LMFDB - Embedded newform 441.2.g.h.67.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.9
Character	$\chi$	$=$	441.67
Dual form			441.2.g.h.79.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.863305 - 1.49529i) q^{2} +(-0.615283 - 1.61908i) q^{3} +(-0.490592 - 0.849731i) q^{4} -3.51231 q^{5} +(-2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(-2.24285 + 1.99239i) q^{9} +O(q^{10})$	\(q+(0.863305 - 1.49529i) q^{2} +(-0.615283 - 1.61908i) q^{3} +(-0.490592 - 0.849731i) q^{4} -3.51231 q^{5} +(-2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(-2.24285 + 1.99239i) q^{9} +(-3.03220 + 5.25192i) q^{10} -6.09064 q^{11} +(-1.07393 + 1.31713i) q^{12} +(-0.560139 + 0.970190i) q^{13} +(2.16106 + 5.68672i) q^{15} +(2.49982 - 4.32982i) q^{16} +(0.601978 - 1.04266i) q^{17} +(1.04293 + 5.07375i) q^{18} +(-1.10269 - 1.90991i) q^{19} +(1.72311 + 2.98452i) q^{20} +(-5.25808 + 9.10727i) q^{22} -1.27339 q^{23} +(-1.08234 - 2.84812i) q^{24} +7.33633 q^{25} +(0.967143 + 1.67514i) q^{26} +(4.60583 + 2.40548i) q^{27} +(-3.10262 - 5.37390i) q^{29} +(10.3689 + 1.67796i) q^{30} +(-0.0942019 - 0.163162i) q^{31} +(-2.55712 - 4.42907i) q^{32} +(3.74747 + 9.86125i) q^{33} +(-1.03938 - 1.80026i) q^{34} +(2.79332 + 0.928373i) q^{36} +(-1.78835 - 3.09752i) q^{37} -3.80782 q^{38} +(1.91546 + 0.309971i) q^{39} -6.17850 q^{40} +(-1.68320 + 2.91538i) q^{41} +(-1.90276 - 3.29567i) q^{43} +(2.98802 + 5.17540i) q^{44} +(7.87760 - 6.99788i) q^{45} +(-1.09932 + 1.90408i) q^{46} +(-2.86035 + 4.95427i) q^{47} +(-8.54843 - 1.38336i) q^{48} +(6.33349 - 10.9699i) q^{50} +(-2.05853 - 0.333123i) q^{51} +1.09920 q^{52} +(4.16913 - 7.22115i) q^{53} +(7.57313 - 4.81037i) q^{54} +21.3922 q^{55} +(-2.41384 + 2.96047i) q^{57} -10.7140 q^{58} +(-5.63427 - 9.75883i) q^{59} +(3.77198 - 4.62618i) q^{60} +(6.00109 - 10.3942i) q^{61} -0.325300 q^{62} +1.16898 q^{64} +(1.96738 - 3.40761i) q^{65} +(17.9806 + 2.90972i) q^{66} +(3.95652 + 6.85289i) q^{67} -1.18130 q^{68} +(0.783494 + 2.06172i) q^{69} -12.2052 q^{71} +(-3.94540 + 3.50480i) q^{72} +(-2.65737 + 4.60269i) q^{73} -6.17557 q^{74} +(-4.51392 - 11.8781i) q^{75} +(-1.08194 + 1.87397i) q^{76} +(2.11712 - 2.59657i) q^{78} +(-4.60855 + 7.98225i) q^{79} +(-8.78016 + 15.2077i) q^{80} +(1.06079 - 8.93727i) q^{81} +(2.90623 + 5.03373i) q^{82} +(-0.624950 - 1.08245i) q^{83} +(-2.11433 + 3.66213i) q^{85} -6.57064 q^{86} +(-6.79179 + 8.32986i) q^{87} -10.7140 q^{88} +(2.77066 + 4.79892i) q^{89} +(-3.66308 - 17.8206i) q^{90} +(0.624715 + 1.08204i) q^{92} +(-0.206213 + 0.252912i) q^{93} +(4.93871 + 8.55409i) q^{94} +(3.87298 + 6.70820i) q^{95} +(-5.59767 + 6.86532i) q^{96} +(-8.24277 - 14.2769i) q^{97} +(13.6604 - 12.1349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} - 8 q^{51} + 32 q^{53} - 12 q^{57} + 56 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} - 168 q^{72} - 136 q^{74} - 60 q^{78} + 12 q^{79} - 40 q^{81} + 12 q^{85} - 152 q^{86} + 16 q^{92} + 112 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.863305	−	1.49529i	0.610449	−	1.05733i	−0.380716	−	0.924692i	$-0.624322\pi$
$2$	0.863305	−	1.49529i	0.610449	−	1.05733i	0.991165	−	0.132637i	$-0.0423443\pi$
$3$	−0.615283	−	1.61908i	−0.355234	−	0.934778i
$3$	−0.615283	−	1.61908i	−0.355234	−	0.934778i
$4$	−0.490592	−	0.849731i	−0.245296	−	0.424865i
$5$	−3.51231			−1.57075			−0.785377	−	0.619018i	$-0.787531\pi$
$5$	−3.51231			−1.57075			−0.785377	+	0.619018i	$0.787531\pi$
$6$	−2.95217	−	0.477737i	−1.20522	−	0.195035i
$7$		0			0
$7$		0			0
$8$	1.75910			0.621935
$9$	−2.24285	+	1.99239i	−0.747618	+	0.664129i
$10$	−3.03220	+	5.25192i	−0.958865	+	1.66080i
$11$	−6.09064			−1.83640			−0.918199	−	0.396120i	$-0.870356\pi$
$11$	−6.09064			−1.83640			−0.918199	+	0.396120i	$0.870356\pi$
$12$	−1.07393	+	1.31713i	−0.310017	+	0.380224i
$13$	−0.560139	+	0.970190i	−0.155355	+	0.269082i	−0.933188	−	0.359388i	$-0.882985\pi$
$13$	−0.560139	+	0.970190i	−0.155355	+	0.269082i	0.777833	+	0.628471i	$0.216319\pi$
$14$		0			0
$15$	2.16106	+	5.68672i	0.557984	+	1.46831i
$16$	2.49982	−	4.32982i	0.624956	−	1.08246i
$17$	0.601978	−	1.04266i	0.146001	−	0.252881i	−0.783745	−	0.621083i	$-0.786693\pi$
$17$	0.601978	−	1.04266i	0.146001	−	0.252881i	0.929746	+	0.368202i	$0.120026\pi$
$18$	1.04293	+	5.07375i	0.245820	+	1.19589i
$19$	−1.10269	−	1.90991i	−0.252974	−	0.438163i	0.711370	−	0.702818i	$-0.248075\pi$
$19$	−1.10269	−	1.90991i	−0.252974	−	0.438163i	−0.964343	+	0.264655i	$0.914742\pi$
$20$	1.72311	+	2.98452i	0.385300	+	0.667359i
$21$		0			0
$22$	−5.25808	+	9.10727i	−1.12103	+	1.94168i
$23$	−1.27339			−0.265520			−0.132760	−	0.991148i	$-0.542384\pi$
$23$	−1.27339			−0.265520			−0.132760	+	0.991148i	$0.542384\pi$
$24$	−1.08234	−	2.84812i	−0.220932	−	0.581371i
$25$	7.33633			1.46727
$26$	0.967143	+	1.67514i	0.189672	+	0.328522i
$27$	4.60583	+	2.40548i	0.886392	+	0.462936i
$28$		0			0
$29$	−3.10262	−	5.37390i	−0.576142	−	0.997907i	−0.995917	−	0.0902789i	$-0.971224\pi$
$29$	−3.10262	−	5.37390i	−0.576142	−	0.997907i	0.419774	−	0.907628i	$-0.362109\pi$
$30$	10.3689	+	1.67796i	1.89310	+	0.306352i
$31$	−0.0942019	−	0.163162i	−0.0169192	−	0.0293048i	0.857442	−	0.514581i	$-0.172052\pi$
$31$	−0.0942019	−	0.163162i	−0.0169192	−	0.0293048i	−0.874361	+	0.485276i	$0.838719\pi$
$32$	−2.55712	−	4.42907i	−0.452040	−	0.782956i
$33$	3.74747	+	9.86125i	0.652350	+	1.71662i
$34$	−1.03938	−	1.80026i	−0.178252	−	0.308742i
$35$		0			0
$36$	2.79332	+	0.928373i	0.465553	+	0.154729i
$37$	−1.78835	−	3.09752i	−0.294003	−	0.509228i	0.680749	−	0.732516i	$-0.261654\pi$
$37$	−1.78835	−	3.09752i	−0.294003	−	0.509228i	−0.974753	+	0.223288i	$0.928321\pi$
$38$	−3.80782			−0.617710
$39$	1.91546	+	0.309971i	0.306719	+	0.0496350i
$40$	−6.17850			−0.976907
$41$	−1.68320	+	2.91538i	−0.262871	+	0.455307i	−0.967004	−	0.254762i	$-0.918003\pi$
$41$	−1.68320	+	2.91538i	−0.262871	+	0.455307i	0.704132	+	0.710069i	$0.251336\pi$
$42$		0			0
$43$	−1.90276	−	3.29567i	−0.290168	−	0.502585i	0.683681	−	0.729781i	$-0.260378\pi$
$43$	−1.90276	−	3.29567i	−0.290168	−	0.502585i	−0.973849	+	0.227195i	$0.927044\pi$
$44$	2.98802	+	5.17540i	0.450461	+	0.780221i
$45$	7.87760	−	6.99788i	1.17432	−	1.04318i
$46$	−1.09932	+	1.90408i	−0.162086	+	0.280742i
$47$	−2.86035	+	4.95427i	−0.417225	+	0.722654i	−0.995659	−	0.0930746i	$-0.970331\pi$
$47$	−2.86035	+	4.95427i	−0.417225	+	0.722654i	0.578434	+	0.815729i	$0.303664\pi$
$48$	−8.54843	−	1.38336i	−1.23386	−	0.199670i
$49$		0			0
$50$	6.33349	−	10.9699i	0.895691	−	1.55138i
$51$	−2.05853	−	0.333123i	−0.288252	−	0.0466466i
$52$	1.09920			0.152432
$53$	4.16913	−	7.22115i	0.572675	−	0.991901i	−0.423615	−	0.905842i	$-0.639239\pi$
$53$	4.16913	−	7.22115i	0.572675	−	0.991901i	0.996290	−	0.0860593i	$-0.0274275\pi$
$54$	7.57313	−	4.81037i	1.03057	−	0.654609i
$55$	21.3922			2.88453
$56$		0			0
$57$	−2.41384	+	2.96047i	−0.319720	+	0.392124i
$58$	−10.7140			−1.40682
$59$	−5.63427	−	9.75883i	−0.733519	−	1.27049i	−0.955370	−	0.295411i	$-0.904543\pi$
$59$	−5.63427	−	9.75883i	−0.733519	−	1.27049i	0.221851	−	0.975081i	$-0.428790\pi$
$60$	3.77198	−	4.62618i	0.486960	−	0.597238i
$61$	6.00109	−	10.3942i	0.768361	−	1.33084i	−0.170091	−	0.985428i	$-0.554406\pi$
$61$	6.00109	−	10.3942i	0.768361	−	1.33084i	0.938451	−	0.345411i	$-0.112261\pi$
$62$	−0.325300			−0.0413131
$63$		0			0
$64$	1.16898			0.146123
$65$	1.96738	−	3.40761i	0.244024	−	0.422662i
$66$	17.9806	+	2.90972i	2.21326	+	0.358162i
$67$	3.95652	+	6.85289i	0.483366	+	0.837214i	0.999818	−	0.0191025i	$-0.00608088\pi$
$67$	3.95652	+	6.85289i	0.483366	+	0.837214i	−0.516452	+	0.856316i	$0.672748\pi$
$68$	−1.18130			−0.143254
$69$	0.783494	+	2.06172i	0.0943217	+	0.248202i
$70$		0			0
$71$	−12.2052			−1.44850			−0.724248	−	0.689540i	$-0.757813\pi$
$71$	−12.2052			−1.44850			−0.724248	+	0.689540i	$0.757813\pi$
$72$	−3.94540	+	3.50480i	−0.464970	+	0.413045i
$73$	−2.65737	+	4.60269i	−0.311021	+	0.538704i	−0.978584	−	0.205849i	$-0.934004\pi$
$73$	−2.65737	+	4.60269i	−0.311021	+	0.538704i	0.667563	+	0.744554i	$0.267338\pi$
$74$	−6.17557			−0.717896
$75$	−4.51392	−	11.8781i	−0.521222	−	1.37157i
$76$	−1.08194	+	1.87397i	−0.124107	+	0.214959i
$77$		0			0
$78$	2.11712	−	2.59657i	0.239717	−	0.294003i
