LMFDB - Embedded newform 820.2.s.c.583.102

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			583.102
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.102

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23475 - 0.689491i) q^{2} -2.13292 q^{3} +(1.04921 - 1.70269i) q^{4} +(-1.66560 + 1.49190i) q^{5} +(-2.63362 + 1.47063i) q^{6} +3.79559i q^{7} +(0.121513 - 2.82582i) q^{8} +1.54935 q^{9} +(-1.02794 + 2.99054i) q^{10} +(1.18738 - 1.18738i) q^{11} +(-2.23787 + 3.63171i) q^{12} -5.25705i q^{13} +(2.61703 + 4.68660i) q^{14} +(3.55260 - 3.18211i) q^{15} +(-1.79834 - 3.57295i) q^{16} -6.80287i q^{17} +(1.91306 - 1.06826i) q^{18} +(0.539583 - 0.539583i) q^{19} +(0.792697 + 4.40132i) q^{20} -8.09570i q^{21} +(0.647426 - 2.28480i) q^{22} +(2.86694 - 2.86694i) q^{23} +(-0.259177 + 6.02724i) q^{24} +(0.548453 - 4.96983i) q^{25} +(-3.62469 - 6.49114i) q^{26} +3.09412 q^{27} +(6.46273 + 3.98236i) q^{28} +(-0.631885 + 0.631885i) q^{29} +(2.19252 - 6.37859i) q^{30} +6.03484i q^{31} +(-4.68401 - 3.17176i) q^{32} +(-2.53258 + 2.53258i) q^{33} +(-4.69052 - 8.39983i) 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} +(4.01345 + 4.88797i) q^{40} +(-1.60372 + 6.19904i) q^{41} +(-5.58191 - 9.99615i) q^{42} +(-6.88851 - 6.88851i) q^{43} +(-0.775937 - 3.26754i) 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} +(-2.74945 - 6.51464i) q^{50} +14.5100i q^{51} +(-8.95115 - 5.51573i) q^{52} -1.29473i q^{53} +(3.82046 - 2.13336i) q^{54} +(-0.206245 + 3.74915i) q^{55} +(10.7256 + 0.461213i) q^{56} +(-1.15089 + 1.15089i) q^{57} +(-0.344540 + 1.21590i) q^{58} -3.32033 q^{59} +(-1.69076 - 9.38767i) q^{60} -9.00272i q^{61} +(4.16096 + 7.45150i) 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} +(-11.3509 - 3.90166i) q^{70} +(4.57139 - 4.57139i) q^{71} +(0.188266 - 4.37818i) q^{72} +(2.83212 - 2.83212i) q^{73} +(3.57885 - 12.6299i) q^{74} +(-1.16981 + 10.6003i) q^{75} +(-0.352611 - 1.48488i) q^{76} +(4.50680 + 4.50680i) q^{77} +(7.73117 + 13.8451i) q^{78} +(3.21799 + 3.21799i) q^{79} +(8.32581 + 3.26817i) q^{80} -11.2476 q^{81} +(2.29400 + 8.76000i) 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} +(-1.59265 + 4.63340i) q^{90} +19.9536 q^{91} +(-1.87351 - 7.88953i) q^{92} -12.8718i q^{93} +(-8.57848 + 4.79027i) q^{94} +(-0.0937245 + 1.70373i) q^{95} +(9.99062 + 6.76511i) q^{96} +13.6640i q^{97} +(-9.14520 + 5.10673i) 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 $

$2$	1.23475	−	0.689491i	0.873099	−	0.487543i
$2$	1.23475	−	0.689491i	0.873099	−	0.487543i
$3$	−2.13292			−1.23144			−0.615721	−	0.787964i	$-0.711135\pi$
$3$	−2.13292			−1.23144			−0.615721	+	0.787964i	$0.711135\pi$
$4$	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
$6$	−2.63362	+	1.47063i	−1.07517	+	0.600382i
$7$			3.79559i			1.43460i	0.696765	+	0.717300i	$0.254622\pi$
$7$			3.79559i			1.43460i	−0.696765	+	0.717300i	$0.745378\pi$
$8$	0.121513	−	2.82582i	0.0429613	−	0.999077i
$9$	1.54935			0.516451
$10$	−1.02794	+	2.99054i	−0.325065	+	0.945692i
$11$	1.18738	−	1.18738i	0.358008	−	0.358008i	−0.505071	−	0.863078i	$-0.668534\pi$
$11$	1.18738	−	1.18738i	0.358008	−	0.358008i	0.863078	+	0.505071i	$0.168534\pi$
$12$	−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	$-0.260025\pi$
$14$	2.61703	+	4.68660i	0.699430	+	1.25255i
$15$	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	$-0.308808\pi$
$18$	1.91306	−	1.06826i	0.450912	−	0.251792i
$19$	0.539583	−	0.539583i	0.123789	−	0.123789i	−0.642498	−	0.766287i	$-0.722102\pi$
$19$	0.539583	−	0.539583i	0.123789	−	0.123789i	0.766287	+	0.642498i	$0.222102\pi$
$20$	0.792697	+	4.40132i	0.177252	+	0.984165i
$21$		−	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	$-0.611080\pi$
$23$	2.86694	−	2.86694i	0.597799	−	0.597799i	0.939726	+	0.341928i	$0.111080\pi$
$24$	−0.259177	+	6.02724i	−0.0529043	+	1.23031i
$25$	0.548453	−	4.96983i	0.109691	−	0.993966i
$26$	−3.62469	−	6.49114i	−0.710860	−	1.27302i
$27$	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	$0.276441\pi$
$30$	2.19252	−	6.37859i	0.400298	−	1.16457i
$31$			6.03484i			1.08389i	0.840414	+	0.541944i	$0.182312\pi$
$31$			6.03484i			1.08389i	−0.840414	+	0.541944i	$0.817688\pi$
$32$	−4.68401	−	3.17176i	−0.828024	−	0.560693i
$33$	−2.53258	+	2.53258i	−0.440866	+	0.440866i
$34$	−4.69052	−	8.39983i	−0.804417	−	1.44056i
$35$	−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
$40$	4.01345	+	4.88797i	0.634582	+	0.772855i
$41$	−1.60372	+	6.19904i	−0.250458	+	0.968127i
$41$	−1.60372	+	6.19904i	−0.250458	+	0.968127i
$42$	−5.58191	−	9.99615i	−0.861307	−	1.54244i
$43$	−6.88851	−	6.88851i	−1.05049	−	1.05049i	−0.998656	−	0.0518314i	$-0.983494\pi$
$43$	−6.88851	−	6.88851i	−1.05049	−	1.05049i	−0.0518314	−	0.998656i	$-0.516506\pi$
$44$	−0.775937	−	3.26754i	−0.116977	−	0.492600i
$45$	−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	$-0.669136\pi$
$47$	−6.94756			−1.01341			−0.506703	+	0.862121i	$0.669136\pi$
$48$	3.83571	+	7.62083i	0.553637	+	1.09997i
$49$	−7.40653			−1.05808
$50$	−2.74945	−	6.51464i	−0.388831	−	0.921309i
$51$			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	$-0.0283422\pi$
$54$	3.82046	−	2.13336i	0.519898	−	0.290314i
$55$	−0.206245	+	3.74915i	−0.0278101	+	0.505535i
$56$	10.7256	+	0.461213i	1.43327	+	0.0616322i
$57$	−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	$-0.569345\pi$
$59$	−3.32033			−0.432270			−0.216135	+	0.976363i	$0.569345\pi$
$60$	−1.69076	−	9.38767i	−0.218276	−	1.21194i
$61$		−	9.00272i		−	1.15268i	−0.817210	−	0.576340i	$-0.804480\pi$
$61$		−	9.00272i		−	1.15268i	0.817210	−	0.576340i	$-0.195520\pi$
$62$	4.16096	+	7.45150i	0.528443	+	0.946342i
$63$			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	$-0.177113\pi$
$67$	13.9012			1.69831			0.849154	+	0.528146i	$0.177113\pi$
$68$	−11.5832	−	7.13761i	−1.40467	−	0.865562i
$69$	−6.11496	+	6.11496i	−0.736154	+	0.736154i
$70$	−11.3509	−	3.90166i	−1.35669	−	0.466337i
$71$	4.57139	−	4.57139i	0.542524	−	0.542524i	−0.381744	−	0.924268i	$-0.624676\pi$
