LMFDB - Embedded newform 525.2.bo.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(4,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 3, 20]))

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

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

chi := DirichletCharacter("525.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bo (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	525.4
Dual form			525.2.bo.a.394.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.459756 - 2.16298i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-2.64003 + 1.17542i) q^{4} +(-2.14884 + 0.618467i) q^{5} +(1.78898 - 1.29977i) q^{6} +(-2.46658 - 0.957073i) q^{7} +(1.15663 + 1.59196i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.459756 - 2.16298i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-2.64003 + 1.17542i) q^{4} +(-2.14884 + 0.618467i) q^{5} +(1.78898 - 1.29977i) q^{6} +(-2.46658 - 0.957073i) q^{7} +(1.15663 + 1.59196i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(2.32567 + 4.36355i) q^{10} +(3.55846 + 3.95207i) q^{11} +(-2.14759 - 1.93370i) q^{12} +(4.64532 - 1.50936i) q^{13} +(-0.936106 + 5.77519i) q^{14} +(-1.43901 - 1.71151i) q^{15} +(-0.955782 + 1.06150i) q^{16} +(-4.68576 + 0.492493i) q^{17} +(1.91505 + 1.10565i) q^{18} +(5.45376 + 2.42817i) q^{19} +(4.94603 - 4.15855i) q^{20} +(-0.128919 - 2.64261i) q^{21} +(6.91224 - 9.51388i) q^{22} +(1.76805 + 8.31803i) q^{23} +(-0.983886 + 1.70414i) q^{24} +(4.23500 - 2.65797i) q^{25} +(-5.40043 - 9.35381i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(7.63679 - 0.372558i) q^{28} +(-0.862469 - 0.626621i) q^{29} +(-3.04037 + 3.89943i) q^{30} +(0.241356 + 2.29635i) q^{31} +(6.14372 + 3.54708i) q^{32} +(-2.16304 + 4.85827i) q^{33} +(3.21956 + 9.90878i) q^{34} +(5.89219 + 0.531094i) q^{35} +(0.893019 - 2.74843i) q^{36} +(-0.112265 - 0.101084i) q^{37} +(2.74469 - 12.9128i) q^{38} +(3.26829 + 3.62980i) q^{39} +(-3.46998 - 2.70553i) q^{40} +(2.37228 + 7.30113i) q^{41} +(-5.65665 + 1.49380i) q^{42} +4.48699i q^{43} +(-14.0398 - 6.25090i) q^{44} +(0.978241 - 2.01073i) q^{45} +(17.1789 - 7.64854i) q^{46} +(-6.51115 - 0.684350i) q^{47} +(-1.35848 - 0.441398i) q^{48} +(5.16802 + 4.72139i) q^{49} +(-7.69621 - 7.93821i) q^{50} +(-2.35578 - 4.08034i) q^{51} +(-10.4897 + 9.44493i) q^{52} +(-2.43158 - 5.46143i) q^{53} +(-0.231144 + 2.19919i) q^{54} +(-10.0908 - 6.29156i) q^{55} +(-1.32929 - 5.03368i) q^{56} +5.96989i q^{57} +(-0.958844 + 2.15360i) q^{58} +(-7.00628 - 1.48923i) q^{59} +(5.81075 + 2.82699i) q^{60} +(-2.59552 + 0.551694i) q^{61} +(4.85599 - 1.57781i) q^{62} +(2.36171 - 1.19262i) q^{63} +(3.96486 - 12.2026i) q^{64} +(-9.04855 + 6.11634i) q^{65} +(11.5028 + 2.44500i) q^{66} +(0.690898 - 0.0726163i) q^{67} +(11.7916 - 6.80791i) q^{68} +(-6.87977 + 4.99845i) q^{69} +(-1.56023 - 12.9889i) q^{70} +(1.71228 + 1.24405i) q^{71} +(-1.95699 - 0.205688i) q^{72} +(-0.502455 + 0.452412i) q^{73} +(-0.167029 + 0.289302i) q^{74} +(4.15070 + 2.78777i) q^{75} -17.2522 q^{76} +(-4.99481 - 13.1538i) q^{77} +(6.34858 - 8.73807i) q^{78} +(0.461592 - 4.39175i) q^{79} +(1.39731 - 2.87212i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(14.7015 - 8.48794i) q^{82} +(-1.66593 - 2.29296i) q^{83} +(3.44651 + 6.82503i) q^{84} +(9.76433 - 3.95627i) q^{85} +(9.70528 - 2.06292i) q^{86} +(0.221649 - 1.04277i) q^{87} +(-2.17573 + 10.2360i) q^{88} +(-13.6646 + 2.90450i) q^{89} +(-4.79893 - 1.19147i) q^{90} +(-12.9026 - 0.722963i) q^{91} +(-14.4449 - 19.8816i) q^{92} +(-1.99965 + 1.15450i) q^{93} +(1.51331 + 14.3981i) q^{94} +(-13.2210 - 1.84477i) q^{95} +(-0.741542 + 7.05530i) q^{96} +(-0.0252936 + 0.0348137i) q^{97} +(7.83625 - 13.3490i) q^{98} -5.31804 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.459756	−	2.16298i	−0.325097	−	1.52946i	−0.772434	−	0.635095i	$-0.780961\pi$
$2$	−0.459756	−	2.16298i	−0.325097	−	1.52946i	0.447338	−	0.894365i	$-0.352372\pi$
$3$	0.406737	+	0.913545i	0.234830	+	0.527436i
$3$	0.406737	+	0.913545i	0.234830	+	0.527436i
$4$	−2.64003	+	1.17542i	−1.32001	+	0.587708i
$5$	−2.14884	+	0.618467i	−0.960989	+	0.276587i
$5$	−2.14884	+	0.618467i	−0.960989	+	0.276587i
$6$	1.78898	−	1.29977i	0.730349	−	0.530630i
$7$	−2.46658	−	0.957073i	−0.932279	−	0.361739i
$7$	−2.46658	−	0.957073i	−0.932279	−	0.361739i
$8$	1.15663	+	1.59196i	0.408930	+	0.562843i
$9$	−0.669131	+	0.743145i	−0.223044	+	0.247715i
$10$	2.32567	+	4.36355i	0.735443	+	1.37988i
$11$	3.55846	+	3.95207i	1.07292	+	1.19159i	0.980632	+	0.195861i	$0.0627503\pi$
$11$	3.55846	+	3.95207i	1.07292	+	1.19159i	0.0922845	+	0.995733i	$0.470583\pi$
$12$	−2.14759	−	1.93370i	−0.619956	−	0.558211i
$13$	4.64532	−	1.50936i	1.28838	−	0.418620i	0.416856	−	0.908973i	$-0.363132\pi$
$13$	4.64532	−	1.50936i	1.28838	−	0.418620i	0.871524	+	0.490352i	$0.163132\pi$
$14$	−0.936106	+	5.77519i	−0.250185	+	1.54348i
$15$	−1.43901	−	1.71151i	−0.371550	−	0.441909i
$16$	−0.955782	+	1.06150i	−0.238945	+	0.265376i
$17$	−4.68576	+	0.492493i	−1.13646	+	0.119447i	−0.654018	−	0.756479i	$-0.726918\pi$
$17$	−4.68576	+	0.492493i	−1.13646	+	0.119447i	−0.482445	+	0.875926i	$0.660251\pi$
$18$	1.91505	+	1.10565i	0.451381	+	0.260605i
$19$	5.45376	+	2.42817i	1.25118	+	0.557061i	0.921994	−	0.387205i	$-0.126559\pi$
$19$	5.45376	+	2.42817i	1.25118	+	0.557061i	0.329185	+	0.944265i	$0.393226\pi$
$20$	4.94603	−	4.15855i	1.10597	−	0.929879i
$21$	−0.128919	−	2.64261i	−0.0281324	−	0.576664i
$22$	6.91224	−	9.51388i	1.47369	−	2.02837i
$23$	1.76805	+	8.31803i	0.368665	+	1.73443i	0.636782	+	0.771044i	$0.280265\pi$
$23$	1.76805	+	8.31803i	0.368665	+	1.73443i	−0.268117	+	0.963386i	$0.586402\pi$
$24$	−0.983886	+	1.70414i	−0.200835	+	0.347856i
$25$	4.23500	−	2.65797i	0.846999	−	0.531594i
$26$	−5.40043	−	9.35381i	−1.05911	−	1.83443i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	7.63679	−	0.372558i	1.44322	−	0.0704069i
$29$	−0.862469	−	0.626621i	−0.160157	−	0.116361i	0.504820	−	0.863224i	$-0.331559\pi$
$29$	−0.862469	−	0.626621i	−0.160157	−	0.116361i	−0.664977	+	0.746864i	$0.731559\pi$
$30$	−3.04037	+	3.89943i	−0.555092	+	0.711935i
$31$	0.241356	+	2.29635i	0.0433488	+	0.412436i	0.994581	+	0.103961i	$0.0331518\pi$
$31$	0.241356	+	2.29635i	0.0433488	+	0.412436i	−0.951233	+	0.308475i	$0.900181\pi$
$32$	6.14372	+	3.54708i	1.08607	+	0.627041i
$33$	−2.16304	+	4.85827i	−0.376537	+	0.845716i
$34$	3.21956	+	9.90878i	0.552150	+	1.69934i
$35$	5.89219	+	0.531094i	0.995962	+	0.0897712i
$36$	0.893019	−	2.74843i	0.148836	−	0.458072i
$37$	−0.112265	−	0.101084i	−0.0184563	−	0.0166181i	0.659851	−	0.751397i	$-0.270619\pi$
$37$	−0.112265	−	0.101084i	−0.0184563	−	0.0166181i	−0.678307	+	0.734778i	$0.737286\pi$
$38$	2.74469	−	12.9128i	0.445248	−	2.09473i
$39$	3.26829	+	3.62980i	0.523345	+	0.581233i
$40$	−3.46998	−	2.70553i	−0.548652	−	0.427782i
$41$	2.37228	+	7.30113i	0.370488	+	1.14024i	0.946473	+	0.322784i	$0.104619\pi$
$41$	2.37228	+	7.30113i	0.370488	+	1.14024i	−0.575985	+	0.817460i	$0.695381\pi$
$42$	−5.65665	+	1.49380i	−0.872839	+	0.230499i
$43$			4.48699i			0.684259i	0.939653	+	0.342130i	$0.111148\pi$
$43$			4.48699i			0.684259i	−0.939653	+	0.342130i	$0.888852\pi$
$44$	−14.0398	−	6.25090i	−2.11657	−	0.942359i
$45$	0.978241	−	2.01073i	0.145828	−	0.299742i
$46$	17.1789	−	7.64854i	2.53289	−	1.12772i
$47$	−6.51115	−	0.684350i	−0.949749	−	0.0998227i	−0.383032	−	0.923735i	$-0.625120\pi$
$47$	−6.51115	−	0.684350i	−0.949749	−	0.0998227i	−0.566717	+	0.823912i	$0.691787\pi$
$48$	−1.35848	−	0.441398i	−0.196080	−	0.0637103i
$49$	5.16802	+	4.72139i	0.738289	+	0.674484i
$50$	−7.69621	−	7.93821i	−1.08841	−	1.12263i
$51$	−2.35578	−	4.08034i	−0.329876	−	0.571361i
$52$	−10.4897	+	9.44493i	−1.45465	+	1.30978i
$53$	−2.43158	−	5.46143i	−0.334004	−	0.750185i	−0.999991	−	0.00422170i	$-0.998656\pi$
$53$	−2.43158	−	5.46143i	−0.334004	−	0.750185i	0.665987	−	0.745963i	$-0.268010\pi$
$54$	−0.231144	+	2.19919i	−0.0314548	+	0.299272i
$55$	−10.0908	−	6.29156i	−1.36064	−	0.848354i
$56$	−1.32929	−	5.03368i	−0.177634	−	0.672653i
$57$			5.96989i			0.790731i
$58$	−0.958844	+	2.15360i	−0.125902	+	0.282781i
$59$	−7.00628	−	1.48923i	−0.912140	−	0.193881i	−0.272141	−	0.962257i	$-0.587732\pi$
$59$	−7.00628	−	1.48923i	−0.912140	−	0.193881i	−0.639999	+	0.768376i	$0.721065\pi$
$60$	5.81075	+	2.82699i	0.750165	+	0.364963i
$61$	−2.59552	+	0.551694i	−0.332322	+	0.0706372i	−0.371051	−	0.928613i	$-0.621002\pi$
$61$	−2.59552	+	0.551694i	−0.332322	+	0.0706372i	0.0387289	+	0.999250i	$0.487669\pi$
$62$	4.85599	−	1.57781i	0.616712	−	0.200382i
$63$	2.36171	−	1.19262i	0.297547	−	0.150256i
$64$	3.96486	−	12.2026i	0.495608	−	1.52532i
$65$	−9.04855	+	6.11634i	−1.12233	+	0.758638i
$66$	11.5028	+	2.44500i	1.41590	+	0.300959i
$67$	0.690898	−	0.0726163i	0.0844066	−	0.00887149i	−0.0622310	−	0.998062i	$-0.519822\pi$
$67$	0.690898	−	0.0726163i	0.0844066	−	0.00887149i	0.146638	+	0.989190i	$0.453155\pi$
$68$	11.7916	−	6.80791i	1.42995	−	0.825580i
$69$	−6.87977	+	4.99845i	−0.828227	+	0.601742i
$70$	−1.56023	−	12.9889i	−0.186483	−	1.55247i
$71$	1.71228	+	1.24405i	0.203211	+	0.147641i	0.684737	−	0.728791i	$-0.259917\pi$
$71$	1.71228	+	1.24405i	0.203211	+	0.147641i	−0.481526	+	0.876432i	$0.659917\pi$
$72$	−1.95699	−	0.205688i	−0.230634	−	0.0242406i
$73$	−0.502455	+	0.452412i	−0.0588079	+	0.0529508i	−0.698011	−	0.716087i	$-0.745931\pi$
