LMFDB - Embedded newform 2268.2.i.g.865.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(865,2268)]

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, 4, 4]))

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.1100711784$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2268.865
Dual form			2268.2.i.g.2053.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})$	$q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(1.50000 + 2.59808i) q^{13} +(-4.00000 + 6.92820i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{29} +3.00000 q^{31} +(5.00000 - 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-3.00000 - 5.19615i) q^{41} +(-5.50000 + 9.52628i) q^{43} +6.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +4.00000 q^{59} -6.00000 q^{61} +6.00000 q^{65} +13.0000 q^{67} -10.0000 q^{71} +(5.50000 - 9.52628i) q^{73} +(1.00000 - 5.19615i) q^{77} -3.00000 q^{79} +(-1.00000 + 1.73205i) q^{83} +(8.00000 + 13.8564i) q^{85} +(-1.50000 + 7.79423i) q^{91} +2.00000 q^{95} +(-5.00000 + 8.66025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 2 * q + 2 * q^5 + 4 * q^7	$ 2 q + 2 q^{5} + 4 q^{7} - 2 q^{11} + 3 q^{13} - 8 q^{17} + q^{19} - 8 q^{23} + q^{25} - 4 q^{29} + 6 q^{31} + 10 q^{35} + q^{37} - 6 q^{41} - 11 q^{43} + 12 q^{47} + 2 q^{49} + 12 q^{53} - 8 q^{55} + 8 q^{59} - 12 q^{61} + 12 q^{65} + 26 q^{67} - 20 q^{71} + 11 q^{73} + 2 q^{77} - 6 q^{79} - 2 q^{83} + 16 q^{85} - 3 q^{91} + 4 q^{95} - 10 q^{97}+O(q^{100}) $ 2 * q + 2 * q^5 + 4 * q^7 - 2 * q^11 + 3 * q^13 - 8 * q^17 + q^19 - 8 * q^23 + q^25 - 4 * q^29 + 6 * q^31 + 10 * q^35 + q^37 - 6 * q^41 - 11 * q^43 + 12 * q^47 + 2 * q^49 + 12 * q^53 - 8 * q^55 + 8 * q^59 - 12 * q^61 + 12 * q^65 + 26 * q^67 - 20 * q^71 + 11 * q^73 + 2 * q^77 - 6 * q^79 - 2 * q^83 + 16 * q^85 - 3 * q^91 + 4 * q^95 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		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	−0.275029	+	0.961436i	$0.588688\pi$
$17$	−4.00000	+	6.92820i	−0.970143	+	1.68034i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	0.618389	+	0.785872i	$0.287786\pi$
$30$		0			0
$31$	3.00000			0.538816			0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000			0.538816			0.269408	+	0.963026i	$0.413172\pi$
$32$		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	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$		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
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	−4.00000			−0.539360
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.00000			0.744208
$66$		0			0
$67$	13.0000			1.58820			0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000			1.58820			0.794101	+	0.607785i	$0.207942\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−10.0000			−1.18678			−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000			−1.18678			−0.593391	+	0.804914i	$0.702211\pi$
$72$		0			0
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	−0.340868	−	0.940111i	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.00000	−	5.19615i	0.113961	−	0.592157i
$78$		0			0
$79$	−3.00000			−0.337526			−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000			−0.337526			−0.168763	+	0.985657i	$0.553977\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	−0.915675	−	0.401920i	$-0.868343\pi$
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	0.805910	+	0.592037i	$0.201676\pi$
$84$		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	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−1.50000	+	7.79423i	−0.157243	+	0.817057i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.00000			0.205196
$96$		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
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$		0			0
$103$	−5.50000	+	9.52628i	−0.541931	+	0.938652i	0.456862	+	0.889538i	$0.348973\pi$
$103$	−5.50000	+	9.52628i	−0.541931	+	0.938652i	−0.998793	+	0.0491146i	$0.984360\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	−0.472708	−	0.881219i	$-0.656723\pi$
