LMFDB - Embedded newform 1008.2.s.d.865.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(289,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1008.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.s (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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1008.865
Dual form			1008.2.s.d.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})$	$q+(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{11} +1.00000 q^{13} +(0.500000 + 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{25} -4.00000 q^{29} +(4.50000 - 7.79423i) q^{31} +(-1.00000 - 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +10.0000 q^{41} -5.00000 q^{43} +(3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(-1.00000 - 1.73205i) q^{65} +(-2.50000 + 4.33013i) q^{67} -6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} +(4.00000 - 3.46410i) q^{77} +(-0.500000 - 0.866025i) q^{79} +6.00000 q^{83} +(8.00000 + 13.8564i) q^{89} +(2.50000 + 0.866025i) q^{91} +(1.00000 - 1.73205i) q^{95} -6.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} + 5 q^{7}+O(q^{10}) $ 2 * q - 2 * q^5 + 5 * q^7	$ 2 q - 2 q^{5} + 5 q^{7} + 2 q^{11} + 2 q^{13} + q^{19} + q^{25} - 8 q^{29} + 9 q^{31} - 2 q^{35} - 3 q^{37} + 20 q^{41} - 10 q^{43} + 6 q^{47} + 11 q^{49} + 12 q^{53} - 8 q^{55} + 12 q^{59} - 10 q^{61} - 2 q^{65} - 5 q^{67} - 12 q^{71} + 3 q^{73} + 8 q^{77} - q^{79} + 12 q^{83} + 16 q^{89} + 5 q^{91} + 2 q^{95} - 12 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 + 5 * q^7 + 2 * q^11 + 2 * q^13 + q^19 + q^25 - 8 * q^29 + 9 * q^31 - 2 * q^35 - 3 * q^37 + 20 * q^41 - 10 * q^43 + 6 * q^47 + 11 * q^49 + 12 * q^53 - 8 * q^55 + 12 * q^59 - 10 * q^61 - 2 * q^65 - 5 * q^67 - 12 * q^71 + 3 * q^73 + 8 * q^77 - q^79 + 12 * q^83 + 16 * q^89 + 5 * q^91 + 2 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	−0.105869	−	0.994380i	$-0.533762\pi$
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	0.914093	−	0.405505i	$-0.132904\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.00000	−	5.19615i	−0.169031	−	0.878310i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	−4.00000			−0.539360
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.00000	−	1.73205i	−0.124035	−	0.214834i
$66$		0			0
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.00000	−	3.46410i	0.455842	−	0.394771i
$78$		0			0
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.00000	+	13.8564i	0.847998	+	1.46878i	0.882992	+	0.469389i	$0.155526\pi$
$89$	8.00000	+	13.8564i	0.847998	+	1.46878i	−0.0349934	+	0.999388i	$0.511141\pi$
$90$		0			0
$91$	2.50000	+	0.866025i	0.262071	+	0.0907841i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$		0			0
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	0.640464	−	0.767988i	$-0.278742\pi$
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	−0.985329	+	0.170664i	$0.945409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$		0			0
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	−0.996962	−	0.0778949i	$-0.975180\pi$
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	0.565940	+	0.824447i	$0.308513\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	15.0000			1.33103			0.665517	−	0.746382i	$-0.268211\pi$
$127$	15.0000			1.33103			0.665517	+	0.746382i	$0.268211\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	0.990972	+	0.134069i	$0.0428042\pi$
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	−0.379379	+	0.925241i	$0.623862\pi$
$132$		0			0
$133$	0.500000	+	2.59808i	0.0433555	+	0.225282i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	3.00000			0.254457			0.127228	−	0.991873i	$-0.459392\pi$