$73$	−0.502455	+	0.452412i	−0.0588079	+	0.0529508i	0.639203	+	0.769038i	$0.279264\pi$
$74$	−0.167029	+	0.289302i	−0.0194167	+	0.0336307i
$75$	4.15070	+	2.78777i	0.479282	+	0.321904i
$76$	−17.2522			−1.97896
$77$	−4.99481	−	13.1538i	−0.569211	−	1.49901i
$78$	6.34858	−	8.73807i	0.718835	−	0.989392i
$79$	0.461592	−	4.39175i	0.0519331	−	0.494111i	−0.937380	−	0.348307i	$-0.886757\pi$
$79$	0.461592	−	4.39175i	0.0519331	−	0.494111i	0.989314	−	0.145804i	$-0.0465767\pi$
$80$	1.39731	−	2.87212i	0.156224	−	0.321112i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	14.7015	−	8.48794i	1.62351	−	0.937336i
$83$	−1.66593	−	2.29296i	−0.182860	−	0.251685i	0.707740	−	0.706473i	$-0.249715\pi$
$83$	−1.66593	−	2.29296i	−0.182860	−	0.251685i	−0.890600	+	0.454788i	$0.849715\pi$
$84$	3.44651	+	6.82503i	0.376045	+	0.744671i
$85$	9.76433	−	3.95627i	1.05909	−	0.429118i
$86$	9.70528	−	2.06292i	1.04655	−	0.222450i
$87$	0.221649	−	1.04277i	0.0237632	−	0.111797i
$88$	−2.17573	+	10.2360i	−0.231934	+	1.09116i
$89$	−13.6646	+	2.90450i	−1.44844	+	0.307876i	−0.863973	−	0.503538i	$-0.832031\pi$
$89$	−13.6646	+	2.90450i	−1.44844	+	0.307876i	−0.584471	+	0.811415i	$0.698698\pi$
$90$	−4.79893	−	1.19147i	−0.505852	−	0.125592i
$91$	−12.9026	−	0.722963i	−1.35256	−	0.0757871i
$92$	−14.4449	−	19.8816i	−1.50598	−	2.07280i
$93$	−1.99965	+	1.15450i	−0.207354	+	0.119716i
$94$	1.51331	+	14.3981i	0.156086	+	1.48506i
$95$	−13.2210	−	1.84477i	−1.35644	−	0.189269i
$96$	−0.741542	+	7.05530i	−0.0756833	+	0.720078i
$97$	−0.0252936	+	0.0348137i	−0.00256818	+	0.00353479i	−0.810299	−	0.586016i	$-0.800695\pi$
$97$	−0.0252936	+	0.0348137i	−0.00256818	+	0.00353479i	0.807731	+	0.589551i	$0.200695\pi$
$98$	7.83625	−	13.3490i	0.791581	−	1.34846i
$99$	−5.31804			−0.534483
$100$	−8.05628	+	11.9950i	−0.805628	+	1.19950i
$101$	−6.98226	+	12.0936i	−0.694761	+	1.20336i	0.275501	+	0.961301i	$0.411156\pi$
$101$	−6.98226	+	12.0936i	−0.694761	+	1.20336i	−0.970261	+	0.242060i	$0.922177\pi$
$102$	−7.74261	+	6.97148i	−0.766633	+	0.690279i
$103$	−11.0951	−	1.16614i	−1.09323	−	0.114903i	−0.459292	−	0.888286i	$-0.651897\pi$
$103$	−11.0951	−	1.16614i	−1.09323	−	0.114903i	−0.633940	+	0.773382i	$0.718563\pi$
$104$	7.77574	+	5.64941i	0.762474	+	0.553970i
$105$	1.91139	+	5.59880i	0.186533	+	0.546387i
$106$	−10.6950	+	7.77040i	−1.03879	+	0.754728i
$107$	14.2626	−	8.23453i	1.37882	−	0.796062i	0.386802	−	0.922163i	$-0.373580\pi$
$107$	14.2626	−	8.23453i	1.37882	−	0.796062i	0.992017	+	0.126101i	$0.0402464\pi$
$108$	2.87404	−	0.302074i	0.276554	−	0.0290670i
$109$	10.4733	+	2.22617i	1.00316	+	0.213228i	0.680075	−	0.733142i	$-0.261947\pi$
$109$	10.4733	+	2.22617i	1.00316	+	0.213228i	0.323084	+	0.946370i	$0.395280\pi$
$110$	−8.96924	+	24.7188i	−0.855184	+	2.35684i
$111$	0.0466825	−	0.143674i	0.00443091	−	0.0136369i
$112$	3.37345	−	1.70353i	0.318761	−	0.160968i
$113$	18.7845	−	6.10346i	1.76710	−	0.574165i	0.769202	−	0.639006i	$-0.220654\pi$
$113$	18.7845	−	6.10346i	1.76710	−	0.574165i	0.997896	+	0.0648410i	$0.0206540\pi$
$114$	12.9128	−	2.74469i	1.20939	−	0.257064i
$115$	−8.94369	−	16.7806i	−0.834003	−	1.56480i
$116$	3.01348	+	0.640535i	0.279795	+	0.0594722i
$117$	−1.98666	+	4.46210i	−0.183666	+	0.412522i
$118$			15.8392i			1.45811i
$119$	12.0291	+	3.26984i	1.10271	+	0.299745i
$120$	1.06026	−	4.27042i	0.0967876	−	0.389834i
$121$	−1.80641	+	17.1868i	−0.164219	+	1.56244i
$122$	2.38661	+	5.36042i	0.216074	+	0.485309i
$123$	−5.70502	+	5.13682i	−0.514404	+	0.463171i
$124$	−3.33635	−	5.77873i	−0.299613	−	0.518945i
$125$	−7.45645	+	8.33075i	−0.666925	+	0.745125i
$126$	−3.66542	−	4.56002i	−0.326542	−	0.406239i
$127$	7.75031	+	2.51823i	0.687729	+	0.223457i	0.631976	−	0.774988i	$-0.282244\pi$
$127$	7.75031	+	2.51823i	0.687729	+	0.223457i	0.0557529	+	0.998445i	$0.482244\pi$
$128$	−14.1063	−	1.48263i	−1.24683	−	0.131047i
$129$	−4.09907	+	1.82502i	−0.360903	+	0.160684i
$130$	17.3897	+	16.7598i	1.52517	+	1.46993i
$131$	10.4666	+	4.66002i	0.914470	+	0.407148i	0.809360	−	0.587313i	$-0.199814\pi$
$131$	10.4666	+	4.66002i	0.914470	+	0.407148i	0.105109	+	0.994461i	$0.466481\pi$
$132$		−	15.3684i		−	1.33765i
$133$	−11.1282	−	11.2089i	−0.964937	−	0.971937i
$134$	−0.474712	−	1.46101i	−0.0410089	−	0.126212i
$135$	2.23478	+	0.0758296i	0.192339	+	0.00652637i
$136$	−6.20371	−	6.88991i	−0.531963	−	0.590805i
$137$	−4.60007	+	21.6416i	−0.393011	+	1.84897i	0.123026	+	0.992403i	$0.460740\pi$
$137$	−4.60007	+	21.6416i	−0.393011	+	1.84897i	−0.516036	+	0.856567i	$0.672593\pi$
$138$	13.9746	+	12.5828i	1.18959	+	1.07112i
$139$	−3.53150	+	10.8688i	−0.299538	+	0.921882i	0.682122	+	0.731239i	$0.261057\pi$
$139$	−3.53150	+	10.8688i	−0.299538	+	0.921882i	−0.981659	+	0.190643i	$0.938943\pi$
$140$	−16.1798	+	5.52367i	−1.36744	+	0.466836i
$141$	−2.02314	−	6.22658i	−0.170379	−	0.524373i
$142$	1.90362	−	4.27560i	0.159748	−	0.358800i
$143$	22.4953	+	12.9877i	1.88115	+	1.08608i
$144$	−0.149308	−	1.42057i	−0.0124423	−	0.118381i
$145$	2.24085	+	0.813096i	0.186092	+	0.0675240i
$146$	1.20957	+	0.878801i	0.100104	+	0.0727301i
$147$	−2.21118	+	6.64159i	−0.182375	+	0.547789i
$148$	0.415199	+	0.134906i	0.0341292	+	0.0110892i
$149$	−0.424981	−	0.736089i	−0.0348158	−	0.0603027i	0.848092	−	0.529848i	$-0.177751\pi$
$149$	−0.424981	−	0.736089i	−0.0348158	−	0.0603027i	−0.882908	+	0.469546i	$0.844418\pi$
$150$	4.12158	−	10.2596i	0.336526	−	0.837692i
$151$	−0.920744	+	1.59478i	−0.0749291	+	0.129781i	−0.901055	−	0.433704i	$-0.857206\pi$
$151$	−0.920744	+	1.59478i	−0.0749291	+	0.129781i	0.826126	+	0.563485i	$0.190540\pi$
$152$	2.44242	+	11.4907i	0.198106	+	0.932017i
$153$	2.76939	−	3.81174i	0.223892	−	0.308161i
$154$	−26.1550	+	16.8512i	−2.10763	+	1.35791i
$155$	−1.93885	−	4.78520i	−0.155732	−	0.384357i
$156$	−12.8949	−	5.74118i	−1.03242	−	0.459662i
$157$	1.38772	+	0.801202i	0.110752	+	0.0639429i	0.554353	−	0.832282i	$-0.312966\pi$
$157$	1.38772	+	0.801202i	0.110752	+	0.0639429i	−0.443601	+	0.896225i	$0.646299\pi$
$158$	−9.71151	+	1.02072i	−0.772606	+	0.0812041i
$159$	4.00025	−	4.44273i	0.317240	−	0.352331i
$160$	−15.3956	−	3.82240i	−1.21713	−	0.302187i
$161$	3.59992	−	22.2092i	0.283713	−	1.75033i
$162$	−2.10308	+	0.683331i	−0.165233	+	0.0536875i
$163$	11.2220	+	10.1043i	0.878971	+	0.791429i	0.979065	−	0.203549i	$-0.0652476\pi$
$163$	11.2220	+	10.1043i	0.878971	+	0.791429i	−0.100094	+	0.994978i	$0.531914\pi$
$164$	−14.8447	−	16.4868i	−1.15918	−	1.28740i
$165$	1.64334	−	11.7774i	0.127934	−	0.916869i
$166$	−4.19371	+	4.65758i	−0.325495	+	0.361499i
$167$	5.25839	+	7.23755i	0.406906	+	0.560059i	0.962460	−	0.271422i	$-0.0874938\pi$
$167$	5.25839	+	7.23755i	0.406906	+	0.560059i	−0.555554	+	0.831480i	$0.687494\pi$
$168$	4.05782	−	3.26175i	0.313068	−	0.251649i
$169$	8.78363	−	6.38168i	0.675664	−	0.490899i
$170$	−13.0466	−	19.3012i	−1.00063	−	1.48033i
$171$	−5.45376	+	2.42817i	−0.417060	+	0.185687i
$172$	−5.27408	−	11.8458i	−0.402145	−	0.903232i
$173$	−5.31873	−	25.0227i	−0.404375	−	1.90244i	−0.430127	−	0.902768i	$-0.641531\pi$
$173$	−5.31873	−	25.0227i	−0.404375	−	1.90244i	0.0257514	−	0.999668i	$-0.491802\pi$
$174$	−2.35741			−0.178715
$175$	−12.9898	+	2.50290i	−0.981938	+	0.189201i
$176$	−7.59625			−0.572589
$177$	−1.48923	−	7.00628i	−0.111937	−	0.526624i
$178$	12.5648	+	28.2209i	0.941769	+	2.11525i
$179$	9.03813	−	4.02404i	0.675542	−	0.300771i	−0.0401431	−	0.999194i	$-0.512781\pi$
$179$	9.03813	−	4.02404i	0.675542	−	0.300771i	0.715685	+	0.698423i	$0.246115\pi$
$180$	−0.219138	+	6.45823i	−0.0163336	+	0.481368i
$181$	0.330025	−	0.239777i	0.0245306	−	0.0178225i	−0.575452	−	0.817835i	$-0.695174\pi$
$181$	0.330025	−	0.239777i	0.0245306	−	0.0178225i	0.599983	+	0.800013i	$0.295174\pi$
$182$	4.36830	+	28.2405i	0.323800	+	2.09333i
$183$	−1.55969	−	2.14673i	−0.115296	−	0.158691i
$184$	−11.1970	+	12.4355i	−0.825455	+	0.916760i
$185$	0.303757	+	0.147781i	0.0223327	+	0.0108651i
$186$	3.41651	+	3.79442i	0.250511	+	0.278220i
$187$	−18.6204	−	16.7659i	−1.36166	−	1.22605i
$188$	17.9940	−	5.84661i	1.31235	−	0.426408i
$189$	2.05010	+	1.67244i	0.149123	+	0.121652i
$190$	2.08823	+	29.4449i	0.151496	+	2.13616i
$191$	5.74803	−	6.38384i	0.415913	−	0.461918i	−0.498388	−	0.866954i	$-0.666074\pi$
$191$	5.74803	−	6.38384i	0.415913	−	0.461918i	0.914301	+	0.405036i	$0.132741\pi$
$192$	12.7603	−	1.34116i	0.920893	−	0.0967898i
$193$	−15.7404	−	9.08772i	−1.13302	−	0.654149i	−0.188326	−	0.982106i	$-0.560306\pi$
$193$	−15.7404	−	9.08772i	−1.13302	−	0.654149i	−0.944692	+	0.327958i	$0.893640\pi$
$194$	0.0869303	+	0.0387039i	0.00624123	+	0.00277877i
$195$	−9.26793	−	5.77852i	−0.663690	−	0.413808i
$196$	−19.1933	−	6.39002i	−1.37095	−	0.456430i
$197$	8.19148	−	11.2746i	0.583619	−	0.803283i	−0.410467	−	0.911875i	$-0.634634\pi$
$197$	8.19148	−	11.2746i	0.583619	−	0.803283i	0.994086	+	0.108593i	$0.0346344\pi$
$198$	2.44500	+	11.5028i	0.173759	+	0.817470i
$199$	5.51303	−	9.54885i	0.390808	−	0.676900i	−0.601748	−	0.798686i	$-0.705529\pi$
$199$	5.51303	−	9.54885i	0.390808	−	0.676900i	0.992556	+	0.121786i	$0.0388622\pi$
$200$	9.12970	+	3.66767i	0.645567	+	0.259343i
$201$	0.347352	+	0.601631i	0.0245003	+	0.0424358i
$202$	29.3684	+	9.54238i	2.06636	+	0.671400i
$203$	1.52763	+	2.37106i	0.107218	+	0.166415i
$204$	11.0154	+	8.00318i	0.771234	+	0.560334i
$205$	−9.61315	−	14.2217i	−0.671411	−	0.993290i
