LMFDB - Embedded newform 912.2.q.b.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(49,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("912.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.q (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:	$7.28235666434$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	912.577
Dual form			912.2.q.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +2.00000 q^{11} +(1.50000 - 2.59808i) q^{13} +(-2.00000 - 3.46410i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{21} +(2.00000 - 3.46410i) q^{23} +(2.50000 - 4.33013i) q^{25} +1.00000 q^{27} +3.00000 q^{31} +(-1.00000 - 1.73205i) q^{33} -5.00000 q^{37} -3.00000 q^{39} +(-2.00000 - 3.46410i) q^{41} +(-4.50000 - 7.79423i) q^{43} +(5.00000 - 8.66025i) q^{47} -6.00000 q^{49} +(-2.00000 + 3.46410i) q^{51} +(2.00000 - 3.46410i) q^{53} +(3.50000 + 2.59808i) q^{57} +(-7.00000 - 12.1244i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(0.500000 - 0.866025i) q^{63} +(1.50000 - 2.59808i) q^{67} -4.00000 q^{69} +(7.00000 + 12.1244i) q^{71} +(5.50000 + 9.52628i) q^{73} -5.00000 q^{75} -2.00000 q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.00000 q^{83} +(7.00000 - 12.1244i) q^{89} +(-1.50000 + 2.59808i) q^{91} +(-1.50000 - 2.59808i) q^{93} +(-1.00000 - 1.73205i) q^{97} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 2 q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 - 2 * q^7 - q^9	$ 2 q - q^{3} - 2 q^{7} - q^{9} + 4 q^{11} + 3 q^{13} - 4 q^{17} - 8 q^{19} + q^{21} + 4 q^{23} + 5 q^{25} + 2 q^{27} + 6 q^{31} - 2 q^{33} - 10 q^{37} - 6 q^{39} - 4 q^{41} - 9 q^{43} + 10 q^{47} - 12 q^{49} - 4 q^{51} + 4 q^{53} + 7 q^{57} - 14 q^{59} - 11 q^{61} + q^{63} + 3 q^{67} - 8 q^{69} + 14 q^{71} + 11 q^{73} - 10 q^{75} - 4 q^{77} + q^{79} - q^{81} - 16 q^{83} + 14 q^{89} - 3 q^{91} - 3 q^{93} - 2 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - q^3 - 2 * q^7 - q^9 + 4 * q^11 + 3 * q^13 - 4 * q^17 - 8 * q^19 + q^21 + 4 * q^23 + 5 * q^25 + 2 * q^27 + 6 * q^31 - 2 * q^33 - 10 * q^37 - 6 * q^39 - 4 * q^41 - 9 * q^43 + 10 * q^47 - 12 * q^49 - 4 * q^51 + 4 * q^53 + 7 * q^57 - 14 * q^59 - 11 * q^61 + q^63 + 3 * q^67 - 8 * q^69 + 14 * q^71 + 11 * q^73 - 10 * q^75 - 4 * q^77 + q^79 - q^81 - 16 * q^83 + 14 * q^89 - 3 * q^91 - 3 * q^93 - 2 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	1.50000	−	2.59808i	0.416025	−	0.720577i	−0.579510	−	0.814965i	$-0.696756\pi$
$13$	1.50000	−	2.59808i	0.416025	−	0.720577i	0.995535	+	0.0943882i	$0.0300895\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$		0			0
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$		0			0
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$		0			0
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		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
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.00000			−0.821995			−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000			−0.821995			−0.410997	+	0.911636i	$0.634819\pi$
$38$		0			0
$39$	−3.00000			−0.480384
$40$		0			0
$41$	−2.00000	−	3.46410i	−0.312348	−	0.541002i	0.666523	−	0.745485i	$-0.267782\pi$
$41$	−2.00000	−	3.46410i	−0.312348	−	0.541002i	−0.978870	+	0.204483i	$0.934449\pi$
$42$		0			0
$43$	−4.50000	−	7.79423i	−0.686244	−	1.18861i	−0.973044	−	0.230618i	$-0.925925\pi$
$43$	−4.50000	−	7.79423i	−0.686244	−	1.18861i	0.286801	−	0.957990i	$-0.407408\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	−0.227844	−	0.973698i	$-0.573168\pi$
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	0.957169	−	0.289530i	$-0.0934991\pi$
$48$		0			0
$49$	−6.00000			−0.857143
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$		0			0
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.50000	+	2.59808i	0.463586	+	0.344124i
$58$		0			0
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.812198	−	0.583382i	$-0.801729\pi$
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.0991242	−	0.995075i	$-0.531604\pi$
$60$		0			0
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	0.262776	+	0.964857i	$0.415362\pi$
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	−0.966978	+	0.254858i	$0.917971\pi$
$62$		0			0
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$		0			0
$69$	−4.00000			−0.481543
$70$		0			0
$71$	7.00000	+	12.1244i	0.830747	+	1.43890i	0.897447	+	0.441123i	$0.145420\pi$
$71$	7.00000	+	12.1244i	0.830747	+	1.43890i	−0.0666994	+	0.997773i	$0.521247\pi$
$72$		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
$75$	−5.00000			−0.577350
$76$		0			0
$77$	−2.00000			−0.227921
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$		0			0
$91$	−1.50000	+	2.59808i	−0.157243	+	0.272352i
$92$		0			0
$93$	−1.50000	−	2.59808i	−0.155543	−	0.269408i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$	−1.00000	+	1.73205i	−0.100504	+	0.174078i
$100$		0			0
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	3.00000			0.295599			0.147799	−	0.989017i	$-0.452781\pi$
