LMFDB - Embedded newform 819.2.fm.f.496.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			496.7
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.f.748.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11902 + 0.567791i) q^{2} +(2.43582 + 1.40632i) q^{4} +(-3.00219 - 3.00219i) q^{5} +(-2.49394 + 0.883331i) q^{7} +(1.26060 + 1.26060i) q^{8} +O(q^{10})$	\(q+(2.11902 + 0.567791i) q^{2} +(2.43582 + 1.40632i) q^{4} +(-3.00219 - 3.00219i) q^{5} +(-2.49394 + 0.883331i) q^{7} +(1.26060 + 1.26060i) q^{8} +(-4.65710 - 8.06633i) q^{10} +(0.698323 - 2.60618i) q^{11} +(-0.373866 - 3.58612i) q^{13} +(-5.78626 + 0.455764i) q^{14} +(-0.857159 - 1.48464i) q^{16} +(0.599399 - 1.03819i) q^{17} +(-1.89568 + 0.507945i) q^{19} +(-3.09075 - 11.5349i) q^{20} +(2.95953 - 5.12605i) q^{22} +(4.65282 - 2.68631i) q^{23} +13.0263i q^{25} +(1.24393 - 7.81134i) q^{26} +(-7.31704 - 1.35564i) q^{28} +(-1.47928 - 2.56220i) q^{29} +(3.36721 + 3.36721i) q^{31} +(-1.89620 - 7.07671i) q^{32} +(1.85961 - 1.85961i) q^{34} +(10.1392 + 4.83535i) q^{35} +(-1.03769 + 3.87273i) q^{37} -4.30539 q^{38} -7.56914i q^{40} +(-1.42770 + 5.32825i) q^{41} +(-9.78317 - 5.64832i) q^{43} +(5.36612 - 5.36612i) q^{44} +(11.3847 - 3.05052i) q^{46} +(-2.97828 + 2.97828i) q^{47} +(5.43945 - 4.40594i) q^{49} +(-7.39621 + 27.6030i) q^{50} +(4.13256 - 9.26092i) q^{52} +11.0603 q^{53} +(-9.92075 + 5.72775i) q^{55} +(-4.25739 - 2.03033i) q^{56} +(-1.67985 - 6.26927i) q^{58} +(-3.14721 - 11.7455i) q^{59} +(4.55683 + 2.63089i) q^{61} +(5.22332 + 9.04706i) q^{62} -12.6437i q^{64} +(-9.64379 + 11.8886i) q^{65} +(4.15530 + 1.11341i) q^{67} +(2.92006 - 1.68590i) q^{68} +(18.7397 + 16.0032i) q^{70} +(-0.800761 - 2.98848i) q^{71} +(-4.78407 + 4.78407i) q^{73} +(-4.39780 + 7.61721i) q^{74} +(-5.33186 - 1.42867i) q^{76} +(0.560542 + 7.11650i) q^{77} -1.16895 q^{79} +(-1.88383 + 7.03054i) q^{80} +(-6.05066 + 10.4801i) q^{82} +(-3.24002 - 3.24002i) q^{83} +(-4.91635 + 1.31733i) q^{85} +(-17.5237 - 17.5237i) q^{86} +(4.16566 - 2.40505i) q^{88} +(4.80209 + 1.28672i) q^{89} +(4.10012 + 8.61330i) q^{91} +15.1113 q^{92} +(-8.00209 + 4.62001i) q^{94} +(7.21613 + 4.16623i) q^{95} +(14.7483 - 3.95180i) q^{97} +(14.0280 - 6.24783i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.11902	+	0.567791i	1.49838	+	0.401489i	0.912556	−	0.408953i	$-0.134106\pi$
$2$	2.11902	+	0.567791i	1.49838	+	0.401489i	0.585820	+	0.810441i	$0.300773\pi$
$3$		0			0
$3$		0			0
$4$	2.43582	+	1.40632i	1.21791	+	0.703161i
$5$	−3.00219	−	3.00219i	−1.34262	−	1.34262i	−0.893442	−	0.449179i	$-0.851717\pi$
$5$	−3.00219	−	3.00219i	−1.34262	−	1.34262i	−0.449179	−	0.893442i	$-0.648283\pi$
$6$		0			0
$7$	−2.49394	+	0.883331i	−0.942620	+	0.333868i
$7$	−2.49394	+	0.883331i	−0.942620	+	0.333868i
$8$	1.26060	+	1.26060i	0.445690	+	0.445690i
$9$		0			0
$10$	−4.65710	−	8.06633i	−1.47270	−	2.55080i
$11$	0.698323	−	2.60618i	0.210552	−	0.785792i	−0.777133	−	0.629337i	$-0.783327\pi$
$11$	0.698323	−	2.60618i	0.210552	−	0.785792i	0.987685	−	0.156455i	$-0.0500068\pi$
$12$		0			0
$13$	−0.373866	−	3.58612i	−0.103692	−	0.994609i
$13$	−0.373866	−	3.58612i	−0.103692	−	0.994609i
$14$	−5.78626	+	0.455764i	−1.54644	+	0.121808i
$15$		0			0
$16$	−0.857159	−	1.48464i	−0.214290	−	0.371161i
$17$	0.599399	−	1.03819i	0.145376	−	0.251798i	−0.784137	−	0.620587i	$-0.786894\pi$
$17$	0.599399	−	1.03819i	0.145376	−	0.251798i	0.929513	+	0.368789i	$0.120228\pi$
$18$		0			0
$19$	−1.89568	+	0.507945i	−0.434898	+	0.116531i	−0.469624	−	0.882866i	$-0.655611\pi$
$19$	−1.89568	+	0.507945i	−0.434898	+	0.116531i	0.0347266	+	0.999397i	$0.488944\pi$
$20$	−3.09075	−	11.5349i	−0.691114	−	2.57927i
$21$		0			0
$22$	2.95953	−	5.12605i	0.630973	−	1.09288i
$23$	4.65282	−	2.68631i	0.970181	−	0.560134i	0.0708893	−	0.997484i	$-0.477416\pi$
$23$	4.65282	−	2.68631i	0.970181	−	0.560134i	0.899291	+	0.437350i	$0.144083\pi$
$24$		0			0
$25$			13.0263i			2.60526i
$26$	1.24393	−	7.81134i	0.243955	−	1.53193i
$27$		0			0
$28$	−7.31704	−	1.35564i	−1.38279	−	0.256193i
$29$	−1.47928	−	2.56220i	−0.274696	−	0.475788i	0.695362	−	0.718659i	$-0.255244\pi$
$29$	−1.47928	−	2.56220i	−0.274696	−	0.475788i	−0.970058	+	0.242872i	$0.921911\pi$
$30$		0			0
$31$	3.36721	+	3.36721i	0.604768	+	0.604768i	0.941574	−	0.336806i	$-0.109347\pi$
$31$	3.36721	+	3.36721i	0.604768	+	0.604768i	−0.336806	+	0.941574i	$0.609347\pi$
$32$	−1.89620	−	7.07671i	−0.335204	−	1.25100i
$33$		0			0
$34$	1.85961	−	1.85961i	0.318921	−	0.318921i
$35$	10.1392	+	4.83535i	1.71384	+	0.817324i
$36$		0			0
$37$	−1.03769	+	3.87273i	−0.170596	+	0.636673i	0.826664	+	0.562696i	$0.190236\pi$
$37$	−1.03769	+	3.87273i	−0.170596	+	0.636673i	−0.997260	+	0.0739770i	$0.976431\pi$
$38$	−4.30539			−0.698426
$39$		0			0
$40$		−	7.56914i		−	1.19679i
$41$	−1.42770	+	5.32825i	−0.222969	+	0.832133i	0.760239	+	0.649644i	$0.225082\pi$
$41$	−1.42770	+	5.32825i	−0.222969	+	0.832133i	−0.983208	+	0.182489i	$0.941585\pi$
$42$		0			0
$43$	−9.78317	−	5.64832i	−1.49192	−	0.861360i	−0.491963	−	0.870616i	$-0.663720\pi$
$43$	−9.78317	−	5.64832i	−1.49192	−	0.861360i	−0.999957	+	0.00925580i	$0.997054\pi$
$44$	5.36612	−	5.36612i	0.808973	−	0.808973i
$45$		0			0
$46$	11.3847	−	3.05052i	1.67858	−	0.449775i
$47$	−2.97828	+	2.97828i	−0.434427	+	0.434427i	−0.890131	−	0.455704i	$-0.849387\pi$
$47$	−2.97828	+	2.97828i	−0.434427	+	0.434427i	0.455704	+	0.890131i	$0.349387\pi$
$48$		0			0
$49$	5.43945	−	4.40594i	0.777065	−	0.629421i
$50$	−7.39621	+	27.6030i	−1.04598	+	3.90366i
$51$		0			0
$52$	4.13256	−	9.26092i	0.573084	−	1.28426i
$53$	11.0603			1.51925			0.759627	−	0.650359i	$-0.225382\pi$
$53$	11.0603			1.51925			0.759627	+	0.650359i	$0.225382\pi$
$54$		0			0
$55$	−9.92075	+	5.72775i	−1.33771	+	0.772329i
$56$	−4.25739	−	2.03033i	−0.568918	−	0.271315i
$57$		0			0
$58$	−1.67985	−	6.26927i	−0.220575	−	0.823196i
$59$	−3.14721	−	11.7455i	−0.409731	−	1.52914i	−0.795160	−	0.606400i	$-0.792613\pi$
$59$	−3.14721	−	11.7455i	−0.409731	−	1.52914i	0.385428	−	0.922738i	$-0.374054\pi$
$60$		0			0
$61$	4.55683	+	2.63089i	0.583442	+	0.336851i	0.762500	−	0.646988i	$-0.223972\pi$
$61$	4.55683	+	2.63089i	0.583442	+	0.336851i	−0.179058	+	0.983839i	$0.557305\pi$
$62$	5.22332	+	9.04706i	0.663362	+	1.14898i
$63$		0			0
$64$		−	12.6437i		−	1.58046i
$65$	−9.64379	+	11.8886i	−1.19616	+	1.47460i
$66$		0			0
$67$	4.15530	+	1.11341i	0.507651	+	0.136025i	0.503549	−	0.863967i	$-0.332028\pi$
$67$	4.15530	+	1.11341i	0.507651	+	0.136025i	0.00410235	+	0.999992i	$0.498694\pi$
$68$	2.92006	−	1.68590i	0.354109	−	0.204445i
$69$		0			0
$70$	18.7397	+	16.0032i	2.23983	+	1.91274i
$71$	−0.800761	−	2.98848i	−0.0950329	−	0.354668i	0.901992	−	0.431754i	$-0.142105\pi$
$71$	−0.800761	−	2.98848i	−0.0950329	−	0.354668i	−0.997024	+	0.0770861i	$0.975438\pi$
$72$		0			0
$73$	−4.78407	+	4.78407i	−0.559933	+	0.559933i	−0.929288	−	0.369355i	$-0.879579\pi$
$73$	−4.78407	+	4.78407i	−0.559933	+	0.559933i	0.369355	+	0.929288i	$0.379579\pi$
$74$	−4.39780	+	7.61721i	−0.511234	+	0.885483i
$75$		0			0
$76$	−5.33186	−	1.42867i	−0.611607	−	0.163879i
$77$	0.560542	+	7.11650i	0.0638797	+	0.811000i
$78$		0			0
$79$	−1.16895			−0.131517			−0.0657584	−	0.997836i	$-0.520947\pi$
$79$	−1.16895			−0.131517			−0.0657584	+	0.997836i	$0.520947\pi$
$80$	−1.88383	+	7.03054i	−0.210618	+	0.786038i
$81$		0			0
$82$	−6.05066	+	10.4801i	−0.668184	+	1.15733i
