LMFDB - Embedded newform 891.2.n.b.190.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(136,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.136"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$891 = 3^{4} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	891.n (of order $15$ , degree $8$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-1,0,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1$ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			190.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	891.190
Dual form			891.2.n.b.136.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.348943 + 0.155360i) q^{2} +(-1.24064 - 1.37787i) q^{4} +(-1.47815 + 0.658114i) q^{5} +(0.978148 - 0.207912i) q^{7} +(-0.454915 - 1.40008i) q^{8} -0.618034 q^{10} +(1.06082 - 3.14240i) q^{11} +(0.442790 + 4.21286i) q^{13} +(0.373619 + 0.0794152i) q^{14} +(-0.328836 + 3.12866i) q^{16} +(-6.35410 - 4.61653i) q^{17} +(-0.263932 - 0.812299i) q^{19} +(2.74064 + 1.22021i) q^{20} +(0.858369 - 0.931709i) q^{22} +(-2.11803 + 3.66854i) q^{23} +(-1.59385 + 1.77015i) q^{25} +(-0.500000 + 1.53884i) q^{26} +(-1.50000 - 1.08981i) q^{28} +(-5.86889 + 1.24747i) q^{29} +(-0.532068 - 5.06229i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(-1.50000 - 2.59808i) q^{34} +(-1.30902 + 0.951057i) q^{35} +(-0.545085 + 1.67760i) q^{37} +(0.0341011 - 0.324451i) q^{38} +(1.59385 + 1.77015i) q^{40} +(-4.14350 - 0.880728i) q^{41} +(-3.35410 - 5.80948i) q^{43} +(-5.64590 + 2.43690i) q^{44} +(-1.30902 + 0.951057i) q^{46} +(-0.729466 + 0.810154i) q^{47} +(-5.48127 + 2.44042i) q^{49} +(-0.831171 + 0.370061i) q^{50} +(5.25542 - 5.83674i) q^{52} +(-2.11803 + 1.53884i) q^{53} +(0.500000 + 5.34307i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(-2.24171 - 0.476491i) q^{58} +(-6.43572 - 7.14759i) q^{59} +(-0.895005 + 8.51540i) q^{61} +(0.600813 - 1.84911i) q^{62} +(3.80902 - 2.76741i) q^{64} +(-3.42705 - 5.93583i) q^{65} +(2.42705 - 4.20378i) q^{67} +(1.52218 + 14.4825i) q^{68} +(-0.604528 + 0.128496i) q^{70} +(-4.30902 - 3.13068i) q^{71} +(2.38197 - 7.33094i) q^{73} +(-0.450835 + 0.500703i) q^{74} +(-0.791796 + 1.37143i) q^{76} +(0.384301 - 3.29428i) q^{77} +(10.0490 + 4.47410i) q^{79} +(-1.57295 - 4.84104i) q^{80} +(-1.30902 - 0.951057i) q^{82} +(-0.781051 + 7.43120i) q^{83} +(12.4305 + 2.64218i) q^{85} +(-0.267834 - 2.54827i) q^{86} +(-4.88220 - 0.0557196i) q^{88} +3.76393 q^{89} +(1.30902 + 4.02874i) q^{91} +(7.68247 - 1.63296i) q^{92} +(-0.380408 + 0.169368i) q^{94} +(0.924716 + 1.02700i) q^{95} +(1.04683 + 0.466079i) q^{97} -2.29180 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - q^{2} + 9 q^{4} - 3 q^{5} - q^{7} - 26 q^{8} + 4 q^{10} - 11 q^{11} - 7 q^{13} - 4 q^{14} - q^{16} - 24 q^{17} - 20 q^{19} + 3 q^{20} - 4 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} - 12 q^{28} + 6 q^{29}+ \cdots - 72 q^{98}+O(q^{100})$ 8 * q - q^2 + 9 * q^4 - 3 * q^5 - q^7 - 26 * q^8 + 4 * q^10 - 11 * q^11 - 7 * q^13 - 4 * q^14 - q^16 - 24 * q^17 - 20 * q^19 + 3 * q^20 - 4 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 - 12 * q^28 + 6 * q^29 + 12 * q^31 - 30 * q^32 - 12 * q^34 - 6 * q^35 + 18 * q^37 - 10 * q^38 + 6 * q^40 - 3 * q^41 - 72 * q^44 - 6 * q^46 + 17 * q^47 - 6 * q^49 + 6 * q^50 - 3 * q^52 - 8 * q^53 + 4 * q^55 + 12 * q^56 + 24 * q^58 - 6 * q^59 + 21 * q^61 + 54 * q^62 + 26 * q^64 - 14 * q^65 + 6 * q^67 - 27 * q^68 - 3 * q^70 - 30 * q^71 + 28 * q^73 - 26 * q^74 - 60 * q^76 + q^77 + 11 * q^79 - 26 * q^80 - 6 * q^82 + 13 * q^83 + 9 * q^85 + 15 * q^86 + 37 * q^88 + 48 * q^89 + 6 * q^91 + 3 * q^92 - 17 * q^94 + 5 * q^95 - 3 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$ .

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.348943	+	0.155360i	0.246740	+	0.109856i	0.526381	−	0.850249i	$-0.323549\pi$
$2$	0.348943	+	0.155360i	0.246740	+	0.109856i	−0.279641	+	0.960105i	$0.590215\pi$
$3$		0			0
$3$		0			0
$4$	−1.24064	−	1.37787i	−0.620318	−	0.688933i
$5$	−1.47815	+	0.658114i	−0.661048	+	0.294317i	−0.709706	−	0.704498i	$-0.751172\pi$
$5$	−1.47815	+	0.658114i	−0.661048	+	0.294317i	0.0486582	+	0.998815i	$0.484506\pi$
$6$		0			0
$7$	0.978148	−	0.207912i	0.369705	−	0.0785832i	−0.0193127	−	0.999813i	$-0.506148\pi$
$7$	0.978148	−	0.207912i	0.369705	−	0.0785832i	0.389018	+	0.921230i	$0.372814\pi$
$8$	−0.454915	−	1.40008i	−0.160837	−	0.495005i
$9$		0			0
$10$	−0.618034			−0.195440
$11$	1.06082	−	3.14240i	0.319850	−	0.947468i
$11$	1.06082	−	3.14240i	0.319850	−	0.947468i
$12$		0			0
$13$	0.442790	+	4.21286i	0.122808	+	1.16844i	0.866241	+	0.499627i	$0.166530\pi$
$13$	0.442790	+	4.21286i	0.122808	+	1.16844i	−0.743433	+	0.668811i	$0.766804\pi$
$14$	0.373619	+	0.0794152i	0.0998539	+	0.0212246i
$15$		0			0
$16$	−0.328836	+	3.12866i	−0.0822090	+	0.782166i
$17$	−6.35410	−	4.61653i	−1.54110	−	1.11967i	−0.949644	−	0.313332i	$-0.898555\pi$
$17$	−6.35410	−	4.61653i	−1.54110	−	1.11967i	−0.591452	−	0.806340i	$-0.701445\pi$
$18$		0			0
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	0.916206	−	0.400707i	$-0.131236\pi$
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	−0.976756	+	0.214353i	$0.931236\pi$
$20$	2.74064	+	1.22021i	0.612825	+	0.272847i
$21$		0			0
$22$	0.858369	−	0.931709i	0.183005	−	0.198641i
$23$	−2.11803	+	3.66854i	−0.441641	+	0.764944i	−0.997811	−	0.0661240i	$-0.978937\pi$
$23$	−2.11803	+	3.66854i	−0.441641	+	0.764944i	0.556171	+	0.831068i	$0.312270\pi$
$24$		0			0
$25$	−1.59385	+	1.77015i	−0.318769	+	0.354029i
$26$	−0.500000	+	1.53884i	−0.0980581	+	0.301792i
$27$		0			0
$28$	−1.50000	−	1.08981i	−0.283473	−	0.205955i
$29$	−5.86889	+	1.24747i	−1.08982	+	0.231649i	−0.717574	−	0.696483i	$-0.754747\pi$
$29$	−5.86889	+	1.24747i	−1.08982	+	0.231649i	−0.372251	+	0.928132i	$0.621414\pi$
$30$		0			0
$31$	−0.532068	−	5.06229i	−0.0955622	−	0.909213i	−0.932319	−	0.361638i	$-0.882218\pi$
$31$	−0.532068	−	5.06229i	−0.0955622	−	0.909213i	0.836756	−	0.547575i	$-0.184449\pi$
$32$	−2.07295	+	3.59045i	−0.366449	+	0.634708i
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	−1.30902	+	0.951057i	−0.221264	+	0.160758i
$36$		0			0
$37$	−0.545085	+	1.67760i	−0.0896114	+	0.275796i	−0.985812	−	0.167854i	$-0.946316\pi$
$37$	−0.545085	+	1.67760i	−0.0896114	+	0.275796i	0.896201	+	0.443649i	$0.146316\pi$
$38$	0.0341011	−	0.324451i	0.00553194	−	0.0526329i
$39$		0			0
$40$	1.59385	+	1.77015i	0.252009	+	0.279885i
$41$	−4.14350	−	0.880728i	−0.647106	−	0.137547i	−0.127345	−	0.991858i	$-0.540646\pi$
$41$	−4.14350	−	0.880728i	−0.647106	−	0.137547i	−0.519761	+	0.854312i	$0.673979\pi$
$42$		0			0
$43$	−3.35410	−	5.80948i	−0.511496	−	0.885937i	−0.999911	−	0.0133254i	$-0.995758\pi$
$43$	−3.35410	−	5.80948i	−0.511496	−	0.885937i	0.488415	−	0.872611i	$-0.337575\pi$
$44$	−5.64590	+	2.43690i	−0.851151	+	0.367376i
$45$		0			0
$46$	−1.30902	+	0.951057i	−0.193004	+	0.140226i
$47$	−0.729466	+	0.810154i	−0.106404	+	0.118173i	−0.793994	−	0.607926i	$-0.792002\pi$
$47$	−0.729466	+	0.810154i	−0.106404	+	0.118173i	0.687590	+	0.726099i	$0.258669\pi$
$48$		0			0
$49$	−5.48127	+	2.44042i	−0.783039	+	0.348631i
$50$	−0.831171	+	0.370061i	−0.117545	+	0.0523346i
$51$		0			0
$52$	5.25542	−	5.83674i	0.728796	−	0.809410i
$53$	−2.11803	+	1.53884i	−0.290934	+	0.211376i	−0.723673	−	0.690143i	$-0.757547\pi$
$53$	−2.11803	+	1.53884i	−0.290934	+	0.211376i	0.432738	+	0.901520i	$0.357547\pi$
$54$		0			0
$55$	0.500000	+	5.34307i	0.0674200	+	0.720459i
$56$	−0.736068	−	1.27491i	−0.0983612	−	0.170367i
$57$		0			0
$58$	−2.24171	−	0.476491i	−0.294352	−	0.0625664i
$59$	−6.43572	−	7.14759i	−0.837859	−	0.930537i	0.160544	−	0.987029i	$-0.448675\pi$
$59$	−6.43572	−	7.14759i	−0.837859	−	0.930537i	−0.998403	+	0.0564915i	$0.982009\pi$
$60$		0			0