$103$	3.00000			0.295599			0.147799	+	0.989017i	$0.452781\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.0000			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$		0			0
$111$	2.50000	+	4.33013i	0.237289	+	0.410997i
$112$		0			0
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.50000	+	2.59808i	0.138675	+	0.240192i
$118$		0			0
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$		0			0
$121$	−7.00000			−0.636364
$122$		0			0
$123$	−2.00000	+	3.46410i	−0.180334	+	0.312348i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	−0.987108	−	0.160055i	$-0.948833\pi$
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	0.632166	+	0.774833i	$0.282166\pi$
$128$		0			0
$129$	−4.50000	+	7.79423i	−0.396203	+	0.686244i
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	4.00000	−	1.73205i	0.346844	−	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	−9.50000	+	16.4545i	−0.805779	+	1.39565i	0.109984	+	0.993933i	$0.464920\pi$
$139$	−9.50000	+	16.4545i	−0.805779	+	1.39565i	−0.915764	+	0.401718i	$0.868413\pi$
$140$		0			0
$141$	−10.0000			−0.842152
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$		0			0
$149$	11.0000	+	19.0526i	0.901155	+	1.56085i	0.825997	+	0.563675i	$0.190613\pi$
$149$	11.0000	+	19.0526i	0.901155	+	1.56085i	0.0751583	+	0.997172i	$0.476054\pi$
$150$		0			0
$151$	20.0000			1.62758			0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000			1.62758			0.813788	+	0.581161i	$0.197401\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$		0			0
$156$		0			0
$157$	10.5000	+	18.1865i	0.837991	+	1.45144i	0.891572	+	0.452880i	$0.149603\pi$
$157$	10.5000	+	18.1865i	0.837991	+	1.45144i	−0.0535803	+	0.998564i	$0.517063\pi$
$158$		0			0
$159$	−4.00000			−0.317221
$160$		0			0
$161$	−2.00000	+	3.46410i	−0.157622	+	0.273009i
$162$		0			0
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	−0.726293	−	0.687386i	$-0.758758\pi$
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	0.958440	+	0.285295i	$0.0920916\pi$
$168$		0			0
$169$	2.00000	+	3.46410i	0.153846	+	0.266469i
$170$		0			0
$171$	0.500000	−	4.33013i	0.0382360	−	0.331133i
$172$		0			0
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.810745	+	0.585399i	$0.199062\pi$
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.101598	+	0.994826i	$0.467605\pi$
$174$		0			0
$175$	−2.50000	+	4.33013i	−0.188982	+	0.327327i
$176$		0			0
$177$	−7.00000	+	12.1244i	−0.526152	+	0.911322i
$178$		0			0
$179$	−4.00000			−0.298974			−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000			−0.298974			−0.149487	+	0.988764i	$0.547762\pi$
$180$		0			0
$181$	9.00000	−	15.5885i	0.668965	−	1.15868i	−0.309229	−	0.950988i	$-0.600071\pi$
$181$	9.00000	−	15.5885i	0.668965	−	1.15868i	0.978194	−	0.207693i	$-0.0665956\pi$
$182$		0			0
$183$	11.0000			0.813143
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$		0			0
$189$	−1.00000			−0.0727393
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	0.999326	−	0.0366998i	$-0.0116845\pi$
$193$	6.50000	+	11.2583i	0.467880	+	0.810392i	−0.531446	+	0.847092i	$0.678351\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	2.50000	−	4.33013i	0.177220	−	0.306955i	−0.763707	−	0.645563i	$-0.776623\pi$
$199$	2.50000	−	4.33013i	0.177220	−	0.306955i	0.940927	+	0.338608i	$0.109956\pi$
$200$		0			0
$201$	−3.00000			−0.211604
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$		0			0
$209$	−8.00000	+	3.46410i	−0.553372	+	0.239617i
$210$		0			0
$211$	12.5000	+	21.6506i	0.860535	+	1.49049i	0.871413	+	0.490550i	$0.163204\pi$
$211$	12.5000	+	21.6506i	0.860535	+	1.49049i	−0.0108774	+	0.999941i	$0.503462\pi$
$212$		0			0
$213$	7.00000	−	12.1244i	0.479632	−	0.830747i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.00000			−0.203653
$218$		0			0
$219$	5.50000	−	9.52628i	0.371656	−	0.643726i
$220$		0			0
$221$	−12.0000			−0.807207
$222$		0			0
$223$	4.50000	+	7.79423i	0.301342	+	0.521940i	0.976440	−	0.215788i	$-0.0692320\pi$
$223$	4.50000	+	7.79423i	0.301342	+	0.521940i	−0.675098	+	0.737728i	$0.735899\pi$
$224$		0			0
$225$	2.50000	+	4.33013i	0.166667	+	0.288675i
$226$		0			0
$227$	−8.00000			−0.530979			−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000			−0.530979			−0.265489	+	0.964114i	$0.585534\pi$
$228$		0			0
$229$	−11.0000			−0.726900			−0.363450	−	0.931614i	$-0.618401\pi$
$229$	−11.0000			−0.726900			−0.363450	+	0.931614i	$0.618401\pi$
$230$		0			0
$231$	1.00000	+	1.73205i	0.0657952	+	0.113961i
$232$		0			0
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.500000	−	0.866025i	0.0324785	−	0.0562544i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	−12.5000	+	21.6506i	−0.805196	+	1.39464i	0.110963	+	0.993825i	$0.464606\pi$
$241$	−12.5000	+	21.6506i	−0.805196	+	1.39464i	−0.916159	+	0.400815i	$0.868727\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.50000	+	12.9904i	−0.0954427	+	0.826558i
$248$		0			0
$249$	4.00000	+	6.92820i	0.253490	+	0.439057i
$250$		0			0
$251$	−9.00000	+	15.5885i	−0.568075	+	0.983935i	0.428681	+	0.903456i	$0.358978\pi$
$251$	−9.00000	+	15.5885i	−0.568075	+	0.983935i	−0.996756	+	0.0804789i	$0.974355\pi$
