LMFDB - Embedded newform 1620.2.x.d.917.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(53,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 9]))

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

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

chi := DirichletCharacter("1620.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.x (of order $12$, degree $4$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 100x^{12} - 408x^{10} + 1191x^{8} - 2040x^{6} + 2500x^{4} - 1500x^{2} + 625 $ x^16 - 12x^14 + 100x^12 - 408x^10 + 1191x^8 - 2040x^6 + 2500x^4 - 1500*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 540)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			917.1
Root			$-1.44919 + 0.836690i$ of defining polynomial
Character	$\chi$	$=$	1620.917
Dual form			1620.2.x.d.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70289 + 1.44919i) q^{5} +(-0.307007 + 0.0822623i) q^{7} +O(q^{10})$	$q+(-1.70289 + 1.44919i) q^{5} +(-0.307007 + 0.0822623i) q^{7} +(2.41131 + 1.39217i) q^{11} +(1.67303 + 0.448288i) q^{13} +(2.78434 - 2.78434i) q^{17} -3.89898i q^{19} +(-2.26732 + 8.46177i) q^{23} +(0.799701 - 4.93563i) q^{25} +(-1.39217 + 2.41131i) q^{29} +(-0.224745 - 0.389270i) q^{31} +(0.403587 - 0.584996i) q^{35} +(3.67423 + 3.67423i) q^{37} +(-8.31779 + 4.80228i) q^{41} +(0.201501 + 0.752011i) q^{43} +(-5.97469 + 3.44949i) q^{49} +(6.19445 + 6.19445i) q^{53} +(-6.12372 + 1.12372i) q^{55} +(6.19445 + 10.7291i) q^{59} +(-6.39898 + 11.0834i) q^{61} +(-3.49865 + 1.66115i) q^{65} +(3.17499 - 11.8492i) q^{67} +9.60455i q^{71} +(-6.22474 + 6.22474i) q^{73} +(-0.854813 - 0.229046i) q^{77} +(8.00853 + 4.62372i) q^{79} +(-4.65829 + 1.24819i) q^{83} +(-0.706403 + 8.77647i) q^{85} +12.3889 q^{89} -0.550510 q^{91} +(5.65036 + 6.63955i) q^{95} +(6.52312 - 1.74786i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 8 q^{25} + 16 q^{31} - 24 q^{43} - 24 q^{61} - 40 q^{67} - 80 q^{73} - 40 q^{85} - 48 q^{91} + 48 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 + 8 * q^25 + 16 * q^31 - 24 * q^43 - 24 * q^61 - 40 * q^67 - 80 * q^73 - 40 * q^85 - 48 * q^91 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.70289	+	1.44919i	−0.761558	+	0.648097i
$5$	−1.70289	+	1.44919i	−0.761558	+	0.648097i
$6$		0			0
$7$	−0.307007	+	0.0822623i	−0.116038	+	0.0310922i	−0.316371	−	0.948636i	$-0.602464\pi$
$7$	−0.307007	+	0.0822623i	−0.116038	+	0.0310922i	0.200333	+	0.979728i	$0.435798\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.41131	+	1.39217i	0.727037	+	0.419755i	0.817337	−	0.576159i	$-0.195449\pi$
$11$	2.41131	+	1.39217i	0.727037	+	0.419755i	−0.0903001	+	0.995915i	$0.528783\pi$
$12$		0			0
$13$	1.67303	+	0.448288i	0.464016	+	0.124333i	0.483250	−	0.875482i	$-0.339456\pi$
$13$	1.67303	+	0.448288i	0.464016	+	0.124333i	−0.0192343	+	0.999815i	$0.506123\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.78434	−	2.78434i	0.675302	−	0.675302i	−0.283632	−	0.958933i	$-0.591539\pi$
$17$	2.78434	−	2.78434i	0.675302	−	0.675302i	0.958933	+	0.283632i	$0.0915393\pi$
$18$		0			0
$19$		−	3.89898i		−	0.894487i	−0.894412	−	0.447244i	$-0.852406\pi$
$19$		−	3.89898i		−	0.894487i	0.894412	−	0.447244i	$-0.147594\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.26732	+	8.46177i	−0.472770	+	1.76440i	0.156978	+	0.987602i	$0.449825\pi$
$23$	−2.26732	+	8.46177i	−0.472770	+	1.76440i	−0.629748	+	0.776799i	$0.716842\pi$
$24$		0			0
$25$	0.799701	−	4.93563i	0.159940	−	0.987127i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.39217	+	2.41131i	−0.258520	+	0.447769i	−0.965846	−	0.259119i	$-0.916568\pi$
$29$	−1.39217	+	2.41131i	−0.258520	+	0.447769i	0.707326	+	0.706887i	$0.249901\pi$
$30$		0			0
$31$	−0.224745	−	0.389270i	−0.0403654	−	0.0699149i	0.845137	−	0.534550i	$-0.179519\pi$
$31$	−0.224745	−	0.389270i	−0.0403654	−	0.0699149i	−0.885502	+	0.464635i	$0.846186\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.403587	−	0.584996i	0.0682187	−	0.0988823i
$36$		0			0
$37$	3.67423	+	3.67423i	0.604040	+	0.604040i	0.941382	−	0.337342i	$-0.109528\pi$
$37$	3.67423	+	3.67423i	0.604040	+	0.604040i	−0.337342	+	0.941382i	$0.609528\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.31779	+	4.80228i	−1.29902	+	0.749990i	−0.980235	−	0.197837i	$-0.936608\pi$
$41$	−8.31779	+	4.80228i	−1.29902	+	0.749990i	−0.318785	+	0.947827i	$0.603275\pi$
$42$		0			0
$43$	0.201501	+	0.752011i	0.0307286	+	0.114681i	0.979587	−	0.201022i	$-0.0644264\pi$
$43$	0.201501	+	0.752011i	0.0307286	+	0.114681i	−0.948858	+	0.315703i	$0.897760\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$47$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$48$		0			0
$49$	−5.97469	+	3.44949i	−0.853527	+	0.492784i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.19445	+	6.19445i	0.850873	+	0.850873i	0.990241	−	0.139368i	$-0.0445071\pi$
$53$	6.19445	+	6.19445i	0.850873	+	0.850873i	−0.139368	+	0.990241i	$0.544507\pi$
$54$		0			0
$55$	−6.12372	+	1.12372i	−0.825723	+	0.151523i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.19445	+	10.7291i	0.806448	+	1.39681i	0.915309	+	0.402752i	$0.131946\pi$
$59$	6.19445	+	10.7291i	0.806448	+	1.39681i	−0.108861	+	0.994057i	$0.534720\pi$
$60$		0			0
$61$	−6.39898	+	11.0834i	−0.819305	+	1.41908i	0.0868894	+	0.996218i	$0.472307\pi$
$61$	−6.39898	+	11.0834i	−0.819305	+	1.41908i	−0.906195	+	0.422861i	$0.861026\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.49865	+	1.66115i	−0.433954	+	0.206041i
$66$		0			0
$67$	3.17499	−	11.8492i	0.387887	−	1.44761i	−0.445679	−	0.895193i	$-0.647038\pi$
$67$	3.17499	−	11.8492i	0.387887	−	1.44761i	0.833566	−	0.552420i	$-0.186296\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			9.60455i			1.13985i	0.821696	+	0.569925i	$0.193028\pi$
$71$			9.60455i			1.13985i	−0.821696	+	0.569925i	$0.806972\pi$
$72$		0			0
$73$	−6.22474	+	6.22474i	−0.728551	+	0.728551i	−0.970331	−	0.241780i	$-0.922269\pi$
$73$	−6.22474	+	6.22474i	−0.728551	+	0.728551i	0.241780	+	0.970331i	$0.422269\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.854813	−	0.229046i	−0.0974149	−	0.0261023i
