LMFDB - Embedded newform 324.2.p.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	324.11
Dual form			324.2.p.a.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41031 - 0.105029i) q^{2} +(-0.330952 - 1.70014i) q^{3} +(1.97794 + 0.296246i) q^{4} +(0.00377236 - 0.0322746i) q^{5} +(0.288181 + 2.43248i) q^{6} +(-0.446224 - 0.888506i) q^{7} +(-2.75839 - 0.625539i) q^{8} +(-2.78094 + 1.12533i) q^{9} +O(q^{10})$	\(q+(-1.41031 - 0.105029i) q^{2} +(-0.330952 - 1.70014i) q^{3} +(1.97794 + 0.296246i) q^{4} +(0.00377236 - 0.0322746i) q^{5} +(0.288181 + 2.43248i) q^{6} +(-0.446224 - 0.888506i) q^{7} +(-2.75839 - 0.625539i) q^{8} +(-2.78094 + 1.12533i) q^{9} +(-0.00870995 + 0.0451209i) q^{10} +(2.16786 - 5.02566i) q^{11} +(-0.150943 - 3.46081i) q^{12} +(1.51950 - 0.360127i) q^{13} +(0.535995 + 1.29993i) q^{14} +(-0.0561197 + 0.00426781i) q^{15} +(3.82448 + 1.17191i) q^{16} +(-5.49614 + 0.969119i) q^{17} +(4.04018 - 1.29498i) q^{18} +(0.388087 + 0.0684303i) q^{19} +(0.0170227 - 0.0627196i) q^{20} +(-1.36290 + 1.05270i) q^{21} +(-3.58519 + 6.86004i) q^{22} +(-7.20224 - 3.61710i) q^{23} +(-0.150609 + 4.89666i) q^{24} +(4.86420 + 1.15284i) q^{25} +(-2.18078 + 0.348299i) q^{26} +(2.83357 + 4.35556i) q^{27} +(-0.619388 - 1.88960i) q^{28} +(-1.60710 + 0.481133i) q^{29} +(0.0795943 - 0.000124733i) q^{30} +(-5.26788 - 8.00942i) q^{31} +(-5.27061 - 2.05444i) q^{32} +(-9.26178 - 2.02241i) q^{33} +(7.85304 - 0.789502i) q^{34} +(-0.0303595 + 0.0110499i) q^{35} +(-5.83390 + 1.40199i) q^{36} +(-6.57185 - 2.39196i) q^{37} +(-0.540136 - 0.137268i) q^{38} +(-1.11515 - 2.46417i) q^{39} +(-0.0305946 + 0.0866660i) q^{40} +(1.69763 - 1.60163i) q^{41} +(2.03268 - 1.34148i) q^{42} +(-4.21206 + 3.13576i) q^{43} +(5.77672 - 9.29823i) q^{44} +(0.0258288 + 0.0939989i) q^{45} +(9.77747 + 5.85767i) q^{46} +(7.16150 + 4.71019i) q^{47} +(0.726696 - 6.88999i) q^{48} +(3.58978 - 4.82192i) q^{49} +(-6.73894 - 2.13673i) q^{50} +(3.46660 + 9.02348i) q^{51} +(3.11215 - 0.262164i) q^{52} +(3.35957 - 1.93965i) q^{53} +(-3.53875 - 6.44028i) q^{54} +(-0.154023 - 0.0889253i) q^{55} +(0.675065 + 2.72997i) q^{56} +(-0.0120974 - 0.682449i) q^{57} +(2.31704 - 0.509755i) q^{58} +(3.05504 + 7.08237i) q^{59} +(-0.112266 - 0.00818379i) q^{60} +(0.0769563 - 1.32129i) q^{61} +(6.58811 + 11.8490i) q^{62} +(2.24078 + 1.96873i) q^{63} +(7.21740 + 3.45096i) q^{64} +(-0.00589087 - 0.0503996i) q^{65} +(12.8495 + 3.82497i) q^{66} +(-2.85205 - 0.853849i) q^{67} +(-11.1581 + 0.288645i) q^{68} +(-3.76597 + 13.4419i) q^{69} +(0.0439768 - 0.0123952i) q^{70} +(4.98620 - 4.18392i) q^{71} +(8.37485 - 1.36450i) q^{72} +(1.85640 + 1.55770i) q^{73} +(9.01711 + 4.06363i) q^{74} +(0.350165 - 8.65134i) q^{75} +(0.747340 + 0.250320i) q^{76} +(-5.43268 + 0.316418i) q^{77} +(1.31389 + 3.59236i) q^{78} +(4.37177 + 4.12455i) q^{79} +(0.0522503 - 0.119012i) q^{80} +(6.46727 - 6.25895i) q^{81} +(-2.56240 + 2.08049i) q^{82} +(7.99493 - 8.47413i) q^{83} +(-3.00760 + 1.67841i) q^{84} +(0.0105445 + 0.181042i) q^{85} +(6.26965 - 3.98000i) q^{86} +(1.34987 + 2.57306i) q^{87} +(-9.12354 + 12.5066i) q^{88} +(4.18508 - 4.98758i) q^{89} +(-0.0265540 - 0.135280i) q^{90} +(-0.998011 - 1.18938i) q^{91} +(-13.1740 - 9.28803i) q^{92} +(-11.8737 + 11.6069i) q^{93} +(-9.60521 - 7.39498i) q^{94} +(0.00367256 - 0.0122672i) q^{95} +(-1.74851 + 9.64068i) q^{96} +(16.7230 - 1.95464i) q^{97} +(-5.56914 + 6.42336i) q^{98} +(-0.373168 + 16.4156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{54}\right)$

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 $

$2$	−1.41031	−	0.105029i	−0.997238	−	0.0742666i
$2$	−1.41031	−	0.105029i	−0.997238	−	0.0742666i
$3$	−0.330952	−	1.70014i	−0.191075	−	0.981575i
$3$	−0.330952	−	1.70014i	−0.191075	−	0.981575i
$4$	1.97794	+	0.296246i	0.988969	+	0.148123i
$5$	0.00377236	−	0.0322746i	0.00168705	−	0.0144336i	−0.992369	−	0.123307i	$-0.960650\pi$
$5$	0.00377236	−	0.0322746i	0.00168705	−	0.0144336i	0.994056	+	0.108873i	$0.0347242\pi$
$6$	0.288181	+	2.43248i	0.117649	+	0.993055i
$7$	−0.446224	−	0.888506i	−0.168657	−	0.335824i	0.793387	−	0.608717i	$-0.208316\pi$
$7$	−0.446224	−	0.888506i	−0.168657	−	0.335824i	−0.962044	+	0.272894i	$0.912019\pi$
$8$	−2.75839	−	0.625539i	−0.975237	−	0.221161i
$9$	−2.78094	+	1.12533i	−0.926980	+	0.375110i
$10$	−0.00870995	+	0.0451209i	−0.00275433	+	0.0142685i
$11$	2.16786	−	5.02566i	0.653634	−	1.51529i	−0.191924	−	0.981410i	$-0.561473\pi$
$11$	2.16786	−	5.02566i	0.653634	−	1.51529i	0.845558	−	0.533884i	$-0.179268\pi$
$12$	−0.150943	−	3.46081i	−0.0435735	−	0.999050i
$13$	1.51950	−	0.360127i	0.421432	−	0.0998813i	−0.0144274	−	0.999896i	$-0.504593\pi$
$13$	1.51950	−	0.360127i	0.421432	−	0.0998813i	0.435860	+	0.900015i	$0.356444\pi$
$14$	0.535995	+	1.29993i	0.143251	+	0.347422i
$15$	−0.0561197	+	0.00426781i	−0.0144900	+	0.00110194i
$16$	3.82448	+	1.17191i	0.956119	+	0.292978i
$17$	−5.49614	+	0.969119i	−1.33301	+	0.235046i	−0.794342	−	0.607471i	$-0.792184\pi$
$17$	−5.49614	+	0.969119i	−1.33301	+	0.235046i	−0.538669	+	0.842517i	$0.681073\pi$
$18$	4.04018	−	1.29498i	0.952279	−	0.305230i
$19$	0.388087	+	0.0684303i	0.0890333	+	0.0156990i	0.217987	−	0.975952i	$-0.430051\pi$
$19$	0.388087	+	0.0684303i	0.0890333	+	0.0156990i	−0.128954	+	0.991651i	$0.541162\pi$
$20$	0.0170227	−	0.0627196i	0.00380639	−	0.0140245i
$21$	−1.36290	+	1.05270i	−0.297410	+	0.229717i
$22$	−3.58519	+	6.86004i	−0.764365	+	1.46257i
$23$	−7.20224	−	3.61710i	−1.50177	−	0.754217i	−0.507555	−	0.861620i	$-0.669450\pi$
$23$	−7.20224	−	3.61710i	−1.50177	−	0.754217i	−0.994216	+	0.107402i	$0.965747\pi$
$24$	−0.150609	+	4.89666i	−0.0307429	+	0.999527i
$25$	4.86420	+	1.15284i	0.972839	+	0.230567i
$26$	−2.18078	+	0.348299i	−0.427686	+	0.0683071i
$27$	2.83357	+	4.35556i	0.545321	+	0.838227i
$28$	−0.619388	−	1.88960i	−0.117053	−	0.357101i
$29$	−1.60710	+	0.481133i	−0.298430	+	0.0893442i	−0.432518	−	0.901625i	$-0.642375\pi$
$29$	−1.60710	+	0.481133i	−0.298430	+	0.0893442i	0.134088	+	0.990969i	$0.457190\pi$
$30$	0.0795943		0.000124733i	0.0145319		2.27730e-5i
$31$	−5.26788	−	8.00942i	−0.946138	−	1.43853i	−0.898152	−	0.439686i	$-0.855090\pi$
$31$	−5.26788	−	8.00942i	−0.946138	−	1.43853i	−0.0479866	−	0.998848i	$-0.515280\pi$
$32$	−5.27061	−	2.05444i	−0.931720	−	0.363177i
$33$	−9.26178	−	2.02241i	−1.61227	−	0.352056i
$34$	7.85304	−	0.789502i	1.34679	−	0.135398i
$35$	−0.0303595	+	0.0110499i	−0.00513169	+	0.00186778i
$36$	−5.83390	+	1.40199i	−0.972317	+	0.233664i
$37$	−6.57185	−	2.39196i	−1.08041	−	0.393236i	−0.260347	−	0.965515i	$-0.583837\pi$
$37$	−6.57185	−	2.39196i	−1.08041	−	0.393236i	−0.820059	+	0.572279i	$0.806059\pi$
$38$	−0.540136	−	0.137268i	−0.0876216	−	0.0222678i
$39$	−1.11515	−	2.46417i	−0.178566	−	0.394583i
$40$	−0.0305946	+	0.0866660i	−0.00483744	+	0.0137031i
$41$	1.69763	−	1.60163i	0.265125	−	0.250132i	−0.542186	−	0.840258i	$-0.682403\pi$
$41$	1.69763	−	1.60163i	0.265125	−	0.250132i	0.807311	+	0.590126i	$0.200922\pi$
$42$	2.03268	−	1.34148i	0.313649	−	0.206995i
$43$	−4.21206	+	3.13576i	−0.642333	+	0.478199i	−0.868368	−	0.495920i	$-0.834831\pi$
$43$	−4.21206	+	3.13576i	−0.642333	+	0.478199i	0.226035	+	0.974119i	$0.427424\pi$
$44$	5.77672	−	9.29823i	0.870874	−	1.40176i
$45$	0.0258288	+	0.0939989i	0.00385033	+	0.0140125i
$46$	9.77747	+	5.85767i	1.44161	+	0.863666i
$47$	7.16150	+	4.71019i	1.04461	+	0.687052i	0.951200	−	0.308576i	$-0.0998523\pi$
$47$	7.16150	+	4.71019i	1.04461	+	0.687052i	0.0934117	+	0.995628i	$0.470223\pi$
$48$	0.726696	−	6.88999i	0.104890	−	0.994484i
$49$	3.58978	−	4.82192i	0.512826	−	0.688845i
$50$	−6.73894	−	2.13673i	−0.953029	−	0.302180i
$51$	3.46660	+	9.02348i	0.485421	+	1.26354i
$52$	3.11215	−	0.262164i	0.431578	−	0.0363556i
$53$	3.35957	−	1.93965i	0.461473	−	0.266431i	−0.251191	−	0.967938i	$-0.580822\pi$
$53$	3.35957	−	1.93965i	0.461473	−	0.266431i	0.712663	+	0.701506i	$0.247489\pi$
$54$	−3.53875	−	6.44028i	−0.481563	−	0.876411i
$55$	−0.154023	−	0.0889253i	−0.0207685	−	0.0119907i
$56$	0.675065	+	2.72997i	0.0902093	+	0.364808i
$57$	−0.0120974	−	0.682449i	−0.00160234	−	0.0903926i
$58$	2.31704	−	0.509755i	0.304242	−	0.0669341i
$59$	3.05504	+	7.08237i	0.397732	+	0.922046i	0.992956	+	0.118486i	$0.0378041\pi$
$59$	3.05504	+	7.08237i	0.397732	+	0.922046i	−0.595224	+	0.803560i	$0.702937\pi$
$60$	−0.112266	−	0.00818379i	−0.0144934	−	0.00105652i
$61$	0.0769563	−	1.32129i	0.00985325	−	0.169174i	−0.989792	−	0.142523i	$-0.954479\pi$
$61$	0.0769563	−	1.32129i	0.00985325	−	0.169174i	0.999645	−	0.0266511i	$-0.00848432\pi$
$62$	6.58811	+	11.8490i	0.836691	+	1.50483i
$63$	2.24078	+	1.96873i	0.282312	+	0.248037i
$64$	7.21740	+	3.45096i	0.902175	+	0.431370i
$65$	−0.00589087	−	0.0503996i	−0.000730673	−	0.00625130i
$66$	12.8495	+	3.82497i	1.58167	+	0.470821i
$67$	−2.85205	−	0.853849i	−0.348434	−	0.104314i	0.107804	−	0.994172i	$-0.465618\pi$
$67$	−2.85205	−	0.853849i	−0.348434	−	0.104314i	−0.456238	+	0.889858i	$0.650803\pi$
$68$	−11.1581	+	0.288645i	−1.35312	+	0.0350033i
$69$	−3.76597	+	13.4419i	−0.453370	+	1.61821i
$70$	0.0439768	−	0.0123952i	0.00525623	−	0.00148151i
$71$	4.98620	−	4.18392i	0.591754	−	0.496540i	−0.297029	−	0.954868i	$-0.595996\pi$
$71$	4.98620	−	4.18392i	0.591754	−	0.496540i	0.888783	+	0.458328i	$0.151552\pi$
$72$	8.37485	−	1.36450i	0.986986	−	0.160808i
$73$	1.85640	+	1.55770i	0.217275	+	0.182315i	0.744928	−	0.667144i	$-0.232484\pi$
$73$	1.85640	+	1.55770i	0.217275	+	0.182315i	−0.527653	+	0.849460i	$0.676928\pi$
$74$	9.01711	+	4.06363i	1.04822	+	0.472388i
$75$	0.350165	−	8.65134i	0.0404335	−	0.998971i
