LMFDB - Embedded newform 43.2.g.a.40.2

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			40.2
Character	$\chi$	$=$	43.40
Dual form			43.2.g.a.14.2

$q$-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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{21}\right)$

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	0.0527802	−	0.998606i	$-0.483192\pi$
$2$	−0.982954	−	0.473366i	−0.695054	−	0.334720i	−0.747834	+	0.663886i	$0.768906\pi$
$3$	0.109070	−	1.45544i	0.0629716	−	0.840298i	−0.872887	−	0.487922i	$-0.837755\pi$
$3$	0.109070	−	1.45544i	0.0629716	−	0.840298i	0.935859	−	0.352375i	$-0.114626\pi$
$4$	−0.504856	−	0.633069i	−0.252428	−	0.316534i
$5$	1.29085	+	0.398175i	0.577286	+	0.178069i	0.569629	−	0.821902i	$-0.307087\pi$
$5$	1.29085	+	0.398175i	0.577286	+	0.178069i	0.00765630	+	0.999971i	$0.497563\pi$
$6$	−0.796166	+	1.37900i	−0.325033	+	0.562974i
$7$	−0.108163	−	0.187343i	−0.0408816	−	0.0708091i	0.844861	−	0.534987i	$-0.179683\pi$
$7$	−0.108163	−	0.187343i	−0.0408816	−	0.0708091i	−0.885742	+	0.464177i	$0.846350\pi$
$8$	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	−0.241397	+	0.970426i	$0.577606\pi$
$11$	−3.76031	+	4.71528i	−1.13378	+	1.42171i	−0.892380	+	0.451285i	$0.850966\pi$
$12$	−0.976457	+	0.665737i	−0.281879	+	0.192182i
$13$	2.10767	−	1.95563i	0.584562	−	0.542395i	−0.331487	−	0.943460i	$-0.607550\pi$
$13$	2.10767	−	1.95563i	0.584562	−	0.542395i	0.916050	+	0.401065i	$0.131360\pi$
$14$	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	−0.261833	−	0.965113i	$-0.584327\pi$
$17$	0.270054	−	0.0833006i	0.0654977	−	0.0202034i	0.327331	+	0.944910i	$0.393851\pi$
$18$	−0.784062	−	0.534564i	−0.184805	−	0.125998i
$19$	1.12457	−	0.169502i	0.257994	−	0.0388863i	−0.0187716	−	0.999824i	$-0.505976\pi$
$19$	1.12457	−	0.169502i	0.257994	−	0.0388863i	0.276766	+	0.960937i	$0.410737\pi$
$20$	−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	−0.998770	−	0.0495821i	$-0.984211\pi$
$23$	−1.44040	−	3.67008i	−0.300344	−	0.765265i	0.698426	−	0.715682i	$-0.253884\pi$
$24$	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	0.813272	+	0.581883i	$0.197684\pi$
$29$	0.515946	+	6.88482i	0.0958088	+	1.27848i	−0.717463	+	0.696596i	$0.754697\pi$
$30$	−1.57681	+	1.46307i	−0.287885	+	0.267119i
$31$	−8.17225	+	5.57174i	−1.46778	+	1.00071i	−0.475100	+	0.879932i	$0.657588\pi$
$31$	−8.17225	+	5.57174i	−1.46778	+	1.00071i	−0.992679	+	0.120783i	$0.961459\pi$
$32$	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	0.369489	+	0.929235i	$0.379533\pi$
$37$	−3.77129	+	6.53207i	−0.619996	+	1.07387i	−0.989486	+	0.144630i	$0.953801\pi$
$38$	−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	0.0366371	−	0.999329i	$-0.488335\pi$
$41$	−4.62195	−	2.22581i	−0.721827	−	0.347613i	−0.758464	+	0.651715i	$0.774050\pi$
$42$	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	0.802409	−	0.596775i	$-0.203551\pi$
$47$	0.288239	+	0.361440i	0.0420439	+	0.0527214i	−0.760365	+	0.649496i	$0.774980\pi$
$48$	−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	0.136539	−	0.990635i	$-0.456402\pi$
$53$	−6.12346	−	5.68174i	−0.841123	−	0.780448i	−0.977661	+	0.210187i	$0.932593\pi$
$54$	−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	−0.697088	−	0.716986i	$-0.745521\pi$
$59$	1.85926	−	8.14595i	0.242055	−	1.06051i	0.939143	−	0.343527i	$-0.111622\pi$
$60$	−1.52554	+	0.470567i	−0.196946	+	0.0607499i
$61$	11.0987	+	7.56700i	1.42105	+	0.968855i	0.998030	+	0.0627337i	$0.0199819\pi$
$61$	11.0987	+	7.56700i	1.42105	+	0.968855i	0.423019	+	0.906121i	$0.360971\pi$
$62$	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	0.242559	−	0.970137i	$-0.422013\pi$
$67$	6.22328	−	0.938008i	0.760294	−	0.114596i	0.517736	+	0.855541i	$0.326775\pi$
$68$	−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	−0.959344	−	0.282238i	$-0.908923\pi$
$71$	−0.540324	+	1.37672i	−0.0641247	+	0.163387i	0.895220	+	0.445625i	$0.147018\pi$
