LMFDB - Embedded newform 380.2.bj.a.207.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			207.11
Character	$\chi$	$=$	380.207
Dual form			380.2.bj.a.123.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20320 - 0.743174i) q^{2} +(-0.0390213 - 0.446015i) q^{3} +(0.895384 + 1.78838i) q^{4} +(0.378999 + 2.20371i) q^{5} +(-0.284517 + 0.565646i) q^{6} +(-3.33202 - 0.892813i) q^{7} +(0.251747 - 2.81720i) q^{8} +(2.75702 - 0.486136i) q^{9} +O(q^{10})$	\(q+(-1.20320 - 0.743174i) q^{2} +(-0.0390213 - 0.446015i) q^{3} +(0.895384 + 1.78838i) q^{4} +(0.378999 + 2.20371i) q^{5} +(-0.284517 + 0.565646i) q^{6} +(-3.33202 - 0.892813i) q^{7} +(0.251747 - 2.81720i) q^{8} +(2.75702 - 0.486136i) q^{9} +(1.18173 - 2.93317i) q^{10} +(0.386458 + 0.223121i) q^{11} +(0.762704 - 0.469140i) q^{12} +(-0.285103 + 3.25874i) q^{13} +(3.34558 + 3.55051i) q^{14} +(0.968101 - 0.255031i) q^{15} +(-2.39657 + 3.20257i) q^{16} +(-4.32774 + 3.03032i) q^{17} +(-3.67853 - 1.46402i) q^{18} +(3.60746 + 2.44667i) q^{19} +(-3.60172 + 2.65097i) q^{20} +(-0.268188 + 1.52097i) q^{21} +(-0.299168 - 0.555665i) q^{22} +(3.54358 + 7.59923i) q^{23} +(-1.26634 - 0.00235225i) q^{24} +(-4.71272 + 1.67041i) q^{25} +(2.76485 - 3.70904i) q^{26} +(-0.672041 - 2.50809i) q^{27} +(-1.38676 - 6.75832i) q^{28} +(3.46690 - 0.611309i) q^{29} +(-1.35435 - 0.412614i) q^{30} +(-3.72546 + 2.15090i) q^{31} +(5.26362 - 2.07226i) q^{32} +(0.0844355 - 0.181072i) q^{33} +(7.45919 - 0.429814i) q^{34} +(0.704670 - 7.68120i) q^{35} +(3.33798 + 4.49530i) q^{36} +(5.30509 + 5.30509i) q^{37} +(-2.52220 - 5.62481i) q^{38} +1.46457 q^{39} +(6.30372 - 0.512939i) q^{40} +(1.12586 + 0.944712i) q^{41} +(1.45303 - 1.63072i) q^{42} +(-7.54666 - 3.51907i) q^{43} +(-0.0529967 + 0.890911i) q^{44} +(2.11621 + 5.89143i) q^{45} +(1.38391 - 11.7769i) q^{46} +(7.00444 + 4.90456i) q^{47} +(1.52191 + 0.943940i) q^{48} +(4.24308 + 2.44974i) q^{49} +(6.91176 + 1.49253i) q^{50} +(1.52044 + 1.81199i) q^{51} +(-6.08313 + 2.40796i) q^{52} +(11.6075 - 5.41266i) q^{53} +(-1.05535 + 3.51718i) q^{54} +(-0.345229 + 0.936205i) q^{55} +(-3.35406 + 9.16221i) q^{56} +(0.950486 - 1.70446i) q^{57} +(-4.62569 - 1.84099i) q^{58} +(-0.568387 + 3.22348i) q^{59} +(1.32291 + 1.50298i) q^{60} +(-12.3322 - 4.48856i) q^{61} +(6.08097 + 0.180707i) q^{62} +(-9.62047 - 0.841682i) q^{63} +(-7.87325 - 1.41844i) q^{64} +(-7.28939 + 0.606775i) q^{65} +(-0.236161 + 0.155116i) q^{66} +(-8.66940 - 6.07038i) q^{67} +(-9.29433 - 5.02632i) q^{68} +(3.25110 - 1.87702i) q^{69} +(-6.55633 + 8.71834i) q^{70} +(2.32643 + 6.39182i) q^{71} +(-0.675473 - 7.88945i) q^{72} +(4.66061 - 0.407751i) q^{73} +(-2.44048 - 10.3257i) q^{74} +(0.928926 + 2.03676i) q^{75} +(-1.14550 + 8.64221i) q^{76} +(-1.08848 - 1.08848i) q^{77} +(-1.76218 - 1.08843i) q^{78} +(-2.65348 - 2.22653i) q^{79} +(-7.96584 - 4.06759i) q^{80} +(6.79972 - 2.47490i) q^{81} +(-0.652555 - 1.97339i) q^{82} +(1.55142 - 5.78996i) q^{83} +(-2.96020 + 0.882233i) q^{84} +(-8.31816 - 8.38861i) q^{85} +(6.46487 + 9.84263i) q^{86} +(-0.407936 - 1.52244i) q^{87} +(0.725868 - 1.03256i) q^{88} +(-6.19419 - 7.38194i) q^{89} +(1.83213 - 8.66129i) q^{90} +(3.85942 - 10.6037i) q^{91} +(-10.4174 + 13.1415i) q^{92} +(1.10470 + 1.57768i) q^{93} +(-4.78280 - 11.1067i) q^{94} +(-4.02454 + 8.87711i) q^{95} +(-1.12965 - 2.26679i) q^{96} +(7.45829 - 5.22235i) q^{97} +(-3.28469 - 6.10088i) q^{98} +(1.17394 + 0.427278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.20320	−	0.743174i	−0.850791	−	0.525503i
$2$	−1.20320	−	0.743174i	−0.850791	−	0.525503i
$3$	−0.0390213	−	0.446015i	−0.0225289	−	0.257507i	−0.999104	−	0.0423288i	$-0.986522\pi$
$3$	−0.0390213	−	0.446015i	−0.0225289	−	0.257507i	0.976575	−	0.215178i	$-0.0690332\pi$
$4$	0.895384	+	1.78838i	0.447692	+	0.894188i
$5$	0.378999	+	2.20371i	0.169494	+	0.985531i
$5$	0.378999	+	2.20371i	0.169494	+	0.985531i
$6$	−0.284517	+	0.565646i	−0.116153	+	0.230924i
$7$	−3.33202	−	0.892813i	−1.25939	−	0.337451i	−0.433431	−	0.901187i	$-0.642697\pi$
$7$	−3.33202	−	0.892813i	−1.25939	−	0.337451i	−0.825955	+	0.563735i	$0.809364\pi$
$8$	0.251747	−	2.81720i	0.0890060	−	0.996031i
$9$	2.75702	−	0.486136i	0.919005	−	0.162045i
$10$	1.18173	−	2.93317i	0.373696	−	0.927551i
$11$	0.386458	+	0.223121i	0.116521	+	0.0672736i	0.557128	−	0.830427i	$-0.311903\pi$
$11$	0.386458	+	0.223121i	0.116521	+	0.0672736i	−0.440607	+	0.897700i	$0.645237\pi$
$12$	0.762704	−	0.469140i	0.220174	−	0.135429i
$13$	−0.285103	+	3.25874i	−0.0790733	+	0.903812i	0.848261	+	0.529578i	$0.177650\pi$
$13$	−0.285103	+	3.25874i	−0.0790733	+	0.903812i	−0.927334	+	0.374234i	$0.877906\pi$
$14$	3.34558	+	3.55051i	0.894143	+	0.948913i
$15$	0.968101	−	0.255031i	0.249963	−	0.0658488i
$16$	−2.39657	+	3.20257i	−0.599143	+	0.800642i
$17$	−4.32774	+	3.03032i	−1.04963	+	0.734959i	−0.965211	−	0.261471i	$-0.915792\pi$
$17$	−4.32774	+	3.03032i	−1.04963	+	0.734959i	−0.0844194	+	0.996430i	$0.526904\pi$
$18$	−3.67853	−	1.46402i	−0.867037	−	0.345074i
$19$	3.60746	+	2.44667i	0.827609	+	0.561305i
$19$	3.60746	+	2.44667i	0.827609	+	0.561305i
$20$	−3.60172	+	2.65097i	−0.805369	+	0.592774i
$21$	−0.268188	+	1.52097i	−0.0585235	+	0.331903i
$22$	−0.299168	−	0.555665i	−0.0637829	−	0.118468i
$23$	3.54358	+	7.59923i	0.738888	+	1.58455i	0.809551	+	0.587050i	$0.199711\pi$
$23$	3.54358	+	7.59923i	0.738888	+	1.58455i	−0.0706632	+	0.997500i	$0.522512\pi$
$24$	−1.26634	−	0.00235225i	−0.258490	−	0.000480151i
$25$	−4.71272	+	1.67041i	−0.942544	+	0.334083i
$26$	2.76485	−	3.70904i	0.542231	−	0.727403i
$27$	−0.672041	−	2.50809i	−0.129334	−	0.482682i
$28$	−1.38676	−	6.75832i	−0.262072	−	1.27720i
$29$	3.46690	−	0.611309i	0.643788	−	0.113517i	0.157784	−	0.987474i	$-0.449565\pi$
$29$	3.46690	−	0.611309i	0.643788	−	0.113517i	0.486004	+	0.873956i	$0.338454\pi$
$30$	−1.35435	−	0.412614i	−0.247270	−	0.0753327i
$31$	−3.72546	+	2.15090i	−0.669113	+	0.386312i	−0.795740	−	0.605638i	$-0.792918\pi$
$31$	−3.72546	+	2.15090i	−0.669113	+	0.386312i	0.126628	+	0.991950i	$0.459585\pi$
$32$	5.26362	−	2.07226i	0.930486	−	0.366327i
$33$	0.0844355	−	0.181072i	0.0146983	−	0.0315207i
$34$	7.45919	−	0.429814i	1.27924	−	0.0737125i
$35$	0.704670	−	7.68120i	0.119111	−	1.29836i
$36$	3.33798	+	4.49530i	0.556331	+	0.749217i
$37$	5.30509	+	5.30509i	0.872151	+	0.872151i	0.992707	−	0.120555i	$-0.0384675\pi$
$37$	5.30509	+	5.30509i	0.872151	+	0.872151i	−0.120555	+	0.992707i	$0.538467\pi$
$38$	−2.52220	−	5.62481i	−0.409155	−	0.912465i
$39$	1.46457			0.234519
$40$	6.30372	−	0.512939i	0.996706	−	0.0811027i
$41$	1.12586	+	0.944712i	0.175830	+	0.147539i	0.726456	−	0.687213i	$-0.241166\pi$
$41$	1.12586	+	0.944712i	0.175830	+	0.147539i	−0.550625	+	0.834753i	$0.685611\pi$
$42$	1.45303	−	1.63072i	0.224208	−	0.251626i
$43$	−7.54666	−	3.51907i	−1.15086	−	0.536653i	−0.248920	−	0.968524i	$-0.580076\pi$
$43$	−7.54666	−	3.51907i	−1.15086	−	0.536653i	−0.901935	+	0.431871i	$0.857854\pi$
$44$	−0.0529967	+	0.890911i	−0.00798956	+	0.134310i
$45$	2.11621	+	5.89143i	0.315466	+	0.878243i
$46$	1.38391	−	11.7769i	0.204047	−	1.73641i
$47$	7.00444	+	4.90456i	1.02170	+	0.715404i	0.959225	−	0.282643i	$-0.0912111\pi$
$47$	7.00444	+	4.90456i	1.02170	+	0.715404i	0.0624770	+	0.998046i	$0.480100\pi$
$48$	1.52191	+	0.943940i	0.219669	+	0.136246i
$49$	4.24308	+	2.44974i	0.606154	+	0.349963i
$50$	6.91176	+	1.49253i	0.977470	+	0.211075i
$51$	1.52044	+	1.81199i	0.212904	+	0.253729i
$52$	−6.08313	+	2.40796i	−0.843579	+	0.333923i
$53$	11.6075	−	5.41266i	1.59441	−	0.743486i	0.596174	−	0.802855i	$-0.296687\pi$
$53$	11.6075	−	5.41266i	1.59441	−	0.743486i	0.998236	+	0.0593699i	$0.0189091\pi$
$54$	−1.05535	+	3.51718i	−0.143615	+	0.478628i
$55$	−0.345229	+	0.936205i	−0.0465506	+	0.126238i
$56$	−3.35406	+	9.16221i	−0.448205	+	1.22435i
$57$	0.950486	−	1.70446i	0.125895	−	0.225761i
$58$	−4.62569	−	1.84099i	−0.607383	−	0.241733i
$59$	−0.568387	+	3.22348i	−0.0739977	+	0.419662i	0.925195	+	0.379492i	$0.123901\pi$
$59$	−0.568387	+	3.22348i	−0.0739977	+	0.419662i	−0.999193	+	0.0401700i	$0.987210\pi$
$60$	1.32291	+	1.50298i	0.170788	+	0.194034i
$61$	−12.3322	−	4.48856i	−1.57898	−	0.574702i	−0.603998	−	0.796986i	$-0.706427\pi$
$61$	−12.3322	−	4.48856i	−1.57898	−	0.574702i	−0.974982	+	0.222284i	$0.928649\pi$
$62$	6.08097	+	0.180707i	0.772284	+	0.0229498i
$63$	−9.62047	−	0.841682i	−1.21207	−	0.106042i
$64$	−7.87325	−	1.41844i	−0.984156	−	0.177306i
$65$	−7.28939	+	0.606775i	−0.904138	+	0.0752612i
$66$	−0.236161	+	0.155116i	−0.0290694	+	0.0190935i
$67$	−8.66940	−	6.07038i	−1.05914	−	0.741615i	−0.0919698	−	0.995762i	$-0.529316\pi$
$67$	−8.66940	−	6.07038i	−1.05914	−	0.741615i	−0.967166	+	0.254147i	$0.918205\pi$
$68$	−9.29433	−	5.02632i	−1.12710	−	0.609531i
$69$	3.25110	−	1.87702i	0.391386	−	0.225967i
$70$	−6.55633	+	8.71834i	−0.783631	+	1.04204i
$71$	2.32643	+	6.39182i	0.276097	+	0.758570i	0.997796	+	0.0663625i	$0.0211394\pi$
$71$	2.32643	+	6.39182i	0.276097	+	0.758570i	−0.721699	+	0.692207i	$0.756638\pi$
$72$	−0.675473	−	7.88945i	−0.0796053	−	0.929781i
$73$	4.66061	−	0.407751i	0.545484	−	0.0477236i	0.188916	−	0.981993i	$-0.439503\pi$
$73$	4.66061	−	0.407751i	0.545484	−	0.0477236i	0.356567	+	0.934270i	$0.383947\pi$
$74$	−2.44048	−	10.3257i	−0.283700	−	1.20034i
$75$	0.928926	+	2.03676i	0.107263	+	0.235185i
$76$	−1.14550	+	8.64221i	−0.131398	+	0.991330i
$77$	−1.08848	−	1.08848i	−0.124044	−	0.124044i
$78$	−1.76218	−	1.08843i	−0.199527	−	0.123241i