$79$	−4.60855	+	7.98225i	−0.518503	+	0.898073i	0.481266	+	0.876575i	$0.340177\pi$
$79$	−4.60855	+	7.98225i	−0.518503	+	0.898073i	−0.999769	+	0.0214988i	$0.993156\pi$
$80$	−8.78016	+	15.2077i	−0.981651	+	1.70027i
$81$	1.06079	−	8.93727i	0.117866	−	0.993030i
$82$	2.90623	+	5.03373i	0.320939	+	0.555883i
$83$	−0.624950	−	1.08245i	−0.0685972	−	0.118814i	0.829687	−	0.558229i	$-0.188519\pi$
$83$	−0.624950	−	1.08245i	−0.0685972	−	0.118814i	−0.898284	+	0.439415i	$0.855186\pi$
$84$		0			0
$85$	−2.11433	+	3.66213i	−0.229332	+	0.397214i
$86$	−6.57064			−0.708531
$87$	−6.79179	+	8.32986i	−0.728156	+	0.893055i
$88$	−10.7140			−1.14212
$89$	2.77066	+	4.79892i	0.293689	+	0.508684i	0.974679	−	0.223608i	$-0.0717837\pi$
$89$	2.77066	+	4.79892i	0.293689	+	0.508684i	−0.680990	+	0.732293i	$0.738450\pi$
$90$	−3.66308	−	17.8206i	−0.386122	−	1.87846i
$91$		0			0
$92$	0.624715	+	1.08204i	0.0651310	+	0.112810i
$93$	−0.206213	+	0.252912i	−0.0213832	+	0.0262257i
$94$	4.93871	+	8.55409i	0.509389	+	0.882287i
$95$	3.87298	+	6.70820i	0.397359	+	0.688246i
$96$	−5.59767	+	6.86532i	−0.571310	+	0.700689i
$97$	−8.24277	−	14.2769i	−0.836926	−	1.44960i	−0.892452	−	0.451142i	$-0.851017\pi$
$97$	−8.24277	−	14.2769i	−0.836926	−	1.44960i	0.0555261	−	0.998457i	$-0.482316\pi$
$98$		0			0
$99$	13.6604	−	12.1349i	1.37292	−	1.21960i
$100$	−3.59915	−	6.23391i	−0.359915	−	0.623391i
$101$	12.9638			1.28995			0.644975	−	0.764203i	$-0.276868\pi$
$101$	12.9638			1.28995			0.644975	+	0.764203i	$0.276868\pi$
$102$	−2.27526	+	2.79051i	−0.225284	+	0.276302i
$103$	−2.70182			−0.266218			−0.133109	−	0.991101i	$-0.542496\pi$
$103$	−2.70182			−0.266218			−0.133109	+	0.991101i	$0.542496\pi$
$104$	−0.985340	+	1.70666i	−0.0966205	+	0.167352i
$105$		0			0
$106$	−7.19847	−	12.4681i	−0.699177	−	1.21101i
$107$	0.0892402	+	0.154569i	0.00862718	+	0.0149427i	0.870307	−	0.492510i	$-0.163921\pi$
$107$	0.0892402	+	0.154569i	0.00862718	+	0.0149427i	−0.861680	+	0.507453i	$0.830587\pi$
$108$	−0.215569	−	5.09382i	−0.0207431	−	0.490153i
$109$	−4.67927	+	8.10473i	−0.448192	+	0.776292i	−0.998268	−	0.0588226i	$-0.981265\pi$
$109$	−4.67927	+	8.10473i	−0.448192	+	0.776292i	0.550076	+	0.835115i	$0.314599\pi$
$110$	18.4680	−	31.9876i	1.76086	−	3.04989i
$111$	−3.91479	+	4.80134i	−0.371575	+	0.455723i
$112$		0			0
$113$	4.21019	−	7.29226i	0.396061	−	0.685998i	−0.597175	−	0.802111i	$-0.703710\pi$
$113$	4.21019	−	7.29226i	0.396061	−	0.685998i	0.993236	+	0.116113i	$0.0370434\pi$
$114$	2.34289	+	6.16517i	0.219431	+	0.577422i
$115$	4.47254			0.417067
$116$	−3.04424	+	5.27278i	−0.282651	+	0.489565i
$117$	−0.676682	−	3.29201i	−0.0625593	−	0.304346i
$118$	−19.4564			−1.79110
$119$		0			0
$120$	3.80152	+	10.0035i	0.347030	+	0.913190i
$121$	26.0959			2.37235
$122$	−10.3615	−	17.9467i	−0.938090	−	1.62482i
$123$	5.75589	+	0.931450i	0.518991	+	0.0839861i
$124$	−0.0924294	+	0.160092i	−0.00830040	+	0.0143767i
$125$	−8.20593			−0.733960
$126$		0			0
$127$	−9.92438			−0.880647			−0.440323	−	0.897839i	$-0.645136\pi$
$127$	−9.92438			−0.880647			−0.440323	+	0.897839i	$0.645136\pi$
$128$	6.12343	−	10.6061i	0.541240	−	0.937455i
$129$	−4.16523	+	5.10849i	−0.366728	+	0.449778i
$130$	−3.39691	−	5.88361i	−0.297928	−	0.516027i
$131$	15.2467			1.33211			0.666055	−	0.745902i	$-0.267981\pi$
$131$	15.2467			1.33211			0.666055	+	0.745902i	$0.267981\pi$
$132$	6.54093	−	8.02219i	0.569314	−	0.698242i
$133$		0			0
$134$	13.6627			1.18028
$135$	−16.1771	−	8.44881i	−1.39230	−	0.727158i
$136$	1.05894	−	1.83413i	0.0908032	−	0.157276i
$137$	6.14700			0.525174			0.262587	−	0.964908i	$-0.415424\pi$
$137$	6.14700			0.525174			0.262587	+	0.964908i	$0.415424\pi$
$138$	3.75926	+	0.608345i	0.320010	+	0.0517858i
$139$	−0.438687	+	0.759829i	−0.0372090	+	0.0644478i	−0.884030	−	0.467430i	$-0.845180\pi$
$139$	−0.438687	+	0.759829i	−0.0372090	+	0.0644478i	0.846821	+	0.531878i	$0.178513\pi$
$140$		0			0
$141$	9.78129	+	1.58286i	0.823733	+	0.133301i
$142$	−10.5368	+	18.2504i	−0.884233	+	1.53154i
$143$	3.41161	−	5.90908i	0.285293	−	0.494142i
$144$	3.01994	+	14.6918i	0.251661	+	1.22431i
$145$	10.8974	+	18.8748i	0.904977	+	1.56747i
$146$	4.58824	+	7.94706i	0.379725	+	0.657703i
$147$		0			0
$148$	−1.75470	+	3.03923i	−0.144236	+	0.249823i
$149$	5.77553			0.473150			0.236575	−	0.971613i	$-0.423975\pi$
$149$	5.77553			0.473150			0.236575	+	0.971613i	$0.423975\pi$
$150$	−21.6581	−	3.50484i	−1.76838	−	0.286169i
$151$	−2.02643			−0.164908			−0.0824541	−	0.996595i	$-0.526276\pi$
$151$	−2.02643			−0.164908			−0.0824541	+	0.996595i	$0.526276\pi$
$152$	−1.93973	−	3.35972i	−0.157333	−	0.272509i
$153$	0.727226	+	3.53790i	0.0587927	+	0.286022i
$154$		0			0
$155$	0.330866	+	0.573077i	0.0265758	+	0.0460307i
$156$	−0.676319	−	1.77969i	−0.0541488	−	0.142490i
$157$	−1.52378	−	2.63927i	−0.121611	−	0.210636i	0.798792	−	0.601607i	$-0.205473\pi$
$157$	−1.52378	−	2.63927i	−0.121611	−	0.210636i	−0.920403	+	0.390971i	$0.872139\pi$
$158$	7.95718	+	13.7822i	0.633039	+	1.09646i
$159$	−14.2568	−	2.30712i	−1.13064	−	0.182967i
$160$	8.98141	+	15.5563i	0.710043	+	1.22983i
$161$		0			0
$162$	−12.4480	−	9.30178i	−0.978008	−	0.730817i
$163$	2.69445	+	4.66693i	0.211046	+	0.365542i	0.952042	−	0.305967i	$-0.0989797\pi$
$163$	2.69445	+	4.66693i	0.211046	+	0.365542i	−0.740996	+	0.671509i	$0.765646\pi$
$164$	3.30306			0.257925
$165$	−13.1623	−	34.6358i	−1.02468	−	2.69639i
$166$	−2.15809			−0.167500
$167$	8.30480	−	14.3843i	0.642645	−	1.11309i	−0.342196	−	0.939629i	$-0.611171\pi$
$167$	8.30480	−	14.3843i	0.642645	−	1.11309i	0.984840	−	0.173464i	$-0.0554961\pi$
$168$		0			0
$169$	5.87249	+	10.1714i	0.451730	+	0.782419i
$170$	3.65063	+	6.32308i	0.279991	+	0.484958i
$171$	6.27844	+	2.08667i	0.480125	+	0.159572i
$172$	−1.86696	+	3.23366i	−0.142354	+	0.246564i
$173$	−8.82516	+	15.2856i	−0.670965	+	1.16214i	0.306666	+	0.951817i	$0.400786\pi$
$173$	−8.82516	+	15.2856i	−0.670965	+	1.16214i	−0.977631	+	0.210328i	$0.932547\pi$
$174$	6.59216	+	17.3469i	0.499750	+	1.31507i
$175$		0			0
$176$	−15.2255	+	26.3714i	−1.14767	+	1.98782i
$177$	−12.3337	+	15.1268i	−0.927057	+	1.13700i
$178$	9.56769			0.717128
$179$	−1.31422	+	2.27630i	−0.0982294	+	0.170138i	−0.910952	−	0.412513i	$-0.864651\pi$
$179$	−1.31422	+	2.27630i	−0.0982294	+	0.170138i	0.812722	+	0.582651i	$0.197985\pi$
$180$	−9.81100	−	3.26073i	−0.731269	−	0.243041i
$181$	−3.97391			−0.295378			−0.147689	−	0.989034i	$-0.547184\pi$
$181$	−3.97391			−0.295378			−0.147689	+	0.989034i	$0.547184\pi$
$182$		0			0
$183$	−20.5214	−	3.32089i	−1.51699	−	0.245487i
$184$	−2.24002			−0.165136
$185$	6.28125	+	10.8794i	0.461806	+	0.799872i
$186$	0.200151	+	0.526687i	0.0146758	+	0.0386186i
$187$	−3.66643	+	6.35045i	−0.268116	+	0.464391i
$188$	5.61306			0.409374
$189$		0			0
$190$	13.3743			0.970270
$191$	9.10295	−	15.7668i	0.658666	−	1.14084i	−0.322295	−	0.946639i	$-0.604454\pi$
$191$	9.10295	−	15.7668i	0.658666	−	1.14084i	0.980961	−	0.194204i	$-0.0622125\pi$
$192$	−0.719254	−	1.89268i	−0.0519077	−	0.136592i
$193$	0.101193	+	0.175271i	0.00728401	+	0.0126163i	0.869644	−	0.493679i	$-0.164348\pi$
$193$	0.101193	+	0.175271i	0.00728401	+	0.0126163i	−0.862360	+	0.506295i	$0.831015\pi$
$194$	−28.4641			−2.04360
$195$	−6.72770	−	1.08871i	−0.481780	−	0.0779644i
$196$		0			0
$197$	−1.63136			−0.116229			−0.0581147	−	0.998310i	$-0.518509\pi$
$197$	−1.63136			−0.116229			−0.0581147	+	0.998310i	$0.518509\pi$
$198$	−6.35208	−	30.9024i	−0.451423	−	2.19614i
$199$	3.14605	−	5.44912i	0.223018	−	0.386278i	−0.732705	−	0.680546i	$-0.761743\pi$
$199$	3.14605	−	5.44912i	0.223018	−	0.386278i	0.955723	+	0.294268i	$0.0950759\pi$
$200$	12.9053			0.912544
$201$	8.66101	−	10.6224i	0.610901	−	0.749246i
$202$	11.1918	−	19.3847i	0.787449	−	1.36390i
$203$		0			0
$204$	0.726835	+	1.91263i	0.0508886	+	0.133911i
$205$	5.91192	−	10.2397i	0.412906	−	0.715174i
$206$	−2.33249	+	4.04000i	−0.162512	+	0.281480i
$207$	2.85603	−	2.53708i	0.198508	−	0.176340i
$208$	2.80050	+	4.85061i	0.194180	+	0.336329i
$209$	6.71607	+	11.6326i	0.464560	+	0.804642i
$210$		0			0
$211$	8.14368	−	14.1053i	0.560634	−	0.971046i	−0.436807	−	0.899555i	$-0.643891\pi$
$211$	8.14368	−	14.1053i	0.560634	−	0.971046i	0.997441	−	0.0714912i	$-0.0227758\pi$
$212$	−8.18138			−0.561899
$213$	7.50967	+	19.7613i	0.514554	+	1.35402i