$252$		0			0
$253$	4.00000	−	6.92820i	0.251478	−	0.435572i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	−0.615948	−	0.787787i	$-0.711227\pi$
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	0.990217	+	0.139533i	$0.0445601\pi$
$258$		0			0
$259$	5.00000			0.310685
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−14.0000			−0.856786
$268$		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
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$	3.00000			0.181568
$274$		0			0
$275$	5.00000	−	8.66025i	0.301511	−	0.522233i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$		0			0
$279$	−1.50000	+	2.59808i	−0.0898027	+	0.155543i
$280$		0			0
$281$	4.00000	−	6.92820i	0.238620	−	0.413302i	−0.721699	−	0.692207i	$-0.756638\pi$
$281$	4.00000	−	6.92820i	0.238620	−	0.413302i	0.960319	+	0.278906i	$0.0899716\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.00000	+	3.46410i	0.118056	+	0.204479i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$		0			0
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.00000			0.116052
$298$		0			0
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$		0			0
$301$	4.50000	+	7.79423i	0.259376	+	0.449252i
$302$		0			0
$303$	−10.0000			−0.574485
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−6.00000	−	10.3923i	−0.342438	−	0.593120i	0.642447	−	0.766330i	$-0.277919\pi$
$307$	−6.00000	−	10.3923i	−0.342438	−	0.593120i	−0.984885	+	0.173210i	$0.944586\pi$
$308$		0			0
$309$	−1.50000	−	2.59808i	−0.0853320	−	0.147799i
$310$		0			0
$311$	−10.0000			−0.567048			−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000			−0.567048			−0.283524	+	0.958965i	$0.591504\pi$
$312$		0			0
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	−0.938269	−	0.345907i	$-0.887571\pi$
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	0.768699	+	0.639611i	$0.220905\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−5.00000	−	8.66025i	−0.279073	−	0.483368i
$322$		0			0
$323$	14.0000	+	10.3923i	0.778981	+	0.578243i
$324$		0			0
$325$	−7.50000	−	12.9904i	−0.416025	−	0.720577i
$326$		0			0
$327$	−7.00000	+	12.1244i	−0.387101	+	0.670478i
$328$		0			0
$329$	−5.00000	+	8.66025i	−0.275659	+	0.477455i
$330$		0			0
$331$	−15.0000			−0.824475			−0.412237	−	0.911077i	$-0.635253\pi$
$331$	−15.0000			−0.824475			−0.412237	+	0.911077i	$0.635253\pi$
$332$		0			0
$333$	2.50000	−	4.33013i	0.136999	−	0.237289i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.50000	+	16.4545i	0.517498	+	0.896333i	0.999793	+	0.0203242i	$0.00646983\pi$
$337$	9.50000	+	16.4545i	0.517498	+	0.896333i	−0.482295	+	0.876009i	$0.660197\pi$
$338$		0			0
$339$	−5.00000	−	8.66025i	−0.271563	−	0.470360i
$340$		0			0
$341$	6.00000			0.324918
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	0.996826	−	0.0796169i	$-0.0253697\pi$
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	−0.567363	+	0.823468i	$0.692036\pi$
$348$		0			0
$349$	−29.0000			−1.55233			−0.776167	−	0.630527i	$-0.782839\pi$
$349$	−29.0000			−1.55233			−0.776167	+	0.630527i	$0.782839\pi$
$350$		0			0
$351$	1.50000	−	2.59808i	0.0800641	−	0.138675i
$352$		0			0
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.00000	−	3.46410i	0.105851	−	0.183340i
$358$		0			0
$359$	−18.0000	−	31.1769i	−0.950004	−	1.64545i	−0.745409	−	0.666608i	$-0.767746\pi$
$359$	−18.0000	−	31.1769i	−0.950004	−	1.64545i	−0.204595	−	0.978847i	$-0.565588\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$		0			0
$363$	3.50000	+	6.06218i	0.183702	+	0.318182i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	11.5000	−	19.9186i	0.600295	−	1.03974i	−0.392481	−	0.919760i	$-0.628383\pi$
$367$	11.5000	−	19.9186i	0.600295	−	1.03974i	0.992776	−	0.119982i	$-0.0382835\pi$
$368$		0			0
$369$	4.00000			0.208232
$370$		0			0
$371$	−2.00000	+	3.46410i	−0.103835	+	0.179847i
$372$		0			0
$373$	26.0000			1.34623			0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000			1.34623			0.673114	+	0.739538i	$0.264956\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		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
$381$	8.00000			0.409852
$382$		0			0
$383$	7.00000	+	12.1244i	0.357683	+	0.619526i	0.987573	−	0.157159i	$-0.0502334\pi$
$383$	7.00000	+	12.1244i	0.357683	+	0.619526i	−0.629890	+	0.776684i	$0.716900\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	9.00000			0.457496
$388$		0			0
$389$	8.00000	−	13.8564i	0.405616	−	0.702548i	−0.588777	−	0.808296i	$-0.700390\pi$
$389$	8.00000	−	13.8564i	0.405616	−	0.702548i	0.994393	+	0.105748i	$0.0337237\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$	−3.00000	+	5.19615i	−0.151330	+	0.262111i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.50000	−	12.9904i	−0.376414	−	0.651969i	0.614123	−	0.789210i	$-0.289510\pi$
$397$	−7.50000	−	12.9904i	−0.376414	−	0.651969i	−0.990538	+	0.137241i	$0.956176\pi$
$398$		0			0
$399$	−3.50000	−	2.59808i	−0.175219	−	0.130066i
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		0			0
$403$	4.50000	−	7.79423i	0.224161	−	0.388258i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.0000			−0.495682
