LMFDB - Embedded newform 820.2.s.c.583.40

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			583.40
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.40

$q$-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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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	$-0.745378\pi$
$7$		−	3.79559i		−	1.43460i	0.696765	−	0.717300i	$-0.254622\pi$
$8$	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	−0.863078	−	0.505071i	$-0.831466\pi$
$11$	−1.18738	+	1.18738i	−0.358008	+	0.358008i	0.505071	+	0.863078i	$0.331466\pi$
$12$	−2.23787	−	3.63171i	−0.646018	−	1.04839i
$13$		−	5.25705i		−	1.45804i	−0.684490	−	0.729022i	$-0.739975\pi$
$13$		−	5.25705i		−	1.45804i	0.684490	−	0.729022i	$-0.260025\pi$
$14$	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	$-0.691192\pi$
$17$		−	6.80287i		−	1.64994i	0.565177	−	0.824969i	$-0.308808\pi$
$18$	−1.06826	+	1.91306i	−0.251792	+	0.450912i
$19$	−0.539583	+	0.539583i	−0.123789	+	0.123789i	−0.766287	−	0.642498i	$-0.777898\pi$
$19$	−0.539583	+	0.539583i	−0.123789	+	0.123789i	0.642498	+	0.766287i	$0.277898\pi$
$20$	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	−0.939726	−	0.341928i	$-0.888920\pi$
$23$	−2.86694	+	2.86694i	−0.597799	+	0.597799i	0.341928	+	0.939726i	$0.388920\pi$
$24$	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	−0.763338	−	0.646000i	$-0.776441\pi$
$29$	−0.631885	+	0.631885i	−0.117338	+	0.117338i	0.646000	+	0.763338i	$0.276441\pi$
$30$	−1.47962	−	6.58060i	−0.270141	−	1.20145i
$31$		−	6.03484i		−	1.08389i	−0.840414	−	0.541944i	$-0.817688\pi$
$31$		−	6.03484i		−	1.08389i	0.840414	−	0.541944i	$-0.182312\pi$
$32$	−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	0.0824524	−	0.996595i	$-0.473725\pi$
$37$	6.56359	−	6.56359i	1.07905	−	1.07905i	0.996595	−	0.0824524i	$-0.0262752\pi$
$38$	−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	0.998656	+	0.0518314i	$0.0165058\pi$
$43$	6.88851	+	6.88851i	1.05049	+	1.05049i	0.0518314	+	0.998656i	$0.483494\pi$
$44$	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	$-0.971658\pi$
$53$		−	1.29473i		−	0.177844i	0.996039	−	0.0889221i	$-0.0283422\pi$
$54$	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	$-0.804480\pi$
$61$		−	9.00272i		−	1.15268i	0.817210	−	0.576340i	$-0.195520\pi$
$62$	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	−0.924268	−	0.381744i	$-0.875324\pi$
$71$	−4.57139	+	4.57139i	−0.542524	+	0.542524i	0.381744	+	0.924268i	$0.375324\pi$
$72$	4.37818	−	0.188266i	0.515974	−	0.0221874i
$73$	2.83212	−	2.83212i	0.331475	−	0.331475i	−0.521672	−	0.853146i	$-0.674691\pi$
$73$	2.83212	−	2.83212i	0.331475	−	0.331475i	0.853146	+	0.521672i	$0.174691\pi$
$74$	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	0.502516	−	0.864568i	$-0.332408\pi$
$79$	−3.21799	−	3.21799i	−0.362052	−	0.362052i	−0.864568	+	0.502516i	$0.832408\pi$
$80$	−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	−0.459332	−	0.888265i	$-0.651911\pi$
$83$	3.90777	−	3.90777i	0.428933	−	0.428933i	0.888265	+	0.459332i	$0.151911\pi$
$84$	−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	−0.794261	−	0.607577i	$-0.792142\pi$
$89$	−1.76118	+	1.76118i	−0.186684	+	0.186684i	0.607577	+	0.794261i	$0.292142\pi$
$90$	−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	$0.244014\pi$
$97$			13.6640i			1.38737i	−0.720278	+	0.693686i	$0.755986\pi$
$98$	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	0.198452	−	0.980111i	$-0.436409\pi$
$101$	11.8444	−	11.8444i	1.17856	−	1.17856i	0.980111	−	0.198452i	$-0.0635914\pi$
$102$	17.9162	+	10.0045i	1.77397	+	0.990593i
$103$	6.27427	+	6.27427i	0.618222	+	0.618222i	0.945075	−	0.326853i	$-0.105988\pi$
