LMFDB - Embedded newform 392.2.bc.a.243.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(3,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 21, 1]))

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

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

chi := DirichletCharacter("392.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.bc (of order $42$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			243.47
Character	$\chi$	$=$	392.243
Dual form			392.2.bc.a.171.47

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29071 - 0.577993i) q^{2} +(2.25676 + 0.885712i) q^{3} +(1.33185 - 1.49204i) q^{4} +(0.346055 - 0.0521594i) q^{5} +(3.42475 - 0.161194i) q^{6} +(-2.27282 + 1.35435i) q^{7} +(0.856640 - 2.69558i) q^{8} +(2.10932 + 1.95716i) q^{9} +O(q^{10})$	\(q+(1.29071 - 0.577993i) q^{2} +(2.25676 + 0.885712i) q^{3} +(1.33185 - 1.49204i) q^{4} +(0.346055 - 0.0521594i) q^{5} +(3.42475 - 0.161194i) q^{6} +(-2.27282 + 1.35435i) q^{7} +(0.856640 - 2.69558i) q^{8} +(2.10932 + 1.95716i) q^{9} +(0.416508 - 0.267340i) q^{10} +(-1.49441 + 1.38661i) q^{11} +(4.32718 - 2.18753i) q^{12} +(-0.125627 - 0.550408i) q^{13} +(-2.15074 + 3.06175i) q^{14} +(0.827161 + 0.188794i) q^{15} +(-0.452356 - 3.97434i) q^{16} +(3.72333 - 0.279025i) q^{17} +(3.85373 + 1.30695i) q^{18} +(-3.51049 - 2.02678i) q^{19} +(0.383069 - 0.585796i) q^{20} +(-6.32878 + 1.04338i) q^{21} +(-1.12740 + 2.65347i) q^{22} +(-1.49317 - 0.111898i) q^{23} +(4.32074 - 5.32454i) q^{24} +(-4.66083 + 1.43768i) q^{25} +(-0.480279 - 0.637804i) q^{26} +(-0.128914 - 0.267694i) q^{27} +(-1.00631 + 5.19493i) q^{28} +(-1.23046 + 2.55507i) q^{29} +(1.17674 - 0.234415i) q^{30} +(0.563337 + 0.975728i) q^{31} +(-2.88100 - 4.86825i) q^{32} +(-4.60067 + 1.80563i) q^{33} +(4.64445 - 2.51220i) q^{34} +(-0.715880 + 0.587230i) q^{35} +(5.72945 - 0.540539i) q^{36} +(3.18351 + 4.66935i) q^{37} +(-5.70247 - 0.586944i) q^{38} +(0.203993 - 1.35341i) q^{39} +(0.155845 - 0.977502i) q^{40} +(3.61147 - 2.88005i) q^{41} +(-7.56554 + 5.00468i) q^{42} +(-0.185374 + 0.232452i) q^{43} +(0.0785463 + 4.07648i) q^{44} +(0.832024 + 0.567264i) q^{45} +(-1.99192 + 0.718615i) q^{46} +(-6.30704 - 1.94546i) q^{47} +(2.49926 - 9.36978i) q^{48} +(3.33146 - 6.15641i) q^{49} +(-5.18480 + 4.54954i) q^{50} +(8.64979 + 2.66811i) q^{51} +(-0.988546 - 0.545620i) q^{52} +(-2.64110 + 3.87379i) q^{53} +(-0.321116 - 0.271002i) q^{54} +(-0.444825 + 0.557792i) q^{55} +(1.70378 + 7.28678i) q^{56} +(-6.12717 - 7.68323i) q^{57} +(-0.111348 + 4.00904i) q^{58} +(-0.580487 + 3.85128i) q^{59} +(1.38334 - 0.982710i) q^{60} +(12.1707 - 8.29783i) q^{61} +(1.29107 + 0.933775i) q^{62} +(-7.44479 - 1.59152i) q^{63} +(-6.53234 - 4.61829i) q^{64} +(-0.0721828 - 0.183919i) q^{65} +(-4.89448 + 4.98970i) q^{66} +(4.11031 + 7.11926i) q^{67} +(4.54260 - 5.92697i) q^{68} +(-3.27062 - 1.57505i) q^{69} +(-0.584577 + 1.17171i) q^{70} +(-0.343595 - 0.713483i) q^{71} +(7.08261 - 4.00926i) q^{72} +(0.852846 + 2.76486i) q^{73} +(6.80783 + 4.18672i) q^{74} +(-11.7917 - 0.883668i) q^{75} +(-7.69947 + 2.53841i) q^{76} +(1.51858 - 5.17549i) q^{77} +(-0.518964 - 1.86476i) q^{78} +(1.15975 + 0.669580i) q^{79} +(-0.363839 - 1.35175i) q^{80} +(-0.698924 - 9.32650i) q^{81} +(2.99670 - 5.80471i) q^{82} +(5.93191 + 1.35392i) q^{83} +(-6.87222 + 10.8324i) q^{84} +(1.27392 - 0.290765i) q^{85} +(-0.104908 + 0.407172i) q^{86} +(-5.03989 + 4.67634i) q^{87} +(2.45756 + 5.21615i) q^{88} +(-10.5335 + 11.3524i) q^{89} +(1.40177 + 0.251268i) q^{90} +(1.03097 + 1.08084i) q^{91} +(-2.15564 + 2.07884i) q^{92} +(0.407101 + 2.70094i) q^{93} +(-9.26500 + 1.13440i) q^{94} +(-1.32054 - 0.518272i) q^{95} +(-2.18985 - 13.5382i) q^{96} -15.4058i q^{97} +(0.741576 - 9.87168i) q^{98} -5.86602 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 22 q^{3} - 13 q^{4} - 14 q^{6} - 4 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 22 * q^3 - 13 * q^4 - 14 * q^6 - 4 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 22 q^{3} - 13 q^{4} - 14 q^{6} - 4 q^{8} - 76 q^{9} - 20 q^{10} - 26 q^{11} - 31 q^{12} + 15 q^{14} - 9 q^{16} - 22 q^{17} - 18 q^{18} - 36 q^{19} - 14 q^{20} - 26 q^{22} + 22 q^{24} + 20 q^{25} - 20 q^{26} - 28 q^{27} - 62 q^{28} - 5 q^{30} - 23 q^{32} - 22 q^{33} - 42 q^{34} - 46 q^{35} - 32 q^{36} - 4 q^{38} - 28 q^{41} + 16 q^{42} - 20 q^{43} + 6 q^{46} - 16 q^{49} - 140 q^{50} - 34 q^{51} + 10 q^{52} + 43 q^{54} + 56 q^{56} - 34 q^{57} - 16 q^{58} - 70 q^{59} + 92 q^{60} + 20 q^{64} - 16 q^{65} + 2 q^{66} - 24 q^{67} + 15 q^{68} - 114 q^{70} + 110 q^{72} - 46 q^{73} - 34 q^{74} - 52 q^{75} - 147 q^{76} + 48 q^{78} + 6 q^{80} + 70 q^{81} - 68 q^{82} - 28 q^{83} + 128 q^{84} - 117 q^{86} + 133 q^{88} - 46 q^{89} - 294 q^{90} - 124 q^{91} - 102 q^{92} - 44 q^{94} + 38 q^{96} - 225 q^{98} - 72 q^{99}+O(q^{100}) $ 648 * q - 13 * q^2 - 22 * q^3 - 13 * q^4 - 14 * q^6 - 4 * q^8 - 76 * q^9 - 20 * q^10 - 26 * q^11 - 31 * q^12 + 15 * q^14 - 9 * q^16 - 22 * q^17 - 18 * q^18 - 36 * q^19 - 14 * q^20 - 26 * q^22 + 22 * q^24 + 20 * q^25 - 20 * q^26 - 28 * q^27 - 62 * q^28 - 5 * q^30 - 23 * q^32 - 22 * q^33 - 42 * q^34 - 46 * q^35 - 32 * q^36 - 4 * q^38 - 28 * q^41 + 16 * q^42 - 20 * q^43 + 6 * q^46 - 16 * q^49 - 140 * q^50 - 34 * q^51 + 10 * q^52 + 43 * q^54 + 56 * q^56 - 34 * q^57 - 16 * q^58 - 70 * q^59 + 92 * q^60 + 20 * q^64 - 16 * q^65 + 2 * q^66 - 24 * q^67 + 15 * q^68 - 114 * q^70 + 110 * q^72 - 46 * q^73 - 34 * q^74 - 52 * q^75 - 147 * q^76 + 48 * q^78 + 6 * q^80 + 70 * q^81 - 68 * q^82 - 28 * q^83 + 128 * q^84 - 117 * q^86 + 133 * q^88 - 46 * q^89 - 294 * q^90 - 124 * q^91 - 102 * q^92 - 44 * q^94 + 38 * q^96 - 225 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{42}\right)$

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 $

$2$	1.29071	−	0.577993i	0.912668	−	0.408702i
$2$	1.29071	−	0.577993i	0.912668	−	0.408702i
$3$	2.25676	+	0.885712i	1.30294	+	0.511366i	0.912430	−	0.409232i	$-0.134204\pi$
$3$	2.25676	+	0.885712i	1.30294	+	0.511366i	0.390510	+	0.920599i	$0.372299\pi$
$4$	1.33185	−	1.49204i	0.665925	−	0.746019i
$5$	0.346055	−	0.0521594i	0.154761	−	0.0233264i	−0.0712050	−	0.997462i	$-0.522684\pi$
$5$	0.346055	−	0.0521594i	0.154761	−	0.0233264i	0.225965	+	0.974135i	$0.427446\pi$
$6$	3.42475	−	0.161194i	1.39815	−	0.0658073i
$7$	−2.27282	+	1.35435i	−0.859047	+	0.511897i
$7$	−2.27282	+	1.35435i	−0.859047	+	0.511897i
$8$	0.856640	−	2.69558i	0.302868	−	0.953033i
$9$	2.10932	+	1.95716i	0.703105	+	0.652386i
$10$	0.416508	−	0.267340i	0.131711	−	0.0845402i
$11$	−1.49441	+	1.38661i	−0.450583	+	0.418080i	−0.872545	−	0.488534i	$-0.837532\pi$
$11$	−1.49441	+	1.38661i	−0.450583	+	0.418080i	0.421962	+	0.906613i	$0.361341\pi$
$12$	4.32718	−	2.18753i	1.24915	−	0.631487i
$13$	−0.125627	−	0.550408i	−0.0348427	−	0.152656i	0.954514	−	0.298166i	$-0.0963748\pi$
$13$	−0.125627	−	0.550408i	−0.0348427	−	0.152656i	−0.989357	+	0.145510i	$0.953518\pi$
$14$	−2.15074	+	3.06175i	−0.574810	+	0.818287i
$15$	0.827161	+	0.188794i	0.213572	+	0.0487464i
$16$	−0.452356	−	3.97434i	−0.113089	−	0.993585i
$17$	3.72333	−	0.279025i	0.903040	−	0.0676735i	0.384889	−	0.922963i	$-0.374240\pi$
$17$	3.72333	−	0.279025i	0.903040	−	0.0676735i	0.518151	+	0.855289i	$0.326621\pi$
$18$	3.85373	+	1.30695i	0.908333	+	0.308051i
$19$	−3.51049	−	2.02678i	−0.805361	−	0.464975i	0.0399816	−	0.999200i	$-0.487270\pi$
$19$	−3.51049	−	2.02678i	−0.805361	−	0.464975i	−0.845342	+	0.534225i	$0.820603\pi$
$20$	0.383069	−	0.585796i	0.0856569	−	0.130988i
$21$	−6.32878	+	1.04338i	−1.38105	+	0.227684i
$22$	−1.12740	+	2.65347i	−0.240362	+	0.565722i
$23$	−1.49317	−	0.111898i	−0.311348	−	0.0233323i	−0.0818601	−	0.996644i	$-0.526086\pi$
$23$	−1.49317	−	0.111898i	−0.311348	−	0.0233323i	−0.229488	+	0.973312i	$0.573705\pi$
$24$	4.32074	−	5.32454i	0.881968	−	1.08687i
$25$	−4.66083	+	1.43768i	−0.932166	+	0.287535i
$26$	−0.480279	−	0.637804i	−0.0941905	−	0.125084i
$27$	−0.128914	−	0.267694i	−0.0248096	−	0.0515177i
$28$	−1.00631	+	5.19493i	−0.190175	+	0.981750i
$29$	−1.23046	+	2.55507i	−0.228490	+	0.474464i	−0.983420	−	0.181341i	$-0.941956\pi$
$29$	−1.23046	+	2.55507i	−0.228490	+	0.474464i	0.754931	+	0.655805i	$0.227671\pi$
$30$	1.17674	−	0.234415i	0.214843	−	0.0427981i
$31$	0.563337	+	0.975728i	0.101178	+	0.175246i	0.912170	−	0.409811i	$-0.134405\pi$
$31$	0.563337	+	0.975728i	0.101178	+	0.175246i	−0.810992	+	0.585057i	$0.801072\pi$
$32$	−2.88100	−	4.86825i	−0.509293	−	0.860593i
$33$	−4.60067	+	1.80563i	−0.800874	+	0.314320i
$34$	4.64445	−	2.51220i	0.796517	−	0.430838i
$35$	−0.715880	+	0.587230i	−0.121006	+	0.0992599i
$36$	5.72945	−	0.540539i	0.954908	−	0.0900898i
$37$	3.18351	+	4.66935i	0.523366	+	0.767637i	0.993362	−	0.115032i	$-0.0366970\pi$
$37$	3.18351	+	4.66935i	0.523366	+	0.767637i	−0.469996	+	0.882669i	$0.655745\pi$
$38$	−5.70247	−	0.586944i	−0.925063	−	0.0952149i
$39$	0.203993	−	1.35341i	0.0326651	−	0.216719i
$40$	0.155845	−	0.977502i	0.0246412	−	0.154557i
$41$	3.61147	−	2.88005i	0.564017	−	0.449789i	−0.299509	−	0.954094i	$-0.596823\pi$
$41$	3.61147	−	2.88005i	0.564017	−	0.449789i	0.863526	+	0.504305i	$0.168251\pi$
$42$	−7.56554	+	5.00468i	−1.16739	+	0.772240i
$43$	−0.185374	+	0.232452i	−0.0282693	+	0.0354486i	−0.795765	−	0.605605i	$-0.792931\pi$
$43$	−0.185374	+	0.232452i	−0.0282693	+	0.0354486i	0.767496	+	0.641054i	$0.221502\pi$
$44$	0.0785463	+	4.07648i	0.0118413	+	0.614553i
$45$	0.832024	+	0.567264i	0.124031	+	0.0845627i
$46$	−1.99192	+	0.718615i	−0.293693	+	0.105954i
$47$	−6.30704	−	1.94546i	−0.919976	−	0.283775i	−0.201631	−	0.979462i	$-0.564624\pi$
$47$	−6.30704	−	1.94546i	−0.919976	−	0.283775i	−0.718345	+	0.695687i	$0.755100\pi$
$48$	2.49926	−	9.36978i	0.360738	−	1.35241i
$49$	3.33146	−	6.15641i	0.475922	−	0.879487i
$50$	−5.18480	+	4.54954i	−0.733242	+	0.643403i
$51$	8.64979	+	2.66811i	1.21121	+	0.373610i
$52$	−0.988546	−	0.545620i	−0.137087	−	0.0756639i
$53$	−2.64110	+	3.87379i	−0.362783	+	0.532105i	−0.963623	−	0.267264i	$-0.913880\pi$