$139$	3.00000			0.254457			0.127228	+	0.991873i	$0.459392\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$		0			0
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	0.508413	−	0.861113i	$-0.330232\pi$
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	−0.999953	+	0.00974235i	$0.996899\pi$
$150$		0			0
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	0.331842	+	0.943335i	$0.392330\pi$
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	−0.982873	+	0.184284i	$0.941004\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−18.0000			−1.44579
$156$		0			0
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.0000			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	0.977064	−	0.212947i	$-0.0683062\pi$
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	−0.672949	+	0.739689i	$0.734973\pi$
$174$		0			0
$175$	2.00000	−	1.73205i	0.151186	−	0.130931i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	−0.900975	−	0.433872i	$-0.857147\pi$
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	0.826231	+	0.563331i	$0.190480\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.00000	−	8.66025i	−0.361787	−	0.626634i	0.626468	−	0.779447i	$-0.284500\pi$
$191$	−5.00000	−	8.66025i	−0.361787	−	0.626634i	−0.988255	+	0.152813i	$0.951167\pi$
$192$		0			0
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.0000	−	3.46410i	−0.701862	−	0.243132i
$204$		0			0
$205$	−10.0000	−	17.3205i	−0.698430	−	1.20972i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.00000			0.138343
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$	18.0000	−	15.5885i	1.22192	−	1.05821i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	0.395860	+	0.918311i	$0.370447\pi$
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	−0.993210	+	0.116331i	$0.962887\pi$
$228$		0			0
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	0.987997	+	0.154475i	$0.0493686\pi$
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	−0.360219	+	0.932868i	$0.617298\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.00000	−	13.8564i	0.127775	−	0.885253i
$246$		0			0
$247$	0.500000	+	0.866025i	0.0318142	+	0.0551039i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	0.912222	+	0.409695i	$0.134365\pi$
$257$	13.0000	+	22.5167i	0.810918	+	1.40455i	−0.101305	+	0.994855i	$0.532302\pi$
$258$		0			0
$259$	−1.50000	−	7.79423i	−0.0932055	−	0.484310i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	−0.921077	−	0.389380i	$-0.872689\pi$
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	0.797752	+	0.602986i	$0.206023\pi$
$264$		0			0
$265$	−24.0000			−1.47431
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$		0			0
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	−0.992522	−	0.122068i	$-0.961047\pi$
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	0.601975	+	0.798515i	$0.294381\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4.00000			0.238620			0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000			0.238620			0.119310	+	0.992857i	$0.461932\pi$
$282$		0			0
$283$	−5.50000	+	9.52628i	−0.326941	+	0.566279i	−0.981903	−	0.189383i	$-0.939351\pi$
$283$	−5.50000	+	9.52628i	−0.326941	+	0.566279i	0.654962	+	0.755662i	$0.272685\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	25.0000	+	8.66025i	1.47570	+	0.511199i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.00000			−0.467365			−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000			−0.467365			−0.233682	+	0.972313i	$0.575078\pi$
$294$		0			0
$295$	−24.0000			−1.39733
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−12.5000	−	4.33013i	−0.720488	−	0.249584i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.0000	+	17.3205i	−0.572598	+	0.991769i
