LMFDB - Embedded newform 441.2.bb.d.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			163.1
Character	$\chi$	$=$	441.163
Dual form			441.2.bb.d.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.940144 - 2.39545i) q^{2} +(-3.38820 + 3.14379i) q^{4} +(0.392378 - 0.267519i) q^{5} +(-1.60453 - 2.10369i) q^{7} +(6.07919 + 2.92758i) q^{8} +O(q^{10})$	\(q+(-0.940144 - 2.39545i) q^{2} +(-3.38820 + 3.14379i) q^{4} +(0.392378 - 0.267519i) q^{5} +(-1.60453 - 2.10369i) q^{7} +(6.07919 + 2.92758i) q^{8} +(-1.00972 - 0.688415i) q^{10} +(-3.28657 - 0.495370i) q^{11} +(-2.76976 + 3.47317i) q^{13} +(-3.53079 + 5.82133i) q^{14} +(0.606748 - 8.09649i) q^{16} +(-0.946896 + 0.292079i) q^{17} +(-0.0478826 + 0.0829351i) q^{19} +(-0.488432 + 2.13996i) q^{20} +(1.90321 + 8.33852i) q^{22} +(0.486025 + 0.149919i) q^{23} +(-1.74431 + 4.44443i) q^{25} +(10.9238 + 3.36954i) q^{26} +(12.0500 + 2.08342i) q^{28} +(-1.47014 + 6.44112i) q^{29} +(0.404047 + 0.699830i) q^{31} +(-7.06990 + 2.18078i) q^{32} +(1.58988 + 1.99364i) q^{34} +(-1.19236 - 0.396200i) q^{35} +(-2.32031 - 2.15293i) q^{37} +(0.243683 + 0.0367293i) q^{38} +(3.16852 - 0.477578i) q^{40} +(-7.92765 - 3.81776i) q^{41} +(6.60449 - 3.18056i) q^{43} +(12.6929 - 8.65385i) q^{44} +(-0.0978108 - 1.30519i) q^{46} +(0.443785 + 1.13075i) q^{47} +(-1.85099 + 6.75084i) q^{49} +12.2863 q^{50} +(-1.53441 - 20.4753i) q^{52} +(0.333215 - 0.309178i) q^{53} +(-1.42210 + 0.684846i) q^{55} +(-3.59550 - 17.4861i) q^{56} +(16.8115 - 2.53393i) q^{58} +(-3.90255 - 2.66071i) q^{59} +(-8.93259 - 8.28823i) q^{61} +(1.29654 - 1.62581i) q^{62} +(1.74620 + 2.18966i) q^{64} +(-0.157655 + 2.10376i) q^{65} +(-3.22934 - 5.59338i) q^{67} +(2.29004 - 3.96646i) q^{68} +(0.171912 + 3.22871i) q^{70} +(-1.45614 - 6.37976i) q^{71} +(-2.26184 + 5.76306i) q^{73} +(-2.97581 + 7.58224i) q^{74} +(-0.0984946 - 0.431533i) q^{76} +(4.23128 + 7.70874i) q^{77} +(-2.49455 + 4.32069i) q^{79} +(-1.92789 - 3.33920i) q^{80} +(-1.69210 + 22.5795i) q^{82} +(10.8545 + 13.6111i) q^{83} +(-0.293405 + 0.367918i) q^{85} +(-13.8280 - 12.8305i) q^{86} +(-18.5294 - 12.6331i) q^{88} +(-9.88950 + 1.49060i) q^{89} +(11.7506 + 0.253917i) q^{91} +(-2.11806 + 1.02001i) q^{92} +(2.29142 - 2.12613i) q^{94} +(0.00339862 + 0.0453514i) q^{95} +4.44708 q^{97} +(17.9115 - 1.91280i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{10}{21}\right)$	$1$

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 $

$2$	−0.940144	−	2.39545i	−0.664782	−	1.69384i	−0.718726	−	0.695294i	$-0.755274\pi$
$2$	−0.940144	−	2.39545i	−0.664782	−	1.69384i	0.0539436	−	0.998544i	$-0.482821\pi$
$3$		0			0
$3$		0			0
$4$	−3.38820	+	3.14379i	−1.69410	+	1.57189i
$5$	0.392378	−	0.267519i	0.175477	−	0.119638i	−0.472396	−	0.881386i	$-0.656611\pi$
$5$	0.392378	−	0.267519i	0.175477	−	0.119638i	0.647873	+	0.761748i	$0.275659\pi$
$6$		0			0
$7$	−1.60453	−	2.10369i	−0.606454	−	0.795119i
$7$	−1.60453	−	2.10369i	−0.606454	−	0.795119i
$8$	6.07919	+	2.92758i	2.14932	+	1.03506i
$9$		0			0
$10$	−1.00972	−	0.688415i	−0.319302	−	0.217696i
$11$	−3.28657	−	0.495370i	−0.990937	−	0.149360i	−0.366486	−	0.930424i	$-0.619439\pi$
$11$	−3.28657	−	0.495370i	−0.990937	−	0.149360i	−0.624451	+	0.781064i	$0.714677\pi$
$12$		0			0
$13$	−2.76976	+	3.47317i	−0.768194	+	0.963284i	−0.999955	−	0.00948840i	$-0.996980\pi$
$13$	−2.76976	+	3.47317i	−0.768194	+	0.963284i	0.231761	+	0.972773i	$0.425551\pi$
$14$	−3.53079	+	5.82133i	−0.943642	+	1.55581i
$15$		0			0
$16$	0.606748	−	8.09649i	0.151687	−	2.02412i
$17$	−0.946896	+	0.292079i	−0.229656	+	0.0708395i	−0.407447	−	0.913229i	$-0.633581\pi$
$17$	−0.946896	+	0.292079i	−0.229656	+	0.0708395i	0.177791	+	0.984068i	$0.443105\pi$
$18$		0			0
$19$	−0.0478826	+	0.0829351i	−0.0109850	+	0.0190266i	−0.871466	−	0.490457i	$-0.836830\pi$
$19$	−0.0478826	+	0.0829351i	−0.0109850	+	0.0190266i	0.860481	+	0.509483i	$0.170163\pi$
$20$	−0.488432	+	2.13996i	−0.109217	+	0.478510i
$21$		0			0
$22$	1.90321	+	8.33852i	0.405766	+	1.77778i
$23$	0.486025	+	0.149919i	0.101343	+	0.0312603i	0.345012	−	0.938598i	$-0.387875\pi$
$23$	0.486025	+	0.149919i	0.101343	+	0.0312603i	−0.243669	+	0.969858i	$0.578351\pi$
$24$		0			0
$25$	−1.74431	+	4.44443i	−0.348862	+	0.888886i
$26$	10.9238	+	3.36954i	2.14233	+	0.660821i
$27$		0			0
$28$	12.0500	+	2.08342i	2.27723	+	0.393729i
$29$	−1.47014	+	6.44112i	−0.272999	+	1.19609i	0.633455	+	0.773780i	$0.281636\pi$
$29$	−1.47014	+	6.44112i	−0.272999	+	1.19609i	−0.906453	+	0.422306i	$0.861221\pi$
$30$		0			0
$31$	0.404047	+	0.699830i	0.0725690	+	0.125693i	0.900027	−	0.435835i	$-0.143547\pi$
$31$	0.404047	+	0.699830i	0.0725690	+	0.125693i	−0.827458	+	0.561528i	$0.810214\pi$
$32$	−7.06990	+	2.18078i	−1.24979	+	0.385510i
$33$		0			0
$34$	1.58988	+	1.99364i	0.272662	+	0.341907i
$35$	−1.19236	−	0.396200i	−0.201545	−	0.0669700i
$36$		0			0
$37$	−2.32031	−	2.15293i	−0.381456	−	0.353940i	0.466019	−	0.884775i	$-0.345688\pi$
$37$	−2.32031	−	2.15293i	−0.381456	−	0.353940i	−0.847475	+	0.530835i	$0.821878\pi$
$38$	0.243683	+	0.0367293i	0.0395306	+	0.00595828i
$39$		0			0
$40$	3.16852	−	0.477578i	0.500988	−	0.0755117i
$41$	−7.92765	−	3.81776i	−1.23809	−	0.596233i	−0.303797	−	0.952737i	$-0.598254\pi$
$41$	−7.92765	−	3.81776i	−1.23809	−	0.596233i	−0.934294	+	0.356504i	$0.883969\pi$
$42$		0			0
$43$	6.60449	−	3.18056i	1.00718	−	0.485030i	0.143808	−	0.989606i	$-0.454065\pi$
$43$	6.60449	−	3.18056i	1.00718	−	0.485030i	0.863368	+	0.504575i	$0.168351\pi$
$44$	12.6929	−	8.65385i	1.91352	−	1.30462i
$45$		0			0
$46$	−0.0978108	−	1.30519i	−0.0144214	−	0.192440i
$47$	0.443785	+	1.13075i	0.0647327	+	0.164936i	0.959580	−	0.281436i	$-0.0908109\pi$
$47$	0.443785	+	1.13075i	0.0647327	+	0.164936i	−0.894847	+	0.446373i	$0.852716\pi$
$48$		0			0
$49$	−1.85099	+	6.75084i	−0.264428	+	0.964406i
$50$	12.2863			1.73755
$51$		0			0
$52$	−1.53441	−	20.4753i	−0.212785	−	2.83942i
$53$	0.333215	−	0.309178i	0.0457705	−	0.0424689i	−0.656956	−	0.753929i	$-0.728156\pi$
$53$	0.333215	−	0.309178i	0.0457705	−	0.0424689i	0.702726	+	0.711460i	$0.251966\pi$
$54$		0			0
$55$	−1.42210	+	0.684846i	−0.191756	+	0.0923447i
$56$	−3.59550	−	17.4861i	−0.480468	−	2.33668i
$57$		0			0
$58$	16.8115	−	2.53393i	2.20746	−	0.332721i
$59$	−3.90255	−	2.66071i	−0.508068	−	0.346395i	0.281999	−	0.959415i	$-0.409002\pi$
$59$	−3.90255	−	2.66071i	−0.508068	−	0.346395i	−0.790068	+	0.613019i	$0.789955\pi$
$60$		0			0
$61$	−8.93259	−	8.28823i	−1.14370	−	1.06120i	−0.997408	−	0.0719582i	$-0.977075\pi$
$61$	−8.93259	−	8.28823i	−1.14370	−	1.06120i	−0.146293	−	0.989241i	$-0.546734\pi$
$62$	1.29654	−	1.62581i	0.164661	−	0.206479i
$63$		0			0
$64$	1.74620	+	2.18966i	0.218275	+	0.273708i
$65$	−0.157655	+	2.10376i	−0.0195547	+	0.260939i
$66$		0			0
$67$	−3.22934	−	5.59338i	−0.394527	−	0.683340i	0.598514	−	0.801112i	$-0.295758\pi$
$67$	−3.22934	−	5.59338i	−0.394527	−	0.683340i	−0.993041	+	0.117772i	$0.962425\pi$
$68$	2.29004	−	3.96646i	0.277708	−	0.481004i
$69$		0			0
$70$	0.171912	+	3.22871i	0.0205474	+	0.385905i
$71$	−1.45614	−	6.37976i	−0.172812	−	0.757139i	−0.984832	−	0.173509i	$-0.944489\pi$
$71$	−1.45614	−	6.37976i	−0.172812	−	0.757139i	0.812020	−	0.583629i	$-0.198368\pi$
$72$		0			0
$73$	−2.26184	+	5.76306i	−0.264728	+	0.674516i	−0.999995	−	0.00326211i	$-0.998962\pi$
$73$	−2.26184	+	5.76306i	−0.264728	+	0.674516i	0.735267	+	0.677778i	$0.237057\pi$
$74$	−2.97581	+	7.58224i	−0.345931	+	0.881417i
$75$		0			0
$76$	−0.0984946	−	0.431533i	−0.0112981	−	0.0495002i
$77$	4.23128	+	7.70874i	0.482199	+	0.878492i
$78$		0			0
$79$	−2.49455	+	4.32069i	−0.280659	+	0.486116i	−0.971547	−	0.236846i	$-0.923886\pi$
$79$	−2.49455	+	4.32069i	−0.280659	+	0.486116i	0.690888	+	0.722962i	$0.257220\pi$
$80$	−1.92789	−	3.33920i	−0.215545	−	0.373334i
$81$		0			0