$53$	−2.64110	+	3.87379i	−0.362783	+	0.532105i	0.600840	+	0.799369i	$0.294833\pi$
$54$	−0.321116	−	0.271002i	−0.0436983	−	0.0368788i
$55$	−0.444825	+	0.557792i	−0.0599801	+	0.0752127i
$56$	1.70378	+	7.28678i	0.227677	+	0.973737i
$57$	−6.12717	−	7.68323i	−0.811564	−	1.01767i
$58$	−0.111348	+	4.00904i	−0.0146207	+	0.526412i
$59$	−0.580487	+	3.85128i	−0.0755729	+	0.501394i	0.918737	+	0.394870i	$0.129210\pi$
$59$	−0.580487	+	3.85128i	−0.0755729	+	0.501394i	−0.994310	+	0.106524i	$0.966028\pi$
$60$	1.38334	−	0.982710i	0.178589	−	0.126867i
$61$	12.1707	−	8.29783i	1.55830	−	1.06243i	0.591688	−	0.806167i	$-0.298462\pi$
$61$	12.1707	−	8.29783i	1.55830	−	1.06243i	0.966607	−	0.256262i	$-0.0824908\pi$
$62$	1.29107	+	0.933775i	0.163966	+	0.118590i
$63$	−7.44479	−	1.59152i	−0.937955	−	0.200513i
$64$	−6.53234	−	4.61829i	−0.816542	−	0.577286i
$65$	−0.0721828	−	0.183919i	−0.00895318	−	0.0228123i
$66$	−4.89448	+	4.98970i	−0.602469	+	0.614189i
$67$	4.11031	+	7.11926i	0.502154	+	0.869756i	0.999997	+	0.00248880i	$0.000792209\pi$
$67$	4.11031	+	7.11926i	0.502154	+	0.869756i	−0.497843	+	0.867267i	$0.665874\pi$
$68$	4.54260	−	5.92697i	0.550871	−	0.718750i
$69$	−3.27062	−	1.57505i	−0.393736	−	0.189613i
$70$	−0.584577	+	1.17171i	−0.0698703	+	0.140047i
$71$	−0.343595	−	0.713483i	−0.0407772	−	0.0846748i	0.879585	−	0.475742i	$-0.157820\pi$
$71$	−0.343595	−	0.713483i	−0.0407772	−	0.0846748i	−0.920362	+	0.391067i	$0.872106\pi$
$72$	7.08261	−	4.00926i	0.834694	−	0.472495i
$73$	0.852846	+	2.76486i	0.0998181	+	0.323602i	0.991684	−	0.128698i	$-0.0410797\pi$
$73$	0.852846	+	2.76486i	0.0998181	+	0.323602i	−0.891866	+	0.452300i	$0.850604\pi$
$74$	6.80783	+	4.18672i	0.791394	+	0.486696i
$75$	−11.7917	−	0.883668i	−1.36159	−	0.102037i
$76$	−7.69947	+	2.53841i	−0.883190	+	0.291176i
$77$	1.51858	−	5.17549i	0.173058	−	0.589802i
$78$	−0.518964	−	1.86476i	−0.0587611	−	0.211142i
$79$	1.15975	+	0.669580i	0.130482	+	0.0753336i	0.563820	−	0.825898i	$-0.309331\pi$
$79$	1.15975	+	0.669580i	0.130482	+	0.0753336i	−0.433338	+	0.901231i	$0.642664\pi$
$80$	−0.363839	−	1.35175i	−0.0406785	−	0.151130i
$81$	−0.698924	−	9.32650i	−0.0776582	−	1.03628i
$82$	2.99670	−	5.80471i	0.330930	−	0.641023i
$83$	5.93191	+	1.35392i	0.651111	+	0.148612i	0.535304	−	0.844660i	$-0.320197\pi$
$83$	5.93191	+	1.35392i	0.651111	+	0.148612i	0.115808	+	0.993272i	$0.463054\pi$
$84$	−6.87222	+	10.8324i	−0.749821	+	1.18191i
$85$	1.27392	−	0.290765i	0.138176	−	0.0315378i
$86$	−0.104908	+	0.407172i	−0.0113126	+	0.0439065i
$87$	−5.03989	+	4.67634i	−0.540333	+	0.501356i
$88$	2.45756	+	5.21615i	0.261977	+	0.556043i
$89$	−10.5335	+	11.3524i	−1.11655	+	1.20335i	−0.139526	+	0.990218i	$0.544558\pi$
$89$	−10.5335	+	11.3524i	−1.11655	+	1.20335i	−0.977023	+	0.213135i	$0.931633\pi$
$90$	1.40177	+	0.251268i	0.147760	+	0.0264860i
$91$	1.03097	+	1.08084i	0.108076	+	0.113303i
$92$	−2.15564	+	2.07884i	−0.224741	+	0.216734i
$93$	0.407101	+	2.70094i	0.0422144	+	0.280074i
$94$	−9.26500	+	1.13440i	−0.955612	+	0.117004i
$95$	−1.32054	−	0.518272i	−0.135484	−	0.0531736i
$96$	−2.18985	−	13.5382i	−0.223500	−	1.38174i
$97$		−	15.4058i		−	1.56422i	−0.623140	−	0.782111i	$-0.714143\pi$
$97$		−	15.4058i		−	1.56422i	0.623140	−	0.782111i	$-0.285857\pi$
$98$	0.741576	−	9.87168i	0.0749104	−	0.997190i
$99$	−5.86602			−0.589557
$100$	−4.06246	+	8.86890i	−0.406246	+	0.886890i
$101$	5.68496	−	14.4851i	0.565675	−	1.44132i	−0.306380	−	0.951909i	$-0.599118\pi$
$101$	5.68496	−	14.4851i	0.565675	−	1.44132i	0.872055	−	0.489407i	$-0.162787\pi$
$102$	12.7065	−	1.55577i	1.25813	−	0.154044i
$103$	−7.50261	+	1.13084i	−0.739254	+	0.111425i	−0.507865	−	0.861437i	$-0.669565\pi$
$103$	−7.50261	+	1.13084i	−0.739254	+	0.111425i	−0.231389	+	0.972861i	$0.574327\pi$
$104$	−1.59129	−	0.132863i	−0.156039	−	0.0130283i
$105$	−2.13568	+	0.691172i	−0.208421	+	0.0674515i
$106$	−1.16987	+	6.52646i	−0.113628	+	0.633906i
$107$	13.2488	+	12.2931i	1.28081	+	1.18842i	0.971390	+	0.237490i	$0.0763247\pi$
$107$	13.2488	+	12.2931i	1.28081	+	1.18842i	0.309418	+	0.950926i	$0.399866\pi$
$108$	−0.571104	−	0.164182i	−0.0549545	−	0.0157984i
$109$	10.8573	+	11.7013i	1.03994	+	1.12078i	0.992541	+	0.121909i	$0.0389015\pi$
$109$	10.8573	+	11.7013i	1.03994	+	1.12078i	0.0473951	+	0.998876i	$0.484908\pi$
$110$	−0.251738	+	0.977052i	−0.0240023	+	0.0931583i
$111$	3.04871	+	13.3573i	0.289371	+	1.26782i
$112$	6.41078	+	8.42032i	0.605762	+	0.795646i
$113$	4.43429	−	19.4279i	0.417143	−	1.82762i	−0.131184	−	0.991358i	$-0.541878\pi$
$113$	4.43429	−	19.4279i	0.417143	−	1.82762i	0.548327	−	0.836264i	$-0.315265\pi$
$114$	−12.3492	−	6.37534i	−1.15661	−	0.597105i
$115$	−0.522556	+	0.0391602i	−0.0487286	+	0.00365171i
$116$	2.17348	+	5.23885i	0.201802	+	0.486415i
$117$	0.812249	−	1.40686i	0.0750924	−	0.130064i
$118$	1.47677	+	5.30639i	0.135948	+	0.488492i
$119$	−8.08457	+	5.67687i	−0.741111	+	0.520398i
$120$	1.21749	−	2.06795i	0.111141	−	0.188777i
$121$	−0.511455	+	6.82489i	−0.0464959	+	0.620445i
$122$	10.9127	−	17.7446i	0.987989	−	1.60652i
$123$	10.7011	−	3.30086i	0.964887	−	0.297628i
$124$	2.20610	+	0.459003i	0.198114	+	0.0412197i
$125$	−3.11445	+	1.49984i	−0.278565	+	0.134150i
$126$	−10.5289	+	2.24885i	−0.937991	+	0.200343i
$127$	−5.63414	+	11.6994i	−0.499949	+	1.03815i	0.486438	+	0.873715i	$0.338296\pi$
$127$	−5.63414	+	11.6994i	−0.499949	+	1.03815i	−0.986387	+	0.164440i	$0.947418\pi$
$128$	−11.1007	−	2.18522i	−0.981170	−	0.193148i
$129$	−0.624230	+	0.360400i	−0.0549604	+	0.0317314i
$130$	−0.199471	−	0.195664i	−0.0174947	−	0.0171609i
$131$	−13.6338	+	5.35089i	−1.19119	+	0.467510i	−0.876369	−	0.481640i	$-0.840041\pi$
$131$	−13.6338	+	5.35089i	−1.19119	+	0.467510i	−0.314826	+	0.949150i	$0.601946\pi$
$132$	−3.43333	+	9.26921i	−0.298833	+	0.806781i
$133$	10.7237	−	0.147922i	0.929862	−	0.0128265i
$134$	9.42008	+	6.81315i	0.813771	+	0.588567i
$135$	−0.0585742	−	0.0859126i	−0.00504127	−	0.00739418i
$136$	2.43742	−	10.2756i	0.209007	−	0.881122i
$137$	−9.62250	−	1.45036i	−0.822105	−	0.123912i	−0.275498	−	0.961302i	$-0.588843\pi$
$137$	−9.62250	−	1.45036i	−0.822105	−	0.123912i	−0.546607	+	0.837389i	$0.684081\pi$
$138$	−5.13178	−	0.142531i	−0.436846	−	0.0121330i
$139$	−10.8438	+	8.64764i	−0.919759	+	0.733484i	−0.964102	−	0.265533i	$-0.914452\pi$
$139$	−10.8438	+	8.64764i	−0.919759	+	0.733484i	0.0443424	+	0.999016i	$0.485881\pi$
$140$	−0.0772749	+	1.85022i	−0.00653092	+	0.156372i
$141$	−12.5103	−	9.97666i	−1.05356	−	0.840187i
$142$	−0.855868	−	0.722302i	−0.0718229	−	0.0606142i
$143$	0.950942	+	0.648341i	0.0795218	+	0.0542170i
$144$	6.82425	−	9.26847i	0.568688	−	0.772372i
$145$	−0.292534	+	0.948373i	−0.0242937	+	0.0787581i
$146$	2.69884	+	3.07569i	0.223358	+	0.254546i
$147$	12.9711	−	10.9428i	1.06984	−	0.902548i
$148$	11.2068	+	1.46895i	0.921194	+	0.120747i
$149$	−5.39789	+	17.4995i	−0.442212	+	1.43362i	0.410800	+	0.911726i	$0.365250\pi$
$149$	−5.39789	+	17.4995i	−0.442212	+	1.43362i	−0.853012	+	0.521891i	$0.825227\pi$
$150$	−15.7304	+	5.67498i	−1.28438	+	0.463360i
$151$	6.81056	−	9.98926i	0.554236	−	0.812914i	−0.442231	−	0.896901i	$-0.645813\pi$
$151$	6.81056	−	9.98926i	0.554236	−	0.812914i	0.996467	+	0.0839868i	$0.0267654\pi$
$152$	−8.47058	+	7.72658i	−0.687054	+	0.626709i
$153$	8.39977	+	6.69859i	0.679081	+	0.541549i
$154$	−1.03136	−	7.55777i	−0.0831093	−	0.609023i
$155$	0.245839	+	0.308272i	0.0197463	+	0.0247610i
$156$	−1.74765	−	2.10690i	−0.139924	−	0.168687i
$157$	16.9905	+	2.56090i	1.35599	+	0.204382i	0.786486	−	0.617609i	$-0.211898\pi$
$157$	16.9905	+	2.56090i	1.35599	+	0.204382i	0.569501	+	0.821991i	$0.307137\pi$
$158$	1.88391	+	0.193907i	0.149875	+	0.0154264i
$159$	−9.39139	+	6.40294i	−0.744786	+	0.507786i
$160$	−1.25091	−	1.53441i	−0.0988930	−	0.121306i
$161$	3.54527	−	1.76796i	0.279406	−	0.139335i
$162$	−6.29275	−	11.6338i	−0.494405	−	0.914038i
$163$	4.42133	+	11.2654i	0.346305	+	0.882372i	0.992836	+	0.119484i	$0.0381239\pi$
$163$	4.42133	+	11.2654i	0.346305	+	0.882372i	−0.646531	+	0.762888i	$0.723781\pi$
$164$	0.512787	−	9.22425i	0.0400419	−	0.720293i
$165$	−1.49791	+	0.864816i	−0.116612	+	0.0673258i
$166$	8.43891	−	1.68109i	0.654986	−	0.130478i
$167$	4.86857	+	2.34458i	0.376741	+	0.181429i	0.612665	−	0.790342i	$-0.290097\pi$
$167$	4.86857	+	2.34458i	0.376741	+	0.181429i	−0.235924	+	0.971772i	$0.575812\pi$
$168$	−2.60897	+	17.9536i	−0.201287	+	1.38515i
$169$	11.4254	−	5.50220i	0.878879	−	0.423246i
$170$	1.47620	−	1.11161i	0.113219	−	0.0852566i
$171$	−3.43799	−	11.1457i	−0.262910	−	0.852333i
$172$	0.0999366	+	0.586176i	0.00762010	+	0.0446955i
$173$	0.785038	−	10.4756i	0.0596853	−	0.796446i	−0.884397	−	0.466736i	$-0.845430\pi$
$173$	0.785038	−	10.4756i	0.0596853	−	0.796446i	0.944082	−	0.329710i	$-0.106951\pi$
$174$	−3.80214	+	8.94880i	−0.288239	+	0.678407i
$175$	8.64613	−	9.57999i	0.653586	−	0.724179i
$176$	6.18688	+	5.31207i	0.466354	+	0.400412i
$177$	−4.72114	+	8.17726i	−0.354863	+	0.614640i
$178$	−7.03405	+	20.7409i	−0.527224	+	1.55460i
$179$	−1.11425	−	14.8686i	−0.0832828	−	1.11133i	−0.869682	−	0.493613i	$-0.835676\pi$
$179$	−1.11425	−	14.8686i	−0.0832828	−	1.11133i	0.786399	−	0.617719i	$-0.211943\pi$
$180$	1.95451	−	0.485901i	0.145681	−	0.0362169i
$181$	4.49470	−	19.6926i	0.334088	−	1.46374i	−0.477047	−	0.878878i	$-0.658293\pi$
$181$	4.49470	−	19.6926i	0.334088	−	1.46374i	0.811135	−	0.584859i	$-0.198850\pi$
$182$	1.95540	+	0.799148i	0.144944	+	0.0592368i
$183$	34.8158	−	7.94647i	2.57366	−	0.587420i
$184$	−1.58074	+	3.92911i	−0.116534	+	0.289658i
$185$	1.34522	+	1.44980i	0.0989026	+	0.106592i
$186$	2.08657	+	3.25082i	0.152995	+	0.238362i
$187$	−5.17730	+	5.57980i	−0.378601	+	0.408035i
$188$	−11.3027	+	6.81928i	−0.824336	+	0.497347i
$189$	0.655551	+	0.433825i	0.0476843	+	0.0315561i
$190$	−2.00398	+	0.0943225i	−0.145384	+	0.00684287i
$191$	−4.09986	−	27.2008i	−0.296656	−	1.96818i	−0.245028	−	0.969516i	$-0.578797\pi$
$191$	−4.09986	−	27.2008i	−0.296656	−	1.96818i	−0.0516279	−	0.998666i	$-0.516441\pi$
