LMFDB - Embedded newform 43.2.g.a.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			14.2
Character	$\chi$	$=$	43.14
Dual form			43.2.g.a.40.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.982954 + 0.473366i) q^{2} +(0.109070 + 1.45544i) q^{3} +(-0.504856 + 0.633069i) q^{4} +(1.29085 - 0.398175i) q^{5} +(-0.796166 - 1.37900i) q^{6} +(-0.108163 + 0.187343i) q^{7} +(0.682116 - 2.98855i) q^{8} +(0.860089 - 0.129637i) q^{9} +O(q^{10})$	\(q+(-0.982954 + 0.473366i) q^{2} +(0.109070 + 1.45544i) q^{3} +(-0.504856 + 0.633069i) q^{4} +(1.29085 - 0.398175i) q^{5} +(-0.796166 - 1.37900i) q^{6} +(-0.108163 + 0.187343i) q^{7} +(0.682116 - 2.98855i) q^{8} +(0.860089 - 0.129637i) q^{9} +(-1.08036 + 1.00243i) q^{10} +(-3.76031 - 4.71528i) q^{11} +(-0.976457 - 0.665737i) q^{12} +(2.10767 + 1.95563i) q^{13} +(0.0176371 - 0.235350i) q^{14} +(0.720312 + 1.83532i) q^{15} +(0.383825 + 1.68165i) q^{16} +(0.270054 + 0.0833006i) q^{17} +(-0.784062 + 0.534564i) q^{18} +(1.12457 + 0.169502i) q^{19} +(-0.399621 + 1.01822i) q^{20} +(-0.284464 - 0.136990i) q^{21} +(5.92827 + 2.85490i) q^{22} +(-1.44040 + 3.67008i) q^{23} +(4.42404 + 0.666817i) q^{24} +(-2.62344 + 1.78863i) q^{25} +(-2.99747 - 0.924598i) q^{26} +(1.25681 + 5.50644i) q^{27} +(-0.0639946 - 0.163056i) q^{28} +(0.515946 - 6.88482i) q^{29} +(-1.57681 - 1.46307i) q^{30} +(-8.17225 - 5.57174i) q^{31} +(2.64918 + 3.32196i) q^{32} +(6.45267 - 5.98720i) q^{33} +(-0.304882 + 0.0459536i) q^{34} +(-0.0650265 + 0.284900i) q^{35} +(-0.352151 + 0.609944i) q^{36} +(-3.77129 - 6.53207i) q^{37} +(-1.18564 + 0.365721i) q^{38} +(-2.61642 + 3.28088i) q^{39} +(-0.309453 - 4.12937i) q^{40} +(-4.62195 + 2.22581i) q^{41} +0.344461 q^{42} +(5.90092 + 2.85993i) q^{43} +4.88351 q^{44} +(1.05863 - 0.509808i) q^{45} +(-0.321443 - 4.28936i) q^{46} +(0.288239 - 0.361440i) q^{47} +(-2.40567 + 0.742051i) q^{48} +(3.47660 + 6.02165i) q^{49} +(1.73205 - 2.99999i) q^{50} +(-0.0917841 + 0.402132i) q^{51} +(-2.30212 + 0.346988i) q^{52} +(-6.12346 + 5.68174i) q^{53} +(-3.84195 - 4.81765i) q^{54} +(-6.73151 - 4.58946i) q^{55} +(0.486104 + 0.451039i) q^{56} +(-0.124042 + 1.65523i) q^{57} +(2.75189 + 7.01170i) q^{58} +(1.85926 + 8.14595i) q^{59} +(-1.52554 - 0.470567i) q^{60} +(11.0987 - 7.56700i) q^{61} +(10.6704 + 1.60831i) q^{62} +(-0.0687427 + 0.175154i) q^{63} +(-7.28468 - 3.50811i) q^{64} +(3.49937 + 1.68521i) q^{65} +(-3.50854 + 8.93961i) q^{66} +(6.22328 + 0.938008i) q^{67} +(-0.189073 + 0.128908i) q^{68} +(-5.49868 - 1.69612i) q^{69} +(-0.0709437 - 0.310825i) q^{70} +(-0.540324 - 1.37672i) q^{71} +(0.199253 - 2.65884i) q^{72} +(0.601198 + 0.557830i) q^{73} +(6.79906 + 4.63552i) q^{74} +(-2.88938 - 3.62317i) q^{75} +(-0.675051 + 0.626356i) q^{76} +(1.29010 - 0.194451i) q^{77} +(1.01876 - 4.46348i) q^{78} +(-3.07798 + 5.33121i) q^{79} +(1.16505 + 2.01792i) q^{80} +(-5.38373 + 1.66066i) q^{81} +(3.48954 - 4.37574i) q^{82} +(-0.538458 - 7.18523i) q^{83} +(0.230338 - 0.110925i) q^{84} +0.381767 q^{85} +(-7.15412 - 0.0178853i) q^{86} +10.0767 q^{87} +(-16.6568 + 8.02150i) q^{88} +(0.331353 + 4.42159i) q^{89} +(-0.799256 + 1.00224i) q^{90} +(-0.594345 + 0.183331i) q^{91} +(-1.59622 - 2.76473i) q^{92} +(7.21798 - 12.5019i) q^{93} +(-0.112232 + 0.491721i) q^{94} +(1.51914 - 0.228974i) q^{95} +(-4.54597 + 4.21804i) q^{96} +(-2.78649 - 3.49415i) q^{97} +(-6.26778 - 4.27330i) q^{98} +(-3.84548 - 3.56808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{10}{21}\right)$

Coefficient data

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

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

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

$2$	−0.982954	+	0.473366i	−0.695054	+	0.334720i	−0.747834	−	0.663886i	$-0.768906\pi$
$2$	−0.982954	+	0.473366i	−0.695054	+	0.334720i	0.0527802	+	0.998606i	$0.483192\pi$
$3$	0.109070	+	1.45544i	0.0629716	+	0.840298i	0.935859	+	0.352375i	$0.114626\pi$
$3$	0.109070	+	1.45544i	0.0629716	+	0.840298i	−0.872887	+	0.487922i	$0.837755\pi$
$4$	−0.504856	+	0.633069i	−0.252428	+	0.316534i
$5$	1.29085	−	0.398175i	0.577286	−	0.178069i	0.00765630	−	0.999971i	$-0.497563\pi$
$5$	1.29085	−	0.398175i	0.577286	−	0.178069i	0.569629	+	0.821902i	$0.307087\pi$
$6$	−0.796166	−	1.37900i	−0.325033	−	0.562974i
$7$	−0.108163	+	0.187343i	−0.0408816	+	0.0708091i	−0.885742	−	0.464177i	$-0.846350\pi$
$7$	−0.108163	+	0.187343i	−0.0408816	+	0.0708091i	0.844861	+	0.534987i	$0.179683\pi$
$8$	0.682116	−	2.98855i	0.241164	−	1.05661i
$9$	0.860089	−	0.129637i	0.286696	−	0.0432125i
$10$	−1.08036	+	1.00243i	−0.341641	+	0.316997i
$11$	−3.76031	−	4.71528i	−1.13378	−	1.42171i	−0.892380	−	0.451285i	$-0.850966\pi$
$11$	−3.76031	−	4.71528i	−1.13378	−	1.42171i	−0.241397	−	0.970426i	$-0.577606\pi$
$12$	−0.976457	−	0.665737i	−0.281879	−	0.192182i
$13$	2.10767	+	1.95563i	0.584562	+	0.542395i	0.916050	−	0.401065i	$-0.131360\pi$
$13$	2.10767	+	1.95563i	0.584562	+	0.542395i	−0.331487	+	0.943460i	$0.607550\pi$
$14$	0.0176371	−	0.235350i	0.00471370	−	0.0629000i
$15$	0.720312	+	1.83532i	0.185984	+	0.473879i
$16$	0.383825	+	1.68165i	0.0959562	+	0.420412i
$17$	0.270054	+	0.0833006i	0.0654977	+	0.0202034i	0.327331	−	0.944910i	$-0.393851\pi$
$17$	0.270054	+	0.0833006i	0.0654977	+	0.0202034i	−0.261833	+	0.965113i	$0.584327\pi$
$18$	−0.784062	+	0.534564i	−0.184805	+	0.125998i
$19$	1.12457	+	0.169502i	0.257994	+	0.0388863i	0.276766	−	0.960937i	$-0.410737\pi$
$19$	1.12457	+	0.169502i	0.257994	+	0.0388863i	−0.0187716	+	0.999824i	$0.505976\pi$
$20$	−0.399621	+	1.01822i	−0.0893580	+	0.227680i
$21$	−0.284464	−	0.136990i	−0.0620751	−	0.0298938i
$22$	5.92827	+	2.85490i	1.26391	+	0.608668i
$23$	−1.44040	+	3.67008i	−0.300344	+	0.765265i	0.698426	+	0.715682i	$0.253884\pi$
$23$	−1.44040	+	3.67008i	−0.300344	+	0.765265i	−0.998770	+	0.0495821i	$0.984211\pi$
$24$	4.42404	+	0.666817i	0.903054	+	0.136113i
$25$	−2.62344	+	1.78863i	−0.524688	+	0.357727i
$26$	−2.99747	−	0.924598i	−0.587853	−	0.181329i
$27$	1.25681	+	5.50644i	0.241873	+	1.05972i
$28$	−0.0639946	−	0.163056i	−0.0120938	−	0.0308146i
$29$	0.515946	−	6.88482i	0.0958088	−	1.27848i	−0.717463	−	0.696596i	$-0.754697\pi$
$29$	0.515946	−	6.88482i	0.0958088	−	1.27848i	0.813272	−	0.581883i	$-0.197684\pi$
$30$	−1.57681	−	1.46307i	−0.287885	−	0.267119i
$31$	−8.17225	−	5.57174i	−1.46778	−	1.00071i	−0.992679	−	0.120783i	$-0.961459\pi$
$31$	−8.17225	−	5.57174i	−1.46778	−	1.00071i	−0.475100	−	0.879932i	$-0.657588\pi$
$32$	2.64918	+	3.32196i	0.468313	+	0.587246i
$33$	6.45267	−	5.98720i	1.12326	−	1.04224i
$34$	−0.304882	+	0.0459536i	−0.0522869	+	0.00788098i
$35$	−0.0650265	+	0.284900i	−0.0109915	+	0.0481568i
$36$	−0.352151	+	0.609944i	−0.0586918	+	0.101657i
$37$	−3.77129	−	6.53207i	−0.619996	−	1.07387i	−0.989486	−	0.144630i	$-0.953801\pi$
$37$	−3.77129	−	6.53207i	−0.619996	−	1.07387i	0.369489	−	0.929235i	$-0.379533\pi$
$38$	−1.18564	+	0.365721i	−0.192336	+	0.0593277i
$39$	−2.61642	+	3.28088i	−0.418962	+	0.525362i
$40$	−0.309453	−	4.12937i	−0.0489289	−	0.652910i
$41$	−4.62195	+	2.22581i	−0.721827	+	0.347613i	−0.758464	−	0.651715i	$-0.774050\pi$
$41$	−4.62195	+	2.22581i	−0.721827	+	0.347613i	0.0366371	+	0.999329i	$0.488335\pi$
$42$	0.344461			0.0531516
$43$	5.90092	+	2.85993i	0.899881	+	0.436135i
$43$	5.90092	+	2.85993i	0.899881	+	0.436135i
$44$	4.88351			0.736217
$45$	1.05863	−	0.509808i	0.157811	−	0.0759977i
$46$	−0.321443	−	4.28936i	−0.0473942	−	0.632431i
$47$	0.288239	−	0.361440i	0.0420439	−	0.0527214i	−0.760365	−	0.649496i	$-0.774980\pi$
$47$	0.288239	−	0.361440i	0.0420439	−	0.0527214i	0.802409	+	0.596775i	$0.203551\pi$
$48$	−2.40567	+	0.742051i	−0.347228	+	0.107106i
$49$	3.47660	+	6.02165i	0.496657	+	0.860236i
$50$	1.73205	−	2.99999i	0.244948	−	0.424263i
$51$	−0.0917841	+	0.402132i	−0.0128523	+	0.0563098i
$52$	−2.30212	+	0.346988i	−0.319246	+	0.0481186i
$53$	−6.12346	+	5.68174i	−0.841123	+	0.780448i	−0.977661	−	0.210187i	$-0.932593\pi$
$53$	−6.12346	+	5.68174i	−0.841123	+	0.780448i	0.136539	+	0.990635i	$0.456402\pi$
$54$	−3.84195	−	4.81765i	−0.522823	−	0.655599i
$55$	−6.73151	−	4.58946i	−0.907676	−	0.618843i
$56$	0.486104	+	0.451039i	0.0649584	+	0.0602726i
$57$	−0.124042	+	1.65523i	−0.0164298	+	0.219240i
$58$	2.75189	+	7.01170i	0.361341	+	0.920681i
$59$	1.85926	+	8.14595i	0.242055	+	1.06051i	0.939143	+	0.343527i	$0.111622\pi$
$59$	1.85926	+	8.14595i	0.242055	+	1.06051i	−0.697088	+	0.716986i	$0.745521\pi$
$60$	−1.52554	−	0.470567i	−0.196946	−	0.0607499i
$61$	11.0987	−	7.56700i	1.42105	−	0.968855i	0.423019	−	0.906121i	$-0.360971\pi$
$61$	11.0987	−	7.56700i	1.42105	−	0.968855i	0.998030	−	0.0627337i	$-0.0199819\pi$
$62$	10.6704	+	1.60831i	1.35514	+	0.204255i
$63$	−0.0687427	+	0.175154i	−0.00866077	+	0.0220673i
$64$	−7.28468	−	3.50811i	−0.910584	−	0.438514i
$65$	3.49937	+	1.68521i	0.434043	+	0.209024i
$66$	−3.50854	+	8.93961i	−0.431871	+	1.10039i
$67$	6.22328	+	0.938008i	0.760294	+	0.114596i	0.517736	−	0.855541i	$-0.326775\pi$
$67$	6.22328	+	0.938008i	0.760294	+	0.114596i	0.242559	+	0.970137i	$0.422013\pi$
$68$	−0.189073	+	0.128908i	−0.0229285	+	0.0156324i
$69$	−5.49868	−	1.69612i	−0.661963	−	0.204189i
$70$	−0.0709437	−	0.310825i	−0.00847939	−	0.0371506i
$71$	−0.540324	−	1.37672i	−0.0641247	−	0.163387i	0.895220	−	0.445625i	$-0.147018\pi$
$71$	−0.540324	−	1.37672i	−0.0641247	−	0.163387i	−0.959344	+	0.282238i	$0.908923\pi$
$72$	0.199253	−	2.65884i	0.0234822	−	0.313348i
$73$	0.601198	+	0.557830i	0.0703649	+	0.0652891i	0.714571	−	0.699563i	$-0.246622\pi$