$103$	6.27427	+	6.27427i	0.618222	+	0.618222i	−0.326853	+	0.945075i	$0.605988\pi$
$104$	−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	0.995353	+	0.0962926i	$0.0306984\pi$
$107$	11.2921	+	11.2921i	1.09165	+	1.09165i	0.0962926	+	0.995353i	$0.469302\pi$
$108$	3.24637	+	5.26834i	0.312382	+	0.506946i
$109$	6.65133	+	6.65133i	0.637082	+	0.637082i	0.949835	−	0.312753i	$-0.101251\pi$
$109$	6.65133	+	6.65133i	0.637082	+	0.637082i	−0.312753	+	0.949835i	$0.601251\pi$
$110$	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	0.235958	−	0.971763i	$-0.424177\pi$
$113$	−7.82171	−	7.82171i	−0.735805	−	0.735805i	−0.971763	+	0.235958i	$0.924177\pi$
$114$	−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	−0.999197	−	0.0400669i	$-0.987243\pi$
$127$	−11.7119	−	11.7119i	−1.03926	−	1.03926i	−0.0400669	−	0.999197i	$-0.512757\pi$
$128$	−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	$-0.838836\pi$
$137$		−	11.3525i		−	0.969909i	0.874539	−	0.484955i	$-0.161164\pi$
$138$	−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	0.0637922	−	0.997963i	$-0.479681\pi$
$149$	−11.4030	−	11.4030i	−0.934171	−	0.934171i	−0.997963	+	0.0637922i	$0.979681\pi$
$150$	12.2821	+	8.75319i	1.00283	+	0.714695i
$151$	−6.73143	+	6.73143i	−0.547796	+	0.547796i	−0.925803	−	0.378007i	$-0.876610\pi$
$151$	−6.73143	+	6.73143i	−0.547796	+	0.547796i	0.378007	+	0.925803i	$0.376610\pi$
$152$	−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	−0.652058	−	0.758169i	$-0.726094\pi$
$163$	1.35473	−	1.35473i	0.106111	−	0.106111i	0.758169	+	0.652058i	$0.226094\pi$
$164$	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	$0.0851945\pi$
$167$			6.83522i			0.528925i	−0.964396	+	0.264462i	$0.914805\pi$
$168$	−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	−0.996699	−	0.0811817i	$-0.974131\pi$
$173$	−12.0418	+	12.0418i	−0.915518	+	0.915518i	0.0811817	+	0.996699i	$0.474131\pi$
$174$	−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	−0.789991	−	0.613119i	$-0.789915\pi$
$179$	−2.36638	+	2.36638i	−0.176872	+	0.176872i	0.613119	+	0.789991i	$0.289915\pi$
$180$	6.64333	+	1.96876i	0.495165	+	0.146742i
$181$	−5.80793	+	5.80793i	−0.431700	+	0.431700i	−0.889206	−	0.457506i	$-0.848743\pi$
$181$	−5.80793	+	5.80793i	−0.431700	+	0.431700i	0.457506	+	0.889206i	$0.348743\pi$
$182$	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	0.246578	−	0.969123i	$-0.420694\pi$
$191$	−9.98578	−	9.98578i	−0.722545	−	0.722545i	−0.969123	+	0.246578i	$0.920694\pi$
$192$	17.0004	−	1.46477i	1.22690	−	0.105711i
$193$			4.94076i			0.355644i	0.984063	+	0.177822i	$0.0569051\pi$
$193$			4.94076i			0.355644i	−0.984063	+	0.177822i	$0.943095\pi$
$194$	−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	0.796547	−	0.604577i	$-0.206658\pi$
$197$	2.69442	+	2.69442i	0.191969	+	0.191969i	−0.604577	+	0.796547i	$0.706658\pi$
$198$	−1.00309	−	3.53995i	−0.0712866	−	0.251574i
$199$	3.98148	−	3.98148i	0.282240	−	0.282240i	−0.551762	−	0.834002i	$-0.686044\pi$
$199$	3.98148	−	3.98148i	0.282240	−	0.282240i	0.834002	+	0.551762i	$0.186044\pi$
$200$	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	0.544738	−	0.838606i	$-0.316629\pi$
$211$	−4.26868	−	4.26868i	−0.293868	−	0.293868i	−0.838606	+	0.544738i	$0.816629\pi$
$212$	−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	−0.249036	−	0.968494i	$-0.580114\pi$
$223$	10.7438	−	10.7438i	0.719458	−	0.719458i	0.968494	+	0.249036i	$0.0801138\pi$
$224$	−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	0.999945	+	0.0104690i	$0.00333245\pi$
$229$	15.2903	+	15.2903i	1.01041	+	1.01041i	0.0104690	+	0.999945i	$0.496668\pi$