$61$	−0.895005	+	8.51540i	−0.114594	+	1.09029i	0.774504	+	0.632568i	$0.217999\pi$
$61$	−0.895005	+	8.51540i	−0.114594	+	1.09029i	−0.889098	+	0.457717i	$0.848667\pi$
$62$	0.600813	−	1.84911i	0.0763033	−	0.234838i
$63$		0			0
$64$	3.80902	−	2.76741i	0.476127	−	0.345927i
$65$	−3.42705	−	5.93583i	−0.425073	−	0.736249i
$66$		0			0
$67$	2.42705	−	4.20378i	0.296511	−	0.513573i	−0.678824	−	0.734301i	$-0.737510\pi$
$67$	2.42705	−	4.20378i	0.296511	−	0.513573i	0.975335	+	0.220728i	$0.0708434\pi$
$68$	1.52218	+	14.4825i	0.184591	+	1.75626i
$69$		0			0
$70$	−0.604528	+	0.128496i	−0.0722550	+	0.0153583i
$71$	−4.30902	−	3.13068i	−0.511386	−	0.371544i	0.301963	−	0.953320i	$-0.402358\pi$
$71$	−4.30902	−	3.13068i	−0.511386	−	0.371544i	−0.813349	+	0.581776i	$0.802358\pi$
$72$		0			0
$73$	2.38197	−	7.33094i	0.278788	−	0.858021i	−0.709404	−	0.704802i	$-0.751036\pi$
$73$	2.38197	−	7.33094i	0.278788	−	0.858021i	0.988192	−	0.153219i	$-0.0489641\pi$
$74$	−0.450835	+	0.500703i	−0.0524085	+	0.0582055i
$75$		0			0
$76$	−0.791796	+	1.37143i	−0.0908252	+	0.157314i
$77$	0.384301	−	3.29428i	0.0437952	−	0.375419i
$78$		0			0
$79$	10.0490	+	4.47410i	1.13060	+	0.503376i	0.884812	−	0.465948i	$-0.154286\pi$
$79$	10.0490	+	4.47410i	1.13060	+	0.503376i	0.245788	+	0.969323i	$0.420953\pi$
$80$	−1.57295	−	4.84104i	−0.175861	−	0.541245i
$81$		0			0
$82$	−1.30902	−	0.951057i	−0.144557	−	0.105027i
$83$	−0.781051	+	7.43120i	−0.0857315	+	0.815680i	0.864185	+	0.503175i	$0.167835\pi$
$83$	−0.781051	+	7.43120i	−0.0857315	+	0.815680i	−0.949916	+	0.312505i	$0.898832\pi$
$84$		0			0
$85$	12.4305	+	2.64218i	1.34828	+	0.286585i
$86$	−0.267834	−	2.54827i	−0.0288813	−	0.274787i
$87$		0			0
$88$	−4.88220	−	0.0557196i	−0.520445	−	0.00593972i
$89$	3.76393			0.398976			0.199488	−	0.979900i	$-0.436072\pi$
$89$	3.76393			0.398976			0.199488	+	0.979900i	$0.436072\pi$
$90$		0			0
$91$	1.30902	+	4.02874i	0.137222	+	0.422327i
$92$	7.68247	−	1.63296i	0.800953	−	0.170248i
$93$		0			0
$94$	−0.380408	+	0.169368i	−0.0392360	+	0.0174690i
$95$	0.924716	+	1.02700i	0.0948738	+	0.105368i
$96$		0			0
$97$	1.04683	+	0.466079i	0.106289	+	0.0473231i	0.459193	−	0.888337i	$-0.348139\pi$
$97$	1.04683	+	0.466079i	0.106289	+	0.0473231i	−0.352903	+	0.935660i	$0.614805\pi$
$98$	−2.29180			−0.231506
$99$		0			0
$100$	4.41641			0.441641
$101$	5.26561	+	2.34440i	0.523948	+	0.233277i	0.651628	−	0.758539i	$-0.274086\pi$
$101$	5.26561	+	2.34440i	0.523948	+	0.233277i	−0.127680	+	0.991815i	$0.540753\pi$
$102$		0			0
$103$	4.64662	+	5.16060i	0.457846	+	0.508489i	0.927224	−	0.374508i	$-0.122188\pi$
$103$	4.64662	+	5.16060i	0.457846	+	0.508489i	−0.469378	+	0.882997i	$0.655522\pi$
$104$	5.69693	−	2.53644i	0.558630	−	0.248718i
$105$		0			0
$106$	−0.978148	+	0.207912i	−0.0950061	+	0.0201942i
$107$	0.781153	+	2.40414i	0.0755169	+	0.232417i	0.981689	−	0.190493i	$-0.0610086\pi$
$107$	0.781153	+	2.40414i	0.0755169	+	0.232417i	−0.906172	+	0.422910i	$0.861009\pi$
$108$		0			0
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$	−0.655625	+	1.94211i	−0.0625114	+	0.185173i
$111$		0			0
$112$	0.328836	+	3.12866i	0.0310721	+	0.295631i
$113$	4.42892	+	0.941396i	0.416638	+	0.0885591i	0.411461	−	0.911428i	$-0.365019\pi$
$113$	4.42892	+	0.941396i	0.416638	+	0.0885591i	0.00517704	+	0.999987i	$0.498352\pi$
$114$		0			0
$115$	0.716449	−	6.81655i	0.0668092	−	0.635647i
$116$	9.00000	+	6.53888i	0.835629	+	0.607120i
$117$		0			0
$118$	−1.13525	−	3.49396i	−0.104509	−	0.321645i
$119$	−7.17508	−	3.19455i	−0.657738	−	0.292844i
$120$		0			0
$121$	−8.74931	−	6.66706i	−0.795391	−	0.606096i
$122$	−1.63525	+	2.83234i	−0.148049	+	0.256428i
$123$		0			0
$124$	−6.31505	+	7.01357i	−0.567108	+	0.629837i
$125$	3.69098	−	11.3597i	0.330132	−	1.01604i
$126$		0			0
$127$	4.61803	+	3.35520i	0.409784	+	0.297726i	0.773514	−	0.633779i	$-0.218497\pi$
$127$	4.61803	+	3.35520i	0.409784	+	0.297726i	−0.363730	+	0.931504i	$0.618497\pi$
$128$	9.86968	−	2.09786i	0.872364	−	0.185427i
$129$		0			0
$130$	−0.273659	−	2.60369i	−0.0240015	−	0.228359i
$131$	6.39919	−	11.0837i	0.559100	−	0.968389i	−0.438472	−	0.898745i	$-0.644480\pi$
$131$	6.39919	−	11.0837i	0.559100	−	0.968389i	0.997572	−	0.0696442i	$-0.0221864\pi$
$132$		0			0
$133$	−0.427051	−	0.739674i	−0.0370300	−	0.0641379i
$134$	1.50000	−	1.08981i	0.129580	−	0.0941456i
$135$		0			0
$136$	−3.57295	+	10.9964i	−0.306378	+	0.942934i
$137$	1.48807	−	14.1581i	0.127135	−	1.20961i	−0.725918	−	0.687781i	$-0.758585\pi$
$137$	1.48807	−	14.1581i	0.127135	−	1.20961i	0.853053	−	0.521825i	$-0.174749\pi$
$138$		0			0
$139$	−3.72191	−	4.13360i	−0.315688	−	0.350607i	0.564328	−	0.825551i	$-0.309135\pi$
$139$	−3.72191	−	4.13360i	−0.315688	−	0.350607i	−0.880016	+	0.474943i	$0.842469\pi$
$140$	2.93444	+	0.623735i	0.248006	+	0.0527152i
$141$		0			0
$142$	−1.01722	−	1.76188i	−0.0853633	−	0.147854i
$143$	13.7082	+	3.07768i	1.14634	+	0.257369i
$144$		0			0
$145$	7.85410	−	5.70634i	0.652248	−	0.473886i
$146$	1.97010	−	2.18802i	0.163047	−	0.181082i
$147$		0			0
$148$	2.98776	−	1.33024i	0.245592	−	0.109345i
$149$	−0.215659	+	0.0960175i	−0.0176675	+	0.00786606i	−0.415551	−	0.909570i	$-0.636411\pi$
$149$	−0.215659	+	0.0960175i	−0.0176675	+	0.00786606i	0.397884	+	0.917436i	$0.369745\pi$
$150$		0			0
$151$	12.6762	−	14.0783i	1.03157	−	1.14568i	0.0423746	−	0.999102i	$-0.486508\pi$
$151$	12.6762	−	14.0783i	1.03157	−	1.14568i	0.989199	−	0.146577i	$-0.0468256\pi$
$152$	−1.01722	+	0.739054i	−0.0825075	+	0.0599452i
$153$		0			0
$154$	0.645898	−	1.08981i	0.0520479	−	0.0878197i
$155$	4.11803	+	7.13264i	0.330768	+	0.572908i
$156$		0			0
$157$	−2.24171	−	0.476491i	−0.178908	−	0.0380281i	0.117586	−	0.993063i	$-0.462484\pi$
$157$	−2.24171	−	0.476491i	−0.178908	−	0.0380281i	−0.296495	+	0.955035i	$0.595818\pi$
$158$	2.81144	+	3.12242i	0.223666	+	0.248406i
$159$		0			0
$160$	0.701198	−	6.67146i	0.0554346	−	0.527425i
$161$	−1.30902	+	4.02874i	−0.103165	+	0.317509i
$162$		0			0
$163$	9.59017	−	6.96767i	0.751160	−	0.545750i	−0.145026	−	0.989428i	$-0.546327\pi$
$163$	9.59017	−	6.96767i	0.751160	−	0.545750i	0.896186	+	0.443678i	$0.146327\pi$
$164$	3.92705	+	6.80185i	0.306651	+	0.531135i
$165$		0			0
$166$	−1.42705	+	2.47172i	−0.110761	+	0.191843i
$167$	−1.78058	−	16.9411i	−0.137786	−	1.31094i	−0.816844	−	0.576859i	$-0.804278\pi$
$167$	−1.78058	−	16.9411i	−0.137786	−	1.31094i	0.679058	−	0.734085i	$-0.262388\pi$
$168$		0			0
$169$	−4.83623	+	1.02797i	−0.372018	+	0.0790748i
$170$	3.92705	+	2.85317i	0.301191	+	0.218828i
$171$		0			0
$172$	−3.84346	+	11.8290i	−0.293061	+	0.901949i
$173$	−7.38348	+	8.20019i	−0.561356	+	0.623449i	−0.955283	−	0.295693i	$-0.904450\pi$
$173$	−7.38348	+	8.20019i	−0.561356	+	0.623449i	0.393927	+	0.919142i	$0.371116\pi$
$174$		0			0
$175$	−1.19098	+	2.06284i	−0.0900299	+	0.155936i
$176$	9.48267	+	4.35229i	0.714783	+	0.328066i
$177$		0			0
$178$	1.31340	+	0.584763i	0.0984434	+	0.0438298i
$179$	5.39919	+	16.6170i	0.403554	+	1.24201i	0.922096	+	0.386960i	$0.126475\pi$
$179$	5.39919	+	16.6170i	0.403554	+	1.24201i	−0.518542	+	0.855052i	$0.673525\pi$
$180$		0			0
$181$	−9.28115	−	6.74315i	−0.689863	−	0.501215i	0.186752	−	0.982407i	$-0.440204\pi$
$181$	−9.28115	−	6.74315i	−0.689863	−	0.501215i	−0.876615	+	0.481192i	$0.840204\pi$
$182$	−0.169131	+	1.60917i	−0.0125368	+	0.119280i
$183$		0			0
$184$	6.09979	+	1.29655i	0.449683	+	0.0955830i
$185$	−0.298335	−	2.83847i	−0.0219340	−	0.208688i
$186$		0			0
$187$	−21.2475	+	15.0698i	−1.55377	+	1.10201i
$188$	2.02129			0.147417
$189$		0			0
$190$	0.163119	+	0.502029i	0.0118339	+	0.0364210i
$191$	−22.6738	+	4.81946i	−1.64062	+	0.348724i	−0.933557	−	0.358428i	$-0.883313\pi$
$191$	−22.6738	+	4.81946i	−1.64062	+	0.348724i	−0.707061	+	0.707153i	$0.749979\pi$
$192$		0			0
