LMFDB - Embedded newform 900.3.u.d.749.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.4
Character	$\chi$	$=$	900.749
Dual form			900.3.u.d.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37034 - 1.83888i) q^{3} +(-7.15437 - 4.13058i) q^{7} +(2.23701 + 8.71756i) q^{9} +O(q^{10})$	\(q+(-2.37034 - 1.83888i) q^{3} +(-7.15437 - 4.13058i) q^{7} +(2.23701 + 8.71756i) q^{9} +(-1.19023 - 0.687179i) q^{11} +(18.6723 - 10.7805i) q^{13} +25.3117 q^{17} +2.49216 q^{19} +(9.36262 + 22.9469i) q^{21} +(-19.1618 - 33.1892i) q^{23} +(10.7281 - 24.7772i) q^{27} +(-37.0732 - 21.4042i) q^{29} +(10.9499 + 18.9658i) q^{31} +(1.55760 + 3.81754i) q^{33} +30.5877i q^{37} +(-64.0837 - 8.78288i) q^{39} +(7.29574 - 4.21220i) q^{41} +(-61.6445 - 35.5905i) q^{43} +(-24.3281 + 42.1375i) q^{47} +(9.62335 + 16.6681i) q^{49} +(-59.9974 - 46.5454i) q^{51} -1.96485 q^{53} +(-5.90725 - 4.58279i) q^{57} +(-3.77749 + 2.18094i) q^{59} +(-18.4907 + 32.0268i) q^{61} +(20.0042 - 71.6088i) q^{63} +(13.9663 - 8.06346i) q^{67} +(-15.6112 + 113.906i) q^{69} +71.5235i q^{71} -122.276i q^{73} +(5.67689 + 9.83266i) q^{77} +(-3.98462 + 6.90157i) q^{79} +(-70.9916 + 39.0024i) q^{81} +(-52.1235 + 90.2806i) q^{83} +(48.5161 + 118.909i) q^{87} +9.37245i q^{89} -178.118 q^{91} +(8.92094 - 65.0910i) q^{93} +(-11.8902 - 6.86481i) q^{97} +(3.32797 - 11.9131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{9}+O(q^{10}) $ 32 * q - 28 * q^9	$ 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) $ 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.37034	−	1.83888i	−0.790113	−	0.612962i
$3$	−2.37034	−	1.83888i	−0.790113	−	0.612962i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−7.15437	−	4.13058i	−1.02205	−	0.590083i	−0.107355	−	0.994221i	$-0.534238\pi$
$7$	−7.15437	−	4.13058i	−1.02205	−	0.590083i	−0.914698	+	0.404138i	$0.867571\pi$
$8$		0			0
$9$	2.23701	+	8.71756i	0.248556	+	0.968617i
$10$		0			0
$11$	−1.19023	−	0.687179i	−0.108203	−	0.0624708i	0.444922	−	0.895569i	$-0.353231\pi$
$11$	−1.19023	−	0.687179i	−0.108203	−	0.0624708i	−0.553125	+	0.833098i	$0.686565\pi$
$12$		0			0
$13$	18.6723	−	10.7805i	1.43633	−	0.829266i	0.438739	−	0.898615i	$-0.355425\pi$
$13$	18.6723	−	10.7805i	1.43633	−	0.829266i	0.997593	+	0.0693484i	$0.0220920\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	25.3117			1.48893			0.744463	−	0.667664i	$-0.232706\pi$
$17$	25.3117			1.48893			0.744463	+	0.667664i	$0.232706\pi$
$18$		0			0
$19$	2.49216			0.131166			0.0655831	−	0.997847i	$-0.479109\pi$
$19$	2.49216			0.131166			0.0655831	+	0.997847i	$0.479109\pi$
$20$		0			0
$21$	9.36262	+	22.9469i	0.445839	+	1.09271i
$22$		0			0
$23$	−19.1618	−	33.1892i	−0.833122	−	1.44301i	−0.895550	−	0.444961i	$-0.853218\pi$
$23$	−19.1618	−	33.1892i	−0.833122	−	1.44301i	0.0624276	−	0.998049i	$-0.480116\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	10.7281	−	24.7772i	0.397338	−	0.917672i
$28$		0			0
$29$	−37.0732	−	21.4042i	−1.27839	−	0.738076i	−0.301834	−	0.953360i	$-0.597599\pi$
$29$	−37.0732	−	21.4042i	−1.27839	−	0.738076i	−0.976551	+	0.215284i	$0.930932\pi$
$30$		0			0
$31$	10.9499	+	18.9658i	0.353223	+	0.611800i	0.986812	−	0.161869i	$-0.0517523\pi$
$31$	10.9499	+	18.9658i	0.353223	+	0.611800i	−0.633589	+	0.773670i	$0.718419\pi$
$32$		0			0
$33$	1.55760	+	3.81754i	0.0472000	+	0.115683i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			30.5877i			0.826693i	0.910574	+	0.413347i	$0.135640\pi$
$37$			30.5877i			0.826693i	−0.910574	+	0.413347i	$0.864360\pi$
$38$		0			0
$39$	−64.0837	−	8.78288i	−1.64317	−	0.225202i
$40$		0			0
$41$	7.29574	−	4.21220i	0.177945	−	0.102736i	−0.408382	−	0.912811i	$-0.633907\pi$
$41$	7.29574	−	4.21220i	0.177945	−	0.102736i	0.586327	+	0.810075i	$0.300573\pi$
$42$		0			0
$43$	−61.6445	−	35.5905i	−1.43359	−	0.827686i	−0.436201	−	0.899849i	$-0.643676\pi$
$43$	−61.6445	−	35.5905i	−1.43359	−	0.827686i	−0.997393	+	0.0721636i	$0.977010\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−24.3281	+	42.1375i	−0.517620	+	0.896544i	0.482171	+	0.876077i	$0.339848\pi$
$47$	−24.3281	+	42.1375i	−0.517620	+	0.896544i	−0.999791	+	0.0204664i	$0.993485\pi$
$48$		0			0
$49$	9.62335	+	16.6681i	0.196395	+	0.340166i
$50$		0			0
$51$	−59.9974	−	46.5454i	−1.17642	−	0.912654i
$52$		0			0
$53$	−1.96485			−0.0370727			−0.0185363	−	0.999828i	$-0.505901\pi$
$53$	−1.96485			−0.0370727			−0.0185363	+	0.999828i	$0.505901\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.90725	−	4.58279i	−0.103636	−	0.0803998i
$58$		0			0
$59$	−3.77749	+	2.18094i	−0.0640253	+	0.0369650i	−0.531671	−	0.846951i	$-0.678436\pi$
$59$	−3.77749	+	2.18094i	−0.0640253	+	0.0369650i	0.467646	+	0.883916i	$0.345102\pi$
$60$		0			0
$61$	−18.4907	+	32.0268i	−0.303126	+	0.525030i	−0.976842	−	0.213960i	$-0.931364\pi$
$61$	−18.4907	+	32.0268i	−0.303126	+	0.525030i	0.673716	+	0.738990i	$0.264697\pi$
$62$		0			0
$63$	20.0042	−	71.6088i	0.317527	−	1.13665i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	13.9663	−	8.06346i	0.208453	−	0.120350i	−0.392139	−	0.919906i	$-0.628265\pi$
$67$	13.9663	−	8.06346i	0.208453	−	0.120350i	0.600592	+	0.799556i	$0.294932\pi$
$68$		0			0
$69$	−15.6112	+	113.906i	−0.226249	+	1.65081i
$70$		0			0
$71$			71.5235i			1.00737i	0.863886	+	0.503687i	$0.168023\pi$
$71$			71.5235i			1.00737i	−0.863886	+	0.503687i	$0.831977\pi$
$72$		0			0
$73$		−	122.276i		−	1.67502i	−0.546422	−	0.837510i	$-0.684011\pi$
$73$		−	122.276i		−	1.67502i	0.546422	−	0.837510i	$-0.315989\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.67689	+	9.83266i	0.0737259	+	0.127697i
$78$		0			0
$79$	−3.98462	+	6.90157i	−0.0504382	+	0.0873616i	−0.890142	−	0.455683i	$-0.849395\pi$
$79$	−3.98462	+	6.90157i	−0.0504382	+	0.0873616i	0.839704	+	0.543044i	$0.182728\pi$
$80$		0			0
$81$	−70.9916	+	39.0024i	−0.876440	+	0.481512i
$82$		0			0
$83$	−52.1235	+	90.2806i	−0.627994	+	1.08772i	0.359960	+	0.932968i	$0.382790\pi$
$83$	−52.1235	+	90.2806i	−0.627994	+	1.08772i	−0.987954	+	0.154750i	$0.950543\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	48.5161	+	118.909i	0.557656	+	1.36676i
$88$		0			0
$89$			9.37245i			0.105308i	0.998613	+	0.0526542i	$0.0167681\pi$
