LMFDB - Embedded newform 552.2.bb.a.13.15

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			13.15
Character	$\chi$	$=$	552.13
Dual form			552.2.bb.a.85.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.817442 - 1.15403i) q^{2} +(0.540641 - 0.841254i) q^{3} +(-0.663576 + 1.88671i) q^{4} +(-2.63955 - 1.20544i) q^{5} +(-1.41278 + 0.0637600i) q^{6} +(3.10238 + 0.910940i) q^{7} +(2.71975 - 0.776488i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.817442 - 1.15403i) q^{2} +(0.540641 - 0.841254i) q^{3} +(-0.663576 + 1.88671i) q^{4} +(-2.63955 - 1.20544i) q^{5} +(-1.41278 + 0.0637600i) q^{6} +(3.10238 + 0.910940i) q^{7} +(2.71975 - 0.776488i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(0.766563 + 4.03151i) q^{10} +(-1.24993 - 1.08307i) q^{11} +(1.22844 + 1.57827i) q^{12} +(-0.884534 - 3.01245i) q^{13} +(-1.48476 - 4.32488i) q^{14} +(-2.44113 + 1.56882i) q^{15} +(-3.11933 - 2.50395i) q^{16} +(-0.685217 - 4.76579i) q^{17} +(-0.710166 + 1.22297i) q^{18} +(-0.389769 - 0.0560403i) q^{19} +(4.02586 - 4.18016i) 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} +(-2.75340 + 3.48328i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(-3.77734 + 5.24880i) q^{28} +(-4.10030 + 0.589534i) q^{29} +(3.80595 + 1.53472i) q^{30} +(-4.60234 + 2.95774i) q^{31} +(-0.339757 + 5.64664i) q^{32} +(-1.58690 + 0.465957i) q^{33} +(-4.93974 + 4.68652i) q^{34} +(-7.09080 - 6.14421i) q^{35} +(1.99187 - 0.180157i) q^{36} +(-3.39103 + 1.54863i) q^{37} +(0.253941 + 0.495615i) q^{38} +(-3.01245 - 0.884534i) q^{39} +(-8.11495 - 1.22893i) q^{40} +(1.52135 - 3.33129i) q^{41} +(-4.44104 - 1.08915i) q^{42} +(5.82692 - 9.06687i) q^{43} +(2.87287 - 1.63956i) q^{44} +2.90178i q^{45} +(4.90161 + 4.68767i) q^{46} +8.73791 q^{47} +(-3.79289 + 1.27041i) q^{48} +(2.90616 + 1.86768i) q^{49} +(1.15213 - 4.69787i) q^{50} +(-4.37969 - 2.00014i) q^{51} +(6.27056 + 0.330129i) q^{52} +(-3.74971 + 12.7704i) q^{53} +(0.644886 + 1.25862i) q^{54} +(1.99368 + 4.36555i) q^{55} +(9.14504 + 0.0685752i) q^{56} +(-0.257869 + 0.297597i) q^{57} +(4.03210 + 4.24996i) q^{58} +(-1.25320 - 4.26802i) q^{59} +(-1.34003 - 5.64674i) q^{60} +(-3.95379 - 6.15222i) q^{61} +(7.17548 + 2.89346i) q^{62} +(-0.460154 - 3.20044i) q^{63} +(6.79413 - 4.22371i) q^{64} +(-1.29656 + 9.01777i) q^{65} +(1.83493 + 1.45044i) 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} +(-1.83615 - 2.15141i) q^{72} +(0.408778 - 2.84311i) q^{73} +(4.55913 + 2.64743i) q^{74} +(3.38552 - 0.486764i) q^{75} +(0.364373 - 0.698193i) q^{76} +(-2.89115 - 4.49871i) q^{77} +(1.44172 + 4.19951i) q^{78} +(-1.26059 + 0.370142i) q^{79} +(5.21528 + 10.3695i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-5.08802 + 0.967452i) q^{82} +(7.35078 - 3.35699i) q^{83} +(2.37339 + 6.01542i) q^{84} +(-3.93622 + 13.4055i) q^{85} +(-15.2266 + 0.687193i) q^{86} +(-1.72084 + 3.76812i) q^{87} +(-4.24050 - 1.97513i) q^{88} +(-0.761319 - 0.489270i) q^{89} +(3.34875 - 2.37204i) q^{90} -10.1515i q^{91} +(1.40293 - 9.48851i) q^{92} +5.47081i q^{93} +(-7.14274 - 10.0838i) q^{94} +(0.961262 + 0.617766i) q^{95} +(4.56657 + 3.33863i) q^{96} +(-4.43100 + 9.70254i) q^{97} +(-0.220263 - 4.88052i) 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 $

$2$	−0.817442	−	1.15403i	−0.578019	−	0.816023i
$2$	−0.817442	−	1.15403i	−0.578019	−	0.816023i
$3$	0.540641	−	0.841254i	0.312139	−	0.485698i
$3$	0.540641	−	0.841254i	0.312139	−	0.485698i
$4$	−0.663576	+	1.88671i	−0.331788	+	0.943354i
$5$	−2.63955	−	1.20544i	−1.18044	−	0.539091i	−0.274129	−	0.961693i	$-0.588389\pi$
$5$	−2.63955	−	1.20544i	−1.18044	−	0.539091i	−0.906315	+	0.422602i	$0.861117\pi$
$6$	−1.41278	+	0.0637600i	−0.576763	+	0.0260299i
$7$	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	$0.381658\pi$
$8$	2.71975	−	0.776488i	0.961579	−	0.274530i
$9$	−0.415415	−	0.909632i	−0.138472	−	0.303211i
$10$	0.766563	+	4.03151i	0.242409	+	1.27487i
$11$	−1.24993	−	1.08307i	−0.376869	−	0.326559i	0.445744	−	0.895160i	$-0.352939\pi$
$11$	−1.24993	−	1.08307i	−0.376869	−	0.326559i	−0.822613	+	0.568602i	$0.807485\pi$
$12$	1.22844	+	1.57827i	0.354621	+	0.455606i
$13$	−0.884534	−	3.01245i	−0.245326	−	0.835502i	−0.986440	−	0.164123i	$-0.947520\pi$
$13$	−0.884534	−	3.01245i	−0.245326	−	0.835502i	0.741114	−	0.671379i	$-0.234298\pi$
$14$	−1.48476	−	4.32488i	−0.396819	−	1.15587i
$15$	−2.44113	+	1.56882i	−0.630298	+	0.405068i
$16$	−3.11933	−	2.50395i	−0.779834	−	0.625987i
$17$	−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	$-0.243921\pi$
$18$	−0.710166	+	1.22297i	−0.167388	+	0.288258i
$19$	−0.389769	−	0.0560403i	−0.0894191	−	0.0128565i	0.0974600	−	0.995239i	$-0.468928\pi$
$19$	−0.389769	−	0.0560403i	−0.0894191	−	0.0128565i	−0.186879	+	0.982383i	$0.559837\pi$
$20$	4.02586	−	4.18016i	0.900210	−	0.934713i
$21$	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
$26$	−2.75340	+	3.48328i	−0.539987	+	0.683128i
$27$	−0.989821	−	0.142315i	−0.190491	−	0.0273885i
$28$	−3.77734	+	5.24880i	−0.713850	+	0.991930i
$29$	−4.10030	+	0.589534i	−0.761406	+	0.109474i	−0.512070	−	0.858943i	$-0.671121\pi$
$29$	−4.10030	+	0.589534i	−0.761406	+	0.109474i	−0.249336	+	0.968417i	$0.580212\pi$
$30$	3.80595	+	1.53472i	0.694869	+	0.280201i
$31$	−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	$0.481658\pi$
$32$	−0.339757	+	5.64664i	−0.0600612	+	0.998195i
$33$	−1.58690	+	0.465957i	−0.276244	+	0.0811126i
$34$	−4.93974	+	4.68652i	−0.847159	+	0.803731i
$35$	−7.09080	−	6.14421i	−1.19856	−	1.03856i
$36$	1.99187	−	0.180157i	0.331978	−	0.0300262i
$37$	−3.39103	+	1.54863i	−0.557481	+	0.254593i	−0.674171	−	0.738575i	$-0.735499\pi$
$37$	−3.39103	+	1.54863i	−0.557481	+	0.254593i	0.116690	+	0.993168i	$0.462772\pi$
$38$	0.253941	+	0.495615i	0.0411947	+	0.0803994i
$39$	−3.01245	−	0.884534i	−0.482378	−	0.141639i
$40$	−8.11495	−	1.22893i	−1.28309	−	0.194311i
$41$	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	$0.0440470\pi$
$42$	−4.44104	−	1.08915i	−0.685268	−	0.168059i
$43$	5.82692	−	9.06687i	0.888597	−	1.38268i	−0.0350272	−	0.999386i	$-0.511152\pi$
$43$	5.82692	−	9.06687i	0.888597	−	1.38268i	0.923625	−	0.383298i	$-0.125212\pi$
$44$	2.87287	−	1.63956i	0.433101	−	0.247172i
$45$			2.90178i			0.432572i
$46$	4.90161	+	4.68767i	0.722703	+	0.691159i
$47$	8.73791			1.27456			0.637278	−	0.770634i	$-0.280060\pi$
$47$	8.73791			1.27456			0.637278	+	0.770634i	$0.280060\pi$
$48$	−3.79289	+	1.27041i	−0.547457	+	0.183369i
$49$	2.90616	+	1.86768i	0.415166	+	0.266811i
$50$	1.15213	−	4.69787i	0.162936	−	0.664378i
$51$	−4.37969	−	2.00014i	−0.613279	−	0.280075i
$52$	6.27056	+	0.330129i	0.869571	+	0.0457807i
$53$	−3.74971	+	12.7704i	−0.515063	+	1.75414i	0.131535	+	0.991312i	$0.458009\pi$
$53$	−3.74971	+	12.7704i	−0.515063	+	1.75414i	−0.646598	+	0.762831i	$0.723809\pi$
$54$	0.644886	+	1.25862i	0.0877579	+	0.171276i
$55$	1.99368	+	4.36555i	0.268828	+	0.588650i
$56$	9.14504	+	0.0685752i	1.22206	+	0.00916374i
$57$	−0.257869	+	0.297597i	−0.0341556	+	0.0394177i
$58$	4.03210	+	4.24996i	0.529440	+	0.558047i
$59$	−1.25320	−	4.26802i	−0.163153	−	0.555649i	−0.999967	−	0.00816090i	$-0.997402\pi$
$59$	−1.25320	−	4.26802i	−0.163153	−	0.555649i	0.836813	−	0.547488i	$-0.184416\pi$
$60$	−1.34003	−	5.64674i	−0.172997	−	0.728991i
$61$	−3.95379	−	6.15222i	−0.506231	−	0.787711i	0.490245	−	0.871584i	$-0.336907\pi$
$61$	−3.95379	−	6.15222i	−0.506231	−	0.787711i	−0.996476	+	0.0838737i	$0.973271\pi$
$62$	7.17548	+	2.89346i	0.911286	+	0.367470i
$63$	−0.460154	−	3.20044i	−0.0579739	−	0.403218i
$64$	6.79413	−	4.22371i	0.849267	−	0.527964i
$65$	−1.29656	+	9.01777i	−0.160818	+	1.11852i
$66$	1.83493	+	1.45044i	0.225864	+	0.178537i
$67$	1.33024	−	1.15266i	0.162515	−	0.140820i	−0.569807	−	0.821778i	$-0.692982\pi$
$67$	1.33024	−	1.15266i	0.162515	−	0.140820i	0.732322	+	0.680959i	$0.238437\pi$
$68$	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	$-0.521167\pi$
