LMFDB - Embedded newform 820.2.j.c.483.18

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			483.18
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23863 + 0.682492i) q^{2} -1.46723i q^{3} +(1.06841 - 1.69071i) q^{4} +(-2.23604 + 0.0119321i) q^{5} +(1.00137 + 1.81736i) q^{6} +1.28612 q^{7} +(-0.169471 + 2.82335i) q^{8} +0.847235 q^{9} +(2.76148 - 1.54086i) q^{10} +(-1.47909 - 1.47909i) q^{11} +(-2.48066 - 1.56760i) q^{12} +3.56889 q^{13} +(-1.59302 + 0.877763i) q^{14} +(0.0175071 + 3.28078i) q^{15} +(-1.71700 - 3.61274i) q^{16} +3.93550 q^{17} +(-1.04941 + 0.578231i) q^{18} +(-2.16695 - 2.16695i) q^{19} +(-2.36883 + 3.79324i) q^{20} -1.88703i q^{21} +(2.84150 + 0.822577i) q^{22} +(-2.24603 + 2.24603i) q^{23} +(4.14250 + 0.248653i) q^{24} +(4.99972 - 0.0533612i) q^{25} +(-4.42054 + 2.43574i) q^{26} -5.64478i q^{27} +(1.37410 - 2.17445i) q^{28} +(1.18647 + 1.18647i) q^{29} +(-2.26079 - 4.05173i) q^{30} +3.46652i q^{31} +(4.59239 + 3.30302i) q^{32} +(-2.17016 + 2.17016i) q^{33} +(-4.87462 + 2.68594i) q^{34} +(-2.87580 + 0.0153461i) q^{35} +(0.905195 - 1.43243i) q^{36} +(7.52111 - 7.52111i) q^{37} +(4.16298 + 1.20513i) q^{38} -5.23639i q^{39} +(0.345254 - 6.31512i) q^{40} +(-6.39275 + 0.364380i) q^{41} +(1.28788 + 2.33733i) q^{42} +(-2.95192 - 2.95192i) q^{43} +(-4.08098 + 0.920434i) q^{44} +(-1.89445 + 0.0101093i) q^{45} +(1.24910 - 4.31490i) q^{46} -11.5638i q^{47} +(-5.30073 + 2.51923i) q^{48} -5.34591 q^{49} +(-6.15638 + 3.47836i) q^{50} -5.77428i q^{51} +(3.81304 - 6.03396i) q^{52} +4.85058 q^{53} +(3.85251 + 6.99180i) q^{54} +(3.32494 + 3.28964i) q^{55} +(-0.217959 + 3.63115i) q^{56} +(-3.17942 + 3.17942i) q^{57} +(-2.27935 - 0.659841i) q^{58} -4.83040 q^{59} +(5.56555 + 3.47562i) q^{60} -10.7064i q^{61} +(-2.36587 - 4.29374i) q^{62} +1.08964 q^{63} +(-7.94256 - 0.956949i) q^{64} +(-7.98017 + 0.0425844i) q^{65} +(1.20691 - 4.16914i) q^{66} -11.9293i q^{67} +(4.20472 - 6.65378i) q^{68} +(3.29544 + 3.29544i) q^{69} +(3.55158 - 1.98172i) q^{70} +(-3.02064 - 3.02064i) q^{71} +(-0.143582 + 2.39204i) q^{72} +(-6.12859 + 6.12859i) q^{73} +(-4.18278 + 14.4490i) q^{74} +(-0.0782932 - 7.33573i) q^{75} +(-5.97888 + 1.34849i) q^{76} +(-1.90228 - 1.90228i) q^{77} +(3.57379 + 6.48595i) q^{78} +(1.61263 - 1.61263i) q^{79} +(3.88238 + 8.05774i) q^{80} -5.74049 q^{81} +(7.66957 - 4.81433i) q^{82} +(0.976800 - 0.976800i) q^{83} +(-3.19042 - 2.01612i) q^{84} +(-8.79991 + 0.0469587i) q^{85} +(5.67099 + 1.64168i) q^{86} +(1.74082 - 1.74082i) q^{87} +(4.42663 - 3.92531i) q^{88} +(-5.53320 - 5.53320i) q^{89} +(2.33962 - 1.30547i) q^{90} +4.59001 q^{91} +(1.39770 + 6.19707i) q^{92} +5.08618 q^{93} +(7.89217 + 14.3232i) q^{94} +(4.87124 + 4.81953i) q^{95} +(4.84629 - 6.73810i) q^{96} +16.9179 q^{97} +(6.62160 - 3.64854i) q^{98} +(-1.25313 - 1.25313i) 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 $

$2$	−1.23863	+	0.682492i	−0.875844	+	0.482594i
$2$	−1.23863	+	0.682492i	−0.875844	+	0.482594i
$3$		−	1.46723i		−	0.847106i	−0.905871	−	0.423553i	$-0.860783\pi$
$3$		−	1.46723i		−	0.847106i	0.905871	−	0.423553i	$-0.139217\pi$
$4$	1.06841	−	1.69071i	0.534205	−	0.845355i
$5$	−2.23604	+	0.0119321i	−0.999986	+	0.00533620i
$5$	−2.23604	+	0.0119321i	−0.999986	+	0.00533620i
$6$	1.00137	+	1.81736i	0.408809	+	0.741932i
$7$	1.28612			0.486106			0.243053	−	0.970013i	$-0.421851\pi$
$7$	1.28612			0.486106			0.243053	+	0.970013i	$0.421851\pi$
$8$	−0.169471	+	2.82335i	−0.0599170	+	0.998203i
$9$	0.847235			0.282412
$10$	2.76148	−	1.54086i	0.873256	−	0.487261i
$11$	−1.47909	−	1.47909i	−0.445961	−	0.445961i	0.448048	−	0.894009i	$-0.352119\pi$
$11$	−1.47909	−	1.47909i	−0.445961	−	0.445961i	−0.894009	+	0.448048i	$0.852119\pi$
$12$	−2.48066	−	1.56760i	−0.716105	−	0.452528i
$13$	3.56889			0.989833			0.494916	−	0.868941i	$-0.335199\pi$
$13$	3.56889			0.989833			0.494916	+	0.868941i	$0.335199\pi$
$14$	−1.59302	+	0.877763i	−0.425753	+	0.234592i
$15$	0.0175071	+	3.28078i	0.00452033	+	0.847094i
$16$	−1.71700	−	3.61274i	−0.429249	−	0.903186i
$17$	3.93550			0.954498			0.477249	−	0.878768i	$-0.341634\pi$
$17$	3.93550			0.954498			0.477249	+	0.878768i	$0.341634\pi$
$18$	−1.04941	+	0.578231i	−0.247349	+	0.136290i
$19$	−2.16695	−	2.16695i	−0.497133	−	0.497133i	0.413411	−	0.910544i	$-0.364337\pi$
$19$	−2.16695	−	2.16695i	−0.497133	−	0.497133i	−0.910544	+	0.413411i	$0.864337\pi$
$20$	−2.36883	+	3.79324i	−0.529687	+	0.848193i
$21$		−	1.88703i		−	0.411783i
$22$	2.84150	+	0.822577i	0.605811	+	0.175374i
$23$	−2.24603	+	2.24603i	−0.468330	+	0.468330i	−0.901373	−	0.433043i	$-0.857440\pi$
$23$	−2.24603	+	2.24603i	−0.468330	+	0.468330i	0.433043	+	0.901373i	$0.357440\pi$
$24$	4.14250	+	0.248653i	0.845584	+	0.0507560i
$25$	4.99972	−	0.0533612i	0.999943	−	0.0106722i
$26$	−4.42054	+	2.43574i	−0.866939	+	0.477688i
$27$		−	5.64478i		−	1.08634i
$28$	1.37410	−	2.17445i	0.259680	−	0.410932i
$29$	1.18647	+	1.18647i	0.220322	+	0.220322i	0.808634	−	0.588312i	$-0.200207\pi$
$29$	1.18647	+	1.18647i	0.220322	+	0.220322i	−0.588312	+	0.808634i	$0.700207\pi$
$30$	−2.26079	−	4.05173i	−0.412762	−	0.739740i
$31$			3.46652i			0.622605i	0.950311	+	0.311303i	$0.100765\pi$
$31$			3.46652i			0.622605i	−0.950311	+	0.311303i	$0.899235\pi$
$32$	4.59239	+	3.30302i	0.811828	+	0.583897i
$33$	−2.17016	+	2.17016i	−0.377776	+	0.377776i
$34$	−4.87462	+	2.68594i	−0.835991	+	0.460635i
$35$	−2.87580	+	0.0153461i	−0.486099	+	0.00259396i
$36$	0.905195	−	1.43243i	0.150866	−	0.238738i
$37$	7.52111	−	7.52111i	1.23646	−	1.23646i	0.275027	−	0.961437i	$-0.411313\pi$
$37$	7.52111	−	7.52111i	1.23646	−	1.23646i	0.961437	−	0.275027i	$-0.0886867\pi$
$38$	4.16298	+	1.20513i	0.675325	+	0.195497i
$39$		−	5.23639i		−	0.838493i
$40$	0.345254	−	6.31512i	0.0545895	−	0.998509i
$41$	−6.39275	+	0.364380i	−0.998380	+	0.0569066i
$41$	−6.39275	+	0.364380i	−0.998380	+	0.0569066i
$42$	1.28788	+	2.33733i	0.198724	+	0.360658i
$43$	−2.95192	−	2.95192i	−0.450163	−	0.450163i	0.445245	−	0.895409i	$-0.353116\pi$
$43$	−2.95192	−	2.95192i	−0.450163	−	0.450163i	−0.895409	+	0.445245i	$0.853116\pi$
$44$	−4.08098	+	0.920434i	−0.615230	+	0.138761i
$45$	−1.89445	+	0.0101093i	−0.282408	+	0.00150701i
$46$	1.24910	−	4.31490i	0.184170	−	0.636197i
$47$		−	11.5638i		−	1.68675i	−0.537327	−	0.843374i	$-0.680566\pi$
$47$		−	11.5638i		−	1.68675i	0.537327	−	0.843374i	$-0.319434\pi$
$48$	−5.30073	+	2.51923i	−0.765094	+	0.363620i
$49$	−5.34591			−0.763701
$50$	−6.15638	+	3.47836i	−0.870644	+	0.491914i
$51$		−	5.77428i		−	0.808561i
$52$	3.81304	−	6.03396i	0.528774	−	0.836760i
$53$	4.85058			0.666278			0.333139	−	0.942878i	$-0.391892\pi$
$53$	4.85058			0.666278			0.333139	+	0.942878i	$0.391892\pi$
$54$	3.85251	+	6.99180i	0.524261	+	0.951463i
$55$	3.32494	+	3.28964i	0.448335	+	0.443575i
$56$	−0.217959	+	3.63115i	−0.0291260	+	0.485233i
$57$	−3.17942	+	3.17942i	−0.421124	+	0.421124i
$58$	−2.27935	−	0.659841i	−0.299293	−	0.0866414i
$59$	−4.83040			−0.628864			−0.314432	−	0.949280i	$-0.601814\pi$
$59$	−4.83040			−0.628864			−0.314432	+	0.949280i	$0.601814\pi$
$60$	5.56555	+	3.47562i	0.718510	+	0.448701i
$61$		−	10.7064i		−	1.37082i	−0.728157	−	0.685410i	$-0.759623\pi$
$61$		−	10.7064i		−	1.37082i	0.728157	−	0.685410i	$-0.240377\pi$
$62$	−2.36587	−	4.29374i	−0.300466	−	0.545305i
$63$	1.08964			0.137282
$64$	−7.94256	−	0.956949i	−0.992820	−	0.119619i
$65$	−7.98017	+	0.0425844i	−0.989819	+	0.00528194i
$66$	1.20691	−	4.16914i	0.148560	−	0.513186i
$67$		−	11.9293i		−	1.45739i	−0.684838	−	0.728695i	$-0.740127\pi$
$67$		−	11.9293i		−	1.45739i	0.684838	−	0.728695i	$-0.259873\pi$
$68$	4.20472	−	6.65378i	0.509898	−	0.806889i
$69$	3.29544	+	3.29544i	0.396725	+	0.396725i
$70$	3.55158	−	1.98172i	0.424495	−	0.236861i
$71$	−3.02064	−	3.02064i	−0.358485	−	0.358485i	0.504770	−	0.863254i	$-0.331577\pi$
$71$	−3.02064	−	3.02064i	−0.358485	−	0.358485i	−0.863254	+	0.504770i	$0.831577\pi$
$72$	−0.143582	+	2.39204i	−0.0169213	+	0.281904i
$73$	−6.12859	+	6.12859i	−0.717297	+	0.717297i	−0.968051	−	0.250754i	$-0.919321\pi$
$73$	−6.12859	+	6.12859i	−0.717297	+	0.717297i	0.250754	+	0.968051i	$0.419321\pi$
$74$	−4.18278	+	14.4490i	−0.486239	+	1.67966i
$75$	−0.0782932	−	7.33573i	−0.00904052	−	0.847058i
$76$	−5.97888	+	1.34849i	−0.685825	+	0.154683i
$77$	−1.90228	−	1.90228i	−0.216784	−	0.216784i
$78$	3.57379	+	6.48595i	0.404652	+	0.734389i
$79$	1.61263	−	1.61263i	0.181435	−	0.181435i	−0.610546	−	0.791981i	$-0.709050\pi$
$79$	1.61263	−	1.61263i	0.181435	−	0.181435i	0.791981	+	0.610546i	$0.209050\pi$
$80$	3.88238	+	8.05774i	0.434063	+	0.900883i
$81$	−5.74049			−0.637832
$82$	7.66957	−	4.81433i	0.846962	−	0.531654i