$78$		0			0
$79$	8.00853	+	4.62372i	0.901030	+	0.520210i	0.877534	−	0.479514i	$-0.159187\pi$
$79$	8.00853	+	4.62372i	0.901030	+	0.520210i	0.0234955	+	0.999724i	$0.492520\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.65829	+	1.24819i	−0.511314	+	0.137006i	−0.505246	−	0.862975i	$-0.668598\pi$
$83$	−4.65829	+	1.24819i	−0.511314	+	0.137006i	−0.00606809	+	0.999982i	$0.501932\pi$
$84$		0			0
$85$	−0.706403	+	8.77647i	−0.0766201	+	0.951942i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.3889			1.31322			0.656610	−	0.754230i	$-0.271990\pi$
$89$	12.3889			1.31322			0.656610	+	0.754230i	$0.271990\pi$
$90$		0			0
$91$	−0.550510			−0.0577092
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.65036	+	6.63955i	0.579715	+	0.681204i
$96$		0			0
$97$	6.52312	−	1.74786i	0.662322	−	0.177469i	0.0880285	−	0.996118i	$-0.471943\pi$
$97$	6.52312	−	1.74786i	0.662322	−	0.177469i	0.574294	+	0.818649i	$0.305277\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−15.5517	−	8.97879i	−1.54745	−	0.893423i	−0.998335	−	0.0576781i	$-0.981630\pi$
$101$	−15.5517	−	8.97879i	−1.54745	−	0.893423i	−0.549118	−	0.835745i	$-0.685036\pi$
$102$		0			0
$103$	8.50316	+	2.27841i	0.837841	+	0.224499i	0.652132	−	0.758106i	$-0.273875\pi$
$103$	8.50316	+	2.27841i	0.837841	+	0.224499i	0.185710	+	0.982605i	$0.440542\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.97879	+	8.97879i	−0.868012	+	0.868012i	−0.992252	−	0.124240i	$-0.960351\pi$
$107$	−8.97879	+	8.97879i	−0.868012	+	0.868012i	0.124240	+	0.992252i	$0.460351\pi$
$108$		0			0
$109$		−	11.3485i		−	1.08699i	−0.839414	−	0.543493i	$-0.817101\pi$
$109$		−	11.3485i		−	1.08699i	0.839414	−	0.543493i	$-0.182899\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.229046	+	0.854813i	−0.0215469	+	0.0804140i	−0.975862	−	0.218388i	$-0.929920\pi$
$113$	−0.229046	+	0.854813i	−0.0215469	+	0.0804140i	0.954315	+	0.298802i	$0.0965869\pi$
$114$		0			0
$115$	−8.40169	−	17.6953i	−0.783462	−	1.65009i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.625766	+	1.08386i	−0.0573639	+	0.0993572i
$120$		0			0
$121$	−1.62372	−	2.81237i	−0.147611	−	0.255670i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.79086	+	9.56378i	0.517950	+	0.855411i
$126$		0			0
$127$	9.89898	+	9.89898i	0.878392	+	0.878392i	0.993368	−	0.114976i	$-0.0366791\pi$
$127$	9.89898	+	9.89898i	0.878392	+	0.878392i	−0.114976	+	0.993368i	$0.536679\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.82262	−	2.78434i	0.421354	−	0.243269i	−0.274302	−	0.961644i	$-0.588447\pi$
$131$	4.82262	−	2.78434i	0.421354	−	0.243269i	0.695657	+	0.718375i	$0.255114\pi$
$132$		0			0
$133$	0.320739	+	1.19701i	0.0278116	+	0.103794i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.24819	−	4.65829i	−0.106640	−	0.397985i	0.891886	−	0.452260i	$-0.149382\pi$
$137$	−1.24819	−	4.65829i	−0.106640	−	0.397985i	−0.998526	+	0.0542749i	$0.982715\pi$
$138$		0			0
$139$	−16.6688	+	9.62372i	−1.41383	+	0.816274i	−0.995746	−	0.0921361i	$-0.970631\pi$
$139$	−16.6688	+	9.62372i	−1.41383	+	0.816274i	−0.418081	+	0.908410i	$0.637297\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.41011	+	3.41011i	0.285167	+	0.285167i
$144$		0			0
$145$	−1.12372	−	6.12372i	−0.0933202	−	0.508548i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.41011	−	5.90648i	−0.279367	−	0.483878i	0.691861	−	0.722031i	$-0.256791\pi$
$149$	−3.41011	−	5.90648i	−0.279367	−	0.483878i	−0.971228	+	0.238153i	$0.923458\pi$
$150$		0			0
$151$	−5.27526	+	9.13701i	−0.429294	+	0.743559i	−0.996811	−	0.0798027i	$-0.974571\pi$
$151$	−5.27526	+	9.13701i	−0.429294	+	0.743559i	0.567517	+	0.823362i	$0.307904\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.946842	+	0.337187i	0.0760522	+	0.0270835i
$156$		0			0
$157$	4.88588	−	18.2343i	0.389936	−	1.45526i	−0.440302	−	0.897850i	$-0.645129\pi$
$157$	4.88588	−	18.2343i	0.389936	−	1.45526i	0.830238	−	0.557410i	$-0.188205\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	2.78434i		−	0.219437i
$162$		0			0
$163$	3.77526	−	3.77526i	0.295701	−	0.295701i	−0.543626	−	0.839327i	$-0.682949\pi$
$163$	3.77526	−	3.77526i	0.295701	−	0.295701i	0.839327	+	0.543626i	$0.182949\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.1201	+	3.51551i	1.01526	+	0.272038i	0.727826	−	0.685762i	$-0.240531\pi$
$167$	13.1201	+	3.51551i	1.01526	+	0.272038i	0.287435	+	0.957800i	$0.407197\pi$
$168$		0			0
$169$	−8.66025	−	5.00000i	−0.666173	−	0.384615i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.60696	+	2.03828i	−0.578346	+	0.154967i	−0.536122	−	0.844141i	$-0.680111\pi$
$173$	−7.60696	+	2.03828i	−0.578346	+	0.154967i	−0.0422247	+	0.999108i	$0.513445\pi$
$174$		0			0
$175$	0.160503	+	1.58106i	0.0121329	+	0.119517i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.60455			−0.717878			−0.358939	−	0.933361i	$-0.616861\pi$
$179$	−9.60455			−0.717878			−0.358939	+	0.933361i	$0.616861\pi$
$180$		0			0
$181$	11.2474			0.836016			0.418008	−	0.908443i	$-0.362728\pi$
$181$	11.2474			0.836016			0.418008	+	0.908443i	$0.362728\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−11.5815	−	0.932174i	−0.851489	−	0.0685348i
$186$		0			0
$187$	10.5902	−	2.83763i	0.774431	−	0.207508i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.7291	+	6.19445i	0.776330	+	0.448214i	0.835128	−	0.550055i	$-0.185393\pi$
$191$	10.7291	+	6.19445i	0.776330	+	0.448214i	−0.0587979	+	0.998270i	$0.518727\pi$
$192$		0			0
$193$	15.8093	+	4.23609i	1.13798	+	0.304920i	0.778138	−	0.628093i	$-0.216164\pi$
$193$	15.8093	+	4.23609i	1.13798	+	0.304920i	0.359841	+	0.933014i	$0.382831\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.82021	−	6.82021i	0.485920	−	0.485920i	−0.421096	−	0.907016i	$-0.638354\pi$
$197$	6.82021	−	6.82021i	0.485920	−	0.485920i	0.907016	+	0.421096i	$0.138354\pi$
$198$		0			0
$199$		−	9.24745i		−	0.655534i	−0.944759	−	0.327767i	$-0.893704\pi$
$199$		−	9.24745i		−	0.655534i	0.944759	−	0.327767i	$-0.106296\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.229046	−	0.854813i	0.0160759	−	0.0599961i
$204$		0			0
