LMFDB - Embedded newform 930.2.s.b.769.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (of order $6$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			769.3
Root			$1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	930.769
Dual form			930.2.s.b.439.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-1.86603 + 1.23205i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.29129 + 1.32288i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-1.86603 + 1.23205i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.29129 + 1.32288i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.23205 - 1.86603i) q^{10} +(-2.32288 + 4.02334i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-4.58258 - 2.64575i) q^{13} +(-1.32288 - 2.29129i) q^{14} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} +(5.19615 - 3.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(2.64575 + 4.58258i) q^{19} +(1.86603 - 1.23205i) q^{20} +(1.32288 - 2.29129i) q^{21} +(-4.02334 - 2.32288i) q^{22} -1.29150i q^{23} +(0.500000 + 0.866025i) q^{24} +(1.96410 - 4.59808i) q^{25} +(2.64575 - 4.58258i) q^{26} +1.00000i q^{27} +(2.29129 - 1.32288i) q^{28} +2.64575 q^{29} +(2.00000 + 1.00000i) q^{30} +(-4.14575 - 3.71655i) q^{31} +1.00000i q^{32} -4.64575i q^{33} +(3.00000 + 5.19615i) q^{34} +(2.64575 - 5.29150i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.46410 + 2.00000i) q^{37} +(-4.58258 + 2.64575i) q^{38} +5.29150 q^{39} +(1.23205 + 1.86603i) q^{40} +(3.64575 - 6.31463i) q^{41} +(2.29129 + 1.32288i) q^{42} +(0.613577 - 0.354249i) q^{43} +(2.32288 - 4.02334i) q^{44} +(0.133975 + 2.23205i) q^{45} +1.29150 q^{46} -1.29150i q^{47} +(-0.866025 + 0.500000i) q^{48} +(4.59808 + 1.96410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(4.58258 + 2.64575i) q^{52} +(-7.18065 - 4.14575i) q^{53} -1.00000 q^{54} +(-0.622413 - 10.3696i) q^{55} +(1.32288 + 2.29129i) q^{56} +(-4.58258 - 2.64575i) q^{57} +2.64575i q^{58} +(2.32288 + 4.02334i) q^{59} +(-1.00000 + 2.00000i) q^{60} +10.0000 q^{61} +(3.71655 - 4.14575i) q^{62} +2.64575i q^{63} -1.00000 q^{64} +(11.8109 - 0.708927i) q^{65} +4.64575 q^{66} +(-0.613577 - 0.354249i) q^{67} +(-5.19615 + 3.00000i) q^{68} +(0.645751 + 1.11847i) q^{69} +(5.29150 + 2.64575i) q^{70} +(7.29150 - 12.6293i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(-12.6293 - 7.29150i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(0.598076 + 4.96410i) q^{75} +(-2.64575 - 4.58258i) q^{76} -12.2915i q^{77} +5.29150i q^{78} +(-3.29150 - 5.70105i) q^{79} +(-1.86603 + 1.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.31463 + 3.64575i) q^{82} +(10.0312 + 5.79150i) q^{83} +(-1.32288 + 2.29129i) q^{84} +(-6.00000 + 12.0000i) q^{85} +(0.354249 + 0.613577i) q^{86} +(-2.29129 + 1.32288i) q^{87} +(4.02334 + 2.32288i) q^{88} -7.29150 q^{89} +(-2.23205 + 0.133975i) q^{90} +14.0000 q^{91} +1.29150i q^{92} +(5.44860 + 1.14575i) q^{93} +1.29150 q^{94} +(-10.5830 - 5.29150i) q^{95} +(-0.500000 - 0.866025i) q^{96} +15.2288i q^{97} +(2.32288 + 4.02334i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9	$ 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{15} + 8 q^{16} + 8 q^{20} + 4 q^{24} - 12 q^{25} + 16 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{36} - 4 q^{40} + 8 q^{41} + 8 q^{44} + 8 q^{45} - 32 q^{46} + 16 q^{50} - 24 q^{51} - 8 q^{54} - 16 q^{55} + 8 q^{59} - 8 q^{60} + 80 q^{61} - 8 q^{64} + 16 q^{66} - 16 q^{69} + 16 q^{71} - 16 q^{74} - 16 q^{75} + 16 q^{79} - 8 q^{80} - 4 q^{81} - 48 q^{85} + 24 q^{86} - 16 q^{89} - 4 q^{90} + 112 q^{91} - 32 q^{94} - 4 q^{96} + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^15 + 8 * q^16 + 8 * q^20 + 4 * q^24 - 12 * q^25 + 16 * q^30 - 12 * q^31 + 24 * q^34 - 4 * q^36 - 4 * q^40 + 8 * q^41 + 8 * q^44 + 8 * q^45 - 32 * q^46 + 16 * q^50 - 24 * q^51 - 8 * q^54 - 16 * q^55 + 8 * q^59 - 8 * q^60 + 80 * q^61 - 8 * q^64 + 16 * q^66 - 16 * q^69 + 16 * q^71 - 16 * q^74 - 16 * q^75 + 16 * q^79 - 8 * q^80 - 4 * q^81 - 48 * q^85 + 24 * q^86 - 16 * q^89 - 4 * q^90 + 112 * q^91 - 32 * q^94 - 4 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−1.00000			−0.500000
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.29129	+	1.32288i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	−2.29129	+	1.32288i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.23205	−	1.86603i	−0.389609	−	0.590089i
$11$	−2.32288	+	4.02334i	−0.700373	+	1.21308i	0.267962	+	0.963429i	$0.413650\pi$
$11$	−2.32288	+	4.02334i	−0.700373	+	1.21308i	−0.968335	+	0.249653i	$0.919684\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−4.58258	−	2.64575i	−1.27098	−	0.733799i	−0.295806	−	0.955248i	$-0.595588\pi$
$13$	−4.58258	−	2.64575i	−1.27098	−	0.733799i	−0.975172	+	0.221449i	$0.928921\pi$
$14$	−1.32288	−	2.29129i	−0.353553	−	0.612372i
$15$	1.00000	−	2.00000i	0.258199	−	0.516398i
$16$	1.00000			0.250000
$17$	5.19615	−	3.00000i	1.26025	−	0.727607i	0.287129	−	0.957892i	$-0.407299\pi$
$17$	5.19615	−	3.00000i	1.26025	−	0.727607i	0.973123	+	0.230285i	$0.0739659\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	2.64575	+	4.58258i	0.606977	+	1.05131i	0.991736	+	0.128298i	$0.0409513\pi$
$19$	2.64575	+	4.58258i	0.606977	+	1.05131i	−0.384759	+	0.923017i	$0.625715\pi$
$20$	1.86603	−	1.23205i	0.417256	−	0.275495i
$21$	1.32288	−	2.29129i	0.288675	−	0.500000i
$22$	−4.02334	−	2.32288i	−0.857779	−	0.495239i
$23$		−	1.29150i		−	0.269297i	−0.990893	−	0.134648i	$-0.957009\pi$
$23$		−	1.29150i		−	0.269297i	0.990893	−	0.134648i	$-0.0429905\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$	2.64575	−	4.58258i	0.518875	−	0.898717i
$27$			1.00000i			0.192450i
$28$	2.29129	−	1.32288i	0.433013	−	0.250000i
$29$	2.64575			0.491304			0.245652	−	0.969358i	$-0.420998\pi$
$29$	2.64575			0.491304			0.245652	+	0.969358i	$0.420998\pi$
$30$	2.00000	+	1.00000i	0.365148	+	0.182574i
$31$	−4.14575	−	3.71655i	−0.744599	−	0.667512i
$31$	−4.14575	−	3.71655i	−0.744599	−	0.667512i
$32$			1.00000i			0.176777i
$33$		−	4.64575i		−	0.808721i
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	2.64575	−	5.29150i	0.447214	−	0.894427i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	−0.756948	−	0.653476i	$-0.773310\pi$
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	0.187453	+	0.982274i	$0.439977\pi$
$38$	−4.58258	+	2.64575i	−0.743392	+	0.429198i
$39$	5.29150			0.847319
$40$	1.23205	+	1.86603i	0.194804	+	0.295045i
$41$	3.64575	−	6.31463i	0.569371	−	0.986179i	−0.427258	−	0.904130i	$-0.640520\pi$
$41$	3.64575	−	6.31463i	0.569371	−	0.986179i	0.996628	−	0.0820490i	$-0.0261464\pi$
$42$	2.29129	+	1.32288i	0.353553	+	0.204124i
$43$	0.613577	−	0.354249i	0.0935696	−	0.0540224i	−0.452485	−	0.891772i	$-0.649462\pi$
$43$	0.613577	−	0.354249i	0.0935696	−	0.0540224i	0.546055	+	0.837750i	$0.316129\pi$
$44$	2.32288	−	4.02334i	0.350187	−	0.606541i
$45$	0.133975	+	2.23205i	0.0199718	+	0.332734i
$46$	1.29150			0.190422
$47$		−	1.29150i		−	0.188385i	−0.995554	−	0.0941925i	$-0.969973\pi$
$47$		−	1.29150i		−	0.188385i	0.995554	−	0.0941925i	$-0.0300269\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$		0			0
$50$	4.59808	+	1.96410i	0.650266	+	0.277766i
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	4.58258	+	2.64575i	0.635489	+	0.366900i
$53$	−7.18065	−	4.14575i	−0.986338	−	0.569463i	−0.0821606	−	0.996619i	$-0.526182\pi$
$53$	−7.18065	−	4.14575i	−0.986338	−	0.569463i	−0.904178	+	0.427156i	$0.859515\pi$
$54$	−1.00000			−0.136083
$55$	−0.622413	−	10.3696i	−0.0839261	−	1.39823i
$56$	1.32288	+	2.29129i	0.176777	+	0.306186i
$57$	−4.58258	−	2.64575i	−0.606977	−	0.350438i
$58$			2.64575i			0.347404i
$59$	2.32288	+	4.02334i	0.302413	+	0.523794i	0.976682	−	0.214692i	$-0.0688746\pi$
$59$	2.32288	+	4.02334i	0.302413	+	0.523794i	−0.674269	+	0.738486i	$0.735541\pi$
$60$	−1.00000	+	2.00000i	−0.129099	+	0.258199i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	3.71655	−	4.14575i	0.472002	−	0.526511i
$63$			2.64575i			0.333333i
$64$	−1.00000			−0.125000
$65$	11.8109	−	0.708927i	1.46496	−	0.0879316i
$66$	4.64575			0.571852
$67$	−0.613577	−	0.354249i	−0.0749603	−	0.0432784i	0.462051	−	0.886853i	$-0.347114\pi$
$67$	−0.613577	−	0.354249i	−0.0749603	−	0.0432784i	−0.537012	+	0.843575i	$0.680447\pi$
$68$	−5.19615	+	3.00000i	−0.630126	+	0.363803i
$69$	0.645751	+	1.11847i	0.0777393	+	0.134648i
$70$	5.29150	+	2.64575i	0.632456	+	0.316228i
$71$	7.29150	−	12.6293i	0.865342	−	1.49882i	−0.00136488	−	0.999999i	$-0.500434\pi$
$71$	7.29150	−	12.6293i	0.865342	−	1.49882i	0.866707	−	0.498818i	$-0.166232\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	−12.6293	−	7.29150i	−1.47814	−	0.853406i	−0.478448	−	0.878116i	$-0.658800\pi$