$306$		0			0
$307$	17.0000			0.970241			0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000			0.970241			0.485121	+	0.874447i	$0.338776\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	0.976764	+	0.214318i	$0.0687530\pi$
$317$	12.0000	+	20.7846i	0.673987	+	1.16738i	−0.302777	+	0.953062i	$0.597914\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.00000	+	15.5885i	0.165395	+	0.859419i
$330$		0			0
$331$	−12.5000	−	21.6506i	−0.687062	−	1.19003i	−0.972784	−	0.231714i	$-0.925567\pi$
$331$	−12.5000	−	21.6506i	−0.687062	−	1.19003i	0.285722	−	0.958313i	$-0.407767\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.0000			0.546358
$336$		0			0
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−9.00000	−	15.5885i	−0.487377	−	0.844162i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.0000	+	27.7128i	−0.858925	+	1.48770i	0.0140303	+	0.999902i	$0.495534\pi$
$347$	−16.0000	+	27.7128i	−0.858925	+	1.48770i	−0.872955	+	0.487800i	$0.837799\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.0000	−	29.4449i	0.904819	−	1.56719i	0.0836583	−	0.996495i	$-0.473340\pi$
$353$	17.0000	−	29.4449i	0.904819	−	1.56719i	0.821160	−	0.570697i	$-0.193327\pi$
$354$		0			0
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.00000			−0.314054
$366$		0			0
$367$	−4.50000	+	7.79423i	−0.234898	+	0.406855i	−0.959243	−	0.282582i	$-0.908809\pi$
$367$	−4.50000	+	7.79423i	−0.234898	+	0.406855i	0.724345	+	0.689438i	$0.242142\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	24.0000	−	20.7846i	1.24602	−	1.07908i
$372$		0			0
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.00000			−0.206010
$378$		0			0
$379$	−3.00000			−0.154100			−0.0770498	−	0.997027i	$-0.524550\pi$
$379$	−3.00000			−0.154100			−0.0770498	+	0.997027i	$0.524550\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$		0			0
$385$	−10.0000	−	3.46410i	−0.509647	−	0.176547i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.00000	+	1.73205i	−0.0503155	+	0.0871489i
$396$		0			0
$397$	4.50000	+	7.79423i	0.225849	+	0.391181i	0.956574	−	0.291491i	$-0.0941512\pi$
$397$	4.50000	+	7.79423i	0.225849	+	0.391181i	−0.730725	+	0.682672i	$0.760818\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.828932	−	0.559350i	$-0.811051\pi$
$401$	−18.0000	−	31.1769i	−0.898877	−	1.55690i	−0.0699455	−	0.997551i	$-0.522283\pi$
$402$		0			0
$403$	4.50000	−	7.79423i	0.224161	−	0.388258i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.00000			−0.297409
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0000	−	20.7846i	1.18096	−	1.02274i
$414$		0			0
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$		0			0
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.00000	−	25.9808i	−0.241967	−	1.25730i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	0.997173	+	0.0751385i	$0.0239399\pi$
$432$		0			0
$433$	31.0000			1.48976			0.744882	−	0.667196i	$-0.232506\pi$
$433$	31.0000			1.48976			0.744882	+	0.667196i	$0.232506\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$	16.0000	−	27.7128i	0.758473	−	1.31371i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	10.0000	−	17.3205i	0.470882	−	0.815591i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.00000	−	5.19615i	−0.0468807	−	0.243599i
$456$		0			0
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	0.965512	−	0.260358i	$-0.0838407\pi$
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	−0.708233	+	0.705979i	$0.750507\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$		0			0
$463$	17.0000			0.790057			0.395029	−	0.918669i	$-0.370735\pi$
