LMFDB - Embedded newform 820.2.s.c.647.40

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(583,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.583"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.40
Character	$\chi$	$=$	820.647
Dual form			820.2.s.c.583.40

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.689491 - 1.23475i) q^{2} +2.13292 q^{3} +(-1.04921 + 1.70269i) q^{4} +(-1.66560 - 1.49190i) q^{5} +(-1.47063 - 2.63362i) q^{6} +3.79559i q^{7} +(2.82582 + 0.121513i) q^{8} +1.54935 q^{9} +(-0.693708 + 3.08525i) q^{10} +(-1.18738 - 1.18738i) q^{11} +(-2.23787 + 3.63171i) q^{12} +5.25705i q^{13} +(4.68660 - 2.61703i) q^{14} +(-3.55260 - 3.18211i) q^{15} +(-1.79834 - 3.57295i) q^{16} +6.80287i q^{17} +(-1.06826 - 1.91306i) q^{18} +(-0.539583 - 0.539583i) q^{19} +(4.28781 - 1.27070i) q^{20} +8.09570i q^{21} +(-0.647426 + 2.28480i) q^{22} +(-2.86694 - 2.86694i) q^{23} +(6.02724 + 0.259177i) q^{24} +(0.548453 + 4.96983i) q^{25} +(6.49114 - 3.62469i) q^{26} -3.09412 q^{27} +(-6.46273 - 3.98236i) q^{28} +(-0.631885 - 0.631885i) q^{29} +(-1.47962 + 6.58060i) q^{30} +6.03484i q^{31} +(-3.17176 + 4.68401i) q^{32} +(-2.53258 - 2.53258i) q^{33} +(8.39983 - 4.69052i) q^{34} +(5.66266 - 6.32194i) q^{35} +(-1.62559 + 2.63807i) q^{36} +(6.56359 + 6.56359i) q^{37} +(-0.294211 + 1.03829i) q^{38} +11.2129i q^{39} +(-4.52540 - 4.41823i) q^{40} +(-1.60372 - 6.19904i) q^{41} +(9.99615 - 5.58191i) q^{42} +(6.88851 - 6.88851i) q^{43} +(3.26754 - 0.775937i) q^{44} +(-2.58060 - 2.31148i) q^{45} +(-1.56322 + 5.51668i) q^{46} +6.94756 q^{47} +(-3.83571 - 7.62083i) q^{48} -7.40653 q^{49} +(5.75833 - 4.10385i) q^{50} +14.5100i q^{51} +(-8.95115 - 5.51573i) q^{52} +1.29473i q^{53} +(2.13336 + 3.82046i) q^{54} +(0.206245 + 3.74915i) q^{55} +(-0.461213 + 10.7256i) q^{56} +(-1.15089 - 1.15089i) q^{57} +(-0.344540 + 1.21590i) q^{58} +3.32033 q^{59} +(9.14556 - 2.71030i) q^{60} +9.00272i q^{61} +(7.45150 - 4.16096i) q^{62} +5.88071i q^{63} +(7.97047 + 0.686746i) q^{64} +(7.84301 - 8.75615i) q^{65} +(-1.38091 + 4.87329i) q^{66} -13.9012 q^{67} +(-11.5832 - 7.13761i) q^{68} +(-6.11496 - 6.11496i) q^{69} +(-11.7104 - 2.63303i) q^{70} +(-4.57139 - 4.57139i) q^{71} +(4.37818 + 0.188266i) q^{72} +(2.83212 + 2.83212i) q^{73} +(3.57885 - 12.6299i) q^{74} +(1.16981 + 10.6003i) q^{75} +(1.48488 - 0.352611i) q^{76} +(4.50680 - 4.50680i) q^{77} +(13.8451 - 7.73117i) q^{78} +(-3.21799 + 3.21799i) q^{79} +(-2.33519 + 8.63405i) q^{80} -11.2476 q^{81} +(-6.54851 + 6.25436i) q^{82} +(3.90777 + 3.90777i) q^{83} +(-13.7845 - 8.49405i) q^{84} +(10.1492 - 11.3309i) q^{85} +(-13.2551 - 3.75601i) q^{86} +(-1.34776 - 1.34776i) q^{87} +(-3.21103 - 3.49959i) q^{88} +(-1.76118 - 1.76118i) q^{89} +(-1.07480 + 4.78014i) q^{90} -19.9536 q^{91} +(7.88953 - 1.87351i) q^{92} +12.8718i q^{93} +(-4.79027 - 8.57848i) q^{94} +(0.0937245 + 1.70373i) q^{95} +(-6.76511 + 9.99062i) q^{96} -13.6640i q^{97} +(5.10673 + 9.14520i) q^{98} +(-1.83966 - 1.83966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.689491	−	1.23475i	−0.487543	−	0.873099i
$2$	−0.689491	−	1.23475i	−0.487543	−	0.873099i
$3$	2.13292			1.23144			0.615721	−	0.787964i	$-0.288865\pi$
$3$	2.13292			1.23144			0.615721	+	0.787964i	$0.288865\pi$
$4$	−1.04921	+	1.70269i	−0.524603	+	0.851347i
$5$	−1.66560	−	1.49190i	−0.744879	−	0.667199i
$5$	−1.66560	−	1.49190i	−0.744879	−	0.667199i
$6$	−1.47063	−	2.63362i	−0.600382	−	1.07517i
$7$			3.79559i			1.43460i	0.696765	+	0.717300i	$0.254622\pi$
$7$			3.79559i			1.43460i	−0.696765	+	0.717300i	$0.745378\pi$
$8$	2.82582	+	0.121513i	0.999077	+	0.0429613i
$9$	1.54935			0.516451
$10$	−0.693708	+	3.08525i	−0.219370	+	0.975642i
$11$	−1.18738	−	1.18738i	−0.358008	−	0.358008i	0.505071	−	0.863078i	$-0.331466\pi$
$11$	−1.18738	−	1.18738i	−0.358008	−	0.358008i	−0.863078	+	0.505071i	$0.831466\pi$
$12$	−2.23787	+	3.63171i	−0.646018	+	1.04839i
$13$			5.25705i			1.45804i	0.684490	+	0.729022i	$0.260025\pi$
$13$			5.25705i			1.45804i	−0.684490	+	0.729022i	$0.739975\pi$
$14$	4.68660	−	2.61703i	1.25255	−	0.699430i
$15$	−3.55260	−	3.18211i	−0.917276	−	0.821617i
$16$	−1.79834	−	3.57295i	−0.449584	−	0.893238i
$17$			6.80287i			1.64994i	0.565177	+	0.824969i	$0.308808\pi$
$17$			6.80287i			1.64994i	−0.565177	+	0.824969i	$0.691192\pi$
$18$	−1.06826	−	1.91306i	−0.251792	−	0.450912i
$19$	−0.539583	−	0.539583i	−0.123789	−	0.123789i	0.642498	−	0.766287i	$-0.277898\pi$
$19$	−0.539583	−	0.539583i	−0.123789	−	0.123789i	−0.766287	+	0.642498i	$0.777898\pi$
$20$	4.28781	−	1.27070i	0.958784	−	0.284136i
$21$			8.09570i			1.76663i
$22$	−0.647426	+	2.28480i	−0.138032	+	0.487120i
$23$	−2.86694	−	2.86694i	−0.597799	−	0.597799i	0.341928	−	0.939726i	$-0.388920\pi$
$23$	−2.86694	−	2.86694i	−0.597799	−	0.597799i	−0.939726	+	0.341928i	$0.888920\pi$
$24$	6.02724	+	0.259177i	1.23031	+	0.0529043i
$25$	0.548453	+	4.96983i	0.109691	+	0.993966i
$26$	6.49114	−	3.62469i	1.27302	−	0.710860i
$27$	−3.09412			−0.595463
$28$	−6.46273	−	3.98236i	−1.22134	−	0.752595i
$29$	−0.631885	−	0.631885i	−0.117338	−	0.117338i	0.646000	−	0.763338i	$-0.276441\pi$
$29$	−0.631885	−	0.631885i	−0.117338	−	0.117338i	−0.763338	+	0.646000i	$0.776441\pi$
$30$	−1.47962	+	6.58060i	−0.270141	+	1.20145i
$31$			6.03484i			1.08389i	0.840414	+	0.541944i	$0.182312\pi$
$31$			6.03484i			1.08389i	−0.840414	+	0.541944i	$0.817688\pi$
$32$	−3.17176	+	4.68401i	−0.560693	+	0.828024i
$33$	−2.53258	−	2.53258i	−0.440866	−	0.440866i
$34$	8.39983	−	4.69052i	1.44056	−	0.804417i
$35$	5.66266	−	6.32194i	0.957164	−	1.06860i
$36$	−1.62559	+	2.63807i	−0.270931	+	0.439679i
$37$	6.56359	+	6.56359i	1.07905	+	1.07905i	0.996595	+	0.0824524i	$0.0262752\pi$
$37$	6.56359	+	6.56359i	1.07905	+	1.07905i	0.0824524	+	0.996595i	$0.473725\pi$
$38$	−0.294211	+	1.03829i	−0.0477274	+	0.168432i
$39$			11.2129i			1.79550i
$40$	−4.52540	−	4.41823i	−0.715528	−	0.698584i
$41$	−1.60372	−	6.19904i	−0.250458	−	0.968127i
$41$	−1.60372	−	6.19904i	−0.250458	−	0.968127i
$42$	9.99615	−	5.58191i	1.54244	−	0.861307i
$43$	6.88851	−	6.88851i	1.05049	−	1.05049i	0.0518314	−	0.998656i	$-0.483494\pi$
$43$	6.88851	−	6.88851i	1.05049	−	1.05049i	0.998656	−	0.0518314i	$-0.0165058\pi$
$44$	3.26754	−	0.775937i	0.492600	−	0.116977i
$45$	−2.58060	−	2.31148i	−0.384693	−	0.344575i
$46$	−1.56322	+	5.51668i	−0.230484	+	0.813390i
$47$	6.94756			1.01341			0.506703	−	0.862121i	$-0.330864\pi$
$47$	6.94756			1.01341			0.506703	+	0.862121i	$0.330864\pi$
$48$	−3.83571	−	7.62083i	−0.553637	−	1.09997i
$49$	−7.40653			−1.05808
$50$	5.75833	−	4.10385i	0.814351	−	0.580372i
$51$			14.5100i			2.03180i
$52$	−8.95115	−	5.51573i	−1.24130	−	0.764894i
$53$			1.29473i			0.177844i	0.996039	+	0.0889221i	$0.0283422\pi$
$53$			1.29473i			0.177844i	−0.996039	+	0.0889221i	$0.971658\pi$
$54$	2.13336	+	3.82046i	0.290314	+	0.519898i
$55$	0.206245	+	3.74915i	0.0278101	+	0.505535i
$56$	−0.461213	+	10.7256i	−0.0616322	+	1.43327i
$57$	−1.15089	−	1.15089i	−0.152439	−	0.152439i
$58$	−0.344540	+	1.21590i	−0.0452403	+	0.159655i
$59$	3.32033			0.432270			0.216135	−	0.976363i	$-0.430655\pi$
$59$	3.32033			0.432270			0.216135	+	0.976363i	$0.430655\pi$
$60$	9.14556	−	2.71030i	1.18069	−	0.349898i
$61$			9.00272i			1.15268i	0.817210	+	0.576340i	$0.195520\pi$
$61$			9.00272i			1.15268i	−0.817210	+	0.576340i	$0.804480\pi$
$62$	7.45150	−	4.16096i	0.946342	−	0.528443i
$63$			5.88071i			0.740900i
$64$	7.97047	+	0.686746i	0.996309	+	0.0858432i
$65$	7.84301	−	8.75615i	0.972806	−	1.08607i
$66$	−1.38091	+	4.87329i	−0.169978	+	0.599860i
$67$	−13.9012			−1.69831			−0.849154	−	0.528146i	$-0.822887\pi$
$67$	−13.9012			−1.69831			−0.849154	+	0.528146i	$0.822887\pi$
$68$	−11.5832	−	7.13761i	−1.40467	−	0.865562i
$69$	−6.11496	−	6.11496i	−0.736154	−	0.736154i
$70$	−11.7104	−	2.63303i	−1.39966	−	0.314708i
$71$	−4.57139	−	4.57139i	−0.542524	−	0.542524i	0.381744	−	0.924268i	$-0.375324\pi$
$71$	−4.57139	−	4.57139i	−0.542524	−	0.542524i	−0.924268	+	0.381744i	$0.875324\pi$
$72$	4.37818	+	0.188266i	0.515974	+	0.0221874i
$73$	2.83212	+	2.83212i	0.331475	+	0.331475i	0.853146	−	0.521672i	$-0.174691\pi$
$73$	2.83212	+	2.83212i	0.331475	+	0.331475i	−0.521672	+	0.853146i	$0.674691\pi$
$74$	3.57885	−	12.6299i	0.416032	−	1.46820i
$75$	1.16981	+	10.6003i	0.135078	+	1.22401i
$76$	1.48488	−	0.352611i	0.170327	−	0.0404473i
$77$	4.50680	−	4.50680i	0.513597	−	0.513597i
$78$	13.8451	−	7.73117i	1.56765	−	0.875383i
$79$	−3.21799	+	3.21799i	−0.362052	+	0.362052i	−0.864568	−	0.502516i	$-0.832408\pi$
$79$	−3.21799	+	3.21799i	−0.362052	+	0.362052i	0.502516	+	0.864568i	$0.332408\pi$
$80$	−2.33519	+	8.63405i	−0.261082	+	0.965317i
