LMFDB - Embedded newform 552.2.bb.a.85.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			85.13
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02595 + 0.973358i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(0.105149 - 1.99723i) q^{4} +(2.63955 - 1.20544i) q^{5} +(1.37351 + 0.336848i) q^{6} +(3.10238 - 0.910940i) q^{7} +(1.83615 + 2.15141i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.02595 + 0.973358i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(0.105149 - 1.99723i) q^{4} +(2.63955 - 1.20544i) q^{5} +(1.37351 + 0.336848i) q^{6} +(3.10238 - 0.910940i) q^{7} +(1.83615 + 2.15141i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-1.53472 + 3.80595i) q^{10} +(1.24993 - 1.08307i) q^{11} +(-1.73703 + 0.991329i) q^{12} +(0.884534 - 3.01245i) q^{13} +(-2.29622 + 3.95430i) q^{14} +(-2.44113 - 1.56882i) q^{15} +(-3.97789 - 0.420015i) q^{16} +(-0.685217 + 4.76579i) q^{17} +(-0.459202 - 1.33758i) q^{18} +(0.389769 - 0.0560403i) q^{19} +(-2.13001 - 5.39856i) q^{20} +(-2.44360 - 2.11739i) q^{21} +(-0.228152 + 2.32781i) q^{22} +(-4.70825 - 0.912357i) q^{23} +(0.817187 - 2.70780i) q^{24} +(2.23984 - 2.58491i) q^{25} +(2.02470 + 3.95159i) q^{26} +(0.989821 - 0.142315i) q^{27} +(-1.49315 - 6.29196i) q^{28} +(4.10030 + 0.589534i) q^{29} +(4.03151 - 0.766563i) q^{30} +(-4.60234 - 2.95774i) q^{31} +(4.48994 - 3.44099i) q^{32} +(-1.58690 - 0.465957i) q^{33} +(-3.93582 - 5.55642i) q^{34} +(7.09080 - 6.14421i) q^{35} +(1.77307 + 0.925328i) q^{36} +(3.39103 + 1.54863i) q^{37} +(-0.345336 + 0.436879i) q^{38} +(-3.01245 + 0.884534i) q^{39} +(7.44001 + 3.46539i) q^{40} +(1.52135 + 3.33129i) q^{41} +(4.56800 - 0.206158i) q^{42} +(-5.82692 - 9.06687i) q^{43} +(-2.03172 - 2.61029i) q^{44} +2.90178i q^{45} +(5.71848 - 3.64678i) q^{46} +8.73791 q^{47} +(1.79727 + 3.57349i) q^{48} +(2.90616 - 1.86768i) q^{49} +(0.218080 + 4.83216i) q^{50} +(4.37969 - 2.00014i) q^{51} +(-5.92355 - 2.08338i) q^{52} +(3.74971 + 12.7704i) q^{53} +(-0.876985 + 1.10946i) q^{54} +(1.99368 - 4.36555i) q^{55} +(7.65622 + 5.00187i) q^{56} +(-0.257869 - 0.297597i) q^{57} +(-4.78053 + 3.38622i) q^{58} +(1.25320 - 4.26802i) q^{59} +(-3.38999 + 4.71055i) q^{60} +(3.95379 - 6.15222i) q^{61} +(7.60072 - 1.44522i) q^{62} +(-0.460154 + 3.20044i) q^{63} +(-1.25714 + 7.90061i) q^{64} +(-1.29656 - 9.01777i) q^{65} +(2.08163 - 1.06658i) q^{66} +(-1.33024 - 1.15266i) q^{67} +(9.44634 + 1.86966i) q^{68} +(1.77795 + 4.45409i) q^{69} +(-1.29429 + 13.2055i) q^{70} +(-8.80218 + 10.1583i) q^{71} +(-2.71975 + 0.776488i) q^{72} +(0.408778 + 2.84311i) q^{73} +(-4.98640 + 1.71186i) q^{74} +(-3.38552 - 0.486764i) q^{75} +(-0.0709417 - 0.784352i) q^{76} +(2.89115 - 4.49871i) q^{77} +(2.22965 - 3.83968i) q^{78} +(-1.26059 - 0.370142i) q^{79} +(-11.0061 + 3.68647i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-4.80336 - 1.93692i) q^{82} +(-7.35078 - 3.35699i) q^{83} +(-4.48588 + 4.65781i) q^{84} +(3.93622 + 13.4055i) q^{85} +(14.8034 + 3.63048i) q^{86} +(-1.72084 - 3.76812i) q^{87} +(4.62519 + 0.700440i) q^{88} +(-0.761319 + 0.489270i) q^{89} +(-2.82447 - 2.97708i) q^{90} -10.1515i q^{91} +(-2.31726 + 9.30754i) q^{92} +5.47081i q^{93} +(-8.96467 + 8.50512i) q^{94} +(0.961262 - 0.617766i) q^{95} +(-5.32219 - 1.91684i) q^{96} +(-4.43100 - 9.70254i) q^{97} +(-1.16366 + 4.74488i) q^{98} +(0.465957 + 1.58690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.02595	+	0.973358i	−0.725457	+	0.688268i
$2$	−1.02595	+	0.973358i	−0.725457	+	0.688268i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$4$	0.105149	−	1.99723i	0.0525746	−	0.998617i
$5$	2.63955	−	1.20544i	1.18044	−	0.539091i	0.274129	−	0.961693i	$-0.411611\pi$
$5$	2.63955	−	1.20544i	1.18044	−	0.539091i	0.906315	+	0.422602i	$0.138883\pi$
$6$	1.37351	+	0.336848i	0.560734	+	0.137517i
$7$	3.10238	−	0.910940i	1.17259	−	0.344303i	0.363276	−	0.931682i	$-0.381658\pi$
$7$	3.10238	−	0.910940i	1.17259	−	0.344303i	0.809312	+	0.587378i	$0.199840\pi$
$8$	1.83615	+	2.15141i	0.649175	+	0.760639i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	−1.53472	+	3.80595i	−0.485322	+	1.20355i
$11$	1.24993	−	1.08307i	0.376869	−	0.326559i	−0.445744	−	0.895160i	$-0.647061\pi$
$11$	1.24993	−	1.08307i	0.376869	−	0.326559i	0.822613	+	0.568602i	$0.192515\pi$
$12$	−1.73703	+	0.991329i	−0.501437	+	0.286172i
$13$	0.884534	−	3.01245i	0.245326	−	0.835502i	−0.741114	−	0.671379i	$-0.765702\pi$
$13$	0.884534	−	3.01245i	0.245326	−	0.835502i	0.986440	−	0.164123i	$-0.0524795\pi$
$14$	−2.29622	+	3.95430i	−0.613689	+	1.05683i
$15$	−2.44113	−	1.56882i	−0.630298	−	0.405068i
$16$	−3.97789	−	0.420015i	−0.994472	−	0.105004i
$17$	−0.685217	+	4.76579i	−0.166189	+	1.15587i	0.720482	+	0.693473i	$0.243921\pi$
$17$	−0.685217	+	4.76579i	−0.166189	+	1.15587i	−0.886672	+	0.462400i	$0.846989\pi$
$18$	−0.459202	−	1.33758i	−0.108235	−	0.315272i
$19$	0.389769	−	0.0560403i	0.0894191	−	0.0128565i	−0.0974600	−	0.995239i	$-0.531072\pi$
$19$	0.389769	−	0.0560403i	0.0894191	−	0.0128565i	0.186879	+	0.982383i	$0.440163\pi$
$20$	−2.13001	−	5.39856i	−0.476284	−	1.20715i
$21$	−2.44360	−	2.11739i	−0.533238	−	0.462053i
$22$	−0.228152	+	2.32781i	−0.0486421	+	0.496291i
$23$	−4.70825	−	0.912357i	−0.981738	−	0.190240i
$23$	−4.70825	−	0.912357i	−0.981738	−	0.190240i
$24$	0.817187	−	2.70780i	0.166808	−	0.552728i
$25$	2.23984	−	2.58491i	0.447968	−	0.516983i
$26$	2.02470	+	3.95159i	0.397076	+	0.774971i
$27$	0.989821	−	0.142315i	0.190491	−	0.0273885i
$28$	−1.49315	−	6.29196i	−0.282178	−	1.18907i
$29$	4.10030	+	0.589534i	0.761406	+	0.109474i	0.512070	−	0.858943i	$-0.328879\pi$
$29$	4.10030	+	0.589534i	0.761406	+	0.109474i	0.249336	+	0.968417i	$0.419788\pi$
$30$	4.03151	−	0.766563i	0.736049	−	0.139955i
$31$	−4.60234	−	2.95774i	−0.826605	−	0.531227i	0.0575927	−	0.998340i	$-0.481658\pi$
$31$	−4.60234	−	2.95774i	−0.826605	−	0.531227i	−0.884197	+	0.467114i	$0.845294\pi$
$32$	4.48994	−	3.44099i	0.793717	−	0.608287i
$33$	−1.58690	−	0.465957i	−0.276244	−	0.0811126i
$34$	−3.93582	−	5.55642i	−0.674987	−	0.952919i
$35$	7.09080	−	6.14421i	1.19856	−	1.03856i
$36$	1.77307	+	0.925328i	0.295511	+	0.154221i
$37$	3.39103	+	1.54863i	0.557481	+	0.254593i	0.674171	−	0.738575i	$-0.264501\pi$
$37$	3.39103	+	1.54863i	0.557481	+	0.254593i	−0.116690	+	0.993168i	$0.537228\pi$
$38$	−0.345336	+	0.436879i	−0.0560210	+	0.0708712i
$39$	−3.01245	+	0.884534i	−0.482378	+	0.141639i
$40$	7.44001	+	3.46539i	1.17637	+	0.547927i
$41$	1.52135	+	3.33129i	0.237595	+	0.520259i	0.990441	−	0.137937i	$-0.0440470\pi$
$41$	1.52135	+	3.33129i	0.237595	+	0.520259i	−0.752847	+	0.658196i	$0.771320\pi$
$42$	4.56800	−	0.206158i	0.704858	−	0.0318109i
$43$	−5.82692	−	9.06687i	−0.888597	−	1.38268i	−0.923625	−	0.383298i	$-0.874788\pi$
$43$	−5.82692	−	9.06687i	−0.888597	−	1.38268i	0.0350272	−	0.999386i	$-0.488848\pi$
$44$	−2.03172	−	2.61029i	−0.306293	−	0.393516i
$45$			2.90178i			0.432572i
$46$	5.71848	−	3.64678i	0.843144	−	0.537688i
$47$	8.73791			1.27456			0.637278	−	0.770634i	$-0.280060\pi$
$47$	8.73791			1.27456			0.637278	+	0.770634i	$0.280060\pi$
$48$	1.79727	+	3.57349i	0.259413	+	0.515789i
$49$	2.90616	−	1.86768i	0.415166	−	0.266811i
$50$	0.218080	+	4.83216i	0.0308412	+	0.683371i
$51$	4.37969	−	2.00014i	0.613279	−	0.280075i
$52$	−5.92355	−	2.08338i	−0.821449	−	0.288913i
$53$	3.74971	+	12.7704i	0.515063	+	1.75414i	0.646598	+	0.762831i	$0.276191\pi$
$53$	3.74971	+	12.7704i	0.515063	+	1.75414i	−0.131535	+	0.991312i	$0.541991\pi$
$54$	−0.876985	+	1.10946i	−0.119342	+	0.150978i
$55$	1.99368	−	4.36555i	0.268828	−	0.588650i
$56$	7.65622	+	5.00187i	1.02311	+	0.668403i
$57$	−0.257869	−	0.297597i	−0.0341556	−	0.0394177i
$58$	−4.78053	+	3.38622i	−0.627714	+	0.444633i
$59$	1.25320	−	4.26802i	0.163153	−	0.555649i	−0.836813	−	0.547488i	$-0.815584\pi$
$59$	1.25320	−	4.26802i	0.163153	−	0.555649i	0.999967	−	0.00816090i	$-0.00259772\pi$
$60$	−3.38999	+	4.71055i	−0.437645	+	0.608130i
$61$	3.95379	−	6.15222i	0.506231	−	0.787711i	−0.490245	−	0.871584i	$-0.663093\pi$
$61$	3.95379	−	6.15222i	0.506231	−	0.787711i	0.996476	+	0.0838737i	$0.0267292\pi$
$62$	7.60072	−	1.44522i	0.965292	−	0.183544i
$63$	−0.460154	+	3.20044i	−0.0579739	+	0.403218i
$64$	−1.25714	+	7.90061i	−0.157143	+	0.987576i
$65$	−1.29656	−	9.01777i	−0.160818	−	1.11852i
$66$	2.08163	−	1.06658i	0.256230	−	0.131286i
$67$	−1.33024	−	1.15266i	−0.162515	−	0.140820i	0.569807	−	0.821778i	$-0.307018\pi$
$67$	−1.33024	−	1.15266i	−0.162515	−	0.140820i	−0.732322	+	0.680959i	$0.761563\pi$
$68$	9.44634	+	1.86966i	1.14554	+	0.226729i
$69$	1.77795	+	4.45409i	0.214040	+	0.536209i
$70$	−1.29429	+	13.2055i	−0.154698	+	1.57836i
$71$	−8.80218	+	10.1583i	−1.04463	+	1.20556i	−0.0664494	+	0.997790i	$0.521167\pi$
$71$	−8.80218	+	10.1583i	−1.04463	+	1.20556i	−0.978177	+	0.207773i	$0.933378\pi$
$72$	−2.71975	+	0.776488i	−0.320526	+	0.0915100i
$73$	0.408778	+	2.84311i	0.0478438	+	0.332761i	0.999660	+	0.0260906i	$0.00830584\pi$
$73$	0.408778	+	2.84311i	0.0478438	+	0.332761i	−0.951816	+	0.306670i	$0.900785\pi$
$74$	−4.98640	+	1.71186i	−0.579657	+	0.199000i
$75$	−3.38552	−	0.486764i	−0.390926	−	0.0562067i
$76$	−0.0709417	−	0.784352i	−0.00813757	−	0.0899714i
$77$	2.89115	−	4.49871i	0.329477	−	0.512676i
$78$	2.22965	−	3.83968i	0.252459	−	0.434758i