$82$	−1.69210	+	22.5795i	−0.186861	+	2.49349i
$83$	10.8545	+	13.6111i	1.19144	+	1.49401i	0.826460	+	0.562995i	$0.190351\pi$
$83$	10.8545	+	13.6111i	1.19144	+	1.49401i	0.364975	+	0.931017i	$0.381078\pi$
$84$		0			0
$85$	−0.293405	+	0.367918i	−0.0318242	+	0.0399063i
$86$	−13.8280	−	12.8305i	−1.49112	−	1.38355i
$87$		0			0
$88$	−18.5294	−	12.6331i	−1.97524	−	1.34670i
$89$	−9.88950	+	1.49060i	−1.04829	+	0.158004i	−0.650524	−	0.759485i	$-0.725451\pi$
$89$	−9.88950	+	1.49060i	−1.04829	+	0.158004i	−0.397761	+	0.917489i	$0.630213\pi$
$90$		0			0
$91$	11.7506	+	0.253917i	1.23180	+	0.0266178i
$92$	−2.11806	+	1.02001i	−0.220823	+	0.106343i
$93$		0			0
$94$	2.29142	−	2.12613i	0.236342	−	0.219293i
$95$	0.00339862	+	0.0453514i	0.000348691	+	0.00465296i
$96$		0			0
$97$	4.44708			0.451532			0.225766	−	0.974182i	$-0.427512\pi$
$97$	4.44708			0.451532			0.225766	+	0.974182i	$0.427512\pi$
$98$	17.9115	−	1.91280i	1.80933	−	0.193222i
$99$		0			0
$100$	−8.06228	−	20.5423i	−0.806228	−	2.05423i
$101$	−0.674598	−	9.00188i	−0.0671250	−	0.895720i	−0.924538	−	0.381091i	$-0.875549\pi$
$101$	−0.674598	−	9.00188i	−0.0671250	−	0.895720i	0.857413	−	0.514630i	$-0.172071\pi$
$102$		0			0
$103$	−15.7301	+	10.7246i	−1.54993	+	1.05672i	−0.579611	+	0.814893i	$0.696796\pi$
$103$	−15.7301	+	10.7246i	−1.54993	+	1.05672i	−0.970318	+	0.241831i	$0.922252\pi$
$104$	−27.0059	+	13.0053i	−2.64814	+	1.27528i
$105$		0			0
$106$	−1.05389	−	0.507526i	−0.102363	−	0.0492953i
$107$	2.20422	−	0.332232i	0.213090	−	0.0321181i	−0.0416297	−	0.999133i	$-0.513255\pi$
$107$	2.20422	−	0.332232i	0.213090	−	0.0321181i	0.254719	+	0.967015i	$0.418017\pi$
$108$		0			0
$109$	0.0227935	+	0.00343556i	0.00218322	+	0.000329067i	0.150134	−	0.988666i	$-0.452030\pi$
$109$	0.0227935	+	0.00343556i	0.00218322	+	0.000329067i	−0.147951	+	0.988995i	$0.547268\pi$
$110$	2.97749	+	2.76271i	0.283893	+	0.263414i
$111$		0			0
$112$	−18.0060	+	11.7146i	−1.70141	+	1.10693i
$113$	−7.50707	−	9.41357i	−0.706206	−	0.885554i	0.291264	−	0.956643i	$-0.405924\pi$
$113$	−7.50707	−	9.41357i	−0.706206	−	0.885554i	−0.997470	+	0.0710887i	$0.977353\pi$
$114$		0			0
$115$	0.230812	−	0.0711961i	0.0215233	−	0.00663907i
$116$	−15.2684	−	26.4456i	−1.41763	−	2.45541i
$117$		0			0
$118$	−2.70464	+	11.8498i	−0.248982	+	1.09086i
$119$	2.13376	+	1.52333i	0.195602	+	0.139643i
$120$		0			0
$121$	0.0448251	+	0.0138267i	0.00407501	+	0.00125697i
$122$	−11.4561	+	29.1897i	−1.03719	+	2.64271i
$123$		0			0
$124$	−3.56911	−	1.10092i	−0.320515	−	0.0988659i
$125$	1.03291	+	4.52549i	0.0923865	+	0.404772i
$126$		0			0
$127$	2.17823	−	9.54347i	0.193287	−	0.846846i	−0.781535	−	0.623861i	$-0.785563\pi$
$127$	2.17823	−	9.54347i	0.193287	−	0.846846i	0.974822	−	0.222984i	$-0.0715799\pi$
$128$	−3.79505	+	6.57323i	−0.335439	+	0.580997i
$129$		0			0
$130$	5.18767	−	1.60018i	0.454989	−	0.140345i
$131$	0.679017	−	9.06086i	0.0593260	−	0.791651i	−0.885617	−	0.464416i	$-0.846264\pi$
$131$	0.679017	−	9.06086i	0.0593260	−	0.791651i	0.944943	−	0.327235i	$-0.106117\pi$
$132$		0			0
$133$	0.251298	−	0.0323415i	0.0217903	−	0.00280436i
$134$	−10.3626	+	12.9943i	−0.895193	+	1.12254i
$135$		0			0
$136$	−6.61144	−	0.996515i	−0.566927	−	0.0854504i
$137$	−8.26875	−	5.63754i	−0.706447	−	0.481647i	0.156025	−	0.987753i	$-0.450132\pi$
$137$	−8.26875	−	5.63754i	−0.706447	−	0.481647i	−0.862471	+	0.506106i	$0.831084\pi$
$138$		0			0
$139$	−13.3259	−	6.41742i	−1.13029	−	0.544319i	−0.227233	−	0.973840i	$-0.572968\pi$
$139$	−13.3259	−	6.41742i	−1.13029	−	0.544319i	−0.903057	+	0.429522i	$0.858682\pi$
$140$	5.28551	−	2.40611i	0.446707	−	0.203354i
$141$		0			0
$142$	−13.9134	+	9.48600i	−1.16759	+	0.796048i
$143$	10.8235	−	10.0427i	0.905107	−	0.839817i
$144$		0			0
$145$	1.14627	+	2.92065i	0.0951925	+	0.242546i
$146$	15.9316			1.31851
$147$		0			0
$148$	14.6300			1.20258
$149$	−4.16942	−	10.6235i	−0.341572	−	0.870312i	−0.993687	−	0.112191i	$-0.964213\pi$
$149$	−4.16942	−	10.6235i	−0.341572	−	0.870312i	0.652114	−	0.758121i	$-0.273882\pi$
$150$		0			0
$151$	7.34630	−	6.81637i	0.597833	−	0.554708i	−0.322139	−	0.946692i	$-0.604402\pi$
$151$	7.34630	−	6.81637i	0.597833	−	0.554708i	0.919972	+	0.391984i	$0.128211\pi$
$152$	−0.533886	+	0.363998i	−0.0433039	+	0.0295241i
$153$		0			0
$154$	14.4879	−	17.3831i	1.16747	−	1.40077i
$155$	0.345757	+	0.166508i	0.0277719	+	0.0133742i
$156$		0			0
$157$	18.2173	+	12.4204i	1.45390	+	0.991253i	0.994689	+	0.102926i	$0.0328205\pi$
$157$	18.2173	+	12.4204i	1.45390	+	0.991253i	0.459212	+	0.888327i	$0.348132\pi$
$158$	12.6952	+	1.91350i	1.00998	+	0.152230i
$159$		0			0
$160$	−2.19068	+	2.74702i	−0.173188	+	0.217171i
$161$	−0.464458	−	1.26299i	−0.0366044	−	0.0995379i
$162$		0			0
$163$	0.702806	−	9.37829i	0.0550480	−	0.734565i	−0.899579	−	0.436759i	$-0.856126\pi$
$163$	0.702806	−	9.37829i	0.0550480	−	0.734565i	0.954627	−	0.297806i	$-0.0962547\pi$
$164$	38.8626	−	11.9875i	3.03466	−	0.936070i
$165$		0			0
$166$	22.3999	−	38.7978i	1.73857	−	3.01129i
$167$	−2.15813	+	9.45539i	−0.167001	+	0.731680i	0.820184	+	0.572100i	$0.193871\pi$
$167$	−2.15813	+	9.45539i	−0.167001	+	0.731680i	−0.987185	+	0.159580i	$0.948986\pi$
$168$		0			0
$169$	−1.49857	−	6.56565i	−0.115274	−	0.505050i
$170$	1.15717	+	0.356940i	0.0887510	+	0.0273761i
$171$		0			0
$172$	−12.3783	+	31.5395i	−0.943839	+	2.40486i
$173$	−11.0232	−	3.40020i	−0.838077	−	0.258513i	−0.154136	−	0.988050i	$-0.549259\pi$
$173$	−11.0232	−	3.40020i	−0.838077	−	0.258513i	−0.683941	+	0.729537i	$0.739736\pi$
$174$		0			0
$175$	12.1485	−	3.46172i	0.918339	−	0.261682i
$176$	−6.00487	+	26.3091i	−0.452634	+	1.98312i
$177$		0			0
$178$	12.8682	+	22.2884i	0.964514	+	1.67059i
$179$	18.6087	−	5.74001i	1.39088	−	0.429028i	0.493289	−	0.869866i	$-0.335795\pi$
$179$	18.6087	−	5.74001i	1.39088	−	0.429028i	0.897587	+	0.440837i	$0.145318\pi$
$180$		0			0
$181$	7.25983	+	9.10354i	0.539619	+	0.676661i	0.974645	−	0.223757i	$-0.0718323\pi$
$181$	7.25983	+	9.10354i	0.539619	+	0.676661i	−0.435026	+	0.900418i	$0.643261\pi$
$182$	−10.4390	−	28.3867i	−0.773792	−	2.10416i
$183$		0			0
$184$	2.51574	+	2.33426i	0.185463	+	0.172084i
$185$	−1.48639	−	0.224037i	−0.109281	−	0.0164715i
$186$		0			0
$187$	3.25672	−	0.490872i	0.238155	−	0.0358961i
$188$	−5.05845	−	2.43602i	−0.368926	−	0.177665i
$189$		0			0
$190$	0.105442	−	0.0507781i	0.00764955	−	0.00368383i
$191$	−17.6671	+	12.0453i	−1.27835	+	0.871564i	−0.996139	−	0.0877886i	$-0.972020\pi$
$191$	−17.6671	+	12.0453i	−1.27835	+	0.871564i	−0.282210	+	0.959353i	$0.591068\pi$
$192$		0			0
$193$	−1.60993	−	21.4831i	−0.115886	−	1.54639i	−0.687695	−	0.726000i	$-0.741377\pi$
$193$	−1.60993	−	21.4831i	−0.115886	−	1.54639i	0.571810	−	0.820386i	$-0.306242\pi$
$194$	−4.18089	−	10.6527i	−0.300171	−	0.764822i
$195$		0			0
$196$	−14.9517	−	28.6923i	−1.06798	−	2.04945i
$197$	−0.704181			−0.0501708			−0.0250854	−	0.999685i	$-0.507986\pi$
$197$	−0.704181			−0.0501708			−0.0250854	+	0.999685i	$0.507986\pi$
$198$		0			0
$199$	0.346169	+	4.61931i	0.0245393	+	0.327454i	0.995941	+	0.0900110i	$0.0286902\pi$
$199$	0.346169	+	4.61931i	0.0245393	+	0.327454i	−0.971402	+	0.237443i	$0.923691\pi$
$200$	−23.6154	+	21.9119i	−1.66986	+	1.54941i
$201$		0			0
$202$	−20.9293	+	10.0790i	−1.47258	+	0.709158i
$203$	15.9090	−	7.24222i	1.11659	−	0.508304i
$204$		0			0
$205$	−4.13196	+	0.622793i	−0.288589	+	0.0434977i
$206$	40.4787	+	27.5979i	2.82028	+	1.92284i
$207$		0			0
$208$	26.4399	+	24.5327i	1.83328	+	1.70103i
$209$	0.198453	−	0.248852i	0.0137273	−	0.0172135i
$210$		0			0
$211$	−4.70611	−	5.90127i	−0.323982	−	0.406260i	0.592992	−	0.805209i	$-0.297947\pi$
$211$	−4.70611	−	5.90127i	−0.323982	−	0.406260i	−0.916973	+	0.398948i	$0.869375\pi$
$212$	−0.157007	+	2.09511i	−0.0107833	+	0.143893i
$213$		0			0