$206$	2.57869	+	24.5346i	0.179666	+	1.70941i
$207$	−7.36456	−	4.25193i	−0.511873	−	0.295530i
$208$	−2.83773	+	6.37364i	−0.196761	+	0.441932i
$209$	9.81069	+	30.1942i	0.678620	+	2.08858i
$210$	11.2313	−	6.70839i	0.775036	−	0.462923i
$211$	3.24393	−	9.98379i	0.223321	−	0.687313i	−0.775136	−	0.631794i	$-0.782319\pi$
$211$	3.24393	−	9.98379i	0.223321	−	0.687313i	0.998458	−	0.0555186i	$-0.0176812\pi$
$212$	12.8389	+	11.5602i	0.881779	+	0.793957i
$213$	−0.440045	+	2.07025i	−0.0301514	+	0.141851i
$214$	−24.3685	−	27.0639i	−1.66579	−	1.85005i
$215$	−2.77506	−	9.64181i	−0.189257	−	0.657566i
$216$	−0.608075	−	1.87146i	−0.0413743	−	0.127337i
$217$	1.60245	−	5.89512i	0.108781	−	0.400187i
$218$		−	23.6770i		−	1.60361i
$219$	−0.617666	−	0.275003i	−0.0417380	−	0.0185829i
$220$	34.0351	+	4.74904i	2.29465	+	0.320180i
$221$	−21.0235	+	9.36026i	−1.41419	+	0.629640i
$222$	−0.332227	−	0.0349185i	−0.0222976	−	0.00234357i
$223$	−13.5179	−	4.39222i	−0.905223	−	0.294125i	−0.180832	−	0.983514i	$-0.557879\pi$
$223$	−13.5179	−	4.39222i	−0.905223	−	0.294125i	−0.724391	+	0.689389i	$0.757879\pi$
$224$	−11.7592	−	14.6291i	−0.785692	−	0.977450i
$225$	−0.858509	+	4.92574i	−0.0572339	+	0.328383i
$226$	−21.8380	−	37.8245i	−1.45264	−	2.51605i
$227$	5.40705	−	4.86853i	0.358878	−	0.323136i	−0.469892	−	0.882724i	$-0.655707\pi$
$227$	5.40705	−	4.86853i	0.358878	−	0.323136i	0.828771	+	0.559588i	$0.189041\pi$
$228$	−7.01710	−	15.7607i	−0.464719	−	1.04378i
$229$	1.56284	−	14.8694i	0.103275	−	0.982597i	−0.813059	−	0.582182i	$-0.802199\pi$
$229$	1.56284	−	14.8694i	0.103275	−	0.982597i	0.916334	−	0.400415i	$-0.131134\pi$
$230$	−32.1843	+	27.0600i	−2.12217	+	1.78429i
$231$	9.98502	−	9.91311i	0.656966	−	0.652235i
$232$		−	2.09778i		−	0.137726i
$233$	−8.15106	+	18.3076i	−0.533994	+	1.19937i	0.422165	+	0.906519i	$0.361270\pi$
$233$	−8.15106	+	18.3076i	−0.533994	+	1.19937i	−0.956158	+	0.292850i	$0.905396\pi$
$234$	10.5648	+	2.24562i	0.690644	+	0.146801i
$235$	14.4147	−	2.55638i	0.940308	−	0.166760i
$236$	20.2472	−	4.30368i	1.31798	−	0.280146i
$237$	4.19981	−	1.36460i	0.272807	−	0.0886404i
$238$	1.54213	−	27.5222i	0.0999613	−	1.78400i
$239$	2.34940	−	7.23072i	0.151970	−	0.467716i	−0.845871	−	0.533387i	$-0.820919\pi$
$239$	2.34940	−	7.23072i	0.151970	−	0.467716i	0.997841	+	0.0656711i	$0.0209188\pi$
$240$	3.19215	+	0.108314i	0.206052	+	0.00699167i
$241$	10.4743	+	2.22638i	0.674708	+	0.143414i	0.532509	−	0.846424i	$-0.321249\pi$
$241$	10.4743	+	2.22638i	0.674708	+	0.143414i	0.142199	+	0.989838i	$0.454583\pi$
$242$	38.0053	−	3.99452i	2.44307	−	0.256777i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	6.20377	−	4.50730i	0.397156	−	0.288550i
$245$	−14.0253	−	6.94924i	−0.896041	−	0.443971i
$246$	13.7338	+	9.97817i	0.875633	+	0.636185i
$247$	28.9995	+	3.04797i	1.84519	+	0.193937i
$248$	−3.37654	+	3.04025i	−0.214410	+	0.193056i
$249$	1.41713	−	2.45454i	0.0898067	−	0.155550i
$250$	21.4474	+	12.2981i	1.35645	+	0.777797i
$251$	2.21499			0.139809			0.0699044	−	0.997554i	$-0.477731\pi$
$251$	2.21499			0.139809			0.0699044	+	0.997554i	$0.477731\pi$
$252$	−4.83315	+	5.92453i	−0.304460	+	0.373211i
$253$	−26.5819	+	36.5869i	−1.67119	+	2.30020i
$254$	1.88363	−	17.9216i	0.118190	−	1.12450i
$255$	7.58575	+	7.31100i	0.475038	+	0.457833i
$256$	0.596225	+	5.67270i	0.0372641	+	0.354544i
$257$	14.0103	−	8.08888i	0.873941	−	0.504570i	0.00528542	−	0.999986i	$-0.498318\pi$
$257$	14.0103	−	8.08888i	0.873941	−	0.504570i	0.868656	+	0.495416i	$0.164984\pi$
$258$	5.83206	+	8.02715i	0.363088	+	0.499748i
$259$	0.180166	+	0.356778i	0.0111950	+	0.0221691i
$260$	16.6992	−	26.7831i	1.03564	−	1.66102i
$261$	1.04277	−	0.221649i	0.0645461	−	0.0137197i
$262$	5.26747	−	24.7815i	0.325426	−	1.53101i
$263$	−4.31044	+	20.2790i	−0.265793	+	1.25046i	0.619342	+	0.785122i	$0.287400\pi$
$263$	−4.31044	+	20.2790i	−0.265793	+	1.25046i	−0.885134	+	0.465335i	$0.845934\pi$
$264$	−10.2360	+	2.17573i	−0.629983	+	0.133907i
$265$	8.60279	+	10.2319i	0.528465	+	0.628538i
$266$	−19.1284	+	29.2235i	−1.17284	+	1.79181i
$267$	−8.21128	−	11.3019i	−0.502522	−	0.691663i
$268$	−1.73864	+	1.00380i	−0.106204	+	0.0613169i
$269$	0.00232099	+	0.0220827i	0.000141513	+	0.00134641i	0.994592	−	0.103855i	$-0.0331179\pi$
$269$	0.00232099	+	0.0220827i	0.000141513	+	0.00134641i	−0.994451	+	0.105202i	$0.966451\pi$
$270$	−0.863437	−	4.86866i	−0.0525471	−	0.296297i
$271$	2.16504	−	20.5990i	0.131517	−	1.25130i	−0.707311	−	0.706903i	$-0.750092\pi$
$271$	2.16504	−	20.5990i	0.131517	−	1.25130i	0.838828	−	0.544397i	$-0.183241\pi$
$272$	3.95578	−	5.44466i	0.239854	−	0.330131i
$273$	−4.58751	−	12.0812i	−0.277649	−	0.731186i
$274$	48.9254			2.95569
$275$	25.5746	+	7.27872i	1.54220	+	0.438923i
$276$	12.2875	−	21.2826i	0.739622	−	1.28106i
$277$	−1.01423	+	0.913221i	−0.0609394	+	0.0548701i	−0.699038	−	0.715085i	$-0.746388\pi$
$277$	−1.01423	+	0.913221i	−0.0609394	+	0.0548701i	0.638098	+	0.769955i	$0.279721\pi$
$278$	25.1327	+	2.64156i	1.50736	+	0.158430i
$279$	−1.86802	−	1.35719i	−0.111835	−	0.0812531i
$280$	5.96959	+	9.99442i	0.356751	+	0.597281i
$281$	−18.9888	+	13.7962i	−1.13278	+	0.823012i	−0.986097	−	0.166172i	$-0.946859\pi$
$281$	−18.9888	+	13.7962i	−1.13278	+	0.823012i	−0.146682	+	0.989184i	$0.546859\pi$
$282$	−12.5378	+	7.23873i	−0.746618	+	0.431060i
$283$	−11.1639	+	1.17337i	−0.663622	+	0.0697495i	−0.430350	−	0.902662i	$-0.641610\pi$
$283$	−11.1639	+	1.17337i	−0.663622	+	0.0697495i	−0.233272	+	0.972412i	$0.574943\pi$
$284$	−5.98275	−	1.27167i	−0.355011	−	0.0754599i
$285$	−3.69218	−	12.8283i	−0.218706	−	0.759884i
$286$	17.7497	−	54.6280i	1.04956	−	3.23022i
$287$	1.13629	−	20.2792i	0.0670732	−	1.19705i
$288$	−6.74695	+	2.19222i	−0.397568	+	0.129178i
$289$	5.08526	−	1.08091i	0.299133	−	0.0635827i
$290$	0.728468	−	5.22075i	0.0427771	−	0.306573i
$291$	−0.0420917	−	0.00894687i	−0.00246746	−	0.000524475i
$292$	0.794721	−	1.78497i	0.0465075	−	0.104458i
$293$			10.8156i			0.631854i	0.948784	+	0.315927i	$0.102315\pi$
$293$			10.8156i			0.631854i	−0.948784	+	0.315927i	$0.897685\pi$
$294$	15.3822	+	1.72923i	0.897111	+	0.100851i
$295$	15.9764	−	1.13304i	0.930182	−	0.0659683i
$296$	0.0310729	−	0.295639i	0.00180607	−	0.0171836i
$297$	−2.16304	−	4.85827i	−0.125512	−	0.281905i
$298$	−1.39676	+	1.25765i	−0.0809121	+	0.0728536i
$299$	20.7681	+	35.9713i	1.20105	+	2.08028i
$300$	−14.2348	−	2.48098i	−0.821844	−	0.143239i
$301$	4.29437	−	11.0675i	0.247524	−	0.637921i
$302$	3.87279	+	1.25835i	0.222854	+	0.0724096i
$303$	−13.8880	−	1.45969i	−0.797846	−	0.0838569i
$304$	−7.79012	+	3.46838i	−0.446794	+	0.198925i
$305$	5.23614	−	2.79074i	0.299820	−	0.159798i
$306$	−9.51797	−	4.23767i	−0.544106	−	0.242252i
$307$			1.24091i			0.0708227i	0.999373	+	0.0354114i	$0.0112741\pi$
$307$			1.24091i			0.0708227i	−0.999373	+	0.0354114i	$0.988726\pi$
$308$	28.6476	+	28.8554i	1.63235	+	1.64419i
$309$	−3.44746	−	10.6102i	−0.196119	−	0.603592i
$310$	−9.45891	+	6.39373i	−0.537230	+	0.363139i
$311$	−7.89063	−	8.76343i	−0.447437	−	0.496929i	0.476660	−	0.879088i	$-0.341847\pi$
$311$	−7.89063	−	8.76343i	−0.447437	−	0.496929i	−0.924097	+	0.382159i	$0.875181\pi$
$312$	−1.99831	+	9.40132i	−0.113132	+	0.532245i
$313$	9.45745	+	8.51553i	0.534567	+	0.481326i	0.891637	−	0.452752i	$-0.149558\pi$
$313$	9.45745	+	8.51553i	0.534567	+	0.481326i	−0.357070	+	0.934078i	$0.616224\pi$
$314$	1.09497	−	3.36998i	0.0617928	−	0.190179i
$315$	−4.33733	+	4.02338i	−0.244381	+	0.226692i
$316$	3.94352	+	12.1369i	0.221840	+	0.682755i
$317$	0.499368	−	1.12160i	0.0280473	−	0.0629953i	−0.898979	−	0.437992i	$-0.855690\pi$
$317$	0.499368	−	1.12160i	0.0280473	−	0.0629953i	0.927026	+	0.374997i	$0.122356\pi$
$318$	−11.4487	−	6.60990i	−0.642010	−	0.370665i
$319$	−0.592614	−	5.63834i	−0.0331800	−	0.315687i
$320$	−0.972936	+	28.6735i	−0.0543888	+	1.60290i
$321$	13.3237	+	9.68027i	0.743659	+	0.540300i
$322$	−49.6933	+	2.42427i	−2.76930	+	0.135099i
$323$	−26.7509	−	8.69188i	−1.48846	−	0.483629i
$324$	1.44493	+	2.50270i	0.0802742	+	0.139039i
$325$	15.6611	−	18.7392i	0.868721	−	1.03947i
$326$	16.6960	−	28.9184i	0.924708	−	1.60164i
$327$	2.22617	+	10.4733i	0.123107	+	0.579174i
$328$	−8.87927	+	12.2213i	−0.490275	+	0.674806i
$329$	15.4053	+	7.91965i	0.849322	+	0.436624i
$330$	−26.2298	+	1.86021i	−1.44390	+	0.102401i
$331$	22.5345	+	10.0330i	1.23861	+	0.551463i	0.918313	−	0.395855i	$-0.129552\pi$
$331$	22.5345	+	10.0330i	1.23861	+	0.551463i	0.320294	+	0.947318i	$0.396218\pi$
$332$	7.09329	+	4.09531i	0.389295	+	0.224759i
$333$	0.150240	−	0.0157909i	0.00823312	−	0.000865335i
$334$	13.2371	−	14.7013i	0.724303	−	0.804420i
$335$	−1.43972	+	0.583338i	−0.0786601	+	0.0318712i
$336$	2.92836	+	2.38891i	0.159755	+	0.130326i
$337$	−21.9321	+	7.12617i	−1.19472	+	0.388187i	−0.837815	−	0.545954i	$-0.816167\pi$
$337$	−21.9321	+	7.12617i	−1.19472	+	0.388187i	−0.356903	+	0.934141i	$0.616167\pi$
$338$	−17.8418	−	16.0648i	−0.970466	−	0.873811i
$339$	13.2161	+	14.6780i	0.717802	+	0.797200i
$340$	−21.1278	+	21.9218i	−1.14582	+	1.18888i
$341$	−8.21647	+	9.12531i	−0.444947	+	0.494164i
$342$	7.75949	+	10.6800i	0.419585	+	0.577510i
$343$	−8.22863	−	16.5919i	−0.444304	−	0.895876i
$344$	−7.14311	+	5.18978i	−0.385131	+	0.279814i
$345$	11.6921	−	14.9958i	0.629483	−	0.807344i
$346$	−51.6782	+	23.0086i	−2.77824	+	1.23695i
$347$	−4.77955	−	10.7351i	−0.256580	−	0.576288i	0.738623	−	0.674118i	$-0.235476\pi$
