LMFDB - Embedded newform 80.2.q.c.29.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,2,Mod(29,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("80.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0] 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.6
Root			$1.32661 + 0.490008i$ of defining polynomial
Character	$\chi$	$=$	80.29
Dual form			80.2.q.c.69.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.490008 + 1.32661i) q^{2} +(1.99154 - 1.99154i) q^{3} +(-1.51978 + 1.30010i) q^{4} +(-2.16225 + 0.569800i) q^{5} +(3.61786 + 1.66612i) q^{6} +1.09033 q^{7} +(-2.46943 - 1.37910i) q^{8} -4.93244i q^{9} +(-1.81542 - 2.58926i) q^{10} +(-2.33225 + 2.33225i) q^{11} +(-0.437515 + 5.61590i) q^{12} +(-1.80775 + 1.80775i) q^{13} +(0.534268 + 1.44644i) q^{14} +(-3.17142 + 5.44098i) q^{15} +(0.619491 - 3.95174i) q^{16} -4.93886i q^{17} +(6.54342 - 2.41694i) q^{18} +(2.03957 + 2.03957i) q^{19} +(2.54536 - 3.67711i) q^{20} +(2.17142 - 2.17142i) q^{21} +(-4.23680 - 1.95116i) q^{22} -1.45791 q^{23} +(-7.66449 + 2.17142i) q^{24} +(4.35066 - 2.46410i) q^{25} +(-3.28398 - 1.51236i) q^{26} +(-3.84853 - 3.84853i) q^{27} +(-1.65706 + 1.41753i) q^{28} +(-0.707323 - 0.707323i) q^{29} +(-8.77208 - 1.54112i) q^{30} +10.1286 q^{31} +(5.54597 - 1.11456i) q^{32} +9.28951i q^{33} +(6.55193 - 2.42008i) q^{34} +(-2.35756 + 0.621268i) q^{35} +(6.41266 + 7.49625i) q^{36} +(-4.35066 - 4.35066i) q^{37} +(-1.70631 + 3.70512i) q^{38} +7.20039i q^{39} +(6.12534 + 1.57488i) q^{40} +10.2753i q^{41} +(3.94465 + 1.81662i) q^{42} +(2.22457 + 2.22457i) q^{43} +(0.512364 - 6.57666i) q^{44} +(2.81051 + 10.6652i) q^{45} +(-0.714386 - 1.93407i) q^{46} +2.09458i q^{47} +(-6.63629 - 9.10377i) q^{48} -5.81119 q^{49} +(5.40076 + 4.56419i) q^{50} +(-9.83592 - 9.83592i) q^{51} +(0.397138 - 5.09763i) q^{52} +(-0.215297 - 0.215297i) q^{53} +(3.21969 - 6.99131i) q^{54} +(3.71399 - 6.37182i) q^{55} +(-2.69248 - 1.50367i) q^{56} +8.12376 q^{57} +(0.591747 - 1.28493i) q^{58} +(-1.16082 + 1.16082i) q^{59} +(-2.25393 - 12.3923i) q^{60} +(-3.46410 - 3.46410i) q^{61} +(4.96309 + 13.4367i) q^{62} -5.37797i q^{63} +(4.19615 + 6.81119i) q^{64} +(2.87875 - 4.93886i) q^{65} +(-12.3236 + 4.55193i) q^{66} +(5.04189 - 5.04189i) q^{67} +(6.42100 + 7.50600i) q^{68} +(-2.90348 + 2.90348i) q^{69} +(-1.97940 - 2.82313i) q^{70} -6.40078i q^{71} +(-6.80234 + 12.1803i) q^{72} -5.24343 q^{73} +(3.63977 - 7.90348i) q^{74} +(3.75714 - 13.5718i) q^{75} +(-5.75135 - 0.448067i) q^{76} +(-2.54291 + 2.54291i) q^{77} +(-9.55211 + 3.52825i) q^{78} +2.61504 q^{79} +(0.912206 + 8.89763i) q^{80} -0.531659 q^{81} +(-13.6313 + 5.03497i) q^{82} +(-5.67856 + 5.67856i) q^{83} +(-0.477033 + 6.12316i) q^{84} +(2.81416 + 10.6790i) q^{85} +(-1.86108 + 4.04120i) q^{86} -2.81732 q^{87} +(8.97572 - 2.54291i) q^{88} -6.87875i q^{89} +(-12.7714 + 8.95446i) q^{90} +(-1.97103 + 1.97103i) q^{91} +(2.21570 - 1.89542i) q^{92} +(20.1715 - 20.1715i) q^{93} +(-2.77868 + 1.02636i) q^{94} +(-5.57221 - 3.24791i) q^{95} +(8.82531 - 13.2647i) q^{96} +3.77310i q^{97} +(-2.84753 - 7.70918i) q^{98} +(11.5037 + 11.5037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36}+ \cdots + 88 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.490008	+	1.32661i	0.346488	+	0.938054i
$2$	0.490008	+	1.32661i	0.346488	+	0.938054i
$3$	1.99154	−	1.99154i	1.14981	−	1.14981i	0.163226	−	0.986589i	$-0.447810\pi$
$3$	1.99154	−	1.99154i	1.14981	−	1.14981i	0.986589	−	0.163226i	$-0.0521899\pi$
$4$	−1.51978	+	1.30010i	−0.759892	+	0.650049i
$5$	−2.16225	+	0.569800i	−0.966988	+	0.254822i
$5$	−2.16225	+	0.569800i	−0.966988	+	0.254822i
$6$	3.61786	+	1.66612i	1.47699	+	0.680192i
$7$	1.09033			0.412104			0.206052	−	0.978541i	$-0.433938\pi$
$7$	1.09033			0.412104			0.206052	+	0.978541i	$0.433938\pi$
$8$	−2.46943	−	1.37910i	−0.873075	−	0.487586i
$9$		−	4.93244i		−	1.64415i
$10$	−1.81542	−	2.58926i	−0.574087	−	0.818794i
$11$	−2.33225	+	2.33225i	−0.703199	+	0.703199i	−0.965096	−	0.261897i	$-0.915652\pi$
$11$	−2.33225	+	2.33225i	−0.703199	+	0.703199i	0.261897	+	0.965096i	$0.415652\pi$
$12$	−0.437515	+	5.61590i	−0.126300	+	1.62117i
$13$	−1.80775	+	1.80775i	−0.501379	+	0.501379i	−0.911866	−	0.410487i	$-0.865359\pi$
$13$	−1.80775	+	1.80775i	−0.501379	+	0.501379i	0.410487	+	0.911866i	$0.365359\pi$
$14$	0.534268	+	1.44644i	0.142789	+	0.386576i
$15$	−3.17142	+	5.44098i	−0.818858	+	1.40486i
$16$	0.619491	−	3.95174i	0.154873	−	0.987934i
$17$		−	4.93886i		−	1.19785i	−0.800806	−	0.598924i	$-0.795595\pi$
$17$		−	4.93886i		−	1.19785i	0.800806	−	0.598924i	$-0.204405\pi$
$18$	6.54342	−	2.41694i	1.54230	−	0.569677i
$19$	2.03957	+	2.03957i	0.467909	+	0.467909i	0.901237	−	0.433327i	$-0.142661\pi$
$19$	2.03957	+	2.03957i	0.467909	+	0.467909i	−0.433327	+	0.901237i	$0.642661\pi$
$20$	2.54536	−	3.67711i	0.569160	−	0.822227i
$21$	2.17142	−	2.17142i	0.473844	−	0.473844i
$22$	−4.23680	−	1.95116i	−0.903289	−	0.415989i
$23$	−1.45791			−0.303995			−0.151997	−	0.988381i	$-0.548570\pi$
$23$	−1.45791			−0.303995			−0.151997	+	0.988381i	$0.548570\pi$
$24$	−7.66449	+	2.17142i	−1.56451	+	0.443240i
$25$	4.35066	−	2.46410i	0.870131	−	0.492820i
$26$	−3.28398	−	1.51236i	−0.644042	−	0.296599i
$27$	−3.84853	−	3.84853i	−0.740650	−	0.740650i
$28$	−1.65706	+	1.41753i	−0.313155	+	0.267888i
$29$	−0.707323	−	0.707323i	−0.131347	−	0.131347i	0.638377	−	0.769724i	$-0.279606\pi$
$29$	−0.707323	−	0.707323i	−0.131347	−	0.131347i	−0.769724	+	0.638377i	$0.779606\pi$
$30$	−8.77208	−	1.54112i	−1.60156	−	0.281368i
$31$	10.1286			1.81915			0.909575	−	0.415541i	$-0.136408\pi$
$31$	10.1286			1.81915			0.909575	+	0.415541i	$0.136408\pi$
$32$	5.54597	−	1.11456i	0.980398	−	0.197028i
$33$			9.28951i			1.61710i
$34$	6.55193	−	2.42008i	1.12365	−	0.415040i
$35$	−2.35756	+	0.621268i	−0.398500	+	0.105013i
$36$	6.41266	+	7.49625i	1.06878	+	1.24938i
$37$	−4.35066	−	4.35066i	−0.715243	−	0.715243i	0.252384	−	0.967627i	$-0.418785\pi$
$37$	−4.35066	−	4.35066i	−0.715243	−	0.715243i	−0.967627	+	0.252384i	$0.918785\pi$
$38$	−1.70631	+	3.70512i	−0.276800	+	0.601049i
$39$			7.20039i			1.15299i
$40$	6.12534	+	1.57488i	0.968501	+	0.249011i
$41$			10.2753i			1.60473i	0.596833	+	0.802365i	$0.296425\pi$
$41$			10.2753i			1.60473i	−0.596833	+	0.802365i	$0.703575\pi$
$42$	3.94465	+	1.81662i	0.608672	+	0.280310i
$43$	2.22457	+	2.22457i	0.339244	+	0.339244i	0.856083	−	0.516839i	$-0.172891\pi$
$43$	2.22457	+	2.22457i	0.339244	+	0.339244i	−0.516839	+	0.856083i	$0.672891\pi$
$44$	0.512364	−	6.57666i	0.0772418	−	0.991469i
$45$	2.81051	+	10.6652i	0.418966	+	1.58987i
$46$	−0.714386	−	1.93407i	−0.105330	−	0.285163i
$47$			2.09458i			0.305525i	0.988263	+	0.152763i	$0.0488170\pi$
$47$			2.09458i			0.305525i	−0.988263	+	0.152763i	$0.951183\pi$
$48$	−6.63629	−	9.10377i	−0.957866	−	1.31402i
$49$	−5.81119			−0.830170
$50$	5.40076	+	4.56419i	0.763782	+	0.645474i
$51$	−9.83592	−	9.83592i	−1.37730	−	1.37730i
$52$	0.397138	−	5.09763i	0.0550732	−	0.706915i
$53$	−0.215297	−	0.215297i	−0.0295733	−	0.0295733i	0.692166	−	0.721739i	$-0.256657\pi$
$53$	−0.215297	−	0.215297i	−0.0295733	−	0.0295733i	−0.721739	+	0.692166i	$0.756657\pi$
$54$	3.21969	−	6.99131i	0.438144	−	0.951396i
$55$	3.71399	−	6.37182i	0.500794	−	0.859175i
$56$	−2.69248	−	1.50367i	−0.359798	−	0.200936i
$57$	8.12376			1.07602
$58$	0.591747	−	1.28493i	0.0777002	−	0.168720i
$59$	−1.16082	+	1.16082i	−0.151126	+	0.151126i	−0.778621	−	0.627495i	$-0.784080\pi$
$59$	−1.16082	+	1.16082i	−0.151126	+	0.151126i	0.627495	+	0.778621i	$0.284080\pi$
$60$	−2.25393	−	12.3923i	−0.290981	−	1.59984i
$61$	−3.46410	−	3.46410i	−0.443533	−	0.443533i	0.449665	−	0.893197i	$-0.351543\pi$
$61$	−3.46410	−	3.46410i	−0.443533	−	0.443533i	−0.893197	+	0.449665i	$0.851543\pi$
$62$	4.96309	+	13.4367i	0.630313	+	1.70646i
$63$		−	5.37797i		−	0.677560i
$64$	4.19615	+	6.81119i	0.524519	+	0.851399i
$65$	2.87875	−	4.93886i	0.357065	−	0.612590i
$66$	−12.3236	+	4.55193i	−1.51692	+	0.560304i
$67$	5.04189	−	5.04189i	0.615965	−	0.615965i	−0.328529	−	0.944494i	$-0.606553\pi$
$67$	5.04189	−	5.04189i	0.615965	−	0.615965i	0.944494	+	0.328529i	$0.106553\pi$
$68$	6.42100	+	7.50600i	0.778660	+	0.910236i
$69$	−2.90348	+	2.90348i	−0.349537	+	0.349537i
$70$	−1.97940	−	2.82313i	−0.236584	−	0.337429i
$71$		−	6.40078i		−	0.759633i	−0.925062	−	0.379817i	$-0.875987\pi$
$71$		−	6.40078i		−	0.759633i	0.925062	−	0.379817i	$-0.124013\pi$
$72$	−6.80234	+	12.1803i	−0.801664	+	1.43546i
$73$	−5.24343			−0.613696			−0.306848	−	0.951758i	$-0.599274\pi$
$73$	−5.24343			−0.613696			−0.306848	+	0.951758i	$0.599274\pi$
$74$	3.63977	−	7.90348i	0.423114	−	0.918760i
$75$	3.75714	−	13.5718i	0.433837	−	1.56714i
$76$	−5.75135	−	0.448067i	−0.659725	−	0.0513968i
$77$	−2.54291	+	2.54291i	−0.289791	+	0.289791i
$78$	−9.55211	+	3.52825i	−1.08156	+	0.399495i