$81$	−11.2476			−1.24973
$82$	−6.54851	+	6.25436i	−0.723162	+	0.690679i
$83$	3.90777	+	3.90777i	0.428933	+	0.428933i	0.888265	−	0.459332i	$-0.151911\pi$
$83$	3.90777	+	3.90777i	0.428933	+	0.428933i	−0.459332	+	0.888265i	$0.651911\pi$
$84$	−13.7845	−	8.49405i	−1.50401	−	0.926777i
$85$	10.1492	−	11.3309i	1.10084	−	1.22901i
$86$	−13.2551	−	3.75601i	−1.42934	−	0.405021i
$87$	−1.34776	−	1.34776i	−0.144495	−	0.144495i
$88$	−3.21103	−	3.49959i	−0.342297	−	0.373057i
$89$	−1.76118	−	1.76118i	−0.186684	−	0.186684i	0.607577	−	0.794261i	$-0.292142\pi$
$89$	−1.76118	−	1.76118i	−0.186684	−	0.186684i	−0.794261	+	0.607577i	$0.792142\pi$
$90$	−1.07480	+	4.78014i	−0.113294	+	0.503871i
$91$	−19.9536			−2.09171
$92$	7.88953	−	1.87351i	0.822541	−	0.195327i
$93$			12.8718i			1.33475i
$94$	−4.79027	−	8.57848i	−0.494079	−	0.884803i
$95$	0.0937245	+	1.70373i	0.00961593	+	0.174799i
$96$	−6.76511	+	9.99062i	−0.690462	+	1.01966i
$97$		−	13.6640i		−	1.38737i	−0.720278	−	0.693686i	$-0.755986\pi$
$97$		−	13.6640i		−	1.38737i	0.720278	−	0.693686i	$-0.244014\pi$
$98$	5.10673	+	9.14520i	0.515858	+	0.923804i
$99$	−1.83966	−	1.83966i	−0.184893	−	0.184893i
$100$	−9.03754	−	4.28052i	−0.903754	−	0.428052i
$101$	11.8444	+	11.8444i	1.17856	+	1.17856i	0.980111	+	0.198452i	$0.0635914\pi$
$101$	11.8444	+	11.8444i	1.17856	+	1.17856i	0.198452	+	0.980111i	$0.436409\pi$
$102$	17.9162	−	10.0045i	1.77397	−	0.990593i
$103$	6.27427	−	6.27427i	0.618222	−	0.618222i	−0.326853	−	0.945075i	$-0.605988\pi$
$103$	6.27427	−	6.27427i	0.618222	−	0.618222i	0.945075	+	0.326853i	$0.105988\pi$
$104$	−0.638799	+	14.8555i	−0.0626394	+	1.45670i
$105$	12.0780	−	13.4842i	1.17869	−	1.31592i
$106$	1.59866	−	0.892701i	0.155276	−	0.0867068i
$107$	11.2921	−	11.2921i	1.09165	−	1.09165i	0.0962926	−	0.995353i	$-0.469302\pi$
$107$	11.2921	−	11.2921i	1.09165	−	1.09165i	0.995353	−	0.0962926i	$-0.0306984\pi$
$108$	3.24637	−	5.26834i	0.312382	−	0.506946i
$109$	6.65133	−	6.65133i	0.637082	−	0.637082i	−0.312753	−	0.949835i	$-0.601251\pi$
$109$	6.65133	−	6.65133i	0.637082	−	0.637082i	0.949835	+	0.312753i	$0.101251\pi$
$110$	4.48705	−	2.83966i	0.427823	−	0.270751i
$111$	13.9996	+	13.9996i	1.32878	+	1.32878i
$112$	13.5615	−	6.82575i	1.28144	−	0.644973i
$113$	−7.82171	+	7.82171i	−0.735805	+	0.735805i	−0.971763	−	0.235958i	$-0.924177\pi$
$113$	−7.82171	+	7.82171i	−0.735805	+	0.735805i	0.235958	+	0.971763i	$0.424177\pi$
$114$	−0.627530	+	2.21458i	−0.0587736	+	0.207415i
$115$	0.497982	+	9.05238i	0.0464371	+	0.844138i
$116$	1.73888	−	0.412930i	0.161451	−	0.0383396i
$117$			8.14503i			0.753008i
$118$	−2.28934	−	4.09977i	−0.210750	−	0.377414i
$119$	−25.8209			−2.36700
$120$	−9.65231	−	9.42374i	−0.881132	−	0.860266i
$121$		−	8.18027i		−	0.743661i
$122$	11.1161	−	6.20729i	1.00640	−	0.561982i
$123$	−3.42060	−	13.2221i	−0.308425	−	1.19219i
$124$	−10.2755	−	6.33178i	−0.922766	−	0.568611i
$125$	6.50100	−	9.09599i	0.581467	−	0.813570i
$126$	7.26120	−	4.05469i	0.646879	−	0.361221i
$127$	−11.7119	+	11.7119i	−1.03926	+	1.03926i	−0.0400669	+	0.999197i	$0.512757\pi$
$127$	−11.7119	+	11.7119i	−1.03926	+	1.03926i	−0.999197	+	0.0400669i	$0.987243\pi$
$128$	−4.64761	−	10.3150i	−0.410794	−	0.911728i
$129$	14.6926	−	14.6926i	1.29361	−	1.29361i
$130$	−16.2193	−	3.64686i	−1.42253	−	0.319851i
$131$	0.293595			0.0256515			0.0128258	−	0.999918i	$-0.495917\pi$
$131$	0.293595			0.0256515			0.0128258	+	0.999918i	$0.495917\pi$
$132$	6.96941	−	1.65501i	0.606609	−	0.144050i
$133$	2.04804	−	2.04804i	0.177587	−	0.177587i
$134$	9.58478	+	17.1645i	0.827999	+	1.48279i
$135$	5.15356	+	4.61612i	0.443548	+	0.397293i
$136$	−0.826636	+	19.2237i	−0.0708835	+	1.64842i
$137$			11.3525i			0.969909i	0.874539	+	0.484955i	$0.161164\pi$
$137$			11.3525i			0.969909i	−0.874539	+	0.484955i	$0.838836\pi$
$138$	−3.33423	+	11.7666i	−0.283828	+	1.00164i
$139$	19.7558			1.67567			0.837833	−	0.545927i	$-0.183822\pi$
$139$	19.7558			1.67567			0.837833	+	0.545927i	$0.183822\pi$
$140$	4.82305	+	16.2748i	0.407622	+	1.37547i
$141$	14.8186			1.24795
$142$	−2.49258	+	8.79644i	−0.209173	+	0.738181i
$143$	6.24210	−	6.24210i	0.521991	−	0.521991i
$144$	−2.78625	−	5.53576i	−0.232188	−	0.461313i
$145$	0.109757	+	1.99518i	0.00911485	+	0.165691i
$146$	1.54424	−	5.44968i	0.127802	−	0.451019i
$147$	−15.7975			−1.30296
$148$	−18.0623	+	4.28923i	−1.48472	+	0.352573i
$149$	−11.4030	+	11.4030i	−0.934171	+	0.934171i	−0.997963	−	0.0637922i	$-0.979681\pi$
$149$	−11.4030	+	11.4030i	−0.934171	+	0.934171i	0.0637922	+	0.997963i	$0.479681\pi$
$150$	12.2821	−	8.75319i	1.00283	−	0.714695i
$151$	−6.73143	−	6.73143i	−0.547796	−	0.547796i	0.378007	−	0.925803i	$-0.376610\pi$
$151$	−6.73143	−	6.73143i	−0.547796	−	0.547796i	−0.925803	+	0.378007i	$0.876610\pi$
$152$	−1.45919	−	1.59033i	−0.118356	−	0.128993i
$153$			10.5400i			0.852112i
$154$	−8.67216	−	2.45737i	−0.698822	−	0.198020i
$155$	9.00339	−	10.0516i	0.723170	−	0.807366i
$156$	−19.0921	−	11.7646i	−1.52859	−	0.941923i
$157$	2.78990			0.222658			0.111329	−	0.993784i	$-0.464489\pi$
$157$	2.78990			0.222658			0.111329	+	0.993784i	$0.464489\pi$
$158$	6.19218	+	1.75463i	0.492623	+	0.139591i
$159$			2.76155i			0.219005i
$160$	12.2710	−	3.06973i	0.970106	−	0.242683i
$161$	10.8817	−	10.8817i	0.857601	−	0.857601i
$162$	7.75509	+	13.8879i	0.609297	+	1.09114i
$163$	1.35473	+	1.35473i	0.106111	+	0.106111i	0.758169	−	0.652058i	$-0.226094\pi$
$163$	1.35473	+	1.35473i	0.106111	+	0.106111i	−0.652058	+	0.758169i	$0.726094\pi$
$164$	12.2377	+	3.77343i	0.955604	+	0.294655i
$165$	0.439905	+	7.99663i	0.0342465	+	0.622537i
$166$	2.13074	−	7.51948i	0.165377	−	0.583624i
$167$		−	6.83522i		−	0.528925i	−0.964396	−	0.264462i	$-0.914805\pi$
$167$		−	6.83522i		−	0.528925i	0.964396	−	0.264462i	$-0.0851945\pi$
$168$	−0.983731	+	22.8770i	−0.0758965	+	1.76500i
$169$	−14.6366			−1.12589
$170$	−20.9886	−	4.71921i	−1.60975	−	0.361947i
$171$	−0.836003	−	0.836003i	−0.0639308	−	0.0639308i
$172$	4.50156	+	18.9565i	0.343241	+	1.44542i
$173$	−12.0418	−	12.0418i	−0.915518	−	0.915518i	0.0811817	−	0.996699i	$-0.474131\pi$
$173$	−12.0418	−	12.0418i	−0.915518	−	0.915518i	−0.996699	+	0.0811817i	$0.974131\pi$
$174$	−0.734877	+	2.59341i	−0.0557109	+	0.196606i
$175$	−18.8634	+	2.08170i	−1.42594	+	0.157362i
$176$	−2.10714	+	6.37774i	−0.158832	+	0.480740i
$177$	7.08200			0.532316
$178$	−0.960295	+	3.38892i	−0.0719771	+	0.254011i
$179$	−2.36638	−	2.36638i	−0.176872	−	0.176872i	0.613119	−	0.789991i	$-0.289915\pi$
$179$	−2.36638	−	2.36638i	−0.176872	−	0.176872i	−0.789991	+	0.613119i	$0.789915\pi$
$180$	6.64333	−	1.96876i	0.495165	−	0.146742i
$181$	−5.80793	−	5.80793i	−0.431700	−	0.431700i	0.457506	−	0.889206i	$-0.348743\pi$
$181$	−5.80793	−	5.80793i	−0.431700	−	0.431700i	−0.889206	+	0.457506i	$0.848743\pi$
$182$	13.7578	+	24.6377i	1.01980	+	1.82627i
$183$			19.2021i			1.41946i
$184$	−7.75308	−	8.44982i	−0.571564	−	0.622929i
$185$	−1.14008	−	20.7246i	−0.0838206	−	1.52370i
$186$	15.8935	−	8.87501i	1.16537	−	0.650747i
$187$	8.07757	−	8.07757i	0.590691	−	0.590691i
$188$	−7.28941	+	11.8296i	−0.531635	+	0.862760i
$189$		−	11.7440i		−	0.854251i
$190$	2.03906	−	1.29043i	0.147929	−	0.0936180i
$191$	−9.98578	+	9.98578i	−0.722545	+	0.722545i	−0.969123	−	0.246578i	$-0.920694\pi$
$191$	−9.98578	+	9.98578i	−0.722545	+	0.722545i	0.246578	+	0.969123i	$0.420694\pi$
$192$	17.0004	+	1.46477i	1.22690	+	0.105711i
$193$		−	4.94076i		−	0.355644i	−0.984063	−	0.177822i	$-0.943095\pi$
$193$		−	4.94076i		−	0.355644i	0.984063	−	0.177822i	$-0.0569051\pi$
$194$	−16.8716	+	9.42122i	−1.21131	+	0.676404i
$195$	16.7285	−	18.6762i	1.19795	−	1.33743i
$196$	7.77097	−	12.6111i	0.555069	−	0.900789i
$197$	2.69442	−	2.69442i	0.191969	−	0.191969i	−0.604577	−	0.796547i	$-0.706658\pi$
$197$	2.69442	−	2.69442i	0.191969	−	0.191969i	0.796547	+	0.604577i	$0.206658\pi$
$198$	−1.00309	+	3.53995i	−0.0712866	+	0.251574i
$199$	3.98148	+	3.98148i	0.282240	+	0.282240i	0.834002	−	0.551762i	$-0.186044\pi$
$199$	3.98148	+	3.98148i	0.282240	+	0.282240i	−0.551762	+	0.834002i	$0.686044\pi$
$200$	0.945928	+	14.1105i	0.0668872	+	0.997761i
$201$	−29.6503			−2.09137
$202$	6.45825	−	22.7915i	0.454401	−	1.60360i
$203$	2.39838	−	2.39838i	0.168333	−	0.168333i
$204$	−24.7061	−	15.2240i	−1.72977	−	1.06589i
$205$	−6.57722	+	12.7177i	−0.459373	+	0.888244i
$206$	−12.0732	−	3.42109i	−0.841179	−	0.238359i
$207$	−4.44190	−	4.44190i	−0.308733	−	0.308733i
$208$	18.7832	−	9.45394i	1.30238	−	0.655513i
$209$			1.28138i			0.0886346i
$210$	−24.9773	−	5.61605i	−1.72359	−	0.387544i
$211$	−4.26868	+	4.26868i	−0.293868	+	0.293868i	−0.838606	−	0.544738i	$-0.816629\pi$