$192$	−10.6514	−	16.2081i	−0.768701	−	1.16972i
$193$	1.14444	−	2.91598i	0.0823786	−	0.209897i	−0.883749	−	0.467960i	$-0.844989\pi$
$193$	1.14444	−	2.91598i	0.0823786	−	0.209897i	0.966128	+	0.258063i	$0.0830843\pi$
$194$	−8.90443	−	19.8844i	−0.639301	−	1.42761i
$195$		−	0.478993i		−	0.0343014i
$196$	−4.74860	−	13.1701i	−0.339186	−	0.940719i
$197$		−	6.22640i		−	0.443612i	−0.975091	−	0.221806i	$-0.928805\pi$
$197$		−	6.22640i		−	0.443612i	0.975091	−	0.221806i	$-0.0711952\pi$
$198$	−7.57131	+	3.39051i	−0.538069	+	0.240953i
$199$	6.63960	−	16.9174i	0.470669	−	1.19924i	−0.476690	−	0.879071i	$-0.658164\pi$
$199$	6.63960	−	16.9174i	0.470669	−	1.19924i	0.947359	−	0.320173i	$-0.103741\pi$
$200$	−0.117280	+	13.7952i	−0.00829292	+	0.975470i
$201$	2.97035	+	19.7070i	0.209512	+	1.39002i
$202$	−1.03463	−	21.9818i	−0.0727963	−	1.54664i
$203$	−0.663853	−	7.47369i	−0.0465934	−	0.524550i
$204$	15.5011	−	9.35230i	1.08530	−	0.654792i
$205$	1.09955	−	1.18503i	0.0767956	−	0.0827660i
$206$	−9.03005	+	5.79603i	−0.629154	+	0.403828i
$207$	−2.93057	−	3.15840i	−0.203689	−	0.219524i
$208$	−2.13068	+	0.748265i	−0.147736	+	0.0518828i
$209$	8.05648	−	1.83884i	0.557278	−	0.127195i
$210$	−2.35705	+	2.12651i	−0.162652	+	0.146743i
$211$	0.133402	−	0.584473i	0.00918378	−	0.0402368i	−0.970128	−	0.242592i	$-0.922002\pi$
$211$	0.133402	−	0.584473i	0.00918378	−	0.0402368i	0.979312	+	0.202355i	$0.0648595\pi$
$212$	2.26229	+	9.09992i	0.155374	+	0.624985i
$213$	−0.143471	−	1.91448i	−0.00983045	−	0.131178i
$214$	24.2056	+	8.20906i	1.65466	+	0.561160i
$215$	−0.0520251	+	0.0901102i	−0.00354808	+	0.00614546i
$216$	−0.832024	+	0.118183i	−0.0566120	+	0.00804130i
$217$	−2.60185	−	1.45470i	−0.176625	−	0.0987516i
$218$	20.7768	+	8.82759i	1.40718	+	0.597880i
$219$	−0.524203	+	6.99500i	−0.0354223	+	0.472678i
$220$	0.239808	+	1.40659i	0.0161679	+	0.0948323i
$221$	−0.621328	−	2.01430i	−0.0417951	−	0.135496i
$222$	11.6554	+	15.4782i	0.782259	+	1.03883i
$223$	22.8956	−	11.0260i	1.53321	−	0.738353i	0.538647	−	0.842532i	$-0.318936\pi$
$223$	22.8956	−	11.0260i	1.53321	−	0.738353i	0.994559	+	0.104179i	$0.0332214\pi$
$224$	13.1413	+	7.16279i	0.878042	+	0.478584i
$225$	−12.6449	−	6.08947i	−0.842995	−	0.405965i
$226$	−5.50581	−	27.6387i	−0.366241	−	1.83850i
$227$	3.92133	−	2.26398i	0.260268	−	0.150266i	−0.364189	−	0.931325i	$-0.618654\pi$
$227$	3.92133	−	2.26398i	0.260268	−	0.150266i	0.624457	+	0.781059i	$0.285320\pi$
$228$	−19.6241	−	1.09093i	−1.29964	−	0.0722486i
$229$	6.44513	+	16.4219i	0.425906	+	1.08519i	0.969337	+	0.245737i	$0.0790300\pi$
$229$	6.44513	+	16.4219i	0.425906	+	1.08519i	−0.543430	+	0.839454i	$0.682875\pi$
$230$	−0.651833	+	0.352578i	−0.0429806	+	0.0232483i
$231$	8.01106	−	10.3348i	0.527089	−	0.679981i
$232$	5.83334	+	5.50557i	0.382977	+	0.361458i
$233$	−21.6826	+	14.7829i	−1.42047	+	0.968462i	−0.422400	+	0.906410i	$0.638812\pi$
$233$	−21.6826	+	14.7829i	−1.42047	+	0.968462i	−0.998073	+	0.0620520i	$0.980236\pi$
$234$	0.235223	−	2.28531i	0.0153770	−	0.149396i
$235$	−2.28406	−	0.344266i	−0.148995	−	0.0224574i
$236$	4.97313	+	5.99543i	0.323723	+	0.390269i
$237$	2.02421	+	2.53828i	0.131487	+	0.164879i
$238$	−7.15362	+	12.0000i	−0.463700	+	0.777845i
$239$	14.1908	+	11.3168i	0.917928	+	0.732023i	0.963716	−	0.266928i	$-0.0860087\pi$
$239$	14.1908	+	11.3168i	0.917928	+	0.732023i	−0.0457889	+	0.998951i	$0.514580\pi$
$240$	0.376161	−	3.37282i	0.0242811	−	0.217715i
$241$	4.09074	−	6.00001i	0.263508	−	0.386495i	−0.671568	−	0.740943i	$-0.734379\pi$
$241$	4.09074	−	6.00001i	0.263508	−	0.386495i	0.935076	+	0.354448i	$0.115331\pi$
$242$	3.28460	+	9.10455i	0.211142	+	0.585263i
$243$	6.42056	−	20.8149i	0.411879	−	1.33528i
$244$	3.82883	−	29.2106i	0.245116	−	1.87002i
$245$	0.831753	−	2.30422i	0.0531387	−	0.147211i
$246$	11.9041	−	10.4456i	0.758980	−	0.665987i
$247$	−0.674544	+	2.18682i	−0.0429202	+	0.139144i
$248$	3.11273	−	0.682674i	0.197659	−	0.0433498i
$249$	12.1877	+	8.30943i	0.772364	+	0.526589i
$250$	−3.15294	+	3.73598i	−0.199410	+	0.236284i
$251$	5.94318	+	4.73952i	0.375130	+	0.299156i	0.792847	−	0.609421i	$-0.208598\pi$
$251$	5.94318	+	4.73952i	0.375130	+	0.299156i	−0.417717	+	0.908577i	$0.637170\pi$
$252$	−12.2899	+	8.98824i	−0.774194	+	0.566206i
$253$	2.38658	−	1.90323i	0.150043	−	0.119655i
$254$	−0.509850	+	18.3570i	−0.0319909	+	1.15182i
$255$	3.13247	+	0.472144i	0.196163	+	0.0295668i
$256$	−15.5907	+	3.59563i	−0.974422	+	0.224727i
$257$	1.17684	+	1.72611i	0.0734095	+	0.107672i	0.861188	−	0.508287i	$-0.169721\pi$
$257$	1.17684	+	1.72611i	0.0734095	+	0.107672i	−0.787778	+	0.615959i	$0.788769\pi$
$258$	−0.597390	+	0.825971i	−0.0371919	+	0.0514227i
$259$	−13.5595	−	6.30102i	−0.842547	−	0.391526i
$260$	−0.370550	−	0.137253i	−0.0229806	−	0.00851204i
$261$	−7.59609	+	2.98125i	−0.470186	+	0.184534i
$262$	−14.5045	+	14.7867i	−0.896093	+	0.913525i
$263$	−18.9703	+	10.9525i	−1.16976	+	0.675360i	−0.953623	−	0.301004i	$-0.902678\pi$
$263$	−18.9703	+	10.9525i	−1.16976	+	0.675360i	−0.216134	+	0.976364i	$0.569345\pi$
$264$	0.926108	+	13.9483i	0.0569980	+	0.858457i
$265$	−0.711912	+	1.47830i	−0.0437324	+	0.0908113i
$266$	13.7556	−	6.38914i	0.843413	−	0.391743i
$267$	−33.8265	+	16.2900i	−2.07015	+	0.996932i
$268$	16.0965	+	3.34905i	0.983251	+	0.204576i
$269$	−23.4453	+	7.23191i	−1.42948	+	0.440938i	−0.910380	−	0.413773i	$-0.864211\pi$
$269$	−23.4453	+	7.23191i	−1.42948	+	0.440938i	−0.519104	+	0.854711i	$0.673734\pi$
$270$	−0.125259	−	0.0770325i	−0.00762302	−	0.00468805i
$271$	−0.121483	+	1.62108i	−0.00737956	+	0.0984733i	−0.999677	−	0.0254023i	$-0.991913\pi$
$271$	−0.121483	+	1.62108i	−0.00737956	+	0.0984733i	0.992298	+	0.123876i	$0.0395324\pi$
$272$	−2.79321	−	14.6716i	−0.169363	−	0.889593i
$273$	1.36935	+	3.35233i	0.0828768	+	0.202893i
$274$	−13.2581	+	3.68974i	−0.800952	+	0.222906i
$275$	4.97171	−	8.61126i	0.299805	−	0.519278i
$276$	−6.70600	+	2.78216i	−0.403654	+	0.167467i
$277$	4.27604	−	0.320445i	0.256922	−	0.0192537i	0.0543538	−	0.998522i	$-0.482690\pi$
$277$	4.27604	−	0.320445i	0.256922	−	0.0192537i	0.202569	+	0.979268i	$0.435071\pi$
$278$	−8.99790	+	17.4292i	−0.539658	+	1.04533i
$279$	−0.721400	+	3.16066i	−0.0431891	+	0.189224i
$280$	0.969675	+	2.43276i	0.0579492	+	0.145385i
$281$	2.53577	+	11.1099i	0.151272	+	0.662764i	0.992517	+	0.122110i	$0.0389660\pi$
$281$	2.53577	+	11.1099i	0.151272	+	0.662764i	−0.841245	+	0.540654i	$0.818177\pi$
$282$	−21.9136	−	5.64607i	−1.30494	−	0.336218i
$283$	7.79216	+	8.39795i	0.463196	+	0.499206i	0.920846	−	0.389926i	$-0.127499\pi$
$283$	7.79216	+	8.39795i	0.463196	+	0.499206i	−0.457650	+	0.889132i	$0.651309\pi$
$284$	−1.52216	−	0.437594i	−0.0903236	−	0.0259664i
$285$	−2.52109	−	2.33923i	−0.149337	−	0.138564i
$286$	1.60212	+	0.287181i	0.0947356	+	0.0169814i
$287$	−4.30763	+	11.4371i	−0.254271	+	0.675108i
$288$	3.45101	−	15.9072i	0.203352	−	0.937343i
$289$	−3.02481	+	0.455916i	−0.177930	+	0.0268186i
$290$	0.170577	+	1.39315i	0.0100166	+	0.0818089i
$291$	13.6451	−	34.7672i	0.799890	−	2.03809i
$292$	5.26114	+	2.40990i	0.307885	+	0.141029i
$293$	−2.83540			−0.165646			−0.0828229	−	0.996564i	$-0.526394\pi$
$293$	−2.83540			−0.165646			−0.0828229	+	0.996564i	$0.526394\pi$
$294$	10.4170	−	21.6212i	0.607533	−	1.26097i
$295$			1.36303i			0.0793588i
$296$	15.3137	−	4.58146i	0.890094	−	0.266292i
$297$	0.563839	+	0.221291i	0.0327173	+	0.0128406i
$298$	3.14750	+	25.7067i	0.182330	+	1.48915i
$299$	0.125993	+	0.835911i	0.00728638	+	0.0483420i
$300$	−17.0233	+	16.4168i	−0.982839	+	0.947825i
$301$	0.106501	−	0.779384i	0.00613862	−	0.0449230i
$302$	3.01672	−	16.8297i	0.173593	−	0.968438i
$303$	25.6592	−	27.6540i	1.47408	−	1.58868i
$304$	−6.46712	+	14.8687i	−0.370915	+	0.852778i
$305$	3.77892	−	3.50632i	0.216380	−	0.200771i
$306$	14.7134	+	3.79092i	0.841108	+	0.216712i
$307$	8.99213	−	2.05239i	0.513208	−	0.117136i	0.0419290	−	0.999121i	$-0.486650\pi$
$307$	8.99213	−	2.05239i	0.513208	−	0.117136i	0.471279	+	0.881984i	$0.343793\pi$
$308$	−5.69952	−	9.15875i	−0.324760	−	0.521868i
$309$	−17.9332	−	4.09313i	−1.02018	−	0.232850i
$310$	0.495485	+	0.255796i	0.0281417	+	0.0145282i
$311$	−1.25429	−	16.7374i	−0.0711244	−	0.949089i	−0.912616	−	0.408819i	$-0.865941\pi$
$311$	−1.25429	−	16.7374i	−0.0711244	−	0.949089i	0.841491	−	0.540271i	$-0.181678\pi$
$312$	−3.47347	−	1.70926i	−0.196647	−	0.0967680i
$313$	20.2802	+	11.7088i	1.14631	+	0.661821i	0.947985	−	0.318316i	$-0.103117\pi$
$313$	20.2802	+	11.7088i	1.14631	+	0.661821i	0.198322	+	0.980137i	$0.436451\pi$
$314$	23.4099	−	6.51499i	1.32110	−	0.367662i
$315$	−2.65932	−	0.162438i	−0.149836	−	0.00915234i
$316$	2.54365	−	0.838607i	0.143091	−	0.0471753i
$317$	−30.0822	−	2.25435i	−1.68958	−	0.126617i	−0.805085	−	0.593159i	$-0.797881\pi$
$317$	−30.0822	−	2.25435i	−1.68958	−	0.126617i	−0.884499	+	0.466542i	$0.845500\pi$
$318$	−8.42068	+	13.6925i	−0.472208	+	0.767836i
$319$	−1.70408	−	5.52449i	−0.0954102	−	0.309312i
$320$	−2.50143	−	1.25746i	−0.139834	−	0.0702941i
$321$	19.0112	+	39.4771i	1.06110	+	2.20340i
$322$	3.55403	−	4.33105i	0.198059	−	0.241360i
$323$	−13.6362	−	6.56685i	−0.758739	−	0.365389i
$324$	−14.8463	−	11.3787i	−0.824797	−	0.632148i
$325$	1.37683	+	2.38475i	0.0763730	+	0.132282i
$326$	12.2179	+	11.9848i	0.676689	+	0.663776i
$327$	14.1382	+	36.0235i	0.781843	+	1.99210i
$328$	−4.66969	−	12.2022i	−0.257840	−	0.673753i
$329$	16.9696	−	4.12026i	0.935566	−	0.227157i
$330$	−1.43350	+	1.98200i	−0.0789116	+	0.109106i
$331$	−9.09424	+	6.20034i	−0.499864	+	0.340802i	−0.786861	−	0.617130i	$-0.788295\pi$
$331$	−9.09424	+	6.20034i	−0.499864	+	0.340802i	0.286997	+	0.957931i	$0.407343\pi$
$332$	9.92050	−	7.04742i	0.544458	−	0.386777i
$333$	−2.42364	+	16.0798i	−0.132814	+	0.881166i
$334$	7.63905	+	0.212168i	0.417990	+	0.0116093i
$335$	1.79373	+	2.24926i	0.0980019	+	0.122890i
$336$	7.00960	+	24.6807i	0.382405	+	1.34645i
$337$	−3.25177	+	4.07760i	−0.177135	+	0.222121i	−0.862471	−	0.506107i	$-0.831084\pi$
