LMFDB - Embedded newform 900.3.u.d.149.4

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			149.4
Character	$\chi$	$=$	900.149
Dual form			900.3.u.d.749.4

$q$-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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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	−0.914698	−	0.404138i	$-0.867571\pi$
$7$	−7.15437	+	4.13058i	−1.02205	+	0.590083i	−0.107355	+	0.994221i	$0.534238\pi$
$8$		0			0
$9$	2.23701	−	8.71756i	0.248556	−	0.968617i
$10$		0			0
$11$	−1.19023	+	0.687179i	−0.108203	+	0.0624708i	−0.553125	−	0.833098i	$-0.686565\pi$
$11$	−1.19023	+	0.687179i	−0.108203	+	0.0624708i	0.444922	+	0.895569i	$0.353231\pi$
$12$		0			0
$13$	18.6723	+	10.7805i	1.43633	+	0.829266i	0.997593	−	0.0693484i	$-0.0220920\pi$
$13$	18.6723	+	10.7805i	1.43633	+	0.829266i	0.438739	+	0.898615i	$0.355425\pi$
$14$		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	0.0624276	+	0.998049i	$0.480116\pi$
$23$	−19.1618	+	33.1892i	−0.833122	+	1.44301i	−0.895550	+	0.444961i	$0.853218\pi$
$24$		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	−0.976551	−	0.215284i	$-0.930932\pi$
$29$	−37.0732	+	21.4042i	−1.27839	+	0.738076i	−0.301834	+	0.953360i	$0.597599\pi$
$30$		0			0
$31$	10.9499	−	18.9658i	0.353223	−	0.611800i	−0.633589	−	0.773670i	$-0.718419\pi$
$31$	10.9499	−	18.9658i	0.353223	−	0.611800i	0.986812	+	0.161869i	$0.0517523\pi$
$32$		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	$-0.864360\pi$
$37$		−	30.5877i		−	0.826693i	0.910574	−	0.413347i	$-0.135640\pi$
$38$		0			0
$39$	−64.0837	+	8.78288i	−1.64317	+	0.225202i
$40$		0			0
$41$	7.29574	+	4.21220i	0.177945	+	0.102736i	0.586327	−	0.810075i	$-0.300573\pi$
$41$	7.29574	+	4.21220i	0.177945	+	0.102736i	−0.408382	+	0.912811i	$0.633907\pi$
$42$		0			0
$43$	−61.6445	+	35.5905i	−1.43359	+	0.827686i	−0.997393	−	0.0721636i	$-0.977010\pi$
$43$	−61.6445	+	35.5905i	−1.43359	+	0.827686i	−0.436201	+	0.899849i	$0.643676\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−24.3281	−	42.1375i	−0.517620	−	0.896544i	−0.999791	−	0.0204664i	$-0.993485\pi$
$47$	−24.3281	−	42.1375i	−0.517620	−	0.896544i	0.482171	−	0.876077i	$-0.339848\pi$
$48$		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	0.467646	−	0.883916i	$-0.345102\pi$
$59$	−3.77749	−	2.18094i	−0.0640253	−	0.0369650i	−0.531671	+	0.846951i	$0.678436\pi$
$60$		0			0
$61$	−18.4907	−	32.0268i	−0.303126	−	0.525030i	0.673716	−	0.738990i	$-0.264697\pi$
$61$	−18.4907	−	32.0268i	−0.303126	−	0.525030i	−0.976842	+	0.213960i	$0.931364\pi$
$62$		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	0.600592	−	0.799556i	$-0.294932\pi$
$67$	13.9663	+	8.06346i	0.208453	+	0.120350i	−0.392139	+	0.919906i	$0.628265\pi$
$68$		0			0
$69$	−15.6112	−	113.906i	−0.226249	−	1.65081i
$70$		0			0
$71$		−	71.5235i		−	1.00737i	−0.863886	−	0.503687i	$-0.831977\pi$
$71$		−	71.5235i		−	1.00737i	0.863886	−	0.503687i	$-0.168023\pi$
$72$		0			0
$73$			122.276i			1.67502i	0.546422	+	0.837510i	$0.315989\pi$
$73$			122.276i			1.67502i	−0.546422	+	0.837510i	$0.684011\pi$
$74$		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	0.839704	−	0.543044i	$-0.182728\pi$
$79$	−3.98462	−	6.90157i	−0.0504382	−	0.0873616i	−0.890142	+	0.455683i	$0.849395\pi$
$80$		0			0
$81$	−70.9916	−	39.0024i	−0.876440	−	0.481512i
$82$		0			0