$83$	−3.24002	−	3.24002i	−0.355639	−	0.355639i	0.506564	−	0.862202i	$-0.330915\pi$
$83$	−3.24002	−	3.24002i	−0.355639	−	0.355639i	−0.862202	+	0.506564i	$0.830915\pi$
$84$		0			0
$85$	−4.91635	+	1.31733i	−0.533253	+	0.142885i
$86$	−17.5237	−	17.5237i	−1.88963	−	1.88963i
$87$		0			0
$88$	4.16566	−	2.40505i	0.444061	−	0.256379i
$89$	4.80209	+	1.28672i	0.509020	+	0.136392i	0.504183	−	0.863597i	$-0.331794\pi$
$89$	4.80209	+	1.28672i	0.509020	+	0.136392i	0.00483713	+	0.999988i	$0.498460\pi$
$90$		0			0
$91$	4.10012	+	8.61330i	0.429810	+	0.902919i
$92$	15.1113			1.57546
$93$		0			0
$94$	−8.00209	+	4.62001i	−0.825352	+	0.476517i
$95$	7.21613	+	4.16623i	0.740359	+	0.427447i
$96$		0			0
$97$	14.7483	−	3.95180i	1.49746	−	0.401244i	0.585214	−	0.810879i	$-0.301010\pi$
$97$	14.7483	−	3.95180i	1.49746	−	0.401244i	0.912250	+	0.409634i	$0.134344\pi$
$98$	14.0280	−	6.24783i	1.41704	−	0.631126i
$99$		0			0
$100$	−18.3192	+	31.7298i	−1.83192	+	3.17298i
$101$	−0.803086	−	1.39099i	−0.0799101	−	0.138408i	0.823301	−	0.567605i	$-0.192130\pi$
$101$	−0.803086	−	1.39099i	−0.0799101	−	0.138408i	−0.903211	+	0.429197i	$0.858797\pi$
$102$		0			0
$103$	14.4997			1.42870			0.714351	−	0.699787i	$-0.246722\pi$
$103$	14.4997			1.42870			0.714351	+	0.699787i	$0.246722\pi$
$104$	4.04937	−	4.99196i	0.397073	−	0.489502i
$105$		0			0
$106$	23.4371	+	6.27995i	2.27641	+	0.609963i
$107$	−1.91021	−	3.30858i	−0.184667	−	0.319852i	0.758797	−	0.651327i	$-0.225787\pi$
$107$	−1.91021	−	3.30858i	−0.184667	−	0.319852i	−0.943464	+	0.331475i	$0.892454\pi$
$108$		0			0
$109$	9.59246	−	9.59246i	0.918791	−	0.918791i	−0.0781507	−	0.996942i	$-0.524902\pi$
$109$	9.59246	−	9.59246i	0.918791	−	0.918791i	0.996942	+	0.0781507i	$0.0249015\pi$
$110$	−24.2745	+	6.50432i	−2.31448	+	0.620163i
$111$		0			0
$112$	3.44913	+	2.94545i	0.325912	+	0.278319i
$113$	1.57880	−	2.73457i	0.148521	−	0.257247i	−0.782160	−	0.623078i	$-0.785882\pi$
$113$	1.57880	−	2.73457i	0.148521	−	0.257247i	0.930681	+	0.365831i	$0.119215\pi$
$114$		0			0
$115$	−22.0335	−	5.90385i	−2.05463	−	0.550537i
$116$		−	8.32140i		−	0.772623i
$117$		0			0
$118$		−	26.6760i		−	2.45573i
$119$	−0.577799	+	3.11865i	−0.0529668	+	0.285886i
$120$		0			0
$121$	3.22177	+	1.86009i	0.292888	+	0.169099i
$122$	8.16224	+	8.16224i	0.738974	+	0.738974i
$123$		0			0
$124$	3.46654	+	12.9373i	0.311304	+	1.16180i
$125$	24.0965	−	24.0965i	2.15526	−	2.15526i
$126$		0			0
$127$	5.77265	−	3.33284i	0.512240	−	0.295742i	−0.221514	−	0.975157i	$-0.571100\pi$
$127$	5.77265	−	3.33284i	0.512240	−	0.295742i	0.733754	+	0.679415i	$0.237767\pi$
$128$	3.38658	−	12.6389i	0.299335	−	1.11713i
$129$		0			0
$130$	−27.1857	+	19.7166i	−2.38434	+	1.72926i
$131$			9.80212i			0.856415i	0.903680	+	0.428207i	$0.140855\pi$
$131$			9.80212i			0.856415i	−0.903680	+	0.428207i	$0.859145\pi$
$132$		0			0
$133$	4.27901	−	2.94129i	0.371038	−	0.255042i
$134$	8.17300	+	4.71868i	0.706039	+	0.407632i
$135$		0			0
$136$	2.06435	−	0.553140i	0.177016	−	0.0474314i
$137$	−6.48757	+	1.73834i	−0.554271	+	0.148516i	−0.525073	−	0.851057i	$-0.675962\pi$
$137$	−6.48757	+	1.73834i	−0.554271	+	0.148516i	−0.0291978	+	0.999574i	$0.509295\pi$
$138$		0			0
$139$	0.304839	+	0.175999i	0.0258561	+	0.0149280i	0.512872	−	0.858465i	$-0.328581\pi$
$139$	0.304839	+	0.175999i	0.0258561	+	0.0149280i	−0.487016	+	0.873393i	$0.661915\pi$
$140$	17.8972	+	26.0371i	1.51259	+	2.20053i
$141$		0			0
$142$		−	6.78733i		−	0.569580i
$143$	−9.60714	−	1.52991i	−0.803389	−	0.127937i
$144$		0			0
$145$	−3.25111	+	12.1333i	−0.269990	+	1.00762i
$146$	−12.8539	+	7.42121i	−1.06380	+	0.614184i
$147$		0			0
$148$	−7.97395	+	7.97395i	−0.655455	+	0.655455i
$149$	−3.05452	−	11.3996i	−0.250236	−	0.933892i	−0.970679	−	0.240379i	$-0.922728\pi$
$149$	−3.05452	−	11.3996i	−0.250236	−	0.933892i	0.720443	−	0.693514i	$-0.243938\pi$
$150$		0			0
$151$	−12.2745	−	12.2745i	−0.998884	−	0.998884i	0.00111530	−	0.999999i	$-0.499645\pi$
$151$	−12.2745	−	12.2745i	−0.998884	−	0.998884i	−0.999999	+	0.00111530i	$0.999645\pi$
$152$	−3.03001	−	1.74938i	−0.245766	−	0.141893i
$153$		0			0
$154$	−2.85288	+	15.3983i	−0.229891	+	1.24083i
$155$		−	20.2180i		−	1.62395i
$156$		0			0
$157$		−	4.41109i		−	0.352043i	−0.984386	−	0.176022i	$-0.943677\pi$
$157$		−	4.41109i		−	0.352043i	0.984386	−	0.176022i	$-0.0563228\pi$
$158$	−2.47702	−	0.663716i	−0.197061	−	0.0528024i
$159$		0			0
$160$	−15.5529	+	26.9384i	−1.22956	+	2.12967i
$161$	−9.23095	+	10.8095i	−0.727501	+	0.851905i
$162$		0			0
$163$	−0.610931	+	0.163698i	−0.0478518	+	0.0128219i	−0.282666	−	0.959219i	$-0.591219\pi$
$163$	−0.610931	+	0.163698i	−0.0478518	+	0.0128219i	0.234814	+	0.972040i	$0.424552\pi$
$164$	−10.9709	+	10.9709i	−0.856680	+	0.856680i
$165$		0			0
$166$	−5.02603	−	8.70534i	−0.390096	−	0.675665i
$167$	−16.3769	−	4.38817i	−1.26728	−	0.339567i	−0.438292	−	0.898833i	$-0.644416\pi$
$167$	−16.3769	−	4.38817i	−1.26728	−	0.339567i	−0.828988	+	0.559266i	$0.811083\pi$
$168$		0			0
$169$	−12.7204	+	2.68145i	−0.978496	+	0.206266i
$170$	−11.1658			−0.856380
$171$		0			0
$172$	−15.8867	−	27.5166i	−1.21135	−	2.09812i
$173$	4.60670	−	7.97903i	0.350241	−	0.606634i	−0.636051	−	0.771647i	$-0.719433\pi$
$173$	4.60670	−	7.97903i	0.350241	−	0.606634i	0.986291	+	0.165013i	$0.0527665\pi$
$174$		0			0
$175$	−11.5065	−	32.4868i	−0.869812	−	2.45577i
$176$	−4.46782	+	1.19715i	−0.336774	+	0.0902384i
$177$		0			0
$178$	9.44515	+	5.45316i	0.707944	+	0.408732i
$179$	−2.35631	+	1.36042i	−0.176119	+	0.101682i	−0.585468	−	0.810696i	$-0.699089\pi$
$179$	−2.35631	+	1.36042i	−0.176119	+	0.101682i	0.409349	+	0.912378i	$0.365756\pi$
$180$		0			0
$181$	15.4525			1.14858			0.574288	−	0.818653i	$-0.305279\pi$
$181$	15.4525			1.14858			0.574288	+	0.818653i	$0.305279\pi$
$182$	3.79771	+	20.5798i	0.281505	+	1.52548i
$183$		0			0
$184$	9.25172	+	2.47899i	0.682046	+	0.182754i
$185$	14.7420	−	8.51132i	1.08386	−	0.625765i
$186$		0			0
$187$	−2.28713	−	2.28713i	−0.167252	−	0.167252i
$188$	−11.4430	+	3.06614i	−0.834566	+	0.223621i
$189$		0			0
$190$	12.9256	+	12.9256i	0.937721	+	0.937721i
$191$	−1.63770	+	2.83658i	−0.118500	+	0.205248i	−0.919173	−	0.393853i	$-0.871142\pi$
$191$	−1.63770	+	2.83658i	−0.118500	+	0.205248i	0.800673	+	0.599101i	$0.204475\pi$
$192$		0			0
$193$	−5.44447	+	20.3190i	−0.391901	+	1.46260i	0.435093	+	0.900385i	$0.356715\pi$
$193$	−5.44447	+	20.3190i	−0.391901	+	1.46260i	−0.826995	+	0.562210i	$0.809951\pi$
$194$	33.4958			2.40486
$195$		0			0
$196$	19.4457	−	3.08247i	1.38898	−	0.220176i
$197$	−20.1959	−	5.41149i	−1.43890	−	0.385553i	−0.546753	−	0.837294i	$-0.684136\pi$
$197$	−20.1959	−	5.41149i	−1.43890	−	0.385553i	−0.892149	+	0.451741i	$0.850803\pi$
$198$		0			0
$199$	12.4685	−	21.5960i	0.883867	−	1.53090i	0.0368601	−	0.999320i	$-0.488264\pi$
$199$	12.4685	−	21.5960i	0.883867	−	1.53090i	0.847007	−	0.531582i	$-0.178402\pi$
$200$	−16.4210	+	16.4210i	−1.16114	+	1.16114i
$201$		0			0
$202$	−0.911969	−	3.40352i	−0.0641659	−	0.239471i
$203$	5.95251	+	5.08326i	0.417784	+	0.356775i
$204$		0			0
$205$	20.2827	−	11.7102i	1.41660	−	0.817876i
$206$	30.7253	+	8.23282i	2.14073	+	0.573608i
$207$		0			0
$208$	−5.00364	+	3.62893i	−0.346940	+	0.251621i
$209$			5.29518i			0.366275i
$210$		0			0
$211$	5.46157	+	9.45972i	0.375990	+	0.651234i	0.990475	−	0.137695i	$-0.0439694\pi$
$211$	5.46157	+	9.45972i	0.375990	+	0.651234i	−0.614485	+	0.788929i	$0.710636\pi$