$205$	7.20491	−	20.2318i	0.503213	−	1.41305i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.42804	−	9.40165i	0.375466	−	0.650325i
$210$		0			0
$211$	6.62372	+	11.4726i	0.455996	+	0.789808i	0.998745	−	0.0500868i	$-0.0159498\pi$
$211$	6.62372	+	11.4726i	0.455996	+	0.789808i	−0.542749	+	0.839895i	$0.682616\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.43294	−	0.988583i	−0.0977257	−	0.0674208i
$216$		0			0
$217$	0.101021	+	0.101021i	0.00685772	+	0.00685772i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.90648	−	3.41011i	0.397313	−	0.229389i
$222$		0			0
$223$	4.68438	+	17.4823i	0.313689	+	1.17070i	0.925204	+	0.379471i	$0.123894\pi$
$223$	4.68438	+	17.4823i	0.313689	+	1.17070i	−0.611515	+	0.791233i	$0.709439\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.78284	+	21.5818i	0.383820	+	1.43244i	0.840018	+	0.542558i	$0.182544\pi$
$227$	5.78284	+	21.5818i	0.383820	+	1.43244i	−0.456198	+	0.889878i	$0.650789\pi$
$228$		0			0
$229$	−1.16781	+	0.674235i	−0.0771710	+	0.0445547i	−0.538089	−	0.842888i	$-0.680854\pi$
$229$	−1.16781	+	0.674235i	−0.0771710	+	0.0445547i	0.460918	+	0.887443i	$0.347520\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.1732	−	15.1732i	−0.994032	−	0.994032i	0.00595067	−	0.999982i	$-0.498106\pi$
$233$	−15.1732	−	15.1732i	−0.994032	−	0.994032i	−0.999982	+	0.00595067i	$0.998106\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.17651	−	7.23393i	−0.270156	−	0.467924i	0.698746	−	0.715370i	$-0.253742\pi$
$239$	−4.17651	−	7.23393i	−0.270156	−	0.467924i	−0.968902	+	0.247446i	$0.920409\pi$
$240$		0			0
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.17531	−	14.5326i	0.330638	−	0.928452i
$246$		0			0
$247$	1.74786	−	6.52312i	0.111214	−	0.415056i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	21.9934i		−	1.38821i	−0.719872	−	0.694107i	$-0.755799\pi$
$251$		−	21.9934i		−	1.38821i	0.719872	−	0.694107i	$-0.244201\pi$
$252$		0			0
$253$	−17.2474	+	17.2474i	−1.08434	+	1.08434i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−28.3340	−	7.59207i	−1.76743	−	0.473580i	−0.779225	−	0.626745i	$-0.784387\pi$
$257$	−28.3340	−	7.59207i	−1.76743	−	0.473580i	−0.988201	+	0.153165i	$0.951054\pi$
$258$		0			0
$259$	−1.43027	−	0.825765i	−0.0888725	−	0.0513106i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	16.9235	−	4.53465i	1.04355	−	0.279618i	0.303966	−	0.952683i	$-0.401689\pi$
$263$	16.9235	−	4.53465i	1.04355	−	0.279618i	0.739584	+	0.673064i	$0.235022\pi$
$264$		0			0
$265$	−19.5254	−	1.57157i	−1.19944	−	0.0965405i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.3889			−0.755364			−0.377682	−	0.925935i	$-0.623279\pi$
$269$	−12.3889			−0.755364			−0.377682	+	0.925935i	$0.623279\pi$
$270$		0			0
$271$	−21.0000			−1.27566			−0.637830	−	0.770178i	$-0.720168\pi$
$271$	−21.0000			−1.27566			−0.637830	+	0.770178i	$0.720168\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.79957	−	10.7880i	0.530634	−	0.650542i
$276$		0			0
$277$	18.9864	−	5.08738i	1.14078	−	0.305671i	0.361515	−	0.932366i	$-0.382260\pi$
$277$	18.9864	−	5.08738i	1.14078	−	0.305671i	0.779264	+	0.626695i	$0.215593\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.3743	+	11.7631i	1.21543	+	0.701729i	0.963937	−	0.266130i	$-0.0857449\pi$
$281$	20.3743	+	11.7631i	1.21543	+	0.701729i	0.251494	+	0.967859i	$0.419078\pi$
$282$		0			0
$283$	−3.82208	−	1.02412i	−0.227199	−	0.0608779i	0.143423	−	0.989661i	$-0.454189\pi$
$283$	−3.82208	−	1.02412i	−0.227199	−	0.0608779i	−0.370623	+	0.928784i	$0.620856\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.15857	−	2.15857i	0.127417	−	0.127417i
$288$		0			0
$289$			1.49490i			0.0879351i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.74456	−	13.9749i	0.218759	−	0.816421i	−0.766050	−	0.642781i	$-0.777780\pi$
$293$	3.74456	−	13.9749i	0.218759	−	0.816421i	0.984809	−	0.173640i	$-0.0555529\pi$
$294$		0			0
$295$	−26.0970	−	9.29360i	−1.51943	−	0.541094i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.58662	+	13.1404i	−0.438745	+	0.759929i
$300$		0			0
$301$	−0.123724	−	0.214297i	−0.00713135	−	0.0123519i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.16509	−	28.1471i	−0.295752	−	1.61170i
$306$		0			0
$307$	13.3485	+	13.3485i	0.761837	+	0.761837i	0.976654	−	0.214817i	$-0.0689155\pi$
$307$	13.3485	+	13.3485i	0.761837	+	0.761837i	−0.214817	+	0.976654i	$0.568915\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.08386	−	0.625766i	0.0614600	−	0.0354839i	−0.468955	−	0.883222i	$-0.655369\pi$
$311$	1.08386	−	0.625766i	0.0614600	−	0.0354839i	0.530415	+	0.847738i	$0.322036\pi$
$312$		0			0
$313$	5.04209	+	18.8173i	0.284996	+	1.06362i	0.948842	+	0.315750i	$0.102256\pi$
$313$	5.04209	+	18.8173i	0.284996	+	1.06362i	−0.663846	+	0.747869i	$0.731077\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.05016	−	30.0436i	−0.452142	−	1.68742i	−0.696357	−	0.717696i	$-0.745197\pi$
$317$	−8.05016	−	30.0436i	−0.452142	−	1.68742i	0.244215	−	0.969721i	$-0.421470\pi$
$318$		0			0
$319$	−6.71391	+	3.87628i	−0.375907	+	0.217030i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.8561	−	10.8561i	−0.604049	−	0.604049i
$324$		0			0
$325$	3.55051	−	7.89898i	0.196947	−	0.438157i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.37628	+	5.84788i	−0.185577	+	0.321429i	−0.943771	−	0.330601i	$-0.892749\pi$
$331$	−3.37628	+	5.84788i	−0.185577	+	0.321429i	0.758194	+	0.652029i	$0.226082\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	11.7651	+	24.7791i	0.642796	+	1.35383i
$336$		0			0
$337$	2.35237	−	8.77915i	0.128142	−	0.478231i	−0.871791	−	0.489879i	$-0.837041\pi$
$337$	2.35237	−	8.77915i	0.128142	−	0.478231i	0.999932	+	0.0116478i	$0.00370770\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	1.25153i		−	0.0677743i
$342$		0			0
$343$	3.12372	−	3.12372i	0.168665	−	0.168665i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.854813	+	0.229046i	0.0458887	+	0.0122959i	0.281690	−	0.959505i	$-0.409105\pi$
$347$	0.854813	+	0.229046i	0.0458887	+	0.0122959i	−0.235802	+	0.971801i	$0.575772\pi$
$348$		0			0
$349$	−11.2583	−	6.50000i	−0.602645	−	0.347937i	0.167437	−	0.985883i	$-0.446451\pi$
