LMFDB - Embedded newform 2268.2.l.g.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(109,2268)]

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, 2, 4]))

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

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

chi := DirichletCharacter("2268.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.l (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:	$18.1100711784$
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 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2268.541
Dual form			2268.2.l.g.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})$	$q+2.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} -2.00000 q^{11} +(1.50000 + 2.59808i) q^{13} +(4.00000 + 6.92820i) q^{17} +(0.500000 - 0.866025i) q^{19} -8.00000 q^{23} -1.00000 q^{25} +(2.00000 - 3.46410i) q^{29} +(-1.50000 + 2.59808i) q^{31} +(-5.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{37} +(3.00000 + 5.19615i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +(2.00000 - 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} +(3.00000 + 5.19615i) q^{65} +(-6.50000 + 11.2583i) q^{67} +10.0000 q^{71} +(5.50000 + 9.52628i) q^{73} +(5.00000 + 1.73205i) q^{77} +(1.50000 + 2.59808i) q^{79} +(1.00000 - 1.73205i) q^{83} +(8.00000 + 13.8564i) q^{85} +(-1.50000 - 7.79423i) q^{91} +(1.00000 - 1.73205i) q^{95} +(-5.00000 + 8.66025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{5} - 5 q^{7}+O(q^{10}) $ 2 * q + 4 * q^5 - 5 * q^7	$ 2 q + 4 q^{5} - 5 q^{7} - 4 q^{11} + 3 q^{13} + 8 q^{17} + q^{19} - 16 q^{23} - 2 q^{25} + 4 q^{29} - 3 q^{31} - 10 q^{35} + q^{37} + 6 q^{41} - 11 q^{43} + 6 q^{47} + 11 q^{49} - 12 q^{53} - 8 q^{55} + 4 q^{59} + 6 q^{61} + 6 q^{65} - 13 q^{67} + 20 q^{71} + 11 q^{73} + 10 q^{77} + 3 q^{79} + 2 q^{83} + 16 q^{85} - 3 q^{91} + 2 q^{95} - 10 q^{97}+O(q^{100}) $ 2 * q + 4 * q^5 - 5 * q^7 - 4 * q^11 + 3 * q^13 + 8 * q^17 + q^19 - 16 * q^23 - 2 * q^25 + 4 * q^29 - 3 * q^31 - 10 * q^35 + q^37 + 6 * q^41 - 11 * q^43 + 6 * q^47 + 11 * q^49 - 12 * q^53 - 8 * q^55 + 4 * q^59 + 6 * q^61 + 6 * q^65 - 13 * q^67 + 20 * q^71 + 11 * q^73 + 10 * q^77 + 3 * q^79 + 2 * q^83 + 16 * q^85 - 3 * q^91 + 2 * q^95 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		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
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	0.995535	−	0.0943882i	$-0.0300895\pi$
$13$	1.50000	+	2.59808i	0.416025	+	0.720577i	−0.579510	+	0.814965i	$0.696756\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.00000	+	6.92820i	0.970143	+	1.68034i	0.695113	+	0.718900i	$0.255354\pi$
$17$	4.00000	+	6.92820i	0.970143	+	1.68034i	0.275029	+	0.961436i	$0.411312\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$		0			0
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.00000	−	1.73205i	−0.845154	−	0.292770i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$		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	−0.902557	−	0.430570i	$-0.858312\pi$
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	0.0783936	−	0.996922i	$-0.475021\pi$
$54$		0			0
$55$	−4.00000			−0.539360
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$		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	0.129307	+	0.991605i	$0.458725\pi$
$67$	−6.50000	+	11.2583i	−0.794101	+	1.37542i	−0.923408	+	0.383819i	$0.874609\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	10.0000			1.18678			0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000			1.18678			0.593391	+	0.804914i	$0.297789\pi$
$72$		0			0
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.00000	+	1.73205i	0.569803	+	0.197386i
$78$		0			0
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.00000	−	1.73205i	0.109764	−	0.190117i	−0.805910	−	0.592037i	$-0.798324\pi$
$83$	1.00000	−	1.73205i	0.109764	−	0.190117i	0.915675	+	0.401920i	$0.131657\pi$
$84$		0			0
$85$	8.00000	+	13.8564i	0.867722	+	1.50294i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−1.50000	−	7.79423i	−0.157243	−	0.817057i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$		0			0
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	0.492287	+	0.870433i	$0.336161\pi$
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	−0.999961	+	0.00888289i	$0.997172\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$		0			0
$103$	11.0000			1.08386			0.541931	−	0.840423i	$-0.317693\pi$
$103$	11.0000			1.08386			0.541931	+	0.840423i	$0.317693\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	0.999512	+	0.0312328i	$0.00994332\pi$
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	−0.472708	+	0.881219i	$0.656723\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	−0.981003	−	0.193993i	$-0.937856\pi$