$193$	−9.00217	+	4.00802i	−0.647990	+	0.288504i	−0.704293	−	0.709910i	$-0.748736\pi$
$193$	−9.00217	+	4.00802i	−0.647990	+	0.288504i	0.0563022	+	0.998414i	$0.482069\pi$
$194$	0.292875	+	0.325270i	0.0210272	+	0.0233530i
$195$		0			0
$196$	10.1628	+	4.52479i	0.725917	+	0.323199i
$197$	16.0344			1.14241			0.571203	−	0.820809i	$-0.306477\pi$
$197$	16.0344			1.14241			0.571203	+	0.820809i	$0.306477\pi$
$198$		0			0
$199$	−6.70820			−0.475532			−0.237766	−	0.971322i	$-0.576415\pi$
$199$	−6.70820			−0.475532			−0.237766	+	0.971322i	$0.576415\pi$
$200$	3.20342	+	1.42625i	0.226516	+	0.100851i
$201$		0			0
$202$	1.47318	+	1.63613i	0.103652	+	0.115117i
$203$	−5.48127	+	2.44042i	−0.384710	+	0.171284i
$204$		0			0
$205$	6.70432	−	1.42505i	0.468250	−	0.0995297i
$206$	0.819660	+	2.52265i	0.0571084	+	0.175762i
$207$		0			0
$208$	−13.3262			−0.924008
$209$	−2.83255	−	0.0323273i	−0.195932	−	0.00223613i
$210$		0			0
$211$	−0.144455	−	1.37440i	−0.00994468	−	0.0946173i	0.988424	−	0.151719i	$-0.0484808\pi$
$211$	−0.144455	−	1.37440i	−0.00994468	−	0.0946173i	−0.998368	+	0.0571015i	$0.981814\pi$
$212$	4.74803	+	1.00922i	0.326096	+	0.0693138i
$213$		0			0
$214$	−0.100928	+	0.960269i	−0.00689932	+	0.0656426i
$215$	8.78115	+	6.37988i	0.598870	+	0.435104i
$216$		0			0
$217$	−1.57295	−	4.84104i	−0.106779	−	0.328631i
$218$	−4.18732	−	1.86431i	−0.283601	−	0.126267i
$219$		0			0
$220$	6.74171	−	7.31774i	0.454526	−	0.493362i
$221$	16.6353	−	28.8131i	1.11901	−	1.93818i
$222$		0			0
$223$	−10.1576	+	11.2812i	−0.680205	+	0.755444i	−0.980095	−	0.198529i	$-0.936383\pi$
$223$	−10.1576	+	11.2812i	−0.680205	+	0.755444i	0.299890	+	0.953974i	$0.403050\pi$
$224$	−1.28115	+	3.94298i	−0.0856006	+	0.263452i
$225$		0			0
$226$	1.39919	+	1.01657i	0.0930725	+	0.0676212i
$227$	−8.97973	+	1.90870i	−0.596005	+	0.126685i	−0.496031	−	0.868305i	$-0.665210\pi$
$227$	−8.97973	+	1.90870i	−0.596005	+	0.126685i	−0.0999749	+	0.994990i	$0.531876\pi$
$228$		0			0
$229$	0.885579	+	8.42572i	0.0585207	+	0.556788i	0.984022	+	0.178044i	$0.0569770\pi$
$229$	0.885579	+	8.42572i	0.0585207	+	0.556788i	−0.925502	+	0.378743i	$0.876356\pi$
$230$	1.30902	−	2.26728i	0.0863140	−	0.149500i
$231$		0			0
$232$	4.41641	+	7.64944i	0.289951	+	0.502211i
$233$	−8.78115	+	6.37988i	−0.575272	+	0.417960i	−0.837017	−	0.547177i	$-0.815702\pi$
$233$	−8.78115	+	6.37988i	−0.575272	+	0.417960i	0.261744	+	0.965137i	$0.415702\pi$
$234$		0			0
$235$	0.545085	−	1.67760i	0.0355574	−	0.109434i
$236$	−1.86404	+	17.7351i	−0.121338	+	1.15446i
$237$		0			0
$238$	−2.00739	−	2.22943i	−0.130120	−	0.144513i
$239$	2.56082	+	0.544320i	0.165646	+	0.0352091i	0.289988	−	0.957030i	$-0.406349\pi$
$239$	2.56082	+	0.544320i	0.165646	+	0.0352091i	−0.124342	+	0.992239i	$0.539682\pi$
$240$		0			0
$241$	−10.8541	−	18.7999i	−0.699174	−	1.21101i	−0.968753	−	0.248027i	$-0.920218\pi$
$241$	−10.8541	−	18.7999i	−0.699174	−	1.21101i	0.269579	−	0.962978i	$-0.413115\pi$
$242$	−2.01722	−	3.68571i	−0.129672	−	0.236927i
$243$		0			0
$244$	12.8435	−	9.33132i	0.822218	−	0.597376i
$245$	6.49606	−	7.21460i	0.415018	−	0.460924i
$246$		0			0
$247$	3.30524	−	1.47159i	0.210307	−	0.0936348i
$248$	−6.84558	+	3.04785i	−0.434695	+	0.193539i
$249$		0			0
$250$	3.05278	−	3.39045i	0.193075	−	0.214431i
$251$	20.2082	−	14.6821i	1.27553	−	0.926727i	0.276122	−	0.961123i	$-0.410951\pi$
$251$	20.2082	−	14.6821i	1.27553	−	0.926727i	0.999408	+	0.0343954i	$0.0109505\pi$
$252$		0			0
$253$	9.28115	+	10.5474i	0.583501	+	0.663108i
$254$	1.09017	+	1.88823i	0.0684033	+	0.118478i
$255$		0			0
$256$	−5.44076	−	1.15647i	−0.340047	−	0.0722793i
$257$	8.52649	+	9.46963i	0.531868	+	0.590699i	0.947867	−	0.318666i	$-0.103235\pi$
$257$	8.52649	+	9.46963i	0.531868	+	0.590699i	−0.415999	+	0.909365i	$0.636568\pi$
$258$		0			0
$259$	−0.184381	+	1.75427i	−0.0114569	+	0.109005i
$260$	−3.92705	+	12.0862i	−0.243545	+	0.749556i
$261$		0			0
$262$	3.95492	−	2.87341i	0.244335	−	0.177520i
$263$	9.13525	+	15.8227i	0.563304	+	0.975671i	0.997205	+	0.0747107i	$0.0238033\pi$
$263$	9.13525	+	15.8227i	0.563304	+	0.975671i	−0.433901	+	0.900960i	$0.642863\pi$
$264$		0			0
$265$	2.11803	−	3.66854i	0.130110	−	0.225357i
$266$	−0.0341011	−	0.324451i	−0.00209088	−	0.0198934i
$267$		0			0
$268$	−8.80333	+	1.87121i	−0.537749	+	0.114302i
$269$	1.14590	+	0.832544i	0.0698666	+	0.0507611i	0.622170	−	0.782882i	$-0.286251\pi$
$269$	1.14590	+	0.832544i	0.0698666	+	0.0507611i	−0.552304	+	0.833643i	$0.686251\pi$
$270$		0			0
$271$	5.06231	−	15.5802i	0.307513	−	0.946428i	−0.671214	−	0.741263i	$-0.734227\pi$
$271$	5.06231	−	15.5802i	0.307513	−	0.946428i	0.978727	−	0.205165i	$-0.0657731\pi$
$272$	16.5330	−	18.3618i	1.00246	−	1.11335i
$273$		0			0
$274$	2.71885	−	4.70918i	0.164252	−	0.284492i
$275$	3.87171	+	6.88631i	0.233473	+	0.415260i
$276$		0			0
$277$	20.2942	+	9.03557i	1.21936	+	0.542895i	0.912585	−	0.408887i	$-0.134083\pi$
$277$	20.2942	+	9.03557i	1.21936	+	0.542895i	0.306776	+	0.951782i	$0.400750\pi$
$278$	−0.656541	−	2.02063i	−0.0393767	−	0.121189i
$279$		0			0
$280$	1.92705	+	1.40008i	0.115163	+	0.0836711i
$281$	3.05600	−	29.0759i	0.182306	−	1.73452i	−0.395603	−	0.918422i	$-0.629464\pi$
$281$	3.05600	−	29.0759i	0.182306	−	1.73452i	0.577908	−	0.816102i	$-0.303869\pi$
$282$		0			0
$283$	−7.53976	−	1.60263i	−0.448192	−	0.0952662i	−0.0217144	−	0.999764i	$-0.506912\pi$
$283$	−7.53976	−	1.60263i	−0.448192	−	0.0952662i	−0.426478	+	0.904498i	$0.640246\pi$
$284$	1.03226	+	9.82129i	0.0612533	+	0.582786i
$285$		0			0
$286$	4.30524	+	3.20364i	0.254574	+	0.189435i
$287$	−4.23607			−0.250047
$288$		0			0
$289$	13.8090	+	42.4998i	0.812295	+	2.49999i
$290$	3.62717	−	0.770979i	0.212995	−	0.0452734i
$291$		0			0
$292$	−13.0562	+	5.81300i	−0.764057	+	0.340180i
$293$	−6.45877	−	7.17319i	−0.377325	−	0.419062i	0.524332	−	0.851514i	$-0.324315\pi$
$293$	−6.45877	−	7.17319i	−0.377325	−	0.419062i	−0.901657	+	0.432452i	$0.857649\pi$
$294$		0			0
$295$	14.2169	+	6.32976i	0.827738	+	0.368533i
$296$	2.59675			0.150933
$297$		0			0
$298$	−0.0901699			−0.00522340
$299$	−16.3929	−	7.29859i	−0.948026	−	0.422089i
$300$		0			0
$301$	−4.48866	−	4.98517i	−0.258722	−	0.287340i
$302$	6.61048	−	2.94317i	0.380390	−	0.169361i
$303$		0			0
$304$	2.62820	−	0.558642i	0.150738	−	0.0320403i
$305$	−4.28115	−	13.1760i	−0.245138	−	0.754458i
$306$		0			0
$307$	−18.9787			−1.08317			−0.541586	−	0.840645i	$-0.682176\pi$
$307$	−18.9787			−1.08317			−0.541586	+	0.840645i	$0.682176\pi$
$308$	−5.01586	+	3.55749i	−0.285805	+	0.202707i
$309$		0			0
$310$	0.328836	+	3.12866i	0.0186766	+	0.177696i
$311$	−19.2230	−	4.08598i	−1.09004	−	0.231695i	−0.372373	−	0.928083i	$-0.621456\pi$
$311$	−19.2230	−	4.08598i	−1.09004	−	0.231695i	−0.717665	+	0.696389i	$0.754789\pi$
$312$		0			0
$313$	1.19916	−	11.4093i	0.0677808	−	0.644891i	−0.906909	−	0.421328i	$-0.861564\pi$
$313$	1.19916	−	11.4093i	0.0677808	−	0.644891i	0.974689	−	0.223564i	$-0.0717691\pi$
$314$	−0.708204	−	0.514540i	−0.0399663	−	0.0290372i
$315$		0			0
$316$	−6.30244	−	19.3969i	−0.354540	−	1.09116i
$317$	26.6576	+	11.8687i	1.49724	+	0.666613i	0.981731	−	0.190272i	$-0.0609370\pi$
$317$	26.6576	+	11.8687i	1.49724	+	0.666613i	0.515507	+	0.856886i	$0.327604\pi$
$318$		0			0
$319$	−2.30581	+	19.7657i	−0.129100	+	1.10667i
$320$	−3.80902	+	6.59741i	−0.212931	+	0.368806i
$321$		0			0
$322$	−1.08268	+	1.20243i	−0.0603352	+	0.0670090i
$323$	−2.07295	+	6.37988i	−0.115342	+	0.354986i
$324$		0			0
$325$	−8.16312	−	5.93085i	−0.452808	−	0.328985i
$326$	4.42892	−	0.941396i	0.245295	−	0.0521391i
$327$		0			0
$328$	0.651847	+	6.20191i	0.0359922	+	0.342443i
$329$	−0.545085	+	0.944115i	−0.0300515	+	0.0520507i
$330$		0			0
$331$	−1.64590	−	2.85078i	−0.0904667	−	0.156693i	0.817241	−	0.576296i	$-0.195503\pi$
