LMFDB - Embedded newform 272.2.l.c.205.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,2,Mod(69,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	272.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17193093498$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.13
Character	$\chi$	$=$	272.205
Dual form			272.2.l.c.69.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.808880 - 1.16005i) q^{2} +(-0.0958959 - 0.0958959i) q^{3} +(-0.691426 - 1.87668i) q^{4} +(-0.447567 + 0.447567i) q^{5} +(-0.188812 + 0.0336756i) q^{6} -0.608862i q^{7} +(-2.73632 - 0.715922i) q^{8} -2.98161i q^{9} +(0.157171 + 0.881227i) q^{10} +(3.40456 - 3.40456i) q^{11} +(-0.113661 + 0.246271i) q^{12} +(-2.42497 - 2.42497i) q^{13} +(-0.706310 - 0.492497i) q^{14} +0.0858396 q^{15} +(-3.04386 + 2.59517i) q^{16} +1.00000 q^{17} +(-3.45881 - 2.41176i) q^{18} +(2.29923 + 2.29923i) q^{19} +(1.14940 + 0.530480i) q^{20} +(-0.0583874 + 0.0583874i) q^{21} +(-1.19558 - 6.70335i) q^{22} +8.44480i q^{23} +(0.193748 + 0.331056i) q^{24} +4.59937i q^{25} +(-4.77459 + 0.851573i) q^{26} +(-0.573612 + 0.573612i) q^{27} +(-1.14264 + 0.420983i) q^{28} +(-1.91539 - 1.91539i) q^{29} +(0.0694340 - 0.0995781i) q^{30} +8.60605 q^{31} +(0.548406 + 5.63021i) q^{32} -0.652968 q^{33} +(0.808880 - 1.16005i) q^{34} +(0.272506 + 0.272506i) q^{35} +(-5.59553 + 2.06156i) q^{36} +(2.39745 - 2.39745i) q^{37} +(4.52702 - 0.807417i) q^{38} +0.465089i q^{39} +(1.54511 - 0.904263i) q^{40} -4.54163i q^{41} +(0.0205038 + 0.114961i) q^{42} +(-2.24913 + 2.24913i) q^{43} +(-8.74329 - 4.03528i) q^{44} +(1.33447 + 1.33447i) q^{45} +(9.79638 + 6.83083i) q^{46} +5.03217 q^{47} +(0.540760 + 0.0430275i) q^{48} +6.62929 q^{49} +(5.33549 + 3.72034i) q^{50} +(-0.0958959 - 0.0958959i) q^{51} +(-2.87421 + 6.22758i) q^{52} +(-8.40199 + 8.40199i) q^{53} +(0.201434 + 1.12940i) q^{54} +3.04754i q^{55} +(-0.435898 + 1.66604i) q^{56} -0.440974i q^{57} +(-3.77126 + 0.672623i) q^{58} +(3.63251 - 3.63251i) q^{59} +(-0.0593517 - 0.161094i) q^{60} +(-4.10191 - 4.10191i) q^{61} +(6.96127 - 9.98344i) q^{62} -1.81539 q^{63} +(6.97491 + 3.91799i) q^{64} +2.17067 q^{65} +(-0.528173 + 0.757474i) q^{66} +(-6.40751 - 6.40751i) q^{67} +(-0.691426 - 1.87668i) q^{68} +(0.809822 - 0.809822i) q^{69} +(0.536546 - 0.0956957i) q^{70} +13.8271i q^{71} +(-2.13460 + 8.15864i) q^{72} -12.6966i q^{73} +(-0.841910 - 4.72042i) q^{74} +(0.441061 - 0.441061i) q^{75} +(2.72517 - 5.90467i) q^{76} +(-2.07291 - 2.07291i) q^{77} +(0.539526 + 0.376202i) q^{78} +2.82341 q^{79} +(0.200819 - 2.52384i) q^{80} -8.83481 q^{81} +(-5.26851 - 3.67364i) q^{82} +(10.0726 + 10.0726i) q^{83} +(0.149945 + 0.0692040i) q^{84} +(-0.447567 + 0.447567i) q^{85} +(0.789825 + 4.42839i) q^{86} +0.367355i q^{87} +(-11.7534 + 6.87858i) q^{88} +5.42631i q^{89} +(2.62747 - 0.468623i) q^{90} +(-1.47647 + 1.47647i) q^{91} +(15.8482 - 5.83895i) q^{92} +(-0.825286 - 0.825286i) q^{93} +(4.07042 - 5.83756i) q^{94} -2.05812 q^{95} +(0.487324 - 0.592504i) q^{96} +14.7965 q^{97} +(5.36230 - 7.69030i) q^{98} +(-10.1511 - 10.1511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	0.808880	−	1.16005i	0.571965	−	0.820278i
$2$	0.808880	−	1.16005i	0.571965	−	0.820278i
$3$	−0.0958959	−	0.0958959i	−0.0553655	−	0.0553655i	0.678882	−	0.734247i	$-0.262465\pi$
$3$	−0.0958959	−	0.0958959i	−0.0553655	−	0.0553655i	−0.734247	+	0.678882i	$0.762465\pi$
$4$	−0.691426	−	1.87668i	−0.345713	−	0.938340i
$5$	−0.447567	+	0.447567i	−0.200158	+	0.200158i	−0.800068	−	0.599910i	$-0.795203\pi$
$5$	−0.447567	+	0.447567i	−0.200158	+	0.200158i	0.599910	+	0.800068i	$0.295203\pi$
$6$	−0.188812	+	0.0336756i	−0.0770823	+	0.0137480i
$7$		−	0.608862i		−	0.230128i	−0.993358	−	0.115064i	$-0.963293\pi$
$7$		−	0.608862i		−	0.230128i	0.993358	−	0.115064i	$-0.0367074\pi$
$8$	−2.73632	−	0.715922i	−0.967436	−	0.253117i
$9$		−	2.98161i		−	0.993869i
$10$	0.157171	+	0.881227i	0.0497019	+	0.278668i
$11$	3.40456	−	3.40456i	1.02651	−	1.02651i	0.0268762	−	0.999639i	$-0.491444\pi$
$11$	3.40456	−	3.40456i	1.02651	−	1.02651i	0.999639	−	0.0268762i	$-0.00855598\pi$
$12$	−0.113661	+	0.246271i	−0.0328111	+	0.0710923i
$13$	−2.42497	−	2.42497i	−0.672566	−	0.672566i	0.285741	−	0.958307i	$-0.407760\pi$
$13$	−2.42497	−	2.42497i	−0.672566	−	0.672566i	−0.958307	+	0.285741i	$0.907760\pi$
$14$	−0.706310	−	0.492497i	−0.188769	−	0.131625i
$15$	0.0858396			0.0221637
$16$	−3.04386	+	2.59517i	−0.760965	+	0.648793i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−3.45881	−	2.41176i	−0.815249	−	0.568458i
$19$	2.29923	+	2.29923i	0.527480	+	0.527480i	0.919820	−	0.392340i	$-0.128334\pi$
$19$	2.29923	+	2.29923i	0.527480	+	0.527480i	−0.392340	+	0.919820i	$0.628334\pi$
$20$	1.14940	+	0.530480i	0.257013	+	0.118619i
$21$	−0.0583874	+	0.0583874i	−0.0127412	+	0.0127412i
$22$	−1.19558	−	6.70335i	−0.254898	−	1.42916i
$23$			8.44480i			1.76086i	0.474173	+	0.880432i	$0.342747\pi$
$23$			8.44480i			1.76086i	−0.474173	+	0.880432i	$0.657253\pi$
$24$	0.193748	+	0.331056i	0.0395487	+	0.0675766i
$25$			4.59937i			0.919874i
$26$	−4.77459	+	0.851573i	−0.936375	+	0.167007i
$27$	−0.573612	+	0.573612i	−0.110392	+	0.110392i
$28$	−1.14264	+	0.420983i	−0.215939	+	0.0795583i
$29$	−1.91539	−	1.91539i	−0.355678	−	0.355678i	0.506539	−	0.862217i	$-0.330925\pi$
$29$	−1.91539	−	1.91539i	−0.355678	−	0.355678i	−0.862217	+	0.506539i	$0.830925\pi$
$30$	0.0694340	−	0.0995781i	0.0126769	−	0.0181804i
$31$	8.60605			1.54569			0.772847	−	0.634593i	$-0.218832\pi$
$31$	8.60605			1.54569			0.772847	+	0.634593i	$0.218832\pi$
$32$	0.548406	+	5.63021i	0.0969454	+	0.995290i
$33$	−0.652968			−0.113667
$34$	0.808880	−	1.16005i	0.138722	−	0.198947i
$35$	0.272506	+	0.272506i	0.0460620	+	0.0460620i
$36$	−5.59553	+	2.06156i	−0.932588	+	0.343593i
$37$	2.39745	−	2.39745i	0.394139	−	0.394139i	−0.482021	−	0.876160i	$-0.660097\pi$
$37$	2.39745	−	2.39745i	0.394139	−	0.394139i	0.876160	+	0.482021i	$0.160097\pi$
$38$	4.52702	−	0.807417i	0.734380	−	0.130980i
$39$			0.465089i			0.0744739i
$40$	1.54511	−	0.904263i	0.244303	−	0.142977i
$41$		−	4.54163i		−	0.709284i	−0.935002	−	0.354642i	$-0.884603\pi$
$41$		−	4.54163i		−	0.709284i	0.935002	−	0.354642i	$-0.115397\pi$
$42$	0.0205038	+	0.114961i	0.00316381	+	0.0177388i
$43$	−2.24913	+	2.24913i	−0.342990	+	0.342990i	−0.857490	−	0.514500i	$-0.827977\pi$
$43$	−2.24913	+	2.24913i	−0.342990	+	0.342990i	0.514500	+	0.857490i	$0.327977\pi$
$44$	−8.74329	−	4.03528i	−1.31810	−	0.608341i
$45$	1.33447	+	1.33447i	0.198931	+	0.198931i
$46$	9.79638	+	6.83083i	1.44440	+	1.00715i
$47$	5.03217			0.734017			0.367008	−	0.930218i	$-0.380382\pi$
$47$	5.03217			0.734017			0.367008	+	0.930218i	$0.380382\pi$
$48$	0.540760	+	0.0430275i	0.0780520	+	0.00621049i
$49$	6.62929			0.947041
$50$	5.33549	+	3.72034i	0.754552	+	0.526135i
$51$	−0.0958959	−	0.0958959i	−0.0134281	−	0.0134281i
$52$	−2.87421	+	6.22758i	−0.398581	+	0.863610i
$53$	−8.40199	+	8.40199i	−1.15410	+	1.15410i	−0.168380	+	0.985722i	$0.553854\pi$
$53$	−8.40199	+	8.40199i	−1.15410	+	1.15410i	−0.985722	+	0.168380i	$0.946146\pi$
$54$	0.201434	+	1.12940i	0.0274118	+	0.153692i
$55$			3.04754i			0.410930i
$56$	−0.435898	+	1.66604i	−0.0582493	+	0.222634i
$57$		−	0.440974i		−	0.0584084i