$89$			9.37245i			0.105308i	−0.998613	+	0.0526542i	$0.983232\pi$
$90$		0			0
$91$	−178.118			−1.95734
$92$		0			0
$93$	8.92094	−	65.0910i	0.0959241	−	0.699903i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.8902	−	6.86481i	−0.122579	−	0.0707713i	0.437457	−	0.899240i	$-0.355879\pi$
$97$	−11.8902	−	6.86481i	−0.122579	−	0.0707713i	−0.560036	+	0.828468i	$0.689213\pi$
$98$		0			0
$99$	3.32797	−	11.9131i	0.0336159	−	0.120334i
$100$		0			0
$101$	−103.509	−	59.7611i	−1.02484	−	0.591694i	−0.109341	−	0.994004i	$-0.534874\pi$
$101$	−103.509	−	59.7611i	−1.02484	−	0.591694i	−0.915503	+	0.402310i	$0.868207\pi$
$102$		0			0
$103$	−69.7254	+	40.2560i	−0.676945	+	0.390835i	−0.798703	−	0.601725i	$-0.794480\pi$
$103$	−69.7254	+	40.2560i	−0.676945	+	0.390835i	0.121758	+	0.992560i	$0.461147\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−74.6987			−0.698119			−0.349060	−	0.937101i	$-0.613499\pi$
$107$	−74.6987			−0.698119			−0.349060	+	0.937101i	$0.613499\pi$
$108$		0			0
$109$	88.2427			0.809566			0.404783	−	0.914413i	$-0.367347\pi$
$109$	88.2427			0.809566			0.404783	+	0.914413i	$0.367347\pi$
$110$		0			0
$111$	56.2472	−	72.5031i	0.506731	−	0.653181i
$112$		0			0
$113$	−79.5718	−	137.822i	−0.704175	−	1.21967i	−0.966988	−	0.254821i	$-0.917984\pi$
$113$	−79.5718	−	137.822i	−0.704175	−	1.21967i	0.262813	−	0.964847i	$-0.415350\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	135.749	+	138.661i	1.16025	+	1.18514i
$118$		0			0
$119$	−181.090	−	104.552i	−1.52176	−	0.878589i
$120$		0			0
$121$	−59.5556	−	103.153i	−0.492195	−	0.852506i
$122$		0			0
$123$	−25.0391	−	3.43169i	−0.203570	−	0.0278999i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	210.083i		−	1.65420i	−0.562055	−	0.827100i	$-0.689989\pi$
$127$		−	210.083i		−	1.65420i	0.562055	−	0.827100i	$-0.310011\pi$
$128$		0			0
$129$	80.6716	+	197.719i	0.625361	+	1.53270i
$130$		0			0
$131$	−5.70580	+	3.29424i	−0.0435557	+	0.0251469i	−0.521620	−	0.853178i	$-0.674672\pi$
$131$	−5.70580	+	3.29424i	−0.0435557	+	0.0251469i	0.478064	+	0.878325i	$0.341339\pi$
$132$		0			0
$133$	−17.8298	−	10.2940i	−0.134059	−	0.0773988i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−107.281	+	185.816i	−0.783072	+	1.35632i	0.147072	+	0.989126i	$0.453015\pi$
$137$	−107.281	+	185.816i	−0.783072	+	1.35632i	−0.930144	+	0.367195i	$0.880318\pi$
$138$		0			0
$139$	−40.7194	−	70.5281i	−0.292946	−	0.507397i	0.681559	−	0.731763i	$-0.261302\pi$
$139$	−40.7194	−	70.5281i	−0.292946	−	0.507397i	−0.974505	+	0.224366i	$0.927969\pi$
$140$		0			0
$141$	135.152	−	55.1436i	0.958525	−	0.391089i
$142$		0			0
$143$	−29.6324			−0.207220
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.84018	−	57.2053i	0.0533346	−	0.389152i
$148$		0			0
$149$	−234.181	+	135.204i	−1.57168	+	0.907412i	−0.575721	+	0.817646i	$0.695279\pi$
$149$	−234.181	+	135.204i	−1.57168	+	0.907412i	−0.995963	+	0.0897663i	$0.971388\pi$
$150$		0			0
$151$	−52.7441	+	91.3555i	−0.349299	+	0.605003i	−0.986125	−	0.166004i	$-0.946914\pi$
$151$	−52.7441	+	91.3555i	−0.349299	+	0.605003i	0.636826	+	0.771007i	$0.280247\pi$
$152$		0			0
$153$	56.6225	+	220.657i	0.370082	+	1.44220i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.28642	−	5.36152i	0.0591492	−	0.0341498i	−0.470134	−	0.882595i	$-0.655794\pi$
$157$	9.28642	−	5.36152i	0.0591492	−	0.0341498i	0.529283	+	0.848445i	$0.322461\pi$
$158$		0			0
$159$	4.65737	+	3.61314i	0.0292916	+	0.0227241i
$160$		0			0
$161$			316.597i			1.96644i
$162$		0			0
$163$		−	155.005i		−	0.950950i	−0.879729	−	0.475475i	$-0.842276\pi$
$163$		−	155.005i		−	0.950950i	0.879729	−	0.475475i	$-0.157724\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	38.0386	+	65.8848i	0.227776	+	0.394519i	0.957149	−	0.289597i	$-0.0935213\pi$
$167$	38.0386	+	65.8848i	0.227776	+	0.394519i	−0.729373	+	0.684117i	$0.760188\pi$
$168$		0			0
$169$	147.937	−	256.234i	0.875365	−	1.51618i
$170$		0			0
$171$	5.57497	+	21.7255i	0.0326021	+	0.127050i
$172$		0			0
$173$	−30.6536	+	53.0935i	−0.177188	+	0.306899i	−0.940916	−	0.338639i	$-0.890033\pi$
$173$	−30.6536	+	53.0935i	−0.177188	+	0.306899i	0.763728	+	0.645538i	$0.223367\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	12.9644	+	1.77682i	0.0732453	+	0.0100385i
$178$		0			0
$179$		−	294.705i		−	1.64640i	−0.567752	−	0.823200i	$-0.692187\pi$
$179$		−	294.705i		−	1.64640i	0.567752	−	0.823200i	$-0.307813\pi$
$180$		0			0
$181$	219.086			1.21042			0.605209	−	0.796067i	$-0.293090\pi$
$181$	219.086			1.21042			0.605209	+	0.796067i	$0.293090\pi$
$182$		0			0
$183$	102.723	−	41.9121i	0.561327	−	0.229028i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−30.1268	−	17.3937i	−0.161106	−	0.0930144i
$188$		0			0
$189$	−179.097	+	132.952i	−0.947603	+	0.703448i
$190$		0			0
$191$	146.319	+	84.4770i	0.766066	+	0.442288i	0.831469	−	0.555571i	$-0.187500\pi$
$191$	146.319	+	84.4770i	0.766066	+	0.442288i	−0.0654037	+	0.997859i	$0.520834\pi$
$192$		0			0
$193$	175.481	−	101.314i	0.909226	−	0.524942i	0.0290438	−	0.999578i	$-0.490754\pi$
$193$	175.481	−	101.314i	0.909226	−	0.524942i	0.880182	+	0.474636i	$0.157420\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−345.227			−1.75242			−0.876211	−	0.481929i	$-0.839936\pi$
$197$	−345.227			−1.75242			−0.876211	+	0.481929i	$0.839936\pi$
$198$		0			0
$199$	313.067			1.57320			0.786601	−	0.617462i	$-0.211839\pi$
$199$	313.067			1.57320			0.786601	+	0.617462i	$0.211839\pi$
$200$		0			0
$201$	−47.9327	−	6.56933i	−0.238471	−	0.0326832i
$202$		0			0
$203$	176.824	+	306.267i	0.871052	+	1.50871i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	246.464	−	241.289i	1.19065	−	1.16565i
$208$		0			0
$209$	−2.96624	−	1.71256i	−0.0141925	−	0.00819405i
$210$		0			0
$211$	−17.2115	−	29.8111i	−0.0815710	−	0.141285i	0.822354	−	0.568976i	$-0.192660\pi$
$211$	−17.2115	−	29.8111i	−0.0815710	−	0.141285i	−0.903925	+	0.427691i	$0.859327\pi$
$212$		0			0
$213$	131.524	−	169.535i	0.617481	−	0.795939i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	180.918i		−	0.833723i
$218$		0			0
$219$	−224.852	+	289.837i	−1.02672	+	1.32345i
$220$		0			0