$349$	−11.2583	−	6.50000i	−0.602645	−	0.347937i	−0.770081	+	0.637946i	$0.779784\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.7270	−	5.55379i	1.10319	−	0.295598i	0.339126	−	0.940741i	$-0.389869\pi$
$353$	20.7270	−	5.55379i	1.10319	−	0.295598i	0.764062	+	0.645143i	$0.223202\pi$
$354$		0			0
$355$	−13.9188	−	16.3555i	−0.738734	−	0.868062i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.03587			0.213005			0.106503	−	0.994312i	$-0.466035\pi$
$359$	4.03587			0.213005			0.106503	+	0.994312i	$0.466035\pi$
$360$		0			0
$361$	3.79796			0.199893
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.57925	−	19.6209i	0.0826619	−	1.02701i
$366$		0			0
$367$	25.3715	−	6.79827i	1.32438	−	0.354867i	0.473763	−	0.880652i	$-0.342895\pi$
$367$	25.3715	−	6.79827i	1.32438	−	0.354867i	0.850617	+	0.525785i	$0.176229\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.41131	−	1.39217i	−0.125189	−	0.0722779i
$372$		0			0
$373$	5.90911	+	1.58334i	0.305962	+	0.0819822i	0.408533	−	0.912743i	$-0.366040\pi$
$373$	5.90911	+	1.58334i	0.305962	+	0.0819822i	−0.102571	+	0.994726i	$0.532707\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.41011	+	3.41011i	−0.175629	+	0.175629i
$378$		0			0
$379$			13.0000i			0.667765i	0.942615	+	0.333883i	$0.108359\pi$
$379$			13.0000i			0.667765i	−0.942615	+	0.333883i	$0.891641\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.61121	−	32.1375i	0.440012	−	1.64215i	−0.288767	−	0.957399i	$-0.593245\pi$
$383$	8.61121	−	32.1375i	0.440012	−	1.64215i	0.728780	−	0.684748i	$-0.240088\pi$
$384$		0			0
$385$	1.78759	−	0.848743i	0.0911039	−	0.0432560i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.35302	−	14.4679i	0.423515	−	0.733549i	−0.572765	−	0.819719i	$-0.694129\pi$
$389$	8.35302	−	14.4679i	0.423515	−	0.733549i	0.996280	+	0.0861698i	$0.0274628\pi$
$390$		0			0
$391$	17.2474	+	29.8735i	0.872241	+	1.51077i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−20.3383	+	3.73215i	−1.02333	+	0.187785i
$396$		0			0
$397$	−16.1464	−	16.1464i	−0.810366	−	0.810366i	0.174323	−	0.984689i	$-0.444226\pi$
$397$	−16.1464	−	16.1464i	−0.810366	−	0.810366i	−0.984689	+	0.174323i	$0.944226\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.32745	+	0.766404i	−0.0662897	+	0.0382724i	−0.532779	−	0.846255i	$-0.678852\pi$
$401$	−1.32745	+	0.766404i	−0.0662897	+	0.0382724i	0.466489	+	0.884527i	$0.345519\pi$
$402$		0			0
$403$	−0.201501	−	0.752011i	−0.0100375	−	0.0374603i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.74456	+	13.9749i	0.185611	+	0.692709i
$408$		0			0
$409$	23.8113	−	13.7474i	1.17739	−	0.679768i	0.221982	−	0.975051i	$-0.428747\pi$
$409$	23.8113	−	13.7474i	1.17739	−	0.679768i	0.955410	+	0.295283i	$0.0954140\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.78434	−	2.78434i	−0.137008	−	0.137008i
$414$		0			0
$415$	6.12372	−	8.87628i	0.300602	−	0.435719i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.1732	−	26.2808i	−0.741261	−	1.28390i	−0.951921	−	0.306342i	$-0.900895\pi$
$419$	−15.1732	−	26.2808i	−0.741261	−	1.28390i	0.210660	−	0.977559i	$-0.432439\pi$
$420$		0			0
$421$	−5.62372	+	9.74058i	−0.274084	+	0.474727i	−0.969904	−	0.243490i	$-0.921708\pi$
$421$	−5.62372	+	9.74058i	−0.274084	+	0.474727i	0.695820	+	0.718216i	$0.255041\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.5158	−	15.9691i	−0.558600	−	0.774616i
$426$		0			0
$427$	1.05279	−	3.92907i	0.0509481	−	0.190141i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			20.7419i			0.999103i	0.866284	+	0.499551i	$0.166502\pi$
$431$			20.7419i			0.999103i	−0.866284	+	0.499551i	$0.833498\pi$
$432$		0			0
$433$	2.79796	−	2.79796i	0.134461	−	0.134461i	−0.636673	−	0.771134i	$-0.719690\pi$
$433$	2.79796	−	2.79796i	0.134461	−	0.134461i	0.771134	+	0.636673i	$0.219690\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	32.9923	+	8.84025i	1.57823	+	0.422887i
$438$		0			0
$439$	−11.3851	−	6.57321i	−0.543383	−	0.313722i	0.203066	−	0.979165i	$-0.434909\pi$
$439$	−11.3851	−	6.57321i	−0.543383	−	0.313722i	−0.746449	+	0.665443i	$0.768243\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.31658	+	2.49637i	−0.442644	+	0.118606i	−0.473256	−	0.880925i	$-0.656921\pi$
$443$	−9.31658	+	2.49637i	−0.442644	+	0.118606i	0.0306113	+	0.999531i	$0.490255\pi$
$444$		0			0
$445$	−21.0970	+	17.9539i	−1.00009	+	0.851094i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−12.3889			−0.584668			−0.292334	−	0.956316i	$-0.594432\pi$
$449$	−12.3889			−0.584668			−0.292334	+	0.956316i	$0.594432\pi$
$450$		0			0
$451$	−26.7423			−1.25925
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.937461	−	0.797794i	0.0439489	−	0.0374011i
$456$		0			0
$457$	30.5286	−	8.18011i	1.42807	−	0.382649i	0.539728	−	0.841839i	$-0.318527\pi$
$457$	30.5286	−	8.18011i	1.42807	−	0.382649i	0.888338	+	0.459190i	$0.151860\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−25.1970	−	14.5475i	−1.17354	−	0.677543i	−0.219028	−	0.975719i	$-0.570289\pi$
$461$	−25.1970	−	14.5475i	−1.17354	−	0.677543i	−0.954511	+	0.298175i	$0.903622\pi$
$462$		0			0
$463$	−1.39704	−	0.374336i	−0.0649259	−	0.0173969i	0.226210	−	0.974079i	$-0.427366\pi$
$463$	−1.39704	−	0.374336i	−0.0649259	−	0.0173969i	−0.291136	+	0.956682i	$0.594033\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.4248	−	16.4248i	0.760048	−	0.760048i	−0.216283	−	0.976331i	$-0.569393\pi$
$467$	16.4248	−	16.4248i	0.760048	−	0.760048i	0.976331	+	0.216283i	$0.0693934\pi$
$468$		0			0
$469$			3.89898i			0.180038i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.561047	+	2.09385i	−0.0257970	+	0.0962755i
$474$		0			0
$475$	−19.2439	−	3.11802i	−0.882972	−	0.143065i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.01794	−	3.49517i	0.0922019	−	0.159698i	−0.816235	−	0.577719i	$-0.803943\pi$
$479$	2.01794	−	3.49517i	0.0922019	−	0.159698i	0.908437	+	0.418021i	$0.137276\pi$
$480$		0			0
$481$	4.50000	+	7.79423i	0.205182	+	0.355386i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.57520	+	12.4297i	−0.389380	+	0.564402i
$486$		0			0
$487$	18.6742	+	18.6742i	0.846210	+	0.846210i	0.989658	−	0.143448i	$-0.0458188\pi$