$83$	0.976800	−	0.976800i	0.107218	−	0.107218i	−0.651463	−	0.758681i	$-0.725844\pi$
$83$	0.976800	−	0.976800i	0.107218	−	0.107218i	0.758681	+	0.651463i	$0.225844\pi$
$84$	−3.19042	−	2.01612i	−0.348103	−	0.219977i
$85$	−8.79991	+	0.0469587i	−0.954484	+	0.00509339i
$86$	5.67099	+	1.64168i	0.611519	+	0.177026i
$87$	1.74082	−	1.74082i	0.186636	−	0.186636i
$88$	4.42663	−	3.92531i	0.471881	−	0.418439i
$89$	−5.53320	−	5.53320i	−0.586518	−	0.586518i	0.350168	−	0.936687i	$-0.386124\pi$
$89$	−5.53320	−	5.53320i	−0.586518	−	0.586518i	−0.936687	+	0.350168i	$0.886124\pi$
$90$	2.33962	−	1.30547i	0.246618	−	0.137608i
$91$	4.59001			0.481163
$92$	1.39770	+	6.19707i	0.145721	+	0.646089i
$93$	5.08618			0.527412
$94$	7.89217	+	14.3232i	0.814015	+	1.47733i
$95$	4.87124	+	4.81953i	0.499779	+	0.494473i
$96$	4.84629	−	6.73810i	0.494622	−	0.687704i
$97$	16.9179			1.71775			0.858876	−	0.512184i	$-0.171163\pi$
$97$	16.9179			1.71775			0.858876	+	0.512184i	$0.171163\pi$
$98$	6.62160	−	3.64854i	0.668883	−	0.368558i
$99$	−1.25313	−	1.25313i	−0.125945	−	0.125945i
$100$	5.25153	−	8.51008i	0.525153	−	0.851008i
$101$	2.82179	+	2.82179i	0.280779	+	0.280779i	0.833420	−	0.552641i	$-0.186380\pi$
$101$	2.82179	+	2.82179i	0.280779	+	0.280779i	−0.552641	+	0.833420i	$0.686380\pi$
$102$	3.94090	+	7.15220i	0.390207	+	0.708173i
$103$	0.749274	+	0.749274i	0.0738282	+	0.0738282i	0.743057	−	0.669228i	$-0.233375\pi$
$103$	0.749274	+	0.749274i	0.0738282	+	0.0738282i	−0.669228	+	0.743057i	$0.733375\pi$
$104$	−0.604823	+	10.0762i	−0.0593078	+	0.988054i
$105$	0.0225162	+	4.21946i	0.00219736	+	0.411777i
$106$	−6.00807	+	3.31048i	−0.583555	+	0.321542i
$107$	2.86997	+	2.86997i	0.277451	+	0.277451i	0.832091	−	0.554640i	$-0.187144\pi$
$107$	2.86997	+	2.86997i	0.277451	+	0.277451i	−0.554640	+	0.832091i	$0.687144\pi$
$108$	−9.54368	−	6.03094i	−0.918341	−	0.580328i
$109$	2.11147	−	2.11147i	0.202242	−	0.202242i	−0.598718	−	0.800960i	$-0.704323\pi$
$109$	2.11147	−	2.11147i	0.202242	−	0.202242i	0.800960	+	0.598718i	$0.204323\pi$
$110$	−6.36352	−	1.80541i	−0.606738	−	0.172139i
$111$	−11.0352	−	11.0352i	−1.04742	−	1.04742i
$112$	−2.20826	−	4.64640i	−0.208661	−	0.439044i
$113$	2.98143	+	2.98143i	0.280469	+	0.280469i	0.833296	−	0.552827i	$-0.186451\pi$
$113$	2.98143	+	2.98143i	0.280469	+	0.280469i	−0.552827	+	0.833296i	$0.686451\pi$
$114$	1.76820	−	6.10805i	0.165607	−	0.572072i
$115$	4.99540	−	5.04900i	0.465824	−	0.470822i
$116$	3.27361	−	0.738338i	0.303947	−	0.0685530i
$117$	3.02369			0.279540
$118$	5.98307	−	3.29670i	0.550787	−	0.303486i
$119$	5.06150			0.463987
$120$	−9.26574	−	0.506568i	−0.845843	−	0.0462431i
$121$		−	6.62461i		−	0.602237i
$122$	7.30706	+	13.2613i	0.661550	+	1.20062i
$123$	0.534629	+	9.37963i	0.0482059	+	0.845733i
$124$	5.86088	+	3.70367i	0.526322	+	0.332599i
$125$	−11.1789	+	0.178975i	−0.999872	+	0.0160080i
$126$	−1.34966	+	0.743672i	−0.120238	+	0.0662515i
$127$	13.7671	+	13.7671i	1.22163	+	1.22163i	0.967051	+	0.254582i	$0.0819378\pi$
$127$	13.7671	+	13.7671i	1.22163	+	1.22163i	0.254582	+	0.967051i	$0.418062\pi$
$128$	10.4910	−	4.23542i	0.927283	−	0.374362i
$129$	−4.33114	+	4.33114i	−0.381336	+	0.381336i
$130$	9.85542	−	5.49915i	0.864378	−	0.482307i
$131$	15.4414			1.34913			0.674563	−	0.738218i	$-0.264332\pi$
$131$	15.4414			1.34913			0.674563	+	0.738218i	$0.264332\pi$
$132$	1.35049	+	5.98773i	0.117545	+	0.521165i
$133$	−2.78695	−	2.78695i	−0.241659	−	0.241659i
$134$	8.14162	+	14.7759i	0.703329	+	1.27645i
$135$	0.0673541	+	12.6219i	0.00579692	+	1.08632i
$136$	−0.666951	+	11.1113i	−0.0571906	+	0.952783i
$137$	−14.5542			−1.24345			−0.621727	−	0.783234i	$-0.713569\pi$
$137$	−14.5542			−1.24345			−0.621727	+	0.783234i	$0.713569\pi$
$138$	−6.33095	−	1.83272i	−0.538926	−	0.156012i
$139$	5.45695			0.462853			0.231426	−	0.972852i	$-0.425661\pi$
$139$	5.45695			0.462853			0.231426	+	0.972852i	$0.425661\pi$
$140$	−3.04659	+	4.87854i	−0.257484	+	0.412312i
$141$	−16.9667			−1.42885
$142$	5.80303	+	1.67990i	0.486979	+	0.140974i
$143$	−5.27870	−	5.27870i	−0.441427	−	0.441427i
$144$	−1.45470	−	3.06084i	−0.121225	−	0.255070i
$145$	−2.66714	−	2.63883i	−0.221494	−	0.219143i
$146$	3.40835	−	11.7738i	0.282077	−	0.974404i
$147$			7.84368i			0.646936i
$148$	−4.68038	−	20.7517i	−0.384725	−	1.70578i
$149$	7.17508	−	7.17508i	0.587805	−	0.587805i	−0.349231	−	0.937037i	$-0.613557\pi$
$149$	7.17508	−	7.17508i	0.587805	−	0.587805i	0.937037	+	0.349231i	$0.113557\pi$
$150$	5.10355	+	9.03283i	0.416703	+	0.737527i
$151$	−2.94945	−	2.94945i	−0.240023	−	0.240023i	0.576837	−	0.816860i	$-0.304287\pi$
$151$	−2.94945	−	2.94945i	−0.240023	−	0.240023i	−0.816860	+	0.576837i	$0.804287\pi$
$152$	6.48529	−	5.75082i	0.526027	−	0.466453i
$153$	3.33429			0.269561
$154$	3.65450	+	1.05793i	0.294488	+	0.0852504i
$155$	−0.0413629	−	7.75126i	−0.00332235	−	0.622596i
$156$	−8.85321	−	5.59461i	−0.708824	−	0.447927i
$157$			7.95371i			0.634775i	0.948296	+	0.317388i	$0.102806\pi$
$157$			7.95371i			0.634775i	−0.948296	+	0.317388i	$0.897194\pi$
$158$	−0.896847	+	3.09806i	−0.0713493	+	0.246468i
$159$		−	7.11691i		−	0.564408i
$160$	−10.3082	−	7.33087i	−0.814932	−	0.579556i
$161$	−2.88865	+	2.88865i	−0.227658	+	0.227658i
$162$	7.11034	−	3.91783i	0.558641	−	0.307814i
$163$	−16.4010	+	16.4010i	−1.28463	+	1.28463i	−0.346619	+	0.938006i	$0.612670\pi$
$163$	−16.4010	+	16.4010i	−1.28463	+	1.28463i	−0.938006	+	0.346619i	$0.887330\pi$
$164$	−6.21402	+	11.1976i	−0.485233	+	0.874385i
$165$	4.82666	−	4.87845i	0.375755	−	0.379787i
$166$	−0.543237	+	1.87655i	−0.0421633	+	0.145649i
$167$	−11.7904			−0.912371			−0.456186	−	0.889885i	$-0.650785\pi$
$167$	−11.7904			−0.912371			−0.456186	+	0.889885i	$0.650785\pi$
$168$	5.32773	+	0.319796i	0.411043	+	0.0246728i
$169$	−0.263007			−0.0202313
$170$	10.8678	−	6.06403i	0.833521	−	0.465090i
$171$	−1.83592	−	1.83592i	−0.140396	−	0.140396i
$172$	−8.14470	+	1.83698i	−0.621027	+	0.140068i
$173$	−2.97299	+	2.97299i	−0.226032	+	0.226032i	−0.811033	−	0.585001i	$-0.801094\pi$
$173$	−2.97299	+	2.97299i	−0.226032	+	0.226032i	0.585001	+	0.811033i	$0.301094\pi$
$174$	−0.968139	+	3.34433i	−0.0733944	+	0.253533i
$175$	6.43021	−	0.0686287i	0.486078	−	0.00518784i
$176$	−2.80397	+	7.88315i	−0.211357	+	0.594215i
$177$			7.08730i			0.532714i
$178$	10.6300	+	3.07723i	0.796749	+	0.230648i
$179$	4.51057	+	4.51057i	0.337136	+	0.337136i	0.855288	−	0.518153i	$-0.173380\pi$
$179$	4.51057	+	4.51057i	0.337136	+	0.337136i	−0.518153	+	0.855288i	$0.673380\pi$
$180$	−2.00696	+	3.21376i	−0.149590	+	0.239540i
$181$	0.0998182	+	0.0998182i	0.00741943	+	0.00741943i	0.710807	−	0.703387i	$-0.248330\pi$
$181$	0.0998182	+	0.0998182i	0.00741943	+	0.00741943i	−0.703387	+	0.710807i	$0.748330\pi$
$182$	−5.68532	+	3.13264i	−0.421424	+	0.232207i
$183$	−15.7088			−1.16123
$184$	−5.96068	−	6.72196i	−0.439427	−	0.495549i
$185$	−16.7277	+	16.9072i	−1.22985	+	1.24304i
$186$	−6.29990	+	3.47128i	−0.461931	+	0.254526i
$187$	−5.82094	−	5.82094i	−0.425669	−	0.425669i
$188$	−19.5510	−	12.3548i	−1.42590	−	0.901070i
$189$		−	7.25984i		−	0.528075i
$190$	−9.32296	−	2.64503i	−0.676358	−	0.191891i
$191$	−2.94462	+	2.94462i	−0.213065	+	0.213065i	−0.805568	−	0.592503i	$-0.798140\pi$
$191$	−2.94462	+	2.94462i	−0.213065	+	0.213065i	0.592503	+	0.805568i	$0.298140\pi$
$192$	−1.40406	+	11.6536i	−0.101330	+	0.841024i
$193$	15.6502			1.12653			0.563264	−	0.826277i	$-0.309546\pi$
$193$	15.6502			1.12653			0.563264	+	0.826277i	$0.309546\pi$
$194$	−20.9550	+	11.5463i	−1.50448	+	0.828978i
$195$	0.0624811	+	11.7088i	0.00447437	+	0.838481i
$196$	−5.71162	+	9.03838i	−0.407973	+	0.645598i
$197$	6.69390	+	6.69390i	0.476921	+	0.476921i	0.904145	−	0.427225i	$-0.140509\pi$
$197$	6.69390	+	6.69390i	0.476921	+	0.476921i	−0.427225	+	0.904145i	$0.640509\pi$
$198$	2.40742	+	0.696917i	0.171088	+	0.0495277i
$199$	13.4968	+	13.4968i	0.956762	+	0.956762i	0.999103	−	0.0423413i	$-0.0134817\pi$
$199$	13.4968	+	13.4968i	0.956762	+	0.956762i	−0.0423413	+	0.999103i	$0.513482\pi$
$200$	−0.696648	+	14.1250i	−0.0492605	+	0.998786i
$201$	−17.5030			−1.23456
$202$	−5.42100	−	1.56931i	−0.381421	−	0.110416i
$203$	1.52594	+	1.52594i	0.107100	+	0.107100i
$204$	−9.76263	−	6.16930i	−0.683521	−	0.431937i
$205$	14.2901	−	0.891046i	0.998062	−	0.0622333i
$206$	−1.43945	−	0.416700i	−0.100291	−	0.0290329i
$207$	−1.90292	+	1.90292i	−0.132262	+	0.132262i
$208$	−6.12778	−	12.8935i	−0.424885	−	0.894003i
$209$			6.41022i			0.443404i
$210$	−2.90764	−	5.21099i	−0.200646	−	0.359592i
$211$	−9.63832	+	9.63832i	−0.663529	+	0.663529i	−0.956210	−	0.292681i	$-0.905453\pi$
$211$	−9.63832	+	9.63832i	−0.663529	+	0.663529i	0.292681	+	0.956210i	$0.405453\pi$
$212$	5.18241	−	8.20091i	0.355929	−	0.563241i
