LMFDB - Embedded newform 552.2.bb.a.13.13

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			13.13
Character	$\chi$	$=$	552.13
Dual form			552.2.bb.a.85.13

$q$-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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$	$-1$	$1$

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	0.906315	−	0.422602i	$-0.138883\pi$
$5$	2.63955	+	1.20544i	1.18044	+	0.539091i	0.274129	+	0.961693i	$0.411611\pi$
$6$	1.37351	−	0.336848i	0.560734	−	0.137517i
$7$	3.10238	+	0.910940i	1.17259	+	0.344303i	0.809312	−	0.587378i	$-0.199840\pi$
$7$	3.10238	+	0.910940i	1.17259	+	0.344303i	0.363276	+	0.931682i	$0.381658\pi$
$8$	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	0.822613	−	0.568602i	$-0.192515\pi$
$11$	1.24993	+	1.08307i	0.376869	+	0.326559i	−0.445744	+	0.895160i	$0.647061\pi$
$12$	−1.73703	−	0.991329i	−0.501437	−	0.286172i
$13$	0.884534	+	3.01245i	0.245326	+	0.835502i	0.986440	+	0.164123i	$0.0524795\pi$
$13$	0.884534	+	3.01245i	0.245326	+	0.835502i	−0.741114	+	0.671379i	$0.765702\pi$
$14$	−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	−0.886672	−	0.462400i	$-0.846989\pi$
$17$	−0.685217	−	4.76579i	−0.166189	−	1.15587i	0.720482	−	0.693473i	$-0.243921\pi$
$18$	−0.459202	+	1.33758i	−0.108235	+	0.315272i
$19$	0.389769	+	0.0560403i	0.0894191	+	0.0128565i	0.186879	−	0.982383i	$-0.440163\pi$
$19$	0.389769	+	0.0560403i	0.0894191	+	0.0128565i	−0.0974600	+	0.995239i	$0.531072\pi$
$20$	−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	0.249336	−	0.968417i	$-0.419788\pi$
$29$	4.10030	−	0.589534i	0.761406	−	0.109474i	0.512070	+	0.858943i	$0.328879\pi$
$30$	4.03151	+	0.766563i	0.736049	+	0.139955i
$31$	−4.60234	+	2.95774i	−0.826605	+	0.531227i	−0.884197	−	0.467114i	$-0.845294\pi$
$31$	−4.60234	+	2.95774i	−0.826605	+	0.531227i	0.0575927	+	0.998340i	$0.481658\pi$
$32$	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	−0.116690	−	0.993168i	$-0.537228\pi$
$37$	3.39103	−	1.54863i	0.557481	−	0.254593i	0.674171	+	0.738575i	$0.264501\pi$
$38$	−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	−0.752847	−	0.658196i	$-0.771320\pi$
$41$	1.52135	−	3.33129i	0.237595	−	0.520259i	0.990441	+	0.137937i	$0.0440470\pi$
$42$	4.56800	+	0.206158i	0.704858	+	0.0318109i
$43$	−5.82692	+	9.06687i	−0.888597	+	1.38268i	0.0350272	+	0.999386i	$0.488848\pi$
$43$	−5.82692	+	9.06687i	−0.888597	+	1.38268i	−0.923625	+	0.383298i	$0.874788\pi$
$44$	−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	−0.131535	−	0.991312i	$-0.541991\pi$
$53$	3.74971	−	12.7704i	0.515063	−	1.75414i	0.646598	−	0.762831i	$-0.276191\pi$
$54$	−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	0.999967	+	0.00816090i	$0.00259772\pi$
$59$	1.25320	+	4.26802i	0.163153	+	0.555649i	−0.836813	+	0.547488i	$0.815584\pi$
$60$	−3.38999	−	4.71055i	−0.437645	−	0.608130i
$61$	3.95379	+	6.15222i	0.506231	+	0.787711i	0.996476	−	0.0838737i	$-0.0267292\pi$
$61$	3.95379	+	6.15222i	0.506231	+	0.787711i	−0.490245	+	0.871584i	$0.663093\pi$
$62$	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	−0.732322	−	0.680959i	$-0.761563\pi$
$67$	−1.33024	+	1.15266i	−0.162515	+	0.140820i	0.569807	+	0.821778i	$0.307018\pi$
$68$	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	−0.978177	−	0.207773i	$-0.933378\pi$
$71$	−8.80218	−	10.1583i	−1.04463	−	1.20556i	−0.0664494	−	0.997790i	$-0.521167\pi$
$72$	−2.71975	−	0.776488i	−0.320526	−	0.0915100i
$73$	0.408778	−	2.84311i	0.0478438	−	0.332761i	−0.951816	−	0.306670i	$-0.900785\pi$
$73$	0.408778	−	2.84311i	0.0478438	−	0.332761i	0.999660	−	0.0260906i	$-0.00830584\pi$
$74$	−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	−0.351876	−	0.936047i	$-0.614456\pi$
$79$	−1.26059	+	0.370142i	−0.141827	+	0.0416442i	0.210048	+	0.977691i	$0.432638\pi$
$80$	−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	−0.775751	−	0.631039i	$-0.782629\pi$
