LMFDB - Embedded newform 2268.2.k.a.1297.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1297,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2268.1297");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.k (of order $3$, degree $2$, 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:	$18.1100711784$
Analytic rank:	$1$
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 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1297.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2268.1297
Dual form			2268.2.k.a.1621.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})$	$q+(-1.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-2.00000 - 3.46410i) q^{11} +3.00000 q^{13} +(-3.50000 - 6.06218i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{29} +(1.50000 + 2.59808i) q^{31} +(4.00000 + 3.46410i) q^{35} +(-5.50000 + 9.52628i) q^{37} -9.00000 q^{41} +5.00000 q^{43} +(-1.50000 + 2.59808i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-1.50000 - 2.59808i) q^{53} +8.00000 q^{55} +(3.50000 + 6.06218i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-3.00000 + 5.19615i) q^{65} +(-6.50000 - 11.2583i) q^{67} -8.00000 q^{71} +(-3.50000 - 6.06218i) q^{73} +(-10.0000 + 3.46410i) q^{77} +(4.50000 - 7.79423i) q^{79} +1.00000 q^{83} +14.0000 q^{85} +(-7.50000 + 12.9904i) q^{89} +(1.50000 - 7.79423i) q^{91} +(-5.00000 - 8.66025i) q^{95} -17.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5} + q^{7}+O(q^{10}) $ 2 * q - 2 * q^5 + q^7	$ 2 q - 2 q^{5} + q^{7} - 4 q^{11} + 6 q^{13} - 7 q^{17} - 5 q^{19} - 4 q^{23} + q^{25} - 2 q^{29} + 3 q^{31} + 8 q^{35} - 11 q^{37} - 18 q^{41} + 10 q^{43} - 3 q^{47} - 13 q^{49} - 3 q^{53} + 16 q^{55} + 7 q^{59} - 3 q^{61} - 6 q^{65} - 13 q^{67} - 16 q^{71} - 7 q^{73} - 20 q^{77} + 9 q^{79} + 2 q^{83} + 28 q^{85} - 15 q^{89} + 3 q^{91} - 10 q^{95} - 34 q^{97}+O(q^{100}) $ 2 * q - 2 * q^5 + q^7 - 4 * q^11 + 6 * q^13 - 7 * q^17 - 5 * q^19 - 4 * q^23 + q^25 - 2 * q^29 + 3 * q^31 + 8 * q^35 - 11 * q^37 - 18 * q^41 + 10 * q^43 - 3 * q^47 - 13 * q^49 - 3 * q^53 + 16 * q^55 + 7 * q^59 - 3 * q^61 - 6 * q^65 - 13 * q^67 - 16 * q^71 - 7 * q^73 - 20 * q^77 + 9 * q^79 + 2 * q^83 + 28 * q^85 - 15 * q^89 + 3 * q^91 - 10 * q^95 - 34 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	3.00000			0.832050			0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	0.0333386	−	0.999444i	$-0.489386\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	0.968709	−	0.248199i	$-0.0798387\pi$
$31$	1.50000	+	2.59808i	0.269408	+	0.466628i	−0.699301	+	0.714827i	$0.746505\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.00000	+	3.46410i	0.676123	+	0.585540i
$36$		0			0
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.0821995	+	0.996616i	$0.526194\pi$
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	0.998726	−	0.0504625i	$-0.0160695\pi$
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	−0.543065	+	0.839691i	$0.682736\pi$
$60$		0			0
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	−0.945931	−	0.324367i	$-0.894849\pi$
$61$	−1.50000	+	2.59808i	−0.192055	+	0.332650i	0.753876	+	0.657017i	$0.228182\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	−0.923408	−	0.383819i	$-0.874609\pi$
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	0.129307	−	0.991605i	$-0.458725\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.0000	+	3.46410i	−1.13961	+	0.394771i
$78$		0			0
$79$	4.50000	−	7.79423i	0.506290	−	0.876919i	−0.493684	−	0.869641i	$-0.664350\pi$
$79$	4.50000	−	7.79423i	0.506290	−	0.876919i	0.999974	−	0.00727784i	$-0.00231663\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.00000			0.109764			0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000			0.109764			0.0548821	+	0.998493i	$0.482522\pi$
$84$		0			0
$85$	14.0000			1.51851
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	0.127842	+	0.991795i	$0.459195\pi$
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	−0.922840	+	0.385183i	$0.874138\pi$
$90$		0			0
$91$	1.50000	−	7.79423i	0.157243	−	0.817057i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.00000	−	8.66025i	−0.512989	−	0.888523i
$96$		0			0
$97$	−17.0000			−1.72609			−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000			−1.72609			−0.863044	+	0.505128i	$0.831445\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	−0.784366	−	0.620298i	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$		0			0
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	0.648292	−	0.761392i	$-0.275484\pi$