$73$	−12.6293	−	7.29150i	−1.47814	−	0.853406i	−0.999695	+	0.0247103i	$0.992134\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$	0.598076	+	4.96410i	0.0690599	+	0.573205i
$76$	−2.64575	−	4.58258i	−0.303488	−	0.525657i
$77$		−	12.2915i		−	1.40075i
$78$			5.29150i			0.599145i
$79$	−3.29150	−	5.70105i	−0.370323	−	0.641418i	0.619292	−	0.785161i	$-0.287420\pi$
$79$	−3.29150	−	5.70105i	−0.370323	−	0.641418i	−0.989615	+	0.143742i	$0.954086\pi$
$80$	−1.86603	+	1.23205i	−0.208628	+	0.137747i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.31463	+	3.64575i	0.697334	+	0.402606i
$83$	10.0312	+	5.79150i	1.10106	+	0.635700i	0.936500	−	0.350666i	$-0.114045\pi$
$83$	10.0312	+	5.79150i	1.10106	+	0.635700i	0.164564	+	0.986366i	$0.447378\pi$
$84$	−1.32288	+	2.29129i	−0.144338	+	0.250000i
$85$	−6.00000	+	12.0000i	−0.650791	+	1.30158i
$86$	0.354249	+	0.613577i	0.0381996	+	0.0661637i
$87$	−2.29129	+	1.32288i	−0.245652	+	0.141827i
$88$	4.02334	+	2.32288i	0.428889	+	0.247619i
$89$	−7.29150			−0.772898			−0.386449	−	0.922311i	$-0.626298\pi$
$89$	−7.29150			−0.772898			−0.386449	+	0.922311i	$0.626298\pi$
$90$	−2.23205	+	0.133975i	−0.235279	+	0.0141222i
$91$	14.0000			1.46760
$92$			1.29150i			0.134648i
$93$	5.44860	+	1.14575i	0.564994	+	0.118809i
$94$	1.29150			0.133208
$95$	−10.5830	−	5.29150i	−1.08579	−	0.542897i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$			15.2288i			1.54625i	0.634256	+	0.773123i	$0.281306\pi$
$97$			15.2288i			1.54625i	−0.634256	+	0.773123i	$0.718694\pi$
$98$		0			0
$99$	2.32288	+	4.02334i	0.233458	+	0.404361i
$100$	−1.96410	+	4.59808i	−0.196410	+	0.459808i
$101$	1.35425			0.134753			0.0673764	−	0.997728i	$-0.478537\pi$
$101$	1.35425			0.134753			0.0673764	+	0.997728i	$0.478537\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$	1.17281	+	0.677124i	0.115561	+	0.0667190i	0.556666	−	0.830736i	$-0.312080\pi$
$103$	1.17281	+	0.677124i	0.115561	+	0.0667190i	−0.441106	+	0.897455i	$0.645414\pi$
$104$	−2.64575	+	4.58258i	−0.259437	+	0.449359i
$105$	0.354463	+	5.90545i	0.0345921	+	0.576313i
$106$	4.14575	−	7.18065i	0.402671	−	0.697447i
$107$	4.33013	−	2.50000i	0.418609	−	0.241684i	−0.275873	−	0.961194i	$-0.588967\pi$
$107$	4.33013	−	2.50000i	0.418609	−	0.241684i	0.694482	+	0.719510i	$0.255634\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	−17.2915			−1.65623			−0.828113	−	0.560562i	$-0.810585\pi$
$109$	−17.2915			−1.65623			−0.828113	+	0.560562i	$0.810585\pi$
$110$	10.3696	−	0.622413i	0.988698	−	0.0593447i
$111$	2.00000	−	3.46410i	0.189832	−	0.328798i
$112$	−2.29129	+	1.32288i	−0.216506	+	0.125000i
$113$	2.34563	+	1.35425i	0.220658	+	0.127397i	0.606255	−	0.795270i	$-0.292671\pi$
$113$	2.34563	+	1.35425i	0.220658	+	0.127397i	−0.385597	+	0.922667i	$0.626004\pi$
$114$	2.64575	−	4.58258i	0.247797	−	0.429198i
$115$	1.59120	+	2.40998i	0.148380	+	0.224731i
$116$	−2.64575			−0.245652
$117$	−4.58258	+	2.64575i	−0.423659	+	0.244600i
$118$	−4.02334	+	2.32288i	−0.370378	+	0.213838i
$119$	−7.93725	+	13.7477i	−0.727607	+	1.26025i
$120$	−2.00000	−	1.00000i	−0.182574	−	0.0912871i
$121$	−5.29150	−	9.16515i	−0.481046	−	0.833196i
$122$			10.0000i			0.905357i
$123$			7.29150i			0.657453i
$124$	4.14575	+	3.71655i	0.372299	+	0.333756i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−2.64575			−0.235702
$127$	−11.4564	+	6.61438i	−1.01659	+	0.586931i	−0.913116	−	0.407700i	$-0.866331\pi$
$127$	−11.4564	+	6.61438i	−1.01659	+	0.586931i	−0.103479	+	0.994632i	$0.532997\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−0.354249	+	0.613577i	−0.0311899	+	0.0540224i
$130$	0.708927	+	11.8109i	0.0621770	+	1.03588i
$131$	−6.64575	−	11.5108i	−0.580642	−	1.00570i	−0.995403	−	0.0957712i	$-0.969468\pi$
$131$	−6.64575	−	11.5108i	−0.580642	−	1.00570i	0.414761	−	0.909930i	$-0.363865\pi$
$132$			4.64575i			0.404361i
$133$	−12.1244	−	7.00000i	−1.05131	−	0.606977i
$134$	0.354249	−	0.613577i	0.0306024	−	0.0530050i
$135$	−1.23205	−	1.86603i	−0.106038	−	0.160602i
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	−9.16515	−	5.29150i	−0.783032	−	0.452084i	0.0544719	−	0.998515i	$-0.482652\pi$
$137$	−9.16515	−	5.29150i	−0.783032	−	0.452084i	−0.837504	+	0.546432i	$0.815986\pi$
$138$	−1.11847	+	0.645751i	−0.0952108	+	0.0549700i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−2.64575	+	5.29150i	−0.223607	+	0.447214i
$141$	0.645751	+	1.11847i	0.0543821	+	0.0941925i
$142$	12.6293	+	7.29150i	1.05982	+	0.611889i
$143$	21.2895	−	12.2915i	1.78032	−	1.02787i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−4.93704	+	3.25970i	−0.409999	+	0.270703i
$146$	7.29150	−	12.6293i	0.603449	−	1.04520i
$147$		0			0
$148$	3.46410	−	2.00000i	0.284747	−	0.164399i
$149$	−6.67712	−	11.5651i	−0.547011	−	0.947451i	−0.998477	−	0.0551631i	$-0.982432\pi$
$149$	−6.67712	−	11.5651i	−0.547011	−	0.947451i	0.451466	−	0.892288i	$-0.350901\pi$
$150$	−4.96410	+	0.598076i	−0.405317	+	0.0488327i
$151$	−22.2915			−1.81406			−0.907028	−	0.421069i	$-0.861655\pi$
$151$	−22.2915			−1.81406			−0.907028	+	0.421069i	$0.861655\pi$
$152$	4.58258	−	2.64575i	0.371696	−	0.214599i
$153$		−	6.00000i		−	0.485071i
$154$	12.2915			0.990478
$155$	12.3151	+	1.82740i	0.989169	+	0.146780i
$156$	−5.29150			−0.423659
$157$		−	9.29150i		−	0.741543i	−0.928724	−	0.370771i	$-0.879093\pi$
$157$		−	9.29150i		−	0.741543i	0.928724	−	0.370771i	$-0.120907\pi$
$158$	5.70105	−	3.29150i	0.453551	−	0.261858i
$159$	8.29150			0.657559
$160$	−1.23205	−	1.86603i	−0.0974022	−	0.147522i
$161$	1.70850	+	2.95920i	0.134648	+	0.233218i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$		−	10.0000i		−	0.783260i	−0.920123	−	0.391630i	$-0.871911\pi$
$163$		−	10.0000i		−	0.783260i	0.920123	−	0.391630i	$-0.128089\pi$
$164$	−3.64575	+	6.31463i	−0.284685	+	0.493089i
$165$	5.72380	+	8.66909i	0.445597	+	0.674888i
$166$	−5.79150	+	10.0312i	−0.449508	+	0.778570i
$167$	8.55157	−	4.93725i	0.661741	−	0.382056i	−0.131199	−	0.991356i	$-0.541883\pi$
$167$	8.55157	−	4.93725i	0.661741	−	0.382056i	0.792940	+	0.609300i	$0.208549\pi$
$168$	−2.29129	−	1.32288i	−0.176777	−	0.102062i
$169$	7.50000	+	12.9904i	0.576923	+	0.999260i
$170$	−12.0000	−	6.00000i	−0.920358	−	0.460179i
$171$	5.29150			0.404651
$172$	−0.613577	+	0.354249i	−0.0467848	+	0.0270112i
$173$	−3.71655	−	2.14575i	−0.282564	−	0.163138i	0.352020	−	0.935993i	$-0.385495\pi$
$173$	−3.71655	−	2.14575i	−0.282564	−	0.163138i	−0.634584	+	0.772854i	$0.718828\pi$
$174$	−1.32288	−	2.29129i	−0.100287	−	0.173702i
$175$	1.58236	+	13.1338i	0.119615	+	0.992820i
$176$	−2.32288	+	4.02334i	−0.175093	+	0.303271i
$177$	−4.02334	−	2.32288i	−0.302413	−	0.174598i
$178$		−	7.29150i		−	0.546521i
$179$	11.6144	+	20.1167i	0.868099	+	1.50359i	0.863936	+	0.503601i	$0.167992\pi$
$179$	11.6144	+	20.1167i	0.868099	+	1.50359i	0.00416298	+	0.999991i	$0.498675\pi$
$180$	−0.133975	−	2.23205i	−0.00998588	−	0.166367i
$181$	5.64575	−	9.77873i	0.419645	−	0.726847i	−0.576258	−	0.817268i	$-0.695488\pi$
$181$	5.64575	−	9.77873i	0.419645	−	0.726847i	0.995904	+	0.0904205i	$0.0288211\pi$
$182$			14.0000i			1.03775i
$183$	−8.66025	+	5.00000i	−0.640184	+	0.369611i
$184$	−1.29150			−0.0952108
$185$	4.00000	−	8.00000i	0.294086	−	0.588172i
$186$	−1.14575	+	5.44860i	−0.0840106	+	0.399511i
$187$			27.8745i			2.03839i
$188$			1.29150i			0.0941925i
$189$	−1.32288	−	2.29129i	−0.0962250	−	0.166667i
$190$	5.29150	−	10.5830i	0.383886	−	0.767772i
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	13.2972	−	7.67712i	0.957151	−	0.552612i	0.0618561	−	0.998085i	$-0.480298\pi$
$193$	13.2972	−	7.67712i	0.957151	−	0.552612i	0.895295	+	0.445474i	$0.146965\pi$
$194$	−15.2288			−1.09336
$195$	−9.87408	+	6.51940i	−0.707097	+	0.466864i
$196$		0			0
$197$	−16.5983	−	9.58301i	−1.18258	−	0.682761i	−0.225967	−	0.974135i	$-0.572554\pi$
$197$	−16.5983	−	9.58301i	−1.18258	−	0.682761i	−0.956609	+	0.291374i	$0.905888\pi$
$198$	−4.02334	+	2.32288i	−0.285926	+	0.165080i
$199$	2.85425	−	4.94370i	0.202332	−	0.350450i	−0.746947	−	0.664883i	$-0.768481\pi$
$199$	2.85425	−	4.94370i	0.202332	−	0.350450i	0.949279	+	0.314434i	$0.101815\pi$
$200$	−4.59808	−	1.96410i	−0.325133	−	0.138883i
$201$	0.708497			0.0499736
$202$			1.35425i			0.0952846i
$203$	−6.06218	+	3.50000i	−0.425481	+	0.245652i
$204$	3.00000	−	5.19615i	0.210042	−	0.363803i
$205$	0.976876	+	16.2750i	0.0682280	+	1.13670i
$206$	−0.677124	+	1.17281i	−0.0471775	+	0.0817138i
$207$	−1.11847	−	0.645751i	−0.0777393	−	0.0448828i
$208$	−4.58258	−	2.64575i	−0.317744	−	0.183450i
$209$	−24.5830			−1.70044
