LMFDB - Embedded newform 731.2.u.b.52.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(52,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("731.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.u (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			52.12
Character	$\chi$	$=$	731.52
Dual form			731.2.u.b.239.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.362567 - 0.454644i) q^{2} +(1.29324 + 0.194925i) q^{3} +(0.369795 - 1.62018i) q^{4} +(-2.61272 - 1.78132i) q^{5} +(-0.380264 - 0.658637i) q^{6} +(-1.55140 + 2.68710i) q^{7} +(-1.91853 + 0.923914i) q^{8} +(-1.23224 - 0.380097i) q^{9} +O(q^{10})$	\(q+(-0.362567 - 0.454644i) q^{2} +(1.29324 + 0.194925i) q^{3} +(0.369795 - 1.62018i) q^{4} +(-2.61272 - 1.78132i) q^{5} +(-0.380264 - 0.658637i) q^{6} +(-1.55140 + 2.68710i) q^{7} +(-1.91853 + 0.923914i) q^{8} +(-1.23224 - 0.380097i) q^{9} +(0.137417 + 1.83370i) q^{10} +(0.975970 + 4.27600i) q^{11} +(0.794047 - 2.02320i) q^{12} +(-0.221321 + 2.95333i) q^{13} +(1.78416 - 0.268919i) q^{14} +(-3.03165 - 2.81296i) q^{15} +(-1.87889 - 0.904828i) q^{16} +(-0.826239 + 0.563320i) q^{17} +(0.273961 + 0.698042i) q^{18} +(-1.68522 + 0.519821i) q^{19} +(-3.85223 + 3.57435i) q^{20} +(-2.53011 + 3.17266i) q^{21} +(1.59021 - 1.99405i) q^{22} +(1.19257 - 1.10655i) q^{23} +(-2.66121 + 0.820875i) q^{24} +(1.82649 + 4.65381i) q^{25} +(1.42296 - 0.970154i) q^{26} +(-5.05449 - 2.43411i) q^{27} +(3.77988 + 3.50722i) q^{28} +(5.74762 - 0.866314i) q^{29} +(-0.179721 + 2.39821i) q^{30} +(-2.61169 + 6.65448i) q^{31} +(1.21752 + 5.33432i) q^{32} +(0.428665 + 5.72014i) q^{33} +(0.555677 + 0.171404i) q^{34} +(8.83995 - 4.25710i) q^{35} +(-1.07150 + 1.85590i) q^{36} +(-1.67543 - 2.90193i) q^{37} +(0.847337 + 0.577704i) q^{38} +(-0.861897 + 3.77622i) q^{39} +(6.65836 + 1.00359i) q^{40} +(-3.40119 - 4.26495i) q^{41} +2.35977 q^{42} +(-4.01300 + 5.18612i) q^{43} +7.28880 q^{44} +(2.54243 + 3.18811i) q^{45} +(-0.935471 - 0.141000i) q^{46} +(2.01338 - 8.82119i) q^{47} +(-2.25349 - 1.53640i) q^{48} +(-1.31367 - 2.27535i) q^{49} +(1.45360 - 2.51772i) q^{50} +(-1.17833 + 0.567454i) q^{51} +(4.70307 + 1.45070i) q^{52} +(0.304993 + 4.06985i) q^{53} +(0.725933 + 3.18052i) q^{54} +(5.06700 - 12.9105i) q^{55} +(0.493750 - 6.58863i) q^{56} +(-2.28072 + 0.343763i) q^{57} +(-2.47776 - 2.29902i) q^{58} +(-8.01457 - 3.85961i) q^{59} +(-5.67859 + 3.87159i) q^{60} +(1.78686 + 4.55284i) q^{61} +(3.97233 - 1.22530i) q^{62} +(2.93306 - 2.72148i) q^{63} +(-0.616687 + 0.773301i) q^{64} +(5.83907 - 7.32196i) q^{65} +(2.44521 - 2.26882i) q^{66} +(-8.56074 + 2.64064i) q^{67} +(0.607140 + 1.54697i) q^{68} +(1.75798 - 1.19857i) q^{69} +(-5.14053 - 2.47555i) q^{70} +(-8.54058 - 7.92450i) q^{71} +(2.71527 - 0.409261i) q^{72} +(-0.398945 + 5.32355i) q^{73} +(-0.711890 + 1.81387i) q^{74} +(1.45494 + 6.37452i) q^{75} +(0.219017 + 2.92258i) q^{76} +(-13.0042 - 4.01125i) q^{77} +(2.02933 - 0.977274i) q^{78} +(-0.340048 + 0.588981i) q^{79} +(3.29723 + 5.71097i) q^{80} +(-2.86581 - 1.95388i) q^{81} +(-0.705879 + 3.09266i) q^{82} +(-10.2321 - 1.54224i) q^{83} +(4.20465 + 5.27247i) q^{84} +3.16218 q^{85} +(3.81282 - 0.0558268i) q^{86} +7.60192 q^{87} +(-5.82308 - 7.30192i) q^{88} +(-13.6258 - 2.05375i) q^{89} +(0.527654 - 2.31180i) q^{90} +(-7.59252 - 5.17649i) q^{91} +(-1.35179 - 2.34137i) q^{92} +(-4.67466 + 8.09676i) q^{93} +(-4.74048 + 2.28290i) q^{94} +(5.32896 + 1.64377i) q^{95} +(0.534761 + 7.13588i) q^{96} +(2.41333 + 10.5735i) q^{97} +(-0.558179 + 1.42222i) q^{98} +(0.422662 - 5.64004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9}+O(q^{10}) $ 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 12 q^{12} - 9 q^{13} - 3 q^{14} - 14 q^{15} - 30 q^{16} - 29 q^{17} - 204 q^{18} - 8 q^{19} + 61 q^{20} + 26 q^{21} + 85 q^{22} - 79 q^{23} - 12 q^{24} + 22 q^{25} - 14 q^{26} + 12 q^{27} - 15 q^{28} + 54 q^{29} - 46 q^{30} - 52 q^{31} + 33 q^{32} + 39 q^{33} + 3 q^{34} + 32 q^{35} - 161 q^{36} + 68 q^{37} - 29 q^{38} + 61 q^{39} + 107 q^{40} + 63 q^{41} - 56 q^{42} - 45 q^{43} - 74 q^{44} + 144 q^{45} - 22 q^{46} - 70 q^{47} + 168 q^{48} - 119 q^{49} + 97 q^{50} - 6 q^{51} + 27 q^{52} + 10 q^{53} - 34 q^{54} - 78 q^{55} - 44 q^{56} - 40 q^{57} - 38 q^{58} - 47 q^{59} - 72 q^{60} - 76 q^{61} - 41 q^{62} + 63 q^{63} - 112 q^{64} - 31 q^{65} - 598 q^{66} - 39 q^{67} - 20 q^{68} - 17 q^{69} - 72 q^{70} - 37 q^{71} + 245 q^{72} + 14 q^{73} + 77 q^{74} - 121 q^{75} + 152 q^{76} + 59 q^{77} + 220 q^{78} + 4 q^{79} - 42 q^{80} - 109 q^{81} + 148 q^{82} + 59 q^{83} + 390 q^{84} + 2 q^{85} + 12 q^{86} - 78 q^{87} + 344 q^{88} - 103 q^{89} - 75 q^{90} + 148 q^{91} + 28 q^{92} + 140 q^{93} + 24 q^{94} - 302 q^{95} + 22 q^{96} + 57 q^{97} - 72 q^{98} - 128 q^{99}+O(q^{100}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 12 * q^12 - 9 * q^13 - 3 * q^14 - 14 * q^15 - 30 * q^16 - 29 * q^17 - 204 * q^18 - 8 * q^19 + 61 * q^20 + 26 * q^21 + 85 * q^22 - 79 * q^23 - 12 * q^24 + 22 * q^25 - 14 * q^26 + 12 * q^27 - 15 * q^28 + 54 * q^29 - 46 * q^30 - 52 * q^31 + 33 * q^32 + 39 * q^33 + 3 * q^34 + 32 * q^35 - 161 * q^36 + 68 * q^37 - 29 * q^38 + 61 * q^39 + 107 * q^40 + 63 * q^41 - 56 * q^42 - 45 * q^43 - 74 * q^44 + 144 * q^45 - 22 * q^46 - 70 * q^47 + 168 * q^48 - 119 * q^49 + 97 * q^50 - 6 * q^51 + 27 * q^52 + 10 * q^53 - 34 * q^54 - 78 * q^55 - 44 * q^56 - 40 * q^57 - 38 * q^58 - 47 * q^59 - 72 * q^60 - 76 * q^61 - 41 * q^62 + 63 * q^63 - 112 * q^64 - 31 * q^65 - 598 * q^66 - 39 * q^67 - 20 * q^68 - 17 * q^69 - 72 * q^70 - 37 * q^71 + 245 * q^72 + 14 * q^73 + 77 * q^74 - 121 * q^75 + 152 * q^76 + 59 * q^77 + 220 * q^78 + 4 * q^79 - 42 * q^80 - 109 * q^81 + 148 * q^82 + 59 * q^83 + 390 * q^84 + 2 * q^85 + 12 * q^86 - 78 * q^87 + 344 * q^88 - 103 * q^89 - 75 * q^90 + 148 * q^91 + 28 * q^92 + 140 * q^93 + 24 * q^94 - 302 * q^95 + 22 * q^96 + 57 * q^97 - 72 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{1}{21}\right)$

Coefficient data

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

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

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

$2$	−0.362567	−	0.454644i	−0.256373	−	0.321482i	0.636943	−	0.770911i	$-0.280199\pi$
$2$	−0.362567	−	0.454644i	−0.256373	−	0.321482i	−0.893316	+	0.449429i	$0.851627\pi$
$3$	1.29324	+	0.194925i	0.746653	+	0.112540i	0.511338	−	0.859380i	$-0.329150\pi$
$3$	1.29324	+	0.194925i	0.746653	+	0.112540i	0.235314	+	0.971919i	$0.424388\pi$
$4$	0.369795	−	1.62018i	0.184898	−	0.810089i
$5$	−2.61272	−	1.78132i	−1.16844	−	0.796631i	−0.185882	−	0.982572i	$-0.559514\pi$
$5$	−2.61272	−	1.78132i	−1.16844	−	0.796631i	−0.982561	+	0.185941i	$0.940467\pi$
$6$	−0.380264	−	0.658637i	−0.155242	−	0.268887i
$7$	−1.55140	+	2.68710i	−0.586373	+	1.01563i	0.408329	+	0.912835i	$0.366111\pi$
$7$	−1.55140	+	2.68710i	−0.586373	+	1.01563i	−0.994703	+	0.102794i	$0.967222\pi$
$8$	−1.91853	+	0.923914i	−0.678302	+	0.326653i
$9$	−1.23224	−	0.380097i	−0.410748	−	0.126699i
$10$	0.137417	+	1.83370i	0.0434551	+	0.579868i
$11$	0.975970	+	4.27600i	0.294266	+	1.28926i	0.878525	+	0.477696i	$0.158528\pi$
$11$	0.975970	+	4.27600i	0.294266	+	1.28926i	−0.584259	+	0.811567i	$0.698615\pi$
$12$	0.794047	−	2.02320i	0.229222	−	0.584047i
$13$	−0.221321	+	2.95333i	−0.0613834	+	0.819105i	0.878529	+	0.477689i	$0.158525\pi$
$13$	−0.221321	+	2.95333i	−0.0613834	+	0.819105i	−0.939912	+	0.341416i	$0.889094\pi$
$14$	1.78416	−	0.268919i	0.476837	−	0.0718715i
$15$	−3.03165	−	2.81296i	−0.782768	−	0.726303i
$16$	−1.87889	−	0.904828i	−0.469724	−	0.226207i
$17$	−0.826239	+	0.563320i	−0.200392	+	0.136625i
$17$	−0.826239	+	0.563320i	−0.200392	+	0.136625i
$18$	0.273961	+	0.698042i	0.0645733	+	0.164530i
$19$	−1.68522	+	0.519821i	−0.386615	+	0.119255i	−0.481969	−	0.876188i	$-0.660078\pi$
$19$	−1.68522	+	0.519821i	−0.386615	+	0.119255i	0.0953534	+	0.995443i	$0.469602\pi$
$20$	−3.85223	+	3.57435i	−0.861384	+	0.799248i
$21$	−2.53011	+	3.17266i	−0.552116	+	0.692331i
$22$	1.59021	−	1.99405i	0.339033	−	0.425134i
$23$	1.19257	−	1.10655i	0.248668	−	0.230731i	−0.545983	−	0.837796i	$-0.683844\pi$
$23$	1.19257	−	1.10655i	0.248668	−	0.230731i	0.794652	+	0.607065i	$0.207653\pi$
$24$	−2.66121	+	0.820875i	−0.543217	+	0.167560i
$25$	1.82649	+	4.65381i	0.365297	+	0.930762i
$26$	1.42296	−	0.970154i	0.279064	−	0.190263i
$27$	−5.05449	−	2.43411i	−0.972737	−	0.468445i
$28$	3.77988	+	3.50722i	0.714331	+	0.662802i
$29$	5.74762	−	0.866314i	1.06731	−	0.160871i	0.408179	−	0.912902i	$-0.366164\pi$
$29$	5.74762	−	0.866314i	1.06731	−	0.160871i	0.659127	+	0.752031i	$0.270926\pi$
$30$	−0.179721	+	2.39821i	−0.0328124	+	0.437850i
$31$	−2.61169	+	6.65448i	−0.469073	+	1.19518i	0.479195	+	0.877709i	$0.340929\pi$
$31$	−2.61169	+	6.65448i	−0.469073	+	1.19518i	−0.948268	+	0.317471i	$0.897166\pi$
$32$	1.21752	+	5.33432i	0.215230	+	0.942984i
$33$	0.428665	+	5.72014i	0.0746210	+	0.995749i
$34$	0.555677	+	0.171404i	0.0952978	+	0.0293955i
$35$	8.83995	−	4.25710i	1.49422	−	0.719581i
$36$	−1.07150	+	1.85590i	−0.178584	+	0.309316i
$37$	−1.67543	−	2.90193i	−0.275439	−	0.477074i	0.694807	−	0.719196i	$-0.255490\pi$
$37$	−1.67543	−	2.90193i	−0.275439	−	0.477074i	−0.970246	+	0.242122i	$0.922157\pi$
$38$	0.847337	+	0.577704i	0.137456	+	0.0937160i
$39$	−0.861897	+	3.77622i	−0.138014	+	0.604679i
$40$	6.65836	+	1.00359i	1.05278	+	0.158681i
$41$	−3.40119	−	4.26495i	−0.531176	−	0.666074i	0.441764	−	0.897131i	$-0.354353\pi$
$41$	−3.40119	−	4.26495i	−0.531176	−	0.666074i	−0.972940	+	0.231058i	$0.925781\pi$
$42$	2.35977			0.364120
$43$	−4.01300	+	5.18612i	−0.611977	+	0.790876i
$43$	−4.01300	+	5.18612i	−0.611977	+	0.790876i
$44$	7.28880			1.09883
$45$	2.54243	+	3.18811i	0.379003	+	0.475255i
$46$	−0.935471	−	0.141000i	−0.137928	−	0.0207892i
$47$	2.01338	−	8.82119i	0.293681	−	1.28670i	−0.585678	−	0.810544i	$-0.699172\pi$