$230$	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	$-0.863213\pi$
$233$		−	12.7190i		−	0.833248i	0.909079	−	0.416624i	$-0.136787\pi$
$234$	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	0.590644	−	0.806932i	$-0.298874\pi$
$239$	−3.34373	−	3.34373i	−0.216288	−	0.216288i	−0.806932	+	0.590644i	$0.798874\pi$
$240$	−4.98077	−	18.4158i	−0.321507	−	1.18873i
$241$			12.6414i			0.814302i	0.913361	+	0.407151i	$0.133478\pi$
$241$			12.6414i			0.814302i	−0.913361	+	0.407151i	$0.866522\pi$
$242$	−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	$0.0149622\pi$
$263$			1.52403i			0.0939759i	−0.998895	+	0.0469880i	$0.985038\pi$
$264$	−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	$-0.533955\pi$
$269$		−	32.6160i		−	1.98863i	0.106471	−	0.994316i	$-0.466045\pi$
$270$	2.14641	+	9.54613i	0.130627	+	0.580959i
$271$			22.5274i			1.36844i	0.729274	+	0.684221i	$0.239858\pi$
$271$			22.5274i			1.36844i	−0.729274	+	0.684221i	$0.760142\pi$
$272$	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	−0.272042	−	0.962285i	$-0.587699\pi$
$277$	11.4879	−	11.4879i	0.690243	−	0.690243i	0.962285	+	0.272042i	$0.0876990\pi$
$278$	−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	−0.449472	−	0.893294i	$-0.648388\pi$
$281$	7.43982	−	7.43982i	0.443822	−	0.443822i	0.893294	+	0.449472i	$0.148388\pi$
$282$	−10.2173	+	18.2972i	−0.608430	+	1.08958i
$283$	2.86216	−	2.86216i	0.170138	−	0.170138i	−0.616902	−	0.787040i	$-0.711613\pi$
$283$	2.86216	−	2.86216i	0.170138	−	0.170138i	0.787040	+	0.616902i	$0.211613\pi$
$284$	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	−0.809891	−	0.586580i	$-0.800474\pi$
$307$	−3.91273	+	3.91273i	−0.223312	+	0.223312i	0.586580	+	0.809891i	$0.300474\pi$
$308$	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	0.587180	−	0.809456i	$-0.300238\pi$
$311$	−3.91988	−	3.91988i	−0.222276	−	0.222276i	−0.809456	+	0.587180i	$0.800238\pi$
$312$	−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	−0.703605	−	0.710592i	$-0.748427\pi$
$331$	0.127120	−	0.127120i	0.00698714	−	0.00698714i	0.710592	+	0.703605i	$0.248427\pi$
$332$	−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	0.747732	−	0.664000i	$-0.231143\pi$
$337$	1.53712	+	1.53712i	0.0837321	+	0.0837321i	−0.664000	+	0.747732i	$0.731143\pi$
$338$	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	0.949920	+	0.312494i	$0.101164\pi$
$353$	23.7186	+	23.7186i	1.26241	+	1.26241i	0.312494	+	0.949920i	$0.398836\pi$
$354$	−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	−0.243250	−	0.969964i	$-0.578213\pi$
$367$	13.9218	−	13.9218i	0.726714	−	0.726714i	0.969964	+	0.243250i	$0.0782134\pi$
$368$	−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	0.974804	−	0.223063i	$-0.0716056\pi$
$373$	14.5185	+	14.5185i	0.751741	+	0.751741i	−0.223063	+	0.974804i	$0.571606\pi$
$374$	−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	$0.00105831\pi$
$383$			0.130134i			0.00664953i	−0.999994	+	0.00332476i	$0.998942\pi$
$384$	−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	$0.0563700\pi$
$401$			7.05550i			0.352335i	−0.984360	+	0.176167i	$0.943630\pi$
$402$	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	$-0.832363\pi$
$409$		−	20.3305i		−	1.00528i	0.864497	−	0.502639i	$-0.167637\pi$
$410$	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	$-0.559350\pi$
$419$		−	40.2294i		−	1.96534i	0.185374	−	0.982668i	$-0.440650\pi$
$420$	10.2872	−	34.7128i	0.501963	−	1.69381i
$421$	−1.28823	−	1.28823i	−0.0627843	−	0.0627843i	0.675017	−	0.737802i	$-0.264136\pi$
$421$	−1.28823	−	1.28823i	−0.0627843	−	0.0627843i	−0.737802	+	0.675017i	$0.764136\pi$
$422$	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	0.705643	−	0.708568i	$-0.250658\pi$
