LMFDB - Embedded newform 1728.2.i.n.1153.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(577,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1728.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1153.3
Root			$0.774115 + 1.18353i$ of defining polynomial
Character	$\chi$	$=$	1728.1153
Dual form			1728.2.i.n.577.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68614 + 2.92048i) q^{5} +(-2.35143 + 4.07279i) q^{7} +O(q^{10})$	$q+(1.68614 + 2.92048i) q^{5} +(-2.35143 + 4.07279i) q^{7} +(-0.437696 + 0.758112i) q^{11} +(-0.686141 - 1.18843i) q^{13} +2.37228 q^{17} -5.57825 q^{19} +(2.35143 + 4.07279i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(2.68614 - 4.65253i) q^{29} +(3.22682 + 5.58902i) q^{31} -15.8593 q^{35} -4.00000 q^{37} +(0.500000 + 0.866025i) q^{41} +(-0.437696 + 0.758112i) q^{43} +(2.35143 - 4.07279i) q^{47} +(-7.55842 - 13.0916i) q^{49} -4.00000 q^{53} -2.95207 q^{55} +(-4.26516 - 7.38747i) q^{59} +(-1.05842 + 1.83324i) q^{61} +(2.31386 - 4.00772i) q^{65} +(-4.26516 - 7.38747i) q^{67} -9.40571 q^{71} +10.3723 q^{73} +(-2.05842 - 3.56529i) q^{77} +(-3.22682 + 5.58902i) q^{79} +(1.47603 - 2.55657i) q^{83} +(4.00000 + 6.92820i) q^{85} -12.7446 q^{89} +6.45364 q^{91} +(-9.40571 - 16.2912i) q^{95} +(-4.50000 + 7.79423i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5}+O(q^{10}) $ 8 * q + 2 * q^5	$ 8 q + 2 q^{5} + 6 q^{13} - 4 q^{17} - 14 q^{25} + 10 q^{29} - 32 q^{37} + 4 q^{41} - 26 q^{49} - 32 q^{53} + 26 q^{61} + 30 q^{65} + 60 q^{73} + 18 q^{77} + 32 q^{85} - 56 q^{89} - 36 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 + 6 * q^13 - 4 * q^17 - 14 * q^25 + 10 * q^29 - 32 * q^37 + 4 * q^41 - 26 * q^49 - 32 * q^53 + 26 * q^61 + 30 * q^65 + 60 * q^73 + 18 * q^77 + 32 * q^85 - 56 * q^89 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.68614	+	2.92048i	0.754065	+	1.30608i	0.945838	+	0.324640i	$0.105243\pi$
$5$	1.68614	+	2.92048i	0.754065	+	1.30608i	−0.191773	+	0.981439i	$0.561424\pi$
$6$		0			0
$7$	−2.35143	+	4.07279i	−0.888756	+	1.53937i	−0.0474088	+	0.998876i	$0.515096\pi$
$7$	−2.35143	+	4.07279i	−0.888756	+	1.53937i	−0.841347	+	0.540495i	$0.818237\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.437696	+	0.758112i	−0.131970	+	0.228579i	−0.924436	−	0.381337i	$-0.875464\pi$
$11$	−0.437696	+	0.758112i	−0.131970	+	0.228579i	0.792466	+	0.609917i	$0.208797\pi$
$12$		0			0
$13$	−0.686141	−	1.18843i	−0.190301	−	0.329611i	0.755049	−	0.655669i	$-0.227613\pi$
$13$	−0.686141	−	1.18843i	−0.190301	−	0.329611i	−0.945350	+	0.326057i	$0.894280\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.37228			0.575363			0.287681	−	0.957726i	$-0.407116\pi$
$17$	2.37228			0.575363			0.287681	+	0.957726i	$0.407116\pi$
$18$		0			0
$19$	−5.57825			−1.27974			−0.639869	−	0.768484i	$-0.721011\pi$
$19$	−5.57825			−1.27974			−0.639869	+	0.768484i	$0.721011\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.35143	+	4.07279i	0.490307	+	0.849236i	0.999938	−	0.0111571i	$-0.00355150\pi$
$23$	2.35143	+	4.07279i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$24$		0			0
$25$	−3.18614	+	5.51856i	−0.637228	+	1.10371i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.68614	−	4.65253i	0.498804	−	0.863954i	−0.501195	−	0.865334i	$-0.667106\pi$
$29$	2.68614	−	4.65253i	0.498804	−	0.863954i	0.999999	+	0.00138070i	$0.000439492\pi$
$30$		0			0
$31$	3.22682	+	5.58902i	0.579554	+	1.00382i	0.995530	+	0.0944415i	$0.0301065\pi$
$31$	3.22682	+	5.58902i	0.579554	+	1.00382i	−0.415976	+	0.909375i	$0.636560\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−15.8593			−2.68072
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	0.902424	−	0.430848i	$-0.141786\pi$
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	−0.824338	+	0.566099i	$0.808452\pi$
$42$		0			0
$43$	−0.437696	+	0.758112i	−0.0667481	+	0.115611i	−0.897468	−	0.441079i	$-0.854596\pi$
$43$	−0.437696	+	0.758112i	−0.0667481	+	0.115611i	0.830720	+	0.556690i	$0.187929\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.35143	−	4.07279i	0.342991	−	0.594078i	−0.641996	−	0.766708i	$-0.721893\pi$
$47$	2.35143	−	4.07279i	0.342991	−	0.594078i	0.984987	+	0.172630i	$0.0552266\pi$
$48$		0			0
$49$	−7.55842	−	13.0916i	−1.07977	−	1.87022i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	−2.95207			−0.398057
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.26516	−	7.38747i	−0.555276	−	0.961767i	−0.997882	−	0.0650505i	$-0.979279\pi$
$59$	−4.26516	−	7.38747i	−0.555276	−	0.961767i	0.442606	−	0.896716i	$-0.354054\pi$
$60$		0			0
$61$	−1.05842	+	1.83324i	−0.135517	+	0.234722i	−0.925795	−	0.378026i	$-0.876603\pi$
$61$	−1.05842	+	1.83324i	−0.135517	+	0.234722i	0.790278	+	0.612749i	$0.209936\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.31386	−	4.00772i	0.286999	−	0.497097i
$66$		0			0
$67$	−4.26516	−	7.38747i	−0.521072	−	0.902523i	−0.999700	−	0.0245053i	$-0.992199\pi$
$67$	−4.26516	−	7.38747i	−0.521072	−	0.902523i	0.478628	−	0.878018i	$-0.341134\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.40571			−1.11625			−0.558126	−	0.829756i	$-0.688480\pi$
$71$	−9.40571			−1.11625			−0.558126	+	0.829756i	$0.688480\pi$
$72$		0			0
$73$	10.3723			1.21398			0.606992	−	0.794708i	$-0.292376\pi$
$73$	10.3723			1.21398			0.606992	+	0.794708i	$0.292376\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.05842	−	3.56529i	−0.234579	−	0.406303i
$78$		0			0
$79$	−3.22682	+	5.58902i	−0.363046	+	0.628813i	−0.988460	−	0.151479i	$-0.951596\pi$
$79$	−3.22682	+	5.58902i	−0.363046	+	0.628813i	0.625415	+	0.780292i	$0.284930\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.47603	−	2.55657i	0.162016	−	0.280620i	−0.773576	−	0.633704i	$-0.781534\pi$
$83$	1.47603	−	2.55657i	0.162016	−	0.280620i	0.935592	+	0.353084i	$0.114867\pi$
$84$		0			0
