LMFDB - Embedded newform 847.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(1,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("847.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.a (trivial)

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:	yes
Analytic conductor:	$6.76332905120$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.76156$ of defining polynomial
Character	$\chi$	$=$	847.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76156 q^{2} +1.76156 q^{3} +5.62620 q^{4} -2.62620 q^{5} -4.86464 q^{6} -1.00000 q^{7} -10.0140 q^{8} +0.103084 q^{9} +O(q^{10})$	\(q-2.76156 q^{2} +1.76156 q^{3} +5.62620 q^{4} -2.62620 q^{5} -4.86464 q^{6} -1.00000 q^{7} -10.0140 q^{8} +0.103084 q^{9} +7.25240 q^{10} +9.91087 q^{12} +2.38776 q^{13} +2.76156 q^{14} -4.62620 q^{15} +16.4017 q^{16} +2.38776 q^{17} -0.284672 q^{18} +1.72928 q^{19} -14.7755 q^{20} -1.76156 q^{21} -0.626198 q^{23} -17.6402 q^{24} +1.89692 q^{25} -6.59392 q^{26} -5.10308 q^{27} -5.62620 q^{28} -1.72928 q^{29} +12.7755 q^{30} -2.23844 q^{31} -25.2663 q^{32} -6.59392 q^{34} +2.62620 q^{35} +0.579969 q^{36} -6.89692 q^{37} -4.77551 q^{38} +4.20617 q^{39} +26.2986 q^{40} -10.3878 q^{41} +4.86464 q^{42} -7.25240 q^{43} -0.270718 q^{45} +1.72928 q^{46} +6.38776 q^{47} +28.8925 q^{48} +1.00000 q^{49} -5.23844 q^{50} +4.20617 q^{51} +13.4340 q^{52} -9.25240 q^{53} +14.0925 q^{54} +10.0140 q^{56} +3.04623 q^{57} +4.77551 q^{58} -1.76156 q^{59} -26.0279 q^{60} +10.3878 q^{61} +6.18159 q^{62} -0.103084 q^{63} +36.9711 q^{64} -6.27072 q^{65} -6.42003 q^{67} +13.4340 q^{68} -1.10308 q^{69} -7.25240 q^{70} +8.08476 q^{71} -1.03228 q^{72} -10.3878 q^{73} +19.0462 q^{74} +3.34153 q^{75} +9.72928 q^{76} -11.6156 q^{78} -15.2524 q^{79} -43.0741 q^{80} -9.29862 q^{81} +28.6864 q^{82} -12.7755 q^{83} -9.91087 q^{84} -6.27072 q^{85} +20.0279 q^{86} -3.04623 q^{87} -14.1493 q^{89} +0.747604 q^{90} -2.38776 q^{91} -3.52311 q^{92} -3.94315 q^{93} -17.6402 q^{94} -4.54144 q^{95} -44.5081 q^{96} -8.35548 q^{97} -2.76156 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - q^{3} + 8 q^{4} + q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - q^3 + 8 * q^4 + q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 + 4 * q^9	$ 3 q - 2 q^{2} - q^{3} + 8 q^{4} + q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} + 2 q^{14} - 5 q^{15} + 10 q^{16} - 8 q^{17} + 18 q^{18} - 14 q^{20} + q^{21} + 7 q^{23} - 20 q^{24} + 2 q^{25} - 12 q^{26} - 19 q^{27} - 8 q^{28} + 8 q^{30} - 13 q^{31} - 34 q^{32} - 12 q^{34} - q^{35} + 18 q^{36} - 17 q^{37} + 16 q^{38} + 20 q^{39} + 36 q^{40} - 16 q^{41} + 12 q^{42} - 4 q^{43} - 6 q^{45} + 4 q^{47} + 36 q^{48} + 3 q^{49} - 22 q^{50} + 20 q^{51} - 10 q^{53} - 8 q^{54} + 6 q^{56} - 16 q^{57} - 16 q^{58} + q^{59} - 30 q^{60} + 16 q^{61} - 4 q^{62} - 4 q^{63} + 34 q^{64} - 24 q^{65} - 3 q^{67} - 7 q^{69} - 4 q^{70} + 5 q^{71} - 2 q^{72} - 16 q^{73} + 32 q^{74} + 20 q^{75} + 24 q^{76} + 28 q^{78} - 28 q^{79} - 56 q^{80} + 15 q^{81} + 28 q^{82} - 8 q^{83} - 2 q^{84} - 24 q^{85} + 12 q^{86} + 16 q^{87} - 21 q^{89} + 20 q^{90} + 8 q^{91} + 2 q^{92} + 17 q^{93} - 20 q^{94} - 24 q^{95} - 20 q^{96} - 11 q^{97} - 2 q^{98}+O(q^{100}) $ 3 * q - 2 * q^2 - q^3 + 8 * q^4 + q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 + 2 * q^14 - 5 * q^15 + 10 * q^16 - 8 * q^17 + 18 * q^18 - 14 * q^20 + q^21 + 7 * q^23 - 20 * q^24 + 2 * q^25 - 12 * q^26 - 19 * q^27 - 8 * q^28 + 8 * q^30 - 13 * q^31 - 34 * q^32 - 12 * q^34 - q^35 + 18 * q^36 - 17 * q^37 + 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 + 12 * q^42 - 4 * q^43 - 6 * q^45 + 4 * q^47 + 36 * q^48 + 3 * q^49 - 22 * q^50 + 20 * q^51 - 10 * q^53 - 8 * q^54 + 6 * q^56 - 16 * q^57 - 16 * q^58 + q^59 - 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 + 34 * q^64 - 24 * q^65 - 3 * q^67 - 7 * q^69 - 4 * q^70 + 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 + 20 * q^75 + 24 * q^76 + 28 * q^78 - 28 * q^79 - 56 * q^80 + 15 * q^81 + 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 + 12 * q^86 + 16 * q^87 - 21 * q^89 + 20 * q^90 + 8 * q^91 + 2 * q^92 + 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 - 11 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−2.76156	−1.95272	−0.976358	−	0.216160i	$-0.930647\pi$
$2$	−2.76156	−1.95272	−0.976358	+	0.216160i	$0.930647\pi$
$3$	1.76156	1.01704	0.508518	−	0.861052i	$-0.330194\pi$
$3$	1.76156	1.01704	0.508518	+	0.861052i	$0.330194\pi$
$4$	5.62620	2.81310
$5$	−2.62620	−1.17447	−0.587236	−	0.809416i	$-0.699784\pi$
$5$	−2.62620	−1.17447	−0.587236	+	0.809416i	$0.699784\pi$
$6$	−4.86464	−1.98598
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.0140	−3.54047
$9$	0.103084	0.0343612
$10$	7.25240	2.29341
$11$	0	0
$11$	0	0
$12$	9.91087	2.86102
$13$	2.38776	0.662244	0.331122	−	0.943588i	$-0.392573\pi$
$13$	2.38776	0.662244	0.331122	+	0.943588i	$0.392573\pi$
$14$	2.76156	0.738057
$15$	−4.62620	−1.19448
$16$	16.4017	4.10043
$17$	2.38776	0.579116	0.289558	−	0.957161i	$-0.406492\pi$
$17$	2.38776	0.579116	0.289558	+	0.957161i	$0.406492\pi$
$18$	−0.284672	−0.0670977
$19$	1.72928	0.396724	0.198362	−	0.980129i	$-0.436438\pi$
$19$	1.72928	0.396724	0.198362	+	0.980129i	$0.436438\pi$
$20$	−14.7755	−3.30390
$21$	−1.76156	−0.384403
$22$	0	0
$23$	−0.626198	−0.130571	−0.0652857	−	0.997867i	$-0.520796\pi$
$23$	−0.626198	−0.130571	−0.0652857	+	0.997867i	$0.520796\pi$
$24$	−17.6402	−3.60078
$25$	1.89692	0.379383
$26$	−6.59392	−1.29317
$27$	−5.10308	−0.982089
$28$	−5.62620	−1.06325
$29$	−1.72928	−0.321120	−0.160560	−	0.987026i	$-0.551330\pi$
$29$	−1.72928	−0.321120	−0.160560	+	0.987026i	$0.551330\pi$
$30$	12.7755	2.33248
$31$	−2.23844	−0.402036	−0.201018	−	0.979588i	$-0.564425\pi$
$31$	−2.23844	−0.402036	−0.201018	+	0.979588i	$0.564425\pi$
$32$	−25.2663	−4.46650
$33$	0	0
$34$	−6.59392	−1.13085
$35$	2.62620	0.443908
$36$	0.579969	0.0966616
$37$	−6.89692	−1.13385	−0.566923	−	0.823771i	$-0.691866\pi$