$211$	−4.26868	+	4.26868i	−0.293868	+	0.293868i	0.544738	+	0.838606i	$0.316629\pi$
$212$	−2.20452	−	1.35843i	−0.151407	−	0.0932976i
$213$	−9.75041	−	9.75041i	−0.668087	−	0.668087i
$214$	−21.7286	−	6.15709i	−1.48534	−	0.420890i
$215$	−21.7505	+	1.19652i	−1.48337	+	0.0816020i
$216$	−8.74341	−	0.375975i	−0.594913	−	0.0255819i
$217$	−22.9058			−1.55495
$218$	−12.7987	−	3.62669i	−0.866841	−	0.245630i
$219$	6.04069	+	6.04069i	0.408192	+	0.408192i
$220$	−6.60004	−	3.58245i	−0.444975	−	0.241529i
$221$	−35.7631			−2.40568
$222$	7.63340	−	26.9386i	0.512320	−	1.80800i
$223$	10.7438	+	10.7438i	0.719458	+	0.719458i	0.968494	−	0.249036i	$-0.0801138\pi$
$223$	10.7438	+	10.7438i	0.719458	+	0.719458i	−0.249036	+	0.968494i	$0.580114\pi$
$224$	−17.7786	−	12.0387i	−1.18788	−	0.804370i
$225$	0.849746	+	7.70001i	0.0566497	+	0.513334i
$226$	15.0508	+	4.26485i	1.00117	+	0.283693i
$227$	4.00580			0.265875			0.132937	−	0.991124i	$-0.457559\pi$
$227$	4.00580			0.265875			0.132937	+	0.991124i	$0.457559\pi$
$228$	3.16713	−	0.752092i	0.209748	−	0.0498085i
$229$	15.2903	−	15.2903i	1.01041	−	1.01041i	0.0104690	−	0.999945i	$-0.496668\pi$
$229$	15.2903	−	15.2903i	1.01041	−	1.01041i	0.999945	−	0.0104690i	$-0.00333245\pi$
$230$	10.8340	−	6.85641i	0.714376	−	0.452098i
$231$	9.61265	−	9.61265i	0.632466	−	0.632466i
$232$	−1.70881	−	1.86237i	−0.112189	−	0.122271i
$233$			12.7190i			0.833248i	0.909079	+	0.416624i	$0.136787\pi$
$233$			12.7190i			0.833248i	−0.909079	+	0.416624i	$0.863213\pi$
$234$	10.0571	−	5.61592i	0.657450	−	0.367124i
$235$	−11.5719	−	10.3651i	−0.754865	−	0.676143i
$236$	−3.48371	+	5.65350i	−0.226770	+	0.368012i
$237$	−6.86372	+	6.86372i	−0.445846	+	0.445846i
$238$	17.8033	+	31.8823i	1.15402	+	2.06663i
$239$	−3.34373	+	3.34373i	−0.216288	+	0.216288i	−0.806932	−	0.590644i	$-0.798874\pi$
$239$	−3.34373	+	3.34373i	−0.216288	+	0.216288i	0.590644	+	0.806932i	$0.298874\pi$
$240$	−4.98077	+	18.4158i	−0.321507	+	1.18873i
$241$		−	12.6414i		−	0.814302i	−0.913361	−	0.407151i	$-0.866522\pi$
$241$		−	12.6414i		−	0.814302i	0.913361	−	0.407151i	$-0.133478\pi$
$242$	−10.1006	+	5.64022i	−0.649290	+	0.362567i
$243$	−14.7078			−0.943507
$244$	−15.3289	−	9.44570i	−0.981331	−	0.604699i
$245$	12.3363	+	11.0498i	0.788138	+	0.705947i
$246$	−13.9674	+	13.3401i	−0.890532	+	0.850531i
$247$	2.83661	−	2.83661i	0.180489	−	0.180489i
$248$	−0.733310	+	17.0533i	−0.0465652	+	1.08289i
$249$	8.33496	+	8.33496i	0.528206	+	0.528206i
$250$	−15.7136	−	1.75550i	−0.993817	−	0.111027i
$251$	−21.7813			−1.37482			−0.687411	−	0.726268i	$-0.741253\pi$
$251$	−21.7813			−1.37482			−0.687411	+	0.726268i	$0.741253\pi$
$252$	−10.0131	−	6.17007i	−0.630763	−	0.388678i
$253$			6.80828i			0.428033i
$254$	22.5365	+	6.38601i	1.41407	+	0.400694i
$255$	21.6475	−	24.1679i	1.35562	−	1.51345i
$256$	−9.53198	+	12.8507i	−0.595749	+	0.803171i
$257$	−14.8162			−0.924207			−0.462104	−	0.886826i	$-0.652905\pi$
$257$	−14.8162			−0.924207			−0.462104	+	0.886826i	$0.652905\pi$
$258$	−28.2721	−	8.01127i	−1.76015	−	0.498760i
$259$	−24.9127	+	24.9127i	−1.54800	+	1.54800i
$260$	6.68012	+	22.5413i	0.414283	+	1.39795i
$261$	−0.979013	−	0.979013i	−0.0605994	−	0.0605994i
$262$	−0.202431	−	0.362516i	−0.0125062	−	0.0223963i
$263$		−	1.52403i		−	0.0939759i	−0.998895	−	0.0469880i	$-0.985038\pi$
$263$		−	1.52403i		−	0.0939759i	0.998895	−	0.0469880i	$-0.0149622\pi$
$264$	−6.84887	−	7.46435i	−0.421519	−	0.459399i
$265$	1.93160	−	2.15650i	0.118658	−	0.132473i
$266$	−3.94091	−	1.11671i	−0.241633	−	0.0684697i
$267$	−3.75645	−	3.75645i	−0.229891	−	0.229891i
$268$	14.5853	−	23.6696i	0.890937	−	1.44585i
$269$			32.6160i			1.98863i	0.106471	+	0.994316i	$0.466045\pi$
$269$			32.6160i			1.98863i	−0.106471	+	0.994316i	$0.533955\pi$
$270$	2.14641	−	9.54613i	0.130627	−	0.580959i
$271$		−	22.5274i		−	1.36844i	−0.729274	−	0.684221i	$-0.760142\pi$
$271$		−	22.5274i		−	1.36844i	0.729274	−	0.684221i	$-0.239858\pi$
$272$	24.3063	−	12.2338i	1.47379	−	0.741786i
$273$	−42.5595			−2.57582
$274$	14.0175	−	7.82744i	0.846826	−	0.472873i
$275$	5.24984	−	6.55228i	0.316577	−	0.395117i
$276$	16.8278	−	3.99606i	1.01291	−	0.240534i
$277$	11.4879	+	11.4879i	0.690243	+	0.690243i	0.962285	−	0.272042i	$-0.0876990\pi$
$277$	11.4879	+	11.4879i	0.690243	+	0.690243i	−0.272042	+	0.962285i	$0.587699\pi$
$278$	−13.6214	−	24.3934i	−0.816960	−	1.46302i
$279$			9.35009i			0.559775i
$280$	16.7698	−	17.1766i	1.00219	−	1.02650i
$281$	7.43982	+	7.43982i	0.443822	+	0.443822i	0.893294	−	0.449472i	$-0.148388\pi$
$281$	7.43982	+	7.43982i	0.443822	+	0.443822i	−0.449472	+	0.893294i	$0.648388\pi$
$282$	−10.2173	−	18.2972i	−0.608430	−	1.08958i
$283$	2.86216	+	2.86216i	0.170138	+	0.170138i	0.787040	−	0.616902i	$-0.211613\pi$
$283$	2.86216	+	2.86216i	0.170138	+	0.170138i	−0.616902	+	0.787040i	$0.711613\pi$
$284$	12.5800	−	2.98735i	0.746486	−	0.177267i
$285$	0.199907	+	3.63393i	0.0118415	+	0.215255i
$286$	−12.0113	−	3.40355i	−0.710243	−	0.201256i
$287$	23.5290	−	6.08705i	1.38887	−	0.359307i
$288$	−4.91417	+	7.25718i	−0.289570	+	0.427633i
$289$	−29.2791			−1.72230
$290$	2.38787	−	1.51118i	0.140220	−	0.0887396i
$291$		−	29.1443i		−	1.70847i
$292$	−7.79372	+	1.85076i	−0.456093	+	0.108308i
$293$	17.6019			1.02831			0.514156	−	0.857697i	$-0.328105\pi$
$293$	17.6019			1.02831			0.514156	+	0.857697i	$0.328105\pi$
$294$	10.8923	+	19.5060i	0.635249	+	1.13761i
$295$	−5.53034	−	4.95361i	−0.321989	−	0.288410i
$296$	17.7499	+	19.3451i	1.03169	+	1.12441i
$297$	3.67388	+	3.67388i	0.213180	+	0.213180i
$298$	21.9421	+	6.21758i	1.27107	+	0.360175i
$299$	15.0717	−	15.0717i	0.871617	−	0.871617i
$300$	−19.2764	−	9.13002i	−1.11292	−	0.527122i
$301$	26.1460	+	26.1460i	1.50703	+	1.50703i
$302$	−3.67037	+	12.9529i	−0.211206	+	0.745355i
$303$	25.2632	+	25.2632i	1.45133	+	1.45133i
$304$	−0.957552	+	2.89825i	−0.0549194	+	0.166226i
$305$	13.4312	−	14.9949i	0.769067	−	0.858608i
$306$	13.0143	−	7.26726i	0.743978	−	0.415442i
$307$	−3.91273	−	3.91273i	−0.223312	−	0.223312i	0.586580	−	0.809891i	$-0.300474\pi$
$307$	−3.91273	−	3.91273i	−0.223312	−	0.223312i	−0.809891	+	0.586580i	$0.800474\pi$
$308$	2.94514	+	12.4023i	0.167815	+	0.706684i
$309$	13.3825	−	13.3825i	0.761305	−	0.761305i
$310$	−18.6190	−	4.18641i	−1.05749	−	0.237772i
$311$	−3.91988	+	3.91988i	−0.222276	+	0.222276i	−0.809456	−	0.587180i	$-0.800238\pi$
$311$	−3.91988	+	3.91988i	−0.222276	+	0.222276i	0.587180	+	0.809456i	$0.300238\pi$
$312$	−1.36251	+	31.6855i	−0.0771368	+	1.79384i
$313$	19.0627			1.07749			0.538743	−	0.842470i	$-0.318899\pi$
$313$	19.0627			1.07749			0.538743	+	0.842470i	$0.318899\pi$
$314$	−1.92361	−	3.44483i	−0.108556	−	0.194403i
$315$	8.77345	−	9.79492i	0.494328	−	0.551881i
$316$	−2.10292	−	8.85558i	−0.118298	−	0.498165i
$317$	4.78035			0.268491			0.134246	−	0.990948i	$-0.457139\pi$
$317$	4.78035			0.268491			0.134246	+	0.990948i	$0.457139\pi$
$318$	3.40982	−	1.90406i	0.191213	−	0.106774i
$319$			1.50057i			0.0840159i
$320$	−12.2511	−	13.0350i	−0.684855	−	0.728679i
$321$	24.0851	−	24.0851i	1.34430	−	1.34430i
$322$	−20.9391	−	5.93335i	−1.16689	−	0.330653i
$323$	3.67071	−	3.67071i	0.204244	−	0.204244i
$324$	11.8010	−	19.1512i	0.655611	−	1.06395i
$325$	−26.1267	+	2.88324i	−1.44925	+	0.159934i
$326$	0.738679	−	2.60683i	0.0409117	−	0.144379i
$327$	14.1868	−	14.1868i	0.784530	−	0.784530i
$328$	−3.77854	−	17.7122i	−0.208635	−	0.977994i
$329$			26.3701i			1.45383i
$330$	9.57052	−	6.05677i	0.526840	−	0.333414i
$331$	0.127120	+	0.127120i	0.00698714	+	0.00698714i	0.710592	−	0.703605i	$-0.248427\pi$
$331$	0.127120	+	0.127120i	0.00698714	+	0.00698714i	−0.703605	+	0.710592i	$0.748427\pi$
$332$	−10.7538	+	2.55368i	−0.590190	+	0.140151i
$333$	10.1693	+	10.1693i	0.557275	+	0.557275i
$334$	−8.43977	+	4.71282i	−0.461804	+	0.257874i
$335$	23.1539	+	20.7393i	1.26503	+	1.13311i
$336$	28.9256	−	14.5588i	1.57802	−	0.794247i
$337$	1.53712	−	1.53712i	0.0837321	−	0.0837321i	−0.664000	−	0.747732i	$-0.731143\pi$
$337$	1.53712	−	1.53712i	0.0837321	−	0.0837321i	0.747732	+	0.664000i	$0.231143\pi$
$338$	10.0918	+	18.0725i	0.548921	+	0.983015i
$339$	−16.6831	+	16.6831i	−0.906101	+	0.906101i
$340$	8.64439	+	29.1694i	0.468808	+	1.58193i
$341$	7.16562	−	7.16562i	0.388040	−	0.388040i
$342$	−0.455837	+	1.60867i	−0.0246489	+	0.0869869i
$343$		−	1.54301i		−	0.0833149i
$344$	20.3027	−	18.6286i	1.09465	−	1.00439i
$345$	1.06216	+	19.3080i	0.0571846	+	1.03951i
$346$	−6.56586	+	23.1712i	−0.352983	+	1.24569i
$347$	4.28660			0.230117			0.115058	−	0.993359i	$-0.463294\pi$
$347$	4.28660			0.230117			0.115058	+	0.993359i	$0.463294\pi$
$348$	3.70890	−	0.880747i	0.198818	−	0.0472130i