$463$	17.0000			0.790057			0.395029	+	0.918669i	$0.370735\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.00000	−	5.19615i	−0.138823	−	0.240449i	0.788228	−	0.615383i	$-0.210999\pi$
$467$	−3.00000	−	5.19615i	−0.138823	−	0.240449i	−0.927052	+	0.374934i	$0.877665\pi$
$468$		0			0
$469$	−10.0000	+	8.66025i	−0.461757	+	0.399893i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$		0			0
$475$	1.00000			0.0458831
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$		0			0
$481$	−1.50000	−	2.59808i	−0.0683941	−	0.118462i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.00000	+	10.3923i	0.272446	+	0.471890i
$486$		0			0
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	−0.265260	−	0.964177i	$-0.585458\pi$
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	0.967632	−	0.252367i	$-0.0812090\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−15.0000	−	5.19615i	−0.672842	−	0.233079i
$498$		0			0
$499$	18.5000	+	32.0429i	0.828174	+	1.43444i	0.899469	+	0.436984i	$0.143953\pi$
$499$	18.5000	+	32.0429i	0.828174	+	1.43444i	−0.0712957	+	0.997455i	$0.522713\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−42.0000			−1.87269			−0.936344	−	0.351085i	$-0.885813\pi$
$503$	−42.0000			−1.87269			−0.936344	+	0.351085i	$0.885813\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$		0			0
$511$	6.00000	−	5.19615i	0.265424	−	0.229864i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.00000	+	12.1244i	−0.308457	+	0.534263i
$516$		0			0
$517$	12.0000			0.527759
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$		0			0
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	0.975652	+	0.219326i	$0.0703858\pi$
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	−0.297884	+	0.954602i	$0.596281\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.0000			0.433148
$534$		0			0
$535$	8.00000	−	13.8564i	0.345870	−	0.599065i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$		0			0
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	18.0000			0.771035
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.00000	−	3.46410i	−0.0852029	−	0.147576i
$552$		0			0
$553$	−0.500000	−	2.59808i	−0.0212622	−	0.110481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$		0			0
$562$		0			0
$563$	13.0000	−	22.5167i	0.547885	−	0.948964i	−0.450535	−	0.892759i	$-0.648767\pi$
$563$	13.0000	−	22.5167i	0.547885	−	0.948964i	0.998419	−	0.0562051i	$-0.0179001\pi$
$564$		0			0
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.0000	−	22.5167i	−0.544988	−	0.943948i	−0.998608	−	0.0527519i	$-0.983201\pi$
$569$	−13.0000	−	22.5167i	−0.544988	−	0.943948i	0.453619	−	0.891196i	$-0.350133\pi$
$570$		0			0
$571$	−9.50000	+	16.4545i	−0.397563	+	0.688599i	−0.993425	−	0.114488i	$-0.963477\pi$
$571$	−9.50000	+	16.4545i	−0.397563	+	0.688599i	0.595862	+	0.803087i	$0.296811\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	−0.633062	−	0.774101i	$-0.718202\pi$
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515357\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.0000	+	5.19615i	0.622305	+	0.215573i
$582$		0			0
$583$	−12.0000	−	20.7846i	−0.496989	−	0.860811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.0000			0.660391			0.330195	−	0.943913i	$-0.392885\pi$
$587$	16.0000			0.660391			0.330195	+	0.943913i	$0.392885\pi$
$588$		0			0
$589$	9.00000			0.370839
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	−9.00000			−0.367118			−0.183559	−	0.983009i	$-0.558762\pi$
$601$	−9.00000			−0.367118			−0.183559	+	0.983009i	$0.558762\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.00000	+	5.19615i	0.121367	+	0.210214i
$612$		0			0
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	0.286300	+	0.958140i	$0.407575\pi$