$433$	−0.0608646	−	0.0608646i	−0.00292496	−	0.00292496i	−0.708568	+	0.705643i	$0.750658\pi$
$434$	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	0.207263	−	0.978285i	$-0.433544\pi$
$439$	−16.1547	−	16.1547i	−0.771022	−	0.771022i	−0.978285	+	0.207263i	$0.933544\pi$
$440$	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	0.922051	−	0.387067i	$-0.126512\pi$
$443$	11.2601	+	11.2601i	0.534984	+	0.534984i	−0.387067	+	0.922051i	$0.626512\pi$
$444$	−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	$-0.846588\pi$
$457$		−	19.8177i		−	0.927032i	0.886088	−	0.463516i	$-0.153412\pi$
$458$	−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	0.880599	+	0.473862i	$0.157140\pi$
$467$	29.2702	+	29.2702i	1.35446	+	1.35446i	0.473862	+	0.880599i	$0.342860\pi$
$468$	−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	0.992560	−	0.121754i	$-0.0388519\pi$
$479$	19.0585	+	19.0585i	0.870806	+	0.870806i	−0.121754	+	0.992560i	$0.538852\pi$
$480$	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	−0.738789	−	0.673937i	$-0.764602\pi$
$487$	−1.43115	+	1.43115i	−0.0648517	+	0.0648517i	0.673937	+	0.738789i	$0.264602\pi$
$488$	−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	$0.0630575\pi$
$491$			8.72193i			0.393615i	−0.980442	+	0.196808i	$0.936943\pi$
$492$	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	0.457371	−	0.889276i	$-0.348791\pi$
$499$	−9.64801	−	9.64801i	−0.431904	−	0.431904i	−0.889276	+	0.457371i	$0.848791\pi$
$500$	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	0.696321	−	0.717730i	$-0.254819\pi$
$509$	−0.483014	−	0.483014i	−0.0214092	−	0.0214092i	−0.717730	+	0.696321i	$0.754819\pi$
$510$	−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	0.591064	−	0.806625i	$-0.298708\pi$
$521$	−4.92026	−	4.92026i	−0.215561	−	0.215561i	−0.806625	+	0.591064i	$0.798708\pi$
$522$	−0.533814	−	1.88385i	−0.0233644	−	0.0824540i
$523$	−22.2043	+	22.2043i	−0.970927	+	0.970927i	−0.999589	−	0.0286619i	$-0.990875\pi$
$523$	−22.2043	+	22.2043i	−0.970927	+	0.970927i	0.0286619	+	0.999589i	$0.490875\pi$
$524$	−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	$-0.886418\pi$
$541$		−	16.2492i		−	0.698607i	0.937010	−	0.349303i	$-0.113582\pi$
$542$	−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	$-0.997753\pi$
$557$		−	0.333252i		−	0.0141203i	0.999975	−	0.00706017i	$-0.00224734\pi$
$558$	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	−0.582267	−	0.812998i	$-0.697834\pi$
$571$	5.51345	−	5.51345i	0.230731	−	0.230731i	0.812998	+	0.582267i	$0.197834\pi$
$572$	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	$0.133824\pi$
$587$			19.7772i			0.816291i	−0.912917	+	0.408146i	$0.866176\pi$
$588$	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	−0.832229	−	0.554431i	$-0.812936\pi$
$601$	−6.81030	+	6.81030i	−0.277798	+	0.277798i	0.554431	+	0.832229i	$0.312936\pi$
$602$	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	−0.154890	+	0.987932i	$0.549502\pi$
$607$	−28.1561	+	28.1561i	−1.14282	+	1.14282i	−0.987932	+	0.154890i	$0.950498\pi$
$608$	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	−0.255878	−	0.966709i	$-0.582364\pi$
$613$	17.5994	−	17.5994i	0.710831	−	0.710831i	0.966709	+	0.255878i	$0.0823645\pi$
$614$	−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	0.996855	+	0.0792413i	$0.0252498\pi$
$617$	26.7297	+	26.7297i	1.07610	+	1.07610i	0.0792413	+	0.996855i	$0.474750\pi$
$618$	−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	$-0.827451\pi$
$631$		−	25.9194i		−	1.03183i	0.856638	−	0.515917i	$-0.172549\pi$
$632$	−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	−0.404397	−	0.914584i	$-0.632518\pi$