$349$	26.6440			1.42622			0.713110	−	0.701053i	$-0.247286\pi$
$349$	26.6440			1.42622			0.713110	+	0.701053i	$0.247286\pi$
$350$	15.5765	+	21.8563i	0.832602	+	1.16827i
$351$		−	16.2659i		−	0.868212i
$352$	9.32776	−	1.79561i	0.497171	−	0.0957062i
$353$	23.7186	−	23.7186i	1.26241	−	1.26241i	0.312494	−	0.949920i	$-0.398836\pi$
$353$	23.7186	−	23.7186i	1.26241	−	1.26241i	0.949920	−	0.312494i	$-0.101164\pi$
$354$	−4.88297	−	8.74448i	−0.259527	−	0.464764i
$355$	0.794042	+	14.4342i	0.0421434	+	0.766087i
$356$	4.84658	−	1.15091i	0.256868	−	0.0609981i
$357$	−55.0740			−2.91483
$358$	−1.29029	+	4.55348i	−0.0681938	+	0.240659i
$359$	24.6134			1.29905			0.649523	−	0.760342i	$-0.274969\pi$
$359$	24.6134			1.29905			0.649523	+	0.760342i	$0.274969\pi$
$360$	−7.01143	−	6.84540i	−0.369535	−	0.360784i
$361$		−	18.4177i		−	0.969353i
$362$	−3.16682	+	11.1758i	−0.166444	+	0.587389i
$363$		−	17.4479i		−	0.915776i
$364$	20.9355	−	33.9749i	1.09732	−	1.78077i
$365$	−0.491934	−	8.94244i	−0.0257490	−	0.468069i
$366$	23.7097	−	13.2397i	1.23933	−	0.692048i
$367$	13.9218	+	13.9218i	0.726714	+	0.726714i	0.969964	−	0.243250i	$-0.0782134\pi$
$367$	13.9218	+	13.9218i	0.726714	+	0.726714i	−0.243250	+	0.969964i	$0.578213\pi$
$368$	−5.08772	+	15.3992i	−0.265216	+	0.802737i
$369$	−2.48472	−	9.60450i	−0.129349	−	0.499990i
$370$	−24.8035	+	15.6971i	−1.28947	+	0.816053i
$371$	−4.91425			−0.255135
$372$	−21.9168	−	13.5052i	−1.13633	−	0.700212i
$373$	14.5185	−	14.5185i	0.751741	−	0.751741i	−0.223063	−	0.974804i	$-0.571606\pi$
$373$	14.5185	−	14.5185i	0.751741	−	0.751741i	0.974804	+	0.223063i	$0.0716056\pi$
$374$	−15.5432	−	4.40436i	−0.803718	−	0.227744i
$375$	13.8661	−	19.4010i	0.716043	−	1.00186i
$376$	19.6325	+	0.844217i	1.01247	+	0.0435372i
$377$	3.32185	−	3.32185i	0.171084	−	0.171084i
$378$	−14.5009	+	8.09739i	−0.745846	+	0.416485i
$379$	15.5630			0.799419			0.399709	−	0.916642i	$-0.369111\pi$
$379$	15.5630			0.799419			0.399709	+	0.916642i	$0.369111\pi$
$380$	−2.99927	−	1.62798i	−0.153860	−	0.0835138i
$381$	−24.9806	+	24.9806i	−1.27979	+	1.27979i
$382$	19.2150	+	5.44482i	0.983126	+	0.278581i
$383$		−	0.130134i		−	0.00664953i	−0.999994	−	0.00332476i	$-0.998942\pi$
$383$		−	0.130134i		−	0.00664953i	0.999994	−	0.00332476i	$-0.00105831\pi$
$384$	−9.91298	−	22.0011i	−0.505869	−	1.12274i
$385$	−14.2302	+	0.782823i	−0.725240	+	0.0398963i
$386$	−6.10060	+	3.40661i	−0.310512	+	0.173392i
$387$	10.6727	−	10.6727i	0.542525	−	0.542525i
$388$	23.2657	+	14.3364i	1.18113	+	0.727819i
$389$	−10.7898			−0.547064			−0.273532	−	0.961863i	$-0.588192\pi$
$389$	−10.7898			−0.547064			−0.273532	+	0.961863i	$0.588192\pi$
$390$	−34.5945	−	7.77846i	−1.75176	−	0.393878i
$391$	19.5034	−	19.5034i	0.986331	−	0.986331i
$392$	−20.9295	−	0.899988i	−1.05710	−	0.0454563i
$393$	0.626215			0.0315884
$394$	−5.18470	−	1.46915i	−0.261202	−	0.0740148i
$395$	10.1608	−	0.558959i	0.511246	−	0.0281243i
$396$	5.06257	−	1.20220i	0.254404	−	0.0604128i
$397$	−2.29560			−0.115213			−0.0576065	−	0.998339i	$-0.518347\pi$
$397$	−2.29560			−0.115213			−0.0576065	+	0.998339i	$0.518347\pi$
$398$	2.17093	−	7.66132i	0.108819	−	0.384027i
$399$	4.36830	−	4.36830i	0.218689	−	0.218689i
$400$	16.7707	−	10.8970i	0.838533	−	0.544851i
$401$		−	7.05550i		−	0.352335i	−0.984360	−	0.176167i	$-0.943630\pi$
$401$		−	7.05550i		−	0.352335i	0.984360	−	0.176167i	$-0.0563700\pi$
$402$	20.4436	+	36.6106i	1.01963	+	1.82597i
$403$	−31.7255			−1.58036
$404$	−32.5946	+	7.74019i	−1.62164	+	0.385089i
$405$	18.7340	+	16.7803i	0.930898	+	0.833818i
$406$	−4.61505	−	1.30773i	−0.229041	−	0.0649018i
$407$		−	15.5869i		−	0.772614i
$408$	−1.76315	+	41.0026i	−0.0872889	+	2.02993i
$409$			20.3305i			1.00528i	0.864497	+	0.502639i	$0.167637\pi$
$409$			20.3305i			1.00528i	−0.864497	+	0.502639i	$0.832363\pi$
$410$	20.2381	−	0.647540i	0.999489	−	0.0319797i
$411$			24.2140i			1.19439i
$412$	4.10016	+	17.2662i	0.202001	+	0.850642i
$413$			12.6026i			0.620134i
$414$	−2.42198	+	8.54728i	−0.119034	+	0.420076i
$415$	−0.678772	−	12.3388i	−0.0333196	−	0.605687i
$416$	−24.6241	−	16.6741i	−1.20729	−	0.817516i
$417$	42.1376			2.06349
$418$	1.58218	−	0.883496i	0.0773868	−	0.0432132i
$419$			40.2294i			1.96534i	0.185374	+	0.982668i	$0.440650\pi$
$419$			40.2294i			1.96534i	−0.185374	+	0.982668i	$0.559350\pi$
$420$	10.2872	+	34.7128i	0.501963	+	1.69381i
$421$	−1.28823	+	1.28823i	−0.0627843	+	0.0627843i	−0.737802	−	0.675017i	$-0.764136\pi$
$421$	−1.28823	+	1.28823i	−0.0627843	+	0.0627843i	0.675017	+	0.737802i	$0.264136\pi$
$422$	8.21395	+	2.32753i	0.399849	+	0.113302i
$423$	10.7642			0.523374
$424$	−0.157326	+	3.65866i	−0.00764041	+	0.177680i
$425$	−33.8091	+	3.73105i	−1.63998	+	0.180983i
$426$	−5.31649	+	18.7621i	−0.257585	+	0.909028i
$427$	−34.1707			−1.65363
$428$	7.37924	+	31.0746i	0.356689	+	1.50205i
$429$	13.3139	−	13.3139i	0.642802	−	0.642802i
$430$	16.4742	+	26.0314i	0.794454	+	1.25534i
$431$	23.7048			1.14182			0.570909	−	0.821013i	$-0.306591\pi$
$431$	23.7048			1.14182			0.570909	+	0.821013i	$0.306591\pi$
$432$	5.56426	+	11.0551i	0.267711	+	0.531890i
$433$	−0.0608646	+	0.0608646i	−0.00292496	+	0.00292496i	−0.708568	−	0.705643i	$-0.750658\pi$
$433$	−0.0608646	+	0.0608646i	−0.00292496	+	0.00292496i	0.705643	+	0.708568i	$0.250658\pi$
$434$	15.7933	+	28.2829i	0.758104	+	1.35762i
$435$	0.234104	+	4.25556i	0.0112244	+	0.204039i
$436$	4.34657	+	18.3038i	0.208163	+	0.876593i
$437$			3.09390i			0.148001i
$438$	3.29373	−	11.6237i	0.157381	−	0.555404i
$439$	−16.1547	+	16.1547i	−0.771022	+	0.771022i	−0.978285	−	0.207263i	$-0.933544\pi$
$439$	−16.1547	+	16.1547i	−0.771022	+	0.771022i	0.207263	+	0.978285i	$0.433544\pi$
$440$	0.127241	+	10.6195i	0.00606600	+	0.506263i
$441$	−11.4753			−0.546444
$442$	24.6583	+	44.1584i	1.17288	+	2.10040i
$443$	11.2601	−	11.2601i	0.534984	−	0.534984i	−0.387067	−	0.922051i	$-0.626512\pi$
$443$	11.2601	−	11.2601i	0.534984	−	0.534984i	0.922051	+	0.387067i	$0.126512\pi$
$444$	−38.5255	+	9.14859i	−1.82834	+	0.434173i
$445$	0.305913	+	5.56092i	0.0145017	+	0.263613i
$446$	5.85814	−	20.6736i	0.277391	−	0.978925i
$447$	−24.3217	+	24.3217i	−1.15038	+	1.15038i
$448$	−2.60661	+	30.2527i	−0.123151	+	1.42930i
$449$	36.0289			1.70031			0.850155	−	0.526533i	$-0.176508\pi$
$449$	36.0289			1.70031			0.850155	+	0.526533i	$0.176508\pi$
$450$	8.92169	−	6.35831i	0.420572	−	0.299734i
$451$	−5.45638	+	9.26481i	−0.256931	+	0.436263i
$452$	−5.11140	−	21.5246i	−0.240420	−	1.01243i
$453$	−14.3576	−	14.3576i	−0.674580	−	0.674580i
$454$	−2.76196	−	4.94616i	−0.129625	−	0.232135i
$455$	33.2348	+	29.7689i	1.55807	+	1.39559i
$456$	−3.11235	−	3.39204i	−0.145749	−	0.158847i
$457$			19.8177i			0.927032i	0.886088	+	0.463516i	$0.153412\pi$
$457$			19.8177i			0.927032i	−0.886088	+	0.463516i	$0.846588\pi$
$458$	−29.4223	−	8.33717i	−1.37481	−	0.389571i
$459$		−	21.0489i		−	0.982478i
$460$	−15.9359	−	8.64989i	−0.743016	−	0.403303i
$461$	5.78625			0.269492			0.134746	−	0.990880i	$-0.456978\pi$
$461$	5.78625			0.269492			0.134746	+	0.990880i	$0.456978\pi$
$462$	−18.4970	−	5.24137i	−0.860559	−	0.243850i
$463$	−13.6863			−0.636056			−0.318028	−	0.948081i	$-0.603021\pi$
$463$	−13.6863			−0.636056			−0.318028	+	0.948081i	$0.603021\pi$
$464$	−1.12135	+	3.39404i	−0.0520576	+	0.157564i
$465$	19.2035	−	21.4393i	0.890542	−	0.994225i
$466$	15.7047	−	8.76962i	0.727508	−	0.406245i
$467$	29.2702	−	29.2702i	1.35446	−	1.35446i	0.473862	−	0.880599i	$-0.342860\pi$
$467$	29.2702	−	29.2702i	1.35446	−	1.35446i	0.880599	−	0.473862i	$-0.157140\pi$
$468$	−13.8685	−	8.54581i	−0.641071	−	0.395030i
$469$		−	52.7635i		−	2.43639i
$470$	−4.81957	+	21.4350i	−0.222310	+	0.988721i
$471$	5.95064			0.274191
$472$	9.38264	+	0.403462i	0.431871	+	0.0185709i
$473$	−16.3585			−0.752165
$474$	13.2074	+	3.74249i	0.606637	+	0.171898i
$475$	2.38570	−	2.97757i	0.109463	−	0.136620i
$476$	27.0915	−	43.9652i	1.24174	−	2.01514i
$477$			2.00599i			0.0918478i
$478$	6.43413	+	1.82319i	0.294290	+	0.0833909i
$479$	19.0585	−	19.0585i	0.870806	−	0.870806i	−0.121754	−	0.992560i	$-0.538852\pi$
$479$	19.0585	−	19.0585i	0.870806	−	0.870806i	0.992560	+	0.121754i	$0.0388519\pi$
$480$	26.1730	−	6.54749i	1.19463	−	0.298851i
$481$	−34.5051	+	34.5051i	−1.57330	+	1.57330i
$482$	−15.6089	+	8.71610i	−0.710966	+	0.397008i
$483$	23.2099	−	23.2099i	1.05609	−	1.05609i
$484$	13.9285	+	8.58279i	0.633114	+	0.390127i
$485$	−20.3854	+	22.7588i	−0.925653	+	1.03342i
$486$	10.1409	+	18.1604i	0.460001	+	0.823774i
$487$	−1.43115	−	1.43115i	−0.0648517	−	0.0648517i	0.673937	−	0.738789i	$-0.264602\pi$
$487$	−1.43115	−	1.43115i	−0.0648517	−	0.0648517i	−0.738789	+	0.673937i	$0.764602\pi$