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	−0.972924	+	0.231127i	$0.925759\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	0.412341	+	0.911030i	$0.364711\pi$
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	−0.995145	+	0.0984169i	$0.968622\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.00000	+	41.5692i	0.320513	+	1.66544i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−15.0000	−	25.9808i	−0.595257	−	1.03102i
$636$		0			0
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	19.0000			0.749287			0.374643	−	0.927169i	$-0.377765\pi$
$643$	19.0000			0.749287			0.374643	+	0.927169i	$0.377765\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.00000	+	1.73205i	−0.0393141	+	0.0680939i	−0.885013	−	0.465566i	$-0.845851\pi$
$647$	−1.00000	+	1.73205i	−0.0393141	+	0.0680939i	0.845699	+	0.533660i	$0.179184\pi$
$648$		0			0
$649$	−12.0000	−	20.7846i	−0.471041	−	0.815867i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		0			0
$655$	14.0000	−	24.2487i	0.547025	−	0.947476i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	−0.123974	−	0.992286i	$-0.539564\pi$
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	0.921331	−	0.388778i	$-0.127103\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.00000	−	3.46410i	0.155113	−	0.134332i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−20.0000			−0.772091
$672$		0			0
$673$	−41.0000			−1.58043			−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000			−1.58043			−0.790217	+	0.612827i	$0.790032\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	0.957984	−	0.286820i	$-0.0925982\pi$
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	−0.727386	+	0.686229i	$0.759265\pi$
$678$		0			0
$679$	−15.0000	−	5.19615i	−0.575647	−	0.199410i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$		0			0
$685$	24.0000			0.916993
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	−18.5000	−	32.0429i	−0.703773	−	1.21897i	−0.967132	−	0.254273i	$-0.918164\pi$
$691$	−18.5000	−	32.0429i	−0.703773	−	1.21897i	0.263359	−	0.964698i	$-0.415170\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.00000	−	5.19615i	−0.113796	−	0.197101i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	1.50000	−	2.59808i	0.0565736	−	0.0979883i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.00000	−	3.46410i	0.150435	−	0.130281i
$708$		0			0
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	−0.997202	−	0.0747503i	$-0.976184\pi$
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	0.433865	−	0.900978i	$-0.357149\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−4.00000			−0.149592
$716$		0			0
$717$		0			0
$718$		0			0
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$		0			0
$721$	−3.50000	−	18.1865i	−0.130347	−	0.677302i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$		0			0
$727$	13.0000			0.482143			0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000			0.482143			0.241072	+	0.970507i	$0.422501\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	0.970642	−	0.240527i	$-0.0773202\pi$
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	−0.693624	+	0.720338i	$0.743987\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.00000	+	8.66025i	0.184177	+	0.319005i
$738$		0			0
$739$	−7.50000	+	12.9904i	−0.275892	+	0.477859i	−0.970360	−	0.241665i	$-0.922307\pi$
$739$	−7.50000	+	12.9904i	−0.275892	+	0.477859i	0.694468	+	0.719524i	$0.255640\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	42.0000			1.54083			0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000			1.54083			0.770415	+	0.637542i	$0.220049\pi$
$744$		0			0