$347$	−4.77955	−	10.7351i	−0.256580	−	0.576288i	−0.995203	+	0.0978307i	$0.968810\pi$
$348$	0.640535	+	3.01348i	0.0343363	+	0.161540i
$349$	−16.8093			−0.899781			−0.449891	−	0.893084i	$-0.648537\pi$
$349$	−16.8093			−0.899781			−0.449891	+	0.893084i	$0.648537\pi$
$350$	11.3859	+	26.9460i	0.608600	+	1.44033i
$351$	−4.88438			−0.260709
$352$	7.84388	+	36.9026i	0.418080	+	1.96691i
$353$	−14.4799	−	32.5224i	−0.770688	−	1.73099i	−0.677714	−	0.735325i	$-0.737029\pi$
$353$	−14.4799	−	32.5224i	−0.770688	−	1.73099i	−0.0929738	−	0.995669i	$-0.529637\pi$
$354$	−14.4698	+	6.44236i	−0.769060	+	0.342408i
$355$	−4.44882	−	1.61426i	−0.236119	−	0.0856761i
$356$	32.6609	−	23.7295i	1.73102	−	1.25766i
$357$	1.90555	+	12.3191i	0.100852	+	0.651997i
$358$	−12.8593	−	17.6992i	−0.679633	−	0.935434i
$359$	3.57727	−	3.97296i	0.188801	−	0.209685i	−0.641312	−	0.767281i	$-0.721609\pi$
$359$	3.57727	−	3.97296i	0.188801	−	0.209685i	0.830113	+	0.557596i	$0.188276\pi$
$360$	4.33247	−	0.768346i	0.228341	−	0.0404954i
$361$	11.1340	+	12.3656i	0.586002	+	0.650821i
$362$	−0.670365	−	0.603599i	−0.0352336	−	0.0317245i
$363$	−16.4357	+	5.34028i	−0.862650	+	0.280292i
$364$	34.9130	−	13.2573i	1.82994	−	0.694871i
$365$	0.799891	−	1.28291i	0.0418682	−	0.0671507i
$366$	−3.92626	+	4.36056i	−0.205229	+	0.227930i
$367$	20.8144	−	2.18768i	1.08650	−	0.114196i	0.455696	−	0.890135i	$-0.349390\pi$
$367$	20.8144	−	2.18768i	1.08650	−	0.114196i	0.630808	+	0.775939i	$0.282724\pi$
$368$	−10.5195	−	6.07343i	−0.548366	−	0.316600i
$369$	−7.01316	−	3.12246i	−0.365090	−	0.162549i
$370$	0.179993	−	0.724964i	0.00935740	−	0.0376891i
$371$	0.770712	+	15.7982i	0.0400134	+	0.820204i
$372$	3.92211	−	5.39833i	0.203352	−	0.279890i
$373$	4.60608	+	21.6699i	0.238494	+	1.12203i	0.920519	+	0.390697i	$0.127766\pi$
$373$	4.60608	+	21.6699i	0.238494	+	1.12203i	−0.682025	+	0.731329i	$0.738901\pi$
$374$	−27.7035	+	47.9839i	−1.43252	+	2.48119i
$375$	−10.6433	−	3.42338i	−0.549619	−	0.176783i
$376$	−6.44152	−	11.1570i	−0.332196	−	0.575381i
$377$	−4.95224	−	1.60908i	−0.255053	−	0.0828719i
$378$	2.67492	−	5.20326i	0.137583	−	0.267627i
$379$	5.04650	+	3.66650i	0.259221	+	0.188335i	0.709804	−	0.704399i	$-0.248784\pi$
$379$	5.04650	+	3.66650i	0.259221	+	0.188335i	−0.450582	+	0.892735i	$0.648784\pi$
$380$	37.0721	−	10.6699i	1.90176	−	0.547355i
$381$	0.851819	+	8.10452i	0.0436400	+	0.415207i
$382$	−16.4508	−	9.49788i	−0.841697	−	0.485954i
$383$	7.45854	−	16.7522i	0.381114	−	0.855995i	−0.616526	−	0.787334i	$-0.711461\pi$
$383$	7.45854	−	16.7522i	0.381114	−	0.855995i	0.997640	−	0.0686609i	$-0.0218727\pi$
$384$	−4.38309	−	13.4898i	−0.223673	−	0.688396i
$385$	18.8682	+	25.1762i	0.961613	+	1.28310i
$386$	−12.4198	+	38.2244i	−0.632153	+	1.94557i
$387$	−3.33448	−	3.00238i	−0.169501	−	0.152620i
$388$	0.0258553	−	0.121640i	0.00131260	−	0.00617531i
$389$	−0.955017	−	1.06065i	−0.0484213	−	0.0537773i	0.718448	−	0.695581i	$-0.244853\pi$
$389$	−0.955017	−	1.06065i	−0.0484213	−	0.0537773i	−0.766869	+	0.641804i	$0.778186\pi$
$390$	−8.23785	+	22.7031i	−0.417140	+	1.14962i
$391$	−12.3812	−	38.1055i	−0.626146	−	1.92708i
$392$	−1.53879	+	13.6882i	−0.0777207	+	0.691358i
$393$			11.4571i			0.577934i
$394$	−28.1529	−	12.5345i	−1.41832	−	0.631477i
$395$	1.72427	+	9.72264i	0.0867575	+	0.489199i
$396$	14.0398	−	6.25090i	0.705524	−	0.314120i
$397$	−32.4639	−	3.41209i	−1.62931	−	0.171248i	−0.754701	−	0.656069i	$-0.772218\pi$
$397$	−32.4639	−	3.41209i	−1.62931	−	0.171248i	−0.874613	+	0.484821i	$0.838885\pi$
$398$	−23.1886	−	7.53444i	−1.16234	−	0.377668i
$399$	5.71361	−	14.7252i	0.286039	−	0.737182i
$400$	−1.22629	+	7.03590i	−0.0613144	+	0.351795i
$401$	−18.7511	−	32.4779i	−0.936387	−	1.62187i	−0.772141	−	0.635451i	$-0.780814\pi$
$401$	−18.7511	−	32.4779i	−0.936387	−	1.62187i	−0.164246	−	0.986419i	$-0.552519\pi$
$402$	1.14162	−	1.02792i	0.0569388	−	0.0512680i
$403$	4.58718	+	10.3030i	0.228504	+	0.513228i
$404$	4.21831	−	40.1345i	0.209869	−	1.99677i
$405$	0.839694	+	2.07242i	0.0417247	+	0.102979i
$406$	4.42621	−	4.39434i	0.219669	−	0.218087i
$407$		−	0.803384i		−	0.0398223i
$408$	3.77097	−	8.46975i	0.186691	−	0.419315i
$409$	11.5718	+	2.45967i	0.572190	+	0.121623i	0.484915	−	0.874561i	$-0.338851\pi$
$409$	11.5718	+	2.45967i	0.572190	+	0.121623i	0.0872756	+	0.996184i	$0.472184\pi$
$410$	−26.3417	+	27.3316i	−1.30092	+	1.34981i
$411$	−21.6416	+	4.60007i	−1.06750	+	0.226905i
$412$	30.6620	−	9.96270i	1.51061	−	0.490827i
$413$	15.8562	+	10.3788i	0.780235	+	0.510709i
$414$	−5.81095	+	17.8843i	−0.285593	+	0.878964i
$415$	4.99794	+	3.89687i	0.245339	+	0.191290i
$416$	33.8934	+	7.20426i	1.66176	+	0.353218i
$417$	−11.3656	+	1.19457i	−0.556574	+	0.0584983i
$418$	60.7990	−	35.1023i	2.97378	−	1.71691i
$419$	2.02840	−	1.47372i	0.0990939	−	0.0719960i	−0.537135	−	0.843496i	$-0.680493\pi$
$419$	2.02840	−	1.47372i	0.0990939	−	0.0719960i	0.636229	+	0.771500i	$0.280493\pi$
$420$	−11.6270	−	12.5343i	−0.567342	−	0.611612i
$421$	4.09800	+	2.97737i	0.199724	+	0.145108i	0.683152	−	0.730276i	$-0.260609\pi$
$421$	4.09800	+	2.97737i	0.199724	+	0.145108i	−0.483428	+	0.875384i	$0.660609\pi$
$422$	−23.0862	−	2.42646i	−1.12382	−	0.118118i
$423$	4.86538	−	4.38081i	0.236563	−	0.213002i
$424$	5.88194	−	10.1878i	0.285652	−	0.494765i
$425$	−18.5351	+	14.5403i	−0.899086	+	0.705309i
$426$	4.68023			0.226758
$427$	6.93006	+	1.12330i	0.335369	+	0.0543604i
$428$	−27.9747	+	38.5039i	−1.35221	+	1.86116i
$429$	−2.71516	+	25.8330i	−0.131089	+	1.24723i
$430$	−19.5792	+	10.4353i	−0.944193	+	0.503234i
$431$	−2.43579	−	23.1750i	−0.117328	−	1.11630i	−0.881794	−	0.471635i	$-0.843664\pi$
$431$	−2.43579	−	23.1750i	−0.117328	−	1.11630i	0.764466	−	0.644664i	$-0.223003\pi$
$432$	1.23702	−	0.714197i	0.0595164	−	0.0343618i
$433$	15.9582	+	21.9645i	0.766901	+	1.05555i	0.996609	+	0.0822885i	$0.0262229\pi$
$433$	15.9582	+	21.9645i	0.766901	+	1.05555i	−0.229708	+	0.973260i	$0.573777\pi$
$434$	−13.4878	−	0.755750i	−0.647434	−	0.0362772i
$435$	0.168635	+	2.37783i	0.00808545	+	0.114008i
$436$	−30.2664	+	6.43333i	−1.44950	+	0.308101i
$437$	−10.5551	+	49.6577i	−0.504918	+	2.37545i
$438$	−0.310850	+	1.46243i	−0.0148530	+	0.0698778i
$439$	35.3892	−	7.52220i	1.68903	−	0.359015i	0.739615	−	0.673030i	$-0.235007\pi$
$439$	35.3892	−	7.52220i	1.68903	−	0.359015i	0.949418	+	0.314015i	$0.101674\pi$
$440$	−1.65535	−	23.3411i	−0.0789156	−	1.11274i
$441$	−6.96676	+	0.681364i	−0.331750	+	0.0324459i
$442$	29.9118	+	41.1700i	1.42276	+	1.95826i
$443$	−6.09008	+	3.51611i	−0.289348	+	0.167055i	−0.637648	−	0.770328i	$-0.720093\pi$
$443$	−6.09008	+	3.51611i	−0.289348	+	0.167055i	0.348300	+	0.937383i	$0.386759\pi$
$444$	0.0456336	+	0.434175i	0.00216567	+	0.0206050i
$445$	27.5666	−	14.6924i	1.30678	−	0.696486i
$446$	−3.28537	+	31.2582i	−0.155567	+	1.48012i
$447$	0.499595	−	0.687634i	0.0236300	−	0.0325240i
$448$	−21.4584	+	26.3040i	−1.01381	+	1.24275i
$449$	1.77377			0.0837096			0.0418548	−	0.999124i	$-0.486673\pi$
$449$	1.77377			0.0837096			0.0418548	+	0.999124i	$0.486673\pi$
$450$	11.0490	−	0.407702i	0.520855	−	0.0192193i
$451$	−20.4129	+	35.3562i	−0.961206	+	1.66486i
$452$	−42.4175	+	38.1929i	−1.99515	+	1.79644i
$453$	−1.83140	−	0.192488i	−0.0860467	−	0.00904387i
$454$	−13.0165	−	9.45702i	−0.610893	−	0.443840i
$455$	28.1727	−	6.42632i	1.32076	−	0.301270i
$456$	−9.50383	+	6.90494i	−0.445058	+	0.323353i
$457$	−21.5845	+	12.4618i	−1.00968	+	0.582939i	−0.911098	−	0.412190i	$-0.864764\pi$
$457$	−21.5845	+	12.4618i	−1.00968	+	0.582939i	−0.0985815	+	0.995129i	$0.531431\pi$
$458$	−32.8807	+	3.45591i	−1.53642	+	0.161484i
$459$	4.60861	+	0.979590i	0.215111	+	0.0457233i
$460$	43.3358	+	33.7887i	2.02054	+	1.57541i
$461$	4.72346	−	14.5373i	0.219993	−	0.677070i	−0.778768	−	0.627312i	$-0.784155\pi$
$461$	4.72346	−	14.5373i	0.219993	−	0.677070i	0.998761	−	0.0497580i	$-0.0158450\pi$
$462$	−26.0326	−	17.0398i	−1.21114	−	0.792764i
$463$	2.45613	−	0.798044i	0.114146	−	0.0370882i	−0.251387	−	0.967887i	$-0.580887\pi$
$463$	2.45613	−	0.798044i	0.114146	−	0.0370882i	0.365533	+	0.930798i	$0.380887\pi$
$464$	1.48949	−	0.316601i	0.0691479	−	0.0146978i
$465$	3.58290	−	3.71755i	0.166153	−	0.172397i
$466$	43.3465	+	9.21358i	2.00799	+	0.426811i
$467$	2.81765	−	6.32855i	0.130385	−	0.292850i	−0.836542	−	0.547903i	$-0.815426\pi$
$467$	2.81765	−	6.32855i	0.130385	−	0.292850i	0.966927	+	0.255053i	$0.0820929\pi$
$468$		−	14.1152i		−	0.652476i
$469$	−1.77365	−	0.482126i	−0.0818997	−	0.0222625i
$470$	−12.1566	−	30.0033i	−0.560743	−	1.38395i
$471$	−0.167497	+	1.59363i	−0.00771785	+	0.0734304i
$472$	−5.73286	−	12.8762i	−0.263876	−	0.592676i
$473$	−17.7329	+	15.9668i	−0.815359	+	0.734153i
$474$	−4.88250	−	8.45674i	−0.224261	−	0.388431i
$475$	29.5507	−	4.21264i	1.35588	−	0.193289i
$476$	−35.6007	+	5.50679i	−1.63175	+	0.252403i
$477$	5.68568	+	1.84739i	0.260329	+	0.0845861i
$478$	−16.7201	−	1.75735i	−0.764758	−	0.0803793i
$479$	5.56423	−	2.47736i	0.254236	−	0.113193i	−0.275662	−	0.961255i	$-0.588897\pi$
$479$	5.56423	−	2.47736i	0.254236	−	0.113193i	0.529898	+	0.848061i	$0.322230\pi$
$480$	−2.77002	−	15.6193i	−0.126433	−	0.712920i
$481$	−0.674080	−	0.300120i	−0.0307354	−	0.0136843i
$482$		−	23.6793i		−	1.07856i
$483$	21.7534	−	5.74462i	0.989813	−	0.261389i
$484$	−15.4327	−	47.4970i	−0.701486	−	2.15895i
