LMFDB - Embedded newform 900.2.n.a.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(181,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("900.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	900.181
Dual form			900.2.n.a.721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.04275 - 0.909491i) q^{5} +0.747238 q^{7} +O(q^{10})$	$q+(-2.04275 - 0.909491i) q^{5} +0.747238 q^{7} +(-0.0646021 - 0.198825i) q^{11} +(-0.773659 + 2.38108i) q^{13} +(-5.51712 - 4.00842i) q^{17} +(-1.00739 - 0.731913i) q^{19} +(-1.00457 - 3.09174i) q^{23} +(3.34565 + 3.71572i) q^{25} +(-4.19332 + 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(-1.52642 - 0.679606i) q^{35} +(0.607352 - 1.86924i) q^{37} +(-0.993096 + 3.05644i) q^{41} -12.7127 q^{43} +(-5.24425 + 3.81017i) q^{47} -6.44163 q^{49} +(3.35177 - 2.43520i) q^{53} +(-0.0488635 + 0.464905i) q^{55} +(-3.61882 + 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(3.74596 - 4.16031i) q^{65} +(-2.35995 - 1.71460i) q^{67} +(5.29912 - 3.85004i) q^{71} +(-0.778516 - 2.39603i) q^{73} +(-0.0482732 - 0.148570i) q^{77} +(8.28621 - 6.02028i) q^{79} +(-4.59240 - 3.33658i) q^{83} +(7.62447 + 13.2060i) q^{85} +(0.284829 + 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} +(1.39218 + 2.41133i) q^{95} +(12.5757 - 9.13679i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q - 5 * q^5 - 8 * q^7	$ 8 q - 5 q^{5} - 8 q^{7} + 2 q^{11} - 7 q^{17} + 5 q^{19} - 7 q^{23} + 5 q^{25} - 27 q^{29} - 3 q^{31} - 20 q^{35} - 9 q^{37} - 20 q^{41} - 68 q^{43} + 7 q^{47} - 8 q^{49} + 11 q^{53} + 5 q^{55} - 2 q^{59} - 14 q^{61} + 35 q^{65} + 28 q^{67} + 15 q^{71} + 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{83} + 10 q^{85} + 5 q^{91} - 5 q^{95} + 34 q^{97}+O(q^{100}) $ 8 * q - 5 * q^5 - 8 * q^7 + 2 * q^11 - 7 * q^17 + 5 * q^19 - 7 * q^23 + 5 * q^25 - 27 * q^29 - 3 * q^31 - 20 * q^35 - 9 * q^37 - 20 * q^41 - 68 * q^43 + 7 * q^47 - 8 * q^49 + 11 * q^53 + 5 * q^55 - 2 * q^59 - 14 * q^61 + 35 * q^65 + 28 * q^67 + 15 * q^71 + 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^83 + 10 * q^85 + 5 * q^91 - 5 * q^95 + 34 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.04275	−	0.909491i	−0.913545	−	0.406737i
$5$	−2.04275	−	0.909491i	−0.913545	−	0.406737i
$6$		0			0
$7$	0.747238			0.282430			0.141215	−	0.989979i	$-0.454899\pi$
$7$	0.747238			0.282430			0.141215	+	0.989979i	$0.454899\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.0646021	−	0.198825i	−0.0194783	−	0.0599480i	0.940845	−	0.338837i	$-0.110034\pi$
$11$	−0.0646021	−	0.198825i	−0.0194783	−	0.0599480i	−0.960323	+	0.278889i	$0.910034\pi$
$12$		0			0
$13$	−0.773659	+	2.38108i	−0.214574	+	0.660392i	0.784609	+	0.619991i	$0.212864\pi$
$13$	−0.773659	+	2.38108i	−0.214574	+	0.660392i	−0.999184	+	0.0404014i	$0.987136\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.51712	−	4.00842i	−1.33810	−	0.972185i	−0.999512	−	0.0312497i	$-0.990051\pi$
$17$	−5.51712	−	4.00842i	−1.33810	−	0.972185i	−0.338586	−	0.940935i	$-0.609949\pi$
$18$		0			0
$19$	−1.00739	−	0.731913i	−0.231112	−	0.167912i	0.466203	−	0.884678i	$-0.345622\pi$
$19$	−1.00739	−	0.731913i	−0.231112	−	0.167912i	−0.697314	+	0.716766i	$0.745622\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.00457	−	3.09174i	−0.209467	−	0.644673i	−0.999500	−	0.0316092i	$-0.989937\pi$
$23$	−1.00457	−	3.09174i	−0.209467	−	0.644673i	0.790033	−	0.613064i	$-0.210063\pi$
$24$		0			0
$25$	3.34565	+	3.71572i	0.669131	+	0.743145i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.19332	+	3.04662i	−0.778680	+	0.565744i	−0.904582	−	0.426299i	$-0.859817\pi$
$29$	−4.19332	+	3.04662i	−0.778680	+	0.565744i	0.125903	+	0.992043i	$0.459817\pi$
$30$		0			0
$31$	−3.02547	−	2.19813i	−0.543390	−	0.394796i	0.281953	−	0.959428i	$-0.409018\pi$
$31$	−3.02547	−	2.19813i	−0.543390	−	0.394796i	−0.825342	+	0.564633i	$0.809018\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.52642	−	0.679606i	−0.258012	−	0.114874i
$36$		0			0
$37$	0.607352	−	1.86924i	0.0998480	−	0.307301i	−0.888639	−	0.458608i	$-0.848348\pi$
$37$	0.607352	−	1.86924i	0.0998480	−	0.307301i	0.988487	+	0.151307i	$0.0483483\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.993096	+	3.05644i	−0.155096	+	0.477335i	−0.998171	−	0.0604609i	$-0.980743\pi$
$41$	−0.993096	+	3.05644i	−0.155096	+	0.477335i	0.843075	+	0.537796i	$0.180743\pi$
$42$		0			0
$43$	−12.7127			−1.93866			−0.969332	−	0.245755i	$-0.920964\pi$
$43$	−12.7127			−1.93866			−0.969332	+	0.245755i	$0.920964\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.24425	+	3.81017i	−0.764952	+	0.555770i	−0.900425	−	0.435011i	$-0.856745\pi$
$47$	−5.24425	+	3.81017i	−0.764952	+	0.555770i	0.135473	+	0.990781i	$0.456745\pi$
$48$		0			0
$49$	−6.44163			−0.920234
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.35177	−	2.43520i	0.460401	−	0.334501i	−0.333288	−	0.942825i	$-0.608158\pi$
$53$	3.35177	−	2.43520i	0.460401	−	0.334501i	0.793688	+	0.608325i	$0.208158\pi$
$54$		0			0
$55$	−0.0488635	+	0.464905i	−0.00658875	+	0.0626877i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.61882	+	11.1376i	−0.471131	+	1.44999i	0.379975	+	0.924997i	$0.375933\pi$
$59$	−3.61882	+	11.1376i	−0.471131	+	1.44999i	−0.851106	+	0.524995i	$0.824067\pi$
$60$		0			0
$61$	−3.85634	−	11.8686i	−0.493753	−	1.51962i	−0.818891	−	0.573949i	$-0.805411\pi$
$61$	−3.85634	−	11.8686i	−0.493753	−	1.51962i	0.325138	−	0.945667i	$-0.394589\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.74596	−	4.16031i	0.464629	−	0.516023i
$66$		0			0
$67$	−2.35995	−	1.71460i	−0.288314	−	0.209472i	0.434222	−	0.900806i	$-0.357023\pi$
$67$	−2.35995	−	1.71460i	−0.288314	−	0.209472i	−0.722535	+	0.691334i	$0.757023\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.29912	−	3.85004i	0.628890	−	0.456916i	−0.227125	−	0.973866i	$-0.572933\pi$
$71$	5.29912	−	3.85004i	0.628890	−	0.456916i	0.856016	+	0.516950i	$0.172933\pi$
$72$		0			0
$73$	−0.778516	−	2.39603i	−0.0911184	−	0.280434i	0.895104	−	0.445857i	$-0.147101\pi$
$73$	−0.778516	−	2.39603i	−0.0911184	−	0.280434i	−0.986223	+	0.165423i	$0.947101\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.0482732	−	0.148570i	−0.00550124	−	0.0169311i