$83$	−52.1235	−	90.2806i	−0.627994	−	1.08772i	−0.987954	−	0.154750i	$-0.950543\pi$
$83$	−52.1235	−	90.2806i	−0.627994	−	1.08772i	0.359960	−	0.932968i	$-0.382790\pi$
$84$		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	$-0.983232\pi$
$89$		−	9.37245i		−	0.105308i	0.998613	−	0.0526542i	$-0.0167681\pi$
$90$		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	−0.560036	−	0.828468i	$-0.689213\pi$
$97$	−11.8902	+	6.86481i	−0.122579	+	0.0707713i	0.437457	+	0.899240i	$0.355879\pi$
$98$		0			0
$99$	3.32797	+	11.9131i	0.0336159	+	0.120334i
$100$		0			0
$101$	−103.509	+	59.7611i	−1.02484	+	0.591694i	−0.915503	−	0.402310i	$-0.868207\pi$
$101$	−103.509	+	59.7611i	−1.02484	+	0.591694i	−0.109341	+	0.994004i	$0.534874\pi$
$102$		0			0
$103$	−69.7254	−	40.2560i	−0.676945	−	0.390835i	0.121758	−	0.992560i	$-0.461147\pi$
$103$	−69.7254	−	40.2560i	−0.676945	−	0.390835i	−0.798703	+	0.601725i	$0.794480\pi$
$104$		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	0.262813	+	0.964847i	$0.415350\pi$
$113$	−79.5718	+	137.822i	−0.704175	+	1.21967i	−0.966988	+	0.254821i	$0.917984\pi$
$114$		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	$0.310011\pi$
$127$			210.083i			1.65420i	−0.562055	+	0.827100i	$0.689989\pi$
$128$		0			0
$129$	80.6716	−	197.719i	0.625361	−	1.53270i
$130$		0			0
$131$	−5.70580	−	3.29424i	−0.0435557	−	0.0251469i	0.478064	−	0.878325i	$-0.341339\pi$
$131$	−5.70580	−	3.29424i	−0.0435557	−	0.0251469i	−0.521620	+	0.853178i	$0.674672\pi$
$132$		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	−0.930144	−	0.367195i	$-0.880318\pi$
$137$	−107.281	−	185.816i	−0.783072	−	1.35632i	0.147072	−	0.989126i	$-0.453015\pi$
$138$		0			0
$139$	−40.7194	+	70.5281i	−0.292946	+	0.507397i	−0.974505	−	0.224366i	$-0.927969\pi$
$139$	−40.7194	+	70.5281i	−0.292946	+	0.507397i	0.681559	+	0.731763i	$0.261302\pi$
$140$		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	−0.995963	−	0.0897663i	$-0.971388\pi$
$149$	−234.181	−	135.204i	−1.57168	−	0.907412i	−0.575721	−	0.817646i	$-0.695279\pi$
$150$		0			0
$151$	−52.7441	−	91.3555i	−0.349299	−	0.605003i	0.636826	−	0.771007i	$-0.280247\pi$
$151$	−52.7441	−	91.3555i	−0.349299	−	0.605003i	−0.986125	+	0.166004i	$0.946914\pi$
$152$		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	0.529283	−	0.848445i	$-0.322461\pi$
$157$	9.28642	+	5.36152i	0.0591492	+	0.0341498i	−0.470134	+	0.882595i	$0.655794\pi$
$158$		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	$0.157724\pi$
$163$			155.005i			0.950950i	−0.879729	+	0.475475i	$0.842276\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	38.0386	−	65.8848i	0.227776	−	0.394519i	−0.729373	−	0.684117i	$-0.760188\pi$
$167$	38.0386	−	65.8848i	0.227776	−	0.394519i	0.957149	+	0.289597i	$0.0935213\pi$
$168$		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	0.763728	−	0.645538i	$-0.223367\pi$
$173$	−30.6536	−	53.0935i	−0.177188	−	0.306899i	−0.940916	+	0.338639i	$0.890033\pi$
$174$		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	$0.307813\pi$
$179$			294.705i			1.64640i	−0.567752	+	0.823200i	$0.692187\pi$
$180$		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	−0.0654037	−	0.997859i	$-0.520834\pi$
$191$	146.319	−	84.4770i	0.766066	−	0.442288i	0.831469	+	0.555571i	$0.187500\pi$
$192$		0			0
$193$	175.481	+	101.314i	0.909226	+	0.524942i	0.880182	−	0.474636i	$-0.157420\pi$