$37$	−6.89692	−1.13385	−0.566923	+	0.823771i	$0.691866\pi$
$38$	−4.77551	−0.774690
$39$	4.20617	0.673526
$40$	26.2986	4.15818
$41$	−10.3878	−1.62229	−0.811147	−	0.584842i	$-0.801157\pi$
$41$	−10.3878	−1.62229	−0.811147	+	0.584842i	$0.801157\pi$
$42$	4.86464	0.750630
$43$	−7.25240	−1.10598	−0.552990	−	0.833188i	$-0.686513\pi$
$43$	−7.25240	−1.10598	−0.552990	+	0.833188i	$0.686513\pi$
$44$	0	0
$45$	−0.270718	−0.0403563
$46$	1.72928	0.254969
$47$	6.38776	0.931750	0.465875	−	0.884851i	$-0.345740\pi$
$47$	6.38776	0.931750	0.465875	+	0.884851i	$0.345740\pi$
$48$	28.8925	4.17028
$49$	1.00000	0.142857
$50$	−5.23844	−0.740828
$51$	4.20617	0.588981
$52$	13.4340	1.86296
$53$	−9.25240	−1.27091	−0.635457	−	0.772136i	$-0.719188\pi$
$53$	−9.25240	−1.27091	−0.635457	+	0.772136i	$0.719188\pi$
$54$	14.0925	1.91774
$55$	0	0
$56$	10.0140	1.33817
$57$	3.04623	0.403483
$58$	4.77551	0.627055
$59$	−1.76156	−0.229335	−0.114668	−	0.993404i	$-0.536580\pi$
$59$	−1.76156	−0.229335	−0.114668	+	0.993404i	$0.536580\pi$
$60$	−26.0279	−3.36019
$61$	10.3878	1.33002	0.665008	−	0.746836i	$-0.268428\pi$
$61$	10.3878	1.33002	0.665008	+	0.746836i	$0.268428\pi$
$62$	6.18159	0.785062
$63$	−0.103084	−0.0129873
$64$	36.9711	4.62138
$65$	−6.27072	−0.777787
$66$	0	0
$67$	−6.42003	−0.784332	−0.392166	−	0.919895i	$-0.628274\pi$
$67$	−6.42003	−0.784332	−0.392166	+	0.919895i	$0.628274\pi$
$68$	13.4340	1.62911
$69$	−1.10308	−0.132796
$70$	−7.25240	−0.866827
$71$	8.08476	0.959485	0.479742	−	0.877409i	$-0.340730\pi$
$71$	8.08476	0.959485	0.479742	+	0.877409i	$0.340730\pi$
$72$	−1.03228	−0.121655
$73$	−10.3878	−1.21579	−0.607897	−	0.794016i	$-0.707987\pi$
$73$	−10.3878	−1.21579	−0.607897	+	0.794016i	$0.707987\pi$
$74$	19.0462	2.21408
$75$	3.34153	0.385846
$76$	9.72928	1.11603
$77$	0	0
$78$	−11.6156	−1.31520
$79$	−15.2524	−1.71603	−0.858014	−	0.513626i	$-0.828302\pi$
$79$	−15.2524	−1.71603	−0.858014	+	0.513626i	$0.828302\pi$
$80$	−43.0741	−4.81583
$81$	−9.29862	−1.03318
$82$	28.6864	3.16788
$83$	−12.7755	−1.40229	−0.701147	−	0.713017i	$-0.747328\pi$
$83$	−12.7755	−1.40229	−0.701147	+	0.713017i	$0.747328\pi$
$84$	−9.91087	−1.08136
$85$	−6.27072	−0.680155
$86$	20.0279	2.15966
$87$	−3.04623	−0.326590
$88$	0	0
$89$	−14.1493	−1.49982	−0.749912	−	0.661538i	$-0.769904\pi$
$89$	−14.1493	−1.49982	−0.749912	+	0.661538i	$0.769904\pi$
$90$	0.747604	0.0788044
$91$	−2.38776	−0.250305
$92$	−3.52311	−0.367310
$93$	−3.94315	−0.408885
$94$	−17.6402	−1.81944
$95$	−4.54144	−0.465942
$96$	−44.5081	−4.54259
$97$	−8.35548	−0.848370	−0.424185	−	0.905575i	$-0.639439\pi$
$97$	−8.35548	−0.848370	−0.424185	+	0.905575i	$0.639439\pi$
$98$	−2.76156	−0.278959
$99$	0	0
$100$	10.6724	1.06724
$101$	13.8463	1.37776	0.688880	−	0.724875i	$-0.258103\pi$
$101$	13.8463	1.37776	0.688880	+	0.724875i	$0.258103\pi$
$102$	−11.6156	−1.15011
$103$	−2.92919	−0.288622	−0.144311	−	0.989532i	$-0.546097\pi$
$103$	−2.92919	−0.288622	−0.144311	+	0.989532i	$0.546097\pi$
$104$	−23.9109	−2.34465
$105$	4.62620	0.451471
$106$	25.5510	2.48173
$107$	−3.45856	−0.334352	−0.167176	−	0.985927i	$-0.553465\pi$
$107$	−3.45856	−0.334352	−0.167176	+	0.985927i	$0.553465\pi$
$108$	−28.7110	−2.76271
$109$	16.2341	1.55494	0.777471	−	0.628919i	$-0.216502\pi$
$109$	16.2341	1.55494	0.777471	+	0.628919i	$0.216502\pi$
$110$	0	0
$111$	−12.1493	−1.15316
$112$	−16.4017	−1.54982
$113$	7.10308	0.668202	0.334101	−	0.942537i	$-0.391567\pi$
$113$	7.10308	0.668202	0.334101	+	0.942537i	$0.391567\pi$
$114$	−8.41233	−0.787887
$115$	1.64452	0.153352
$116$	−9.72928	−0.903341
$117$	0.246139	0.0227555
$118$	4.86464	0.447826
$119$	−2.38776	−0.218885
$120$	46.3265	4.22901
$121$	0	0
$122$	−28.6864	−2.59714
$123$	−18.2986	−1.64993
$124$	−12.5939	−1.13097
$125$	8.14931	0.728897
$126$	0.284672	0.0253606
$127$	4.54144	0.402987	0.201494	−	0.979490i	$-0.435420\pi$
$127$	4.54144	0.402987	0.201494	+	0.979490i	$0.435420\pi$
$128$	−51.5650	−4.55774
$129$	−12.7755	−1.12482
$130$	17.3169	1.51880
$131$	6.27072	0.547875	0.273938	−	0.961747i	$-0.411674\pi$
$131$	6.27072	0.547875	0.273938	+	0.961747i	$0.411674\pi$
$132$	0	0
$133$	−1.72928	−0.149948
$134$	17.7293	1.53158
$135$	13.4017	1.15344
$136$	−23.9109	−2.05034
$137$	9.40171	0.803242	0.401621	−	0.915806i	$-0.368447\pi$
$137$	9.40171	0.803242	0.401621	+	0.915806i	$0.368447\pi$
$138$	3.04623	0.259312
$139$	−15.8217	−1.34198	−0.670991	−	0.741465i	$-0.734131\pi$
$139$	−15.8217	−1.34198	−0.670991	+	0.741465i	$0.734131\pi$
$140$	14.7755	1.24876
$141$	11.2524	0.947623
$142$	−22.3265	−1.87360
$143$	0	0
$144$	1.69075	0.140896
$145$	4.54144	0.377146
$146$	28.6864	2.37410
$147$	1.76156	0.145291
$148$	−38.8034	−3.18962
$149$	−3.45856	−0.283337	−0.141668	−	0.989914i	$-0.545247\pi$
$149$	−3.45856	−0.283337	−0.141668	+	0.989914i	$0.545247\pi$
$150$	−9.22782	−0.753448
$151$	10.2986	0.838090	0.419045	−	0.907965i	$-0.362365\pi$
$151$	10.2986	0.838090	0.419045	+	0.907965i	$0.362365\pi$
$152$	−17.3169	−1.40459
$153$	0.246139	0.0198991
$154$	0	0
$155$	5.87859	0.472180
$156$	23.6647	1.89469
$157$	11.3372	0.904804	0.452402	−	0.891814i	$-0.350567\pi$
$157$	11.3372	0.904804	0.452402	+	0.891814i	$0.350567\pi$
$158$	42.1204	3.35092
$159$	−16.2986	−1.29257
$160$	66.3544	5.24578
$161$	0.626198	0.0493513
$162$	25.6787	2.01751
$163$	−9.72928	−0.762056	−0.381028	−	0.924563i	$-0.624430\pi$
$163$	−9.72928	−0.762056	−0.381028	+	0.924563i	$0.624430\pi$
$164$	−58.4436	−4.56368
$165$	0	0
$166$	35.2803	2.73828
$167$	−22.5048	−1.74147	−0.870737	−	0.491750i	$-0.836357\pi$
$167$	−22.5048	−1.74147	−0.870737	+	0.491750i	$0.836357\pi$
$168$	17.6402	1.36097
$169$	−7.29862	−0.561433
$170$	17.3169	1.32815
$171$	0.178261	0.0136319
$172$	−40.8034	−3.11123
$173$	−6.92919	−0.526817	−0.263408	−	0.964684i	$-0.584847\pi$
$173$	−6.92919	−0.526817	−0.263408	+	0.964684i	$0.584847\pi$
$174$	8.41233	0.637737
$175$	−1.89692	−0.143393
$176$	0	0
$177$	−3.10308	−0.233242
$178$	39.0741	2.92873
$179$	13.9431	1.04216	0.521080	−	0.853508i	$-0.325529\pi$