$214$	0.308166			0.0210658
$215$	6.68308	+	11.5754i	0.455782	+	0.789438i
$216$	8.10210	+	4.23148i	0.551278	+	0.287916i
$217$		0			0
$218$	8.07927	+	13.9937i	0.547197	+	0.947773i
$219$	9.08717	+	1.47054i	0.614054	+	0.0993696i
$220$	−10.4949	−	18.1776i	−0.707563	−	1.22554i
$221$	0.674383	+	1.16807i	0.0453639	+	0.0785726i
$222$	3.79972	+	9.99876i	0.255021	+	0.671073i
$223$	9.98472	+	17.2940i	0.668626	+	1.15809i	0.978288	+	0.207248i	$0.0664507\pi$
$223$	9.98472	+	17.2940i	0.668626	+	1.15809i	−0.309662	+	0.950847i	$0.600216\pi$
$224$		0			0
$225$	−16.4543	+	14.6168i	−1.09695	+	0.974454i
$226$	−7.26936	−	12.5909i	−0.483551	−	0.837534i
$227$	−3.61283			−0.239792			−0.119896	−	0.992786i	$-0.538256\pi$
$227$	−3.61283			−0.239792			−0.119896	+	0.992786i	$0.538256\pi$
$228$	3.69981	+	0.598725i	0.245026	+	0.0396515i
$229$	−13.7147			−0.906290			−0.453145	−	0.891437i	$-0.649698\pi$
$229$	−13.7147			−0.906290			−0.453145	+	0.891437i	$0.649698\pi$
$230$	3.86117	−	6.68774i	0.254598	−	0.440976i
$231$		0			0
$232$	−5.45781	−	9.45321i	−0.358323	−	0.620634i
$233$	12.6271	+	21.8707i	0.827227	+	1.43280i	0.900205	+	0.435466i	$0.143417\pi$
$233$	12.6271	+	21.8707i	0.827227	+	1.43280i	−0.0729776	+	0.997334i	$0.523250\pi$
$234$	−5.50669	−	1.83017i	−0.359983	−	0.119642i
$235$	10.0464	−	17.4009i	0.655357	−	1.13511i
$236$	−5.52825	+	9.57521i	−0.359859	+	0.623293i
$237$	15.7595	+	2.55029i	1.02369	+	0.165659i
$238$		0			0
$239$	−4.49495	+	7.78549i	−0.290754	+	0.503601i	−0.973988	−	0.226598i	$-0.927240\pi$
$239$	−4.49495	+	7.78549i	−0.290754	+	0.503601i	0.683234	+	0.730200i	$0.260573\pi$
$240$	30.0248	+	4.85877i	1.93809	+	0.313633i
$241$	−9.25724			−0.596311			−0.298156	−	0.954517i	$-0.596371\pi$
$241$	−9.25724			−0.596311			−0.298156	+	0.954517i	$0.596371\pi$
$242$	22.5287	−	39.0209i	1.44820	−	2.50836i
$243$	−15.1229	+	3.78144i	−0.970132	+	0.242579i
$244$	−11.7763			−0.753903
$245$		0			0
$246$	6.36188	−	7.80259i	0.405619	−	0.497475i
$247$	2.47063			0.157203
$248$	−0.165710	−	0.287019i	−0.0105226	−	0.0182257i
$249$	−1.36805	+	1.67786i	−0.0866965	+	0.106330i
$250$	−7.08422	+	12.2702i	−0.448045	+	0.776037i
$251$	−20.6517			−1.30353			−0.651763	−	0.758422i	$-0.725970\pi$
$251$	−20.6517			−1.30353			−0.651763	+	0.758422i	$0.725970\pi$
$252$		0			0
$253$	7.75576			0.487600
$254$	−8.56777	+	14.8398i	−0.537590	+	0.931133i
$255$	7.23021	+	1.17003i	0.452773	+	0.0732703i
$256$	−9.40380	−	16.2879i	−0.587738	−	1.01799i
$257$	2.44579			0.152564			0.0762819	−	0.997086i	$-0.475695\pi$
$257$	2.44579			0.152564			0.0762819	+	0.997086i	$0.475695\pi$
$258$	4.04280	+	10.6384i	0.251694	+	0.662318i
$259$		0			0
$260$	−3.86073			−0.239432
$261$	17.6656	+	5.87125i	1.09347	+	0.363421i
$262$	13.1626	−	22.7982i	0.813186	−	1.40848i
$263$	−24.5628			−1.51460			−0.757302	−	0.653065i	$-0.773483\pi$
$263$	−24.5628			−1.51460			−0.757302	+	0.653065i	$0.773483\pi$
$264$	6.59216	+	17.3469i	0.405719	+	1.06763i
$265$	−14.6433	+	25.3629i	−0.899531	+	1.55803i
$266$		0			0
$267$	6.06510	−	7.43861i	0.371178	−	0.455236i
$268$	3.88207	−	6.72395i	0.237135	−	0.410730i
$269$	−14.7851	+	25.6086i	−0.901466	+	1.56139i	−0.0758746	+	0.997117i	$0.524175\pi$
$269$	−14.7851	+	25.6086i	−0.901466	+	1.56139i	−0.825592	+	0.564268i	$0.809158\pi$
$270$	−26.5992	+	16.8955i	−1.61877	+	1.02823i
$271$	−12.3958	−	21.4701i	−0.752989	−	1.30421i	−0.946368	−	0.323090i	$-0.895278\pi$
$271$	−12.3958	−	21.4701i	−0.752989	−	1.30421i	0.193380	−	0.981124i	$-0.438055\pi$
$272$	−3.00968	−	5.21291i	−0.182488	−	0.316079i
$273$		0			0
$274$	5.30674	−	9.19154i	0.320592	−	0.555281i
$275$	−44.6830			−2.69448
$276$	1.36753	−	1.67722i	0.0823157	−	0.100957i
$277$	1.87850			0.112868			0.0564340	−	0.998406i	$-0.482027\pi$
$277$	1.87850			0.112868			0.0564340	+	0.998406i	$0.482027\pi$
$278$	0.757442	+	1.31193i	0.0454284	+	0.0786842i
$279$	0.536364	+	0.178263i	0.0321113	+	0.0106723i
$280$		0			0
$281$	6.03965	+	10.4610i	0.360295	+	0.624049i	0.988009	−	0.154395i	$-0.0493427\pi$
$281$	6.03965	+	10.4610i	0.360295	+	0.624049i	−0.627714	+	0.778444i	$0.716009\pi$
$282$	10.8111	−	13.2594i	0.643790	−	0.789583i
$283$	−13.9859	−	24.2244i	−0.831378	−	1.43999i	−0.896946	−	0.442140i	$-0.854219\pi$
$283$	−13.9859	−	24.2244i	−0.831378	−	1.43999i	0.0655680	−	0.997848i	$-0.479114\pi$
$284$	5.98779	+	10.3712i	0.355310	+	0.615415i
$285$	8.47814	−	10.3981i	0.502202	−	0.615931i
$286$	−5.89052	−	10.2027i	−0.348314	−	0.603297i
$287$		0			0
$288$	14.5597	+	4.83897i	0.857937	+	0.285139i
$289$	7.77524	+	13.4671i	0.457367	+	0.792183i
$290$	37.6310			2.20977
$291$	−18.0438	+	22.1300i	−1.05775	+	1.29729i
$292$	5.21473			0.305169
$293$	4.41163	−	7.64117i	0.257730	−	0.446402i	−0.707903	−	0.706309i	$-0.750359\pi$
$293$	4.41163	−	7.64117i	0.257730	−	0.446402i	0.965634	+	0.259908i	$0.0836921\pi$
$294$		0			0
$295$	19.7893	+	34.2761i	1.15218	+	1.99563i
$296$	−3.14589	−	5.44883i	−0.182851	−	0.316707i
$297$	−28.0524	−	14.6509i	−1.62777	−	0.850134i
$298$	4.98604	−	8.63608i	0.288834	−	0.500275i
$299$	0.713276	−	1.23543i	0.0412498	−	0.0714467i
$300$	−7.87871	+	9.66293i	−0.454878	+	0.557889i
$301$		0			0
$302$	−1.74942	+	3.03009i	−0.100668	+	0.174362i
$303$	−7.97643	−	20.9895i	−0.458234	−	1.20582i
$304$	−11.0261			−0.632389
$305$	−21.0777	+	36.5076i	−1.20691	+	2.09042i
$306$	5.91800	+	1.96687i	0.338309	+	0.112439i
$307$	−1.05532			−0.0602304			−0.0301152	−	0.999546i	$-0.509587\pi$
$307$	−1.05532			−0.0602304			−0.0301152	+	0.999546i	$0.509587\pi$
$308$		0			0
$309$	1.66238	+	4.37446i	0.0945696	+	0.248855i
$310$	1.14255			0.0648927
$311$	1.53608	+	2.66056i	0.0871029	+	0.150867i	0.906285	−	0.422666i	$-0.138906\pi$
$311$	1.53608	+	2.66056i	0.0871029	+	0.150867i	−0.819182	+	0.573533i	$0.805572\pi$
$312$	3.36948	+	0.545269i	0.190759	+	0.0308698i
$313$	14.0810	−	24.3891i	0.795907	−	1.37855i	−0.126355	−	0.991985i	$-0.540328\pi$
$313$	14.0810	−	24.3891i	0.795907	−	1.37855i	0.922262	−	0.386566i	$-0.126339\pi$
$314$	−5.26196			−0.296949
$315$		0			0
$316$	9.04368			0.508747
$317$	−6.42324	+	11.1254i	−0.360765	+	0.624863i	−0.988087	−	0.153897i	$-0.950818\pi$
$317$	−6.42324	+	11.1254i	−0.360765	+	0.624863i	0.627322	+	0.778760i	$0.284151\pi$
$318$	−15.7578	+	19.3263i	−0.883654	+	1.08377i
$319$	18.8969	+	32.7305i	1.05803	+	1.83255i
$320$	−4.10582			−0.229523
$321$	0.195351	−	0.239591i	0.0109034	−	0.0133726i
$322$		0			0
$323$	−2.65517			−0.147738
$324$	−8.11468	+	3.48317i	−0.450816	+	0.193509i
$325$	−4.10937	+	7.11763i	−0.227947	+	0.394815i
$326$	9.30454			0.515331
$327$	16.0013	+	2.58942i	0.884873	+	0.143195i
$328$	−2.96091	+	5.12845i	−0.163489	+	0.283171i
$329$		0			0
$330$	−63.1535	−	10.2199i	−3.47649	−	0.562585i
$331$	10.7780	−	18.6681i	0.592413	−	1.02609i	−0.401493	−	0.915862i	$-0.631509\pi$
$331$	10.7780	−	18.6681i	0.592413	−	1.02609i	0.993906	−	0.110228i	$-0.0351581\pi$
$332$	−0.613191	+	1.06208i	−0.0336532	+	0.0582891i
$333$	10.1825	+	3.38419i	0.557995	+	0.185452i
$334$	−14.3392	−	24.8361i	−0.784604	−	1.35897i
$335$	−13.8965	−	24.0695i	−0.759248	−	1.31506i
$336$		0			0
$337$	6.30340	−	10.9178i	0.343368	−	0.594731i	−0.641688	−	0.766966i	$-0.721766\pi$
$337$	6.30340	−	10.9178i	0.343368	−	0.594731i	0.985056	+	0.172235i	$0.0550989\pi$
$338$	20.2790			1.10303
$339$	−14.3972	−	2.32984i	−0.781950	−	0.126540i
$340$	4.14910			0.225017
$341$	0.573750	+	0.993764i	0.0310703	+	0.0538153i
$342$	8.54039	−	7.58665i	0.461811	−	0.410239i
$343$		0			0
$344$	−3.34714	−	5.79741i	−0.180466	−	0.312575i
$345$	−2.75188	−	7.24141i	−0.148156	−	0.389864i
$346$	15.2376	+	26.3923i	0.819179	+	1.41886i
$347$	−11.5683	−	20.0369i	−0.621020	−	1.07564i	−0.989296	−	0.145922i	$-0.953385\pi$
$347$	−11.5683	−	20.0369i	−0.621020	−	1.07564i	0.368276	−	0.929716i	$-0.379948\pi$
$348$	10.4101	+	1.68463i	0.558042	+	0.0903055i
$349$	−8.24346	−	14.2781i	−0.441262	−	0.764289i	0.556521	−	0.830833i	$-0.312136\pi$
$349$	−8.24346	−	14.2781i	−0.441262	−	0.764289i	−0.997783	+	0.0665448i	$0.978802\pi$
$350$		0			0
$351$	−4.91368	+	3.12112i	−0.262273	+	0.166593i
$352$	15.5745	+	26.9759i	0.830124	+	1.43782i
$353$	24.4875			1.30334			0.651669	−	0.758503i	$-0.274069\pi$
$353$	24.4875			1.30334			0.651669	+	0.758503i	$0.274069\pi$
$354$	11.9712	+	31.5015i	0.636260	+	1.67428i