$58$	−3.77126	+	0.672623i	−0.495190	+	0.0883197i
$59$	3.63251	−	3.63251i	0.472912	−	0.472912i	−0.429944	−	0.902856i	$-0.641467\pi$
$59$	3.63251	−	3.63251i	0.472912	−	0.472912i	0.902856	+	0.429944i	$0.141467\pi$
$60$	−0.0593517	−	0.161094i	−0.00766228	−	0.0207971i
$61$	−4.10191	−	4.10191i	−0.525196	−	0.525196i	0.393940	−	0.919136i	$-0.371112\pi$
$61$	−4.10191	−	4.10191i	−0.525196	−	0.525196i	−0.919136	+	0.393940i	$0.871112\pi$
$62$	6.96127	−	9.98344i	0.884082	−	1.26790i
$63$	−1.81539			−0.228717
$64$	6.97491	+	3.91799i	0.871864	+	0.489748i
$65$	2.17067			0.269239
$66$	−0.528173	+	0.757474i	−0.0650136	+	0.0932387i
$67$	−6.40751	−	6.40751i	−0.782802	−	0.782802i	0.197501	−	0.980303i	$-0.436717\pi$
$67$	−6.40751	−	6.40751i	−0.782802	−	0.782802i	−0.980303	+	0.197501i	$0.936717\pi$
$68$	−0.691426	−	1.87668i	−0.0838477	−	0.227581i
$69$	0.809822	−	0.809822i	0.0974912	−	0.0974912i
$70$	0.536546	−	0.0956957i	0.0641295	−	0.0114378i
$71$			13.8271i			1.64098i	0.571660	+	0.820490i	$0.306299\pi$
$71$			13.8271i			1.64098i	−0.571660	+	0.820490i	$0.693701\pi$
$72$	−2.13460	+	8.15864i	−0.251565	+	0.961505i
$73$		−	12.6966i		−	1.48602i	−0.669279	−	0.743011i	$-0.733397\pi$
$73$		−	12.6966i		−	1.48602i	0.669279	−	0.743011i	$-0.266603\pi$
$74$	−0.841910	−	4.72042i	−0.0978701	−	0.548737i
$75$	0.441061	−	0.441061i	0.0509293	−	0.0509293i
$76$	2.72517	−	5.90467i	0.312599	−	0.677312i
$77$	−2.07291	−	2.07291i	−0.236230	−	0.236230i
$78$	0.539526	+	0.376202i	0.0610893	+	0.0425964i
$79$	2.82341			0.317659			0.158829	−	0.987306i	$-0.449228\pi$
$79$	2.82341			0.317659			0.158829	+	0.987306i	$0.449228\pi$
$80$	0.200819	−	2.52384i	0.0224522	−	0.282174i
$81$	−8.83481			−0.981646
$82$	−5.26851	−	3.67364i	−0.581810	−	0.405685i
$83$	10.0726	+	10.0726i	1.10561	+	1.10561i	0.993720	+	0.111893i	$0.0356915\pi$
$83$	10.0726	+	10.0726i	1.10561	+	1.10561i	0.111893	+	0.993720i	$0.464308\pi$
$84$	0.149945	+	0.0692040i	0.0163604	+	0.00755077i
$85$	−0.447567	+	0.447567i	−0.0485454	+	0.0485454i
$86$	0.789825	+	4.42839i	0.0851690	+	0.477525i
$87$			0.367355i			0.0393846i
$88$	−11.7534	+	6.87858i	−1.25292	+	0.733259i
$89$			5.42631i			0.575188i	0.957752	+	0.287594i	$0.0928553\pi$
$89$			5.42631i			0.575188i	−0.957752	+	0.287594i	$0.907145\pi$
$90$	2.62747	−	0.468623i	0.276960	−	0.0493972i
$91$	−1.47647	+	1.47647i	−0.154776	+	0.154776i
$92$	15.8482	−	5.83895i	1.65229	−	0.608753i
$93$	−0.825286	−	0.825286i	−0.0855781	−	0.0855781i
$94$	4.07042	−	5.83756i	0.419832	−	0.602098i
$95$	−2.05812			−0.211158
$96$	0.487324	−	0.592504i	0.0497373	−	0.0604722i
$97$	14.7965			1.50235			0.751177	−	0.660101i	$-0.229486\pi$
$97$	14.7965			1.50235			0.751177	+	0.660101i	$0.229486\pi$
$98$	5.36230	−	7.69030i	0.541674	−	0.776837i
$99$	−10.1511	−	10.1511i	−1.02022	−	1.02022i
$100$	8.63155	−	3.18012i	0.863155	−	0.318012i
$101$	−9.93863	+	9.93863i	−0.988931	+	0.988931i	−0.999939	−	0.0110083i	$-0.996496\pi$
$101$	−9.93863	+	9.93863i	−0.988931	+	0.988931i	0.0110083	+	0.999939i	$0.496496\pi$
$102$	−0.188812	+	0.0336756i	−0.0186952	+	0.00333438i
$103$		−	3.07006i		−	0.302502i	−0.988495	−	0.151251i	$-0.951670\pi$
$103$		−	3.07006i		−	0.302502i	0.988495	−	0.151251i	$-0.0483302\pi$
$104$	4.89941	+	8.37159i	0.480426	+	0.820902i
$105$		−	0.0522645i		−	0.00510049i
$106$	2.95052	+	16.5429i	0.286579	+	1.60679i
$107$	2.77668	−	2.77668i	0.268432	−	0.268432i	−0.560036	−	0.828468i	$-0.689213\pi$
$107$	2.77668	−	2.77668i	0.268432	−	0.268432i	0.828468	+	0.560036i	$0.189213\pi$
$108$	1.47310	+	0.679876i	0.141749	+	0.0654211i
$109$	−5.94317	−	5.94317i	−0.569253	−	0.569253i	0.362666	−	0.931919i	$-0.381866\pi$
$109$	−5.94317	−	5.94317i	−0.569253	−	0.569253i	−0.931919	+	0.362666i	$0.881866\pi$
$110$	3.53529	+	2.46509i	0.337077	+	0.235037i
$111$	−0.459812			−0.0436434
$112$	1.58010	+	1.85329i	0.149306	+	0.175120i
$113$	−6.66004			−0.626524			−0.313262	−	0.949667i	$-0.601422\pi$
$113$	−6.66004			−0.626524			−0.313262	+	0.949667i	$0.601422\pi$
$114$	−0.511551	−	0.356695i	−0.0479111	−	0.0334075i
$115$	−3.77961	−	3.77961i	−0.352451	−	0.352451i
$116$	−2.27022	+	4.91891i	−0.210785	+	0.456710i
$117$	−7.23031	+	7.23031i	−0.668442	+	0.668442i
$118$	−1.27562	−	7.15215i	−0.117431	−	0.658409i
$119$		−	0.608862i		−	0.0558143i
$120$	−0.234885	−	0.0614545i	−0.0214420	−	0.00561000i
$121$		−	12.1821i		−	1.10747i
$122$	−8.07638	+	1.44046i	−0.731201	+	0.130413i
$123$	−0.435524	+	0.435524i	−0.0392699	+	0.0392699i
$124$	−5.95045	−	16.1508i	−0.534366	−	1.45039i
$125$	−4.29636	−	4.29636i	−0.384278	−	0.384278i
$126$	−1.46843	+	2.10594i	−0.130818	+	0.187612i
$127$	−10.6582			−0.945760			−0.472880	−	0.881127i	$-0.656786\pi$
$127$	−10.6582			−0.945760			−0.472880	+	0.881127i	$0.656786\pi$
$128$	10.1869	−	4.92205i	0.900405	−	0.435052i
$129$	0.431366			0.0379796
$130$	1.75581	−	2.51808i	0.153995	−	0.220851i
$131$	−5.48630	−	5.48630i	−0.479340	−	0.479340i	0.425580	−	0.904921i	$-0.360070\pi$
$131$	−5.48630	−	5.48630i	−0.479340	−	0.479340i	−0.904921	+	0.425580i	$0.860070\pi$
$132$	0.451479	+	1.22541i	0.0392962	+	0.106658i
$133$	1.39992	−	1.39992i	0.121388	−	0.121388i
$134$	−12.6159	+	2.25012i	−1.08985	+	0.194380i
$135$		−	0.513459i		−	0.0441915i
$136$	−2.73632	−	0.715922i	−0.234638	−	0.0613898i
$137$			20.3339i			1.73724i	0.495476	+	0.868621i	$0.334993\pi$
$137$			20.3339i			1.73724i	−0.495476	+	0.868621i	$0.665007\pi$
$138$	−0.284384	−	1.59448i	−0.0242084	−	0.135731i
$139$	3.16393	−	3.16393i	0.268361	−	0.268361i	−0.560078	−	0.828440i	$-0.689229\pi$
$139$	3.16393	−	3.16393i	0.268361	−	0.268361i	0.828440	+	0.560078i	$0.189229\pi$
$140$	0.322990	−	0.699825i	0.0272976	−	0.0591460i
$141$	−0.482564	−	0.482564i	−0.0406392	−	0.0406392i
$142$	16.0402	+	11.1845i	1.34606	+	0.938583i
$143$	−16.5119			−1.38080
$144$	7.73778	+	9.07560i	0.644815	+	0.756300i
$145$	1.71452			0.142384
$146$	−14.7286	−	10.2700i	−1.21895	−	0.849952i
$147$	−0.635722	−	0.635722i	−0.0524334	−	0.0524334i
$148$	−6.15692	−	2.84159i	−0.506095	−	0.233578i
$149$	1.44394	−	1.44394i	0.118292	−	0.118292i	−0.645483	−	0.763775i	$-0.723344\pi$
$149$	1.44394	−	1.44394i	0.118292	−	0.118292i	0.763775	+	0.645483i	$0.223344\pi$
$150$	−0.154887	−	0.868417i	−0.0126464	−	0.0709060i
$151$		−	2.89635i		−	0.235701i	−0.993031	−	0.117851i	$-0.962400\pi$
$151$		−	2.89635i		−	0.235701i	0.993031	−	0.117851i	$-0.0376004\pi$
$152$	−4.64536	−	7.93751i	−0.376789	−	0.643817i
$153$		−	2.98161i		−	0.241049i
$154$	−4.08141	+	0.727941i	−0.328890	+	0.0586592i
$155$	−3.85178	+	3.85178i	−0.309383	+	0.309383i
$156$	0.872824	−	0.321575i	0.0698819	−	0.0257466i
$157$	−0.649273	−	0.649273i	−0.0518177	−	0.0518177i	0.680723	−	0.732541i	$-0.261666\pi$
$157$	−0.649273	−	0.649273i	−0.0518177	−	0.0518177i	−0.732541	+	0.680723i	$0.761666\pi$
$158$	2.28380	−	3.27530i	0.181690	−	0.260569i
$159$	1.61143			0.127795
$160$	−2.76534	−	2.27445i	−0.218619	−	0.179811i
$161$	5.14172			0.405225
$162$	−7.14630	+	10.2488i	−0.561467	+	0.805222i
$163$	1.05218	+	1.05218i	0.0824134	+	0.0824134i	0.747112	−	0.664698i	$-0.231440\pi$
$163$	1.05218	+	1.05218i	0.0824134	+	0.0824134i	−0.664698	+	0.747112i	$0.731440\pi$
$164$	−8.52319	+	3.14020i	−0.665549	+	0.245209i
$165$	0.292247	−	0.292247i	0.0227514	−	0.0227514i