$213$	−4.43198	+	4.43198i	−0.303674	+	0.303674i
$214$	−5.51357	−	1.59610i	−0.376900	−	0.109107i
$215$	6.63582	+	6.56537i	0.452559	+	0.447755i
$216$	15.9372	+	0.956625i	1.08439	+	0.0650901i
$217$			4.45834i			0.302652i
$218$	−1.17427	+	4.05639i	−0.0795316	+	0.274733i
$219$	8.99205	+	8.99205i	0.607626	+	0.607626i
$220$	9.11423	−	2.10682i	0.614481	−	0.142042i
$221$	14.0454			0.944793
$222$	21.2000	+	6.13711i	1.42285	+	0.411896i
$223$	0.504028	−	0.504028i	0.0337522	−	0.0337522i	−0.690029	−	0.723781i	$-0.742402\pi$
$223$	0.504028	−	0.504028i	0.0337522	−	0.0337522i	0.723781	+	0.690029i	$0.242402\pi$
$224$	5.90635	+	4.24806i	0.394634	+	0.283836i
$225$	4.23594	−	0.0452095i	0.282396	−	0.00301397i
$226$	−5.72768	−	1.65809i	−0.381000	−	0.110294i
$227$		−	24.1402i		−	1.60224i	−0.598504	−	0.801120i	$-0.704238\pi$
$227$		−	24.1402i		−	1.60224i	0.598504	−	0.801120i	$-0.295762\pi$
$228$	1.97855	+	8.77240i	0.131033	+	0.580966i
$229$	−4.53806	+	4.53806i	−0.299883	+	0.299883i	−0.840968	−	0.541085i	$-0.818014\pi$
$229$	−4.53806	+	4.53806i	−0.299883	+	0.299883i	0.541085	+	0.840968i	$0.318014\pi$
$230$	−2.74156	+	9.66317i	−0.180773	+	0.637171i
$231$	−2.79108	+	2.79108i	−0.183639	+	0.183639i
$232$	−3.55088	+	3.14874i	−0.233127	+	0.206725i
$233$	9.45756			0.619586			0.309793	−	0.950804i	$-0.399740\pi$
$233$	9.45756			0.619586			0.309793	+	0.950804i	$0.399740\pi$
$234$	−3.74524	+	2.06364i	−0.244834	+	0.134905i
$235$	0.137980	+	25.8570i	0.00900082	+	1.68672i
$236$	−5.16085	+	8.16680i	−0.335942	+	0.531613i
$237$	−2.36610	−	2.36610i	−0.153695	−	0.153695i
$238$	−6.26933	+	3.45443i	−0.406380	+	0.223918i
$239$	9.35836	−	9.35836i	0.605342	−	0.605342i	−0.336383	−	0.941725i	$-0.609204\pi$
$239$	9.35836	−	9.35836i	0.605342	−	0.605342i	0.941725	+	0.336383i	$0.109204\pi$
$240$	11.8226	−	5.69634i	0.763143	−	0.367697i
$241$			16.2896i			1.04931i	0.851316	+	0.524654i	$0.175805\pi$
$241$			16.2896i			1.04931i	−0.851316	+	0.524654i	$0.824195\pi$
$242$	4.52124	+	8.20544i	0.290636	+	0.527466i
$243$		−	8.51172i		−	0.546027i
$244$	−18.1015	−	11.4389i	−1.15883	−	0.732299i
$245$	11.9536	−	0.0637879i	0.763690	−	0.00407526i
$246$	−7.06373	−	11.2530i	−0.450367	−	0.717466i
$247$	−7.73362	−	7.73362i	−0.492079	−	0.492079i
$248$	−9.78718	−	0.587474i	−0.621487	−	0.0373046i
$249$	−1.43319	−	1.43319i	−0.0908248	−	0.0908248i
$250$	13.7244	−	7.85119i	0.868006	−	0.496553i
$251$	−28.5412			−1.80150			−0.900751	−	0.434336i	$-0.856983\pi$
$251$	−28.5412			−1.80150			−0.900751	+	0.434336i	$0.856983\pi$
$252$	1.16419	−	1.84227i	0.0733368	−	0.116052i
$253$	6.64414			0.417714
$254$	−26.4483	−	7.65642i	−1.65951	−	0.480407i
$255$	0.0688993	+	12.9115i	0.00431464	+	0.808549i
$256$	−10.1038	+	12.4061i	−0.631490	+	0.775384i
$257$			28.6033i			1.78423i	0.451813	+	0.892113i	$0.350777\pi$
$257$			28.6033i			1.78423i	−0.451813	+	0.892113i	$0.649223\pi$
$258$	2.40872	−	8.32065i	0.149960	−	0.518021i
$259$	9.67302	−	9.67302i	0.601052	−	0.601052i
$260$	−8.45410	+	13.5377i	−0.524301	+	0.839570i
$261$	1.00522	+	1.00522i	0.0622214	+	0.0622214i
$262$	−19.1262	+	10.5387i	−1.18162	+	0.651080i
$263$	28.1358			1.73493			0.867464	−	0.497501i	$-0.165749\pi$
$263$	28.1358			1.73493			0.867464	+	0.497501i	$0.165749\pi$
$264$	−5.75933	−	6.49489i	−0.354462	−	0.399733i
$265$	−10.8461	+	0.0578776i	−0.666268	+	0.00355539i
$266$	5.35407	+	1.54993i	0.328279	+	0.0950324i
$267$	−8.11848	+	8.11848i	−0.496843	+	0.496843i
$268$	−20.1689	−	12.7453i	−1.23201	−	0.778546i
$269$		−	11.0488i		−	0.673659i	−0.941566	−	0.336830i	$-0.890645\pi$
$269$		−	11.0488i		−	0.673659i	0.941566	−	0.336830i	$-0.109355\pi$
$270$	−8.69779	−	15.5879i	−0.529331	−	0.948652i
$271$			13.4267i			0.815617i	0.913068	+	0.407808i	$0.133707\pi$
$271$			13.4267i			0.815617i	−0.913068	+	0.407808i	$0.866293\pi$
$272$	−6.75724	−	14.2179i	−0.409718	−	0.862089i
$273$		−	6.73460i		−	0.407596i
$274$	18.0273	−	9.93315i	1.08907	−	0.600084i
$275$	−7.47394	−	7.31608i	−0.450695	−	0.441176i
$276$	9.09252	−	2.05075i	0.547306	−	0.123441i
$277$	7.52652	−	7.52652i	0.452225	−	0.452225i	−0.443868	−	0.896092i	$-0.646394\pi$
$277$	7.52652	−	7.52652i	0.452225	−	0.452225i	0.896092	+	0.443868i	$0.146394\pi$
$278$	−6.75915	+	3.72432i	−0.405387	+	0.223370i
$279$			2.93696i			0.175831i
$280$	0.444037	−	8.12198i	0.0265363	−	0.485381i
$281$	−3.27477	−	3.27477i	−0.195356	−	0.195356i	0.602650	−	0.798006i	$-0.294112\pi$
$281$	−3.27477	−	3.27477i	−0.195356	−	0.195356i	−0.798006	+	0.602650i	$0.794112\pi$
$282$	21.0155	−	11.5796i	1.25145	−	0.689557i
$283$	4.45351	−	4.45351i	0.264734	−	0.264734i	−0.562240	−	0.826974i	$-0.690060\pi$
$283$	4.45351	−	4.45351i	0.264734	−	0.264734i	0.826974	+	0.562240i	$0.190060\pi$
$284$	−8.33432	+	1.87974i	−0.494551	+	0.111542i
$285$	7.07136	−	7.14723i	0.418871	−	0.423366i
$286$	10.1410	+	2.93569i	0.599651	+	0.173591i
$287$	−8.22181	+	0.468635i	−0.485318	+	0.0276626i
$288$	3.89084	+	2.79843i	0.229270	+	0.164899i
$289$	−1.51188			−0.0889339
$290$	5.10458	+	1.44823i	0.299752	+	0.0850431i
$291$		−	24.8224i		−	1.45512i
$292$	3.81381	+	16.9095i	0.223187	+	0.989554i
$293$			14.1239i			0.825126i	0.910929	+	0.412563i	$0.135366\pi$
$293$			14.1239i			0.825126i	−0.910929	+	0.412563i	$0.864634\pi$
$294$	−5.35324	−	9.71542i	−0.312208	−	0.566615i
$295$	10.8009	−	0.0576368i	0.628855	−	0.00335574i
$296$	19.9601	+	22.5093i	1.16016	+	1.30833i
$297$	−8.34912	+	8.34912i	−0.484465	+	0.484465i
$298$	−3.99034	+	13.7842i	−0.231154	+	0.798497i
$299$	−8.01584	+	8.01584i	−0.463568	+	0.463568i
$300$	−12.4862	−	7.70520i	−0.720894	−	0.444860i
$301$	−3.79651	−	3.79651i	−0.218827	−	0.218827i
$302$	5.66625	+	1.64030i	0.326056	+	0.0943889i
$303$	4.14022	−	4.14022i	0.237849	−	0.237849i
$304$	−4.10799	+	11.5493i	−0.235610	+	0.662398i
$305$	0.127750	+	23.9400i	0.00731497	+	1.37080i
$306$	−4.12995	+	2.27563i	−0.236094	+	0.130089i
$307$	−5.15749	+	5.15749i	−0.294354	+	0.294354i	−0.838797	−	0.544444i	$-0.816741\pi$
$307$	−5.15749	+	5.15749i	−0.294354	+	0.294354i	0.544444	+	0.838797i	$0.316741\pi$
$308$	−5.24861	+	1.18378i	−0.299067	+	0.0674524i
$309$	1.09936	−	1.09936i	0.0625403	−	0.0625403i
$310$	5.34140	+	9.57272i	0.303371	+	0.543694i
$311$	19.4726	−	19.4726i	1.10419	−	1.10419i	0.110293	−	0.993899i	$-0.464821\pi$
$311$	19.4726	−	19.4726i	1.10419	−	1.10419i	0.993899	−	0.110293i	$-0.0351789\pi$
$312$	14.7841	+	0.887415i	0.836987	+	0.0502400i
$313$		−	27.6903i		−	1.56515i	−0.622556	−	0.782575i	$-0.713906\pi$
$313$		−	27.6903i		−	1.56515i	0.622556	−	0.782575i	$-0.286094\pi$
$314$	−5.42834	−	9.85170i	−0.306339	−	0.555964i
$315$	−2.43648	+	0.0130017i	−0.137280	+	0.000732564i
$316$	−1.00354	−	4.44944i	−0.0564535	−	0.250301i
$317$		−	21.3917i		−	1.20148i	−0.799445	−	0.600740i	$-0.794873\pi$
$317$		−	21.3917i		−	1.20148i	0.799445	−	0.600740i	$-0.205127\pi$
$318$	4.85723	+	8.81522i	0.272380	+	0.494333i
$319$		−	3.50978i		−	0.196510i
$320$	17.7713	+	2.04500i	0.993444	+	0.114319i
$321$	4.21091	−	4.21091i	0.235030	−	0.235030i
$322$	1.60649	−	5.54946i	0.0895263	−	0.309259i
$323$	−8.52804	−	8.52804i	−0.474513	−	0.474513i
$324$	−6.13320	+	9.70550i	−0.340733	+	0.539194i
$325$	17.8434	−	0.190441i	0.989776	−	0.0105637i
$326$	9.12123	−	31.5083i	0.505178	−	1.74508i
$327$	−3.09801	−	3.09801i	−0.171320	−	0.171320i
$328$	0.0546134	−	18.1107i	0.00301552	−	0.999995i
$329$		−	14.8723i		−	0.819938i
$330$	−2.64895	+	9.33675i	−0.145820	+	0.513971i
$331$	−5.16514	−	5.16514i	−0.283902	−	0.283902i	0.550761	−	0.834663i	$-0.314338\pi$
$331$	−5.16514	−	5.16514i	−0.283902	−	0.283902i	−0.834663	+	0.550761i	$0.814338\pi$
$332$	−0.607862	−	2.69511i	−0.0333608	−	0.147913i
$333$	6.37215	−	6.37215i	0.349192	−	0.349192i
$334$	14.6040	−	8.04687i	0.799095	−	0.440305i
$335$	0.142341	+	26.6743i	0.00777693	+	1.45737i
$336$	−6.81735	+	3.24002i	−0.371917	+	0.176758i
$337$	15.5492	+	15.5492i	0.847019	+	0.847019i	0.989760	−	0.142741i	$-0.0455916\pi$
$337$	15.5492	+	15.5492i	0.847019	+	0.847019i	−0.142741	+	0.989760i	$0.545592\pi$
$338$	0.325768	−	0.179500i	0.0177195	−	0.00976352i
$339$	4.37444	−	4.37444i	0.237587	−	0.237587i
$340$	−9.32252	+	14.9283i	−0.505585	+	0.809599i
$341$	5.12728	−	5.12728i	0.277658	−	0.277658i
$342$	3.52703	+	1.02103i	0.190720	+	0.0552108i
$343$	−15.8783			−0.857345
$344$	8.83455	−	7.83402i	0.476327	−	0.422382i
$345$	−7.40805	−	7.32941i	−0.398836	−	0.394602i
$346$	1.65339	−	5.71147i	0.0888870	−	0.307051i
$347$			9.46621i			0.508173i	0.967182	+	0.254086i	$0.0817748\pi$
$347$			9.46621i			0.508173i	−0.967182	+	0.254086i	$0.918225\pi$
$348$	−1.08331	−	4.80314i	−0.0580716	−	0.257475i
$349$	−15.7685			−0.844070			−0.422035	−	0.906580i	$-0.638684\pi$