$485$	0.0328207	−	0.0904522i	0.00149031	−	0.00410722i
$486$	−1.47965	−	1.64332i	−0.0671184	−	0.0745425i
$487$	2.52820	−	11.8943i	0.114564	−	0.538980i	−0.883009	−	0.469355i	$-0.844486\pi$
$487$	2.52820	−	11.8943i	0.114564	−	0.538980i	0.997573	−	0.0696251i	$-0.0221803\pi$
$488$	−3.88032	−	3.49386i	−0.175654	−	0.158160i
$489$	−4.66635	+	14.3615i	−0.211020	+	0.649452i
$490$	−8.58289	+	33.5314i	−0.387735	+	1.51479i
$491$	4.05623	+	12.4838i	0.183055	+	0.563386i	0.999909	−	0.0134584i	$-0.00428407\pi$
$491$	4.05623	+	12.4838i	0.183055	+	0.563386i	−0.816854	+	0.576844i	$0.804284\pi$
$492$	9.02350	−	20.2671i	0.406811	−	0.913712i
$493$	4.34993	+	2.51143i	0.195911	+	0.113109i
$494$	−6.73998	−	64.1266i	−0.303246	−	2.88519i
$495$	11.4276	−	3.28903i	0.513632	−	0.147831i
$496$	−2.66826	−	1.93861i	−0.119809	−	0.0870460i
$497$	−3.03284	−	4.70732i	−0.136041	−	0.211152i
$498$	−5.96065	−	1.93673i	−0.267103	−	0.0867871i
$499$	−16.6021	−	28.7557i	−0.743212	−	1.28728i	−0.951025	−	0.309113i	$-0.899968\pi$
$499$	−16.6021	−	28.7557i	−0.743212	−	1.28728i	0.207813	−	0.978169i	$-0.433365\pi$
$500$	9.89313	−	30.7578i	0.442434	−	1.37553i
$501$	−4.47305	+	7.74755i	−0.199841	+	0.346135i
$502$	−1.01835	−	4.79098i	−0.0454514	−	0.213832i
$503$	8.47454	−	11.6642i	0.377861	−	0.520081i	−0.577155	−	0.816634i	$-0.695837\pi$
$503$	8.47454	−	11.6642i	0.377861	−	0.520081i	0.955016	+	0.296553i	$0.0958373\pi$
$504$	4.63022	+	2.38033i	0.206246	+	0.106028i
$505$	7.52422	−	30.3055i	0.334823	−	1.34858i
$506$	91.3580	+	40.6752i	4.06136	+	1.80823i
$507$	9.40258	+	5.42858i	0.417583	+	0.241092i
$508$	−23.4210	+	2.46165i	−1.03914	+	0.109218i
$509$	17.4065	−	19.3318i	0.771527	−	0.856868i	−0.221450	−	0.975172i	$-0.571079\pi$
$509$	17.4065	−	19.3318i	0.771527	−	0.856868i	0.992977	+	0.118304i	$0.0377456\pi$
$510$	12.3260	−	19.7691i	0.545803	−	0.875391i
$511$	1.67234	−	0.635025i	0.0739798	−	0.0280918i
$512$	−14.9837	+	4.86849i	−0.662191	+	0.215159i
$513$	−4.43649	−	3.99463i	−0.195876	−	0.176367i
$514$	−23.9374	−	26.5852i	−1.05584	−	1.17262i
$515$	24.5627	−	4.35610i	1.08236	−	0.191953i
$516$	8.67649	−	9.63622i	0.381961	−	0.424211i
$517$	−20.4651	−	28.1678i	−0.900053	−	1.23882i
$518$	0.688872	−	0.553728i	0.0302673	−	0.0243294i
$519$	20.6960	−	15.0365i	0.908454	−	0.660030i
$520$	−20.2028	−	7.33061i	−0.885950	−	0.321469i
$521$	8.82755	−	3.93028i	0.386742	−	0.172189i	−0.204149	−	0.978940i	$-0.565443\pi$
$521$	8.82755	−	3.93028i	0.386742	−	0.172189i	0.590891	+	0.806751i	$0.298776\pi$
$522$	−0.958844	−	2.15360i	−0.0419675	−	0.0942605i
$523$	−2.91784	−	13.7274i	−0.127588	−	0.600256i	−0.994759	−	0.102245i	$-0.967397\pi$
$523$	−2.91784	−	13.7274i	−0.127588	−	0.600256i	0.867171	−	0.498011i	$-0.165936\pi$
$524$	−33.1095			−1.44640
$525$	−7.56995	−	10.8488i	−0.330380	−	0.473479i
$526$	45.8449			1.99893
$527$	−2.26187	−	10.6413i	−0.0985286	−	0.463541i
$528$	−3.08967	−	6.93952i	−0.134461	−	0.302004i
$529$	−45.0521	+	20.0585i	−1.95879	+	0.872109i
$530$	18.1761	−	23.3118i	0.789521	−	1.01260i
$531$	5.79483	−	4.21019i	0.251474	−	0.182707i
$532$	42.5539	+	16.5116i	1.84495	+	0.715869i
$533$	22.0400	+	30.3355i	0.954658	+	1.31397i
$534$	−20.6705	+	22.9570i	−0.894502	+	0.993445i
$535$	−25.5552	+	26.5156i	−1.10485	+	1.14637i
$536$	0.914714	+	1.01589i	0.0395096	+	0.0438799i
$537$	7.35228	+	6.62002i	0.317274	+	0.285675i
$538$	0.0466975	−	0.0151729i	0.00201327	−	0.000654151i
$539$	−0.269058	+	37.2253i	−0.0115891	+	1.60341i
$540$	−5.98902	+	2.42661i	−0.257726	+	0.104424i
$541$	−9.92158	+	11.0190i	−0.426562	+	0.473745i	−0.917664	−	0.397357i	$-0.869928\pi$
$541$	−9.92158	+	11.0190i	−0.426562	+	0.473745i	0.491102	+	0.871102i	$0.336594\pi$
$542$	−45.5506	+	4.78757i	−1.95657	+	0.205644i
$543$	0.353281	+	0.203967i	0.0151607	+	0.00875305i
$544$	−30.5349	−	13.5950i	−1.30917	−	0.582881i
$545$	−23.8822	+	1.69372i	−1.02300	+	0.0725510i
$546$	−24.0222	+	15.4771i	−1.02806	+	0.662359i
$547$	2.10777	−	2.90110i	0.0901218	−	0.124042i	−0.761575	−	0.648076i	$-0.775574\pi$
$547$	2.10777	−	2.90110i	0.0901218	−	0.124042i	0.851697	+	0.524034i	$0.175574\pi$
$548$	−13.2936	−	62.5415i	−0.567875	−	2.67164i
$549$	1.32675	−	2.29800i	0.0566244	−	0.0980763i
$550$	3.98569	−	58.6637i	0.169950	−	2.50143i
$551$	−3.18216	−	5.51166i	−0.135565	−	0.234805i
$552$	−15.9147	−	5.17099i	−0.677373	−	0.220092i
$553$	−5.34178	+	10.3908i	−0.227156	+	0.441863i
$554$	2.44158	+	1.77391i	0.103733	+	0.0753663i
$555$	−0.0114554	+	0.337604i	−0.000486255	+	0.0143305i
$556$	−3.45215	−	32.8450i	−0.146404	−	1.39294i
$557$	30.3707	+	17.5345i	1.28685	+	0.742961i	0.978090	−	0.208181i	$-0.0667542\pi$
$557$	30.3707	+	17.5345i	1.28685	+	0.742961i	0.308755	+	0.951141i	$0.400088\pi$
$558$	−2.07675	+	4.66447i	−0.0879160	+	0.197463i
$559$	6.77247	+	20.8435i	0.286445	+	0.881586i
$560$	−6.19541	+	5.74697i	−0.261804	+	0.242854i
$561$	7.74282	−	23.8299i	0.326902	−	1.00610i
$562$	38.5711	+	34.7296i	1.62703	+	1.46498i
$563$	0.364890	−	1.71667i	0.0153783	−	0.0723492i	−0.969789	−	0.243944i	$-0.921559\pi$
$563$	0.364890	−	1.71667i	0.0153783	−	0.0723492i	0.985168	+	0.171595i	$0.0548920\pi$
$564$	12.6600	+	14.0603i	0.533081	+	0.592046i
$565$	−36.5900	+	24.7329i	−1.53935	+	1.04052i
$566$	7.67063	+	23.6078i	0.322420	+	0.992308i
$567$	−0.694002	+	2.55311i	−0.0291453	+	0.107220i
$568$			4.16479i			0.174751i
$569$	25.0835	+	11.1679i	1.05155	+	0.468182i	0.858397	−	0.512985i	$-0.171461\pi$
$569$	25.0835	+	11.1679i	1.05155	+	0.468182i	0.193157	+	0.981168i	$0.438127\pi$
$570$	−26.0499	+	13.8840i	−1.09111	+	0.581537i
$571$	−2.89028	+	1.28684i	−0.120955	+	0.0538525i	−0.466322	−	0.884615i	$-0.654421\pi$
$571$	−2.89028	+	1.28684i	−0.120955	+	0.0538525i	0.345367	+	0.938468i	$0.387754\pi$
$572$	−74.6540	−	7.84645i	−3.12144	−	0.328077i
$573$	8.16986	+	2.65455i	0.341301	+	0.110895i
$574$	−44.3861	+	6.86573i	−1.85264	+	0.286570i
$575$	29.5968	+	30.5274i	1.23427	+	1.27308i
$576$	6.41528	+	11.1116i	0.267303	+	0.462983i
$577$	0.00207815	−	0.00187117i	8.65144e−5	−	7.78979e-5i	−0.669087	−	0.743184i	$-0.733315\pi$
$577$	0.00207815	−	0.00187117i	8.65144e−5	−	7.78979e-5i	0.669174	+	0.743106i	$0.266648\pi$
$578$	−4.67596	−	10.5024i	−0.194494	−	0.436841i
$579$	1.89985	−	18.0759i	0.0789551	−	0.751208i
$580$	−6.87163	+	0.487334i	−0.285329	+	0.0202355i
$581$	1.91463	+	7.25018i	0.0794320	+	0.300788i
$582$			0.0951570i			0.00394439i
$583$	12.9313	−	29.0441i	0.535558	−	1.20288i
$584$	−1.30138	−	0.276616i	−0.0538513	−	0.0114464i
$585$	1.50933	−	10.8170i	0.0624033	−	0.447228i
$586$	23.3939	−	4.97254i	0.966395	−	0.205414i
$587$	−13.7338	+	4.46237i	−0.566853	+	0.184182i	−0.578402	−	0.815752i	$-0.696324\pi$
$587$	−13.7338	+	4.46237i	−0.566853	+	0.184182i	0.0115493	+	0.999933i	$0.496324\pi$
$588$	−1.96905	−	20.1330i	−0.0812024	−	0.830272i
$589$	−4.25963	+	13.1098i	−0.175515	+	0.540179i
$590$	−9.79600	−	34.0357i	−0.403295	−	1.40123i
$591$	13.6316	+	2.89750i	0.560731	+	0.119187i
$592$	0.214602	−	0.0225556i	0.00882010	−	0.000927029i
$593$	18.2808	−	10.5544i	0.750702	−	0.433418i	−0.0752457	−	0.997165i	$-0.523974\pi$
$593$	18.2808	−	10.5544i	0.750702	−	0.433418i	0.825947	+	0.563747i	$0.190641\pi$
$594$	−9.51388	+	6.91224i	−0.390359	+	0.283612i
$595$	−27.8709	+	0.413287i	−1.14260	+	0.0169431i
$596$	1.98717	+	1.44376i	0.0813977	+	0.0591389i
$597$	10.9657	+	1.15254i	0.448794	+	0.0471702i
$598$	68.2571	−	61.4590i	2.79124	−	2.51324i
$599$	15.0429	−	26.0551i	0.614638	−	1.06458i	−0.375810	−	0.926697i	$-0.622635\pi$
$599$	15.0429	−	26.0551i	0.614638	−	1.06458i	0.990448	−	0.137887i	$-0.0440312\pi$
$600$	0.362802	+	9.83217i	0.0148113	+	0.401397i
$601$	10.2591			0.418476			0.209238	−	0.977865i	$-0.432902\pi$
$601$	10.2591			0.418476			0.209238	+	0.977865i	$0.432902\pi$
$602$	−25.9132	−	4.20030i	−1.05614	−	0.171191i
$603$	−0.408337	+	0.562027i	−0.0166288	+	0.0228875i
$604$	0.556265	−	5.29251i	0.0226341	−	0.215349i
$605$	−6.74782	−	38.0489i	−0.274338	−	1.54691i
$606$	3.22782	+	30.7106i	0.131121	+	1.24753i
$607$	−20.6044	+	11.8960i	−0.836308	+	0.482843i	−0.856008	−	0.516963i	$-0.827062\pi$
$607$	−20.6044	+	11.8960i	−0.836308	+	0.482843i	0.0196994	+	0.999806i	$0.493729\pi$
$608$	24.8935	+	34.2629i	1.00956	+	1.38955i
$609$	−1.54472	+	2.35995i	−0.0625954	+	0.0956301i
$610$	−8.44368	−	10.0426i	−0.341875	−	0.406614i
$611$	−31.2793	+	6.64863i	−1.26543	+	0.268975i
$612$	−2.83089	+	13.3183i	−0.114432	+	0.538359i
$613$	−4.90078	+	23.0563i	−0.197941	+	0.931237i	0.761246	+	0.648463i	$0.224588\pi$
$613$	−4.90078	+	23.0563i	−0.197941	+	0.931237i	−0.959187	+	0.282774i	$0.908745\pi$
$614$	2.68408	−	0.570518i	0.108320	−	0.0230242i
$615$	9.08219	−	14.5666i	0.366229	−	0.587380i
$616$	15.1632	−	23.1656i	0.610943	−	0.933368i
$617$	−13.2325	−	18.2130i	−0.532721	−	0.733228i	0.454821	−	0.890583i	$-0.349703\pi$
$617$	−13.2325	−	18.2130i	−0.532721	−	0.733228i	−0.987542	+	0.157355i	$0.949703\pi$
$618$	−21.3646	+	12.3349i	−0.859412	+	0.496182i
$619$	−0.334854	−	3.18593i	−0.0134589	−	0.128053i	0.985729	−	0.168338i	$-0.0538401\pi$
$619$	−0.334854	−	3.18593i	−0.0134589	−	0.128053i	−0.999188	+	0.0402850i	$0.987173\pi$
$620$	10.7432	+	10.3541i	0.431458	+	0.415831i
$621$	0.888896	−	8.45728i	0.0356702	−	0.339379i
$622$	−15.3274	+	21.0963i	−0.614572	+	0.845886i
$623$	36.4846	+	5.91383i	1.46173	+	0.236933i
$624$	−6.97682			−0.279296
$625$	10.8704	−	22.5130i	0.434815	−	0.900520i