$85$	4.00000	+	6.92820i	0.433861	+	0.751469i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−12.7446			−1.35092			−0.675460	−	0.737396i	$-0.736055\pi$
$89$	−12.7446			−1.35092			−0.675460	+	0.737396i	$0.736055\pi$
$90$		0			0
$91$	6.45364			0.676525
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.40571	−	16.2912i	−0.965005	−	1.67144i
$96$		0			0
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	−0.998796	−	0.0490655i	$-0.984376\pi$
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	0.541890	+	0.840450i	$0.317709\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.05842	+	1.83324i	−0.105317	+	0.182414i	−0.913868	−	0.406012i	$-0.866919\pi$
$101$	−1.05842	+	1.83324i	−0.105317	+	0.182414i	0.808551	+	0.588426i	$0.200252\pi$
$102$		0			0
$103$	2.35143	+	4.07279i	0.231693	+	0.401304i	0.958306	−	0.285742i	$-0.0922402\pi$
$103$	2.35143	+	4.07279i	0.231693	+	0.401304i	−0.726613	+	0.687047i	$0.758907\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.57825			0.539270			0.269635	−	0.962963i	$-0.413097\pi$
$107$	5.57825			0.539270			0.269635	+	0.962963i	$0.413097\pi$
$108$		0			0
$109$	5.48913			0.525763			0.262881	−	0.964828i	$-0.415327\pi$
$109$	5.48913			0.525763			0.262881	+	0.964828i	$0.415327\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.68614	+	15.0448i	0.817123	+	1.41530i	0.907793	+	0.419418i	$0.137766\pi$
$113$	8.68614	+	15.0448i	0.817123	+	1.41530i	−0.0906698	+	0.995881i	$0.528901\pi$
$114$		0			0
$115$	−7.92967	+	13.7346i	−0.739446	+	1.28076i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.57825	+	9.66181i	−0.511357	+	0.885696i
$120$		0			0
$121$	5.11684	+	8.86263i	0.465168	+	0.805694i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.62772			−0.413916
$126$		0			0
$127$	−11.1565			−0.989979			−0.494989	−	0.868899i	$-0.664828\pi$
$127$	−11.1565			−0.989979			−0.494989	+	0.868899i	$0.664828\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.22682	−	5.58902i	−0.281929	−	0.488315i	0.689931	−	0.723875i	$-0.257641\pi$
$131$	−3.22682	−	5.58902i	−0.281929	−	0.488315i	−0.971860	+	0.235560i	$0.924307\pi$
$132$		0			0
$133$	13.1168	−	22.7190i	1.13737	−	1.96999i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.24456	−	9.08385i	0.448073	−	0.776086i	−0.550187	−	0.835041i	$-0.685444\pi$
$137$	5.24456	−	9.08385i	0.448073	−	0.776086i	0.998261	+	0.0589556i	$0.0187770\pi$
$138$		0			0
$139$	9.84341	+	17.0493i	0.834907	+	1.44610i	0.894106	+	0.447855i	$0.147812\pi$
$139$	9.84341	+	17.0493i	0.834907	+	1.44610i	−0.0591995	+	0.998246i	$0.518855\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.20128			0.100456
$144$		0			0
$145$	18.1168			1.50452
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.68614	+	15.0448i	0.711596	+	1.23252i	0.964258	+	0.264966i	$0.0853608\pi$
$149$	8.68614	+	15.0448i	0.711596	+	1.23252i	−0.252661	+	0.967555i	$0.581306\pi$
$150$		0			0
$151$	2.35143	−	4.07279i	0.191356	−	0.331439i	−0.754344	−	0.656480i	$-0.772045\pi$
$151$	2.35143	−	4.07279i	0.191356	−	0.331439i	0.945700	+	0.325041i	$0.105378\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.8817	+	18.8477i	−0.874043	+	1.51389i
$156$		0			0
$157$	7.05842	+	12.2255i	0.563323	+	0.975705i	0.997203	+	0.0747341i	$0.0238108\pi$
$157$	7.05842	+	12.2255i	0.563323	+	0.975705i	−0.433880	+	0.900971i	$0.642856\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−22.1168			−1.74305
$162$		0			0
$163$	−18.8114			−1.47342			−0.736712	−	0.676207i	$-0.763623\pi$
$163$	−18.8114			−1.47342			−0.736712	+	0.676207i	$0.763623\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.22682	+	5.58902i	0.249699	+	0.432491i	0.963442	−	0.267916i	$-0.0863351\pi$
$167$	3.22682	+	5.58902i	0.249699	+	0.432491i	−0.713743	+	0.700407i	$0.753002\pi$
$168$		0			0
$169$	5.55842	−	9.62747i	0.427571	−	0.740575i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.68614	+	4.65253i	−0.204223	+	0.353725i	−0.949885	−	0.312599i	$-0.898800\pi$
$173$	−2.68614	+	4.65253i	−0.204223	+	0.353725i	0.745662	+	0.666325i	$0.232134\pi$
$174$		0			0
$175$	−14.9840	−	25.9530i	−1.13268	−	1.96186i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	18.8114			1.40603			0.703016	−	0.711174i	$-0.251836\pi$
$179$	18.8114			1.40603			0.703016	+	0.711174i	$0.251836\pi$
$180$		0			0
$181$	−26.2337			−1.94993			−0.974967	−	0.222348i	$-0.928628\pi$
$181$	−26.2337			−1.94993			−0.974967	+	0.222348i	$0.928628\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.74456	−	11.6819i	−0.495870	−	0.858872i
$186$		0			0
$187$	−1.03834	+	1.79846i	−0.0759308	+	0.131516i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.80507	+	15.2508i	−0.637112	+	1.10351i	0.348951	+	0.937141i	$0.386538\pi$
$191$	−8.80507	+	15.2508i	−0.637112	+	1.10351i	−0.986063	+	0.166370i	$0.946795\pi$
$192$		0			0
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	0.847469	−	0.530845i	$-0.178125\pi$
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	−0.883460	+	0.468507i	$0.844792\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.7446			−0.765518			−0.382759	−	0.923848i	$-0.625026\pi$
$197$	−10.7446			−0.765518			−0.382759	+	0.923848i	$0.625026\pi$
$198$		0			0
$199$	17.0606			1.20940			0.604698	−	0.796455i	$-0.293294\pi$
$199$	17.0606			1.20940			0.604698	+	0.796455i	$0.293294\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.6325	+	21.8802i	0.886630	+	1.53569i
$204$		0			0
$205$	−1.68614	+	2.92048i	−0.117765	+	0.203975i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.44158	−	4.22894i	0.168887	−	0.292522i
$210$		0			0
$211$	7.92967	+	13.7346i	0.545901	+	0.945529i	0.998550	+	0.0538397i	$0.0171460\pi$
$211$	7.92967	+	13.7346i	0.545901	+	0.945529i	−0.452648	+	0.891689i	$0.649521\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.95207			−0.201329
$216$		0			0
$217$	−30.3505			−2.06033