$71$	4.57139	−	4.57139i	0.542524	−	0.542524i	0.924268	+	0.381744i	$0.124676\pi$
$72$	0.188266	−	4.37818i	0.0221874	−	0.515974i
$73$	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
$76$	−0.352611	−	1.48488i	−0.0404473	−	0.170327i
$77$	4.50680	+	4.50680i	0.513597	+	0.513597i
$78$	7.73117	+	13.8451i	0.875383	+	1.56765i
$79$	3.21799	+	3.21799i	0.362052	+	0.362052i	0.864568	−	0.502516i	$-0.167592\pi$
$79$	3.21799	+	3.21799i	0.362052	+	0.362052i	−0.502516	+	0.864568i	$0.667592\pi$
$80$	8.32581	+	3.26817i	0.930853	+	0.365393i
$81$	−11.2476			−1.24973
$82$	2.29400	+	8.76000i	0.253329	+	0.967380i
$83$	−3.90777	+	3.90777i	−0.428933	+	0.428933i	−0.888265	−	0.459332i	$-0.848089\pi$
$83$	−3.90777	+	3.90777i	−0.428933	+	0.428933i	0.459332	+	0.888265i	$0.348089\pi$
$84$	−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	$0.292142\pi$
$90$	−1.59265	+	4.63340i	−0.167880	+	0.488403i
$91$	19.9536			2.09171
$92$	−1.87351	−	7.88953i	−0.195327	−	0.822541i
$93$		−	12.8718i		−	1.33475i
$94$	−8.57848	+	4.79027i	−0.884803	+	0.494079i
$95$	−0.0937245	+	1.70373i	−0.00961593	+	0.174799i
$96$	9.99062	+	6.76511i	1.01966	+	0.690462i
$97$			13.6640i			1.38737i	0.720278	+	0.693686i	$0.244014\pi$
$97$			13.6640i			1.38737i	−0.720278	+	0.693686i	$0.755986\pi$
$98$	−9.14520	+	5.10673i	−0.923804	+	0.515858i
$99$	1.83966	−	1.83966i	0.184893	−	0.184893i
$100$	−7.88666	−	6.14822i	−0.788666	−	0.614822i
$101$	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	$-0.0635914\pi$
$102$	10.0045	+	17.9162i	0.990593	+	1.77397i
$103$	−6.27427	−	6.27427i	−0.618222	−	0.618222i	0.326853	−	0.945075i	$-0.394012\pi$
$103$	−6.27427	−	6.27427i	−0.618222	−	0.618222i	−0.945075	+	0.326853i	$0.894012\pi$
$104$	−14.8555	−	0.638799i	−1.45670	−	0.0626394i
$105$	12.0780	+	13.4842i	1.17869	+	1.31592i
$106$	−0.892701	−	1.59866i	−0.0867068	−	0.155276i
$107$	−11.2921	−	11.2921i	−1.09165	−	1.09165i	−0.995353	−	0.0962926i	$-0.969302\pi$
$107$	−11.2921	−	11.2921i	−1.09165	−	1.09165i	−0.0962926	−	0.995353i	$-0.530698\pi$
$108$	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	$0.601251\pi$
$110$	2.33034	+	4.77145i	0.222189	+	0.454940i
$111$	−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
$116$	0.412930	+	1.73888i	0.0383396	+	0.161451i
$117$		−	8.14503i		−	0.753008i
$118$	−4.09977	+	2.28934i	−0.377414	+	0.210750i
$119$	25.8209			2.36700
$120$	−8.56037	−	10.4256i	−0.781452	−	0.951727i
$121$			8.18027i			0.743661i
$122$	−6.20729	−	11.1161i	−0.561982	−	1.00640i
$123$	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
$126$	4.05469	+	7.26120i	0.361221	+	0.646879i
$127$	11.7119	+	11.7119i	1.03926	+	1.03926i	0.999197	+	0.0400669i	$0.0127571\pi$
$127$	11.7119	+	11.7119i	1.03926	+	1.03926i	0.0400669	+	0.999197i	$0.487243\pi$
$128$	−10.3150	+	4.64761i	−0.911728	+	0.410794i
$129$	14.6926	+	14.6926i	1.29361	+	1.29361i
$130$	15.7214	+	5.40396i	1.37886	+	0.473959i
$131$	−0.293595			−0.0256515			−0.0128258	−	0.999918i	$-0.504083\pi$
$131$	−0.293595			−0.0256515			−0.0128258	+	0.999918i	$0.504083\pi$
$132$	1.65501	+	6.96941i	0.144050	+	0.606609i
$133$	2.04804	+	2.04804i	0.177587	+	0.177587i
$134$	17.1645	−	9.58478i	1.48279	−	0.827999i
$135$	−5.15356	+	4.61612i	−0.443548	+	0.397293i
$136$	−19.2237	−	0.826636i	−1.64842	−	0.0708835i
$137$		−	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	$-0.816178\pi$
$139$	−19.7558			−1.67567			−0.837833	+	0.545927i	$0.816178\pi$
$140$	−16.7056	+	3.00875i	−1.41188	+	0.254286i
$141$	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
$148$	−4.28923	−	18.0623i	−0.352573	−	1.48472i
$149$	−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	$0.979681\pi$
$150$	5.86436	+	13.8952i	0.478823	+	1.13454i
$151$	6.73143	−	6.73143i	0.547796	−	0.547796i	−0.378007	−	0.925803i	$-0.623390\pi$
$151$	6.73143	−	6.73143i	0.547796	−	0.547796i	0.925803	+	0.378007i	$0.123390\pi$
$152$	−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
$160$	12.5336	−	1.70520i	0.990872	−	0.134808i
$161$	10.8817	+	10.8817i	0.857601	+	0.857601i
$162$	−13.8879	+	7.75509i	−1.09114	+	0.609297i
$163$	−1.35473	+	1.35473i	−0.106111	+	0.106111i	−0.758169	−	0.652058i	$-0.773906\pi$
$163$	−1.35473	+	1.35473i	−0.106111	+	0.106111i	0.652058	+	0.758169i	$0.273906\pi$
$164$	8.87244	+	9.23470i	0.692821	+	0.721109i
$165$	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	$-0.0851945\pi$
$168$	−22.8770	−	0.983731i	−1.76500	−	0.0758965i
$169$	−14.6366			−1.12589
$170$	20.3443	+	6.99298i	1.56033	+	0.536337i
$171$	0.836003	−	0.836003i	0.0639308	−	0.0639308i
$172$	−18.9565	+	4.50156i	−1.44542	+	0.343241i
$173$	−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
$176$	−6.37774	−	2.10714i	−0.480740	−	0.158832i
$177$	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	$-0.710085\pi$
$179$	2.36638	−	2.36638i	0.176872	−	0.176872i	0.789991	+	0.613119i	$0.210085\pi$
$180$	1.22817	+	6.81920i	0.0915421	+	0.508273i
$181$	−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	$0.348743\pi$
$182$	24.6377	−	13.7578i	1.82627	−	1.01980i
$183$			19.2021i			1.41946i
$184$	−7.75308	−	8.44982i	−0.571564	−	0.622929i
$185$	−1.14008	+	20.7246i	−0.0838206	+	1.52370i
$186$	−8.87501	−	15.8935i	−0.650747	−	1.16537i
$187$	−8.07757	−	8.07757i	−0.590691	−	0.590691i
$188$	−7.28941	+	11.8296i	−0.531635	+	0.862760i
$189$			11.7440i			0.854251i
$190$	1.05898	+	2.16830i	0.0768267	+	0.157305i
$191$	9.98578	+	9.98578i	0.722545	+	0.722545i	0.969123	−	0.246578i	$-0.0793060\pi$
$191$	9.98578	+	9.98578i	0.722545	+	0.722545i	−0.246578	+	0.969123i	$0.579306\pi$
$192$	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	$0.943095\pi$
$194$	9.42122	+	16.8716i	0.676404	+	1.21131i
$195$	−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	−0.834002	−	0.551762i	$-0.813956\pi$
$199$	−3.98148	+	3.98148i	−0.282240	+	0.282240i	0.551762	+	0.834002i	$0.313956\pi$
$200$	−13.9772	−	2.15372i	−0.988336	−	0.152291i
$201$	−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
$210$	24.2105	+	8.32193i	1.67068	+	0.574268i