$72$	−1.83615	−	2.15141i	−0.216392	−	0.253546i
$73$	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	$-0.00830584\pi$
$74$	4.55913	+	2.64743i	0.529989	+	0.307758i
$75$	3.38552	−	0.486764i	0.390926	−	0.0562067i
$76$	0.364373	−	0.698193i	0.0417964	−	0.0800883i
$77$	−2.89115	−	4.49871i	−0.329477	−	0.512676i
$78$	1.44172	+	4.19951i	0.163243	+	0.475501i
$79$	−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	$0.432638\pi$
$80$	5.21528	+	10.3695i	0.583086	+	1.15934i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−5.08802	+	0.967452i	−0.561878	+	0.106837i
$83$	7.35078	−	3.35699i	0.806852	−	0.368477i	0.0311014	−	0.999516i	$-0.490099\pi$
$83$	7.35078	−	3.35699i	0.806852	−	0.368477i	0.775751	+	0.631039i	$0.217371\pi$
$84$	2.37339	+	6.01542i	0.258958	+	0.656336i
$85$	−3.93622	+	13.4055i	−0.426943	+	1.45403i
$86$	−15.2266	+	0.687193i	−1.64193	+	0.0741019i
$87$	−1.72084	+	3.76812i	−0.184494	+	0.403984i
$88$	−4.24050	−	1.97513i	−0.452039	−	0.210550i
$89$	−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	$0.697091\pi$
$90$	3.34875	−	2.37204i	0.352989	−	0.250035i
$91$		−	10.1515i		−	1.06417i
$92$	1.40293	−	9.48851i	0.146265	−	0.989245i
$93$			5.47081i			0.567297i
$94$	−7.14274	−	10.0838i	−0.736718	−	1.04007i
$95$	0.961262	+	0.617766i	0.0986234	+	0.0633814i
$96$	4.56657	+	3.33863i	0.466074	+	0.340747i
$97$	−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	$0.954218\pi$
$98$	−0.220263	−	4.88052i	−0.0222499	−	0.493007i
$99$	−0.465957	+	1.58690i	−0.0468304	+	0.159490i
$100$	−6.36328	+	2.51064i	−0.636328	+	0.251064i
$101$	17.6857	−	8.07677i	1.75979	−	0.803669i	0.774544	−	0.632520i	$-0.217979\pi$
$101$	17.6857	−	8.07677i	1.75979	−	0.803669i	0.985245	−	0.171149i	$-0.0547478\pi$
$102$	1.27192	+	6.68930i	0.125939	+	0.662339i
$103$	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	$0.182352\pi$
$104$	−4.74485	−	7.50629i	−0.465270	−	0.736052i
$105$	−9.00242	+	2.64335i	−0.878546	+	0.257964i
$106$	17.8026	−	6.11174i	1.72914	−	0.593625i
$107$	−5.97553	−	9.29811i	−0.577677	−	0.898882i	0.422295	−	0.906459i	$-0.361225\pi$
$107$	−5.97553	−	9.29811i	−0.577677	−	0.898882i	−0.999971	+	0.00757633i	$0.997588\pi$
$108$	0.925328	−	1.77307i	0.0890397	−	0.170613i
$109$	−2.95934	+	0.425488i	−0.283453	+	0.0407544i	−0.282575	−	0.959245i	$-0.591189\pi$
$109$	−2.95934	+	0.425488i	−0.283453	+	0.0407544i	−0.000878016		1.00000i	$0.500279\pi$
$110$	3.40826	−	5.86935i	0.324965	−	0.559621i
$111$	−0.530537	+	3.68996i	−0.0503563	+	0.350236i
$112$	−7.39641	−	10.6097i	−0.698895	−	1.00252i
$113$	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
$118$	−3.90101	+	4.93510i	−0.359117	+	0.454313i
$119$	2.21555	−	15.4095i	0.203099	−	1.41258i
$120$	−5.42111	+	6.16232i	−0.494878	+	0.562540i
$121$	−1.17618	−	8.18050i	−0.106925	−	0.743682i
$122$	−3.86785	+	9.59188i	−0.350179	+	0.868408i
$123$	−1.97995	−	3.08087i	−0.178526	−	0.277792i
$124$	−2.52640	−	10.6460i	−0.226877	−	0.956035i
$125$	1.29142	+	4.39817i	0.115508	+	0.393384i
$126$	−3.31726	+	3.14721i	−0.295525	+	0.280376i
$127$	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	$0.177667\pi$
$128$	−10.4281	−	4.38800i	−0.921723	−	0.387848i
$129$	−4.47726	−	9.80384i	−0.394201	−	0.863180i
$130$	11.4666	−	5.87524i	1.00569	−	0.515292i
$131$	−0.608616	+	2.07276i	−0.0531751	+	0.181098i	−0.981798	−	0.189926i	$-0.939175\pi$
$131$	−0.608616	+	2.07276i	−0.0531751	+	0.181098i	0.928623	+	0.371024i	$0.120993\pi$
$132$	0.173906	−	3.30322i	0.0151366	−	0.287508i
$133$	−1.15816	−	0.528914i	−0.100425	−	0.0458627i
$134$	−2.41760	−	0.592906i	−0.208849	−	0.0512193i
$135$	2.44113	+	1.56882i	0.210099	+	0.135023i
$136$	−5.56420	−	12.4297i	−0.477126	−	1.06584i
$137$	12.8472			1.09761			0.548805	−	0.835950i	$-0.315083\pi$
$137$	12.8472			1.09761			0.548805	+	0.835950i	$0.315083\pi$
$138$	6.59353	−	1.58915i	0.561278	−	0.135278i
$139$			6.43812i			0.546074i	0.962003	+	0.273037i	$0.0880282\pi$
$139$			6.43812i			0.546074i	−0.962003	+	0.273037i	$0.911972\pi$
$140$	16.2976	−	9.30112i	1.37740	−	0.786088i
$141$	4.72407	−	7.35080i	0.397839	−	0.619049i
$142$	−4.52767	+	18.4618i	−0.379954	+	1.54928i
$143$	−2.15709	+	4.72337i	−0.180385	+	0.394988i
$144$	−0.981853	+	3.87762i	−0.0818210	+	0.323135i
$145$	11.5336	+	3.38657i	0.957813	+	0.281239i
$146$	−3.61519	+	1.85234i	−0.299195	+	0.153301i
$147$	3.14238	−	1.43508i	0.259179	−	0.118363i
$148$	−0.671609	−	7.42551i	−0.0552059	−	0.610373i
$149$	13.3170	+	11.5392i	1.09097	+	0.945331i	0.998729	−	0.0504057i	$-0.0160514\pi$
$149$	13.3170	+	11.5392i	1.09097	+	0.945331i	0.0922413	+	0.995737i	$0.470597\pi$
$150$	−3.32921	−	3.50909i	−0.271829	−	0.286516i
$151$	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	$0.185856\pi$
$152$	−1.10359	+	0.150235i	−0.0895130	+	0.0121857i
$153$	−4.05046	+	2.60307i	−0.327461	+	0.210446i
$154$	−2.82831	+	7.01391i	−0.227912	+	0.565197i
$155$	15.7135	−	2.25926i	1.26214	−	0.181468i
$156$	3.66784	−	5.09665i	0.293663	−	0.408059i
$157$	8.00036	+	1.15028i	0.638498	+	0.0918022i	0.453958	−	0.891023i	$-0.350011\pi$
$157$	8.00036	+	1.15028i	0.638498	+	0.0918022i	0.184540	+	0.982825i	$0.440921\pi$
$158$	1.45761	+	1.15219i	0.115961	+	0.0916631i
$159$	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	$-0.743959\pi$
$163$	−1.01116	+	0.876175i	−0.0792002	+	0.0686274i	0.614361	+	0.789025i	$0.289414\pi$
$164$	5.27563	+	5.08090i	0.411958	+	0.396752i
$165$	4.75040	+	0.683004i	0.369818	+	0.0531718i
$166$	−9.88290	−	5.73888i	−0.767062	−	0.445424i
$167$	−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	$-0.354641\pi$
$168$	5.00187	−	7.65622i	0.385903	−	0.590690i
$169$	2.64386	−	1.69911i	0.203374	−	0.130700i
$170$	18.6880	−	6.41573i	1.43331	−	0.492064i
$171$	0.110940	+	0.377826i	0.00848378	+	0.0288931i
$172$	13.2399	+	17.0103i	1.00954	+	1.29702i
$173$	−0.942503	−	0.816684i	−0.0716572	−	0.0620913i	0.618296	−	0.785945i	$-0.287823\pi$
$173$	−0.942503	−	0.816684i	−0.0716572	−	0.0620913i	−0.689953	+	0.723854i	$0.742369\pi$
$174$	5.75521	−	1.09431i	0.436301	−	0.0829597i
$175$	4.59413	+	10.0597i	0.347284	+	0.760445i
$176$	1.18700	+	6.50823i	0.0894735	+	0.490576i
$177$	−4.26802	−	1.25320i	−0.320804	−	0.0941966i
$178$	0.0577016	+	1.27854i	0.00432492	+	0.0958303i
$179$	23.7424	+	10.8428i	1.77459	+	0.810427i	0.978791	+	0.204863i	$0.0656749\pi$
$179$	23.7424	+	10.8428i	1.77459	+	0.810427i	0.795797	+	0.605564i	$0.207052\pi$
$180$	−5.47481	−	1.92555i	−0.408068	−	0.143522i
$181$	1.07296	−	1.66955i	0.0797521	−	0.124097i	−0.799086	−	0.601217i	$-0.794683\pi$
$181$	1.07296	−	1.66955i	0.0797521	−	0.124097i	0.878838	+	0.477120i	$0.158319\pi$
$182$	−11.7152	+	8.29827i	−0.868385	+	0.615109i
$183$	−7.31316			−0.540604
$184$	−12.0968	+	6.13729i	−0.891791	+	0.452447i
$185$	10.8176			0.795324
$186$	6.31349	−	4.47207i	0.462927	−	0.327908i
$187$	−4.30522	+	6.69905i	−0.314829	+	0.489883i
$188$	−5.79827	+	16.4859i	−0.422882	+	1.20236i
$189$	−2.94116	−	1.34318i	−0.213938	−	0.0977022i
$190$	−0.0728556	−	1.61431i	−0.00528550	−	0.117115i
$191$	−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	$0.800624\pi$
$192$	0.119971	−	7.99910i	0.00865817	−	0.577285i
$193$	−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	$-0.524502\pi$
$194$	14.8191	−	2.81776i	1.06395	−	0.202303i
$195$	6.88526	+	5.96611i	0.493063	+	0.427242i
$196$	−5.45221	+	4.24373i	−0.389444	+	0.303124i
$197$	−1.70982	−	5.82310i	−0.121819	−	0.414879i	0.875891	−	0.482509i	$-0.160274\pi$
$197$	−1.70982	−	5.82310i	−0.121819	−	0.414879i	−0.997710	+	0.0676302i	$0.978456\pi$
$198$	2.21223	−	0.759473i	0.157216	−	0.0539734i
$199$	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	$0.149641\pi$
$200$	8.09897	+	5.29112i	0.572684	+	0.374139i
$201$	−0.250497	−	1.74225i	−0.0176687	−	0.122889i
$202$	−23.7779	−	13.8075i	−1.67300	−	0.971493i
$203$	−13.2577	−	1.90617i	−0.930508	−	0.133787i
$204$	6.67993	−	6.93596i	0.467689	−	0.485614i