$214$	−2.86813	−	4.96774i	−0.196061	−	0.339588i
$215$	1.74060	−	3.01481i	0.118708	−	0.205608i
$216$		0			0
$217$	0.823919	−	1.97288i	0.0559313	−	0.133928i
$218$	−0.0131994	−	0.0578305i	−0.000893978	−	0.00391677i
$219$		0			0
$220$	2.66534	−	6.79117i	0.179697	−	0.457860i
$221$	1.60824	−	4.09772i	0.108182	−	0.275643i
$222$		0			0
$223$	4.86902	+	21.3326i	0.326054	+	1.42854i	0.826582	+	0.562816i	$0.190282\pi$
$223$	4.86902	+	21.3326i	0.326054	+	1.42854i	−0.500529	+	0.865720i	$0.666861\pi$
$224$	15.9315	+	11.3737i	1.06447	+	0.759940i
$225$		0			0
$226$	−15.4920	+	26.8329i	−1.03051	+	1.78490i
$227$	0.0931095	+	0.161270i	0.00617989	+	0.0107039i	0.869099	−	0.494639i	$-0.164700\pi$
$227$	0.0931095	+	0.161270i	0.00617989	+	0.0107039i	−0.862919	+	0.505342i	$0.831366\pi$
$228$		0			0
$229$	1.07215	−	14.3069i	0.0708497	−	0.945424i	−0.842618	−	0.538512i	$-0.818987\pi$
$229$	1.07215	−	14.3069i	0.0708497	−	0.945424i	0.913467	−	0.406912i	$-0.133394\pi$
$230$	−0.387543	−	0.485964i	−0.0255538	−	0.0320435i
$231$		0			0
$232$	−27.7942	+	34.8528i	−1.82478	+	2.28820i
$233$	10.4779	+	9.72211i	0.686433	+	0.636917i	0.944232	−	0.329282i	$-0.106807\pi$
$233$	10.4779	+	9.72211i	0.686433	+	0.636917i	−0.257799	+	0.966199i	$0.582997\pi$
$234$		0			0
$235$	0.476627	+	0.324959i	0.0310917	+	0.0211980i
$236$	21.5873	−	3.25376i	1.40521	−	0.211802i
$237$		0			0
$238$	1.64300	−	6.54346i	0.106500	−	0.424150i
$239$	23.7061	−	11.4162i	1.53342	−	0.738455i	0.538836	−	0.842411i	$-0.318864\pi$
$239$	23.7061	−	11.4162i	1.53342	−	0.738455i	0.994582	+	0.103955i	$0.0331499\pi$
$240$		0			0
$241$	8.94423	−	8.29903i	0.576149	−	0.534588i	−0.337377	−	0.941370i	$-0.609540\pi$
$241$	8.94423	−	8.29903i	0.576149	−	0.534588i	0.913525	+	0.406782i	$0.133349\pi$
$242$	−0.00902088	−	0.120375i	−0.000579884	−	0.00773802i
$243$		0			0
$244$	56.3218			3.60563
$245$	1.07969	+	3.14406i	0.0689787	+	0.200867i
$246$		0			0
$247$	−0.155424	−	0.396015i	−0.00988941	−	0.0251978i
$248$	0.407468	+	5.43728i	0.0258742	+	0.345267i
$249$		0			0
$250$	9.86948	−	6.72890i	0.624201	−	0.425573i
$251$	−22.4122	+	10.7931i	−1.41464	+	0.681256i	−0.976073	−	0.217441i	$-0.930229\pi$
$251$	−22.4122	+	10.7931i	−1.41464	+	0.681256i	−0.438569	+	0.898697i	$0.644515\pi$
$252$		0			0
$253$	−1.52309	−	0.733481i	−0.0957558	−	0.0461136i
$254$	−24.9087	+	3.75439i	−1.56291	+	0.235571i
$255$		0			0
$256$	24.8525	+	3.74592i	1.55328	+	0.234120i
$257$	3.22480	+	2.99217i	0.201157	+	0.186647i	0.774319	−	0.632796i	$-0.218093\pi$
$257$	3.22480	+	2.99217i	0.201157	+	0.186647i	−0.573161	+	0.819442i	$0.694283\pi$
$258$		0			0
$259$	−0.806098	+	8.33563i	−0.0500885	+	0.517951i
$260$	−6.07961	−	7.62359i	−0.377041	−	0.472795i
$261$		0			0
$262$	−22.3432	+	6.89196i	−1.38037	+	0.425787i
$263$	−3.40636	−	5.89999i	−0.210045	−	0.363809i	0.741683	−	0.670750i	$-0.234028\pi$
$263$	−3.40636	−	5.89999i	−0.210045	−	0.363809i	−0.951728	+	0.306941i	$0.900694\pi$
$264$		0			0
$265$	0.0480352	−	0.210456i	0.00295078	−	0.0129282i
$266$	−0.313729	−	0.571566i	−0.0192360	−	0.0350450i
$267$		0			0
$268$	28.5260	+	8.79912i	1.74251	+	0.537492i
$269$	−9.00683	+	22.9490i	−0.549156	+	1.39923i	0.339480	+	0.940613i	$0.389749\pi$
$269$	−9.00683	+	22.9490i	−0.549156	+	1.39923i	−0.888636	+	0.458613i	$0.848346\pi$
$270$		0			0
$271$	−2.50940	−	0.774046i	−0.152435	−	0.0470200i	0.217599	−	0.976038i	$-0.430178\pi$
$271$	−2.50940	−	0.774046i	−0.152435	−	0.0470200i	−0.370034	+	0.929018i	$0.620654\pi$
$272$	1.79028	+	7.84375i	0.108552	+	0.475597i
$273$		0			0
$274$	−5.73061	+	25.1074i	−0.346199	+	1.51680i
$275$	7.93443	−	13.7428i	0.478464	−	0.828724i
$276$		0			0
$277$	15.1913	−	4.68590i	0.912757	−	0.281548i	0.197413	−	0.980320i	$-0.436746\pi$
$277$	15.1913	−	4.68590i	0.912757	−	0.281548i	0.715344	+	0.698772i	$0.246270\pi$
$278$	−2.84432	+	37.9548i	−0.170591	+	2.27638i
$279$		0			0
$280$	−6.08865	−	5.89930i	−0.363867	−	0.352550i
$281$	−9.15377	+	11.4785i	−0.546068	+	0.684748i	−0.975914	−	0.218154i	$-0.929996\pi$
$281$	−9.15377	+	11.4785i	−0.546068	+	0.684748i	0.429846	+	0.902902i	$0.358568\pi$
$282$		0			0
$283$	−0.312407	−	0.0470878i	−0.0185707	−	0.00279908i	0.139750	−	0.990187i	$-0.455370\pi$
$283$	−0.312407	−	0.0470878i	−0.0185707	−	0.00279908i	−0.158321	+	0.987388i	$0.550608\pi$
$284$	24.9903	+	17.0381i	1.48290	+	1.01103i
$285$		0			0
$286$	−34.2325	−	16.4855i	−2.02421	−	0.974809i
$287$	4.68876	+	22.8030i	0.276769	+	1.34602i
$288$		0			0
$289$	−13.2348	+	9.02330i	−0.778515	+	0.530783i
$290$	5.91860	−	5.49166i	0.347552	−	0.322481i
$291$		0			0
$292$	−10.4543	−	26.6371i	−0.611792	−	1.55882i
$293$	13.4547			0.786029			0.393015	−	0.919532i	$-0.371432\pi$
$293$	13.4547			0.786029			0.393015	+	0.919532i	$0.371432\pi$
$294$		0			0
$295$	−2.24307			−0.130596
$296$	−7.80270	−	19.8809i	−0.453523	−	1.15556i
$297$		0			0
$298$	−21.5282	+	19.9753i	−1.24710	+	1.15714i
$299$	−1.86687	+	1.27281i	−0.107964	+	0.0736085i
$300$		0			0
$301$	−17.2880	−	8.79050i	−0.996462	−	0.506676i
$302$	−23.2348	−	11.1893i	−1.33701	−	0.643872i
$303$		0			0
$304$	0.642430	+	0.438001i	0.0368459	+	0.0251211i
$305$	−5.72221	−	0.862485i	−0.327653	−	0.0493858i
$306$		0			0
$307$	11.4060	−	14.3026i	0.650972	−	0.816293i	−0.341355	−	0.939934i	$-0.610886\pi$
$307$	11.4060	−	14.3026i	0.650972	−	0.816293i	0.992327	+	0.123641i	$0.0394573\pi$
$308$	−38.5710	−	12.8165i	−2.19779	−	0.730287i
$309$		0			0
$310$	0.0737994	−	0.984785i	0.00419152	−	0.0559320i
$311$	7.19576	−	2.21960i	0.408034	−	0.125862i	−0.0839420	−	0.996471i	$-0.526751\pi$
$311$	7.19576	−	2.21960i	0.408034	−	0.125862i	0.491976	+	0.870609i	$0.336275\pi$
$312$		0			0
$313$	−9.28638	+	16.0845i	−0.524897	+	0.909149i	0.474682	+	0.880157i	$0.342563\pi$
$313$	−9.28638	+	16.0845i	−0.524897	+	0.909149i	−0.999580	+	0.0289916i	$0.990770\pi$
$314$	12.6254	−	55.3156i	0.712494	−	3.12164i
$315$		0			0
$316$	−5.13130	−	22.4817i	−0.288658	−	1.26469i
$317$	14.7822	+	4.55971i	0.830252	+	0.256099i	0.680614	−	0.732642i	$-0.261713\pi$
$317$	14.7822	+	4.55971i	0.830252	+	0.256099i	0.149638	+	0.988741i	$0.452189\pi$
$318$		0			0
$319$	8.02246	−	20.4409i	0.449172	−	1.14447i
$320$	1.27095	+	0.392035i	0.0710481	+	0.0219154i
$321$		0			0
$322$	−2.58878	+	2.29998i	−0.144267	+	0.128173i
$323$	0.0211163	−	0.0925164i	0.00117494	−	0.00514775i
$324$		0			0
$325$	−10.6049	−	18.3683i	−0.588257	−	1.01889i
$326$	−23.1260	+	7.13341i	−1.28083	+	0.395083i
$327$		0			0
$328$	−37.0169	−	46.4177i	−2.04391	−	2.56299i
$329$	1.66667	−	2.74789i	0.0918865	−	0.151496i
$330$		0			0
$331$	4.37900	+	4.06312i	0.240692	+	0.223329i	0.791290	−	0.611441i	$-0.209410\pi$
$331$	4.37900	+	4.06312i	0.240692	+	0.223329i	−0.550598	+	0.834770i	$0.685600\pi$
$332$	−79.5675	−	11.9929i	−4.36684	−	0.658195i
$333$		0			0
$334$	24.6788	−	3.71974i	1.35037	−	0.203535i
$335$	−2.76346	−	1.33081i	−0.150984	−	0.0727100i
$336$		0			0
$337$	−8.43617	+	4.06265i	−0.459548	+	0.221306i	−0.649310	−	0.760523i	$-0.724942\pi$
$337$	−8.43617	+	4.06265i	−0.459548	+	0.221306i	0.189763	+	0.981830i	$0.439228\pi$
$338$	−14.3188	+	9.76239i	−0.778840	+	0.531004i
$339$		0			0
$340$	−0.162543	−	2.16898i	−0.00881512	−	0.117630i
$341$	−0.981253	−	2.50019i	−0.0531378	−	0.135393i
$342$		0			0
$343$	17.1716	−	6.93798i	0.927180	−	0.374616i
$344$	49.4613			2.66677
$345$		0			0
$346$	2.21837	+	29.6021i	0.119261	+	1.59142i
$347$	13.3053	−	12.3455i	0.714266	−	0.662742i	−0.236860	−	0.971544i	$-0.576118\pi$
$347$	13.3053	−	12.3455i	0.714266	−	0.662742i	0.951126	+	0.308802i	$0.0999279\pi$
$348$		0			0
$349$	−13.7787	+	6.63546i	−0.737556	+	0.355188i	−0.764651	−	0.644445i	$-0.777089\pi$
$349$	−13.7787	+	6.63546i	−0.737556	+	0.355188i	0.0270952	+	0.999633i	$0.491374\pi$
$350$	−19.7137	−	25.8465i	−1.05374	−	1.38156i
$351$		0			0
$352$	24.3160	−	3.66505i	1.29605	−	0.195348i