$79$	2.61504			0.294215			0.147107	−	0.989121i	$-0.453004\pi$
$79$	2.61504			0.294215			0.147107	+	0.989121i	$0.453004\pi$
$80$	0.912206	+	8.89763i	0.101988	+	0.994786i
$81$	−0.531659			−0.0590733
$82$	−13.6313	+	5.03497i	−1.50532	+	0.556020i
$83$	−5.67856	+	5.67856i	−0.623303	+	0.623303i	−0.946375	−	0.323071i	$-0.895285\pi$
$83$	−5.67856	+	5.67856i	−0.623303	+	0.623303i	0.323071	+	0.946375i	$0.395285\pi$
$84$	−0.477033	+	6.12316i	−0.0520486	+	0.668092i
$85$	2.81416	+	10.6790i	0.305239	+	1.15831i
$86$	−1.86108	+	4.04120i	−0.200686	+	0.435774i
$87$	−2.81732			−0.302048
$88$	8.97572	−	2.54291i	0.956815	−	0.271075i
$89$		−	6.87875i		−	0.729146i	−0.931175	−	0.364573i	$-0.881215\pi$
$89$		−	6.87875i		−	0.729146i	0.931175	−	0.364573i	$-0.118785\pi$
$90$	−12.7714	+	8.95446i	−1.34622	+	0.943883i
$91$	−1.97103	+	1.97103i	−0.206620	+	0.206620i
$92$	2.21570	−	1.89542i	0.231003	−	0.197611i
$93$	20.1715	−	20.1715i	2.09168	−	2.09168i
$94$	−2.77868	+	1.02636i	−0.286599	+	0.105861i
$95$	−5.57221	−	3.24791i	−0.571696	−	0.333229i
$96$	8.82531	−	13.2647i	0.900730	−	1.35382i
$97$			3.77310i			0.383100i	0.981483	+	0.191550i	$0.0613515\pi$
$97$			3.77310i			0.383100i	−0.981483	+	0.191550i	$0.938649\pi$
$98$	−2.84753	−	7.70918i	−0.287644	−	0.778745i
$99$	11.5037	+	11.5037i	1.15616	+	1.15616i
$100$	−3.40849	+	9.40118i	−0.340849	+	0.940118i
$101$	−0.707323	+	0.707323i	−0.0703813	+	0.0703813i	−0.741421	−	0.671040i	$-0.765848\pi$
$101$	−0.707323	+	0.707323i	−0.0703813	+	0.0703813i	0.671040	+	0.741421i	$0.265848\pi$
$102$	8.22874	−	17.8681i	0.814767	−	1.76921i
$103$	−12.9320			−1.27422			−0.637112	−	0.770771i	$-0.719871\pi$
$103$	−12.9320			−1.27422			−0.637112	+	0.770771i	$0.719871\pi$
$104$	6.95717	−	1.97103i	0.682207	−	0.193276i
$105$	−3.45789	+	5.93244i	−0.337455	+	0.578947i
$106$	0.180117	−	0.391111i	0.0174946	−	0.0379881i
$107$	−1.56094	−	1.56094i	−0.150902	−	0.150902i	0.627619	−	0.778521i	$-0.284030\pi$
$107$	−1.56094	−	1.56094i	−0.150902	−	0.150902i	−0.778521	+	0.627619i	$0.784030\pi$
$108$	10.8524	+	0.845472i	1.04427	+	0.0813556i
$109$	−7.13283	−	7.13283i	−0.683202	−	0.683202i	0.277519	−	0.960720i	$-0.410488\pi$
$109$	−7.13283	−	7.13283i	−0.683202	−	0.683202i	−0.960720	+	0.277519i	$0.910488\pi$
$110$	10.2728	+	1.80477i	0.979472	+	0.172078i
$111$	−17.3290			−1.64479
$112$	0.675447	−	4.30868i	0.0638238	−	0.407132i
$113$		−	9.23949i		−	0.869178i	−0.900629	−	0.434589i	$-0.856894\pi$
$113$		−	9.23949i		−	0.869178i	0.900629	−	0.434589i	$-0.143106\pi$
$114$	3.98070	+	10.7771i	0.372827	+	1.00936i
$115$	3.15236	−	0.830715i	0.293959	−	0.0774646i
$116$	1.99457	+	0.155390i	0.185191	+	0.0144276i
$117$	8.91661	+	8.91661i	0.824341	+	0.824341i
$118$	−2.10877	−	0.971145i	−0.194128	−	0.0894012i
$119$		−	5.38496i		−	0.493639i
$120$	15.3353	−	9.06239i	1.39991	−	0.827280i
$121$			0.121253i			0.0110230i
$122$	2.89807	−	6.29295i	0.262379	−	0.569737i
$123$	20.4636	+	20.4636i	1.84514	+	1.84514i
$124$	−15.3933	+	13.1682i	−1.38236	+	1.18254i
$125$	−8.00316	+	7.80701i	−0.715825	+	0.698280i
$126$	7.13446	−	2.63525i	0.635589	−	0.234766i
$127$		−	1.99608i		−	0.177124i	−0.996071	−	0.0885618i	$-0.971773\pi$
$127$		−	1.99608i		−	0.177124i	0.996071	−	0.0885618i	$-0.0282271\pi$
$128$	−6.97964	+	8.90419i	−0.616919	+	0.787027i
$129$	8.86065			0.780136
$130$	7.96254	+	1.39890i	0.698361	+	0.122691i
$131$	11.2894	+	11.2894i	0.986361	+	0.986361i	0.999908	−	0.0135473i	$-0.00431238\pi$
$131$	11.2894	+	11.2894i	0.986361	+	0.986361i	−0.0135473	+	0.999908i	$0.504312\pi$
$132$	−12.0773	−	14.1181i	−1.05119	−	1.22882i
$133$	2.22380	+	2.22380i	0.192827	+	0.192827i
$134$	9.15919	+	4.21806i	0.791234	+	0.364385i
$135$	10.5144	+	6.12859i	0.904934	+	0.527465i
$136$	−6.81119	+	12.1962i	−0.584055	+	1.04581i
$137$	−15.9429			−1.36210			−0.681049	−	0.732238i	$-0.738476\pi$
$137$	−15.9429			−1.36210			−0.681049	+	0.732238i	$0.738476\pi$
$138$	−5.27450	−	2.42905i	−0.448996	−	0.206775i
$139$	3.79635	−	3.79635i	0.322002	−	0.322002i	−0.527533	−	0.849535i	$-0.676883\pi$
$139$	3.79635	−	3.79635i	0.322002	−	0.322002i	0.849535	+	0.527533i	$0.176883\pi$
$140$	2.77527	−	4.00925i	0.234553	−	0.338843i
$141$	4.17142	+	4.17142i	0.351297	+	0.351297i
$142$	8.49134	−	3.13643i	0.712577	−	0.263204i
$143$		−	8.43222i		−	0.705138i
$144$	−19.4917	−	3.05560i	−1.62431	−	0.254634i
$145$	1.93244	+	1.12638i	0.160481	+	0.0935405i
$146$	−2.56932	−	6.95598i	−0.212638	−	0.575681i
$147$	−11.5732	+	11.5732i	−0.954542	+	0.954542i
$148$	12.2683	+	0.955782i	1.00845	+	0.0785648i
$149$	13.3290	−	13.3290i	1.09195	−	1.09195i	0.0966330	−	0.995320i	$-0.469193\pi$
$149$	13.3290	−	13.3290i	1.09195	−	1.09195i	0.995320	−	0.0966330i	$-0.0308073\pi$
$150$	19.8456	−	1.66605i	1.62038	−	0.136032i
$151$			5.60117i			0.455817i	0.973683	+	0.227909i	$0.0731887\pi$
$151$			5.60117i			0.455817i	−0.973683	+	0.227909i	$0.926811\pi$
$152$	−2.22380	−	7.84935i	−0.180374	−	0.636666i
$153$	−24.3606			−1.96944
$154$	−4.61949	−	2.12740i	−0.372249	−	0.171431i
$155$	−21.9006	+	5.77128i	−1.75910	+	0.463560i
$156$	−9.36121	−	10.9430i	−0.749497	−	0.876145i
$157$	−7.11951	+	7.11951i	−0.568199	+	0.568199i	−0.931624	−	0.363425i	$-0.881607\pi$
$157$	−7.11951	+	7.11951i	−0.568199	+	0.568199i	0.363425	+	0.931624i	$0.381607\pi$
$158$	1.28139	+	3.46913i	0.101942	+	0.275989i
$159$	−0.857542			−0.0680075
$160$	−11.3567	+	5.57005i	−0.897826	+	0.440351i
$161$	−1.58959			−0.125277
$162$	−0.260517	−	0.705304i	−0.0204682	−	0.0554139i
$163$	−0.546047	+	0.546047i	−0.0427697	+	0.0427697i	−0.728168	−	0.685398i	$-0.759628\pi$
$163$	−0.546047	+	0.546047i	−0.0427697	+	0.0427697i	0.685398	+	0.728168i	$0.259628\pi$
$164$	−13.3589	−	15.6162i	−1.04315	−	1.21942i
$165$	−5.29317	−	20.0863i	−0.412072	−	1.56371i
$166$	−10.3158	−	4.75069i	−0.800659	−	0.368725i
$167$	21.3103			1.64904			0.824519	−	0.565834i	$-0.191446\pi$
$167$	21.3103			1.64904			0.824519	+	0.565834i	$0.191446\pi$
$168$	−8.35679	+	2.36756i	−0.644741	+	0.182661i
$169$			6.46410i			0.497239i
$170$	−12.7880	+	8.96611i	−0.980792	+	0.687669i
$171$	10.0601	−	10.0601i	0.769312	−	0.769312i
$172$	−6.27304	−	0.488710i	−0.478315	−	0.0372638i
$173$	2.64673	−	2.64673i	0.201227	−	0.201227i	−0.599299	−	0.800525i	$-0.704554\pi$
$173$	2.64673	−	2.64673i	0.201227	−	0.201227i	0.800525	+	0.599299i	$0.204554\pi$
$174$	−1.38051	−	3.73748i	−0.104656	−	0.283338i
$175$	4.74363	−	2.68667i	0.358585	−	0.203093i
$176$	7.77162	+	10.6612i	0.585808	+	0.803621i
$177$			4.62364i			0.347534i
$178$	9.12541	−	3.37064i	0.683978	−	0.252640i
$179$	−13.4747	−	13.4747i	−1.00715	−	1.00715i	−0.999974	−	0.00717240i	$-0.997717\pi$
$179$	−13.4747	−	13.4747i	−1.00715	−	1.00715i	−0.00717240	−	0.999974i	$-0.502283\pi$
$180$	−18.1371	−	12.5548i	−1.35186	−	0.935782i
$181$	−1.63553	+	1.63553i	−0.121568	+	0.121568i	−0.765273	−	0.643706i	$-0.777396\pi$
$181$	−1.63553	+	1.63553i	−0.121568	+	0.121568i	0.643706	+	0.765273i	$0.277396\pi$
$182$	−3.58061	−	1.64897i	−0.265413	−	0.122230i
$183$	−13.7978			−1.01996
$184$	3.60020	+	2.01060i	0.265410	+	0.148224i
$185$	11.8862	+	6.92820i	0.873892	+	0.509372i
$186$	36.6438	+	16.8755i	2.68686	+	1.23737i
$187$	11.5186	+	11.5186i	0.842326	+	0.842326i
$188$	−2.72315	−	3.18330i	−0.198606	−	0.232166i
$189$	−4.19615	−	4.19615i	−0.305225	−	0.305225i
$190$	1.57829	−	8.98365i	0.114501	−	0.651742i
$191$	5.07180			0.366982			0.183491	−	0.983021i	$-0.441260\pi$
$191$	5.07180			0.366982			0.183491	+	0.983021i	$0.441260\pi$
$192$	21.9215	+	5.20794i	1.58205	+	0.375851i
$193$			22.0369i			1.58625i	0.609058	+	0.793126i	$0.291548\pi$
$193$			22.0369i			1.58625i	−0.609058	+	0.793126i	$0.708452\pi$
$194$	−5.00543	+	1.84885i	−0.359369	+	0.132740i
$195$	−4.10278	−	15.5691i	−0.293806	−	1.11492i
$196$	8.83176	−	7.55512i	0.630840	−	0.539651i
$197$	8.06997	+	8.06997i	0.574961	+	0.574961i	0.933511	−	0.358549i	$-0.116729\pi$
$197$	8.06997	+	8.06997i	0.574961	+	0.574961i	−0.358549	+	0.933511i	$0.616729\pi$
$198$	−9.62399	+	20.8978i	−0.683947	+	1.48514i
$199$			21.8564i			1.54936i	0.632354	+	0.774680i	$0.282089\pi$
$199$			21.8564i			1.54936i	−0.632354	+	0.774680i	$0.717911\pi$
$200$	−14.1419	+	0.0849223i	−0.999982	+	0.00600491i
$201$		−	20.0822i		−	1.41649i
$202$	−1.28493	−	0.591747i	−0.0904077	−	0.0416352i
$203$	−0.771212	−	0.771212i	−0.0541285	−	0.0541285i
$204$	27.7361	+	2.16082i	1.94192	+	0.151288i
$205$	−5.85486	−	22.2178i	−0.408921	−	1.55176i
$206$	−6.33676	−	17.1557i	−0.441503	−	1.19529i
$207$			7.19104i			0.499812i
$208$	6.02386	+	8.26363i	0.417679	+	0.572979i
$209$	−9.51356			−0.658067
$210$	−9.56442	−	1.68032i	−0.660008	−	0.115953i
$211$	5.18203	+	5.18203i	0.356745	+	0.356745i	0.862612	−	0.505866i	$-0.168827\pi$
$211$	5.18203	+	5.18203i	0.356745	+	0.356745i	−0.505866	+	0.862612i	$0.668827\pi$
$212$	0.607111	+	0.0472978i	0.0416966	+	0.00324843i
$213$	−12.7474	−	12.7474i	−0.873437	−	0.873437i