$83$	−7.35078	+	3.35699i	−0.806852	+	0.368477i	−0.0311014	+	0.999516i	$0.509901\pi$
$84$	−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	0.499669	−	0.866217i	$-0.333455\pi$
$89$	−0.761319	−	0.489270i	−0.0806996	−	0.0518625i	−0.580368	+	0.814354i	$0.697091\pi$
$90$	−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	0.539774	+	0.841810i	$0.318510\pi$
$97$	−4.43100	+	9.70254i	−0.449900	+	0.985144i	−0.989674	+	0.143334i	$0.954218\pi$
$98$	−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	−0.774544	+	0.632520i	$0.782021\pi$
$101$	−17.6857	+	8.07677i	−1.75979	+	0.803669i	−0.985245	+	0.171149i	$0.945252\pi$
$102$	−2.54650	−	6.31505i	−0.252141	−	0.625283i
$103$	1.86962	−	2.15765i	0.184219	−	0.212600i	−0.656127	−	0.754651i	$-0.727806\pi$
$103$	1.86962	−	2.15765i	0.184219	−	0.212600i	0.840346	+	0.542051i	$0.182352\pi$
$104$	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	0.999971	−	0.00757633i	$-0.00241164\pi$
$107$	5.97553	+	9.29811i	0.577677	+	0.898882i	−0.422295	+	0.906459i	$0.638775\pi$
$108$	−0.180157	+	1.99187i	−0.0173356	+	0.191668i
$109$	2.95934	−	0.425488i	0.283453	−	0.0407544i	0.000878016	−	1.00000i	$-0.499721\pi$
$109$	2.95934	−	0.425488i	0.283453	−	0.0407544i	0.282575	+	0.959245i	$0.408811\pi$
$110$	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	0.989440	+	0.144944i	$0.0463001\pi$
$113$	10.5461	+	12.1709i	0.992096	+	1.14494i	0.00265623	+	0.999996i	$0.499154\pi$
$114$	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	−0.644950	−	0.764225i	$-0.723122\pi$
$127$	2.29087	−	2.64381i	0.203282	−	0.234600i	0.848232	+	0.529625i	$0.177667\pi$
$128$	−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	−0.928623	−	0.371024i	$-0.879007\pi$
$131$	0.608616	−	2.07276i	0.0531751	−	0.181098i	0.981798	+	0.189926i	$0.0608249\pi$
$132$	−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	$-0.911972\pi$
$139$		−	6.43812i		−	0.546074i	0.962003	−	0.273037i	$-0.0880282\pi$
$140$	−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	−0.0922413	−	0.995737i	$-0.529403\pi$
$149$	−13.3170	−	11.5392i	−1.09097	−	0.945331i	−0.998729	+	0.0504057i	$0.983949\pi$
$150$	3.94717	+	2.79592i	0.322285	+	0.228286i
$151$	15.2149	−	4.46750i	1.23817	−	0.363560i	0.403844	−	0.914828i	$-0.367674\pi$
$151$	15.2149	−	4.46750i	1.23817	−	0.363560i	0.834329	+	0.551267i	$0.185856\pi$
$152$	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	−0.184540	−	0.982825i	$-0.559079\pi$
$157$	−8.00036	−	1.15028i	−0.638498	−	0.0918022i	−0.453958	+	0.891023i	$0.649989\pi$
$158$	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	−0.614361	−	0.789025i	$-0.710586\pi$
$163$	1.01116	−	0.876175i	0.0792002	−	0.0686274i	0.693561	+	0.720398i	$0.256041\pi$
$164$	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	−0.675954	−	0.736944i	$-0.736268\pi$
$167$	−3.03690	−	21.1221i	−0.235002	−	1.63447i	0.440952	−	0.897531i	$-0.354641\pi$
$168$	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	0.689953	−	0.723854i	$-0.257631\pi$
$173$	0.942503	+	0.816684i	0.0716572	+	0.0620913i	−0.618296	+	0.785945i	$0.712177\pi$
$174$	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	−0.978791	−	0.204863i	$-0.934325\pi$
$179$	−23.7424	−	10.8428i	−1.77459	−	0.810427i	−0.795797	−	0.605564i	$-0.792948\pi$
$180$	5.79554	−	0.305120i	0.431974	−	0.0227423i
$181$	−1.07296	+	1.66955i	−0.0797521	+	0.124097i	−0.878838	−	0.477120i	$-0.841681\pi$
$181$	−1.07296	+	1.66955i	−0.0797521	+	0.124097i	0.799086	+	0.601217i	$0.205317\pi$
$182$	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	−0.364634	−	0.931151i	$-0.618806\pi$
$191$	−16.2361	−	4.76735i	−1.17480	−	0.344953i	−0.810168	+	0.586198i	$0.800624\pi$
$192$	7.32608	+	3.21382i	0.528714	+	0.231937i
$193$	−10.8368	−	23.7294i	−0.780052	−	1.70808i	−0.703154	−	0.711037i	$-0.748226\pi$