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	0.322498	−	0.946570i	$-0.395477\pi$
$114$		0			0
$115$	−16.0000			−1.49201
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.00000	−	20.7846i	−0.366679	−	1.90532i
$120$		0			0
$121$	−7.00000			−0.636364
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	3.00000			0.266207			0.133103	−	0.991102i	$-0.457506\pi$
$127$	3.00000			0.266207			0.133103	+	0.991102i	$0.457506\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.00000			0.174741			0.0873704	−	0.996176i	$-0.472154\pi$
$131$	2.00000			0.174741			0.0873704	+	0.996176i	$0.472154\pi$
$132$		0			0
$133$	−2.00000	+	1.73205i	−0.173422	+	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.00000			−0.341743			−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000			−0.341743			−0.170872	+	0.985293i	$0.554658\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$		0			0
$145$	4.00000	−	6.92820i	0.332182	−	0.575356i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	20.0000	+	6.92820i	1.57622	+	0.546019i
$162$		0			0
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	0.824737	−	0.565516i	$-0.191323\pi$
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	−0.902120	+	0.431486i	$0.857990\pi$
$168$		0			0
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.00000	+	13.8564i	0.608229	+	1.05348i	0.991532	+	0.129861i	$0.0414530\pi$
$173$	8.00000	+	13.8564i	0.608229	+	1.05348i	−0.383304	+	0.923622i	$0.625214\pi$
$174$		0			0
$175$	2.50000	+	0.866025i	0.188982	+	0.0654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$		0			0
$181$	−15.0000			−1.11494			−0.557471	−	0.830197i	$-0.688228\pi$
$181$	−15.0000			−1.11494			−0.557471	+	0.830197i	$0.688228\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$		0			0
$187$	−8.00000	−	13.8564i	−0.585018	−	1.01328i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		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
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$		0			0
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.00000	+	6.92820i	−0.561490	+	0.486265i
$204$		0			0
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.00000	+	1.73205i	−0.0691714	+	0.119808i
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.0000	+	19.0526i	−0.750194	+	1.29937i
$216$		0			0
$217$	6.00000	−	5.19615i	0.407307	−	0.352738i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−12.0000	+	20.7846i	−0.807207	+	1.39812i
$222$		0			0
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	−0.968309	−	0.249756i	$-0.919650\pi$
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	0.700449	+	0.713702i	$0.252983\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.0000			1.19470			0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000			1.19470			0.597351	+	0.801980i	$0.296220\pi$
$228$		0			0
$229$	1.00000			0.0660819			0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000			0.0660819			0.0330409	+	0.999454i	$0.489481\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	−0.540301	−	0.841472i	$-0.681690\pi$
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	0.998886	+	0.0471787i	$0.0150230\pi$
$234$		0			0
$235$	6.00000	+	10.3923i	0.391397	+	0.677919i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.00000	+	15.5885i	0.582162	+	1.00833i	0.995223	+	0.0976302i	$0.0311262\pi$
$239$	9.00000	+	15.5885i	0.582162	+	1.00833i	−0.413061	+	0.910703i	$0.635540\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.0000	+	8.66025i	0.702764	+	0.553283i
$246$		0			0
$247$	3.00000			0.190885
$248$		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
$257$	−18.0000			−1.12281			−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000			−1.12281			−0.561405	+	0.827541i	$0.689739\pi$
$258$		0			0
$259$	−2.00000	+	1.73205i	−0.124274	+	0.107624i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$		0			0
$265$	−12.0000	−	20.7846i	−0.737154	−	1.27679i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.00000	−	1.73205i	−0.0609711	−	0.105605i	0.833929	−	0.551872i	$-0.186086\pi$
$269$	−1.00000	−	1.73205i	−0.0609711	−	0.105605i	−0.894900	+	0.446267i	$0.852753\pi$
$270$		0			0
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.00000			0.120605
$276$		0			0
$277$	17.0000			1.02143			0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000			1.02143			0.510716	+	0.859750i	$0.329381\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.0000	−	17.3205i	0.596550	−	1.03325i	−0.396776	−	0.917915i	$-0.629871\pi$
$281$	10.0000	−	17.3205i	0.596550	−	1.03325i	0.993326	−	0.115339i	$-0.0367956\pi$
$282$		0			0
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	0.432360	+	0.901701i	$0.357681\pi$
