LMFDB - Embedded newform 3456.2.i.i.1153.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3456,2,Mod(1153,3456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("3456.1153");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3456 = 2^{7} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3456.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:	$27.5962989386$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 2x^11 + 3x^10 - 8x^9 + 22x^8 - 42x^7 + 51x^6 - 126x^5 + 198x^4 - 216x^3 + 243x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 1152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1153.3
Root			$-1.28252 + 1.16410i$ of defining polynomial
Character	$\chi$	$=$	3456.1153
Dual form			3456.2.i.i.2305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05471 - 1.82681i) q^{5} +(1.43914 - 2.49267i) q^{7} +O(q^{10})$	$q+(-1.05471 - 1.82681i) q^{5} +(1.43914 - 2.49267i) q^{7} +(1.21325 - 2.10141i) q^{11} +(-3.30008 - 5.71590i) q^{13} +7.56848 q^{17} +6.25779 q^{19} +(2.63611 + 4.56587i) q^{23} +(0.275172 - 0.476612i) q^{25} +(-1.57821 + 2.73353i) q^{29} +(-1.79039 - 3.10104i) q^{31} -6.07151 q^{35} +6.70957 q^{37} +(1.74537 + 3.02306i) q^{41} +(3.12570 - 5.41388i) q^{43} +(-1.32972 + 2.30314i) q^{47} +(-0.642255 - 1.11242i) q^{49} +0.953009 q^{53} -5.11850 q^{55} +(-4.84757 - 8.39624i) q^{59} +(-2.57821 + 4.46558i) q^{61} +(-6.96125 + 12.0572i) q^{65} +(0.949546 + 1.64466i) q^{67} -5.82491 q^{71} -5.01222 q^{73} +(-3.49207 - 6.04844i) q^{77} +(6.49996 - 11.2583i) q^{79} +(-1.54502 + 2.67606i) q^{83} +(-7.98256 - 13.8262i) q^{85} +2.95301 q^{89} -18.9971 q^{91} +(-6.60015 - 11.4318i) q^{95} +(-5.51242 + 9.54779i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{5} - 6 q^{7}+O(q^{10}) $ 12 * q - 2 * q^5 - 6 * q^7	$ 12 q - 2 q^{5} - 6 q^{7} - 4 q^{11} - 10 q^{13} - 4 q^{17} + 4 q^{19} + 8 q^{23} - 14 q^{25} - 2 q^{29} - 8 q^{31} - 8 q^{35} + 2 q^{41} - 2 q^{43} - 14 q^{47} - 18 q^{49} + 24 q^{53} + 16 q^{55} - 6 q^{59} - 14 q^{61} + 8 q^{65} + 4 q^{67} - 28 q^{71} + 60 q^{73} + 2 q^{77} - 16 q^{79} - 24 q^{83} - 16 q^{85} + 48 q^{89} - 52 q^{91} - 20 q^{95} - 14 q^{97}+O(q^{100}) $ 12 * q - 2 * q^5 - 6 * q^7 - 4 * q^11 - 10 * q^13 - 4 * q^17 + 4 * q^19 + 8 * q^23 - 14 * q^25 - 2 * q^29 - 8 * q^31 - 8 * q^35 + 2 * q^41 - 2 * q^43 - 14 * q^47 - 18 * q^49 + 24 * q^53 + 16 * q^55 - 6 * q^59 - 14 * q^61 + 8 * q^65 + 4 * q^67 - 28 * q^71 + 60 * q^73 + 2 * q^77 - 16 * q^79 - 24 * q^83 - 16 * q^85 + 48 * q^89 - 52 * q^91 - 20 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times$.

$n$	$2053$	$2431$	$2945$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−1.05471	−	1.82681i	−0.471681	−	0.816975i	0.527794	−	0.849372i	$-0.323019\pi$
$5$	−1.05471	−	1.82681i	−0.471681	−	0.816975i	−0.999475	+	0.0323971i	$0.989686\pi$
$6$		0			0
$7$	1.43914	−	2.49267i	0.543944	−	0.942139i	−0.454728	−	0.890630i	$-0.650264\pi$
$7$	1.43914	−	2.49267i	0.543944	−	0.942139i	0.998673	−	0.0515089i	$-0.0164031\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.21325	−	2.10141i	0.365808	−	0.633598i	−0.623097	−	0.782144i	$-0.714126\pi$
$11$	1.21325	−	2.10141i	0.365808	−	0.633598i	0.988905	+	0.148546i	$0.0474594\pi$
$12$		0			0
$13$	−3.30008	−	5.71590i	−0.915277	−	1.58531i	−0.806496	−	0.591240i	$-0.798639\pi$
$13$	−3.30008	−	5.71590i	−0.915277	−	1.58531i	−0.108781	−	0.994066i	$-0.534695\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.56848			1.83563			0.917813	−	0.397013i	$-0.129953\pi$
$17$	7.56848			1.83563			0.917813	+	0.397013i	$0.129953\pi$
$18$		0			0
$19$	6.25779			1.43563			0.717817	−	0.696231i	$-0.245141\pi$
$19$	6.25779			1.43563			0.717817	+	0.696231i	$0.245141\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.63611	+	4.56587i	0.549666	+	0.952050i	0.998297	+	0.0583329i	$0.0185785\pi$
$23$	2.63611	+	4.56587i	0.549666	+	0.952050i	−0.448631	+	0.893717i	$0.648088\pi$
$24$		0			0
$25$	0.275172	−	0.476612i	0.0550344	−	0.0953223i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.57821	+	2.73353i	−0.293065	+	0.507604i	−0.974533	−	0.224244i	$-0.928009\pi$
$29$	−1.57821	+	2.73353i	−0.293065	+	0.507604i	0.681468	+	0.731848i	$0.261342\pi$
$30$		0			0
$31$	−1.79039	−	3.10104i	−0.321563	−	0.556964i	0.659248	−	0.751926i	$-0.270875\pi$
$31$	−1.79039	−	3.10104i	−0.321563	−	0.556964i	−0.980811	+	0.194962i	$0.937542\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.07151			−1.02627
$36$		0			0
$37$	6.70957			1.10305			0.551524	−	0.834159i	$-0.314047\pi$
$37$	6.70957			1.10305			0.551524	+	0.834159i	$0.314047\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.74537	+	3.02306i	0.272580	+	0.472123i	0.969522	−	0.245005i	$-0.0787896\pi$
$41$	1.74537	+	3.02306i	0.272580	+	0.472123i	−0.696941	+	0.717128i	$0.745456\pi$
$42$		0			0
$43$	3.12570	−	5.41388i	0.476665	−	0.825608i	−0.522977	−	0.852347i	$-0.675179\pi$
$43$	3.12570	−	5.41388i	0.476665	−	0.825608i	0.999642	+	0.0267383i	$0.00851207\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.32972	+	2.30314i	−0.193960	+	0.335948i	−0.946559	−	0.322531i	$-0.895466\pi$
$47$	−1.32972	+	2.30314i	−0.193960	+	0.335948i	0.752599	+	0.658479i	$0.228800\pi$
$48$		0			0
$49$	−0.642255	−	1.11242i	−0.0917508	−	0.158917i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.953009			0.130906			0.0654529	−	0.997856i	$-0.479151\pi$
$53$	0.953009			0.130906			0.0654529	+	0.997856i	$0.479151\pi$
$54$		0			0
$55$	−5.11850			−0.690178
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.84757	−	8.39624i	−0.631100	−	1.09310i	−0.987327	−	0.158698i	$-0.949270\pi$
$59$	−4.84757	−	8.39624i	−0.631100	−	1.09310i	0.356227	−	0.934400i	$-0.384063\pi$
$60$		0			0
$61$	−2.57821	+	4.46558i	−0.330105	+	0.571759i	−0.982532	−	0.186092i	$-0.940418\pi$
$61$	−2.57821	+	4.46558i	−0.330105	+	0.571759i	0.652427	+	0.757852i	$0.273751\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.96125	+	12.0572i	−0.863437	+	1.49552i
$66$		0			0
$67$	0.949546	+	1.64466i	0.116005	+	0.200927i	0.918181	−	0.396161i	$-0.129658\pi$
