LMFDB - Embedded newform 528.2.t.b.133.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,2,Mod(133,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("528.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	528.t (of order $4$, degree $2$, 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:	$4.21610122672$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			133.6
Character	$\chi$	$=$	528.133
Dual form			528.2.t.b.397.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.899005 + 1.09169i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-0.383579 - 1.96287i) q^{4} +(-0.245391 - 0.245391i) q^{5} +(-0.136250 - 1.40763i) q^{6} -2.09093i q^{7} +(2.48769 + 1.34588i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.899005 + 1.09169i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-0.383579 - 1.96287i) q^{4} +(-0.245391 - 0.245391i) q^{5} +(-0.136250 - 1.40763i) q^{6} -2.09093i q^{7} +(2.48769 + 1.34588i) q^{8} -1.00000i q^{9} +(0.488500 - 0.0472835i) q^{10} +(0.707107 + 0.707107i) q^{11} +(1.65919 + 1.11673i) q^{12} +(-4.34278 + 4.34278i) q^{13} +(2.28265 + 1.87976i) q^{14} +0.347036 q^{15} +(-3.70573 + 1.50583i) q^{16} +2.50293 q^{17} +(1.09169 + 0.899005i) q^{18} +(-4.96229 + 4.96229i) q^{19} +(-0.387545 + 0.575799i) q^{20} +(1.47851 + 1.47851i) q^{21} +(-1.40763 + 0.136250i) q^{22} +6.14677i q^{23} +(-2.71074 + 0.807380i) q^{24} -4.87957i q^{25} +(-0.836793 - 8.64516i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.10424 + 0.802039i) q^{28} +(-1.30284 + 1.30284i) q^{29} +(-0.311987 + 0.378856i) q^{30} -8.61940 q^{31} +(1.68757 - 5.39927i) q^{32} -1.00000 q^{33} +(-2.25015 + 2.73243i) q^{34} +(-0.513097 + 0.513097i) q^{35} +(-1.96287 + 0.383579i) q^{36} +(5.65915 + 5.65915i) q^{37} +(-0.956164 - 9.87841i) q^{38} -6.14162i q^{39} +(-0.280190 - 0.940726i) q^{40} +4.91298i q^{41} +(-2.94327 + 0.284889i) q^{42} +(-5.98401 - 5.98401i) q^{43} +(1.11673 - 1.65919i) q^{44} +(-0.245391 + 0.245391i) q^{45} +(-6.71037 - 5.52598i) q^{46} -5.47116 q^{47} +(1.55556 - 3.68513i) q^{48} +2.62799 q^{49} +(5.32698 + 4.38676i) q^{50} +(-1.76984 + 1.76984i) q^{51} +(10.1901 + 6.85852i) q^{52} +(2.63883 + 2.63883i) q^{53} +(-1.40763 + 0.136250i) q^{54} -0.347036i q^{55} +(2.81415 - 5.20160i) q^{56} -7.01774i q^{57} +(-0.251039 - 2.59356i) q^{58} +(-8.02589 - 8.02589i) q^{59} +(-0.133116 - 0.681187i) q^{60} +(-0.865814 + 0.865814i) q^{61} +(7.74889 - 9.40973i) q^{62} -2.09093 q^{63} +(4.37720 + 6.69628i) q^{64} +2.13136 q^{65} +(0.899005 - 1.09169i) q^{66} +(-0.215658 + 0.215658i) q^{67} +(-0.960072 - 4.91293i) q^{68} +(-4.34642 - 4.34642i) q^{69} +(-0.0988667 - 1.02142i) q^{70} +13.8412i q^{71} +(1.34588 - 2.48769i) q^{72} +6.77148i q^{73} +(-11.2657 + 1.09044i) q^{74} +(3.45037 + 3.45037i) q^{75} +(11.6438 + 7.83691i) q^{76} +(1.47851 - 1.47851i) q^{77} +(6.70475 + 5.52135i) q^{78} -8.77144 q^{79} +(1.27887 + 0.539837i) q^{80} -1.00000 q^{81} +(-5.36345 - 4.41679i) q^{82} +(-3.00773 + 3.00773i) q^{83} +(2.33501 - 3.46926i) q^{84} +(-0.614198 - 0.614198i) q^{85} +(11.9123 - 1.15303i) q^{86} -1.84249i q^{87} +(0.807380 + 2.71074i) q^{88} -13.7112i q^{89} +(-0.0472835 - 0.488500i) q^{90} +(9.08047 + 9.08047i) q^{91} +(12.0653 - 2.35777i) q^{92} +(6.09484 - 6.09484i) q^{93} +(4.91860 - 5.97281i) q^{94} +2.43541 q^{95} +(2.62457 + 5.01115i) q^{96} -12.9265 q^{97} +(-2.36258 + 2.86896i) q^{98} +(0.707107 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{8}+O(q^{10}) $ 40 * q + 12 * q^8	$ 40 q + 12 q^{8} + 8 q^{10} + 16 q^{14} - 8 q^{15} + 20 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{22} - 16 q^{24} - 20 q^{28} + 20 q^{30} + 8 q^{31} + 40 q^{32} - 40 q^{33} + 20 q^{34} - 24 q^{35} + 4 q^{36} - 60 q^{38} - 56 q^{40} + 20 q^{42} + 8 q^{44} + 76 q^{46} - 64 q^{47} + 32 q^{48} - 40 q^{49} - 12 q^{50} - 8 q^{51} + 36 q^{52} - 4 q^{54} - 20 q^{56} + 12 q^{58} - 16 q^{59} - 12 q^{60} - 64 q^{61} + 68 q^{62} + 24 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{67} - 4 q^{68} - 16 q^{69} - 116 q^{70} - 12 q^{76} + 28 q^{78} - 72 q^{79} + 40 q^{80} - 40 q^{81} - 24 q^{82} + 16 q^{85} - 64 q^{86} - 12 q^{90} + 16 q^{91} + 20 q^{92} + 32 q^{93} + 104 q^{94} + 128 q^{95} - 20 q^{96} - 32 q^{97} + 36 q^{98}+O(q^{100}) $ 40 * q + 12 * q^8 + 8 * q^10 + 16 * q^14 - 8 * q^15 + 20 * q^16 + 8 * q^19 - 8 * q^20 - 4 * q^22 - 16 * q^24 - 20 * q^28 + 20 * q^30 + 8 * q^31 + 40 * q^32 - 40 * q^33 + 20 * q^34 - 24 * q^35 + 4 * q^36 - 60 * q^38 - 56 * q^40 + 20 * q^42 + 8 * q^44 + 76 * q^46 - 64 * q^47 + 32 * q^48 - 40 * q^49 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^54 - 20 * q^56 + 12 * q^58 - 16 * q^59 - 12 * q^60 - 64 * q^61 + 68 * q^62 + 24 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^67 - 4 * q^68 - 16 * q^69 - 116 * q^70 - 12 * q^76 + 28 * q^78 - 72 * q^79 + 40 * q^80 - 40 * q^81 - 24 * q^82 + 16 * q^85 - 64 * q^86 - 12 * q^90 + 16 * q^91 + 20 * q^92 + 32 * q^93 + 104 * q^94 + 128 * q^95 - 20 * q^96 - 32 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.899005	+	1.09169i	−0.635693	+	0.771942i
$2$	−0.899005	+	1.09169i	−0.635693	+	0.771942i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−0.383579	−	1.96287i	−0.191790	−	0.981436i
$5$	−0.245391	−	0.245391i	−0.109742	−	0.109742i	0.650103	−	0.759846i	$-0.274726\pi$
$5$	−0.245391	−	0.245391i	−0.109742	−	0.109742i	−0.759846	+	0.650103i	$0.774726\pi$
$6$	−0.136250	−	1.40763i	−0.0556236	−	0.574665i
$7$		−	2.09093i		−	0.790299i	−0.918617	−	0.395149i	$-0.870693\pi$
$7$		−	2.09093i		−	0.790299i	0.918617	−	0.395149i	$-0.129307\pi$
$8$	2.48769	+	1.34588i	0.879531	+	0.475841i
$9$		−	1.00000i		−	0.333333i
$10$	0.488500	−	0.0472835i	0.154477	−	0.0149524i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	1.65919	+	1.11673i	0.478967	+	0.322372i
$13$	−4.34278	+	4.34278i	−1.20447	+	1.20447i	−0.231679	+	0.972792i	$0.574422\pi$
$13$	−4.34278	+	4.34278i	−1.20447	+	1.20447i	−0.972792	+	0.231679i	$0.925578\pi$
$14$	2.28265	+	1.87976i	0.610065	+	0.502387i
$15$	0.347036			0.0896043
$16$	−3.70573	+	1.50583i	−0.926433	+	0.376458i
$17$	2.50293			0.607050			0.303525	−	0.952824i	$-0.401836\pi$
$17$	2.50293			0.607050			0.303525	+	0.952824i	$0.401836\pi$
$18$	1.09169	+	0.899005i	0.257314	+	0.211898i
$19$	−4.96229	+	4.96229i	−1.13843	+	1.13843i	−0.149695	+	0.988732i	$0.547829\pi$
$19$	−4.96229	+	4.96229i	−1.13843	+	1.13843i	−0.988732	+	0.149695i	$0.952171\pi$
$20$	−0.387545	+	0.575799i	−0.0866577	+	0.128753i
$21$	1.47851	+	1.47851i	0.322638	+	0.322638i
$22$	−1.40763	+	0.136250i	−0.300109	+	0.0290485i
$23$			6.14677i			1.28169i	0.767670	+	0.640845i	$0.221416\pi$
$23$			6.14677i			1.28169i	−0.767670	+	0.640845i	$0.778584\pi$
$24$	−2.71074	+	0.807380i	−0.553328	+	0.164806i
$25$		−	4.87957i		−	0.975913i
$26$	−0.836793	−	8.64516i	−0.164109	−	1.69546i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−4.10424	+	0.802039i	−0.775628	+	0.151571i
$29$	−1.30284	+	1.30284i	−0.241931	+	0.241931i	−0.817649	−	0.575717i	$-0.804723\pi$
$29$	−1.30284	+	1.30284i	−0.241931	+	0.241931i	0.575717	+	0.817649i	$0.304723\pi$
$30$	−0.311987	+	0.378856i	−0.0569608	+	0.0691693i
$31$	−8.61940			−1.54809			−0.774045	−	0.633130i	$-0.781770\pi$
$31$	−8.61940			−1.54809			−0.774045	+	0.633130i	$0.781770\pi$
$32$	1.68757	−	5.39927i	0.298323	−	0.954465i
$33$	−1.00000			−0.174078
$34$	−2.25015	+	2.73243i	−0.385897	+	0.468607i
$35$	−0.513097	+	0.513097i	−0.0867293	+	0.0867293i
$36$	−1.96287	+	0.383579i	−0.327145	+	0.0639299i
$37$	5.65915	+	5.65915i	0.930359	+	0.930359i	0.997728	−	0.0673694i	$-0.0214606\pi$
$37$	5.65915	+	5.65915i	0.930359	+	0.930359i	−0.0673694	+	0.997728i	$0.521461\pi$
$38$	−0.956164	−	9.87841i	−0.155110	−	1.60249i
$39$		−	6.14162i		−	0.983446i
$40$	−0.280190	−	0.940726i	−0.0443019	−	0.148742i
$41$			4.91298i			0.767278i	0.923483	+	0.383639i	$0.125329\pi$
$41$			4.91298i			0.767278i	−0.923483	+	0.383639i	$0.874671\pi$
$42$	−2.94327	+	0.284889i	−0.454157	+	0.0439593i
$43$	−5.98401	−	5.98401i	−0.912553	−	0.912553i	0.0839195	−	0.996473i	$-0.473256\pi$
$43$	−5.98401	−	5.98401i	−0.912553	−	0.912553i	−0.996473	+	0.0839195i	$0.973256\pi$
$44$	1.11673	−	1.65919i	0.168353	−	0.250133i
$45$	−0.245391	+	0.245391i	−0.0365808	+	0.0365808i
$46$	−6.71037	−	5.52598i	−0.989390	−	0.814761i
$47$	−5.47116			−0.798050			−0.399025	−	0.916940i	$-0.630651\pi$
$47$	−5.47116			−0.798050			−0.399025	+	0.916940i	$0.630651\pi$
$48$	1.55556	−	3.68513i	0.224526	−	0.531903i
$49$	2.62799			0.375428
$50$	5.32698	+	4.38676i	0.753349	+	0.620381i
$51$	−1.76984	+	1.76984i	−0.247827	+	0.247827i
$52$	10.1901	+	6.85852i	1.41312	+	0.951106i
$53$	2.63883	+	2.63883i	0.362472	+	0.362472i	0.864722	−	0.502250i	$-0.167494\pi$
$53$	2.63883	+	2.63883i	0.362472	+	0.362472i	−0.502250	+	0.864722i	$0.667494\pi$
$54$	−1.40763	+	0.136250i	−0.191555	+	0.0185412i
$55$		−	0.347036i		−	0.0467943i
$56$	2.81415	−	5.20160i	0.376057	−	0.695092i
$57$		−	7.01774i		−	0.929522i
$58$	−0.251039	−	2.59356i	−0.0329630	−	0.340551i