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	−0.997076	+	0.0764162i	$0.975652\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.00000	−	15.5885i	−0.177084	−	0.920158i
$288$		0			0
$289$	−23.5000	+	40.7032i	−1.38235	+	2.39431i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	−0.968099	−	0.250568i	$-0.919383\pi$
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	0.267052	−	0.963682i	$-0.413951\pi$
$294$		0			0
$295$	4.00000	−	6.92820i	0.232889	−	0.403376i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−12.0000	−	20.7846i	−0.693978	−	1.20201i
$300$		0			0
$301$	22.0000	−	19.0526i	1.26806	−	1.09817i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.00000	+	10.3923i	0.343559	+	0.595062i
$306$		0			0
$307$	−23.0000			−1.31268			−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000			−1.31268			−0.656340	+	0.754466i	$0.727896\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.00000	+	1.73205i	−0.0567048	+	0.0982156i	−0.892984	−	0.450088i	$-0.851393\pi$
$311$	−1.00000	+	1.73205i	−0.0567048	+	0.0982156i	0.836280	+	0.548303i	$0.184726\pi$
$312$		0			0
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	0.999748	−	0.0224310i	$-0.00714060\pi$
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	−0.519300	+	0.854592i	$0.673807\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	−0.976764	−	0.214318i	$-0.931247\pi$
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	0.302777	−	0.953062i	$-0.402086\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.00000			0.445132
$324$		0			0
$325$	−1.50000	−	2.59808i	−0.0832050	−	0.144115i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.00000	−	15.5885i	−0.165395	−	0.859419i
$330$		0			0
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.0000	+	22.5167i	−0.710266	+	1.23022i
$336$		0			0
$337$	−10.5000	−	18.1865i	−0.571971	−	0.990684i	−0.996363	−	0.0852050i	$-0.972845\pi$
$337$	−10.5000	−	18.1865i	−0.571971	−	0.990684i	0.424392	−	0.905479i	$-0.360488\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	−0.340293	−	0.940319i	$-0.610526\pi$
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	0.984487	−	0.175457i	$-0.0561403\pi$
$348$		0			0
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	−0.615581	−	0.788074i	$-0.711079\pi$
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	0.990282	+	0.139072i	$0.0444119\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$	20.0000			1.06149
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.0000	+	19.0526i	0.575766	+	0.997257i
$366$		0			0
$367$	5.00000			0.260998			0.130499	−	0.991448i	$-0.458342\pi$
$367$	5.00000			0.260998			0.130499	+	0.991448i	$0.458342\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.00000	+	31.1769i	0.311504	+	1.61862i
$372$		0			0
$373$	−5.00000			−0.258890			−0.129445	−	0.991587i	$-0.541320\pi$
$373$	−5.00000			−0.258890			−0.129445	+	0.991587i	$0.541320\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	13.0000			0.667765			0.333883	−	0.942615i	$-0.391641\pi$
$379$	13.0000			0.667765			0.333883	+	0.942615i	$0.391641\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	28.0000			1.43073			0.715367	−	0.698749i	$-0.246260\pi$
$383$	28.0000			1.43073			0.715367	+	0.698749i	$0.246260\pi$
$384$		0			0
$385$	10.0000	+	3.46410i	0.509647	+	0.176547i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$		0			0
$391$	−32.0000	−	55.4256i	−1.61831	−	2.80299i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.00000	+	5.19615i	0.150946	+	0.261447i
$396$		0			0
$397$	−1.50000	+	2.59808i	−0.0752828	+	0.130394i	−0.901209	−	0.433384i	$-0.857319\pi$
$397$	−1.50000	+	2.59808i	−0.0752828	+	0.130394i	0.825926	+	0.563778i	$0.190653\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.0000			0.599251			0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000			0.599251			0.299626	+	0.954057i	$0.403138\pi$
$402$		0			0
$403$	−9.00000			−0.448322
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.00000	+	1.73205i	−0.0495682	+	0.0858546i
$408$		0			0
$409$	9.50000	−	16.4545i	0.469745	−	0.813622i	−0.529657	−	0.848212i	$-0.677679\pi$
$409$	9.50000	−	16.4545i	0.469745	−	0.813622i	0.999402	+	0.0345902i	$0.0110126\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.00000	+	6.92820i	−0.393654	+	0.340915i
$414$		0			0
$415$	2.00000	−	3.46410i	0.0981761	−	0.170046i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	0.997665	−	0.0683046i	$-0.0217590\pi$
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	−0.557986	+	0.829851i	$0.688426\pi$
$420$		0			0
$421$	13.5000	−	23.3827i	0.657950	−	1.13960i	−0.323196	−	0.946332i	$-0.604757\pi$
$421$	13.5000	−	23.3827i	0.657950	−	1.13960i	0.981146	−	0.193270i	$-0.0619094\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.00000	−	6.92820i	−0.194029	−	0.336067i