$211$	4.26868	+	4.26868i	0.293868	+	0.293868i	0.838606	−	0.544738i	$-0.183371\pi$
$211$	4.26868	+	4.26868i	0.293868	+	0.293868i	−0.544738	+	0.838606i	$0.683371\pi$
$212$	−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
$216$	0.375975	−	8.74341i	0.0255819	−	0.594913i
$217$	−22.9058			−1.55495
$218$	12.7987	+	3.62669i	0.866841	+	0.245630i
$219$	−6.04069	+	6.04069i	−0.408192	+	0.408192i
$220$	6.16726	+	4.28480i	0.415796	+	0.288881i
$221$	−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	$-0.919886\pi$
$223$	−10.7438	+	10.7438i	−0.719458	+	0.719458i	0.249036	+	0.968494i	$0.419886\pi$
$224$	12.0387	−	17.7786i	0.804370	−	1.18788i
$225$	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	$-0.542441\pi$
$227$	−4.00580			−0.265875			−0.132937	+	0.991124i	$0.542441\pi$
$228$	0.752092	+	3.16713i	0.0498085	+	0.209748i
$229$	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	$0.496668\pi$
$230$	5.62665	+	11.5208i	0.371010	+	0.759656i
$231$	−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	$-0.136787\pi$
$234$	−5.61592	−	10.0571i	−0.367124	−	0.657450i
$235$	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
$238$	31.8823	−	17.8033i	2.06663	−	1.15402i
$239$	3.34373	+	3.34373i	0.216288	+	0.216288i	0.806932	−	0.590644i	$-0.201126\pi$
$239$	3.34373	+	3.34373i	0.216288	+	0.216288i	−0.590644	+	0.806932i	$0.701126\pi$
$240$	−17.7583	−	6.97075i	−1.14629	−	0.449960i
$241$			12.6414i			0.814302i	0.913361	+	0.407151i	$0.133478\pi$
$241$			12.6414i			0.814302i	−0.913361	+	0.407151i	$0.866522\pi$
$242$	5.64022	+	10.1006i	0.362567	+	0.649290i
$243$	14.7078			0.943507
$244$	−15.3289	−	9.44570i	−0.981331	−	0.604699i
$245$	12.3363	−	11.0498i	0.788138	−	0.705947i
$246$	−4.89291	−	18.6844i	−0.311961	−	1.19127i
$247$	−2.83661	−	2.83661i	−0.180489	−	0.180489i
$248$	17.0533	+	0.733310i	1.08289	+	0.0465652i
$249$	8.33496	−	8.33496i	0.528206	−	0.528206i
$250$	14.2987	+	6.74888i	0.904329	+	0.426837i
$251$	21.7813			1.37482			0.687411	−	0.726268i	$-0.258747\pi$
$251$	21.7813			1.37482			0.687411	+	0.726268i	$0.258747\pi$
$252$	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
$260$	23.1380	−	4.16725i	1.43496	−	0.258442i
$261$	−0.979013	+	0.979013i	−0.0605994	+	0.0605994i
$262$	−0.362516	+	0.202431i	−0.0223963	+	0.0125062i
$263$		−	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	$-0.533955\pi$
$269$		−	32.6160i		−	1.98863i	0.106471	−	0.994316i	$-0.466045\pi$
$270$	−3.18058	+	9.25308i	−0.193564	+	0.563125i
$271$		−	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
$274$	−7.82744	−	14.0175i	−0.472873	−	0.846826i
$275$	−5.24984	−	6.55228i	−0.316577	−	0.395117i
$276$	3.99606	+	16.8278i	0.240534	+	1.01291i
$277$	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	$0.0876990\pi$
$278$	−24.3934	+	13.6214i	−1.46302	+	0.816960i
$279$			9.35009i			0.559775i
$280$	−18.5527	+	15.2334i	−1.10874	+	0.910371i
$281$	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	$0.148388\pi$
$282$	18.2972	−	10.2173i	1.08958	−	0.608430i
$283$	−2.86216	+	2.86216i	−0.170138	+	0.170138i	−0.787040	−	0.616902i	$-0.788387\pi$
$283$	−2.86216	+	2.86216i	−0.170138	+	0.170138i	0.616902	+	0.787040i	$0.288387\pi$
$284$	−2.98735	−	12.5800i	−0.177267	−	0.746486i
$285$	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
$288$	−7.25718	−	4.91417i	−0.427633	−	0.289570i
$289$	−29.2791			−1.72230
$290$	−1.24013	−	2.53922i	−0.0728232	−	0.149108i
$291$		−	29.1443i		−	1.70847i
$292$	−1.85076	−	7.79372i	−0.108308	−	0.456093i
$293$	17.6019			1.02831			0.514156	−	0.857697i	$-0.328105\pi$
$293$	17.6019			1.02831			0.514156	+	0.857697i	$0.328105\pi$
$294$	19.5060	−	10.8923i	1.13761	−	0.635249i
$295$	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
$300$	16.8216	+	13.1137i	0.971197	+	0.757118i
$301$	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
$304$	−2.89825	−	0.957552i	−0.166226	−	0.0549194i
$305$	13.4312	+	14.9949i	0.769067	+	0.858608i
$306$	−7.26726	−	13.0143i	−0.415442	−	0.743978i
$307$	3.91273	−	3.91273i	0.223312	−	0.223312i	−0.586580	−	0.809891i	$-0.699526\pi$
$307$	3.91273	−	3.91273i	0.223312	−	0.223312i	0.809891	+	0.586580i	$0.199526\pi$
$308$	12.4023	−	2.94514i	0.706684	−	0.167815i
$309$	13.3825	+	13.3825i	0.761305	+	0.761305i
$310$	−18.0474	−	6.20348i	−1.02502	−	0.352334i
$311$	3.91988	+	3.91988i	0.222276	+	0.222276i	0.809456	−	0.587180i	$-0.199762\pi$
$311$	3.91988	+	3.91988i	0.222276	+	0.222276i	−0.587180	+	0.809456i	$0.699762\pi$
$312$	31.6855	+	1.36251i	1.79384	+	0.0771368i
$313$	19.0627			1.07749			0.538743	−	0.842470i	$-0.318899\pi$
$313$	19.0627			1.07749			0.538743	+	0.842470i	$0.318899\pi$
$314$	3.44483	−	1.92361i	0.194403	−	0.108556i
$315$	−8.77345	−	9.79492i	−0.494328	−	0.551881i
$316$	8.85558	−	2.10292i	0.498165	−	0.118298i
$317$	4.78035			0.268491			0.134246	−	0.990948i	$-0.457139\pi$
$317$	4.78035			0.268491			0.134246	+	0.990948i	$0.457139\pi$
$318$	1.90406	+	3.40982i	0.106774	+	0.191213i
$319$			1.50057i			0.0840159i
$320$	14.3002	−	10.7473i	0.799404	−	0.600793i
$321$	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
$328$	17.3225	+	5.28507i	0.956474	+	0.291819i
$329$		−	26.3701i		−	1.45383i
$330$	−4.97043	−	10.1771i	−0.273613	−	0.560233i
$331$	−0.127120	+	0.127120i	−0.00698714	+	0.00698714i	−0.710592	−	0.703605i	$-0.751573\pi$
$331$	−0.127120	+	0.127120i	−0.00698714	+	0.00698714i	0.703605	+	0.710592i	$0.251573\pi$
$332$	2.55368	+	10.7538i	0.140151	+	0.590190i
$333$	10.1693	−	10.1693i	0.557275	−	0.557275i
$334$	−4.71282	−	8.43977i	−0.257874	−	0.461804i
$335$	−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	$0.731143\pi$
$338$	−18.0725	+	10.0918i	−0.983015	+	0.548921i
$339$	16.6831	+	16.6831i	0.906101	+	0.906101i
$340$	29.9416	−	5.39261i	1.62381	−	0.292456i
$341$	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	$-0.536706\pi$
$347$	−4.28660			−0.230117			−0.115058	+	0.993359i	$0.536706\pi$
$348$	−0.880747	−	3.70890i	−0.0472130	−	0.198818i
$349$	26.6440			1.42622			0.713110	−	0.701053i	$-0.247286\pi$