$166$	19.8323	−	3.53719i	1.53928	−	0.274539i
$167$		−	1.65720i		−	0.128238i	−0.997942	−	0.0641188i	$-0.979576\pi$
$167$		−	1.65720i		−	0.128238i	0.997942	−	0.0641188i	$-0.0204237\pi$
$168$	0.201568	−	0.117966i	0.0155513	−	0.00910127i
$169$		−	1.23905i		−	0.0953112i
$170$	0.157171	+	0.881227i	0.0120545	+	0.0675870i
$171$	6.85540	−	6.85540i	0.524246	−	0.524246i
$172$	5.77602	+	2.66580i	0.440417	+	0.203265i
$173$	6.75435	+	6.75435i	0.513524	+	0.513524i	0.915604	−	0.402080i	$-0.131713\pi$
$173$	6.75435	+	6.75435i	0.513524	+	0.513524i	−0.402080	+	0.915604i	$0.631713\pi$
$174$	0.426150	+	0.297146i	0.0323064	+	0.0225266i
$175$	2.80038			0.211689
$176$	−1.52759	+	19.1984i	−0.115147	+	1.44714i
$177$	−0.696686			−0.0523661
$178$	6.29478	+	4.38923i	0.471814	+	0.328987i
$179$	−17.8532	−	17.8532i	−1.33441	−	1.33441i	−0.901375	−	0.433039i	$-0.857441\pi$
$179$	−17.8532	−	17.8532i	−1.33441	−	1.33441i	−0.433039	−	0.901375i	$-0.642559\pi$
$180$	1.58168	−	3.42706i	0.117892	−	0.255438i
$181$	8.39506	−	8.39506i	0.624000	−	0.624000i	−0.322552	−	0.946552i	$-0.604541\pi$
$181$	8.39506	−	8.39506i	0.624000	−	0.624000i	0.946552	+	0.322552i	$0.104541\pi$
$182$	0.518491	+	2.90707i	0.0384331	+	0.215486i
$183$			0.786714i			0.0581556i
$184$	6.04582	−	23.1077i	0.445704	−	1.70352i
$185$			2.14604i			0.157780i
$186$	−1.62493	+	0.289814i	−0.119146	+	0.0212502i
$187$	3.40456	−	3.40456i	0.248966	−	0.248966i
$188$	−3.47937	−	9.44377i	−0.253759	−	0.688758i
$189$	0.349251	+	0.349251i	0.0254042	+	0.0254042i
$190$	−1.66477	+	2.38752i	−0.120775	+	0.173209i
$191$	−10.9854			−0.794877			−0.397438	−	0.917629i	$-0.630101\pi$
$191$	−10.9854			−0.794877			−0.397438	+	0.917629i	$0.630101\pi$
$192$	−0.293147	−	1.04458i	−0.0211560	−	0.0753864i
$193$	−15.6527			−1.12671			−0.563355	−	0.826215i	$-0.690490\pi$
$193$	−15.6527			−1.12671			−0.563355	+	0.826215i	$0.690490\pi$
$194$	11.9686	−	17.1646i	0.859293	−	1.23235i
$195$	−0.208158	−	0.208158i	−0.0149065	−	0.0149065i
$196$	−4.58366	−	12.4411i	−0.327404	−	0.888647i
$197$	7.10694	−	7.10694i	0.506349	−	0.506349i	−0.407055	−	0.913404i	$-0.633444\pi$
$197$	7.10694	−	7.10694i	0.506349	−	0.506349i	0.913404	+	0.407055i	$0.133444\pi$
$198$	−19.9867	+	3.56474i	−1.42040	+	0.253335i
$199$			19.5859i			1.38841i	0.719778	+	0.694205i	$0.244244\pi$
$199$			19.5859i			1.38841i	−0.719778	+	0.694205i	$0.755756\pi$
$200$	3.29279	−	12.5854i	0.232835	−	0.889919i
$201$			1.22891i			0.0866805i
$202$	3.49014	+	19.5685i	0.245565	+	1.37683i
$203$	−1.16621	+	1.16621i	−0.0818516	+	0.0818516i
$204$	−0.113661	+	0.246271i	−0.00795787	+	0.0172424i
$205$	2.03268	+	2.03268i	0.141969	+	0.141969i
$206$	−3.56142	−	2.48331i	−0.248136	−	0.173020i
$207$	25.1791			1.75007
$208$	13.6745	+	1.08806i	0.948155	+	0.0754434i
$209$	15.6558			1.08293
$210$	−0.0606294	−	0.0422757i	−0.00418382	−	0.00291730i
$211$	−0.654065	−	0.654065i	−0.0450277	−	0.0450277i	0.684234	−	0.729262i	$-0.260137\pi$
$211$	−0.654065	−	0.654065i	−0.0450277	−	0.0450277i	−0.729262	+	0.684234i	$0.760137\pi$
$212$	21.5772	+	9.95850i	1.48193	+	0.683953i
$213$	1.32597	−	1.32597i	0.0908538	−	0.0908538i
$214$	−0.975083	−	5.46709i	−0.0666553	−	0.373722i
$215$		−	2.01327i		−	0.137304i
$216$	1.98025	−	1.15893i	0.134739	−	0.0788549i
$217$		−	5.23990i		−	0.355708i
$218$	−11.7017	+	2.08706i	−0.792538	+	0.141353i
$219$	−1.21755	+	1.21755i	−0.0822744	+	0.0822744i
$220$	5.71926	−	2.10715i	0.385592	−	0.142064i
$221$	−2.42497	−	2.42497i	−0.163121	−	0.163121i
$222$	−0.371933	+	0.533404i	−0.0249625	+	0.0357998i
$223$	11.0892			0.742591			0.371295	−	0.928515i	$-0.378914\pi$
$223$	11.0892			0.742591			0.371295	+	0.928515i	$0.378914\pi$
$224$	3.42802	−	0.333904i	0.229044	−	0.0223099i
$225$	13.7135			0.914234
$226$	−5.38717	+	7.72597i	−0.358349	+	0.513924i
$227$	−2.69606	−	2.69606i	−0.178944	−	0.178944i	0.611952	−	0.790895i	$-0.290385\pi$
$227$	−2.69606	−	2.69606i	−0.178944	−	0.178944i	−0.790895	+	0.611952i	$0.790385\pi$
$228$	−0.827567	+	0.304901i	−0.0548070	+	0.0201925i
$229$	−2.65416	+	2.65416i	−0.175392	+	0.175392i	−0.789343	−	0.613952i	$-0.789579\pi$
$229$	−2.65416	+	2.65416i	−0.175392	+	0.175392i	0.613952	+	0.789343i	$0.289579\pi$
$230$	−7.44179	+	1.32728i	−0.490697	+	0.0875183i
$231$			0.397568i			0.0261580i
$232$	3.86984	+	6.61238i	0.254068	+	0.434124i
$233$			15.9083i			1.04219i	0.853499	+	0.521095i	$0.174476\pi$
$233$			15.9083i			1.04219i	−0.853499	+	0.521095i	$0.825524\pi$
$234$	2.53906	+	14.2360i	0.165983	+	0.930634i
$235$	−2.25223	+	2.25223i	−0.146919	+	0.146919i
$236$	−9.32867	−	4.30545i	−0.607245	−	0.280261i
$237$	−0.270754	−	0.270754i	−0.0175874	−	0.0175874i
$238$	−0.706310	−	0.492497i	−0.0457833	−	0.0319238i
$239$	8.12977			0.525871			0.262936	−	0.964813i	$-0.415309\pi$
$239$	8.12977			0.525871			0.262936	+	0.964813i	$0.415309\pi$
$240$	−0.261284	+	0.222768i	−0.0168658	+	0.0143796i
$241$	20.7325			1.33550			0.667748	−	0.744387i	$-0.267258\pi$
$241$	20.7325			1.33550			0.667748	+	0.744387i	$0.267258\pi$
$242$	−14.1319	−	9.85388i	−0.908430	−	0.633431i
$243$	2.56806	+	2.56806i	0.164741	+	0.164741i
$244$	−4.86181	+	10.5342i	−0.311246	+	0.674380i
$245$	−2.96705	+	2.96705i	−0.189558	+	0.189558i
$246$	0.152942	+	0.857516i	0.00975125	+	0.0546732i
$247$		−	11.1511i		−	0.709529i
$248$	−23.5489	−	6.16127i	−1.49536	−	0.391241i
$249$		−	1.93185i		−	0.122426i
$250$	−8.45922	+	1.50874i	−0.535008	+	0.0954214i
$251$	−7.90356	+	7.90356i	−0.498868	+	0.498868i	−0.911085	−	0.412217i	$-0.864754\pi$
$251$	−7.90356	+	7.90356i	−0.498868	+	0.498868i	0.412217	+	0.911085i	$0.364754\pi$
$252$	1.25521	+	3.40690i	0.0790706	+	0.214615i
$253$	28.7509	+	28.7509i	1.80755	+	1.80755i
$254$	−8.62118	+	12.3640i	−0.540941	+	0.775786i
$255$	0.0858396			0.00537549
$256$	2.53018	−	15.7987i	0.158136	−	0.987417i
$257$	−1.95377			−0.121873			−0.0609364	−	0.998142i	$-0.519409\pi$
$257$	−1.95377			−0.121873			−0.0609364	+	0.998142i	$0.519409\pi$
$258$	0.348923	−	0.500405i	0.0217230	−	0.0311539i
$259$	−1.45972	−	1.45972i	−0.0907025	−	0.0907025i
$260$	−1.50086	−	4.07366i	−0.0930792	−	0.252637i
$261$	−5.71093	+	5.71093i	−0.353498	+	0.353498i
$262$	−10.8021	+	1.92662i	−0.667358	+	0.119027i
$263$		−	1.40161i		−	0.0864269i	−0.999066	−	0.0432134i	$-0.986240\pi$
$263$		−	1.40161i		−	0.0864269i	0.999066	−	0.0432134i	$-0.0137595\pi$
$264$	1.78673	+	0.467474i	0.109966	+	0.0287710i
$265$		−	7.52090i		−	0.462005i
$266$	−0.491606	−	2.75633i	−0.0301423	−	0.169002i
$267$	0.520361	−	0.520361i	0.0318456	−	0.0318456i
$268$	−7.59453	+	16.4552i	−0.463910	+	1.00516i
$269$	17.5625	+	17.5625i	1.07080	+	1.07080i	0.997295	+	0.0735097i	$0.0234200\pi$
$269$	17.5625	+	17.5625i	1.07080	+	1.07080i	0.0735097	+	0.997295i	$0.476580\pi$
$270$	−0.595637	−	0.415327i	−0.0362493	−	0.0252760i
$271$	−26.3658			−1.60161			−0.800805	−	0.598925i	$-0.795595\pi$
$271$	−26.3658			−1.60161			−0.800805	+	0.598925i	$0.795595\pi$
$272$	−3.04386	+	2.59517i	−0.184561	+	0.157355i
$273$	0.283175			0.0171386
$274$	23.5883	+	16.4477i	1.42502	+	0.993641i
$275$	15.6588	+	15.6588i	0.944264	+	0.944264i
$276$	−2.07971	−	0.959846i	−0.125184	−	0.0577759i
$277$	−5.33899	+	5.33899i	−0.320789	+	0.320789i	−0.849070	−	0.528281i	$-0.822837\pi$