$212$	26.9410	+	15.5544i	1.85032	+	1.06828i
$213$		0			0
$214$	−2.16919	−	8.09554i	−0.148283	−	0.553400i
$215$	12.4136	+	46.3283i	0.846602	+	3.15956i
$216$		0			0
$217$	−11.3720	−	5.42325i	−0.771979	−	0.368154i
$218$	25.7731	−	14.8801i	1.74558	−	1.00781i
$219$		0			0
$220$	−32.2202			−2.17229
$221$	−3.94716	−	1.76137i	−0.265515	−	0.118483i
$222$		0			0
$223$	3.99267	−	14.9009i	0.267369	−	0.997835i	−0.693415	−	0.720538i	$-0.743895\pi$
$223$	3.99267	−	14.9009i	0.267369	−	0.997835i	0.960784	−	0.277297i	$-0.0894385\pi$
$224$	10.9801	+	15.9739i	0.733637	+	1.06730i
$225$		0			0
$226$	4.89819	−	4.89819i	0.325823	−	0.325823i
$227$	−18.6556	+	4.99875i	−1.23822	+	0.331779i	−0.817773	−	0.575541i	$-0.804792\pi$
$227$	−18.6556	+	4.99875i	−1.23822	+	0.331779i	−0.420442	+	0.907319i	$0.638125\pi$
$228$		0			0
$229$	−12.6136	+	12.6136i	−0.833528	+	0.833528i	−0.987998	−	0.154470i	$-0.950633\pi$
$229$	−12.6136	+	12.6136i	−0.833528	+	0.833528i	0.154470	+	0.987998i	$0.450633\pi$
$230$	−43.3373	−	25.0208i	−2.85758	−	1.64982i
$231$		0			0
$232$	1.36512	−	5.09470i	0.0896245	−	0.334483i
$233$			24.9418i			1.63399i	0.576643	+	0.816996i	$0.304362\pi$
$233$			24.9418i			1.63399i	−0.576643	+	0.816996i	$0.695638\pi$
$234$		0			0
$235$	17.8827			1.16654
$236$	8.85197	−	33.0360i	0.576214	−	2.15046i
$237$		0			0
$238$	−2.99511	+	6.28042i	−0.194144	+	0.407099i
$239$	4.67931	−	4.67931i	0.302680	−	0.302680i	−0.539382	−	0.842061i	$-0.681342\pi$
$239$	4.67931	−	4.67931i	0.302680	−	0.302680i	0.842061	+	0.539382i	$0.181342\pi$
$240$		0			0
$241$	0.169033	+	0.630839i	0.0108884	+	0.0406359i	0.971156	−	0.238444i	$-0.0766373\pi$
$241$	0.169033	+	0.630839i	0.0108884	+	0.0406359i	−0.960268	+	0.279080i	$0.909971\pi$
$242$	5.77086	+	5.77086i	0.370965	+	0.370965i
$243$		0			0
$244$	7.39975	+	12.8167i	0.473721	+	0.820508i
$245$	−29.5578	−	3.10279i	−1.88838	−	0.198230i
$246$		0			0
$247$	2.53028	+	6.60821i	0.160998	+	0.420470i
$248$			8.48941i			0.539078i
$249$		0			0
$250$	64.7428	−	37.3793i	4.09470	−	2.36407i
$251$	9.89477	−	17.1382i	0.624552	−	1.08176i	−0.364075	−	0.931370i	$-0.618615\pi$
$251$	9.89477	−	17.1382i	0.624552	−	1.08176i	0.988627	−	0.150386i	$-0.0480518\pi$
$252$		0			0
$253$	−3.75182	−	14.0020i	−0.235875	−	0.880298i
$254$	14.1247	−	3.78471i	0.886265	−	0.237474i
$255$		0			0
$256$	1.70879	−	2.95971i	0.106799	−	0.184982i
$257$	−7.97194	−	13.8078i	−0.497276	−	0.861307i	0.502719	−	0.864450i	$-0.332333\pi$
$257$	−7.97194	−	13.8078i	−0.497276	−	0.861307i	−0.999995	+	0.00314245i	$0.999000\pi$
$258$		0			0
$259$	−0.832955	−	10.5750i	−0.0517573	−	0.657097i
$260$	−40.2098	+	15.3963i	−2.49371	+	0.954838i
$261$		0			0
$262$	−5.56555	+	20.7709i	−0.343841	+	1.28323i
$263$	0.217727	+	0.377114i	0.0134256	+	0.0232538i	0.872660	−	0.488328i	$-0.162393\pi$
$263$	0.217727	+	0.377114i	0.0134256	+	0.0232538i	−0.859235	+	0.511582i	$0.829060\pi$
$264$		0			0
$265$	−33.2052	−	33.2052i	−2.03978	−	2.03978i
$266$	10.7374	−	3.80308i	0.658350	−	0.233182i
$267$		0			0
$268$	8.55576	+	8.55576i	0.522626	+	0.522626i
$269$	14.2630	+	8.23477i	0.869633	+	0.502083i	0.867226	−	0.497914i	$-0.165901\pi$
$269$	14.2630	+	8.23477i	0.869633	+	0.502083i	0.00240680	+	0.999997i	$0.499234\pi$
$270$		0			0
$271$	22.4966	+	6.02794i	1.36657	+	0.366171i	0.866224	−	0.499655i	$-0.166540\pi$
$271$	22.4966	+	6.02794i	1.36657	+	0.366171i	0.500345	+	0.865826i	$0.333207\pi$
$272$	−2.05512			−0.124610
$273$		0			0
$274$	−14.7343			−0.890133
$275$	33.9489	+	9.09658i	2.04719	+	0.548544i
$276$		0			0
$277$	7.08167	+	4.08860i	0.425496	+	0.245660i	0.697426	−	0.716657i	$-0.254329\pi$
$277$	7.08167	+	4.08860i	0.425496	+	0.245660i	−0.271930	+	0.962317i	$0.587662\pi$
$278$	0.546031	+	0.546031i	0.0327488	+	0.0327488i
$279$		0			0
$280$	6.68605	+	18.8770i	0.399568	+	1.12811i
$281$	−3.14177	−	3.14177i	−0.187422	−	0.187422i	0.607159	−	0.794581i	$-0.292309\pi$
$281$	−3.14177	−	3.14177i	−0.187422	−	0.187422i	−0.794581	+	0.607159i	$0.792309\pi$
$282$		0			0
$283$	−6.35147	−	11.0011i	−0.377555	−	0.653945i	0.613151	−	0.789966i	$-0.289902\pi$
$283$	−6.35147	−	11.0011i	−0.377555	−	0.653945i	−0.990706	+	0.136021i	$0.956569\pi$
$284$	2.25226	−	8.40554i	0.133647	−	0.498777i
$285$		0			0
$286$	−19.4891	−	8.69675i	−1.15241	−	0.514250i
$287$	−1.14601	−	14.5495i	−0.0676469	−	0.858827i
$288$		0			0
$289$	7.78144	+	13.4779i	0.457732	+	0.792815i
$290$	−13.7783	+	23.8648i	−0.809092	+	1.40139i
$291$		0			0
$292$	−18.3811	+	4.92520i	−1.07567	+	0.288226i
$293$	−1.47718	−	5.51290i	−0.0862977	−	0.322067i	0.909259	−	0.416231i	$-0.136649\pi$
$293$	−1.47718	−	5.51290i	−0.0862977	−	0.322067i	−0.995557	+	0.0941633i	$0.969982\pi$
$294$		0			0
$295$	−25.8138	+	44.7109i	−1.50294	+	2.60317i
$296$	−6.19009	+	3.57385i	−0.359792	+	0.207726i
$297$		0			0
$298$		−	25.8904i		−	1.49979i
$299$	−11.3729	−	15.6812i	−0.657714	−	0.906870i
$300$		0			0
$301$	29.3880	+	5.44478i	1.69389	+	0.313832i
$302$	−19.0406	−	32.9793i	−1.09566	−	1.89774i
$303$		0			0
$304$	2.37901	+	2.37901i	0.136446	+	0.136446i
$305$	−5.78205	−	21.5789i	−0.331079	−	1.23560i
$306$		0			0
$307$	−10.2283	+	10.2283i	−0.583760	+	0.583760i	−0.935934	−	0.352174i	$-0.885442\pi$
$307$	−10.2283	+	10.2283i	−0.583760	+	0.583760i	0.352174	+	0.935934i	$0.385442\pi$
$308$	−8.64271	+	18.1228i	−0.492464	+	1.03264i
$309$		0			0
$310$	11.4796	−	42.8424i	0.651997	−	2.43328i
$311$	14.6147			0.828724			0.414362	−	0.910112i	$-0.364005\pi$
$311$	14.6147			0.828724			0.414362	+	0.910112i	$0.364005\pi$
$312$		0			0
$313$			17.9984i			1.01733i	0.860965	+	0.508665i	$0.169861\pi$
$313$			17.9984i			1.01733i	−0.860965	+	0.508665i	$0.830139\pi$
$314$	2.50457	−	9.34720i	0.141341	−	0.527493i
$315$		0			0
$316$	−2.84734	−	1.64392i	−0.160176	−	0.0924775i
$317$	12.0835	−	12.0835i	0.678674	−	0.678674i	−0.281026	−	0.959700i	$-0.590675\pi$
$317$	12.0835	−	12.0835i	0.678674	−	0.678674i	0.959700	+	0.281026i	$0.0906747\pi$
$318$		0			0
$319$	−7.71056	+	2.06604i	−0.431708	+	0.115676i
$320$	−37.9588	+	37.9588i	−2.12196	+	2.12196i
$321$		0			0
$322$	−25.6981	+	17.6643i	−1.43210	+	0.984391i
$323$	−0.608923	+	2.27253i	−0.0338814	+	0.126447i
$324$		0			0
$325$	46.7138	−	4.87009i	2.59122	−	0.270144i
$326$	−1.38752			−0.0768478
$327$		0			0
$328$	−8.51656	+	4.91704i	−0.470248	+	0.271498i
$329$	4.79684	−	10.0585i	0.264458	−	0.554541i
$330$		0			0
$331$	2.57122	+	9.59594i	0.141327	+	0.527441i	0.999891	+	0.0147345i	$0.00469030\pi$
$331$	2.57122	+	9.59594i	0.141327	+	0.527441i	−0.858564	+	0.512706i	$0.828643\pi$
$332$	−3.33560	−	12.4486i	−0.183065	−	0.683208i
$333$		0			0
$334$	−32.2114	−	18.5973i	−1.76253	−	1.01760i
$335$	−9.13234	−	15.8177i	−0.498953	−	0.864212i
$336$		0			0
$337$		−	6.44780i		−	0.351234i	−0.984459	−	0.175617i	$-0.943808\pi$
$337$		−	6.44780i		−	0.351234i	0.984459	−	0.175617i	$-0.0561920\pi$
$338$	−28.4774	−	1.54049i	−1.54897	−	0.0837915i
$339$		0			0
$340$	−13.8280	−	3.70519i	−0.749926	−	0.200942i
$341$	11.1269	−	6.42414i	0.602558	−	0.347887i
$342$		0			0
$343$	−9.67375	+	15.7930i	−0.522334	+	0.852741i
$344$	−5.21241	−	19.4530i	−0.281034	−	1.04883i
$345$		0			0
$346$	14.2921	−	14.2921i	0.768349	−	0.768349i
$347$	−6.00501	+	10.4010i	−0.322366	+	0.558354i	−0.980976	−	0.194131i	$-0.937811\pi$
$347$	−6.00501	+	10.4010i	−0.322366	+	0.558354i	0.658610	+	0.752484i	$0.271145\pi$
$348$		0			0
$349$	−24.5954	−	6.59031i	−1.31656	−	0.352771i	−0.468872	−	0.883266i	$-0.655339\pi$