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	−0.983531	+	0.180741i	$0.942150\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.00000			−0.0940721			−0.0470360	−	0.998893i	$-0.514978\pi$
$113$	−1.00000			−0.0940721			−0.0470360	+	0.998893i	$0.514978\pi$
$114$		0			0
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−17.5000	+	6.06218i	−1.60422	+	0.555719i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$	10.0000	+	8.66025i	0.867110	+	0.750939i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.00000	−	12.1244i	−0.598050	−	1.03585i	−0.993109	−	0.117198i	$-0.962609\pi$
$137$	−7.00000	−	12.1244i	−0.598050	−	1.03585i	0.395058	−	0.918656i	$-0.370724\pi$
$138$		0			0
$139$	−5.00000			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$		0			0
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.00000			−0.481932
$156$		0			0
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.00000	+	6.92820i	0.630488	+	0.546019i
$162$		0			0
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	−0.206518	−	0.978443i	$-0.566213\pi$
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	0.950615	−	0.310372i	$-0.100454\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	23.0000			1.77979			0.889897	−	0.456162i	$-0.150776\pi$
$167$	23.0000			1.77979			0.889897	+	0.456162i	$0.150776\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.500000	−	0.866025i	0.0380143	−	0.0658427i	−0.846392	−	0.532560i	$-0.821230\pi$
$173$	0.500000	−	0.866025i	0.0380143	−	0.0658427i	0.884407	+	0.466717i	$0.154563\pi$
$174$		0			0
$175$	2.50000	−	0.866025i	0.188982	−	0.0654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	0.929114	+	0.369792i	$0.120571\pi$
$179$	10.5000	+	18.1865i	0.784807	+	1.35933i	−0.144308	+	0.989533i	$0.546095\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−11.0000	−	19.0526i	−0.808736	−	1.40077i
$186$		0			0
$187$	−14.0000	+	24.2487i	−1.02378	+	1.77324i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$		0			0
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−26.0000			−1.85242			−0.926212	−	0.377004i	$-0.876954\pi$
$197$	−26.0000			−1.85242			−0.926212	+	0.377004i	$0.876954\pi$
$198$		0			0
$199$	6.50000	+	11.2583i	0.460773	+	0.798082i	0.999000	−	0.0447181i	$-0.0142390\pi$
$199$	6.50000	+	11.2583i	0.460773	+	0.798082i	−0.538227	+	0.842800i	$0.680906\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.500000	+	2.59808i	−0.0350931	+	0.182349i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	20.0000			1.38343
$210$		0			0
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$		0			0
$217$	7.50000	−	2.59808i	0.509133	−	0.176369i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−10.5000	−	18.1865i	−0.706306	−	1.22336i
$222$		0			0
$223$	−7.00000			−0.468755			−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000			−0.468755			−0.234377	+	0.972146i	$0.575305\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.5000	−	25.1147i	0.949927	−	1.64532i	0.204354	−	0.978897i	$-0.434491\pi$
$233$	14.5000	−	25.1147i	0.949927	−	1.64532i	0.745573	−	0.666424i	$-0.232176\pi$
$234$		0			0
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−21.0000			−1.35838			−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000			−1.35838			−0.679189	+	0.733964i	$0.737668\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.0000	−	8.66025i	0.702764	−	0.553283i
$246$		0			0
$247$	−7.50000	+	12.9904i	−0.477214	+	0.826558i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	16.0000			1.00591
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$	22.0000	+	19.0526i	1.36701	+	1.18387i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.500000	+	0.866025i	0.0304855	+	0.0528025i	0.880866	−	0.473366i	$-0.156961\pi$
$269$	0.500000	+	0.866025i	0.0304855	+	0.0528025i	−0.850380	+	0.526169i	$0.823628\pi$
$270$		0			0
$271$	1.50000	−	2.59808i	0.0911185	−	0.157822i	−0.816864	−	0.576831i	$-0.804289\pi$
$271$	1.50000	−	2.59808i	0.0911185	−	0.157822i	0.907982	+	0.419009i	$0.137622\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−17.0000			−1.01413			−0.507067	−	0.861906i	$-0.669271\pi$
$281$	−17.0000			−1.01413			−0.507067	+	0.861906i	$0.669271\pi$
$282$		0			0
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	0.850782	−	0.525519i	$-0.176129\pi$
$283$	−0.500000	−	0.866025i	−0.0297219	−	0.0514799i	−0.880504	+	0.474039i	$0.842796\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.50000	+	23.3827i	−0.265627	+	1.38024i
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	27.0000			1.57736			0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000			1.57736			0.788678	+	0.614806i	$0.210766\pi$