$214$	1.30589	−	2.83564i	0.0892687	−	0.193840i
$215$	−6.07765	−	3.54252i	−0.414492	−	0.241598i
$216$	4.19615	+	14.8112i	0.285512	+	1.00777i
$217$	11.0435			0.749679
$218$	5.96734	−	12.9576i	0.404159	−	0.877601i
$219$	−10.4425	+	10.4425i	−0.705637	+	0.705637i
$220$	2.63952	+	14.5123i	0.177957	+	0.978421i
$221$	8.92820	+	8.92820i	0.600576	+	0.600576i
$222$	−8.49134	−	22.9888i	−0.569901	−	1.54291i
$223$		−	18.7097i		−	1.25289i	−0.779465	−	0.626446i	$-0.784509\pi$
$223$		−	18.7097i		−	1.25289i	0.779465	−	0.626446i	$-0.215491\pi$
$224$	6.04691	−	1.21523i	0.404026	−	0.0811962i
$225$	−12.1540	−	21.4594i	−0.810269	−	1.43062i
$226$	12.2572	−	4.52742i	0.815336	−	0.301160i
$227$	−8.68435	+	8.68435i	−0.576401	+	0.576401i	−0.933910	−	0.357509i	$-0.883626\pi$
$227$	−8.68435	+	8.68435i	−0.576401	+	0.576401i	0.357509	+	0.933910i	$0.383626\pi$
$228$	−12.3464	+	10.5617i	−0.817658	+	0.699464i
$229$	−4.22936	+	4.22936i	−0.279484	+	0.279484i	−0.832903	−	0.553419i	$-0.813323\pi$
$229$	−4.22936	+	4.22936i	−0.279484	+	0.279484i	0.553419	+	0.832903i	$0.313323\pi$
$230$	2.64672	+	3.77489i	0.174519	+	0.248909i
$231$			10.1286i			0.666413i
$232$	0.771212	+	2.72215i	0.0506326	+	0.178718i
$233$	19.7054			1.29094			0.645472	−	0.763784i	$-0.276661\pi$
$233$	19.7054			1.29094			0.645472	+	0.763784i	$0.276661\pi$
$234$	−7.45965	+	16.1981i	−0.487652	+	1.05890i
$235$	−1.19349	−	4.52900i	−0.0778547	−	0.295439i
$236$	0.255017	−	3.27338i	0.0166002	−	0.213079i
$237$	5.20794	−	5.20794i	0.338292	−	0.338292i
$238$	7.14374	−	2.63867i	0.463060	−	0.171040i
$239$	−0.957886			−0.0619605			−0.0309803	−	0.999520i	$-0.509863\pi$
$239$	−0.957886			−0.0619605			−0.0309803	+	0.999520i	$0.509863\pi$
$240$	19.5367	+	15.9033i	1.26109	+	1.02655i
$241$	10.4599			0.673779			0.336889	−	0.941544i	$-0.390625\pi$
$241$	10.4599			0.673779			0.336889	+	0.941544i	$0.390625\pi$
$242$	−0.160855	+	0.0594147i	−0.0103401	+	0.00381932i
$243$	10.4868	−	10.4868i	0.672727	−	0.672727i
$244$	9.76836	+	0.761018i	0.625355	+	0.0487192i
$245$	12.5652	−	3.31122i	0.802764	−	0.211546i
$246$	−17.1199	+	37.1746i	−1.09153	+	2.37016i
$247$	−7.37405			−0.469200
$248$	−25.0118	−	13.9684i	−1.58825	−	0.886992i
$249$			22.6181i			1.43337i
$250$	−14.2785	−	6.79157i	−0.903049	−	0.429537i
$251$	7.29013	−	7.29013i	0.460149	−	0.460149i	−0.438555	−	0.898704i	$-0.644510\pi$
$251$	7.29013	−	7.29013i	0.460149	−	0.460149i	0.898704	+	0.438555i	$0.144510\pi$
$252$	6.99189	+	8.17335i	0.440447	+	0.514873i
$253$	3.40020	−	3.40020i	0.213769	−	0.213769i
$254$	2.64802	−	0.978096i	0.166152	−	0.0613712i
$255$	26.8722	+	15.6632i	1.68280	+	0.980868i
$256$	−15.2325	−	4.89613i	−0.952029	−	0.306008i
$257$		−	20.2830i		−	1.26522i	−0.774472	−	0.632608i	$-0.781984\pi$
$257$		−	20.2830i		−	1.26522i	0.774472	−	0.632608i	$-0.218016\pi$
$258$	4.34179	+	11.7546i	0.270308	+	0.731810i
$259$	−4.74363	−	4.74363i	−0.294755	−	0.294755i
$260$	2.04592	+	11.2487i	0.126883	+	0.697612i
$261$	−3.48883	+	3.48883i	−0.215953	+	0.215953i
$262$	−9.44474	+	20.5085i	−0.583498	+	1.26702i
$263$	20.2075			1.24605			0.623025	−	0.782202i	$-0.285904\pi$
$263$	20.2075			1.24605			0.623025	+	0.782202i	$0.285904\pi$
$264$	12.8112	−	22.9398i	0.788474	−	1.41185i
$265$	0.588201	+	0.342849i	0.0361329	+	0.0210611i
$266$	−1.86043	+	4.03978i	−0.114070	+	0.247695i
$267$	−13.6993	−	13.6993i	−0.838382	−	0.838382i
$268$	−1.10764	+	14.2175i	−0.0676598	+	0.868475i
$269$	16.2657	+	16.2657i	0.991735	+	0.991735i	0.999966	−	0.00823090i	$-0.00262000\pi$
$269$	16.2657	+	16.2657i	0.991735	+	0.991735i	−0.00823090	+	0.999966i	$0.502620\pi$
$270$	−2.97812	+	16.9515i	−0.181243	+	1.03164i
$271$	−24.4714			−1.48653			−0.743267	−	0.668995i	$-0.766725\pi$
$271$	−24.4714			−1.48653			−0.743267	+	0.668995i	$0.766725\pi$
$272$	−19.5171	−	3.05958i	−1.18340	−	0.185514i
$273$			7.85077i			0.475150i
$274$	−7.81217	−	21.1501i	−0.471950	−	1.27772i
$275$	−4.39991	+	15.8937i	−0.265324	+	0.958426i
$276$	0.637855	−	8.18746i	0.0383944	−	0.492827i
$277$	−13.7978	−	13.7978i	−0.829028	−	0.829028i	0.158354	−	0.987382i	$-0.449381\pi$
$277$	−13.7978	−	13.7978i	−0.829028	−	0.829028i	−0.987382	+	0.158354i	$0.949381\pi$
$278$	6.89651	+	3.17603i	0.413625	+	0.190486i
$279$		−	49.9587i		−	2.99095i
$280$	6.67861	+	1.71714i	0.399123	+	0.102619i
$281$		−	16.5673i		−	0.988319i	−0.869371	−	0.494160i	$-0.835476\pi$
$281$		−	16.5673i		−	0.988319i	0.869371	−	0.494160i	$-0.164524\pi$
$282$	−3.48982	+	7.57788i	−0.207816	+	0.451256i
$283$	−13.6823	−	13.6823i	−0.813330	−	0.813330i	0.171802	−	0.985132i	$-0.445041\pi$
$283$	−13.6823	−	13.6823i	−0.813330	−	0.813330i	−0.985132	+	0.171802i	$0.945041\pi$
$284$	8.32164	+	9.72781i	0.493799	+	0.577239i
$285$	−17.5656	+	4.62892i	−1.04050	+	0.274193i
$286$	11.1863	−	4.13186i	0.661458	−	0.244322i
$287$			11.2034i			0.661317i
$288$	−5.49750	−	27.3552i	−0.323943	−	1.61192i
$289$	−7.39230			−0.434841
$290$	−0.547350	+	3.11553i	−0.0321415	+	0.182950i
$291$	7.51427	+	7.51427i	0.440495	+	0.440495i
$292$	7.96888	−	6.81697i	0.466343	−	0.398933i
$293$	23.0518	+	23.0518i	1.34670	+	1.34670i	0.889219	+	0.457482i	$0.151249\pi$
$293$	23.0518	+	23.0518i	1.34670	+	1.34670i	0.457482	+	0.889219i	$0.348751\pi$
$294$	−21.0241	−	9.68216i	−1.22615	−	0.564675i
$295$	1.84855	−	3.17142i	0.107627	−	0.184647i
$296$	4.74363	+	16.7436i	0.275718	+	0.973204i
$297$	17.9514			1.04165
$298$	24.2137	+	11.1511i	1.40266	+	0.645963i
$299$	2.63553	−	2.63553i	0.152416	−	0.152416i
$300$	11.9347	+	25.5109i	0.689049	+	1.47287i
$301$	2.42551	+	2.42551i	0.139804	+	0.139804i
$302$	−7.43057	+	2.74462i	−0.427581	+	0.157935i
$303$			2.81732i			0.161851i
$304$	9.32334	−	6.79635i	0.534730	−	0.389797i
$305$	9.46410	+	5.51641i	0.541913	+	0.315869i
$306$	−11.9369	−	32.3170i	−0.682387	−	1.84744i
$307$	23.3518	−	23.3518i	1.33276	−	1.33276i	0.429867	−	0.902892i	$-0.358560\pi$
$307$	23.3518	−	23.3518i	1.33276	−	1.33276i	0.902892	−	0.429867i	$-0.141440\pi$
$308$	0.558644	−	7.17070i	0.0318317	−	0.408589i
$309$	−25.7545	+	25.7545i	−1.46512	+	1.46512i
$310$	−18.3877	−	26.2255i	−1.04435	−	1.48951i
$311$		−	17.8004i		−	1.00937i	−0.863304	−	0.504685i	$-0.831609\pi$
$311$		−	17.8004i		−	1.00937i	0.863304	−	0.504685i	$-0.168391\pi$
$312$	9.93008	−	17.7809i	0.562180	−	1.00664i
$313$	−23.7909			−1.34474			−0.672370	−	0.740216i	$-0.734723\pi$
$313$	−23.7909			−1.34474			−0.672370	+	0.740216i	$0.734723\pi$
$314$	−12.9334	−	5.95619i	−0.729875	−	0.336127i
$315$	3.06437	+	11.6285i	0.172658	+	0.655193i
$316$	−3.97429	+	3.39980i	−0.223571	+	0.191254i
$317$	−13.6940	+	13.6940i	−0.769129	+	0.769129i	−0.977953	−	0.208824i	$-0.933036\pi$
$317$	−13.6940	+	13.6940i	−0.769129	+	0.769129i	0.208824	+	0.977953i	$0.433036\pi$
$318$	−0.420202	−	1.13762i	−0.0235638	−	0.0637948i
$319$	3.29930			0.184725
$320$	−12.9542	−	12.3365i	−0.724159	−	0.689633i
$321$	−6.21736			−0.347019
$322$	−0.778913	−	2.10877i	−0.0434071	−	0.117517i
$323$	10.0731	−	10.0731i	0.560485	−	0.560485i
$324$	0.808008	−	0.691209i	0.0448893	−	0.0384005i
$325$	−3.41041	+	12.3194i	−0.189176	+	0.683355i
$326$	−0.991959	−	0.456824i	−0.0549395	−	0.0253011i
$327$	−28.4106			−1.57111
$328$	14.1707	−	25.3741i	0.782445	−	1.40105i
$329$			2.28377i			0.125908i
$330$	24.0529	−	16.8644i	1.32407	−	0.928354i
$331$	1.96043	−	1.96043i	0.107755	−	0.107755i	−0.651174	−	0.758929i	$-0.725723\pi$
$331$	1.96043	−	1.96043i	0.107755	−	0.107755i	0.758929	+	0.651174i	$0.225723\pi$
$332$	1.24751	−	16.0129i	0.0684658	−	0.878821i
$333$	−21.4594	+	21.4594i	−1.17597	+	1.17597i
$334$	10.4422	+	28.2704i	0.571372	+	1.54689i
$335$	−8.02897	+	13.7747i	−0.438669	+	0.752593i
$336$	−7.23572	−	9.92608i	−0.394741	−	0.541512i
$337$			18.5606i			1.01106i	0.862809	+	0.505530i	$0.168703\pi$
$337$			18.5606i			1.01106i	−0.862809	+	0.505530i	$0.831297\pi$
$338$	−8.57534	+	3.16746i	−0.466437	+	0.172287i
$339$	−18.4008	−	18.4008i	−0.999393	−	0.999393i
$340$	−18.1607	−	12.5712i	−0.984904	−	0.681767i
$341$	−23.6224	+	23.6224i	−1.27922	+	1.27922i
$342$	18.2753	+	8.41626i	0.988214	+	0.455099i
$343$	−13.9684			−0.754221
$344$	−2.42551	−	8.56134i	−0.130775	−	0.461597i
$345$	4.62364	−	7.93244i	0.248928	−	0.427068i
$346$	4.80809	+	2.21425i	0.258484	+	0.119039i
$347$	−8.01007	−	8.01007i	−0.430003	−	0.430003i	0.458626	−	0.888629i	$-0.348342\pi$
$347$	−8.01007	−	8.01007i	−0.430003	−	0.430003i	−0.888629	+	0.458626i	$0.848342\pi$
$348$	4.28172	−	3.66279i	0.229524	−	0.196346i
$349$	19.2579	+	19.2579i	1.03085	+	1.03085i	0.999509	+	0.0313434i	$0.00997854\pi$
$349$	19.2579	+	19.2579i	1.03085	+	1.03085i	0.0313434	+	0.999509i	$0.490021\pi$
$350$	5.88858	+	4.97646i	0.314758	+	0.266003i
$351$	13.9143			0.742693
$352$	−10.3351	+	15.5340i	−0.550865	+	0.827965i
$353$			6.05459i			0.322253i	0.986934	+	0.161127i	$0.0515127\pi$
$353$			6.05459i			0.322253i	−0.986934	+	0.161127i	$0.948487\pi$