$426$		0			0
$427$	−3.00000	−	15.5885i	−0.145180	−	0.754378i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$		0			0
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.00000	+	6.92820i	−0.191346	+	0.331421i
$438$		0			0
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	−0.996284	−	0.0861252i	$-0.972552\pi$
$439$	−12.0000	−	20.7846i	−0.572729	−	0.991995i	0.423556	−	0.905870i	$-0.360782\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	0.814595	−	0.580030i	$-0.196959\pi$
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	−0.909618	+	0.415445i	$0.863626\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−22.0000			−1.03824			−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000			−1.03824			−0.519122	+	0.854700i	$0.673741\pi$
$450$		0			0
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.00000	−	15.5885i	−0.140642	−	0.730798i
$456$		0			0
$457$	−6.50000	−	11.2583i	−0.304057	−	0.526642i	0.672994	−	0.739648i	$-0.265008\pi$
$457$	−6.50000	−	11.2583i	−0.304057	−	0.526642i	−0.977051	+	0.213006i	$0.931675\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.00000	−	3.46410i	0.0931493	−	0.161339i	−0.815685	−	0.578496i	$-0.803640\pi$
$461$	2.00000	−	3.46410i	0.0931493	−	0.161339i	0.908835	+	0.417156i	$0.136973\pi$
$462$		0			0
$463$	5.50000	+	9.52628i	0.255607	+	0.442724i	0.965060	−	0.262029i	$-0.0843915\pi$
$463$	5.50000	+	9.52628i	0.255607	+	0.442724i	−0.709453	+	0.704752i	$0.751058\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.0000	−	29.4449i	0.786666	−	1.36255i	−0.141332	−	0.989962i	$-0.545139\pi$
$467$	17.0000	−	29.4449i	0.786666	−	1.36255i	0.927999	−	0.372584i	$-0.121528\pi$
$468$		0			0
$469$	26.0000	−	22.5167i	1.20057	−	1.03972i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	11.0000	−	19.0526i	0.505781	−	0.876038i
$474$		0			0
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	28.0000			1.27935			0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000			1.27935			0.639676	+	0.768644i	$0.279068\pi$
$480$		0			0
$481$	3.00000			0.136788
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−10.0000	+	17.3205i	−0.454077	+	0.786484i
$486$		0			0
$487$	9.50000	+	16.4545i	0.430486	+	0.745624i	0.996915	−	0.0784867i	$-0.0250088\pi$
$487$	9.50000	+	16.4545i	0.430486	+	0.745624i	−0.566429	+	0.824110i	$0.691675\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.0000	−	31.1769i	−0.812329	−	1.40699i	−0.911230	−	0.411897i	$-0.864866\pi$
$491$	−18.0000	−	31.1769i	−0.812329	−	1.40699i	0.0989017	−	0.995097i	$-0.468467\pi$
$492$		0			0
$493$	32.0000			1.44121
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−25.0000	−	8.66025i	−1.12140	−	0.388465i
$498$		0			0
$499$	−29.0000			−1.29822			−0.649109	−	0.760695i	$-0.724858\pi$
$499$	−29.0000			−1.29822			−0.649109	+	0.760695i	$0.724858\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	30.0000			1.33763			0.668817	−	0.743427i	$-0.266801\pi$
$503$	30.0000			1.33763			0.668817	+	0.743427i	$0.266801\pi$
$504$		0			0
$505$	−20.0000			−0.889988
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−18.0000			−0.797836			−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000			−0.797836			−0.398918	+	0.916987i	$0.630614\pi$
$510$		0			0
$511$	−5.50000	−	28.5788i	−0.243306	−	1.26425i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	22.0000			0.969436
$516$		0			0
$517$	−6.00000	−	10.3923i	−0.263880	−	0.457053i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−18.0000	−	31.1769i	−0.788594	−	1.36589i	−0.926828	−	0.375486i	$-0.877476\pi$
$521$	−18.0000	−	31.1769i	−0.788594	−	1.36589i	0.138234	−	0.990400i	$-0.455857\pi$
$522$		0			0
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	−0.297884	−	0.954602i	$-0.596281\pi$
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	0.975652	−	0.219326i	$-0.0703858\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.0000			−1.04546
$528$		0			0
$529$	41.0000			1.78261
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11.0000	−	8.66025i	−0.473804	−	0.373024i
$540$		0			0
$541$	7.50000	−	12.9904i	0.322450	−	0.558500i	−0.658543	−	0.752543i	$-0.728827\pi$
$541$	7.50000	−	12.9904i	0.322450	−	0.558500i	0.980993	+	0.194043i	$0.0621602\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	11.0000	+	19.0526i	0.471188	+	0.816122i
$546$		0			0
$547$	6.00000	−	10.3923i	0.256541	−	0.444343i	−0.708772	−	0.705438i	$-0.750750\pi$
$547$	6.00000	−	10.3923i	0.256541	−	0.444343i	0.965313	+	0.261095i	$0.0840836\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.00000	−	3.46410i	−0.0852029	−	0.147576i
$552$		0			0
$553$	−1.50000	−	7.79423i	−0.0637865	−	0.331444i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.0000	+	19.0526i	0.466085	+	0.807283i	0.999250	−	0.0387286i	$-0.0123308\pi$