$72$	0.199253	+	2.65884i	0.0234822	+	0.313348i
$73$	0.601198	−	0.557830i	0.0703649	−	0.0652891i	−0.644206	−	0.764852i	$-0.722812\pi$
$73$	0.601198	−	0.557830i	0.0703649	−	0.0652891i	0.714571	+	0.699563i	$0.246622\pi$
$74$	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	0.639290	−	0.768966i	$-0.279228\pi$
$79$	−3.07798	−	5.33121i	−0.346299	−	0.599808i	−0.985589	+	0.169158i	$0.945895\pi$
$80$	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	0.886369	+	0.462979i	$0.153220\pi$
$83$	−0.538458	+	7.18523i	−0.0591035	+	0.788681i	−0.945473	+	0.325702i	$0.894399\pi$
$84$	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	−0.951716	−	0.306981i	$-0.900681\pi$
$89$	0.331353	−	4.42159i	0.0351233	−	0.468688i	0.986839	−	0.161707i	$-0.0516999\pi$
$90$	−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	−0.902905	−	0.429841i	$-0.858570\pi$
$97$	−2.78649	+	3.49415i	−0.282925	+	0.354777i	0.619979	+	0.784618i	$0.287141\pi$
$98$	−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	−0.974916	−	0.222572i	$-0.928555\pi$
$101$	−1.09407	+	2.78765i	−0.108864	+	0.277382i	0.866052	+	0.499954i	$0.166650\pi$
$102$	−0.100136	+	0.438725i	−0.00991496	+	0.0434403i
$103$	8.07350	−	2.49034i	0.795505	−	0.245381i	0.129746	−	0.991547i	$-0.458584\pi$
$103$	8.07350	−	2.49034i	0.795505	−	0.245381i	0.665760	+	0.746166i	$0.268108\pi$
$104$	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	−0.686407	−	0.727217i	$-0.740813\pi$
$107$	−5.64595	+	2.71894i	−0.545814	+	0.262850i	0.140593	+	0.990067i	$0.455099\pi$
$108$	−4.12047	+	1.98431i	−0.396492	+	0.190941i
$109$	0.0776988	+	0.197973i	0.00744219	+	0.0189624i	0.934547	−	0.355841i	$-0.115805\pi$
$109$	0.0776988	+	0.197973i	0.00744219	+	0.0189624i	−0.927104	+	0.374803i	$0.877710\pi$
$110$	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	−0.716380	−	0.697710i	$-0.754202\pi$
$113$	2.46387	−	10.7949i	0.231781	−	1.01550i	0.948161	−	0.317789i	$-0.102940\pi$
$114$	−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	0.0946062	−	0.995515i	$-0.469841\pi$
$127$	−7.04038	−	3.39047i	−0.624733	−	0.300855i	−0.719339	+	0.694659i	$0.755555\pi$
$128$	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	0.975876	−	0.218327i	$-0.0700601\pi$
$131$	16.1797	+	7.79174i	1.41363	+	0.680768i	0.437753	+	0.899095i	$0.355774\pi$
$132$	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	−0.976075	−	0.217434i	$-0.930231\pi$
$137$	−2.23563	−	9.79494i	−0.191003	−	0.836839i	0.785072	−	0.619404i	$-0.212626\pi$
$138$	6.20783	+	0.935681i	0.528446	+	0.0796504i
$139$	9.10473	+	8.44795i	0.772253	+	0.716546i	0.964292	−	0.264841i	$-0.0853195\pi$
$139$	9.10473	+	8.44795i	0.772253	+	0.716546i	−0.192039	+	0.981387i	$0.561510\pi$
$140$	−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	0.864809	−	0.502101i	$-0.167440\pi$
$149$	−1.35074	−	3.44162i	−0.110657	−	0.281948i	−0.975465	+	0.220153i	$0.929344\pi$
$150$	4.55522	−	2.19368i	0.371932	−	0.179113i
$151$	10.3773	−	4.99744i	0.844492	−	0.406686i	0.0389621	−	0.999241i	$-0.487595\pi$
$151$	10.3773	−	4.99744i	0.844492	−	0.406686i	0.805530	+	0.592555i	$0.201881\pi$
$152$	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	0.229914	+	0.973211i	$0.426156\pi$
$157$	−7.52520	+	19.1739i	−0.600577	+	1.53024i	−0.830490	+	0.557033i	$0.811940\pi$
$158$	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	−0.124329	−	0.992241i	$-0.539678\pi$
$163$	−6.83812	−	1.03068i	−0.535603	−	0.0807292i	−0.411274	+	0.911512i	$0.634916\pi$
$164$	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	0.423396	−	0.905945i	$-0.360838\pi$
$167$	3.39723	+	1.04791i	0.262886	+	0.0810895i	−0.160510	+	0.987034i	$0.551314\pi$
$168$	−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	0.946705	−	0.322103i	$-0.104390\pi$
$179$	2.60094	+	4.50496i	0.194403	+	0.336717i	−0.752301	+	0.658819i	$0.771056\pi$
$180$	−0.211710	−	0.927563i	−0.0157800	−	0.0691365i