$78$		0			0
$79$	8.28621	−	6.02028i	0.932271	−	0.677335i	−0.0142765	−	0.999898i	$-0.504545\pi$
$79$	8.28621	−	6.02028i	0.932271	−	0.677335i	0.946548	+	0.322563i	$0.104545\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.59240	−	3.33658i	−0.504082	−	0.366237i	0.306492	−	0.951873i	$-0.400845\pi$
$83$	−4.59240	−	3.33658i	−0.504082	−	0.366237i	−0.810574	+	0.585636i	$0.800845\pi$
$84$		0			0
$85$	7.62447	+	13.2060i	0.826990	+	1.43239i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.284829	+	0.876615i	0.0301919	+	0.0929210i	0.965017	−	0.262188i	$-0.0844439\pi$
$89$	0.284829	+	0.876615i	0.0301919	+	0.0929210i	−0.934825	+	0.355109i	$0.884444\pi$
$90$		0			0
$91$	−0.578108	+	1.77923i	−0.0606022	+	0.186514i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.39218	+	2.41133i	0.142835	+	0.247397i
$96$		0			0
$97$	12.5757	−	9.13679i	1.27687	−	0.927700i	0.277416	−	0.960750i	$-0.410522\pi$
$97$	12.5757	−	9.13679i	1.27687	−	0.927700i	0.999454	+	0.0330496i	$0.0105219\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	11.0405			1.09857			0.549285	−	0.835635i	$-0.314900\pi$
$101$	11.0405			1.09857			0.549285	+	0.835635i	$0.314900\pi$
$102$		0			0
$103$	−11.2326	+	8.16097i	−1.10678	+	0.804124i	−0.982154	−	0.188079i	$-0.939774\pi$
$103$	−11.2326	+	8.16097i	−1.10678	+	0.804124i	−0.124628	+	0.992203i	$0.539774\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.02510			−0.0991002			−0.0495501	−	0.998772i	$-0.515779\pi$
$107$	−1.02510			−0.0991002			−0.0495501	+	0.998772i	$0.515779\pi$
$108$		0			0
$109$	−2.07199	+	6.37694i	−0.198461	+	0.610800i	0.801458	+	0.598051i	$0.204058\pi$
$109$	−2.07199	+	6.37694i	−0.198461	+	0.610800i	−0.999919	+	0.0127488i	$0.995942\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.57151	+	7.91428i	−0.241907	+	0.744513i	0.754223	+	0.656618i	$0.228014\pi$
$113$	−2.57151	+	7.91428i	−0.241907	+	0.744513i	−0.996130	+	0.0878944i	$0.971986\pi$
$114$		0			0
$115$	−0.759830	+	7.22930i	−0.0708546	+	0.674136i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.12260	−	2.99525i	−0.377918	−	0.274574i
$120$		0			0
$121$	8.86383	−	6.43995i	0.805803	−	0.585450i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$		0			0
$127$	−4.49195	−	13.8248i	−0.398597	−	1.22675i	−0.926125	−	0.377217i	$-0.876881\pi$
$127$	−4.49195	−	13.8248i	−0.398597	−	1.22675i	0.527529	−	0.849537i	$-0.323119\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.00611	+	4.36370i	0.524757	+	0.381258i	0.818393	−	0.574659i	$-0.194865\pi$
$131$	6.00611	+	4.36370i	0.524757	+	0.381258i	−0.293636	+	0.955917i	$0.594865\pi$
$132$		0			0
$133$	−0.752762	−	0.546913i	−0.0652727	−	0.0474234i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.26676	−	6.97636i	0.193662	−	0.596030i	−0.806328	−	0.591469i	$-0.798548\pi$
$137$	2.26676	−	6.97636i	0.193662	−	0.596030i	0.999990	−	0.00456114i	$-0.00145186\pi$
$138$		0			0
$139$	6.10219	+	18.7806i	0.517581	+	1.59295i	0.778536	+	0.627600i	$0.215963\pi$
$139$	6.10219	+	18.7806i	0.517581	+	1.59295i	−0.260954	+	0.965351i	$0.584037\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.523398			0.0437687
$144$		0			0
$145$	11.3368	−	2.40971i	0.941468	−	0.200115i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	21.7551			1.78224			0.891122	−	0.453763i	$-0.149919\pi$
$149$	21.7551			1.78224			0.891122	+	0.453763i	$0.149919\pi$
$150$		0			0
$151$	10.1308			0.824432			0.412216	−	0.911086i	$-0.364755\pi$
$151$	10.1308			0.824432			0.412216	+	0.911086i	$0.364755\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.18109	+	7.24186i	0.335833	+	0.581680i
$156$		0			0
$157$	−9.99520			−0.797704			−0.398852	−	0.917015i	$-0.630591\pi$
$157$	−9.99520			−0.797704			−0.398852	+	0.917015i	$0.630591\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.750652	−	2.31027i	−0.0591597	−	0.182075i
$162$		0			0
$163$	−0.792035	+	2.43763i	−0.0620369	+	0.190930i	−0.977272	−	0.211991i	$-0.932005\pi$
$163$	−0.792035	+	2.43763i	−0.0620369	+	0.190930i	0.915235	+	0.402921i	$0.132005\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.8690	−	12.2560i	−1.30536	−	0.948401i	−0.305369	−	0.952234i	$-0.598780\pi$
$167$	−16.8690	−	12.2560i	−1.30536	−	0.948401i	−0.999993	+	0.00383355i	$0.998780\pi$
$168$		0			0
$169$	5.44624	+	3.95692i	0.418941	+	0.304379i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.635016	−	1.95438i	−0.0482794	−	0.148589i	0.924011	−	0.382367i	$-0.124891\pi$
$173$	−0.635016	−	1.95438i	−0.0482794	−	0.148589i	−0.972290	+	0.233778i	$0.924891\pi$
$174$		0			0
$175$	2.50000	+	2.77653i	0.188982	+	0.209886i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−15.8247	+	11.4973i	−1.18279	+	0.859349i	−0.992484	−	0.122375i	$-0.960949\pi$
$179$	−15.8247	+	11.4973i	−1.18279	+	0.859349i	−0.190309	+	0.981724i	$0.560949\pi$
$180$		0			0
$181$	5.96251	+	4.33202i	0.443190	+	0.321996i	0.786901	−	0.617079i	$-0.211684\pi$
$181$	5.96251	+	4.33202i	0.443190	+	0.321996i	−0.343711	+	0.939075i	$0.611684\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.94072	+	3.26600i	−0.216206	+	0.240121i
$186$		0			0
$187$	−0.440557	+	1.35589i	−0.0322167	+	0.0991528i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.693806	−	2.13532i	0.0502021	−	0.154506i	−0.922813	−	0.385249i	$-0.874116\pi$
$191$	0.693806	−	2.13532i	0.0502021	−	0.154506i	0.973015	+	0.230743i	$0.0741156\pi$
$192$		0			0
$193$	1.10589			0.0796035			0.0398018	−	0.999208i	$-0.487327\pi$
$193$	1.10589			0.0796035			0.0398018	+	0.999208i	$0.487327\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.6953	−	12.1299i	1.18949	−	0.864217i	0.196282	−	0.980547i	$-0.437113\pi$
$197$	16.6953	−	12.1299i	1.18949	−	0.864217i	0.993211	+	0.116331i	$0.0371132\pi$
$198$		0			0
$199$	−12.3822			−0.877749			−0.438874	−	0.898548i	$-0.644623\pi$
$199$	−12.3822			−0.877749			−0.438874	+	0.898548i	$0.644623\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.13341	+	2.27655i	−0.219922	+	0.159783i
$204$		0			0
$205$	4.80845	−	5.34032i	0.335837	−	0.372984i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0804429	+	0.247578i	−0.00556435	+	0.0171253i