$294$		0			0
$295$	−14.0000			−0.815112
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$		0			0
$301$	2.50000	−	12.9904i	0.144098	−	0.748753i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.5000	+	26.8468i	0.878924	+	1.52234i	0.852523	+	0.522690i	$0.175072\pi$
$311$	15.5000	+	26.8468i	0.878924	+	1.52234i	0.0264017	+	0.999651i	$0.491595\pi$
$312$		0			0
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	−0.711535	−	0.702650i	$-0.752000\pi$
$317$	4.50000	−	7.79423i	0.252745	−	0.437767i	0.964281	+	0.264883i	$0.0853332\pi$
$318$		0			0
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	35.0000			1.94745
$324$		0			0
$325$	1.50000	+	2.59808i	0.0832050	+	0.144115i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.00000	+	5.19615i	0.330791	+	0.286473i
$330$		0			0
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	−0.285722	−	0.958313i	$-0.592233\pi$
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	0.972784	−	0.231714i	$-0.0744333\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	26.0000			1.42053
$336$		0			0
$337$	3.00000			0.163420			0.0817102	−	0.996656i	$-0.473962\pi$
$337$	3.00000			0.163420			0.0817102	+	0.996656i	$0.473962\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.50000	+	12.9904i	0.402621	+	0.697360i	0.994041	−	0.109003i	$-0.0347659\pi$
$347$	7.50000	+	12.9904i	0.402621	+	0.697360i	−0.591420	+	0.806363i	$0.701433\pi$
$348$		0			0
$349$	−5.00000			−0.267644			−0.133822	−	0.991005i	$-0.542725\pi$
$349$	−5.00000			−0.267644			−0.133822	+	0.991005i	$0.542725\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$		0			0
$355$	8.00000	−	13.8564i	0.424596	−	0.735422i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.5000	−	26.8468i	0.818059	−	1.41692i	−0.0890519	−	0.996027i	$-0.528384\pi$
$359$	15.5000	−	26.8468i	0.818059	−	1.41692i	0.907111	−	0.420892i	$-0.138283\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	14.0000			0.732793
$366$		0			0
$367$	−16.0000	−	27.7128i	−0.835193	−	1.44660i	−0.893873	−	0.448320i	$-0.852022\pi$
$367$	−16.0000	−	27.7128i	−0.835193	−	1.44660i	0.0586798	−	0.998277i	$-0.481311\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.50000	+	2.59808i	−0.389381	+	0.134885i
$372$		0			0
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	0.427051	+	0.904227i	$0.359552\pi$
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	−0.996610	+	0.0822766i	$0.973781\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.00000			−0.154508
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.00000	+	13.8564i	−0.408781	+	0.708029i	−0.994753	−	0.102302i	$-0.967379\pi$
$383$	−8.00000	+	13.8564i	−0.408781	+	0.708029i	0.585973	+	0.810331i	$0.300713\pi$
$384$		0			0
$385$	4.00000	−	20.7846i	0.203859	−	1.05928i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−13.0000	−	22.5167i	−0.659126	−	1.14164i	−0.980842	−	0.194804i	$-0.937593\pi$
$389$	−13.0000	−	22.5167i	−0.659126	−	1.14164i	0.321716	−	0.946836i	$-0.395740\pi$
$390$		0			0
$391$	28.0000			1.41602
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.00000	+	15.5885i	0.452839	+	0.784340i
$396$		0			0
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	−0.472526	−	0.881317i	$-0.656658\pi$
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	0.999506	−	0.0314391i	$-0.0100090\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$		0			0
$403$	4.50000	+	7.79423i	0.224161	+	0.388258i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	44.0000			2.18100
$408$		0			0
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	−0.996701	−	0.0811615i	$-0.974137\pi$
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	0.428063	−	0.903749i	$-0.359196\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	17.5000	−	6.06218i	0.861119	−	0.298300i
$414$		0			0
$415$	−1.00000	+	1.73205i	−0.0490881	+	0.0850230i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.0000			0.732798			0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000			0.732798			0.366399	+	0.930458i	$0.380591\pi$
$420$		0			0
$421$	−9.00000			−0.438633			−0.219317	−	0.975654i	$-0.570383\pi$
$421$	−9.00000			−0.438633			−0.219317	+	0.975654i	$0.570383\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.50000	−	6.06218i	0.169775	−	0.294059i
$426$		0			0
$427$	6.00000	+	5.19615i	0.290360	+	0.251459i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−19.5000	−	33.7750i	−0.939282	−	1.62688i	−0.766814	−	0.641869i	$-0.778159\pi$
$431$	−19.5000	−	33.7750i	−0.939282	−	1.62688i	−0.172468	−	0.985015i	$-0.555174\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.0000	−	17.3205i	−0.478365	−	0.828552i
