LMFDB - Embedded newform 900.3.u.c.149.2

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.2
Character	$\chi$	$=$	900.149
Dual form			900.3.u.c.749.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.87949 - 0.841761i) q^{3} +(10.3705 - 5.98742i) q^{7} +(7.58288 + 4.84768i) q^{9} +O(q^{10})$	\(q+(-2.87949 - 0.841761i) q^{3} +(10.3705 - 5.98742i) q^{7} +(7.58288 + 4.84768i) q^{9} +(7.43429 - 4.29219i) q^{11} +(14.4628 + 8.35009i) q^{13} +22.1715 q^{17} -26.9572 q^{19} +(-34.9017 + 8.51119i) q^{21} +(-19.3998 + 33.6015i) q^{23} +(-17.7542 - 20.3418i) q^{27} +(-8.44943 + 4.87828i) q^{29} +(6.01648 - 10.4208i) q^{31} +(-25.0199 + 6.10140i) q^{33} +25.0544i q^{37} +(-34.6166 - 36.2181i) q^{39} +(34.8030 + 20.0935i) q^{41} +(67.8113 - 39.1509i) q^{43} +(37.1715 + 64.3830i) q^{47} +(47.1983 - 81.7498i) q^{49} +(-63.8424 - 18.6631i) q^{51} +13.0311 q^{53} +(77.6229 + 22.6915i) q^{57} +(-32.9009 - 18.9954i) q^{59} +(-4.56537 - 7.90745i) q^{61} +(107.663 + 4.87104i) q^{63} +(-20.8770 - 12.0533i) q^{67} +(84.1460 - 80.4251i) q^{69} +43.7125i q^{71} +7.68710i q^{73} +(51.3982 - 89.0244i) q^{77} +(-19.3250 - 33.4718i) q^{79} +(34.0001 + 73.5187i) q^{81} +(-42.1875 - 73.0708i) q^{83} +(28.4364 - 6.93454i) q^{87} +61.5351i q^{89} +199.982 q^{91} +(-26.0962 + 24.9422i) q^{93} +(54.2630 - 31.3288i) q^{97} +(77.1805 + 3.49189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 52 q^{9}+O(q^{10}) $ 24 * q - 52 * q^9	$ 24 q - 52 q^{9} + 96 q^{11} - 144 q^{19} - 256 q^{21} - 300 q^{29} - 24 q^{31} - 80 q^{39} + 180 q^{41} - 96 q^{49} - 288 q^{51} - 96 q^{59} - 156 q^{61} + 300 q^{69} - 240 q^{79} + 868 q^{81} + 240 q^{91} + 240 q^{99}+O(q^{100}) $ 24 * q - 52 * q^9 + 96 * q^11 - 144 * q^19 - 256 * q^21 - 300 * q^29 - 24 * q^31 - 80 * q^39 + 180 * q^41 - 96 * q^49 - 288 * q^51 - 96 * q^59 - 156 * q^61 + 300 * q^69 - 240 * q^79 + 868 * q^81 + 240 * q^91 + 240 * 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
$3$	−2.87949	−	0.841761i	−0.959829	−	0.280587i
$3$	−2.87949	−	0.841761i	−0.959829	−	0.280587i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	10.3705	−	5.98742i	1.48150	−	0.855345i	0.481721	−	0.876324i	$-0.340012\pi$
$7$	10.3705	−	5.98742i	1.48150	−	0.855345i	0.999780	+	0.0209794i	$0.00667844\pi$
$8$		0			0
$9$	7.58288	+	4.84768i	0.842542	+	0.538631i
$10$		0			0
$11$	7.43429	−	4.29219i	0.675845	−	0.390199i	−0.122443	−	0.992476i	$-0.539073\pi$
$11$	7.43429	−	4.29219i	0.675845	−	0.390199i	0.798288	+	0.602277i	$0.205740\pi$
$12$		0			0
$13$	14.4628	+	8.35009i	1.11252	+	0.642314i	0.939481	−	0.342601i	$-0.111308\pi$
$13$	14.4628	+	8.35009i	1.11252	+	0.642314i	0.173040	+	0.984915i	$0.444641\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	22.1715			1.30420			0.652102	−	0.758131i	$-0.273887\pi$
$17$	22.1715			1.30420			0.652102	+	0.758131i	$0.273887\pi$
$18$		0			0
$19$	−26.9572			−1.41880			−0.709400	−	0.704806i	$-0.751034\pi$
$19$	−26.9572			−1.41880			−0.709400	+	0.704806i	$0.751034\pi$
$20$		0			0
$21$	−34.9017	+	8.51119i	−1.66199	+	0.405295i
$22$		0			0
$23$	−19.3998	+	33.6015i	−0.843472	+	1.46094i	0.0434704	+	0.999055i	$0.486159\pi$
$23$	−19.3998	+	33.6015i	−0.843472	+	1.46094i	−0.886942	+	0.461881i	$0.847175\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−17.7542	−	20.3418i	−0.657563	−	0.753400i
$28$		0			0
$29$	−8.44943	+	4.87828i	−0.291360	+	0.168217i	−0.638555	−	0.769576i	$-0.720467\pi$
$29$	−8.44943	+	4.87828i	−0.291360	+	0.168217i	0.347195	+	0.937793i	$0.387134\pi$
$30$		0			0
$31$	6.01648	−	10.4208i	0.194080	−	0.336156i	−0.752519	−	0.658571i	$-0.771161\pi$
$31$	6.01648	−	10.4208i	0.194080	−	0.336156i	0.946598	+	0.322415i	$0.104495\pi$
$32$		0			0
$33$	−25.0199	+	6.10140i	−0.758180	+	0.184891i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			25.0544i			0.677147i	0.940940	+	0.338574i	$0.109944\pi$
$37$			25.0544i			0.677147i	−0.940940	+	0.338574i	$0.890056\pi$
$38$		0			0
$39$	−34.6166	−	36.2181i	−0.887604	−	0.928670i
$40$		0			0
$41$	34.8030	+	20.0935i	0.848854	+	0.490086i	0.860264	−	0.509849i	$-0.170299\pi$
$41$	34.8030	+	20.0935i	0.848854	+	0.490086i	−0.0114101	+	0.999935i	$0.503632\pi$
$42$		0			0
$43$	67.8113	−	39.1509i	1.57701	−	0.910485i	0.581732	−	0.813381i	$-0.302375\pi$
$43$	67.8113	−	39.1509i	1.57701	−	0.910485i	0.995274	−	0.0971043i	$-0.0309580\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	37.1715	+	64.3830i	0.790883	+	1.36985i	0.925421	+	0.378942i	$0.123712\pi$
$47$	37.1715	+	64.3830i	0.790883	+	1.36985i	−0.134537	+	0.990909i	$0.542955\pi$
$48$		0			0
$49$	47.1983	−	81.7498i	0.963231	−	1.66836i
$50$		0			0
$51$	−63.8424	−	18.6631i	−1.25181	−	0.365943i
$52$		0			0
$53$	13.0311			0.245869			0.122934	−	0.992415i	$-0.460770\pi$
$53$	13.0311			0.245869			0.122934	+	0.992415i	$0.460770\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	77.6229	+	22.6915i	1.36181	+	0.398097i
$58$		0			0
$59$	−32.9009	−	18.9954i	−0.557643	−	0.321955i	0.194556	−	0.980891i	$-0.437673\pi$
$59$	−32.9009	−	18.9954i	−0.557643	−	0.321955i	−0.752199	+	0.658936i	$0.771007\pi$
$60$		0			0
$61$	−4.56537	−	7.90745i	−0.0748421	−	0.129630i	0.826175	−	0.563413i	$-0.190512\pi$
$61$	−4.56537	−	7.90745i	−0.0748421	−	0.129630i	−0.901018	+	0.433783i	$0.857179\pi$
$62$		0			0
$63$	107.663	+	4.87104i	1.70894	+	0.0773180i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−20.8770	−	12.0533i	−0.311597	−	0.179901i	0.336044	−	0.941846i	$-0.390911\pi$
$67$	−20.8770	−	12.0533i	−0.311597	−	0.179901i	−0.647641	+	0.761946i	$0.724244\pi$
$68$		0			0
$69$	84.1460	−	80.4251i	1.21951	−	1.16558i
$70$		0			0
$71$			43.7125i			0.615668i	0.951440	+	0.307834i	$0.0996042\pi$
$71$			43.7125i			0.615668i	−0.951440	+	0.307834i	$0.900396\pi$
$72$		0			0
$73$			7.68710i			0.105303i	0.998613	+	0.0526514i	$0.0167672\pi$
$73$			7.68710i			0.105303i	−0.998613	+	0.0526514i	$0.983233\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	51.3982	−	89.0244i	0.667510	−	1.15616i
$78$		0			0
$79$	−19.3250	−	33.4718i	−0.244620	−	0.423694i	0.717405	−	0.696657i	$-0.245330\pi$
$79$	−19.3250	−	33.4718i	−0.244620	−	0.423694i	−0.962025	+	0.272963i	$0.911997\pi$
$80$		0			0
$81$	34.0001	+	73.5187i	0.419754	+	0.907638i
$82$		0			0
$83$	−42.1875	−	73.0708i	−0.508283	−	0.880372i	−0.999954	−	0.00959062i	$-0.996947\pi$