$210$		0			0
$211$	6.37422	+	19.6178i	0.438820	+	1.35055i	0.889121	+	0.457671i	$0.151316\pi$
$211$	6.37422	+	19.6178i	0.438820	+	1.35055i	−0.450302	+	0.892876i	$0.648684\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	25.9688	+	11.5621i	1.77106	+	0.788526i
$216$		0			0
$217$	−2.26074	−	1.64253i	−0.153469	−	0.111502i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	13.8127	−	10.0355i	0.929145	−	0.675063i
$222$		0			0
$223$	−1.28385	−	3.95129i	−0.0859732	−	0.264598i	0.898823	−	0.438312i	$-0.144423\pi$
$223$	−1.28385	−	3.95129i	−0.0859732	−	0.264598i	−0.984796	+	0.173713i	$0.944423\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.30175	+	22.4725i	0.484634	+	1.49155i	0.832510	+	0.554010i	$0.186903\pi$
$227$	7.30175	+	22.4725i	0.484634	+	1.49155i	−0.347876	+	0.937541i	$0.613097\pi$
$228$		0			0
$229$	−14.7565	+	10.7212i	−0.975139	+	0.708480i	−0.956617	−	0.291348i	$-0.905896\pi$
$229$	−14.7565	+	10.7212i	−0.975139	+	0.708480i	−0.0185221	+	0.999828i	$0.505896\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.83438	+	1.33276i	0.120174	+	0.0873117i	0.646249	−	0.763127i	$-0.276337\pi$
$233$	1.83438	+	1.33276i	0.120174	+	0.0873117i	−0.526075	+	0.850438i	$0.676337\pi$
$234$		0			0
$235$	14.1780	−	3.01363i	0.924871	−	0.196587i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.28631	−	16.2696i	−0.341943	−	1.05239i	−0.963200	−	0.268786i	$-0.913378\pi$
$239$	−5.28631	−	16.2696i	−0.341943	−	1.05239i	0.621257	−	0.783607i	$-0.286622\pi$
$240$		0			0
$241$	8.71435	−	26.8200i	0.561341	−	1.72763i	−0.117240	−	0.993104i	$-0.537405\pi$
$241$	8.71435	−	26.8200i	0.561341	−	1.72763i	0.678581	−	0.734526i	$-0.262595\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	13.1586	+	5.85861i	0.840675	+	0.374293i
$246$		0			0
$247$	2.52212	−	1.83243i	0.160479	−	0.116595i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−23.9575			−1.51219			−0.756093	−	0.654464i	$-0.772894\pi$
$251$	−23.9575			−1.51219			−0.756093	+	0.654464i	$0.772894\pi$
$252$		0			0
$253$	−0.549819	+	0.399467i	−0.0345668	+	0.0251142i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	28.5421			1.78041			0.890204	−	0.455561i	$-0.150561\pi$
$257$	28.5421			1.78041			0.890204	+	0.455561i	$0.150561\pi$
$258$		0			0
$259$	0.453837	−	1.39677i	0.0282000	−	0.0867908i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.09911	−	3.38270i	0.0677738	−	0.208586i	−0.911434	−	0.411447i	$-0.865024\pi$
$263$	1.09911	−	3.38270i	0.0677738	−	0.208586i	0.979208	+	0.202860i	$0.0650237\pi$
$264$		0			0
$265$	−9.06161	+	1.92611i	−0.556650	+	0.118320i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	23.6733	+	17.1997i	1.44339	+	1.04868i	0.987321	+	0.158736i	$0.0507419\pi$
$269$	23.6733	+	17.1997i	1.44339	+	1.04868i	0.456066	+	0.889946i	$0.349258\pi$
$270$		0			0
$271$	20.0784	−	14.5878i	1.21968	−	0.886147i	0.223603	−	0.974680i	$-0.428218\pi$
$271$	20.0784	−	14.5878i	1.21968	−	0.886147i	0.996073	+	0.0885338i	$0.0282181\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.522642	−	0.905243i	0.0315165	−	0.0545882i
$276$		0			0
$277$	−5.38539	−	16.5745i	−0.323577	−	0.995867i	−0.972079	−	0.234654i	$-0.924604\pi$
$277$	−5.38539	−	16.5745i	−0.323577	−	0.995867i	0.648502	−	0.761213i	$-0.275396\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.03664	+	2.20625i	0.181151	+	0.131614i	0.674665	−	0.738124i	$-0.264288\pi$
$281$	3.03664	+	2.20625i	0.181151	+	0.131614i	−0.493515	+	0.869738i	$0.664288\pi$
$282$		0			0
$283$	−13.2464	−	9.62409i	−0.787418	−	0.572093i	0.119778	−	0.992801i	$-0.461782\pi$
$283$	−13.2464	−	9.62409i	−0.787418	−	0.572093i	−0.907196	+	0.420708i	$0.861782\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.742080	+	2.28389i	−0.0438036	+	0.134814i
$288$		0			0
$289$	9.11787	+	28.0619i	0.536345	+	1.65070i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.70991			−0.508838			−0.254419	−	0.967094i	$-0.581884\pi$
$293$	−8.70991			−0.508838			−0.254419	+	0.967094i	$0.581884\pi$
$294$		0			0
$295$	17.5219	−	19.4600i	1.02016	−	1.13301i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.13888			0.470683
$300$		0			0
$301$	−9.49939			−0.547536
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.91684	+	27.7518i	−0.167018	+	1.58907i
$306$		0			0
$307$	−17.7123			−1.01090			−0.505448	−	0.862857i	$-0.668673\pi$
$307$	−17.7123			−1.01090			−0.505448	+	0.862857i	$0.668673\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.26921	−	19.2946i	−0.355494	−	1.09410i	−0.955722	−	0.294270i	$-0.904924\pi$
$311$	−6.26921	−	19.2946i	−0.355494	−	1.09410i	0.600228	−	0.799829i	$-0.295076\pi$
$312$		0			0
$313$	6.41831	−	19.7535i	0.362785	−	1.11654i	−0.588572	−	0.808445i	$-0.700310\pi$
$313$	6.41831	−	19.7535i	0.362785	−	1.11654i	0.951357	−	0.308091i	$-0.0996902\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.5633	−	9.85429i	−0.761789	−	0.553472i	0.137670	−	0.990478i	$-0.456039\pi$
$317$	−13.5633	−	9.85429i	−0.761789	−	0.553472i	−0.899458	+	0.437006i	$0.856039\pi$
$318$		0			0
$319$	0.876642	+	0.636918i	0.0490825	+	0.0356606i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.62408	+	8.07610i	0.146008	+	0.449366i
$324$		0			0
$325$	−11.4358	+	5.09156i	−0.634345	+	0.282429i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.91870	+	2.84711i	−0.216045	+	0.156966i
$330$		0			0
$331$	21.2090	+	15.4092i	1.16575	+	0.846968i	0.990494	−	0.137555i	$-0.0439243\pi$
$331$	21.2090	+	15.4092i	1.16575	+	0.846968i	0.175257	+	0.984523i	$0.443924\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.26137	+	5.64886i	0.178188	+	0.308630i
$336$		0			0
$337$	−8.03519	+	24.7298i	−0.437705	+	1.34712i	0.452584	+	0.891722i	$0.350502\pi$
$337$	−8.03519	+	24.7298i	−0.437705	+	1.34712i	−0.890289	+	0.455395i	$0.849498\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.241591	+	0.743542i	−0.0130829	+	0.0402651i
$342$		0			0
$343$	−10.0441			−0.542331
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.72256	−	2.70460i	0.199838	−	0.145191i	−0.483366	−	0.875418i	$-0.660586\pi$
$347$	3.72256	−	2.70460i	0.199838	−	0.145191i	0.683204	+	0.730228i	$0.260586\pi$
$348$		0			0