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.62772	−	2.81929i	−0.109492	−	0.189646i
$222$		0			0
$223$	−2.35143	+	4.07279i	−0.157463	+	0.272734i	−0.933953	−	0.357395i	$-0.883665\pi$
$223$	−2.35143	+	4.07279i	−0.157463	+	0.272734i	0.776490	+	0.630130i	$0.216998\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.7188	−	18.5655i	0.711432	−	1.23224i	−0.252888	−	0.967496i	$-0.581380\pi$
$227$	10.7188	−	18.5655i	0.711432	−	1.23224i	0.964320	−	0.264740i	$-0.0852862\pi$
$228$		0			0
$229$	0.686141	+	1.18843i	0.0453415	+	0.0785337i	0.887805	−	0.460219i	$-0.152229\pi$
$229$	0.686141	+	1.18843i	0.0453415	+	0.0785337i	−0.842464	+	0.538753i	$0.818896\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	25.8614			1.69424			0.847119	−	0.531404i	$-0.178335\pi$
$233$	25.8614			1.69424			0.847119	+	0.531404i	$0.178335\pi$
$234$		0			0
$235$	15.8593			1.03455
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.80507	−	15.2508i	−0.569552	−	0.986494i	−0.996610	−	0.0822694i	$-0.973783\pi$
$239$	−8.80507	−	15.2508i	−0.569552	−	0.986494i	0.427058	−	0.904224i	$-0.359550\pi$
$240$		0			0
$241$	−5.87228	+	10.1711i	−0.378267	+	0.655177i	−0.990810	−	0.135260i	$-0.956813\pi$
$241$	−5.87228	+	10.1711i	−0.378267	+	0.655177i	0.612543	+	0.790437i	$0.290147\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	25.4891	−	44.1485i	1.62844	−	2.82054i
$246$		0			0
$247$	3.82746	+	6.62936i	0.243536	+	0.421816i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	16.7347			1.05629			0.528144	−	0.849155i	$-0.322888\pi$
$251$	16.7347			1.05629			0.528144	+	0.849155i	$0.322888\pi$
$252$		0			0
$253$	−4.11684			−0.258824
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.24456	+	14.2800i	0.514282	+	0.890762i	0.999863	+	0.0165703i	$0.00527474\pi$
$257$	8.24456	+	14.2800i	0.514282	+	0.890762i	−0.485581	+	0.874192i	$0.661392\pi$
$258$		0			0
$259$	9.40571	−	16.2912i	0.584442	−	1.01228i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.80507	−	15.2508i	0.542944	−	0.940406i	−0.455790	−	0.890088i	$-0.650643\pi$
$263$	8.80507	−	15.2508i	0.542944	−	0.940406i	0.998733	−	0.0503185i	$-0.0160236\pi$
$264$		0			0
$265$	−6.74456	−	11.6819i	−0.414315	−	0.717615i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−13.4891			−0.822446			−0.411223	−	0.911535i	$-0.634898\pi$
$269$	−13.4891			−0.822446			−0.411223	+	0.911535i	$0.634898\pi$
$270$		0			0
$271$	−22.3130			−1.35542			−0.677709	−	0.735330i	$-0.737027\pi$
$271$	−22.3130			−1.35542			−0.677709	+	0.735330i	$0.737027\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.78912	−	4.83090i	−0.168190	−	0.291314i
$276$		0			0
$277$	−2.05842	+	3.56529i	−0.123679	+	0.214218i	−0.921216	−	0.389052i	$-0.872803\pi$
$277$	−2.05842	+	3.56529i	−0.123679	+	0.214218i	0.797537	+	0.603270i	$0.206136\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.43070	+	2.47805i	−0.0853486	+	0.147828i	−0.905540	−	0.424262i	$-0.860534\pi$
$281$	−1.43070	+	2.47805i	−0.0853486	+	0.147828i	0.820191	+	0.572090i	$0.193867\pi$
$282$		0			0
$283$	−7.92967	−	13.7346i	−0.471370	−	0.816437i	0.528093	−	0.849186i	$-0.322907\pi$
$283$	−7.92967	−	13.7346i	−0.471370	−	0.816437i	−0.999464	+	0.0327491i	$0.989574\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.70285			−0.277601
$288$		0			0
$289$	−11.3723			−0.668958
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.31386	+	12.6680i	0.427280	+	0.740071i	0.996630	−	0.0820241i	$-0.0261384\pi$
$293$	7.31386	+	12.6680i	0.427280	+	0.740071i	−0.569350	+	0.822095i	$0.692805\pi$
$294$		0			0
$295$	14.3833	−	24.9126i	0.837429	−	1.45047i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.22682	−	5.58902i	0.186612	−	0.323221i
$300$		0			0
$301$	−2.05842	−	3.56529i	−0.118645	−	0.205500i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.13859			−0.408755
$306$		0			0
$307$	20.8881			1.19215			0.596073	−	0.802930i	$-0.296727\pi$
$307$	20.8881			1.19215			0.596073	+	0.802930i	$0.296727\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.5079	+	23.3964i	0.765964	+	1.32669i	0.939735	+	0.341903i	$0.111071\pi$
$311$	13.5079	+	23.3964i	0.765964	+	1.32669i	−0.173771	+	0.984786i	$0.555595\pi$
$312$		0			0
$313$	7.61684	−	13.1928i	0.430529	−	0.745699i	−0.566389	−	0.824138i	$-0.691660\pi$
$313$	7.61684	−	13.1928i	0.430529	−	0.745699i	0.996919	+	0.0784388i	$0.0249935\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.31386	+	2.27567i	−0.0737937	+	0.127814i	−0.900561	−	0.434730i	$-0.856844\pi$
$317$	−1.31386	+	2.27567i	−0.0737937	+	0.127814i	0.826767	+	0.562544i	$0.190177\pi$
$318$		0			0
$319$	2.35143	+	4.07279i	0.131655	+	0.228033i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.2332			−0.736313
$324$		0			0
$325$	8.74456			0.485061
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.0584	+	19.1537i	0.609671	+	1.05598i
$330$		0			0
$331$	4.97760	−	8.62146i	0.273594	−	0.473879i	−0.696186	−	0.717862i	$-0.745121\pi$
$331$	4.97760	−	8.62146i	0.273594	−	0.473879i	0.969779	+	0.243983i	$0.0784542\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	14.3833	−	24.9126i	0.785844	−	1.36112i
$336$		0			0
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.64947			−0.305936
$342$		0			0
$343$	38.1723			2.06111
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.26516	+	7.38747i	0.228966	+	0.396580i	0.957502	−	0.288427i	$-0.0931323\pi$
$347$	4.26516	+	7.38747i	0.228966	+	0.396580i	−0.728536	+	0.685007i	$0.759799\pi$
$348$		0			0
$349$	−2.94158	+	5.09496i	−0.157459	+	0.272727i	−0.933952	−	0.357399i	$-0.883664\pi$
$349$	−2.94158	+	5.09496i	−0.157459	+	0.272727i	0.776493	+	0.630126i	$0.216997\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.61684	−	13.1928i	0.405404	−	0.702180i	−0.588965	−	0.808159i	$-0.700464\pi$
$353$	7.61684	−	13.1928i	0.405404	−	0.702180i	0.994368	+	0.105979i	$0.0337976\pi$
$354$		0			0