$408$		0			0
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	−0.210017	−	0.977698i	$-0.567352\pi$
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	0.951720	−	0.306968i	$-0.0993146\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$		0			0
$413$	7.00000	+	12.1244i	0.344447	+	0.596601i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	19.0000			0.930434
$418$		0			0
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$		0			0
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	0.718076	−	0.695965i	$-0.245023\pi$
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	−0.961761	+	0.273890i	$0.911690\pi$
$422$		0			0
$423$	5.00000	+	8.66025i	0.243108	+	0.421076i
$424$		0			0
$425$	−20.0000			−0.970143
$426$		0			0
$427$	5.50000	−	9.52628i	0.266164	−	0.461009i
$428$		0			0
$429$	−6.00000			−0.289683
$430$		0			0
$431$	−5.00000	+	8.66025i	−0.240842	+	0.417150i	−0.960954	−	0.276707i	$-0.910757\pi$
$431$	−5.00000	+	8.66025i	−0.240842	+	0.417150i	0.720113	+	0.693857i	$0.244090\pi$
$432$		0			0
$433$	4.50000	−	7.79423i	0.216256	−	0.374567i	−0.737404	−	0.675452i	$-0.763949\pi$
$433$	4.50000	−	7.79423i	0.216256	−	0.374567i	0.953660	+	0.300885i	$0.0972820\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.00000	+	17.3205i	−0.0956730	+	0.828552i
$438$		0			0
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	0.998595	−	0.0529862i	$-0.0168739\pi$
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	−0.545185	+	0.838316i	$0.683541\pi$
$440$		0			0
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$		0			0
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	−0.426414	−	0.904528i	$-0.640223\pi$
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	0.996551	−	0.0829786i	$-0.0264433\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	11.0000	−	19.0526i	0.520282	−	0.901155i
$448$		0			0
$449$	−36.0000			−1.69895			−0.849473	−	0.527633i	$-0.823080\pi$
$449$	−36.0000			−1.69895			−0.849473	+	0.527633i	$0.823080\pi$
$450$		0			0
$451$	−4.00000	−	6.92820i	−0.188353	−	0.326236i
$452$		0			0
$453$	−10.0000	−	17.3205i	−0.469841	−	0.813788i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$		0			0
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$		0			0
$463$	9.00000			0.418265			0.209133	−	0.977887i	$-0.432936\pi$
$463$	9.00000			0.418265			0.209133	+	0.977887i	$0.432936\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$	−1.50000	+	2.59808i	−0.0692636	+	0.119968i
$470$		0			0
$471$	10.5000	−	18.1865i	0.483814	−	0.837991i
$472$		0			0
$473$	−9.00000	−	15.5885i	−0.413820	−	0.716758i
$474$		0			0
$475$	−2.50000	+	21.6506i	−0.114708	+	0.993399i
$476$		0			0
$477$	2.00000	+	3.46410i	0.0915737	+	0.158610i
$478$		0			0
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	−7.50000	+	12.9904i	−0.341971	+	0.592310i
$482$		0			0
$483$	4.00000			0.182006
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$		0			0
$489$	5.50000	+	9.52628i	0.248719	+	0.430793i
$490$		0			0
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	0.975898	+	0.218229i	$0.0700279\pi$
$491$	15.0000	+	25.9808i	0.676941	+	1.17250i	−0.298957	+	0.954267i	$0.596639\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.00000	−	12.1244i	−0.313993	−	0.543852i
$498$		0			0
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	0.916542	−	0.399937i	$-0.130968\pi$
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	−0.804627	+	0.593780i	$0.797635\pi$
$500$		0			0
$501$	−6.00000			−0.268060
$502$		0			0
$503$	8.00000	−	13.8564i	0.356702	−	0.617827i	−0.630705	−	0.776022i	$-0.717234\pi$
$503$	8.00000	−	13.8564i	0.356702	−	0.617827i	0.987408	+	0.158196i	$0.0505677\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.00000	−	3.46410i	0.0888231	−	0.153846i
$508$		0			0
$509$	−13.0000	+	22.5167i	−0.576215	+	0.998033i	0.419694	+	0.907666i	$0.362138\pi$
$509$	−13.0000	+	22.5167i	−0.576215	+	0.998033i	−0.995908	+	0.0903676i	$0.971196\pi$
$510$		0			0
$511$	−5.50000	−	9.52628i	−0.243306	−	0.421418i
$512$		0			0
$513$	−4.00000	+	1.73205i	−0.176604	+	0.0764719i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	10.0000	−	17.3205i	0.439799	−	0.761755i
$518$		0			0
$519$	12.0000	−	20.7846i	0.526742	−	0.912343i
$520$		0			0
$521$	34.0000			1.48957			0.744784	−	0.667306i	$-0.232553\pi$
$521$	34.0000			1.48957			0.744784	+	0.667306i	$0.232553\pi$
$522$		0			0
$523$	18.5000	−	32.0429i	0.808949	−	1.40114i	−0.104644	−	0.994510i	$-0.533370\pi$
$523$	18.5000	−	32.0429i	0.808949	−	1.40114i	0.913593	−	0.406630i	$-0.133296\pi$
$524$		0			0
$525$	5.00000			0.218218
$526$		0			0
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	14.0000			0.607548
$532$		0			0
$533$	−12.0000			−0.519778
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.00000	+	3.46410i	0.0863064	+	0.149487i
$538$		0			0
$539$	−12.0000			−0.516877
$540$		0			0
$541$	15.5000	−	26.8468i	0.666397	−	1.15423i	−0.312507	−	0.949915i	$-0.601169\pi$
$541$	15.5000	−	26.8468i	0.666397	−	1.15423i	0.978905	−	0.204318i	$-0.0654977\pi$