$76$	0.747340	+	0.250320i	0.0857258	+	0.0287137i
$77$	−5.43268	+	0.316418i	−0.619111	+	0.0360591i
$78$	1.31389	+	3.59236i	0.148769	+	0.406755i
$79$	4.37177	+	4.12455i	0.491862	+	0.464048i	0.891758	−	0.452512i	$-0.149472\pi$
$79$	4.37177	+	4.12455i	0.491862	+	0.464048i	−0.399896	+	0.916561i	$0.630954\pi$
$80$	0.0522503	−	0.119012i	0.00584176	−	0.0133060i
$81$	6.46727	−	6.25895i	0.718586	−	0.695438i
$82$	−2.56240	+	2.08049i	−0.282969	+	0.229752i
$83$	7.99493	−	8.47413i	0.877557	−	0.930156i	−0.120484	−	0.992715i	$-0.538445\pi$
$83$	7.99493	−	8.47413i	0.877557	−	0.930156i	0.998041	+	0.0625588i	$0.0199261\pi$
$84$	−3.00760	+	1.67841i	−0.328156	+	0.183130i
$85$	0.0105445	+	0.181042i	0.00114371	+	0.0196367i
$86$	6.26965	−	3.98000i	0.676073	−	0.429175i
$87$	1.34987	+	2.57306i	0.144721	+	0.275861i
$88$	−9.12354	+	12.5066i	−0.972573	+	1.33321i
$89$	4.18508	−	4.98758i	0.443617	−	0.528683i	−0.497182	−	0.867646i	$-0.665632\pi$
$89$	4.18508	−	4.98758i	0.443617	−	0.528683i	0.940800	+	0.338964i	$0.110076\pi$
$90$	−0.0265540	−	0.135280i	−0.00279903	−	0.0142598i
$91$	−0.998011	−	1.18938i	−0.104620	−	0.124681i
$92$	−13.1740	−	9.28803i	−1.37349	−	0.968344i
$93$	−11.8737	+	11.6069i	−1.23125	+	1.20357i
$94$	−9.60521	−	7.39498i	−0.990702	−	0.762734i
$95$	0.00367256	−	0.0122672i	0.000376797	−	0.00125859i
$96$	−1.74851	+	9.64068i	−0.178457	+	0.983948i
$97$	16.7230	−	1.95464i	1.69796	−	0.198464i	0.788728	−	0.614743i	$-0.210740\pi$
$97$	16.7230	−	1.95464i	1.69796	−	0.198464i	0.909237	+	0.416279i	$0.136666\pi$
$98$	−5.56914	+	6.42336i	−0.562568	+	0.648857i
$99$	−0.373168	+	16.4156i	−0.0375048	+	1.64983i
$100$	9.27956	+	3.72124i	0.927956	+	0.372124i
$101$	12.8954	+	0.751070i	1.28314	+	0.0747343i	0.686117	−	0.727491i	$-0.259314\pi$
$101$	12.8954	+	0.751070i	1.28314	+	0.0747343i	0.597021	+	0.802226i	$0.296351\pi$
$102$	−3.94124	−	13.0900i	−0.390241	−	1.29610i
$103$	−3.77204	+	1.62710i	−0.371670	+	0.160323i	−0.573718	−	0.819053i	$-0.694500\pi$
$103$	−3.77204	+	1.62710i	−0.371670	+	0.160323i	0.202048	+	0.979376i	$0.435240\pi$
$104$	−4.41663	+	0.0428663i	−0.433086	+	0.00420338i
$105$	0.0288340	+	0.0479583i	0.00281391	+	0.00468025i
$106$	−4.94175	+	2.38265i	−0.479985	+	0.231423i
$107$	1.71144	−	2.96431i	0.165451	−	0.286570i	−0.771364	−	0.636394i	$-0.780425\pi$
$107$	1.71144	−	2.96431i	0.165451	−	0.286570i	0.936816	+	0.349824i	$0.113759\pi$
$108$	4.31431	+	9.45445i	0.415145	+	0.909755i
$109$	0.134908	+	0.233667i	0.0129218	+	0.0223813i	0.872414	−	0.488768i	$-0.162553\pi$
$109$	0.134908	+	0.233667i	0.0129218	+	0.0223813i	−0.859492	+	0.511149i	$0.829220\pi$
$110$	0.207880	+	0.141589i	0.0198206	+	0.0135000i
$111$	−1.89169	+	11.9647i	−0.179552	+	1.13564i
$112$	−0.665323	−	3.92101i	−0.0628671	−	0.370500i
$113$	11.6466	+	8.67057i	1.09562	+	0.815659i	0.984014	−	0.178094i	$-0.0569930\pi$
$113$	11.6466	+	8.67057i	1.09562	+	0.815659i	0.111607	+	0.993752i	$0.464400\pi$
$114$	−0.0546159	+	0.963734i	−0.00511525	+	0.0902620i
$115$	−0.143910	+	0.218804i	−0.0134197	+	0.0204036i
$116$	−3.32127	+	0.475555i	−0.308372	+	0.0441542i
$117$	−3.82037	+	2.71142i	−0.353193	+	0.250671i
$118$	−3.56469	−	10.3092i	−0.328156	−	0.949038i
$119$	3.31358	+	4.45091i	0.303755	+	0.408014i
$120$	0.157470	+	0.0233328i	0.0143749	+	0.00212998i
$121$	−13.0090	−	13.7887i	−1.18264	−	1.25352i
$122$	−0.247306	+	1.85534i	−0.0223900	+	0.167975i
$123$	−3.28482	−	2.35614i	−0.296183	−	0.212446i
$124$	−8.04677	−	17.4027i	−0.722621	−	1.56281i
$125$	0.111125	−	0.305314i	0.00993935	−	0.0273081i
$126$	−2.95342	−	3.01187i	−0.263112	−	0.268319i
$127$	−2.80049	−	7.69428i	−0.248503	−	0.682757i	−0.999742	−	0.0227260i	$-0.992765\pi$
$127$	−2.80049	−	7.69428i	−0.248503	−	0.682757i	0.751239	−	0.660031i	$-0.229457\pi$
$128$	−9.81631	−	5.62495i	−0.867647	−	0.497180i
$129$	6.72522	+	6.12330i	0.592122	+	0.539126i
$130$	0.00301453	+	0.0716977i	0.000264391	+	0.00628830i
$131$	−4.87826	+	3.20848i	−0.426216	+	0.280326i	−0.744440	−	0.667689i	$-0.767284\pi$
$131$	−4.87826	+	3.20848i	−0.426216	+	0.280326i	0.318225	+	0.948015i	$0.396913\pi$
$132$	−17.7201	−	6.74396i	−1.54234	−	0.586986i
$133$	−0.112373	−	0.375353i	−0.00974400	−	0.0325472i
$134$	3.93260	+	1.50374i	0.339725	+	0.129903i
$135$	0.151263	−	0.0750216i	0.0130186	−	0.00645684i
$136$	15.7667	+	0.764848i	1.35198	+	0.0655852i
$137$	3.15393	−	13.3075i	0.269458	−	1.13693i	−0.654993	−	0.755635i	$-0.727328\pi$
$137$	3.15393	−	13.3075i	0.269458	−	1.13693i	0.924452	−	0.381300i	$-0.124523\pi$
$138$	6.72297	−	18.5617i	0.572297	−	1.58007i
$139$	1.91094	−	3.80499i	0.162083	−	0.322735i	−0.797901	−	0.602789i	$-0.794056\pi$
$139$	1.91094	−	3.80499i	0.162083	−	0.322735i	0.959984	+	0.280054i	$0.0903524\pi$
$140$	−0.0633226	+	0.0128622i	−0.00535174	+	0.00108706i
$141$	5.63786	−	13.7344i	0.474794	−	1.15664i
$142$	−7.47152	+	5.37692i	−0.626996	+	0.451221i
$143$	1.48418	−	8.41718i	0.124113	−	0.703880i
$144$	−11.9544	+	1.04477i	−0.996203	+	0.0870643i
$145$	0.00946583	+	0.0536834i	0.000786094	+	0.00445816i
$146$	−2.45449	−	2.39182i	−0.203135	−	0.197948i
$147$	−9.38597	−	4.50731i	−0.774142	−	0.371756i
$148$	−12.2901	−	6.67803i	−1.01024	−	0.548931i
$149$	5.43406	+	22.9281i	0.445176	+	1.87834i	0.477092	+	0.878853i	$0.341691\pi$
$149$	5.43406	+	22.9281i	0.445176	+	1.87834i	−0.0319164	+	0.999491i	$0.510161\pi$
$150$	−1.40248	+	12.1643i	−0.114512	+	0.993209i
$151$	−1.62762	−	0.702088i	−0.132454	−	0.0571351i	0.328821	−	0.944392i	$-0.393349\pi$
$151$	−1.62762	−	0.702088i	−0.132454	−	0.0571351i	−0.461275	+	0.887257i	$0.652608\pi$
$152$	−1.02769	−	0.431521i	−0.0833566	−	0.0350010i
$153$	14.1939	−	8.88003i	1.14751	−	0.717908i
$154$	7.69499	+	0.124342i	0.620080	+	0.0100198i
$155$	−0.278373	+	0.139804i	−0.0223594	+	0.0112293i
$156$	−1.47569	−	5.20433i	−0.118150	−	0.416680i
$157$	−4.99607	−	0.583957i	−0.398730	−	0.0466048i	−0.0856346	−	0.996327i	$-0.527292\pi$
$157$	−4.99607	−	0.583957i	−0.398730	−	0.0466048i	−0.313095	+	0.949722i	$0.601366\pi$
$158$	−5.73234	−	6.27605i	−0.456041	−	0.499296i
$159$	−4.40953	−	5.06980i	−0.349698	−	0.402062i
$160$	−0.0861888	+	0.162356i	−0.00681382	+	0.0128354i
$161$			8.01327i			0.631534i
$162$	−9.77821	+	8.14779i	−0.768249	+	0.640151i
$163$		−	3.05985i		−	0.239666i	−0.992794	−	0.119833i	$-0.961764\pi$
$163$		−	3.05985i		−	0.239666i	0.992794	−	0.119833i	$-0.0382359\pi$
$164$	3.83228	−	2.66501i	0.299251	−	0.208102i
$165$	−0.100211	+	0.291291i	−0.00780142	+	0.0226769i
$166$	−12.1653	+	11.1114i	−0.944213	+	0.862415i
$167$	−21.1256	−	2.46922i	−1.63474	−	0.191074i	−0.751416	−	0.659828i	$-0.770629\pi$
$167$	−21.1256	−	2.46922i	−1.63474	−	0.191074i	−0.883329	+	0.468754i	$0.844703\pi$
$168$	4.41792	−	2.05119i	0.340850	−	0.158253i
$169$	−9.43805	+	4.73997i	−0.726004	+	0.364613i
$170$	0.00414364	−	0.256432i	0.000317803	−	0.0196674i
$171$	−1.15625	+	0.246425i	−0.0884210	+	0.0188446i
$172$	−9.26015	+	4.95453i	−0.706080	+	0.377780i
$173$	−9.12461	−	3.93597i	−0.693731	−	0.299246i	0.0198660	−	0.999803i	$-0.493676\pi$
$173$	−9.12461	−	3.93597i	−0.693731	−	0.299246i	−0.713597	+	0.700556i	$0.752935\pi$
$174$	−1.63348	−	3.77058i	−0.123834	−	0.285847i
$175$	−1.14622	−	4.83629i	−0.0866462	−	0.365589i
$176$	14.1806	−	16.6800i	1.06890	−	1.25730i
$177$	11.0299	−	7.53791i	0.829061	−	0.566584i
$178$	−6.42609	+	6.59447i	−0.481656	+	0.494277i
$179$	1.99745	+	11.3281i	0.149296	+	0.846701i	0.963817	+	0.266566i	$0.0858890\pi$
$179$	1.99745	+	11.3281i	0.149296	+	0.846701i	−0.814520	+	0.580135i	$0.803000\pi$
$180$	0.0232410	+	0.193576i	0.00173228	+	0.0144283i
$181$	1.25484	−	7.11653i	0.0932712	−	0.528967i	−0.901992	−	0.431752i	$-0.857895\pi$
$181$	1.25484	−	7.11653i	0.0932712	−	0.528967i	0.995263	−	0.0972150i	$-0.0309934\pi$
$182$	1.28258	+	1.78222i	0.0950714	+	0.132107i
$183$	−2.27184	+	0.306447i	−0.167939	+	0.0226532i
$184$	17.6039	+	14.4826i	1.29778	+	1.06767i
$185$	−0.101991	+	0.203080i	−0.00749852	+	0.0149308i
$186$	17.9646	−	15.1222i	1.31723	−	1.10881i
$187$	−7.04440	+	29.7227i	−0.515138	+	2.17354i
$188$	12.7696	+	11.4380i	0.931320	+	0.834204i
$189$	2.60553	−	4.46120i	0.189524	−	0.324505i
$190$	−0.00646786	+	0.0169148i	−0.000469228	+	0.00122713i
$191$	−2.64443	−	8.83301i	−0.191344	−	0.639134i	−0.998789	−	0.0491917i	$-0.984335\pi$
$191$	−2.64443	−	8.83301i	−0.191344	−	0.639134i	0.807445	−	0.589943i	$-0.200850\pi$
$192$	3.47849	−	13.4127i	0.251039	−	0.967977i
$193$	10.0055	−	6.58070i	0.720209	−	0.473689i	−0.135743	−	0.990744i	$-0.543342\pi$
$193$	10.0055	−	6.58070i	0.720209	−	0.473689i	0.855952	+	0.517055i	$0.172972\pi$
$194$	−23.7899	+	1.00025i	−1.70801	+	0.0718134i
$195$	−0.0837367	+	0.0266952i	−0.00599651	+	0.00191168i
$196$	8.52884	−	8.47399i	0.609203	−	0.605285i
$197$	8.75781	+	24.0619i	0.623968	+	1.71434i	0.697059	+	0.717014i	$0.254492\pi$
$197$	8.75781	+	24.0619i	0.623968	+	1.71434i	−0.0730904	+	0.997325i	$0.523286\pi$
$198$	2.25040	−	23.1119i	0.159929	−	1.64249i
$199$	0.550405	−	1.51223i	0.0390172	−	0.107199i	−0.918654	−	0.395063i	$-0.870723\pi$
$199$	0.550405	−	1.51223i	0.0390172	−	0.107199i	0.957671	+	0.287864i	$0.0929451\pi$
$200$	−12.6962	−	6.22271i	−0.897757	−	0.440012i
$201$	−0.507768	+	5.13147i	−0.0358152	+	0.361946i
$202$	−18.1076	−	2.41363i	−1.27404	−	0.169822i
$203$	1.14462	+	1.21322i	0.0803363	+	0.0851515i
$204$	4.18354	+	18.8748i	0.292907	+	1.32150i
$205$	−0.0452878	−	0.0608321i	−0.00316304	−	0.00424870i
$206$	5.49063	−	1.89854i	0.382550	−	0.132277i
$207$	24.0994	+	1.95406i	1.67503	+	0.135816i
$208$	6.23331	+	0.403419i	0.432203	+	0.0279721i
$209$	1.18523	−	1.80205i	0.0819838	−	0.124650i
$210$	−0.0356278	−	0.0706644i	−0.00245855	−	0.00487630i
