0.746985 + 0.331588i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

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