$542$		0			0
$543$	−18.0000			−0.772454
$544$		0			0
$545$		0			0
$546$		0			0
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	−0.724157	−	0.689635i	$-0.757771\pi$
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	0.959320	+	0.282321i	$0.0911043\pi$
$548$		0			0
$549$	−5.50000	−	9.52628i	−0.234734	−	0.406572i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−0.500000	−	0.866025i	−0.0212622	−	0.0368271i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	0.240561	+	0.970634i	$0.422669\pi$
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	−0.960874	+	0.276985i	$0.910665\pi$
$558$		0			0
$559$	−27.0000			−1.14198
$560$		0			0
$561$	−4.00000	+	6.92820i	−0.168880	+	0.292509i
$562$		0			0
$563$	6.00000			0.252870			0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000			0.252870			0.126435	+	0.991975i	$0.459647\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$		0			0
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	7.00000			0.292941			0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000			0.292941			0.146470	+	0.989215i	$0.453209\pi$
$572$		0			0
$573$	−4.00000	−	6.92820i	−0.167102	−	0.289430i
$574$		0			0
$575$	−10.0000	−	17.3205i	−0.417029	−	0.722315i
$576$		0			0
$577$	−14.0000			−0.582828			−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000			−0.582828			−0.291414	+	0.956597i	$0.594126\pi$
$578$		0			0
$579$	6.50000	−	11.2583i	0.270131	−	0.467880i
$580$		0			0
$581$	8.00000			0.331896
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.00000	−	1.73205i	−0.0412744	−	0.0714894i	0.844650	−	0.535319i	$-0.179808\pi$
$587$	−1.00000	−	1.73205i	−0.0412744	−	0.0714894i	−0.885925	+	0.463829i	$0.846475\pi$
$588$		0			0
$589$	−12.0000	+	5.19615i	−0.494451	+	0.214104i
$590$		0			0
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$		0			0
$593$	−17.0000	+	29.4449i	−0.698106	+	1.20916i	0.271016	+	0.962575i	$0.412640\pi$
$593$	−17.0000	+	29.4449i	−0.698106	+	1.20916i	−0.969122	+	0.246581i	$0.920693\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.00000			−0.204636
$598$		0			0
$599$	−23.0000	+	39.8372i	−0.939755	+	1.62770i	−0.173826	+	0.984776i	$0.555613\pi$
$599$	−23.0000	+	39.8372i	−0.939755	+	1.62770i	−0.765928	+	0.642926i	$0.777720\pi$
$600$		0			0
$601$	27.0000			1.10135			0.550676	−	0.834719i	$-0.314370\pi$
$601$	27.0000			1.10135			0.550676	+	0.834719i	$0.314370\pi$
$602$		0			0
$603$	1.50000	+	2.59808i	0.0610847	+	0.105802i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−5.00000			−0.202944			−0.101472	−	0.994838i	$-0.532355\pi$
$607$	−5.00000			−0.202944			−0.101472	+	0.994838i	$0.532355\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−15.0000	−	25.9808i	−0.606835	−	1.05107i
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	−0.0398207	−	0.999207i	$-0.512679\pi$
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	0.885249	−	0.465118i	$-0.153988\pi$
$618$		0			0
$619$	−1.00000			−0.0401934			−0.0200967	−	0.999798i	$-0.506397\pi$
$619$	−1.00000			−0.0401934			−0.0200967	+	0.999798i	$0.506397\pi$
$620$		0			0
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$		0			0
$623$	−7.00000	+	12.1244i	−0.280449	+	0.485752i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$	7.00000	+	5.19615i	0.279553	+	0.207514i
$628$		0			0
$629$	10.0000	+	17.3205i	0.398726	+	0.690614i
$630$		0			0
$631$	8.50000	−	14.7224i	0.338380	−	0.586091i	−0.645748	−	0.763550i	$-0.723455\pi$
$631$	8.50000	−	14.7224i	0.338380	−	0.586091i	0.984128	+	0.177459i	$0.0567879\pi$
$632$		0			0
$633$	12.5000	−	21.6506i	0.496830	−	0.860535i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$		0			0
$639$	−14.0000			−0.553831
$640$		0			0
$641$	7.00000	+	12.1244i	0.276483	+	0.478883i	0.970508	−	0.241068i	$-0.0774976\pi$
$641$	7.00000	+	12.1244i	0.276483	+	0.478883i	−0.694025	+	0.719951i	$0.744164\pi$
$642$		0			0
$643$	18.5000	+	32.0429i	0.729569	+	1.26365i	0.957066	+	0.289871i	$0.0936125\pi$
$643$	18.5000	+	32.0429i	0.729569	+	1.26365i	−0.227497	+	0.973779i	$0.573054\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−48.0000			−1.88707			−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000			−1.88707			−0.943537	+	0.331266i	$0.892524\pi$
$648$		0			0
$649$	−14.0000	−	24.2487i	−0.549548	−	0.951845i
$650$		0			0
$651$	1.50000	+	2.59808i	0.0587896	+	0.101827i
$652$		0			0
$653$	−42.0000			−1.64359			−0.821794	−	0.569785i	$-0.807026\pi$
$653$	−42.0000			−1.64359			−0.821794	+	0.569785i	$0.807026\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−11.0000			−0.429151
$658$		0			0
$659$	−7.00000	+	12.1244i	−0.272681	+	0.472298i	−0.969548	−	0.244903i	$-0.921244\pi$
$659$	−7.00000	+	12.1244i	−0.272681	+	0.472298i	0.696866	+	0.717201i	$0.254577\pi$
$660$		0			0
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	−0.946729	−	0.322031i	$-0.895634\pi$
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	0.752252	+	0.658876i	$0.228968\pi$
$662$		0			0
$663$	6.00000	+	10.3923i	0.233021	+	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	4.50000	−	7.79423i	0.173980	−	0.301342i