$354$	−6.13376	+	2.26562i	−0.326006	+	0.120416i
$355$	3.64717	+	13.8401i	0.193572	+	0.734556i
$356$	8.94304	+	10.4542i	0.473980	+	0.554072i
$357$	−10.7244	−	10.7244i	−0.567593	−	0.567593i
$358$	11.2730	−	24.4784i	0.595794	−	1.29372i
$359$			8.74167i			0.461368i	0.973029	+	0.230684i	$0.0740964\pi$
$359$			8.74167i			0.461368i	−0.973029	+	0.230684i	$0.925904\pi$
$360$	7.76803	−	30.2129i	0.409411	−	1.59236i
$361$		−	10.6803i		−	0.562122i
$362$	−2.97112	−	1.36828i	−0.156159	−	0.0719154i
$363$	0.241479	+	0.241479i	0.0126744	+	0.0126744i
$364$	0.433010	−	5.55808i	0.0226959	−	0.291323i
$365$	11.3376	−	2.98770i	0.593437	−	0.156384i
$366$	−6.76102	−	18.3043i	−0.353404	−	0.956779i
$367$			22.7558i			1.18784i	0.804524	+	0.593920i	$0.202421\pi$
$367$			22.7558i			1.18784i	−0.804524	+	0.593920i	$0.797579\pi$
$368$	−0.903160	+	5.76126i	−0.0470805	+	0.300327i
$369$	50.6823			2.63841
$370$	−3.36668	+	19.1632i	−0.175025	+	0.996249i
$371$	−0.234743	−	0.234743i	−0.0121873	−	0.0121873i
$372$	−4.43141	+	56.8812i	−0.229758	+	2.94915i
$373$	−19.1172	−	19.1172i	−0.989851	−	0.989851i	0.0100979	−	0.999949i	$-0.496786\pi$
$373$	−19.1172	−	19.1172i	−0.989851	−	0.989851i	−0.999949	+	0.0100979i	$0.996786\pi$
$374$	−9.63650	+	20.9249i	−0.498292	+	1.08200i
$375$	−0.390645	+	31.4865i	−0.0201728	+	1.62596i
$376$	2.88863	−	5.17240i	0.148970	−	0.266746i
$377$	2.55732			0.131709
$378$	3.51051	−	7.62280i	0.180561	−	0.392075i
$379$	19.2110	−	19.2110i	0.986802	−	0.986802i	−0.0131116	−	0.999914i	$-0.504174\pi$
$379$	19.2110	−	19.2110i	0.986802	−	0.986802i	0.999914	+	0.0131116i	$0.00417366\pi$
$380$	12.6912	−	2.30829i	0.651043	−	0.118413i
$381$	−3.97527	−	3.97527i	−0.203659	−	0.203659i
$382$	2.48522	+	6.72829i	0.127155	+	0.344249i
$383$			20.7721i			1.06140i	0.847558	+	0.530702i	$0.178072\pi$
$383$			20.7721i			1.06140i	−0.847558	+	0.530702i	$0.821928\pi$
$384$	3.83281	+	31.6332i	0.195592	+	1.61428i
$385$	4.04946	−	6.94736i	0.206379	−	0.354070i
$386$	−29.2344	+	10.7983i	−1.48799	+	0.549617i
$387$	10.9726	−	10.9726i	0.557768	−	0.557768i
$388$	−4.90540	−	5.73430i	−0.249034	−	0.291115i
$389$	22.9514	−	22.9514i	1.16368	−	1.16368i	0.180017	−	0.983664i	$-0.442385\pi$
$389$	22.9514	−	22.9514i	1.16368	−	1.16368i	0.983664	−	0.180017i	$-0.0576152\pi$
$390$	18.6437	−	13.0717i	0.944058	−	0.661914i
$391$			7.20039i			0.364139i
$392$	14.3503	+	8.01423i	0.724800	+	0.404780i
$393$	44.9666			2.26826
$394$	−6.75135	+	14.6600i	−0.340128	+	0.738562i
$395$	−5.65437	+	1.49005i	−0.284502	+	0.0749725i
$396$	−32.4390	−	2.52721i	−1.63012	−	0.126997i
$397$	19.9562	−	19.9562i	1.00157	−	1.00157i	0.00157311	−	0.999999i	$-0.499499\pi$
$397$	19.9562	−	19.9562i	1.00157	−	1.00157i	0.999999	−	0.00157311i	$-0.000500736\pi$
$398$	−28.9949	+	10.7098i	−1.45338	+	0.536834i
$399$	8.85754			0.443432
$400$	−7.04229	−	18.7191i	−0.352115	−	0.935957i
$401$	−35.5367			−1.77462			−0.887310	−	0.461174i	$-0.847428\pi$
$401$	−35.5367			−1.77462			−0.887310	+	0.461174i	$0.847428\pi$
$402$	26.6413	−	9.84046i	1.32875	−	0.490797i
$403$	−18.3099	+	18.3099i	−0.912083	+	0.912083i
$404$	0.155390	−	1.99457i	0.00773092	−	0.0992334i
$405$	1.14958	−	0.302940i	0.0571231	−	0.0150532i
$406$	0.645198	−	1.40100i	0.0320206	−	0.0695303i
$407$	20.2936			1.00592
$408$	10.7244	+	37.8538i	0.530935	+	1.87404i
$409$		−	6.50932i		−	0.321865i	−0.986965	−	0.160933i	$-0.948550\pi$
$409$		−	6.50932i		−	0.321865i	0.986965	−	0.160933i	$-0.0514502\pi$
$410$	26.6054	−	18.6540i	1.31394	−	0.921255i
$411$	−31.7510	+	31.7510i	−1.56616	+	1.56616i
$412$	19.6538	−	16.8128i	0.968274	−	0.828308i
$413$	−1.26567	+	1.26567i	−0.0622798	+	0.0622798i
$414$	−9.53970	+	3.52367i	−0.468851	+	0.173179i
$415$	9.04283	−	15.5141i	0.443895	−	0.761558i
$416$	−8.01086	+	12.0405i	−0.392765	+	0.590336i
$417$		−	15.1211i		−	0.740485i
$418$	−4.66172	−	12.6208i	−0.228012	−	0.617302i
$419$	10.8597	+	10.8597i	0.530529	+	0.530529i	0.920730	−	0.390200i	$-0.127594\pi$
$419$	10.8597	+	10.8597i	0.530529	+	0.530529i	−0.390200	+	0.920730i	$0.627594\pi$
$420$	−2.45751	−	13.5116i	−0.119914	−	0.659300i
$421$	17.0865	−	17.0865i	0.832744	−	0.832744i	−0.155147	−	0.987891i	$-0.549585\pi$
$421$	17.0865	−	17.0865i	0.832744	−	0.832744i	0.987891	+	0.155147i	$0.0495852\pi$
$422$	−4.33529	+	9.41376i	−0.211039	+	0.458255i
$423$	10.3314			0.502328
$424$	0.234743	+	0.828575i	0.0114001	+	0.0402392i
$425$	−12.1698	−	21.4873i	−0.590324	−	1.04229i
$426$	10.6645	−	23.1571i	0.516696	−	1.12197i
$427$	−3.77700	−	3.77700i	−0.182782	−	0.182782i
$428$	4.40168	+	0.342919i	0.212763	+	0.0165756i
$429$	−16.7931	−	16.7931i	−0.810778	−	0.810778i
$430$	1.72145	−	9.79853i	0.0830157	−	0.472527i
$431$	24.6877			1.18916			0.594581	−	0.804036i	$-0.297318\pi$
$431$	24.6877			1.18916			0.594581	+	0.804036i	$0.297318\pi$
$432$	−17.5925	+	12.8243i	−0.846420	+	0.617007i
$433$		−	34.7872i		−	1.67176i	−0.548909	−	0.835882i	$-0.684957\pi$
$433$		−	34.7872i		−	1.67176i	0.548909	−	0.835882i	$-0.315043\pi$
$434$	5.41139	+	14.6504i	0.259755	+	0.703240i
$435$	6.09175	−	1.60531i	0.292077	−	0.0769687i
$436$	20.1138	+	1.56699i	0.963274	+	0.0750452i
$437$	−2.97350	−	2.97350i	−0.142242	−	0.142242i
$438$	−18.9700	−	8.73619i	−0.906421	−	0.417431i
$439$		−	1.12777i		−	0.0538257i	−0.999638	−	0.0269128i	$-0.991432\pi$
$439$		−	1.12777i		−	0.0538257i	0.999638	−	0.0269128i	$-0.00856766\pi$
$440$	−17.9588	+	10.6128i	−0.856153	+	0.505944i
$441$			28.6634i			1.36492i
$442$	−7.46935	+	16.2191i	−0.355281	+	0.771465i
$443$	1.20401	+	1.20401i	0.0572043	+	0.0572043i	0.735130	−	0.677926i	$-0.237121\pi$
$443$	1.20401	+	1.20401i	0.0572043	+	0.0572043i	−0.677926	+	0.735130i	$0.737121\pi$
$444$	26.3363	−	22.5294i	1.24987	−	1.06920i
$445$	3.91951	+	14.8736i	0.185803	+	0.705075i
$446$	24.8204	−	9.16788i	1.17528	−	0.434112i
$447$		−	53.0903i		−	2.51109i
$448$	4.57517	+	7.42642i	0.216157	+	0.350865i
$449$	−18.1896			−0.858422			−0.429211	−	0.903204i	$-0.641208\pi$
$449$	−18.1896			−0.858422			−0.429211	+	0.903204i	$0.641208\pi$
$450$	22.5126	−	26.6389i	1.06125	−	1.25577i
$451$	−23.9645	−	23.9645i	−1.12844	−	1.12844i
$452$	12.0122	+	14.0420i	0.565008	+	0.660482i
$453$	11.1549	+	11.1549i	0.524105	+	0.524105i
$454$	−15.7761	−	7.26534i	−0.740411	−	0.340979i
$455$	3.13877	−	5.38496i	0.147148	−	0.252451i
$456$	−20.0610	−	11.2035i	−0.939444	−	0.524652i
$457$	−4.25060			−0.198835			−0.0994174	−	0.995046i	$-0.531698\pi$
$457$	−4.25060			−0.198835			−0.0994174	+	0.995046i	$0.531698\pi$
$458$	−7.68312	−	3.53829i	−0.359009	−	0.165333i
$459$	−19.0073	+	19.0073i	−0.887187	+	0.887187i
$460$	−3.71090	+	5.36088i	−0.173021	+	0.249953i
$461$	−25.7081	−	25.7081i	−1.19735	−	1.19735i	−0.974958	−	0.222390i	$-0.928614\pi$
$461$	−25.7081	−	25.7081i	−1.19735	−	1.19735i	−0.222390	−	0.974958i	$-0.571386\pi$
$462$	−13.4367	+	4.96309i	−0.625131	+	0.230904i
$463$			32.8289i			1.52569i	0.646582	+	0.762844i	$0.276198\pi$
$463$			32.8289i			1.52569i	−0.646582	+	0.762844i	$0.723802\pi$
$464$	−3.23334	+	2.35697i	−0.150104	+	0.109420i
$465$	−32.1221	+	55.1095i	−1.48963	+	2.55564i
$466$	9.65580	+	26.1414i	0.447296	+	1.21098i
$467$	−17.1611	+	17.1611i	−0.794123	+	0.794123i	−0.982162	−	0.188039i	$-0.939787\pi$
$467$	−17.1611	+	17.1611i	−0.794123	+	0.794123i	0.188039	+	0.982162i	$0.439787\pi$
$468$	−25.1438	−	1.95886i	−1.16227	−	0.0905484i
$469$	5.49731	−	5.49731i	0.253842	−	0.253842i
$470$	5.42339	−	3.80254i	0.250162	−	0.175398i
$471$			28.3575i			1.30665i
$472$	4.46746	−	1.26567i	0.205631	−	0.0582574i
$473$	−10.3765			−0.477112
$474$	9.46084	+	4.35697i	0.434551	+	0.200122i
$475$	13.8992	+	3.84776i	0.637738	+	0.176547i
$476$	7.00098	+	8.18398i	0.320889	+	0.375112i
$477$	−1.06194	+	1.06194i	−0.0486228	+	0.0486228i
$478$	−0.469372	−	1.27074i	−0.0214686	−	0.0581223i
$479$	−25.2711			−1.15466			−0.577332	−	0.816510i	$-0.695906\pi$
$479$	−25.2711			−1.15466			−0.577332	+	0.816510i	$0.695906\pi$
$480$	−11.5243	+	33.7102i	−0.526011	+	1.53866i
$481$	15.7298			0.717216
$482$	5.12541	+	13.8762i	0.233456	+	0.632041i
$483$	−3.16573	+	3.16573i	−0.144046	+	0.144046i
$484$	−0.157640	−	0.184278i	−0.00716546	−	0.00837626i
$485$	−2.14991	−	8.15839i	−0.0976226	−	0.370454i
$486$	19.0505	+	8.77325i	0.864146	+	0.397963i
$487$	12.9056			0.584807			0.292404	−	0.956295i	$-0.405545\pi$
$487$	12.9056			0.584807			0.292404	+	0.956295i	$0.405545\pi$
$488$	3.77700	+	13.3317i	0.170977	+	0.603498i
$489$			2.17495i			0.0983545i
$490$	10.5498	+	15.0467i	0.476590	+	0.679739i
$491$	10.3909	−	10.3909i	0.468935	−	0.468935i	−0.432635	−	0.901569i	$-0.642416\pi$
$491$	10.3909	−	10.3909i	0.468935	−	0.468935i	0.901569	+	0.432635i	$0.142416\pi$
$492$	−57.7050	−	4.49559i	−2.60154	−	0.202677i
$493$	−3.49337	+	3.49337i	−0.157333	+	0.157333i
$494$	−3.61334	−	9.78249i	−0.162572	−	0.440135i
$495$	−31.4286	−	18.3190i	−1.41261	−	0.823379i
$496$	6.27458	−	40.0255i	0.281737	−	1.79720i
