LMFDB - Embedded newform 2268.2.k.f.1621.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(1297,2268)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2268, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2268.1297"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.6
Root			$1.68442 + 0.403398i$ of defining polynomial
Character	$\chi$	$=$	2268.1621
Dual form			2268.2.k.f.1297.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80173 + 3.12069i) q^{5} +(2.62435 - 0.335842i) q^{7} +(-3.01334 + 5.21926i) q^{11} +5.11278 q^{13} +(-0.111006 + 0.192269i) q^{17} +(1.71161 + 2.96460i) q^{19} +(-0.509880 - 0.883137i) q^{23} +(-3.99245 + 6.91513i) q^{25} -5.67359 q^{29} +(2.52322 - 4.37035i) q^{31} +(5.77642 + 7.58467i) q^{35} +(1.68526 + 2.91896i) q^{37} +0.191162 q^{41} -3.42323 q^{43} +(-1.03506 - 1.79278i) q^{47} +(6.77442 - 1.76274i) q^{49} +(2.65207 - 4.59353i) q^{53} -21.7169 q^{55} +(3.79814 - 6.57858i) q^{59} +(-0.891408 - 1.54396i) q^{61} +(9.21184 + 15.9554i) q^{65} +(-6.49235 + 11.2451i) q^{67} -5.89560 q^{71} +(6.30519 - 10.9209i) q^{73} +(-6.15522 + 14.7092i) q^{77} +(-6.30763 - 10.9251i) q^{79} -7.19891 q^{83} -0.800013 q^{85} +(4.44697 + 7.70238i) q^{89} +(13.4177 - 1.71709i) q^{91} +(-6.16773 + 10.6828i) q^{95} +5.45982 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{5} - 3 q^{7} - 2 q^{11} - 4 q^{13} - 2 q^{17} + 7 q^{19} - 11 q^{23} - 9 q^{25} + 2 q^{29} - q^{31} + 19 q^{35} + 10 q^{37} - 66 q^{41} - 14 q^{43} + 3 q^{47} + 17 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots + 36 q^{97}+O(q^{100}) $ 14 * q + 2 * q^5 - 3 * q^7 - 2 * q^11 - 4 * q^13 - 2 * q^17 + 7 * q^19 - 11 * q^23 - 9 * q^25 + 2 * q^29 - q^31 + 19 * q^35 + 10 * q^37 - 66 * q^41 - 14 * q^43 + 3 * q^47 + 17 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 28 * q^77 - 10 * q^79 - 50 * q^83 - 16 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 + 36 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.80173	+	3.12069i	0.805757	+	1.39561i	0.915779	+	0.401684i	$0.131575\pi$
$5$	1.80173	+	3.12069i	0.805757	+	1.39561i	−0.110021	+	0.993929i	$0.535092\pi$
$6$		0			0
$7$	2.62435	−	0.335842i	0.991911	−	0.126937i
$7$	2.62435	−	0.335842i	0.991911	−	0.126937i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.01334	+	5.21926i	−0.908557	+	1.57367i	−0.0924872	+	0.995714i	$0.529482\pi$
$11$	−3.01334	+	5.21926i	−0.908557	+	1.57367i	−0.816070	+	0.577953i	$0.803852\pi$
$12$		0			0
$13$	5.11278			1.41803			0.709015	−	0.705193i	$-0.249140\pi$
$13$	5.11278			1.41803			0.709015	+	0.705193i	$0.249140\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.111006	+	0.192269i	−0.0269230	+	0.0466320i	−0.879173	−	0.476503i	$-0.841904\pi$
$17$	−0.111006	+	0.192269i	−0.0269230	+	0.0466320i	0.852250	+	0.523135i	$0.175238\pi$
$18$		0			0
$19$	1.71161	+	2.96460i	0.392671	+	0.680127i	0.992801	−	0.119776i	$-0.0382177\pi$
$19$	1.71161	+	2.96460i	0.392671	+	0.680127i	−0.600130	+	0.799903i	$0.704884\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.509880	−	0.883137i	−0.106317	−	0.184147i	0.807958	−	0.589240i	$-0.200573\pi$
$23$	−0.509880	−	0.883137i	−0.106317	−	0.184147i	−0.914276	+	0.405093i	$0.867239\pi$
$24$		0			0
$25$	−3.99245	+	6.91513i	−0.798490	+	1.38303i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.67359			−1.05356			−0.526779	−	0.850002i	$-0.676601\pi$
$29$	−5.67359			−1.05356			−0.526779	+	0.850002i	$0.676601\pi$
$30$		0			0
$31$	2.52322	−	4.37035i	0.453184	−	0.784938i	−0.545398	−	0.838177i	$-0.683621\pi$
$31$	2.52322	−	4.37035i	0.453184	−	0.784938i	0.998582	+	0.0532395i	$0.0169547\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.77642	+	7.58467i	0.976394	+	1.28204i
$36$		0			0
$37$	1.68526	+	2.91896i	0.277055	+	0.479874i	0.970652	−	0.240490i	$-0.0773082\pi$
$37$	1.68526	+	2.91896i	0.277055	+	0.479874i	−0.693596	+	0.720364i	$0.743975\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.191162			0.0298544			0.0149272	−	0.999889i	$-0.495248\pi$
$41$	0.191162			0.0298544			0.0149272	+	0.999889i	$0.495248\pi$
$42$		0			0
$43$	−3.42323			−0.522038			−0.261019	−	0.965334i	$-0.584058\pi$
$43$	−3.42323			−0.522038			−0.261019	+	0.965334i	$0.584058\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.03506	−	1.79278i	−0.150980	−	0.261504i	0.780608	−	0.625021i	$-0.214909\pi$
$47$	−1.03506	−	1.79278i	−0.150980	−	0.261504i	−0.931588	+	0.363516i	$0.881576\pi$
$48$		0			0
$49$	6.77442	−	1.76274i	0.967774	−	0.251819i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.65207	−	4.59353i	0.364290	−	0.630969i	−0.624372	−	0.781127i	$-0.714645\pi$
$53$	2.65207	−	4.59353i	0.364290	−	0.630969i	0.988662	+	0.150158i	$0.0479782\pi$
$54$		0			0
$55$	−21.7169			−2.92831
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.79814	−	6.57858i	0.494476	−	0.856458i	−0.505503	−	0.862825i	$-0.668693\pi$
$59$	3.79814	−	6.57858i	0.494476	−	0.856458i	0.999980	+	0.00636650i	$0.00202653\pi$
$60$		0			0
$61$	−0.891408	−	1.54396i	−0.114133	−	0.197684i	0.803300	−	0.595575i	$-0.203076\pi$
$61$	−0.891408	−	1.54396i	−0.114133	−	0.197684i	−0.917433	+	0.397891i	$0.869742\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.21184	+	15.9554i	1.14259	+	1.97902i
$66$		0			0
$67$	−6.49235	+	11.2451i	−0.793167	+	1.37380i	0.130830	+	0.991405i	$0.458236\pi$
$67$	−6.49235	+	11.2451i	−0.793167	+	1.37380i	−0.923997	+	0.382400i	$0.875098\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.89560			−0.699679			−0.349839	−	0.936810i	$-0.613764\pi$
$71$	−5.89560			−0.699679			−0.349839	+	0.936810i	$0.613764\pi$
$72$		0			0
$73$	6.30519	−	10.9209i	0.737967	−	1.27820i	−0.215442	−	0.976517i	$-0.569119\pi$
$73$	6.30519	−	10.9209i	0.737967	−	1.27820i	0.953409	−	0.301680i	$-0.0975473\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.15522	+	14.7092i	−0.701452	+	1.67627i
$78$		0			0
$79$	−6.30763	−	10.9251i	−0.709664	−	1.22917i	−0.964982	−	0.262317i	$-0.915514\pi$
$79$	−6.30763	−	10.9251i	−0.709664	−	1.22917i	0.255318	−	0.966857i	$-0.417820\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.19891			−0.790184			−0.395092	−	0.918642i	$-0.629287\pi$