$181$	2.74306	+	0.413450i	0.203890	+	0.0307315i	0.250193	−	0.968196i	$-0.419506\pi$
$181$	2.74306	+	0.413450i	0.203890	+	0.0307315i	−0.0463029	+	0.998927i	$0.514744\pi$
$182$	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	−0.0242502	−	0.999706i	$-0.507720\pi$
$191$	3.41700	−	0.515030i	0.247245	−	0.0372662i	0.271496	+	0.962440i	$0.412482\pi$
$192$	4.31130	+	10.9850i	0.311142	+	0.792776i
$193$	16.4497	−	7.92174i	1.18407	−	0.570219i	0.264977	−	0.964255i	$-0.414636\pi$
$193$	16.4497	−	7.92174i	1.18407	−	0.570219i	0.919095	+	0.394035i	$0.128921\pi$
$194$	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	0.824607	−	0.565705i	$-0.191396\pi$
$197$	8.41116	+	5.73463i	0.599270	+	0.408575i	−0.225337	+	0.974281i	$0.572348\pi$
$198$	5.46894	−	1.68694i	0.388661	−	0.119886i
$199$	−2.04642	+	8.96595i	−0.145067	+	0.635579i	0.849147	+	0.528157i	$0.177117\pi$
$199$	−2.04642	+	8.96595i	−0.145067	+	0.635579i	−0.994214	+	0.107422i	$0.965740\pi$
$200$	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	−0.999105	−	0.0423025i	$-0.986531\pi$
$211$	−11.8825	−	14.9002i	−0.818025	−	1.02577i	0.181080	−	0.983468i	$-0.442041\pi$
$212$	−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	0.999748	+	0.0224455i	$0.00714523\pi$
$223$	1.62391	+	7.11481i	0.108745	+	0.476443i	−0.891003	+	0.453997i	$0.849998\pi$
$224$	−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	−0.0527382	−	0.998608i	$-0.516795\pi$
$227$	12.9206	−	8.80914i	0.857573	−	0.584683i	0.910311	+	0.413925i	$0.135842\pi$
$228$	−0.985251	+	0.914179i	−0.0652498	+	0.0605430i
$229$	−0.0803517	−	1.07222i	−0.00530979	−	0.0708542i	0.993919	−	0.110110i	$-0.0351203\pi$
$229$	−0.0803517	−	1.07222i	−0.00530979	−	0.0708542i	−0.999229	+	0.0392558i	$0.987501\pi$
$230$	−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	0.526705	−	0.850048i	$-0.323427\pi$
$233$	−1.10140	−	0.750923i	−0.0721552	−	0.0491946i	−0.598860	+	0.800853i	$0.704380\pi$
$234$	−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	−0.606444	−	0.795126i	$-0.707405\pi$
$239$	−14.7110	+	2.21733i	−0.951579	+	0.143427i	−0.345134	+	0.938553i	$0.612167\pi$
$240$	−2.80989	−	1.91575i	−0.181378	−	0.123661i
$241$	22.8421	−	7.04584i	1.47139	−	0.453862i	0.547590	−	0.836747i	$-0.315545\pi$
$241$	22.8421	−	7.04584i	1.47139	−	0.453862i	0.923796	+	0.382885i	$0.125069\pi$
$242$	−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	0.983574	+	0.180504i	$0.0577729\pi$
$251$	10.2680	+	17.7846i	0.648108	+	1.12256i	−0.335466	+	0.942052i	$0.608894\pi$
$252$	−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	0.470823	−	0.882227i	$-0.343957\pi$
$263$	5.88459	+	1.81516i	0.362860	+	0.111927i	−0.107964	+	0.994155i	$0.534433\pi$
$264$	−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	−0.409621	−	0.912256i	$-0.634339\pi$
$269$	9.36364	−	11.7416i	0.570911	−	0.715900i	0.980533	+	0.196355i	$0.0629106\pi$
$270$	−6.87765	+	4.68910i	−0.418560	+	0.285370i
$271$	−2.26842	+	2.10479i	−0.137797	+	0.127857i	−0.746060	−	0.665878i	$-0.768057\pi$
$271$	−2.26842	+	2.10479i	−0.137797	+	0.127857i	0.608263	+	0.793735i	$0.291866\pi$
$272$	−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	−0.581760	−	0.813360i	$-0.697636\pi$
$277$	−14.9446	+	2.25253i	−0.897932	+	0.135341i	−0.316172	+	0.948702i	$0.602398\pi$
$278$	−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	0.999402	−	0.0345883i	$-0.0110120\pi$
$281$	4.07782	+	10.3901i	0.243262	+	0.619822i	−0.756139	+	0.654411i	$0.772917\pi$
$282$	−0.727911	+	0.109715i	−0.0433465	+	0.00653343i
$283$	−13.2949	−	9.06431i	−0.790300	−	0.538818i	0.0995704	−	0.995031i	$-0.468253\pi$
$283$	−13.2949	−	9.06431i	−0.790300	−	0.538818i	−0.889871	+	0.456213i	$0.849206\pi$
$284$	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	0.976127	+	0.217203i	$0.0696933\pi$
$293$	3.26781	+	14.3172i	0.190908	+	0.836421i	−0.785219	+	0.619218i	$0.787450\pi$
$294$	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	−0.866430	−	0.499299i	$-0.833591\pi$