$277$	−5.33899	+	5.33899i	−0.320789	+	0.320789i	0.528281	+	0.849070i	$0.322837\pi$
$278$	−1.11107	−	6.22956i	−0.0666378	−	0.373624i
$279$		−	25.6599i		−	1.53622i
$280$	−0.550572	−	0.940759i	−0.0329030	−	0.0562211i
$281$			10.8569i			0.647670i	0.946114	+	0.323835i	$0.104972\pi$
$281$			10.8569i			0.647670i	−0.946114	+	0.323835i	$0.895028\pi$
$282$	−0.950135	+	0.169461i	−0.0565797	+	0.0100913i
$283$	−9.41355	+	9.41355i	−0.559577	+	0.559577i	−0.929187	−	0.369610i	$-0.879491\pi$
$283$	−9.41355	+	9.41355i	−0.559577	+	0.559577i	0.369610	+	0.929187i	$0.379491\pi$
$284$	25.9491	−	9.56045i	1.53980	−	0.567308i
$285$	0.197365	+	0.197365i	0.0116909	+	0.0116909i
$286$	−13.3562	+	19.1546i	−0.789767	+	1.13264i
$287$	−2.76523			−0.163226
$288$	16.7871	−	1.63513i	0.989188	−	0.0963510i
$289$	1.00000			0.0588235
$290$	1.38685	−	1.98893i	0.0814384	−	0.116794i
$291$	−1.41892	−	1.41892i	−0.0831786	−	0.0831786i
$292$	−23.8274	+	8.77874i	−1.39439	+	0.513737i
$293$	−16.3133	+	16.3133i	−0.953035	+	0.953035i	−0.998946	−	0.0459108i	$-0.985381\pi$
$293$	−16.3133	+	16.3133i	−0.953035	+	0.953035i	0.0459108	+	0.998946i	$0.485381\pi$
$294$	−1.25169	+	0.223245i	−0.0730001	+	0.0130199i
$295$			3.25158i			0.189314i
$296$	−8.27659	+	4.84381i	−0.481067	+	0.281541i
$297$			3.90580i			0.226637i
$298$	−0.507068	−	2.84302i	−0.0293736	−	0.164692i
$299$	20.4784	−	20.4784i	1.18430	−	1.18430i
$300$	−1.13269	−	0.522769i	−0.0653959	−	0.0301821i
$301$	1.36941	+	1.36941i	0.0789317	+	0.0789317i
$302$	−3.35990	−	2.34280i	−0.193341	−	0.134813i
$303$	1.90615			0.109505
$304$	−12.9654	−	1.03164i	−0.743619	−	0.0591687i
$305$	3.67176			0.210244
$306$	−3.45881	−	2.41176i	−0.197727	−	0.137871i
$307$	18.3821	+	18.3821i	1.04912	+	1.04912i	0.998730	+	0.0503912i	$0.0160468\pi$
$307$	18.3821	+	18.3821i	1.04912	+	1.04912i	0.0503912	+	0.998730i	$0.483953\pi$
$308$	−2.45693	+	5.32346i	−0.139996	+	0.303332i
$309$	−0.294406	+	0.294406i	−0.0167482	+	0.0167482i
$310$	1.35262	+	7.58389i	0.0768239	+	0.430736i
$311$		−	15.2732i		−	0.866063i	−0.901379	−	0.433032i	$-0.857444\pi$
$311$		−	15.2732i		−	0.866063i	0.901379	−	0.433032i	$-0.142556\pi$
$312$	0.332968	−	1.27263i	0.0188506	−	0.0720487i
$313$			16.6333i			0.940172i	0.882621	+	0.470086i	$0.155777\pi$
$313$			16.6333i			0.940172i	−0.882621	+	0.470086i	$0.844223\pi$
$314$	−1.27837	+	0.228004i	−0.0721428	+	0.0128670i
$315$	0.812507	−	0.812507i	0.0457796	−	0.0457796i
$316$	−1.95218	−	5.29865i	−0.109819	−	0.298072i
$317$	−15.2096	−	15.2096i	−0.854257	−	0.854257i	0.136397	−	0.990654i	$-0.456448\pi$
$317$	−15.2096	−	15.2096i	−0.854257	−	0.854257i	−0.990654	+	0.136397i	$0.956448\pi$
$318$	1.30346	−	1.86934i	0.0730942	−	0.104827i
$319$	−13.0421			−0.730218
$320$	−4.87530	+	1.36818i	−0.272537	+	0.0764834i
$321$	−0.532545			−0.0297238
$322$	4.15904	−	5.96465i	0.231774	−	0.332397i
$323$	2.29923	+	2.29923i	0.127933	+	0.127933i
$324$	6.10862	+	16.5801i	0.339368	+	0.921118i
$325$	11.1533	−	11.1533i	0.618675	−	0.618675i
$326$	2.07167	−	0.369494i	0.114739	−	0.0204644i
$327$			1.13985i			0.0630340i
$328$	−3.25146	+	12.4274i	−0.179532	+	0.686186i
$329$		−	3.06390i		−	0.168918i
$330$	−0.102628	−	0.575413i	−0.00564947	−	0.0316754i
$331$	−2.34497	+	2.34497i	−0.128891	+	0.128891i	−0.768609	−	0.639718i	$-0.779051\pi$
$331$	−2.34497	+	2.34497i	−0.128891	+	0.128891i	0.639718	+	0.768609i	$0.279051\pi$
$332$	11.9386	−	25.8676i	0.655217	−	1.41967i
$333$	−7.14827	−	7.14827i	−0.391723	−	0.391723i
$334$	−1.92243	−	1.34047i	−0.105191	−	0.0733474i
$335$	5.73557			0.313368
$336$	0.0261979	−	0.329249i	0.00142921	−	0.0179620i
$337$	10.6127			0.578110			0.289055	−	0.957312i	$-0.406659\pi$
$337$	10.6127			0.578110			0.289055	+	0.957312i	$0.406659\pi$
$338$	−1.43735	−	1.00224i	−0.0781817	−	0.0545146i
$339$	0.638671	+	0.638671i	0.0346878	+	0.0346878i
$340$	1.14940	+	0.530480i	0.0623349	+	0.0287693i
$341$	29.2999	−	29.2999i	1.58668	−	1.58668i
$342$	−2.40740	−	13.4978i	−0.130177	−	0.729878i
$343$		−	8.29836i		−	0.448069i
$344$	7.76456	−	4.54415i	0.418637	−	0.245004i
$345$			0.724899i			0.0390272i
$346$	13.2988	−	2.37192i	0.714950	−	0.127515i
$347$	−4.33651	+	4.33651i	−0.232796	+	0.232796i	−0.813859	−	0.581063i	$-0.802637\pi$
$347$	−4.33651	+	4.33651i	−0.232796	+	0.232796i	0.581063	+	0.813859i	$0.302637\pi$
$348$	0.689409	−	0.253999i	0.0369562	−	0.0136158i
$349$	17.9297	+	17.9297i	0.959754	+	0.959754i	0.999221	−	0.0394669i	$-0.0125660\pi$
$349$	17.9297	+	17.9297i	0.959754	+	0.959754i	−0.0394669	+	0.999221i	$0.512566\pi$
$350$	2.26517	−	3.24858i	0.121079	−	0.173644i
$351$	2.78198			0.148491
$352$	21.0355	+	17.3013i	1.12120	+	0.922164i
$353$	−29.3573			−1.56253			−0.781265	−	0.624199i	$-0.785425\pi$
$353$	−29.3573			−1.56253			−0.781265	+	0.624199i	$0.785425\pi$
$354$	−0.563535	+	0.808189i	−0.0299516	+	0.0429548i
$355$	−6.18857	−	6.18857i	−0.328455	−	0.328455i
$356$	10.1835	−	3.75189i	0.539722	−	0.198850i
$357$	−0.0583874	+	0.0583874i	−0.00309019	+	0.00309019i
$358$	−35.1518	+	6.26950i	−1.85783	+	0.331353i
$359$			10.3083i			0.544049i	0.962290	+	0.272025i	$0.0876932\pi$
$359$			10.3083i			0.544049i	−0.962290	+	0.272025i	$0.912307\pi$
$360$	−2.69616	−	4.60691i	−0.142100	−	0.242805i
$361$		−	8.42708i		−	0.443530i
$362$	−2.94808	−	16.5293i	−0.154948	−	0.868760i
$363$	−1.16822	+	1.16822i	−0.0613154	+	0.0613154i
$364$	3.79174	+	1.75000i	0.198741	+	0.0917247i
$365$	5.68256	+	5.68256i	0.297439	+	0.297439i
$366$	0.912626	+	0.636357i	0.0477037	+	0.0332629i
$367$	3.75481			0.196000			0.0979998	−	0.995186i	$-0.468756\pi$
$367$	3.75481			0.196000			0.0979998	+	0.995186i	$0.468756\pi$
$368$	−21.9157	−	25.7048i	−1.14244	−	1.33996i
$369$	−13.5414			−0.704935
$370$	2.48951	+	1.73589i	0.129424	+	0.0902446i
$371$	5.11566	+	5.11566i	0.265592	+	0.265592i
$372$	−0.978174	+	2.11942i	−0.0507160	+	0.109887i
$373$	20.3092	−	20.3092i	1.05157	−	1.05157i	0.0529738	−	0.998596i	$-0.483130\pi$
$373$	20.3092	−	20.3092i	1.05157	−	1.05157i	0.998596	−	0.0529738i	$-0.0168700\pi$
$374$	−1.19558	−	6.70335i	−0.0618218	−	0.346622i
$375$			0.824006i			0.0425515i
$376$	−13.7696	−	3.60264i	−0.710114	−	0.185792i
$377$			9.28950i			0.478434i
$378$	0.687650	−	0.122646i	0.0353689	−	0.00630822i
$379$	−2.21342	+	2.21342i	−0.113696	+	0.113696i	−0.761666	−	0.647970i	$-0.775618\pi$
$379$	−2.21342	+	2.21342i	−0.113696	+	0.113696i	0.647970	+	0.761666i	$0.275618\pi$
$380$	1.42304	+	3.86243i	0.0730002	+	0.198138i
$381$	1.02208	+	1.02208i	0.0523625	+	0.0523625i
$382$	−8.88589	+	12.7436i	−0.454642	+	0.652020i
$383$	−19.5256			−0.997713			−0.498857	−	0.866685i	$-0.666247\pi$
$383$	−19.5256			−0.997713			−0.498857	+	0.866685i	$0.666247\pi$
$384$	−1.44889	−	0.504879i	−0.0739383	−	0.0257645i
$385$	1.85553			0.0945666
$386$	−12.6612	+	18.1580i	−0.644438	+	0.924215i
$387$	6.70604	+	6.70604i	0.340887	+	0.340887i
$388$	−10.2307	−	27.7683i	−0.519383	−	1.40972i
$389$	19.1361	−	19.1361i	0.970237	−	0.970237i	−0.0293325	−	0.999570i	$-0.509338\pi$
$389$	19.1361	−	19.1361i	0.970237	−	0.970237i	0.999570	+	0.0293325i	$0.00933818\pi$
$390$	−0.409849	+	0.0730987i	−0.0207535	+	0.00370150i
$391$			8.44480i			0.427072i
$392$	−18.1399	−	4.74605i	−0.916201	−	0.239712i
$393$			1.05223i			0.0530779i
$394$	−2.49573	−	13.9931i	−0.125733	−	0.704960i