$349$	26.6440			1.42622			0.713110	+	0.701053i	$0.247286\pi$
$350$	24.7269	−	10.4358i	1.32171	−	0.557817i
$351$		−	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	$0.398836\pi$
$354$	8.74448	−	4.88297i	0.464764	−	0.259527i
$355$	−0.794042	+	14.4342i	−0.0421434	+	0.766087i
$356$	1.15091	+	4.84658i	0.0609981	+	0.256868i
$357$	−55.0740			−2.91483
$358$	1.29029	−	4.55348i	0.0681938	−	0.240659i
$359$	−24.6134			−1.29905			−0.649523	−	0.760342i	$-0.725031\pi$
$359$	−24.6134			−1.29905			−0.649523	+	0.760342i	$0.725031\pi$
$360$	6.21825	+	7.57318i	0.327730	+	0.399142i
$361$			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
$366$	13.2397	+	23.7097i	0.692048	+	1.23933i
$367$	−13.9218	+	13.9218i	−0.726714	+	0.726714i	−0.969964	−	0.243250i	$-0.921787\pi$
$367$	−13.9218	+	13.9218i	−0.726714	+	0.726714i	0.243250	+	0.969964i	$0.421787\pi$
$368$	−15.3992	−	5.08772i	−0.802737	−	0.265216i
$369$	−2.48472	+	9.60450i	−0.129349	+	0.499990i
$370$	12.8817	+	26.3757i	0.669686	+	1.37121i
$371$	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
$376$	−0.844217	+	19.6325i	−0.0435372	+	1.01247i
$377$	3.32185	+	3.32185i	0.171084	+	0.171084i
$378$	8.09739	+	14.5009i	0.416485	+	0.745846i
$379$	−15.5630			−0.799419			−0.399709	−	0.916642i	$-0.630889\pi$
$379$	−15.5630			−0.799419			−0.399709	+	0.916642i	$0.630889\pi$
$380$	2.80260	+	1.94715i	0.143770	+	0.0998868i
$381$	−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	$-0.00105831\pi$
$384$	22.0011	−	9.91298i	1.12274	−	0.505869i
$385$	−14.2302	−	0.782823i	−0.725240	−	0.0398963i
$386$	3.40661	+	6.10060i	0.173392	+	0.310512i
$387$	−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	$0.588192\pi$
$390$	−33.5326	−	11.5262i	−1.69799	−	0.583653i
$391$	−19.5034	−	19.5034i	−0.986331	−	0.986331i
$392$	−0.899988	+	20.9295i	−0.0454563	+	1.05710i
$393$	0.626215			0.0315884
$394$	5.18470	+	1.46915i	0.261202	+	0.0740148i
$395$	−10.1608	−	0.558959i	−0.511246	−	0.0281243i
$396$	−1.20220	−	5.06257i	−0.0604128	−	0.254404i
$397$	−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
$400$	−18.7433	+	6.97783i	−0.937163	+	0.348891i
$401$			7.05550i			0.352335i	0.984360	+	0.176167i	$0.0563700\pi$
$401$			7.05550i			0.352335i	−0.984360	+	0.176167i	$0.943630\pi$
$402$	−36.6106	+	20.4436i	−1.82597	+	1.01963i
$403$	31.7255			1.58036
$404$	−7.74019	−	32.5946i	−0.385089	−	1.62164i
$405$	18.7340	−	16.7803i	0.930898	−	0.833818i
$406$	−4.61505	−	1.30773i	−0.229041	−	0.0649018i
$407$		−	15.5869i		−	0.772614i
$408$	41.0026	+	1.76315i	2.02993	+	0.0872889i
$409$		−	20.3305i		−	1.00528i	−0.864497	−	0.502639i	$-0.832363\pi$
$409$		−	20.3305i		−	1.00528i	0.864497	−	0.502639i	$-0.167637\pi$
$410$	−16.8899	−	11.1682i	−0.834135	−	0.551560i
$411$			24.2140i			1.19439i
$412$	−17.2662	+	4.10016i	−0.850642	+	0.202001i
$413$		−	12.6026i		−	0.620134i
$414$	2.42198	−	8.54728i	0.119034	−	0.420076i
$415$	0.678772	−	12.3388i	0.0333196	−	0.605687i
$416$	−16.6741	+	24.6241i	−0.817516	+	1.20729i
$417$	42.1376			2.06349
$418$	−0.883496	−	1.58218i	−0.0432132	−	0.0773868i
$419$			40.2294i			1.96534i	0.185374	+	0.982668i	$0.440650\pi$
$419$			40.2294i			1.96534i	−0.185374	+	0.982668i	$0.559350\pi$
$420$	35.6318	−	6.41743i	1.73865	−	0.313139i
$421$	−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
$424$	−3.65866	−	0.157326i	−0.177680	−	0.00764041i
$425$	−33.8091	−	3.73105i	−1.63998	−	0.180983i
$426$	−5.31649	+	18.7621i	−0.257585	+	0.909028i
$427$	34.1707			1.65363
$428$	−31.0746	+	7.37924i	−1.50205	+	0.356689i
$429$	13.3139	+	13.3139i	0.642802	+	0.642802i
$430$	27.6814	−	13.5193i	1.33491	−	0.651961i
$431$	−23.7048			−1.14182			−0.570909	−	0.821013i	$-0.693409\pi$
$431$	−23.7048			−1.14182			−0.570909	+	0.821013i	$0.693409\pi$
$432$	−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	$0.750658\pi$
$434$	−28.2829	+	15.7933i	−1.35762	+	0.758104i
$435$	−0.234104	+	4.25556i	−0.0112244	+	0.204039i
$436$	18.3038	−	4.34657i	0.876593	−	0.208163i
$437$		−	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	$-0.0664557\pi$
$439$	16.1547	+	16.1547i	0.771022	+	0.771022i	−0.207263	+	0.978285i	$0.566456\pi$
$440$	10.5693	+	1.03838i	0.503873	+	0.0495028i
$441$	−11.4753			−0.546444
$442$	−44.1584	+	24.6583i	−2.10040	+	1.17288i
$443$	−11.2601	−	11.2601i	−0.534984	−	0.534984i	0.387067	−	0.922051i	$-0.373488\pi$
$443$	−11.2601	−	11.2601i	−0.534984	−	0.534984i	−0.922051	+	0.387067i	$0.873488\pi$
$444$	9.14859	+	38.5255i	0.434173	+	1.82834i
$445$	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	$0.176508\pi$
$450$	−4.25987	−	10.0935i	−0.200812	−	0.475811i
$451$	5.45638	+	9.26481i	0.256931	+	0.436263i
$452$	−21.5246	+	5.11140i	−1.01243	+	0.240420i
$453$	−14.3576	+	14.3576i	−0.674580	+	0.674580i
$454$	−4.94616	+	2.76196i	−0.232135	+	0.129625i
$455$	−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
$460$	14.8909	+	10.3457i	0.694294	+	0.482371i
$461$	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	$-0.396979\pi$
$463$	13.6863			0.636056			0.318028	+	0.948081i	$0.396979\pi$
$464$	3.39404	+	1.12135i	0.157564	+	0.0520576i
$465$	19.2035	+	21.4393i	0.890542	+	0.994225i
$466$	−8.76962	−	15.7047i	−0.406245	−	0.727508i
$467$	−29.2702	−	29.2702i	−1.35446	−	1.35446i	−0.880599	−	0.473862i	$-0.842860\pi$
$467$	−29.2702	−	29.2702i	−1.35446	−	1.35446i	−0.473862	−	0.880599i	$-0.657140\pi$
$468$	−13.8685	−	8.54581i	−0.641071	−	0.395030i
$469$			52.7635i			2.43639i
$470$	7.14170	−	20.7769i	0.329422	−	0.958369i
$471$	−5.95064			−0.274191
$472$	−0.403462	+	9.38264i	−0.0185709	+	0.431871i
$473$	−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	$-0.461148\pi$
$479$	−19.0585	−	19.0585i	−0.870806	−	0.870806i	−0.992560	+	0.121754i	$0.961148\pi$
$480$	−26.7333	+	3.63705i	−1.22020	+	0.166008i
$481$	−34.5051	−	34.5051i	−1.57330	−	1.57330i
$482$	8.71610	+	15.6089i	0.397008	+	0.710966i
$483$	−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
$486$	18.1604	−	10.1409i	0.823774	−	0.460001i