$488$	−1.09395	+	25.4400i	−0.0495206	+	1.15162i
$489$	2.88954	+	2.88954i	0.130670	+	0.130670i
$490$	5.13797	−	22.8510i	0.232110	−	1.03230i
$491$		−	8.72193i		−	0.393615i	−0.980442	−	0.196808i	$-0.936943\pi$
$491$		−	8.72193i		−	0.393615i	0.980442	−	0.196808i	$-0.0630575\pi$
$492$	26.1020	+	8.04843i	1.17677	+	0.362851i
$493$	4.29863	−	4.29863i	0.193601	−	0.193601i
$494$	−5.45832	−	1.54669i	−0.245582	−	0.0695887i
$495$	0.319546	+	5.80875i	0.0143625	+	0.261084i
$496$	21.5622	−	10.8527i	0.968171	−	0.487299i
$497$	17.3511	−	17.3511i	0.778305	−	0.778305i
$498$	4.54470	−	16.0384i	0.203653	−	0.718700i
$499$	−9.64801	+	9.64801i	−0.431904	+	0.431904i	−0.889276	−	0.457371i	$-0.848791\pi$
$499$	−9.64801	+	9.64801i	−0.431904	+	0.431904i	0.457371	+	0.889276i	$0.348791\pi$
$500$	8.66681	+	20.6128i	0.387591	+	0.921831i
$501$		−	14.5790i		−	0.651341i
$502$	15.0180	+	26.8944i	0.670286	+	1.20036i
$503$	−15.3459			−0.684238			−0.342119	−	0.939657i	$-0.611145\pi$
$503$	−15.3459			−0.684238			−0.342119	+	0.939657i	$0.611145\pi$
$504$	−0.714582	+	16.6178i	−0.0318300	+	0.740216i
$505$	−2.05735	−	37.3988i	−0.0915510	−	1.66422i
$506$	8.40651	−	4.69424i	0.373715	−	0.208685i
$507$	−31.2187			−1.38647
$508$	−7.65360	−	32.2300i	−0.339574	−	1.42997i
$509$	−0.483014	+	0.483014i	−0.0214092	+	0.0214092i	−0.717730	−	0.696321i	$-0.754819\pi$
$509$	−0.483014	+	0.483014i	−0.0214092	+	0.0214092i	0.696321	+	0.717730i	$0.254819\pi$
$510$	−44.7669	−	10.0657i	−1.98231	−	0.445716i
$511$	−10.7496	+	10.7496i	−0.475534	+	0.475534i
$512$	22.4396	+	2.90913i	0.991701	+	0.128567i
$513$	1.66953	+	1.66953i	0.0737116	+	0.0737116i
$514$	10.2156	+	18.2942i	0.450591	+	0.806924i
$515$	−19.8110	+	1.08983i	−0.872978	+	0.0480236i
$516$	9.60147	+	40.4327i	0.422681	+	1.77995i
$517$	−8.24937	−	8.24937i	−0.362807	−	0.362807i
$518$	47.9380	+	13.5838i	2.10628	+	0.596840i
$519$	−25.6841	−	25.6841i	−1.12741	−	1.12741i
$520$	23.2269	−	23.7902i	1.01857	−	1.04327i
$521$	−4.92026	+	4.92026i	−0.215561	+	0.215561i	−0.806625	−	0.591064i	$-0.798708\pi$
$521$	−4.92026	+	4.92026i	−0.215561	+	0.215561i	0.591064	+	0.806625i	$0.298708\pi$
$522$	−0.533814	+	1.88385i	−0.0233644	+	0.0824540i
$523$	−22.2043	−	22.2043i	−0.970927	−	0.970927i	0.0286619	−	0.999589i	$-0.490875\pi$
$523$	−22.2043	−	22.2043i	−0.970927	−	0.970927i	−0.999589	+	0.0286619i	$0.990875\pi$
$524$	−0.308041	+	0.499902i	−0.0134568	+	0.0218383i
$525$	−40.2342	+	4.44011i	−1.75597	+	0.193782i
$526$	−1.88180	+	1.05081i	−0.0820502	+	0.0458173i
$527$	−41.0542			−1.78835
$528$	−4.49436	+	13.6032i	−0.195592	+	0.592004i
$529$		−	6.56130i		−	0.285274i
$530$	−3.99455	−	0.898161i	−0.173512	−	0.0390136i
$531$	5.14436			0.223246
$532$	1.33837	+	5.63599i	0.0580256	+	0.244351i
$533$	32.5887	−	8.43082i	1.41157	−	0.365179i
$534$	−2.04823	+	7.22831i	−0.0886357	+	0.312799i
$535$	−35.6548	+	1.96141i	−1.54149	+	0.0847992i
$536$	−39.2824	−	1.68918i	−1.69674	−	0.0729614i
$537$	−5.04730	−	5.04730i	−0.217807	−	0.217807i
$538$	40.2725	−	22.4884i	1.73627	−	0.969544i
$539$	8.79434	+	8.79434i	0.378799	+	0.378799i
$540$	−13.2670	+	3.93168i	−0.570921	+	0.169193i
$541$			16.2492i			0.698607i	0.937010	+	0.349303i	$0.113582\pi$
$541$			16.2492i			0.698607i	−0.937010	+	0.349303i	$0.886418\pi$
$542$	−27.8157	+	15.5324i	−1.19479	+	0.667175i
$543$	−12.3879	−	12.3879i	−0.531614	−	0.531614i
$544$	−31.8647	−	21.5771i	−1.36619	−	0.925110i
$545$	−21.0016	+	1.15532i	−0.899610	+	0.0494886i
$546$	29.3444	+	52.5503i	1.25582	+	2.24894i
$547$	23.9813			1.02537			0.512684	−	0.858578i	$-0.328651\pi$
$547$	23.9813			1.02537			0.512684	+	0.858578i	$0.328651\pi$
$548$	−19.3298	−	11.9111i	−0.825729	−	0.508817i
$549$			13.9484i			0.595302i
$550$	−11.7101	−	1.96449i	−0.499322	−	0.0837663i
$551$			0.681909i			0.0290503i
$552$	−16.5367	−	18.0228i	−0.703849	−	0.767101i
$553$	−12.2142	−	12.2142i	−0.519400	−	0.519400i
$554$	6.26388	−	22.1055i	0.266127	−	0.939174i
$555$	−2.43171	−	44.2038i	−0.103220	−	1.87635i
$556$	−20.7279	+	33.6381i	−0.879059	+	1.42657i
$557$			0.333252i			0.0141203i	0.999975	+	0.00706017i	$0.00224734\pi$
$557$			0.333252i			0.0141203i	−0.999975	+	0.00706017i	$0.997753\pi$
$558$	11.5450	−	6.44680i	0.488739	−	0.272915i
$559$	36.2132	+	36.2132i	1.53166	+	1.53166i
$560$	−32.7714	−	8.86342i	−1.38484	−	0.374548i
$561$	17.2288	−	17.2288i	0.727401	−	0.727401i
$562$	4.05662	−	14.3160i	0.171118	−	0.603883i
$563$	2.33241			0.0982992			0.0491496	−	0.998791i	$-0.484349\pi$
$563$	2.33241			0.0982992			0.0491496	+	0.998791i	$0.484349\pi$
$564$	−15.5477	+	25.2315i	−0.654678	+	1.06244i
$565$	24.6971	−	1.35862i	1.03901	−	0.0571574i
$566$	1.56061	−	5.50748i	0.0655975	−	0.231497i
$567$		−	42.6912i		−	1.79286i
$568$	−12.3624	−	13.4734i	−0.518716	−	0.565331i
$569$	14.2563			0.597655			0.298827	−	0.954307i	$-0.403405\pi$
$569$	14.2563			0.597655			0.298827	+	0.954307i	$0.403405\pi$
$570$	4.34915	−	2.75240i	0.182166	−	0.115285i
$571$	5.51345	+	5.51345i	0.230731	+	0.230731i	0.812998	−	0.582267i	$-0.197834\pi$
$571$	5.51345	+	5.51345i	0.230731	+	0.230731i	−0.582267	+	0.812998i	$0.697834\pi$
$572$	4.07914	+	17.1776i	0.170558	+	0.718233i
$573$	−21.2989	+	21.2989i	−0.889773	+	0.889773i
$574$	−23.7390	−	24.8555i	−0.990848	−	1.03745i
$575$	12.6758	−	15.8206i	0.528618	−	0.659764i
$576$	12.3491	+	1.06401i	0.514544	+	0.0443338i
$577$	24.6132			1.02466			0.512331	−	0.858788i	$-0.328782\pi$
$577$	24.6132			1.02466			0.512331	+	0.858788i	$0.328782\pi$
$578$	20.1876	+	36.1523i	0.839695	+	1.50374i
$579$		−	10.5383i		−	0.437955i
$580$	−3.51234	−	1.90647i	−0.145842	−	0.0791619i
$581$	−14.8323	+	14.8323i	−0.615347	+	0.615347i
$582$	−35.9859	+	20.0947i	−1.49166	+	0.832953i
$583$	1.53733	−	1.53733i	0.0636696	−	0.0636696i
$584$	7.65892	+	8.34720i	0.316928	+	0.345409i
$585$	12.1516	−	13.5664i	0.502406	−	0.560900i
$586$	−12.1363	−	21.7339i	−0.501347	−	0.897818i
$587$		−	19.7772i		−	0.816291i	−0.912917	−	0.408146i	$-0.866176\pi$
$587$		−	19.7772i		−	0.816291i	0.912917	−	0.408146i	$-0.133824\pi$
$588$	16.5749	−	26.8984i	0.683536	−	1.10927i
$589$	3.25629	−	3.25629i	0.134173	−	0.134173i
$590$	−2.30334	+	10.2440i	−0.0948269	+	0.421741i
$591$	5.74698	−	5.74698i	0.236399	−	0.236399i
$592$	11.6479	−	35.2549i	0.478724	−	1.44897i
$593$	4.91495			0.201833			0.100916	−	0.994895i	$-0.467823\pi$
$593$	4.91495			0.201833			0.100916	+	0.994895i	$0.467823\pi$
$594$	2.00321	−	7.06943i	0.0821928	−	0.290062i
$595$	43.0074	+	38.5223i	1.76313	+	1.57926i
$596$	−7.45174	−	31.3799i	−0.305235	−	1.28537i
$597$	8.49219	+	8.49219i	0.347562	+	0.347562i
$598$	−29.0015	−	8.21793i	−1.18596	−	0.336056i
$599$	1.03660			0.0423544			0.0211772	−	0.999776i	$-0.493259\pi$
$599$	1.03660			0.0423544			0.0211772	+	0.999776i	$0.493259\pi$
$600$	2.01759	+	30.0965i	0.0823677	+	1.22868i
$601$	−6.81030	−	6.81030i	−0.277798	−	0.277798i	0.554431	−	0.832229i	$-0.312936\pi$
$601$	−6.81030	−	6.81030i	−0.277798	−	0.277798i	−0.832229	+	0.554431i	$0.812936\pi$
$602$	14.2563	−	50.3111i	0.581043	−	2.05053i
$603$	−21.5379			−0.877092
$604$	18.5242	−	4.39892i	0.753740	−	0.178989i
$605$	−12.2042	+	13.6251i	−0.496170	+	0.553938i
$606$	13.7749	−	48.6124i	0.559569	−	1.97474i
$607$	−28.1561	−	28.1561i	−1.14282	−	1.14282i	−0.987932	−	0.154890i	$-0.950498\pi$
$607$	−28.1561	−	28.1561i	−1.14282	−	1.14282i	−0.154890	−	0.987932i	$-0.549502\pi$
$608$	4.23884	−	0.815983i	0.171908	−	0.0330925i
$609$	5.11555	−	5.11555i	0.207293	−	0.207293i
$610$	−27.7756	−	6.24526i	−1.12460	−	0.252863i
$611$			36.5237i			1.47759i
$612$	−17.9465	−	11.0587i	−0.725443	−	0.447020i
$613$	17.5994	+	17.5994i	0.710831	+	0.710831i	0.966709	−	0.255878i	$-0.0823645\pi$
$613$	17.5994	+	17.5994i	0.710831	+	0.710831i	−0.255878	+	0.966709i	$0.582364\pi$
$614$	−2.13345	+	7.52903i	−0.0860989	+	0.303847i
$615$	−14.0287	+	27.1259i	−0.565691	+	1.09382i
$616$	13.2830	−	12.1877i	0.535188	−	0.491058i
$617$	26.7297	−	26.7297i	1.07610	−	1.07610i	0.0792413	−	0.996855i	$-0.474750\pi$
$617$	26.7297	−	26.7297i	1.07610	−	1.07610i	0.996855	−	0.0792413i	$-0.0252498\pi$
$618$	−25.7512	−	7.29692i	−1.03586	−	0.293525i
$619$	24.1522			0.970759			0.485380	−	0.874303i	$-0.338681\pi$
$619$	24.1522			0.970759			0.485380	+	0.874303i	$0.338681\pi$
$620$	7.66845	+	25.8762i	0.307972	+	1.03922i
$621$	8.87065	+	8.87065i	0.355967	+	0.355967i
$622$	7.54279	+	2.13735i	0.302438	+	0.0856998i
$623$	6.68471	−	6.68471i	0.267817	−	0.267817i
$624$	40.0631	−	20.1645i	1.60381	−	0.807227i
$625$	−24.3984	+	5.45143i	−0.975936	+	0.218057i
$626$	−13.1435	−	23.5376i	−0.525321	−	0.940752i
$627$			2.73307i			0.109148i
$628$	−2.92718	+	4.75035i	−0.116807	+	0.189560i
$629$	−44.6513	+	44.6513i	−1.78036	+	1.78036i