$349$	−24.5954	−	6.59031i	−1.31656	−	0.352771i	−0.847688	+	0.530495i	$0.822006\pi$
$350$	−5.93692	−	75.3736i	−0.317342	−	4.02889i
$351$		0			0
$352$	−19.7673			−1.05360
$353$	2.43053	−	9.07084i	0.129364	−	0.482792i	−0.870594	−	0.492003i	$-0.836265\pi$
$353$	2.43053	−	9.07084i	0.129364	−	0.482792i	0.999958	+	0.00921021i	$0.00293174\pi$
$354$		0			0
$355$	−6.56796	+	11.3760i	−0.348591	+	0.603777i
$356$	9.88750	+	9.88750i	0.524036	+	0.524036i
$357$		0			0
$358$	−5.76551	+	1.54486i	−0.304716	+	0.0816485i
$359$	16.2790	+	16.2790i	0.859171	+	0.859171i	0.991240	−	0.132070i	$-0.0421622\pi$
$359$	16.2790	+	16.2790i	0.859171	+	0.859171i	−0.132070	+	0.991240i	$0.542162\pi$
$360$		0			0
$361$	−13.1189	+	7.57420i	−0.690469	+	0.398642i
$362$	32.7442	+	8.77379i	1.72100	+	0.461140i
$363$		0			0
$364$	−2.12591	+	26.7466i	−0.111428	+	1.40190i
$365$	28.7254			1.50356
$366$		0			0
$367$	−19.6200	+	11.3276i	−1.02416	+	0.591297i	−0.915305	−	0.402761i	$-0.868051\pi$
$367$	−19.6200	+	11.3276i	−1.02416	+	0.591297i	−0.108851	+	0.994058i	$0.534717\pi$
$368$	−7.97642	−	4.60519i	−0.415799	−	0.240062i
$369$		0			0
$370$	36.0714	−	9.66529i	1.87526	−	0.502475i
$371$	−27.5838	+	9.76993i	−1.43208	+	0.507230i
$372$		0			0
$373$	11.0535	−	19.1453i	0.572330	−	0.991305i	−0.423996	−	0.905664i	$-0.639373\pi$
$373$	11.0535	−	19.1453i	0.572330	−	0.991305i	0.996326	−	0.0856409i	$-0.0272938\pi$
$374$	−3.54787	−	6.14510i	−0.183456	−	0.317755i
$375$		0			0
$376$	−7.50885			−0.387240
$377$	−8.63527	+	6.26280i	−0.444739	+	0.322551i
$378$		0			0
$379$	−1.03041	−	0.276097i	−0.0529284	−	0.0141821i	0.232258	−	0.972654i	$-0.425389\pi$
$379$	−1.03041	−	0.276097i	−0.0529284	−	0.0141821i	−0.285186	+	0.958472i	$0.592055\pi$
$380$	11.7181	+	20.2964i	0.601128	+	1.04118i
$381$		0			0
$382$	−5.08092	+	5.08092i	−0.259962	+	0.259962i
$383$	12.0580	−	3.23092i	0.616133	−	0.165092i	0.0627635	−	0.998028i	$-0.480009\pi$
$383$	12.0580	−	3.23092i	0.616133	−	0.165092i	0.553369	+	0.832936i	$0.313342\pi$
$384$		0			0
$385$	19.6822	−	23.0479i	1.00310	−	1.17463i
$386$	−23.0739	+	39.9652i	−1.17443	+	2.03417i
$387$		0			0
$388$	41.4818	+	11.1150i	2.10592	+	0.564279i
$389$			19.0137i			0.964031i	0.876163	+	0.482015i	$0.160095\pi$
$389$			19.0137i			0.964031i	−0.876163	+	0.482015i	$0.839905\pi$
$390$		0			0
$391$		−	6.44068i		−	0.325719i
$392$	12.4111	+	1.30284i	0.626856	+	0.0658035i
$393$		0			0
$394$	−39.7231	−	22.9341i	−2.00122	−	1.15541i
$395$	3.50940	+	3.50940i	0.176577	+	0.176577i
$396$		0			0
$397$	0.702815	+	2.62294i	0.0352733	+	0.131642i	0.981317	−	0.192397i	$-0.0616260\pi$
$397$	0.702815	+	2.62294i	0.0352733	+	0.131642i	−0.946044	+	0.324038i	$0.894959\pi$
$398$	38.6830	−	38.6830i	1.93900	−	1.93900i
$399$		0			0
$400$	19.3394	−	11.1656i	0.966970	−	0.558281i
$401$	−0.821135	+	3.06452i	−0.0410055	+	0.153035i	−0.983393	−	0.181488i	$-0.941909\pi$
$401$	−0.821135	+	3.06452i	−0.0410055	+	0.153035i	0.942388	+	0.334523i	$0.108575\pi$
$402$		0			0
$403$	10.8163	−	13.3341i	0.538799	−	0.664218i
$404$		−	4.51759i		−	0.224759i
$405$		0			0
$406$	9.72728	+	14.1513i	0.482757	+	0.702318i
$407$	9.36838	+	5.40884i	0.464373	+	0.268106i
$408$		0			0
$409$	2.97815	−	0.797992i	0.147260	−	0.0394582i	−0.184436	−	0.982845i	$-0.559046\pi$
$409$	2.97815	−	0.797992i	0.147260	−	0.0394582i	0.331696	+	0.943386i	$0.392379\pi$
$410$	49.6284	−	13.2979i	2.45097	−	0.656735i
$411$		0			0
$412$	35.3188	+	20.3913i	1.74003	+	1.00461i
$413$	18.2241	+	26.5126i	0.896751	+	1.30460i
$414$		0			0
$415$			19.4543i			0.954976i
$416$	−24.6690	+	9.44572i	−1.20950	+	0.463115i
$417$		0			0
$418$	−3.00655	+	11.2206i	−0.147055	+	0.548818i
$419$	−29.0623	+	16.7791i	−1.41979	+	0.819715i	−0.996280	−	0.0861779i	$-0.972535\pi$
$419$	−29.0623	+	16.7791i	−1.41979	+	0.819715i	−0.423508	+	0.905893i	$0.639201\pi$
$420$		0			0
$421$	18.2634	−	18.2634i	0.890104	−	0.890104i	−0.104429	−	0.994532i	$-0.533301\pi$
$421$	18.2634	−	18.2634i	0.890104	−	0.890104i	0.994532	+	0.104429i	$0.0333014\pi$
$422$	6.20205	+	23.1464i	0.301911	+	1.12675i
$423$		0			0
$424$	13.9427	+	13.9427i	0.677116	+	0.677116i
$425$	13.5238	+	7.80795i	0.655999	+	0.378741i
$426$		0			0
$427$	−13.6884	−	2.53608i	−0.662428	−	0.122730i
$428$		−	10.7455i		−	0.519402i
$429$		0			0
$430$			105.219i			5.07411i
$431$	16.9380	+	4.53851i	0.815873	+	0.218612i	0.642541	−	0.766251i	$-0.277880\pi$
$431$	16.9380	+	4.53851i	0.815873	+	0.218612i	0.173331	+	0.984864i	$0.444547\pi$
$432$		0			0
$433$	17.6656	−	30.5978i	0.848957	−	1.47044i	−0.0331835	−	0.999449i	$-0.510565\pi$
$433$	17.6656	−	30.5978i	0.848957	−	1.47044i	0.882140	−	0.470987i	$-0.156102\pi$
$434$	−21.0182	−	17.9489i	−1.00890	−	0.861574i
$435$		0			0
$436$	36.8556	−	9.87543i	1.76506	−	0.472947i
$437$	−7.45575	+	7.45575i	−0.356657	+	0.356657i
$438$		0			0
$439$	9.35887	+	16.2100i	0.446674	+	0.773663i	0.998167	−	0.0605168i	$-0.0192749\pi$
$439$	9.35887	+	16.2100i	0.446674	+	0.773663i	−0.551493	+	0.834180i	$0.685942\pi$
$440$	−19.7265	−	5.28570i	−0.940425	−	0.251986i
$441$		0			0
$442$	−7.36404	−	5.97354i	−0.350272	−	0.284133i
$443$	−30.4948			−1.44885			−0.724426	−	0.689353i	$-0.757895\pi$
$443$	−30.4948			−1.44885			−0.724426	+	0.689353i	$0.757895\pi$
$444$		0			0
$445$	−10.5538	−	18.2798i	−0.500299	−	0.866544i
$446$	16.9211	−	29.3083i	0.801239	−	1.38779i
$447$		0			0
$448$	11.1686	+	31.5326i	0.527666	+	1.48978i
$449$	19.0888	−	5.11484i	0.900859	−	0.241384i	0.221474	−	0.975166i	$-0.428913\pi$
$449$	19.0888	−	5.11484i	0.900859	−	0.241384i	0.679385	+	0.733782i	$0.262247\pi$
$450$		0			0
$451$	12.8894	+	7.44168i	0.606937	+	0.350415i
$452$	7.69138	−	4.44062i	0.361772	−	0.208869i
$453$		0			0
$454$	−42.3699			−1.98852
$455$	13.5494	−	38.1681i	0.635207	−	1.78935i
$456$		0			0
$457$	7.87442	+	2.10994i	0.368350	+	0.0986990i	0.438246	−	0.898855i	$-0.355600\pi$
$457$	7.87442	+	2.10994i	0.368350	+	0.0986990i	−0.0698958	+	0.997554i	$0.522267\pi$
$458$	−33.8903	+	19.5666i	−1.58359	+	0.914286i
$459$		0			0
$460$	−45.3669	−	45.3669i	−2.11524	−	2.11524i
$461$	32.2015	−	8.62836i	1.49977	−	0.401863i	0.586748	−	0.809769i	$-0.300408\pi$
$461$	32.2015	−	8.62836i	1.49977	−	0.401863i	0.913024	+	0.407907i	$0.133741\pi$
$462$		0			0
$463$	1.66118	+	1.66118i	0.0772018	+	0.0772018i	0.744653	−	0.667452i	$-0.232615\pi$
$463$	1.66118	+	1.66118i	0.0772018	+	0.0772018i	−0.667452	+	0.744653i	$0.732615\pi$
$464$	−2.53596	+	4.39242i	−0.117729	+	0.203913i
$465$		0			0
$466$	−14.1617	+	52.8523i	−0.656029	+	2.44833i
$467$	−12.2930			−0.568854			−0.284427	−	0.958698i	$-0.591803\pi$
$467$	−12.2930			−0.568854			−0.284427	+	0.958698i	$0.591803\pi$
$468$		0			0
$469$	−11.3466	+	0.893731i	−0.523936	+	0.0412687i
$470$	37.8939	+	10.1537i	1.74792	+	0.468353i
$471$		0			0
$472$	10.8391	−	18.7738i	0.498908	−	0.864135i
$473$	−21.5523	+	21.5523i	−0.990978	+	0.990978i
$474$		0			0
$475$	−6.61664	−	24.6937i	−0.303592	−	1.13302i
$476$	−5.79324	+	6.78390i	−0.265533	+	0.310939i
$477$		0			0
$478$	12.5724	−	7.25871i	0.575050	−	0.332005i
$479$	22.8035	+	6.11018i	1.04192	+	0.279181i	0.738908	−	0.673806i	$-0.235342\pi$
$479$	22.8035	+	6.11018i	1.04192	+	0.279181i	0.303010	+	0.952987i	$0.402008\pi$
$480$		0			0
$481$	14.2760	+	2.27341i	0.650930	+	0.103659i
$482$			1.43274i			0.0652594i
$483$		0			0
$484$	5.23177	+	9.06169i	0.237808	+	0.411895i