$349$	−29.2108			−1.56362			−0.781810	−	0.623516i	$-0.785703\pi$
$349$	−29.2108			−1.56362			−0.781810	+	0.623516i	$0.785703\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−22.7505	+	16.5292i	−1.21088	+	0.879759i	−0.995311	−	0.0967283i	$-0.969162\pi$
$353$	−22.7505	+	16.5292i	−1.21088	+	0.879759i	−0.215574	+	0.976488i	$0.569162\pi$
$354$		0			0
$355$	−14.3264	+	3.04516i	−0.760364	+	0.161620i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.90570	−	8.94282i	0.153357	−	0.471984i	−0.844634	−	0.535345i	$-0.820182\pi$
$359$	2.90570	−	8.94282i	0.153357	−	0.471984i	0.997991	+	0.0633604i	$0.0201817\pi$
$360$		0			0
$361$	−5.39218	−	16.5954i	−0.283799	−	0.873444i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.588850	+	5.60253i	−0.0308218	+	0.293250i
$366$		0			0
$367$	−17.8033	−	12.9349i	−0.929326	−	0.675195i	0.0165016	−	0.999864i	$-0.494747\pi$
$367$	−17.8033	−	12.9349i	−0.929326	−	0.675195i	−0.945828	+	0.324669i	$0.894747\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.50457	−	1.81968i	0.130031	−	0.0944728i
$372$		0			0
$373$	5.75384	+	17.7085i	0.297923	+	0.916911i	0.982224	+	0.187712i	$0.0601072\pi$
$373$	5.75384	+	17.7085i	0.297923	+	0.916911i	−0.684302	+	0.729199i	$0.739893\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.01005	−	12.3417i	−0.206528	−	0.635628i
$378$		0			0
$379$	13.6515	−	9.91838i	0.701230	−	0.509473i	−0.179103	−	0.983830i	$-0.557320\pi$
$379$	13.6515	−	9.91838i	0.701230	−	0.509473i	0.880332	+	0.474357i	$0.157320\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.32847	−	5.32445i	−0.374467	−	0.272066i	0.384594	−	0.923086i	$-0.374342\pi$
$383$	−7.32847	−	5.32445i	−0.374467	−	0.272066i	−0.759061	+	0.651020i	$0.774342\pi$
$384$		0			0
$385$	−0.0365126	+	0.347395i	−0.00186086	+	0.0177049i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.2225	−	31.4616i	−0.518301	−	1.59517i	−0.777194	−	0.629261i	$-0.783358\pi$
$389$	−10.2225	−	31.4616i	−0.518301	−	1.59517i	0.258893	−	0.965906i	$-0.416642\pi$
$390$		0			0
$391$	−6.85069	+	21.0843i	−0.346454	+	1.06628i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−22.4020	+	4.76170i	−1.12717	+	0.239587i
$396$		0			0
$397$	17.5773	−	12.7706i	0.882177	−	0.640939i	−0.0516494	−	0.998665i	$-0.516448\pi$
$397$	17.5773	−	12.7706i	0.882177	−	0.640939i	0.933827	+	0.357726i	$0.116448\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−20.1663			−1.00706			−0.503529	−	0.863978i	$-0.667965\pi$
$401$	−20.1663			−1.00706			−0.503529	+	0.863978i	$0.667965\pi$
$402$		0			0
$403$	7.57460	−	5.50327i	0.377318	−	0.274137i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.410887			−0.0203669
$408$		0			0
$409$	−4.34139	+	13.3614i	−0.214668	+	0.660679i	0.784509	+	0.620117i	$0.212915\pi$
$409$	−4.34139	+	13.3614i	−0.214668	+	0.660679i	−0.999177	+	0.0405623i	$0.987085\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.70412	+	8.32244i	−0.133061	+	0.409520i
$414$		0			0
$415$	6.34655	+	10.9925i	0.311540	+	0.539602i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−16.3919	−	11.9094i	−0.800794	−	0.581811i	0.110353	−	0.993892i	$-0.464802\pi$
$419$	−16.3919	−	11.9094i	−0.800794	−	0.581811i	−0.911147	+	0.412081i	$0.864802\pi$
$420$		0			0
$421$	−3.54258	+	2.57384i	−0.172655	+	0.125441i	−0.670757	−	0.741677i	$-0.734031\pi$
$421$	−3.54258	+	2.57384i	−0.172655	+	0.125441i	0.498102	+	0.867119i	$0.334031\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.56418	−	33.9109i	−0.172888	−	1.64492i
$426$		0			0
$427$	−2.88160	−	8.86866i	−0.139450	−	0.429184i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.944967	+	0.686559i	0.0455175	+	0.0330704i	0.610311	−	0.792162i	$-0.291044\pi$
$431$	0.944967	+	0.686559i	0.0455175	+	0.0330704i	−0.564794	+	0.825232i	$0.691044\pi$
$432$		0			0
$433$	−1.81940	−	1.32187i	−0.0874347	−	0.0635250i	0.543209	−	0.839597i	$-0.317209\pi$
$433$	−1.81940	−	1.32187i	−0.0874347	−	0.0635250i	−0.630644	+	0.776072i	$0.717209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.25089	+	3.84985i	−0.0598383	+	0.184163i
$438$		0			0
$439$	6.83477	+	21.0353i	0.326206	+	1.00396i	0.970893	+	0.239512i	$0.0769875\pi$
$439$	6.83477	+	21.0353i	0.326206	+	1.00396i	−0.644688	+	0.764446i	$0.723013\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−28.1534			−1.33761			−0.668804	−	0.743439i	$-0.733193\pi$
$443$	−28.1534			−1.33761			−0.668804	+	0.743439i	$0.733193\pi$
$444$		0			0
$445$	0.215438	−	2.04975i	0.0102127	−	0.0971677i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−16.5924			−0.783044			−0.391522	−	0.920169i	$-0.628051\pi$
$449$	−16.5924			−0.783044			−0.391522	+	0.920169i	$0.628051\pi$
$450$		0			0
$451$	0.671852			0.0316363
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.79912	−	3.10874i	0.131225	−	0.145740i
$456$		0			0
$457$	−11.1599			−0.522039			−0.261019	−	0.965334i	$-0.584059\pi$
$457$	−11.1599			−0.522039			−0.261019	+	0.965334i	$0.584059\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.93631	−	5.95935i	−0.0901830	−	0.277555i	0.895785	−	0.444487i	$-0.146614\pi$
$461$	−1.93631	−	5.95935i	−0.0901830	−	0.277555i	−0.985968	+	0.166932i	$0.946614\pi$
$462$		0			0
$463$	−5.26243	+	16.1961i	−0.244566	+	0.752696i	0.751142	+	0.660141i	$0.229503\pi$
$463$	−5.26243	+	16.1961i	−0.244566	+	0.752696i	−0.995708	+	0.0925550i	$0.970497\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.1159	−	10.9823i	−0.699481	−	0.508202i	0.180282	−	0.983615i	$-0.442299\pi$
$467$	−15.1159	−	10.9823i	−0.699481	−	0.508202i	−0.879763	+	0.475413i	$0.842299\pi$
$468$		0			0
$469$	−1.76344	−	1.28122i	−0.0814283	−	0.0591611i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.821266	+	2.52760i	0.0377618	+	0.116219i
$474$		0			0
$475$	−0.650797	−	6.19192i	−0.0298606	−	0.284105i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.38111	−	1.72998i	0.108796	−	0.0790448i	−0.532057	−	0.846708i	$-0.678581\pi$
$479$	2.38111	−	1.72998i	0.108796	−	0.0790448i	0.640853	+	0.767664i	$0.278581\pi$
$480$		0			0
$481$	3.98092	+	2.89230i	0.181514	+	0.131878i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−33.9989	+	7.22668i	−1.54381	+	0.328147i
$486$		0			0