$349$	−15.7685			−0.844070			−0.422035	+	0.906580i	$0.638684\pi$
$350$	−7.91782	+	4.47357i	−0.423225	+	0.239122i
$351$		−	20.1456i		−	1.07529i
$352$	−1.90710	−	11.6780i	−0.101649	−	0.622439i
$353$	2.27725	+	2.27725i	0.121206	+	0.121206i	0.765108	−	0.643902i	$-0.222686\pi$
$353$	2.27725	+	2.27725i	0.121206	+	0.121206i	−0.643902	+	0.765108i	$0.722686\pi$
$354$	−4.83702	−	8.77855i	−0.257085	−	0.466575i
$355$	6.79031	+	6.71823i	0.360392	+	0.356567i
$356$	−15.2668	+	3.44331i	−0.809137	+	0.182495i
$357$		−	7.42639i		−	0.393046i
$358$	−8.66535	−	2.50850i	−0.457978	−	0.132578i
$359$	30.8709			1.62930			0.814651	−	0.579952i	$-0.196929\pi$
$359$	30.8709			1.62930			0.814651	+	0.579952i	$0.196929\pi$
$360$	0.292512	−	5.35040i	0.0154167	−	0.281991i
$361$		−	9.60863i		−	0.505717i
$362$	−0.191763	−	0.0555128i	−0.0100788	−	0.00291769i
$363$	−9.71983			−0.510159
$364$	4.90401	−	7.76037i	0.257040	−	0.406754i
$365$	13.6306	−	13.7769i	0.713459	−	0.721114i
$366$	19.4574	−	10.7211i	1.01706	−	0.560403i
$367$	−18.6788	+	18.6788i	−0.975027	+	0.975027i	−0.999696	−	0.0246685i	$-0.992147\pi$
$367$	−18.6788	+	18.6788i	−0.975027	+	0.975027i	0.0246685	+	0.999696i	$0.492147\pi$
$368$	11.9708	+	4.25790i	0.624019	+	0.221959i
$369$	−5.41616	+	0.308716i	−0.281954	+	0.0160711i
$370$	9.18045	−	32.3583i	0.477269	−	1.68223i
$371$	6.23840			0.323882
$372$	5.43413	−	8.59926i	0.281746	−	0.445851i
$373$	−7.60595	−	7.60595i	−0.393821	−	0.393821i	0.482226	−	0.876047i	$-0.339829\pi$
$373$	−7.60595	−	7.60595i	−0.393821	−	0.393821i	−0.876047	+	0.482226i	$0.839829\pi$
$374$	11.1827	+	3.23725i	0.578245	+	0.167394i
$375$	0.262597	+	16.4020i	0.0135605	+	0.846997i
$376$	32.6485	+	1.95972i	1.68372	+	0.101065i
$377$	4.23438	+	4.23438i	0.218082	+	0.218082i
$378$	4.95478	+	8.99226i	0.254846	+	0.462512i
$379$	24.6682			1.26712			0.633561	−	0.773693i	$-0.281593\pi$
$379$	24.6682			1.26712			0.633561	+	0.773693i	$0.281593\pi$
$380$	13.3529	−	3.08662i	0.684990	−	0.158340i
$381$	20.1995	−	20.1995i	1.03485	−	1.03485i
$382$	1.63762	−	5.65697i	0.0837877	−	0.289436i
$383$	25.0902			1.28205			0.641024	−	0.767521i	$-0.278510\pi$
$383$	25.0902			1.28205			0.641024	+	0.767521i	$0.278510\pi$
$384$	−6.21434	−	15.3927i	−0.317124	−	0.785506i
$385$	4.27625	+	4.23086i	0.217938	+	0.215624i
$386$	−19.3848	+	10.6811i	−0.986662	+	0.543656i
$387$	−2.50097	−	2.50097i	−0.127131	−	0.127131i
$388$	18.0753	−	28.6032i	0.917632	−	1.45211i
$389$	6.50144			0.329636			0.164818	−	0.986324i	$-0.447296\pi$
$389$	6.50144			0.329636			0.164818	+	0.986324i	$0.447296\pi$
$390$	−8.06851	−	14.4602i	−0.408565	−	0.732219i
$391$	−8.83924	+	8.83924i	−0.447020	+	0.447020i
$392$	0.905975	−	15.0933i	0.0457587	−	0.762329i
$393$		−	22.6562i		−	1.14285i
$394$	−12.8598	−	3.72274i	−0.647867	−	0.187549i
$395$	−3.58666	+	3.62514i	−0.180464	+	0.182401i
$396$	−3.45755	+	0.779824i	−0.173748	+	0.0391876i
$397$		−	3.70813i		−	0.186106i	−0.995661	−	0.0930530i	$-0.970337\pi$
$397$		−	3.70813i		−	0.186106i	0.995661	−	0.0930530i	$-0.0296626\pi$
$398$	−25.9290	−	7.50609i	−1.29970	−	0.376246i
$399$	−4.08910	+	4.08910i	−0.204711	+	0.204711i
$400$	−8.77728	−	17.9711i	−0.438864	−	0.898553i
$401$			23.4516i			1.17111i	0.810631	+	0.585557i	$0.199124\pi$
$401$			23.4516i			1.17111i	−0.810631	+	0.585557i	$0.800876\pi$
$402$	21.6797	−	11.9456i	1.08129	−	0.595794i
$403$			12.3716i			0.616275i
$404$	7.78566	−	1.75600i	0.387351	−	0.0873641i
$405$	12.8359	−	0.0684961i	0.637823	−	0.00340360i
$406$	−2.93151	−	0.848632i	−0.145488	−	0.0421169i
$407$	−22.2487			−1.10283
$408$	16.3028	+	0.978571i	0.807108	+	0.0484465i
$409$		−	25.2591i		−	1.24898i	−0.781032	−	0.624491i	$-0.785306\pi$
$409$		−	25.2591i		−	1.24898i	0.781032	−	0.624491i	$-0.214694\pi$
$410$	−17.0920	+	10.8565i	−0.844113	+	0.536166i
$411$			21.3544i			1.05334i
$412$	2.06734	−	0.466273i	0.101850	−	0.0229716i
$413$	−6.21245			−0.305694
$414$	1.05829	−	3.65573i	0.0520119	−	0.179670i
$415$	−2.17251	+	2.19582i	−0.106644	+	0.107788i
$416$	16.3898	+	11.7881i	0.803574	+	0.577960i
$417$		−	8.00661i		−	0.392085i
$418$	−4.37492	−	7.93990i	−0.213984	−	0.388353i
$419$			39.6006i			1.93462i	0.253605	+	0.967308i	$0.418384\pi$
$419$			39.6006i			1.93462i	−0.253605	+	0.967308i	$0.581616\pi$
$420$	7.15794	+	4.47005i	0.349272	+	0.218116i
$421$	12.1330	−	12.1330i	0.591328	−	0.591328i	−0.346662	−	0.937990i	$-0.612685\pi$
$421$	12.1330	−	12.1330i	0.591328	−	0.591328i	0.937990	+	0.346662i	$0.112685\pi$
$422$	5.36024	−	18.5164i	0.260933	−	0.901363i
$423$		−	9.79723i		−	0.476357i
$424$	−0.822031	+	13.6949i	−0.0399213	+	0.665081i
$425$	19.6764	−	0.210003i	0.954443	−	0.0101866i
$426$	2.46480	−	8.51438i	0.119420	−	0.412523i
$427$		−	13.7697i		−	0.666364i
$428$	7.91860	−	1.78598i	0.382760	−	0.0863287i
$429$	−7.74507	+	7.74507i	−0.373935	+	0.373935i
$430$	−12.7001	−	3.60318i	−0.612455	−	0.173761i
$431$	−15.7548			−0.758884			−0.379442	−	0.925216i	$-0.623884\pi$
$431$	−15.7548			−0.758884			−0.379442	+	0.925216i	$0.623884\pi$
$432$	−20.3931	+	9.69208i	−0.981166	+	0.466310i
$433$	−14.1701	−	14.1701i	−0.680969	−	0.680969i	0.279249	−	0.960219i	$-0.409914\pi$
$433$	−14.1701	−	14.1701i	−0.680969	−	0.680969i	−0.960219	+	0.279249i	$0.909914\pi$
$434$	−3.04278	−	5.52224i	−0.146058	−	0.265076i
$435$	−3.87177	+	3.91331i	−0.185637	+	0.187629i
$436$	−1.31396	−	5.82579i	−0.0629275	−	0.279005i
$437$	9.73409			0.465644
$438$	−17.2748	−	5.00083i	−0.825423	−	0.238949i
$439$	7.10413	−	7.10413i	0.339061	−	0.339061i	−0.516953	−	0.856014i	$-0.672934\pi$
$439$	7.10413	−	7.10413i	0.339061	−	0.339061i	0.856014	+	0.516953i	$0.172934\pi$
$440$	−9.85127	+	8.82995i	−0.469641	+	0.420951i
$441$	−4.52924			−0.215678
$442$	−17.3970	+	9.58584i	−0.827491	+	0.455952i
$443$	27.0461	+	27.0461i	1.28500	+	1.28500i	0.937785	+	0.347215i	$0.112873\pi$
$443$	27.0461	+	27.0461i	1.28500	+	1.28500i	0.347215	+	0.937785i	$0.387127\pi$
$444$	−30.4475	+	6.86720i	−1.44497	+	0.325903i
$445$	12.4385	+	12.3064i	0.589640	+	0.583380i
$446$	−0.280309	+	0.968299i	−0.0132730	+	0.0458503i
$447$	−10.5275	−	10.5275i	−0.497933	−	0.497933i
$448$	−10.2150	−	1.23075i	−0.482616	−	0.0581473i
$449$	1.54303			0.0728201			0.0364100	−	0.999337i	$-0.488408\pi$
$449$	1.54303			0.0728201			0.0364100	+	0.999337i	$0.488408\pi$
$450$	−5.21590	+	2.94699i	−0.245880	+	0.138922i
$451$	9.99437	+	8.91648i	0.470617	+	0.419860i
$452$	8.22611	−	1.85534i	0.386924	−	0.0872678i
$453$	−4.32752	+	4.32752i	−0.203325	+	0.203325i
$454$	16.4755	+	29.9008i	0.773232	+	1.40331i
$455$	−10.2634	+	0.0547684i	−0.481157	+	0.00256758i
$456$	−8.43778	−	9.51542i	−0.395135	−	0.445600i
$457$	−2.41526			−0.112981			−0.0564906	−	0.998403i	$-0.517991\pi$
$457$	−2.41526			−0.112981			−0.0564906	+	0.998403i	$0.517991\pi$
$458$	2.52379	−	8.71816i	0.117929	−	0.407373i
$459$		−	22.2150i		−	1.03691i
$460$	−3.19926	−	13.8402i	−0.149166	−	0.645302i
$461$	17.7954			0.828814			0.414407	−	0.910092i	$-0.363989\pi$
$461$	17.7954			0.828814			0.414407	+	0.910092i	$0.363989\pi$
$462$	1.55223	−	5.36200i	0.0722161	−	0.249463i
$463$			35.6081i			1.65485i	0.561577	+	0.827424i	$0.310195\pi$
$463$			35.6081i			1.65485i	−0.561577	+	0.827424i	$0.689805\pi$
$464$	2.24924	−	6.32357i	0.104418	−	0.293564i
$465$	−11.3729	+	0.0606888i	−0.527405	+	0.00281438i
$466$	−11.7144	+	6.45471i	−0.542660	+	0.299009i
$467$	−23.7712	−	23.7712i	−1.10000	−	1.10000i	−0.994410	−	0.105590i	$-0.966327\pi$
$467$	−23.7712	−	23.7712i	−1.10000	−	1.10000i	−0.105590	−	0.994410i	$-0.533673\pi$
$468$	3.23054	−	5.11218i	0.149332	−	0.236311i
$469$		−	15.3424i		−	0.708446i
$470$	−17.8181	−	31.9331i	−0.821887	−	1.47296i
$471$	11.6699			0.537722
$472$	0.818611	−	13.6379i	0.0376796	−	0.627734i
$473$			8.73228i			0.401511i
$474$	4.54557	+	1.31588i	0.208785	+	0.0604404i
$475$	−10.9498	−	10.7185i	−0.502410	−	0.491799i
$476$	5.40776	−	8.55753i	0.247864	−	0.392234i
$477$	4.10958			0.188165
$478$	−5.20455	+	17.9786i	−0.238051	+	0.822320i
$479$	6.07402	−	6.07402i	0.277529	−	0.277529i	−0.554593	−	0.832122i	$-0.687126\pi$
$479$	6.07402	−	6.07402i	0.277529	−	0.277529i	0.832122	+	0.554593i	$0.187126\pi$
$480$	−10.7561	+	15.1245i	−0.490945	+	0.690334i
$481$	26.8420	−	26.8420i	1.22389	−	1.22389i
$482$	−11.1175	−	20.1768i	−0.506390	−	0.919029i
$483$	4.23832	+	4.23832i	0.192850	+	0.192850i
$484$	−11.2003	−	7.07780i	−0.509104	−	0.321718i
$485$	−37.8290	+	0.201866i	−1.71773	+	0.00916627i
$486$	5.80918	+	10.5429i	0.263510	+	0.478235i
$487$	8.78469	−	8.78469i	0.398072	−	0.398072i	−0.479480	−	0.877553i	$-0.659175\pi$
$487$	8.78469	−	8.78469i	0.398072	−	0.398072i	0.877553	+	0.479480i	$0.159175\pi$
$488$	30.2280	+	1.81443i	1.36836	+	0.0821354i