$355$	42.8686			2.27523
$356$	2.71852	−	4.70862i	0.144081	−	0.249556i
$357$		0			0
$358$	2.26915	+	3.93028i	0.119928	+	0.207722i
$359$	−10.2389	−	17.7342i	−0.540386	−	0.935977i	−0.998882	−	0.0472797i	$-0.984945\pi$
$359$	−10.2389	−	17.7342i	−0.540386	−	0.935977i	0.458495	−	0.888697i	$-0.348389\pi$
$360$	13.8575	−	12.3100i	0.730353	−	0.648792i
$361$	7.06816	−	12.2424i	0.372009	−	0.644338i
$362$	−3.43070	+	5.94214i	−0.180313	+	0.312312i
$363$	−16.0564	−	42.2514i	−0.842740	−	2.21762i
$364$		0			0
$365$	9.33349	−	16.1661i	0.488537	−	0.846172i
$366$	−22.6819	+	27.8185i	−1.18560	+	1.45410i
$367$	−22.2539			−1.16164			−0.580821	−	0.814031i	$-0.697268\pi$
$367$	−22.2539			−1.16164			−0.580821	+	0.814031i	$0.697268\pi$
$368$	−3.18325	+	5.51355i	−0.165938	+	0.287414i
$369$	−2.03341	−	9.89237i	−0.105855	−	0.514976i
$370$	21.6905			1.12764
$371$		0			0
$372$	0.316073	+	0.0511487i	0.0163876	+	0.00265194i
$373$	−32.5369			−1.68469			−0.842347	−	0.538935i	$-0.818827\pi$
$373$	−32.5369			−1.68469			−0.842347	+	0.538935i	$0.818827\pi$
$374$	6.33050	+	10.9647i	0.327342	+	0.566974i
$375$	5.04896	+	13.2861i	0.260727	+	0.686090i
$376$	−5.03163	+	8.71504i	−0.259487	+	0.449444i
$377$	6.95160			0.358026
$378$		0			0
$379$	1.54440			0.0793306			0.0396653	−	0.999213i	$-0.487371\pi$
$379$	1.54440			0.0793306			0.0396653	+	0.999213i	$0.487371\pi$
$380$	3.80011	−	6.58198i	0.194941	−	0.337648i
$381$	6.10630	+	16.0684i	0.312835	+	0.823209i
$382$	−15.7173	−	27.2231i	−0.804165	−	1.39285i
$383$	−31.6294			−1.61619			−0.808093	−	0.589055i	$-0.799500\pi$
$383$	−31.6294			−1.61619			−0.808093	+	0.589055i	$0.799500\pi$
$384$	−20.9398	−	3.38859i	−1.06858	−	0.172923i
$385$		0			0
$386$	0.349441			0.0177861
$387$	10.8339	+	3.60068i	0.550716	+	0.183033i
$388$	−8.08767	+	14.0083i	−0.410589	+	0.711162i
$389$	−5.24626			−0.265996			−0.132998	−	0.991116i	$-0.542460\pi$
$389$	−5.24626			−0.265996			−0.132998	+	0.991116i	$0.542460\pi$
$390$	−7.43600	+	9.11996i	−0.376536	+	0.461807i
$391$	−0.766552	+	1.32771i	−0.0387662	+	0.0671451i
$392$		0			0
$393$	−9.38103	−	24.6857i	−0.473210	−	1.24523i
$394$	−1.40836	+	2.43935i	−0.0709521	+	0.122893i
$395$	16.1867	−	28.0362i	0.814440	−	1.41065i
$396$	−17.0131	−	5.65438i	−0.854940	−	0.284143i
$397$	0.0138175	+	0.0239325i	0.000693478	+	0.00120114i	0.866372	−	0.499399i	$-0.166446\pi$
$397$	0.0138175	+	0.0239325i	0.000693478	+	0.00120114i	−0.865678	+	0.500600i	$0.833113\pi$
$398$	−5.43201	−	9.40851i	−0.272282	−	0.471606i
$399$		0			0
$400$	18.3395	−	31.7650i	0.916977	−	1.58825i
$401$	12.1377			0.606127			0.303064	−	0.952970i	$-0.401991\pi$
$401$	12.1377			0.606127			0.303064	+	0.952970i	$0.401991\pi$
$402$	−8.40644	−	22.1211i	−0.419275	−	1.10330i
$403$	0.211065			0.0105139
$404$	−6.35996	−	11.0158i	−0.316420	−	0.548055i
$405$	−3.72583	+	31.3905i	−0.185138	+	1.55980i
$406$		0			0
$407$	10.8922	+	18.8659i	0.539907	+	0.935146i
$408$	−3.62116	−	0.585997i	−0.179274	−	0.0290112i
$409$	15.6726	+	27.1458i	0.774963	+	1.34227i	0.934816	+	0.355134i	$0.115565\pi$
$409$	15.6726	+	27.1458i	0.774963	+	1.34227i	−0.159853	+	0.987141i	$0.551102\pi$
$410$	−10.2076	−	17.6800i	−0.504116	−	0.873155i
$411$	−3.78214	−	9.95250i	−0.186559	−	0.490921i
$412$	1.32549	+	2.29582i	0.0653022	+	0.113107i
$413$		0			0
$414$	−1.32805	−	6.46086i	−0.0652701	−	0.317534i
$415$	2.19502	+	3.80189i	0.107749	+	0.186627i
$416$	5.72938			0.280906
$417$	1.50014	+	0.242761i	0.0734623	+	0.0118881i
$418$	23.1921			1.13436
$419$	−7.44319	+	12.8920i	−0.363623	+	0.629814i	−0.988554	−	0.150866i	$-0.951794\pi$
$419$	−7.44319	+	12.8920i	−0.363623	+	0.629814i	0.624931	+	0.780680i	$0.285127\pi$
$420$		0			0
$421$	−4.54213	−	7.86721i	−0.221370	−	0.383424i	0.733854	−	0.679307i	$-0.237720\pi$
$421$	−4.54213	−	7.86721i	−0.221370	−	0.383424i	−0.955224	+	0.295883i	$0.904386\pi$
$422$	−14.0610	−	24.3543i	−0.684477	−	1.18555i
$423$	−3.45547	−	16.8106i	−0.168011	−	0.817360i
$424$	7.33392	−	12.7027i	0.356166	−	0.616898i
$425$	4.41631	−	7.64927i	0.214223	−	0.371044i
$426$	36.0320	+	5.83089i	1.74575	+	0.282508i
$427$		0			0
$428$	0.0875611	−	0.151660i	0.00423243	−	0.00733078i
$429$	−11.6664	−	1.88792i	−0.563258	−	0.0911496i
$430$	23.0781			1.11293
$431$	8.31776	−	14.4068i	0.400652	−	0.693950i	−0.593152	−	0.805090i	$-0.702117\pi$
$431$	8.31776	−	14.4068i	0.400652	−	0.693950i	0.993805	+	0.111140i	$0.0354502\pi$
$432$	21.9291	−	13.9291i	1.05506	−	0.670165i
$433$	−19.7423			−0.948756			−0.474378	−	0.880321i	$-0.657327\pi$
$433$	−19.7423			−0.948756			−0.474378	+	0.880321i	$0.657327\pi$
$434$		0			0
$435$	23.8549	−	29.2571i	1.14375	−	1.40277i
$436$	9.18244			0.439759
$437$	1.40415	+	2.43206i	0.0671696	+	0.116341i
$438$	10.0439	−	12.3184i	0.479915	−	0.588597i
$439$	−3.36757	+	5.83280i	−0.160725	+	0.278384i	−0.935129	−	0.354307i	$-0.884717\pi$
$439$	−3.36757	+	5.83280i	−0.160725	+	0.278384i	0.774404	+	0.632692i	$0.218050\pi$
$440$	37.6310			1.79399
$441$		0			0
$442$	2.32879			0.110769
$443$	−14.3202	+	24.8033i	−0.680372	+	1.17844i	0.294496	+	0.955653i	$0.404848\pi$
$443$	−14.3202	+	24.8033i	−0.680372	+	1.17844i	−0.974867	+	0.222786i	$0.928485\pi$
$444$	6.00041	+	0.971019i	0.284767	+	0.0460825i
$445$	−9.73141	−	16.8553i	−0.461313	−	0.799017i
$446$	34.4794			1.63265
$447$	−3.55358	−	9.35105i	−0.168079	−	0.442290i
$448$		0			0
$449$	−6.66872			−0.314716			−0.157358	−	0.987542i	$-0.550298\pi$
$449$	−6.66872			−0.314716			−0.157358	+	0.987542i	$0.550298\pi$
$450$	7.65124	+	37.2227i	0.360683	+	1.75470i
$451$	10.2518	−	17.7566i	0.482736	−	0.836124i
$452$	−8.26194			−0.388609
$453$	1.24683	+	3.28095i	0.0585810	+	0.154153i
$454$	−3.11898	+	5.40223i	−0.146381	+	0.253539i
$455$		0			0
$456$	−4.24617	+	5.20776i	−0.198845	+	0.243876i
$457$	14.3287	−	24.8180i	0.670266	−	1.16093i	−0.307563	−	0.951528i	$-0.599513\pi$
$457$	14.3287	−	24.8180i	0.670266	−	1.16093i	0.977829	−	0.209407i	$-0.0671533\pi$
$458$	−11.8399	+	20.5074i	−0.553244	+	0.958246i
$459$	5.28070	−	3.35425i	0.246482	−	0.156563i
$460$	−2.19419	−	3.80045i	−0.102305	−	0.177197i
$461$	10.0087	+	17.3355i	0.466150	+	0.807395i	0.999253	−	0.0386554i	$-0.0123075\pi$
$461$	10.0087	+	17.3355i	0.466150	+	0.807395i	−0.533103	+	0.846050i	$0.678974\pi$
$462$		0			0
$463$	−4.95789	+	8.58731i	−0.230413	+	0.399086i	−0.957930	−	0.287003i	$-0.907341\pi$
$463$	−4.95789	+	8.58731i	−0.230413	+	0.399086i	0.727517	+	0.686090i	$0.240674\pi$
$464$	−31.0240			−1.44025
$465$	0.724283	−	0.888304i	0.0335878	−	0.0411941i
$466$	43.6041			2.01992
$467$	−8.04035	−	13.9263i	−0.372063	−	0.644432i	0.617820	−	0.786320i	$-0.288016\pi$
$467$	−8.04035	−	13.9263i	−0.372063	−	0.644432i	−0.989883	+	0.141888i	$0.954683\pi$
$468$	−2.46535	+	2.19003i	−0.113961	+	0.101234i
$469$		0			0
$470$	−17.3463	−	30.0446i	−0.800124	−	1.38586i
$471$	−3.33563	+	4.09102i	−0.153698	+	0.188504i
$472$	−9.91123	−	17.1667i	−0.456201	−	0.790164i
$473$	11.5890	+	20.0728i	0.532863	+	0.922946i
$474$	17.4187	−	21.3633i	0.800066	−	0.981249i
$475$	−8.08967	−	14.0117i	−0.371180	−	0.642902i
$476$		0			0
$477$	5.03657	+	24.5025i	0.230609	+	1.12189i
$478$	7.76103	+	13.4425i	0.354981	+	0.614846i
$479$	−8.20255			−0.374784			−0.187392	−	0.982285i	$-0.560003\pi$
$479$	−8.20255			−0.374784			−0.187392	+	0.982285i	$0.560003\pi$
$480$	19.6608	−	24.1131i	0.897387	−	1.10061i
$481$	4.00690			0.182699
$482$	−7.99183	+	13.8423i	−0.364018	+	0.630497i
$483$		0			0
$484$	−12.8024	−	22.1745i	−0.581929	−	1.00793i
$485$	28.9512	+	50.1449i	1.31460	+	2.27696i
$486$	−7.40130	+	25.8776i	−0.335730	+	1.17383i
$487$	−1.36840	+	2.37014i	−0.0620081	+	0.107401i	−0.895363	−	0.445337i	$-0.853084\pi$
$487$	−1.36840	+	2.37014i	−0.0620081	+	0.107401i	0.833355	+	0.552738i	$0.186417\pi$
$488$	10.5565	−	18.2844i	0.477871	−	0.827696i
$489$	5.89829	−	7.23402i	0.266730	−	0.327134i
$490$		0			0
$491$	9.85482	−	17.0690i	0.444742	−	0.770315i	−0.553293	−	0.832987i	$-0.686629\pi$
$491$	9.85482	−	17.0690i	0.444742	−	0.770315i	0.998034	+	0.0626719i	$0.0199622\pi$
$492$	−2.03231	−	5.34792i	−0.0916237	−	0.241103i
$493$	−7.47084			−0.336470
$494$	2.13291	−	3.69431i	0.0959642	−	0.166215i
$495$	−47.9796	+	42.6216i	−2.15652	+	1.91570i
$496$	−0.941952			−0.0422949
$497$		0			0
$498$	1.32784	+	3.49413i	0.0595018	+	0.156576i