$497$		−	6.97894i		−	0.313048i
$498$	−30.0054	+	11.0831i	−1.34458	+	0.496644i
$499$	−19.8755	−	19.8755i	−0.889749	−	0.889749i	0.104750	−	0.994499i	$-0.466596\pi$
$499$	−19.8755	−	19.8755i	−0.889749	−	0.889749i	−0.994499	+	0.104750i	$0.966596\pi$
$500$	2.01321	−	22.2699i	0.0900334	−	0.995939i
$501$	42.4402	−	42.4402i	1.89609	−	1.89609i
$502$	13.2434	+	6.09894i	0.591081	+	0.272209i
$503$	12.8059			0.570989			0.285494	−	0.958380i	$-0.407842\pi$
$503$	12.8059			0.570989			0.285494	+	0.958380i	$0.407842\pi$
$504$	−7.41677	+	13.2805i	−0.330369	+	0.591561i
$505$	1.12638	−	1.93244i	0.0501231	−	0.0859925i
$506$	6.17686	+	2.84461i	0.274595	+	0.126458i
$507$	12.8735	+	12.8735i	0.571732	+	0.571732i
$508$	2.59510	+	3.03362i	0.115139	+	0.134595i
$509$	5.77064	+	5.77064i	0.255779	+	0.255779i	0.823335	−	0.567556i	$-0.192111\pi$
$509$	5.77064	+	5.77064i	0.255779	+	0.255779i	−0.567556	+	0.823335i	$0.692111\pi$
$510$	−7.61136	+	43.3240i	−0.337037	+	1.91842i
$511$	−5.71704			−0.252907
$512$	−0.968769	−	22.6067i	−0.0428139	−	0.999083i
$513$		−	15.6987i		−	0.693114i
$514$	26.9076	−	9.93881i	1.18684	−	0.438382i
$515$	27.9622	−	7.36864i	1.23216	−	0.324701i
$516$	−13.4663	+	11.5197i	−0.592820	+	0.507127i
$517$	−4.88507	−	4.88507i	−0.214845	−	0.214845i
$518$	3.96853	−	8.61736i	0.174367	−	0.378625i
$519$		−	10.5421i		−	0.462747i
$520$	−13.9201	+	8.22606i	−0.610435	+	0.360737i
$521$			18.9514i			0.830274i	0.909759	+	0.415137i	$0.136266\pi$
$521$			18.9514i			0.830274i	−0.909759	+	0.415137i	$0.863734\pi$
$522$	−6.33787	−	2.91876i	−0.277401	−	0.127751i
$523$	7.32161	+	7.32161i	0.320152	+	0.320152i	0.848825	−	0.528674i	$-0.177310\pi$
$523$	7.32161	+	7.32161i	0.320152	+	0.320152i	−0.528674	+	0.848825i	$0.677310\pi$
$524$	−31.8348	−	2.48014i	−1.39071	−	0.108345i
$525$	4.09651	−	14.7977i	0.178786	−	0.645826i
$526$	9.90185	+	26.8075i	0.431741	+	1.16886i
$527$		−	50.0237i		−	2.17907i
$528$	36.7097	+	5.75477i	1.59759	+	0.250444i
$529$	−20.8745			−0.907587
$530$	−0.166604	+	0.948312i	−0.00723680	+	0.0411920i
$531$	5.72569	+	5.72569i	0.248474	+	0.248474i
$532$	−6.27084	−	0.488539i	−0.271875	−	0.0211808i
$533$	−18.5751	−	18.5751i	−0.804578	−	0.804578i
$534$	11.4608	−	24.8864i	0.495959	−	1.07694i
$535$	4.26458	+	2.48573i	0.184374	+	0.107467i
$536$	−19.4039	+	5.49731i	−0.838120	+	0.237448i
$537$	−53.6708			−2.31606
$538$	−13.6079	+	29.5485i	−0.586677	+	1.27393i
$539$	13.5531	−	13.5531i	0.583774	−	0.583774i
$540$	−23.9474	+	4.35558i	−1.03053	+	0.187434i
$541$	−6.08576	−	6.08576i	−0.261647	−	0.261647i	0.564076	−	0.825723i	$-0.309233\pi$
$541$	−6.08576	−	6.08576i	−0.261647	−	0.261647i	−0.825723	+	0.564076i	$0.809233\pi$
$542$	−11.9912	−	32.4640i	−0.515066	−	1.39445i
$543$			6.51442i			0.279561i
$544$	−5.50465	−	27.3907i	−0.236010	−	1.17437i
$545$	19.4873	+	11.3587i	0.834743	+	0.486553i
$546$	−10.4149	+	3.84694i	−0.445717	+	0.164634i
$547$	3.68638	−	3.68638i	0.157618	−	0.157618i	−0.623892	−	0.781510i	$-0.714450\pi$
$547$	3.68638	−	3.68638i	0.157618	−	0.157618i	0.781510	+	0.623892i	$0.214450\pi$
$548$	24.2298	−	20.7274i	1.03505	−	0.885430i
$549$	−17.0865	+	17.0865i	−0.729233	+	0.729233i
$550$	−23.2407	+	1.95107i	−0.990987	+	0.0831941i
$551$		−	2.88527i		−	0.122917i
$552$	11.1741	−	3.16573i	0.475602	−	0.134743i
$553$	2.85124			0.121247
$554$	11.5432	−	25.0653i	0.490425	−	1.06492i
$555$	37.4696	−	9.87406i	1.59050	−	0.419130i
$556$	−0.834008	+	10.7053i	−0.0353698	+	0.454004i
$557$	3.92396	−	3.92396i	0.166264	−	0.166264i	−0.619071	−	0.785335i	$-0.712491\pi$
$557$	3.92396	−	3.92396i	0.166264	−	0.166264i	0.785335	+	0.619071i	$0.212491\pi$
$558$	66.2757	−	24.4802i	2.80567	−	1.03633i
$559$	−8.04293			−0.340180
$560$	0.994601	+	9.70132i	0.0420296	+	0.409956i
$561$	45.8796			1.93704
$562$	21.9783	−	8.11808i	0.927097	−	0.342441i
$563$	−2.42213	+	2.42213i	−0.102081	+	0.102081i	−0.756303	−	0.654222i	$-0.772996\pi$
$563$	−2.42213	+	2.42213i	−0.102081	+	0.102081i	0.654222	+	0.756303i	$0.272996\pi$
$564$	−11.7629	−	0.916407i	−0.495309	−	0.0385877i
$565$	5.26466	+	19.9781i	0.221486	+	0.840484i
$566$	11.4467	−	24.8555i	0.481139	−	1.04476i
$567$	−0.579682			−0.0243444
$568$	−8.82734	+	15.8063i	−0.370387	+	0.663217i
$569$		−	0.577163i		−	0.0241959i	−0.999927	−	0.0120980i	$-0.996149\pi$
$569$		−	0.577163i		−	0.0241959i	0.999927	−	0.0120980i	$-0.00385099\pi$
$570$	−14.7480	−	21.0345i	−0.617728	−	0.881038i
$571$	−18.5485	+	18.5485i	−0.776229	+	0.776229i	−0.979187	−	0.202959i	$-0.934944\pi$
$571$	−18.5485	+	18.5485i	−0.776229	+	0.776229i	0.202959	+	0.979187i	$0.434944\pi$
$572$	10.9627	+	12.8152i	0.458374	+	0.535829i
$573$	10.1007	−	10.1007i	0.421962	−	0.421962i
$574$	−14.8626	+	5.48976i	−0.620351	+	0.229138i
$575$	−6.34285	+	3.59243i	−0.264515	+	0.149815i
$576$	33.5958	−	20.6973i	1.39982	−	0.862387i
$577$			9.63346i			0.401046i	0.979689	+	0.200523i	$0.0642642\pi$
$577$			9.63346i			0.401046i	−0.979689	+	0.200523i	$0.935736\pi$
$578$	−3.62229	−	9.80670i	−0.150667	−	0.407905i
$579$	43.8873	+	43.8873i	1.82390	+	1.82390i
$580$	−4.40130	+	0.800514i	−0.182754	+	0.0332395i
$581$	−6.19148	+	6.19148i	−0.256866	+	0.256866i
$582$	−6.28645	+	13.6506i	−0.260582	+	0.565834i
$583$	1.00425			0.0415918
$584$	12.9483	+	7.23122i	0.535803	+	0.299230i
$585$	−24.3606	−	14.1993i	−1.00719	−	0.587067i
$586$	−19.2852	+	41.8763i	−0.796663	+	1.72989i
$587$	17.5202	+	17.5202i	0.723136	+	0.723136i	0.969243	−	0.246107i	$-0.0791513\pi$
$587$	17.5202	+	17.5202i	0.723136	+	0.723136i	−0.246107	+	0.969243i	$0.579151\pi$
$588$	2.54248	−	32.6351i	0.104850	−	1.34585i
$589$	20.6580	+	20.6580i	0.851197	+	0.851197i
$590$	5.11305	+	0.898283i	0.210501	+	0.0369817i
$591$	32.1433			1.32220
$592$	−19.8878	+	14.4975i	−0.817385	+	0.595842i
$593$		−	15.7065i		−	0.644988i	−0.946571	−	0.322494i	$-0.895479\pi$
$593$		−	15.7065i		−	0.644988i	0.946571	−	0.322494i	$-0.104521\pi$
$594$	8.79635	+	23.8146i	0.360919	+	0.977123i
$595$	3.06835	+	11.6436i	0.125790	+	0.477343i
$596$	−2.92820	+	37.5862i	−0.119944	+	1.53959i
$597$	43.5279	+	43.5279i	1.78148	+	1.78148i
$598$	4.78774	+	2.20489i	0.195785	+	0.0901645i
$599$			29.6865i			1.21296i	0.795099	+	0.606479i	$0.207419\pi$
$599$			29.6865i			1.21296i	−0.795099	+	0.606479i	$0.792581\pi$
$600$	−27.9950	+	28.3332i	−1.14289	+	1.15670i
$601$			13.3688i			0.545325i	0.962110	+	0.272663i	$0.0879043\pi$
$601$			13.3688i			0.545325i	−0.962110	+	0.272663i	$0.912096\pi$
$602$	−2.02919	+	4.40622i	−0.0827034	+	0.179584i
$603$	−24.8689	−	24.8689i	−1.01274	−	1.01274i
$604$	−7.28207	−	8.51258i	−0.296303	−	0.346372i
$605$	−0.0690897	−	0.262178i	−0.00280890	−	0.0106591i
$606$	−3.73748	+	1.38051i	−0.151825	+	0.0560793i
$607$			39.5508i			1.60532i	0.596439	+	0.802659i	$0.296582\pi$
$607$			39.5508i			1.60532i	−0.596439	+	0.802659i	$0.703418\pi$
$608$	13.5846	+	9.03816i	0.550929	+	0.366546i
$609$	−3.07180			−0.124475
$610$	−2.68064	+	15.2582i	−0.108536	+	0.617788i
$611$	−3.78646	−	3.78646i	−0.153184	−	0.153184i
$612$	37.0229	−	31.6712i	1.49656	−	1.28023i
$613$	15.1788	+	15.1788i	0.613067	+	0.613067i	0.943744	−	0.330677i	$-0.107277\pi$
$613$	15.1788	+	15.1788i	0.613067	+	0.613067i	−0.330677	+	0.943744i	$0.607277\pi$
$614$	42.4213	+	19.5362i	1.71199	+	0.788416i
$615$	−55.9077	−	32.5873i	−2.25441	−	1.31405i
$616$	9.78646	−	2.77260i	0.394308	−	0.111711i
$617$	−18.6184			−0.749549			−0.374774	−	0.927116i	$-0.622280\pi$
$617$	−18.6184			−0.749549			−0.374774	+	0.927116i	$0.622280\pi$
$618$	−46.7861	−	21.5463i	−1.88201	−	0.866717i
$619$	−15.6388	+	15.6388i	−0.628576	+	0.628576i	−0.947710	−	0.319134i	$-0.896608\pi$
$619$	−15.6388	+	15.6388i	−0.628576	+	0.628576i	0.319134	+	0.947710i	$0.396608\pi$
$620$	25.7809	−	37.2440i	1.03539	−	1.49575i
$621$	5.61080	+	5.61080i	0.225154	+	0.225154i
$622$	23.6142	−	8.72235i	0.946844	−	0.349734i
$623$		−	7.50008i		−	0.300484i
$624$	28.4541	+	4.46058i	1.13907	+	0.178566i
$625$	12.8564	−	21.4409i	0.514256	−	0.857637i
$626$	−11.6577	−	31.5612i	−0.465936	−	1.26144i
$627$	−18.9466	+	18.9466i	−0.756655	+	0.756655i
$628$	1.56406	−	20.0762i	0.0624129	−	0.801127i
$629$	−21.4873	+	21.4873i	−0.856753	+	0.856753i
$630$	−13.9249	+	9.76328i	−0.554783	+	0.388978i
$631$		−	32.2591i		−	1.28422i	−0.766614	−	0.642108i	$-0.778060\pi$
$631$		−	32.2591i		−	1.28422i	0.766614	−	0.642108i	$-0.221940\pi$
$632$	−6.45765	−	3.60640i	−0.256871	−	0.143455i
$633$	20.6404			0.820382
$634$	−24.8767	−	11.4564i	−0.987979	−	0.454991i
$635$	1.13737	+	4.31603i	0.0451351	+	0.171276i
$636$	1.30328	−	1.11489i	0.0516784	−	0.0442082i
$637$	10.5052	−	10.5052i	0.416230	−	0.416230i
$638$	1.61668	+	4.37689i	0.0640051	+	0.173283i
$639$	−31.5715			−1.24895
$640$	10.0181	−	23.2301i	0.396001	−	0.918250i
$641$	−8.87760			−0.350644			−0.175322	−	0.984511i	$-0.556097\pi$
$641$	−8.87760			−0.350644			−0.175322	+	0.984511i	$0.556097\pi$