$67$	0.949546	+	1.64466i	0.116005	+	0.200927i	−0.802176	+	0.597088i	$0.796324\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.82491			−0.691290			−0.345645	−	0.938365i	$-0.612340\pi$
$71$	−5.82491			−0.691290			−0.345645	+	0.938365i	$0.612340\pi$
$72$		0			0
$73$	−5.01222			−0.586636			−0.293318	−	0.956015i	$-0.594760\pi$
$73$	−5.01222			−0.586636			−0.293318	+	0.956015i	$0.594760\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.49207	−	6.04844i	−0.397958	−	0.689284i
$78$		0			0
$79$	6.49996	−	11.2583i	0.731303	−	1.26665i	−0.225024	−	0.974353i	$-0.572246\pi$
$79$	6.49996	−	11.2583i	0.731303	−	1.26665i	0.956327	−	0.292301i	$-0.0944207\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.54502	+	2.67606i	−0.169588	+	0.293735i	−0.938275	−	0.345890i	$-0.887577\pi$
$83$	−1.54502	+	2.67606i	−0.169588	+	0.293735i	0.768687	+	0.639625i	$0.220910\pi$
$84$		0			0
$85$	−7.98256	−	13.8262i	−0.865830	−	1.49966i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.95301			0.313018			0.156509	−	0.987677i	$-0.449976\pi$
$89$	2.95301			0.313018			0.156509	+	0.987677i	$0.449976\pi$
$90$		0			0
$91$	−18.9971			−1.99144
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.60015	−	11.4318i	−0.677161	−	1.17288i
$96$		0			0
$97$	−5.51242	+	9.54779i	−0.559702	+	0.969432i	0.437820	+	0.899063i	$0.355751\pi$
$97$	−5.51242	+	9.54779i	−0.559702	+	0.969432i	−0.997521	+	0.0703686i	$0.977582\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.82357	−	3.15852i	0.181452	−	0.314284i	−0.760923	−	0.648842i	$-0.775254\pi$
$101$	1.82357	−	3.15852i	0.181452	−	0.314284i	0.942375	+	0.334558i	$0.108587\pi$
$102$		0			0
$103$	−5.43914	−	9.42087i	−0.535935	−	0.928266i	−0.999117	−	0.0420031i	$-0.986626\pi$
$103$	−5.43914	−	9.42087i	−0.535935	−	0.928266i	0.463183	−	0.886263i	$-0.346707\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.94922			0.575133			0.287567	−	0.957761i	$-0.407154\pi$
$107$	5.94922			0.575133			0.287567	+	0.957761i	$0.407154\pi$
$108$		0			0
$109$	−9.87113			−0.945483			−0.472741	−	0.881201i	$-0.656735\pi$
$109$	−9.87113			−0.945483			−0.472741	+	0.881201i	$0.656735\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.51518	+	13.0167i	0.706969	+	1.22451i	0.965976	+	0.258630i	$0.0832711\pi$
$113$	7.51518	+	13.0167i	0.706969	+	1.22451i	−0.259008	+	0.965875i	$0.583396\pi$
$114$		0			0
$115$	5.56066	−	9.63134i	0.518534	−	0.898128i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.8921	−	18.8657i	0.998478	−	1.72942i
$120$		0			0
$121$	2.55606	+	4.42722i	0.232369	+	0.402475i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.7080			−1.04720
$126$		0			0
$127$	8.07789			0.716797			0.358398	−	0.933569i	$-0.383323\pi$
$127$	8.07789			0.716797			0.358398	+	0.933569i	$0.383323\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−11.1329	−	19.2827i	−0.972684	−	1.68474i	−0.687375	−	0.726303i	$-0.741237\pi$
$131$	−11.1329	−	19.2827i	−0.972684	−	1.68474i	−0.285309	−	0.958435i	$-0.592096\pi$
$132$		0			0
$133$	9.00584	−	15.5986i	0.780905	−	1.35257i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.62365	−	8.00839i	0.395025	−	0.684203i	−0.598079	−	0.801437i	$-0.704069\pi$
$137$	4.62365	−	8.00839i	0.395025	−	0.684203i	0.993104	+	0.117234i	$0.0374026\pi$
$138$		0			0
$139$	4.20256	+	7.27905i	0.356456	+	0.617401i	0.987366	−	0.158456i	$-0.0506515\pi$
$139$	4.20256	+	7.27905i	0.356456	+	0.617401i	−0.630910	+	0.775856i	$0.717318\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−16.0152			−1.33926
$144$		0			0
$145$	6.65820			0.552934
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.17836	+	10.7012i	0.506151	+	0.876679i	0.999975	+	0.00711709i	$0.00226546\pi$
$149$	6.17836	+	10.7012i	0.506151	+	0.876679i	−0.493824	+	0.869562i	$0.664401\pi$
$150$		0			0
$151$	−4.91424	+	8.51171i	−0.399915	+	0.692673i	−0.993715	−	0.111940i	$-0.964294\pi$
$151$	−4.91424	+	8.51171i	−0.399915	+	0.692673i	0.593800	+	0.804613i	$0.297627\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.77668	+	6.54141i	−0.303350	+	0.525418i
$156$		0			0
$157$	0.108083	+	0.187206i	0.00862598	+	0.0149406i	0.870306	−	0.492511i	$-0.163921\pi$
$157$	0.108083	+	0.187206i	0.00862598	+	0.0149406i	−0.861680	+	0.507452i	$0.830588\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	15.1749			1.19595
$162$		0			0
$163$	−5.78116			−0.452815			−0.226408	−	0.974033i	$-0.572698\pi$
$163$	−5.78116			−0.452815			−0.226408	+	0.974033i	$0.572698\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.818646	−	1.41794i	−0.0633487	−	0.109723i	0.832612	−	0.553857i	$-0.186845\pi$
$167$	−0.818646	−	1.41794i	−0.0633487	−	0.109723i	−0.895960	+	0.444134i	$0.853511\pi$
$168$		0			0
$169$	−15.2810	+	26.4675i	−1.17546	+	2.03596i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.99228	+	5.18278i	−0.227499	+	0.394040i	−0.957066	−	0.289869i	$-0.906388\pi$
$173$	−2.99228	+	5.18278i	−0.227499	+	0.394040i	0.729567	+	0.683909i	$0.239721\pi$
$174$		0			0
$175$	−0.792022	−	1.37182i	−0.0598713	−	0.103700i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.51313			−0.711045			−0.355522	−	0.934668i	$-0.615697\pi$
$179$	−9.51313			−0.711045			−0.355522	+	0.934668i	$0.615697\pi$
$180$		0			0
$181$	23.7526			1.76551			0.882757	−	0.469830i	$-0.155685\pi$
$181$	23.7526			1.76551			0.882757	+	0.469830i	$0.155685\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.07666	−	12.2571i	−0.520286	−	0.901162i
$186$		0			0
$187$	9.18244	−	15.9045i	0.671487	−	1.16305i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.14164	+	7.17352i	−0.299678	+	0.519058i	−0.976062	−	0.217491i	$-0.930213\pi$
$191$	−4.14164	+	7.17352i	−0.299678	+	0.519058i	0.676384	+	0.736549i	$0.263546\pi$
$192$		0			0
$193$	5.00315	+	8.66572i	0.360135	+	0.623772i	0.987983	−	0.154564i	$-0.0493973\pi$
$193$	5.00315	+	8.66572i	0.360135	+	0.623772i	−0.627848	+	0.778336i	$0.716064\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.556259			0.0396318			0.0198159	−	0.999804i	$-0.493692\pi$