$179$	13.9431	1.04216	0.521080	+	0.853508i	$0.325529\pi$
$180$	−1.52311	−0.113526
$181$	3.16763	0.235448	0.117724	−	0.993046i	$-0.462440\pi$
$181$	3.16763	0.235448	0.117724	+	0.993046i	$0.462440\pi$
$182$	6.59392	0.488774
$183$	18.2986	1.35267
$184$	6.27072	0.462283
$185$	18.1127	1.33167
$186$	10.8892	0.798436
$187$	0	0
$188$	35.9388	2.62110
$189$	5.10308	0.371195
$190$	12.5414	0.909851
$191$	18.3555	1.32816	0.664078	−	0.747663i	$-0.268824\pi$
$191$	18.3555	1.32816	0.664078	+	0.747663i	$0.268824\pi$
$192$	65.1266	4.70011
$193$	3.04623	0.219272	0.109636	−	0.993972i	$-0.465031\pi$
$193$	3.04623	0.219272	0.109636	+	0.993972i	$0.465031\pi$
$194$	23.0741	1.65663
$195$	−11.0462	−0.791037
$196$	5.62620	0.401871
$197$	−4.95377	−0.352942	−0.176471	−	0.984306i	$-0.556468\pi$
$197$	−4.95377	−0.352942	−0.176471	+	0.984306i	$0.556468\pi$
$198$	0	0
$199$	15.7047	1.11328	0.556638	−	0.830755i	$-0.312091\pi$
$199$	15.7047	1.11328	0.556638	+	0.830755i	$0.312091\pi$
$200$	−18.9956	−1.34319
$201$	−11.3093	−0.797693
$202$	−38.2374	−2.69037
$203$	1.72928	0.121372
$204$	23.6647	1.65686
$205$	27.2803	1.90534
$206$	8.08913	0.563596
$207$	−0.0645508	−0.00448659
$208$	39.1633	2.71548
$209$	0	0
$210$	−12.7755	−0.881594
$211$	−17.5510	−1.20826	−0.604131	−	0.796885i	$-0.706480\pi$
$211$	−17.5510	−1.20826	−0.604131	+	0.796885i	$0.706480\pi$
$212$	−52.0558	−3.57521
$213$	14.2418	0.975830
$214$	9.55102	0.652894
$215$	19.0462	1.29894
$216$	51.1020	3.47705
$217$	2.23844	0.151955
$218$	−44.8313	−3.03636
$219$	−18.2986	−1.23651
$220$	0	0
$221$	5.70138	0.383516
$222$	33.5510	2.25180
$223$	−22.2943	−1.49293	−0.746467	−	0.665423i	$-0.768251\pi$
$223$	−22.2943	−1.49293	−0.746467	+	0.665423i	$0.768251\pi$
$224$	25.2663	1.68818
$225$	0.195541	0.0130361
$226$	−19.6156	−1.30481
$227$	−14.2707	−0.947181	−0.473590	−	0.880745i	$-0.657042\pi$
$227$	−14.2707	−0.947181	−0.473590	+	0.880745i	$0.657042\pi$
$228$	17.1387	1.13504
$229$	−3.87859	−0.256305	−0.128152	−	0.991754i	$-0.540905\pi$
$229$	−3.87859	−0.256305	−0.128152	+	0.991754i	$0.540905\pi$
$230$	−4.54144	−0.299453
$231$	0	0
$232$	17.3169	1.13691
$233$	−6.68305	−0.437821	−0.218911	−	0.975745i	$-0.570250\pi$
$233$	−6.68305	−0.437821	−0.218911	+	0.975745i	$0.570250\pi$
$234$	−0.679726	−0.0444351
$235$	−16.7755	−1.09431
$236$	−9.91087	−0.645143
$237$	−26.8680	−1.74526
$238$	6.59392	0.427421
$239$	4.54144	0.293761	0.146881	−	0.989154i	$-0.453077\pi$
$239$	4.54144	0.293761	0.146881	+	0.989154i	$0.453077\pi$
$240$	−75.8776	−4.89787
$241$	3.70470	0.238641	0.119320	−	0.992856i	$-0.461928\pi$
$241$	3.70470	0.238641	0.119320	+	0.992856i	$0.461928\pi$
$242$	0	0
$243$	−1.07081	−0.0686924
$244$	58.4436	3.74147
$245$	−2.62620	−0.167782
$246$	50.5327	3.22185
$247$	4.12910	0.262728
$248$	22.4157	1.42340
$249$	−22.5048	−1.42618
$250$	−22.5048	−1.42333
$251$	8.50916	0.537093	0.268547	−	0.963267i	$-0.413457\pi$
$251$	8.50916	0.537093	0.268547	+	0.963267i	$0.413457\pi$
$252$	−0.579969	−0.0365346
$253$	0	0
$254$	−12.5414	−0.786920
$255$	−11.0462	−0.691742
$256$	68.4575	4.27860
$257$	−2.95377	−0.184251	−0.0921256	−	0.995747i	$-0.529366\pi$
$257$	−2.95377	−0.184251	−0.0921256	+	0.995747i	$0.529366\pi$
$258$	35.2803	2.19646
$259$	6.89692	0.428554
$260$	−35.2803	−2.18799
$261$	−0.178261	−0.0110341
$262$	−17.3169	−1.06984
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	24.2986	1.49265
$266$	4.77551	0.292805
$267$	−24.9248	−1.52537
$268$	−36.1204	−2.20640
$269$	−6.77551	−0.413110	−0.206555	−	0.978435i	$-0.566225\pi$
$269$	−6.77551	−0.413110	−0.206555	+	0.978435i	$0.566225\pi$
$270$	−37.0096	−2.25233
$271$	−3.45856	−0.210093	−0.105046	−	0.994467i	$-0.533499\pi$
$271$	−3.45856	−0.210093	−0.105046	+	0.994467i	$0.533499\pi$
$272$	39.1633	2.37462
$273$	−4.20617	−0.254569
$274$	−25.9634	−1.56850
$275$	0	0
$276$	−6.20617	−0.373567
$277$	11.4586	0.688478	0.344239	−	0.938882i	$-0.388137\pi$
$277$	11.4586	0.688478	0.344239	+	0.938882i	$0.388137\pi$
$278$	43.6926	2.62051
$279$	−0.230747	−0.0138145
$280$	−26.2986	−1.57164
$281$	22.3265	1.33189	0.665945	−	0.746001i	$-0.268029\pi$
$281$	22.3265	1.33189	0.665945	+	0.746001i	$0.268029\pi$
$282$	−31.0741	−1.85044
$283$	12.3632	0.734915	0.367457	−	0.930040i	$-0.380228\pi$
$283$	12.3632	0.734915	0.367457	+	0.930040i	$0.380228\pi$
$284$	45.4865	2.69913
$285$	−8.00000	−0.473879
$286$	0	0
$287$	10.3878	0.613170
$288$	−2.60455	−0.153475
$289$	−11.2986	−0.664625
$290$	−12.5414	−0.736459
$291$	−14.7187	−0.862823
$292$	−58.4436	−3.42015
$293$	−2.15368	−0.125819	−0.0629097	−	0.998019i	$-0.520038\pi$
$293$	−2.15368	−0.125819	−0.0629097	+	0.998019i	$0.520038\pi$
$294$	−4.86464	−0.283712
$295$	4.62620	0.269348
$296$	69.0654	4.01434
$297$	0	0
$298$	9.55102	0.553276
$299$	−1.49521	−0.0864701
$300$	18.8001	1.08542
$301$	7.25240	0.418021
$302$	−28.4402	−1.63655
$303$	24.3911	1.40123
$304$	28.3632	1.62674
$305$	−27.2803	−1.56207
$306$	−0.679726	−0.0388573
$307$	31.8217	1.81616	0.908081	−	0.418794i	$-0.137547\pi$
$307$	31.8217	1.81616	0.908081	+	0.418794i	$0.137547\pi$
$308$	0	0
$309$	−5.15994	−0.293539
$310$	−16.2341	−0.922033
$311$	−10.9292	−0.619738	−0.309869	−	0.950779i	$-0.600285\pi$
$311$	−10.9292	−0.619738	−0.309869	+	0.950779i	$0.600285\pi$
$312$	−42.1204	−2.38460
$313$	7.40171	0.418369	0.209185	−	0.977876i	$-0.432919\pi$
$313$	7.40171	0.418369	0.209185	+	0.977876i	$0.432919\pi$
$314$	−31.3082	−1.76682
$315$	0.270718	0.0152532
$316$	−85.8130	−4.82736
$317$	−8.89692	−0.499701	−0.249850	−	0.968284i	$-0.580381\pi$
$317$	−8.89692	−0.499701	−0.249850	+	0.968284i	$0.580381\pi$
$318$	45.0096	2.52401
$319$	0	0
$320$	−97.0933	−5.42768
$321$	−6.09246	−0.340048
$322$	−1.72928	−0.0963691
$323$	4.12910	0.229749
$324$	−52.3159	−2.90644
$325$	4.52937	0.251244
$326$	26.8680	1.48808
$327$	28.5972	1.58143
$328$	104.022	5.74368
$329$	−6.38776	−0.352168
$330$	0	0
$331$	8.56165	0.470591	0.235295	−	0.971924i	$-0.424394\pi$
$331$	8.56165	0.470591	0.235295	+	0.971924i	$0.424394\pi$