$499$	−33.0960			−1.48158			−0.740789	−	0.671737i	$-0.765548\pi$
$499$	−33.0960			−1.48158			−0.740789	+	0.671737i	$0.765548\pi$
$500$	4.02576	+	6.97283i	0.180038	+	0.311834i
$501$	−28.3992	−	4.59572i	−1.26878	−	0.205322i
$502$	−17.8288	+	30.8803i	−0.795737	+	1.37826i
$503$	12.1860			0.543346			0.271673	−	0.962390i	$-0.412423\pi$
$503$	12.1860			0.543346			0.271673	+	0.962390i	$0.412423\pi$
$504$		0			0
$505$	−45.5331			−2.02619
$506$	6.69559	−	11.5971i	0.297655	−	0.515554i
$507$	12.8552	−	15.7664i	0.570918	−	0.700208i
$508$	4.86882	+	8.43305i	0.216019	+	0.374156i
$509$	13.6393			0.604551			0.302276	−	0.953221i	$-0.402254\pi$
$509$	13.6393			0.604551			0.302276	+	0.953221i	$0.402254\pi$
$510$	7.99142	−	9.80116i	0.353866	−	0.434002i
$511$		0			0
$512$	−7.97968			−0.352656
$513$	−0.484527	−	11.4492i	−0.0213924	−	0.505495i
$514$	2.11146	−	3.65715i	0.0931325	−	0.161310i
$515$	9.48962			0.418163
$516$	6.38427	+	1.03314i	0.281052	+	0.0454814i
$517$	17.4214	−	30.1747i	0.766190	−	1.32708i
$518$		0			0
$519$	30.1787	+	4.88368i	1.32470	+	0.214370i
$520$	3.46082	−	5.99432i	0.151767	−	0.262868i
$521$	17.7745	−	30.7863i	0.778714	−	1.34877i	−0.153969	−	0.988076i	$-0.549206\pi$
$521$	17.7745	−	30.7863i	0.778714	−	1.34877i	0.932683	−	0.360697i	$-0.117461\pi$
$522$	24.0300	−	21.3465i	1.05177	−	0.934311i
$523$	−13.3593	−	23.1391i	−0.584163	−	1.01180i	−0.994979	−	0.100082i	$-0.968089\pi$
$523$	−13.3593	−	23.1391i	−0.584163	−	1.01180i	0.410816	−	0.911718i	$-0.365244\pi$
$524$	−7.47991	−	12.9556i	−0.326761	−	0.565967i
$525$		0			0
$526$	−21.2052	+	36.7284i	−0.924589	+	1.60143i
$527$	−0.226830			−0.00988086
$528$	52.0654	+	8.42552i	2.26586	+	0.366674i
$529$	−21.3785			−0.929499
$530$	25.2833	+	43.7919i	1.09824	+	1.90220i
$531$	32.0802	+	10.6620i	1.39216	+	0.462692i
$532$		0			0
$533$	−1.88565	−	3.26604i	−0.0816766	−	0.141468i
$534$	−5.88683	−	15.4909i	−0.254748	−	0.670356i
$535$	−0.313440	−	0.542893i	−0.0135512	−	0.0234713i
$536$	6.95990	+	12.0549i	0.300622	+	0.520693i
$537$	4.49413	+	0.727265i	0.193936	+	0.0313838i
$538$	25.5282	+	44.2161i	1.10060	+	1.90629i
$539$		0			0
$540$	0.757146	+	17.8911i	0.0325824	+	0.769910i
$541$	−18.7927	−	32.5500i	−0.807963	−	1.39943i	−0.914272	−	0.405100i	$-0.867237\pi$
$541$	−18.7927	−	32.5500i	−0.807963	−	1.39943i	0.106309	−	0.994333i	$-0.466097\pi$
$542$	−42.8053			−1.83864
$543$	2.44508	+	6.43408i	0.104928	+	0.276113i
$544$	−6.15733			−0.263993
$545$	16.4350	−	28.4663i	0.704000	−	1.21936i
$546$		0			0
$547$	−9.13381	−	15.8202i	−0.390533	−	0.676424i	0.601986	−	0.798506i	$-0.294376\pi$
$547$	−9.13381	−	15.8202i	−0.390533	−	0.676424i	−0.992520	+	0.122082i	$0.961043\pi$
$548$	−3.01567	−	5.22329i	−0.128823	−	0.223128i
$549$	7.24968	+	35.2691i	0.309409	+	1.50525i
$550$	−38.5750	+	66.8139i	−1.64485	+	2.84896i
$551$	−6.84243	+	11.8514i	−0.291498	+	0.504889i
$552$	1.37824	+	3.62677i	0.0586619	+	0.154366i
$553$		0			0
$554$	1.62172	−	2.80890i	0.0689002	−	0.119339i
$555$	13.7500	−	16.8638i	0.583653	−	0.715828i
$556$	0.860866			0.0365089
$557$	1.94636	−	3.37119i	0.0824698	−	0.142842i	−0.821840	−	0.569718i	$-0.807053\pi$
$557$	1.94636	−	3.37119i	0.0824698	−	0.142842i	0.904310	+	0.426876i	$0.140386\pi$
$558$	0.729600	−	0.648123i	0.0308864	−	0.0274372i
$559$	4.26324			0.180316
$560$		0			0
$561$	12.5378	+	2.02893i	0.529346	+	0.0856617i
$562$	20.8562			0.879767
$563$	1.66428	+	2.88261i	0.0701409	+	0.121488i	0.898963	−	0.438025i	$-0.144322\pi$
$563$	1.66428	+	2.88261i	0.0701409	+	0.121488i	−0.828822	+	0.559512i	$0.810988\pi$
$564$	−3.45362	−	9.08800i	−0.145424	−	0.382674i
$565$	−14.7875	+	25.6127i	−0.622115	+	1.07753i
$566$	−48.2965			−2.03006
$567$		0			0
$568$	−21.4702			−0.900870
$569$	18.3122	−	31.7177i	0.767688	−	1.32967i	−0.171126	−	0.985249i	$-0.554741\pi$
$569$	18.3122	−	31.7177i	0.767688	−	1.32967i	0.938814	−	0.344425i	$-0.111926\pi$
$570$	−8.22895	−	21.6540i	−0.344673	−	0.906987i
$571$	11.2912	+	19.5569i	0.472522	+	0.818432i	0.999506	−	0.0314435i	$-0.0100104\pi$
$571$	11.2912	+	19.5569i	0.472522	+	0.818432i	−0.526984	+	0.849875i	$0.676677\pi$
$572$	−6.69483			−0.279925
$573$	−31.1286	−	5.03740i	−1.30042	−	0.210441i
$574$		0			0
$575$	−9.34201			−0.389589
$576$	−2.62185	+	2.32906i	−0.109244	+	0.0970442i
$577$	11.2725	−	19.5245i	0.469279	−	0.812815i	−0.530104	−	0.847932i	$-0.677847\pi$
$577$	11.2725	−	19.5245i	0.469279	−	0.812815i	0.999383	+	0.0351177i	$0.0111806\pi$
$578$	26.8496			1.11680
$579$	0.221516	−	0.271680i	0.00920588	−	0.0112906i
$580$	10.6923	−	18.5197i	0.443975	−	0.768987i
$581$		0			0
$582$	17.5135	+	46.0857i	0.725957	+	1.91031i
$583$	−25.3927	+	43.9814i	−1.05166	+	1.82152i
$584$	−4.67457	+	8.09659i	−0.193435	+	0.335039i
$585$	2.37672	+	11.5626i	0.0982652	+	0.478053i
$586$	−7.61717	−	13.1933i	−0.314662	−	0.545011i
$587$	12.1198	+	20.9921i	0.500237	+	0.866436i	1.00000		0.000273884i	$8.71801e-5\pi$
$587$	12.1198	+	20.9921i	0.500237	+	0.866436i	−0.499763	+	0.866162i	$0.666579\pi$
$588$		0			0
$589$	−0.207750	+	0.359834i	−0.00856020	+	0.0148267i
$590$	68.3368			2.81338
$591$	1.00375	+	2.64130i	0.0412886	+	0.108649i
$592$	−17.8822			−0.734956
$593$	−22.8663	−	39.6056i	−0.939007	−	1.62641i	−0.767328	−	0.641255i	$-0.778414\pi$
$593$	−22.8663	−	39.6056i	−0.939007	−	1.62641i	−0.171680	−	0.985153i	$-0.554919\pi$
$594$	−46.1252	+	29.2983i	−1.89254	+	1.20212i
$595$		0			0
$596$	−2.83343	−	4.90764i	−0.116062	−	0.201025i
$597$	−10.7583	−	1.74097i	−0.440308	−	0.0712530i
$598$	−1.23155	−	2.13311i	−0.0503618	−	0.0872292i
$599$	15.0834	+	26.1252i	0.616290	+	1.06745i	0.990157	+	0.139963i	$0.0446985\pi$
$599$	15.0834	+	26.1252i	0.616290	+	1.06745i	−0.373866	+	0.927483i	$0.621968\pi$
$600$	−7.94042	−	20.8948i	−0.324166	−	0.853026i
$601$	−7.36933	−	12.7641i	−0.300601	−	0.520657i	0.675671	−	0.737203i	$-0.263854\pi$
$601$	−7.36933	−	12.7641i	−0.300601	−	0.520657i	−0.976272	+	0.216547i	$0.930521\pi$
$602$		0			0
$603$	−22.5275	−	7.48712i	−0.917391	−	0.304899i
$604$	0.994149	+	1.72192i	0.0404513	+	0.0700638i
$605$	−91.6569			−3.72638
$606$	−38.2715	−	6.19331i	−1.55467	−	0.251586i
$607$	6.07836			0.246713			0.123356	−	0.992362i	$-0.460634\pi$
$607$	6.07836			0.246713			0.123356	+	0.992362i	$0.460634\pi$
$608$	−5.63941	+	9.76774i	−0.228708	+	0.396134i
$609$		0			0
$610$	36.3930	+	63.0345i	1.47351	+	2.55219i
$611$	−3.20439	−	5.55016i	−0.129636	−	0.224535i
$612$	2.64949	−	2.35361i	0.107099	−	0.0951391i
$613$	−5.88668	+	10.1960i	−0.237761	+	0.411814i	−0.960071	−	0.279755i	$-0.909747\pi$
$613$	−5.88668	+	10.1960i	−0.237761	+	0.411814i	0.722311	+	0.691569i	$0.243080\pi$
$614$	−0.911065	+	1.57801i	−0.0367676	+	0.0636833i
$615$	−20.2165	−	3.27154i	−0.815207	−	0.131921i
$616$		0			0
$617$	−16.0319	+	27.7680i	−0.645418	+	1.11790i	0.338786	+	0.940863i	$0.389984\pi$
$617$	−16.0319	+	27.7680i	−0.645418	+	1.11790i	−0.984205	+	0.177034i	$0.943350\pi$
$618$	7.97623	+	1.29076i	0.320851	+	0.0519219i
$619$	12.5518			0.504498			0.252249	−	0.967662i	$-0.418830\pi$
$619$	12.5518			0.504498			0.252249	+	0.967662i	$0.418830\pi$
$620$	0.324641	−	0.562294i	0.0130379	−	0.0225823i
$621$	−5.86501	−	3.06312i	−0.235355	−	0.122919i
$622$	5.30441			0.212688
$623$		0			0
$624$	6.13043	−	7.51873i	0.245414	−	0.300990i
$625$	−7.85989			−0.314396
$626$	−24.3125	−	42.1104i	−0.971721	−	1.68307i
$627$	14.7018	−	18.0312i	0.587134	−	0.720096i
$628$	−1.49511	+	2.58961i	−0.0596614	+	0.103337i
$629$	−4.30619			−0.171699
$630$		0			0
$631$	33.4642			1.33219			0.666095	−	0.745867i	$-0.267964\pi$
$631$	33.4642			1.33219			0.666095	+	0.745867i	$0.267964\pi$
$632$	−8.10690	+	14.0416i	−0.322475	+	0.558543i
$633$	−27.8482	−	4.50656i	−1.10687	−	0.179120i
$634$	11.0904	+	19.2092i	0.440457	+	0.762894i
$635$	34.8575			1.38328
$636$	5.03386	+	13.2463i	0.199606	+	0.525251i
$637$		0			0
$638$	65.2553			2.58348
$639$	27.3746	−	24.3176i	1.08292	−	0.961988i
$640$	−21.5074	+	37.2519i	−0.850155	+	1.47251i
$641$	−18.9837			−0.749809			−0.374905	−	0.927063i	$-0.622325\pi$
$641$	−18.9837			−0.749809			−0.374905	+	0.927063i	$0.622325\pi$
$642$	−0.189609	−	0.498947i	−0.00748329	−	0.0196918i
$643$	−4.81347	+	8.33718i	−0.189825	+	0.328786i	−0.945192	−	0.326516i	$-0.894125\pi$
$643$	−4.81347	+	8.33718i	−0.189825	+	0.328786i	0.755367	+	0.655302i	$0.227459\pi$