$487$	18.6742	+	18.6742i	0.846210	+	0.846210i	−0.143448	+	0.989658i	$0.545819\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	34.5986	−	19.9755i	1.56141	−	0.901482i	0.564298	−	0.825571i	$-0.309147\pi$
$491$	34.5986	−	19.9755i	1.56141	−	0.901482i	0.997115	−	0.0759113i	$-0.0241866\pi$
$492$		0			0
$493$	2.83763	+	10.5902i	0.127800	+	0.476958i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.790093	−	2.94867i	−0.0354405	−	0.132266i
$498$		0			0
$499$	0.778539	−	0.449490i	0.0348522	−	0.0201219i	−0.482473	−	0.875911i	$-0.660261\pi$
$499$	0.778539	−	0.449490i	0.0348522	−	0.0201219i	0.517325	+	0.855789i	$0.326928\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.5833	+	18.5833i	0.828590	+	0.828590i	0.987322	−	0.158732i	$-0.0507404\pi$
$503$	18.5833	+	18.5833i	0.828590	+	0.828590i	−0.158732	+	0.987322i	$0.550740\pi$
$504$		0			0
$505$	39.4949	−	7.24745i	1.75750	−	0.322507i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.21238	−	14.2243i	−0.364007	−	0.630479i	0.624609	−	0.780938i	$-0.285258\pi$
$509$	−8.21238	−	14.2243i	−0.364007	−	0.630479i	−0.988616	+	0.150458i	$0.951925\pi$
$510$		0			0
$511$	1.39898	−	2.42310i	0.0618872	−	0.107192i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−17.7818	+	8.44279i	−0.783562	+	0.372034i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	15.1732i		−	0.664751i	−0.943147	−	0.332376i	$-0.892150\pi$
$521$		−	15.1732i		−	0.664751i	0.943147	−	0.332376i	$-0.107850\pi$
$522$		0			0
$523$	27.9217	−	27.9217i	1.22093	−	1.22093i	0.253628	−	0.967302i	$-0.418376\pi$
$523$	27.9217	−	27.9217i	1.22093	−	1.22093i	0.967302	−	0.253628i	$-0.0816240\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.70963	−	0.458093i	−0.0744724	−	0.0199548i
$528$		0			0
$529$	−46.5422	−	26.8712i	−2.02358	−	1.16831i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−16.0687	+	4.30560i	−0.696014	+	0.186496i
$534$		0			0
$535$	2.27797	−	28.3019i	0.0984852	−	1.22360i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.2091			−0.827395
$540$		0			0
$541$	10.5505			0.453602			0.226801	−	0.973941i	$-0.427173\pi$
$541$	10.5505			0.453602			0.226801	+	0.973941i	$0.427173\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.4461	+	19.3252i	0.704473	+	0.827803i
$546$		0			0
$547$	32.2016	−	8.62840i	1.37684	−	0.368924i	0.506869	−	0.862023i	$-0.330803\pi$
$547$	32.2016	−	8.62840i	1.37684	−	0.368924i	0.869973	+	0.493100i	$0.164136\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.40165	+	5.42804i	0.400524	+	0.231242i
$552$		0			0
$553$	−2.83903	−	0.760717i	−0.120728	−	0.0323490i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−23.5263	+	23.5263i	−0.996839	+	0.996839i	−0.999995	−	0.00315559i	$-0.998996\pi$
$557$	−23.5263	+	23.5263i	−0.996839	+	0.996839i	0.00315559	+	0.999995i	$0.498996\pi$
$558$		0			0
$559$			1.34847i			0.0570342i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.05742	−	11.4104i	0.128855	−	0.480893i	−0.871093	−	0.491118i	$-0.836588\pi$
$563$	3.05742	−	11.4104i	0.128855	−	0.480893i	0.999948	+	0.0102256i	$0.00325496\pi$
$564$		0			0
$565$	−0.848743	−	1.78759i	−0.0357069	−	0.0752044i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.97879	−	15.5517i	0.376410	−	0.651962i	−0.614127	−	0.789207i	$-0.710492\pi$
$569$	8.97879	−	15.5517i	0.376410	−	0.651962i	0.990537	+	0.137246i	$0.0438250\pi$
$570$		0			0
$571$	4.72474	+	8.18350i	0.197724	+	0.342469i	0.947790	−	0.318894i	$-0.103312\pi$
$571$	4.72474	+	8.18350i	0.197724	+	0.342469i	−0.750066	+	0.661363i	$0.769978\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	39.9510	+	17.9576i	1.66607	+	0.748883i
$576$		0			0
$577$	−22.0227	−	22.0227i	−0.916817	−	0.916817i	0.0799794	−	0.996797i	$-0.474515\pi$
$577$	−22.0227	−	22.0227i	−0.916817	−	0.916817i	−0.996797	+	0.0799794i	$0.974515\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.32745	−	0.766404i	0.0550719	−	0.0317958i
$582$		0			0
$583$	6.31300	+	23.5605i	0.261458	+	0.975774i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.74456	−	13.9749i	−0.154554	−	0.576805i	−0.999143	−	0.0413892i	$-0.986822\pi$
$587$	−3.74456	−	13.9749i	−0.154554	−	0.576805i	0.844589	−	0.535416i	$-0.179845\pi$
$588$		0			0
$589$	−1.51775	+	0.876276i	−0.0625380	+	0.0361063i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	8.97879	+	8.97879i	0.368715	+	0.368715i	0.867008	−	0.498294i	$-0.166040\pi$
$593$	8.97879	+	8.97879i	0.368715	+	0.368715i	−0.498294	+	0.867008i	$0.666040\pi$
$594$		0			0
$595$	−0.505103	−	2.75255i	−0.0207072	−	0.112844i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.1912	+	29.7760i	0.702412	+	1.21661i	0.967617	+	0.252422i	$0.0812270\pi$
$599$	17.1912	+	29.7760i	0.702412	+	1.21661i	−0.265205	+	0.964192i	$0.585440\pi$
$600$		0			0
$601$	7.02270	−	12.1637i	0.286462	−	0.496167i	−0.686501	−	0.727129i	$-0.740854\pi$
$601$	7.02270	−	12.1637i	0.286462	−	0.496167i	0.972963	+	0.230962i	$0.0741874\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.84069	+	2.43609i	0.278114	+	0.0990412i
$606$		0			0
$607$	1.34486	−	5.01910i	0.0545863	−	0.203719i	−0.933247	−	0.359235i	$-0.883038\pi$
$607$	1.34486	−	5.01910i	0.0545863	−	0.203719i	0.987833	+	0.155517i	$0.0497042\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−31.2247	+	31.2247i	−1.26116	+	1.26116i	−0.310622	+	0.950533i	$0.600537\pi$
$613$	−31.2247	+	31.2247i	−1.26116	+	1.26116i	−0.950533	+	0.310622i	$0.899463\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−16.0687	−	4.30560i	−0.646903	−	0.173337i	−0.0795746	−	0.996829i	$-0.525356\pi$
$617$	−16.0687	−	4.30560i	−0.646903	−	0.173337i	−0.567328	+	0.823492i	$0.692023\pi$
$618$		0			0
$619$	1.43027	+	0.825765i	0.0574873	+	0.0331903i	0.528468	−	0.848953i	$-0.322767\pi$
$619$	1.43027	+	0.825765i	0.0574873	+	0.0331903i	−0.470981	+	0.882143i	$0.656100\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.80348	+	1.01914i	−0.152383	+	0.0408310i
$624$		0			0
$625$	−23.7210	−	7.89406i	−0.948838	−	0.315763i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	20.4606			0.815819
$630$		0			0