$83$	−7.19891			−0.790184			−0.395092	+	0.918642i	$0.629287\pi$
$84$		0			0
$85$	−0.800013			−0.0867736
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.44697	+	7.70238i	0.471378	+	0.816451i	0.999464	−	0.0327404i	$-0.0104235\pi$
$89$	4.44697	+	7.70238i	0.471378	+	0.816451i	−0.528086	+	0.849191i	$0.677090\pi$
$90$		0			0
$91$	13.4177	−	1.71709i	1.40656	−	0.180000i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.16773	+	10.6828i	−0.632796	+	1.09603i
$96$		0			0
$97$	5.45982			0.554361			0.277181	−	0.960818i	$-0.410600\pi$
$97$	5.45982			0.554361			0.277181	+	0.960818i	$0.410600\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.98645	+	3.44063i	−0.197659	+	0.342355i	−0.947769	−	0.318958i	$-0.896667\pi$
$101$	−1.98645	+	3.44063i	−0.197659	+	0.342355i	0.750110	+	0.661313i	$0.230001\pi$
$102$		0			0
$103$	−1.77894	−	3.08121i	−0.175284	−	0.303601i	0.764975	−	0.644059i	$-0.222751\pi$
$103$	−1.77894	−	3.08121i	−0.175284	−	0.303601i	−0.940260	+	0.340458i	$0.889418\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.23035	+	2.13102i	0.118942	+	0.206014i	0.919349	−	0.393444i	$-0.128716\pi$
$107$	1.23035	+	2.13102i	0.118942	+	0.206014i	−0.800407	+	0.599457i	$0.795383\pi$
$108$		0			0
$109$	−2.97628	+	5.15506i	−0.285075	+	0.493765i	−0.972627	−	0.232370i	$-0.925352\pi$
$109$	−2.97628	+	5.15506i	−0.285075	+	0.493765i	0.687552	+	0.726135i	$0.258685\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.05949			0.664101			0.332050	−	0.943262i	$-0.392260\pi$
$113$	7.05949			0.664101			0.332050	+	0.943262i	$0.392260\pi$
$114$		0			0
$115$	1.83733	−	3.18235i	0.171332	−	0.296755i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.226748	+	0.541861i	−0.0207859	+	0.0496723i
$120$		0			0
$121$	−12.6605	−	21.9286i	−1.15095	−	1.99351i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.7560			−0.962042
$126$		0			0
$127$	2.76393			0.245259			0.122629	−	0.992453i	$-0.460867\pi$
$127$	2.76393			0.245259			0.122629	+	0.992453i	$0.460867\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.22748	+	7.32221i	0.369357	+	0.639744i	0.989465	−	0.144772i	$-0.0462448\pi$
$131$	4.22748	+	7.32221i	0.369357	+	0.639744i	−0.620108	+	0.784516i	$0.712911\pi$
$132$		0			0
$133$	5.48751	+	7.20532i	0.475828	+	0.624781i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.04286	−	15.6627i	0.772584	−	1.33815i	−0.163559	−	0.986534i	$-0.552297\pi$
$137$	9.04286	−	15.6627i	0.772584	−	1.33815i	0.936143	−	0.351621i	$-0.114369\pi$
$138$		0			0
$139$	−12.0187			−1.01941			−0.509707	−	0.860348i	$-0.670246\pi$
$139$	−12.0187			−1.01941			−0.509707	+	0.860348i	$0.670246\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−15.4066	+	26.6850i	−1.28836	+	2.23151i
$144$		0			0
$145$	−10.2223	−	17.7055i	−0.848912	−	1.47036i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.49026	−	4.31325i	−0.204010	−	0.353355i	0.745807	−	0.666162i	$-0.232064\pi$
$149$	−2.49026	−	4.31325i	−0.204010	−	0.353355i	−0.949817	+	0.312807i	$0.898731\pi$
$150$		0			0
$151$	0.0921906	−	0.159679i	0.00750237	−	0.0129945i	−0.862250	−	0.506483i	$-0.830945\pi$
$151$	0.0921906	−	0.159679i	0.00750237	−	0.0129945i	0.869752	+	0.493489i	$0.164279\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	18.1846			1.46063
$156$		0			0
$157$	−2.16698	+	3.75332i	−0.172944	+	0.299548i	−0.939448	−	0.342692i	$-0.888661\pi$
$157$	−2.16698	+	3.75332i	−0.172944	+	0.299548i	0.766504	+	0.642240i	$0.221995\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.63470	−	2.14642i	−0.128832	−	0.169162i
$162$		0			0
$163$	11.8652	+	20.5511i	0.929353	+	1.60969i	0.784407	+	0.620247i	$0.212967\pi$
$163$	11.8652	+	20.5511i	0.929353	+	1.60969i	0.144946	+	0.989440i	$0.453699\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.18889			0.246764			0.123382	−	0.992359i	$-0.460626\pi$
$167$	3.18889			0.246764			0.123382	+	0.992359i	$0.460626\pi$
$168$		0			0
$169$	13.1405			1.01081
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.6530	+	18.4515i	0.809932	+	1.40284i	0.912910	+	0.408160i	$0.133830\pi$
$173$	10.6530	+	18.4515i	0.809932	+	1.40284i	−0.102978	+	0.994684i	$0.532837\pi$
$174$		0			0
$175$	−8.15519	+	19.4885i	−0.616475	+	1.47320i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.250143	+	0.433260i	−0.0186965	+	0.0323833i	−0.875222	−	0.483721i	$-0.839285\pi$
$179$	−0.250143	+	0.433260i	−0.0186965	+	0.0323833i	0.856526	+	0.516104i	$0.172618\pi$
$180$		0			0
$181$	5.88424			0.437372			0.218686	−	0.975795i	$-0.429823\pi$
$181$	5.88424			0.437372			0.218686	+	0.975795i	$0.429823\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.07276	+	10.5183i	−0.446478	+	0.773323i
$186$		0			0
$187$	−0.669001	−	1.15874i	−0.0489222	−	0.0847357i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.94466	−	6.83235i	−0.285425	−	0.494371i	0.687287	−	0.726386i	$-0.258802\pi$
$191$	−3.94466	−	6.83235i	−0.285425	−	0.494371i	−0.972712	+	0.232015i	$0.925468\pi$
$192$		0			0
$193$	−9.50508	+	16.4633i	−0.684190	+	1.18505i	0.289500	+	0.957178i	$0.406511\pi$
$193$	−9.50508	+	16.4633i	−0.684190	+	1.18505i	−0.973691	+	0.227875i	$0.926822\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.72107			0.692597			0.346299	−	0.938124i	$-0.387438\pi$
$197$	9.72107			0.692597			0.346299	+	0.938124i	$0.387438\pi$
$198$		0			0
$199$	−7.54581	+	13.0697i	−0.534908	+	0.926489i	0.464259	+	0.885699i	$0.346321\pi$
$199$	−7.54581	+	13.0697i	−0.534908	+	0.926489i	−0.999168	+	0.0407893i	$0.987013\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−14.8895	+	1.90543i	−1.04504	+	0.133735i
$204$		0			0
$205$	0.344421	+	0.596555i	0.0240554	+	0.0416652i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−20.6307			−1.42706
$210$		0			0
$211$	17.5035			1.20499			0.602494	−	0.798124i	$-0.294174\pi$
$211$	17.5035			1.20499			0.602494	+	0.798124i	$0.294174\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.16773	−	10.6828i	−0.420636	−	0.728562i
$216$		0			0
$217$	5.15407	−	12.3167i	0.349881	−	0.836114i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.567551	+	0.983028i	−0.0381776	+	0.0661256i