$221$	472.628	−	272.872i	2.13859	−	1.23472i
$222$		0			0
$223$	−185.711	−	107.220i	−0.832785	−	0.480808i	0.0220206	−	0.999758i	$-0.492990\pi$
$223$	−185.711	−	107.220i	−0.832785	−	0.480808i	−0.854805	+	0.518949i	$0.826323\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	218.068	−	377.705i	0.960653	−	1.66390i	0.239789	−	0.970825i	$-0.422922\pi$
$227$	218.068	−	377.705i	0.960653	−	1.66390i	0.720865	−	0.693076i	$-0.243745\pi$
$228$		0			0
$229$	181.933	+	315.117i	0.794466	+	1.37605i	0.923178	+	0.384373i	$0.125582\pi$
$229$	181.933	+	315.117i	0.794466	+	1.37605i	−0.128712	+	0.991682i	$0.541084\pi$
$230$		0			0
$231$	4.62499	−	33.7459i	0.0200216	−	0.146086i
$232$		0			0
$233$	−192.385			−0.825685			−0.412843	−	0.910802i	$-0.635464\pi$
$233$	−192.385			−0.825685			−0.412843	+	0.910802i	$0.635464\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	22.1361	−	9.03179i	0.0934012	−	0.0381088i
$238$		0			0
$239$	229.644	−	132.585i	0.960853	−	0.554749i	0.0644178	−	0.997923i	$-0.479481\pi$
$239$	229.644	−	132.585i	0.960853	−	0.554749i	0.896436	+	0.443174i	$0.146148\pi$
$240$		0			0
$241$	−61.4106	+	106.366i	−0.254816	+	0.441354i	−0.964845	−	0.262818i	$-0.915348\pi$
$241$	−61.4106	+	106.366i	−0.254816	+	0.441354i	0.710030	+	0.704172i	$0.248681\pi$
$242$		0			0
$243$	239.995	+	38.0964i	0.987634	+	0.156775i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	46.5343	−	26.8666i	0.188398	−	0.108772i
$248$		0			0
$249$	289.566	−	118.146i	1.16292	−	0.474483i
$250$		0			0
$251$		−	218.969i		−	0.872388i	−0.899853	−	0.436194i	$-0.856326\pi$
$251$		−	218.969i		−	0.872388i	0.899853	−	0.436194i	$-0.143674\pi$
$252$		0			0
$253$			52.6704i			0.208183i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	205.943	+	356.703i	0.801334	+	1.38795i	0.918738	+	0.394867i	$0.129209\pi$
$257$	205.943	+	356.703i	0.801334	+	1.38795i	−0.117404	+	0.993084i	$0.537457\pi$
$258$		0			0
$259$	126.345	−	218.835i	0.487817	−	0.844925i
$260$		0			0
$261$	103.660	−	371.069i	0.397163	−	1.42172i
$262$		0			0
$263$	−206.048	+	356.886i	−0.783453	+	1.35698i	0.146466	+	0.989216i	$0.453210\pi$
$263$	−206.048	+	356.886i	−0.783453	+	1.35698i	−0.929919	+	0.367765i	$0.880123\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	17.2349	−	22.2159i	0.0645500	−	0.0832055i
$268$		0			0
$269$		−	384.725i		−	1.43020i	−0.699020	−	0.715102i	$-0.746380\pi$
$269$		−	384.725i		−	1.43020i	0.699020	−	0.715102i	$-0.253620\pi$
$270$		0			0
$271$	−148.889			−0.549405			−0.274702	−	0.961529i	$-0.588579\pi$
$271$	−148.889			−0.549405			−0.274702	+	0.961529i	$0.588579\pi$
$272$		0			0
$273$	422.200	+	327.539i	1.54652	+	1.19978i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−458.764	−	264.867i	−1.65619	−	0.956200i	−0.974451	−	0.224602i	$-0.927892\pi$
$277$	−458.764	−	264.867i	−1.65619	−	0.956200i	−0.681737	−	0.731598i	$-0.738775\pi$
$278$		0			0
$279$	−140.841	+	137.883i	−0.504805	+	0.494205i
$280$		0			0
$281$	81.2085	+	46.8857i	0.288998	+	0.166853i	0.637490	−	0.770459i	$-0.279973\pi$
$281$	81.2085	+	46.8857i	0.288998	+	0.166853i	−0.348492	+	0.937312i	$0.613306\pi$
$282$		0			0
$283$	−43.7017	+	25.2312i	−0.154423	+	0.0891561i	−0.575220	−	0.817999i	$-0.695084\pi$
$283$	−43.7017	+	25.2312i	−0.154423	+	0.0891561i	0.420797	+	0.907155i	$0.361750\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−69.5952			−0.242492
$288$		0			0
$289$	351.684			1.21690
$290$		0			0
$291$	15.5602	+	38.1367i	0.0534715	+	0.131054i
$292$		0			0
$293$	118.016	+	204.410i	0.402785	+	0.697643i	0.994061	−	0.108826i	$-0.0347090\pi$
$293$	118.016	+	204.410i	0.402785	+	0.697643i	−0.591276	+	0.806469i	$0.701376\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−29.7953	+	22.1183i	−0.100321	+	0.0744725i
$298$		0			0
$299$	−715.591	−	413.146i	−2.39328	−	1.38176i
$300$		0			0
$301$	294.019	+	509.255i	0.976806	+	1.69188i
$302$		0			0
$303$	135.458	+	331.996i	0.447057	+	1.09570i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			78.3780i			0.255303i	0.991819	+	0.127651i	$0.0407439\pi$
$307$			78.3780i			0.255303i	−0.991819	+	0.127651i	$0.959256\pi$
$308$		0			0
$309$	239.299	+	32.7967i	0.774430	+	0.106138i
$310$		0			0
$311$	−217.139	+	125.365i	−0.698195	+	0.403103i	−0.806675	−	0.590995i	$-0.798735\pi$
$311$	−217.139	+	125.365i	−0.698195	+	0.403103i	0.108480	+	0.994099i	$0.465402\pi$
$312$		0			0
$313$	108.756	+	62.7902i	0.347463	+	0.200608i	0.663567	−	0.748117i	$-0.269042\pi$
$313$	108.756	+	62.7902i	0.347463	+	0.200608i	−0.316104	+	0.948724i	$0.602375\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−79.2443	+	137.255i	−0.249982	+	0.432982i	−0.963521	−	0.267634i	$-0.913758\pi$
$317$	−79.2443	+	137.255i	−0.249982	+	0.432982i	0.713538	+	0.700616i	$0.247091\pi$
$318$		0			0
$319$	29.4170	+	50.9518i	0.0922164	+	0.159724i
$320$		0			0
$321$	177.061	+	137.362i	0.551593	+	0.427920i
$322$		0			0
$323$	63.0808			0.195297
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−209.165	−	162.268i	−0.639648	−	0.496233i
$328$		0			0
$329$	348.105	−	200.978i	1.05807	−	0.610877i
$330$		0			0
$331$	235.780	−	408.383i	0.712327	−	1.23379i	−0.251655	−	0.967817i	$-0.580975\pi$
$331$	235.780	−	408.383i	0.712327	−	1.23379i	0.963982	−	0.265969i	$-0.0856919\pi$
$332$		0			0
$333$	−266.650	+	68.4247i	−0.800750	+	0.205480i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−83.2869	+	48.0857i	−0.247142	+	0.142688i	−0.618455	−	0.785820i	$-0.712241\pi$
$337$	−83.2869	+	48.0857i	−0.247142	+	0.142688i	0.371313	+	0.928508i	$0.378908\pi$
$338$		0			0
$339$	−64.8275	+	473.009i	−0.191231	+	1.39531i
$340$		0			0
$341$		−	30.0982i		−	0.0882645i
$342$		0			0
$343$			245.797i			0.716608i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	135.894	+	235.376i	0.391626	+	0.678317i	0.992664	−	0.120904i	$-0.0385793\pi$
$347$	135.894	+	235.376i	0.391626	+	0.678317i	−0.601038	+	0.799220i	$0.705246\pi$
$348$		0			0
$349$	166.723	−	288.773i	0.477717	−	0.827430i	−0.521957	−	0.852972i	$-0.674798\pi$
$349$	166.723	−	288.773i	0.477717	−	0.827430i	0.999674	+	0.0255418i	$0.00813110\pi$
$350$		0			0
$351$	−66.7903	−	578.301i	−0.190286	−	1.64758i
$352$		0			0