$307$	−0.0141820	+	0.0245640i	−0.000809410	+	0.00140194i	0.865620	+	0.500701i	$0.166924\pi$
$308$	−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	0.864263	−	0.503040i	$-0.167785\pi$
$311$	7.53405	+	6.99057i	0.427217	+	0.396399i	−0.437047	+	0.899439i	$0.643976\pi$
$312$	8.02037	−	10.0572i	0.454064	−	0.569378i
$313$	14.8130	−	10.0994i	0.837283	−	0.570850i	−0.0670152	−	0.997752i	$-0.521348\pi$
$313$	14.8130	−	10.0994i	0.837283	−	0.570850i	0.904298	+	0.426902i	$0.140395\pi$
$314$	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	−0.636566	−	0.771222i	$-0.719646\pi$
$317$	4.83536	−	21.1851i	0.271581	−	1.18987i	0.908147	−	0.418652i	$-0.137497\pi$
$318$	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	−0.900116	−	0.435650i	$-0.856518\pi$
$331$	−9.69617	+	8.99673i	−0.532950	+	0.494505i	0.367166	+	0.930155i	$0.380328\pi$
$332$	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	0.965400	−	0.260775i	$-0.0839780\pi$
$337$	4.71536	+	8.16725i	0.256862	+	0.444898i	−0.708537	+	0.705673i	$0.750645\pi$
$338$	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	0.845526	+	0.533935i	$0.179287\pi$
$347$	−1.30647	+	17.4336i	−0.0701351	+	0.935887i	−0.915661	+	0.401952i	$0.868332\pi$
$348$	−5.08728	−	6.37925i	−0.272707	−	0.341964i
$349$	8.91802	+	2.75084i	0.477370	+	0.147249i	0.524097	−	0.851658i	$-0.324403\pi$
$349$	8.91802	+	2.75084i	0.477370	+	0.147249i	−0.0467268	+	0.998908i	$0.514879\pi$
$350$	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	−0.130125	−	0.991498i	$-0.541538\pi$
$353$	−10.2719	−	1.54824i	−0.546718	−	0.0824045i	−0.416593	+	0.909093i	$0.636776\pi$
$354$	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	−0.788065	−	0.615593i	$-0.788917\pi$
$359$	3.94742	−	10.0579i	0.208337	−	0.530834i	0.996402	+	0.0847587i	$0.0270119\pi$
$360$	−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	0.987838	+	0.155488i	$0.0496951\pi$
$367$	7.07784	+	18.0340i	0.369460	+	0.941369i	−0.618377	+	0.785881i	$0.712210\pi$
$368$	−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	0.522737	+	0.852494i	$0.324911\pi$
$373$	2.56665	+	34.2496i	0.132896	+	1.77338i	−0.389841	+	0.920882i	$0.627470\pi$
$374$	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	0.958036	−	0.286649i	$-0.0925414\pi$
$379$	−0.574248	−	2.51594i	−0.0294971	−	0.129235i	−0.987533	+	0.157414i	$0.949684\pi$
$380$	−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	0.955633	−	0.294559i	$-0.0951727\pi$
$383$	8.92040	+	11.1858i	0.455811	+	0.571569i	−0.499822	+	0.866128i	$0.666601\pi$
$384$	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	0.758210	−	0.652010i	$-0.226074\pi$
$389$	14.2240	+	6.84991i	0.721185	+	0.347304i	−0.0370254	+	0.999314i	$0.511788\pi$
$390$	−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	0.999992	−	0.00390325i	$-0.00124245\pi$
$397$	21.3361	+	19.7970i	1.07083	+	0.993585i	0.0708372	+	0.997488i	$0.477433\pi$
$398$	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	0.958075	+	0.286519i	$0.0924980\pi$
$401$	1.06942	+	14.2704i	0.0534043	+	0.712631i	−0.904670	+	0.426112i	$0.859883\pi$
$402$	−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	−0.963884	−	0.266321i	$-0.914192\pi$
$409$	−27.4363	+	13.2126i	−1.35664	+	0.653322i	−0.392754	+	0.919644i	$0.628478\pi$
$410$	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	0.154459	−	0.987999i	$-0.450637\pi$
$419$	22.1749	−	27.8065i	1.08332	−	1.35844i	0.928858	−	0.370437i	$-0.120792\pi$
$420$	0.253164	+	0.234902i	0.0123531	+	0.0114620i
$421$	−16.3130	−	2.45879i	−0.795047	−	0.119834i	−0.261056	−	0.965324i	$-0.584071\pi$
$421$	−16.3130	−	2.45879i	−0.795047	−	0.119834i	−0.533992	+	0.845490i	$0.679309\pi$
$422$	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	−0.876130	−	0.482074i	$-0.839884\pi$
$433$	1.29146	−	17.2334i	0.0620638	−	0.828184i	0.938194	−	0.346110i	$-0.112497\pi$