$222$		0			0
$223$	−10.0067			−0.670101			−0.335051	−	0.942200i	$-0.608753\pi$
$223$	−10.0067			−0.670101			−0.335051	+	0.942200i	$0.608753\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.13317	+	1.96270i	−0.0752110	+	0.130269i	−0.901178	−	0.433449i	$-0.857296\pi$
$227$	−1.13317	+	1.96270i	−0.0752110	+	0.130269i	0.825967	+	0.563718i	$0.190630\pi$
$228$		0			0
$229$	2.51228	+	4.35140i	0.166016	+	0.287549i	0.937016	−	0.349287i	$-0.113576\pi$
$229$	2.51228	+	4.35140i	0.166016	+	0.287549i	−0.770999	+	0.636836i	$0.780243\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.72393	+	13.3782i	0.506011	+	0.876438i	0.999976	+	0.00695541i	$0.00221399\pi$
$233$	7.72393	+	13.3782i	0.506011	+	0.876438i	−0.493964	+	0.869482i	$0.664453\pi$
$234$		0			0
$235$	3.72981	−	6.46022i	0.243306	−	0.421418i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.25381			−0.598579			−0.299290	−	0.954162i	$-0.596750\pi$
$239$	−9.25381			−0.598579			−0.299290	+	0.954162i	$0.596750\pi$
$240$		0			0
$241$	8.16387	−	14.1402i	0.525881	−	0.910853i	−0.473664	−	0.880705i	$-0.657069\pi$
$241$	8.16387	−	14.1402i	0.525881	−	0.910853i	0.999545	−	0.0301474i	$-0.00959768\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	17.7066	+	17.9649i	1.13123	+	1.14773i
$246$		0			0
$247$	8.75111	+	15.1574i	0.556820	+	0.964440i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.54803			−0.476427			−0.238214	−	0.971213i	$-0.576562\pi$
$251$	−7.54803			−0.476427			−0.238214	+	0.971213i	$0.576562\pi$
$252$		0			0
$253$	6.14577			0.386381
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.6463	+	21.9041i	0.788856	+	1.36634i	0.926668	+	0.375880i	$0.122659\pi$
$257$	12.6463	+	21.9041i	0.788856	+	1.36634i	−0.137813	+	0.990458i	$0.544007\pi$
$258$		0			0
$259$	5.40302	+	7.09438i	0.335727	+	0.440823i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11.7490	−	20.3499i	0.724474	−	1.25483i	−0.234716	−	0.972064i	$-0.575416\pi$
$263$	11.7490	−	20.3499i	0.724474	−	1.25483i	0.959190	−	0.282762i	$-0.0912505\pi$
$264$		0			0
$265$	19.1133			1.17412
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.9078	−	24.0891i	0.847975	−	1.46874i	−0.0350378	−	0.999386i	$-0.511155\pi$
$269$	13.9078	−	24.0891i	0.847975	−	1.46874i	0.883013	−	0.469349i	$-0.155512\pi$
$270$		0			0
$271$	−9.57834	−	16.5902i	−0.581843	−	1.00778i	−0.995261	−	0.0972397i	$-0.968999\pi$
$271$	−9.57834	−	16.5902i	−0.581843	−	1.00778i	0.413418	−	0.910541i	$-0.364335\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−24.0612	−	41.6753i	−1.45095	−	2.51312i
$276$		0			0
$277$	−13.7905	+	23.8859i	−0.828593	+	1.43516i	0.0705495	+	0.997508i	$0.477525\pi$
$277$	−13.7905	+	23.8859i	−0.828593	+	1.43516i	−0.899142	+	0.437657i	$0.855809\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.385182			0.0229780			0.0114890	−	0.999934i	$-0.496343\pi$
$281$	0.385182			0.0229780			0.0114890	+	0.999934i	$0.496343\pi$
$282$		0			0
$283$	7.49904	−	12.9887i	0.445772	−	0.772099i	−0.552334	−	0.833623i	$-0.686263\pi$
$283$	7.49904	−	12.9887i	0.445772	−	0.772099i	0.998106	+	0.0615239i	$0.0195960\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.501675	−	0.0642002i	0.0296129	−	0.00378962i
$288$		0			0
$289$	8.47536	+	14.6797i	0.498550	+	0.863514i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	22.4647			1.31240			0.656200	−	0.754587i	$-0.272163\pi$
$293$	22.4647			1.31240			0.656200	+	0.754587i	$0.272163\pi$
$294$		0			0
$295$	27.3729			1.59371
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.60690	−	4.51529i	−0.150761	−	0.261126i
$300$		0			0
$301$	−8.98375	+	1.14967i	−0.517815	+	0.0662656i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.21215	−	5.56361i	0.183927	−	0.318571i
$306$		0			0
$307$	6.90792			0.394256			0.197128	−	0.980378i	$-0.436839\pi$
$307$	6.90792			0.394256			0.197128	+	0.980378i	$0.436839\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.5890	−	20.0727i	0.657152	−	1.13822i	−0.324198	−	0.945989i	$-0.605094\pi$
$311$	11.5890	−	20.0727i	0.657152	−	1.13822i	0.981350	−	0.192231i	$-0.0615722\pi$
$312$		0			0
$313$	−8.21883	−	14.2354i	−0.464556	−	0.804635i	0.534625	−	0.845089i	$-0.320453\pi$
$313$	−8.21883	−	14.2354i	−0.464556	−	0.804635i	−0.999181	+	0.0404546i	$0.987119\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.18401	−	12.4431i	−0.403494	−	0.698873i	0.590651	−	0.806927i	$-0.298871\pi$
$317$	−7.18401	−	12.4431i	−0.403494	−	0.698873i	−0.994145	+	0.108055i	$0.965538\pi$
$318$		0			0
$319$	17.0965	−	29.6119i	0.957218	−	1.65795i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.760001			−0.0422876
$324$		0			0
$325$	−20.4125	+	35.3555i	−1.13228	+	1.96117i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.31846	−	4.35727i	−0.182953	−	0.240224i
$330$		0			0
$331$	−1.87582	−	3.24902i	−0.103105	−	0.178582i	0.809858	−	0.586626i	$-0.199544\pi$
$331$	−1.87582	−	3.24902i	−0.103105	−	0.178582i	−0.912962	+	0.408044i	$0.866211\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−46.7898			−2.55640
$336$		0			0
$337$	5.54341			0.301969			0.150984	−	0.988536i	$-0.451756\pi$
$337$	5.54341			0.301969			0.150984	+	0.988536i	$0.451756\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	15.2067	+	26.3387i	0.823487	+	1.42632i
$342$		0			0
$343$	17.1864	−	6.90117i	0.927981	−	0.372628i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.77609	−	6.54037i	0.202711	−	0.351106i	−0.746690	−	0.665172i	$-0.768358\pi$
$347$	3.77609	−	6.54037i	0.202711	−	0.351106i	0.949401	+	0.314066i	$0.101691\pi$
$348$		0			0
$349$	18.2036			0.974415			0.487207	−	0.873286i	$-0.338016\pi$
$349$	18.2036			0.974415			0.487207	+	0.873286i	$0.338016\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.266224	+	0.461114i	−0.0141697	+	0.0245426i	−0.873023	−	0.487678i	$-0.837844\pi$
$353$	−0.266224	+	0.461114i	−0.0141697	+	0.0245426i	0.858854	+	0.512221i	$0.171177\pi$
$354$		0			0
$355$	−10.6223	−	18.3983i	−0.563771	−	0.976481i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.0550	−	22.6118i	−0.689014	−	1.19341i	−0.972157	−	0.234330i	$-0.924710\pi$