$59$	−8.02589	−	8.02589i	−1.04488	−	1.04488i	−0.998944	−	0.0459382i	$-0.985372\pi$
$59$	−8.02589	−	8.02589i	−1.04488	−	1.04488i	−0.0459382	−	0.998944i	$-0.514628\pi$
$60$	−0.133116	−	0.681187i	−0.0171852	−	0.0879409i
$61$	−0.865814	+	0.865814i	−0.110856	+	0.110856i	−0.760359	−	0.649503i	$-0.774977\pi$
$61$	−0.865814	+	0.865814i	−0.110856	+	0.110856i	0.649503	+	0.760359i	$0.274977\pi$
$62$	7.74889	−	9.40973i	0.984110	−	1.19504i
$63$	−2.09093			−0.263433
$64$	4.37720	+	6.69628i	0.547150	+	0.837034i
$65$	2.13136			0.264363
$66$	0.899005	−	1.09169i	0.110660	−	0.134378i
$67$	−0.215658	+	0.215658i	−0.0263469	+	0.0263469i	−0.720157	−	0.693811i	$-0.755930\pi$
$67$	−0.215658	+	0.215658i	−0.0263469	+	0.0263469i	0.693811	+	0.720157i	$0.255930\pi$
$68$	−0.960072	−	4.91293i	−0.116426	−	0.595780i
$69$	−4.34642	−	4.34642i	−0.523248	−	0.523248i
$70$	−0.0988667	−	1.02142i	−0.0118168	−	0.122083i
$71$			13.8412i			1.64264i	0.570465	+	0.821322i	$0.306763\pi$
$71$			13.8412i			1.64264i	−0.570465	+	0.821322i	$0.693237\pi$
$72$	1.34588	−	2.48769i	0.158614	−	0.293177i
$73$			6.77148i			0.792541i	0.918134	+	0.396271i	$0.129696\pi$
$73$			6.77148i			0.792541i	−0.918134	+	0.396271i	$0.870304\pi$
$74$	−11.2657	+	1.09044i	−1.30961	+	0.126761i
$75$	3.45037	+	3.45037i	0.398415	+	0.398415i
$76$	11.6438	+	7.83691i	1.33563	+	0.898955i
$77$	1.47851	−	1.47851i	0.168492	−	0.168492i
$78$	6.70475	+	5.52135i	0.759164	+	0.625170i
$79$	−8.77144			−0.986864			−0.493432	−	0.869784i	$-0.664258\pi$
$79$	−8.77144			−0.986864			−0.493432	+	0.869784i	$0.664258\pi$
$80$	1.27887	+	0.539837i	0.142982	+	0.0603556i
$81$	−1.00000			−0.111111
$82$	−5.36345	−	4.41679i	−0.592294	−	0.487753i
$83$	−3.00773	+	3.00773i	−0.330141	+	0.330141i	−0.852640	−	0.522499i	$-0.825000\pi$
$83$	−3.00773	+	3.00773i	−0.330141	+	0.330141i	0.522499	+	0.852640i	$0.325000\pi$
$84$	2.33501	−	3.46926i	0.254770	−	0.378527i
$85$	−0.614198	−	0.614198i	−0.0666191	−	0.0666191i
$86$	11.9123	−	1.15303i	1.28454	−	0.124335i
$87$		−	1.84249i		−	0.197536i
$88$	0.807380	+	2.71074i	0.0860670	+	0.288966i
$89$		−	13.7112i		−	1.45339i	−0.686963	−	0.726693i	$-0.741056\pi$
$89$		−	13.7112i		−	1.45339i	0.686963	−	0.726693i	$-0.258944\pi$
$90$	−0.0472835	−	0.488500i	−0.00498412	−	0.0514924i
$91$	9.08047	+	9.08047i	0.951892	+	0.951892i
$92$	12.0653	−	2.35777i	1.25790	−	0.245815i
$93$	6.09484	−	6.09484i	0.632005	−	0.632005i
$94$	4.91860	−	5.97281i	0.507315	−	0.616049i
$95$	2.43541			0.249868
$96$	2.62457	+	5.01115i	0.267869	+	0.511448i
$97$	−12.9265			−1.31249			−0.656245	−	0.754548i	$-0.727856\pi$
$97$	−12.9265			−1.31249			−0.656245	+	0.754548i	$0.727856\pi$
$98$	−2.36258	+	2.86896i	−0.238657	+	0.289809i
$99$	0.707107	−	0.707107i	0.0710669	−	0.0710669i
$100$	−9.57796	+	1.87170i	−0.957796	+	0.187170i
$101$	6.59939	+	6.59939i	0.656664	+	0.656664i	0.954589	−	0.297925i	$-0.0962947\pi$
$101$	6.59939	+	6.59939i	0.656664	+	0.656664i	−0.297925	+	0.954589i	$0.596295\pi$
$102$	−0.341023	−	3.52321i	−0.0337663	−	0.348850i
$103$		−	13.4679i		−	1.32703i	−0.748163	−	0.663515i	$-0.769064\pi$
$103$		−	13.4679i		−	1.32703i	0.748163	−	0.663515i	$-0.230936\pi$
$104$	−16.6484	+	4.95862i	−1.63251	+	0.486233i
$105$		−	0.725629i		−	0.0708142i
$106$	−5.25312	+	0.508466i	−0.510228	+	0.0493866i
$107$	13.2553	+	13.2553i	1.28143	+	1.28143i	0.939851	+	0.341584i	$0.110963\pi$
$107$	13.2553	+	13.2553i	1.28143	+	1.28143i	0.341584	+	0.939851i	$0.389037\pi$
$108$	1.11673	−	1.65919i	0.107457	−	0.159656i
$109$	−8.05315	+	8.05315i	−0.771352	+	0.771352i	−0.978343	−	0.206991i	$-0.933633\pi$
$109$	−8.05315	+	8.05315i	−0.771352	+	0.771352i	0.206991	+	0.978343i	$0.433633\pi$
$110$	0.378856	+	0.311987i	0.0361225	+	0.0297468i
$111$	−8.00325			−0.759635
$112$	3.14860	+	7.74845i	0.297515	+	0.732159i
$113$	19.1658			1.80296			0.901481	−	0.432818i	$-0.142481\pi$
$113$	19.1658			1.80296			0.901481	+	0.432818i	$0.142481\pi$
$114$	7.66120	+	6.30898i	0.717537	+	0.590890i
$115$	1.50836	−	1.50836i	0.140656	−	0.140656i
$116$	3.05705	+	2.05756i	0.283840	+	0.191040i
$117$	4.34278	+	4.34278i	0.401490	+	0.401490i
$118$	15.9771	−	1.54648i	1.47081	−	0.142365i
$119$		−	5.23346i		−	0.479751i
$120$	0.863318	+	0.467070i	0.0788098	+	0.0426374i
$121$			1.00000i			0.0909091i
$122$	−0.166830	−	1.72357i	−0.0151041	−	0.156045i
$123$	−3.47400	−	3.47400i	−0.313240	−	0.313240i
$124$	3.30622	+	16.9188i	0.296908	+	1.51935i
$125$	−2.42436	+	2.42436i	−0.216841	+	0.216841i
$126$	1.87976	−	2.28265i	0.167462	−	0.203355i
$127$	14.5036			1.28699			0.643495	−	0.765450i	$-0.277484\pi$
$127$	14.5036			1.28699			0.643495	+	0.765450i	$0.277484\pi$
$128$	−11.2454	−	1.24143i	−0.993962	−	0.109728i
$129$	8.46267			0.745096
$130$	−1.91611	+	2.32679i	−0.168054	+	0.204073i
$131$	−4.38366	+	4.38366i	−0.383002	+	0.383002i	−0.872183	−	0.489180i	$-0.837296\pi$
$131$	−4.38366	+	4.38366i	−0.383002	+	0.383002i	0.489180	+	0.872183i	$0.337296\pi$
$132$	0.383579	+	1.96287i	0.0333863	+	0.170846i
$133$	10.3758	+	10.3758i	0.899698	+	0.899698i
$134$	−0.0415543	−	0.429310i	−0.00358975	−	0.0370868i
$135$		−	0.347036i		−	0.0298681i
$136$	6.22651	+	3.36865i	0.533919	+	0.288859i
$137$		−	5.04371i		−	0.430914i	−0.976513	−	0.215457i	$-0.930876\pi$
$137$		−	5.04371i		−	0.430914i	0.976513	−	0.215457i	$-0.0691240\pi$
$138$	8.65240	−	0.837494i	0.736542	−	0.0712922i
$139$	6.52621	+	6.52621i	0.553546	+	0.553546i	0.927462	−	0.373916i	$-0.121985\pi$
$139$	6.52621	+	6.52621i	0.553546	+	0.553546i	−0.373916	+	0.927462i	$0.621985\pi$
$140$	1.20396	+	0.810331i	0.101753	+	0.0684855i
$141$	3.86869	−	3.86869i	0.325803	−	0.325803i
$142$	−15.1103	−	12.4433i	−1.26803	−	1.04422i
$143$	−6.14162			−0.513588
$144$	1.50583	+	3.70573i	0.125486	+	0.308811i
$145$	0.639411			0.0531002
$146$	−7.39236	−	6.08759i	−0.611796	−	0.503813i
$147$	−1.85827	+	1.85827i	−0.153268	+	0.153268i
$148$	8.93746	−	13.2789i	0.734654	−	1.09152i
$149$	4.44620	+	4.44620i	0.364247	+	0.364247i	0.865374	−	0.501127i	$-0.167081\pi$
$149$	4.44620	+	4.44620i	0.364247	+	0.364247i	−0.501127	+	0.865374i	$0.667081\pi$
$150$	−6.86865	+	0.664839i	−0.560823	+	0.0542838i
$151$			2.79880i			0.227763i	0.993494	+	0.113882i	$0.0363284\pi$
$151$			2.79880i			0.227763i	−0.993494	+	0.113882i	$0.963672\pi$
$152$	−19.0233	+	5.66598i	−1.54299	+	0.459572i
$153$		−	2.50293i		−	0.202350i
$154$	0.284889	+	2.94327i	0.0229570	+	0.237176i
$155$	2.11513	+	2.11513i	0.169891	+	0.169891i
$156$	−12.0552	+	2.35580i	−0.965190	+	0.188615i
$157$	7.33141	−	7.33141i	0.585110	−	0.585110i	−0.351193	−	0.936303i	$-0.614224\pi$
$157$	7.33141	−	7.33141i	0.585110	−	0.585110i	0.936303	+	0.351193i	$0.114224\pi$
$158$	7.88557	−	9.57570i	0.627342	−	0.761802i
$159$	−3.73188			−0.295957
$160$	−1.73905	+	0.910820i	−0.137484	+	0.0720066i
$161$	12.8525			1.01292
$162$	0.899005	−	1.09169i	0.0706325	−	0.0857714i
$163$	12.9157	−	12.9157i	1.01163	−	1.01163i	0.0117006	−	0.999932i	$-0.496275\pi$
$163$	12.9157	−	12.9157i	1.01163	−	1.01163i	0.999932	−	0.0117006i	$-0.00372450\pi$
$164$	9.64354	−	1.88452i	0.753034	−	0.147156i
$165$	0.245391	+	0.245391i	0.0191037	+	0.0191037i
$166$	−0.579547	−	5.98748i	−0.0449816	−	0.464718i
$167$		−	3.59646i		−	0.278302i	−0.990271	−	0.139151i	$-0.955563\pi$
$167$		−	3.59646i		−	0.278302i	0.990271	−	0.139151i	$-0.0444374\pi$
$168$	1.68818	+	5.66799i	0.130246	+	0.437295i
$169$		−	24.7195i		−	1.90150i
$170$	1.22268	−	0.118347i	0.0937754	−	0.00907682i
$171$	4.96229	+	4.96229i	0.379476	+	0.379476i
$172$	−9.45050	+	14.0412i	−0.720594	+	1.07063i
$173$	−9.09948	+	9.09948i	−0.691821	+	0.691821i	−0.962632	−	0.270811i	$-0.912708\pi$
$173$	−9.09948	+	9.09948i	−0.691821	+	0.691821i	0.270811	+	0.962632i	$0.412708\pi$
$174$	2.01143	+	1.65641i	0.152486	+	0.125572i
$175$	−10.2029			−0.771263
$176$	−3.68513	−	1.55556i	−0.277778	−	0.117255i
$177$	11.3503			0.853143
$178$	14.9684	+	12.3264i	1.12193	+	0.923906i
$179$	−2.48751	+	2.48751i	−0.185925	+	0.185925i	−0.793932	−	0.608007i	$-0.791969\pi$
$179$	−2.48751	+	2.48751i	−0.185925	+	0.185925i	0.608007	+	0.793932i	$0.291969\pi$
$180$	0.575799	+	0.387545i	0.0429175	+	0.0288859i
$181$	−10.5130	−	10.5130i	−0.781425	−	0.781425i	0.198646	−	0.980071i	$-0.436346\pi$
$181$	−10.5130	−	10.5130i	−0.781425	−	0.781425i	−0.980071	+	0.198646i	$0.936346\pi$
$182$	−18.0765	+	1.74968i	−1.33992	+	0.129695i
$183$		−	1.22445i		−	0.0905137i
$184$	−8.27283	+	15.2913i	−0.609881	+	1.12729i
$185$		−	2.77741i		−	0.204200i
$186$	1.17439	+	12.1330i	0.0861104	+	0.889633i
$187$	1.76984	+	1.76984i	0.129423	+	0.129423i
$188$	2.09862	+	10.7392i	0.153058	+	0.783235i
$189$	1.47851	−	1.47851i	0.107546	−	0.107546i
$190$	−2.18944	+	2.65871i	−0.158839	+	0.192883i
$191$	−27.3173			−1.97661			−0.988305	−	0.152488i	$-0.951271\pi$
$191$	−27.3173			−1.97661			−0.988305	+	0.152488i	$0.951271\pi$
$192$	−7.83013	−	1.63983i	−0.565091	−	0.118345i
$193$	11.1300			0.801153			0.400576	−	0.916263i	$-0.368810\pi$
$193$	11.1300			0.801153			0.400576	+	0.916263i	$0.368810\pi$
$194$	11.6210	−	14.1118i	0.834340	−	1.01317i