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	0.999512	−	0.0312328i	$-0.00994332\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	0.981003	+	0.193993i	$0.0621440\pi$
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	−0.322498	+	0.946570i	$0.604523\pi$
$114$		0			0
$115$	8.00000	+	13.8564i	0.746004	+	1.29212i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−20.0000	+	6.92820i	−1.83340	+	0.635107i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	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
$131$	1.00000	−	1.73205i	0.0873704	−	0.151330i	−0.819028	−	0.573753i	$-0.805487\pi$
$131$	1.00000	−	1.73205i	0.0873704	−	0.151330i	0.906399	+	0.422423i	$0.138820\pi$
$132$		0			0
$133$	−0.500000	+	2.59808i	−0.0433555	+	0.225282i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	0.767853	−	0.640626i	$-0.221325\pi$
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	−0.938725	+	0.344668i	$0.887992\pi$
$138$		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
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	−0.508413	−	0.861113i	$-0.669768\pi$
$149$	6.00000	−	10.3923i	0.491539	−	0.851371i	0.999953	+	0.00974235i	$0.00310113\pi$
$150$		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
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$		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	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.00000	+	1.73205i	0.0773823	+	0.134030i	0.902120	−	0.431486i	$-0.142010\pi$
$167$	1.00000	+	1.73205i	0.0773823	+	0.134030i	−0.824737	+	0.565516i	$0.808677\pi$
$168$		0			0
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	16.0000			1.21646			0.608229	−	0.793762i	$-0.291880\pi$
$173$	16.0000			1.21646			0.608229	+	0.793762i	$0.291880\pi$
$174$		0			0
$175$	−0.500000	+	2.59808i	−0.0377964	+	0.196396i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$		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
$185$	2.00000			0.147043
$186$		0			0
$187$	16.0000			1.17004
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.00000			0.434145			0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000			0.434145			0.217072	+	0.976156i	$0.430349\pi$
$192$		0			0
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$		0			0
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.0000	+	3.46410i	−0.701862	+	0.243132i
$204$		0			0
$205$	−12.0000			−0.838116
$206$		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
$221$	−24.0000			−1.61441
$222$		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
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$		0			0
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	−0.882073	−	0.471113i	$-0.843853\pi$
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	0.849032	+	0.528341i	$0.177186\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	0.540301	−	0.841472i	$-0.318310\pi$
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	−0.998886	+	0.0471787i	$0.984977\pi$
$234$		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	$-0.968874\pi$
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	0.413061	−	0.910703i	$-0.364460\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	13.0000	+	5.19615i	0.830540	+	0.331970i
$246$		0			0
$247$	−1.50000	+	2.59808i	−0.0954427	+	0.165312i
$248$		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
$259$	−0.500000	+	2.59808i	−0.0310685	+	0.161437i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		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	$-0.813914\pi$
$269$	1.00000	−	1.73205i	0.0609711	−	0.105605i	0.894900	+	0.446267i	$0.147247\pi$
$270$		0			0
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	0.957328	+	0.289003i	$0.0933238\pi$
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	−0.228380	+	0.973572i	$0.573343\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$		0			0
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.0000	+	17.3205i	−0.596550	+	1.03325i	0.396776	+	0.917915i	$0.370129\pi$