$644$		0			0
$645$	14.6296	−	17.9426i	0.576039	−	0.706490i
$646$	−2.29222	+	3.97025i	−0.0901864	+	0.156207i
$647$	−3.90607	+	6.76551i	−0.153564	+	0.265980i	−0.932535	−	0.361079i	$-0.882408\pi$
$647$	−3.90607	+	6.76551i	−0.153564	+	0.265980i	0.778972	+	0.627059i	$0.215742\pi$
$648$	1.86604	−	15.7215i	0.0733048	−	0.617600i
$649$	34.3163	+	59.4375i	1.34703	+	2.33313i
$650$	7.09528	+	12.2894i	0.278300	+	0.482029i
$651$		0			0
$652$	2.64376	−	4.57912i	0.103537	−	0.179332i
$653$	31.7429			1.24219			0.621097	−	0.783734i	$-0.286687\pi$
$653$	31.7429			1.24219			0.621097	+	0.783734i	$0.286687\pi$
$654$	17.6859	−	21.6911i	0.691574	−	0.848189i
$655$	−53.5512			−2.09242
$656$	8.41540	+	14.5759i	0.328566	+	0.569093i
$657$	−3.21026	−	15.6177i	−0.125244	−	0.609303i
$658$		0			0
$659$	3.10685	+	5.38122i	0.121026	+	0.209623i	0.920172	−	0.391513i	$-0.128048\pi$
$659$	3.10685	+	5.38122i	0.121026	+	0.209623i	−0.799147	+	0.601136i	$0.794715\pi$
$660$	−22.9738	+	28.1764i	−0.894253	+	1.09677i
$661$	13.7631	+	23.8384i	0.535324	+	0.927208i	0.999148	+	0.0412802i	$0.0131436\pi$
$661$	13.7631	+	23.8384i	0.535324	+	0.927208i	−0.463824	+	0.885927i	$0.653523\pi$
$662$	−18.6094	−	32.2325i	−0.723276	−	1.25275i
$663$	1.47626	−	1.81057i	0.0573331	−	0.0703168i
$664$	−1.09935	−	1.90413i	−0.0426630	−	0.0738945i
$665$		0			0
$666$	13.8509	−	12.3041i	0.536712	−	0.476775i
$667$	3.95084	+	6.84306i	0.152977	+	0.264964i
$668$	−16.2971			−0.630553
$669$	21.8570	−	26.8068i	0.845042	−	1.03641i
$670$	−47.9878			−1.85393
$671$	−36.5505	+	63.3073i	−1.41102	+	2.44395i
$672$		0			0
$673$	−8.10894	−	14.0451i	−0.312577	−	0.541399i	0.666343	−	0.745646i	$-0.267859\pi$
$673$	−8.10894	−	14.0451i	−0.312577	−	0.541399i	−0.978919	+	0.204247i	$0.934526\pi$
$674$	−10.8835	−	18.8508i	−0.419217	−	0.726106i
$675$	33.7899	+	17.6474i	1.30057	+	0.679250i
$676$	5.76199	−	9.98006i	0.221615	−	0.383849i
$677$	−10.2545	+	17.7613i	−0.394112	+	0.682623i	−0.992987	−	0.118220i	$-0.962281\pi$
$677$	−10.2545	+	17.7613i	−0.394112	+	0.682623i	0.598875	+	0.800842i	$0.295615\pi$
$678$	−15.9130	+	19.5167i	−0.611135	+	0.749532i
$679$		0			0
$680$	−3.71932	+	6.44205i	−0.142629	+	0.247041i
$681$	2.22291	+	5.84947i	0.0851822	+	0.224152i
$682$	1.98128			0.0758673
$683$	0.0561542	−	0.0972618i	0.00214868	−	0.00372162i	−0.864949	−	0.501860i	$-0.832649\pi$
$683$	0.0561542	−	0.0972618i	0.00214868	−	0.00372162i	0.867098	+	0.498138i	$0.165983\pi$
$684$	−1.30705	−	6.35869i	−0.0499762	−	0.243131i
$685$	−21.5902			−0.824918
$686$		0			0
$687$	8.43839	+	22.2052i	0.321945	+	0.847179i
$688$	−19.0262			−0.725368
$689$	4.67059	+	8.08970i	0.177935	+	0.308193i
$690$	−13.2037	−	2.13670i	−0.502657	−	0.0813427i
$691$	9.43351	−	16.3393i	0.358868	−	0.621577i	−0.628904	−	0.777483i	$-0.716496\pi$
$691$	9.43351	−	16.3393i	0.358868	−	0.621577i	0.987772	+	0.155906i	$0.0498296\pi$
$692$	17.3182			0.658340
$693$		0			0
$694$	−39.9480			−1.51640
$695$	1.54081	−	2.66876i	0.0584461	−	0.101232i
$696$	−11.9474	+	14.6530i	−0.452866	+	0.555422i
$697$	2.02650	+	3.51000i	0.0767590	+	0.132951i
$698$	−28.4665			−1.07747
$699$	27.6413	−	33.9010i	1.04549	−	1.28225i
$700$		0			0
$701$	−3.16006			−0.119354			−0.0596770	−	0.998218i	$-0.519007\pi$
$701$	−3.16006			−0.119354			−0.0596770	+	0.998218i	$0.519007\pi$
$702$	0.424968	+	10.0419i	0.0160394	+	0.379005i
$703$	−3.94398	+	6.83118i	−0.148750	+	0.257643i
$704$	−7.11984			−0.268339
$705$	−34.3549	−	5.55951i	−1.29388	−	0.209383i
$706$	21.1402	−	36.6159i	0.795622	−	1.37806i
$707$		0			0
$708$	18.9045	+	3.05923i	0.710475	+	0.114973i
$709$	10.7606	−	18.6378i	0.404121	−	0.699959i	−0.590097	−	0.807332i	$-0.700911\pi$
$709$	10.7606	−	18.6378i	0.404121	−	0.699959i	0.994219	+	0.107373i	$0.0342440\pi$
$710$	37.0087	−	64.1009i	1.38891	−	2.40567i
$711$	−5.56741	−	27.0850i	−0.208794	−	1.01577i
$712$	4.87385	+	8.44176i	0.182655	+	0.316368i
$713$	0.119956	+	0.207769i	0.00449237	+	0.00778102i
$714$		0			0
$715$	−11.9826	+	20.7545i	−0.448125	+	0.776175i
$716$	2.57898			0.0963812
$717$	15.3710	+	2.48742i	0.574041	+	0.0928945i
$718$	−35.3570			−1.31951
$719$	−9.41508	−	16.3074i	−0.351123	−	0.608163i	0.635323	−	0.772246i	$-0.280867\pi$
$719$	−9.41508	−	16.3074i	−0.351123	−	0.608163i	−0.986447	+	0.164083i	$0.947533\pi$
$720$	−10.6070	−	51.6021i	−0.395298	−	1.92310i
$721$		0			0
$722$	−12.2040	−	21.1379i	−0.454185	−	0.786671i
$723$	5.69582	+	14.9882i	0.211830	+	0.557419i
$724$	1.94957	+	3.37675i	0.0724551	+	0.125496i
$725$	−22.7618	−	39.4247i	−0.845354	−	1.46420i
$726$	−77.0396	−	12.4670i	−2.85921	−	0.462693i
$727$	19.5426	+	33.8489i	0.724797	+	1.25538i	0.959058	+	0.283211i	$0.0913996\pi$
$727$	19.5426	+	33.8489i	0.724797	+	1.25538i	−0.234261	+	0.972174i	$0.575267\pi$
$728$		0			0
$729$	15.4273	+	22.1585i	0.571381	+	0.820685i
$730$	−16.1153	−	27.9125i	−0.596454	−	1.03309i
$731$	−4.58167			−0.169459
$732$	7.24578	+	19.0669i	0.267812	+	0.704732i
$733$	−18.5985			−0.686951			−0.343475	−	0.939162i	$-0.611604\pi$
$733$	−18.5985			−0.686951			−0.343475	+	0.939162i	$0.611604\pi$
$734$	−19.2119	+	33.2759i	−0.709123	+	1.22824i
$735$		0			0
$736$	3.25621	+	5.63993i	0.120026	+	0.207890i
$737$	−24.0977	−	41.7385i	−0.887651	−	1.53746i
$738$	−16.5474	−	5.49960i	−0.609118	−	0.202443i
$739$	−2.75068	+	4.76432i	−0.101185	+	0.175258i	−0.912173	−	0.409805i	$-0.865597\pi$
$739$	−2.75068	+	4.76432i	−0.101185	+	0.175258i	0.810988	+	0.585063i	$0.198930\pi$
$740$	6.16306	−	10.6747i	0.226559	−	0.392411i
$741$	−1.52014	−	4.00016i	−0.0558436	−	0.146949i
$742$		0			0
$743$	10.2326	−	17.7234i	0.375399	−	0.650210i	−0.614988	−	0.788537i	$-0.710839\pi$
$743$	10.2326	−	17.7234i	0.375399	−	0.650210i	0.990387	+	0.138327i	$0.0441725\pi$
$744$	−0.362748	+	0.444896i	−0.0132990	+	0.0163107i
$745$	−20.2855			−0.743201
$746$	−28.0892	+	48.6520i	−1.02842	+	1.78128i
$747$	3.55832	+	1.18262i	0.130192	+	0.0432700i
$748$	7.19489			0.263071
$749$		0			0
$750$	24.2253	+	3.92027i	0.884583	+	0.143148i
$751$	38.0460			1.38832			0.694159	−	0.719822i	$-0.255777\pi$
$751$	38.0460			1.38832			0.694159	+	0.719822i	$0.255777\pi$
$752$	14.3007	+	24.7696i	0.521494	+	0.903254i
$753$	12.7067	+	33.4369i	0.463057	+	1.21851i
$754$	6.00135	−	10.3946i	0.218556	−	0.378551i
$755$	7.11744			0.259030
$756$		0			0
$757$	−51.0780			−1.85646			−0.928230	−	0.372006i	$-0.878670\pi$
$757$	−51.0780			−1.85646			−0.928230	+	0.372006i	$0.878670\pi$
$758$	1.33329	−	2.30933i	0.0484273	−	0.0838786i
$759$	−4.77198	−	12.5572i	−0.173212	−	0.455798i
$760$	6.81295	+	11.8004i	0.247132	+	0.428045i
$761$	40.0749			1.45271			0.726357	−	0.687317i	$-0.241212\pi$
$761$	40.0749			1.45271			0.726357	+	0.687317i	$0.241212\pi$
$762$	29.2985	+	4.74124i	1.06137	+	0.171757i
$763$		0			0
$764$	−17.8633			−0.646273
$765$	−2.55424	−	12.4262i	−0.0923489	−	0.449270i
$766$	−27.3058	+	47.2951i	−0.986599	+	1.70884i
$767$	12.6239			0.455822
$768$	−20.5854	+	25.2472i	−0.742812	+	0.911029i
$769$	−22.4828	+	38.9414i	−0.810751	+	1.40426i	0.101587	+	0.994827i	$0.467608\pi$
$769$	−22.4828	+	38.9414i	−0.810751	+	1.40426i	−0.912339	+	0.409436i	$0.865726\pi$
$770$		0			0
$771$	−1.50485	−	3.95993i	−0.0541958	−	0.142613i
$772$	0.0992886	−	0.171973i	0.00357348	−	0.00618944i
$773$	−12.1781	+	21.0930i	−0.438014	+	0.758663i	−0.997536	−	0.0701524i	$-0.977651\pi$
$773$	−12.1781	+	21.0930i	−0.438014	+	0.758663i	0.559522	+	0.828816i	$0.310985\pi$
$774$	14.7370	−	13.0913i	0.529710	−	0.470556i
$775$	−0.691096	−	1.19701i	−0.0248249	−	0.0429980i
$776$	−14.4998	−	25.1145i	−0.520514	−	0.901556i
$777$		0			0
$778$	−4.52913	+	7.84468i	−0.162377	+	0.281245i
$779$	7.42416			0.265998
$780$	2.37544	+	6.25084i	0.0850545	+	0.223816i
$781$	74.3377			2.66001
$782$	1.32354	+	2.29243i	0.0473296	+	0.0819773i
$783$	−1.36331	−	32.2145i	−0.0487207	−	1.15125i
$784$		0			0
$785$	5.35200	+	9.26993i	0.191021	+	0.330858i
$786$	−45.0109	−	7.28391i	−1.60549	−	0.259809i
$787$	20.7617	+	35.9603i	0.740073	+	1.28184i	0.952461	+	0.304659i	$0.0985426\pi$
$787$	20.7617	+	35.9603i	0.740073	+	1.28184i	−0.212388	+	0.977185i	$0.568124\pi$
$788$	0.800331	+	1.38621i	0.0285106	+	0.0493818i
$789$	15.1130	+	39.7691i	0.538038	+	1.41582i
$790$	−27.9481	−	48.4075i	−0.994349	−	1.72226i
$791$		0			0