$434$	−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	−0.302197	−	0.953245i	$-0.597720\pi$
$439$	−18.2692	−	2.75364i	−0.871943	−	0.131424i	−0.569745	+	0.821821i	$0.692958\pi$
$440$	−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	−0.508863	−	0.860848i	$-0.669934\pi$
$443$	6.55737	−	6.08435i	0.311550	−	0.289076i	0.820413	+	0.571771i	$0.193744\pi$
$444$	−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	0.342132	−	0.939652i	$-0.388851\pi$
$449$	20.0461	−	3.02146i	0.946032	−	0.142591i	0.603900	+	0.797060i	$0.293613\pi$
$450$	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	−0.887527	−	0.460755i	$-0.847579\pi$
$457$	2.39474	−	10.4921i	0.112021	−	0.490797i	0.999549	−	0.0300423i	$-0.00956421\pi$
$458$	−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	−0.716012	−	0.698088i	$-0.754034\pi$
$461$	−7.03749	+	4.79808i	−0.327769	+	0.223469i	0.388243	+	0.921557i	$0.373082\pi$
$462$	−1.29528	+	1.62423i	−0.0602620	+	0.0755662i
$463$	1.66719	+	1.54693i	0.0774811	+	0.0718919i	0.717963	−	0.696082i	$-0.245075\pi$
$463$	1.66719	+	1.54693i	0.0774811	+	0.0718919i	−0.640482	+	0.767973i	$0.721265\pi$
$464$	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	−0.268560	−	0.963263i	$-0.586548\pi$
$467$	15.1256	−	26.1983i	0.699930	−	1.21231i	0.968490	−	0.249052i	$-0.0801189\pi$
$468$	−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	−0.978413	−	0.206661i	$-0.933740\pi$
$479$	−6.78977	+	11.7602i	−0.310233	+	0.537338i	0.668180	+	0.744000i	$0.267074\pi$
$480$	−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	−0.597765	−	0.801672i	$-0.703944\pi$
$487$	−2.78410	−	37.1512i	−0.126159	−	1.68348i	0.471605	−	0.881810i	$-0.343675\pi$
$488$	−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	0.882023	−	0.471206i	$-0.156181\pi$
$491$	16.9652	+	11.5667i	0.765629	+	0.521997i	−0.116394	+	0.993203i	$0.537134\pi$
$492$	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	−0.142056	−	0.989859i	$-0.545371\pi$
$499$	6.66084	−	2.05460i	0.298180	−	0.0919763i	0.440235	+	0.897882i	$0.354895\pi$
$500$	−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	−0.863136	−	0.504971i	$-0.831503\pi$
$503$	−9.51112	+	8.82503i	−0.424080	+	0.393488i	0.439057	+	0.898459i	$0.355313\pi$
$504$	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	−0.980467	−	0.196686i	$-0.936982\pi$
$509$	−14.9031	−	25.8129i	−0.660568	−	1.14414i	0.319898	−	0.947452i	$-0.396351\pi$
$510$	−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	−0.437256	−	0.899337i	$-0.644050\pi$
$521$	−29.7906	−	9.18917i	−1.30515	−	0.402585i	−0.867892	+	0.496752i	$0.834526\pi$
$522$	3.27585	−	5.67393i	0.143380	−	0.248341i
$523$	−6.95091	−	12.0393i	−0.303942	−	0.526443i	0.673083	−	0.739567i	$-0.264970\pi$
$523$	−6.95091	−	12.0393i	−0.303942	−	0.526443i	−0.977025	+	0.213124i	$0.931636\pi$
$524$	−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	0.135916	−	0.990720i	$-0.456602\pi$
$541$	−17.1344	−	11.6820i	−0.736664	−	0.502249i	−0.872580	+	0.488472i	$0.837555\pi$
$542$	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	−0.144928	−	0.989442i	$-0.546295\pi$
$547$	16.9135	−	11.5314i	0.723169	−	0.493049i	0.868098	+	0.496394i	$0.165343\pi$
$548$	−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	0.730578	−	0.682829i	$-0.239251\pi$
$557$	15.3932	+	7.41296i	0.652229	+	0.314097i	−0.0783489	+	0.996926i	$0.524965\pi$
$558$	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	0.611483	−	0.791258i	$-0.290573\pi$
$563$	−7.02348	−	8.80717i	−0.296004	−	0.371178i	−0.907487	+	0.420080i	$0.862002\pi$
$564$	−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	0.793931	−	0.608007i	$-0.208031\pi$
$569$	5.89078	+	5.46585i	0.246955	+	0.229140i	−0.546977	+	0.837148i	$0.684221\pi$
$570$	−1.52524	+	1.91259i	−0.0638854	+	0.0801098i
$571$	−24.0538	+	16.3996i	−1.00662	+	0.686302i	−0.950050	−	0.312096i	$-0.898969\pi$
$571$	−24.0538	+	16.3996i	−1.00662	+	0.686302i	−0.0565700	+	0.998399i	$0.518016\pi$