$197$	0.556259			0.0396318			0.0198159	+	0.999804i	$0.493692\pi$
$198$		0			0
$199$	21.5526			1.52782			0.763912	−	0.645320i	$-0.223276\pi$
$199$	21.5526			1.52782			0.763912	+	0.645320i	$0.223276\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.54252	+	7.86788i	0.318823	+	0.552217i
$204$		0			0
$205$	3.68171	−	6.37691i	0.257142	−	0.445383i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	7.59225	−	13.1502i	0.525167	−	0.909615i
$210$		0			0
$211$	−8.32984	−	14.4277i	−0.573450	−	0.993245i	−0.996208	−	0.0870022i	$-0.972271\pi$
$211$	−8.32984	−	14.4277i	−0.573450	−	0.993245i	0.422758	−	0.906243i	$-0.361062\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.1868			−0.899335
$216$		0			0
$217$	−10.3065			−0.699650
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−24.9766	−	43.2607i	−1.68011	−	2.91003i
$222$		0			0
$223$	−4.49251	+	7.78126i	−0.300841	+	0.521072i	−0.976327	−	0.216301i	$-0.930601\pi$
$223$	−4.49251	+	7.78126i	−0.300841	+	0.521072i	0.675486	+	0.737373i	$0.263934\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.32448	+	9.22226i	−0.353398	+	0.612103i	−0.986842	−	0.161685i	$-0.948307\pi$
$227$	−5.32448	+	9.22226i	−0.353398	+	0.612103i	0.633445	+	0.773788i	$0.281640\pi$
$228$		0			0
$229$	5.50786	+	9.53988i	0.363969	+	0.630413i	0.988610	−	0.150499i	$-0.0480880\pi$
$229$	5.50786	+	9.53988i	0.363969	+	0.630413i	−0.624641	+	0.780912i	$0.714755\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−27.2595			−1.78583			−0.892915	−	0.450225i	$-0.851344\pi$
$233$	−27.2595			−1.78583			−0.892915	+	0.450225i	$0.851344\pi$
$234$		0			0
$235$	5.60988			0.365948
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.82295	−	10.0856i	−0.376655	−	0.652386i	0.613918	−	0.789370i	$-0.289593\pi$
$239$	−5.82295	−	10.0856i	−0.376655	−	0.652386i	−0.990573	+	0.136984i	$0.956259\pi$
$240$		0			0
$241$	9.83554	−	17.0356i	0.633563	−	1.09736i	−0.353255	−	0.935527i	$-0.614925\pi$
$241$	9.83554	−	17.0356i	0.633563	−	1.09736i	0.986818	−	0.161835i	$-0.0517414\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.35479	+	2.34656i	−0.0865542	+	0.149916i
$246$		0			0
$247$	−20.6512	−	35.7689i	−1.31400	−	2.27592i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−23.3802			−1.47575			−0.737873	−	0.674940i	$-0.764170\pi$
$251$	−23.3802			−1.47575			−0.737873	+	0.674940i	$0.764170\pi$
$252$		0			0
$253$	12.7930			0.804289
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.89037	+	3.27421i	0.117918	+	0.204240i	0.918942	−	0.394392i	$-0.129045\pi$
$257$	1.89037	+	3.27421i	0.117918	+	0.204240i	−0.801024	+	0.598632i	$0.795711\pi$
$258$		0			0
$259$	9.65603	−	16.7247i	0.599996	−	1.03922i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.3638	+	17.9507i	−0.639060	+	1.10689i	0.346579	+	0.938021i	$0.387343\pi$
$263$	−10.3638	+	17.9507i	−0.639060	+	1.10689i	−0.985639	+	0.168864i	$0.945990\pi$
$264$		0			0
$265$	−1.00515	−	1.74097i	−0.0617458	−	0.106947i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.965772			0.0588842			0.0294421	−	0.999566i	$-0.490627\pi$
$269$	0.965772			0.0588842			0.0294421	+	0.999566i	$0.490627\pi$
$270$		0			0
$271$	4.28219			0.260124			0.130062	−	0.991506i	$-0.458482\pi$
$271$	4.28219			0.260124			0.130062	+	0.991506i	$0.458482\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.667703	−	1.15650i	−0.0402640	−	0.0697393i
$276$		0			0
$277$	−4.83619	+	8.37653i	−0.290579	+	0.503297i	−0.973947	−	0.226777i	$-0.927181\pi$
$277$	−4.83619	+	8.37653i	−0.290579	+	0.503297i	0.683368	+	0.730074i	$0.260514\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.34848	+	12.7279i	−0.438373	+	0.759285i	−0.997564	−	0.0697540i	$-0.977779\pi$
$281$	−7.34848	+	12.7279i	−0.438373	+	0.759285i	0.559191	+	0.829039i	$0.311112\pi$
$282$		0			0
$283$	−7.90174	−	13.6862i	−0.469710	−	0.813561i	0.529690	−	0.848191i	$-0.322308\pi$
$283$	−7.90174	−	13.6862i	−0.469710	−	0.813561i	−0.999400	+	0.0346299i	$0.988975\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.0473			0.593074
$288$		0			0
$289$	40.2819			2.36952
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.99866	−	5.19384i	−0.175184	−	0.303427i	0.765041	−	0.643981i	$-0.222719\pi$
$293$	−2.99866	−	5.19384i	−0.175184	−	0.303427i	−0.940225	+	0.340554i	$0.889385\pi$
$294$		0			0
$295$	−10.2256	+	17.7112i	−0.595356	+	1.03119i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	17.3987	−	30.1355i	1.00619	−	1.74278i
$300$		0			0
$301$	−8.99666	−	15.5827i	−0.518559	−	0.898170i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	10.8770			0.622818
$306$		0			0
$307$	−11.7568			−0.670994			−0.335497	−	0.942041i	$-0.608904\pi$
$307$	−11.7568			−0.670994			−0.335497	+	0.942041i	$0.608904\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−16.1797	−	28.0240i	−0.917465	−	1.58910i	−0.803252	−	0.595640i	$-0.796899\pi$
$311$	−16.1797	−	28.0240i	−0.917465	−	1.58910i	−0.114213	−	0.993456i	$-0.536435\pi$
$312$		0			0
$313$	−14.6062	+	25.2987i	−0.825591	+	1.42997i	0.0758750	+	0.997117i	$0.475825\pi$
$313$	−14.6062	+	25.2987i	−0.825591	+	1.42997i	−0.901466	+	0.432849i	$0.857508\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.7011	−	23.7310i	0.769530	−	1.33286i	−0.168288	−	0.985738i	$-0.553824\pi$
$317$	13.7011	−	23.7310i	0.769530	−	1.33286i	0.937818	−	0.347127i	$-0.112843\pi$
$318$		0			0
$319$	3.82951	+	6.63291i	0.214411	+	0.371371i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	47.3619			2.63529
$324$		0			0
$325$	−3.63235			−0.201487
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.82731	+	6.62910i	0.211007	+	0.365474i
$330$		0			0
$331$	−1.08930	+	1.88673i	−0.0598735	+	0.103704i	−0.894408	−	0.447251i	$-0.852403\pi$
$331$	−1.08930	+	1.88673i	−0.0598735	+	0.103704i	0.834535	+	0.550955i	$0.185736\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.00299	−	3.46928i	0.109435	−	0.189547i
$336$		0			0
$337$	−0.715700	−	1.23963i	−0.0389866	−	0.0675268i	0.845874	−	0.533383i	$-0.179080\pi$