$487$	−4.33109	+	13.3297i	−0.196261	+	0.604028i	0.803699	+	0.595036i	$0.202862\pi$
$487$	−4.33109	+	13.3297i	−0.196261	+	0.604028i	−0.999960	+	0.00899199i	$0.997138\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.76416	+	8.50720i	−0.124745	+	0.383925i	−0.993854	−	0.110695i	$-0.964692\pi$
$491$	−2.76416	+	8.50720i	−0.124745	+	0.383925i	0.869110	+	0.494619i	$0.164692\pi$
$492$		0			0
$493$	35.3472			1.59196
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.95971	−	2.87690i	0.177617	−	0.129046i
$498$		0			0
$499$	−2.39366			−0.107155			−0.0535774	−	0.998564i	$-0.517062\pi$
$499$	−2.39366			−0.107155			−0.0535774	+	0.998564i	$0.517062\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.81519	−	4.95152i	0.303874	−	0.220777i	−0.425389	−	0.905010i	$-0.639863\pi$
$503$	6.81519	−	4.95152i	0.303874	−	0.220777i	0.729264	+	0.684233i	$0.239863\pi$
$504$		0			0
$505$	−22.5530	−	10.0412i	−1.00359	−	0.446829i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.98528	+	30.7315i	−0.442590	+	1.36215i	0.442516	+	0.896761i	$0.354086\pi$
$509$	−9.98528	+	30.7315i	−0.442590	+	1.36215i	−0.885106	+	0.465390i	$0.845914\pi$
$510$		0			0
$511$	−0.581737	−	1.79040i	−0.0257345	−	0.0792027i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	30.3677	−	6.45486i	1.33816	−	0.284435i
$516$		0			0
$517$	1.09635	+	0.796543i	0.0482173	+	0.0350319i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.88427	−	2.09554i	0.126362	−	0.0918074i	−0.522809	−	0.852450i	$-0.675116\pi$
$521$	2.88427	−	2.09554i	0.126362	−	0.0918074i	0.649171	+	0.760642i	$0.275116\pi$
$522$		0			0
$523$	−10.0241	−	30.8511i	−0.438325	−	1.34903i	−0.889640	−	0.456662i	$-0.849045\pi$
$523$	−10.0241	−	30.8511i	−0.438325	−	1.34903i	0.451315	−	0.892365i	$-0.350955\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.88082	+	24.2547i	0.343294	+	1.05655i
$528$		0			0
$529$	10.0577	−	7.30732i	0.437290	−	0.317710i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.50929	−	4.72928i	−0.281949	−	0.204848i
$534$		0			0
$535$	2.09402	+	0.932320i	0.0905326	+	0.0403077i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.416143	+	1.28076i	0.0179246	+	0.0551661i
$540$		0			0
$541$	−3.40378	+	10.4757i	−0.146340	+	0.450388i	−0.997181	−	0.0750356i	$-0.976093\pi$
$541$	−3.40378	+	10.4757i	−0.146340	+	0.450388i	0.850841	+	0.525423i	$0.176093\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	10.0323	−	11.1420i	0.429738	−	0.477272i
$546$		0			0
$547$	4.31795	−	3.13718i	0.184622	−	0.134136i	−0.491635	−	0.870801i	$-0.663601\pi$
$547$	4.31795	−	3.13718i	0.184622	−	0.134136i	0.676258	+	0.736665i	$0.263601\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.45418			0.274957
$552$		0			0
$553$	6.19177	−	4.49859i	0.263301	−	0.191299i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.0652731			0.00276571			0.00138286	−	0.999999i	$-0.499560\pi$
$557$	0.0652731			0.00276571			0.00138286	+	0.999999i	$0.499560\pi$
$558$		0			0
$559$	9.83527	−	30.2699i	0.415988	−	1.28028i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.88197	−	27.3359i	0.374330	−	1.15207i	−0.569599	−	0.821923i	$-0.692902\pi$
$563$	8.88197	−	27.3359i	0.374330	−	1.15207i	0.943929	−	0.330147i	$-0.107098\pi$
$564$		0			0
$565$	12.4509	−	13.8281i	0.523814	−	0.581754i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.68501	−	4.85694i	−0.280250	−	0.203614i	0.438776	−	0.898596i	$-0.355412\pi$
$569$	−6.68501	−	4.85694i	−0.280250	−	0.203614i	−0.719026	+	0.694983i	$0.755412\pi$
$570$		0			0
$571$	−9.49451	+	6.89817i	−0.397333	+	0.288679i	−0.768454	−	0.639905i	$-0.778974\pi$
$571$	−9.49451	+	6.89817i	−0.397333	+	0.288679i	0.371121	+	0.928585i	$0.378974\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.12713	−	14.0766i	0.338925	−	0.587035i
$576$		0			0
$577$	6.60944	+	20.3418i	0.275154	+	0.846838i	0.989178	+	0.146717i	$0.0468707\pi$
$577$	6.60944	+	20.3418i	0.275154	+	0.846838i	−0.714024	+	0.700121i	$0.753129\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.43162	−	2.49322i	−0.142368	−	0.103436i
$582$		0			0
$583$	−0.700710	−	0.509096i	−0.0290204	−	0.0210846i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.7412	+	39.2133i	−0.525885	+	1.61851i	0.236674	+	0.971589i	$0.423943\pi$
$587$	−12.7412	+	39.2133i	−0.525885	+	1.61851i	−0.762559	+	0.646918i	$0.776057\pi$
$588$		0			0
$589$	1.43899	+	4.42876i	0.0592925	+	0.182484i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	23.2238			0.953685			0.476843	−	0.878989i	$-0.341781\pi$
$593$	23.2238			0.953685			0.476843	+	0.878989i	$0.341781\pi$
$594$		0			0
$595$	5.69730	+	9.86801i	0.233566	+	0.404549i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	22.6226			0.924335			0.462168	−	0.886793i	$-0.347072\pi$
$599$	22.6226			0.924335			0.462168	+	0.886793i	$0.347072\pi$
$600$		0			0
$601$	−12.9540			−0.528405			−0.264203	−	0.964467i	$-0.585109\pi$
$601$	−12.9540			−0.528405			−0.264203	+	0.964467i	$0.585109\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−23.9637	+	5.09363i	−0.974261	+	0.207086i
$606$		0			0
$607$	4.54036			0.184288			0.0921439	−	0.995746i	$-0.470628\pi$
$607$	4.54036			0.184288			0.0921439	+	0.995746i	$0.470628\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.01505	−	15.4347i	−0.202887	−	0.624423i
$612$		0			0
$613$	−7.83471	+	24.1128i	−0.316441	+	0.973905i	0.658716	+	0.752391i	$0.271100\pi$
$613$	−7.83471	+	24.1128i	−0.316441	+	0.973905i	−0.975157	+	0.221514i	$0.928900\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−36.5829	−	26.5790i	−1.47277	−	1.07003i	−0.979799	−	0.199986i	$-0.935910\pi$
$617$	−36.5829	−	26.5790i	−1.47277	−	1.07003i	−0.492972	−	0.870045i	$-0.664090\pi$
$618$		0			0
$619$	−25.3666	−	18.4299i	−1.01957	−	0.740762i	−0.0533766	−	0.998574i	$-0.516998\pi$
$619$	−25.3666	−	18.4299i	−1.01957	−	0.740762i	−0.966195	+	0.257812i	$0.916998\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.212835	+	0.655040i	0.00852707	+	0.0262436i
$624$		0			0
$625$	−2.61321	+	24.8630i	−0.104528	+	0.994522i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−10.8435	+	7.87828i	−0.432360	+	0.314128i
$630$		0			0
$631$	−25.8455	−	18.7779i	−1.02889	−	0.747535i	−0.0608071	−	0.998150i	$-0.519367\pi$