$73$	0.601198	+	0.557830i	0.0703649	+	0.0652891i	−0.644206	+	0.764852i	$0.722812\pi$
$74$	6.79906	+	4.63552i	0.790375	+	0.538869i
$75$	−2.88938	−	3.62317i	−0.333637	−	0.418368i
$76$	−0.675051	+	0.626356i	−0.0774337	+	0.0718480i
$77$	1.29010	−	0.194451i	0.147021	−	0.0221598i
$78$	1.01876	−	4.46348i	0.115352	−	0.505390i
$79$	−3.07798	+	5.33121i	−0.346299	+	0.599808i	−0.985589	−	0.169158i	$-0.945895\pi$
$79$	−3.07798	+	5.33121i	−0.346299	+	0.599808i	0.639290	+	0.768966i	$0.279228\pi$
$80$	1.16505	+	2.01792i	0.130256	+	0.225611i
$81$	−5.38373	+	1.66066i	−0.598192	+	0.184518i
$82$	3.48954	−	4.37574i	0.385355	−	0.483220i
$83$	−0.538458	−	7.18523i	−0.0591035	−	0.788681i	−0.945473	−	0.325702i	$-0.894399\pi$
$83$	−0.538458	−	7.18523i	−0.0591035	−	0.788681i	0.886369	−	0.462979i	$-0.153220\pi$
$84$	0.230338	−	0.110925i	0.0251319	−	0.0121029i
$85$	0.381767			0.0414085
$86$	−7.15412	−	0.0178853i	−0.771449	−	0.00192862i
$87$	10.0767			1.08034
$88$	−16.6568	+	8.02150i	−1.77562	+	0.855095i
$89$	0.331353	+	4.42159i	0.0351233	+	0.468688i	0.986839	+	0.161707i	$0.0516999\pi$
$89$	0.331353	+	4.42159i	0.0351233	+	0.468688i	−0.951716	+	0.306981i	$0.900681\pi$
$90$	−0.799256	+	1.00224i	−0.0842490	+	0.105645i
$91$	−0.594345	+	0.183331i	−0.0623043	+	0.0192183i
$92$	−1.59622	−	2.76473i	−0.166417	−	0.288243i
$93$	7.21798	−	12.5019i	0.748470	−	1.29639i
$94$	−0.112232	+	0.491721i	−0.0115759	+	0.0507172i
$95$	1.51914	−	0.228974i	0.155861	−	0.0234922i
$96$	−4.54597	+	4.21804i	−0.463971	+	0.430502i
$97$	−2.78649	−	3.49415i	−0.282925	−	0.354777i	0.619979	−	0.784618i	$-0.287141\pi$
$97$	−2.78649	−	3.49415i	−0.282925	−	0.354777i	−0.902905	+	0.429841i	$0.858570\pi$
$98$	−6.26778	−	4.27330i	−0.633142	−	0.431669i
$99$	−3.84548	−	3.56808i	−0.386485	−	0.358606i
$100$	0.192132	−	2.56382i	0.0192132	−	0.256382i
$101$	−1.09407	−	2.78765i	−0.108864	−	0.277382i	0.866052	−	0.499954i	$-0.166650\pi$
$101$	−1.09407	−	2.78765i	−0.108864	−	0.277382i	−0.974916	+	0.222572i	$0.928555\pi$
$102$	−0.100136	−	0.438725i	−0.00991496	−	0.0434403i
$103$	8.07350	+	2.49034i	0.795505	+	0.245381i	0.665760	−	0.746166i	$-0.268108\pi$
$103$	8.07350	+	2.49034i	0.795505	+	0.245381i	0.129746	+	0.991547i	$0.458584\pi$
$104$	7.28217	−	4.96490i	0.714076	−	0.486848i
$105$	−0.421746	−	0.0635680i	−0.0411582	−	0.00620360i
$106$	3.32954	−	8.48353i	0.323394	−	0.823994i
$107$	−5.64595	−	2.71894i	−0.545814	−	0.262850i	0.140593	−	0.990067i	$-0.455099\pi$
$107$	−5.64595	−	2.71894i	−0.545814	−	0.262850i	−0.686407	+	0.727217i	$0.740813\pi$
$108$	−4.12047	−	1.98431i	−0.396492	−	0.190941i
$109$	0.0776988	−	0.197973i	0.00744219	−	0.0189624i	−0.927104	−	0.374803i	$-0.877710\pi$
$109$	0.0776988	−	0.197973i	0.00744219	−	0.0189624i	0.934547	+	0.355841i	$0.115805\pi$
$110$	8.78926	+	1.32477i	0.838023	+	0.126312i
$111$	9.09569	−	6.20133i	0.863324	−	0.588605i
$112$	−0.356561	−	0.109984i	−0.0336918	−	0.0103925i
$113$	2.46387	+	10.7949i	0.231781	+	1.01550i	0.948161	+	0.317789i	$0.102940\pi$
$113$	2.46387	+	10.7949i	0.231781	+	1.01550i	−0.716380	+	0.697710i	$0.754202\pi$
$114$	−0.661601	−	1.68573i	−0.0619646	−	0.157883i
$115$	−0.398009	+	5.31105i	−0.0371145	+	0.495258i
$116$	4.09809	+	3.80247i	0.380498	+	0.353051i
$117$	2.06631	+	1.40878i	0.191030	+	0.130242i
$118$	−5.68358	−	7.12699i	−0.523216	−	0.656093i
$119$	−0.0448155	+	0.0415827i	−0.00410823	+	0.00381188i
$120$	5.97629	−	0.900780i	0.545558	−	0.0822296i
$121$	−5.64621	+	24.7377i	−0.513292	+	2.24888i
$122$	−7.32760	+	12.6918i	−0.663410	+	1.14906i
$123$	−3.74365	−	6.48419i	−0.337553	−	0.584659i
$124$	7.65310	−	2.36067i	0.687269	−	0.211994i
$125$	−6.88554	+	8.63419i	−0.615861	+	0.772265i
$126$	−0.0153408	−	0.204708i	−0.00136667	−	0.0182369i
$127$	−7.04038	+	3.39047i	−0.624733	+	0.300855i	−0.719339	−	0.694659i	$-0.755555\pi$
$127$	−7.04038	+	3.39047i	−0.624733	+	0.300855i	0.0946062	+	0.995515i	$0.469841\pi$
$128$	0.323224			0.0285692
$129$	−3.51883	+	8.90035i	−0.309816	+	0.783632i
$130$	−4.23744			−0.371648
$131$	16.1797	−	7.79174i	1.41363	−	0.680768i	0.437753	−	0.899095i	$-0.355774\pi$
$131$	16.1797	−	7.79174i	1.41363	−	0.680768i	0.975876	+	0.218327i	$0.0700601\pi$
$132$	0.532645	+	7.10765i	0.0463608	+	0.618642i
$133$	−0.153391	+	0.192347i	−0.0133007	+	0.0166786i
$134$	−6.56122	+	2.02387i	−0.566803	+	0.174836i
$135$	3.81488	+	6.60757i	0.328333	+	0.568689i
$136$	0.433156	−	0.750248i	0.0371428	−	0.0643332i
$137$	−2.23563	+	9.79494i	−0.191003	+	0.836839i	0.785072	+	0.619404i	$0.212626\pi$
$137$	−2.23563	+	9.79494i	−0.191003	+	0.836839i	−0.976075	+	0.217434i	$0.930231\pi$
$138$	6.20783	−	0.935681i	0.528446	−	0.0796504i
$139$	9.10473	−	8.44795i	0.772253	−	0.716546i	−0.192039	−	0.981387i	$-0.561510\pi$
$139$	9.10473	−	8.44795i	0.772253	−	0.716546i	0.964292	+	0.264841i	$0.0853195\pi$
$140$	−0.147532	−	0.184999i	−0.0124687	−	0.0156353i
$141$	0.557491	+	0.380091i	0.0469492	+	0.0320095i
$142$	1.18281	+	1.09749i	0.0992590	+	0.0920989i
$143$	1.29586	−	17.2920i	0.108365	−	1.44603i
$144$	0.548128	+	1.39661i	0.0456773	+	0.116384i
$145$	−2.07535	−	9.09271i	−0.172349	−	0.755109i
$146$	−0.855008	−	0.263735i	−0.0707610	−	0.0218269i
$147$	−8.38495	+	5.71676i	−0.691579	+	0.471510i
$148$	6.03921	+	0.910264i	0.496420	+	0.0748232i
$149$	−1.35074	+	3.44162i	−0.110657	+	0.281948i	−0.975465	−	0.220153i	$-0.929344\pi$
$149$	−1.35074	+	3.44162i	−0.110657	+	0.281948i	0.864809	+	0.502101i	$0.167440\pi$
$150$	4.55522	+	2.19368i	0.371932	+	0.179113i
$151$	10.3773	+	4.99744i	0.844492	+	0.406686i	0.805530	−	0.592555i	$-0.201881\pi$
$151$	10.3773	+	4.99744i	0.844492	+	0.406686i	0.0389621	+	0.999241i	$0.487595\pi$
$152$	1.27365	−	3.24521i	0.103307	−	0.263221i
$153$	0.243069	+	0.0366368i	0.0196510	+	0.00296191i
$154$	−1.17606	+	0.801827i	−0.0947699	+	0.0646130i
$155$	−12.7677	−	3.93831i	−1.02552	−	0.316332i
$156$	−0.756112	−	3.31274i	−0.0605374	−	0.265232i
$157$	−7.52520	−	19.1739i	−0.600577	−	1.53024i	−0.830490	−	0.557033i	$-0.811940\pi$
$157$	−7.52520	−	19.1739i	−0.600577	−	1.53024i	0.229914	−	0.973211i	$-0.426156\pi$
$158$	0.501897	−	6.69734i	0.0399287	−	0.532812i
$159$	−8.93731	−	8.29262i	−0.708775	−	0.657647i
$160$	4.74241	+	3.23332i	0.374921	+	0.255617i
$161$	−0.531767	−	0.666815i	−0.0419091	−	0.0525524i
$162$	4.50586	−	4.18083i	0.354014	−	0.328477i
$163$	−6.83812	+	1.03068i	−0.535603	+	0.0807292i	−0.411274	−	0.911512i	$-0.634916\pi$
$163$	−6.83812	+	1.03068i	−0.535603	+	0.0807292i	−0.124329	+	0.992241i	$0.539678\pi$
$164$	0.924323	−	4.04972i	0.0721775	−	0.316230i
$165$	5.94547	−	10.2979i	0.462855	−	0.801688i
$166$	3.93052	+	6.80786i	0.305068	+	0.528393i
$167$	3.39723	−	1.04791i	0.262886	−	0.0810895i	−0.160510	−	0.987034i	$-0.551314\pi$
$167$	3.39723	−	1.04791i	0.262886	−	0.0810895i	0.423396	+	0.905945i	$0.360838\pi$
$168$	−0.603440	+	0.756689i	−0.0465564	+	0.0583799i
$169$	−0.353715	−	4.72000i	−0.0272089	−	0.363077i
$170$	−0.375260	+	0.180716i	−0.0287811	+	0.0138603i
$171$	0.989203			0.0756463
$172$	−4.78964	+	2.29184i	−0.365207	+	0.174751i
$173$	−24.0563			−1.82897			−0.914483	−	0.404623i	$-0.867403\pi$
$173$	−24.0563			−1.82897			−0.914483	+	0.404623i	$0.867403\pi$
$174$	−9.90494	+	4.76997i	−0.750892	+	0.361610i
$175$	−0.0513297	−	0.684947i	−0.00388016	−	0.0517771i
$176$	6.48614	−	8.13336i	0.488911	−	0.613075i
$177$	−11.6531	+	3.59452i	−0.875904	+	0.270181i
$178$	−2.41874	−	4.18937i	−0.181292	−	0.314007i
$179$	2.60094	−	4.50496i	0.194403	−	0.336717i	−0.752301	−	0.658819i	$-0.771056\pi$
$179$	2.60094	−	4.50496i	0.194403	−	0.336717i	0.946705	+	0.322103i	$0.104390\pi$
$180$	−0.211710	+	0.927563i	−0.0157800	+	0.0691365i
$181$	2.74306	−	0.413450i	0.203890	−	0.0307315i	−0.0463029	−	0.998927i	$-0.514744\pi$
$181$	2.74306	−	0.413450i	0.203890	−	0.0307315i	0.250193	+	0.968196i	$0.419506\pi$
$182$	0.497431	−	0.461549i	0.0368721	−	0.0342123i
$183$	12.2238	+	15.3282i	0.903612	+	1.13309i
$184$	9.98568	+	6.80812i	0.736154	+	0.501902i
$185$	−7.46908	−	6.93029i	−0.549137	−	0.509525i
$186$	−1.17697	+	15.7056i	−0.0862995	+	1.15159i
$187$	−0.622701	−	1.58662i	−0.0455364	−	0.116025i
$188$	0.0832974	+	0.364950i	0.00607509	+	0.0266167i
$189$	−1.16753	−	0.360137i	−0.0849256	−	0.0261961i
$190$	−1.38486	+	0.944181i	−0.100468	+	0.0684981i
$191$	3.41700	+	0.515030i	0.247245	+	0.0372662i	0.271496	−	0.962440i	$-0.412482\pi$
$191$	3.41700	+	0.515030i	0.247245	+	0.0372662i	−0.0242502	+	0.999706i	$0.507720\pi$
$192$	4.31130	−	10.9850i	0.311142	−	0.792776i
$193$	16.4497	+	7.92174i	1.18407	+	0.570219i	0.919095	−	0.394035i	$-0.128921\pi$
$193$	16.4497	+	7.92174i	1.18407	+	0.570219i	0.264977	+	0.964255i	$0.414636\pi$
$194$	4.39300	+	2.11556i	0.315399	+	0.151888i
$195$	−2.07104	+	5.27692i	−0.148310	+	0.377888i
$196$	−5.56730	−	0.839136i	−0.397664	−	0.0599383i
$197$	8.41116	−	5.73463i	0.599270	−	0.408575i	−0.225337	−	0.974281i	$-0.572348\pi$
$197$	8.41116	−	5.73463i	0.599270	−	0.408575i	0.824607	+	0.565705i	$0.191396\pi$
$198$	5.46894	+	1.68694i	0.388661	+	0.119886i
$199$	−2.04642	−	8.96595i	−0.145067	−	0.635579i	−0.994214	−	0.107422i	$-0.965740\pi$
$199$	−2.04642	−	8.96595i	−0.145067	−	0.635579i	0.849147	−	0.528157i	$-0.177117\pi$
$200$	3.55592	+	9.06033i	0.251441	+	0.640662i
$201$	−0.686440	+	9.15990i	−0.0484177	+	0.646090i
$202$	2.39500	+	2.22224i	0.168512	+	0.156356i
$203$	1.23402	+	0.841340i	0.0866111	+	0.0590505i
$204$	−0.208240	−	0.261124i	−0.0145797	−	0.0182824i
$205$	−5.07998	+	4.71353i	−0.354801	+	0.329207i