$337$	−0.715700	−	1.23963i	−0.0389866	−	0.0675268i	−0.884860	+	0.465856i	$0.845746\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.68874			−0.470522
$342$		0			0
$343$	16.4508			0.888259
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.1223	+	22.7285i	0.704441	+	1.22013i	0.966893	+	0.255183i	$0.0821357\pi$
$347$	13.1223	+	22.7285i	0.704441	+	1.22013i	−0.262452	+	0.964945i	$0.584531\pi$
$348$		0			0
$349$	−17.1673	+	29.7346i	−0.918944	+	1.59166i	−0.117923	+	0.993023i	$0.537623\pi$
$349$	−17.1673	+	29.7346i	−0.918944	+	1.59166i	−0.801022	+	0.598635i	$0.795710\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.28933	−	3.96523i	0.121849	−	0.211048i	−0.798648	−	0.601798i	$-0.794451\pi$
$353$	2.28933	−	3.96523i	0.121849	−	0.211048i	0.920497	+	0.390750i	$0.127784\pi$
$354$		0			0
$355$	6.14359	+	10.6410i	0.326068	+	0.564766i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.0591			0.689231			0.344616	−	0.938744i	$-0.388009\pi$
$359$	13.0591			0.689231			0.344616	+	0.938744i	$0.388009\pi$
$360$		0			0
$361$	20.1599			1.06105
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.28644	+	9.15639i	0.276705	+	0.479267i
$366$		0			0
$367$	−1.70626	+	2.95533i	−0.0890660	+	0.154267i	−0.907117	−	0.420879i	$-0.861722\pi$
$367$	−1.70626	+	2.95533i	−0.0890660	+	0.154267i	0.818051	+	0.575146i	$0.195055\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.37151	−	2.37553i	0.0712055	−	0.123332i
$372$		0			0
$373$	−6.42179	−	11.1229i	−0.332508	−	0.575921i	0.650495	−	0.759511i	$-0.274561\pi$
$373$	−6.42179	−	11.1229i	−0.332508	−	0.575921i	−0.983003	+	0.183590i	$0.941228\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	20.8328			1.07294
$378$		0			0
$379$	12.1642			0.624833			0.312417	−	0.949945i	$-0.398862\pi$
$379$	12.1642			0.624833			0.312417	+	0.949945i	$0.398862\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.84072	+	15.3126i	0.451740	+	0.782436i	0.998494	−	0.0548568i	$-0.0174702\pi$
$383$	8.84072	+	15.3126i	0.451740	+	0.782436i	−0.546755	+	0.837293i	$0.684137\pi$
$384$		0			0
$385$	−7.36625	+	12.7587i	−0.375419	+	0.650244i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.77658	+	6.54123i	−0.191480	+	0.331654i	−0.945741	−	0.324921i	$-0.894662\pi$
$389$	−3.77658	+	6.54123i	−0.191480	+	0.331654i	0.754261	+	0.656575i	$0.227995\pi$
$390$		0			0
$391$	19.9513	+	34.5567i	1.00898	+	1.74761i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−27.4223			−1.37977
$396$		0			0
$397$	−7.97075			−0.400040			−0.200020	−	0.979792i	$-0.564101\pi$
$397$	−7.97075			−0.400040			−0.200020	+	0.979792i	$0.564101\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.53771	+	6.12750i	0.176665	+	0.305993i	0.940736	−	0.339139i	$-0.110136\pi$
$401$	3.53771	+	6.12750i	0.176665	+	0.305993i	−0.764071	+	0.645132i	$0.776802\pi$
$402$		0			0
$403$	−11.8168	+	20.4674i	−0.588639	+	1.01955i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.14038	−	14.0995i	0.403503	−	0.698889i
$408$		0			0
$409$	−16.0499	−	27.7993i	−0.793619	−	1.37459i	−0.923713	−	0.383086i	$-0.874861\pi$
$409$	−16.0499	−	27.7993i	−0.793619	−	1.37459i	0.130094	−	0.991502i	$-0.458472\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−27.9054			−1.37313
$414$		0			0
$415$	6.51820			0.319966
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.63571	+	9.76133i	0.275322	+	0.476872i	0.970216	−	0.242240i	$-0.0778821\pi$
$419$	5.63571	+	9.76133i	0.275322	+	0.476872i	−0.694894	+	0.719112i	$0.744549\pi$
$420$		0			0
$421$	−4.82872	+	8.36359i	−0.235337	+	0.407616i	−0.959371	−	0.282149i	$-0.908953\pi$
$421$	−4.82872	+	8.36359i	−0.235337	+	0.407616i	0.724033	+	0.689765i	$0.242286\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.08263	−	3.60723i	0.101023	−	0.174976i
$426$		0			0
$427$	7.42081	+	12.8532i	0.359118	+	0.622011i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	40.1842			1.93560			0.967802	−	0.251711i	$-0.0809933\pi$
$431$	40.1842			1.93560			0.967802	+	0.251711i	$0.0809933\pi$
$432$		0			0
$433$	16.1510			0.776168			0.388084	−	0.921624i	$-0.373137\pi$
$433$	16.1510			0.776168			0.388084	+	0.921624i	$0.373137\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	16.4962	+	28.5723i	0.789120	+	1.36680i
$438$		0			0
$439$	9.25383	−	16.0281i	0.441661	−	0.764980i	−0.556152	−	0.831081i	$-0.687723\pi$
$439$	9.25383	−	16.0281i	0.441661	−	0.764980i	0.997813	+	0.0661011i	$0.0210560\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.72586	+	2.98927i	−0.0819979	+	0.142025i	−0.904108	−	0.427304i	$-0.859463\pi$
$443$	−1.72586	+	2.98927i	−0.0819979	+	0.142025i	0.822110	+	0.569329i	$0.192797\pi$
$444$		0			0
$445$	−3.11457	−	5.39459i	−0.147645	−	0.255728i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.83790			−0.464279			−0.232140	−	0.972682i	$-0.574573\pi$
$449$	−9.83790			−0.464279			−0.232140	+	0.972682i	$0.574573\pi$
$450$		0			0
$451$	8.47025			0.398848
$452$		0			0
$453$		0			0
$454$		0			0
$455$	20.0364	+	34.7041i	0.939323	+	1.62696i
$456$		0			0
$457$	0.0111990	−	0.0193973i	0.000523869	−	0.000907367i	−0.865763	−	0.500454i	$-0.833167\pi$
$457$	0.0111990	−	0.0193973i	0.000523869	−	0.000907367i	0.866287	+	0.499546i	$0.166500\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.50986	+	13.0075i	−0.349769	+	0.605818i	−0.986208	−	0.165509i	$-0.947073\pi$
$461$	−7.50986	+	13.0075i	−0.349769	+	0.605818i	0.636439	+	0.771327i	$0.280407\pi$
$462$		0			0
$463$	−16.2691	−	28.1790i	−0.756091	−	1.30959i	−0.944830	−	0.327561i	$-0.893773\pi$
$463$	−16.2691	−	28.1790i	−0.756091	−	1.30959i	0.188738	−	0.982027i	$-0.439560\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.2983			−0.476550			−0.238275	−	0.971198i	$-0.576582\pi$
$467$	−10.2983			−0.476550			−0.238275	+	0.971198i	$0.576582\pi$
$468$		0			0
$469$	5.46612			0.252402
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.58450	−	13.1367i	−0.348736	−	0.604028i
$474$		0			0
$475$	1.72197	−	2.98253i	0.0790093	−	0.136848i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.79020	+	6.56481i	−0.173178	+	0.299954i	−0.939529	−	0.342468i	$-0.888737\pi$