$79$	−1.26059	−	0.370142i	−0.141827	−	0.0416442i	0.210048	−	0.977691i	$-0.432638\pi$
$79$	−1.26059	−	0.370142i	−0.141827	−	0.0416442i	−0.351876	+	0.936047i	$0.614456\pi$
$80$	−11.0061	+	3.68647i	−1.23052	+	0.412159i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−4.80336	−	1.93692i	−0.530442	−	0.213897i
$83$	−7.35078	−	3.35699i	−0.806852	−	0.368477i	−0.0311014	−	0.999516i	$-0.509901\pi$
$83$	−7.35078	−	3.35699i	−0.806852	−	0.368477i	−0.775751	+	0.631039i	$0.782629\pi$
$84$	−4.48588	+	4.65781i	−0.489449	+	0.508208i
$85$	3.93622	+	13.4055i	0.426943	+	1.45403i
$86$	14.8034	+	3.63048i	1.59630	+	0.391485i
$87$	−1.72084	−	3.76812i	−0.184494	−	0.403984i
$88$	4.62519	+	0.700440i	0.493047	+	0.0746671i
$89$	−0.761319	+	0.489270i	−0.0806996	+	0.0518625i	−0.580368	−	0.814354i	$-0.697091\pi$
$89$	−0.761319	+	0.489270i	−0.0806996	+	0.0518625i	0.499669	+	0.866217i	$0.333455\pi$
$90$	−2.82447	−	2.97708i	−0.297725	−	0.313812i
$91$		−	10.1515i		−	1.06417i
$92$	−2.31726	+	9.30754i	−0.241591	+	0.970378i
$93$			5.47081i			0.567297i
$94$	−8.96467	+	8.50512i	−0.924635	+	0.877236i
$95$	0.961262	−	0.617766i	0.0986234	−	0.0633814i
$96$	−5.32219	−	1.91684i	−0.543194	−	0.195636i
$97$	−4.43100	−	9.70254i	−0.449900	−	0.985144i	−0.989674	−	0.143334i	$-0.954218\pi$
$97$	−4.43100	−	9.70254i	−0.449900	−	0.985144i	0.539774	−	0.841810i	$-0.318510\pi$
$98$	−1.16366	+	4.74488i	−0.117547	+	0.479305i
$99$	0.465957	+	1.58690i	0.0468304	+	0.159490i
$100$	−4.92716	−	4.74529i	−0.492716	−	0.474529i
$101$	−17.6857	−	8.07677i	−1.75979	−	0.803669i	−0.985245	−	0.171149i	$-0.945252\pi$
$101$	−17.6857	−	8.07677i	−1.75979	−	0.803669i	−0.774544	−	0.632520i	$-0.782021\pi$
$102$	−2.54650	+	6.31505i	−0.252141	+	0.625283i
$103$	1.86962	+	2.15765i	0.184219	+	0.212600i	0.840346	−	0.542051i	$-0.182352\pi$
$103$	1.86962	+	2.15765i	0.184219	+	0.212600i	−0.656127	+	0.754651i	$0.727806\pi$
$104$	8.10515	−	3.62829i	0.794775	−	0.355783i
$105$	−9.00242	−	2.64335i	−0.878546	−	0.257964i
$106$	−16.2771	−	9.45194i	−1.58098	−	0.918053i
$107$	5.97553	−	9.29811i	0.577677	−	0.898882i	−0.422295	−	0.906459i	$-0.638775\pi$
$107$	5.97553	−	9.29811i	0.577677	−	0.898882i	0.999971	+	0.00757633i	$0.00241164\pi$
$108$	−0.180157	−	1.99187i	−0.0173356	−	0.191668i
$109$	2.95934	+	0.425488i	0.283453	+	0.0407544i	0.282575	−	0.959245i	$-0.408811\pi$
$109$	2.95934	+	0.425488i	0.283453	+	0.0407544i	0.000878016		1.00000i	$0.499721\pi$
$110$	2.20382	+	6.41940i	0.210126	+	0.612066i
$111$	−0.530537	−	3.68996i	−0.0503563	−	0.350236i
$112$	−12.7235	+	2.32057i	−1.20226	+	0.219273i
$113$	10.5461	−	12.1709i	0.992096	−	1.14494i	0.00265623	−	0.999996i	$-0.499154\pi$
$113$	10.5461	−	12.1709i	0.992096	−	1.14494i	0.989440	−	0.144944i	$-0.0463001\pi$
$114$	0.554229	+	0.0543207i	0.0519083	+	0.00508760i
$115$	−13.5275	+	3.26731i	−1.26144	+	0.304678i
$116$	1.60858	−	8.12727i	0.149353	−	0.754598i
$117$	2.37277	+	2.05602i	0.219363	+	0.190079i
$118$	2.86859	+	5.59860i	0.264075	+	0.515392i
$119$	2.21555	+	15.4095i	0.203099	+	1.41258i
$120$	−1.10710	−	8.13247i	−0.101064	−	0.742389i
$121$	−1.17618	+	8.18050i	−0.106925	+	0.743682i
$122$	1.93192	+	10.1603i	0.174907	+	0.919872i
$123$	1.97995	−	3.08087i	0.178526	−	0.277792i
$124$	−6.39124	+	8.88094i	−0.573950	+	0.797532i
$125$	−1.29142	+	4.39817i	−0.115508	+	0.393384i
$126$	−2.64308	−	3.73139i	−0.235464	−	0.332418i
$127$	2.29087	+	2.64381i	0.203282	+	0.234600i	0.848232	−	0.529625i	$-0.177667\pi$
$127$	2.29087	+	2.64381i	0.203282	+	0.234600i	−0.644950	+	0.764225i	$0.723122\pi$
$128$	−6.40035	−	9.32928i	−0.565717	−	0.824600i
$129$	−4.47726	+	9.80384i	−0.394201	+	0.863180i
$130$	10.1077	+	7.98977i	0.886506	+	0.700749i
$131$	0.608616	+	2.07276i	0.0531751	+	0.181098i	0.981798	−	0.189926i	$-0.0608249\pi$
$131$	0.608616	+	2.07276i	0.0531751	+	0.181098i	−0.928623	+	0.371024i	$0.879007\pi$
$132$	−1.09749	+	3.12042i	−0.0955239	+	0.271598i
$133$	1.15816	−	0.528914i	0.100425	−	0.0458627i
$134$	2.48671	−	0.112228i	0.214819	−	0.00969501i
$135$	2.44113	−	1.56882i	0.210099	−	0.135023i
$136$	−11.5113	+	7.27649i	−0.987088	+	0.623954i
$137$	12.8472			1.09761			0.548805	−	0.835950i	$-0.315083\pi$
$137$	12.8472			1.09761			0.548805	+	0.835950i	$0.315083\pi$
$138$	−6.15951	−	2.83910i	−0.524332	−	0.241680i
$139$			6.43812i			0.546074i	0.962003	+	0.273037i	$0.0880282\pi$
$139$			6.43812i			0.546074i	−0.962003	+	0.273037i	$0.911972\pi$
$140$	−11.5258	−	14.8081i	−0.974111	−	1.25151i
$141$	−4.72407	−	7.35080i	−0.397839	−	0.619049i
$142$	−0.857017	−	18.9895i	−0.0719193	−	1.59357i
$143$	−2.15709	−	4.72337i	−0.180385	−	0.394988i
$144$	2.03453	−	3.44393i	0.169544	−	0.286994i
$145$	11.5336	−	3.38657i	0.957813	−	0.281239i
$146$	−3.18675	−	2.51900i	−0.263737	−	0.208474i
$147$	−3.14238	−	1.43508i	−0.259179	−	0.118363i
$148$	3.44954	−	6.60983i	0.283550	−	0.543325i
$149$	−13.3170	+	11.5392i	−1.09097	+	0.945331i	−0.998729	−	0.0504057i	$-0.983949\pi$
$149$	−13.3170	+	11.5392i	−1.09097	+	0.945331i	−0.0922413	+	0.995737i	$0.529403\pi$
$150$	3.94717	−	2.79592i	0.322285	−	0.228286i
$151$	15.2149	+	4.46750i	1.23817	+	0.363560i	0.834329	−	0.551267i	$-0.185856\pi$
$151$	15.2149	+	4.46750i	1.23817	+	0.363560i	0.403844	+	0.914828i	$0.367674\pi$
$152$	0.836238	+	0.735655i	0.0678279	+	0.0596695i
$153$	−4.05046	−	2.60307i	−0.327461	−	0.210446i
$154$	1.41268	+	7.42958i	0.113837	+	0.598692i
$155$	−15.7135	−	2.25926i	−1.26214	−	0.181468i
$156$	1.44987	+	6.10957i	0.116082	+	0.489157i
$157$	−8.00036	+	1.15028i	−0.638498	+	0.0918022i	−0.453958	−	0.891023i	$-0.649989\pi$
$157$	−8.00036	+	1.15028i	−0.638498	+	0.0918022i	−0.184540	+	0.982825i	$0.559079\pi$
$158$	1.65358	−	0.847255i	0.131552	−	0.0674040i
$159$	8.71586	−	10.0586i	0.691212	−	0.797702i
$160$	7.70351	−	14.4951i	0.609016	−	1.14593i
$161$	−15.4379	+	1.45846i	−1.21667	+	0.114942i
$162$	1.40747	+	0.137948i	0.110581	+	0.0108382i
$163$	1.01116	+	0.876175i	0.0792002	+	0.0686274i	0.693561	−	0.720398i	$-0.256041\pi$
$163$	1.01116	+	0.876175i	0.0792002	+	0.0686274i	−0.614361	+	0.789025i	$0.710586\pi$
$164$	6.81333	−	2.68820i	0.532031	−	0.209913i
$165$	−4.75040	+	0.683004i	−0.369818	+	0.0531718i
$166$	10.8091	−	3.71083i	0.838947	−	0.288016i
$167$	−3.03690	+	21.1221i	−0.235002	+	1.63447i	0.440952	+	0.897531i	$0.354641\pi$
$167$	−3.03690	+	21.1221i	−0.235002	+	1.63447i	−0.675954	+	0.736944i	$0.736268\pi$
$168$	0.0685752	−	9.14504i	0.00529069	−	0.705555i
$169$	2.64386	+	1.69911i	0.203374	+	0.130700i
$170$	−17.0868	−	9.92207i	−1.31049	−	0.760988i
$171$	−0.110940	+	0.377826i	−0.00848378	+	0.0288931i
$172$	−18.7214	+	10.6844i	−1.42749	+	0.814674i
$173$	0.942503	−	0.816684i	0.0716572	−	0.0620913i	−0.618296	−	0.785945i	$-0.712177\pi$
$173$	0.942503	−	0.816684i	0.0716572	−	0.0620913i	0.689953	+	0.723854i	$0.257631\pi$
$174$	5.43322	+	2.19091i	0.411892	+	0.166092i
$175$	4.59413	−	10.0597i	0.347284	−	0.760445i
$176$	−5.42699	+	3.78335i	−0.409075	+	0.285181i
$177$	−4.26802	+	1.25320i	−0.320804	+	0.0941966i
$178$	0.304841	−	1.24300i	0.0228488	−	0.0931669i
$179$	−23.7424	+	10.8428i	−1.77459	+	0.810427i	−0.795797	+	0.605564i	$0.792948\pi$
$179$	−23.7424	+	10.8428i	−1.77459	+	0.810427i	−0.978791	+	0.204863i	$0.934325\pi$
$180$	5.79554	+	0.305120i	0.431974	+	0.0227423i
$181$	−1.07296	−	1.66955i	−0.0797521	−	0.124097i	0.799086	−	0.601217i	$-0.205317\pi$
$181$	−1.07296	−	1.66955i	−0.0797521	−	0.124097i	−0.878838	+	0.477120i	$0.841681\pi$
$182$	9.88105	+	10.4149i	0.732432	+	0.772007i
$183$	−7.31316			−0.540604
$184$	−6.68217	−	11.8046i	−0.492616	−	0.870247i
$185$	10.8176			0.795324
$186$	−5.32506	−	5.61278i	−0.390452	−	0.411549i
$187$	4.30522	+	6.69905i	0.314829	+	0.489883i
$188$	0.918785	−	17.4517i	0.0670093	−	1.27279i
$189$	2.94116	−	1.34318i	0.213938	−	0.0977022i
$190$	−0.384901	+	1.56945i	−0.0279236	+	0.113860i
$191$	−16.2361	+	4.76735i	−1.17480	+	0.344953i	−0.810168	−	0.586198i	$-0.800624\pi$
$191$	−16.2361	+	4.76735i	−1.17480	+	0.344953i	−0.364634	+	0.931151i	$0.618806\pi$
$192$	7.32608	−	3.21382i	0.528714	−	0.231937i
$193$	−10.8368	+	23.7294i	−0.780052	+	1.70808i	−0.0768979	+	0.997039i	$0.524502\pi$
$193$	−10.8368	+	23.7294i	−0.780052	+	1.70808i	−0.703154	+	0.711037i	$0.748226\pi$
$194$	13.9900	+	5.64138i	1.00443	+	0.405027i
$195$	−6.88526	+	5.96611i	−0.493063	+	0.427242i
$196$	−3.42460	−	6.00066i	−0.244615	−	0.428619i
$197$	1.70982	−	5.82310i	0.121819	−	0.414879i	−0.875891	−	0.482509i	$-0.839726\pi$
$197$	1.70982	−	5.82310i	0.121819	−	0.414879i	0.997710	+	0.0676302i	$0.0215438\pi$
$198$	−2.02267	−	1.17454i	−0.143745	−	0.0834710i
$199$	11.9882	+	7.70434i	0.849820	+	0.546146i	0.891519	−	0.452984i	$-0.149641\pi$
$199$	11.9882	+	7.70434i	0.849820	+	0.546146i	−0.0416984	+	0.999130i	$0.513277\pi$
$200$	9.67389	+	0.0725408i	0.684047	+	0.00512941i
$201$	−0.250497	+	1.74225i	−0.0176687	+	0.122889i
$202$	26.0062	−	8.92811i	1.82979	−	0.628180i
$203$	13.2577	−	1.90617i	0.930508	−	0.133787i
$204$	−3.53422	−	8.95758i	−0.247445	−	0.627156i
$205$	8.03135	+	6.95921i	0.560934	+	0.486052i
$206$	−4.01830	−	0.393839i	−0.279969	−	0.0274401i
$207$	2.78579	−	3.90377i	0.193626	−	0.271331i
$208$	−4.78385	+	11.6117i	−0.331700	+	0.805124i
$209$	0.426489	−	0.492194i	0.0295009	−	0.0340458i
$210$	11.8090	−	6.05063i	0.814896	−	0.417533i
$211$	−6.54025	+	0.940346i	−0.450249	+	0.0647361i	−0.363710	−	0.931512i	$-0.618490\pi$
