LMFDB - Embedded newform 820.2.j.c.483.81

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(483,820)] 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, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.483"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.j (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			483.81
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.81

$q$-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} -2.13292i q^{3} +(-1.04921 - 1.70269i) q^{4} +(1.66560 - 1.49190i) q^{5} +(-2.63362 - 1.47063i) q^{6} -3.79559 q^{7} +(-2.82582 + 0.121513i) q^{8} -1.54935 q^{9} +(-0.693708 - 3.08525i) q^{10} +(1.18738 + 1.18738i) q^{11} +(-3.63171 + 2.23787i) q^{12} -5.25705 q^{13} +(-2.61703 + 4.68660i) q^{14} +(-3.18211 - 3.55260i) q^{15} +(-1.79834 + 3.57295i) q^{16} +6.80287 q^{17} +(-1.06826 + 1.91306i) q^{18} +(-0.539583 - 0.539583i) q^{19} +(-4.28781 - 1.27070i) q^{20} +8.09570i q^{21} +(2.28480 - 0.647426i) 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} -3.09412i q^{27} +(3.98236 + 6.46273i) q^{28} +(0.631885 + 0.631885i) q^{29} +(-6.58060 + 1.47962i) q^{30} -6.03484i q^{31} +(3.17176 + 4.68401i) q^{32} +(2.53258 - 2.53258i) q^{33} +(4.69052 - 8.39983i) q^{34} +(-6.32194 + 5.66266i) q^{35} +(1.62559 + 2.63807i) q^{36} +(6.56359 - 6.56359i) q^{37} +(-1.03829 + 0.294211i) 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} +(0.775937 - 3.26754i) q^{44} +(-2.58060 + 2.31148i) q^{45} +(1.56322 + 5.51668i) q^{46} +6.94756i q^{47} +(7.62083 + 3.83571i) q^{48} +7.40653 q^{49} +(-5.75833 - 4.10385i) q^{50} -14.5100i q^{51} +(5.51573 + 8.95115i) q^{52} -1.29473 q^{53} +(-3.82046 - 2.13336i) q^{54} +(3.74915 + 0.206245i) q^{55} +(10.7256 - 0.461213i) q^{56} +(-1.15089 + 1.15089i) q^{57} +(1.21590 - 0.344540i) q^{58} +3.32033 q^{59} +(-2.71030 + 9.14556i) q^{60} +9.00272i q^{61} +(-7.45150 - 4.16096i) q^{62} +5.88071 q^{63} +(7.97047 - 0.686746i) q^{64} +(-8.75615 + 7.84301i) q^{65} +(-1.38091 - 4.87329i) q^{66} -13.9012i q^{67} +(-7.13761 - 11.5832i) q^{68} +(6.11496 + 6.11496i) q^{69} +(2.63303 + 11.7104i) 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} +(-10.6003 - 1.16981i) q^{75} +(-0.352611 + 1.48488i) 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} +(-8.76000 - 2.29400i) q^{82} +(3.90777 - 3.90777i) q^{83} +(13.7845 - 8.49405i) q^{84} +(11.3309 - 10.1492i) q^{85} +(-13.2551 + 3.75601i) q^{86} +(1.34776 - 1.34776i) q^{87} +(-3.49959 - 3.21103i) q^{88} +(1.76118 + 1.76118i) q^{89} +(1.07480 + 4.78014i) q^{90} +19.9536 q^{91} +(7.88953 + 1.87351i) q^{92} -12.8718 q^{93} +(8.57848 + 4.79027i) q^{94} +(-1.70373 - 0.0937245i) q^{95} +(9.99062 - 6.76511i) q^{96} -13.6640 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} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * 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 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

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

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

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
$3$		−	2.13292i		−	1.23144i	−0.787964	−	0.615721i	$-0.788865\pi$
$3$		−	2.13292i		−	1.23144i	0.787964	−	0.615721i	$-0.211135\pi$
$4$	−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
$7$	−3.79559			−1.43460			−0.717300	−	0.696765i	$-0.754622\pi$
$7$	−3.79559			−1.43460			−0.717300	+	0.696765i	$0.754622\pi$
$8$	−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	$-0.168534\pi$
$11$	1.18738	+	1.18738i	0.358008	+	0.358008i	−0.505071	+	0.863078i	$0.668534\pi$
$12$	−3.63171	+	2.23787i	−1.04839	+	0.646018i
$13$	−5.25705			−1.45804			−0.729022	−	0.684490i	$-0.760025\pi$
$13$	−5.25705			−1.45804			−0.729022	+	0.684490i	$0.760025\pi$
$14$	−2.61703	+	4.68660i	−0.699430	+	1.25255i
$15$	−3.18211	−	3.55260i	−0.821617	−	0.917276i
$16$	−1.79834	+	3.57295i	−0.449584	+	0.893238i
$17$	6.80287			1.64994			0.824969	−	0.565177i	$-0.191192\pi$
$17$	6.80287			1.64994			0.824969	+	0.565177i	$0.191192\pi$
$18$	−1.06826	+	1.91306i	−0.251792	+	0.450912i
$19$	−0.539583	−	0.539583i	−0.123789	−	0.123789i	0.642498	−	0.766287i	$-0.277898\pi$
$19$	−0.539583	−	0.539583i	−0.123789	−	0.123789i	−0.766287	+	0.642498i	$0.777898\pi$
$20$	−4.28781	−	1.27070i	−0.958784	−	0.284136i
$21$			8.09570i			1.76663i
$22$	2.28480	−	0.647426i	0.487120	−	0.138032i
$23$	−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	$0.388920\pi$
$24$	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
$27$		−	3.09412i		−	0.595463i
$28$	3.98236	+	6.46273i	0.752595	+	1.22134i
$29$	0.631885	+	0.631885i	0.117338	+	0.117338i	0.763338	−	0.646000i	$-0.223559\pi$
$29$	0.631885	+	0.631885i	0.117338	+	0.117338i	−0.646000	+	0.763338i	$0.723559\pi$
$30$	−6.58060	+	1.47962i	−1.20145	+	0.270141i
$31$		−	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
$34$	4.69052	−	8.39983i	0.804417	−	1.44056i
$35$	−6.32194	+	5.66266i	−1.06860	+	0.957164i
$36$	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	$-0.0262752\pi$
$38$	−1.03829	+	0.294211i	−0.168432	+	0.0477274i
$39$			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	$-0.983494\pi$
$43$	−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
$47$			6.94756i			1.01341i	0.862121	+	0.506703i	$0.169136\pi$
$47$			6.94756i			1.01341i	−0.862121	+	0.506703i	$0.830864\pi$
$48$	7.62083	+	3.83571i	1.09997	+	0.553637i
$49$	7.40653			1.05808
$50$	−5.75833	−	4.10385i	−0.814351	−	0.580372i
$51$		−	14.5100i		−	2.03180i
$52$	5.51573	+	8.95115i	0.764894	+	1.24130i
$53$	−1.29473			−0.177844			−0.0889221	−	0.996039i	$-0.528342\pi$
$53$	−1.29473			−0.177844			−0.0889221	+	0.996039i	$0.528342\pi$
$54$	−3.82046	−	2.13336i	−0.519898	−	0.290314i
$55$	3.74915	+	0.206245i	0.505535	+	0.0278101i
$56$	10.7256	−	0.461213i	1.43327	−	0.0616322i
$57$	−1.15089	+	1.15089i	−0.152439	+	0.152439i
$58$	1.21590	−	0.344540i	0.159655	−	0.0452403i
$59$	3.32033			0.432270			0.216135	−	0.976363i	$-0.430655\pi$
$59$	3.32033			0.432270			0.216135	+	0.976363i	$0.430655\pi$
$60$	−2.71030	+	9.14556i	−0.349898	+	1.18069i
$61$			9.00272i			1.15268i	0.817210	+	0.576340i	$0.195520\pi$
$61$			9.00272i			1.15268i	−0.817210	+	0.576340i	$0.804480\pi$
$62$	−7.45150	−	4.16096i	−0.946342	−	0.528443i
$63$	5.88071			0.740900
$64$	7.97047	−	0.686746i	0.996309	−	0.0858432i
$65$	−8.75615	+	7.84301i	−1.08607	+	0.972806i
$66$	−1.38091	−	4.87329i	−0.169978	−	0.599860i
$67$		−	13.9012i		−	1.69831i	−0.528146	−	0.849154i	$-0.677113\pi$
$67$		−	13.9012i		−	1.69831i	0.528146	−	0.849154i	$-0.322887\pi$
$68$	−7.13761	−	11.5832i	−0.865562	−	1.40467i
$69$	6.11496	+	6.11496i	0.736154	+	0.736154i
$70$	2.63303	+	11.7104i	0.314708	+	1.39966i
$71$	4.57139	+	4.57139i	0.542524	+	0.542524i	0.924268	−	0.381744i	$-0.124676\pi$
$71$	4.57139	+	4.57139i	0.542524	+	0.542524i	−0.381744	+	0.924268i	$0.624676\pi$
$72$	4.37818	−	0.188266i	0.515974	−	0.0221874i