$359$	−13.0550	−	22.6118i	−0.689014	−	1.19341i	0.283143	−	0.959078i	$-0.408623\pi$
$360$		0			0
$361$	3.64075	−	6.30597i	0.191618	−	0.331893i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	45.4410			2.37849
$366$		0			0
$367$	−10.5921	+	18.3461i	−0.552904	+	0.957658i	0.445159	+	0.895451i	$0.353147\pi$
$367$	−10.5921	+	18.3461i	−0.552904	+	0.957658i	−0.998063	+	0.0622062i	$0.980186\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.41727	−	12.9457i	0.281251	−	0.672107i
$372$		0			0
$373$	−9.00427	−	15.5959i	−0.466223	−	0.807523i	0.533032	−	0.846095i	$-0.321052\pi$
$373$	−9.00427	−	15.5959i	−0.466223	−	0.807523i	−0.999256	+	0.0385721i	$0.987719\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−29.0078			−1.49398
$378$		0			0
$379$	−15.9120			−0.817343			−0.408672	−	0.912681i	$-0.634008\pi$
$379$	−15.9120			−0.817343			−0.408672	+	0.912681i	$0.634008\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.154293	−	0.267243i	−0.00788400	−	0.0136555i	0.862056	−	0.506812i	$-0.169176\pi$
$383$	−0.154293	−	0.267243i	−0.00788400	−	0.0136555i	−0.869940	+	0.493157i	$0.835843\pi$
$384$		0			0
$385$	−56.9927	+	7.29346i	−2.90462	+	0.371709i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.38753	−	4.13533i	0.121053	−	0.209669i	−0.799130	−	0.601158i	$-0.794706\pi$
$389$	2.38753	−	4.13533i	0.121053	−	0.209669i	0.920183	+	0.391488i	$0.128040\pi$
$390$		0			0
$391$	0.226400			0.0114495
$392$		0			0
$393$		0			0
$394$		0			0
$395$	22.7293	−	39.3683i	1.14363	−	1.98083i
$396$		0			0
$397$	−4.75029	−	8.22774i	−0.238410	−	0.412939i	0.721848	−	0.692052i	$-0.243293\pi$
$397$	−4.75029	−	8.22774i	−0.238410	−	0.412939i	−0.960258	+	0.279113i	$0.909960\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.67088	−	16.7505i	−0.482941	−	0.836478i	0.516867	−	0.856066i	$-0.327098\pi$
$401$	−9.67088	−	16.7505i	−0.482941	−	0.836478i	−0.999808	+	0.0195874i	$0.993765\pi$
$402$		0			0
$403$	12.9007	−	22.3446i	0.642629	−	1.11307i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−20.3131			−1.00688
$408$		0			0
$409$	5.34036	−	9.24977i	0.264064	−	0.457372i	−0.703254	−	0.710939i	$-0.748270\pi$
$409$	5.34036	−	9.24977i	0.264064	−	0.457372i	0.967318	+	0.253567i	$0.0816037\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.75829	−	18.5401i	0.381761	−	0.912297i
$414$		0			0
$415$	−12.9705	−	22.4655i	−0.636696	−	1.10279i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−35.0547			−1.71253			−0.856267	−	0.516533i	$-0.827222\pi$
$419$	−35.0547			−1.71253			−0.856267	+	0.516533i	$0.827222\pi$
$420$		0			0
$421$	−31.7305			−1.54645			−0.773226	−	0.634130i	$-0.781358\pi$
$421$	−31.7305			−1.54645			−0.773226	+	0.634130i	$0.781358\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.886375	−	1.53525i	−0.0429955	−	0.0744704i
$426$		0			0
$427$	−2.85790	−	3.75253i	−0.138303	−	0.181598i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.4768	−	30.2707i	0.841829	−	1.45809i	−0.0465186	−	0.998917i	$-0.514813\pi$
$431$	17.4768	−	30.2707i	0.841829	−	1.45809i	0.888347	−	0.459172i	$-0.151854\pi$
$432$		0			0
$433$	−28.3369			−1.36178			−0.680891	−	0.732385i	$-0.738407\pi$
$433$	−28.3369			−1.36178			−0.680891	+	0.732385i	$0.738407\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.74543	−	3.02318i	0.0834955	−	0.144618i
$438$		0			0
$439$	4.85457	+	8.40837i	0.231696	+	0.401310i	0.958307	−	0.285739i	$-0.0922391\pi$
$439$	4.85457	+	8.40837i	0.231696	+	0.401310i	−0.726611	+	0.687049i	$0.758906\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.03961	−	8.72885i	−0.239439	−	0.414720i	0.721114	−	0.692816i	$-0.243630\pi$
$443$	−5.03961	−	8.72885i	−0.239439	−	0.414720i	−0.960553	+	0.278096i	$0.910297\pi$
$444$		0			0
$445$	−16.0245	+	27.7552i	−0.759633	+	1.31572i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	28.9202			1.36483			0.682414	−	0.730966i	$-0.260930\pi$
$449$	28.9202			1.36483			0.682414	+	0.730966i	$0.260930\pi$
$450$		0			0
$451$	−0.576035	+	0.997723i	−0.0271245	+	0.0469809i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	29.5336	+	38.7788i	1.38456	+	1.81798i
$456$		0			0
$457$	4.10680	+	7.11318i	0.192108	+	0.332741i	0.945949	−	0.324317i	$-0.105134\pi$
$457$	4.10680	+	7.11318i	0.192108	+	0.332741i	−0.753841	+	0.657057i	$0.771801\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	28.1032			1.30890			0.654448	−	0.756107i	$-0.272901\pi$
$461$	28.1032			1.30890			0.654448	+	0.756107i	$0.272901\pi$
$462$		0			0
$463$	−3.09793			−0.143973			−0.0719866	−	0.997406i	$-0.522934\pi$
$463$	−3.09793			−0.143973			−0.0719866	+	0.997406i	$0.522934\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.75954	−	9.97582i	−0.266520	−	0.461626i	0.701441	−	0.712728i	$-0.252540\pi$
$467$	−5.75954	−	9.97582i	−0.266520	−	0.461626i	−0.967961	+	0.251102i	$0.919207\pi$
$468$		0			0
$469$	−13.2616	+	31.6914i	−0.612365	+	1.46337i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	10.3154	−	17.8667i	0.474301	−	0.821513i
$474$		0			0
$475$	−27.3341			−1.25418
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−20.3542	+	35.2545i	−0.930007	+	1.61082i	−0.146704	+	0.989180i	$0.546867\pi$
$479$	−20.3542	+	35.2545i	−0.930007	+	1.61082i	−0.783303	+	0.621640i	$0.786467\pi$
$480$		0			0
$481$	8.61637	+	14.9240i	0.392873	+	0.680475i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.83712	+	17.0384i	0.446681	+	0.773673i
$486$		0			0
$487$	16.7955	−	29.0907i	0.761077	−	1.31822i	−0.181219	−	0.983443i	$-0.558004\pi$
$487$	16.7955	−	29.0907i	0.761077	−	1.31822i	0.942296	−	0.334781i	$-0.108662\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.45980			−0.291527			−0.145763	−	0.989319i	$-0.546564\pi$
$491$	−6.45980			−0.291527			−0.145763	+	0.989319i	$0.546564\pi$
$492$		0			0
$493$	0.629804	−	1.09085i	0.0283650	−	0.0491295i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−15.4721	+	1.97999i	−0.694019	+	0.0888148i
$498$		0			0
$499$	6.00584	+	10.4024i	0.268859	+	0.465677i	0.968567	−	0.248752i	$-0.0800203\pi$