$193$	−10.8368	−	23.7294i	−0.780052	−	1.70808i	−0.0768979	−	0.997039i	$-0.524502\pi$
$194$	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	0.997710	−	0.0676302i	$-0.0215438\pi$
$197$	1.70982	+	5.82310i	0.121819	+	0.414879i	−0.875891	+	0.482509i	$0.839726\pi$
$198$	−2.02267	+	1.17454i	−0.143745	+	0.0834710i
$199$	11.9882	−	7.70434i	0.849820	−	0.546146i	−0.0416984	−	0.999130i	$-0.513277\pi$
$199$	11.9882	−	7.70434i	0.849820	−	0.546146i	0.891519	+	0.452984i	$0.149641\pi$
$200$	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	−0.0865395	−	0.996248i	$-0.527581\pi$
$211$	−6.54025	−	0.940346i	−0.450249	−	0.0647361i	−0.363710	+	0.931512i	$0.618490\pi$
$212$	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	0.993662	+	0.112413i	$0.0358580\pi$
$223$	28.2291	+	8.28880i	1.89036	+	0.555059i	0.896696	+	0.442646i	$0.145960\pi$
$224$	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	0.291746	−	0.956496i	$-0.405764\pi$
$227$	15.6784	−	24.3960i	1.04061	−	1.61922i	0.748864	−	0.662724i	$-0.230600\pi$
$228$	−0.621485	−	0.483733i	−0.0411589	−	0.0320360i
$229$		−	22.1268i		−	1.46218i	−0.682282	−	0.731089i	$-0.739012\pi$
$229$		−	22.1268i		−	1.46218i	0.682282	−	0.731089i	$-0.260988\pi$
$230$	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	0.322538	−	0.946557i	$-0.395464\pi$
$233$	−6.17433	−	3.96800i	−0.404494	−	0.259952i	−0.727031	+	0.686604i	$0.759100\pi$
$234$	−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	0.923456	−	0.383704i	$-0.125352\pi$
$239$	0.444260	+	0.972794i	0.0287368	+	0.0629248i	−0.894719	+	0.446629i	$0.852624\pi$
$240$	9.05162	−	7.26591i	0.584280	−	0.469012i
$241$	11.2918	−	13.0314i	0.727369	−	0.839429i	−0.264803	−	0.964302i	$-0.585307\pi$
$241$	11.2918	−	13.0314i	0.727369	−	0.839429i	0.992173	+	0.124873i	$0.0398525\pi$
$242$	−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	−0.740016	−	0.672590i	$-0.765182\pi$
$251$	−2.84520	+	2.46538i	−0.179587	+	0.155613i	0.560428	+	0.828203i	$0.310637\pi$
$252$	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	0.704405	+	0.709799i	$0.251214\pi$
$257$	−2.74839	+	19.1155i	−0.171440	+	1.19239i	−0.875845	+	0.482593i	$0.839695\pi$
$258$	−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	−0.690427	−	0.723402i	$-0.742578\pi$
$263$	−14.2737	+	4.19112i	−0.880152	+	0.258436i	−0.189724	+	0.981837i	$0.560759\pi$
$264$	−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	−0.331938	−	0.943301i	$-0.607703\pi$
$269$	7.50016	−	25.5432i	0.457293	−	1.55740i	0.789231	−	0.614096i	$-0.210479\pi$
$270$	−0.977458	−	3.98563i	−0.0594862	−	0.242558i
$271$	−2.87150	+	6.28771i	−0.174431	+	0.381951i	−0.976574	−	0.215181i	$-0.930966\pi$
$271$	−2.87150	+	6.28771i	−0.174431	+	0.381951i	0.802143	+	0.597132i	$0.203693\pi$
$272$	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	$-0.972055\pi$
$277$		−	2.91857i		−	0.175360i	0.996149	−	0.0876799i	$-0.0279453\pi$
$278$	−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	0.503031	+	0.864268i	$0.332218\pi$
$281$	−8.03880	+	17.6025i	−0.479555	+	1.05008i	−0.982586	+	0.185810i	$0.940509\pi$
$282$	12.0016	−	2.94335i	0.714686	−	0.175274i
$283$	−5.26341	+	17.9255i	−0.312877	+	1.06556i	0.641541	+	0.767089i	$0.278295\pi$
$283$	−5.26341	+	17.9255i	−0.312877	+	1.06556i	−0.954418	+	0.298473i	$0.903523\pi$
$284$	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	−0.164941	−	0.986303i	$-0.552743\pi$
$293$	−0.775885	+	0.111555i	−0.0453277	+	0.00651714i	0.119614	+	0.992821i	$0.461834\pi$
$294$	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	0.888064	+	0.459720i	$0.152050\pi$
$307$	16.4233	+	25.5551i	0.937325	+	1.45851i	0.0492612	+	0.998786i	$0.484313\pi$
$308$	−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	−0.643541	−	0.765412i	$-0.722535\pi$
$311$	3.62696	−	4.18573i	0.205666	−	0.237351i	0.849206	+	0.528061i	$0.177081\pi$
