LMFDB - Embedded newform 441.2.g.h.67.10

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			67.10
Character	$\chi$	$=$	441.67
Dual form			441.2.g.h.79.10

$q$-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	$-0.212469\pi$
$5$	3.51231			1.57075			0.785377	+	0.619018i	$0.212469\pi$
$6$	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	−0.777833	−	0.628471i	$-0.783681\pi$
$13$	0.560139	−	0.970190i	0.155355	−	0.269082i	0.933188	+	0.359388i	$0.117015\pi$
$14$		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	−0.929746	−	0.368202i	$-0.879974\pi$
$17$	−0.601978	+	1.04266i	−0.146001	+	0.252881i	0.783745	+	0.621083i	$0.213307\pi$
$18$	1.04293	+	5.07375i	0.245820	+	1.19589i
$19$	1.10269	+	1.90991i	0.252974	+	0.438163i	0.964343	−	0.264655i	$-0.0852581\pi$
$19$	1.10269	+	1.90991i	0.252974	+	0.438163i	−0.711370	+	0.702818i	$0.751925\pi$
$20$	−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	0.874361	−	0.485276i	$-0.161281\pi$
$31$	0.0942019	+	0.163162i	0.0169192	+	0.0293048i	−0.857442	+	0.514581i	$0.827948\pi$
$32$	−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	−0.704132	−	0.710069i	$-0.748664\pi$
$41$	1.68320	−	2.91538i	0.262871	−	0.455307i	0.967004	+	0.254762i	$0.0819972\pi$
$42$		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	−0.578434	−	0.815729i	$-0.696336\pi$
$47$	2.86035	−	4.95427i	0.417225	−	0.722654i	0.995659	+	0.0930746i	$0.0296695\pi$
$48$	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	$0.0954567\pi$
$59$	5.63427	+	9.75883i	0.733519	+	1.27049i	−0.221851	+	0.975081i	$0.571210\pi$
$60$	3.77198	−	4.62618i	0.486960	−	0.597238i
$61$	−6.00109	+	10.3942i	−0.768361	+	1.33084i	0.170091	+	0.985428i	$0.445594\pi$
$61$	−6.00109	+	10.3942i	−0.768361	+	1.33084i	−0.938451	+	0.345411i	$0.887739\pi$
$62$	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	−0.667563	−	0.744554i	$-0.732662\pi$
$73$	2.65737	−	4.60269i	0.311021	−	0.538704i	0.978584	+	0.205849i	$0.0659957\pi$
$74$	−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	0.898284	−	0.439415i	$-0.144814\pi$
$83$	0.624950	+	1.08245i	0.0685972	+	0.118814i	−0.829687	+	0.558229i	$0.811481\pi$
$84$		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	0.680990	−	0.732293i	$-0.261550\pi$
$89$	−2.77066	−	4.79892i	−0.293689	−	0.508684i	−0.974679	+	0.223608i	$0.928216\pi$
$90$	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	$0.148983\pi$
$97$	8.24277	+	14.2769i	0.836926	+	1.44960i	−0.0555261	+	0.998457i	$0.517684\pi$
$98$		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	$-0.723132\pi$
$101$	−12.9638			−1.28995			−0.644975	+	0.764203i	$0.723132\pi$
$102$	−2.27526	+	2.79051i	−0.225284	+	0.276302i
$103$	2.70182			0.266218			0.133109	−	0.991101i	$-0.457504\pi$
$103$	2.70182			0.266218			0.133109	+	0.991101i	$0.457504\pi$
$104$	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	$-0.732019\pi$
$131$	−15.2467			−1.33211			−0.666055	+	0.745902i	$0.732019\pi$
$132$	−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	−0.846821	−	0.531878i	$-0.821487\pi$
$139$	0.438687	−	0.759829i	0.0372090	−	0.0644478i	0.884030	+	0.467430i	$0.154820\pi$
$140$		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	0.920403	−	0.390971i	$-0.127861\pi$
$157$	1.52378	+	2.63927i	0.121611	+	0.210636i	−0.798792	+	0.601607i	$0.794527\pi$
$158$	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	$0.388829\pi$
$167$	−8.30480	+	14.3843i	−0.642645	+	1.11309i	−0.984840	+	0.173464i	$0.944504\pi$
$168$		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	$-0.599214\pi$
$173$	8.82516	−	15.2856i	0.670965	−	1.16214i	0.977631	−	0.210328i	$-0.0674531\pi$
$174$	−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	$-0.452816\pi$
$181$	3.97391			0.295378			0.147689	+	0.989034i	$0.452816\pi$
$182$		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	−0.955723	−	0.294268i	$-0.904924\pi$