$355$	−15.8593	−	27.4692i	−0.841727	−	1.45791i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	33.4695			1.76645			0.883226	−	0.468948i	$-0.155367\pi$
$359$	33.4695			1.76645			0.883226	+	0.468948i	$0.155367\pi$
$360$		0			0
$361$	12.1168			0.637729
$362$		0			0
$363$		0			0
$364$		0			0
$365$	17.4891	+	30.2921i	0.915423	+	1.58556i
$366$		0			0
$367$	15.5846	−	26.9933i	0.813509	−	1.40904i	−0.0968838	−	0.995296i	$-0.530888\pi$
$367$	15.5846	−	26.9933i	0.813509	−	1.40904i	0.910393	−	0.413744i	$-0.135779\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.40571	−	16.2912i	0.488320	−	0.845795i
$372$		0			0
$373$	0.0584220	+	0.101190i	0.00302498	+	0.00523941i	0.867534	−	0.497378i	$-0.165704\pi$
$373$	0.0584220	+	0.101190i	0.00302498	+	0.00523941i	−0.864509	+	0.502617i	$0.832370\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.37228			−0.379692
$378$		0			0
$379$	3.82746			0.196604			0.0983018	−	0.995157i	$-0.468659\pi$
$379$	3.82746			0.196604			0.0983018	+	0.995157i	$0.468659\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.8817	+	18.8477i	0.556031	+	0.963074i	0.997823	+	0.0659564i	$0.0210098\pi$
$383$	10.8817	+	18.8477i	0.556031	+	0.963074i	−0.441791	+	0.897118i	$0.645657\pi$
$384$		0			0
$385$	6.94158	−	12.0232i	0.353776	−	0.612757i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.1753	+	28.0164i	−0.820119	+	1.42049i	0.0854750	+	0.996340i	$0.472759\pi$
$389$	−16.1753	+	28.0164i	−0.820119	+	1.42049i	−0.905594	+	0.424147i	$0.860574\pi$
$390$		0			0
$391$	5.57825	+	9.66181i	0.282104	+	0.488619i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−21.7635			−1.09504
$396$		0			0
$397$	4.00000			0.200754			0.100377	−	0.994949i	$-0.467995\pi$
$397$	4.00000			0.200754			0.100377	+	0.994949i	$0.467995\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.98913	−	15.5696i	−0.448895	−	0.777510i	0.549419	−	0.835547i	$-0.314849\pi$
$401$	−8.98913	−	15.5696i	−0.448895	−	0.777510i	−0.998314	+	0.0580372i	$0.981516\pi$
$402$		0			0
$403$	4.42810	−	7.66970i	0.220580	−	0.382055i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.75079	−	3.03245i	0.0867832	−	0.150313i
$408$		0			0
$409$	14.8723	+	25.7595i	0.735387	+	1.27373i	0.954553	+	0.298040i	$0.0963329\pi$
$409$	14.8723	+	25.7595i	0.735387	+	1.27373i	−0.219166	+	0.975688i	$0.570334\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	40.1168			1.97402
$414$		0			0
$415$	9.95521			0.488682
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.92967	−	13.7346i	−0.387390	−	0.670979i	0.604708	−	0.796448i	$-0.293290\pi$
$419$	−7.92967	−	13.7346i	−0.387390	−	0.670979i	−0.992098	+	0.125468i	$0.959957\pi$
$420$		0			0
$421$	−8.31386	+	14.4000i	−0.405193	+	0.701814i	−0.994344	−	0.106208i	$-0.966129\pi$
$421$	−8.31386	+	14.4000i	−0.405193	+	0.701814i	0.589151	+	0.808023i	$0.299462\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.55842	+	13.0916i	−0.366637	+	0.635034i
$426$		0			0
$427$	−4.97760	−	8.62146i	−0.240883	−	0.417222i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.1565			0.537389			0.268695	−	0.963225i	$-0.413408\pi$
$431$	11.1565			0.537389			0.268695	+	0.963225i	$0.413408\pi$
$432$		0			0
$433$	−0.883156			−0.0424418			−0.0212209	−	0.999775i	$-0.506755\pi$
$433$	−0.883156			−0.0424418			−0.0212209	+	0.999775i	$0.506755\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−13.1168	−	22.7190i	−0.627464	−	1.08680i
$438$		0			0
$439$	−10.8817	+	18.8477i	−0.519357	+	0.899553i	0.480390	+	0.877055i	$0.340495\pi$
$439$	−10.8817	+	18.8477i	−0.519357	+	0.899553i	−0.999747	+	0.0224981i	$0.992838\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.7188	+	18.5655i	−0.509265	+	0.882074i	0.490677	+	0.871342i	$0.336750\pi$
$443$	−10.7188	+	18.5655i	−0.509265	+	0.882074i	−0.999942	+	0.0107321i	$0.996584\pi$
$444$		0			0
$445$	−21.4891	−	37.2203i	−1.01868	−	1.76441i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.883156			0.0416787			0.0208394	−	0.999783i	$-0.493366\pi$
$449$	0.883156			0.0416787			0.0208394	+	0.999783i	$0.493366\pi$
$450$		0			0
$451$	−0.875393			−0.0412206
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.8817	+	18.8477i	0.510144	+	0.883595i
$456$		0			0
$457$	−9.98913	+	17.3017i	−0.467272	+	0.809338i	−0.999301	−	0.0373879i	$-0.988096\pi$
$457$	−9.98913	+	17.3017i	−0.467272	+	0.809338i	0.532029	+	0.846726i	$0.321430\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.94158	−	10.2911i	0.276727	−	0.479305i	−0.693842	−	0.720127i	$-0.744084\pi$
$461$	5.94158	−	10.2911i	0.276727	−	0.479305i	0.970569	+	0.240822i	$0.0774169\pi$
$462$		0			0
$463$	−0.274750	−	0.475881i	−0.0127687	−	0.0221161i	0.859570	−	0.511017i	$-0.170731\pi$
$463$	−0.274750	−	0.475881i	−0.0127687	−	0.0221161i	−0.872339	+	0.488901i	$0.837398\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.73160			0.450325			0.225162	−	0.974321i	$-0.427709\pi$
$467$	9.73160			0.450325			0.225162	+	0.974321i	$0.427709\pi$
$468$		0			0
$469$	40.1168			1.85242
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.383156	−	0.663646i	−0.0176175	−	0.0305145i
$474$		0			0
$475$	17.7731	−	30.7839i	0.815485	−	1.41246i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.35143	+	4.07279i	−0.107439	+	0.186091i	−0.914732	−	0.404061i	$-0.867599\pi$
$479$	−2.35143	+	4.07279i	−0.107439	+	0.186091i	0.807293	+	0.590151i	$0.200932\pi$
$480$		0			0
$481$	2.74456	+	4.75372i	0.125141	+	0.216751i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−30.3505			−1.37815
$486$		0			0
$487$	−11.1565			−0.505549			−0.252775	−	0.967525i	$-0.581343\pi$
$487$	−11.1565			−0.505549			−0.252775	+	0.967525i	$0.581343\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.1245	+	34.8567i	0.908206	+	1.57306i	0.816554	+	0.577268i	$0.195881\pi$
$491$	20.1245	+	34.8567i	0.908206	+	1.57306i	0.0916519	+	0.995791i	$0.470785\pi$
$492$		0			0