$73$	−2.83212	+	2.83212i	−0.331475	+	0.331475i	−0.853146	−	0.521672i	$-0.825309\pi$
$73$	−2.83212	+	2.83212i	−0.331475	+	0.331475i	0.521672	+	0.853146i	$0.325309\pi$
$74$	−3.57885	−	12.6299i	−0.416032	−	1.46820i
$75$	−10.6003	−	1.16981i	−1.22401	−	0.135078i
$76$	−0.352611	+	1.48488i	−0.0404473	+	0.170327i
$77$	−4.50680	−	4.50680i	−0.513597	−	0.513597i
$78$	13.8451	+	7.73117i	1.56765	+	0.875383i
$79$	−3.21799	+	3.21799i	−0.362052	+	0.362052i	−0.864568	−	0.502516i	$-0.832408\pi$
$79$	−3.21799	+	3.21799i	−0.362052	+	0.362052i	0.502516	+	0.864568i	$0.332408\pi$
$80$	2.33519	+	8.63405i	0.261082	+	0.965317i
$81$	−11.2476			−1.24973
$82$	−8.76000	−	2.29400i	−0.967380	−	0.253329i
$83$	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
$85$	11.3309	−	10.1492i	1.22901	−	1.10084i
$86$	−13.2551	+	3.75601i	−1.42934	+	0.405021i
$87$	1.34776	−	1.34776i	0.144495	−	0.144495i
$88$	−3.49959	−	3.21103i	−0.373057	−	0.342297i
$89$	1.76118	+	1.76118i	0.186684	+	0.186684i	0.794261	−	0.607577i	$-0.207858\pi$
$89$	1.76118	+	1.76118i	0.186684	+	0.186684i	−0.607577	+	0.794261i	$0.707858\pi$
$90$	1.07480	+	4.78014i	0.113294	+	0.503871i
$91$	19.9536			2.09171
$92$	7.88953	+	1.87351i	0.822541	+	0.195327i
$93$	−12.8718			−1.33475
$94$	8.57848	+	4.79027i	0.884803	+	0.494079i
$95$	−1.70373	−	0.0937245i	−0.174799	−	0.00961593i
$96$	9.99062	−	6.76511i	1.01966	−	0.690462i
$97$	−13.6640			−1.38737			−0.693686	−	0.720278i	$-0.744014\pi$
$97$	−13.6640			−1.38737			−0.693686	+	0.720278i	$0.744014\pi$
$98$	5.10673	−	9.14520i	0.515858	−	0.923804i
$99$	−1.83966	−	1.83966i	−0.184893	−	0.184893i
$100$	−9.03754	+	4.28052i	−0.903754	+	0.428052i
$101$	11.8444	+	11.8444i	1.17856	+	1.17856i	0.980111	+	0.198452i	$0.0635914\pi$
$101$	11.8444	+	11.8444i	1.17856	+	1.17856i	0.198452	+	0.980111i	$0.436409\pi$
$102$	−17.9162	−	10.0045i	−1.77397	−	0.990593i
$103$	−6.27427	−	6.27427i	−0.618222	−	0.618222i	0.326853	−	0.945075i	$-0.394012\pi$
$103$	−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	$0.0306984\pi$
$107$	11.2921	+	11.2921i	1.09165	+	1.09165i	0.0962926	+	0.995353i	$0.469302\pi$
$108$	−5.26834	+	3.24637i	−0.506946	+	0.312382i
$109$	−6.65133	+	6.65133i	−0.637082	+	0.637082i	−0.949835	−	0.312753i	$-0.898749\pi$
$109$	−6.65133	+	6.65133i	−0.637082	+	0.637082i	0.312753	+	0.949835i	$0.398749\pi$
$110$	2.83966	−	4.48705i	0.270751	−	0.427823i
$111$	−13.9996	−	13.9996i	−1.32878	−	1.32878i
$112$	6.82575	−	13.5615i	0.644973	−	1.28144i
$113$	−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
$117$	8.14503			0.753008
$118$	2.28934	−	4.09977i	0.210750	−	0.377414i
$119$	−25.8209			−2.36700
$120$	9.42374	+	9.65231i	0.860266	+	0.881132i
$121$		−	8.18027i		−	0.743661i
$122$	11.1161	+	6.20729i	1.00640	+	0.561982i
$123$	−13.2221	+	3.42060i	−1.19219	+	0.308425i
$124$	−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	$-0.987243\pi$
$127$	−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
$130$	3.64686	+	16.2193i	0.319851	+	1.42253i
$131$	−0.293595			−0.0256515			−0.0128258	−	0.999918i	$-0.504083\pi$
$131$	−0.293595			−0.0256515			−0.0128258	+	0.999918i	$0.504083\pi$
$132$	−6.96941	−	1.65501i	−0.606609	−	0.144050i
$133$	2.04804	+	2.04804i	0.177587	+	0.177587i
$134$	−17.1645	−	9.58478i	−1.48279	−	0.827999i
$135$	−4.61612	−	5.15356i	−0.397293	−	0.443548i
$136$	−19.2237	+	0.826636i	−1.64842	+	0.0708835i
$137$	11.3525			0.969909			0.484955	−	0.874539i	$-0.338836\pi$
$137$	11.3525			0.969909			0.484955	+	0.874539i	$0.338836\pi$
$138$	11.7666	−	3.33423i	1.00164	−	0.283828i
$139$	19.7558			1.67567			0.837833	−	0.545927i	$-0.183822\pi$
$139$	19.7558			1.67567			0.837833	+	0.545927i	$0.183822\pi$
$140$	16.2748	+	4.82305i	1.37547	+	0.407622i
$141$	14.8186			1.24795
$142$	8.79644	−	2.49258i	0.738181	−	0.209173i
$143$	−6.24210	−	6.24210i	−0.521991	−	0.521991i
$144$	2.78625	−	5.53576i	0.232188	−	0.461313i
$145$	1.99518	+	0.109757i	0.165691	+	0.00911485i
$146$	1.54424	+	5.44968i	0.127802	+	0.451019i
$147$		−	15.7975i		−	1.30296i
$148$	−18.0623	−	4.28923i	−1.48472	−	0.352573i
$149$	11.4030	−	11.4030i	0.934171	−	0.934171i	−0.0637922	−	0.997963i	$-0.520319\pi$
$149$	11.4030	−	11.4030i	0.934171	−	0.934171i	0.997963	+	0.0637922i	$0.0203195\pi$
$150$	−8.75319	+	12.2821i	−0.714695	+	1.00283i
$151$	6.73143	+	6.73143i	0.547796	+	0.547796i	0.925803	−	0.378007i	$-0.123390\pi$
$151$	6.73143	+	6.73143i	0.547796	+	0.547796i	−0.378007	+	0.925803i	$0.623390\pi$
$152$	1.59033	+	1.45919i	0.128993	+	0.118356i
$153$	−10.5400			−0.852112
$154$	−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
$157$		−	2.78990i		−	0.222658i	−0.993784	−	0.111329i	$-0.964489\pi$
$157$		−	2.78990i		−	0.222658i	0.993784	−	0.111329i	$-0.0355108\pi$
$158$	1.75463	+	6.19218i	0.139591	+	0.492623i
$159$			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	$0.226094\pi$
$164$	−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
$167$	6.83522			0.528925			0.264462	−	0.964396i	$-0.414805\pi$
$167$	6.83522			0.528925			0.264462	+	0.964396i	$0.414805\pi$
$168$	−0.983731	−	22.8770i	−0.0758965	−	1.76500i
$169$	14.6366			1.12589
$170$	−4.71921	−	20.9886i	−0.361947	−	1.60975i
$171$	0.836003	+	0.836003i	0.0639308	+	0.0639308i
$172$	−4.50156	+	18.9565i	−0.343241	+	1.44542i
$173$	12.0418	−	12.0418i	0.915518	−	0.915518i	−0.0811817	−	0.996699i	$-0.525869\pi$
$173$	12.0418	−	12.0418i	0.915518	−	0.915518i	0.996699	+	0.0811817i	$0.0258694\pi$
$174$	−0.734877	−	2.59341i	−0.0557109	−	0.196606i
$175$	−2.08170	+	18.8634i	−0.157362	+	1.42594i
$176$	−6.37774	+	2.10714i	−0.480740	+	0.158832i
$177$		−	7.08200i		−	0.532316i
$178$	3.38892	−	0.960295i	0.254011	−	0.0719771i
$179$	−2.36638	−	2.36638i	−0.176872	−	0.176872i	0.613119	−	0.789991i	$-0.289915\pi$
$179$	−2.36638	−	2.36638i	−0.176872	−	0.176872i	−0.789991	+	0.613119i	$0.789915\pi$
$180$	6.64333	+	1.96876i	0.495165	+	0.146742i
$181$	−5.80793	−	5.80793i	−0.431700	−	0.431700i	0.457506	−	0.889206i	$-0.348743\pi$
$181$	−5.80793	−	5.80793i	−0.431700	−	0.431700i	−0.889206	+	0.457506i	$0.848743\pi$
$182$	13.7578	−	24.6377i	1.01980	−	1.82627i
$183$	19.2021			1.41946
$184$	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
$188$	11.8296	−	7.28941i	0.862760	−	0.531635i
$189$			11.7440i			0.854251i
$190$	−1.29043	+	2.03906i	−0.0936180	+	0.147929i
$191$	9.98578	−	9.98578i	0.722545	−	0.722545i	−0.246578	−	0.969123i	$-0.579306\pi$
$191$	9.98578	−	9.98578i	0.722545	−	0.722545i	0.969123	+	0.246578i	$0.0793060\pi$
$192$	−1.46477	−	17.0004i	−0.105711	−	1.22690i
$193$	4.94076			0.355644			0.177822	−	0.984063i	$-0.443095\pi$
$193$	4.94076			0.355644			0.177822	+	0.984063i	$0.443095\pi$
$194$	−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	0.604577	−	0.796547i	$-0.293342\pi$
$197$	−2.69442	−	2.69442i	−0.191969	−	0.191969i	−0.796547	+	0.604577i	$0.793342\pi$
$198$	−3.53995	+	1.00309i	−0.251574	+	0.0712866i