$193$	175.481	+	101.314i	0.909226	+	0.524942i	0.0290438	+	0.999578i	$0.490754\pi$
$194$		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	−0.903925	−	0.427691i	$-0.859327\pi$
$211$	−17.2115	+	29.8111i	−0.0815710	+	0.141285i	0.822354	+	0.568976i	$0.192660\pi$
$212$		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	−0.854805	−	0.518949i	$-0.826323\pi$
$223$	−185.711	+	107.220i	−0.832785	+	0.480808i	0.0220206	+	0.999758i	$0.492990\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	218.068	+	377.705i	0.960653	+	1.66390i	0.720865	+	0.693076i	$0.243745\pi$
$227$	218.068	+	377.705i	0.960653	+	1.66390i	0.239789	+	0.970825i	$0.422922\pi$
$228$		0			0
$229$	181.933	−	315.117i	0.794466	−	1.37605i	−0.128712	−	0.991682i	$-0.541084\pi$
$229$	181.933	−	315.117i	0.794466	−	1.37605i	0.923178	−	0.384373i	$-0.125582\pi$
$230$		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	0.896436	−	0.443174i	$-0.146148\pi$
$239$	229.644	+	132.585i	0.960853	+	0.554749i	0.0644178	+	0.997923i	$0.479481\pi$
$240$		0			0
$241$	−61.4106	−	106.366i	−0.254816	−	0.441354i	0.710030	−	0.704172i	$-0.248681\pi$
$241$	−61.4106	−	106.366i	−0.254816	−	0.441354i	−0.964845	+	0.262818i	$0.915348\pi$
$242$		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	$0.143674\pi$
$251$			218.969i			0.872388i	−0.899853	+	0.436194i	$0.856326\pi$
$252$		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	−0.117404	−	0.993084i	$-0.537457\pi$
$257$	205.943	−	356.703i	0.801334	−	1.38795i	0.918738	−	0.394867i	$-0.129209\pi$
$258$		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	−0.929919	−	0.367765i	$-0.880123\pi$
$263$	−206.048	−	356.886i	−0.783453	−	1.35698i	0.146466	−	0.989216i	$-0.453210\pi$
$264$		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	$0.253620\pi$
$269$			384.725i			1.43020i	−0.699020	+	0.715102i	$0.746380\pi$
$270$		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	−0.681737	+	0.731598i	$0.738775\pi$
$277$	−458.764	+	264.867i	−1.65619	+	0.956200i	−0.974451	+	0.224602i	$0.927892\pi$
$278$		0			0
$279$	−140.841	−	137.883i	−0.504805	−	0.494205i
$280$		0			0
$281$	81.2085	−	46.8857i	0.288998	−	0.166853i	−0.348492	−	0.937312i	$-0.613306\pi$
$281$	81.2085	−	46.8857i	0.288998	−	0.166853i	0.637490	+	0.770459i	$0.279973\pi$
$282$		0			0
$283$	−43.7017	−	25.2312i	−0.154423	−	0.0891561i	0.420797	−	0.907155i	$-0.361750\pi$
$283$	−43.7017	−	25.2312i	−0.154423	−	0.0891561i	−0.575220	+	0.817999i	$0.695084\pi$
$284$		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	−0.591276	−	0.806469i	$-0.701376\pi$
$293$	118.016	−	204.410i	0.402785	−	0.697643i	0.994061	+	0.108826i	$0.0347090\pi$
$294$		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	$-0.959256\pi$
$307$		−	78.3780i		−	0.255303i	0.991819	−	0.127651i	$-0.0407439\pi$
$308$		0			0
$309$	239.299	−	32.7967i	0.774430	−	0.106138i
$310$		0			0
$311$	−217.139	−	125.365i	−0.698195	−	0.403103i	0.108480	−	0.994099i	$-0.465402\pi$
$311$	−217.139	−	125.365i	−0.698195	−	0.403103i	−0.806675	+	0.590995i	$0.798735\pi$
$312$		0			0
$313$	108.756	−	62.7902i	0.347463	−	0.200608i	−0.316104	−	0.948724i	$-0.602375\pi$
$313$	108.756	−	62.7902i	0.347463	−	0.200608i	0.663567	+	0.748117i	$0.269042\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−79.2443	−	137.255i	−0.249982	−	0.432982i	0.713538	−	0.700616i	$-0.247091\pi$