$631$	−35.4949			−1.41303			−0.706515	−	0.707698i	$-0.749734\pi$
$631$	−35.4949			−1.41303			−0.706515	+	0.707698i	$0.749734\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−31.2024	−	2.51143i	−1.23823	−	0.0996629i
$636$		0			0
$637$	−11.5422	+	3.09273i	−0.457319	+	0.122538i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6.99034	−	4.03587i	−0.276102	−	0.159407i	0.355556	−	0.934655i	$-0.384292\pi$
$641$	−6.99034	−	4.03587i	−0.276102	−	0.159407i	−0.631657	+	0.775248i	$0.717625\pi$
$642$		0			0
$643$	17.1443	+	4.59381i	0.676106	+	0.181162i	0.580504	−	0.814258i	$-0.302856\pi$
$643$	17.1443	+	4.59381i	0.676106	+	0.181162i	0.0956021	+	0.995420i	$0.469522\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.0147	+	13.0147i	−0.511659	+	0.511659i	−0.915035	−	0.403375i	$-0.867837\pi$
$647$	−13.0147	+	13.0147i	−0.511659	+	0.511659i	0.403375	+	0.915035i	$0.367837\pi$
$648$		0			0
$649$			34.4949i			1.35404i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.05016	+	30.0436i	−0.315027	+	1.17570i	0.608937	+	0.793218i	$0.291596\pi$
$653$	−8.05016	+	30.0436i	−0.315027	+	1.17570i	−0.923964	+	0.382479i	$0.875071\pi$
$654$		0			0
$655$	−4.17738	+	11.7303i	−0.163224	+	0.458342i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.7778	+	42.9164i	−0.965206	+	1.67179i	−0.256144	+	0.966639i	$0.582452\pi$
$659$	−24.7778	+	42.9164i	−0.965206	+	1.67179i	−0.709062	+	0.705146i	$0.750881\pi$
$660$		0			0
$661$	0.500000	+	0.866025i	0.0194477	+	0.0336845i	0.875585	−	0.483063i	$-0.160476\pi$
$661$	0.500000	+	0.866025i	0.0194477	+	0.0336845i	−0.856138	+	0.516748i	$0.827143\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.28089	−	1.57358i	−0.0884490	−	0.0610208i
$666$		0			0
$667$	−17.2474	−	17.2474i	−0.667824	−	0.667824i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−30.8598	+	17.8169i	−1.19133	+	0.687815i
$672$		0			0
$673$	6.68734	+	24.9575i	0.257778	+	0.962041i	0.966524	+	0.256577i	$0.0825946\pi$
$673$	6.68734	+	24.9575i	0.257778	+	0.962041i	−0.708746	+	0.705464i	$0.750739\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.07656	+	15.2139i	0.156675	+	0.584718i	0.998956	+	0.0456802i	$0.0145455\pi$
$677$	4.07656	+	15.2139i	0.156675	+	0.584718i	−0.842281	+	0.539038i	$0.818788\pi$
$678$		0			0
$679$	−1.85886	+	1.07321i	−0.0713366	+	0.0411862i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−20.1161	−	20.1161i	−0.769723	−	0.769723i	0.208335	−	0.978058i	$-0.433196\pi$
$683$	−20.1161	−	20.1161i	−0.769723	−	0.769723i	−0.978058	+	0.208335i	$0.933196\pi$
$684$		0			0
$685$	8.87628	+	6.12372i	0.339145	+	0.233975i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.58662	+	13.1404i	0.289027	+	0.500610i
$690$		0			0
$691$	0.123724	−	0.214297i	0.00470670	−	0.00815224i	−0.863662	−	0.504071i	$-0.831835\pi$
$691$	0.123724	−	0.214297i	0.00470670	−	0.00815224i	0.868369	+	0.495918i	$0.165168\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	14.4386	−	40.5444i	0.547687	−	1.53794i
$696$		0			0
$697$	−9.78838	+	36.5307i	−0.370761	+	1.38370i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			17.6763i			0.667625i	0.942640	+	0.333812i	$0.108335\pi$
$701$			17.6763i			0.667625i	−0.942640	+	0.333812i	$0.891665\pi$
$702$		0			0
$703$	14.3258	−	14.3258i	0.540306	−	0.540306i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.51310	+	1.47723i	0.207342	+	0.0555570i
$708$		0			0
$709$	−7.22999	−	4.17423i	−0.271528	−	0.156767i	0.358054	−	0.933701i	$-0.383440\pi$
$709$	−7.22999	−	4.17423i	−0.271528	−	0.156767i	−0.629582	+	0.776934i	$0.716774\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.80348	−	1.01914i	0.142441	−	0.0381671i
$714$		0			0
$715$	−10.7489	−	0.865163i	−0.401988	−	0.0323553i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	49.8369			1.85860			0.929300	−	0.369325i	$-0.120411\pi$
$719$	49.8369			1.85860			0.929300	+	0.369325i	$0.120411\pi$
$720$		0			0
$721$	−2.79796			−0.104201
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.7880	+	8.79957i	0.400657	+	0.326808i
$726$		0			0
$727$	18.9864	−	5.08738i	0.704165	−	0.188680i	0.111070	−	0.993813i	$-0.464572\pi$
$727$	18.9864	−	5.08738i	0.704165	−	0.188680i	0.593095	+	0.805132i	$0.297906\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.65490	+	1.53281i	0.0981951	+	0.0566929i
$732$		0			0
$733$	3.48406	+	0.933552i	0.128687	+	0.0344815i	0.322588	−	0.946540i	$-0.395447\pi$
$733$	3.48406	+	0.933552i	0.128687	+	0.0344815i	−0.193901	+	0.981021i	$0.562114\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.1520	−	24.1520i	0.889651	−	0.889651i
$738$		0			0
$739$			26.2474i			0.965528i	0.875750	+	0.482764i	$0.160367\pi$
$739$			26.2474i			0.965528i	−0.875750	+	0.482764i	$0.839633\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.5848	+	46.9672i	−0.461692	+	1.72306i	0.205939	+	0.978565i	$0.433975\pi$
$743$	−12.5848	+	46.9672i	−0.461692	+	1.72306i	−0.667631	+	0.744493i	$0.732691\pi$
$744$		0			0
$745$	14.3667	+	5.11622i	0.526354	+	0.187444i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.01794	−	3.49517i	0.0737338	−	0.127711i
$750$		0			0
$751$	−4.50000	−	7.79423i	−0.164207	−	0.284415i	0.772166	−	0.635421i	$-0.219173\pi$
$751$	−4.50000	−	7.79423i	−0.164207	−	0.284415i	−0.936374	+	0.351005i	$0.885840\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.25805	−	23.2042i	−0.154966	−	0.844488i
$756$		0			0
$757$	19.7196	+	19.7196i	0.716723	+	0.716723i	0.967933	−	0.251210i	$-0.0808285\pi$
$757$	19.7196	+	19.7196i	0.716723	+	0.716723i	−0.251210	+	0.967933i	$0.580828\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−20.1307	+	11.6225i	−0.729739	+	0.421315i	−0.818327	−	0.574753i	$-0.805098\pi$
$761$	−20.1307	+	11.6225i	−0.729739	+	0.421315i	0.0885878	+	0.996068i	$0.471765\pi$
$762$		0			0
$763$	0.933552	+	3.48406i	0.0337968	+	0.126132i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.55379	+	20.7270i	0.200536	+	0.748409i
$768$		0			0
$769$	25.7576	−	14.8712i	0.928844	−	0.536268i	0.0423981	−	0.999101i	$-0.486500\pi$
$769$	25.7576	−	14.8712i	0.928844	−	0.536268i	0.886446	+	0.462833i	$0.153167\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.41011	+	3.41011i	0.122653	+	0.122653i	0.765769	−	0.643116i	$-0.222359\pi$