$281$	−10.0000	+	17.3205i	−0.596550	+	1.03325i	−0.993326	+	0.115339i	$0.963204\pi$
$282$		0			0
$283$	19.0000			1.12943			0.564716	−	0.825285i	$-0.308986\pi$
$283$	19.0000			1.12943			0.564716	+	0.825285i	$0.308986\pi$
$284$		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	$0.0806172\pi$
$293$	12.0000	+	20.7846i	0.701047	+	1.21425i	−0.267052	+	0.963682i	$0.586049\pi$
$294$		0			0
$295$	4.00000	−	6.92820i	0.232889	−	0.403376i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−24.0000			−1.38796
$300$		0			0
$301$	−27.5000	+	9.52628i	−1.58507	+	0.549086i
$302$		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
$311$	−2.00000			−0.113410			−0.0567048	−	0.998391i	$-0.518059\pi$
$311$	−2.00000			−0.113410			−0.0567048	+	0.998391i	$0.518059\pi$
$312$		0			0
$313$	−17.0000			−0.960897			−0.480448	−	0.877023i	$-0.659526\pi$
$313$	−17.0000			−0.960897			−0.480448	+	0.877023i	$0.659526\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−24.0000			−1.34797			−0.673987	−	0.738743i	$-0.735420\pi$
$317$	−24.0000			−1.34797			−0.673987	+	0.738743i	$0.735420\pi$
$318$		0			0
$319$	8.00000			0.447914
$320$		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
$329$	12.0000	+	10.3923i	0.661581	+	0.572946i
$330$		0			0
$331$	17.0000			0.934405			0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000			0.934405			0.467202	+	0.884150i	$0.345262\pi$
$332$		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
$347$	24.0000			1.28839			0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000			1.28839			0.644194	+	0.764862i	$0.277193\pi$
$348$		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
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	0.934751	−	0.355303i	$-0.115622\pi$
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	−0.775077	+	0.631867i	$0.782289\pi$
$354$		0			0
$355$	−10.0000	+	17.3205i	−0.530745	+	0.919277i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$		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
$367$	−2.50000	−	4.33013i	−0.130499	−	0.226031i	0.793370	−	0.608740i	$-0.208325\pi$
$367$	−2.50000	−	4.33013i	−0.130499	−	0.226031i	−0.923869	+	0.382709i	$0.874991\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	30.0000	−	10.3923i	1.55752	−	0.539542i
$372$		0			0
$373$	2.50000	−	4.33013i	0.129445	−	0.224205i	−0.794017	−	0.607896i	$-0.792014\pi$
$373$	2.50000	−	4.33013i	0.129445	−	0.224205i	0.923462	+	0.383691i	$0.125347\pi$
$374$		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
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	−0.247451	−	0.968900i	$-0.579593\pi$
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	0.962818	−	0.270151i	$-0.0870736\pi$
$384$		0			0
$385$	−8.00000	−	6.92820i	−0.407718	−	0.353094i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$		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	0.825926	−	0.563778i	$-0.190653\pi$
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	−0.901209	+	0.433384i	$0.857319\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$		0			0
$403$	4.50000	+	7.79423i	0.224161	+	0.388258i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.00000	−	1.73205i	0.0495682	−	0.0858546i
$408$		0			0
$409$	−19.0000			−0.939490			−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000			−0.939490			−0.469745	+	0.882802i	$0.655654\pi$
$410$		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	0.557986	−	0.829851i	$-0.311574\pi$
$419$	−9.00000	−	15.5885i	−0.439679	−	0.761546i	−0.997665	+	0.0683046i	$0.978241\pi$
$420$		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
$425$	−8.00000			−0.388057
$426$		0			0
$427$	−12.0000	−	10.3923i	−0.580721	−	0.502919i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$		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
$437$	−8.00000			−0.382692
$438$		0			0
$439$	24.0000			1.14546			0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000			1.14546			0.572729	+	0.819745i	$0.305885\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.0000			1.03824			0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000			1.03824			0.519122	+	0.854700i	$0.326259\pi$