$206$	−9.11472	+	1.37382i	−0.635053	+	0.0957188i
$207$	−0.763092	+	3.34332i	−0.0530385	+	0.232377i
$208$	−2.47971	+	4.29498i	−0.171937	+	0.297803i
$209$	−3.42949	−	5.94004i	−0.237222	−	0.410881i
$210$	0.444648	−	0.137156i	0.0306836	−	0.00946465i
$211$	−11.8825	+	14.9002i	−0.818025	+	1.02577i	0.181080	+	0.983468i	$0.442041\pi$
$211$	−11.8825	+	14.9002i	−0.818025	+	1.02577i	−0.999105	+	0.0423025i	$0.986531\pi$
$212$	−0.505471	−	6.74504i	−0.0347159	−	0.463251i
$213$	1.94480	−	0.936567i	0.133256	−	0.0641725i
$214$	6.83676			0.467352
$215$	8.75595	+	1.34214i	0.597151	+	0.0915334i
$216$	17.3136			1.17804
$217$	1.92776	−	0.928360i	0.130865	−	0.0630212i
$218$	0.0173394	+	0.231379i	0.00117437	+	0.0156709i
$219$	−0.746315	+	0.935849i	−0.0504313	+	0.0632388i
$220$	6.30389	−	1.94449i	0.425008	−	0.131098i
$221$	0.406279	+	0.703696i	0.0273293	+	0.0473357i
$222$	−6.00514	+	10.4012i	−0.403039	+	0.698084i
$223$	1.62391	−	7.11481i	0.108745	−	0.476443i	−0.891003	−	0.453997i	$-0.849998\pi$
$223$	1.62391	−	7.11481i	0.108745	−	0.476443i	0.999748	−	0.0224455i	$-0.00714523\pi$
$224$	−0.908889	+	0.136993i	−0.0607277	+	0.00915323i
$225$	−2.02452	+	1.87848i	−0.134968	+	0.125232i
$226$	−7.53181	−	9.44459i	−0.501008	−	0.628245i
$227$	12.9206	+	8.80914i	0.857573	+	0.584683i	0.910311	−	0.413925i	$-0.135842\pi$
$227$	12.9206	+	8.80914i	0.857573	+	0.584683i	−0.0527382	+	0.998608i	$0.516795\pi$
$228$	−0.985251	−	0.914179i	−0.0652498	−	0.0605430i
$229$	−0.0803517	+	1.07222i	−0.00530979	+	0.0708542i	−0.999229	−	0.0392558i	$-0.987501\pi$
$229$	−0.0803517	+	1.07222i	−0.00530979	+	0.0708542i	0.993919	+	0.110110i	$0.0351203\pi$
$230$	−2.12285	−	5.40893i	−0.139976	−	0.356654i
$231$	0.423723	+	1.85645i	0.0278790	+	0.122146i
$232$	−20.2237	−	6.23818i	−1.32775	−	0.409556i
$233$	−1.10140	+	0.750923i	−0.0721552	+	0.0491946i	−0.598860	−	0.800853i	$-0.704380\pi$
$233$	−1.10140	+	0.750923i	−0.0721552	+	0.0491946i	0.526705	+	0.850048i	$0.323427\pi$
$234$	−2.69795	−	0.406651i	−0.176371	−	0.0265836i
$235$	0.228157	−	0.581334i	0.0148833	−	0.0379220i
$236$	−6.09561	−	2.93549i	−0.396790	−	0.191084i
$237$	−8.09496	−	3.89833i	−0.525824	−	0.253224i
$238$	0.0243678	−	0.0620881i	0.00157953	−	0.00402457i
$239$	−14.7110	−	2.21733i	−0.951579	−	0.143427i	−0.345134	−	0.938553i	$-0.612167\pi$
$239$	−14.7110	−	2.21733i	−0.951579	−	0.143427i	−0.606444	+	0.795126i	$0.707405\pi$
$240$	−2.80989	+	1.91575i	−0.181378	+	0.123661i
$241$	22.8421	+	7.04584i	1.47139	+	0.453862i	0.923796	−	0.382885i	$-0.125069\pi$
$241$	22.8421	+	7.04584i	1.47139	+	0.453862i	0.547590	+	0.836747i	$0.315545\pi$
$242$	−6.16000	−	26.9887i	−0.395980	−	1.73490i
$243$	3.18621	+	8.11832i	0.204395	+	0.520790i
$244$	−0.812834	+	10.8465i	−0.0520363	+	0.694377i
$245$	6.88544	+	6.38876i	0.439895	+	0.408163i
$246$	6.74923	+	4.60154i	0.430315	+	0.293384i
$247$	2.03874	+	2.55650i	0.129722	+	0.162666i
$248$	−22.2258	+	20.6226i	−1.41134	+	1.30953i
$249$	10.3989	−	1.56739i	0.659005	−	0.0993290i
$250$	2.68104	−	11.7464i	0.169564	−	0.742907i
$251$	10.2680	−	17.7846i	0.648108	−	1.12256i	−0.335466	−	0.942052i	$-0.608894\pi$
$251$	10.2680	−	17.7846i	0.648108	−	1.12256i	0.983574	−	0.180504i	$-0.0577729\pi$
$252$	−0.0761792	−	0.131946i	−0.00479884	−	0.00831183i
$253$	22.7218	−	7.00875i	1.42851	−	0.440637i
$254$	5.31544	−	6.66535i	0.333520	−	0.418221i
$255$	0.0416394	+	0.555639i	0.00260756	+	0.0347954i
$256$	14.2516	−	6.86323i	0.890727	−	0.428952i
$257$	−22.8388			−1.42464			−0.712322	−	0.701853i	$-0.752356\pi$
$257$	−22.8388			−1.42464			−0.712322	+	0.701853i	$0.752356\pi$
$258$	−0.754269	−	10.4143i	−0.0469588	−	0.648368i
$259$	1.63165			0.101386
$260$	−2.83353	+	1.36456i	−0.175728	+	0.0846261i
$261$	−0.448772	−	5.98844i	−0.0277783	−	0.370675i
$262$	−12.2156	+	15.3179i	−0.754681	+	0.946340i
$263$	5.88459	−	1.81516i	0.362860	−	0.111927i	−0.107964	−	0.994155i	$-0.534433\pi$
$263$	5.88459	−	1.81516i	0.362860	−	0.111927i	0.470823	+	0.882227i	$0.343957\pi$
$264$	−13.4916	−	23.3681i	−0.830348	−	1.43820i
$265$	−5.64215	+	9.77249i	−0.346594	+	0.600319i
$266$	0.0597263	−	0.261678i	0.00366206	−	0.0160445i
$267$	−6.39922	+	0.964527i	−0.391626	+	0.0590281i
$268$	−3.73568	+	3.46621i	−0.228193	+	0.211732i
$269$	9.36364	+	11.7416i	0.570911	+	0.715900i	0.980533	−	0.196355i	$-0.0629106\pi$
$269$	9.36364	+	11.7416i	0.570911	+	0.715900i	−0.409621	+	0.912256i	$0.634339\pi$
$270$	−6.87765	−	4.68910i	−0.418560	−	0.285370i
$271$	−2.26842	−	2.10479i	−0.137797	−	0.127857i	0.608263	−	0.793735i	$-0.291866\pi$
$271$	−2.26842	−	2.10479i	−0.137797	−	0.127857i	−0.746060	+	0.665878i	$0.768057\pi$
$272$	−0.0364288	+	0.486108i	−0.00220882	+	0.0294746i
$273$	−0.331652	−	0.845037i	−0.0200725	−	0.0511440i
$274$	−2.43907	−	10.6863i	−0.147349	−	0.645580i
$275$	18.2989	+	5.64446i	1.10346	+	0.340373i
$276$	3.84980	−	2.62475i	0.231731	−	0.157991i
$277$	−14.9446	−	2.25253i	−0.897932	−	0.135341i	−0.316172	−	0.948702i	$-0.602398\pi$
$277$	−14.9446	−	2.25253i	−0.897932	−	0.135341i	−0.581760	+	0.813360i	$0.697636\pi$
$278$	−4.95056	+	12.6138i	−0.296915	+	0.756527i
$279$	−7.75116	−	3.73276i	−0.464050	−	0.223475i
$280$	0.807080	+	0.388669i	0.0482322	+	0.0232274i
$281$	4.07782	−	10.3901i	0.243262	−	0.619822i	−0.756139	−	0.654411i	$-0.772917\pi$
$281$	4.07782	−	10.3901i	0.243262	−	0.619822i	0.999402	+	0.0345883i	$0.0110120\pi$
$282$	−0.727911	−	0.109715i	−0.0433465	−	0.00653343i
$283$	−13.2949	+	9.06431i	−0.790300	+	0.538818i	−0.889871	−	0.456213i	$-0.849206\pi$
$283$	−13.2949	+	9.06431i	−0.790300	+	0.538818i	0.0995704	+	0.995031i	$0.468253\pi$
$284$	1.14435	+	0.352984i	0.0679045	+	0.0209458i
$285$	0.498950	+	2.18604i	0.0295553	+	0.129490i
$286$	6.91169	+	17.6107i	0.408697	+	1.04134i
$287$	0.0829312	−	1.10664i	0.00489527	−	0.0653229i
$288$	2.70918	+	2.51375i	0.159640	+	0.148124i
$289$	−13.9801	−	9.53145i	−0.822357	−	0.560674i
$290$	6.34416	+	7.95532i	0.372542	+	0.467152i
$291$	4.78160	−	4.43667i	0.280302	−	0.260082i
$292$	−0.656663	+	0.0989760i	−0.0384283	+	0.00579213i
$293$	3.26781	−	14.3172i	0.190908	−	0.836421i	−0.785219	−	0.619218i	$-0.787450\pi$
$293$	3.26781	−	14.3172i	0.190908	−	0.836421i	0.976127	−	0.217203i	$-0.0696933\pi$
$294$	5.53590	−	9.58846i	0.322860	−	0.559210i
$295$	5.64354	+	9.77490i	0.328580	+	0.569116i
$296$	−22.0938	+	6.81505i	−1.28418	+	0.396117i
$297$	21.2384	−	26.6322i	1.23238	−	1.54536i
$298$	−0.301433	−	4.02235i	−0.0174616	−	0.233008i
$299$	−10.2132	+	4.91842i	−0.590645	+	0.284440i
$300$	3.75244			0.216647
$301$	−1.17405	+	0.796159i	−0.0676709	+	0.0458898i
$302$	−12.5660			−0.723094
$303$	3.93792	−	1.89640i	0.226228	−	0.108946i
$304$	0.146596	+	1.95619i	0.00840786	+	0.112195i
$305$	11.3138	−	14.1871i	0.647828	−	0.812351i
$306$	−0.256268	+	0.0790483i	−0.0146499	+	0.00451889i
$307$	−0.0141820	−	0.0245640i	−0.000809410	−	0.00140194i	0.865620	−	0.500701i	$-0.166924\pi$
$307$	−0.0141820	−	0.0245640i	−0.000809410	−	0.00140194i	−0.866430	+	0.499299i	$0.833591\pi$
$308$	−0.528214	+	0.914893i	−0.0300978	+	0.0521309i
$309$	−2.74397	+	12.0221i	−0.156099	+	0.683913i
$310$	14.4143	−	2.17261i	0.818677	−	0.123396i
$311$	7.53405	−	6.99057i	0.427217	−	0.396399i	−0.437047	−	0.899439i	$-0.643976\pi$
$311$	7.53405	−	6.99057i	0.427217	−	0.396399i	0.864263	+	0.503040i	$0.167785\pi$
$312$	8.02037	+	10.0572i	0.454064	+	0.569378i
$313$	14.8130	+	10.0994i	0.837283	+	0.570850i	0.904298	−	0.426902i	$-0.140395\pi$
$313$	14.8130	+	10.0994i	0.837283	+	0.570850i	−0.0670152	+	0.997752i	$0.521348\pi$
$314$	16.4732	+	15.2849i	0.929637	+	0.862577i
$315$	−0.0189949	+	0.253469i	−0.00107024	+	0.0142813i
$316$	−1.82109	−	4.64006i	−0.102444	−	0.261024i
$317$	4.83536	+	21.1851i	0.271581	+	1.18987i	0.908147	+	0.418652i	$0.137497\pi$
$317$	4.83536	+	21.1851i	0.271581	+	1.18987i	−0.636566	+	0.771222i	$0.719646\pi$
$318$	12.7104	+	3.92064i	0.712765	+	0.219859i
$319$	−34.4040	+	23.4563i	−1.92625	+	1.31330i
$320$	−10.8003	−	1.62788i	−0.603753	−	0.0910012i
$321$	3.34145	−	8.51388i	0.186502	−	0.475199i
$322$	0.838350	+	0.403728i	0.0467194	+	0.0224989i
$323$	0.289575	+	0.139452i	0.0161124	+	0.00775931i
$324$	1.66669	−	4.24666i	0.0925940	−	0.235926i
$325$	−9.02726	−	1.36064i	−0.500742	−	0.0754747i
$326$	6.23367	−	4.25005i	0.345251	−	0.235388i
$327$	0.296612	+	0.0914928i	0.0164027	+	0.00505956i
$328$	3.49924	+	15.3312i	0.193213	+	0.846522i
$329$	0.0365366	+	0.0930938i	0.00201433	+	0.00513243i
$330$	−0.969473	+	12.9367i	−0.0533677	+	0.712143i
$331$	−9.69617	−	8.99673i	−0.532950	−	0.494505i	0.367166	−	0.930155i	$-0.380328\pi$
$331$	−9.69617	−	8.99673i	−0.532950	−	0.494505i	−0.900116	+	0.435650i	$0.856518\pi$
$332$	4.82059	+	3.28662i	0.264564	+	0.180377i
$333$	−4.09044	−	5.12926i	−0.224155	−	0.281081i
$334$	−2.84328	+	2.63818i	−0.155577	+	0.144355i
$335$	8.40681	−	1.26712i	0.459313	−	0.0692303i
$336$	0.121185	−	0.530948i	0.00661120	−	0.0289656i
$337$	4.71536	−	8.16725i	0.256862	−	0.444898i	−0.708537	−	0.705673i	$-0.750645\pi$
$337$	4.71536	−	8.16725i	0.256862	−	0.444898i	0.965400	+	0.260775i	$0.0839780\pi$
$338$	2.58197	+	4.47211i	0.140441	+	0.243251i
$339$	−15.4426	+	4.76341i	−0.838726	+	0.258713i
$340$	−0.192737	+	0.241685i	−0.0104527	+	0.0131072i
$341$	4.45786	+	59.4860i	0.241406	+	3.22135i
$342$	−0.972341	+	0.468255i	−0.0525782	+	0.0253203i
$343$	−3.01843			−0.162980
$344$	12.5721	−	15.6844i	0.677844	−	0.845644i
$345$	−7.77332			−0.418502
$346$	23.6462	−	11.3874i	1.27123	−	0.612192i