$312$	−7.43429	+	4.85688i	−0.420884	+	0.274967i
$313$	11.3612	+	24.8775i	0.642172	+	1.40616i	0.898242	+	0.439501i	$0.144845\pi$
$313$	11.3612	+	24.8775i	0.642172	+	1.40616i	−0.256070	+	0.966658i	$0.582428\pi$
$314$	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	0.866583	−	0.499033i	$-0.166312\pi$
$317$	18.8181	+	8.59394i	1.05693	+	0.482683i	0.190347	+	0.981717i	$0.439039\pi$
$318$	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	0.179718	−	0.983718i	$-0.442481\pi$
$331$	18.9367	−	8.64808i	1.04085	−	0.475342i	0.861135	+	0.508376i	$0.169754\pi$
$332$	−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	−0.464034	−	0.885817i	$-0.653599\pi$
$337$	2.73466	−	1.75746i	0.148967	−	0.0957350i	0.613001	+	0.790082i	$0.289962\pi$
$338$	−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	−0.939208	−	0.343349i	$-0.888439\pi$
$347$	−13.6546	+	11.8318i	−0.733017	+	0.635163i	0.206191	+	0.978512i	$0.433893\pi$
$348$	−7.70675	−	3.04071i	−0.413125	−	0.162999i
$349$	−33.4436	−	4.80846i	−1.79019	−	0.257391i	−0.834344	−	0.551245i	$-0.814153\pi$
$349$	−33.4436	−	4.80846i	−1.79019	−	0.257391i	−0.955850	+	0.293853i	$0.905062\pi$
$350$	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	−0.383405	−	0.923581i	$-0.625248\pi$
$353$	5.58842	−	3.59146i	0.297442	−	0.191154i	0.680846	+	0.732426i	$0.261612\pi$
$354$	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	0.717864	−	0.696183i	$-0.245120\pi$
$359$	−5.27450	−	11.5495i	−0.278377	−	0.609561i	−0.996241	+	0.0866221i	$0.972393\pi$
$360$	−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	0.946594	−	0.322429i	$-0.104499\pi$
$373$	25.5476	+	11.6672i	1.32281	+	0.604105i	0.376211	+	0.926534i	$0.377227\pi$
$374$	−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	−0.952943	−	0.303148i	$-0.901962\pi$
$379$	−27.0336	−	23.4248i	−1.38862	−	1.20325i	−0.435681	−	0.900101i	$-0.643492\pi$
$380$	−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	−0.586809	−	0.809726i	$-0.699616\pi$
$383$	−1.84011	+	1.18257i	−0.0940253	+	0.0604264i	0.492783	+	0.870152i	$0.335980\pi$
$384$	−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	−0.979736	−	0.200295i	$-0.935810\pi$
$389$	−18.1632	+	15.7385i	−0.920910	+	0.797973i	0.0588257	+	0.998268i	$0.481264\pi$
$390$	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	0.217924	−	0.975966i	$-0.430071\pi$
$397$	13.9869	−	2.01101i	0.701983	−	0.100930i	0.484058	+	0.875036i	$0.339162\pi$
$398$	−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	−0.464767	−	0.885433i	$-0.653862\pi$
$401$	−7.55046	+	2.21702i	−0.377052	+	0.110712i	0.0877146	+	0.996146i	$0.472044\pi$
$402$	−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	−0.671661	−	0.740858i	$-0.734419\pi$
$409$	6.63514	−	14.5289i	0.328087	−	0.718410i	0.999748	+	0.0224487i	$0.00714625\pi$
$410$	−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	0.644611	−	0.764511i	$-0.277019\pi$
$419$	10.0088	+	4.57088i	0.488963	+	0.223302i	−0.155648	+	0.987813i	$0.549747\pi$
$420$	−6.22598	−	17.7020i	−0.303797	−	0.863769i
$421$	−6.37343	+	21.7059i	−0.310622	+	1.05788i	0.645219	+	0.763998i	$0.276766\pi$
$421$	−6.37343	+	21.7059i	−0.310622	+	1.05788i	−0.955841	+	0.293884i	$0.905052\pi$
$422$	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	−0.930152	−	0.367174i	$-0.880326\pi$
$431$	−2.92978	−	20.3771i	−0.141122	−	0.981528i	0.789030	−	0.614355i	$-0.210584\pi$
$432$	−3.99717	−	0.150372i	−0.192314	−	0.00723479i
$433$	−4.02574	+	27.9997i	−0.193465	+	1.34558i	0.629285	+	0.777175i	$0.283348\pi$
$433$	−4.02574	+	27.9997i	−0.193465	+	1.34558i	−0.822750	+	0.568404i	$0.807561\pi$
$434$	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	0.438472	−	0.898745i	$-0.355520\pi$
$439$	−10.7596	−	12.4172i	−0.513526	−	0.592641i	−0.951998	+	0.306104i	$0.900974\pi$