$631$	−25.8455	−	18.7779i	−1.02889	−	0.747535i	−0.968087	+	0.250614i	$0.919367\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.39760	+	32.3260i	−0.134830	+	1.28282i
$636$		0			0
$637$	4.98363	−	15.3380i	0.197459	−	0.607715i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.7727	+	39.3103i	−0.504491	+	1.55267i	0.297132	+	0.954836i	$0.403970\pi$
$641$	−12.7727	+	39.3103i	−0.504491	+	1.55267i	−0.801624	+	0.597829i	$0.796030\pi$
$642$		0			0
$643$	−33.2313			−1.31052			−0.655258	−	0.755406i	$-0.727440\pi$
$643$	−33.2313			−1.31052			−0.655258	+	0.755406i	$0.727440\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	27.2571	−	19.8034i	1.07159	−	0.778553i	0.0953892	−	0.995440i	$-0.469590\pi$
$647$	27.2571	−	19.8034i	1.07159	−	0.778553i	0.976197	+	0.216887i	$0.0695904\pi$
$648$		0			0
$649$	2.44822			0.0961009
$650$		0			0
$651$		0			0
$652$		0			0
$653$	17.6754	−	12.8419i	0.691692	−	0.502544i	−0.185524	−	0.982640i	$-0.559398\pi$
$653$	17.6754	−	12.8419i	0.691692	−	0.502544i	0.877216	+	0.480096i	$0.159398\pi$
$654$		0			0
$655$	−8.30025	−	14.3764i	−0.324317	−	0.561734i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.48829	−	10.7359i	0.135884	−	0.418209i	−0.859842	−	0.510560i	$-0.829438\pi$
$659$	3.48829	−	10.7359i	0.135884	−	0.418209i	0.995727	+	0.0923507i	$0.0294381\pi$
$660$		0			0
$661$	−11.3014	−	34.7821i	−0.439573	−	1.35287i	−0.888327	−	0.459211i	$-0.848132\pi$
$661$	−11.3014	−	34.7821i	−0.439573	−	1.35287i	0.448754	−	0.893655i	$-0.351868\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.04029	+	1.80184i	0.0403408	+	0.0698722i
$666$		0			0
$667$	13.6319	+	9.90412i	0.527828	+	0.383489i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.11064	+	1.53347i	−0.0814804	+	0.0591990i
$672$		0			0
$673$	2.37563	+	7.31143i	0.0915737	+	0.281835i	0.986346	−	0.164689i	$-0.0526619\pi$
$673$	2.37563	+	7.31143i	0.0915737	+	0.281835i	−0.894772	+	0.446523i	$0.852662\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.5253	+	35.4711i	0.442952	+	1.36327i	0.884714	+	0.466133i	$0.154353\pi$
$677$	11.5253	+	35.4711i	0.442952	+	1.36327i	−0.441763	+	0.897132i	$0.645647\pi$
$678$		0			0
$679$	9.39705	−	6.82736i	0.360626	−	0.262010i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	29.5125	+	21.4421i	1.12926	+	0.820458i	0.985587	−	0.169166i	$-0.0541075\pi$
$683$	29.5125	+	21.4421i	1.12926	+	0.820458i	0.143676	+	0.989625i	$0.454108\pi$
$684$		0			0
$685$	−10.9753	+	12.1894i	−0.419346	+	0.465731i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.20528	+	9.86483i	0.122111	+	0.375820i
$690$		0			0
$691$	−9.99734	+	30.7686i	−0.380317	+	1.17049i	0.559504	+	0.828827i	$0.310992\pi$
$691$	−9.99734	+	30.7686i	−0.380317	+	1.17049i	−0.939821	+	0.341667i	$0.889008\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.61555	−	43.9140i	0.175078	−	1.66575i
$696$		0			0
$697$	17.7305	−	12.8820i	0.671591	−	0.487940i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−5.27498			−0.199233			−0.0996166	−	0.995026i	$-0.531762\pi$
$701$	−5.27498			−0.199233			−0.0996166	+	0.995026i	$0.531762\pi$
$702$		0			0
$703$	−1.97996	+	1.43853i	−0.0746756	+	0.0542550i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.24988			0.310268
$708$		0			0
$709$	9.03055	−	27.7932i	0.339149	−	1.04379i	−0.625493	−	0.780230i	$-0.715102\pi$
$709$	9.03055	−	27.7932i	0.339149	−	1.04379i	0.964642	−	0.263564i	$-0.0848981\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.75677	+	11.5621i	−0.140692	+	0.433005i
$714$		0			0
$715$	−1.06917	−	0.476025i	−0.0399847	−	0.0178023i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	35.5675	+	25.8413i	1.32644	+	0.963718i	0.999828	+	0.0185605i	$0.00590834\pi$
$719$	35.5675	+	25.8413i	1.32644	+	0.963718i	0.326616	+	0.945157i	$0.394092\pi$
$720$		0			0
$721$	−8.39344	+	6.09819i	−0.312588	+	0.227108i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−25.3498	−	5.38827i	−0.941468	−	0.200115i
$726$		0			0
$727$	9.24768	+	28.4614i	0.342977	+	1.05558i	0.962658	+	0.270721i	$0.0872622\pi$
$727$	9.24768	+	28.4614i	0.342977	+	1.05558i	−0.619680	+	0.784854i	$0.712738\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	70.1373	+	50.9577i	2.59412	+	1.88474i
$732$		0			0
$733$	13.3702	+	9.71402i	0.493840	+	0.358795i	0.806659	−	0.591017i	$-0.201273\pi$
$733$	13.3702	+	9.71402i	0.493840	+	0.358795i	−0.312819	+	0.949813i	$0.601273\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.188448	+	0.579984i	−0.00694158	+	0.0213640i
$738$		0			0
$739$	−15.7285	−	48.4073i	−0.578581	−	1.78069i	−0.623648	−	0.781706i	$-0.714350\pi$
$739$	−15.7285	−	48.4073i	−0.578581	−	1.78069i	0.0450666	−	0.998984i	$-0.485650\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	28.6937			1.05267			0.526336	−	0.850277i	$-0.323566\pi$
$743$	28.6937			1.05267			0.526336	+	0.850277i	$0.323566\pi$
$744$		0			0
$745$	−44.4402	−	19.7860i	−1.62816	−	0.724904i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.765995			−0.0279888
$750$		0			0
$751$	−0.927935			−0.0338608			−0.0169304	−	0.999857i	$-0.505389\pi$
$751$	−0.927935			−0.0338608			−0.0169304	+	0.999857i	$0.505389\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−20.6947	−	9.21385i	−0.753156	−	0.335327i
$756$		0			0
$757$	41.4243			1.50559			0.752796	−	0.658254i	$-0.228705\pi$
$757$	41.4243			1.50559			0.752796	+	0.658254i	$0.228705\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.17031	−	3.60185i	−0.0424237	−	0.130567i	0.927601	−	0.373572i	$-0.121867\pi$
$761$	−1.17031	−	3.60185i	−0.0424237	−	0.130567i	−0.970025	+	0.243005i	$0.921867\pi$
$762$		0			0
$763$	−1.54827	+	4.76509i	−0.0560513	+	0.172508i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−23.7197	−	17.2334i	−0.856470	−	0.622262i
$768$		0			0
$769$	1.06014	+	0.770234i	0.0382295	+	0.0277753i	0.606736	−	0.794903i	$-0.292479\pi$
$769$	1.06014	+	0.770234i	0.0382295	+	0.0277753i	−0.568506	+	0.822679i	$0.692479\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.00241	−	27.7066i	−0.323794	−	0.996536i	−0.971982	−	0.235055i	$-0.924473\pi$
$773$	−9.00241	−	27.7066i	−0.323794	−	0.996536i	0.648188	−	0.761480i	$-0.275527\pi$