$317$	−79.2443	−	137.255i	−0.249982	−	0.432982i	−0.963521	+	0.267634i	$0.913758\pi$
$318$		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	0.963982	+	0.265969i	$0.0856919\pi$
$331$	235.780	+	408.383i	0.712327	+	1.23379i	−0.251655	+	0.967817i	$0.580975\pi$
$332$		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	0.371313	−	0.928508i	$-0.378908\pi$
$337$	−83.2869	−	48.0857i	−0.247142	−	0.142688i	−0.618455	+	0.785820i	$0.712241\pi$
$338$		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	−0.601038	−	0.799220i	$-0.705246\pi$
$347$	135.894	−	235.376i	0.391626	−	0.678317i	0.992664	+	0.120904i	$0.0385793\pi$
$348$		0			0
$349$	166.723	+	288.773i	0.477717	+	0.827430i	0.999674	−	0.0255418i	$-0.00813110\pi$
$349$	166.723	+	288.773i	0.477717	+	0.827430i	−0.521957	+	0.852972i	$0.674798\pi$
$350$		0			0
$351$	−66.7903	+	578.301i	−0.190286	+	1.64758i
$352$		0			0
$353$	−168.782	−	292.339i	−0.478136	−	0.828156i	0.521550	−	0.853221i	$-0.325354\pi$
$353$	−168.782	−	292.339i	−0.478136	−	0.828156i	−0.999686	+	0.0250648i	$0.992021\pi$
$354$		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	$-0.651075\pi$
$359$		−	638.638i		−	1.77894i	0.456997	−	0.889468i	$-0.348925\pi$
$360$		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	−0.634384	−	0.773018i	$-0.718746\pi$
$367$	−103.539	+	59.7781i	−0.282122	+	0.162883i	0.352262	+	0.935902i	$0.385413\pi$
$368$		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	0.614555	−	0.788874i	$-0.289336\pi$
$373$	89.0157	+	51.3932i	0.238648	+	0.137783i	−0.375907	+	0.926657i	$0.622669\pi$
$374$		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	−0.978814	−	0.204754i	$-0.934361\pi$
$383$	−119.529	+	207.029i	−0.312085	+	0.540547i	0.666729	+	0.745301i	$0.267694\pi$
$384$		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	−0.651097	−	0.758995i	$-0.725691\pi$
$389$	−124.222	+	71.7196i	−0.319337	+	0.184369i	0.331760	+	0.943364i	$0.392357\pi$
$390$		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	$0.0744731\pi$
$397$			184.077i			0.463671i	−0.972755	+	0.231836i	$0.925527\pi$
$398$		0			0
$399$	23.3331	−	57.1873i	0.0584790	−	0.143327i
$400$		0			0
$401$	102.303	+	59.0645i	0.255119	+	0.147293i	0.622106	−	0.782933i	$-0.286277\pi$
$401$	102.303	+	59.0645i	0.255119	+	0.147293i	−0.366987	+	0.930226i	$0.619611\pi$
$402$		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	0.195028	+	0.980798i	$0.437520\pi$
$409$	−307.520	+	532.640i	−0.751882	+	1.30230i	−0.946910	+	0.321499i	$0.895813\pi$
$410$		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	0.645040	−	0.764149i	$-0.276841\pi$
$419$	128.125	+	73.9729i	0.305787	+	0.176546i	−0.339253	+	0.940695i	$0.610174\pi$
$420$		0			0
$421$	42.4834	+	73.5835i	0.100911	+	0.174783i	0.912060	−	0.410056i	$-0.134491\pi$
$421$	42.4834	+	73.5835i	0.100911	+	0.174783i	−0.811149	+	0.584839i	$0.801158\pi$
$422$		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	$-0.836964\pi$
$431$		−	422.458i		−	0.980180i	0.871672	−	0.490090i	$-0.163036\pi$
$432$		0			0
$433$			534.169i			1.23365i	0.787102	+	0.616823i	$0.211581\pi$
$433$			534.169i			1.23365i	−0.787102	+	0.616823i	$0.788419\pi$
$434$		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	0.830443	−	0.557104i	$-0.188088\pi$
$439$	−29.5206	−	51.1312i	−0.0672452	−	0.116472i	−0.897688	+	0.440632i	$0.854754\pi$
$440$		0			0