$485$	−56.1413	−	32.4132i	−2.54925	−	1.47181i
$486$		0			0
$487$	−2.73616	−	10.2115i	−0.123987	−	0.462726i	0.875814	−	0.482648i	$-0.160325\pi$
$487$	−2.73616	−	10.2115i	−0.123987	−	0.462726i	−0.999802	+	0.0199217i	$0.993658\pi$
$488$	2.42785	+	9.06085i	0.109903	+	0.410165i
$489$		0			0
$490$	−60.8719	−	23.3575i	−2.74991	−	1.05518i
$491$	−9.46863	+	5.46672i	−0.427313	+	0.246710i	−0.698201	−	0.715901i	$-0.746016\pi$
$491$	−9.46863	+	5.46672i	−0.427313	+	0.246710i	0.270888	+	0.962611i	$0.412683\pi$
$492$		0			0
$493$	−3.54672			−0.159736
$494$	1.60964	+	15.4396i	0.0724210	+	0.694661i
$495$		0			0
$496$	2.11287	−	7.88533i	0.0948705	−	0.354062i
$497$	4.63687	+	6.74575i	0.207992	+	0.302588i
$498$		0			0
$499$	−21.1483	+	21.1483i	−0.946727	+	0.946727i	−0.998651	−	0.0519238i	$-0.983465\pi$
$499$	−21.1483	+	21.1483i	−0.946727	+	0.946727i	0.0519238	+	0.998651i	$0.483465\pi$
$500$	92.5823	−	24.8073i	4.14041	−	1.10942i
$501$		0			0
$502$	30.6982	−	30.6982i	1.37013	−	1.37013i
$503$	−6.00891	−	3.46924i	−0.267924	−	0.154686i	0.360020	−	0.932945i	$-0.382770\pi$
$503$	−6.00891	−	3.46924i	−0.267924	−	0.154686i	−0.627944	+	0.778259i	$0.716103\pi$
$504$		0			0
$505$	−1.76499	+	6.58703i	−0.0785409	+	0.293119i
$506$		−	31.8008i		−	1.41372i
$507$		0			0
$508$	18.7482			0.831817
$509$	−2.48325	+	9.26762i	−0.110068	+	0.410780i	−0.998871	−	0.0475103i	$-0.984871\pi$
$509$	−2.48325	+	9.26762i	−0.110068	+	0.410780i	0.888803	+	0.458290i	$0.151538\pi$
$510$		0			0
$511$	7.70526	−	16.1571i	0.340861	−	0.714748i
$512$	−13.2032	+	13.2032i	−0.583504	+	0.583504i
$513$		0			0
$514$	−9.05279	−	33.7855i	−0.399301	−	1.49021i
$515$	−43.5310	−	43.5310i	−1.91821	−	1.91821i
$516$		0			0
$517$	5.68213	+	9.84174i	0.249900	+	0.432839i
$518$	4.23932	−	22.8816i	0.186265	−	1.00536i
$519$		0			0
$520$	−27.1438	+	2.82984i	−1.19033	+	0.124097i
$521$		−	17.8193i		−	0.780676i	−0.920672	−	0.390338i	$-0.872358\pi$
$521$		−	17.8193i		−	0.780676i	0.920672	−	0.390338i	$-0.127642\pi$
$522$		0			0
$523$	−6.40070	+	3.69545i	−0.279883	+	0.161591i	−0.633370	−	0.773849i	$-0.718329\pi$
$523$	−6.40070	+	3.69545i	−0.279883	+	0.161591i	0.353487	+	0.935439i	$0.384996\pi$
$524$	−13.7849	+	23.8762i	−0.602198	+	1.04304i
$525$		0			0
$526$	0.247246	+	0.922736i	0.0107805	+	0.0402332i
$527$	5.51410	−	1.47750i	0.240198	−	0.0643608i
$528$		0			0
$529$	2.93251	−	5.07925i	0.127500	−	0.220837i
$530$	−51.5090	−	89.2163i	−2.23741	−	3.87531i
$531$		0			0
$532$	14.5593	−	1.14679i	0.631227	−	0.0497196i
$533$	19.6415	+	3.12785i	0.850767	+	0.135482i
$534$		0			0
$535$	−4.19817	+	15.6678i	−0.181503	+	0.677377i
$536$	3.83461	+	6.64175i	0.165630	+	0.286880i
$537$		0			0
$538$	25.5481	+	25.5481i	1.10146	+	1.10146i
$539$	−7.68418	−	17.2530i	−0.330981	−	0.743138i
$540$		0			0
$541$	−17.3442	−	17.3442i	−0.745687	−	0.745687i	0.227979	−	0.973666i	$-0.426788\pi$
$541$	−17.3442	−	17.3442i	−0.745687	−	0.745687i	−0.973666	+	0.227979i	$0.926788\pi$
$542$	44.2481	+	25.5467i	1.90062	+	1.09732i
$543$		0			0
$544$	−8.48354	−	2.27316i	−0.363729	−	0.0974608i
$545$	−57.5968			−2.46718
$546$		0			0
$547$	26.8037			1.14604			0.573022	−	0.819540i	$-0.305771\pi$
$547$	26.8037			1.14604			0.573022	+	0.819540i	$0.305771\pi$
$548$	−18.2472	−	4.88933i	−0.779483	−	0.208862i
$549$		0			0
$550$	66.7735	+	38.5517i	2.84723	+	1.64385i
$551$	4.10570	+	4.10570i	0.174909	+	0.174909i
$552$		0			0
$553$	2.91528	−	1.03257i	0.123970	−	0.0439092i
$554$	12.6847	+	12.6847i	0.538923	+	0.538923i
$555$		0			0
$556$	0.495023	+	0.857405i	0.0209936	+	0.0363621i
$557$	3.42508	−	12.7826i	0.145125	−	0.541615i	−0.854624	−	0.519247i	$-0.826213\pi$
$557$	3.42508	−	12.7826i	0.145125	−	0.541615i	0.999750	−	0.0223686i	$-0.00712072\pi$
$558$		0			0
$559$	−16.5979	+	37.1953i	−0.702017	+	1.57319i
$560$	−1.51214	−	19.1978i	−0.0638997	−	0.811254i
$561$		0			0
$562$	−4.87361	−	8.44134i	−0.205581	−	0.356077i
$563$	−8.52959	+	14.7737i	−0.359479	+	0.622636i	−0.987874	−	0.155258i	$-0.950379\pi$
$563$	−8.52959	+	14.7737i	−0.359479	+	0.622636i	0.628395	+	0.777895i	$0.283712\pi$
$564$		0			0
$565$	−12.9496	+	3.46983i	−0.544793	+	0.145977i
$566$	−7.21260	−	26.9178i	−0.303168	−	1.13144i
$567$		0			0
$568$	2.75784	−	4.77673i	0.115717	−	0.200427i
$569$	26.6276	−	15.3735i	1.11629	−	0.644489i	0.175837	−	0.984419i	$-0.443737\pi$
$569$	26.6276	−	15.3735i	1.11629	−	0.644489i	0.940450	+	0.339931i	$0.110404\pi$
$570$		0			0
$571$			4.14822i			0.173598i	0.996226	+	0.0867988i	$0.0276637\pi$
$571$			4.14822i			0.173598i	−0.996226	+	0.0867988i	$0.972336\pi$
$572$	−21.2497	−	17.2373i	−0.888496	−	0.720728i
$573$		0			0
$574$	5.83262	−	31.4813i	0.243449	−	1.31401i
$575$	34.9927	+	60.6091i	1.45930	+	2.52757i
$576$		0			0
$577$	−8.22860	−	8.22860i	−0.342561	−	0.342561i	0.514768	−	0.857329i	$-0.327878\pi$
$577$	−8.22860	−	8.22860i	−0.342561	−	0.342561i	−0.857329	+	0.514768i	$0.827878\pi$
$578$	8.83646	+	32.9781i	0.367548	+	1.37171i
$579$		0			0
$580$	−24.9824	+	24.9824i	−1.03734	+	1.03734i
$581$	10.9424	+	5.21840i	0.453968	+	0.216496i
$582$		0			0
$583$	7.72369	−	28.8252i	0.319883	−	1.19382i
$584$	−12.0616			−0.499113
$585$		0			0
$586$		−	12.5207i		−	0.517225i
$587$	2.86420	−	10.6893i	0.118218	−	0.441196i	−0.881289	−	0.472577i	$-0.843324\pi$
$587$	2.86420	−	10.6893i	0.118218	−	0.441196i	0.999508	+	0.0313808i	$0.00999044\pi$
$588$		0			0
$589$	−8.09348	−	4.67278i	−0.333486	−	0.192538i
$590$	−80.0865	+	80.0865i	−3.29711	+	3.29711i
$591$		0			0
$592$	6.63909	−	1.77894i	0.272865	−	0.0731139i
$593$	−9.97769	+	9.97769i	−0.409734	+	0.409734i	−0.881646	−	0.471911i	$-0.843564\pi$
$593$	−9.97769	+	9.97769i	−0.409734	+	0.409734i	0.471911	+	0.881646i	$0.343564\pi$
$594$		0			0
$595$	11.0974	−	7.62811i	0.454951	−	0.312722i
$596$	8.59127	−	32.0631i	0.351912	−	1.31335i
$597$		0			0
$598$	−15.1959	−	39.6864i	−0.621406	−	1.62290i
$599$	−34.7079			−1.41813			−0.709063	−	0.705145i	$-0.750882\pi$
$599$	−34.7079			−1.41813			−0.709063	+	0.705145i	$0.750882\pi$
$600$		0			0
$601$	11.2636	−	6.50302i	0.459450	−	0.265264i	−0.252363	−	0.967633i	$-0.581208\pi$
$601$	11.2636	−	6.50302i	0.459450	−	0.265264i	0.711813	+	0.702369i	$0.247874\pi$
$602$	59.1823	+	28.2238i	2.41209	+	1.15032i
$603$		0			0
$604$	−12.6366	−	47.1604i	−0.514175	−	1.91893i
$605$	−4.08802	−	15.2567i	−0.166202	−	0.620273i
$606$		0			0
$607$	−18.9672	−	10.9507i	−0.769856	−	0.444477i	0.0629670	−	0.998016i	$-0.479944\pi$
$607$	−18.9672	−	10.9507i	−0.769856	−	0.444477i	−0.832823	+	0.553539i	$0.813277\pi$
$608$	7.18915	+	12.4520i	0.291559	+	0.504994i
$609$		0			0
$610$		−	49.0092i		−	1.98432i
$611$	11.7939	+	9.56698i	0.477132	+	0.387039i
$612$		0			0
$613$	−10.3087	−	2.76221i	−0.416365	−	0.111565i	0.0445537	−	0.999007i	$-0.485813\pi$
$613$	−10.3087	−	2.76221i	−0.416365	−	0.111565i	−0.460919	+	0.887442i	$0.652480\pi$
$614$	−27.4815	+	15.8665i	−1.10906	+	0.640319i
$615$		0			0
$616$	−8.26445	+	9.67769i	−0.332984	+	0.389925i
$617$	−5.78797	−	21.6010i	−0.233015	−	0.869624i	−0.979034	−	0.203699i	$-0.934704\pi$
$617$	−5.78797	−	21.6010i	−0.233015	−	0.869624i	0.746019	−	0.665925i	$-0.231963\pi$
$618$		0			0
$619$	−5.50453	+	5.50453i	−0.221246	+	0.221246i	−0.809023	−	0.587777i	$-0.800003\pi$
$619$	−5.50453	+	5.50453i	−0.221246	+	0.221246i	0.587777	+	0.809023i	$0.300003\pi$
$620$	28.4330	−	49.2474i	1.14190	−	1.97782i
$621$		0			0
$622$	30.9689	+	8.29810i	1.24174	+	0.332723i