$332$	−71.8776	−3.94479
$333$	−0.710960	−0.0389604
$334$	62.1483	3.40060
$335$	16.8603	0.921175
$336$	−28.8925	−1.57622
$337$	9.72928	0.529988	0.264994	−	0.964250i	$-0.414630\pi$
$337$	9.72928	0.529988	0.264994	+	0.964250i	$0.414630\pi$
$338$	20.1556	1.09632
$339$	12.5125	0.679585
$340$	−35.2803	−1.91334
$341$	0	0
$342$	−0.492277	−0.0266193
$343$	−1.00000	−0.0539949
$344$	72.6252	3.91569
$345$	2.89692	0.155965
$346$	19.1354	1.02872
$347$	−14.8401	−0.796656	−0.398328	−	0.917243i	$-0.630409\pi$
$347$	−14.8401	−0.796656	−0.398328	+	0.917243i	$0.630409\pi$
$348$	−17.1387	−0.918730
$349$	−16.2461	−0.869636	−0.434818	−	0.900518i	$-0.643187\pi$
$349$	−16.2461	−0.869636	−0.434818	+	0.900518i	$0.643187\pi$
$350$	5.23844	0.280007
$351$	−12.1849	−0.650383
$352$	0	0
$353$	30.8603	1.64253	0.821263	−	0.570549i	$-0.193270\pi$
$353$	30.8603	1.64253	0.821263	+	0.570549i	$0.193270\pi$
$354$	8.56934	0.455455
$355$	−21.2322	−1.12689
$356$	−79.6068	−4.21915
$357$	−4.20617	−0.222614
$358$	−38.5048	−2.03504
$359$	11.7938	0.622455	0.311227	−	0.950335i	$-0.399260\pi$
$359$	11.7938	0.622455	0.311227	+	0.950335i	$0.399260\pi$
$360$	2.71096	0.142880
$361$	−16.0096	−0.842610
$362$	−8.74760	−0.459764
$363$	0	0
$364$	−13.4340	−0.704132
$365$	27.2803	1.42792
$366$	−50.5327	−2.64139
$367$	−3.55539	−0.185590	−0.0927949	−	0.995685i	$-0.529580\pi$
$367$	−3.55539	−0.185590	−0.0927949	+	0.995685i	$0.529580\pi$
$368$	−10.2707	−0.535398
$369$	−1.07081	−0.0557441
$370$	−50.0192	−2.60037
$371$	9.25240	0.480360
$372$	−22.1849	−1.15023
$373$	−22.5048	−1.16525	−0.582627	−	0.812740i	$-0.697975\pi$
$373$	−22.5048	−1.16525	−0.582627	+	0.812740i	$0.697975\pi$
$374$	0	0
$375$	14.3555	0.741314
$376$	−63.9667	−3.29883
$377$	−4.12910	−0.212660
$378$	−14.0925	−0.724838
$379$	23.4296	1.20350	0.601749	−	0.798685i	$-0.294471\pi$
$379$	23.4296	1.20350	0.601749	+	0.798685i	$0.294471\pi$
$380$	−25.5510	−1.31074
$381$	8.00000	0.409852
$382$	−50.6897	−2.59351
$383$	−3.42629	−0.175075	−0.0875376	−	0.996161i	$-0.527900\pi$
$383$	−3.42629	−0.175075	−0.0875376	+	0.996161i	$0.527900\pi$
$384$	−90.8347	−4.63539
$385$	0	0
$386$	−8.41233	−0.428177
$387$	−0.747604	−0.0380028
$388$	−47.0096	−2.38655
$389$	8.05685	0.408499	0.204249	−	0.978919i	$-0.434525\pi$
$389$	8.05685	0.408499	0.204249	+	0.978919i	$0.434525\pi$
$390$	30.5048	1.54467
$391$	−1.49521	−0.0756159
$392$	−10.0140	−0.505781
$393$	11.0462	0.557209
$394$	13.6801	0.689195
$395$	40.0558	2.01543
$396$	0	0
$397$	−26.3632	−1.32313	−0.661565	−	0.749888i	$-0.730107\pi$
$397$	−26.3632	−1.32313	−0.661565	+	0.749888i	$0.730107\pi$
$398$	−43.3694	−2.17391
$399$	−3.04623	−0.152502
$400$	31.1127	1.55563
$401$	−22.5972	−1.12845	−0.564226	−	0.825620i	$-0.690825\pi$
$401$	−22.5972	−1.12845	−0.564226	+	0.825620i	$0.690825\pi$
$402$	31.2311	1.55767
$403$	−5.34485	−0.266246
$404$	77.9021	3.87578
$405$	24.4200	1.21344
$406$	−4.77551	−0.237005
$407$	0	0
$408$	−42.1204	−2.08527
$409$	−9.30488	−0.460097	−0.230048	−	0.973179i	$-0.573888\pi$
$409$	−9.30488	−0.460097	−0.230048	+	0.973179i	$0.573888\pi$
$410$	−75.3361	−3.72059
$411$	16.5616	0.816926
$412$	−16.4802	−0.811922
$413$	1.76156	0.0866806
$414$	0.178261	0.00876104
$415$	33.5510	1.64695
$416$	−60.3299	−2.95791
$417$	−27.8709	−1.36484
$418$	0	0
$419$	−13.8463	−0.676437	−0.338218	−	0.941068i	$-0.609824\pi$
$419$	−13.8463	−0.676437	−0.338218	+	0.941068i	$0.609824\pi$
$420$	26.0279	1.27003
$421$	−35.7572	−1.74270	−0.871349	−	0.490663i	$-0.836755\pi$
$421$	−35.7572	−1.74270	−0.871349	+	0.490663i	$0.836755\pi$
$422$	48.4681	2.35939
$423$	0.658473	0.0320161
$424$	92.6531	4.49963
$425$	4.52937	0.219707
$426$	−39.3295	−1.90552
$427$	−10.3878	−0.502699
$428$	−19.4586	−0.940565
$429$	0	0
$430$	−52.5972	−2.53646
$431$	31.3082	1.50806	0.754032	−	0.656838i	$-0.228106\pi$
$431$	31.3082	1.50806	0.754032	+	0.656838i	$0.228106\pi$
$432$	−83.6993	−4.02698
$433$	21.6079	1.03841	0.519204	−	0.854650i	$-0.326228\pi$
$433$	21.6079	1.03841	0.519204	+	0.854650i	$0.326228\pi$
$434$	−6.18159	−0.296726
$435$	8.00000	0.383571
$436$	91.3361	4.37421
$437$	−1.08287	−0.0518008
$438$	50.5327	2.41455
$439$	−15.5877	−0.743959	−0.371979	−	0.928241i	$-0.621321\pi$
$439$	−15.5877	−0.743959	−0.371979	+	0.928241i	$0.621321\pi$
$440$	0	0
$441$	0.103084	0.00490875
$442$	−15.7447	−0.748898
$443$	23.4942	1.11624	0.558121	−	0.829760i	$-0.311523\pi$
$443$	23.4942	1.11624	0.558121	+	0.829760i	$0.311523\pi$
$444$	−68.3544	−3.24396
$445$	37.1589	1.76150
$446$	61.5669	2.91528
$447$	−6.09246	−0.288163
$448$	−36.9711	−1.74672
$449$	22.7832	1.07521	0.537603	−	0.843198i	$-0.319330\pi$
$449$	22.7832	1.07521	0.537603	+	0.843198i	$0.319330\pi$
$450$	−0.539998	−0.0254558
$451$	0	0
$452$	39.9634	1.87972
$453$	18.1416	0.852368
$454$	39.4094	1.84957
$455$	6.27072	0.293976
$456$	−30.5048	−1.42852
$457$	14.5048	0.678506	0.339253	−	0.940695i	$-0.389826\pi$
$457$	14.5048	0.678506	0.339253	+	0.940695i	$0.389826\pi$
$458$	10.7110	0.500490
$459$	−12.1849	−0.568743
$460$	9.25240	0.431395
$461$	31.1633	1.45142	0.725709	−	0.688002i	$-0.241512\pi$
$461$	31.1633	1.45142	0.725709	+	0.688002i	$0.241512\pi$
$462$	0	0
$463$	−5.87859	−0.273201	−0.136601	−	0.990626i	$-0.543618\pi$
$463$	−5.87859	−0.273201	−0.136601	+	0.990626i	$0.543618\pi$
$464$	−28.3632	−1.31673
$465$	10.3555	0.480224
$466$	18.4556	0.854941
$467$	−23.7249	−1.09786	−0.548929	−	0.835869i	$-0.684964\pi$
$467$	−23.7249	−1.09786	−0.548929	+	0.835869i	$0.684964\pi$
$468$	1.38482	0.0640136
$469$	6.42003	0.296449
$470$	46.3265	2.13688
$471$	19.9711	0.920217
$472$	17.6402	0.811954
$473$	0	0
$474$	74.1974	3.40800
$475$	3.28030	0.150511
$476$	−13.4340	−0.615746
$477$	−0.953771	−0.0436702
$478$	−12.5414	−0.573632
$479$	−8.41233	−0.384369	−0.192185	−	0.981359i	$-0.561557\pi$
$479$	−8.41233	−0.384369	−0.192185	+	0.981359i	$0.561557\pi$
$480$	116.887	5.33514
$481$	−16.4681	−0.750883
$482$	−10.2307	−0.465998
$483$	1.10308	0.0501920
$484$	0	0
$485$	21.9431	0.996387