$670$		0			0
$671$	−11.0000	+	19.0526i	−0.424650	+	0.735516i
$672$		0			0
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$		0			0
$675$	2.50000	−	4.33013i	0.0962250	−	0.166667i
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		0			0
$679$	1.00000	+	1.73205i	0.0383765	+	0.0664700i
$680$		0			0
$681$	4.00000	+	6.92820i	0.153280	+	0.265489i
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	5.50000	+	9.52628i	0.209838	+	0.363450i
$688$		0			0
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	−4.00000			−0.152167			−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000			−0.152167			−0.0760836	+	0.997101i	$0.524242\pi$
$692$		0			0
$693$	1.00000	−	1.73205i	0.0379869	−	0.0657952i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−8.00000	+	13.8564i	−0.303022	+	0.524849i
$698$		0			0
$699$	−9.00000	+	15.5885i	−0.340411	+	0.589610i
$700$		0			0
$701$	22.0000	+	38.1051i	0.830929	+	1.43921i	0.897303	+	0.441416i	$0.145524\pi$
$701$	22.0000	+	38.1051i	0.830929	+	1.43921i	−0.0663742	+	0.997795i	$0.521143\pi$
$702$		0			0
$703$	20.0000	−	8.66025i	0.754314	−	0.326628i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.00000	+	8.66025i	−0.188044	+	0.325702i
$708$		0			0
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	0.995228	−	0.0975728i	$-0.0311079\pi$
$710$		0			0
$711$	−1.00000			−0.0375029
$712$		0			0
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$		0			0
$719$	20.0000	+	34.6410i	0.745874	+	1.29189i	0.949785	+	0.312903i	$0.101301\pi$
$719$	20.0000	+	34.6410i	0.745874	+	1.29189i	−0.203911	+	0.978989i	$0.565365\pi$
$720$		0			0
$721$	−3.00000			−0.111726
$722$		0			0
$723$	25.0000			0.929760
$724$		0			0
$725$		0			0
$726$		0			0
$727$	8.50000	+	14.7224i	0.315248	+	0.546025i	0.979490	−	0.201492i	$-0.0645791\pi$
$727$	8.50000	+	14.7224i	0.315248	+	0.546025i	−0.664243	+	0.747517i	$0.731246\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−18.0000	+	31.1769i	−0.665754	+	1.15312i
$732$		0			0
$733$	−2.00000			−0.0738717			−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000			−0.0738717			−0.0369358	+	0.999318i	$0.511760\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$		0			0
$739$	−2.50000	−	4.33013i	−0.0919640	−	0.159286i	0.816373	−	0.577524i	$-0.195981\pi$
$739$	−2.50000	−	4.33013i	−0.0919640	−	0.159286i	−0.908337	+	0.418238i	$0.862648\pi$
$740$		0			0
$741$	12.0000	−	5.19615i	0.440831	−	0.190885i
$742$		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
$745$		0			0
$746$		0			0
$747$	4.00000	−	6.92820i	0.146352	−	0.253490i
$748$		0			0
$749$	−10.0000			−0.365392
$750$		0			0
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$		0			0
$753$	18.0000			0.655956
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.50000	−	4.33013i	−0.0908640	−	0.157381i	0.817011	−	0.576622i	$-0.195630\pi$
$757$	−2.50000	−	4.33013i	−0.0908640	−	0.157381i	−0.907875	+	0.419241i	$0.862296\pi$
$758$		0			0
$759$	−8.00000			−0.290382
$760$		0			0
$761$	−34.0000			−1.23250			−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000			−1.23250			−0.616250	+	0.787551i	$0.711349\pi$
$762$		0			0
$763$	7.00000	+	12.1244i	0.253417	+	0.438931i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−42.0000			−1.51653
$768$		0			0
$769$	−13.5000	+	23.3827i	−0.486822	+	0.843201i	−0.999885	−	0.0151499i	$-0.995177\pi$
$769$	−13.5000	+	23.3827i	−0.486822	+	0.843201i	0.513063	+	0.858351i	$0.328511\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$		0			0
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		0			0
$775$	7.50000	−	12.9904i	0.269408	−	0.466628i
$776$		0			0
$777$	−2.50000	−	4.33013i	−0.0896870	−	0.155342i
$778$		0			0
$779$	14.0000	+	10.3923i	0.501602	+	0.372343i
$780$		0			0
$781$	14.0000	+	24.2487i	0.500959	+	0.867687i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	47.0000			1.67537			0.837685	−	0.546154i	$-0.183909\pi$
$787$	47.0000			1.67537			0.837685	+	0.546154i	$0.183909\pi$
$788$		0			0
$789$	9.00000	−	15.5885i	0.320408	−	0.554964i
$790$		0			0
$791$	−10.0000			−0.355559
$792$		0			0
$793$	16.5000	+	28.5788i	0.585932	+	1.01486i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	26.0000			0.920967			0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000			0.920967			0.460484	+	0.887668i	$0.347676\pi$
$798$		0			0
$799$	−40.0000			−1.41510
$800$		0			0
$801$	7.00000	+	12.1244i	0.247333	+	0.428393i
$802$		0			0
$803$	11.0000	+	19.0526i	0.388182	+	0.672350i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.00000	+	1.73205i	−0.0352017	+	0.0609711i
$808$		0			0
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$		0			0
$811$	2.00000	−	3.46410i	0.0702295	−	0.121641i	−0.828772	−	0.559586i	$-0.810960\pi$
$811$	2.00000	−	3.46410i	0.0702295	−	0.121641i	0.899002	+	0.437945i	$0.144294\pi$
$812$		0			0
$813$	−8.00000	+	13.8564i	−0.280572	+	0.485965i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	31.5000	+	23.3827i	1.10205	+	0.818057i
$818$		0			0
$819$	−1.50000	−	2.59808i	−0.0524142	−	0.0907841i