$572$	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	0.433401	−	0.901201i	$-0.357313\pi$
$577$	−5.93710	−	4.04784i	−0.247165	−	0.168514i	−0.680565	+	0.732687i	$0.738266\pi$
$578$	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	0.511381	+	0.859354i	$0.329134\pi$
$587$	−10.8541	+	27.6558i	−0.447997	+	1.14148i	−0.959378	+	0.282123i	$0.908961\pi$
$588$	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	−0.542130	−	0.840295i	$-0.682382\pi$
$593$	−31.8484	−	4.80037i	−1.30786	−	0.197127i	−0.765726	+	0.643167i	$0.777620\pi$
$594$	−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	0.924494	+	0.381196i	$0.124488\pi$
$599$	−1.13778	+	15.1826i	−0.0464885	+	0.620346i	−0.970983	+	0.239150i	$0.923131\pi$
$600$	−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	0.108148	−	0.994135i	$-0.465508\pi$
$607$	−8.93135	−	2.75496i	−0.362512	−	0.111820i	−0.470660	+	0.882315i	$0.655984\pi$
$608$	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	−0.224233	−	0.974536i	$-0.571988\pi$
$613$	19.2070	−	24.0849i	0.775765	−	0.972779i	0.999998	+	0.00175653i	$0.000559122\pi$
$614$	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	−0.956331	−	0.292285i	$-0.905584\pi$
$617$	−1.40309	+	3.57502i	−0.0564864	+	0.143925i	0.899845	+	0.436210i	$0.143680\pi$
$618$	−2.99366	+	13.1161i	−0.120423	+	0.527606i
$619$	32.6404	−	10.0682i	1.31193	−	0.404676i	0.441629	−	0.897198i	$-0.354401\pi$
$619$	32.6404	−	10.0682i	1.31193	−	0.404676i	0.870300	+	0.492521i	$0.163925\pi$
$620$	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	−0.994013	−	0.109257i	$-0.965153\pi$
$631$	−0.687936	−	9.17986i	−0.0273863	−	0.365445i	0.966627	−	0.256187i	$-0.0824663\pi$
$632$	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	0.821744	−	0.569857i	$-0.193001\pi$
$641$	2.10948	+	2.64521i	0.0833196	+	0.104479i	−0.738424	+	0.674336i	$0.764430\pi$
$642$	0.745686	−	9.95049i	0.0294299	−	0.392714i
$643$	−10.1874	−	4.90598i	−0.401751	−	0.193473i	0.222087	−	0.975027i	$-0.428713\pi$
$643$	−10.1874	−	4.90598i	−0.401751	−	0.193473i	−0.623838	+	0.781554i	$0.714427\pi$
$644$	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	0.790873	−	0.611981i	$-0.209627\pi$
$647$	20.4890	+	9.86700i	0.805507	+	0.387912i	0.0146350	+	0.999893i	$0.495341\pi$
$648$	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	−0.953841	−	0.300312i	$-0.902909\pi$
$653$	−5.74350	−	25.1639i	−0.224760	−	0.984739i	0.729081	−	0.684428i	$-0.239948\pi$
$654$	−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	0.992191	+	0.124729i	$0.0398060\pi$
$659$	0.761704	+	10.1642i	0.0296718	+	0.395942i	−0.962519	+	0.271214i	$0.912575\pi$
$660$	3.51765	−	8.96283i	0.136924	−	0.348878i
$661$	2.96298	−	12.9817i	0.115247	−	0.504928i	−0.884049	−	0.467395i	$-0.845193\pi$
$661$	2.96298	−	12.9817i	0.115247	−	0.504928i	0.999295	−	0.0375336i	$-0.0119501\pi$
$662$	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	−0.968417	−	0.249336i	$-0.919788\pi$
$673$	−2.30694	+	5.87798i	−0.0889259	+	0.226579i	0.879491	+	0.475915i	$0.157883\pi$
$674$	−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	−0.988939	−	0.148325i	$-0.952612\pi$
$677$	−16.2431	+	20.3682i	−0.624273	+	0.782814i	0.364666	+	0.931139i	$0.381183\pi$
$678$	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	−0.801930	−	0.597418i	$-0.796193\pi$
$683$	−47.0692	−	14.5189i	−1.80105	−	0.555551i	−0.999123	+	0.0418665i	$0.986670\pi$
$684$	−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	0.272978	+	0.962020i	$0.411991\pi$
$691$	−3.68891	+	49.2251i	−0.140333	+	1.87261i	−0.413311	+	0.910590i	$0.635628\pi$
$692$	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	−0.399712	−	0.916641i	$-0.630890\pi$
$701$	12.8277	−	11.9024i	0.484495	−	0.449546i	0.884207	+	0.467095i	$0.154699\pi$
$702$	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	−0.887007	−	0.461756i	$-0.847220\pi$