$205$	−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
$210$	10.4095	+	8.22829i	0.718321	+	0.567806i
$211$	6.54025	+	0.940346i	0.450249	+	0.0647361i	0.363710	−	0.931512i	$-0.381510\pi$
$211$	6.54025	+	0.940346i	0.450249	+	0.0647361i	0.0865395	+	0.996248i	$0.472419\pi$
$212$	−21.6057	−	15.5487i	−1.48389	−	1.06789i
$213$	−13.3045	+	1.91290i	−0.911608	+	0.131069i
$214$	−5.84566	+	14.4966i	−0.399601	+	0.990969i
$215$	−26.3101	+	16.9085i	−1.79433	+	1.15315i
$216$	−2.80258	+	0.381523i	−0.190691	+	0.0259594i
$217$	−16.9725	+	4.98358i	−1.15217	+	0.338308i
$218$	2.91011	+	3.06735i	0.197098	+	0.207747i
$219$	−2.17078	−	1.88099i	−0.146687	−	0.127105i
$220$	−9.55947	+	0.864618i	−0.644499	+	0.0582925i
$221$	−13.7506	+	6.27968i	−0.924964	+	0.422417i
$222$	4.69202	−	2.40408i	0.314908	−	0.161351i
$223$	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	$0.145960\pi$
$224$	−6.19781	+	17.2085i	−0.414109	+	1.14979i
$225$	1.42086	−	3.11124i	0.0947238	−	0.207416i
$226$	5.42472	−	22.1196i	0.360847	−	1.47137i
$227$	−15.6784	+	24.3960i	−1.04061	+	1.61922i	−0.291746	+	0.956496i	$0.594236\pi$
$227$	−15.6784	+	24.3960i	−1.04061	+	1.61922i	−0.748864	+	0.662724i	$0.769400\pi$
$228$	−0.390363	−	0.684002i	−0.0258524	−	0.0452991i
$229$			22.1268i			1.46218i	0.682282	+	0.731089i	$0.260988\pi$
$229$			22.1268i			1.46218i	−0.682282	+	0.731089i	$0.739012\pi$
$230$	−7.28734	−	18.2820i	−0.480513	−	1.20548i
$231$	−5.34763			−0.351848
$232$	−10.6940	+	4.78722i	−0.702098	+	0.314296i
$233$	−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	$0.759100\pi$
$234$	4.31231	+	1.05757i	0.281904	+	0.0691358i
$235$	−23.0642	−	10.5331i	−1.50454	−	0.687101i
$236$	8.88411	+	0.467725i	0.578306	+	0.0304463i
$237$	−0.370142	+	1.26059i	−0.0240433	+	0.0818840i
$238$	−19.5941	+	10.0395i	−1.27010	+	0.650767i
$239$	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	$0.852624\pi$
$240$	11.5430	+	1.21879i	0.745095	+	0.0786727i
$241$	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	$0.0398525\pi$
$242$	−8.47910	+	8.04444i	−0.545057	+	0.517116i
$243$	0.281733	+	0.959493i	0.0180732	+	0.0615515i
$244$	14.2311	−	3.37718i	0.911051	−	0.216202i
$245$	−5.41958	−	8.43304i	−0.346245	−	0.538767i
$246$	−1.93692	+	4.80336i	−0.123493	+	0.306251i
$247$	0.175946	+	1.22373i	0.0111951	+	0.0778639i
$248$	−10.2206	+	11.6180i	−0.649008	+	0.737744i
$249$	1.15005	−	7.99879i	0.0728816	−	0.506903i
$250$	4.01997	−	5.08559i	0.254245	−	0.321641i
$251$	2.84520	−	2.46538i	0.179587	−	0.155613i	−0.560428	−	0.828203i	$-0.689363\pi$
$251$	2.84520	−	2.46538i	0.179587	−	0.155613i	0.740016	+	0.672590i	$0.234818\pi$
$252$	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
$256$	3.46049	+	15.6213i	0.216281	+	0.976331i
$257$	−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	$0.839695\pi$
$258$	−7.65403	+	13.1810i	−0.476519	+	0.820612i
$259$	−11.9310	+	1.71541i	−0.741353	+	0.106590i
$260$	−16.1535	−	8.43020i	−1.00180	−	0.522819i
$261$	2.23958	+	3.48486i	0.138627	+	0.215707i
$262$	2.88953	−	0.991997i	0.178516	−	0.0612858i
$263$	−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	$0.560759\pi$
$264$	−3.95418	+	2.49950i	−0.243363	+	0.153833i
$265$	25.2915	−	29.1880i	1.55364	−	1.79300i
$266$	0.336346	+	1.76891i	0.0206227	+	0.108459i
$267$	−0.823200	+	0.375943i	−0.0503790	+	0.0230073i
$268$	1.29202	+	3.27466i	0.0789226	+	0.200031i
$269$	−7.50016	+	25.5432i	−0.457293	+	1.55740i	0.331938	+	0.943301i	$0.392297\pi$
$269$	−7.50016	+	25.5432i	−0.457293	+	1.55740i	−0.789231	+	0.614096i	$0.789521\pi$
$270$	−0.185017	−	4.09956i	−0.0112598	−	0.249492i
$271$	−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	$0.203693\pi$
$272$	−9.79586	+	16.5818i	−0.593961	+	1.00542i
$273$	−8.53999	−	5.48832i	−0.516864	−	0.332168i
$274$	−10.5019	−	14.8261i	−0.634440	−	0.895676i
$275$		−	5.65688i		−	0.341122i
$276$	−7.22376	−	6.31009i	−0.434819	−	0.379823i
$277$			2.91857i			0.175360i	0.996149	+	0.0876799i	$0.0279453\pi$
$277$			2.91857i			0.175360i	−0.996149	+	0.0876799i	$0.972055\pi$
$278$	7.42979	−	5.26279i	0.445609	−	0.315641i
$279$	4.60234	+	2.95774i	0.275535	+	0.177076i
$280$	−24.0562	−	11.2048i	−1.43763	−	0.669617i
$281$	−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	$0.940509\pi$
$282$	−12.3447	+	0.557129i	−0.735117	+	0.0331766i
$283$	5.26341	−	17.9255i	0.312877	−	1.06556i	−0.641541	−	0.767089i	$-0.721705\pi$
$283$	5.26341	−	17.9255i	0.312877	−	1.06556i	0.954418	−	0.298473i	$-0.0964772\pi$
$284$	25.0066	−	9.86637i	1.48387	−	0.585461i
$285$	1.03940	−	0.474676i	0.0615685	−	0.0281174i
$286$	7.21421	−	1.37173i	0.426585	−	0.0811122i
$287$	7.75440	−	8.94905i	0.457727	−	0.528246i
$288$	5.27751	−	2.03665i	0.310980	−	0.120010i
$289$	−5.93182	+	1.74174i	−0.348931	+	0.102455i
$290$	−5.51985	−	16.0785i	−0.324137	−	0.944160i
$291$	5.76672	+	8.97319i	0.338051	+	0.526018i
$292$	5.09287	+	2.65786i	0.298037	+	0.155540i
$293$	0.775885	−	0.111555i	0.0453277	−	0.00651714i	−0.119614	−	0.992821i	$-0.538166\pi$
$293$	0.775885	−	0.111555i	0.0453277	−	0.00651714i	0.164941	+	0.986303i	$0.447257\pi$
$294$	−4.22483	−	2.45331i	−0.246397	−	0.143080i
$295$	−1.83696	+	12.7763i	−0.106952	+	0.743867i
$296$	−8.02027	+	6.84498i	−0.466168	+	0.397857i
$297$	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
$302$	−17.5930	−	13.9066i	−1.01236	−	0.800233i
$303$	2.76698	−	19.2448i	0.158959	−	1.10558i
$304$	1.07550	+	1.15077i	0.0616840	+	0.0660012i
$305$	3.02009	+	21.0052i	0.172930	+	1.20275i
$306$	6.31505	+	2.54650i	0.361007	+	0.145574i
$307$	−16.4233	−	25.5551i	−0.937325	−	1.45851i	−0.888064	−	0.459720i	$-0.847950\pi$
$307$	−16.4233	−	25.5551i	−0.937325	−	1.45851i	−0.0492612	−	0.998786i	$-0.515687\pi$
$308$	10.4063	−	2.46951i	0.592951	−	0.140714i
$309$	−0.804342	−	2.73934i	−0.0457574	−	0.155836i
$310$	−15.4521	−	16.2871i	−0.877623	−	0.925043i
$311$	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	$0.177081\pi$
$312$	−8.87995	−	0.0665873i	−0.502728	−	0.00376977i
$313$	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	$0.582428\pi$
$314$	−5.21238	−	10.1730i	−0.294151	−	0.574093i
$315$	−2.64335	+	9.00242i	−0.148936	+	0.507229i
$316$	0.138146	−	2.62398i	0.00777130	−	0.147610i
$317$	−18.8181	−	8.59394i	−1.05693	−	0.482683i	−0.190347	−	0.981717i	$-0.560961\pi$
$317$	−18.8181	−	8.59394i	−1.05693	−	0.482683i	−0.866583	+	0.499033i	$0.833688\pi$
$318$	4.48327	−	18.2807i	0.251409	−	1.02513i
$319$	5.76360	+	3.70404i	0.322700	+	0.207386i
$320$	−23.0249	+	2.95877i	−1.28713	+	0.165400i
$321$	−11.0527			−0.616901
$322$	10.9365	+	19.0080i	0.609465	+	1.05927i
$323$			1.89596i			0.105494i
$324$	−0.991329	−	1.73703i	−0.0550738	−	0.0965016i
$325$	5.80570	−	9.03385i	0.322042	−	0.501108i
$326$	1.83770	+	0.450688i	0.101781	+	0.0249613i
$327$	−1.24199	+	2.71959i	−0.0686824	+	0.150394i
$328$	1.55099	−	10.2416i	0.0856390	−	0.565497i
$329$	27.1083	+	7.95972i	1.49453	+	0.438833i
$330$	−3.09497	−	6.04042i	−0.170372	−	0.332514i
$331$	−18.9367	+	8.64808i	−1.04085	+	0.475342i	−0.861135	−	0.508376i	$-0.830246\pi$
$331$	−18.9367	+	8.64808i	−1.04085	+	0.475342i	−0.179718	+	0.983718i	$0.557519\pi$
$332$	1.45586	+	16.0964i	0.0799005	+	0.883404i
$333$	2.81737	+	2.44126i	0.154391	+	0.133780i
$334$	−21.8930	+	20.7707i	−1.19793	+	1.13652i
$335$	−4.90071	+	1.43898i	−0.267754	+	0.0786198i
$336$	−12.9243	+	0.486206i	−0.705076	+	0.0265247i
$337$	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	$0.289962\pi$
$338$	−4.12202	−	1.66218i	−0.224209	−	0.0904105i
$339$	15.9405	−	2.29189i	0.865767	−	0.124479i
$340$	−22.6804	−	16.3221i	−1.23001	−	0.885190i
$341$	8.95606	+	1.28769i	0.484998	+	0.0697322i
$342$	0.345336	−	0.436879i	0.0186737	−	0.0236237i
$343$	−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	$-0.566107\pi$
$347$	13.6546	−	11.8318i	0.733017	−	0.635163i	0.939208	+	0.343349i	$0.111561\pi$
$348$	−5.96743	−	5.74716i	−0.319888	−	0.308080i
$349$	33.4436	+	4.80846i	1.79019	+	0.257391i	0.955850	−	0.293853i	$-0.0949378\pi$