$450$		0			0
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	12.0000	+	10.3923i	0.562569	+	0.487199i
$456$		0			0
$457$	13.0000			0.608114			0.304057	−	0.952654i	$-0.401659\pi$
$457$	13.0000			0.608114			0.304057	+	0.952654i	$0.401659\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.00000	+	3.46410i	−0.0931493	+	0.161339i	−0.908835	−	0.417156i	$-0.863027\pi$
$461$	−2.00000	+	3.46410i	−0.0931493	+	0.161339i	0.815685	+	0.578496i	$0.196360\pi$
$462$		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	−0.927999	−	0.372584i	$-0.878472\pi$
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	0.141332	−	0.989962i	$-0.454861\pi$
$468$		0			0
$469$	26.0000	+	22.5167i	1.20057	+	1.03972i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	22.0000			1.01156
$474$		0			0
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.0000	+	24.2487i	0.639676	+	1.10795i	0.985504	+	0.169654i	$0.0542649\pi$
$479$	14.0000	+	24.2487i	0.639676	+	1.10795i	−0.345827	+	0.938298i	$0.612402\pi$
$480$		0			0
$481$	−1.50000	+	2.59808i	−0.0683941	+	0.118462i
$482$		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	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	0.996915	+	0.0784867i	$0.0250088\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	0.911230	+	0.411897i	$0.135134\pi$
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	−0.0989017	+	0.995097i	$0.531533\pi$
$492$		0			0
$493$	−16.0000	−	27.7128i	−0.720604	−	1.24812i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−20.0000	−	17.3205i	−0.897123	−	0.776931i
$498$		0			0
$499$	14.5000	−	25.1147i	0.649109	−	1.12429i	−0.334227	−	0.942493i	$-0.608475\pi$
$499$	14.5000	−	25.1147i	0.649109	−	1.12429i	0.983336	−	0.181797i	$-0.0581915\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−30.0000			−1.33763			−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000			−1.33763			−0.668817	+	0.743427i	$0.733199\pi$
$504$		0			0
$505$	−20.0000			−0.889988
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$		0			0
$511$	27.5000	−	9.52628i	1.21653	−	0.421418i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.0000	+	19.0526i	0.484718	+	0.839556i
$516$		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	−0.138234	−	0.990400i	$-0.544143\pi$
$521$	18.0000	−	31.1769i	0.788594	−	1.36589i	0.926828	−	0.375486i	$-0.122524\pi$
$522$		0			0
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	0.975652	+	0.219326i	$0.0703858\pi$
$523$	15.5000	+	26.8468i	0.677768	+	1.17393i	−0.297884	+	0.954602i	$0.596281\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		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	0.980993	−	0.194043i	$-0.0621602\pi$
$541$	7.50000	+	12.9904i	0.322450	+	0.558500i	−0.658543	+	0.752543i	$0.728827\pi$
$542$		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
$551$	−4.00000			−0.170406
$552$		0			0
$553$	−6.00000	−	5.19615i	−0.255146	−	0.220963i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.0000	+	19.0526i	−0.466085	+	0.807283i	−0.999250	−	0.0387286i	$-0.987669\pi$
$557$	−11.0000	+	19.0526i	−0.466085	+	0.807283i	0.533165	+	0.846011i	$0.321003\pi$
$558$		0			0
$559$	−33.0000			−1.39575
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−46.0000			−1.93867			−0.969334	−	0.245745i	$-0.920967\pi$
$563$	−46.0000			−1.93867			−0.969334	+	0.245745i	$0.920967\pi$
$564$		0			0
$565$	28.0000			1.17797
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$	−21.0000			−0.878823			−0.439411	−	0.898286i	$-0.644813\pi$
$571$	−21.0000			−0.878823			−0.439411	+	0.898286i	$0.644813\pi$
$572$		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	−0.0246713	−	0.999696i	$-0.507854\pi$
$577$	20.5000	−	35.5070i	0.853426	−	1.47818i	0.878097	−	0.478482i	$-0.158813\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.00000	+	1.73205i	−0.207435	+	0.0718576i
$582$		0			0
$583$	−24.0000			−0.993978