$709$	−28.7314	+	13.8363i	−1.07903	+	0.519634i	−0.192025	+	0.981390i	$0.561505\pi$
$710$	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	0.332677	−	0.943041i	$-0.392048\pi$
$719$	35.7184	−	24.3524i	1.33207	−	0.908190i	0.999393	+	0.0348509i	$0.0110956\pi$
$720$	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	0.731015	−	0.682361i	$-0.239047\pi$
$727$	−2.61281	−	3.27636i	−0.0969039	−	0.121514i	−0.827919	+	0.560848i	$0.810475\pi$
$728$	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	−0.999831	−	0.0184045i	$-0.994141\pi$
$733$	−44.3364	−	21.3513i	−1.63760	−	0.788629i	−0.637773	−	0.770224i	$-0.720144\pi$
$734$	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	0.984156	−	0.177307i	$-0.0567387\pi$
$739$	0.558133	+	2.44534i	0.0205313	+	0.0899533i	−0.963624	+	0.267261i	$0.913882\pi$
$740$	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	−0.262357	−	0.964971i	$-0.584500\pi$
$743$	14.7210	−	10.0366i	0.540059	−	0.368206i	0.802416	+	0.596765i	$0.203547\pi$
$744$	−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	0.916908	+	0.399099i	$0.130677\pi$
$751$	14.1468	+	36.0454i	0.516223	+	1.31532i	−0.400684	+	0.916216i	$0.631228\pi$
$752$	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	0.293246	−	0.956037i	$-0.405265\pi$
$757$	29.5522	−	9.11563i	1.07409	−	0.331313i	0.780846	+	0.624724i	$0.214788\pi$
$758$	−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	0.144300	−	0.989534i	$-0.453907\pi$
$761$	31.4994	−	29.2271i	1.14185	−	1.05948i	0.997551	−	0.0699487i	$-0.0222836\pi$
$762$	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	0.486896	−	0.873460i	$-0.338129\pi$
$769$	11.0134	+	3.39717i	0.397152	+	0.122505i	−0.0897448	+	0.995965i	$0.528605\pi$
$770$	−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	−0.800574	−	0.599234i	$-0.795472\pi$
$787$	−7.37365	+	6.84175i	−0.262842	+	0.243882i	0.537732	+	0.843116i	$0.319281\pi$
$788$	−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	−0.907390	−	0.420290i	$-0.861928\pi$
$797$	−14.9088	−	37.9869i	−0.528096	−	1.34557i	0.379294	−	0.925276i	$-0.376167\pi$
$798$	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	0.735221	+	0.677827i	$0.237078\pi$
$809$	10.4359	+	45.7228i	0.366908	+	1.60753i	−0.368313	+	0.929702i	$0.620065\pi$
$810$	4.15169	+	7.19094i	0.145876	+	0.252664i
$811$	−17.1357	+	29.6798i	−0.601714	+	1.04220i	0.390847	+	0.920456i	$0.372182\pi$
$811$	−17.1357	+	29.6798i	−0.601714	+	1.04220i	−0.992562	+	0.121744i	$0.961151\pi$
$812$	−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	0.539447	−	0.842020i	$-0.318633\pi$
$821$	−11.5042	−	14.4258i	−0.401500	−	0.503465i	−0.940947	+	0.338555i	$0.890062\pi$
$822$	15.2872	+	4.71546i	0.533201	+	0.164471i
$823$	−4.59427	+	7.95750i	−0.160146	+	0.277381i	−0.934921	−	0.354856i	$-0.884530\pi$
$823$	−4.59427	+	7.95750i	−0.160146	+	0.277381i	0.774775	+	0.632237i	$0.217863\pi$
$824$	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	0.0558380	−	0.998440i	$-0.482217\pi$
$827$	−26.9067	−	24.9658i	−0.935637	−	0.868145i	−0.991475	+	0.130295i	$0.958407\pi$
$828$	−1.73130	+	2.17099i	−0.0601669	+	0.0754470i
$829$	3.75599	−	2.56079i	0.130451	−	0.0889400i	−0.496336	−	0.868130i	$-0.665322\pi$
$829$	3.75599	−	2.56079i	0.130451	−	0.0889400i	0.626788	+	0.779190i	$0.284369\pi$
$830$	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	−0.0212370	−	0.999774i	$-0.506760\pi$
$839$	21.6424	−	10.4224i	0.747177	−	0.359822i	0.768414	+	0.639953i	$0.221046\pi$
$840$	−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	0.880043	+	0.474894i	$0.157514\pi$
$853$	24.8630	+	43.0639i	0.851292	+	1.47448i	−0.0287512	+	0.999587i	$0.509153\pi$
$854$	−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	0.750183	+	0.661230i	$0.229965\pi$
$857$	−2.63975	+	35.2251i	−0.0901723	+	1.20327i	−0.840356	+	0.542036i	$0.817654\pi$
$858$	−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	−0.771842	−	0.635814i	$-0.780664\pi$