$774$		0			0
$775$	−1.95452	−	18.5960i	−0.0702083	−	0.667987i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.23748	−	2.35217i	0.115995	−	0.0842752i
$780$		0			0
$781$	−1.10782	−	0.804877i	−0.0396409	−	0.0288008i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	20.4177	+	9.09055i	0.728739	+	0.324455i
$786$		0			0
$787$	−14.4050	+	44.3341i	−0.513484	+	1.58034i	0.272540	+	0.962145i	$0.412136\pi$
$787$	−14.4050	+	44.3341i	−0.513484	+	1.58034i	−0.786023	+	0.618197i	$0.787864\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.92153	+	5.91385i	−0.0683217	+	0.210272i
$792$		0			0
$793$	31.2435			1.10949
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.1308	+	8.08703i	−0.394275	+	0.286457i	−0.767205	−	0.641402i	$-0.778353\pi$
$797$	−11.1308	+	8.08703i	−0.394275	+	0.286457i	0.372930	+	0.927859i	$0.378353\pi$
$798$		0			0
$799$	44.2059			1.56389
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.426096	+	0.309577i	−0.0150366	+	0.0109247i
$804$		0			0
$805$	−0.567774	+	5.40201i	−0.0200114	+	0.190396i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.08886	+	9.50654i	−0.108599	+	0.334232i	−0.990558	−	0.137093i	$-0.956224\pi$
$809$	−3.08886	+	9.50654i	−0.108599	+	0.334232i	0.881960	+	0.471325i	$0.156224\pi$
$810$		0			0
$811$	5.72277	+	17.6129i	0.200954	+	0.618472i	0.999855	+	0.0170101i	$0.00541474\pi$
$811$	5.72277	+	17.6129i	0.200954	+	0.618472i	−0.798902	+	0.601462i	$0.794585\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.83493	−	4.25912i	0.134332	−	0.149191i
$816$		0			0
$817$	12.8066	+	9.30457i	0.448048	+	0.325526i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.9081	−	16.6437i	0.799498	−	0.580869i	−0.111269	−	0.993790i	$-0.535491\pi$
$821$	22.9081	−	16.6437i	0.799498	−	0.580869i	0.910767	+	0.412921i	$0.135491\pi$
$822$		0			0
$823$	3.70366	+	11.3987i	0.129101	+	0.397333i	0.994626	−	0.103533i	$-0.0330148\pi$
$823$	3.70366	+	11.3987i	0.129101	+	0.397333i	−0.865525	+	0.500866i	$0.833015\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.13191	−	12.7167i	−0.143681	−	0.442204i	0.853158	−	0.521652i	$-0.174684\pi$
$827$	−4.13191	−	12.7167i	−0.143681	−	0.442204i	−0.996839	+	0.0794485i	$0.974684\pi$
$828$		0			0
$829$	13.3909	−	9.72909i	0.465087	−	0.337905i	−0.330437	−	0.943828i	$-0.607196\pi$
$829$	13.3909	−	9.72909i	0.465087	−	0.337905i	0.795523	+	0.605923i	$0.207196\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	35.5393	+	25.8208i	1.23136	+	0.894637i
$834$		0			0
$835$	23.3124	+	40.3782i	0.806758	+	1.39735i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.56589	−	23.2854i	−0.261204	−	0.803902i	−0.992544	−	0.121889i	$-0.961105\pi$
$839$	−7.56589	−	23.2854i	−0.261204	−	0.803902i	0.731340	−	0.682013i	$-0.238895\pi$
$840$		0			0
$841$	−0.659493	+	2.02971i	−0.0227411	+	0.0699900i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−7.52652	−	13.0363i	−0.258920	−	0.448463i
$846$		0			0
$847$	6.62339	−	4.81218i	0.227582	−	0.165348i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.38933			−0.219023
$852$		0			0
$853$	−15.4809	+	11.2475i	−0.530055	+	0.385108i	−0.820379	−	0.571821i	$-0.806237\pi$
$853$	−15.4809	+	11.2475i	−0.530055	+	0.385108i	0.290323	+	0.956929i	$0.406237\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.43367			0.253929			0.126965	−	0.991907i	$-0.459477\pi$
$857$	7.43367			0.253929			0.126965	+	0.991907i	$0.459477\pi$
$858$		0			0
$859$	12.7368	−	39.1999i	0.434575	−	1.33748i	−0.458947	−	0.888464i	$-0.651773\pi$
$859$	12.7368	−	39.1999i	0.434575	−	1.33748i	0.893522	−	0.449020i	$-0.148227\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	11.7794	−	36.2532i	0.400975	−	1.23407i	−0.523234	−	0.852189i	$-0.675275\pi$
$863$	11.7794	−	36.2532i	0.400975	−	1.23407i	0.924210	−	0.381886i	$-0.124725\pi$
$864$		0			0
$865$	−0.480310	+	4.56985i	−0.0163310	+	0.155380i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.73229	−	1.25858i	−0.0587639	−	0.0426945i
$870$		0			0
$871$	5.90840	−	4.29270i	0.200198	−	0.145453i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.58164	−	7.94549i	−0.0872755	−	0.268606i
$876$		0			0
$877$	8.96931	+	27.6047i	0.302872	+	0.932145i	0.980463	+	0.196705i	$0.0630242\pi$
$877$	8.96931	+	27.6047i	0.302872	+	0.932145i	−0.677591	+	0.735439i	$0.736976\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.8503	−	20.2344i	−0.938300	−	0.681715i	0.00971098	−	0.999953i	$-0.496909\pi$
$881$	−27.8503	−	20.2344i	−0.938300	−	0.681715i	−0.948011	+	0.318238i	$0.896909\pi$
$882$		0			0
$883$	31.3921	+	22.8077i	1.05643	+	0.767539i	0.973424	−	0.229010i	$-0.0735490\pi$
$883$	31.3921	+	22.8077i	1.05643	+	0.767539i	0.0830028	+	0.996549i	$0.473549\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.78288	+	5.48715i	−0.0598634	+	0.184241i	−0.976516	−	0.215444i	$-0.930880\pi$
$887$	−1.78288	+	5.48715i	−0.0598634	+	0.184241i	0.916653	+	0.399684i	$0.130880\pi$
$888$		0			0
$889$	−3.35656	−	10.3304i	−0.112575	−	0.346472i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.07173			0.270110
$894$		0			0
$895$	42.7826	−	9.09372i	1.43006	−	0.303970i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	19.3836			0.646480
$900$		0			0
$901$	−28.2534			−0.941257
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.23999	−	14.2721i	−0.273906	−	0.474420i
$906$		0			0
$907$	31.7260			1.05345			0.526723	−	0.850037i	$-0.323421\pi$
$907$	31.7260			1.05345			0.526723	+	0.850037i	$0.323421\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.95450	+	15.2484i	0.164150	+	0.505202i	0.998973	−	0.0453174i	$-0.0144299\pi$
$911$	4.95450	+	15.2484i	0.164150	+	0.505202i	−0.834823	+	0.550519i	$0.814430\pi$
$912$		0			0
$913$	−0.366716	+	1.12863i	−0.0121365	+	0.0373523i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.48800	+	3.26072i	0.148207	+	0.107679i
$918$		0			0
$919$	8.82328	+	6.41049i	0.291053	+	0.211462i	0.723724	−	0.690089i	$-0.242429\pi$
$919$	8.82328	+	6.41049i	0.291053	+	0.211462i	−0.432671	+	0.901552i	$0.642429\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.06753	+	15.5962i	0.166800	+	0.513357i
$924$		0			0