$199$	3.98148	+	3.98148i	0.282240	+	0.282240i	0.834002	−	0.551762i	$-0.186044\pi$
$199$	3.98148	+	3.98148i	0.282240	+	0.282240i	−0.551762	+	0.834002i	$0.686044\pi$
$200$	−0.945928	+	14.1105i	−0.0668872	+	0.997761i
$201$	−29.6503			−2.09137
$202$	22.7915	−	6.45825i	1.60360	−	0.454401i
$203$	−2.39838	−	2.39838i	−0.168333	−	0.168333i
$204$	−24.7061	+	15.2240i	−1.72977	+	1.06589i
$205$	−11.9195	−	7.93254i	−0.832495	−	0.554033i
$206$	−12.0732	+	3.42109i	−0.841179	+	0.238359i
$207$	4.44190	−	4.44190i	0.308733	−	0.308733i
$208$	9.45394	−	18.7832i	0.655513	−	1.30238i
$209$		−	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	$-0.683371\pi$
$211$	4.26868	−	4.26868i	0.293868	−	0.293868i	0.838606	+	0.544738i	$0.183371\pi$
$212$	1.35843	+	2.20452i	0.0932976	+	0.151407i
$213$	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
$217$			22.9058i			1.55495i
$218$	3.62669	+	12.7987i	0.245630	+	0.866841i
$219$	6.04069	+	6.04069i	0.408192	+	0.408192i
$220$	−3.58245	−	6.60004i	−0.241529	−	0.444975i
$221$	−35.7631			−2.40568
$222$	−26.9386	+	7.63340i	−1.80800	+	0.512320i
$223$	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	$0.0801138\pi$
$224$	−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
$227$			4.00580i			0.265875i	0.991124	+	0.132937i	$0.0424409\pi$
$227$			4.00580i			0.265875i	−0.991124	+	0.132937i	$0.957559\pi$
$228$	3.16713	+	0.752092i	0.209748	+	0.0498085i
$229$	−15.2903	+	15.2903i	−1.01041	+	1.01041i	−0.0104690	+	0.999945i	$0.503332\pi$
$229$	−15.2903	+	15.2903i	−1.01041	+	1.01041i	−0.999945	+	0.0104690i	$0.996668\pi$
$230$	10.8340	+	6.85641i	0.714376	+	0.452098i
$231$	−9.61265	+	9.61265i	−0.632466	+	0.632466i
$232$	−1.86237	−	1.70881i	−0.122271	−	0.112189i
$233$	−12.7190			−0.833248			−0.416624	−	0.909079i	$-0.636787\pi$
$233$	−12.7190			−0.833248			−0.416624	+	0.909079i	$0.636787\pi$
$234$	5.61592	−	10.0571i	0.367124	−	0.657450i
$235$	10.3651	+	11.5719i	0.676143	+	0.754865i
$236$	−3.48371	−	5.65350i	−0.226770	−	0.368012i
$237$	6.86372	+	6.86372i	0.445846	+	0.445846i
$238$	−17.8033	+	31.8823i	−1.15402	+	2.06663i
$239$	−3.34373	+	3.34373i	−0.216288	+	0.216288i	−0.806932	−	0.590644i	$-0.798874\pi$
$239$	−3.34373	+	3.34373i	−0.216288	+	0.216288i	0.590644	+	0.806932i	$0.298874\pi$
$240$	18.4158	−	4.98077i	1.18873	−	0.321507i
$241$		−	12.6414i		−	0.814302i	−0.913361	−	0.407151i	$-0.866522\pi$
$241$		−	12.6414i		−	0.814302i	0.913361	−	0.407151i	$-0.133478\pi$
$242$	−10.1006	−	5.64022i	−0.649290	−	0.362567i
$243$			14.7078i			0.943507i
$244$	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
$248$	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	$-0.258747\pi$
$251$	21.7813			1.37482			0.687411	+	0.726268i	$0.258747\pi$
$252$	−6.17007	−	10.0131i	−0.388678	−	0.630763i
$253$	−6.80828			−0.428033
$254$	−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
$257$			14.8162i			0.924207i	0.886826	+	0.462104i	$0.152905\pi$
$257$			14.8162i			0.924207i	−0.886826	+	0.462104i	$0.847095\pi$
$258$	8.01127	+	28.2721i	0.498760	+	1.76015i
$259$	−24.9127	+	24.9127i	−1.54800	+	1.54800i
$260$	22.5413	+	6.68012i	1.39795	+	0.414283i
$261$	−0.979013	−	0.979013i	−0.0605994	−	0.0605994i
$262$	−0.202431	+	0.362516i	−0.0125062	+	0.0223963i
$263$	−1.52403			−0.0939759			−0.0469880	−	0.998895i	$-0.514962\pi$
$263$	−1.52403			−0.0939759			−0.0469880	+	0.998895i	$0.514962\pi$
$264$	−6.84887	+	7.46435i	−0.421519	+	0.459399i
$265$	−2.15650	+	1.93160i	−0.132473	+	0.118658i
$266$	3.94091	−	1.11671i	0.241633	−	0.0684697i
$267$	3.75645	−	3.75645i	0.229891	−	0.229891i
$268$	−23.6696	+	14.5853i	−1.44585	+	0.890937i
$269$		−	32.6160i		−	1.98863i	−0.106471	−	0.994316i	$-0.533955\pi$
$269$		−	32.6160i		−	1.98863i	0.106471	−	0.994316i	$-0.466045\pi$
$270$	−9.54613	+	2.14641i	−0.580959	+	0.130627i
$271$			22.5274i			1.36844i	0.729274	+	0.684221i	$0.239858\pi$
$271$			22.5274i			1.36844i	−0.729274	+	0.684221i	$0.760142\pi$
$272$	−12.2338	+	24.3063i	−0.741786	+	1.47379i
$273$		−	42.5595i		−	2.57582i
$274$	7.82744	−	14.0175i	0.472873	−	0.846826i
$275$	6.55228	−	5.24984i	0.395117	−	0.316577i
$276$	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	$0.0876990\pi$
$278$	13.6214	−	24.3934i	0.816960	−	1.46302i
$279$			9.35009i			0.559775i
$280$	17.1766	−	16.7698i	1.02650	−	1.00219i
$281$	7.43982	+	7.43982i	0.443822	+	0.443822i	0.893294	−	0.449472i	$-0.148388\pi$
$281$	7.43982	+	7.43982i	0.443822	+	0.443822i	−0.449472	+	0.893294i	$0.648388\pi$
$282$	10.2173	−	18.2972i	0.608430	−	1.08958i
$283$	2.86216	−	2.86216i	0.170138	−	0.170138i	−0.616902	−	0.787040i	$-0.711613\pi$
$283$	2.86216	−	2.86216i	0.170138	−	0.170138i	0.787040	+	0.616902i	$0.211613\pi$
$284$	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
$287$	6.08705	+	23.5290i	0.359307	+	1.38887i
$288$	−4.91417	−	7.25718i	−0.289570	−	0.427633i
$289$	29.2791			1.72230
$290$	1.51118	−	2.38787i	0.0887396	−	0.140220i
$291$			29.1443i			1.70847i
$292$	7.79372	+	1.85076i	0.456093	+	0.108308i
$293$			17.6019i			1.02831i	0.857697	+	0.514156i	$0.171895\pi$
$293$			17.6019i			1.02831i	−0.857697	+	0.514156i	$0.828105\pi$
$294$	−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
$298$	−6.21758	−	21.9421i	−0.360175	−	1.27107i
$299$	15.0717	−	15.0717i	0.871617	−	0.871617i
$300$	9.13002	+	19.2764i	0.527122	+	1.11292i
$301$	26.1460	+	26.1460i	1.50703	+	1.50703i
$302$	12.9529	−	3.67037i	0.745355	−	0.211206i
$303$	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	$0.199526\pi$
$308$	−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	$-0.699762\pi$
$311$	3.91988	−	3.91988i	0.222276	−	0.222276i	0.809456	+	0.587180i	$0.199762\pi$
$312$	−1.36251	−	31.6855i	−0.0771368	−	1.79384i
$313$			19.0627i			1.07749i	0.842470	+	0.538743i	$0.181101\pi$
$313$			19.0627i			1.07749i	−0.842470	+	0.538743i	$0.818899\pi$
$314$	−3.44483	−	1.92361i	−0.194403	−	0.108556i
$315$	9.79492	−	8.77345i	0.551881	−	0.494328i
$316$	8.85558	+	2.10292i	0.498165	+	0.118298i
$317$		−	4.78035i		−	0.268491i	−0.990948	−	0.134246i	$-0.957139\pi$
$317$		−	4.78035i		−	0.268491i	0.990948	−	0.134246i	$-0.0428612\pi$
$318$	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
$322$	−5.93335	−	20.9391i	−0.330653	−	1.16689i
$323$	−3.67071	−	3.67071i	−0.204244	−	0.204244i
$324$	11.8010	+	19.1512i	0.655611	+	1.06395i
$325$	−2.88324	+	26.1267i	−0.159934	+	1.44925i
$326$	−0.738679	−	2.60683i	−0.0409117	−	0.144379i
$327$	14.1868	+	14.1868i	0.784530	+	0.784530i
$328$	5.28507	+	17.3225i	0.291819	+	0.956474i
$329$		−	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	$-0.251573\pi$
$331$	−0.127120	−	0.127120i	−0.00698714	−	0.00698714i	−0.710592	+	0.703605i	$0.751573\pi$
$332$	−10.7538	−	2.55368i	−0.590190	−	0.140151i
$333$	−10.1693	+	10.1693i	−0.557275	+	0.557275i
$334$	4.71282	−	8.43977i	0.257874	−	0.461804i
$335$	−20.7393	−	23.1539i	−1.13311	−	1.26503i
$336$	−28.9256	−	14.5588i	−1.57802	−	0.794247i