$626$	14.0708	−	24.3714i	0.562383	−	0.974076i
$627$	−23.5934	+	21.2436i	−0.942230	+	0.848388i
$628$	−4.60537	−	0.484044i	−0.183774	−	0.0193155i
$629$	0.575831	+	0.418366i	0.0229599	+	0.0166813i
$630$	10.6966	+	7.53179i	0.426163	+	0.300074i
$631$	−8.74137	+	6.35098i	−0.347988	+	0.252828i	−0.748025	−	0.663671i	$-0.768998\pi$
$631$	−8.74137	+	6.35098i	−0.347988	+	0.252828i	0.400036	+	0.916499i	$0.368998\pi$
$632$	7.52539	−	4.34479i	0.299344	−	0.172826i
$633$	10.4401	−	1.09730i	0.414956	−	0.0436136i
$634$	−2.65559	−	0.564463i	−0.105467	−	0.0224177i
$635$	−18.2116	−	0.617947i	−0.722705	−	0.0245225i
$636$	−5.33871	+	16.4309i	−0.211694	+	0.651526i
$637$	31.1334	+	14.1320i	1.23355	+	0.559930i
$638$	−11.9232	+	3.87408i	−0.472043	+	0.153376i
$639$	−2.07025	+	0.440045i	−0.0818978	+	0.0174079i
$640$	31.2290	−	5.53834i	1.23444	−	0.218922i
$641$	18.1026	+	3.84783i	0.715010	+	0.151980i	0.551032	−	0.834484i	$-0.314234\pi$
$641$	18.1026	+	3.84783i	0.715010	+	0.151980i	0.163978	+	0.986464i	$0.447567\pi$
$642$	14.8126	−	33.2696i	0.584606	−	1.31305i
$643$			27.8187i			1.09706i	0.836130	+	0.548531i	$0.184813\pi$
$643$			27.8187i			1.09706i	−0.836130	+	0.548531i	$0.815187\pi$
$644$	16.6012	+	62.8644i	0.654179	+	2.47720i
$645$	7.67951	−	6.45682i	0.302380	−	0.254237i
$646$	−6.50152	+	61.8578i	−0.255799	+	2.43376i
$647$	−5.17305	−	11.6189i	−0.203374	−	0.456785i	0.782848	−	0.622213i	$-0.213766\pi$
$647$	−5.17305	−	11.6189i	−0.203374	−	0.456785i	−0.986222	+	0.165428i	$0.947099\pi$
$648$	1.46234	−	1.31670i	0.0574461	−	0.0517247i
$649$	−19.0460	−	32.9887i	−0.747622	−	1.29492i
$650$	−47.7329	−	25.2592i	−1.87224	−	0.990747i
$651$	6.03723	−	0.933851i	0.236618	−	0.0366005i
$652$	−41.5030	−	13.4851i	−1.62538	−	0.528119i
$653$	25.2481	+	2.65368i	0.988033	+	0.103846i	0.584737	−	0.811223i	$-0.301198\pi$
$653$	25.2481	+	2.65368i	0.988033	+	0.103846i	0.403296	+	0.915070i	$0.367864\pi$
$654$	21.6300	−	9.63031i	0.845802	−	0.376575i
$655$	−25.3730	−	3.54039i	−0.991407	−	0.138334i
$656$	−10.0175	−	4.46010i	−0.391120	−	0.174138i
$657$		−	0.676119i		−	0.0263779i
$658$	10.0474	−	36.9625i	0.391688	−	1.44095i
$659$	4.09655	+	12.6079i	0.159579	+	0.491133i	0.998596	−	0.0529719i	$-0.0168694\pi$
$659$	4.09655	+	12.6079i	0.159579	+	0.491133i	−0.839017	+	0.544105i	$0.816869\pi$
$660$	9.50487	+	33.0242i	0.369977	+	1.28547i
$661$	8.18041	+	9.08527i	0.318181	+	0.353376i	0.880925	−	0.473255i	$-0.156921\pi$
$661$	8.18041	+	9.08527i	0.318181	+	0.353376i	−0.562744	+	0.826631i	$0.690254\pi$
$662$	11.3408	−	53.3544i	0.440774	−	2.07368i
$663$	−17.1021	−	15.3988i	−0.664189	−	0.598038i
$664$	1.72344	−	5.30420i	0.0668824	−	0.205843i
$665$	30.8450	+	17.2037i	1.19612	+	0.667132i
$666$	−0.103229	−	0.317707i	−0.00400005	−	0.0123109i
$667$	3.68736	−	8.28195i	0.142775	−	0.320678i
$668$	−22.3894	−	12.9265i	−0.866273	−	0.500143i
$669$	−1.48572	−	14.1357i	−0.0574411	−	0.546516i
$670$	1.92367	+	2.84589i	0.0743178	+	0.109946i
$671$	−11.4164	−	8.29449i	−0.440725	−	0.320205i
$672$	8.58150	−	16.6927i	0.331039	−	0.643936i
$673$	−1.09283	−	0.355083i	−0.0421256	−	0.0136874i	0.287878	−	0.957667i	$-0.407050\pi$
$673$	−1.09283	−	0.355083i	−0.0421256	−	0.0136874i	−0.330004	+	0.943980i	$0.607050\pi$
$674$	25.4972	+	44.1625i	0.982116	+	1.70107i
$675$	−4.84908	+	1.21919i	−0.186641	+	0.0469268i
$676$	−15.6879	+	27.1722i	−0.603380	+	1.04509i
$677$	10.5821	+	49.7849i	0.406704	+	1.91339i	0.407084	+	0.913391i	$0.366546\pi$
$677$	10.5821	+	49.7849i	0.406704	+	1.91339i	−0.000379925		1.00000i	$0.500121\pi$
$678$	25.6721	−	35.3346i	0.985930	−	1.35702i
$679$	0.0957079	−	0.0616629i	0.00367293	−	0.00236640i
$680$	17.5919	+	10.9685i	0.674620	+	0.420623i
$681$	6.64687	+	2.95938i	0.254709	+	0.113404i
$682$	23.5155	+	13.5767i	0.900454	+	0.519877i
$683$	22.4057	−	2.35494i	0.857331	−	0.0901091i	0.334346	−	0.942451i	$-0.391485\pi$
$683$	22.4057	−	2.35494i	0.857331	−	0.0901091i	0.522986	+	0.852341i	$0.324818\pi$
$684$	11.5440	−	12.8209i	0.441395	−	0.490219i
$685$	−3.49984	−	49.3493i	−0.133722	−	1.88554i
$686$	−32.1047	+	25.4266i	−1.22576	+	0.970792i
$687$	14.2195	−	4.62020i	0.542509	−	0.176272i
$688$	−4.76295	−	4.28858i	−0.181586	−	0.163501i
$689$	−19.5387	−	21.7000i	−0.744366	−	0.826703i
$690$	−37.8111	−	18.3955i	−1.43944	−	0.700304i
$691$	−7.77228	+	8.63199i	−0.295671	+	0.328376i	−0.872616	−	0.488407i	$-0.837578\pi$
$691$	−7.77228	+	8.63199i	−0.295671	+	0.328376i	0.576945	+	0.816783i	$0.304245\pi$
$692$	43.4536	+	59.8088i	1.65186	+	2.27359i
$693$	13.1174	+	5.08975i	0.498287	+	0.193343i
$694$	−21.0223	+	15.2736i	−0.797996	+	0.579778i
$695$	0.866593	−	25.5395i	0.0328718	−	0.968767i
$696$	1.91642	−	0.853246i	0.0726418	−	0.0323422i
$697$	−14.7117	−	33.0430i	−0.557245	−	1.25159i
$698$	7.72818	+	36.3582i	0.292516	+	1.37618i
$699$	−20.0401			−0.757988
$700$	31.3515	−	21.8762i	1.18498	−	0.826841i
$701$	22.8498			0.863025			0.431512	−	0.902107i	$-0.357980\pi$
$701$	22.8498			0.863025			0.431512	+	0.902107i	$0.357980\pi$
$702$	2.24562	+	10.5648i	0.0847556	+	0.398744i
$703$	−0.366819	−	0.823888i	−0.0138348	−	0.0310735i
$704$	62.3343	−	27.7530i	2.34931	−	1.04598i
$705$	8.19834	+	12.1287i	0.308767	+	0.456792i
$706$	−63.6882	+	46.2722i	−2.39694	+	1.74148i
$707$	28.7968	−	23.1474i	1.08301	−	0.870546i
$708$	12.1669	+	16.7463i	0.457260	+	0.629365i
$709$	6.70378	−	7.44530i	0.251766	−	0.279614i	−0.603993	−	0.796990i	$-0.706424\pi$
$709$	6.70378	−	7.44530i	0.251766	−	0.279614i	0.855758	+	0.517376i	$0.173091\pi$
$710$	−1.44625	+	10.3649i	−0.0542767	+	0.388987i
$711$	2.95484	+	3.28169i	0.110815	+	0.123073i
$712$	−20.4287	−	18.3941i	−0.765598	−	0.689347i
$713$	−18.6744	+	6.06767i	−0.699360	+	0.227236i
$714$	25.7700	−	9.78546i	0.964417	−	0.366212i
$715$	−56.3711	−	13.9957i	−2.10816	−	0.523411i
$716$	−19.1310	+	21.2471i	−0.714959	+	0.794042i
$717$	7.56118	−	0.794712i	0.282377	−	0.0296791i
$718$	−10.2381	−	5.91098i	−0.382083	−	0.220596i
$719$	12.4108	+	5.52564i	0.462844	+	0.206072i	0.624892	−	0.780711i	$-0.285143\pi$
$719$	12.4108	+	5.52564i	0.462844	+	0.206072i	−0.162047	+	0.986783i	$0.551810\pi$
$720$	1.19941	+	2.96023i	0.0446995	+	0.110321i
$721$	26.2508	+	13.4952i	0.977632	+	0.502587i
$722$	21.6276	−	29.7679i	0.804897	−	1.10785i
$723$	2.22638	+	10.4743i	0.0827999	+	0.389543i
$724$	−0.589437	+	1.02093i	−0.0219063	+	0.0379427i
$725$	−5.31809	−	0.361318i	−0.197509	−	0.0134190i
$726$	19.1073	+	33.0949i	0.709140	+	1.22827i
$727$	−6.90068	−	2.24217i	−0.255932	−	0.0831574i	0.178241	−	0.983987i	$-0.442959\pi$
$727$	−6.90068	−	2.24217i	−0.255932	−	0.0831574i	−0.434173	+	0.900829i	$0.642959\pi$
$728$	−13.7726	−	21.3767i	−0.510446	−	0.792272i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−3.14267	−	1.14032i	−0.116315	−	0.0422052i
$731$	−2.20981	−	21.0249i	−0.0817328	−	0.777636i
$732$	6.64092	+	3.83414i	0.245456	+	0.141714i
$733$	−11.1190	+	24.9736i	−0.410689	+	0.922422i	0.583230	+	0.812307i	$0.301789\pi$
$733$	−11.1190	+	24.9736i	−0.410689	+	0.922422i	−0.993919	+	0.110115i	$0.964878\pi$
$734$	−14.3015	−	44.0154i	−0.527877	−	1.62464i
$735$	0.643859	−	15.6392i	0.0237491	−	0.576862i
$736$	−18.6423	+	57.3751i	−0.687164	+	2.11487i
$737$	2.74552	+	2.47208i	0.101132	+	0.0910601i
$738$	−3.52948	+	16.6049i	−0.129922	+	0.611235i
$739$	27.7710	+	30.8428i	1.02157	+	1.13457i	0.990840	+	0.135044i	$0.0431175\pi$
$739$	27.7710	+	30.8428i	1.02157	+	1.13457i	0.0307330	+	0.999528i	$0.490216\pi$
$740$	−0.975630	−	0.0331046i	−0.0358649	−	0.00121695i
$741$	9.01069	+	27.7320i	0.331016	+	1.01876i
$742$	33.8170	−	8.93038i	1.24146	−	0.327844i
$743$		−	27.5794i		−	1.01179i	−0.862595	−	0.505896i	$-0.831162\pi$
$743$		−	27.5794i		−	1.01179i	0.862595	−	0.505896i	$-0.168838\pi$
$744$	−4.15077	−	1.84804i	−0.152174	−	0.0677524i
$745$	1.36846	+	1.31890i	0.0501365	+	0.0483207i
$746$	44.7540	−	19.9258i	1.63856	−	0.729534i
$747$	2.81873	+	0.296260i	0.103132	+	0.0108396i
$748$	68.8654	+	22.3757i	2.51797	+	0.818138i
$749$	−43.0609	+	6.66075i	−1.57341	+	0.243378i
$750$	−2.51138	+	24.5953i	−0.0917026	+	0.898092i
$751$	−7.22159	−	12.5082i	−0.263519	−	0.456429i	0.703655	−	0.710542i	$-0.251550\pi$
$751$	−7.22159	−	12.5082i	−0.263519	−	0.456429i	−0.967175	+	0.254113i	$0.918217\pi$
$752$	6.94968	−	6.25752i	0.253429	−	0.228188i
$753$	0.900916	+	2.02349i	0.0328312	+	0.0737401i
$754$	−1.20359	+	11.4514i	−0.0438322	+	0.417035i
$755$	0.992212	−	3.99636i	0.0361103	−	0.145442i
$756$	−7.37815	−	2.00557i	−0.268341	−	0.0729421i
$757$			43.0197i			1.56358i	0.623543	+	0.781789i	$0.285693\pi$
$757$			43.0197i			1.56358i	−0.623543	+	0.781789i	$0.714307\pi$
$758$	5.61041	−	12.6012i	0.203779	−	0.457696i
$759$	−44.2356	−	9.40257i	−1.60565	−	0.341292i
$760$	−12.3550	−	23.1810i	−0.448162	−	0.840864i
$761$	25.3991	−	5.39874i	0.920716	−	0.195704i	0.276913	−	0.960895i	$-0.410689\pi$
$761$	25.3991	−	5.39874i	0.920716	−	0.195704i	0.643804	+	0.765191i	$0.277355\pi$
$762$	17.1383	−	5.56857i	0.620855	−	0.201728i
$763$	−23.7026	−	15.5147i	−0.858091	−	0.561670i
$764$	−7.67130	+	23.6098i	−0.277538	+	0.854174i
$765$	−3.59353	+	9.90358i	−0.129924	+	0.358065i
$766$	−39.6637	−	8.43079i	−1.43311	−	0.304617i
$767$	−34.7942	+	3.65702i	−1.25635	+	0.132047i
$768$	−4.93977	+	2.85198i	−0.178248	+	0.102912i
$769$	−4.91040	+	3.56761i	−0.177074	+	0.128651i	−0.672792	−	0.739832i	$-0.734905\pi$