$195$	−1.50710	+	1.50710i	−0.107926	+	0.107926i
$196$	−1.00804	−	5.15842i	−0.0720032	−	0.368458i
$197$	−8.39958	−	8.39958i	−0.598446	−	0.598446i	0.341453	−	0.939899i	$-0.389081\pi$
$197$	−8.39958	−	8.39958i	−0.598446	−	0.598446i	−0.939899	+	0.341453i	$0.889081\pi$
$198$	0.136250	+	1.40763i	0.00968283	+	0.100036i
$199$		−	4.71019i		−	0.333896i	−0.985966	−	0.166948i	$-0.946609\pi$
$199$		−	4.71019i		−	0.333896i	0.985966	−	0.166948i	$-0.0533912\pi$
$200$	6.56732	−	12.1388i	0.464380	−	0.858346i
$201$		−	0.304987i		−	0.0215121i
$202$	−13.1374	+	1.27161i	−0.924343	+	0.0894701i
$203$	2.72415	+	2.72415i	0.191198	+	0.191198i
$204$	4.15284	+	2.79509i	0.290757	+	0.195696i
$205$	1.20560	−	1.20560i	0.0842029	−	0.0842029i
$206$	14.7028	+	12.1077i	1.02439	+	0.843583i
$207$	6.14677			0.427230
$208$	9.55369	−	22.6327i	0.662429	−	1.56930i
$209$	−7.01774			−0.485427
$210$	0.792163	+	0.652345i	0.0546644	+	0.0450160i
$211$	4.52045	−	4.52045i	0.311201	−	0.311201i	−0.534174	−	0.845375i	$-0.679377\pi$
$211$	4.52045	−	4.52045i	0.311201	−	0.311201i	0.845375	+	0.534174i	$0.179377\pi$
$212$	4.16749	−	6.19190i	0.286225	−	0.425261i
$213$	−9.78718	−	9.78718i	−0.670607	−	0.670607i
$214$	−26.3872	+	2.55410i	−1.80379	+	0.174595i
$215$			2.93685i			0.200292i
$216$	0.807380	+	2.71074i	0.0549352	+	0.184443i
$217$			18.0226i			1.22345i
$218$	−1.55173	−	16.0314i	−0.105096	−	1.08578i
$219$	−4.78816	−	4.78816i	−0.323554	−	0.323554i
$220$	−0.681187	+	0.133116i	−0.0459256	+	0.00897466i
$221$	−10.8697	+	10.8697i	−0.731174	+	0.731174i
$222$	7.19496	−	8.73707i	0.482894	−	0.586394i
$223$	18.3819			1.23094			0.615471	−	0.788160i	$-0.288966\pi$
$223$	18.3819			1.23094			0.615471	+	0.788160i	$0.288966\pi$
$224$	−11.2895	−	3.52859i	−0.754313	−	0.235764i
$225$	−4.87957			−0.325304
$226$	−17.2301	+	20.9231i	−1.14613	+	1.39178i
$227$	9.82137	−	9.82137i	0.651867	−	0.651867i	−0.301575	−	0.953442i	$-0.597512\pi$
$227$	9.82137	−	9.82137i	0.651867	−	0.651867i	0.953442	+	0.301575i	$0.0975124\pi$
$228$	−13.7749	+	2.69186i	−0.912267	+	0.178273i
$229$	−16.0713	−	16.0713i	−1.06202	−	1.06202i	−0.997945	−	0.0640742i	$-0.979591\pi$
$229$	−16.0713	−	16.0713i	−1.06202	−	1.06202i	−0.0640742	−	0.997945i	$-0.520409\pi$
$230$	0.290641	+	3.00270i	0.0191643	+	0.197992i
$231$			2.09093i			0.137573i
$232$	−4.99453	+	1.48759i	−0.327907	+	0.0976652i
$233$		−	17.1666i		−	1.12462i	−0.826927	−	0.562310i	$-0.809913\pi$
$233$		−	17.1666i		−	1.12462i	0.826927	−	0.562310i	$-0.190087\pi$
$234$	−8.64516	+	0.836793i	−0.565152	+	0.0547029i
$235$	1.34258	+	1.34258i	0.0875799	+	0.0875799i
$236$	−12.6752	+	18.8324i	−0.825088	+	1.22588i
$237$	6.20234	−	6.20234i	0.402885	−	0.402885i
$238$	5.71332	+	4.70491i	0.370340	+	0.304974i
$239$	5.18755			0.335555			0.167777	−	0.985825i	$-0.446341\pi$
$239$	5.18755			0.335555			0.167777	+	0.985825i	$0.446341\pi$
$240$	−1.28602	+	0.522578i	−0.0830124	+	0.0337323i
$241$	12.5630			0.809257			0.404628	−	0.914481i	$-0.367401\pi$
$241$	12.5630			0.809257			0.404628	+	0.914481i	$0.367401\pi$
$242$	−1.09169	−	0.899005i	−0.0701766	−	0.0577902i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	2.03159	+	1.36737i	0.130059	+	0.0875372i
$245$	−0.644888	−	0.644888i	−0.0412004	−	0.0412004i
$246$	6.91568	−	0.669391i	0.440927	−	0.0426788i
$247$		−	43.1003i		−	2.74241i
$248$	−21.4424	−	11.6007i	−1.36159	−	0.736645i
$249$		−	4.25357i		−	0.269559i
$250$	−0.467140	−	4.82617i	−0.0295445	−	0.305234i
$251$	9.69825	+	9.69825i	0.612148	+	0.612148i	0.943505	−	0.331357i	$-0.107507\pi$
$251$	9.69825	+	9.69825i	0.612148	+	0.612148i	−0.331357	+	0.943505i	$0.607507\pi$
$252$	0.802039	+	4.10424i	0.0505237	+	0.258543i
$253$	−4.34642	+	4.34642i	−0.273257	+	0.273257i
$254$	−13.0388	+	15.8335i	−0.818130	+	0.993482i
$255$	0.868607			0.0543943
$256$	11.4649	−	11.1604i	0.716558	−	0.697527i
$257$	−7.21019			−0.449759			−0.224880	−	0.974387i	$-0.572199\pi$
$257$	−7.21019			−0.449759			−0.224880	+	0.974387i	$0.572199\pi$
$258$	−7.60798	+	9.23862i	−0.473652	+	0.575171i
$259$	11.8329	−	11.8329i	0.735261	−	0.735261i
$260$	−0.817547	−	4.18359i	−0.0507021	−	0.259455i
$261$	1.30284	+	1.30284i	0.0806437	+	0.0806437i
$262$	−0.844670	−	8.72654i	−0.0521839	−	0.539127i
$263$			17.5909i			1.08470i	0.840151	+	0.542352i	$0.182466\pi$
$263$			17.5909i			1.08470i	−0.840151	+	0.542352i	$0.817534\pi$
$264$	−2.48769	−	1.34588i	−0.153107	−	0.0828333i
$265$		−	1.29510i		−	0.0795571i
$266$	−20.6551	+	1.99928i	−1.26645	+	0.122583i
$267$	9.69529	+	9.69529i	0.593342	+	0.593342i
$268$	0.506032	+	0.340588i	0.0309108	+	0.0208047i
$269$	3.46271	−	3.46271i	0.211125	−	0.211125i	−0.593620	−	0.804745i	$-0.702302\pi$
$269$	3.46271	−	3.46271i	0.211125	−	0.211125i	0.804745	+	0.593620i	$0.202302\pi$
$270$	0.378856	+	0.311987i	0.0230564	+	0.0189869i
$271$	−23.4609			−1.42515			−0.712575	−	0.701596i	$-0.752471\pi$
$271$	−23.4609			−1.42515			−0.712575	+	0.701596i	$0.752471\pi$
$272$	−9.27519	+	3.76900i	−0.562391	+	0.228529i
$273$	−12.8417			−0.777217
$274$	5.50618	+	4.53432i	0.332640	+	0.273929i
$275$	3.45037	−	3.45037i	0.208065	−	0.208065i
$276$	−6.86427	+	10.1987i	−0.413181	+	0.613888i
$277$	2.14756	+	2.14756i	0.129034	+	0.129034i	0.768674	−	0.639640i	$-0.220917\pi$
$277$	2.14756	+	2.14756i	0.129034	+	0.129034i	−0.639640	+	0.768674i	$0.720917\pi$
$278$	−12.9917	+	1.25751i	−0.779191	+	0.0754204i
$279$			8.61940i			0.516030i
$280$	−1.96700	+	0.585858i	−0.117550	+	0.0350117i
$281$			8.13203i			0.485116i	0.970137	+	0.242558i	$0.0779865\pi$
$281$			8.13203i			0.485116i	−0.970137	+	0.242558i	$0.922013\pi$
$282$	0.745443	+	7.70139i	0.0443905	+	0.458611i
$283$	−0.206112	−	0.206112i	−0.0122521	−	0.0122521i	0.700954	−	0.713206i	$-0.252758\pi$
$283$	−0.206112	−	0.206112i	−0.0122521	−	0.0122521i	−0.713206	+	0.700954i	$0.752758\pi$
$284$	27.1684	−	5.30918i	1.61215	−	0.315042i
$285$	−1.72209	+	1.72209i	−0.102008	+	0.102008i
$286$	5.52135	−	6.70475i	0.326484	−	0.396460i
$287$	10.2727			0.606379
$288$	−5.39927	−	1.68757i	−0.318155	−	0.0994409i
$289$	−10.7353			−0.631491
$290$	−0.574834	+	0.698040i	−0.0337554	+	0.0409903i
$291$	9.14043	−	9.14043i	0.535821	−	0.535821i
$292$	13.2915	−	2.59740i	0.777829	−	0.152001i
$293$	7.14647	+	7.14647i	0.417501	+	0.417501i	0.884342	−	0.466841i	$-0.154608\pi$
$293$	7.14647	+	7.14647i	0.417501	+	0.417501i	−0.466841	+	0.884342i	$0.654608\pi$
$294$	−0.358063	−	3.69926i	−0.0208827	−	0.215745i
$295$			3.93897i			0.229336i
$296$	6.46166	+	21.6948i	0.375576	+	1.26098i
$297$			1.00000i			0.0580259i
$298$	−8.85104	+	0.856721i	−0.512727	+	0.0496285i
$299$	−26.6941	−	26.6941i	−1.54376	−	1.54376i
$300$	5.44915	−	8.09614i	0.314607	−	0.467431i
$301$	−12.5122	+	12.5122i	−0.721190	+	0.721190i
$302$	−3.05542	−	2.51613i	−0.175820	−	0.144787i
$303$	−9.33295			−0.536164
$304$	10.9165	−	25.8613i	0.626107	−	1.48325i
$305$	0.424927			0.0243312
$306$	2.73243	+	2.25015i	0.156202	+	0.128632i
$307$	−8.01785	+	8.01785i	−0.457603	+	0.457603i	−0.897868	−	0.440265i	$-0.854885\pi$
$307$	−8.01785	+	8.01785i	−0.457603	+	0.457603i	0.440265	+	0.897868i	$0.354885\pi$
$308$	−3.46926	−	2.33501i	−0.197679	−	0.133049i
$309$	9.52323	+	9.52323i	0.541758	+	0.541758i
$310$	−4.21058	+	0.407555i	−0.239145	+	0.0231476i
$311$			0.00693950i			0.000393503i	1.00000		0.000196751i	$6.26279e-5\pi$
$311$			0.00693950i			0.000393503i	−1.00000		0.000196751i	$0.999937\pi$
$312$	8.26590	−	15.2784i	0.467964	−	0.864972i
$313$			8.83753i			0.499527i	0.968307	+	0.249763i	$0.0803529\pi$
$313$			8.83753i			0.499527i	−0.968307	+	0.249763i	$0.919647\pi$
$314$	1.41266	+	14.5946i	0.0797210	+	0.823622i
$315$	0.513097	+	0.513097i	0.0289098	+	0.0289098i
$316$	3.36454	+	17.2172i	0.189270	+	0.968544i
$317$	−8.51379	+	8.51379i	−0.478182	+	0.478182i	−0.904550	−	0.426368i	$-0.859793\pi$
$317$	−8.51379	+	8.51379i	−0.478182	+	0.478182i	0.426368	+	0.904550i	$0.359793\pi$
$318$	3.35498	−	4.07406i	0.188138	−	0.228462i
$319$	−1.84249			−0.103160
$320$	0.569081	−	2.71734i	0.0318126	−	0.151904i
$321$	−18.7458			−1.04629
$322$	−11.5545	+	14.0309i	−0.643904	+	0.781914i
$323$	−12.4203	+	12.4203i	−0.691082	+	0.691082i
$324$	0.383579	+	1.96287i	0.0213100	+	0.109048i
$325$	21.1909	+	21.1909i	1.17546	+	1.17546i
$326$	2.48867	+	25.7111i	0.137834	+	1.42401i
$327$		−	11.3889i		−	0.629806i
$328$	−6.61229	+	12.2220i	−0.365102	+	0.674845i
$329$			11.4398i			0.630698i
$330$	−0.488500	+	0.0472835i	−0.0268910	+	0.00260287i
$331$	−9.64848	−	9.64848i	−0.530329	−	0.530329i	0.390342	−	0.920670i	$-0.372357\pi$
$331$	−9.64848	−	9.64848i	−0.530329	−	0.530329i	−0.920670	+	0.390342i	$0.872357\pi$
$332$	7.05749	+	4.75009i	0.387330	+	0.260695i
$333$	5.65915	−	5.65915i	0.310120	−	0.310120i
$334$	3.92622	+	3.23323i	0.214833	+	0.176915i
$335$	0.105841			0.00578273
$336$	−7.70537	−	3.25258i	−0.420363	−	0.177443i
$337$	−10.4238			−0.567823			−0.283911	−	0.958851i	$-0.591632\pi$
$337$	−10.4238			−0.567823			−0.283911	+	0.958851i	$0.591632\pi$
$338$	26.9861	+	22.2230i	1.46785	+	1.20877i
$339$	−13.5522	+	13.5522i	−0.736056	+	0.736056i