$395$	−1.26367	+	1.26367i	−0.0635819	+	0.0635819i
$396$	−12.0316	+	26.0690i	−0.604611	+	1.31002i
$397$	−26.8450	−	26.8450i	−1.34731	−	1.34731i	−0.888570	−	0.458740i	$-0.848301\pi$
$397$	−26.8450	−	26.8450i	−1.34731	−	1.34731i	−0.458740	−	0.888570i	$-0.651699\pi$
$398$	22.7206	+	15.8427i	1.13888	+	0.794121i
$399$	−0.268492			−0.0134414
$400$	−11.9361	−	13.9998i	−0.596807	−	0.699992i
$401$	−10.9982			−0.549222			−0.274611	−	0.961555i	$-0.588549\pi$
$401$	−10.9982			−0.549222			−0.274611	+	0.961555i	$0.588549\pi$
$402$	1.42559	+	0.994039i	0.0711021	+	0.0495782i
$403$	−20.8694	−	20.8694i	−1.03958	−	1.03958i
$404$	25.5235	+	11.7798i	1.26984	+	0.586068i
$405$	3.95417	−	3.95417i	0.196484	−	0.196484i
$406$	0.409535	+	2.29618i	0.0203249	+	0.113957i
$407$		−	16.3246i		−	0.809179i
$408$	0.193748	+	0.331056i	0.00959196	+	0.0163897i
$409$		−	19.2606i		−	0.952373i	−0.879344	−	0.476187i	$-0.842019\pi$
$409$		−	19.2606i		−	0.952373i	0.879344	−	0.476187i	$-0.157981\pi$
$410$	4.00221	−	0.713814i	0.197655	−	0.0352528i
$411$	1.94994	−	1.94994i	0.0961834	−	0.0961834i
$412$	−5.76152	+	2.12272i	−0.283850	+	0.104579i
$413$	−2.21170	−	2.21170i	−0.108831	−	0.108831i
$414$	20.3669	−	29.2090i	1.00098	−	1.43554i
$415$	−9.01634			−0.442594
$416$	12.3232	−	14.9830i	0.604195	−	0.734600i
$417$	−0.606817			−0.0297160
$418$	12.6636	−	18.1614i	0.619399	−	0.888305i
$419$	22.4250	+	22.4250i	1.09553	+	1.09553i	0.994926	+	0.100605i	$0.0320777\pi$
$419$	22.4250	+	22.4250i	1.09553	+	1.09553i	0.100605	+	0.994926i	$0.467922\pi$
$420$	−0.0980838	+	0.0361370i	−0.00478600	+	0.00176331i
$421$	−0.813332	+	0.813332i	−0.0396394	+	0.0396394i	−0.726649	−	0.687009i	$-0.758923\pi$
$421$	−0.813332	+	0.813332i	−0.0396394	+	0.0396394i	0.687009	+	0.726649i	$0.258923\pi$
$422$	−1.28781	+	0.229687i	−0.0626895	+	0.0111810i
$423$		−	15.0039i		−	0.729517i
$424$	29.0057	−	16.9754i	1.40864	−	0.824397i
$425$			4.59937i			0.223102i
$426$	−0.465638	−	2.61074i	−0.0225602	−	0.126491i
$427$	−2.49750	+	2.49750i	−0.120863	+	0.120863i
$428$	−7.13081	−	3.29108i	−0.344681	−	0.159080i
$429$	1.58343	+	1.58343i	0.0764486	+	0.0764486i
$430$	−2.33550	−	1.62850i	−0.112628	−	0.0785331i
$431$	11.3460			0.546518			0.273259	−	0.961941i	$-0.411898\pi$
$431$	11.3460			0.546518			0.273259	+	0.961941i	$0.411898\pi$
$432$	0.257374	−	3.23462i	0.0123829	−	0.155626i
$433$	−24.1903			−1.16251			−0.581256	−	0.813720i	$-0.697439\pi$
$433$	−24.1903			−1.16251			−0.581256	+	0.813720i	$0.697439\pi$
$434$	−6.07854	−	4.23845i	−0.291779	−	0.203452i
$435$	−0.164416	−	0.164416i	−0.00788314	−	0.00788314i
$436$	−7.04418	+	15.2627i	−0.337355	+	0.730951i
$437$	−19.4166	+	19.4166i	−0.928820	+	0.928820i
$438$	0.427565	+	2.39727i	0.0204299	+	0.114546i
$439$		−	24.3351i		−	1.16145i	−0.814099	−	0.580726i	$-0.802769\pi$
$439$		−	24.3351i		−	1.16145i	0.814099	−	0.580726i	$-0.197231\pi$
$440$	2.18180	−	8.33905i	0.104013	−	0.397548i
$441$		−	19.7659i		−	0.941235i
$442$	−4.77459	+	0.851573i	−0.227104	+	0.0405052i
$443$	−16.7909	+	16.7909i	−0.797761	+	0.797761i	−0.982742	−	0.184981i	$-0.940778\pi$
$443$	−16.7909	+	16.7909i	−0.797761	+	0.797761i	0.184981	+	0.982742i	$0.440778\pi$
$444$	0.317926	+	0.862920i	0.0150881	+	0.0409524i
$445$	−2.42863	−	2.42863i	−0.115128	−	0.115128i
$446$	8.96987	−	12.8641i	0.424736	−	0.609131i
$447$	−0.276937			−0.0130987
$448$	2.38551	−	4.24676i	0.112705	−	0.200641i
$449$	−36.7989			−1.73665			−0.868324	−	0.495997i	$-0.834803\pi$
$449$	−36.7989			−1.73665			−0.868324	+	0.495997i	$0.834803\pi$
$450$	11.0926	−	15.9083i	0.522910	−	0.749926i
$451$	−15.4623	−	15.4623i	−0.728090	−	0.728090i
$452$	4.60492	+	12.4988i	0.216597	+	0.587892i
$453$	−0.277748	+	0.277748i	−0.0130497	+	0.0130497i
$454$	−5.30834	+	0.946770i	−0.249133	+	0.0444341i
$455$		−	1.32164i		−	0.0619594i
$456$	−0.315703	+	1.20665i	−0.0147841	+	0.0565064i
$457$			8.70262i			0.407092i	0.979065	+	0.203546i	$0.0652466\pi$
$457$			8.70262i			0.407092i	−0.979065	+	0.203546i	$0.934753\pi$
$458$	0.932056	+	5.22585i	0.0435521	+	0.244188i
$459$	−0.573612	+	0.573612i	−0.0267739	+	0.0267739i
$460$	−4.47980	+	9.70645i	−0.208872	+	0.452565i
$461$	−9.82718	−	9.82718i	−0.457697	−	0.457697i	0.440202	−	0.897899i	$-0.354907\pi$
$461$	−9.82718	−	9.82718i	−0.457697	−	0.457697i	−0.897899	+	0.440202i	$0.854907\pi$
$462$	0.461198	+	0.321584i	0.0214569	+	0.0149615i
$463$	23.8196			1.10699			0.553495	−	0.832852i	$-0.313294\pi$
$463$	23.8196			1.10699			0.553495	+	0.832852i	$0.313294\pi$
$464$	10.8009	+	0.859414i	0.501420	+	0.0398973i
$465$	0.738741			0.0342583
$466$	18.4544	+	12.8679i	0.854885	+	0.596095i
$467$	7.59613	+	7.59613i	0.351507	+	0.351507i	0.860670	−	0.509163i	$-0.170045\pi$
$467$	7.59613	+	7.59613i	0.351507	+	0.351507i	−0.509163	+	0.860670i	$0.670045\pi$
$468$	18.5682	+	8.56976i	0.858315	+	0.396137i
$469$	−3.90129	+	3.90129i	−0.180145	+	0.180145i
$470$	0.790912	+	4.43448i	0.0364820	+	0.204547i
$471$			0.124525i			0.00573783i
$472$	−12.5403	+	7.33912i	−0.577214	+	0.337810i
$473$			15.3146i			0.704168i
$474$	−0.533095	+	0.0950802i	−0.0244859	+	0.00436718i
$475$	−10.5750	+	10.5750i	−0.485215	+	0.485215i
$476$	−1.14264	+	0.420983i	−0.0523728	+	0.0192957i
$477$	25.0514	+	25.0514i	1.14703	+	1.14703i
$478$	6.57601	−	9.43093i	0.300780	−	0.431361i
$479$	6.12832			0.280010			0.140005	−	0.990151i	$-0.455288\pi$
$479$	6.12832			0.280010			0.140005	+	0.990151i	$0.455288\pi$
$480$	0.0470749	+	0.483295i	0.00214867	+	0.0220593i
$481$	−11.6275			−0.530169
$482$	16.7701	−	24.0507i	0.763857	−	1.09548i
$483$	−0.493070	−	0.493070i	−0.0224355	−	0.0224355i
$484$	−22.8620	+	8.42303i	−1.03918	+	0.382865i
$485$	−6.62241	+	6.62241i	−0.300708	+	0.300708i
$486$	5.05632	−	0.901821i	0.229359	−	0.0409074i
$487$			5.14859i			0.233305i	0.993173	+	0.116652i	$0.0372164\pi$
$487$			5.14859i			0.233305i	−0.993173	+	0.116652i	$0.962784\pi$
$488$	8.28751	+	14.1608i	0.375158	+	0.641030i
$489$		−	0.201800i		−	0.00912572i
$490$	1.04193	+	5.84190i	0.0470698	+	0.263910i
$491$	0.0848303	−	0.0848303i	0.00382834	−	0.00382834i	−0.705190	−	0.709018i	$-0.749138\pi$
$491$	0.0848303	−	0.0848303i	0.00382834	−	0.00382834i	0.709018	+	0.705190i	$0.249138\pi$
$492$	1.11847	+	0.516207i	0.0504246	+	0.0232724i
$493$	−1.91539	−	1.91539i	−0.0862646	−	0.0862646i
$494$	−12.9359	−	9.01993i	−0.582012	−	0.405826i
$495$	9.08657			0.408411
$496$	−26.1956	+	22.3342i	−1.17622	+	1.00283i
$497$	8.41883			0.377636
$498$	−2.24104	−	1.56263i	−0.100423	−	0.0700232i
$499$	21.1562	+	21.1562i	0.947080	+	0.947080i	0.998668	−	0.0515880i	$-0.0164283\pi$
$499$	21.1562	+	21.1562i	0.947080	+	0.947080i	−0.0515880	+	0.998668i	$0.516428\pi$
$500$	−5.09228	+	11.0335i	−0.227734	+	0.493433i
$501$	−0.158918	+	0.158918i	−0.00709995	+	0.00709995i
$502$	2.77548	+	15.5615i	0.123876	+	0.694545i
$503$		−	4.93831i		−	0.220188i	−0.993921	−	0.110094i	$-0.964885\pi$
$503$		−	4.93831i		−	0.220188i	0.993921	−	0.110094i	$-0.0351153\pi$
$504$	4.96749	+	1.29968i	0.221269	+	0.0578922i
$505$		−	8.89640i		−	0.395885i
$506$	56.6084	−	10.0964i	2.51655	−	0.448840i
$507$	−0.118819	+	0.118819i	−0.00527696	+	0.00527696i
$508$	7.36933	+	20.0020i	0.326961	+	0.887444i
$509$	−18.6934	−	18.6934i	−0.828573	−	0.828573i	0.158747	−	0.987319i	$-0.449255\pi$