$557$	11.0000	+	19.0526i	0.466085	+	0.807283i	−0.533165	+	0.846011i	$0.678997\pi$
$558$		0			0
$559$	−33.0000			−1.39575
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−23.0000	+	39.8372i	−0.969334	+	1.67894i	−0.271846	+	0.962341i	$0.587634\pi$
$563$	−23.0000	+	39.8372i	−0.969334	+	1.67894i	−0.697489	+	0.716596i	$0.745699\pi$
$564$		0			0
$565$	−14.0000	−	24.2487i	−0.588984	−	1.02015i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	10.5000	−	18.1865i	0.439411	−	0.761083i	−0.558233	−	0.829684i	$-0.688520\pi$
$571$	10.5000	−	18.1865i	0.439411	−	0.761083i	0.997644	+	0.0686016i	$0.0218537\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.00000			0.333623
$576$		0			0
$577$	20.5000	+	35.5070i	0.853426	+	1.47818i	0.878097	+	0.478482i	$0.158813\pi$
$577$	20.5000	+	35.5070i	0.853426	+	1.47818i	−0.0246713	+	0.999696i	$0.507854\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.00000	+	3.46410i	−0.165948	+	0.143715i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.0000	−	27.7128i	0.660391	−	1.14383i	−0.320122	−	0.947376i	$-0.603724\pi$
$587$	16.0000	−	27.7128i	0.660391	−	1.14383i	0.980513	−	0.196454i	$-0.0629426\pi$
$588$		0			0
$589$	1.50000	+	2.59808i	0.0618064	+	0.107052i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$		0			0
$595$	−8.00000	−	41.5692i	−0.327968	−	1.70417i
$596$		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
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.0000			−0.569181
$606$		0			0
$607$	−3.00000			−0.121766			−0.0608831	−	0.998145i	$-0.519392\pi$
$607$	−3.00000			−0.121766			−0.0608831	+	0.998145i	$0.519392\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.00000	+	15.5885i	−0.364101	+	0.630641i
$612$		0			0
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	0.991917	+	0.126885i	$0.0404979\pi$
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	−0.386073	+	0.922468i	$0.626169\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.0000	+	22.5167i	0.523360	+	0.906487i	0.999630	+	0.0271876i	$0.00865514\pi$
$617$	13.0000	+	22.5167i	0.523360	+	0.906487i	−0.476270	+	0.879299i	$0.658012\pi$
$618$		0			0
$619$	−11.0000			−0.442127			−0.221064	−	0.975259i	$-0.570953\pi$
$619$	−11.0000			−0.442127			−0.221064	+	0.975259i	$0.570953\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	8.00000			0.318981
$630$		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
$635$	6.00000			0.238103
$636$		0			0
$637$	−3.00000	+	20.7846i	−0.118864	+	0.823516i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	40.0000			1.57991			0.789953	−	0.613168i	$-0.210105\pi$
$641$	40.0000			1.57991			0.789953	+	0.613168i	$0.210105\pi$
$642$		0			0
$643$	−17.5000	−	30.3109i	−0.690133	−	1.19534i	−0.971794	−	0.235831i	$-0.924219\pi$
$643$	−17.5000	−	30.3109i	−0.690133	−	1.19534i	0.281661	−	0.959514i	$-0.409114\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$		0			0
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$		0			0
$655$	4.00000			0.156293
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	0.453221	+	0.891398i	$0.350275\pi$
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	−0.998584	+	0.0531977i	$0.983059\pi$
$660$		0			0
$661$	14.5000	−	25.1147i	0.563985	−	0.976850i	−0.433159	−	0.901318i	$-0.642601\pi$
$661$	14.5000	−	25.1147i	0.563985	−	0.976850i	0.997143	−	0.0755324i	$-0.0240656\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.00000	+	3.46410i	−0.155113	+	0.134332i
$666$		0			0
$667$	−16.0000	+	27.7128i	−0.619522	+	1.07304i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.00000	−	10.3923i	−0.231627	−	0.401190i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$		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
$679$	20.0000	−	17.3205i	0.767530	−	0.664700i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	0.972242	+	0.233977i	$0.0751739\pi$
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	−0.283491	+	0.958975i	$0.591493\pi$
$684$		0			0
$685$	−8.00000			−0.305664
$686$		0			0
$687$		0			0
$688$		0			0
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	21.5000	+	37.2391i	0.817899	+	1.41664i	0.907228	+	0.420640i	$0.138194\pi$
$691$	21.5000	+	37.2391i	0.817899	+	1.41664i	−0.0893292	+	0.996002i	$0.528472\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.00000	+	8.66025i	0.189661	+	0.328502i
$696$		0			0
$697$	−24.0000	+	41.5692i	−0.909065	+	1.57455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	8.00000			0.302156			0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000			0.302156			0.151078	+	0.988522i	$0.451726\pi$
$702$		0			0
$703$	−0.500000	−	0.866025i	−0.0188579	−	0.0326628i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	25.0000	+	8.66025i	0.940222	+	0.325702i