$441$	−123.778	−	121.179i	−0.280676	−	0.274782i
$442$		0			0
$443$	32.4581	+	56.2191i	0.0732689	+	0.126905i	0.900332	−	0.435203i	$-0.143324\pi$
$443$	32.4581	+	56.2191i	0.0732689	+	0.126905i	−0.827063	+	0.562109i	$0.809990\pi$
$444$		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	$-0.793183\pi$
$449$		−	543.268i		−	1.20995i	0.796244	−	0.604976i	$-0.206817\pi$
$450$		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	0.367427	−	0.930052i	$-0.380239\pi$
$457$	619.962	−	357.935i	1.35659	−	0.783228i	0.989163	+	0.146825i	$0.0469053\pi$
$458$		0			0
$459$	271.547	+	627.153i	0.591607	+	1.36635i
$460$		0			0
$461$	130.777	−	75.5039i	0.283680	−	0.163783i	−0.351408	−	0.936222i	$-0.614297\pi$
$461$	130.777	−	75.5039i	0.283680	−	0.163783i	0.635088	+	0.772440i	$0.280964\pi$
$462$		0			0
$463$	−284.185	−	164.074i	−0.613790	−	0.354372i	0.160658	−	0.987010i	$-0.448639\pi$
$463$	−284.185	−	164.074i	−0.613790	−	0.354372i	−0.774447	+	0.632639i	$0.781972\pi$
$464$		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	−0.869622	−	0.493718i	$-0.835638\pi$
$479$	−420.016	+	242.497i	−0.876861	+	0.506256i	−0.00723877	+	0.999974i	$0.502304\pi$
$480$		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	$0.287205\pi$
$487$			764.340i			1.56949i	−0.619821	+	0.784743i	$0.712795\pi$
$488$		0			0
$489$	−285.036	−	367.414i	−0.582896	−	0.751358i
$490$		0			0
$491$	−387.463	−	223.702i	−0.789129	−	0.455604i	0.0505265	−	0.998723i	$-0.483910\pi$
$491$	−387.463	−	223.702i	−0.789129	−	0.455604i	−0.839656	+	0.543119i	$0.817243\pi$
$492$		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	−0.662468	−	0.749090i	$-0.730491\pi$
$499$	158.431	−	274.410i	0.317497	−	0.549920i	0.979965	+	0.199170i	$0.0638244\pi$
$500$		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	0.630017	−	0.776581i	$-0.283048\pi$
$509$	138.696	+	80.0759i	0.272486	+	0.157320i	−0.357531	+	0.933901i	$0.616381\pi$
$510$		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	$0.0832346\pi$
$521$			269.377i			0.517039i	−0.966006	+	0.258519i	$0.916765\pi$
$522$		0			0
$523$		−	224.057i		−	0.428407i	−0.976789	−	0.214204i	$-0.931284\pi$
$523$		−	224.057i		−	0.428407i	0.976789	−	0.214204i	$-0.0687156\pi$
$524$		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	−0.723437	−	0.690391i	$-0.757439\pi$
$547$	−266.531	+	153.882i	−0.487259	+	0.281319i	0.236178	+	0.971710i	$0.424105\pi$
$548$		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	0.182648	+	0.983178i	$0.441533\pi$
$563$	−427.955	+	741.240i	−0.760133	+	1.31659i	−0.942781	+	0.333411i	$0.891800\pi$
$564$		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	−0.679447	−	0.733725i	$-0.737780\pi$
$569$	−218.351	+	126.065i	−0.383746	+	0.221556i	0.295701	+	0.955281i	$0.404447\pi$
$570$		0			0
$571$	−185.624	+	321.511i	−0.325087	+	0.563066i	−0.981530	−	0.191309i	$-0.938727\pi$
$571$	−185.624	+	321.511i	−0.325087	+	0.563066i	0.656443	+	0.754375i	$0.272060\pi$
$572$		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	$-0.773877\pi$
$577$		−	752.555i		−	1.30425i	0.758109	−	0.652127i	$-0.226123\pi$
$578$		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	0.974860	+	0.222816i	$0.0715250\pi$
$587$	399.392	+	691.767i	0.680395	+	1.17848i	−0.294466	+	0.955662i	$0.595142\pi$
$588$		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	0.590811	−	0.806810i	$-0.298808\pi$