$509$	−18.6934	−	18.6934i	−0.828573	−	0.828573i	−0.987319	+	0.158747i	$0.949255\pi$
$510$	0.0694340	−	0.0995781i	0.00307459	−	0.00440939i
$511$	−7.73047			−0.341976
$512$	−16.2806	−	15.7144i	−0.719509	−	0.694483i
$513$	−2.63773			−0.116459
$514$	−1.58037	+	2.26647i	−0.0697070	+	0.0999697i
$515$	1.37406	+	1.37406i	0.0605481	+	0.0605481i
$516$	−0.298257	−	0.809536i	−0.0131300	−	0.0356378i
$517$	17.1323	−	17.1323i	0.753479	−	0.753479i
$518$	−2.87408	+	0.512607i	−0.126280	+	0.0225227i
$519$		−	1.29543i		−	0.0568631i
$520$	−5.93965	−	1.55403i	−0.260471	−	0.0681488i
$521$		−	17.7856i		−	0.779200i	−0.920984	−	0.389600i	$-0.872613\pi$
$521$		−	17.7856i		−	0.779200i	0.920984	−	0.389600i	$-0.127387\pi$
$522$	2.00550	+	11.2444i	0.0877783	+	0.492155i
$523$	−22.9804	+	22.9804i	−1.00486	+	1.00486i	−0.00487572	+	0.999988i	$0.501552\pi$
$523$	−22.9804	+	22.9804i	−1.00486	+	1.00486i	−0.999988	+	0.00487572i	$0.998448\pi$
$524$	−6.50266	+	14.0894i	−0.284070	+	0.615498i
$525$	−0.268545	−	0.268545i	−0.0117203	−	0.0117203i
$526$	−1.62593	−	1.13373i	−0.0708941	−	0.0494331i
$527$	8.60605			0.374886
$528$	1.98754	−	1.69456i	0.0864967	−	0.0737464i
$529$	−48.3147			−2.10064
$530$	−8.72461	−	6.08351i	−0.378973	−	0.264251i
$531$	−10.8307	−	10.8307i	−0.470013	−	0.470013i
$532$	−3.59513	−	1.65926i	−0.155869	−	0.0719379i
$533$	−11.0133	+	11.0133i	−0.477040	+	0.477040i
$534$	−0.182734	−	1.02455i	−0.00790769	−	0.0443368i
$535$			2.48550i			0.107458i
$536$	12.9457	+	22.1203i	0.559170	+	0.955451i
$537$			3.42411i			0.147761i
$538$	34.5793	−	6.16739i	1.49082	−	0.265895i
$539$	22.5698	−	22.5698i	0.972152	−	0.972152i
$540$	−0.963599	+	0.355019i	−0.0414667	+	0.0152776i
$541$	8.43580	+	8.43580i	0.362683	+	0.362683i	0.864800	−	0.502117i	$-0.167445\pi$
$541$	8.43580	+	8.43580i	0.362683	+	0.362683i	−0.502117	+	0.864800i	$0.667445\pi$
$542$	−21.3268	+	30.5857i	−0.916065	+	1.31377i
$543$	−1.61010			−0.0690962
$544$	0.548406	+	5.63021i	0.0235127	+	0.241393i
$545$	5.31993			0.227881
$546$	0.229055	−	0.328497i	0.00980265	−	0.0140584i
$547$	9.29903	+	9.29903i	0.397598	+	0.397598i	0.877385	−	0.479787i	$-0.159286\pi$
$547$	9.29903	+	9.29903i	0.397598	+	0.397598i	−0.479787	+	0.877385i	$0.659286\pi$
$548$	38.1602	−	14.0594i	1.63012	−	0.600587i
$549$	−12.2303	+	12.2303i	−0.521977	+	0.521977i
$550$	30.8312	−	5.49889i	1.31464	−	0.234474i
$551$		−	8.80783i		−	0.375226i
$552$	−2.79570	+	1.63616i	−0.118993	+	0.0696398i
$553$		−	1.71907i		−	0.0731023i
$554$	1.87489	+	10.5121i	0.0796563	+	0.446616i
$555$	0.205797	−	0.205797i	0.00873558	−	0.00873558i
$556$	−8.12532	−	3.75007i	−0.344590	−	0.159038i
$557$	−18.9984	−	18.9984i	−0.804988	−	0.804988i	0.178883	−	0.983870i	$-0.442752\pi$
$557$	−18.9984	−	18.9984i	−0.804988	−	0.804988i	−0.983870	+	0.178883i	$0.942752\pi$
$558$	−29.7667	−	20.7558i	−1.26013	−	0.878662i
$559$	10.9082			0.461366
$560$	−1.53667	−	0.122271i	−0.0649363	−	0.00516689i
$561$	−0.652968			−0.0275683
$562$	12.5946	+	8.78195i	0.531269	+	0.370444i
$563$	32.0489	+	32.0489i	1.35070	+	1.35070i	0.884878	+	0.465822i	$0.154241\pi$
$563$	32.0489	+	32.0489i	1.35070	+	1.35070i	0.465822	+	0.884878i	$0.345759\pi$
$564$	−0.571962	+	1.23928i	−0.0240839	+	0.0521829i
$565$	2.98081	−	2.98081i	0.125404	−	0.125404i
$566$	3.30574	+	18.5346i	0.138951	+	0.779068i
$567$			5.37918i			0.225904i
$568$	9.89916	−	37.8355i	0.415360	−	1.58754i
$569$			6.24532i			0.261817i	0.991394	+	0.130909i	$0.0417895\pi$
$569$			6.24532i			0.261817i	−0.991394	+	0.130909i	$0.958211\pi$
$570$	0.388598	−	0.0693084i	0.0162766	−	0.00290301i
$571$	−21.2572	+	21.2572i	−0.889587	+	0.889587i	−0.994483	−	0.104897i	$-0.966549\pi$
$571$	−21.2572	+	21.2572i	−0.889587	+	0.889587i	0.104897	+	0.994483i	$0.466549\pi$
$572$	11.4168	+	30.9876i	0.477359	+	1.29566i
$573$	1.05346	+	1.05346i	0.0440088	+	0.0440088i
$574$	−2.23674	+	3.20780i	−0.0933597	+	0.133891i
$575$	−38.8408			−1.61977
$576$	11.6819	−	20.7964i	0.486746	−	0.866519i
$577$	−18.7832			−0.781955			−0.390977	−	0.920400i	$-0.627863\pi$
$577$	−18.7832			−0.781955			−0.390977	+	0.920400i	$0.627863\pi$
$578$	0.808880	−	1.16005i	0.0336450	−	0.0482517i
$579$	1.50103	+	1.50103i	0.0623809	+	0.0623809i
$580$	−1.18547	−	3.21762i	−0.0492238	−	0.133604i
$581$	6.13284	−	6.13284i	0.254433	−	0.254433i
$582$	−2.79376	+	0.498281i	−0.115805	+	0.0206544i
$583$			57.2103i			2.36941i
$584$	−9.08976	+	34.7419i	−0.376137	+	1.43763i
$585$		−	6.47209i		−	0.267588i
$586$	5.72873	+	32.1198i	0.236652	+	1.32686i
$587$	25.1712	−	25.1712i	1.03893	−	1.03893i	0.0397141	−	0.999211i	$-0.487355\pi$
$587$	25.1712	−	25.1712i	1.03893	−	1.03893i	0.999211	−	0.0397141i	$-0.0126447\pi$
$588$	−0.753492	+	1.63260i	−0.0310735	+	0.0673273i
$589$	19.7873	+	19.7873i	0.815322	+	0.815322i
$590$	3.77199	+	2.63014i	0.155290	+	0.108281i
$591$	−1.36305			−0.0560685
$592$	−1.07571	+	13.5193i	−0.0442116	+	0.555640i
$593$	−3.70296			−0.152062			−0.0760312	−	0.997105i	$-0.524225\pi$
$593$	−3.70296			−0.152062			−0.0760312	+	0.997105i	$0.524225\pi$
$594$	4.53092	+	3.15932i	0.185906	+	0.129629i
$595$	0.272506	+	0.272506i	0.0111717	+	0.0111717i
$596$	−3.70820	−	1.71144i	−0.151894	−	0.0701034i
$597$	1.87821	−	1.87821i	0.0768701	−	0.0768701i
$598$	−7.19137	−	40.3205i	−0.294077	−	1.64883i
$599$			8.39789i			0.343129i	0.985173	+	0.171564i	$0.0548821\pi$
$599$			8.39789i			0.343129i	−0.985173	+	0.171564i	$0.945118\pi$
$600$	−1.52265	+	0.891119i	−0.0621619	+	0.0363798i
$601$		−	33.9424i		−	1.38454i	−0.721638	−	0.692270i	$-0.756611\pi$
$601$		−	33.9424i		−	1.38454i	0.721638	−	0.692270i	$-0.243389\pi$
$602$	2.69628	−	0.480895i	0.109892	−	0.0195998i
$603$	−19.1047	+	19.1047i	−0.778003	+	0.778003i
$604$	−5.43552	+	2.00261i	−0.221168	+	0.0814850i
$605$	5.45231	+	5.45231i	0.221668	+	0.221668i
$606$	1.54185	−	2.21123i	0.0626332	−	0.0898249i
$607$	−38.3466			−1.55644			−0.778220	−	0.627992i	$-0.783877\pi$
$607$	−38.3466			−1.55644			−0.778220	+	0.627992i	$0.783877\pi$
$608$	−11.6842	+	14.2061i	−0.473858	+	0.576132i
$609$	0.223669			0.00906352
$610$	2.97001	−	4.25942i	0.120252	−	0.172459i
$611$	−12.2028	−	12.2028i	−0.493674	−	0.493674i
$612$	−5.59553	+	2.06156i	−0.226186	+	0.0833336i
$613$	−13.9857	+	13.9857i	−0.564879	+	0.564879i	−0.930689	−	0.365810i	$-0.880792\pi$
$613$	−13.9857	+	13.9857i	−0.564879	+	0.564879i	0.365810	+	0.930689i	$0.380792\pi$
$614$	36.1930	−	6.45521i	1.46063	−	0.260511i
$615$		−	0.389852i		−	0.0157203i
$616$	4.18811	+	7.15619i	0.168744	+	0.288331i
$617$			17.0510i			0.686447i	0.939254	+	0.343223i	$0.111519\pi$
$617$			17.0510i			0.686447i	−0.939254	+	0.343223i	$0.888481\pi$
$618$	0.103386	+	0.579665i	0.00415880	+	0.0233175i
$619$	−20.1561	+	20.1561i	−0.810144	+	0.810144i	−0.984655	−	0.174511i	$-0.944165\pi$
$619$	−20.1561	+	20.1561i	−0.810144	+	0.810144i	0.174511	+	0.984655i	$0.444165\pi$
$620$	9.89179	+	4.56534i	0.397264	+	0.183349i
$621$	−4.84404	−	4.84404i	−0.194385	−	0.194385i
$622$	−17.7176	−	12.3542i	−0.710413	−	0.495358i
$623$	3.30388			0.132367
$624$	−1.20699	−	1.41567i	−0.0483181	−	0.0566721i
$625$	−19.1510			−0.766041
$626$	19.2955	+	13.4544i	0.771203	+	0.537745i
$627$	−1.50132	−	1.50132i	−0.0599571	−	0.0599571i
$628$	−0.769554	+	1.66740i	−0.0307086	+	0.0665366i