$83$	−42.1875	−	73.0708i	−0.508283	−	0.880372i	0.491671	−	0.870781i	$-0.336386\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	28.4364	−	6.93454i	0.326855	−	0.0797074i
$88$		0			0
$89$			61.5351i			0.691406i	0.938344	+	0.345703i	$0.112360\pi$
$89$			61.5351i			0.691406i	−0.938344	+	0.345703i	$0.887640\pi$
$90$		0			0
$91$	199.982			2.19760
$92$		0			0
$93$	−26.0962	+	24.9422i	−0.280604	+	0.268196i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	54.2630	−	31.3288i	0.559413	−	0.322977i	−0.193497	−	0.981101i	$-0.561983\pi$
$97$	54.2630	−	31.3288i	0.559413	−	0.322977i	0.752910	+	0.658124i	$0.228650\pi$
$98$		0			0
$99$	77.1805	+	3.49189i	0.779601	+	0.0352716i
$100$		0			0
$101$	−36.0279	+	20.8007i	−0.356712	+	0.205948i	−0.667638	−	0.744486i	$-0.732694\pi$
$101$	−36.0279	+	20.8007i	−0.356712	+	0.205948i	0.310925	+	0.950434i	$0.399361\pi$
$102$		0			0
$103$	13.4144	+	7.74480i	0.130237	+	0.0751923i	0.563703	−	0.825978i	$-0.309376\pi$
$103$	13.4144	+	7.74480i	0.130237	+	0.0751923i	−0.433466	+	0.901170i	$0.642710\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	195.752			1.82946			0.914729	−	0.404067i	$-0.132404\pi$
$107$	195.752			1.82946			0.914729	+	0.404067i	$0.132404\pi$
$108$		0			0
$109$	86.4249			0.792889			0.396444	−	0.918059i	$-0.370244\pi$
$109$	86.4249			0.792889			0.396444	+	0.918059i	$0.370244\pi$
$110$		0			0
$111$	21.0899	−	72.1439i	0.189999	−	0.649945i
$112$		0			0
$113$	50.9210	−	88.1977i	0.450628	−	0.780511i	−0.547797	−	0.836611i	$-0.684533\pi$
$113$	50.9210	−	88.1977i	0.450628	−	0.780511i	0.998425	+	0.0561004i	$0.0178667\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	69.1909	+	133.429i	0.591375	+	1.14041i
$118$		0			0
$119$	229.929	−	132.750i	1.93218	−	1.11554i
$120$		0			0
$121$	−23.6542	+	40.9703i	−0.195489	+	0.338598i
$122$		0			0
$123$	−83.3008	−	87.1548i	−0.677243	−	0.708576i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	93.7585i		−	0.738256i	−0.929379	−	0.369128i	$-0.879656\pi$
$127$		−	93.7585i		−	0.738256i	0.929379	−	0.369128i	$-0.120344\pi$
$128$		0			0
$129$	−228.217	+	55.6535i	−1.76913	+	0.431422i
$130$		0			0
$131$	−119.315	−	68.8867i	−0.910804	−	0.525853i	−0.0301140	−	0.999546i	$-0.509587\pi$
$131$	−119.315	−	68.8867i	−0.910804	−	0.525853i	−0.880690	+	0.473694i	$0.842920\pi$
$132$		0			0
$133$	−279.560	+	161.404i	−2.10196	+	1.21356i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	47.8412	+	82.8634i	0.349206	+	0.604842i	0.986109	−	0.166102i	$-0.0531180\pi$
$137$	47.8412	+	82.8634i	0.349206	+	0.604842i	−0.636903	+	0.770944i	$0.719785\pi$
$138$		0			0
$139$	40.8322	−	70.7235i	0.293757	−	0.508802i	−0.680938	−	0.732341i	$-0.738428\pi$
$139$	40.8322	−	70.7235i	0.293757	−	0.508802i	0.974695	+	0.223539i	$0.0717610\pi$
$140$		0			0
$141$	−52.8398	−	216.679i	−0.374750	−	1.53673i
$142$		0			0
$143$	143.361			1.00252
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−204.721	+	195.668i	−1.39266	+	1.33107i
$148$		0			0
$149$	−85.2595	−	49.2246i	−0.572211	−	0.330366i	0.185821	−	0.982584i	$-0.440506\pi$
$149$	−85.2595	−	49.2246i	−0.572211	−	0.330366i	−0.758032	+	0.652217i	$0.773839\pi$
$150$		0			0
$151$	−92.5938	−	160.377i	−0.613204	−	1.06210i	−0.990697	−	0.136088i	$-0.956547\pi$
$151$	−92.5938	−	160.377i	−0.613204	−	1.06210i	0.377492	−	0.926013i	$-0.376786\pi$
$152$		0			0
$153$	168.123	+	107.480i	1.09885	+	0.702484i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−160.367	−	92.5876i	−1.02144	−	0.589730i	−0.106921	−	0.994267i	$-0.534099\pi$
$157$	−160.367	−	92.5876i	−1.02144	−	0.589730i	−0.914522	+	0.404537i	$0.867433\pi$
$158$		0			0
$159$	−37.5227	−	10.9690i	−0.235992	−	0.0689876i
$160$		0			0
$161$			464.620i			2.88584i
$162$		0			0
$163$		−	180.426i		−	1.10691i	−0.832880	−	0.553454i	$-0.813309\pi$
$163$		−	180.426i		−	1.10691i	0.832880	−	0.553454i	$-0.186691\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	83.1659	−	144.047i	0.497999	−	0.862560i	−0.501998	−	0.864869i	$-0.667402\pi$
$167$	83.1659	−	144.047i	0.497999	−	0.862560i	0.999997	+	0.00230886i	$0.000734932\pi$
$168$		0			0
$169$	54.9479	+	95.1725i	0.325135	+	0.563151i
$170$		0			0
$171$	−204.413	−	130.680i	−1.19540	−	0.764210i
$172$		0			0
$173$	75.4211	+	130.633i	0.435960	+	0.755105i	0.997373	−	0.0724307i	$-0.0230756\pi$
$173$	75.4211	+	130.633i	0.435960	+	0.755105i	−0.561414	+	0.827535i	$0.689742\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	78.7482	+	82.3916i	0.444905	+	0.465489i
$178$		0			0
$179$			181.881i			1.01610i	0.861329	+	0.508048i	$0.169633\pi$
$179$			181.881i			1.01610i	−0.861329	+	0.508048i	$0.830367\pi$
$180$		0			0
$181$	120.345			0.664887			0.332444	−	0.943123i	$-0.392127\pi$
$181$	120.345			0.664887			0.332444	+	0.943123i	$0.392127\pi$
$182$		0			0
$183$	6.48973	+	26.6123i	0.0354630	+	0.145423i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	164.829	−	95.1641i	0.881439	−	0.508899i
$188$		0			0
$189$	−305.915	−	104.653i	−1.61860	−	0.553719i
$190$		0			0
$191$	5.73186	−	3.30929i	0.0300098	−	0.0173261i	−0.484920	−	0.874558i	$-0.661151\pi$
$191$	5.73186	−	3.30929i	0.0300098	−	0.0173261i	0.514930	+	0.857232i	$0.327818\pi$
$192$		0			0
$193$	147.954	+	85.4213i	0.766601	+	0.442597i	0.831661	−	0.555284i	$-0.187390\pi$
$193$	147.954	+	85.4213i	0.766601	+	0.442597i	−0.0650597	+	0.997881i	$0.520724\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−200.181			−1.01615			−0.508074	−	0.861313i	$-0.669642\pi$
$197$	−200.181			−1.01615			−0.508074	+	0.861313i	$0.669642\pi$
$198$		0			0
$199$	−96.3228			−0.484034			−0.242017	−	0.970272i	$-0.577809\pi$
$199$	−96.3228			−0.484034			−0.242017	+	0.970272i	$0.577809\pi$
$200$		0			0
$201$	49.9690	+	52.2808i	0.248602	+	0.260104i
$202$		0			0
$203$	−58.4166	+	101.181i	−0.287767	+	0.498426i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−309.996	+	160.752i	−1.49756	+	0.776580i
$208$		0			0
$209$	−200.408	+	115.705i	−0.958889	+	0.553615i
$210$		0			0
$211$	163.796	−	283.703i	0.776284	−	1.34456i	−0.157787	−	0.987473i	$-0.550436\pi$
$211$	163.796	−	283.703i	0.776284	−	1.34456i	0.934070	−	0.357089i	$-0.116231\pi$
$212$		0			0
$213$	36.7954	−	125.869i	0.172749	−	0.590936i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	144.093i		−	0.664021i
$218$		0			0