$210$	−5.90545	+	0.354463i	−0.407515	+	0.0244603i
$211$	−2.29150	−	3.96900i	−0.157754	−	0.273237i	0.776305	−	0.630358i	$-0.217092\pi$
$211$	−2.29150	−	3.96900i	−0.157754	−	0.273237i	−0.934058	+	0.357121i	$0.883758\pi$
$212$	7.18065	+	4.14575i	0.493169	+	0.284731i
$213$			14.5830i			0.999211i
$214$	2.50000	+	4.33013i	0.170896	+	0.296001i
$215$	−0.708497	+	1.41699i	−0.0483191	+	0.0966382i
$216$	1.00000			0.0680414
$217$	14.4156	+	3.03137i	0.978598	+	0.205783i
$218$		−	17.2915i		−	1.17113i
$219$	14.5830			0.985428
$220$	0.622413	+	10.3696i	0.0419631	+	0.699115i
$221$	−31.7490			−2.13567
$222$	3.46410	+	2.00000i	0.232495	+	0.134231i
$223$	−18.4933	+	10.6771i	−1.23840	+	0.714993i	−0.968768	−	0.247969i	$-0.920237\pi$
$223$	−18.4933	+	10.6771i	−1.23840	+	0.714993i	−0.269636	+	0.962962i	$0.586904\pi$
$224$	−1.32288	−	2.29129i	−0.0883883	−	0.153093i
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	−1.35425	+	2.34563i	−0.0900833	+	0.156029i
$227$	−12.9904	−	7.50000i	−0.862202	−	0.497792i	0.00254715	−	0.999997i	$-0.499189\pi$
$227$	−12.9904	−	7.50000i	−0.862202	−	0.497792i	−0.864749	+	0.502204i	$0.832523\pi$
$228$	4.58258	+	2.64575i	0.303488	+	0.175219i
$229$	12.5830	+	21.7944i	0.831508	+	1.44021i	0.896842	+	0.442351i	$0.145856\pi$
$229$	12.5830	+	21.7944i	0.831508	+	1.44021i	−0.0653335	+	0.997863i	$0.520811\pi$
$230$	−2.40998	+	1.59120i	−0.158909	+	0.104920i
$231$	6.14575	+	10.6448i	0.404361	+	0.700373i
$232$		−	2.64575i		−	0.173702i
$233$		−	3.29150i		−	0.215634i	−0.994171	−	0.107817i	$-0.965614\pi$
$233$		−	3.29150i		−	0.215634i	0.994171	−	0.107817i	$-0.0343860\pi$
$234$	−2.64575	−	4.58258i	−0.172958	−	0.299572i
$235$	1.59120	+	2.40998i	0.103798	+	0.157210i
$236$	−2.32288	−	4.02334i	−0.151206	−	0.261897i
$237$	5.70105	+	3.29150i	0.370323	+	0.213806i
$238$	−13.7477	−	7.93725i	−0.891133	−	0.514496i
$239$	1.70850	−	2.95920i	0.110514	−	0.191415i	−0.805464	−	0.592645i	$-0.798084\pi$
$239$	1.70850	−	2.95920i	0.110514	−	0.191415i	0.915977	+	0.401230i	$0.131417\pi$
$240$	1.00000	−	2.00000i	0.0645497	−	0.129099i
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	−0.976068	−	0.217465i	$-0.930221\pi$
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	0.299704	−	0.954032i	$-0.403112\pi$
$242$	9.16515	−	5.29150i	0.589158	−	0.340151i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	−7.29150			−0.464889
$247$		−	28.0000i		−	1.78160i
$248$	−3.71655	+	4.14575i	−0.236001	+	0.263255i
$249$	−11.5830			−0.734043
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	−10.6458	−	18.4390i	−0.671954	−	1.16386i	−0.977349	−	0.211633i	$-0.932122\pi$
$251$	−10.6458	−	18.4390i	−0.671954	−	1.16386i	0.305395	−	0.952226i	$-0.401211\pi$
$252$		−	2.64575i		−	0.166667i
$253$	5.19615	+	3.00000i	0.326679	+	0.188608i
$254$	−6.61438	−	11.4564i	−0.415023	−	0.718841i
$255$	−0.803848	−	13.3923i	−0.0503389	−	0.838659i
$256$	1.00000			0.0625000
$257$	4.58258	+	2.64575i	0.285853	+	0.165037i	0.636070	−	0.771631i	$-0.280559\pi$
$257$	4.58258	+	2.64575i	0.285853	+	0.165037i	−0.350217	+	0.936669i	$0.613892\pi$
$258$	−0.613577	−	0.354249i	−0.0381996	−	0.0220546i
$259$	5.29150	−	9.16515i	0.328798	−	0.569495i
$260$	−11.8109	+	0.708927i	−0.732481	+	0.0439658i
$261$	1.32288	−	2.29129i	0.0818839	−	0.141827i
$262$	11.5108	−	6.64575i	0.711138	−	0.410576i
$263$			19.1660i			1.18183i	0.806735	+	0.590913i	$0.201233\pi$
$263$			19.1660i			1.18183i	−0.806735	+	0.590913i	$0.798767\pi$
$264$	−4.64575			−0.285926
$265$	18.5071	−	1.11085i	1.13688	−	0.0682390i
$266$	7.00000	−	12.1244i	0.429198	−	0.743392i
$267$	6.31463	−	3.64575i	0.386449	−	0.223116i
$268$	0.613577	+	0.354249i	0.0374802	+	0.0216392i
$269$	4.00000	−	6.92820i	0.243884	−	0.422420i	−0.717933	−	0.696112i	$-0.754912\pi$
$269$	4.00000	−	6.92820i	0.243884	−	0.422420i	0.961817	+	0.273692i	$0.0882449\pi$
$270$	1.86603	−	1.23205i	0.113563	−	0.0749802i
$271$	−11.7085			−0.711241			−0.355620	−	0.934631i	$-0.615730\pi$
$271$	−11.7085			−0.711241			−0.355620	+	0.934631i	$0.615730\pi$
$272$	5.19615	−	3.00000i	0.315063	−	0.181902i
$273$	−12.1244	+	7.00000i	−0.733799	+	0.423659i
$274$	5.29150	−	9.16515i	0.319671	−	0.553687i
$275$	13.9373	+	18.5830i	0.840448	+	1.12060i
$276$	−0.645751	−	1.11847i	−0.0388697	−	0.0673242i
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$		−	4.00000i		−	0.239904i
$279$	−5.29150	+	1.73205i	−0.316794	+	0.103695i
$280$	−5.29150	−	2.64575i	−0.316228	−	0.158114i
$281$	−2.58301			−0.154089			−0.0770446	−	0.997028i	$-0.524548\pi$
$281$	−2.58301			−0.154089			−0.0770446	+	0.997028i	$0.524548\pi$
$282$	−1.11847	+	0.645751i	−0.0666042	+	0.0384539i
$283$			29.2915i			1.74120i	0.491992	+	0.870600i	$0.336269\pi$
$283$			29.2915i			1.74120i	−0.491992	+	0.870600i	$0.663731\pi$
$284$	−7.29150	+	12.6293i	−0.432671	+	0.749408i
$285$	11.8109	−	0.708927i	0.699617	−	0.0419932i
$286$	12.2915	+	21.2895i	0.726812	+	1.25887i
$287$			19.2915i			1.13874i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$	−3.25970	−	4.93704i	−0.191416	−	0.289913i
$291$	−7.61438	−	13.1885i	−0.446363	−	0.773123i
$292$	12.6293	+	7.29150i	0.739071	+	0.426703i
$293$	21.0371	−	12.1458i	1.22900	−	0.709562i	0.262178	−	0.965020i	$-0.415559\pi$
$293$	21.0371	−	12.1458i	1.22900	−	0.709562i	0.966820	+	0.255457i	$0.0822260\pi$
$294$		0			0
$295$	−9.29150	−	4.64575i	−0.540972	−	0.270486i
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−4.02334	−	2.32288i	−0.233458	−	0.134787i
$298$	11.5651	−	6.67712i	0.669949	−	0.386795i
$299$	−3.41699	+	5.91841i	−0.197610	+	0.342270i
$300$	−0.598076	−	4.96410i	−0.0345299	−	0.286603i
$301$	−0.937254	+	1.62337i	−0.0540224	+	0.0935696i
$302$		−	22.2915i		−	1.28273i
$303$	−1.17281	+	0.677124i	−0.0673764	+	0.0388998i
$304$	2.64575	+	4.58258i	0.151744	+	0.262829i
$305$	−18.6603	+	12.3205i	−1.06848	+	0.705470i
$306$	6.00000			0.342997
$307$	−15.4798	+	8.93725i	−0.883478	+	0.510076i	−0.871803	−	0.489856i	$-0.837049\pi$
$307$	−15.4798	+	8.93725i	−0.883478	+	0.510076i	−0.0116741	+	0.999932i	$0.503716\pi$
$308$			12.2915i			0.700373i
$309$	−1.35425			−0.0770405
$310$	−1.82740	+	12.3151i	−0.103789	+	0.699448i
$311$	19.8745			1.12698			0.563490	−	0.826123i	$-0.309458\pi$
$311$	19.8745			1.12698			0.563490	+	0.826123i	$0.309458\pi$
$312$		−	5.29150i		−	0.299572i
$313$	−1.67771	+	0.968627i	−0.0948298	+	0.0547500i	−0.546665	−	0.837351i	$-0.684103\pi$
$313$	−1.67771	+	0.968627i	−0.0948298	+	0.0547500i	0.451835	+	0.892101i	$0.350770\pi$
$314$	9.29150			0.524350
$315$	−3.25970	−	4.93704i	−0.183663	−	0.278171i
$316$	3.29150	+	5.70105i	0.185161	+	0.320709i
$317$	4.94370	−	2.85425i	0.277666	−	0.160311i	−0.354700	−	0.934980i	$-0.615417\pi$
$317$	4.94370	−	2.85425i	0.277666	−	0.160311i	0.632366	+	0.774669i	$0.282084\pi$
$318$			8.29150i			0.464964i
$319$	−6.14575	+	10.6448i	−0.344096	+	0.595992i
$320$	1.86603	−	1.23205i	0.104314	−	0.0688737i
$321$	−2.50000	+	4.33013i	−0.139536	+	0.241684i
$322$	−2.95920	+	1.70850i	−0.164910	+	0.0952108i
$323$	27.4955	+	15.8745i	1.52989	+	0.883281i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−21.1660	+	15.8745i	−1.17408	+	0.880559i
$326$	10.0000			0.553849
$327$	14.9749	−	8.64575i	0.828113	−	0.478111i
$328$	−6.31463	−	3.64575i	−0.348667	−	0.201303i
$329$	1.70850	+	2.95920i	0.0941925	+	0.163146i
$330$	−8.66909	+	5.72380i	−0.477218	+	0.315085i
$331$	11.5830	−	20.0624i	0.636660	−	1.10273i	−0.349501	−	0.936936i	$-0.613649\pi$
$331$	11.5830	−	20.0624i	0.636660	−	1.10273i	0.986161	−	0.165791i	$-0.0530177\pi$
$332$	−10.0312	−	5.79150i	−0.550532	−	0.317850i
$333$			4.00000i			0.219199i
$334$	4.93725	+	8.55157i	0.270155	+	0.467921i
$335$	1.58140	−	0.0949207i	0.0864012	−	0.00518607i
$336$	1.32288	−	2.29129i	0.0721688	−	0.125000i
$337$		−	23.1033i		−	1.25852i	−0.777197	−	0.629258i	$-0.783359\pi$
$337$		−	23.1033i		−	1.25852i	0.777197	−	0.629258i	$-0.216641\pi$
$338$	−12.9904	+	7.50000i	−0.706584	+	0.407946i
$339$	−2.70850			−0.147105
$340$	6.00000	−	12.0000i	0.325396	−	0.650791i
$341$	24.5830	−	8.04668i	1.33124	−	0.435752i
$342$			5.29150i			0.286132i
$343$		−	18.5203i		−	1.00000i
$344$	−0.354249	−	0.613577i	−0.0190998	−	0.0330818i
$345$	−2.58301	−	1.29150i	−0.139064	−	0.0695322i
$346$	2.14575	−	3.71655i	0.115356	−	0.199803i
$347$	−15.2273	+	8.79150i	−0.817446	+	0.471953i	−0.849535	−	0.527532i	$-0.823117\pi$
$347$	−15.2273	+	8.79150i	−0.817446	+	0.471953i	0.0320890	+	0.999485i	$0.489784\pi$
$348$	2.29129	−	1.32288i	0.122826	−	0.0709136i
$349$	−5.29150			−0.283248			−0.141624	−	0.989921i	$-0.545232\pi$
$349$	−5.29150			−0.283248			−0.141624	+	0.989921i	$0.545232\pi$
$350$	−13.1338	+	1.58236i	−0.702030	+	0.0845807i