$211$	8.40566	+	6.25778i	0.578669	+	0.430803i	0.846291	−	0.532721i	$-0.178830\pi$
$211$	8.40566	+	6.25778i	0.578669	+	0.430803i	−0.267622	+	0.963524i	$0.586238\pi$
$212$	7.21964	−	2.84125i	0.495847	−	0.195138i
$213$	−8.76344	−	7.09256i	−0.600461	−	0.485974i
$214$	−2.72500	+	4.00084i	−0.186277	+	0.273491i
$215$	0.0853160	+	0.147772i	0.00581850	+	0.0100779i
$216$	−5.09152	−	13.7868i	−0.346434	−	0.938074i
$217$	−4.76576	+	8.25453i	−0.323521	+	0.560354i
$218$	−0.165720	−	0.343712i	−0.0112240	−	0.0232791i
$219$	2.03393	−	3.67166i	0.137440	−	0.248108i
$220$	−0.278304	−	0.221518i	−0.0187633	−	0.0149347i
$221$	−8.00236	+	3.45188i	−0.538297	+	0.232199i
$222$	3.92451	−	16.6752i	0.263396	−	1.11917i
$223$	−23.3866	−	1.36211i	−1.56608	−	0.0912138i	−0.746973	−	0.664855i	$-0.768493\pi$
$223$	−23.3866	−	1.36211i	−1.56608	−	0.0912138i	−0.819107	+	0.573641i	$0.805531\pi$
$224$	0.526492	+	5.59970i	0.0351777	+	0.374146i
$225$	−14.8244	+	2.26785i	−0.988291	+	0.151190i
$226$	−15.5146	−	13.4514i	−1.03202	−	0.894774i
$227$	22.7306	−	2.65683i	1.50868	−	0.176340i	0.678819	−	0.734306i	$-0.262492\pi$
$227$	22.7306	−	2.65683i	1.50868	−	0.176340i	0.829864	+	0.557966i	$0.188418\pi$
$228$	0.178245	−	1.35343i	0.0118046	−	0.0896328i
$229$	0.900767	−	3.00877i	0.0595243	−	0.198825i	−0.923055	−	0.384667i	$-0.874316\pi$
$229$	0.900767	−	3.00877i	0.0595243	−	0.198825i	0.982580	+	0.185842i	$0.0595013\pi$
$230$	0.225938	−	0.293467i	0.0148979	−	0.0193506i
$231$	2.33591	+	9.13159i	0.153692	+	0.600815i
$232$	4.73396	−	0.321850i	0.310800	−	0.0211305i
$233$	−12.0023	−	14.3037i	−0.786295	−	0.937070i	0.212905	−	0.977073i	$-0.431708\pi$
$233$	−12.0023	−	14.3037i	−0.786295	−	0.937070i	−0.999200	+	0.0400032i	$0.987263\pi$
$234$	5.67267	−	3.42270i	0.370834	−	0.223749i
$235$	0.179035	−	0.213366i	0.0116790	−	0.0139184i
$236$	3.94455	+	14.9135i	0.256768	+	0.970788i
$237$	5.56546	−	8.79764i	0.361516	−	0.571468i
$238$	−4.20570	−	6.62518i	−0.272615	−	0.429447i
$239$	1.01712	+	17.4633i	0.0657920	+	1.12960i	0.856071	+	0.516858i	$0.172898\pi$
$239$	1.01712	+	17.4633i	0.0657920	+	1.12960i	−0.790279	+	0.612747i	$0.790065\pi$
$240$	−0.219630	−	0.0494453i	−0.0141771	−	0.00319168i
$241$	−8.31228	+	8.81050i	−0.535441	+	0.567534i	−0.937458	−	0.348098i	$-0.886828\pi$
$241$	−8.31228	+	8.81050i	−0.535441	+	0.567534i	0.402017	+	0.915632i	$0.368309\pi$
$242$	16.8985	+	20.8127i	1.08628	+	1.33789i
$243$	−12.7814	−	8.92385i	−0.819929	−	0.572465i
$244$	0.543642	−	2.59063i	0.0348031	−	0.165848i
$245$	−0.142083	−	0.134049i	−0.00907737	−	0.00856406i
$246$	4.38515	+	3.66788i	0.279587	+	0.233856i
$247$	0.614341	−	0.0357813i	0.0390896	−	0.00227671i
$248$	9.52064	+	25.3883i	0.604561	+	1.61216i
$249$	−17.0531	−	10.7880i	−1.08070	−	0.683659i
$250$	−0.188788	+	0.418916i	−0.0119400	+	0.0264946i
$251$	0.569519	+	0.477883i	0.0359477	+	0.0301637i	0.660585	−	0.750752i	$-0.270309\pi$
$251$	0.569519	+	0.477883i	0.0359477	+	0.0301637i	−0.624637	+	0.780915i	$0.714753\pi$
$252$	3.84890	+	4.55786i	0.242458	+	0.287118i
$253$	−33.7917	+	28.3546i	−2.12447	+	1.78264i
$254$	3.14143	+	11.1454i	0.197111	+	0.699327i
$255$	0.304306	−	0.0778432i	0.0190564	−	0.00487473i
$256$	13.2532	+	8.96391i	0.828327	+	0.560244i
$257$	18.6131	+	5.57239i	1.16105	+	0.347596i	0.808671	−	0.588261i	$-0.200187\pi$
$257$	18.6131	+	5.57239i	1.16105	+	0.347596i	0.352380	+	0.935857i	$0.385372\pi$
$258$	−8.84151	−	9.34208i	−0.550448	−	0.581612i
$259$	0.807252	+	6.90648i	0.0501602	+	0.429148i
$260$	0.00327892	−	0.101432i	0.000203350	−	0.00629057i
$261$	3.92781	−	3.14652i	0.243125	−	0.194764i
$262$	7.21683	−	4.01259i	0.445857	−	0.247899i
$263$	−0.586735	+	10.0738i	−0.0361796	+	0.621180i	0.930674	+	0.365849i	$0.119221\pi$
$263$	−0.586735	+	10.0738i	−0.0361796	+	0.621180i	−0.966854	+	0.255331i	$0.917816\pi$
$264$	24.2825	+	11.3722i	1.49448	+	0.699910i
$265$	−0.0499279	−	0.115746i	−0.00306704	−	0.00711021i
$266$	0.119058	+	0.541166i	0.00729992	+	0.0331810i
$267$	−9.86464	−	5.46456i	−0.603706	−	0.334426i
$268$	−5.38824	−	2.53377i	−0.329139	−	0.154775i
$269$	−16.1995	−	9.35276i	−0.987698	−	0.570248i	−0.0831129	−	0.996540i	$-0.526486\pi$
$269$	−16.1995	−	9.35276i	−0.987698	−	0.570248i	−0.904586	+	0.426292i	$0.859820\pi$
$270$	−0.221207	+	0.0899167i	−0.0134622	+	0.00547215i
$271$	18.3097	−	10.5711i	1.11224	−	0.642150i	0.172829	−	0.984952i	$-0.444709\pi$
$271$	18.3097	−	10.5711i	1.11224	−	0.642150i	0.939408	+	0.342801i	$0.111376\pi$
$272$	−22.1556	−	2.73463i	−1.34338	−	0.165811i
$273$	−1.69182	+	2.09039i	−0.102394	+	0.126516i
$274$	−5.84568	+	18.4364i	−0.353151	+	1.11378i
$275$	16.3387	−	21.9466i	0.985258	−	1.32343i
$276$	−11.4310	+	25.4716i	−0.688064	+	1.53321i
$277$	23.7029	+	15.5896i	1.42417	+	0.936690i	0.999509	+	0.0313367i	$0.00997641\pi$
$277$	23.7029	+	15.5896i	1.42417	+	0.936690i	0.424659	+	0.905353i	$0.360394\pi$
$278$	−3.09464	+	5.16550i	−0.185604	+	0.309806i
$279$	23.6629	+	16.3456i	1.41666	+	0.978587i
$280$	0.0906553	−	0.0114890i	0.00541769	−	0.000686599i
$281$	−4.31000	+	3.20868i	−0.257113	+	0.191414i	−0.717996	−	0.696047i	$-0.754940\pi$
$281$	−4.31000	+	3.20868i	−0.257113	+	0.191414i	0.460883	+	0.887461i	$0.347533\pi$
$282$	−9.39363	+	18.7776i	−0.559383	+	1.11819i
$283$	15.4857	−	14.6100i	0.920532	−	0.868477i	−0.0711138	−	0.997468i	$-0.522655\pi$
$283$	15.4857	−	14.6100i	0.920532	−	0.868477i	0.991646	+	0.128991i	$0.0411739\pi$
$284$	11.1019	−	6.79839i	0.658775	−	0.403411i
$285$	−0.0220714	−	0.00218401i	−0.00130740	−	0.000129369i
$286$	−2.97719	+	11.7149i	−0.176045	+	0.692718i
$287$	−2.18058	−	0.793666i	−0.128716	−	0.0468486i
$288$	16.9692	−	0.217888i	0.999918	−	0.0128392i
$289$	13.2936	−	4.83849i	0.781979	−	0.284617i
$290$	−0.00771143	−	0.0767043i	−0.000452831	−	0.00450423i
$291$	−8.85767	−	27.7845i	−0.519246	−	1.62876i
$292$	3.21038	+	3.63099i	0.187873	+	0.212488i
$293$	−6.61681	−	10.0604i	−0.386558	−	0.587733i	0.588822	−	0.808262i	$-0.299592\pi$
$293$	−6.61681	−	10.0604i	−0.386558	−	0.587733i	−0.975380	+	0.220530i	$0.929221\pi$
$294$	12.7637	+	7.34249i	0.744395	+	0.428223i
$295$	0.240105	−	0.0718827i	0.0139795	−	0.00418518i
$296$	16.6315	+	10.7089i	0.966684	+	0.622442i
$297$	28.0323	−	4.79835i	1.62660	−	0.278428i
$298$	−5.25559	−	32.9064i	−0.304448	−	1.90622i
$299$	−12.2464	−	2.90245i	−0.708227	−	0.167853i
$300$	3.25553	−	17.0081i	0.187958	−	0.981962i
$301$	4.66567	+	2.34319i	0.268924	+	0.135059i
$302$	2.22171	+	1.16111i	0.127845	+	0.0668143i
$303$	−2.99083	−	22.1725i	−0.171819	−	1.27378i
$304$	1.40404	+	0.716515i	0.0805270	+	0.0410949i
$305$	−0.0423537	−	0.00746811i	−0.00242517	−	0.000427623i
$306$	−20.9504	+	11.0328i	−1.19765	+	0.630704i
$307$	4.84434	−	0.854188i	0.276481	−	0.0487511i	−0.0336882	−	0.999432i	$-0.510725\pi$
$307$	4.84434	−	0.854188i	0.276481	−	0.0487511i	0.310169	+	0.950681i	$0.399614\pi$
$308$	−10.8392	−	0.983556i	−0.617623	−	0.0560433i
$309$	4.01466	+	5.87450i	0.228386	+	0.334188i
$310$	0.407275	−	0.167930i	0.0231317	−	0.00953776i
$311$	−15.5123	+	3.67648i	−0.879622	+	0.208474i	−0.645525	−	0.763739i	$-0.723361\pi$
$311$	−15.5123	+	3.67648i	−0.879622	+	0.208474i	−0.234097	+	0.972213i	$0.575213\pi$
$312$	1.53457	+	7.49470i	0.0868780	+	0.424304i
$313$	13.4172	−	31.1045i	0.758382	−	1.75813i	0.113923	−	0.993490i	$-0.463658\pi$
$313$	13.4172	−	31.1045i	0.758382	−	1.75813i	0.644460	−	0.764638i	$-0.277082\pi$
$314$	6.98466	+	1.34829i	0.394167	+	0.0760884i
$315$	0.0719931	−	0.0648936i	0.00405635	−	0.00365634i
$316$	7.42520	+	9.45322i	0.417700	+	0.531785i
$317$	4.90781	+	9.77226i	0.275650	+	0.548865i	0.988276	−	0.152680i	$-0.0487904\pi$
$317$	4.90781	+	9.77226i	0.275650	+	0.548865i	−0.712625	+	0.701545i	$0.752494\pi$
$318$	5.68632	+	7.61311i	0.318873	+	0.426922i
$319$	−1.06595	+	9.11976i	−0.0596815	+	0.510608i
$320$	0.138605	−	0.219920i	0.00774824	−	0.0122939i
$321$	−5.60614	−	1.92865i	−0.312904	−	0.107647i
$322$	0.841625	−	11.3012i	0.0469019	−	0.629790i
$323$	−2.19930			−0.122372
$324$	14.6460	−	10.4639i	0.813669	−	0.581328i
$325$	7.80630			0.433015
$326$	−0.321372	+	4.31533i	−0.0177992	+	0.239004i
$327$	0.352619	−	0.306695i	0.0194999	−	0.0169603i
$328$	−5.68460	+	3.35598i	−0.313879	+	0.185303i
$329$	0.989397	−	8.46483i	0.0545472	−	0.466681i
$330$	0.171922	−	0.400285i	0.00946402	−	0.0220349i
$331$	14.1498	+	28.1745i	0.777743	+	1.54861i	0.834998	+	0.550253i	$0.185469\pi$
$331$	14.1498	+	28.1745i	0.777743	+	1.54861i	−0.0572551	+	0.998360i	$0.518235\pi$
$332$	18.3239	−	14.3928i	1.00565	−	0.789909i
$333$	20.9677	−	0.743596i	1.14902	−	0.0407488i
$334$	29.5342	+	5.70116i	1.61604	+	0.311954i
$335$	−0.0383166	+	0.0888278i	−0.00209346	+	0.00485318i
$336$	−6.44606	+	2.42881i	−0.351662	+	0.132502i
$337$	−21.2901	+	5.04584i	−1.15974	+	0.274865i	−0.765064	−	0.643954i	$-0.777293\pi$
$337$	−21.2901	+	5.04584i	−1.15974	+	0.274865i	−0.394680	+	0.918819i	$0.629145\pi$
$338$	13.8084	−	5.69354i	0.751077	−	0.309688i
$339$	10.8867	−	22.6704i	0.591285	−	1.23129i
$340$	−0.0327766	+	0.361213i	−0.00177756	+	0.0195895i
$341$	−51.6726	+	9.11128i	−2.79823	+	0.493403i
$342$	1.65656	−	0.226095i	0.0895763	−	0.0122258i
$343$	−12.7403	−	2.24645i	−0.687909	−	0.121297i
$344$	13.5800	−	6.01484i	0.732186	−	0.324298i
$345$	0.419625	+	0.172253i	0.0225918	+	0.00927378i
$346$	12.4551	+	6.50928i	0.669591	+	0.349941i
$347$	−18.8346	−	9.45911i	−1.01110	−	0.507791i	−0.135470	−	0.990781i	$-0.543254\pi$
$347$	−18.8346	−	9.45911i	−1.01110	−	0.507791i	−0.875626	+	0.482990i	$0.839551\pi$
$348$	1.90769	+	5.48924i	0.102263	+	0.294254i
$349$	−22.7755	−	5.39789i	−1.21914	−	0.288942i	−0.429817	−	0.902916i	$-0.641422\pi$