$331$	−1.64590	−	2.85078i	−0.0904667	−	0.156693i	−0.907708	+	0.419603i	$0.862169\pi$
$332$	11.2082	−	8.14324i	0.615130	−	0.446918i
$333$		0			0
$334$	2.01064	−	6.18812i	0.110017	−	0.338599i
$335$	−0.820977	+	7.81108i	−0.0448548	+	0.426765i
$336$		0			0
$337$	2.79719	+	3.10660i	0.152373	+	0.169227i	0.814499	−	0.580166i	$-0.197012\pi$
$337$	2.79719	+	3.10660i	0.152373	+	0.169227i	−0.662126	+	0.749393i	$0.730346\pi$
$338$	−1.84727	−	0.392650i	−0.100478	−	0.0213574i
$339$		0			0
$340$	−11.7812	−	20.4056i	−0.638923	−	1.10665i
$341$	−16.4721	−	3.69822i	−0.892016	−	0.200270i
$342$		0			0
$343$	−10.5172	+	7.64121i	−0.567877	+	0.412586i
$344$	−6.60792	+	7.33884i	−0.356275	+	0.395684i
$345$		0			0
$346$	−3.85039	+	1.71431i	−0.206999	+	0.0921617i
$347$	9.56677	−	4.25940i	0.513571	−	0.228657i	−0.133552	−	0.991042i	$-0.542638\pi$
$347$	9.56677	−	4.25940i	0.513571	−	0.228657i	0.647124	+	0.762385i	$0.275972\pi$
$348$		0			0
$349$	−0.473881	+	0.526298i	−0.0253663	+	0.0281721i	−0.755694	−	0.654924i	$-0.772700\pi$
$349$	−0.473881	+	0.526298i	−0.0253663	+	0.0281721i	0.730328	+	0.683096i	$0.239367\pi$
$350$	−0.736068	+	0.534785i	−0.0393445	+	0.0285854i
$351$		0			0
$352$	9.08359	+	10.3229i	0.484157	+	0.550211i
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270130\pi$
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	−0.980352	+	0.197256i	$0.936797\pi$
$354$		0			0
$355$	8.42971	+	1.79179i	0.447403	+	0.0950983i
$356$	−4.66967	−	5.18620i	−0.247492	−	0.274868i
$357$		0			0
$358$	−0.697598	+	6.63720i	−0.0368692	+	0.350787i
$359$	−1.14590	+	3.52671i	−0.0604782	+	0.186133i	−0.976731	−	0.214468i	$-0.931198\pi$
$359$	−1.14590	+	3.52671i	−0.0604782	+	0.186133i	0.916253	+	0.400600i	$0.131198\pi$
$360$		0			0
$361$	14.7812	−	10.7391i	0.777955	−	0.565218i
$362$	−2.19098	−	3.79489i	−0.115156	−	0.199455i
$363$		0			0
$364$	3.92705	−	6.80185i	0.205833	−	0.356514i
$365$	1.30369	+	12.4038i	0.0682384	+	0.649245i
$366$		0			0
$367$	−28.2236	+	5.99911i	−1.47326	+	0.313151i	−0.873419	−	0.486970i	$-0.838102\pi$
$367$	−28.2236	+	5.99911i	−1.47326	+	0.313151i	−0.599839	+	0.800120i	$0.704769\pi$
$368$	−10.7812	−	7.83297i	−0.562006	−	0.408322i
$369$		0			0
$370$	0.336881	−	1.03681i	0.0175136	−	0.0539014i
$371$	−1.75181	+	1.94558i	−0.0909493	+	0.101009i
$372$		0			0
$373$	17.4443	−	30.2144i	0.903230	−	1.56444i	0.0799547	−	0.996799i	$-0.474522\pi$
$373$	17.4443	−	30.2144i	0.903230	−	1.56444i	0.823275	−	0.567642i	$-0.192144\pi$
$374$	−9.75542	+	1.95749i	−0.504441	+	0.101220i
$375$		0			0
$376$	1.46613	+	0.652763i	0.0756098	+	0.0336637i
$377$	−7.85410	−	24.1724i	−0.404507	−	1.24494i
$378$		0			0
$379$	−8.80902	−	6.40013i	−0.452489	−	0.328752i	0.338089	−	0.941114i	$-0.390220\pi$
$379$	−8.80902	−	6.40013i	−0.452489	−	0.328752i	−0.790578	+	0.612362i	$0.790220\pi$
$380$	0.267834	−	2.54827i	0.0137396	−	0.130723i
$381$		0			0
$382$	−8.66062	−	1.84087i	−0.443116	−	0.0941872i
$383$	0.0740275	+	0.704324i	0.00378263	+	0.0359893i	0.996250	−	0.0865167i	$-0.0275736\pi$
$383$	0.0740275	+	0.704324i	0.00378263	+	0.0359893i	−0.992468	+	0.122506i	$0.960907\pi$
$384$		0			0
$385$	1.59996	+	5.12235i	0.0815415	+	0.261059i
$386$	−3.76393			−0.191579
$387$		0			0
$388$	−0.656541	−	2.02063i	−0.0333308	−	0.102582i
$389$	5.61716	−	1.19396i	0.284801	−	0.0605363i	−0.0632961	−	0.997995i	$-0.520161\pi$
$389$	5.61716	−	1.19396i	0.284801	−	0.0605363i	0.348097	+	0.937458i	$0.386828\pi$
$390$		0			0
$391$	30.3941	−	13.5323i	1.53710	−	0.684360i
$392$	5.91031	+	6.56406i	0.298516	+	0.331535i
$393$		0			0
$394$	5.59511	+	2.49110i	0.281878	+	0.125500i
$395$	−17.7984			−0.895533
$396$		0			0
$397$	−5.29180			−0.265588			−0.132794	−	0.991144i	$-0.542395\pi$
$397$	−5.29180			−0.265588			−0.132794	+	0.991144i	$0.542395\pi$
$398$	−2.34078	−	1.04218i	−0.117333	−	0.0522399i
$399$		0			0
$400$	−5.01408	−	5.56870i	−0.250704	−	0.278435i
$401$	−26.2068	+	11.6680i	−1.30871	+	0.582673i	−0.938180	−	0.346149i	$-0.887489\pi$
$401$	−26.2068	+	11.6680i	−1.30871	+	0.582673i	−0.370526	+	0.928822i	$0.620822\pi$
$402$		0			0
$403$	21.0911	−	4.48306i	1.05062	−	0.223317i
$404$	−3.30244	−	10.1639i	−0.164302	−	0.505671i
$405$		0			0
$406$	−2.29180			−0.113740
$407$	4.69344	+	3.49251i	0.232645	+	0.173117i
$408$		0			0
$409$	−0.258409	−	2.45859i	−0.0127775	−	0.121570i	0.986274	−	0.165118i	$-0.0528004\pi$
$409$	−0.258409	−	2.45859i	−0.0127775	−	0.121570i	−0.999051	+	0.0435482i	$0.986134\pi$
$410$	2.56082	+	0.544320i	0.126470	+	0.0268820i
$411$		0			0
$412$	1.34584	−	12.8049i	0.0663050	−	0.630850i
$413$	−7.78115	−	5.65334i	−0.382886	−	0.278183i
$414$		0			0
$415$	−3.73607	−	11.4984i	−0.183396	−	0.564436i
$416$	−16.0440	−	7.14323i	−0.786620	−	0.350226i
$417$		0			0
$418$	−0.983377	−	0.451344i	−0.0480986	−	0.0220760i
$419$	−12.2254	+	21.1751i	−0.597251	+	1.03447i	0.395974	+	0.918262i	$0.370407\pi$
$419$	−12.2254	+	21.1751i	−0.597251	+	1.03447i	−0.993225	+	0.116207i	$0.962926\pi$
$420$		0			0
$421$	−18.4055	+	20.4414i	−0.897029	+	0.996251i	0.102970	+	0.994684i	$0.467165\pi$
$421$	−18.4055	+	20.4414i	−0.897029	+	0.996251i	−0.999999	+	0.00156699i	$0.999501\pi$
$422$	0.163119	−	0.502029i	0.00794051	−	0.0244384i
$423$		0			0
$424$	3.11803	+	2.26538i	0.151425	+	0.110017i
$425$	18.2994	−	3.88965i	0.887651	−	0.188676i
$426$		0			0
$427$	0.895005	+	8.51540i	0.0433123	+	0.412089i
$428$	2.34346	−	4.05899i	0.113275	−	0.196199i
$429$		0			0
$430$	2.07295	+	3.59045i	0.0999665	+	0.173147i
$431$	−13.8262	+	10.0453i	−0.665986	+	0.483867i	−0.868679	−	0.495375i	$-0.835031\pi$
$431$	−13.8262	+	10.0453i	−0.665986	+	0.483867i	0.202693	+	0.979242i	$0.435031\pi$
$432$		0			0
$433$	−8.43769	+	25.9686i	−0.405490	+	1.24797i	0.514996	+	0.857193i	$0.327793\pi$
$433$	−8.43769	+	25.9686i	−0.405490	+	1.24797i	−0.920486	+	0.390776i	$0.872207\pi$
$434$	0.203232	−	1.93362i	0.00975544	−	0.0928168i
$435$		0			0
$436$	14.8876	+	16.5344i	0.712988	+	0.791854i
$437$	3.53897	+	0.752232i	0.169292	+	0.0359841i
$438$		0			0
$439$	−18.3541	−	31.7902i	−0.875993	−	1.51727i	−0.855701	−	0.517471i	$-0.826873\pi$
$439$	−18.3541	−	31.7902i	−0.875993	−	1.51727i	−0.0202928	−	0.999794i	$-0.506460\pi$
$440$	7.25329	−	3.13068i	0.345787	−	0.149250i
$441$		0			0
$442$	10.2812	−	7.46969i	0.489025	−	0.355297i
$443$	−11.7745	+	13.0769i	−0.559424	+	0.621304i	−0.954812	−	0.297211i	$-0.903944\pi$
$443$	−11.7745	+	13.0769i	−0.559424	+	0.621304i	0.395387	+	0.918514i	$0.370610\pi$
$444$		0			0
$445$	−5.56365	+	2.47710i	−0.263742	+	0.117426i
$446$	−5.29708	+	2.35841i	−0.250824	+	0.111674i
$447$		0			0
$448$	3.15040	−	3.49888i	0.148843	−	0.165306i
$449$	−21.7984	+	15.8374i	−1.02873	+	0.747415i	−0.968054	−	0.250742i	$-0.919325\pi$
$449$	−21.7984	+	15.8374i	−1.02873	+	0.747415i	−0.0606750	+	0.998158i	$0.519325\pi$
$450$		0			0
$451$	−7.16312	+	12.0862i	−0.337298	+	0.569118i
$452$	−4.19756	−	7.27039i	−0.197437	−	0.341970i
$453$		0			0
$454$	−3.42995	−	0.729059i	−0.160976	−	0.0342164i
$455$	−4.58629	−	5.09359i	−0.215009	−	0.238791i
$456$		0			0
$457$	2.40193	−	22.8528i	0.112358	−	1.06901i	−0.782498	−	0.622654i	$-0.786055\pi$
$457$	2.40193	−	22.8528i	0.112358	−	1.06901i	0.894855	−	0.446357i	$-0.147279\pi$
$458$	−1.00000	+	3.07768i	−0.0467269	+	0.143811i
$459$		0			0
$460$	−10.2812	+	7.46969i	−0.479361	+	0.348276i
$461$	−12.1353	−	21.0189i	−0.565195	−	0.978947i	−0.997031	−	0.0769948i	$-0.975468\pi$
$461$	−12.1353	−	21.0189i	−0.565195	−	0.978947i	0.431836	−	0.901952i	$-0.357866\pi$
$462$		0			0
$463$	−17.6353	+	30.5452i	−0.819580	+	1.41955i	0.0864124	+	0.996259i	$0.472460\pi$
$463$	−17.6353	+	30.5452i	−0.819580	+	1.41955i	−0.905992	+	0.423294i	$0.860874\pi$
$464$	−1.97302	−	18.7720i	−0.0915949	−	0.871468i
$465$		0			0
$466$	−4.05530	+	0.861981i	−0.187858	+	0.0399305i