$489$	24.0640	+	24.0640i	1.08821	+	1.08821i
$490$	−14.7626	+	8.23727i	−0.666907	+	0.372122i
$491$		−	0.498440i		−	0.0224943i	−0.999937	−	0.0112471i	$-0.996420\pi$
$491$		−	0.498440i		−	0.0224943i	0.999937	−	0.0112471i	$-0.00358015\pi$
$492$	16.4294	+	9.11740i	0.740696	+	0.411044i
$493$	4.66934	+	4.66934i	0.210297	+	0.210297i
$494$	14.8572	+	4.30097i	0.668459	+	0.193510i
$495$	2.81701	+	2.78710i	0.126615	+	0.125271i
$496$	12.5236	−	5.95200i	0.562328	−	0.267253i
$497$	−3.88490	−	3.88490i	−0.174261	−	0.174261i
$498$	2.75333	+	0.797053i	0.123380	+	0.0357168i
$499$	0.352401	−	0.352401i	0.0157757	−	0.0157757i	−0.699175	−	0.714951i	$-0.746449\pi$
$499$	0.352401	−	0.352401i	0.0157757	−	0.0157757i	0.714951	+	0.699175i	$0.246449\pi$
$500$	−11.6411	+	19.0915i	−0.520604	+	0.853798i
$501$			17.2993i			0.772875i
$502$	35.3519	−	19.4791i	1.57783	−	0.869395i
$503$			16.9621i			0.756305i	0.925743	+	0.378152i	$0.123440\pi$
$503$			16.9621i			0.756305i	−0.925743	+	0.378152i	$0.876560\pi$
$504$	−0.184663	+	3.07644i	−0.00822552	+	0.137035i
$505$	−6.34330	−	6.27596i	−0.282273	−	0.279276i
$506$	−8.22964	+	4.53457i	−0.365852	+	0.201586i
$507$			0.385892i			0.0171381i
$508$	37.9851	−	8.56726i	1.68532	−	0.380111i
$509$	−28.7794	+	28.7794i	−1.27562	+	1.27562i	−0.332530	+	0.943093i	$0.607902\pi$
$509$	−28.7794	+	28.7794i	−1.27562	+	1.27562i	−0.943093	+	0.332530i	$0.892098\pi$
$510$	−8.89733	−	15.9455i	−0.393980	−	0.706081i
$511$	−7.88207	+	7.88207i	−0.348682	+	0.348682i
$512$	4.04783	−	22.2624i	0.178890	−	0.983869i
$513$	−12.2320	+	12.2320i	−0.540055	+	0.540055i
$514$	−19.5215	−	35.4289i	−0.861057	−	1.56270i
$515$	−1.68434	−	1.66646i	−0.0742211	−	0.0734332i
$516$	2.69527	+	11.9501i	0.118652	+	0.526076i
$517$	−17.1038	+	17.1038i	−0.752224	+	0.752224i
$518$	−5.37954	+	18.5830i	−0.236363	+	0.816492i
$519$	4.36206	+	4.36206i	0.191473	+	0.191473i
$520$	1.23218	−	22.5380i	0.0540345	−	0.988357i
$521$	−11.3728	+	11.3728i	−0.498253	+	0.498253i	−0.910894	−	0.412641i	$-0.864606\pi$
$521$	−11.3728	+	11.3728i	−0.498253	+	0.498253i	0.412641	+	0.910894i	$0.364606\pi$
$522$	−1.93115	−	0.559041i	−0.0845240	−	0.0244686i
$523$	−23.7630	+	23.7630i	−1.03909	+	1.03909i	−0.0398809	+	0.999204i	$0.512698\pi$
$523$	−23.7630	+	23.7630i	−1.03909	+	1.03909i	−0.999204	+	0.0398809i	$0.987302\pi$
$524$	16.4978	−	26.1070i	0.720710	−	1.14049i
$525$	−0.100694	−	9.43460i	−0.00439465	−	0.411760i
$526$	−34.8498	+	19.2024i	−1.51953	+	0.837266i
$527$			13.6425i			0.594275i
$528$	11.5664	+	4.11407i	0.503363	+	0.179042i
$529$			12.9107i			0.561335i
$530$	13.3948	−	7.47404i	0.581831	−	0.324651i
$531$	−4.09248			−0.177599
$532$	−7.68953	+	1.73432i	−0.333384	+	0.0751922i
$533$	−22.8150	+	1.30043i	−0.988229	+	0.0563280i
$534$	4.51500	−	15.5966i	0.195383	−	0.674931i
$535$	−6.45161	−	6.38312i	−0.278928	−	0.275966i
$536$	33.6804	+	2.02166i	1.45477	+	0.0873224i
$537$	6.61804	−	6.61804i	0.285590	−	0.285590i
$538$	7.54074	+	13.6854i	0.325104	+	0.590021i
$539$	7.90706	+	7.90706i	0.340581	+	0.340581i
$540$	21.4120	+	13.3715i	0.921425	+	0.575419i
$541$			13.1974i			0.567402i	0.958913	+	0.283701i	$0.0915623\pi$
$541$			13.1974i			0.567402i	−0.958913	+	0.283701i	$0.908438\pi$
$542$	−9.16364	−	16.6308i	−0.393612	−	0.714353i
$543$	0.146456	−	0.146456i	0.00628504	−	0.00628504i
$544$	18.0733	+	12.9990i	0.774888	+	0.557328i
$545$	−4.69613	+	4.74651i	−0.201160	+	0.203318i
$546$	4.59631	+	8.34168i	0.196704	+	0.356991i
$547$			39.3760i			1.68360i	0.539791	+	0.841799i	$0.318503\pi$
$547$			39.3760i			1.68360i	−0.539791	+	0.841799i	$0.681497\pi$
$548$	−15.5499	+	24.6070i	−0.664259	+	1.05116i
$549$		−	9.07088i		−	0.387136i
$550$	14.2506	+	3.96103i	0.607648	+	0.168899i
$551$		−	5.14204i		−	0.219058i
$552$	−9.86266	+	8.74569i	−0.419783	+	0.372241i
$553$	2.07403	−	2.07403i	0.0881967	−	0.0881967i
$554$	−4.18579	+	14.4594i	−0.177837	+	0.614319i
$555$	24.8068	+	24.5434i	1.05299	+	1.04181i
$556$	5.83026	−	9.22612i	0.247258	−	0.391275i
$557$	−32.4284			−1.37403			−0.687017	−	0.726641i	$-0.741080\pi$
$557$	−32.4284			−1.37403			−0.687017	+	0.726641i	$0.741080\pi$
$558$	−2.00445	−	3.63780i	−0.0848551	−	0.154001i
$559$	−10.5351	−	10.5351i	−0.445586	−	0.445586i
$560$	4.99318	+	10.3632i	0.211001	+	0.437924i
$561$	−8.54065	+	8.54065i	−0.360587	+	0.360587i
$562$	6.29123	+	1.82123i	0.265380	+	0.0768238i
$563$		−	39.9231i		−	1.68256i	−0.540602	−	0.841278i	$-0.681804\pi$
$563$		−	39.9231i		−	1.68256i	0.540602	−	0.841278i	$-0.318196\pi$
$564$	−18.1274	+	28.6858i	−0.763301	+	1.20789i
$565$	−6.70215	−	6.63100i	−0.281962	−	0.278968i
$566$	−2.47677	+	8.55573i	−0.104106	+	0.359624i
$567$	−7.38293			−0.310054
$568$	9.04024	−	8.01641i	0.379320	−	0.336361i
$569$	−14.6032			−0.612198			−0.306099	−	0.952000i	$-0.599024\pi$
$569$	−14.6032			−0.612198			−0.306099	+	0.952000i	$0.599024\pi$
$570$	−3.88087	+	13.6789i	−0.162552	+	0.572947i
$571$	6.13007	+	6.13007i	0.256535	+	0.256535i	0.823643	−	0.567108i	$-0.191938\pi$
$571$	6.13007	+	6.13007i	0.256535	+	0.256535i	−0.567108	+	0.823643i	$0.691938\pi$
$572$	−14.5646	+	3.28493i	−0.608975	+	0.137350i
$573$	4.32043	+	4.32043i	0.180489	+	0.180489i
$574$	9.86395	−	6.19178i	0.411713	−	0.258440i
$575$	−11.1097	+	11.3494i	−0.463305	+	0.473301i
$576$	−6.72922	−	0.810761i	−0.280384	−	0.0337817i
$577$			6.08319i			0.253246i	0.991951	+	0.126623i	$0.0404139\pi$
$577$			6.08319i			0.253246i	−0.991951	+	0.126623i	$0.959586\pi$
$578$	1.87266	−	1.03184i	0.0778922	−	0.0429190i
$579$		−	22.9625i		−	0.954288i
$580$	−7.31110	+	1.69001i	−0.303577	+	0.0701739i
$581$	1.25628	−	1.25628i	0.0521192	−	0.0521192i
$582$	16.9411	+	30.7458i	0.702232	+	1.27446i
$583$	−7.17442	−	7.17442i	−0.297134	−	0.297134i
$584$	−16.2645	−	18.3417i	−0.673030	−	0.758986i
$585$	−6.76108	+	0.0360790i	−0.279536	+	0.00149168i
$586$	−9.63942	−	17.4943i	−0.398201	−	0.722681i
$587$	20.8479			0.860485			0.430243	−	0.902713i	$-0.358428\pi$
$587$	20.8479			0.860485			0.430243	+	0.902713i	$0.358428\pi$
$588$	13.2614	+	8.38027i	0.546890	+	0.345596i
$589$	7.51178	−	7.51178i	0.309518	−	0.309518i
$590$	−13.3390	+	7.44294i	−0.549159	+	0.306421i
$591$	9.82149	−	9.82149i	0.404002	−	0.404002i
$592$	−40.0856	−	14.2581i	−1.64751	−	0.586005i
$593$		−	33.8476i		−	1.38996i	−0.719031	−	0.694978i	$-0.755414\pi$
$593$		−	33.8476i		−	1.38996i	0.719031	−	0.694978i	$-0.244586\pi$
$594$	4.64327	−	16.0397i	0.190516	−	0.658116i
$595$	−11.3177	+	0.0603944i	−0.463980	+	0.00247593i
$596$	−4.46504	−	19.7969i	−0.182895	−	0.810913i
$597$	19.8029	−	19.8029i	0.810479	−	0.810479i
$598$	4.45792	−	15.3994i	0.182298	−	0.629729i
$599$	15.4148			0.629832			0.314916	−	0.949119i	$-0.398024\pi$
$599$	15.4148			0.629832			0.314916	+	0.949119i	$0.398024\pi$
$600$	20.7246	+	1.02214i	0.846077	+	0.0417288i
$601$	10.1606	+	10.1606i	0.414459	+	0.414459i	0.883289	−	0.468829i	$-0.155324\pi$
$601$	10.1606	+	10.1606i	0.414459	+	0.414459i	−0.468829	+	0.883289i	$0.655324\pi$
$602$	7.29355	+	2.11138i	0.297263	+	0.0860536i
$603$		−	10.1069i		−	0.411584i
$604$	−8.13789	+	1.83544i	−0.331126	+	0.0746830i
$605$	0.0790455	+	14.8129i	0.00321366	+	0.602229i
$606$	−2.30254	+	7.95386i	−0.0935341	+	0.323104i
$607$	5.34766	−	5.34766i	0.217055	−	0.217055i	−0.590201	−	0.807256i	$-0.700952\pi$
$607$	5.34766	−	5.34766i	0.217055	−	0.217055i	0.807256	+	0.590201i	$0.200952\pi$
$608$	−2.79402	−	17.1090i	−0.113312	−	0.693861i
$609$	2.23890	−	2.23890i	0.0907248	−	0.0907248i
$610$	−16.4971	−	29.5656i	−0.667948	−	1.19708i
$611$		−	41.2698i		−	1.66960i
$612$	3.56239	−	5.63732i	0.144001	−	0.227875i
$613$	−25.3444	+	25.3444i	−1.02365	+	1.02365i	−0.0239365	+	0.999713i	$0.507620\pi$
$613$	−25.3444	+	25.3444i	−1.02365	+	1.02365i	−0.999713	+	0.0239365i	$0.992380\pi$
$614$	2.86828	−	9.90818i	0.115754	−	0.399861i
$615$	−1.30737	−	20.9668i	−0.0527182	−	0.845464i
$616$	5.69316	−	5.04840i	0.229384	−	0.203406i
$617$	19.0158	+	19.0158i	0.765549	+	0.765549i	0.977319	−	0.211771i	$-0.0679230\pi$
$617$	19.0158	+	19.0158i	0.765549	+	0.765549i	−0.211771	+	0.977319i	$0.567923\pi$
$618$	−0.611396	+	2.11200i	−0.0245939	+	0.0849571i
$619$	−10.4838			−0.421379			−0.210689	−	0.977553i	$-0.567571\pi$
$619$	−10.4838			−0.421379			−0.210689	+	0.977553i	$0.567571\pi$
$620$	−13.1493	−	8.21160i	−0.528090	−	0.329786i
$621$	12.6783	+	12.6783i	0.508765	+	0.508765i
$622$	−10.8295	+	37.4093i	−0.434223	+	1.49998i
$623$	−7.11634	−	7.11634i	−0.285110	−	0.285110i
$624$	−18.9177	+	8.99086i	−0.757315	+	0.359923i
$625$	24.9943	−	0.533582i	0.999772	−	0.0213433i
$626$	18.8984	+	34.2981i	0.755333	+	1.37083i
$627$	9.40527			0.375610
$628$	13.4474	+	8.49783i	0.536610	+	0.339100i
$629$	29.5993	−	29.5993i	1.18020	−	1.18020i