$349$	33.4436	+	4.80846i	1.79019	+	0.257391i	0.834344	+	0.551245i	$0.185847\pi$
$350$	7.85382	−	13.5250i	0.419804	−	0.722943i
$351$	0.446815	+	3.10767i	0.0238492	+	0.165875i
$352$	6.54039	−	6.68994i	0.348604	−	0.356575i
$353$	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	$0.261612\pi$
$354$	2.04263	+	5.94985i	0.108564	+	0.316231i
$355$	10.9886	+	37.4238i	0.583215	+	1.98625i
$356$	1.42830	−	1.11172i	0.0756999	−	0.0589210i
$357$	−11.7654	−	10.1948i	−0.622694	−	0.539567i
$358$	−6.89511	−	36.2628i	−0.364418	−	1.91655i
$359$	−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	$0.972393\pi$
$360$	2.25320	+	7.89213i	0.118754	+	0.415952i
$361$	−18.0816	−	5.30923i	−0.951662	−	0.279433i
$362$	−2.80379	+	0.126538i	−0.147364	+	0.00665069i
$363$	−7.51777	−	3.43325i	−0.394580	−	0.180199i
$364$	19.1529	+	6.73629i	1.00389	+	0.353078i
$365$	−4.50620	+	7.01178i	−0.235865	+	0.367014i
$366$	5.97808	+	8.43961i	0.312479	+	0.441145i
$367$	−14.0461			−0.733199			−0.366599	−	0.930379i	$-0.619478\pi$
$367$	−14.0461			−0.733199			−0.366599	+	0.930379i	$0.619478\pi$
$368$	16.9711	+	8.94326i	0.884680	+	0.466200i
$369$	−3.66223			−0.190648
$370$	−8.84274	−	12.4838i	−0.459712	−	0.649003i
$371$	−23.2661	+	36.2027i	−1.20791	+	1.87955i
$372$	−10.3218	−	3.63030i	−0.535162	−	0.188222i
$373$	−25.5476	−	11.6672i	−1.32281	−	0.604105i	−0.376211	−	0.926534i	$-0.622773\pi$
$373$	−25.5476	−	11.6672i	−1.32281	−	0.604105i	−0.946594	+	0.322429i	$0.895501\pi$
$374$	11.2502	−	0.507732i	0.581733	−	0.0262542i
$375$	4.39817	+	1.29142i	0.227121	+	0.0666886i
$376$	23.7650	−	6.78489i	1.22559	−	0.349904i
$377$	5.40279	+	11.8305i	0.278258	+	0.609300i
$378$	0.854154	+	4.49216i	0.0439329	+	0.231052i
$379$	27.0336	+	23.4248i	1.38862	+	1.20325i	0.952943	+	0.303148i	$0.0980377\pi$
$379$	27.0336	+	23.4248i	1.38862	+	1.20325i	0.435681	+	0.900101i	$0.356508\pi$
$380$	−1.80341	+	1.40369i	−0.0925132	+	0.0720076i
$381$	−0.985573	−	3.35655i	−0.0504924	−	0.171961i
$382$	7.77040	+	22.6340i	0.397568	+	1.15806i
$383$	−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	$0.335980\pi$
$384$	−9.32928	+	6.40035i	−0.476083	+	0.326617i
$385$	2.20839	+	15.3597i	0.112550	+	0.782803i
$386$	−18.5259	+	31.9034i	−0.942945	+	1.62384i
$387$	−10.6681	−	1.53384i	−0.542290	−	0.0779696i
$388$	−15.3656	−	14.7984i	−0.780068	−	0.751274i
$389$	18.1632	−	15.7385i	0.920910	−	0.797973i	−0.0588257	−	0.998268i	$-0.518736\pi$
$389$	18.1632	−	15.7385i	0.920910	−	0.797973i	0.979736	+	0.200295i	$0.0641901\pi$
$390$	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
$394$	−5.32236	+	6.73323i	−0.268137	+	0.339215i
$395$	3.77357	+	0.542558i	0.189869	+	0.0272990i
$396$	−2.68482	−	1.93215i	−0.134917	−	0.0970944i
$397$	−13.9869	+	2.01101i	−0.701983	+	0.100930i	−0.484058	−	0.875036i	$-0.660838\pi$
$397$	−13.9869	+	2.01101i	−0.701983	+	0.100930i	−0.217924	+	0.975966i	$0.569929\pi$
$398$	−18.6907	−	7.53689i	−0.936880	−	0.377790i
$399$	−1.07110	+	0.688354i	−0.0536221	+	0.0344608i
$400$	−0.514323	−	13.6717i	−0.0257161	−	0.683583i
$401$	−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	$0.472044\pi$
$402$	−1.80584	+	1.71327i	−0.0900671	+	0.0854500i
$403$	12.9810	+	11.2481i	0.646628	+	0.560307i
$404$	3.50273	+	38.7272i	0.174267	+	1.92675i
$405$	2.63955	−	1.20544i	0.131160	−	0.0598990i
$406$	8.63763	+	16.8580i	0.428678	+	0.836648i
$407$	5.91583	+	1.73704i	0.293237	+	0.0861021i
$408$	−13.4648	−	2.03911i	−0.666605	−	0.100951i
$409$	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	$0.00714625\pi$
$410$	14.5963	+	3.57968i	0.720860	+	0.176788i
$411$	6.94572	−	10.8078i	0.342607	−	0.533107i
$412$	2.83023	+	4.95919i	0.139435	+	0.244322i
$413$		−	14.3826i		−	0.707722i
$414$	2.22785	−	6.40599i	0.109493	−	0.314837i
$415$	−23.4494			−1.15109
$416$	17.3107	−	3.97115i	0.848729	−	0.194702i
$417$	5.41609	+	3.48071i	0.265227	+	0.170451i
$418$	0.219378	−	0.894522i	0.0107301	−	0.0437525i
$419$	−10.0088	−	4.57088i	−0.488963	−	0.223302i	0.155648	−	0.987813i	$-0.450253\pi$
$419$	−10.0088	−	4.57088i	−0.488963	−	0.223302i	−0.644611	+	0.764511i	$0.722981\pi$
$420$	0.986560	−	18.7390i	0.0481392	−	0.914370i
$421$	6.37343	−	21.7059i	0.310622	−	1.05788i	−0.645219	−	0.763998i	$-0.723234\pi$
$421$	6.37343	−	21.7059i	0.310622	−	1.05788i	0.955841	−	0.293884i	$-0.0949480\pi$
$422$	−4.26109	−	8.31633i	−0.207426	−	0.404832i
$423$	−3.62986	−	7.94829i	−0.176490	−	0.386459i
$424$	−0.282277	+	37.6438i	−0.0137086	+	1.82815i
$425$	10.7844	−	12.4458i	0.523119	−	0.603712i
$426$	13.0832	+	13.7901i	0.633883	+	0.668133i
$427$	−6.66185	−	22.6882i	−0.322389	−	1.09796i
$428$	21.5080	−	5.10408i	1.03963	−	0.246715i
$429$	2.80734	+	4.36830i	0.135540	+	0.210904i
$430$	41.0198	+	16.5410i	1.97815	+	0.797675i
$431$	−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	$-0.210584\pi$
$432$	2.73124	+	2.92239i	0.131407	+	0.140603i
$433$	−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	$0.807561\pi$
$434$	19.6253	+	15.5130i	0.942043	+	0.744649i
$435$	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	$0.900974\pi$
$440$	8.81211	+	10.3252i	0.420101	+	0.492232i
$441$	0.491635	−	3.41940i	0.0234112	−	0.162828i
$442$	18.4873	+	10.7353i	0.879349	+	0.510627i
$443$	−1.93107	+	0.277645i	−0.0917477	+	0.0131913i	−0.188036	−	0.982162i	$-0.560212\pi$
$443$	−1.93107	+	0.277645i	−0.0917477	+	0.0131913i	0.0962881	+	0.995354i	$0.469303\pi$
$444$	−6.60983	−	3.44954i	−0.313689	−	0.163708i
$445$	1.41975	+	2.20918i	0.0673028	+	0.104725i
$446$	−13.5101	−	39.3528i	−0.639722	−	1.86341i
$447$	16.9071	−	4.96438i	0.799680	−	0.234807i
$448$	24.9255	−	6.91451i	1.17762	−	0.326680i
$449$	−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	$0.334898\pi$
$450$	−4.75194	+	0.903549i	−0.224009	+	0.0425937i
$451$	−5.50960	+	2.51615i	−0.259437	+	0.118481i
$452$	−29.9610	+	11.8212i	−1.40925	+	0.556021i
$453$	4.46750	−	15.2149i	0.209902	−	0.714859i
$454$	40.9699	−	1.84901i	1.92281	−	0.0867785i
$455$	−12.2371	+	26.7954i	−0.573682	+	1.25619i
$456$	−0.470260	+	1.00962i	−0.0220220	+	0.0472799i
$457$	−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	$0.782469\pi$
$458$	25.5350	−	18.0874i	1.19317	−	0.845167i
$459$			4.81479i			0.224735i
$460$	−15.1410	+	23.3543i	−0.705951	+	1.08890i
$461$		−	33.7864i		−	1.57359i	−0.617214	−	0.786796i	$-0.711739\pi$
$461$		−	33.7864i		−	1.57359i	0.617214	−	0.786796i	$-0.288261\pi$
$462$	4.37138	+	6.17133i	0.203375	+	0.287116i
$463$	−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	$0.794359\pi$
$464$	14.2664	+	8.42798i	0.662299	+	0.391259i
$465$	6.59475	−	14.4405i	0.305824	−	0.669662i
$466$	0.467962	+	10.3690i	0.0216779	+	0.480334i
$467$	−5.06583	+	17.2526i	−0.234419	+	0.798357i	0.755306	+	0.655372i	$0.227488\pi$
$467$	−5.06583	+	17.2526i	−0.234419	+	0.798357i	−0.989725	+	0.142985i	$0.954330\pi$
$468$	−2.30459	−	5.84105i	−0.106530	−	0.270002i
$469$	5.17692	−	2.36422i	0.239048	−	0.109169i
$470$	6.69816	+	35.2270i	0.308963	+	1.62490i
$471$	5.29300	−	6.10844i	0.243888	−	0.281462i
$472$	−6.72248	−	10.6349i	−0.309427	−	0.489510i
$473$	−17.1033	+	5.02199i	−0.786412	+	0.230911i
$474$	1.75733	−	0.603302i	0.0807167	−	0.0277106i
$475$	−0.728161	−	1.13304i	−0.0334103	−	0.0519875i
$476$	27.6030	+	14.4054i	1.26518	+	0.660272i
$477$	13.1740	−	1.89414i	0.603196	−	0.0867266i
$478$	0.759478	−	1.30789i	0.0347377	−	0.0598217i
$479$	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	$-0.125383\pi$
$480$	−8.02918	−	14.3172i	−0.366480	−	0.653489i
$481$	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
$486$	0.876985	−	1.10946i	0.0397808	−	0.0503261i
$487$	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	$-0.143326\pi$
$488$	−15.5305	−	13.6625i	−0.703031	−	0.618470i
$489$	0.190411	+	1.32434i	0.00861069	+	0.0598887i
$490$	−5.30179	+	13.1479i	−0.239510	+	0.593961i
$491$	−10.9491	−	17.0372i	−0.494127	−	0.768877i	0.501211	−	0.865325i	$-0.332888\pi$