$199$	−3.14605	+	5.44912i	−0.223018	+	0.386278i	0.732705	+	0.680546i	$0.238257\pi$
$200$	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	$-0.933549\pi$
$223$	−9.98472	−	17.2940i	−0.668626	−	1.15809i	0.309662	−	0.950847i	$-0.399784\pi$
$224$		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	$-0.461744\pi$
$227$	3.61283			0.239792			0.119896	+	0.992786i	$0.461744\pi$
$228$	3.69981	+	0.598725i	0.245026	+	0.0396515i
$229$	13.7147			0.906290			0.453145	−	0.891437i	$-0.350302\pi$
$229$	13.7147			0.906290			0.453145	+	0.891437i	$0.350302\pi$
$230$	−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	$-0.403629\pi$
$241$	9.25724			0.596311			0.298156	+	0.954517i	$0.403629\pi$
$242$	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	$-0.274030\pi$
$251$	20.6517			1.30353			0.651763	+	0.758422i	$0.274030\pi$
$252$		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	$-0.524305\pi$
$257$	−2.44579			−0.152564			−0.0762819	+	0.997086i	$0.524305\pi$
$258$	−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	$-0.475825\pi$
$269$	14.7851	−	25.6086i	0.901466	−	1.56139i	0.825592	−	0.564268i	$-0.190842\pi$
$270$	−26.5992	+	16.8955i	−1.61877	+	1.02823i
$271$	12.3958	+	21.4701i	0.752989	+	1.30421i	0.946368	+	0.323090i	$0.104722\pi$
$271$	12.3958	+	21.4701i	0.752989	+	1.30421i	−0.193380	+	0.981124i	$0.561945\pi$
$272$	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	$0.145781\pi$
$283$	13.9859	+	24.2244i	0.831378	+	1.43999i	−0.0655680	+	0.997848i	$0.520886\pi$
$284$	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	−0.965634	−	0.259908i	$-0.916308\pi$
$293$	−4.41163	+	7.64117i	−0.257730	+	0.446402i	0.707903	+	0.706309i	$0.249641\pi$
$294$		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	$-0.490413\pi$
$307$	1.05532			0.0602304			0.0301152	+	0.999546i	$0.490413\pi$
$308$		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	0.819182	−	0.573533i	$-0.194428\pi$
$311$	−1.53608	−	2.66056i	−0.0871029	−	0.150867i	−0.906285	+	0.422666i	$0.861094\pi$
$312$	3.36948	+	0.545269i	0.190759	+	0.0308698i
$313$	−14.0810	+	24.3891i	−0.795907	+	1.37855i	0.126355	+	0.991985i	$0.459672\pi$
$313$	−14.0810	+	24.3891i	−0.795907	+	1.37855i	−0.922262	+	0.386566i	$0.873661\pi$
$314$	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	0.997783	−	0.0665448i	$-0.0211975\pi$
$349$	8.24346	+	14.2781i	0.441262	+	0.764289i	−0.556521	+	0.830833i	$0.687864\pi$
$350$		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	$-0.725931\pi$
$353$	−24.4875			−1.30334			−0.651669	+	0.758503i	$0.725931\pi$
$354$	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	$-0.302732\pi$
$367$	22.2539			1.16164			0.580821	+	0.814031i	$0.302732\pi$
$368$	−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	$-0.200500\pi$
$383$	31.6294			1.61619			0.808093	+	0.589055i	$0.200500\pi$
$384$	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	0.865678	−	0.500600i	$-0.166887\pi$
$397$	−0.0138175	−	0.0239325i	−0.000693478	−	0.00120114i	−0.866372	+	0.499399i	$0.833554\pi$
$398$	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	$-0.884435\pi$
$409$	−15.6726	−	27.1458i	−0.774963	−	1.34227i	0.159853	−	0.987141i	$-0.448898\pi$
$410$	−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	−0.624931	−	0.780680i	$-0.714873\pi$
$419$	7.44319	−	12.8920i	0.363623	−	0.629814i	0.988554	+	0.150866i	$0.0482061\pi$
$420$		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	$-0.342673\pi$
$433$	19.7423			0.948756			0.474378	+	0.880321i	$0.342673\pi$
$434$		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	−0.774404	−	0.632692i	$-0.781950\pi$
$439$	3.36757	−	5.83280i	0.160725	−	0.278384i	0.935129	+	0.354307i	$0.115283\pi$
$440$	−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	0.533103	−	0.846050i	$-0.321026\pi$