$438$		0			0
$439$	10.5000	−	18.1865i	0.501138	−	0.867996i	−0.498861	−	0.866682i	$-0.666248\pi$
$439$	10.5000	−	18.1865i	0.501138	−	0.867996i	0.999999	−	0.00131415i	$-0.000418308\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.5000	−	25.1147i	0.688916	−	1.19324i	−0.283273	−	0.959039i	$-0.591420\pi$
$443$	14.5000	−	25.1147i	0.688916	−	1.19324i	0.972189	−	0.234198i	$-0.0752464\pi$
$444$		0			0
$445$	−15.0000	−	25.9808i	−0.711068	−	1.23161i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$		0			0
$451$	18.0000	+	31.1769i	0.847587	+	1.46806i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	12.0000	+	10.3923i	0.562569	+	0.487199i
$456$		0			0
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	0.233890	+	0.972263i	$0.424854\pi$
$457$	−15.5000	+	26.8468i	−0.725059	+	1.25584i	−0.958950	+	0.283577i	$0.908479\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	23.0000			1.07122			0.535608	−	0.844466i	$-0.320082\pi$
$461$	23.0000			1.07122			0.535608	+	0.844466i	$0.320082\pi$
$462$		0			0
$463$	−5.00000			−0.232370			−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000			−0.232370			−0.116185	+	0.993228i	$0.537067\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.50000	+	14.7224i	−0.393333	+	0.681273i	−0.992887	−	0.119062i	$-0.962011\pi$
$467$	−8.50000	+	14.7224i	−0.393333	+	0.681273i	0.599554	+	0.800334i	$0.295345\pi$
$468$		0			0
$469$	−32.5000	+	11.2583i	−1.50071	+	0.519861i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.0000	−	17.3205i	−0.459800	−	0.796398i
$474$		0			0
$475$	−5.00000			−0.229416
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	0.942821	−	0.333300i	$-0.108162\pi$
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	−0.760056	+	0.649857i	$0.774829\pi$
$480$		0			0
$481$	−16.5000	+	28.5788i	−0.752335	+	1.30308i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	17.0000	−	29.4449i	0.771930	−	1.33702i
$486$		0			0
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	0.877132	−	0.480250i	$-0.159454\pi$
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	−0.854475	+	0.519493i	$0.826121\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.00000			−0.406164			−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000			−0.406164			−0.203082	+	0.979162i	$0.565096\pi$
$492$		0			0
$493$	3.50000	+	6.06218i	0.157632	+	0.273027i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.00000	+	20.7846i	−0.179425	+	0.932317i
$498$		0			0
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	4.00000			0.177998
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	−17.5000	+	6.06218i	−0.774154	+	0.268175i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$		0			0
$517$	12.0000			0.527759
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$		0			0
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.5000	−	18.1865i	0.457387	−	0.792218i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−27.0000			−1.16950
$534$		0			0
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.00000	+	27.7128i	0.172292	+	1.19368i
$540$		0			0
$541$	16.5000	−	28.5788i	0.709390	−	1.22870i	−0.255693	−	0.966758i	$-0.582304\pi$
$541$	16.5000	−	28.5788i	0.709390	−	1.22870i	0.965084	−	0.261942i	$-0.0843630\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14.0000			0.599694
$546$		0			0
$547$	33.0000			1.41098			0.705489	−	0.708721i	$-0.250727\pi$
$547$	33.0000			1.41098			0.705489	+	0.708721i	$0.250727\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.50000	−	4.33013i	0.106504	−	0.184470i
$552$		0			0
$553$	−18.0000	−	15.5885i	−0.765438	−	0.662889i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.50000	−	9.52628i	−0.233042	−	0.403641i	0.725660	−	0.688054i	$-0.241535\pi$
$557$	−5.50000	−	9.52628i	−0.233042	−	0.403641i	−0.958702	+	0.284413i	$0.908201\pi$
$558$		0			0
$559$	15.0000			0.634432
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.50000	−	11.2583i	−0.273942	−	0.474482i	0.695925	−	0.718114i	$-0.254994\pi$
$563$	−6.50000	−	11.2583i	−0.273942	−	0.474482i	−0.969868	+	0.243632i	$0.921661\pi$
$564$		0			0
$565$	1.00000	−	1.73205i	0.0420703	−	0.0728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.5000	+	23.3827i	−0.565949	+	0.980253i	0.431011	+	0.902347i	$0.358157\pi$
$569$	−13.5000	+	23.3827i	−0.565949	+	0.980253i	−0.996961	+	0.0779066i	$0.975176\pi$
$570$		0			0
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	0.895704	−	0.444651i	$-0.146672\pi$