$47$	2.01338	−	8.82119i	0.293681	−	1.28670i	0.879359	−	0.476159i	$-0.157971\pi$
$48$	−2.25349	−	1.53640i	−0.325263	−	0.221761i
$49$	−1.31367	−	2.27535i	−0.187667	−	0.325049i
$50$	1.45360	−	2.51772i	0.205571	−	0.356059i
$51$	−1.17833	+	0.567454i	−0.164999	+	0.0794594i
$52$	4.70307	+	1.45070i	0.652198	+	0.201177i
$53$	0.304993	+	4.06985i	0.0418940	+	0.559037i	0.978175	+	0.207784i	$0.0666251\pi$
$53$	0.304993	+	4.06985i	0.0418940	+	0.559037i	−0.936281	+	0.351253i	$0.885756\pi$
$54$	0.725933	+	3.18052i	0.0987870	+	0.432814i
$55$	5.06700	−	12.9105i	0.683234	−	1.74085i
$56$	0.493750	−	6.58863i	0.0659801	−	0.880443i
$57$	−2.28072	+	0.343763i	−0.302088	+	0.0455325i
$58$	−2.47776	−	2.29902i	−0.325346	−	0.301877i
$59$	−8.01457	−	3.85961i	−1.04341	−	0.502479i	−0.167961	−	0.985794i	$-0.553718\pi$
$59$	−8.01457	−	3.85961i	−1.04341	−	0.502479i	−0.875447	+	0.483315i	$0.839433\pi$
$60$	−5.67859	+	3.87159i	−0.733102	+	0.499821i
$61$	1.78686	+	4.55284i	0.228784	+	0.582931i	0.998458	−	0.0555049i	$-0.0176768\pi$
$61$	1.78686	+	4.55284i	0.228784	+	0.582931i	−0.769675	+	0.638436i	$0.779582\pi$
$62$	3.97233	−	1.22530i	0.504486	−	0.155613i
$63$	2.93306	−	2.72148i	0.369531	−	0.342874i
$64$	−0.616687	+	0.773301i	−0.0770858	+	0.0966626i
$65$	5.83907	−	7.32196i	0.724247	−	0.908178i
$66$	2.44521	−	2.26882i	0.300984	−	0.279273i
$67$	−8.56074	+	2.64064i	−1.04586	+	0.322605i	−0.769633	−	0.638487i	$-0.779561\pi$
$67$	−8.56074	+	2.64064i	−1.04586	+	0.322605i	−0.276228	+	0.961092i	$0.589085\pi$
$68$	0.607140	+	1.54697i	0.0736265	+	0.187597i
$69$	1.75798	−	1.19857i	0.211635	−	0.144291i
$70$	−5.14053	−	2.47555i	−0.614411	−	0.295885i
$71$	−8.54058	−	7.92450i	−1.01358	−	0.940465i	−0.0153469	−	0.999882i	$-0.504885\pi$
$71$	−8.54058	−	7.92450i	−1.01358	−	0.940465i	−0.998233	+	0.0594173i	$0.981076\pi$
$72$	2.71527	−	0.409261i	0.319998	−	0.0482319i
$73$	−0.398945	+	5.32355i	−0.0466929	+	0.623074i	0.923944	+	0.382527i	$0.124946\pi$
$73$	−0.398945	+	5.32355i	−0.0466929	+	0.623074i	−0.970637	+	0.240547i	$0.922673\pi$
$74$	−0.711890	+	1.81387i	−0.0827555	+	0.210858i
$75$	1.45494	+	6.37452i	0.168002	+	0.736066i
$76$	0.219017	+	2.92258i	0.0251230	+	0.335243i
$77$	−13.0042	−	4.01125i	−1.48196	−	0.457125i
$78$	2.02933	−	0.977274i	0.229776	−	0.110654i
$79$	−0.340048	+	0.588981i	−0.0382584	+	0.0662656i	−0.884521	−	0.466501i	$-0.845514\pi$
$79$	−0.340048	+	0.588981i	−0.0382584	+	0.0662656i	0.846262	+	0.532767i	$0.178848\pi$
$80$	3.29723	+	5.71097i	0.368642	+	0.638506i
$81$	−2.86581	−	1.95388i	−0.318423	−	0.217097i
$82$	−0.705879	+	3.09266i	−0.0779513	+	0.341527i
$83$	−10.2321	−	1.54224i	−1.12311	−	0.169282i	−0.438881	−	0.898545i	$-0.644625\pi$
$83$	−10.2321	−	1.54224i	−1.12311	−	0.169282i	−0.684234	+	0.729263i	$0.739863\pi$
$84$	4.20465	+	5.27247i	0.458765	+	0.575273i
$85$	3.16218			0.342987
$86$	3.81282	−	0.0558268i	0.411147	−	0.00601996i
$87$	7.60192			0.815011
$88$	−5.82308	−	7.30192i	−0.620743	−	0.778387i
$89$	−13.6258	−	2.05375i	−1.44433	−	0.217697i	−0.620352	−	0.784324i	$-0.713010\pi$
$89$	−13.6258	−	2.05375i	−1.44433	−	0.217697i	−0.823975	+	0.566626i	$0.808248\pi$
$90$	0.527654	−	2.31180i	0.0556196	−	0.243685i
$91$	−7.59252	−	5.17649i	−0.795913	−	0.542644i
$92$	−1.35179	−	2.34137i	−0.140934	−	0.244105i
$93$	−4.67466	+	8.09676i	−0.484740	+	0.839594i
$94$	−4.74048	+	2.28290i	−0.488944	+	0.235463i
$95$	5.32896	+	1.64377i	0.546740	+	0.168647i
$96$	0.534761	+	7.13588i	0.0545788	+	0.728303i
$97$	2.41333	+	10.5735i	0.245036	+	1.07357i	0.936364	+	0.351032i	$0.114169\pi$
$97$	2.41333	+	10.5735i	0.245036	+	1.07357i	−0.691328	+	0.722542i	$0.742974\pi$
$98$	−0.558179	+	1.42222i	−0.0563846	+	0.143666i
$99$	0.422662	−	5.64004i	0.0424792	−	0.566845i
$100$	8.21543	−	1.23828i	0.821543	−	0.123828i
$101$	8.41065	+	7.80395i	0.836891	+	0.776522i	0.976915	−	0.213627i	$-0.0685276\pi$
$101$	8.41065	+	7.80395i	0.836891	+	0.776522i	−0.140024	+	0.990148i	$0.544718\pi$
$102$	0.685213	+	0.329981i	0.0678462	+	0.0326730i
$103$	−3.92710	+	2.67745i	−0.386948	+	0.263817i	−0.741133	−	0.671359i	$-0.765711\pi$
$103$	−3.92710	+	2.67745i	−0.386948	+	0.263817i	0.354184	+	0.935176i	$0.384759\pi$
$104$	−2.30401	−	5.87052i	−0.225927	−	0.575652i
$105$	12.2620	−	3.78233i	1.19665	−	0.369117i
$106$	1.73975	−	1.61425i	0.168980	−	0.156790i
$107$	4.87546	−	6.11363i	0.471328	−	0.591027i	−0.488168	−	0.872750i	$-0.662334\pi$
$107$	4.87546	−	6.11363i	0.471328	−	0.591027i	0.959496	+	0.281723i	$0.0909059\pi$
$108$	−5.81282	+	7.28905i	−0.559339	+	0.701389i
$109$	−2.79755	+	2.59574i	−0.267956	+	0.248627i	−0.802694	−	0.596391i	$-0.796601\pi$
$109$	−2.79755	+	2.59574i	−0.267956	+	0.248627i	0.534738	+	0.845018i	$0.320410\pi$
$110$	−7.70681	+	2.37724i	−0.734815	+	0.226661i
$111$	−1.60108	−	4.07947i	−0.151967	−	0.387207i
$112$	5.34628	−	3.64503i	0.505176	−	0.344423i
$113$	13.3771	+	6.44209i	1.25842	+	0.606021i	0.939755	−	0.341848i	$-0.111053\pi$
$113$	13.3771	+	6.44209i	1.25842	+	0.606021i	0.318660	+	0.947869i	$0.396767\pi$
$114$	0.983201	+	0.912277i	0.0920852	+	0.0854426i
$115$	−5.08697	+	0.766737i	−0.474362	+	0.0714986i
$116$	0.721858	−	9.63253i	0.0670229	−	0.894358i
$117$	1.39527	−	3.55509i	0.128993	−	0.328668i
$118$	1.15106	+	5.04314i	0.105964	+	0.464259i
$119$	−0.231872	−	3.09412i	−0.0212557	−	0.283638i
$120$	8.41523	+	2.59576i	0.768202	+	0.236959i
$121$	−7.42103	+	3.57378i	−0.674639	+	0.324889i
$122$	1.42207	−	2.46309i	0.128748	−	0.222998i
$123$	−3.56721	−	6.17858i	−0.321644	−	0.557104i
$124$	9.81565	+	6.69220i	0.881471	+	0.600977i
$125$	−0.000422805		0.00185243i	−3.78168e−5		0.000165686i
$126$	−2.30073	−	0.346780i	−0.204966	−	0.0308936i
$127$	5.11757	+	6.41723i	0.454111	+	0.569437i	0.955201	−	0.295958i	$-0.0956390\pi$
$127$	5.11757	+	6.41723i	0.454111	+	0.569437i	−0.501090	+	0.865395i	$0.667068\pi$
$128$	11.5182			1.01807
$129$	−6.20068	+	5.92467i	−0.545939	+	0.521638i
$130$	−5.44594			−0.477640
$131$	−14.1283	−	17.7163i	−1.23439	−	1.54788i	−0.727993	−	0.685584i	$-0.759547\pi$
$131$	−14.1283	−	17.7163i	−1.23439	−	1.54788i	−0.506402	−	0.862298i	$-0.669025\pi$
$132$	9.42617	+	1.42077i	0.820442	+	0.123662i
$133$	1.21763	−	5.33479i	0.105582	−	0.462585i
$134$	4.30439	+	2.93468i	0.371843	+	0.253518i
$135$	8.87001	+	15.3633i	0.763409	+	1.32226i
$136$	1.06470	−	1.84412i	0.0912975	−	0.158132i
$137$	5.26271	−	2.53439i	0.449623	−	0.216527i	−0.195348	−	0.980734i	$-0.562584\pi$
$137$	5.26271	−	2.53439i	0.449623	−	0.216527i	0.644971	+	0.764207i	$0.276869\pi$
$138$	−1.18230	−	0.364693i	−0.100644	−	0.0310447i
$139$	−1.36856	−	18.2622i	−0.116080	−	1.54898i	−0.686196	−	0.727417i	$-0.740721\pi$
$139$	−1.36856	−	18.2622i	−0.116080	−	1.54898i	0.570116	−	0.821564i	$-0.306898\pi$
$140$	−3.62828	−	15.8966i	−0.306646	−	1.34350i
$141$	4.32325	−	11.0155i	0.364083	−	0.927669i
$142$	−0.506298	+	6.75608i	−0.0424876	+	0.566958i
$143$	−12.8444	+	1.93599i	−1.07411	+	0.161895i
$144$	1.97133	+	1.82913i	0.164278	+	0.152427i
$145$	−16.5601	−	7.97492i	−1.37524	−	0.662281i
$146$	2.56496	−	1.74876i	0.212278	−	0.144729i
$147$	−1.25537	−	3.19864i	−0.103541	−	0.263819i
$148$	−5.32121	+	1.64138i	−0.437401	+	0.134920i
$149$	−15.1596	+	14.0660i	−1.24192	+	1.15234i	−0.259484	+	0.965747i	$0.583552\pi$
$149$	−15.1596	+	14.0660i	−1.24192	+	1.15234i	−0.982438	+	0.186588i	$0.940257\pi$
$150$	2.37062	−	2.97267i	0.193561	−	0.242717i
$151$	−8.55575	+	10.7286i	−0.696257	+	0.873078i	−0.996738	−	0.0807094i	$-0.974281\pi$
$151$	−8.55575	+	10.7286i	−0.696257	+	0.873078i	0.300481	+	0.953788i	$0.402853\pi$
$152$	2.75287	−	2.55429i	0.223287	−	0.207180i
$153$	1.23224	−	0.380097i	0.0996210	−	0.0307290i
$154$	2.89118	+	7.36661i	0.232978	+	0.593619i
$155$	18.6774	−	12.7340i	1.50020	−	1.02282i
$156$	5.79942	+	2.79285i	0.464325	+	0.223607i
$157$	0.850517	+	0.789164i	0.0678786	+	0.0629822i	0.713383	−	0.700775i	$-0.247162\pi$
$157$	0.850517	+	0.789164i	0.0678786	+	0.0629822i	−0.645504	+	0.763757i	$0.723353\pi$
$158$	0.391067	−	0.0589439i	0.0311116	−	0.00468932i
$159$	−0.398884	+	5.32274i	−0.0316336	+	0.422121i
$160$	6.32109	−	16.1059i	0.499726	−	1.27328i
$161$	1.12324	+	4.92125i	0.0885240	+	0.387849i
$162$	0.150729	+	2.01133i	0.0118424	+	0.158025i
$163$	−0.254701	−	0.0785649i	−0.0199497	−	0.00615368i	0.284764	−	0.958598i	$-0.408085\pi$
$163$	−0.254701	−	0.0785649i	−0.0199497	−	0.00615368i	−0.304714	+	0.952444i	$0.598561\pi$
$164$	−8.16773	+	3.93337i	−0.637792	+	0.307145i
$165$	9.06942	−	15.7087i	0.706054	−	1.22292i
$166$	3.00864	+	5.21111i	0.233515	+	0.404460i
$167$	10.8423	+	7.39215i	0.839002	+	0.572022i	0.904813	−	0.425810i	$-0.140011\pi$
$167$	10.8423	+	7.39215i	0.839002	+	0.572022i	−0.0658103	+	0.997832i	$0.520963\pi$
$168$	1.92282	−	8.42444i	0.148349	−	0.649960i
$169$	4.18165	+	0.630283i	0.321666	+	0.0484833i
$170$	−1.14650	−	1.43767i	−0.0879327	−	0.110264i
$171$	2.27418			0.173911
$172$	6.91845	+	8.41958i	0.527527	+	0.641987i
$173$	17.9175			1.36224			0.681121	−	0.732171i	$-0.261493\pi$
$173$	17.9175			1.36224			0.681121	+	0.732171i	$0.261493\pi$
$174$	−2.75620	−	3.45617i	−0.208947	−	0.262011i
$175$	−15.3389	−	2.31196i	−1.15951	−	0.174768i
$176$	2.03530	−	8.91724i	0.153417	−	0.672162i
$177$	−9.61243	−	6.55364i	−0.722514	−	0.492602i
$178$	4.00652	+	6.93949i	0.300301	+	0.520137i
$179$	11.8063	−	20.4492i	0.882448	−	1.52844i	0.0338367	−	0.999427i	$-0.489227\pi$
$179$	11.8063	−	20.4492i	0.882448	−	1.52844i	0.848611	−	0.529017i	$-0.177439\pi$
$180$	6.10548	−	2.94024i	0.455076	−	0.219153i
$181$	1.72133	+	0.530958i	0.127945	+	0.0394658i	0.358066	−	0.933696i	$-0.383436\pi$
$181$	1.72133	+	0.530958i	0.127945	+	0.0394658i	−0.230121	+	0.973162i	$0.573912\pi$
$182$	0.399332	+	5.32872i	0.0296005	+	0.394991i
$183$	1.42338	+	6.23622i	0.105219	+	0.460995i
$184$	−1.26563	+	3.22477i	−0.0933034	+	0.237733i
$185$	−0.791842	+	10.5664i	−0.0582174	+	0.776857i
$186$	5.37602	−	0.810304i	0.394189	−	0.0594144i
$187$	−3.21514	−	2.98322i	−0.235114	−	0.218154i