$792$	24.0300	−	21.3465i	0.853869	−	0.758515i
$793$	6.72289	+	11.6444i	0.238737	+	0.413504i
$794$	0.0477147			0.00169333
$795$	50.0744	+	8.10333i	1.77596	+	0.287395i
$796$	−6.17372			−0.218822
$797$	17.3018	−	29.9676i	0.612861	−	1.06151i	−0.377895	−	0.925848i	$-0.623352\pi$
$797$	17.3018	−	29.9676i	0.612861	−	1.06151i	0.990756	−	0.135657i	$-0.0433146\pi$
$798$		0			0
$799$	3.44373	+	5.96472i	0.121831	+	0.211017i
$800$	−18.7599	−	32.4931i	−0.663263	−	1.14880i
$801$	−15.7755	−	5.24305i	−0.557399	−	0.185254i
$802$	10.4785	−	18.1494i	0.370010	−	0.640876i
$803$	16.1851	−	28.0333i	0.571158	−	0.989275i
$804$	−13.2752	−	2.14827i	−0.468180	−	0.0757635i
$805$		0			0
$806$	0.182213	−	0.315603i	0.00641819	−	0.0111166i
$807$	50.5595	+	8.18182i	1.77978	+	0.288014i
$808$	22.8047			0.802266
$809$	5.62597	−	9.74446i	0.197799	−	0.342597i	−0.750016	−	0.661420i	$-0.769954\pi$
$809$	5.62597	−	9.74446i	0.197799	−	0.342597i	0.947814	+	0.318823i	$0.103287\pi$
$810$	43.7213	+	32.6707i	1.53621	+	1.14793i
$811$	29.6803			1.04222			0.521108	−	0.853491i	$-0.325519\pi$
$811$	29.6803			1.04222			0.521108	+	0.853491i	$0.325519\pi$
$812$		0			0
$813$	−27.1349	+	33.2799i	−0.951664	+	1.16718i
$814$	37.6132			1.31834
$815$	−9.46376	−	16.3917i	−0.331501	−	0.574177i
$816$	−6.58833	+	8.08033i	−0.230638	+	0.282868i
$817$	−4.19629	+	7.26819i	−0.146810	+	0.254282i
$818$	54.1211			1.89230
$819$		0			0
$820$	−11.6014			−0.405137
$821$	−17.3215	+	30.0018i	−0.604526	+	1.04707i	0.387600	+	0.921828i	$0.373304\pi$
$821$	−17.3215	+	30.0018i	−0.604526	+	1.04707i	−0.992126	+	0.125242i	$0.960029\pi$
$822$	−18.1470	−	2.93665i	−0.632949	−	0.102427i
$823$	−18.1935	−	31.5121i	−0.634186	−	1.09844i	−0.986687	−	0.162631i	$-0.948002\pi$
$823$	−18.1935	−	31.5121i	−0.634186	−	1.09844i	0.352501	−	0.935811i	$-0.385331\pi$
$824$	−4.75276			−0.165570
$825$	27.4927	+	72.3454i	0.957171	+	2.51874i
$826$		0			0
$827$	−24.3576			−0.846997			−0.423498	−	0.905897i	$-0.639198\pi$
$827$	−24.3576			−0.846997			−0.423498	+	0.905897i	$0.639198\pi$
$828$	−3.55698	−	1.18218i	−0.123614	−	0.0410836i
$829$	19.5851	−	33.9224i	0.680219	−	1.17817i	−0.294694	−	0.955592i	$-0.595218\pi$
$829$	19.5851	−	33.9224i	0.680219	−	1.17817i	0.974914	−	0.222583i	$-0.0714488\pi$
$830$	7.57989			0.263102
$831$	−1.15581	−	3.04144i	−0.0400945	−	0.105506i
$832$	−0.654792	+	1.13413i	−0.0227008	+	0.0393190i
$833$		0			0
$834$	1.65808	−	2.03357i	0.0574146	−	0.0704167i
$835$	−29.1690	+	50.5223i	−1.00944	+	1.74839i
$836$	6.58970	−	11.4137i	0.227910	−	0.394751i
$837$	−0.0413928	−	0.978099i	−0.00143075	−	0.0338080i
$838$	12.8515	+	22.2594i	0.443947	+	0.768939i
$839$	17.1739	+	29.7460i	0.592907	+	1.02695i	0.993839	+	0.110838i	$0.0353534\pi$
$839$	17.1739	+	29.7460i	0.592907	+	1.02695i	−0.400931	+	0.916108i	$0.631313\pi$
$840$		0			0
$841$	−4.75250	+	8.23157i	−0.163879	+	0.283847i
$842$	−15.6850			−0.540541
$843$	13.2211	−	16.2151i	0.455358	−	0.558479i
$844$	−15.9809			−0.550085
$845$	−20.6260	−	35.7253i	−0.709556	−	1.22899i
$846$	−28.1199	−	9.34577i	−0.966781	−	0.321314i
$847$		0			0
$848$	−20.8442	−	36.1032i	−0.715793	−	1.23979i
$849$	−30.6159	+	37.5492i	−1.05074	+	1.28869i
$850$	−7.62525	−	13.2073i	−0.261544	−	0.453007i
$851$	2.27727	+	3.94434i	0.0780637	+	0.135210i
$852$	13.1076	−	16.0759i	0.449058	−	0.550752i
$853$	16.3371	+	28.2967i	0.559373	+	0.968862i	0.997549	+	0.0699730i	$0.0222913\pi$
$853$	16.3371	+	28.2967i	0.559373	+	0.968862i	−0.438176	+	0.898889i	$0.644375\pi$
$854$		0			0
$855$	−22.0518	−	7.32904i	−0.754157	−	0.250648i
$856$	0.156982	+	0.271901i	0.00536555	+	0.00929340i
$857$	57.6679			1.96990			0.984950	−	0.172841i	$-0.0552945\pi$
$857$	57.6679			1.96990			0.984950	+	0.172841i	$0.0552945\pi$
$858$	−12.8946	+	15.8148i	−0.440216	+	0.539907i
$859$	−29.9768			−1.02279			−0.511397	−	0.859344i	$-0.670872\pi$
$859$	−29.9768			−1.02279			−0.511397	+	0.859344i	$0.670872\pi$
$860$	6.55733	−	11.3576i	0.223603	−	0.387292i
$861$		0			0
$862$	−14.3615	−	24.8749i	−0.489156	−	0.847243i
$863$	11.5888	+	20.0724i	0.394487	+	0.683272i	0.993036	−	0.117815i	$-0.0375889\pi$
$863$	11.5888	+	20.0724i	0.394487	+	0.683272i	−0.598548	+	0.801087i	$0.704256\pi$
$864$	−1.12361	−	26.5506i	−0.0382261	−	0.903271i
$865$	30.9967	−	53.6879i	1.05392	−	1.82544i
$866$	−17.0437	+	29.5205i	−0.579167	+	1.00315i
$867$	17.0204	−	20.8748i	0.578043	−	0.708947i
$868$		0			0
$869$	28.0690	−	48.6170i	0.952177	−	1.64922i
$870$	−23.1537	−	60.9277i	−0.784985	−	2.06564i
$871$	−8.86480			−0.300372
$872$	−8.23129	+	14.2570i	−0.278747	+	0.482803i
$873$	46.9324	+	15.5982i	1.58842	+	0.527919i
$874$	4.84884			0.164014
$875$		0			0
$876$	−3.20853	−	8.44308i	−0.108406	−	0.285265i
$877$	−0.739956			−0.0249865			−0.0124933	−	0.999922i	$-0.503977\pi$
$877$	−0.739956			−0.0249865			−0.0124933	+	0.999922i	$0.503977\pi$
$878$	5.81448	+	10.0710i	0.196229	+	0.339879i
$879$	−15.0861	−	2.44131i	−0.508841	−	0.0823435i
$880$	53.4768	−	92.6245i	1.80270	−	3.12237i
$881$	18.0285			0.607395			0.303697	−	0.952769i	$-0.401779\pi$
$881$	18.0285			0.607395			0.303697	+	0.952769i	$0.401779\pi$
$882$		0			0
$883$	43.0928			1.45019			0.725095	−	0.688649i	$-0.241796\pi$
$883$	43.0928			1.45019			0.725095	+	0.688649i	$0.241796\pi$
$884$	0.661694	−	1.14609i	0.0222552	−	0.0385471i
$885$	43.3198	−	53.1300i	1.45618	−	1.78594i
$886$	24.7254	+	42.8256i	0.830664	+	1.43875i
$887$	30.9527			1.03929			0.519645	−	0.854382i	$-0.326064\pi$
$887$	30.9527			1.03929			0.519645	+	0.854382i	$0.326064\pi$
$888$	−6.88650	+	8.44602i	−0.231096	+	0.283430i
$889$		0			0
$890$	−33.6047			−1.12643
$891$	−6.46090	+	54.4337i	−0.216448	+	1.82360i
$892$	9.79685	−	16.9686i	0.328023	−	0.568152i
$893$	12.6163			0.422187
$894$	−17.0504	−	2.75918i	−0.570249	−	0.0922809i
$895$	4.61595	−	7.99506i	0.154294	−	0.267245i
$896$		0			0
$897$	−2.43913	−	0.394713i	−0.0814401	−	0.0131791i
$898$	−5.75714	+	9.97165i	−0.192118	+	0.332758i
$899$	−0.584545	+	1.01246i	−0.0194957	+	0.0337675i
$900$	20.4927	+	6.81085i	0.683090	+	0.227028i
$901$	−5.01945	−	8.69395i	−0.167222	−	0.289637i
$902$	−17.7008	−	30.6587i	−0.589372	−	1.02082i
$903$		0			0
$904$	7.40614	−	12.8278i	0.246324	−	0.426646i
$905$	13.9576			0.463966
$906$	5.98236	+	0.968099i	0.198751	+	0.0321629i
$907$	−42.8083			−1.42143			−0.710714	−	0.703481i	$-0.751628\pi$
$907$	−42.8083			−1.42143			−0.710714	+	0.703481i	$0.751628\pi$
$908$	1.77243	+	3.06993i	0.0588200	+	0.101879i
$909$	−29.0760	+	25.8290i	−0.964391	+	0.856694i
$910$		0			0
$911$	3.04869	+	5.28049i	0.101008	+	0.174950i	0.912100	−	0.409968i	$-0.134460\pi$
$911$	3.04869	+	5.28049i	0.101008	+	0.174950i	−0.811092	+	0.584918i	$0.801127\pi$
$912$	6.78416	+	17.8521i	0.224646	+	0.591143i
$913$	3.80635	+	6.59278i	0.125972	+	0.218189i
$914$	−24.7400	−	42.8509i	−0.818327	−	1.41738i
$915$	72.0776	+	11.6640i	2.38281	+	0.385600i
$916$	6.72830	+	11.6538i	0.222309	+	0.385051i
$917$		0			0
$918$	−0.456710	−	10.7919i	−0.0150737	−	0.356186i
$919$	−12.4307	−	21.5305i	−0.410050	−	0.710227i	0.584845	−	0.811145i	$-0.301155\pi$
$919$	−12.4307	−	21.5305i	−0.410050	−	0.710227i	−0.994895	+	0.100918i	$0.967822\pi$
$920$	7.86764			0.259388
$921$	0.649321	+	1.70865i	0.0213959	+	0.0563020i
$922$	34.5621			1.13824
$923$	6.83664	−	11.8414i	0.225031	−	0.389764i
$924$		0			0
$925$	−13.1199	−	22.7244i	−0.431381	−	0.747174i
$926$	8.56034	+	14.8269i	0.281310	+	0.487244i
$927$	6.05978	−	5.38306i	0.199029	−	0.176803i
$928$	−15.8676	+	27.4834i	−0.520878	+	0.902188i
$929$	−20.9201	+	36.2347i	−0.686366	+	1.18882i	0.286639	+	0.958039i	$0.407462\pi$
$929$	−20.9201	+	36.2347i	−0.686366	+	1.18882i	−0.973005	+	0.230783i	$0.925871\pi$
$930$	−0.702994	−	1.84989i	−0.0230521	−	0.0606603i
$931$		0			0
$932$	12.3895	−	21.4592i	0.405831	−	0.702920i
$933$	3.36255	−	4.12403i	0.110085	−	0.135015i
$934$	−27.7651			−0.908502
$935$	12.8776	−	22.3047i	0.421144	−	0.729443i
$936$	−1.19035	−	5.79097i	−0.0389078	−	0.189284i
$937$	29.2537			0.955676			0.477838	−	0.878448i	$-0.341421\pi$
$937$	29.2537			0.955676			0.477838	+	0.878448i	$0.341421\pi$
$938$		0			0
$939$	−48.1517	−	7.79218i	−1.57137	−	0.254288i
$940$	−19.7148			−0.643026
$941$	−1.67869	−	2.90757i	−0.0547236	−	0.0947841i	0.837366	−	0.546643i	$-0.184094\pi$