$642$	−3.04655	−	8.24800i	−0.120238	−	0.325523i
$643$	−19.5500	+	19.5500i	−0.770977	+	0.770977i	−0.978277	−	0.207301i	$-0.933532\pi$
$643$	−19.5500	+	19.5500i	−0.770977	+	0.770977i	0.207301	+	0.978277i	$0.433532\pi$
$644$	2.41584	−	2.06663i	0.0951974	−	0.0814365i
$645$	−19.1589	+	5.04880i	−0.754382	+	0.198796i
$646$	18.2990	+	8.42721i	0.719966	+	0.331564i
$647$	−33.1992			−1.30519			−0.652597	−	0.757705i	$-0.726321\pi$
$647$	−33.1992			−1.30519			−0.652597	+	0.757705i	$0.726321\pi$
$648$	1.31289	+	0.733213i	0.0515754	+	0.0288033i
$649$		−	5.41465i		−	0.212543i
$650$	−18.0141	+	1.51230i	−0.706571	+	0.0593171i
$651$	21.9935	−	21.9935i	0.861992	−	0.861992i
$652$	0.119959	−	1.53979i	0.00469797	−	0.0603028i
$653$	−10.3869	+	10.3869i	−0.406472	+	0.406472i	−0.880506	−	0.474034i	$-0.842797\pi$
$653$	−10.3869	+	10.3869i	−0.406472	+	0.406472i	0.474034	+	0.880506i	$0.342797\pi$
$654$	−13.9214	−	37.6898i	−0.544371	−	1.47379i
$655$	−30.8433	−	17.9778i	−1.20515	−	0.702452i
$656$	40.6053	+	6.36545i	1.58537	+	0.248529i
$657$			25.8629i			1.00901i
$658$	−3.02967	+	1.11906i	−0.118109	+	0.0436257i
$659$	3.29013	+	3.29013i	0.128165	+	0.128165i	0.768280	−	0.640114i	$-0.221113\pi$
$659$	3.29013	+	3.29013i	0.128165	+	0.128165i	−0.640114	+	0.768280i	$0.721113\pi$
$660$	34.1586	+	23.6451i	1.32962	+	0.920386i
$661$	−8.43866	+	8.43866i	−0.328226	+	0.328226i	−0.851912	−	0.523686i	$-0.824557\pi$
$661$	−8.43866	+	8.43866i	−0.328226	+	0.328226i	0.523686	+	0.851912i	$0.324557\pi$
$662$	3.56135	+	1.64010i	0.138416	+	0.0637443i
$663$	35.5617			1.38110
$664$	21.8541	−	6.19148i	0.848105	−	0.240276i
$665$	−6.07552	−	3.54128i	−0.235599	−	0.137325i
$666$	−38.9834	−	17.9529i	−1.51058	−	0.695662i
$667$	1.03121	+	1.03121i	0.0399286	+	0.0399286i
$668$	−32.3870	+	27.7054i	−1.25309	+	1.07196i
$669$	−37.2610	−	37.2610i	−1.44059	−	1.44059i
$670$	−22.2079	−	3.90159i	−0.857967	−	0.150731i
$671$	16.1583			0.623783
$672$	9.62247	−	14.4628i	0.371195	−	0.557916i
$673$			7.49618i			0.288956i	0.989508	+	0.144478i	$0.0461504\pi$
$673$			7.49618i			0.288956i	−0.989508	+	0.144478i	$0.953850\pi$
$674$	−24.6226	+	9.09483i	−0.948429	+	0.350320i
$675$	−26.2268	−	7.26046i	−1.00947	−	0.279455i
$676$	−8.40396	−	9.82404i	−0.323229	−	0.377848i
$677$	11.2336	+	11.2336i	0.431741	+	0.431741i	0.889220	−	0.457479i	$-0.151248\pi$
$677$	11.2336	+	11.2336i	0.431741	+	0.431741i	−0.457479	+	0.889220i	$0.651248\pi$
$678$	15.3941	−	33.4272i	0.591208	−	1.28376i
$679$			4.11391i			0.157877i
$680$	7.77813	−	30.2522i	0.298278	−	1.16012i
$681$			34.5904i			1.32551i
$682$	−42.9128	−	19.7625i	−1.64322	−	0.756746i
$683$	−24.1607	−	24.1607i	−0.924482	−	0.924482i	0.0728605	−	0.997342i	$-0.476787\pi$
$683$	−24.1607	−	24.1607i	−0.924482	−	0.924482i	−0.997342	+	0.0728605i	$0.976787\pi$
$684$	−2.21006	+	28.3682i	−0.0845039	+	1.08468i
$685$	34.4726	−	9.08429i	1.31713	−	0.347093i
$686$	−6.84461	−	18.5306i	−0.261328	−	0.707500i
$687$			16.8458i			0.642709i
$688$	10.1690	−	7.41283i	0.387691	−	0.282611i
$689$	0.778403			0.0296548
$690$	12.7889	+	2.24681i	0.486864	+	0.0855345i
$691$	20.6744	+	20.6744i	0.786490	+	0.786490i	0.980917	−	0.194427i	$-0.0622846\pi$
$691$	20.6744	+	20.6744i	0.786490	+	0.786490i	−0.194427	+	0.980917i	$0.562285\pi$
$692$	−0.581451	+	7.46345i	−0.0221034	+	0.283718i
$693$	12.5427	+	12.5427i	0.476460	+	0.476460i
$694$	6.70124	−	14.5512i	0.254376	−	0.552357i
$695$	−6.04550	+	10.3718i	−0.229319	+	0.393425i
$696$	6.95717	+	3.88537i	0.263711	+	0.147275i
$697$	50.7482			1.92222
$698$	−16.1112	+	34.9842i	−0.609818	+	1.32417i
$699$	39.2440	−	39.2440i	1.48435	−	1.48435i
$700$	−3.71636	+	10.2504i	−0.140465	+	0.387427i
$701$	−5.10967	−	5.10967i	−0.192990	−	0.192990i	0.603997	−	0.796987i	$-0.293574\pi$
$701$	−5.10967	−	5.10967i	−0.192990	−	0.192990i	−0.796987	+	0.603997i	$0.793574\pi$
$702$	6.81814	+	18.4589i	0.257334	+	0.696686i
$703$		−	17.7469i		−	0.669338i
$704$	−25.6718	−	6.09891i	−0.967544	−	0.229861i
$705$	−11.3965	−	6.64279i	−0.429219	−	0.250182i
$706$	−8.03207	+	2.96679i	−0.302291	+	0.111657i
$707$	−0.771212	+	0.771212i	−0.0290044	+	0.0290044i
$708$	−6.01119	−	7.02694i	−0.225914	−	0.264089i
$709$	13.7429	−	13.7429i	0.516126	−	0.516126i	−0.400271	−	0.916397i	$-0.631084\pi$
$709$	13.7429	−	13.7429i	0.516126	−	0.516126i	0.916397	+	0.400271i	$0.131084\pi$
$710$	−16.5733	+	11.6201i	−0.621983	+	0.436095i
$711$		−	12.8985i		−	0.483732i
$712$	−9.48650	+	16.9866i	−0.355522	+	0.636599i
$713$	−14.7665			−0.553011
$714$	8.97201	−	19.4820i	0.335769	−	0.729097i
$715$	4.80468	+	18.2326i	0.179685	+	0.681860i
$716$	37.9971	+	2.96022i	1.42002	+	0.110628i
$717$	−1.90767	+	1.90767i	−0.0712431	+	0.0712431i
$718$	−11.5968	+	4.28349i	−0.432788	+	0.159858i
$719$	23.0266			0.858747			0.429373	−	0.903127i	$-0.358734\pi$
$719$	23.0266			0.858747			0.429373	+	0.903127i	$0.358734\pi$
$720$	43.8871	−	4.49940i	1.63557	−	0.167683i
$721$	−14.1001			−0.525114
$722$	14.1686	−	5.23344i	0.527301	−	0.194768i
$723$	20.8312	−	20.8312i	0.774721	−	0.774721i
$724$	0.359304	−	4.61199i	0.0133534	−	0.171403i
$725$	−4.82023	−	1.33440i	−0.179019	−	0.0495585i
$726$	−0.202022	+	0.438675i	−0.00749773	+	0.0162807i
$727$	−43.6601			−1.61926			−0.809631	−	0.586939i	$-0.800333\pi$
$727$	−43.6601			−1.61926			−0.809631	+	0.586939i	$0.800333\pi$
$728$	7.58558	−	2.14907i	0.281140	−	0.0796498i
$729$		−	43.3646i		−	1.60610i
$730$	9.51903	+	13.5766i	0.352315	+	0.502491i
$731$	10.9869	−	10.9869i	0.406363	−	0.406363i
$732$	20.9696	−	17.9385i	0.775061	−	0.663025i
$733$	−20.4799	+	20.4799i	−0.756444	+	0.756444i	−0.975673	−	0.219229i	$-0.929646\pi$
$733$	−20.4799	+	20.4799i	−0.756444	+	0.756444i	0.219229	+	0.975673i	$0.429646\pi$
$734$	−30.1880	+	11.1505i	−1.11426	+	0.411572i
$735$	18.4297	−	31.6186i	0.679792	−	1.16627i
$736$	−8.08550	+	1.62492i	−0.298036	+	0.0598955i
$737$			23.5179i			0.866292i
$738$	24.8347	+	67.2356i	0.914178	+	2.47498i
$739$	−5.57362	−	5.57362i	−0.205029	−	0.205029i	0.597122	−	0.802151i	$-0.296311\pi$
$739$	−5.57362	−	5.57362i	−0.205029	−	0.205029i	−0.802151	+	0.597122i	$0.796311\pi$
$740$	−27.0718	+	4.92386i	−0.995180	+	0.181005i
$741$	−14.6857	+	14.6857i	−0.539493	+	0.539493i
$742$	0.196387	−	0.426439i	0.00720958	−	0.0156551i
$743$	−13.1917			−0.483957			−0.241978	−	0.970282i	$-0.577796\pi$
$743$	−13.1917			−0.483957			−0.241978	+	0.970282i	$0.577796\pi$
$744$	−77.6305	+	21.9935i	−2.84607	+	0.806320i
$745$	−21.2257	+	36.4155i	−0.777651	+	1.33416i
$746$	15.9935	−	34.7286i	0.585563	−	1.27151i
$747$	28.0092	+	28.0092i	1.02480	+	1.02480i
$748$	−32.4812	−	2.53049i	−1.18763	−	0.0925240i
$749$	−1.70194	−	1.70194i	−0.0621875	−	0.0621875i
$750$	−41.9618	+	14.9104i	−1.53223	+	0.544452i
$751$	−16.1003			−0.587510			−0.293755	−	0.955881i	$-0.594905\pi$
$751$	−16.1003			−0.587510			−0.293755	+	0.955881i	$0.594905\pi$
$752$	8.27721	+	1.29757i	0.301839	+	0.0473175i
$753$		−	29.0371i		−	1.05817i
$754$	1.25311	+	3.39257i	0.0456355	+	0.123550i
$755$	−3.19155	−	12.1111i	−0.116152	−	0.440770i
$756$	11.8327	+	0.921840i	0.430350	+	0.0335270i
$757$	−23.2342	−	23.2342i	−0.844463	−	0.844463i	0.144973	−	0.989436i	$-0.453691\pi$
$757$	−23.2342	−	23.2342i	−0.844463	−	0.844463i	−0.989436	+	0.144973i	$0.953691\pi$
$758$	34.8990	+	16.0719i	1.26759	+	0.583759i
$759$		−	13.5432i		−	0.491588i
$760$	9.28096	+	15.7051i	0.336656	+	0.569685i
$761$			15.4641i			0.560573i	0.959916	+	0.280287i	$0.0904295\pi$
$761$			15.4641i			0.560573i	−0.959916	+	0.280287i	$0.909570\pi$
$762$	3.32572	−	7.22155i	0.120478	−	0.261609i
$763$	−7.77711	−	7.77711i	−0.281550	−	0.281550i
$764$	−7.70804	+	6.59383i	−0.278867	+	0.238556i
$765$	52.6738	−	13.8807i	1.90442	−	0.501857i
$766$	−27.5565	+	10.1785i	−0.995655	+	0.367764i
$767$		−	4.19694i		−	0.151543i
$768$	−40.0868	+	20.5852i	−1.44651	+	0.742804i
$769$	20.7352			0.747729			0.373864	−	0.927483i	$-0.378033\pi$
$769$	20.7352			0.747729			0.373864	+	0.927483i	$0.378033\pi$
$770$	11.2007	+	1.96779i	0.403645	+	0.0709141i
$771$	−40.3943	−	40.3943i	−1.45476	−	1.45476i
$772$	−28.6501	−	33.4914i	−1.03114	−	1.20538i
$773$	−9.64112	−	9.64112i	−0.346767	−	0.346767i	0.512137	−	0.858904i	$-0.328854\pi$
$773$	−9.64112	−	9.64112i	−0.346767	−	0.346767i	−0.858904	+	0.512137i	$0.828854\pi$
$774$	19.9330	+	9.17968i	0.716476	+	0.329957i
$775$	44.0660	−	24.9579i	1.58290	−	0.896514i
$776$	5.20349	−	9.31740i	0.186795	−	0.334475i
$777$	−18.8942			−0.677827
$778$	41.6938	+	19.2011i	1.49480	+	0.688395i
$779$	−20.9572	+	20.9572i	−0.750869	+	0.750869i
$780$	26.4766	+	18.3276i	0.948016	+	0.656233i
$781$	14.9282	+	14.9282i	0.534173	+	0.534173i
$782$	−9.55211	+	3.52825i	−0.341583	+	0.126170i
$783$			5.44431i			0.194564i
$784$	−3.59998	+	22.9643i	−0.128571	+	0.820153i
$785$	11.3375	−	19.4509i	0.404651	−	0.694231i
$786$	22.0340	+	59.6531i	0.785926	+	2.12776i