$630$	3.00902	−	1.67898i	0.119882	−	0.0668922i
$631$		−	10.0445i		−	0.399865i	−0.979810	−	0.199933i	$-0.935928\pi$
$631$		−	10.0445i		−	0.399865i	0.979810	−	0.199933i	$-0.0640724\pi$
$632$	4.27972	+	4.82631i	0.170238	+	0.191980i
$633$	14.1416	+	14.1416i	0.562079	+	0.562079i
$634$	14.5997	+	26.4965i	0.579827	+	1.05231i
$635$	−30.9480	−	30.6195i	−1.22813	−	1.21510i
$636$	−12.0326	−	7.60378i	−0.477125	−	0.301510i
$637$	−19.0790			−0.755936
$638$	2.39539	+	4.34732i	0.0948346	+	0.172112i
$639$	−2.55920	−	2.55920i	−0.101240	−	0.101240i
$640$	−23.4077	+	9.59574i	−0.925272	+	0.379305i
$641$	−31.8596	−	31.8596i	−1.25838	−	1.25838i	−0.951866	−	0.306513i	$-0.900838\pi$
$641$	−31.8596	−	31.8596i	−1.25838	−	1.25838i	−0.306513	−	0.951866i	$-0.599162\pi$
$642$	−2.34185	+	8.08968i	−0.0924256	+	0.319274i
$643$		−	6.56095i		−	0.258739i	−0.991596	−	0.129369i	$-0.958705\pi$
$643$		−	6.56095i		−	0.258739i	0.991596	−	0.129369i	$-0.0412953\pi$
$644$	1.79761	+	7.97014i	0.0708356	+	0.314068i
$645$	9.63291	−	9.73627i	0.379296	−	0.383365i
$646$	16.3834	+	4.74277i	0.644596	+	0.186602i
$647$	23.0155	−	23.0155i	0.904832	−	0.904832i	−0.0910174	−	0.995849i	$-0.529012\pi$
$647$	23.0155	−	23.0155i	0.904832	−	0.904832i	0.995849	+	0.0910174i	$0.0290119\pi$
$648$	0.972845	−	16.2074i	0.0382169	−	0.636686i
$649$	7.14457	+	7.14457i	0.280449	+	0.280449i
$650$	−21.9715	+	12.4139i	−0.861792	+	0.486913i
$651$	6.54142			0.256378
$652$	10.2063	+	45.2523i	0.399711	+	1.77222i
$653$	3.86895			0.151404			0.0757019	−	0.997130i	$-0.475880\pi$
$653$	3.86895			0.151404			0.0757019	+	0.997130i	$0.475880\pi$
$654$	5.95166	+	1.72292i	0.232728	+	0.0673717i
$655$	−34.5276	+	0.184249i	−1.34911	+	0.00719920i
$656$	12.2927	+	22.4697i	0.479951	+	0.877295i
$657$	−5.19236	+	5.19236i	−0.202573	+	0.202573i
$658$	10.1502	+	18.4213i	0.395698	+	0.718138i
$659$	−11.2541	+	11.2541i	−0.438399	+	0.438399i	−0.891473	−	0.453074i	$-0.850327\pi$
$659$	−11.2541	+	11.2541i	−0.438399	+	0.438399i	0.453074	+	0.891473i	$0.350327\pi$
$660$	−3.09119	−	13.3727i	−0.120324	−	0.520531i
$661$			44.5712i			1.73362i	0.498638	+	0.866810i	$0.333834\pi$
$661$			44.5712i			1.73362i	−0.498638	+	0.866810i	$0.666166\pi$
$662$	9.92287	+	2.87254i	0.385663	+	0.111644i
$663$		−	20.6078i		−	0.800340i
$664$	2.59231	+	2.92338i	0.100601	+	0.113449i
$665$	6.26498	+	6.19847i	0.242945	+	0.240366i
$666$	−3.54380	+	12.2417i	−0.137320	+	0.474356i
$667$	−5.32969			−0.206366
$668$	−12.5970	+	19.9342i	−0.487394	+	0.771277i
$669$	−0.739525	−	0.739525i	−0.0285917	−	0.0285917i
$670$	−18.3813	−	32.9424i	−0.710130	−	1.27268i
$671$	−15.8358	+	15.8358i	−0.611333	+	0.611333i
$672$	6.23288	−	8.66597i	0.240439	−	0.334297i
$673$			1.80452i			0.0695590i	0.999395	+	0.0347795i	$0.0110729\pi$
$673$			1.80452i			0.0695590i	−0.999395	+	0.0347795i	$0.988927\pi$
$674$	−29.8719	−	8.64751i	−1.15062	−	0.333090i
$675$	−0.301212	−	28.2223i	−0.0115937	−	1.08628i
$676$	−0.280999	+	0.444668i	−0.0108077	+	0.0171026i
$677$	−31.3321	−	31.3321i	−1.20419	−	1.20419i	−0.972880	−	0.231309i	$-0.925699\pi$
$677$	−31.3321	−	31.3321i	−1.20419	−	1.20419i	−0.231309	−	0.972880i	$-0.574301\pi$
$678$	−2.43279	+	8.40383i	−0.0934309	+	0.322747i
$679$	21.7584			0.835009
$680$	1.35875	−	24.8531i	0.0521056	−	0.953075i
$681$	−35.4192			−1.35727
$682$	−2.85148	+	9.85013i	−0.109189	+	0.377181i
$683$	−12.6562			−0.484276			−0.242138	−	0.970242i	$-0.577849\pi$
$683$	−12.6562			−0.484276			−0.242138	+	0.970242i	$0.577849\pi$
$684$	−5.06552	+	1.14249i	−0.193685	+	0.0436842i
$685$	32.5438	−	0.173663i	1.24344	−	0.00663532i
$686$	19.6673	−	10.8368i	0.750901	−	0.413750i
$687$	6.65837	+	6.65837i	0.254033	+	0.254033i
$688$	−5.59609	+	15.7330i	−0.213349	+	0.599813i
$689$	17.3112			0.659504
$690$	14.1781	+	4.02250i	0.539751	+	0.153134i
$691$	3.80789	−	3.80789i	0.144859	−	0.144859i	−0.630958	−	0.775817i	$-0.717338\pi$
$691$	3.80789	−	3.80789i	0.144859	−	0.144859i	0.775817	+	0.630958i	$0.217338\pi$
$692$	1.85009	+	8.20283i	0.0703298	+	0.311825i
$693$	−1.61167	−	1.61167i	−0.0612225	−	0.0612225i
$694$	−6.46061	−	11.7251i	−0.245241	−	0.445080i
$695$	−12.2019	+	0.0651129i	−0.462846	+	0.00246987i
$696$	4.61993	+	5.20996i	0.175118	+	0.197483i
$697$	−25.1586	+	1.43402i	−0.952951	+	0.0543172i
$698$	19.5314	−	10.7619i	0.739274	−	0.407343i
$699$		−	13.8764i		−	0.524854i
$700$	6.75407	−	10.9449i	0.255280	−	0.413680i
$701$	37.1403			1.40277			0.701385	−	0.712782i	$-0.252565\pi$
$701$	37.1403			1.40277			0.701385	+	0.712782i	$0.252565\pi$
$702$	13.7492	+	24.9530i	0.518931	+	0.941789i
$703$	−32.5958			−1.22937
$704$	10.3323	+	13.1631i	0.389414	+	0.496104i
$705$	37.9382	−	0.202448i	1.42883	−	0.00762465i
$706$	−4.37487	−	1.26646i	−0.164650	−	0.0476640i
$707$	3.62915	+	3.62915i	0.136488	+	0.136488i
$708$	11.9826	+	7.57215i	0.450333	+	0.284579i
$709$	3.79099	+	3.79099i	0.142373	+	0.142373i	0.774701	−	0.632328i	$-0.217900\pi$
$709$	3.79099	+	3.79099i	0.142373	+	0.142373i	−0.632328	+	0.774701i	$0.717900\pi$
$710$	−12.9958	−	3.68707i	−0.487725	−	0.138373i
$711$	1.36628	−	1.36628i	0.0512394	−	0.0512394i
$712$	16.5599	−	14.6844i	0.620607	−	0.550322i
$713$	−7.78591	−	7.78591i	−0.291584	−	0.291584i
$714$	5.06845	+	9.19855i	0.189682	+	0.344247i
$715$	11.8663	+	11.7404i	0.443776	+	0.439065i
$716$	12.4452	−	2.80692i	0.465099	−	0.104900i
$717$	−13.7309	−	13.7309i	−0.512789	−	0.512789i
$718$	−38.2376	+	21.0691i	−1.42701	+	0.786292i
$719$	10.0223	+	10.0223i	0.373769	+	0.373769i	0.868848	−	0.495079i	$-0.164861\pi$
$719$	10.0223	+	10.0223i	0.373769	+	0.373769i	−0.495079	+	0.868848i	$0.664861\pi$
$720$	3.28929	+	6.82680i	0.122584	+	0.254420i
$721$	0.963653	+	0.963653i	0.0358883	+	0.0358883i
$722$	6.55781	+	11.9015i	0.244056	+	0.442929i
$723$	23.9006			0.888874
$724$	0.275410	−	0.0621168i	0.0102355	−	0.00230855i
$725$	5.99532	+	5.86869i	0.222660	+	0.217958i
$726$	12.0393	−	6.63370i	0.446819	−	0.246200i
$727$	8.14188			0.301966			0.150983	−	0.988536i	$-0.451756\pi$
$727$	8.14188			0.301966			0.150983	+	0.988536i	$0.451756\pi$
$728$	−0.777872	+	12.9592i	−0.0288299	+	0.480299i
$729$	−29.7101			−1.10037
$730$	−7.48070	+	26.3672i	−0.276873	+	0.975895i
$731$	−11.6173	−	11.6173i	−0.429680	−	0.429680i
$732$	−16.7835	+	26.5591i	−0.620335	+	0.981651i
$733$	0.303050	−	0.303050i	0.0111934	−	0.0111934i	−0.701488	−	0.712681i	$-0.747481\pi$
$733$	0.303050	−	0.303050i	0.0111934	−	0.0111934i	0.712681	+	0.701488i	$0.247481\pi$
$734$	10.3880	−	35.8843i	0.383429	−	1.32451i
$735$	−0.0935916	−	17.5387i	−0.00345218	−	0.646926i
$736$	−17.7333	+	2.89598i	−0.653659	+	0.106747i
$737$	−17.6444	+	17.6444i	−0.649940	+	0.649940i
$738$	6.49793	−	4.07887i	0.239192	−	0.150145i
$739$	−44.2806			−1.62889			−0.814444	−	0.580242i	$-0.802958\pi$
$739$	−44.2806			−1.62889			−0.814444	+	0.580242i	$0.802958\pi$
$740$	10.7131	+	46.3456i	0.393822	+	1.70370i
$741$	−11.3470	+	11.3470i	−0.416843	+	0.416843i
$742$	−7.72707	+	4.25765i	−0.283670	+	0.156303i
$743$	1.12779	+	1.12779i	0.0413745	+	0.0413745i	0.727491	−	0.686117i	$-0.240686\pi$
$743$	1.12779	+	1.12779i	0.0413745	+	0.0413745i	−0.686117	+	0.727491i	$0.740686\pi$
$744$	−0.861959	+	14.3600i	−0.0316010	+	0.526465i
$745$	−15.9581	+	16.1293i	−0.584660	+	0.590934i
$746$	14.6120	+	4.22997i	0.534982	+	0.154870i
$747$	0.827580	−	0.827580i	0.0302796	−	0.0302796i
$748$	−16.0607	+	3.62236i	−0.587236	+	0.132447i
$749$	3.69112	+	3.69112i	0.134871	+	0.134871i
$750$	−11.5195	−	20.1368i	−0.420633	−	0.735293i
$751$	27.3352	+	27.3352i	0.997477	+	0.997477i	0.999997	−	0.00251969i	$-0.000802042\pi$
$751$	27.3352	+	27.3352i	0.997477	+	0.997477i	−0.00251969	+	0.999997i	$0.500802\pi$
$752$	−41.7769	+	19.8550i	−1.52345	+	0.724036i
$753$			41.8764i			1.52606i
$754$	−8.13476	−	2.35490i	−0.296250	−	0.0857605i
$755$	6.63027	+	6.55989i	0.241300	+	0.238739i
$756$	−12.2743	−	7.75649i	−0.446411	−	0.282101i
$757$	−13.5476			−0.492394			−0.246197	−	0.969220i	$-0.579181\pi$
$757$	−13.5476			−0.492394			−0.246197	+	0.969220i	$0.579181\pi$
$758$	−30.5548	+	16.8358i	−1.10980	+	0.611506i
$759$		−	9.74849i		−	0.353848i
$760$	−14.4327	+	12.9364i	−0.523530	+	0.469254i
$761$	−36.2323			−1.31342			−0.656710	−	0.754143i	$-0.728053\pi$
$761$	−36.2323			−1.31342			−0.656710	+	0.754143i	$0.728053\pi$
$762$	−11.2337	+	38.8057i	−0.406955	+	1.40578i
$763$	2.71559	−	2.71559i	0.0983110	−	0.0983110i
$764$	1.83243	+	8.12455i	0.0662951	+	0.293936i
$765$	−7.45559	+	0.0397851i	−0.269558	+	0.00143843i
$766$	−31.0774	+	17.1238i	−1.12287	+	0.618709i
$767$	−17.2392			−0.622470
$768$	18.2027	+	14.8247i	0.656832	+	0.534939i
$769$			51.8886i			1.87115i	0.353128	+	0.935575i	$0.385118\pi$
$769$			51.8886i			1.87115i	−0.353128	+	0.935575i	$0.614882\pi$