$349$	−22.7755	−	5.39789i	−1.21914	−	0.288942i	−0.789327	+	0.613973i	$0.789570\pi$
$350$	1.10858	+	6.94105i	0.0592559	+	0.371015i
$351$	5.87416	+	5.59780i	0.313539	+	0.298789i
$352$	−21.7508	+	22.0345i	−1.15932	+	1.17445i
$353$	27.3527	−	8.18885i	1.45583	−	0.435848i	0.541463	−	0.840724i	$-0.317871\pi$
$353$	27.3527	−	8.18885i	1.45583	−	0.435848i	0.914372	+	0.404876i	$0.132685\pi$
$354$	−16.3473	+	9.47231i	−0.868849	+	0.503448i
$355$	−0.116225	−	0.176711i	−0.00616856	−	0.00937884i
$356$	9.75538	−	8.62531i	0.517034	−	0.457141i
$357$	6.47053	−	7.10659i	0.342457	−	0.376120i
$358$	−1.62724	−	16.1859i	−0.0860023	−	0.855450i
$359$	2.55128	−	0.928590i	0.134651	−	0.0490091i	−0.273815	−	0.961782i	$-0.588286\pi$
$359$	2.55128	−	0.928590i	0.134651	−	0.0490091i	0.408467	+	0.912773i	$0.366064\pi$
$360$	−0.0124459	−	0.275442i	−0.000655956	−	0.0145171i
$361$	−17.7082	−	6.44527i	−0.932012	−	0.339225i
$362$	−2.51715	+	9.90470i	−0.132298	+	0.520580i
$363$	−19.1374	+	26.6805i	−1.00445	+	1.40036i
$364$	−1.62165	−	2.64818i	−0.0849978	−	0.138803i
$365$	0.0572772	−	0.0540383i	0.00299803	−	0.00282849i
$366$	3.23618	−	0.193575i	0.169158	−	0.0101183i
$367$	25.1932	−	18.7557i	1.31508	−	0.979038i	0.315530	−	0.948916i	$-0.397818\pi$
$367$	25.1932	−	18.7557i	1.31508	−	0.979038i	0.999546	−	0.0301219i	$-0.00958956\pi$
$368$	−23.3059	−	22.2739i	−1.21490	−	1.16111i
$369$	−2.91864	+	6.36443i	−0.151939	+	0.331319i
$370$	0.165168	−	0.275694i	0.00858667	−	0.0143327i
$371$	−3.22251	−	2.11948i	−0.167304	−	0.110038i
$372$	−26.9239	+	19.4401i	−1.39594	+	1.00792i
$373$	−12.0829	+	16.2302i	−0.625630	+	0.840367i	−0.996077	−	0.0884865i	$-0.971797\pi$
$373$	−12.0829	+	16.2302i	−0.625630	+	0.840367i	0.370447	+	0.928853i	$0.379204\pi$
$374$	13.0565	−	41.1783i	0.675136	−	2.12928i
$375$	−0.555854	−	0.0878840i	−0.0287042	−	0.00453831i
$376$	−16.8078	−	17.4723i	−0.866795	−	0.901066i
$377$	−2.26871	+	1.30984i	−0.116844	+	0.0674602i
$378$	−4.14315	+	6.01801i	−0.213101	+	0.309533i
$379$	−19.8735	−	11.4740i	−1.02083	−	0.589379i	−0.106488	−	0.994314i	$-0.533961\pi$
$379$	−19.8735	−	11.4740i	−1.02083	−	0.589379i	−0.914345	+	0.404935i	$0.867294\pi$
$380$	0.0108982	−	0.0231758i	0.000559067	−	0.00118889i
$381$	−12.1545	+	7.30765i	−0.622694	+	0.374382i
$382$	2.80174	+	12.7350i	0.143350	+	0.651580i
$383$	0.420235	+	0.974214i	0.0214730	+	0.0497800i	0.928615	−	0.371044i	$-0.121000\pi$
$383$	0.420235	+	0.974214i	0.0214730	+	0.0497800i	−0.907142	+	0.420824i	$0.861741\pi$
$384$	−6.31446	+	18.5507i	−0.322234	+	0.946660i
$385$	−0.0102818	+	0.176531i	−0.000524007	+	0.00899686i
$386$	−14.8020	+	8.22995i	−0.753399	+	0.418893i
$387$	8.18473	−	13.4603i	0.416053	−	0.684226i
$388$	33.6561	+	1.08797i	1.70863	+	0.0552334i
$389$	−2.54964	−	21.8136i	−0.129272	−	1.10599i	−0.889692	−	0.456560i	$-0.849081\pi$
$389$	−2.54964	−	21.8136i	−0.129272	−	1.10599i	0.760421	−	0.649431i	$-0.224993\pi$
$390$	0.120898	−	0.0288536i	0.00612193	−	0.00146106i
$391$	43.0899	+	12.9003i	2.17915	+	0.652395i
$392$	−12.9183	+	11.0552i	−0.652473	+	0.558370i
$393$	7.06933	+	7.23186i	0.356601	+	0.364799i
$394$	−9.82402	−	34.8545i	−0.494927	−	1.75594i
$395$	0.149610	−	0.125538i	0.00752770	−	0.00631649i
$396$	−5.60117	+	32.3585i	−0.281469	+	1.62608i
$397$	20.1401	+	16.8995i	1.01080	+	0.848164i	0.988444	−	0.151586i	$-0.0484381\pi$
$397$	20.1401	+	16.8995i	1.01080	+	0.848164i	0.0223582	+	0.999750i	$0.492883\pi$
$398$	−0.935068	+	2.07490i	−0.0468707	+	0.104005i
$399$	−0.600962	+	0.315274i	−0.0300857	+	0.0157834i
$400$	17.2520	+	10.1094i	0.862599	+	0.505470i
$401$	−3.48447	+	0.202947i	−0.174006	+	0.0101347i	−0.144927	−	0.989442i	$-0.546295\pi$
$401$	−3.48447	+	0.202947i	−0.174006	+	0.0101347i	−0.0290795	+	0.999577i	$0.509258\pi$
$402$	1.25506	−	7.18362i	0.0625968	−	0.358287i
$403$	−10.8889	−	10.2732i	−0.542416	−	0.511743i
$404$	25.2837	+	5.30577i	1.25791	+	0.263972i
$405$	−0.177608	−	0.232339i	−0.00882541	−	0.0115450i
$406$	−1.48684	−	1.83123i	−0.0737905	−	0.0908826i
$407$	−26.2680	+	27.8425i	−1.30206	+	1.38010i
$408$	−3.91768	−	27.0587i	−0.193954	−	1.33961i
$409$	0.100200	+	1.72037i	0.00495457	+	0.0850667i	0.999879	−	0.0155587i	$-0.00495268\pi$
$409$	0.100200	+	1.72037i	0.00495457	+	0.0850667i	−0.994924	+	0.100625i	$0.967916\pi$
$410$	0.0574807	+	0.0905486i	0.00283877	+	0.00447188i
$411$	−23.6684	−	0.957981i	−1.16747	−	0.0472537i
$412$	−7.94288	+	2.10085i	−0.391318	+	0.103501i
$413$	4.92949	−	5.87474i	0.242565	−	0.289077i
$414$	−33.7824	−	5.28696i	−1.66031	−	0.259840i
$415$	−0.243339	−	0.290000i	−0.0119451	−	0.0142356i
$416$	−8.74852	−	1.22362i	−0.428932	−	0.0599931i
$417$	−7.10143	−	1.98959i	−0.347759	−	0.0974305i
$418$	−1.86080	+	2.41696i	−0.0910147	+	0.118217i
$419$	1.19135	−	3.97938i	0.0582011	−	0.194405i	−0.923945	−	0.382526i	$-0.875054\pi$
$419$	1.19135	−	3.97938i	0.0582011	−	0.194405i	0.982146	+	0.188120i	$0.0602395\pi$
$420$	0.0428243	+	0.103400i	0.00208961	+	0.00504543i
$421$	−2.64793	+	0.309499i	−0.129052	+	0.0150841i	−0.180374	−	0.983598i	$-0.557731\pi$
$421$	−2.64793	+	0.309499i	−0.129052	+	0.0150841i	0.0513215	+	0.998682i	$0.483657\pi$
$422$	−11.1973	−	9.70824i	−0.545077	−	0.472590i
$423$	−25.2162	−	5.03973i	−1.22605	−	0.245040i
$424$	−10.4803	+	3.24876i	−0.508969	+	0.157774i
$425$	−27.8516	−	1.62217i	−1.35100	−	0.0786868i
$426$	11.6142	+	10.9231i	0.562711	+	0.529226i
$427$	−1.20831	+	0.521215i	−0.0584744	+	0.0252234i
$428$	4.26329	−	5.35621i	0.206074	−	0.258902i
$429$	−14.8016	+	0.262378i	−0.714626	+	0.0126677i
$430$	−0.104802	−	0.217364i	−0.00505398	−	0.0104822i
$431$	−9.87937	+	17.1116i	−0.475872	+	0.824235i	−0.999618	−	0.0276396i	$-0.991201\pi$
$431$	−9.87937	+	17.1116i	−0.475872	+	0.824235i	0.523746	+	0.851875i	$0.324534\pi$
$432$	5.73260	+	19.9784i	0.275810	+	0.961212i
$433$	−10.2404	−	17.7368i	−0.492120	−	0.852377i	0.507839	−	0.861452i	$-0.330445\pi$
$433$	−10.2404	−	17.7368i	−0.492120	−	0.852377i	−0.999959	+	0.00907492i	$0.997111\pi$
$434$	7.58815	−	11.1409i	0.364243	−	0.534780i
$435$	0.0881365	−	0.0338598i	0.00422582	−	0.00162346i
$436$	0.197616	+	0.502145i	0.00946410	+	0.0240484i
$437$	−2.54758	−	1.89660i	−0.121867	−	0.0907267i
$438$	−3.25410	+	4.96455i	−0.155487	+	0.237215i
$439$	6.52388	−	9.91907i	0.311368	−	0.473412i	−0.645572	−	0.763700i	$-0.723381\pi$
$439$	6.52388	−	9.91907i	0.311368	−	0.473412i	0.956939	+	0.290288i	$0.0937512\pi$
$440$	0.369229	+	0.341638i	0.0176023	+	0.0162869i
$441$	−4.55674	+	17.4492i	−0.216988	+	0.830912i
$442$	11.6483	−	4.02774i	0.554055	−	0.191580i
$443$	5.44671	+	7.31620i	0.258781	+	0.347603i	0.912458	−	0.409170i	$-0.134182\pi$
$443$	5.44671	+	7.31620i	0.258781	+	0.347603i	−0.653677	+	0.756774i	$0.726774\pi$
$444$	−7.28614	+	23.1050i	−0.345785	+	1.09651i
$445$	−0.145185	−	0.153887i	−0.00688241	−	0.00729492i
$446$	32.8392	+	4.37726i	1.55498	+	0.207269i
$447$	37.1825	−	16.8268i	1.75867	−	0.795879i
$448$	−0.154385	−	7.95261i	−0.00729400	−	0.375725i
$449$	6.80376	−	18.6932i	0.321089	−	0.882186i	−0.669190	−	0.743091i	$-0.733359\pi$
$449$	6.80376	−	18.6932i	0.321089	−	0.882186i	0.990279	−	0.139094i	$-0.0444190\pi$
$450$	21.1451	−	1.64138i	0.996790	−	0.0773755i
$451$	−4.36903	−	12.0038i	−0.205729	−	0.565237i
$452$	20.4676	+	20.6001i	0.962716	+	0.968948i
$453$	−0.654982	+	2.99954i	−0.0307737	+	0.140931i
$454$	−32.3362	+	1.35957i	−1.51761	+	0.0638079i
$455$	−0.0421517	+	0.0277236i	−0.00197610	+	0.00129970i
$456$	−0.393529	+	1.89003i	−0.0184287	+	0.0885086i
$457$	9.43111	+	31.5021i	0.441169	+	1.47361i	0.832847	+	0.553504i	$0.186710\pi$
$457$	9.43111	+	31.5021i	0.441169	+	1.47361i	−0.391678	+	0.920102i	$0.628105\pi$
$458$	−1.58637	+	4.14869i	−0.0741260	+	0.193855i
$459$	−19.7948	−	21.1927i	−0.923941	−	0.989190i
$460$	−0.349464	+	0.390148i	−0.0162939	+	0.0181908i
$461$	5.47610	−	23.1055i	0.255047	−	1.07613i	−0.683219	−	0.730214i	$-0.739420\pi$
$461$	5.47610	−	23.1055i	0.255047	−	1.07613i	0.938266	−	0.345915i	$-0.112431\pi$
$462$	−2.33527	−	13.1237i	−0.108647	−	0.610569i
$463$	10.8651	−	21.6342i	0.504944	−	1.00543i	−0.486351	−	0.873764i	$-0.661672\pi$
$463$	10.8651	−	21.6342i	0.504944	−	1.00543i	0.991295	−	0.131662i	$-0.0420313\pi$
$464$	−6.71015	−	0.0432951i	−0.311511	−	0.00200993i
$465$	0.329814	+	0.427004i	0.0152948	+	0.0198018i
$466$	15.4246	+	21.4333i	0.714530	+	0.992877i
$467$	2.79176	−	15.8329i	0.129187	−	0.732659i	−0.849545	−	0.527517i	$-0.823123\pi$
$467$	2.79176	−	15.8329i	0.129187	−	0.732659i	0.978732	−	0.205142i	$-0.0657656\pi$
$468$	−8.35970	+	4.23126i	−0.386427	+	0.195590i
$469$	0.514006	+	2.91507i	0.0237346	+	0.134606i
$470$	−0.274904	+	0.282108i	−0.0126804	+	0.0130127i
$471$	0.660652	+	8.68727i	0.0304412	+	0.400288i
$472$	−3.99667	−	21.4470i	−0.183962	−	0.987176i
$473$	6.62813	+	27.9663i	0.304762	+	1.28589i
$474$	−8.77302	+	11.8228i	−0.402958	+	0.543041i
$475$	1.80884	+	0.780259i	0.0829955	+	0.0358008i
$476$	5.23549	+	9.78526i	0.239968	+	0.448507i
$477$	−7.16003	+	9.17467i	−0.327835	+	0.420079i
$478$	0.399695	−	24.7354i	0.0182816	−	1.13137i
$479$	−7.00056	+	3.51581i	−0.319864	+	0.160642i	−0.601485	−	0.798884i	$-0.705424\pi$
$479$	−7.00056	+	3.51581i	−0.319864	+	0.160642i	0.281621	+	0.959526i	$0.409128\pi$
$480$	0.304553	+	0.0928006i	0.0139009	+	0.00423575i
$481$	−10.8473	−	1.26787i	−0.494595	−	0.0578099i
$482$	12.6482	−	11.5525i	0.576111	−	0.526201i
$483$	13.6237	−	2.65201i	0.619898	−	0.120671i
$484$	−21.6461	−	31.1271i	−0.983915	−	1.41487i
$485$		−	0.547102i		−	0.0248426i
$486$	17.0885	+	13.9278i	0.775150	+	0.631777i
$487$			2.00793i			0.0909878i	0.998965	+	0.0454939i	$0.0144862\pi$