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	−0.832931	+	0.553377i	$0.813339\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	0.783930	−	0.620850i	$-0.213212\pi$
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	−0.929636	+	0.368478i	$0.879879\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.500000	−	2.59808i	0.0207435	−	0.107786i
$582$		0			0
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	37.0000			1.52715			0.763577	−	0.645717i	$-0.223441\pi$
$587$	37.0000			1.52715			0.763577	+	0.645717i	$0.223441\pi$
$588$		0			0
$589$	−15.0000			−0.618064
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−13.5000	+	23.3827i	−0.554379	+	0.960212i	0.443573	+	0.896238i	$0.353711\pi$
$593$	−13.5000	+	23.3827i	−0.554379	+	0.960212i	−0.997952	+	0.0639736i	$0.979623\pi$
$594$		0			0
$595$	7.00000	−	36.3731i	0.286972	−	1.49115i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.50000	+	2.59808i	0.0612883	+	0.106155i	0.895042	−	0.445983i	$-0.147146\pi$
$599$	1.50000	+	2.59808i	0.0612883	+	0.106155i	−0.833753	+	0.552137i	$0.813812\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	24.0000	−	41.5692i	0.974130	−	1.68724i	0.291353	−	0.956616i	$-0.405895\pi$
$607$	24.0000	−	41.5692i	0.974130	−	1.68724i	0.682777	−	0.730627i	$-0.260772\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.50000	+	7.79423i	−0.182051	+	0.315321i
$612$		0			0
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	0.942478	−	0.334269i	$-0.108489\pi$
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	−0.760724	+	0.649075i	$0.775156\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	43.0000			1.73111			0.865557	−	0.500810i	$-0.166964\pi$
$617$	43.0000			1.73111			0.865557	+	0.500810i	$0.166964\pi$
$618$		0			0
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	30.0000	+	25.9808i	1.20192	+	1.04090i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	77.0000			3.07019
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−19.5000	−	7.79423i	−0.772618	−	0.308819i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	0.885098	−	0.465404i	$-0.154091\pi$
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	−0.845601	+	0.533816i	$0.820758\pi$
$642$		0			0
$643$	−13.0000			−0.512670			−0.256335	−	0.966588i	$-0.582515\pi$
$643$	−13.0000			−0.512670			−0.256335	+	0.966588i	$0.582515\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	0.835033	−	0.550200i	$-0.185449\pi$
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	−0.894004	+	0.448059i	$0.852115\pi$
$648$		0			0
$649$	14.0000	−	24.2487i	0.549548	−	0.951845i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$		0			0
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	25.0000			0.973862			0.486931	−	0.873441i	$-0.338116\pi$
$659$	25.0000			0.973862			0.486931	+	0.873441i	$0.338116\pi$
$660$		0			0
$661$	8.50000	+	14.7224i	0.330612	+	0.572636i	0.982632	−	0.185565i	$-0.0594116\pi$
$661$	8.50000	+	14.7224i	0.330612	+	0.572636i	−0.652020	+	0.758202i	$0.726078\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−25.0000	+	8.66025i	−0.969458	+	0.335830i
$666$		0			0
$667$	2.00000	−	3.46410i	0.0774403	−	0.134131i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	12.0000			0.463255
$672$		0			0
$673$	−25.0000			−0.963679			−0.481840	−	0.876259i	$-0.660031\pi$
$673$	−25.0000			−0.963679			−0.481840	+	0.876259i	$0.660031\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	0.480913	+	0.876768i	$0.340305\pi$
$677$	−13.5000	+	23.3827i	−0.518847	+	0.898670i	−0.999760	+	0.0219013i	$0.993028\pi$
$678$		0			0
$679$	−8.50000	+	44.1673i	−0.326200	+	1.69499i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	0.993940	−	0.109926i	$-0.0350613\pi$
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	−0.592168	+	0.805814i	$0.701728\pi$
$684$		0			0
$685$	28.0000			1.06983
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.50000	−	7.79423i	−0.171436	−	0.296936i
$690$		0			0
$691$	−5.50000	+	9.52628i	−0.209230	+	0.362397i	−0.951472	−	0.307735i	$-0.900429\pi$
$691$	−5.50000	+	9.52628i	−0.209230	+	0.362397i	0.742242	+	0.670132i	$0.233762\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.00000	−	8.66025i	0.189661	−	0.328502i
$696$		0			0
$697$	31.5000	+	54.5596i	1.19315	+	2.06659i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−22.0000			−0.830929			−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000			−0.830929			−0.415464	+	0.909610i	$0.636381\pi$
$702$		0			0
$703$	−27.5000	−	47.6314i	−1.03718	−	1.79645i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.00000	+	1.73205i	−0.188044	+	0.0651405i
$708$		0			0