$641$	12.9169	−	12.9169i	0.510187	−	0.510187i	0.914584	+	0.404397i	$0.132518\pi$
$642$	−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	−0.807706	−	0.589586i	$-0.799291\pi$
$647$	−5.54813	+	5.54813i	−0.218119	+	0.218119i	0.589586	+	0.807706i	$0.299291\pi$
$648$	−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	$0.127201\pi$
$653$			19.8841i			0.778126i	−0.921211	+	0.389063i	$0.872799\pi$
$654$	−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	0.452136	−	0.891949i	$-0.350662\pi$
$659$	−11.2904	−	11.2904i	−0.439813	−	0.439813i	−0.891949	+	0.452136i	$0.850662\pi$
$660$	−14.0774	+	7.64109i	−0.547961	+	0.297429i
$661$			7.08423i			0.275545i	0.990464	+	0.137772i	$0.0439942\pi$
$661$			7.08423i			0.275545i	−0.990464	+	0.137772i	$0.956006\pi$
$662$	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	0.278636	−	0.960397i	$-0.410118\pi$
$677$	−17.7389	−	17.7389i	−0.681761	−	0.681761i	−0.960397	+	0.278636i	$0.910118\pi$
$678$	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	$-0.831282\pi$
$683$		−	26.4254i		−	1.01114i	0.862786	−	0.505570i	$-0.168718\pi$
$684$	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	0.00555091	−	0.999985i	$-0.498233\pi$
$691$	−26.1406	−	26.1406i	−0.994434	−	0.994434i	−0.999985	+	0.00555091i	$0.998233\pi$
$692$	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	−0.275102	−	0.961415i	$-0.588712\pi$
$709$	18.2745	−	18.2745i	0.686313	−	0.686313i	0.961415	+	0.275102i	$0.0887116\pi$
$710$	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	−0.0294593	+	0.999566i	$0.509379\pi$
$719$	−27.5925	+	27.5925i	−1.02903	+	1.02903i	−0.999566	+	0.0294593i	$0.990621\pi$
$720$	−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	$-0.686186\pi$
$727$		−	44.9610i		−	1.66751i	0.552134	−	0.833756i	$-0.313814\pi$
$728$	−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	−0.856071	−	0.516858i	$-0.827101\pi$
$733$	−9.18384	+	9.18384i	−0.339213	+	0.339213i	0.516858	+	0.856071i	$0.327101\pi$
$734$	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	0.527347	−	0.849650i	$-0.323187\pi$
$743$	−8.78535	−	8.78535i	−0.322303	−	0.322303i	−0.849650	+	0.527347i	$0.823187\pi$
$744$	−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	−0.868665	−	0.495400i	$-0.835022\pi$
$751$	−10.2291	+	10.2291i	−0.373265	+	0.373265i	0.495400	+	0.868665i	$0.335022\pi$
$752$	−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	$-0.830951\pi$
$757$		−	27.8696i		−	1.01294i	0.862259	−	0.506468i	$-0.169049\pi$
$758$	−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	$0.0644278\pi$
$769$			11.1493i			0.402053i	−0.979586	+	0.201027i	$0.935572\pi$
$770$	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	−0.229342	−	0.973346i	$-0.573657\pi$
$787$	20.8719	−	20.8719i	0.744004	−	0.744004i	0.973346	+	0.229342i	$0.0736575\pi$
$788$	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	−0.993379	−	0.114881i	$-0.963351\pi$
$797$	−24.8010	+	24.8010i	−0.878498	+	0.878498i	0.114881	+	0.993379i	$0.463351\pi$
$798$	−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	−0.990341	−	0.138650i	$-0.955724\pi$
$809$	−24.2246	+	24.2246i	−0.851691	+	0.851691i	0.138650	+	0.990341i	$0.455724\pi$
$810$	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	$-0.948268\pi$
$827$		−	9.30624i		−	0.323610i	0.986823	−	0.161805i	$-0.0517315\pi$
$828$	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	−0.990833	−	0.135090i	$-0.956867\pi$
$839$	−24.7870	+	24.7870i	−0.855743	+	0.855743i	0.135090	+	0.990833i	$0.456867\pi$
$840$	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	−0.186738	−	0.982410i	$-0.559791\pi$