$440$	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	−0.0962881	−	0.995354i	$-0.530697\pi$
$443$	1.93107	−	0.277645i	0.0917477	−	0.0131913i	0.188036	+	0.982162i	$0.439788\pi$
$444$	−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	−0.930184	−	0.367094i	$-0.880353\pi$
$449$	−9.20577	+	10.6240i	−0.434447	+	0.501379i	0.495737	+	0.868473i	$0.334898\pi$
$450$	−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	0.252241	−	0.967664i	$-0.418832\pi$
$457$	−11.1846	−	7.18789i	−0.523192	−	0.336235i	−0.775434	+	0.631429i	$0.782469\pi$
$458$	−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	$0.288261\pi$
$461$			33.7864i			1.57359i	−0.617214	+	0.786796i	$0.711739\pi$
$462$	5.48640	+	5.20516i	0.255251	+	0.242166i
$463$	−12.5349	−	8.05572i	−0.582548	−	0.374381i	0.215926	−	0.976410i	$-0.430723\pi$
$463$	−12.5349	−	8.05572i	−0.582548	−	0.374381i	−0.798475	+	0.602029i	$0.794359\pi$
$464$	−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	−0.755306	−	0.655372i	$-0.772512\pi$
$467$	5.06583	−	17.2526i	0.234419	−	0.798357i	0.989725	−	0.142985i	$-0.0456701\pi$
$468$	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	−0.777885	−	0.628407i	$-0.783707\pi$
$479$	3.18514	−	22.1531i	0.145533	−	1.01220i	0.923418	−	0.383796i	$-0.125383\pi$
$480$	−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	−0.741247	−	0.671232i	$-0.765765\pi$
$487$	3.51064	−	24.4170i	0.159082	−	1.10644i	0.900329	−	0.435209i	$-0.143326\pi$
$488$	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	0.995338	−	0.0964485i	$-0.0307483\pi$
$491$	10.9491	+	17.0372i	0.494127	+	0.768877i	−0.501211	+	0.865325i	$0.667112\pi$
$492$	−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	−0.878113	−	0.478454i	$-0.841198\pi$
$499$	2.66438	−	9.07406i	0.119274	−	0.406211i	0.997387	+	0.0722429i	$0.0230157\pi$
$500$	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	0.773134	−	0.634243i	$-0.218688\pi$
$503$	11.6036	+	7.45715i	0.517377	+	0.332498i	−0.255757	+	0.966741i	$0.582325\pi$
$504$	−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	−0.998798	−	0.0490096i	$-0.984393\pi$
$509$	−12.1672	+	18.9325i	−0.539302	+	0.839170i	0.459497	+	0.888180i	$0.348030\pi$
$510$	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	−0.438027	−	0.898962i	$-0.644322\pi$
$521$	4.51338	−	2.90058i	0.197735	−	0.127077i	0.635762	+	0.771885i	$0.280686\pi$
$522$	−1.09431	+	5.75521i	−0.0478968	+	0.251899i
$523$	2.57719	−	0.370544i	0.112693	−	0.0162027i	−0.0857378	−	0.996318i	$-0.527325\pi$
$523$	2.57719	−	0.370544i	0.112693	−	0.0162027i	0.198430	+	0.980115i	$0.436416\pi$
$524$	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	0.722831	−	0.691025i	$-0.242840\pi$
$541$	3.29608	+	2.85607i	0.141709	+	0.122792i	−0.581122	+	0.813817i	$0.697386\pi$
$542$	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	0.128039	−	0.991769i	$-0.459132\pi$
$547$	−12.5744	−	5.74253i	−0.537642	−	0.245533i	−0.665681	+	0.746236i	$0.731859\pi$
$548$	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	0.500615	−	0.865670i	$-0.333107\pi$
$557$	4.11170	+	1.87775i	0.174218	+	0.0795628i	−0.326397	+	0.945233i	$0.605835\pi$
$558$	−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	0.108740	−	0.994070i	$-0.465319\pi$
$563$	−20.3995	−	17.6763i	−0.859737	−	0.744967i	−0.968477	+	0.249104i	$0.919864\pi$
$564$	−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	0.984061	+	0.177832i	$0.0569084\pi$
$569$	2.14594	+	14.9253i	0.0899625	+	0.625703i	−0.894098	+	0.447871i	$0.852182\pi$
$570$	1.52840	+	0.524709i	0.0640175	+	0.0219777i
$571$	19.6583	+	2.82643i	0.822674	+	0.118283i	0.540781	−	0.841163i	$-0.318129\pi$
$571$	19.6583	+	2.82643i	0.822674	+	0.118283i	0.281892	+	0.959446i	$0.409038\pi$
$572$	−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	0.313124	−	0.949712i	$-0.398624\pi$
$577$	−16.1296	−	18.6145i	−0.671484	−	0.774934i	−0.984608	+	0.174779i	$0.944079\pi$