$461$	−10.0087	−	17.3355i	−0.466150	−	0.807395i	−0.999253	+	0.0386554i	$0.987693\pi$
$462$		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	0.989883	−	0.141888i	$-0.0453172\pi$
$467$	8.04035	+	13.9263i	0.372063	+	0.644432i	−0.617820	+	0.786320i	$0.711984\pi$
$468$	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	$-0.439997\pi$
$479$	8.20255			0.374784			0.187392	+	0.982285i	$0.439997\pi$
$480$	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	$-0.587577\pi$
$503$	−12.1860			−0.543346			−0.271673	+	0.962390i	$0.587577\pi$
$504$		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	$-0.597746\pi$
$509$	−13.6393			−0.604551			−0.302276	+	0.953221i	$0.597746\pi$
$510$	−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	$0.450794\pi$
$521$	−17.7745	+	30.7863i	−0.778714	+	1.34877i	−0.932683	+	0.360697i	$0.882539\pi$
$522$	24.0300	−	21.3465i	1.05177	−	0.934311i
$523$	13.3593	+	23.1391i	0.584163	+	1.01180i	0.994979	+	0.100082i	$0.0319105\pi$
$523$	13.3593	+	23.1391i	0.584163	+	1.01180i	−0.410816	+	0.911718i	$0.634756\pi$
$524$	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	0.828822	−	0.559512i	$-0.189012\pi$
$563$	−1.66428	−	2.88261i	−0.0701409	−	0.121488i	−0.898963	+	0.438025i	$0.855678\pi$
$564$	−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	−0.999383	−	0.0351177i	$-0.988819\pi$
$577$	−11.2725	+	19.5245i	−0.469279	+	0.812815i	0.530104	+	0.847932i	$0.322153\pi$
$578$	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	$-0.999913\pi$
$587$	−12.1198	−	20.9921i	−0.500237	−	0.866436i	0.499763	−	0.866162i	$-0.333421\pi$
$588$		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	$0.221586\pi$
$593$	22.8663	+	39.6056i	0.939007	+	1.62641i	0.171680	+	0.985153i	$0.445081\pi$
$594$	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	0.976272	−	0.216547i	$-0.0694794\pi$
$601$	7.36933	+	12.7641i	0.300601	+	0.520657i	−0.675671	+	0.737203i	$0.736146\pi$
$602$		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	$-0.539366\pi$
$607$	−6.07836			−0.246713			−0.123356	+	0.992362i	$0.539366\pi$
$608$	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	$-0.581170\pi$
$619$	−12.5518			−0.504498			−0.252249	+	0.967662i	$0.581170\pi$
$620$	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	−0.755367	−	0.655302i	$-0.772541\pi$
$643$	4.81347	−	8.33718i	0.189825	−	0.328786i	0.945192	+	0.326516i	$0.105875\pi$
$644$		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	−0.778972	−	0.627059i	$-0.784258\pi$
$647$	3.90607	−	6.76551i	0.153564	−	0.265980i	0.932535	+	0.361079i	$0.117592\pi$
$648$	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	$-0.986856\pi$
$661$	−13.7631	−	23.8384i	−0.535324	−	0.927208i	0.463824	−	0.885927i	$-0.346477\pi$
$662$	−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	−0.598875	−	0.800842i	$-0.704385\pi$
$677$	10.2545	−	17.7613i	0.394112	−	0.682623i	0.992987	+	0.118220i	$0.0377188\pi$
$678$	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	−0.987772	−	0.155906i	$-0.950170\pi$
$691$	−9.43351	+	16.3393i	−0.358868	+	0.621577i	0.628904	+	0.777483i	$0.283504\pi$
$692$	−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	0.986447	−	0.164083i	$-0.0524665\pi$
$719$	9.41508	+	16.3074i	0.351123	+	0.608163i	−0.635323	+	0.772246i	$0.719133\pi$
$720$	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	$-0.908600\pi$
$727$	−19.5426	−	33.8489i	−0.724797	−	1.25538i	0.234261	−	0.972174i	$-0.424733\pi$
$728$		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	$-0.388396\pi$
$733$	18.5985			0.686951			0.343475	+	0.939162i	$0.388396\pi$
$734$	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	$-0.758788\pi$
$761$	−40.0749			−1.45271			−0.726357	+	0.687317i	$0.758788\pi$
$762$	−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	$-0.532392\pi$
$769$	22.4828	−	38.9414i	0.810751	−	1.40426i	0.912339	−	0.409436i	$-0.134274\pi$