$219$	6.47070	−	22.1349i	0.0295466	−	0.101073i
$220$		0			0
$221$	320.661	+	185.134i	1.45095	+	0.837709i
$222$		0			0
$223$	46.7687	−	27.0019i	0.209725	−	0.121085i	−0.391459	−	0.920196i	$-0.628029\pi$
$223$	46.7687	−	27.0019i	0.209725	−	0.121085i	0.601184	+	0.799111i	$0.294696\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−114.956	−	199.109i	−0.506413	−	0.877133i	−0.999972	−	0.00742111i	$-0.997638\pi$
$227$	−114.956	−	199.109i	−0.506413	−	0.877133i	0.493559	−	0.869712i	$-0.335696\pi$
$228$		0			0
$229$	−8.83249	+	15.2983i	−0.0385698	+	0.0668049i	−0.884666	−	0.466225i	$-0.845614\pi$
$229$	−8.83249	+	15.2983i	−0.0385698	+	0.0668049i	0.846096	+	0.533030i	$0.178947\pi$
$230$		0			0
$231$	−222.938	+	213.079i	−0.965098	+	0.922422i
$232$		0			0
$233$	−399.853			−1.71611			−0.858054	−	0.513560i	$-0.828326\pi$
$233$	−399.853			−1.71611			−0.858054	+	0.513560i	$0.828326\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	27.4707	+	112.649i	0.115910	+	0.475311i
$238$		0			0
$239$	97.0062	+	56.0066i	0.405884	+	0.234337i	0.689020	−	0.724743i	$-0.258041\pi$
$239$	97.0062	+	56.0066i	0.405884	+	0.234337i	−0.283136	+	0.959080i	$0.591375\pi$
$240$		0			0
$241$	18.6167	+	32.2451i	0.0772478	+	0.133797i	0.902062	−	0.431607i	$-0.142053\pi$
$241$	18.6167	+	32.2451i	0.0772478	+	0.133797i	−0.824814	+	0.565405i	$0.808720\pi$
$242$		0			0
$243$	−36.0175	−	240.316i	−0.148220	−	0.988954i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−389.876	−	225.095i	−1.57845	−	0.911316i
$248$		0			0
$249$	59.9700	+	245.918i	0.240844	+	0.987623i
$250$		0			0
$251$			426.106i			1.69763i	0.528686	+	0.848817i	$0.322685\pi$
$251$			426.106i			1.69763i	−0.528686	+	0.848817i	$0.677315\pi$
$252$		0			0
$253$			333.071i			1.31649i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−77.8523	+	134.844i	−0.302927	+	0.524685i	−0.976798	−	0.214164i	$-0.931297\pi$
$257$	−77.8523	+	134.844i	−0.302927	+	0.524685i	0.673870	+	0.738850i	$0.264631\pi$
$258$		0			0
$259$	150.011	+	259.827i	0.579195	+	1.00319i
$260$		0			0
$261$	−87.7194	−	3.96871i	−0.336090	−	0.0152058i
$262$		0			0
$263$	142.667	+	247.107i	0.542461	+	0.939569i	0.998762	+	0.0497440i	$0.0158405\pi$
$263$	142.667	+	247.107i	0.542461	+	0.939569i	−0.456301	+	0.889825i	$0.650826\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	51.7979	−	177.190i	0.193999	−	0.663631i
$268$		0			0
$269$		−	112.337i		−	0.417611i	−0.977957	−	0.208806i	$-0.933042\pi$
$269$		−	112.337i		−	0.417611i	0.977957	−	0.208806i	$-0.0669576\pi$
$270$		0			0
$271$	39.2503			0.144835			0.0724175	−	0.997374i	$-0.476929\pi$
$271$	39.2503			0.144835			0.0724175	+	0.997374i	$0.476929\pi$
$272$		0			0
$273$	−575.845	−	168.337i	−2.10932	−	0.616618i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−409.507	+	236.429i	−1.47836	+	0.853534i	−0.999701	−	0.0244650i	$-0.992212\pi$
$277$	−409.507	+	236.429i	−1.47836	+	0.853534i	−0.478663	+	0.877999i	$0.658878\pi$
$278$		0			0
$279$	96.1391	−	49.8540i	0.344584	−	0.178688i
$280$		0			0
$281$	104.091	−	60.0971i	0.370431	−	0.213869i	−0.303216	−	0.952922i	$-0.598060\pi$
$281$	104.091	−	60.0971i	0.370431	−	0.213869i	0.673647	+	0.739053i	$0.264727\pi$
$282$		0			0
$283$	181.872	+	105.004i	0.642658	+	0.371039i	0.785638	−	0.618687i	$-0.212335\pi$
$283$	181.872	+	105.004i	0.642658	+	0.371039i	−0.142980	+	0.989726i	$0.545668\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	481.233			1.67677
$288$		0			0
$289$	202.574			0.700947
$290$		0			0
$291$	−182.621	+	44.5343i	−0.627564	+	0.153039i
$292$		0			0
$293$	70.4835	−	122.081i	0.240558	−	0.416659i	−0.720315	−	0.693647i	$-0.756003\pi$
$293$	70.4835	−	122.081i	0.240558	−	0.416659i	0.960873	+	0.276988i	$0.0893362\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−219.301	−	75.0223i	−0.738386	−	0.252600i
$298$		0			0
$299$	−561.151	+	323.981i	−1.87676	+	1.08355i
$300$		0			0
$301$	468.825	−	812.028i	1.55756	−	2.69777i
$302$		0			0
$303$	121.251	−	29.5685i	0.400169	−	0.0975858i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	83.3870i		−	0.271619i	−0.990735	−	0.135809i	$-0.956637\pi$
$307$		−	83.3870i		−	0.271619i	0.990735	−	0.135809i	$-0.0433635\pi$
$308$		0			0
$309$	−32.1073	−	33.5928i	−0.103907	−	0.108714i
$310$		0			0
$311$	−354.823	−	204.857i	−1.14091	−	0.658704i	−0.194254	−	0.980951i	$-0.562229\pi$
$311$	−354.823	−	204.857i	−1.14091	−	0.658704i	−0.946656	+	0.322247i	$0.895562\pi$
$312$		0			0
$313$	201.134	−	116.125i	0.642602	−	0.371007i	−0.143014	−	0.989721i	$-0.545679\pi$
$313$	201.134	−	116.125i	0.642602	−	0.371007i	0.785616	+	0.618714i	$0.212346\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	156.512	+	271.087i	0.493730	+	0.855165i	0.999974	−	0.00722536i	$-0.00229992\pi$
$317$	156.512	+	271.087i	0.493730	+	0.855165i	−0.506244	+	0.862390i	$0.668967\pi$
$318$		0			0
$319$	−41.8770	+	72.5331i	−0.131276	+	0.227377i
$320$		0			0
$321$	−563.665	−	164.776i	−1.75597	−	0.513322i
$322$		0			0
$323$	−597.681			−1.85041
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−248.859	−	72.7491i	−0.761037	−	0.222474i
$328$		0			0
$329$	770.975	+	445.123i	2.34339	+	1.35296i
$330$		0			0
$331$	−39.3215	−	68.1068i	−0.118796	−	0.205761i	0.800495	−	0.599340i	$-0.204570\pi$
$331$	−39.3215	−	68.1068i	−0.118796	−	0.205761i	−0.919291	+	0.393579i	$0.871237\pi$
$332$		0			0
$333$	−121.456	+	189.985i	−0.364732	+	0.570525i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−116.656	−	67.3515i	−0.346161	−	0.199856i	0.316832	−	0.948482i	$-0.397381\pi$
$337$	−116.656	−	67.3515i	−0.346161	−	0.199856i	−0.662993	+	0.748626i	$0.730714\pi$
$338$		0			0
$339$	−220.868	+	211.101i	−0.651527	+	0.622716i
$340$		0			0
$341$		−	103.295i		−	0.302919i
$342$		0			0
$343$		−	543.617i		−	1.58489i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−35.3923	+	61.3013i	−0.101995	+	0.176661i	−0.912507	−	0.409062i	$-0.865856\pi$
$347$	−35.3923	+	61.3013i	−0.101995	+	0.176661i	0.810511	+	0.585723i	$0.199189\pi$
$348$		0			0
$349$	−182.024	−	315.274i	−0.521557	−	0.903364i	−0.999686	−	0.0250738i	$-0.992018\pi$
$349$	−182.024	−	315.274i	−0.521557	−	0.903364i	0.478128	−	0.878290i	$-0.341315\pi$
$350$		0			0
$351$	−86.9193	−	442.448i	−0.247633	−	1.26053i
$352$		0			0
$353$	4.46473	+	7.73314i	0.0126480	+	0.0219069i	0.872280	−	0.489007i	$-0.162641\pi$