$353$	4.80914	+	3.27881i	0.255965	+	0.174514i	0.684503	−	0.729010i	$-0.260019\pi$
$353$	4.80914	+	3.27881i	0.255965	+	0.174514i	−0.428539	+	0.903523i	$0.640971\pi$
$354$		0			0
$355$	−2.27807	−	2.11374i	−0.120907	−	0.112185i
$356$	28.8214	−	36.1409i	1.52753	−	1.91547i
$357$		0			0
$358$	−31.2447	−	39.1796i	−1.65133	−	2.07071i
$359$	0.236123	−	3.15085i	0.0124621	−	0.166295i	−0.987500	−	0.157617i	$-0.949619\pi$
$359$	0.236123	−	3.15085i	0.0124621	−	0.166295i	0.999962	−	0.00867776i	$-0.00276225\pi$
$360$		0			0
$361$	9.49541	+	16.4465i	0.499759	+	0.865607i
$362$	14.9818	−	25.9492i	0.787424	−	1.36386i
$363$		0			0
$364$	−40.6117	+	36.0811i	−2.12863	+	1.89116i
$365$	0.654234	+	2.86639i	0.0342442	+	0.150033i
$366$		0			0
$367$	−7.73318	+	19.7038i	−0.403669	+	1.02853i	0.574089	+	0.818793i	$0.305357\pi$
$367$	−7.73318	+	19.7038i	−0.403669	+	1.02853i	−0.977758	+	0.209739i	$0.932739\pi$
$368$	1.50871	−	3.84413i	0.0786470	−	0.200389i
$369$		0			0
$370$	0.860750	+	3.77119i	0.0447483	+	0.196055i
$371$	−1.18507	−	0.204895i	−0.0615255	−	0.0106376i
$372$		0			0
$373$	−13.5570	+	23.4814i	−0.701956	+	1.21582i	0.265823	+	0.964022i	$0.414356\pi$
$373$	−13.5570	+	23.4814i	−0.701956	+	1.21582i	−0.967779	+	0.251801i	$0.918977\pi$
$374$	−4.23765	−	7.33982i	−0.219124	−	0.379533i
$375$		0			0
$376$	−0.612499	+	8.17323i	−0.0315872	+	0.421502i
$377$	−18.2992	−	22.9464i	−0.942455	−	1.18180i
$378$		0			0
$379$	15.4532	−	19.3777i	0.793777	−	0.995365i	−0.206081	−	0.978535i	$-0.566071\pi$
$379$	15.4532	−	19.3777i	0.793777	−	0.995365i	0.999858	−	0.0168304i	$-0.00535754\pi$
$380$	−0.154090	−	0.142975i	−0.00790467	−	0.00733446i
$381$		0			0
$382$	45.4634	+	30.9964i	2.32611	+	1.58592i
$383$	−5.46679	+	0.823986i	−0.279340	+	0.0421037i	−0.287218	−	0.957865i	$-0.592730\pi$
$383$	−5.46679	+	0.823986i	−0.279340	+	0.0421037i	0.00787813	+	0.999969i	$0.497492\pi$
$384$		0			0
$385$	3.72250	+	1.89280i	0.189716	+	0.0964658i
$386$	−49.9480	+	24.0537i	−2.54229	+	1.22430i
$387$		0			0
$388$	−15.0676	+	13.9807i	−0.764940	+	0.709760i
$389$	1.52341	+	20.3284i	0.0772398	+	1.03069i	0.892337	+	0.451369i	$0.149064\pi$
$389$	1.52341	+	20.3284i	0.0772398	+	1.03069i	−0.815097	+	0.579324i	$0.803317\pi$
$390$		0			0
$391$	−0.504004			−0.0254886
$392$	−31.0162	+	35.6207i	−1.56655	+	1.79912i
$393$		0			0
$394$	0.662031	+	1.68683i	0.0333526	+	0.0849812i
$395$	0.177059	+	2.36269i	0.00890880	+	0.118880i
$396$		0			0
$397$	−7.17037	+	4.88868i	−0.359871	+	0.245356i	−0.729735	−	0.683730i	$-0.760357\pi$
$397$	−7.17037	+	4.88868i	−0.359871	+	0.245356i	0.369864	+	0.929086i	$0.379404\pi$
$398$	10.7399	−	5.17204i	0.538340	−	0.259251i
$399$		0			0
$400$	34.9259	+	16.8194i	1.74630	+	0.840972i
$401$	21.7897	−	3.28428i	1.08813	−	0.164009i	0.419610	−	0.907705i	$-0.362167\pi$
$401$	21.7897	−	3.28428i	1.08813	−	0.164009i	0.668518	+	0.743696i	$0.266929\pi$
$402$		0			0
$403$	−3.54974	−	0.535038i	−0.176825	−	0.0266521i
$404$	30.5857	+	28.3793i	1.52169	+	1.41193i
$405$		0			0
$406$	−32.3051	−	31.3004i	−1.60327	−	1.55341i
$407$	6.55934	+	8.22516i	0.325135	+	0.407706i
$408$		0			0
$409$	12.0431	−	3.71479i	0.595491	−	0.183685i	0.0176638	−	0.999844i	$-0.494377\pi$
$409$	12.0431	−	3.71479i	0.595491	−	0.183685i	0.577827	+	0.816159i	$0.303901\pi$
$410$	5.37651	+	9.31238i	0.265527	+	0.459906i
$411$		0			0
$412$	19.5808	−	85.7890i	0.964675	−	4.22652i
$413$	0.664435	+	12.4789i	0.0326947	+	0.614047i
$414$		0			0
$415$	7.90030	+	2.43692i	0.387810	+	0.119624i
$416$	12.0077	−	30.5952i	0.588727	−	1.50005i
$417$		0			0
$418$	−0.782686	−	0.241427i	−0.0382824	−	0.0118086i
$419$	−1.64545	−	7.20917i	−0.0803853	−	0.352191i	0.918700	−	0.394956i	$-0.129240\pi$
$419$	−1.64545	−	7.20917i	−0.0803853	−	0.352191i	−0.999085	+	0.0427655i	$0.986383\pi$
$420$		0			0
$421$	−5.62826	+	24.6590i	−0.274305	+	1.20181i	0.630571	+	0.776131i	$0.282821\pi$
$421$	−5.62826	+	24.6590i	−0.274305	+	1.20181i	−0.904876	+	0.425676i	$0.860036\pi$
$422$	−9.71177	+	16.8213i	−0.472762	+	0.818847i
$423$		0			0
$424$	2.93082	−	0.904037i	0.142333	−	0.0439039i
$425$	0.353557	−	4.71789i	0.0171500	−	0.228851i
$426$		0			0
$427$	−3.10327	+	32.0901i	−0.150178	+	1.55295i
$428$	−6.42385	+	8.05526i	−0.310509	+	0.389366i
$429$		0			0
$430$	−8.85823	−	1.33516i	−0.427182	−	0.0643873i
$431$	9.28854	+	6.33282i	0.447413	+	0.305041i	0.765986	−	0.642857i	$-0.222251\pi$
$431$	9.28854	+	6.33282i	0.447413	+	0.305041i	−0.318573	+	0.947898i	$0.603204\pi$
$432$		0			0
$433$	19.5411	+	9.41049i	0.939085	+	0.452239i	0.839846	−	0.542824i	$-0.182645\pi$
$433$	19.5411	+	9.41049i	0.939085	+	0.452239i	0.0992386	+	0.995064i	$0.468359\pi$
$434$	−5.50054	−	0.118860i	−0.264035	−	0.00570548i
$435$		0			0
$436$	−0.0880294	+	0.0600174i	−0.00421584	+	0.00287431i
$437$	−0.0357057	+	0.0331300i	−0.00170804	+	0.00158483i
$438$		0			0
$439$	−11.8434	−	30.1765i	−0.565256	−	1.44025i	−0.872498	−	0.488617i	$-0.837502\pi$
$439$	−11.8434	−	30.1765i	−0.565256	−	1.44025i	0.307243	−	0.951631i	$-0.400594\pi$
$440$	−10.6501			−0.507726
$441$		0			0
$442$	−11.3279			−0.538811
$443$	−3.87445	−	9.87193i	−0.184081	−	0.469030i	0.808809	−	0.588072i	$-0.200113\pi$
$443$	−3.87445	−	9.87193i	−0.184081	−	0.469030i	−0.992889	+	0.119042i	$0.962018\pi$
$444$		0			0
$445$	−3.48166	+	3.23051i	−0.165047	+	0.153141i
$446$	46.5235	−	31.7192i	2.20295	−	1.50195i
$447$		0			0
$448$	1.80454	−	7.18682i	0.0852567	−	0.339545i
$449$	−8.79991	−	4.23781i	−0.415293	−	0.199995i	0.214557	−	0.976712i	$-0.431169\pi$
$449$	−8.79991	−	4.23781i	−0.415293	−	0.199995i	−0.629850	+	0.776717i	$0.716884\pi$
$450$		0			0
$451$	24.1635	+	16.4744i	1.13782	+	0.775750i
$452$	55.0297	+	8.29439i	2.58838	+	0.390135i
$453$		0			0
$454$	0.298778	−	0.374656i	0.0140224	−	0.0175835i
$455$	4.67861	−	3.04388i	0.219337	−	0.142699i
$456$		0			0
$457$	0.680971	−	9.08693i	0.0318545	−	0.425069i	−0.958365	−	0.285547i	$-0.907825\pi$
$457$	0.680971	−	9.08693i	0.0318545	−	0.425069i	0.990219	−	0.139521i	$-0.0445564\pi$
$458$	−35.2793	+	10.8822i	−1.64849	+	0.508493i
$459$		0			0
$460$	−0.558211	+	0.966850i	−0.0260267	+	0.0450796i
$461$	−7.27998	+	31.8957i	−0.339063	+	1.48553i	0.461963	+	0.886899i	$0.347145\pi$
$461$	−7.27998	+	31.8957i	−0.339063	+	1.48553i	−0.801025	+	0.598631i	$0.795712\pi$
$462$		0			0
$463$	3.30364	+	14.4742i	0.153533	+	0.672672i	0.991842	+	0.127476i	$0.0406877\pi$
$463$	3.30364	+	14.4742i	0.153533	+	0.672672i	−0.838309	+	0.545196i	$0.816455\pi$
$464$	51.2584	+	15.8111i	2.37961	+	0.734013i
$465$		0			0
$466$	13.4380	−	34.2396i	0.622505	−	1.58612i
$467$	−14.1464	−	4.36358i	−0.654616	−	0.201922i	−0.0503832	−	0.998730i	$-0.516044\pi$
$467$	−14.1464	−	4.36358i	−0.654616	−	0.201922i	−0.604233	+	0.796808i	$0.706520\pi$
$468$		0			0
$469$	−6.58516	+	15.7682i	−0.304074	+	0.728110i
$470$	0.330324	−	1.44724i	0.0152367	−	0.0667564i
$471$		0			0
$472$	−15.9349	−	27.6000i	−0.733461	−	1.27039i
$473$	−23.2817	+	7.18144i	−1.07049	+	0.330203i
$474$		0			0
$475$	−0.285077	−	0.357475i	−0.0130802	−	0.0164021i
$476$	−12.0186	+	1.54677i	−0.550872	+	0.0708960i
$477$		0			0
$478$	−49.6341	−	46.0537i	−2.27021	−	2.10645i
$479$	−2.87255	−	0.432967i	−0.131250	−	0.0197828i	0.0830886	−	0.996542i	$-0.473522\pi$
$479$	−2.87255	−	0.432967i	−0.131250	−	0.0197828i	−0.214339	+	0.976759i	$0.568760\pi$
$480$		0			0
$481$	13.9042	−	2.09572i	0.633977	−	0.0955566i
$482$	−28.2888	−	13.6232i	−1.28852	−	0.620518i
$483$		0			0
$484$	−0.195344	+	0.0940729i	−0.00887929	+	0.00427604i
$485$	1.74494	−	1.18968i	0.0792335	−	0.0540205i
$486$		0			0
$487$	0.849960	+	11.3419i	0.0385154	+	0.513952i	0.982782	+	0.184770i	$0.0591539\pi$
$487$	0.849960	+	11.3419i	0.0385154	+	0.513952i	−0.944266	+	0.329182i	$0.893227\pi$
$488$	−30.0384	−	76.5366i	−1.35977	−	3.46465i
$489$		0			0