$467$	−12.0451	−	8.75127i	−0.557380	−	0.404960i	0.273119	−	0.961980i	$-0.411945\pi$
$467$	−12.0451	−	8.75127i	−0.557380	−	0.404960i	−0.830499	+	0.557020i	$0.811945\pi$
$468$		0			0
$469$	1.50000	−	4.61653i	0.0692636	−	0.213171i
$470$	0.450835	−	0.500703i	0.0207955	−	0.0230957i
$471$		0			0
$472$	−7.07953	+	12.2621i	−0.325862	+	0.564409i
$473$	−21.8138	+	4.37709i	−1.00300	+	0.201259i
$474$		0			0
$475$	1.85856	+	0.827482i	0.0852764	+	0.0379675i
$476$	4.50000	+	13.8496i	0.206257	+	0.634794i
$477$		0			0
$478$	0.809017	+	0.587785i	0.0370036	+	0.0268847i
$479$	−3.20046	+	30.4503i	−0.146233	+	1.39131i	0.637614	+	0.770356i	$0.279921\pi$
$479$	−3.20046	+	30.4503i	−0.146233	+	1.39131i	−0.783847	+	0.620954i	$0.786745\pi$
$480$		0			0
$481$	−7.30885	−	1.55354i	−0.333255	−	0.0708355i
$482$	−0.866729	−	8.24637i	−0.0394784	−	0.375612i
$483$		0			0
$484$	1.66840	+	20.3268i	0.0758362	+	0.923944i
$485$	−1.85410			−0.0841904
$486$		0			0
$487$	0.218847	+	0.673542i	0.00991691	+	0.0305211i	0.955893	−	0.293717i	$-0.0948922\pi$
$487$	0.218847	+	0.673542i	0.00991691	+	0.0305211i	−0.945976	+	0.324238i	$0.894892\pi$
$488$	12.3294	−	2.62070i	0.558127	−	0.118634i
$489$		0			0
$490$	3.38761	−	1.50826i	0.153037	−	0.0681364i
$491$	19.4651	+	21.6182i	0.878449	+	0.975616i	0.999856	−	0.0169867i	$-0.00540729\pi$
$491$	19.4651	+	21.6182i	0.878449	+	0.975616i	−0.121407	+	0.992603i	$0.538741\pi$
$492$		0			0
$493$	43.0505	+	19.1673i	1.93890	+	0.863252i
$494$	1.38197			0.0621776
$495$		0			0
$496$	16.0132			0.719012
$497$	−4.86576	−	2.16638i	−0.218259	−	0.0971753i
$498$		0			0
$499$	−16.6306	−	18.4702i	−0.744490	−	0.826840i	0.245289	−	0.969450i	$-0.421117\pi$
$499$	−16.6306	−	18.4702i	−0.744490	−	0.826840i	−0.989779	+	0.142610i	$0.954450\pi$
$500$	−20.2313	+	9.00755i	−0.904771	+	0.402830i
$501$		0			0
$502$	9.33253	−	1.98369i	0.416531	−	0.0885364i
$503$	7.00000	+	21.5438i	0.312115	+	0.960590i	0.976926	+	0.213579i	$0.0685119\pi$
$503$	7.00000	+	21.5438i	0.312115	+	0.960590i	−0.664811	+	0.747011i	$0.731488\pi$
$504$		0			0
$505$	−9.32624			−0.415012
$506$	1.59996	+	5.12235i	0.0711269	+	0.227716i
$507$		0			0
$508$	−1.10629	−	10.5256i	−0.0490835	−	0.466999i
$509$	−3.66086	−	0.778140i	−0.162265	−	0.0344904i	0.126063	−	0.992022i	$-0.459766\pi$
$509$	−3.66086	−	0.778140i	−0.162265	−	0.0344904i	−0.288328	+	0.957532i	$0.593099\pi$
$510$		0			0
$511$	0.805727	−	7.66598i	0.0356433	−	0.339123i
$512$	−18.0451	−	13.1105i	−0.797488	−	0.579409i
$513$		0			0
$514$	1.50407	+	4.62904i	0.0663415	+	0.204178i
$515$	−10.2647	−	4.57012i	−0.452315	−	0.201384i
$516$		0			0
$517$	1.77199	+	3.15170i	0.0779320	+	0.138612i
$518$	−0.336881	+	0.583495i	−0.0148017	+	0.0256373i
$519$		0			0
$520$	−6.75164	+	7.49846i	−0.296079	+	0.328829i
$521$	2.76393	−	8.50651i	0.121090	−	0.372677i	−0.872078	−	0.489366i	$-0.837228\pi$
$521$	2.76393	−	8.50651i	0.121090	−	0.372677i	0.993168	+	0.116689i	$0.0372282\pi$
$522$		0			0
$523$	12.3541	+	8.97578i	0.540207	+	0.392483i	0.824162	−	0.566354i	$-0.191647\pi$
$523$	12.3541	+	8.97578i	0.540207	+	0.392483i	−0.283955	+	0.958838i	$0.591647\pi$
$524$	−23.2109	+	4.93364i	−1.01397	+	0.215527i
$525$		0			0
$526$	0.729474	+	6.94048i	0.0318066	+	0.302619i
$527$	−19.9894	+	34.6226i	−0.870750	+	1.50818i
$528$		0			0
$529$	2.52786	+	4.37839i	0.109907	+	0.190365i
$530$	1.30902	−	0.951057i	0.0568601	−	0.0413113i
$531$		0			0
$532$	−0.489357	+	1.50609i	−0.0212163	+	0.0652971i
$533$	1.87569	−	17.8460i	0.0812450	−	0.772995i
$534$		0			0
$535$	−2.73686	−	3.03959i	−0.118325	−	0.131413i
$536$	−6.98974	−	1.48572i	−0.301911	−	0.0641731i
$537$		0			0
$538$	0.270510	+	0.468537i	0.0116625	+	0.0202001i
$539$	1.85410	+	19.8132i	0.0798618	+	0.853414i
$540$		0			0
$541$	36.8156	−	26.7481i	1.58283	−	1.14999i	0.669462	−	0.742846i	$-0.266525\pi$
$541$	36.8156	−	26.7481i	1.58283	−	1.14999i	0.913364	−	0.407144i	$-0.133475\pi$
$542$	4.18699	−	4.65012i	0.179847	−	0.199740i
$543$		0			0
$544$	29.7471	−	13.2443i	1.27540	−	0.567844i
$545$	17.7378	−	7.89736i	0.759803	−	0.338286i
$546$		0			0
$547$	7.85736	−	8.72649i	0.335957	−	0.373118i	−0.551369	−	0.834262i	$-0.685894\pi$
$547$	7.85736	−	8.72649i	0.335957	−	0.373118i	0.887325	+	0.461144i	$0.152561\pi$
$548$	−21.3541	+	15.5147i	−0.912202	+	0.662754i
$549$		0			0
$550$	0.281153	+	3.00444i	0.0119884	+	0.128110i
$551$	2.56231	+	4.43804i	0.109158	+	0.189067i
$552$		0			0
$553$	10.7596	+	2.28703i	0.457546	+	0.0972543i
$554$	5.67777	+	6.30580i	0.241225	+	0.267908i
$555$		0			0
$556$	−1.07801	+	10.2566i	−0.0457178	+	0.434976i
$557$	12.5557	−	38.6426i	0.532003	−	1.63734i	−0.218033	−	0.975941i	$-0.569964\pi$
$557$	12.5557	−	38.6426i	0.532003	−	1.63734i	0.750037	−	0.661396i	$-0.230036\pi$
$558$		0			0
$559$	22.9894	−	16.7027i	0.972346	−	0.706451i
$560$	−2.54508	−	4.40822i	−0.107549	−	0.186281i
$561$		0			0
$562$	5.58359	−	9.67107i	0.235530	−	0.407949i
$563$	−0.898605	−	8.54965i	−0.0378717	−	0.360325i	−0.997003	−	0.0773635i	$-0.975350\pi$
$563$	−0.898605	−	8.54965i	−0.0378717	−	0.360325i	0.959131	−	0.282961i	$-0.0913169\pi$
$564$		0			0
$565$	−7.16614	+	1.52321i	−0.301482	+	0.0640819i
$566$	−2.38197	−	1.73060i	−0.100121	−	0.0727425i
$567$		0			0
$568$	−2.42299	+	7.45718i	−0.101666	+	0.312896i
$569$	−7.90890	+	8.78372i	−0.331558	+	0.368233i	−0.885755	−	0.464153i	$-0.846359\pi$
$569$	−7.90890	+	8.78372i	−0.331558	+	0.368233i	0.554197	+	0.832386i	$0.313025\pi$
$570$		0			0
$571$	−1.04508	+	1.81014i	−0.0437354	+	0.0757520i	−0.887064	−	0.461646i	$-0.847259\pi$
$571$	−1.04508	+	1.81014i	−0.0437354	+	0.0757520i	0.843329	+	0.537398i	$0.180593\pi$
$572$	−12.7663	−	22.7064i	−0.533784	−	0.949401i
$573$		0			0
$574$	−1.47815	−	0.658114i	−0.0616967	−	0.0274691i
$575$	−3.11803	−	9.59632i	−0.130031	−	0.400194i
$576$		0			0
$577$	−14.7984	−	10.7516i	−0.616064	−	0.447597i	0.235480	−	0.971879i	$-0.424334\pi$
$577$	−14.7984	−	10.7516i	−0.616064	−	0.447597i	−0.851545	+	0.524282i	$0.824334\pi$
$578$	−1.78418	+	16.9754i	−0.0742123	+	0.706083i
$579$		0			0
$580$	−17.6067	−	3.74241i	−0.731077	−	0.155395i
$581$	0.781051	+	7.43120i	0.0324035	+	0.308298i
$582$		0			0
$583$	2.58879	+	8.28814i	0.107217	+	0.343260i
$584$	−11.3475			−0.469564
$585$		0			0
$586$	−1.13932	−	3.50647i	−0.0470649	−	0.144851i
$587$	37.2915	−	7.92655i	1.53918	−	0.327164i	0.641264	−	0.767320i	$-0.278410\pi$
$587$	37.2915	−	7.92655i	1.53918	−	0.327164i	0.897921	+	0.440157i	$0.145077\pi$
$588$		0			0
$589$	−3.97166	+	1.76830i	−0.163649	+	0.0728614i
$590$	3.97749	+	4.41745i	0.163751	+	0.181864i
$591$		0			0
$592$	−5.06940	−	2.25704i	−0.208351	−	0.0927639i
$593$	−15.0344			−0.617391			−0.308695	−	0.951161i	$-0.599892\pi$
$593$	−15.0344			−0.617391			−0.308695	+	0.951161i	$0.599892\pi$
$594$		0			0
$595$	12.7082			0.520986
$596$	0.399853	+	0.178026i	0.0163786	+	0.00729224i
$597$		0			0
$598$	−4.58629	−	5.09359i	−0.187547	−	0.208292i
$599$	17.0399	−	7.58665i	0.696231	−	0.309982i	−0.0279331	−	0.999610i	$-0.508893\pi$
$599$	17.0399	−	7.58665i	0.696231	−	0.309982i	0.724164	+	0.689628i	$0.242226\pi$
$600$		0			0
$601$	−28.2573	+	6.00627i	−1.15264	+	0.245001i	−0.744310	−	0.667835i	$-0.767221\pi$
$601$	−28.2573	+	6.00627i	−1.15264	+	0.245001i	−0.408328	+	0.912835i	$0.633888\pi$
$602$	−0.791796	−	2.43690i	−0.0322712	−	0.0993205i
$603$		0			0
$604$	−35.1246			−1.42920
$605$	17.3204	+	4.09685i	0.704176	+	0.166561i
$606$		0			0
$607$	−0.372362	−	3.54279i	−0.0151137	−	0.143797i	0.984363	−	0.176154i	$-0.0563656\pi$
$607$	−0.372362	−	3.54279i	−0.0151137	−	0.143797i	−0.999476	+	0.0323562i	$0.989699\pi$
$608$	3.46364	+	0.736219i	0.140469	+	0.0298576i
$609$		0			0
$610$	0.553143	−	5.26281i	0.0223961	−	0.213085i
$611$	−3.73607	−	2.71441i	−0.151145	−	0.109813i
$612$		0			0
$613$	−8.56231	−	26.3521i	−0.345828	−	1.06435i	−0.961139	−	0.276065i	$-0.910969\pi$