$499$	6.00584	+	10.4024i	0.268859	+	0.465677i	−0.699709	+	0.714428i	$0.746687\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−34.3935			−1.53353			−0.766765	−	0.641928i	$-0.778135\pi$
$503$	−34.3935			−1.53353			−0.766765	+	0.641928i	$0.778135\pi$
$504$		0			0
$505$	−14.3162			−0.637060
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.7523	−	27.2838i	−0.698208	−	1.20933i	−0.969087	−	0.246718i	$-0.920648\pi$
$509$	−15.7523	−	27.2838i	−0.698208	−	1.20933i	0.270879	−	0.962613i	$-0.412686\pi$
$510$		0			0
$511$	12.8793	−	30.7778i	0.569748	−	1.36153i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.41033	−	11.1030i	0.282473	−	0.489258i
$516$		0			0
$517$	12.4760			0.548695
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.3195	+	23.0701i	−0.583539	+	1.01072i	0.411517	+	0.911402i	$0.364999\pi$
$521$	−13.3195	+	23.0701i	−0.583539	+	1.01072i	−0.995056	+	0.0993168i	$0.968334\pi$
$522$		0			0
$523$	15.2006	+	26.3282i	0.664676	+	1.15125i	0.979373	+	0.202060i	$0.0647637\pi$
$523$	15.2006	+	26.3282i	0.664676	+	1.15125i	−0.314697	+	0.949192i	$0.601903\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.560188	+	0.970273i	0.0244022	+	0.0422658i
$528$		0			0
$529$	10.9800	−	19.0180i	0.477393	−	0.826869i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.977368			0.0423345
$534$		0			0
$535$	−4.43350	+	7.67904i	−0.191677	+	0.331994i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11.2135	+	40.6692i	−0.482998	+	1.75175i
$540$		0			0
$541$	−1.25855	−	2.17988i	−0.0541094	−	0.0937202i	0.837702	−	0.546128i	$-0.183899\pi$
$541$	−1.25855	−	2.17988i	−0.0541094	−	0.0937202i	−0.891811	+	0.452407i	$0.850565\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−21.4498			−0.918807
$546$		0			0
$547$	−18.5157			−0.791674			−0.395837	−	0.918321i	$-0.629546\pi$
$547$	−18.5157			−0.791674			−0.395837	+	0.918321i	$0.629546\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.71099	−	16.8199i	−0.413702	−	0.716553i
$552$		0			0
$553$	−20.2225	−	26.5530i	−0.859950	−	1.12915i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.2124	−	21.1524i	0.517454	−	0.896257i	−0.482340	−	0.875984i	$-0.660213\pi$
$557$	12.2124	−	21.1524i	0.517454	−	0.896257i	0.999794	−	0.0202733i	$-0.00645364\pi$
$558$		0			0
$559$	−17.5022			−0.740265
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.3700	−	21.4255i	0.521334	−	0.902976i	−0.478359	−	0.878165i	$-0.658768\pi$
$563$	12.3700	−	21.4255i	0.521334	−	0.902976i	0.999692	−	0.0248116i	$-0.00789858\pi$
$564$		0			0
$565$	12.7193	+	22.0304i	0.535104	+	0.926828i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.35982	+	14.4796i	0.350462	+	0.607018i	0.986330	−	0.164780i	$-0.0526913\pi$
$569$	8.35982	+	14.4796i	0.350462	+	0.607018i	−0.635869	+	0.771797i	$0.719358\pi$
$570$		0			0
$571$	14.8135	−	25.6578i	0.619926	−	1.07374i	−0.369573	−	0.929202i	$-0.620496\pi$
$571$	14.8135	−	25.6578i	0.619926	−	1.07374i	0.989499	−	0.144542i	$-0.0461708\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.14267			0.339573
$576$		0			0
$577$	15.3341	−	26.5594i	0.638367	−	1.10568i	−0.347425	−	0.937708i	$-0.612944\pi$
$577$	15.3341	−	26.5594i	0.638367	−	1.10568i	0.985791	−	0.167976i	$-0.0537230\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−18.8925	+	2.41770i	−0.783792	+	0.100303i
$582$		0			0
$583$	15.9832	+	27.6837i	0.661957	+	1.14654i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.7722			0.650989			0.325495	−	0.945544i	$-0.394469\pi$
$587$	15.7722			0.650989			0.325495	+	0.945544i	$0.394469\pi$
$588$		0			0
$589$	17.2751			0.711810
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.53339	+	2.65591i	0.0629688	+	0.109065i	0.895791	−	0.444475i	$-0.146610\pi$
$593$	1.53339	+	2.65591i	0.0629688	+	0.109065i	−0.832822	+	0.553540i	$0.813276\pi$
$594$		0			0
$595$	−2.09951	+	0.268678i	−0.0860717	+	0.0110147i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	16.1696	−	28.0066i	0.660673	−	1.14432i	−0.319766	−	0.947496i	$-0.603604\pi$
$599$	16.1696	−	28.0066i	0.660673	−	1.14432i	0.980439	−	0.196822i	$-0.0630622\pi$
$600$		0			0
$601$	29.9679			1.22242			0.611208	−	0.791470i	$-0.290684\pi$
$601$	29.9679			1.22242			0.611208	+	0.791470i	$0.290684\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	45.6215	−	79.0187i	1.85478	−	3.21257i
$606$		0			0
$607$	10.1275	+	17.5414i	0.411064	+	0.711984i	0.995006	−	0.0998113i	$-0.0318239\pi$
$607$	10.1275	+	17.5414i	0.411064	+	0.711984i	−0.583942	+	0.811795i	$0.698491\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.29206	−	9.16611i	−0.214094	−	0.370821i
$612$		0			0
$613$	12.5419	−	21.7233i	0.506564	−	0.877395i	−0.493407	−	0.869799i	$-0.664249\pi$
$613$	12.5419	−	21.7233i	0.506564	−	0.877395i	0.999971	−	0.00759665i	$-0.00241811\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−42.0944			−1.69466			−0.847328	−	0.531070i	$-0.821790\pi$
$617$	−42.0944			−1.69466			−0.847328	+	0.531070i	$0.821790\pi$
$618$		0			0
$619$	7.41252	−	12.8389i	0.297934	−	0.516037i	−0.677729	−	0.735312i	$-0.737036\pi$
$619$	7.41252	−	12.8389i	0.297934	−	0.516037i	0.975663	+	0.219275i	$0.0703690\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14.2572	+	18.7203i	0.571202	+	0.750011i
$624$		0			0
$625$	0.582932	+	1.00967i	0.0233173	+	0.0403867i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.748299			−0.0298366
$630$		0			0
$631$	20.6414			0.821722			0.410861	−	0.911698i	$-0.365228\pi$
$631$	20.6414			0.821722			0.410861	+	0.911698i	$0.365228\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.97984	+	8.62534i	0.197619	+	0.342286i
$636$		0			0
$637$	34.6361	−	9.01248i	1.37233	−	0.357088i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.776633	−	1.34517i	0.0306752	−	0.0531309i	−0.850280	−	0.526330i	$-0.823568\pi$
$641$	0.776633	−	1.34517i	0.0306752	−	0.0531309i	0.880955	+	0.473199i	$0.156901\pi$
$642$		0			0
$643$	21.4121			0.844412			0.422206	−	0.906500i	$-0.361256\pi$
$643$	21.4121			0.844412			0.422206	+	0.906500i	$0.361256\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.7637	−	25.5715i	0.580422	−	1.00532i	−0.415008	−	0.909818i	$-0.636221\pi$