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.0000	+	27.7128i	−0.660391	+	1.14383i	0.320122	+	0.947376i	$0.396276\pi$
$587$	−16.0000	+	27.7128i	−0.660391	+	1.14383i	−0.980513	+	0.196454i	$0.937057\pi$
$588$		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	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$		0			0
$595$	−8.00000	+	41.5692i	−0.327968	+	1.70417i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		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
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	1.50000	−	2.59808i	0.0608831	−	0.105453i	−0.833977	−	0.551799i	$-0.813942\pi$
$607$	1.50000	−	2.59808i	0.0608831	−	0.105453i	0.894860	+	0.446346i	$0.147275\pi$
$608$		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	−0.386073	−	0.922468i	$-0.626169\pi$
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	0.991917	−	0.126885i	$-0.0404979\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.0000	−	22.5167i	−0.523360	−	0.906487i	−0.999630	−	0.0271876i	$-0.991345\pi$
$617$	−13.0000	−	22.5167i	−0.523360	−	0.906487i	0.476270	−	0.879299i	$-0.341988\pi$
$618$		0			0
$619$	5.50000	+	9.52628i	0.221064	+	0.382893i	0.955131	−	0.296183i	$-0.0957138\pi$
$619$	5.50000	+	9.52628i	0.221064	+	0.382893i	−0.734068	+	0.679076i	$0.762380\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		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
$635$	3.00000	−	5.19615i	0.119051	−	0.206203i
$636$		0			0
$637$	−16.5000	+	12.9904i	−0.653754	+	0.514698i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.0000	+	34.6410i	0.789953	+	1.36824i	0.925995	+	0.377535i	$0.123228\pi$
$641$	20.0000	+	34.6410i	0.789953	+	1.36824i	−0.136043	+	0.990703i	$0.543438\pi$
$642$		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	$-0.870963\pi$
$647$	−3.00000	+	5.19615i	−0.117942	+	0.204282i	0.801010	+	0.598651i	$0.204296\pi$
$648$		0			0
$649$	−4.00000	−	6.92820i	−0.157014	−	0.271956i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$		0			0
$655$	−2.00000	−	3.46410i	−0.0781465	−	0.135354i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.0000	−	24.2487i	0.545363	−	0.944596i	−0.453221	−	0.891398i	$-0.649725\pi$
$659$	14.0000	−	24.2487i	0.545363	−	0.944596i	0.998584	−	0.0531977i	$-0.0169414\pi$
$660$		0			0
$661$	−29.0000			−1.12797			−0.563985	−	0.825785i	$-0.690732\pi$
$661$	−29.0000			−1.12797			−0.563985	+	0.825785i	$0.690732\pi$
$662$		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
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$		0			0
$679$	−25.0000	+	8.66025i	−0.959412	+	0.332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	0.283491	+	0.958975i	$0.408507\pi$
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	−0.972242	+	0.233977i	$0.924826\pi$
$684$		0			0
$685$	−8.00000			−0.305664
$686$		0			0
$687$		0			0
$688$		0			0
$689$	36.0000			1.37149
$690$		0			0
$691$	−43.0000			−1.63580			−0.817899	−	0.575362i	$-0.804861\pi$
$691$	−43.0000			−1.63580			−0.817899	+	0.575362i	$0.804861\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	10.0000			0.379322
$696$		0			0
$697$	48.0000			1.81813
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.00000			−0.302156			−0.151078	−	0.988522i	$-0.548274\pi$
$701$	−8.00000			−0.302156			−0.151078	+	0.988522i	$0.548274\pi$
$702$		0			0
$703$	−0.500000	+	0.866025i	−0.0188579	+	0.0326628i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.00000	−	25.9808i	0.188044	−	0.977107i
$708$		0			0
$709$	14.0000			0.525781			0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000			0.525781			0.262891	+	0.964826i	$0.415324\pi$
$710$		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	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$		0			0
$721$	−27.5000	+	9.52628i	−1.02415	+	0.354777i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.00000			−0.148556
$726$		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
$731$	−44.0000	−	76.2102i	−1.62740	−	2.81874i
$732$		0			0