$623$	−13.1127	+	1.03284i	−0.525349	+	0.0413800i
$624$		0			0
$625$	−79.5531			−3.18213
$626$	−10.2193	+	38.1390i	−0.408446	+	1.52434i
$627$		0			0
$628$	6.20341	−	10.7446i	0.247543	−	0.428757i
$629$	3.39863	+	3.39863i	0.135512	+	0.135512i
$630$		0			0
$631$	−20.7278	+	5.55399i	−0.825160	+	0.221101i	−0.646601	−	0.762828i	$-0.723810\pi$
$631$	−20.7278	+	5.55399i	−0.825160	+	0.221101i	−0.178559	+	0.983929i	$0.557143\pi$
$632$	−1.47358	−	1.47358i	−0.0586157	−	0.0586157i
$633$		0			0
$634$	32.4660	−	18.7442i	1.28939	−	0.744429i
$635$	−27.3364	−	7.32477i	−1.08481	−	0.290675i
$636$		0			0
$637$	−17.8339	−	17.8593i	−0.706603	−	0.707610i
$638$	−17.5119			−0.693304
$639$		0			0
$640$	−48.1116	+	27.7772i	−1.90178	+	1.09799i
$641$	40.6530	+	23.4710i	1.60570	+	0.927050i	0.990318	+	0.138818i	$0.0443304\pi$
$641$	40.6530	+	23.4710i	1.60570	+	0.927050i	0.615379	+	0.788231i	$0.289003\pi$
$642$		0			0
$643$	22.4152	−	6.00613i	0.883968	−	0.236859i	0.211850	−	0.977302i	$-0.432051\pi$
$643$	22.4152	−	6.00613i	0.883968	−	0.236859i	0.672118	+	0.740444i	$0.265385\pi$
$644$	−37.6866	+	13.3482i	−1.48506	+	0.525995i
$645$		0			0
$646$	−2.58064	+	4.46981i	−0.101534	+	0.175862i
$647$	6.98028	+	12.0902i	0.274423	+	0.475315i	0.969989	−	0.243147i	$-0.0781798\pi$
$647$	6.98028	+	12.0902i	0.274423	+	0.475315i	−0.695566	+	0.718462i	$0.744846\pi$
$648$		0			0
$649$	−32.8087			−1.28786
$650$	101.753	+	16.2038i	3.99108	+	0.635567i
$651$		0			0
$652$	−1.71833	−	0.460426i	−0.0672951	−	0.0180317i
$653$	13.4921	+	23.3689i	0.527985	+	0.914497i	0.999468	+	0.0326216i	$0.0103856\pi$
$653$	13.4921	+	23.3689i	0.527985	+	0.914497i	−0.471483	+	0.881875i	$0.656281\pi$
$654$		0			0
$655$	29.4278	−	29.4278i	1.14984	−	1.14984i
$656$	9.13431	−	2.44753i	0.356635	−	0.0955601i
$657$		0			0
$658$	15.8757	−	18.5905i	0.618900	−	0.724733i
$659$	−2.76889	+	4.79586i	−0.107861	+	0.186820i	−0.914903	−	0.403673i	$-0.867733\pi$
$659$	−2.76889	+	4.79586i	−0.107861	+	0.186820i	0.807043	+	0.590493i	$0.201067\pi$
$660$		0			0
$661$	36.8331	+	9.86941i	1.43264	+	0.383875i	0.889951	−	0.456057i	$-0.150739\pi$
$661$	36.8331	+	9.86941i	1.43264	+	0.383875i	0.542692	+	0.839932i	$0.317405\pi$
$662$			21.7939i			0.847046i
$663$		0			0
$664$		−	8.16876i		−	0.317009i
$665$	−21.6767	−	4.01610i	−0.840588	−	0.155738i
$666$		0			0
$667$	−13.7657	−	7.94763i	−0.533010	−	0.307733i
$668$	−33.7200	−	33.7200i	−1.30466	−	1.30466i
$669$		0			0
$670$	−10.3705	−	38.7033i	−0.400648	−	1.49524i
$671$	10.0387	−	10.0387i	0.387540	−	0.387540i
$672$		0			0
$673$	5.72219	−	3.30371i	0.220574	−	0.127349i	−0.385642	−	0.922649i	$-0.626020\pi$
$673$	5.72219	−	3.30371i	0.220574	−	0.127349i	0.606216	+	0.795300i	$0.292687\pi$
$674$	3.66100	−	13.6630i	0.141016	−	0.526281i
$675$		0			0
$676$	−34.7557	−	11.3575i	−1.33676	−	0.436827i
$677$			21.3320i			0.819855i	0.912118	+	0.409928i	$0.134446\pi$
$677$			21.3320i			0.819855i	−0.912118	+	0.409928i	$0.865554\pi$
$678$		0			0
$679$	−33.2906	+	22.8832i	−1.27758	+	0.878176i
$680$	−7.85819	−	4.53693i	−0.301348	−	0.173983i
$681$		0			0
$682$	27.2258	−	7.29513i	1.04253	−	0.279345i
$683$	1.32430	−	0.354846i	0.0506730	−	0.0135778i	−0.233393	−	0.972382i	$-0.574983\pi$
$683$	1.32430	−	0.354846i	0.0506730	−	0.0135778i	0.284067	+	0.958805i	$0.408316\pi$
$684$		0			0
$685$	24.6958	+	14.2581i	0.943576	+	0.544774i
$686$	−29.4660	+	27.9730i	−1.12502	+	1.06802i
$687$		0			0
$688$			19.3660i			0.738323i
$689$	−4.13508	−	39.6636i	−0.157534	−	1.51106i
$690$		0			0
$691$	8.87327	−	33.1155i	0.337555	−	1.25977i	−0.563517	−	0.826104i	$-0.690552\pi$
$691$	8.87327	−	33.1155i	0.337555	−	1.25977i	0.901072	−	0.433669i	$-0.142781\pi$
$692$	22.4422	−	12.9570i	0.853124	−	0.492551i
$693$		0			0
$694$	−18.6303	+	18.6303i	−0.707197	+	0.707197i
$695$	−0.386803	−	1.44357i	−0.0146723	−	0.0547577i
$696$		0			0
$697$	4.67597	+	4.67597i	0.177115	+	0.177115i
$698$	−48.3762	−	27.9300i	−1.83107	−	1.05717i
$699$		0			0
$700$	17.6590	−	95.3140i	0.667449	−	3.60253i
$701$		−	42.5906i		−	1.60862i	−0.594208	−	0.804312i	$-0.702534\pi$
$701$		−	42.5906i		−	1.60862i	0.594208	−	0.804312i	$-0.297466\pi$
$702$		0			0
$703$		−	7.86853i		−	0.296767i
$704$	−32.9518	−	8.82940i	−1.24192	−	0.332771i
$705$		0			0
$706$	10.3007	−	17.8413i	0.387671	−	0.671466i
$707$	3.23155	+	2.75964i	0.121535	+	0.103787i
$708$		0			0
$709$	37.3239	−	10.0009i	1.40173	−	0.375592i	0.522764	−	0.852478i	$-0.324901\pi$
$709$	37.3239	−	10.0009i	1.40173	−	0.375592i	0.878965	+	0.476886i	$0.158234\pi$
$710$	−20.3769	+	20.3769i	−0.764730	+	0.764730i
$711$		0			0
$712$	4.43148	+	7.67556i	0.166077	+	0.287654i
$713$	24.7124	+	6.62166i	0.925486	+	0.247983i
$714$		0			0
$715$	24.2494	+	33.4355i	0.906876	+	1.25042i
$716$	−7.65273			−0.285996
$717$		0			0
$718$	25.2525	+	43.7385i	0.942413	+	1.63231i
$719$	−25.0297	+	43.3527i	−0.933450	+	1.61678i	−0.156076	+	0.987745i	$0.549884\pi$
$719$	−25.0297	+	43.3527i	−0.933450	+	1.61678i	−0.777375	+	0.629038i	$0.783449\pi$
$720$		0			0
$721$	−36.1615	+	12.8081i	−1.34672	+	0.476997i
$722$	−32.0998	+	8.60112i	−1.19463	+	0.320101i
$723$		0			0
$724$	37.6396	+	21.7312i	1.39886	+	0.807634i
$725$	33.3759	−	19.2696i	1.23955	−	0.715655i
$726$		0			0
$727$	5.22923			0.193941			0.0969707	−	0.995287i	$-0.469085\pi$
$727$	5.22923			0.193941			0.0969707	+	0.995287i	$0.469085\pi$
$728$	−5.68932	+	16.0266i	−0.210860	+	0.593984i
$729$		0			0
$730$	60.8698	+	16.3100i	2.25289	+	0.603661i
$731$	−11.7280	+	6.77119i	−0.433777	+	0.250442i
$732$		0			0
$733$	−10.0406	−	10.0406i	−0.370858	−	0.370858i	0.496932	−	0.867790i	$-0.334460\pi$
$733$	−10.0406	−	10.0406i	−0.370858	−	0.370858i	−0.867790	+	0.496932i	$0.834460\pi$
$734$	−48.0070	+	12.8634i	−1.77197	+	0.474798i
$735$		0			0
$736$	−27.8329	−	27.8329i	−1.02593	−	1.02593i
$737$	5.80349	−	10.0519i	0.213774	−	0.370268i
$738$		0			0
$739$	−1.48318	+	5.53532i	−0.0545598	+	0.203620i	−0.987825	−	0.155567i	$-0.950279\pi$
$739$	−1.48318	+	5.53532i	−0.0545598	+	0.203620i	0.933265	+	0.359187i	$0.116946\pi$
$740$	47.8786			1.76005
$741$		0			0
$742$	−63.9979	+	5.04090i	−2.34944	+	0.185057i
$743$	−0.617584	−	0.165481i	−0.0226569	−	0.00607091i	0.247473	−	0.968895i	$-0.420400\pi$
$743$	−0.617584	−	0.165481i	−0.0226569	−	0.00607091i	−0.270130	+	0.962824i	$0.587067\pi$
$744$		0			0
$745$	−25.0536	+	43.3941i	−0.917892	+	1.58984i
$746$	34.2932	−	34.2932i	1.25556	−	1.25556i
$747$		0			0
$748$	−2.35460	−	8.78749i	−0.0860928	−	0.321303i
$749$	7.68650	+	6.56404i	0.280859	+	0.239845i
$750$		0			0
$751$	−22.0888	+	12.7530i	−0.806031	+	0.465362i	−0.845576	−	0.533856i	$-0.820743\pi$
$751$	−22.0888	+	12.7530i	−0.806031	+	0.465362i	0.0395448	+	0.999218i	$0.487409\pi$
$752$	6.97454	+	1.86882i	0.254335	+	0.0681490i
$753$		0			0
$754$	−21.8543	+	8.36799i	−0.795887	+	0.304744i
$755$			73.7008i			2.68225i
$756$		0			0
$757$	8.06785	+	13.9739i	0.293231	+	0.507891i	0.974572	−	0.224075i	$-0.0719362\pi$
$757$	8.06785	+	13.9739i	0.293231	+	0.507891i	−0.681341	+	0.731966i	$0.738603\pi$
$758$	−2.02669	−	1.17011i	−0.0736127	−	0.0425003i
$759$		0			0
$760$	3.84470	+	14.3486i	0.139462	+	0.520479i
$761$	6.42639	+	23.9836i	0.232957	+	0.869406i	0.979059	+	0.203575i	$0.0652561\pi$
$761$	6.42639	+	23.9836i	0.232957	+	0.869406i	−0.746103	+	0.665831i	$0.768077\pi$
$762$		0			0
$763$	−15.4497	+	32.3963i	−0.559316	+	1.17283i
$764$	−7.97831	+	4.60628i	−0.288645	+	0.166649i
$765$		0			0