$79$	−2.65348	−	2.22653i	−0.298540	−	0.250504i	0.481197	−	0.876613i	$-0.340202\pi$
$79$	−2.65348	−	2.22653i	−0.298540	−	0.250504i	−0.779736	+	0.626108i	$0.784647\pi$
$80$	−7.96584	−	4.06759i	−0.890608	−	0.454771i
$81$	6.79972	−	2.47490i	0.755524	−	0.274988i
$82$	−0.652555	−	1.97339i	−0.0720626	−	0.217925i
$83$	1.55142	−	5.78996i	0.170290	−	0.635531i	−0.827016	−	0.562178i	$-0.809963\pi$
$83$	1.55142	−	5.78996i	0.170290	−	0.635531i	0.997306	−	0.0733527i	$-0.0233699\pi$
$84$	−2.96020	+	0.882233i	−0.322984	+	0.0962595i
$85$	−8.31816	−	8.38861i	−0.902231	−	0.909873i
$86$	6.46487	+	9.84263i	0.697125	+	1.06136i
$87$	−0.407936	−	1.52244i	−0.0437353	−	0.163222i
$88$	0.725868	−	1.03256i	0.0773777	−	0.110071i
$89$	−6.19419	−	7.38194i	−0.656582	−	0.782484i	0.330309	−	0.943873i	$-0.392847\pi$
$89$	−6.19419	−	7.38194i	−0.656582	−	0.782484i	−0.986891	+	0.161389i	$0.948403\pi$
$90$	1.83213	−	8.66129i	0.193124	−	0.912980i
$91$	3.85942	−	10.6037i	0.404577	−	1.11157i
$92$	−10.4174	+	13.1415i	−1.08609	+	1.37009i
$93$	1.10470	+	1.57768i	0.114553	+	0.163598i
$94$	−4.78280	−	11.1067i	−0.493308	−	1.14557i
$95$	−4.02454	+	8.87711i	−0.412910	+	0.910772i
$96$	−1.12965	−	2.26679i	−0.115295	−	0.231354i
$97$	7.45829	−	5.22235i	0.757275	−	0.530250i	−0.129987	−	0.991516i	$-0.541494\pi$
$97$	7.45829	−	5.22235i	0.757275	−	0.530250i	0.887262	+	0.461266i	$0.152605\pi$
$98$	−3.28469	−	6.10088i	−0.331804	−	0.616282i
$99$	1.17394	+	0.427278i	0.117985	+	0.0429431i
$100$	−7.20702	−	6.93245i	−0.720702	−	0.693245i
$101$	−8.57681	+	7.19680i	−0.853424	+	0.716108i	−0.960541	−	0.278138i	$-0.910283\pi$
$101$	−8.57681	+	7.19680i	−0.853424	+	0.716108i	0.107117	+	0.994246i	$0.465838\pi$
$102$	−0.482771	−	3.31014i	−0.0478014	−	0.327753i
$103$	−5.61715	+	1.50511i	−0.553474	+	0.148303i	−0.524706	−	0.851283i	$-0.675825\pi$
$103$	−5.61715	+	1.50511i	−0.553474	+	0.148303i	−0.0287675	+	0.999586i	$0.509158\pi$
$104$	9.10876	+	1.62357i	0.893187	+	0.159204i
$105$	−3.45343	−	0.0145634i	−0.337020	−	0.00142125i
$106$	−17.9887	−	2.11387i	−1.74721	−	0.205317i
$107$	3.27382	+	0.877217i	0.316492	+	0.0848037i	0.413568	−	0.910473i	$-0.364282\pi$
$107$	3.27382	+	0.877217i	0.316492	+	0.0848037i	−0.0970762	+	0.995277i	$0.530949\pi$
$108$	3.88367	−	3.44757i	0.373707	−	0.331742i
$109$	4.21774	+	11.5882i	0.403987	+	1.10994i	0.960299	+	0.278971i	$0.0899934\pi$
$109$	4.21774	+	11.5882i	0.403987	+	1.10994i	−0.556313	+	0.830973i	$0.687784\pi$
$110$	1.11114	−	0.869878i	0.105943	−	0.0829396i
$111$	2.15914	−	2.57316i	0.204936	−	0.244234i
$112$	10.8447	−	8.53133i	1.02473	−	0.806135i
$113$	6.82874	−	6.82874i	0.642394	−	0.642394i	−0.308750	−	0.951143i	$-0.599911\pi$
$113$	6.82874	−	6.82874i	0.642394	−	0.642394i	0.951143	+	0.308750i	$0.0999105\pi$
$114$	−2.41033	+	1.34443i	−0.225748	+	0.125917i
$115$	−15.4035	+	10.6891i	−1.43639	+	0.996768i
$116$	4.19746	+	5.65277i	0.389725	+	0.524847i
$117$	0.798159	+	9.12300i	0.0737899	+	0.843422i
$118$	3.07949	−	3.45609i	0.283490	−	0.318158i
$119$	17.1256	−	6.23322i	1.56990	−	0.571398i
$120$	−0.474758	−	2.79154i	−0.0433392	−	0.254832i
$121$	−5.40043	−	9.35383i	−0.490949	−	0.850348i
$122$	11.5024	+	14.5656i	1.04138	+	1.31871i
$123$	0.377423	−	0.539016i	0.0340311	−	0.0486015i
$124$	−7.18233	−	4.73664i	−0.644992	−	0.425363i
$125$	−5.46723	−	9.75240i	−0.489004	−	0.872282i
$126$	10.9498	+	8.16240i	0.975489	+	0.727164i
$127$	0.950399	−	10.8631i	0.0843343	−	0.963946i	−0.829674	−	0.558249i	$-0.811473\pi$
$127$	0.950399	−	10.8631i	0.0843343	−	0.963946i	0.914008	−	0.405697i	$-0.132971\pi$
$128$	8.41895	+	7.55787i	0.744137	+	0.668027i
$129$	−1.27508	+	3.50325i	−0.112264	+	0.308444i
$130$	9.22154	+	4.68722i	0.808783	+	0.411096i
$131$	2.29659	+	0.404950i	0.200654	+	0.0353807i	0.273072	−	0.961994i	$-0.411960\pi$
$131$	2.29659	+	0.404950i	0.200654	+	0.0353807i	−0.0724179	+	0.997374i	$0.523072\pi$
$132$	0.399428	−	0.0111271i	0.0347657	−	0.000968493i
$133$	−9.83573	−	11.3732i	−0.852866	−	0.986178i
$134$	5.91968	+	13.7468i	0.511382	+	1.18754i
$135$	5.27242	−	2.43155i	0.453777	−	0.209275i
$136$	7.44751	+	12.9550i	0.638619	+	1.11088i
$137$	4.30300	+	9.22781i	0.367630	+	0.788385i	0.999907	+	0.0136425i	$0.00434268\pi$
$137$	4.30300	+	9.22781i	0.367630	+	0.788385i	−0.632277	+	0.774742i	$0.717880\pi$
$138$	−5.30668	−	0.157697i	−0.451735	−	0.0134241i
$139$	−8.46883	+	7.10619i	−0.718317	+	0.602739i	−0.926919	−	0.375261i	$-0.877553\pi$
$139$	−8.46883	+	7.10619i	−0.718317	+	0.602739i	0.208602	+	0.978001i	$0.433109\pi$
$140$	14.3678	−	5.61741i	1.21430	−	0.474758i
$141$	1.91419	−	3.31547i	0.161204	−	0.279213i
$142$	1.95107	−	9.41959i	0.163730	−	0.790474i
$143$	−0.837275	+	1.19575i	−0.0700165	+	0.0999939i
$144$	−5.05051	+	9.99459i	−0.420876	+	0.832883i
$145$	2.66110	+	7.40838i	0.220993	+	0.615233i
$146$	−5.91069	−	2.97304i	−0.489172	−	0.246051i
$147$	0.927053	−	1.98807i	0.0764620	−	0.163973i
$148$	−4.73740	+	14.2376i	−0.389412	+	1.17032i
$149$	7.99621	−	9.52952i	0.655075	−	0.780688i	−0.331595	−	0.943422i	$-0.607587\pi$
$149$	7.99621	−	9.52952i	0.655075	−	0.780688i	0.986670	+	0.162734i	$0.0520311\pi$
$150$	0.395985	−	3.14099i	0.0323320	−	0.256461i
$151$			6.17619i			0.502611i	0.967908	+	0.251306i	$0.0808600\pi$
$151$			6.17619i			0.502611i	−0.967908	+	0.251306i	$0.919140\pi$
$152$	7.80094	−	9.54701i	0.632740	−	0.774364i
$153$	−10.4585	+	10.4585i	−0.845520	+	0.845520i
$154$	0.500730	+	2.11859i	0.0403500	+	0.170721i
$155$	−6.15191	−	7.39467i	−0.494133	−	0.593954i
$156$	1.31136	+	2.61921i	0.104993	+	0.209704i
$157$	−14.8355	−	6.91793i	−1.18401	−	0.552111i	−0.272003	−	0.962296i	$-0.587686\pi$
$157$	−14.8355	−	6.91793i	−1.18401	−	0.552111i	−0.912002	+	0.410185i	$0.865464\pi$
$158$	1.53797	+	4.65096i	0.122354	+	0.370011i
$159$	−2.86707	−	4.96590i	−0.227373	−	0.393822i
$160$	6.56158	+	10.8141i	0.518738	+	0.854933i
$161$	−5.02260	−	28.4846i	−0.395836	−	2.24490i
$162$	−10.0207	−	2.07558i	−0.787301	−	0.163073i
$163$	7.98685	−	2.14007i	0.625578	−	0.167623i	0.0679159	−	0.997691i	$-0.478365\pi$
$163$	7.98685	−	2.14007i	0.625578	−	0.167623i	0.557662	+	0.830068i	$0.311698\pi$
$164$	−0.681419	+	2.85935i	−0.0532098	+	0.223277i
$165$	0.431033	+	0.117445i	0.0335559	+	0.00914311i
$166$	−6.16962	+	5.81352i	−0.478855	+	0.451216i
$167$	2.98981	−	1.39417i	0.231358	−	0.107884i	−0.303482	−	0.952837i	$-0.598149\pi$
$167$	2.98981	−	1.39417i	0.231358	−	0.107884i	0.534841	+	0.844953i	$0.320372\pi$
$168$	4.21737	+	1.13844i	0.325377	+	0.0878326i
$169$	2.26438	+	0.399272i	0.174183	+	0.0307132i
$170$	3.77422	+	16.2750i	0.289469	+	1.24824i
$171$	11.1353	+	4.99180i	0.851534	+	0.381732i
$172$	−0.463752	−	16.6472i	−0.0353608	−	1.26934i
$173$	−2.24990	−	3.21320i	−0.171057	−	0.244295i	0.724465	−	0.689311i	$-0.242087\pi$
$173$	−2.24990	−	3.21320i	−0.171057	−	0.244295i	−0.895522	+	0.445016i	$0.853198\pi$
$174$	−0.640608	+	2.13497i	−0.0485643	+	0.161851i
$175$	17.1943	−	1.35828i	1.29976	−	0.102676i
$176$	−1.64074	+	0.702930i	−0.123675	+	0.0529853i
$177$	1.45990	+	0.127725i	0.109733	+	0.00960038i
$178$	1.96678	+	13.4853i	0.147416	+	1.01077i
$179$	4.19025	−	7.25773i	0.313194	−	0.542468i	−0.665858	−	0.746079i	$-0.731934\pi$
$179$	4.19025	−	7.25773i	0.313194	−	0.542468i	0.979052	+	0.203610i	$0.0652676\pi$
$180$	−8.64127	+	9.05968i	−0.644082	+	0.675269i
$181$	−1.00005	−	5.67159i	−0.0743334	−	0.421566i	−0.999153	−	0.0411588i	$-0.986895\pi$
$181$	−1.00005	−	5.67159i	−0.0743334	−	0.421566i	0.924819	−	0.380407i	$-0.124216\pi$
$182$	−12.5240	+	9.89011i	−0.928342	+	0.733104i
$183$	−1.52075	+	5.67551i	−0.112417	+	0.419546i
$184$	22.3007	−	8.06990i	1.64403	−	0.594921i
$185$	−9.68028	+	13.7015i	−0.711708	+	1.00736i
$186$	−0.156689	−	2.71926i	−0.0114890	−	0.199386i
$187$	−2.34862	+	0.205477i	−0.171748	+	0.0150260i
$188$	−2.49953	+	16.9180i	−0.182297	+	1.23387i
$189$			8.95702i			0.651528i
$190$	11.4396	−	7.69001i	0.829914	−	0.557892i
$191$		−	9.86117i		−	0.713529i	−0.934194	−	0.356765i	$-0.883880\pi$
$191$		−	9.86117i		−	0.713529i	0.934194	−	0.356765i	$-0.116120\pi$
$192$	−0.325424	+	3.56694i	−0.0234854	+	0.257422i
$193$	18.5686	−	1.62454i	1.33660	−	0.116937i	0.603665	−	0.797238i	$-0.293707\pi$
$193$	18.5686	−	1.62454i	1.33660	−	0.116937i	0.732933	+	0.680301i	$0.238151\pi$
$194$	−12.8549	+	0.740729i	−0.922931	+	0.0531812i
$195$	0.555072	+	3.22750i	0.0397496	+	0.231126i
$196$	−0.581873	+	9.78168i	−0.0415624	+	0.698692i
$197$	−0.282010	+	1.05248i	−0.0200924	+	0.0749859i	−0.975244	−	0.221131i	$-0.929025\pi$
$197$	−0.282010	+	1.05248i	−0.0200924	+	0.0749859i	0.955152	+	0.296117i	$0.0956918\pi$
$198$	−1.09494	−	1.38654i	−0.0778140	−	0.0985372i
$199$	2.94729	+	16.7149i	0.208928	+	1.18489i	0.891138	+	0.453732i	$0.149908\pi$
$199$	2.94729	+	16.7149i	0.208928	+	1.18489i	−0.682211	+	0.731156i	$0.738981\pi$
$200$	3.51948	+	13.6972i	0.248865	+	0.968538i
$201$	−2.36919	+	4.10356i	−0.167110	+	0.289443i
$202$	15.6681	−	2.28513i	1.10240	−	0.160781i
$203$	−12.0976	−	1.05840i	−0.849084	−	0.0742852i
$204$	−1.87914	+	4.34155i	−0.131566	+	0.303969i
$205$	−1.65517	+	2.83913i	−0.115602	+	0.198293i
$206$	7.87711	+	2.36357i	0.548825	+	0.164678i
$207$	13.4640	+	19.2285i	0.935811	+	1.33648i
$208$	−9.75307	−	8.72288i	−0.676254	−	0.604823i
$209$	0.848226	+	1.75044i	0.0586730	+	0.121080i
$210$	4.14435	+	2.58402i	0.285987	+	0.178315i
$211$	10.1663	+	1.79259i	0.699875	+	0.123407i	0.512253	−	0.858834i	$-0.328811\pi$