$647$	14.7637	−	25.5715i	0.580422	−	1.00532i	0.995429	−	0.0955019i	$-0.0304456\pi$
$648$		0			0
$649$	22.8902	+	39.6470i	0.898520	+	1.55628i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.03041	+	13.9091i	0.314254	+	0.544304i	0.979279	−	0.202517i	$-0.0649123\pi$
$653$	8.03041	+	13.9091i	0.314254	+	0.544304i	−0.665025	+	0.746822i	$0.731579\pi$
$654$		0			0
$655$	−15.2335	+	26.3853i	−0.595224	+	1.03096i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	28.4200			1.10709			0.553543	−	0.832821i	$-0.313276\pi$
$659$	28.4200			1.10709			0.553543	+	0.832821i	$0.313276\pi$
$660$		0			0
$661$	−16.9884	+	29.4248i	−0.660773	+	1.14449i	0.319640	+	0.947539i	$0.396438\pi$
$661$	−16.9884	+	29.4248i	−0.660773	+	1.14449i	−0.980413	+	0.196953i	$0.936895\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.5985	+	30.1068i	−0.488550	+	1.16749i
$666$		0			0
$667$	2.89285	+	5.01055i	0.112011	+	0.194009i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.7445			0.414786
$672$		0			0
$673$	1.61404			0.0622166			0.0311083	−	0.999516i	$-0.490096\pi$
$673$	1.61404			0.0622166			0.0311083	+	0.999516i	$0.490096\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.3479	−	23.1193i	−0.513002	−	0.888545i	−0.999886	−	0.0150790i	$-0.995200\pi$
$677$	−13.3479	−	23.1193i	−0.513002	−	0.888545i	0.486884	−	0.873466i	$-0.338133\pi$
$678$		0			0
$679$	14.3285	−	1.83364i	0.549877	−	0.0703687i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	17.6183	−	30.5158i	0.674146	−	1.16765i	−0.302572	−	0.953126i	$-0.597845\pi$
$683$	17.6183	−	30.5158i	0.674146	−	1.16765i	0.976718	−	0.214528i	$-0.0688214\pi$
$684$		0			0
$685$	65.1711			2.49006
$686$		0			0
$687$		0			0
$688$		0			0
$689$	13.5595	−	23.4857i	0.516575	−	0.894734i
$690$		0			0
$691$	14.3904	+	24.9248i	0.547435	+	0.948185i	0.998449	+	0.0556685i	$0.0177290\pi$
$691$	14.3904	+	24.9248i	0.547435	+	0.948185i	−0.451014	+	0.892517i	$0.648938\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−21.6545	−	37.5066i	−0.821401	−	1.42271i
$696$		0			0
$697$	−0.0212202	+	0.0367544i	−0.000803771	+	0.00139217i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−17.2044			−0.649800			−0.324900	−	0.945748i	$-0.605331\pi$
$701$	−17.2044			−0.649800			−0.324900	+	0.945748i	$0.605331\pi$
$702$		0			0
$703$	−5.76903	+	9.99226i	−0.217583	+	0.376865i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.05762	+	9.69654i	−0.152603	+	0.364676i
$708$		0			0
$709$	−22.8211	−	39.5272i	−0.857063	−	1.48448i	−0.874718	−	0.484633i	$-0.838953\pi$
$709$	−22.8211	−	39.5272i	−0.857063	−	1.48448i	0.0176546	−	0.999844i	$-0.494380\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−5.14616			−0.192725
$714$		0			0
$715$	−111.034			−4.15243
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.1857	−	19.3741i	−0.417155	−	0.722533i	0.578497	−	0.815684i	$-0.303639\pi$
$719$	−11.1857	−	19.3741i	−0.417155	−	0.722533i	−0.995652	+	0.0931513i	$0.970306\pi$
$720$		0			0
$721$	−5.70336	−	7.48874i	−0.212404	−	0.278895i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	22.6515	−	39.2336i	0.841256	−	1.45710i
$726$		0			0
$727$	36.6062			1.35765			0.678824	−	0.734301i	$-0.262490\pi$
$727$	36.6062			1.35765			0.678824	+	0.734301i	$0.262490\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.380000	−	0.658180i	0.0140548	−	0.0243437i
$732$		0			0
$733$	19.9734	+	34.5950i	0.737736	+	1.27780i	0.953513	+	0.301353i	$0.0974383\pi$
$733$	19.9734	+	34.5950i	0.737736	+	1.27780i	−0.215777	+	0.976443i	$0.569228\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−39.1273	−	67.7706i	−1.44127	−	2.49636i
$738$		0			0
$739$	5.42140	−	9.39015i	0.199430	−	0.345422i	−0.748914	−	0.662667i	$-0.769424\pi$
$739$	5.42140	−	9.39015i	0.199430	−	0.345422i	0.948344	+	0.317245i	$0.102758\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.48707			−0.201301			−0.100651	−	0.994922i	$-0.532092\pi$
$743$	−5.48707			−0.201301			−0.100651	+	0.994922i	$0.532092\pi$
$744$		0			0
$745$	8.97353	−	15.5426i	0.328765	−	0.569437i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.94454	+	5.17934i	0.144131	+	0.189249i
$750$		0			0
$751$	13.5621	+	23.4902i	0.494888	+	0.857171i	0.999983	−	0.00589323i	$-0.00187588\pi$
$751$	13.5621	+	23.4902i	0.494888	+	0.857171i	−0.505095	+	0.863064i	$0.668543\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.664410			0.0241804
$756$		0			0
$757$	−36.5294			−1.32768			−0.663842	−	0.747872i	$-0.731075\pi$
$757$	−36.5294			−1.32768			−0.663842	+	0.747872i	$0.731075\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.4394	+	45.7944i	0.958429	+	1.66005i	0.726319	+	0.687358i	$0.241230\pi$
$761$	26.4394	+	45.7944i	0.958429	+	1.66005i	0.232110	+	0.972690i	$0.425437\pi$
$762$		0			0
$763$	−6.07950	+	14.5282i	−0.220093	+	0.525958i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	19.4191	−	33.6348i	0.701183	−	1.21448i
$768$		0			0
$769$	−45.8762			−1.65434			−0.827169	−	0.561954i	$-0.810050\pi$
$769$	−45.8762			−1.65434			−0.827169	+	0.561954i	$0.810050\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.61224	+	13.1848i	−0.273793	+	0.474224i	−0.969830	−	0.243782i	$-0.921612\pi$
$773$	−7.61224	+	13.1848i	−0.273793	+	0.474224i	0.696037	+	0.718006i	$0.254945\pi$
$774$		0			0
$775$	20.1477	+	34.8968i	0.723726	+	1.25353i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.327195	+	0.566718i	0.0117230	+	0.0203048i
$780$		0			0
$781$	17.7655	−	30.7707i	0.635698	−	1.10106i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.6172			−0.557403
$786$		0			0
$787$	−10.5617	+	18.2935i	−0.376485	+	0.652091i	−0.990548	−	0.137166i	$-0.956201\pi$
$787$	−10.5617	+	18.2935i	−0.376485	+	0.652091i	0.614063	+	0.789257i	$0.289534\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18.5266	−	2.37088i	0.658729	−	0.0842986i
$792$		0			0
$793$	−4.55758	−	7.89395i	−0.161844	−	0.280322i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−54.1063			−1.91654			−0.958272	−	0.285856i	$-0.907722\pi$
$797$	−54.1063			−1.91654			−0.958272	+	0.285856i	$0.907722\pi$
$798$		0			0
$799$	0.459595			0.0162593
$800$		0			0
$801$		0			0
$802$		0			0