$578$	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	0.780115	−	0.625636i	$-0.215160\pi$
$587$	6.58689	+	5.70757i	0.271870	+	0.235577i	−0.508245	+	0.861212i	$0.669706\pi$
$588$	−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	−0.713638	−	0.700515i	$-0.752954\pi$
$593$	6.89417	−	15.0961i	0.283109	−	0.619923i	0.996747	+	0.0805917i	$0.0256810\pi$
$594$	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	0.640019	−	0.768359i	$-0.278926\pi$
$601$	5.07392	+	3.26081i	0.206970	+	0.133011i	−0.433050	+	0.901370i	$0.642563\pi$
$602$	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	0.989549	+	0.144199i	$0.0460606\pi$
$607$	11.0994	+	24.3043i	0.450511	+	0.986481i	−0.539038	+	0.842281i	$0.681212\pi$
$608$	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	0.847163	−	0.531334i	$-0.178309\pi$
$613$	0.295137	+	0.459243i	0.0119205	+	0.0185486i	−0.835242	+	0.549882i	$0.814673\pi$
$614$	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	0.895441	+	0.445179i	$0.146860\pi$
$617$	−2.21444	+	15.4017i	−0.0891498	+	0.620051i	−0.984591	+	0.174871i	$0.944049\pi$
$618$	1.84114	−	3.59334i	0.0740615	−	0.144545i
$619$	−28.2193	+	24.4521i	−1.13423	+	0.982814i	−0.999967	−	0.00813192i	$-0.997412\pi$
$619$	−28.2193	+	24.4521i	−1.13423	+	0.982814i	−0.134261	+	0.990946i	$0.542866\pi$
$620$	−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	0.439560	−	0.898213i	$-0.355134\pi$
$631$	32.5288	−	9.55133i	1.29495	−	0.380232i	0.855392	+	0.517981i	$0.173316\pi$
$632$	−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	0.190513	−	0.981685i	$-0.438985\pi$
$641$	−15.7811	−	10.1419i	−0.623316	−	0.400581i	−0.813830	+	0.581104i	$0.802621\pi$
$642$	11.3395	+	10.7582i	0.447535	+	0.424593i
$643$		−	40.0856i		−	1.58082i	−0.612577	−	0.790411i	$-0.709867\pi$
$643$		−	40.0856i		−	1.58082i	0.612577	−	0.790411i	$-0.290133\pi$
$644$	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	0.238219	−	0.971212i	$-0.423437\pi$
$647$	−13.8950	−	8.92974i	−0.546267	−	0.351064i	−0.784486	+	0.620147i	$0.787073\pi$
$648$	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	−0.342536	−	0.939505i	$-0.611286\pi$
$653$	3.65881	−	1.67092i	0.143180	−	0.0653883i	0.485717	+	0.874116i	$0.338559\pi$
$654$	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	0.549308	−	0.835620i	$-0.314891\pi$
$659$	−11.2693	−	17.5353i	−0.438989	−	0.683080i	−0.988297	+	0.152540i	$0.951255\pi$
$660$	0.864618	−	9.55947i	0.0336552	−	0.372102i
$661$	3.37009	−	0.484546i	0.131081	−	0.0188466i	−0.0764619	−	0.997073i	$-0.524362\pi$
$661$	3.37009	−	0.484546i	0.131081	−	0.0188466i	0.207543	+	0.978226i	$0.433453\pi$
$662$	−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	0.593456	+	0.804867i	$0.297763\pi$
$673$	6.50622	+	45.2517i	0.250796	+	1.74433i	−0.342659	+	0.939460i	$0.611328\pi$
$674$	−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	0.975532	−	0.219857i	$-0.0705592\pi$
$677$	0.936652	+	3.18994i	0.0359984	+	0.122599i	−0.939534	+	0.342457i	$0.888741\pi$
$678$	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	0.757511	+	0.652822i	$0.226415\pi$
$683$	−6.08118	+	20.7106i	−0.232690	+	0.792470i	−0.990201	+	0.139647i	$0.955403\pi$
$684$	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	$0.402635\pi$
$691$			50.1334i			1.90716i	−0.301134	+	0.953582i	$0.597365\pi$
$692$	−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	−0.988598	−	0.150576i	$-0.951887\pi$
$701$	−33.8457	−	29.3275i	−1.27833	−	1.10768i	−0.289736	−	0.957107i	$-0.593567\pi$
$702$	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	0.875943	−	0.482414i	$-0.160240\pi$
$709$	42.0839	+	6.05075i	1.58049	+	0.227241i	0.704550	+	0.709655i	$0.251149\pi$
$710$	−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	−0.998031	−	0.0627241i	$-0.980021\pi$