$211$	−6.54025	+	0.940346i	−0.450249	+	0.0647361i	−0.0865395	+	0.996248i	$0.527581\pi$
$212$	25.8997	−	6.14626i	1.77880	−	0.422127i
$213$	13.3045	+	1.91290i	0.911608	+	0.131069i
$214$	2.91979	+	15.3557i	0.199593	+	1.04970i
$215$	−26.3101	−	16.9085i	−1.79433	−	1.15315i
$216$	2.12363	+	1.86820i	0.144495	+	0.127115i
$217$	−16.9725	−	4.98358i	−1.15217	−	0.338308i
$218$	−3.45028	+	2.44396i	−0.233683	+	0.165526i
$219$	2.17078	−	1.88099i	0.146687	−	0.127105i
$220$	−8.50939	−	4.44088i	−0.573703	−	0.299404i
$221$	13.7506	+	6.27968i	0.924964	+	0.422417i
$222$	4.13596	+	3.26932i	0.277587	+	0.219422i
$223$	28.2291	−	8.28880i	1.89036	−	0.555059i	0.896696	−	0.442646i	$-0.145960\pi$
$223$	28.2291	−	8.28880i	1.89036	−	0.555059i	0.993662	−	0.112413i	$-0.0358580\pi$
$224$	10.7950	−	14.7653i	0.721268	−	0.986550i
$225$	1.42086	+	3.11124i	0.0947238	+	0.207416i
$226$	1.02681	+	22.7519i	0.0683027	+	1.51343i
$227$	15.6784	+	24.3960i	1.04061	+	1.61922i	0.748864	+	0.662724i	$0.230600\pi$
$227$	15.6784	+	24.3960i	1.04061	+	1.61922i	0.291746	+	0.956496i	$0.405764\pi$
$228$	−0.621485	+	0.483733i	−0.0411589	+	0.0320360i
$229$			22.1268i			1.46218i	0.682282	+	0.731089i	$0.260988\pi$
$229$			22.1268i			1.46218i	−0.682282	+	0.731089i	$0.739012\pi$
$230$	10.6982	−	16.5192i	0.705422	−	1.08924i
$231$	−5.34763			−0.351848
$232$	6.26041	+	9.90390i	0.411016	+	0.650223i
$233$	−6.17433	+	3.96800i	−0.404494	+	0.259952i	−0.727031	−	0.686604i	$-0.759100\pi$
$233$	−6.17433	+	3.96800i	−0.404494	+	0.259952i	0.322538	+	0.946557i	$0.395464\pi$
$234$	−4.43558	+	0.200182i	−0.289963	+	0.0130863i
$235$	23.0642	−	10.5331i	1.50454	−	0.687101i
$236$	−8.39246	−	2.95172i	−0.546303	−	0.192141i
$237$	0.370142	+	1.26059i	0.0240433	+	0.0818840i
$238$	−17.2720	−	13.6528i	−1.11957	−	0.884981i
$239$	0.444260	−	0.972794i	0.0287368	−	0.0629248i	−0.894719	−	0.446629i	$-0.852624\pi$
$239$	0.444260	−	0.972794i	0.0287368	−	0.0629248i	0.923456	+	0.383704i	$0.125352\pi$
$240$	9.05162	+	7.26591i	0.584280	+	0.469012i
$241$	11.2918	+	13.0314i	0.727369	+	0.839429i	0.992173	−	0.124873i	$-0.0398525\pi$
$241$	11.2918	+	13.0314i	0.727369	+	0.839429i	−0.264803	+	0.964302i	$0.585307\pi$
$242$	−6.75586	−	9.53763i	−0.434283	−	0.613102i
$243$	−0.281733	+	0.959493i	−0.0180732	+	0.0615515i
$244$	−11.8717	−	8.54355i	−0.760006	−	0.546944i
$245$	5.41958	−	8.43304i	0.346245	−	0.538767i
$246$	0.967452	+	5.08802i	0.0616825	+	0.324400i
$247$	0.175946	−	1.22373i	0.0111951	−	0.0778639i
$248$	−2.08724	−	15.3324i	−0.132540	−	0.973607i
$249$	1.15005	+	7.99879i	0.0728816	+	0.506903i
$250$	−2.95606	−	5.76932i	−0.186958	−	0.364884i
$251$	−2.84520	−	2.46538i	−0.179587	−	0.155613i	0.560428	−	0.828203i	$-0.310637\pi$
$251$	−2.84520	−	2.46538i	−0.179587	−	0.155613i	−0.740016	+	0.672590i	$0.765182\pi$
$252$	6.34364	+	1.25556i	0.399612	+	0.0790928i
$253$	−6.87314	+	3.95899i	−0.432111	+	0.248899i
$254$	−4.92369	−	0.482578i	−0.308940	−	0.0302796i
$255$	9.14937	−	10.5589i	0.572956	−	0.661226i
$256$	15.6472	+	3.34155i	0.977948	+	0.208847i
$257$	−2.74839	−	19.1155i	−0.171440	−	1.19239i	−0.875845	−	0.482593i	$-0.839695\pi$
$257$	−2.74839	−	19.1155i	−0.171440	−	1.19239i	0.704405	−	0.709799i	$-0.251214\pi$
$258$	−4.94919	−	14.4162i	−0.308123	−	0.897516i
$259$	11.9310	+	1.71541i	0.741353	+	0.106590i
$260$	−18.1469	+	1.64132i	−1.12542	+	0.101790i
$261$	−2.23958	+	3.48486i	−0.138627	+	0.215707i
$262$	−2.64194	−	1.53414i	−0.163220	−	0.0947798i
$263$	−14.2737	−	4.19112i	−0.880152	−	0.258436i	−0.189724	−	0.981837i	$-0.560759\pi$
$263$	−14.2737	−	4.19112i	−0.880152	−	0.258436i	−0.690427	+	0.723402i	$0.742578\pi$
$264$	−1.91132	−	4.26964i	−0.117634	−	0.262778i
$265$	25.2915	+	29.1880i	1.55364	+	1.79300i
$266$	−0.673393	+	1.66995i	−0.0412884	+	0.102391i
$267$	0.823200	+	0.375943i	0.0503790	+	0.0230073i
$268$	−2.44201	+	2.53560i	−0.149169	+	0.154887i
$269$	7.50016	+	25.5432i	0.457293	+	1.55740i	0.789231	+	0.614096i	$0.210479\pi$
$269$	7.50016	+	25.5432i	0.457293	+	1.55740i	−0.331938	+	0.943301i	$0.607703\pi$
$270$	−0.977458	+	3.98563i	−0.0594862	+	0.242558i
$271$	−2.87150	−	6.28771i	−0.174431	−	0.381951i	0.802143	−	0.597132i	$-0.203693\pi$
$271$	−2.87150	−	6.28771i	−0.174431	−	0.381951i	−0.976574	+	0.215181i	$0.930966\pi$
$272$	4.72742	−	18.6700i	0.286642	−	1.13203i
$273$	−8.53999	+	5.48832i	−0.516864	+	0.332168i
$274$	−13.1806	+	12.5049i	−0.796269	+	0.755450i
$275$		−	5.65688i		−	0.341122i
$276$	9.08281	−	3.08263i	0.546721	−	0.185553i
$277$			2.91857i			0.175360i	0.996149	+	0.0876799i	$0.0279453\pi$
$277$			2.91857i			0.175360i	−0.996149	+	0.0876799i	$0.972055\pi$
$278$	−6.26660	−	6.60519i	−0.375845	−	0.396153i
$279$	4.60234	−	2.95774i	0.275535	−	0.177076i
$280$	26.2385	+	3.97356i	1.56805	+	0.237466i
$281$	−8.03880	−	17.6025i	−0.479555	−	1.05008i	−0.982586	−	0.185810i	$-0.940509\pi$
$281$	−8.03880	−	17.6025i	−0.479555	−	1.05008i	0.503031	−	0.864268i	$-0.332218\pi$
$282$	12.0016	+	2.94335i	0.714686	+	0.175274i
$283$	−5.26341	−	17.9255i	−0.312877	−	1.06556i	−0.954418	−	0.298473i	$-0.903523\pi$
$283$	−5.26341	−	17.9255i	−0.312877	−	1.06556i	0.641541	−	0.767089i	$-0.278295\pi$
$284$	19.3629	+	18.6481i	1.14898	+	1.10656i
$285$	−1.03940	−	0.474676i	−0.0615685	−	0.0281174i
$286$	6.81059	+	2.74632i	0.402719	+	0.162393i
$287$	7.75440	+	8.94905i	0.457727	+	0.528246i
$288$	1.26485	+	5.51363i	0.0745319	+	0.324894i
$289$	−5.93182	−	1.74174i	−0.348931	−	0.102455i
$290$	−8.53656	+	14.7008i	−0.501284	+	0.863259i
$291$	−5.76672	+	8.97319i	−0.338051	+	0.526018i
$292$	5.72134	−	0.517474i	0.334816	−	0.0302829i
$293$	−0.775885	−	0.111555i	−0.0453277	−	0.00651714i	0.119614	−	0.992821i	$-0.461834\pi$
$293$	−0.775885	−	0.111555i	−0.0453277	−	0.00651714i	−0.164941	+	0.986303i	$0.552743\pi$
$294$	4.62077	−	1.58634i	0.269488	−	0.0925173i
$295$	−1.83696	−	12.7763i	−0.106952	−	0.743867i
$296$	2.89468	+	10.1390i	0.168250	+	0.589317i
$297$	1.08307	−	1.24993i	0.0628462	−	0.0725284i
$298$	2.43077	−	24.8009i	0.140811	−	1.43668i
$299$	−6.91303	+	13.3763i	−0.399791	+	0.773574i
$300$	−1.32817	+	6.71049i	−0.0766817	+	0.387430i
$301$	−26.3367	−	22.8209i	−1.51802	−	1.31537i
$302$	−19.9582	+	10.2261i	−1.14847	+	0.588447i
$303$	2.76698	+	19.2448i	0.158959	+	1.10558i
$304$	−1.57399	+	0.0592131i	−0.0902748	+	0.00339611i
$305$	3.02009	−	21.0052i	0.172930	−	1.20275i
$306$	6.68930	−	1.27192i	0.382402	−	0.0727110i
$307$	16.4233	−	25.5551i	0.937325	−	1.45851i	0.0492612	−	0.998786i	$-0.484313\pi$
$307$	16.4233	−	25.5551i	0.937325	−	1.45851i	0.888064	−	0.459720i	$-0.152050\pi$
$308$	−8.68098	−	6.24733i	−0.494645	−	0.355975i
$309$	0.804342	−	2.73934i	0.0457574	−	0.155836i
$310$	18.3204	−	12.9770i	1.04053	−	0.737043i
$311$	3.62696	+	4.18573i	0.205666	+	0.237351i	0.849206	−	0.528061i	$-0.177081\pi$
$311$	3.62696	+	4.18573i	0.205666	+	0.237351i	−0.643541	+	0.765412i	$0.722535\pi$
$312$	−7.43429	−	4.85688i	−0.420884	−	0.274967i
$313$	11.3612	−	24.8775i	0.642172	−	1.40616i	−0.256070	−	0.966658i	$-0.582428\pi$
$313$	11.3612	−	24.8775i	0.642172	−	1.40616i	0.898242	−	0.439501i	$-0.144845\pi$
$314$	7.08834	−	8.96734i	0.400018	−	0.506056i
$315$	2.64335	+	9.00242i	0.148936	+	0.507229i
$316$	−0.871810	+	2.47877i	−0.0490431	+	0.139442i
$317$	18.8181	−	8.59394i	1.05693	−	0.482683i	0.190347	−	0.981717i	$-0.439039\pi$
$317$	18.8181	−	8.59394i	1.05693	−	0.482683i	0.866583	+	0.499033i	$0.166312\pi$
$318$	0.848612	+	18.8033i	0.0475878	+	1.05444i
$319$	5.76360	−	3.70404i	0.322700	−	0.207386i
$320$	6.20545	+	22.3695i	0.346895	+	1.25049i
$321$	−11.0527			−0.616901
$322$	14.4189	−	16.5229i	0.803533	−	0.920784i
$323$			1.89596i			0.105494i
$324$	−1.57827	+	1.22844i	−0.0876815	+	0.0682469i
$325$	−5.80570	−	9.03385i	−0.322042	−	0.501108i
$326$	−1.89023	+	0.0853081i	−0.104690	+	0.00472478i
$327$	−1.24199	−	2.71959i	−0.0686824	−	0.150394i
$328$	−4.37355	+	9.38977i	−0.241489	+	0.518463i
$329$	27.1083	−	7.95972i	1.49453	−	0.438833i
$330$	4.20887	−	5.32456i	0.231690	−	0.293108i
$331$	18.9367	+	8.64808i	1.04085	+	0.475342i	0.861135	−	0.508376i	$-0.169754\pi$
$331$	18.9367	+	8.64808i	1.04085	+	0.475342i	0.179718	+	0.983718i	$0.442481\pi$
$332$	−7.47762	+	14.3282i	−0.410388	+	0.786364i
$333$	−2.81737	+	2.44126i	−0.154391	+	0.133780i
$334$	−17.4436	−	24.6262i	−0.954473	−	1.34748i
$335$	−4.90071	−	1.43898i	−0.267754	−	0.0786198i
$336$	8.83104	+	9.44911i	0.481773	+	0.515491i
$337$	2.73466	+	1.75746i	0.148967	+	0.0957350i	0.613001	−	0.790082i	$-0.289962\pi$
$337$	2.73466	+	1.75746i	0.148967	+	0.0957350i	−0.464034	+	0.885817i	$0.653599\pi$
$338$	−4.36631	+	0.830223i	−0.237496	+	0.0451582i
$339$	−15.9405	−	2.29189i	−0.865767	−	0.124479i
$340$	27.1879	−	6.45197i	1.47447	−	0.349907i
$341$	−8.95606	+	1.28769i	−0.484998	+	0.0697322i
$342$	−0.253941	−	0.495615i	−0.0137316	−	0.0267998i
$343$	−7.50710	+	8.66365i	−0.405345	+	0.467793i
$344$	8.80749	−	29.1842i	0.474868	−	1.57351i
$345$	10.0621	+	9.61359i	0.541727	+	0.517578i
$346$	−0.172036	+	1.75527i	−0.00924873	+	0.0943639i
$347$	−13.6546	−	11.8318i	−0.733017	−	0.635163i	0.206191	−	0.978512i	$-0.433893\pi$
$347$	−13.6546	−	11.8318i	−0.733017	−	0.635163i	−0.939208	+	0.343349i	$0.888439\pi$
$348$	−7.70675	+	3.04071i	−0.413125	+	0.162999i
$349$	−33.4436	+	4.80846i	−1.79019	+	0.257391i	−0.955850	−	0.293853i	$-0.905062\pi$