$803$	37.9994	+	65.8169i	1.34097	+	2.32263i
$804$		0			0
$805$	3.75303	−	8.96864i	0.132277	−	0.316103i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−27.3280	+	47.3335i	−0.960803	+	1.66416i	−0.240310	+	0.970696i	$0.577249\pi$
$809$	−27.3280	+	47.3335i	−0.960803	+	1.66416i	−0.720493	+	0.693463i	$0.756084\pi$
$810$		0			0
$811$	−12.7853			−0.448954			−0.224477	−	0.974479i	$-0.572067\pi$
$811$	−12.7853			−0.448954			−0.224477	+	0.974479i	$0.572067\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−42.7557	+	74.0550i	−1.49767	+	2.59403i
$816$		0			0
$817$	−5.85925	−	10.1485i	−0.204989	−	0.355052i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.7302	+	30.7095i	0.618787	+	1.07177i	0.989707	+	0.143105i	$0.0457088\pi$
$821$	17.7302	+	30.7095i	0.618787	+	1.07177i	−0.370921	+	0.928664i	$0.620958\pi$
$822$		0			0
$823$	−3.95726	+	6.85417i	−0.137941	+	0.238921i	−0.926717	−	0.375760i	$-0.877382\pi$
$823$	−3.95726	+	6.85417i	−0.137941	+	0.238921i	0.788776	+	0.614681i	$0.210715\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−45.6562			−1.58762			−0.793811	−	0.608164i	$-0.791906\pi$
$827$	−45.6562			−1.58762			−0.793811	+	0.608164i	$0.791906\pi$
$828$		0			0
$829$	21.0443	−	36.4498i	0.730898	−	1.26595i	−0.225602	−	0.974220i	$-0.572435\pi$
$829$	21.0443	−	36.4498i	0.730898	−	1.26595i	0.956500	−	0.291733i	$-0.0942318\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.413085	+	1.49818i	−0.0143125	+	0.0519090i
$834$		0			0
$835$	5.74552	+	9.95154i	0.198832	+	0.344387i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−20.7196			−0.715320			−0.357660	−	0.933852i	$-0.616425\pi$
$839$	−20.7196			−0.715320			−0.357660	+	0.933852i	$0.616425\pi$
$840$		0			0
$841$	3.18957			0.109985
$842$		0			0
$843$		0			0
$844$		0			0
$845$	23.6757	+	41.0075i	0.814468	+	1.41070i
$846$		0			0
$847$	−40.5901	−	53.2963i	−1.39469	−	1.83128i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.71856	−	2.97663i	0.0589115	−	0.102038i
$852$		0			0
$853$	−15.5188			−0.531355			−0.265678	−	0.964062i	$-0.585596\pi$
$853$	−15.5188			−0.531355			−0.265678	+	0.964062i	$0.585596\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.24091	−	2.14933i	0.0423888	−	0.0734196i	−0.844053	−	0.536260i	$-0.819837\pi$
$857$	1.24091	−	2.14933i	0.0423888	−	0.0734196i	0.886441	+	0.462841i	$0.153170\pi$
$858$		0			0
$859$	−17.5198	−	30.3452i	−0.597768	−	1.03537i	−0.993150	−	0.116848i	$-0.962721\pi$
$859$	−17.5198	−	30.3452i	−0.597768	−	1.03537i	0.395382	−	0.918517i	$-0.370612\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.4778	+	25.0763i	0.492831	+	0.853608i	0.999966	−	0.00825876i	$-0.00262887\pi$
$863$	14.4778	+	25.0763i	0.492831	+	0.853608i	−0.507135	+	0.861866i	$0.669296\pi$
$864$		0			0
$865$	−38.3876	+	66.4893i	−1.30522	+	2.26070i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	76.0282			2.57908
$870$		0			0
$871$	−33.1940	+	57.4936i	−1.12473	+	1.94810i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−28.2274	+	3.61231i	−0.954260	+	0.122118i
$876$		0			0
$877$	−9.79611	−	16.9674i	−0.330791	−	0.572947i	0.651876	−	0.758325i	$-0.273982\pi$
$877$	−9.79611	−	16.9674i	−0.330791	−	0.572947i	−0.982667	+	0.185379i	$0.940649\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	15.9010			0.535717			0.267858	−	0.963458i	$-0.413684\pi$
$881$	15.9010			0.535717			0.267858	+	0.963458i	$0.413684\pi$
$882$		0			0
$883$	0.329844			0.0111001			0.00555007	−	0.999985i	$-0.498233\pi$
$883$	0.329844			0.0111001			0.00555007	+	0.999985i	$0.498233\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.31301	−	10.9345i	−0.211970	−	0.367143i	0.740361	−	0.672210i	$-0.234655\pi$
$887$	−6.31301	−	10.9345i	−0.211970	−	0.367143i	−0.952331	+	0.305066i	$0.901321\pi$
$888$		0			0
$889$	7.25351	−	0.928243i	0.243275	−	0.0311323i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.54326	−	6.13711i	0.118571	−	0.205371i
$894$		0			0
$895$	−1.80276			−0.0602595
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−14.3157	+	24.7956i	−0.477456	+	0.826978i
$900$		0			0
$901$	0.588794	+	1.01982i	0.0196156	+	0.0339752i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.6018	+	18.3629i	0.352416	+	0.610402i
$906$		0			0
$907$	4.94626	−	8.56717i	0.164238	−	0.284468i	−0.772147	−	0.635445i	$-0.780817\pi$
$907$	4.94626	−	8.56717i	0.164238	−	0.284468i	0.936384	+	0.350976i	$0.114150\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	59.6371			1.97586			0.987932	−	0.154889i	$-0.0495020\pi$
$911$	59.6371			1.97586			0.987932	+	0.154889i	$0.0495020\pi$
$912$		0			0
$913$	21.6928	−	37.5730i	0.717927	−	1.24349i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.5535	+	17.7963i	0.447576	+	0.587685i
$918$		0			0
$919$	3.84759	+	6.66423i	0.126920	+	0.219833i	0.922482	−	0.386040i	$-0.126157\pi$
$919$	3.84759	+	6.66423i	0.126920	+	0.219833i	−0.795562	+	0.605873i	$0.792824\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−30.1429			−0.992166
$924$		0			0
$925$	−26.9133			−0.884903
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.8357	+	23.9642i	0.453936	+	0.786240i	0.998626	−	0.0523969i	$-0.0166861\pi$
$929$	13.8357	+	23.9642i	0.453936	+	0.786240i	−0.544690	+	0.838637i	$0.683353\pi$
$930$		0			0
$931$	16.8210	+	17.0663i	0.551286	+	0.559327i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.41071	−	4.17548i	0.0788388	−	0.136553i
$936$		0			0
$937$	44.7712			1.46261			0.731305	−	0.682051i	$-0.238912\pi$
$937$	44.7712			1.46261			0.731305	+	0.682051i	$0.238912\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.0046	−	34.6490i	0.652132	−	1.12953i	−0.330472	−	0.943816i	$-0.607208\pi$
$941$	20.0046	−	34.6490i	0.652132	−	1.12953i	0.982605	−	0.185710i	$-0.0594586\pi$
$942$		0			0
$943$	−0.0974694	−	0.168822i	−0.00317404	−	0.00549760i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−22.4634	−	38.9078i	−0.729963	−	1.26433i	−0.956898	−	0.290423i	$-0.906204\pi$
$947$	−22.4634	−	38.9078i	−0.729963	−	1.26433i	0.226935	−	0.973910i	$-0.427129\pi$
$948$		0			0