$820$		0			0
$821$	−24.0000	+	41.5692i	−0.837606	+	1.45078i	0.0542853	+	0.998525i	$0.482712\pi$
$821$	−24.0000	+	41.5692i	−0.837606	+	1.45078i	−0.891891	+	0.452250i	$0.850621\pi$
$822$		0			0
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	−0.829060	−	0.559159i	$-0.811124\pi$
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	0.898776	+	0.438408i	$0.144457\pi$
$824$		0			0
$825$	−10.0000			−0.348155
$826$		0			0
$827$	18.0000	−	31.1769i	0.625921	−	1.08413i	−0.362441	−	0.932007i	$-0.618056\pi$
$827$	18.0000	−	31.1769i	0.625921	−	1.08413i	0.988362	−	0.152121i	$-0.0486102\pi$
$828$		0			0
$829$	−31.0000			−1.07667			−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000			−1.07667			−0.538337	+	0.842729i	$0.680947\pi$
$830$		0			0
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$		0			0
$833$	12.0000	+	20.7846i	0.415775	+	0.720144i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.00000			0.103695
$838$		0			0
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	0.743670	−	0.668546i	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$		0			0
$843$	−8.00000			−0.275535
$844$		0			0
$845$		0			0
$846$		0			0
$847$	7.00000			0.240523
$848$		0			0
$849$	−10.0000	+	17.3205i	−0.343199	+	0.594438i
$850$		0			0
$851$	−10.0000	+	17.3205i	−0.342796	+	0.593739i
$852$		0			0
$853$	−1.50000	−	2.59808i	−0.0513590	−	0.0889564i	0.839203	−	0.543818i	$-0.183022\pi$
$853$	−1.50000	−	2.59808i	−0.0513590	−	0.0889564i	−0.890562	+	0.454862i	$0.849689\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	0.244701	−	0.969599i	$-0.421310\pi$
$858$		0			0
$859$	3.50000	−	6.06218i	0.119418	−	0.206839i	−0.800119	−	0.599841i	$-0.795230\pi$
$859$	3.50000	−	6.06218i	0.119418	−	0.206839i	0.919537	+	0.393003i	$0.128564\pi$
$860$		0			0
$861$	2.00000	−	3.46410i	0.0681598	−	0.118056i
$862$		0			0
$863$	22.0000			0.748889			0.374444	−	0.927249i	$-0.377833\pi$
$863$	22.0000			0.748889			0.374444	+	0.927249i	$0.377833\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	1.00000	+	1.73205i	0.0339227	+	0.0587558i
$870$		0			0
$871$	−4.50000	−	7.79423i	−0.152477	−	0.264097i
$872$		0			0
$873$	2.00000			0.0676897
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.5000	+	21.6506i	0.422095	+	0.731090i	0.996144	−	0.0877308i	$-0.0279615\pi$
$877$	12.5000	+	21.6506i	0.422095	+	0.731090i	−0.574049	+	0.818821i	$0.694628\pi$
$878$		0			0
$879$	−7.00000	−	12.1244i	−0.236104	−	0.408944i
$880$		0			0
$881$	36.0000			1.21287			0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000			1.21287			0.606435	+	0.795133i	$0.292599\pi$
$882$		0			0
$883$	−4.50000	+	7.79423i	−0.151437	+	0.262297i	−0.931756	−	0.363085i	$-0.881723\pi$
$883$	−4.50000	+	7.79423i	−0.151437	+	0.262297i	0.780319	+	0.625382i	$0.215057\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.00000	−	15.5885i	0.302190	−	0.523409i	−0.674441	−	0.738328i	$-0.735615\pi$
$887$	9.00000	−	15.5885i	0.302190	−	0.523409i	0.976632	+	0.214919i	$0.0689488\pi$
$888$		0			0
$889$	4.00000	−	6.92820i	0.134156	−	0.232364i
$890$		0			0
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$		0			0
$893$	−5.00000	+	43.3013i	−0.167319	+	1.44902i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−6.00000	+	10.3923i	−0.200334	+	0.346989i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−16.0000			−0.533037
$902$		0			0
$903$	4.50000	−	7.79423i	0.149751	−	0.259376i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	26.0000	+	45.0333i	0.863316	+	1.49531i	0.868710	+	0.495321i	$0.164950\pi$
$907$	26.0000	+	45.0333i	0.863316	+	1.49531i	−0.00539395	+	0.999985i	$0.501717\pi$
$908$		0			0
$909$	5.00000	+	8.66025i	0.165840	+	0.287242i
$910$		0			0
$911$	60.0000			1.98789			0.993944	−	0.109885i	$-0.0350482\pi$
$911$	60.0000			1.98789			0.993944	+	0.109885i	$0.0350482\pi$
$912$		0			0
$913$	−16.0000			−0.529523
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.00000	+	5.19615i	0.0990687	+	0.171592i
$918$		0			0
$919$	−55.0000			−1.81428			−0.907141	−	0.420826i	$-0.861740\pi$
$919$	−55.0000			−1.81428			−0.907141	+	0.420826i	$0.861740\pi$
$920$		0			0
$921$	−6.00000	+	10.3923i	−0.197707	+	0.342438i
$922$		0			0
$923$	42.0000			1.38245
$924$		0			0
$925$	−12.5000	+	21.6506i	−0.410997	+	0.711868i
$926$		0			0
$927$	−1.50000	+	2.59808i	−0.0492665	+	0.0853320i
$928$		0			0
$929$	−6.00000	−	10.3923i	−0.196854	−	0.340960i	0.750653	−	0.660697i	$-0.229739\pi$
$929$	−6.00000	−	10.3923i	−0.196854	−	0.340960i	−0.947507	+	0.319736i	$0.896406\pi$
$930$		0			0
$931$	24.0000	−	10.3923i	0.786568	−	0.340594i
$932$		0			0
$933$	5.00000	+	8.66025i	0.163693	+	0.283524i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	−0.586349	−	0.810059i	$-0.699435\pi$
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	0.994706	+	0.102763i	$0.0327685\pi$
$938$		0			0
$939$	6.00000			0.195803
$940$		0			0
$941$	16.0000	−	27.7128i	0.521585	−	0.903412i	−0.478100	−	0.878306i	$-0.658674\pi$
$941$	16.0000	−	27.7128i	0.521585	−	0.903412i	0.999685	−	0.0251063i	$-0.00799243\pi$
$942$		0			0