$347$	−1.30647	−	17.4336i	−0.0701351	−	0.935887i	−0.915661	−	0.401952i	$-0.868332\pi$
$347$	−1.30647	−	17.4336i	−0.0701351	−	0.935887i	0.845526	−	0.533935i	$-0.179287\pi$
$348$	−5.08728	+	6.37925i	−0.272707	+	0.341964i
$349$	8.91802	−	2.75084i	0.477370	−	0.147249i	−0.0467268	−	0.998908i	$-0.514879\pi$
$349$	8.91802	−	2.75084i	0.477370	−	0.147249i	0.524097	+	0.851658i	$0.324403\pi$
$350$	0.374685	+	0.648974i	0.0200278	+	0.0346891i
$351$	−8.11964	+	14.0636i	−0.433394	+	0.750661i
$352$	5.70226	−	24.9832i	0.303932	−	1.33161i
$353$	−10.2719	+	1.54824i	−0.546718	+	0.0824045i	−0.416593	−	0.909093i	$-0.636776\pi$
$353$	−10.2719	+	1.54824i	−0.546718	+	0.0824045i	−0.130125	+	0.991498i	$0.541538\pi$
$354$	9.75298	−	9.04945i	0.518365	−	0.480973i
$355$	−1.24565	−	1.56200i	−0.0661124	−	0.0829024i
$356$	−2.96646	−	2.02250i	−0.157222	−	0.107192i
$357$	−0.0654091	−	0.0606908i	−0.00346182	−	0.00321210i
$358$	−0.424111	+	5.65937i	−0.0224150	+	0.299107i
$359$	3.94742	+	10.0579i	0.208337	+	0.530834i	0.996402	−	0.0847587i	$-0.0270119\pi$
$359$	3.94742	+	10.0579i	0.208337	+	0.530834i	−0.788065	+	0.615593i	$0.788917\pi$
$360$	−0.801478	−	3.51150i	−0.0422416	−	0.185073i
$361$	−16.9200	−	5.21912i	−0.890524	−	0.274690i
$362$	−2.50059	+	1.70487i	−0.131428	+	0.0896062i
$363$	−36.6200	−	5.51957i	−1.92205	−	0.289703i
$364$	0.183997	−	0.468817i	0.00964407	−	0.0245727i
$365$	0.998170	+	0.480694i	0.0522466	+	0.0251606i
$366$	−19.2713	−	9.28058i	−1.00733	−	0.485104i
$367$	7.07784	−	18.0340i	0.369460	−	0.941369i	−0.618377	−	0.785881i	$-0.712210\pi$
$367$	7.07784	−	18.0340i	0.369460	−	0.941369i	0.987838	−	0.155488i	$-0.0496951\pi$
$368$	−6.72464	−	1.01358i	−0.350546	−	0.0528363i
$369$	−3.68673	+	2.51357i	−0.191924	+	0.130851i
$370$	10.6223	+	3.27655i	0.552228	+	0.170340i
$371$	−0.402106	−	1.76174i	−0.0208763	−	0.0914651i
$372$	4.27053	+	10.8811i	0.221417	+	0.564161i
$373$	2.56665	−	34.2496i	0.132896	−	1.77338i	−0.389841	−	0.920882i	$-0.627470\pi$
$373$	2.56665	−	34.2496i	0.132896	−	1.77338i	0.522737	−	0.852494i	$-0.324911\pi$
$374$	1.36314	+	1.26481i	0.0704861	+	0.0654016i
$375$	−13.3175	−	9.07974i	−0.687715	−	0.468876i
$376$	−0.883567	−	1.10796i	−0.0455665	−	0.0571386i
$377$	14.5516	−	13.5019i	0.749447	−	0.695385i
$378$	1.31811	−	0.198673i	0.0677962	−	0.0102186i
$379$	−0.574248	+	2.51594i	−0.0294971	+	0.129235i	−0.987533	−	0.157414i	$-0.949684\pi$
$379$	−0.574248	+	2.51594i	−0.0294971	+	0.129235i	0.958036	+	0.286649i	$0.0925414\pi$
$380$	−0.621991	+	1.07732i	−0.0319075	+	0.0552654i
$381$	−5.70251	−	9.87704i	−0.292148	−	0.506016i
$382$	−3.60255	+	1.11124i	−0.184323	+	0.0568560i
$383$	8.92040	−	11.1858i	0.455811	−	0.571569i	−0.499822	−	0.866128i	$-0.666601\pi$
$383$	8.92040	−	11.1858i	0.455811	−	0.571569i	0.955633	+	0.294559i	$0.0951727\pi$
$384$	0.0352540	+	0.470432i	0.00179905	+	0.0240066i
$385$	1.58790	−	0.764693i	0.0809270	−	0.0389724i
$386$	−19.9191			−1.01386
$387$	5.44606	+	1.69481i	0.276839	+	0.0861521i
$388$	3.61881			0.183717
$389$	14.2240	−	6.84991i	0.721185	−	0.347304i	−0.0370254	−	0.999314i	$-0.511788\pi$
$389$	14.2240	−	6.84991i	0.721185	−	0.347304i	0.758210	+	0.652010i	$0.226074\pi$
$390$	−0.462177	−	6.16733i	−0.0234033	−	0.312295i
$391$	−0.694706	+	0.871133i	−0.0351328	+	0.0440551i
$392$	20.3674	−	6.28252i	1.02871	−	0.317315i
$393$	13.1051	+	22.6987i	0.661066	+	1.14500i
$394$	−5.55321	+	9.61843i	−0.279766	+	0.484570i
$395$	−1.85045	+	8.10736i	−0.0931064	+	0.407926i
$396$	4.20025	−	0.633086i	0.211071	−	0.0318138i
$397$	21.3361	−	19.7970i	1.07083	−	0.993585i	0.0708372	−	0.997488i	$-0.477433\pi$
$397$	21.3361	−	19.7970i	1.07083	−	0.993585i	0.999992	+	0.00390325i	$0.00124245\pi$
$398$	6.25571	+	7.84441i	0.313570	+	0.393205i
$399$	−0.296679	−	0.202272i	−0.0148525	−	0.0101263i
$400$	−4.01479	−	3.72518i	−0.200740	−	0.186259i
$401$	1.06942	−	14.2704i	0.0534043	−	0.712631i	−0.904670	−	0.426112i	$-0.859883\pi$
$401$	1.06942	−	14.2704i	0.0534043	−	0.712631i	0.958075	−	0.286519i	$-0.0924980\pi$
$402$	−3.66125	−	9.32871i	−0.182606	−	0.465274i
$403$	−6.32812	−	27.7253i	−0.315226	−	1.38110i
$404$	2.31712	+	0.714738i	0.115281	+	0.0355596i
$405$	−6.28835	+	4.28733i	−0.312471	+	0.213039i
$406$	−1.61125	−	0.242856i	−0.0799648	−	0.0120527i
$407$	−16.6193	+	42.3453i	−0.823789	+	2.09898i
$408$	1.13918	+	0.548602i	0.0563980	+	0.0271598i
$409$	−27.4363	−	13.2126i	−1.35664	−	0.653322i	−0.392754	−	0.919644i	$-0.628478\pi$
$409$	−27.4363	−	13.2126i	−1.35664	−	0.653322i	−0.963884	+	0.266321i	$0.914192\pi$
$410$	2.76216	−	7.03787i	0.136413	−	0.347576i
$411$	−14.4998	−	2.18549i	−0.715221	−	0.107802i
$412$	−5.65251	+	3.85382i	−0.278479	+	0.189864i
$413$	−1.72719	−	0.532768i	−0.0849895	−	0.0262158i
$414$	−0.832531	−	3.64756i	−0.0409167	−	0.179268i
$415$	−3.55604	−	9.06065i	−0.174559	−	0.444770i
$416$	−0.912946	+	12.1824i	−0.0447608	+	0.597292i
$417$	13.2885	+	12.3300i	0.650742	+	0.603800i
$418$	6.18284	+	4.21539i	0.302413	+	0.206181i
$419$	22.1749	+	27.8065i	1.08332	+	1.35844i	0.928858	+	0.370437i	$0.120792\pi$
$419$	22.1749	+	27.8065i	1.08332	+	1.35844i	0.154459	+	0.987999i	$0.450637\pi$
$420$	0.253164	−	0.234902i	0.0123531	−	0.0114620i
$421$	−16.3130	+	2.45879i	−0.795047	+	0.119834i	−0.533992	−	0.845490i	$-0.679309\pi$
$421$	−16.3130	+	2.45879i	−0.795047	+	0.119834i	−0.261056	+	0.965324i	$0.584071\pi$
$422$	4.62672	−	20.2710i	0.225225	−	0.986775i
$423$	0.201055	−	0.348237i	0.00977561	−	0.0169318i
$424$	12.8032	+	22.1759i	0.621780	+	1.07696i
$425$	−0.857465	+	0.264493i	−0.0415932	+	0.0128298i
$426$	−1.46831	+	1.84121i	−0.0711400	+	0.0892067i
$427$	0.217156	+	2.89774i	0.0105089	+	0.140231i
$428$	4.57167	−	2.20160i	0.220980	−	0.106418i
$429$	25.3088			1.22192
$430$	−9.24202	+	2.82550i	−0.445690	+	0.136258i
$431$	−9.05750			−0.436285			−0.218142	−	0.975917i	$-0.570000\pi$
$431$	−9.05750			−0.436285			−0.218142	+	0.975917i	$0.570000\pi$
$432$	−8.77750	+	4.22702i	−0.422308	+	0.203373i
$433$	1.29146	+	17.2334i	0.0620638	+	0.828184i	0.938194	+	0.346110i	$0.112497\pi$
$433$	1.29146	+	17.2334i	0.0620638	+	0.828184i	−0.876130	+	0.482074i	$0.839884\pi$
$434$	−1.45545	+	1.82507i	−0.0698636	+	0.0876062i
$435$	13.0075	−	4.01229i	0.623663	−	0.192375i
$436$	0.0861040	+	0.149137i	0.00412364	+	0.00714235i
$437$	−2.24191	+	3.88311i	−0.107245	+	0.185754i
$438$	0.290594	−	1.27318i	0.0138851	−	0.0608347i
$439$	−18.2692	+	2.75364i	−0.871943	+	0.131424i	−0.569745	−	0.821821i	$-0.692958\pi$
$439$	−18.2692	+	2.75364i	−0.871943	+	0.131424i	−0.302197	+	0.953245i	$0.597720\pi$
$440$	−18.3075	+	16.9869i	−0.872775	+	0.809817i
$441$	3.77082	+	4.72845i	0.179563	+	0.225165i
$442$	−0.732459	−	0.499382i	−0.0348395	−	0.0237532i
$443$	6.55737	+	6.08435i	0.311550	+	0.289076i	0.820413	−	0.571771i	$-0.193744\pi$
$443$	6.55737	+	6.08435i	0.311550	+	0.289076i	−0.508863	+	0.860848i	$0.669934\pi$
$444$	−0.666137	+	8.88897i	−0.0316134	+	0.421852i
$445$	2.18829	+	5.57568i	0.103735	+	0.264313i
$446$	1.77168	+	7.76223i	0.0838914	+	0.367552i
$447$	−5.15639	−	1.59054i	−0.243889	−	0.0752297i
$448$	1.44515	−	0.985287i	0.0682770	−	0.0465504i
$449$	20.0461	+	3.02146i	0.946032	+	0.142591i	0.603900	−	0.797060i	$-0.293613\pi$
$449$	20.0461	+	3.02146i	0.946032	+	0.142591i	0.342132	+	0.939652i	$0.388851\pi$
$450$	1.10080	−	2.80480i	0.0518923	−	0.132219i
$451$	27.8753	+	13.4240i	1.31260	+	0.632113i
$452$	−8.07782	−	3.89007i	−0.379949	−	0.182974i
$453$	−6.14162	+	15.6486i	−0.288558	+	0.735235i
$454$	−16.8703	−	2.54279i	−0.791764	−	0.119339i
$455$	−0.694213	+	0.473306i	−0.0325452	+	0.0221889i
$456$	4.86212	+	1.49976i	0.227689	+	0.0702329i
$457$	2.39474	+	10.4921i	0.112021	+	0.490797i	0.999549	+	0.0300423i	$0.00956421\pi$
$457$	2.39474	+	10.4921i	0.112021	+	0.490797i	−0.887527	+	0.460755i	$0.847579\pi$
$458$	−0.428570	−	1.09198i	−0.0200257	−	0.0510248i
$459$	−0.119284	+	1.59173i	−0.00556768	+	0.0742956i
$460$	−3.16133	−	2.93328i	−0.147398	−	0.136765i
$461$	−7.03749	−	4.79808i	−0.327769	−	0.223469i	0.388243	−	0.921557i	$-0.373082\pi$
$461$	−7.03749	−	4.79808i	−0.327769	−	0.223469i	−0.716012	+	0.698088i	$0.754034\pi$
$462$	−1.29528	−	1.62423i	−0.0602620	−	0.0755662i
$463$	1.66719	−	1.54693i	0.0774811	−	0.0718919i	−0.640482	−	0.767973i	$-0.721265\pi$
$463$	1.66719	−	1.54693i	0.0774811	−	0.0718919i	0.717963	+	0.696082i	$0.245075\pi$
$464$	11.7759	−	1.77493i	0.546681	−	0.0823989i
$465$	4.33939	−	19.0121i	0.201234	−	0.881666i
$466$	0.727166	−	1.25949i	0.0336853	−	0.0583447i
$467$	15.1256	+	26.1983i	0.699930	+	1.21231i	0.968490	+	0.249052i	$0.0801189\pi$
$467$	15.1256	+	26.1983i	0.699930	+	1.21231i	−0.268560	+	0.963263i	$0.586548\pi$
$468$	−1.93504	+	0.596882i	−0.0894474	+	0.0275909i
$469$	−0.848855	+	1.06443i	−0.0391965	+	0.0491509i
$470$	0.0509160	+	0.679426i	0.00234858	+	0.0313396i
$471$	27.0857	−	13.0438i	1.24804	−	0.601025i
$472$	25.6128			1.17892
$473$	−8.70393	−	38.5787i	−0.400207	−	1.77385i
$474$	9.80231			0.450235
$475$	−3.25342	+	1.56676i	−0.149277	+	0.0718881i
$476$	−0.00369937	−	0.0493646i	−0.000169560	−	0.00226262i
$477$	−4.53015	+	5.68063i	−0.207422	+	0.260098i
$478$	15.5099	−	4.78417i	0.709406	−	0.218823i
$479$	−6.78977	−	11.7602i	−0.310233	−	0.537338i	0.668180	−	0.744000i	$-0.267074\pi$
$479$	−6.78977	−	11.7602i	−0.310233	−	0.537338i	−0.978413	+	0.206661i	$0.933740\pi$
$480$	−4.18865	+	7.25495i	−0.191185	+	0.331142i
$481$	4.82568	−	21.1427i	0.220032	−	0.964024i
$482$	−25.7880	+	3.88691i	−1.17461	+	0.177044i
$483$	0.912508	−	0.846683i	0.0415205	−	0.0385254i