$353$	4.46473	+	7.73314i	0.0126480	+	0.0219069i	−0.859632	+	0.510913i	$0.829307\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−773.822	+	188.706i	−2.16757	+	0.528587i
$358$		0			0
$359$			320.413i			0.892516i	0.894904	+	0.446258i	$0.147244\pi$
$359$			320.413i			0.892516i	−0.894904	+	0.446258i	$0.852756\pi$
$360$		0			0
$361$	365.692			1.01300
$362$		0			0
$363$	102.599	−	98.0622i	0.282642	−	0.270144i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−115.412	+	66.6334i	−0.314475	+	0.181562i	−0.648927	−	0.760850i	$-0.724782\pi$
$367$	−115.412	+	66.6334i	−0.314475	+	0.181562i	0.334452	+	0.942413i	$0.391449\pi$
$368$		0			0
$369$	166.500	+	321.081i	0.451220	+	0.870137i
$370$		0			0
$371$	135.139	−	78.0223i	0.364255	−	0.210303i
$372$		0			0
$373$	−619.796	−	357.839i	−1.66165	−	0.959355i	−0.971927	−	0.235284i	$-0.924398\pi$
$373$	−619.796	−	357.839i	−1.66165	−	0.959355i	−0.689725	−	0.724071i	$-0.742269\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−162.936			−0.432192
$378$		0			0
$379$	−45.4400			−0.119894			−0.0599472	−	0.998202i	$-0.519093\pi$
$379$	−45.4400			−0.119894			−0.0599472	+	0.998202i	$0.519093\pi$
$380$		0			0
$381$	−78.9222	+	269.976i	−0.207145	+	0.708599i
$382$		0			0
$383$	349.952	−	606.135i	0.913713	−	1.58260i	0.104938	−	0.994479i	$-0.466536\pi$
$383$	349.952	−	606.135i	0.913713	−	1.58260i	0.808775	−	0.588118i	$-0.200131\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	703.995	+	31.8510i	1.81911	+	0.0823024i
$388$		0			0
$389$	98.3531	−	56.7842i	0.252836	−	0.145975i	−0.368226	−	0.929736i	$-0.620035\pi$
$389$	98.3531	−	56.7842i	0.252836	−	0.145975i	0.621062	+	0.783761i	$0.286702\pi$
$390$		0			0
$391$	−430.123	+	744.995i	−1.10006	+	1.90536i
$392$		0			0
$393$	285.581	+	298.793i	0.726668	+	0.760288i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	614.028i		−	1.54667i	−0.633998	−	0.773335i	$-0.718587\pi$
$397$		−	614.028i		−	1.54667i	0.633998	−	0.773335i	$-0.281413\pi$
$398$		0			0
$399$	940.853	−	229.438i	2.35803	−	0.575033i
$400$		0			0
$401$	639.856	+	369.421i	1.59565	+	0.921250i	0.992312	+	0.123765i	$0.0394969\pi$
$401$	639.856	+	369.421i	1.59565	+	0.921250i	0.603339	+	0.797484i	$0.293836\pi$
$402$		0			0
$403$	174.030	−	100.476i	0.431836	−	0.249321i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	107.538	+	186.262i	0.264222	+	0.457646i
$408$		0			0
$409$	274.589	−	475.602i	0.671366	−	1.16284i	−0.306151	−	0.951983i	$-0.599041\pi$
$409$	274.589	−	475.602i	0.671366	−	1.16284i	0.977517	−	0.210857i	$-0.0676255\pi$
$410$		0			0
$411$	−68.0069	−	278.875i	−0.165467	−	0.678528i
$412$		0			0
$413$	−454.933			−1.10153
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−177.108	+	169.276i	−0.424720	+	0.405938i
$418$		0			0
$419$	−168.477	−	97.2700i	−0.402092	−	0.232148i	0.285294	−	0.958440i	$-0.407909\pi$
$419$	−168.477	−	97.2700i	−0.402092	−	0.232148i	−0.687386	+	0.726292i	$0.741242\pi$
$420$		0			0
$421$	301.120	+	521.555i	0.715249	+	1.23885i	0.962863	+	0.269989i	$0.0870200\pi$
$421$	301.120	+	521.555i	0.715249	+	1.23885i	−0.247615	+	0.968859i	$0.579647\pi$
$422$		0			0
$423$	−30.2407	+	668.404i	−0.0714911	+	1.58015i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−94.6904	−	54.6695i	−0.221757	−	0.128032i
$428$		0			0
$429$	−412.805	−	120.675i	−0.962249	−	0.281294i
$430$		0			0
$431$			148.264i			0.344001i	0.985097	+	0.172000i	$0.0550231\pi$
$431$			148.264i			0.344001i	−0.985097	+	0.172000i	$0.944977\pi$
$432$		0			0
$433$			405.637i			0.936805i	0.883515	+	0.468402i	$0.155170\pi$
$433$			405.637i			0.936805i	−0.883515	+	0.468402i	$0.844830\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	522.966	−	905.803i	1.19672	−	2.07278i
$438$		0			0
$439$	55.5992	+	96.3007i	0.126650	+	0.219364i	0.922377	−	0.386292i	$-0.126244\pi$
$439$	55.5992	+	96.3007i	0.126650	+	0.219364i	−0.795727	+	0.605656i	$0.792911\pi$
$440$		0			0
$441$	754.196	−	391.097i	1.71019	−	0.886841i
$442$		0			0
$443$	155.408	+	269.175i	0.350808	+	0.607618i	0.986391	−	0.164415i	$-0.0525735\pi$
$443$	155.408	+	269.175i	0.350808	+	0.607618i	−0.635583	+	0.772033i	$0.719240\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	204.068	+	213.510i	0.456528	+	0.477650i
$448$		0			0
$449$		−	371.254i		−	0.826846i	−0.910539	−	0.413423i	$-0.864333\pi$
$449$		−	371.254i		−	0.826846i	0.910539	−	0.413423i	$-0.135667\pi$
$450$		0			0
$451$	344.981			0.764924
$452$		0			0
$453$	131.623	+	539.746i	0.290559	+	1.19149i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−226.691	+	130.880i	−0.496041	+	0.286390i	−0.727077	−	0.686556i	$-0.759122\pi$
$457$	−226.691	+	130.880i	−0.496041	+	0.286390i	0.231036	+	0.972945i	$0.425788\pi$
$458$		0			0
$459$	−393.637	−	451.007i	−0.857596	−	0.982586i
$460$		0			0
$461$	−360.223	+	207.975i	−0.781394	+	0.451138i	−0.836924	−	0.547319i	$-0.815649\pi$
$461$	−360.223	+	207.975i	−0.781394	+	0.451138i	0.0555299	+	0.998457i	$0.482315\pi$
$462$		0			0
$463$	116.882	+	67.4817i	0.252444	+	0.145749i	0.620883	−	0.783903i	$-0.286774\pi$
$463$	116.882	+	67.4817i	0.252444	+	0.145749i	−0.368439	+	0.929652i	$0.620108\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−342.345			−0.733073			−0.366537	−	0.930404i	$-0.619457\pi$
$467$	−342.345			−0.733073			−0.366537	+	0.930404i	$0.619457\pi$
$468$		0			0
$469$	−288.673			−0.615508
$470$		0			0
$471$	383.836	+	401.595i	0.814939	+	0.852643i
$472$		0			0
$473$	336.086	−	582.118i	0.710541	−	1.23069i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	98.8129	+	63.1703i	0.207155	+	0.132433i
$478$		0			0
$479$	−302.469	+	174.630i	−0.631458	+	0.364573i	−0.781317	−	0.624135i	$-0.785452\pi$
$479$	−302.469	+	174.630i	−0.631458	+	0.364573i	0.149858	+	0.988707i	$0.452118\pi$
$480$		0			0
$481$	−209.207	+	362.357i	−0.434941	+	0.753340i
$482$		0			0
$483$	391.099	−	1337.87i	0.809728	−	2.76991i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			744.059i			1.52784i	0.645310	+	0.763921i	$0.276728\pi$
$487$			744.059i			1.52784i	−0.645310	+	0.763921i	$0.723272\pi$
$488$		0			0
$489$	−151.876	+	519.534i	−0.310584	+	1.06244i
$490$		0			0
$491$	−663.655	−	383.162i	−1.35164	−	0.780370i	−0.363161	−	0.931726i	$-0.618302\pi$
$491$	−663.655	−	383.162i	−1.35164	−	0.780370i	−0.988479	+	0.151357i	$0.951636\pi$
$492$		0			0