$770$		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	−0.559522	−	0.828816i	$-0.689015\pi$
$773$	12.1781	−	21.0930i	0.438014	−	0.758663i	0.997536	+	0.0701524i	$0.0223485\pi$
$774$	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	$-0.901457\pi$
$787$	−20.7617	−	35.9603i	−0.740073	−	1.28184i	0.212388	−	0.977185i	$-0.431876\pi$
$788$	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	$0.376648\pi$
$797$	−17.3018	+	29.9676i	−0.612861	+	1.06151i	−0.990756	+	0.135657i	$0.956685\pi$
$798$		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	$-0.674481\pi$
$811$	−29.6803			−1.04222			−0.521108	+	0.853491i	$0.674481\pi$
$812$		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	$0.404782\pi$
$829$	−19.5851	+	33.9224i	−0.680219	+	1.17817i	−0.974914	+	0.222583i	$0.928551\pi$
$830$	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	$-0.964647\pi$
$839$	−17.1739	−	29.7460i	−0.592907	−	1.02695i	0.400931	−	0.916108i	$-0.368687\pi$
$840$		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	$-0.977709\pi$
$853$	−16.3371	−	28.2967i	−0.559373	−	0.968862i	0.438176	−	0.898889i	$-0.355625\pi$
$854$		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	$-0.944705\pi$
$857$	−57.6679			−1.96990			−0.984950	+	0.172841i	$0.944705\pi$
$858$	−12.8946	+	15.8148i	−0.440216	+	0.539907i
$859$	29.9768			1.02279			0.511397	−	0.859344i	$-0.329128\pi$
$859$	29.9768			1.02279			0.511397	+	0.859344i	$0.329128\pi$
$860$	−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	$-0.598221\pi$
$881$	−18.0285			−0.607395			−0.303697	+	0.952769i	$0.598221\pi$
$882$		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	$-0.673936\pi$
$887$	−30.9527			−1.03929			−0.519645	+	0.854382i	$0.673936\pi$
$888$	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	$-0.592538\pi$
$929$	20.9201	−	36.2347i	0.686366	−	1.18882i	0.973005	−	0.230783i	$-0.0741287\pi$
$930$	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	$-0.658579\pi$
$937$	−29.2537			−0.955676			−0.477838	+	0.878448i	$0.658579\pi$
$938$		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	0.892090	−	0.451859i	$-0.149239\pi$
$941$	1.67869	+	2.90757i	0.0547236	+	0.0947841i	−0.837366	+	0.546643i	$0.815906\pi$
$942$	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	$-0.858654\pi$
$971$	−25.6627	−	44.4491i	−0.823555	−	1.42644i	0.0794635	−	0.996838i	$-0.474679\pi$
$972$	−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	$-0.417850\pi$
$983$	16.0041			0.510453			0.255226	+	0.966881i	$0.417850\pi$
$984$	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	$-0.725162\pi$
$997$	−41.0375			−1.29967			−0.649835	+	0.760075i	$0.725162\pi$
$998$	−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.67.10		24
3.2	odd	2		1323.2.g.h.361.3		24
7.2	even	3		441.2.h.h.373.3		24
7.3	odd	6		441.2.f.h.148.9	✓	24
7.4	even	3		441.2.f.h.148.10	yes	24
7.5	odd	6		441.2.h.h.373.4		24
7.6	odd	2	inner	441.2.g.h.67.9		24
9.2	odd	6		1323.2.h.h.802.9		24
9.7	even	3		441.2.h.h.214.3		24
21.2	odd	6		1323.2.h.h.226.9		24
21.5	even	6		1323.2.h.h.226.10		24
21.11	odd	6		1323.2.f.h.442.4		24
21.17	even	6		1323.2.f.h.442.3		24
21.20	even	2		1323.2.g.h.361.4		24
63.2	odd	6		1323.2.g.h.667.3		24
63.4	even	3		3969.2.a.bh.1.4		12
63.11	odd	6		1323.2.f.h.883.4		24
63.16	even	3	inner	441.2.g.h.79.10		24
63.20	even	6		1323.2.h.h.802.10		24
63.25	even	3		441.2.f.h.295.10	yes	24
63.31	odd	6		3969.2.a.bh.1.3		12
63.32	odd	6		3969.2.a.bi.1.9		12
63.34	odd	6		441.2.h.h.214.4		24
63.38	even	6		1323.2.f.h.883.3		24
63.47	even	6		1323.2.g.h.667.4		24
63.52	odd	6		441.2.f.h.295.9	yes	24
63.59	even	6		3969.2.a.bi.1.10		12
63.61	odd	6	inner	441.2.g.h.79.9		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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

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