$349$	−33.4436	+	4.80846i	−1.79019	+	0.257391i	−0.834344	+	0.551245i	$0.814153\pi$
$350$	5.07838	+	14.7925i	0.271451	+	0.790694i
$351$	0.446815	−	3.10767i	0.0238492	−	0.165875i
$352$	1.88528	−	9.16394i	0.100486	−	0.488439i
$353$	5.58842	+	3.59146i	0.297442	+	0.191154i	0.680846	−	0.732426i	$-0.261612\pi$
$353$	5.58842	+	3.59146i	0.297442	+	0.191154i	−0.383405	+	0.923581i	$0.625248\pi$
$354$	3.15896	−	5.44004i	0.167897	−	0.289135i
$355$	−10.9886	+	37.4238i	−0.583215	+	1.98625i
$356$	0.897134	+	1.57198i	0.0475480	+	0.0833147i
$357$	11.7654	−	10.1948i	0.622694	−	0.539567i
$358$	13.8046	−	34.2340i	0.729595	−	1.80932i
$359$	−5.27450	+	11.5495i	−0.278377	+	0.609561i	−0.996241	−	0.0866221i	$-0.972393\pi$
$359$	−5.27450	+	11.5495i	−0.278377	+	0.609561i	0.717864	+	0.696183i	$0.245120\pi$
$360$	−6.24292	+	5.32809i	−0.329031	+	0.280815i
$361$	−18.0816	+	5.30923i	−0.951662	+	0.279433i
$362$	2.72587	+	0.668507i	0.143269	+	0.0351360i
$363$	7.51777	−	3.43325i	0.394580	−	0.180199i
$364$	−20.2749	−	1.06742i	−1.06270	−	0.0559482i
$365$	4.50620	+	7.01178i	0.235865	+	0.367014i
$366$	7.50294	−	7.11832i	0.392185	−	0.372080i
$367$	−14.0461			−0.733199			−0.366599	−	0.930379i	$-0.619478\pi$
$367$	−14.0461			−0.733199			−0.366599	+	0.930379i	$0.619478\pi$
$368$	18.3457	+	5.60679i	0.956335	+	0.292274i
$369$	−3.66223			−0.190648
$370$	−11.0983	+	10.5294i	−0.576973	+	0.547396i
$371$	23.2661	+	36.2027i	1.20791	+	1.87955i
$372$	10.9265	+	0.575252i	0.566512	+	0.0298254i
$373$	25.5476	−	11.6672i	1.32281	−	0.604105i	0.376211	−	0.926534i	$-0.377227\pi$
$373$	25.5476	−	11.6672i	1.32281	−	0.604105i	0.946594	+	0.322429i	$0.104499\pi$
$374$	−10.9375	−	2.68238i	−0.565565	−	0.138702i
$375$	4.39817	−	1.29142i	0.227121	−	0.0666886i
$376$	16.0441	+	18.7988i	0.827410	+	0.969477i
$377$	5.40279	−	11.8305i	0.278258	−	0.609300i
$378$	−1.71009	+	4.24084i	−0.0879574	+	0.218125i
$379$	−27.0336	+	23.4248i	−1.38862	+	1.20325i	−0.435681	+	0.900101i	$0.643492\pi$
$379$	−27.0336	+	23.4248i	−1.38862	+	1.20325i	−0.952943	+	0.303148i	$0.901962\pi$
$380$	−1.13275	−	1.98482i	−0.0581087	−	0.101819i
$381$	0.985573	−	3.35655i	0.0504924	−	0.171961i
$382$	12.0171	−	20.6946i	0.614848	−	1.05883i
$383$	−1.84011	−	1.18257i	−0.0940253	−	0.0604264i	0.492783	−	0.870152i	$-0.335980\pi$
$383$	−1.84011	−	1.18257i	−0.0940253	−	0.0604264i	−0.586809	+	0.809726i	$0.699616\pi$
$384$	−4.38800	+	10.4281i	−0.223924	+	0.532157i
$385$	2.20839	−	15.3597i	0.112550	−	0.782803i
$386$	−11.9791	−	34.8933i	−0.609720	−	1.77602i
$387$	10.6681	−	1.53384i	0.542290	−	0.0779696i
$388$	−19.8442	+	7.82954i	−1.00743	+	0.397484i
$389$	−18.1632	−	15.7385i	−0.920910	−	0.797973i	0.0588257	−	0.998268i	$-0.481264\pi$
$389$	−18.1632	−	15.7385i	−0.920910	−	0.797973i	−0.979736	+	0.200295i	$0.935810\pi$
$390$	1.25677	−	12.8228i	0.0636393	−	0.649305i
$391$	7.57427	−	21.8133i	0.383047	−	1.10315i
$392$	9.35427	+	2.82302i	0.472462	+	0.142584i
$393$	1.41467	−	1.63262i	0.0713607	−	0.0823547i
$394$	3.91377	+	7.63847i	0.197173	+	0.384821i
$395$	−3.77357	+	0.542558i	−0.189869	+	0.0272990i
$396$	3.21841	−	0.763763i	0.161731	−	0.0383805i
$397$	13.9869	+	2.01101i	0.701983	+	0.100930i	0.484058	−	0.875036i	$-0.339162\pi$
$397$	13.9869	+	2.01101i	0.701983	+	0.100930i	0.217924	+	0.975966i	$0.430071\pi$
$398$	−19.7984	+	3.76452i	−0.992403	+	0.188699i
$399$	−1.07110	−	0.688354i	−0.0536221	−	0.0344608i
$400$	−9.99554	+	9.34173i	−0.499777	+	0.467087i
$401$	−7.55046	−	2.21702i	−0.377052	−	0.110712i	0.0877146	−	0.996146i	$-0.472044\pi$
$401$	−7.55046	−	2.21702i	−0.377052	−	0.110712i	−0.464767	+	0.885433i	$0.653862\pi$
$402$	−1.43883	−	2.03128i	−0.0717624	−	0.101311i
$403$	−12.9810	+	11.2481i	−0.646628	+	0.560307i
$404$	−17.9908	+	34.4731i	−0.895078	+	1.71510i
$405$	−2.63955	−	1.20544i	−0.131160	−	0.0598990i
$406$	−11.7464	+	14.8601i	−0.582962	+	0.737496i
$407$	5.91583	−	1.73704i	0.293237	−	0.0861021i
$408$	12.3449	+	5.74997i	0.611162	+	0.284666i
$409$	6.63514	+	14.5289i	0.328087	+	0.718410i	0.999748	−	0.0224487i	$-0.00714625\pi$
$409$	6.63514	+	14.5289i	0.328087	+	0.718410i	−0.671661	+	0.740858i	$0.734419\pi$
$410$	−15.0136	+	0.677577i	−0.741467	+	0.0334632i
$411$	−6.94572	−	10.8078i	−0.342607	−	0.533107i
$412$	4.50593	−	3.50719i	0.221991	−	0.172787i
$413$		−	14.3826i		−	0.707722i
$414$	0.941683	+	6.71664i	0.0462812	+	0.330105i
$415$	−23.4494			−1.15109
$416$	−6.39430	−	16.5694i	−0.313506	−	0.812381i
$417$	5.41609	−	3.48071i	0.265227	−	0.170451i
$418$	0.0415247	+	0.920094i	0.00203104	+	0.0450032i
$419$	10.0088	−	4.57088i	0.488963	−	0.223302i	−0.155648	−	0.987813i	$-0.549747\pi$
$419$	10.0088	−	4.57088i	0.488963	−	0.223302i	0.644611	+	0.764511i	$0.277019\pi$
$420$	−6.22598	+	17.7020i	−0.303797	+	0.863769i
$421$	−6.37343	−	21.7059i	−0.310622	−	1.05788i	−0.955841	−	0.293884i	$-0.905052\pi$
$421$	−6.37343	−	21.7059i	−0.310622	−	1.05788i	0.645219	−	0.763998i	$-0.276766\pi$
$422$	5.79468	−	7.33075i	0.282081	−	0.356855i
$423$	−3.62986	+	7.94829i	−0.176490	+	0.386459i
$424$	−20.5893	+	31.5154i	−0.999903	+	1.53052i
$425$	10.7844	+	12.4458i	0.523119	+	0.603712i
$426$	−15.5117	+	10.9875i	−0.751543	+	0.532346i
$427$	6.66185	−	22.6882i	0.322389	−	1.09796i
$428$	−17.9422	−	12.9122i	−0.867268	−	0.624136i
$429$	−2.80734	+	4.36830i	−0.135540	+	0.210904i
$430$	43.4508	−	8.26187i	2.09538	−	0.398423i
$431$	−2.92978	+	20.3771i	−0.141122	+	0.981528i	0.789030	+	0.614355i	$0.210584\pi$
$431$	−2.92978	+	20.3771i	−0.141122	+	0.981528i	−0.930152	+	0.367174i	$0.880326\pi$
$432$	−3.99717	+	0.150372i	−0.192314	+	0.00723479i
$433$	−4.02574	−	27.9997i	−0.193465	−	1.34558i	−0.822750	−	0.568404i	$-0.807561\pi$
$433$	−4.02574	−	27.9997i	−0.193465	−	1.34558i	0.629285	−	0.777175i	$-0.283348\pi$
$434$	22.2638	−	11.4074i	1.06870	−	0.547574i
$435$	−9.08450	−	7.87176i	−0.435568	−	0.377422i
$436$	1.16097	−	5.86575i	0.0556004	−	0.280918i
$437$	−1.88626	−	0.0917568i	−0.0902320	−	0.00438932i
$438$	−0.396234	+	4.04274i	−0.0189328	+	0.193170i
$439$	−10.7596	+	12.4172i	−0.513526	+	0.592641i	−0.951998	−	0.306104i	$-0.900974\pi$
$439$	−10.7596	+	12.4172i	−0.513526	+	0.592641i	0.438472	+	0.898745i	$0.355520\pi$
$440$	13.0528	−	3.72656i	0.622267	−	0.177657i
$441$	0.491635	+	3.41940i	0.0234112	+	0.162828i
$442$	−20.2198	+	6.94159i	−0.961758	+	0.330178i
$443$	1.93107	+	0.277645i	0.0917477	+	0.0131913i	0.188036	−	0.982162i	$-0.439788\pi$
$443$	1.93107	+	0.277645i	0.0917477	+	0.0131913i	−0.0962881	+	0.995354i	$0.530697\pi$
$444$	−7.42551	+	0.671609i	−0.352399	+	0.0318732i
$445$	−1.41975	+	2.20918i	−0.0673028	+	0.104725i
$446$	−20.8937	+	35.9809i	−0.989343	+	1.70374i
$447$	16.9071	+	4.96438i	0.799680	+	0.234807i
$448$	3.29686	+	25.6558i	0.155762	+	1.21212i
$449$	−9.20577	−	10.6240i	−0.434447	−	0.501379i	0.495737	−	0.868473i	$-0.334898\pi$
$449$	−9.20577	−	10.6240i	−0.434447	−	0.501379i	−0.930184	+	0.367094i	$0.880353\pi$
$450$	−4.48608	−	1.80898i	−0.211476	−	0.0852761i
$451$	5.50960	+	2.51615i	0.259437	+	0.118481i
$452$	−23.1992	−	22.3428i	−1.09120	−	1.05092i
$453$	−4.46750	−	15.2149i	−0.209902	−	0.714859i
$454$	−39.8313	−	9.76844i	−1.86937	−	0.458456i
$455$	−12.2371	−	26.7954i	−0.573682	−	1.25619i
$456$	0.166768	−	1.10121i	0.00780963	−	0.0515691i
$457$	−11.1846	+	7.18789i	−0.523192	+	0.336235i	−0.775434	−	0.631429i	$-0.782469\pi$
$457$	−11.1846	+	7.18789i	−0.523192	+	0.336235i	0.252241	+	0.967664i	$0.418832\pi$
$458$	−21.5373	−	22.7010i	−1.00637	−	1.06075i
$459$			4.81479i			0.224735i
$460$	5.10318	+	27.3611i	0.237937	+	1.27572i
$461$		−	33.7864i		−	1.57359i	−0.617214	−	0.786796i	$-0.711739\pi$
$461$		−	33.7864i		−	1.57359i	0.617214	−	0.786796i	$-0.288261\pi$
$462$	5.48640	−	5.20516i	0.255251	−	0.242166i
$463$	−12.5349	+	8.05572i	−0.582548	+	0.374381i	−0.798475	−	0.602029i	$-0.794359\pi$
$463$	−12.5349	+	8.05572i	−0.582548	+	0.374381i	0.215926	+	0.976410i	$0.430723\pi$
$464$	−16.0629	−	4.06729i	−0.745702	−	0.188819i
$465$	6.59475	+	14.4405i	0.305824	+	0.669662i
$466$	2.47227	−	10.0808i	0.114526	−	0.466984i
$467$	5.06583	+	17.2526i	0.234419	+	0.798357i	0.989725	+	0.142985i	$0.0456701\pi$
$467$	5.06583	+	17.2526i	0.234419	+	0.798357i	−0.755306	+	0.655372i	$0.772512\pi$
$468$	4.35584	−	4.52279i	0.201349	−	0.209066i
$469$	−5.17692	−	2.36422i	−0.239048	−	0.109169i
$470$	−13.4103	+	33.2561i	−0.618570	+	1.53399i
$471$	5.29300	+	6.10844i	0.243888	+	0.281462i
$472$	11.4833	−	5.14055i	0.528563	−	0.236613i
$473$	−17.1033	−	5.02199i	−0.786412	−	0.230911i
$474$	−1.60675	−	0.933020i	−0.0738005	−	0.0428550i
$475$	0.728161	−	1.13304i	0.0334103	−	0.0519875i
$476$	31.0093	−	2.80467i	1.42131	−	0.128552i
$477$	−13.1740	−	1.89414i	−0.603196	−	0.0867266i
$478$	0.491088	+	1.43046i	0.0224618	+	0.0654279i
$479$	3.18514	+	22.1531i	0.145533	+	1.01220i	0.923418	+	0.383796i	$0.125383\pi$
$479$	3.18514	+	22.1531i	0.145533	+	1.01220i	−0.777885	+	0.628407i	$0.783707\pi$
$480$	−16.3588	+	1.35601i	−0.746676	+	0.0618930i
$481$	7.66464	−	8.84547i	0.349478	−	0.403319i
$482$	−24.2691	−	2.37865i	−1.10543	−	0.108344i
$483$	9.57327	+	12.1987i	0.435599	+	0.555058i
$484$	16.2147	+	3.20928i	0.737032	+	0.145876i
$485$	−23.3917	−	20.2691i	−1.06216	−	0.920370i
$486$	−0.644886	−	1.25862i	−0.0292526	−	0.0570921i