$188$	−13.5474	−	6.52406i	−0.988043	−	0.475816i
$189$	14.3822	−	9.80564i	1.04615	−	0.713255i
$190$	−1.18477	−	3.01876i	−0.0859526	−	0.219004i
$191$	−4.03553	+	1.24480i	−0.292001	+	0.0900703i	−0.437295	−	0.899318i	$-0.644063\pi$
$191$	−4.03553	+	1.24480i	−0.292001	+	0.0900703i	0.145294	+	0.989389i	$0.453587\pi$
$192$	−0.948260	+	0.879856i	−0.0684347	+	0.0634982i
$193$	3.43129	−	4.30270i	0.246989	−	0.309715i	−0.642847	−	0.765995i	$-0.722247\pi$
$193$	3.43129	−	4.30270i	0.246989	−	0.309715i	0.889836	+	0.456280i	$0.150818\pi$
$194$	3.93217	−	4.93079i	0.282314	−	0.354010i
$195$	8.97855	−	8.33088i	0.642967	−	0.596587i
$196$	−4.17225	+	1.28697i	−0.298018	+	0.0919264i
$197$	4.43171	+	11.2918i	0.315746	+	0.804509i	0.997348	+	0.0727848i	$0.0231886\pi$
$197$	4.43171	+	11.2918i	0.315746	+	0.804509i	−0.681601	+	0.731724i	$0.738716\pi$
$198$	−2.71745	+	1.85273i	−0.193121	+	0.131668i
$199$	−18.7904	−	9.04897i	−1.33201	−	0.641464i	−0.373799	−	0.927510i	$-0.621945\pi$
$199$	−18.7904	−	9.04897i	−1.33201	−	0.641464i	−0.958216	+	0.286045i	$0.907659\pi$
$200$	−7.80388	−	7.24094i	−0.551818	−	0.512012i
$201$	−11.5858	+	1.74628i	−0.817201	+	0.123173i
$202$	0.498596	−	6.65330i	0.0350811	−	0.468125i
$203$	−6.58897	+	16.7884i	−0.462455	+	1.17832i
$204$	0.483636	+	2.11895i	0.0338613	+	0.148356i
$205$	1.28909	+	17.2017i	0.0900340	+	1.20142i
$206$	2.64112	+	0.814678i	0.184016	+	0.0567613i
$207$	−1.89013	+	0.910240i	−0.131373	+	0.0632661i
$208$	3.08809	−	5.34873i	0.214120	−	0.370868i
$209$	−3.86748	−	6.69866i	−0.267519	−	0.463356i
$210$	−6.16540	−	4.20350i	−0.425453	−	0.290069i
$211$	2.52325	−	11.0551i	0.173708	−	0.761064i	−0.810743	−	0.585402i	$-0.800937\pi$
$211$	2.52325	−	11.0551i	0.173708	−	0.761064i	0.984451	−	0.175661i	$-0.0562063\pi$
$212$	6.70667	+	1.01087i	0.460616	+	0.0694266i
$213$	−9.50034	−	11.9130i	−0.650953	−	0.816269i
$214$	−4.54720			−0.310840
$215$	19.7230	−	6.40143i	1.34510	−	0.436574i
$216$	11.9461			0.812828
$217$	−13.8295	−	17.3416i	−0.938806	−	1.17723i
$218$	2.19444	+	0.330758i	0.148626	+	0.0224018i
$219$	−1.55362	+	6.80686i	−0.104984	+	0.459965i
$220$	−19.0436	−	12.9837i	−1.28392	−	0.875360i
$221$	−1.48080	−	2.56483i	−0.0996096	−	0.172529i
$222$	−1.27421	+	2.20700i	−0.0855195	+	0.148124i
$223$	2.54190	−	1.22411i	0.170218	−	0.0819727i	−0.346835	−	0.937926i	$-0.612743\pi$
$223$	2.54190	−	1.22411i	0.170218	−	0.0819727i	0.517053	+	0.855954i	$0.327029\pi$
$224$	−16.2227	−	5.00405i	−1.08393	−	0.334347i
$225$	−0.481777	−	6.42887i	−0.0321185	−	0.428591i
$226$	−1.92124	−	8.41752i	−0.127799	−	0.559925i
$227$	4.34843	−	11.0796i	0.288615	−	0.735380i	−0.710871	−	0.703323i	$-0.751699\pi$
$227$	4.34843	−	11.0796i	0.288615	−	0.735380i	0.999486	−	0.0320570i	$-0.0102058\pi$
$228$	−0.286441	+	3.82229i	−0.0189700	+	0.253137i
$229$	17.9936	−	2.71210i	1.18905	−	0.179221i	0.475430	−	0.879753i	$-0.342292\pi$
$229$	17.9936	−	2.71210i	1.18905	−	0.179221i	0.713620	+	0.700533i	$0.247054\pi$
$230$	2.19296	+	2.03477i	0.144599	+	0.134168i
$231$	−16.0356	−	7.72235i	−1.05507	−	0.508093i
$232$	−10.2266	+	6.97235i	−0.671407	+	0.457758i
$233$	−7.71911	−	19.6680i	−0.505696	−	1.28849i	−0.924766	−	0.380537i	$-0.875739\pi$
$233$	−7.71911	−	19.6680i	−0.505696	−	1.28849i	0.419070	−	0.907954i	$-0.362356\pi$
$234$	−2.12218	+	0.654606i	−0.138731	+	0.0427929i
$235$	−20.9738	+	19.4608i	−1.36818	+	1.26948i
$236$	−9.21701	+	11.5578i	−0.599976	+	0.752346i
$237$	−0.554571	+	0.695410i	−0.0360233	+	0.0451718i
$238$	−1.32265	+	1.22724i	−0.0857349	+	0.0795504i
$239$	10.1776	−	3.13936i	0.658331	−	0.203068i	0.0524503	−	0.998624i	$-0.483297\pi$
$239$	10.1776	−	3.13936i	0.658331	−	0.203068i	0.605881	+	0.795555i	$0.292821\pi$
$240$	3.15090	+	8.02837i	0.203390	+	0.518229i
$241$	14.2570	−	9.72028i	0.918376	−	0.626138i	−0.00912490	−	0.999958i	$-0.502905\pi$
$241$	14.2570	−	9.72028i	0.918376	−	0.626138i	0.927501	+	0.373820i	$0.121952\pi$
$242$	4.31541	+	2.07819i	0.277405	+	0.133591i
$243$	9.01207	+	8.36198i	0.578124	+	0.536421i
$244$	8.03718	−	1.21141i	0.514528	−	0.0775526i
$245$	−0.620868	+	8.28491i	−0.0396658	+	0.529303i
$246$	−1.51571	+	3.86196i	−0.0966379	+	0.246229i
$247$	−1.16223	−	5.09204i	−0.0739506	−	0.323999i
$248$	−1.13757	−	15.1798i	−0.0722356	−	0.963917i
$249$	−12.9319	−	3.98896i	−0.819526	−	0.252790i
$250$	0.000995491	0	0.000479403i	6.29604e−5	0	3.03201e-5i
$251$	−6.54699	+	11.3397i	−0.413243	+	0.715757i	−0.995242	−	0.0974319i	$-0.968937\pi$
$251$	−6.54699	+	11.3397i	−0.413243	+	0.715757i	0.582000	+	0.813189i	$0.302271\pi$
$252$	−3.32465	−	5.75847i	−0.209433	−	0.362749i
$253$	5.89550	+	4.01949i	0.370647	+	0.252703i
$254$	1.06210	−	4.65334i	0.0666418	−	0.291977i
$255$	4.08946	+	0.616387i	0.256092	+	0.0385997i
$256$	−2.94273	−	3.69007i	−0.183921	−	0.230629i
$257$	15.3091			0.954957			0.477478	−	0.878644i	$-0.341551\pi$
$257$	15.3091			0.954957			0.477478	+	0.878644i	$0.341551\pi$
$258$	4.94177	+	0.671015i	0.307661	+	0.0417755i
$259$	10.3970			0.646040
$260$	−9.70362	−	12.1680i	−0.601793	−	0.754625i
$261$	−7.41175	−	1.11714i	−0.458776	−	0.0691493i
$262$	−2.93217	+	12.8467i	−0.181150	+	0.793671i
$263$	9.96315	+	6.79276i	0.614354	+	0.418860i	0.830119	−	0.557586i	$-0.188272\pi$
$263$	9.96315	+	6.79276i	0.614354	+	0.418860i	−0.215765	+	0.976445i	$0.569225\pi$
$264$	−6.10732	−	10.5782i	−0.375880	−	0.651043i
$265$	6.45285	−	11.1767i	0.396395	−	0.686577i
$266$	−2.86691	+	1.38063i	−0.175781	+	0.0846518i
$267$	−17.2210	−	5.31199i	−1.05391	−	0.325088i
$268$	1.11259	+	14.8464i	0.0679620	+	0.906890i
$269$	0.936611	+	4.10356i	0.0571062	+	0.250198i	0.995422	−	0.0955822i	$-0.0304713\pi$
$269$	0.936611	+	4.10356i	0.0571062	+	0.250198i	−0.938315	+	0.345781i	$0.887614\pi$
$270$	3.76887	−	9.60292i	0.229366	−	0.584415i
$271$	1.26401	−	16.8671i	0.0767834	−	1.02460i	−0.817156	−	0.576416i	$-0.804451\pi$
$271$	1.26401	−	16.8671i	0.0767834	−	1.02460i	0.893940	−	0.448187i	$-0.147930\pi$
$272$	2.06212	−	0.310815i	0.125035	−	0.0188459i
$273$	−8.80993	−	8.17442i	−0.533201	−	0.494738i
$274$	−3.06032	−	1.47377i	−0.184881	−	0.0890340i
$275$	−18.1171	+	12.3520i	−1.09250	+	0.744856i
$276$	−1.29180	−	3.29146i	−0.0777573	−	0.198122i
$277$	15.3584	−	4.73743i	0.922794	−	0.284644i	0.203279	−	0.979121i	$-0.434840\pi$
$277$	15.3584	−	4.73743i	0.922794	−	0.284644i	0.719515	+	0.694477i	$0.244364\pi$
$278$	−7.80661	+	7.24348i	−0.468209	+	0.434435i
$279$	5.74758	−	7.20724i	0.344099	−	0.431486i
$280$	−13.0265	+	16.3347i	−0.778482	+	0.976186i
$281$	−8.39899	+	7.79312i	−0.501042	+	0.464899i	−0.889741	−	0.456466i	$-0.849115\pi$
$281$	−8.39899	+	7.79312i	−0.501042	+	0.464899i	0.388699	+	0.921365i	$0.372925\pi$
$282$	−6.57558	+	2.02830i	−0.391570	+	0.120783i
$283$	4.50121	+	11.4689i	0.267569	+	0.681756i	1.00000		0.000913496i	$0.000290775\pi$
$283$	4.50121	+	11.4689i	0.267569	+	0.681756i	−0.732430	+	0.680842i	$0.761614\pi$
$284$	−15.9974	+	10.9068i	−0.949269	+	0.647201i
$285$	6.57122	+	3.16453i	0.389245	+	0.187451i
$286$	5.53714	+	5.13772i	0.327418	+	0.303800i
$287$	16.7369	−	2.52269i	0.987951	−	0.148910i
$288$	0.527272	−	7.03596i	0.0310698	−	0.414598i
$289$	0.365341	−	0.930874i	0.0214906	−	0.0547573i
$290$	2.37839	+	10.4204i	0.139664	+	0.611906i
$291$	1.05998	+	14.1445i	0.0621371	+	0.829163i
$292$	8.47757	+	2.61498i	0.496112	+	0.153030i
$293$	−18.7588	+	9.03377i	−1.09590	+	0.527758i	−0.892368	−	0.451309i	$-0.850957\pi$
$293$	−18.7588	+	9.03377i	−1.09590	+	0.527758i	−0.203534	+	0.979068i	$0.565243\pi$
$294$	−0.999085	+	1.73047i	−0.0582678	+	0.100923i
$295$	14.0646	+	24.3606i	0.818872	+	1.41833i
$296$	5.89549	+	4.01948i	0.342668	+	0.233627i
$297$	5.47525	−	23.9886i	0.317706	−	1.39196i
$298$	11.8914	+	1.79234i	0.688851	+	0.103828i
$299$	3.00405	+	3.76695i	0.173728	+	0.217849i
$300$	10.8659			0.627343
$301$	−7.70986	−	18.8291i	−0.444389	−	1.08529i
$302$	7.97971			0.459181
$303$	9.35581	+	11.7318i	0.537478	+	0.673975i
$304$	3.63669	+	0.548143i	0.208579	+	0.0314382i
$305$	3.44151	−	15.0783i	0.197060	−	0.863378i
$306$	−0.619579	−	0.422422i	−0.0354190	−	0.0241482i
$307$	16.9928	+	29.4324i	0.969831	+	1.67980i	0.696033	+	0.718010i	$0.254947\pi$
$307$	16.9928	+	29.4324i	0.969831	+	1.67980i	0.273798	+	0.961787i	$0.411720\pi$
$308$	−11.3078	+	19.5857i	−0.644323	+	1.11600i
$309$	−5.60058	+	2.69710i	−0.318606	+	0.153433i
$310$	−12.5612	−	3.87463i	−0.713430	−	0.220064i
$311$	2.58429	+	34.4850i	0.146542	+	1.95547i	0.269367	+	0.963038i	$0.413186\pi$
$311$	2.58429	+	34.4850i	0.146542	+	1.95547i	−0.122825	+	0.992428i	$0.539195\pi$
$312$	−1.83533	−	8.04110i	−0.103905	−	0.455237i
$313$	−2.32802	+	5.93170i	−0.131588	+	0.335280i	−0.981448	−	0.191728i	$-0.938591\pi$
$313$	−2.32802	+	5.93170i	−0.131588	+	0.335280i	0.849861	+	0.527008i	$0.176686\pi$
$314$	0.0504199	−	0.672807i	0.00284536	−	0.0379687i
$315$	−12.5111	+	1.88574i	−0.704920	+	0.106250i
$316$	0.828506	+	0.768741i	0.0466071	+	0.0432451i
$317$	19.5988	+	9.43827i	1.10078	+	0.530106i	0.893903	−	0.448261i	$-0.147957\pi$
$317$	19.5988	+	9.43827i	1.10078	+	0.530106i	0.206874	+	0.978368i	$0.433671\pi$
$318$	2.56458	−	1.74850i	0.143814	−	0.0980509i
$319$	9.31387	+	23.7313i	0.521476	+	1.32870i
$320$	2.98873	−	0.921900i	0.167075	−	0.0515358i
$321$	7.49684	−	6.95605i	0.418433	−	0.388249i
$322$	1.83017	−	2.29496i	0.101991	−	0.127893i
$323$	1.09957	−	1.37881i	0.0611815	−	0.0767192i
$324$	−4.22539	+	3.92059i	−0.234744	+	0.217811i
$325$	−14.1485	+	4.36422i	−0.784815	+	0.242083i
$326$	0.0566271	+	0.144283i	0.00313628	+	0.00799112i
$327$	−4.12388	+	2.81161i	−0.228051	+	0.155482i
$328$	10.4657	+	5.04002i	0.577873	+	0.278289i
$329$	20.5799	+	19.0953i	1.13460	+	1.05276i
$330$	−10.4301	+	1.57209i	−0.574160	+	0.0865407i
$331$	−0.789781	+	10.5389i	−0.0434103	+	0.579270i	0.932510	+	0.361144i	$0.117614\pi$
$331$	−0.789781	+	10.5389i	−0.0434103	+	0.579270i	−0.975920	+	0.218127i	$0.930005\pi$
$332$	−6.28246	+	16.0075i	−0.344795	+	0.878523i