$340$	−0.969998	+	1.44118i	−0.0526055	+	0.0781592i
$341$	−6.09484	−	6.09484i	−0.330054	−	0.330054i
$342$	−9.87841	+	0.956164i	−0.534163	+	0.0517034i
$343$		−	20.1315i		−	1.08700i
$344$	−6.83259	−	22.9401i	−0.368388	−	1.23685i
$345$			2.13315i			0.114845i
$346$	−1.75334	−	18.1143i	−0.0942603	−	0.973831i
$347$	−9.99269	−	9.99269i	−0.536436	−	0.536436i	0.386044	−	0.922480i	$-0.373841\pi$
$347$	−9.99269	−	9.99269i	−0.536436	−	0.536436i	−0.922480	+	0.386044i	$0.873841\pi$
$348$	−3.61658	+	0.706742i	−0.193869	+	0.0378854i
$349$	7.21564	−	7.21564i	0.386245	−	0.386245i	−0.487101	−	0.873346i	$-0.661946\pi$
$349$	7.21564	−	7.21564i	0.386245	−	0.386245i	0.873346	+	0.487101i	$0.161946\pi$
$350$	9.17242	−	11.1384i	0.490286	−	0.595370i
$351$	−6.14162			−0.327815
$352$	5.01115	−	2.62457i	0.267095	−	0.139890i
$353$	20.0988			1.06975			0.534875	−	0.844931i	$-0.320359\pi$
$353$	20.0988			1.06975			0.534875	+	0.844931i	$0.320359\pi$
$354$	−10.2040	+	12.3911i	−0.542337	+	0.658577i
$355$	3.39650	−	3.39650i	0.180268	−	0.180268i
$356$	−26.9133	+	5.25933i	−1.42640	+	0.278744i
$357$	3.70062	+	3.70062i	0.195857	+	0.195857i
$358$	−0.479309	−	4.95188i	−0.0253322	−	0.261715i
$359$			16.9788i			0.896108i	0.894006	+	0.448054i	$0.147883\pi$
$359$			16.9788i			0.896108i	−0.894006	+	0.448054i	$0.852117\pi$
$360$	−0.940726	+	0.280190i	−0.0495806	+	0.0147673i
$361$		−	30.2487i		−	1.59203i
$362$	20.9282	−	2.02571i	1.09996	−	0.106469i
$363$	−0.707107	−	0.707107i	−0.0371135	−	0.0371135i
$364$	14.3407	−	21.3069i	0.751658	−	1.11678i
$365$	1.66166	−	1.66166i	0.0869754	−	0.0869754i
$366$	1.33672	+	1.10078i	0.0698713	+	0.0575389i
$367$	11.9588			0.624246			0.312123	−	0.950042i	$-0.398960\pi$
$367$	11.9588			0.624246			0.312123	+	0.950042i	$0.398960\pi$
$368$	−9.25601	−	22.7783i	−0.482503	−	1.18740i
$369$	4.91298			0.255759
$370$	3.03208	+	2.49691i	0.157630	+	0.129808i
$371$	5.51763	−	5.51763i	0.286461	−	0.286461i
$372$	−14.3012	−	9.62554i	−0.741485	−	0.499061i
$373$	−7.17331	−	7.17331i	−0.371420	−	0.371420i	0.496574	−	0.867994i	$-0.334591\pi$
$373$	−7.17331	−	7.17331i	−0.371420	−	0.371420i	−0.867994	+	0.496574i	$0.834591\pi$
$374$	−3.52321	+	0.341023i	−0.182181	+	0.0176339i
$375$		−	3.42856i		−	0.177050i
$376$	−13.6105	−	7.36353i	−0.701910	−	0.379745i
$377$		−	11.3159i		−	0.582798i
$378$	0.284889	+	2.94327i	0.0146531	+	0.151386i
$379$	17.7457	+	17.7457i	0.911536	+	0.911536i	0.996393	−	0.0848572i	$-0.0270434\pi$
$379$	17.7457	+	17.7457i	0.911536	+	0.911536i	−0.0848572	+	0.996393i	$0.527043\pi$
$380$	−0.934172	−	4.78039i	−0.0479220	−	0.245229i
$381$	−10.2556	+	10.2556i	−0.525411	+	0.525411i
$382$	24.5584	−	29.8221i	1.25652	−	1.52583i
$383$	18.4143			0.940927			0.470463	−	0.882420i	$-0.344087\pi$
$383$	18.4143			0.940927			0.470463	+	0.882420i	$0.344087\pi$
$384$	8.82952	−	7.07387i	0.450580	−	0.360987i
$385$	−0.725629			−0.0369815
$386$	−10.0059	+	12.1505i	−0.509287	+	0.618444i
$387$	−5.98401	+	5.98401i	−0.304184	+	0.304184i
$388$	4.95834	+	25.3731i	0.251722	+	1.28812i
$389$	−8.00441	−	8.00441i	−0.405840	−	0.405840i	0.474445	−	0.880285i	$-0.342649\pi$
$389$	−8.00441	−	8.00441i	−0.405840	−	0.405840i	−0.880285	+	0.474445i	$0.842649\pi$
$390$	−0.290397	−	3.00018i	−0.0147048	−	0.151920i
$391$			15.3849i			0.778049i
$392$	6.53764	+	3.53697i	0.330200	+	0.178644i
$393$		−	6.19943i		−	0.312720i
$394$	16.7210	−	1.61848i	0.842393	−	0.0815379i
$395$	2.15244	+	2.15244i	0.108301	+	0.108301i
$396$	−1.65919	−	1.11673i	−0.0833775	−	0.0561177i
$397$	−10.2024	+	10.2024i	−0.512043	+	0.512043i	−0.915152	−	0.403109i	$-0.867930\pi$
$397$	−10.2024	+	10.2024i	−0.512043	+	0.512043i	0.403109	+	0.915152i	$0.367930\pi$
$398$	5.14207	+	4.23448i	0.257749	+	0.212255i
$399$	−14.6736			−0.734600
$400$	7.34782	+	18.0824i	0.367391	+	0.904119i
$401$	30.3556			1.51589			0.757944	−	0.652320i	$-0.226204\pi$
$401$	30.3556			1.51589			0.757944	+	0.652320i	$0.226204\pi$
$402$	0.332952	+	0.274185i	0.0166061	+	0.0136751i
$403$	37.4322	−	37.4322i	1.86463	−	1.86463i
$404$	10.4224	−	15.4851i	0.518532	−	0.770415i
$405$	0.245391	+	0.245391i	0.0121936	+	0.0121936i
$406$	−5.42296	+	0.524906i	−0.269137	+	0.0260506i
$407$			8.00325i			0.396706i
$408$	−6.78480	+	2.02082i	−0.335898	+	0.100045i
$409$			30.4165i			1.50400i	0.659165	+	0.751999i	$0.270910\pi$
$409$			30.4165i			1.50400i	−0.659165	+	0.751999i	$0.729090\pi$
$410$	0.232303	+	2.39999i	0.0114726	+	0.118527i
$411$	3.56644	+	3.56644i	0.175920	+	0.175920i
$412$	−26.4357	+	5.16600i	−1.30239	+	0.254510i
$413$	−16.7816	+	16.7816i	−0.825769	+	0.825769i
$414$	−5.52598	+	6.71037i	−0.271587	+	0.329797i
$415$	1.47614			0.0724610
$416$	16.1191	+	30.7766i	0.790304	+	1.50895i
$417$	−9.22946			−0.451969
$418$	6.30898	−	7.66120i	0.308582	−	0.374722i
$419$	14.8821	−	14.8821i	0.727036	−	0.727036i	−0.242992	−	0.970028i	$-0.578129\pi$
$419$	14.8821	−	14.8821i	0.727036	−	0.727036i	0.970028	+	0.242992i	$0.0781289\pi$
$420$	−1.42432	+	0.278336i	−0.0694996	+	0.0135814i
$421$	16.7779	+	16.7779i	0.817706	+	0.817706i	0.985775	−	0.168069i	$-0.0537533\pi$
$421$	16.7779	+	16.7779i	0.817706	+	0.817706i	−0.168069	+	0.985775i	$0.553753\pi$
$422$	0.871028	+	8.99885i	0.0424010	+	0.438057i
$423$			5.47116i			0.266017i
$424$	3.01304	+	10.1162i	0.146326	+	0.491284i
$425$		−	12.2132i		−	0.592428i
$426$	19.4833	−	1.88585i	0.943970	−	0.0913699i
$427$	1.81036	+	1.81036i	0.0876095	+	0.0876095i
$428$	20.9339	−	31.1028i	1.01188	−	1.50341i
$429$	4.34278	−	4.34278i	0.209671	−	0.209671i
$430$	−3.20613	−	2.64024i	−0.154613	−	0.127324i
$431$	15.0634			0.725579			0.362790	−	0.931871i	$-0.381824\pi$
$431$	15.0634			0.725579			0.362790	+	0.931871i	$0.381824\pi$
$432$	−3.68513	−	1.55556i	−0.177301	−	0.0748421i
$433$	−13.1030			−0.629688			−0.314844	−	0.949143i	$-0.601952\pi$
$433$	−13.1030			−0.629688			−0.314844	+	0.949143i	$0.601952\pi$
$434$	−19.6751	−	16.2024i	−0.944436	−	0.777741i
$435$	−0.452132	+	0.452132i	−0.0216781	+	0.0216781i
$436$	18.8963	+	12.7183i	0.904970	+	0.609095i
$437$	−30.5020	−	30.5020i	−1.45911	−	1.45911i
$438$	9.53177	−	0.922610i	0.455445	−	0.0440840i
$439$		−	10.9067i		−	0.520549i	−0.965535	−	0.260275i	$-0.916187\pi$
$439$		−	10.9067i		−	0.520549i	0.965535	−	0.260275i	$-0.0838131\pi$
$440$	0.467070	−	0.863318i	0.0222667	−	0.0411571i
$441$		−	2.62799i		−	0.125143i
$442$	−2.09443	−	21.6382i	−0.0996221	−	1.02923i
$443$	18.3910	+	18.3910i	0.873782	+	0.873782i	0.992882	−	0.119100i	$-0.0380010\pi$
$443$	18.3910	+	18.3910i	0.873782	+	0.873782i	−0.119100	+	0.992882i	$0.538001\pi$
$444$	3.06988	+	15.7094i	0.145690	+	0.745533i
$445$	−3.36461	+	3.36461i	−0.159498	+	0.159498i
$446$	−16.5254	+	20.0673i	−0.782500	+	0.950215i
$447$	−6.28788			−0.297407
$448$	14.0015	−	9.15244i	0.661507	−	0.432412i
$449$	−0.323178			−0.0152517			−0.00762586	−	0.999971i	$-0.502427\pi$
$449$	−0.323178			−0.0152517			−0.00762586	+	0.999971i	$0.502427\pi$
$450$	4.38676	−	5.32698i	0.206794	−	0.251116i
$451$	−3.47400	+	3.47400i	−0.163584	+	0.163584i
$452$	−7.35158	−	37.6199i	−0.345789	−	1.76949i
$453$	−1.97905	−	1.97905i	−0.0929839	−	0.0929839i
$454$	1.89244	+	19.5514i	0.0888166	+	0.917591i
$455$		−	4.45654i		−	0.208926i
$456$	9.44505	−	17.4580i	0.442305	−	0.817544i
$457$			15.7651i			0.737458i	0.929537	+	0.368729i	$0.120207\pi$
$457$			15.7651i			0.737458i	−0.929537	+	0.368729i	$0.879793\pi$
$458$	31.9930	−	3.09671i	1.49494	−	0.144700i
$459$	1.76984	+	1.76984i	0.0826090	+	0.0826090i
$460$	−3.53930	−	2.38215i	−0.165021	−	0.111068i
$461$	6.38169	−	6.38169i	0.297225	−	0.297225i	−0.542701	−	0.839926i	$-0.682598\pi$
$461$	6.38169	−	6.38169i	0.297225	−	0.297225i	0.839926	+	0.542701i	$0.182598\pi$
$462$	−2.28265	−	1.87976i	−0.106199	−	0.0874544i
$463$	−5.69727			−0.264775			−0.132387	−	0.991198i	$-0.542264\pi$
$463$	−5.69727			−0.264775			−0.132387	+	0.991198i	$0.542264\pi$
$464$	2.86612	−	6.78984i	0.133056	−	0.315210i
$465$	−2.99124			−0.138716
$466$	18.7406	+	15.4328i	0.868141	+	0.714912i
$467$	7.55326	−	7.55326i	0.349523	−	0.349523i	−0.510409	−	0.859932i	$-0.670506\pi$
$467$	7.55326	−	7.55326i	0.349523	−	0.349523i	0.859932	+	0.510409i	$0.170506\pi$
$468$	6.85852	−	10.1901i	0.317035	−	0.471039i
$469$	0.450927	+	0.450927i	0.0208219	+	0.0208219i
$470$	−2.67266	+	0.258695i	−0.123281	+	0.0119327i
$471$			10.3682i			0.477740i
$472$	−9.16403	−	30.7678i	−0.421809	−	1.41620i
$473$		−	8.46267i		−	0.389114i
$474$	1.19510	+	12.3470i	0.0548929	+	0.567116i
$475$	24.2138	+	24.2138i	1.11101	+	1.11101i
$476$	−10.2726	+	2.00745i	−0.470845	+	0.0920112i
$477$	2.63883	−	2.63883i	0.120824	−	0.120824i
$478$	−4.66364	+	5.66321i	−0.213310	+	0.259029i
$479$	−8.83700			−0.403773			−0.201887	−	0.979409i	$-0.564707\pi$
$479$	−8.83700			−0.403773			−0.201887	+	0.979409i	$0.564707\pi$
$480$	0.585647	−	1.87374i	0.0267310	−	0.0855242i
$481$	−49.1529			−2.24118
$482$	−11.2942	+	13.7150i	−0.514439	+	0.624699i
$483$	−9.08808	+	9.08808i	−0.413522	+	0.413522i
$484$	1.96287	−	0.383579i	0.0892215	−	0.0174354i
$485$	3.17206	+	3.17206i	0.144036	+	0.144036i