$629$	2.39745	−	2.39745i	0.0955927	−	0.0955927i
$630$	−0.285327	−	1.59977i	−0.0113677	−	0.0637363i
$631$		−	5.55501i		−	0.221141i	−0.993868	−	0.110571i	$-0.964732\pi$
$631$		−	5.55501i		−	0.221141i	0.993868	−	0.110571i	$-0.0352679\pi$
$632$	−7.72577	−	2.02134i	−0.307314	−	0.0804048i
$633$			0.125444i			0.00498596i
$634$	−29.9467	+	5.34114i	−1.18933	+	0.212124i
$635$	4.77024	−	4.77024i	0.189301	−	0.189301i
$636$	−1.11419	−	3.02415i	−0.0441804	−	0.119915i
$637$	−16.0758	−	16.0758i	−0.636947	−	0.636947i
$638$	−10.5495	+	15.1295i	−0.417659	+	0.598982i
$639$	41.2271			1.63092
$640$	−2.35638	+	6.76227i	−0.0931441	+	0.267302i
$641$	46.4400			1.83427			0.917134	−	0.398579i	$-0.130497\pi$
$641$	46.4400			1.83427			0.917134	+	0.398579i	$0.130497\pi$
$642$	−0.430765	+	0.617778i	−0.0170009	+	0.0243818i
$643$	24.3358	+	24.3358i	0.959711	+	0.959711i	0.999219	−	0.0395087i	$-0.0125793\pi$
$643$	24.3358	+	24.3358i	0.959711	+	0.959711i	−0.0395087	+	0.999219i	$0.512579\pi$
$644$	−3.55512	−	9.64937i	−0.140091	−	0.380239i
$645$	−0.193065	+	0.193065i	−0.00760192	+	0.00760192i
$646$	4.52702	−	0.807417i	0.178113	−	0.0317674i
$647$		−	33.1871i		−	1.30472i	−0.757909	−	0.652361i	$-0.773779\pi$
$647$		−	33.1871i		−	1.30472i	0.757909	−	0.652361i	$-0.226221\pi$
$648$	24.1749	+	6.32504i	0.949679	+	0.248471i
$649$		−	24.7342i		−	0.970903i
$650$	−3.91670	−	21.9601i	−0.153626	−	0.861346i
$651$	−0.502485	+	0.502485i	−0.0196940	+	0.0196940i
$652$	1.24711	−	2.70212i	0.0488404	−	0.105823i
$653$	25.1203	+	25.1203i	0.983033	+	0.983033i	0.999858	−	0.0168254i	$-0.00535593\pi$
$653$	25.1203	+	25.1203i	0.983033	+	0.983033i	−0.0168254	+	0.999858i	$0.505356\pi$
$654$	1.32228	+	0.922004i	0.0517054	+	0.0360532i
$655$	4.91097			0.191887
$656$	11.7863	+	13.8241i	0.460178	+	0.539740i
$657$	−37.8562			−1.47691
$658$	−3.55427	−	2.47832i	−0.138560	−	0.0966152i
$659$	22.9394	+	22.9394i	0.893593	+	0.893593i	0.994859	−	0.101266i	$-0.0322894\pi$
$659$	22.9394	+	22.9394i	0.893593	+	0.893593i	−0.101266	+	0.994859i	$0.532289\pi$
$660$	−0.750520	−	0.346387i	−0.0292140	−	0.0134831i
$661$	26.1598	−	26.1598i	1.01750	−	1.01750i	0.0176527	−	0.999844i	$-0.494381\pi$
$661$	26.1598	−	26.1598i	1.01750	−	1.01750i	0.999844	−	0.0176527i	$-0.00561931\pi$
$662$	0.823478	+	4.61707i	0.0320054	+	0.179447i
$663$			0.465089i			0.0180626i
$664$	−20.3507	−	34.7731i	−0.789761	−	1.34946i
$665$			1.25311i			0.0485935i
$666$	−14.0744	+	2.51025i	−0.545373	+	0.0972701i
$667$	16.1751	−	16.1751i	0.626301	−	0.626301i
$668$	−3.11003	+	1.14583i	−0.120331	+	0.0443334i
$669$	−1.06341	−	1.06341i	−0.0411139	−	0.0411139i
$670$	4.63939	−	6.65354i	0.179235	−	0.257049i
$671$	−27.9305			−1.07824
$672$	−0.360753	−	0.296713i	−0.0139164	−	0.0114460i
$673$	35.8860			1.38330			0.691651	−	0.722232i	$-0.256884\pi$
$673$	35.8860			1.38330			0.691651	+	0.722232i	$0.256884\pi$
$674$	8.58440	−	12.3112i	0.330659	−	0.474211i
$675$	−2.63825	−	2.63825i	−0.101546	−	0.101546i
$676$	−2.32529	+	0.856708i	−0.0894343	+	0.0329503i
$677$	27.3189	−	27.3189i	1.04995	−	1.04995i	0.0512670	−	0.998685i	$-0.483674\pi$
$677$	27.3189	−	27.3189i	1.04995	−	1.04995i	0.998685	−	0.0512670i	$-0.0163259\pi$
$678$	1.25750	−	0.224281i	0.0482939	−	0.00861346i
$679$		−	9.00901i		−	0.345734i
$680$	1.54511	−	0.904263i	0.0592522	−	0.0346769i
$681$			0.517082i			0.0198146i
$682$	−10.2892	−	57.6894i	−0.393994	−	2.20904i
$683$	14.7494	−	14.7494i	0.564371	−	0.564371i	−0.366175	−	0.930546i	$-0.619333\pi$
$683$	14.7494	−	14.7494i	0.564371	−	0.564371i	0.930546	+	0.366175i	$0.119333\pi$
$684$	−17.6054	−	8.12540i	−0.673160	−	0.310683i
$685$	−9.10078	−	9.10078i	−0.347723	−	0.347723i
$686$	−9.62650	−	6.71238i	−0.367541	−	0.256280i
$687$	0.509046			0.0194213
$688$	1.00916	−	12.6829i	0.0384740	−	0.483533i
$689$	40.7492			1.55242
$690$	0.840918	+	0.586356i	0.0320132	+	0.0223222i
$691$	22.3536	+	22.3536i	0.850371	+	0.850371i	0.990179	−	0.139807i	$-0.0446483\pi$
$691$	22.3536	+	22.3536i	0.850371	+	0.850371i	−0.139807	+	0.990179i	$0.544648\pi$
$692$	8.00563	−	17.3459i	0.304328	−	0.659392i
$693$	−6.18061	+	6.18061i	−0.234782	+	0.234782i
$694$	1.52285	+	8.53828i	0.0578064	+	0.324109i
$695$			2.83214i			0.107429i
$696$	0.262998	−	1.00520i	0.00996891	−	0.0381021i
$697$		−	4.54163i		−	0.172027i
$698$	35.3023	−	6.29634i	1.33621	−	0.238320i
$699$	1.52554	−	1.52554i	0.0577014	−	0.0577014i
$700$	−1.93626	−	5.25542i	−0.0731836	−	0.198636i
$701$	−23.2968	−	23.2968i	−0.879907	−	0.879907i	0.113618	−	0.993525i	$-0.463756\pi$
$701$	−23.2968	−	23.2968i	−0.879907	−	0.879907i	−0.993525	+	0.113618i	$0.963756\pi$
$702$	2.25029	−	3.22724i	0.0849317	−	0.121804i
$703$	11.0246			0.415801
$704$	37.0856	−	10.4075i	1.39772	−	0.392247i
$705$	0.431959			0.0162685
$706$	−23.7465	+	34.0559i	−0.893712	+	1.28171i
$707$	6.05126	+	6.05126i	0.227581	+	0.227581i
$708$	0.481706	+	1.30746i	0.0181036	+	0.0491372i
$709$	−20.3230	+	20.3230i	−0.763247	+	0.763247i	−0.976908	−	0.213661i	$-0.931461\pi$
$709$	−20.3230	+	20.3230i	−0.763247	+	0.763247i	0.213661	+	0.976908i	$0.431461\pi$
$710$	−12.1849	+	2.17323i	−0.457289	+	0.0815599i
$711$		−	8.41831i		−	0.315711i
$712$	3.88482	−	14.8481i	0.145590	−	0.556457i
$713$			72.6764i			2.72175i
$714$	0.0205038	+	0.114961i	0.000767336	+	0.00430230i
$715$	7.39019	−	7.39019i	0.276377	−	0.276377i
$716$	−21.1606	+	45.8490i	−0.790811	+	1.71346i
$717$	−0.779612	−	0.779612i	−0.0291151	−	0.0291151i
$718$	11.9581	+	8.33814i	0.446272	+	0.311177i
$719$	44.9144			1.67502			0.837512	−	0.546418i	$-0.184009\pi$
$719$	44.9144			1.67502			0.837512	+	0.546418i	$0.184009\pi$
$720$	−7.52511	−	0.598762i	−0.280444	−	0.0223146i
$721$	−1.86924			−0.0696143
$722$	−9.77582	−	6.81649i	−0.363818	−	0.253684i
$723$	−1.98816	−	1.98816i	−0.0739405	−	0.0739405i
$724$	−21.5594	−	9.95029i	−0.801249	−	0.369800i
$725$	8.80956	−	8.80956i	0.327179	−	0.327179i
$726$	0.410241	+	2.30013i	0.0152255	+	0.0853660i
$727$		−	21.6605i		−	0.803344i	−0.915784	−	0.401672i	$-0.868429\pi$
$727$		−	21.6605i		−	0.803344i	0.915784	−	0.401672i	$-0.131571\pi$
$728$	5.09714	−	2.98306i	0.188913	−	0.110560i
$729$			26.0119i			0.963404i
$730$	11.1886	−	1.99554i	0.414107	−	0.0738581i
$731$	−2.24913	+	2.24913i	−0.0831872	+	0.0831872i
$732$	1.47641	−	0.543954i	0.0545697	−	0.0201051i
$733$	−34.2629	−	34.2629i	−1.26553	−	1.26553i	−0.948373	−	0.317158i	$-0.897271\pi$
$733$	−34.2629	−	34.2629i	−1.26553	−	1.26553i	−0.317158	−	0.948373i	$-0.602729\pi$
$734$	3.03719	−	4.35576i	0.112105	−	0.160774i
$735$	0.569056			0.0209899
$736$	−47.5460	+	4.63118i	−1.75257	+	0.170708i
$737$	−43.6296			−1.60712
$738$	−10.9533	+	15.7086i	−0.403198	+	0.578243i
$739$	−38.0567	−	38.0567i	−1.39994	−	1.39994i	−0.800187	−	0.599751i	$-0.795266\pi$
$739$	−38.0567	−	38.0567i	−1.39994	−	1.39994i	−0.599751	−	0.800187i	$-0.704734\pi$
$740$	4.02743	−	1.48383i	0.148051	−	0.0545466i
$741$	−1.06935	+	1.06935i	−0.0392835	+	0.0392835i
$742$	10.0724	−	1.79646i	0.369768	−	0.0659500i
$743$		−	8.82982i		−	0.323935i	−0.986796	−	0.161967i	$-0.948216\pi$
$743$		−	8.82982i		−	0.323935i	0.986796	−	0.161967i	$-0.0517839\pi$
$744$	1.66741	+	2.84909i	0.0611301	+	0.104453i
$745$			1.29252i			0.0473543i
$746$	−7.13195	−	39.9873i	−0.261119	−	1.46404i