$493$	6.37228	−	11.0371i	0.286993	−	0.497087i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.1168	−	38.3075i	0.992076	−	1.71833i
$498$		0			0
$499$	−6.89134	−	11.9361i	−0.308499	−	0.534335i	0.669536	−	0.742780i	$-0.266493\pi$
$499$	−6.89134	−	11.9361i	−0.308499	−	0.534335i	−0.978034	+	0.208445i	$0.933160\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	31.7187			1.41427			0.707133	−	0.707080i	$-0.249988\pi$
$503$	31.7187			1.41427			0.707133	+	0.707080i	$0.249988\pi$
$504$		0			0
$505$	−7.13859			−0.317663
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−19.1753	−	33.2125i	−0.849929	−	1.47212i	−0.881271	−	0.472611i	$-0.843312\pi$
$509$	−19.1753	−	33.2125i	−0.849929	−	1.47212i	0.0313424	−	0.999509i	$-0.490022\pi$
$510$		0			0
$511$	−24.3897	+	42.2441i	−1.07894	+	1.86877i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.92967	+	13.7346i	−0.349423	+	0.605219i
$516$		0			0
$517$	2.05842	+	3.56529i	0.0905293	+	0.156801i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−35.3505			−1.54873			−0.774367	−	0.632736i	$-0.781932\pi$
$521$	−35.3505			−1.54873			−0.774367	+	0.632736i	$0.781932\pi$
$522$		0			0
$523$	−12.9073			−0.564396			−0.282198	−	0.959356i	$-0.591064\pi$
$523$	−12.9073			−0.564396			−0.282198	+	0.959356i	$0.591064\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.65492	+	13.2587i	0.333454	+	0.577559i
$528$		0			0
$529$	0.441578	−	0.764836i	0.0191990	−	0.0332537i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.686141	−	1.18843i	0.0297201	−	0.0514766i
$534$		0			0
$535$	9.40571	+	16.2912i	0.406644	+	0.704329i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	13.2332			0.569993
$540$		0			0
$541$	2.74456			0.117998			0.0589990	−	0.998258i	$-0.481209\pi$
$541$	2.74456			0.117998			0.0589990	+	0.998258i	$0.481209\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.25544	+	16.0309i	0.396459	+	0.686688i
$546$		0			0
$547$	−5.14055	+	8.90370i	−0.219794	+	0.380695i	−0.954745	−	0.297426i	$-0.903872\pi$
$547$	−5.14055	+	8.90370i	−0.219794	+	0.380695i	0.734951	+	0.678120i	$0.237205\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−14.9840	+	25.9530i	−0.638338	+	1.10563i
$552$		0			0
$553$	−15.1753	−	26.2843i	−0.645318	−	1.11772i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.25544			−0.307423			−0.153711	−	0.988116i	$-0.549123\pi$
$557$	−7.25544			−0.307423			−0.153711	+	0.988116i	$0.549123\pi$
$558$		0			0
$559$	1.20128			0.0508089
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.38977	−	5.87125i	−0.142862	−	0.247444i	0.785711	−	0.618593i	$-0.212297\pi$
$563$	−3.38977	−	5.87125i	−0.142862	−	0.247444i	−0.928573	+	0.371150i	$0.878964\pi$
$564$		0			0
$565$	−29.2921	+	50.7354i	−1.23233	+	2.13446i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.1277	+	24.4699i	−0.592265	+	1.02583i	0.401662	+	0.915788i	$0.368433\pi$
$569$	−14.1277	+	24.4699i	−0.592265	+	1.02583i	−0.993927	+	0.110045i	$0.964901\pi$
$570$		0			0
$571$	20.1245	+	34.8567i	0.842184	+	1.45871i	0.888044	+	0.459758i	$0.152064\pi$
$571$	20.1245	+	34.8567i	0.842184	+	1.45871i	−0.0458596	+	0.998948i	$0.514603\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−29.9679			−1.24975
$576$		0			0
$577$	0.883156			0.0367663			0.0183831	−	0.999831i	$-0.494148\pi$
$577$	0.883156			0.0367663			0.0183831	+	0.999831i	$0.494148\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.94158	+	12.0232i	0.287985	+	0.498805i
$582$		0			0
$583$	1.75079	−	3.03245i	0.0725101	−	0.125591i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.2491	−	33.3404i	0.794496	−	1.37611i	−0.128663	−	0.991688i	$-0.541068\pi$
$587$	19.2491	−	33.3404i	0.794496	−	1.37611i	0.923159	−	0.384419i	$-0.125598\pi$
$588$		0			0
$589$	−18.0000	−	31.1769i	−0.741677	−	1.28462i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−39.7228			−1.63122			−0.815610	−	0.578602i	$-0.803599\pi$
$593$	−39.7228			−1.63122			−0.815610	+	0.578602i	$0.803599\pi$
$594$		0			0
$595$	−37.6228			−1.54239
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−15.5846	−	26.9933i	−0.636769	−	1.10292i	−0.986137	−	0.165931i	$-0.946937\pi$
$599$	−15.5846	−	26.9933i	−0.636769	−	1.10292i	0.349368	−	0.936986i	$-0.386396\pi$
$600$		0			0
$601$	18.6168	−	32.2453i	0.759397	−	1.31531i	−0.183762	−	0.982971i	$-0.558827\pi$
$601$	18.6168	−	32.2453i	0.759397	−	1.31531i	0.943159	−	0.332343i	$-0.107839\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−17.2554	+	29.8873i	−0.701533	+	1.21509i
$606$		0			0
$607$	0.274750	+	0.475881i	0.0111518	+	0.0193154i	0.871547	−	0.490311i	$-0.163117\pi$
$607$	0.274750	+	0.475881i	0.0111518	+	0.0193154i	−0.860396	+	0.509627i	$0.829784\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.45364			−0.261086
$612$		0			0
$613$	32.4674			1.31134			0.655672	−	0.755045i	$-0.272385\pi$
$613$	32.4674			1.31134			0.655672	+	0.755045i	$0.272385\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.1277	−	22.7379i	−0.528502	−	0.915392i	−0.999448	−	0.0332302i	$-0.989421\pi$
$617$	−13.1277	−	22.7379i	−0.528502	−	0.915392i	0.470946	−	0.882162i	$-0.343913\pi$
$618$		0			0
$619$	−5.14055	+	8.90370i	−0.206616	+	0.357870i	−0.950646	−	0.310276i	$-0.899578\pi$
$619$	−5.14055	+	8.90370i	−0.206616	+	0.357870i	0.744030	+	0.668146i	$0.232912\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	29.9679	−	51.9060i	1.20064	−	2.07957i
$624$		0			0
$625$	8.12772	+	14.0776i	0.325109	+	0.563105i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.48913			−0.378356
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−18.8114	−	32.5823i	−0.746508	−	1.29299i
$636$		0			0
$637$	−10.3723	+	17.9653i	−0.410965	+	0.711812i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.12772	−	1.95327i	0.0445422	−	0.0771494i	−0.842895	−	0.538078i	$-0.819150\pi$
$641$	1.12772	−	1.95327i	0.0445422	−	0.0771494i	0.887437	+	0.460929i	$0.152484\pi$