$770$	−8.18422	−	2.32196i	−0.294939	−	0.0836777i
$771$	41.9676			1.51143
$772$	16.7209	−	26.4600i	0.601797	−	0.952315i
$773$			9.33295i			0.335683i	0.985814	+	0.167841i	$0.0536796\pi$
$773$			9.33295i			0.335683i	−0.985814	+	0.167841i	$0.946320\pi$
$774$	4.80467	+	1.39089i	0.172700	+	0.0499944i
$775$	0.184978	+	17.3316i	0.00664460	+	0.622570i
$776$	−2.86709	+	47.7651i	−0.102922	+	1.71467i
$777$	−14.1925	−	14.1925i	−0.509155	−	0.509155i
$778$	−8.05288	+	4.43718i	−0.288710	+	0.159081i
$779$	14.6424	+	13.0632i	0.524618	+	0.468037i
$780$	19.8629	+	12.4041i	0.711204	+	0.444139i
$781$			8.93559i			0.319740i
$782$	4.91585	−	16.9813i	0.175790	−	0.607249i
$783$	6.69735	−	6.69735i	0.239344	−	0.239344i
$784$	9.17891	+	19.3134i	0.327818	+	0.689764i
$785$	−0.0949045	−	17.7848i	−0.00338729	−	0.634766i
$786$	15.4626	+	28.0626i	0.551534	+	1.00096i
$787$	−11.8195	+	11.8195i	−0.421319	+	0.421319i	−0.885658	−	0.464339i	$-0.846292\pi$
$787$	−11.8195	+	11.8195i	−0.421319	+	0.421319i	0.464339	+	0.885658i	$0.346292\pi$
$788$	18.4693	−	4.16561i	0.657941	−	0.148394i
$789$		−	41.2817i		−	1.46967i
$790$	1.96842	−	6.93808i	0.0700331	−	0.246846i
$791$	3.83446	+	3.83446i	0.136338	+	0.136338i
$792$	3.75040	−	3.32566i	0.133265	−	0.118172i
$793$		−	38.2102i		−	1.35688i
$794$	2.53077	+	4.59301i	0.0898137	+	0.163000i
$795$	0.0849197	+	15.9137i	0.00301179	+	0.564400i
$796$	37.2393	−	8.39904i	1.31991	−	0.297696i
$797$	0.0505684	−	0.0505684i	0.00179122	−	0.00179122i	−0.706211	−	0.708002i	$-0.749597\pi$
$797$	0.0505684	−	0.0505684i	0.00179122	−	0.00179122i	0.708002	+	0.706211i	$0.249597\pi$
$798$	2.27411	−	7.85566i	0.0805025	−	0.278087i
$799$		−	45.5091i		−	1.61000i
$800$	23.1369	+	16.2691i	0.818013	+	0.575199i
$801$	−4.68793	−	4.68793i	−0.165640	−	0.165640i
$802$	−16.0055	−	29.0478i	−0.565173	−	1.02571i
$803$	18.1294			0.639773
$804$	−18.7004	+	29.5924i	−0.659511	+	1.04364i
$805$	6.42467	−	6.49360i	0.226440	−	0.228869i
$806$	−8.44353	−	15.3239i	−0.297411	−	0.539761i
$807$	−16.2112			−0.570661
$808$	−8.44510	+	7.48868i	−0.297098	+	0.263451i
$809$	0.257463	+	0.257463i	0.00905191	+	0.00905191i	0.711618	−	0.702566i	$-0.247963\pi$
$809$	0.257463	+	0.257463i	0.00905191	+	0.00905191i	−0.702566	+	0.711618i	$0.747963\pi$
$810$	−15.8522	+	8.84526i	−0.556991	+	0.310791i
$811$	3.37999			0.118687			0.0593437	−	0.998238i	$-0.481099\pi$
$811$	3.37999			0.118687			0.0593437	+	0.998238i	$0.481099\pi$
$812$	4.21024	−	0.949588i	0.147750	−	0.0333240i
$813$	19.7001			0.690913
$814$	27.5580	−	15.1846i	0.965907	−	0.532219i
$815$	36.4775	−	36.8689i	1.27775	−	1.29146i
$816$	−20.8610	+	9.91442i	−0.730281	+	0.347074i
$817$			12.7933i			0.447582i
$818$	17.2391	+	31.2867i	0.602752	+	1.09391i
$819$	3.88882			0.135886
$820$	13.7612	−	25.1124i	0.480561	−	0.876962i
$821$	−3.10612			−0.108404			−0.0542021	−	0.998530i	$-0.517262\pi$
$821$	−3.10612			−0.108404			−0.0542021	+	0.998530i	$0.517262\pi$
$822$	−14.5742	−	26.4503i	−0.508334	−	0.922559i
$823$			39.3682i			1.37229i	0.727466	+	0.686144i	$0.240698\pi$
$823$			39.3682i			1.37229i	−0.727466	+	0.686144i	$0.759302\pi$
$824$	−2.24244	+	1.98848i	−0.0781191	+	0.0692720i
$825$	−10.7344	+	10.9660i	−0.373723	+	0.381787i
$826$	7.69492	−	4.23994i	0.267741	−	0.147526i
$827$	40.8752			1.42137			0.710685	−	0.703510i	$-0.248385\pi$
$827$	40.8752			1.42137			0.710685	+	0.703510i	$0.248385\pi$
$828$	1.18418	+	5.25037i	0.0411532	+	0.182463i
$829$	8.53575			0.296459			0.148229	−	0.988953i	$-0.452643\pi$
$829$	8.53575			0.296459			0.148229	+	0.988953i	$0.452643\pi$
$830$	1.19231	−	4.20252i	0.0413855	−	0.145872i
$831$	−11.0431	−	11.0431i	−0.383082	−	0.383082i
$832$	−28.3461	−	3.41525i	−0.982726	−	0.118402i
$833$	−21.0388			−0.728951
$834$	5.46444	+	9.91722i	0.189218	+	0.343405i
$835$	26.3638	−	0.140685i	0.912358	−	0.00486860i
$836$	10.8378	+	6.84875i	0.374834	+	0.236869i
$837$	19.5677			0.676360
$838$	−27.0271	−	49.0505i	−0.933635	−	1.69442i
$839$	4.33479	+	4.33479i	0.149653	+	0.149653i	0.777963	−	0.628310i	$-0.216253\pi$
$839$	4.33479	+	4.33479i	0.149653	+	0.149653i	−0.628310	+	0.777963i	$0.716253\pi$
$840$	−11.9168	−	0.651504i	−0.411169	−	0.0224790i
$841$		−	26.1846i		−	0.902917i
$842$	−6.74765	+	23.3090i	−0.232539	+	0.803283i
$843$	−4.80484	+	4.80484i	−0.165487	+	0.165487i
$844$	5.99792	+	26.5933i	0.206457	+	0.915378i
$845$	0.588093	−	0.00313823i	0.0202310	−	0.000107958i
$846$	6.68652	+	12.1351i	0.229887	+	0.417215i
$847$		−	8.52001i		−	0.292751i
$848$	−8.32843	−	17.5239i	−0.285999	−	0.601773i
$849$	−6.53432	−	6.53432i	−0.224257	−	0.224257i
$850$	−24.2284	+	13.6891i	−0.831028	+	0.469531i
$851$			33.7853i			1.15815i
$852$	2.75802	+	12.2284i	0.0944881	+	0.418937i
$853$	37.3151	−	37.3151i	1.27764	−	1.27764i	0.335662	−	0.941983i	$-0.391040\pi$
$853$	37.3151	−	37.3151i	1.27764	−	1.27764i	0.941983	−	0.335662i	$-0.108960\pi$
$854$	9.39772	+	17.0556i	0.321583	+	0.583631i
$855$	4.12709	+	4.08328i	0.141143	+	0.139645i
$856$	−8.58931	+	7.61655i	−0.293576	+	0.260328i
$857$	−21.5814	+	21.5814i	−0.737206	+	0.737206i	−0.972036	−	0.234830i	$-0.924547\pi$
$857$	−21.5814	+	21.5814i	−0.737206	+	0.737206i	0.234830	+	0.972036i	$0.424547\pi$
$858$	4.30733	−	14.8792i	0.147050	−	0.507968i
$859$		−	13.3468i		−	0.455388i	−0.973733	−	0.227694i	$-0.926881\pi$
$859$		−	13.3468i		−	0.455388i	0.973733	−	0.227694i	$-0.0731186\pi$
$860$	18.1899	−	4.20473i	0.620271	−	0.143380i
$861$	0.687595	+	12.0633i	0.0234332	+	0.411116i
$862$	19.5144	−	10.7525i	0.664664	−	0.366233i
$863$	−16.7806	−	16.7806i	−0.571218	−	0.571218i	0.361251	−	0.932469i	$-0.382350\pi$
$863$	−16.7806	−	16.7806i	−0.571218	−	0.571218i	−0.932469	+	0.361251i	$0.882350\pi$
$864$	18.6448	−	25.9230i	0.634309	−	0.881920i
$865$	6.61223	−	6.68318i	0.224823	−	0.227235i
$866$	27.2224	+	7.88052i	0.925055	+	0.267791i
$867$			2.21827i			0.0753364i
$868$	7.53776	+	4.76334i	0.255848	+	0.161678i
$869$	−4.77044			−0.161826
$870$	2.12489	−	7.48960i	0.0720405	−	0.253921i
$871$		−	42.5742i		−	1.44257i
$872$	5.60357	+	6.31924i	0.189761	+	0.213996i
$873$	14.3334			0.485113
$874$	−12.0569	+	6.64343i	−0.407832	+	0.224717i
$875$	−14.3774	+	0.230182i	−0.486044	+	0.00778158i
$876$	24.8101	−	5.59574i	0.838257	−	0.189063i
$877$	−12.9060	+	12.9060i	−0.435805	+	0.435805i	−0.890597	−	0.454792i	$-0.849713\pi$
$877$	−12.9060	+	12.9060i	−0.435805	+	0.435805i	0.454792	+	0.890597i	$0.349713\pi$
$878$	−3.95088	+	13.6479i	−0.133336	+	0.460594i
$879$	20.7230			0.698969
$880$	6.17572	−	17.6605i	0.208183	−	0.595334i
$881$		−	14.1422i		−	0.476461i	−0.971209	−	0.238231i	$-0.923433\pi$
$881$		−	14.1422i		−	0.476461i	0.971209	−	0.238231i	$-0.0765674\pi$
$882$	5.61006	−	3.09117i	0.188900	−	0.104085i
$883$	2.83439			0.0953849			0.0476925	−	0.998862i	$-0.484813\pi$
$883$	2.83439			0.0953849			0.0476925	+	0.998862i	$0.484813\pi$
$884$	15.0062	−	23.7466i	0.504713	−	0.798685i
$885$	−0.0845664	−	15.8475i	−0.00284267	−	0.532707i
$886$	−51.9589	−	15.0414i	−1.74559	−	0.505326i
$887$			14.1527i			0.475201i	0.971363	+	0.237600i	$0.0763609\pi$
$887$			14.1527i			0.475201i	−0.971363	+	0.237600i	$0.923639\pi$
$888$	33.0263	−	29.2861i	1.10829	−	0.982776i
$889$	17.7061	+	17.7061i	0.593843	+	0.593843i
$890$	−23.8057	−	6.75396i	−0.797968	−	0.226393i
$891$	8.49067	+	8.49067i	0.284448	+	0.284448i
$892$	−0.313656	−	1.39067i	−0.0105020	−	0.0465632i
$893$	−25.0581	+	25.0581i	−0.838538	+	0.838538i
$894$	20.2246	+	5.85475i	0.676412	+	0.195812i
$895$	−10.1396	−	10.0320i	−0.338930	−	0.335332i
$896$	13.4926	−	5.44724i	0.450758	−	0.181980i
$897$	11.7611	+	11.7611i	0.392691	+	0.392691i
$898$	−1.91124	+	1.05310i	−0.0637790	+	0.0351426i
$899$	−4.11292	+	4.11292i	−0.137173	+	0.137173i
$900$	4.44928	−	7.21004i	0.148309	−	0.240335i
$901$	19.0894			0.635961
$902$	−18.4648	−	4.22314i	−0.614809	−	0.140615i
$903$	−5.57035	+	5.57035i	−0.185370	+	0.185370i
$904$	−8.92286	+	7.91233i	−0.296770	+	0.263160i
$905$	−0.224388	−	0.222006i	−0.00745891	−	0.00737973i
$906$	2.40670	−	8.31370i	0.0799574	−	0.276204i
$907$	40.0546	−	40.0546i	1.32999	−	1.32999i	0.424617	−	0.905373i	$-0.360409\pi$
$907$	40.0546	−	40.0546i	1.32999	−	1.32999i	0.905373	−	0.424617i	$-0.139591\pi$
$908$	−40.8140	−	25.7916i	−1.35446	−	0.855925i
$909$	2.39072	+	2.39072i	0.0792952	+	0.0792952i
$910$	12.6752	−	7.07254i	0.420179	−	0.234452i
$911$	−7.30397			−0.241991			−0.120996	−	0.992653i	$-0.538609\pi$
$911$	−7.30397			−0.241991			−0.120996	+	0.992653i	$0.538609\pi$
$912$	16.9455	+	6.02737i	0.561121	+	0.199586i
$913$	−2.88954			−0.0956299
$914$	2.99162	−	1.64840i	0.0989539	−	0.0545241i
$915$	35.1255	−	0.187439i	1.16121	−	0.00619655i
$916$	2.82403	+	12.5210i	0.0933085	+	0.413707i