$490$	6.51637	−	5.54220i	0.294379	−	0.250371i
$491$	28.2106			1.27313			0.636563	−	0.771224i	$-0.280355\pi$
$491$	28.2106			1.27313			0.636563	+	0.771224i	$0.280355\pi$
$492$		0			0
$493$	−0.489241	−	6.52847i	−0.0220343	−	0.294027i
$494$	−0.802511	+	0.744622i	−0.0361067	+	0.0335021i
$495$		0			0
$496$	5.91132	−	2.84674i	0.265426	−	0.127822i
$497$	−11.0846	+	13.2998i	−0.497213	+	0.596576i
$498$		0			0
$499$	−2.76296	+	0.416449i	−0.123687	+	0.0186428i	−0.210594	−	0.977574i	$-0.567540\pi$
$499$	−2.76296	+	0.416449i	−0.123687	+	0.0186428i	0.0869070	+	0.996216i	$0.472302\pi$
$500$	−17.7269	−	12.0860i	−0.792770	−	0.540501i
$501$		0			0
$502$	46.9250	+	43.5401i	2.09437	+	1.94329i
$503$	−4.30121	+	5.39354i	−0.191781	+	0.240486i	−0.868420	−	0.495829i	$-0.834864\pi$
$503$	−4.30121	+	5.39354i	−0.191781	+	0.240486i	0.676639	+	0.736315i	$0.263436\pi$
$504$		0			0
$505$	−2.67287	−	3.35167i	−0.118941	−	0.149148i
$506$	−0.325093	+	4.33806i	−0.0144521	+	0.192850i
$507$		0			0
$508$	22.6223	+	39.1830i	1.00370	+	1.73847i
$509$	−13.9711	+	24.1987i	−0.619260	+	1.07259i	0.370361	+	0.928888i	$0.379234\pi$
$509$	−13.9711	+	24.1987i	−0.619260	+	1.07259i	−0.989621	+	0.143702i	$0.954099\pi$
$510$		0			0
$511$	15.7529	−	4.48879i	0.696865	−	0.198572i
$512$	−11.0139	−	48.2550i	−0.486750	−	2.13259i
$513$		0			0
$514$	4.13583	−	10.5379i	0.182423	−	0.464807i
$515$	−3.30311	+	8.41618i	−0.145552	+	0.370861i
$516$		0			0
$517$	−0.898391	−	3.93611i	−0.0395112	−	0.173110i
$518$	20.7254	−	5.90573i	0.910623	−	0.259483i
$519$		0			0
$520$	−7.11735	+	12.3276i	−0.312116	+	0.540601i
$521$	−0.538018	−	0.931875i	−0.0235710	−	0.0408262i	0.853999	−	0.520274i	$-0.174170\pi$
$521$	−0.538018	−	0.931875i	−0.0235710	−	0.0408262i	−0.877570	+	0.479448i	$0.840837\pi$
$522$		0			0
$523$	−1.14859	+	15.3269i	−0.0502243	+	0.670196i	0.914103	+	0.405483i	$0.132897\pi$
$523$	−1.14859	+	15.3269i	−0.0502243	+	0.670196i	−0.964327	+	0.264714i	$0.914723\pi$
$524$	26.1848	+	32.8346i	1.14389	+	1.43439i
$525$		0			0
$526$	−10.9306	+	13.7066i	−0.476599	+	0.597636i
$527$	−0.586996	−	0.544653i	−0.0255700	−	0.0237255i
$528$		0			0
$529$	−18.7897	−	12.8106i	−0.816946	−	0.556984i
$530$	−0.549296	+	0.0827931i	−0.0238599	+	0.00359630i
$531$		0			0
$532$	−0.749773	+	0.899608i	−0.0325068	+	0.0390029i
$533$	35.2174	−	16.9598i	1.52544	−	0.734611i
$534$		0			0
$535$	0.776009	−	0.720031i	0.0335498	−	0.0311296i
$536$	−3.25668	−	43.4574i	−0.140667	−	1.87707i
$537$		0			0
$538$	63.4409			2.73513
$539$	9.42758	−	21.2702i	0.406075	−	0.916170i
$540$		0			0
$541$	−7.85826	−	20.0225i	−0.337853	−	0.860836i	−0.994315	−	0.106477i	$-0.966043\pi$
$541$	−7.85826	−	20.0225i	−0.337853	−	0.860836i	0.656462	−	0.754359i	$-0.272052\pi$
$542$	0.505007	+	6.73884i	0.0216919	+	0.289458i
$543$		0			0
$544$	6.05751	−	4.12994i	0.259713	−	0.177070i
$545$	0.00986274	−	0.00474964i	0.000422473	−	0.000203452i
$546$		0			0
$547$	1.79194	+	0.862953i	0.0766178	+	0.0368972i	0.471800	−	0.881705i	$-0.343604\pi$
$547$	1.79194	+	0.862953i	0.0766178	+	0.0368972i	−0.395182	+	0.918603i	$0.629319\pi$
$548$	45.7393	−	6.89410i	1.95389	−	0.294501i
$549$		0			0
$550$	−40.3798	−	6.08627i	−1.72180	−	0.259519i
$551$	−0.463800	−	0.430344i	−0.0197586	−	0.0183333i
$552$		0			0
$553$	13.0920	−	1.68490i	0.556726	−	0.0716494i
$554$	−25.5068	−	31.9846i	−1.08368	−	1.35889i
$555$		0			0
$556$	65.3258	−	20.1504i	2.77043	−	0.854565i
$557$	−2.53699	−	4.39420i	−0.107496	−	0.186188i	0.807259	−	0.590197i	$-0.200950\pi$
$557$	−2.53699	−	4.39420i	−0.107496	−	0.186188i	−0.914755	+	0.404009i	$0.867617\pi$
$558$		0			0
$559$	−7.24625	+	31.7479i	−0.306484	+	1.34279i
$560$	−3.93129	+	9.41351i	−0.166127	+	0.397793i
$561$		0			0
$562$	36.1019	+	11.1360i	1.52287	+	0.469743i
$563$	14.5629	−	37.1056i	0.613752	−	1.56382i	−0.198244	−	0.980153i	$-0.563524\pi$
$563$	14.5629	−	37.1056i	0.613752	−	1.56382i	0.811996	−	0.583663i	$-0.198381\pi$
$564$		0			0
$565$	−5.46392	−	1.68540i	−0.229869	−	0.0709051i
$566$	0.180911	+	0.792624i	0.00760427	+	0.0333165i
$567$		0			0
$568$	9.82514	−	43.0467i	0.412254	−	1.80620i
$569$	−2.46008	+	4.26099i	−0.103132	+	0.178630i	−0.912974	−	0.408019i	$-0.866220\pi$
$569$	−2.46008	+	4.26099i	−0.103132	+	0.178630i	0.809841	+	0.586649i	$0.199553\pi$
$570$		0			0
$571$	−30.1825	+	9.31008i	−1.26310	+	0.389615i	−0.852753	−	0.522315i	$-0.825069\pi$
$571$	−30.1825	+	9.31008i	−1.26310	+	0.389615i	−0.410347	+	0.911930i	$0.634592\pi$
$572$	−5.09991	+	68.0536i	−0.213238	+	2.84546i
$573$		0			0
$574$	50.2152	−	32.6698i	2.09594	−	1.36361i
$575$	−1.51408	+	1.89860i	−0.0631417	+	0.0791772i
$576$		0			0
$577$	−26.4136	−	3.98121i	−1.09961	−	0.165740i	−0.425927	−	0.904758i	$-0.640052\pi$
$577$	−26.4136	−	3.98121i	−1.09961	−	0.165740i	−0.673686	+	0.739018i	$0.735290\pi$
$578$	34.0574	+	23.2200i	1.41660	+	0.965823i
$579$		0			0
$580$	−13.0657	−	6.29210i	−0.542523	−	0.261265i
$581$	11.2172	−	44.6738i	0.465367	−	1.85338i
$582$		0			0
$583$	−1.24829	+	0.851069i	−0.0516989	+	0.0352477i
$584$	−30.6220	+	28.4130i	−1.26715	+	1.17574i
$585$		0			0
$586$	−12.6493	−	32.2299i	−0.522538	−	1.33141i
$587$	5.03276			0.207724			0.103862	−	0.994592i	$-0.466880\pi$
$587$	5.03276			0.207724			0.103862	+	0.994592i	$0.466880\pi$
$588$		0			0
$589$	−0.0773873			−0.00318869
$590$	2.10881	+	5.37315i	0.0868181	+	0.221209i
$591$		0			0
$592$	−18.8390	+	17.4800i	−0.774278	+	0.718425i
$593$	−5.50233	+	3.75143i	−0.225954	+	0.154053i	−0.671006	−	0.741452i	$-0.734138\pi$
$593$	−5.50233	+	3.75143i	−0.225954	+	0.154053i	0.445052	+	0.895505i	$0.353185\pi$
$594$		0			0
$595$	1.24476	+	0.0268978i	0.0510302	+	0.00110270i
$596$	47.5249	+	22.8868i	1.94669	+	0.937479i
$597$		0			0
$598$	4.80407	+	3.27536i	0.196453	+	0.133940i
$599$	−24.6001	−	3.70787i	−1.00513	−	0.151500i	−0.374210	−	0.927344i	$-0.622086\pi$
$599$	−24.6001	−	3.70787i	−1.00513	−	0.151500i	−0.630924	+	0.775844i	$0.717324\pi$
$600$		0			0
$601$	−19.1772	+	24.0474i	−0.782252	+	0.980914i	0.217736	+	0.976008i	$0.430133\pi$
$601$	−19.1772	+	24.0474i	−0.782252	+	0.980914i	−0.999988	+	0.00490571i	$0.998438\pi$
$602$	−4.80400	+	49.6768i	−0.195796	+	2.02467i
$603$		0			0
$604$	−3.46149	+	46.1904i	−0.140846	+	1.87946i
$605$	0.0212873	−	0.00656626i	0.000865452	−	0.000266957i
$606$		0			0
$607$	−3.07018	+	5.31770i	−0.124615	+	0.215839i	−0.921582	−	0.388183i	$-0.873103\pi$
$607$	−3.07018	+	5.31770i	−0.124615	+	0.215839i	0.796968	+	0.604022i	$0.206436\pi$
$608$	0.157662	−	0.690764i	0.00639405	−	0.0280142i
$609$		0			0
$610$	3.31367	+	14.5181i	0.134166	+	0.587822i
$611$	−5.15645	−	1.59055i	−0.208608	−	0.0643469i
$612$		0			0
$613$	6.77013	−	17.2500i	0.273443	−	0.696721i	−0.726511	−	0.687155i	$-0.758860\pi$
$613$	6.77013	−	17.2500i	0.273443	−	0.696721i	0.999954	−	0.00956674i	$-0.00304524\pi$
$614$	−44.9844	−	13.8758i	−1.81542	−	0.559984i
$615$		0			0
$616$	3.15476	+	59.2503i	0.127109	+	2.38726i
$617$	−3.41751	+	14.9731i	−0.137584	+	0.602794i	0.858378	+	0.513017i	$0.171472\pi$
$617$	−3.41751	+	14.9731i	−0.137584	+	0.602794i	−0.995962	+	0.0897762i	$0.971385\pi$
$618$		0			0
$619$	−8.53609	−	14.7849i	−0.343094	−	0.594257i	0.641911	−	0.766779i	$-0.278142\pi$
$619$	−8.53609	−	14.7849i	−0.343094	−	0.594257i	−0.985006	+	0.172522i	$0.944808\pi$
$620$	−1.69496	+	0.522825i	−0.0680712	+	0.0209972i
$621$		0			0
$622$	−12.0820	−	15.1503i	−0.484443	−	0.607472i
$623$	19.0037	+	18.4127i	0.761368	+	0.737689i
$624$		0			0
$625$	−15.8837	−	14.7380i	−0.635349	−	0.589518i
$626$	47.2601	+	7.12331i	1.88889	+	0.284705i
$627$		0			0
$628$	−100.771	+	15.1888i	−4.02119	+	0.606098i
$629$	2.82592	+	1.36089i	0.112677	+	0.0542622i
$630$		0			0
$631$	−0.144508	+	0.0695915i	−0.00575278	+	0.00277039i	−0.436758	−	0.899579i	$-0.643873\pi$