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	−0.529943	−	0.848034i	$-0.677787\pi$
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	0.999390	+	0.0349269i	$0.0111198\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−12.0000			−0.449404
$714$		0			0
$715$	24.0000			0.897549
$716$		0			0
$717$		0			0
$718$		0			0
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$		0			0
$721$	16.0000	+	13.8564i	0.595871	+	0.516040i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.500000	−	0.866025i	−0.0185695	−	0.0321634i
$726$		0			0
$727$	−47.0000			−1.74313			−0.871567	−	0.490277i	$-0.836896\pi$
$727$	−47.0000			−1.74313			−0.871567	+	0.490277i	$0.836896\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−17.5000	−	30.3109i	−0.647261	−	1.12109i
$732$		0			0
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	0.443940	+	0.896056i	$0.353580\pi$
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	−0.997978	+	0.0635649i	$0.979753\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−26.0000	+	45.0333i	−0.957722	+	1.65882i
$738$		0			0
$739$	10.5000	+	18.1865i	0.386249	+	0.669002i	0.991942	−	0.126696i	$-0.0404373\pi$
$739$	10.5000	+	18.1865i	0.386249	+	0.669002i	−0.605693	+	0.795699i	$0.707104\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$		0			0
$745$	6.00000	+	10.3923i	0.219823	+	0.380745i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$		0			0
$751$	12.0000	−	20.7846i	0.437886	−	0.758441i	−0.559640	−	0.828736i	$-0.689061\pi$
$751$	12.0000	−	20.7846i	0.437886	−	0.758441i	0.997526	+	0.0702946i	$0.0223939\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.00000	−	1.73205i	0.0362500	−	0.0627868i	−0.847331	−	0.531065i	$-0.821792\pi$
$761$	1.00000	−	1.73205i	0.0362500	−	0.0627868i	0.883581	+	0.468278i	$0.155125\pi$
$762$		0			0
$763$	−17.5000	+	6.06218i	−0.633543	+	0.219466i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.5000	+	18.1865i	0.379133	+	0.656678i
$768$		0			0
$769$	−5.00000			−0.180305			−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000			−0.180305			−0.0901523	+	0.995928i	$0.528735\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−11.5000	−	19.9186i	−0.413626	−	0.716422i	0.581657	−	0.813434i	$-0.302405\pi$
$773$	−11.5000	−	19.9186i	−0.413626	−	0.716422i	−0.995283	+	0.0970125i	$0.969071\pi$
$774$		0			0
$775$	−1.50000	+	2.59808i	−0.0538816	+	0.0933257i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	22.5000	−	38.9711i	0.806146	−	1.39629i
$780$		0			0
$781$	16.0000	+	27.7128i	0.572525	+	0.991642i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−26.0000			−0.927980
$786$		0			0
$787$	−10.5000	−	18.1865i	−0.374285	−	0.648280i	0.615935	−	0.787797i	$-0.288778\pi$
$787$	−10.5000	−	18.1865i	−0.374285	−	0.648280i	−0.990220	+	0.139517i	$0.955445\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.500000	+	2.59808i	−0.0177780	+	0.0923770i
$792$		0			0
$793$	−4.50000	+	7.79423i	−0.159800	+	0.276781i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.0000			0.531327			0.265664	−	0.964066i	$-0.414409\pi$
$797$	15.0000			0.531327			0.265664	+	0.964066i	$0.414409\pi$
$798$		0			0
$799$	21.0000			0.742927
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−14.0000	+	24.2487i	−0.494049	+	0.855718i
$804$		0			0
$805$	−20.0000	+	6.92820i	−0.704907	+	0.244187i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.500000	+	0.866025i	0.0175791	+	0.0304478i	0.874681	−	0.484699i	$-0.161071\pi$
$809$	0.500000	+	0.866025i	0.0175791	+	0.0304478i	−0.857102	+	0.515147i	$0.827737\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	19.0000	+	32.9090i	0.665541	+	1.15275i
$816$		0			0
$817$	−12.5000	+	21.6506i	−0.437320	+	0.757460i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	26.5000	−	45.8993i	0.924856	−	1.60190i	0.133064	−	0.991107i	$-0.457518\pi$
$821$	26.5000	−	45.8993i	0.924856	−	1.60190i	0.791792	−	0.610791i	$-0.209148\pi$
$822$		0			0
$823$	11.5000	+	19.9186i	0.400865	+	0.694318i	0.993831	−	0.110910i	$-0.0353764\pi$
$823$	11.5000	+	19.9186i	0.400865	+	0.694318i	−0.592966	+	0.805228i	$0.702043\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−9.50000	−	16.4545i	−0.329949	−	0.571488i	0.652553	−	0.757743i	$-0.273698\pi$
$829$	−9.50000	−	16.4545i	−0.329949	−	0.571488i	−0.982501	+	0.186256i	$0.940365\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7.00000	+	48.4974i	0.242536	+	1.68034i
$834$		0			0
$835$	−23.0000	+	39.8372i	−0.795948	+	1.37862i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−23.0000			−0.794048			−0.397024	−	0.917808i	$-0.629957\pi$