$333$	0.961523	+	4.21271i	0.0526911	+	0.230855i
$334$	−0.570256	−	7.60953i	−0.0312030	−	0.416375i
$335$	27.0706	+	8.35018i	1.47903	+	0.456219i
$336$	7.62453	−	3.67178i	0.415952	−	0.200312i
$337$	8.01245	−	13.8780i	0.436466	−	0.755981i	−0.560948	−	0.827851i	$-0.689563\pi$
$337$	8.01245	−	13.8780i	0.436466	−	0.755981i	0.997414	+	0.0718698i	$0.0228966\pi$
$338$	−1.22957	−	2.12968i	−0.0668800	−	0.115840i
$339$	16.0441	+	10.9387i	0.871398	+	0.594109i
$340$	1.16936	−	5.12330i	0.0634174	−	0.277850i
$341$	−31.0035	−	4.67302i	−1.67893	−	0.253058i
$342$	−0.824541	−	1.03394i	−0.0445861	−	0.0559092i
$343$	−13.5675			−0.732574
$344$	2.90752	−	13.6574i	0.156763	−	0.736357i
$345$	−6.72813			−0.362230
$346$	−6.49628	−	8.14608i	−0.349242	−	0.437936i
$347$	−7.11186	−	1.07194i	−0.381784	−	0.0575447i	−0.0446535	−	0.999003i	$-0.514218\pi$
$347$	−7.11186	−	1.07194i	−0.381784	−	0.0575447i	−0.337131	+	0.941458i	$0.609456\pi$
$348$	2.81115	−	12.3165i	0.150694	−	0.660232i
$349$	7.17992	+	4.89519i	0.384332	+	0.262033i	0.740039	−	0.672564i	$-0.234807\pi$
$349$	7.17992	+	4.89519i	0.384332	+	0.262033i	−0.355706	+	0.934598i	$0.615760\pi$
$350$	4.51024	+	7.81196i	0.241082	+	0.417567i
$351$	8.30739	−	14.3888i	0.443416	−	0.768019i
$352$	−21.6213	+	10.4123i	−1.15242	+	0.554976i
$353$	−9.18936	−	2.83454i	−0.489100	−	0.150867i	0.0403892	−	0.999184i	$-0.487140\pi$
$353$	−9.18936	−	2.83454i	−0.489100	−	0.150867i	−0.529489	+	0.848317i	$0.677616\pi$
$354$	0.505570	+	6.74636i	0.0268707	+	0.358565i
$355$	8.19805	+	35.9180i	0.435107	+	1.90633i
$356$	−8.36618	+	21.3167i	−0.443407	+	1.12978i
$357$	0.303254	−	4.04664i	0.0160499	−	0.214171i
$358$	−13.5777	+	2.04651i	−0.717603	+	0.108161i
$359$	−0.342610	−	0.317896i	−0.0180823	−	0.0167779i	0.671080	−	0.741385i	$-0.265831\pi$
$359$	−0.342610	−	0.317896i	−0.0180823	−	0.0167779i	−0.689162	+	0.724607i	$0.742021\pi$
$360$	−7.82326	−	3.76748i	−0.412322	−	0.198564i
$361$	−13.1288	+	8.95106i	−0.690989	+	0.471108i
$362$	−0.382698	−	0.975098i	−0.0201141	−	0.0512500i
$363$	−10.2938	+	3.17521i	−0.540284	+	0.166656i
$364$	−11.1945	+	10.3870i	−0.586752	+	0.544427i
$365$	10.5253	−	13.1983i	0.550918	−	0.690829i
$366$	2.31919	−	2.90817i	0.121226	−	0.152013i
$367$	3.97946	−	3.69240i	0.207726	−	0.192742i	−0.569448	−	0.822027i	$-0.692843\pi$
$367$	3.97946	−	3.69240i	0.207726	−	0.192742i	0.777174	+	0.629286i	$0.216652\pi$
$368$	−3.24195	+	1.00001i	−0.168998	+	0.0521291i
$369$	2.56999	+	6.54824i	0.133789	+	0.340888i
$370$	5.09105	−	3.47102i	0.264671	−	0.180450i
$371$	−11.4093	−	5.49441i	−0.592339	−	0.285255i
$372$	11.3895	+	10.5679i	0.590519	+	0.547922i
$373$	−10.6935	+	1.61178i	−0.553687	+	0.0834549i	−0.419925	−	0.907559i	$-0.637944\pi$
$373$	−10.6935	+	1.61178i	−0.553687	+	0.0834549i	−0.133762	+	0.991014i	$0.542706\pi$
$374$	−0.190598	+	2.54336i	−0.00985561	+	0.131514i
$375$	−0.000907873		0.00231322i	−4.68824e−5		0.000119454i
$376$	4.28730	+	18.7839i	0.221100	+	0.968705i
$377$	1.28644	+	17.1663i	0.0662549	+	0.884111i
$378$	−9.67259	−	2.98360i	−0.497504	−	0.153460i
$379$	−11.6238	+	5.59773i	−0.597075	+	0.287536i	−0.707910	−	0.706303i	$-0.750362\pi$
$379$	−11.6238	+	5.59773i	−0.597075	+	0.287536i	0.110835	+	0.993839i	$0.464647\pi$
$380$	4.63382	−	8.02601i	0.237710	−	0.411726i
$381$	5.36737	+	9.29656i	0.274979	+	0.476277i
$382$	2.02909	+	1.38341i	0.103817	+	0.0707814i
$383$	4.13991	−	18.1381i	0.211540	−	0.926816i	−0.751982	−	0.659184i	$-0.770902\pi$
$383$	4.13991	−	18.1381i	0.211540	−	0.926816i	0.963521	−	0.267632i	$-0.0862410\pi$
$384$	14.8958	+	2.24518i	0.760146	+	0.114574i
$385$	26.8309	+	33.6449i	1.36743	+	1.71470i
$386$	−3.20026			−0.162889
$387$	6.91622	−	4.86523i	0.351571	−	0.247314i
$388$	18.0233			0.914997
$389$	4.76032	+	5.96925i	0.241358	+	0.302653i	0.887726	−	0.460373i	$-0.152284\pi$
$389$	4.76032	+	5.96925i	0.241358	+	0.302653i	−0.646368	+	0.763026i	$0.723713\pi$
$390$	−7.04291	−	1.06155i	−0.356631	−	0.0537535i
$391$	−0.362010	+	1.58607i	−0.0183076	+	0.0802110i
$392$	4.62254	+	3.15159i	0.233473	+	0.159179i
$393$	−14.8179	−	25.6654i	−0.747466	−	1.29465i
$394$	3.52697	−	6.10889i	0.177686	−	0.307761i
$395$	1.93762	−	0.933106i	0.0974920	−	0.0469497i
$396$	−8.98157	−	2.77045i	−0.451341	−	0.139220i
$397$	0.594886	+	7.93820i	0.0298565	+	0.398407i	0.992033	+	0.125980i	$0.0402074\pi$
$397$	0.594886	+	7.93820i	0.0298565	+	0.398407i	−0.962176	+	0.272427i	$0.912174\pi$
$398$	2.69870	+	11.8238i	0.135274	+	0.592673i
$399$	2.61457	−	6.66183i	0.130892	−	0.333508i
$400$	0.779123	−	10.3967i	0.0389561	−	0.519834i
$401$	−36.3048	+	5.47207i	−1.81298	+	0.273262i	−0.966032	−	0.258421i	$-0.916798\pi$
$401$	−36.3048	+	5.47207i	−1.81298	+	0.273262i	−0.846944	+	0.531683i	$0.821560\pi$
$402$	4.99457	+	4.63428i	0.249106	+	0.231137i
$403$	−19.0748	−	9.18595i	−0.950184	−	0.457585i
$404$	15.7540	−	10.7409i	0.783791	−	0.534380i
$405$	4.00707	+	10.2099i	0.199113	+	0.507332i
$406$	10.0217	−	3.09128i	0.497369	−	0.153418i
$407$	10.7735	−	9.99634i	0.534022	−	0.495500i
$408$	1.73638	−	2.17735i	0.0859636	−	0.107795i
$409$	−9.65609	+	12.1084i	−0.477463	+	0.598720i	−0.960981	−	0.276615i	$-0.910787\pi$
$409$	−9.65609	+	12.1084i	−0.477463	+	0.598720i	0.483518	+	0.875335i	$0.339359\pi$
$410$	7.35328	−	6.82284i	0.363153	−	0.336956i
$411$	7.29996	−	2.25174i	0.360080	−	0.111070i
$412$	2.88573	+	7.35271i	0.142169	+	0.362242i
$413$	22.8049	−	15.5481i	1.12216	−	0.765074i
$414$	1.09913	+	0.529315i	0.0540195	+	0.0260144i
$415$	23.9863	+	22.2560i	1.17744	+	1.09250i
$416$	−16.0234	+	2.41515i	−0.785614	+	0.118412i
$417$	1.78987	−	23.8842i	0.0876505	−	1.16961i
$418$	−1.64329	+	4.18704i	−0.0803760	+	0.204795i
$419$	−6.99850	−	30.6624i	−0.341899	−	1.49796i	−0.795061	−	0.606530i	$-0.792561\pi$
$419$	−6.99850	−	30.6624i	−0.341899	−	1.49796i	0.453161	−	0.891429i	$-0.350296\pi$
$420$	−1.59361	−	21.2653i	−0.0777604	−	1.03764i
$421$	0.251838	+	0.0776818i	0.0122738	+	0.00378598i	0.300886	−	0.953660i	$-0.402718\pi$
$421$	0.251838	+	0.0776818i	0.0122738	+	0.00378598i	−0.288612	+	0.957446i	$0.593194\pi$
$422$	−5.94098	+	2.86102i	−0.289202	+	0.139272i
$423$	−5.83388	+	10.1046i	−0.283653	+	0.491301i
$424$	−4.34533	−	7.52633i	−0.211028	−	0.365511i
$425$	−4.13070	−	2.81626i	−0.200368	−	0.136609i
$426$	−1.97169	+	8.63855i	−0.0955288	+	0.418539i
$427$	−15.0061	−	2.26180i	−0.726194	−	0.109456i
$428$	−8.10225	−	10.1599i	−0.391637	−	0.491097i
$429$	−16.9883			−0.820203
$430$	−10.0613	−	6.64599i	−0.485197	−	0.320498i
$431$	−5.71625			−0.275342			−0.137671	−	0.990478i	$-0.543962\pi$
$431$	−5.71625			−0.275342			−0.137671	+	0.990478i	$0.543962\pi$
$432$	7.29439	+	9.14688i	0.350952	+	0.440080i
$433$	−30.9167	−	4.65994i	−1.48576	−	0.223942i	−0.644514	−	0.764593i	$-0.722940\pi$
$433$	−30.9167	−	4.65994i	−1.48576	−	0.223942i	−0.841247	+	0.540650i	$0.818178\pi$
$434$	−2.87016	+	12.5750i	−0.137772	+	0.603618i
$435$	−19.8617	−	13.5415i	−0.952294	−	0.649263i
$436$	3.17105	+	5.49242i	0.151866	+	0.263039i
$437$	−1.43454	+	2.48469i	−0.0686232	+	0.118859i
$438$	3.65799	−	1.76160i	0.174786	−	0.0841723i
$439$	−5.23230	−	1.61395i	−0.249724	−	0.0770296i	0.167366	−	0.985895i	$-0.446474\pi$
$439$	−5.23230	−	1.61395i	−0.249724	−	0.0770296i	−0.417090	+	0.908865i	$0.636950\pi$
$440$	2.20702	+	29.4506i	0.105216	+	1.40400i
$441$	0.753911	+	3.30310i	0.0359005	+	0.157291i
$442$	−0.629193	+	1.60316i	−0.0299277	+	0.0762545i
$443$	−2.44051	+	32.5663i	−0.115952	+	1.54727i	0.571231	+	0.820789i	$0.306466\pi$
$443$	−2.44051	+	32.5663i	−0.115952	+	1.54727i	−0.687183	+	0.726484i	$0.741153\pi$
$444$	−7.20155	+	1.08546i	−0.341770	+	0.0515136i
$445$	31.9419	+	29.6377i	1.51419	+	1.40496i
$446$	−1.47814	−	0.711836i	−0.0699921	−	0.0337064i
$447$	−22.3468	+	15.2358i	−1.05697	+	0.720629i
$448$	−1.12121	−	2.85680i	−0.0529722	−	0.134971i
$449$	28.9564	−	8.93186i	1.36654	−	0.421520i	0.477208	−	0.878791i	$-0.341649\pi$
$449$	28.9564	−	8.93186i	1.36654	−	0.421520i	0.889328	+	0.457270i	$0.151173\pi$
$450$	−2.74817	+	2.54993i	−0.129550	+	0.120205i
$451$	14.9175	−	18.7059i	0.702437	−	0.880829i
$452$	15.3841	−	19.2911i	0.723609	−	0.907377i
$453$	−13.1559	+	12.2069i	−0.618118	+	0.573530i
$454$	−6.61387	+	2.04011i	−0.310404	+	0.0957471i
$455$	10.6161	+	27.0494i	0.497692	+	1.26810i
$456$	4.05801	−	2.76670i	0.190034	−	0.129563i
$457$	−11.6272	−	5.59936i	−0.543897	−	0.261927i	0.141698	−	0.989910i	$-0.454744\pi$
$457$	−11.6272	−	5.59936i	−0.543897	−	0.261927i	−0.685595	+	0.727983i	$0.740458\pi$
$458$	−7.75692	−	7.19737i	−0.362457	−	0.336311i
$459$	5.54740	−	0.836136i	0.258930	−	0.0390275i
$460$	−0.638885	+	8.52533i	−0.0297882	+	0.397496i
$461$	1.60636	−	4.09295i	0.0748159	−	0.190628i	−0.888573	−	0.458735i	$-0.848303\pi$
$461$	1.60636	−	4.09295i	0.0748159	−	0.190628i	0.963389	+	0.268107i	$0.0863981\pi$
$462$	2.30306	+	10.0904i	0.107148	+	0.469446i
$463$	0.526910	+	7.03112i	0.0244876	+	0.326764i	0.995972	+	0.0896616i	$0.0285786\pi$
$463$	0.526910	+	7.03112i	0.0244876	+	0.326764i	−0.971485	+	0.237102i	$0.923802\pi$
$464$	−11.5830	−	3.57289i	−0.537729	−	0.165867i
$465$	26.6365	−	12.8275i	1.23524	−	0.594859i
$466$	−6.14323	+	10.6404i	−0.284580	+	0.492907i
$467$	−18.9788	−	32.8722i	−0.878232	−	1.52114i	−0.853280	−	0.521454i	$-0.825390\pi$
$467$	−18.9788	−	32.8722i	−0.878232	−	1.52114i	−0.0249524	−	0.999689i	$-0.507943\pi$
$468$	−5.24392	−	3.57524i	−0.242400	−	0.165266i
$469$	6.18546	−	27.1003i	0.285618	−	1.25137i
$470$	16.4521	+	2.47976i	0.758880	+	0.114383i
$471$	0.946095	+	1.18637i	0.0435938	+	0.0546649i
$472$	18.9421			0.871882
$473$	−26.0924	−	12.0981i	−1.19973	−	0.556271i
$474$	0.517233			0.0237573
$475$	−5.49717	−	6.89323i	−0.252227	−	0.316283i
$476$	−5.09877	−	0.768516i	−0.233702	−	0.0352249i
$477$	1.17111	−	5.13097i	0.0536215	−	0.234931i
$478$	−5.11733	−	3.48894i	−0.234061	−	0.159580i
$479$	−13.6852	−	23.7034i	−0.625291	−	1.08304i	−0.988484	−	0.151322i	$-0.951647\pi$
$479$	−13.6852	−	23.7034i	−0.625291	−	1.08304i	0.363193	−	0.931714i	$-0.381686\pi$