$487$	1.43115	−	1.43115i	0.0648517	−	0.0648517i	−0.673937	−	0.738789i	$-0.735398\pi$
$487$	1.43115	−	1.43115i	0.0648517	−	0.0648517i	0.738789	+	0.673937i	$0.235398\pi$
$488$	−25.4400	−	1.09395i	−1.15162	−	0.0495206i
$489$	2.88954	−	2.88954i	0.130670	−	0.130670i
$490$	7.61350	−	22.1495i	0.343943	−	1.00061i
$491$		−	8.72193i		−	0.393615i	−0.980442	−	0.196808i	$-0.936943\pi$
$491$		−	8.72193i		−	0.393615i	0.980442	−	0.196808i	$-0.0630575\pi$
$492$	−18.9242	−	19.6969i	−0.853170	−	0.888005i
$493$	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	$-0.151209\pi$
$499$	9.64801	+	9.64801i	0.431904	+	0.431904i	−0.457371	+	0.889276i	$0.651209\pi$
$500$	22.3086	−	1.52565i	0.997670	−	0.0682292i
$501$			14.5790i			0.651341i
$502$	26.8944	−	15.0180i	1.20036	−	0.670286i
$503$	15.3459			0.684238			0.342119	−	0.939657i	$-0.388855\pi$
$503$	15.3459			0.684238			0.342119	+	0.939657i	$0.388855\pi$
$504$	16.6178	+	0.714582i	0.740216	+	0.0318300i
$505$	−2.05735	+	37.3988i	−0.0915510	+	1.66422i
$506$	−4.69424	−	8.40651i	−0.208685	−	0.373715i
$507$	31.2187			1.38647
$508$	32.2300	−	7.65360i	1.42997	−	0.339574i
$509$	−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	$0.754819\pi$
$510$	−43.3927	−	14.9155i	−1.92146	−	0.660468i
$511$	10.7496	+	10.7496i	0.475534	+	0.475534i
$512$	−2.90913	+	22.4396i	−0.128567	+	0.991701i
$513$	1.66953	−	1.66953i	0.0737116	−	0.0737116i
$514$	−18.2942	+	10.2156i	−0.806924	+	0.450591i
$515$	19.8110	+	1.08983i	0.872978	+	0.0480236i
$516$	40.4327	−	9.60147i	1.77995	−	0.422681i
$517$	−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
$520$	25.6963	−	21.0989i	1.12686	−	0.925249i
$521$	−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	−0.0286619	−	0.999589i	$-0.509125\pi$
$523$	22.2043	−	22.2043i	0.970927	−	0.970927i	0.999589	+	0.0286619i	$0.00912462\pi$
$524$	−0.308041	+	0.499902i	−0.0134568	+	0.0218383i
$525$	−40.2342	−	4.44011i	−1.75597	−	0.193782i
$526$	−1.05081	−	1.88180i	−0.0458173	−	0.0820502i
$527$	41.0542			1.78835
$528$	13.6032	+	4.49436i	0.592004	+	0.195592i
$529$			6.56130i			0.285274i
$530$	3.87193	+	1.33091i	0.168186	+	0.0578109i
$531$	−5.14436			−0.223246
$532$	5.63599	−	1.33837i	0.244351	−	0.0580256i
$533$	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
$536$	1.68918	−	39.2824i	0.0729614	−	1.69674i
$537$	−5.04730	+	5.04730i	−0.217807	+	0.217807i
$538$	−22.4884	−	40.2725i	−0.969544	−	1.73627i
$539$	−8.79434	+	8.79434i	−0.378799	+	0.378799i
$540$	2.45270	+	13.6182i	0.105547	+	0.586034i
$541$		−	16.2492i		−	0.698607i	−0.937010	−	0.349303i	$-0.886418\pi$
$541$		−	16.2492i		−	0.698607i	0.937010	−	0.349303i	$-0.113582\pi$
$542$	−15.5324	−	27.8157i	−0.667175	−	1.19479i
$543$	12.3879	−	12.3879i	0.531614	−	0.531614i
$544$	−21.5771	+	31.8647i	−0.925110	+	1.36619i
$545$	−21.0016	−	1.15532i	−0.899610	−	0.0494886i
$546$	−52.5503	+	29.3444i	−2.24894	+	1.25582i
$547$	−23.9813			−1.02537			−0.512684	−	0.858578i	$-0.671349\pi$
$547$	−23.9813			−1.02537			−0.512684	+	0.858578i	$0.671349\pi$
$548$	−19.3298	−	11.9111i	−0.825729	−	0.508817i
$549$		−	13.9484i		−	0.595302i
$550$	−11.0000	−	4.47070i	−0.469040	−	0.190631i
$551$			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	$-0.00224734\pi$
$558$	6.44680	+	11.5450i	0.272915	+	0.488739i
$559$	−36.2132	+	36.2132i	−1.53166	+	1.53166i
$560$	−12.4046	+	31.6014i	−0.524192	+	1.33540i
$561$	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	$-0.515651\pi$
$563$	−2.33241			−0.0982992			−0.0491496	+	0.998791i	$0.515651\pi$
$564$	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	$0.403405\pi$
$570$	−2.25873	−	4.62482i	−0.0946076	−	0.193712i
$571$	−5.51345	+	5.51345i	−0.230731	+	0.230731i	−0.812998	−	0.582267i	$-0.802166\pi$
$571$	−5.51345	+	5.51345i	−0.230731	+	0.230731i	0.582267	+	0.812998i	$0.302166\pi$
$572$	−17.1776	+	4.07914i	−0.718233	+	0.170558i
$573$	−21.2989	−	21.2989i	−0.889773	−	0.889773i
$574$	−33.2494	+	8.70707i	−1.38780	+	0.363426i
$575$	−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	$0.328782\pi$
$578$	−36.1523	+	20.1876i	−1.50374	+	0.839695i
$579$		−	10.5383i		−	0.437955i
$580$	−3.28202	−	2.28024i	−0.136279	−	0.0946817i
$581$	−14.8323	−	14.8323i	−0.615347	−	0.615347i
$582$	−20.0947	−	35.9859i	−0.832953	−	1.49166i
$583$	−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
$586$	21.7339	−	12.1363i	0.897818	−	0.501347i
$587$		−	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
$590$	3.41311	−	9.92957i	0.140516	−	0.408794i
$591$	−5.74698	−	5.74698i	−0.236399	−	0.236399i
$592$	−35.2549	−	11.6479i	−1.44897	−	0.478724i
$593$	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
$596$	−31.3799	+	7.45174i	−1.28537	+	0.305235i
$597$	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	$-0.506741\pi$
$599$	−1.03660			−0.0423544			−0.0211772	+	0.999776i	$0.506741\pi$
$600$	29.8122	+	4.59372i	1.21708	+	0.187538i
$601$	−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
$604$	−4.39892	−	18.5242i	−0.178989	−	0.753740i
$605$	−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	$-0.450498\pi$
$607$	28.1561	−	28.1561i	1.14282	−	1.14282i	0.987932	−	0.154890i	$-0.0495024\pi$
$608$	−4.23884	+	0.815983i	−0.171908	+	0.0330925i
$609$	5.11555	+	5.11555i	0.207293	+	0.207293i
$610$	26.9230	+	9.25430i	1.09008	+	0.374696i
$611$			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	$-0.661319\pi$
$619$	−24.1522			−0.970759			−0.485380	+	0.874303i	$0.661319\pi$
$620$	−26.5613	+	4.78380i	−1.06673	+	0.192122i
$621$	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
$626$	23.5376	−	13.1435i	0.940752	−	0.525321i
$627$			2.73307i			0.109148i
$628$	2.92718	−	4.75035i	0.116807	−	0.189560i
$629$	−44.6513	−	44.6513i	−1.78036	−	1.78036i
$630$	−17.5865	−	6.04504i	−0.700663	−	0.240840i
$631$			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
$634$	5.90253	−	3.29601i	0.234420	−	0.130901i
$635$	−36.9804	−	2.03434i	−1.46752	−	0.0807302i
$636$	4.70207	+	2.89743i	0.186449	+	0.114891i
$637$			38.9365i			1.54272i
$638$	1.03463	+	1.85283i	0.0409614	+	0.0733541i