$773$	3.41011	+	3.41011i	0.122653	+	0.122653i	−0.643116	+	0.765769i	$0.722359\pi$
$774$		0			0
$775$	−2.10102	+	0.797959i	−0.0754709	+	0.0286635i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	18.7240	+	32.4309i	0.670856	+	1.16196i
$780$		0			0
$781$	−13.3712	+	23.1596i	−0.478458	+	0.828714i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	18.1049	+	38.1317i	0.646191	+	1.36098i
$786$		0			0
$787$	6.39527	−	23.8675i	0.227967	−	0.850783i	−0.753228	−	0.657760i	$-0.771504\pi$
$787$	6.39527	−	23.8675i	0.227967	−	0.850783i	0.981194	−	0.193023i	$-0.0618292\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	0.281275i		−	0.0100010i
$792$		0			0
$793$	−15.6742	+	15.6742i	−0.556608	+	0.556608i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−30.0436	−	8.05016i	−1.06420	−	0.285151i	−0.316092	−	0.948729i	$-0.602371\pi$
$797$	−30.0436	−	8.05016i	−1.06420	−	0.285151i	−0.748108	+	0.663577i	$0.769037\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−23.6757	+	6.34388i	−0.835497	+	0.223871i
$804$		0			0
$805$	4.03504	+	4.74144i	0.142216	+	0.167114i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.25153			−0.0440015			−0.0220008	−	0.999758i	$-0.507004\pi$
$809$	−1.25153			−0.0440015			−0.0220008	+	0.999758i	$0.507004\pi$
$810$		0			0
$811$	−19.5505			−0.686511			−0.343256	−	0.939242i	$-0.611530\pi$
$811$	−19.5505			−0.686511			−0.343256	+	0.939242i	$0.611530\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.957803	+	11.8999i	−0.0335504	+	0.416836i
$816$		0			0
$817$	2.93208	−	0.785647i	0.102580	−	0.0274863i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.5517	+	8.97879i	0.542759	+	0.313362i	0.746196	−	0.665726i	$-0.231878\pi$
$821$	15.5517	+	8.97879i	0.542759	+	0.313362i	−0.203438	+	0.979088i	$0.565211\pi$
$822$		0			0
$823$	−42.3778	−	11.3551i	−1.47720	−	0.395814i	−0.571805	−	0.820390i	$-0.693757\pi$
$823$	−42.3778	−	11.3551i	−1.47720	−	0.395814i	−0.905392	+	0.424576i	$0.860423\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.82021	+	6.82021i	−0.237162	+	0.237162i	−0.815674	−	0.578512i	$-0.803634\pi$
$827$	−6.82021	+	6.82021i	−0.237162	+	0.237162i	0.578512	+	0.815674i	$0.303634\pi$
$828$		0			0
$829$		−	49.2474i		−	1.71043i	−0.518270	−	0.855217i	$-0.673424\pi$
$829$		−	49.2474i		−	1.71043i	0.518270	−	0.855217i	$-0.326576\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.03102	+	26.2401i	−0.243610	+	0.909167i
$834$		0			0
$835$	−27.4367	+	13.0269i	−0.949487	+	0.450815i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.3889	−	21.4582i	0.427712	−	0.740819i	−0.568957	−	0.822367i	$-0.692653\pi$
$839$	12.3889	−	21.4582i	0.427712	−	0.740819i	0.996669	+	0.0815479i	$0.0259864\pi$
$840$		0			0
$841$	10.6237	+	18.4008i	0.366335	+	0.634511i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	21.9934	−	4.03587i	0.756598	−	0.138838i
$846$		0			0
$847$	0.729847	+	0.729847i	0.0250779	+	0.0250779i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−39.4212	+	22.7599i	−1.35134	+	0.780198i
$852$		0			0
$853$	−1.27091	−	4.74310i	−0.0435152	−	0.162401i	0.940749	−	0.339103i	$-0.110124\pi$
$853$	−1.27091	−	4.74310i	−0.0435152	−	0.162401i	−0.984264	+	0.176702i	$0.943457\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.24819	−	4.65829i	−0.0426372	−	0.159124i	0.941325	−	0.337502i	$-0.109582\pi$
$857$	−1.24819	−	4.65829i	−0.0426372	−	0.159124i	−0.983962	+	0.178377i	$0.942915\pi$
$858$		0			0
$859$	4.54442	−	2.62372i	0.155054	−	0.0895203i	−0.420466	−	0.907308i	$-0.638133\pi$
$859$	4.54442	−	2.62372i	0.155054	−	0.0895203i	0.575519	+	0.817788i	$0.304800\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.8561	+	10.8561i	0.369545	+	0.369545i	0.867311	−	0.497766i	$-0.165846\pi$
$863$	10.8561	+	10.8561i	0.369545	+	0.369545i	−0.497766	+	0.867311i	$0.665846\pi$
$864$		0			0
$865$	10.0000	−	14.4949i	0.340010	−	0.492841i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.8740	+	22.2985i	0.436721	+	0.756423i
$870$		0			0
$871$	10.6237	−	18.4008i	0.359971	−	0.623488i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.56457	−	2.45978i	−0.0866984	−	0.0831558i
$876$		0			0
$877$	3.74252	−	13.9673i	0.126376	−	0.471641i	−0.873509	−	0.486808i	$-0.838161\pi$
$877$	3.74252	−	13.9673i	0.126376	−	0.471641i	0.999885	+	0.0151668i	$0.00482792\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	2.78434i		−	0.0938068i	−0.998899	−	0.0469034i	$-0.985065\pi$
$881$		−	2.78434i		−	0.0938068i	0.998899	−	0.0469034i	$-0.0149353\pi$
$882$		0			0
$883$	22.9217	−	22.9217i	0.771376	−	0.771376i	−0.206971	−	0.978347i	$-0.566361\pi$
$883$	22.9217	−	22.9217i	0.771376	−	0.771376i	0.978347	+	0.206971i	$0.0663606\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−18.6332	−	4.99274i	−0.625641	−	0.167640i	−0.0679499	−	0.997689i	$-0.521646\pi$
$887$	−18.6332	−	4.99274i	−0.625641	−	0.167640i	−0.557691	+	0.830049i	$0.688312\pi$
$888$		0			0
$889$	−3.85337	−	2.22474i	−0.129238	−	0.0746155i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	16.3555	−	13.9188i	0.546706	−	0.465255i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.25153			0.0417409
$900$		0			0
$901$	34.4949			1.14919
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−19.1532	+	16.2997i	−0.636675	+	0.541820i
$906$		0			0
$907$	−18.6794	+	5.00512i	−0.620238	+	0.166192i	−0.555236	−	0.831693i	$-0.687372\pi$
$907$	−18.6794	+	5.00512i	−0.620238	+	0.166192i	−0.0650019	+	0.997885i	$0.520705\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.73876	−	2.15857i	−0.123871	−	0.0715168i	0.436784	−	0.899566i	$-0.356117\pi$
$911$	−3.73876	−	2.15857i	−0.123871	−	0.0715168i	−0.560655	+	0.828049i	$0.689451\pi$
$912$		0			0
$913$	−12.9703	−	3.47537i	−0.429253	−	0.115018i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.25153	+	1.25153i	−0.0413292	+	0.0413292i
$918$		0			0
$919$			18.6515i			0.615257i	0.951507	+	0.307629i	$0.0995354\pi$
$919$			18.6515i			0.615257i	−0.951507	+	0.307629i	$0.900465\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.30560	+	16.0687i	−0.141721	+	0.528909i