$642$		0			0
$643$	1.31309	+	2.27434i	0.0517832	+	0.0896911i	0.890755	−	0.454484i	$-0.150176\pi$
$643$	1.31309	+	2.27434i	0.0517832	+	0.0896911i	−0.838972	+	0.544175i	$0.816843\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.15335			0.163285			0.0816426	−	0.996662i	$-0.473983\pi$
$647$	4.15335			0.163285			0.0816426	+	0.996662i	$0.473983\pi$
$648$		0			0
$649$	7.46738			0.293120
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.9416	−	20.6834i	−0.467310	−	0.809405i	0.531992	−	0.846749i	$-0.321443\pi$
$653$	−11.9416	−	20.6834i	−0.467310	−	0.809405i	−0.999302	+	0.0373444i	$0.988110\pi$
$654$		0			0
$655$	10.8817	−	18.8477i	0.425185	−	0.736442i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−20.2875	+	35.1389i	−0.790287	+	1.36882i	0.135502	+	0.990777i	$0.456735\pi$
$659$	−20.2875	+	35.1389i	−0.790287	+	1.36882i	−0.925789	+	0.378040i	$0.876598\pi$
$660$		0			0
$661$	7.05842	+	12.2255i	0.274541	+	0.475519i	0.970019	−	0.243028i	$-0.0781408\pi$
$661$	7.05842	+	12.2255i	0.274541	+	0.475519i	−0.695478	+	0.718547i	$0.744807\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	88.4674			3.43062
$666$		0			0
$667$	25.2651			0.978267
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.926535	−	1.60481i	−0.0357685	−	0.0619528i
$672$		0			0
$673$	14.1753	−	24.5523i	0.546416	−	0.946421i	−0.452100	−	0.891967i	$-0.649325\pi$
$673$	14.1753	−	24.5523i	0.546416	−	0.946421i	0.998516	−	0.0544536i	$-0.0173417\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	25.1753	−	43.6048i	0.967564	−	1.67587i	0.265002	−	0.964248i	$-0.414627\pi$
$677$	25.1753	−	43.6048i	0.967564	−	1.67587i	0.702562	−	0.711622i	$-0.252039\pi$
$678$		0			0
$679$	−21.1628	−	36.6551i	−0.812156	−	1.40669i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−9.73160			−0.372369			−0.186185	−	0.982515i	$-0.559612\pi$
$683$	−9.73160			−0.372369			−0.186185	+	0.982515i	$0.559612\pi$
$684$		0			0
$685$	35.3723			1.35151
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.74456	+	4.75372i	0.104560	+	0.181102i
$690$		0			0
$691$	−9.13096	+	15.8153i	−0.347358	+	0.601642i	−0.985779	−	0.168045i	$-0.946254\pi$
$691$	−9.13096	+	15.8153i	−0.347358	+	0.601642i	0.638421	+	0.769687i	$0.279588\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−33.1947	+	57.4950i	−1.25915	+	2.18091i
$696$		0			0
$697$	1.18614	+	2.05446i	0.0449283	+	0.0778181i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	23.2554			0.878346			0.439173	−	0.898403i	$-0.355272\pi$
$701$	23.2554			0.878346			0.439173	+	0.898403i	$0.355272\pi$
$702$		0			0
$703$	22.3130			0.841550
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.97760	−	8.62146i	−0.187202	−	0.324244i
$708$		0			0
$709$	13.8030	−	23.9075i	0.518382	−	0.897864i	−0.481390	−	0.876507i	$-0.659868\pi$
$709$	13.8030	−	23.9075i	0.518382	−	0.897864i	0.999772	−	0.0213574i	$-0.00679878\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−15.1753	+	26.2843i	−0.568318	+	0.984356i
$714$		0			0
$715$	2.02554	+	3.50833i	0.0757507	+	0.131204i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.3098			0.570961			0.285481	−	0.958385i	$-0.407847\pi$
$719$	15.3098			0.570961			0.285481	+	0.958385i	$0.407847\pi$
$720$		0			0
$721$	−22.1168			−0.823674
$722$		0			0
$723$		0			0
$724$		0			0
$725$	17.1168	+	29.6472i	0.635704	+	1.10107i
$726$		0			0
$727$	10.0064	−	17.3315i	0.371115	−	0.642790i	−0.618622	−	0.785689i	$-0.712309\pi$
$727$	10.0064	−	17.3315i	0.371115	−	0.642790i	0.989737	+	0.142898i	$0.0456422\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.03834	+	1.79846i	−0.0384043	+	0.0665183i
$732$		0			0
$733$	20.0584	+	34.7422i	0.740875	+	1.28323i	0.952097	+	0.305795i	$0.0989221\pi$
$733$	20.0584	+	34.7422i	0.740875	+	1.28323i	−0.211223	+	0.977438i	$0.567745\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.46738			0.275064
$738$		0			0
$739$	7.32903			0.269603			0.134801	−	0.990873i	$-0.456960\pi$
$739$	7.32903			0.269603			0.134801	+	0.990873i	$0.456960\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.6644	−	42.7200i	−0.904850	−	1.56725i	−0.821119	−	0.570757i	$-0.806650\pi$
$743$	−24.6644	−	42.7200i	−0.904850	−	1.56725i	−0.0837309	−	0.996488i	$-0.526684\pi$
$744$		0			0
$745$	−29.2921	+	50.7354i	−1.07318	+	1.85880i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−13.1168	+	22.7190i	−0.479279	+	0.830136i
$750$		0			0
$751$	−10.8817	−	18.8477i	−0.397081	−	0.687764i	0.596284	−	0.802774i	$-0.296643\pi$
$751$	−10.8817	−	18.8477i	−0.397081	−	0.687764i	−0.993364	+	0.115010i	$0.963310\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	15.8593			0.577181
$756$		0			0
$757$	−34.4674			−1.25274			−0.626369	−	0.779527i	$-0.715460\pi$
$757$	−34.4674			−1.25274			−0.626369	+	0.779527i	$0.715460\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.31386	+	12.6680i	0.265127	+	0.459214i	0.967597	−	0.252500i	$-0.0812527\pi$
$761$	7.31386	+	12.6680i	0.265127	+	0.459214i	−0.702470	+	0.711714i	$0.747919\pi$
$762$		0			0
$763$	−12.9073	+	22.3561i	−0.467275	+	0.809344i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.85300	+	10.1377i	−0.211339	+	0.366051i
$768$		0			0
$769$	16.0584	+	27.8140i	0.579082	+	1.00300i	0.995585	+	0.0938645i	$0.0299220\pi$
$769$	16.0584	+	27.8140i	0.579082	+	1.00300i	−0.416503	+	0.909134i	$0.636745\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.25544			−0.260960			−0.130480	−	0.991451i	$-0.541652\pi$
$773$	−7.25544			−0.260960			−0.130480	+	0.991451i	$0.541652\pi$
$774$		0			0
$775$	−41.1244			−1.47723
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.78912	−	4.83090i	−0.0999307	−	0.173085i
$780$		0			0
$781$	4.11684	−	7.13058i	0.147312	−	0.255152i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−23.8030	+	41.2280i	−0.849565	+	1.47149i
$786$		0			0