$719$	−1.55787	−	10.8352i	−0.0580987	−	0.404085i	0.939932	−	0.341361i	$-0.110888\pi$
$720$	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	0.999996	+	0.00271897i	$0.000865476\pi$
$727$	9.36134	+	20.4985i	0.347193	+	0.760246i	−0.652803	+	0.757527i	$0.726407\pi$
$728$	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	−0.752627	−	0.658447i	$-0.771214\pi$
$733$	4.30394	−	6.69705i	0.158969	−	0.247361i	0.911597	+	0.411085i	$0.134850\pi$
$734$	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	−0.847963	−	0.530055i	$-0.822171\pi$
$739$	−0.368407	+	0.573252i	−0.0135521	+	0.0210874i	0.834411	+	0.551142i	$0.185808\pi$
$740$	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	0.643882	−	0.765125i	$-0.277323\pi$
$743$	21.0402	+	6.17797i	0.771892	+	0.226648i	0.128010	+	0.991773i	$0.459141\pi$
$744$	−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	−0.966761	−	0.255681i	$-0.917700\pi$
$751$	−31.1257	+	20.0033i	−1.13579	+	0.729930i	−0.169031	+	0.985611i	$0.554064\pi$
$752$	−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	−0.0141427	−	0.999900i	$-0.504502\pi$
$757$	26.7864	−	23.2105i	0.973567	−	0.843601i	0.987710	+	0.156299i	$0.0499565\pi$
$758$	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	0.645663	−	0.763622i	$-0.276581\pi$
$761$	−5.57445	−	6.43326i	−0.202074	−	0.233205i	−0.847737	+	0.530417i	$0.822035\pi$
$762$	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	−0.820194	−	0.572086i	$-0.806135\pi$
$769$	−33.3018	+	9.77828i	−1.20089	+	0.352614i	−0.380698	+	0.924699i	$0.624316\pi$
$770$	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	0.884548	−	0.466450i	$-0.154467\pi$
$773$	50.4990	−	23.0621i	1.81632	−	0.829487i	0.931775	−	0.363037i	$-0.118260\pi$
$774$	−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	−0.403618	−	0.914928i	$-0.632247\pi$
$787$	−38.1356	−	17.4159i	−1.35939	−	0.620812i	−0.955770	+	0.294116i	$0.904975\pi$
$788$	−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	0.890545	−	0.454895i	$-0.150323\pi$
$797$	3.01543	+	4.69211i	0.106812	+	0.166203i	−0.783733	+	0.621098i	$0.786687\pi$
$798$	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	0.565385	+	0.824827i	$0.308728\pi$
$809$	−5.95818	+	41.4401i	−0.209479	+	1.45696i	−0.774864	+	0.632128i	$0.782182\pi$
$810$	3.88138	+	1.33250i	0.136378	+	0.0468194i
$811$	25.2397	−	3.62893i	0.886287	−	0.127429i	0.315888	−	0.948796i	$-0.397698\pi$
$811$	25.2397	−	3.62893i	0.886287	−	0.127429i	0.570399	+	0.821368i	$0.306789\pi$
$812$	−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	0.245729	+	0.969339i	$0.420973\pi$
$821$	−13.8983	+	47.3334i	−0.485055	+	1.65195i	−0.730784	+	0.682609i	$0.760845\pi$
$822$	17.6458	−	4.32755i	0.615467	−	0.150941i
$823$	−6.89921	+	15.1072i	−0.240491	+	0.526602i	−0.990937	−	0.134330i	$-0.957112\pi$
$823$	−6.89921	+	15.1072i	−0.240491	+	0.526602i	0.750445	+	0.660932i	$0.229839\pi$
$824$	−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	$0.147351\pi$
$827$			25.6840i			0.893118i	−0.894754	+	0.446559i	$0.852649\pi$
$828$	−7.50381	+	5.97435i	−0.260776	+	0.207623i
$829$			18.6090i			0.646316i	0.946345	+	0.323158i	$0.104744\pi$
$829$			18.6090i			0.646316i	−0.946345	+	0.323158i	$0.895256\pi$
$830$	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	−0.0719621	−	0.997407i	$-0.522926\pi$
$839$	26.8086	−	30.9387i	0.925534	−	1.06812i	0.997496	−	0.0707163i	$-0.0225285\pi$
$840$	−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	−0.631749	−	0.775173i	$-0.717663\pi$
$853$	1.33256	−	1.15467i	0.0456259	−	0.0395350i	0.677375	+	0.735638i	$0.263117\pi$
$854$	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	−0.967985	−	0.251007i	$-0.919238\pi$
$857$	−3.21807	−	22.3821i	−0.109927	−	0.764559i	0.858058	−	0.513552i	$-0.171671\pi$
$858$	−1.37173	+	7.21421i	−0.0468302	+	0.246289i
$859$	24.5621	+	38.2194i	0.838048	+	1.30403i	0.950612	+	0.310383i	$0.100457\pi$