$484$	−12.8101	−	16.0634i	−0.582279	−	0.730154i
$485$	−4.98822	−	3.40091i	−0.226504	−	0.154428i
$486$	−6.97483	−	6.47170i	−0.316385	−	0.293562i
$487$	−2.78410	+	37.1512i	−0.126159	+	1.68348i	0.471605	+	0.881810i	$0.343675\pi$
$487$	−2.78410	+	37.1512i	−0.126159	+	1.68348i	−0.597765	+	0.801672i	$0.703944\pi$
$488$	−15.0437	−	38.3307i	−0.680996	−	1.73515i
$489$	−2.24593	−	9.84005i	−0.101564	−	0.444982i
$490$	−9.79229	−	3.02052i	−0.442371	−	0.136453i
$491$	16.9652	−	11.5667i	0.765629	−	0.521997i	−0.116394	−	0.993203i	$-0.537134\pi$
$491$	16.9652	−	11.5667i	0.765629	−	0.521997i	0.882023	+	0.471206i	$0.156181\pi$
$492$	5.99494	+	0.903592i	0.270273	+	0.0407371i
$493$	0.712843	−	1.81629i	0.0321048	−	0.0818018i
$494$	−3.21414	−	1.54785i	−0.144611	−	0.0696411i
$495$	−6.38466	−	3.07469i	−0.286969	−	0.138197i
$496$	6.23299	−	15.8814i	0.279870	−	0.713096i
$497$	0.316363	+	0.0476840i	0.0141908	+	0.00213892i
$498$	−9.47972	+	6.46316i	−0.424796	+	0.289621i
$499$	6.66084	+	2.05460i	0.298180	+	0.0919763i	0.440235	−	0.897882i	$-0.354895\pi$
$499$	6.66084	+	2.05460i	0.298180	+	0.0919763i	−0.142056	+	0.989859i	$0.545371\pi$
$500$	−1.98984	−	8.71804i	−0.0889882	−	0.389883i
$501$	1.89570	+	4.83017i	0.0846937	+	0.215796i
$502$	−1.67430	+	22.3420i	−0.0747277	+	0.997172i
$503$	−9.51112	−	8.82503i	−0.424080	−	0.393488i	0.439057	−	0.898459i	$-0.355313\pi$
$503$	−9.51112	−	8.82503i	−0.424080	−	0.393488i	−0.863136	+	0.504971i	$0.831503\pi$
$504$	0.476564	+	0.324916i	0.0212279	+	0.0144729i
$505$	−2.52226	−	3.16281i	−0.112239	−	0.140743i
$506$	−19.0168	+	17.6450i	−0.845400	+	0.784417i
$507$	6.83109	−	1.02962i	0.303379	−	0.0457271i
$508$	1.40798	−	6.16874i	0.0624688	−	0.273694i
$509$	−14.9031	+	25.8129i	−0.660568	+	1.14414i	0.319898	+	0.947452i	$0.396351\pi$
$509$	−14.9031	+	25.8129i	−0.660568	+	1.14414i	−0.980467	+	0.196686i	$0.936982\pi$
$510$	−0.303950	−	0.526457i	−0.0134591	−	0.0233119i
$511$	−0.169533	+	0.0522939i	−0.00749969	+	0.00231335i
$512$	−11.1629	+	13.9979i	−0.493337	+	0.618625i
$513$	0.480019	+	6.40541i	0.0211934	+	0.282806i
$514$	22.4495	−	10.8111i	0.990204	−	0.476857i
$515$	11.4133			0.502929
$516$	−3.85803	−	6.72106i	−0.169840	−	0.295878i
$517$	−2.78816			−0.122623
$518$	−1.60384	+	0.772368i	−0.0704686	+	0.0339359i
$519$	−2.62382	−	35.0125i	−0.115173	−	1.53688i
$520$	7.42329	−	9.30852i	0.325533	−	0.408205i
$521$	−29.7906	+	9.18917i	−1.30515	+	0.402585i	−0.867892	−	0.496752i	$-0.834526\pi$
$521$	−29.7906	+	9.18917i	−1.30515	+	0.402585i	−0.437256	+	0.899337i	$0.644050\pi$
$522$	3.27585	+	5.67393i	0.143380	+	0.248341i
$523$	−6.95091	+	12.0393i	−0.303942	+	0.526443i	−0.977025	−	0.213124i	$-0.931636\pi$
$523$	−6.95091	+	12.0393i	−0.303942	+	0.526443i	0.673083	+	0.739567i	$0.264970\pi$
$524$	−3.23571	+	14.1766i	−0.141353	+	0.619307i
$525$	0.991300	−	0.149414i	0.0432639	−	0.00652098i
$526$	−4.92505	+	4.56978i	−0.214742	+	0.199252i
$527$	−1.74282	−	2.18542i	−0.0759183	−	0.0951986i
$528$	12.5450	+	8.55307i	0.545953	+	0.372225i
$529$	5.46546	+	5.07120i	0.237629	+	0.220487i
$530$	0.920012	−	12.2767i	0.0399628	−	0.533266i
$531$	2.65515	+	6.76521i	0.115224	+	0.293585i
$532$	−0.0443282	−	0.194215i	−0.00192187	−	0.00842027i
$533$	−14.0944	−	4.34755i	−0.610496	−	0.188313i
$534$	5.83356	−	3.97726i	0.252443	−	0.172113i
$535$	−8.37069	−	1.26168i	−0.361896	−	0.0545471i
$536$	7.04828	−	17.9587i	0.304439	−	0.775699i
$537$	6.84038	+	3.29415i	0.295184	+	0.142153i
$538$	−14.7621	−	7.10906i	−0.636440	−	0.306493i
$539$	15.3207	−	39.0365i	0.659908	−	1.68142i
$540$	−6.10901	−	0.920785i	−0.262890	−	0.0396243i
$541$	−17.1344	+	11.6820i	−0.736664	+	0.502249i	−0.872580	−	0.488472i	$-0.837555\pi$
$541$	−17.1344	+	11.6820i	−0.736664	+	0.502249i	0.135916	+	0.990720i	$0.456602\pi$
$542$	3.22609	+	0.995118i	0.138573	+	0.0427440i
$543$	0.900937	+	3.94726i	0.0386629	+	0.169393i
$544$	0.438699	+	1.11779i	0.0188091	+	0.0479247i
$545$	0.0214696	−	0.286491i	0.000919655	−	0.0122719i
$546$	0.726011	+	0.673640i	0.0310704	+	0.0288291i
$547$	16.9135	+	11.5314i	0.723169	+	0.493049i	0.868098	−	0.496394i	$-0.165343\pi$
$547$	16.9135	+	11.5314i	0.723169	+	0.493049i	−0.144928	+	0.989442i	$0.546295\pi$
$548$	−5.07220	−	6.36034i	−0.216674	−	0.271700i
$549$	8.56494	−	7.94710i	0.365543	−	0.339174i
$550$	−20.6589	+	3.11382i	−0.880896	+	0.132774i
$551$	1.74721	−	7.65501i	0.0744335	−	0.326114i
$552$	−8.81966	+	15.2761i	−0.375390	+	0.650194i
$553$	−0.665844	−	1.15328i	−0.0283146	−	0.0490423i
$554$	15.7561	−	4.86011i	0.669413	−	0.206486i
$555$	9.27195	−	11.6267i	0.393573	−	0.493524i
$556$	0.751563	+	10.0289i	0.0318734	+	0.425321i
$557$	15.3932	−	7.41296i	0.652229	−	0.314097i	−0.0783489	−	0.996926i	$-0.524965\pi$
$557$	15.3932	−	7.41296i	0.652229	−	0.314097i	0.730578	+	0.682829i	$0.239251\pi$
$558$	9.38600			0.397341
$559$	6.84422	+	17.5678i	0.289480	+	0.743039i
$560$	−0.504059			−0.0213004
$561$	2.24130	−	1.07936i	0.0946280	−	0.0455704i
$562$	0.910015	+	12.1433i	0.0383867	+	0.512235i
$563$	−7.02348	+	8.80717i	−0.296004	+	0.371178i	−0.907487	−	0.420080i	$-0.862002\pi$
$563$	−7.02348	+	8.80717i	−0.296004	+	0.371178i	0.611483	+	0.791258i	$0.290573\pi$
$564$	−0.522077	+	0.161039i	−0.0219834	+	0.00678098i
$565$	7.47874	+	12.9536i	0.314633	+	0.544960i
$566$	8.77755	−	15.2032i	0.368948	−	0.639037i
$567$	0.271205	−	1.18823i	0.0113895	−	0.0499008i
$568$	−4.48296	+	0.675698i	−0.188101	+	0.0283517i
$569$	5.89078	−	5.46585i	0.246955	−	0.229140i	−0.546977	−	0.837148i	$-0.684221\pi$
$569$	5.89078	−	5.46585i	0.246955	−	0.229140i	0.793931	+	0.608007i	$0.208031\pi$
$570$	−1.52524	−	1.91259i	−0.0638854	−	0.0801098i
$571$	−24.0538	−	16.3996i	−1.00662	−	0.686302i	−0.0565700	−	0.998399i	$-0.518016\pi$
$571$	−24.0538	−	16.3996i	−1.00662	−	0.686302i	−0.950050	+	0.312096i	$0.898969\pi$
$572$	10.2928	+	9.55035i	0.430365	+	0.399320i
$573$	−0.376902	+	5.02941i	−0.0157453	+	0.210106i
$574$	0.442328	+	1.12703i	0.0184624	+	0.0470414i
$575$	−2.78562	−	12.2046i	−0.116168	−	0.508967i
$576$	−6.72025	−	2.07292i	−0.280010	−	0.0863718i
$577$	−5.93710	+	4.04784i	−0.247165	+	0.168514i	−0.680565	−	0.732687i	$-0.738266\pi$
$577$	−5.93710	+	4.04784i	−0.247165	+	0.168514i	0.433401	+	0.901201i	$0.357313\pi$
$578$	18.2536	+	2.75129i	0.759251	+	0.114439i
$579$	−9.73544	+	24.8055i	−0.404591	+	1.03088i
$580$	6.80407	+	3.27667i	0.282523	+	0.136056i
$581$	1.40434	+	0.676297i	0.0582620	+	0.0280575i
$582$	−2.59992	+	6.62449i	−0.107770	+	0.274594i
$583$	49.8172	+	7.50873i	2.06322	+	0.310980i
$584$	2.07719	−	1.41620i	0.0859547	−	0.0586029i
$585$	3.22823	+	0.995778i	0.133471	+	0.0411703i
$586$	3.56517	+	15.6200i	0.147276	+	0.645258i
$587$	−10.8541	−	27.6558i	−0.447997	−	1.14148i	−0.959378	−	0.282123i	$-0.908961\pi$
$587$	−10.8541	−	27.6558i	−0.447997	−	1.14148i	0.511381	−	0.859354i	$-0.329134\pi$
$588$	0.614084	−	8.19439i	0.0253244	−	0.337931i
$589$	−8.24584	−	7.65102i	−0.339764	−	0.315255i
$590$	−10.1744	−	6.93682i	−0.418875	−	0.285584i
$591$	9.26380	+	11.6164i	0.381062	+	0.477837i
$592$	9.53712	−	8.84915i	0.391973	−	0.363698i
$593$	−31.8484	+	4.80037i	−1.30786	+	0.197127i	−0.765726	−	0.643167i	$-0.777620\pi$
$593$	−31.8484	+	4.80037i	−1.30786	+	0.197127i	−0.542130	+	0.840295i	$0.682382\pi$
$594$	−8.26966	+	36.2318i	−0.339308	+	1.48661i
$595$	−0.0412930	+	0.0715215i	−0.00169285	+	0.00293210i
$596$	−1.49686	−	2.59263i	−0.0613136	−	0.106198i
$597$	12.8262	−	3.95635i	0.524940	−	0.161923i
$598$	7.71091	−	9.66917i	0.315322	−	0.395402i
$599$	−1.13778	−	15.1826i	−0.0464885	−	0.620346i	−0.970983	−	0.239150i	$-0.923131\pi$
$599$	−1.13778	−	15.1826i	−0.0464885	−	0.620346i	0.924494	−	0.381196i	$-0.124488\pi$
$600$	−12.7989	+	6.16363i	−0.522513	+	0.251629i
$601$	−14.8489			−0.605699			−0.302849	−	0.953038i	$-0.597938\pi$
$601$	−14.8489			−0.605699			−0.302849	+	0.953038i	$0.597938\pi$
$602$	0.777159	−	1.33834i	0.0316747	−	0.0545467i
$603$	5.47417			0.222925
$604$	−8.40276	+	4.04656i	−0.341904	+	0.164652i
$605$	2.56150	+	34.1808i	0.104140	+	1.38965i
$606$	−2.97311	+	3.72816i	−0.120774	+	0.151446i
$607$	−8.93135	+	2.75496i	−0.362512	+	0.111820i	−0.470660	−	0.882315i	$-0.655984\pi$
$607$	−8.93135	+	2.75496i	−0.362512	+	0.111820i	0.108148	+	0.994135i	$0.465508\pi$
$608$	2.41611	+	4.18482i	0.0979860	+	0.169717i
$609$	−1.08992	+	1.88780i	−0.0441659	+	0.0764976i
$610$	−4.40529	+	19.3009i	−0.178365	+	0.781469i
$611$	1.31435	−	0.198107i	0.0531731	−	0.00801455i
$612$	−0.145908	+	0.135383i	−0.00589800	+	0.00547254i
$613$	19.2070	+	24.0849i	0.775765	+	0.972779i	0.999998	−	0.00175653i	$-0.000559122\pi$
$613$	19.2070	+	24.0849i	0.775765	+	0.972779i	−0.224233	+	0.974536i	$0.571988\pi$
$614$	0.0255680	+	0.0174320i	0.00103184	+	0.000703497i
$615$	−7.41433	−	6.87949i	−0.298974	−	0.277408i
$616$	0.298872	−	3.98817i	0.0120419	−	0.160688i
$617$	−1.40309	−	3.57502i	−0.0564864	−	0.143925i	0.899845	−	0.436210i	$-0.143680\pi$
$617$	−1.40309	−	3.57502i	−0.0564864	−	0.143925i	−0.956331	+	0.292285i	$0.905584\pi$
$618$	−2.99366	−	13.1161i	−0.120423	−	0.527606i
$619$	32.6404	+	10.0682i	1.31193	+	0.404676i	0.870300	−	0.492521i	$-0.163925\pi$
$619$	32.6404	+	10.0682i	1.31193	+	0.404676i	0.441629	+	0.897198i	$0.354401\pi$
$620$	8.93905	−	6.09454i	0.359001	−	0.244763i
$621$	−22.0194	−	3.31889i	−0.883608	−	0.133182i
$622$	−4.09653	+	10.4378i	−0.164256	+	0.418517i
$623$	−0.864195	−	0.416175i	−0.0346233	−	0.0166737i
$624$	−6.52153	−	3.14060i	−0.261070	−	0.125725i
$625$	0.349803	−	0.891285i	0.0139921	−	0.0356514i