$839$	−23.0000			−0.794048			−0.397024	+	0.917808i	$0.629957\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.00000	−	6.92820i	0.137604	−	0.238337i
$846$		0			0
$847$	10.0000	+	8.66025i	0.343604	+	0.297570i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−22.0000	−	38.1051i	−0.754150	−	1.30623i
$852$		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
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	−22.0000	+	38.1051i	−0.750630	+	1.30013i	0.196887	+	0.980426i	$0.436917\pi$
$859$	−22.0000	+	38.1051i	−0.750630	+	1.30013i	−0.947518	+	0.319704i	$0.896417\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−20.5000	+	35.5070i	−0.697828	+	1.20867i	0.271390	+	0.962470i	$0.412517\pi$
$863$	−20.5000	+	35.5070i	−0.697828	+	1.20867i	−0.969218	+	0.246204i	$0.920817\pi$
$864$		0			0
$865$	1.00000	+	1.73205i	0.0340010	+	0.0588915i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−36.0000			−1.22122
$870$		0			0
$871$	−19.5000	−	33.7750i	−0.660732	−	1.14442i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.00000	+	31.1769i	−0.202837	+	1.05397i
$876$		0			0
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	−0.343495	−	0.939155i	$-0.611611\pi$
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	0.985079	−	0.172102i	$-0.0550559\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	−0.948999	−	0.315279i	$-0.897902\pi$
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	0.747539	+	0.664218i	$0.231235\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.50000	−	12.9904i	−0.250978	−	0.434707i
$894$		0			0
$895$	−42.0000			−1.40391
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.50000	−	2.59808i	−0.0500278	−	0.0866507i
$900$		0			0
$901$	−10.5000	+	18.1865i	−0.349806	+	0.605881i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.00000	−	10.3923i	0.199447	−	0.345452i
$906$		0			0
$907$	−18.0000	−	31.1769i	−0.597680	−	1.03521i	−0.993163	−	0.116739i	$-0.962756\pi$
$907$	−18.0000	−	31.1769i	−0.597680	−	1.03521i	0.395482	−	0.918474i	$-0.370577\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−39.0000			−1.29213			−0.646064	−	0.763283i	$-0.723586\pi$
$911$	−39.0000			−1.29213			−0.646064	+	0.763283i	$0.723586\pi$
$912$		0			0
$913$	−2.00000	−	3.46410i	−0.0661903	−	0.114645i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.00000	−	6.92820i	−0.264183	−	0.228789i
$918$		0			0
$919$	17.5000	−	30.3109i	0.577272	−	0.999864i	−0.418519	−	0.908208i	$-0.637451\pi$
$919$	17.5000	−	30.3109i	0.577272	−	0.999864i	0.995791	−	0.0916559i	$-0.0292160\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−24.0000			−0.789970
$924$		0			0
$925$	−11.0000			−0.361678
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.50000	+	2.59808i	−0.0492134	+	0.0852401i	−0.889583	−	0.456774i	$-0.849005\pi$
$929$	−1.50000	+	2.59808i	−0.0492134	+	0.0852401i	0.840369	+	0.542014i	$0.182338\pi$
$930$		0			0
$931$	27.5000	−	21.6506i	0.901276	−	0.709571i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−28.0000	−	48.4974i	−0.915698	−	1.58604i
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−29.5000	−	51.0955i	−0.961673	−	1.66567i	−0.718301	−	0.695733i	$-0.755080\pi$
$941$	−29.5000	−	51.0955i	−0.961673	−	1.66567i	−0.243372	−	0.969933i	$-0.578253\pi$
$942$		0			0
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.5000	−	21.6506i	0.406195	−	0.703551i	−0.588264	−	0.808669i	$-0.700189\pi$
$947$	12.5000	−	21.6506i	0.406195	−	0.703551i	0.994460	+	0.105118i	$0.0335219\pi$
$948$		0			0
$949$	−10.5000	−	18.1865i	−0.340844	−	0.590360i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	−15.0000	−	25.9808i	−0.485389	−	0.840718i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−35.0000	+	12.1244i	−1.13021	+	0.391516i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.00000			−0.0643823
$966$		0			0
$967$	47.0000			1.51142			0.755709	−	0.654907i	$-0.227292\pi$
$967$	47.0000			1.51142			0.755709	+	0.654907i	$0.227292\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$		0			0
$973$	−2.50000	+	12.9904i	−0.0801463	+	0.416452i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	0.841033	−	0.540984i	$-0.181948\pi$
$977$	−1.50000	−	2.59808i	−0.0479893	−	0.0831198i	−0.889022	+	0.457864i	$0.848615\pi$
$978$		0			0
$979$	60.0000			1.91761
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$		0			0
$985$	26.0000	−	45.0333i	0.828429	−	1.43488i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−10.0000	+	17.3205i	−0.317982	+	0.550760i
$990$		0			0
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	0.994537	+	0.104389i	$0.0332887\pi$