$493$	−187.336	+	108.159i	−0.379993	+	0.219389i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	261.725	+	453.320i	0.526609	+	0.912113i
$498$		0			0
$499$	−444.348	+	769.633i	−0.890477	+	1.54235i	−0.0511717	+	0.998690i	$0.516296\pi$
$499$	−444.348	+	769.633i	−0.890477	+	1.54235i	−0.839305	+	0.543661i	$0.817038\pi$
$500$		0			0
$501$	−360.728	+	344.777i	−0.720017	+	0.688178i
$502$		0			0
$503$	−188.524			−0.374800			−0.187400	−	0.982284i	$-0.560006\pi$
$503$	−188.524			−0.374800			−0.187400	+	0.982284i	$0.560006\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−78.1091	−	320.301i	−0.154061	−	0.631757i
$508$		0			0
$509$	67.0370	+	38.7038i	0.131703	+	0.0760389i	0.564404	−	0.825499i	$-0.309106\pi$
$509$	67.0370	+	38.7038i	0.131703	+	0.0760389i	−0.432701	+	0.901538i	$0.642439\pi$
$510$		0			0
$511$	46.0259	+	79.7191i	0.0900702	+	0.156006i
$512$		0			0
$513$	478.604	+	548.358i	0.932951	+	1.06892i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	552.688	+	319.094i	1.06903	+	0.617204i
$518$		0			0
$519$	−107.212	−	439.643i	−0.206574	−	0.847096i
$520$		0			0
$521$		−	558.234i		−	1.07147i	−0.844387	−	0.535734i	$-0.820035\pi$
$521$		−	558.234i		−	1.07147i	0.844387	−	0.535734i	$-0.179965\pi$
$522$		0			0
$523$			927.119i			1.77269i	0.463022	+	0.886347i	$0.346765\pi$
$523$			927.119i			1.77269i	−0.463022	+	0.886347i	$0.653235\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	133.394	−	231.045i	0.253120	−	0.438416i
$528$		0			0
$529$	−488.208	−	845.601i	−0.922888	−	1.59849i
$530$		0			0
$531$	−157.400	−	303.533i	−0.296423	−	0.571624i
$532$		0			0
$533$	335.565	+	581.216i	0.629579	+	1.09046i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	153.100	−	523.724i	0.285103	−	0.975278i
$538$		0			0
$539$		−	810.336i		−	1.50341i
$540$		0			0
$541$	−870.887			−1.60977			−0.804886	−	0.593429i	$-0.797774\pi$
$541$	−870.887			−1.60977			−0.804886	+	0.593429i	$0.797774\pi$
$542$		0			0
$543$	−346.531	−	101.301i	−0.638178	−	0.186559i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−151.801	+	87.6421i	−0.277515	+	0.160223i	−0.632298	−	0.774725i	$-0.717888\pi$
$547$	−151.801	+	87.6421i	−0.277515	+	0.160223i	0.354783	+	0.934949i	$0.384555\pi$
$548$		0			0
$549$	3.71414	−	82.0927i	0.00676528	−	0.149531i
$550$		0			0
$551$	227.773	−	131.505i	0.413382	−	0.238666i
$552$		0			0
$553$	−400.820	−	231.413i	−0.724809	−	0.418469i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.6793			−0.0461029			−0.0230515	−	0.999734i	$-0.507338\pi$
$557$	−25.6793			−0.0461029			−0.0230515	+	0.999734i	$0.507338\pi$
$558$		0			0
$559$	1307.65			2.33927
$560$		0			0
$561$	−554.728	+	135.277i	−0.988821	+	0.241136i
$562$		0			0
$563$	249.991	−	432.998i	0.444035	−	0.769090i	−0.553950	−	0.832550i	$-0.686880\pi$
$563$	249.991	−	432.998i	0.444035	−	0.769090i	0.997984	+	0.0634596i	$0.0202134\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	792.785	+	558.854i	1.39821	+	0.985632i
$568$		0			0
$569$	163.726	−	94.5273i	0.287744	−	0.166129i	−0.349180	−	0.937056i	$-0.613540\pi$
$569$	163.726	−	94.5273i	0.287744	−	0.166129i	0.636924	+	0.770927i	$0.280207\pi$
$570$		0			0
$571$	491.393	−	851.117i	0.860583	−	1.49057i	−0.0107848	−	0.999942i	$-0.503433\pi$
$571$	491.393	−	851.117i	0.860583	−	1.49057i	0.871367	−	0.490631i	$-0.163234\pi$
$572$		0			0
$573$	−19.2905	+	4.70420i	−0.0336657	+	0.00820978i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	348.901i		−	0.604681i	−0.953200	−	0.302341i	$-0.902232\pi$
$577$		−	348.901i		−	0.604681i	0.953200	−	0.302341i	$-0.0977680\pi$
$578$		0			0
$579$	−354.127	−	370.511i	−0.611619	−	0.639916i
$580$		0			0
$581$	−875.011	−	505.188i	−1.50604	−	0.869514i
$582$		0			0
$583$	96.8766	−	55.9318i	0.166169	−	0.0959378i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−282.746	−	489.730i	−0.481679	−	0.834292i	0.518100	−	0.855320i	$-0.326640\pi$
$587$	−282.746	−	489.730i	−0.481679	−	0.834292i	−0.999779	+	0.0210277i	$0.993306\pi$
$588$		0			0
$589$	−162.187	+	280.917i	−0.275361	+	0.476939i
$590$		0			0
$591$	576.419	+	168.505i	0.975328	+	0.285118i
$592$		0			0
$593$	664.718			1.12094			0.560471	−	0.828174i	$-0.310620\pi$
$593$	664.718			1.12094			0.560471	+	0.828174i	$0.310620\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	277.360	+	81.0807i	0.464590	+	0.135814i
$598$		0			0
$599$	−728.790	−	420.767i	−1.21668	−	0.702449i	−0.252472	−	0.967604i	$-0.581243\pi$
$599$	−728.790	−	420.767i	−1.21668	−	0.702449i	−0.964206	+	0.265155i	$0.914577\pi$
$600$		0			0
$601$	−412.452	−	714.388i	−0.686276	−	1.18866i	−0.973034	−	0.230662i	$-0.925911\pi$
$601$	−412.452	−	714.388i	−0.686276	−	1.18866i	0.286758	−	0.958003i	$-0.407422\pi$
$602$		0			0
$603$	−99.8770	−	192.604i	−0.165633	−	0.319409i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	789.319	+	455.713i	1.30036	+	0.750763i	0.980466	−	0.196690i	$-0.0630192\pi$
$607$	789.319	+	455.713i	1.30036	+	0.750763i	0.319895	+	0.947453i	$0.396352\pi$
$608$		0			0
$609$	253.380	−	242.175i	0.416059	−	0.397660i
$610$		0			0
$611$			1241.54i			2.03198i
$612$		0			0
$613$		−	222.488i		−	0.362949i	−0.983396	−	0.181475i	$-0.941913\pi$
$613$		−	222.488i		−	0.362949i	0.983396	−	0.181475i	$-0.0580870\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−355.212	+	615.245i	−0.575708	+	0.997156i	0.420256	+	0.907406i	$0.361940\pi$
$617$	−355.212	+	615.245i	−0.575708	+	0.997156i	−0.995964	+	0.0897507i	$0.971393\pi$
$618$		0			0
$619$	160.056	+	277.226i	0.258573	+	0.447861i	0.965860	−	0.259065i	$-0.0834145\pi$
$619$	160.056	+	277.226i	0.258573	+	0.447861i	−0.707287	+	0.706926i	$0.750081\pi$
$620$		0			0
$621$	1027.94	−	201.941i	1.65530	−	0.325186i
$622$		0			0
$623$	368.436	+	638.151i	0.591391	+	1.02432i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	674.468	−	164.477i	1.07571	−	0.262324i
$628$		0			0
$629$			555.494i			0.883138i
$630$		0			0
$631$	−1051.94			−1.66711			−0.833553	−	0.552439i	$-0.813697\pi$
$631$	−1051.94			−1.66711			−0.833553	+	0.552439i	$0.813697\pi$
$632$		0			0
$633$	−710.458	+	679.041i	−1.12237	+	1.07273i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1365.24	−	788.220i	2.14323	−	1.23739i
$638$		0			0
$639$	−211.904	+	331.466i	−0.331618	+	0.518726i
$640$		0			0
$641$	762.966	−	440.499i	1.19027	−	0.687205i	0.231906	−	0.972738i	$-0.425504\pi$