$631$	−0.144508	+	0.0695915i	−0.00575278	+	0.00277039i	0.431005	+	0.902349i	$0.358159\pi$
$632$	−27.8140	+	18.9633i	−1.10638	+	0.754319i
$633$		0			0
$634$	−2.97486	−	39.6968i	−0.118147	−	1.57656i
$635$	−1.69837	−	4.32737i	−0.0673976	−	0.171726i
$636$		0			0
$637$	−18.3200	−	25.1270i	−0.725865	−	0.995569i
$638$	−56.5074			−2.23715
$639$		0			0
$640$	0.269366	+	3.59444i	0.0106476	+	0.142083i
$641$	−20.0051	+	18.5620i	−0.790153	+	0.733155i	−0.968013	−	0.250901i	$-0.919273\pi$
$641$	−20.0051	+	18.5620i	−0.790153	+	0.733155i	0.177860	+	0.984056i	$0.443083\pi$
$642$		0			0
$643$	−19.2156	+	9.25377i	−0.757791	+	0.364933i	−0.772546	−	0.634958i	$-0.781017\pi$
$643$	−19.2156	+	9.25377i	−0.757791	+	0.364933i	0.0147555	+	0.999891i	$0.495303\pi$
$644$	5.54426	+	2.81912i	0.218474	+	0.111089i
$645$		0			0
$646$	−0.241471	+	0.0363958i	−0.00950053	+	0.00143198i
$647$	22.2387	+	15.1621i	0.874293	+	0.596083i	0.915164	−	0.403082i	$-0.132061\pi$
$647$	22.2387	+	15.1621i	0.874293	+	0.596083i	−0.0408713	+	0.999164i	$0.513013\pi$
$648$		0			0
$649$	11.5079	+	10.6778i	0.451726	+	0.419141i
$650$	−34.0301	+	42.6724i	−1.33477	+	1.67375i
$651$		0			0
$652$	27.1021	+	33.9850i	1.06140	+	1.33095i
$653$	−0.572776	+	7.64317i	−0.0224145	+	0.299100i	0.974719	+	0.223435i	$0.0717271\pi$
$653$	−0.572776	+	7.64317i	−0.0224145	+	0.299100i	−0.997133	+	0.0756652i	$0.975892\pi$
$654$		0			0
$655$	−2.15752	−	3.73693i	−0.0843013	−	0.146014i
$656$	−35.7205	+	61.8697i	−1.39465	+	2.41561i
$657$		0			0
$658$	−8.14935	−	1.40900i	−0.317695	−	0.0549287i
$659$	−3.81431	−	16.7116i	−0.148584	−	0.650991i	−0.993279	−	0.115743i	$-0.963075\pi$
$659$	−3.81431	−	16.7116i	−0.148584	−	0.650991i	0.844695	−	0.535248i	$-0.179782\pi$
$660$		0			0
$661$	−0.799902	+	2.03812i	−0.0311126	+	0.0792736i	−0.945586	−	0.325373i	$-0.894510\pi$
$661$	−0.799902	+	2.03812i	−0.0311126	+	0.0792736i	0.914473	+	0.404646i	$0.132605\pi$
$662$	5.61610	−	14.3096i	0.218276	−	0.556158i
$663$		0			0
$664$	26.1389	+	114.522i	1.01438	+	4.44431i
$665$	0.0899520	−	0.0799172i	0.00348819	−	0.00309905i
$666$		0			0
$667$	−1.68017	+	2.91014i	−0.0650566	+	0.112681i
$668$	−22.4136	−	38.8214i	−0.867206	−	1.50205i
$669$		0			0
$670$	−0.589841	+	7.87088i	−0.0227875	+	0.304078i
$671$	25.2518	+	31.6648i	0.974835	+	1.22240i
$672$		0			0
$673$	18.3387	−	22.9960i	0.706905	−	0.886430i	−0.290614	−	0.956841i	$-0.593859\pi$
$673$	18.3387	−	22.9960i	0.706905	−	0.886430i	0.997518	+	0.0704102i	$0.0224308\pi$
$674$	17.6631	+	16.3889i	0.680356	+	0.631278i
$675$		0			0
$676$	25.7184	+	17.5345i	0.989170	+	0.674405i
$677$	−28.5543	+	4.30387i	−1.09743	+	0.165411i	−0.672706	−	0.739910i	$-0.734868\pi$
$677$	−28.5543	+	4.30387i	−1.09743	+	0.165411i	−0.424727	+	0.905322i	$0.639630\pi$
$678$		0			0
$679$	−7.13545	−	9.35525i	−0.273833	−	0.359022i
$680$	−2.86077	+	1.37768i	−0.109706	+	0.0528315i
$681$		0			0
$682$	−5.06656	+	4.70108i	−0.194009	+	0.180014i
$683$	−2.98912	−	39.8871i	−0.114376	−	1.52624i	−0.699111	−	0.715013i	$-0.746421\pi$
$683$	−2.98912	−	39.8871i	−0.114376	−	1.52624i	0.584735	−	0.811224i	$-0.301198\pi$
$684$		0			0
$685$	−4.75262			−0.181588
$686$	−32.7634	−	34.6110i	−1.25091	−	1.32145i
$687$		0			0
$688$	−21.7441	−	55.4030i	−0.828985	−	2.11222i
$689$	0.150903	+	2.01366i	0.00574895	+	0.0767144i
$690$		0			0
$691$	30.1322	−	20.5438i	1.14628	−	0.781523i	0.167390	−	0.985891i	$-0.446466\pi$
$691$	30.1322	−	20.5438i	1.14628	−	0.781523i	0.978894	+	0.204368i	$0.0655138\pi$
$692$	48.0382	−	23.1340i	1.82614	−	0.879422i
$693$		0			0
$694$	−42.0819	−	20.2656i	−1.59741	−	0.769271i
$695$	−6.94558	+	1.04688i	−0.263461	+	0.0397104i
$696$		0			0
$697$	8.62175	+	1.29952i	0.326572	+	0.0492228i
$698$	28.8488	+	26.7678i	1.09194	+	1.01318i
$699$		0			0
$700$	−30.2785	+	49.9212i	−1.14442	+	1.88685i
$701$	26.0103	+	32.6159i	0.982396	+	1.23189i	0.972732	+	0.231933i	$0.0745049\pi$
$701$	26.0103	+	32.6159i	0.982396	+	1.23189i	0.00966455	+	0.999953i	$0.496924\pi$
$702$		0			0
$703$	0.289656	−	0.0893470i	0.0109246	−	0.00336978i
$704$	−4.65430	−	8.06149i	−0.175416	−	0.303829i
$705$		0			0
$706$	3.33295	−	14.6026i	0.125437	−	0.549576i
$707$	−17.8547	+	15.8629i	−0.671496	+	0.596585i
$708$		0			0
$709$	−1.12441	−	0.346833i	−0.0422279	−	0.0130256i	0.273569	−	0.961852i	$-0.411796\pi$
$709$	−1.12441	−	0.346833i	−0.0422279	−	0.0130256i	−0.315797	+	0.948827i	$0.602272\pi$
$710$	−2.92163	+	7.44420i	−0.109647	+	0.279376i
$711$		0			0
$712$	−64.4840	−	19.8907i	−2.41664	−	0.745435i
$713$	0.0914593	+	0.400710i	0.00342518	+	0.0150067i
$714$		0			0
$715$	1.56028	−	6.83605i	0.0583513	−	0.255654i
$716$	−45.0044	+	77.9499i	−1.68189	+	2.91313i
$717$		0			0
$718$	−7.76968	+	2.39663i	−0.289962	+	0.0894413i
$719$	1.35967	−	18.1435i	0.0507070	−	0.676638i	−0.912706	−	0.408617i	$-0.866011\pi$
$719$	1.35967	−	18.1435i	0.0507070	−	0.676638i	0.963413	−	0.268021i	$-0.0863697\pi$
$720$		0			0
$721$	47.8005	+	15.8833i	1.78018	+	0.591524i
$722$	30.4698	−	38.2079i	1.13397	−	1.42195i
$723$		0			0
$724$	−53.2173	−	8.02122i	−1.97781	−	0.298106i
$725$	−26.0627	−	17.7693i	−0.967945	−	0.659934i
$726$		0			0
$727$	−11.8289	−	5.69651i	−0.438710	−	0.211272i	0.201473	−	0.979494i	$-0.435427\pi$
$727$	−11.8289	−	5.69651i	−0.438710	−	0.211272i	−0.640183	+	0.768222i	$0.721142\pi$
$728$	70.6908	+	35.9445i	2.61998	+	1.33219i
$729$		0			0
$730$	6.25120	−	4.26200i	0.231367	−	0.157744i
$731$	−5.32480	+	4.94069i	−0.196945	+	0.182738i
$732$		0			0
$733$	2.13659	+	5.44394i	0.0789167	+	0.201077i	0.964887	−	0.262666i	$-0.0846016\pi$
$733$	2.13659	+	5.44394i	0.0789167	+	0.201077i	−0.885970	+	0.463742i	$0.846506\pi$
$734$	54.4698			2.01052
$735$		0			0
$736$	−3.76309			−0.138709
$737$	7.84265	+	19.9827i	0.288888	+	0.736074i
$738$		0			0
$739$	28.3138	−	26.2713i	1.04154	−	0.966407i	0.0420742	−	0.999114i	$-0.486603\pi$
$739$	28.3138	−	26.2713i	1.04154	−	0.966407i	0.999465	+	0.0327074i	$0.0104129\pi$
$740$	5.74050	−	3.91381i	0.211025	−	0.143874i
$741$		0			0
$742$	0.623316	+	3.03139i	0.0228827	+	0.111286i
$743$	−44.8870	−	21.6164i	−1.64674	−	0.793030i	−0.999528	−	0.0307245i	$-0.990219\pi$
$743$	−44.8870	−	21.6164i	−1.64674	−	0.793030i	−0.647217	−	0.762306i	$-0.724067\pi$
$744$		0			0
$745$	−4.47798	−	3.05304i	−0.164061	−	0.111855i
$746$	68.9941	+	10.3992i	2.52605	+	0.380741i
$747$		0			0
$748$	−9.49123	+	11.9016i	−0.347034	+	0.435166i
$749$	−4.23564	−	4.10391i	−0.154767	−	0.149954i
$750$		0			0
$751$	−0.579555	+	7.73363i	−0.0211483	+	0.282204i	0.976596	+	0.215080i	$0.0690013\pi$
$751$	−0.579555	+	7.73363i	−0.0211483	+	0.282204i	−0.997745	+	0.0671238i	$0.978618\pi$
$752$	9.42433	−	2.90702i	0.343670	−	0.106008i
$753$		0			0
$754$	−37.7631	+	65.4076i	−1.37525	+	2.38200i
$755$	1.05902	−	4.63987i	0.0385417	−	0.168862i
$756$		0			0
$757$	3.42419	+	15.0024i	0.124454	+	0.545270i	0.998258	+	0.0589922i	$0.0187887\pi$
$757$	3.42419	+	15.0024i	0.124454	+	0.545270i	−0.873804	+	0.486278i	$0.838354\pi$
$758$	−60.9465	−	18.7995i	−2.21368	−	0.682829i
$759$		0			0
$760$	−0.112109	+	0.285649i	−0.00406663	+	0.0103616i
$761$	18.8242	+	5.80649i	0.682376	+	0.210485i	0.616514	−	0.787344i	$-0.288544\pi$
$761$	18.8242	+	5.80649i	0.682376	+	0.210485i	0.0658614	+	0.997829i	$0.479020\pi$
$762$		0			0
$763$	−0.0293454	−	0.0534627i	−0.00106237	−	0.00193548i
$764$	21.9920	−	96.3534i	0.795644	−	3.48594i
$765$		0			0
$766$	7.11338	+	12.3207i	0.257017	+	0.445166i
$767$	20.0502	−	6.18468i	0.723972	−	0.223316i
$768$		0			0
$769$	4.66168	+	5.84556i	0.168104	+	0.210796i	0.858747	−	0.512400i	$-0.171244\pi$
$769$	4.66168	+	5.84556i	0.168104	+	0.210796i	−0.690642	+	0.723196i	$0.742672\pi$
$770$	1.03441	−	10.6965i	0.0372776	−	0.385477i
$771$		0			0
$772$	72.9930	+	67.7276i	2.62708	+	2.43757i
$773$	−3.58460	−	0.540291i	−0.128929	−	0.0194329i	0.0842607	−	0.996444i	$-0.473147\pi$