$769$	−4.91040	+	3.56761i	−0.177074	+	0.128651i	0.495718	+	0.868484i	$0.334905\pi$
$770$	45.7810	−	52.3865i	1.64983	−	1.88788i
$771$	13.0881	+	9.50905i	0.471356	+	0.342460i
$772$	52.2369	+	5.49032i	1.88005	+	0.197601i
$773$	−0.512624	+	0.461568i	−0.0184378	+	0.0166015i	−0.678298	−	0.734787i	$-0.737282\pi$
$773$	−0.512624	+	0.461568i	−0.0184378	+	0.0166015i	0.659860	+	0.751388i	$0.270615\pi$
$774$	−4.96105	+	8.59279i	−0.178321	+	0.308862i
$775$	7.12576	+	9.08351i	0.255965	+	0.326289i
$776$	−0.0846773			−0.00303974
$777$	−0.252653	+	0.309705i	−0.00906386	+	0.0111106i
$778$	−1.85510	+	2.55333i	−0.0665086	+	0.0915412i
$779$	−4.79054	+	45.5789i	−0.171639	+	1.63303i
$780$	31.2597	+	4.36178i	1.11928	+	0.156177i
$781$	1.17653	+	11.1940i	0.0420996	+	0.400551i
$782$	−76.7293	+	44.2997i	−2.74383	+	1.58415i
$783$	0.626621	+	0.862469i	0.0223936	+	0.0308221i
$784$	−9.95127	+	0.973256i	−0.355403	+	0.0347591i
$785$	−3.47751	−	0.863391i	−0.124118	−	0.0308157i
$786$	24.7815	−	5.26747i	0.883927	−	0.187885i
$787$	−7.90771	+	37.2029i	−0.281879	+	1.32614i	0.578165	+	0.815920i	$0.303769\pi$
$787$	−7.90771	+	37.2029i	−0.281879	+	1.32614i	−0.860045	+	0.510219i	$0.829564\pi$
$788$	−8.37339	+	39.3937i	−0.298289	+	1.40334i
$789$	−20.2790	+	4.31044i	−0.721952	+	0.153456i
$790$	20.2372	−	8.19961i	0.720006	−	0.291729i
$791$	−52.1749	−	2.92348i	−1.85513	−	0.103947i
$792$	−6.15099	−	8.46611i	−0.218566	−	0.300830i
$793$	−11.2243	+	6.48036i	−0.398587	+	0.230124i
$794$	7.54517	+	71.7875i	0.267768	+	2.54764i
$795$	−5.84820	+	12.0207i	−0.207414	+	0.426331i
$796$	−3.33068	+	31.6893i	−0.118053	+	1.12320i
$797$	−8.35817	+	11.5040i	−0.296062	+	0.407494i	−0.930971	−	0.365093i	$-0.881037\pi$
$797$	−8.35817	+	11.5040i	−0.296062	+	0.407494i	0.634910	+	0.772586i	$0.281037\pi$
$798$	−34.4772	−	5.58845i	−1.22048	−	0.197829i
$799$	30.8467			1.09128
$800$	35.4467	−	1.30796i	1.25323	−	0.0462434i
$801$	6.98493	−	12.0983i	0.246801	−	0.427471i
$802$	−61.6282	+	55.4903i	−2.17617	+	1.95943i
$803$	−3.57593	−	0.375845i	−0.126192	−	0.0132633i
$804$	−1.62419	−	1.18004i	−0.0572806	−	0.0416168i
$805$	6.00005	+	49.9505i	0.211474	+	1.76052i
$806$	20.1762	−	14.6589i	0.710676	−	0.516336i
$807$	−0.0192295	+	0.0111022i	−0.000676912	+	0.000390815i
$808$	−27.3285	+	2.87234i	−0.961412	+	0.101048i
$809$	−13.5015	−	2.86982i	−0.474686	−	0.100898i	−0.0356447	−	0.999365i	$-0.511348\pi$
$809$	−13.5015	−	2.86982i	−0.474686	−	0.100898i	−0.439041	+	0.898467i	$0.644682\pi$
$810$	4.09655	−	2.76905i	0.143938	−	0.0972945i
$811$	8.35839	−	25.7245i	0.293503	−	0.903309i	−0.690218	−	0.723602i	$-0.742485\pi$
$811$	8.35839	−	25.7245i	0.293503	−	0.903309i	0.983720	−	0.179707i	$-0.0575148\pi$
$812$	−6.81995	−	4.46405i	−0.239333	−	0.156658i
$813$	19.6987	−	6.40050i	0.690864	−	0.224475i
$814$	−1.73771	+	0.369361i	−0.0609065	+	0.0129461i
$815$	−30.3633	−	14.7721i	−1.06358	−	0.517443i
$816$	6.58291	+	1.39924i	0.230448	+	0.0489832i
$817$	−10.8952	+	24.4710i	−0.381174	+	0.856131i
$818$		−	26.1605i		−	0.914681i
$819$	9.17080	−	9.10476i	0.320454	−	0.318146i
$820$	42.0954	+	26.2464i	1.47004	+	0.916562i
$821$	5.74997	−	54.7073i	0.200675	−	1.90930i	−0.178444	−	0.983950i	$-0.557106\pi$
$821$	5.74997	−	54.7073i	0.200675	−	1.90930i	0.379119	−	0.925348i	$-0.376227\pi$
$822$	19.8998	+	44.6956i	0.694084	+	1.55894i
$823$	29.7333	−	26.7720i	1.03644	−	0.933213i	0.0386209	−	0.999254i	$-0.487704\pi$
$823$	29.7333	−	26.7720i	1.03644	−	0.933213i	0.997817	+	0.0660412i	$0.0210369\pi$
$824$	−10.9764	−	19.0117i	−0.382382	−	0.662305i
$825$	3.75266	+	26.3240i	0.130651	+	0.916485i
$826$	15.1592	−	39.0685i	0.527457	−	1.35937i
$827$	2.43840	+	0.792286i	0.0847916	+	0.0275505i	0.351106	−	0.936336i	$-0.385806\pi$
$827$	2.43840	+	0.792286i	0.0847916	+	0.0275505i	−0.266314	+	0.963886i	$0.585806\pi$
$828$	24.4404	+	2.56879i	0.849364	+	0.0892717i
$829$	35.7991	−	15.9388i	1.24336	−	0.553577i	0.323646	−	0.946178i	$-0.395091\pi$
$829$	35.7991	−	15.9388i	1.24336	−	0.553577i	0.919709	+	0.392601i	$0.128425\pi$
$830$	6.13103	−	12.6021i	0.212811	−	0.437424i
$831$	−1.24680	−	0.555109i	−0.0432508	−	0.0192565i
$832$		−	62.6693i		−	2.17267i
$833$	−26.5414	−	19.5781i	−0.919604	−	0.678340i
$834$	7.80922	+	24.0343i	0.270411	+	0.832240i
$835$	−15.7756	−	12.3002i	−0.545937	−	0.425665i
$836$	−61.3912	−	68.1819i	−2.12326	−	2.35812i
$837$	0.480067	−	2.25854i	0.0165936	−	0.0780665i
$838$	−4.12020	−	3.70985i	−0.142330	−	0.128155i
$839$	−11.4319	+	35.1837i	−0.394672	+	1.21468i	0.534545	+	0.845140i	$0.320483\pi$
$839$	−11.4319	+	35.1837i	−0.394672	+	1.21468i	−0.929217	+	0.369535i	$0.879517\pi$
$840$	−6.70231	+	9.51859i	−0.231252	+	0.328423i
$841$	−8.61029	−	26.4998i	−0.296907	−	0.913785i
$842$	4.55592	−	10.2328i	0.157007	−	0.352644i
$843$	−20.3269	−	11.7357i	−0.700096	−	0.404200i
$844$	3.17104	+	30.1705i	0.109152	+	1.03851i
$845$	−14.9277	+	19.1456i	−0.513529	+	0.658628i
$846$	−11.7125	−	8.50963i	−0.402684	−	0.292567i
$847$	20.9047	−	40.6638i	0.718294	−	1.39722i
$848$	8.12139	+	2.63880i	0.278890	+	0.0906167i
$849$	−5.61267	−	9.72144i	−0.192626	−	0.333639i
$850$	39.9721	+	33.4062i	1.37103	+	1.14582i
$851$	0.642330	−	1.11255i	0.0220188	−	0.0381377i
$852$	−1.27167	−	5.98275i	−0.0435668	−	0.204966i
$853$	−31.0492	+	42.7356i	−1.06311	+	1.46324i	−0.186239	+	0.982504i	$0.559630\pi$
$853$	−31.0492	+	42.7356i	−1.06311	+	1.46324i	−0.876866	+	0.480734i	$0.840370\pi$
$854$	−0.756458	−	15.5060i	−0.0258854	−	0.530606i
$855$	10.2175	−	8.59072i	0.349431	−	0.293796i
$856$	29.6056	+	13.1813i	1.01190	+	0.450526i
$857$	−2.80510	−	1.61953i	−0.0958206	−	0.0553220i	0.451324	−	0.892360i	$-0.350952\pi$
$857$	−2.80510	−	1.61953i	−0.0958206	−	0.0553220i	−0.547145	+	0.837038i	$0.684285\pi$
$858$	57.1247	−	6.00404i	1.95020	−	0.204975i
$859$	−11.6643	+	12.9545i	−0.397981	+	0.442003i	−0.908513	−	0.417856i	$-0.862782\pi$
$859$	−11.6643	+	12.9545i	−0.397981	+	0.442003i	0.510532	+	0.859859i	$0.329448\pi$
$860$	18.6594	+	22.1928i	0.636279	+	0.756768i
$861$	18.9882	−	7.21026i	0.647116	−	0.245725i
$862$	−49.0072	+	15.9234i	−1.66919	+	0.542354i
$863$	26.3467	+	23.7227i	0.896853	+	0.807530i	0.982008	−	0.188838i	$-0.0604720\pi$
$863$	26.3467	+	23.7227i	0.896853	+	0.807530i	−0.0851554	+	0.996368i	$0.527139\pi$
$864$	−4.74692	−	5.27199i	−0.161493	−	0.179357i
$865$	26.9048	+	50.4801i	0.914790	+	1.71638i
$866$	40.1720	−	44.6156i	1.36510	−	1.51610i
$867$	3.05582	+	4.20597i	0.103781	+	0.142842i
$868$	2.69871	+	17.4468i	0.0916001	+	0.592183i
$869$	18.9991	−	13.8036i	0.644499	−	0.468256i
$870$	5.06568	−	1.45798i	0.171743	−	0.0494301i
$871$	3.09984	−	1.38014i	0.105034	−	0.0467642i
$872$	8.56972	+	19.2479i	0.290207	+	0.651817i
$873$	−0.00894687	−	0.0420917i	−0.000302806	−	0.00142459i
$874$	112.262			3.79730
$875$	26.3650	−	13.4121i	0.891301	−	0.453412i
$876$	1.95390			0.0660160
$877$	−9.03572	−	42.5097i	−0.305115	−	1.43545i	−0.817119	−	0.576468i	$-0.804430\pi$
$877$	−9.03572	−	42.5097i	−0.305115	−	1.43545i	0.512005	−	0.858983i	$-0.328903\pi$
$878$	−32.5408	−	73.0878i	−1.09820	−	2.46659i
$879$	−9.88054	+	4.39910i	−0.333262	+	0.148378i
$880$	16.3231	−	4.69803i	0.550251	−	0.158371i
$881$	10.0613	−	7.30995i	0.338973	−	0.246278i	−0.405255	−	0.914204i	$-0.632817\pi$
$881$	10.0613	−	7.30995i	0.338973	−	0.246278i	0.744228	+	0.667925i	$0.232817\pi$
$882$	4.67679	+	14.7557i	0.157476	+	0.496851i
$883$	−29.9457	−	41.2167i	−1.00775	−	1.38705i	−0.920445	−	0.390872i	$-0.872174\pi$
$883$	−29.9457	−	41.2167i	−1.00775	−	1.38705i	−0.0873082	−	0.996181i	$-0.527826\pi$
$884$	44.5004	−	49.4227i	1.49671	−	1.66227i
$885$	7.53327	+	14.1343i	0.253228	+	0.475120i
$886$	10.4052	+	11.5562i	0.349571	+	0.388237i
$887$	−30.6414	−	27.5896i	−1.02884	−	0.926369i	−0.0315148	−	0.999503i	$-0.510033\pi$
$887$	−30.6414	−	27.5896i	−1.02884	−	0.926369i	−0.997322	+	0.0731343i	$0.976700\pi$
$888$	0.282718	−	0.0918606i	0.00948739	−	0.00308264i
$889$	−16.7066	−	13.6290i	−0.560322	−	0.457103i
$890$	−44.4533	−	52.8712i	−1.49008	−	1.77225i
$891$	3.55846	−	3.95207i	0.119213	−	0.132399i
$892$	40.8502	−	4.29353i	1.36777	−	0.143758i
$893$	−33.8486	−	19.5425i	−1.13270	−	0.653964i
$894$	−1.71703	−	0.764472i	−0.0574261	−	0.0255678i
$895$	−16.9327	+	14.2368i	−0.565999	+	0.475883i
$896$	33.3752	+	17.1577i	1.11499	+	0.573200i
$897$	−24.4143	+	33.6034i	−0.815170	+	1.12199i
$898$	−0.815504	−	3.83664i	−0.0272137	−	0.128030i
$899$	1.23078	−	2.13177i	0.0410487	−	0.0710984i
$900$	−3.52331	−	14.0132i	−0.117444	−	0.467107i
$901$	14.0835	+	24.3934i	0.469190	+	0.812661i
$902$	85.8598	+	27.8975i	2.85882	+	0.928886i
$903$	11.8574	−	0.578457i	0.394588	−	0.0192499i
$904$	31.4431	+	22.8448i	1.04578	+	0.759806i
$905$	−0.560875	+	0.719352i	−0.0186441	+	0.0239121i
$906$	0.425649	+	4.04978i	0.0141413	+	0.134545i
$907$	23.0688	+	13.3188i	0.765988	+	0.442243i	0.831442	−	0.555612i	$-0.187516\pi$
$907$	23.0688	+	13.3188i	0.765988	+	0.442243i	−0.0654535	+	0.997856i	$0.520849\pi$
$908$	−8.55221	+	19.2086i	−0.283815	+	0.637459i
$909$	−4.31527	−	13.2810i	−0.143129	−	0.440504i
$910$	−26.8526	−	57.9826i	−0.890155	−	1.92210i
$911$	−6.72489	+	20.6971i	−0.222805	+	0.685724i	0.775702	+	0.631100i	$0.217396\pi$
$911$	−6.72489	+	20.6971i	−0.222805	+	0.685724i	−0.998507	+	0.0546246i	$0.982604\pi$
$912$	−6.33705	−	5.70591i	−0.209841	−	0.188942i
$913$	3.13378	−	14.7433i	0.103713	−	0.487932i
$914$	36.8783	+	40.9575i	1.21982	+	1.35475i