$641$	762.966	−	440.499i	1.19027	−	0.687205i	0.958369	+	0.285533i	$0.0921705\pi$
$642$		0			0
$643$	707.819	+	408.659i	1.10081	+	0.635551i	0.936433	−	0.350847i	$-0.114106\pi$
$643$	707.819	+	408.659i	1.10081	+	0.635551i	0.164374	+	0.986398i	$0.447440\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−299.497			−0.462901			−0.231451	−	0.972847i	$-0.574347\pi$
$647$	−299.497			−0.462901			−0.231451	+	0.972847i	$0.574347\pi$
$648$		0			0
$649$	−326.127			−0.502507
$650$		0			0
$651$	−121.291	+	414.912i	−0.186316	+	0.637346i
$652$		0			0
$653$	−377.726	+	654.241i	−0.578447	+	1.00190i	0.417210	+	0.908810i	$0.363008\pi$
$653$	−377.726	+	654.241i	−0.578447	+	1.00190i	−0.995658	+	0.0930902i	$0.970326\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−37.2646	+	58.2903i	−0.0567193	+	0.0887219i
$658$		0			0
$659$	538.168	−	310.712i	0.816644	−	0.471490i	−0.0326137	−	0.999468i	$-0.510383\pi$
$659$	538.168	−	310.712i	0.816644	−	0.471490i	0.849258	+	0.527978i	$0.177050\pi$
$660$		0			0
$661$	24.8919	−	43.1140i	0.0376580	−	0.0652255i	−0.846582	−	0.532258i	$-0.821344\pi$
$661$	24.8919	−	43.1140i	0.0376580	−	0.0652255i	0.884240	+	0.467033i	$0.154677\pi$
$662$		0			0
$663$	−767.500	−	803.009i	−1.15762	−	1.21118i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	378.552i		−	0.567544i
$668$		0			0
$669$	−157.399	+	38.3836i	−0.235275	+	0.0573746i
$670$		0			0
$671$	−67.8805	−	39.1908i	−0.101163	−	0.0584066i
$672$		0			0
$673$	210.090	−	121.295i	0.312169	−	0.180231i	−0.335728	−	0.941959i	$-0.608982\pi$
$673$	210.090	−	121.295i	0.312169	−	0.180231i	0.647897	+	0.761728i	$0.275649\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	408.572	+	707.668i	0.603504	+	1.04530i	0.992286	+	0.123970i	$0.0395628\pi$
$677$	408.572	+	707.668i	0.603504	+	1.04530i	−0.388782	+	0.921330i	$0.627104\pi$
$678$		0			0
$679$	375.157	−	649.791i	0.552514	−	0.956982i
$680$		0			0
$681$	163.411	+	670.098i	0.239958	+	0.983990i
$682$		0			0
$683$	−911.627			−1.33474			−0.667369	−	0.744727i	$-0.732580\pi$
$683$	−911.627			−1.33474			−0.667369	+	0.744727i	$0.732580\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	38.3106	−	36.6165i	0.0557650	−	0.0532991i
$688$		0			0
$689$	188.465	+	108.810i	0.273534	+	0.157925i
$690$		0			0
$691$	197.429	+	341.957i	0.285715	+	0.494872i	0.972782	−	0.231721i	$-0.0744357\pi$
$691$	197.429	+	341.957i	0.285715	+	0.494872i	−0.687068	+	0.726594i	$0.741102\pi$
$692$		0			0
$693$	821.308	−	425.899i	1.18515	−	0.614573i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	771.634	+	445.503i	1.10708	+	0.639172i
$698$		0			0
$699$	1151.37	+	336.581i	1.64717	+	0.481517i
$700$		0			0
$701$			1256.28i			1.79213i	0.443925	+	0.896064i	$0.353586\pi$
$701$			1256.28i			1.79213i	−0.443925	+	0.896064i	$0.646414\pi$
$702$		0			0
$703$		−	675.398i		−	0.960737i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−249.085	+	431.428i	−0.352313	+	0.610224i
$708$		0			0
$709$	−211.556	−	366.426i	−0.298387	−	0.516821i	0.677380	−	0.735633i	$-0.263115\pi$
$709$	−211.556	−	366.426i	−0.298387	−	0.516821i	−0.975767	+	0.218812i	$0.929782\pi$
$710$		0			0
$711$	15.7217	−	347.494i	0.0221122	−	0.488740i
$712$		0			0
$713$	233.437	+	404.325i	0.327402	+	0.567076i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−232.184	−	242.926i	−0.323827	−	0.338809i
$718$		0			0
$719$		−	1290.42i		−	1.79474i	−0.441283	−	0.897368i	$-0.645477\pi$
$719$		−	1290.42i		−	1.79474i	0.441283	−	0.897368i	$-0.354523\pi$
$720$		0			0
$721$	185.485			0.257261
$722$		0			0
$723$	−26.4639	−	108.520i	−0.0366029	−	0.150097i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	959.948	−	554.226i	1.32042	−	0.762347i	0.336628	−	0.941638i	$-0.390714\pi$
$727$	959.948	−	554.226i	1.32042	−	0.762347i	0.983796	+	0.179291i	$0.0573803\pi$
$728$		0			0
$729$	−98.5766	+	722.304i	−0.135222	+	0.990815i
$730$		0			0
$731$	1503.47	−	868.032i	2.05674	−	1.18746i
$732$		0			0
$733$	−397.974	−	229.770i	−0.542939	−	0.313466i	0.203330	−	0.979110i	$-0.434823\pi$
$733$	−397.974	−	229.770i	−0.542939	−	0.313466i	−0.746269	+	0.665644i	$0.768157\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−206.941			−0.280788
$738$		0			0
$739$	−620.936			−0.840238			−0.420119	−	0.907469i	$-0.638012\pi$
$739$	−620.936			−0.840238			−0.420119	+	0.907469i	$0.638012\pi$
$740$		0			0
$741$	933.166	+	976.340i	1.25933	+	1.31760i
$742$		0			0
$743$	−254.499	+	440.805i	−0.342529	+	0.593278i	−0.984902	−	0.173115i	$-0.944617\pi$
$743$	−254.499	+	440.805i	−0.342529	+	0.593278i	0.642373	+	0.766392i	$0.277950\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	34.3214	−	758.598i	0.0459457	−	1.01553i
$748$		0			0
$749$	2030.05	−	1172.05i	2.71035	−	1.56482i
$750$		0			0
$751$	−416.456	+	721.324i	−0.554536	+	0.960484i	0.443404	+	0.896322i	$0.353771\pi$
$751$	−416.456	+	721.324i	−0.554536	+	0.960484i	−0.997939	+	0.0641621i	$0.979563\pi$
$752$		0			0
$753$	358.680	−	1226.97i	0.476334	−	1.62944i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			1174.63i			1.55169i	0.630924	+	0.775845i	$0.282676\pi$
$757$			1174.63i			1.55169i	−0.630924	+	0.775845i	$0.717324\pi$
$758$		0			0
$759$	280.366	−	959.074i	0.369389	−	1.26360i
$760$		0			0
$761$	−594.035	−	342.966i	−0.780598	−	0.450678i	0.0560442	−	0.998428i	$-0.482151\pi$
$761$	−594.035	−	342.966i	−0.780598	−	0.450678i	−0.836642	+	0.547750i	$0.815485\pi$
$762$		0			0
$763$	896.270	−	517.462i	1.17467	−	0.678194i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−317.226	−	549.451i	−0.413593	−	0.716364i
$768$		0			0
$769$	−196.412	+	340.196i	−0.255412	+	0.442387i	−0.965007	−	0.262223i	$-0.915545\pi$
$769$	−196.412	+	340.196i	−0.255412	+	0.442387i	0.709595	+	0.704610i	$0.248878\pi$
$770$		0			0
$771$	337.681	−	322.749i	0.437978	−	0.418611i
$772$		0			0
$773$	250.268			0.323761			0.161881	−	0.986810i	$-0.448244\pi$
$773$	250.268			0.323761			0.161881	+	0.986810i	$0.448244\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−213.243	−	874.443i	−0.274444	−	1.12541i
$778$		0			0
$779$	−938.192	−	541.666i	−1.20435	−	0.695335i
$780$		0			0
$781$	187.622	+	324.971i	0.240233	+	0.416096i
$782$		0			0
$783$	249.246	+	85.2666i	0.318322	+	0.108897i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−466.707	−	269.454i	−0.593021	−	0.342381i	0.173270	−	0.984874i	$-0.444567\pi$