$773$	−3.58460	−	0.540291i	−0.128929	−	0.0194329i	−0.213190	+	0.977011i	$0.568385\pi$
$774$		0			0
$775$	−3.81513	+	0.575038i	−0.137044	+	0.0206560i
$776$	27.0346	+	13.0192i	0.970485	+	0.467361i
$777$		0			0
$778$	47.2635	−	22.7609i	1.69448	−	0.816018i
$779$	0.696222	−	0.474676i	0.0249447	−	0.0170070i
$780$		0			0
$781$	1.62535	+	21.6888i	0.0581597	+	0.776088i
$782$	0.473836	+	1.20732i	0.0169444	+	0.0431735i
$783$		0			0
$784$	53.5350	+	19.0826i	1.91196	+	0.681521i
$785$	10.4708			0.373718
$786$		0			0
$787$	−0.742587	−	9.90913i	−0.0264704	−	0.353222i	−0.994675	−	0.103063i	$-0.967136\pi$
$787$	−0.742587	−	9.90913i	−0.0264704	−	0.353222i	0.968205	−	0.250160i	$-0.0804832\pi$
$788$	2.38590	−	2.21379i	0.0849942	−	0.0788631i
$789$		0			0
$790$	5.49323	−	2.64540i	0.195440	−	0.0941191i
$791$	−7.75791	+	30.8968i	−0.275839	+	1.09856i
$792$		0			0
$793$	53.5276	−	8.06799i	1.90082	−	0.286503i
$794$	18.4518	+	12.5802i	0.654828	+	0.446454i
$795$		0			0
$796$	−15.6950	−	14.5628i	−0.556295	−	0.516166i
$797$	23.0743	−	28.9342i	0.817333	−	1.02490i	−0.181803	−	0.983335i	$-0.558193\pi$
$797$	23.0743	−	28.9342i	0.817333	−	1.02490i	0.999136	−	0.0415680i	$-0.0132353\pi$
$798$		0			0
$799$	−0.750485	−	0.941078i	−0.0265503	−	0.0332930i
$800$	2.63980	−	35.2256i	0.0933309	−	1.24541i
$801$		0			0
$802$	−28.3528	−	49.1085i	−1.00117	−	1.73408i
$803$	10.2885	−	17.8202i	0.363074	−	0.628863i
$804$		0			0
$805$	−0.520118	−	0.371320i	−0.0183318	−	0.0130873i
$806$	2.05562	+	9.00624i	0.0724060	+	0.317231i
$807$		0			0
$808$	22.2527	−	56.6990i	0.782848	−	1.99466i
$809$	20.5742	−	52.4222i	0.723351	−	1.84307i	0.230139	−	0.973158i	$-0.426082\pi$
$809$	20.5742	−	52.4222i	0.723351	−	1.84307i	0.493212	−	0.869909i	$-0.335823\pi$
$810$		0			0
$811$	−6.89358	−	30.2027i	−0.242066	−	1.06056i	−0.939133	−	0.343555i	$-0.888369\pi$
$811$	−6.89358	−	30.2027i	−0.242066	−	1.06056i	0.697066	−	0.717007i	$-0.254488\pi$
$812$	−31.1347	+	74.5525i	−1.09262	+	2.61628i
$813$		0			0
$814$	13.5362	−	23.4454i	0.474444	−	0.821761i
$815$	−2.23311	−	3.86785i	−0.0782223	−	0.135485i
$816$		0			0
$817$	−0.0524605	+	0.700037i	−0.00183536	+	0.0244912i
$818$	−20.2208	−	25.3561i	−0.707003	−	0.886554i
$819$		0			0
$820$	12.0420	−	15.1001i	0.420524	−	0.527320i
$821$	−21.2369	−	19.7049i	−0.741171	−	0.687706i	0.216270	−	0.976334i	$-0.430611\pi$
$821$	−21.2369	−	19.7049i	−0.741171	−	0.687706i	−0.957442	+	0.288627i	$0.906801\pi$
$822$		0			0
$823$	7.77366	+	5.29999i	0.270973	+	0.184746i	0.691181	−	0.722682i	$-0.257091\pi$
$823$	7.77366	+	5.29999i	0.270973	+	0.184746i	−0.420208	+	0.907428i	$0.638043\pi$
$824$	−127.023	+	19.1456i	−4.42506	+	0.666970i
$825$		0			0
$826$	29.2679	−	13.3236i	1.01836	−	0.463587i
$827$	−9.28130	+	4.46964i	−0.322742	+	0.155425i	−0.588239	−	0.808687i	$-0.700178\pi$
$827$	−9.28130	+	4.46964i	−0.322742	+	0.155425i	0.265496	+	0.964112i	$0.414464\pi$
$828$		0			0
$829$	16.1589	−	14.9933i	0.561222	−	0.520738i	−0.347754	−	0.937586i	$-0.613056\pi$
$829$	16.1589	−	14.9933i	0.561222	−	0.520738i	0.908976	+	0.416848i	$0.136865\pi$
$830$	−1.58990	−	21.2158i	−0.0551864	−	0.736411i
$831$		0			0
$832$	−12.4416			−0.431336
$833$	−0.219078	−	6.93298i	−0.00759060	−	0.240214i
$834$		0			0
$835$	1.68269	+	4.28743i	0.0582320	+	0.148373i
$836$	0.109940	+	1.46705i	0.00380237	+	0.0507391i
$837$		0			0
$838$	−15.7222	+	10.7192i	−0.543115	+	0.370290i
$839$	−33.4865	+	16.1263i	−1.15608	+	0.556740i	−0.910855	−	0.412725i	$-0.864577\pi$
$839$	−33.4865	+	16.1263i	−1.15608	+	0.556740i	−0.245227	+	0.969466i	$0.578863\pi$
$840$		0			0
$841$	−13.1986	−	6.35610i	−0.455123	−	0.219176i
$842$	64.3608	−	9.70082i	2.21802	−	0.334313i
$843$		0			0
$844$	34.4976	+	5.19967i	1.18746	+	0.178980i
$845$	−2.34444	−	2.17532i	−0.0806512	−	0.0748334i
$846$		0			0
$847$	−0.0428360	−	0.116483i	−0.00147186	−	0.00400241i
$848$	−2.30108	−	2.88546i	−0.0790193	−	0.0990871i
$849$		0			0
$850$	−11.6339	+	3.58857i	−0.399038	+	0.123087i
$851$	−0.804963	−	1.39424i	−0.0275938	−	0.0477938i
$852$		0			0
$853$	3.63364	−	15.9200i	0.124413	−	0.545091i	−0.873851	−	0.486195i	$-0.838385\pi$
$853$	3.63364	−	15.9200i	0.124413	−	0.545091i	0.998264	−	0.0588965i	$-0.0187582\pi$
$854$	79.7876	−	22.7355i	2.73027	−	0.777994i
$855$		0			0
$856$	14.3725	+	4.43332i	0.491241	+	0.151528i
$857$	20.3165	−	51.7656i	0.693998	−	1.76828i	0.0557541	−	0.998445i	$-0.482244\pi$
$857$	20.3165	−	51.7656i	0.693998	−	1.76828i	0.638244	−	0.769834i	$-0.279661\pi$
$858$		0			0
$859$	−45.2053	−	13.9440i	−1.54239	−	0.475763i	−0.597144	−	0.802134i	$-0.703698\pi$
$859$	−45.2053	−	13.9440i	−1.54239	−	0.475763i	−0.945242	+	0.326371i	$0.894174\pi$
$860$	3.58042	+	15.6868i	0.122091	+	0.534917i
$861$		0			0
$862$	6.43737	−	28.2040i	0.219258	−	0.960631i
$863$	7.34385	−	12.7199i	0.249988	−	0.432991i	−0.713534	−	0.700620i	$-0.752907\pi$
$863$	7.34385	−	12.7199i	0.249988	−	0.432991i	0.963522	+	0.267629i	$0.0862401\pi$
$864$		0			0
$865$	−5.23488	+	1.61475i	−0.177991	+	0.0549030i
$866$	4.17091	−	55.6569i	0.141733	−	1.89130i
$867$		0			0
$868$	3.41073	+	9.27474i	0.115768	+	0.314805i
$869$	10.3389	−	12.9645i	0.350722	−	0.439791i
$870$		0			0
$871$	28.3713	+	4.27628i	0.961324	+	0.144896i
$872$	0.128508	+	0.0876151i	0.00435182	+	0.00296702i
$873$		0			0
$874$	0.112930	+	0.0543841i	0.00381991	+	0.00183957i
$875$	7.86287	−	9.43418i	0.265814	−	0.318934i
$876$		0			0
$877$	36.6895	−	25.0145i	1.23892	−	0.844680i	0.246688	−	0.969095i	$-0.420658\pi$
$877$	36.6895	−	25.0145i	1.23892	−	0.844680i	0.992230	+	0.124415i	$0.0397054\pi$
$878$	−61.1518	+	56.7406i	−2.06377	+	1.91490i
$879$		0			0
$880$	4.68199	+	11.9295i	0.157830	+	0.402144i
$881$	−43.7802			−1.47499			−0.737496	−	0.675352i	$-0.763992\pi$
$881$	−43.7802			−1.47499			−0.737496	+	0.675352i	$0.763992\pi$
$882$		0			0
$883$	−10.6151			−0.357226			−0.178613	−	0.983919i	$-0.557161\pi$
$883$	−10.6151			−0.357226			−0.178613	+	0.983919i	$0.557161\pi$
$884$	7.43334	+	18.9398i	0.250010	+	0.637016i
$885$		0			0
$886$	−20.0052	+	18.5621i	−0.672087	+	0.623605i
$887$	−44.2024	+	30.1367i	−1.48417	+	1.01189i	−0.494399	+	0.869235i	$0.664612\pi$
$887$	−44.2024	+	30.1367i	−1.48417	+	1.01189i	−0.989772	+	0.142656i	$0.954436\pi$
$888$		0			0
$889$	−23.5715	+	10.7304i	−0.790563	+	0.359887i
$890$	11.0118	+	5.30300i	0.369116	+	0.177757i
$891$		0			0
$892$	−83.5623	−	56.9718i	−2.79787	−	1.90756i
$893$	−0.115028	−	0.0173377i	−0.00384927	−	0.000580183i
$894$		0			0
$895$	5.76607	−	7.23042i	0.192738	−	0.241686i
$896$	19.9173	−	2.56331i	0.665389	−	0.0856341i
$897$		0			0
$898$	−1.87828	+	25.0639i	−0.0626789	+	0.836392i
$899$	−5.10170	+	1.57366i	−0.170151	+	0.0524847i
$900$		0			0
$901$	−0.225215	+	0.390084i	−0.00750301	+	0.0129956i
$902$	16.7464	−	73.3709i	0.557595	−	2.44298i
$903$		0			0
$904$	−18.0779	−	79.2044i	−0.601261	−	2.63430i
$905$	5.28397	+	1.62989i	0.175645	+	0.0541793i
$906$		0			0
$907$	−11.0509	+	28.1571i	−0.366938	+	0.934943i	0.621513	+	0.783404i	$0.286518\pi$
$907$	−11.0509	+	28.1571i	−0.366938	+	0.934943i	−0.988451	+	0.151539i	$0.951577\pi$
$908$	−0.822473	−	0.253699i	−0.0272947	−	0.00841931i
$909$		0			0
$910$	−11.6900	−	8.34569i	−0.387521	−	0.276657i
$911$	−1.42613	+	6.24826i	−0.0472496	+	0.207014i	−0.993043	−	0.117756i	$-0.962430\pi$
$911$	−1.42613	+	6.24826i	−0.0472496	+	0.207014i	0.945793	+	0.324770i	$0.105287\pi$
$912$		0			0
$913$	−28.9315	−	50.1108i	−0.957492	−	1.65842i
$914$	−22.4075	+	6.91179i	−0.741174	+	0.228622i
$915$		0			0
$916$	41.3451	+	51.8451i	1.36608	+	1.71301i
$917$	−20.1507	+	13.1099i	−0.665435	+	0.432928i
$918$		0			0
$919$	16.8799	+	15.6622i	0.556816	+	0.516650i	0.907616	−	0.419801i	$-0.137900\pi$
$919$	16.8799	+	15.6622i	0.556816	+	0.516650i	−0.350800	+	0.936450i	$0.614090\pi$