$211$	10.1663	+	1.79259i	0.699875	+	0.123407i	0.187622	+	0.982241i	$0.439922\pi$
$212$	20.0730	+	15.9121i	1.37862	+	1.09285i
$213$	2.76007	−	1.28704i	0.189117	−	0.0881866i
$214$	−3.28713	−	3.48848i	−0.224704	−	0.238468i
$215$	4.89484	−	17.9644i	0.333825	−	1.22516i
$216$	−7.23498	+	1.26187i	−0.492278	+	0.0858594i
$217$	14.3337	−	3.84069i	0.973033	−	0.260723i
$218$	3.53723	−	17.0774i	0.239571	−	1.15663i
$219$	−0.363726	−	2.06279i	−0.0245783	−	0.139391i
$220$	−1.98340	+	0.220865i	−0.133721	+	0.0148907i
$221$	−8.64116	−	14.9669i	−0.581268	−	1.00679i
$222$	−4.51019	+	1.49141i	−0.302704	+	0.100097i
$223$	26.0971	+	12.1693i	1.74759	+	0.814915i	0.985976	+	0.166886i	$0.0533713\pi$
$223$	26.0971	+	12.1693i	1.74759	+	0.814915i	0.761616	+	0.648029i	$0.224406\pi$
$224$	−19.3887	+	2.20539i	−1.29546	+	0.147354i
$225$	−12.1810	+	6.89638i	−0.812066	+	0.459759i
$226$	−13.2913	+	3.14140i	−0.884123	+	0.208963i
$227$	5.70112	−	5.70112i	0.378396	−	0.378396i	−0.492127	−	0.870523i	$-0.663780\pi$
$227$	5.70112	−	5.70112i	0.378396	−	0.378396i	0.870523	+	0.492127i	$0.163780\pi$
$228$	3.89926	+	0.173682i	0.258235	+	0.0115024i
$229$		−	5.78501i		−	0.382284i	−0.981562	−	0.191142i	$-0.938781\pi$
$229$		−	5.78501i		−	0.382284i	0.981562	−	0.191142i	$-0.0612191\pi$
$230$	26.4774	−	1.41368i	1.74587	−	0.0932156i
$231$	−0.443005	+	0.527952i	−0.0291476	+	0.0347367i
$232$	−0.849397	−	9.92086i	−0.0557656	−	0.651337i
$233$	−3.49933	+	7.50434i	−0.229249	+	0.491626i	−0.986960	−	0.160964i	$-0.948540\pi$
$233$	−3.49933	+	7.50434i	−0.229249	+	0.491626i	0.757711	+	0.652590i	$0.226317\pi$
$234$	5.81963	−	11.5700i	0.380441	−	0.756353i
$235$	−8.15357	+	17.2946i	−0.531881	+	1.12818i
$236$	−6.27372	+	1.86977i	−0.408384	+	0.121711i
$237$	−0.889525	+	1.27037i	−0.0577809	+	0.0825196i
$238$	−25.2379	−	5.22751i	−1.63593	−	0.338849i
$239$	6.95020	−	12.0381i	0.449571	−	0.778679i	−0.548787	−	0.835962i	$-0.684910\pi$
$239$	6.95020	−	12.0381i	0.449571	−	0.778679i	0.998358	+	0.0572826i	$0.0182436\pi$
$240$	−1.50337	+	3.71161i	−0.0970422	+	0.239583i
$241$	6.48250	−	5.43946i	0.417575	−	0.350387i	−0.409665	−	0.912236i	$-0.634354\pi$
$241$	6.48250	−	5.43946i	0.417575	−	0.350387i	0.827240	+	0.561849i	$0.189910\pi$
$242$	−0.453715	+	15.2680i	−0.0291659	+	0.981464i
$243$	−4.66125	−	9.99607i	−0.299019	−	0.641248i
$244$	−3.01485	−	26.0736i	−0.193006	−	1.66919i
$245$	−3.79041	+	10.2790i	−0.242161	+	0.656701i
$246$	−0.854699	+	0.368054i	−0.0544936	+	0.0234662i
$247$	−9.00158	+	11.0582i	−0.572757	+	0.703619i
$248$	5.12163	+	11.0369i	0.325224	+	0.700841i
$249$	−2.64295	−	0.466023i	−0.167490	−	0.0295330i
$250$	−0.669557	+	15.7972i	−0.0423465	+	0.999103i
$251$	4.06815	−	11.1772i	0.256779	−	0.705496i	−0.742582	−	0.669755i	$-0.766399\pi$
$251$	4.06815	−	11.1772i	0.256779	−	0.705496i	0.999361	−	0.0357401i	$-0.0113789\pi$
$252$	−7.10877	−	17.9586i	−0.447811	−	1.13129i
$253$	−0.326108	+	3.72743i	−0.0205022	+	0.234342i
$254$	−9.21671	+	12.3642i	−0.578308	+	0.775799i
$255$	−3.41686	+	4.03736i	−0.213972	+	0.252829i
$256$	−4.51287	−	15.3504i	−0.282054	−	0.959398i
$257$	−5.75587	+	8.22023i	−0.359041	+	0.512764i	−0.957517	−	0.288377i	$-0.906884\pi$
$257$	−5.75587	+	8.22023i	−0.359041	+	0.512764i	0.598476	+	0.801141i	$0.295773\pi$
$258$	4.13770	−	3.26750i	0.257602	−	0.203426i
$259$	−12.9402	−	22.4131i	−0.804066	−	1.39268i
$260$	−7.61195	−	12.4929i	−0.472073	−	0.774775i
$261$	9.26113	−	3.37078i	0.573250	−	0.208646i
$262$	−2.46231	−	2.19400i	−0.152122	−	0.135546i
$263$	2.01709	+	23.0554i	0.124379	+	1.42166i	0.760134	+	0.649766i	$0.225133\pi$
$263$	2.01709	+	23.0554i	0.124379	+	1.42166i	−0.635755	+	0.771891i	$0.719311\pi$
$264$	−0.488861	−	0.283456i	−0.0300873	−	0.0174455i
$265$	16.3272	+	23.5282i	1.00297	+	1.44532i
$266$	3.38212	+	20.9939i	0.207371	+	1.28722i
$267$	−3.05075	+	3.05075i	−0.186703	+	0.186703i
$268$	3.09367	−	20.9395i	0.188976	−	1.27908i
$269$	−0.331898	+	0.395540i	−0.0202362	+	0.0241165i	−0.776068	−	0.630650i	$-0.782788\pi$
$269$	−0.331898	+	0.395540i	−0.0202362	+	0.0241165i	0.755831	+	0.654766i	$0.227233\pi$
$270$	−8.15084	−	0.992678i	−0.496044	−	0.0604124i
$271$	−4.44948	−	12.2248i	−0.270286	−	0.742606i	−0.998368	−	0.0571150i	$-0.981810\pi$
$271$	−4.44948	−	12.2248i	−0.270286	−	0.742606i	0.728081	−	0.685491i	$-0.240412\pi$
$272$	0.666956	−	21.1222i	0.0404401	−	1.28072i
$273$	−4.87999	−	1.30759i	−0.295351	−	0.0791389i
$274$	1.68050	−	14.3008i	0.101523	−	0.863942i
$275$	−2.19397	−	0.405965i	−0.132301	−	0.0244806i
$276$	6.26781	+	4.13353i	0.377278	+	0.248809i
$277$	8.10395	−	2.17145i	0.486919	−	0.130470i	−0.00700347	−	0.999975i	$-0.502229\pi$
$277$	8.10395	−	2.17145i	0.486919	−	0.130470i	0.493923	+	0.869506i	$0.335563\pi$
$278$	15.4708	−	2.25636i	0.927880	−	0.135328i
$279$	−9.22553	+	7.74114i	−0.552318	+	0.463450i
$280$	−21.4621	−	3.91892i	−1.28261	−	0.234200i
$281$	−11.7806	−	4.28778i	−0.702770	−	0.255787i	−0.0341768	−	0.999416i	$-0.510881\pi$
$281$	−11.7806	−	4.28778i	−0.702770	−	0.255787i	−0.668593	+	0.743628i	$0.733103\pi$
$282$	−4.76712	+	2.56660i	−0.283878	+	0.152839i
$283$	11.9175	−	8.34470i	0.708420	−	0.496041i	−0.162970	−	0.986631i	$-0.552108\pi$
$283$	11.9175	−	8.34470i	0.708420	−	0.496041i	0.871391	+	0.490590i	$0.163219\pi$
$284$	−9.34793	+	9.88367i	−0.554697	+	0.586488i
$285$	4.11637	+	1.44861i	0.243833	+	0.0858084i
$286$	1.89606	−	0.816490i	0.112117	−	0.0482801i
$287$	−2.90795	−	4.15299i	−0.171651	−	0.245143i
$288$	13.5045	−	8.27209i	0.795760	−	0.487438i
$289$	3.73217	−	10.2540i	0.219539	−	0.603179i
$290$	2.30388	−	10.8914i	0.135288	−	0.639567i
$291$	−2.62028	−	3.12273i	−0.153604	−	0.183058i
$292$	4.90225	+	7.96984i	0.286883	+	0.466399i
$293$	1.98529	+	7.40920i	0.115982	+	0.432850i	0.999358	−	0.0358137i	$-0.0114023\pi$
$293$	1.98529	+	7.40920i	0.115982	+	0.432850i	−0.883377	+	0.468664i	$0.844736\pi$
$294$	−2.59291	+	1.70309i	−0.151222	+	0.0993260i
$295$	−7.31905	−	0.0308651i	−0.426132	−	0.00179704i
$296$	16.2810	−	13.6100i	0.946317	−	0.791063i
$297$	0.299894	−	1.11922i	0.0174016	−	0.0649436i
$298$	−16.7031	+	5.52334i	−0.967587	+	0.319959i
$299$	−25.7742	+	9.38105i	−1.49056	+	0.542520i
$300$	−2.81075	+	3.48495i	−0.162279	+	0.201204i
$301$	22.0038	+	18.4634i	1.26828	+	1.06421i
$302$	4.58999	−	7.43120i	0.264124	−	0.427618i
$303$	3.54456	+	3.54456i	0.203630	+	0.203630i
$304$	−16.4812	+	5.68951i	−0.945261	+	0.326316i
$305$	5.21761	−	28.8779i	0.298759	−	1.65354i
$306$	20.3562	−	4.81119i	1.16368	−	0.275037i
$307$	−30.5792	+	2.67533i	−1.74524	+	0.152689i	−0.914665	−	0.404212i	$-0.867546\pi$
$307$	−30.5792	+	2.67533i	−1.74524	+	0.152689i	−0.830579	+	0.556901i	$0.811990\pi$
$308$	0.972003	−	2.92122i	0.0553850	−	0.166452i
$309$	0.890490	+	2.44660i	0.0506582	+	0.139182i
$310$	1.90646	+	13.4692i	0.108279	+	0.765000i
$311$	11.3145	−	6.53244i	0.641588	−	0.370421i	−0.143638	−	0.989630i	$-0.545880\pi$
$311$	11.3145	−	6.53244i	0.641588	−	0.370421i	0.785226	+	0.619209i	$0.212547\pi$
$312$	0.368702	−	4.12600i	0.0208737	−	0.233589i
$313$	5.38424	+	3.77009i	0.304335	+	0.213098i	0.715761	−	0.698346i	$-0.246080\pi$
$313$	5.38424	+	3.77009i	0.304335	+	0.213098i	−0.411426	+	0.911443i	$0.634969\pi$
$314$	12.7089	+	19.3491i	0.717206	+	1.09193i
$315$	−1.79132	−	21.5198i	−0.100930	−	1.21250i
$316$	1.60599	−	6.73902i	0.0903441	−	0.379099i
$317$	−33.3764	−	2.92005i	−1.87460	−	0.164007i	−0.907779	−	0.419449i	$-0.862223\pi$
$317$	−33.3764	−	2.92005i	−1.87460	−	0.164007i	−0.966824	+	0.255443i	$0.917779\pi$
$318$	−0.240875	+	8.10571i	−0.0135076	+	0.454546i
$319$	1.47621	+	0.537296i	0.0826518	+	0.0300828i
$320$	0.141892	−	17.8880i	0.00793202	−	0.999969i
$321$	0.263503	−	1.49440i	0.0147073	−	0.0834094i
$322$	−15.1258	+	38.0053i	−0.842928	+	2.11795i
$323$	−23.0263	+	0.343187i	−1.28122	+	0.0190954i
$324$	10.5144	+	9.94447i	0.584134	+	0.552471i
$325$	−4.09983	−	15.8338i	−0.227418	−	0.878300i
$326$	−11.2002	−	3.36069i	−0.620323	−	0.186131i
$327$	5.00391	−	2.33336i	0.276717	−	0.129035i
$328$	2.94488	−	2.93396i	0.162604	−	0.162001i
$329$	−18.9601	−	22.5958i	−1.04530	−	1.24574i
$330$	−0.431337	−	0.461643i	−0.0237443	−	0.0254126i
$331$	13.3821	+	7.72617i	0.735547	+	0.424669i	0.820448	−	0.571721i	$-0.193724\pi$
$331$	13.3821	+	7.72617i	0.735547	+	0.424669i	−0.0849007	+	0.996389i	$0.527057\pi$
$332$	11.7437	−	2.40973i	0.644522	−	0.132251i
$333$	17.2052	+	12.0472i	0.942840	+	0.660184i
$334$	−4.63345	−	0.544481i	−0.253531	−	0.0297927i
$335$	10.0917	−	21.4055i	0.551368	−	1.16951i
$336$	−4.22828	−	4.50401i	−0.230672	−	0.245714i
$337$	−19.0447	−	8.88070i	−1.03743	−	0.483763i	−0.172162	−	0.985069i	$-0.555075\pi$
$337$	−19.0447	−	8.88070i	−1.03743	−	0.483763i	−0.865270	+	0.501306i	$0.832853\pi$
$338$	−2.42778	−	2.16324i	−0.132054	−	0.117665i
$339$	−3.31219	−	2.77926i	−0.179893	−	0.150948i
$340$	7.55404	−	22.3870i	0.409675	−	1.21411i
$341$	−1.91964			−0.103955
$342$	−9.68817	−	14.2816i	−0.523876	−	0.772259i
$343$	5.12359	+	5.12359i	0.276648	+	0.276648i
$344$	−11.8138	+	20.3746i	−0.636956	+	1.09852i
$345$	5.36859	+	6.45311i	0.289035	+	0.347424i
$346$	0.319122	+	5.53819i	0.0171561	+	0.297735i
$347$	6.71658	−	14.4037i	0.360565	−	0.773234i	−0.639426	−	0.768853i	$-0.720828\pi$
$347$	6.71658	−	14.4037i	0.360565	−	0.773234i	0.999990	−	0.00438074i	$-0.00139444\pi$
$348$	2.35743	−	2.09271i	0.126372	−	0.112181i
$349$	7.23066	−	4.17463i	0.387049	−	0.223463i	−0.293832	−	0.955857i	$-0.594931\pi$
$349$	7.23066	−	4.17463i	0.387049	−	0.223463i	0.680881	+	0.732394i	$0.261597\pi$