$639$	7.08269	−	7.08269i	0.280187	−	0.280187i
$640$	10.2469	−	23.1301i	0.405046	−	0.914296i
$641$	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	$-0.653618\pi$
$643$	−23.5362			−0.928176			−0.464088	+	0.885789i	$0.653618\pi$
$644$	29.9455	−	7.11110i	1.18002	−	0.280216i
$645$	−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	$-0.700709\pi$
$647$	5.54813	−	5.54813i	0.218119	−	0.218119i	0.807706	+	0.589586i	$0.200709\pi$
$648$	−1.36672	+	31.7835i	−0.0536900	+	1.24858i
$649$	−3.94248	+	3.94248i	−0.154756	+	0.154756i
$650$	−34.2478	+	14.4540i	−1.34331	+	0.566933i
$651$	48.8562			1.91483
$652$	0.885304	+	3.72809i	0.0346712	+	0.146003i
$653$			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
$656$	25.0329	−	5.41796i	0.977370	−	0.211536i
$657$	4.38795	−	4.38795i	0.171190	−	0.171190i
$658$	−18.1819	−	32.5604i	−0.708806	−	1.26934i
$659$	11.2904	+	11.2904i	0.439813	+	0.439813i	0.891949	−	0.452136i	$-0.149338\pi$
$659$	11.2904	+	11.2904i	0.439813	+	0.439813i	−0.452136	+	0.891949i	$0.649338\pi$
$660$	−13.1543	−	9.13913i	−0.512029	−	0.355740i
$661$			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
$670$	−14.2897	+	41.5722i	−0.552060	+	1.60608i
$671$	−10.6896	−	10.6896i	−0.412668	−	0.412668i
$672$	−25.6776	+	37.9203i	−0.990536	+	1.46281i
$673$	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
$680$	33.2522	−	27.3030i	1.27516	−	1.04702i
$681$	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	$0.831282\pi$
$684$	−0.546319	−	2.30060i	−0.0208890	−	0.0879656i
$685$	16.9368	+	18.9087i	0.647123	+	0.722465i
$686$	−1.06389	−	1.90523i	−0.0406196	−	0.0727421i
$687$	−32.6131	−	32.6131i	−1.24427	−	1.24427i
$688$	−12.2245	+	37.0001i	−0.466053	+	1.41062i
$689$	−6.80644			−0.259305
$690$	−12.0012	−	24.5729i	−0.456877	−	0.935473i
$691$	26.1406	+	26.1406i	0.994434	+	0.994434i	0.999985	−	0.00555091i	$-0.00176692\pi$
$691$	26.1406	+	26.1406i	0.994434	+	0.994434i	−0.00555091	+	0.999985i	$0.501767\pi$
$692$	7.86915	+	33.1377i	0.299140	+	1.25971i
$693$	6.98262	+	6.98262i	0.265248	+	0.265248i
$694$	−5.29287	+	2.95557i	−0.200915	+	0.112192i
$695$	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
$698$	32.8986	−	18.3708i	1.24523	−	0.695344i
$699$			27.1286i			1.02610i
$700$	23.3361	−	29.9346i	0.882023	−	1.13142i
$701$	10.0862			0.380949			0.190475	−	0.981692i	$-0.438997\pi$
$701$	10.0862			0.380949			0.190475	+	0.981692i	$0.438997\pi$
$702$	−11.2152	−	20.0843i	−0.423291	−	0.758034i
$703$		−	7.08320i		−	0.267148i
$704$	−10.2794	+	8.64852i	−0.387419	+	0.325953i
$705$	−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	$0.0887116\pi$
$710$	8.97179	+	18.3701i	0.336705	+	0.689416i
$711$	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
$714$	−68.0025	+	37.9730i	−2.54493	+	1.42110i
$715$	19.7095	+	1.08424i	0.737092	+	0.0405483i
$716$	−1.54640	−	6.51204i	−0.0577918	−	0.243366i
$717$	−7.13191	−	7.13191i	−0.266346	−	0.266346i
$718$	−30.3913	+	16.9707i	−1.13419	+	0.633341i
$719$	27.5925	−	27.5925i	1.02903	−	1.02903i	0.0294593	−	0.999566i	$-0.490621\pi$
$719$	27.5925	−	27.5925i	1.02903	−	1.02903i	0.999566	−	0.0294593i	$-0.00937853\pi$
$720$	12.8996	+	5.06355i	0.480740	+	0.188707i
$721$	23.8146	−	23.8146i	0.886901	−	0.886901i
$722$	12.6988	+	22.7412i	0.472602	+	0.846341i
$723$		−	26.9630i		−	1.00277i
$724$	3.79542	+	15.9828i	0.141056	+	0.593997i
$725$	2.79380	+	3.48692i	0.103759	+	0.129501i
$726$	−12.0301	−	21.5437i	−0.446481	−	0.799563i
$727$			44.9610i			1.66751i	0.552134	+	0.833756i	$0.313814\pi$
$727$			44.9610i			1.66751i	−0.552134	+	0.833756i	$0.686186\pi$
$728$	2.42462	−	56.3853i	0.0898625	−	2.08978i
$729$	2.37209			0.0878551
$730$	5.55831	+	11.3808i	0.205722	+	0.421224i
$731$	−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
$738$	3.55421	+	13.5723i	0.130832	+	0.499604i
$739$	2.64278			0.0972161			0.0486081	−	0.998818i	$-0.484521\pi$
$739$	2.64278			0.0972161			0.0486081	+	0.998818i	$0.484521\pi$
$740$	34.0914	+	23.6855i	1.25322	+	0.870697i
$741$	6.05027	+	6.05027i	0.222262	+	0.222262i
$742$	6.06786	−	3.38833i	0.222758	−	0.124390i
$743$	8.78535	+	8.78535i	0.322303	+	0.322303i	0.849650	−	0.527347i	$-0.176813\pi$
$743$	8.78535	+	8.78535i	0.322303	+	0.322303i	−0.527347	+	0.849650i	$0.676813\pi$
$744$	−36.3734	−	1.56409i	−1.33351	−	0.0573424i
$745$	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
$748$	−22.2287	+	5.27860i	−0.812761	+	0.193005i
$749$	42.8601	−	42.8601i	1.56607	−	1.56607i
$750$	−30.4980	−	14.3948i	−1.11363	−	0.525625i
$751$	10.2291	−	10.2291i	0.373265	−	0.373265i	−0.495400	−	0.868665i	$-0.664978\pi$
$751$	10.2291	−	10.2291i	0.373265	−	0.373265i	0.868665	+	0.495400i	$0.164978\pi$
$752$	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	$-0.169049\pi$
$758$	−19.2164	+	10.7306i	−0.697972	+	0.389751i
$759$			14.5215i			0.527098i
$760$	4.80305	+	0.471874i	0.174225	+	0.0171167i
$761$	−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
$764$	27.4799	−	6.52559i	0.994186	−	0.236088i
$765$	15.7247	+	17.5555i	0.568528	+	0.634721i
$766$	−0.0897260	−	0.160682i	−0.00324193	−	0.00580569i
$767$			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	$0.935572\pi$
$770$	−18.1105	+	8.84502i	−0.652657	+	0.318752i
$771$	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
$776$	38.6120	+	1.66035i	1.38609	+	0.0596032i
$777$	−53.1368	−	53.1368i	−1.90627	−	1.90627i
$778$	−13.3227	+	7.43946i	−0.477641	+	0.266718i
$779$	2.47956	+	4.21023i	0.0888394	+	0.150847i
$780$	−49.3515	+	8.88841i	−1.76707	+	0.318256i
$781$		−	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
$786$	0.773217	−	0.431769i	0.0275797	−	0.0154007i
$787$	−20.8719	+	20.8719i	−0.744004	+	0.744004i	−0.973346	−	0.229342i	$-0.926343\pi$
$787$	−20.8719	+	20.8719i	−0.744004	+	0.744004i	0.229342	+	0.973346i	$0.426343\pi$
$788$	7.41477	−	1.76077i	0.264140	−	0.0627249i
$789$			3.25064i			0.115726i
$790$	−12.9314	+	6.31561i	−0.460080	+	0.224699i
$791$	29.6880	−	29.6880i	1.05559	−	1.05559i
$792$	−4.97501	−	5.42210i	−0.176779	−	0.192666i