$787$	−4.42810	−	7.66970i	−0.157845	−	0.273395i	0.776246	−	0.630430i	$-0.217121\pi$
$787$	−4.42810	−	7.66970i	−0.157845	−	0.273395i	−0.934091	+	0.357034i	$0.883788\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−81.6993			−2.90489
$792$		0			0
$793$	2.90491			0.103156
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.54755	+	14.8048i	0.302770	+	0.524412i	0.976762	−	0.214326i	$-0.0687554\pi$
$797$	8.54755	+	14.8048i	0.302770	+	0.524412i	−0.673993	+	0.738738i	$0.735422\pi$
$798$		0			0
$799$	5.57825	−	9.66181i	0.197344	−	0.341810i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.53991	+	7.86335i	−0.160210	+	0.277492i
$804$		0			0
$805$	−37.2921	−	64.5918i	−1.31437	−	2.27656i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.3723			0.645935			0.322968	−	0.946410i	$-0.395320\pi$
$809$	18.3723			0.645935			0.322968	+	0.946410i	$0.395320\pi$
$810$		0			0
$811$	50.2042			1.76291			0.881454	−	0.472269i	$-0.156565\pi$
$811$	50.2042			1.76291			0.881454	+	0.472269i	$0.156565\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−31.7187	−	54.9384i	−1.11106	−	1.92441i
$816$		0			0
$817$	2.44158	−	4.22894i	0.0854200	−	0.147952i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.31386	+	2.27567i	−0.0458540	+	0.0794215i	−0.888041	−	0.459763i	$-0.847934\pi$
$821$	−1.31386	+	2.27567i	−0.0458540	+	0.0794215i	0.842187	+	0.539185i	$0.181268\pi$
$822$		0			0
$823$	10.8817	+	18.8477i	0.379314	+	0.656991i	0.990963	−	0.134139i	$-0.0428268\pi$
$823$	10.8817	+	18.8477i	0.379314	+	0.656991i	−0.611649	+	0.791129i	$0.709493\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.8114			0.654137			0.327069	−	0.945001i	$-0.393939\pi$
$827$	18.8114			0.654137			0.327069	+	0.945001i	$0.393939\pi$
$828$		0			0
$829$	−26.2337			−0.911134			−0.455567	−	0.890202i	$-0.650563\pi$
$829$	−26.2337			−0.911134			−0.455567	+	0.890202i	$0.650563\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−17.9307	−	31.0569i	−0.621262	−	1.07606i
$834$		0			0
$835$	−10.8817	+	18.8477i	−0.376578	+	0.652253i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.22682	+	5.58902i	−0.111402	+	0.192954i	−0.916336	−	0.400411i	$-0.868868\pi$
$839$	−3.22682	+	5.58902i	−0.111402	+	0.192954i	0.804934	+	0.593365i	$0.202201\pi$
$840$		0			0
$841$	0.0692967	+	0.120025i	0.00238954	+	0.00413881i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	37.4891			1.28967
$846$		0			0
$847$	−48.1275			−1.65368
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−9.40571	−	16.2912i	−0.322424	−	0.558454i
$852$		0			0
$853$	−1.94158	+	3.36291i	−0.0664784	+	0.115144i	−0.897349	−	0.441322i	$-0.854510\pi$
$853$	−1.94158	+	3.36291i	−0.0664784	+	0.115144i	0.830870	+	0.556466i	$0.187843\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.54755	−	16.5368i	0.326138	−	0.564888i	−0.655604	−	0.755105i	$-0.727586\pi$
$857$	9.54755	−	16.5368i	0.326138	−	0.564888i	0.981742	+	0.190217i	$0.0609193\pi$
$858$		0			0
$859$	1.31309	+	2.27434i	0.0448020	+	0.0775994i	0.887557	−	0.460698i	$-0.152401\pi$
$859$	1.31309	+	2.27434i	0.0448020	+	0.0775994i	−0.842755	+	0.538298i	$0.819068\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−37.6228			−1.28070			−0.640348	−	0.768085i	$-0.721210\pi$
$863$	−37.6228			−1.28070			−0.640348	+	0.768085i	$0.721210\pi$
$864$		0			0
$865$	−18.1168			−0.615991
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.82473	−	4.89258i	−0.0958225	−	0.165970i
$870$		0			0
$871$	−5.85300	+	10.1377i	−0.198321	+	0.343502i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	10.8817	−	18.8477i	0.367870	−	0.637170i
$876$		0			0
$877$	19.1753	+	33.2125i	0.647503	+	1.12151i	0.983717	+	0.179722i	$0.0575199\pi$
$877$	19.1753	+	33.2125i	0.647503	+	1.12151i	−0.336215	+	0.941785i	$0.609147\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	30.2337			1.01860			0.509299	−	0.860589i	$-0.329905\pi$
$881$	30.2337			1.01860			0.509299	+	0.860589i	$0.329905\pi$
$882$		0			0
$883$	−32.0446			−1.07839			−0.539193	−	0.842182i	$-0.681271\pi$
$883$	−32.0446			−1.07839			−0.539193	+	0.842182i	$0.681271\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.8817	−	18.8477i	−0.365373	−	0.632845i	0.623463	−	0.781853i	$-0.285725\pi$
$887$	−10.8817	−	18.8477i	−0.365373	−	0.632845i	−0.988836	+	0.149008i	$0.952392\pi$
$888$		0			0
$889$	26.2337	−	45.4381i	0.879850	−	1.52394i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13.1168	+	22.7190i	−0.438938	+	0.760264i
$894$		0			0
$895$	31.7187	+	54.9384i	1.06024	+	1.83639i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	34.6708			1.15633
$900$		0			0
$901$	−9.48913			−0.316129
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−44.2337	−	76.6150i	−1.47038	−	2.54677i
$906$		0			0
$907$	−17.1724	+	29.7435i	−0.570201	+	0.987618i	0.426343	+	0.904561i	$0.359802\pi$
$907$	−17.1724	+	29.7435i	−0.570201	+	0.987618i	−0.996545	+	0.0830565i	$0.973532\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11.4312	+	19.7995i	−0.378734	+	0.655987i	−0.990878	−	0.134759i	$-0.956974\pi$
$911$	−11.4312	+	19.7995i	−0.378734	+	0.655987i	0.612144	+	0.790746i	$0.290307\pi$
$912$		0			0
$913$	1.29211	+	2.23800i	0.0427626	+	0.0740670i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	30.3505			1.00226
$918$		0			0
$919$	−26.4663			−0.873044			−0.436522	−	0.899694i	$-0.643790\pi$
$919$	−26.4663			−0.873044			−0.436522	+	0.899694i	$0.643790\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.45364	+	11.1780i	0.212424	+	0.367929i
$924$		0			0
$925$	12.7446	−	22.0742i	0.419039	−	0.725796i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15.3139	−	26.5244i	0.502431	−	0.870237i	−0.497565	−	0.867427i	$-0.665772\pi$
$929$	15.3139	−	26.5244i	0.502431	−	0.870237i	0.999996	−	0.00280985i	$-0.000894404\pi$
$930$		0			0
$931$	42.1627	+	73.0280i	1.38183	+	2.39340i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.00314			−0.229027