$353$	−168.782	+	292.339i	−0.478136	+	0.828156i	−0.999686	−	0.0250648i	$-0.992021\pi$
$353$	−168.782	+	292.339i	−0.478136	+	0.828156i	0.521550	+	0.853221i	$0.325354\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	236.984	+	580.827i	0.663821	+	1.62697i
$358$		0			0
$359$			638.638i			1.77894i	0.456997	+	0.889468i	$0.348925\pi$
$359$			638.638i			1.77894i	−0.456997	+	0.889468i	$0.651075\pi$
$360$		0			0
$361$	−354.789			−0.982795
$362$		0			0
$363$	−48.5202	+	354.024i	−0.133664	+	0.975273i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−103.539	−	59.7781i	−0.282122	−	0.162883i	0.352262	−	0.935902i	$-0.385413\pi$
$367$	−103.539	−	59.7781i	−0.282122	−	0.162883i	−0.634384	+	0.773018i	$0.718746\pi$
$368$		0			0
$369$	53.0407	+	54.1783i	0.143742	+	0.146825i
$370$		0			0
$371$	14.0573	+	8.11598i	0.0378903	+	0.0218760i
$372$		0			0
$373$	89.0157	−	51.3932i	0.238648	−	0.137783i	−0.375907	−	0.926657i	$-0.622669\pi$
$373$	89.0157	−	51.3932i	0.238648	−	0.137783i	0.614555	+	0.788874i	$0.289336\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−922.989			−2.44825
$378$		0			0
$379$	546.990			1.44325			0.721623	−	0.692286i	$-0.243396\pi$
$379$	546.990			1.44325			0.721623	+	0.692286i	$0.243396\pi$
$380$		0			0
$381$	−386.319	+	497.969i	−1.01396	+	1.30700i
$382$		0			0
$383$	−119.529	−	207.029i	−0.312085	−	0.540547i	0.666729	−	0.745301i	$-0.267694\pi$
$383$	−119.529	−	207.029i	−0.312085	−	0.540547i	−0.978814	+	0.204754i	$0.934361\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	172.363	−	617.006i	0.445382	−	1.59433i
$388$		0			0
$389$	−124.222	−	71.7196i	−0.319337	−	0.184369i	0.331760	−	0.943364i	$-0.392357\pi$
$389$	−124.222	−	71.7196i	−0.319337	−	0.184369i	−0.651097	+	0.758995i	$0.725691\pi$
$390$		0			0
$391$	−485.019	−	840.077i	−1.24046	−	2.14853i
$392$		0			0
$393$	19.5824	+	2.68383i	0.0498280	+	0.00682909i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	184.077i		−	0.463671i	−0.972755	−	0.231836i	$-0.925527\pi$
$397$		−	184.077i		−	0.463671i	0.972755	−	0.231836i	$-0.0744731\pi$
$398$		0			0
$399$	23.3331	+	57.1873i	0.0584790	+	0.143327i
$400$		0			0
$401$	102.303	−	59.0645i	0.255119	−	0.147293i	−0.366987	−	0.930226i	$-0.619611\pi$
$401$	102.303	−	59.0645i	0.255119	−	0.147293i	0.622106	+	0.782933i	$0.286277\pi$
$402$		0			0
$403$	408.920	+	236.090i	1.01469	+	0.585832i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.0192	−	36.4063i	0.0516442	−	0.0894504i
$408$		0			0
$409$	−307.520	−	532.640i	−0.751882	−	1.30230i	−0.946910	−	0.321499i	$-0.895813\pi$
$409$	−307.520	−	532.640i	−0.751882	−	1.30230i	0.195028	−	0.980798i	$-0.437520\pi$
$410$		0			0
$411$	595.986	−	243.169i	1.45009	−	0.591653i
$412$		0			0
$413$	36.0341			0.0872496
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−33.1743	+	242.054i	−0.0795547	+	0.580465i
$418$		0			0
$419$	128.125	−	73.9729i	0.305787	−	0.176546i	−0.339253	−	0.940695i	$-0.610174\pi$
$419$	128.125	−	73.9729i	0.305787	−	0.176546i	0.645040	+	0.764149i	$0.276841\pi$
$420$		0			0
$421$	42.4834	−	73.5835i	0.100911	−	0.174783i	−0.811149	−	0.584839i	$-0.801158\pi$
$421$	42.4834	−	73.5835i	0.100911	−	0.174783i	0.912060	+	0.410056i	$0.134491\pi$
$422$		0			0
$423$	−421.759	−	117.820i	−0.997065	−	0.278534i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	264.578	−	152.754i	0.619622	−	0.357739i
$428$		0			0
$429$	70.2388	+	54.4906i	0.163727	+	0.127018i
$430$		0			0
$431$			422.458i			0.980180i	0.871672	+	0.490090i	$0.163036\pi$
$431$			422.458i			0.980180i	−0.871672	+	0.490090i	$0.836964\pi$
$432$		0			0
$433$		−	534.169i		−	1.23365i	−0.787102	−	0.616823i	$-0.788419\pi$
$433$		−	534.169i		−	1.23365i	0.787102	−	0.616823i	$-0.211581\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−47.7542	−	82.7128i	−0.109277	−	0.189274i
$438$		0			0
$439$	−29.5206	+	51.1312i	−0.0672452	+	0.116472i	−0.897688	−	0.440632i	$-0.854754\pi$
$439$	−29.5206	+	51.1312i	−0.0672452	+	0.116472i	0.830443	+	0.557104i	$0.188088\pi$
$440$		0			0
$441$	−123.778	+	121.179i	−0.280676	+	0.274782i
$442$		0			0
$443$	32.4581	−	56.2191i	0.0732689	−	0.126905i	−0.827063	−	0.562109i	$-0.809990\pi$
$443$	32.4581	−	56.2191i	0.0732689	−	0.126905i	0.900332	+	0.435203i	$0.143324\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	803.713	+	110.152i	1.79802	+	0.246424i
$448$		0			0
$449$			543.268i			1.20995i	0.796244	+	0.604976i	$0.206817\pi$
$449$			543.268i			1.20995i	−0.796244	+	0.604976i	$0.793183\pi$
$450$		0			0
$451$	−11.5781			−0.0256721
$452$		0			0
$453$	293.014	−	119.553i	0.646829	−	0.263914i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	619.962	+	357.935i	1.35659	+	0.783228i	0.989163	−	0.146825i	$-0.0469053\pi$
$457$	619.962	+	357.935i	1.35659	+	0.783228i	0.367427	+	0.930052i	$0.380239\pi$
$458$		0			0
$459$	271.547	−	627.153i	0.591607	−	1.36635i
$460$		0			0
$461$	130.777	+	75.5039i	0.283680	+	0.163783i	0.635088	−	0.772440i	$-0.280964\pi$
$461$	130.777	+	75.5039i	0.283680	+	0.163783i	−0.351408	+	0.936222i	$0.614297\pi$
$462$		0			0
$463$	−284.185	+	164.074i	−0.613790	+	0.354372i	−0.774447	−	0.632639i	$-0.781972\pi$
$463$	−284.185	+	164.074i	−0.613790	+	0.354372i	0.160658	+	0.987010i	$0.448639\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	30.8948			0.0661558			0.0330779	−	0.999453i	$-0.489469\pi$
$467$	30.8948			0.0661558			0.0330779	+	0.999453i	$0.489469\pi$
$468$		0			0
$469$	−133.227			−0.284066
$470$		0			0
$471$	−31.8712	−	4.36805i	−0.0676671	−	0.00927399i
$472$		0			0
$473$	48.9141	+	84.7216i	0.103412	+	0.179115i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−4.39539	−	17.1287i	−0.00921465	−	0.0359093i
$478$		0			0
$479$	−420.016	−	242.497i	−0.876861	−	0.506256i	−0.00723877	−	0.999974i	$-0.502304\pi$
$479$	−420.016	−	242.497i	−0.876861	−	0.506256i	−0.869622	+	0.493718i	$0.835638\pi$
$480$		0			0
$481$	329.749	+	571.142i	0.685549	+	1.18741i
$482$		0			0
$483$	582.186	−	750.443i	1.20535	−	1.55371i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	764.340i		−	1.56949i	−0.619821	−	0.784743i	$-0.712795\pi$
$487$		−	764.340i		−	1.56949i	0.619821	−	0.784743i	$-0.287205\pi$
$488$		0			0