$486$	2.95710	0.134137
$487$	24.7957	1.12360	0.561801	−	0.827273i	$-0.310109\pi$
$487$	24.7957	1.12360	0.561801	+	0.827273i	$0.310109\pi$
$488$	−104.022	−4.70888
$489$	−17.1387	−0.775038
$490$	7.25240	0.327630
$491$	−12.2062	−0.550857	−0.275428	−	0.961322i	$-0.588820\pi$
$491$	−12.2062	−0.550857	−0.275428	+	0.961322i	$0.588820\pi$
$492$	−102.952	−4.64142
$493$	−4.12910	−0.185965
$494$	−11.4028	−0.513034
$495$	0	0
$496$	−36.7143	−1.64852
$497$	−8.08476	−0.362651
$498$	62.1483	2.78493
$499$	22.3265	0.999473	0.499736	−	0.866178i	$-0.333430\pi$
$499$	22.3265	0.999473	0.499736	+	0.866178i	$0.333430\pi$
$500$	45.8496	2.05046
$501$	−39.6435	−1.77114
$502$	−23.4985	−1.04879
$503$	4.54144	0.202493	0.101246	−	0.994861i	$-0.467717\pi$
$503$	4.54144	0.202493	0.101246	+	0.994861i	$0.467717\pi$
$504$	1.03228	0.0459812
$505$	−36.3632	−1.61814
$506$	0	0
$507$	−12.8569	−0.570997
$508$	25.5510	1.13364
$509$	4.12141	0.182678	0.0913391	−	0.995820i	$-0.470885\pi$
$509$	4.12141	0.182678	0.0913391	+	0.995820i	$0.470885\pi$
$510$	30.5048	1.35077
$511$	10.3878	0.459527
$512$	−85.9194	−3.79714
$513$	−8.82467	−0.389619
$514$	8.15701	0.359790
$515$	7.69264	0.338978
$516$	−71.8776	−3.16423
$517$	0	0
$518$	−19.0462	−0.836843
$519$	−12.2062	−0.535791
$520$	62.7947	2.75373
$521$	39.2880	1.72124	0.860619	−	0.509249i	$-0.170077\pi$
$521$	39.2880	1.72124	0.860619	+	0.509249i	$0.170077\pi$
$522$	0.492277	0.0215464
$523$	2.14162	0.0936464	0.0468232	−	0.998903i	$-0.485090\pi$
$523$	2.14162	0.0936464	0.0468232	+	0.998903i	$0.485090\pi$
$524$	35.2803	1.54123
$525$	−3.34153	−0.145836
$526$	−44.1849	−1.92655
$527$	−5.34485	−0.232825
$528$	0	0
$529$	−22.6079	−0.982951
$530$	−67.1020	−2.91473
$531$	−0.181588	−0.00788024
$532$	−9.72928	−0.421818
$533$	−24.8034	−1.07436
$534$	68.8313	2.97862
$535$	9.08287	0.392687
$536$	64.2899	2.77690
$537$	24.5616	1.05991
$538$	18.7110	0.806687
$539$	0	0
$540$	75.4007	3.24473
$541$	43.0462	1.85070	0.925351	−	0.379112i	$-0.123770\pi$
$541$	43.0462	1.85070	0.925351	+	0.379112i	$0.123770\pi$
$542$	9.55102	0.410251
$543$	5.57997	0.239459
$544$	−60.3299	−2.58662
$545$	−42.6339	−1.82624
$546$	11.6156	0.497101
$547$	29.0096	1.24036	0.620180	−	0.784459i	$-0.287060\pi$
$547$	29.0096	1.24036	0.620180	+	0.784459i	$0.287060\pi$
$548$	52.8959	2.25960
$549$	1.07081	0.0457010
$550$	0	0
$551$	−2.99042	−0.127396
$552$	11.0462	0.470159
$553$	15.2524	0.648598
$554$	−31.6435	−1.34440
$555$	31.9065	1.35436
$556$	−89.0162	−3.77513
$557$	1.49521	0.0633540	0.0316770	−	0.999498i	$-0.489915\pi$
$557$	1.49521	0.0633540	0.0316770	+	0.999498i	$0.489915\pi$
$558$	0.637221	0.0269757
$559$	−17.3169	−0.732429
$560$	43.0741	1.82021
$561$	0	0
$562$	−61.6560	−2.60080
$563$	−6.27072	−0.264279	−0.132140	−	0.991231i	$-0.542185\pi$
$563$	−6.27072	−0.264279	−0.132140	+	0.991231i	$0.542185\pi$
$564$	63.3082	2.66576
$565$	−18.6541	−0.784784
$566$	−34.1416	−1.43508
$567$	9.29862	0.390506
$568$	−80.9604	−3.39702
$569$	−7.82174	−0.327904	−0.163952	−	0.986468i	$-0.552424\pi$
$569$	−7.82174	−0.327904	−0.163952	+	0.986468i	$0.552424\pi$
$570$	22.0925	0.925351
$571$	15.1753	0.635068	0.317534	−	0.948247i	$-0.397145\pi$
$571$	15.1753	0.635068	0.317534	+	0.948247i	$0.397145\pi$
$572$	0	0
$573$	32.3342	1.35078
$574$	−28.6864	−1.19735
$575$	−1.18785	−0.0495366
$576$	3.81111	0.158796
$577$	23.6445	0.984334	0.492167	−	0.870501i	$-0.336205\pi$
$577$	23.6445	0.984334	0.492167	+	0.870501i	$0.336205\pi$
$578$	31.2018	1.29782
$579$	5.36611	0.223008
$580$	25.5510	1.06095
$581$	12.7755	0.530017
$582$	40.6464	1.68485
$583$	0	0
$584$	104.022	4.30448
$585$	−0.646409	−0.0267257
$586$	5.94751	0.245690
$587$	−10.1537	−0.419087	−0.209544	−	0.977799i	$-0.567198\pi$
$587$	−10.1537	−0.419087	−0.209544	+	0.977799i	$0.567198\pi$
$588$	9.91087	0.408717
$589$	−3.87090	−0.159498
$590$	−12.7755	−0.525959
$591$	−8.72635	−0.358954
$592$	−113.121	−4.64925
$593$	−33.7972	−1.38788	−0.693942	−	0.720031i	$-0.744127\pi$
$593$	−33.7972	−1.38788	−0.693942	+	0.720031i	$0.744127\pi$
$594$	0	0
$595$	6.27072	0.257074
$596$	−19.4586	−0.797054
$597$	27.6647	1.13224
$598$	4.12910	0.168852
$599$	−18.3265	−0.748802	−0.374401	−	0.927267i	$-0.622152\pi$
$599$	−18.3265	−0.748802	−0.374401	+	0.927267i	$0.622152\pi$
$600$	−33.4619	−1.36608
$601$	−48.4802	−1.97755	−0.988775	−	0.149415i	$-0.952261\pi$
$601$	−48.4802	−1.97755	−0.988775	+	0.149415i	$0.952261\pi$
$602$	−20.0279	−0.816277
$603$	−0.661801	−0.0269506
$604$	57.9421	2.35763
$605$	0	0
$606$	−67.3574	−2.73621
$607$	20.5972	0.836017	0.418008	−	0.908443i	$-0.362728\pi$
$607$	20.5972	0.836017	0.418008	+	0.908443i	$0.362728\pi$
$608$	−43.6926	−1.77197
$609$	3.04623	0.123439
$610$	75.3361	3.05027
$611$	15.2524	0.617046
$612$	1.38482	0.0559782
$613$	−18.8122	−0.759816	−0.379908	−	0.925024i	$-0.624044\pi$
$613$	−18.8122	−0.759816	−0.379908	+	0.925024i	$0.624044\pi$
$614$	−87.8776	−3.54645
$615$	48.0558	1.93780
$616$	0	0
$617$	−14.2062	−0.571919	−0.285959	−	0.958242i	$-0.592312\pi$
$617$	−14.2062	−0.571919	−0.285959	+	0.958242i	$0.592312\pi$
$618$	14.2495	0.573198
$619$	−16.0235	−0.644040	−0.322020	−	0.946733i	$-0.604362\pi$
$619$	−16.0235	−0.644040	−0.322020	+	0.946733i	$0.604362\pi$
$620$	33.0741	1.32829
$621$	3.19554	0.128233
$622$	30.1816	1.21017
$623$	14.1493	0.566880
$624$	68.9883	2.76174
$625$	−30.8863	−1.23545
$626$	−20.4402	−0.816956
$627$	0	0
$628$	63.7851	2.54530
$629$	−16.4681	−0.656628
$630$	−0.747604	−0.0297853
$631$	15.1955	0.604925	0.302462	−	0.953161i	$-0.402191\pi$
$631$	15.1955	0.604925	0.302462	+	0.953161i	$0.402191\pi$
$632$	152.737	6.07554
$633$	−30.9171	−1.22885
$634$	24.5693	0.975773
$635$	−11.9267	−0.473297
$636$	−91.6993	−3.63611
$637$	2.38776	0.0946063
$638$	0	0
$639$	0.833407	0.0329691
$640$	135.420	5.35294
$641$	−10.2264	−0.403918	−0.201959	−	0.979394i	$-0.564731\pi$
$641$	−10.2264	−0.403918	−0.201959	+	0.979394i	$0.564731\pi$
$642$	16.8247	0.664017
$643$	20.5650	0.811003	0.405502	−	0.914094i	$-0.367097\pi$