$479$	−3.79020	+	6.56481i	−0.173178	+	0.299954i	0.766351	+	0.642422i	$0.222070\pi$
$480$		0			0
$481$	−22.1421	−	38.3513i	−1.00959	−	1.74867i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	23.2560			1.05600
$486$		0			0
$487$	20.6214			0.934444			0.467222	−	0.884140i	$-0.345255\pi$
$487$	20.6214			0.934444			0.467222	+	0.884140i	$0.345255\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.98229	+	6.89752i	0.179718	+	0.311281i	0.941784	−	0.336219i	$-0.109148\pi$
$491$	3.98229	+	6.89752i	0.179718	+	0.311281i	−0.762066	+	0.647499i	$0.775815\pi$
$492$		0			0
$493$	−11.9446	+	20.6887i	−0.537959	+	0.931772i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.38287	+	14.5196i	−0.376023	+	0.651291i
$498$		0			0
$499$	10.5911	+	18.3444i	0.474125	+	0.821208i	0.999561	−	0.0296248i	$-0.00943125\pi$
$499$	10.5911	+	18.3444i	0.474125	+	0.821208i	−0.525436	+	0.850833i	$0.676098\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−19.0876			−0.851073			−0.425536	−	0.904941i	$-0.639915\pi$
$503$	−19.0876			−0.851073			−0.425536	+	0.904941i	$0.639915\pi$
$504$		0			0
$505$	−7.69336			−0.342350
$506$		0			0
$507$		0			0
$508$		0			0
$509$	18.3596	+	31.7998i	0.813776	+	1.40950i	0.910204	+	0.414161i	$0.135925\pi$
$509$	18.3596	+	31.7998i	0.813776	+	1.40950i	−0.0964283	+	0.995340i	$0.530742\pi$
$510$		0			0
$511$	−7.21330	+	12.4938i	−0.319097	+	0.552693i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−11.4734	+	19.8726i	−0.505580	+	0.875690i
$516$		0			0
$517$	3.22656	+	5.58857i	0.141904	+	0.245785i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−20.5620			−0.900839			−0.450419	−	0.892817i	$-0.648725\pi$
$521$	−20.5620			−0.900839			−0.450419	+	0.892817i	$0.648725\pi$
$522$		0			0
$523$	−16.2754			−0.711672			−0.355836	−	0.934548i	$-0.615804\pi$
$523$	−16.2754			−0.711672			−0.355836	+	0.934548i	$0.615804\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.5505	−	23.4702i	−0.590270	−	1.02238i
$528$		0			0
$529$	−2.39812	+	4.15367i	−0.104266	+	0.180594i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	11.5197	−	19.9527i	0.498973	−	0.864246i
$534$		0			0
$535$	−6.27471	−	10.8681i	−0.271279	−	0.469870i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.11686			−0.134253
$540$		0			0
$541$	3.19402			0.137322			0.0686609	−	0.997640i	$-0.478127\pi$
$541$	3.19402			0.137322			0.0686609	+	0.997640i	$0.478127\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	10.4112	+	18.0327i	0.445966	+	0.772436i
$546$		0			0
$547$	−7.43936	+	12.8854i	−0.318084	+	0.550938i	−0.980088	−	0.198562i	$-0.936373\pi$
$547$	−7.43936	+	12.8854i	−0.318084	+	0.550938i	0.662004	+	0.749500i	$0.269706\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.87608	+	17.1059i	−0.420735	+	0.728734i
$552$		0			0
$553$	−18.7087	−	32.4045i	−0.795576	−	1.37798i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.76686			−0.244350			−0.122175	−	0.992509i	$-0.538987\pi$
$557$	−5.76686			−0.244350			−0.122175	+	0.992509i	$0.538987\pi$
$558$		0			0
$559$	−41.2602			−1.74512
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.76738	−	8.25734i	−0.200921	−	0.348005i	0.747904	−	0.663806i	$-0.231060\pi$
$563$	−4.76738	−	8.25734i	−0.200921	−	0.348005i	−0.948825	+	0.315801i	$0.897727\pi$
$564$		0			0
$565$	15.8527	−	27.4576i	0.666927	−	1.15515i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.27200	−	7.39933i	0.179092	−	0.310196i	−0.762478	−	0.647014i	$-0.776017\pi$
$569$	4.27200	−	7.39933i	0.179092	−	0.310196i	0.941570	+	0.336818i	$0.109351\pi$
$570$		0			0
$571$	18.1444	+	31.4270i	0.759318	+	1.31518i	0.943199	+	0.332229i	$0.107801\pi$
$571$	18.1444	+	31.4270i	0.759318	+	1.31518i	−0.183881	+	0.982949i	$0.558866\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.90153			0.121002
$576$		0			0
$577$	−6.11652			−0.254634			−0.127317	−	0.991862i	$-0.540637\pi$
$577$	−6.11652			−0.254634			−0.127317	+	0.991862i	$0.540637\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.44701	+	7.70245i	0.184493	+	0.319551i
$582$		0			0
$583$	1.15624	−	2.00266i	0.0478864	−	0.0829417i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.92500	+	3.33419i	−0.0794532	+	0.137617i	−0.903014	−	0.429611i	$-0.858651\pi$
$587$	−1.92500	+	3.33419i	−0.0794532	+	0.137617i	0.823561	+	0.567228i	$0.191984\pi$
$588$		0			0
$589$	−11.2039	−	19.4057i	−0.461647	−	0.799597i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.6462			−0.683579			−0.341789	−	0.939777i	$-0.611033\pi$
$593$	−16.6462			−0.683579			−0.341789	+	0.939777i	$0.611033\pi$
$594$		0			0
$595$	−45.9521			−1.88385
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.8791	+	30.9675i	0.730520	+	1.26530i	0.956661	+	0.291203i	$0.0940557\pi$
$599$	17.8791	+	30.9675i	0.730520	+	1.26530i	−0.226141	+	0.974095i	$0.572611\pi$
$600$		0			0
$601$	6.77202	−	11.7295i	0.276236	−	0.478455i	−0.694210	−	0.719773i	$-0.744246\pi$
$601$	6.77202	−	11.7295i	0.276236	−	0.478455i	0.970446	+	0.241317i	$0.0775794\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.39181	−	9.33888i	0.219208	−	0.379679i
$606$		0			0
$607$	−14.0131	−	24.2714i	−0.568775	−	0.985147i	−0.996688	−	0.0813266i	$-0.974084\pi$
$607$	−14.0131	−	24.2714i	−0.568775	−	0.985147i	0.427913	−	0.903820i	$-0.359249\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17.5527			0.710107
$612$		0			0
$613$	37.6283			1.51979			0.759897	−	0.650043i	$-0.225249\pi$
$613$	37.6283			1.51979			0.759897	+	0.650043i	$0.225249\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.57241	−	9.65169i	−0.224337	−	0.388562i	0.731784	−	0.681537i	$-0.238688\pi$
$617$	−5.57241	−	9.65169i	−0.224337	−	0.388562i	−0.956120	+	0.292975i	$0.905355\pi$
$618$		0			0
$619$	9.54119	−	16.5258i	0.383493	−	0.664229i	−0.608066	−	0.793886i	$-0.708054\pi$
$619$	9.54119	−	16.5258i	0.383493	−	0.664229i	0.991559	+	0.129658i	$0.0413878\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.24980	−	7.36086i	0.170265	−	0.294907i
$624$		0			0
$625$	10.9727	+	19.0053i	0.438908	+	0.760211i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	50.7813			2.02478