$480$	11.3141	−	19.5966i	0.516417	−	0.894460i
$481$	8.94115	−	4.30583i	0.407681	−	0.196329i
$482$	−9.58839	−	2.95763i	−0.436739	−	0.134716i
$483$	0.493351	+	6.58331i	0.0224482	+	0.299551i
$484$	3.04590	+	13.3450i	0.138450	+	0.606589i
$485$	12.5294	−	31.9244i	0.568931	−	1.44961i
$486$	0.534249	−	7.12905i	0.0242340	−	0.323380i
$487$	−39.8757	+	6.01029i	−1.80694	+	0.272352i	−0.964047	−	0.265732i	$-0.914387\pi$
$487$	−39.8757	+	6.01029i	−1.80694	+	0.272352i	−0.842891	+	0.538084i	$0.819148\pi$
$488$	−7.63457	−	7.08384i	−0.345601	−	0.320671i
$489$	−0.314076	−	0.151251i	−0.0142030	−	0.00683980i
$490$	3.99179	−	2.72156i	0.180331	−	0.122947i
$491$	2.32329	+	5.91964i	0.104849	+	0.267150i	0.973665	−	0.227985i	$-0.0732138\pi$
$491$	2.32329	+	5.91964i	0.104849	+	0.267150i	−0.868816	+	0.495135i	$0.835119\pi$
$492$	−11.3295	+	3.49470i	−0.510775	+	0.157553i
$493$	−4.26089	+	3.95353i	−0.191901	+	0.178058i
$494$	−1.89368	+	2.37460i	−0.0852008	+	0.106838i
$495$	−11.1510	+	13.9829i	−0.501201	+	0.628486i
$496$	10.9282	−	10.1399i	0.490693	−	0.455296i
$497$	34.5438	−	10.6553i	1.54950	−	0.477957i
$498$	2.87511	+	7.32567i	0.128837	+	0.328271i
$499$	14.8230	−	10.1061i	0.663568	−	0.452413i	−0.184123	−	0.982903i	$-0.558944\pi$
$499$	14.8230	−	10.1061i	0.663568	−	0.452413i	0.847691	+	0.530490i	$0.177992\pi$
$500$	0.00284492	+	0.00137004i	0.000127229	+	6.12700e-5i
$501$	12.5808	+	11.6733i	0.562068	+	0.521523i
$502$	7.52926	−	1.13485i	0.336047	−	0.0506510i
$503$	−1.60834	+	21.4618i	−0.0717122	+	0.956933i	0.839064	+	0.544033i	$0.183103\pi$
$503$	−1.60834	+	21.4618i	−0.0717122	+	0.956933i	−0.910776	+	0.412900i	$0.864516\pi$
$504$	−3.11274	+	7.93113i	−0.138652	+	0.353280i
$505$	−8.07333	−	35.3716i	−0.359259	−	1.57401i
$506$	−0.310077	−	4.13769i	−0.0137846	−	0.183943i
$507$	5.28503	+	1.63022i	0.234716	+	0.0724004i
$508$	12.2895	−	5.91831i	0.545258	−	0.262583i
$509$	−6.87313	+	11.9046i	−0.304646	+	0.527663i	−0.977182	−	0.212401i	$-0.931872\pi$
$509$	−6.87313	+	11.9046i	−0.304646	+	0.527663i	0.672536	+	0.740064i	$0.265205\pi$
$510$	−1.20247	−	2.08273i	−0.0532461	−	0.0922249i
$511$	−13.6860	−	9.33094i	−0.605432	−	0.412777i
$512$	4.51534	−	19.7830i	0.199552	−	0.874293i
$513$	9.78321	+	1.47458i	0.431939	+	0.0651044i
$514$	−5.55057	−	6.96020i	−0.244825	−	0.307001i
$515$	15.0298			0.662292
$516$	7.30604	+	12.2371i	0.321630	+	0.538709i
$517$	39.6844			1.74532
$518$	−3.76962	−	4.72695i	−0.165627	−	0.207690i
$519$	23.1716	+	3.49256i	1.01712	+	0.153306i
$520$	−4.43755	+	19.4422i	−0.194599	+	0.852596i
$521$	13.5247	+	9.22101i	0.592530	+	0.403980i	0.822126	−	0.569306i	$-0.192788\pi$
$521$	13.5247	+	9.22101i	0.592530	+	0.403980i	−0.229596	+	0.973286i	$0.573740\pi$
$522$	2.17935	+	3.77475i	0.0953876	+	0.165216i
$523$	−0.329874	+	0.571359i	−0.0144244	+	0.0249838i	−0.873148	−	0.487456i	$-0.837925\pi$
$523$	−0.329874	+	0.571359i	−0.0144244	+	0.0249838i	0.858723	+	0.512440i	$0.171258\pi$
$524$	−33.9282	+	16.3389i	−1.48216	+	0.713770i
$525$	−19.3862	−	5.97984i	−0.846082	−	0.260982i
$526$	−0.524017	−	6.99252i	−0.0228482	−	0.304888i
$527$	−1.59072	−	6.96940i	−0.0692929	−	0.303592i
$528$	4.37033	−	11.1354i	0.190194	−	0.484606i
$529$	−1.52101	+	20.2964i	−0.0661307	+	0.882453i
$530$	−7.42099	+	1.11853i	−0.322347	+	0.0485860i
$531$	8.40887	+	7.80229i	0.364914	+	0.338591i
$532$	−8.19305	−	3.94556i	−0.355214	−	0.171062i
$533$	13.3485	−	9.10088i	0.578190	−	0.394203i
$534$	3.82871	+	9.75540i	0.165685	+	0.422157i
$535$	−23.6285	+	7.28844i	−1.02155	+	0.315107i
$536$	13.9843	−	12.9755i	0.604030	−	0.560457i
$537$	19.2545	−	24.1444i	0.830893	−	1.04191i
$538$	1.52607	−	1.91364i	0.0657938	−	0.0825028i
$539$	8.44728	−	7.83793i	0.363850	−	0.337604i
$540$	28.1714	−	8.68973i	1.21230	−	0.373946i
$541$	12.5838	+	32.0630i	0.541019	+	1.37849i	0.896181	+	0.443690i	$0.146331\pi$
$541$	12.5838	+	32.0630i	0.541019	+	1.37849i	−0.355161	+	0.934805i	$0.615574\pi$
$542$	−8.12682	+	5.54077i	−0.349077	+	0.237996i
$543$	2.12259	+	1.02219i	0.0910891	+	0.0438662i
$544$	−4.01090	−	3.72157i	−0.171966	−	0.159561i
$545$	11.9331	−	1.79862i	0.511156	−	0.0770444i
$546$	−0.522266	+	6.96915i	−0.0223509	+	0.298252i
$547$	−1.71593	+	4.37211i	−0.0733677	+	0.186938i	−0.962853	−	0.270026i	$-0.912968\pi$
$547$	−1.71593	+	4.37211i	−0.0733677	+	0.186938i	0.889485	+	0.456964i	$0.151063\pi$
$548$	−2.16003	−	9.46373i	−0.0922721	−	0.404270i
$549$	−0.471324	−	6.28938i	−0.0201156	−	0.268424i
$550$	12.1844	+	3.75840i	0.519546	+	0.160259i
$551$	−9.23566	+	4.44766i	−0.393452	+	0.189477i
$552$	−2.26535	+	3.92370i	−0.0964197	+	0.167004i
$553$	−1.05510	−	1.82749i	−0.0448675	−	0.0777127i
$554$	−7.72227	−	5.26495i	−0.328088	−	0.223686i
$555$	−3.08369	+	13.5105i	−0.130896	+	0.573491i
$556$	−30.0941	−	4.53596i	−1.27628	−	0.192368i
$557$	13.3289	+	16.7139i	0.564765	+	0.708193i	0.979431	−	0.201781i	$-0.0646729\pi$
$557$	13.3289	+	16.7139i	0.564765	+	0.708193i	−0.414666	+	0.909974i	$0.636102\pi$
$558$	−5.36061			−0.226933
$559$	−14.4281	−	12.9995i	−0.610245	−	0.549820i
$560$	−20.4613			−0.864647
$561$	−3.57645	−	4.48473i	−0.150998	−	0.189345i
$562$	6.58829	+	0.993025i	0.277910	+	0.0418882i
$563$	−4.06810	+	17.8235i	−0.171450	+	0.751172i	0.813952	+	0.580931i	$0.197312\pi$
$563$	−4.06810	+	17.8235i	−0.171450	+	0.751172i	−0.985403	+	0.170240i	$0.945546\pi$
$564$	−16.2483	−	11.0779i	−0.684177	−	0.466464i
$565$	−23.4753	−	40.6603i	−0.987612	−	1.71059i
$566$	3.58228	−	6.20469i	0.150574	−	0.260803i
$567$	9.69628	−	4.66948i	0.407205	−	0.196100i
$568$	23.7069	+	7.31261i	0.994719	+	0.306830i
$569$	2.91961	+	38.9594i	0.122396	+	1.63326i	0.633498	+	0.773744i	$0.281618\pi$
$569$	2.91961	+	38.9594i	0.122396	+	1.63326i	−0.511102	+	0.859520i	$0.670763\pi$
$570$	−0.943768	−	4.13492i	−0.0395301	−	0.173193i
$571$	−11.0002	+	28.0282i	−0.460346	+	1.17294i	0.492722	+	0.870187i	$0.336002\pi$
$571$	−11.0002	+	28.0282i	−0.460346	+	1.17294i	−0.953068	+	0.302755i	$0.902093\pi$
$572$	−1.61316	+	21.5262i	−0.0674498	+	0.900055i
$573$	−5.46155	+	0.823197i	−0.228160	+	0.0343895i
$574$	−7.21518	−	6.69471i	−0.301156	−	0.279432i
$575$	7.32787	+	3.52891i	0.305593	+	0.147166i
$576$	1.05384	−	0.718494i	0.0439099	−	0.0299373i
$577$	−15.3278	−	39.0547i	−0.638106	−	1.62587i	−0.772556	−	0.634946i	$-0.781022\pi$
$577$	−15.3278	−	39.0547i	−0.638106	−	1.62587i	0.134451	−	0.990920i	$-0.457073\pi$
$578$	−0.555677	+	0.171404i	−0.0231131	+	0.00712945i
$579$	5.27618	−	4.89558i	0.219271	−	0.203453i
$580$	−19.0446	+	23.8812i	−0.790785	+	0.991614i
$581$	20.0181	−	25.1020i	0.830492	−	1.04140i
$582$	6.04638	−	5.61022i	0.250630	−	0.232551i
$583$	−17.1050	+	5.27620i	−0.708418	+	0.218518i
$584$	−4.15311	−	10.5820i	−0.171857	−	0.437885i
$585$	−9.97821	+	6.80303i	−0.412548	+	0.281271i
$586$	10.9085	+	5.25324i	0.450625	+	0.217009i
$587$	−8.45879	−	7.84861i	−0.349132	−	0.323947i	0.486040	−	0.873937i	$-0.338441\pi$
$587$	−8.45879	−	7.84861i	−0.349132	−	0.323947i	−0.835171	+	0.549990i	$0.814632\pi$
$588$	−5.64659	+	0.851087i	−0.232861	+	0.0350982i
$589$	0.942130	−	12.5718i	0.0388198	−	0.518014i
$590$	5.97605	−	15.2267i	0.246030	−	0.626874i
$591$	3.53021	+	15.4669i	0.145214	+	0.636223i
$592$	0.522209	+	6.96839i	0.0214627	+	0.286399i
$593$	−36.3742	−	11.2200i	−1.49371	−	0.460749i	−0.562985	−	0.826467i	$-0.690347\pi$
$593$	−36.3742	−	11.2200i	−1.49371	−	0.460749i	−0.930726	+	0.365718i	$0.880823\pi$
$594$	−12.8914	+	6.20818i	−0.528942	+	0.254725i
$595$	−4.90580	+	8.49710i	−0.201118	+	0.348347i
$596$	17.1836	+	29.7628i	0.703866	+	1.21913i
$597$	−22.5366	−	15.3652i	−0.922362	−	0.628856i
$598$	0.623457	−	2.73154i	0.0254950	−	0.111701i
$599$	−46.5368	−	7.01429i	−1.90144	−	0.286596i	−0.909741	−	0.415176i	$-0.863720\pi$
$599$	−46.5368	−	7.01429i	−1.90144	−	0.286596i	−0.991699	+	0.128579i	$0.958958\pi$
$600$	−8.68086	−	10.8855i	−0.354395	−	0.444397i
$601$	−36.1135			−1.47310			−0.736551	−	0.676382i	$-0.763547\pi$
$601$	−36.1135			−1.47310			−0.736551	+	0.676382i	$0.763547\pi$
$602$	−5.76518	+	10.3320i	−0.234971	+	0.421102i
$603$	11.5526			0.470459
$604$	14.2183	+	17.8292i	0.578535	+	0.725460i
$605$	25.7551	+	3.88196i	1.04709	+	0.157824i
$606$	1.94170	−	8.50713i	0.0788761	−	0.345579i
$607$	3.37208	+	2.29904i	0.136868	+	0.0933153i	0.629819	−	0.776742i	$-0.283129\pi$
$607$	3.37208	+	2.29904i	0.136868	+	0.0933153i	−0.492950	+	0.870057i	$0.664082\pi$
$608$	−4.82468	−	8.35659i	−0.195667	−	0.338905i
$609$	−11.7936	+	20.4271i	−0.477901	+	0.827749i
$610$	−8.10301	+	3.90221i	−0.328081	+	0.157996i
$611$	25.6062	+	7.89848i	1.03592	+	0.319538i
$612$	−0.160147	−	2.13701i	−0.00647355	−	0.0863836i
$613$	−5.46762	−	23.9552i	−0.220835	−	0.967543i	−0.956851	−	0.290578i	$-0.906152\pi$
$613$	−5.46762	−	23.9552i	−0.220835	−	0.967543i	0.736016	−	0.676964i	$-0.236705\pi$
$614$	7.22025	−	18.3969i	0.291386	−	0.742438i
$615$	−1.68593	+	22.4972i	−0.0679834	+	0.907176i
$616$	28.6549	−	4.31903i	1.15454	−	0.174019i
$617$	1.59858	+	1.48327i	0.0643566	+	0.0597142i	0.711695	−	0.702488i	$-0.247928\pi$
$617$	1.59858	+	1.48327i	0.0643566	+	0.0597142i	−0.647339	+	0.762202i	$0.724118\pi$
$618$	3.25680	+	1.56839i	0.131008	+	0.0630901i
$619$	−30.1129	+	20.5306i	−1.21034	+	0.825195i	−0.988696	−	0.149933i	$-0.952094\pi$
$619$	−30.1129	+	20.5306i	−1.21034	+	0.825195i	−0.221642	+	0.975128i	$0.571142\pi$
$620$	−13.7246	−	34.9696i	−0.551192	−	1.40441i
$621$	−8.72130	+	2.69016i	−0.349974	+	0.107953i
$622$	14.7414	−	13.6780i	0.591077	−	0.548440i
$623$	26.6576	−	33.4276i	1.06801	−	1.33925i
$624$	5.03624	−	6.31525i	0.201611	−	0.252812i
$625$	18.3285	−	17.0064i	0.733140	−	0.680254i
$626$	3.54088	−	1.09222i	0.141522	−	0.0436537i
$627$	−3.69584	−	9.41685i	−0.147598	−	0.376073i
$628$	1.59310	−	1.08616i	0.0635718	−	0.0433425i
$629$	3.01902	+	1.45388i	0.120376	+	0.0579701i
$630$	5.39344	+	5.00438i	0.214880	+	0.199379i
$631$	47.6395	−	7.18050i	1.89650	−	0.285851i	0.905990	−	0.423300i	$-0.139128\pi$