$337$	−3.25177	+	4.07760i	−0.177135	+	0.222121i	0.685335	+	0.728228i	$0.259656\pi$
$338$	11.5667	−	13.7055i	0.629143	−	0.745483i
$339$	27.2146	−	39.9165i	1.47810	−	2.16797i
$340$	1.26284	−	2.28800i	0.0684872	−	0.124084i
$341$	−2.19482	−	0.677012i	−0.118856	−	0.0366622i
$342$	−10.8796	−	12.3987i	−0.588300	−	0.670445i
$343$	0.766136	+	18.5044i	0.0413674	+	0.999144i
$344$	0.467794	+	0.698819i	0.0252218	+	0.0376778i
$345$	−1.21397	−	0.374459i	−0.0653578	−	0.0201602i
$346$	−5.04157	−	13.9747i	−0.271036	−	0.751284i
$347$	−19.9815	−	13.6231i	−1.07266	−	0.731329i	−0.107823	−	0.994170i	$-0.534388\pi$
$347$	−19.9815	−	13.6231i	−1.07266	−	0.731329i	−0.964839	+	0.262841i	$0.915340\pi$
$348$	0.264896	+	13.7479i	0.0141999	+	0.736964i
$349$	−10.4934	+	13.1583i	−0.561699	+	0.704349i	−0.978871	−	0.204479i	$-0.934450\pi$
$349$	−10.4934	+	13.1583i	−0.561699	+	0.704349i	0.417172	+	0.908828i	$0.363021\pi$
$350$	5.62245	−	17.3624i	0.300533	−	0.928057i
$351$	−0.131146	+	0.104585i	−0.00700003	+	0.00558234i
$352$	11.0558	+	3.28035i	0.589275	+	0.174843i
$353$	−0.697834	+	4.62983i	−0.0371420	+	0.246421i	−0.999696	−	0.0246703i	$-0.992146\pi$
$353$	−0.697834	+	4.62983i	−0.0371420	+	0.246421i	0.962554	+	0.271091i	$0.0873845\pi$
$354$	−1.36722	+	13.2832i	−0.0726667	+	0.705996i
$355$	−0.156118	−	0.228983i	−0.00828586	−	0.0121531i
$356$	2.90920	+	30.8361i	0.154187	+	1.63431i
$357$	−23.2730	+	5.65073i	−1.23174	+	0.299068i
$358$	−10.0321	−	18.5470i	−0.530214	−	0.980239i
$359$	−17.3213	+	6.79811i	−0.914183	+	0.358791i	−0.775355	−	0.631526i	$-0.782429\pi$
$359$	−17.3213	+	6.79811i	−0.914183	+	0.358791i	−0.138829	+	0.990316i	$0.544334\pi$
$360$	2.24185	−	1.75685i	0.118156	−	0.0925940i
$361$	−1.28433	−	2.22452i	−0.0675963	−	0.117080i
$362$	−5.58082	−	28.0152i	−0.293321	−	1.47245i
$363$	−7.19912	+	14.9491i	−0.377856	+	0.784626i
$364$	2.98575	−	0.0987415i	0.156496	−	0.00517546i
$365$	0.439345	+	0.912310i	0.0229964	+	0.0477525i
$366$	40.3440	−	30.3798i	2.10881	−	1.58798i
$367$	−24.1707	+	7.45568i	−1.26170	+	0.389183i	−0.852243	−	0.523146i	$-0.824758\pi$
$367$	−24.1707	+	7.45568i	−1.26170	+	0.389183i	−0.409458	+	0.912329i	$0.634282\pi$
$368$	0.230725	+	5.98499i	0.0120274	+	0.311989i
$369$	13.2545	+	0.993284i	0.689999	+	0.0517083i
$370$	2.57426	+	1.09374i	0.133829	+	0.0568610i
$371$	0.756288	−	12.3814i	0.0392645	−	0.642811i
$372$	4.57210	+	2.98983i	0.237052	+	0.155016i
$373$	21.6126	+	12.4781i	1.11906	+	0.646089i	0.941161	−	0.337959i	$-0.109737\pi$
$373$	21.6126	+	12.4781i	1.11906	+	0.646089i	0.177899	+	0.984049i	$0.443070\pi$
$374$	−3.45729	+	10.1943i	−0.178772	+	0.527136i
$375$	−8.35698	+	0.626269i	−0.431553	+	0.0323404i
$376$	−10.6470	+	15.3346i	−0.549078	+	0.790821i
$377$	1.56091	+	0.356267i	0.0803908	+	0.0183487i
$378$	1.09687	+	0.181037i	0.0564170	+	0.00931153i
$379$	2.48350	+	10.8809i	0.127569	+	0.558916i	0.997801	+	0.0662747i	$0.0211114\pi$
$379$	2.48350	+	10.8809i	0.127569	+	0.558916i	−0.870233	+	0.492641i	$0.836031\pi$
$380$	−2.53204	+	1.28003i	−0.129891	+	0.0656642i
$381$	−23.0772	+	21.4125i	−1.18228	+	1.09700i
$382$	−21.0136	−	32.7386i	−1.07515	−	1.67505i
$383$	−13.8048	−	12.8090i	−0.705392	−	0.654508i	0.243576	−	0.969882i	$-0.421680\pi$
$383$	−13.8048	−	12.8090i	−0.705392	−	0.654508i	−0.948967	+	0.315374i	$0.897870\pi$
$384$	−23.1161	−	14.7635i	−1.17964	−	0.753397i
$385$	0.255560	−	1.87021i	0.0130246	−	0.0953149i
$386$	−0.208281	−	4.42516i	−0.0106012	−	0.225235i
$387$	−0.845958	+	0.127508i	−0.0430025	+	0.00648158i
$388$	−22.9860	−	20.5182i	−1.16694	−	1.04165i
$389$	−14.9471	−	5.86629i	−0.757846	−	0.297433i	−0.0452202	−	0.998977i	$-0.514399\pi$
$389$	−14.9471	−	5.86629i	−0.757846	−	0.297433i	−0.712626	+	0.701544i	$0.752494\pi$
$390$	−0.276855	−	0.618240i	−0.0140191	−	0.0313058i
$391$	−5.59079			−0.282739
$392$	−13.7413	−	14.2540i	−0.694038	−	0.719938i
$393$	−35.5076			−1.79112
$394$	−3.59881	−	8.03645i	−0.181305	−	0.404871i
$395$	0.436261	+	0.171220i	0.0219507	+	0.00861500i
$396$	−7.81265	+	8.75232i	−0.392600	+	0.439821i
$397$	1.70220	−	0.256565i	0.0854308	−	0.0128766i	−0.106188	−	0.994346i	$-0.533864\pi$
$397$	1.70220	−	0.256565i	0.0854308	−	0.0128766i	0.191619	+	0.981469i	$0.438626\pi$
$398$	−1.20837	−	25.6731i	−0.0605700	−	1.28688i
$399$	24.3318	+	9.16428i	1.21811	+	0.458788i
$400$	7.82216	+	17.8734i	0.391108	+	0.893669i
$401$	−15.7047	−	14.5719i	−0.784257	−	0.727684i	0.182549	−	0.983197i	$-0.441565\pi$
$401$	−15.7047	−	14.5719i	−0.784257	−	0.727684i	−0.966806	+	0.255513i	$0.917756\pi$
$402$	15.2244	+	23.7191i	0.759322	+	1.18300i
$403$	0.466278	−	0.432643i	0.0232270	−	0.0215515i
$404$	−14.0407	−	27.7741i	−0.698553	−	1.38181i
$405$	−0.728331	−	3.19103i	−0.0361910	−	0.158563i
$406$	−5.17658	−	9.26264i	−0.256909	−	0.459697i
$407$	−11.2321	−	2.56365i	−0.556753	−	0.127075i
$408$	14.6019	−	21.0306i	0.722900	−	1.04117i
$409$	−0.428166	+	0.0320866i	−0.0211714	+	0.00158658i	−0.0853116	−	0.996354i	$-0.527189\pi$
$409$	−0.428166	+	0.0320866i	−0.0211714	+	0.00158658i	0.0641402	+	0.997941i	$0.479570\pi$
$410$	0.734254	−	2.16505i	0.0362622	−	0.106924i
$411$	−20.4311	−	11.7959i	−1.00779	−	0.581847i
$412$	−8.30509	+	12.7003i	−0.409162	+	0.625698i
$413$	−3.89664	−	9.53946i	−0.191741	−	0.469406i
$414$	−5.60804	−	2.38273i	−0.275620	−	0.117105i
$415$	2.12339	+	0.159126i	0.104233	+	0.00781118i
$416$	−2.31759	+	2.19731i	−0.113629	+	0.107732i
$417$	−32.1312	+	9.91115i	−1.57347	+	0.485351i
$418$	9.33572	−	7.02999i	0.456625	−	0.343848i
$419$	−0.181760	−	0.377429i	−0.00887957	−	0.0184386i	0.896482	−	0.443080i	$-0.146114\pi$
$419$	−0.181760	−	0.377429i	−0.00887957	−	0.0184386i	−0.905361	+	0.424642i	$0.860400\pi$
$420$	−1.81315	+	4.10706i	−0.0884729	+	0.200404i
$421$	−12.8420	+	26.6667i	−0.625881	+	1.29966i	0.311134	+	0.950366i	$0.399291\pi$
$421$	−12.8420	+	26.6667i	−0.625881	+	1.29966i	−0.937015	+	0.349289i	$0.886423\pi$
$422$	−0.165638	−	0.831489i	−0.00806313	−	0.0404762i
$423$	−9.49595	−	16.4475i	−0.461709	−	0.799704i
$424$	8.17964	+	10.4378i	0.397238	+	0.506902i
$425$	−16.9527	+	6.65343i	−0.822324	+	0.322739i
$426$	−1.29174	−	2.38811i	−0.0625848	−	0.115704i
$427$	−16.4236	+	35.3429i	−0.794795	+	1.71036i
$428$	35.9871	−	3.39517i	1.73950	−	0.164112i
$429$	1.57180	+	2.30541i	0.0758873	+	0.111306i
$430$	−0.0150662	+	0.146376i	−0.000726556	+	0.00705887i
$431$	−3.50414	+	23.2484i	−0.168788	+	1.11984i	0.730638	+	0.682765i	$0.239223\pi$
$431$	−3.50414	+	23.2484i	−0.168788	+	1.11984i	−0.899426	+	0.437073i	$0.856015\pi$
$432$	−1.00559	+	0.633442i	−0.0483815	+	0.0304765i
$433$	26.7139	−	21.3036i	1.28379	−	1.02379i	0.285938	−	0.958248i	$-0.407695\pi$
$433$	26.7139	−	21.3036i	1.28379	−	1.02379i	0.997850	−	0.0655386i	$-0.0208766\pi$
$434$	−4.19903	−	0.373746i	−0.201560	−	0.0179404i
$435$	−1.50017	+	1.88115i	−0.0719274	+	0.0901941i
$436$	31.9191	−	0.615021i	1.52865	−	0.0294542i
$437$	5.01497	+	3.41915i	0.239898	+	0.163560i
$438$	3.36646	+	9.33148i	0.160856	+	0.445875i
$439$	−9.13154	−	2.81671i	−0.435824	−	0.134434i	0.0690764	−	0.997611i	$-0.477995\pi$
$439$	−9.13154	−	2.81671i	−0.435824	−	0.134434i	−0.504901	+	0.863177i	$0.668471\pi$
$440$	1.12252	+	1.67689i	0.0535141	+	0.0799426i
$441$	19.0762	−	6.46562i	0.908389	−	0.307887i
$442$	−1.96620	−	2.24074i	−0.0935226	−	0.106581i
$443$	−10.1562	−	3.13279i	−0.482538	−	0.148843i	0.0439364	−	0.999034i	$-0.486010\pi$
$443$	−10.1562	−	3.13279i	−0.482538	−	0.148843i	−0.526474	+	0.850191i	$0.676486\pi$
$444$	23.9900	+	13.2411i	1.13851	+	0.628394i
$445$	−3.05304	+	4.47798i	−0.144728	+	0.212277i
$446$	23.1786	−	27.4648i	1.09754	−	1.30050i
$447$	−27.6813	+	34.7112i	−1.30928	+	1.64178i
$448$	21.1016	+	1.64947i	0.996959	+	0.0779302i
$449$	−1.37258	−	1.72116i	−0.0647760	−	0.0812266i	0.748388	−	0.663261i	$-0.230828\pi$
$449$	−1.37258	−	1.72116i	−0.0647760	−	0.0812266i	−0.813164	+	0.582035i	$0.802257\pi$
$450$	−19.8406	−	0.551055i	−0.935293	−	0.0259770i
$451$	−1.40351	+	9.31171i	−0.0660889	+	0.438471i
$452$	−23.0813	−	32.4911i	−1.08566	−	1.52826i
$453$	24.2174	−	16.5111i	1.13783	−	0.775761i
$454$	3.75272	−	5.18864i	0.176124	−	0.243515i
$455$	0.413150	+	0.320254i	0.0193688	+	0.0150137i
$456$	−25.9596	+	9.93454i	−1.21567	+	0.465227i
$457$	−10.6448	−	27.1226i	−0.497944	−	1.26874i	−0.930221	−	0.367000i	$-0.880385\pi$
$457$	−10.6448	−	27.1226i	−0.497944	−	1.26874i	0.432277	−	0.901741i	$-0.357710\pi$
$458$	17.8105	+	17.4707i	0.832231	+	0.816350i
$459$	−0.554684	−	0.960741i	−0.0258904	−	0.0448435i
$460$	−0.637538	+	0.831829i	−0.0297253	+	0.0387842i
$461$	−4.70136	−	2.26405i	−0.218964	−	0.105448i	0.321186	−	0.947016i	$-0.395918\pi$
$461$	−4.70136	−	2.26405i	−0.218964	−	0.105448i	−0.540150	+	0.841568i	$0.681633\pi$
$462$	4.36648	−	17.9696i	0.203147	−	0.836019i
$463$	−0.151399	−	0.314383i	−0.00703610	−	0.0146106i	0.897421	−	0.441175i	$-0.145438\pi$
$463$	−0.151399	−	0.314383i	−0.00703610	−	0.0146106i	−0.904457	+	0.426564i	$0.859724\pi$
$464$	10.7113	+	3.73445i	0.497260	+	0.173367i
$465$	0.281759	+	0.913439i	0.0130662	+	0.0423597i
$466$	−19.4414	+	31.6128i	−0.900607	+	1.46443i
$467$	22.4280	+	1.68074i	1.03784	+	0.0777755i	0.582736	−	0.812662i	$-0.301982\pi$
$467$	22.4280	+	1.68074i	1.03784	+	0.0777755i	0.455106	+	0.890437i	$0.349601\pi$
$468$	−1.01729	−	3.08563i	−0.0470243	−	0.142633i
$469$	−18.9840	−	10.6140i	−0.876599	−	0.490110i
$470$	−3.14703	+	0.875821i	−0.145162	+	0.0403986i
$471$	36.0751	+	20.8280i	1.66225	+	0.959703i
$472$	9.88417	+	4.86391i	0.454956	+	0.223879i
$473$	−0.0452952	−	0.604422i	−0.00208267	−	0.0277913i
$474$	4.07977	+	2.10620i	0.187390	+	0.0967409i
$475$	19.2756	+	4.39954i	0.884427	+	0.201865i
$476$	−2.29732	+	19.6232i	−0.105297	+	0.899429i
$477$	−13.1525	+	3.00198i	−0.602213	+	0.137451i
$478$	24.8572	+	6.40448i	1.13694	+	0.292934i
$479$	−16.3691	+	15.1883i	−0.747924	+	0.693972i	−0.958971	−	0.283504i	$-0.908503\pi$
$479$	−16.3691	+	15.1883i	−0.747924	+	0.693972i	0.211047	+	0.977476i	$0.432313\pi$
$480$	−1.46395	−	4.57074i	−0.0668199	−	0.208625i