$630$		0			0
$631$	−29.7049			−1.18253			−0.591267	−	0.806476i	$-0.701372\pi$
$631$	−29.7049			−1.18253			−0.591267	+	0.806476i	$0.701372\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.51984	−	14.7568i	−0.338099	−	0.585605i
$636$		0			0
$637$	−4.23898	+	7.34214i	−0.167955	+	0.290906i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.60138	−	16.6301i	0.379232	−	0.656848i	−0.611719	−	0.791075i	$-0.709522\pi$
$641$	9.60138	−	16.6301i	0.379232	−	0.656848i	0.990951	+	0.134227i	$0.0428551\pi$
$642$		0			0
$643$	3.52181	+	6.09995i	0.138887	+	0.240559i	0.927075	−	0.374875i	$-0.122314\pi$
$643$	3.52181	+	6.09995i	0.138887	+	0.240559i	−0.788189	+	0.615434i	$0.788981\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−36.8474			−1.44862			−0.724311	−	0.689473i	$-0.757842\pi$
$647$	−36.8474			−1.44862			−0.724311	+	0.689473i	$0.757842\pi$
$648$		0			0
$649$	−23.5252			−0.923446
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.6354	+	35.7416i	0.807526	+	1.39868i	0.914572	+	0.404422i	$0.132527\pi$
$653$	20.6354	+	35.7416i	0.807526	+	1.39868i	−0.107046	+	0.994254i	$0.534139\pi$
$654$		0			0
$655$	−23.4839	+	40.6754i	−0.917593	+	1.58932i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7.79606	−	13.5032i	0.303691	−	0.526009i	−0.673278	−	0.739390i	$-0.735114\pi$
$659$	7.79606	−	13.5032i	0.303691	−	0.526009i	0.976969	+	0.213381i	$0.0684475\pi$
$660$		0			0
$661$	0.273228	+	0.473246i	0.0106274	+	0.0184071i	0.871290	−	0.490768i	$-0.163284\pi$
$661$	0.273228	+	0.473246i	0.0106274	+	0.0184071i	−0.860663	+	0.509175i	$0.829950\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−37.9942			−1.47335
$666$		0			0
$667$	−16.6413			−0.644353
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.25601	+	10.8357i	0.241510	+	0.418308i
$672$		0			0
$673$	7.71994	−	13.3713i	0.297582	−	0.515427i	−0.678000	−	0.735061i	$-0.737153\pi$
$673$	7.71994	−	13.3713i	0.297582	−	0.515427i	0.975582	+	0.219635i	$0.0704866\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−20.7394	+	35.9216i	−0.797079	+	1.38058i	0.124432	+	0.992228i	$0.460289\pi$
$677$	−20.7394	+	35.9216i	−0.797079	+	1.38058i	−0.921511	+	0.388353i	$0.873044\pi$
$678$		0			0
$679$	15.8663	+	27.4812i	0.608893	+	1.05463i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.83506			−0.299800			−0.149900	−	0.988701i	$-0.547895\pi$
$683$	−7.83506			−0.299800			−0.149900	+	0.988701i	$0.547895\pi$
$684$		0			0
$685$	−19.5064			−0.745303
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.14500	−	5.44730i	−0.119815	−	0.207526i
$690$		0			0
$691$	11.8366	−	20.5016i	0.450286	−	0.779918i	−0.548118	−	0.836401i	$-0.684655\pi$
$691$	11.8366	−	20.5016i	0.450286	−	0.779918i	0.998404	+	0.0564831i	$0.0179887\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.86497	−	15.3546i	0.336267	−	0.582432i
$696$		0			0
$697$	13.2098	+	22.8800i	0.500356	+	0.866642i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−7.14909			−0.270017			−0.135009	−	0.990844i	$-0.543106\pi$
$701$	−7.14909			−0.270017			−0.135009	+	0.990844i	$0.543106\pi$
$702$		0			0
$703$	41.9871			1.58357
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.24876	−	9.09111i	−0.197400	−	0.341906i
$708$		0			0
$709$	−19.3826	+	33.5716i	−0.727928	+	1.26081i	0.229830	+	0.973231i	$0.426183\pi$
$709$	−19.3826	+	33.5716i	−0.727928	+	1.26081i	−0.957757	+	0.287577i	$0.907150\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.43931	−	16.3494i	0.353505	−	0.612289i
$714$		0			0
$715$	16.8914	+	29.2568i	0.631704	+	1.09414i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	38.3429			1.42995			0.714975	−	0.699151i	$-0.246438\pi$
$719$	38.3429			1.42995			0.714975	+	0.699151i	$0.246438\pi$
$720$		0			0
$721$	−31.3108			−1.16607
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.868556	+	1.50438i	0.0322574	+	0.0558714i
$726$		0			0
$727$	−21.9734	+	38.0591i	−0.814950	+	1.41154i	0.0944136	+	0.995533i	$0.469902\pi$
$727$	−21.9734	+	38.0591i	−0.814950	+	1.41154i	−0.909364	+	0.416002i	$0.863431\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	23.6568	−	40.9748i	0.874979	−	1.51551i
$732$		0			0
$733$	24.7222	+	42.8202i	0.913137	+	1.58160i	0.809606	+	0.586973i	$0.199681\pi$
$733$	24.7222	+	42.8202i	0.913137	+	1.58160i	0.103531	+	0.994626i	$0.466986\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.60814			0.169743
$738$		0			0
$739$	9.25073			0.340294			0.170147	−	0.985419i	$-0.445576\pi$
$739$	9.25073			0.340294			0.170147	+	0.985419i	$0.445576\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	20.6473	+	35.7621i	0.757475	+	1.31198i	0.944135	+	0.329560i	$0.106900\pi$
$743$	20.6473	+	35.7621i	0.757475	+	1.31198i	−0.186660	+	0.982425i	$0.559766\pi$
$744$		0			0
$745$	13.0328	−	22.5734i	0.477483	−	0.827025i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.56178	−	14.8294i	0.312840	−	0.541856i
$750$		0			0
$751$	10.2101	+	17.6845i	0.372573	+	0.645315i	0.989961	−	0.141344i	$-0.0451423\pi$
$751$	10.2101	+	17.6845i	0.372573	+	0.645315i	−0.617388	+	0.786659i	$0.711809\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.7324			0.754529
$756$		0			0
$757$	−7.74944			−0.281658			−0.140829	−	0.990034i	$-0.544977\pi$
$757$	−7.74944			−0.281658			−0.140829	+	0.990034i	$0.544977\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.3416	−	23.1084i	−0.483634	−	0.837679i	0.516189	−	0.856475i	$-0.327350\pi$
$761$	−13.3416	−	23.1084i	−0.483634	−	0.837679i	−0.999823	+	0.0187955i	$0.994017\pi$
$762$		0			0
$763$	−14.2059	+	24.6054i	−0.514290	+	0.890776i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−31.9947	+	55.4165i	−1.15526	+	2.00097i
$768$		0			0
$769$	−24.5226	−	42.4744i	−0.884307	−	1.53166i	−0.846506	−	0.532379i	$-0.821298\pi$
$769$	−24.5226	−	42.4744i	−0.884307	−	1.53166i	−0.0378010	−	0.999285i	$-0.512035\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	12.1406			0.436665			0.218333	−	0.975874i	$-0.429938\pi$
$773$	12.1406			0.436665			0.218333	+	0.975874i	$0.429938\pi$