$626$	−19.3412	−	2.91522i	−0.773031	−	0.116516i
$627$	8.27131	−	5.63928i	0.330324	−	0.225211i
$628$	15.9375	+	4.91608i	0.635977	+	0.196173i
$629$	−0.474327	−	2.07816i	−0.0189126	−	0.0828617i
$630$	−0.101312	−	0.258140i	−0.00403638	−	0.0102845i
$631$	−0.687936	+	9.17986i	−0.0273863	+	0.365445i	0.966627	+	0.256187i	$0.0824663\pi$
$631$	−0.687936	+	9.17986i	−0.0273863	+	0.365445i	−0.994013	+	0.109257i	$0.965153\pi$
$632$	13.8330	+	12.8352i	0.550248	+	0.510556i
$633$	−22.9823	−	15.6691i	−0.913465	−	0.622790i
$634$	−14.7812	−	18.5351i	−0.587038	−	0.736123i
$635$	−7.73808	+	7.17989i	−0.307076	+	0.284925i
$636$	9.76185	−	1.47136i	0.387083	−	0.0583433i
$637$	−4.44860	+	19.4906i	−0.176260	+	0.772246i
$638$	22.7142	−	39.3421i	0.899263	−	1.55757i
$639$	−0.643201	−	1.11406i	−0.0254447	−	0.0440714i
$640$	0.417233	−	0.128699i	0.0164926	−	0.00508729i
$641$	2.10948	−	2.64521i	0.0833196	−	0.104479i	−0.738424	−	0.674336i	$-0.764430\pi$
$641$	2.10948	−	2.64521i	0.0833196	−	0.104479i	0.821744	+	0.569857i	$0.193001\pi$
$642$	0.745686	+	9.95049i	0.0294299	+	0.392714i
$643$	−10.1874	+	4.90598i	−0.401751	+	0.193473i	−0.623838	−	0.781554i	$-0.714427\pi$
$643$	−10.1874	+	4.90598i	−0.401751	+	0.193473i	0.222087	+	0.975027i	$0.428713\pi$
$644$	0.690605			0.0272137
$645$	−0.998394	+	12.8901i	−0.0393117	+	0.507548i
$646$	−0.350651			−0.0137962
$647$	20.4890	−	9.86700i	0.805507	−	0.387912i	0.0146350	−	0.999893i	$-0.495341\pi$
$647$	20.4890	−	9.86700i	0.805507	−	0.387912i	0.790873	+	0.611981i	$0.209627\pi$
$648$	1.29063	+	17.2223i	0.0507008	+	0.676555i
$649$	31.4191	−	39.3983i	1.23331	−	1.54652i
$650$	9.51746	−	2.93575i	0.373306	−	0.115150i
$651$	1.56143	+	2.70448i	0.0611973	+	0.105997i
$652$	2.79977	−	4.84935i	0.109648	−	0.189915i
$653$	−5.74350	+	25.1639i	−0.224760	+	0.984739i	0.729081	+	0.684428i	$0.239948\pi$
$653$	−5.74350	+	25.1639i	−0.224760	+	0.984739i	−0.953841	+	0.300312i	$0.902909\pi$
$654$	−0.334866	+	0.0504729i	−0.0130943	+	0.00197365i
$655$	17.7831	−	16.5003i	0.694844	−	0.644721i
$656$	−5.51705	−	6.91816i	−0.215404	−	0.270109i
$657$	0.589399	+	0.401846i	0.0229947	+	0.0156775i
$658$	−0.0799813	−	0.0742118i	−0.00311799	−	0.00289308i
$659$	0.761704	−	10.1642i	0.0296718	−	0.395942i	−0.962519	−	0.271214i	$-0.912575\pi$
$659$	0.761704	−	10.1642i	0.0296718	−	0.395942i	0.992191	−	0.124729i	$-0.0398060\pi$
$660$	3.51765	+	8.96283i	0.136924	+	0.348878i
$661$	2.96298	+	12.9817i	0.115247	+	0.504928i	0.999295	+	0.0375336i	$0.0119501\pi$
$661$	2.96298	+	12.9817i	0.115247	+	0.504928i	−0.884049	+	0.467395i	$0.845193\pi$
$662$	13.7896	+	4.25354i	0.535949	+	0.165318i
$663$	−0.979873	+	0.668066i	−0.0380551	+	0.0259455i
$664$	−21.8407	−	3.29195i	−0.847583	−	0.127753i
$665$	−0.121418	+	0.309367i	−0.00470838	+	0.0119967i
$666$	6.44874	+	3.10555i	0.249883	+	0.120338i
$667$	24.5247	+	11.8105i	0.949600	+	0.457303i
$668$	−1.05171	+	2.67972i	−0.0406920	+	0.103682i
$669$	10.5323	+	1.58749i	0.407201	+	0.0613757i
$670$	−7.66370	+	5.22502i	−0.296075	+	0.201860i
$671$	−77.4153	−	23.8795i	−2.98858	−	0.921856i
$672$	−0.298517	−	1.30789i	−0.0115156	−	0.0504530i
$673$	−2.30694	−	5.87798i	−0.0889259	−	0.226579i	0.879491	−	0.475915i	$-0.157883\pi$
$673$	−2.30694	−	5.87798i	−0.0889259	−	0.226579i	−0.968417	+	0.249336i	$0.919788\pi$
$674$	−0.768890	+	10.2601i	−0.0296165	+	0.395205i
$675$	−13.1462	−	12.1979i	−0.505997	−	0.469496i
$676$	3.16666	+	2.15899i	0.121795	+	0.0830382i
$677$	−16.2431	−	20.3682i	−0.624273	−	0.782814i	0.364666	−	0.931139i	$-0.381183\pi$
$677$	−16.2431	−	20.3682i	−0.624273	−	0.782814i	−0.988939	+	0.148325i	$0.952612\pi$
$678$	12.9245	−	11.9922i	0.496363	−	0.460558i
$679$	0.955999	−	0.144094i	0.0366879	−	0.00552981i
$680$	0.260410	−	1.14093i	0.00998625	−	0.0437526i
$681$	−11.4119	+	19.7660i	−0.437305	+	0.757435i
$682$	−32.5405	−	56.3618i	−1.24604	−	2.15820i
$683$	−47.0692	+	14.5189i	−1.80105	+	0.555551i	−0.999123	−	0.0418665i	$-0.986670\pi$
$683$	−47.0692	+	14.5189i	−1.80105	+	0.555551i	−0.801930	+	0.597418i	$0.796193\pi$
$684$	−0.499405	+	0.626234i	−0.0190952	+	0.0239446i
$685$	1.01423	+	13.5340i	0.0387518	+	0.517107i
$686$	2.96698	−	1.42882i	0.113280	−	0.0545527i
$687$	−1.56931			−0.0598730
$688$	−2.54447	+	11.0210i	−0.0970070	+	0.420171i
$689$	−24.0176			−0.914999
$690$	7.64082	−	3.67963i	0.290881	−	0.140081i
$691$	−3.68891	−	49.2251i	−0.140333	−	1.87261i	−0.413311	−	0.910590i	$-0.635628\pi$
$691$	−3.68891	−	49.2251i	−0.140333	−	1.87261i	0.272978	−	0.962020i	$-0.411991\pi$
$692$	12.1450	−	15.2293i	0.461682	−	0.578931i
$693$	1.08439	−	0.334491i	0.0411927	−	0.0127063i
$694$	9.53670	+	16.5180i	0.362008	+	0.627016i
$695$	8.38908	−	14.5303i	0.318216	−	0.551166i
$696$	6.87349	−	30.1147i	0.260539	−	1.14150i
$697$	−1.43359	+	0.216078i	−0.0543009	+	0.00818455i
$698$	−7.46385	+	6.92544i	−0.282511	+	0.262132i
$699$	−1.21305	−	1.52112i	−0.0458818	−	0.0575340i
$700$	0.459533	+	0.313304i	0.0173687	+	0.0118418i
$701$	12.8277	+	11.9024i	0.484495	+	0.449546i	0.884207	−	0.467095i	$-0.154699\pi$
$701$	12.8277	+	11.9024i	0.484495	+	0.449546i	−0.399712	+	0.916641i	$0.630890\pi$
$702$	1.32399	−	17.6675i	0.0499709	−	0.666815i
$703$	−3.13388	−	7.98500i	−0.118197	−	0.301160i
$704$	10.8509	+	47.5409i	0.408959	+	1.79177i
$705$	0.870981	+	0.268662i	0.0328030	+	0.0101184i
$706$	9.36392	−	6.38421i	0.352416	−	0.240273i
$707$	0.640585	+	0.0965527i	0.0240917	+	0.00363124i
$708$	3.60758	−	9.19196i	0.135581	−	0.345455i
$709$	−28.7314	−	13.8363i	−1.07903	−	0.519634i	−0.192025	−	0.981390i	$-0.561505\pi$
$709$	−28.7314	−	13.8363i	−1.07903	−	0.519634i	−0.887007	+	0.461756i	$0.847220\pi$
$710$	1.96382	+	0.945725i	0.0737008	+	0.0354924i
$711$	−1.95621	+	4.98433i	−0.0733635	+	0.186927i
$712$	13.4402	+	2.02578i	0.503691	+	0.0759192i
$713$	32.2201	−	21.9673i	1.20665	−	0.822680i
$714$	0.0930231	+	0.0286938i	0.00348130	+	0.00107384i
$715$	−5.21249	−	22.8374i	−0.194936	−	0.854071i
$716$	1.53885	+	3.92093i	0.0575096	+	0.146532i
$717$	1.62266	−	21.6529i	0.0605993	−	0.808641i
$718$	−8.64119	−	8.01785i	−0.322486	−	0.299224i
$719$	35.7184	+	24.3524i	1.33207	+	0.908190i	0.999393	−	0.0348509i	$-0.0110956\pi$
$719$	35.7184	+	24.3524i	1.33207	+	0.908190i	0.332677	+	0.943041i	$0.392048\pi$
$720$	1.26364	+	1.58456i	0.0470932	+	0.0590531i
$721$	−1.33980	+	1.24315i	−0.0498968	+	0.0462974i
$722$	19.1021	−	2.87918i	0.710906	−	0.107152i
$723$	−7.76340	+	34.0137i	−0.288724	+	1.26498i
$724$	−1.12311	+	1.94528i	−0.0417400	+	0.0722958i
$725$	10.9609	+	18.9848i	0.407076	+	0.705077i
$726$	38.6086	−	11.9092i	1.43290	−	0.441990i
$727$	−2.61281	+	3.27636i	−0.0969039	+	0.121514i	−0.827919	−	0.560848i	$-0.810475\pi$
$727$	−2.61281	+	3.27636i	−0.0969039	+	0.121514i	0.731015	+	0.682361i	$0.239047\pi$
$728$	0.142481	+	1.90128i	0.00528071	+	0.0704662i
$729$	−26.6965	+	12.8563i	−0.988757	+	0.476161i
$730$	−1.20870			−0.0447360
$731$	1.35533	+	1.26388i	0.0501288	+	0.0467464i
$732$	−15.8751			−0.586760
$733$	−44.3364	+	21.3513i	−1.63760	+	0.788629i	−0.637773	+	0.770224i	$0.720144\pi$
$733$	−44.3364	+	21.3513i	−1.63760	+	0.788629i	−0.999831	+	0.0184045i	$0.994141\pi$
$734$	1.57951	+	21.0771i	0.0583007	+	0.777968i
$735$	−8.54744	+	10.7182i	−0.315277	+	0.395345i
$736$	−16.0077	+	4.93774i	−0.590053	+	0.182007i
$737$	−18.9785	−	32.8717i	−0.699082	−	1.21085i
$738$	2.43405	−	4.21590i	0.0895987	−	0.155189i
$739$	0.558133	−	2.44534i	0.0205313	−	0.0899533i	−0.963624	−	0.267261i	$-0.913882\pi$
$739$	0.558133	−	2.44534i	0.0205313	−	0.0899533i	0.984156	+	0.177307i	$0.0567387\pi$
$740$	8.15815	−	1.22964i	0.299900	−	0.0452026i
$741$	−3.49846	+	3.24609i	−0.128519	+	0.119248i
$742$	1.22920	+	1.54137i	0.0451254	+	0.0565854i
$743$	14.7210	+	10.0366i	0.540059	+	0.368206i	0.802416	−	0.596765i	$-0.203547\pi$
$743$	14.7210	+	10.0366i	0.540059	+	0.368206i	−0.262357	+	0.964971i	$0.584500\pi$
$744$	−32.4390	−	30.0990i	−1.18927	−	1.10348i
$745$	−0.373233	+	4.98044i	−0.0136742	+	0.182469i
$746$	13.6897	+	34.8807i	0.501215	+	1.27707i
$747$	−1.39460	−	6.11013i	−0.0510256	−	0.223558i
$748$	1.31881	+	0.406800i	0.0482205	+	0.0148741i
$749$	1.12006	−	0.763641i	0.0409260	−	0.0279028i
$750$	17.3886	+	2.62091i	0.634941	+	0.0957019i
$751$	14.1468	−	36.0454i	0.516223	−	1.31532i	−0.400684	−	0.916216i	$-0.631228\pi$
$751$	14.1468	−	36.0454i	0.516223	−	1.31532i	0.916908	−	0.399099i	$-0.130677\pi$
$752$	0.718447	+	0.345986i	0.0261991	+	0.0126168i
$753$	27.0044	+	13.0046i	0.984094	+	0.473915i
$754$	−7.91223	+	20.1600i	−0.288146	+	0.734185i
$755$	15.3854	+	2.31897i	0.559932	+	0.0843961i
$756$	0.817428	−	0.557313i	0.0297296	−	0.0202693i
$757$	29.5522	+	9.11563i	1.07409	+	0.331313i	0.780846	−	0.624724i	$-0.214788\pi$
$757$	29.5522	+	9.11563i	1.07409	+	0.331313i	0.293246	+	0.956037i	$0.405265\pi$
$758$	−0.626503	−	2.74489i	−0.0227556	−	0.0996988i
$759$	12.6791	+	32.3058i	0.460221	+	1.17262i
$760$	0.351933	−	4.69621i	0.0127659	−	0.170350i
$761$	31.4994	+	29.2271i	1.14185	+	1.05948i	0.997551	+	0.0699487i	$0.0222836\pi$
$761$	31.4994	+	29.2271i	1.14185	+	1.05948i	0.144300	+	0.989534i	$0.453907\pi$
$762$	10.2808	+	7.00930i	0.372433	+	0.253920i
$763$	0.0286848	+	0.0359696i	0.00103846	+	0.00130219i
$764$	−2.05114	+	1.90318i	−0.0742077	+	0.0688546i
$765$	0.328354	−	0.0494914i	0.0118717	−	0.00178936i
$766$	−3.47336	+	15.2178i	−0.125498	+	0.549841i
$767$	−12.0118	+	20.8050i	−0.433720	+	0.751225i
$768$	11.5434	+	19.9938i	0.416538	+	0.721464i