$481$	2.17011	−	2.33883i	0.0989487	−	0.106641i
$482$	1.81198	−	10.1087i	0.0825336	−	0.460438i
$483$	9.56671	−	0.849767i	0.435300	−	0.0386657i
$484$	9.50182	+	9.85283i	0.431901	+	0.447856i
$485$	−0.803557	−	5.33125i	−0.0364876	−	0.242080i
$486$	−3.74382	−	30.5770i	−0.169823	−	1.38700i
$487$	−24.6663	−	9.68083i	−1.11774	−	0.438680i	−0.266698	−	0.963780i	$-0.585933\pi$
$487$	−24.6663	−	9.68083i	−1.11774	−	0.438680i	−0.851041	+	0.525100i	$0.824028\pi$
$488$	−11.9416	−	39.9153i	−0.540571	−	1.80688i
$489$			29.3392i			1.32677i
$490$	−0.258275	−	3.45482i	−0.0116677	−	0.156073i
$491$	10.4351			0.470930			0.235465	−	0.971883i	$-0.424339\pi$
$491$	10.4351			0.470930			0.235465	+	0.971883i	$0.424339\pi$
$492$	9.32727	−	20.3627i	0.420506	−	0.918022i
$493$	−3.86846	+	9.85668i	−0.174227	+	0.443922i
$494$	0.393326	+	3.21242i	0.0176966	+	0.144534i
$495$	−2.02996	+	0.305968i	−0.0912401	+	0.0137522i
$496$	3.62305	−	2.68027i	0.162680	−	0.120348i
$497$	1.74724	+	1.15627i	0.0783743	+	0.0518659i
$498$	20.5335	+	3.68064i	0.920130	+	0.164934i
$499$	−5.29337	−	4.91153i	−0.236964	−	0.219870i	0.552748	−	0.833349i	$-0.313579\pi$
$499$	−5.29337	−	4.91153i	−0.236964	−	0.219870i	−0.789711	+	0.613478i	$0.789770\pi$
$500$	−1.91016	+	6.64443i	−0.0854249	+	0.297148i
$501$	8.91057	+	9.60331i	0.398095	+	0.429044i
$502$	10.4103	+	2.68223i	0.464635	+	0.119714i
$503$	−1.53128	−	6.70899i	−0.0682765	−	0.299139i	0.929248	−	0.369456i	$-0.120456\pi$
$503$	−1.53128	−	6.70899i	−0.0682765	−	0.299139i	−0.997525	+	0.0703171i	$0.977599\pi$
$504$	−10.6676	+	18.7047i	−0.475172	+	0.833173i
$505$	1.21178	−	5.30915i	0.0539235	−	0.236254i
$506$	1.98032	−	3.83594i	0.0880359	−	0.170528i
$507$	30.6578	−	2.29748i	1.36156	−	0.102035i
$508$	9.95214	+	23.9882i	0.441555	+	1.06430i
$509$	−0.865112	+	1.49842i	−0.0383454	+	0.0664162i	−0.884561	−	0.466424i	$-0.845542\pi$
$509$	−0.865112	+	1.49842i	−0.0383454	+	0.0664162i	0.846216	+	0.532840i	$0.178875\pi$
$510$	4.31600	−	1.20114i	0.191115	−	0.0531876i
$511$	−5.68297	−	5.12899i	−0.251400	−	0.226893i
$512$	−18.0448	+	13.6522i	−0.797477	+	0.603350i
$513$	−0.0900037	+	1.20102i	−0.00397376	+	0.0530261i
$514$	2.51664	+	1.54770i	0.111004	+	0.0682661i
$515$	−2.53733	+	0.782663i	−0.111808	+	0.0344882i
$516$	−0.293651	+	1.41137i	−0.0129273	+	0.0621322i
$517$	12.1229	−	5.83810i	0.533166	−	0.256759i
$518$	−21.1433	−	0.295474i	−0.928983	−	0.0129824i
$519$	11.0500	−	22.9456i	0.485042	−	1.00720i
$520$	−0.557603	+	0.0370225i	−0.0244525	+	0.00162355i
$521$	−8.66831	+	5.00465i	−0.379765	+	0.219258i	−0.677716	−	0.735324i	$-0.737030\pi$
$521$	−8.66831	+	5.00465i	−0.379765	+	0.219258i	0.297951	+	0.954581i	$0.403697\pi$
$522$	−8.08119	+	8.23840i	−0.353704	+	0.360585i
$523$	10.4871	−	4.11588i	0.458569	−	0.179975i	−0.124801	−	0.992182i	$-0.539829\pi$
$523$	10.4871	−	4.11588i	0.458569	−	0.179975i	0.583370	+	0.812207i	$0.301734\pi$
$524$	−10.1745	+	27.4688i	−0.444475	+	1.19998i
$525$	27.9973	−	13.9617i	1.22190	−	0.609341i
$526$	−18.1546	+	25.1011i	−0.791578	+	1.09446i
$527$	2.36974	+	3.47577i	0.103228	+	0.151407i
$528$	9.25733	+	17.4678i	0.402874	+	0.760191i
$529$	−20.5261	−	3.09381i	−0.892438	−	0.134513i
$530$	−0.0644231	+	2.31953i	−0.00279836	+	0.100754i
$531$	−8.76199	+	6.98745i	−0.380238	+	0.303230i
$532$	14.0616	−	16.1972i	0.609649	−	0.702236i
$533$	−2.03890	−	1.62597i	−0.0883146	−	0.0704286i
$534$	−34.2446	+	40.5771i	−1.48191	+	1.75594i
$535$	5.22601	+	3.56303i	0.225940	+	0.154043i
$536$	22.7116	−	4.98103i	0.980992	−	0.215148i
$537$	10.6547	−	34.5417i	0.459785	−	1.49059i
$538$	−26.0810	+	22.8855i	−1.12443	+	0.986663i
$539$	3.55799	+	13.8197i	0.153253	+	0.595255i
$540$	−0.206197	−	0.0270277i	−0.00887330	−	0.00116309i
$541$	−4.08518	+	13.2438i	−0.175636	+	0.569397i	0.824359	+	0.566068i	$0.191536\pi$
$541$	−4.08518	+	13.2438i	−0.175636	+	0.569397i	−0.999994	+	0.00332915i	$0.998940\pi$
$542$	0.780171	+	2.16255i	0.0335112	+	0.0928895i
$543$	27.5854	−	40.4604i	1.18380	−	1.73632i
$544$	−12.0853	−	17.3222i	−0.518151	−	0.742684i
$545$	4.36754	+	3.48300i	0.187085	+	0.149195i
$546$	3.70505	+	3.53541i	0.158562	+	0.151301i
$547$	15.1095	+	18.9467i	0.646036	+	0.810103i	0.991743	−	0.128239i	$-0.0409325\pi$
$547$	15.1095	+	18.9467i	0.646036	+	0.810103i	−0.345708	+	0.938342i	$0.612361\pi$
$548$	−14.9797	+	12.4255i	−0.639901	+	0.530790i
$549$	41.9120	+	6.31721i	1.78876	+	0.269612i
$550$	1.43978	−	13.9882i	0.0613924	−	0.596460i
$551$	9.49805	−	6.47566i	0.404631	−	0.275872i
$552$	−7.04741	+	7.46698i	−0.299958	+	0.317816i
$553$	−3.54275	+	0.0488685i	−0.150653	+	0.00207810i
$554$	5.33390	−	2.88512i	0.226616	−	0.122577i
$555$	1.75173	+	4.46333i	0.0743568	+	0.189458i
$556$	−1.53969	+	27.6967i	−0.0652976	+	1.17460i
$557$	20.2864	−	11.7123i	0.859562	−	0.496268i	−0.00430385	−	0.999991i	$-0.501370\pi$
$557$	20.2864	−	11.7123i	0.859562	−	0.496268i	0.863865	+	0.503723i	$0.168037\pi$
$558$	0.895722	+	4.49645i	0.0379189	+	0.190350i
$559$	0.151231	+	0.0728292i	0.00639641	+	0.00308035i
$560$	2.65768	+	2.57951i	0.112308	+	0.109004i
$561$	−16.6260	+	8.00666i	−0.701950	+	0.338041i
$562$	9.69441	+	12.8740i	0.408934	+	0.543058i
$563$	1.71301	+	5.55344i	0.0721948	+	0.234050i	0.984477	−	0.175512i	$-0.0561579\pi$
$563$	1.71301	+	5.55344i	0.0721948	+	0.234050i	−0.912283	+	0.409561i	$0.865682\pi$
$564$	−31.5474	+	5.37849i	−1.32839	+	0.226475i
$565$	0.521161	−	6.95441i	0.0219254	−	0.292574i
$566$	14.9113	+	6.33548i	0.626771	+	0.266300i
$567$	14.2199	+	20.2509i	0.597180	+	0.850458i
$568$	−2.21759	+	0.314991i	−0.0930480	+	0.0132167i
$569$	2.09814	−	3.63409i	0.0879588	−	0.152349i	−0.818689	−	0.574237i	$-0.805299\pi$
$569$	2.09814	−	3.63409i	0.0879588	−	0.152349i	0.906648	+	0.421888i	$0.138632\pi$
$570$	−4.60605	−	1.56209i	−0.192926	−	0.0654287i
$571$	0.0660617	+	0.881532i	0.00276460	+	0.0368910i	0.998415	−	0.0562718i	$-0.0179213\pi$
$571$	0.0660617	+	0.881532i	0.00276460	+	0.0368910i	−0.995651	+	0.0931628i	$0.970302\pi$
$572$	2.23386	−	0.555349i	0.0934024	−	0.0232203i
$573$	14.8397	−	65.0170i	0.619937	−	2.71612i
$574$	1.05064	+	17.2517i	0.0438530	+	0.720071i
$575$	7.12030	−	1.62516i	0.296937	−	0.0677739i
$576$	−4.74003	−	22.5262i	−0.197501	−	0.938594i
$577$	−2.50564	−	2.70044i	−0.104311	−	0.112421i	0.678738	−	0.734381i	$-0.262527\pi$
$577$	−2.50564	−	2.70044i	−0.104311	−	0.112421i	−0.783049	+	0.621960i	$0.786337\pi$
$578$	−3.64062	+	2.33677i	−0.151430	+	0.0971969i
$579$	5.16545	−	5.56703i	0.214669	−	0.231358i
$580$	1.02540	+	1.69956i	0.0425773	+	0.0705705i
$581$	−15.3159	+	4.95667i	−0.635409	+	0.205638i
$582$	−2.48333	−	52.7610i	−0.102937	−	2.18701i
$583$	−1.42454	−	9.45123i	−0.0589986	−	0.391430i
$584$	8.18349	+	0.0695717i	0.338635	+	0.00287890i
$585$	0.207702	−	0.529216i	0.00858742	−	0.0218804i
$586$	−3.65967	+	1.63884i	−0.151180	+	0.0676999i
$587$		−	8.41598i		−	0.347365i	−0.984802	−	0.173682i	$-0.944433\pi$
$587$		−	8.41598i		−	0.347365i	0.984802	−	0.173682i	$-0.0555666\pi$
$588$	0.948451	−	33.9276i	0.0391134	−	1.39915i
$589$		−	4.56704i		−	0.188182i
$590$	0.787822	+	1.75927i	0.0324341	+	0.0724282i
$591$	5.51480	−	14.0515i	0.226848	−	0.578000i
$592$	17.1175	−	14.7646i	0.703525	−	0.606820i
$593$	3.81557	+	25.3147i	0.156687	+	1.03955i	0.919545	+	0.392984i	$0.128557\pi$
$593$	3.81557	+	25.3147i	0.156687	+	1.03955i	−0.762859	+	0.646565i	$0.776205\pi$
$594$	0.855656	−	0.0402736i	0.0351080	−	0.00165244i
$595$	−2.50160	+	2.38620i	−0.102556	+	0.0978245i
$596$	18.9208	+	31.3606i	0.775026	+	1.28458i
$597$	29.9679	−	32.2978i	1.22651	−	1.32186i
$598$	0.645771	+	1.00609i	0.0264075	+	0.0411422i
$599$	−12.1182	−	13.0603i	−0.495136	−	0.533630i	0.435202	−	0.900333i	$-0.356677\pi$
$599$	−12.1182	−	13.0603i	−0.495136	−	0.533630i	−0.930338	+	0.366703i	$0.880486\pi$
$600$	−12.4833	+	31.0286i	−0.509628	+	1.26674i
$601$	5.90149	−	1.34698i	0.240727	−	0.0549443i	−0.100455	−	0.994942i	$-0.532030\pi$
$601$	5.90149	−	1.34698i	0.240727	−	0.0549443i	0.341182	+	0.939997i	$0.389173\pi$
$602$	−0.313017	−	1.06751i	−0.0127576	−	0.0435086i
$603$	−5.26359	+	23.0613i	−0.214350	+	0.939128i
$604$	−5.83371	−	23.4658i	−0.237370	−	0.954810i
$605$	0.178991	+	2.38846i	0.00727701	+	0.0971049i
$606$	17.1347	−	50.5241i	0.696048	−	2.05240i
$607$	−9.75373	+	16.8940i	−0.395892	+	0.685705i	−0.993215	−	0.116296i	$-0.962898\pi$
$607$	−9.75373	+	16.8940i	−0.395892	+	0.685705i	0.597323	+	0.802001i	$0.296231\pi$
$608$	0.246830	+	22.9291i	0.0100103	+	0.929896i
$609$	5.12138	−	17.4543i	0.207529	−	0.707283i
$610$	2.85084	−	6.70982i	0.115427	−	0.271673i
$611$	−0.278464	+	3.71585i	−0.0112655	+	0.150327i
$612$	21.1818	−	3.61126i	0.856223	−	0.145977i
$613$	−11.0228	−	35.7352i	−0.445208	−	1.44333i	−0.848958	−	0.528460i	$-0.822770\pi$
$613$	−11.0228	−	35.7352i	−0.445208	−	1.44333i	0.403750	−	0.914869i	$-0.367707\pi$
$614$	10.4199	−	7.84642i	0.420514	−	0.316656i
$615$	3.53100	−	1.70044i	0.142384	−	0.0685684i
$616$	−12.6501	−	8.52698i	−0.509687	−	0.343562i
$617$	−3.91200	−	1.88392i	−0.157491	−	0.0758438i	0.353478	−	0.935443i	$-0.384999\pi$
$617$	−3.91200	−	1.88392i	−0.157491	−	0.0758438i	−0.510969	+	0.859599i	$0.670713\pi$
$618$	−25.5123	+	5.08221i	−1.02625	+	0.204436i
$619$	−10.1142	+	5.83942i	−0.406523	+	0.234706i	−0.689295	−	0.724481i	$-0.742079\pi$
$619$	−10.1142	+	5.83942i	−0.406523	+	0.234706i	0.282772	+	0.959187i	$0.408746\pi$
$620$	0.787375	+	0.0437711i	0.0316217	+	0.00175789i
$621$	0.162537	+	0.414138i	0.00652239	+	0.0166188i
$622$	−11.2930	−	20.8781i	−0.452808	−	0.837134i
$623$	8.56562	−	40.0681i	0.343174	−	1.60529i
$624$	−5.47118	−	0.198517i	−0.219022	−	0.00794705i
$625$	19.1505	−	13.0566i	0.766019	−	0.522263i
$626$	32.9434	+	3.39080i	1.31668	+	0.135524i
$627$	19.8102	+	2.98591i	0.791144	+	0.119246i
$628$	26.4497	−	21.9397i	1.05546	−	0.875489i
$629$	13.1561	+	16.4973i	0.524569	+	0.657788i
$630$	−3.52629	+	1.32741i	−0.140491	+	0.0528852i
$631$	−29.9151	−	23.8565i	−1.19090	−	0.949713i	−0.191409	−	0.981510i	$-0.561306\pi$