$949$	32.2371	−	55.8362i	1.04646	−	1.81252i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	40.8038			1.32176			0.660882	−	0.750490i	$-0.270182\pi$
$953$	40.8038			1.32176			0.660882	+	0.750490i	$0.270182\pi$
$954$		0			0
$955$	14.2144	−	24.6201i	0.459967	−	0.796687i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.4714	−	44.1414i	0.596474	−	1.42540i
$960$		0			0
$961$	2.76670	+	4.79206i	0.0892483	+	0.154583i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−68.5023			−2.20517
$966$		0			0
$967$	19.2658			0.619546			0.309773	−	0.950811i	$-0.399747\pi$
$967$	19.2658			0.619546			0.309773	+	0.950811i	$0.399747\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	29.8684	+	51.7336i	0.958523	+	1.66021i	0.726093	+	0.687597i	$0.241334\pi$
$971$	29.8684	+	51.7336i	0.958523	+	1.66021i	0.232430	+	0.972613i	$0.425332\pi$
$972$		0			0
$973$	−31.5413	+	4.03640i	−1.01117	+	0.129401i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.7758	+	51.5732i	−0.952613	+	1.64997i	−0.212873	+	0.977080i	$0.568282\pi$
$977$	−29.7758	+	51.5732i	−0.952613	+	1.64997i	−0.739739	+	0.672893i	$0.765051\pi$
$978$		0			0
$979$	−53.6010			−1.71310
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.06414	+	7.03930i	−0.129626	+	0.224519i	−0.923532	−	0.383522i	$-0.874711\pi$
$983$	−4.06414	+	7.03930i	−0.129626	+	0.224519i	0.793906	+	0.608041i	$0.208044\pi$
$984$		0			0
$985$	17.5147	+	30.3364i	0.558066	+	0.966598i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.74543	+	3.02318i	0.0555016	+	0.0961316i
$990$		0			0
$991$	−27.6811	+	47.9451i	−0.879320	+	1.52303i	−0.0272305	+	0.999629i	$0.508669\pi$
$991$	−27.6811	+	47.9451i	−0.879320	+	1.52303i	−0.852089	+	0.523397i	$0.824665\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−54.3820			−1.72403
$996$		0			0
$997$	4.83187	−	8.36904i	0.153027	−	0.265050i	−0.779312	−	0.626636i	$-0.784431\pi$
$997$	4.83187	−	8.36904i	0.153027	−	0.265050i	0.932339	+	0.361586i	$0.117765\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.k.f.1621.6		14
3.2	odd	2		2268.2.k.e.1621.2		14
7.2	even	3	inner	2268.2.k.f.1297.6		14
9.2	odd	6		252.2.l.b.193.7	yes	14
9.4	even	3		756.2.i.b.613.6		14
9.5	odd	6		252.2.i.b.25.3	✓	14
9.7	even	3		756.2.l.b.361.2		14
21.2	odd	6		2268.2.k.e.1297.2		14
36.7	odd	6		3024.2.t.j.1873.2		14
36.11	even	6		1008.2.t.j.193.1		14
36.23	even	6		1008.2.q.j.529.5		14
36.31	odd	6		3024.2.q.j.2881.6		14
63.2	odd	6		252.2.i.b.121.3	yes	14
63.4	even	3		5292.2.j.h.3529.6		14
63.5	even	6		1764.2.l.i.961.1		14
63.11	odd	6		1764.2.j.g.589.2		14
63.13	odd	6		5292.2.i.i.2125.2		14
63.16	even	3		756.2.i.b.37.6		14
63.20	even	6		1764.2.l.i.949.1		14
63.23	odd	6		252.2.l.b.205.7	yes	14
63.25	even	3		5292.2.j.h.1765.6		14
63.31	odd	6		5292.2.j.g.3529.2		14
63.32	odd	6		1764.2.j.g.1177.2		14
63.34	odd	6		5292.2.l.i.361.6		14
63.38	even	6		1764.2.j.h.589.6		14
63.40	odd	6		5292.2.l.i.3313.6		14
63.41	even	6		1764.2.i.i.1537.5		14
63.47	even	6		1764.2.i.i.373.5		14
63.52	odd	6		5292.2.j.g.1765.2		14
63.58	even	3		756.2.l.b.289.2		14
63.59	even	6		1764.2.j.h.1177.6		14
63.61	odd	6		5292.2.i.i.1549.2		14
252.23	even	6		1008.2.t.j.961.1		14
252.79	odd	6		3024.2.q.j.2305.6		14
252.191	even	6		1008.2.q.j.625.5		14
252.247	odd	6		3024.2.t.j.289.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.3	✓	14	9.5	odd	6
252.2.i.b.121.3	yes	14	63.2	odd	6
252.2.l.b.193.7	yes	14	9.2	odd	6
252.2.l.b.205.7	yes	14	63.23	odd	6
756.2.i.b.37.6		14	63.16	even	3
756.2.i.b.613.6		14	9.4	even	3
756.2.l.b.289.2		14	63.58	even	3
756.2.l.b.361.2		14	9.7	even	3
1008.2.q.j.529.5		14	36.23	even	6
1008.2.q.j.625.5		14	252.191	even	6
1008.2.t.j.193.1		14	36.11	even	6
1008.2.t.j.961.1		14	252.23	even	6
1764.2.i.i.373.5		14	63.47	even	6
1764.2.i.i.1537.5		14	63.41	even	6
1764.2.j.g.589.2		14	63.11	odd	6
1764.2.j.g.1177.2		14	63.32	odd	6
1764.2.j.h.589.6		14	63.38	even	6
1764.2.j.h.1177.6		14	63.59	even	6
1764.2.l.i.949.1		14	63.20	even	6
1764.2.l.i.961.1		14	63.5	even	6
2268.2.k.e.1297.2		14	21.2	odd	6
2268.2.k.e.1621.2		14	3.2	odd	2
2268.2.k.f.1297.6		14	7.2	even	3	inner
2268.2.k.f.1621.6		14	1.1	even	1	trivial
3024.2.q.j.2305.6		14	252.79	odd	6
3024.2.q.j.2881.6		14	36.31	odd	6
3024.2.t.j.289.2		14	252.247	odd	6
3024.2.t.j.1873.2		14	36.7	odd	6
5292.2.i.i.1549.2		14	63.61	odd	6
5292.2.i.i.2125.2		14	63.13	odd	6
5292.2.j.g.1765.2		14	63.52	odd	6
5292.2.j.g.3529.2		14	63.31	odd	6
5292.2.j.h.1765.6		14	63.25	even	3
5292.2.j.h.3529.6		14	63.4	even	3
5292.2.l.i.361.6		14	63.34	odd	6
5292.2.l.i.3313.6		14	63.40	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80173 + 3.12069i) q^{5} +(2.62435 - 0.335842i) q^{7} +(-3.01334 + 5.21926i) q^{11} +5.11278 q^{13} +(-0.111006 + 0.192269i) q^{17} +(1.71161 + 2.96460i) q^{19} +(-0.509880 - 0.883137i) q^{23} +(-3.99245 + 6.91513i) q^{25} -5.67359 q^{29} +(2.52322 - 4.37035i) q^{31} +(5.77642 + 7.58467i) q^{35} +(1.68526 + 2.91896i) q^{37} +0.191162 q^{41} -3.42323 q^{43} +(-1.03506 - 1.79278i) q^{47} +(6.77442 - 1.76274i) q^{49} +(2.65207 - 4.59353i) q^{53} -21.7169 q^{55} +(3.79814 - 6.57858i) q^{59} +(-0.891408 - 1.54396i) q^{61} +(9.21184 + 15.9554i) q^{65} +(-6.49235 + 11.2451i) q^{67} -5.89560 q^{71} +(6.30519 - 10.9209i) q^{73} +(-6.15522 + 14.7092i) q^{77} +(-6.30763 - 10.9251i) q^{79} -7.19891 q^{83} -0.800013 q^{85} +(4.44697 + 7.70238i) q^{89} +(13.4177 - 1.71709i) q^{91} +(-6.16773 + 10.6828i) q^{95} +5.45982 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5} - 3 q^{7} - 2 q^{11} - 4 q^{13} - 2 q^{17} + 7 q^{19} - 11 q^{23} - 9 q^{25} + 2 q^{29} - q^{31} + 19 q^{35} + 10 q^{37} - 66 q^{41} - 14 q^{43} + 3 q^{47} + 17 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots + 36 q^{97}+O(q^{100}) \) 14 * q + 2 * q^5 - 3 * q^7 - 2 * q^11 - 4 * q^13 - 2 * q^17 + 7 * q^19 - 11 * q^23 - 9 * q^25 + 2 * q^29 - q^31 + 19 * q^35 + 10 * q^37 - 66 * q^41 - 14 * q^43 + 3 * q^47 + 17 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 28 * q^77 - 10 * q^79 - 50 * q^83 - 16 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 + 36 * q^97

Introduction

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