$337$	−1.53712	−	1.53712i	−0.0837321	−	0.0837321i	0.664000	−	0.747732i	$-0.268857\pi$
$337$	−1.53712	−	1.53712i	−0.0837321	−	0.0837321i	−0.747732	+	0.664000i	$0.768857\pi$
$338$	10.0918	−	18.0725i	0.548921	−	0.983015i
$339$	−16.6831	+	16.6831i	−0.906101	+	0.906101i
$340$	−29.1694	−	8.64439i	−1.58193	−	0.468808i
$341$	7.16562	−	7.16562i	0.388040	−	0.388040i
$342$	1.60867	−	0.455837i	0.0869869	−	0.0246489i
$343$	−1.54301			−0.0833149
$344$	20.3027	+	18.6286i	1.09465	+	1.00439i
$345$	19.3080	+	1.06216i	1.03951	+	0.0571846i
$346$	−6.56586	−	23.1712i	−0.352983	−	1.24569i
$347$			4.28660i			0.230117i	0.993359	+	0.115058i	$0.0367055\pi$
$347$			4.28660i			0.230117i	−0.993359	+	0.115058i	$0.963294\pi$
$348$	−3.70890	−	0.880747i	−0.198818	−	0.0472130i
$349$	−26.6440			−1.42622			−0.713110	−	0.701053i	$-0.752714\pi$
$349$	−26.6440			−1.42622			−0.713110	+	0.701053i	$0.752714\pi$
$350$	21.8563	+	15.5765i	1.16827	+	0.832602i
$351$			16.2659i			0.868212i
$352$	−1.79561	+	9.32776i	−0.0957062	+	0.497171i
$353$	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
$355$	14.4342	+	0.794042i	0.766087	+	0.0421434i
$356$	1.15091	−	4.84658i	0.0609981	−	0.256868i
$357$			55.0740i			2.91483i
$358$	−4.55348	+	1.29029i	−0.240659	+	0.0681938i
$359$	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
$362$	−11.1758	+	3.16682i	−0.587389	+	0.166444i
$363$	−17.4479			−0.915776
$364$	−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	$0.421787\pi$
$368$	−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
$372$	13.5052	+	21.9168i	0.700212	+	1.13633i
$373$	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
$375$	−19.4010	+	13.8661i	−1.00186	+	0.716043i
$376$	−0.844217	−	19.6325i	−0.0435372	−	1.01247i
$377$	−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	$0.369111\pi$
$380$	1.62798	+	2.99927i	0.0835138	+	0.153860i
$381$	−24.9806	+	24.9806i	−1.27979	+	1.27979i
$382$	−5.44482	−	19.2150i	−0.278581	−	0.983126i
$383$	−0.130134			−0.00664953			−0.00332476	−	0.999994i	$-0.501058\pi$
$383$	−0.130134			−0.00664953			−0.00332476	+	0.999994i	$0.501058\pi$
$384$	−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
$388$	14.3364	+	23.2657i	0.727819	+	1.18113i
$389$	10.7898			0.547064			0.273532	−	0.961863i	$-0.411808\pi$
$389$	10.7898			0.547064			0.273532	+	0.961863i	$0.411808\pi$
$390$	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
$393$			0.626215i			0.0315884i
$394$	−5.18470	+	1.46915i	−0.261202	+	0.0740148i
$395$	−0.558959	+	10.1608i	−0.0281243	+	0.511246i
$396$	−1.20220	+	5.06257i	−0.0604128	+	0.254404i
$397$			2.29560i			0.115213i	0.998339	+	0.0576065i	$0.0183469\pi$
$397$			2.29560i			0.115213i	−0.998339	+	0.0576065i	$0.981653\pi$
$398$	7.66132	−	2.17093i	0.384027	−	0.108819i
$399$	4.36830	−	4.36830i	0.218689	−	0.218689i
$400$	16.7707	+	10.8970i	0.838533	+	0.544851i
$401$		−	7.05550i		−	0.352335i	−0.984360	−	0.176167i	$-0.943630\pi$
$401$		−	7.05550i		−	0.352335i	0.984360	−	0.176167i	$-0.0563700\pi$
$402$	−20.4436	+	36.6106i	−1.01963	+	1.82597i
$403$			31.7255i			1.58036i
$404$	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
$407$	15.5869			0.772614
$408$	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	$-0.167637\pi$
$410$	−18.0131	+	9.24819i	−0.889603	+	0.456735i
$411$		−	24.2140i		−	1.19439i
$412$	−4.10016	+	17.2662i	−0.202001	+	0.850642i
$413$	−12.6026			−0.620134
$414$	−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
$417$		−	42.1376i		−	2.06349i
$418$	−1.58218	−	0.883496i	−0.0773868	−	0.0432132i
$419$			40.2294i			1.96534i	0.185374	+	0.982668i	$0.440650\pi$
$419$			40.2294i			1.96534i	−0.185374	+	0.982668i	$0.559350\pi$
$420$	10.2872	−	34.7128i	0.501963	−	1.69381i
$421$	−1.28823	+	1.28823i	−0.0627843	+	0.0627843i	−0.737802	−	0.675017i	$-0.764136\pi$
$421$	−1.28823	+	1.28823i	−0.0627843	+	0.0627843i	0.675017	+	0.737802i	$0.264136\pi$
$422$	−2.32753	−	8.21395i	−0.113302	−	0.399849i
$423$		−	10.7642i		−	0.523374i
$424$	3.65866	−	0.157326i	0.177680	−	0.00764041i
$425$	3.73105	−	33.8091i	0.180983	−	1.63998i
$426$	−5.31649	−	18.7621i	−0.257585	−	0.909028i
$427$		−	34.1707i		−	1.65363i
$428$	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	$-0.693409\pi$
$431$	−23.7048			−1.14182			−0.570909	+	0.821013i	$0.693409\pi$
$432$	11.0551	+	5.56426i	0.531890	+	0.267711i
$433$	−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
$437$	3.09390			0.148001
$438$	11.6237	−	3.29373i	0.555404	−	0.157381i
$439$	−16.1547	+	16.1547i	−0.771022	+	0.771022i	−0.978285	−	0.207263i	$-0.933544\pi$
$439$	−16.1547	+	16.1547i	−0.771022	+	0.771022i	0.207263	+	0.978285i	$0.433544\pi$
$440$	−10.6195	−	0.127241i	−0.506263	−	0.00606600i
$441$	−11.4753			−0.546444
$442$	−24.6583	+	44.1584i	−1.17288	+	2.10040i
$443$	−11.2601	−	11.2601i	−0.534984	−	0.534984i	0.387067	−	0.922051i	$-0.373488\pi$
$443$	−11.2601	−	11.2601i	−0.534984	−	0.534984i	−0.922051	+	0.387067i	$0.873488\pi$
$444$	−9.14859	+	38.5255i	−0.434173	+	1.82834i
$445$	5.56092	+	0.305913i	0.263613	+	0.0145017i
$446$	−5.85814	−	20.6736i	−0.277391	−	0.978925i
$447$	−24.3217	−	24.3217i	−1.15038	−	1.15038i
$448$	−30.2527	+	2.60661i	−1.42930	+	0.123151i
$449$	−36.0289			−1.70031			−0.850155	−	0.526533i	$-0.823492\pi$
$449$	−36.0289			−1.70031			−0.850155	+	0.526533i	$0.823492\pi$
$450$	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
$454$	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
$457$	19.8177			0.927032			0.463516	−	0.886088i	$-0.346588\pi$
$457$	19.8177			0.927032			0.463516	+	0.886088i	$0.346588\pi$
$458$	8.33717	+	29.4223i	0.389571	+	1.37481i
$459$		−	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	$0.456978\pi$
$462$	5.24137	+	18.4970i	0.243850	+	0.860559i
$463$			13.6863i			0.636056i	0.948081	+	0.318028i	$0.103021\pi$
$463$			13.6863i			0.636056i	−0.948081	+	0.318028i	$0.896979\pi$
$464$	−3.39404	+	1.12135i	−0.157564	+	0.0520576i
$465$	−21.4393	+	19.2035i	−0.994225	+	0.890542i
$466$	−8.76962	+	15.7047i	−0.406245	+	0.727508i
$467$	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	$0.342860\pi$
$468$	−8.54581	−	13.8685i	−0.395030	−	0.641071i
$469$			52.7635i			2.43639i
$470$	21.4350	−	4.81957i	0.988721	−	0.222310i
$471$	−5.95064			−0.274191
$472$	−9.38264	+	0.403462i	−0.431871	+	0.0185709i
$473$		−	16.3585i		−	0.752165i
$474$	13.2074	−	3.74249i	0.606637	−	0.171898i
$475$	−2.97757	+	2.38570i	−0.136620	+	0.109463i
$476$	27.0915	+	43.9652i	1.24174	+	2.01514i
$477$	2.00599			0.0918478
$478$	1.82319	+	6.43413i	0.0833909	+	0.294290i
$479$	19.0585	−	19.0585i	0.870806	−	0.870806i	−0.121754	−	0.992560i	$-0.538852\pi$
$479$	19.0585	−	19.0585i	0.870806	−	0.870806i	0.992560	+	0.121754i	$0.0388519\pi$
$480$	6.54749	−	26.1730i	0.298851	−	1.19463i
$481$	−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
$485$	−22.7588	+	20.3854i	−1.03342	+	0.925653i
$486$	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	$0.235398\pi$