$853$	23.2385	−	23.2385i	0.795672	−	0.795672i	0.982410	+	0.186738i	$0.0597914\pi$
$854$	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	−0.215805	−	0.976437i	$-0.569237\pi$
$857$	22.2672	−	22.2672i	0.760632	−	0.760632i	0.976437	+	0.215805i	$0.0692374\pi$
$858$	−25.6191	+	7.25951i	−0.874623	+	0.247836i
$859$		−	46.8265i		−	1.59770i	−0.601530	−	0.798851i	$-0.705442\pi$
$859$		−	46.8265i		−	1.59770i	0.601530	−	0.798851i	$-0.294558\pi$
$860$	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	0.999543	+	0.0302260i	$0.00962271\pi$
$863$	30.2514	+	30.2514i	1.02977	+	1.02977i	0.0302260	+	0.999543i	$0.490377\pi$
$864$	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	−0.851509	−	0.524341i	$-0.824312\pi$
$877$	−9.68882	+	9.68882i	−0.327168	+	0.327168i	0.524341	+	0.851509i	$0.324312\pi$
$878$	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	$-0.734158\pi$
$881$		−	44.0125i		−	1.48282i	0.671054	−	0.741409i	$-0.265842\pi$
$882$	7.91212	−	14.1691i	0.266415	−	0.477099i
$883$		−	52.2259i		−	1.75754i	−0.477245	−	0.878770i	$-0.658365\pi$
$883$		−	52.2259i		−	1.75754i	0.477245	−	0.878770i	$-0.341635\pi$
$884$	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	−0.977440	−	0.211212i	$-0.932259\pi$
$907$	−23.0761	+	23.0761i	−0.766229	+	0.766229i	0.211212	+	0.977440i	$0.432259\pi$
$908$	−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	−0.0896774	+	0.995971i	$0.528584\pi$
$919$	−32.9114	+	32.9114i	−1.08565	+	1.08565i	−0.995971	+	0.0896774i	$0.971416\pi$
$920$	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	0.849406	−	0.527740i	$-0.176960\pi$
$929$	9.80422	+	9.80422i	0.321666	+	0.321666i	−0.527740	+	0.849406i	$0.676960\pi$
$930$	−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	$0.175860\pi$
$937$			32.1288i			1.04960i	−0.851225	+	0.524801i	$0.824140\pi$
$938$	−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	$0.273684\pi$
$941$			46.4869i			1.51543i	−0.652587	+	0.757714i	$0.726316\pi$
$942$	−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	0.678797	−	0.734326i	$-0.262501\pi$
$947$	−1.70879	−	1.70879i	−0.0555281	−	0.0555281i	−0.734326	+	0.678797i	$0.762501\pi$
$948$	−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	0.975075	+	0.221878i	$0.0712185\pi$
$953$	36.9507	+	36.9507i	1.19695	+	1.19695i	0.221878	+	0.975075i	$0.428781\pi$
$954$	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	−0.367274	−	0.930113i	$-0.619709\pi$
$971$	17.5385	−	17.5385i	0.562838	−	0.562838i	0.930113	+	0.367274i	$0.119709\pi$
$972$	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	−0.664069	−	0.747671i	$-0.731172\pi$
$983$	2.62116	−	2.62116i	0.0836021	−	0.0836021i	0.747671	+	0.664069i	$0.231172\pi$
$984$	−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	−0.703293	−	0.710900i	$-0.748288\pi$
$991$	0.239446	−	0.239446i	0.00760624	−	0.00760624i	0.710900	+	0.703293i	$0.248288\pi$
$992$	−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.583.40	yes	240
4.3	odd	2	inner	820.2.s.c.583.102	yes	240
5.2	odd	4		820.2.j.c.747.19	yes	240
20.7	even	4		820.2.j.c.747.81	yes	240
41.32	even	4		820.2.j.c.483.81	yes	240
164.155	odd	4		820.2.j.c.483.19	✓	240
205.32	odd	4	inner	820.2.s.c.647.102	yes	240
820.647	even	4	inner	820.2.s.c.647.40	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.19	✓	240	164.155	odd	4
820.2.j.c.483.81	yes	240	41.32	even	4
820.2.j.c.747.19	yes	240	5.2	odd	4
820.2.j.c.747.81	yes	240	20.7	even	4
820.2.s.c.583.40	yes	240	1.1	even	1	trivial
820.2.s.c.583.102	yes	240	4.3	odd	2	inner
820.2.s.c.647.40	yes	240	820.647	even	4	inner
820.2.s.c.647.102	yes	240	205.32	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Related objects

Downloads

Learn more