$489$	−285.036	+	367.414i	−0.582896	+	0.751358i
$490$		0			0
$491$	−387.463	+	223.702i	−0.789129	+	0.455604i	−0.839656	−	0.543119i	$-0.817243\pi$
$491$	−387.463	+	223.702i	−0.789129	+	0.455604i	0.0505265	+	0.998723i	$0.483910\pi$
$492$		0			0
$493$	−938.386	−	541.778i	−1.90342	−	1.09894i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	295.433	−	511.706i	0.594434	−	1.02959i
$498$		0			0
$499$	158.431	+	274.410i	0.317497	+	0.549920i	0.979965	−	0.199170i	$-0.0638244\pi$
$499$	158.431	+	274.410i	0.317497	+	0.549920i	−0.662468	+	0.749090i	$0.730491\pi$
$500$		0			0
$501$	30.9902	−	226.118i	0.0618566	−	0.451333i
$502$		0			0
$503$	630.817			1.25411			0.627054	−	0.778976i	$-0.284260\pi$
$503$	630.817			1.25411			0.627054	+	0.778976i	$0.284260\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−821.845	+	335.322i	−1.62100	+	0.661385i
$508$		0			0
$509$	138.696	−	80.0759i	0.272486	−	0.157320i	−0.357531	−	0.933901i	$-0.616381\pi$
$509$	138.696	−	80.0759i	0.272486	−	0.157320i	0.630017	+	0.776581i	$0.283048\pi$
$510$		0			0
$511$	−505.072	+	874.811i	−0.988400	+	1.71196i
$512$		0			0
$513$	26.7362	−	61.7485i	0.0521173	−	0.120368i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	57.9121	−	33.4355i	0.112016	−	0.0646722i
$518$		0			0
$519$	170.292	−	69.4812i	0.328116	−	0.133875i
$520$		0			0
$521$		−	269.377i		−	0.517039i	−0.966006	−	0.258519i	$-0.916765\pi$
$521$		−	269.377i		−	0.517039i	0.966006	−	0.258519i	$-0.0832346\pi$
$522$		0			0
$523$			224.057i			0.428407i	0.976789	+	0.214204i	$0.0687156\pi$
$523$			224.057i			0.428407i	−0.976789	+	0.214204i	$0.931284\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	277.161	+	480.058i	0.525923	+	0.910925i
$528$		0			0
$529$	−469.850	+	813.805i	−0.888186	+	1.53838i
$530$		0			0
$531$	−27.4627	−	28.0517i	−0.0517188	−	0.0528281i
$532$		0			0
$533$	90.8188	−	157.303i	0.170392	−	0.295127i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−541.929	+	698.552i	−1.00918	+	1.30084i
$538$		0			0
$539$		−	26.4519i		−	0.0490758i
$540$		0			0
$541$	705.258			1.30362			0.651809	−	0.758383i	$-0.274010\pi$
$541$	705.258			1.30362			0.651809	+	0.758383i	$0.274010\pi$
$542$		0			0
$543$	−519.307	−	402.873i	−0.956366	−	0.741939i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−266.531	−	153.882i	−0.487259	−	0.281319i	0.236178	−	0.971710i	$-0.424105\pi$
$547$	−266.531	−	153.882i	−0.487259	−	0.281319i	−0.723437	+	0.690391i	$0.757439\pi$
$548$		0			0
$549$	−320.559	−	89.5495i	−0.583897	−	0.163114i
$550$		0			0
$551$	−92.3921	−	53.3426i	−0.167681	−	0.0968106i
$552$		0			0
$553$	57.0149	−	32.9176i	0.103101	−	0.0595255i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−530.424			−0.952287			−0.476143	−	0.879368i	$-0.657966\pi$
$557$	−530.424			−0.952287			−0.476143	+	0.879368i	$0.657966\pi$
$558$		0			0
$559$	−1534.73			−2.74549
$560$		0			0
$561$	39.4256	+	96.6285i	0.0702774	+	0.172243i
$562$		0			0
$563$	−427.955	−	741.240i	−0.760133	−	1.31659i	−0.942781	−	0.333411i	$-0.891800\pi$
$563$	−427.955	−	741.240i	−0.760133	−	1.31659i	0.182648	−	0.983178i	$-0.441533\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	669.003	+	14.1985i	1.17990	+	0.0250414i
$568$		0			0
$569$	−218.351	−	126.065i	−0.383746	−	0.221556i	0.295701	−	0.955281i	$-0.404447\pi$
$569$	−218.351	−	126.065i	−0.383746	−	0.221556i	−0.679447	+	0.733725i	$0.737780\pi$
$570$		0			0
$571$	−185.624	−	321.511i	−0.325087	−	0.563066i	0.656443	−	0.754375i	$-0.272060\pi$
$571$	−185.624	−	321.511i	−0.325087	−	0.563066i	−0.981530	+	0.191309i	$0.938727\pi$
$572$		0			0
$573$	−191.481	−	469.302i	−0.334172	−	0.819026i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			752.555i			1.30425i	0.758109	+	0.652127i	$0.226123\pi$
$577$			752.555i			1.30425i	−0.758109	+	0.652127i	$0.773877\pi$
$578$		0			0
$579$	−602.253	−	82.5407i	−1.04016	−	0.142557i
$580$		0			0
$581$	745.822	−	430.600i	1.28369	−	0.741137i
$582$		0			0
$583$	2.33862	+	1.35021i	0.00401136	+	0.00231596i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	399.392	−	691.767i	0.680395	−	1.17848i	−0.294466	−	0.955662i	$-0.595142\pi$
$587$	399.392	−	691.767i	0.680395	−	1.17848i	0.974860	−	0.222816i	$-0.0715250\pi$
$588$		0			0
$589$	27.2889	+	47.2658i	0.0463309	+	0.0802475i
$590$		0			0
$591$	818.305	+	634.833i	1.38461	+	1.07417i
$592$		0			0
$593$	−684.110			−1.15364			−0.576821	−	0.816871i	$-0.695707\pi$
$593$	−684.110			−1.15364			−0.576821	+	0.816871i	$0.695707\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−742.075	−	575.694i	−1.24301	−	0.964312i
$598$		0			0
$599$	112.311	−	64.8430i	0.187498	−	0.108252i	−0.403313	−	0.915062i	$-0.632141\pi$
$599$	112.311	−	64.8430i	0.187498	−	0.108252i	0.590811	+	0.806810i	$0.298808\pi$
$600$		0			0
$601$	−110.390	+	191.201i	−0.183677	+	0.318139i	−0.943130	−	0.332424i	$-0.892133\pi$
$601$	−110.390	+	191.201i	−0.183677	+	0.318139i	0.759453	+	0.650563i	$0.225467\pi$
$602$		0			0
$603$	101.536	+	103.714i	0.168385	+	0.171997i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−437.376	+	252.519i	−0.720553	+	0.416011i	−0.814956	−	0.579523i	$-0.803239\pi$
$607$	−437.376	+	252.519i	−0.720553	+	0.416011i	0.0944034	+	0.995534i	$0.469906\pi$
$608$		0			0
$609$	144.059	−	1051.12i	0.236550	−	1.72597i
$610$		0			0
$611$			1049.07i			1.71698i
$612$		0			0
$613$		−	582.009i		−	0.949444i	−0.880136	−	0.474722i	$-0.842549\pi$
$613$		−	582.009i		−	0.949444i	0.880136	−	0.474722i	$-0.157451\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	301.668	+	522.504i	0.488927	+	0.846846i	0.999919	−	0.0127394i	$-0.00405517\pi$
$617$	301.668	+	522.504i	0.488927	+	0.846846i	−0.510992	+	0.859585i	$0.670722\pi$
$618$		0			0
$619$	160.899	−	278.685i	0.259933	−	0.450218i	−0.706290	−	0.707922i	$-0.749633\pi$
$619$	160.899	−	278.685i	0.259933	−	0.450218i	0.966224	+	0.257704i	$0.0829661\pi$
$620$		0			0
$621$	−1027.91	+	118.717i	−1.65524	+	0.191171i
$622$		0			0
$623$	38.7136	−	67.0540i	0.0621407	−	0.107631i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.88179	+	9.51390i	0.00619105	+	0.0151737i
$628$		0			0
$629$			774.227i			1.23088i
$630$		0			0