$733$	−22.5000	+	38.9711i	−0.831056	+	1.43943i	0.0661448	+	0.997810i	$0.478930\pi$
$733$	−22.5000	+	38.9711i	−0.831056	+	1.43943i	−0.897201	+	0.441622i	$0.854403\pi$
$734$		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	−0.771310	−	0.636460i	$-0.780398\pi$
$739$	4.50000	−	7.79423i	0.165535	−	0.286715i	0.936845	+	0.349744i	$0.113732\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	9.00000	+	15.5885i	0.330178	+	0.571885i	0.982547	−	0.186017i	$-0.0595579\pi$
$743$	9.00000	+	15.5885i	0.330178	+	0.571885i	−0.652369	+	0.757902i	$0.726225\pi$
$744$		0			0
$745$	−12.0000	−	20.7846i	−0.439646	−	0.761489i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	−0.969801	−	0.243898i	$-0.921574\pi$
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	0.696122	+	0.717923i	$0.254907\pi$
$752$		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
$761$	−4.00000	+	6.92820i	−0.145000	+	0.251147i	−0.929373	−	0.369142i	$-0.879652\pi$
$761$	−4.00000	+	6.92820i	−0.145000	+	0.251147i	0.784373	+	0.620289i	$0.212985\pi$
$762$		0			0
$763$	27.5000	−	9.52628i	0.995567	−	0.344874i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.00000	+	10.3923i	0.216647	+	0.375244i
$768$		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	$-0.962811\pi$
$773$	−11.0000	+	19.0526i	−0.395643	+	0.685273i	0.597540	+	0.801839i	$0.296145\pi$
$774$		0			0
$775$	1.50000	+	2.59808i	0.0538816	+	0.0933257i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$		0			0
$781$	10.0000	+	17.3205i	0.357828	+	0.619777i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.00000	−	3.46410i	0.0713831	−	0.123639i
$786$		0			0
$787$	24.0000			0.855508			0.427754	−	0.903895i	$-0.359305\pi$
$787$	24.0000			0.855508			0.427754	+	0.903895i	$0.359305\pi$
$788$		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	$0.156806\pi$
$797$	24.0000	+	41.5692i	0.850124	+	1.47246i	−0.0309726	+	0.999520i	$0.509860\pi$
$798$		0			0
$799$	−24.0000	+	41.5692i	−0.849059	+	1.47061i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−22.0000			−0.776363
$804$		0			0
$805$	−8.00000	+	41.5692i	−0.281963	+	1.46512i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.0000	+	19.0526i	−0.386739	+	0.669852i	−0.992009	−	0.126168i	$-0.959732\pi$
$809$	−11.0000	+	19.0526i	−0.386739	+	0.669852i	0.605269	+	0.796021i	$0.293065\pi$
$810$		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
$815$	8.00000			0.280228
$816$		0			0
$817$	−11.0000			−0.384841
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.00000			0.0698005			0.0349002	−	0.999391i	$-0.488889\pi$
$821$	2.00000			0.0698005			0.0349002	+	0.999391i	$0.488889\pi$
$822$		0			0
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	54.0000			1.87776			0.938882	−	0.344239i	$-0.111863\pi$
$827$	54.0000			1.87776			0.938882	+	0.344239i	$0.111863\pi$
$828$		0			0
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	−0.754567	−	0.656223i	$-0.772153\pi$
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	0.945589	+	0.325362i	$0.105486\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−52.0000	−	20.7846i	−1.80169	−	0.720144i
$834$		0			0
$835$	4.00000			0.138426
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	−0.829435	−	0.558604i	$-0.811337\pi$
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	0.898482	+	0.439010i	$0.144671\pi$
$840$		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
$851$	−8.00000			−0.274236
$852$		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		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	−0.926161	−	0.377128i	$-0.876912\pi$
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	0.789683	+	0.613515i	$0.210245\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−23.0000	−	39.8372i	−0.782929	−	1.35607i	−0.930228	−	0.366981i	$-0.880391\pi$
$863$	−23.0000	−	39.8372i	−0.782929	−	1.35607i	0.147299	−	0.989092i	$-0.452942\pi$
$864$		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
$871$	19.5000	+	33.7750i	0.660732	+	1.14442i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	24.0000	+	20.7846i	0.811348	+	0.702648i