$915$	4.67920	+	3.64835i	0.154690	+	0.120611i
$916$	13.3518	+	41.0926i	0.441155	+	1.35774i
$917$	−21.3567	−	21.5116i	−0.705260	−	0.710375i
$918$		−	10.4187i		−	0.343869i
$919$	32.7977	+	14.6025i	1.08190	+	0.481691i	0.868710	−	0.495320i	$-0.164949\pi$
$919$	32.7977	+	14.6025i	1.08190	+	0.481691i	0.213186	+	0.977012i	$0.431616\pi$
$920$	16.3696	−	33.6469i	0.539689	−	1.10931i
$921$	−1.13363	+	0.504725i	−0.0373544	+	0.0166313i
$922$	−33.6156	−	3.53314i	−1.10707	−	0.116358i
$923$	9.83182	+	3.19455i	0.323618	+	0.105150i
$924$	−14.7087	+	37.9074i	−0.483881	+	1.24706i
$925$	−0.744122	−	0.129693i	−0.0244666	−	0.00426428i
$926$	−2.85537	−	4.94565i	−0.0938334	−	0.162524i
$927$	8.29067	−	7.46496i	0.272301	−	0.245181i
$928$	−3.07610	−	6.90903i	−0.100978	−	0.226800i
$929$	0.201921	−	1.92115i	0.00662480	−	0.0630307i	−0.990710	−	0.135991i	$-0.956578\pi$
$929$	0.201921	−	1.92115i	0.00662480	−	0.0630307i	0.997335	+	0.0729606i	$0.0232447\pi$
$930$	−9.68825	−	6.04059i	−0.317690	−	0.198079i
$931$	16.7208	+	38.2982i	0.548003	+	1.25517i
$932$		−	57.9134i		−	1.89702i
$933$	4.79639	−	10.7729i	0.157027	−	0.352688i
$934$	−14.9840	−	3.18494i	−0.490290	−	0.104214i
$935$	50.3815	+	24.5111i	1.64765	+	0.801598i
$936$	−9.40132	+	1.99831i	−0.307292	+	0.0653169i
$937$	−11.1958	+	3.63775i	−0.365752	+	0.118840i	−0.486126	−	0.873889i	$-0.661590\pi$
$937$	−11.1958	+	3.63775i	−0.365752	+	0.118840i	0.120374	+	0.992729i	$0.461590\pi$
$938$	−0.227381	+	4.05804i	−0.00742426	+	0.132500i
$939$	−3.93263	+	12.1034i	−0.128336	+	0.394979i
$940$	−35.0503	+	23.6921i	−1.14321	+	0.772752i
$941$	8.78108	+	1.86648i	0.286255	+	0.0608454i	0.348801	−	0.937197i	$-0.386589\pi$
$941$	8.78108	+	1.86648i	0.286255	+	0.0608454i	−0.0625464	+	0.998042i	$0.519922\pi$
$942$	3.52399	−	0.370387i	0.114818	−	0.0120678i
$943$	−56.5367	+	32.6415i	−1.84109	+	1.06295i
$944$	8.27730	−	6.01381i	0.269403	−	0.195733i
$945$	−5.43969	−	2.32589i	−0.176953	−	0.0756611i
$946$	42.6887	+	31.0151i	1.38793	+	1.00839i
$947$	−54.0569	−	5.68161i	−1.75661	−	0.184628i	−0.829273	−	0.558844i	$-0.811245\pi$
$947$	−54.0569	−	5.68161i	−1.75661	−	0.184628i	−0.927341	+	0.374217i	$0.877912\pi$
$948$	−9.48364	+	8.53911i	−0.308014	+	0.277337i
$949$	−1.65121	+	2.85998i	−0.0536006	+	0.0928390i
$950$	−22.6980	−	61.9808i	−0.736420	−	2.01092i
$951$	1.22774			0.0398123
$952$	8.70778	+	22.9319i	0.282221	+	0.743228i
$953$	−0.621189	+	0.854993i	−0.0201223	+	0.0276959i	−0.818960	−	0.573851i	$-0.805449\pi$
$953$	−0.621189	+	0.854993i	−0.0201223	+	0.0276959i	0.798837	+	0.601547i	$0.205449\pi$
$954$	1.38184	−	13.1474i	0.0447389	−	0.425662i
$955$	−8.40339	+	17.2728i	−0.271927	+	0.558934i
$956$	2.29661	+	21.8508i	0.0742778	+	0.706706i
$957$	4.90985	−	2.83470i	0.158713	−	0.0916329i
$958$	−7.91667	−	10.8964i	−0.255776	−	0.352045i
$959$	32.0591	−	48.9782i	1.03524	−	1.58159i
$960$	−26.5903	+	10.7737i	−0.858198	+	0.347721i
$961$	25.1076	−	5.33679i	0.809923	−	0.172154i
$962$	−0.339241	+	1.59601i	−0.0109376	+	0.0514573i
$963$	−3.42411	+	16.1092i	−0.110340	+	0.519111i
$964$	−30.2693	+	6.43394i	−0.974909	+	0.207223i
$965$	39.4440	+	9.79311i	1.26975	+	0.315251i
$966$	−22.4268	−	44.4110i	−0.721569	−	1.42890i
$967$	−13.3274	−	18.3436i	−0.428581	−	0.589892i	0.539045	−	0.842277i	$-0.318785\pi$
$967$	−13.3274	−	18.3436i	−0.428581	−	0.589892i	−0.967627	+	0.252385i	$0.918785\pi$
$968$	−29.4501	+	17.0030i	−0.946563	+	0.546498i
$969$	−2.94013	−	27.9734i	−0.0944505	−	0.898636i
$970$	−0.210736	−	0.0294047i	−0.00676633	−	0.000944128i
$971$	5.44629	−	51.8180i	0.174780	−	1.66292i	−0.458274	−	0.888811i	$-0.651532\pi$
$971$	5.44629	−	51.8180i	0.174780	−	1.66292i	0.633054	−	0.774108i	$-0.281801\pi$
$972$	−1.69862	+	2.33795i	−0.0544833	+	0.0749899i
$973$	19.1130	−	23.4289i	0.612734	−	0.751097i
$974$	−26.8894			−0.861593
$975$	23.4891	+	6.68518i	0.752253	+	0.214097i
$976$	1.89512	−	3.28245i	0.0606614	−	0.105069i
$977$	2.60944	−	2.34955i	0.0834835	−	0.0751689i	−0.626332	−	0.779556i	$-0.715445\pi$
$977$	2.60944	−	2.34955i	0.0834835	−	0.0751689i	0.709816	+	0.704387i	$0.248778\pi$
$978$	33.2092	+	3.49042i	1.06191	+	0.111611i
$979$	−60.1037	−	43.6679i	−1.92092	−	1.39563i
$980$	45.1953	+	1.86067i	1.44371	+	0.0594368i
$981$	−8.66236	+	6.29357i	−0.276568	+	0.200938i
$982$	25.1373	−	14.5131i	0.802165	−	0.463130i
$983$	27.6131	−	2.90226i	0.880722	−	0.0925676i	0.346638	−	0.937999i	$-0.387323\pi$
$983$	27.6131	−	2.90226i	0.880722	−	0.0925676i	0.534084	+	0.845431i	$0.320657\pi$
$984$	−14.7762	−	3.14078i	−0.471048	−	0.100124i
$985$	−10.6292	+	29.2935i	−0.338674	+	0.933367i
$986$	3.43228	−	10.5635i	0.109306	−	0.336409i
$987$	−0.969058	+	17.2947i	−0.0308455	+	0.550495i
$988$	−80.1420	+	26.0397i	−2.54966	+	0.828433i
$989$	−37.3229	+	7.93323i	−1.18680	+	0.252262i
$990$	−12.3680	−	23.2055i	−0.393082	−	0.737520i
$991$	46.3520	+	9.85241i	1.47242	+	0.312972i	0.873101	−	0.487539i	$-0.162105\pi$
$991$	46.3520	+	9.85241i	1.47242	+	0.312972i	0.599317	+	0.800512i	$0.295439\pi$
$992$	−6.66250	+	14.9642i	−0.211535	+	0.475115i
$993$			24.6671i			0.782785i
$994$	−8.78749	+	8.72420i	−0.278722	+	0.276715i
$995$	−5.94095	+	23.9285i	−0.188341	+	0.758586i
$996$	−0.856153	+	8.14575i	−0.0271282	+	0.258108i
$997$	10.4513	+	23.4741i	0.330997	+	0.743431i	1.00000		0.000171484i	$5.45849e-5\pi$
$997$	10.4513	+	23.4741i	0.330997	+	0.743431i	−0.669003	+	0.743260i	$0.733279\pi$
$998$	−54.5651	+	49.1307i	−1.72723	+	1.55520i
$999$	0.0755339	+	0.130829i	0.00238979	+	0.00413923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bo.a.4.6	✓	320
7.2	even	3	inner	525.2.bo.a.79.6	yes	320
25.19	even	10	inner	525.2.bo.a.319.6	yes	320
175.44	even	30	inner	525.2.bo.a.394.6	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bo.a.4.6	✓	320	1.1	even	1	trivial
525.2.bo.a.79.6	yes	320	7.2	even	3	inner
525.2.bo.a.319.6	yes	320	25.19	even	10	inner
525.2.bo.a.394.6	yes	320	175.44	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bo (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.459756 - 2.16298i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-2.64003 + 1.17542i) q^{4} +(-2.14884 + 0.618467i) q^{5} +(1.78898 - 1.29977i) q^{6} +(-2.46658 - 0.957073i) q^{7} +(1.15663 + 1.59196i) q^{8} +(-0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.459756 - 2.16298i) q^{2} +(0.406737 + 0.913545i) q^{3} +(-2.64003 + 1.17542i) q^{4} +(-2.14884 + 0.618467i) q^{5} +(1.78898 - 1.29977i) q^{6} +(-2.46658 - 0.957073i) q^{7} +(1.15663 + 1.59196i) q^{8} +(-0.669131 + 0.743145i) q^{9} +(2.32567 + 4.36355i) q^{10} +(3.55846 + 3.95207i) q^{11} +(-2.14759 - 1.93370i) q^{12} +(4.64532 - 1.50936i) q^{13} +(-0.936106 + 5.77519i) q^{14} +(-1.43901 - 1.71151i) q^{15} +(-0.955782 + 1.06150i) q^{16} +(-4.68576 + 0.492493i) q^{17} +(1.91505 + 1.10565i) q^{18} +(5.45376 + 2.42817i) q^{19} +(4.94603 - 4.15855i) q^{20} +(-0.128919 - 2.64261i) q^{21} +(6.91224 - 9.51388i) q^{22} +(1.76805 + 8.31803i) q^{23} +(-0.983886 + 1.70414i) q^{24} +(4.23500 - 2.65797i) q^{25} +(-5.40043 - 9.35381i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(7.63679 - 0.372558i) q^{28} +(-0.862469 - 0.626621i) q^{29} +(-3.04037 + 3.89943i) q^{30} +(0.241356 + 2.29635i) q^{31} +(6.14372 + 3.54708i) q^{32} +(-2.16304 + 4.85827i) q^{33} +(3.21956 + 9.90878i) q^{34} +(5.89219 + 0.531094i) q^{35} +(0.893019 - 2.74843i) q^{36} +(-0.112265 - 0.101084i) q^{37} +(2.74469 - 12.9128i) q^{38} +(3.26829 + 3.62980i) q^{39} +(-3.46998 - 2.70553i) q^{40} +(2.37228 + 7.30113i) q^{41} +(-5.65665 + 1.49380i) q^{42} +4.48699i q^{43} +(-14.0398 - 6.25090i) q^{44} +(0.978241 - 2.01073i) q^{45} +(17.1789 - 7.64854i) q^{46} +(-6.51115 - 0.684350i) q^{47} +(-1.35848 - 0.441398i) q^{48} +(5.16802 + 4.72139i) q^{49} +(-7.69621 - 7.93821i) q^{50} +(-2.35578 - 4.08034i) q^{51} +(-10.4897 + 9.44493i) q^{52} +(-2.43158 - 5.46143i) q^{53} +(-0.231144 + 2.19919i) q^{54} +(-10.0908 - 6.29156i) q^{55} +(-1.32929 - 5.03368i) q^{56} +5.96989i q^{57} +(-0.958844 + 2.15360i) q^{58} +(-7.00628 - 1.48923i) q^{59} +(5.81075 + 2.82699i) q^{60} +(-2.59552 + 0.551694i) q^{61} +(4.85599 - 1.57781i) q^{62} +(2.36171 - 1.19262i) q^{63} +(3.96486 - 12.2026i) q^{64} +(-9.04855 + 6.11634i) q^{65} +(11.5028 + 2.44500i) q^{66} +(0.690898 - 0.0726163i) q^{67} +(11.7916 - 6.80791i) q^{68} +(-6.87977 + 4.99845i) q^{69} +(-1.56023 - 12.9889i) q^{70} +(1.71228 + 1.24405i) q^{71} +(-1.95699 - 0.205688i) q^{72} +(-0.502455 + 0.452412i) q^{73} +(-0.167029 + 0.289302i) q^{74} +(4.15070 + 2.78777i) q^{75} -17.2522 q^{76} +(-4.99481 - 13.1538i) q^{77} +(6.34858 - 8.73807i) q^{78} +(0.461592 - 4.39175i) q^{79} +(1.39731 - 2.87212i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(14.7015 - 8.48794i) q^{82} +(-1.66593 - 2.29296i) q^{83} +(3.44651 + 6.82503i) q^{84} +(9.76433 - 3.95627i) q^{85} +(9.70528 - 2.06292i) q^{86} +(0.221649 - 1.04277i) q^{87} +(-2.17573 + 10.2360i) q^{88} +(-13.6646 + 2.90450i) q^{89} +(-4.79893 - 1.19147i) q^{90} +(-12.9026 - 0.722963i) q^{91} +(-14.4449 - 19.8816i) q^{92} +(-1.99965 + 1.15450i) q^{93} +(1.51331 + 14.3981i) q^{94} +(-13.2210 - 1.84477i) q^{95} +(-0.741542 + 7.05530i) q^{96} +(-0.0252936 + 0.0348137i) q^{97} +(7.83625 - 13.3490i) q^{98} -5.31804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Introduction

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