$351$	2.64575	−	4.58258i	0.141220	−	0.244600i
$352$	−4.02334	−	2.32288i	−0.214445	−	0.123810i
$353$	−28.8313	+	16.6458i	−1.53453	+	0.885964i	−0.535390	+	0.844605i	$0.679835\pi$
$353$	−28.8313	+	16.6458i	−1.53453	+	0.885964i	−0.999144	+	0.0413591i	$0.986831\pi$
$354$	2.32288	−	4.02334i	0.123459	−	0.213838i
$355$	1.95375	+	32.5500i	0.103694	+	1.72758i
$356$	7.29150			0.386449
$357$		−	15.8745i		−	0.840168i
$358$	−20.1167	+	11.6144i	−1.06320	+	0.613839i
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	−0.524588	−	0.851356i	$-0.675781\pi$
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	0.999590	+	0.0286287i	$0.00911406\pi$
$360$	2.23205	−	0.133975i	0.117639	−	0.00706108i
$361$	−4.50000	+	7.79423i	−0.236842	+	0.410223i
$362$	9.77873	+	5.64575i	0.513959	+	0.296734i
$363$	9.16515	+	5.29150i	0.481046	+	0.277732i
$364$	−14.0000			−0.733799
$365$	32.5500	−	1.95375i	1.70375	−	0.102264i
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	15.9847	+	9.22876i	0.834393	+	0.481737i	0.855355	−	0.518043i	$-0.173339\pi$
$367$	15.9847	+	9.22876i	0.834393	+	0.481737i	−0.0209612	+	0.999780i	$0.506673\pi$
$368$		−	1.29150i		−	0.0673242i
$369$	−3.64575	−	6.31463i	−0.189790	−	0.328726i
$370$	8.00000	+	4.00000i	0.415900	+	0.207950i
$371$	21.9373			1.13893
$372$	−5.44860	−	1.14575i	−0.282497	−	0.0594044i
$373$		−	27.1660i		−	1.40660i	−0.710892	−	0.703301i	$-0.751708\pi$
$373$		−	27.1660i		−	1.40660i	0.710892	−	0.703301i	$-0.248292\pi$
$374$	−27.8745			−1.44136
$375$	−7.23205	−	8.52628i	−0.373461	−	0.440295i
$376$	−1.29150			−0.0666042
$377$	−12.1244	−	7.00000i	−0.624436	−	0.360518i
$378$	2.29129	−	1.32288i	0.117851	−	0.0680414i
$379$	−7.64575	−	13.2428i	−0.392736	−	0.680238i	0.600073	−	0.799945i	$-0.295138\pi$
$379$	−7.64575	−	13.2428i	−0.392736	−	0.680238i	−0.992809	+	0.119706i	$0.961805\pi$
$380$	10.5830	+	5.29150i	0.542897	+	0.271448i
$381$	6.61438	−	11.4564i	0.338865	−	0.586931i
$382$	−6.92820	−	4.00000i	−0.354478	−	0.204658i
$383$	31.5731	+	18.2288i	1.61331	+	0.931446i	0.988596	+	0.150594i	$0.0481186\pi$
$383$	31.5731	+	18.2288i	1.61331	+	0.931446i	0.624716	+	0.780852i	$0.285215\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	15.1438	+	22.9363i	0.771797	+	1.16894i
$386$	7.67712	+	13.2972i	0.390755	+	0.676808i
$387$		−	0.708497i		−	0.0360149i
$388$		−	15.2288i		−	0.773123i
$389$	−8.00000	−	13.8564i	−0.405616	−	0.702548i	0.588777	−	0.808296i	$-0.299610\pi$
$389$	−8.00000	−	13.8564i	−0.405616	−	0.702548i	−0.994393	+	0.105748i	$0.966276\pi$
$390$	−6.51940	−	9.87408i	−0.330123	−	0.499993i
$391$	−3.87451	−	6.71084i	−0.195942	−	0.339382i
$392$		0			0
$393$	11.5108	+	6.64575i	0.580642	+	0.335234i
$394$	9.58301	−	16.5983i	0.482785	−	0.836208i
$395$	13.1660	+	6.58301i	0.662454	+	0.331227i
$396$	−2.32288	−	4.02334i	−0.116729	−	0.202180i
$397$	4.47390	−	2.58301i	0.224538	−	0.129637i	−0.383512	−	0.923536i	$-0.625285\pi$
$397$	4.47390	−	2.58301i	0.224538	−	0.129637i	0.608050	+	0.793899i	$0.291952\pi$
$398$	4.94370	+	2.85425i	0.247805	+	0.143071i
$399$	14.0000			0.700877
$400$	1.96410	−	4.59808i	0.0982051	−	0.229904i
$401$	−22.0000			−1.09863			−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000			−1.09863			−0.549314	+	0.835616i	$0.685111\pi$
$402$			0.708497i			0.0353366i
$403$	9.16515	+	28.0000i	0.456549	+	1.39478i
$404$	−1.35425			−0.0673764
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$	−3.50000	−	6.06218i	−0.173702	−	0.300861i
$407$		−	18.5830i		−	0.921125i
$408$	5.19615	+	3.00000i	0.257248	+	0.148522i
$409$	15.7915	+	27.3517i	0.780840	+	1.35245i	0.931453	+	0.363861i	$0.118542\pi$
$409$	15.7915	+	27.3517i	0.780840	+	1.35245i	−0.150614	+	0.988593i	$0.548125\pi$
$410$	−16.2750	+	0.976876i	−0.803765	+	0.0482445i
$411$	10.5830			0.522021
$412$	−1.17281	−	0.677124i	−0.0577804	−	0.0333595i
$413$	−10.6448	−	6.14575i	−0.523794	−	0.302413i
$414$	0.645751	−	1.11847i	0.0317369	−	0.0549700i
$415$	−25.8539	+	1.55183i	−1.26912	+	0.0761763i
$416$	2.64575	−	4.58258i	0.129719	−	0.224679i
$417$	3.46410	−	2.00000i	0.169638	−	0.0979404i
$418$		−	24.5830i		−	1.20239i
$419$	−1.93725			−0.0946410			−0.0473205	−	0.998880i	$-0.515068\pi$
$419$	−1.93725			−0.0946410			−0.0473205	+	0.998880i	$0.515068\pi$
$420$	−0.354463	−	5.90545i	−0.0172960	−	0.288157i
$421$	−0.0627461	+	0.108679i	−0.00305806	+	0.00529671i	−0.867550	−	0.497349i	$-0.834307\pi$
$421$	−0.0627461	+	0.108679i	−0.00305806	+	0.00529671i	0.864492	+	0.502646i	$0.167640\pi$
$422$	3.96900	−	2.29150i	0.193208	−	0.111549i
$423$	−1.11847	−	0.645751i	−0.0543821	−	0.0313975i
$424$	−4.14575	+	7.18065i	−0.201335	+	0.348723i
$425$	−3.58846	−	29.7846i	−0.174066	−	1.44477i
$426$	−14.5830			−0.706549
$427$	−22.9129	+	13.2288i	−1.10883	+	0.640184i
$428$	−4.33013	+	2.50000i	−0.209305	+	0.120842i
$429$	−12.2915	+	21.2895i	−0.593439	+	1.02787i
$430$	−1.41699	−	0.708497i	−0.0683336	−	0.0341668i
$431$	17.5203	+	30.3460i	0.843921	+	1.46171i	0.886555	+	0.462624i	$0.153092\pi$
$431$	17.5203	+	30.3460i	0.843921	+	1.46171i	−0.0426336	+	0.999091i	$0.513575\pi$
$432$			1.00000i			0.0481125i
$433$		−	33.1660i		−	1.59386i	−0.604074	−	0.796928i	$-0.706457\pi$
$433$		−	33.1660i		−	1.59386i	0.604074	−	0.796928i	$-0.293543\pi$
$434$	−3.03137	+	14.4156i	−0.145511	+	0.691973i
$435$	2.64575	−	5.29150i	0.126854	−	0.253708i
$436$	17.2915			0.828113
$437$	5.91841	−	3.41699i	0.283116	−	0.163457i
$438$			14.5830i			0.696803i
$439$	13.4373	−	23.2740i	0.641325	−	1.11081i	−0.343812	−	0.939038i	$-0.611718\pi$
$439$	13.4373	−	23.2740i	0.641325	−	1.11081i	0.985137	−	0.171769i	$-0.0549483\pi$
$440$	−10.3696	+	0.622413i	−0.494349	+	0.0296724i
$441$		0			0
$442$		−	31.7490i		−	1.51015i
$443$	−6.92820	−	4.00000i	−0.329169	−	0.190046i	0.326303	−	0.945265i	$-0.394197\pi$
$443$	−6.92820	−	4.00000i	−0.329169	−	0.190046i	−0.655472	+	0.755219i	$0.727530\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$	13.6061	−	8.98350i	0.644992	−	0.425859i
$446$	−10.6771	−	18.4933i	−0.505576	−	0.875684i
$447$	11.5651	+	6.67712i	0.547011	+	0.315817i
$448$	2.29129	−	1.32288i	0.108253	−	0.0625000i
$449$	29.1660			1.37643			0.688215	−	0.725507i	$-0.258395\pi$
$449$	29.1660			1.37643			0.688215	+	0.725507i	$0.258395\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$	16.9373	+	29.3362i	0.797544	+	1.38139i
$452$	−2.34563	−	1.35425i	−0.110329	−	0.0636985i
$453$	19.3050	−	11.1458i	0.907028	−	0.523673i
$454$	7.50000	−	12.9904i	0.351992	−	0.609669i
$455$	−26.1244	+	17.2487i	−1.22473	+	0.808632i
$456$	−2.64575	+	4.58258i	−0.123899	+	0.214599i
$457$			25.1660i			1.17722i	0.808418	+	0.588608i	$0.200324\pi$
$457$			25.1660i			1.17722i	−0.808418	+	0.588608i	$0.799676\pi$
$458$	−21.7944	+	12.5830i	−1.01839	+	0.587965i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$	−1.59120	−	2.40998i	−0.0741899	−	0.112366i
$461$	9.22876			0.429826			0.214913	−	0.976633i	$-0.431053\pi$
$461$	9.22876			0.429826			0.214913	+	0.976633i	$0.431053\pi$
$462$	−10.6448	+	6.14575i	−0.495239	+	0.285926i
$463$		−	18.6458i		−	0.866542i	−0.901264	−	0.433271i	$-0.857359\pi$
$463$		−	18.6458i		−	0.866542i	0.901264	−	0.433271i	$-0.142641\pi$
$464$	2.64575			0.122826
$465$	−11.5789	+	4.57495i	−0.536956	+	0.212158i
$466$	3.29150			0.152476
$467$			36.7490i			1.70054i	0.526345	+	0.850271i	$0.323562\pi$
$467$			36.7490i			1.70054i	−0.526345	+	0.850271i	$0.676438\pi$
$468$	4.58258	−	2.64575i	0.211830	−	0.122300i
$469$	1.87451			0.0865567
$470$	−2.40998	+	1.59120i	−0.111164	+	0.0733964i
$471$	4.64575	+	8.04668i	0.214065	+	0.370771i
$472$	4.02334	−	2.32288i	0.185189	−	0.106919i
$473$			3.29150i			0.151343i
$474$	−3.29150	+	5.70105i	−0.151184	+	0.261858i
$475$	26.2676	−	3.16472i	1.20524	−	0.145207i
$476$	7.93725	−	13.7477i	0.363803	−	0.630126i
$477$	−7.18065	+	4.14575i	−0.328779	+	0.189821i
$478$	2.95920	+	1.70850i	0.135351	+	0.0781449i
$479$	16.2915	+	28.2177i	0.744378	+	1.28930i	0.950485	+	0.310771i	$0.100587\pi$
$479$	16.2915	+	28.2177i	0.744378	+	1.28930i	−0.206107	+	0.978529i	$0.566080\pi$
$480$	2.00000	+	1.00000i	0.0912871	+	0.0456435i
$481$	21.1660			0.965087
$482$	18.1865	−	10.5000i	0.828374	−	0.478262i
$483$	−2.95920	−	1.70850i	−0.134648	−	0.0777393i
$484$	5.29150	+	9.16515i	0.240523	+	0.416598i
$485$	−18.7626	−	28.4172i	−0.851966	−	1.29036i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−7.99234	−	4.61438i	−0.362167	−	0.209097i	0.307864	−	0.951430i	$-0.400386\pi$
$487$	−7.99234	−	4.61438i	−0.362167	−	0.209097i	−0.670031	+	0.742333i	$0.733719\pi$
$488$		−	10.0000i		−	0.452679i
$489$	5.00000	+	8.66025i	0.226108	+	0.391630i
$490$		0			0