$487$	3.51064	+	24.4170i	0.159082	+	1.10644i	0.900329	+	0.435209i	$0.143326\pi$
$487$	3.51064	+	24.4170i	0.159082	+	1.10644i	−0.741247	+	0.671232i	$0.765765\pi$
$488$	20.4957	−	2.79014i	0.927796	−	0.126304i
$489$	0.190411	−	1.32434i	0.00861069	−	0.0598887i
$490$	2.64814	+	13.9271i	0.119631	+	0.629161i
$491$	10.9491	−	17.0372i	0.494127	−	0.768877i	−0.501211	−	0.865325i	$-0.667112\pi$
$491$	10.9491	−	17.0372i	0.494127	−	0.768877i	0.995338	+	0.0964485i	$0.0307483\pi$
$492$	−5.94502	−	4.27838i	−0.268022	−	0.192884i
$493$	−5.61919	+	19.1372i	−0.253075	+	0.861896i
$494$	1.01061	+	1.42674i	0.0454697	+	0.0641922i
$495$	3.14284	+	3.62703i	0.141260	+	0.163023i
$496$	17.0653	+	13.6986i	0.766254	+	0.615086i
$497$	−18.0541	+	39.5330i	−0.809838	+	1.77330i
$498$	−8.96558	−	7.08695i	−0.401757	−	0.317574i
$499$	2.66438	+	9.07406i	0.119274	+	0.406211i	0.997387	−	0.0722429i	$-0.0230157\pi$
$499$	2.66438	+	9.07406i	0.119274	+	0.406211i	−0.878113	+	0.478454i	$0.841198\pi$
$500$	8.64839	+	3.04173i	0.386768	+	0.136030i
$501$	19.4109	−	8.86465i	0.867214	−	0.396044i
$502$	5.31873	−	0.240040i	0.237387	−	0.0107135i
$503$	11.6036	−	7.45715i	0.517377	−	0.332498i	−0.255757	−	0.966741i	$-0.582325\pi$
$503$	11.6036	−	7.45715i	0.517377	−	0.332498i	0.773134	+	0.634243i	$0.218688\pi$
$504$	−7.73037	+	4.88649i	−0.344338	+	0.217662i
$505$	−56.4183			−2.51058
$506$	3.19799	−	10.7517i	0.142168	−	0.477974i
$507$		−	3.14276i		−	0.139575i
$508$	5.52119	−	4.29741i	0.244963	−	0.190667i
$509$	−12.1672	−	18.9325i	−0.539302	−	0.839170i	0.459497	−	0.888180i	$-0.348030\pi$
$509$	−12.1672	−	18.9325i	−0.539302	−	0.839170i	−0.998798	+	0.0490096i	$0.984393\pi$
$510$	0.890821	+	19.7386i	0.0394462	+	0.874038i
$511$	3.85809	+	8.44803i	0.170672	+	0.373719i
$512$	−19.3057	+	11.8020i	−0.853202	+	0.521581i
$513$	0.377826	−	0.110940i	0.0166814	−	0.00489811i
$514$	21.4259	+	16.9364i	0.945057	+	0.747032i
$515$	7.53588	+	3.44152i	0.332071	+	0.151652i
$516$	19.1098	+	9.97301i	0.841261	+	0.439037i
$517$	10.9218	−	9.46379i	0.480340	−	0.416217i
$518$	−13.9103	+	9.85316i	−0.611182	+	0.432923i
$519$	−1.19659	−	0.351352i	−0.0525246	−	0.0154226i
$520$	17.0203	−	19.3474i	0.746388	−	0.848438i
$521$	4.51338	+	2.90058i	0.197735	+	0.127077i	0.635762	−	0.771885i	$-0.280686\pi$
$521$	4.51338	+	2.90058i	0.197735	+	0.127077i	−0.438027	+	0.898962i	$0.644322\pi$
$522$	−1.09431	−	5.75521i	−0.0478968	−	0.251899i
$523$	2.57719	+	0.370544i	0.112693	+	0.0162027i	0.198430	−	0.980115i	$-0.436416\pi$
$523$	2.57719	+	0.370544i	0.112693	+	0.0162027i	−0.0857378	+	0.996318i	$0.527325\pi$
$524$	4.20378	−	0.997600i	0.183643	−	0.0435804i
$525$	−10.9466	+	1.57388i	−0.477747	+	0.0686897i
$526$	18.7235	−	9.59349i	0.816385	−	0.418296i
$527$	17.2496	−	19.9071i	0.751403	−	0.867166i
$528$	6.11681	+	2.52005i	0.266200	+	0.109671i
$529$	21.3352	+	8.59121i	0.927618	+	0.373531i
$530$	−54.3582	−	5.32771i	−2.36117	−	0.231421i
$531$	3.36173	+	2.91296i	0.145887	+	0.126411i
$532$	−0.934586	−	2.36873i	−0.0405194	−	0.102698i
$533$	11.3810	−	1.63634i	0.492966	−	0.0708778i
$534$	−1.21049	+	0.415569i	−0.0523830	+	0.0179834i
$535$	4.56439	−	31.7460i	0.197336	−	1.37250i
$536$	0.0373307	−	4.97835i	0.00161244	−	0.215032i
$537$	21.9576	+	14.1113i	0.947541	+	0.608947i
$538$	−32.5575	−	18.9057i	−1.40365	−	0.815084i
$539$	1.60967	−	5.48205i	0.0693336	−	0.236128i
$540$	−2.87662	−	5.04047i	−0.123790	−	0.216908i
$541$	3.29608	−	2.85607i	0.141709	−	0.122792i	−0.581122	−	0.813817i	$-0.697386\pi$
$541$	3.29608	−	2.85607i	0.141709	−	0.122792i	0.722831	+	0.691025i	$0.242840\pi$
$542$	9.06621	+	3.65588i	0.389427	+	0.157034i
$543$	−0.824432	+	1.80525i	−0.0353798	+	0.0774709i
$544$	13.3225	+	23.7559i	0.571196	+	1.01853i
$545$	8.32422	−	2.44421i	0.356571	−	0.104699i
$546$	3.41951	−	13.9432i	0.146342	−	0.596714i
$547$	−12.5744	+	5.74253i	−0.537642	+	0.245533i	−0.665681	−	0.746236i	$-0.731859\pi$
$547$	−12.5744	+	5.74253i	−0.537642	+	0.245533i	0.128039	+	0.991769i	$0.459132\pi$
$548$	1.35087	−	25.6589i	0.0577065	−	1.09609i
$549$	3.95379	+	6.15222i	0.168744	+	0.262570i
$550$	5.50616	+	5.80368i	0.234784	+	0.247470i
$551$	1.63121			0.0694917
$552$	−6.31801	+	12.0034i	−0.268912	+	0.510901i
$553$	−4.24800			−0.180643
$554$	−2.84081	−	2.99431i	−0.120695	−	0.127216i
$555$	−5.84842	−	9.10032i	−0.248252	−	0.386287i
$556$	12.8584	+	0.676964i	0.545319	+	0.0287097i
$557$	4.11170	−	1.87775i	0.174218	−	0.0795628i	−0.326397	−	0.945233i	$-0.605835\pi$
$557$	4.11170	−	1.87775i	0.174218	−	0.0795628i	0.500615	+	0.865670i	$0.333107\pi$
$558$	−1.84283	+	7.51422i	−0.0780132	+	0.318102i
$559$	−32.4676	+	9.53334i	−1.37323	+	0.403217i
$560$	−30.7871	+	21.4627i	−1.30099	+	0.906967i
$561$	3.30802	−	7.24356i	0.139665	−	0.305823i
$562$	25.3810	+	10.2347i	1.07063	+	0.431724i
$563$	−20.3995	+	17.6763i	−0.859737	+	0.744967i	−0.968477	−	0.249104i	$-0.919864\pi$
$563$	−20.3995	+	17.6763i	−0.859737	+	0.744967i	0.108740	+	0.994070i	$0.465319\pi$
$564$	−15.1780	+	8.66215i	−0.639109	+	0.364742i
$565$	13.1658	−	44.8384i	0.553887	−	1.88637i
$566$	22.8479	+	13.2675i	0.960370	+	0.557675i
$567$	−2.72007	−	1.74808i	−0.114232	−	0.0734125i
$568$	−38.0167	−	0.285072i	−1.59514	−	0.0119614i
$569$	2.14594	−	14.9253i	0.0899625	−	0.625703i	−0.894098	−	0.447871i	$-0.852182\pi$
$569$	2.14594	−	14.9253i	0.0899625	−	0.625703i	0.984061	−	0.177832i	$-0.0569084\pi$
$570$	1.52840	−	0.524709i	0.0640175	−	0.0219777i
$571$	19.6583	−	2.82643i	0.822674	−	0.118283i	0.281892	−	0.959446i	$-0.409038\pi$
$571$	19.6583	−	2.82643i	0.822674	−	0.118283i	0.540781	+	0.841163i	$0.318129\pi$
$572$	−9.66049	+	3.81155i	−0.403925	+	0.159369i
$573$	12.7884	+	11.0812i	0.534245	+	0.462926i
$574$	−16.6663	−	1.63348i	−0.695636	−	0.0681802i
$575$	−12.9041	+	10.1269i	−0.538138	+	0.422320i
$576$	−6.66441	−	4.42557i	−0.277684	−	0.184399i
$577$	−16.1296	+	18.6145i	−0.671484	+	0.774934i	−0.984608	−	0.174779i	$-0.944079\pi$
$577$	−16.1296	+	18.6145i	−0.671484	+	0.774934i	0.313124	+	0.949712i	$0.398624\pi$
$578$	7.78110	−	3.98685i	0.323651	−	0.165831i
$579$	25.8212	−	3.71253i	1.07309	−	0.154288i
$580$	−5.55103	−	23.3914i	−0.230494	−	0.971275i
$581$	−25.8629	−	3.71852i	−1.07297	−	0.154270i
$582$	−2.81776	−	14.8191i	−0.116800	−	0.614273i
$583$	18.5181	+	11.9009i	0.766941	+	0.492883i
$584$	−5.36613	+	6.09981i	−0.222052	+	0.252412i
$585$	8.74146	+	2.56672i	0.361415	+	0.106121i
$586$	0.904603	−	0.640764i	0.0373688	−	0.0264697i
$587$	6.58689	−	5.70757i	0.271870	−	0.235577i	−0.508245	−	0.861212i	$-0.669706\pi$
$587$	6.58689	−	5.70757i	0.271870	−	0.235577i	0.780115	+	0.625636i	$0.215160\pi$
$588$	−3.19660	+	6.12516i	−0.131826	+	0.252598i
$589$	−1.95960	−	0.894920i	−0.0807440	−	0.0368745i
$590$	14.3206	+	11.3199i	0.589569	+	0.466032i
$591$	−5.82310	+	1.70982i	−0.239530	+	0.0703324i
$592$	−12.8387	−	7.58456i	−0.527666	−	0.311723i
$593$	6.89417	+	15.0961i	0.283109	+	0.619923i	0.996747	−	0.0805917i	$-0.0256810\pi$
$593$	6.89417	+	15.0961i	0.283109	+	0.619923i	−0.713638	+	0.700515i	$0.752954\pi$
$594$	0.105452	+	2.33659i	0.00432677	+	0.0958712i
$595$	24.4233	+	38.0034i	1.00126	+	1.55799i
$596$	21.6463	+	27.8105i	0.886666	+	1.13916i
$597$		−	14.2504i		−	0.583230i
$598$	−5.92753	−	20.4523i	−0.242395	−	0.836357i
$599$	29.8588			1.22000			0.609998	−	0.792403i	$-0.291170\pi$
$599$	29.8588			1.22000			0.609998	+	0.792403i	$0.291170\pi$
$600$	−5.16907	−	8.17741i	−0.211027	−	0.333841i
$601$	5.07392	−	3.26081i	0.206970	−	0.133011i	−0.433050	−	0.901370i	$-0.642563\pi$
$601$	5.07392	−	3.26081i	0.206970	−	0.133011i	0.640019	+	0.768359i	$0.278926\pi$
$602$	49.2330	−	2.22194i	2.00659	−	0.0905593i
$603$	1.60110	−	0.731198i	0.0652018	−	0.0297767i
$604$	10.5225	−	29.9180i	0.428154	−	1.21735i
$605$	6.75655	+	23.0107i	0.274693	+	0.935517i
$606$	−21.5708	−	17.0509i	−0.876255	−	0.692646i
$607$	11.0994	−	24.3043i	0.450511	−	0.986481i	−0.539038	−	0.842281i	$-0.681212\pi$
$607$	11.0994	−	24.3043i	0.450511	−	0.986481i	0.989549	−	0.144199i	$-0.0460606\pi$
$608$	1.55721	−	1.59281i	0.0631530	−	0.0645970i
$609$	−8.77123	−	10.1225i	−0.355428	−	0.410186i
$610$	17.3471	+	24.4899i	0.702363	+	0.991567i
$611$	7.72898	−	26.3225i	0.312681	−	1.06489i
$612$	−5.62485	+	7.81601i	−0.227371	+	0.315944i
$613$	0.295137	−	0.459243i	0.0119205	−	0.0185486i	−0.835242	−	0.549882i	$-0.814673\pi$
$613$	0.295137	−	0.459243i	0.0119205	−	0.0185486i	0.847163	+	0.531334i	$0.178309\pi$
$614$	8.02479	+	42.2040i	0.323854	+	1.70321i
$615$	1.51238	−	10.5188i	0.0609850	−	0.424160i
$616$	14.9871	−	2.04024i	0.603849	−	0.0822038i
$617$	−2.21444	−	15.4017i	−0.0891498	−	0.620051i	−0.984591	−	0.174871i	$-0.944049\pi$
$617$	−2.21444	−	15.4017i	−0.0891498	−	0.620051i	0.895441	−	0.445179i	$-0.146860\pi$
$618$	1.84114	+	3.59334i	0.0740615	+	0.144545i
$619$	−28.2193	−	24.4521i	−1.13423	−	0.982814i	−0.134261	−	0.990946i	$-0.542866\pi$
$619$	−28.2193	−	24.4521i	−1.13423	−	0.982814i	−0.999967	+	0.00813192i	$0.997412\pi$
$620$	−6.16454	+	31.1460i	−0.247574	+	1.25085i
$621$	−4.79017	−	0.233017i	−0.192223	−	0.00935065i
$622$	−7.79529	−	0.764027i	−0.312563	−	0.0306347i
$623$	−1.91620	+	2.21142i	−0.0767710	+	0.0885985i
$624$	12.3547	−	2.25330i	0.494584	−	0.0902043i
$625$	4.32680	+	30.0935i	0.173072	+	1.20374i
$626$	12.5587	+	36.5816i	0.501947	+	1.46209i
$627$	−0.644638	−	0.0926849i	−0.0257443	−	0.00370148i