$787$	−466.707	−	269.454i	−0.593021	−	0.342381i	−0.766291	+	0.642494i	$0.777900\pi$
$788$		0			0
$789$	−202.803	−	831.632i	−0.257038	−	1.05403i
$790$		0			0
$791$		−	1219.54i		−	1.54177i
$792$		0			0
$793$		−	152.485i		−	0.192289i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	120.351	−	208.455i	0.151006	−	0.261549i	−0.780592	−	0.625041i	$-0.785082\pi$
$797$	120.351	−	208.455i	0.151006	−	0.261549i	0.931597	+	0.363492i	$0.118416\pi$
$798$		0			0
$799$	824.147	+	1427.46i	1.03147	+	1.78656i
$800$		0			0
$801$	−298.302	+	466.613i	−0.372413	+	0.582538i
$802$		0			0
$803$	32.9945	+	57.1481i	0.0410890	+	0.0711683i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−94.5613	+	323.474i	−0.117176	+	0.400835i
$808$		0			0
$809$			608.095i			0.751662i	0.926688	+	0.375831i	$0.122643\pi$
$809$			608.095i			0.751662i	−0.926688	+	0.375831i	$0.877357\pi$
$810$		0			0
$811$	−1166.65			−1.43853			−0.719266	−	0.694735i	$-0.755522\pi$
$811$	−1166.65			−1.43853			−0.719266	+	0.694735i	$0.755522\pi$
$812$		0			0
$813$	−113.021	−	33.0394i	−0.139017	−	0.0406388i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1828.00	+	1055.40i	−2.23746	+	1.29180i
$818$		0			0
$819$	1516.44	+	969.447i	1.85157	+	1.18370i
$820$		0			0
$821$	351.855	−	203.143i	0.428568	−	0.247434i	−0.270168	−	0.962813i	$-0.587079\pi$
$821$	351.855	−	203.143i	0.428568	−	0.247434i	0.698737	+	0.715379i	$0.253746\pi$
$822$		0			0
$823$	585.761	+	338.189i	0.711738	+	0.410922i	0.811704	−	0.584069i	$-0.198540\pi$
$823$	585.761	+	338.189i	0.711738	+	0.410922i	−0.0999661	+	0.994991i	$0.531873\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−351.096			−0.424542			−0.212271	−	0.977211i	$-0.568086\pi$
$827$	−351.096			−0.424542			−0.212271	+	0.977211i	$0.568086\pi$
$828$		0			0
$829$	−24.0890			−0.0290579			−0.0145290	−	0.999894i	$-0.504625\pi$
$829$	−24.0890			−0.0290579			−0.0145290	+	0.999894i	$0.504625\pi$
$830$		0			0
$831$	1378.19	−	336.087i	1.65847	−	0.404436i
$832$		0			0
$833$	1046.46	−	1812.51i	1.25625	−	2.17589i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−318.796	+	62.6279i	−0.380880	+	0.0748242i
$838$		0			0
$839$	−1078.79	+	622.840i	−1.28581	+	0.742361i	−0.977903	−	0.209057i	$-0.932960\pi$
$839$	−1078.79	+	622.840i	−1.28581	+	0.742361i	−0.307903	+	0.951418i	$0.599627\pi$
$840$		0			0
$841$	−372.905	+	645.890i	−0.443406	+	0.768002i
$842$		0			0
$843$	−350.316	+	85.4288i	−0.415559	+	0.101339i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			566.511i			0.668844i
$848$		0			0
$849$	−435.310	−	455.451i	−0.512733	−	0.536455i
$850$		0			0
$851$	−841.867	−	486.052i	−0.989268	−	0.571154i
$852$		0			0
$853$	−651.823	+	376.330i	−0.764154	+	0.441185i	−0.830785	−	0.556593i	$-0.812108\pi$
$853$	−651.823	+	376.330i	−0.764154	+	0.441185i	0.0666312	+	0.997778i	$0.478775\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−236.059	−	408.865i	−0.275448	−	0.477089i	0.694800	−	0.719203i	$-0.255493\pi$
$857$	−236.059	−	408.865i	−0.275448	−	0.477089i	−0.970248	+	0.242113i	$0.922159\pi$
$858$		0			0
$859$	73.2644	−	126.898i	0.0852904	−	0.147727i	−0.820225	−	0.572042i	$-0.806152\pi$
$859$	73.2644	−	126.898i	0.0852904	−	0.147727i	0.905515	+	0.424314i	$0.139485\pi$
$860$		0			0
$861$	−1385.70	−	405.083i	−1.60941	−	0.470480i
$862$		0			0
$863$	784.829			0.909419			0.454709	−	0.890640i	$-0.349743\pi$
$863$	784.829			0.909419			0.454709	+	0.890640i	$0.349743\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−583.308	−	170.519i	−0.672789	−	0.196677i
$868$		0			0
$869$	−287.335	−	165.893i	−0.330650	−	0.190901i
$870$		0			0
$871$	−201.293	−	348.649i	−0.231105	−	0.400286i
$872$		0			0
$873$	563.342	+	25.4874i	0.645294	+	0.0291952i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1418.00	+	818.684i	1.61688	+	0.933505i	0.987721	+	0.156226i	$0.0499327\pi$
$877$	1418.00	+	818.684i	1.61688	+	0.933505i	0.629156	+	0.777279i	$0.283401\pi$
$878$		0			0
$879$	−305.719	+	292.200i	−0.347804	+	0.332424i
$880$		0			0
$881$		−	1368.39i		−	1.55323i	−0.629977	−	0.776614i	$-0.716936\pi$
$881$		−	1368.39i		−	1.55323i	0.629977	−	0.776614i	$-0.283064\pi$
$882$		0			0
$883$			623.608i			0.706238i	0.935578	+	0.353119i	$0.114879\pi$
$883$			623.608i			0.706238i	−0.935578	+	0.353119i	$0.885121\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−687.672	+	1191.08i	−0.775278	+	1.34282i	0.159360	+	0.987221i	$0.449057\pi$
$887$	−687.672	+	1191.08i	−0.775278	+	1.34282i	−0.934638	+	0.355601i	$0.884276\pi$
$888$		0			0
$889$	−561.371	−	972.323i	−0.631463	−	1.09373i
$890$		0			0
$891$	568.322	+	400.625i	0.637848	+	0.449635i
$892$		0			0
$893$	−1002.04	−	1735.59i	−1.12211	−	1.94354i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1888.54	−	460.543i	2.10540	−	0.513426i
$898$		0			0
$899$			117.400i			0.130590i
$900$		0			0
$901$	288.918			0.320663
$902$		0			0
$903$	−2033.51	+	1943.59i	−2.25195	+	2.15237i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−545.676	+	315.046i	−0.601627	+	0.347349i	−0.769681	−	0.638428i	$-0.779585\pi$
$907$	−545.676	+	315.046i	−0.601627	+	0.347349i	0.168054	+	0.985778i	$0.446252\pi$
$908$		0			0
$909$	−374.031	−	16.9223i	−0.411475	−	0.0186164i
$910$		0			0
$911$	−24.0956	+	13.9116i	−0.0264496	+	0.0152707i	−0.513167	−	0.858289i	$-0.671528\pi$
$911$	−24.0956	+	13.9116i	−0.0264496	+	0.0152707i	0.486717	+	0.873560i	$0.338194\pi$
$912$		0			0
$913$	−627.268	−	362.153i	−0.687040	−	0.396663i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1649.81			−1.79914
$918$		0			0
$919$	−1574.63			−1.71342			−0.856709	−	0.515800i	$-0.827495\pi$
$919$	−1574.63			−1.71342			−0.856709	+	0.515800i	$0.827495\pi$
$920$		0			0
$921$	−70.1919	+	240.112i	−0.0762127	+	0.260708i
$922$		0			0
$923$	−365.003	+	632.203i	−0.395453	+	0.684944i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	64.1754	+	123.757i	0.0692291	+	0.133502i
$928$		0			0
$929$	−771.004	+	445.139i	−0.829929	+	0.479160i	−0.853828	−	0.520555i	$-0.825725\pi$
$929$	−771.004	+	445.139i	−0.829929	+	0.479160i	0.0238995	+	0.999714i	$0.492392\pi$
$930$		0			0
$931$	−1272.33	+	2203.75i	−1.36663	+	2.36708i
$932$		0			0
$933$	849.267	+	888.559i	0.910254	+	0.952368i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			943.059i			1.00647i	0.864151	+	0.503233i	$0.167856\pi$