$631$	−453.251			−0.718306			−0.359153	−	0.933279i	$-0.616934\pi$
$631$	−453.251			−0.718306			−0.359153	+	0.933279i	$0.616934\pi$
$632$		0			0
$633$	−14.0223	+	102.312i	−0.0221521	+	0.161631i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	359.380	+	207.488i	0.564176	+	0.325727i
$638$		0			0
$639$	−623.510	+	159.998i	−0.975760	+	0.250389i
$640$		0			0
$641$	−1098.13	−	634.006i	−1.71315	−	0.989089i	−0.930236	−	0.366963i	$-0.880398\pi$
$641$	−1098.13	−	634.006i	−1.71315	−	0.989089i	−0.782917	−	0.622126i	$-0.786269\pi$
$642$		0			0
$643$	295.058	−	170.352i	0.458877	−	0.264933i	−0.252695	−	0.967546i	$-0.581317\pi$
$643$	295.058	−	170.352i	0.458877	−	0.264933i	0.711572	+	0.702613i	$0.247984\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	460.508			0.711759			0.355879	−	0.934532i	$-0.384181\pi$
$647$	460.508			0.711759			0.355879	+	0.934532i	$0.384181\pi$
$648$		0			0
$649$	5.99477			0.00923693
$650$		0			0
$651$	−332.687	+	428.837i	−0.511040	+	0.658735i
$652$		0			0
$653$	−421.100	−	729.367i	−0.644870	−	1.11695i	−0.984331	−	0.176328i	$-0.943578\pi$
$653$	−421.100	−	729.367i	−0.644870	−	1.11695i	0.339461	−	0.940620i	$-0.389755\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1065.95	−	273.533i	1.62245	−	0.416336i
$658$		0			0
$659$	651.160	+	375.948i	0.988104	+	0.570482i	0.904707	−	0.426035i	$-0.140090\pi$
$659$	651.160	+	375.948i	0.988104	+	0.570482i	0.0833967	+	0.996516i	$0.473423\pi$
$660$		0			0
$661$	−45.6212	−	79.0183i	−0.0690185	−	0.119544i	0.829451	−	0.558579i	$-0.188653\pi$
$661$	−45.6212	−	79.0183i	−0.0690185	−	0.119544i	−0.898470	+	0.439036i	$0.855320\pi$
$662$		0			0
$663$	−1622.07	−	222.310i	−2.44656	−	0.335309i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			1640.57i			2.45963i
$668$		0			0
$669$	243.032	+	595.649i	0.363277	+	0.890358i
$670$		0			0
$671$	44.0163	−	25.4128i	0.0655981	−	0.0378731i
$672$		0			0
$673$	940.583	+	543.046i	1.39760	+	0.806903i	0.994140	−	0.108096i	$-0.0344754\pi$
$673$	940.583	+	543.046i	1.39760	+	0.806903i	0.403456	+	0.914999i	$0.367809\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	384.990	−	666.823i	0.568671	−	0.984967i	−0.428027	−	0.903766i	$-0.640791\pi$
$677$	384.990	−	666.823i	0.568671	−	0.984967i	0.996698	−	0.0812011i	$-0.0258756\pi$
$678$		0			0
$679$	56.7113	+	98.2269i	0.0835218	+	0.144664i
$680$		0			0
$681$	−1211.45	+	494.287i	−1.77893	+	0.725825i
$682$		0			0
$683$	993.247			1.45424			0.727121	−	0.686510i	$-0.240858\pi$
$683$	993.247			1.45424			0.727121	+	0.686510i	$0.240858\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	148.221	−	1081.49i	0.215751	−	1.57422i
$688$		0			0
$689$	−36.6883	+	21.1820i	−0.0532487	+	0.0307431i
$690$		0			0
$691$	461.866	−	799.975i	0.668402	−	1.15771i	−0.309949	−	0.950753i	$-0.600312\pi$
$691$	461.866	−	799.975i	0.668402	−	1.15771i	0.978351	−	0.206953i	$-0.0663547\pi$
$692$		0			0
$693$	−73.0176	+	71.4843i	−0.105364	+	0.103152i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	184.668	−	106.618i	0.264947	−	0.152967i
$698$		0			0
$699$	456.017	+	353.773i	0.652384	+	0.506113i
$700$		0			0
$701$		−	163.654i		−	0.233458i	−0.993164	−	0.116729i	$-0.962759\pi$
$701$		−	163.654i		−	0.233458i	0.993164	−	0.116729i	$-0.0372409\pi$
$702$		0			0
$703$			76.2292i			0.108434i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	493.696	+	855.106i	0.698297	+	1.20949i
$708$		0			0
$709$	−11.5863	+	20.0680i	−0.0163417	+	0.0283047i	−0.874081	−	0.485781i	$-0.838535\pi$
$709$	−11.5863	+	20.0680i	−0.0163417	+	0.0283047i	0.857739	+	0.514086i	$0.171869\pi$
$710$		0			0
$711$	−69.0784	−	19.2973i	−0.0971567	−	0.0271411i
$712$		0			0
$713$	419.641	−	726.839i	0.588556	−	1.01941i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−788.142	−	108.018i	−1.09922	−	0.150652i
$718$		0			0
$719$			122.596i			0.170509i	0.996359	+	0.0852545i	$0.0271703\pi$
$719$			122.596i			0.170509i	−0.996359	+	0.0852545i	$0.972830\pi$
$720$		0			0
$721$	665.122			0.922499
$722$		0			0
$723$	341.159	−	139.197i	0.471866	−	0.192527i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	332.525	+	191.983i	0.457393	+	0.264076i	0.710947	−	0.703245i	$-0.248266\pi$
$727$	332.525	+	191.983i	0.457393	+	0.264076i	−0.253554	+	0.967321i	$0.581600\pi$
$728$		0			0
$729$	−498.815	−	531.625i	−0.684245	−	0.729252i
$730$		0			0
$731$	−1560.33	−	900.857i	−2.13451	−	1.23236i
$732$		0			0
$733$	9.48169	−	5.47425i	0.0129355	−	0.00746829i	−0.493518	−	0.869735i	$-0.664289\pi$
$733$	9.48169	−	5.47425i	0.0129355	−	0.00746829i	0.506454	+	0.862267i	$0.330956\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−22.1642			−0.0300735
$738$		0			0
$739$	−429.537			−0.581241			−0.290621	−	0.956838i	$-0.593862\pi$
$739$	−429.537			−0.581241			−0.290621	+	0.956838i	$0.593862\pi$
$740$		0			0
$741$	−159.707	−	21.8883i	−0.215528	−	0.0295389i
$742$		0			0
$743$	−489.716	−	848.213i	−0.659106	−	1.14161i	−0.980847	−	0.194778i	$-0.937601\pi$
$743$	−489.716	−	848.213i	−0.659106	−	1.14161i	0.321741	−	0.946828i	$-0.395732\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−903.626	−	252.432i	−1.20967	−	0.337927i
$748$		0			0
$749$	534.423	+	308.549i	0.713515	+	0.411948i
$750$		0			0
$751$	50.7936	+	87.9772i	0.0676347	+	0.117147i	0.897860	−	0.440282i	$-0.145121\pi$
$751$	50.7936	+	87.9772i	0.0676347	+	0.117147i	−0.830225	+	0.557428i	$0.811788\pi$
$752$		0			0
$753$	−402.659	+	519.031i	−0.534740	+	0.689284i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	264.365i		−	0.349227i	−0.984637	−	0.174614i	$-0.944132\pi$
$757$		−	264.365i		−	0.349227i	0.984637	−	0.174614i	$-0.0558676\pi$
$758$		0			0
$759$	96.8548	−	124.847i	0.127608	−	0.164488i
$760$		0			0
$761$	217.673	−	125.674i	0.286036	−	0.165143i	−0.350117	−	0.936706i	$-0.613858\pi$
$761$	217.673	−	125.674i	0.286036	−	0.165143i	0.636153	+	0.771563i	$0.280525\pi$
$762$		0			0
$763$	−631.321	−	364.493i	−0.827419	−	0.477711i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−47.0230	+	81.4462i	−0.0613077	+	0.106188i
$768$		0			0
$769$	179.852	+	311.512i	0.233878	+	0.405088i	0.958946	−	0.283589i	$-0.0915252\pi$
$769$	179.852	+	311.512i	0.233878	+	0.405088i	−0.725068	+	0.688677i	$0.758192\pi$