$599$	112.311	+	64.8430i	0.187498	+	0.108252i	−0.403313	+	0.915062i	$0.632141\pi$
$600$		0			0
$601$	−110.390	−	191.201i	−0.183677	−	0.318139i	0.759453	−	0.650563i	$-0.225467\pi$
$601$	−110.390	−	191.201i	−0.183677	−	0.318139i	−0.943130	+	0.332424i	$0.892133\pi$
$602$		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	0.0944034	−	0.995534i	$-0.469906\pi$
$607$	−437.376	−	252.519i	−0.720553	−	0.416011i	−0.814956	+	0.579523i	$0.803239\pi$
$608$		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	$0.157451\pi$
$613$			582.009i			0.949444i	−0.880136	+	0.474722i	$0.842549\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	301.668	−	522.504i	0.488927	−	0.846846i	−0.510992	−	0.859585i	$-0.670722\pi$
$617$	301.668	−	522.504i	0.488927	−	0.846846i	0.999919	+	0.0127394i	$0.00405517\pi$
$618$		0			0
$619$	160.899	+	278.685i	0.259933	+	0.450218i	0.966224	−	0.257704i	$-0.0829661\pi$
$619$	160.899	+	278.685i	0.259933	+	0.450218i	−0.706290	+	0.707922i	$0.749633\pi$
$620$		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	−0.782917	+	0.622126i	$0.786269\pi$
$641$	−1098.13	+	634.006i	−1.71315	+	0.989089i	−0.930236	+	0.366963i	$0.880398\pi$
$642$		0			0
$643$	295.058	+	170.352i	0.458877	+	0.264933i	0.711572	−	0.702613i	$-0.247984\pi$
$643$	295.058	+	170.352i	0.458877	+	0.264933i	−0.252695	+	0.967546i	$0.581317\pi$
$644$		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	0.339461	+	0.940620i	$0.389755\pi$
$653$	−421.100	+	729.367i	−0.644870	+	1.11695i	−0.984331	+	0.176328i	$0.943578\pi$
$654$		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	0.0833967	−	0.996516i	$-0.473423\pi$
$659$	651.160	−	375.948i	0.988104	−	0.570482i	0.904707	+	0.426035i	$0.140090\pi$
$660$		0			0
$661$	−45.6212	+	79.0183i	−0.0690185	+	0.119544i	−0.898470	−	0.439036i	$-0.855320\pi$
$661$	−45.6212	+	79.0183i	−0.0690185	+	0.119544i	0.829451	+	0.558579i	$0.188653\pi$
$662$		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	0.403456	−	0.914999i	$-0.367809\pi$
$673$	940.583	−	543.046i	1.39760	−	0.806903i	0.994140	+	0.108096i	$0.0344754\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	384.990	+	666.823i	0.568671	+	0.984967i	0.996698	+	0.0812011i	$0.0258756\pi$
$677$	384.990	+	666.823i	0.568671	+	0.984967i	−0.428027	+	0.903766i	$0.640791\pi$
$678$		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	0.978351	+	0.206953i	$0.0663547\pi$
$691$	461.866	+	799.975i	0.668402	+	1.15771i	−0.309949	+	0.950753i	$0.600312\pi$
$692$		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	$0.0372409\pi$
$701$			163.654i			0.233458i	−0.993164	+	0.116729i	$0.962759\pi$
$702$		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	0.857739	−	0.514086i	$-0.171869\pi$
$709$	−11.5863	−	20.0680i	−0.0163417	−	0.0283047i	−0.874081	+	0.485781i	$0.838535\pi$
$710$		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	$-0.972830\pi$
$719$		−	122.596i		−	0.170509i	0.996359	−	0.0852545i	$-0.0271703\pi$
$720$		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	−0.253554	−	0.967321i	$-0.581600\pi$
$727$	332.525	−	191.983i	0.457393	−	0.264076i	0.710947	+	0.703245i	$0.248266\pi$
$728$		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	0.506454	−	0.862267i	$-0.330956\pi$
$733$	9.48169	+	5.47425i	0.0129355	+	0.00746829i	−0.493518	+	0.869735i	$0.664289\pi$