$924$		0			0
$925$	21.0730	−	15.1964i	0.692875	−	0.499654i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−28.3285	+	49.0665i	−0.929429	+	1.60982i	−0.145150	+	0.989410i	$0.546367\pi$
$929$	−28.3285	+	49.0665i	−0.929429	+	1.60982i	−0.784279	+	0.620409i	$0.786967\pi$
$930$		0			0
$931$	13.4495	+	23.2952i	0.440789	+	0.763469i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−13.9217	+	20.1794i	−0.455288	+	0.659936i
$936$		0			0
$937$	−9.77526	−	9.77526i	−0.319344	−	0.319344i	0.529171	−	0.848515i	$-0.322503\pi$
$937$	−9.77526	−	9.77526i	−0.319344	−	0.319344i	−0.848515	+	0.529171i	$0.822503\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.1404	+	7.58662i	−0.428365	+	0.247317i	−0.698650	−	0.715464i	$-0.746215\pi$
$941$	−13.1404	+	7.58662i	−0.428365	+	0.247317i	0.270285	+	0.962780i	$0.412882\pi$
$942$		0			0
$943$	−21.7766	−	81.2715i	−0.709145	−	2.64657i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.01188	−	22.4366i	−0.195360	−	0.729093i	−0.992173	−	0.124868i	$-0.960149\pi$
$947$	−6.01188	−	22.4366i	−0.195360	−	0.729093i	0.796813	−	0.604225i	$-0.206517\pi$
$948$		0			0
$949$	−13.2047	+	7.62372i	−0.428642	+	0.247477i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	23.5263	+	23.5263i	0.762090	+	0.762090i	0.976700	−	0.214610i	$-0.0688480\pi$
$953$	23.5263	+	23.5263i	0.762090	+	0.762090i	−0.214610	+	0.976700i	$0.568848\pi$
$954$		0			0
$955$	−27.2474	+	5.00000i	−0.881707	+	0.161796i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.766404	+	1.32745i	0.0247485	+	0.0428656i
$960$		0			0
$961$	15.3990	−	26.6718i	0.496741	−	0.860381i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−33.0605	+	15.6971i	−1.06425	+	0.505306i
$966$		0			0
$967$	−11.4660	+	42.7918i	−0.368723	+	1.37609i	0.493581	+	0.869700i	$0.335688\pi$
$967$	−11.4660	+	42.7918i	−0.368723	+	1.37609i	−0.862304	+	0.506391i	$0.830979\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	2.50306i		−	0.0803272i	−0.999193	−	0.0401636i	$-0.987212\pi$
$971$		−	2.50306i		−	0.0803272i	0.999193	−	0.0401636i	$-0.0127879\pi$
$972$		0			0
$973$	4.32577	−	4.32577i	0.138678	−	0.138678i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	46.1123	+	12.3558i	1.47526	+	0.395296i	0.904733	−	0.425980i	$-0.140070\pi$
$977$	46.1123	+	12.3558i	1.47526	+	0.395296i	0.570532	+	0.821276i	$0.306737\pi$
$978$		0			0
$979$	29.8735	+	17.2474i	0.954760	+	0.551231i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	35.0861	−	9.40130i	1.11907	−	0.299855i	0.348565	−	0.937285i	$-0.386669\pi$
$983$	35.0861	−	9.40130i	1.11907	−	0.299855i	0.770509	+	0.637430i	$0.220002\pi$
$984$		0			0
$985$	−1.73033	+	21.4979i	−0.0551328	+	0.684980i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.82021			−0.216870
$990$		0			0
$991$	35.0454			1.11325			0.556627	−	0.830763i	$-0.312095\pi$
$991$	35.0454			1.11325			0.556627	+	0.830763i	$0.312095\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	13.4013	+	15.7474i	0.424850	+	0.499227i
$996$		0			0
$997$	0.137997	−	0.0369761i	0.00437040	−	0.00117104i	−0.256633	−	0.966509i	$-0.582613\pi$
$997$	0.137997	−	0.0369761i	0.00437040	−	0.00117104i	0.261004	+	0.965338i	$0.415947\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.x.d.917.1		16
3.2	odd	2	inner	1620.2.x.d.917.4		16
5.3	odd	4	inner	1620.2.x.d.593.1		16
9.2	odd	6		540.2.j.a.377.3	yes	8
9.4	even	3	inner	1620.2.x.d.377.4		16
9.5	odd	6	inner	1620.2.x.d.377.1		16
9.7	even	3		540.2.j.a.377.2	yes	8
15.8	even	4	inner	1620.2.x.d.593.4		16
36.7	odd	6		2160.2.w.e.1457.2		8
36.11	even	6		2160.2.w.e.1457.3		8
45.2	even	12		2700.2.j.j.593.2		8
45.7	odd	12		2700.2.j.j.593.1		8
45.13	odd	12	inner	1620.2.x.d.53.4		16
45.23	even	12	inner	1620.2.x.d.53.1		16
45.29	odd	6		2700.2.j.j.1457.2		8
45.34	even	6		2700.2.j.j.1457.1		8
45.38	even	12		540.2.j.a.53.2	✓	8
45.43	odd	12		540.2.j.a.53.3	yes	8
180.43	even	12		2160.2.w.e.593.3		8
180.83	odd	12		2160.2.w.e.593.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.j.a.53.2	✓	8	45.38	even	12
540.2.j.a.53.3	yes	8	45.43	odd	12
540.2.j.a.377.2	yes	8	9.7	even	3
540.2.j.a.377.3	yes	8	9.2	odd	6
1620.2.x.d.53.1		16	45.23	even	12	inner
1620.2.x.d.53.4		16	45.13	odd	12	inner
1620.2.x.d.377.1		16	9.5	odd	6	inner
1620.2.x.d.377.4		16	9.4	even	3	inner
1620.2.x.d.593.1		16	5.3	odd	4	inner
1620.2.x.d.593.4		16	15.8	even	4	inner
1620.2.x.d.917.1		16	1.1	even	1	trivial
1620.2.x.d.917.4		16	3.2	odd	2	inner
2160.2.w.e.593.2		8	180.83	odd	12
2160.2.w.e.593.3		8	180.43	even	12
2160.2.w.e.1457.2		8	36.7	odd	6
2160.2.w.e.1457.3		8	36.11	even	6
2700.2.j.j.593.1		8	45.7	odd	12
2700.2.j.j.593.2		8	45.2	even	12
2700.2.j.j.1457.1		8	45.34	even	6
2700.2.j.j.1457.2		8	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70289 + 1.44919i) q^{5} +(-0.307007 + 0.0822623i) q^{7} +O(q^{10})\)	\(q+(-1.70289 + 1.44919i) q^{5} +(-0.307007 + 0.0822623i) q^{7} +(2.41131 + 1.39217i) q^{11} +(1.67303 + 0.448288i) q^{13} +(2.78434 - 2.78434i) q^{17} -3.89898i q^{19} +(-2.26732 + 8.46177i) q^{23} +(0.799701 - 4.93563i) q^{25} +(-1.39217 + 2.41131i) q^{29} +(-0.224745 - 0.389270i) q^{31} +(0.403587 - 0.584996i) q^{35} +(3.67423 + 3.67423i) q^{37} +(-8.31779 + 4.80228i) q^{41} +(0.201501 + 0.752011i) q^{43} +(-5.97469 + 3.44949i) q^{49} +(6.19445 + 6.19445i) q^{53} +(-6.12372 + 1.12372i) q^{55} +(6.19445 + 10.7291i) q^{59} +(-6.39898 + 11.0834i) q^{61} +(-3.49865 + 1.66115i) q^{65} +(3.17499 - 11.8492i) q^{67} +9.60455i q^{71} +(-6.22474 + 6.22474i) q^{73} +(-0.854813 - 0.229046i) q^{77} +(8.00853 + 4.62372i) q^{79} +(-4.65829 + 1.24819i) q^{83} +(-0.706403 + 8.77647i) q^{85} +12.3889 q^{89} -0.550510 q^{91} +(5.65036 + 6.63955i) q^{95} +(6.52312 - 1.74786i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 8 q^{25} + 16 q^{31} - 24 q^{43} - 24 q^{61} - 40 q^{67} - 80 q^{73} - 40 q^{85} - 48 q^{91} + 48 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 + 8 * q^25 + 16 * q^31 - 24 * q^43 - 24 * q^61 - 40 * q^67 - 80 * q^73 - 40 * q^85 - 48 * q^91 + 48 * q^97

Introduction

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