$643$	20.5650	0.811003	0.405502	+	0.914094i	$0.367097\pi$
$644$	3.52311	0.138830
$645$	33.5510	1.32107
$646$	−11.4028	−0.448635
$647$	−25.4542	−1.00071	−0.500354	−	0.865821i	$-0.666797\pi$
$647$	−25.4542	−1.00071	−0.500354	+	0.865821i	$0.666797\pi$
$648$	93.1160	3.65794
$649$	0	0
$650$	−12.5081	−0.490609
$651$	3.94315	0.154544
$652$	−54.7389	−2.14374
$653$	−45.2514	−1.77082	−0.885411	−	0.464809i	$-0.846123\pi$
$653$	−45.2514	−1.77082	−0.885411	+	0.464809i	$0.846123\pi$
$654$	−78.9729	−3.08809
$655$	−16.4681	−0.643464
$656$	−170.377	−6.65210
$657$	−1.07081	−0.0417762
$658$	17.6402	0.687685
$659$	50.3544	1.96153	0.980765	−	0.195191i	$-0.0625327\pi$
$659$	50.3544	1.96153	0.980765	+	0.195191i	$0.0625327\pi$
$660$	0	0
$661$	−23.2234	−0.903287	−0.451644	−	0.892198i	$-0.649162\pi$
$661$	−23.2234	−0.903287	−0.451644	+	0.892198i	$0.649162\pi$
$662$	−23.6435	−0.918930
$663$	10.0433	0.390049
$664$	127.933	4.96478
$665$	4.54144	0.176109
$666$	1.96336	0.0760785
$667$	1.08287	0.0419290
$668$	−126.616	−4.89894
$669$	−39.2726	−1.51837
$670$	−46.5606	−1.79879
$671$	0	0
$672$	44.5081	1.71694
$673$	3.22449	0.124295	0.0621475	−	0.998067i	$-0.480205\pi$
$673$	3.22449	0.124295	0.0621475	+	0.998067i	$0.480205\pi$
$674$	−26.8680	−1.03492
$675$	−9.68012	−0.372588
$676$	−41.0635	−1.57937
$677$	−42.6218	−1.63809	−0.819045	−	0.573729i	$-0.805496\pi$
$677$	−42.6218	−1.63809	−0.819045	+	0.573729i	$0.805496\pi$
$678$	−34.5540	−1.32704
$679$	8.35548	0.320654
$680$	62.7947	2.40807
$681$	−25.1387	−0.963317
$682$	0	0
$683$	15.5877	0.596445	0.298223	−	0.954496i	$-0.403606\pi$
$683$	15.5877	0.596445	0.298223	+	0.954496i	$0.403606\pi$
$684$	1.00293	0.0383480
$685$	−24.6907	−0.943385
$686$	2.76156	0.105437
$687$	−6.83237	−0.260671
$688$	−118.952	−4.53499
$689$	−22.0925	−0.841656
$690$	−8.00000	−0.304555
$691$	41.9311	1.59513	0.797567	−	0.603231i	$-0.206120\pi$
$691$	41.9311	1.59513	0.797567	+	0.603231i	$0.206120\pi$
$692$	−38.9850	−1.48199
$693$	0	0
$694$	40.9817	1.55564
$695$	41.5510	1.57612
$696$	30.5048	1.15628
$697$	−24.8034	−0.939496
$698$	44.8646	1.69815
$699$	−11.7726	−0.445280
$700$	−10.6724	−0.403380
$701$	15.4094	0.582005	0.291003	−	0.956722i	$-0.406011\pi$
$701$	15.4094	0.582005	0.291003	+	0.956722i	$0.406011\pi$
$702$	33.6493	1.27001
$703$	−11.9267	−0.449824
$704$	0	0
$705$	−29.5510	−1.11296
$706$	−85.2224	−3.20739
$707$	−13.8463	−0.520744
$708$	−17.4586	−0.656133
$709$	2.86027	0.107420	0.0537099	−	0.998557i	$-0.482895\pi$
$709$	2.86027	0.107420	0.0537099	+	0.998557i	$0.482895\pi$
$710$	58.6339	2.20049
$711$	−1.57227	−0.0589649
$712$	141.691	5.31008
$713$	1.40171	0.0524944
$714$	11.6156	0.434702
$715$	0	0
$716$	78.4469	2.93170
$717$	8.00000	0.298765
$718$	−32.5693	−1.21548
$719$	−34.4725	−1.28561	−0.642804	−	0.766031i	$-0.722229\pi$
$719$	−34.4725	−1.28561	−0.642804	+	0.766031i	$0.722229\pi$
$720$	−4.44024	−0.165478
$721$	2.92919	0.109089
$722$	44.2114	1.64538
$723$	6.52604	0.242706
$724$	17.8217	0.662340
$725$	−3.28030	−0.121827
$726$	0	0
$727$	−40.3309	−1.49579	−0.747895	−	0.663817i	$-0.768935\pi$
$727$	−40.3309	−1.49579	−0.747895	+	0.663817i	$0.768935\pi$
$728$	23.9109	0.886196
$729$	26.0096	0.963318
$730$	−75.3361	−2.78831
$731$	−17.3169	−0.640490
$732$	102.952	3.80520
$733$	28.7634	1.06240	0.531201	−	0.847246i	$-0.321741\pi$
$733$	28.7634	1.06240	0.531201	+	0.847246i	$0.321741\pi$
$734$	9.81841	0.362404
$735$	−4.62620	−0.170640
$736$	15.8217	0.583197
$737$	0	0
$738$	2.95710	0.108852
$739$	−35.1020	−1.29125	−0.645625	−	0.763655i	$-0.723403\pi$
$739$	−35.1020	−1.29125	−0.645625	+	0.763655i	$0.723403\pi$
$740$	101.905	3.74612
$741$	7.27365	0.267204
$742$	−25.5510	−0.938007
$743$	32.4681	1.19114	0.595570	−	0.803303i	$-0.296926\pi$
$743$	32.4681	1.19114	0.595570	+	0.803303i	$0.296926\pi$
$744$	39.4865	1.44764
$745$	9.08287	0.332771
$746$	62.1483	2.27541
$747$	−1.31695	−0.0481846
$748$	0	0
$749$	3.45856	0.126373
$750$	−39.6435	−1.44758
$751$	−28.3834	−1.03572	−0.517862	−	0.855464i	$-0.673272\pi$
$751$	−28.3834	−1.03572	−0.517862	+	0.855464i	$0.673272\pi$
$752$	104.770	3.82057
$753$	14.9894	0.546243
$754$	11.4028	0.415264
$755$	−27.0462	−0.984313
$756$	28.7110	1.04421
$757$	−17.0462	−0.619556	−0.309778	−	0.950809i	$-0.600255\pi$
$757$	−17.0462	−0.619556	−0.309778	+	0.950809i	$0.600255\pi$
$758$	−64.7022	−2.35009
$759$	0	0
$760$	45.4777	1.64965
$761$	−27.9388	−1.01278	−0.506390	−	0.862305i	$-0.669020\pi$
$761$	−27.9388	−1.01278	−0.506390	+	0.862305i	$0.669020\pi$
$762$	−22.0925	−0.800325
$763$	−16.2341	−0.587713
$764$	103.272	3.73623
$765$	−0.646409	−0.0233710
$766$	9.46189	0.341872
$767$	−4.20617	−0.151876
$768$	120.592	4.35148
$769$	−6.69512	−0.241432	−0.120716	−	0.992687i	$-0.538519\pi$
$769$	−6.69512	−0.241432	−0.120716	+	0.992687i	$0.538519\pi$
$770$	0	0
$771$	−5.20324	−0.187390
$772$	17.1387	0.616835
$773$	27.9142	1.00400	0.502002	−	0.864866i	$-0.332597\pi$
$773$	27.9142	1.00400	0.502002	+	0.864866i	$0.332597\pi$
$774$	2.06455	0.0742087
$775$	−4.24614	−0.152526
$776$	83.6714	3.00363
$777$	12.1493	0.435854
$778$	−22.2495	−0.797682
$779$	−17.9634	−0.643604
$780$	−62.1483	−2.22527
$781$	0	0
$782$	4.12910	0.147656
$783$	8.82467	0.315368
$784$	16.4017	0.585775
$785$	−29.7736	−1.06267
$786$	−30.5048	−1.08807
$787$	−21.8584	−0.779167	−0.389584	−	0.920991i	$-0.627381\pi$
$787$	−21.8584	−0.779167	−0.389584	+	0.920991i	$0.627381\pi$
$788$	−27.8709	−0.992860
$789$	28.1849	1.00341
$790$	−110.616	−3.93556
$791$	−7.10308	−0.252557
$792$	0	0
$793$	24.8034	0.880795
$794$	72.8034	2.58370
$795$	42.8034	1.51808
$796$	88.3578	3.13176
$797$	−34.6262	−1.22652	−0.613261	−	0.789880i	$-0.710143\pi$
$797$	−34.6262	−1.22652	−0.613261	+	0.789880i	$0.710143\pi$
$798$	8.41233	0.297793
$799$	15.2524	0.539591
$800$	−47.9282	−1.69452
$801$	−1.45856	−0.0515358
$802$	62.4036	2.20355
$803$	0	0
$804$	−63.6281	−2.24399
$805$	−1.64452	−0.0579617
$806$	14.7601	0.519903
$807$	−11.9354	−0.420148
$808$	−138.656	−4.87791