$628$	1.45614	+	16.0995i	0.0581064	+	0.642442i
$629$	−9.70403	+	15.0998i	−0.386925	+	0.602067i
$630$	−11.4745	−	6.66311i	−0.457156	−	0.265465i
$631$	32.5288	+	9.55133i	1.29495	+	0.380232i	0.855392	−	0.517981i	$-0.173316\pi$
$631$	32.5288	+	9.55133i	1.29495	+	0.380232i	0.439560	+	0.898213i	$0.355134\pi$
$632$	−1.51829	−	3.39168i	−0.0603945	−	0.134914i
$633$	4.32699	+	4.99362i	0.171983	+	0.198478i
$634$	−10.9415	+	27.1337i	−0.434541	+	1.07762i
$635$	9.23384	+	4.21695i	0.366434	+	0.167345i
$636$	−19.1730	−	18.4653i	−0.760258	−	0.732195i
$637$	−3.05568	−	10.4067i	−0.121070	−	0.412327i
$638$	−2.30781	+	9.41021i	−0.0913672	+	0.372554i
$639$	−5.58372	−	12.2266i	−0.220888	−	0.483678i
$640$	−28.1400	−	16.9099i	−1.11233	−	0.668421i
$641$	−15.7811	+	10.1419i	−0.623316	+	0.400581i	−0.813830	−	0.581104i	$-0.802621\pi$
$641$	−15.7811	+	10.1419i	−0.623316	+	0.400581i	0.190513	+	0.981685i	$0.438985\pi$
$642$	11.3395	−	10.7582i	0.447535	−	0.424593i
$643$			40.0856i			1.58082i	0.612577	+	0.790411i	$0.290133\pi$
$643$			40.0856i			1.58082i	−0.612577	+	0.790411i	$0.709867\pi$
$644$	1.28960	+	30.9864i	0.0508173	+	1.22103i
$645$			31.2748i			1.23145i
$646$	−1.84544	−	1.94516i	−0.0726080	−	0.0765312i
$647$	−13.8950	+	8.92974i	−0.546267	+	0.351064i	−0.784486	−	0.620147i	$-0.787073\pi$
$647$	−13.8950	+	8.92974i	−0.546267	+	0.351064i	0.238219	+	0.971212i	$0.423437\pi$
$648$	0.423509	−	2.79654i	0.0166370	−	0.109858i
$649$	−3.05616	−	6.69205i	−0.119965	−	0.262686i
$650$	14.7495	+	3.61726i	0.578524	+	0.141880i
$651$	4.98358	+	16.9725i	0.195322	+	0.665206i
$652$	1.85625	−	1.92739i	0.0726964	−	0.0754826i
$653$	3.65881	+	1.67092i	0.143180	+	0.0653883i	0.485717	−	0.874116i	$-0.338559\pi$
$653$	3.65881	+	1.67092i	0.143180	+	0.0653883i	−0.342536	+	0.939505i	$0.611286\pi$
$654$	3.92136	+	1.58126i	0.153337	+	0.0618321i
$655$	4.10507	+	4.73750i	0.160398	+	0.185109i
$656$	−4.65256	−	13.8905i	−0.181652	−	0.542332i
$657$	−2.75600	−	0.809234i	−0.107522	−	0.0315712i
$658$	−20.0641	+	34.5524i	−0.782181	+	1.34699i
$659$	−11.2693	+	17.5353i	−0.438989	+	0.683080i	−0.988297	−	0.152540i	$-0.951255\pi$
$659$	−11.2693	+	17.5353i	−0.438989	+	0.683080i	0.549308	+	0.835620i	$0.314891\pi$
$660$	0.864618	+	9.55947i	0.0336552	+	0.372102i
$661$	3.37009	+	0.484546i	0.131081	+	0.0188466i	0.207543	−	0.978226i	$-0.433453\pi$
$661$	3.37009	+	0.484546i	0.131081	+	0.0188466i	−0.0764619	+	0.997073i	$0.524362\pi$
$662$	−27.8458	+	9.55964i	−1.08226	+	0.371546i
$663$	−2.15132	−	14.9628i	−0.0835505	−	0.581106i
$664$	−6.27483	−	21.9785i	−0.243511	−	0.852930i
$665$	2.41945	−	2.79220i	0.0938223	−	0.108277i
$666$	0.514257	−	5.24692i	0.0199271	−	0.203314i
$667$	−18.7674	−	6.51661i	−0.726675	−	0.252324i
$668$	41.8664	+	8.28636i	1.61986	+	0.320609i
$669$	−22.2348	−	19.2665i	−0.859646	−	0.744887i
$670$	6.42853	−	3.29382i	0.248356	−	0.127251i
$671$	−1.72133	−	11.9721i	−0.0664511	−	0.462178i
$672$	−18.2576	−	1.09855i	−0.704301	−	0.0423777i
$673$	6.50622	−	45.2517i	0.250796	−	1.74433i	−0.342659	−	0.939460i	$-0.611328\pi$
$673$	6.50622	−	45.2517i	0.250796	−	1.74433i	0.593456	−	0.804867i	$-0.297763\pi$
$674$	−4.51627	+	0.858737i	−0.173960	+	0.0330773i
$675$	1.84917	−	2.87737i	0.0711746	−	0.110750i
$676$	3.67151	−	5.10175i	0.141212	−	0.196221i
$677$	0.936652	−	3.18994i	0.0359984	−	0.122599i	−0.939534	−	0.342457i	$-0.888741\pi$
$677$	0.936652	−	3.18994i	0.0359984	−	0.122599i	0.975532	+	0.219857i	$0.0705592\pi$
$678$	18.5850	−	13.1644i	0.713751	−	0.505576i
$679$	−22.5851	−	26.0646i	−0.866736	−	1.00027i
$680$	−21.6133	+	33.0829i	−0.828834	+	1.26867i
$681$	12.0469	−	26.3790i	0.461637	−	1.01084i
$682$	7.93510	−	10.0386i	0.303851	−	0.384396i
$683$	−6.08118	−	20.7106i	−0.232690	−	0.792470i	−0.990201	−	0.139647i	$-0.955403\pi$
$683$	−6.08118	−	20.7106i	−0.232690	−	0.792470i	0.757511	−	0.652822i	$-0.226415\pi$
$684$	0.742942	+	0.261301i	0.0284071	+	0.00999109i
$685$	33.9109	−	15.4866i	1.29567	−	0.591712i
$686$	−0.730922	−	16.1956i	−0.0279067	−	0.618350i
$687$	18.6142	−	11.9626i	0.710177	−	0.456403i
$688$	19.3706	+	38.5144i	0.738498	+	1.46835i
$689$	41.7868			1.59195
$690$	−19.6807	−	0.0690037i	−0.749232	−	0.00262693i
$691$		−	50.1334i		−	1.90716i	−0.301134	−	0.953582i	$-0.597365\pi$
$691$		−	50.1334i		−	1.90716i	0.301134	−	0.953582i	$-0.402635\pi$
$692$	−1.53201	−	1.96827i	−0.0582381	−	0.0748225i
$693$	2.89115	+	4.49871i	0.109826	+	0.170892i
$694$	25.5255	−	1.15199i	0.968934	−	0.0437289i
$695$	7.76079	+	16.9938i	0.294384	+	0.644610i
$696$	4.94705	−	10.6210i	0.187518	−	0.402590i
$697$	−16.9187	+	4.96776i	−0.640840	+	0.188167i
$698$	29.6311	−	37.4858i	1.12155	−	1.41886i
$699$	6.67619	+	3.04891i	0.252517	+	0.115320i
$700$	−19.6086	−	10.2333i	−0.741135	−	0.386783i
$701$	−33.8457	+	29.3275i	−1.27833	+	1.10768i	−0.289736	+	0.957107i	$0.593567\pi$
$701$	−33.8457	+	29.3275i	−1.27833	+	1.10768i	−0.988598	+	0.150576i	$0.951887\pi$
$702$	2.56646	+	3.62322i	0.0968649	+	0.136750i
$703$	1.40850	+	0.413574i	0.0531227	+	0.0155982i
$704$	6.98559	+	11.2368i	0.263279	+	0.423503i
$705$	−21.3304	−	13.7082i	−0.803350	−	0.516282i
$706$	−9.22923	+	1.75487i	−0.347346	+	0.0660455i
$707$	−62.2251	−	8.94661i	−2.34021	−	0.336472i
$708$	2.05416	+	8.65601i	0.0772002	+	0.325313i
$709$	42.0839	−	6.05075i	1.58049	−	0.227241i	0.704550	−	0.709655i	$-0.251149\pi$
$709$	42.0839	−	6.05075i	1.58049	−	0.227241i	0.875943	+	0.482414i	$0.160240\pi$
$710$	−25.1530	−	49.0908i	−0.943973	−	1.84234i
$711$	0.860360	−	0.992908i	0.0322660	−	0.0372370i
$712$	−2.45051	−	0.739539i	−0.0918368	−	0.0277154i
$713$	18.9704	+	18.1248i	0.710449	+	0.678778i
$714$	−2.14756	+	21.9114i	−0.0803705	+	0.820013i
$715$	−11.3875	−	9.86733i	−0.425869	−	0.369017i
$716$	19.1591	+	48.5592i	0.716008	+	1.81474i
$717$	−1.05855	+	0.152197i	−0.0395324	+	0.00568389i
$718$	−5.83046	−	16.9832i	−0.217591	−	0.633808i
$719$	−1.55787	+	10.8352i	−0.0580987	+	0.404085i	0.939932	+	0.341361i	$0.110888\pi$
$719$	−1.55787	+	10.8352i	−0.0580987	+	0.404085i	−0.998031	+	0.0627241i	$0.980021\pi$
$720$	1.21879	−	11.5430i	0.0454217	−	0.430181i
$721$	7.76575	+	4.99075i	0.289212	+	0.185865i
$722$	13.3830	−	23.0469i	0.498065	−	0.857715i
$723$	4.85793	−	16.5446i	0.180669	−	0.615301i
$724$	−3.44730	+	1.96739i	−0.128118	+	0.0731175i
$725$	10.7079	−	9.27846i	0.397682	−	0.344593i
$726$	−4.37108	+	10.8398i	−0.162226	+	0.402304i
$727$	9.36134	−	20.4985i	0.347193	−	0.760246i	−0.652803	−	0.757527i	$-0.726407\pi$
$727$	9.36134	−	20.4985i	0.347193	−	0.760246i	0.999996	−	0.00271897i	$-0.000865476\pi$
$728$	21.8401	−	18.6396i	0.809447	−	0.690831i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	−11.4481	−	2.80760i	−0.423714	−	0.103914i
$731$	47.2035	−	21.5571i	1.74588	−	0.797318i
$732$	−0.768973	+	14.6061i	−0.0284221	+	0.539856i
$733$	4.30394	+	6.69705i	0.158969	+	0.247361i	0.911597	−	0.411085i	$-0.134850\pi$
$733$	4.30394	+	6.69705i	0.158969	+	0.247361i	−0.752627	+	0.658447i	$0.771214\pi$
$734$	14.4106	−	13.6718i	0.531904	−	0.504637i
$735$	−10.0244			−0.369754
$736$	−24.2792	+	12.1046i	−0.894942	+	0.446182i
$737$	−2.91113			−0.107233
$738$	3.75727	−	3.56466i	0.138307	−	0.131217i
$739$	−0.368407	−	0.573252i	−0.0135521	−	0.0210874i	0.834411	−	0.551142i	$-0.185808\pi$
$739$	−0.368407	−	0.573252i	−0.0135521	−	0.0210874i	−0.847963	+	0.530055i	$0.822171\pi$
$740$	1.13746	−	21.6052i	0.0418139	−	0.794224i
$741$	−1.12459	+	0.513582i	−0.0413128	+	0.0188669i
$742$	−59.1080	−	14.4960i	−2.16992	−	0.532164i
$743$	21.0402	−	6.17797i	0.771892	−	0.226648i	0.128010	−	0.991773i	$-0.459141\pi$
$743$	21.0402	−	6.17797i	0.771892	−	0.226648i	0.643882	+	0.765125i	$0.277323\pi$
$744$	−11.7700	+	10.0452i	−0.431508	+	0.368275i
$745$	−21.2410	+	46.5113i	−0.778210	+	1.70404i
$746$	−14.8542	+	36.8369i	−0.543852	+	1.34870i
$747$	6.10724	−	5.29196i	0.223452	−	0.193623i
$748$	13.8323	−	7.89413i	0.505757	−	0.288638i
$749$	10.0683	−	34.2896i	0.367889	−	1.25291i
$750$	−3.25529	+	5.60593i	−0.118867	+	0.204700i
$751$	−31.1257	−	20.0033i	−1.13579	−	0.729930i	−0.169031	−	0.985611i	$-0.554064\pi$
$751$	−31.1257	−	20.0033i	−1.13579	−	0.729930i	−0.966761	+	0.255681i	$0.917700\pi$
$752$	−34.7584	−	3.67006i	−1.26751	−	0.133833i
$753$	−0.535778	+	3.72642i	−0.0195248	+	0.135798i
$754$	5.97228	+	17.3963i	0.217498	+	0.633537i
$755$	45.5459	−	6.54851i	1.65759	−	0.238325i
$756$	−2.37339	−	6.01542i	−0.0863193	−	0.218779i
$757$	26.7864	+	23.2105i	0.973567	+	0.843601i	0.987710	−	0.156299i	$-0.0499565\pi$
$757$	26.7864	+	23.2105i	0.973567	+	0.843601i	−0.0141427	+	0.999900i	$0.504502\pi$
$758$	4.93448	−	50.3460i	0.179228	−	1.82865i
$759$	7.04641	+	3.64166i	0.255769	+	0.132184i
$760$	3.09409	+	0.933763i	0.112234	+	0.0338711i
$761$	−5.57445	+	6.43326i	−0.202074	+	0.233205i	−0.847737	−	0.530417i	$-0.822035\pi$
$761$	−5.57445	+	6.43326i	−0.202074	+	0.233205i	0.645663	+	0.763622i	$0.276581\pi$
$762$	2.25598	+	4.40297i	0.0817255	+	0.159503i
$763$	9.56857	−	1.37575i	0.346405	−	0.0498056i
$764$	7.81429	+	32.9286i	0.282711	+	1.19131i
$765$	−13.8293	−	1.98835i	−0.499998	−	0.0718889i
$766$	3.03893	−	0.577831i	0.109801	−	0.0208779i
$767$	−11.7487	−	7.55042i	−0.424220	−	0.272630i
$768$	−5.64841	−	14.9698i	−0.203820	−	0.540177i
$769$	−33.3018	−	9.77828i	−1.20089	−	0.352614i	−0.380698	−	0.924699i	$-0.624316\pi$