$745$	−12.0000	+	20.7846i	−0.439646	+	0.761489i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.00000	+	20.7846i	0.146157	+	0.759453i
$750$		0			0
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	0.959906	−	0.280321i	$-0.0904408\pi$
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	−0.722718	+	0.691143i	$0.757107\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	32.0000			1.16460
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.861996	−	0.506915i	$-0.830786\pi$
$761$	−24.0000	−	41.5692i	−0.869999	−	1.50688i	−0.00800331	−	0.999968i	$-0.502548\pi$
$762$		0			0
$763$	−18.0000	+	15.5885i	−0.651644	+	0.564340i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$		0			0
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.0000	+	29.4449i	−0.611448	+	1.05906i	0.379549	+	0.925172i	$0.376079\pi$
$773$	−17.0000	+	29.4449i	−0.611448	+	1.05906i	−0.990997	+	0.133887i	$0.957254\pi$
$774$		0			0
$775$	−4.50000	−	7.79423i	−0.161645	−	0.279977i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.00000	+	8.66025i	0.179144	+	0.310286i
$780$		0			0
$781$	−6.00000	+	10.3923i	−0.214697	+	0.371866i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−28.0000			−0.999363
$786$		0			0
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	−0.250832	−	0.968031i	$-0.580704\pi$
$787$	20.0000	−	34.6410i	0.712923	−	1.23482i	0.963755	−	0.266788i	$-0.0859624\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−25.0000	−	8.66025i	−0.888898	−	0.307923i
$792$		0			0
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$	−2.50000	−	4.33013i	−0.0874639	−	0.151492i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	0.882948	−	0.469471i	$-0.155555\pi$
$821$	1.00000	+	1.73205i	0.0349002	+	0.0604490i	−0.848048	+	0.529920i	$0.822222\pi$
$822$		0			0
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	14.0000	+	24.2487i	0.484490	+	0.839161i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−44.0000			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$		0			0
$844$		0			0
$845$	12.0000	+	20.7846i	0.412813	+	0.715012i
$846$		0			0
$847$	3.50000	+	18.1865i	0.120261	+	0.624897i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	0.451958	+	0.892039i	$0.350726\pi$
$857$	−16.0000	+	27.7128i	−0.546550	+	0.946652i	−0.998508	+	0.0546125i	$0.982608\pi$
$858$		0			0
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	−0.974249	−	0.225475i	$-0.927607\pi$
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	0.291858	−	0.956462i	$-0.405727\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.0000	+	46.7654i	0.919091	+	1.59191i	0.800799	+	0.598933i	$0.204408\pi$
$863$	27.0000	+	46.7654i	0.919091	+	1.59191i	0.118291	+	0.992979i	$0.462258\pi$
$864$		0			0
$865$	8.00000	−	13.8564i	0.272008	−	0.471132i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.00000			−0.0678454
$870$		0			0
$871$	−2.50000	+	4.33013i	−0.0847093	+	0.146721i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−30.0000	−	10.3923i	−1.01419	−	0.351324i
$876$		0			0
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	0.985079	+	0.172102i	$0.0550559\pi$
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	−0.343495	+	0.939155i	$0.611611\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−24.0000			−0.808581			−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000			−0.808581			−0.404290	+	0.914631i	$0.632481\pi$
$882$		0			0
$883$	13.0000			0.437485			0.218742	−	0.975783i	$-0.429805\pi$
$883$	13.0000			0.437485			0.218742	+	0.975783i	$0.429805\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.0000	+	29.4449i	0.570804	+	0.988662i	0.996484	+	0.0837878i	$0.0267018\pi$
$887$	17.0000	+	29.4449i	0.570804	+	0.988662i	−0.425679	+	0.904874i	$0.639965\pi$