$809$	−35.0462	−1.23216	−0.616080	−	0.787684i	$-0.711280\pi$
$809$	−35.0462	−1.23216	−0.616080	+	0.787684i	$0.711280\pi$
$810$	−67.4373	−2.36951
$811$	18.1416	0.637038	0.318519	−	0.947916i	$-0.396814\pi$
$811$	18.1416	0.637038	0.318519	+	0.947916i	$0.396814\pi$
$812$	9.72928	0.341431
$813$	−6.09246	−0.213672
$814$	0	0
$815$	25.5510	0.895013
$816$	68.9883	2.41507
$817$	−12.5414	−0.438769
$818$	25.6960	0.898438
$819$	−0.246139	−0.00860078
$820$	153.484	5.35991
$821$	3.45856	0.120705	0.0603524	−	0.998177i	$-0.480778\pi$
$821$	3.45856	0.120705	0.0603524	+	0.998177i	$0.480778\pi$
$822$	−45.7359	−1.59522
$823$	−33.5308	−1.16881	−0.584405	−	0.811462i	$-0.698672\pi$
$823$	−33.5308	−1.16881	−0.584405	+	0.811462i	$0.698672\pi$
$824$	29.3328	1.02186
$825$	0	0
$826$	−4.86464	−0.169263
$827$	26.2986	0.914493	0.457246	−	0.889340i	$-0.348836\pi$
$827$	26.2986	0.914493	0.457246	+	0.889340i	$0.348836\pi$
$828$	−0.363176	−0.0126212
$829$	−29.0019	−1.00728	−0.503639	−	0.863914i	$-0.668006\pi$
$829$	−29.0019	−1.00728	−0.503639	+	0.863914i	$0.668006\pi$
$830$	−92.6531	−3.21603
$831$	20.1849	0.700207
$832$	88.2778	3.06048
$833$	2.38776	0.0827308
$834$	76.9671	2.66515
$835$	59.1020	2.04531
$836$	0	0
$837$	11.4230	0.394835
$838$	38.2374	1.32089
$839$	29.1710	1.00709	0.503547	−	0.863968i	$-0.332028\pi$
$839$	29.1710	1.00709	0.503547	+	0.863968i	$0.332028\pi$
$840$	−46.3265	−1.59842
$841$	−26.0096	−0.896882
$842$	98.7455	3.40300
$843$	39.3295	1.35458
$844$	−98.7455	−3.39896
$845$	19.1676	0.659387
$846$	−1.81841	−0.0625183
$847$	0	0
$848$	−151.755	−5.21129
$849$	21.7784	0.747434
$850$	−12.5081	−0.429025
$851$	4.31884	0.148048
$852$	80.1270	2.74511
$853$	−10.6218	−0.363685	−0.181842	−	0.983328i	$-0.558206\pi$
$853$	−10.6218	−0.363685	−0.181842	+	0.983328i	$0.558206\pi$
$854$	28.6864	0.981628
$855$	−0.468148	−0.0160103
$856$	34.6339	1.18376
$857$	−37.8463	−1.29281	−0.646403	−	0.762996i	$-0.723727\pi$
$857$	−37.8463	−1.29281	−0.646403	+	0.762996i	$0.723727\pi$
$858$	0	0
$859$	−19.0785	−0.650950	−0.325475	−	0.945551i	$-0.605524\pi$
$859$	−19.0785	−0.650950	−0.325475	+	0.945551i	$0.605524\pi$
$860$	107.158	3.65405
$861$	18.2986	0.623615
$862$	−86.4594	−2.94482
$863$	11.1753	0.380413	0.190206	−	0.981744i	$-0.439084\pi$
$863$	11.1753	0.380413	0.190206	+	0.981744i	$0.439084\pi$
$864$	128.936	4.38650
$865$	18.1974	0.618731
$866$	−59.6714	−2.02772
$867$	−19.9032	−0.675947
$868$	12.5939	0.427466
$869$	0	0
$870$	−22.0925	−0.749004
$871$	−15.3295	−0.519419
$872$	−162.567	−5.50522
$873$	−0.861314	−0.0291511
$874$	2.99042	0.101152
$875$	−8.14931	−0.275497
$876$	−102.952	−3.47842
$877$	5.85838	0.197824	0.0989118	−	0.995096i	$-0.468464\pi$
$877$	5.85838	0.197824	0.0989118	+	0.995096i	$0.468464\pi$
$878$	43.0462	1.45274
$879$	−3.79383	−0.127963
$880$	0	0
$881$	−25.9065	−0.872812	−0.436406	−	0.899750i	$-0.643749\pi$
$881$	−25.9065	−0.872812	−0.436406	+	0.899750i	$0.643749\pi$
$882$	−0.284672	−0.00958539
$883$	13.4219	0.451684	0.225842	−	0.974164i	$-0.427487\pi$
$883$	13.4219	0.451684	0.225842	+	0.974164i	$0.427487\pi$
$884$	32.0771	1.07887
$885$	8.14931	0.273936
$886$	−64.8805	−2.17970
$887$	49.6068	1.66563	0.832817	−	0.553548i	$-0.186726\pi$
$887$	49.6068	1.66563	0.832817	+	0.553548i	$0.186726\pi$
$888$	121.663	4.08273
$889$	−4.54144	−0.152315
$890$	−102.616	−3.43971
$891$	0	0
$892$	−125.432	−4.19977
$893$	11.0462	0.369648
$894$	16.8247	0.562701
$895$	−36.6175	−1.22399
$896$	51.5650	1.72266
$897$	−2.63389	−0.0879432
$898$	−62.9171	−2.09957
$899$	3.87090	0.129102
$900$	1.10015	0.0366718
$901$	−22.0925	−0.736006
$902$	0	0
$903$	12.7755	0.425142
$904$	−71.1299	−2.36575
$905$	−8.31884	−0.276527
$906$	−50.0991	−1.66443
$907$	−47.8776	−1.58975	−0.794874	−	0.606775i	$-0.792463\pi$
$907$	−47.8776	−1.58975	−0.794874	+	0.606775i	$0.792463\pi$
$908$	−80.2899	−2.66451
$909$	1.42733	0.0473415
$910$	−17.3169	−0.574051
$911$	22.8122	0.755800	0.377900	−	0.925846i	$-0.376646\pi$
$911$	22.8122	0.755800	0.377900	+	0.925846i	$0.376646\pi$
$912$	49.9634	1.65445
$913$	0	0
$914$	−40.0558	−1.32493
$915$	−48.0558	−1.58868
$916$	−21.8217	−0.721011
$917$	−6.27072	−0.207077
$918$	33.6493	1.11059
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	−16.4681	−0.542939
$921$	56.0558	1.84710
$922$	−86.0591	−2.83421
$923$	19.3044	0.635413
$924$	0	0
$925$	−13.0829	−0.430162
$926$	16.2341	0.533485
$927$	−0.301952	−0.00991740
$928$	43.6926	1.43428
$929$	−16.0366	−0.526145	−0.263073	−	0.964776i	$-0.584736\pi$
$929$	−16.0366	−0.526145	−0.263073	+	0.964776i	$0.584736\pi$
$930$	−28.5972	−0.937741
$931$	1.72928	0.0566749
$932$	−37.6002	−1.23163
$933$	−19.2524	−0.630295
$934$	65.5177	2.14380
$935$	0	0
$936$	−2.46482	−0.0805652
$937$	25.3049	0.826674	0.413337	−	0.910578i	$-0.364363\pi$
$937$	25.3049	0.826674	0.413337	+	0.910578i	$0.364363\pi$
$938$	−17.7293	−0.578882
$939$	13.0385	0.425496
$940$	−94.3823	−3.07841
$941$	−20.5294	−0.669238	−0.334619	−	0.942353i	$-0.608608\pi$
$941$	−20.5294	−0.669238	−0.334619	+	0.942353i	$0.608608\pi$
$942$	−55.1512	−1.79692
$943$	6.50479	0.211825
$944$	−28.8925	−0.940372
$945$	−13.4017	−0.435958
$946$	0	0
$947$	−16.6907	−0.542376	−0.271188	−	0.962526i	$-0.587417\pi$
$947$	−16.6907	−0.542376	−0.271188	+	0.962526i	$0.587417\pi$
$948$	−151.165	−4.90960
$949$	−24.8034	−0.805153
$950$	−9.05874	−0.293904
$951$	−15.6724	−0.508213
$952$	23.9109	0.774956
$953$	−56.4681	−1.82918	−0.914591	−	0.404379i	$-0.867488\pi$
$953$	−56.4681	−1.82918	−0.914591	+	0.404379i	$0.867488\pi$
$954$	2.63389	0.0852755
$955$	−48.2051	−1.55988
$956$	25.5510	0.826379
$957$	0	0
$958$	23.2311	0.750564
$959$	−9.40171	−0.303597
$960$	−171.035	−5.52014
$961$	−25.9894	−0.838367
$962$	45.4777	1.46626
$963$	−0.356522	−0.0114887
$964$	20.8434	0.671320
$965$	−8.00000	−0.257529
$966$	−3.04623	−0.0980108
$967$	−47.3082	−1.52133	−0.760665	−	0.649145i	$-0.775127\pi$
$967$	−47.3082	−1.52133	−0.760665	+	0.649145i	$0.775127\pi$
$968$	0	0
$969$	7.27365	0.233663
$970$	−60.5972	−1.94566