$863$	2.53059	−	33.7684i	0.0861424	−	1.14949i	0.857984	−	0.513676i	$-0.171717\pi$
$864$	−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	−0.571231	−	0.820789i	$-0.693534\pi$
$877$	−17.2010	+	5.30581i	−0.580837	+	0.179164i	−0.00960602	+	0.999954i	$0.503058\pi$
$878$	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	0.00859074	−	0.999963i	$-0.497265\pi$
$881$	23.6192	−	11.3744i	0.795750	−	0.383213i	0.787159	+	0.616750i	$0.211551\pi$
$882$	−5.94483	+	2.86288i	−0.200173	+	0.0963982i
$883$	−18.1802	−	46.3225i	−0.611814	−	1.55888i	−0.814829	−	0.579701i	$-0.803169\pi$
$883$	−18.1802	−	46.3225i	−0.611814	−	1.55888i	0.203016	−	0.979176i	$-0.434926\pi$
$884$	−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	−0.932730	−	0.360577i	$-0.882580\pi$
$887$	1.90844	−	8.36143i	0.0640792	−	0.280749i	0.996809	+	0.0798277i	$0.0254370\pi$
$888$	−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	0.399387	−	0.916782i	$-0.369223\pi$
$907$	−17.5664	−	22.0275i	−0.583282	−	0.731412i	−0.982669	+	0.185370i	$0.940652\pi$
$908$	−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	0.981553	+	0.191189i	$0.0612342\pi$
$911$	5.43767	+	23.8240i	0.180158	+	0.789324i	−0.801395	+	0.598135i	$0.795909\pi$
$912$	−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	−0.882014	−	0.471223i	$-0.843813\pi$
$919$	3.55017	−	15.5543i	0.117109	−	0.513089i	0.999123	−	0.0418659i	$-0.0133302\pi$
$920$	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	−0.391195	−	0.920308i	$-0.627938\pi$
$929$	−5.97357	+	1.84260i	−0.195987	+	0.0604539i	0.195208	+	0.980762i	$0.437462\pi$
$930$	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	0.943165	−	0.332324i	$-0.107833\pi$
$937$	53.4604	+	8.05785i	1.74647	+	0.263239i	0.803309	+	0.595563i	$0.203071\pi$
$938$	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	0.740326	−	0.672248i	$-0.234671\pi$
$941$	29.8574	+	9.20978i	0.973322	+	0.300230i	0.232996	+	0.972478i	$0.425147\pi$
$942$	−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	0.999537	−	0.0304252i	$-0.00968613\pi$
$953$	14.6148	+	25.3136i	0.473420	+	0.819987i	−0.526118	+	0.850412i	$0.676353\pi$
$954$	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	−0.765324	−	0.643645i	$-0.777421\pi$
$967$	−22.9889	+	11.0709i	−0.739274	+	0.356015i	0.0260504	+	0.999661i	$0.491707\pi$
$968$	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	0.806788	−	0.590841i	$-0.201204\pi$
$971$	17.1865	+	11.7176i	0.551542	+	0.376035i	−0.255246	+	0.966876i	$0.582156\pi$
$972$	−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	−0.785958	−	0.618280i	$-0.787830\pi$
$977$	−15.5522	+	10.6033i	−0.497559	+	0.339230i	0.288398	+	0.957510i	$0.406877\pi$
$978$	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	−0.632504	−	0.774557i	$-0.717973\pi$
$983$	11.1156	−	19.2529i	0.354534	−	0.614071i	0.987038	+	0.160486i	$0.0513062\pi$
$984$	−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	0.201518	−	0.979485i	$-0.435413\pi$
$991$	−13.8081	−	6.64964i	−0.438630	−	0.211233i	−0.640148	+	0.768252i	$0.721127\pi$
$992$	−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	0.943759	−	0.330634i	$-0.107263\pi$
$997$	−1.57862	−	6.91637i	−0.0499953	−	0.219044i	−0.993754	+	0.111591i	$0.964405\pi$
$998$	−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.40.2	yes	36
3.2	odd	2		387.2.y.c.298.2		36
4.3	odd	2		688.2.bg.c.513.1		36
43.10	even	21		1849.2.a.n.1.13		18
43.14	even	21	inner	43.2.g.a.14.2	✓	36
43.33	odd	42		1849.2.a.o.1.6		18
129.14	odd	42		387.2.y.c.100.2		36
172.143	odd	42		688.2.bg.c.401.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.14.2	✓	36	43.14	even	21	inner
43.2.g.a.40.2	yes	36	1.1	even	1	trivial
387.2.y.c.100.2		36	129.14	odd	42
387.2.y.c.298.2		36	3.2	odd	2
688.2.bg.c.401.1		36	172.143	odd	42
688.2.bg.c.513.1		36	4.3	odd	2
1849.2.a.n.1.13		18	43.10	even	21
1849.2.a.o.1.6		18	43.33	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