$487$			2.00793i			0.0909878i	−0.998965	+	0.0454939i	$0.985514\pi$
$488$	−1.03879	+	3.59649i	−0.0470240	+	0.162805i
$489$	−5.20216	+	1.01266i	−0.235250	+	0.0457942i
$490$	0.186302	+	0.203973i	0.00841628	+	0.00921456i
$491$	4.30748	+	0.503472i	0.194394	+	0.0227214i	0.212733	−	0.977110i	$-0.431764\pi$
$491$	4.30748	+	0.503472i	0.194394	+	0.0227214i	−0.0183388	+	0.999832i	$0.505838\pi$
$492$	−5.79918	−	5.63341i	−0.261447	−	0.253974i
$493$	8.36656	−	4.20185i	0.376811	−	0.189242i
$494$	−0.870168	−	0.0140609i	−0.0391507	−	0.000632630i
$495$	0.528400	+	0.0739694i	0.0237498	+	0.00332468i
$496$	−10.7605	−	36.8053i	−0.483162	−	1.65261i
$497$	−5.94241	−	2.56330i	−0.266553	−	0.114980i
$498$	22.9171	+	17.0054i	1.02694	+	0.762031i
$499$	7.23533	+	30.5283i	0.323898	+	1.36663i	0.854693	+	0.519133i	$0.173745\pi$
$499$	7.23533	+	30.5283i	0.323898	+	1.36663i	−0.530795	+	0.847500i	$0.678107\pi$
$500$	0.310247	−	0.570972i	0.0138747	−	0.0255346i
$501$	2.79352	+	36.7336i	0.124805	+	1.64113i
$502$	−0.753006	−	0.733779i	−0.0336083	−	0.0327501i
$503$	1.41962	+	8.05104i	0.0632975	+	0.358978i	0.999962	+	0.00874931i	$0.00278503\pi$
$503$	1.41962	+	8.05104i	0.0632975	+	0.358978i	−0.936664	+	0.350229i	$0.886104\pi$
$504$	−4.94943	−	6.83223i	−0.220465	−	0.304332i
$505$	0.0728864	−	0.413359i	0.00324340	−	0.0183943i
$506$	50.6348	−	36.4397i	2.25099	−	1.61994i
$507$	11.1821	+	14.4773i	0.496616	+	0.642959i
$508$	−3.25979	−	16.0484i	−0.144630	−	0.712034i
$509$	15.8519	−	31.5637i	0.702623	−	1.39904i	−0.204793	−	0.978805i	$-0.565652\pi$
$509$	15.8519	−	31.5637i	0.702623	−	1.39904i	0.907416	−	0.420233i	$-0.138052\pi$
$510$	−0.437341	+	0.0778219i	−0.0193658	+	0.00344601i
$511$	0.555658	−	2.34451i	0.0245809	−	0.103715i
$512$	−17.7497	−	14.0338i	−0.784433	−	0.620214i
$513$	0.801622	+	1.88424i	0.0353925	+	0.0831911i
$514$	−25.6649	−	9.81369i	−1.13203	−	0.432863i
$515$	0.0382844	+	0.127879i	0.00168701	+	0.00563502i
$516$	11.4881	+	14.1038i	0.505734	+	0.620886i
$517$	39.1969	−	25.7802i	1.72388	−	1.13381i
$518$	−0.413094	−	9.82505i	−0.0181503	−	0.431688i
$519$	−3.67189	+	16.8157i	−0.161178	+	0.738128i
$520$	−0.0152776	+	0.142707i	−0.000669968	+	0.00625810i
$521$	−10.0547	−	27.6250i	−0.440504	−	1.21028i	−0.939161	−	0.343476i	$-0.888396\pi$
$521$	−10.0547	−	27.6250i	−0.440504	−	1.21028i	0.498657	−	0.866799i	$-0.333827\pi$
$522$	−5.86990	+	4.02502i	−0.256918	+	0.176170i
$523$	−13.0308	+	35.8018i	−0.569797	+	1.56550i	0.235025	+	0.971989i	$0.424483\pi$
$523$	−13.0308	+	35.8018i	−0.569797	+	1.56550i	−0.804823	+	0.593516i	$0.797740\pi$
$524$	−10.5994	+	4.90101i	−0.463037	+	0.214102i
$525$	−7.84302	+	3.54932i	−0.342297	+	0.154905i
$526$	1.88552	−	14.1456i	0.0822127	−	0.616778i
$527$	36.7151	+	38.9157i	1.59933	+	1.69520i
$528$	−33.0514	−	18.5886i	−1.43838	−	0.808967i
$529$	25.0542	+	33.6536i	1.08931	+	1.46320i
$530$	0.0582570	+	0.168481i	0.00253052	+	0.00731835i
$531$	−16.4659	−	16.2577i	−0.714558	−	0.705525i
$532$	−0.111071	−	0.775715i	−0.00481552	−	0.0336315i
$533$	2.00275	−	3.04503i	0.0867486	−	0.131895i
$534$	13.3382	+	8.74279i	0.577202	+	0.378337i
$535$	−0.0892156	−	0.0664185i	−0.00385713	−	0.00287152i
$536$	7.33295	+	4.13932i	0.316735	+	0.178791i
$537$	18.5983	−	7.14499i	0.802574	−	0.308329i
$538$	21.8639	+	14.8917i	0.942620	+	0.642026i
$539$	−16.4512	−	28.4943i	−0.708602	−	1.22734i
$540$	0.321414	−	0.103577i	0.0138314	−	0.00445725i
$541$	−13.8143	+	23.9271i	−0.593924	+	1.02871i	0.399774	+	0.916614i	$0.369089\pi$
$541$	−13.8143	+	23.9271i	−0.593924	+	1.02871i	−0.993698	+	0.112093i	$0.964245\pi$
$542$	−26.9326	+	12.9855i	−1.15686	+	0.557775i
$543$	−12.5144	+	0.221835i	−0.537043	+	0.00951984i
$544$	30.9590	+	6.18365i	1.32736	+	0.265122i
$545$	0.00805043	−	0.00347262i	0.000344843	−	0.000148751i
$546$	2.60554	−	2.77040i	0.111507	−	0.118562i
$547$	−30.6229	−	1.78358i	−1.30934	−	0.0762603i	−0.610773	−	0.791806i	$-0.709141\pi$
$547$	−30.6229	−	1.78358i	−1.30934	−	0.0762603i	−0.698566	+	0.715546i	$0.746178\pi$
$548$	10.1806	−	25.3870i	0.434892	−	1.08448i
$549$	1.27287	+	3.76103i	0.0543249	+	0.160517i
$550$	−25.3476	+	29.2355i	−1.08082	+	1.24660i
$551$	−0.656618	+	0.0767477i	−0.0279729	+	0.00326956i
$552$	18.7964	−	34.7222i	0.800030	−	1.47787i
$553$	1.71390	−	5.72482i	0.0728823	−	0.243444i
$554$	−31.7910	−	24.4757i	−1.35067	−	1.03987i
$555$	0.379019	+	0.106189i	0.0160885	+	0.00450746i
$556$	4.90692	−	6.95992i	0.208100	−	0.295166i
$557$	7.43567	+	8.86149i	0.315060	+	0.375473i	0.900213	−	0.435449i	$-0.143410\pi$
$557$	7.43567	+	8.86149i	0.315060	+	0.375473i	−0.585154	+	0.810922i	$0.698966\pi$
$558$	−31.6552	−	25.5377i	−1.34007	−	1.08110i
$559$	−5.27093	+	6.28165i	−0.222937	+	0.265686i
$560$	−0.129059	+	0.00668159i	−0.00545372	+	0.000282349i
$561$	52.8640	+	2.13968i	2.23192	+	0.0903374i
$562$	6.41544	−	4.07255i	0.270619	−	0.171790i
$563$	1.38398	+	23.7620i	0.0583276	+	1.00145i	0.892816	+	0.450422i	$0.148726\pi$
$563$	1.38398	+	23.7620i	0.0583276	+	1.00145i	−0.834488	+	0.551026i	$0.814237\pi$
$564$	15.2201	−	25.4956i	0.640882	−	1.07356i
$565$	0.323774	−	0.343181i	0.0136213	−	0.0144377i
$566$	−23.3741	+	18.9782i	−0.982489	+	0.797714i
$567$	−8.44696	−	2.95331i	−0.354739	−	0.124028i
$568$	−16.3711	+	8.42181i	−0.686916	+	0.353371i
$569$	−10.6142	−	10.0140i	−0.444971	−	0.419809i	0.430866	−	0.902416i	$-0.358208\pi$
$569$	−10.6142	−	10.0140i	−0.444971	−	0.419809i	−0.875837	+	0.482607i	$0.839690\pi$
$570$	0.0308981	+	0.00539825i	0.00129418	+	0.000226108i
$571$	8.73689	−	0.508866i	0.365628	−	0.0212954i	0.125652	−	0.992074i	$-0.459898\pi$
$571$	8.73689	−	0.508866i	0.365628	−	0.0212954i	0.239975	+	0.970779i	$0.422861\pi$
$572$	5.42916	−	16.2090i	0.227005	−	0.677731i
$573$	−14.1422	+	7.41920i	−0.590797	+	0.309942i
$574$	2.99193	+	1.34834i	0.124881	+	0.0562785i
$575$	−30.8632	−	25.8973i	−1.28708	−	1.07999i
$576$	−23.9546	−	1.47496i	−0.998110	−	0.0614568i
$577$	6.85918	−	5.75553i	0.285551	−	0.239606i	−0.488749	−	0.872425i	$-0.662547\pi$
$577$	6.85918	−	5.75553i	0.285551	−	0.239606i	0.774300	+	0.632819i	$0.218102\pi$
$578$	−19.2563	+	5.42754i	−0.800957	+	0.225756i
$579$	−14.4994	−	14.8328i	−0.602576	−	0.616429i
$580$	0.00281932	+	0.108987i	0.000117066	+	0.00452542i
$581$	−11.0968	−	3.32218i	−0.460375	−	0.137827i
$582$	9.57387	+	40.1151i	0.396850	+	1.66282i
$583$	−2.46494	−	21.0889i	−0.102088	−	0.873415i
$584$	−4.14626	−	5.45800i	−0.171574	−	0.225854i
$585$	0.0730983	+	0.133529i	0.00302224	+	0.00552075i
$586$	8.27511	+	14.8832i	0.341841	+	0.614818i
$587$	−1.67560	+	28.7690i	−0.0691596	+	1.18742i	0.767994	+	0.640457i	$0.221255\pi$
$587$	−1.67560	+	28.7690i	−0.0691596	+	1.18742i	−0.837154	+	0.546967i	$0.815782\pi$
$588$	−17.2296	−	11.6957i	−0.710537	−	0.482324i
$589$	−1.49631	−	3.46883i	−0.0616544	−	0.142931i
$590$	−0.346172	+	0.0761589i	−0.0142517	+	0.00313541i
$591$	38.0101	−	22.8528i	1.56353	−	0.940040i
$592$	−22.3307	−	16.8496i	−0.917787	−	0.692516i
$593$	14.1368	+	8.16190i	0.580530	+	0.335169i	0.761344	−	0.648348i	$-0.224540\pi$
$593$	14.1368	+	8.16190i	0.580530	+	0.335169i	−0.180814	+	0.983517i	$0.557873\pi$
$594$	−40.0382	+	3.82294i	−1.64279	+	0.156857i
$595$	0.156151	−	0.0901540i	0.00640158	−	0.00369595i
$596$	3.95587	+	46.9602i	0.162039	+	1.92356i
$597$	−2.75315	−	0.435291i	−0.112679	−	0.0178153i
$598$	16.9663	+	5.37957i	0.693805	+	0.219987i
$599$	−1.50854	+	2.02632i	−0.0616374	+	0.0827933i	−0.831873	−	0.554966i	$-0.812731\pi$
$599$	−1.50854	+	2.02632i	−0.0616374	+	0.0827933i	0.770236	+	0.637759i	$0.220139\pi$
$600$	−6.37764	+	23.6447i	−0.260366	+	0.965291i
$601$	−6.59614	−	4.33835i	−0.269062	−	0.176965i	0.407807	−	0.913068i	$-0.366294\pi$
$601$	−6.59614	−	4.33835i	−0.269062	−	0.176965i	−0.676870	+	0.736103i	$0.736664\pi$
$602$	−6.33392	−	3.79464i	−0.258151	−	0.154658i
$603$	8.89226	−	0.834994i	0.362121	−	0.0340036i
$604$	−3.01135	−	1.87086i	−0.122530	−	0.0761244i
$605$	−0.494100	+	0.367844i	−0.0200880	+	0.0149550i
$606$	1.88924	+	31.5842i	0.0767450	+	1.28302i
$607$	−15.4747	+	14.5996i	−0.628099	+	0.592581i	−0.933032	−	0.359793i	$-0.882847\pi$
$607$	−15.4747	+	14.5996i	−0.628099	+	0.592581i	0.304933	+	0.952374i	$0.401366\pi$
$608$	−1.90487	−	1.15797i	−0.0772527	−	0.0469619i
$609$	1.68383	−	2.34752i	0.0682323	−	0.0951265i
$610$	0.0589475	+	0.0149807i	0.00238671	+	0.000606551i
$611$	12.5781	+	4.57807i	0.508857	+	0.185209i
$612$	30.7053	−	13.3593i	1.24119	−	0.540016i
$613$	−9.88208	+	3.59678i	−0.399133	+	0.145273i	−0.533785	−	0.845620i	$-0.679231\pi$
$613$	−9.88208	+	3.59678i	−0.399133	+	0.145273i	0.134651	+	0.990893i	$0.457009\pi$
$614$	−6.92173	+	0.695873i	−0.279338	+	0.0280831i
$615$	−0.0884349	+	0.0971281i	−0.00356604	+	0.00391658i
$616$	15.1834	+	2.52555i	0.611755	+	0.101757i
$617$	−18.9769	−	28.8529i	−0.763980	−	1.16157i	−0.982594	−	0.185764i	$-0.940524\pi$
$617$	−18.9769	−	28.8529i	−0.763980	−	1.16157i	0.218615	−	0.975811i	$-0.429846\pi$
$618$	−5.04491	−	8.70650i	−0.202936	−	0.350227i
$619$	45.2325	−	13.5417i	1.81805	−	0.544288i	0.818505	−	0.574500i	$-0.194803\pi$
$619$	45.2325	−	13.5417i	1.81805	−	0.544288i	0.999544	+	0.0302116i	$0.00961813\pi$
$620$	−0.592021	+	0.194057i	−0.0237761	+	0.00779351i
$621$	−4.65358	−	41.6191i	−0.186742	−	1.67012i
$622$	22.2633	−	3.55573i	0.892675	−	0.142572i
$623$	−6.29898	−	1.49289i	−0.252363	−	0.0598112i
$624$	−1.37706	−	10.7310i	−0.0551265	−	0.429584i
$625$	22.3267	+	11.2129i	0.893067	+	0.448515i
$626$	−22.1892	+	42.4577i	−0.886858	+	1.69695i
$627$	−3.45598	−	1.41866i	−0.138019	−	0.0566557i
$628$	−9.70892	−	2.63510i	−0.387428	−	0.105152i
$629$	38.4379	+	6.77765i	1.53262	+	0.270242i