$876$		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
$881$	48.0000			1.61716			0.808581	−	0.588386i	$-0.200236\pi$
$881$	48.0000			1.61716			0.808581	+	0.588386i	$0.200236\pi$
$882$		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
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	−0.811256	−	0.584692i	$-0.801215\pi$
$887$	3.00000	−	5.19615i	0.100730	−	0.174470i	0.911986	+	0.410222i	$0.134549\pi$
$888$		0			0
$889$	6.00000	+	5.19615i	0.201234	+	0.174273i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.00000	+	5.19615i	0.100391	+	0.173883i
$894$		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
$905$	−15.0000	+	25.9808i	−0.498617	+	0.863630i
$906$		0			0
$907$	−10.5000	−	18.1865i	−0.348647	−	0.603874i	0.637363	−	0.770564i	$-0.280025\pi$
$907$	−10.5000	−	18.1865i	−0.348647	−	0.603874i	−0.986009	+	0.166690i	$0.946692\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	0.127585	+	0.991828i	$0.459277\pi$
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	−0.922740	+	0.385422i	$0.874056\pi$
$912$		0			0
$913$	4.00000			0.132381
$914$		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	0.942367	−	0.334581i	$-0.108595\pi$
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	−0.760939	+	0.648824i	$0.775261\pi$
$920$		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
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$		0			0
$931$	−5.50000	+	4.33013i	−0.180255	+	0.141914i
$932$		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
$941$	52.0000			1.69515			0.847576	−	0.530674i	$-0.178061\pi$
$941$	52.0000			1.69515			0.847576	+	0.530674i	$0.178061\pi$
$942$		0			0
$943$	48.0000			1.56310
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.0000			0.324956			0.162478	−	0.986712i	$-0.448051\pi$
$947$	10.0000			0.324956			0.162478	+	0.986712i	$0.448051\pi$
$948$		0			0
$949$	33.0000			1.07123
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−28.0000			−0.907009			−0.453504	−	0.891254i	$-0.649826\pi$
$953$	−28.0000			−0.907009			−0.453504	+	0.891254i	$0.649826\pi$
$954$		0			0
$955$	6.00000	−	10.3923i	0.194155	−	0.336287i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.00000	−	10.3923i	0.0645834	−	0.335585i
$960$		0			0
$961$	−22.0000			−0.709677
$962$		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	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$		0			0
$973$	−2.50000	+	12.9904i	−0.0801463	+	0.416452i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.0000			−0.575871			−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000			−0.575871			−0.287936	+	0.957650i	$0.592969\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.00000	+	10.3923i	0.191370	+	0.331463i	0.945705	−	0.325027i	$-0.105374\pi$
$983$	6.00000	+	10.3923i	0.191370	+	0.331463i	−0.754334	+	0.656490i	$0.772040\pi$
$984$		0			0
$985$	8.00000	−	13.8564i	0.254901	−	0.441502i
$986$		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	−0.940062	−	0.341004i	$-0.889233\pi$
$991$	−5.50000	+	9.52628i	−0.174713	+	0.302612i	0.765349	+	0.643616i	$0.222567\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.00000	+	13.8564i	0.253617	+	0.439278i
$996$		0			0
$997$	0.500000	+	0.866025i	0.0158352	+	0.0274273i	0.873834	−	0.486224i	$-0.161626\pi$
$997$	0.500000	+	0.866025i	0.0158352	+	0.0274273i	−0.857999	+	0.513651i	$0.828293\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.i.g.865.1		2
3.2	odd	2		2268.2.i.b.865.1		2
7.2	even	3		2268.2.l.b.541.1		2
9.2	odd	6		252.2.k.a.109.1		2
9.4	even	3		2268.2.l.b.109.1		2
9.5	odd	6		2268.2.l.g.109.1		2
9.7	even	3		84.2.i.a.25.1	✓	2
21.2	odd	6		2268.2.l.g.541.1		2
36.7	odd	6		336.2.q.c.193.1		2
36.11	even	6		1008.2.s.c.865.1		2
45.7	odd	12		2100.2.bc.a.949.1		4
45.34	even	6		2100.2.q.b.1201.1		2
45.43	odd	12		2100.2.bc.a.949.2		4
63.2	odd	6		252.2.k.a.37.1		2
63.11	odd	6		1764.2.a.h.1.1		1
63.16	even	3		84.2.i.a.37.1	yes	2
63.20	even	6		1764.2.k.j.361.1		2
63.23	odd	6		2268.2.i.b.2053.1		2