$630$	−18.1435	−	4.07949i	−0.722853	−	0.162531i
$631$			25.9194i			1.03183i	0.856638	+	0.515917i	$0.172549\pi$
$631$			25.9194i			1.03183i	−0.856638	+	0.515917i	$0.827451\pi$
$632$	−9.48447	+	8.70242i	−0.377272	+	0.346164i
$633$	−9.10475	+	9.10475i	−0.361881	+	0.361881i
$634$	−3.29601	−	5.90253i	−0.130901	−	0.234420i
$635$	36.9804	−	2.03434i	1.46752	−	0.0807302i
$636$	−4.70207	−	2.89743i	−0.186449	−	0.114891i
$637$		−	38.9365i		−	1.54272i
$638$	1.85283	−	1.03463i	0.0733541	−	0.0409614i
$639$	−7.08269	−	7.08269i	−0.280187	−	0.280187i
$640$	−7.64796	+	24.1145i	−0.302312	+	0.953209i
$641$	12.9169	+	12.9169i	0.510187	+	0.510187i	0.914584	−	0.404397i	$-0.132518\pi$
$641$	12.9169	+	12.9169i	0.510187	+	0.510187i	−0.404397	+	0.914584i	$0.632518\pi$
$642$	−46.3455	−	13.1326i	−1.82911	−	0.518301i
$643$	23.5362			0.928176			0.464088	−	0.885789i	$-0.346382\pi$
$643$	23.5362			0.928176			0.464088	+	0.885789i	$0.346382\pi$
$644$	7.11110	+	29.9455i	0.280216	+	1.18002i
$645$	−46.3921	+	2.55208i	−1.82669	+	0.100488i
$646$	−7.06333	−	2.00148i	−0.277903	−	0.0787473i
$647$	−5.54813	−	5.54813i	−0.218119	−	0.218119i	0.589586	−	0.807706i	$-0.299291\pi$
$647$	−5.54813	−	5.54813i	−0.218119	−	0.218119i	−0.807706	+	0.589586i	$0.799291\pi$
$648$	−31.7835	−	1.36672i	−1.24858	−	0.0536900i
$649$	−3.94248	−	3.94248i	−0.154756	−	0.154756i
$650$	21.5742	+	30.2719i	0.846208	+	1.18736i
$651$	−48.8562			−1.91483
$652$	−3.72809	+	0.885304i	−0.146003	+	0.0346712i
$653$		−	19.8841i		−	0.778126i	−0.921211	−	0.389063i	$-0.872799\pi$
$653$		−	19.8841i		−	0.778126i	0.921211	−	0.389063i	$-0.127201\pi$
$654$	−27.2987	−	7.73544i	−1.06746	−	0.302480i
$655$	−0.489012	−	0.438015i	−0.0191073	−	0.0171147i
$656$	−19.2649	+	16.8780i	−0.752166	+	0.658973i
$657$	4.38795	+	4.38795i	0.171190	+	0.171190i
$658$	32.5604	−	18.1819i	1.26934	−	0.708806i
$659$	−11.2904	+	11.2904i	−0.439813	+	0.439813i	−0.891949	−	0.452136i	$-0.850662\pi$
$659$	−11.2904	+	11.2904i	−0.439813	+	0.439813i	0.452136	+	0.891949i	$0.350662\pi$
$660$	−14.0774	−	7.64109i	−0.547961	−	0.297429i
$661$		−	7.08423i		−	0.275545i	−0.990464	−	0.137772i	$-0.956006\pi$
$661$		−	7.08423i		−	0.275545i	0.990464	−	0.137772i	$-0.0439942\pi$
$662$	0.0693131	−	0.244609i	0.00269393	−	0.00950700i
$663$	−76.2798			−2.96246
$664$	10.5678	+	11.5175i	0.410110	+	0.446965i
$665$	−6.46668	+	0.355740i	−0.250767	+	0.0137950i
$666$	5.54489	−	19.5682i	0.214860	−	0.758252i
$667$			3.62315i			0.140289i
$668$	11.6383	+	7.17155i	0.450299	+	0.277475i
$669$	22.9157	+	22.9157i	0.885971	+	0.885971i
$670$	9.64340	−	42.8888i	0.372557	−	1.65694i
$671$	10.6896	−	10.6896i	0.412668	−	0.412668i
$672$	−37.9203	−	25.6776i	−1.46281	−	0.990536i
$673$	20.1396			0.776325			0.388163	−	0.921591i	$-0.373110\pi$
$673$	20.1396			0.776325			0.388163	+	0.921591i	$0.373110\pi$
$674$	−2.95778	−	0.838124i	−0.113929	−	0.0322833i
$675$	−1.69698	−	15.3772i	−0.0653167	−	0.591870i
$676$	15.3568	−	24.9217i	0.590646	−	0.958525i
$677$	−17.7389	+	17.7389i	−0.681761	+	0.681761i	−0.960397	−	0.278636i	$-0.910118\pi$
$677$	−17.7389	+	17.7389i	−0.681761	+	0.681761i	0.278636	+	0.960397i	$0.410118\pi$
$678$	32.1023	+	9.09658i	1.23288	+	0.349352i
$679$	51.8631			1.99032
$680$	30.0567	−	30.7857i	1.15262	−	1.18058i
$681$	8.54406			0.327409
$682$	−13.7884	−	3.90711i	−0.527984	−	0.149611i
$683$			26.4254i			1.01114i	0.862786	+	0.505570i	$0.168718\pi$
$683$			26.4254i			1.01114i	−0.862786	+	0.505570i	$0.831282\pi$
$684$	2.30060	−	0.546319i	0.0879656	−	0.0208890i
$685$	16.9368	−	18.9087i	0.647123	−	0.722465i
$686$	−1.90523	+	1.06389i	−0.0727421	+	0.0406196i
$687$	32.6131	−	32.6131i	1.24427	−	1.24427i
$688$	−37.0001	−	12.2245i	−1.41062	−	0.466053i
$689$	−6.80644			−0.259305
$690$	23.1082	−	14.6242i	0.879713	−	0.556733i
$691$	−26.1406	+	26.1406i	−0.994434	+	0.994434i	−0.999985	−	0.00555091i	$-0.998233\pi$
$691$	−26.1406	+	26.1406i	−0.994434	+	0.994434i	0.00555091	+	0.999985i	$0.498233\pi$
$692$	33.1377	−	7.86915i	1.25971	−	0.299140i
$693$	6.98262	−	6.98262i	0.265248	−	0.265248i
$694$	−2.95557	−	5.29287i	−0.112192	−	0.200915i
$695$	−32.9053	−	29.4737i	−1.24817	−	1.11800i
$696$	−3.64475	−	3.97229i	−0.138154	−	0.150569i
$697$	42.1713	−	10.9099i	1.59735	−	0.413241i
$698$	−18.3708	−	32.8986i	−0.695344	−	1.24523i
$699$			27.1286i			1.02610i
$700$	16.2471	−	34.3028i	0.614084	−	1.29652i
$701$	10.0862			0.380949			0.190475	−	0.981692i	$-0.438997\pi$
$701$	10.0862			0.380949			0.190475	+	0.981692i	$0.438997\pi$
$702$	−20.0843	+	11.2152i	−0.758034	+	0.423291i
$703$		−	7.08320i		−	0.267148i
$704$	−8.64852	−	10.2794i	−0.325953	−	0.387419i
$705$	−24.6819	−	22.1079i	−0.929572	−	0.832631i
$706$	−45.6403	−	12.9327i	−1.71769	−	0.486730i
$707$	−44.9566	+	44.9566i	−1.69077	+	1.69077i
$708$	−7.43047	+	12.0585i	−0.279254	+	0.453185i
$709$	18.2745	+	18.2745i	0.686313	+	0.686313i	0.961415	−	0.275102i	$-0.0887116\pi$
$709$	18.2745	+	18.2745i	0.686313	+	0.686313i	−0.275102	+	0.961415i	$0.588712\pi$
$710$	17.2751	−	10.9327i	0.648323	−	0.410296i
$711$	−4.98580	+	4.98580i	−0.186982	+	0.186982i
$712$	−4.76276	−	5.19077i	−0.178492	−	0.194532i
$713$	17.3015	−	17.3015i	0.647947	−	0.647947i
$714$	37.9730	+	68.0025i	1.42110	+	2.54493i
$715$	−19.7095	+	1.08424i	−0.737092	+	0.0405483i
$716$	6.51204	−	1.54640i	0.243366	−	0.0577918i
$717$	−7.13191	+	7.13191i	−0.266346	+	0.266346i
$718$	−16.9707	−	30.3913i	−0.633341	−	1.13419i
$719$	−27.5925	−	27.5925i	−1.02903	−	1.02903i	−0.999566	−	0.0294593i	$-0.990621\pi$
$719$	−27.5925	−	27.5925i	−1.02903	−	1.02903i	−0.0294593	−	0.999566i	$-0.509379\pi$
$720$	−3.61803	+	13.3772i	−0.134836	+	0.498538i
$721$	23.8146	+	23.8146i	0.886901	+	0.886901i
$722$	−22.7412	+	12.6988i	−0.846341	+	0.472602i
$723$		−	26.9630i		−	1.00277i
$724$	15.9828	−	3.79542i	0.593997	−	0.141056i
$725$	2.79380	−	3.48692i	0.103759	−	0.129501i
$726$	−21.5437	+	12.0301i	−0.799563	+	0.446481i
$727$			44.9610i			1.66751i	0.552134	+	0.833756i	$0.313814\pi$
$727$			44.9610i			1.66751i	−0.552134	+	0.833756i	$0.686186\pi$
$728$	−56.3853	−	2.42462i	−2.08978	−	0.0898625i
$729$	2.37209			0.0878551
$730$	−10.7025	+	6.77314i	−0.396116	+	0.250685i
$731$	46.8616	+	46.8616i	1.73324	+	1.73324i
$732$	−32.6953	−	20.1469i	−1.20845	−	0.744652i
$733$	−9.18384	−	9.18384i	−0.339213	−	0.339213i	0.516858	−	0.856071i	$-0.327101\pi$
$733$	−9.18384	−	9.18384i	−0.339213	−	0.339213i	−0.856071	+	0.516858i	$0.827101\pi$
$734$	7.59099	−	26.7889i	0.280188	−	0.988798i
$735$	26.3124	+	23.5684i	0.970547	+	0.869333i
$736$	22.5220	−	4.33553i	0.830173	−	0.159810i
$737$	16.5060	+	16.5060i	0.608007	+	0.608007i
$738$	−10.1459	+	9.69021i	−0.373477	+	0.356702i
$739$	−2.64278			−0.0972161			−0.0486081	−	0.998818i	$-0.515479\pi$
$739$	−2.64278			−0.0972161			−0.0486081	+	0.998818i	$0.515479\pi$
$740$	36.4838	+	19.8031i	1.34117	+	0.727977i
$741$	6.05027	−	6.05027i	0.222262	−	0.222262i
$742$	3.38833	+	6.06786i	0.124390	+	0.222758i
$743$	−8.78535	+	8.78535i	−0.322303	+	0.322303i	−0.849650	−	0.527347i	$-0.823187\pi$
$743$	−8.78535	+	8.78535i	−0.322303	+	0.322303i	0.527347	+	0.849650i	$0.323187\pi$
$744$	−1.56409	+	36.3734i	−0.0573424	+	1.33351i
$745$	36.0050	−	1.98068i	1.31912	−	0.0725666i
$746$	−27.9371	−	7.91634i	−1.02285	−	0.289838i
$747$	6.05451	+	6.05451i	0.221523	+	0.221523i
$748$	5.27860	+	22.2287i	0.193005	+	0.812761i
$749$	42.8601	+	42.8601i	1.56607	+	1.56607i
$750$	−33.5159	−	3.74433i	−1.22383	−	0.136724i
$751$	−10.2291	−	10.2291i	−0.373265	−	0.373265i	0.495400	−	0.868665i	$-0.335022\pi$
$751$	−10.2291	−	10.2291i	−0.373265	−	0.373265i	−0.868665	+	0.495400i	$0.835022\pi$
$752$	−12.4940	−	24.8233i	−0.455611	−	0.905212i
$753$	−46.4578			−1.69302
$754$	−6.39204	−	1.81127i	−0.232784	−	0.0659624i
$755$	1.16924	+	21.2545i	0.0425529	+	0.773532i
$756$	19.9965	+	12.3219i	0.727264	+	0.448142i
$757$			27.8696i			1.01294i	0.862259	+	0.506468i	$0.169049\pi$
$757$			27.8696i			1.01294i	−0.862259	+	0.506468i	$0.830951\pi$
$758$	−10.7306	−	19.2164i	−0.389751	−	0.697972i
$759$			14.5215i			0.527098i
$760$	0.0578227	+	4.82583i	0.00209745	+	0.175051i
$761$	−43.6459			−1.58216			−0.791081	−	0.611712i	$-0.790481\pi$
$761$	−43.6459			−1.58216			−0.791081	+	0.611712i	$0.790481\pi$
$762$	48.0686	+	13.6208i	1.74134	+	0.493431i
$763$	25.2457	+	25.2457i	0.913957	+	0.913957i
$764$	−6.52559	−	27.4799i	−0.236088	−	0.994186i
$765$	15.7247	−	17.5555i	0.568528	−	0.634721i
$766$	−0.160682	+	0.0897260i	−0.00580569	+	0.00324193i
$767$			17.4551i			0.630269i
$768$	−20.3310	+	27.4096i	−0.733630	+	0.989059i
$769$		−	11.1493i		−	0.402053i	−0.979586	−	0.201027i	$-0.935572\pi$