$350$	−21.6976	−	11.1440i	−1.15978	−	0.595674i
$351$	8.36482	−	1.47494i	0.446481	−	0.0787267i
$352$	2.49653	+	0.373587i	0.133066	+	0.0199122i
$353$	6.70076	+	25.0076i	0.356645	+	1.33102i	0.878401	+	0.477924i	$0.158611\pi$
$353$	6.70076	+	25.0076i	0.356645	+	1.33102i	−0.521756	+	0.853095i	$0.674723\pi$
$354$	−1.66163	−	1.23864i	−0.0883148	−	0.0658329i
$355$	−13.2040	+	7.54929i	−0.700797	+	0.400675i
$356$	7.65551	−	17.6872i	0.405741	−	0.937420i
$357$	−3.44837	−	7.39506i	−0.182507	−	0.391388i
$358$	−10.4355	+	5.61842i	−0.551532	+	0.296943i
$359$	−6.12019	+	34.7093i	−0.323011	+	1.83189i	0.200286	+	0.979737i	$0.435813\pi$
$359$	−6.12019	+	34.7093i	−0.323011	+	1.83189i	−0.523297	+	0.852150i	$0.675298\pi$
$360$	17.1301	−	4.47865i	0.902836	−	0.236045i
$361$	7.02758	+	17.6526i	0.369873	+	0.929083i
$362$	−3.01171	+	7.56727i	−0.158292	+	0.397727i
$363$	−3.96122	+	2.77367i	−0.207910	+	0.145580i
$364$	22.4190	−	2.59227i	1.17507	−	0.135872i
$365$	2.66494	+	10.1161i	0.139489	+	0.529502i
$366$	6.04766	−	5.69860i	0.316116	−	0.297871i
$367$	−1.11633	+	12.7597i	−0.0582719	+	0.666051i	0.909745	+	0.415167i	$0.136277\pi$
$367$	−1.11633	+	12.7597i	−0.0582719	+	0.666051i	−0.968017	+	0.250884i	$0.919279\pi$
$368$	−32.8295	−	6.86357i	−1.71136	−	0.357788i
$369$	3.56328	+	2.05726i	0.185497	+	0.107097i
$370$	21.8299	−	9.29156i	1.13488	−	0.483045i
$371$	−43.5089	+	7.67179i	−2.25887	+	0.398299i
$372$	−1.83235	+	3.38826i	−0.0950030	+	0.175673i
$373$	3.66858	+	0.982992i	0.189952	+	0.0508974i	0.352541	−	0.935796i	$-0.385318\pi$
$373$	3.66858	+	0.982992i	0.189952	+	0.0508974i	−0.162589	+	0.986694i	$0.551984\pi$
$374$	2.97856	+	1.49820i	0.154018	+	0.0774701i
$375$	−4.13638	+	2.81902i	−0.213602	+	0.145574i
$376$	15.5805	−	18.4982i	0.803502	−	0.953972i
$377$	1.00367	+	11.4720i	0.0516918	+	0.590840i
$378$	6.65663	−	10.7771i	0.342380	−	0.554314i
$379$	27.4821			1.41166			0.705829	−	0.708382i	$-0.250575\pi$
$379$	27.4821			1.41166			0.705829	+	0.708382i	$0.250575\pi$
$380$	−19.4791	+	0.751027i	−0.999258	+	0.0385269i
$381$	−4.88220			−0.250123
$382$	−7.32857	+	11.8650i	−0.374962	+	0.607064i
$383$	0.330111	+	3.77319i	0.0168679	+	0.192801i	0.999953	+	0.00965372i	$0.00307292\pi$
$383$	0.330111	+	3.77319i	0.0168679	+	0.192801i	−0.983086	+	0.183147i	$0.941372\pi$
$384$	3.04241	−	4.04990i	0.155257	−	0.206670i
$385$	1.98617	−	2.81123i	0.101224	−	0.143274i
$386$	−23.5491	−	11.8451i	−1.19862	−	0.602897i
$387$	−22.5170	−	6.03342i	−1.14460	−	0.306696i
$388$	16.0176	+	8.66221i	0.813169	+	0.439757i
$389$	1.15337	−	0.203370i	0.0584780	−	0.0103113i	−0.144333	−	0.989529i	$-0.546104\pi$
$389$	1.15337	−	0.203370i	0.0584780	−	0.0103113i	0.202811	+	0.979218i	$0.434992\pi$
$390$	1.73073	−	4.29585i	0.0876391	−	0.217529i
$391$	−38.3638	−	22.1493i	−1.94014	−	1.12014i
$392$	7.96960	−	11.3369i	0.402526	−	0.572600i
$393$	0.0909982	−	1.04011i	0.00459025	−	0.0524668i
$394$	1.12149	−	1.05676i	0.0564998	−	0.0532387i
$395$	3.90098	−	6.69136i	0.196279	−	0.336679i
$396$	0.286991	+	2.48202i	0.0144219	+	0.124726i
$397$	−1.87730	+	1.31450i	−0.0942190	+	0.0659729i	−0.619737	−	0.784810i	$-0.712761\pi$
$397$	−1.87730	+	1.31450i	−0.0942190	+	0.0659729i	0.525518	+	0.850783i	$0.323872\pi$
$398$	8.87590	−	22.3017i	0.444909	−	1.11788i
$399$	−4.68880	+	4.83068i	−0.234734	+	0.241836i
$400$	5.94477	−	19.0961i	0.297238	−	0.954803i
$401$	−2.74821	+	15.5859i	−0.137239	+	0.778322i	0.836035	+	0.548676i	$0.184868\pi$
$401$	−2.74821	+	15.5859i	−0.137239	+	0.778322i	−0.973274	+	0.229646i	$0.926243\pi$
$402$	5.90027	−	3.17668i	0.294279	−	0.158439i
$403$	−5.94708	−	12.7535i	−0.296245	−	0.635299i
$404$	−20.5501	−	8.89465i	−1.02241	−	0.442526i
$405$	8.03105	+	14.0467i	0.399066	+	0.697984i
$406$	13.7692	+	10.2641i	0.683356	+	0.509398i
$407$	0.866513	+	3.23387i	0.0429515	+	0.160297i
$408$	5.48751	−	3.82722i	0.271672	−	0.189476i
$409$	5.72529	−	1.00952i	0.283098	−	0.0499177i	−0.0302963	−	0.999541i	$-0.509645\pi$
$409$	5.72529	−	1.00952i	0.283098	−	0.0499177i	0.313394	+	0.949623i	$0.398534\pi$
$410$	4.10147	−	2.18596i	0.202557	−	0.107957i
$411$	3.94783	−	2.27928i	0.194732	−	0.112429i
$412$	−7.72121	−	8.69792i	−0.380397	−	0.428516i
$413$	4.77184	−	10.2332i	0.234807	−	0.503545i
$414$	−1.90971	−	33.1419i	−0.0938569	−	1.62883i
$415$	13.3474	+	1.22449i	0.655199	+	0.0601077i
$416$	5.25229	+	17.7436i	0.257514	+	0.869952i
$417$	3.49994	+	3.49994i	0.171393	+	0.171393i
$418$	0.280294	−	2.73651i	0.0137096	−	0.133847i
$419$	−3.41996			−0.167076			−0.0835379	−	0.996505i	$-0.526622\pi$
$419$	−3.41996			−0.167076			−0.0835379	+	0.996505i	$0.526622\pi$
$420$	−3.06610	−	6.18907i	−0.149611	−	0.301996i
$421$	−8.91647	−	7.48181i	−0.434562	−	0.364641i	0.399108	−	0.916904i	$-0.369320\pi$
$421$	−8.91647	−	7.48181i	−0.434562	−	0.364641i	−0.833670	+	0.552263i	$0.813764\pi$
$422$	−10.8999	−	9.71216i	−0.530597	−	0.472781i
$423$	21.6956	+	10.1168i	1.05488	+	0.491898i
$424$	−12.3264	−	34.0632i	−0.598623	−	1.65426i
$425$	15.3335	−	21.5101i	0.743786	−	1.04339i
$426$	−4.27741	−	0.502643i	−0.207241	−	0.0243531i
$427$	37.0838	+	25.9664i	1.79461	+	1.25660i
$428$	1.36253	+	6.64026i	0.0658605	+	0.320969i
$429$	0.565996	+	0.326778i	0.0273265	+	0.0157770i
$430$	−19.2402	+	17.9771i	−0.927843	+	0.866932i
$431$	19.8917	+	23.7060i	0.958149	+	1.14188i	0.989812	+	0.142379i	$0.0454753\pi$
$431$	19.8917	+	23.7060i	0.958149	+	1.14188i	−0.0316629	+	0.999499i	$0.510080\pi$
$432$	9.64293	+	3.85857i	0.463946	+	0.185645i
$433$	−9.94484	+	4.63735i	−0.477918	+	0.222857i	−0.646623	−	0.762810i	$-0.723819\pi$
$433$	−9.94484	+	4.63735i	−0.477918	+	0.222857i	0.168705	+	0.985667i	$0.446042\pi$
$434$	−20.1006	−	6.03128i	−0.964859	−	0.289511i
$435$	3.20041	−	1.47598i	0.153448	−	0.0707677i
$436$	−16.9475	+	17.9188i	−0.811637	+	0.858153i
$437$	−5.80951	+	36.0839i	−0.277906	+	1.72613i
$438$	−1.09538	+	2.75227i	−0.0523393	+	0.131508i
$439$	−3.87605	+	21.9822i	−0.184994	+	1.04915i	0.740970	+	0.671538i	$0.234366\pi$
$439$	−3.87605	+	21.9822i	−0.184994	+	1.04915i	−0.925964	+	0.377613i	$0.876745\pi$
$440$	2.55057	+	1.20827i	0.121594	+	0.0576018i
$441$	12.8892	+	4.69127i	0.613769	+	0.223394i
$442$	−0.725983	+	24.4301i	−0.0345315	+	1.16202i
$443$	1.30243	+	0.113948i	0.0618803	+	0.00541382i	0.118054	−	0.993007i	$-0.462334\pi$
$443$	1.30243	+	0.113948i	0.0618803	+	0.00541382i	−0.0561735	+	0.998421i	$0.517890\pi$
$444$	6.53504	+	1.55738i	0.310139	+	0.0739101i
$445$	13.9201	−	16.4480i	0.659876	−	0.779709i
$446$	−22.3562	−	34.0368i	−1.05860	−	1.61169i
$447$	−4.56233	−	3.19458i	−0.215791	−	0.151098i
$448$	24.9674	+	11.7556i	1.17960	+	0.555401i
$449$	13.9593	−	8.05942i	0.658781	−	0.380348i	−0.133031	−	0.991112i	$-0.542471\pi$
$449$	13.9593	−	8.05942i	0.658781	−	0.380348i	0.791813	+	0.610764i	$0.209138\pi$
$450$	19.7814	+	0.754871i	0.932504	+	0.0355849i
$451$	0.224313	+	0.616295i	0.0105625	+	0.0290202i
$452$	18.3267	+	6.09800i	0.862015	+	0.286826i
$453$	2.75468	−	0.241003i	0.129426	−	0.0113233i
$454$	−11.0965	+	2.62267i	−0.520785	+	0.123088i
$455$	24.8302	+	4.48627i	1.16406	+	0.210320i
$456$	−4.56251	−	3.10680i	−0.213659	−	0.145489i
$457$	−3.36009	−	3.36009i	−0.157178	−	0.157178i	0.624137	−	0.781315i	$-0.285451\pi$
$457$	−3.36009	−	3.36009i	−0.157178	−	0.157178i	−0.781315	+	0.624137i	$0.785451\pi$
$458$	−4.29927	+	6.96052i	−0.200892	+	0.325244i
$459$	10.5087	+	8.81787i	0.490505	+	0.411583i
$460$	−32.9083	−	17.9764i	−1.53436	−	0.838154i
$461$	11.1338	−	4.05236i	0.518551	−	0.188737i	−0.0694683	−	0.997584i	$-0.522130\pi$
$461$	11.1338	−	4.05236i	0.518551	−	0.188737i	0.588019	+	0.808847i	$0.299908\pi$
$462$	0.925384	−	0.306003i	0.0430528	−	0.0142366i
$463$	3.37178	−	12.5836i	0.156700	−	0.584812i	−0.842254	−	0.539081i	$-0.818772\pi$
$463$	3.37178	−	12.5836i	0.156700	−	0.584812i	0.998954	−	0.0457307i	$-0.0145616\pi$
$464$	−6.35093	+	12.5680i	−0.294835	+	0.583457i
$465$	−3.05808	+	3.03239i	−0.141815	+	0.140624i
$466$	9.78743	−	6.42862i	0.453394	−	0.297800i
$467$	1.87006	+	6.97914i	0.0865359	+	0.322956i	0.995601	−	0.0936986i	$-0.0298690\pi$
$467$	1.87006	+	6.97914i	0.0865359	+	0.322956i	−0.909065	+	0.416655i	$0.863202\pi$
$468$	−15.6007	+	9.59600i	−0.721142	+	0.443575i
$469$	23.4669	+	27.9668i	1.08360	+	1.29139i
$470$	22.6633	−	14.7494i	1.04538	−	0.680337i
$471$	−2.50660	+	6.88683i	−0.115498	+	0.317328i
$472$	8.93811	+	2.41276i	0.411410	+	0.111056i
$473$	−2.13129	−	3.04379i	−0.0979967	−	0.139954i
$474$	2.01439	−	0.867442i	0.0925238	−	0.0398429i
$475$	−21.0879	−	5.50453i	−0.967580	−	0.252565i
$476$	26.4814	+	25.0459i	1.21377	+	1.14798i
$477$	29.3707	−	20.5656i	1.34479	−	0.941634i
$478$	−17.3089	+	9.31904i	−0.791690	+	0.426243i
$479$	9.32926	+	3.39557i	0.426265	+	0.155148i	0.546239	−	0.837629i	$-0.316059\pi$
$479$	9.32926	+	3.39557i	0.426265	+	0.155148i	−0.119974	+	0.992777i	$0.538281\pi$
$480$	4.56723	−	3.34855i	0.208465	−	0.152840i
$481$	−18.8004	+	15.7754i	−0.857225	+	0.719297i
$482$	−11.8422	+	1.72714i	−0.539398	+	0.0786691i
$483$	−12.5086	+	3.35166i	−0.569159	+	0.152506i
$484$	11.8927	−	18.0333i	0.540577	−	0.819694i
$485$	14.3353	+	14.4567i	0.650931	+	0.656444i
$486$	−1.82041	+	15.4914i	−0.0825754	+	0.702704i
$487$	−39.6070	−	10.6127i	−1.79477	−	0.480906i	−0.801624	−	0.597828i	$-0.796031\pi$
$487$	−39.6070	−	10.6127i	−1.79477	−	0.480906i	−0.993141	+	0.116922i	$0.962697\pi$
$488$	−15.7498	+	33.6124i	−0.712960	+	1.52156i