$888$		0			0
$889$	37.5000	+	12.9904i	1.25771	+	0.435683i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$		0			0
$895$	4.00000			0.133705
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−13.0000	−	22.5167i	−0.432135	−	0.748479i
$906$		0			0
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	0.376228	+	0.926527i	$0.377221\pi$
$907$	−18.5000	+	32.0429i	−0.614282	+	1.06397i	−0.990510	+	0.137441i	$0.956112\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		0			0
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.00000	+	36.3731i	0.231160	+	1.20114i
$918$		0			0
$919$	11.5000	+	19.9186i	0.379350	+	0.657053i	0.990968	−	0.134100i	$-0.0428143\pi$
$919$	11.5000	+	19.9186i	0.379350	+	0.657053i	−0.611618	+	0.791153i	$0.709481\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.00000			−0.197492
$924$		0			0
$925$	−3.00000			−0.0986394
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$	−1.00000	+	6.92820i	−0.0327737	+	0.227063i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	15.0000			0.490029			0.245014	−	0.969519i	$-0.421207\pi$
$937$	15.0000			0.490029			0.245014	+	0.969519i	$0.421207\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2.00000	+	3.46410i	−0.0651981	+	0.112926i	−0.896782	−	0.442473i	$-0.854101\pi$
$941$	−2.00000	+	3.46410i	−0.0651981	+	0.112926i	0.831584	+	0.555399i	$0.187435\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.00000	+	8.66025i	0.162478	+	0.281420i	0.935757	−	0.352646i	$-0.114718\pi$
$947$	5.00000	+	8.66025i	0.162478	+	0.281420i	−0.773279	+	0.634066i	$0.781385\pi$
$948$		0			0
$949$	1.50000	−	2.59808i	0.0486921	−	0.0843371i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−44.0000			−1.42530			−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000			−1.42530			−0.712650	+	0.701520i	$0.752505\pi$
$954$		0			0
$955$	−10.0000	+	17.3205i	−0.323592	+	0.560478i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−24.0000	+	20.7846i	−0.775000	+	0.671170i
$960$		0			0
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	22.0000			0.708205
$966$		0			0
$967$	−19.0000			−0.610999			−0.305499	−	0.952192i	$-0.598823\pi$
$967$	−19.0000			−0.610999			−0.305499	+	0.952192i	$0.598823\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$		0			0
$973$	7.50000	+	2.59808i	0.240439	+	0.0832905i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$	32.0000			1.02272
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	16.0000	+	27.7128i	0.509802	+	0.883004i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	0.968864	+	0.247592i	$0.0796392\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	−0.976333	−	0.216274i	$-0.930610\pi$
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	0.675465	+	0.737392i	$0.263943\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.s.d.865.1		2
3.2	odd	2		336.2.q.f.193.1		2
4.3	odd	2		63.2.e.b.46.1		2
7.2	even	3	inner	1008.2.s.d.289.1		2
7.3	odd	6		7056.2.a.m.1.1		1
7.4	even	3		7056.2.a.bp.1.1		1
12.11	even	2		21.2.e.a.4.1	✓	2
21.2	odd	6		336.2.q.f.289.1		2
21.5	even	6		2352.2.q.c.961.1		2
21.11	odd	6		2352.2.a.d.1.1		1
21.17	even	6		2352.2.a.w.1.1		1
21.20	even	2		2352.2.q.c.1537.1		2
24.5	odd	2		1344.2.q.c.193.1		2
24.11	even	2		1344.2.q.m.193.1		2
28.3	even	6		441.2.a.a.1.1		1
28.11	odd	6		441.2.a.b.1.1		1
28.19	even	6		441.2.e.e.226.1		2
28.23	odd	6		63.2.e.b.37.1		2
28.27	even	2		441.2.e.e.361.1		2
36.7	odd	6		567.2.g.f.109.1		2
36.11	even	6		567.2.g.a.109.1		2
36.23	even	6		567.2.h.f.298.1		2
36.31	odd	6		567.2.h.a.298.1		2
60.23	odd	4		525.2.r.e.424.1		4
60.47	odd	4		525.2.r.e.424.2		4
60.59	even	2		525.2.i.e.151.1		2
84.11	even	6		147.2.a.c.1.1		1