$941$	−1.67869	−	2.90757i	−0.0547236	−	0.0947841i	−0.892090	+	0.451859i	$0.850761\pi$
$942$	3.23759	+	8.51954i	0.105486	+	0.277582i
$943$	2.14337	−	3.71242i	0.0697976	−	0.120893i
$944$	−56.3387			−1.83367
$945$		0			0
$946$	40.0194			1.30114
$947$	−2.63300	+	4.56050i	−0.0855612	+	0.148196i	−0.905630	−	0.424068i	$-0.860602\pi$
$947$	−2.63300	+	4.56050i	−0.0855612	+	0.148196i	0.820069	+	0.572265i	$0.193935\pi$
$948$	−5.56442	−	14.6425i	−0.180724	−	0.475565i
$949$	−2.97699	−	5.15630i	−0.0966372	−	0.167381i
$950$	−27.9354			−0.906345
$951$	21.9650	+	3.55450i	0.712264	+	0.115263i
$952$		0			0
$953$	56.2520			1.82218			0.911090	−	0.412208i	$-0.135242\pi$
$953$	56.2520			1.82218			0.911090	+	0.412208i	$0.135242\pi$
$954$	40.9864	+	13.6220i	1.32698	+	0.441030i
$955$	−31.9724	+	55.3778i	−1.03460	+	1.79198i
$956$	8.82075			0.285284
$957$	41.3663	−	50.7342i	1.33718	−	1.64000i
$958$	−7.08131	+	12.2652i	−0.228787	+	0.396270i
$959$		0			0
$960$	2.52624	+	6.64767i	0.0815341	+	0.214553i
$961$	15.4823	−	26.8160i	0.499427	−	0.865034i
$962$	3.45918	−	5.99148i	0.111528	−	0.193173i
$963$	−0.508113	−	0.168874i	−0.0163737	−	0.00544188i
$964$	4.54153	+	7.86616i	0.146273	+	0.253352i
$965$	−0.355420	−	0.615606i	−0.0114414	−	0.0198171i
$966$		0			0
$967$	−6.88641	+	11.9276i	−0.221452	+	0.383566i	−0.955249	−	0.295803i	$-0.904413\pi$
$967$	−6.88641	+	11.9276i	−0.221452	+	0.383566i	0.733797	+	0.679369i	$0.237746\pi$
$968$	45.9052			1.47545
$969$	1.63368	+	4.29894i	0.0524814	+	0.138102i
$970$	99.9748			3.21000
$971$	25.6627	+	44.4491i	0.823555	+	1.42644i	0.903019	+	0.429602i	$0.141346\pi$
$971$	25.6627	+	44.4491i	0.823555	+	1.42644i	−0.0794635	+	0.996838i	$0.525321\pi$
$972$	10.6324	+	10.9952i	0.341033	+	0.352671i
$973$		0			0
$974$	2.36269	+	4.09230i	0.0757055	+	0.131126i
$975$	14.0525	+	2.27405i	0.450039	+	0.0728278i
$976$	−30.0033	−	51.9673i	−0.960383	−	1.66343i
$977$	−8.84252	−	15.3157i	−0.282897	−	0.489992i	0.689200	−	0.724571i	$-0.257962\pi$
$977$	−8.84252	−	15.3157i	−0.282897	−	0.489992i	−0.972097	+	0.234579i	$0.924629\pi$
$978$	−5.72492	−	15.0648i	−0.183063	−	0.481720i
$979$	−16.8751	−	29.2285i	−0.539329	−	0.934146i
$980$		0			0
$981$	−5.65284	−	27.5006i	−0.180481	−	0.878027i
$982$	−17.0154	−	29.4716i	−0.542984	−	0.940476i
$983$	−16.0041			−0.510453			−0.255226	−	0.966881i	$-0.582150\pi$
$983$	−16.0041			−0.510453			−0.255226	+	0.966881i	$0.582150\pi$
$984$	10.1252	+	1.63851i	0.322779	+	0.0522339i
$985$	5.72984			0.182568
$986$	−6.44961	+	11.1711i	−0.205397	+	0.355759i
$987$		0			0
$988$	−1.21207	−	2.09937i	−0.0385612	−	0.0667899i
$989$	2.42295	+	4.19667i	0.0770454	+	0.133446i
$990$	22.3105	+	108.539i	0.709074	+	3.44959i
$991$	5.43319	−	9.41055i	0.172591	−	0.298936i	−0.766734	−	0.641965i	$-0.778120\pi$
$991$	5.43319	−	9.41055i	0.172591	−	0.298936i	0.939325	+	0.343029i	$0.111453\pi$
$992$	−0.481771	+	0.834453i	−0.0152963	+	0.0264939i
$993$	−36.8567	−	5.96435i	−1.16961	−	0.189273i
$994$		0			0
$995$	−11.0499	+	19.1390i	−0.350306	+	0.606748i
$996$	2.09688	+	0.339329i	0.0664421	+	0.0107520i
$997$	41.0375			1.29967			0.649835	−	0.760075i	$-0.274838\pi$
$997$	41.0375			1.29967			0.649835	+	0.760075i	$0.274838\pi$
$998$	−28.5719	+	49.4880i	−0.904428	+	1.56652i
$999$	−0.785812	−	18.5685i	−0.0248620	−	0.587480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.h.67.9		24
3.2	odd	2		1323.2.g.h.361.4		24
7.2	even	3		441.2.h.h.373.4		24
7.3	odd	6		441.2.f.h.148.10	yes	24
7.4	even	3		441.2.f.h.148.9	✓	24
7.5	odd	6		441.2.h.h.373.3		24
7.6	odd	2	inner	441.2.g.h.67.10		24
9.2	odd	6		1323.2.h.h.802.10		24
9.7	even	3		441.2.h.h.214.4		24
21.2	odd	6		1323.2.h.h.226.10		24
21.5	even	6		1323.2.h.h.226.9		24
21.11	odd	6		1323.2.f.h.442.3		24
21.17	even	6		1323.2.f.h.442.4		24
21.20	even	2		1323.2.g.h.361.3		24
63.2	odd	6		1323.2.g.h.667.4		24
63.4	even	3		3969.2.a.bh.1.3		12
63.11	odd	6		1323.2.f.h.883.3		24
63.16	even	3	inner	441.2.g.h.79.9		24
63.20	even	6		1323.2.h.h.802.9		24
63.25	even	3		441.2.f.h.295.9	yes	24
63.31	odd	6		3969.2.a.bh.1.4		12
63.32	odd	6		3969.2.a.bi.1.10		12
63.34	odd	6		441.2.h.h.214.3		24
63.38	even	6		1323.2.f.h.883.4		24
63.47	even	6		1323.2.g.h.667.3		24
63.52	odd	6		441.2.f.h.295.10	yes	24
63.59	even	6		3969.2.a.bi.1.9		12
63.61	odd	6	inner	441.2.g.h.79.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.9	✓	24	7.4	even	3
441.2.f.h.148.10	yes	24	7.3	odd	6
441.2.f.h.295.9	yes	24	63.25	even	3
441.2.f.h.295.10	yes	24	63.52	odd	6
441.2.g.h.67.9		24	1.1	even	1	trivial
441.2.g.h.67.10		24	7.6	odd	2	inner
441.2.g.h.79.9		24	63.16	even	3	inner
441.2.g.h.79.10		24	63.61	odd	6	inner
441.2.h.h.214.3		24	63.34	odd	6
441.2.h.h.214.4		24	9.7	even	3
441.2.h.h.373.3		24	7.5	odd	6
441.2.h.h.373.4		24	7.2	even	3
1323.2.f.h.442.3		24	21.11	odd	6
1323.2.f.h.442.4		24	21.17	even	6
1323.2.f.h.883.3		24	63.11	odd	6
1323.2.f.h.883.4		24	63.38	even	6
1323.2.g.h.361.3		24	21.20	even	2
1323.2.g.h.361.4		24	3.2	odd	2
1323.2.g.h.667.3		24	63.47	even	6
1323.2.g.h.667.4		24	63.2	odd	6
1323.2.h.h.226.9		24	21.5	even	6
1323.2.h.h.226.10		24	21.2	odd	6
1323.2.h.h.802.9		24	63.20	even	6
1323.2.h.h.802.10		24	9.2	odd	6
3969.2.a.bh.1.3		12	63.4	even	3
3969.2.a.bh.1.4		12	63.31	odd	6
3969.2.a.bi.1.9		12	63.59	even	6
3969.2.a.bi.1.10		12	63.32	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.863305 - 1.49529i) q^{2} +(-0.615283 - 1.61908i) q^{3} +(-0.490592 - 0.849731i) q^{4} -3.51231 q^{5} +(-2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(-2.24285 + 1.99239i) q^{9} +O(q^{10})\)	\(q+(0.863305 - 1.49529i) q^{2} +(-0.615283 - 1.61908i) q^{3} +(-0.490592 - 0.849731i) q^{4} -3.51231 q^{5} +(-2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(-2.24285 + 1.99239i) q^{9} +(-3.03220 + 5.25192i) q^{10} -6.09064 q^{11} +(-1.07393 + 1.31713i) q^{12} +(-0.560139 + 0.970190i) q^{13} +(2.16106 + 5.68672i) q^{15} +(2.49982 - 4.32982i) q^{16} +(0.601978 - 1.04266i) q^{17} +(1.04293 + 5.07375i) q^{18} +(-1.10269 - 1.90991i) q^{19} +(1.72311 + 2.98452i) q^{20} +(-5.25808 + 9.10727i) q^{22} -1.27339 q^{23} +(-1.08234 - 2.84812i) q^{24} +7.33633 q^{25} +(0.967143 + 1.67514i) q^{26} +(4.60583 + 2.40548i) q^{27} +(-3.10262 - 5.37390i) q^{29} +(10.3689 + 1.67796i) q^{30} +(-0.0942019 - 0.163162i) q^{31} +(-2.55712 - 4.42907i) q^{32} +(3.74747 + 9.86125i) q^{33} +(-1.03938 - 1.80026i) q^{34} +(2.79332 + 0.928373i) q^{36} +(-1.78835 - 3.09752i) q^{37} -3.80782 q^{38} +(1.91546 + 0.309971i) q^{39} -6.17850 q^{40} +(-1.68320 + 2.91538i) q^{41} +(-1.90276 - 3.29567i) q^{43} +(2.98802 + 5.17540i) q^{44} +(7.87760 - 6.99788i) q^{45} +(-1.09932 + 1.90408i) q^{46} +(-2.86035 + 4.95427i) q^{47} +(-8.54843 - 1.38336i) q^{48} +(6.33349 - 10.9699i) q^{50} +(-2.05853 - 0.333123i) q^{51} +1.09920 q^{52} +(4.16913 - 7.22115i) q^{53} +(7.57313 - 4.81037i) q^{54} +21.3922 q^{55} +(-2.41384 + 2.96047i) q^{57} -10.7140 q^{58} +(-5.63427 - 9.75883i) q^{59} +(3.77198 - 4.62618i) q^{60} +(6.00109 - 10.3942i) q^{61} -0.325300 q^{62} +1.16898 q^{64} +(1.96738 - 3.40761i) q^{65} +(17.9806 + 2.90972i) q^{66} +(3.95652 + 6.85289i) q^{67} -1.18130 q^{68} +(0.783494 + 2.06172i) q^{69} -12.2052 q^{71} +(-3.94540 + 3.50480i) q^{72} +(-2.65737 + 4.60269i) q^{73} -6.17557 q^{74} +(-4.51392 - 11.8781i) q^{75} +(-1.08194 + 1.87397i) q^{76} +(2.11712 - 2.59657i) q^{78} +(-4.60855 + 7.98225i) q^{79} +(-8.78016 + 15.2077i) q^{80} +(1.06079 - 8.93727i) q^{81} +(2.90623 + 5.03373i) q^{82} +(-0.624950 - 1.08245i) q^{83} +(-2.11433 + 3.66213i) q^{85} -6.57064 q^{86} +(-6.79179 + 8.32986i) q^{87} -10.7140 q^{88} +(2.77066 + 4.79892i) q^{89} +(-3.66308 - 17.8206i) q^{90} +(0.624715 + 1.08204i) q^{92} +(-0.206213 + 0.252912i) q^{93} +(4.93871 + 8.55409i) q^{94} +(3.87298 + 6.70820i) q^{95} +(-5.59767 + 6.86532i) q^{96} +(-8.24277 - 14.2769i) q^{97} +(13.6604 - 12.1349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} - 8 q^{51} + 32 q^{53} - 12 q^{57} + 56 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} - 168 q^{72} - 136 q^{74} - 60 q^{78} + 12 q^{79} - 40 q^{81} + 12 q^{85} - 152 q^{86} + 16 q^{92} + 112 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Introduction

L-functions

Modular forms

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