$631$	−29.9151	−	23.8565i	−1.19090	−	0.949713i	−0.999494	+	0.0317971i	$0.989877\pi$
$632$	2.79839	−	2.55260i	0.111314	−	0.101537i
$633$	0.818731	−	1.20086i	0.0325416	−	0.0477298i
$634$	−40.1303	+	14.4776i	−1.59378	+	0.574978i
$635$	−1.33949	+	4.34251i	−0.0531560	+	0.172327i
$636$	−2.95448	+	22.5401i	−0.117153	+	0.893772i
$637$	−3.80706	−	1.06025i	−0.150841	−	0.0420086i
$638$	−5.39259	−	6.14556i	−0.213495	−	0.243305i
$639$	0.671648	−	2.17743i	0.0265700	−	0.0861378i
$640$	−3.95542	−	0.177201i	−0.156352	−	0.00700448i
$641$	34.3595	+	23.4259i	1.35712	+	0.925267i	0.999961	−	0.00877770i	$-0.00279407\pi$
$641$	34.3595	+	23.4259i	1.35712	+	0.925267i	0.357156	+	0.934045i	$0.383746\pi$
$642$	47.3553	+	39.9651i	1.86897	+	1.57729i
$643$	−22.5235	−	17.9619i	−0.888242	−	0.708349i	0.0690068	−	0.997616i	$-0.478017\pi$
$643$	−22.5235	−	17.9619i	−0.888242	−	0.708349i	−0.957248	+	0.289267i	$0.906588\pi$
$644$	2.08390	−	7.64433i	0.0821172	−	0.301229i
$645$	−0.197220	+	0.157278i	−0.00776552	+	0.00619280i
$646$	−21.3959	−	0.594255i	−0.841812	−	0.0233806i
$647$	37.5919	+	5.66606i	1.47789	+	0.222756i	0.837983	−	0.545697i	$-0.183735\pi$
$647$	37.5919	+	5.66606i	1.47789	+	0.222756i	0.639906	+	0.768453i	$0.278973\pi$
$648$	−25.7391	−	6.10544i	−1.01113	−	0.239844i
$649$	−4.47275	−	6.56031i	−0.175571	−	0.257515i
$650$	3.15546	+	2.28221i	0.123767	+	0.0895156i
$651$	−4.58329	−	5.58740i	−0.179633	−	0.218987i
$652$	22.6969	+	8.40698i	0.888879	+	0.329243i
$653$	−17.8446	+	7.00351i	−0.698315	+	0.274068i	−0.687825	−	0.725876i	$-0.741434\pi$
$653$	−17.8446	+	7.00351i	−0.698315	+	0.274068i	−0.0104900	+	0.999945i	$0.503339\pi$
$654$	39.0696	+	38.3240i	1.52774	+	1.49859i
$655$	−4.43896	+	2.56284i	−0.173445	+	0.100138i
$656$	−13.0800	−	13.0504i	−0.510687	−	0.509533i
$657$	−3.61235	+	7.50112i	−0.140931	+	0.292647i
$658$	19.5213	−	15.1264i	0.761021	−	0.589687i
$659$	23.6024	−	11.3663i	0.919419	−	0.442769i	0.0865555	−	0.996247i	$-0.472414\pi$
$659$	23.6024	−	11.3663i	0.919419	−	0.442769i	0.832864	+	0.553478i	$0.186700\pi$
$660$	−0.704645	+	3.38674i	−0.0274283	+	0.131829i
$661$	−12.8488	+	3.96333i	−0.499761	+	0.154156i	−0.534379	−	0.845245i	$-0.679455\pi$
$661$	−12.8488	+	3.96333i	−0.499761	+	0.154156i	0.0346186	+	0.999401i	$0.488978\pi$
$662$	−8.15424	+	13.2592i	−0.316924	+	0.515335i
$663$	0.381900	−	5.09610i	0.0148318	−	0.197916i
$664$	8.73111	−	14.8301i	0.338833	−	0.575520i
$665$	3.70327	−	0.610530i	0.143607	−	0.0236754i
$666$	6.16579	+	22.1551i	0.238919	+	0.858494i
$667$	2.12319	−	3.67747i	0.0822102	−	0.142392i
$668$	9.98241	−	4.14147i	0.386231	−	0.160238i
$669$	61.4358	−	4.60397i	2.37524	−	0.178000i
$670$	3.61524	+	1.86638i	0.139669	+	0.0721045i
$671$	−6.68215	+	29.2764i	−0.257962	+	1.13020i
$672$	23.3126	+	27.8041i	0.899304	+	1.07257i
$673$	2.70156	+	11.8363i	0.104137	+	0.456256i	0.999931	+	0.0117848i	$0.00375131\pi$
$673$	2.70156	+	11.8363i	0.104137	+	0.456256i	−0.895793	+	0.444471i	$0.853392\pi$
$674$	−1.84027	+	7.14248i	−0.0708845	+	0.275118i
$675$	0.985705	+	1.06234i	0.0379398	+	0.0408894i
$676$	7.00746	−	24.3753i	0.269518	−	0.937510i
$677$	9.10290	+	8.44626i	0.349853	+	0.324616i	0.835450	−	0.549567i	$-0.185207\pi$
$677$	9.10290	+	8.44626i	0.349853	+	0.324616i	−0.485597	+	0.874183i	$0.661398\pi$
$678$	12.0547	−	67.2504i	0.462956	−	2.58274i
$679$	20.8649	+	35.0147i	0.800721	+	1.34374i
$680$	0.307513	−	3.68304i	0.0117926	−	0.141238i
$681$	10.8547	−	1.63609i	0.415954	−	0.0626950i
$682$	−3.22417	+	0.394765i	−0.123460	+	0.0151163i
$683$	−0.585086	+	1.49077i	−0.0223877	+	0.0570429i	−0.941631	−	0.336648i	$-0.890707\pi$
$683$	−0.585086	+	1.49077i	−0.0223877	+	0.0570429i	0.919243	+	0.393691i	$0.128802\pi$
$684$	−21.2087	−	9.71477i	−0.810935	−	0.371454i
$685$	−3.40556			−0.130120
$686$	11.6843	+	23.4409i	0.446107	+	0.894979i
$687$			42.7688i			1.63173i
$688$	1.00770	+	0.631589i	0.0384181	+	0.0240791i
$689$	2.46396	+	0.967032i	0.0938693	+	0.0368410i
$690$	−1.78331	+	0.218347i	−0.0678895	+	0.00831233i
$691$	−2.53453	−	16.8155i	−0.0964181	−	0.639692i	−0.983883	−	0.178816i	$-0.942773\pi$
$691$	−2.53453	−	16.8155i	−0.0964181	−	0.639692i	0.887464	−	0.460876i	$-0.152465\pi$
$692$	−14.5845	−	15.1232i	−0.554418	−	0.574899i
$693$	13.3324	−	7.94465i	0.506457	−	0.301792i
$694$	−33.6643	−	6.03434i	−1.27788	−	0.229060i
$695$	−3.30150	+	3.55817i	−0.125233	+	0.134969i
$696$	8.28808	+	17.5914i	0.314159	+	0.666800i
$697$	12.6431	−	11.7311i	0.478891	−	0.444346i
$698$	−5.93851	+	23.0486i	−0.224776	+	0.872404i
$699$	−62.0257	+	14.1570i	−2.34603	+	0.535466i
$700$	−2.77838	−	25.6595i	−0.105013	−	0.969836i
$701$	−3.50144	−	0.799180i	−0.132248	−	0.0301846i	0.155885	−	0.987775i	$-0.450177\pi$
$701$	−3.50144	−	0.799180i	−0.132248	−	0.0301846i	−0.288132	+	0.957591i	$0.593034\pi$
$702$	−0.108821	+	0.210790i	−0.00410719	+	0.00795575i
$703$	−1.71192	−	22.8440i	−0.0645662	−	0.861577i
$704$	16.1658	−	2.15619i	0.609272	−	0.0812645i
$705$	−4.84964	−	2.79994i	−0.182648	−	0.105452i
$706$	1.77531	+	6.37909i	0.0668145	+	0.240080i
$707$	6.69695	+	40.6214i	0.251865	+	1.52773i
$708$	5.91293	+	17.9350i	0.222222	+	0.674038i
$709$	−21.7332	−	1.62868i	−0.816208	−	0.0611663i	−0.339918	−	0.940455i	$-0.610399\pi$
$709$	−21.7332	−	1.62868i	−0.816208	−	0.0611663i	−0.476289	+	0.879289i	$0.658019\pi$
$710$	−0.333852	−	0.205315i	−0.0125293	−	0.00770532i
$711$	1.13580	+	3.68216i	0.0425957	+	0.138092i
$712$	21.5780	+	38.1188i	0.808668	+	1.42856i
$713$	−0.731977	−	1.51997i	−0.0274128	−	0.0569232i
$714$	−26.7725	+	20.7451i	−1.00194	+	0.776364i
$715$	0.362895	+	0.174761i	0.0135715	+	0.00653570i
$716$	−23.6685	−	18.1402i	−0.884535	−	0.677933i
$717$	22.0018	+	38.1083i	0.821673	+	1.42318i
$718$	−18.4275	+	18.7860i	−0.687707	+	0.701086i
$719$	−8.44406	−	21.5151i	−0.314910	−	0.802379i	−0.997439	−	0.0715198i	$-0.977215\pi$
$719$	−8.44406	−	21.5151i	−0.314910	−	0.802379i	0.682529	−	0.730859i	$-0.260880\pi$
$720$	1.87813	−	3.56335i	0.0699938	−	0.132798i
$721$	15.5206	−	12.7314i	0.578016	−	0.474141i
$722$	−2.94345	−	2.12887i	−0.109544	−	0.0792285i
$723$	14.5461	−	9.91736i	0.540975	−	0.368831i
$724$	−23.3958	−	32.9338i	−0.869498	−	1.22397i
$725$	2.06159	−	13.6777i	0.0765654	−	0.507978i
$726$	−0.651470	+	23.4560i	−0.0241783	+	0.870533i
$727$	−25.9345	−	32.5208i	−0.961856	−	1.20613i	−0.978496	−	0.206267i	$-0.933868\pi$
$727$	−25.9345	−	32.5208i	−0.961856	−	1.20613i	0.0166401	−	0.999862i	$-0.494703\pi$
$728$	3.79666	−	1.85319i	0.140714	−	0.0686838i
$729$	15.4319	−	19.3509i	0.571550	−	0.716701i
$730$	1.09437	+	0.923586i	0.0405046	+	0.0341835i
$731$	−0.625349	+	0.917219i	−0.0231294	+	0.0339246i
$732$	34.5129	−	62.5300i	1.27563	−	2.31117i
$733$	36.0249	+	11.1122i	1.33061	+	0.410439i	0.876884	−	0.480702i	$-0.159618\pi$
$733$	36.0249	+	11.1122i	1.33061	+	0.410439i	0.453727	+	0.891141i	$0.350094\pi$
$734$	−26.8880	+	23.5936i	−0.992454	+	0.870856i
$735$	3.91794	−	4.46338i	0.144516	−	0.164634i
$736$	3.75708	+	7.59151i	0.138488	+	0.279827i
$737$	−16.0142	−	4.93972i	−0.589889	−	0.181957i
$738$	17.6817	−	6.37894i	0.650873	−	0.234812i
$739$	−32.8206	−	22.3767i	−1.20732	−	0.823140i	−0.219033	−	0.975717i	$-0.570290\pi$
$739$	−32.8206	−	22.3767i	−1.20732	−	0.823140i	−0.988291	+	0.152578i	$0.951243\pi$
$740$	3.95479	−	0.0762015i	0.145381	−	0.00280122i
$741$	−3.45917	+	4.33767i	−0.127076	+	0.159348i
$742$	−6.18022	−	16.4179i	−0.226883	−	0.602720i
$743$	20.9313	−	16.6922i	0.767896	−	0.612377i	−0.159180	−	0.987250i	$-0.550885\pi$
$743$	20.9313	−	16.6922i	0.767896	−	0.612377i	0.927076	+	0.374873i	$0.122314\pi$
$744$	7.62934	+	1.21636i	0.279705	+	0.0445938i
$745$	−0.955202	+	6.33735i	−0.0349959	+	0.232183i
$746$	35.1078	+	3.61358i	1.28539	+	0.132302i
$747$	9.86243	+	14.4655i	0.360847	+	0.529266i
$748$	1.42989	+	15.1562i	0.0522821	+	0.554164i
$749$	−46.7613	−	9.99647i	−1.70862	−	0.365263i
$750$	−10.4244	+	5.63860i	−0.380647	+	0.205893i
$751$	14.3044	−	5.61404i	0.521973	−	0.204859i	−0.0897016	−	0.995969i	$-0.528591\pi$
$751$	14.3044	−	5.61404i	0.521973	−	0.204859i	0.611675	+	0.791109i	$0.290496\pi$
$752$	−4.87891	+	25.9464i	−0.177916	+	0.946166i
$753$	9.21446	+	15.9599i	0.335793	+	0.581611i
$754$	2.22059	−	0.442357i	0.0808692	−	0.0161097i
$755$	1.83579	−	3.81207i	0.0668114	−	0.138735i
$756$	1.52038	−	0.400319i	0.0552956	−	0.0145594i
$757$	19.6628	+	40.8302i	0.714657	+	1.48400i	0.868387	+	0.495887i	$0.165157\pi$
$757$	19.6628	+	40.8302i	0.714657	+	1.48400i	−0.153731	+	0.988113i	$0.549129\pi$
$758$	9.49457	+	12.6086i	0.344858	+	0.457967i
$759$	7.07164	−	2.18131i	0.256684	−	0.0791767i
$760$	−2.52827	+	3.11564i	−0.0917100	+	0.113016i
$761$	−3.14552	−	0.235724i	−0.114025	−	0.00854499i	0.0175954	−	0.999845i	$-0.494399\pi$
$761$	−3.14552	−	0.235724i	−0.114025	−	0.00854499i	−0.131620	+	0.991300i	$0.542018\pi$
$762$	−17.4096	+	40.9757i	−0.630684	+	1.48439i
$763$	−40.5244	−	11.8905i	−1.46708	−	0.430466i
$764$	−46.0451	−	30.1102i	−1.66585	−	1.08935i
$765$	3.25618	+	1.87995i	0.117727	+	0.0679699i
$766$	−25.2214	−	8.55356i	−0.911287	−	0.309053i
$767$	2.19270	−	0.164320i	0.0791737	−	0.00593325i
$768$	−38.3692	−	5.69445i	−1.38453	−	0.205481i
$769$	−48.7747	−	11.1325i	−1.75886	−	0.401448i	−0.783381	−	0.621541i	$-0.786507\pi$
$769$	−48.7747	−	11.1325i	−1.75886	−	0.401448i	−0.975479	+	0.220093i	$0.929364\pi$
$770$	−0.751116	−	2.56161i	−0.0270683	−	0.0923140i
$771$	1.12701	+	4.93776i	0.0405884	+	0.177829i
$772$	−2.82654	−	5.59120i	−0.101729	−	0.201232i
$773$	−10.7334	+	9.95911i	−0.386052	+	0.358204i	−0.849195	−	0.528080i	$-0.822912\pi$
$773$	−10.7334	+	9.95911i	−0.386052	+	0.358204i	0.463143	+	0.886284i	$0.346722\pi$
$774$	−1.01819	+	0.653533i	−0.0365979	+	0.0234907i
$775$	−4.02840	−	3.73781i	−0.144704	−	0.134266i
$776$	−41.5276	−	13.1972i	−1.49075	−	0.473753i
$777$	−25.0196	−	26.2297i	−0.897575	−	0.940985i
$778$	−22.6829	+	1.06763i	−0.813223	+	0.0382764i
$779$	−18.5152	+	2.79072i	−0.663378	+	0.0999881i
$780$	−0.714677	−	0.637947i	−0.0255895	−	0.0228422i
$781$	1.50280	+	0.589805i	0.0537744	+	0.0211049i