$770$		0			0
$771$	167.782	−	1224.21i	0.217617	−	1.58782i
$772$		0			0
$773$	−455.149			−0.588808			−0.294404	−	0.955681i	$-0.595121\pi$
$773$	−455.149			−0.588808			−0.294404	+	0.955681i	$0.595121\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−701.893	+	286.381i	−0.903337	+	0.368572i
$778$		0			0
$779$	18.1821	−	10.4974i	0.0233403	−	0.0134755i
$780$		0			0
$781$	49.1494	−	85.1293i	0.0629314	−	0.109000i
$782$		0			0
$783$	−928.061	+	688.941i	−1.18526	+	0.879873i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1137.46	+	656.715i	−1.44532	+	0.834454i	−0.998197	−	0.0600202i	$-0.980883\pi$
$787$	−1137.46	+	656.715i	−1.44532	+	0.834454i	−0.447120	+	0.894474i	$0.647550\pi$
$788$		0			0
$789$	1144.68	−	467.041i	1.45079	−	0.591941i
$790$		0			0
$791$			1314.71i			1.66209i
$792$		0			0
$793$			797.353i			1.00549i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	222.359	+	385.136i	0.278995	+	0.483233i	0.971135	−	0.238530i	$-0.0766655\pi$
$797$	222.359	+	385.136i	0.278995	+	0.483233i	−0.692141	+	0.721763i	$0.743332\pi$
$798$		0			0
$799$	−615.787	+	1066.57i	−0.770697	+	1.33489i
$800$		0			0
$801$	−81.7049	+	20.9662i	−0.102004	+	0.0261751i
$802$		0			0
$803$	−84.0258	+	145.537i	−0.104640	+	0.181242i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−707.465	+	911.928i	−0.876660	+	1.13002i
$808$		0			0
$809$			718.402i			0.888012i	0.896024	+	0.444006i	$0.146443\pi$
$809$			718.402i			0.888012i	−0.896024	+	0.444006i	$0.853557\pi$
$810$		0			0
$811$	−899.465			−1.10908			−0.554541	−	0.832157i	$-0.687106\pi$
$811$	−899.465			−1.10908			−0.554541	+	0.832157i	$0.687106\pi$
$812$		0			0
$813$	352.916	+	273.789i	0.434092	+	0.336764i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−153.628	−	88.6970i	−0.188039	−	0.108564i
$818$		0			0
$819$	−398.451	−	1552.76i	−0.486509	−	1.89592i
$820$		0			0
$821$	−1327.63	−	766.507i	−1.61709	−	0.933626i	−0.987669	−	0.156559i	$-0.949960\pi$
$821$	−1327.63	−	766.507i	−1.61709	−	0.933626i	−0.629418	−	0.777067i	$-0.716707\pi$
$822$		0			0
$823$	−684.403	+	395.140i	−0.831595	+	0.480122i	−0.854399	−	0.519618i	$-0.826074\pi$
$823$	−684.403	+	395.140i	−0.831595	+	0.480122i	0.0228034	+	0.999740i	$0.492741\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−608.168			−0.735390			−0.367695	−	0.929946i	$-0.619853\pi$
$827$	−608.168			−0.735390			−0.367695	+	0.929946i	$0.619853\pi$
$828$		0			0
$829$	−1293.97			−1.56088			−0.780441	−	0.625229i	$-0.785006\pi$
$829$	−1293.97			−1.56088			−0.780441	+	0.625229i	$0.785006\pi$
$830$		0			0
$831$	600.365	+	1471.44i	0.722461	+	1.77068i
$832$		0			0
$833$	243.584	+	421.899i	0.292417	+	0.506482i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	587.391	−	67.8401i	0.701781	−	0.0810515i
$838$		0			0
$839$	1075.31	+	620.832i	1.28166	+	0.739966i	0.977152	−	0.212543i	$-0.0681747\pi$
$839$	1075.31	+	620.832i	1.28166	+	0.739966i	0.304508	+	0.952510i	$0.401508\pi$
$840$		0			0
$841$	495.780	+	858.717i	0.589513	+	1.02107i
$842$		0			0
$843$	−106.274	−	260.468i	−0.126067	−	0.308978i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			983.996i			1.16174i
$848$		0			0
$849$	149.985	+	20.5559i	0.176661	+	0.0242119i
$850$		0			0
$851$	1015.18	−	586.115i	1.19293	−	0.688737i
$852$		0			0
$853$	996.935	+	575.580i	1.16874	+	0.674772i	0.953383	−	0.301764i	$-0.0975753\pi$
$853$	996.935	+	575.580i	1.16874	+	0.674772i	0.215356	+	0.976536i	$0.430909\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	824.101	−	1427.38i	0.961611	−	1.66556i	0.243155	−	0.969987i	$-0.421818\pi$
$857$	824.101	−	1427.38i	0.961611	−	1.66556i	0.718456	−	0.695572i	$-0.244849\pi$
$858$		0			0
$859$	−279.406	−	483.945i	−0.325269	−	0.563382i	0.656298	−	0.754502i	$-0.272121\pi$
$859$	−279.406	−	483.945i	−0.325269	−	0.563382i	−0.981567	+	0.191120i	$0.938788\pi$
$860$		0			0
$861$	164.964	+	127.978i	0.191596	+	0.148638i
$862$		0			0
$863$	1222.64			1.41673			0.708365	−	0.705846i	$-0.249433\pi$
$863$	1222.64			1.41673			0.708365	+	0.705846i	$0.249433\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−833.610	−	646.706i	−0.961488	−	0.745913i
$868$		0			0
$869$	9.48522	−	5.47629i	0.0109151	−	0.00630184i
$870$		0			0
$871$	173.856	−	301.127i	0.199605	−	0.345725i
$872$		0			0
$873$	33.2460	−	119.010i	0.0380824	−	0.136323i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1028.99	−	594.086i	1.17330	−	0.677407i	0.218848	−	0.975759i	$-0.429770\pi$
$877$	1028.99	−	594.086i	1.17330	−	0.677407i	0.954456	+	0.298352i	$0.0964368\pi$
$878$		0			0
$879$	96.1480	−	701.537i	0.109383	−	0.798108i
$880$		0			0
$881$		−	663.144i		−	0.752717i	−0.926474	−	0.376359i	$-0.877176\pi$
$881$		−	663.144i		−	0.752717i	0.926474	−	0.376359i	$-0.122824\pi$
$882$		0			0
$883$			1447.52i			1.63932i	0.572852	+	0.819659i	$0.305837\pi$
$883$			1447.52i			1.63932i	−0.572852	+	0.819659i	$0.694163\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−323.166	−	559.739i	−0.364335	−	0.631047i	0.624334	−	0.781158i	$-0.285370\pi$
$887$	−323.166	−	559.739i	−0.364335	−	0.631047i	−0.988669	+	0.150110i	$0.952037\pi$
$888$		0			0
$889$	−867.766	+	1503.01i	−0.976114	+	1.69068i
$890$		0			0
$891$	111.298	+	2.36211i	0.124913	+	0.00265108i
$892$		0			0
$893$	−60.6295	+	105.013i	−0.0678942	+	0.117596i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	936.463	+	2295.19i	1.04399	+	2.55874i
$898$		0			0
$899$		−	937.497i		−	1.04282i
$900$		0			0
$901$	−49.7338			−0.0551985
$902$		0			0
$903$	239.538	−	1747.77i	0.265269	−	1.93552i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	625.829	+	361.322i	0.689999	+	0.398371i	0.803612	−	0.595154i	$-0.202909\pi$
$907$	625.829	+	361.322i	0.689999	+	0.398371i	−0.113613	+	0.993525i	$0.536242\pi$
$908$		0			0
$909$	289.420	−	1036.03i	0.318394	−	1.13975i
$910$		0			0
$911$	1278.01	+	737.862i	1.40287	+	0.809947i	0.994686	−	0.102952i	$-0.0328289\pi$
$911$	1278.01	+	737.862i	1.40287	+	0.809947i	0.408184	+	0.912900i	$0.366162\pi$
$912$		0			0
$913$	124.078	−	71.6363i	0.135901	−	0.0784626i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	54.4285			0.0593550
$918$		0			0