$925$	8.97756	−	3.99707i	0.295180	−	0.131423i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.3021	−	13.2973i	0.600473	−	0.436269i	−0.245573	−	0.969378i	$-0.578976\pi$
$929$	18.3021	−	13.2973i	0.600473	−	0.436269i	0.846047	+	0.533108i	$0.178976\pi$
$930$		0			0
$931$	6.48925	+	4.71472i	0.212677	+	0.154519i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.13312	−	2.36907i	0.0697605	−	0.0774768i
$936$		0			0
$937$	−1.59323	+	4.90347i	−0.0520487	+	0.160189i	−0.973702	−	0.227824i	$-0.926839\pi$
$937$	−1.59323	+	4.90347i	−0.0520487	+	0.160189i	0.921654	+	0.388014i	$0.126839\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.84942	+	11.8473i	−0.125488	+	0.386211i	−0.993990	−	0.109475i	$-0.965083\pi$
$941$	−3.84942	+	11.8473i	−0.125488	+	0.386211i	0.868502	+	0.495686i	$0.165083\pi$
$942$		0			0
$943$	10.4474			0.340213
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.4795	−	9.79345i	0.438026	−	0.318244i	−0.346824	−	0.937930i	$-0.612740\pi$
$947$	13.4795	−	9.79345i	0.438026	−	0.318244i	0.784850	+	0.619686i	$0.212740\pi$
$948$		0			0
$949$	6.30743			0.204748
$950$		0			0
$951$		0			0
$952$		0			0
$953$	41.9537	−	30.4812i	1.35901	−	0.987382i	0.360508	−	0.932756i	$-0.382604\pi$
$953$	41.9537	−	30.4812i	1.35901	−	0.987382i	0.998507	−	0.0546255i	$-0.0173965\pi$
$954$		0			0
$955$	−3.35932	+	3.73091i	−0.108705	+	0.120729i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.69381	−	5.21300i	0.0546959	−	0.168337i
$960$		0			0
$961$	−5.25786	−	16.1820i	−0.169608	−	0.522001i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.25905	−	1.00579i	−0.0727214	−	0.0323777i
$966$		0			0
$967$	−10.3327	−	7.50713i	−0.332277	−	0.241413i	0.409119	−	0.912481i	$-0.365836\pi$
$967$	−10.3327	−	7.50713i	−0.332277	−	0.241413i	−0.741396	+	0.671068i	$0.765836\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.5679	+	9.13110i	−0.403323	+	0.293031i	−0.770893	−	0.636965i	$-0.780190\pi$
$971$	−12.5679	+	9.13110i	−0.403323	+	0.293031i	0.367570	+	0.929996i	$0.380190\pi$
$972$		0			0
$973$	4.55979	+	14.0336i	0.146180	+	0.449896i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.2613	+	31.5811i	0.328288	+	1.01037i	0.969934	+	0.243367i	$0.0782518\pi$
$977$	10.2613	+	31.5811i	0.328288	+	1.01037i	−0.641646	+	0.767001i	$0.721748\pi$
$978$		0			0
$979$	0.155892	−	0.113262i	0.00498234	−	0.00361988i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−39.7183	−	28.8570i	−1.26682	−	0.920395i	−0.267745	−	0.963490i	$-0.586278\pi$
$983$	−39.7183	−	28.8570i	−1.26682	−	0.920395i	−0.999071	+	0.0430944i	$0.986278\pi$
$984$		0			0
$985$	−45.1364	+	9.59403i	−1.43816	+	0.305691i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.7707	+	39.3043i	0.406086	+	1.24980i
$990$		0			0
$991$	−7.91583	+	24.3624i	−0.251455	+	0.773898i	0.743053	+	0.669233i	$0.233377\pi$
$991$	−7.91583	+	24.3624i	−0.251455	+	0.773898i	−0.994508	+	0.104665i	$0.966623\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	25.2937	+	11.2615i	0.801863	+	0.357013i
$996$		0			0
$997$	8.76157	−	6.36565i	0.277482	−	0.201602i	−0.440337	−	0.897833i	$-0.645141\pi$
$997$	8.76157	−	6.36565i	0.277482	−	0.201602i	0.717818	+	0.696231i	$0.245141\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.n.a.181.1		8
3.2	odd	2		300.2.m.a.181.2	yes	8
15.2	even	4		1500.2.o.a.349.4		16
15.8	even	4		1500.2.o.a.349.1		16
15.14	odd	2		1500.2.m.b.901.1		8
25.21	even	5	inner	900.2.n.a.721.1		8
75.2	even	20		7500.2.d.d.1249.4		8
75.11	odd	10		7500.2.a.g.1.4		4
75.14	odd	10		7500.2.a.d.1.1		4
75.23	even	20		7500.2.d.d.1249.5		8
75.29	odd	10		1500.2.m.b.601.1		8
75.47	even	20		1500.2.o.a.649.2		16
75.53	even	20		1500.2.o.a.649.3		16
75.71	odd	10		300.2.m.a.121.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.121.2	✓	8	75.71	odd	10
300.2.m.a.181.2	yes	8	3.2	odd	2
900.2.n.a.181.1		8	1.1	even	1	trivial
900.2.n.a.721.1		8	25.21	even	5	inner
1500.2.m.b.601.1		8	75.29	odd	10
1500.2.m.b.901.1		8	15.14	odd	2
1500.2.o.a.349.1		16	15.8	even	4
1500.2.o.a.349.4		16	15.2	even	4
1500.2.o.a.649.2		16	75.47	even	20
1500.2.o.a.649.3		16	75.53	even	20
7500.2.a.d.1.1		4	75.14	odd	10
7500.2.a.g.1.4		4	75.11	odd	10
7500.2.d.d.1249.4		8	75.2	even	20
7500.2.d.d.1249.5		8	75.23	even	20

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.04275 - 0.909491i) q^{5} +0.747238 q^{7} +O(q^{10})\)	\(q+(-2.04275 - 0.909491i) q^{5} +0.747238 q^{7} +(-0.0646021 - 0.198825i) q^{11} +(-0.773659 + 2.38108i) q^{13} +(-5.51712 - 4.00842i) q^{17} +(-1.00739 - 0.731913i) q^{19} +(-1.00457 - 3.09174i) q^{23} +(3.34565 + 3.71572i) q^{25} +(-4.19332 + 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(-1.52642 - 0.679606i) q^{35} +(0.607352 - 1.86924i) q^{37} +(-0.993096 + 3.05644i) q^{41} -12.7127 q^{43} +(-5.24425 + 3.81017i) q^{47} -6.44163 q^{49} +(3.35177 - 2.43520i) q^{53} +(-0.0488635 + 0.464905i) q^{55} +(-3.61882 + 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(3.74596 - 4.16031i) q^{65} +(-2.35995 - 1.71460i) q^{67} +(5.29912 - 3.85004i) q^{71} +(-0.778516 - 2.39603i) q^{73} +(-0.0482732 - 0.148570i) q^{77} +(8.28621 - 6.02028i) q^{79} +(-4.59240 - 3.33658i) q^{83} +(7.62447 + 13.2060i) q^{85} +(0.284829 + 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} +(1.39218 + 2.41133i) q^{95} +(12.5757 - 9.13679i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q - 5 * q^5 - 8 * q^7	\( 8 q - 5 q^{5} - 8 q^{7} + 2 q^{11} - 7 q^{17} + 5 q^{19} - 7 q^{23} + 5 q^{25} - 27 q^{29} - 3 q^{31} - 20 q^{35} - 9 q^{37} - 20 q^{41} - 68 q^{43} + 7 q^{47} - 8 q^{49} + 11 q^{53} + 5 q^{55} - 2 q^{59} - 14 q^{61} + 35 q^{65} + 28 q^{67} + 15 q^{71} + 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{83} + 10 q^{85} + 5 q^{91} - 5 q^{95} + 34 q^{97}+O(q^{100}) \) 8 * q - 5 * q^5 - 8 * q^7 + 2 * q^11 - 7 * q^17 + 5 * q^19 - 7 * q^23 + 5 * q^25 - 27 * q^29 - 3 * q^31 - 20 * q^35 - 9 * q^37 - 20 * q^41 - 68 * q^43 + 7 * q^47 - 8 * q^49 + 11 * q^53 + 5 * q^55 - 2 * q^59 - 14 * q^61 + 35 * q^65 + 28 * q^67 + 15 * q^71 + 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^83 + 10 * q^85 + 5 * q^91 - 5 * q^95 + 34 * q^97

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