$708$		0			0
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.0000	−	20.7846i	0.449404	−	0.778390i
$714$		0			0
$715$	−6.00000	−	10.3923i	−0.224387	−	0.388650i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	−27.5000	−	9.52628i	−1.02415	−	0.354777i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.00000	+	3.46410i	−0.0742781	+	0.128654i
$726$		0			0
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	−0.570049	−	0.821611i	$-0.693076\pi$
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	0.996560	+	0.0828714i	$0.0264091\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−88.0000			−3.25480
$732$		0			0
$733$	45.0000			1.66211			0.831056	−	0.556188i	$-0.187737\pi$
$733$	45.0000			1.66211			0.831056	+	0.556188i	$0.187737\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.0000	−	22.5167i	0.478861	−	0.829412i
$738$		0			0
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	0.936845	−	0.349744i	$-0.113732\pi$
$739$	4.50000	+	7.79423i	0.165535	+	0.286715i	−0.771310	+	0.636460i	$0.780398\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	0.652369	−	0.757902i	$-0.273775\pi$
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	−0.982547	+	0.186017i	$0.940442\pi$
$744$		0			0
$745$	24.0000			0.879292
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	15.0000			0.547358			0.273679	−	0.961821i	$-0.411759\pi$
$751$	15.0000			0.547358			0.273679	+	0.961821i	$0.411759\pi$
$752$		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
$761$	−8.00000			−0.290000			−0.145000	−	0.989432i	$-0.546318\pi$
$761$	−8.00000			−0.290000			−0.145000	+	0.989432i	$0.546318\pi$
$762$		0			0
$763$	−5.50000	−	28.5788i	−0.199113	−	1.03462i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.0000			0.433295
$768$		0			0
$769$	−15.5000	−	26.8468i	−0.558944	−	0.968120i	−0.997585	−	0.0694574i	$-0.977873\pi$
$769$	−15.5000	−	26.8468i	−0.558944	−	0.968120i	0.438641	−	0.898663i	$-0.355460\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.0000	+	19.0526i	0.395643	+	0.685273i	0.993183	−	0.116566i	$-0.0371886\pi$
$773$	11.0000	+	19.0526i	0.395643	+	0.685273i	−0.597540	+	0.801839i	$0.703855\pi$
$774$		0			0
$775$	1.50000	−	2.59808i	0.0538816	−	0.0933257i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000			0.214972
$780$		0			0
$781$	−20.0000			−0.715656
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.00000	+	3.46410i	−0.0713831	+	0.123639i
$786$		0			0
$787$	−12.0000	+	20.7846i	−0.427754	+	0.740891i	−0.996673	−	0.0815020i	$-0.974028\pi$
$787$	−12.0000	+	20.7846i	−0.427754	+	0.740891i	0.568919	+	0.822393i	$0.307362\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	7.00000	+	36.3731i	0.248891	+	1.29328i
$792$		0			0
$793$	−9.00000	+	15.5885i	−0.319599	+	0.553562i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.0000	−	41.5692i	−0.850124	−	1.47246i	−0.881096	−	0.472937i	$-0.843194\pi$
$797$	−24.0000	−	41.5692i	−0.850124	−	1.47246i	0.0309726	−	0.999520i	$-0.490140\pi$
$798$		0			0
$799$	−24.0000	+	41.5692i	−0.849059	+	1.47061i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−11.0000	−	19.0526i	−0.388182	−	0.672350i
$804$		0			0
$805$	40.0000	+	13.8564i	1.40981	+	0.488374i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	11.0000	+	19.0526i	0.386739	+	0.669852i	0.992009	−	0.126168i	$-0.0402680\pi$
$809$	11.0000	+	19.0526i	0.386739	+	0.669852i	−0.605269	+	0.796021i	$0.706935\pi$
$810$		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
$817$	5.50000	+	9.52628i	0.192421	+	0.333282i
$818$		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
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−54.0000			−1.87776			−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000			−1.87776			−0.938882	+	0.344239i	$0.888137\pi$
$828$		0			0
$829$	5.50000	+	9.52628i	0.191023	+	0.330861i	0.945589	−	0.325362i	$-0.105486\pi$
$829$	5.50000	+	9.52628i	0.191023	+	0.330861i	−0.754567	+	0.656223i	$0.772153\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.00000	+	55.4256i	−0.277184	+	1.92038i
$834$		0			0
$835$	−2.00000	−	3.46410i	−0.0692129	−	0.119880i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	−0.898482	−	0.439010i	$-0.855329\pi$
$839$	−2.00000	+	3.46410i	−0.0690477	+	0.119594i	0.829435	+	0.558604i	$0.188663\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.00000	−	6.92820i	0.137604	−	0.238337i
$846$		0			0
$847$	17.5000	+	6.06218i	0.601307	+	0.208299i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.00000	+	6.92820i	−0.137118	+	0.237496i
$852$		0			0
$853$	−11.5000	+	19.9186i	−0.393753	+	0.681999i	−0.992941	−	0.118609i	$-0.962157\pi$
$853$	−11.5000	+	19.9186i	−0.393753	+	0.681999i	0.599189	+	0.800608i	$0.295490\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	8.00000			0.272956			0.136478	−	0.990643i	$-0.456422\pi$