$489$	−1.26616	−	3.47875i	−0.0572578	−	0.157314i
$490$	12.1997	−	9.55075i	0.551127	−	0.431459i
$491$	−8.36278	+	9.96638i	−0.377407	+	0.449776i	−0.920994	−	0.389577i	$-0.872621\pi$
$491$	−8.36278	+	9.96638i	−0.377407	+	0.449776i	0.543587	+	0.839353i	$0.317066\pi$
$492$	1.30190	+	0.192348i	0.0586943	+	0.00867170i
$493$	−13.1514	+	13.1514i	−0.592309	+	0.592309i
$494$	19.0489	−	6.61554i	0.857051	−	0.297647i
$495$	−0.496678	+	2.74896i	−0.0223240	+	0.123557i
$496$	2.03995	−	17.0858i	0.0915966	−	0.767176i
$497$	−2.04503	−	23.3748i	−0.0917320	−	1.04850i
$498$	2.83366	+	2.52489i	0.126979	+	0.113143i
$499$	1.92260	−	0.699771i	0.0860676	−	0.0313260i	−0.298628	−	0.954370i	$-0.596529\pi$
$499$	1.92260	−	0.699771i	0.0860676	−	0.0313260i	0.384695	+	0.923044i	$0.374307\pi$
$500$	12.5457	−	18.5096i	0.561060	−	0.827775i
$501$	−0.738487	−	1.27910i	−0.0329932	−	0.0571459i
$502$	−13.2014	+	10.4250i	−0.589206	+	0.465291i
$503$	4.90313	−	7.00239i	0.218620	−	0.312221i	−0.694829	−	0.719175i	$-0.744520\pi$
$503$	4.90313	−	7.00239i	0.218620	−	0.312221i	0.913449	+	0.406954i	$0.133409\pi$
$504$	−4.79311	+	26.8909i	−0.213502	+	1.19782i
$505$	−19.1103	−	16.1733i	−0.850397	−	0.719701i
$506$	3.16250	−	4.24249i	0.140590	−	0.188602i
$507$	0.0897223	−	1.02553i	0.00398471	−	0.0455454i
$508$	20.2783	−	8.02699i	0.899704	−	0.356140i
$509$	9.45345	−	25.9732i	0.419017	−	1.15124i	−0.533246	−	0.845960i	$-0.679028\pi$
$509$	9.45345	−	25.9732i	0.419017	−	1.15124i	0.952263	−	0.305279i	$-0.0987498\pi$
$510$	7.11164	−	2.31843i	0.314909	−	0.102662i
$511$	−15.8933	−	2.80242i	−0.703079	−	0.123972i
$512$	−5.97811	+	21.8234i	−0.264198	+	0.964469i
$513$	3.71212	−	10.6921i	0.163894	−	0.472068i
$514$	13.0345	−	5.61298i	0.574929	−	0.247578i
$515$	−5.44573	−	11.8082i	−0.239967	−	0.520329i
$516$	−7.40680	+	0.856435i	−0.326066	+	0.0377025i
$517$	1.61261	+	3.45824i	0.0709223	+	0.152093i
$518$	−1.08717	+	36.5843i	−0.0477674	+	1.60742i
$519$	−1.34534	+	1.12887i	−0.0590539	+	0.0495521i
$520$	−0.125675	+	20.6884i	−0.00551122	+	0.907248i
$521$	4.08486	−	7.07518i	0.178961	−	0.309969i	−0.762564	−	0.646913i	$-0.776060\pi$
$521$	4.08486	−	7.07518i	0.178961	−	0.309969i	0.941525	+	0.336943i	$0.109393\pi$
$522$	−13.6481	−	2.82691i	−0.597360	−	0.123731i
$523$	20.2023	−	28.8518i	0.883383	−	1.26160i	−0.0808982	−	0.996722i	$-0.525779\pi$
$523$	20.2023	−	28.8518i	0.883383	−	1.26160i	0.964281	−	0.264880i	$-0.0853322\pi$
$524$	1.33212	+	4.46974i	0.0581941	+	0.195262i
$525$	−1.27675	−	7.61590i	−0.0557221	−	0.332385i
$526$	14.7072	−	29.2393i	0.641265	−	1.27490i
$527$	9.60493	−	20.5978i	0.418397	−	0.897256i
$528$	0.377541	+	0.704364i	0.0164304	+	0.0306535i
$529$	−30.4073	+	36.2380i	−1.32206	+	1.57556i
$530$	−2.15934	−	40.4431i	−0.0937957	−	1.75673i
$531$			9.16351i			0.397662i
$532$	11.5327	−	27.7733i	0.500007	−	1.20413i
$533$	−3.39956	+	3.39956i	−0.147251	+	0.147251i
$534$	5.93791	−	1.40343i	0.256959	−	0.0607323i
$535$	−0.692361	+	7.54702i	−0.0299334	+	0.326286i
$536$	−19.2840	+	22.8952i	−0.832941	+	0.988924i
$537$	−3.40057	−	1.58571i	−0.146745	−	0.0684285i
$538$	0.693295	−	0.229257i	0.0298901	−	0.00988395i
$539$	1.09318	+	1.89344i	0.0470866	+	0.0815564i
$540$	9.06937	+	7.25188i	0.390283	+	0.312071i
$541$	5.33108	+	30.2340i	0.229201	+	1.29986i	0.854489	+	0.519469i	$0.173870\pi$
$541$	5.33108	+	30.2340i	0.229201	+	1.29986i	−0.625288	+	0.780394i	$0.715019\pi$
$542$	−3.73157	+	18.0157i	−0.160285	+	0.773839i
$543$	−2.49059	+	0.667352i	−0.106881	+	0.0286388i
$544$	−16.5000	+	24.9186i	−0.707431	+	1.06838i
$545$	−23.9385	+	13.6866i	−1.02541	+	0.586270i
$546$	4.89984	+	5.19998i	0.209694	+	0.222538i
$547$	21.3228	−	9.94299i	0.911698	−	0.425132i	0.0905793	−	0.995889i	$-0.471128\pi$
$547$	21.3228	−	9.94299i	0.911698	−	0.425132i	0.821119	+	0.570758i	$0.193350\pi$
$548$	−12.6499	+	15.9578i	−0.540379	+	0.681684i
$549$	−36.1822	−	6.37990i	−1.54422	−	0.272288i
$550$	2.33809	+	2.11896i	0.0996963	+	0.0903528i
$551$	14.0024	+	6.27711i	0.596522	+	0.267414i
$552$	−4.46950	−	9.63154i	−0.190234	−	0.409945i
$553$	6.85357	+	9.78791i	0.291443	+	0.416224i
$554$	−11.3644	−	3.40996i	−0.482829	−	0.144875i
$555$	6.48883	+	3.78290i	0.275435	+	0.160575i
$556$	−20.2914	−	8.78268i	−0.860547	−	0.372468i
$557$	19.2762	+	1.68645i	0.816760	+	0.0714572i	0.487876	−	0.872913i	$-0.337772\pi$
$557$	19.2762	+	1.68645i	0.816760	+	0.0714572i	0.328884	+	0.944370i	$0.393327\pi$
$558$	16.8532	−	2.45797i	0.713452	−	0.104054i
$559$	13.6193	−	23.5893i	0.576035	−	0.997723i
$560$	22.9108	+	20.6653i	0.968157	+	0.873269i
$561$	0.183292	+	1.03950i	0.00773859	+	0.0438877i
$562$	10.9878	+	13.9141i	0.463493	+	0.586930i
$563$	6.63772	−	24.7723i	0.279746	−	1.04403i	−0.672847	−	0.739782i	$-0.734929\pi$
$563$	6.63772	−	24.7723i	0.279746	−	1.04403i	0.952593	−	0.304246i	$-0.0984046\pi$
$564$	7.64323	+	0.454665i	0.321838	+	0.0191449i
$565$	17.6367	+	12.4605i	0.741981	+	0.524217i
$566$	−20.5407	+	1.18360i	−0.863389	+	0.0497503i
$567$	−24.8664	+	2.17553i	−1.04429	+	0.0913637i
$568$	18.5927	−	4.94491i	0.780133	−	0.207484i
$569$		−	10.5808i		−	0.443572i	−0.975095	−	0.221786i	$-0.928811\pi$
$569$		−	10.5808i		−	0.443572i	0.975095	−	0.221786i	$-0.0711886\pi$
$570$	−3.87625	−	4.80215i	−0.162358	−	0.201140i
$571$		−	14.5819i		−	0.610232i	−0.952315	−	0.305116i	$-0.901305\pi$
$571$		−	14.5819i		−	0.610232i	0.952315	−	0.305116i	$-0.0986952\pi$
$572$	−2.88814	−	0.426704i	−0.120759	−	0.0178414i
$573$	−4.39823	+	0.384795i	−0.183739	+	0.0160751i
$574$	0.412459	+	7.15799i	0.0172157	+	0.298769i
$575$	−29.3938	−	29.8938i	−1.22580	−	1.24666i
$576$	−22.3962	−	0.0832032i	−0.933176	−	0.00346680i
$577$	−7.19473	+	26.8511i	−0.299521	+	1.11783i	0.638040	+	0.770003i	$0.279745\pi$
$577$	−7.19473	+	26.8511i	−0.299521	+	1.11783i	−0.937560	+	0.347822i	$0.886921\pi$
$578$	−12.1111	+	9.56403i	−0.503755	+	0.397811i
$579$	−1.44914	−	8.21849i	−0.0602242	−	0.341549i
$580$	−10.8663	+	11.3924i	−0.451197	+	0.473044i
$581$	−10.3387	+	17.9072i	−0.428922	+	0.742914i
$582$	0.831993	+	5.70460i	0.0344872	+	0.236463i
$583$	5.69348	+	0.498115i	0.235800	+	0.0206298i
$584$	0.0245797	−	13.2325i	0.00101712	−	0.547566i
$585$	−19.8020	+	5.21653i	−0.818712	+	0.215677i
$586$	3.11762	−	10.3902i	0.128788	−	0.429214i
$587$	17.6324	+	25.1816i	0.727766	+	1.03936i	0.997084	+	0.0763058i	$0.0243125\pi$
$587$	17.6324	+	25.1816i	0.727766	+	1.03936i	−0.269319	+	0.963051i	$0.586799\pi$
$588$	4.38548	−	0.122169i	0.180854	−	0.00503818i
$589$	−18.7020	−	1.35571i	−0.770603	−	0.0558610i
$590$	8.78335	+	5.47647i	0.361605	+	0.225463i
$591$	0.480425	+	0.0847119i	0.0197621	+	0.00348458i
$592$	−29.7039	+	4.27587i	−1.22082	+	0.175737i
$593$	−30.9490	+	14.4317i	−1.27092	+	0.592640i	−0.936792	−	0.349887i	$-0.886220\pi$
$593$	−30.9490	+	14.4317i	−1.27092	+	0.592640i	−0.334129	+	0.942527i	$0.608442\pi$
$594$	−1.19261	+	1.12377i	−0.0489332	+	0.0461089i
$595$	20.2268	+	35.3776i	0.829219	+	1.45034i
$596$	24.2020	+	5.76765i	0.991354	+	0.236252i
$597$	7.34009	−	1.96677i	0.300410	−	0.0804946i
$598$	37.9833	+	7.86745i	1.55325	+	0.321724i
$599$	−6.24257	−	35.4033i	−0.255064	−	1.44654i	−0.795908	−	0.605418i	$-0.793006\pi$
$599$	−6.24257	−	35.4033i	−0.255064	−	1.44654i	0.540843	−	0.841123i	$-0.318105\pi$
$600$	5.97183	−	2.10422i	0.243799	−	0.0859045i
$601$	−2.11945	−	3.67099i	−0.0864541	−	0.149743i	0.819556	−	0.572999i	$-0.194220\pi$
$601$	−2.11945	−	3.67099i	−0.0864541	−	0.149743i	−0.906010	+	0.423257i	$0.860887\pi$
$602$	−12.7535	−	38.5678i	−0.519793	−	1.57191i
$603$	−26.8527	−	12.5216i	−1.09353	−	0.509920i
$604$	−11.0454	+	5.53007i	−0.449429	+	0.225015i
$605$	18.5664	−	15.4461i	0.754832	−	0.627974i
$606$	−1.63059	−	6.89904i	−0.0662383	−	0.280254i
$607$	29.0169	−	29.0169i	1.17776	−	1.17776i	0.197446	−	0.980314i	$-0.436735\pi$
$607$	29.0169	−	29.0169i	1.17776	−	1.17776i	0.980314	−	0.197446i	$-0.0632648\pi$
$608$	24.0585	+	5.40277i	0.975700	+	0.219111i
$609$			5.43701i			0.220319i
$610$	−27.7391	+	30.8683i	−1.12312	+	1.24982i
$611$	−17.9797	+	21.4274i	−0.727380	+	0.866858i
$612$	−28.0681	−	9.33935i	−1.13459	−	0.377521i
$613$	−0.239200	+	0.512966i	−0.00966120	+	0.0207185i	−0.911079	−	0.412231i	$-0.864750\pi$
$613$	−0.239200	+	0.512966i	−0.00966120	+	0.0207185i	0.901418	+	0.432950i	$0.142527\pi$
$614$	38.7811	+	19.5067i	1.56508	+	0.787225i
$615$	1.33088	+	0.627446i	0.0536663	+	0.0253011i
$616$	−3.34049	+	2.79245i	−0.134592	+	0.112511i
$617$	4.73694	−	6.76505i	0.190702	−	0.272351i	−0.712403	−	0.701771i	$-0.752393\pi$
$617$	4.73694	−	6.76505i	0.190702	−	0.272351i	0.903105	+	0.429420i	$0.141282\pi$
$618$	0.746813	−	3.60554i	0.0300412	−	0.145036i
$619$	18.3268	−	31.7429i	0.736614	−	1.27585i	−0.217397	−	0.976083i	$-0.569757\pi$
$619$	18.3268	−	31.7429i	0.736614	−	1.27585i	0.954011	−	0.299770i	$-0.0969100\pi$
$620$	7.71612	−	17.6230i	0.309887	−	0.707756i
$621$	16.6781	−	13.9946i	0.669271	−	0.561585i
$622$	−18.4684	−	0.548820i	−0.740515	−	0.0220057i
$623$	14.0485	+	30.1270i	0.562840	+	1.20701i
$624$	−3.50996	+	4.69040i	−0.140511	+	0.187766i
$625$	19.4194	−	15.7444i	0.776778	−	0.629775i
$626$	−3.67649	−	8.53760i	−0.146942	−	0.341231i
$627$	0.747623	−	0.446626i	0.0298572	−	0.0178365i
$628$	−0.911663	−	32.7257i	−0.0363793	−	1.30590i
$629$	−39.0351	−	6.88295i	−1.55643	−	0.274441i
$630$	−13.8376	+	27.2239i	−0.551304	+	1.08462i
$631$	−4.39988	+	12.0886i	−0.175156	+	0.481238i	−0.995942	−	0.0899983i	$-0.971314\pi$
$631$	−4.39988	+	12.0886i	−0.175156	+	0.481238i	0.820786	+	0.571236i	$0.193536\pi$