$937$			943.059i			1.00647i	−0.864151	+	0.503233i	$0.832144\pi$
$938$		0			0
$939$	−676.913	+	165.073i	−0.720888	+	0.175797i
$940$		0			0
$941$	−1341.95	−	774.773i	−1.42608	−	0.823350i	−0.429276	−	0.903173i	$-0.641231\pi$
$941$	−1341.95	−	774.773i	−1.42608	−	0.823350i	−0.996809	+	0.0798230i	$0.974564\pi$
$942$		0			0
$943$	−1350.35	+	779.623i	−1.43197	+	0.826747i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−246.504	−	426.957i	−0.260299	−	0.450852i	0.706022	−	0.708190i	$-0.250488\pi$
$947$	−246.504	−	426.957i	−0.260299	−	0.450852i	−0.966321	+	0.257338i	$0.917155\pi$
$948$		0			0
$949$	−64.1879	+	111.177i	−0.0676374	+	0.117151i
$950$		0			0
$951$	−222.484	−	912.338i	−0.233948	−	0.959346i
$952$		0			0
$953$	−1588.42			−1.66675			−0.833377	−	0.552706i	$-0.813595\pi$
$953$	−1588.42			−1.66675			−0.833377	+	0.552706i	$0.813595\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	181.640	−	173.608i	0.189801	−	0.181408i
$958$		0			0
$959$	992.275	+	572.891i	1.03470	+	0.597383i
$960$		0			0
$961$	408.104	+	706.857i	0.424666	+	0.735543i
$962$		0			0
$963$	1484.36	+	948.943i	1.54140	+	0.985403i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−544.974	−	314.641i	−0.563572	−	0.325378i	0.191006	−	0.981589i	$-0.438825\pi$
$967$	−544.974	−	314.641i	−0.563572	−	0.325378i	−0.754578	+	0.656210i	$0.772158\pi$
$968$		0			0
$969$	1721.01	+	503.104i	1.77607	+	0.519200i
$970$		0			0
$971$		−	547.967i		−	0.564332i	−0.959366	−	0.282166i	$-0.908947\pi$
$971$		−	547.967i		−	0.564332i	0.959366	−	0.282166i	$-0.0910529\pi$
$972$		0			0
$973$		−	977.918i		−	1.00505i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	883.292	−	1529.91i	0.904086	−	1.56592i	0.0819454	−	0.996637i	$-0.473887\pi$
$977$	883.292	−	1529.91i	0.904086	−	1.56592i	0.822140	−	0.569285i	$-0.192780\pi$
$978$		0			0
$979$	264.120	+	457.470i	0.269786	+	0.467283i
$980$		0			0
$981$	655.349	+	418.960i	0.668042	+	0.427074i
$982$		0			0
$983$	765.891	+	1326.56i	0.779136	+	1.34950i	0.932440	+	0.361324i	$0.117675\pi$
$983$	765.891	+	1326.56i	0.779136	+	1.34950i	−0.153304	+	0.988179i	$0.548991\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1845.33	−	1930.70i	−1.86963	−	1.95613i
$988$		0			0
$989$			3038.08i			3.07187i
$990$		0			0
$991$	1431.39			1.44439			0.722193	−	0.691692i	$-0.243134\pi$
$991$	1431.39			1.44439			0.722193	+	0.691692i	$0.243134\pi$
$992$		0			0
$993$	55.8960	+	229.212i	0.0562900	+	0.230828i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	72.5120	−	41.8648i	0.0727302	−	0.0419908i	−0.463194	−	0.886257i	$-0.653297\pi$
$997$	72.5120	−	41.8648i	0.0727302	−	0.0419908i	0.535924	+	0.844266i	$0.319963\pi$
$998$		0			0
$999$	509.652	−	444.822i	0.510162	−	0.445267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.c.149.2		24
3.2	odd	2		2700.3.u.c.449.12		24
5.2	odd	4		900.3.p.c.401.3		12
5.3	odd	4		180.3.o.b.41.4	✓	12
5.4	even	2	inner	900.3.u.c.149.11		24
9.2	odd	6	inner	900.3.u.c.749.11		24
9.7	even	3		2700.3.u.c.2249.1		24
15.2	even	4		2700.3.p.c.2501.6		12
15.8	even	4		540.3.o.b.341.1		12
15.14	odd	2		2700.3.u.c.449.1		24
20.3	even	4		720.3.bs.b.401.3		12
45.2	even	12		900.3.p.c.101.3		12
45.7	odd	12		2700.3.p.c.1601.6		12
45.13	odd	12		1620.3.g.b.161.6		12
45.23	even	12		1620.3.g.b.161.12		12
45.29	odd	6	inner	900.3.u.c.749.2		24
45.34	even	6		2700.3.u.c.2249.12		24
45.38	even	12		180.3.o.b.101.4	yes	12
45.43	odd	12		540.3.o.b.521.1		12
60.23	odd	4		2160.3.bs.b.881.3		12
180.43	even	12		2160.3.bs.b.1601.3		12
180.83	odd	12		720.3.bs.b.641.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.b.41.4	✓	12	5.3	odd	4
180.3.o.b.101.4	yes	12	45.38	even	12
540.3.o.b.341.1		12	15.8	even	4
540.3.o.b.521.1		12	45.43	odd	12
720.3.bs.b.401.3		12	20.3	even	4
720.3.bs.b.641.3		12	180.83	odd	12
900.3.p.c.101.3		12	45.2	even	12
900.3.p.c.401.3		12	5.2	odd	4
900.3.u.c.149.2		24	1.1	even	1	trivial
900.3.u.c.149.11		24	5.4	even	2	inner
900.3.u.c.749.2		24	45.29	odd	6	inner
900.3.u.c.749.11		24	9.2	odd	6	inner
1620.3.g.b.161.6		12	45.13	odd	12
1620.3.g.b.161.12		12	45.23	even	12
2160.3.bs.b.881.3		12	60.23	odd	4
2160.3.bs.b.1601.3		12	180.43	even	12
2700.3.p.c.1601.6		12	45.7	odd	12
2700.3.p.c.2501.6		12	15.2	even	4
2700.3.u.c.449.1		24	15.14	odd	2
2700.3.u.c.449.12		24	3.2	odd	2
2700.3.u.c.2249.1		24	9.7	even	3
2700.3.u.c.2249.12		24	45.34	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.87949 - 0.841761i) q^{3} +(10.3705 - 5.98742i) q^{7} +(7.58288 + 4.84768i) q^{9} +O(q^{10})\)	\(q+(-2.87949 - 0.841761i) q^{3} +(10.3705 - 5.98742i) q^{7} +(7.58288 + 4.84768i) q^{9} +(7.43429 - 4.29219i) q^{11} +(14.4628 + 8.35009i) q^{13} +22.1715 q^{17} -26.9572 q^{19} +(-34.9017 + 8.51119i) q^{21} +(-19.3998 + 33.6015i) q^{23} +(-17.7542 - 20.3418i) q^{27} +(-8.44943 + 4.87828i) q^{29} +(6.01648 - 10.4208i) q^{31} +(-25.0199 + 6.10140i) q^{33} +25.0544i q^{37} +(-34.6166 - 36.2181i) q^{39} +(34.8030 + 20.0935i) q^{41} +(67.8113 - 39.1509i) q^{43} +(37.1715 + 64.3830i) q^{47} +(47.1983 - 81.7498i) q^{49} +(-63.8424 - 18.6631i) q^{51} +13.0311 q^{53} +(77.6229 + 22.6915i) q^{57} +(-32.9009 - 18.9954i) q^{59} +(-4.56537 - 7.90745i) q^{61} +(107.663 + 4.87104i) q^{63} +(-20.8770 - 12.0533i) q^{67} +(84.1460 - 80.4251i) q^{69} +43.7125i q^{71} +7.68710i q^{73} +(51.3982 - 89.0244i) q^{77} +(-19.3250 - 33.4718i) q^{79} +(34.0001 + 73.5187i) q^{81} +(-42.1875 - 73.0708i) q^{83} +(28.4364 - 6.93454i) q^{87} +61.5351i q^{89} +199.982 q^{91} +(-26.0962 + 24.9422i) q^{93} +(54.2630 - 31.3288i) q^{97} +(77.1805 + 3.49189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 52 q^{9}+O(q^{10}) \) 24 * q - 52 * q^9	\( 24 q - 52 q^{9} + 96 q^{11} - 144 q^{19} - 256 q^{21} - 300 q^{29} - 24 q^{31} - 80 q^{39} + 180 q^{41} - 96 q^{49} - 288 q^{51} - 96 q^{59} - 156 q^{61} + 300 q^{69} - 240 q^{79} + 868 q^{81} + 240 q^{91} + 240 q^{99}+O(q^{100}) \) 24 * q - 52 * q^9 + 96 * q^11 - 144 * q^19 - 256 * q^21 - 300 * q^29 - 24 * q^31 - 80 * q^39 + 180 * q^41 - 96 * q^49 - 288 * q^51 - 96 * q^59 - 156 * q^61 + 300 * q^69 - 240 * q^79 + 868 * q^81 + 240 * q^91 + 240 * q^99

Introduction

L-functions

Modular forms

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Database

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