$486$	0.136250	+	1.40763i	0.00618040	+	0.0638516i
$487$			12.3676i			0.560429i	0.959937	+	0.280215i	$0.0904057\pi$
$487$			12.3676i			0.560429i	−0.959937	+	0.280215i	$0.909594\pi$
$488$	−3.31916	+	0.988593i	−0.150251	+	0.0447515i
$489$			18.2655i			0.825994i
$490$	1.28378	−	0.124261i	0.0579951	−	0.00561353i
$491$	12.7536	+	12.7536i	0.575560	+	0.575560i	0.933677	−	0.358117i	$-0.116581\pi$
$491$	12.7536	+	12.7536i	0.575560	+	0.575560i	−0.358117	+	0.933677i	$0.616581\pi$
$492$	−5.48646	+	8.15157i	−0.247349	+	0.367501i
$493$	−3.26092	+	3.26092i	−0.146864	+	0.146864i
$494$	47.0522	+	38.7474i	2.11698	+	1.74333i
$495$	−0.347036			−0.0155981
$496$	31.9412	−	12.9794i	1.43420	−	0.582792i
$497$	28.9410			1.29818
$498$	4.64359	+	3.82398i	0.208084	+	0.171357i
$499$	−18.0121	+	18.0121i	−0.806332	+	0.806332i	−0.984077	−	0.177744i	$-0.943120\pi$
$499$	−18.0121	+	18.0121i	−0.806332	+	0.806332i	0.177744	+	0.984077i	$0.443120\pi$
$500$	5.68865	+	3.82878i	0.254404	+	0.171228i
$501$	2.54308	+	2.54308i	0.113616	+	0.113616i
$502$	−19.3063	+	1.86872i	−0.861681	+	0.0834049i
$503$			11.9339i			0.532106i	0.963958	+	0.266053i	$0.0857196\pi$
$503$			11.9339i			0.532106i	−0.963958	+	0.266053i	$0.914280\pi$
$504$	−5.20160	−	2.81415i	−0.231697	−	0.125352i
$505$		−	3.23887i		−	0.144128i
$506$	−0.837494	−	8.65240i	−0.0372312	−	0.384646i
$507$	17.4793	+	17.4793i	0.776284	+	0.776284i
$508$	−5.56329	−	28.4688i	−0.246831	−	1.26310i
$509$	−14.9505	+	14.9505i	−0.662668	+	0.662668i	−0.956008	−	0.293340i	$-0.905233\pi$
$509$	−14.9505	+	14.9505i	−0.662668	+	0.662668i	0.293340	+	0.956008i	$0.405233\pi$
$510$	−0.780882	+	0.948250i	−0.0345780	+	0.0419892i
$511$	14.1587			0.626344
$512$	1.87672	+	22.5495i	0.0829402	+	0.996555i
$513$	−7.01774			−0.309841
$514$	6.48200	−	7.87130i	0.285909	−	0.347188i
$515$	−3.30490	+	3.30490i	−0.145631	+	0.145631i
$516$	−3.24610	−	16.6111i	−0.142902	−	0.731264i
$517$	−3.86869	−	3.86869i	−0.170145	−	0.170145i
$518$	2.28004	+	23.5557i	0.100179	+	1.03498i
$519$		−	12.8686i		−	0.564869i
$520$	5.30217	+	2.86856i	0.232516	+	0.125795i
$521$			38.0440i			1.66674i	0.552716	+	0.833370i	$0.313592\pi$
$521$			38.0440i			1.66674i	−0.552716	+	0.833370i	$0.686408\pi$
$522$	−2.59356	+	0.251039i	−0.113517	+	0.0109877i
$523$	−7.99590	−	7.99590i	−0.349636	−	0.349636i	0.510338	−	0.859974i	$-0.329520\pi$
$523$	−7.99590	−	7.99590i	−0.349636	−	0.349636i	−0.859974	+	0.510338i	$0.829520\pi$
$524$	10.2860	+	6.92309i	0.449348	+	0.302436i
$525$	7.21450	−	7.21450i	0.314867	−	0.314867i
$526$	−19.2039	−	15.8144i	−0.837329	−	0.689538i
$527$	−21.5738			−0.939768
$528$	3.70573	−	1.50583i	0.161271	−	0.0655330i
$529$	−14.7828			−0.642728
$530$	1.41384	+	1.16430i	0.0614135	+	0.0505738i
$531$	−8.02589	+	8.02589i	−0.348294	+	0.348294i
$532$	16.3865	−	24.3464i	0.710443	−	1.05555i
$533$	−21.3360	−	21.3360i	−0.924164	−	0.924164i
$534$	−19.3004	+	1.86815i	−0.835209	+	0.0808426i
$535$		−	6.50546i		−	0.281256i
$536$	−0.826742	+	0.246240i	−0.0357098	+	0.0106360i
$537$		−	3.51787i		−	0.151807i
$538$	0.667215	+	6.89320i	0.0287657	+	0.297187i
$539$	1.85827	+	1.85827i	0.0800415	+	0.0800415i
$540$	−0.681187	+	0.133116i	−0.0293136	+	0.00572839i
$541$	−8.26526	+	8.26526i	−0.355351	+	0.355351i	−0.862096	−	0.506745i	$-0.830849\pi$
$541$	−8.26526	+	8.26526i	−0.355351	+	0.355351i	0.506745	+	0.862096i	$0.330849\pi$
$542$	21.0915	−	25.6121i	0.905957	−	1.10013i
$543$	14.8676			0.638031
$544$	4.22387	−	13.5140i	0.181097	−	0.579408i
$545$	3.95235			0.169300
$546$	11.5448	−	14.0192i	0.494071	−	0.599966i
$547$	1.23113	−	1.23113i	0.0526392	−	0.0526392i	−0.680297	−	0.732936i	$-0.738149\pi$
$547$	1.23113	−	1.23113i	0.0526392	−	0.0526392i	0.732936	+	0.680297i	$0.238149\pi$
$548$	−9.90016	+	1.93466i	−0.422914	+	0.0826447i
$549$	0.865814	+	0.865814i	0.0369521	+	0.0369521i
$550$	0.664839	+	6.86865i	0.0283488	+	0.292880i
$551$		−	12.9301i		−	0.550842i
$552$	−4.96278	−	16.6623i	−0.211230	−	0.709195i
$553$			18.3405i			0.779917i
$554$	−4.27513	+	0.413804i	−0.181633	+	0.0175808i
$555$	1.96393	+	1.96393i	0.0833641	+	0.0833641i
$556$	10.3068	−	15.3134i	0.437106	−	0.649435i
$557$	−4.27351	+	4.27351i	−0.181074	+	0.181074i	−0.791824	−	0.610749i	$-0.790868\pi$
$557$	−4.27351	+	4.27351i	−0.181074	+	0.181074i	0.610749	+	0.791824i	$0.290868\pi$
$558$	−9.40973	−	7.74889i	−0.398346	−	0.328037i
$559$	51.9745			2.19829
$560$	1.12876	−	2.67404i	0.0476989	−	0.112999i
$561$	−2.50293			−0.105674
$562$	−8.87767	−	7.31074i	−0.374482	−	0.308385i
$563$	0.369648	−	0.369648i	0.0155788	−	0.0155788i	−0.699274	−	0.714853i	$-0.746493\pi$
$563$	0.369648	−	0.369648i	0.0155788	−	0.0155788i	0.714853	+	0.699274i	$0.246493\pi$
$564$	−9.07770	−	6.10980i	−0.382240	−	0.257269i
$565$	−4.70311	−	4.70311i	−0.197861	−	0.197861i
$566$	0.410307	−	0.0397150i	0.0172465	−	0.00166934i
$567$			2.09093i			0.0878110i
$568$	−18.6286	+	34.4325i	−0.781638	+	1.44476i
$569$		−	36.3587i		−	1.52423i	−0.647439	−	0.762117i	$-0.724160\pi$
$569$		−	36.3587i		−	1.52423i	0.647439	−	0.762117i	$-0.275840\pi$
$570$	−0.331823	−	3.42816i	−0.0138985	−	0.143590i
$571$	−1.49254	−	1.49254i	−0.0624607	−	0.0624607i	0.675186	−	0.737647i	$-0.264063\pi$
$571$	−1.49254	−	1.49254i	−0.0624607	−	0.0624607i	−0.737647	+	0.675186i	$0.764063\pi$
$572$	2.35580	+	12.0552i	0.0985009	+	0.504054i
$573$	19.3162	−	19.3162i	0.806948	−	0.806948i
$574$	−9.23522	+	11.2146i	−0.385471	+	0.468089i
$575$	29.9936			1.25082
$576$	6.69628	−	4.37720i	0.279011	−	0.182383i
$577$	12.5047			0.520577			0.260288	−	0.965531i	$-0.416182\pi$
$577$	12.5047			0.520577			0.260288	+	0.965531i	$0.416182\pi$
$578$	9.65113	−	11.7197i	0.401434	−	0.487474i
$579$	−7.87008	+	7.87008i	−0.327069	+	0.327069i
$580$	−0.245265	−	1.25508i	−0.0101841	−	0.0521145i
$581$	6.28897	+	6.28897i	0.260910	+	0.260910i
$582$	1.76123	+	18.1958i	0.0730054	+	0.754241i
$583$			3.73188i			0.154559i
$584$	−9.11361	+	16.8453i	−0.377124	+	0.697065i
$585$		−	2.13136i		−	0.0881210i
$586$	−14.2264	+	1.37702i	−0.587689	+	0.0568843i
$587$	−31.6252	−	31.6252i	−1.30531	−	1.30531i	−0.924759	−	0.380553i	$-0.875734\pi$
$587$	−31.6252	−	31.6252i	−1.30531	−	1.30531i	−0.380553	−	0.924759i	$-0.624266\pi$
$588$	4.36035	+	2.93476i	0.179818	+	0.121027i
$589$	42.7720	−	42.7720i	1.76239	−	1.76239i
$590$	−4.30014	−	3.54116i	−0.177034	−	0.145787i
$591$	11.8788			0.488629
$592$	−29.4930	−	12.4496i	−1.21216	−	0.511674i
$593$	−8.29924			−0.340809			−0.170404	−	0.985374i	$-0.554507\pi$
$593$	−8.29924			−0.340809			−0.170404	+	0.985374i	$0.554507\pi$
$594$	−1.09169	−	0.899005i	−0.0447926	−	0.0368866i
$595$	−1.28425	+	1.28425i	−0.0526490	+	0.0526490i
$596$	7.02186	−	10.4328i	0.287627	−	0.427344i
$597$	3.33060	+	3.33060i	0.136313	+	0.136313i
$598$	53.1398	−	5.14357i	2.17305	−	0.210336i
$599$			3.70055i			0.151200i	0.997138	+	0.0756002i	$0.0240873\pi$
$599$			3.70055i			0.151200i	−0.997138	+	0.0756002i	$0.975913\pi$
$600$	3.93966	+	13.2273i	0.160836	+	0.540001i
$601$			45.7480i			1.86610i	0.359745	+	0.933051i	$0.382864\pi$
$601$			45.7480i			1.86610i	−0.359745	+	0.933051i	$0.617136\pi$
$602$	−2.41092	−	24.9079i	−0.0982617	−	1.01517i
$603$	0.215658	+	0.215658i	0.00878228	+	0.00878228i
$604$	5.49368	−	1.07356i	0.223535	−	0.0436826i
$605$	0.245391	−	0.245391i	0.00997658	−	0.00997658i
$606$	8.39037	−	10.1887i	0.340835	−	0.413887i
$607$	−6.34206			−0.257416			−0.128708	−	0.991683i	$-0.541083\pi$
$607$	−6.34206			−0.257416			−0.128708	+	0.991683i	$0.541083\pi$
$608$	18.4185	+	35.1670i	0.746970	+	1.42621i
$609$	−3.85253			−0.156112
$610$	−0.382012	+	0.463889i	−0.0154672	+	0.0187823i
$611$	23.7600	−	23.7600i	0.961228	−	0.961228i
$612$	−4.91293	+	0.960072i	−0.198593	+	0.0388086i
$613$	7.34810	+	7.34810i	0.296787	+	0.296787i	0.839754	−	0.542967i	$-0.182699\pi$
$613$	7.34810	+	7.34810i	0.296787	+	0.296787i	−0.542967	+	0.839754i	$0.682699\pi$
$614$	−1.54493	−	15.9611i	−0.0623482	−	0.644138i
$615$			1.70498i			0.0687514i
$616$	5.66799	−	1.68818i	0.228370	−	0.0680186i
$617$			16.5554i			0.666496i	0.942839	+	0.333248i	$0.108145\pi$
$617$			16.5554i			0.666496i	−0.942839	+	0.333248i	$0.891855\pi$
$618$	−18.9579	+	1.83499i	−0.762597	+	0.0738142i
$619$	−16.3152	−	16.3152i	−0.655762	−	0.655762i	0.298612	−	0.954374i	$-0.403476\pi$
$619$	−16.3152	−	16.3152i	−0.655762	−	0.655762i	−0.954374	+	0.298612i	$0.903476\pi$
$620$	3.34041	−	4.96305i	0.134154	−	0.199321i
$621$	−4.34642	+	4.34642i	−0.174416	+	0.174416i
$622$	−0.00757579	−	0.00623865i	−0.000303761	−	0.000250147i
$623$	−28.6692			−1.14861
$624$	9.24826	+	22.7592i	0.370227	+	0.911098i
$625$	−23.2080			−0.928320
$626$	−9.64786	−	7.94499i	−0.385606	−	0.317546i
$627$	4.96229	−	4.96229i	0.198175	−	0.198175i
$628$	−17.2028	−	11.5784i	−0.686466	−	0.462030i
$629$	14.1645	+	14.1645i	0.564774	+	0.564774i
$630$	−1.02142	+	0.0988667i	−0.0406944	+	0.00393894i
$631$		−	36.5383i		−	1.45457i	−0.686337	−	0.727284i	$-0.740782\pi$
$631$		−	36.5383i		−	1.45457i	0.686337	−	0.727284i	$-0.259218\pi$
$632$	−21.8206	−	11.8053i	−0.867977	−	0.469590i