$774$		0			0
$775$	−1.97066			−0.0707881
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.9221	+	18.9177i	0.391326	+	0.677796i
$780$		0			0
$781$	−7.06706	+	12.2405i	−0.252879	+	0.438000i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.227993	−	0.394895i	0.00813742	−	0.0140944i
$786$		0			0
$787$	24.2553	+	42.0114i	0.864608	+	1.49754i	0.867436	+	0.497549i	$0.165766\pi$
$787$	24.2553	+	42.0114i	0.864608	+	1.49754i	−0.00282812	+	0.999996i	$0.500900\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	43.2616			1.53821
$792$		0			0
$793$	34.0331			1.20855
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.54989	−	4.41654i	−0.0903218	−	0.156442i	0.817325	−	0.576177i	$-0.195456\pi$
$797$	−2.54989	−	4.41654i	−0.0903218	−	0.156442i	−0.907647	+	0.419735i	$0.862123\pi$
$798$		0			0
$799$	−10.0640	+	17.4313i	−0.356037	+	0.616675i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.08107	+	10.5327i	−0.214596	+	0.371692i
$804$		0			0
$805$	−16.0051	−	27.7217i	−0.564107	−	0.977063i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	38.1416			1.34099			0.670494	−	0.741915i	$-0.266082\pi$
$809$	38.1416			1.34099			0.670494	+	0.741915i	$0.266082\pi$
$810$		0			0
$811$	−2.88343			−0.101251			−0.0506255	−	0.998718i	$-0.516122\pi$
$811$	−2.88343			−0.101251			−0.0506255	+	0.998718i	$0.516122\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.09745	+	10.5611i	0.213584	+	0.369939i
$816$		0			0
$817$	19.5600	−	33.8789i	0.684317	−	1.18527i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.84327	+	10.1208i	−0.203931	+	0.353220i	−0.949792	−	0.312883i	$-0.898705\pi$
$821$	−5.84327	+	10.1208i	−0.203931	+	0.353220i	0.745860	+	0.666102i	$0.232039\pi$
$822$		0			0
$823$	−5.91203	−	10.2399i	−0.206080	−	0.356942i	0.744396	−	0.667738i	$-0.232738\pi$
$823$	−5.91203	−	10.2399i	−0.206080	−	0.356942i	−0.950476	+	0.310797i	$0.899404\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.5265			0.957192			0.478596	−	0.878035i	$-0.341146\pi$
$827$	27.5265			0.957192			0.478596	+	0.878035i	$0.341146\pi$
$828$		0			0
$829$	27.7398			0.963443			0.481721	−	0.876324i	$-0.340012\pi$
$829$	27.7398			0.963443			0.481721	+	0.876324i	$0.340012\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.86090	−	8.41932i	−0.168420	−	0.291712i
$834$		0			0
$835$	−1.72687	+	2.99102i	−0.0597608	+	0.103509i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.7349	−	22.0574i	0.439656	−	0.761507i	−0.558007	−	0.829837i	$-0.688434\pi$
$839$	12.7349	−	22.0574i	0.439656	−	0.761507i	0.997663	+	0.0683295i	$0.0217669\pi$
$840$		0			0
$841$	9.51853	+	16.4866i	0.328225	+	0.568503i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	64.4682			2.21777
$846$		0			0
$847$	14.7141			0.505583
$848$		0			0
$849$		0			0
$850$		0			0
$851$	17.6872	+	30.6351i	0.606308	+	1.05016i
$852$		0			0
$853$	−15.2819	+	26.4690i	−0.523241	+	0.906280i	0.476393	+	0.879232i	$0.341944\pi$
$853$	−15.2819	+	26.4690i	−0.523241	+	0.906280i	−0.999634	+	0.0270477i	$0.991389\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.69252	+	13.3238i	−0.262772	+	0.455134i	−0.966977	−	0.254862i	$-0.917970\pi$
$857$	−7.69252	+	13.3238i	−0.262772	+	0.455134i	0.704206	+	0.709996i	$0.251303\pi$
$858$		0			0
$859$	9.19471	+	15.9257i	0.313720	+	0.543378i	0.979164	−	0.203069i	$-0.0650915\pi$
$859$	9.19471	+	15.9257i	0.313720	+	0.543378i	−0.665445	+	0.746447i	$0.731758\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	35.5698			1.21081			0.605404	−	0.795918i	$-0.293011\pi$
$863$	35.5698			1.21081			0.605404	+	0.795918i	$0.293011\pi$
$864$		0			0
$865$	12.6240			0.429227
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−15.7721	−	27.3181i	−0.535033	−	0.926704i
$870$		0			0
$871$	6.26715	−	10.8550i	0.212354	−	0.367808i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−16.8495	+	29.1842i	−0.569616	+	0.986605i
$876$		0			0
$877$	−11.1127	−	19.2477i	−0.375249	−	0.649950i	0.615115	−	0.788437i	$-0.289109\pi$
$877$	−11.1127	−	19.2477i	−0.375249	−	0.649950i	−0.990364	+	0.138487i	$0.955776\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−38.5586			−1.29907			−0.649536	−	0.760331i	$-0.725037\pi$
$881$	−38.5586			−1.29907			−0.649536	+	0.760331i	$0.725037\pi$
$882$		0			0
$883$	10.4984			0.353298			0.176649	−	0.984274i	$-0.443474\pi$
$883$	10.4984			0.353298			0.176649	+	0.984274i	$0.443474\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.0186	−	39.8693i	−0.772888	−	1.33868i	−0.935974	−	0.352069i	$-0.885478\pi$
$887$	−23.0186	−	39.8693i	−0.772888	−	1.33868i	0.163087	−	0.986612i	$-0.447855\pi$
$888$		0			0
$889$	11.6252	−	20.1355i	0.389898	−	0.675322i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.32111	+	14.4126i	−0.278455	+	0.482299i
$894$		0			0
$895$	10.0336	+	17.3787i	0.335386	+	0.580906i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.3024			0.376956
$900$		0			0
$901$	7.21283			0.240294
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−25.0521	−	43.3914i	−0.832759	−	1.44238i
$906$		0			0
$907$	−8.68354	+	15.0403i	−0.288332	+	0.499406i	−0.973412	−	0.229062i	$-0.926434\pi$
$907$	−8.68354	+	15.0403i	−0.288332	+	0.499406i	0.685080	+	0.728468i	$0.259767\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.29095	−	2.23599i	0.0427711	−	0.0740817i	−0.843847	−	0.536583i	$-0.819715\pi$
$911$	1.29095	−	2.23599i	0.0427711	−	0.0740817i	0.886618	+	0.462502i	$0.153048\pi$
$912$		0			0
$913$	3.74899	+	6.49344i	0.124073	+	0.214902i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−64.0871			−2.11634
$918$		0			0
$919$	−34.8909			−1.15095			−0.575473	−	0.817821i	$-0.695182\pi$
$919$	−34.8909			−1.15095			−0.575473	+	0.817821i	$0.695182\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	19.2226	+	33.2946i	0.632721	+	1.09591i
$924$		0			0
$925$	1.84629	−	3.19786i	0.0607055	−	0.105145i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.38201	+	7.58986i	−0.143769	+	0.249015i	−0.928913	−	0.370298i	$-0.879256\pi$
$929$	−4.38201	+	7.58986i	−0.143769	+	0.249015i	0.785144	+	0.619313i	$0.212589\pi$