$491$	8.90588	−	15.4254i	0.401917	−	0.696140i	−0.592040	−	0.805908i	$-0.701677\pi$
$491$	8.90588	−	15.4254i	0.401917	−	0.696140i	0.993957	+	0.109768i	$0.0350108\pi$
$492$		−	7.29150i		−	0.328726i
$493$	13.7477	−	7.93725i	0.619166	−	0.357476i
$494$	28.0000			1.25978
$495$	−9.29150	−	4.64575i	−0.417622	−	0.208811i
$496$	−4.14575	−	3.71655i	−0.186150	−	0.166878i
$497$			38.5830i			1.73068i
$498$		−	11.5830i		−	0.519047i
$499$	−18.2288	−	31.5731i	−0.816031	−	1.41341i	−0.908585	−	0.417700i	$-0.862836\pi$
$499$	−18.2288	−	31.5731i	−0.816031	−	1.41341i	0.0925539	−	0.995708i	$-0.470497\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	−4.93725	+	8.55157i	−0.220580	+	0.382056i
$502$	18.4390	−	10.6458i	0.822972	−	0.475143i
$503$	6.92820	−	4.00000i	0.308913	−	0.178351i	−0.337527	−	0.941316i	$-0.609590\pi$
$503$	6.92820	−	4.00000i	0.308913	−	0.178351i	0.646440	+	0.762965i	$0.276257\pi$
$504$	2.64575			0.117851
$505$	−2.52706	+	1.66850i	−0.112453	+	0.0742474i
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$	−12.9904	−	7.50000i	−0.576923	−	0.333087i
$508$	11.4564	−	6.61438i	0.508297	−	0.293466i
$509$	−1.32288	+	2.29129i	−0.0586354	+	0.101560i	−0.893853	−	0.448360i	$-0.852008\pi$
$509$	−1.32288	+	2.29129i	−0.0586354	+	0.101560i	0.835218	+	0.549920i	$0.185342\pi$
$510$	13.3923	−	0.803848i	0.593021	−	0.0355950i
$511$	38.5830			1.70681
$512$			1.00000i			0.0441942i
$513$	−4.58258	+	2.64575i	−0.202326	+	0.116813i
$514$	−2.64575	+	4.58258i	−0.116699	+	0.202129i
$515$	−3.02275	+	0.181435i	−0.133198	+	0.00799498i
$516$	0.354249	−	0.613577i	0.0155949	−	0.0270112i
$517$	5.19615	+	3.00000i	0.228527	+	0.131940i
$518$	9.16515	+	5.29150i	0.402694	+	0.232495i
$519$	4.29150			0.188376
$520$	−0.708927	−	11.8109i	−0.0310885	−	0.517942i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	2.29129	+	1.32288i	0.100287	+	0.0579007i
$523$			1.87451i			0.0819665i	0.999160	+	0.0409833i	$0.0130490\pi$
$523$			1.87451i			0.0819665i	−0.999160	+	0.0409833i	$0.986951\pi$
$524$	6.64575	+	11.5108i	0.290321	+	0.502851i
$525$	−7.93725	−	10.5830i	−0.346410	−	0.461880i
$526$	−19.1660			−0.835678
$527$	−32.6916	−	6.87451i	−1.42407	−	0.299458i
$528$		−	4.64575i		−	0.202180i
$529$	21.3320			0.927479
$530$	1.11085	+	18.5071i	0.0482523	+	0.803895i
$531$	4.64575			0.201608
$532$	12.1244	+	7.00000i	0.525657	+	0.303488i
$533$	−33.4139	+	19.2915i	−1.44732	+	0.835608i
$534$	3.64575	+	6.31463i	0.157767	+	0.273261i
$535$	−5.00000	+	10.0000i	−0.216169	+	0.432338i
$536$	−0.354249	+	0.613577i	−0.0153012	+	0.0265025i
$537$	−20.1167	−	11.6144i	−0.868099	−	0.501197i
$538$	6.92820	+	4.00000i	0.298696	+	0.172452i
$539$		0			0
$540$	1.23205	+	1.86603i	0.0530190	+	0.0803009i
$541$	−1.93725	−	3.35542i	−0.0832891	−	0.144261i	0.821372	−	0.570393i	$-0.193209\pi$
$541$	−1.93725	−	3.35542i	−0.0832891	−	0.144261i	−0.904661	+	0.426132i	$0.859876\pi$
$542$		−	11.7085i		−	0.502923i
$543$			11.2915i			0.484565i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	32.2664	−	21.3040i	1.38214	−	0.912564i
$546$	−7.00000	−	12.1244i	−0.299572	−	0.518875i
$547$	11.0059	+	6.35425i	0.470578	+	0.271688i	0.716481	−	0.697606i	$-0.245751\pi$
$547$	11.0059	+	6.35425i	0.470578	+	0.271688i	−0.245904	+	0.969294i	$0.579085\pi$
$548$	9.16515	+	5.29150i	0.391516	+	0.226042i
$549$	5.00000	−	8.66025i	0.213395	−	0.369611i
$550$	−18.5830	+	13.9373i	−0.792382	+	0.594287i
$551$	7.00000	+	12.1244i	0.298210	+	0.516515i
$552$	1.11847	−	0.645751i	0.0476054	−	0.0274850i
$553$	15.0836	+	8.70850i	0.641418	+	0.370323i
$554$	2.00000			0.0849719
$555$	0.535898	+	8.92820i	0.0227476	+	0.378981i
$556$	4.00000			0.169638
$557$		−	6.29150i		−	0.266580i	−0.991077	−	0.133290i	$-0.957446\pi$
$557$		−	6.29150i		−	0.266580i	0.991077	−	0.133290i	$-0.0425541\pi$
$558$	−1.73205	−	5.29150i	−0.0733236	−	0.224007i
$559$	−3.74902			−0.158566
$560$	2.64575	−	5.29150i	0.111803	−	0.223607i
$561$	−13.9373	−	24.1400i	−0.588431	−	1.01919i
$562$		−	2.58301i		−	0.108958i
$563$	−7.28933	−	4.20850i	−0.307209	−	0.177367i	0.338468	−	0.940978i	$-0.390091\pi$
$563$	−7.28933	−	4.20850i	−0.307209	−	0.177367i	−0.645677	+	0.763611i	$0.723425\pi$
$564$	−0.645751	−	1.11847i	−0.0271910	−	0.0470963i
$565$	−6.04550	+	0.362870i	−0.254336	+	0.0152660i
$566$	−29.2915			−1.23121
$567$	2.29129	+	1.32288i	0.0962250	+	0.0555556i
$568$	−12.6293	−	7.29150i	−0.529912	−	0.305945i
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$	0.708927	+	11.8109i	0.0296937	+	0.494704i
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	−0.0554391	−	0.998462i	$-0.517656\pi$
$571$	20.0000	−	34.6410i	0.836974	−	1.44968i	0.892413	−	0.451219i	$-0.149011\pi$
$572$	−21.2895	+	12.2915i	−0.890159	+	0.513934i
$573$		−	8.00000i		−	0.334205i
$574$	−19.2915			−0.805212
$575$	−5.93843	−	2.53664i	−0.247650	−	0.105785i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−24.0314	+	13.8745i	−1.00044	+	0.577603i	−0.908378	−	0.418150i	$-0.862679\pi$
$577$	−24.0314	+	13.8745i	−1.00044	+	0.577603i	−0.0920604	+	0.995753i	$0.529345\pi$
$578$	16.4545	+	9.50000i	0.684416	+	0.395148i
$579$	−7.67712	+	13.2972i	−0.319050	+	0.552612i
$580$	4.93704	−	3.25970i	0.204999	−	0.135352i
$581$	−30.6458			−1.27140
$582$	13.1885	−	7.61438i	0.546681	−	0.315626i
$583$	33.3595	−	19.2601i	1.38161	−	0.797673i
$584$	−7.29150	+	12.6293i	−0.301725	+	0.522602i
$585$	5.29150	−	10.5830i	0.218777	−	0.437553i
$586$	12.1458	+	21.0371i	0.501736	+	0.869033i
$587$			3.00000i			0.123823i	0.998082	+	0.0619116i	$0.0197197\pi$
$587$			3.00000i			0.123823i	−0.998082	+	0.0619116i	$0.980280\pi$
$588$		0			0
$589$	6.06275	−	28.8313i	0.249811	−	1.18797i
$590$	4.64575	−	9.29150i	0.191263	−	0.382525i
$591$	19.1660			0.788384
$592$	−3.46410	+	2.00000i	−0.142374	+	0.0821995i
$593$			28.4575i			1.16861i	0.811534	+	0.584305i	$0.198633\pi$
$593$			28.4575i			1.16861i	−0.811534	+	0.584305i	$0.801367\pi$
$594$	2.32288	−	4.02334i	0.0953087	−	0.165080i
$595$	−2.12678	−	35.4327i	−0.0871895	−	1.45260i
$596$	6.67712	+	11.5651i	0.273506	+	0.473726i
$597$			5.70850i			0.233633i
$598$	−5.91841	−	3.41699i	−0.242022	−	0.139731i
$599$	3.64575	−	6.31463i	0.148961	−	0.258009i	−0.781882	−	0.623426i	$-0.785740\pi$
$599$	3.64575	−	6.31463i	0.148961	−	0.258009i	0.930844	+	0.365417i	$0.119074\pi$
$600$	4.96410	−	0.598076i	0.202659	−	0.0244164i
$601$	−17.5830	−	30.4547i	−0.717226	−	1.24227i	−0.962095	−	0.272715i	$-0.912078\pi$
$601$	−17.5830	−	30.4547i	−0.717226	−	1.24227i	0.244869	−	0.969556i	$-0.421255\pi$
$602$	−1.62337	−	0.937254i	−0.0661637	−	0.0381996i
$603$	−0.613577	+	0.354249i	−0.0249868	+	0.0144261i
$604$	22.2915			0.907028
$605$	21.1660	+	10.5830i	0.860521	+	0.430260i
$606$	−0.677124	−	1.17281i	−0.0275063	−	0.0476423i
$607$	−23.1302	−	13.3542i	−0.938827	−	0.542032i	−0.0492348	−	0.998787i	$-0.515678\pi$
$607$	−23.1302	−	13.3542i	−0.938827	−	0.542032i	−0.889593	+	0.456755i	$0.849012\pi$
$608$	−4.58258	+	2.64575i	−0.185848	+	0.107299i
$609$	3.50000	−	6.06218i	0.141827	−	0.245652i
$610$	−12.3205	−	18.6603i	−0.498843	−	0.755532i
$611$	−3.41699	+	5.91841i	−0.138237	+	0.239433i
$612$			6.00000i			0.242536i
$613$	23.6351	−	13.6458i	0.954614	−	0.551147i	0.0601029	−	0.998192i	$-0.480857\pi$
$613$	23.6351	−	13.6458i	0.954614	−	0.551147i	0.894511	+	0.447045i	$0.147524\pi$
$614$	−8.93725	−	15.4798i	−0.360678	−	0.624713i
$615$	−8.98350	−	13.6061i	−0.362250	−	0.548652i
$616$	−12.2915			−0.495239
$617$	2.95920	−	1.70850i	0.119133	−	0.0687815i	−0.439249	−	0.898365i	$-0.644756\pi$
$617$	2.95920	−	1.70850i	0.119133	−	0.0687815i	0.558382	+	0.829584i	$0.311422\pi$
$618$		−	1.35425i		−	0.0544759i
$619$	−6.58301			−0.264593			−0.132297	−	0.991210i	$-0.542235\pi$
$619$	−6.58301			−0.264593			−0.132297	+	0.991210i	$0.542235\pi$
$620$	−12.3151	−	1.82740i	−0.494585	−	0.0733902i
$621$	1.29150			0.0518262
$622$			19.8745i			0.796895i
$623$	16.7069	−	9.64575i	0.669349	−	0.386449i
$624$	5.29150			0.211830
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	−0.968627	−	1.67771i	−0.0387141	−	0.0670548i
$627$	21.2895	−	12.2915i	0.850221	−	0.490875i
$628$			9.29150i			0.370771i
$629$	−12.0000	+	20.7846i	−0.478471	+	0.828737i
$630$	4.93704	−	3.25970i	0.196696	−	0.129870i
$631$	−2.43725	+	4.22145i	−0.0970255	+	0.168053i	−0.910452	−	0.413614i	$-0.864266\pi$
$631$	−2.43725	+	4.22145i	−0.0970255	+	0.168053i	0.813427	+	0.581668i	$0.197600\pi$
$632$	−5.70105	+	3.29150i	−0.226776	+	0.130929i
$633$	3.96900	+	2.29150i	0.157754	+	0.0910791i
$634$	2.85425	+	4.94370i	0.113357	+	0.196340i
$635$	13.2288	−	26.4575i	0.524967	−	1.04993i
$636$	−8.29150			−0.328779
$637$		0			0