$769$	11.0134	−	3.39717i	0.397152	−	0.122505i	−0.0897448	−	0.995965i	$-0.528605\pi$
$769$	11.0134	−	3.39717i	0.397152	−	0.122505i	0.486896	+	0.873460i	$0.338129\pi$
$770$	−1.19886	+	1.50332i	−0.0432038	+	0.0541758i
$771$	−2.49103	−	33.2404i	−0.0897121	−	1.19712i
$772$	−13.3197	+	6.41443i	−0.479387	+	0.230861i
$773$	−24.2393			−0.871828			−0.435914	−	0.899988i	$-0.643575\pi$
$773$	−24.2393			−0.871828			−0.435914	+	0.899988i	$0.643575\pi$
$774$	−6.15550	+	0.912060i	−0.221255	+	0.0327833i
$775$	31.4052			1.12811
$776$	−12.3431	+	5.94414i	−0.443093	+	0.213382i
$777$	0.177964	+	2.37477i	0.00638443	+	0.0851943i
$778$	−10.7390	+	13.4663i	−0.385013	+	0.482790i
$779$	−5.57498	+	1.71965i	−0.199744	+	0.0616130i
$780$	−2.29508	−	3.97519i	−0.0821770	−	0.142335i
$781$	−4.45985	+	7.72469i	−0.159586	+	0.276411i
$782$	0.270499	−	1.18513i	0.00967303	−	0.0423803i
$783$	38.5593	−	5.81189i	1.37800	−	0.207700i
$784$	−8.79188	+	8.15768i	−0.313996	+	0.291346i
$785$	−17.3485	−	21.7543i	−0.619194	−	0.776444i
$786$	−23.6265	−	16.1083i	−0.842731	−	0.574564i
$787$	−7.37365	−	6.84175i	−0.262842	−	0.243882i	0.537732	−	0.843116i	$-0.319281\pi$
$787$	−7.37365	−	6.84175i	−0.262842	−	0.243882i	−0.800574	+	0.599234i	$0.795472\pi$
$788$	−0.616004	+	8.22000i	−0.0219442	+	0.292825i
$789$	3.28368	+	8.36668i	0.116902	+	0.297862i
$790$	−2.01884	−	8.84511i	−0.0718271	−	0.314695i
$791$	−2.28885	−	0.706017i	−0.0813821	−	0.0251031i
$792$	−13.2864	+	9.05854i	−0.472113	+	0.321881i
$793$	38.1907	+	5.75633i	1.35619	+	0.204413i
$794$	−11.6012	+	29.5594i	−0.411711	+	1.04902i
$795$	−14.8386	−	7.14591i	−0.526272	−	0.253439i
$796$	6.70921	+	3.23098i	0.237802	+	0.114519i
$797$	−14.9088	+	37.9869i	−0.528096	+	1.34557i	0.379294	+	0.925276i	$0.376167\pi$
$797$	−14.9088	+	37.9869i	−0.528096	+	1.34557i	−0.907390	+	0.420290i	$0.861928\pi$
$798$	0.387371	+	0.0583868i	0.0137128	+	0.00206687i
$799$	0.107948	−	0.0735978i	0.00381893	−	0.00260370i
$800$	−12.8917	−	3.97657i	−0.455792	−	0.140593i
$801$	0.858197	+	3.76001i	0.0303229	+	0.132853i
$802$	5.70394	+	14.5334i	0.201413	+	0.513192i
$803$	0.369635	−	4.93243i	0.0130441	−	0.174062i
$804$	−5.45230	−	5.05899i	−0.192288	−	0.178417i
$805$	−0.951940	−	0.649022i	−0.0335515	−	0.0228750i
$806$	19.3445	+	24.2572i	0.681380	+	0.854423i
$807$	−16.0679	+	14.9089i	−0.565618	+	0.524817i
$808$	−9.07731	+	1.36818i	−0.319339	+	0.0481326i
$809$	10.4359	−	45.7228i	0.366908	−	1.60753i	−0.368313	−	0.929702i	$-0.620065\pi$
$809$	10.4359	−	45.7228i	0.366908	−	1.60753i	0.735221	−	0.677827i	$-0.237078\pi$
$810$	4.15169	−	7.19094i	0.145876	−	0.252664i
$811$	−17.1357	−	29.6798i	−0.601714	−	1.04220i	−0.992562	−	0.121744i	$-0.961151\pi$
$811$	−17.1357	−	29.6798i	−0.601714	−	1.04220i	0.390847	−	0.920456i	$-0.372182\pi$
$812$	−1.15563	+	0.356464i	−0.0405546	+	0.0125094i
$813$	2.81598	−	3.53112i	0.0987606	−	0.123842i
$814$	−3.70880	−	49.4905i	−0.129993	−	1.73464i
$815$	−8.41660	+	4.05322i	−0.294821	+	0.141978i
$816$	−0.711474			−0.0249066
$817$	6.15123	+	4.21640i	0.215204	+	0.147513i
$818$	33.2230			1.16162
$819$	−0.487423	+	0.234730i	−0.0170319	+	0.00820215i
$820$	−0.419334	−	5.59563i	−0.0146438	−	0.195408i
$821$	−11.5042	+	14.4258i	−0.401500	+	0.503465i	−0.940947	−	0.338555i	$-0.890062\pi$
$821$	−11.5042	+	14.4258i	−0.401500	+	0.503465i	0.539447	+	0.842020i	$0.318633\pi$
$822$	15.2872	−	4.71546i	0.533201	−	0.164471i
$823$	−4.59427	−	7.95750i	−0.160146	−	0.277381i	0.774775	−	0.632237i	$-0.217863\pi$
$823$	−4.59427	−	7.95750i	−0.160146	−	0.277381i	−0.934921	+	0.354856i	$0.884530\pi$
$824$	12.9496	−	22.4293i	0.451120	−	0.781362i
$825$	−6.21930	+	27.2485i	−0.216528	+	0.948672i
$826$	1.94994	−	0.293907i	0.0678472	−	0.0102263i
$827$	−26.9067	+	24.9658i	−0.935637	+	0.868145i	−0.991475	−	0.130295i	$-0.958407\pi$
$827$	−26.9067	+	24.9658i	−0.935637	+	0.868145i	0.0558380	+	0.998440i	$0.482217\pi$
$828$	−1.73130	−	2.17099i	−0.0601669	−	0.0754470i
$829$	3.75599	+	2.56079i	0.130451	+	0.0889400i	0.626788	−	0.779190i	$-0.284369\pi$
$829$	3.75599	+	2.56079i	0.130451	+	0.0889400i	−0.496336	+	0.868130i	$0.665322\pi$
$830$	7.78443	+	7.22290i	0.270202	+	0.250710i
$831$	1.64842	−	21.9966i	0.0571829	−	0.763053i
$832$	−8.49311	−	21.6401i	−0.294446	−	0.750235i
$833$	0.437263	+	1.91577i	0.0151503	+	0.0663776i
$834$	−18.8986	−	5.82944i	−0.654405	−	0.201857i
$835$	3.96807	−	2.70538i	0.137321	−	0.0936236i
$836$	5.49185	+	0.827763i	0.189940	+	0.0286288i
$837$	20.4095	−	52.0026i	0.705457	−	1.79747i
$838$	−34.9596	−	16.8357i	−1.20766	−	0.581578i
$839$	21.6424	+	10.4224i	0.747177	+	0.359822i	0.768414	−	0.639953i	$-0.221046\pi$
$839$	21.6424	+	10.4224i	0.747177	+	0.359822i	−0.0212370	+	0.999774i	$0.506760\pi$
$840$	−0.477656	+	1.21705i	−0.0164807	+	0.0419921i
$841$	−18.4585	−	2.78217i	−0.636500	−	0.0959369i
$842$	14.8710	−	10.1389i	0.512490	−	0.349410i
$843$	15.5669	+	4.80176i	0.536154	+	0.165382i
$844$	−3.43390	−	15.0449i	−0.118200	−	0.517866i
$845$	−2.33598	−	5.95197i	−0.0803601	−	0.204754i
$846$	−0.0327841	+	0.437473i	−0.00112714	+	0.0150406i
$847$	−4.02372	−	3.73347i	−0.138257	−	0.128284i
$848$	−11.9050	−	8.11671i	−0.408820	−	0.278729i
$849$	−14.6426	−	18.3613i	−0.502534	−	0.630157i
$850$	0.717647	−	0.665879i	0.0246151	−	0.0228395i
$851$	29.4054	−	4.43215i	1.00800	−	0.151932i
$852$	−0.388933	+	1.70403i	−0.0133246	+	0.0583789i
$853$	24.8630	−	43.0639i	0.851292	−	1.47448i	−0.0287512	−	0.999587i	$-0.509153\pi$
$853$	24.8630	−	43.0639i	0.851292	−	1.47448i	0.880043	−	0.474894i	$-0.157514\pi$
$854$	−1.58515	−	2.74555i	−0.0542426	−	0.0939509i
$855$	1.27691	−	0.393876i	0.0436695	−	0.0134703i
$856$	−11.9769	+	15.0185i	−0.409361	+	0.513323i
$857$	−2.63975	−	35.2251i	−0.0901723	−	1.20327i	−0.840356	−	0.542036i	$-0.817654\pi$
$857$	−2.63975	−	35.2251i	−0.0901723	−	1.20327i	0.750183	−	0.661230i	$-0.229965\pi$
$858$	−24.8774	+	11.9803i	−0.849302	+	0.409002i
$859$	8.58814			0.293024			0.146512	−	0.989209i	$-0.453195\pi$
$859$	8.58814			0.293024			0.146512	+	0.989209i	$0.453195\pi$
$860$	−5.27016	+	4.86553i	−0.179711	+	0.165913i
$861$	1.61969			0.0551989
$862$	8.90311	−	4.28751i	0.303241	−	0.146033i
$863$	2.53059	+	33.7684i	0.0861424	+	1.14949i	0.857984	+	0.513676i	$0.171717\pi$
$863$	2.53059	+	33.7684i	0.0861424	+	1.14949i	−0.771842	+	0.635814i	$0.780664\pi$
$864$	−14.9627	+	18.7626i	−0.509041	+	0.638317i
$865$	−31.0531	+	9.57861i	−1.05584	+	0.325682i
$866$	−9.42715	−	16.3283i	−0.320348	−	0.554858i
$867$	12.3476	−	21.3867i	0.419347	−	0.726331i
$868$	−0.385524	+	1.68909i	−0.0130856	+	0.0573315i
$869$	36.7123	−	5.53349i	1.24538	−	0.187711i
$870$	−10.8865	+	10.1012i	−0.369088	+	0.342463i
$871$	11.2822	+	14.1474i	0.382283	+	0.479368i
$872$	−0.538653	−	0.367247i	−0.0182411	−	0.0124366i
$873$	−2.84960	−	2.64404i	−0.0964444	−	0.0894873i
$874$	0.365568	−	4.87817i	0.0123655	−	0.165006i
$875$	−0.872799	−	2.22386i	−0.0295060	−	0.0751800i
$876$	−0.215676	−	0.944937i	−0.00728701	−	0.0319265i
$877$	−17.2010	−	5.30581i	−0.580837	−	0.179164i	−0.00960602	−	0.999954i	$-0.503058\pi$
$877$	−17.2010	−	5.30581i	−0.580837	−	0.179164i	−0.571231	+	0.820789i	$0.693534\pi$
$878$	16.6543	−	11.3547i	0.562057	−	0.383204i
$879$	21.1943	+	3.19452i	0.714864	+	0.107748i
$880$	5.13414	−	13.0816i	0.173072	−	0.440980i
$881$	23.6192	+	11.3744i	0.795750	+	0.383213i	0.787159	−	0.616750i	$-0.211551\pi$
$881$	23.6192	+	11.3744i	0.795750	+	0.383213i	0.00859074	+	0.999963i	$0.497265\pi$
$882$	−5.94483	−	2.86288i	−0.200173	−	0.0963982i
$883$	−18.1802	+	46.3225i	−0.611814	+	1.55888i	0.203016	+	0.979176i	$0.434926\pi$
$883$	−18.1802	+	46.3225i	−0.611814	+	1.55888i	−0.814829	+	0.579701i	$0.803169\pi$
$884$	−0.650600	−	0.0980622i	−0.0218821	−	0.00329819i
$885$	−13.6112	+	9.27997i	−0.457536	+	0.311943i
$886$	−9.32572	−	2.87660i	−0.313304	−	0.0966414i
$887$	1.90844	+	8.36143i	0.0640792	+	0.280749i	0.996809	−	0.0798277i	$-0.0254370\pi$
$887$	1.90844	+	8.36143i	0.0640792	+	0.280749i	−0.932730	+	0.360577i	$0.882580\pi$
$888$	−12.3287	−	31.4129i	−0.413723	−	1.05415i
$889$	0.126325	−	1.68569i	0.00423680	−	0.0565362i
$890$	−4.79033	−	4.44478i	−0.160572	−	0.148989i
$891$	28.0750	+	19.1412i	0.940547	+	0.641254i
$892$	3.68432	+	4.62000i	0.123360	+	0.154689i
$893$	0.385409	−	0.357607i	0.0128972	−	0.0119669i
$894$	5.82140	−	0.877435i	0.194697	−	0.0293458i
$895$	1.56366	−	6.85086i	0.0522675	−	0.228999i
$896$	−0.0349607	+	0.0605537i	−0.00116796	+	0.00202296i
$897$	−8.27242	−	14.3282i	−0.276208	−	0.478406i
$898$	−21.1346	+	6.51917i	−0.705271	+	0.217547i
$899$	−42.5769	+	53.3898i	−1.42002	+	1.78065i
$900$	−0.167117	−	2.23002i	−0.00557056	−	0.0743340i
$901$	−2.12696	+	1.02429i	−0.0708592	+	0.0341240i
$902$	−33.7546			−1.12391
$903$	−1.28681	−	1.62191i	−0.0428225	−	0.0539739i
$904$	33.9417			1.12888
$905$	3.37626	−	1.62592i	0.112231	−	0.0540474i
$906$	−1.37058	−	18.2891i	−0.0455344	−	0.607614i
$907$	−17.5664	+	22.0275i	−0.583282	+	0.731412i	−0.982669	−	0.185370i	$-0.940652\pi$
$907$	−17.5664	+	22.0275i	−0.583282	+	0.731412i	0.399387	+	0.916782i	$0.369223\pi$
$908$	−12.0998	+	3.73231i	−0.401548	+	0.123861i
$909$	−1.30238	−	2.25579i	−0.0431973	−	0.0748200i
$910$	0.458332	−	0.793855i	0.0151936	−	0.0263160i
$911$	5.43767	−	23.8240i	0.180158	−	0.789324i	−0.801395	−	0.598135i	$-0.795909\pi$
$911$	5.43767	−	23.8240i	0.180158	−	0.789324i	0.981553	−	0.191189i	$-0.0612342\pi$
$912$	−2.83112	+	0.426723i	−0.0937478	+	0.0141302i
$913$	−31.8556	+	29.5577i	−1.05427	+	0.978217i
$914$	−7.32050	−	9.17962i	−0.242141	−	0.303635i