$630$	−0.108348	+	0.0839586i	−0.00431669	+	0.00334499i
$631$	−9.46338	+	1.66865i	−0.376731	+	0.0664279i	−0.358808	−	0.933411i	$-0.616817\pi$
$631$	−9.46338	+	1.66865i	−0.376731	+	0.0664279i	−0.0179236	+	0.999839i	$0.505706\pi$
$632$	−9.47896	−	14.1118i	−0.377053	−	0.561338i
$633$	7.85722	−	16.3618i	0.312297	−	0.650323i
$634$	−5.89516	−	14.2974i	−0.234127	−	0.567821i
$635$	−0.258894	+	0.0613590i	−0.0102739	+	0.00243496i
$636$	−7.21986	−	11.3341i	−0.286286	−	0.449425i
$637$	3.71816	−	8.61966i	0.147319	−	0.341523i
$638$	2.46115	−	12.7497i	0.0974379	−	0.504766i
$639$	−9.15806	+	17.2464i	−0.362287	+	0.682256i
$640$	−0.218573	+	0.295598i	−0.00863988	+	0.0116845i
$641$	−4.94780	−	9.85187i	−0.195426	−	0.389125i	0.774482	−	0.632596i	$-0.218010\pi$
$641$	−4.94780	−	9.85187i	−0.195426	−	0.389125i	−0.969908	+	0.243470i	$0.921714\pi$
$642$	7.70382	+	3.30879i	0.304045	+	0.130588i
$643$	−1.15354	+	9.86914i	−0.0454910	+	0.389201i	0.951243	+	0.308443i	$0.0998080\pi$
$643$	−1.15354	+	9.86914i	−0.0454910	+	0.389201i	−0.996734	+	0.0807575i	$0.974266\pi$
$644$	−2.37390	+	15.8497i	−0.0935448	+	0.624567i
$645$	0.222997	−	0.193954i	0.00878049	−	0.00763694i
$646$	3.10169	+	0.230990i	0.122034	+	0.00908819i
$647$	−21.8417			−0.858687			−0.429344	−	0.903141i	$-0.641255\pi$
$647$	−21.8417			−0.858687			−0.429344	+	0.903141i	$0.641255\pi$
$648$	−21.7545	+	13.2191i	−0.854596	+	0.519294i
$649$	42.2165			1.65714
$650$	−11.0093	−	0.819886i	−0.431820	−	0.0321586i
$651$	15.6111	+	5.37059i	0.611847	+	0.210490i
$652$	0.906468	−	6.05219i	0.0355000	−	0.237022i
$653$	−4.18927	+	35.8415i	−0.163939	+	1.40258i	0.621388	+	0.783503i	$0.286569\pi$
$653$	−4.18927	+	35.8415i	−0.163939	+	1.40258i	−0.785327	+	0.619082i	$0.787505\pi$
$654$	−0.529513	+	0.395499i	−0.0207056	+	0.0154652i
$655$	0.0851499	+	0.169547i	0.00332708	+	0.00662476i
$656$	8.36951	−	4.13592i	0.326774	−	0.161481i
$657$	−6.91547	−	2.24282i	−0.269798	−	0.0875009i
$658$	−2.28441	+	11.8341i	−0.0890554	+	0.461341i
$659$	−6.31417	+	14.6379i	−0.245965	+	0.570211i	−0.995814	−	0.0913975i	$-0.970867\pi$
$659$	−6.31417	+	14.6379i	−0.245965	+	0.570211i	0.749849	+	0.661608i	$0.230126\pi$
$660$	−0.284505	+	0.546468i	−0.0110743	+	0.0212712i
$661$	5.46213	−	1.29455i	0.212452	−	0.0503521i	−0.123011	−	0.992405i	$-0.539255\pi$
$661$	5.46213	−	1.29455i	0.212452	−	0.0503521i	0.335464	+	0.942053i	$0.391107\pi$
$662$	−16.9964	−	41.2209i	−0.660585	−	1.60210i
$663$	8.51708	+	12.4627i	0.330776	+	0.484012i
$664$	−27.3540	+	18.3738i	−1.06154	+	0.713041i
$665$	−0.0125383	+	0.00221084i	−0.000486213	+	8.57325e-5i
$666$	−29.6490	−	1.15351i	−1.14887	−	0.0446977i
$667$	13.3150	+	2.34779i	0.515559	+	0.0909070i
$668$	−41.0535	−	11.1423i	−1.58841	−	0.431110i
$669$	5.42405	+	40.2112i	0.209706	+	1.55465i
$670$	0.0633677	−	0.121250i	0.00244811	−	0.00468431i
$671$	−6.47352	−	3.25112i	−0.249907	−	0.125508i
$672$	9.34603	−	2.74834i	0.360531	−	0.106020i
$673$	−26.7637	−	6.34312i	−1.03167	−	0.244509i	−0.320289	−	0.947320i	$-0.603780\pi$
$673$	−26.7637	−	6.34312i	−1.03167	−	0.244509i	−0.711377	+	0.702811i	$0.751928\pi$
$674$	30.5555	−	4.88012i	1.17696	−	0.187975i
$675$	8.76181	+	24.4529i	0.337242	+	0.941194i
$676$	−20.0721	+	6.57937i	−0.772003	+	0.253053i
$677$	19.4419	−	5.82053i	0.747214	−	0.223701i	0.109513	−	0.993985i	$-0.465071\pi$
$677$	19.4419	−	5.82053i	0.747214	−	0.223701i	0.637701	+	0.770284i	$0.279886\pi$
$678$	−17.7347	+	30.8288i	−0.681095	+	1.18397i
$679$	−9.19892	−	13.9863i	−0.353022	−	0.536744i
$680$	0.0841628	−	0.505979i	0.00322750	−	0.0194034i
$681$	−12.0397	−	37.7659i	−0.461363	−	1.44719i
$682$	73.8313	−	7.42259i	2.82715	−	0.284226i
$683$	46.1276	−	16.7891i	1.76502	−	0.642417i	0.765026	−	0.643999i	$-0.222726\pi$
$683$	46.1276	−	16.7891i	1.76502	−	0.642417i	0.999999	+	0.00158267i	$0.000503780\pi$
$684$	−2.36000	+	0.144878i	−0.0902369	+	0.00553954i
$685$	−0.417595	−	0.151992i	−0.0159555	−	0.00580733i
$686$	17.7317	+	4.50628i	0.677001	+	0.172051i
$687$	−5.41344	−	0.535669i	−0.206536	−	0.0204371i
$688$	−19.7838	+	7.05648i	−0.754249	+	0.269026i
$689$	4.40633	−	4.15716i	0.167868	−	0.158375i
$690$	−0.573708	−	0.287002i	−0.0218407	−	0.0109260i
$691$	13.8108	−	10.2818i	0.525388	−	0.391137i	−0.301533	−	0.953456i	$-0.597498\pi$
$691$	13.8108	−	10.2818i	0.525388	−	0.391137i	0.826920	+	0.562319i	$0.190091\pi$
$692$	−16.8819	−	10.4882i	−0.641753	−	0.398703i
$693$	14.7519	−	6.99349i	0.560378	−	0.265661i
$694$	25.5691	+	15.3184i	0.970592	+	0.581480i
$695$	−0.115596	−	0.0760284i	−0.00438479	−	0.00288392i
$696$	−2.11391	−	7.94188i	−0.0801274	−	0.301036i
$697$	−7.77824	+	10.4480i	−0.294622	+	0.395746i
$698$	31.5535	+	10.0048i	1.19432	+	0.378686i
$699$	−20.3462	+	25.1394i	−0.769563	+	0.950859i
$700$	−0.834423	−	9.90545i	−0.0315382	−	0.374391i
$701$	−7.09886	+	4.09853i	−0.268120	+	0.154799i	−0.628033	−	0.778187i	$-0.716140\pi$
$701$	−7.09886	+	4.09853i	−0.268120	+	0.154799i	0.359913	+	0.932986i	$0.382806\pi$
$702$	−7.69644	−	8.51158i	−0.290483	−	0.321249i
$703$	−2.38677	−	1.37800i	−0.0900188	−	0.0519724i
$704$	32.9897	−	28.7910i	1.24334	−	1.08510i
$705$	−0.422003	−	0.233771i	−0.0158936	−	0.00880431i
$706$	−39.4357	+	8.67598i	−1.48418	+	0.326525i
$707$	−5.08690	−	11.7928i	−0.191313	−	0.443512i
$708$	24.0496	−	11.6419i	0.903839	−	0.437531i
$709$	0.470677	−	8.08121i	0.0176766	−	0.303496i	−0.977869	−	0.209217i	$-0.932908\pi$
$709$	0.470677	−	8.08121i	0.0176766	−	0.303496i	0.995546	−	0.0942789i	$-0.0300545\pi$
$710$	0.145353	+	0.261424i	0.00545499	+	0.00981106i
$711$	−16.7991	−	6.55046i	−0.630016	−	0.245661i
$712$	−14.6640	+	11.1398i	−0.549556	+	0.417480i
$713$	8.96964	+	76.7401i	0.335916	+	2.87394i
$714$	−9.87184	+	9.34288i	−0.369444	+	0.349649i
$715$	−0.266062	−	0.0796537i	−0.00995015	−	0.00297888i
$716$	0.594924	+	22.9980i	0.0222334	+	0.859475i
$717$	29.3533	−	7.50874i	1.09622	−	0.280419i
$718$	−3.69562	+	1.04164i	−0.137919	+	0.0388737i
$719$	−24.1664	+	20.2780i	−0.901255	+	0.756243i	−0.970435	−	0.241361i	$-0.922406\pi$
$719$	−24.1664	+	20.2780i	−0.901255	+	0.756243i	0.0691799	+	0.997604i	$0.477962\pi$
$720$	−0.0113768	+	0.389765i	−0.000423990	+	0.0145257i
$721$	3.12886	+	2.62543i	0.116525	+	0.0977760i
$722$	24.2971	+	10.9497i	0.904245	+	0.407505i
$723$	17.7300	+	11.2162i	0.659387	+	0.417134i
$724$	4.59023	−	13.7043i	0.170595	−	0.509317i
$725$	−8.37191	+	0.487608i	−0.310925	+	0.0181093i
$726$	29.7919	−	35.6178i	1.10568	−	1.32190i
$727$	31.1749	+	29.4120i	1.15621	+	1.09083i	0.994579	+	0.103979i	$0.0331575\pi$
$727$	31.1749	+	29.4120i	1.15621	+	1.09083i	0.161633	+	0.986851i	$0.448324\pi$
$728$	2.00890	+	3.90508i	0.0744546	+	0.144732i
$729$	−10.9417	+	24.6836i	−0.405249	+	0.914206i
$730$	−0.0864541	+	0.0701949i	−0.00319981	+	0.00259803i
$731$	20.1112	−	21.3166i	0.743838	−	0.788422i
$732$	−4.58435	−	0.0668919i	−0.169442	−	0.00247240i
$733$	−1.57230	−	26.9953i	−0.0580741	−	0.997094i	−0.893947	−	0.448172i	$-0.852075\pi$
$733$	−1.57230	−	26.9953i	−0.0580741	−	0.997094i	0.835873	−	0.548923i	$-0.184962\pi$
$734$	−37.5001	+	23.8052i	−1.38415	+	0.878668i
$735$	−0.180879	+	0.285925i	−0.00667181	+	0.0105465i
$736$	30.5290	+	33.8609i	1.12532	+	1.24813i
$737$	−10.4740	+	12.4824i	−0.385815	+	0.459796i
$738$	4.78464	−	8.66926i	0.176125	−	0.319120i
$739$	25.3085	+	30.1615i	0.930989	+	1.10951i	0.993766	+	0.111482i	$0.0355597\pi$
$739$	25.3085	+	30.1615i	0.930989	+	1.10951i	−0.0627774	+	0.998028i	$0.519996\pi$
$740$	−0.261893	+	0.371466i	−0.00962739	+	0.0136554i
$741$	−0.264150	−	1.03262i	−0.00970381	−	0.0379343i
$742$	4.32213	+	3.32758i	0.158670	+	0.122159i
$743$	11.9390	−	39.8790i	0.437999	−	1.46302i	−0.399579	−	0.916699i	$-0.630844\pi$
$743$	11.9390	−	39.8790i	0.437999	−	1.46302i	0.837578	−	0.546318i	$-0.183971\pi$
$744$	40.0128	−	24.5887i	1.46694	−	0.901466i
$745$	0.760494	−	0.0888890i	0.0278624	−	0.00325664i
$746$	18.7453	−	21.6205i	0.686313	−	0.791583i
$747$	−12.6972	+	32.5630i	−0.464568	+	1.19142i
$748$	−22.7386	+	56.7027i	−0.831406	+	2.07326i
$749$	−3.39749	−	0.197881i	−0.124142	−	0.00723043i
$750$	0.774694	+	0.182324i	0.0282878	+	0.00665754i
$751$	−10.7414	+	4.63337i	−0.391958	+	0.169074i	−0.582932	−	0.812521i	$-0.698095\pi$
$751$	−10.7414	+	4.63337i	−0.391958	+	0.169074i	0.190974	+	0.981595i	$0.438835\pi$
$752$	21.8690	+	26.4067i	0.797482	+	0.962952i
$753$	0.623984	−	1.12642i	0.0227392	−	0.0410489i
$754$	3.33715	−	1.60900i	0.121532	−	0.0585962i
$755$	−0.0287996	+	0.0498823i	−0.00104812	+	0.00181540i
$756$	6.47518	−	8.05210i	0.235500	−	0.292852i
$757$	5.90132	+	10.2214i	0.214487	+	0.371503i	0.953114	−	0.302612i	$-0.0978586\pi$
$757$	5.90132	+	10.2214i	0.214487	+	0.371503i	−0.738627	+	0.674115i	$0.764525\pi$
$758$	26.8227	+	18.2691i	0.974243	+	0.663565i
$759$	59.3903	+	48.0666i	2.15573	+	1.74471i
$760$	−0.0178040	+	0.0315404i	−0.000645818	+	0.00114409i
$761$	−1.95914	−	1.45853i	−0.0710190	−	0.0528716i	0.561064	−	0.827773i	$-0.310392\pi$
$761$	−1.95914	−	1.45853i	−0.0710190	−	0.0528716i	−0.632083	+	0.774901i	$0.717800\pi$
$762$	17.9091	−	9.02947i	0.648779	−	0.327103i
$763$	0.147416	−	0.224134i	0.00533680	−	0.00811421i
$764$	−2.61377	−	18.2546i	−0.0945630	−	0.660427i
$765$	−0.233055	−	0.491600i	−0.00842612	−	0.0177738i
$766$	−0.490340	−	1.41808i	−0.0177167	−	0.0512373i
$767$	7.19267	+	9.66143i	0.259712	+	0.348854i
$768$	10.8537	−	25.4990i	0.391649	−	0.920115i
$769$	19.7729	+	20.9581i	0.713030	+	0.755768i	0.978026	−	0.208482i	$-0.0668522\pi$
$769$	19.7729	+	20.9581i	0.713030	+	0.755768i	−0.264996	+	0.964249i	$0.585371\pi$
$770$	0.0330413	−	0.247883i	0.00119073	−	0.00893310i