$638$	−10.6448	−	6.14575i	−0.421430	−	0.243313i
$639$	−7.29150	−	12.6293i	−0.288447	−	0.499606i
$640$	1.23205	+	1.86603i	0.0487011	+	0.0737611i
$641$	−12.5203	+	21.6857i	−0.494521	+	0.856535i	−0.999980	−	0.00631566i	$-0.997990\pi$
$641$	−12.5203	+	21.6857i	−0.494521	+	0.856535i	0.505460	+	0.862850i	$0.331323\pi$
$642$	−4.33013	−	2.50000i	−0.170896	−	0.0986671i
$643$		−	7.87451i		−	0.310540i	−0.987872	−	0.155270i	$-0.950375\pi$
$643$		−	7.87451i		−	0.310540i	0.987872	−	0.155270i	$-0.0496248\pi$
$644$	−1.70850	−	2.95920i	−0.0673242	−	0.116609i
$645$	−0.0949207	−	1.58140i	−0.00373750	−	0.0622676i
$646$	−15.8745	+	27.4955i	−0.624574	+	1.08179i
$647$			2.00000i			0.0786281i	0.999227	+	0.0393141i	$0.0125173\pi$
$647$			2.00000i			0.0786281i	−0.999227	+	0.0393141i	$0.987483\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−21.5830			−0.847207
$650$	−15.8745	−	21.1660i	−0.622649	−	0.830199i
$651$	−14.0000	+	4.58258i	−0.548703	+	0.179605i
$652$			10.0000i			0.391630i
$653$			30.8745i			1.20821i	0.796904	+	0.604106i	$0.206470\pi$
$653$			30.8745i			1.20821i	−0.796904	+	0.604106i	$0.793530\pi$
$654$	8.64575	+	14.9749i	0.338076	+	0.585564i
$655$	26.5830	+	13.2915i	1.03868	+	0.519342i
$656$	3.64575	−	6.31463i	0.142343	−	0.246545i
$657$	−12.6293	+	7.29150i	−0.492714	+	0.284469i
$658$	−2.95920	+	1.70850i	−0.115362	+	0.0666042i
$659$	−49.9373			−1.94528			−0.972640	−	0.232319i	$-0.925369\pi$
$659$	−49.9373			−1.94528			−0.972640	+	0.232319i	$0.925369\pi$
$660$	−5.72380	−	8.66909i	−0.222799	−	0.337444i
$661$	−23.2288	+	40.2334i	−0.903494	+	1.56490i	−0.0805677	+	0.996749i	$0.525673\pi$
$661$	−23.2288	+	40.2334i	−0.903494	+	1.56490i	−0.822926	+	0.568148i	$0.807660\pi$
$662$	20.0624	+	11.5830i	0.779746	+	0.450186i
$663$	27.4955	−	15.8745i	1.06783	−	0.616515i
$664$	5.79150	−	10.0312i	0.224754	−	0.389285i
$665$	31.2487	−	1.87564i	1.21177	−	0.0727344i
$666$	−4.00000			−0.154997
$667$		−	3.41699i		−	0.132307i
$668$	−8.55157	+	4.93725i	−0.330870	+	0.191028i
$669$	10.6771	−	18.4933i	0.412801	−	0.714993i
$670$	0.0949207	+	1.58140i	0.00366710	+	0.0610949i
$671$	−23.2288	+	40.2334i	−0.896736	+	1.55319i
$672$	2.29129	+	1.32288i	0.0883883	+	0.0510310i
$673$	−38.5557	−	22.2601i	−1.48621	−	0.858065i	−0.486335	−	0.873772i	$-0.661667\pi$
$673$	−38.5557	−	22.2601i	−1.48621	−	0.858065i	−0.999877	+	0.0157073i	$0.995000\pi$
$674$	23.1033			0.889904
$675$	4.59808	+	1.96410i	0.176980	+	0.0755983i
$676$	−7.50000	−	12.9904i	−0.288462	−	0.499630i
$677$	−17.0681	−	9.85425i	−0.655979	−	0.378730i	0.134764	−	0.990878i	$-0.456972\pi$
$677$	−17.0681	−	9.85425i	−0.655979	−	0.378730i	−0.790743	+	0.612148i	$0.790306\pi$
$678$		−	2.70850i		−	0.104019i
$679$	−20.1458	−	34.8935i	−0.773123	−	1.33909i
$680$	12.0000	+	6.00000i	0.460179	+	0.230089i
$681$	15.0000			0.574801
$682$	8.04668	+	24.5830i	0.308123	+	0.941332i
$683$		−	20.1660i		−	0.771631i	−0.922576	−	0.385815i	$-0.873920\pi$
$683$		−	20.1660i		−	0.771631i	0.922576	−	0.385815i	$-0.126080\pi$
$684$	−5.29150			−0.202326
$685$	23.6218	−	1.41785i	0.902543	−	0.0541734i
$686$	18.5203			0.707107
$687$	−21.7944	−	12.5830i	−0.831508	−	0.480072i
$688$	0.613577	−	0.354249i	0.0233924	−	0.0135056i
$689$	21.9373	+	37.9964i	0.835743	+	1.44755i
$690$	1.29150	−	2.58301i	0.0491667	−	0.0983333i
$691$	−20.5830	+	35.6508i	−0.783014	+	1.35622i	0.147164	+	0.989112i	$0.452986\pi$
$691$	−20.5830	+	35.6508i	−0.783014	+	1.35622i	−0.930178	+	0.367109i	$0.880348\pi$
$692$	3.71655	+	2.14575i	0.141282	+	0.0815692i
$693$	−10.6448	−	6.14575i	−0.404361	−	0.233458i
$694$	−8.79150	−	15.2273i	−0.333721	−	0.578022i
$695$	7.46410	−	4.92820i	0.283130	−	0.186937i
$696$	1.32288	+	2.29129i	0.0501435	+	0.0868510i
$697$		−	43.7490i		−	1.65711i
$698$		−	5.29150i		−	0.200286i
$699$	1.64575	+	2.85052i	0.0622480	+	0.107817i
$700$	−1.58236	−	13.1338i	−0.0598076	−	0.496410i
$701$	24.6144	+	42.6334i	0.929672	+	1.61024i	0.783869	+	0.620926i	$0.213243\pi$
$701$	24.6144	+	42.6334i	0.929672	+	1.61024i	0.145803	+	0.989314i	$0.453423\pi$
$702$	4.58258	+	2.64575i	0.172958	+	0.0998574i
$703$	−18.3303	−	10.5830i	−0.691340	−	0.399146i
$704$	2.32288	−	4.02334i	0.0875467	−	0.151635i
$705$	−2.58301	−	1.29150i	−0.0972816	−	0.0486408i
$706$	−16.6458	−	28.8313i	−0.626471	−	1.08508i
$707$	−3.10297	+	1.79150i	−0.116699	+	0.0673764i
$708$	4.02334	+	2.32288i	0.151206	+	0.0872990i
$709$	−23.2915			−0.874731			−0.437365	−	0.899284i	$-0.644088\pi$
$709$	−23.2915			−0.874731			−0.437365	+	0.899284i	$0.644088\pi$
$710$	−32.5500	+	1.95375i	−1.22158	+	0.0733230i
$711$	−6.58301			−0.246882
$712$			7.29150i			0.273261i
$713$	−4.79993	+	5.35425i	−0.179759	+	0.200518i
$714$	15.8745			0.594089
$715$	−24.5830	+	49.1660i	−0.919352	+	1.83870i
$716$	−11.6144	−	20.1167i	−0.434050	−	0.751796i
$717$			3.41699i			0.127610i
$718$	15.5885	+	9.00000i	0.581756	+	0.335877i
$719$	−7.29150	−	12.6293i	−0.271927	−	0.470992i	0.697428	−	0.716655i	$-0.254328\pi$
$719$	−7.29150	−	12.6293i	−0.271927	−	0.470992i	−0.969355	+	0.245663i	$0.920994\pi$
$720$	0.133975	+	2.23205i	0.00499294	+	0.0831836i
$721$	−3.58301			−0.133438
$722$	−7.79423	−	4.50000i	−0.290071	−	0.167473i
$723$	18.1865	+	10.5000i	0.676364	+	0.390499i
$724$	−5.64575	+	9.77873i	−0.209823	+	0.363424i
$725$	5.19652	−	12.1654i	0.192994	−	0.451810i
$726$	−5.29150	+	9.16515i	−0.196386	+	0.340151i
$727$	21.8487	−	12.6144i	0.810325	−	0.467841i	−0.0367437	−	0.999325i	$-0.511699\pi$
$727$	21.8487	−	12.6144i	0.810325	−	0.467841i	0.847069	+	0.531483i	$0.178365\pi$
$728$		−	14.0000i		−	0.518875i
$729$	−1.00000			−0.0370370
$730$	1.95375	+	32.5500i	0.0723116	+	1.20473i
$731$	2.12549	−	3.68146i	0.0786142	−	0.136164i
$732$	8.66025	−	5.00000i	0.320092	−	0.184805i
$733$	10.5010	+	6.06275i	0.387863	+	0.223933i	0.681234	−	0.732066i	$-0.261444\pi$
$733$	10.5010	+	6.06275i	0.387863	+	0.223933i	−0.293371	+	0.955999i	$0.594777\pi$
$734$	−9.22876	+	15.9847i	−0.340640	+	0.590005i
$735$		0			0
$736$	1.29150			0.0476054
$737$	2.85052	−	1.64575i	0.105000	−	0.0606220i
$738$	6.31463	−	3.64575i	0.232445	−	0.134202i
$739$	−19.6458	+	34.0274i	−0.722681	+	1.25172i	0.237241	+	0.971451i	$0.423757\pi$
$739$	−19.6458	+	34.0274i	−0.722681	+	1.25172i	−0.959922	+	0.280269i	$0.909576\pi$
$740$	−4.00000	+	8.00000i	−0.147043	+	0.294086i
$741$	14.0000	+	24.2487i	0.514303	+	0.890799i
$742$			21.9373i			0.805342i
$743$			18.5830i			0.681744i	0.940110	+	0.340872i	$0.110722\pi$
$743$			18.5830i			0.681744i	−0.940110	+	0.340872i	$0.889278\pi$
$744$	1.14575	−	5.44860i	0.0420053	−	0.199755i
$745$	26.7085	+	13.3542i	0.978524	+	0.489262i
$746$	27.1660			0.994618
$747$	10.0312	−	5.79150i	0.367022	−	0.211900i
$748$		−	27.8745i		−	1.01919i
$749$	−6.61438	+	11.4564i	−0.241684	+	0.418609i
$750$	8.52628	−	7.23205i	0.311336	−	0.264077i
$751$	−23.1458	−	40.0896i	−0.844600	−	1.46289i	−0.885968	−	0.463747i	$-0.846505\pi$
$751$	−23.1458	−	40.0896i	−0.844600	−	1.46289i	0.0413673	−	0.999144i	$-0.486829\pi$
$752$		−	1.29150i		−	0.0470963i
$753$	18.4390	+	10.6458i	0.671954	+	0.387953i
$754$	7.00000	−	12.1244i	0.254925	−	0.441543i
$755$	41.5965	−	27.4643i	1.51385	−	0.999527i
$756$	1.32288	+	2.29129i	0.0481125	+	0.0833333i
$757$	−32.8003	−	18.9373i	−1.19215	−	0.688286i	−0.233354	−	0.972392i	$-0.574970\pi$
$757$	−32.8003	−	18.9373i	−1.19215	−	0.688286i	−0.958793	+	0.284106i	$0.908303\pi$
$758$	13.2428	−	7.64575i	0.481001	−	0.277706i
$759$	−6.00000			−0.217786
$760$	−5.29150	+	10.5830i	−0.191943	+	0.383886i
$761$	−12.0000	−	20.7846i	−0.435000	−	0.753442i	0.562296	−	0.826936i	$-0.309918\pi$
$761$	−12.0000	−	20.7846i	−0.435000	−	0.753442i	−0.997296	+	0.0734946i	$0.976585\pi$
$762$	11.4564	+	6.61438i	0.415023	+	0.239614i
$763$	39.6198	−	22.8745i	1.43433	−	0.828113i
$764$	4.00000	−	6.92820i	0.144715	−	0.250654i
$765$	7.39230	+	11.1962i	0.267269	+	0.404798i
$766$	−18.2288	+	31.5731i	−0.658632	+	1.14078i
$767$		−	24.5830i		−	0.887641i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	13.7915	+	23.8876i	0.497334	+	0.861408i	0.999995	−	0.00307535i	$-0.000978916\pi$
$769$	13.7915	+	23.8876i	0.497334	+	0.861408i	−0.502661	+	0.864484i	$0.667646\pi$
$770$	−22.9363	+	15.1438i	−0.826565	+	0.545743i
$771$	−5.29150			−0.190569
$772$	−13.2972	+	7.67712i	−0.478576	+	0.276306i
$773$			47.1660i			1.69644i	0.529641	+	0.848222i	$0.322327\pi$
$773$			47.1660i			1.69644i	−0.529641	+	0.848222i	$0.677673\pi$
$774$	0.708497			0.0254664
$775$	−25.2317	+	11.7628i	−0.906348	+	0.422532i
$776$	15.2288			0.546681
$777$			10.5830i			0.379663i
$778$	13.8564	−	8.00000i	0.496776	−	0.286814i
$779$	38.5830			1.38238
$780$	9.87408	−	6.51940i	0.353549	−	0.233432i