$971$	−25.2355	−0.809846	−0.404923	−	0.914351i	$-0.632702\pi$
$971$	−25.2355	−0.809846	−0.404923	+	0.914351i	$0.632702\pi$
$972$	−6.02458	−0.193238
$973$	15.8217	0.507222
$974$	−68.4748	−2.19407
$975$	7.97875	0.255524
$976$	170.377	5.45363
$977$	7.10308	0.227248	0.113624	−	0.993524i	$-0.463754\pi$
$977$	7.10308	0.227248	0.113624	+	0.993524i	$0.463754\pi$
$978$	47.3295	1.51343
$979$	0	0
$980$	−14.7755	−0.471986
$981$	1.67347	0.0534297
$982$	33.7080	1.07567
$983$	−14.1893	−0.452568	−0.226284	−	0.974061i	$-0.572658\pi$
$983$	−14.1893	−0.452568	−0.226284	+	0.974061i	$0.572658\pi$
$984$	183.242	5.84153
$985$	13.0096	0.414520
$986$	11.4028	0.363138
$987$	−11.2524	−0.358168
$988$	23.2311	0.739081
$989$	4.54144	0.144409
$990$	0	0
$991$	4.23407	0.134500	0.0672499	−	0.997736i	$-0.478578\pi$
$991$	4.23407	0.134500	0.0672499	+	0.997736i	$0.478578\pi$
$992$	56.5573	1.79570
$993$	15.0818	0.478607
$994$	22.3265	0.708155
$995$	−41.2437	−1.30751
$996$	−126.616	−4.01199
$997$	27.7047	0.877417	0.438708	−	0.898629i	$-0.355436\pi$
$997$	27.7047	0.877417	0.438708	+	0.898629i	$0.355436\pi$
$998$	−61.6560	−1.95169
$999$	35.1955	1.11354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.a.i.1.1	✓	3
3.2	odd	2		7623.2.a.ce.1.3		3
7.6	odd	2		5929.2.a.t.1.1		3
11.2	odd	10		847.2.f.t.323.1		12
11.3	even	5		847.2.f.u.372.1		12
11.4	even	5		847.2.f.u.148.1		12
11.5	even	5		847.2.f.u.729.3		12
11.6	odd	10		847.2.f.t.729.1		12
11.7	odd	10		847.2.f.t.148.3		12
11.8	odd	10		847.2.f.t.372.3		12
11.9	even	5		847.2.f.u.323.3		12
11.10	odd	2		847.2.a.j.1.3	yes	3
33.32	even	2		7623.2.a.bz.1.1		3
77.76	even	2		5929.2.a.y.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.1	✓	3	1.1	even	1	trivial
847.2.a.j.1.3	yes	3	11.10	odd	2
847.2.f.t.148.3		12	11.7	odd	10
847.2.f.t.323.1		12	11.2	odd	10
847.2.f.t.372.3		12	11.8	odd	10
847.2.f.t.729.1		12	11.6	odd	10
847.2.f.u.148.1		12	11.4	even	5
847.2.f.u.323.3		12	11.9	even	5
847.2.f.u.372.1		12	11.3	even	5
847.2.f.u.729.3		12	11.5	even	5
5929.2.a.t.1.1		3	7.6	odd	2
5929.2.a.y.1.3		3	77.76	even	2
7623.2.a.bz.1.1		3	33.32	even	2
7623.2.a.ce.1.3		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76156 q^{2} +1.76156 q^{3} +5.62620 q^{4} -2.62620 q^{5} -4.86464 q^{6} -1.00000 q^{7} -10.0140 q^{8} +0.103084 q^{9} +O(q^{10})\)	\(q-2.76156 q^{2} +1.76156 q^{3} +5.62620 q^{4} -2.62620 q^{5} -4.86464 q^{6} -1.00000 q^{7} -10.0140 q^{8} +0.103084 q^{9} +7.25240 q^{10} +9.91087 q^{12} +2.38776 q^{13} +2.76156 q^{14} -4.62620 q^{15} +16.4017 q^{16} +2.38776 q^{17} -0.284672 q^{18} +1.72928 q^{19} -14.7755 q^{20} -1.76156 q^{21} -0.626198 q^{23} -17.6402 q^{24} +1.89692 q^{25} -6.59392 q^{26} -5.10308 q^{27} -5.62620 q^{28} -1.72928 q^{29} +12.7755 q^{30} -2.23844 q^{31} -25.2663 q^{32} -6.59392 q^{34} +2.62620 q^{35} +0.579969 q^{36} -6.89692 q^{37} -4.77551 q^{38} +4.20617 q^{39} +26.2986 q^{40} -10.3878 q^{41} +4.86464 q^{42} -7.25240 q^{43} -0.270718 q^{45} +1.72928 q^{46} +6.38776 q^{47} +28.8925 q^{48} +1.00000 q^{49} -5.23844 q^{50} +4.20617 q^{51} +13.4340 q^{52} -9.25240 q^{53} +14.0925 q^{54} +10.0140 q^{56} +3.04623 q^{57} +4.77551 q^{58} -1.76156 q^{59} -26.0279 q^{60} +10.3878 q^{61} +6.18159 q^{62} -0.103084 q^{63} +36.9711 q^{64} -6.27072 q^{65} -6.42003 q^{67} +13.4340 q^{68} -1.10308 q^{69} -7.25240 q^{70} +8.08476 q^{71} -1.03228 q^{72} -10.3878 q^{73} +19.0462 q^{74} +3.34153 q^{75} +9.72928 q^{76} -11.6156 q^{78} -15.2524 q^{79} -43.0741 q^{80} -9.29862 q^{81} +28.6864 q^{82} -12.7755 q^{83} -9.91087 q^{84} -6.27072 q^{85} +20.0279 q^{86} -3.04623 q^{87} -14.1493 q^{89} +0.747604 q^{90} -2.38776 q^{91} -3.52311 q^{92} -3.94315 q^{93} -17.6402 q^{94} -4.54144 q^{95} -44.5081 q^{96} -8.35548 q^{97} -2.76156 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - q^{3} + 8 q^{4} + q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - q^3 + 8 * q^4 + q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 + 4 * q^9	\( 3 q - 2 q^{2} - q^{3} + 8 q^{4} + q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} + 2 q^{14} - 5 q^{15} + 10 q^{16} - 8 q^{17} + 18 q^{18} - 14 q^{20} + q^{21} + 7 q^{23} - 20 q^{24} + 2 q^{25} - 12 q^{26} - 19 q^{27} - 8 q^{28} + 8 q^{30} - 13 q^{31} - 34 q^{32} - 12 q^{34} - q^{35} + 18 q^{36} - 17 q^{37} + 16 q^{38} + 20 q^{39} + 36 q^{40} - 16 q^{41} + 12 q^{42} - 4 q^{43} - 6 q^{45} + 4 q^{47} + 36 q^{48} + 3 q^{49} - 22 q^{50} + 20 q^{51} - 10 q^{53} - 8 q^{54} + 6 q^{56} - 16 q^{57} - 16 q^{58} + q^{59} - 30 q^{60} + 16 q^{61} - 4 q^{62} - 4 q^{63} + 34 q^{64} - 24 q^{65} - 3 q^{67} - 7 q^{69} - 4 q^{70} + 5 q^{71} - 2 q^{72} - 16 q^{73} + 32 q^{74} + 20 q^{75} + 24 q^{76} + 28 q^{78} - 28 q^{79} - 56 q^{80} + 15 q^{81} + 28 q^{82} - 8 q^{83} - 2 q^{84} - 24 q^{85} + 12 q^{86} + 16 q^{87} - 21 q^{89} + 20 q^{90} + 8 q^{91} + 2 q^{92} + 17 q^{93} - 20 q^{94} - 24 q^{95} - 20 q^{96} - 11 q^{97} - 2 q^{98}+O(q^{100}) \) 3 * q - 2 * q^2 - q^3 + 8 * q^4 + q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 + 2 * q^14 - 5 * q^15 + 10 * q^16 - 8 * q^17 + 18 * q^18 - 14 * q^20 + q^21 + 7 * q^23 - 20 * q^24 + 2 * q^25 - 12 * q^26 - 19 * q^27 - 8 * q^28 + 8 * q^30 - 13 * q^31 - 34 * q^32 - 12 * q^34 - q^35 + 18 * q^36 - 17 * q^37 + 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 + 12 * q^42 - 4 * q^43 - 6 * q^45 + 4 * q^47 + 36 * q^48 + 3 * q^49 - 22 * q^50 + 20 * q^51 - 10 * q^53 - 8 * q^54 + 6 * q^56 - 16 * q^57 - 16 * q^58 + q^59 - 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 + 34 * q^64 - 24 * q^65 - 3 * q^67 - 7 * q^69 - 4 * q^70 + 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 + 20 * q^75 + 24 * q^76 + 28 * q^78 - 28 * q^79 - 56 * q^80 + 15 * q^81 + 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 + 12 * q^86 + 16 * q^87 - 21 * q^89 + 20 * q^90 + 8 * q^91 + 2 * q^92 + 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 - 11 * q^97 - 2 * q^98

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