$491$	−10.9491	−	17.0372i	−0.494127	−	0.768877i	−0.995338	+	0.0964485i	$0.969252\pi$
$492$	7.12655	−	1.69120i	0.321290	−	0.0762454i
$493$	5.61919	+	19.1372i	0.253075	+	0.861896i
$494$	1.26839	−	1.20337i	0.0570678	−	0.0541423i
$495$	3.14284	−	3.62703i	0.141260	−	0.163023i
$496$	21.7623	+	2.29782i	0.977155	+	0.103175i
$497$	−18.0541	−	39.5330i	−0.809838	−	1.77330i
$498$	−10.1710	+	5.21135i	−0.455771	+	0.233526i
$499$	−2.66438	+	9.07406i	−0.119274	+	0.406211i	−0.997387	−	0.0722429i	$-0.976984\pi$
$499$	−2.66438	+	9.07406i	−0.119274	+	0.406211i	0.878113	+	0.478454i	$0.158802\pi$
$500$	−9.15502	−	0.481988i	−0.409425	−	0.0215552i
$501$	−19.4109	−	8.86465i	−0.867214	−	0.396044i
$502$	−5.17091	−	1.26814i	−0.230789	−	0.0566000i
$503$	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	$0.582325\pi$
$504$	−3.73661	−	8.34711i	−0.166442	−	0.371810i
$505$	−56.4183			−2.51058
$506$	−1.04960	−	11.1681i	−0.0466604	−	0.496481i
$507$		−	3.14276i		−	0.139575i
$508$	3.46793	+	6.07657i	0.153864	+	0.269604i
$509$	12.1672	−	18.9325i	0.539302	−	0.839170i	−0.459497	−	0.888180i	$-0.651970\pi$
$509$	12.1672	−	18.9325i	0.539302	−	0.839170i	0.998798	+	0.0490096i	$0.0156065\pi$
$510$	4.70626	−	19.1900i	0.208397	−	0.849747i
$511$	3.85809	−	8.44803i	0.170672	−	0.373719i
$512$	15.1987	−	16.7630i	0.671695	−	0.740828i
$513$	0.377826	+	0.110940i	0.0166814	+	0.00489811i
$514$	24.3065	−	12.4541i	1.07211	−	0.549326i
$515$	−7.53588	+	3.44152i	−0.332071	+	0.151652i
$516$	21.4680	−	1.94170i	0.945075	−	0.0854785i
$517$	−10.9218	−	9.46379i	−0.480340	−	0.416217i
$518$	11.7325	+	12.3664i	0.515497	+	0.543350i
$519$	−1.19659	+	0.351352i	−0.0525246	+	0.0154226i
$520$	3.47587	+	25.5329i	0.152427	+	1.11969i
$521$	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	$0.280686\pi$
$522$	2.19091	−	5.43322i	0.0958934	−	0.237806i
$523$	−2.57719	+	0.370544i	−0.112693	+	0.0162027i	−0.198430	−	0.980115i	$-0.563584\pi$
$523$	−2.57719	+	0.370544i	−0.112693	+	0.0162027i	0.0857378	+	0.996318i	$0.472675\pi$
$524$	−3.50682	−	2.52371i	−0.153196	−	0.110249i
$525$	10.9466	+	1.57388i	0.477747	+	0.0686897i
$526$	16.5046	+	13.0462i	0.719634	+	0.568843i
$527$	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
$532$	1.76643	−	1.83414i	0.0765847	−	0.0795199i
$533$	−11.3810	−	1.63634i	−0.492966	−	0.0708778i
$534$	1.10677	+	0.642687i	0.0478945	+	0.0278118i
$535$	4.56439	+	31.7460i	0.197336	+	1.37250i
$536$	2.72290	−	4.16787i	0.117612	−	0.180025i
$537$	21.9576	−	14.1113i	0.947541	−	0.608947i
$538$	35.6086	−	12.2247i	1.53520	−	0.527044i
$539$	−1.60967	−	5.48205i	−0.0693336	−	0.236128i
$540$	−4.57978	+	3.56467i	−0.197083	+	0.153399i
$541$	−3.29608	−	2.85607i	−0.141709	−	0.122792i	0.581122	−	0.813817i	$-0.302614\pi$
$541$	−3.29608	−	2.85607i	−0.141709	−	0.122792i	−0.722831	+	0.691025i	$0.757160\pi$
$542$	9.60350	−	1.82604i	0.412505	−	0.0784351i
$543$	−0.824432	−	1.80525i	−0.0353798	−	0.0774709i
$544$	27.1435	−	2.24996i	1.16377	−	0.0964663i
$545$	8.32422	+	2.44421i	0.356571	+	0.104699i
$546$	0.647260	+	14.3418i	0.0277002	+	0.613772i
$547$	12.5744	+	5.74253i	0.537642	+	0.245533i	0.665681	−	0.746236i	$-0.268141\pi$
$547$	12.5744	+	5.74253i	0.537642	+	0.245533i	−0.128039	+	0.991769i	$0.540868\pi$
$548$	−8.52510	+	24.2389i	−0.364174	+	1.03544i
$549$	−3.95379	+	6.15222i	−0.168744	+	0.262570i
$550$	−6.52821	+	4.62417i	−0.278364	+	0.197175i
$551$	1.63121			0.0694917
$552$	−1.37704	+	13.4946i	−0.0586105	+	0.574368i
$553$	−4.24800			−0.180643
$554$	3.36812	−	2.38576i	0.143098	−	0.101361i
$555$	5.84842	−	9.10032i	0.248252	−	0.386287i
$556$	−12.1469	−	4.27218i	−0.515141	−	0.181181i
$557$	−4.11170	−	1.87775i	−0.174218	−	0.0795628i	0.326397	−	0.945233i	$-0.394165\pi$
$557$	−4.11170	−	1.87775i	−0.174218	−	0.0795628i	−0.500615	+	0.865670i	$0.666893\pi$
$558$	−0.348819	−	7.72903i	−0.0147667	−	0.327196i
$559$	−32.4676	−	9.53334i	−1.37323	−	0.403217i
$560$	6.73379	+	36.9209i	0.284555	+	1.56019i
$561$	3.30802	+	7.24356i	0.139665	+	0.305823i
$562$	26.8851	−	5.11202i	1.13408	−	0.215637i
$563$	20.3995	+	17.6763i	0.859737	+	0.744967i	0.968477	−	0.249104i	$-0.0801360\pi$
$563$	20.3995	+	17.6763i	0.859737	+	0.744967i	−0.108740	+	0.994070i	$0.534681\pi$
$564$	10.7340	+	13.7908i	0.451984	+	0.580696i
$565$	−13.1658	−	44.8384i	−0.553887	−	1.88637i
$566$	−24.9891	+	8.57894i	−1.05037	+	0.360600i
$567$	−2.72007	+	1.74808i	−0.114232	+	0.0734125i
$568$	−31.8275	−	20.7932i	−1.33545	−	0.872462i
$569$	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	$0.852182\pi$
$570$	−1.39744	−	0.811474i	−0.0585322	−	0.0339889i
$571$	−19.6583	−	2.82643i	−0.822674	−	0.118283i	−0.281892	−	0.959446i	$-0.590962\pi$
$571$	−19.6583	−	2.82643i	−0.822674	−	0.118283i	−0.540781	+	0.841163i	$0.681871\pi$
$572$	−7.48022	−	7.20411i	−0.312764	−	0.301219i
$573$	−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	$0.944079\pi$
$578$	6.85895	+	5.42174i	0.285295	+	0.225515i
$579$	−25.8212	−	3.71253i	−1.07309	−	0.154288i
$580$	−14.0429	+	19.5133i	−0.583099	+	0.810245i
$581$	25.8629	−	3.71852i	1.07297	−	0.154270i
$582$	5.64138	−	13.9900i	0.233843	−	0.579906i
$583$	18.5181	−	11.9009i	0.766941	−	0.492883i
$584$	−1.09587	−	8.04998i	−0.0453473	−	0.333110i
$585$	8.74146	−	2.56672i	0.361415	−	0.106121i
$586$	−0.762980	−	0.804206i	−0.0315184	−	0.0332214i
$587$	−6.58689	−	5.70757i	−0.271870	−	0.235577i	0.508245	−	0.861212i	$-0.330294\pi$
$587$	−6.58689	−	5.70757i	−0.271870	−	0.235577i	−0.780115	+	0.625636i	$0.784840\pi$
$588$	0.622363	+	6.88103i	0.0256658	+	0.283769i
$589$	1.95960	−	0.894920i	0.0807440	−	0.0368745i
$590$	16.2459	−	8.32401i	0.668833	−	0.342694i
$591$	−5.82310	−	1.70982i	−0.239530	−	0.0703324i
$592$	14.4554	+	3.66026i	0.594114	+	0.150436i
$593$	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	$0.0256810\pi$
$594$	0.557111	−	2.27165i	0.0228585	−	0.0932068i
$595$	−24.4233	+	38.0034i	−1.00126	+	1.55799i
$596$	−30.6080	+	17.4681i	−1.25375	+	0.715522i
$597$		−	14.2504i		−	0.583230i
$598$	9.78570	−	18.9122i	0.400167	−	0.773379i
$599$	29.8588			1.22000			0.609998	−	0.792403i	$-0.291170\pi$
$599$	29.8588			1.22000			0.609998	+	0.792403i	$0.291170\pi$
$600$	8.82981	−	3.95269i	0.360476	−	0.161368i
$601$	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	$0.642563\pi$
$602$	−47.8647	−	11.7386i	−1.95082	−	0.478430i
$603$	−1.60110	−	0.731198i	−0.0652018	−	0.0297767i
$604$	−1.66738	+	31.6706i	−0.0678447	+	1.28866i
$605$	−6.75655	+	23.0107i	−0.274693	+	0.935517i
$606$	−24.4709	+	12.5383i	−0.994062	+	0.509334i
$607$	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	$0.681212\pi$
$608$	0.448866	−	2.18185i	0.0182039	−	0.0884855i
$609$	−8.77123	+	10.1225i	−0.355428	+	0.410186i
$610$	21.7719	−	20.6558i	0.881517	−	0.836329i
$611$	−7.72898	−	26.3225i	−0.312681	−	1.06489i
$612$	−2.22345	−	9.36938i	−0.0898777	−	0.378735i
$613$	−0.295137	−	0.459243i	−0.0119205	−	0.0185486i	0.835242	−	0.549882i	$-0.185327\pi$
$613$	−0.295137	−	0.459243i	−0.0119205	−	0.0185486i	−0.847163	+	0.531334i	$0.821691\pi$
$614$	−16.0663	+	39.8428i	−0.648383	+	1.60792i
$615$	1.51238	+	10.5188i	0.0609850	+	0.424160i
$616$	−11.3564	−	9.99045i	−0.457563	−	0.402527i
$617$	−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	$0.944049\pi$
$618$	−2.50378	+	3.16749i	−0.100717	+	0.127415i
$619$	28.2193	−	24.4521i	1.13423	−	0.982814i	0.134261	−	0.990946i	$-0.457134\pi$
$619$	28.2193	−	24.4521i	1.13423	−	0.982814i	0.999967	+	0.00813192i	$0.00258850\pi$
$620$	−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
$624$	7.18200	+	10.3022i	0.287510	+	0.412417i
$625$	4.32680	−	30.0935i	0.173072	−	1.20374i
$626$	19.4223	−	33.4471i	0.776271	−	1.33681i
$627$	0.644638	−	0.0926849i	0.0257443	−	0.00370148i
$628$	−7.47908	+	14.3310i	−0.298448	+	0.571871i
$629$	9.70403	+	15.0998i	0.386925	+	0.602067i
$630$	12.5499	−	4.30845i	0.499998	−	0.171653i
$631$	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	$0.173316\pi$