$633$			6.39289i			0.254094i
$634$	−1.64049	−	16.9484i	−0.0651521	−	0.673106i
$635$	−3.55907	−	3.55907i	−0.141237	−	0.141237i
$636$	1.43147	+	7.32519i	0.0567615	+	0.290463i
$637$	−11.4128	+	11.4128i	−0.452192	+	0.452192i
$638$	1.65641	−	2.01143i	0.0655779	−	0.0796334i
$639$	13.8412			0.547548
$640$	2.45489	+	3.06416i	0.0970379	+	0.121122i
$641$	−25.8942			−1.02276			−0.511379	−	0.859355i	$-0.670865\pi$
$641$	−25.8942			−1.02276			−0.511379	+	0.859355i	$0.670865\pi$
$642$	16.8526	−	20.4646i	0.665117	−	0.807673i
$643$	1.14029	−	1.14029i	0.0449685	−	0.0449685i	−0.684265	−	0.729233i	$-0.739877\pi$
$643$	1.14029	−	1.14029i	0.0449685	−	0.0449685i	0.729233	+	0.684265i	$0.239877\pi$
$644$	−4.92995	−	25.2278i	−0.194267	−	0.994114i
$645$	−2.07667	−	2.07667i	−0.0817687	−	0.0817687i
$646$	−2.39321	−	24.7250i	−0.0941596	−	0.972791i
$647$			39.0312i			1.53447i	0.641364	+	0.767237i	$0.278369\pi$
$647$			39.0312i			1.53447i	−0.641364	+	0.767237i	$0.721631\pi$
$648$	−2.48769	−	1.34588i	−0.0977257	−	0.0528712i
$649$		−	11.3503i		−	0.445539i
$650$	−42.1846	+	4.08319i	−1.65462	+	0.160156i
$651$	−12.7439	−	12.7439i	−0.499473	−	0.499473i
$652$	−30.3060	−	20.3976i	−1.18687	−	0.798832i
$653$	−22.9879	+	22.9879i	−0.899586	+	0.899586i	−0.995399	−	0.0958135i	$-0.969455\pi$
$653$	−22.9879	+	22.9879i	−0.899586	+	0.899586i	0.0958135	+	0.995399i	$0.469455\pi$
$654$	12.4331	+	10.2387i	0.486174	+	0.400363i
$655$	2.15143			0.0840632
$656$	−7.39812	−	18.2062i	−0.288848	−	0.710832i
$657$	6.77148			0.264180
$658$	−12.4888	−	10.2845i	−0.486862	−	0.400930i
$659$	−4.68103	+	4.68103i	−0.182347	+	0.182347i	−0.792378	−	0.610031i	$-0.791157\pi$
$659$	−4.68103	+	4.68103i	−0.182347	+	0.182347i	0.610031	+	0.792378i	$0.291157\pi$
$660$	0.387545	−	0.575799i	0.0150852	−	0.0224130i
$661$	14.8273	+	14.8273i	0.576713	+	0.576713i	0.933996	−	0.357283i	$-0.116297\pi$
$661$	14.8273	+	14.8273i	0.576713	+	0.576713i	−0.357283	+	0.933996i	$0.616297\pi$
$662$	19.2072	−	1.85913i	0.746509	−	0.0722570i
$663$		−	15.3720i		−	0.597001i
$664$	−11.5304	+	3.43425i	−0.447464	+	0.133275i
$665$		−	5.09228i		−	0.197470i
$666$	1.09044	+	11.2657i	0.0422536	+	0.436535i
$667$	−8.00825	−	8.00825i	−0.310081	−	0.310081i
$668$	−7.05938	+	1.37953i	−0.273136	+	0.0533755i
$669$	−12.9979	+	12.9979i	−0.502530	+	0.502530i
$670$	−0.0951520	+	0.115546i	−0.00367604	+	0.00446394i
$671$	−1.22445			−0.0472692
$672$	10.4780	−	5.48780i	0.404197	−	0.211696i
$673$	9.18516			0.354062			0.177031	−	0.984205i	$-0.443351\pi$
$673$	9.18516			0.354062			0.177031	+	0.984205i	$0.443351\pi$
$674$	9.37109	−	11.3796i	0.360961	−	0.438326i
$675$	3.45037	−	3.45037i	0.132805	−	0.132805i
$676$	−48.5212	+	9.48189i	−1.86620	+	0.364688i
$677$	−16.7815	−	16.7815i	−0.644964	−	0.644964i	0.306808	−	0.951772i	$-0.400739\pi$
$677$	−16.7815	−	16.7815i	−0.644964	−	0.644964i	−0.951772	+	0.306808i	$0.900739\pi$
$678$	−2.61132	−	26.9784i	−0.100287	−	1.03610i
$679$			27.0285i			1.03726i
$680$	−0.701296	−	2.35457i	−0.0268935	−	0.0902937i
$681$			13.8895i			0.532247i
$682$	12.1330	−	1.17439i	0.464596	−	0.0449697i
$683$	−33.2648	−	33.2648i	−1.27284	−	1.27284i	−0.944589	−	0.328254i	$-0.893540\pi$
$683$	−33.2648	−	33.2648i	−1.27284	−	1.27284i	−0.328254	−	0.944589i	$-0.606460\pi$
$684$	7.83691	−	11.6438i	0.299652	−	0.445211i
$685$	−1.23768	+	1.23768i	−0.0472895	+	0.0472895i
$686$	21.9774	+	18.0983i	0.839100	+	0.690997i
$687$	22.7282			0.867135
$688$	31.1861	+	13.1642i	1.18896	+	0.501881i
$689$	−22.9198			−0.873174
$690$	−2.32874	−	1.91771i	−0.0886536	−	0.0730061i
$691$	−27.7382	+	27.7382i	−1.05521	+	1.05521i	−0.0568273	+	0.998384i	$0.518098\pi$
$691$	−27.7382	+	27.7382i	−1.05521	+	1.05521i	−0.998384	+	0.0568273i	$0.981902\pi$
$692$	21.3515	+	14.3707i	0.811662	+	0.546294i
$693$	−1.47851	−	1.47851i	−0.0561641	−	0.0561641i
$694$	19.8924	−	1.92545i	0.755106	−	0.0730891i
$695$		−	3.20295i		−	0.121495i
$696$	2.47978	−	4.58355i	0.0939958	−	0.173739i
$697$			12.2968i			0.465776i
$698$	1.39035	+	14.3642i	0.0526256	+	0.543691i
$699$	12.1386	+	12.1386i	0.459124	+	0.459124i
$700$	3.91360	+	20.0269i	0.147920	+	0.756945i
$701$	−20.9709	+	20.9709i	−0.792061	+	0.792061i	−0.981829	−	0.189768i	$-0.939227\pi$
$701$	−20.9709	+	20.9709i	−0.792061	+	0.792061i	0.189768	+	0.981829i	$0.439227\pi$
$702$	5.52135	−	6.70475i	0.208390	−	0.253055i
$703$	−56.1647			−2.11829
$704$	−1.63983	+	7.83013i	−0.0618035	+	0.295109i
$705$	−1.89869			−0.0715087
$706$	−18.0689	+	21.9417i	−0.680033	+	0.825786i
$707$	13.7989	−	13.7989i	0.518961	−	0.518961i
$708$	−4.35375	−	22.2792i	−0.163624	−	0.837305i
$709$	−35.1665	−	35.1665i	−1.32071	−	1.32071i	−0.913204	−	0.407502i	$-0.866400\pi$
$709$	−35.1665	−	35.1665i	−1.32071	−	1.32071i	−0.407502	−	0.913204i	$-0.633600\pi$
$710$	0.654459	+	6.76141i	0.0245614	+	0.253751i
$711$			8.77144i			0.328955i
$712$	18.4537	−	34.1092i	0.691581	−	1.27830i
$713$		−	52.9815i		−	1.98417i
$714$	−7.36680	+	0.713057i	−0.275696	+	0.0266855i
$715$	1.50710	+	1.50710i	0.0563624	+	0.0563624i
$716$	5.83683	+	3.92851i	0.218132	+	0.146815i
$717$	−3.66815	+	3.66815i	−0.136990	+	0.136990i
$718$	−18.5356	−	15.2641i	−0.691744	−	0.569650i
$719$	8.81360			0.328692			0.164346	−	0.986403i	$-0.447449\pi$
$719$	8.81360			0.328692			0.164346	+	0.986403i	$0.447449\pi$
$720$	0.539837	−	1.27887i	0.0201185	−	0.0476608i
$721$	−28.1604			−1.04875
$722$	33.0222	+	27.1937i	1.22896	+	1.01204i
$723$	−8.88341	+	8.88341i	−0.330378	+	0.330378i
$724$	−16.6031	+	24.6683i	−0.617050	+	0.916788i
$725$	6.35729	+	6.35729i	0.236104	+	0.236104i
$726$	1.40763	−	0.136250i	0.0522422	−	0.00505669i
$727$			11.1043i			0.411835i	0.978569	+	0.205917i	$0.0660178\pi$
$727$			11.1043i			0.411835i	−0.978569	+	0.205917i	$0.933982\pi$
$728$	10.3682	+	34.8106i	0.384269	+	1.29017i
$729$			1.00000i			0.0370370i
$730$	0.320179	+	3.30787i	0.0118504	+	0.122430i
$731$	−14.9776	−	14.9776i	−0.553965	−	0.553965i
$732$	−2.40343	+	0.469672i	−0.0888334	+	0.0173596i
$733$	28.7471	−	28.7471i	1.06180	−	1.06180i	0.0638369	−	0.997960i	$-0.479666\pi$
$733$	28.7471	−	28.7471i	1.06180	−	1.06180i	0.997960	−	0.0638369i	$-0.0203338\pi$
$734$	−10.7511	+	13.0554i	−0.396829	+	0.481882i
$735$	0.912009			0.0336399
$736$	33.1881	+	10.3731i	1.22333	+	0.382357i
$737$	−0.304987			−0.0112343
$738$	−4.41679	+	5.36345i	−0.162584	+	0.197431i
$739$	−29.1265	+	29.1265i	−1.07143	+	1.07143i	−0.0741904	+	0.997244i	$0.523637\pi$
$739$	−29.1265	+	29.1265i	−1.07143	+	1.07143i	−0.997244	+	0.0741904i	$0.976363\pi$
$740$	−5.45171	+	1.06536i	−0.200409	+	0.0391634i
$741$	30.4765	+	30.4765i	1.11958	+	1.11958i
$742$	1.06317	+	10.9839i	0.0390302	+	0.403233i
$743$			16.7569i			0.614751i	0.951588	+	0.307376i	$0.0994508\pi$
$743$			16.7569i			0.614751i	−0.951588	+	0.307376i	$0.900549\pi$
$744$	23.3650	−	6.95913i	0.856603	−	0.255134i
$745$		−	2.18212i		−	0.0799467i
$746$	14.2799	−	1.38220i	0.522824	−	0.0506058i
$747$	3.00773	+	3.00773i	0.110047	+	0.110047i
$748$	2.79509	−	4.15284i	0.102199	−	0.151843i
$749$	27.7159	−	27.7159i	1.01272	−	1.01272i
$750$	3.74293	+	3.08230i	0.136673	+	0.112550i
$751$	34.5796			1.26183			0.630914	−	0.775853i	$-0.282680\pi$
$751$	34.5796			1.26183			0.630914	+	0.775853i	$0.282680\pi$
$752$	20.2747	−	8.23865i	0.739340	−	0.300433i
$753$	−13.7154			−0.499817
$754$	12.3535	+	10.1730i	0.449887	+	0.370481i
$755$	0.686801	−	0.686801i	0.0249953	−	0.0249953i
$756$	−3.46926	−	2.33501i	−0.126176	−	0.0849234i
$757$	24.0808	+	24.0808i	0.875232	+	0.875232i	0.993037	−	0.117805i	$-0.0375857\pi$
$757$	24.0808	+	24.0808i	0.875232	+	0.875232i	−0.117805	+	0.993037i	$0.537586\pi$
$758$	−35.3263	+	3.41935i	−1.28311	+	0.124196i
$759$		−	6.14677i		−	0.223114i
$760$	6.05854	+	3.27777i	0.219766	+	0.118897i
$761$			10.2180i			0.370402i	0.982701	+	0.185201i	$0.0592936\pi$
$761$			10.2180i			0.370402i	−0.982701	+	0.185201i	$0.940706\pi$
$762$	−1.97611	−	20.4158i	−0.0715871	−	0.739587i
$763$	16.8386	+	16.8386i	0.609598	+	0.609598i
$764$	10.4783	+	53.6204i	0.379093	+	1.93992i
$765$	−0.614198	+	0.614198i	−0.0222064	+	0.0222064i
$766$	−16.5546	+	20.1027i	−0.598140	+	0.726341i
$767$	69.7094			2.51706
$768$	−0.215306	+	15.9986i	−0.00776920	+	0.577298i
$769$	−35.6406			−1.28523			−0.642617	−	0.766188i	$-0.722151\pi$
$769$	−35.6406			−1.28523			−0.642617	+	0.766188i	$0.722151\pi$
$770$	0.652345	−	0.792163i	0.0235089	−	0.0285476i
$771$	5.09837	−	5.09837i	0.183613	−	0.183613i
$772$	−4.26923	−	21.8467i	−0.153653	−	0.786280i
$773$	−16.8666	−	16.8666i	−0.606649	−	0.606649i	0.335420	−	0.942069i	$-0.391122\pi$
$773$	−16.8666	−	16.8666i	−0.606649	−	0.606649i	−0.942069	+	0.335420i	$0.891122\pi$
$774$	−1.15303	−	11.9123i	−0.0414450	−	0.428180i
$775$			42.0590i			1.51080i
$776$	−32.1572	−	17.3976i	−1.15438	−	0.624536i
$777$			16.7343i			0.600338i
$778$	15.9344	−	1.54234i	0.571274	−	0.0552955i
$779$	−24.3796	−	24.3796i	−0.873490	−	0.873490i
$780$	3.53634	+	2.38015i	0.126621	+	0.0852232i
$781$	−9.78718	+	9.78718i	−0.350213	+	0.350213i