$632$	−6.94059	+	6.91486i	−0.276082	+	0.275058i
$633$	0.402821	−	4.60426i	0.0160107	−	0.183003i
$634$	37.9884	+	28.3179i	1.50871	+	1.12465i
$635$	24.2994	−	2.02270i	0.964293	−	0.0802685i
$636$	6.31377	−	9.57378i	0.250357	−	0.379625i
$637$	−9.19280	+	13.1287i	−0.364232	+	0.520177i
$638$	−1.37687	−	1.74355i	−0.0545108	−	0.0690280i
$639$	9.52131	+	16.4914i	0.376657	+	0.652389i
$640$	−13.4646	+	21.4174i	−0.532235	+	0.846596i
$641$	25.7632	−	9.37704i	1.01759	−	0.370371i	0.221244	−	0.975218i	$-0.428988\pi$
$641$	25.7632	−	9.37704i	1.01759	−	0.370371i	0.796341	+	0.604847i	$0.206766\pi$
$642$	−1.42765	+	1.60224i	−0.0563448	+	0.0632353i
$643$	1.53996	+	17.6018i	0.0607302	+	0.694149i	0.964144	+	0.265380i	$0.0854972\pi$
$643$	1.53996	+	17.6018i	0.0607302	+	0.694149i	−0.903414	+	0.428770i	$0.858947\pi$
$644$	46.4440	−	34.4869i	1.83015	−	1.35898i
$645$	−8.20341	−	1.48218i	−0.323009	−	0.0583607i
$646$	27.9604	+	16.6997i	1.10009	+	0.657039i
$647$	−23.4275	+	23.4275i	−0.921028	+	0.921028i	−0.997102	−	0.0760737i	$-0.975762\pi$
$647$	−23.4275	+	23.4275i	−0.921028	+	0.921028i	0.0760737	+	0.997102i	$0.475762\pi$
$648$	−5.26047	−	19.7792i	−0.206651	−	0.777001i
$649$	−0.938885	+	1.11892i	−0.0368545	+	0.0439214i
$650$	−6.83433	+	22.0981i	−0.268064	+	0.866759i
$651$	−2.27233	−	6.24317i	−0.0890595	−	0.244689i
$652$	10.9785	+	12.3673i	0.429953	+	0.484341i
$653$	−35.6289	−	9.54674i	−1.39427	−	0.373593i	−0.517984	−	0.855390i	$-0.673317\pi$
$653$	−35.6289	−	9.54674i	−1.39427	−	0.373593i	−0.876283	+	0.481797i	$0.839984\pi$
$654$	−7.75481	−	0.911274i	−0.303237	−	0.0356337i
$655$	−0.0219900	+	5.21450i	−0.000859221	+	0.203747i
$656$	−5.72372	+	1.34158i	−0.223474	+	0.0523800i
$657$	12.6512	−	3.38987i	0.493569	−	0.132251i
$658$	6.02021	+	41.2779i	0.234692	+	1.60918i
$659$	4.91188	−	4.12156i	0.191340	−	0.160553i	−0.542085	−	0.840324i	$-0.682365\pi$
$659$	4.91188	−	4.12156i	0.191340	−	0.160553i	0.733425	+	0.679770i	$0.237921\pi$
$660$	0.175904	+	0.876008i	0.00684705	+	0.0340986i
$661$	−9.24146	−	3.36362i	−0.359451	−	0.130830i	0.155981	−	0.987760i	$-0.450146\pi$
$661$	−9.24146	−	3.36362i	−0.359451	−	0.130830i	−0.515432	+	0.856931i	$0.672368\pi$
$662$	−10.3595	−	19.2414i	−0.402633	−	0.747837i
$663$	−6.33829	+	4.43812i	−0.246159	+	0.172362i
$664$	−15.9209	−	5.82826i	−0.617852	−	0.226180i
$665$	21.3355	−	25.9856i	0.827354	−	1.00768i
$666$	−11.7481	−	27.2817i	−0.455231	−	1.05714i
$667$	16.9307	+	24.1796i	0.655561	+	0.936238i
$668$	5.17033	+	4.09858i	0.200046	+	0.158579i
$669$	4.40934	−	12.1146i	0.170475	−	0.468376i
$670$	−28.0504	+	18.2553i	−1.08368	+	0.705263i
$671$	−3.76439	−	4.48622i	−0.145323	−	0.173189i
$672$	1.74021	+	8.56158i	0.0671299	+	0.330270i
$673$	−1.45474	−	5.42917i	−0.0560762	−	0.209279i	0.932203	−	0.361935i	$-0.117884\pi$
$673$	−1.45474	−	5.42917i	−0.0560762	−	0.209279i	−0.988279	+	0.152656i	$0.951217\pi$
$674$	16.3147	+	24.8388i	0.628420	+	0.956755i
$675$	7.35669	+	10.6973i	0.283159	+	0.411741i
$676$	1.31345	+	4.40707i	0.0505172	+	0.169503i
$677$	9.86949	−	36.8334i	0.379315	−	1.41562i	−0.467620	−	0.883929i	$-0.654889\pi$
$677$	9.86949	−	36.8334i	0.379315	−	1.41562i	0.846936	−	0.531695i	$-0.178445\pi$
$678$	1.91976	+	5.80553i	0.0737278	+	0.222960i
$679$	−29.5138	+	10.7421i	−1.13263	+	0.412245i
$680$	−25.7265	+	21.3221i	−0.986566	+	0.817666i
$681$	−2.76525	−	2.32032i	−0.105965	−	0.0889149i
$682$	2.30972	+	1.42663i	0.0884437	+	0.0546285i
$683$	1.93287	+	1.93287i	0.0739593	+	0.0739593i	0.743119	−	0.669159i	$-0.233346\pi$
$683$	1.93287	+	1.93287i	0.0739593	+	0.0739593i	−0.669159	+	0.743119i	$0.733346\pi$
$684$	1.04312	+	24.3836i	0.0398846	+	0.932330i
$685$	−18.7046	+	12.9799i	−0.714667	+	0.495937i
$686$	−2.35699	−	9.97243i	−0.0899903	−	0.380749i
$687$	−2.58020	+	0.225738i	−0.0984408	+	0.00861245i
$688$	29.3562	−	15.7350i	1.11919	−	0.599891i
$689$	14.3291	+	39.3689i	0.545896	+	1.49984i
$690$	−1.66371	−	11.7542i	−0.0633363	−	0.447474i
$691$	−4.27417	+	2.46769i	−0.162597	+	0.0938754i	−0.579090	−	0.815263i	$-0.696592\pi$
$691$	−4.27417	+	2.46769i	−0.162597	+	0.0938754i	0.416494	+	0.909139i	$0.363259\pi$
$692$	3.73187	−	6.90072i	0.141865	−	0.262326i
$693$	−3.53011	−	2.47181i	−0.134098	−	0.0938962i
$694$	−18.7859	+	12.3390i	−0.713102	+	0.468383i
$695$	−18.8697	−	15.9696i	−0.715769	−	0.605763i
$696$	−4.39171	+	0.765969i	−0.166467	+	0.0290340i
$697$	−7.73522	−	0.676744i	−0.292992	−	0.0256335i
$698$	−11.8024	−	0.350729i	−0.446728	−	0.0132753i
$699$	3.48360	+	1.26793i	0.131762	+	0.0479574i
$700$	17.8246	+	29.5336i	0.673706	+	1.11626i
$701$	1.31181	−	7.43966i	0.0495465	−	0.280992i	−0.949961	−	0.312368i	$-0.898878\pi$
$701$	1.31181	−	7.43966i	0.0495465	−	0.280992i	0.999508	+	0.0313760i	$0.00998894\pi$
$702$	−11.1607	−	4.44187i	−0.421234	−	0.167647i
$703$	6.15809	+	32.1177i	0.232257	+	1.21134i
$704$	−2.72619	−	2.30486i	−0.102747	−	0.0868676i
$705$	8.03182	+	2.96176i	0.302496	+	0.111546i
$706$	10.5226	−	35.0690i	0.396024	−	1.31984i
$707$	35.0035	−	16.3224i	1.31644	−	0.613867i
$708$	1.07875	+	2.72521i	0.0405420	+	0.102420i
$709$	−4.67111	−	5.56681i	−0.175427	−	0.209066i	0.671165	−	0.741308i	$-0.265794\pi$
$709$	−4.67111	−	5.56681i	−0.175427	−	0.209066i	−0.846592	+	0.532242i	$0.821350\pi$
$710$	21.4975	+	0.729585i	0.806789	+	0.0273809i
$711$	−8.39808	−	4.84863i	−0.314953	−	0.181838i
$712$	−22.3558	+	15.5919i	−0.837819	+	0.584331i
$713$	−29.5466	−	20.6888i	−1.10653	−	0.774801i
$714$	−1.34673	+	11.4605i	−0.0504002	+	0.428898i
$715$	−2.95243	−	1.39193i	−0.110414	−	0.0520551i
$716$	16.7314	+	0.995286i	0.625283	+	0.0371956i
$717$	−5.64038	−	2.63015i	−0.210644	−	0.0982248i
$718$	33.1589	−	37.2139i	1.23748	−	1.38881i
$719$	0.988430	+	0.829391i	0.0368622	+	0.0309311i	0.661033	−	0.750357i	$-0.270118\pi$
$719$	0.988430	+	0.829391i	0.0368622	+	0.0309311i	−0.624170	+	0.781288i	$0.714563\pi$
$720$	−23.9394	−	7.34194i	−0.892168	−	0.273618i
$721$	20.0602			0.747082
$722$	4.66334	−	26.4623i	0.173552	−	0.984825i
$723$	−2.67904	−	2.67904i	−0.0996345	−	0.0996345i
$724$	9.24749	−	6.86672i	0.343680	−	0.255200i
$725$	−15.3174	+	8.67209i	−0.568874	+	0.322073i
$726$	6.82746	−	0.393413i	0.253391	−	0.0146009i
$727$	−7.70100	+	16.5149i	−0.285614	+	0.612502i	−0.995804	−	0.0915080i	$-0.970831\pi$
$727$	−7.70100	+	16.5149i	−0.285614	+	0.612502i	0.710190	+	0.704010i	$0.248609\pi$
$728$	−28.9010	−	13.5422i	−1.07114	−	0.501907i
$729$	14.5235	−	8.38512i	0.537906	−	0.310560i
$730$	4.31159	−	14.1522i	0.159579	−	0.523798i
$731$	43.3239	−	7.63917i	1.60239	−	0.282545i
$732$	−11.5116	+	2.36210i	−0.425481	+	0.0873055i
$733$	−3.77105	−	14.0737i	−0.139287	−	0.519825i	−0.999943	−	0.0106395i	$-0.996613\pi$
$733$	−3.77105	−	14.0737i	−0.139287	−	0.519825i	0.860657	−	0.509186i	$-0.170053\pi$
$734$	10.8259	−	14.5229i	0.399589	−	0.536049i
$735$	4.73249	+	1.28948i	0.174561	+	0.0475633i
$736$	34.3997	+	32.6563i	1.26799	+	1.20373i
$737$	−1.99592	−	4.28027i	−0.0735208	−	0.157666i
$738$	−2.75844	−	5.12344i	−0.101540	−	0.188596i
$739$	−6.62280	+	37.5598i	−0.243624	+	1.38166i	0.580043	+	0.814586i	$0.303036\pi$
$739$	−6.62280	+	37.5598i	−0.243624	+	1.38166i	−0.823667	+	0.567073i	$0.808076\pi$
$740$	−33.1711	−	5.04384i	−1.21939	−	0.185415i
$741$	5.28340	+	3.58333i	0.194090	+	0.131637i
$742$	58.0514	+	23.1040i	2.13113	+	0.848173i
$743$	31.9380	−	22.3632i	1.17169	−	0.820427i	0.184952	−	0.982747i	$-0.440787\pi$
$743$	31.9380	−	22.3632i	1.17169	−	0.820427i	0.986738	+	0.162321i	$0.0518980\pi$
$744$	4.72275	−	2.71500i	0.173145	−	0.0995367i
$745$	24.0309	+	14.0097i	0.880424	+	0.513275i
$746$	−3.68350	−	3.90913i	−0.134863	−	0.143123i
$747$	1.46257	−	16.7172i	0.0535125	−	0.611651i
$748$	−2.47038	−	4.01623i	−0.0903262	−	0.146848i
$749$	−10.1252	−	5.84581i	−0.369968	−	0.213601i
$750$	7.07192	−	0.317794i	0.258230	−	0.0116042i
$751$	45.9210	−	8.09712i	1.67568	−	0.295468i	0.746581	−	0.665294i	$-0.231694\pi$
$751$	45.9210	−	8.09712i	1.67568	−	0.295468i	0.929101	+	0.369826i	$0.120583\pi$
$752$	−32.4938	+	10.6780i	−1.18493	+	0.389388i
$753$	−5.14392	−	1.37831i	−0.187455	−	0.0502284i
$754$	7.31810	−	14.5491i	0.266509	−	0.529846i
$755$	−13.6106	+	2.34077i	−0.495339	+	0.0851894i
$756$	−16.0185	+	8.01998i	−0.582588	+	0.291684i
$757$	−4.49451	−	51.3725i	−0.163356	−	1.86717i	−0.429280	−	0.903171i	$-0.641233\pi$
$757$	−4.49451	−	51.3725i	−0.163356	−	1.86717i	0.265925	−	0.963994i	$-0.414323\pi$
$758$	−33.0664	−	20.4240i	−1.20103	−	0.741831i
$759$	1.67522			0.0608065
$760$	23.9954	+	13.5727i	0.870406	+	0.492335i
$761$	32.8286			1.19003			0.595017	−	0.803713i	$-0.297145\pi$
$761$	32.8286			1.19003			0.595017	+	0.803713i	$0.297145\pi$
$762$	5.87427	+	3.62832i	0.212802	+	0.131440i
$763$	−3.70756	−	42.3777i	−0.134223	−	1.53417i
$764$	17.6355	−	8.82954i	0.638029	−	0.319441i
$765$	−27.0113	−	19.0838i	−0.976596	−	0.689976i
$766$	2.40695	−	4.78523i	0.0869665	−	0.172897i
$767$	−10.3424	−	2.77125i	−0.373444	−	0.100064i
$768$	−6.67040	+	2.61180i	−0.240697	+	0.0942452i
$769$	7.26149	−	1.28040i	0.261856	−	0.0461723i	−0.0411787	−	0.999152i	$-0.513111\pi$
$769$	7.26149	−	1.28040i	0.261856	−	0.0461723i	0.303035	+	0.952980i	$0.402000\pi$
$770$	−4.47899	+	1.90641i	−0.161412	+	0.0687022i
$771$	3.89095	+	2.24644i	0.140129	+	0.0809036i
$772$	19.5313	+	31.7530i	0.702948	+	1.14282i
$773$	2.53198	−	28.9407i	0.0910690	−	1.04092i	−0.803891	−	0.594777i	$-0.797240\pi$