$771$	3.31380	−	33.4890i	0.119343	−	1.20608i
$772$	21.7397	−	10.0521i	0.782429	−	0.361784i
$773$	−9.71810	+	26.7003i	−0.349536	+	0.960342i	0.632981	+	0.774168i	$0.281831\pi$
$773$	−9.71810	+	26.7003i	−0.349536	+	0.960342i	−0.982517	+	0.186175i	$0.940391\pi$
$774$	−12.9567	+	18.1236i	−0.465719	+	0.651438i
$775$	−16.3904	−	45.0324i	−0.588762	−	1.61761i
$776$	−47.3512	−	5.06924i	−1.69981	−	0.181975i
$777$	11.4748	−	3.65815i	0.411657	−	0.131236i
$778$	1.30472	+	31.0316i	0.0467766	+	1.11254i
$779$	0.768428	−	0.505403i	0.0275318	−	0.0181079i
$780$	−0.173534	+	0.0279947i	−0.00621353	+	0.00100237i
$781$	−10.2176	−	34.1291i	−0.365614	−	1.22124i
$782$	−59.4152	−	22.7191i	−2.12468	−	0.812432i
$783$	−6.64943	−	5.63648i	−0.237631	−	0.201431i
$784$	19.3799	−	14.2344i	0.692140	−	0.508371i
$785$	−0.0376939	+	0.159043i	−0.00134535	+	0.00567649i
$786$	−9.21038	−	10.9416i	−0.328524	−	0.390275i
$787$	−22.2981	+	44.3991i	−0.794840	+	1.58266i	0.0177659	+	0.999842i	$0.494345\pi$
$787$	−22.2981	+	44.3991i	−0.794840	+	1.58266i	−0.812606	+	0.582814i	$0.801952\pi$
$788$	10.1942	+	50.1874i	0.363152	+	1.78785i
$789$	17.3211	−	2.33643i	0.616648	−	0.0831791i
$790$	−0.224181	+	0.161333i	−0.00797601	+	0.00573999i
$791$	2.50686	−	14.2171i	0.0891336	−	0.505502i
$792$	11.2980	−	45.0472i	0.401455	−	1.60068i
$793$	−0.358897	−	2.03541i	−0.0127448	−	0.0722794i
$794$	−26.6288	−	25.9489i	−0.945021	−	0.920890i
$795$	−0.180260	+	0.123191i	−0.00639317	+	0.00436912i
$796$	1.53666	−	2.82803i	0.0544654	−	0.100237i
$797$	−8.89662	−	37.5378i	−0.315134	−	1.32966i	−0.868074	−	0.496435i	$-0.834642\pi$
$797$	−8.89662	−	37.5378i	−0.315134	−	1.32966i	0.552939	−	0.833222i	$-0.313506\pi$
$798$	0.880655	−	0.381515i	0.0311748	−	0.0135055i
$799$	−43.9253	−	18.9475i	−1.55397	−	0.670316i
$800$	−23.2688	−	16.0693i	−0.822677	−	0.568137i
$801$	−6.02579	+	18.5798i	−0.212911	+	0.656484i
$802$	4.93549	+	0.0797519i	0.174278	+	0.00281614i
$803$	11.8529	−	5.95275i	0.418280	−	0.210068i
$804$	−2.52451	+	9.99930i	−0.0890327	+	0.352648i
$805$	0.258625	+	0.0302289i	0.00911533	+	0.00106543i
$806$	14.2778	+	15.6320i	0.502913	+	0.550613i
$807$	−10.5397	+	30.6366i	−0.371017	+	1.07846i
$808$	−35.1006	−	10.1383i	−1.23484	−	0.356664i
$809$		−	20.8872i		−	0.734354i	−0.930151	−	0.367177i	$-0.880324\pi$
$809$		−	20.8872i		−	0.734354i	0.930151	−	0.367177i	$-0.119676\pi$
$810$	0.226080	+	0.346324i	0.00794363	+	0.0121686i
$811$			35.4387i			1.24442i	0.782850	+	0.622210i	$0.213765\pi$
$811$			35.4387i			1.24442i	−0.782850	+	0.622210i	$0.786235\pi$
$812$	1.90457	+	2.73877i	0.0668372	+	0.0961118i
$813$	−24.0320	−	27.6305i	−0.842840	−	0.969046i
$814$	39.9703	−	36.5076i	1.40096	−	1.27959i
$815$	−0.0987553	−	0.0115428i	−0.00345925	−	0.000404328i
$816$	2.68319	+	38.5726i	0.0939303	+	1.35031i
$817$	−1.84923	+	0.928717i	−0.0646963	+	0.0324917i
$818$	0.0393754	−	2.43677i	0.00137673	−	0.0851997i
$819$	4.11386	+	2.18452i	0.143750	+	0.0763331i
$820$	−0.0715552	−	0.133739i	−0.00249882	−	0.00467035i
$821$	38.0257	+	16.4027i	1.32711	+	0.572458i	0.937327	−	0.348450i	$-0.113292\pi$
$821$	38.0257	+	16.4027i	1.32711	+	0.572458i	0.389779	+	0.920908i	$0.372551\pi$
$822$	33.2791	+	3.83691i	1.16074	+	0.133828i
$823$	−8.50542	−	35.8872i	−0.296480	−	1.25095i	−0.893625	−	0.448815i	$-0.851846\pi$
$823$	−8.50542	−	35.8872i	−0.296480	−	1.25095i	0.597144	−	0.802134i	$-0.296302\pi$
$824$	11.4226	−	2.12861i	0.397924	−	0.0741537i
$825$	−42.7196	−	20.5147i	−1.48731	−	0.714230i
$826$	−7.56912	+	7.76746i	−0.263363	+	0.270264i
$827$	−2.78047	−	15.7688i	−0.0966865	−	0.548336i	−0.994218	−	0.107385i	$-0.965752\pi$
$827$	−2.78047	−	15.7688i	−0.0966865	−	0.548336i	0.897531	−	0.440951i	$-0.145359\pi$
$828$	47.0883	+	11.0044i	1.63643	+	0.382428i
$829$	6.45173	−	36.5896i	0.224078	−	1.27081i	−0.640362	−	0.768073i	$-0.721216\pi$
$829$	6.45173	−	36.5896i	0.224078	−	1.27081i	0.864440	−	0.502736i	$-0.167673\pi$
$830$	0.312725	+	0.434547i	0.0108548	+	0.0150834i
$831$	18.6600	−	45.4576i	0.647309	−	1.57691i
$832$	12.2096	+	2.64453i	0.423292	+	0.0916827i
$833$	−15.0570	+	29.9809i	−0.521693	+	1.03878i
$834$	9.80624	+	3.55179i	0.339562	+	0.122988i
$835$	−0.159386	+	0.672504i	−0.00551579	+	0.0232730i
$836$	2.87815	−	3.21322i	0.0995430	−	0.111132i
$837$	19.9585	−	45.6398i	0.689868	−	1.57754i
$838$	−2.09812	+	5.48702i	−0.0724782	+	0.189546i
$839$	−6.46924	−	21.6088i	−0.223343	−	0.746017i	−0.994059	−	0.108839i	$-0.965287\pi$
$839$	−6.46924	−	21.6088i	−0.223343	−	0.746017i	0.770717	−	0.637178i	$-0.219898\pi$
$840$	−0.0495354	−	0.150324i	−0.00170914	−	0.00518668i
$841$	−21.8779	+	14.3893i	−0.754409	+	0.496183i
$842$	3.76691	−	0.158380i	0.129816	−	0.00545812i
$843$	6.88160	+	6.26568i	0.237015	+	0.215802i
$844$	14.7720	+	14.8676i	0.508474	+	0.511765i
$845$	0.117377	+	0.322490i	0.00403788	+	0.0110940i
$846$	35.0333	+	9.75600i	1.20447	+	0.335418i
$847$	−6.44644	+	17.7114i	−0.221502	+	0.608572i
$848$	15.1217	−	3.48102i	0.519281	−	0.119539i
$849$	−29.9641	−	21.4927i	−1.02837	−	0.737627i
$850$	39.1089	+	5.21298i	1.34142	+	0.178804i
$851$	38.6801	+	40.9985i	1.32594	+	1.40541i
$852$	−15.2324	−	16.6248i	−0.521853	−	0.569556i
$853$	−7.22713	−	9.70773i	−0.247452	−	0.332386i	0.660991	−	0.750394i	$-0.270136\pi$
$853$	−7.22713	−	9.70773i	−0.247452	−	0.332386i	−0.908444	+	0.418007i	$0.862729\pi$
$854$	1.75884	−	0.608166i	0.0601861	−	0.0208110i
$855$	0.00359146	+	0.0382472i	0.000122825	+	0.00130803i
$856$	−6.57511	+	7.10613i	−0.224733	+	0.242883i
$857$	−16.9724	+	25.8053i	−0.579766	+	0.881492i	−0.999660	−	0.0260816i	$-0.991697\pi$
$857$	−16.9724	+	25.8053i	−0.579766	+	0.881492i	0.419894	+	0.907573i	$0.362067\pi$
$858$	20.9023	+	1.18456i	0.713593	+	0.0404401i
$859$	−9.11061	−	6.78260i	−0.310850	−	0.231419i	0.430416	−	0.902631i	$-0.358367\pi$
$859$	−9.11061	−	6.78260i	−0.310850	−	0.231419i	−0.741266	+	0.671211i	$0.765774\pi$
$860$	0.124973	+	0.317558i	0.00426154	+	0.0108286i
$861$	−0.627675	+	3.96995i	−0.0213911	+	0.135296i
$862$	15.7302	−	23.0950i	0.535771	−	0.786618i
$863$	1.43333	+	2.48260i	0.0487911	+	0.0845087i	0.889390	−	0.457150i	$-0.151130\pi$
$863$	1.43333	+	2.48260i	0.0487911	+	0.0845087i	−0.840598	+	0.541659i	$0.817796\pi$
$864$	−5.98642	−	28.7778i	−0.203662	−	0.979041i
$865$	−0.161453	+	0.279645i	−0.00548957	+	0.00950822i
$866$	12.5792	+	26.0899i	0.427458	+	0.886572i
$867$	−12.6257	−	20.9997i	−0.428790	−	0.713188i
$868$	−11.8717	+	14.9151i	−0.402953	+	0.506252i
$869$	30.2060	−	13.0296i	1.02467	−	0.441998i
$870$	−0.127856	+	0.0384959i	−0.00433472	+	0.00130513i
$871$	−4.64118	−	0.270318i	−0.157260	−	0.00915937i
$872$	−0.225960	−	0.728935i	−0.00765197	−	0.0246848i
$873$	−44.3061	+	24.2546i	−1.49953	+	0.820895i
$874$	3.39367	+	2.94236i	0.114793	+	0.0995269i
$875$	−0.320860	+	0.0375032i	−0.0108471	+	0.00126784i
$876$	5.11071	−	6.65977i	0.172675	−	0.225013i
$877$	−5.24695	+	17.5260i	−0.177177	+	0.591812i	0.822556	+	0.568685i	$0.192548\pi$
$877$	−5.24695	+	17.5260i	−0.177177	+	0.591812i	−0.999733	+	0.0231275i	$0.992638\pi$
$878$	−10.2425	+	13.3038i	−0.345667	+	0.448980i
$879$	−14.9142	+	14.5790i	−0.503042	+	0.491737i
$880$	−0.484845	−	0.520594i	−0.0163441	−	0.0175492i
$881$	4.95360	+	5.90347i	0.166891	+	0.198893i	0.843008	−	0.537902i	$-0.180783\pi$
$881$	4.95360	+	5.90347i	0.166891	+	0.198893i	−0.676116	+	0.736795i	$0.736338\pi$
$882$	8.25907	−	24.1301i	0.278097	−	0.812503i
$883$	−15.2404	+	18.1628i	−0.512880	+	0.611227i	−0.958882	−	0.283805i	$-0.908403\pi$
$883$	−15.2404	+	18.1628i	−0.512880	+	0.611227i	0.446002	+	0.895032i	$0.352848\pi$
$884$	−16.8508	+	4.45694i	−0.566753	+	0.149903i
$885$	−0.201674	−	0.384422i	−0.00677919	−	0.0129222i
$886$	−6.91313	−	10.8902i	−0.232251	−	0.365862i
$887$	0.515565	+	8.85190i	0.0173110	+	0.297218i	0.995841	+	0.0911119i	$0.0290421\pi$
$887$	0.515565	+	8.85190i	0.0173110	+	0.297218i	−0.978530	+	0.206106i	$0.933921\pi$
$888$	12.7024	−	31.8199i	0.426265	−	1.06781i
$889$	−5.58676	+	5.92162i	−0.187374	+	0.198605i
$890$	0.188592	+	0.232276i	0.00632163	+	0.00778591i
$891$	−17.4352	−	46.0708i	−0.584102	−	1.54343i
$892$	−45.8536	−	9.62235i	−1.53529	−	0.322180i
$893$	2.45697	+	2.31803i	0.0822192	+	0.0775698i
$894$	−54.2061	+	19.8257i	−1.81292	+	0.663070i
$895$	0.373144	−	0.0217332i	0.0124728	−	0.000726460i
$896$	−0.617523	+	11.2318i	−0.0206300	+	0.375229i
$897$	−0.881595	+	21.7811i	−0.0294356	+	0.727251i
$898$	−11.5587	+	25.6485i	−0.385720	+	0.855903i
$899$	12.3196	+	10.3374i	0.410881	+	0.344770i
$900$	−29.9935	+	0.0940063i	−0.999784	+	0.00313354i
$901$	−16.5849	+	13.9164i	−0.552524	+	0.463623i
$902$	4.90093	+	17.3879i	0.163183	+	0.578955i
$903$	2.43963	−	8.70776i	0.0811857	−	0.289776i
$904$	−26.7021	−	31.2022i	−0.888097	−	1.03777i
$905$	−0.224949	−	0.0673454i	−0.00747757	−	0.00223864i
$906$	1.23876	−	4.16149i	0.0411552	−	0.138256i
$907$	−3.74968	−	32.0806i	−0.124506	−	1.06522i	−0.900615	−	0.434619i	$-0.856883\pi$
$907$	−3.74968	−	32.0806i	−0.124506	−	1.06522i	0.776108	−	0.630600i	$-0.217191\pi$
$908$	45.7468	+	1.47882i	1.51816	+	0.0490762i
$909$	−36.7065	+	12.4229i	−1.21748	+	0.412040i
$910$	0.0623587	−	0.0346717i	0.00206717	−	0.00114936i
$911$	0.400792	−	6.88133i	0.0132788	−	0.227989i	−0.985139	−	0.171759i	$-0.945055\pi$
$911$	0.400792	−	6.88133i	0.0132788	−	0.227989i	0.998418	−	0.0562298i	$-0.0179079\pi$
$912$	0.753505	−	2.62419i	0.0249510	−	0.0868956i
$913$	−25.2562	−	58.5505i	−0.835859	−	1.93774i
$914$	−9.99214	−	45.4182i	−0.330511	−	1.50230i
$915$	0.00132024	+	0.0744788i	4.36458e−5	+	0.00246219i
$916$	2.67300	−	5.68431i	0.0883183	−	0.187815i
$917$	5.02755	+	2.90266i	0.166024	+	0.0958543i