$769$	−33.3018	−	9.77828i	−1.20089	−	0.352614i	−0.820194	+	0.572086i	$0.806135\pi$
$770$	12.6848	+	17.9078i	0.457128	+	0.645354i
$771$	−14.5951	+	12.6467i	−0.525629	+	0.455460i
$772$	46.2536	+	24.1388i	1.66470	+	0.868775i
$773$	50.4990	+	23.0621i	1.81632	+	0.829487i	0.931775	+	0.363037i	$0.118260\pi$
$773$	50.4990	+	23.0621i	1.81632	+	0.829487i	0.884548	+	0.466450i	$0.154467\pi$
$774$	−9.45197	+	11.9575i	−0.339744	+	0.429805i
$775$	−17.9540	+	5.27178i	−0.644928	+	0.189368i
$776$	12.7382	−	27.3482i	0.457275	−	0.981743i
$777$	−5.00726	−	10.9644i	−0.179635	−	0.393345i
$778$	33.9537	−	1.53236i	1.21730	−	0.0549379i
$779$	0.779660	+	1.21318i	0.0279342	+	0.0434665i
$780$	11.1917	+	14.3788i	0.400728	+	0.514844i
$781$			22.2305i			0.795471i
$782$	13.4614	+	29.7519i	0.481377	+	1.06393i
$783$	4.14246			0.148040
$784$	−12.3448	+	6.20877i	−0.440887	+	0.221742i
$785$	−19.7308	+	12.6802i	−0.704222	+	0.452576i
$786$	0.137738	+	3.05197i	0.00491296	+	0.108860i
$787$	−38.1356	+	17.4159i	−1.35939	+	0.620812i	−0.955770	−	0.294116i	$-0.904975\pi$
$787$	−38.1356	+	17.4159i	−1.35939	+	0.620812i	−0.403618	+	0.914928i	$0.632247\pi$
$788$	−11.4503	−	4.02720i	−0.407900	−	0.143463i
$789$	4.19112	+	14.2737i	0.149208	+	0.508156i
$790$	3.34340	−	4.22967i	0.118953	−	0.150485i
$791$	21.6311	−	47.3656i	0.769114	−	1.68413i
$792$	−2.55852	+	3.91625i	−0.0909129	+	0.139158i
$793$	−15.0360	−	17.3524i	−0.533943	−	0.616203i
$794$	−16.3073	+	11.5511i	−0.578725	+	0.409932i
$795$	10.8808	−	37.0568i	0.385904	−	1.31427i
$796$	16.6479	−	23.1331i	0.590070	−	0.819932i
$797$	3.01543	−	4.69211i	0.106812	−	0.166203i	−0.783733	−	0.621098i	$-0.786687\pi$
$797$	3.01543	−	4.69211i	0.106812	−	0.166203i	0.890545	+	0.454895i	$0.150323\pi$
$798$	1.76891	−	0.336346i	0.0626188	−	0.0119065i
$799$	−5.98737	+	41.6430i	−0.211818	+	1.47322i
$800$	1.16208	−	19.3134i	0.0410858	−	0.682831i
$801$	−0.128792	−	0.895770i	−0.00455065	−	0.0316505i
$802$	9.90435	−	5.07475i	0.349735	−	0.179196i
$803$	3.59024	+	3.11096i	0.126697	+	0.109783i
$804$	3.45333	+	0.683497i	0.121790	+	0.0241051i
$805$	−38.9910	+	22.4591i	−1.37425	+	0.791581i
$806$	2.36943	−	24.1751i	0.0834597	−	0.851532i
$807$	17.4334	−	20.1192i	0.613686	−	0.708231i
$808$	−15.0970	−	52.8793i	−0.531110	−	1.86029i
$809$	−5.95818	−	41.4401i	−0.209479	−	1.45696i	−0.774864	−	0.632128i	$-0.782182\pi$
$809$	−5.95818	−	41.4401i	−0.209479	−	1.45696i	0.565385	−	0.824827i	$-0.308728\pi$
$810$	3.88138	−	1.33250i	0.136378	−	0.0468194i
$811$	25.2397	+	3.62893i	0.886287	+	0.127429i	0.570399	−	0.821368i	$-0.306789\pi$
$811$	25.2397	+	3.62893i	0.886287	+	0.127429i	0.315888	+	0.948796i	$0.397698\pi$
$812$	−2.41303	−	26.6792i	−0.0846807	−	0.936255i
$813$	−3.73711	+	5.81505i	−0.131066	+	0.203943i
$814$	−4.37858	+	7.54034i	−0.153469	+	0.264289i
$815$	3.72519	+	1.09381i	0.130488	+	0.0383147i
$816$	−18.2620	+	6.11679i	−0.639298	+	0.214130i
$817$	−2.77926	−	3.20744i	−0.0972341	−	0.112214i
$818$	−20.9492	−	8.44760i	−0.732471	−	0.295363i
$819$	9.23413	+	4.21709i	0.322667	+	0.147357i
$820$	14.7437	−	15.3087i	0.514871	−	0.534604i
$821$	−13.8983	−	47.3334i	−0.485055	−	1.65195i	−0.730784	−	0.682609i	$-0.760845\pi$
$821$	−13.8983	−	47.3334i	−0.485055	−	1.65195i	0.245729	−	0.969339i	$-0.420973\pi$
$822$	17.6458	+	4.32755i	0.615467	+	0.150941i
$823$	−6.89921	−	15.1072i	−0.240491	−	0.526602i	0.750445	−	0.660932i	$-0.229839\pi$
$823$	−6.89921	−	15.1072i	−0.240491	−	0.526602i	−0.990937	+	0.134330i	$0.957112\pi$
$824$	−1.20911	+	7.98408i	−0.0421214	+	0.278139i
$825$	−4.75887	+	3.05834i	−0.165682	+	0.106478i
$826$	13.9994	+	14.7558i	0.487102	+	0.513422i
$827$		−	25.6840i		−	0.893118i	−0.894754	−	0.446559i	$-0.852649\pi$
$827$		−	25.6840i		−	0.893118i	0.894754	−	0.446559i	$-0.147351\pi$
$828$	−7.50381	−	5.97435i	−0.260776	−	0.207623i
$829$		−	18.6090i		−	0.646316i	−0.946345	−	0.323158i	$-0.895256\pi$
$829$		−	18.6090i		−	0.646316i	0.946345	−	0.323158i	$-0.104744\pi$
$830$	24.0579	−	22.8247i	0.835063	−	0.792256i
$831$	2.45526	−	1.57790i	0.0851719	−	0.0547367i
$832$	22.6882	+	10.7754i	0.786571	+	0.373571i
$833$	6.90959	+	15.1299i	0.239403	+	0.524220i
$834$	−2.16867	+	8.84283i	−0.0750948	+	0.306202i
$835$	17.4454	+	59.4136i	0.603723	+	2.05609i
$836$	−0.938183	−	0.903552i	−0.0324477	−	0.0312500i
$837$	−4.97643	−	2.27266i	−0.172010	−	0.0785545i
$838$	−5.81946	+	14.4317i	−0.201030	+	0.498534i
$839$	26.8086	+	30.9387i	0.925534	+	1.06812i	0.997496	+	0.0707163i	$0.0225285\pi$
$839$	26.8086	+	30.9387i	0.925534	+	1.06812i	−0.0719621	+	0.997407i	$0.522926\pi$
$840$	−10.8428	−	24.2215i	−0.374113	−	0.835720i
$841$	−11.3604	−	3.33572i	−0.391738	−	0.115025i
$842$	27.6665	+	16.0656i	0.953449	+	0.553656i
$843$	−10.4621	+	16.2793i	−0.360333	+	0.560689i
$844$	1.19039	+	13.1613i	0.0409749	+	0.453030i
$845$	9.02678	+	1.29786i	0.310531	+	0.0446476i
$846$	−4.01247	−	11.6877i	−0.137952	−	0.401832i
$847$	3.80300	+	26.4504i	0.130673	+	0.908848i
$848$	−9.55220	−	52.3740i	−0.328024	−	1.79853i
$849$	−12.2343	+	14.1191i	−0.419880	+	0.484567i
$850$	−23.1785	−	2.27175i	−0.795015	−	0.0779205i
$851$	−14.5529	−	10.3852i	−0.498867	−	0.355999i
$852$	5.21946	−	26.3710i	0.178816	−	0.903457i
$853$	1.33256	+	1.15467i	0.0456259	+	0.0395350i	0.677375	−	0.735638i	$-0.263117\pi$
$853$	1.33256	+	1.15467i	0.0456259	+	0.0395350i	−0.631749	+	0.775173i	$0.717663\pi$
$854$	15.2490	+	29.7613i	0.521809	+	1.01841i
$855$	0.162617	+	1.13102i	0.00556137	+	0.0386802i
$856$	30.9760	−	4.21685i	1.05874	−	0.144129i
$857$	−3.21807	+	22.3821i	−0.109927	+	0.764559i	0.858058	+	0.513552i	$0.171671\pi$
$857$	−3.21807	+	22.3821i	−0.109927	+	0.764559i	−0.967985	+	0.251007i	$0.919238\pi$
$858$	−1.37173	−	7.21421i	−0.0468302	−	0.246289i
$859$	24.5621	−	38.2194i	0.838048	−	1.30403i	−0.112564	−	0.993644i	$-0.535906\pi$
$859$	24.5621	−	38.2194i	0.838048	−	1.30403i	0.950612	−	0.310383i	$-0.100457\pi$
$860$	−36.5366	+	50.7695i	−1.24589	+	1.73122i
$861$	3.33608	−	11.3616i	0.113693	−	0.387203i
$862$	−16.8284	−	23.7576i	−0.573176	−	0.809186i
$863$	−11.1175	−	12.8302i	−0.378443	−	0.436746i	0.534291	−	0.845300i	$-0.320579\pi$
$863$	−11.1175	−	12.8302i	−0.378443	−	0.436746i	−0.912734	+	0.408554i	$0.866033\pi$
$864$	3.95454	−	4.04495i	0.134536	−	0.137612i
$865$	1.50332	−	3.29181i	0.0511145	−	0.111925i
$866$	31.3839	+	24.8078i	1.06647	+	0.843003i
$867$	1.74174	+	5.93182i	0.0591526	+	0.201455i
$868$	−11.7380	+	33.3741i	−0.398415	+	1.13279i
$869$	−1.97654	+	0.902655i	−0.0670495	+	0.0306205i
$870$	16.9823	−	0.766428i	0.575754	−	0.0259843i
$871$	−4.64897	+	2.98771i	−0.157524	+	0.101235i
$872$	4.51837	+	7.14801i	0.153011	+	0.242062i
$873$	10.6664			0.361005
$874$	2.02452	−	1.74187i	0.0684804	−	0.0589195i
$875$			14.8212i			0.501048i
$876$	−3.52852	−	4.53333i	−0.119218	−	0.153167i
$877$	−13.5946	−	21.1537i	−0.459058	−	0.714308i	0.532146	−	0.846653i	$-0.321386\pi$
$877$	−13.5946	−	21.1537i	−0.459058	−	0.714308i	−0.991204	+	0.132345i	$0.957749\pi$
$878$	−1.04760	−	23.2123i	−0.0353547	−	0.783379i
$879$	0.325629	+	0.713028i	0.0109832	+	0.0240498i
$880$	−9.76423	+	16.5283i	−0.329152	+	0.557168i
$881$	33.3210	−	9.78392i	1.12261	−	0.329629i	0.332812	−	0.942993i	$-0.392002\pi$
$881$	33.3210	−	9.78392i	1.12261	−	0.329629i	0.789800	+	0.613364i	$0.210184\pi$
$882$	−3.83269	−	3.02959i	−0.129053	−	0.102012i
$883$	−1.76315	−	0.805202i	−0.0593346	−	0.0270972i	0.385527	−	0.922697i	$-0.374020\pi$
$883$	−1.76315	−	0.805202i	−0.0593346	−	0.0270972i	−0.444861	+	0.895599i	$0.646747\pi$
$884$	13.9879	−	26.8028i	0.470463	−	0.901477i
$885$	−9.75500	+	8.45276i	−0.327911	+	0.284136i
$886$	−2.25143	+	1.59477i	−0.0756381	+	0.0535773i
$887$	−11.7349	−	3.44568i	−0.394020	−	0.115695i	0.0787199	−	0.996897i	$-0.474917\pi$
$887$	−11.7349	−	3.44568i	−0.394020	−	0.115695i	−0.472740	+	0.881202i	$0.656735\pi$
$888$	6.96449	−	7.91671i	0.233713	−	0.265668i
$889$	9.51550	+	6.11524i	0.319140	+	0.205099i
$890$	−0.693725	−	3.64844i	−0.0232537	−	0.122296i
$891$	−1.63706	−	0.235374i	−0.0548437	−	0.00788533i
$892$	−13.5864	−	57.2516i	−0.454907	−	1.91693i
$893$	3.40577	−	0.489676i	0.113970	−	0.0163864i
$894$	−22.1780	+	11.3635i	−0.741743	+	0.380052i
$895$	−49.5989	+	57.2401i	−1.65791	+	1.91333i
$896$	−28.3547	−	23.1126i	−0.947265	−	0.772138i
$897$	14.9904	−	1.41618i	0.500514	−	0.0472849i
$898$	19.7856	+	1.93922i	0.660256	+	0.0647125i
$899$	−17.1273	−	14.8409i	−0.571227	−	0.494971i
$900$	6.36328	−	2.51064i	0.212109	−	0.0836880i
$901$	−63.4301	+	9.11988i	−2.11316	+	0.303827i
$902$	−8.10170	+	2.78137i	−0.269757	+	0.0926094i
$903$	−4.95945	+	34.4937i	−0.165040	+	1.14788i
$904$	45.5488	+	0.341553i	1.51493	+	0.0113599i
$905$	−4.84467	−	3.11348i	−0.161042	−	0.103496i
$906$	19.3930	+	11.2613i	0.644289	+	0.374131i
$907$	7.86999	−	26.8027i	0.261319	−	0.889970i	−0.719408	−	0.694587i	$-0.755587\pi$
$907$	7.86999	−	26.8027i	0.261319	−	0.889970i	0.980727	−	0.195382i	$-0.0625948\pi$
$908$	50.3731	−	28.7481i	1.67169	−	0.954040i
$909$	14.6938	−	12.7322i	0.487362	−	0.422301i
$910$	38.6362	+	15.5797i	1.28078	+	0.516464i
$911$	−17.8874	+	39.1680i	−0.592637	+	1.29769i	0.341199	+	0.939991i	$0.389167\pi$
$911$	−17.8874	+	39.1680i	−0.592637	+	1.29769i	−0.933836	+	0.357702i	$0.883560\pi$
$912$	0.900779	+	1.29212i	0.0298278	+	0.0427862i
$913$	−12.8238	+	3.76542i	−0.424407	+	0.124617i