$787$	20.1485	−	20.1485i	0.718216	−	0.718216i	−0.250024	−	0.968240i	$-0.580438\pi$
$787$	20.1485	−	20.1485i	0.718216	−	0.718216i	0.968240	+	0.250024i	$0.0804384\pi$
$788$	−22.7564	−	1.77287i	−0.810662	−	0.0631557i
$789$	40.2440	−	40.2440i	1.43273	−	1.43273i
$790$	−4.74740	−	6.77100i	−0.168905	−	0.240901i
$791$		−	10.0741i		−	0.358192i
$792$	−12.5427	−	44.2722i	−0.445687	−	1.57315i
$793$	12.5244			0.444756
$794$	36.2527	+	16.6954i	1.28656	+	0.592496i
$795$	1.85422	−	0.488628i	0.0657625	−	0.0173298i
$796$	−28.4155	−	33.2170i	−1.00716	−	1.17735i
$797$	19.9707	−	19.9707i	0.707399	−	0.707399i	−0.258588	−	0.965988i	$-0.583257\pi$
$797$	19.9707	−	19.9707i	0.707399	−	0.707399i	0.965988	+	0.258588i	$0.0832573\pi$
$798$	4.34026	+	11.7505i	0.153644	+	0.415963i
$799$	10.3448			0.365973
$800$	21.3822	−	18.5149i	0.755975	−	0.654600i
$801$	−33.9290			−1.19882
$802$	−17.4133	−	47.1433i	−0.614884	−	1.66469i
$803$	12.2290	−	12.2290i	0.431551	−	0.431551i
$804$	26.1089	+	30.5207i	0.920789	+	1.07638i
$805$	3.43710	−	0.905750i	0.121142	−	0.0319235i
$806$	−33.2621	−	15.3181i	−1.17161	−	0.539558i
$807$	64.7874			2.28062
$808$	2.72215	−	0.771212i	0.0957650	−	0.0271312i
$809$			16.2764i			0.572249i	0.958192	+	0.286125i	$0.0923671\pi$
$809$			16.2764i			0.572249i	−0.958192	+	0.286125i	$0.907633\pi$
$810$	0.965186	+	1.37660i	0.0339132	+	0.0483689i
$811$	−27.7616	+	27.7616i	−0.974841	+	0.974841i	−0.999691	−	0.0248504i	$-0.992089\pi$
$811$	−27.7616	+	27.7616i	−0.974841	+	0.974841i	0.0248504	+	0.999691i	$0.492089\pi$
$812$	2.17473	+	0.169425i	0.0763180	+	0.00594566i
$813$	−48.7358	+	48.7358i	−1.70924	+	1.70924i
$814$	9.94402	+	26.9217i	0.348538	+	0.943604i
$815$	0.869553	−	1.49183i	0.0304591	−	0.0522565i
$816$	−44.9622	+	32.7757i	−1.57399	+	1.14738i
$817$			9.07435i			0.317471i
$818$	8.63532	−	3.18962i	0.301927	−	0.111522i
$819$	9.72201	+	9.72201i	0.339714	+	0.339714i
$820$	37.7834	+	26.1543i	1.31945	+	0.913348i
$821$	7.26795	−	7.26795i	0.253653	−	0.253653i	−0.568813	−	0.822467i	$-0.692597\pi$
$821$	7.26795	−	7.26795i	0.253653	−	0.253653i	0.822467	+	0.568813i	$0.192597\pi$
$822$	−57.6794	−	26.5629i	−2.01180	−	0.926488i
$823$	44.1075			1.53749			0.768746	−	0.639554i	$-0.220881\pi$
$823$	44.1075			1.53749			0.768746	+	0.639554i	$0.220881\pi$
$824$	31.9346	+	17.8345i	1.11249	+	0.621295i
$825$	22.8903	+	40.4155i	0.796938	+	1.40709i
$826$	−2.29925	−	1.05886i	−0.0800010	−	0.0368426i
$827$	−12.9202	−	12.9202i	−0.449279	−	0.449279i	0.445836	−	0.895115i	$-0.352907\pi$
$827$	−12.9202	−	12.9202i	−0.449279	−	0.449279i	−0.895115	+	0.445836i	$0.852907\pi$
$828$	−9.34906	−	10.9288i	−0.324902	−	0.379803i
$829$	−16.1583	−	16.1583i	−0.561200	−	0.561200i	0.368448	−	0.929648i	$-0.379889\pi$
$829$	−16.1583	−	16.1583i	−0.561200	−	0.561200i	−0.929648	+	0.368448i	$0.879889\pi$
$830$	25.0122	+	4.39426i	0.868187	+	0.152527i
$831$	−54.9576			−1.90646
$832$	−19.8985	−	4.72733i	−0.689856	−	0.163891i
$833$			28.7006i			0.994418i
$834$	20.0598	−	7.40948i	0.694616	−	0.256569i
$835$	−46.0781	+	12.1426i	−1.59460	+	0.420212i
$836$	14.4586	−	12.3686i	0.500060	−	0.427775i
$837$	−38.9802	−	38.9802i	−1.34735	−	1.34735i
$838$	−9.08521	+	19.7279i	−0.313844	+	0.681488i
$839$			50.4452i			1.74156i	0.491673	+	0.870780i	$0.336386\pi$
$839$			50.4452i			1.74156i	−0.491673	+	0.870780i	$0.663614\pi$
$840$	16.7204	−	9.88096i	0.576910	−	0.340926i
$841$		−	27.9994i		−	0.965496i
$842$	31.0396	+	14.2946i	1.06970	+	0.492624i
$843$	−32.9943	−	32.9943i	−1.13638	−	1.13638i
$844$	−14.6127	−	1.13842i	−0.502990	−	0.0391861i
$845$	−3.68325	−	13.9770i	−0.126708	−	0.480824i
$846$	5.06245	+	13.7057i	0.174051	+	0.471211i
$847$			0.132205i			0.00454261i
$848$	−0.984170	+	0.717421i	−0.0337965	+	0.0246363i
$849$	−54.4977			−1.87036
$850$	22.5419	−	26.6736i	0.773180	−	0.914895i
$851$	6.34285	+	6.34285i	0.217430	+	0.217430i
$852$	35.9462	+	2.80044i	1.23150	+	0.0959414i
$853$	26.2184	+	26.2184i	0.897701	+	0.897701i	0.995232	−	0.0975316i	$-0.0310947\pi$
$853$	26.2184	+	26.2184i	0.897701	+	0.897701i	−0.0975316	+	0.995232i	$0.531095\pi$
$854$	3.15984	−	6.86136i	0.108128	−	0.234791i
$855$	−16.0201	+	27.4846i	−0.547877	+	0.939953i
$856$	1.70194	+	6.00734i	0.0581710	+	0.205327i
$857$	31.6388			1.08076			0.540380	−	0.841421i	$-0.318280\pi$
$857$	31.6388			1.08076			0.540380	+	0.841421i	$0.318280\pi$
$858$	14.0491	−	30.5066i	0.479629	−	1.04148i
$859$	14.1168	−	14.1168i	0.481657	−	0.481657i	−0.424003	−	0.905661i	$-0.639376\pi$
$859$	14.1168	−	14.1168i	0.481657	−	0.481657i	0.905661	+	0.424003i	$0.139376\pi$
$860$	13.8423	−	2.51767i	0.472020	−	0.0858517i
$861$	22.3120	+	22.3120i	0.760392	+	0.760392i
$862$	12.0971	+	32.7509i	0.412030	+	1.11550i
$863$			1.50248i			0.0511449i	0.999673	+	0.0255724i	$0.00814085\pi$
$863$			1.50248i			0.0511449i	−0.999673	+	0.0255724i	$0.991859\pi$
$864$	−25.6332	−	17.0544i	−0.872061	−	0.580203i
$865$	−4.21478	+	7.23099i	−0.143307	+	0.245861i
$866$	46.1490	−	17.0460i	1.56821	−	0.579246i
$867$	−14.7221	+	14.7221i	−0.499987	+	0.499987i
$868$	−16.7837	+	14.3576i	−0.569676	+	0.487328i
$869$	−6.09891	+	6.09891i	−0.206891	+	0.206891i
$870$	5.11462	+	7.29476i	0.173402	+	0.247316i
$871$			18.2289i			0.617664i
$872$	7.77711	+	27.4509i	0.263366	+	0.929606i
$873$	18.6106			0.629874
$874$	2.48764	−	5.40171i	0.0841455	−	0.182716i
$875$	−8.72605	+	8.51218i	−0.294994	+	0.287764i
$876$	2.29408	−	29.4466i	0.0775096	−	0.994907i
$877$	−26.9903	+	26.9903i	−0.911398	+	0.911398i	−0.996382	−	0.0849842i	$-0.972916\pi$
$877$	−26.9903	+	26.9903i	−0.911398	+	0.911398i	0.0849842	+	0.996382i	$0.472916\pi$
$878$	1.49611	−	0.552618i	0.0504914	−	0.0186499i
$879$	91.8171			3.09691
$880$	−22.8790	−	18.6240i	−0.771250	−	0.627814i
$881$	−0.184858			−0.00622802			−0.00311401	−	0.999995i	$-0.500991\pi$
$881$	−0.184858			−0.00622802			−0.00311401	+	0.999995i	$0.500991\pi$
$882$	−38.0251	+	14.0453i	−1.28037	+	0.472929i
$883$	17.9054	−	17.9054i	0.602564	−	0.602564i	−0.338428	−	0.940992i	$-0.609895\pi$
$883$	17.9054	−	17.9054i	0.602564	−	0.602564i	0.940992	+	0.338428i	$0.109895\pi$
$884$	−25.1765	−	1.96141i	−0.846777	−	0.0659693i
$885$	−2.63455	−	9.99747i	−0.0885595	−	0.336061i
$886$	−1.00728	+	2.18723i	−0.0338402	+	0.0734813i
$887$	−12.7152			−0.426936			−0.213468	−	0.976950i	$-0.568476\pi$
$887$	−12.7152			−0.426936			−0.213468	+	0.976950i	$0.568476\pi$
$888$	42.7927	+	23.8984i	1.43603	+	0.801979i
$889$		−	2.17638i		−	0.0729934i
$890$	−17.8108	+	12.4878i	−0.597021	+	0.418593i
$891$	1.23996	−	1.23996i	0.0415403	−	0.0415403i
$892$	24.3244	+	28.4347i	0.814441	+	0.952063i
$893$	−4.27203	+	4.27203i	−0.142958	+	0.142958i
$894$	70.4302	−	26.0147i	2.35554	−	0.870061i
$895$	36.8136	+	21.4578i	1.23054	+	0.717255i
$896$	−7.61008	+	9.70847i	−0.254235	+	0.324337i
$897$		−	10.4975i		−	0.350501i
$898$	−8.91306	−	24.1305i	−0.297433	−	0.805246i
$899$	−7.16419	−	7.16419i	−0.238939	−	0.238939i
$900$	46.3708	+	16.8122i	1.54569	+	0.560405i
$901$	−1.06332	+	1.06332i	−0.0354243	+	0.0354243i
$902$	20.0487	−	43.5343i	0.667550	−	1.44954i
$903$	9.66099			0.321498
$904$	−12.7422	+	22.8162i	−0.423799	+	0.758857i
$905$	2.60449	−	4.46834i	0.0865763	−	0.148533i
$906$	−9.33225	+	20.2643i	−0.310043	+	0.673235i
$907$	0.807340	+	0.807340i	0.0268073	+	0.0268073i	0.720383	−	0.693576i	$-0.243966\pi$
$907$	0.807340	+	0.807340i	0.0268073	+	0.0268073i	−0.693576	+	0.720383i	$0.743966\pi$
$908$	1.90784	−	24.4888i	0.0633138	−	0.812691i
$909$	3.48883	+	3.48883i	0.115717	+	0.115717i
$910$	8.68176	+	1.52525i	0.287798	+	0.0505616i
$911$	−9.38640			−0.310985			−0.155493	−	0.987837i	$-0.549696\pi$
$911$	−9.38640			−0.310985			−0.155493	+	0.987837i	$0.549696\pi$
$912$	5.03260	−	32.1030i	0.166646	−	1.06304i
$913$		−	26.4876i		−	0.876612i
$914$	−2.08283	−	5.63889i	−0.0688939	−	0.186518i
$915$	29.8342	−	7.86198i	0.986290	−	0.259909i
$916$	0.929134	−	11.9263i	0.0306995	−	0.394056i
$917$	12.3091	+	12.3091i	0.406484	+	0.406484i
$918$	−34.5291	−	15.9016i	−1.13963	−	0.524830i
$919$		−	13.6402i		−	0.449949i	−0.974365	−	0.224974i	$-0.927770\pi$
$919$		−	13.6402i		−	0.449949i	0.974365	−	0.224974i	$-0.0722298\pi$
$920$	−8.93017	−	2.29603i	−0.294419	−	0.0756980i
$921$		−	93.0121i		−	3.06485i
$922$	21.5075	−	46.7019i	0.708311	−	1.53804i
$923$	11.5710	+	11.5710i	0.380864	+	0.380864i
$924$	−13.1682	−	15.3933i	−0.433201	−	0.506402i
$925$	−29.6487	−	8.20775i	−0.974842	−	0.269869i
$926$	−43.5511	+	16.0864i	−1.43118	+	0.528632i
$927$			63.7862i			2.09501i
$928$	−4.71114	−	3.13444i	−0.154651	−	0.102893i
$929$	18.0314			0.591590			0.295795	−	0.955252i	$-0.404416\pi$
$929$	18.0314			0.591590			0.295795	+	0.955252i	$0.404416\pi$
$930$	−88.8488	−	15.6094i	−2.91347	−	0.511851i
$931$	−11.8523	−	11.8523i	−0.388444	−	0.388444i
$932$	−29.9480	+	25.6189i	−0.980978	+	0.839177i
$933$	−35.4502	−	35.4502i	−1.16059	−	1.16059i