$918$	25.6909	+	31.9673i	0.847926	+	1.05508i
$919$	36.6983	−	21.1878i	1.21057	−	0.698920i	0.247683	−	0.968841i	$-0.420331\pi$
$919$	36.6983	−	21.1878i	1.21057	−	0.698920i	0.962882	+	0.269921i	$0.0869976\pi$
$920$	0.533829	−	0.513525i	0.0175998	−	0.0169304i
$921$	−3.05548	−	7.95336i	−0.100682	−	0.262072i
$922$	−10.1497	+	32.0107i	−0.334263	+	1.05422i
$923$	6.06977	−	8.15312i	0.199789	−	0.268363i
$924$	1.91509	+	18.7537i	0.0630017	+	0.616952i
$925$	−29.2093	−	19.2112i	−0.960394	−	0.631661i
$926$	−17.5953	+	29.3697i	−0.578219	+	0.965148i
$927$	8.65880	−	8.76965i	0.284392	−	0.288033i
$928$	9.45883	+	0.765819i	0.310501	+	0.0251392i
$929$	−33.5414	+	24.9707i	−1.10046	+	0.819260i	−0.984742	−	0.174022i	$-0.944324\pi$
$929$	−33.5414	+	24.9707i	−1.10046	+	0.819260i	−0.115716	+	0.993282i	$0.536916\pi$
$930$	−0.420292	−	0.636847i	−0.0137819	−	0.0208830i
$931$	1.72311	−	1.62567i	0.0564728	−	0.0532793i
$932$	−19.5023	−	31.8476i	−0.638820	−	1.04320i
$933$	11.3844	+	25.1563i	0.372707	+	0.823581i
$934$	−5.60016	+	22.0360i	−0.183243	+	0.721041i
$935$	0.932713	+	0.339480i	0.0305030	+	0.0111022i
$936$	12.2342	−	5.08937i	0.399886	−	0.166351i
$937$	−22.2649	+	8.10376i	−0.727362	+	0.264738i	−0.679048	−	0.734094i	$-0.737607\pi$
$937$	−22.2649	+	8.10376i	−0.727362	+	0.264738i	−0.0483144	+	0.998832i	$0.515385\pi$
$938$	−0.418740	−	4.16514i	−0.0136724	−	0.135997i
$939$	−57.3223	−	12.5169i	−1.87064	−	0.408475i
$940$	0.417329	−	0.368986i	0.0136118	−	0.0120350i
$941$	−5.30779	−	8.07010i	−0.173029	−	0.263078i	0.738554	−	0.674195i	$-0.235509\pi$
$941$	−5.30779	−	8.07010i	−0.173029	−	0.263078i	−0.911583	+	0.411117i	$0.865139\pi$
$942$	−0.0193085	−	12.3211i	−0.000629105	−	0.401444i
$943$	−18.0200	+	5.39482i	−0.586811	+	0.175680i
$944$	3.38399	+	30.6666i	0.110140	+	0.998112i
$945$	−0.134154	−	0.100922i	−0.00436404	−	0.00328298i
$946$	−6.41043	−	40.1372i	−0.208421	−	1.30497i
$947$	−9.22998	−	2.18754i	−0.299934	−	0.0710856i	0.0778935	−	0.996962i	$-0.475181\pi$
$947$	−9.22998	−	2.18754i	−0.299934	−	0.0710856i	−0.377827	+	0.925876i	$0.623329\pi$
$948$	13.6144	−	15.7524i	0.442175	−	0.511615i
$949$	3.38176	+	1.69838i	0.109777	+	0.0551319i
$950$	−2.46908	−	1.29039i	−0.0801075	−	0.0418657i
$951$	14.9899	−	11.5781i	0.486082	−	0.375446i
$952$	−6.35592	−	14.3501i	−0.205997	−	0.465090i
$953$	19.3885	+	3.41871i	0.628054	+	0.110743i	0.478610	−	0.878027i	$-0.341141\pi$
$953$	19.3885	+	3.41871i	0.628054	+	0.110743i	0.149444	+	0.988770i	$0.452252\pi$
$954$	11.0614	−	12.1871i	0.358128	−	0.394572i
$955$	−0.295057	+	0.0520266i	−0.00954784	+	0.00168354i
$956$	−3.16163	+	34.8426i	−0.102254	+	1.12689i
$957$	15.8576	−	1.20595i	0.512604	−	0.0389827i
$958$	10.2422	−	4.22312i	0.330911	−	0.136443i
$959$	−13.2311	+	3.13584i	−0.427256	+	0.101261i
$960$	−0.419767	−	0.162864i	−0.0135479	−	0.00525642i
$961$	−24.1218	+	55.9205i	−0.778121	+	1.80389i
$962$	15.1649	+	2.92737i	0.488936	+	0.0943821i
$963$	−1.42360	+	10.1695i	−0.0458750	+	0.327708i
$964$	−19.0512	+	14.9641i	−0.613599	+	0.481963i
$965$	−0.174645	−	0.347747i	−0.00562202	−	0.0111944i
$966$	−19.4921	+	2.30927i	−0.627148	+	0.0742995i
$967$	−0.543073	+	4.64628i	−0.0174640	+	0.149414i	−0.999157	−	0.0410569i	$-0.986928\pi$
$967$	−0.543073	+	4.64628i	−0.0174640	+	0.149414i	0.981693	+	0.190471i	$0.0610016\pi$
$968$	27.2585	+	46.1723i	0.876121	+	1.48403i
$969$	0.727863	+	3.73912i	0.0233823	+	0.120118i
$970$	−0.0574615	+	0.771582i	−0.00184498	+	0.0247740i
$971$	−18.2701			−0.586316			−0.293158	−	0.956064i	$-0.594706\pi$
$971$	−18.2701			−0.586316			−0.293158	+	0.956064i	$0.594706\pi$
$972$	−22.6372	−	21.4373i	−0.726089	−	0.687600i
$973$	−4.23346			−0.135718
$974$	0.210890	−	2.83179i	0.00675736	−	0.0907365i
$975$	−2.58351	−	13.2718i	−0.0827385	−	0.425037i
$976$	1.84275	−	4.96305i	0.0589851	−	0.158863i
$977$	−1.66785	+	14.2694i	−0.0533592	+	0.456517i	0.939975	+	0.341244i	$0.110848\pi$
$977$	−1.66785	+	14.2694i	−0.0533592	+	0.456517i	−0.993334	+	0.115273i	$0.963226\pi$
$978$	7.44301	−	0.881789i	0.238001	−	0.0281965i
$979$	−15.9932	−	31.8452i	−0.511146	−	1.01778i
$980$	−0.241321	−	0.307232i	−0.00770871	−	0.00981416i
$981$	−0.638123	−	0.497999i	−0.0203737	−	0.0158999i
$982$	−6.02200	−	1.16246i	−0.192170	−	0.0370956i
$983$	16.4247	−	38.0768i	0.523868	−	1.21446i	−0.426827	−	0.904333i	$-0.640369\pi$
$983$	16.4247	−	38.0768i	0.523868	−	1.21446i	0.950695	−	0.310129i	$-0.100372\pi$
$984$	7.58696	+	8.55393i	0.241863	+	0.272689i
$985$	0.809625	−	0.191885i	0.0257968	−	0.00611395i
$986$	−12.2407	+	5.04717i	−0.389825	+	0.160735i
$987$	−14.7188	+	1.11934i	−0.468506	+	0.0356290i
$988$	1.22573	+	0.111223i	0.0389956	+	0.00353847i
$989$	41.6786	−	7.34906i	1.32530	−	0.233687i
$990$	−0.737437	−	0.159817i	−0.0234373	−	0.00507931i
$991$	−42.0886	−	7.42136i	−1.33699	−	0.235747i	−0.540982	−	0.841034i	$-0.681947\pi$
$991$	−42.0886	−	7.42136i	−1.33699	−	0.235747i	−0.796007	+	0.605287i	$0.793058\pi$
$992$	11.3100	+	53.0370i	0.359094	+	1.68393i
$993$	43.2177	−	33.3810i	1.37147	−	1.05931i
$994$	8.11140	+	4.23917i	0.257278	+	0.134458i
$995$	−0.0467301	−	0.0234688i	−0.00148144	−	0.000744010i
$996$	−30.5341	−	26.3898i	−0.967511	−	0.836194i
$997$	−19.8182	−	4.69700i	−0.627649	−	0.148755i	−0.0955318	−	0.995426i	$-0.530455\pi$
$997$	−19.8182	−	4.69700i	−0.627649	−	0.148755i	−0.532117	+	0.846671i	$0.678603\pi$
$998$	−6.99770	−	43.8142i	−0.221508	−	1.38691i
$999$	−8.20351	−	35.4019i	−0.259548	−	1.12007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.11.3	✓	936
3.2	odd	2		972.2.p.a.359.50		936
4.3	odd	2	inner	324.2.p.a.11.24	yes	936
12.11	even	2		972.2.p.a.359.29		936
81.22	even	27		972.2.p.a.287.29		936
81.59	odd	54	inner	324.2.p.a.59.24	yes	936
324.59	even	54	inner	324.2.p.a.59.3	yes	936
324.103	odd	54		972.2.p.a.287.50		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.11.3	✓	936	1.1	even	1	trivial
324.2.p.a.11.24	yes	936	4.3	odd	2	inner
324.2.p.a.59.3	yes	936	324.59	even	54	inner
324.2.p.a.59.24	yes	936	81.59	odd	54	inner
972.2.p.a.287.29		936	81.22	even	27
972.2.p.a.287.50		936	324.103	odd	54
972.2.p.a.359.29		936	12.11	even	2
972.2.p.a.359.50		936	3.2	odd	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41031 - 0.105029i) q^{2} +(-0.330952 - 1.70014i) q^{3} +(1.97794 + 0.296246i) q^{4} +(0.00377236 - 0.0322746i) q^{5} +(0.288181 + 2.43248i) q^{6} +(-0.446224 - 0.888506i) q^{7} +(-2.75839 - 0.625539i) q^{8} +(-2.78094 + 1.12533i) q^{9} +O(q^{10})\)	\(q+(-1.41031 - 0.105029i) q^{2} +(-0.330952 - 1.70014i) q^{3} +(1.97794 + 0.296246i) q^{4} +(0.00377236 - 0.0322746i) q^{5} +(0.288181 + 2.43248i) q^{6} +(-0.446224 - 0.888506i) q^{7} +(-2.75839 - 0.625539i) q^{8} +(-2.78094 + 1.12533i) q^{9} +(-0.00870995 + 0.0451209i) q^{10} +(2.16786 - 5.02566i) q^{11} +(-0.150943 - 3.46081i) q^{12} +(1.51950 - 0.360127i) q^{13} +(0.535995 + 1.29993i) q^{14} +(-0.0561197 + 0.00426781i) q^{15} +(3.82448 + 1.17191i) q^{16} +(-5.49614 + 0.969119i) q^{17} +(4.04018 - 1.29498i) q^{18} +(0.388087 + 0.0684303i) q^{19} +(0.0170227 - 0.0627196i) q^{20} +(-1.36290 + 1.05270i) q^{21} +(-3.58519 + 6.86004i) q^{22} +(-7.20224 - 3.61710i) q^{23} +(-0.150609 + 4.89666i) q^{24} +(4.86420 + 1.15284i) q^{25} +(-2.18078 + 0.348299i) q^{26} +(2.83357 + 4.35556i) q^{27} +(-0.619388 - 1.88960i) q^{28} +(-1.60710 + 0.481133i) q^{29} +(0.0795943 - 0.000124733i) q^{30} +(-5.26788 - 8.00942i) q^{31} +(-5.27061 - 2.05444i) q^{32} +(-9.26178 - 2.02241i) q^{33} +(7.85304 - 0.789502i) q^{34} +(-0.0303595 + 0.0110499i) q^{35} +(-5.83390 + 1.40199i) q^{36} +(-6.57185 - 2.39196i) q^{37} +(-0.540136 - 0.137268i) q^{38} +(-1.11515 - 2.46417i) q^{39} +(-0.0305946 + 0.0866660i) q^{40} +(1.69763 - 1.60163i) q^{41} +(2.03268 - 1.34148i) q^{42} +(-4.21206 + 3.13576i) q^{43} +(5.77672 - 9.29823i) q^{44} +(0.0258288 + 0.0939989i) q^{45} +(9.77747 + 5.85767i) q^{46} +(7.16150 + 4.71019i) q^{47} +(0.726696 - 6.88999i) q^{48} +(3.58978 - 4.82192i) q^{49} +(-6.73894 - 2.13673i) q^{50} +(3.46660 + 9.02348i) q^{51} +(3.11215 - 0.262164i) q^{52} +(3.35957 - 1.93965i) q^{53} +(-3.53875 - 6.44028i) q^{54} +(-0.154023 - 0.0889253i) q^{55} +(0.675065 + 2.72997i) q^{56} +(-0.0120974 - 0.682449i) q^{57} +(2.31704 - 0.509755i) q^{58} +(3.05504 + 7.08237i) q^{59} +(-0.112266 - 0.00818379i) q^{60} +(0.0769563 - 1.32129i) q^{61} +(6.58811 + 11.8490i) q^{62} +(2.24078 + 1.96873i) q^{63} +(7.21740 + 3.45096i) q^{64} +(-0.00589087 - 0.0503996i) q^{65} +(12.8495 + 3.82497i) q^{66} +(-2.85205 - 0.853849i) q^{67} +(-11.1581 + 0.288645i) q^{68} +(-3.76597 + 13.4419i) q^{69} +(0.0439768 - 0.0123952i) q^{70} +(4.98620 - 4.18392i) q^{71} +(8.37485 - 1.36450i) q^{72} +(1.85640 + 1.55770i) q^{73} +(9.01711 + 4.06363i) q^{74} +(0.350165 - 8.65134i) q^{75} +(0.747340 + 0.250320i) q^{76} +(-5.43268 + 0.316418i) q^{77} +(1.31389 + 3.59236i) q^{78} +(4.37177 + 4.12455i) q^{79} +(0.0522503 - 0.119012i) q^{80} +(6.46727 - 6.25895i) q^{81} +(-2.56240 + 2.08049i) q^{82} +(7.99493 - 8.47413i) q^{83} +(-3.00760 + 1.67841i) q^{84} +(0.0105445 + 0.181042i) q^{85} +(6.26965 - 3.98000i) q^{86} +(1.34987 + 2.57306i) q^{87} +(-9.12354 + 12.5066i) q^{88} +(4.18508 - 4.98758i) q^{89} +(-0.0265540 - 0.135280i) q^{90} +(-0.998011 - 1.18938i) q^{91} +(-13.1740 - 9.28803i) q^{92} +(-11.8737 + 11.6069i) q^{93} +(-9.60521 - 7.39498i) q^{94} +(0.00367256 - 0.0122672i) q^{95} +(-1.74851 + 9.64068i) q^{96} +(16.7230 - 1.95464i) q^{97} +(-5.56914 + 6.42336i) q^{98} +(-0.373168 + 16.4156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

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