$632$	−3.14108	+	1.98553i	−0.124945	+	0.0789800i
$633$	4.32699	−	4.99362i	0.171983	−	0.198478i
$634$	5.46504	+	28.7417i	0.217044	+	1.14148i
$635$	−9.23384	+	4.21695i	−0.366434	+	0.167345i
$636$	−24.7613	+	9.76961i	−0.981851	+	0.387390i
$637$	3.05568	−	10.4067i	0.121070	−	0.412327i
$638$	−0.436833	−	9.67921i	−0.0172944	−	0.383204i
$639$	−5.58372	+	12.2266i	−0.220888	+	0.483678i
$640$	22.2361	+	24.1528i	0.878958	+	0.954725i
$641$	−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	$0.802621\pi$
$642$	9.03493	+	12.7551i	0.356580	+	0.503405i
$643$			40.0856i			1.58082i	0.612577	+	0.790411i	$0.290133\pi$
$643$			40.0856i			1.58082i	−0.612577	+	0.790411i	$0.709867\pi$
$644$	12.9959	−	28.1590i	0.512109	−	1.10962i
$645$			31.2748i			1.23145i
$646$	2.18799	−	1.54983i	0.0860854	−	0.0609774i
$647$	−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	$0.787073\pi$
$648$	−1.19423	+	2.56395i	−0.0469138	+	0.100721i
$649$	−3.05616	+	6.69205i	−0.119965	+	0.262686i
$650$	−15.1712	+	0.684690i	−0.595062	+	0.0268558i
$651$	−4.98358	+	16.9725i	−0.195322	+	0.665206i
$652$	−0.982106	−	2.48917i	−0.0384622	−	0.0974835i
$653$	−3.65881	+	1.67092i	−0.143180	+	0.0653883i	−0.485717	−	0.874116i	$-0.661441\pi$
$653$	−3.65881	+	1.67092i	−0.143180	+	0.0653883i	0.342536	+	0.939505i	$0.388714\pi$
$654$	4.15375	−	0.789806i	0.162424	−	0.0308839i
$655$	4.10507	−	4.73750i	0.160398	−	0.185109i
$656$	−13.0870	+	6.58202i	−0.510960	+	0.256985i
$657$	−2.75600	+	0.809234i	−0.107522	+	0.0315712i
$658$	−12.9737	−	37.7904i	−0.505768	−	1.47322i
$659$	11.2693	+	17.5353i	0.438989	+	0.683080i	0.988297	−	0.152540i	$-0.0487452\pi$
$659$	11.2693	+	17.5353i	0.438989	+	0.683080i	−0.549308	+	0.835620i	$0.685109\pi$
$660$	−4.44088	+	8.50939i	−0.172861	+	0.331227i
$661$	−3.37009	+	0.484546i	−0.131081	+	0.0188466i	−0.207543	−	0.978226i	$-0.566547\pi$
$661$	−3.37009	+	0.484546i	−0.131081	+	0.0188466i	0.0764619	+	0.997073i	$0.475638\pi$
$662$	25.4598	+	14.7842i	0.989523	+	0.574604i
$663$	−2.15132	+	14.9628i	−0.0835505	+	0.581106i
$664$	17.3856	−	14.8380i	0.674694	−	0.575825i
$665$	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
$670$	5.66667	+	4.47929i	0.218923	+	0.173050i
$671$	−1.72133	+	11.9721i	−0.0664511	+	0.462178i
$672$	11.1259	+	14.5176i	0.429192	+	0.560027i
$673$	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	$0.611328\pi$
$674$	−4.26360	−	1.71926i	−0.164228	−	0.0662235i
$675$	−1.84917	−	2.87737i	−0.0711746	−	0.110750i
$676$	1.45131	+	6.11568i	0.0558198	+	0.235218i
$677$	−0.936652	−	3.18994i	−0.0359984	−	0.122599i	0.939534	−	0.342457i	$-0.111259\pi$
$677$	−0.936652	−	3.18994i	−0.0359984	−	0.122599i	−0.975532	+	0.219857i	$0.929441\pi$
$678$	−15.6753	−	16.5223i	−0.602007	−	0.634535i
$679$	−22.5851	+	26.0646i	−0.866736	+	1.00027i
$680$	−0.296317	+	39.5162i	−0.0113632	+	1.51538i
$681$	12.0469	+	26.3790i	0.461637	+	1.01084i
$682$	−5.83503	−	11.3882i	−0.223435	−	0.436076i
$683$	6.08118	−	20.7106i	0.232690	−	0.792470i	−0.757511	−	0.652822i	$-0.773585\pi$
$683$	6.08118	−	20.7106i	0.232690	−	0.792470i	0.990201	−	0.139647i	$-0.0445969\pi$
$684$	−0.786465	−	0.0414054i	−0.0300712	−	0.00158317i
$685$	−33.9109	−	15.4866i	−1.29567	−	0.591712i
$686$	−3.86151	+	15.7455i	−0.147433	+	0.601165i
$687$	18.6142	+	11.9626i	0.710177	+	0.456403i
$688$	−40.8791	+	13.6923i	−1.55850	+	0.522014i
$689$	41.7868			1.59195
$690$	−19.3196	−	3.75347i	−0.735484	−	0.142892i
$691$		−	50.1334i		−	1.90716i	−0.301134	−	0.953582i	$-0.597365\pi$
$691$		−	50.1334i		−	1.90716i	0.301134	−	0.953582i	$-0.402635\pi$
$692$	2.16627	−	1.23630i	0.0823491	−	0.0469970i
$693$	−2.89115	+	4.49871i	−0.109826	+	0.170892i
$694$	−24.8161	−	6.08603i	−0.942005	−	0.231023i
$695$	7.76079	−	16.9938i	0.294384	−	0.644610i
$696$	−1.75437	+	11.5846i	−0.0664992	+	0.439112i
$697$	−16.9187	−	4.96776i	−0.640840	−	0.188167i
$698$	−21.7891	−	42.5256i	−0.824729	−	1.60962i
$699$	−6.67619	+	3.04891i	−0.252517	+	0.115320i
$700$	−22.0283	+	1.99238i	−0.832593	+	0.0753049i
$701$	33.8457	+	29.3275i	1.27833	+	1.10768i	0.988598	+	0.150576i	$0.0481129\pi$
$701$	33.8457	+	29.3275i	1.27833	+	1.10768i	0.289736	+	0.957107i	$0.406433\pi$
$702$	3.22110	−	3.05598i	0.121573	−	0.115340i
$703$	1.40850	−	0.413574i	0.0531227	−	0.0155982i
$704$	−13.0668	−	2.07918i	−0.492473	−	0.0783621i
$705$	−21.3304	+	13.7082i	−0.803350	+	0.516282i
$706$	−8.71287	−	3.51340i	−0.327913	−	0.132229i
$707$	62.2251	−	8.94661i	2.34021	−	0.336472i
$708$	5.19659	−	7.22091i	0.195300	−	0.271379i
$709$	−42.0839	−	6.05075i	−1.58049	−	0.227241i	−0.704550	−	0.709655i	$-0.748851\pi$
$709$	−42.0839	−	6.05075i	−1.58049	−	0.227241i	−0.875943	+	0.482414i	$0.839760\pi$
$710$	34.2056	−	43.2730i	1.28372	−	1.62401i
$711$	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
$716$	−36.2120	+	37.5999i	−1.35331	+	1.40517i
$717$	1.05855	+	0.152197i	0.0395324	+	0.00568389i
$718$	−9.01693	+	15.5280i	−0.336509	+	0.579500i
$719$	−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	$-0.110888\pi$
$720$	7.26591	−	9.05162i	0.270784	−	0.337334i
$721$	7.76575	−	4.99075i	0.289212	−	0.185865i
$722$	8.65364	+	25.2067i	0.322055	+	0.938097i
$723$	−4.85793	−	16.5446i	−0.180669	−	0.615301i
$724$	2.43797	+	3.13223i	0.0906064	+	0.116408i
$725$	−10.7079	−	9.27846i	−0.397682	−	0.344593i
$726$	2.18327	+	11.4822i	0.0810286	+	0.426145i
$727$	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	$0.726407\pi$
$728$	−7.88252	−	27.6096i	−0.292146	−	1.02328i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	11.7754	−	0.531434i	0.435826	−	0.0196693i
$731$	−47.2035	−	21.5571i	−1.74588	−	0.797318i
$732$	4.85283	−	13.7978i	0.179366	−	0.509981i
$733$	−4.30394	+	6.69705i	−0.158969	+	0.247361i	−0.911597	−	0.411085i	$-0.865150\pi$
$733$	−4.30394	+	6.69705i	−0.158969	+	0.247361i	0.752627	+	0.658447i	$0.228786\pi$
$734$	11.4818	+	16.2096i	0.423803	+	0.598307i
$735$	−10.0244			−0.369754
$736$	−3.55209	−	26.8958i	−0.130932	−	0.991391i
$737$	−2.91113			−0.107233
$738$	2.99367	+	4.22633i	0.110198	+	0.155573i
$739$	0.368407	−	0.573252i	0.0135521	−	0.0210874i	−0.834411	−	0.551142i	$-0.814192\pi$
$739$	0.368407	−	0.573252i	0.0135521	−	0.0210874i	0.847963	+	0.530055i	$0.177829\pi$
$740$	−7.17828	+	20.4096i	−0.263879	+	0.750272i
$741$	1.12459	+	0.513582i	0.0413128	+	0.0188669i
$742$	60.7977	−	2.74386i	2.23195	−	0.100730i
$743$	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	$0.459141\pi$
$744$	4.24802	+	14.8793i	0.155740	+	0.545500i
$745$	−21.2410	−	46.5113i	−0.778210	−	1.70404i
$746$	7.41938	+	39.0200i	0.271643	+	1.42862i
$747$	−6.10724	−	5.29196i	−0.223452	−	0.193623i
$748$	−9.78231	−	12.5680i	−0.357677	−	0.459532i
$749$	−10.0683	−	34.2896i	−0.367889	−	1.25291i
$750$	−2.10491	−	6.13129i	−0.0768606	−	0.223883i
$751$	−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	$0.554064\pi$
$752$	−27.2565	−	21.8793i	−0.993941	−	0.797855i
$753$	−0.535778	−	3.72642i	−0.0195248	−	0.135798i
$754$	9.23625	−	15.9057i	0.336365	−	0.579252i
$755$	−45.5459	−	6.54851i	−1.65759	−	0.238325i
$756$	4.48588	−	4.65781i	0.163150	−	0.169403i
$757$	−26.7864	+	23.2105i	−0.973567	+	0.843601i	−0.987710	−	0.156299i	$-0.950044\pi$
$757$	−26.7864	+	23.2105i	−0.973567	+	0.843601i	0.0141427	+	0.999900i	$0.495498\pi$
$758$	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	$0.822035\pi$
$762$	−3.06792	+	3.88117i	−0.111139	+	0.140600i
$763$	−9.56857	−	1.37575i	−0.346405	−	0.0498056i
$764$	19.7685	−	27.4693i	0.715198	−	0.993803i
$765$	13.8293	−	1.98835i	0.499998	−	0.0718889i
$766$	2.86891	+	1.15687i	0.103658	+	0.0417992i
$767$	−11.7487	+	7.55042i	−0.424220	+	0.272630i
$768$	15.0124	+	5.53436i	0.541712	+	0.199704i
$769$	−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	$0.624316\pi$
$770$	15.9203	−	15.1042i	0.573729	−	0.544318i
$771$	14.5951	+	12.6467i	0.525629	+	0.455460i
$772$	51.9614	−	4.69971i	1.87013	−	0.169146i