$930$		0			0
$931$	−4.01910	−	6.96128i	−0.131721	−	0.228147i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−38.7393			−1.26691
$936$		0			0
$937$	39.6212			1.29437			0.647184	−	0.762334i	$-0.275946\pi$
$937$	39.6212			1.29437			0.647184	+	0.762334i	$0.275946\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.5675	−	23.4995i	−0.442287	−	0.766063i	0.555572	−	0.831468i	$-0.312499\pi$
$941$	−13.5675	−	23.4995i	−0.442287	−	0.766063i	−0.997859	+	0.0654053i	$0.979166\pi$
$942$		0			0
$943$	−9.20195	+	15.9382i	−0.299657	+	0.519020i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.06166	−	1.83886i	0.0344995	−	0.0597548i	−0.848260	−	0.529580i	$-0.822350\pi$
$947$	1.06166	−	1.83886i	0.0344995	−	0.0597548i	0.882760	+	0.469825i	$0.155683\pi$
$948$		0			0
$949$	16.5407	+	28.6494i	0.536934	+	0.929998i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.523434			0.0169557			0.00847784	−	0.999964i	$-0.497301\pi$
$953$	0.523434			0.0169557			0.00847784	+	0.999964i	$0.497301\pi$
$954$		0			0
$955$	17.4729			0.565410
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−13.3082	−	23.0504i	−0.429743	−	0.744337i
$960$		0			0
$961$	9.08902	−	15.7426i	0.293194	−	0.507827i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10.5538	−	18.2796i	0.339737	−	0.588442i
$966$		0			0
$967$	2.74196	+	4.74922i	0.0881756	+	0.152725i	0.906740	−	0.421690i	$-0.138563\pi$
$967$	2.74196	+	4.74922i	0.0881756	+	0.152725i	−0.818564	+	0.574415i	$0.805230\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.813501			0.0261065			0.0130532	−	0.999915i	$-0.495845\pi$
$971$	0.813501			0.0261065			0.0130532	+	0.999915i	$0.495845\pi$
$972$		0			0
$973$	24.1923			0.775570
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.85335	−	17.0665i	−0.315237	−	0.546006i	0.664251	−	0.747509i	$-0.268751\pi$
$977$	−9.85335	−	17.0665i	−0.315237	−	0.546006i	−0.979488	+	0.201504i	$0.935417\pi$
$978$		0			0
$979$	3.58273	−	6.20547i	0.114505	−	0.198328i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	27.9588	−	48.4261i	0.891747	−	1.54455i	0.0539681	−	0.998543i	$-0.482813\pi$
$983$	27.9588	−	48.4261i	0.891747	−	1.54455i	0.837779	−	0.546009i	$-0.183854\pi$
$984$		0			0
$985$	−0.586692	−	1.01618i	−0.0186936	−	0.0323782i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	32.9588			1.04803
$990$		0			0
$991$	22.4053			0.711727			0.355863	−	0.934538i	$-0.384187\pi$
$991$	22.4053			0.711727			0.355863	+	0.934538i	$0.384187\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−22.7318	−	39.3726i	−0.720646	−	1.24819i
$996$		0			0
$997$	−16.6132	+	28.7749i	−0.526146	+	0.911311i	0.473390	+	0.880853i	$0.343030\pi$
$997$	−16.6132	+	28.7749i	−0.526146	+	0.911311i	−0.999536	+	0.0304585i	$0.990303\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3456.2.i.i.1153.3		12
3.2	odd	2		1152.2.i.l.385.3	yes	12
4.3	odd	2		3456.2.i.j.1153.3		12
8.3	odd	2		3456.2.i.l.1153.4		12
8.5	even	2		3456.2.i.k.1153.4		12
9.4	even	3	inner	3456.2.i.i.2305.3		12
9.5	odd	6		1152.2.i.l.769.3	yes	12
12.11	even	2		1152.2.i.j.385.4	yes	12
24.5	odd	2		1152.2.i.i.385.4	✓	12
24.11	even	2		1152.2.i.k.385.3	yes	12
36.23	even	6		1152.2.i.j.769.4	yes	12
36.31	odd	6		3456.2.i.j.2305.3		12
72.5	odd	6		1152.2.i.i.769.4	yes	12
72.13	even	6		3456.2.i.k.2305.4		12
72.59	even	6		1152.2.i.k.769.3	yes	12
72.67	odd	6		3456.2.i.l.2305.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.i.385.4	✓	12	24.5	odd	2
1152.2.i.i.769.4	yes	12	72.5	odd	6
1152.2.i.j.385.4	yes	12	12.11	even	2
1152.2.i.j.769.4	yes	12	36.23	even	6
1152.2.i.k.385.3	yes	12	24.11	even	2
1152.2.i.k.769.3	yes	12	72.59	even	6
1152.2.i.l.385.3	yes	12	3.2	odd	2
1152.2.i.l.769.3	yes	12	9.5	odd	6
3456.2.i.i.1153.3		12	1.1	even	1	trivial
3456.2.i.i.2305.3		12	9.4	even	3	inner
3456.2.i.j.1153.3		12	4.3	odd	2
3456.2.i.j.2305.3		12	36.31	odd	6
3456.2.i.k.1153.4		12	8.5	even	2
3456.2.i.k.2305.4		12	72.13	even	6
3456.2.i.l.1153.4		12	8.3	odd	2
3456.2.i.l.2305.4		12	72.67	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:	\( N \)	\(=\)	\( 3456 = 2^{7} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3456.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.05471 - 1.82681i) q^{5} +(1.43914 - 2.49267i) q^{7} +O(q^{10})\)	\(q+(-1.05471 - 1.82681i) q^{5} +(1.43914 - 2.49267i) q^{7} +(1.21325 - 2.10141i) q^{11} +(-3.30008 - 5.71590i) q^{13} +7.56848 q^{17} +6.25779 q^{19} +(2.63611 + 4.56587i) q^{23} +(0.275172 - 0.476612i) q^{25} +(-1.57821 + 2.73353i) q^{29} +(-1.79039 - 3.10104i) q^{31} -6.07151 q^{35} +6.70957 q^{37} +(1.74537 + 3.02306i) q^{41} +(3.12570 - 5.41388i) q^{43} +(-1.32972 + 2.30314i) q^{47} +(-0.642255 - 1.11242i) q^{49} +0.953009 q^{53} -5.11850 q^{55} +(-4.84757 - 8.39624i) q^{59} +(-2.57821 + 4.46558i) q^{61} +(-6.96125 + 12.0572i) q^{65} +(0.949546 + 1.64466i) q^{67} -5.82491 q^{71} -5.01222 q^{73} +(-3.49207 - 6.04844i) q^{77} +(6.49996 - 11.2583i) q^{79} +(-1.54502 + 2.67606i) q^{83} +(-7.98256 - 13.8262i) q^{85} +2.95301 q^{89} -18.9971 q^{91} +(-6.60015 - 11.4318i) q^{95} +(-5.51242 + 9.54779i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{5} - 6 q^{7}+O(q^{10}) \) 12 * q - 2 * q^5 - 6 * q^7	\( 12 q - 2 q^{5} - 6 q^{7} - 4 q^{11} - 10 q^{13} - 4 q^{17} + 4 q^{19} + 8 q^{23} - 14 q^{25} - 2 q^{29} - 8 q^{31} - 8 q^{35} + 2 q^{41} - 2 q^{43} - 14 q^{47} - 18 q^{49} + 24 q^{53} + 16 q^{55} - 6 q^{59} - 14 q^{61} + 8 q^{65} + 4 q^{67} - 28 q^{71} + 60 q^{73} + 2 q^{77} - 16 q^{79} - 24 q^{83} - 16 q^{85} + 48 q^{89} - 52 q^{91} - 20 q^{95} - 14 q^{97}+O(q^{100}) \) 12 * q - 2 * q^5 - 6 * q^7 - 4 * q^11 - 10 * q^13 - 4 * q^17 + 4 * q^19 + 8 * q^23 - 14 * q^25 - 2 * q^29 - 8 * q^31 - 8 * q^35 + 2 * q^41 - 2 * q^43 - 14 * q^47 - 18 * q^49 + 24 * q^53 + 16 * q^55 - 6 * q^59 - 14 * q^61 + 8 * q^65 + 4 * q^67 - 28 * q^71 + 60 * q^73 + 2 * q^77 - 16 * q^79 - 24 * q^83 - 16 * q^85 + 48 * q^89 - 52 * q^91 - 20 * q^95 - 14 * q^97

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