$613$	−8.56231	−	26.3521i	−0.345828	−	1.06435i	0.615311	−	0.788285i	$-0.289031\pi$
$614$	−6.62250	−	2.94852i	−0.267262	−	0.118993i
$615$		0			0
$616$	−4.78710	+	0.960565i	−0.192878	+	0.0387023i
$617$	−5.59017	+	9.68246i	−0.225052	+	0.389801i	−0.956335	−	0.292273i	$-0.905588\pi$
$617$	−5.59017	+	9.68246i	−0.225052	+	0.389801i	0.731283	+	0.682074i	$0.238922\pi$
$618$		0			0
$619$	−10.7895	+	11.9829i	−0.433665	+	0.481634i	−0.919877	−	0.392207i	$-0.871712\pi$
$619$	−10.7895	+	11.9829i	−0.433665	+	0.481634i	0.486212	+	0.873841i	$0.338378\pi$
$620$	4.71885	−	14.5231i	0.189513	−	0.583262i
$621$		0			0
$622$	−6.07295	−	4.41226i	−0.243503	−	0.176915i
$623$	3.68168	−	0.782565i	0.147503	−	0.0313528i
$624$		0			0
$625$	0.775226	+	7.37578i	0.0310090	+	0.295031i
$626$	2.19098	−	3.79489i	0.0875693	−	0.151674i
$627$		0			0
$628$	2.12461	+	3.67994i	0.0847812	+	0.146845i
$629$	11.2082	−	8.14324i	0.446900	−	0.324692i
$630$		0			0
$631$	−9.95492	+	30.6381i	−0.396299	+	1.21968i	0.531646	+	0.846966i	$0.321574\pi$
$631$	−9.95492	+	30.6381i	−0.396299	+	1.21968i	−0.927945	+	0.372716i	$0.878426\pi$
$632$	1.69268	−	16.1048i	0.0673312	−	0.640614i
$633$		0			0
$634$	7.45806	+	8.28302i	0.296197	+	0.328961i
$635$	−9.03424	−	1.92029i	−0.358513	−	0.0762042i
$636$		0			0
$637$	−12.7082	−	22.0113i	−0.503517	−	0.872118i
$638$	−3.87539	+	6.53888i	−0.153428	+	0.258877i
$639$		0			0
$640$	−13.2082	+	9.59632i	−0.522100	+	0.379328i
$641$	9.30749	−	10.3370i	0.367624	−	0.408288i	−0.530744	−	0.847532i	$-0.678087\pi$
$641$	9.30749	−	10.3370i	0.367624	−	0.408288i	0.898367	+	0.439245i	$0.144754\pi$
$642$		0			0
$643$	12.9229	−	5.75366i	0.509630	−	0.226902i	−0.135779	−	0.990739i	$-0.543354\pi$
$643$	12.9229	−	5.75366i	0.509630	−	0.226902i	0.645409	+	0.763837i	$0.276687\pi$
$644$	7.17508	−	3.19455i	0.282738	−	0.125883i
$645$		0			0
$646$	−1.71452	+	1.90416i	−0.0674568	+	0.0749183i
$647$	12.9164	−	9.38432i	0.507796	−	0.368936i	−0.304191	−	0.952611i	$-0.598386\pi$
$647$	12.9164	−	9.38432i	0.507796	−	0.368936i	0.811987	+	0.583676i	$0.198386\pi$
$648$		0			0
$649$	−29.2877	+	12.6412i	−1.14964	+	0.496212i
$650$	−1.92705	−	3.33775i	−0.0755852	−	0.130917i
$651$		0			0
$652$	−21.4984	−	4.56963i	−0.841943	−	0.178961i
$653$	2.26298	+	2.51329i	0.0885571	+	0.0983527i	0.785795	−	0.618488i	$-0.212254\pi$
$653$	2.26298	+	2.51329i	0.0885571	+	0.0983527i	−0.697237	+	0.716840i	$0.745588\pi$
$654$		0			0
$655$	−2.16460	+	20.5948i	−0.0845778	+	0.804704i
$656$	4.11803	−	12.6740i	0.160782	−	0.494837i
$657$		0			0
$658$	−0.336881	+	0.244758i	−0.0131330	+	0.00954168i
$659$	−0.437694	−	0.758108i	−0.0170501	−	0.0295317i	0.857374	−	0.514693i	$-0.172094\pi$
$659$	−0.437694	−	0.758108i	−0.0170501	−	0.0295317i	−0.874425	+	0.485161i	$0.838761\pi$
$660$		0			0
$661$	−8.21885	+	14.2355i	−0.319676	+	0.553695i	−0.980420	−	0.196916i	$-0.936907\pi$
$661$	−8.21885	+	14.2355i	−0.319676	+	0.553695i	0.660744	+	0.750611i	$0.270241\pi$
$662$	−0.131429	−	1.25047i	−0.00510814	−	0.0486008i
$663$		0			0
$664$	10.7596	−	2.28703i	0.417554	−	0.0887539i
$665$	1.11803	+	0.812299i	0.0433555	+	0.0314996i
$666$		0			0
$667$	7.85410	−	24.1724i	0.304112	−	0.935961i
$668$	−21.1335	+	23.4712i	−0.817682	+	0.908127i
$669$		0			0
$670$	−1.50000	+	2.59808i	−0.0579501	+	0.100372i
$671$	25.8093	+	11.8458i	0.996358	+	0.457302i
$672$		0			0
$673$	−16.2911	−	7.25326i	−0.627975	−	0.279593i	0.0679701	−	0.997687i	$-0.478348\pi$
$673$	−16.2911	−	7.25326i	−0.627975	−	0.279593i	−0.695945	+	0.718095i	$0.745014\pi$
$674$	0.493422	+	1.51860i	0.0190059	+	0.0584942i
$675$		0			0
$676$	7.41641	+	5.38834i	0.285246	+	0.207244i
$677$	2.34898	−	22.3490i	0.0902786	−	0.858943i	−0.851871	−	0.523751i	$-0.824532\pi$
$677$	2.34898	−	22.3490i	0.0902786	−	0.858943i	0.942150	−	0.335192i	$-0.108801\pi$
$678$		0			0
$679$	1.12086	+	0.238246i	0.0430146	+	0.00914303i
$680$	−1.95554	−	18.6057i	−0.0749915	−	0.713497i
$681$		0			0
$682$	−5.17329	−	3.84957i	−0.198095	−	0.147408i
$683$	49.0689			1.87757			0.938784	−	0.344505i	$-0.111953\pi$
$683$	49.0689			1.87757			0.938784	+	0.344505i	$0.111953\pi$
$684$		0			0
$685$	7.11803	+	21.9071i	0.271966	+	0.837026i
$686$	−4.85705	+	1.03240i	−0.185443	+	0.0394171i
$687$		0			0
$688$	19.2788	−	8.58350i	0.734999	−	0.327243i
$689$	−7.42077	−	8.24160i	−0.282709	−	0.313980i
$690$		0			0
$691$	29.8295	+	13.2810i	1.13477	+	0.505231i	0.886163	−	0.463373i	$-0.153361\pi$
$691$	29.8295	+	13.2810i	1.13477	+	0.505231i	0.248605	+	0.968605i	$0.420028\pi$
$692$	20.4590			0.777734
$693$		0			0
$694$	4.00000			0.151838
$695$	8.22191	+	3.66063i	0.311875	+	0.138856i
$696$		0			0
$697$	22.2623	+	24.7248i	0.843245	+	0.936519i
$698$	−0.247123	+	0.110026i	−0.00935374	+	0.00416456i
$699$		0			0
$700$	4.31990	−	0.918223i	0.163277	−	0.0347056i
$701$	3.15248	+	9.70232i	0.119067	+	0.366452i	0.992774	−	0.120002i	$-0.0382902\pi$
$701$	3.15248	+	9.70232i	0.119067	+	0.366452i	−0.873706	+	0.486454i	$0.838290\pi$
$702$		0			0
$703$	1.50658			0.0568217
$704$	−4.65561	−	14.9052i	−0.175465	−	0.561760i
$705$		0			0
$706$	−0.479116	−	4.55848i	−0.0180318	−	0.171561i
$707$	5.63798	+	1.19839i	0.212038	+	0.0450701i
$708$		0			0
$709$	4.20359	−	39.9945i	0.157869	−	1.50202i	−0.573028	−	0.819536i	$-0.694231\pi$
$709$	4.20359	−	39.9945i	0.157869	−	1.50202i	0.730897	−	0.682488i	$-0.239102\pi$
$710$	2.66312	+	1.93487i	0.0999451	+	0.0726143i
$711$		0			0
$712$	−1.71227	−	5.26982i	−0.0641700	−	0.197495i
$713$	19.6981	+	8.77018i	0.737701	+	0.328446i
$714$		0			0
$715$	−22.2882	+	4.47229i	−0.833532	+	0.167254i
$716$	16.1976	−	28.0550i	0.605331	−	1.04846i
$717$		0			0
$718$	−0.947762	+	1.05260i	−0.0353702	+	0.0392825i
$719$	−14.3647	+	44.2101i	−0.535715	+	1.64876i	0.206385	+	0.978471i	$0.433830\pi$
$719$	−14.3647	+	44.2101i	−0.535715	+	1.64876i	−0.742100	+	0.670289i	$0.766170\pi$
$720$		0			0
$721$	5.61803	+	4.08174i	0.209227	+	0.152012i
$722$	6.82621	−	1.45096i	0.254045	−	0.0539990i
$723$		0			0
$724$	2.22337	+	21.1540i	0.0826310	+	0.786182i
$725$	7.14590	−	12.3771i	0.265392	−	0.459672i
$726$		0			0
$727$	7.92705	+	13.7301i	0.293998	+	0.509220i	0.974751	−	0.223293i	$-0.0716807\pi$
$727$	7.92705	+	13.7301i	0.293998	+	0.509220i	−0.680753	+	0.732513i	$0.738347\pi$
$728$	5.04508	−	3.66547i	0.186983	−	0.135851i
$729$		0			0
$730$	−1.47214	+	4.53077i	−0.0544862	+	0.167691i
$731$	−5.50728	+	52.3983i	−0.203694	+	1.93802i
$732$		0			0
$733$	−33.1867	−	36.8576i	−1.22578	−	1.36137i	−0.911110	−	0.412164i	$-0.864773\pi$
$733$	−33.1867	−	36.8576i	−1.22578	−	1.36137i	−0.314669	−	0.949201i	$-0.601894\pi$
$734$	−10.7804	−	2.29145i	−0.397913	−	0.0845791i
$735$		0			0
$736$	−8.78115	−	15.2094i	−0.323678	−	0.560626i
$737$	−10.6353	−	12.0862i	−0.391755	−	0.445202i
$738$		0			0
$739$	−2.42705	+	1.76336i	−0.0892805	+	0.0648661i	−0.631530	−	0.775351i	$-0.717573\pi$
$739$	−2.42705	+	1.76336i	−0.0892805	+	0.0648661i	0.542250	+	0.840218i	$0.317573\pi$
$740$	−3.54090	+	3.93257i	−0.130166	+	0.144564i
$741$		0			0
$742$	−0.913545	+	0.406737i	−0.0335373	+	0.0149318i
$743$	6.49664	−	2.89249i	0.238339	−	0.106115i	−0.284092	−	0.958797i	$-0.591692\pi$
$743$	6.49664	−	2.89249i	0.238339	−	0.106115i	0.522430	+	0.852682i	$0.325025\pi$
$744$		0			0
$745$	0.255585	−	0.283856i	0.00936392	−	0.0103997i
$746$	10.7812	−	7.83297i	0.394726	−	0.286785i
$747$		0			0
$748$	47.1246	+	10.5801i	1.72305	+	0.386848i
$749$	1.26393	+	2.18919i	0.0461831	+	0.0799914i
$750$		0			0
$751$	−22.3547	−	4.75163i	−0.815734	−	0.173390i	−0.218893	−	0.975749i	$-0.570244\pi$
$751$	−22.3547	−	4.75163i	−0.815734	−	0.173390i	−0.596841	+	0.802359i	$0.703578\pi$
$752$	−2.29483	−	2.54866i	−0.0836837	−	0.0929402i
$753$		0			0
$754$	1.01478	−	9.65502i	0.0369562	−	0.351615i