$773$	−50.4990	+	23.0621i	−1.81632	+	0.829487i	−0.884548	+	0.466450i	$0.845533\pi$
$773$	−50.4990	+	23.0621i	−1.81632	+	0.829487i	−0.931775	+	0.363037i	$0.881740\pi$
$774$	6.95046	+	13.5652i	0.249829	+	0.487589i
$775$	−17.9540	−	5.27178i	−0.644928	−	0.189368i
$776$	−4.51733	+	29.8292i	−0.162163	+	1.07080i
$777$	−5.00726	+	10.9644i	−0.179635	+	0.393345i
$778$	−33.0101	−	8.09557i	−1.18347	−	0.290240i
$779$	−0.779660	+	1.21318i	−0.0279342	+	0.0434665i
$780$	−15.8252	+	9.03150i	−0.566633	+	0.323380i
$781$			22.2305i			0.795471i
$782$	18.9818	−	26.5721i	0.678786	−	0.950216i
$783$	4.14246			0.148040
$784$	−4.38872	−	13.1028i	−0.156740	−	0.467956i
$785$	−19.7308	−	12.6802i	−0.704222	−	0.452576i
$786$	0.727679	−	2.96715i	0.0259555	−	0.105835i
$787$	38.1356	+	17.4159i	1.35939	+	0.620812i	0.955770	−	0.294116i	$-0.0950252\pi$
$787$	38.1356	+	17.4159i	1.35939	+	0.620812i	0.403618	+	0.914928i	$0.367753\pi$
$788$	12.1211	+	0.638144i	0.431796	+	0.0227329i
$789$	−4.19112	+	14.2737i	−0.149208	+	0.508156i
$790$	−2.45855	−	4.79833i	−0.0874713	−	0.170717i
$791$	21.6311	+	47.3656i	0.769114	+	1.68413i
$792$	−0.0350770	+	4.67780i	−0.00124641	+	0.166218i
$793$	−15.0360	+	17.3524i	−0.533943	+	0.616203i
$794$	13.7543	+	14.4974i	0.488120	+	0.514495i
$795$	−10.8808	−	37.0568i	−0.385904	−	1.31427i
$796$	6.58077	+	27.7306i	0.233249	+	0.982886i
$797$	−3.01543	−	4.69211i	−0.106812	−	0.166203i	0.783733	−	0.621098i	$-0.213313\pi$
$797$	−3.01543	−	4.69211i	−0.106812	−	0.166203i	−0.890545	+	0.454895i	$0.849677\pi$
$798$	1.66995	+	0.673393i	0.0591154	+	0.0238379i
$799$	−5.98737	−	41.6430i	−0.211818	−	1.47322i
$800$	−15.3571	+	11.7693i	−0.542955	+	0.416109i
$801$	−0.128792	+	0.895770i	−0.00455065	+	0.0316505i
$802$	8.73057	+	6.90119i	0.308287	+	0.243689i
$803$	−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
$808$	41.8291	−	35.6995i	1.47154	−	1.25591i
$809$	−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	$0.782182\pi$
$810$	−3.54880	−	2.06075i	−0.124692	−	0.0724072i
$811$	−25.2397	+	3.62893i	−0.886287	+	0.127429i	−0.570399	−	0.821368i	$-0.693211\pi$
$811$	−25.2397	+	3.62893i	−0.886287	+	0.127429i	−0.315888	+	0.948796i	$0.602302\pi$
$812$	12.3939	−	23.7485i	0.434940	−	0.833410i
$813$	3.73711	+	5.81505i	0.131066	+	0.203943i
$814$	−2.83125	−	8.24698i	−0.0992351	−	0.289057i
$815$	3.72519	−	1.09381i	0.130488	−	0.0383147i
$816$	8.65348	+	17.2056i	0.302932	+	0.602317i
$817$	−2.77926	+	3.20744i	−0.0972341	+	0.112214i
$818$	−22.1907	+	4.21941i	−0.775879	+	0.147528i
$819$	−9.23413	+	4.21709i	−0.322667	+	0.147357i
$820$	−7.80058	−	19.7708i	−0.272408	−	0.690425i
$821$	13.8983	−	47.3334i	0.485055	−	1.65195i	−0.245729	−	0.969339i	$-0.579027\pi$
$821$	13.8983	−	47.3334i	0.485055	−	1.65195i	0.730784	−	0.682609i	$-0.239155\pi$
$822$	−18.1502	+	0.819138i	−0.633062	+	0.0285707i
$823$	−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	$0.229839\pi$
$824$	3.40951	−	7.32003i	0.118776	−	0.255005i
$825$	−4.75887	−	3.05834i	−0.165682	−	0.106478i
$826$	−16.5980	+	11.7570i	−0.577518	+	0.409077i
$827$		−	25.6840i		−	0.893118i	−0.894754	−	0.446559i	$-0.852649\pi$
$827$		−	25.6840i		−	0.893118i	0.894754	−	0.446559i	$-0.147351\pi$
$828$	−9.21385	+	2.66552i	−0.320203	+	0.0926332i
$829$		−	18.6090i		−	0.646316i	−0.946345	−	0.323158i	$-0.895256\pi$
$829$		−	18.6090i		−	0.646316i	0.946345	−	0.323158i	$-0.104744\pi$
$830$	19.1685	+	27.0614i	0.665350	+	0.939313i
$831$	2.45526	+	1.57790i	0.0851719	+	0.0547367i
$832$	−18.7334	−	16.7309i	−0.649462	−	0.580041i
$833$	6.90959	−	15.1299i	0.239403	−	0.524220i
$834$	−0.410494	−	9.09562i	−0.0142143	−	0.314956i
$835$	−17.4454	+	59.4136i	−0.603723	+	2.05609i
$836$	−1.21164	+	0.478052i	−0.0419053	+	0.0165338i
$837$	4.97643	−	2.27266i	0.172010	−	0.0785545i
$838$	2.90670	+	15.2869i	0.100410	+	0.528078i
$839$	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	$-0.0225285\pi$
$840$	−22.4318	+	14.1795i	−0.773972	+	0.489240i
$841$	−11.3604	+	3.33572i	−0.391738	+	0.115025i
$842$	−30.2592	+	10.3882i	−1.04280	+	0.358001i
$843$	10.4621	+	16.2793i	0.360333	+	0.560689i
$844$	−6.11411	+	11.7155i	−0.210456	+	0.403266i
$845$	−9.02678	+	1.29786i	−0.310531	+	0.0446476i
$846$	−6.20537	+	10.6862i	−0.213345	+	0.367400i
$847$	3.80300	−	26.4504i	0.130673	−	0.908848i
$848$	43.6729	−	30.4459i	1.49973	−	1.04552i
$849$	−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	$-0.736883\pi$
$853$	−1.33256	+	1.15467i	−0.0456259	+	0.0395350i	0.631749	+	0.775173i	$0.282337\pi$
$854$	−20.7372	+	26.2343i	−0.709612	+	0.897718i
$855$	0.162617	−	1.13102i	0.00556137	−	0.0386802i
$856$	−23.4719	−	20.6487i	−0.802251	−	0.705756i
$857$	−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	$-0.171671\pi$
$858$	2.74632	−	6.81059i	0.0937579	−	0.232510i
$859$	−24.5621	−	38.2194i	−0.838048	−	1.30403i	−0.950612	−	0.310383i	$-0.899543\pi$
$859$	−24.5621	−	38.2194i	−0.838048	−	1.30403i	0.112564	−	0.993644i	$-0.464094\pi$
$860$	−14.4426	−	60.8595i	−0.492488	−	2.07529i
$861$	−3.33608	−	11.3616i	−0.113693	−	0.387203i
$862$	−21.1208	+	20.0381i	−0.719378	+	0.682501i
$863$	−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	$0.320579\pi$
$864$	1.13990	−	5.54081i	0.0387802	−	0.188502i
$865$	1.50332	+	3.29181i	0.0511145	+	0.111925i
$866$	35.6033	−	18.2423i	1.20985	−	0.619898i
$867$	−1.74174	+	5.93182i	−0.0591526	+	0.201455i
$868$	1.85999	−	35.3292i	0.0631322	−	1.19915i
$869$	1.97654	+	0.902655i	0.0670495	+	0.0306205i
$870$	−16.5103	−	4.04908i	−0.559752	−	0.137277i
$871$	−4.64897	−	2.98771i	−0.157524	−	0.101235i
$872$	−7.71828	+	3.45511i	−0.261374	+	0.117005i
$873$	10.6664			0.361005
$874$	−1.64780	−	2.10179i	−0.0557376	−	0.0710943i
$875$			14.8212i			0.501048i
$876$	4.98935	−	2.84744i	0.168574	−	0.0962061i
$877$	13.5946	−	21.1537i	0.459058	−	0.714308i	−0.532146	−	0.846653i	$-0.678614\pi$
$877$	13.5946	−	21.1537i	0.459058	−	0.714308i	0.991204	+	0.132345i	$0.0422506\pi$
$878$	−5.53451	+	22.5672i	−0.186781	+	0.761607i
$879$	0.325629	−	0.713028i	0.0109832	−	0.0240498i
$880$	4.71215	−	18.6097i	0.158847	−	0.627332i
$881$	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	$0.392002\pi$
$882$	−4.34797	+	2.22780i	−0.146404	+	0.0750138i
$883$	1.76315	−	0.805202i	0.0593346	−	0.0270972i	−0.385527	−	0.922697i	$-0.625980\pi$
$883$	1.76315	−	0.805202i	0.0593346	−	0.0270972i	0.444861	+	0.895599i	$0.353253\pi$
$884$	−2.72337	−	30.1104i	−0.0915968	−	1.01272i
$885$	9.75500	+	8.45276i	0.327911	+	0.284136i
$886$	1.89895	+	2.00155i	0.0637963	+	0.0672434i
$887$	−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	$0.474917\pi$
$888$	1.42228	+	10.4478i	0.0477287	+	0.350604i
$889$	9.51550	−	6.11524i	0.319140	−	0.205099i
$890$	1.38890	−	3.44432i	0.0465559	−	0.115454i
$891$	1.63706	−	0.235374i	0.0548437	−	0.00788533i
$892$	−34.3707	+	47.7598i	−1.15082	+	1.59911i
$893$	−3.40577	−	0.489676i	−0.113970	−	0.0163864i
$894$	−19.5497	−	15.4533i	−0.653838	−	0.516834i
$895$	−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
$900$	4.92716	+	4.74529i	0.164239	+	0.158176i
$901$	63.4301	+	9.11988i	2.11316	+	0.303827i
$902$	7.40750	+	4.30144i	0.246643	+	0.143222i
$903$	−4.95945	−	34.4937i	−0.165040	−	1.14788i
$904$	38.1334	+	24.9129i	1.26830	+	0.828590i
$905$	−4.84467	+	3.11348i	−0.161042	+	0.103496i
$906$	−21.2104	+	7.28168i	−0.704669	+	0.241918i
$907$	−7.86999	−	26.8027i	−0.261319	−	0.889970i	−0.980727	−	0.195382i	$-0.937405\pi$
$907$	−7.86999	−	26.8027i	−0.261319	−	0.889970i	0.719408	−	0.694587i	$-0.244413\pi$
$908$	−35.6244	−	45.7691i	−1.18224	−	1.51890i
$909$	−14.6938	−	12.7322i	−0.487362	−	0.422301i
$910$	40.9259	−	7.78177i	1.35668	−	0.257963i
$911$	−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	$-0.389167\pi$
$912$	1.54955	−	0.282613i	0.0513106	−	0.00935826i
$913$	−12.8238	−	3.76542i	−0.424407	−	0.124617i
$914$	0.847697	+	18.7830i	0.0280393	+	0.621287i
$915$	19.3035	+	8.81559i	0.638153	+	0.291435i