$769$		−	11.1493i		−	0.402053i	0.979586	−	0.201027i	$-0.0644278\pi$
$770$	10.7782	+	17.0310i	0.388419	+	0.613755i
$771$	−31.6017			−1.13811
$772$	8.41261	+	5.18388i	0.302776	+	0.186572i
$773$	2.22633			0.0800755			0.0400378	−	0.999198i	$-0.487252\pi$
$773$	2.22633			0.0800755			0.0400378	+	0.999198i	$0.487252\pi$
$774$	−20.5369	−	5.81938i	−0.738182	−	0.209173i
$775$	−29.9921	+	3.30982i	−1.07735	+	0.118892i
$776$	1.66035	−	38.6120i	0.0596032	−	1.38609i
$777$	−53.1368	+	53.1368i	−1.90627	+	1.90627i
$778$	7.43946	+	13.3227i	0.266718	+	0.477641i
$779$	−2.47956	+	4.21023i	−0.0888394	+	0.150847i
$780$	14.2482	+	48.0787i	0.510166	+	1.72149i
$781$			10.8559i			0.388455i
$782$	−37.5293	−	10.6344i	−1.34204	−	0.380285i
$783$	1.95513	+	1.95513i	0.0698705	+	0.0698705i
$784$	13.3194	+	26.4632i	0.475694	+	0.945113i
$785$	−4.64686	−	4.16226i	−0.165854	−	0.148557i
$786$	−0.431769	−	0.773217i	−0.0154007	−	0.0275797i
$787$	20.8719	+	20.8719i	0.744004	+	0.744004i	0.973346	−	0.229342i	$-0.0736575\pi$
$787$	20.8719	+	20.8719i	0.744004	+	0.744004i	−0.229342	+	0.973346i	$0.573657\pi$
$788$	1.76077	+	7.41477i	0.0627249	+	0.264140i
$789$		−	3.25064i		−	0.115726i
$790$	−7.69596	−	12.1606i	−0.273810	−	0.432656i
$791$	−29.6880	−	29.6880i	−1.05559	−	1.05559i
$792$	−4.97501	−	5.42210i	−0.176779	−	0.192666i
$793$	−47.3278			−1.68066
$794$	1.58280	+	2.83449i	0.0561713	+	0.100592i
$795$	4.11996	−	4.59964i	0.146120	−	0.163132i
$796$	−10.9566	+	2.60185i	−0.388348	+	0.0922203i
$797$	−24.8010	−	24.8010i	−0.878498	−	0.878498i	0.114881	−	0.993379i	$-0.463351\pi$
$797$	−24.8010	−	24.8010i	−0.878498	−	0.878498i	−0.993379	+	0.114881i	$0.963351\pi$
$798$	−8.40565	−	2.38185i	−0.297557	−	0.0843165i
$799$			47.2633i			1.67206i
$800$	−25.0183	−	13.1942i	−0.884530	−	0.466484i
$801$	−2.72868	−	2.72868i	−0.0964133	−	0.0964133i
$802$	−8.71177	+	4.86470i	−0.307623	+	0.171779i
$803$		−	6.72559i		−	0.237341i
$804$	31.1092	−	50.4853i	1.09714	−	1.78048i
$805$	−34.3591	+	1.89014i	−1.21100	+	0.0666186i
$806$	21.8744	+	39.1729i	0.770493	+	1.37981i
$807$			69.5673i			2.44889i
$808$	32.0309	+	34.9094i	1.12684	+	1.22811i
$809$	−24.2246	−	24.2246i	−0.851691	−	0.851691i	0.138650	−	0.990341i	$-0.455724\pi$
$809$	−24.2246	−	24.2246i	−0.851691	−	0.851691i	−0.990341	+	0.138650i	$0.955724\pi$
$810$	7.80252	−	34.7016i	0.274153	−	1.21929i
$811$	−0.574172			−0.0201619			−0.0100810	−	0.999949i	$-0.503209\pi$
$811$	−0.574172			−0.0201619			−0.0100810	+	0.999949i	$0.503209\pi$
$812$	1.56731	+	6.60010i	0.0550019	+	0.231618i
$813$		−	48.0492i		−	1.68516i
$814$	−19.2459	+	10.7470i	−0.674568	+	0.376683i
$815$	−0.235315	−	4.27758i	−0.00824272	−	0.149837i
$816$	51.8435	−	26.0938i	1.81489	−	0.913467i
$817$	−7.43384			−0.260077
$818$	25.1030	−	14.0177i	0.877706	−	0.490116i
$819$	−30.9152			−1.08026
$820$	−14.7535	−	24.5425i	−0.515216	−	0.857061i
$821$	21.9550			0.766234			0.383117	−	0.923700i	$-0.374851\pi$
$821$	21.9550			0.766234			0.383117	+	0.923700i	$0.374851\pi$
$822$	29.8982	−	16.6953i	1.04282	−	0.582316i
$823$	19.3515			0.674550			0.337275	−	0.941406i	$-0.390495\pi$
$823$	19.3515			0.674550			0.337275	+	0.941406i	$0.390495\pi$
$824$	18.4923	−	16.9675i	0.644211	−	0.591092i
$825$	11.1975	−	13.9755i	0.389847	−	0.486564i
$826$	15.5611	−	8.68938i	0.541438	−	0.302342i
$827$			9.30624i			0.323610i	0.986823	+	0.161805i	$0.0517315\pi$
$827$			9.30624i			0.323610i	−0.986823	+	0.161805i	$0.948268\pi$
$828$	12.2237	−	2.90273i	0.424802	−	0.100877i
$829$	−10.3721			−0.360238			−0.180119	−	0.983645i	$-0.557648\pi$
$829$	−10.3721			−0.360238			−0.180119	+	0.983645i	$0.557648\pi$
$830$	−14.7673	+	9.34559i	−0.512580	+	0.324390i
$831$	24.5029	+	24.5029i	0.849995	+	0.849995i
$832$	−3.61026	+	41.9012i	−0.125163	+	1.45266i
$833$		−	50.3857i		−	1.74576i
$834$	−29.0535	−	52.0293i	−1.00604	−	1.80163i
$835$	−10.1975	+	11.3847i	−0.352898	+	0.393985i
$836$	−2.18179	−	1.34443i	−0.0754588	−	0.0464980i
$837$		−	18.6725i		−	0.645416i
$838$	49.6732	−	27.7378i	1.71593	−	0.958187i
$839$	−24.7870	−	24.7870i	−0.855743	−	0.855743i	0.135090	−	0.990833i	$-0.456867\pi$
$839$	−24.7870	−	24.7870i	−0.855743	−	0.855743i	−0.990833	+	0.135090i	$0.956867\pi$
$840$	35.7687	−	36.6362i	1.23414	−	1.26407i
$841$		−	28.2014i		−	0.972464i
$842$	2.47885	+	0.702415i	0.0854270	+	0.0242068i
$843$	15.8685	+	15.8685i	0.546542	+	0.546542i
$844$	−2.78953	−	11.7470i	−0.0960197	−	0.404347i
$845$	24.3787	+	21.8364i	0.838654	+	0.751194i
$846$	−7.42182	−	13.2911i	−0.255167	−	0.456957i
$847$	31.0490			1.06686
$848$	4.62599	−	2.32835i	0.158857	−	0.0799559i
$849$	6.10476	+	6.10476i	0.209515	+	0.209515i
$850$	27.9180	+	39.1732i	0.957579	+	1.34363i
$851$		−	37.6348i		−	1.29011i
$852$	26.8322	−	6.37179i	0.919255	−	0.218294i
$853$	23.2385	+	23.2385i	0.795672	+	0.795672i	0.982410	−	0.186738i	$-0.0597914\pi$
$853$	23.2385	+	23.2385i	0.795672	+	0.795672i	−0.186738	+	0.982410i	$0.559791\pi$
$854$	23.5603	+	42.1922i	0.806219	+	1.44379i
$855$	0.145212	+	2.63968i	0.00496615	+	0.0902753i
$856$	33.2814	−	30.5372i	1.13754	−	1.04374i
$857$	22.2672	+	22.2672i	0.760632	+	0.760632i	0.976437	−	0.215805i	$-0.0692374\pi$
$857$	22.2672	+	22.2672i	0.760632	+	0.760632i	−0.215805	+	0.976437i	$0.569237\pi$
$858$	−25.6191	−	7.25951i	−0.874623	−	0.247836i
$859$			46.8265i			1.59770i	0.601530	+	0.798851i	$0.294558\pi$
$859$			46.8265i			1.59770i	−0.601530	+	0.798851i	$0.705442\pi$
$860$	20.7834	−	38.2898i	0.708709	−	1.30567i
$861$	50.1856	−	12.9832i	1.71032	−	0.442466i
$862$	−16.3442	−	29.2694i	−0.556686	−	0.996921i
$863$	30.2514	−	30.2514i	1.02977	−	1.02977i	0.0302260	−	0.999543i	$-0.490377\pi$
$863$	30.2514	−	30.2514i	1.02977	−	1.02977i	0.999543	−	0.0302260i	$-0.00962271\pi$
$864$	9.81380	−	14.4929i	0.333872	−	0.493058i
$865$	2.09163	+	38.0219i	0.0711176	+	1.29278i
$866$	0.117118	+	0.0331869i	0.00397983	+	0.00112774i
$867$	−62.4499			−2.12091
$868$	24.0329	−	39.0016i	0.815729	−	1.32380i
$869$	7.64193			0.259235
$870$	5.09313	−	3.22323i	0.172673	−	0.109278i
$871$		−	73.0796i		−	2.47621i
$872$	19.6037	−	17.9872i	0.663864	−	0.609124i
$873$		−	21.1704i		−	0.716509i
$874$	3.82019	−	2.13322i	0.129220	−	0.0721571i
$875$	34.5247	+	24.6751i	1.16715	+	0.834172i
$876$	−16.6234	+	3.94753i	−0.561652	+	0.133375i
$877$	−9.68882	−	9.68882i	−0.327168	−	0.327168i	0.524341	−	0.851509i	$-0.324312\pi$
$877$	−9.68882	−	9.68882i	−0.327168	−	0.327168i	−0.851509	+	0.524341i	$0.824312\pi$
$878$	31.0855	+	8.80847i	1.04909	+	0.297272i
$879$	37.5434			1.26631
$880$	13.0246	−	7.47913i	0.439060	−	0.252121i
$881$			44.0125i			1.48282i	0.671054	+	0.741409i	$0.265842\pi$
$881$			44.0125i			1.48282i	−0.671054	+	0.741409i	$0.734158\pi$
$882$	7.91212	+	14.1691i	0.266415	+	0.477099i
$883$			52.2259i			1.75754i	0.477245	+	0.878770i	$0.341635\pi$
$883$			52.2259i			1.75754i	−0.477245	+	0.878770i	$0.658365\pi$
$884$	37.5228	−	60.8936i	1.26203	−	2.04807i
$885$	−11.7958	−	10.5657i	−0.396511	−	0.355161i
$886$	−21.6671	−	6.13966i	−0.727922	−	0.206266i
$887$	−49.4435			−1.66015			−0.830075	−	0.557652i	$-0.811702\pi$
$887$	−49.4435			−1.66015			−0.830075	+	0.557652i	$0.811702\pi$
$888$	37.8592	+	41.2615i	1.27047	+	1.38464i
$889$	−44.4536	−	44.4536i	−1.49093	−	1.49093i
$890$	6.65541	−	4.21193i	0.223090	−	0.141184i
$891$	13.3551	+	13.3551i	0.447413	+	0.447413i
$892$	−29.5659	+	7.02095i	−0.989938	+	0.235079i
$893$	−3.74878	−	3.74878i	−0.125448	−	0.125448i
$894$	46.8008	+	13.2616i	1.56525	+	0.443534i
$895$	0.411036	+	7.47185i	0.0137394	+	0.249757i
$896$	39.1516	−	17.6404i	1.30796	−	0.589325i
$897$	32.1467	−	32.1467i	1.07335	−	1.07335i
$898$	−24.8416	−	44.4866i	−0.828975	−	1.48454i
$899$	3.81332	−	3.81332i	0.127181	−	0.127181i
$900$	−14.0023	−	6.63204i	−0.466744	−	0.221068i
$901$	−8.80785			−0.293432
$902$	15.2018	+	0.349258i	0.506166	+	0.0116290i
$903$	55.7673	+	55.7673i	1.85582	+	1.85582i
$904$	−23.0532	+	21.1523i	−0.766736	+	0.703514i
$905$	1.00883	+	18.3386i	0.0335345	+	0.609594i
$906$	−7.82860	+	27.6275i	−0.260088	+	0.917862i
$907$	−23.0761	−	23.0761i	−0.766229	−	0.766229i	0.211212	−	0.977440i	$-0.432259\pi$
$907$	−23.0761	−	23.0761i	−0.766229	−	0.766229i	−0.977440	+	0.211212i	$0.932259\pi$
$908$	−4.20291	+	6.82066i	−0.139479	+	0.226352i
$909$	18.3512	+	18.3512i	0.608670	+	0.608670i
$910$	13.8420	−	61.5620i	0.458858	−	2.04076i
$911$	−33.1983			−1.09991			−0.549954	−	0.835195i	$-0.685355\pi$
$911$	−33.1983			−1.09991			−0.549954	+	0.835195i	$0.685355\pi$
$912$	−2.04238	+	6.18175i	−0.0676301	+	0.204698i
$913$		−	9.27998i		−	0.307123i
$914$	24.4699	−	13.6641i	0.809391	−	0.451969i
$915$	28.6477	−	31.9830i	0.947062	−	1.05733i
$916$	9.99207	+	42.0775i	0.330147	+	1.39028i