$859$	8.00000			0.272956			0.136478	+	0.990643i	$0.456422\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	23.0000	−	39.8372i	0.782929	−	1.35607i	−0.147299	−	0.989092i	$-0.547058\pi$
$863$	23.0000	−	39.8372i	0.782929	−	1.35607i	0.930228	−	0.366981i	$-0.119609\pi$
$864$		0			0
$865$	16.0000	+	27.7128i	0.544016	+	0.942264i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$		0			0
$871$	−39.0000			−1.32146
$872$		0			0
$873$		0			0
$874$		0			0
$875$	30.0000	+	10.3923i	1.01419	+	0.351324i
$876$		0			0
$877$	−38.0000			−1.28317			−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000			−1.28317			−0.641584	+	0.767052i	$0.721723\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−48.0000			−1.61716			−0.808581	−	0.588386i	$-0.799764\pi$
$881$	−48.0000			−1.61716			−0.808581	+	0.588386i	$0.799764\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.00000			0.201460			0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000			0.201460			0.100730	+	0.994914i	$0.467882\pi$
$888$		0			0
$889$	−7.50000	−	2.59808i	−0.251542	−	0.0871367i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.00000			0.200782
$894$		0			0
$895$	6.00000	+	10.3923i	0.200558	+	0.347376i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$		0			0
$901$	48.0000	−	83.1384i	1.59911	−	2.76974i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−30.0000			−0.997234
$906$		0			0
$907$	21.0000			0.697294			0.348647	−	0.937254i	$-0.386641\pi$
$907$	21.0000			0.697294			0.348647	+	0.937254i	$0.386641\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	24.0000	−	41.5692i	0.795155	−	1.37725i	−0.127585	−	0.991828i	$-0.540723\pi$
$911$	24.0000	−	41.5692i	0.795155	−	1.37725i	0.922740	−	0.385422i	$-0.125944\pi$
$912$		0			0
$913$	−2.00000	+	3.46410i	−0.0661903	+	0.114645i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.00000	−	1.73205i	−0.165115	−	0.0571974i
$918$		0			0
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	−0.760939	−	0.648824i	$-0.775261\pi$
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	0.942367	+	0.334581i	$0.108595\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	15.0000	+	25.9808i	0.493731	+	0.855167i
$924$		0			0
$925$	−0.500000	+	0.866025i	−0.0164399	+	0.0284747i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$	6.50000	−	2.59808i	0.213029	−	0.0851485i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.0000	−	27.7128i	−0.523256	−	0.906306i
$936$		0			0
$937$	−49.0000			−1.60076			−0.800380	−	0.599493i	$-0.795369\pi$
$937$	−49.0000			−1.60076			−0.800380	+	0.599493i	$0.795369\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	26.0000	−	45.0333i	0.847576	−	1.46804i	−0.0357896	−	0.999359i	$-0.511395\pi$
$941$	26.0000	−	45.0333i	0.847576	−	1.46804i	0.883365	−	0.468685i	$-0.155272\pi$
$942$		0			0
$943$	−24.0000	−	41.5692i	−0.781548	−	1.35368i
$944$		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
$949$	−16.5000	+	28.5788i	−0.535613	+	0.927708i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	28.0000			0.907009			0.453504	−	0.891254i	$-0.350174\pi$
$953$	28.0000			0.907009			0.453504	+	0.891254i	$0.350174\pi$
$954$		0			0
$955$	6.00000	+	10.3923i	0.194155	+	0.336287i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	10.0000	+	3.46410i	0.322917	+	0.111862i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−11.0000	+	19.0526i	−0.354103	+	0.613324i
$966$		0			0
$967$	15.5000	+	26.8468i	0.498446	+	0.863334i	0.999998	−	0.00179302i	$-0.000570736\pi$
$967$	15.5000	+	26.8468i	0.498446	+	0.863334i	−0.501552	+	0.865128i	$0.667237\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	−0.418101	−	0.908401i	$-0.637304\pi$
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	0.995748	−	0.0921142i	$-0.0293625\pi$
$972$		0			0
$973$	−2.50000	−	12.9904i	−0.0801463	−	0.416452i
$974$		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
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12.0000			0.382741			0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000			0.382741			0.191370	+	0.981518i	$0.438707\pi$
$984$		0			0
$985$	−16.0000			−0.509802
$986$		0			0
$987$		0			0
$988$		0			0
$989$	44.0000	−	76.2102i	1.39912	−	2.42334i
$990$		0			0
$991$	−5.50000	−	9.52628i	−0.174713	−	0.302612i	0.765349	−	0.643616i	$-0.222567\pi$
$991$	−5.50000	−	9.52628i	−0.174713	−	0.302612i	−0.940062	+	0.341004i	$0.889233\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−8.00000	−	13.8564i	−0.253617	−	0.439278i
$996$		0			0
$997$	−1.00000			−0.0316703			−0.0158352	−	0.999875i	$-0.505041\pi$
$997$	−1.00000			−0.0316703			−0.0158352	+	0.999875i	$0.505041\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.l.g.541.1		2