$920$	1.61158	+	0.242907i	0.0531323	+	0.00800840i
$921$		0			0
$922$	83.2487	−	12.5477i	2.74165	−	0.413237i
$923$	26.1912	+	12.6130i	0.862093	+	0.415162i
$924$		0			0
$925$	13.6159	−	6.55707i	0.447688	−	0.215595i
$926$	31.5663	−	21.5215i	1.03733	−	0.707241i
$927$		0			0
$928$	−3.65287	−	48.7441i	−0.119911	−	1.60010i
$929$	14.4606	+	36.8449i	0.474435	+	1.20884i	0.945173	+	0.326569i	$0.105892\pi$
$929$	14.4606	+	36.8449i	0.474435	+	1.20884i	−0.470738	+	0.882273i	$0.656012\pi$
$930$		0			0
$931$	−0.471251	−	0.476760i	−0.0154446	−	0.0156252i
$932$	−66.0656			−2.16405
$933$		0			0
$934$	2.84690	+	37.9893i	0.0931536	+	1.24305i
$935$	1.14655	−	1.06384i	0.0374962	−	0.0347914i
$936$		0			0
$937$	−4.00389	+	1.92817i	−0.130801	+	0.0629906i	−0.498140	−	0.867097i	$-0.665983\pi$
$937$	−4.00389	+	1.92817i	−0.130801	+	0.0629906i	0.367338	+	0.930087i	$0.380269\pi$
$938$	43.9630	+	0.949990i	1.43544	+	0.0310183i
$939$		0			0
$940$	−2.63651	+	0.397390i	−0.0859934	+	0.0129614i
$941$	−40.1193	−	27.3529i	−1.30785	−	0.891678i	−0.309604	−	0.950866i	$-0.600197\pi$
$941$	−40.1193	−	27.3529i	−1.30785	−	0.891678i	−0.998247	+	0.0591878i	$0.981149\pi$
$942$		0			0
$943$	−3.28069	−	3.04403i	−0.106834	−	0.0991273i
$944$	−23.9103	+	29.9825i	−0.778213	+	0.975849i
$945$		0			0
$946$	39.0909	+	49.0184i	1.27095	+	1.59373i
$947$	2.37743	−	31.7246i	0.0772560	−	1.03091i	−0.815024	−	0.579427i	$-0.803276\pi$
$947$	2.37743	−	31.7246i	0.0772560	−	1.03091i	0.892280	−	0.451482i	$-0.149105\pi$
$948$		0			0
$949$	−13.7514	−	23.8181i	−0.446388	−	0.773167i
$950$	−0.588300	+	1.01897i	−0.0190870	+	0.0330596i
$951$		0			0
$952$	8.51188	+	15.5073i	0.275872	+	0.502596i
$953$	10.8967	+	47.7418i	0.352980	+	1.54651i	0.770260	+	0.637730i	$0.220126\pi$
$953$	10.8967	+	47.7418i	0.352980	+	1.54651i	−0.417280	+	0.908778i	$0.637017\pi$
$954$		0			0
$955$	−3.70987	+	9.45259i	−0.120049	+	0.305879i
$956$	−44.4306	+	113.207i	−1.43699	+	3.66139i
$957$		0			0
$958$	1.66346	+	7.28809i	0.0537440	+	0.235468i
$959$	1.40781	+	26.4404i	0.0454605	+	0.853806i
$960$		0			0
$961$	15.1735	−	26.2813i	0.489467	−	0.847783i
$962$	−18.0921	−	31.3365i	−0.583314	−	1.01033i
$963$		0			0
$964$	−4.21442	+	56.2375i	−0.135737	+	1.81129i
$965$	−6.37884	−	7.99881i	−0.205342	−	0.257491i
$966$		0			0
$967$	21.9539	−	27.5294i	0.705991	−	0.885285i	−0.291464	−	0.956582i	$-0.594142\pi$
$967$	21.9539	−	27.5294i	0.705991	−	0.885285i	0.997455	+	0.0712968i	$0.0227137\pi$
$968$	0.232021	+	0.215284i	0.00745744	+	0.00691950i
$969$		0			0
$970$	−4.49030	−	3.06144i	−0.144175	−	0.0982968i
$971$	27.5185	−	4.14775i	0.883111	−	0.133108i	0.308198	−	0.951322i	$-0.400274\pi$
$971$	27.5185	−	4.14775i	0.883111	−	0.133108i	0.574913	+	0.818215i	$0.305036\pi$
$972$		0			0
$973$	7.88153	+	38.3305i	0.252670	+	1.22882i
$974$	26.3699	−	12.6991i	0.844946	−	0.406905i
$975$		0			0
$976$	−72.5254	+	67.2937i	−2.32148	+	2.15402i
$977$	1.64054	+	21.8915i	0.0524856	+	0.700372i	0.959937	+	0.280215i	$0.0904058\pi$
$977$	1.64054	+	21.8915i	0.0524856	+	0.700372i	−0.907452	+	0.420157i	$0.861975\pi$
$978$		0			0
$979$	33.2409			1.06238
$980$	−13.5424	−	7.25838i	−0.432598	−	0.231860i
$981$		0			0
$982$	−26.5220	−	67.5770i	−0.846352	−	2.15647i
$983$	2.98037	+	39.7703i	0.0950590	+	1.26847i	0.817048	+	0.576570i	$0.195609\pi$
$983$	2.98037	+	39.7703i	0.0950590	+	1.26847i	−0.721989	+	0.691905i	$0.756772\pi$
$984$		0			0
$985$	−0.276305	+	0.188382i	−0.00880381	+	0.00600234i
$986$	−15.1787	+	7.30965i	−0.483387	+	0.232787i
$987$		0			0
$988$	1.77159	+	0.853155i	0.0563619	+	0.0271425i
$989$	3.68678	−	0.555692i	0.117233	−	0.0176700i
$990$		0			0
$991$	−17.0601	−	2.57139i	−0.541931	−	0.0816830i	−0.127628	−	0.991822i	$-0.540737\pi$
$991$	−17.0601	−	2.57139i	−0.541931	−	0.0816830i	−0.414303	+	0.910139i	$0.635975\pi$
$992$	−4.38275	−	4.06659i	−0.139152	−	0.129114i
$993$		0			0
$994$	42.2800	+	14.0489i	1.34104	+	0.445605i
$995$	1.37158	+	1.71991i	0.0434820	+	0.0545248i
$996$		0			0
$997$	−37.0425	+	11.4261i	−1.17315	+	0.361868i	−0.819261	−	0.573421i	$-0.805616\pi$
$997$	−37.0425	+	11.4261i	−1.17315	+	0.361868i	−0.353886	+	0.935289i	$0.615140\pi$
$998$	3.59516	+	6.22700i	0.113803	+	0.197112i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.163.1		48
3.2	odd	2		49.2.g.a.16.4	✓	48
12.11	even	2		784.2.bg.c.65.4		48
21.2	odd	6		343.2.e.d.295.8		48
21.5	even	6		343.2.e.c.295.8		48
21.11	odd	6		343.2.g.i.165.1		48
21.17	even	6		343.2.g.h.165.1		48
21.20	even	2		343.2.g.g.226.4		48
49.46	even	21	inner	441.2.bb.d.46.1		48
147.5	even	42		343.2.e.c.50.8		48
147.8	odd	14		343.2.g.i.79.1		48
147.41	even	14		343.2.g.h.79.1		48
147.44	odd	42		343.2.e.d.50.8		48
147.86	odd	42		2401.2.a.h.1.24		24
147.95	odd	42		49.2.g.a.46.4	yes	48
147.101	even	42		343.2.g.g.214.4		48
147.110	even	42		2401.2.a.i.1.24		24
588.95	even	42		784.2.bg.c.193.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.16.4	✓	48	3.2	odd	2
49.2.g.a.46.4	yes	48	147.95	odd	42
343.2.e.c.50.8		48	147.5	even	42
343.2.e.c.295.8		48	21.5	even	6
343.2.e.d.50.8		48	147.44	odd	42
343.2.e.d.295.8		48	21.2	odd	6
343.2.g.g.214.4		48	147.101	even	42
343.2.g.g.226.4		48	21.20	even	2
343.2.g.h.79.1		48	147.41	even	14
343.2.g.h.165.1		48	21.17	even	6
343.2.g.i.79.1		48	147.8	odd	14
343.2.g.i.165.1		48	21.11	odd	6
441.2.bb.d.46.1		48	49.46	even	21	inner
441.2.bb.d.163.1		48	1.1	even	1	trivial
784.2.bg.c.65.4		48	12.11	even	2
784.2.bg.c.193.4		48	588.95	even	42
2401.2.a.h.1.24		24	147.86	odd	42
2401.2.a.i.1.24		24	147.110	even	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.940144 - 2.39545i) q^{2} +(-3.38820 + 3.14379i) q^{4} +(0.392378 - 0.267519i) q^{5} +(-1.60453 - 2.10369i) q^{7} +(6.07919 + 2.92758i) q^{8} +O(q^{10})\)	\(q+(-0.940144 - 2.39545i) q^{2} +(-3.38820 + 3.14379i) q^{4} +(0.392378 - 0.267519i) q^{5} +(-1.60453 - 2.10369i) q^{7} +(6.07919 + 2.92758i) q^{8} +(-1.00972 - 0.688415i) q^{10} +(-3.28657 - 0.495370i) q^{11} +(-2.76976 + 3.47317i) q^{13} +(-3.53079 + 5.82133i) q^{14} +(0.606748 - 8.09649i) q^{16} +(-0.946896 + 0.292079i) q^{17} +(-0.0478826 + 0.0829351i) q^{19} +(-0.488432 + 2.13996i) q^{20} +(1.90321 + 8.33852i) q^{22} +(0.486025 + 0.149919i) q^{23} +(-1.74431 + 4.44443i) q^{25} +(10.9238 + 3.36954i) q^{26} +(12.0500 + 2.08342i) q^{28} +(-1.47014 + 6.44112i) q^{29} +(0.404047 + 0.699830i) q^{31} +(-7.06990 + 2.18078i) q^{32} +(1.58988 + 1.99364i) q^{34} +(-1.19236 - 0.396200i) q^{35} +(-2.32031 - 2.15293i) q^{37} +(0.243683 + 0.0367293i) q^{38} +(3.16852 - 0.477578i) q^{40} +(-7.92765 - 3.81776i) q^{41} +(6.60449 - 3.18056i) q^{43} +(12.6929 - 8.65385i) q^{44} +(-0.0978108 - 1.30519i) q^{46} +(0.443785 + 1.13075i) q^{47} +(-1.85099 + 6.75084i) q^{49} +12.2863 q^{50} +(-1.53441 - 20.4753i) q^{52} +(0.333215 - 0.309178i) q^{53} +(-1.42210 + 0.684846i) q^{55} +(-3.59550 - 17.4861i) q^{56} +(16.8115 - 2.53393i) q^{58} +(-3.90255 - 2.66071i) q^{59} +(-8.93259 - 8.28823i) q^{61} +(1.29654 - 1.62581i) q^{62} +(1.74620 + 2.18966i) q^{64} +(-0.157655 + 2.10376i) q^{65} +(-3.22934 - 5.59338i) q^{67} +(2.29004 - 3.96646i) q^{68} +(0.171912 + 3.22871i) q^{70} +(-1.45614 - 6.37976i) q^{71} +(-2.26184 + 5.76306i) q^{73} +(-2.97581 + 7.58224i) q^{74} +(-0.0984946 - 0.431533i) q^{76} +(4.23128 + 7.70874i) q^{77} +(-2.49455 + 4.32069i) q^{79} +(-1.92789 - 3.33920i) q^{80} +(-1.69210 + 22.5795i) q^{82} +(10.8545 + 13.6111i) q^{83} +(-0.293405 + 0.367918i) q^{85} +(-13.8280 - 12.8305i) q^{86} +(-18.5294 - 12.6331i) q^{88} +(-9.88950 + 1.49060i) q^{89} +(11.7506 + 0.253917i) q^{91} +(-2.11806 + 1.02001i) q^{92} +(2.29142 - 2.12613i) q^{94} +(0.00339862 + 0.0453514i) q^{95} +4.44708 q^{97} +(17.9115 - 1.91280i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

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