$488$	−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	$0.936943\pi$
$492$	19.6969	+	18.9242i	0.888005	+	0.853170i
$493$	4.29863	+	4.29863i	0.193601	+	0.193601i
$494$	5.45832	−	1.54669i	0.245582	−	0.0695887i
$495$	−5.80875	−	0.319546i	−0.261084	−	0.0143625i
$496$	21.5622	+	10.8527i	0.968171	+	0.487299i
$497$	−17.3511	−	17.3511i	−0.778305	−	0.778305i
$498$	−16.0384	+	4.54470i	−0.718700	+	0.203653i
$499$	−9.64801	+	9.64801i	−0.431904	+	0.431904i	−0.889276	−	0.457371i	$-0.848791\pi$
$499$	−9.64801	+	9.64801i	−0.431904	+	0.431904i	0.457371	+	0.889276i	$0.348791\pi$
$500$	−8.66681	+	20.6128i	−0.387591	+	0.921831i
$501$		−	14.5790i		−	0.651341i
$502$	15.0180	−	26.8944i	0.670286	−	1.20036i
$503$			15.3459i			0.684238i	0.939657	+	0.342119i	$0.111145\pi$
$503$			15.3459i			0.684238i	−0.939657	+	0.342119i	$0.888855\pi$
$504$	−16.6178	+	0.714582i	−0.740216	+	0.0318300i
$505$	37.3988	+	2.05735i	1.66422	+	0.0915510i
$506$	−4.69424	+	8.40651i	−0.208685	+	0.373715i
$507$		−	31.2187i		−	1.38647i
$508$	−7.65360	+	32.2300i	−0.339574	+	1.42997i
$509$	0.483014	−	0.483014i	0.0214092	−	0.0214092i	−0.696321	−	0.717730i	$-0.745181\pi$
$509$	0.483014	−	0.483014i	0.0214092	−	0.0214092i	0.717730	+	0.696321i	$0.245181\pi$
$510$	−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
$514$	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
$518$	13.5838	+	47.9380i	0.596840	+	2.10628i
$519$	−25.6841	−	25.6841i	−1.12741	−	1.12741i
$520$	23.7902	−	23.2269i	1.04327	−	1.01857i
$521$	−4.92026	+	4.92026i	−0.215561	+	0.215561i	−0.806625	−	0.591064i	$-0.798708\pi$
$521$	−4.92026	+	4.92026i	−0.215561	+	0.215561i	0.591064	+	0.806625i	$0.298708\pi$
$522$	−1.88385	+	0.533814i	−0.0824540	+	0.0233644i
$523$	−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
$526$	−1.05081	+	1.88180i	−0.0458173	+	0.0820502i
$527$		−	41.0542i		−	1.78835i
$528$	4.49436	+	13.6032i	0.195592	+	0.592004i
$529$			6.56130i			0.285274i
$530$	0.898161	+	3.99455i	0.0390136	+	0.173512i
$531$	−5.14436			−0.223246
$532$	1.33837	−	5.63599i	0.0580256	−	0.244351i
$533$	8.43082	+	32.5887i	0.365179	+	1.41157i
$534$	−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
$538$	−40.2725	−	22.4884i	−1.73627	−	0.969544i
$539$	8.79434	+	8.79434i	0.378799	+	0.378799i
$540$	−3.93168	+	13.2670i	−0.169193	+	0.570921i
$541$			16.2492i			0.698607i	0.937010	+	0.349303i	$0.113582\pi$
$541$			16.2492i			0.698607i	−0.937010	+	0.349303i	$0.886418\pi$
$542$	27.8157	+	15.5324i	1.19479	+	0.667175i
$543$	−12.3879	+	12.3879i	−0.531614	+	0.531614i
$544$	21.5771	+	31.8647i	0.925110	+	1.36619i
$545$	−1.15532	+	21.0016i	−0.0494886	+	0.899610i
$546$	−52.5503	−	29.3444i	−2.24894	−	1.25582i
$547$			23.9813i			1.02537i	0.858578	+	0.512684i	$0.171349\pi$
$547$			23.9813i			1.02537i	−0.858578	+	0.512684i	$0.828651\pi$
$548$	−11.9111	−	19.3298i	−0.508817	−	0.825729i
$549$		−	13.9484i		−	0.595302i
$550$	−1.96449	−	11.7101i	−0.0837663	−	0.499322i
$551$		−	0.681909i		−	0.0290503i
$552$	−18.0228	−	16.5367i	−0.767101	−	0.703849i
$553$	12.2142	−	12.2142i	0.519400	−	0.519400i
$554$	−6.26388	−	22.1055i	−0.266127	−	0.939174i
$555$	−44.2038	−	2.43171i	−1.87635	−	0.103220i
$556$	−20.7279	−	33.6381i	−0.879059	−	1.42657i
$557$	0.333252			0.0141203			0.00706017	−	0.999975i	$-0.497753\pi$
$557$	0.333252			0.0141203			0.00706017	+	0.999975i	$0.497753\pi$
$558$	11.5450	+	6.44680i	0.488739	+	0.272915i
$559$	36.2132	+	36.2132i	1.53166	+	1.53166i
$560$	−8.86342	−	32.7714i	−0.374548	−	1.38484i
$561$	17.2288	−	17.2288i	0.727401	−	0.727401i
$562$	14.3160	−	4.05662i	0.603883	−	0.171118i
$563$		−	2.33241i		−	0.0982992i	−0.998791	−	0.0491496i	$-0.984349\pi$
$563$		−	2.33241i		−	0.0982992i	0.998791	−	0.0491496i	$-0.0156511\pi$
$564$	−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
$567$	42.6912			1.79286
$568$	−13.4734	−	12.3624i	−0.565331	−	0.518716i
$569$	−14.2563			−0.597655			−0.298827	−	0.954307i	$-0.596595\pi$
$569$	−14.2563			−0.597655			−0.298827	+	0.954307i	$0.596595\pi$
$570$	4.34915	+	2.75240i	0.182166	+	0.115285i
$571$	−5.51345	−	5.51345i	−0.230731	−	0.230731i	0.582267	−	0.812998i	$-0.302166\pi$
$571$	−5.51345	−	5.51345i	−0.230731	−	0.230731i	−0.812998	+	0.582267i	$0.802166\pi$
$572$	−4.07914	+	17.1776i	−0.170558	+	0.718233i
$573$	−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
$577$		−	24.6132i		−	1.02466i	−0.858788	−	0.512331i	$-0.828782\pi$
$577$		−	24.6132i		−	1.02466i	0.858788	−	0.512331i	$-0.171218\pi$
$578$	20.1876	−	36.1523i	0.839695	−	1.50374i
$579$		−	10.5383i		−	0.437955i
$580$	−1.90647	−	3.51234i	−0.0791619	−	0.145842i
$581$	−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
$585$	13.5664	−	12.1516i	0.560900	−	0.502406i
$586$	21.7339	+	12.1363i	0.897818	+	0.501347i
$587$	19.7772			0.816291			0.408146	−	0.912917i	$-0.366176\pi$
$587$	19.7772			0.816291			0.408146	+	0.912917i	$0.366176\pi$
$588$	−26.8984	+	16.5749i	−1.10927	+	0.683536i
$589$	−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
$593$			4.91495i			0.201833i	0.994895	+	0.100916i	$0.0321775\pi$
$593$			4.91495i			0.201833i	−0.994895	+	0.100916i	$0.967823\pi$
$594$	−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
$598$	−8.21793	−	29.0015i	−0.336056	−	1.18596i
$599$	1.03660			0.0423544			0.0211772	−	0.999776i	$-0.493259\pi$
$599$	1.03660			0.0423544			0.0211772	+	0.999776i	$0.493259\pi$
$600$	30.0965	+	2.01759i	1.22868	+	0.0823677i
$601$	−6.81030	−	6.81030i	−0.277798	−	0.277798i	0.554431	−	0.832229i	$-0.312936\pi$
$601$	−6.81030	−	6.81030i	−0.277798	−	0.277798i	−0.832229	+	0.554431i	$0.812936\pi$
$602$	50.3111	−	14.2563i	2.05053	−	0.581043i
$603$			21.5379i			0.877092i
$604$	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	$-0.0495024\pi$
$608$	0.815983	−	4.23884i	0.0330925	−	0.171908i
$609$	−5.11555	+	5.11555i	−0.207293	+	0.207293i
$610$	27.7756	−	6.24526i	1.12460	−	0.252863i
$611$		−	36.5237i		−	1.47759i
$612$	11.0587	+	17.9465i	0.447020	+	0.725443i
$613$	−17.5994	+	17.5994i	−0.710831	+	0.710831i	−0.966709	−	0.255878i	$-0.917636\pi$
$613$	−17.5994	+	17.5994i	−0.710831	+	0.710831i	0.255878	+	0.966709i	$0.417636\pi$
$614$	−2.13345	−	7.52903i	−0.0860989	−	0.303847i
$615$	−16.9195	+	25.4234i	−0.682259	+	1.02517i
$616$	13.2830	+	12.1877i	0.535188	+	0.491058i
$617$	−26.7297	−	26.7297i	−1.07610	−	1.07610i	−0.996855	−	0.0792413i	$-0.974750\pi$
$617$	−26.7297	−	26.7297i	−1.07610	−	1.07610i	−0.0792413	−	0.996855i	$-0.525250\pi$
$618$	7.29692	+	25.7512i	0.293525	+	1.03586i
$619$	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
$622$	−2.13735	−	7.54279i	−0.0856998	−	0.302438i
$623$	−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
$627$	−2.73307			−0.109148
$628$	−4.75035	+	2.92718i	−0.189560	+	0.116807i
$629$	44.6513	−	44.6513i	1.78036	−	1.78036i
$630$	−4.07949	−	18.1435i	−0.162531	−	0.722853i
$631$		−	25.9194i		−	1.03183i	−0.856638	−	0.515917i	$-0.827451\pi$
$631$		−	25.9194i		−	1.03183i	0.856638	−	0.515917i	$-0.172549\pi$