63.25	even	3		588.2.a.a.1.1		1
63.34	odd	6		588.2.i.b.361.1		2
63.38	even	6		1764.2.a.c.1.1		1
63.47	even	6		1764.2.k.j.1549.1		2
63.52	odd	6		588.2.a.f.1.1		1
63.58	even	3	inner	2268.2.i.g.2053.1		2
63.61	odd	6		588.2.i.b.373.1		2
72.43	odd	6		1344.2.q.n.193.1		2
72.61	even	6		1344.2.q.b.193.1		2
252.11	even	6		7056.2.a.bs.1.1		1
252.79	odd	6		336.2.q.c.289.1		2
252.115	even	6		2352.2.a.k.1.1		1
252.151	odd	6		2352.2.a.o.1.1		1
252.187	even	6		2352.2.q.q.961.1		2
252.191	even	6		1008.2.s.c.289.1		2
252.223	even	6		2352.2.q.q.1537.1		2
252.227	odd	6		7056.2.a.o.1.1		1
315.79	even	6		2100.2.q.b.1801.1		2
315.142	odd	12		2100.2.bc.a.1549.2		4
315.268	odd	12		2100.2.bc.a.1549.1		4
504.115	even	6		9408.2.a.bx.1.1		1
504.205	even	6		1344.2.q.b.961.1		2
504.277	even	6		9408.2.a.cx.1.1		1
504.331	odd	6		1344.2.q.n.961.1		2
504.403	odd	6		9408.2.a.bi.1.1		1
504.493	odd	6		9408.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.i.a.25.1	✓	2	9.7	even	3
84.2.i.a.37.1	yes	2	63.16	even	3
252.2.k.a.37.1		2	63.2	odd	6
252.2.k.a.109.1		2	9.2	odd	6
336.2.q.c.193.1		2	36.7	odd	6
336.2.q.c.289.1		2	252.79	odd	6
588.2.a.a.1.1		1	63.25	even	3
588.2.a.f.1.1		1	63.52	odd	6
588.2.i.b.361.1		2	63.34	odd	6
588.2.i.b.373.1		2	63.61	odd	6
1008.2.s.c.289.1		2	252.191	even	6
1008.2.s.c.865.1		2	36.11	even	6
1344.2.q.b.193.1		2	72.61	even	6
1344.2.q.b.961.1		2	504.205	even	6
1344.2.q.n.193.1		2	72.43	odd	6
1344.2.q.n.961.1		2	504.331	odd	6
1764.2.a.c.1.1		1	63.38	even	6
1764.2.a.h.1.1		1	63.11	odd	6
1764.2.k.j.361.1		2	63.20	even	6
1764.2.k.j.1549.1		2	63.47	even	6
2100.2.q.b.1201.1		2	45.34	even	6
2100.2.q.b.1801.1		2	315.79	even	6
2100.2.bc.a.949.1		4	45.7	odd	12
2100.2.bc.a.949.2		4	45.43	odd	12
2100.2.bc.a.1549.1		4	315.268	odd	12
2100.2.bc.a.1549.2		4	315.142	odd	12
2268.2.i.b.865.1		2	3.2	odd	2
2268.2.i.b.2053.1		2	63.23	odd	6
2268.2.i.g.865.1		2	1.1	even	1	trivial
2268.2.i.g.2053.1		2	63.58	even	3	inner
2268.2.l.b.109.1		2	9.4	even	3
2268.2.l.b.541.1		2	7.2	even	3
2268.2.l.g.109.1		2	9.5	odd	6
2268.2.l.g.541.1		2	21.2	odd	6
2352.2.a.k.1.1		1	252.115	even	6
2352.2.a.o.1.1		1	252.151	odd	6
2352.2.q.q.961.1		2	252.187	even	6
2352.2.q.q.1537.1		2	252.223	even	6
7056.2.a.o.1.1		1	252.227	odd	6
7056.2.a.bs.1.1		1	252.11	even	6
9408.2.a.i.1.1		1	504.493	odd	6
9408.2.a.bi.1.1		1	504.403	odd	6
9408.2.a.bx.1.1		1	504.115	even	6
9408.2.a.cx.1.1		1	504.277	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.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(1.50000 + 2.59808i) q^{13} +(-4.00000 + 6.92820i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{29} +3.00000 q^{31} +(5.00000 - 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-3.00000 - 5.19615i) q^{41} +(-5.50000 + 9.52628i) q^{43} +6.00000 q^{47} +(1.00000 + 6.92820i) q^{49} +(6.00000 - 10.3923i) q^{53} -4.00000 q^{55} +4.00000 q^{59} -6.00000 q^{61} +6.00000 q^{65} +13.0000 q^{67} -10.0000 q^{71} +(5.50000 - 9.52628i) q^{73} +(1.00000 - 5.19615i) q^{77} -3.00000 q^{79} +(-1.00000 + 1.73205i) q^{83} +(8.00000 + 13.8564i) q^{85} +(-1.50000 + 7.79423i) q^{91} +2.00000 q^{95} +(-5.00000 + 8.66025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 2 * q + 2 * q^5 + 4 * q^7	\( 2 q + 2 q^{5} + 4 q^{7} - 2 q^{11} + 3 q^{13} - 8 q^{17} + q^{19} - 8 q^{23} + q^{25} - 4 q^{29} + 6 q^{31} + 10 q^{35} + q^{37} - 6 q^{41} - 11 q^{43} + 12 q^{47} + 2 q^{49} + 12 q^{53} - 8 q^{55} + 8 q^{59} - 12 q^{61} + 12 q^{65} + 26 q^{67} - 20 q^{71} + 11 q^{73} + 2 q^{77} - 6 q^{79} - 2 q^{83} + 16 q^{85} - 3 q^{91} + 4 q^{95} - 10 q^{97}+O(q^{100}) \) 2 * q + 2 * q^5 + 4 * q^7 - 2 * q^11 + 3 * q^13 - 8 * q^17 + q^19 - 8 * q^23 + q^25 - 4 * q^29 + 6 * q^31 + 10 * q^35 + q^37 - 6 * q^41 - 11 * q^43 + 12 * q^47 + 2 * q^49 + 12 * q^53 - 8 * q^55 + 8 * q^59 - 12 * q^61 + 12 * q^65 + 26 * q^67 - 20 * q^71 + 11 * q^73 + 2 * q^77 - 6 * q^79 - 2 * q^83 + 16 * q^85 - 3 * q^91 + 4 * q^95 - 10 * q^97

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