$782$	−7.21607	+	3.23144i	−0.258046	+	0.115556i
$783$	0.842598			0.0301120
$784$	−25.9747	−	10.4555i	−0.927667	−	0.373409i
$785$	6.01321			0.214621
$786$	−45.8300	+	20.5232i	−1.63470	+	0.732037i
$787$	38.6902	+	15.1848i	1.37916	+	0.541279i	0.934993	−	0.354666i	$-0.115406\pi$
$787$	38.6902	+	15.1848i	1.37916	+	0.541279i	0.444164	+	0.895946i	$0.353501\pi$
$788$	−9.29002	−	8.29262i	−0.330943	−	0.295412i
$789$	−52.5121	+	7.91492i	−1.86948	+	0.281779i
$790$	0.662049	−	0.0311610i	0.0235546	−	0.00110866i
$791$	16.2339	+	50.1618i	0.577210	+	1.78355i
$792$	−5.02506	+	15.8123i	−0.178558	+	0.561867i
$793$	−6.09616	−	5.65641i	−0.216481	−	0.200865i
$794$	2.04874	−	1.31501i	0.0727072	−	0.0466679i
$795$	−2.91596	+	2.70562i	−0.103419	+	0.0959584i
$796$	−16.3985	−	32.4380i	−0.581229	−	1.14973i
$797$	−3.11653	−	13.6544i	−0.110393	−	0.483663i	−0.999655	−	0.0262653i	$-0.991639\pi$
$797$	−3.11653	−	13.6544i	−0.110393	−	0.483663i	0.889262	−	0.457398i	$-0.151219\pi$
$798$	36.7021	−	2.23519i	1.29924	−	0.0791250i
$799$	−24.0260	−	5.48378i	−0.849979	−	0.194002i
$800$	20.4268	+	18.5481i	0.722197	+	0.655776i
$801$	−44.4370	+	3.33009i	−1.57010	+	0.117663i
$802$	−28.6926	−	9.73078i	−1.01317	−	0.343606i
$803$	−5.10830	−	2.94928i	−0.180268	−	0.104078i
$804$	33.3596	+	21.8149i	1.17650	+	0.769351i
$805$	1.13464	−	0.796730i	0.0399909	−	0.0280810i
$806$	0.351764	−	0.827921i	0.0123904	−	0.0291623i
$807$	−59.3157	−	4.44510i	−2.08801	−	0.156475i
$808$	−34.1757	−	27.7328i	−1.20230	−	0.975636i
$809$	−44.8251	+	13.8267i	−1.57597	+	0.486122i	−0.954723	−	0.297496i	$-0.903849\pi$
$809$	−44.8251	+	13.8267i	−1.57597	+	0.486122i	−0.621244	+	0.783617i	$0.713372\pi$
$810$	−2.78445	−	3.69771i	−0.0978356	−	0.129924i
$811$	−16.0090	−	33.2430i	−0.562152	−	1.16732i	−0.967433	−	0.253128i	$-0.918541\pi$
$811$	−16.0090	−	33.2430i	−0.562152	−	1.16732i	0.405281	−	0.914192i	$-0.367174\pi$
$812$	−12.0352	−	8.96333i	−0.422352	−	0.314551i
$813$	−1.70996	+	3.55078i	−0.0599711	+	0.124531i
$814$	−15.9791	+	3.18314i	−0.560067	+	0.111569i
$815$	2.11762	+	3.66782i	0.0741769	+	0.128478i
$816$	6.69118	−	35.5841i	0.234238	−	1.24569i
$817$	1.12188	−	0.440306i	0.0392497	−	0.0154044i
$818$	−0.534091	+	0.288891i	−0.0186741	+	0.0101008i
$819$	0.0592810	+	4.29761i	0.00207145	+	0.150171i
$820$	−0.303679	−	3.21884i	−0.0106049	−	0.112407i
$821$	18.6914	+	27.4152i	0.652333	+	0.956796i	0.999817	+	0.0191108i	$0.00608352\pi$
$821$	18.6914	+	27.4152i	0.652333	+	0.956796i	−0.347485	+	0.937686i	$0.612964\pi$
$822$	−33.1884	−	3.41602i	−1.15758	−	0.119147i
$823$	−4.00631	+	26.5801i	−0.139651	+	0.926525i	0.803773	+	0.594936i	$0.202823\pi$
$823$	−4.00631	+	26.5801i	−0.139651	+	0.926525i	−0.943424	+	0.331589i	$0.892415\pi$
$824$	−3.37877	+	21.1926i	−0.117705	+	0.738280i
$825$	18.8470	−	15.0300i	0.656170	−	0.523278i
$826$	−10.5432	−	10.0604i	−0.366843	−	0.350047i
$827$	25.9895	−	32.5898i	0.903743	−	1.13326i	−0.0868236	−	0.996224i	$-0.527672\pi$
$827$	25.9895	−	32.5898i	0.903743	−	1.13326i	0.990566	−	0.137034i	$-0.0437569\pi$
$828$	−8.61554	+	0.166005i	−0.299411	+	0.00576909i
$829$	11.8516	+	8.08032i	0.411625	+	0.280641i	0.751376	−	0.659874i	$-0.229390\pi$
$829$	11.8516	+	8.08032i	0.411625	+	0.280641i	−0.339751	+	0.940515i	$0.610343\pi$
$830$	2.83264	−	1.02192i	0.0983224	−	0.0354712i
$831$	9.93381	+	3.06418i	0.344600	+	0.106295i
$832$	−1.72130	+	4.17563i	−0.0596755	+	0.144764i
$833$	10.6863	−	23.8519i	0.370259	−	0.826419i
$834$	−35.7434	+	31.3640i	−1.23769	+	1.08605i
$835$	1.80709	+	0.557412i	0.0625368	+	0.0192900i
$836$	7.98640	−	14.4696i	0.276215	−	0.500443i
$837$	0.188574	−	0.276587i	0.00651807	−	0.00956025i
$838$	−0.452751	−	0.382094i	−0.0156400	−	0.0131992i
$839$	−19.4473	+	24.3861i	−0.671394	+	0.841902i	−0.994530	−	0.104451i	$-0.966692\pi$
$839$	−19.4473	+	24.3861i	−0.671394	+	0.841902i	0.323136	+	0.946353i	$0.395263\pi$
$840$	0.0335981	+	6.34900i	0.00115924	+	0.219061i
$841$	13.0669	+	16.3853i	0.450581	+	0.565011i
$842$	−1.16211	+	41.8415i	−0.0400490	+	1.44195i
$843$	−4.11759	+	27.3184i	−0.141817	+	0.940897i
$844$	−0.694384	−	0.977471i	−0.0239017	−	0.0336459i
$845$	3.66684	−	2.50001i	0.126143	−	0.0860028i
$846$	−21.7630	−	15.7403i	−0.748228	−	0.541162i
$847$	−8.08086	−	16.2045i	−0.277662	−	0.556792i
$848$	16.5905	+	8.74431i	0.569719	+	0.300281i
$849$	10.1469	+	25.8538i	0.348239	+	0.887299i
$850$	−18.0353	+	18.3861i	−0.618605	+	0.630639i
$851$	−4.23104	−	7.32837i	−0.145038	−	0.251213i
$852$	−3.04756	−	2.33574i	−0.104408	−	0.0800211i
$853$	−11.9805	−	5.76949i	−0.410203	−	0.197543i	0.217390	−	0.976085i	$-0.430246\pi$
$853$	−11.9805	−	5.76949i	−0.410203	−	0.197543i	−0.627593	+	0.778541i	$0.715960\pi$
$854$	−0.770155	+	55.1101i	−0.0263542	+	1.88583i
$855$	−1.77109	−	3.67770i	−0.0605699	−	0.125775i
$856$	44.4864	−	25.1825i	1.52051	−	0.860718i
$857$	−3.33020	−	10.7963i	−0.113758	−	0.368793i	0.880734	−	0.473612i	$-0.157050\pi$
$857$	−3.33020	−	10.7963i	−0.113758	−	0.368793i	−0.994491	+	0.104819i	$0.966574\pi$
$858$	3.36125	+	2.06712i	0.114751	+	0.0705703i
$859$	11.6058	+	0.869736i	0.395986	+	0.0296750i	0.271235	−	0.962513i	$-0.412568\pi$
$859$	11.6058	+	0.869736i	0.395986	+	0.0296750i	0.124751	+	0.992188i	$0.460187\pi$
$860$	0.0651582	+	0.197637i	0.00222188	+	0.00673935i
$861$	−19.8512	+	21.9954i	−0.676528	+	0.749600i
$862$	8.91461	+	32.0323i	0.303633	+	1.09102i
$863$	21.4107	+	12.3615i	0.728828	+	0.420789i	0.817993	−	0.575228i	$-0.195087\pi$
$863$	21.4107	+	12.3615i	0.728828	+	0.420789i	−0.0891654	+	0.996017i	$0.528420\pi$
$864$	−0.931797	+	1.39881i	−0.0317004	+	0.0475886i
$865$	−0.274735	−	3.66608i	−0.00934127	−	0.124651i
$866$	22.1665	−	42.9372i	0.753248	−	1.45906i
$867$	−7.23007	−	1.65022i	−0.245546	−	0.0560443i
$868$	−5.63574	+	1.94461i	−0.191289	+	0.0660044i
$869$	−2.66159	+	0.607491i	−0.0902883	+	0.0206077i
$870$	−0.848985	+	3.29510i	−0.0287833	+	0.111714i
$871$	3.40213	−	3.15672i	0.115277	−	0.106961i
$872$	40.8427	−	19.2428i	1.38311	−	0.651643i
$873$	30.1516	−	32.4957i	1.02048	−	1.09981i
$874$	8.44909	+	1.51450i	0.285795	+	0.0512288i
$875$	5.04728	−	7.62693i	0.170629	−	0.257837i
$876$	9.73864	+	10.0984i	0.329038	+	0.341194i
$877$	−1.39051	−	9.22546i	−0.0469543	−	0.311522i	−0.999963	−	0.00857929i	$-0.997269\pi$
$877$	−1.39051	−	9.22546i	−0.0469543	−	0.311522i	0.953009	−	0.302942i	$-0.0979690\pi$
$878$	−13.4142	+	1.64242i	−0.452706	+	0.0554289i
$879$	−6.39881	−	2.51135i	−0.215827	−	0.0847057i
$880$	2.41808	+	1.51556i	0.0815133	+	0.0510896i
$881$			41.5645i			1.40034i	0.713975	+	0.700171i	$0.246893\pi$
$881$			41.5645i			1.40034i	−0.713975	+	0.700171i	$0.753107\pi$
$882$	20.8847	−	19.3711i	0.703223	−	0.652259i
$883$	44.1975			1.48737			0.743683	−	0.668533i	$-0.233077\pi$
$883$	44.1975			1.48737			0.743683	+	0.668533i	$0.233077\pi$
$884$	−3.83292	−	1.75569i	−0.128915	−	0.0590504i
$885$	−1.20725	+	3.07603i	−0.0405814	+	0.103400i
$886$	−14.9195	+	1.82672i	−0.501229	+	0.0613700i
$887$	23.5879	−	3.55530i	0.792004	−	0.119375i	0.259433	−	0.965761i	$-0.416464\pi$
$887$	23.5879	−	3.55530i	0.792004	−	0.119375i	0.532570	+	0.846386i	$0.321226\pi$
$888$	38.6173	+	3.22432i	1.29591	+	0.108201i
$889$	−3.03972	−	34.2213i	−0.101949	−	1.14775i
$890$	−1.35233	+	7.54439i	−0.0453304	+	0.252889i
$891$	13.9767	+	12.9685i	0.468238	+	0.434461i
$892$	14.0424	−	48.8461i	0.470174	−	1.63549i
$893$	18.1977	+	19.6125i	0.608964	+	0.656307i
$894$	−15.6656	+	60.8016i	−0.523936	+	2.03351i
$895$	−1.16113	−	5.08724i	−0.0388122	−	0.170048i
$896$	28.1894	−	10.0676i	0.941742	−	0.336335i
$897$	−0.456040	+	1.99804i	−0.0152267	+	0.0667127i
$898$	−2.76642	−	1.42817i	−0.0923165	−	0.0476588i
$899$	−3.18621	+	0.238774i	−0.106266	+	0.00796354i
$900$	−25.9269	+	10.7564i	−0.864229	+	0.358548i
$901$	−8.75281	+	15.1603i	−0.291598	+	0.505063i
$902$	3.57057	+	12.8299i	0.118887	+	0.427189i
$903$	0.930657	−	1.66455i	0.0309703	−	0.0553928i
$904$	−48.5709	−	28.5957i	−1.61544	−	0.951079i
$905$	0.528261	−	7.04915i	0.0175600	−	0.234322i
$906$	21.7142	−	35.3085i	0.721407	−	1.17305i
$907$	−23.7711	+	7.33240i	−0.789305	+	0.243468i	−0.663095	−	0.748535i	$-0.730757\pi$
$907$	−23.7711	+	7.33240i	−0.789305	+	0.243468i	−0.126210	+	0.992004i	$0.540281\pi$
$908$	1.84467	−	8.86605i	0.0612177	−	0.294230i
$909$	40.3409	−	19.4272i	1.33802	−	0.644359i
$910$	0.718360	+	0.174557i	0.0238134	+	0.00578650i
$911$	−3.43449	+	7.13180i	−0.113790	+	0.236287i	−0.950084	−	0.311994i	$-0.899003\pi$
$911$	−3.43449	+	7.13180i	−0.113790	+	0.236287i	0.836294	+	0.548281i	$0.184717\pi$
$912$	−27.7641	+	27.8270i	−0.919362	+	0.921445i
$913$	−10.7421	+	6.20195i	−0.355511	+	0.205255i
$914$	−29.4160	−	28.8547i	−0.972995	−	0.954428i
$915$	11.6337	−	4.56589i	0.384598	−	0.150944i
$916$	33.0861	+	12.2551i	1.09319	+	0.404921i
$917$	23.7403	−	30.6267i	0.783975	−	1.01138i
$918$	−1.27124	−	0.919432i	−0.0419570	−	0.0303458i
$919$	23.8352	+	34.9598i	0.786251	+	1.15322i	0.984896	+	0.173147i	$0.0553936\pi$
$919$	23.8352	+	34.9598i	0.786251	+	1.15322i	−0.198645	+	0.980072i	$0.563654\pi$
$920$	−0.342083	+	1.44214i	−0.0112781	+	0.0475459i
$921$	22.1109	+	3.33268i	0.728579	+	0.109816i
$922$	−7.37668	−	0.204881i	−0.242938	−	0.00674740i
$923$	−0.349542	+	0.278750i	−0.0115053	+	0.00917517i
$924$	−4.75042	−	25.7172i	−0.156277	−	0.846034i
$925$	−21.5508	−	17.1862i	−0.708587	−	0.565079i
$926$	−0.377122	−	0.318269i	−0.0123930	−	0.0104590i
$927$	−18.0386	−	12.2985i	−0.592465	−	0.403936i
$928$	15.9836	−	1.37098i	0.524689	−	0.0450045i
$929$	−6.55131	+	21.2388i	−0.214942	+	0.696823i	0.782321	+	0.622876i	$0.214036\pi$
$929$	−6.55131	+	21.2388i	−0.214942	+	0.696823i	−0.997262	+	0.0739474i	$0.976440\pi$
$930$	0.891629	+	1.01613i	0.0292377	+	0.0333201i
$931$	−24.1727	+	14.8599i	−0.792229	+	0.487012i
$932$	−6.82122	+	52.0399i	−0.223437	+	1.70462i
$933$	11.9939	−	38.8831i	0.392661	−	1.27298i
$934$	29.9194	−	10.7938i	0.978992	−	0.353186i
$935$	−1.50059	+	2.20096i	−0.0490745	+	0.0719791i
$936$	−3.09649	−	3.39465i	−0.101212	−	0.110958i