$631$	47.6395	−	7.18050i	1.89650	−	0.285851i	0.990509	+	0.137448i	$0.0438901\pi$
$632$	0.108224	−	1.44415i	0.00430493	−	0.0574453i
$633$	5.41808	−	13.8050i	0.215349	−	0.548701i
$634$	−2.81480	−	12.3325i	−0.111790	−	0.489785i
$635$	−1.93962	−	25.8824i	−0.0769715	−	1.02711i
$636$	8.47629	+	2.61459i	0.336107	+	0.103675i
$637$	7.01058	−	3.37612i	0.277769	−	0.133767i
$638$	7.41242	−	12.8387i	0.293460	−	0.508288i
$639$	7.51199	+	13.0112i	0.297170	+	0.514713i
$640$	−30.0937	−	20.5176i	−1.18956	−	0.811028i
$641$	−2.49158	+	10.9163i	−0.0984114	+	0.431168i	−0.999999	−	0.00142820i	$-0.999545\pi$
$641$	−2.49158	+	10.9163i	−0.0984114	+	0.431168i	0.901588	+	0.432597i	$0.142403\pi$
$642$	−5.88063	−	0.886362i	−0.232090	−	0.0349819i
$643$	5.62414	+	7.05245i	0.221794	+	0.278121i	0.880262	−	0.474487i	$-0.157367\pi$
$643$	5.62414	+	7.05245i	0.221794	+	0.278121i	−0.658468	+	0.752609i	$0.728795\pi$
$644$	8.38868			0.330560
$645$	26.7543	−	4.43409i	1.05345	−	0.174592i
$646$	−1.02553			−0.0403491
$647$	2.13094	+	2.67212i	0.0837760	+	0.105052i	0.821953	−	0.569555i	$-0.192885\pi$
$647$	2.13094	+	2.67212i	0.0837760	+	0.105052i	−0.738177	+	0.674607i	$0.764313\pi$
$648$	7.30335	+	1.10080i	0.286903	+	0.0432436i
$649$	8.68174	−	38.0372i	0.340788	−	1.49309i
$650$	7.11392	+	4.85019i	0.279031	+	0.190240i
$651$	−14.5045	−	25.1226i	−0.568477	−	0.984632i
$652$	−0.221476	+	0.383608i	−0.00867369	+	0.0150233i
$653$	−8.02803	+	3.86610i	−0.314161	+	0.151292i	−0.584319	−	0.811524i	$-0.698638\pi$
$653$	−8.02803	+	3.86610i	−0.314161	+	0.151292i	0.270158	+	0.962816i	$0.412924\pi$
$654$	2.77346	+	0.855500i	0.108451	+	0.0334527i
$655$	5.35480	+	71.4548i	0.209229	+	2.79197i
$656$	2.53142	+	11.0909i	0.0988354	+	0.433026i
$657$	2.51506	−	6.40827i	0.0981218	−	0.250010i
$658$	1.22000	−	16.2798i	0.0475607	−	0.634654i
$659$	−31.9787	+	4.82001i	−1.24571	+	0.187761i	−0.738615	−	0.674127i	$-0.764520\pi$
$659$	−31.9787	+	4.82001i	−1.24571	+	0.187761i	−0.507098	+	0.861888i	$0.669282\pi$
$660$	−22.0971	−	20.5031i	−0.860127	−	0.798082i
$661$	19.8027	+	9.53649i	0.770237	+	0.370926i	0.777366	−	0.629048i	$-0.216555\pi$
$661$	19.8027	+	9.53649i	0.770237	+	0.370926i	−0.00712972	+	0.999975i	$0.502269\pi$
$662$	5.07779	−	3.46198i	0.197354	−	0.134554i
$663$	−1.41509	−	3.60558i	−0.0549574	−	0.140029i
$664$	21.0554	−	6.49473i	0.817107	−	0.252044i
$665$	−12.6843	+	11.7693i	−0.491876	+	0.456395i
$666$	1.56667	−	1.96454i	0.0607071	−	0.0761243i
$667$	5.89583	−	7.39314i	0.228288	−	0.286264i
$668$	15.9860	−	14.8329i	0.618518	−	0.573901i
$669$	3.52589	−	1.08759i	0.136319	−	0.0420488i
$670$	−6.01854	−	15.3350i	−0.232517	−	0.592443i
$671$	−17.7240	+	12.0840i	−0.684229	+	0.466499i
$672$	−20.0045	−	9.63364i	−0.771689	−	0.371626i
$673$	2.89831	+	2.68924i	0.111722	+	0.103662i	0.734056	−	0.679089i	$-0.237625\pi$
$673$	2.89831	+	2.68924i	0.111722	+	0.103662i	−0.622334	+	0.782752i	$0.713816\pi$
$674$	−9.21458	+	1.38887i	−0.354932	+	0.0534975i
$675$	2.09595	−	27.9685i	0.0806731	−	1.07651i
$676$	2.56753	−	6.54195i	0.0987510	−	0.251614i
$677$	1.49356	+	6.54371i	0.0574021	+	0.251495i	0.995485	−	0.0949147i	$-0.0302578\pi$
$677$	1.49356	+	6.54371i	0.0574021	+	0.251495i	−0.938083	+	0.346410i	$0.887401\pi$
$678$	−0.843849	−	11.2604i	−0.0324078	−	0.432452i
$679$	−32.1560	−	9.91881i	−1.23403	−	0.380649i
$680$	−6.06673	+	2.92159i	−0.232649	+	0.112038i
$681$	7.78325	−	13.4810i	0.298255	−	0.516592i
$682$	9.11627	+	15.7898i	0.349080	+	0.604624i
$683$	4.97608	+	3.39263i	0.190404	+	0.129815i	0.654770	−	0.755828i	$-0.272765\pi$
$683$	4.97608	+	3.39263i	0.190404	+	0.129815i	−0.464366	+	0.885643i	$0.653718\pi$
$684$	0.840980	−	3.68458i	0.0321557	−	0.140883i
$685$	−18.2645	−	2.75293i	−0.697852	−	0.105184i
$686$	4.91911	+	6.16837i	0.187812	+	0.235509i
$687$	23.7987			0.907977
$688$	12.2325	−	6.11310i	0.466361	−	0.233060i
$689$	−12.0871			−0.460481
$690$	2.43939	+	3.05890i	0.0928661	+	0.116450i
$691$	−20.7046	−	3.12072i	−0.787640	−	0.118718i	−0.257108	−	0.966383i	$-0.582770\pi$
$691$	−20.7046	−	3.12072i	−0.787640	−	0.118718i	−0.530532	+	0.847665i	$0.678008\pi$
$692$	6.62580	−	29.0295i	0.251875	−	1.10354i
$693$	14.4996	+	9.88568i	0.550795	+	0.375526i
$694$	2.09117	+	3.62201i	0.0793797	+	0.137490i
$695$	−28.9552	+	50.1519i	−1.09833	+	1.90237i
$696$	−14.5845	+	7.02352i	−0.552824	+	0.266226i
$697$	5.21272	+	1.60791i	0.197446	+	0.0609040i
$698$	−0.377631	−	5.03914i	−0.0142936	−	0.190734i
$699$	−6.14889	−	26.9401i	−0.232572	−	1.01897i
$700$	−9.41802	+	23.9967i	−0.355968	+	0.906991i
$701$	−1.60166	+	21.3727i	−0.0604939	+	0.807235i	0.881624	+	0.471953i	$0.156451\pi$
$701$	−1.60166	+	21.3727i	−0.0604939	+	0.807235i	−0.942118	+	0.335282i	$0.891168\pi$
$702$	−9.55377	+	1.44000i	−0.360584	+	0.0543493i
$703$	4.33194	+	4.01946i	0.163382	+	0.151597i
$704$	−3.90850	−	1.88224i	−0.147307	−	0.0709395i
$705$	−30.9175	+	21.0792i	−1.16442	+	0.793888i
$706$	2.04305	+	5.20560i	0.0768910	+	0.195915i
$707$	−34.0183	+	10.4932i	−1.27939	+	0.394639i
$708$	−14.1727	+	13.1503i	−0.532643	+	0.494220i
$709$	26.6840	−	33.4607i	1.00214	−	1.25664i	0.0358051	−	0.999359i	$-0.488600\pi$
$709$	26.6840	−	33.4607i	1.00214	−	1.25664i	0.966335	−	0.257286i	$-0.0828281\pi$
$710$	13.3576	−	16.7499i	0.501300	−	0.628611i
$711$	0.642892	−	0.596517i	0.0241103	−	0.0223711i
$712$	28.0389	−	8.64885i	1.05080	−	0.324129i
$713$	4.24885	+	10.8259i	0.159121	+	0.405433i
$714$	−1.94973	+	1.32930i	−0.0729668	+	0.0497479i
$715$	37.0075	+	17.8219i	1.38400	+	0.666500i
$716$	−28.7654	−	26.6904i	−1.07501	−	0.997467i
$717$	13.7740	−	2.07609i	0.514398	−	0.0775331i
$718$	−0.0203105	+	0.271024i	−0.000757979	+	0.0101145i
$719$	4.17475	−	10.6371i	0.155692	−	0.396697i	−0.831650	−	0.555299i	$-0.812604\pi$
$719$	4.17475	−	10.6371i	0.155692	−	0.396697i	0.987342	+	0.158603i	$0.0506989\pi$
$720$	−1.89227	−	8.29058i	−0.0705207	−	0.308972i
$721$	−1.10208	−	14.7063i	−0.0410438	−	0.547691i
$722$	8.82961	+	2.72357i	0.328604	+	0.101361i
$723$	20.3325	−	9.79161i	0.756174	−	0.364154i
$724$	1.49679	−	2.59251i	0.0556276	−	0.0963498i
$725$	14.5296	+	25.1660i	0.539616	+	0.934642i
$726$	5.17578	+	3.52878i	0.192091	+	0.130965i
$727$	−6.29235	+	27.5686i	−0.233370	+	1.02246i	0.713452	+	0.700705i	$0.247131\pi$
$727$	−6.29235	+	27.5686i	−0.233370	+	1.02246i	−0.946822	+	0.321758i	$0.895726\pi$
$728$	19.3491	+	2.91641i	0.717125	+	0.108089i
$729$	16.5125	+	20.7061i	0.611576	+	0.766892i
$730$	−9.81663			−0.363330
$731$	0.394251	−	6.54558i	0.0145819	−	0.242097i
$732$	10.6301			0.392901
$733$	30.1893	+	37.8562i	1.11507	+	1.39825i	0.907511	+	0.420029i	$0.137980\pi$
$733$	30.1893	+	37.8562i	1.11507	+	1.39825i	0.207558	+	0.978223i	$0.433448\pi$
$734$	−3.12155	−	0.470497i	−0.115218	−	0.0173664i
$735$	−2.41786	+	10.5934i	−0.0891842	+	0.390742i
$736$	7.35465	+	5.01432i	0.271096	+	0.184830i
$737$	−19.6464	−	34.0286i	−0.723685	−	1.25346i
$738$	2.04532	−	3.54260i	0.0752894	−	0.130405i
$739$	46.5108	−	22.3984i	1.71093	−	0.823939i	0.719316	−	0.694683i	$-0.244455\pi$
$739$	46.5108	−	22.3984i	1.71093	−	0.823939i	0.991611	−	0.129256i	$-0.0412589\pi$
$740$	16.8266	+	5.19033i	0.618559	+	0.190800i
$741$	−0.510472	−	6.81178i	−0.0187527	−	0.250237i
$742$	1.63861	+	7.17924i	0.0601554	+	0.263558i
$743$	10.5006	−	26.7552i	0.385231	−	0.981553i	−0.598374	−	0.801217i	$-0.704186\pi$
$743$	10.5006	−	26.7552i	0.385231	−	0.981553i	0.983605	−	0.180336i	$-0.0577185\pi$
$744$	1.48776	−	19.8528i	0.0545441	−	0.727840i
$745$	64.6639	−	9.74651i	2.36910	−	0.357085i
$746$	4.60988	+	4.27734i	0.168780	+	0.156605i
$747$	12.0222	+	5.78958i	0.439869	+	0.211830i
$748$	−6.02229	+	4.10593i	−0.220197	+	0.150128i
$749$	8.86416	+	22.5855i	0.323889	+	0.825257i
$750$	0.00138086		0.000425938i	5.04218e−5		1.55531e-5i
$751$	−29.0819	+	26.9841i	−1.06122	+	0.984664i	−0.999909	−	0.0134550i	$-0.995717\pi$
$751$	−29.0819	+	26.9841i	−1.06122	+	0.984664i	−0.0613059	+	0.998119i	$0.519527\pi$
$752$	−11.7646	+	14.7523i	−0.429010	+	0.537962i
$753$	−10.6772	+	13.3888i	−0.389100	+	0.487916i
$754$	7.33815	−	6.80881i	0.267240	−	0.247962i
$755$	41.4648	−	12.7902i	1.50906	−	0.465483i
$756$	−10.5684	−	26.9279i	−0.384369	−	0.979356i
$757$	3.15269	−	2.14947i	0.114587	−	0.0781238i	−0.504671	−	0.863312i	$-0.668386\pi$
$757$	3.15269	−	2.14947i	0.114587	−	0.0781238i	0.619257	+	0.785188i	$0.287434\pi$
$758$	6.75938	+	3.25514i	0.245512	+	0.118232i
$759$	6.84081	+	6.34734i	0.248306	+	0.230394i
$760$	−11.7425	+	1.76989i	−0.425944	+	0.0642007i
$761$	−2.36740	+	31.5908i	−0.0858183	+	1.14517i	0.773525	+	0.633766i	$0.218492\pi$
$761$	−2.36740	+	31.5908i	−0.0858183	+	1.14517i	−0.859343	+	0.511400i	$0.829127\pi$
$762$	2.28060	−	5.81086i	0.0826172	−	0.210505i
$763$	−2.63492	−	11.5443i	−0.0953904	−	0.417933i
$764$	0.524473	+	6.99860i	0.0189748	+	0.253201i
$765$	−3.89658	−	1.20194i	−0.140881	−	0.0434561i
$766$	−9.74739	+	4.69410i	−0.352188	+	0.169605i
$767$	13.1725	−	22.8154i	0.475631	−	0.823817i
$768$	−3.08637	−	5.34575i	−0.111370	−	0.192898i
$769$	−13.0916	−	8.92568i	−0.472094	−	0.321868i	0.303795	−	0.952737i	$-0.401746\pi$
$769$	−13.0916	−	8.92568i	−0.472094	−	0.321868i	−0.775889	+	0.630869i	$0.782698\pi$
$770$	5.56846	−	24.3970i	0.200673	−	0.879207i
$771$	19.7984	+	2.98412i	0.713021	+	0.107471i
$772$	−5.70226	−	7.15041i	−0.205229	−	0.257349i
$773$	15.9982			0.575415			0.287707	−	0.957718i	$-0.407107\pi$
$773$	15.9982			0.575415			0.287707	+	0.957718i	$0.407107\pi$
$774$	−4.71954	−	1.38045i	−0.169640	−	0.0496191i
$775$	−35.7389			−1.28378
$776$	−14.3990	−	18.0558i	−0.516894	−	0.648165i
$777$	13.4459	+	2.02664i	0.482368	+	0.0727052i
$778$	0.987952	−	4.32850i	0.0354198	−	0.155184i
$779$	7.94875	+	5.41936i	0.284793	+	0.194169i
$780$	−10.1773	−	17.6276i	−0.364405	−	0.631168i
$781$	25.5498	−	44.2536i	0.914245	−	1.58352i
$782$	0.852350	−	0.410470i	0.0304800	−	0.0146784i
$783$	−31.1600	−	9.61158i	−1.11357	−	0.343490i