$773$	2.53198	−	28.9407i	0.0910690	−	1.04092i	0.894960	−	0.446147i	$-0.147204\pi$
$774$	22.6086	+	23.9935i	0.812650	+	0.862428i
$775$	13.9642	−	16.3596i	0.501608	−	0.587655i
$776$	−12.8348	−	22.3262i	−0.460743	−	0.801465i
$777$	−9.49165	+	6.64613i	−0.340511	+	0.238428i
$778$	−1.53887	−	0.612458i	−0.0551712	−	0.0219577i
$779$	1.75011	+	6.16263i	0.0627042	+	0.220799i
$780$	−5.27498	+	3.88253i	−0.188875	+	0.139017i
$781$	−0.527085	+	2.98925i	−0.0188606	+	0.106964i
$782$	29.6985	+	55.1611i	1.06202	+	1.97256i
$783$	−3.86312	−	8.28449i	−0.138057	−	0.296063i
$784$	−18.0143	+	7.71776i	−0.643369	+	0.275634i
$785$	9.62248	−	35.3152i	0.343441	−	1.26045i
$786$	−0.882475	+	1.18384i	−0.0314768	+	0.0422261i
$787$	2.20426	+	8.22640i	0.0785733	+	0.293240i	0.994020	−	0.109200i	$-0.0348290\pi$
$787$	2.20426	+	8.22640i	0.0785733	+	0.293240i	−0.915446	+	0.402440i	$0.868162\pi$
$788$	−2.13473	+	0.438031i	−0.0760467	+	0.0156042i
$789$	10.2044	−	1.79930i	0.363285	−	0.0640569i
$790$	−9.66650	+	5.15195i	−0.343919	+	0.183298i
$791$	−28.8503	+	16.6567i	−1.02580	+	0.592245i
$792$	1.49926	−	3.19965i	0.0532740	−	0.113695i
$793$	18.1430	−	38.9079i	0.644278	−	1.38166i
$794$	3.23567	−	0.186446i	0.114830	−	0.00661673i
$795$	9.85682	−	8.20027i	0.349585	−	0.290834i
$796$	−27.2535	+	20.2371i	−0.965976	+	0.717285i
$797$	24.4199	+	24.4199i	0.864996	+	0.864996i	0.991913	−	0.126917i	$-0.0405083\pi$
$797$	24.4199	+	24.4199i	0.864996	+	0.864996i	−0.126917	+	0.991913i	$0.540508\pi$
$798$	9.23160	−	2.32768i	0.326795	−	0.0823991i
$799$	−45.1757			−1.59820
$800$	−21.3445	+	18.5584i	−0.754640	+	0.656139i
$801$	−20.6661	−	17.3409i	−0.730201	−	0.612711i
$802$	14.8897	−	16.7106i	0.525773	−	0.590070i
$803$	1.89211	+	0.882305i	0.0667710	+	0.0311359i
$804$	−9.46004	−	0.562740i	−0.333630	−	0.0198463i
$805$	60.8683	−	21.8640i	2.14533	−	0.770605i
$806$	−2.32258	+	19.7648i	−0.0818093	+	0.696185i
$807$	0.189368	+	0.132597i	0.00666607	+	0.00466763i
$808$	18.1156	+	25.9744i	0.637306	+	0.913775i
$809$	13.6535	+	7.88287i	0.480033	+	0.277147i	0.720430	−	0.693528i	$-0.243944\pi$
$809$	13.6535	+	7.88287i	0.480033	+	0.277147i	−0.240397	+	0.970675i	$0.577278\pi$
$810$	0.776144	−	22.8694i	0.0272709	−	0.803550i
$811$	−29.1352	−	34.7219i	−1.02307	−	1.21925i	−0.975412	−	0.220388i	$-0.929268\pi$
$811$	−29.1352	−	34.7219i	−1.02307	−	1.21925i	−0.0476613	−	0.998864i	$-0.515177\pi$
$812$	−8.93917	−	22.5827i	−0.313703	−	0.792497i
$813$	−5.27884	+	2.46156i	−0.185137	+	0.0863308i
$814$	1.36074	−	4.53497i	0.0476939	−	0.158951i
$815$	7.74312	+	16.7897i	0.271229	+	0.588116i
$816$	−9.44687	+	0.526744i	−0.330707	+	0.0184397i
$817$	−18.6143	−	31.1591i	−0.651232	−	1.09012i
$818$	−7.63893	−	3.04023i	−0.267089	−	0.106299i
$819$	5.48565	−	31.1107i	0.191684	−	1.08709i
$820$	−6.55944	−	0.417962i	−0.229066	−	0.0145959i
$821$	−15.8208	−	5.75831i	−0.552150	−	0.200966i	0.0508513	−	0.998706i	$-0.483807\pi$
$821$	−15.8208	−	5.75831i	−0.552150	−	0.200966i	−0.603002	+	0.797740i	$0.706029\pi$
$822$	−6.44394	−	0.191493i	−0.224758	−	0.00667908i
$823$	−25.9862	−	2.27350i	−0.905821	−	0.0792491i	−0.375283	−	0.926910i	$-0.622455\pi$
$823$	−25.9862	−	2.27350i	−0.905821	−	0.0792491i	−0.530538	+	0.847661i	$0.678010\pi$
$824$	2.82610	+	16.2035i	0.0984518	+	0.564477i
$825$	−0.0954549	+	0.994386i	−0.00332331	+	0.0346201i
$826$	−13.3466	+	8.76634i	−0.464387	+	0.305020i
$827$	−33.9620	−	23.7805i	−1.18098	−	0.826928i	−0.192949	−	0.981209i	$-0.561805\pi$
$827$	−33.9620	−	23.7805i	−1.18098	−	0.826928i	−0.988027	+	0.154281i	$0.950694\pi$
$828$	−22.3324	+	41.2956i	−0.776106	+	1.43512i
$829$	−22.3556	+	12.9070i	−0.776441	+	0.448278i	−0.835167	−	0.549996i	$-0.814629\pi$
$829$	−22.3556	+	12.9070i	−0.776441	+	0.448278i	0.0587266	+	0.998274i	$0.481296\pi$
$830$	−15.1496	−	11.3928i	−0.525851	−	0.395448i
$831$	−1.28472	−	3.52975i	−0.0445666	−	0.122446i
$832$	6.86703	−	25.2525i	0.238071	−	0.875472i
$833$	−25.7864	+	2.25602i	−0.893447	+	0.0781665i
$834$	−1.61006	−	6.81219i	−0.0557519	−	0.235887i
$835$	4.20549	+	6.06029i	0.145537	+	0.209725i
$836$	−2.37095	+	3.08426i	−0.0820011	+	0.106671i
$837$	7.89831	+	7.89831i	0.273005	+	0.273005i
$838$	4.11490	+	2.54162i	0.142147	+	0.0877989i
$839$	−36.5756	−	30.6906i	−1.26273	−	1.05956i	−0.995386	−	0.0959543i	$-0.969410\pi$
$839$	−36.5756	−	30.6906i	−1.26273	−	1.05956i	−0.267343	−	0.963601i	$-0.586146\pi$
$840$	−0.910419	+	9.72534i	−0.0314124	+	0.335556i
$841$	−15.6054	+	5.67989i	−0.538116	+	0.195858i
$842$	5.16802	+	15.6286i	0.178102	+	0.538597i
$843$	−1.45272	+	5.42163i	−0.0500344	+	0.186731i
$844$	5.89690	+	19.7862i	0.202980	+	0.681068i
$845$	−0.0216817	+	5.14138i	−0.000745872	+	0.176869i
$846$	−18.5856	−	28.2962i	−0.638987	−	0.972844i
$847$	9.64315	+	35.9887i	0.331343	+	1.23659i
$848$	−10.4838	+	50.1456i	−0.360015	+	1.72201i
$849$	−4.18690	−	4.98975i	−0.143694	−	0.171248i
$850$	−34.4351	+	14.4855i	−1.18111	+	0.496849i
$851$	−21.5156	+	59.1136i	−0.737545	+	2.02639i
$852$	4.77304	+	3.78364i	0.163522	+	0.129625i
$853$	−28.6031	−	40.8494i	−0.979351	−	1.39866i	−0.916230	−	0.400652i	$-0.868784\pi$
$853$	−28.6031	−	40.8494i	−0.979351	−	1.39866i	−0.0631206	−	0.998006i	$-0.520105\pi$
$854$	−25.3217	−	58.8025i	−0.866492	−	2.01218i
$855$	−6.78025	+	26.4308i	−0.231880	+	0.903915i
$856$	3.29547	−	9.00217i	0.112637	−	0.307688i
$857$	2.33479	−	1.63483i	0.0797547	−	0.0558449i	−0.533019	−	0.846103i	$-0.678943\pi$
$857$	2.33479	−	1.63483i	0.0797547	−	0.0558449i	0.612774	+	0.790258i	$0.290054\pi$
$858$	−0.438154	−	0.813813i	−0.0149583	−	0.0277831i
$859$	12.2784	+	4.46898i	0.418934	+	0.152480i	0.542882	−	0.839809i	$-0.317333\pi$
$859$	12.2784	+	4.46898i	0.418934	+	0.152480i	−0.123948	+	0.992289i	$0.539555\pi$
$860$	36.5099	−	7.33125i	1.24498	−	0.249994i
$861$	−1.73882	+	1.45905i	−0.0592589	+	0.0497241i
$862$	−6.31602	−	43.3061i	−0.215124	−	1.47501i
$863$	−13.4874	+	3.61394i	−0.459117	+	0.123020i	−0.480962	−	0.876741i	$-0.659713\pi$
$863$	−13.4874	+	3.61394i	−0.459117	+	0.123020i	0.0218452	+	0.999761i	$0.493046\pi$
$864$	−8.73479	−	11.8090i	−0.297164	−	0.401751i
$865$	6.22826	−	6.17595i	0.211767	−	0.209989i
$866$	15.4120	+	1.81108i	0.523721	+	0.0615429i
$867$	−4.71910	−	1.26448i	−0.160269	−	0.0429439i
$868$	19.7027	+	22.1951i	0.668755	+	0.753350i
$869$	−0.528670	−	1.45251i	−0.0179339	−	0.0492730i
$870$	−4.94765	−	0.602566i	−0.167741	−	0.0204289i
$871$	22.2535	−	26.5206i	0.754030	−	0.898618i
$872$	33.7080	−	8.96495i	1.14150	−	0.303592i
$873$	18.0239	−	18.0239i	0.610015	−	0.610015i
$874$	33.8067	−	39.0988i	1.14353	−	1.32254i
$875$	9.50987	+	37.3764i	0.321492	+	1.26355i
$876$	3.36338	−	2.49747i	0.113638	−	0.0843818i
$877$	1.14320	+	13.0669i	0.0386033	+	0.441238i	0.990760	+	0.135627i	$0.0433049\pi$
$877$	1.14320	+	13.0669i	0.0386033	+	0.441238i	−0.952157	+	0.305610i	$0.901140\pi$
$878$	21.0002	−	23.5684i	0.708724	−	0.795394i
$879$	3.22715	−	1.17459i	0.108849	−	0.0396178i
$880$	−2.17089	−	3.34930i	−0.0731808	−	0.112905i
$881$	17.9364	+	31.0667i	0.604291	+	1.04666i	0.992163	+	0.124950i	$0.0398771\pi$
$881$	17.9364	+	31.0667i	0.604291	+	1.04666i	−0.387872	+	0.921713i	$0.626790\pi$
$882$	−12.0218	−	15.2234i	−0.404795	−	0.512599i
$883$	−11.0586	+	15.7934i	−0.372153	+	0.531490i	−0.960925	−	0.276810i	$-0.910723\pi$
$883$	−11.0586	+	15.7934i	−0.372153	+	0.531490i	0.588772	+	0.808299i	$0.299612\pi$
$884$	19.0293	−	28.8548i	0.640026	−	0.970492i
$885$	0.271832	+	3.26561i	0.00913755	+	0.109772i
$886$	−1.48240	−	1.10503i	−0.0498022	−	0.0371243i
$887$	−0.867673	+	9.91755i	−0.0291336	+	0.332999i	0.967615	+	0.252429i	$0.0812295\pi$
$887$	−0.867673	+	9.91755i	−0.0291336	+	0.332999i	−0.996749	+	0.0805696i	$0.974326\pi$
$888$	−6.70556	−	6.73052i	−0.225024	−	0.225861i
$889$	−12.8655	+	35.3476i	−0.431494	+	1.18552i
$890$	−28.9724	+	9.44515i	−0.971157	+	0.316602i
$891$	3.18001	+	0.560721i	0.106534	+	0.0187849i
$892$	1.60370	+	57.5676i	0.0536959	+	1.92751i
$893$	13.2684	+	34.8306i	0.444010	+	1.16556i
$894$	3.11527	+	7.23433i	0.104190	+	0.241952i
$895$	17.5821	+	6.48345i	0.587704	+	0.216718i
$896$	−21.3044	−	32.6995i	−0.711729	−	1.09241i
$897$	5.18984	+	11.1296i	0.173284	+	0.371608i
$898$	−22.7854	−	0.677109i	−0.760360	−	0.0225954i
$899$	−11.6010	+	9.73436i	−0.386914	+	0.324659i
$900$	−23.2400	−	15.6093i	−0.774666	−	0.520309i
$901$	−33.8321	+	58.5989i	−1.12711	+	1.95221i
$902$	0.188121	−	0.908231i	0.00626374	−	0.0302408i
$903$	7.37633	−	10.5345i	0.245469	−	0.350566i
$904$	−17.5188	−	20.9570i	−0.582667	−	0.697021i
$905$	12.1195	−	4.35336i	0.402867	−	0.144711i
$906$	−3.49354	−	1.75723i	−0.116065	−	0.0583800i
$907$	24.4850	−	52.5082i	0.813011	−	1.74351i	0.158636	−	0.987337i	$-0.449290\pi$
$907$	24.4850	−	52.5082i	0.813011	−	1.74351i	0.654375	−	0.756171i	$-0.272932\pi$
$908$	15.3004	+	5.09105i	0.507763	+	0.168952i
$909$	−20.1478	+	24.0112i	−0.668259	+	0.796401i
$910$	−26.5416	−	23.8510i	−0.879845	−	0.790653i
$911$		−	59.1633i		−	1.96017i	−0.198583	−	0.980084i	$-0.563634\pi$
$911$		−	59.1633i		−	1.96017i	0.198583	−	0.980084i	$-0.436366\pi$
$912$	3.18072	+	7.12885i	0.105324	+	0.236060i
$913$	1.89142	−	1.89142i	0.0625969	−	0.0625969i
$914$	1.54573	+	6.54000i	0.0511283	+	0.216324i
$915$	−13.0836	−	1.20028i	−0.432530	−	0.0396801i
$916$	10.3458	−	5.17980i	0.341834	−	0.171146i
$917$	−7.29073	−	3.39972i	−0.240761	−	0.112269i
$918$	−6.09090	−	18.4195i	−0.201030	−	0.607933i
$919$	−16.1923	−	28.0459i	−0.534134	−	0.925148i	−0.999205	−	0.0398742i	$-0.987304\pi$