$937$	−39.6162	−	31.5929i	−1.29421	−	1.03209i	−0.997010	−	0.0772778i	$-0.975377\pi$
$937$	−39.6162	−	31.5929i	−1.29421	−	1.03209i	−0.297196	−	0.954817i	$-0.596051\pi$
$938$	−30.6376	−	2.72698i	−1.00035	−	0.0890391i
$939$	35.3970	+	44.3864i	1.15514	+	1.44850i
$940$	−3.55568	+	2.94939i	−0.115973	+	0.0961985i
$941$	−7.55481	−	1.13871i	−0.246280	−	0.0371207i	0.0247421	−	0.999694i	$-0.492124\pi$
$941$	−7.55481	−	1.13871i	−0.246280	−	0.0371207i	−0.271022	+	0.962573i	$0.587362\pi$
$942$	58.6009	+	6.03167i	1.90932	+	0.196522i
$943$	−5.71482	+	3.89630i	−0.186100	+	0.126881i
$944$	15.5689	+	0.564904i	0.506723	+	0.0183861i
$945$	0.249485	+	0.115934i	0.00811574	+	0.00377134i
$946$	−0.407814	−	0.753951i	−0.0132592	−	0.0245131i
$947$	−4.72384	−	12.0361i	−0.153504	−	0.391122i	0.833348	−	0.552749i	$-0.186421\pi$
$947$	−4.72384	−	12.0361i	−0.153504	−	0.391122i	−0.986852	+	0.161627i	$0.948326\pi$
$948$	6.48316	+	0.360407i	0.210563	+	0.0117055i
$949$	1.41466	−	0.816755i	0.0459218	−	0.0265130i
$950$	27.4221	−	5.46266i	0.889690	−	0.177232i
$951$	−65.8915	−	31.7317i	−2.13668	−	1.02897i
$952$	8.37692	+	26.6557i	0.271497	+	0.863915i
$953$	45.8151	−	22.0634i	1.48410	−	0.714704i	0.495970	−	0.868340i	$-0.334812\pi$
$953$	45.8151	−	22.0634i	1.48410	−	0.714704i	0.988128	+	0.153636i	$0.0490982\pi$
$954$	−15.2409	+	11.4767i	−0.493444	+	0.371573i
$955$	−2.83756	−	9.19913i	−0.0918212	−	0.297677i
$956$	35.7851	−	6.10097i	1.15737	−	0.197319i
$957$	1.04741	−	13.9768i	0.0338581	−	0.451805i
$958$	−12.3490	+	29.0649i	−0.398978	+	0.939044i
$959$	23.8345	−	9.73585i	0.769657	−	0.314387i
$960$	−4.53139	−	5.05333i	−0.146250	−	0.163096i
$961$	14.8653	−	25.7475i	0.479526	−	0.830563i
$962$	1.44916	−	4.27305i	0.0467227	−	0.137769i
$963$	3.88637	+	51.8599i	0.125236	+	1.67116i
$964$	−3.50400	−	14.0947i	−0.112856	−	0.453958i
$965$	0.243943	−	1.06878i	0.00785280	−	0.0344054i
$966$	11.8567	−	6.62629i	0.381482	−	0.213197i
$967$	−2.13902	+	0.488217i	−0.0687862	+	0.0157000i	−0.256776	−	0.966471i	$-0.582660\pi$
$967$	−2.13902	+	0.488217i	−0.0687862	+	0.0157000i	0.187989	+	0.982171i	$0.439803\pi$
$968$	17.9589	+	7.22514i	0.577222	+	0.232225i
$969$	−24.9573	−	26.8976i	−0.801744	−	0.864074i
$970$	−4.11858	−	6.41663i	−0.132240	−	0.206026i
$971$	−29.8790	+	32.2019i	−0.958862	+	1.03341i	0.0405520	+	0.999177i	$0.487088\pi$
$971$	−29.8790	+	32.2019i	−0.958862	+	1.03341i	−0.999414	+	0.0342300i	$0.989102\pi$
$972$	−22.5055	−	37.3021i	−0.721863	−	1.19646i
$973$	12.9341	−	34.3409i	0.414648	−	1.10092i
$974$	−37.4325	+	1.76185i	−1.19941	+	0.0564534i
$975$	0.994982	+	6.60128i	0.0318649	+	0.211410i
$976$	−38.4839	−	44.6168i	−1.23184	−	1.42815i
$977$	−18.3855	+	46.8455i	−0.588204	+	1.49872i	0.258153	+	0.966104i	$0.416886\pi$
$977$	−18.3855	+	46.8455i	−0.588204	+	1.49872i	−0.846357	+	0.532616i	$0.821209\pi$
$978$	16.9579	+	37.8684i	0.542253	+	1.21090i
$979$		−	31.5711i		−	1.00902i
$980$	−2.33022	−	4.30989i	−0.0744362	−	0.137674i
$981$			45.9312i			1.46647i
$982$	13.4687	−	6.03142i	0.429803	−	0.192470i
$983$	18.7196	−	47.6968i	0.597064	−	1.52129i	−0.238071	−	0.971248i	$-0.576515\pi$
$983$	18.7196	−	47.6968i	0.597064	−	1.52129i	0.835135	−	0.550045i	$-0.185390\pi$
$984$	0.269270	−	31.6734i	0.00858402	−	1.00971i
$985$	−0.324765	−	2.15468i	−0.0103479	−	0.0686537i
$986$	0.704037	+	14.9580i	0.0224211	+	0.476361i
$987$	41.9457	+	5.73179i	1.33515	+	0.182445i
$988$	2.36442	+	3.91896i	0.0752224	+	0.124679i
$989$	0.302806	−	0.326348i	0.00962868	−	0.0103773i
$990$	−2.44324	+	1.56822i	−0.0776513	+	0.0498413i
$991$	7.54898	+	8.13586i	0.239801	+	0.258444i	0.841473	−	0.540299i	$-0.181689\pi$
$991$	7.54898	+	8.13586i	0.239801	+	0.258444i	−0.601672	+	0.798743i	$0.705498\pi$
$992$	3.12712	−	5.55354i	0.0992861	−	0.176325i
$993$	−26.0152	+	5.93780i	−0.825568	+	0.188430i
$994$	2.92349	+	0.482517i	0.0927274	+	0.0153045i
$995$	1.41526	−	6.20068i	0.0448669	−	0.196575i
$996$	28.6302	−	7.11760i	0.907181	−	0.225530i
$997$	−2.81739	−	37.5954i	−0.0892276	−	1.19066i	−0.844613	−	0.535378i	$-0.820169\pi$
$997$	−2.81739	−	37.5954i	−0.0892276	−	1.19066i	0.755385	−	0.655281i	$-0.227450\pi$
$998$	−9.67101	−	3.27982i	−0.306131	−	0.103821i
$999$	0.839555	−	1.45415i	0.0265624	−	0.0460073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.bc.a.243.47	yes	648
8.3	odd	2	inner	392.2.bc.a.243.38	yes	648
49.24	odd	42	inner	392.2.bc.a.171.38	✓	648
392.171	even	42	inner	392.2.bc.a.171.47	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.bc.a.171.38	✓	648	49.24	odd	42	inner
392.2.bc.a.171.47	yes	648	392.171	even	42	inner
392.2.bc.a.243.38	yes	648	8.3	odd	2	inner
392.2.bc.a.243.47	yes	648	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.bc (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29071 - 0.577993i) q^{2} +(2.25676 + 0.885712i) q^{3} +(1.33185 - 1.49204i) q^{4} +(0.346055 - 0.0521594i) q^{5} +(3.42475 - 0.161194i) q^{6} +(-2.27282 + 1.35435i) q^{7} +(0.856640 - 2.69558i) q^{8} +(2.10932 + 1.95716i) q^{9} +O(q^{10})\)	\(q+(1.29071 - 0.577993i) q^{2} +(2.25676 + 0.885712i) q^{3} +(1.33185 - 1.49204i) q^{4} +(0.346055 - 0.0521594i) q^{5} +(3.42475 - 0.161194i) q^{6} +(-2.27282 + 1.35435i) q^{7} +(0.856640 - 2.69558i) q^{8} +(2.10932 + 1.95716i) q^{9} +(0.416508 - 0.267340i) q^{10} +(-1.49441 + 1.38661i) q^{11} +(4.32718 - 2.18753i) q^{12} +(-0.125627 - 0.550408i) q^{13} +(-2.15074 + 3.06175i) q^{14} +(0.827161 + 0.188794i) q^{15} +(-0.452356 - 3.97434i) q^{16} +(3.72333 - 0.279025i) q^{17} +(3.85373 + 1.30695i) q^{18} +(-3.51049 - 2.02678i) q^{19} +(0.383069 - 0.585796i) q^{20} +(-6.32878 + 1.04338i) q^{21} +(-1.12740 + 2.65347i) q^{22} +(-1.49317 - 0.111898i) q^{23} +(4.32074 - 5.32454i) q^{24} +(-4.66083 + 1.43768i) q^{25} +(-0.480279 - 0.637804i) q^{26} +(-0.128914 - 0.267694i) q^{27} +(-1.00631 + 5.19493i) q^{28} +(-1.23046 + 2.55507i) q^{29} +(1.17674 - 0.234415i) q^{30} +(0.563337 + 0.975728i) q^{31} +(-2.88100 - 4.86825i) q^{32} +(-4.60067 + 1.80563i) q^{33} +(4.64445 - 2.51220i) q^{34} +(-0.715880 + 0.587230i) q^{35} +(5.72945 - 0.540539i) q^{36} +(3.18351 + 4.66935i) q^{37} +(-5.70247 - 0.586944i) q^{38} +(0.203993 - 1.35341i) q^{39} +(0.155845 - 0.977502i) q^{40} +(3.61147 - 2.88005i) q^{41} +(-7.56554 + 5.00468i) q^{42} +(-0.185374 + 0.232452i) q^{43} +(0.0785463 + 4.07648i) q^{44} +(0.832024 + 0.567264i) q^{45} +(-1.99192 + 0.718615i) q^{46} +(-6.30704 - 1.94546i) q^{47} +(2.49926 - 9.36978i) q^{48} +(3.33146 - 6.15641i) q^{49} +(-5.18480 + 4.54954i) q^{50} +(8.64979 + 2.66811i) q^{51} +(-0.988546 - 0.545620i) q^{52} +(-2.64110 + 3.87379i) q^{53} +(-0.321116 - 0.271002i) q^{54} +(-0.444825 + 0.557792i) q^{55} +(1.70378 + 7.28678i) q^{56} +(-6.12717 - 7.68323i) q^{57} +(-0.111348 + 4.00904i) q^{58} +(-0.580487 + 3.85128i) q^{59} +(1.38334 - 0.982710i) q^{60} +(12.1707 - 8.29783i) q^{61} +(1.29107 + 0.933775i) q^{62} +(-7.44479 - 1.59152i) q^{63} +(-6.53234 - 4.61829i) q^{64} +(-0.0721828 - 0.183919i) q^{65} +(-4.89448 + 4.98970i) q^{66} +(4.11031 + 7.11926i) q^{67} +(4.54260 - 5.92697i) q^{68} +(-3.27062 - 1.57505i) q^{69} +(-0.584577 + 1.17171i) q^{70} +(-0.343595 - 0.713483i) q^{71} +(7.08261 - 4.00926i) q^{72} +(0.852846 + 2.76486i) q^{73} +(6.80783 + 4.18672i) q^{74} +(-11.7917 - 0.883668i) q^{75} +(-7.69947 + 2.53841i) q^{76} +(1.51858 - 5.17549i) q^{77} +(-0.518964 - 1.86476i) q^{78} +(1.15975 + 0.669580i) q^{79} +(-0.363839 - 1.35175i) q^{80} +(-0.698924 - 9.32650i) q^{81} +(2.99670 - 5.80471i) q^{82} +(5.93191 + 1.35392i) q^{83} +(-6.87222 + 10.8324i) q^{84} +(1.27392 - 0.290765i) q^{85} +(-0.104908 + 0.407172i) q^{86} +(-5.03989 + 4.67634i) q^{87} +(2.45756 + 5.21615i) q^{88} +(-10.5335 + 11.3524i) q^{89} +(1.40177 + 0.251268i) q^{90} +(1.03097 + 1.08084i) q^{91} +(-2.15564 + 2.07884i) q^{92} +(0.407101 + 2.70094i) q^{93} +(-9.26500 + 1.13440i) q^{94} +(-1.32054 - 0.518272i) q^{95} +(-2.18985 - 13.5382i) q^{96} -15.4058i q^{97} +(0.741576 - 9.87168i) q^{98} -5.86602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 22 q^{3} - 13 q^{4} - 14 q^{6} - 4 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 22 * q^3 - 13 * q^4 - 14 * q^6 - 4 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 22 q^{3} - 13 q^{4} - 14 q^{6} - 4 q^{8} - 76 q^{9} - 20 q^{10} - 26 q^{11} - 31 q^{12} + 15 q^{14} - 9 q^{16} - 22 q^{17} - 18 q^{18} - 36 q^{19} - 14 q^{20} - 26 q^{22} + 22 q^{24} + 20 q^{25} - 20 q^{26} - 28 q^{27} - 62 q^{28} - 5 q^{30} - 23 q^{32} - 22 q^{33} - 42 q^{34} - 46 q^{35} - 32 q^{36} - 4 q^{38} - 28 q^{41} + 16 q^{42} - 20 q^{43} + 6 q^{46} - 16 q^{49} - 140 q^{50} - 34 q^{51} + 10 q^{52} + 43 q^{54} + 56 q^{56} - 34 q^{57} - 16 q^{58} - 70 q^{59} + 92 q^{60} + 20 q^{64} - 16 q^{65} + 2 q^{66} - 24 q^{67} + 15 q^{68} - 114 q^{70} + 110 q^{72} - 46 q^{73} - 34 q^{74} - 52 q^{75} - 147 q^{76} + 48 q^{78} + 6 q^{80} + 70 q^{81} - 68 q^{82} - 28 q^{83} + 128 q^{84} - 117 q^{86} + 133 q^{88} - 46 q^{89} - 294 q^{90} - 124 q^{91} - 102 q^{92} - 44 q^{94} + 38 q^{96} - 225 q^{98} - 72 q^{99}+O(q^{100}) \) 648 * q - 13 * q^2 - 22 * q^3 - 13 * q^4 - 14 * q^6 - 4 * q^8 - 76 * q^9 - 20 * q^10 - 26 * q^11 - 31 * q^12 + 15 * q^14 - 9 * q^16 - 22 * q^17 - 18 * q^18 - 36 * q^19 - 14 * q^20 - 26 * q^22 + 22 * q^24 + 20 * q^25 - 20 * q^26 - 28 * q^27 - 62 * q^28 - 5 * q^30 - 23 * q^32 - 22 * q^33 - 42 * q^34 - 46 * q^35 - 32 * q^36 - 4 * q^38 - 28 * q^41 + 16 * q^42 - 20 * q^43 + 6 * q^46 - 16 * q^49 - 140 * q^50 - 34 * q^51 + 10 * q^52 + 43 * q^54 + 56 * q^56 - 34 * q^57 - 16 * q^58 - 70 * q^59 + 92 * q^60 + 20 * q^64 - 16 * q^65 + 2 * q^66 - 24 * q^67 + 15 * q^68 - 114 * q^70 + 110 * q^72 - 46 * q^73 - 34 * q^74 - 52 * q^75 - 147 * q^76 + 48 * q^78 + 6 * q^80 + 70 * q^81 - 68 * q^82 - 28 * q^83 + 128 * q^84 - 117 * q^86 + 133 * q^88 - 46 * q^89 - 294 * q^90 - 124 * q^91 - 102 * q^92 - 44 * q^94 + 38 * q^96 - 225 * q^98 - 72 * q^99

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