$784$	0.409454	+	5.46378i	0.0146233	+	0.195135i
$785$	−0.816406	−	3.57691i	−0.0291388	−	0.127665i
$786$	−6.29614	+	16.0423i	−0.224576	+	0.572210i
$787$	2.11881	−	28.2736i	0.0755274	−	1.00784i	−0.822747	−	0.568408i	$-0.807560\pi$
$787$	2.11881	−	28.2736i	0.0755274	−	1.00784i	0.898274	−	0.439435i	$-0.144821\pi$
$788$	19.9336	−	3.00450i	0.710104	−	0.107031i
$789$	11.5607	+	10.7267i	0.411571	+	0.381882i
$790$	−1.12675	−	0.542612i	−0.0400878	−	0.0193053i
$791$	−38.0638	+	25.9515i	−1.35339	+	0.922728i
$792$	4.40002	+	11.2111i	0.156348	+	0.398368i
$793$	−13.8415	+	4.26953i	−0.491525	+	0.151616i
$794$	3.39337	−	3.14859i	0.120426	−	0.111739i
$795$	10.5237	−	13.1963i	0.373237	−	0.468024i
$796$	−21.6095	+	27.0975i	−0.765930	+	0.960446i
$797$	5.33835	−	4.95326i	0.189094	−	0.175454i	−0.579945	−	0.814656i	$-0.696926\pi$
$797$	5.33835	−	4.95326i	0.189094	−	0.175454i	0.769039	+	0.639202i	$0.220735\pi$
$798$	−3.97672	+	1.22665i	−0.140774	+	0.0434231i
$799$	3.30562	+	8.42258i	0.116944	+	0.297970i
$800$	−22.6011	+	15.4092i	−0.799070	+	0.544797i
$801$	16.0096	+	7.70983i	0.565672	+	0.272413i
$802$	15.6508	+	14.5218i	0.552647	+	0.512782i
$803$	−23.1529	+	3.48973i	−0.817047	+	0.123150i
$804$	−1.45509	+	19.4169i	−0.0513172	+	0.684780i
$805$	5.83161	−	14.8587i	0.205537	−	0.523700i
$806$	2.73955	+	12.0028i	0.0964966	+	0.422779i
$807$	0.411378	+	5.48946i	0.0144812	+	0.193238i
$808$	−23.3462	−	7.20136i	−0.821318	−	0.253343i
$809$	−6.67268	+	3.21339i	−0.234599	+	0.112977i	−0.547490	−	0.836812i	$-0.684417\pi$
$809$	−6.67268	+	3.21339i	−0.234599	+	0.112977i	0.312891	+	0.949789i	$0.398702\pi$
$810$	3.18902	−	5.52354i	0.112051	−	0.194078i
$811$	13.7810	+	23.8694i	0.483917	+	0.838169i	0.999829	−	0.0184723i	$-0.00588025\pi$
$811$	13.7810	+	23.8694i	0.483917	+	0.838169i	−0.515912	+	0.856641i	$0.672547\pi$
$812$	24.7637	+	16.8836i	0.869035	+	0.592498i
$813$	4.92249	−	21.5668i	0.172639	−	0.756382i
$814$	−8.45088	−	1.27377i	−0.296203	−	0.0446455i
$815$	0.525513	+	0.658972i	0.0184079	+	0.0230828i
$816$	2.72741			0.0954783
$817$	4.06692	−	10.8258i	0.142284	−	0.378746i
$818$	9.00597			0.314886
$819$	7.38827	+	9.26459i	0.258167	+	0.323731i
$820$	28.3466	+	4.27256i	0.989905	+	0.149204i
$821$	4.43484	−	19.4303i	0.154777	−	0.678122i	−0.836681	−	0.547691i	$-0.815507\pi$
$821$	4.43484	−	19.4303i	0.154777	−	0.678122i	0.991457	−	0.130431i	$-0.0416360\pi$
$822$	−3.67046	−	2.50248i	−0.128022	−	0.0872839i
$823$	17.3378	+	30.0300i	0.604358	+	1.04678i	0.992153	+	0.125033i	$0.0399036\pi$
$823$	17.3378	+	30.0300i	0.604358	+	1.04678i	−0.387795	+	0.921746i	$0.626763\pi$
$824$	5.06051	−	8.76506i	0.176291	−	0.305345i
$825$	−25.8375	+	12.4427i	−0.899546	+	0.433199i
$826$	−15.3372	−	4.73089i	−0.533649	−	0.164609i
$827$	−0.772694	−	10.3109i	−0.0268692	−	0.358545i	−0.994392	−	0.105760i	$-0.966273\pi$
$827$	−0.772694	−	10.3109i	−0.0268692	−	0.358545i	0.967522	−	0.252785i	$-0.0813465\pi$
$828$	0.775789	+	3.39896i	0.0269605	+	0.118122i
$829$	3.34519	−	8.52339i	0.116183	−	0.296030i	−0.860939	−	0.508708i	$-0.830123\pi$
$829$	3.34519	−	8.52339i	0.116183	−	0.296030i	0.977122	+	0.212678i	$0.0682186\pi$
$830$	1.42194	−	18.9745i	0.0493563	−	0.658615i
$831$	20.7855	−	3.13291i	0.721041	−	0.108679i
$832$	−2.14732	−	1.99242i	−0.0744450	−	0.0690749i
$833$	2.36715	+	1.13996i	0.0820170	+	0.0394973i
$834$	−11.5078	+	7.84585i	−0.398481	+	0.271680i
$835$	−15.1601	−	38.6272i	−0.524636	−	1.33675i
$836$	−12.2832	+	3.78887i	−0.424823	+	0.131041i
$837$	29.3985	−	27.2778i	1.01616	−	0.942860i
$838$	−11.4031	+	14.2990i	−0.393913	+	0.493951i
$839$	−10.7002	+	13.4177i	−0.369413	+	0.463230i	−0.931443	−	0.363887i	$-0.881449\pi$
$839$	−10.7002	+	13.4177i	−0.369413	+	0.463230i	0.562030	+	0.827117i	$0.310021\pi$
$840$	−20.0304	+	18.5855i	−0.691116	+	0.641262i
$841$	4.57302	−	1.41059i	0.157690	−	0.0486410i
$842$	−0.0559905	−	0.142661i	−0.00192956	−	0.00491644i
$843$	−12.3810	+	8.44121i	−0.426424	+	0.290731i
$844$	−16.9781	−	8.17624i	−0.584411	−	0.281438i
$845$	−9.80275	−	9.09562i	−0.337225	−	0.312899i
$846$	6.70915	−	1.01124i	0.230665	−	0.0347672i
$847$	1.90987	−	25.4854i	0.0656238	−	0.875689i
$848$	3.10946	−	7.92278i	0.106779	−	0.272069i
$849$	3.58558	+	15.7094i	0.123057	+	0.539147i
$850$	0.217256	+	2.89908i	0.00745182	+	0.0994376i
$851$	−5.20919	−	1.60682i	−0.178569	−	0.0550811i
$852$	−22.8144	+	10.9869i	−0.781610	+	0.376404i
$853$	−24.6019	+	42.6117i	−0.842353	+	1.45900i	0.0455474	+	0.998962i	$0.485497\pi$
$853$	−24.6019	+	42.6117i	−0.842353	+	1.45900i	−0.887900	+	0.460036i	$0.847837\pi$
$854$	4.41238	+	7.64247i	0.150989	+	0.261520i
$855$	−5.94179	−	4.05104i	−0.203205	−	0.138543i
$856$	−3.70523	+	16.2337i	−0.126642	+	0.554855i
$857$	47.8968	+	7.21928i	1.63612	+	0.246606i	0.901787	−	0.432181i	$-0.142256\pi$
$857$	47.8968	+	7.21928i	1.63612	+	0.246606i	0.734336	+	0.678787i	$0.237494\pi$
$858$	6.15939	+	7.72363i	0.210278	+	0.263680i
$859$	−49.1922			−1.67842			−0.839208	−	0.543810i	$-0.816981\pi$
$859$	−49.1922			−1.67842			−0.839208	+	0.543810i	$0.816981\pi$
$860$	−3.07799	−	34.3220i	−0.104959	−	1.17037i
$861$	22.1366			0.754414
$862$	2.07252	+	2.59886i	0.0705904	+	0.0885175i
$863$	34.0175	+	5.12731i	1.15797	+	0.174536i	0.699806	−	0.714333i	$-0.253270\pi$
$863$	34.0175	+	5.12731i	1.15797	+	0.174536i	0.458162	+	0.888869i	$0.348508\pi$
$864$	6.83038	−	29.9258i	0.232374	−	1.01810i
$865$	−46.8133	−	31.9168i	−1.59170	−	1.08520i
$866$	9.09074	+	15.7456i	0.308916	+	0.535058i
$867$	0.653924	−	1.13263i	0.0222084	−	0.0384661i
$868$	−33.2106	+	15.9934i	−1.12724	+	0.542850i
$869$	−2.85036	−	0.879220i	−0.0966919	−	0.0298255i
$870$	1.04463	+	13.9397i	0.0354164	+	0.472599i
$871$	−5.90399	−	25.8671i	−0.200049	−	0.876473i
$872$	2.96893	−	7.56470i	0.100541	−	0.256173i
$873$	1.04514	−	13.9464i	0.0353725	−	0.472014i
$874$	1.64977	−	0.248662i	0.0558042	−	0.00841112i
$875$	−0.00432173	−	0.00400998i	−0.000146101	−	0.000135562i
$876$	10.4538	+	5.03429i	0.353201	+	0.170093i
$877$	5.64299	−	3.84733i	0.190550	−	0.129915i	−0.464287	−	0.885685i	$-0.653689\pi$
$877$	5.64299	−	3.84733i	0.190550	−	0.129915i	0.654838	+	0.755770i	$0.272737\pi$
$878$	1.16328	+	2.96400i	0.0392589	+	0.100030i
$879$	−26.0206	+	8.02628i	−0.877652	+	0.270720i
$880$	−21.2021	+	19.6727i	−0.714724	+	0.663167i
$881$	−11.8214	+	14.8236i	−0.398274	+	0.499420i	−0.940019	−	0.341123i	$-0.889193\pi$
$881$	−11.8214	+	14.8236i	−0.398274	+	0.499420i	0.541744	+	0.840543i	$0.317764\pi$
$882$	1.22839	−	1.54036i	0.0413621	−	0.0518665i
$883$	−28.6166	+	26.5523i	−0.963025	+	0.893557i	−0.994371	−	0.105952i	$-0.966211\pi$
$883$	−28.6166	+	26.5523i	−0.963025	+	0.893557i	0.0313462	+	0.999509i	$0.490021\pi$
$884$	−4.70307	+	1.45070i	−0.158181	+	0.0487925i
$885$	13.4404	+	34.2456i	0.451795	+	1.15115i
$886$	15.6909	−	10.6979i	0.527147	−	0.359403i
$887$	−2.95585	−	1.42346i	−0.0992476	−	0.0477951i	0.383601	−	0.923499i	$-0.374684\pi$
$887$	−2.95585	−	1.42346i	−0.0992476	−	0.0477951i	−0.482849	+	0.875704i	$0.660398\pi$
$888$	6.84079	+	6.34733i	0.229562	+	0.213002i
$889$	−25.1831	+	3.79574i	−0.844614	+	0.127305i
$890$	1.89356	−	25.2678i	0.0634723	−	0.846979i
$891$	5.55784	−	14.1611i	0.186195	−	0.474416i
$892$	−1.04330	−	4.57100i	−0.0349323	−	0.153048i
$893$	1.19246	+	15.9122i	0.0399040	+	0.532482i
$894$	15.0291	+	4.63586i	0.502647	+	0.155046i
$895$	−67.2732	+	32.3971i	−2.24870	+	1.08291i
$896$	−17.8693	+	30.9505i	−0.596970	+	1.03398i
$897$	3.15068	+	5.45714i	0.105198	+	0.182209i
$898$	−14.5594	−	9.92645i	−0.485854	−	0.331250i
$899$	−9.24613	+	40.5099i	−0.308376	+	1.35108i
$900$	−10.5941	−	1.59680i	−0.353136	−	0.0532266i
$901$	−2.54462	−	3.19086i	−0.0847737	−	0.106303i
$902$	−13.9131			−0.463257
$903$	−6.30046	−	25.8534i	−0.209666	−	0.860346i
$904$	−31.6163			−1.05154
$905$	−3.55153	−	4.45348i	−0.118057	−	0.148039i
$906$	10.3197	+	1.55544i	0.342848	+	0.0516761i
$907$	7.37955	−	32.3319i	0.245034	−	1.07356i	−0.691332	−	0.722538i	$-0.742976\pi$
$907$	7.37955	−	32.3319i	0.245034	−	1.07356i	0.936366	−	0.351026i	$-0.114167\pi$
$908$	−16.3429	−	11.1424i	−0.542359	−	0.369774i
$909$	−7.39772	−	12.8132i	−0.245367	−	0.424988i
$910$	8.44882	−	14.6338i	0.280076	−	0.485105i
$911$	36.7475	−	17.6966i	1.21750	−	0.586316i	0.288884	−	0.957364i	$-0.406716\pi$
$911$	36.7475	−	17.6966i	1.21750	−	0.586316i	0.928614	+	0.371048i	$0.121001\pi$
$912$	4.59627	+	1.41776i	0.152198	+	0.0469468i
$913$	−3.39158	−	45.2575i	−0.112245	−	1.49780i
$914$	1.66991	+	7.31637i	0.0552358	+	0.242004i
$915$	7.38983	−	18.8290i	0.244300	−	0.622466i
$916$	2.25986	−	30.1558i	0.0746679	−	0.996374i
$917$	69.5241	−	10.4791i	2.29589	−	0.346050i
$918$	−2.39144	−	2.21894i	−0.0789294	−	0.0732358i
$919$	3.08851	+	1.48735i	0.101881	+	0.0490631i	0.484130	−	0.874996i	$-0.339136\pi$
$919$	3.08851	+	1.48735i	0.101881	+	0.0490631i	−0.382249	+	0.924059i	$0.624850\pi$
$920$	9.05109	−	6.17093i	0.298405	−	0.203449i
$921$	16.2387	+	41.3755i	0.535083	+	1.36337i
$922$	−2.44325	+	0.753643i	−0.0804641	+	0.0248199i
$923$	25.2938	−	23.4692i	0.832557	−	0.772500i
$924$	−18.4415	+	23.1249i	−0.606680	+	0.760753i
$925$	10.4449	−	13.0975i	0.343425	−	0.430642i
$926$	3.00562	−	2.78880i	0.0987707	−	0.0916458i
$927$	5.85683	−	1.80659i	0.192364	−	0.0593363i
$928$	11.6191	+	29.6049i	0.381414	+	0.971828i
$929$	−5.51510	+	3.76013i	−0.180944	+	0.123366i	−0.650405	−	0.759588i	$-0.725401\pi$
$929$	−5.51510	+	3.76013i	−0.180944	+	0.123366i	0.469461	+	0.882953i	$0.344448\pi$
$930$	−15.4894	−	7.45932i	−0.507918	−	0.244601i
$931$	3.39659	+	3.15158i	0.111319	+	0.103289i
$932$	−34.7201	+	5.23321i	−1.13729	+	0.171420i
$933$	−3.37986	+	45.1012i	−0.110652	+	1.47655i
$934$	−8.06407	+	20.5469i	−0.263865	+	0.672316i
$935$	3.08619	+	13.5215i	0.100929	+	0.442200i
$936$	0.607734	+	8.10965i	0.0198644	+	0.265072i
$937$	40.4211	+	12.4682i	1.32050	+	0.407320i	0.873330	−	0.487130i	$-0.161956\pi$
$937$	40.4211	+	12.4682i	1.32050	+	0.407320i	0.447169	+	0.894450i	$0.352432\pi$