$934$	−31.1752	−	14.3570i	−1.02008	−	0.469777i
$935$	−31.4695	−	18.3428i	−1.02916	−	0.599875i
$936$	−9.72201	−	34.3158i	−0.317774	−	1.12165i
$937$	15.1318			0.494334			0.247167	−	0.968973i	$-0.420500\pi$
$937$	15.1318			0.494334			0.247167	+	0.968973i	$0.420500\pi$
$938$	9.98650	+	4.59906i	0.326071	+	0.150164i
$939$	−47.3804	+	47.3804i	−1.54620	+	1.54620i
$940$	7.70199	+	5.33145i	0.251211	+	0.173893i
$941$	−5.08494	−	5.08494i	−0.165764	−	0.165764i	0.619350	−	0.785115i	$-0.287396\pi$
$941$	−5.08494	−	5.08494i	−0.165764	−	0.165764i	−0.785115	+	0.619350i	$0.787396\pi$
$942$	−37.6194	+	13.8954i	−1.22571	+	0.452737i
$943$		−	14.9804i		−	0.487829i
$944$	3.86814	+	5.30638i	0.125897	+	0.172708i
$945$	11.4641	+	6.68216i	0.372927	+	0.217371i
$946$	−5.08457	−	13.7656i	−0.165314	−	0.447557i
$947$	−2.36920	+	2.36920i	−0.0769885	+	0.0769885i	−0.744552	−	0.667564i	$-0.767337\pi$
$947$	−2.36920	+	2.36920i	−0.0769885	+	0.0769885i	0.667564	+	0.744552i	$0.267337\pi$
$948$	−1.14412	+	14.6858i	−0.0371592	+	0.476972i
$949$	9.47879	−	9.47879i	0.307694	−	0.307694i
$950$	1.70623	+	20.3242i	0.0553574	+	0.659404i
$951$			54.5441i			1.76871i
$952$	−7.42642	+	13.2978i	−0.240692	+	0.430984i
$953$	35.0311			1.13477			0.567384	−	0.823454i	$-0.307956\pi$
$953$	35.0311			1.13477			0.567384	+	0.823454i	$0.307956\pi$
$954$	−1.92913	−	0.888419i	−0.0624580	−	0.0287636i
$955$	−10.9665	+	2.88991i	−0.354867	+	0.0935153i
$956$	1.45578	−	1.24535i	0.0470833	−	0.0402774i
$957$	6.57068	−	6.57068i	0.212400	−	0.212400i
$958$	−12.3830	−	33.5248i	−0.400077	−	1.08314i
$959$	−17.3830			−0.561327
$960$	−50.3673	+	1.23001i	−1.62560	+	0.0396985i
$961$	71.5884			2.30930
$962$	7.70771	+	20.8673i	0.248507	+	0.672787i
$963$	−7.69927	+	7.69927i	−0.248105	+	0.248105i
$964$	−15.8967	+	13.5988i	−0.512000	+	0.437989i
$965$	−12.5566	−	47.6493i	−0.404212	−	1.53389i
$966$	−5.75093	−	2.64846i	−0.185033	−	0.0852127i
$967$	−54.2039			−1.74308			−0.871541	−	0.490323i	$-0.836879\pi$
$967$	−54.2039			−1.74308			−0.871541	+	0.490323i	$0.836879\pi$
$968$	0.167220	−	0.299424i	0.00537464	−	0.00962386i
$969$		−	40.1221i		−	1.28891i
$970$	9.76952	−	6.84977i	0.313681	−	0.219933i
$971$	20.8327	−	20.8327i	0.668552	−	0.668552i	−0.288829	−	0.957381i	$-0.593266\pi$
$971$	20.8327	−	20.8327i	0.668552	−	0.668552i	0.957381	+	0.288829i	$0.0932659\pi$
$972$	−2.30381	+	29.5715i	−0.0738946	+	0.948505i
$973$	4.13926	−	4.13926i	0.132698	−	0.132698i
$974$	6.32383	+	17.1207i	0.202629	+	0.548581i
$975$	17.7425	+	31.3264i	0.568215	+	1.00325i
$976$	−15.8352	+	11.5432i	−0.506872	+	0.369490i
$977$		−	5.03891i		−	0.161209i	−0.996746	−	0.0806045i	$-0.974315\pi$
$977$		−	5.03891i		−	0.161209i	0.996746	−	0.0806045i	$-0.0256851\pi$
$978$	−2.88531	+	1.06574i	−0.0922619	+	0.0340786i
$979$	16.0429	+	16.0429i	0.512734	+	0.512734i
$980$	−14.7916	+	21.3684i	−0.472499	+	0.682588i
$981$	−35.1823	+	35.1823i	−1.12328	+	1.12328i
$982$	18.8763	+	8.69304i	0.602366	+	0.277406i
$983$	−40.6047			−1.29509			−0.647545	−	0.762027i	$-0.724204\pi$
$983$	−40.6047			−1.29509			−0.647545	+	0.762027i	$0.724204\pi$
$984$	−22.3120	−	78.7549i	−0.711281	−	2.51061i
$985$	−22.0476	−	12.8510i	−0.702494	−	0.409468i
$986$	−6.34611	−	2.92256i	−0.202101	−	0.0930731i
$987$	4.54821	+	4.54821i	0.144771	+	0.144771i
$988$	11.2070	−	9.58699i	0.356541	−	0.305003i
$989$	−3.24322	−	3.24322i	−0.103128	−	0.103128i
$990$	8.90193	−	50.6700i	0.282922	−	1.61040i
$991$	−18.5421			−0.589009			−0.294505	−	0.955650i	$-0.595155\pi$
$991$	−18.5421			−0.589009			−0.294505	+	0.955650i	$0.595155\pi$
$992$	56.1729	−	11.2889i	1.78349	−	0.358424i
$993$		−	7.80854i		−	0.247797i
$994$	9.25833	−	3.41973i	0.293656	−	0.108467i
$995$	−12.4538	−	47.2590i	−0.394812	−	1.49821i
$996$	−29.4058	−	34.3747i	−0.931758	−	1.08920i
$997$	11.0618	+	11.0618i	0.350330	+	0.350330i	0.860232	−	0.509902i	$-0.170318\pi$
$997$	11.0618	+	11.0618i	0.350330	+	0.350330i	−0.509902	+	0.860232i	$0.670318\pi$
$998$	16.6279	−	36.1062i	0.526346	−	1.14292i
$999$			33.4873i			1.05949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.q.c.29.6	yes	16
3.2	odd	2		720.2.bm.f.109.3		16
4.3	odd	2		320.2.q.c.209.1		16
5.2	odd	4		400.2.l.i.301.2		16
5.3	odd	4		400.2.l.i.301.7		16
5.4	even	2	inner	80.2.q.c.29.3	✓	16
8.3	odd	2		640.2.q.f.289.8		16
8.5	even	2		640.2.q.e.289.1		16
15.14	odd	2		720.2.bm.f.109.6		16
16.3	odd	4		640.2.q.f.609.1		16
16.5	even	4	inner	80.2.q.c.69.3	yes	16
16.11	odd	4		320.2.q.c.49.8		16
16.13	even	4		640.2.q.e.609.8		16
20.3	even	4		1600.2.l.h.401.1		16
20.7	even	4		1600.2.l.h.401.8		16
20.19	odd	2		320.2.q.c.209.8		16
40.19	odd	2		640.2.q.f.289.1		16
40.29	even	2		640.2.q.e.289.8		16
48.5	odd	4		720.2.bm.f.469.6		16
80.19	odd	4		640.2.q.f.609.8		16
80.27	even	4		1600.2.l.h.1201.8		16
80.29	even	4		640.2.q.e.609.1		16
80.37	odd	4		400.2.l.i.101.2		16
80.43	even	4		1600.2.l.h.1201.1		16
80.53	odd	4		400.2.l.i.101.7		16
80.59	odd	4		320.2.q.c.49.1		16
80.69	even	4	inner	80.2.q.c.69.6	yes	16
240.149	odd	4		720.2.bm.f.469.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.3	✓	16	5.4	even	2	inner
80.2.q.c.29.6	yes	16	1.1	even	1	trivial
80.2.q.c.69.3	yes	16	16.5	even	4	inner
80.2.q.c.69.6	yes	16	80.69	even	4	inner
320.2.q.c.49.1		16	80.59	odd	4
320.2.q.c.49.8		16	16.11	odd	4
320.2.q.c.209.1		16	4.3	odd	2
320.2.q.c.209.8		16	20.19	odd	2
400.2.l.i.101.2		16	80.37	odd	4
400.2.l.i.101.7		16	80.53	odd	4
400.2.l.i.301.2		16	5.2	odd	4
400.2.l.i.301.7		16	5.3	odd	4
640.2.q.e.289.1		16	8.5	even	2
640.2.q.e.289.8		16	40.29	even	2
640.2.q.e.609.1		16	80.29	even	4
640.2.q.e.609.8		16	16.13	even	4
640.2.q.f.289.1		16	40.19	odd	2
640.2.q.f.289.8		16	8.3	odd	2
640.2.q.f.609.1		16	16.3	odd	4
640.2.q.f.609.8		16	80.19	odd	4
720.2.bm.f.109.3		16	3.2	odd	2
720.2.bm.f.109.6		16	15.14	odd	2
720.2.bm.f.469.3		16	240.149	odd	4
720.2.bm.f.469.6		16	48.5	odd	4
1600.2.l.h.401.1		16	20.3	even	4
1600.2.l.h.401.8		16	20.7	even	4
1600.2.l.h.1201.1		16	80.43	even	4
1600.2.l.h.1201.8		16	80.27	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.490008 + 1.32661i) q^{2} +(1.99154 - 1.99154i) q^{3} +(-1.51978 + 1.30010i) q^{4} +(-2.16225 + 0.569800i) q^{5} +(3.61786 + 1.66612i) q^{6} +1.09033 q^{7} +(-2.46943 - 1.37910i) q^{8} -4.93244i q^{9} +(-1.81542 - 2.58926i) q^{10} +(-2.33225 + 2.33225i) q^{11} +(-0.437515 + 5.61590i) q^{12} +(-1.80775 + 1.80775i) q^{13} +(0.534268 + 1.44644i) q^{14} +(-3.17142 + 5.44098i) q^{15} +(0.619491 - 3.95174i) q^{16} -4.93886i q^{17} +(6.54342 - 2.41694i) q^{18} +(2.03957 + 2.03957i) q^{19} +(2.54536 - 3.67711i) q^{20} +(2.17142 - 2.17142i) q^{21} +(-4.23680 - 1.95116i) q^{22} -1.45791 q^{23} +(-7.66449 + 2.17142i) q^{24} +(4.35066 - 2.46410i) q^{25} +(-3.28398 - 1.51236i) q^{26} +(-3.84853 - 3.84853i) q^{27} +(-1.65706 + 1.41753i) q^{28} +(-0.707323 - 0.707323i) q^{29} +(-8.77208 - 1.54112i) q^{30} +10.1286 q^{31} +(5.54597 - 1.11456i) q^{32} +9.28951i q^{33} +(6.55193 - 2.42008i) q^{34} +(-2.35756 + 0.621268i) q^{35} +(6.41266 + 7.49625i) q^{36} +(-4.35066 - 4.35066i) q^{37} +(-1.70631 + 3.70512i) q^{38} +7.20039i q^{39} +(6.12534 + 1.57488i) q^{40} +10.2753i q^{41} +(3.94465 + 1.81662i) q^{42} +(2.22457 + 2.22457i) q^{43} +(0.512364 - 6.57666i) q^{44} +(2.81051 + 10.6652i) q^{45} +(-0.714386 - 1.93407i) q^{46} +2.09458i q^{47} +(-6.63629 - 9.10377i) q^{48} -5.81119 q^{49} +(5.40076 + 4.56419i) q^{50} +(-9.83592 - 9.83592i) q^{51} +(0.397138 - 5.09763i) q^{52} +(-0.215297 - 0.215297i) q^{53} +(3.21969 - 6.99131i) q^{54} +(3.71399 - 6.37182i) q^{55} +(-2.69248 - 1.50367i) q^{56} +8.12376 q^{57} +(0.591747 - 1.28493i) q^{58} +(-1.16082 + 1.16082i) q^{59} +(-2.25393 - 12.3923i) q^{60} +(-3.46410 - 3.46410i) q^{61} +(4.96309 + 13.4367i) q^{62} -5.37797i q^{63} +(4.19615 + 6.81119i) q^{64} +(2.87875 - 4.93886i) q^{65} +(-12.3236 + 4.55193i) q^{66} +(5.04189 - 5.04189i) q^{67} +(6.42100 + 7.50600i) q^{68} +(-2.90348 + 2.90348i) q^{69} +(-1.97940 - 2.82313i) q^{70} -6.40078i q^{71} +(-6.80234 + 12.1803i) q^{72} -5.24343 q^{73} +(3.63977 - 7.90348i) q^{74} +(3.75714 - 13.5718i) q^{75} +(-5.75135 - 0.448067i) q^{76} +(-2.54291 + 2.54291i) q^{77} +(-9.55211 + 3.52825i) q^{78} +2.61504 q^{79} +(0.912206 + 8.89763i) q^{80} -0.531659 q^{81} +(-13.6313 + 5.03497i) q^{82} +(-5.67856 + 5.67856i) q^{83} +(-0.477033 + 6.12316i) q^{84} +(2.81416 + 10.6790i) q^{85} +(-1.86108 + 4.04120i) q^{86} -2.81732 q^{87} +(8.97572 - 2.54291i) q^{88} -6.87875i q^{89} +(-12.7714 + 8.95446i) q^{90} +(-1.97103 + 1.97103i) q^{91} +(2.21570 - 1.89542i) q^{92} +(20.1715 - 20.1715i) q^{93} +(-2.77868 + 1.02636i) q^{94} +(-5.57221 - 3.24791i) q^{95} +(8.82531 - 13.2647i) q^{96} +3.77310i q^{97} +(-2.84753 - 7.70918i) q^{98} +(11.5037 + 11.5037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36}+ \cdots + 88 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more