$632$	8.70242	−	9.48447i	0.346164	−	0.377272i
$633$	−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
$637$	−38.9365			−1.54272
$638$	1.85283	+	1.03463i	0.0733541	+	0.0409614i
$639$	−7.08269	−	7.08269i	−0.280187	−	0.280187i
$640$	−7.64796	−	24.1145i	−0.302312	−	0.953209i
$641$	12.9169	+	12.9169i	0.510187	+	0.510187i	0.914584	−	0.404397i	$-0.132518\pi$
$641$	12.9169	+	12.9169i	0.510187	+	0.510187i	−0.404397	+	0.914584i	$0.632518\pi$
$642$	−13.1326	−	46.3455i	−0.518301	−	1.82911i
$643$		−	23.5362i		−	0.928176i	−0.885789	−	0.464088i	$-0.846382\pi$
$643$		−	23.5362i		−	0.928176i	0.885789	−	0.464088i	$-0.153618\pi$
$644$	−29.9455	−	7.11110i	−1.18002	−	0.280216i
$645$	−2.55208	+	46.3921i	−0.100488	+	1.82669i
$646$	−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	$0.200709\pi$
$648$	31.7835	−	1.36672i	1.24858	−	0.0536900i
$649$	3.94248	+	3.94248i	0.154756	+	0.154756i
$650$	30.2719	+	21.5742i	1.18736	+	0.846208i
$651$	48.8562			1.91483
$652$	−3.72809	−	0.885304i	−0.146003	−	0.0346712i
$653$	19.8841			0.778126			0.389063	−	0.921211i	$-0.372799\pi$
$653$	19.8841			0.778126			0.389063	+	0.921211i	$0.372799\pi$
$654$	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
$658$	−32.5604	−	18.1819i	−1.26934	−	0.708806i
$659$	−11.2904	+	11.2904i	−0.439813	+	0.439813i	−0.891949	−	0.452136i	$-0.850662\pi$
$659$	−11.2904	+	11.2904i	−0.439813	+	0.439813i	0.452136	+	0.891949i	$0.350662\pi$
$660$	−14.0774	+	7.64109i	−0.547961	+	0.297429i
$661$		−	7.08423i		−	0.275545i	−0.990464	−	0.137772i	$-0.956006\pi$
$661$		−	7.08423i		−	0.275545i	0.990464	−	0.137772i	$-0.0439942\pi$
$662$	−0.244609	+	0.0693131i	−0.00950700	+	0.00269393i
$663$			76.2798i			2.96246i
$664$	−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
$667$	−3.62315			−0.140289
$668$	−7.17155	−	11.6383i	−0.277475	−	0.450299i
$669$	−22.9157	−	22.9157i	−0.885971	−	0.885971i
$670$	−42.8888	+	9.64340i	−1.65694	+	0.372557i
$671$	−10.6896	+	10.6896i	−0.412668	+	0.412668i
$672$	−37.9203	+	25.6776i	−1.46281	+	0.990536i
$673$			20.1396i			0.776325i	0.921591	+	0.388163i	$0.126890\pi$
$673$			20.1396i			0.776325i	−0.921591	+	0.388163i	$0.873110\pi$
$674$	−2.95778	+	0.838124i	−0.113929	+	0.0322833i
$675$	−15.3772	−	1.69698i	−0.591870	−	0.0653167i
$676$	−15.3568	−	24.9217i	−0.590646	−	0.958525i
$677$	17.7389	+	17.7389i	0.681761	+	0.681761i	0.960397	−	0.278636i	$-0.0898822\pi$
$677$	17.7389	+	17.7389i	0.681761	+	0.681761i	−0.278636	+	0.960397i	$0.589882\pi$
$678$	9.09658	+	32.1023i	0.349352	+	1.23288i
$679$	51.8631			1.99032
$680$	−30.7857	+	30.0567i	−1.18058	+	1.15262i
$681$	8.54406			0.327409
$682$	−3.90711	−	13.7884i	−0.149611	−	0.527984i
$683$	26.4254			1.01114			0.505570	−	0.862786i	$-0.331282\pi$
$683$	26.4254			1.01114			0.505570	+	0.862786i	$0.331282\pi$
$684$	0.546319	−	2.30060i	0.0208890	−	0.0879656i
$685$	18.9087	−	16.9368i	0.722465	−	0.647123i
$686$	−1.06389	+	1.90523i	−0.0406196	+	0.0727421i
$687$	32.6131	+	32.6131i	1.24427	+	1.24427i
$688$	37.0001	−	12.2245i	1.41062	−	0.466053i
$689$	6.80644			0.259305
$690$	14.6242	−	23.1082i	0.556733	−	0.879713i
$691$	26.1406	−	26.1406i	0.994434	−	0.994434i	−0.00555091	−	0.999985i	$-0.501767\pi$
$691$	26.1406	−	26.1406i	0.994434	−	0.994434i	0.999985	+	0.00555091i	$0.00176692\pi$
$692$	−33.1377	−	7.86915i	−1.25971	−	0.299140i
$693$	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
$697$	−10.9099	−	42.1713i	−0.413241	−	1.59735i
$698$	−18.3708	+	32.8986i	−0.695344	+	1.24523i
$699$			27.1286i			1.02610i
$700$	34.3028	−	16.2471i	1.29652	−	0.614084i
$701$	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
$703$	−7.08320			−0.267148
$704$	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
$708$	−12.0585	+	7.43047i	−0.453185	+	0.279254i
$709$	−18.2745	−	18.2745i	−0.686313	−	0.686313i	0.275102	−	0.961415i	$-0.411288\pi$
$709$	−18.2745	−	18.2745i	−0.686313	−	0.686313i	−0.961415	+	0.275102i	$0.911288\pi$
$710$	10.9327	−	17.2751i	0.410296	−	0.648323i
$711$	4.98580	−	4.98580i	0.186982	−	0.186982i
$712$	−5.19077	−	4.76276i	−0.194532	−	0.178492i
$713$	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
$718$	16.9707	−	30.3913i	0.633341	−	1.13419i
$719$	−27.5925	−	27.5925i	−1.02903	−	1.02903i	−0.999566	−	0.0294593i	$-0.990621\pi$
$719$	−27.5925	−	27.5925i	−1.02903	−	1.02903i	−0.0294593	−	0.999566i	$-0.509379\pi$
$720$	−3.61803	−	13.3772i	−0.134836	−	0.498538i
$721$	23.8146	+	23.8146i	0.886901	+	0.886901i
$722$	−22.7412	−	12.6988i	−0.846341	−	0.472602i
$723$	−26.9630			−1.00277
$724$	−3.79542	+	15.9828i	−0.141056	+	0.593997i
$725$	3.48692	−	2.79380i	0.129501	−	0.103759i
$726$	−12.0301	+	21.5437i	−0.446481	+	0.799563i
$727$	−44.9610			−1.66751			−0.833756	−	0.552134i	$-0.813814\pi$
$727$	−44.9610			−1.66751			−0.833756	+	0.552134i	$0.813814\pi$
$728$	−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
$732$	−20.1469	−	32.6953i	−0.744652	−	1.20845i
$733$	9.18384	−	9.18384i	0.339213	−	0.339213i	−0.516858	−	0.856071i	$-0.672899\pi$
$733$	9.18384	−	9.18384i	0.339213	−	0.339213i	0.856071	+	0.516858i	$0.172899\pi$
$734$	7.59099	+	26.7889i	0.280188	+	0.988798i
$735$	−23.5684	−	26.3124i	−0.869333	−	0.970547i
$736$	−22.5220	−	4.33553i	−0.830173	−	0.159810i
$737$	16.5060	−	16.5060i	0.608007	−	0.608007i
$738$	13.5723	+	3.55421i	0.499604	+	0.130832i
$739$	−2.64278			−0.0972161			−0.0486081	−	0.998818i	$-0.515479\pi$
$739$	−2.64278			−0.0972161			−0.0486081	+	0.998818i	$0.515479\pi$
$740$	−36.4838	+	19.8031i	−1.34117	+	0.727977i
$741$	6.05027	−	6.05027i	0.222262	−	0.222262i
$742$	3.38833	−	6.06786i	0.124390	−	0.222758i
$743$	8.78535	+	8.78535i	0.322303	+	0.322303i	0.849650	−	0.527347i	$-0.176813\pi$
$743$	8.78535	+	8.78535i	0.322303	+	0.322303i	−0.527347	+	0.849650i	$0.676813\pi$
$744$	36.3734	−	1.56409i	1.33351	−	0.0573424i
$745$	1.98068	−	36.0050i	0.0725666	−	1.31912i
$746$	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
$750$	3.74433	+	33.5159i	0.136724	+	1.22383i
$751$	10.2291	+	10.2291i	0.373265	+	0.373265i	0.868665	−	0.495400i	$-0.164978\pi$
$751$	10.2291	+	10.2291i	0.373265	+	0.373265i	−0.495400	+	0.868665i	$0.664978\pi$
$752$	−24.8233	−	12.4940i	−0.905212	−	0.455611i
$753$		−	46.4578i		−	1.69302i
$754$	−6.39204	+	1.81127i	−0.232784	+	0.0659624i
$755$	21.2545	+	1.16924i	0.773532	+	0.0425529i
$756$	19.9965	−	12.3219i	0.727264	−	0.448142i
$757$	27.8696			1.01294			0.506468	−	0.862259i	$-0.330951\pi$
$757$	27.8696			1.01294			0.506468	+	0.862259i	$0.330951\pi$
$758$	10.7306	−	19.2164i	0.389751	−	0.697972i
$759$			14.5215i			0.527098i
$760$	4.82583	+	0.0578227i	0.175051	+	0.00209745i
$761$	−43.6459			−1.58216			−0.791081	−	0.611712i	$-0.790481\pi$
$761$	−43.6459			−1.58216			−0.791081	+	0.611712i	$0.790481\pi$
$762$	13.6208	+	48.0686i	0.493431	+	1.74134i
$763$	25.2457	−	25.2457i	0.913957	−	0.913957i
$764$	−27.4799	−	6.52559i	−0.994186	−	0.236088i