$766$	27.3856			0.989481
$767$	−40.9442	+	15.6775i	−1.47841	+	0.566082i
$768$		0			0
$769$	−3.09729	+	11.5592i	−0.111691	+	0.416837i	−0.999018	−	0.0443040i	$-0.985893\pi$
$769$	−3.09729	+	11.5592i	−0.111691	+	0.416837i	0.887327	+	0.461141i	$0.152560\pi$
$770$	54.7935	−	37.6637i	1.97462	−	1.35731i
$771$		0			0
$772$	−41.8368	+	41.8368i	−1.50574	+	1.50574i
$773$	−1.00730	+	0.269904i	−0.0362299	+	0.00970777i	−0.276888	−	0.960902i	$-0.589303\pi$
$773$	−1.00730	+	0.269904i	−0.0362299	+	0.00970777i	0.240659	+	0.970610i	$0.422637\pi$
$774$		0			0
$775$	−43.8623	+	43.8623i	−1.57558	+	1.57558i
$776$	23.5734	+	13.6101i	0.846235	+	0.488574i
$777$		0			0
$778$	−10.7958	+	40.2904i	−0.387047	+	1.44448i
$779$		−	10.8258i		−	0.387875i
$780$		0			0
$781$	−8.34771			−0.298704
$782$	3.65696	−	13.6480i	0.130773	−	0.488050i
$783$		0			0
$784$	−11.2037	−	4.29905i	−0.400133	−	0.153538i
$785$	−13.2429	+	13.2429i	−0.472660	+	0.472660i
$786$		0			0
$787$	12.4106	+	46.3169i	0.442389	+	1.65102i	0.722738	+	0.691122i	$0.242883\pi$
$787$	12.4106	+	46.3169i	0.442389	+	1.65102i	−0.280349	+	0.959898i	$0.590450\pi$
$788$	−41.5834	−	41.5834i	−1.48135	−	1.48135i
$789$		0			0
$790$	5.44390	+	9.42910i	0.193685	+	0.335472i
$791$	−1.52191	+	8.21446i	−0.0541129	+	0.292072i
$792$		0			0
$793$	7.73102	−	17.3249i	0.274537	−	0.615226i
$794$			5.95712i			0.211410i
$795$		0			0
$796$	60.7420	−	35.0694i	2.15294	−	1.24300i
$797$	22.8940	−	39.6535i	0.810946	−	1.40460i	−0.101257	−	0.994860i	$-0.532287\pi$
$797$	22.8940	−	39.6535i	0.810946	−	1.40460i	0.912203	−	0.409739i	$-0.134380\pi$
$798$		0			0
$799$	1.30684	+	4.87720i	0.0462327	+	0.172543i
$800$	92.1834	−	24.7005i	3.25917	−	0.873293i
$801$		0			0
$802$	−3.48001	+	6.02755i	−0.122883	+	0.212840i
$803$	9.12732	+	15.8090i	0.322096	+	0.557887i
$804$		0			0
$805$	60.1652	−	4.73901i	2.12054	−	0.167028i
$806$	30.4910	−	22.1138i	1.07400	−	0.778926i
$807$		0			0
$808$	0.741108	−	2.76585i	0.0260721	−	0.0973023i
$809$	14.8591	+	25.7367i	0.522418	+	0.904855i	0.999660	+	0.0260831i	$0.00830344\pi$
$809$	14.8591	+	25.7367i	0.522418	+	0.904855i	−0.477241	+	0.878772i	$0.658363\pi$
$810$		0			0
$811$	34.3752	+	34.3752i	1.20708	+	1.20708i	0.971970	+	0.235107i	$0.0755440\pi$
$811$	34.3752	+	34.3752i	1.20708	+	1.20708i	0.235107	+	0.971970i	$0.424456\pi$
$812$	7.35055	+	20.7531i	0.257954	+	0.728290i
$813$		0			0
$814$	16.7807	+	16.7807i	0.588164	+	0.588164i
$815$	2.32559	+	1.34268i	0.0814617	+	0.0470319i
$816$		0			0
$817$	21.4148	+	5.73807i	0.749207	+	0.200750i
$818$	6.76385			0.236493
$819$		0			0
$820$	65.8733			2.30039
$821$	30.4555	+	8.16053i	1.06291	+	0.284805i	0.747575	−	0.664177i	$-0.231218\pi$
$821$	30.4555	+	8.16053i	1.06291	+	0.284805i	0.315330	+	0.948982i	$0.397885\pi$
$822$		0			0
$823$	−1.78884	−	1.03279i	−0.0623550	−	0.0360007i	0.468498	−	0.883464i	$-0.344795\pi$
$823$	−1.78884	−	1.03279i	−0.0623550	−	0.0360007i	−0.530853	+	0.847464i	$0.678129\pi$
$824$	18.2784	+	18.2784i	0.636758	+	0.636758i
$825$		0			0
$826$	23.5637	+	66.5283i	0.819887	+	2.31482i
$827$	−15.5395	−	15.5395i	−0.540360	−	0.540360i	0.383275	−	0.923634i	$-0.374796\pi$
$827$	−15.5395	−	15.5395i	−0.540360	−	0.540360i	−0.923634	+	0.383275i	$0.874796\pi$
$828$		0			0
$829$	7.58600	+	13.1393i	0.263473	+	0.456348i	0.967162	−	0.254159i	$-0.0817987\pi$
$829$	7.58600	+	13.1393i	0.263473	+	0.456348i	−0.703690	+	0.710508i	$0.748465\pi$
$830$	−11.0460	+	41.2242i	−0.383412	+	1.43091i
$831$		0			0
$832$	−45.3418	+	4.72706i	−1.57194	+	0.163881i
$833$	−1.31380	−	8.28810i	−0.0455205	−	0.287166i
$834$		0			0
$835$	35.9924	+	62.3406i	1.24557	+	2.15739i
$836$	−7.44673	+	12.8981i	−0.257550	+	0.446091i
$837$		0			0
$838$	−71.1108	+	19.0541i	−2.45648	+	0.658212i
$839$	14.3405	+	53.5194i	0.495088	+	1.84769i	0.529535	+	0.848288i	$0.322366\pi$
$839$	14.3405	+	53.5194i	0.495088	+	1.84769i	−0.0344471	+	0.999407i	$0.510967\pi$
$840$		0			0
$841$	10.1234	−	17.5343i	0.349084	−	0.604631i
$842$	49.0703	−	28.3308i	1.69108	−	0.976343i
$843$		0			0
$844$			30.7229i			1.05753i
$845$	46.2395	+	30.1390i	1.59069	+	1.03681i
$846$		0			0
$847$	−9.67797	−	1.79306i	−0.332539	−	0.0616103i
$848$	−9.48046	−	16.4206i	−0.325560	−	0.563887i
$849$		0			0
$850$	24.2239	+	24.2239i	0.830873	+	0.830873i
$851$	5.57514	+	20.8067i	0.191113	+	0.713244i
$852$		0			0
$853$	−31.2556	+	31.2556i	−1.07017	+	1.07017i	−0.0728280	+	0.997345i	$0.523202\pi$
$853$	−31.2556	+	31.2556i	−1.07017	+	1.07017i	−0.997345	+	0.0728280i	$0.976798\pi$
$854$	−27.5661	−	13.1462i	−0.943291	−	0.449852i
$855$		0			0
$856$	1.76279	−	6.57881i	0.0602508	−	0.224859i
$857$	4.67560			0.159715			0.0798577	−	0.996806i	$-0.474553\pi$
$857$	4.67560			0.159715			0.0798577	+	0.996806i	$0.474553\pi$
$858$		0			0
$859$		−	4.70689i		−	0.160597i	−0.996771	−	0.0802986i	$-0.974413\pi$
$859$		−	4.70689i		−	0.160597i	0.996771	−	0.0802986i	$-0.0255874\pi$
$860$	−34.9151	+	130.305i	−1.19060	+	4.44337i
$861$		0			0
$862$	33.3150	+	19.2344i	1.13471	+	0.655127i
$863$	31.1015	−	31.1015i	1.05871	−	1.05871i	0.0605431	−	0.998166i	$-0.480717\pi$
$863$	31.1015	−	31.1015i	1.05871	−	1.05871i	0.998166	−	0.0605431i	$-0.0192833\pi$
$864$		0			0
$865$	−37.7848	+	10.1244i	−1.28472	+	0.344240i
$866$	54.8070	−	54.8070i	1.86242	−	1.86242i
$867$		0			0
$868$	−20.0732	−	29.2027i	−0.681330	−	0.991205i
$869$	−0.816302	+	3.04648i	−0.0276912	+	0.103345i
$870$		0			0
$871$	2.43929	−	15.3177i	0.0826522	−	0.519019i
$872$	24.1845			0.818992
$873$		0			0
$874$	−20.0322	+	11.5656i	−0.677599	+	0.391212i
$875$	−38.8100	+	81.3804i	−1.31202	+	2.75116i
$876$		0			0
$877$	6.66722	+	24.8824i	0.225136	+	0.840220i	0.982350	+	0.187052i	$0.0598934\pi$
$877$	6.66722	+	24.8824i	0.225136	+	0.840220i	−0.757214	+	0.653167i	$0.773440\pi$
$878$	10.6278	+	39.6633i	0.358669	+	1.33857i
$879$		0			0
$880$	17.0073	+	9.81918i	0.573316	+	0.331004i
$881$	9.58023	+	16.5935i	0.322766	+	0.559048i	0.981058	−	0.193716i	$-0.0620539\pi$
$881$	9.58023	+	16.5935i	0.322766	+	0.559048i	−0.658291	+	0.752763i	$0.728721\pi$
$882$		0			0
$883$			8.19989i			0.275948i	0.990436	+	0.137974i	$0.0440591\pi$
$883$			8.19989i			0.275948i	−0.990436	+	0.137974i	$0.955941\pi$
$884$	−7.13753	−	9.84137i	−0.240061	−	0.331001i
$885$		0			0
$886$	−64.6192	−	17.3147i	−2.17092	−	0.581697i
$887$	3.31720	−	1.91519i	0.111381	−	0.0643057i	−0.443275	−	0.896386i	$-0.646183\pi$
$887$	3.31720	−	1.91519i	0.111381	−	0.0643057i	0.554655	+	0.832080i	$0.312850\pi$
$888$		0			0
$889$	−11.4526	+	13.4111i	−0.384109	+	0.449792i
$890$	−11.9847	−	44.7276i	−0.401729	−	1.49927i
$891$		0			0
$892$	30.6808	−	30.6808i	1.02727	−	1.02727i
$893$	4.13305	−	7.15866i	0.138307	−	0.239555i
$894$		0			0
$895$	11.1583	+	2.98986i	0.372982	+	0.0999401i
$896$	2.71840	+	34.5121i	0.0908154	+	1.15297i
$897$		0			0
$898$	43.3539			1.44674
$899$	3.64639	−	13.6085i	0.121614	−	0.453869i
$900$		0			0
$901$	6.62955	−	11.4827i	0.220862	−	0.382545i
$902$	23.0876	+	23.0876i	0.768732	+	0.768732i
$903$		0			0
$904$	5.43745	−	1.45696i	0.180847	−	0.0484578i
$905$	−46.3914	−	46.3914i	−1.54210	−	1.54210i
$906$		0			0
$907$	26.5418	−	15.3239i	0.881305	−	0.508821i	0.0102163	−	0.999948i	$-0.496748\pi$
$907$	26.5418	−	15.3239i	0.881305	−	0.508821i	0.871088	+	0.491126i	$0.163415\pi$
$908$	−52.4716	−	14.0597i	−1.74133	−	0.466588i
$909$		0			0
$910$	50.3831	−	73.1859i	1.67018	−	2.42609i