$755$	−9.47214	+	29.1522i	−0.344726	+	1.06096i
$756$		0			0
$757$	−4.04508	+	2.93893i	−0.147021	+	0.106817i	−0.658864	−	0.752262i	$-0.728963\pi$
$757$	−4.04508	+	2.93893i	−0.147021	+	0.106817i	0.511843	+	0.859079i	$0.328963\pi$
$758$	−2.07953	−	3.60185i	−0.0755318	−	0.130825i
$759$		0			0
$760$	1.01722	−	1.76188i	0.0368985	−	0.0639100i
$761$	4.46422	+	42.4742i	0.161828	+	1.53969i	0.710527	+	0.703670i	$0.248457\pi$
$761$	4.46422	+	42.4742i	0.161828	+	1.53969i	−0.548699	+	0.836020i	$0.684877\pi$
$762$		0			0
$763$	−11.7378	+	2.49494i	−0.424936	+	0.0903229i
$764$	34.7705	+	25.2623i	1.25795	+	0.913956i
$765$		0			0
$766$	−0.0835921	+	0.257270i	−0.00302031	+	0.00929555i
$767$	27.2622	−	30.2777i	0.984379	−	1.09326i
$768$		0			0
$769$	−1.75329	+	3.03679i	−0.0632252	+	0.109509i	−0.895905	−	0.444245i	$-0.853472\pi$
$769$	−1.75329	+	3.03679i	−0.0632252	+	0.109509i	0.832680	+	0.553754i	$0.186805\pi$
$770$	−0.237511	+	2.03598i	−0.00855931	+	0.0733716i
$771$		0			0
$772$	16.6909	+	7.43129i	0.600720	+	0.267458i
$773$	−1.48936	−	4.58377i	−0.0535684	−	0.164867i	0.920693	−	0.390287i	$-0.127624\pi$
$773$	−1.48936	−	4.58377i	−0.0535684	−	0.164867i	−0.974262	+	0.225421i	$0.927624\pi$
$774$		0			0
$775$	9.80902	+	7.12667i	0.352350	+	0.255997i
$776$	0.176331	−	1.67768i	0.00632991	−	0.0602251i
$777$		0			0
$778$	2.14556	+	0.456053i	0.0769221	+	0.0163503i
$779$	0.378188	+	3.59821i	0.0135500	+	0.128919i
$780$		0			0
$781$	−14.4090	+	10.2195i	−0.515593	+	0.365684i
$782$	12.7082			0.454444
$783$		0			0
$784$	−5.83282	−	17.9516i	−0.208315	−	0.641127i
$785$	3.62717	−	0.770979i	0.129459	−	0.0275174i
$786$		0			0
$787$	3.38761	−	1.50826i	0.120755	−	0.0537637i	−0.345470	−	0.938430i	$-0.612280\pi$
$787$	3.38761	−	1.50826i	0.120755	−	0.0537637i	0.466225	+	0.884666i	$0.345614\pi$
$788$	−19.8929	−	22.0933i	−0.708656	−	0.787042i
$789$		0			0
$790$	−6.21062	−	2.76515i	−0.220964	−	0.0983795i
$791$	4.52786			0.160992
$792$		0			0
$793$	−36.2705			−1.28800
$794$	−1.84654	−	0.822131i	−0.0655311	−	0.0291763i
$795$		0			0
$796$	8.32244	+	9.24301i	0.294981	+	0.327610i
$797$	44.3444	−	19.7434i	1.57076	−	0.699348i	0.577623	−	0.816304i	$-0.303980\pi$
$797$	44.3444	−	19.7434i	1.57076	−	0.699348i	0.993137	+	0.116956i	$0.0373137\pi$
$798$		0			0
$799$	8.37520	−	1.78020i	0.296293	−	0.0629791i
$800$	−3.05166	−	9.39205i	−0.107893	−	0.332059i
$801$		0			0
$802$	−10.9574			−0.386920
$803$	−20.5099	−	15.2619i	−0.723777	−	0.538581i
$804$		0			0
$805$	−0.716449	−	6.81655i	−0.0252515	−	0.240252i
$806$	8.05609	+	1.71237i	0.283764	+	0.0603158i
$807$		0			0
$808$	0.886954	−	8.43881i	0.0312030	−	0.296876i
$809$	12.8713	+	9.35156i	0.452532	+	0.328783i	0.790594	−	0.612340i	$-0.209772\pi$
$809$	12.8713	+	9.35156i	0.452532	+	0.328783i	−0.338063	+	0.941124i	$0.609772\pi$
$810$		0			0
$811$	5.07953	+	15.6332i	0.178366	+	0.548955i	0.999771	−	0.0213905i	$-0.00680931\pi$
$811$	5.07953	+	15.6332i	0.178366	+	0.548955i	−0.821405	+	0.570346i	$0.806809\pi$
$812$	10.1628	+	4.52479i	0.356646	+	0.158789i
$813$		0			0
$814$	1.09515	+	1.94786i	0.0383850	+	0.0682724i
$815$	−9.59017	+	16.6107i	−0.335929	+	0.581846i
$816$		0			0
$817$	−3.83378	+	4.25784i	−0.134127	+	0.148963i
$818$	0.291796	−	0.898056i	0.0102024	−	0.0313998i
$819$		0			0
$820$	−10.2812	−	7.46969i	−0.359033	−	0.260853i
$821$	−8.40889	+	1.78736i	−0.293472	+	0.0623794i	−0.352295	−	0.935889i	$-0.614599\pi$
$821$	−8.40889	+	1.78736i	−0.293472	+	0.0623794i	0.0588228	+	0.998268i	$0.481265\pi$
$822$		0			0
$823$	−2.70026	−	25.6913i	−0.0941253	−	0.895542i	−0.935080	−	0.354437i	$-0.884673\pi$
$823$	−2.70026	−	25.6913i	−0.0941253	−	0.895542i	0.840955	−	0.541106i	$-0.181994\pi$
$824$	5.11146	−	8.85330i	0.178066	−	0.308419i
$825$		0			0
$826$	−1.83688	−	3.18157i	−0.0639133	−	0.110701i
$827$	16.7082	−	12.1392i	0.581001	−	0.422122i	−0.258084	−	0.966123i	$-0.583091\pi$
$827$	16.7082	−	12.1392i	0.581001	−	0.422122i	0.839085	+	0.544000i	$0.183091\pi$
$828$		0			0
$829$	13.1008	−	40.3202i	0.455010	−	1.40038i	−0.416113	−	0.909313i	$-0.636608\pi$
$829$	13.1008	−	40.3202i	0.455010	−	1.40038i	0.871123	−	0.491064i	$-0.163392\pi$
$830$	0.482716	−	4.59274i	0.0167553	−	0.159416i
$831$		0			0
$832$	13.3453	+	14.8215i	0.462666	+	0.513842i
$833$	46.0948	+	9.79776i	1.59709	+	0.339472i
$834$		0			0
$835$	13.7812	+	23.8697i	0.476916	+	0.826044i
$836$	3.46962	+	3.94298i	0.119999	+	0.136371i
$837$		0			0
$838$	−7.55573	+	5.48956i	−0.261008	+	0.189634i
$839$	−23.9768	+	26.6290i	−0.827772	+	0.919334i	−0.997813	−	0.0661029i	$-0.978943\pi$
$839$	−23.9768	+	26.6290i	−0.827772	+	0.919334i	0.170041	+	0.985437i	$0.445610\pi$
$840$		0			0
$841$	6.39482	−	2.84716i	0.220511	−	0.0981778i
$842$	−9.59824	+	4.27341i	−0.330777	+	0.147271i
$843$		0			0
$844$	−1.71452	+	1.90416i	−0.0590161	+	0.0655440i
$845$	6.47214	−	4.70228i	0.222648	−	0.161763i
$846$		0			0
$847$	−9.94427	−	4.70228i	−0.341689	−	0.161572i
$848$	−4.11803	−	7.13264i	−0.141414	−	0.244936i
$849$		0			0
$850$	6.98974	+	1.48572i	0.239746	+	0.0509596i
$851$	−4.99983	−	5.55288i	−0.171392	−	0.190350i
$852$		0			0
$853$	0.226532	−	2.15531i	0.00775632	−	0.0737965i	−0.989959	−	0.141355i	$-0.954854\pi$
$853$	0.226532	−	2.15531i	0.00775632	−	0.0737965i	0.997715	+	0.0675583i	$0.0215209\pi$
$854$	−1.01064	+	3.11044i	−0.0345835	+	0.106437i
$855$		0			0
$856$	3.01064	−	2.18736i	0.102902	−	0.0747624i
$857$	16.1180	+	27.9173i	0.550582	+	0.953635i	0.998233	+	0.0594269i	$0.0189273\pi$
$857$	16.1180	+	27.9173i	0.550582	+	0.953635i	−0.447651	+	0.894208i	$0.647739\pi$
$858$		0			0
$859$	3.79180	−	6.56758i	0.129374	−	0.224083i	−0.794060	−	0.607839i	$-0.792036\pi$
$859$	3.79180	−	6.56758i	0.129374	−	0.224083i	0.923434	+	0.383756i	$0.125370\pi$
$860$	−2.10359	−	20.0144i	−0.0717320	−	0.682484i
$861$		0			0
$862$	−6.38521	+	1.35722i	−0.217481	+	0.0462271i
$863$	29.0344	+	21.0948i	0.988344	+	0.718074i	0.959558	−	0.281512i	$-0.0908358\pi$
$863$	29.0344	+	21.0948i	0.988344	+	0.718074i	0.0287861	+	0.999586i	$0.490836\pi$
$864$		0			0
$865$	5.51722	−	16.9803i	0.187591	−	0.577346i
$866$	−6.97874	+	7.75068i	−0.237147	+	0.263379i
$867$		0			0
$868$	−4.71885	+	8.17328i	−0.160168	+	0.277419i
$869$	24.7196	−	26.8317i	0.838556	−	0.910203i
$870$		0			0
$871$	18.7846	+	8.36344i	0.636492	+	0.283384i
$872$	5.45898	+	16.8010i	0.184864	+	0.568954i
$873$		0			0
$874$	1.11803	+	0.812299i	0.0378181	+	0.0274764i
$875$	1.24852	−	11.8788i	0.0422076	−	0.401578i
$876$		0			0
$877$	39.1804	+	8.32805i	1.32303	+	0.281218i	0.814669	−	0.579926i	$-0.196919\pi$
$877$	39.1804	+	8.32805i	1.32303	+	0.281218i	0.508360	+	0.861145i	$0.330252\pi$
$878$	−1.46562	−	13.9445i	−0.0494624	−	0.470603i
$879$		0			0
$880$	−16.8811	−	0.192660i	−0.569061	−	0.00649457i
$881$	−30.7984			−1.03762			−0.518812	−	0.854888i	$-0.673625\pi$
$881$	−30.7984			−1.03762			−0.518812	+	0.854888i	$0.673625\pi$
$882$		0			0
$883$	5.85410	+	18.0171i	0.197006	+	0.606323i	0.999947	+	0.0102644i	$0.00326732\pi$
$883$	5.85410	+	18.0171i	0.197006	+	0.606323i	−0.802941	+	0.596058i	$0.796733\pi$
$884$	−60.3389	+	12.8254i	−2.02942	+	0.431366i
$885$		0			0
$886$	−6.14027	+	2.73382i	−0.206286	+	0.0918446i
$887$	−20.3986	−	22.6550i	−0.684919	−	0.760680i	0.295980	−	0.955194i	$-0.404354\pi$
$887$	−20.3986	−	22.6550i	−0.684919	−	0.760680i	−0.980900	+	0.194514i	$0.937687\pi$
$888$		0			0
$889$	5.21470	+	2.32174i	0.174896	+	0.0778685i
$890$	−2.32624			−0.0779757
$891$		0			0
$892$	28.1459			0.942394
$893$	0.850617	+	0.378719i	0.0284648	+	0.0126734i
$894$		0			0
$895$	−18.9167	−	21.0091i	−0.632314	−	0.702256i
$896$	9.21783	−	4.10404i	0.307946	−	0.137106i
$897$		0			0
$898$	−10.0669	+	2.13978i	−0.335937	+	0.0714055i
$899$	9.43769	+	29.0462i	0.314765	+	0.968746i
$900$		0			0
$901$	20.5623			0.685030