$936$		0			0
$937$	−22.2337			−0.726343			−0.363171	−	0.931722i	$-0.618306\pi$
$937$	−22.2337			−0.726343			−0.363171	+	0.931722i	$0.618306\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.54755	−	14.8048i	−0.278642	−	0.482622i	0.692405	−	0.721509i	$-0.256551\pi$
$941$	−8.54755	−	14.8048i	−0.278642	−	0.482622i	−0.971048	+	0.238886i	$0.923218\pi$
$942$		0			0
$943$	−2.35143	+	4.07279i	−0.0765730	+	0.132628i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.51437	+	4.35502i	−0.0817062	+	0.141519i	−0.903983	−	0.427569i	$-0.859370\pi$
$947$	−2.51437	+	4.35502i	−0.0817062	+	0.141519i	0.822277	+	0.569088i	$0.192704\pi$
$948$		0			0
$949$	−7.11684	−	12.3267i	−0.231023	−	0.400143i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.60597			−0.278775			−0.139387	−	0.990238i	$-0.544513\pi$
$953$	−8.60597			−0.278775			−0.139387	+	0.990238i	$0.544513\pi$
$954$		0			0
$955$	−59.3863			−1.92170
$956$		0			0
$957$		0			0
$958$		0			0
$959$	24.6644	+	42.7200i	0.796456	+	1.37950i
$960$		0			0
$961$	−5.32473	+	9.22271i	−0.171766	+	0.297507i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.68614	−	2.92048i	0.0542788	−	0.0940136i
$966$		0			0
$967$	−24.6644	−	42.7200i	−0.793154	−	1.37378i	−0.924005	−	0.382381i	$-0.875104\pi$
$967$	−24.6644	−	42.7200i	−0.793154	−	1.37378i	0.130850	−	0.991402i	$-0.458229\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−57.5333			−1.84633			−0.923165	−	0.384404i	$-0.874407\pi$
$971$	−57.5333			−1.84633			−0.923165	+	0.384404i	$0.874407\pi$
$972$		0			0
$973$	−92.5842			−2.96811
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.6168	+	39.1735i	0.723577	+	1.25327i	0.959557	+	0.281514i	$0.0908366\pi$
$977$	22.6168	+	39.1735i	0.723577	+	1.25327i	−0.235980	+	0.971758i	$0.575830\pi$
$978$		0			0
$979$	5.57825	−	9.66181i	0.178282	−	0.308793i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	29.6932	−	51.4301i	0.947065	−	1.64036i	0.195502	−	0.980703i	$-0.437367\pi$
$983$	29.6932	−	51.4301i	0.947065	−	1.64036i	0.751563	−	0.659661i	$-0.229300\pi$
$984$		0			0
$985$	−18.1168	−	31.3793i	−0.577251	−	0.999827i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.11684			−0.130908
$990$		0			0
$991$	7.00314			0.222462			0.111231	−	0.993795i	$-0.464521\pi$
$991$	7.00314			0.222462			0.111231	+	0.993795i	$0.464521\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	28.7666	+	49.8253i	0.911963	+	1.57957i
$996$		0			0
$997$	−5.17527	+	8.96382i	−0.163902	+	0.283887i	−0.936265	−	0.351295i	$-0.885742\pi$
$997$	−5.17527	+	8.96382i	−0.163902	+	0.283887i	0.772363	+	0.635182i	$0.219075\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.i.n.1153.3		8
3.2	odd	2		576.2.i.n.385.3		8
4.3	odd	2	inner	1728.2.i.n.1153.4		8
8.3	odd	2		864.2.i.f.289.2		8
8.5	even	2		864.2.i.f.289.1		8
9.2	odd	6		5184.2.a.cf.1.4		4
9.4	even	3	inner	1728.2.i.n.577.3		8
9.5	odd	6		576.2.i.n.193.3		8
9.7	even	3		5184.2.a.cc.1.2		4
12.11	even	2		576.2.i.n.385.2		8
24.5	odd	2		288.2.i.f.97.2	✓	8
24.11	even	2		288.2.i.f.97.3	yes	8
36.7	odd	6		5184.2.a.cc.1.1		4
36.11	even	6		5184.2.a.cf.1.3		4
36.23	even	6		576.2.i.n.193.2		8
36.31	odd	6	inner	1728.2.i.n.577.4		8
72.5	odd	6		288.2.i.f.193.2	yes	8
72.11	even	6		2592.2.a.u.1.1		4
72.13	even	6		864.2.i.f.577.1		8
72.29	odd	6		2592.2.a.u.1.2		4
72.43	odd	6		2592.2.a.x.1.3		4
72.59	even	6		288.2.i.f.193.3	yes	8
72.61	even	6		2592.2.a.x.1.4		4
72.67	odd	6		864.2.i.f.577.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.i.f.97.2	✓	8	24.5	odd	2
288.2.i.f.97.3	yes	8	24.11	even	2
288.2.i.f.193.2	yes	8	72.5	odd	6
288.2.i.f.193.3	yes	8	72.59	even	6
576.2.i.n.193.2		8	36.23	even	6
576.2.i.n.193.3		8	9.5	odd	6
576.2.i.n.385.2		8	12.11	even	2
576.2.i.n.385.3		8	3.2	odd	2
864.2.i.f.289.1		8	8.5	even	2
864.2.i.f.289.2		8	8.3	odd	2
864.2.i.f.577.1		8	72.13	even	6
864.2.i.f.577.2		8	72.67	odd	6
1728.2.i.n.577.3		8	9.4	even	3	inner
1728.2.i.n.577.4		8	36.31	odd	6	inner
1728.2.i.n.1153.3		8	1.1	even	1	trivial
1728.2.i.n.1153.4		8	4.3	odd	2	inner
2592.2.a.u.1.1		4	72.11	even	6
2592.2.a.u.1.2		4	72.29	odd	6
2592.2.a.x.1.3		4	72.43	odd	6
2592.2.a.x.1.4		4	72.61	even	6
5184.2.a.cc.1.1		4	36.7	odd	6
5184.2.a.cc.1.2		4	9.7	even	3
5184.2.a.cf.1.3		4	36.11	even	6
5184.2.a.cf.1.4		4	9.2	odd	6

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68614 + 2.92048i) q^{5} +(-2.35143 + 4.07279i) q^{7} +O(q^{10})\)	\(q+(1.68614 + 2.92048i) q^{5} +(-2.35143 + 4.07279i) q^{7} +(-0.437696 + 0.758112i) q^{11} +(-0.686141 - 1.18843i) q^{13} +2.37228 q^{17} -5.57825 q^{19} +(2.35143 + 4.07279i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(2.68614 - 4.65253i) q^{29} +(3.22682 + 5.58902i) q^{31} -15.8593 q^{35} -4.00000 q^{37} +(0.500000 + 0.866025i) q^{41} +(-0.437696 + 0.758112i) q^{43} +(2.35143 - 4.07279i) q^{47} +(-7.55842 - 13.0916i) q^{49} -4.00000 q^{53} -2.95207 q^{55} +(-4.26516 - 7.38747i) q^{59} +(-1.05842 + 1.83324i) q^{61} +(2.31386 - 4.00772i) q^{65} +(-4.26516 - 7.38747i) q^{67} -9.40571 q^{71} +10.3723 q^{73} +(-2.05842 - 3.56529i) q^{77} +(-3.22682 + 5.58902i) q^{79} +(1.47603 - 2.55657i) q^{83} +(4.00000 + 6.92820i) q^{85} -12.7446 q^{89} +6.45364 q^{91} +(-9.40571 - 16.2912i) q^{95} +(-4.50000 + 7.79423i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5}+O(q^{10}) \) 8 * q + 2 * q^5	\( 8 q + 2 q^{5} + 6 q^{13} - 4 q^{17} - 14 q^{25} + 10 q^{29} - 32 q^{37} + 4 q^{41} - 26 q^{49} - 32 q^{53} + 26 q^{61} + 30 q^{65} + 60 q^{73} + 18 q^{77} + 32 q^{85} - 56 q^{89} - 36 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 + 6 * q^13 - 4 * q^17 - 14 * q^25 + 10 * q^29 - 32 * q^37 + 4 * q^41 - 26 * q^49 - 32 * q^53 + 26 * q^61 + 30 * q^65 + 60 * q^73 + 18 * q^77 + 32 * q^85 - 56 * q^89 - 36 * q^97

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