$781$	33.8745	+	58.6724i	1.21213	+	2.09946i
$782$	6.71084	−	3.87451i	0.239979	−	0.138552i
$783$			2.64575i			0.0945514i
$784$		0			0
$785$	11.4476	+	17.3382i	0.408582	+	0.618826i
$786$	−6.64575	+	11.5108i	−0.237046	+	0.410576i
$787$	12.7379	−	7.35425i	0.454058	−	0.262151i	−0.255484	−	0.966813i	$-0.582235\pi$
$787$	12.7379	−	7.35425i	0.454058	−	0.262151i	0.709543	+	0.704663i	$0.248902\pi$
$788$	16.5983	+	9.58301i	0.591288	+	0.341380i
$789$	−9.58301	−	16.5983i	−0.341164	−	0.590913i
$790$	−6.58301	+	13.1660i	−0.234213	+	0.468426i
$791$	−7.16601			−0.254794
$792$	4.02334	−	2.32288i	0.142963	−	0.0825398i
$793$	−45.8258	−	26.4575i	−1.62732	−	0.939534i
$794$	2.58301	+	4.47390i	0.0916674	+	0.158773i
$795$	−15.4722	+	10.2156i	−0.548741	+	0.362308i
$796$	−2.85425	+	4.94370i	−0.101166	+	0.175225i
$797$	−18.2952	−	10.5627i	−0.648050	−	0.374152i	0.139659	−	0.990200i	$-0.455399\pi$
$797$	−18.2952	−	10.5627i	−0.648050	−	0.374152i	−0.787709	+	0.616048i	$0.788733\pi$
$798$			14.0000i			0.495595i
$799$	−3.87451	−	6.71084i	−0.137070	−	0.237413i
$800$	4.59808	+	1.96410i	0.162567	+	0.0694415i
$801$	−3.64575	+	6.31463i	−0.128816	+	0.223116i
$802$		−	22.0000i		−	0.776847i
$803$	58.6724	−	33.8745i	2.07050	−	1.19541i
$804$	−0.708497			−0.0249868
$805$	−6.83399	−	3.41699i	−0.240866	−	0.120433i
$806$	−28.0000	+	9.16515i	−0.986258	+	0.322829i
$807$			8.00000i			0.281613i
$808$		−	1.35425i		−	0.0476423i
$809$	−11.7085	−	20.2797i	−0.411649	−	0.712997i	0.583421	−	0.812170i	$-0.301714\pi$
$809$	−11.7085	−	20.2797i	−0.411649	−	0.712997i	−0.995070	+	0.0991729i	$0.968380\pi$
$810$	−1.00000	+	2.00000i	−0.0351364	+	0.0702728i
$811$	−2.64575	+	4.58258i	−0.0929049	+	0.160916i	−0.908732	−	0.417379i	$-0.862949\pi$
$811$	−2.64575	+	4.58258i	−0.0929049	+	0.160916i	0.815827	+	0.578295i	$0.196282\pi$
$812$	6.06218	−	3.50000i	0.212741	−	0.122826i
$813$	10.1399	−	5.85425i	0.355620	−	0.205317i
$814$	18.5830			0.651334
$815$	12.3205	+	18.6603i	0.431569	+	0.653640i
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	3.24674	+	1.87451i	0.113589	+	0.0655807i
$818$	−27.3517	+	15.7915i	−0.956329	+	0.552137i
$819$	7.00000	−	12.1244i	0.244600	−	0.423659i
$820$	−0.976876	−	16.2750i	−0.0341140	−	0.568348i
$821$	−9.10326			−0.317706			−0.158853	−	0.987302i	$-0.550780\pi$
$821$	−9.10326			−0.317706			−0.158853	+	0.987302i	$0.550780\pi$
$822$			10.5830i			0.369125i
$823$	−19.6118	+	11.3229i	−0.683624	+	0.394691i	−0.801219	−	0.598371i	$-0.795815\pi$
$823$	−19.6118	+	11.3229i	−0.683624	+	0.394691i	0.117595	+	0.993062i	$0.462482\pi$
$824$	0.677124	−	1.17281i	0.0235887	−	0.0408569i
$825$	−21.3615	−	9.12473i	−0.743713	−	0.317682i
$826$	6.14575	−	10.6448i	0.213838	−	0.370378i
$827$	−29.9498	−	17.2915i	−1.04146	−	0.601284i	−0.121210	−	0.992627i	$-0.538677\pi$
$827$	−29.9498	−	17.2915i	−1.04146	−	0.601284i	−0.920245	+	0.391342i	$0.872011\pi$
$828$	1.11847	+	0.645751i	0.0388697	+	0.0224414i
$829$	−45.7490			−1.58893			−0.794464	−	0.607311i	$-0.792248\pi$
$829$	−45.7490			−1.58893			−0.794464	+	0.607311i	$0.792248\pi$
$830$	−1.55183	−	25.8539i	−0.0538648	−	0.897400i
$831$	1.00000	+	1.73205i	0.0346896	+	0.0600842i
$832$	4.58258	+	2.64575i	0.158872	+	0.0917249i
$833$		0			0
$834$	2.00000	+	3.46410i	0.0692543	+	0.119952i
$835$	−9.87451	+	19.7490i	−0.341721	+	0.683443i
$836$	24.5830			0.850221
$837$	3.71655	−	4.14575i	0.128463	−	0.143298i
$838$		−	1.93725i		−	0.0669213i
$839$	−42.0000			−1.45000			−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000			−1.45000			−0.725001	+	0.688748i	$0.758161\pi$
$840$	5.90545	−	0.354463i	0.203757	−	0.0122302i
$841$	−22.0000			−0.758621
$842$	−0.108679	−	0.0627461i	−0.00374534	−	0.00216237i
$843$	2.23695	−	1.29150i	0.0770446	−	0.0444817i
$844$	2.29150	+	3.96900i	0.0788768	+	0.136619i
$845$	−30.0000	−	15.0000i	−1.03203	−	0.516016i
$846$	0.645751	−	1.11847i	0.0222014	−	0.0384539i
$847$	24.2487	+	14.0000i	0.833196	+	0.481046i
$848$	−7.18065	−	4.14575i	−0.246585	−	0.142366i
$849$	−14.6458	−	25.3672i	−0.502641	−	0.870600i
$850$	29.7846	−	3.58846i	1.02160	−	0.123083i
$851$	2.58301	+	4.47390i	0.0885443	+	0.153363i
$852$		−	14.5830i		−	0.499606i
$853$			12.4575i			0.426537i	0.976994	+	0.213269i	$0.0684109\pi$
$853$			12.4575i			0.426537i	−0.976994	+	0.213269i	$0.931589\pi$
$854$	−13.2288	−	22.9129i	−0.452679	−	0.784063i
$855$	−9.87408	+	6.51940i	−0.337686	+	0.222959i
$856$	−2.50000	−	4.33013i	−0.0854482	−	0.148001i
$857$	46.6567	+	26.9373i	1.59376	+	0.920159i	0.992654	+	0.120992i	$0.0386075\pi$
$857$	46.6567	+	26.9373i	1.59376	+	0.920159i	0.601109	+	0.799167i	$0.294726\pi$
$858$	−21.2895	−	12.2915i	−0.726812	−	0.419625i
$859$	9.64575	−	16.7069i	0.329109	−	0.570033i	−0.653226	−	0.757163i	$-0.726585\pi$
$859$	9.64575	−	16.7069i	0.329109	−	0.570033i	0.982335	+	0.187129i	$0.0599184\pi$
$860$	0.708497	−	1.41699i	0.0241596	−	0.0483191i
$861$	−9.64575	−	16.7069i	−0.328726	−	0.569371i
$862$	−30.3460	+	17.5203i	−1.03359	+	0.596742i
$863$	−30.9596	−	17.8745i	−1.05388	−	0.608455i	−0.130144	−	0.991495i	$-0.541544\pi$
$863$	−30.9596	−	17.8745i	−1.05388	−	0.608455i	−0.923732	+	0.383040i	$0.874877\pi$
$864$	−1.00000			−0.0340207
$865$	9.57885	−	0.574952i	0.325691	−	0.0195490i
$866$	33.1660			1.12703
$867$			19.0000i			0.645274i
$868$	−14.4156	−	3.03137i	−0.489299	−	0.102892i
$869$	30.5830			1.03746
$870$	5.29150	+	2.64575i	0.179399	+	0.0896994i
$871$	1.87451	+	3.24674i	0.0635153	+	0.110012i
$872$			17.2915i			0.585564i
$873$	13.1885	+	7.61438i	0.446363	+	0.257708i
$874$	3.41699	+	5.91841i	0.115582	+	0.200193i
$875$	−19.1342	−	22.5584i	−0.646854	−	0.762614i
$876$	−14.5830			−0.492714
$877$	−13.7477	−	7.93725i	−0.464228	−	0.268022i	0.249593	−	0.968351i	$-0.419703\pi$
$877$	−13.7477	−	7.93725i	−0.464228	−	0.268022i	−0.713820	+	0.700329i	$0.753037\pi$
$878$	23.2740	+	13.4373i	0.785460	+	0.453485i
$879$	−12.1458	+	21.0371i	−0.409666	+	0.709562i
$880$	−0.622413	−	10.3696i	−0.0209815	−	0.349558i
$881$	12.0000	−	20.7846i	0.404290	−	0.700251i	−0.589948	−	0.807441i	$-0.700852\pi$
$881$	12.0000	−	20.7846i	0.404290	−	0.700251i	0.994239	+	0.107190i	$0.0341852\pi$
$882$		0			0
$883$		−	8.00000i		−	0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$		−	8.00000i		−	0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$	31.7490			1.06783
$885$	10.3696	−	0.622413i	0.348569	−	0.0209222i
$886$	4.00000	−	6.92820i	0.134383	−	0.232758i
$887$	−43.5888	+	25.1660i	−1.46357	+	0.844992i	−0.999174	−	0.0406363i	$-0.987062\pi$
$887$	−43.5888	+	25.1660i	−1.46357	+	0.844992i	−0.464395	+	0.885628i	$0.653728\pi$
$888$	−3.46410	−	2.00000i	−0.116248	−	0.0671156i
$889$	17.5000	−	30.3109i	0.586931	−	1.01659i
$890$	8.98350	+	13.6061i	0.301128	+	0.456078i
$891$	4.64575			0.155639
$892$	18.4933	−	10.6771i	0.619202	−	0.357497i
$893$	5.91841	−	3.41699i	0.198052	−	0.114345i
$894$	−6.67712	+	11.5651i	−0.223316	+	0.386795i
$895$	−46.4575	−	23.2288i	−1.55290	−	0.776452i
$896$	1.32288	+	2.29129i	0.0441942	+	0.0765466i
$897$		−	6.83399i		−	0.228180i
$898$			29.1660i			0.973282i
$899$	−10.9686	−	9.83307i	−0.365824	−	0.327951i
$900$	3.00000	+	4.00000i	0.100000	+	0.133333i
$901$	−49.7490			−1.65738
$902$	−29.3362	+	16.9373i	−0.976788	+	0.563949i
$903$		−	1.87451i		−	0.0623797i
$904$	1.35425	−	2.34563i	0.0450416	−	0.0780144i
$905$	1.51277	+	25.2032i	0.0502863	+	0.837783i
$906$	11.1458	+	19.3050i	0.370293	+	0.641366i
$907$			36.5830i			1.21472i	0.794427	+	0.607359i	$0.207771\pi$
$907$			36.5830i			1.21472i	−0.794427	+	0.607359i	$0.792229\pi$
$908$	12.9904	+	7.50000i	0.431101	+	0.248896i
$909$	0.677124	−	1.17281i	0.0224588	−	0.0388998i
$910$	−17.2487	−	26.1244i	−0.571789	−	0.866014i
$911$	−14.3542	−	24.8623i	−0.475577	−	0.823724i	0.524031	−	0.851699i	$-0.324428\pi$
$911$	−14.3542	−	24.8623i	−0.475577	−	0.823724i	−0.999609	+	0.0279747i	$0.991094\pi$
$912$	−4.58258	−	2.64575i	−0.151744	−	0.0876096i
$913$	−46.6024	+	26.9059i	−1.54231	+	0.890455i
$914$	−25.1660			−0.832418
$915$	10.0000	−	20.0000i	0.330590	−	0.661180i
$916$	−12.5830	−	21.7944i	−0.415754	−	0.720107i
$917$	30.4547	+	17.5830i	1.00570	+	0.580642i
$918$	−5.19615	+	3.00000i	−0.171499	+	0.0990148i
$919$	−17.7288	+	30.7071i	−0.584818	+	1.01293i	0.410080	+	0.912049i	$0.365501\pi$
$919$	−17.7288	+	30.7071i	−0.584818	+	1.01293i	−0.994898	+	0.100885i	$0.967833\pi$
$920$	2.40998	−	1.59120i	0.0794546	−	0.0524602i
$921$	8.93725	−	15.4798i	0.294493	−	0.510076i
$922$			9.22876i			0.303933i
$923$	−66.8277	+	38.5830i	−2.19966	+	1.26998i
$924$	−6.14575	−	10.6448i	−0.202180	−	0.350187i
$925$	2.39230	+	19.8564i	0.0786585	+	0.652875i
$926$	18.6458			0.612737