$734$		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	0.321741	+	0.946828i	$0.395732\pi$
$743$	−489.716	+	848.213i	−0.659106	+	1.14161i	−0.980847	+	0.194778i	$0.937601\pi$
$744$		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	−0.830225	−	0.557428i	$-0.811788\pi$
$751$	50.7936	−	87.9772i	0.0676347	−	0.117147i	0.897860	+	0.440282i	$0.145121\pi$
$752$		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	$0.0558676\pi$
$757$			264.365i			0.349227i	−0.984637	+	0.174614i	$0.944132\pi$
$758$		0			0
$759$	96.8548	+	124.847i	0.127608	+	0.164488i
$760$		0			0
$761$	217.673	+	125.674i	0.286036	+	0.165143i	0.636153	−	0.771563i	$-0.280525\pi$
$761$	217.673	+	125.674i	0.286036	+	0.165143i	−0.350117	+	0.936706i	$0.613858\pi$
$762$		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	−0.725068	−	0.688677i	$-0.758192\pi$
$769$	179.852	−	311.512i	0.233878	−	0.405088i	0.958946	+	0.283589i	$0.0915252\pi$
$770$		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	−0.447120	−	0.894474i	$-0.647550\pi$
$787$	−1137.46	−	656.715i	−1.44532	−	0.834454i	−0.998197	+	0.0600202i	$0.980883\pi$
$788$		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	−0.692141	−	0.721763i	$-0.743332\pi$
$797$	222.359	−	385.136i	0.278995	−	0.483233i	0.971135	+	0.238530i	$0.0766655\pi$
$798$		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	$-0.853557\pi$
$809$		−	718.402i		−	0.888012i	0.896024	−	0.444006i	$-0.146443\pi$
$810$		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	−0.629418	+	0.777067i	$0.716707\pi$
$821$	−1327.63	+	766.507i	−1.61709	+	0.933626i	−0.987669	+	0.156559i	$0.949960\pi$
$822$		0			0
$823$	−684.403	−	395.140i	−0.831595	−	0.480122i	0.0228034	−	0.999740i	$-0.492741\pi$
$823$	−684.403	−	395.140i	−0.831595	−	0.480122i	−0.854399	+	0.519618i	$0.826074\pi$
$824$		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	0.304508	−	0.952510i	$-0.401508\pi$
$839$	1075.31	−	620.832i	1.28166	−	0.739966i	0.977152	+	0.212543i	$0.0681747\pi$
$840$		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	0.215356	−	0.976536i	$-0.430909\pi$
$853$	996.935	−	575.580i	1.16874	−	0.674772i	0.953383	+	0.301764i	$0.0975753\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	824.101	+	1427.38i	0.961611	+	1.66556i	0.718456	+	0.695572i	$0.244849\pi$
$857$	824.101	+	1427.38i	0.961611	+	1.66556i	0.243155	+	0.969987i	$0.421818\pi$
$858$		0			0
$859$	−279.406	+	483.945i	−0.325269	+	0.563382i	−0.981567	−	0.191120i	$-0.938788\pi$
$859$	−279.406	+	483.945i	−0.325269	+	0.563382i	0.656298	+	0.754502i	$0.272121\pi$
$860$		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	0.954456	−	0.298352i	$-0.0964368\pi$
$877$	1028.99	+	594.086i	1.17330	+	0.677407i	0.218848	+	0.975759i	$0.429770\pi$
$878$		0			0
$879$	96.1480	+	701.537i	0.109383	+	0.798108i
$880$		0			0
$881$			663.144i			0.752717i	0.926474	+	0.376359i	$0.122824\pi$
$881$			663.144i			0.752717i	−0.926474	+	0.376359i	$0.877176\pi$
$882$		0			0
$883$		−	1447.52i		−	1.63932i	−0.572852	−	0.819659i	$-0.694163\pi$
$883$		−	1447.52i		−	1.63932i	0.572852	−	0.819659i	$-0.305837\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−323.166	+	559.739i	−0.364335	+	0.631047i	−0.988669	−	0.150110i	$-0.952037\pi$
$887$	−323.166	+	559.739i	−0.364335	+	0.631047i	0.624334	+	0.781158i	$0.285370\pi$