84.23	even	6		21.2.e.a.16.1	yes	2
84.47	odd	6		147.2.e.a.79.1		2
84.59	odd	6		147.2.a.b.1.1		1
84.83	odd	2		147.2.e.a.67.1		2
168.11	even	6		9408.2.a.bg.1.1		1
168.53	odd	6		9408.2.a.cv.1.1		1
168.59	odd	6		9408.2.a.bz.1.1		1
168.101	even	6		9408.2.a.k.1.1		1
168.107	even	6		1344.2.q.m.961.1		2
168.149	odd	6		1344.2.q.c.961.1		2
252.23	even	6		567.2.g.a.541.1		2
252.79	odd	6		567.2.h.a.352.1		2
252.191	even	6		567.2.h.f.352.1		2
252.247	odd	6		567.2.g.f.541.1		2
420.23	odd	12		525.2.r.e.499.2		4
420.59	odd	6		3675.2.a.c.1.1		1
420.107	odd	12		525.2.r.e.499.1		4
420.179	even	6		3675.2.a.a.1.1		1
420.359	even	6		525.2.i.e.226.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.e.a.4.1	✓	2	12.11	even	2
21.2.e.a.16.1	yes	2	84.23	even	6
63.2.e.b.37.1		2	28.23	odd	6
63.2.e.b.46.1		2	4.3	odd	2
147.2.a.b.1.1		1	84.59	odd	6
147.2.a.c.1.1		1	84.11	even	6
147.2.e.a.67.1		2	84.83	odd	2
147.2.e.a.79.1		2	84.47	odd	6
336.2.q.f.193.1		2	3.2	odd	2
336.2.q.f.289.1		2	21.2	odd	6
441.2.a.a.1.1		1	28.3	even	6
441.2.a.b.1.1		1	28.11	odd	6
441.2.e.e.226.1		2	28.19	even	6
441.2.e.e.361.1		2	28.27	even	2
525.2.i.e.151.1		2	60.59	even	2
525.2.i.e.226.1		2	420.359	even	6
525.2.r.e.424.1		4	60.23	odd	4
525.2.r.e.424.2		4	60.47	odd	4
525.2.r.e.499.1		4	420.107	odd	12
525.2.r.e.499.2		4	420.23	odd	12
567.2.g.a.109.1		2	36.11	even	6
567.2.g.a.541.1		2	252.23	even	6
567.2.g.f.109.1		2	36.7	odd	6
567.2.g.f.541.1		2	252.247	odd	6
567.2.h.a.298.1		2	36.31	odd	6
567.2.h.a.352.1		2	252.79	odd	6
567.2.h.f.298.1		2	36.23	even	6
567.2.h.f.352.1		2	252.191	even	6
1008.2.s.d.289.1		2	7.2	even	3	inner
1008.2.s.d.865.1		2	1.1	even	1	trivial
1344.2.q.c.193.1		2	24.5	odd	2
1344.2.q.c.961.1		2	168.149	odd	6
1344.2.q.m.193.1		2	24.11	even	2
1344.2.q.m.961.1		2	168.107	even	6
2352.2.a.d.1.1		1	21.11	odd	6
2352.2.a.w.1.1		1	21.17	even	6
2352.2.q.c.961.1		2	21.5	even	6
2352.2.q.c.1537.1		2	21.20	even	2
3675.2.a.a.1.1		1	420.179	even	6
3675.2.a.c.1.1		1	420.59	odd	6
7056.2.a.m.1.1		1	7.3	odd	6
7056.2.a.bp.1.1		1	7.4	even	3
9408.2.a.k.1.1		1	168.101	even	6
9408.2.a.bg.1.1		1	168.11	even	6
9408.2.a.bz.1.1		1	168.59	odd	6
9408.2.a.cv.1.1		1	168.53	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{11} +1.00000 q^{13} +(0.500000 + 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{25} -4.00000 q^{29} +(4.50000 - 7.79423i) q^{31} +(-1.00000 - 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} +10.0000 q^{41} -5.00000 q^{43} +(3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-5.00000 - 8.66025i) q^{61} +(-1.00000 - 1.73205i) q^{65} +(-2.50000 + 4.33013i) q^{67} -6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} +(4.00000 - 3.46410i) q^{77} +(-0.500000 - 0.866025i) q^{79} +6.00000 q^{83} +(8.00000 + 13.8564i) q^{89} +(2.50000 + 0.866025i) q^{91} +(1.00000 - 1.73205i) q^{95} -6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} + 5 q^{7}+O(q^{10}) \) 2 * q - 2 * q^5 + 5 * q^7	\( 2 q - 2 q^{5} + 5 q^{7} + 2 q^{11} + 2 q^{13} + q^{19} + q^{25} - 8 q^{29} + 9 q^{31} - 2 q^{35} - 3 q^{37} + 20 q^{41} - 10 q^{43} + 6 q^{47} + 11 q^{49} + 12 q^{53} - 8 q^{55} + 12 q^{59} - 10 q^{61} - 2 q^{65} - 5 q^{67} - 12 q^{71} + 3 q^{73} + 8 q^{77} - q^{79} + 12 q^{83} + 16 q^{89} + 5 q^{91} + 2 q^{95} - 12 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 + 5 * q^7 + 2 * q^11 + 2 * q^13 + q^19 + q^25 - 8 * q^29 + 9 * q^31 - 2 * q^35 - 3 * q^37 + 20 * q^41 - 10 * q^43 + 6 * q^47 + 11 * q^49 + 12 * q^53 - 8 * q^55 + 12 * q^59 - 10 * q^61 - 2 * q^65 - 5 * q^67 - 12 * q^71 + 3 * q^73 + 8 * q^77 - q^79 + 12 * q^83 + 16 * q^89 + 5 * q^91 + 2 * q^95 - 12 * q^97

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