$914$	4.47843	−	18.2610i	0.148133	−	0.604020i
$915$	−19.3035	+	8.81559i	−0.638153	+	0.291435i
$916$	44.1923	+	2.32661i	1.46016	+	0.0768734i
$917$	3.77632	+	5.87606i	0.124705	+	0.194045i
$918$	−4.68652	−	4.93974i	−0.154678	−	0.163036i
$919$	−14.2897			−0.471375			−0.235688	−	0.971829i	$-0.575734\pi$
$919$	−14.2897			−0.471375			−0.235688	+	0.971829i	$0.575734\pi$
$920$	−31.8677	−	23.1039i	−1.05065	−	0.761712i
$921$	−30.3774			−1.00097
$922$	32.8863	+	34.6632i	1.08305	+	1.14157i
$923$	22.8154	+	35.5014i	0.750977	+	1.16854i
$924$	−0.562299	+	10.6805i	−0.0184983	+	0.351362i
$925$	11.5984	−	5.29683i	0.381354	−	0.174159i
$926$	5.01914	−	20.4658i	0.164939	−	0.672547i
$927$	−2.73934	+	0.804342i	−0.0899717	+	0.0264181i
$928$	20.4387	−	11.4621i	0.670932	−	0.376263i
$929$	5.56401	−	12.1835i	0.182549	−	0.399727i	−0.796129	−	0.605127i	$-0.793122\pi$
$929$	5.56401	−	12.1835i	0.182549	−	0.399727i	0.978678	+	0.205400i	$0.0658495\pi$
$930$	−20.8217	−	8.39618i	−0.682769	−	0.275322i
$931$	1.02807	−	0.890824i	0.0336935	−	0.0291956i
$932$	7.27580	+	12.7488i	0.238327	+	0.417601i
$933$	1.56038	−	5.31417i	0.0510845	−	0.173978i
$934$	−21.9903	−	12.7695i	−0.719544	−	0.417831i
$935$	19.4392	+	12.4928i	0.635729	+	0.408558i
$936$	−0.0665873	+	8.87995i	−0.00217648	+	0.290250i
$937$	0.655584	−	4.55969i	0.0214170	−	0.148958i	−0.976307	−	0.216391i	$-0.930572\pi$
$937$	0.655584	−	4.55969i	0.0214170	−	0.148958i	0.997724	+	0.0674322i	$0.0214806\pi$
$938$	7.61249	−	2.61342i	0.248557	−	0.0853312i
$939$	−27.0706	+	3.89216i	−0.883416	+	0.127016i
$940$	−18.6118	−	47.1721i	−0.607050	−	1.53858i
$941$	5.19347	+	4.50017i	0.169302	+	0.146701i	0.735391	−	0.677643i	$-0.236999\pi$
$941$	5.19347	+	4.50017i	0.169302	+	0.146701i	−0.566089	+	0.824344i	$0.691544\pi$
$942$	−11.3761	−	1.11498i	−0.370652	−	0.0363281i
$943$	−4.12356	−	17.0725i	−0.134282	−	0.555958i
$944$	−6.77774	+	16.4513i	−0.220597	+	0.535446i
$945$	6.14421	−	7.09080i	0.199871	−	0.230664i
$946$	22.4354	−	11.4953i	0.729437	−	0.373746i
$947$	−34.4627	+	4.95498i	−1.11989	+	0.161015i	−0.677298	−	0.735709i	$-0.736849\pi$
$947$	−34.4627	+	4.95498i	−1.11989	+	0.161015i	−0.442589	+	0.896725i	$0.645940\pi$
$948$	2.55661	−	0.606710i	0.0830348	−	0.0197050i
$949$	8.92630	+	1.28341i	0.289760	+	0.0416612i
$950$	0.355797	+	1.87121i	0.0115436	+	0.0607099i
$951$	−17.4035	−	11.1846i	−0.564347	−	0.362684i
$952$	−29.0840	+	33.0606i	−0.942619	+	1.07150i
$953$	48.4033	+	14.2125i	1.56794	+	0.460388i	0.946400	−	0.322996i	$-0.104690\pi$
$953$	48.4033	+	14.2125i	1.56794	+	0.460388i	0.621538	+	0.783384i	$0.286508\pi$
$954$	15.3596	−	10.8797i	0.497284	−	0.352244i
$955$	−37.1092	+	32.1553i	−1.20083	+	1.04052i
$956$	−1.89618	−	0.989581i	−0.0613270	−	0.0320053i
$957$	−6.23208	−	2.84609i	−0.201454	−	0.0920011i
$958$	−24.8307	−	19.6277i	−0.802244	−	0.634144i
$959$	39.8569	−	11.7030i	1.28705	−	0.377911i
$960$	15.4635	−	17.3142i	0.499082	−	0.558814i
$961$	−0.444586	−	0.973508i	−0.0143415	−	0.0314035i
$962$	0.746262	+	16.5355i	0.0240604	+	0.533124i
$963$	5.97553	+	9.29811i	0.192559	+	0.299627i
$964$	27.2142	−	21.1821i	0.876509	−	0.682231i
$965$			75.6981i			2.43681i
$966$	−21.6954	−	3.19700i	−0.698037	−	0.102862i
$967$	−14.2706			−0.458910			−0.229455	−	0.973319i	$-0.573694\pi$
$967$	−14.2706			−0.458910			−0.229455	+	0.973319i	$0.573694\pi$
$968$	−19.7593	+	12.4901i	−0.635087	+	0.401449i
$969$	1.59498	−	1.02503i	0.0512381	−	0.0329287i
$970$	43.7278	−	1.97348i	1.40402	−	0.0633646i
$971$	−14.9312	+	6.81885i	−0.479165	+	0.218827i	−0.640330	−	0.768100i	$-0.721202\pi$
$971$	−14.9312	+	6.81885i	−0.479165	+	0.218827i	0.161165	+	0.986928i	$0.448475\pi$
$972$	1.88671	+	0.663576i	0.0605162	+	0.0212842i
$973$	5.86474	+	19.9735i	0.188015	+	0.640320i
$974$	−27.3683	−	21.6336i	−0.876936	−	0.693184i
$975$	−4.46096	+	9.76813i	−0.142865	+	0.312831i
$976$	−18.3118	+	22.8122i	−0.586145	+	0.730200i
$977$	−19.2389	−	22.2029i	−0.615506	−	0.710332i	0.359341	−	0.933206i	$-0.383002\pi$
$977$	−19.2389	−	22.2029i	−0.615506	−	0.710332i	−0.974847	+	0.222874i	$0.928456\pi$
$978$	1.09370	+	1.54404i	0.0349728	+	0.0493731i
$979$	−0.421682	+	1.43612i	−0.0134770	+	0.0458985i
$980$	−16.2729	−	11.7109i	−0.519818	−	0.374091i
$981$	−1.61639	+	2.51515i	−0.0516074	+	0.0803026i
$982$	5.35000	+	28.1367i	0.170725	+	0.897878i
$983$	2.22237	−	15.4569i	0.0708825	−	0.492999i	−0.923196	−	0.384331i	$-0.874432\pi$
$983$	2.22237	−	15.4569i	0.0708825	−	0.492999i	0.994078	−	0.108668i	$-0.0346586\pi$
$984$	10.2637	−	1.39723i	0.327195	−	0.0445420i
$985$	−2.50627	−	17.4315i	−0.0798563	−	0.555413i
$986$	−12.8623	−	25.1033i	−0.409620	−	0.799452i
$987$	−21.3520	−	18.5016i	−0.679642	−	0.588913i
$988$	−2.42557	−	0.480078i	−0.0771677	−	0.0152733i
$989$	19.1624	+	48.0053i	0.609328	+	1.52648i
$990$	−6.75479	−	0.662046i	−0.214681	−	0.0210412i
$991$	−16.4224	+	18.9525i	−0.521676	+	0.602046i	−0.954050	−	0.299649i	$-0.903131\pi$
$991$	−16.4224	+	18.9525i	−0.521676	+	0.602046i	0.432374	+	0.901694i	$0.357676\pi$
$992$	−30.8418	+	2.55652i	−0.979228	+	0.0811696i
$993$	−2.96270	−	20.6060i	−0.0940185	−	0.653913i
$994$	−19.9571	−	58.1320i	−0.633002	−	1.84384i
$995$	40.9306	+	5.88493i	1.29759	+	0.186565i
$996$	16.0964	−	1.45586i	0.510033	−	0.0461306i
$997$	−28.9284	+	45.0135i	−0.916171	+	1.42559i	−0.0112855	+	0.999936i	$0.503592\pi$
$997$	−28.9284	+	45.0135i	−0.916171	+	1.42559i	−0.904886	+	0.425654i	$0.860044\pi$
$998$	−11.5658	−	6.71614i	−0.366110	−	0.212596i
$999$	3.57690	+	1.05027i	0.113168	+	0.0332292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.13	yes	480
8.5	even	2	inner	552.2.bb.a.85.15	yes	480
23.13	even	11	inner	552.2.bb.a.13.15	yes	480
184.13	even	22	inner	552.2.bb.a.13.13	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.13	✓	480	184.13	even	22	inner
552.2.bb.a.13.15	yes	480	23.13	even	11	inner
552.2.bb.a.85.13	yes	480	1.1	even	1	trivial
552.2.bb.a.85.15	yes	480	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02595 + 0.973358i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(0.105149 - 1.99723i) q^{4} +(2.63955 - 1.20544i) q^{5} +(1.37351 + 0.336848i) q^{6} +(3.10238 - 0.910940i) q^{7} +(1.83615 + 2.15141i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.02595 + 0.973358i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(0.105149 - 1.99723i) q^{4} +(2.63955 - 1.20544i) q^{5} +(1.37351 + 0.336848i) q^{6} +(3.10238 - 0.910940i) q^{7} +(1.83615 + 2.15141i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-1.53472 + 3.80595i) q^{10} +(1.24993 - 1.08307i) q^{11} +(-1.73703 + 0.991329i) q^{12} +(0.884534 - 3.01245i) q^{13} +(-2.29622 + 3.95430i) q^{14} +(-2.44113 - 1.56882i) q^{15} +(-3.97789 - 0.420015i) q^{16} +(-0.685217 + 4.76579i) q^{17} +(-0.459202 - 1.33758i) q^{18} +(0.389769 - 0.0560403i) q^{19} +(-2.13001 - 5.39856i) q^{20} +(-2.44360 - 2.11739i) q^{21} +(-0.228152 + 2.32781i) q^{22} +(-4.70825 - 0.912357i) q^{23} +(0.817187 - 2.70780i) q^{24} +(2.23984 - 2.58491i) q^{25} +(2.02470 + 3.95159i) q^{26} +(0.989821 - 0.142315i) q^{27} +(-1.49315 - 6.29196i) q^{28} +(4.10030 + 0.589534i) q^{29} +(4.03151 - 0.766563i) q^{30} +(-4.60234 - 2.95774i) q^{31} +(4.48994 - 3.44099i) q^{32} +(-1.58690 - 0.465957i) q^{33} +(-3.93582 - 5.55642i) q^{34} +(7.09080 - 6.14421i) q^{35} +(1.77307 + 0.925328i) q^{36} +(3.39103 + 1.54863i) q^{37} +(-0.345336 + 0.436879i) q^{38} +(-3.01245 + 0.884534i) q^{39} +(7.44001 + 3.46539i) q^{40} +(1.52135 + 3.33129i) q^{41} +(4.56800 - 0.206158i) q^{42} +(-5.82692 - 9.06687i) q^{43} +(-2.03172 - 2.61029i) q^{44} +2.90178i q^{45} +(5.71848 - 3.64678i) q^{46} +8.73791 q^{47} +(1.79727 + 3.57349i) q^{48} +(2.90616 - 1.86768i) q^{49} +(0.218080 + 4.83216i) q^{50} +(4.37969 - 2.00014i) q^{51} +(-5.92355 - 2.08338i) q^{52} +(3.74971 + 12.7704i) q^{53} +(-0.876985 + 1.10946i) q^{54} +(1.99368 - 4.36555i) q^{55} +(7.65622 + 5.00187i) q^{56} +(-0.257869 - 0.297597i) q^{57} +(-4.78053 + 3.38622i) q^{58} +(1.25320 - 4.26802i) q^{59} +(-3.38999 + 4.71055i) q^{60} +(3.95379 - 6.15222i) q^{61} +(7.60072 - 1.44522i) q^{62} +(-0.460154 + 3.20044i) q^{63} +(-1.25714 + 7.90061i) q^{64} +(-1.29656 - 9.01777i) q^{65} +(2.08163 - 1.06658i) q^{66} +(-1.33024 - 1.15266i) q^{67} +(9.44634 + 1.86966i) q^{68} +(1.77795 + 4.45409i) q^{69} +(-1.29429 + 13.2055i) q^{70} +(-8.80218 + 10.1583i) q^{71} +(-2.71975 + 0.776488i) q^{72} +(0.408778 + 2.84311i) q^{73} +(-4.98640 + 1.71186i) q^{74} +(-3.38552 - 0.486764i) q^{75} +(-0.0709417 - 0.784352i) q^{76} +(2.89115 - 4.49871i) q^{77} +(2.22965 - 3.83968i) q^{78} +(-1.26059 - 0.370142i) q^{79} +(-11.0061 + 3.68647i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-4.80336 - 1.93692i) q^{82} +(-7.35078 - 3.35699i) q^{83} +(-4.48588 + 4.65781i) q^{84} +(3.93622 + 13.4055i) q^{85} +(14.8034 + 3.63048i) q^{86} +(-1.72084 - 3.76812i) q^{87} +(4.62519 + 0.700440i) q^{88} +(-0.761319 + 0.489270i) q^{89} +(-2.82447 - 2.97708i) q^{90} -10.1515i q^{91} +(-2.31726 + 9.30754i) q^{92} +5.47081i q^{93} +(-8.96467 + 8.50512i) q^{94} +(0.961262 - 0.617766i) q^{95} +(-5.32219 - 1.91684i) q^{96} +(-4.43100 - 9.70254i) q^{97} +(-1.16366 + 4.74488i) q^{98} +(0.465957 + 1.58690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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