$917$			1.11437i			0.0367996i
$918$	−25.9901	+	14.5130i	−0.857800	+	0.479001i
$919$	−32.9114	−	32.9114i	−1.08565	−	1.08565i	−0.995971	−	0.0896774i	$-0.971416\pi$
$919$	−32.9114	−	32.9114i	−1.08565	−	1.08565i	−0.0896774	−	0.995971i	$-0.528584\pi$
$920$	0.307227	+	25.6409i	0.0101290	+	0.845354i
$921$	−8.34555	−	8.34555i	−0.274995	−	0.274995i
$922$	−3.98956	−	7.14456i	−0.131389	−	0.235293i
$923$	24.0320	−	24.0320i	0.791024	−	0.791024i
$924$	6.28176	+	26.4530i	0.206655	+	0.870241i
$925$	−29.0201	+	36.2197i	−0.954175	+	1.19090i
$926$	9.43657	+	16.8991i	0.310105	+	0.555340i
$927$	9.72105	−	9.72105i	0.319281	−	0.319281i
$928$	4.96394	−	0.955567i	0.162949	−	0.0313680i
$929$	9.80422	−	9.80422i	0.321666	−	0.321666i	−0.527740	−	0.849406i	$-0.676960\pi$
$929$	9.80422	−	9.80422i	0.321666	−	0.321666i	0.849406	+	0.527740i	$0.176960\pi$
$930$	−39.7128	−	8.92929i	−1.30223	−	0.292803i
$931$	3.99643	+	3.99643i	0.130978	+	0.130978i
$932$	−21.6565	−	13.3448i	−0.709383	−	0.437124i
$933$	−8.36080	+	8.36080i	−0.273720	+	0.273720i
$934$	−56.3228	−	15.9598i	−1.84294	−	0.522220i
$935$	−25.5050	+	1.40306i	−0.834101	+	0.0458849i
$936$	−0.989725	+	23.0163i	−0.0323502	+	0.752313i
$937$		−	32.1288i		−	1.04960i	−0.851225	−	0.524801i	$-0.824140\pi$
$937$		−	32.1288i		−	1.04960i	0.851225	−	0.524801i	$-0.175860\pi$
$938$	−65.1496	+	36.3799i	−2.12721	+	1.18785i
$939$	40.6592			1.32686
$940$	29.7898	−	8.82824i	0.971637	−	0.287945i
$941$		−	46.4869i		−	1.51543i	−0.652587	−	0.757714i	$-0.726316\pi$
$941$		−	46.4869i		−	1.51543i	0.652587	−	0.757714i	$-0.273684\pi$
$942$	−4.10291	−	7.34754i	−0.133680	−	0.239396i
$943$	−13.1745	+	22.3700i	−0.429022	+	0.728469i
$944$	−5.97106	−	11.8634i	−0.194342	−	0.386120i
$945$	−17.5209	+	19.5608i	−0.569956	+	0.636314i
$946$	11.2790	+	20.1986i	0.366713	+	0.656714i
$947$	−1.70879	+	1.70879i	−0.0555281	+	0.0555281i	−0.734326	−	0.678797i	$-0.762501\pi$
$947$	−1.70879	+	1.70879i	−0.0555281	+	0.0555281i	0.678797	+	0.734326i	$0.262501\pi$
$948$	−4.48536	−	18.8883i	−0.145678	−	0.613462i
$949$	−14.8886	+	14.8886i	−0.483305	+	0.483305i
$950$	−5.32146	−	0.892730i	−0.172651	−	0.0289640i
$951$	10.1961			0.330632
$952$	−72.9652	−	3.13757i	−2.36482	−	0.101689i
$953$	36.9507	−	36.9507i	1.19695	−	1.19695i	0.221878	−	0.975075i	$-0.428781\pi$
$953$	36.9507	−	36.9507i	1.19695	−	1.19695i	0.975075	−	0.221878i	$-0.0712185\pi$
$954$	2.47689	−	1.38311i	0.0801922	−	0.0447798i
$955$	31.5301	−	1.73451i	1.02029	−	0.0561275i
$956$	−2.18509	−	9.20161i	−0.0706709	−	0.297601i
$957$			3.20060i			0.103461i
$958$	−36.6732	−	10.3918i	−1.18486	−	0.335744i
$959$	−43.0895			−1.39143
$960$	−26.1305	−	27.8026i	−0.843360	−	0.897326i
$961$	−5.41926			−0.174815
$962$	66.3961	+	18.8142i	2.14070	+	0.606594i
$963$	17.4954	−	17.4954i	0.563781	−	0.563781i
$964$	21.5244	+	13.2634i	0.693254	+	0.427185i
$965$	−7.37114	+	8.22934i	−0.237285	+	0.264912i
$966$	−44.6614	−	12.6554i	−1.43696	−	0.407180i
$967$	−27.9108			−0.897550			−0.448775	−	0.893645i	$-0.648140\pi$
$967$	−27.9108			−0.897550			−0.448775	+	0.893645i	$0.648140\pi$
$968$	0.994008	−	23.1159i	0.0319486	−	0.742975i
$969$	7.82934	−	7.82934i	0.251515	−	0.251515i
$970$	42.1569	+	9.47884i	1.35358	+	0.304347i
$971$	17.5385	+	17.5385i	0.562838	+	0.562838i	0.930113	−	0.367274i	$-0.119709\pi$
$971$	17.5385	+	17.5385i	0.562838	+	0.562838i	−0.367274	+	0.930113i	$0.619709\pi$
$972$	15.4315	−	25.0429i	0.494966	−	0.803252i
$973$			74.9850i			2.40391i
$974$	−0.780346	+	2.75388i	−0.0250039	+	0.0882399i
$975$	−55.7261	+	6.14973i	−1.78466	+	0.196949i
$976$	32.1663	−	16.1899i	1.02962	−	0.518226i
$977$	−31.3371			−1.00256			−0.501282	−	0.865284i	$-0.667138\pi$
$977$	−31.3371			−1.00256			−0.501282	+	0.865284i	$0.667138\pi$
$978$	1.57554	−	5.56017i	0.0503803	−	0.177795i
$979$			4.18236i			0.133669i
$980$	−31.7578	+	9.41145i	−1.01447	+	0.300638i
$981$	10.3053	−	10.3053i	0.329021	−	0.329021i
$982$	−10.7694	+	6.01369i	−0.343665	+	0.191905i
$983$	2.62116	+	2.62116i	0.0836021	+	0.0836021i	0.747671	−	0.664069i	$-0.231172\pi$
$983$	2.62116	+	2.62116i	0.0836021	+	0.0836021i	−0.664069	+	0.747671i	$0.731172\pi$
$984$	−8.05933	−	37.7788i	−0.256922	−	1.20434i
$985$	−8.50764	+	0.468016i	−0.271076	+	0.0149122i
$986$	−8.27160	−	2.34386i	−0.263421	−	0.0746438i
$987$			56.2453i			1.79031i
$988$	1.85370	+	7.80608i	0.0589739	+	0.248344i
$989$	−39.4979			−1.25596
$990$	6.95202	−	4.39964i	0.220950	−	0.139830i
$991$	0.239446	+	0.239446i	0.00760624	+	0.00760624i	0.710900	−	0.703293i	$-0.248288\pi$
$991$	0.239446	+	0.239446i	0.00760624	+	0.00760624i	−0.703293	+	0.710900i	$0.748288\pi$
$992$	−28.2672	−	19.1411i	−0.897485	−	0.607729i
$993$	0.271137	+	0.271137i	0.00860427	+	0.00860427i
$994$	−33.3877	−	9.46084i	−1.05899	−	0.300079i
$995$	−0.691576	−	12.5715i	−0.0219244	−	0.398545i
$996$	−22.9370	+	5.44680i	−0.726786	+	0.172588i
$997$	−47.2742			−1.49719			−0.748594	−	0.663029i	$-0.769271\pi$
$997$	−47.2742			−1.49719			−0.748594	+	0.663029i	$0.769271\pi$
$998$	18.5651	+	5.26065i	0.587667	+	0.166523i
$999$	−20.3085	−	20.3085i	−0.642533	−	0.642533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.s.c.647.40	yes	240
4.3	odd	2	inner	820.2.s.c.647.102	yes	240
5.3	odd	4		820.2.j.c.483.19	✓	240
20.3	even	4		820.2.j.c.483.81	yes	240
41.9	even	4		820.2.j.c.747.81	yes	240
164.91	odd	4		820.2.j.c.747.19	yes	240
205.173	odd	4	inner	820.2.s.c.583.102	yes	240
820.583	even	4	inner	820.2.s.c.583.40	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.19	✓	240	5.3	odd	4
820.2.j.c.483.81	yes	240	20.3	even	4
820.2.j.c.747.19	yes	240	164.91	odd	4
820.2.j.c.747.81	yes	240	41.9	even	4
820.2.s.c.583.40	yes	240	820.583	even	4	inner
820.2.s.c.583.102	yes	240	205.173	odd	4	inner
820.2.s.c.647.40	yes	240	1.1	even	1	trivial
820.2.s.c.647.102	yes	240	4.3	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.689491 - 1.23475i) q^{2} +2.13292 q^{3} +(-1.04921 + 1.70269i) q^{4} +(-1.66560 - 1.49190i) q^{5} +(-1.47063 - 2.63362i) q^{6} +3.79559i q^{7} +(2.82582 + 0.121513i) q^{8} +1.54935 q^{9} +(-0.693708 + 3.08525i) q^{10} +(-1.18738 - 1.18738i) q^{11} +(-2.23787 + 3.63171i) q^{12} +5.25705i q^{13} +(4.68660 - 2.61703i) q^{14} +(-3.55260 - 3.18211i) q^{15} +(-1.79834 - 3.57295i) q^{16} +6.80287i q^{17} +(-1.06826 - 1.91306i) q^{18} +(-0.539583 - 0.539583i) q^{19} +(4.28781 - 1.27070i) q^{20} +8.09570i q^{21} +(-0.647426 + 2.28480i) q^{22} +(-2.86694 - 2.86694i) q^{23} +(6.02724 + 0.259177i) q^{24} +(0.548453 + 4.96983i) q^{25} +(6.49114 - 3.62469i) q^{26} -3.09412 q^{27} +(-6.46273 - 3.98236i) q^{28} +(-0.631885 - 0.631885i) q^{29} +(-1.47962 + 6.58060i) q^{30} +6.03484i q^{31} +(-3.17176 + 4.68401i) q^{32} +(-2.53258 - 2.53258i) q^{33} +(8.39983 - 4.69052i) q^{34} +(5.66266 - 6.32194i) q^{35} +(-1.62559 + 2.63807i) q^{36} +(6.56359 + 6.56359i) q^{37} +(-0.294211 + 1.03829i) q^{38} +11.2129i q^{39} +(-4.52540 - 4.41823i) q^{40} +(-1.60372 - 6.19904i) q^{41} +(9.99615 - 5.58191i) q^{42} +(6.88851 - 6.88851i) q^{43} +(3.26754 - 0.775937i) q^{44} +(-2.58060 - 2.31148i) q^{45} +(-1.56322 + 5.51668i) q^{46} +6.94756 q^{47} +(-3.83571 - 7.62083i) q^{48} -7.40653 q^{49} +(5.75833 - 4.10385i) q^{50} +14.5100i q^{51} +(-8.95115 - 5.51573i) q^{52} +1.29473i q^{53} +(2.13336 + 3.82046i) q^{54} +(0.206245 + 3.74915i) q^{55} +(-0.461213 + 10.7256i) q^{56} +(-1.15089 - 1.15089i) q^{57} +(-0.344540 + 1.21590i) q^{58} +3.32033 q^{59} +(9.14556 - 2.71030i) q^{60} +9.00272i q^{61} +(7.45150 - 4.16096i) q^{62} +5.88071i q^{63} +(7.97047 + 0.686746i) q^{64} +(7.84301 - 8.75615i) q^{65} +(-1.38091 + 4.87329i) q^{66} -13.9012 q^{67} +(-11.5832 - 7.13761i) q^{68} +(-6.11496 - 6.11496i) q^{69} +(-11.7104 - 2.63303i) q^{70} +(-4.57139 - 4.57139i) q^{71} +(4.37818 + 0.188266i) q^{72} +(2.83212 + 2.83212i) q^{73} +(3.57885 - 12.6299i) q^{74} +(1.16981 + 10.6003i) q^{75} +(1.48488 - 0.352611i) q^{76} +(4.50680 - 4.50680i) q^{77} +(13.8451 - 7.73117i) q^{78} +(-3.21799 + 3.21799i) q^{79} +(-2.33519 + 8.63405i) q^{80} -11.2476 q^{81} +(-6.54851 + 6.25436i) q^{82} +(3.90777 + 3.90777i) q^{83} +(-13.7845 - 8.49405i) q^{84} +(10.1492 - 11.3309i) q^{85} +(-13.2551 - 3.75601i) q^{86} +(-1.34776 - 1.34776i) q^{87} +(-3.21103 - 3.49959i) q^{88} +(-1.76118 - 1.76118i) q^{89} +(-1.07480 + 4.78014i) q^{90} -19.9536 q^{91} +(7.88953 - 1.87351i) q^{92} +12.8718i q^{93} +(-4.79027 - 8.57848i) q^{94} +(0.0937245 + 1.70373i) q^{95} +(-6.76511 + 9.99062i) q^{96} -13.6640i q^{97} +(5.10673 + 9.14520i) q^{98} +(-1.83966 - 1.83966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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