3.2	odd	2		2268.2.l.b.541.1		2
7.4	even	3		2268.2.i.b.865.1		2
9.2	odd	6		84.2.i.a.37.1	yes	2
9.4	even	3		2268.2.i.b.2053.1		2
9.5	odd	6		2268.2.i.g.2053.1		2
9.7	even	3		252.2.k.a.37.1		2
21.11	odd	6		2268.2.i.g.865.1		2
36.7	odd	6		1008.2.s.c.289.1		2
36.11	even	6		336.2.q.c.289.1		2
45.2	even	12		2100.2.bc.a.1549.2		4
45.29	odd	6		2100.2.q.b.1801.1		2
45.38	even	12		2100.2.bc.a.1549.1		4
63.2	odd	6		588.2.a.a.1.1		1
63.4	even	3	inner	2268.2.l.g.109.1		2
63.11	odd	6		84.2.i.a.25.1	✓	2
63.16	even	3		1764.2.a.h.1.1		1
63.20	even	6		588.2.i.b.373.1		2
63.25	even	3		252.2.k.a.109.1		2
63.32	odd	6		2268.2.l.b.109.1		2
63.34	odd	6		1764.2.k.j.1549.1		2
63.38	even	6		588.2.i.b.361.1		2
63.47	even	6		588.2.a.f.1.1		1
63.52	odd	6		1764.2.k.j.361.1		2
63.61	odd	6		1764.2.a.c.1.1		1
72.11	even	6		1344.2.q.n.961.1		2
72.29	odd	6		1344.2.q.b.961.1		2
252.11	even	6		336.2.q.c.193.1		2
252.47	odd	6		2352.2.a.k.1.1		1
252.79	odd	6		7056.2.a.bs.1.1		1
252.83	odd	6		2352.2.q.q.961.1		2
252.151	odd	6		1008.2.s.c.865.1		2
252.187	even	6		7056.2.a.o.1.1		1
252.191	even	6		2352.2.a.o.1.1		1
252.227	odd	6		2352.2.q.q.1537.1		2
315.74	odd	6		2100.2.q.b.1201.1		2
315.137	even	12		2100.2.bc.a.949.1		4
315.263	even	12		2100.2.bc.a.949.2		4
504.11	even	6		1344.2.q.n.193.1		2
504.173	even	6		9408.2.a.i.1.1		1
504.299	odd	6		9408.2.a.bx.1.1		1
504.317	odd	6		9408.2.a.cx.1.1		1
504.389	odd	6		1344.2.q.b.193.1		2
504.443	even	6		9408.2.a.bi.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.i.a.25.1	✓	2	63.11	odd	6
84.2.i.a.37.1	yes	2	9.2	odd	6
252.2.k.a.37.1		2	9.7	even	3
252.2.k.a.109.1		2	63.25	even	3
336.2.q.c.193.1		2	252.11	even	6
336.2.q.c.289.1		2	36.11	even	6
588.2.a.a.1.1		1	63.2	odd	6
588.2.a.f.1.1		1	63.47	even	6
588.2.i.b.361.1		2	63.38	even	6
588.2.i.b.373.1		2	63.20	even	6
1008.2.s.c.289.1		2	36.7	odd	6
1008.2.s.c.865.1		2	252.151	odd	6
1344.2.q.b.193.1		2	504.389	odd	6
1344.2.q.b.961.1		2	72.29	odd	6
1344.2.q.n.193.1		2	504.11	even	6
1344.2.q.n.961.1		2	72.11	even	6
1764.2.a.c.1.1		1	63.61	odd	6
1764.2.a.h.1.1		1	63.16	even	3
1764.2.k.j.361.1		2	63.52	odd	6
1764.2.k.j.1549.1		2	63.34	odd	6
2100.2.q.b.1201.1		2	315.74	odd	6
2100.2.q.b.1801.1		2	45.29	odd	6
2100.2.bc.a.949.1		4	315.137	even	12
2100.2.bc.a.949.2		4	315.263	even	12
2100.2.bc.a.1549.1		4	45.38	even	12
2100.2.bc.a.1549.2		4	45.2	even	12
2268.2.i.b.865.1		2	7.4	even	3
2268.2.i.b.2053.1		2	9.4	even	3
2268.2.i.g.865.1		2	21.11	odd	6
2268.2.i.g.2053.1		2	9.5	odd	6
2268.2.l.b.109.1		2	63.32	odd	6
2268.2.l.b.541.1		2	3.2	odd	2
2268.2.l.g.109.1		2	63.4	even	3	inner
2268.2.l.g.541.1		2	1.1	even	1	trivial
2352.2.a.k.1.1		1	252.47	odd	6
2352.2.a.o.1.1		1	252.191	even	6
2352.2.q.q.961.1		2	252.83	odd	6
2352.2.q.q.1537.1		2	252.227	odd	6
7056.2.a.o.1.1		1	252.187	even	6
7056.2.a.bs.1.1		1	252.79	odd	6
9408.2.a.i.1.1		1	504.173	even	6
9408.2.a.bi.1.1		1	504.443	even	6
9408.2.a.bx.1.1		1	504.299	odd	6
9408.2.a.cx.1.1		1	504.317	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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+2.00000 q^{5} +(-2.50000 - 0.866025i) q^{7} -2.00000 q^{11} +(1.50000 + 2.59808i) q^{13} +(4.00000 + 6.92820i) q^{17} +(0.500000 - 0.866025i) q^{19} -8.00000 q^{23} -1.00000 q^{25} +(2.00000 - 3.46410i) q^{29} +(-1.50000 + 2.59808i) q^{31} +(-5.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{37} +(3.00000 + 5.19615i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +(2.00000 - 3.46410i) q^{59} +(3.00000 + 5.19615i) q^{61} +(3.00000 + 5.19615i) q^{65} +(-6.50000 + 11.2583i) q^{67} +10.0000 q^{71} +(5.50000 + 9.52628i) q^{73} +(5.00000 + 1.73205i) q^{77} +(1.50000 + 2.59808i) q^{79} +(1.00000 - 1.73205i) q^{83} +(8.00000 + 13.8564i) q^{85} +(-1.50000 - 7.79423i) q^{91} +(1.00000 - 1.73205i) q^{95} +(-5.00000 + 8.66025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{5} - 5 q^{7}+O(q^{10}) \) 2 * q + 4 * q^5 - 5 * q^7	\( 2 q + 4 q^{5} - 5 q^{7} - 4 q^{11} + 3 q^{13} + 8 q^{17} + q^{19} - 16 q^{23} - 2 q^{25} + 4 q^{29} - 3 q^{31} - 10 q^{35} + q^{37} + 6 q^{41} - 11 q^{43} + 6 q^{47} + 11 q^{49} - 12 q^{53} - 8 q^{55} + 4 q^{59} + 6 q^{61} + 6 q^{65} - 13 q^{67} + 20 q^{71} + 11 q^{73} + 10 q^{77} + 3 q^{79} + 2 q^{83} + 16 q^{85} - 3 q^{91} + 2 q^{95} - 10 q^{97}+O(q^{100}) \) 2 * q + 4 * q^5 - 5 * q^7 - 4 * q^11 + 3 * q^13 + 8 * q^17 + q^19 - 16 * q^23 - 2 * q^25 + 4 * q^29 - 3 * q^31 - 10 * q^35 + q^37 + 6 * q^41 - 11 * q^43 + 6 * q^47 + 11 * q^49 - 12 * q^53 - 8 * q^55 + 4 * q^59 + 6 * q^61 + 6 * q^65 - 13 * q^67 + 20 * q^71 + 11 * q^73 + 10 * q^77 + 3 * q^79 + 2 * q^83 + 16 * q^85 - 3 * q^91 + 2 * q^95 - 10 * q^97

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