$859$	24.5621	+	38.2194i	0.838048	+	1.30403i	−0.112564	+	0.993644i	$0.535906\pi$
$860$	−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	−0.912734	−	0.408554i	$-0.866033\pi$
$863$	−11.1175	+	12.8302i	−0.378443	+	0.436746i	0.534291	+	0.845300i	$0.320579\pi$
$864$	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	−0.991204	−	0.132345i	$-0.957749\pi$
$877$	−13.5946	+	21.1537i	−0.459058	+	0.714308i	0.532146	+	0.846653i	$0.321386\pi$
$878$	−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	0.789800	−	0.613364i	$-0.210184\pi$
$881$	33.3210	+	9.78392i	1.12261	+	0.329629i	0.332812	+	0.942993i	$0.392002\pi$
$882$	−3.83269	+	3.02959i	−0.129053	+	0.102012i
$883$	−1.76315	+	0.805202i	−0.0593346	+	0.0270972i	−0.444861	−	0.895599i	$-0.646747\pi$
$883$	−1.76315	+	0.805202i	−0.0593346	+	0.0270972i	0.385527	+	0.922697i	$0.374020\pi$
$884$	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	−0.472740	−	0.881202i	$-0.656735\pi$
$887$	−11.7349	+	3.44568i	−0.394020	+	0.115695i	0.0787199	+	0.996897i	$0.474917\pi$
$888$	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	0.980727	+	0.195382i	$0.0625948\pi$
$907$	7.86999	+	26.8027i	0.261319	+	0.889970i	−0.719408	+	0.694587i	$0.755587\pi$
$908$	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	−0.933836	−	0.357702i	$-0.883560\pi$
$911$	−17.8874	−	39.1680i	−0.592637	−	1.29769i	0.341199	−	0.939991i	$-0.389167\pi$
$912$	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	0.978678	−	0.205400i	$-0.0658495\pi$
$929$	5.56401	+	12.1835i	0.182549	+	0.399727i	−0.796129	+	0.605127i	$0.793122\pi$
$930$	−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	0.997724	−	0.0674322i	$-0.0214806\pi$
$937$	0.655584	+	4.55969i	0.0214170	+	0.148958i	−0.976307	+	0.216391i	$0.930572\pi$
$938$	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	−0.566089	−	0.824344i	$-0.691544\pi$
$941$	5.19347	−	4.50017i	0.169302	−	0.146701i	0.735391	+	0.677643i	$0.236999\pi$
$942$	−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	−0.442589	−	0.896725i	$-0.645940\pi$
$947$	−34.4627	−	4.95498i	−1.11989	−	0.161015i	−0.677298	+	0.735709i	$0.736849\pi$
$948$	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	0.621538	−	0.783384i	$-0.286508\pi$
$953$	48.4033	−	14.2125i	1.56794	−	0.460388i	0.946400	+	0.322996i	$0.104690\pi$
$954$	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	0.161165	−	0.986928i	$-0.448475\pi$
$971$	−14.9312	−	6.81885i	−0.479165	−	0.218827i	−0.640330	+	0.768100i	$0.721202\pi$
$972$	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	−0.974847	−	0.222874i	$-0.928456\pi$
$977$	−19.2389	+	22.2029i	−0.615506	+	0.710332i	0.359341	+	0.933206i	$0.383002\pi$
$978$	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	0.994078	+	0.108668i	$0.0346586\pi$
$983$	2.22237	+	15.4569i	0.0708825	+	0.492999i	−0.923196	+	0.384331i	$0.874432\pi$
$984$	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	0.432374	−	0.901694i	$-0.357676\pi$
$991$	−16.4224	−	18.9525i	−0.521676	−	0.602046i	−0.954050	+	0.299649i	$0.903131\pi$
$992$	−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	−0.904886	−	0.425654i	$-0.860044\pi$
$997$	−28.9284	−	45.0135i	−0.916171	−	1.42559i	−0.0112855	−	0.999936i	$-0.503592\pi$
$998$	−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.13.13	✓	480
8.5	even	2	inner	552.2.bb.a.13.15	yes	480
23.16	even	11	inner	552.2.bb.a.85.15	yes	480
184.85	even	22	inner	552.2.bb.a.85.13	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.13	✓	480	1.1	even	1	trivial
552.2.bb.a.13.15	yes	480	8.5	even	2	inner
552.2.bb.a.85.13	yes	480	184.85	even	22	inner
552.2.bb.a.85.15	yes	480	23.16	even	11	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

Fields

Representations

Groups

Database

Properties

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