$911$	17.6785			0.585714			0.292857	−	0.956156i	$-0.405394\pi$
$911$	17.6785			0.585714			0.292857	+	0.956156i	$0.405394\pi$
$912$		0			0
$913$	−10.7067	+	6.18149i	−0.354339	+	0.204578i
$914$	15.4881	+	8.94204i	0.512300	+	0.295776i
$915$		0			0
$916$	−48.4631	+	12.9857i	−1.60127	+	0.429058i
$917$	−8.65851	−	24.4459i	−0.285929	−	0.807274i
$918$		0			0
$919$	6.76666	−	11.7202i	0.223212	−	0.386614i	−0.732570	−	0.680692i	$-0.761679\pi$
$919$	6.76666	−	11.7202i	0.223212	−	0.386614i	0.955781	+	0.294078i	$0.0950126\pi$
$920$	−20.3330	−	35.2178i	−0.670360	−	1.16110i
$921$		0			0
$922$	73.1348			2.40856
$923$	−10.4177	+	3.98892i	−0.342902	+	0.131297i
$924$		0			0
$925$	−50.4474	−	13.5173i	−1.65870	−	0.444447i
$926$	2.57688	+	4.46329i	0.0846816	+	0.146673i
$927$		0			0
$928$	−15.3269	+	15.3269i	−0.503130	+	0.503130i
$929$	−48.9198	+	13.1080i	−1.60501	+	0.430060i	−0.946549	−	0.322559i	$-0.895457\pi$
$929$	−48.9198	+	13.1080i	−1.60501	+	0.430060i	−0.658456	+	0.752619i	$0.728790\pi$
$930$		0			0
$931$	−8.07346	+	11.1152i	−0.264597	+	0.364285i
$932$	−35.0762	+	60.7538i	−1.14896	+	1.99006i
$933$		0			0
$934$	−26.0492	−	6.97987i	−0.852357	−	0.228388i
$935$			13.7328i			0.449111i
$936$		0			0
$937$		−	24.1481i		−	0.788885i	−0.918921	−	0.394443i	$-0.870938\pi$
$937$		−	24.1481i		−	0.788885i	0.918921	−	0.394443i	$-0.129062\pi$
$938$	−24.5511	−	4.54864i	−0.801622	−	0.148518i
$939$		0			0
$940$	43.5592	+	25.1489i	1.42074	+	0.820267i
$941$	11.0345	+	11.0345i	0.359716	+	0.359716i	0.863708	−	0.503992i	$-0.168136\pi$
$941$	11.0345	+	11.0345i	0.359716	+	0.359716i	−0.503992	+	0.863708i	$0.668136\pi$
$942$		0			0
$943$	7.67049	+	28.6266i	0.249785	+	0.932212i
$944$	−14.7403	+	14.7403i	−0.479755	+	0.479755i
$945$		0			0
$946$	−57.9071	+	33.4327i	−1.88272	+	1.08699i
$947$	6.74864	−	25.1863i	0.219301	−	0.818444i	−0.765307	−	0.643666i	$-0.777413\pi$
$947$	6.74864	−	25.1863i	0.219301	−	0.818444i	0.984608	−	0.174778i	$-0.0559207\pi$
$948$		0			0
$949$	18.9448	+	15.3676i	0.614976	+	0.498855i
$950$		−	56.0833i		−	1.81958i
$951$		0			0
$952$	−4.65975	+	3.20300i	−0.151023	+	0.103810i
$953$	−2.70119	−	1.55953i	−0.0875001	−	0.0505182i	0.455612	−	0.890179i	$-0.349421\pi$
$953$	−2.70119	−	1.55953i	−0.0875001	−	0.0505182i	−0.543112	+	0.839661i	$0.682754\pi$
$954$		0			0
$955$	13.4327	−	3.59927i	0.434671	−	0.116470i
$956$	17.9786	−	4.81735i	0.581470	−	0.155804i
$957$		0			0
$958$	44.8518	+	25.8952i	1.44910	+	0.836636i
$959$	14.6441	−	10.0660i	0.472882	−	0.325048i
$960$		0			0
$961$		−	8.32384i		−	0.268511i
$962$	28.9604	+	12.9232i	0.933720	+	0.416661i
$963$		0			0
$964$	−0.475429	+	1.77433i	−0.0153126	+	0.0571472i
$965$	77.3469	−	44.6563i	2.48989	−	1.43754i
$966$		0			0
$967$	10.4152	−	10.4152i	0.334930	−	0.334930i	−0.519525	−	0.854455i	$-0.673891\pi$
$967$	10.4152	−	10.4152i	0.334930	−	0.334930i	0.854455	+	0.519525i	$0.173891\pi$
$968$	1.71654	+	6.40620i	0.0551715	+	0.205903i
$969$		0			0
$970$	−100.561	−	100.561i	−3.22881	−	3.22881i
$971$	−17.7603	−	10.2539i	−0.569955	−	0.329064i	0.187176	−	0.982326i	$-0.440066\pi$
$971$	−17.7603	−	10.2539i	−0.569955	−	0.329064i	−0.757131	+	0.653263i	$0.773400\pi$
$972$		0			0
$973$	−0.915716	−	0.169657i	−0.0293565	−	0.00543895i
$974$		−	23.1919i		−	0.743117i
$975$		0			0
$976$		−	9.02035i		−	0.288734i
$977$	−21.0235	−	5.63323i	−0.672601	−	0.180223i	−0.0936748	−	0.995603i	$-0.529861\pi$
$977$	−21.0235	−	5.63323i	−0.672601	−	0.180223i	−0.578926	+	0.815380i	$0.696528\pi$
$978$		0			0
$979$	6.70682	−	11.6166i	0.214351	−	0.371267i
$980$	−67.6339	−	49.1256i	−2.16049	−	1.56926i
$981$		0			0
$982$	−23.1682	+	6.20790i	−0.739327	+	0.198102i
$983$	−4.97085	+	4.97085i	−0.158546	+	0.158546i	−0.781922	−	0.623376i	$-0.785760\pi$
$983$	−4.97085	+	4.97085i	−0.158546	+	0.158546i	0.623376	+	0.781922i	$0.285760\pi$
$984$		0			0
$985$	44.3858	+	76.8784i	1.41425	+	2.44955i
$986$	−7.51559	−	2.01380i	−0.239345	−	0.0641323i
$987$		0			0
$988$	−3.12997	+	19.6548i	−0.0995775	+	0.625303i
$989$	−60.6925			−1.92991
$990$		0			0
$991$	−16.0062	−	27.7236i	−0.508454	−	0.880668i	−0.999952	−	0.00978927i	$-0.996884\pi$
$991$	−16.0062	−	27.7236i	−0.508454	−	0.880668i	0.491498	−	0.870879i	$-0.336449\pi$
$992$	17.4438	−	30.2136i	0.553843	−	0.959283i
$993$		0			0
$994$	5.99546	+	16.9272i	0.190164	+	0.536897i
$995$	−102.268	+	27.4027i	−3.24212	+	0.868723i
$996$		0			0
$997$	−38.9153	−	22.4677i	−1.23246	−	0.711561i	−0.264917	−	0.964271i	$-0.585345\pi$
$997$	−38.9153	−	22.4677i	−1.23246	−	0.711561i	−0.967542	+	0.252711i	$0.918678\pi$
$998$	−56.8215	+	32.8059i	−1.79865	+	1.03845i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.496.7		32
3.2	odd	2		273.2.by.c.223.2	yes	32
7.6	odd	2		819.2.fm.e.496.7		32
13.7	odd	12		819.2.fm.e.748.7		32
21.20	even	2		273.2.by.d.223.2	yes	32
39.20	even	12		273.2.by.d.202.2	yes	32
91.20	even	12	inner	819.2.fm.f.748.7		32
273.20	odd	12		273.2.by.c.202.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.2	✓	32	273.20	odd	12
273.2.by.c.223.2	yes	32	3.2	odd	2
273.2.by.d.202.2	yes	32	39.20	even	12
273.2.by.d.223.2	yes	32	21.20	even	2
819.2.fm.e.496.7		32	7.6	odd	2
819.2.fm.e.748.7		32	13.7	odd	12
819.2.fm.f.496.7		32	1.1	even	1	trivial
819.2.fm.f.748.7		32	91.20	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.11902 + 0.567791i) q^{2} +(2.43582 + 1.40632i) q^{4} +(-3.00219 - 3.00219i) q^{5} +(-2.49394 + 0.883331i) q^{7} +(1.26060 + 1.26060i) q^{8} +O(q^{10})\)	\(q+(2.11902 + 0.567791i) q^{2} +(2.43582 + 1.40632i) q^{4} +(-3.00219 - 3.00219i) q^{5} +(-2.49394 + 0.883331i) q^{7} +(1.26060 + 1.26060i) q^{8} +(-4.65710 - 8.06633i) q^{10} +(0.698323 - 2.60618i) q^{11} +(-0.373866 - 3.58612i) q^{13} +(-5.78626 + 0.455764i) q^{14} +(-0.857159 - 1.48464i) q^{16} +(0.599399 - 1.03819i) q^{17} +(-1.89568 + 0.507945i) q^{19} +(-3.09075 - 11.5349i) q^{20} +(2.95953 - 5.12605i) q^{22} +(4.65282 - 2.68631i) q^{23} +13.0263i q^{25} +(1.24393 - 7.81134i) q^{26} +(-7.31704 - 1.35564i) q^{28} +(-1.47928 - 2.56220i) q^{29} +(3.36721 + 3.36721i) q^{31} +(-1.89620 - 7.07671i) q^{32} +(1.85961 - 1.85961i) q^{34} +(10.1392 + 4.83535i) q^{35} +(-1.03769 + 3.87273i) q^{37} -4.30539 q^{38} -7.56914i q^{40} +(-1.42770 + 5.32825i) q^{41} +(-9.78317 - 5.64832i) q^{43} +(5.36612 - 5.36612i) q^{44} +(11.3847 - 3.05052i) q^{46} +(-2.97828 + 2.97828i) q^{47} +(5.43945 - 4.40594i) q^{49} +(-7.39621 + 27.6030i) q^{50} +(4.13256 - 9.26092i) q^{52} +11.0603 q^{53} +(-9.92075 + 5.72775i) q^{55} +(-4.25739 - 2.03033i) q^{56} +(-1.67985 - 6.26927i) q^{58} +(-3.14721 - 11.7455i) q^{59} +(4.55683 + 2.63089i) q^{61} +(5.22332 + 9.04706i) q^{62} -12.6437i q^{64} +(-9.64379 + 11.8886i) q^{65} +(4.15530 + 1.11341i) q^{67} +(2.92006 - 1.68590i) q^{68} +(18.7397 + 16.0032i) q^{70} +(-0.800761 - 2.98848i) q^{71} +(-4.78407 + 4.78407i) q^{73} +(-4.39780 + 7.61721i) q^{74} +(-5.33186 - 1.42867i) q^{76} +(0.560542 + 7.11650i) q^{77} -1.16895 q^{79} +(-1.88383 + 7.03054i) q^{80} +(-6.05066 + 10.4801i) q^{82} +(-3.24002 - 3.24002i) q^{83} +(-4.91635 + 1.31733i) q^{85} +(-17.5237 - 17.5237i) q^{86} +(4.16566 - 2.40505i) q^{88} +(4.80209 + 1.28672i) q^{89} +(4.10012 + 8.61330i) q^{91} +15.1113 q^{92} +(-8.00209 + 4.62001i) q^{94} +(7.21613 + 4.16623i) q^{95} +(14.7483 - 3.95180i) q^{97} +(14.0280 - 6.24783i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

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