$927$	1.17281	−	0.677124i	0.0385203	−	0.0222397i
$928$			2.64575i			0.0868510i
$929$	6.70850			0.220099			0.110049	−	0.993926i	$-0.464899\pi$
$929$	6.70850			0.220099			0.110049	+	0.993926i	$0.464899\pi$
$930$	−4.57495	−	11.5789i	−0.150019	−	0.379686i
$931$		0			0
$932$			3.29150i			0.107817i
$933$	−17.2118	+	9.93725i	−0.563490	+	0.325331i
$934$	−36.7490			−1.20246
$935$	−34.3428	−	52.0145i	−1.12313	−	1.70106i
$936$	2.64575	+	4.58258i	0.0864791	+	0.149786i
$937$	12.6293	−	7.29150i	0.412580	−	0.238203i	−0.279318	−	0.960199i	$-0.590108\pi$
$937$	12.6293	−	7.29150i	0.412580	−	0.238203i	0.691898	+	0.721996i	$0.256775\pi$
$938$			1.87451i			0.0612049i
$939$	0.968627	−	1.67771i	0.0316099	−	0.0547500i
$940$	−1.59120	−	2.40998i	−0.0518991	−	0.0786048i
$941$	−12.5516	+	21.7401i	−0.409172	+	0.708706i	−0.994797	−	0.101876i	$-0.967516\pi$
$941$	−12.5516	+	21.7401i	−0.409172	+	0.708706i	0.585626	+	0.810582i	$0.300849\pi$
$942$	−8.04668	+	4.64575i	−0.262175	+	0.151367i
$943$	−8.15536	−	4.70850i	−0.265575	−	0.153330i
$944$	2.32288	+	4.02334i	0.0756032	+	0.130949i
$945$	5.29150	+	2.64575i	0.172133	+	0.0860663i
$946$	−3.29150			−0.107016
$947$	−3.46410	+	2.00000i	−0.112568	+	0.0649913i	−0.555227	−	0.831699i	$-0.687369\pi$
$947$	−3.46410	+	2.00000i	−0.112568	+	0.0649913i	0.442659	+	0.896690i	$0.354035\pi$
$948$	−5.70105	−	3.29150i	−0.185161	−	0.106903i
$949$	38.5830	+	66.8277i	1.25246	+	2.16932i
$950$	3.16472	+	26.2676i	0.102677	+	0.852232i
$951$	−2.85425	+	4.94370i	−0.0925554	+	0.160311i
$952$	13.7477	+	7.93725i	0.445566	+	0.257248i
$953$		−	28.5830i		−	0.925894i	−0.886386	−	0.462947i	$-0.846792\pi$
$953$		−	28.5830i		−	0.925894i	0.886386	−	0.462947i	$-0.153208\pi$
$954$	−4.14575	−	7.18065i	−0.134224	−	0.232482i
$955$	−1.07180	−	17.8564i	−0.0346825	−	0.577820i
$956$	−1.70850	+	2.95920i	−0.0552568	+	0.0957075i
$957$		−	12.2915i		−	0.397328i
$958$	−28.2177	+	16.2915i	−0.911673	+	0.526355i
$959$	28.0000			0.904167
$960$	−1.00000	+	2.00000i	−0.0322749	+	0.0645497i
$961$	3.37451	+	30.8158i	0.108855	+	0.994058i
$962$			21.1660i			0.682420i
$963$		−	5.00000i		−	0.161123i
$964$	10.5000	+	18.1865i	0.338182	+	0.585749i
$965$	−15.3542	+	30.7085i	−0.494271	+	0.988542i
$966$	1.70850	−	2.95920i	0.0549700	−	0.0952108i
$967$	−22.9129	+	13.2288i	−0.736828	+	0.425408i	−0.820915	−	0.571050i	$-0.806536\pi$
$967$	−22.9129	+	13.2288i	−0.736828	+	0.425408i	0.0840866	+	0.996458i	$0.473203\pi$
$968$	−9.16515	+	5.29150i	−0.294579	+	0.170075i
$969$	−31.7490			−1.01993
$970$	28.4172	−	18.7626i	0.912423	−	0.602431i
$971$	−25.5516	+	44.2567i	−0.819991	+	1.42027i	0.0856972	+	0.996321i	$0.472688\pi$
$971$	−25.5516	+	44.2567i	−0.819991	+	1.42027i	−0.905688	+	0.423945i	$0.860645\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	9.16515	−	5.29150i	0.293821	−	0.169638i
$974$	4.61438	−	7.99234i	0.147854	−	0.256091i
$975$	10.3930	−	24.3307i	0.332844	−	0.779207i
$976$	10.0000			0.320092
$977$			30.5830i			0.978437i	0.872161	+	0.489219i	$0.162718\pi$
$977$			30.5830i			0.978437i	−0.872161	+	0.489219i	$0.837282\pi$
$978$	−8.66025	+	5.00000i	−0.276924	+	0.159882i
$979$	16.9373	−	29.3362i	0.541317	−	0.937589i
$980$		0			0
$981$	−8.64575	+	14.9749i	−0.276038	+	0.478111i
$982$	15.4254	+	8.90588i	0.492246	+	0.284198i
$983$	−7.54178	−	4.35425i	−0.240545	−	0.138879i	0.374882	−	0.927073i	$-0.377683\pi$
$983$	−7.54178	−	4.35425i	−0.240545	−	0.138879i	−0.615427	+	0.788194i	$0.711017\pi$
$984$	7.29150			0.232445
$985$	42.7795	−	2.56776i	1.36307	−	0.0818156i
$986$	7.93725	+	13.7477i	0.252774	+	0.437817i
$987$	−2.95920	−	1.70850i	−0.0941925	−	0.0543821i
$988$			28.0000i			0.890799i
$989$	−0.457513	−	0.792436i	−0.0145481	−	0.0251980i
$990$	4.64575	−	9.29150i	0.147652	−	0.295303i
$991$	−2.58301			−0.0820519			−0.0410259	−	0.999158i	$-0.513063\pi$
$991$	−2.58301			−0.0820519			−0.0410259	+	0.999158i	$0.513063\pi$
$992$	3.71655	−	4.14575i	0.118001	−	0.131628i
$993$			23.1660i			0.735151i
$994$	−38.5830			−1.22378
$995$	0.764794	+	12.7417i	0.0242456	+	0.403938i
$996$	11.5830			0.367022
$997$	−1.84073	−	1.06275i	−0.0582965	−	0.0336575i	0.470568	−	0.882363i	$-0.344049\pi$
$997$	−1.84073	−	1.06275i	−0.0582965	−	0.0336575i	−0.528865	+	0.848706i	$0.677382\pi$
$998$	31.5731	−	18.2288i	0.999430	−	0.577021i
$999$	−2.00000	−	3.46410i	−0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.b.769.3	yes	8
5.4	even	2	inner	930.2.s.b.769.2	yes	8
31.5	even	3	inner	930.2.s.b.439.4	yes	8
155.129	even	6	inner	930.2.s.b.439.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.b.439.1	✓	8	155.129	even	6	inner
930.2.s.b.439.4	yes	8	31.5	even	3	inner
930.2.s.b.769.2	yes	8	5.4	even	2	inner
930.2.s.b.769.3	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-1.86603 + 1.23205i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.29129 + 1.32288i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-1.86603 + 1.23205i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.29129 + 1.32288i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.23205 - 1.86603i) q^{10} +(-2.32288 + 4.02334i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-4.58258 - 2.64575i) q^{13} +(-1.32288 - 2.29129i) q^{14} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} +(5.19615 - 3.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(2.64575 + 4.58258i) q^{19} +(1.86603 - 1.23205i) q^{20} +(1.32288 - 2.29129i) q^{21} +(-4.02334 - 2.32288i) q^{22} -1.29150i q^{23} +(0.500000 + 0.866025i) q^{24} +(1.96410 - 4.59808i) q^{25} +(2.64575 - 4.58258i) q^{26} +1.00000i q^{27} +(2.29129 - 1.32288i) q^{28} +2.64575 q^{29} +(2.00000 + 1.00000i) q^{30} +(-4.14575 - 3.71655i) q^{31} +1.00000i q^{32} -4.64575i q^{33} +(3.00000 + 5.19615i) q^{34} +(2.64575 - 5.29150i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.46410 + 2.00000i) q^{37} +(-4.58258 + 2.64575i) q^{38} +5.29150 q^{39} +(1.23205 + 1.86603i) q^{40} +(3.64575 - 6.31463i) q^{41} +(2.29129 + 1.32288i) q^{42} +(0.613577 - 0.354249i) q^{43} +(2.32288 - 4.02334i) q^{44} +(0.133975 + 2.23205i) q^{45} +1.29150 q^{46} -1.29150i q^{47} +(-0.866025 + 0.500000i) q^{48} +(4.59808 + 1.96410i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(4.58258 + 2.64575i) q^{52} +(-7.18065 - 4.14575i) q^{53} -1.00000 q^{54} +(-0.622413 - 10.3696i) q^{55} +(1.32288 + 2.29129i) q^{56} +(-4.58258 - 2.64575i) q^{57} +2.64575i q^{58} +(2.32288 + 4.02334i) q^{59} +(-1.00000 + 2.00000i) q^{60} +10.0000 q^{61} +(3.71655 - 4.14575i) q^{62} +2.64575i q^{63} -1.00000 q^{64} +(11.8109 - 0.708927i) q^{65} +4.64575 q^{66} +(-0.613577 - 0.354249i) q^{67} +(-5.19615 + 3.00000i) q^{68} +(0.645751 + 1.11847i) q^{69} +(5.29150 + 2.64575i) q^{70} +(7.29150 - 12.6293i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(-12.6293 - 7.29150i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(0.598076 + 4.96410i) q^{75} +(-2.64575 - 4.58258i) q^{76} -12.2915i q^{77} +5.29150i q^{78} +(-3.29150 - 5.70105i) q^{79} +(-1.86603 + 1.23205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.31463 + 3.64575i) q^{82} +(10.0312 + 5.79150i) q^{83} +(-1.32288 + 2.29129i) q^{84} +(-6.00000 + 12.0000i) q^{85} +(0.354249 + 0.613577i) q^{86} +(-2.29129 + 1.32288i) q^{87} +(4.02334 + 2.32288i) q^{88} -7.29150 q^{89} +(-2.23205 + 0.133975i) q^{90} +14.0000 q^{91} +1.29150i q^{92} +(5.44860 + 1.14575i) q^{93} +1.29150 q^{94} +(-10.5830 - 5.29150i) q^{95} +(-0.500000 - 0.866025i) q^{96} +15.2288i q^{97} +(2.32288 + 4.02334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9	\( 8 q - 8 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{15} + 8 q^{16} + 8 q^{20} + 4 q^{24} - 12 q^{25} + 16 q^{30} - 12 q^{31} + 24 q^{34} - 4 q^{36} - 4 q^{40} + 8 q^{41} + 8 q^{44} + 8 q^{45} - 32 q^{46} + 16 q^{50} - 24 q^{51} - 8 q^{54} - 16 q^{55} + 8 q^{59} - 8 q^{60} + 80 q^{61} - 8 q^{64} + 16 q^{66} - 16 q^{69} + 16 q^{71} - 16 q^{74} - 16 q^{75} + 16 q^{79} - 8 q^{80} - 4 q^{81} - 48 q^{85} + 24 q^{86} - 16 q^{89} - 4 q^{90} + 112 q^{91} - 32 q^{94} - 4 q^{96} + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^15 + 8 * q^16 + 8 * q^20 + 4 * q^24 - 12 * q^25 + 16 * q^30 - 12 * q^31 + 24 * q^34 - 4 * q^36 - 4 * q^40 + 8 * q^41 + 8 * q^44 + 8 * q^45 - 32 * q^46 + 16 * q^50 - 24 * q^51 - 8 * q^54 - 16 * q^55 + 8 * q^59 - 8 * q^60 + 80 * q^61 - 8 * q^64 + 16 * q^66 - 16 * q^69 + 16 * q^71 - 16 * q^74 - 16 * q^75 + 16 * q^79 - 8 * q^80 - 4 * q^81 - 48 * q^85 + 24 * q^86 - 16 * q^89 - 4 * q^90 + 112 * q^91 - 32 * q^94 - 4 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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