$765$	−17.5555	+	15.7247i	−0.634721	+	0.568528i
$766$	−0.0897260	+	0.160682i	−0.00324193	+	0.00580569i
$767$	−17.4551			−0.630269
$768$	−27.4096	+	20.3310i	−0.989059	+	0.733630i
$769$			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
$772$	−5.18388	−	8.41261i	−0.186572	−	0.302776i
$773$			2.22633i			0.0800755i	0.999198	+	0.0400378i	$0.0127478\pi$
$773$			2.22633i			0.0800755i	−0.999198	+	0.0400378i	$0.987252\pi$
$774$	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
$778$	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
$782$	10.6344	+	37.5293i	0.380285	+	1.34204i
$783$	1.95513	−	1.95513i	0.0698705	−	0.0698705i
$784$	−13.3194	+	26.4632i	−0.475694	+	0.945113i
$785$	−4.16226	−	4.64686i	−0.148557	−	0.165854i
$786$	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	$0.426343\pi$
$788$	−1.76077	+	7.41477i	−0.0627249	+	0.264140i
$789$			3.25064i			0.115726i
$790$	12.1606	+	7.69596i	0.432656	+	0.273810i
$791$	29.6880	+	29.6880i	1.05559	+	1.05559i
$792$	5.42210	+	4.97501i	0.192666	+	0.176779i
$793$		−	47.3278i		−	1.68066i
$794$	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	$0.463351\pi$
$798$	−2.38185	−	8.40565i	−0.0843165	−	0.297557i
$799$			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
$803$	−6.72559			−0.237341
$804$	31.1092	+	50.4853i	1.09714	+	1.78048i
$805$	1.89014	−	34.3591i	0.0666186	−	1.21100i
$806$	39.1729	+	21.8744i	1.37981	+	0.770493i
$807$	−69.5673			−2.44889
$808$	−34.9094	−	32.0309i	−1.22811	−	1.12684i
$809$	24.2246	+	24.2246i	0.851691	+	0.851691i	0.990341	−	0.138650i	$-0.0442764\pi$
$809$	24.2246	+	24.2246i	0.851691	+	0.851691i	−0.138650	+	0.990341i	$0.544276\pi$
$810$	7.80252	+	34.7016i	0.274153	+	1.21929i
$811$	0.574172			0.0201619			0.0100810	−	0.999949i	$-0.496791\pi$
$811$	0.574172			0.0201619			0.0100810	+	0.999949i	$0.496791\pi$
$812$	−1.56731	+	6.60010i	−0.0550019	+	0.231618i
$813$	48.0492			1.68516
$814$	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
$817$			7.43384i			0.260077i
$818$	−25.1030	−	14.0177i	−0.877706	−	0.490116i
$819$	−30.9152			−1.08026
$820$	−1.00067	+	28.6182i	−0.0349449	+	0.999389i
$821$	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
$823$		−	19.3515i		−	0.674550i	−0.941406	−	0.337275i	$-0.890495\pi$
$823$		−	19.3515i		−	0.674550i	0.941406	−	0.337275i	$-0.109505\pi$
$824$	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
$827$	−9.30624			−0.323610			−0.161805	−	0.986823i	$-0.551732\pi$
$827$	−9.30624			−0.323610			−0.161805	+	0.986823i	$0.551732\pi$
$828$	−12.2237	−	2.90273i	−0.424802	−	0.100877i
$829$	10.3721			0.360238			0.180119	−	0.983645i	$-0.442352\pi$
$829$	10.3721			0.360238			0.180119	+	0.983645i	$0.442352\pi$
$830$	−14.7673	−	9.34559i	−0.512580	−	0.324390i
$831$	−24.5029	−	24.5029i	−0.849995	−	0.849995i
$832$	−41.9012	+	3.61026i	−1.45266	+	0.125163i
$833$	50.3857			1.74576
$834$	−52.0293	−	29.0535i	−1.80163	−	1.00604i
$835$	11.3847	−	10.1975i	0.393985	−	0.352898i
$836$	−2.18179	+	1.34443i	−0.0754588	+	0.0464980i
$837$	−18.6725			−0.645416
$838$	49.6732	+	27.7378i	1.71593	+	0.958187i
$839$	−24.7870	−	24.7870i	−0.855743	−	0.855743i	0.135090	−	0.990833i	$-0.456867\pi$
$839$	−24.7870	−	24.7870i	−0.855743	−	0.855743i	−0.990833	+	0.135090i	$0.956867\pi$
$840$	−35.7687	−	36.6362i	−1.23414	−	1.26407i
$841$		−	28.2014i		−	0.972464i
$842$	0.702415	+	2.47885i	0.0242068	+	0.0854270i
$843$	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
$847$			31.0490i			1.06686i
$848$	2.32835	−	4.62599i	0.0799559	−	0.158857i
$849$	−6.10476	−	6.10476i	−0.209515	−	0.209515i
$850$	−39.1732	−	27.9180i	−1.34363	−	0.957579i
$851$			37.6348i			1.29011i
$852$	−26.8322	−	6.37179i	−0.919255	−	0.218294i
$853$	−23.2385	+	23.2385i	−0.795672	+	0.795672i	−0.982410	−	0.186738i	$-0.940209\pi$
$853$	−23.2385	+	23.2385i	−0.795672	+	0.795672i	0.186738	+	0.982410i	$0.440209\pi$
$854$	−42.1922	−	23.5603i	−1.44379	−	0.806219i
$855$	2.63968	+	0.145212i	0.0902753	+	0.00496615i
$856$	−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	$0.0692374\pi$
$858$	7.25951	+	25.6191i	0.247836	+	0.874623i
$859$			46.8265i			1.59770i	0.601530	+	0.798851i	$0.294558\pi$
$859$			46.8265i			1.59770i	−0.601530	+	0.798851i	$0.705442\pi$
$860$	20.7834	+	38.2898i	0.708709	+	1.30567i
$861$	50.1856	−	12.9832i	1.71032	−	0.442466i
$862$	−16.3442	+	29.2694i	−0.556686	+	0.996921i
$863$	−30.2514	−	30.2514i	−1.02977	−	1.02977i	−0.999543	−	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
$867$		−	62.4499i		−	2.12091i
$868$	39.0016	−	24.0329i	1.32380	−	0.815729i
$869$	−7.64193			−0.259235
$870$	−5.09313	−	3.22323i	−0.172673	−	0.109278i
$871$			73.0796i			2.47621i
$872$	17.9872	−	19.6037i	0.609124	−	0.663864i
$873$	21.1704			0.716509
$874$	2.13322	−	3.82019i	0.0721571	−	0.129220i
$875$	24.6751	+	34.5247i	0.834172	+	1.16715i
$876$	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	$0.324312\pi$
$878$	8.80847	+	31.0855i	0.297272	+	1.04909i
$879$	37.5434			1.26631
$880$	−7.47913	+	13.0246i	−0.252121	+	0.439060i
$881$			44.0125i			1.48282i	0.671054	+	0.741409i	$0.265842\pi$
$881$			44.0125i			1.48282i	−0.671054	+	0.741409i	$0.734158\pi$
$882$	−7.91212	+	14.1691i	−0.266415	+	0.477099i
$883$	52.2259			1.75754			0.878770	−	0.477245i	$-0.158365\pi$
$883$	52.2259			1.75754			0.878770	+	0.477245i	$0.158365\pi$
$884$	37.5228	+	60.8936i	1.26203	+	2.04807i
$885$	−10.5657	−	11.7958i	−0.355161	−	0.396511i
$886$	−21.6671	+	6.13966i	−0.727922	+	0.206266i
$887$		−	49.4435i		−	1.66015i	−0.557652	−	0.830075i	$-0.688298\pi$
$887$		−	49.4435i		−	1.66015i	0.557652	−	0.830075i	$-0.311702\pi$
$888$	41.2615	+	37.8592i	1.38464	+	1.27047i
$889$	44.4536	+	44.4536i	1.49093	+	1.49093i
$890$	4.21193	−	6.65541i	0.141184	−	0.223090i
$891$	−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
$895$	−7.47185	−	0.411036i	−0.249757	−	0.0137394i
$896$	−17.6404	+	39.1516i	−0.589325	+	1.30796i
$897$	−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
$902$	−7.67758	−	13.1253i	−0.255636	−	0.437023i
$903$	55.7673	−	55.7673i	1.85582	−	1.85582i
$904$	23.0532	+	21.1523i	0.766736	+	0.703514i
$905$	−18.3386	−	1.00883i	−0.609594	−	0.0335345i
$906$	−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	$0.0677409\pi$
$908$	6.82066	−	4.20291i	0.226352	−	0.139479i
$909$	−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	$-0.314645\pi$
$911$	33.1983			1.09991			0.549954	+	0.835195i	$0.314645\pi$
$912$	−2.04238	−	6.18175i	−0.0676301	−	0.204698i
$913$	9.27998			0.307123
$914$	13.6641	−	24.4699i	0.451969	−	0.809391i
$915$	31.9830	−	28.6477i	1.05733	−	0.947062i
$916$	42.0775	+	9.99207i	1.39028	+	0.330147i
$917$	1.11437			0.0367996
$918$	−25.9901	−	14.5130i	−0.857800	−	0.479001i
$919$	−32.9114	−	32.9114i	−1.08565	−	1.08565i	−0.995971	−	0.0896774i	$-0.971416\pi$
$919$	−32.9114	−	32.9114i	−1.08565	−	1.08565i	−0.0896774	−	0.995971i	$-0.528584\pi$
$920$	0.307227	−	25.6409i	0.0101290	−	0.845354i