$991$	18.5000	+	32.0429i	0.587672	+	1.01788i	−0.406865	+	0.913488i	$0.633378\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−26.0000			−0.824255
$996$		0			0
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	0.985961	−	0.166978i	$-0.0534008\pi$
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	−0.637587	+	0.770378i	$0.720067\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.k.a.1297.1		2
3.2	odd	2		2268.2.k.b.1297.1		2
7.4	even	3	inner	2268.2.k.a.1621.1		2
9.2	odd	6		756.2.i.a.37.1		2
9.4	even	3		252.2.l.a.205.1	yes	2
9.5	odd	6		756.2.l.a.289.1		2
9.7	even	3		252.2.i.a.121.1	yes	2
21.11	odd	6		2268.2.k.b.1621.1		2
36.7	odd	6		1008.2.q.f.625.1		2
36.11	even	6		3024.2.q.e.2305.1		2
36.23	even	6		3024.2.t.b.289.1		2
36.31	odd	6		1008.2.t.b.961.1		2
63.2	odd	6		5292.2.j.c.1765.1		2
63.4	even	3		252.2.i.a.25.1	✓	2
63.5	even	6		5292.2.j.b.3529.1		2
63.11	odd	6		756.2.l.a.361.1		2
63.13	odd	6		1764.2.l.b.961.1		2
63.16	even	3		1764.2.j.c.589.1		2
63.20	even	6		5292.2.i.b.1549.1		2
63.23	odd	6		5292.2.j.c.3529.1		2
63.25	even	3		252.2.l.a.193.1	yes	2
63.31	odd	6		1764.2.i.b.1537.1		2
63.32	odd	6		756.2.i.a.613.1		2
63.34	odd	6		1764.2.i.b.373.1		2
63.38	even	6		5292.2.l.b.361.1		2
63.40	odd	6		1764.2.j.a.1177.1		2
63.41	even	6		5292.2.l.b.3313.1		2
63.47	even	6		5292.2.j.b.1765.1		2
63.52	odd	6		1764.2.l.b.949.1		2
63.58	even	3		1764.2.j.c.1177.1		2
63.59	even	6		5292.2.i.b.2125.1		2
63.61	odd	6		1764.2.j.a.589.1		2
252.11	even	6		3024.2.t.b.1873.1		2
252.67	odd	6		1008.2.q.f.529.1		2
252.95	even	6		3024.2.q.e.2881.1		2
252.151	odd	6		1008.2.t.b.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.a.25.1	✓	2	63.4	even	3
252.2.i.a.121.1	yes	2	9.7	even	3
252.2.l.a.193.1	yes	2	63.25	even	3
252.2.l.a.205.1	yes	2	9.4	even	3
756.2.i.a.37.1		2	9.2	odd	6
756.2.i.a.613.1		2	63.32	odd	6
756.2.l.a.289.1		2	9.5	odd	6
756.2.l.a.361.1		2	63.11	odd	6
1008.2.q.f.529.1		2	252.67	odd	6
1008.2.q.f.625.1		2	36.7	odd	6
1008.2.t.b.193.1		2	252.151	odd	6
1008.2.t.b.961.1		2	36.31	odd	6
1764.2.i.b.373.1		2	63.34	odd	6
1764.2.i.b.1537.1		2	63.31	odd	6
1764.2.j.a.589.1		2	63.61	odd	6
1764.2.j.a.1177.1		2	63.40	odd	6
1764.2.j.c.589.1		2	63.16	even	3
1764.2.j.c.1177.1		2	63.58	even	3
1764.2.l.b.949.1		2	63.52	odd	6
1764.2.l.b.961.1		2	63.13	odd	6
2268.2.k.a.1297.1		2	1.1	even	1	trivial
2268.2.k.a.1621.1		2	7.4	even	3	inner
2268.2.k.b.1297.1		2	3.2	odd	2
2268.2.k.b.1621.1		2	21.11	odd	6
3024.2.q.e.2305.1		2	36.11	even	6
3024.2.q.e.2881.1		2	252.95	even	6
3024.2.t.b.289.1		2	36.23	even	6
3024.2.t.b.1873.1		2	252.11	even	6
5292.2.i.b.1549.1		2	63.20	even	6
5292.2.i.b.2125.1		2	63.59	even	6
5292.2.j.b.1765.1		2	63.47	even	6
5292.2.j.b.3529.1		2	63.5	even	6
5292.2.j.c.1765.1		2	63.2	odd	6
5292.2.j.c.3529.1		2	63.23	odd	6
5292.2.l.b.361.1		2	63.38	even	6
5292.2.l.b.3313.1		2	63.41	even	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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-2.00000 - 3.46410i) q^{11} +3.00000 q^{13} +(-3.50000 - 6.06218i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{29} +(1.50000 + 2.59808i) q^{31} +(4.00000 + 3.46410i) q^{35} +(-5.50000 + 9.52628i) q^{37} -9.00000 q^{41} +5.00000 q^{43} +(-1.50000 + 2.59808i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-1.50000 - 2.59808i) q^{53} +8.00000 q^{55} +(3.50000 + 6.06218i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(-3.00000 + 5.19615i) q^{65} +(-6.50000 - 11.2583i) q^{67} -8.00000 q^{71} +(-3.50000 - 6.06218i) q^{73} +(-10.0000 + 3.46410i) q^{77} +(4.50000 - 7.79423i) q^{79} +1.00000 q^{83} +14.0000 q^{85} +(-7.50000 + 12.9904i) q^{89} +(1.50000 - 7.79423i) q^{91} +(-5.00000 - 8.66025i) q^{95} -17.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5} + q^{7}+O(q^{10}) \) 2 * q - 2 * q^5 + q^7	\( 2 q - 2 q^{5} + q^{7} - 4 q^{11} + 6 q^{13} - 7 q^{17} - 5 q^{19} - 4 q^{23} + q^{25} - 2 q^{29} + 3 q^{31} + 8 q^{35} - 11 q^{37} - 18 q^{41} + 10 q^{43} - 3 q^{47} - 13 q^{49} - 3 q^{53} + 16 q^{55} + 7 q^{59} - 3 q^{61} - 6 q^{65} - 13 q^{67} - 16 q^{71} - 7 q^{73} - 20 q^{77} + 9 q^{79} + 2 q^{83} + 28 q^{85} - 15 q^{89} + 3 q^{91} - 10 q^{95} - 34 q^{97}+O(q^{100}) \) 2 * q - 2 * q^5 + q^7 - 4 * q^11 + 6 * q^13 - 7 * q^17 - 5 * q^19 - 4 * q^23 + q^25 - 2 * q^29 + 3 * q^31 + 8 * q^35 - 11 * q^37 - 18 * q^41 + 10 * q^43 - 3 * q^47 - 13 * q^49 - 3 * q^53 + 16 * q^55 + 7 * q^59 - 3 * q^61 - 6 * q^65 - 13 * q^67 - 16 * q^71 - 7 * q^73 - 20 * q^77 + 9 * q^79 + 2 * q^83 + 28 * q^85 - 15 * q^89 + 3 * q^91 - 10 * q^95 - 34 * q^97

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