$902$	−4.37723	+	3.10455i	−0.145746	+	0.103370i
$903$		0			0
$904$	−0.696748	−	6.62912i	−0.0231735	−	0.220481i
$905$	18.1567	+	3.85932i	0.603548	+	0.128288i
$906$		0			0
$907$	−3.28168	+	31.2231i	−0.108967	+	1.03675i	0.794259	+	0.607580i	$0.207860\pi$
$907$	−3.28168	+	31.2231i	−0.108967	+	1.03675i	−0.903225	+	0.429167i	$0.858807\pi$
$908$	13.7705	+	10.0049i	0.456990	+	0.332023i
$909$		0			0
$910$	−0.809017	−	2.48990i	−0.0268187	−	0.0825393i
$911$	9.68061	+	4.31009i	0.320733	+	0.142800i	0.560787	−	0.827960i	$-0.310499\pi$
$911$	9.68061	+	4.31009i	0.320733	+	0.142800i	−0.240054	+	0.970759i	$0.577165\pi$
$912$		0			0
$913$	22.5232	+	10.3376i	0.745410	+	0.342124i
$914$	4.38854	−	7.60118i	0.145160	−	0.251425i
$915$		0			0
$916$	10.5108	−	11.6735i	0.347288	−	0.385702i
$917$	3.95492	−	12.1720i	0.130603	−	0.401954i
$918$		0			0
$919$	4.57295	+	3.32244i	0.150848	+	0.109597i	0.660649	−	0.750695i	$-0.270281\pi$
$919$	4.57295	+	3.32244i	0.150848	+	0.109597i	−0.509801	+	0.860292i	$0.670281\pi$
$920$	−9.86968	+	2.09786i	−0.325394	+	0.0691645i
$921$		0			0
$922$	−0.969032	−	9.21973i	−0.0319134	−	0.303635i
$923$	11.2812	−	19.5395i	0.371324	−	0.643151i
$924$		0			0
$925$	−2.10081	−	3.63871i	−0.0690743	−	0.119640i
$926$	−10.8992	+	7.91872i	−0.358170	+	0.260225i
$927$		0			0
$928$	7.68692	−	23.6579i	0.252335	−	0.776609i
$929$	0.0740275	−	0.704324i	0.00242876	−	0.0231081i	−0.993240	−	0.116075i	$-0.962969\pi$
$929$	0.0740275	−	0.704324i	0.00242876	−	0.0231081i	0.995669	+	0.0929673i	$0.0296352\pi$
$930$		0			0
$931$	3.42903	+	3.80833i	0.112382	+	0.124813i
$932$	19.6848	+	4.18414i	0.644798	+	0.137056i
$933$		0			0
$934$	−2.84346	−	4.92502i	−0.0930408	−	0.161151i
$935$	21.4894	−	36.2587i	0.702777	−	1.18578i
$936$		0			0
$937$	−8.37132	+	6.08212i	−0.273479	+	0.198694i	−0.716068	−	0.698030i	$-0.754060\pi$
$937$	−8.37132	+	6.08212i	−0.273479	+	0.198694i	0.442589	+	0.896725i	$0.354060\pi$
$938$	1.24064	−	1.37787i	0.0405082	−	0.0449889i
$939$		0			0
$940$	−2.98776	+	1.33024i	−0.0974500	+	0.0433875i
$941$	−37.8672	+	16.8596i	−1.23444	+	0.549607i	−0.917081	−	0.398700i	$-0.869461\pi$
$941$	−37.8672	+	16.8596i	−1.23444	+	0.549607i	−0.317355	+	0.948307i	$0.602795\pi$
$942$		0			0
$943$	12.0071	−	13.3352i	0.391004	−	0.434254i
$944$	24.4787	−	17.7848i	0.796714	−	0.578847i
$945$		0			0
$946$	−8.29180	−	1.86162i	−0.269590	−	0.0605266i
$947$	20.6976	+	35.8492i	0.672580	+	1.16494i	0.977170	+	0.212460i	$0.0681474\pi$
$947$	20.6976	+	35.8492i	0.672580	+	1.16494i	−0.304589	+	0.952484i	$0.598519\pi$
$948$		0			0
$949$	31.9389	+	6.78883i	1.03678	+	0.220375i
$950$	0.519973	+	0.577489i	0.0168702	+	0.0187362i
$951$		0			0
$952$	−1.20859	+	11.4990i	−0.0391706	+	0.372684i
$953$	−13.1803	+	40.5649i	−0.426953	+	1.31403i	0.474159	+	0.880439i	$0.342752\pi$
$953$	−13.1803	+	40.5649i	−0.426953	+	1.31403i	−0.901112	+	0.433587i	$0.857248\pi$
$954$		0			0
$955$	30.3435	−	22.0458i	0.981891	−	0.713386i
$956$	−2.42705	−	4.20378i	−0.0784964	−	0.135960i
$957$		0			0
$958$	−5.84752	+	10.1282i	−0.188925	+	0.327228i
$959$	−1.48807	−	14.1581i	−0.0480524	−	0.457188i
$960$		0			0
$961$	4.97894	−	1.05831i	0.160611	−	0.0341389i
$962$	−2.30902	−	1.67760i	−0.0744457	−	0.0540880i
$963$		0			0
$964$	−12.4377	+	38.2793i	−0.400591	+	1.23289i
$965$	10.6688	−	11.8489i	0.343441	−	0.381430i
$966$		0			0
$967$	10.4615	−	18.1198i	0.336419	−	0.582695i	−0.647337	−	0.762204i	$-0.724118\pi$
$967$	10.4615	−	18.1198i	0.336419	−	0.582695i	0.983756	+	0.179509i	$0.0574509\pi$
$968$	−5.35425	+	15.2827i	−0.172092	+	0.491205i
$969$		0			0
$970$	−0.646976	−	0.288052i	−0.0207732	−	0.00924881i
$971$	12.9787	+	39.9444i	0.416507	+	1.28188i	0.910896	+	0.412635i	$0.135392\pi$
$971$	12.9787	+	39.9444i	0.416507	+	1.28188i	−0.494389	+	0.869240i	$0.664608\pi$
$972$		0			0
$973$	−4.50000	−	3.26944i	−0.144263	−	0.104813i
$974$	−0.0282760	+	0.269028i	−0.000906021	+	0.00862021i
$975$		0			0
$976$	−26.3475	−	5.60034i	−0.843364	−	0.179262i
$977$	5.07974	+	48.3305i	0.162515	+	1.54623i	0.706851	+	0.707363i	$0.250115\pi$
$977$	5.07974	+	48.3305i	0.162515	+	1.54623i	−0.544335	+	0.838868i	$0.683218\pi$
$978$		0			0
$979$	3.99287	−	11.8278i	0.127613	−	0.378017i
$980$	−18.0000			−0.574989
$981$		0			0
$982$	3.43363	+	10.5676i	0.109571	+	0.337226i
$983$	−42.9295	+	9.12494i	−1.36924	+	0.291040i	−0.833115	−	0.553100i	$-0.813445\pi$
$983$	−42.9295	+	9.12494i	−1.36924	+	0.291040i	−0.536123	+	0.844140i	$0.680112\pi$
$984$		0			0
$985$	−23.7013	+	10.5525i	−0.755185	+	0.336230i
$986$	12.0444	+	13.3766i	0.383570	+	0.425998i
$987$		0			0
$988$	−6.12825	−	2.72847i	−0.194966	−	0.0868043i
$989$	28.4164			0.903589
$990$		0			0
$991$	−38.7426			−1.23070			−0.615350	−	0.788254i	$-0.710985\pi$
$991$	−38.7426			−1.23070			−0.615350	+	0.788254i	$0.710985\pi$
$992$	19.2788	+	8.58350i	0.612104	+	0.272526i
$993$		0			0
$994$	−1.36131	−	1.51188i	−0.0431780	−	0.0479541i
$995$	9.91572	−	4.41476i	0.314349	−	0.139957i
$996$		0			0
$997$	44.7976	−	9.52202i	1.41875	−	0.301565i	0.566227	−	0.824249i	$-0.308403\pi$
$997$	44.7976	−	9.52202i	1.41875	−	0.301565i	0.852526	+	0.522684i	$0.175069\pi$
$998$	−2.93363	−	9.02878i	−0.0928624	−	0.285801i
$999$		0			0

Display

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.b.190.1		8
3.2	odd	2		891.2.n.c.190.1		8
9.2	odd	6		891.2.n.c.784.1		8
9.4	even	3		99.2.f.a.91.1		4
9.5	odd	6		33.2.e.b.25.1	yes	4
9.7	even	3	inner	891.2.n.b.784.1		8
11.4	even	5	inner	891.2.n.b.433.1		8
33.26	odd	10		891.2.n.c.433.1		8
36.23	even	6		528.2.y.b.289.1		4
45.14	odd	6		825.2.n.c.751.1		4
45.23	even	12		825.2.bx.d.124.1		8
45.32	even	12		825.2.bx.d.124.2		8
99.4	even	15		99.2.f.a.37.1		4
99.5	odd	30		363.2.e.k.130.1		4
99.13	odd	30		1089.2.a.l.1.2		2
99.14	odd	30		363.2.e.k.148.1		4
99.31	even	15		1089.2.a.t.1.1		2
99.32	even	6		363.2.e.f.124.1		4
99.41	even	30		363.2.e.b.148.1		4
99.50	even	30		363.2.e.b.130.1		4
99.59	odd	30		33.2.e.b.4.1	✓	4
99.68	even	30		363.2.a.i.1.1		2
99.70	even	15	inner	891.2.n.b.136.1		8
99.86	odd	30		363.2.a.d.1.2		2
99.92	odd	30		891.2.n.c.136.1		8
99.95	even	30		363.2.e.f.202.1		4
396.59	even	30		528.2.y.b.433.1		4
396.167	odd	30		5808.2.a.ci.1.2		2
396.383	even	30		5808.2.a.cj.1.2		2
495.59	odd	30		825.2.n.c.301.1		4
495.158	even	60		825.2.bx.d.499.2		8
495.257	even	60		825.2.bx.d.499.1		8
495.284	odd	30		9075.2.a.cb.1.1		2
495.464	even	30		9075.2.a.u.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.4.1	✓	4	99.59	odd	30
33.2.e.b.25.1	yes	4	9.5	odd	6
99.2.f.a.37.1		4	99.4	even	15
99.2.f.a.91.1		4	9.4	even	3
363.2.a.d.1.2		2	99.86	odd	30
363.2.a.i.1.1		2	99.68	even	30
363.2.e.b.130.1		4	99.50	even	30
363.2.e.b.148.1		4	99.41	even	30
363.2.e.f.124.1		4	99.32	even	6
363.2.e.f.202.1		4	99.95	even	30
363.2.e.k.130.1		4	99.5	odd	30
363.2.e.k.148.1		4	99.14	odd	30
528.2.y.b.289.1		4	36.23	even	6
528.2.y.b.433.1		4	396.59	even	30
825.2.n.c.301.1		4	495.59	odd	30
825.2.n.c.751.1		4	45.14	odd	6
825.2.bx.d.124.1		8	45.23	even	12
825.2.bx.d.124.2		8	45.32	even	12
825.2.bx.d.499.1		8	495.257	even	60
825.2.bx.d.499.2		8	495.158	even	60
891.2.n.b.136.1		8	99.70	even	15	inner
891.2.n.b.190.1		8	1.1	even	1	trivial
891.2.n.b.433.1		8	11.4	even	5	inner
891.2.n.b.784.1		8	9.7	even	3	inner
891.2.n.c.136.1		8	99.92	odd	30
891.2.n.c.190.1		8	3.2	odd	2
891.2.n.c.433.1		8	33.26	odd	10
891.2.n.c.784.1		8	9.2	odd	6
1089.2.a.l.1.2		2	99.13	odd	30
1089.2.a.t.1.1		2	99.31	even	15
5808.2.a.ci.1.2		2	396.167	odd	30
5808.2.a.cj.1.2		2	396.383	even	30
9075.2.a.u.1.2		2	495.464	even	30
9075.2.a.cb.1.1		2	495.284	odd	30

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	891.2.n.b.190.1

Level	$891$
Weight	$2$
Character	891.190
Analytic conductor	$7.115$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$