$921$	−8.34555	−	8.34555i	−0.274995	−	0.274995i
$922$	3.98956	−	7.14456i	0.131389	−	0.235293i
$923$	−24.0320	−	24.0320i	−0.791024	−	0.791024i
$924$	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
$928$	−0.955567	+	4.96394i	−0.0313680	+	0.162949i
$929$	−9.80422	+	9.80422i	−0.321666	+	0.321666i	−0.849406	−	0.527740i	$-0.823040\pi$
$929$	−9.80422	+	9.80422i	−0.321666	+	0.321666i	0.527740	+	0.849406i	$0.323040\pi$
$930$	8.92929	+	39.7128i	0.292803	+	1.30223i
$931$	−3.99643	−	3.99643i	−0.130978	−	0.130978i
$932$	13.3448	+	21.6565i	0.437124	+	0.709383i
$933$	−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
$937$	−32.1288			−1.04960			−0.524801	−	0.851225i	$-0.675860\pi$
$937$	−32.1288			−1.04960			−0.524801	+	0.851225i	$0.675860\pi$
$938$	65.1496	+	36.3799i	2.12721	+	1.18785i
$939$	40.6592			1.32686
$940$	8.82824	−	29.7898i	0.287945	−	0.971637i
$941$		−	46.4869i		−	1.51543i	−0.652587	−	0.757714i	$-0.726316\pi$
$941$		−	46.4869i		−	1.51543i	0.652587	−	0.757714i	$-0.273684\pi$
$942$	−4.10291	+	7.34754i	−0.133680	+	0.239396i
$943$	22.3700	+	13.1745i	0.728469	+	0.429022i
$944$	−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	0.678797	−	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
$950$	0.892730	+	5.32146i	0.0289640	+	0.172651i
$951$	−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	$0.428781\pi$
$954$	1.38311	−	2.47689i	0.0447798	−	0.0801922i
$955$	1.73451	−	31.5301i	0.0561275	−	1.02029i
$956$	9.20161	+	2.18509i	0.297601	+	0.0706709i
$957$	3.20060			0.103461
$958$	−10.3918	−	36.6732i	−0.335744	−	1.18486i
$959$	−43.0895			−1.39143
$960$	−27.8026	−	26.1305i	−0.897326	−	0.843360i
$961$	−5.41926			−0.174815
$962$	18.8142	+	66.3961i	0.606594	+	2.14070i
$963$	−17.4954	−	17.4954i	−0.563781	−	0.563781i
$964$	−21.5244	+	13.2634i	−0.693254	+	0.427185i
$965$	8.22934	−	7.37114i	0.264912	−	0.237285i
$966$	−44.6614	+	12.6554i	−1.43696	+	0.407180i
$967$		−	27.9108i		−	0.897550i	−0.893645	−	0.448775i	$-0.851860\pi$
$967$		−	27.9108i		−	0.897550i	0.893645	−	0.448775i	$-0.148140\pi$
$968$	0.994008	+	23.1159i	0.0319486	+	0.742975i
$969$	−7.82934	+	7.82934i	−0.251515	+	0.251515i
$970$	9.47884	+	42.1569i	0.304347	+	1.35358i
$971$	−17.5385	−	17.5385i	−0.562838	−	0.562838i	0.367274	−	0.930113i	$-0.380291\pi$
$971$	−17.5385	−	17.5385i	−0.562838	−	0.562838i	−0.930113	+	0.367274i	$0.880291\pi$
$972$	25.0429	−	15.4315i	0.803252	−	0.494966i
$973$	−74.9850			−2.40391
$974$	−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
$977$			31.3371i			1.00256i	0.865284	+	0.501282i	$0.167138\pi$
$977$			31.3371i			1.00256i	−0.865284	+	0.501282i	$0.832862\pi$
$978$	−5.56017	+	1.57554i	−0.177795	+	0.0503803i
$979$			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	$0.231172\pi$
$984$	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
$987$	−56.2453			−1.79031
$988$	1.85370	−	7.80608i	0.0589739	−	0.248344i
$989$	39.4979			1.25596
$990$	−4.39964	+	6.95202i	−0.139830	+	0.220950i
$991$	−0.239446	−	0.239446i	−0.00760624	−	0.00760624i	0.703293	−	0.710900i	$-0.251712\pi$
$991$	−0.239446	−	0.239446i	−0.00760624	−	0.00760624i	−0.710900	+	0.703293i	$0.751712\pi$
$992$	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
$995$	12.5715	+	0.691576i	0.398545	+	0.0219244i
$996$	−5.44680	+	22.9370i	−0.172588	+	0.726786i
$997$			47.2742i			1.49719i	0.663029	+	0.748594i	$0.269271\pi$
$997$			47.2742i			1.49719i	−0.663029	+	0.748594i	$0.730729\pi$
$998$	5.26065	+	18.5651i	0.166523	+	0.587667i
$999$	−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.j.c.483.81	yes	240
4.3	odd	2	inner	820.2.j.c.483.19	✓	240
5.2	odd	4		820.2.s.c.647.102	yes	240
20.7	even	4		820.2.s.c.647.40	yes	240
41.9	even	4		820.2.s.c.583.40	yes	240
164.91	odd	4		820.2.s.c.583.102	yes	240
205.132	odd	4	inner	820.2.j.c.747.19	yes	240
820.747	even	4	inner	820.2.j.c.747.81	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.19	✓	240	4.3	odd	2	inner
820.2.j.c.483.81	yes	240	1.1	even	1	trivial
820.2.j.c.747.19	yes	240	205.132	odd	4	inner
820.2.j.c.747.81	yes	240	820.747	even	4	inner
820.2.s.c.583.40	yes	240	41.9	even	4
820.2.s.c.583.102	yes	240	164.91	odd	4
820.2.s.c.647.40	yes	240	20.7	even	4
820.2.s.c.647.102	yes	240	5.2	odd	4

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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.689491 - 1.23475i) q^{2} -2.13292i q^{3} +(-1.04921 - 1.70269i) q^{4} +(1.66560 - 1.49190i) q^{5} +(-2.63362 - 1.47063i) q^{6} -3.79559 q^{7} +(-2.82582 + 0.121513i) q^{8} -1.54935 q^{9} +(-0.693708 - 3.08525i) q^{10} +(1.18738 + 1.18738i) q^{11} +(-3.63171 + 2.23787i) q^{12} -5.25705 q^{13} +(-2.61703 + 4.68660i) q^{14} +(-3.18211 - 3.55260i) q^{15} +(-1.79834 + 3.57295i) q^{16} +6.80287 q^{17} +(-1.06826 + 1.91306i) q^{18} +(-0.539583 - 0.539583i) q^{19} +(-4.28781 - 1.27070i) q^{20} +8.09570i q^{21} +(2.28480 - 0.647426i) 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} -3.09412i q^{27} +(3.98236 + 6.46273i) q^{28} +(0.631885 + 0.631885i) q^{29} +(-6.58060 + 1.47962i) q^{30} -6.03484i q^{31} +(3.17176 + 4.68401i) q^{32} +(2.53258 - 2.53258i) q^{33} +(4.69052 - 8.39983i) q^{34} +(-6.32194 + 5.66266i) q^{35} +(1.62559 + 2.63807i) q^{36} +(6.56359 - 6.56359i) q^{37} +(-1.03829 + 0.294211i) 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} +(0.775937 - 3.26754i) q^{44} +(-2.58060 + 2.31148i) q^{45} +(1.56322 + 5.51668i) q^{46} +6.94756i q^{47} +(7.62083 + 3.83571i) q^{48} +7.40653 q^{49} +(-5.75833 - 4.10385i) q^{50} -14.5100i q^{51} +(5.51573 + 8.95115i) q^{52} -1.29473 q^{53} +(-3.82046 - 2.13336i) q^{54} +(3.74915 + 0.206245i) q^{55} +(10.7256 - 0.461213i) q^{56} +(-1.15089 + 1.15089i) q^{57} +(1.21590 - 0.344540i) q^{58} +3.32033 q^{59} +(-2.71030 + 9.14556i) q^{60} +9.00272i q^{61} +(-7.45150 - 4.16096i) q^{62} +5.88071 q^{63} +(7.97047 - 0.686746i) q^{64} +(-8.75615 + 7.84301i) q^{65} +(-1.38091 - 4.87329i) q^{66} -13.9012i q^{67} +(-7.13761 - 11.5832i) q^{68} +(6.11496 + 6.11496i) q^{69} +(2.63303 + 11.7104i) 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} +(-10.6003 - 1.16981i) q^{75} +(-0.352611 + 1.48488i) 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} +(-8.76000 - 2.29400i) q^{82} +(3.90777 - 3.90777i) q^{83} +(13.7845 - 8.49405i) q^{84} +(11.3309 - 10.1492i) q^{85} +(-13.2551 + 3.75601i) q^{86} +(1.34776 - 1.34776i) q^{87} +(-3.49959 - 3.21103i) q^{88} +(1.76118 + 1.76118i) q^{89} +(1.07480 + 4.78014i) q^{90} +19.9536 q^{91} +(7.88953 + 1.87351i) q^{92} -12.8718 q^{93} +(8.57848 + 4.79027i) q^{94} +(-1.70373 - 0.0937245i) q^{95} +(9.99062 - 6.76511i) q^{96} -13.6640 q^{97} +(5.10673 - 9.14520i) q^{98} +(-1.83966 - 1.83966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * 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 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

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