$919$	−16.1923	−	28.0459i	−0.534134	−	0.925148i	0.465070	−	0.885274i	$-0.346029\pi$
$920$	26.2357	+	46.0858i	0.864965	+	1.51940i
$921$	2.38648	+	13.5344i	0.0786370	+	0.445973i
$922$	−16.4077	−	3.39852i	−0.540360	−	0.111924i
$923$	−21.4926	+	5.75892i	−0.707437	+	0.189557i
$924$	−1.34084	−	0.319538i	−0.0441103	−	0.0105120i
$925$	−33.8631	−	16.1397i	−1.11341	−	0.530670i
$926$	−13.4088	+	12.6348i	−0.440639	+	0.415206i
$927$	−14.7549	+	6.88031i	−0.484614	+	0.225979i
$928$	16.9817	−	10.4020i	0.557451	−	0.341463i
$929$	−12.6343	−	2.22778i	−0.414520	−	0.0730910i	−0.0375008	−	0.999297i	$-0.511940\pi$
$929$	−12.6343	−	2.22778i	−0.414520	−	0.0730910i	−0.377019	+	0.926206i	$0.623051\pi$
$930$	5.93308	−	1.37589i	0.194553	−	0.0451174i
$931$	9.31303	+	19.2188i	0.305222	+	0.629870i
$932$	−16.5538	+	0.461151i	−0.542239	+	0.0151055i
$933$	−3.35508	−	4.79155i	−0.109840	−	0.156868i
$934$	2.93667	−	9.78709i	0.0960907	−	0.320243i
$935$	−1.34294	−	5.09780i	−0.0439187	−	0.166716i
$936$	25.9023	+	0.0481140i	0.846642	+	0.00157265i
$937$	−1.05756	−	0.0925241i	−0.0345488	−	0.00302263i	0.0698682	−	0.997556i	$-0.477742\pi$
$937$	−1.05756	−	0.0925241i	−0.0345488	−	0.00302263i	−0.104417	+	0.994534i	$0.533298\pi$
$938$	−7.45122	−	51.0897i	−0.243291	−	1.66814i
$939$	1.47142	−	2.54857i	0.0480178	−	0.0831693i
$940$	−38.2298	+	0.903670i	−1.24692	+	0.0294745i
$941$	−4.86661	−	27.5999i	−0.158647	−	0.899731i	−0.955375	−	0.295394i	$-0.904549\pi$
$941$	−4.86661	−	27.5999i	−0.158647	−	0.899731i	0.796729	−	0.604337i	$-0.206562\pi$
$942$	8.13405	−	6.42339i	0.265022	−	0.209286i
$943$	−3.18950	+	11.9034i	−0.103864	+	0.387627i
$944$	−8.96124	−	9.54561i	−0.291663	−	0.310683i
$945$	−19.7387	+	3.39471i	−0.642101	+	0.110430i
$946$	0.302298	+	5.24621i	0.00982855	+	0.170569i
$947$	29.9903	−	2.62381i	0.974553	−	0.0852624i	0.411259	−	0.911519i	$-0.365089\pi$
$947$	29.9903	−	2.62381i	0.974553	−	0.0852624i	0.563294	+	0.826256i	$0.309534\pi$
$948$	−3.06837	−	0.453332i	−0.0996561	−	0.0147235i
$949$			15.3040i			0.496789i
$950$	21.2822	+	22.2950i	0.690485	+	0.723347i
$951$			15.0003i			0.486418i
$952$	−13.2489	−	49.8155i	−0.429399	−	1.61453i
$953$	−14.2134	+	1.24351i	−0.460417	+	0.0402813i	−0.315005	−	0.949090i	$-0.602006\pi$
$953$	−14.2134	+	1.24351i	−0.460417	+	0.0402813i	−0.145412	+	0.989371i	$0.546451\pi$
$954$	−50.6227	+	2.91699i	−1.63897	+	0.0944409i
$955$	21.7312	−	3.73738i	0.703205	−	0.120939i
$956$	27.7517	+	1.65084i	0.897555	+	0.0533920i
$957$	0.182039	−	0.679377i	0.00588447	−	0.0219611i
$958$	−8.70147	−	11.0188i	−0.281132	−	0.356002i
$959$	−6.09898	−	34.5890i	−0.196946	−	1.11694i
$960$	−7.98385	+	0.634726i	−0.257678	+	0.0204857i
$961$	−6.24729	+	10.8206i	−0.201526	+	0.349052i
$962$	34.3446	−	5.00902i	1.10731	−	0.161497i
$963$	9.45241	+	0.826979i	0.304600	+	0.0266490i
$964$	15.5321	+	6.72273i	0.500256	+	0.216525i
$965$	10.6175	+	40.3042i	0.341790	+	1.29744i
$966$	17.5412	+	5.26332i	0.564378	+	0.169345i
$967$	−18.1658	−	25.9434i	−0.584171	−	0.834283i	0.412899	−	0.910777i	$-0.364516\pi$
$967$	−18.1658	−	25.9434i	−0.584171	−	0.834283i	−0.997070	+	0.0764939i	$0.975627\pi$
$968$	−27.7112	+	12.8593i	−0.890670	+	0.413314i
$969$	1.05158	+	10.2567i	0.0337817	+	0.329493i
$970$	−6.50437	−	28.0479i	−0.208843	−	0.900563i
$971$	−22.0616	−	3.89005i	−0.707989	−	0.124838i	−0.191953	−	0.981404i	$-0.561482\pi$
$971$	−22.0616	−	3.89005i	−0.707989	−	0.124838i	−0.516036	+	0.856567i	$0.672593\pi$
$972$	13.7031	−	17.2864i	0.439528	−	0.554461i
$973$	34.5628	−	16.1169i	1.10803	−	0.516685i
$974$	39.7681	+	42.2041i	1.27425	+	1.35231i
$975$	−6.90212	+	2.44644i	−0.221045	+	0.0783489i
$976$	43.9300	−	28.7376i	1.40617	−	0.919869i
$977$	−27.2250	+	7.29492i	−0.871005	+	0.233385i	−0.666522	−	0.745485i	$-0.732218\pi$
$977$	−27.2250	+	7.29492i	−0.871005	+	0.233385i	−0.204483	+	0.978870i	$0.565551\pi$
$978$	−1.06187	+	5.12661i	−0.0339549	+	0.163931i
$979$	−0.746721	−	4.23486i	−0.0238653	−	0.135347i
$980$	−21.7766	+	2.42497i	−0.695627	+	0.0774628i
$981$	17.2618	+	29.8983i	0.551127	+	0.954581i
$982$	17.4689	−	5.77655i	0.557454	−	0.184337i
$983$	51.0526	+	23.8062i	1.62833	+	0.759301i	0.999829	−	0.0185105i	$-0.00589240\pi$
$983$	51.0526	+	23.8062i	1.62833	+	0.759301i	0.628498	+	0.777811i	$0.283670\pi$
$984$	−1.42350	−	1.19897i	−0.0453796	−	0.0382219i
$985$	−2.42624	−	0.222582i	−0.0773065	−	0.00709206i
$986$	25.5975	−	6.04999i	0.815192	−	0.192671i
$987$	−9.33820	+	9.33820i	−0.297238	+	0.297238i
$988$	−27.8362	−	6.19682i	−0.885586	−	0.197147i
$989$		−	69.8190i		−	2.22011i
$990$	2.64056	−	2.93843i	0.0839225	−	0.0933896i
$991$	−14.9530	+	17.8202i	−0.474996	+	0.566079i	−0.949336	−	0.314263i	$-0.898242\pi$
$991$	−14.9530	+	17.8202i	−0.474996	+	0.566079i	0.474340	+	0.880342i	$0.342687\pi$
$992$	−15.1522	+	19.0416i	−0.481083	+	0.604572i
$993$	2.92380	−	6.27011i	0.0927840	−	0.198976i
$994$	−14.9109	+	29.6443i	−0.472946	+	0.940261i
$995$	−35.7178	+	12.8299i	−1.13233	+	0.406736i
$996$	−1.53303	−	5.14386i	−0.0485760	−	0.162989i
$997$	−10.4180	+	14.8784i	−0.329941	+	0.471205i	−0.949510	−	0.313738i	$-0.898419\pi$
$997$	−10.4180	+	14.8784i	−0.329941	+	0.471205i	0.619568	+	0.784943i	$0.287308\pi$
$998$	−2.83333	−	0.586865i	−0.0896875	−	0.0185769i
$999$	9.74041	−	16.8709i	0.308173	−	0.533771i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.207.11	yes	672
4.3	odd	2	inner	380.2.bj.a.207.33	yes	672
5.3	odd	4	inner	380.2.bj.a.283.17	yes	672
19.9	even	9	inner	380.2.bj.a.47.52	yes	672
20.3	even	4	inner	380.2.bj.a.283.52	yes	672
76.47	odd	18	inner	380.2.bj.a.47.17	✓	672
95.28	odd	36	inner	380.2.bj.a.123.33	yes	672
380.123	even	36	inner	380.2.bj.a.123.11	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.47.17	✓	672	76.47	odd	18	inner
380.2.bj.a.47.52	yes	672	19.9	even	9	inner
380.2.bj.a.123.11	yes	672	380.123	even	36	inner
380.2.bj.a.123.33	yes	672	95.28	odd	36	inner
380.2.bj.a.207.11	yes	672	1.1	even	1	trivial
380.2.bj.a.207.33	yes	672	4.3	odd	2	inner
380.2.bj.a.283.17	yes	672	5.3	odd	4	inner
380.2.bj.a.283.52	yes	672	20.3	even	4	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20320 - 0.743174i) q^{2} +(-0.0390213 - 0.446015i) q^{3} +(0.895384 + 1.78838i) q^{4} +(0.378999 + 2.20371i) q^{5} +(-0.284517 + 0.565646i) q^{6} +(-3.33202 - 0.892813i) q^{7} +(0.251747 - 2.81720i) q^{8} +(2.75702 - 0.486136i) q^{9} +O(q^{10})\)	\(q+(-1.20320 - 0.743174i) q^{2} +(-0.0390213 - 0.446015i) q^{3} +(0.895384 + 1.78838i) q^{4} +(0.378999 + 2.20371i) q^{5} +(-0.284517 + 0.565646i) q^{6} +(-3.33202 - 0.892813i) q^{7} +(0.251747 - 2.81720i) q^{8} +(2.75702 - 0.486136i) q^{9} +(1.18173 - 2.93317i) q^{10} +(0.386458 + 0.223121i) q^{11} +(0.762704 - 0.469140i) q^{12} +(-0.285103 + 3.25874i) q^{13} +(3.34558 + 3.55051i) q^{14} +(0.968101 - 0.255031i) q^{15} +(-2.39657 + 3.20257i) q^{16} +(-4.32774 + 3.03032i) q^{17} +(-3.67853 - 1.46402i) q^{18} +(3.60746 + 2.44667i) q^{19} +(-3.60172 + 2.65097i) q^{20} +(-0.268188 + 1.52097i) q^{21} +(-0.299168 - 0.555665i) q^{22} +(3.54358 + 7.59923i) q^{23} +(-1.26634 - 0.00235225i) q^{24} +(-4.71272 + 1.67041i) q^{25} +(2.76485 - 3.70904i) q^{26} +(-0.672041 - 2.50809i) q^{27} +(-1.38676 - 6.75832i) q^{28} +(3.46690 - 0.611309i) q^{29} +(-1.35435 - 0.412614i) q^{30} +(-3.72546 + 2.15090i) q^{31} +(5.26362 - 2.07226i) q^{32} +(0.0844355 - 0.181072i) q^{33} +(7.45919 - 0.429814i) q^{34} +(0.704670 - 7.68120i) q^{35} +(3.33798 + 4.49530i) q^{36} +(5.30509 + 5.30509i) q^{37} +(-2.52220 - 5.62481i) q^{38} +1.46457 q^{39} +(6.30372 - 0.512939i) q^{40} +(1.12586 + 0.944712i) q^{41} +(1.45303 - 1.63072i) q^{42} +(-7.54666 - 3.51907i) q^{43} +(-0.0529967 + 0.890911i) q^{44} +(2.11621 + 5.89143i) q^{45} +(1.38391 - 11.7769i) q^{46} +(7.00444 + 4.90456i) q^{47} +(1.52191 + 0.943940i) q^{48} +(4.24308 + 2.44974i) q^{49} +(6.91176 + 1.49253i) q^{50} +(1.52044 + 1.81199i) q^{51} +(-6.08313 + 2.40796i) q^{52} +(11.6075 - 5.41266i) q^{53} +(-1.05535 + 3.51718i) q^{54} +(-0.345229 + 0.936205i) q^{55} +(-3.35406 + 9.16221i) q^{56} +(0.950486 - 1.70446i) q^{57} +(-4.62569 - 1.84099i) q^{58} +(-0.568387 + 3.22348i) q^{59} +(1.32291 + 1.50298i) q^{60} +(-12.3322 - 4.48856i) q^{61} +(6.08097 + 0.180707i) q^{62} +(-9.62047 - 0.841682i) q^{63} +(-7.87325 - 1.41844i) q^{64} +(-7.28939 + 0.606775i) q^{65} +(-0.236161 + 0.155116i) q^{66} +(-8.66940 - 6.07038i) q^{67} +(-9.29433 - 5.02632i) q^{68} +(3.25110 - 1.87702i) q^{69} +(-6.55633 + 8.71834i) q^{70} +(2.32643 + 6.39182i) q^{71} +(-0.675473 - 7.88945i) q^{72} +(4.66061 - 0.407751i) q^{73} +(-2.44048 - 10.3257i) q^{74} +(0.928926 + 2.03676i) q^{75} +(-1.14550 + 8.64221i) q^{76} +(-1.08848 - 1.08848i) q^{77} +(-1.76218 - 1.08843i) q^{78} +(-2.65348 - 2.22653i) q^{79} +(-7.96584 - 4.06759i) q^{80} +(6.79972 - 2.47490i) q^{81} +(-0.652555 - 1.97339i) q^{82} +(1.55142 - 5.78996i) q^{83} +(-2.96020 + 0.882233i) q^{84} +(-8.31816 - 8.38861i) q^{85} +(6.46487 + 9.84263i) q^{86} +(-0.407936 - 1.52244i) q^{87} +(0.725868 - 1.03256i) q^{88} +(-6.19419 - 7.38194i) q^{89} +(1.83213 - 8.66129i) q^{90} +(3.85942 - 10.6037i) q^{91} +(-10.4174 + 13.1415i) q^{92} +(1.10470 + 1.57768i) q^{93} +(-4.78280 - 11.1067i) q^{94} +(-4.02454 + 8.87711i) q^{95} +(-1.12965 - 2.26679i) q^{96} +(7.45829 - 5.22235i) q^{97} +(-3.28469 - 6.10088i) q^{98} +(1.17394 + 0.427278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

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