$915$	21.8824	+	14.9192i	0.723411	+	0.493213i
$916$	−0.638222	−	0.592184i	−0.0210875	−	0.0195663i
$917$	−0.290311	+	3.87394i	−0.00958692	+	0.127929i
$918$	−0.636220	−	1.62106i	−0.0209984	−	0.0535030i
$919$	3.55017	+	15.5543i	0.117109	+	0.513089i	0.999123	+	0.0418659i	$0.0133302\pi$
$919$	3.55017	+	15.5543i	0.117109	+	0.513089i	−0.882014	+	0.471223i	$0.843813\pi$
$920$	15.6008	+	4.81222i	0.514345	+	0.158654i
$921$	0.0342045	−	0.0233202i	0.00112708	−	0.000768427i
$922$	9.18878	+	1.38499i	0.302616	+	0.0456121i
$923$	1.55354	−	3.95835i	0.0511353	−	0.130291i
$924$	−1.38918	−	0.668995i	−0.0457007	−	0.0220083i
$925$	21.5772	+	10.3910i	0.709455	+	0.341656i
$926$	−0.906512	+	2.30975i	−0.0297898	+	0.0759032i
$927$	7.26677	+	1.09529i	0.238672	+	0.0359740i
$928$	24.2380	−	16.5252i	0.795650	−	0.542465i
$929$	−5.97357	−	1.84260i	−0.195987	−	0.0604539i	0.195208	−	0.980762i	$-0.437462\pi$
$929$	−5.97357	−	1.84260i	−0.195987	−	0.0604539i	−0.391195	+	0.920308i	$0.627938\pi$
$930$	4.73426	+	20.7422i	0.155243	+	0.680162i
$931$	2.88900	+	7.36105i	0.0946832	+	0.241249i
$932$	0.0806629	−	1.07637i	0.00264220	−	0.0352577i
$933$	10.9961	+	10.2029i	0.359996	+	0.334027i
$934$	−27.2692	−	18.5918i	−0.892275	−	0.608343i
$935$	−1.43556	−	1.80014i	−0.0469480	−	0.0588709i
$936$	5.61967	−	5.21430i	0.183685	−	0.170435i
$937$	53.4604	−	8.05785i	1.74647	−	0.263239i	0.803309	−	0.595563i	$-0.203071\pi$
$937$	53.4604	−	8.05785i	1.74647	−	0.263239i	0.943165	+	0.332324i	$0.107833\pi$
$938$	0.330521	−	1.44811i	0.0107919	−	0.0472823i
$939$	−13.0833	+	22.6610i	−0.426959	+	0.739514i
$940$	0.252838	+	0.437929i	0.00824667	+	0.0142837i
$941$	29.8574	−	9.20978i	0.973322	−	0.300230i	0.232996	−	0.972478i	$-0.425147\pi$
$941$	29.8574	−	9.20978i	0.973322	−	0.300230i	0.740326	+	0.672248i	$0.234671\pi$
$942$	−20.4495	+	25.6429i	−0.666280	+	0.835489i
$943$	−1.51146	−	20.1690i	−0.0492198	−	0.656792i
$944$	−12.9850	+	6.25324i	−0.422625	+	0.203526i
$945$	−1.65051			−0.0536911
$946$	26.8174	+	33.8010i	0.871909	+	1.09896i
$947$	−38.7946			−1.26066			−0.630328	−	0.776329i	$-0.717080\pi$
$947$	−38.7946			−1.26066			−0.630328	+	0.776329i	$0.717080\pi$
$948$	6.55470	−	3.15658i	0.212887	−	0.102521i
$949$	0.176216	+	2.35144i	0.00572022	+	0.0763311i
$950$	2.45631	−	3.08012i	0.0796932	−	0.0999321i
$951$	−30.3062	+	9.34823i	−0.982747	+	0.303137i
$952$	0.0937025	+	0.162298i	0.00303692	+	0.00526009i
$953$	14.6148	−	25.3136i	0.473420	−	0.819987i	−0.526118	−	0.850412i	$-0.676353\pi$
$953$	14.6148	−	25.3136i	0.473420	−	0.819987i	0.999537	+	0.0304252i	$0.00968613\pi$
$954$	1.76392	−	7.72822i	0.0571089	−	0.250211i
$955$	4.61591	−	0.695736i	0.149367	−	0.0225135i
$956$	8.83068	−	8.19367i	0.285605	−	0.265002i
$957$	−37.8916	−	47.5145i	−1.22486	−	1.53593i
$958$	12.2409	+	8.34572i	0.395486	+	0.269638i
$959$	−1.59320	−	1.47828i	−0.0514472	−	0.0477361i
$960$	1.19129	−	15.8967i	0.0384488	−	0.513063i
$961$	24.4157	+	62.2103i	0.787604	+	2.00678i
$962$	5.26480	+	23.0666i	0.169744	+	0.743698i
$963$	−5.20849	−	1.60661i	−0.167841	−	0.0517722i
$964$	−15.9924	+	10.9035i	−0.515082	+	0.351177i
$965$	24.3883	+	3.67594i	0.785087	+	0.118333i
$966$	−0.496162	+	1.26420i	−0.0159638	+	0.0406750i
$967$	−22.9889	−	11.0709i	−0.739274	−	0.356015i	0.0260504	−	0.999661i	$-0.491707\pi$
$967$	−22.9889	−	11.0709i	−0.739274	−	0.356015i	−0.765324	+	0.643645i	$0.777421\pi$
$968$	70.0783	+	33.7479i	2.25240	+	1.08470i
$969$	−0.171380	+	0.436668i	−0.00550551	+	0.0140278i
$970$	6.51307	+	0.981688i	0.209122	+	0.0315201i
$971$	17.1865	−	11.7176i	0.551542	−	0.376035i	−0.255246	−	0.966876i	$-0.582156\pi$
$971$	17.1865	−	11.7176i	0.551542	−	0.376035i	0.806788	+	0.590841i	$0.201204\pi$
$972$	−6.74803	−	2.08149i	−0.216443	−	0.0667639i
$973$	0.597875	+	2.61946i	0.0191670	+	0.0839761i
$974$	−14.8495	−	37.8358i	−0.475808	−	1.21234i
$975$	0.995724	−	13.2870i	0.0318887	−	0.425525i
$976$	16.9850	+	15.7598i	0.543676	+	0.504458i
$977$	−15.5522	−	10.6033i	−0.497559	−	0.339230i	0.288398	−	0.957510i	$-0.406877\pi$
$977$	−15.5522	−	10.6033i	−0.497559	−	0.339230i	−0.785958	+	0.618280i	$0.787830\pi$
$978$	6.86559	+	8.60917i	0.219537	+	0.275291i
$979$	19.6031	−	18.1890i	0.626517	−	0.581323i
$980$	−7.52068	+	1.13356i	−0.240239	+	0.0362102i
$981$	0.0411631	−	0.180347i	0.00131424	−	0.00575804i
$982$	−11.2007	+	19.4003i	−0.357430	+	0.619087i
$983$	11.1156	+	19.2529i	0.354534	+	0.614071i	0.987038	−	0.160486i	$-0.0513062\pi$
$983$	11.1156	+	19.2529i	0.354534	+	0.614071i	−0.632504	+	0.774557i	$0.717973\pi$
$984$	−21.9319	+	6.76509i	−0.699163	+	0.215663i
$985$	8.57416	−	10.7517i	0.273195	−	0.342576i
$986$	0.159080	+	2.12277i	0.00506613	+	0.0676028i
$987$	−0.131507	+	0.0633305i	−0.00418592	+	0.00201583i
$988$	−2.64771			−0.0842348
$989$	−18.9958	+	17.5374i	−0.604033	+	0.557657i
$990$	7.73128			0.245716
$991$	−13.8081	+	6.64964i	−0.438630	+	0.211233i	−0.640148	−	0.768252i	$-0.721127\pi$
$991$	−13.8081	+	6.64964i	−0.438630	+	0.211233i	0.201518	+	0.979485i	$0.435413\pi$
$992$	−3.14060	−	41.9084i	−0.0997143	−	1.33059i
$993$	12.0366	−	15.0934i	0.381971	−	0.478976i
$994$	−0.333542	+	0.102884i	−0.0105793	+	0.00326328i
$995$	−6.21163	−	10.7589i	−0.196922	−	0.341079i
$996$	−4.25769	+	7.37454i	−0.134910	+	0.233671i
$997$	−1.57862	+	6.91637i	−0.0499953	+	0.219044i	−0.993754	−	0.111591i	$-0.964405\pi$
$997$	−1.57862	+	6.91637i	−0.0499953	+	0.219044i	0.943759	+	0.330634i	$0.107263\pi$
$998$	−7.51987	+	1.13344i	−0.238037	+	0.0358784i
$999$	31.2287	−	28.9760i	0.988031	−	0.916759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.14.2	✓	36
3.2	odd	2		387.2.y.c.100.2		36
4.3	odd	2		688.2.bg.c.401.1		36
43.13	even	21		1849.2.a.n.1.13		18
43.30	odd	42		1849.2.a.o.1.6		18
43.40	even	21	inner	43.2.g.a.40.2	yes	36
129.83	odd	42		387.2.y.c.298.2		36
172.83	odd	42		688.2.bg.c.513.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.14.2	✓	36	1.1	even	1	trivial
43.2.g.a.40.2	yes	36	43.40	even	21	inner
387.2.y.c.100.2		36	3.2	odd	2
387.2.y.c.298.2		36	129.83	odd	42
688.2.bg.c.401.1		36	4.3	odd	2
688.2.bg.c.513.1		36	172.83	odd	42
1849.2.a.n.1.13		18	43.13	even	21
1849.2.a.o.1.6		18	43.30	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.982954 + 0.473366i) q^{2} +(0.109070 + 1.45544i) q^{3} +(-0.504856 + 0.633069i) q^{4} +(1.29085 - 0.398175i) q^{5} +(-0.796166 - 1.37900i) q^{6} +(-0.108163 + 0.187343i) q^{7} +(0.682116 - 2.98855i) q^{8} +(0.860089 - 0.129637i) q^{9} +O(q^{10})\)	\(q+(-0.982954 + 0.473366i) q^{2} +(0.109070 + 1.45544i) q^{3} +(-0.504856 + 0.633069i) q^{4} +(1.29085 - 0.398175i) q^{5} +(-0.796166 - 1.37900i) q^{6} +(-0.108163 + 0.187343i) q^{7} +(0.682116 - 2.98855i) q^{8} +(0.860089 - 0.129637i) q^{9} +(-1.08036 + 1.00243i) q^{10} +(-3.76031 - 4.71528i) q^{11} +(-0.976457 - 0.665737i) q^{12} +(2.10767 + 1.95563i) q^{13} +(0.0176371 - 0.235350i) q^{14} +(0.720312 + 1.83532i) q^{15} +(0.383825 + 1.68165i) q^{16} +(0.270054 + 0.0833006i) q^{17} +(-0.784062 + 0.534564i) q^{18} +(1.12457 + 0.169502i) q^{19} +(-0.399621 + 1.01822i) q^{20} +(-0.284464 - 0.136990i) q^{21} +(5.92827 + 2.85490i) q^{22} +(-1.44040 + 3.67008i) q^{23} +(4.42404 + 0.666817i) q^{24} +(-2.62344 + 1.78863i) q^{25} +(-2.99747 - 0.924598i) q^{26} +(1.25681 + 5.50644i) q^{27} +(-0.0639946 - 0.163056i) q^{28} +(0.515946 - 6.88482i) q^{29} +(-1.57681 - 1.46307i) q^{30} +(-8.17225 - 5.57174i) q^{31} +(2.64918 + 3.32196i) q^{32} +(6.45267 - 5.98720i) q^{33} +(-0.304882 + 0.0459536i) q^{34} +(-0.0650265 + 0.284900i) q^{35} +(-0.352151 + 0.609944i) q^{36} +(-3.77129 - 6.53207i) q^{37} +(-1.18564 + 0.365721i) q^{38} +(-2.61642 + 3.28088i) q^{39} +(-0.309453 - 4.12937i) q^{40} +(-4.62195 + 2.22581i) q^{41} +0.344461 q^{42} +(5.90092 + 2.85993i) q^{43} +4.88351 q^{44} +(1.05863 - 0.509808i) q^{45} +(-0.321443 - 4.28936i) q^{46} +(0.288239 - 0.361440i) q^{47} +(-2.40567 + 0.742051i) q^{48} +(3.47660 + 6.02165i) q^{49} +(1.73205 - 2.99999i) q^{50} +(-0.0917841 + 0.402132i) q^{51} +(-2.30212 + 0.346988i) q^{52} +(-6.12346 + 5.68174i) q^{53} +(-3.84195 - 4.81765i) q^{54} +(-6.73151 - 4.58946i) q^{55} +(0.486104 + 0.451039i) q^{56} +(-0.124042 + 1.65523i) q^{57} +(2.75189 + 7.01170i) q^{58} +(1.85926 + 8.14595i) q^{59} +(-1.52554 - 0.470567i) q^{60} +(11.0987 - 7.56700i) q^{61} +(10.6704 + 1.60831i) q^{62} +(-0.0687427 + 0.175154i) q^{63} +(-7.28468 - 3.50811i) q^{64} +(3.49937 + 1.68521i) q^{65} +(-3.50854 + 8.93961i) q^{66} +(6.22328 + 0.938008i) q^{67} +(-0.189073 + 0.128908i) q^{68} +(-5.49868 - 1.69612i) q^{69} +(-0.0709437 - 0.310825i) q^{70} +(-0.540324 - 1.37672i) q^{71} +(0.199253 - 2.65884i) q^{72} +(0.601198 + 0.557830i) q^{73} +(6.79906 + 4.63552i) q^{74} +(-2.88938 - 3.62317i) q^{75} +(-0.675051 + 0.626356i) q^{76} +(1.29010 - 0.194451i) q^{77} +(1.01876 - 4.46348i) q^{78} +(-3.07798 + 5.33121i) q^{79} +(1.16505 + 2.01792i) q^{80} +(-5.38373 + 1.66066i) q^{81} +(3.48954 - 4.37574i) q^{82} +(-0.538458 - 7.18523i) q^{83} +(0.230338 - 0.110925i) q^{84} +0.381767 q^{85} +(-7.15412 - 0.0178853i) q^{86} +10.0767 q^{87} +(-16.6568 + 8.02150i) q^{88} +(0.331353 + 4.42159i) q^{89} +(-0.799256 + 1.00224i) q^{90} +(-0.594345 + 0.183331i) q^{91} +(-1.59622 - 2.76473i) q^{92} +(7.21798 - 12.5019i) q^{93} +(-0.112232 + 0.491721i) q^{94} +(1.51914 - 0.228974i) q^{95} +(-4.54597 + 4.21804i) q^{96} +(-2.78649 - 3.49415i) q^{97} +(-6.26778 - 4.27330i) q^{98} +(-3.84548 - 3.56808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more