$793$	−47.3278			−1.68066
$794$	−2.83449	+	1.58280i	−0.100592	+	0.0561713i
$795$	−4.11996	−	4.59964i	−0.146120	−	0.163132i
$796$	2.60185	+	10.9566i	0.0922203	+	0.388348i
$797$	−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
$800$	−18.3321	+	21.5392i	−0.648136	+	0.761524i
$801$	−2.72868	+	2.72868i	−0.0964133	+	0.0964133i
$802$	4.86470	+	8.71177i	0.171779	+	0.307623i
$803$		−	6.72559i		−	0.237341i
$804$	−31.1092	+	50.4853i	−1.09714	+	1.78048i
$805$	−34.3591	−	1.89014i	−1.21100	−	0.0666186i
$806$	39.1729	−	21.8744i	1.37981	−	0.770493i
$807$			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	$0.455724\pi$
$810$	11.5619	−	33.6363i	0.406243	−	1.18186i
$811$	0.574172			0.0201619			0.0100810	−	0.999949i	$-0.496791\pi$
$811$	0.574172			0.0201619			0.0100810	+	0.999949i	$0.496791\pi$
$812$	−6.60010	+	1.56731i	−0.231618	+	0.0550019i
$813$			48.0492i			1.68516i
$814$	−10.7470	−	19.2459i	−0.376683	−	0.674568i
$815$	0.235315	−	4.27758i	0.00824272	−	0.149837i
$816$	51.8435	−	26.0938i	1.81489	−	0.913467i
$817$	−7.43384			−0.260077
$818$	−14.0177	−	25.1030i	−0.490116	−	0.877706i
$819$	30.9152			1.08026
$820$	−28.5552	−	2.14451i	−0.997192	−	0.0748895i
$821$	21.9550			0.766234			0.383117	−	0.923700i	$-0.374851\pi$
$821$	21.9550			0.766234			0.383117	+	0.923700i	$0.374851\pi$
$822$	16.6953	+	29.8982i	0.582316	+	1.04282i
$823$	−19.3515			−0.674550			−0.337275	−	0.941406i	$-0.609505\pi$
$823$	−19.3515			−0.674550			−0.337275	+	0.941406i	$0.609505\pi$
$824$	−18.4923	+	16.9675i	−0.644211	+	0.591092i
$825$	11.1975	+	13.9755i	0.389847	+	0.486564i
$826$	−8.68938	−	15.5611i	−0.302342	−	0.541438i
$827$			9.30624i			0.323610i	0.986823	+	0.161805i	$0.0517315\pi$
$827$			9.30624i			0.323610i	−0.986823	+	0.161805i	$0.948268\pi$
$828$	−2.90273	−	12.2237i	−0.100877	−	0.424802i
$829$	−10.3721			−0.360238			−0.180119	−	0.983645i	$-0.557648\pi$
$829$	−10.3721			−0.360238			−0.180119	+	0.983645i	$0.557648\pi$
$830$	−7.66937	−	15.7033i	−0.266208	−	0.545069i
$831$	−24.5029	+	24.5029i	−0.849995	+	0.849995i
$832$	−3.61026	+	41.9012i	−0.125163	+	1.45266i
$833$			50.3857i			1.74576i
$834$	52.0293	−	29.0535i	1.80163	−	1.00604i
$835$	10.1975	+	11.3847i	0.352898	+	0.393985i
$836$	−2.18179	−	1.34443i	−0.0754588	−	0.0464980i
$837$			18.6725i			0.645416i
$838$	27.7378	+	49.6732i	0.958187	+	1.71593i
$839$	24.7870	−	24.7870i	0.855743	−	0.855743i	−0.135090	−	0.990833i	$-0.543133\pi$
$839$	24.7870	−	24.7870i	0.855743	−	0.855743i	0.990833	+	0.135090i	$0.0431325\pi$
$840$	39.5715	−	32.4917i	1.36535	−	1.12107i
$841$			28.2014i			0.972464i
$842$	−2.47885	−	0.702415i	−0.0854270	−	0.0242068i
$843$	−15.8685	+	15.8685i	−0.546542	+	0.546542i
$844$	11.7470	−	2.78953i	0.404347	−	0.0960197i
$845$	24.3787	−	21.8364i	0.838654	−	0.751194i
$846$	−13.2911	+	7.42182i	−0.456957	+	0.255167i
$847$	−31.0490			−1.06686
$848$	−4.62599	+	2.32835i	−0.158857	+	0.0799559i
$849$	6.10476	−	6.10476i	0.209515	−	0.209515i
$850$	−44.3183	+	18.7042i	−1.52010	+	0.641547i
$851$		−	37.6348i		−	1.29011i
$852$	6.37179	+	26.8322i	0.218294	+	0.919255i
$853$	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	$0.0597914\pi$
$854$	42.1922	−	23.5603i	1.44379	−	0.806219i
$855$	−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	$0.294558\pi$
$859$			46.8265i			1.59770i	−0.601530	+	0.798851i	$0.705442\pi$
$860$	24.8580	−	35.7790i	0.847652	−	1.22005i
$861$	50.1856	+	12.9832i	1.71032	+	0.442466i
$862$	−29.2694	+	16.3442i	−0.996921	+	0.556686i
$863$	−30.2514	−	30.2514i	−1.02977	−	1.02977i	−0.999543	−	0.0302260i	$-0.990377\pi$
$863$	−30.2514	−	30.2514i	−1.02977	−	1.02977i	−0.0302260	−	0.999543i	$-0.509623\pi$
$864$	−14.4929	−	9.81380i	−0.493058	−	0.333872i
$865$	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
$870$	2.64511	+	5.41596i	0.0896776	+	0.183618i
$871$		−	73.0796i		−	2.47621i
$872$	19.6037	−	17.9872i	0.663864	−	0.609124i
$873$			21.1704i			0.716509i
$874$	−2.13322	−	3.82019i	−0.0721571	−	0.129220i
$875$	−34.5247	+	24.6751i	−1.16715	+	0.834172i
$876$	3.94753	+	16.6234i	0.133375	+	0.561652i
$877$	−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
$880$	13.7664	−	6.00532i	0.464066	−	0.202439i
$881$		−	44.0125i		−	1.48282i	−0.671054	−	0.741409i	$-0.734158\pi$
$881$		−	44.0125i		−	1.48282i	0.671054	−	0.741409i	$-0.265842\pi$
$882$	−14.1691	+	7.91212i	−0.477099	+	0.266415i
$883$			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	$-0.188298\pi$
$887$	49.4435			1.66015			0.830075	+	0.557652i	$0.188298\pi$
$888$	37.8592	+	41.2615i	1.27047	+	1.38464i
$889$	−44.4536	+	44.4536i	−1.49093	+	1.49093i
$890$	−3.45648	−	7.07726i	−0.115861	−	0.237230i
$891$	−13.3551	+	13.3551i	−0.447413	+	0.447413i
$892$	7.02095	+	29.5659i	0.235079	+	0.989938i
$893$	−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
$896$	−17.6404	−	39.1516i	−0.589325	−	1.30796i
$897$	32.1467	+	32.1467i	1.07335	+	1.07335i
$898$	44.4866	−	24.8416i	1.48454	−	0.828975i
$899$	−3.81332	−	3.81332i	−0.127181	−	0.127181i
$900$	−12.2192	−	9.52576i	−0.407307	−	0.317525i
$901$	−8.80785			−0.293432
$902$	13.1253	+	7.67758i	0.437023	+	0.255636i
$903$	−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	$-0.567741\pi$
$907$	23.0761	−	23.0761i	0.766229	−	0.766229i	0.977440	+	0.211212i	$0.0677409\pi$
$908$	−4.20291	+	6.82066i	−0.139479	+	0.226352i
$909$	18.3512	−	18.3512i	0.608670	−	0.608670i
$910$	−20.5112	+	59.6721i	−0.679941	+	1.97811i
$911$	33.1983			1.09991			0.549954	−	0.835195i	$-0.314645\pi$
$911$	33.1983			1.09991			0.549954	+	0.835195i	$0.314645\pi$
$912$	6.18175	+	2.04238i	0.204698	+	0.0676301i
$913$			9.27998i			0.307123i
$914$	−13.6641	−	24.4699i	−0.451969	−	0.809391i
$915$	−28.6477	−	31.9830i	−0.947062	−	1.05733i
$916$	42.0775	−	9.99207i	1.39028	−	0.330147i
$917$		−	1.11437i		−	0.0367996i
$918$	−14.5130	−	25.9901i	−0.479001	−	0.857800i
$919$	32.9114	−	32.9114i	1.08565	−	1.08565i	0.0896774	−	0.995971i	$-0.471416\pi$
$919$	32.9114	−	32.9114i	1.08565	−	1.08565i	0.995971	−	0.0896774i	$-0.0285836\pi$