$917$	19.8595			0.655818
$918$	15.1616	+	27.5162i	0.500406	+	0.908169i
$919$	−18.7652	−	18.7652i	−0.619007	−	0.619007i	0.326269	−	0.945277i	$-0.394208\pi$
$919$	−18.7652	−	18.7652i	−0.619007	−	0.619007i	−0.945277	+	0.326269i	$0.894208\pi$
$920$	13.4085	+	14.9594i	0.442065	+	0.493197i
$921$	7.56723	+	7.56723i	0.249349	+	0.249349i
$922$	−22.0419	+	12.1452i	−0.725912	+	0.399981i
$923$	−10.7804	−	10.7804i	−0.354840	−	0.354840i
$924$	1.73688	+	7.70091i	0.0571393	+	0.253341i
$925$	37.2021	−	38.0048i	1.22320	−	1.24959i
$926$	−24.3022	−	44.1053i	−0.798621	−	1.44939i
$927$	0.634812	+	0.634812i	0.0208499	+	0.0208499i
$928$	1.52980	+	9.36766i	0.0502182	+	0.307508i
$929$	19.2540	−	19.2540i	0.631703	−	0.631703i	−0.316792	−	0.948495i	$-0.602606\pi$
$929$	19.2540	−	19.2540i	0.631703	−	0.631703i	0.948495	+	0.316792i	$0.102606\pi$
$930$	14.0454	−	7.83707i	0.460566	−	0.256988i
$931$	11.5843	+	11.5843i	0.379661	+	0.379661i
$932$	10.1046	−	15.9900i	0.330986	−	0.523770i
$933$	−28.5708	−	28.5708i	−0.935367	−	0.935367i
$934$	45.6674	+	13.2201i	1.49428	+	0.432575i
$935$	13.0853	+	12.9464i	0.427934	+	0.423392i
$936$	−0.512427	+	8.53693i	−0.0167492	+	0.279038i
$937$	−33.0039			−1.07819			−0.539096	−	0.842244i	$-0.681234\pi$
$937$	−33.0039			−1.07819			−0.539096	+	0.842244i	$0.681234\pi$
$938$	10.4711	+	19.0036i	0.341892	+	0.620488i
$939$	−40.6281			−1.32585
$940$	43.8641	+	27.3926i	1.43069	+	0.893448i
$941$		−	23.2020i		−	0.756365i	−0.925731	−	0.378183i	$-0.876549\pi$
$941$		−	23.2020i		−	0.756365i	0.925731	−	0.378183i	$-0.123451\pi$
$942$	−14.4547	+	7.96462i	−0.470960	+	0.259501i
$943$	13.5399	−	15.1767i	0.440920	−	0.494222i
$944$	8.29378	+	17.4510i	0.269939	+	0.567981i
$945$	0.0866251	+	16.2333i	0.00281792	+	0.528068i
$946$	−5.95971	−	10.8161i	−0.193767	−	0.351661i
$947$	24.0280	+	24.0280i	0.780806	+	0.780806i	0.979967	−	0.199161i	$-0.0638217\pi$
$947$	24.0280	+	24.0280i	0.780806	+	0.780806i	−0.199161	+	0.979967i	$0.563822\pi$
$948$	−6.52836	+	1.47242i	−0.212031	+	0.0478221i
$949$	−21.8723	+	21.8723i	−0.710004	+	0.710004i
$950$	20.8780	+	5.80315i	0.677373	+	0.188279i
$951$	−31.3866			−1.01778
$952$	−0.857776	+	14.2904i	−0.0278007	+	0.463153i
$953$	36.3970	+	36.3970i	1.17902	+	1.17902i	0.979996	+	0.199020i	$0.0637757\pi$
$953$	36.3970	+	36.3970i	1.17902	+	1.17902i	0.199020	+	0.979996i	$0.436224\pi$
$954$	−5.09025	+	2.80475i	−0.164803	+	0.0908072i
$955$	6.54913	−	6.61941i	0.211925	−	0.214199i
$956$	−5.82370	−	25.8208i	−0.188352	−	0.835106i
$957$	−5.14965			−0.166465
$958$	−3.37800	+	11.6689i	−0.109138	+	0.377006i
$959$	−18.7184			−0.604450
$960$	3.00049	−	26.0745i	0.0968403	−	0.841552i
$961$	18.9832			0.612363
$962$	−14.9279	+	51.5668i	−0.481295	+	1.66258i
$963$	2.43154	+	2.43154i	0.0783554	+	0.0783554i
$964$	27.5410	+	17.4040i	0.887037	+	0.560545i
$965$	−34.9944	+	0.186740i	−1.12651	+	0.00601137i
$966$	−8.14233	−	2.35709i	−0.261975	−	0.0758383i
$967$		−	34.3028i		−	1.10311i	−0.834140	−	0.551553i	$-0.814036\pi$
$967$		−	34.3028i		−	1.10311i	0.834140	−	0.551553i	$-0.185964\pi$
$968$	18.7036	+	1.12268i	0.601155	+	0.0360842i
$969$	−12.5126	+	12.5126i	−0.401962	+	0.401962i
$970$	46.7184	−	26.0680i	1.50004	−	0.836994i
$971$	−19.8206	−	19.8206i	−0.636073	−	0.636073i	0.313512	−	0.949584i	$-0.398495\pi$
$971$	−19.8206	−	19.8206i	−0.636073	−	0.636073i	−0.949584	+	0.313512i	$0.898495\pi$
$972$	−14.3909	−	9.09402i	−0.461587	−	0.291691i
$973$	7.01827			0.224995
$974$	−4.88551	+	16.8765i	−0.156542	+	0.540756i
$975$	−0.279420	−	26.1804i	−0.00894860	−	0.838445i
$976$	−38.6797	+	18.3829i	−1.23811	+	0.588424i
$977$		−	17.1665i		−	0.549204i	−0.961558	−	0.274602i	$-0.911454\pi$
$977$		−	17.1665i		−	0.549204i	0.961558	−	0.274602i	$-0.0885461\pi$
$978$	−46.2300	−	13.3829i	−1.47827	−	0.427939i
$979$			16.3682i			0.523129i
$980$	12.6636	−	20.2783i	0.404522	−	0.647766i
$981$	1.78891	−	1.78891i	0.0571155	−	0.0571155i
$982$	0.340181	+	0.617383i	0.0108556	+	0.0197015i
$983$	−1.72618	+	1.72618i	−0.0550566	+	0.0550566i	−0.734099	−	0.679042i	$-0.762395\pi$
$983$	−1.72618	+	1.72618i	−0.0550566	+	0.0550566i	0.679042	+	0.734099i	$0.262395\pi$
$984$	−26.5725	−	0.0801304i	−0.847102	−	0.00255446i
$985$	−15.0477	−	14.8879i	−0.479459	−	0.474369i
$986$	−8.97038	−	2.59680i	−0.285675	−	0.0826990i
$987$	−21.8211			−0.694574
$988$	−21.3380	+	4.81263i	−0.678852	+	0.153110i
$989$	13.2602			0.421650
$990$	−5.39140	−	1.52960i	−0.171350	−	0.0486140i
$991$	36.6871	+	36.6871i	1.16540	+	1.16540i	0.983275	+	0.182129i	$0.0582989\pi$
$991$	36.6871	+	36.6871i	1.16540	+	1.16540i	0.182129	+	0.983275i	$0.441701\pi$
$992$	−11.4500	+	15.9196i	−0.363537	+	0.505448i
$993$	−7.57846	+	7.57846i	−0.240495	+	0.240495i
$994$	7.46336	+	2.16054i	0.236723	+	0.0685282i
$995$	−30.3404	−	30.0183i	−0.961854	−	0.951643i
$996$	−3.95435	+	0.891873i	−0.125298	+	0.0282601i
$997$		−	17.0088i		−	0.538676i	−0.963046	−	0.269338i	$-0.913195\pi$
$997$		−	17.0088i		−	0.538676i	0.963046	−	0.269338i	$-0.0868048\pi$
$998$	−0.195984	+	0.677006i	−0.00620377	+	0.0214302i
$999$	−42.4550	−	42.4550i	−1.34322	−	1.34322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.j.c.483.18	✓	240
4.3	odd	2	inner	820.2.j.c.483.80	yes	240
5.2	odd	4		820.2.s.c.647.41	yes	240
20.7	even	4		820.2.s.c.647.103	yes	240
41.9	even	4		820.2.s.c.583.103	yes	240
164.91	odd	4		820.2.s.c.583.41	yes	240
205.132	odd	4	inner	820.2.j.c.747.80	yes	240
820.747	even	4	inner	820.2.j.c.747.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.18	✓	240	1.1	even	1	trivial
820.2.j.c.483.80	yes	240	4.3	odd	2	inner
820.2.j.c.747.18	yes	240	820.747	even	4	inner
820.2.j.c.747.80	yes	240	205.132	odd	4	inner
820.2.s.c.583.41	yes	240	164.91	odd	4
820.2.s.c.583.103	yes	240	41.9	even	4
820.2.s.c.647.41	yes	240	5.2	odd	4
820.2.s.c.647.103	yes	240	20.7	even	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+(-1.23863 + 0.682492i) q^{2} -1.46723i q^{3} +(1.06841 - 1.69071i) q^{4} +(-2.23604 + 0.0119321i) q^{5} +(1.00137 + 1.81736i) q^{6} +1.28612 q^{7} +(-0.169471 + 2.82335i) q^{8} +0.847235 q^{9} +(2.76148 - 1.54086i) q^{10} +(-1.47909 - 1.47909i) q^{11} +(-2.48066 - 1.56760i) q^{12} +3.56889 q^{13} +(-1.59302 + 0.877763i) q^{14} +(0.0175071 + 3.28078i) q^{15} +(-1.71700 - 3.61274i) q^{16} +3.93550 q^{17} +(-1.04941 + 0.578231i) q^{18} +(-2.16695 - 2.16695i) q^{19} +(-2.36883 + 3.79324i) q^{20} -1.88703i q^{21} +(2.84150 + 0.822577i) q^{22} +(-2.24603 + 2.24603i) q^{23} +(4.14250 + 0.248653i) q^{24} +(4.99972 - 0.0533612i) q^{25} +(-4.42054 + 2.43574i) q^{26} -5.64478i q^{27} +(1.37410 - 2.17445i) q^{28} +(1.18647 + 1.18647i) q^{29} +(-2.26079 - 4.05173i) q^{30} +3.46652i q^{31} +(4.59239 + 3.30302i) q^{32} +(-2.17016 + 2.17016i) q^{33} +(-4.87462 + 2.68594i) q^{34} +(-2.87580 + 0.0153461i) q^{35} +(0.905195 - 1.43243i) q^{36} +(7.52111 - 7.52111i) q^{37} +(4.16298 + 1.20513i) q^{38} -5.23639i q^{39} +(0.345254 - 6.31512i) q^{40} +(-6.39275 + 0.364380i) q^{41} +(1.28788 + 2.33733i) q^{42} +(-2.95192 - 2.95192i) q^{43} +(-4.08098 + 0.920434i) q^{44} +(-1.89445 + 0.0101093i) q^{45} +(1.24910 - 4.31490i) q^{46} -11.5638i q^{47} +(-5.30073 + 2.51923i) q^{48} -5.34591 q^{49} +(-6.15638 + 3.47836i) q^{50} -5.77428i q^{51} +(3.81304 - 6.03396i) q^{52} +4.85058 q^{53} +(3.85251 + 6.99180i) q^{54} +(3.32494 + 3.28964i) q^{55} +(-0.217959 + 3.63115i) q^{56} +(-3.17942 + 3.17942i) q^{57} +(-2.27935 - 0.659841i) q^{58} -4.83040 q^{59} +(5.56555 + 3.47562i) q^{60} -10.7064i q^{61} +(-2.36587 - 4.29374i) q^{62} +1.08964 q^{63} +(-7.94256 - 0.956949i) q^{64} +(-7.98017 + 0.0425844i) q^{65} +(1.20691 - 4.16914i) q^{66} -11.9293i q^{67} +(4.20472 - 6.65378i) q^{68} +(3.29544 + 3.29544i) q^{69} +(3.55158 - 1.98172i) q^{70} +(-3.02064 - 3.02064i) q^{71} +(-0.143582 + 2.39204i) q^{72} +(-6.12859 + 6.12859i) q^{73} +(-4.18278 + 14.4490i) q^{74} +(-0.0782932 - 7.33573i) q^{75} +(-5.97888 + 1.34849i) q^{76} +(-1.90228 - 1.90228i) q^{77} +(3.57379 + 6.48595i) q^{78} +(1.61263 - 1.61263i) q^{79} +(3.88238 + 8.05774i) q^{80} -5.74049 q^{81} +(7.66957 - 4.81433i) q^{82} +(0.976800 - 0.976800i) q^{83} +(-3.19042 - 2.01612i) q^{84} +(-8.79991 + 0.0469587i) q^{85} +(5.67099 + 1.64168i) q^{86} +(1.74082 - 1.74082i) q^{87} +(4.42663 - 3.92531i) q^{88} +(-5.53320 - 5.53320i) q^{89} +(2.33962 - 1.30547i) q^{90} +4.59001 q^{91} +(1.39770 + 6.19707i) q^{92} +5.08618 q^{93} +(7.89217 + 14.3232i) q^{94} +(4.87124 + 4.81953i) q^{95} +(4.84629 - 6.73810i) q^{96} +16.9179 q^{97} +(6.62160 - 3.64854i) q^{98} +(-1.25313 - 1.25313i) 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

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