$919$	1283.57			1.39670			0.698351	−	0.715755i	$-0.253917\pi$
$919$	1283.57			1.39670			0.698351	+	0.715755i	$0.253917\pi$
$920$		0			0
$921$	144.128	−	185.782i	0.156491	−	0.201718i
$922$		0			0
$923$	771.057	+	1335.51i	0.835381	+	1.44692i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−506.910	−	517.782i	−0.546828	−	0.558557i
$928$		0			0
$929$	486.909	+	281.117i	0.524121	+	0.302601i	0.738619	−	0.674123i	$-0.235478\pi$
$929$	486.909	+	281.117i	0.524121	+	0.302601i	−0.214498	+	0.976724i	$0.568812\pi$
$930$		0			0
$931$	23.9829	+	41.5396i	0.0257604	+	0.0446182i
$932$		0			0
$933$	745.224	+	102.135i	0.798740	+	0.109470i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	1337.27i		−	1.42718i	−0.700562	−	0.713592i	$-0.747067\pi$
$937$		−	1337.27i		−	1.42718i	0.700562	−	0.713592i	$-0.252933\pi$
$938$		0			0
$939$	−142.324	−	348.824i	−0.151570	−	0.371484i
$940$		0			0
$941$	918.441	−	530.262i	0.976026	−	0.563509i	0.0749581	−	0.997187i	$-0.476118\pi$
$941$	918.441	−	530.262i	0.976026	−	0.563509i	0.901068	+	0.433678i	$0.142784\pi$
$942$		0			0
$943$	−279.599	−	161.427i	−0.296500	−	0.171184i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	721.938	−	1250.43i	0.762342	−	1.32042i	−0.179298	−	0.983795i	$-0.557383\pi$
$947$	721.938	−	1250.43i	0.762342	−	1.32042i	0.941640	−	0.336621i	$-0.109284\pi$
$948$		0			0
$949$	−1318.20	−	2283.18i	−1.38904	−	2.40588i
$950$		0			0
$951$	440.232	−	179.620i	0.462915	−	0.188875i
$952$		0			0
$953$	854.631			0.896780			0.448390	−	0.893838i	$-0.351998\pi$
$953$	854.631			0.896780			0.448390	+	0.893838i	$0.351998\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	23.9662	−	174.868i	0.0250430	−	0.182725i
$958$		0			0
$959$	1535.05	−	886.264i	1.60068	−	0.924154i
$960$		0			0
$961$	240.699	−	416.902i	0.250467	−	0.433821i
$962$		0			0
$963$	−167.101	−	651.191i	−0.173522	−	0.676210i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	108.975	−	62.9165i	0.112693	−	0.0650636i	−0.442594	−	0.896722i	$-0.645942\pi$
$967$	108.975	−	62.9165i	0.112693	−	0.0650636i	0.555287	+	0.831659i	$0.312608\pi$
$968$		0			0
$969$	−149.523	−	115.998i	−0.154306	−	0.119709i
$970$		0			0
$971$			20.0762i			0.0206758i	0.999947	+	0.0103379i	$0.00329072\pi$
$971$			20.0762i			0.0206758i	−0.999947	+	0.0103379i	$0.996709\pi$
$972$		0			0
$973$			672.779i			0.691449i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−653.401	−	1131.72i	−0.668783	−	1.15837i	−0.978245	−	0.207455i	$-0.933482\pi$
$977$	−653.401	−	1131.72i	−0.668783	−	1.15837i	0.309461	−	0.950912i	$-0.399851\pi$
$978$		0			0
$979$	6.44055	−	11.1554i	0.00657870	−	0.0113946i
$980$		0			0
$981$	197.399	+	769.261i	0.201223	+	0.784160i
$982$		0			0
$983$	−639.237	+	1107.19i	−0.650292	+	1.12634i	0.332760	+	0.943011i	$0.392020\pi$
$983$	−639.237	+	1107.19i	−0.650292	+	1.12634i	−0.983052	+	0.183327i	$0.941313\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1194.70	−	163.738i	−1.21044	−	0.165895i
$988$		0			0
$989$			2727.91i			2.75825i
$990$		0			0
$991$	1017.87			1.02711			0.513557	−	0.858055i	$-0.328327\pi$
$991$	1017.87			1.02711			0.513557	+	0.858055i	$0.328327\pi$
$992$		0			0
$993$	−1309.85	+	534.434i	−1.31908	+	0.538201i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	357.116	+	206.181i	0.358191	+	0.206802i	0.668287	−	0.743904i	$-0.267028\pi$
$997$	357.116	+	206.181i	0.358191	+	0.206802i	−0.310096	+	0.950705i	$0.600361\pi$
$998$		0			0
$999$	757.875	+	328.148i	0.758634	+	0.328477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.d.749.4		32
3.2	odd	2		2700.3.u.d.2249.4		32
5.2	odd	4		900.3.p.d.101.3	✓	16
5.3	odd	4		900.3.p.e.101.6	yes	16
5.4	even	2	inner	900.3.u.d.749.13		32
9.4	even	3		2700.3.u.d.449.13		32
9.5	odd	6	inner	900.3.u.d.149.13		32
15.2	even	4		2700.3.p.e.1601.7		16
15.8	even	4		2700.3.p.d.1601.2		16
15.14	odd	2		2700.3.u.d.2249.13		32
45.4	even	6		2700.3.u.d.449.4		32
45.13	odd	12		2700.3.p.d.2501.2		16
45.14	odd	6	inner	900.3.u.d.149.4		32
45.22	odd	12		2700.3.p.e.2501.7		16
45.23	even	12		900.3.p.e.401.6	yes	16
45.32	even	12		900.3.p.d.401.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.3	✓	16	5.2	odd	4
900.3.p.d.401.3	yes	16	45.32	even	12
900.3.p.e.101.6	yes	16	5.3	odd	4
900.3.p.e.401.6	yes	16	45.23	even	12
900.3.u.d.149.4		32	45.14	odd	6	inner
900.3.u.d.149.13		32	9.5	odd	6	inner
900.3.u.d.749.4		32	1.1	even	1	trivial
900.3.u.d.749.13		32	5.4	even	2	inner
2700.3.p.d.1601.2		16	15.8	even	4
2700.3.p.d.2501.2		16	45.13	odd	12
2700.3.p.e.1601.7		16	15.2	even	4
2700.3.p.e.2501.7		16	45.22	odd	12
2700.3.u.d.449.4		32	45.4	even	6
2700.3.u.d.449.13		32	9.4	even	3
2700.3.u.d.2249.4		32	3.2	odd	2
2700.3.u.d.2249.13		32	15.14	odd	2

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.37034 - 1.83888i) q^{3} +(-7.15437 - 4.13058i) q^{7} +(2.23701 + 8.71756i) q^{9} +O(q^{10})\)	\(q+(-2.37034 - 1.83888i) q^{3} +(-7.15437 - 4.13058i) q^{7} +(2.23701 + 8.71756i) q^{9} +(-1.19023 - 0.687179i) q^{11} +(18.6723 - 10.7805i) q^{13} +25.3117 q^{17} +2.49216 q^{19} +(9.36262 + 22.9469i) q^{21} +(-19.1618 - 33.1892i) q^{23} +(10.7281 - 24.7772i) q^{27} +(-37.0732 - 21.4042i) q^{29} +(10.9499 + 18.9658i) q^{31} +(1.55760 + 3.81754i) q^{33} +30.5877i q^{37} +(-64.0837 - 8.78288i) q^{39} +(7.29574 - 4.21220i) q^{41} +(-61.6445 - 35.5905i) q^{43} +(-24.3281 + 42.1375i) q^{47} +(9.62335 + 16.6681i) q^{49} +(-59.9974 - 46.5454i) q^{51} -1.96485 q^{53} +(-5.90725 - 4.58279i) q^{57} +(-3.77749 + 2.18094i) q^{59} +(-18.4907 + 32.0268i) q^{61} +(20.0042 - 71.6088i) q^{63} +(13.9663 - 8.06346i) q^{67} +(-15.6112 + 113.906i) q^{69} +71.5235i q^{71} -122.276i q^{73} +(5.67689 + 9.83266i) q^{77} +(-3.98462 + 6.90157i) q^{79} +(-70.9916 + 39.0024i) q^{81} +(-52.1235 + 90.2806i) q^{83} +(48.5161 + 118.909i) q^{87} +9.37245i q^{89} -178.118 q^{91} +(8.92094 - 65.0910i) q^{93} +(-11.8902 - 6.86481i) q^{97} +(3.32797 - 11.9131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{9}+O(q^{10}) \) 32 * q - 28 * q^9	\( 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) \) 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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