$943$	−16.0000			−0.521032
$944$		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
$949$	33.0000			1.07123
$950$		0			0
$951$	12.0000			0.389127
$952$		0			0
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	0.999869	−	0.0162081i	$-0.00515944\pi$
$953$	15.0000	+	25.9808i	0.485898	+	0.841599i	−0.513971	+	0.857808i	$0.671826\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$		0			0
$961$	−22.0000			−0.709677
$962$		0			0
$963$	−5.00000	+	8.66025i	−0.161123	+	0.279073i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	25.5000	+	44.1673i	0.820025	+	1.42032i	0.905663	+	0.423998i	$0.139374\pi$
$967$	25.5000	+	44.1673i	0.820025	+	1.42032i	−0.0856383	+	0.996326i	$0.527293\pi$
$968$		0			0
$969$	2.00000	−	17.3205i	0.0642493	−	0.556415i
$970$		0			0
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	0.910140	−	0.414301i	$-0.135974\pi$
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	−0.813865	+	0.581054i	$0.802641\pi$
$972$		0			0
$973$	9.50000	−	16.4545i	0.304556	−	0.527506i
$974$		0			0
$975$	−7.50000	+	12.9904i	−0.240192	+	0.416025i
$976$		0			0
$977$	−42.0000			−1.34370			−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000			−1.34370			−0.671850	+	0.740688i	$0.734500\pi$
$978$		0			0
$979$	14.0000	−	24.2487i	0.447442	−	0.774992i
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	0.814209	−	0.580572i	$-0.197171\pi$
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	−0.909894	+	0.414840i	$0.863838\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	10.0000			0.318304
$988$		0			0
$989$	−36.0000			−1.14473
$990$		0			0
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	0.698853	−	0.715265i	$-0.253694\pi$
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	−0.968864	+	0.247592i	$0.920361\pi$
$992$		0			0
$993$	7.50000	+	12.9904i	0.238005	+	0.412237i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	24.5000	−	42.4352i	0.775923	−	1.34394i	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	24.5000	−	42.4352i	0.775923	−	1.34394i	0.934274	−	0.356555i	$-0.116049\pi$
$998$		0			0
$999$	−5.00000			−0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.q.b.577.1		2
3.2	odd	2		2736.2.s.k.577.1		2
4.3	odd	2		114.2.e.b.7.1	✓	2
12.11	even	2		342.2.g.c.235.1		2
19.11	even	3	inner	912.2.q.b.49.1		2
57.11	odd	6		2736.2.s.k.1873.1		2
76.7	odd	6		2166.2.a.b.1.1		1
76.11	odd	6		114.2.e.b.49.1	yes	2
76.31	even	6		2166.2.a.h.1.1		1
228.11	even	6		342.2.g.c.163.1		2
228.83	even	6		6498.2.a.u.1.1		1
228.107	odd	6		6498.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.e.b.7.1	✓	2	4.3	odd	2
114.2.e.b.49.1	yes	2	76.11	odd	6
342.2.g.c.163.1		2	228.11	even	6
342.2.g.c.235.1		2	12.11	even	2
912.2.q.b.49.1		2	19.11	even	3	inner
912.2.q.b.577.1		2	1.1	even	1	trivial
2166.2.a.b.1.1		1	76.7	odd	6
2166.2.a.h.1.1		1	76.31	even	6
2736.2.s.k.577.1		2	3.2	odd	2
2736.2.s.k.1873.1		2	57.11	odd	6
6498.2.a.g.1.1		1	228.107	odd	6
6498.2.a.u.1.1		1	228.83	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} -1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +2.00000 q^{11} +(1.50000 - 2.59808i) q^{13} +(-2.00000 - 3.46410i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{21} +(2.00000 - 3.46410i) q^{23} +(2.50000 - 4.33013i) q^{25} +1.00000 q^{27} +3.00000 q^{31} +(-1.00000 - 1.73205i) q^{33} -5.00000 q^{37} -3.00000 q^{39} +(-2.00000 - 3.46410i) q^{41} +(-4.50000 - 7.79423i) q^{43} +(5.00000 - 8.66025i) q^{47} -6.00000 q^{49} +(-2.00000 + 3.46410i) q^{51} +(2.00000 - 3.46410i) q^{53} +(3.50000 + 2.59808i) q^{57} +(-7.00000 - 12.1244i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(0.500000 - 0.866025i) q^{63} +(1.50000 - 2.59808i) q^{67} -4.00000 q^{69} +(7.00000 + 12.1244i) q^{71} +(5.50000 + 9.52628i) q^{73} -5.00000 q^{75} -2.00000 q^{77} +(0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.00000 q^{83} +(7.00000 - 12.1244i) q^{89} +(-1.50000 + 2.59808i) q^{91} +(-1.50000 - 2.59808i) q^{93} +(-1.00000 - 1.73205i) q^{97} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 2 q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 - 2 * q^7 - q^9	\( 2 q - q^{3} - 2 q^{7} - q^{9} + 4 q^{11} + 3 q^{13} - 4 q^{17} - 8 q^{19} + q^{21} + 4 q^{23} + 5 q^{25} + 2 q^{27} + 6 q^{31} - 2 q^{33} - 10 q^{37} - 6 q^{39} - 4 q^{41} - 9 q^{43} + 10 q^{47} - 12 q^{49} - 4 q^{51} + 4 q^{53} + 7 q^{57} - 14 q^{59} - 11 q^{61} + q^{63} + 3 q^{67} - 8 q^{69} + 14 q^{71} + 11 q^{73} - 10 q^{75} - 4 q^{77} + q^{79} - q^{81} - 16 q^{83} + 14 q^{89} - 3 q^{91} - 3 q^{93} - 2 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - q^3 - 2 * q^7 - q^9 + 4 * q^11 + 3 * q^13 - 4 * q^17 - 8 * q^19 + q^21 + 4 * q^23 + 5 * q^25 + 2 * q^27 + 6 * q^31 - 2 * q^33 - 10 * q^37 - 6 * q^39 - 4 * q^41 - 9 * q^43 + 10 * q^47 - 12 * q^49 - 4 * q^51 + 4 * q^53 + 7 * q^57 - 14 * q^59 - 11 * q^61 + q^63 + 3 * q^67 - 8 * q^69 + 14 * q^71 + 11 * q^73 - 10 * q^75 - 4 * q^77 + q^79 - q^81 - 16 * q^83 + 14 * q^89 - 3 * q^91 - 3 * q^93 - 2 * q^97 - 2 * q^99

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