$888$		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	−0.113613	−	0.993525i	$-0.536242\pi$
$907$	625.829	−	361.322i	0.689999	−	0.398371i	0.803612	+	0.595154i	$0.202909\pi$
$908$		0			0
$909$	289.420	+	1036.03i	0.318394	+	1.13975i
$910$		0			0
$911$	1278.01	−	737.862i	1.40287	−	0.809947i	0.408184	−	0.912900i	$-0.366162\pi$
$911$	1278.01	−	737.862i	1.40287	−	0.809947i	0.994686	+	0.102952i	$0.0328289\pi$
$912$		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	−0.214498	−	0.976724i	$-0.568812\pi$
$929$	486.909	−	281.117i	0.524121	−	0.302601i	0.738619	+	0.674123i	$0.235478\pi$
$930$		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	$0.252933\pi$
$937$			1337.27i			1.42718i	−0.700562	+	0.713592i	$0.747067\pi$
$938$		0			0
$939$	−142.324	+	348.824i	−0.151570	+	0.371484i
$940$		0			0
$941$	918.441	+	530.262i	0.976026	+	0.563509i	0.901068	−	0.433678i	$-0.142784\pi$
$941$	918.441	+	530.262i	0.976026	+	0.563509i	0.0749581	+	0.997187i	$0.476118\pi$
$942$		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	0.941640	+	0.336621i	$0.109284\pi$
$947$	721.938	+	1250.43i	0.762342	+	1.32042i	−0.179298	+	0.983795i	$0.557383\pi$
$948$		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	0.555287	−	0.831659i	$-0.312608\pi$
$967$	108.975	+	62.9165i	0.112693	+	0.0650636i	−0.442594	+	0.896722i	$0.645942\pi$
$968$		0			0
$969$	−149.523	+	115.998i	−0.154306	+	0.119709i
$970$		0			0
$971$		−	20.0762i		−	0.0206758i	−0.999947	−	0.0103379i	$-0.996709\pi$
$971$		−	20.0762i		−	0.0206758i	0.999947	−	0.0103379i	$-0.00329072\pi$
$972$		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	0.309461	+	0.950912i	$0.399851\pi$
$977$	−653.401	+	1131.72i	−0.668783	+	1.15837i	−0.978245	+	0.207455i	$0.933482\pi$
$978$		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	−0.983052	−	0.183327i	$-0.941313\pi$
$983$	−639.237	−	1107.19i	−0.650292	−	1.12634i	0.332760	−	0.943011i	$-0.392020\pi$
$984$		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	−0.310096	−	0.950705i	$-0.600361\pi$
$997$	357.116	−	206.181i	0.358191	−	0.206802i	0.668287	+	0.743904i	$0.267028\pi$
$998$		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.149.4		32
3.2	odd	2		2700.3.u.d.449.4		32
5.2	odd	4		900.3.p.e.401.6	yes	16
5.3	odd	4		900.3.p.d.401.3	yes	16
5.4	even	2	inner	900.3.u.d.149.13		32
9.2	odd	6	inner	900.3.u.d.749.13		32
9.7	even	3		2700.3.u.d.2249.13		32
15.2	even	4		2700.3.p.d.2501.2		16
15.8	even	4		2700.3.p.e.2501.7		16
15.14	odd	2		2700.3.u.d.449.13		32
45.2	even	12		900.3.p.e.101.6	yes	16
45.7	odd	12		2700.3.p.d.1601.2		16
45.29	odd	6	inner	900.3.u.d.749.4		32
45.34	even	6		2700.3.u.d.2249.4		32
45.38	even	12		900.3.p.d.101.3	✓	16
45.43	odd	12		2700.3.p.e.1601.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.3	✓	16	45.38	even	12
900.3.p.d.401.3	yes	16	5.3	odd	4
900.3.p.e.101.6	yes	16	45.2	even	12
900.3.p.e.401.6	yes	16	5.2	odd	4
900.3.u.d.149.4		32	1.1	even	1	trivial
900.3.u.d.149.13		32	5.4	even	2	inner
900.3.u.d.749.4		32	45.29	odd	6	inner
900.3.u.d.749.13		32	9.2	odd	6	inner
2700.3.p.d.1601.2		16	45.7	odd	12
2700.3.p.d.2501.2		16	15.2	even	4
2700.3.p.e.1601.7		16	45.43	odd	12
2700.3.p.e.2501.7		16	15.8	even	4
2700.3.u.d.449.4		32	3.2	odd	2
2700.3.u.d.449.13		32	15.14	odd	2
2700.3.u.d.2249.4		32	45.34	even	6
2700.3.u.d.2249.13		32	9.7	even	3

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more