$920$	25.5198	+	2.50719i	0.841364	+	0.0826595i
$921$	−8.34555	+	8.34555i	−0.274995	+	0.274995i
$922$	7.14456	−	3.98956i	0.235293	−	0.131389i
$923$	−24.0320	−	24.0320i	−0.791024	−	0.791024i
$924$	−26.4530	+	6.28176i	−0.870241	+	0.206655i
$925$	−29.0201	−	36.2197i	−0.954175	−	1.19090i
$926$	16.8991	−	9.43657i	0.555340	−	0.310105i
$927$	−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	$0.676960\pi$
$930$	38.4937	+	13.2315i	1.26226	+	0.433879i
$931$	−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
$936$	−23.0163	−	0.989725i	−0.752313	−	0.0323502i
$937$			32.1288i			1.04960i	0.851225	+	0.524801i	$0.175860\pi$
$937$			32.1288i			1.04960i	−0.851225	+	0.524801i	$0.824140\pi$
$938$	36.3799	+	65.1496i	1.18785	+	2.12721i
$939$	−40.6592			−1.32686
$940$	−5.50730	−	30.5784i	−0.179628	−	0.997358i
$941$			46.4869i			1.51543i	0.652587	+	0.757714i	$0.273684\pi$
$941$			46.4869i			1.51543i	−0.652587	+	0.757714i	$0.726316\pi$
$942$	−7.34754	+	4.10291i	−0.239396	+	0.133680i
$943$	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
$946$	−20.1986	+	11.2790i	−0.656714	+	0.366713i
$947$	1.70879	+	1.70879i	0.0555281	+	0.0555281i	0.734326	−	0.678797i	$-0.237499\pi$
$947$	1.70879	+	1.70879i	0.0555281	+	0.0555281i	−0.678797	+	0.734326i	$0.737499\pi$
$948$	−18.8883	+	4.48536i	−0.613462	+	0.145678i
$949$	−14.8886	−	14.8886i	−0.483305	−	0.483305i
$950$	−4.99874	−	2.03163i	−0.162181	−	0.0659148i
$951$	−10.1961			−0.330632
$952$	3.13757	−	72.9652i	0.101689	−	2.36482i
$953$	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	$0.428781\pi$
$954$	−1.38311	−	2.47689i	−0.0447798	−	0.0801922i
$955$	−31.5301	−	1.73451i	−1.02029	−	0.0561275i
$956$	9.20161	−	2.18509i	0.297601	−	0.0706709i
$957$		−	3.20060i		−	0.103461i
$958$	−36.6732	−	10.3918i	−1.18486	−	0.335744i
$959$	43.0895			1.39143
$960$	−30.5012	+	22.9232i	−0.984420	+	0.739843i
$961$	−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	$-0.351860\pi$
$967$	27.9108			0.897550			0.448775	+	0.893645i	$0.351860\pi$
$968$	23.1159	+	0.994008i	0.742975	+	0.0319486i
$969$	7.82934	+	7.82934i	0.251515	+	0.251515i
$970$	−40.8628	−	14.0459i	−1.31203	−	0.450985i
$971$	−17.5385	+	17.5385i	−0.562838	+	0.562838i	−0.930113	−	0.367274i	$-0.880291\pi$
$971$	−17.5385	+	17.5385i	−0.562838	+	0.562838i	0.367274	+	0.930113i	$0.380291\pi$
$972$	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
$980$	−5.87113	−	32.5985i	−0.187546	−	1.04132i
$981$	10.3053	+	10.3053i	0.329021	+	0.329021i
$982$	−6.01369	−	10.7694i	−0.191905	−	0.343665i
$983$	−2.62116	+	2.62116i	−0.0836021	+	0.0836021i	−0.747671	−	0.664069i	$-0.768828\pi$
$983$	−2.62116	+	2.62116i	−0.0836021	+	0.0836021i	0.664069	+	0.747671i	$0.268828\pi$
$984$	−36.9475	−	11.2726i	−1.17784	−	0.359358i
$985$	−8.50764	−	0.468016i	−0.271076	−	0.0149122i
$986$	8.27160	+	2.34386i	0.263421	+	0.0746438i
$987$			56.2453i			1.79031i
$988$	−7.80608	+	1.85370i	−0.248344	+	0.0589739i
$989$	−39.4979			−1.25596
$990$	3.61052	+	7.39266i	0.114750	+	0.234954i
$991$	−0.239446	+	0.239446i	−0.00760624	+	0.00760624i	−0.710900	−	0.703293i	$-0.751712\pi$
$991$	−0.239446	+	0.239446i	−0.00760624	+	0.00760624i	0.703293	+	0.710900i	$0.251712\pi$
$992$	19.1411	−	28.2672i	0.607729	−	0.897485i
$993$	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
$996$	−5.44680	−	22.9370i	−0.172588	−	0.726786i
$997$	−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.583.102	yes	240
4.3	odd	2	inner	820.2.s.c.583.40	yes	240
5.2	odd	4		820.2.j.c.747.81	yes	240
20.7	even	4		820.2.j.c.747.19	yes	240
41.32	even	4		820.2.j.c.483.19	✓	240
164.155	odd	4		820.2.j.c.483.81	yes	240
205.32	odd	4	inner	820.2.s.c.647.40	yes	240
820.647	even	4	inner	820.2.s.c.647.102	yes	240

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(1.23475 - 0.689491i) q^{2} -2.13292 q^{3} +(1.04921 - 1.70269i) q^{4} +(-1.66560 + 1.49190i) q^{5} +(-2.63362 + 1.47063i) q^{6} +3.79559i q^{7} +(0.121513 - 2.82582i) q^{8} +1.54935 q^{9} +(-1.02794 + 2.99054i) q^{10} +(1.18738 - 1.18738i) q^{11} +(-2.23787 + 3.63171i) q^{12} -5.25705i q^{13} +(2.61703 + 4.68660i) q^{14} +(3.55260 - 3.18211i) q^{15} +(-1.79834 - 3.57295i) q^{16} -6.80287i q^{17} +(1.91306 - 1.06826i) q^{18} +(0.539583 - 0.539583i) q^{19} +(0.792697 + 4.40132i) q^{20} -8.09570i q^{21} +(0.647426 - 2.28480i) q^{22} +(2.86694 - 2.86694i) q^{23} +(-0.259177 + 6.02724i) q^{24} +(0.548453 - 4.96983i) q^{25} +(-3.62469 - 6.49114i) q^{26} +3.09412 q^{27} +(6.46273 + 3.98236i) q^{28} +(-0.631885 + 0.631885i) q^{29} +(2.19252 - 6.37859i) q^{30} +6.03484i q^{31} +(-4.68401 - 3.17176i) q^{32} +(-2.53258 + 2.53258i) q^{33} +(-4.69052 - 8.39983i) 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} +(4.01345 + 4.88797i) q^{40} +(-1.60372 + 6.19904i) q^{41} +(-5.58191 - 9.99615i) q^{42} +(-6.88851 - 6.88851i) q^{43} +(-0.775937 - 3.26754i) 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} +(-2.74945 - 6.51464i) q^{50} +14.5100i q^{51} +(-8.95115 - 5.51573i) q^{52} -1.29473i q^{53} +(3.82046 - 2.13336i) q^{54} +(-0.206245 + 3.74915i) q^{55} +(10.7256 + 0.461213i) q^{56} +(-1.15089 + 1.15089i) q^{57} +(-0.344540 + 1.21590i) q^{58} -3.32033 q^{59} +(-1.69076 - 9.38767i) q^{60} -9.00272i q^{61} +(4.16096 + 7.45150i) 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} +(-11.3509 - 3.90166i) q^{70} +(4.57139 - 4.57139i) q^{71} +(0.188266 - 4.37818i) q^{72} +(2.83212 - 2.83212i) q^{73} +(3.57885 - 12.6299i) q^{74} +(-1.16981 + 10.6003i) q^{75} +(-0.352611 - 1.48488i) q^{76} +(4.50680 + 4.50680i) q^{77} +(7.73117 + 13.8451i) q^{78} +(3.21799 + 3.21799i) q^{79} +(8.32581 + 3.26817i) q^{80} -11.2476 q^{81} +(2.29400 + 8.76000i) 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} +(-1.59265 + 4.63340i) q^{90} +19.9536 q^{91} +(-1.87351 - 7.88953i) q^{92} -12.8718i q^{93} +(-8.57848 + 4.79027i) q^{94} +(-0.0937245 + 1.70373i) q^{95} +(9.99062 + 6.76511i) q^{96} +13.6640i q^{97} +(-9.14520 + 5.10673i) 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