$782$	−16.7956	−	13.8311i	−0.600609	−	0.494600i
$783$	−1.84249			−0.0658453
$784$	−9.73865	+	3.95732i	−0.347809	+	0.141333i
$785$	−3.59813			−0.128423
$786$	6.76787	+	5.57332i	0.241402	+	0.198794i
$787$	−19.2350	+	19.2350i	−0.685653	+	0.685653i	−0.961268	−	0.275615i	$-0.911119\pi$
$787$	−19.2350	+	19.2350i	−0.685653	+	0.685653i	0.275615	+	0.961268i	$0.411119\pi$
$788$	−13.2654	+	19.7092i	−0.472560	+	0.702112i
$789$	−12.4387	−	12.4387i	−0.442829	−	0.442829i
$790$	−4.28485	+	0.414744i	−0.152448	+	0.0147559i
$791$		−	40.0743i		−	1.42488i
$792$	2.71074	−	0.807380i	0.0963221	−	0.0286890i
$793$		−	7.52009i		−	0.267046i
$794$	−1.96586	−	20.3099i	−0.0697657	−	0.720770i
$795$	0.915770	+	0.915770i	0.0324790	+	0.0324790i
$796$	−9.24549	+	1.80673i	−0.327698	+	0.0640378i
$797$	22.3569	−	22.3569i	0.791922	−	0.791922i	−0.189885	−	0.981806i	$-0.560811\pi$
$797$	22.3569	−	22.3569i	0.791922	−	0.791922i	0.981806	+	0.189885i	$0.0608114\pi$
$798$	13.1917	−	16.0191i	0.466980	−	0.567069i
$799$	−13.6939			−0.484456
$800$	−26.3461	−	8.23460i	−0.931475	−	0.291137i
$801$	−13.7112			−0.484462
$802$	−27.2899	+	33.1390i	−0.963639	+	1.17018i
$803$	−4.78816	+	4.78816i	−0.168970	+	0.168970i
$804$	−0.598650	+	0.116987i	−0.0211128	+	0.00412580i
$805$	−3.15389	−	3.15389i	−0.111160	−	0.111160i
$806$	7.21266	+	74.5161i	0.254055	+	2.62472i
$807$			4.89701i			0.172383i
$808$	7.53523	+	25.2992i	0.265089	+	0.890024i
$809$		−	36.0085i		−	1.26599i	−0.774156	−	0.632995i	$-0.781825\pi$
$809$		−	36.0085i		−	1.26599i	0.774156	−	0.632995i	$-0.218175\pi$
$810$	−0.488500	+	0.0472835i	−0.0171641	+	0.00166137i
$811$	−1.76770	−	1.76770i	−0.0620723	−	0.0620723i	0.675389	−	0.737462i	$-0.263976\pi$
$811$	−1.76770	−	1.76770i	−0.0620723	−	0.0620723i	−0.737462	+	0.675389i	$0.763976\pi$
$812$	4.30223	−	6.39209i	0.150979	−	0.224318i
$813$	16.5894	−	16.5894i	0.581815	−	0.581815i
$814$	−8.73707	−	7.19496i	−0.306234	−	0.252183i
$815$	−6.33878			−0.222038
$816$	3.89347	−	9.22363i	0.136299	−	0.322892i
$817$	59.3888			2.07775
$818$	−33.2054	−	27.3446i	−1.16100	−	0.956080i
$819$	9.08047	−	9.08047i	0.317297	−	0.317297i
$820$	−2.82889	−	1.90400i	−0.0987890	−	0.0664905i
$821$	−25.2471	−	25.2471i	−0.881129	−	0.881129i	0.112520	−	0.993649i	$-0.464108\pi$
$821$	−25.2471	−	25.2471i	−0.881129	−	0.881129i	−0.993649	+	0.112520i	$0.964108\pi$
$822$	−7.09971	+	0.687204i	−0.247631	+	0.0239690i
$823$			13.7006i			0.477574i	0.971072	+	0.238787i	$0.0767498\pi$
$823$			13.7006i			0.477574i	−0.971072	+	0.238787i	$0.923250\pi$
$824$	18.1262	−	33.5039i	0.631455	−	1.16716i
$825$			4.87957i			0.169885i
$826$	−3.23358	−	33.4071i	−0.112511	−	1.16238i
$827$	−2.50531	−	2.50531i	−0.0871180	−	0.0871180i	0.662205	−	0.749323i	$-0.269621\pi$
$827$	−2.50531	−	2.50531i	−0.0871180	−	0.0871180i	−0.749323	+	0.662205i	$0.769621\pi$
$828$	−2.35777	−	12.0653i	−0.0819383	−	0.419299i
$829$	3.40676	−	3.40676i	0.118322	−	0.118322i	−0.645467	−	0.763788i	$-0.723337\pi$
$829$	3.40676	−	3.40676i	0.118322	−	0.118322i	0.763788	+	0.645467i	$0.223337\pi$
$830$	−1.32706	+	1.61149i	−0.0460629	+	0.0559357i
$831$	−3.03710			−0.105356
$832$	−48.0897	−	10.0712i	−1.66721	−	0.349157i
$833$	6.57769			0.227903
$834$	8.29733	−	10.0757i	0.287313	−	0.348894i
$835$	−0.882540	+	0.882540i	−0.0305415	+	0.0305415i
$836$	2.69186	+	13.7749i	0.0930999	+	0.476416i
$837$	−6.09484	−	6.09484i	−0.210668	−	0.210668i
$838$	2.86756	+	29.6257i	0.0990583	+	1.02340i
$839$		−	4.02698i		−	0.139027i	−0.997581	−	0.0695135i	$-0.977855\pi$
$839$		−	4.02698i		−	0.139027i	0.997581	−	0.0695135i	$-0.0221447\pi$
$840$	0.976612	−	1.80514i	0.0336963	−	0.0622833i
$841$			25.6052i			0.882939i
$842$	−33.3997	+	3.23287i	−1.15103	+	0.111412i
$843$	−5.75022	−	5.75022i	−0.198048	−	0.198048i
$844$	−10.6070	−	7.13912i	−0.365109	−	0.245739i
$845$	−6.06596	+	6.06596i	−0.208675	+	0.208675i
$846$	−5.97281	−	4.91860i	−0.205350	−	0.169105i
$847$	2.09093			0.0718453
$848$	−13.7525	−	5.80517i	−0.472262	−	0.199350i
$849$	0.291487			0.0100038
$850$	13.3331	+	10.9797i	0.457320	+	0.376602i
$851$	−34.7855	+	34.7855i	−1.19243	+	1.19243i
$852$	−15.4568	+	22.9652i	−0.529542	+	0.786773i
$853$	27.8488	+	27.8488i	0.953525	+	0.953525i	0.998967	−	0.0454424i	$-0.0144698\pi$
$853$	27.8488	+	27.8488i	0.953525	+	0.953525i	−0.0454424	+	0.998967i	$0.514470\pi$
$854$	−3.60388	+	0.348831i	−0.123322	+	0.0119368i
$855$		−	2.43541i		−	0.0832892i
$856$	15.1350	+	50.8150i	0.517302	+	1.73682i
$857$			48.8725i			1.66945i	0.550665	+	0.834726i	$0.314374\pi$
$857$			48.8725i			1.66945i	−0.550665	+	0.834726i	$0.685626\pi$
$858$	0.836793	+	8.64516i	0.0285676	+	0.295141i
$859$	0.647258	+	0.647258i	0.0220841	+	0.0220841i	0.718063	−	0.695978i	$-0.245029\pi$
$859$	0.647258	+	0.647258i	0.0220841	+	0.0220841i	−0.695978	+	0.718063i	$0.745029\pi$
$860$	5.76466	−	1.12651i	0.196573	−	0.0384138i
$861$	−7.26390	+	7.26390i	−0.247553	+	0.247553i
$862$	−13.5421	+	16.4446i	−0.461246	+	0.560105i
$863$	12.3289			0.419682			0.209841	−	0.977735i	$-0.432705\pi$
$863$	12.3289			0.419682			0.209841	+	0.977735i	$0.432705\pi$
$864$	5.01115	−	2.62457i	0.170483	−	0.0892896i
$865$	4.46587			0.151844
$866$	11.7796	−	14.3044i	0.400288	−	0.486083i
$867$	7.59103	−	7.59103i	0.257805	−	0.257805i
$868$	35.3761	−	6.91310i	1.20074	−	0.234646i
$869$	−6.20234	−	6.20234i	−0.210400	−	0.210400i
$870$	−0.0871195	−	0.900058i	−0.00295363	−	0.0305148i
$871$		−	1.87311i		−	0.0634680i
$872$	−30.8723	+	9.19515i	−1.04547	+	0.311387i
$873$			12.9265i			0.437496i
$874$	60.7203	−	5.87732i	2.05390	−	0.198803i
$875$	5.06918	+	5.06918i	0.171370	+	0.171370i
$876$	−7.56190	+	11.2352i	−0.255493	+	0.379601i
$877$	−31.2205	+	31.2205i	−1.05424	+	1.05424i	−0.0557984	+	0.998442i	$0.517770\pi$
$877$	−31.2205	+	31.2205i	−1.05424	+	1.05424i	−0.998442	+	0.0557984i	$0.982230\pi$
$878$	11.9068	+	9.80519i	0.401834	+	0.330909i
$879$	−10.1066			−0.340888
$880$	0.522578	+	1.28602i	0.0176161	+	0.0433518i
$881$	15.8071			0.532556			0.266278	−	0.963896i	$-0.414206\pi$
$881$	15.8071			0.532556			0.266278	+	0.963896i	$0.414206\pi$
$882$	2.86896	+	2.36258i	0.0966029	+	0.0795522i
$883$	−5.45798	+	5.45798i	−0.183676	+	0.183676i	−0.792955	−	0.609280i	$-0.791459\pi$
$883$	−5.45798	+	5.45798i	−0.183676	+	0.183676i	0.609280	+	0.792955i	$0.291459\pi$
$884$	25.5052	+	17.1664i	0.857832	+	0.577369i
$885$	−2.78527	−	2.78527i	−0.0936260	−	0.0936260i
$886$	−36.6109	+	3.54368i	−1.22997	+	0.119052i
$887$			24.5612i			0.824685i	0.911029	+	0.412342i	$0.135289\pi$
$887$			24.5612i			0.824685i	−0.911029	+	0.412342i	$0.864711\pi$
$888$	−19.9096	−	10.7714i	−0.668122	−	0.361465i
$889$		−	30.3261i		−	1.01711i
$890$	−0.648314	−	6.69792i	−0.0217315	−	0.224515i
$891$	−0.707107	−	0.707107i	−0.0236890	−	0.0236890i
$892$	−7.05090	−	36.0813i	−0.236082	−	1.20809i
$893$	27.1495	−	27.1495i	0.908522	−	0.908522i
$894$	5.65284	−	6.86443i	0.189059	−	0.229581i
$895$	1.22083			0.0408078
$896$	−2.59576	+	23.5134i	−0.0867181	+	0.785527i
$897$	37.7511			1.26047
$898$	0.290539	−	0.352811i	0.00969540	−	0.0117734i
$899$	11.2297	−	11.2297i	0.374531	−	0.374531i
$900$	1.87170	+	9.57796i	0.0623900	+	0.319265i
$901$	6.60482	+	6.60482i	0.220038	+	0.220038i
$902$	−0.669391	−	6.91568i	−0.0222883	−	0.230267i
$903$		−	17.6949i		−	0.588849i
$904$	47.6784	+	25.7948i	1.58576	+	0.857924i
$905$			5.15960i			0.171511i
$906$	3.93969	−	0.381335i	0.130887	−	0.0126690i
$907$	17.1661	+	17.1661i	0.569990	+	0.569990i	0.932126	−	0.362135i	$-0.117952\pi$
$907$	17.1661	+	17.1661i	0.569990	+	0.569990i	−0.362135	+	0.932126i	$0.617952\pi$
$908$	−23.0454	−	15.5108i	−0.764788	−	0.514745i
$909$	6.59939	−	6.59939i	0.218888	−	0.218888i
$910$	4.86517	+	4.00645i	0.161279	+	0.132813i
$911$	46.2830			1.53342			0.766712	−	0.641991i	$-0.221891\pi$
$911$	46.2830			1.53342			0.766712	+	0.641991i	$0.221891\pi$
$912$	10.5675	+	26.0059i	0.349927	+	0.861141i
$913$	−4.25357			−0.140773
$914$	−17.2106	−	14.1729i	−0.569275	−	0.468797i
$915$	−0.300469	+	0.300469i	−0.00993319	+	0.00993319i
$916$	−25.3812	+	37.7105i	−0.838620	+	1.24599i
$917$	9.16595	+	9.16595i	0.302686	+	0.302686i
$918$	−3.52321	+	0.341023i	−0.116283	+	0.0112554i
$919$		−	12.4764i		−	0.411558i	−0.978599	−	0.205779i	$-0.934027\pi$
$919$		−	12.4764i		−	0.411558i	0.978599	−	0.205779i	$-0.0659728\pi$
$920$	5.78242	−	1.72226i	0.190641	−	0.0567813i
$921$		−	11.3390i		−	0.373631i
$922$	1.22966	+	12.7040i	0.0404968	+	0.418384i
$923$	−60.1092	−	60.1092i	−1.97852	−	1.97852i
$924$	4.10424	−	0.802039i	0.135019	−	0.0263851i
$925$	27.6142	−	27.6142i	0.907949	−	0.907949i
$926$	5.12187	−	6.21966i	0.168315	−	0.204391i
$927$	−13.4679			−0.442343
$928$	4.83575	+	9.23301i	0.158741	+	0.303088i
$929$	2.07236			0.0679920			0.0339960	−	0.999422i	$-0.489177\pi$
$929$	2.07236			0.0679920			0.0339960	+	0.999422i	$0.489177\pi$
$930$	2.68914	−	3.26551i	0.0881805	−	0.107080i
$931$	−13.0409	+	13.0409i	−0.427397	+	0.427397i
$932$	−33.6958	+	6.58474i	−1.10374	+	0.215690i
$933$	−0.00490697	−	0.00490697i	−0.000160647	−	0.000160647i
$934$	1.45541	+	15.0362i	0.0476224	+	0.492001i