$916$	−41.7467	−	14.6828i	−1.37935	−	0.485133i
$917$	−3.77632	+	5.87606i	−0.124705	+	0.194045i
$918$	5.55642	−	3.93582i	0.183389	−	0.129901i
$919$	−14.2897			−0.471375			−0.235688	−	0.971829i	$-0.575734\pi$
$919$	−14.2897			−0.471375			−0.235688	+	0.971829i	$0.575734\pi$
$920$	39.3284	−	1.61763i	1.29662	−	0.0533316i
$921$	−30.3774			−1.00097
$922$	−38.9906	+	27.6185i	−1.28409	+	0.909566i
$923$	−22.8154	+	35.5014i	−0.750977	+	1.16854i
$924$	3.54856	−	10.0894i	0.116739	−	0.331917i
$925$	−11.5984	−	5.29683i	−0.381354	−	0.174159i
$926$	0.950044	+	21.0508i	0.0312204	+	0.691773i
$927$	−2.73934	−	0.804342i	−0.0899717	−	0.0264181i
$928$	−1.93578	−	23.3532i	−0.0635451	−	0.766607i
$929$	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	$0.793122\pi$
$930$	−22.0556	+	4.19372i	−0.723232	+	0.137518i
$931$	−1.02807	−	0.890824i	−0.0336935	−	0.0291956i
$932$	11.5836	−	9.01609i	0.379433	−	0.295332i
$933$	−1.56038	−	5.31417i	−0.0510845	−	0.173978i
$934$	24.0511	−	8.25691i	0.786977	−	0.270175i
$935$	19.4392	−	12.4928i	0.635729	−	0.408558i
$936$	−4.85688	+	7.43429i	−0.158752	+	0.242997i
$937$	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	$0.930572\pi$
$938$	−6.96021	−	4.04171i	−0.227259	−	0.131967i
$939$	27.0706	+	3.89216i	0.883416	+	0.127016i
$940$	35.1776	−	36.5259i	1.14737	−	1.19134i
$941$	−5.19347	+	4.50017i	−0.169302	+	0.146701i	−0.735391	−	0.677643i	$-0.763001\pi$
$941$	−5.19347	+	4.50017i	−0.169302	+	0.146701i	0.566089	+	0.824344i	$0.308456\pi$
$942$	−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
$946$	19.7765	+	15.6326i	0.642990	+	0.508259i
$947$	34.4627	+	4.95498i	1.11989	+	0.161015i	0.677298	−	0.735709i	$-0.263151\pi$
$947$	34.4627	+	4.95498i	1.11989	+	0.161015i	0.442589	+	0.896725i	$0.354060\pi$
$948$	−2.13274	−	1.53485i	−0.0692683	−	0.0498495i
$949$	−8.92630	+	1.28341i	−0.289760	+	0.0416612i
$950$	−0.712335	+	1.76652i	−0.0231112	+	0.0573134i
$951$	−17.4035	+	11.1846i	−0.564347	+	0.362684i
$952$	−5.93952	−	43.6303i	−0.192501	−	1.41407i
$953$	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	$0.104690\pi$
$954$	−12.9549	−	13.6549i	−0.419430	−	0.442093i
$955$	37.1092	+	32.1553i	1.20083	+	1.04052i
$956$	−2.13018	+	0.192667i	−0.0688949	+	0.00623129i
$957$	6.23208	−	2.84609i	0.201454	−	0.0920011i
$958$	−28.1691	+	14.4332i	−0.910102	+	0.466314i
$959$	39.8569	+	11.7030i	1.28705	+	0.377911i
$960$	−9.95913	+	20.9694i	−0.321430	+	0.676785i
$961$	−0.444586	+	0.973508i	−0.0143415	+	0.0314035i
$962$	3.94254	−	16.0759i	0.127113	−	0.518308i
$963$	−5.97553	+	9.29811i	−0.192559	+	0.299627i
$964$	17.0936	+	29.9517i	0.550546	+	0.964679i
$965$			75.6981i			2.43681i
$966$	21.9032	+	1.07615i	0.704725	+	0.0346247i
$967$	−14.2706			−0.458910			−0.229455	−	0.973319i	$-0.573694\pi$
$967$	−14.2706			−0.458910			−0.229455	+	0.973319i	$0.573694\pi$
$968$	−9.55098	−	21.3357i	−0.306980	−	0.685755i
$969$	1.59498	+	1.02503i	0.0512381	+	0.0329287i
$970$	−42.5125	−	10.4260i	−1.36499	−	0.334759i
$971$	14.9312	+	6.81885i	0.479165	+	0.218827i	0.640330	−	0.768100i	$-0.278798\pi$
$971$	14.9312	+	6.81885i	0.479165	+	0.218827i	−0.161165	+	0.986928i	$0.551525\pi$
$972$	−1.99723	−	0.105149i	−0.0640613	−	0.00337266i
$973$	−5.86474	+	19.9735i	−0.188015	+	0.640320i
$974$	−31.0478	+	15.9081i	−0.994835	+	0.509730i
$975$	−4.46096	−	9.76813i	−0.142865	−	0.312831i
$976$	−3.07164	+	29.0909i	−0.0983207	+	0.931177i
$977$	−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	$0.383002\pi$
$978$	1.37268	−	1.30231i	0.0438934	−	0.0416433i
$979$	0.421682	+	1.43612i	0.0134770	+	0.0458985i
$980$	19.5070	−	4.62921i	0.623128	−	0.147875i
$981$	1.61639	+	2.51515i	0.0516074	+	0.0803026i
$982$	−10.7111	+	26.5625i	−0.341806	+	0.847645i
$983$	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	$0.874432\pi$
$984$	−7.77724	−	6.84179i	−0.247930	−	0.218108i
$985$	−2.50627	+	17.4315i	−0.0798563	+	0.555413i
$986$	17.4916	−	22.1283i	0.557044	−	0.704707i
$987$	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	$0.903131\pi$
$992$	−15.1376	−	26.9927i	−0.480621	−	0.857018i
$993$	−2.96270	+	20.6060i	−0.0940185	+	0.653913i
$994$	−30.8641	+	53.1510i	−0.978950	+	1.68585i
$995$	−40.9306	+	5.88493i	−1.29759	+	0.186565i
$996$	14.3282	+	7.47762i	0.454007	+	0.236937i
$997$	28.9284	+	45.0135i	0.916171	+	1.42559i	0.904886	+	0.425654i	$0.139956\pi$
$997$	28.9284	+	45.0135i	0.916171	+	1.42559i	0.0112855	+	0.999936i	$0.496408\pi$
$998$	12.6497	−	4.34274i	0.400420	−	0.137467i
$999$	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.13.15	yes	480
8.5	even	2	inner	552.2.bb.a.13.13	✓	480
23.16	even	11	inner	552.2.bb.a.85.13	yes	480
184.85	even	22	inner	552.2.bb.a.85.15	yes	480

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

\(f(q)\)	\(=\)	\(q+(-0.817442 - 1.15403i) q^{2} +(0.540641 - 0.841254i) q^{3} +(-0.663576 + 1.88671i) q^{4} +(-2.63955 - 1.20544i) q^{5} +(-1.41278 + 0.0637600i) q^{6} +(3.10238 + 0.910940i) q^{7} +(2.71975 - 0.776488i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.817442 - 1.15403i) q^{2} +(0.540641 - 0.841254i) q^{3} +(-0.663576 + 1.88671i) q^{4} +(-2.63955 - 1.20544i) q^{5} +(-1.41278 + 0.0637600i) q^{6} +(3.10238 + 0.910940i) q^{7} +(2.71975 - 0.776488i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(0.766563 + 4.03151i) q^{10} +(-1.24993 - 1.08307i) q^{11} +(1.22844 + 1.57827i) q^{12} +(-0.884534 - 3.01245i) q^{13} +(-1.48476 - 4.32488i) q^{14} +(-2.44113 + 1.56882i) q^{15} +(-3.11933 - 2.50395i) q^{16} +(-0.685217 - 4.76579i) q^{17} +(-0.710166 + 1.22297i) q^{18} +(-0.389769 - 0.0560403i) q^{19} +(4.02586 - 4.18016i) 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} +(-2.75340 + 3.48328i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(-3.77734 + 5.24880i) q^{28} +(-4.10030 + 0.589534i) q^{29} +(3.80595 + 1.53472i) q^{30} +(-4.60234 + 2.95774i) q^{31} +(-0.339757 + 5.64664i) q^{32} +(-1.58690 + 0.465957i) q^{33} +(-4.93974 + 4.68652i) q^{34} +(-7.09080 - 6.14421i) q^{35} +(1.99187 - 0.180157i) q^{36} +(-3.39103 + 1.54863i) q^{37} +(0.253941 + 0.495615i) q^{38} +(-3.01245 - 0.884534i) q^{39} +(-8.11495 - 1.22893i) q^{40} +(1.52135 - 3.33129i) q^{41} +(-4.44104 - 1.08915i) q^{42} +(5.82692 - 9.06687i) q^{43} +(2.87287 - 1.63956i) q^{44} +2.90178i q^{45} +(4.90161 + 4.68767i) q^{46} +8.73791 q^{47} +(-3.79289 + 1.27041i) q^{48} +(2.90616 + 1.86768i) q^{49} +(1.15213 - 4.69787i) q^{50} +(-4.37969 - 2.00014i) q^{51} +(6.27056 + 0.330129i) q^{52} +(-3.74971 + 12.7704i) q^{53} +(0.644886 + 1.25862i) q^{54} +(1.99368 + 4.36555i) q^{55} +(9.14504 + 0.0685752i) q^{56} +(-0.257869 + 0.297597i) q^{57} +(4.03210 + 4.24996i) q^{58} +(-1.25320 - 4.26802i) q^{59} +(-1.34003 - 5.64674i) q^{60} +(-3.95379 - 6.15222i) q^{61} +(7.17548 + 2.89346i) q^{62} +(-0.460154 - 3.20044i) q^{63} +(6.79413 - 4.22371i) q^{64} +(-1.29656 + 9.01777i) q^{65} +(1.83493 + 1.45044i) 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} +(-1.83615 - 2.15141i) q^{72} +(0.408778 - 2.84311i) q^{73} +(4.55913 + 2.64743i) q^{74} +(3.38552 - 0.486764i) q^{75} +(0.364373 - 0.698193i) q^{76} +(-2.89115 - 4.49871i) q^{77} +(1.44172 + 4.19951i) q^{78} +(-1.26059 + 0.370142i) q^{79} +(5.21528 + 10.3695i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-5.08802 + 0.967452i) q^{82} +(7.35078 - 3.35699i) q^{83} +(2.37339 + 6.01542i) q^{84} +(-3.93622 + 13.4055i) q^{85} +(-15.2266 + 0.687193i) q^{86} +(-1.72084 + 3.76812i) q^{87} +(-4.24050 - 1.97513i) q^{88} +(-0.761319 - 0.489270i) q^{89} +(3.34875 - 2.37204i) q^{90} -10.1515i q^{91} +(1.40293 - 9.48851i) q^{92} +5.47081i q^{93} +(-7.14274 - 10.0838i) q^{94} +(0.961262 + 0.617766i) q^{95} +(4.56657 + 3.33863i) q^{96} +(-4.43100 + 9.70254i) q^{97} +(-0.220263 - 4.88052i) 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

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Database

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