$938$	−14.5636	+	7.01346i	−0.475519	+	0.228998i
$939$	−4.16693	+	7.21733i	−0.135983	+	0.235529i
$940$	23.7740	+	41.1777i	0.775422	+	1.34307i
$941$	−37.1299	−	25.3148i	−1.21040	−	0.825237i	−0.221697	−	0.975116i	$-0.571159\pi$
$941$	−37.1299	−	25.3148i	−1.21040	−	0.825237i	−0.988704	+	0.149878i	$0.952112\pi$
$942$	0.196352	−	0.860273i	0.00639749	−	0.0280292i
$943$	−8.77552	−	1.32270i	−0.285770	−	0.0430729i
$944$	11.5662	+	14.5036i	0.376449	+	0.472052i
$945$	−55.0437			−1.79057
$946$	3.95991	+	16.2491i	0.128748	+	0.528305i
$947$	33.5215			1.08930			0.544652	−	0.838662i	$-0.316662\pi$
$947$	33.5215			1.08930			0.544652	+	0.838662i	$0.316662\pi$
$948$	0.921611	+	1.15566i	0.0299325	+	0.0375342i
$949$	−15.6339	−	2.35643i	−0.507497	−	0.0764928i
$950$	−1.14088	+	4.99851i	−0.0370150	+	0.162173i
$951$	23.5062	+	16.0262i	0.762240	+	0.519686i
$952$	3.30355	+	5.72192i	0.107069	+	0.185449i
$953$	−5.05249	+	8.75117i	−0.163666	+	0.283478i	−0.936181	−	0.351519i	$-0.885665\pi$
$953$	−5.05249	+	8.75117i	−0.163666	+	0.283478i	0.772515	+	0.634997i	$0.218999\pi$
$954$	−2.75737	+	1.32788i	−0.0892732	+	0.0429917i
$955$	12.7611	+	3.93627i	0.412939	+	0.127375i
$956$	−1.32271	−	17.6504i	−0.0427796	−	0.570854i
$957$	7.41924	+	32.5058i	0.239830	+	1.05076i
$958$	−5.81483	+	14.8159i	−0.187869	+	0.478681i
$959$	−1.35440	+	18.0733i	−0.0437360	+	0.583616i
$960$	4.04484	−	0.609662i	0.130547	−	0.0196767i
$961$	−14.7365	−	13.6735i	−0.475372	−	0.441081i
$962$	−5.19938	−	2.50389i	−0.167635	−	0.0807286i
$963$	−8.33152	+	5.68033i	−0.268480	+	0.183046i
$964$	−10.4764	−	26.6935i	−0.337422	−	0.859738i
$965$	−16.6295	+	5.12951i	−0.535321	+	0.165125i
$966$	2.81419	−	2.61119i	0.0905451	−	0.0840136i
$967$	25.6785	−	32.1998i	0.825764	−	1.03548i	−0.172958	−	0.984929i	$-0.555332\pi$
$967$	25.6785	−	32.1998i	0.825764	−	1.03548i	0.998722	−	0.0505460i	$-0.0160962\pi$
$968$	10.9356	−	13.7128i	0.351483	−	0.440746i
$969$	1.69077	−	1.56880i	0.0543153	−	0.0503972i
$970$	−19.0570	+	5.87830i	−0.611883	+	0.188741i
$971$	15.1028	+	38.4814i	0.484673	+	1.23493i	0.938946	+	0.344064i	$0.111804\pi$
$971$	15.1028	+	38.4814i	0.484673	+	1.23493i	−0.454273	+	0.890862i	$0.650101\pi$
$972$	16.8805	−	11.5089i	0.541443	−	0.369149i
$973$	51.1956	+	24.6545i	1.64125	+	0.790387i
$974$	17.1901	+	15.9501i	0.550807	+	0.511074i
$975$	−19.1480	+	2.88610i	−0.613228	+	0.0924293i
$976$	0.762219	−	10.1711i	0.0243980	−	0.325569i
$977$	−14.5992	+	37.1981i	−0.467070	+	1.19007i	0.482326	+	0.875992i	$0.339792\pi$
$977$	−14.5992	+	37.1981i	−0.467070	+	1.19007i	−0.949396	+	0.314082i	$0.898303\pi$
$978$	0.0451080	+	0.197631i	0.00144240	+	0.00631955i
$979$	−4.51647	−	60.2682i	−0.144347	−	1.92618i
$980$	13.1934	+	4.06963i	0.421449	+	0.130000i
$981$	4.43389	−	2.13525i	0.141563	−	0.0681733i
$982$	1.84898	−	3.20253i	0.0590034	−	0.102197i
$983$	3.50696	+	6.07424i	0.111855	+	0.193738i	0.916518	−	0.399993i	$-0.130988\pi$
$983$	3.50696	+	6.07424i	0.111855	+	0.193738i	−0.804663	+	0.593731i	$0.797654\pi$
$984$	12.5523	+	8.55799i	0.400152	+	0.272819i
$985$	8.53554	−	37.3966i	0.271965	−	1.19156i
$986$	3.34231	+	0.503772i	0.106441	+	0.0160434i
$987$	22.8926	+	28.7064i	0.728678	+	0.913734i
$988$	−8.67980			−0.276141
$989$	0.952884	+	10.6254i	0.0302999	+	0.337868i
$990$	10.4002			0.330541
$991$	−28.0487	−	35.1719i	−0.890995	−	1.11727i	−0.992477	−	0.122435i	$-0.960930\pi$
$991$	−28.0487	−	35.1719i	−0.890995	−	1.11727i	0.101481	−	0.994837i	$-0.467642\pi$
$992$	−38.6769	−	5.82961i	−1.22799	−	0.185090i
$993$	−3.07567	+	13.4754i	−0.0976034	+	0.427628i
$994$	−17.3688	−	11.8418i	−0.550905	−	0.375600i
$995$	32.9748	+	57.1141i	1.04537	+	1.81064i
$996$	−11.2450	+	19.4769i	−0.356311	+	0.617149i
$997$	−18.7660	+	9.03723i	−0.594325	+	0.286212i	−0.706767	−	0.707446i	$-0.749847\pi$
$997$	−18.7660	+	9.03723i	−0.594325	+	0.286212i	0.112442	+	0.993658i	$0.464133\pi$
$998$	−9.96902	−	3.07503i	−0.315564	−	0.0973385i
$999$	1.40481	+	18.7460i	0.0444464	+	0.593096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.u.b.52.12	✓	348
43.24	even	21	inner	731.2.u.b.239.12	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.u.b.52.12	✓	348	1.1	even	1	trivial
731.2.u.b.239.12	yes	348	43.24	even	21	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.u (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.362567 - 0.454644i) q^{2} +(1.29324 + 0.194925i) q^{3} +(0.369795 - 1.62018i) q^{4} +(-2.61272 - 1.78132i) q^{5} +(-0.380264 - 0.658637i) q^{6} +(-1.55140 + 2.68710i) q^{7} +(-1.91853 + 0.923914i) q^{8} +(-1.23224 - 0.380097i) q^{9} +O(q^{10})\)	\(q+(-0.362567 - 0.454644i) q^{2} +(1.29324 + 0.194925i) q^{3} +(0.369795 - 1.62018i) q^{4} +(-2.61272 - 1.78132i) q^{5} +(-0.380264 - 0.658637i) q^{6} +(-1.55140 + 2.68710i) q^{7} +(-1.91853 + 0.923914i) q^{8} +(-1.23224 - 0.380097i) q^{9} +(0.137417 + 1.83370i) q^{10} +(0.975970 + 4.27600i) q^{11} +(0.794047 - 2.02320i) q^{12} +(-0.221321 + 2.95333i) q^{13} +(1.78416 - 0.268919i) q^{14} +(-3.03165 - 2.81296i) q^{15} +(-1.87889 - 0.904828i) q^{16} +(-0.826239 + 0.563320i) q^{17} +(0.273961 + 0.698042i) q^{18} +(-1.68522 + 0.519821i) q^{19} +(-3.85223 + 3.57435i) q^{20} +(-2.53011 + 3.17266i) q^{21} +(1.59021 - 1.99405i) q^{22} +(1.19257 - 1.10655i) q^{23} +(-2.66121 + 0.820875i) q^{24} +(1.82649 + 4.65381i) q^{25} +(1.42296 - 0.970154i) q^{26} +(-5.05449 - 2.43411i) q^{27} +(3.77988 + 3.50722i) q^{28} +(5.74762 - 0.866314i) q^{29} +(-0.179721 + 2.39821i) q^{30} +(-2.61169 + 6.65448i) q^{31} +(1.21752 + 5.33432i) q^{32} +(0.428665 + 5.72014i) q^{33} +(0.555677 + 0.171404i) q^{34} +(8.83995 - 4.25710i) q^{35} +(-1.07150 + 1.85590i) q^{36} +(-1.67543 - 2.90193i) q^{37} +(0.847337 + 0.577704i) q^{38} +(-0.861897 + 3.77622i) q^{39} +(6.65836 + 1.00359i) q^{40} +(-3.40119 - 4.26495i) q^{41} +2.35977 q^{42} +(-4.01300 + 5.18612i) q^{43} +7.28880 q^{44} +(2.54243 + 3.18811i) q^{45} +(-0.935471 - 0.141000i) q^{46} +(2.01338 - 8.82119i) q^{47} +(-2.25349 - 1.53640i) q^{48} +(-1.31367 - 2.27535i) q^{49} +(1.45360 - 2.51772i) q^{50} +(-1.17833 + 0.567454i) q^{51} +(4.70307 + 1.45070i) q^{52} +(0.304993 + 4.06985i) q^{53} +(0.725933 + 3.18052i) q^{54} +(5.06700 - 12.9105i) q^{55} +(0.493750 - 6.58863i) q^{56} +(-2.28072 + 0.343763i) q^{57} +(-2.47776 - 2.29902i) q^{58} +(-8.01457 - 3.85961i) q^{59} +(-5.67859 + 3.87159i) q^{60} +(1.78686 + 4.55284i) q^{61} +(3.97233 - 1.22530i) q^{62} +(2.93306 - 2.72148i) q^{63} +(-0.616687 + 0.773301i) q^{64} +(5.83907 - 7.32196i) q^{65} +(2.44521 - 2.26882i) q^{66} +(-8.56074 + 2.64064i) q^{67} +(0.607140 + 1.54697i) q^{68} +(1.75798 - 1.19857i) q^{69} +(-5.14053 - 2.47555i) q^{70} +(-8.54058 - 7.92450i) q^{71} +(2.71527 - 0.409261i) q^{72} +(-0.398945 + 5.32355i) q^{73} +(-0.711890 + 1.81387i) q^{74} +(1.45494 + 6.37452i) q^{75} +(0.219017 + 2.92258i) q^{76} +(-13.0042 - 4.01125i) q^{77} +(2.02933 - 0.977274i) q^{78} +(-0.340048 + 0.588981i) q^{79} +(3.29723 + 5.71097i) q^{80} +(-2.86581 - 1.95388i) q^{81} +(-0.705879 + 3.09266i) q^{82} +(-10.2321 - 1.54224i) q^{83} +(4.20465 + 5.27247i) q^{84} +3.16218 q^{85} +(3.81282 - 0.0558268i) q^{86} +7.60192 q^{87} +(-5.82308 - 7.30192i) q^{88} +(-13.6258 - 2.05375i) q^{89} +(0.527654 - 2.31180i) q^{90} +(-7.59252 - 5.17649i) q^{91} +(-1.35179 - 2.34137i) q^{92} +(-4.67466 + 8.09676i) q^{93} +(-4.74048 + 2.28290i) q^{94} +(5.32896 + 1.64377i) q^{95} +(0.534761 + 7.13588i) q^{96} +(2.41333 + 10.5735i) q^{97} +(-0.558179 + 1.42222i) q^{98} +(0.422662 - 5.64004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 12 q^{12} - 9 q^{13} - 3 q^{14} - 14 q^{15} - 30 q^{16} - 29 q^{17} - 204 q^{18} - 8 q^{19} + 61 q^{20} + 26 q^{21} + 85 q^{22} - 79 q^{23} - 12 q^{24} + 22 q^{25} - 14 q^{26} + 12 q^{27} - 15 q^{28} + 54 q^{29} - 46 q^{30} - 52 q^{31} + 33 q^{32} + 39 q^{33} + 3 q^{34} + 32 q^{35} - 161 q^{36} + 68 q^{37} - 29 q^{38} + 61 q^{39} + 107 q^{40} + 63 q^{41} - 56 q^{42} - 45 q^{43} - 74 q^{44} + 144 q^{45} - 22 q^{46} - 70 q^{47} + 168 q^{48} - 119 q^{49} + 97 q^{50} - 6 q^{51} + 27 q^{52} + 10 q^{53} - 34 q^{54} - 78 q^{55} - 44 q^{56} - 40 q^{57} - 38 q^{58} - 47 q^{59} - 72 q^{60} - 76 q^{61} - 41 q^{62} + 63 q^{63} - 112 q^{64} - 31 q^{65} - 598 q^{66} - 39 q^{67} - 20 q^{68} - 17 q^{69} - 72 q^{70} - 37 q^{71} + 245 q^{72} + 14 q^{73} + 77 q^{74} - 121 q^{75} + 152 q^{76} + 59 q^{77} + 220 q^{78} + 4 q^{79} - 42 q^{80} - 109 q^{81} + 148 q^{82} + 59 q^{83} + 390 q^{84} + 2 q^{85} + 12 q^{86} - 78 q^{87} + 344 q^{88} - 103 q^{89} - 75 q^{90} + 148 q^{91} + 28 q^{92} + 140 q^{93} + 24 q^{94} - 302 q^{95} + 22 q^{96} + 57 q^{97} - 72 q^{98} - 128 q^{99}+O(q^{100}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 12 * q^12 - 9 * q^13 - 3 * q^14 - 14 * q^15 - 30 * q^16 - 29 * q^17 - 204 * q^18 - 8 * q^19 + 61 * q^20 + 26 * q^21 + 85 * q^22 - 79 * q^23 - 12 * q^24 + 22 * q^25 - 14 * q^26 + 12 * q^27 - 15 * q^28 + 54 * q^29 - 46 * q^30 - 52 * q^31 + 33 * q^32 + 39 * q^33 + 3 * q^34 + 32 * q^35 - 161 * q^36 + 68 * q^37 - 29 * q^38 + 61 * q^39 + 107 * q^40 + 63 * q^41 - 56 * q^42 - 45 * q^43 - 74 * q^44 + 144 * q^45 - 22 * q^46 - 70 * q^47 + 168 * q^48 - 119 * q^49 + 97 * q^50 - 6 * q^51 + 27 * q^52 + 10 * q^53 - 34 * q^54 - 78 * q^55 - 44 * q^56 - 40 * q^57 - 38 * q^58 - 47 * q^59 - 72 * q^60 - 76 * q^61 - 41 * q^62 + 63 * q^63 - 112 * q^64 - 31 * q^65 - 598 * q^66 - 39 * q^67 - 20 * q^68 - 17 * q^69 - 72 * q^70 - 37 * q^71 + 245 * q^72 + 14 * q^73 + 77 * q^74 - 121 * q^75 + 152 * q^76 + 59 * q^77 + 220 * q^78 + 4 * q^79 - 42 * q^80 - 109 * q^81 + 148 * q^82 + 59 * q^83 + 390 * q^84 + 2 * q^85 + 12 * q^86 - 78 * q^87 + 344 * q^88 - 103 * q^89 - 75 * q^90 + 148 * q^91 + 28 * q^92 + 140 * q^93 + 24 * q^94 - 302 * q^95 + 22 * q^96 + 57 * q^97 - 72 * q^98 - 128 * q^99

Introduction

L-functions

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