$935$		−	0.868607i		−	0.0284065i
$936$	4.95862	+	16.6484i	0.162078	+	0.544169i
$937$		−	21.3291i		−	0.696793i	−0.937347	−	0.348396i	$-0.886726\pi$
$937$		−	21.3291i		−	0.696793i	0.937347	−	0.348396i	$-0.113274\pi$
$938$	−0.897659	+	0.0868873i	−0.0293096	+	0.00283697i
$939$	−6.24908	−	6.24908i	−0.203931	−	0.203931i
$940$	2.12032	−	3.15029i	0.0691572	−	0.102751i
$941$	35.0731	−	35.0731i	1.14335	−	1.14335i	0.155516	−	0.987833i	$-0.450296\pi$
$941$	35.0731	−	35.0731i	1.14335	−	1.14335i	0.987833	−	0.155516i	$-0.0497041\pi$
$942$	−11.3188	−	9.32105i	−0.368788	−	0.303696i
$943$	−30.1989			−0.983412
$944$	41.8275	+	17.6562i	1.36137	+	0.574659i
$945$	−0.725629			−0.0236047
$946$	9.23862	+	7.60798i	0.300373	+	0.247357i
$947$	−20.5222	+	20.5222i	−0.666881	+	0.666881i	−0.956993	−	0.290112i	$-0.906308\pi$
$947$	−20.5222	+	20.5222i	−0.666881	+	0.666881i	0.290112	+	0.956993i	$0.406308\pi$
$948$	−14.5535	−	9.79531i	−0.472675	−	0.318137i
$949$	−29.4070	−	29.4070i	−0.954593	−	0.954593i
$950$	−48.2024	+	4.66566i	−1.56389	+	0.151374i
$951$		−	12.0403i		−	0.390434i
$952$	7.04362	−	13.0192i	0.228285	−	0.421956i
$953$			42.0643i			1.36260i	0.732006	+	0.681298i	$0.238584\pi$
$953$			42.0643i			1.36260i	−0.732006	+	0.681298i	$0.761416\pi$
$954$	0.508466	+	5.25312i	0.0164622	+	0.170076i
$955$	6.70343	+	6.70343i	0.216918	+	0.216918i
$956$	−1.98984	−	10.1825i	−0.0643559	−	0.329326i
$957$	1.30284	−	1.30284i	0.0421148	−	0.0421148i
$958$	7.94451	−	9.64728i	0.256676	−	0.311689i
$959$	−10.5461			−0.340550
$960$	1.51905	+	2.32385i	0.0490270	+	0.0750019i
$961$	43.2941			1.39658
$962$	44.1887	−	53.6598i	1.42470	−	1.73006i
$963$	13.2553	−	13.2553i	0.427145	−	0.427145i
$964$	−4.81892	−	24.6596i	−0.155207	−	0.794234i
$965$	−2.73120	−	2.73120i	−0.0879204	−	0.0879204i
$966$	−1.75115	−	18.0916i	−0.0563422	−	0.582088i
$967$		−	16.4476i		−	0.528919i	−0.964397	−	0.264460i	$-0.914806\pi$
$967$		−	16.4476i		−	0.528919i	0.964397	−	0.264460i	$-0.0851936\pi$
$968$	−1.34588	+	2.48769i	−0.0432583	+	0.0799574i
$969$		−	17.5649i		−	0.564266i
$970$	−6.31460	+	0.611211i	−0.202750	+	0.0196248i
$971$	8.03131	+	8.03131i	0.257737	+	0.257737i	0.824133	−	0.566396i	$-0.191663\pi$
$971$	8.03131	+	8.03131i	0.257737	+	0.257737i	−0.566396	+	0.824133i	$0.691663\pi$
$972$	−1.65919	−	1.11673i	−0.0532186	−	0.0358191i
$973$	13.6459	−	13.6459i	0.437467	−	0.437467i
$974$	−13.5016	−	11.1185i	−0.432619	−	0.356261i
$975$	−29.9684			−0.959758
$976$	1.90471	−	4.51225i	0.0609681	−	0.144434i
$977$	−31.1307			−0.995959			−0.497979	−	0.867189i	$-0.665925\pi$
$977$	−31.1307			−0.995959			−0.497979	+	0.867189i	$0.665925\pi$
$978$	−19.9403	−	16.4208i	−0.637620	−	0.525078i
$979$	9.69529	−	9.69529i	0.309863	−	0.309863i
$980$	−1.01847	+	1.51320i	−0.0325337	+	0.0483373i
$981$	8.05315	+	8.05315i	0.257117	+	0.257117i
$982$	−25.3885	+	2.45743i	−0.810178	+	0.0784198i
$983$			27.3465i			0.872218i	0.899894	+	0.436109i	$0.143644\pi$
$983$			27.3465i			0.872218i	−0.899894	+	0.436109i	$0.856356\pi$
$984$	−3.96664	−	13.3178i	−0.126452	−	0.424557i
$985$			4.12237i			0.131350i
$986$	−0.628333	−	6.49149i	−0.0200102	−	0.206731i
$987$	−8.08918	−	8.08918i	−0.257481	−	0.257481i
$988$	−84.6004	+	16.5324i	−2.69150	+	0.525965i
$989$	36.7823	−	36.7823i	1.16961	−	1.16961i
$990$	0.311987	−	0.378856i	0.00991560	−	0.0120408i
$991$	26.2096			0.832576			0.416288	−	0.909233i	$-0.363331\pi$
$991$	26.2096			0.832576			0.416288	+	0.909233i	$0.363331\pi$
$992$	−14.5458	+	46.5385i	−0.461831	+	1.47760i
$993$	13.6450			0.433011
$994$	−26.0181	+	31.5946i	−0.825243	+	1.00212i
$995$	−1.15584	+	1.15584i	−0.0366426	+	0.0366426i
$996$	−8.34922	+	1.63158i	−0.264555	+	0.0516987i
$997$	−30.7653	−	30.7653i	−0.974346	−	0.974346i	0.0253327	−	0.999679i	$-0.491935\pi$
$997$	−30.7653	−	30.7653i	−0.974346	−	0.974346i	−0.999679	+	0.0253327i	$0.991935\pi$
$998$	−3.47068	−	35.8566i	−0.109862	−	1.13502i
$999$			8.00325i			0.253212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.t.b.133.6	✓	40
4.3	odd	2		2112.2.t.b.1585.15		40
16.3	odd	4		2112.2.t.b.529.15		40
16.13	even	4	inner	528.2.t.b.397.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
528.2.t.b.133.6	✓	40	1.1	even	1	trivial
528.2.t.b.397.6	yes	40	16.13	even	4	inner
2112.2.t.b.529.15		40	16.3	odd	4
2112.2.t.b.1585.15		40	4.3	odd	2

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:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.899005 + 1.09169i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-0.383579 - 1.96287i) q^{4} +(-0.245391 - 0.245391i) q^{5} +(-0.136250 - 1.40763i) q^{6} -2.09093i q^{7} +(2.48769 + 1.34588i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.899005 + 1.09169i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-0.383579 - 1.96287i) q^{4} +(-0.245391 - 0.245391i) q^{5} +(-0.136250 - 1.40763i) q^{6} -2.09093i q^{7} +(2.48769 + 1.34588i) q^{8} -1.00000i q^{9} +(0.488500 - 0.0472835i) q^{10} +(0.707107 + 0.707107i) q^{11} +(1.65919 + 1.11673i) q^{12} +(-4.34278 + 4.34278i) q^{13} +(2.28265 + 1.87976i) q^{14} +0.347036 q^{15} +(-3.70573 + 1.50583i) q^{16} +2.50293 q^{17} +(1.09169 + 0.899005i) q^{18} +(-4.96229 + 4.96229i) q^{19} +(-0.387545 + 0.575799i) q^{20} +(1.47851 + 1.47851i) q^{21} +(-1.40763 + 0.136250i) q^{22} +6.14677i q^{23} +(-2.71074 + 0.807380i) q^{24} -4.87957i q^{25} +(-0.836793 - 8.64516i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-4.10424 + 0.802039i) q^{28} +(-1.30284 + 1.30284i) q^{29} +(-0.311987 + 0.378856i) q^{30} -8.61940 q^{31} +(1.68757 - 5.39927i) q^{32} -1.00000 q^{33} +(-2.25015 + 2.73243i) q^{34} +(-0.513097 + 0.513097i) q^{35} +(-1.96287 + 0.383579i) q^{36} +(5.65915 + 5.65915i) q^{37} +(-0.956164 - 9.87841i) q^{38} -6.14162i q^{39} +(-0.280190 - 0.940726i) q^{40} +4.91298i q^{41} +(-2.94327 + 0.284889i) q^{42} +(-5.98401 - 5.98401i) q^{43} +(1.11673 - 1.65919i) q^{44} +(-0.245391 + 0.245391i) q^{45} +(-6.71037 - 5.52598i) q^{46} -5.47116 q^{47} +(1.55556 - 3.68513i) q^{48} +2.62799 q^{49} +(5.32698 + 4.38676i) q^{50} +(-1.76984 + 1.76984i) q^{51} +(10.1901 + 6.85852i) q^{52} +(2.63883 + 2.63883i) q^{53} +(-1.40763 + 0.136250i) q^{54} -0.347036i q^{55} +(2.81415 - 5.20160i) q^{56} -7.01774i q^{57} +(-0.251039 - 2.59356i) q^{58} +(-8.02589 - 8.02589i) q^{59} +(-0.133116 - 0.681187i) q^{60} +(-0.865814 + 0.865814i) q^{61} +(7.74889 - 9.40973i) q^{62} -2.09093 q^{63} +(4.37720 + 6.69628i) q^{64} +2.13136 q^{65} +(0.899005 - 1.09169i) q^{66} +(-0.215658 + 0.215658i) q^{67} +(-0.960072 - 4.91293i) q^{68} +(-4.34642 - 4.34642i) q^{69} +(-0.0988667 - 1.02142i) q^{70} +13.8412i q^{71} +(1.34588 - 2.48769i) q^{72} +6.77148i q^{73} +(-11.2657 + 1.09044i) q^{74} +(3.45037 + 3.45037i) q^{75} +(11.6438 + 7.83691i) q^{76} +(1.47851 - 1.47851i) q^{77} +(6.70475 + 5.52135i) q^{78} -8.77144 q^{79} +(1.27887 + 0.539837i) q^{80} -1.00000 q^{81} +(-5.36345 - 4.41679i) q^{82} +(-3.00773 + 3.00773i) q^{83} +(2.33501 - 3.46926i) q^{84} +(-0.614198 - 0.614198i) q^{85} +(11.9123 - 1.15303i) q^{86} -1.84249i q^{87} +(0.807380 + 2.71074i) q^{88} -13.7112i q^{89} +(-0.0472835 - 0.488500i) q^{90} +(9.08047 + 9.08047i) q^{91} +(12.0653 - 2.35777i) q^{92} +(6.09484 - 6.09484i) q^{93} +(4.91860 - 5.97281i) q^{94} +2.43541 q^{95} +(2.62457 + 5.01115i) q^{96} -12.9265 q^{97} +(-2.36258 + 2.86896i) q^{98} +(0.707107 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{8}+O(q^{10}) \) 40 * q + 12 * q^8	\( 40 q + 12 q^{8} + 8 q^{10} + 16 q^{14} - 8 q^{15} + 20 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{22} - 16 q^{24} - 20 q^{28} + 20 q^{30} + 8 q^{31} + 40 q^{32} - 40 q^{33} + 20 q^{34} - 24 q^{35} + 4 q^{36} - 60 q^{38} - 56 q^{40} + 20 q^{42} + 8 q^{44} + 76 q^{46} - 64 q^{47} + 32 q^{48} - 40 q^{49} - 12 q^{50} - 8 q^{51} + 36 q^{52} - 4 q^{54} - 20 q^{56} + 12 q^{58} - 16 q^{59} - 12 q^{60} - 64 q^{61} + 68 q^{62} + 24 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{67} - 4 q^{68} - 16 q^{69} - 116 q^{70} - 12 q^{76} + 28 q^{78} - 72 q^{79} + 40 q^{80} - 40 q^{81} - 24 q^{82} + 16 q^{85} - 64 q^{86} - 12 q^{90} + 16 q^{91} + 20 q^{92} + 32 q^{93} + 104 q^{94} + 128 q^{95} - 20 q^{96} - 32 q^{97} + 36 q^{98}+O(q^{100}) \) 40 * q + 12 * q^8 + 8 * q^10 + 16 * q^14 - 8 * q^15 + 20 * q^16 + 8 * q^19 - 8 * q^20 - 4 * q^22 - 16 * q^24 - 20 * q^28 + 20 * q^30 + 8 * q^31 + 40 * q^32 - 40 * q^33 + 20 * q^34 - 24 * q^35 + 4 * q^36 - 60 * q^38 - 56 * q^40 + 20 * q^42 + 8 * q^44 + 76 * q^46 - 64 * q^47 + 32 * q^48 - 40 * q^49 - 12 * q^50 - 8 * q^51 + 36 * q^52 - 4 * q^54 - 20 * q^56 + 12 * q^58 - 16 * q^59 - 12 * q^60 - 64 * q^61 + 68 * q^62 + 24 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^67 - 4 * q^68 - 16 * q^69 - 116 * q^70 - 12 * q^76 + 28 * q^78 - 72 * q^79 + 40 * q^80 - 40 * q^81 - 24 * q^82 + 16 * q^85 - 64 * q^86 - 12 * q^90 + 16 * q^91 + 20 * q^92 + 32 * q^93 + 104 * q^94 + 128 * q^95 - 20 * q^96 - 32 * q^97 + 36 * q^98

Introduction

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