$747$	30.0326	−	30.0326i	1.09884	−	1.09884i
$748$	−8.74329	−	4.03528i	−0.319686	−	0.147544i
$749$	−1.69062	−	1.69062i	−0.0617738	−	0.0617738i
$750$	0.955887	+	0.666522i	0.0349041	+	0.0243380i
$751$	11.4767			0.418791			0.209395	−	0.977831i	$-0.432850\pi$
$751$	11.4767			0.418791			0.209395	+	0.977831i	$0.432850\pi$
$752$	−15.3172	+	13.0593i	−0.558561	+	0.476225i
$753$	1.51584			0.0552402
$754$	10.7763	+	7.51409i	0.392449	+	0.273647i
$755$	1.29631	+	1.29631i	0.0471775	+	0.0471775i
$756$	0.413951	−	0.896913i	0.0150553	−	0.0326204i
$757$	−25.0038	+	25.0038i	−0.908777	+	0.908777i	−0.996174	−	0.0873968i	$-0.972145\pi$
$757$	−25.0038	+	25.0038i	−0.908777	+	0.908777i	0.0873968	+	0.996174i	$0.472145\pi$
$758$	0.777283	+	4.35806i	0.0282322	+	0.158292i
$759$		−	5.51419i		−	0.200152i
$760$	5.63167	+	1.47345i	0.204282	+	0.0534477i
$761$		−	7.22929i		−	0.262062i	−0.991378	−	0.131031i	$-0.958171\pi$
$761$		−	7.22929i		−	0.262062i	0.991378	−	0.131031i	$-0.0418287\pi$
$762$	2.01239	−	0.358921i	0.0729013	−	0.0130023i
$763$	−3.61857	+	3.61857i	−0.131001	+	0.131001i
$764$	7.59560	+	20.6161i	0.274799	+	0.745865i
$765$	1.33447	+	1.33447i	0.0482478	+	0.0482478i
$766$	−15.7939	+	22.6507i	−0.570657	+	0.818402i
$767$	−17.6174			−0.636129
$768$	−1.75766	+	1.27240i	−0.0634242	+	0.0459136i
$769$	20.6947			0.746269			0.373135	−	0.927777i	$-0.378283\pi$
$769$	20.6947			0.746269			0.373135	+	0.927777i	$0.378283\pi$
$770$	1.50090	−	2.15251i	0.0540888	−	0.0775710i
$771$	0.187359	+	0.187359i	0.00674756	+	0.00674756i
$772$	10.8227	+	29.3752i	0.389518	+	1.05724i
$773$	13.4277	−	13.4277i	0.482961	−	0.482961i	−0.423115	−	0.906076i	$-0.639063\pi$
$773$	13.4277	−	13.4277i	0.482961	−	0.482961i	0.906076	+	0.423115i	$0.139063\pi$
$774$	13.2037	−	2.35495i	0.474598	−	0.0846469i
$775$			39.5824i			1.42184i
$776$	−40.4879	−	10.5931i	−1.45343	−	0.380271i
$777$			0.279962i			0.0100436i
$778$	−6.71998	−	37.6776i	−0.240923	−	1.35081i
$779$	10.4423	−	10.4423i	0.374133	−	0.374133i
$780$	−0.246721	+	0.534573i	−0.00883402	+	0.0191408i
$781$	47.0754	+	47.0754i	1.68449	+	1.68449i
$782$	9.79638	+	6.83083i	0.350318	+	0.244270i
$783$	2.19738			0.0785278
$784$	−20.1786	+	17.2041i	−0.720665	+	0.614433i
$785$	0.581186			0.0207434
$786$	1.22064	+	0.851126i	0.0435386	+	0.0303587i
$787$	−21.6660	−	21.6660i	−0.772308	−	0.772308i	0.206201	−	0.978510i	$-0.433890\pi$
$787$	−21.6660	−	21.6660i	−0.772308	−	0.772308i	−0.978510	+	0.206201i	$0.933890\pi$
$788$	−18.2514	−	8.42354i	−0.650179	−	0.300076i
$789$	−0.134409	+	0.134409i	−0.00478507	+	0.00478507i
$790$	0.443759	+	2.48807i	0.0157883	+	0.0885215i
$791$			4.05505i			0.144181i
$792$	20.5092	+	35.0440i	0.728764	+	1.24523i
$793$			19.8940i			0.706458i
$794$	−52.8558	+	9.42711i	−1.87578	+	0.334556i
$795$	−0.721224	+	0.721224i	−0.0255792	+	0.0255792i
$796$	36.7565	−	13.5422i	1.30280	−	0.479991i
$797$	−1.59575	−	1.59575i	−0.0565243	−	0.0565243i	0.678280	−	0.734804i	$-0.262726\pi$
$797$	−1.59575	−	1.59575i	−0.0565243	−	0.0565243i	−0.734804	+	0.678280i	$0.762726\pi$
$798$	−0.217178	+	0.311464i	−0.00768802	+	0.0110257i
$799$	5.03217			0.178025
$800$	−25.8954	+	2.52232i	−0.915541	+	0.0891775i
$801$	16.1791			0.571661
$802$	−8.89620	+	12.7584i	−0.314136	+	0.450515i
$803$	−43.2263	−	43.2263i	−1.52542	−	1.52542i
$804$	2.30627	−	0.849699i	0.0813358	−	0.0299666i
$805$	−2.30126	+	2.30126i	−0.0811089	+	0.0811089i
$806$	−41.0904	+	7.32868i	−1.44735	+	0.258142i
$807$		−	3.36834i		−	0.118571i
$808$	34.3106	−	20.0800i	1.20704	−	0.706412i
$809$		−	41.7205i		−	1.46682i	−0.679789	−	0.733408i	$-0.737929\pi$
$809$		−	41.7205i		−	1.46682i	0.679789	−	0.733408i	$-0.262071\pi$
$810$	−1.38858	−	7.78547i	−0.0487897	−	0.273554i
$811$	−5.85439	+	5.85439i	−0.205576	+	0.205576i	−0.802384	−	0.596808i	$-0.796435\pi$
$811$	−5.85439	+	5.85439i	−0.205576	+	0.205576i	0.596808	+	0.802384i	$0.296435\pi$
$812$	2.99494	+	1.38225i	0.105102	+	0.0485075i
$813$	2.52838	+	2.52838i	0.0886740	+	0.0886740i
$814$	−18.9373	−	13.2046i	−0.663752	−	0.462822i
$815$	−0.941844			−0.0329914
$816$	0.540760	+	0.0430275i	0.0189304	+	0.00150627i
$817$	−10.3426			−0.361840
$818$	−22.3432	−	15.5795i	−0.781211	−	0.544724i
$819$	4.40226	+	4.40226i	0.153827	+	0.153827i
$820$	2.40925	−	5.22014i	0.0841345	−	0.182295i
$821$	21.6806	−	21.6806i	0.756656	−	0.756656i	−0.219056	−	0.975712i	$-0.570298\pi$
$821$	21.6806	−	21.6806i	0.756656	−	0.756656i	0.975712	+	0.219056i	$0.0702977\pi$
$822$	−0.684757	−	3.83929i	−0.0238836	−	0.133911i
$823$		−	0.871155i		−	0.0303666i	−0.999885	−	0.0151833i	$-0.995167\pi$
$823$		−	0.871155i		−	0.0303666i	0.999885	−	0.0151833i	$-0.00483317\pi$
$824$	−2.19792	+	8.40067i	−0.0765683	+	0.292651i
$825$		−	3.00324i		−	0.104559i
$826$	−4.35467	+	0.776678i	−0.151519	+	0.0270241i
$827$	4.84149	−	4.84149i	0.168355	−	0.168355i	−0.617901	−	0.786256i	$-0.712017\pi$
$827$	4.84149	−	4.84149i	0.168355	−	0.168355i	0.786256	+	0.617901i	$0.212017\pi$
$828$	−17.4095	−	47.2531i	−0.605021	−	1.64216i
$829$	−3.86675	−	3.86675i	−0.134298	−	0.134298i	0.636762	−	0.771060i	$-0.280273\pi$
$829$	−3.86675	−	3.86675i	−0.134298	−	0.134298i	−0.771060	+	0.636762i	$0.780273\pi$
$830$	−7.29313	+	10.4594i	−0.253148	+	0.363051i
$831$	1.02398			0.0355213
$832$	−7.41295	−	26.4149i	−0.256998	−	0.915773i
$833$	6.62929			0.229691
$834$	−0.490842	+	0.703937i	−0.0169965	+	0.0243754i
$835$	0.741705	+	0.741705i	0.0256678	+	0.0256678i
$836$	−10.8248	−	29.3809i	−0.374383	−	1.01616i
$837$	−4.93654	+	4.93654i	−0.170632	+	0.170632i
$838$	44.1532	−	7.87494i	1.52525	−	0.272035i
$839$			31.6810i			1.09375i	0.837214	+	0.546875i	$0.184183\pi$
$839$			31.6810i			1.09375i	−0.837214	+	0.546875i	$0.815817\pi$
$840$	−0.0374173	+	0.143013i	−0.00129102	+	0.00493440i
$841$		−	21.6626i		−	0.746986i
$842$	0.285617	+	1.60139i	0.00984300	+	0.0551877i
$843$	1.04113	−	1.04113i	0.0358586	−	0.0358586i
$844$	−0.775234	+	1.67971i	−0.0266846	+	0.0578179i
$845$	0.554555	+	0.554555i	0.0190773	+	0.0190773i
$846$	−17.4053	−	12.1364i	−0.598407	−	0.417258i
$847$	−7.41724			−0.254859
$848$	3.76989	−	47.3791i	0.129459	−	1.62701i
$849$	1.80544			0.0619626
$850$	5.33549	+	3.72034i	0.183006	+	0.127607i
$851$	20.2460	+	20.2460i	0.694025	+	0.694025i
$852$	−3.40523	−	1.57161i	−0.116661	−	0.0538424i
$853$	1.64443	−	1.64443i	0.0563042	−	0.0563042i	−0.678394	−	0.734698i	$-0.737324\pi$
$853$	1.64443	−	1.64443i	0.0563042	−	0.0563042i	0.734698	+	0.678394i	$0.237324\pi$
$854$	0.877044	+	4.91740i	0.0300118	+	0.168270i
$855$			6.13650i			0.209864i
$856$	−9.58578	+	5.61001i	−0.327635	+	0.191746i
$857$			1.43180i			0.0489095i	0.999701	+	0.0244547i	$0.00778496\pi$
$857$			1.43180i			0.0489095i	−0.999701	+	0.0244547i	$0.992215\pi$
$858$	3.11766	−	0.556050i	0.106435	−	0.0189832i
$859$	−34.7594	+	34.7594i	−1.18598	+	1.18598i	−0.207806	+	0.978170i	$0.566632\pi$
$859$	−34.7594	+	34.7594i	−1.18598	+	1.18598i	−0.978170	+	0.207806i	$0.933368\pi$
$860$	−3.77827	+	1.39203i	−0.128838	+	0.0474678i
$861$	0.265174	+	0.265174i	0.00903711	+	0.00903711i
$862$	9.17755	−	13.1619i	0.312589	−	0.448297i
$863$	−14.5240			−0.494403			−0.247201	−	0.968964i	$-0.579511\pi$
$863$	−14.5240			−0.494403			−0.247201	+	0.968964i	$0.579511\pi$
$864$	−3.54413	−	2.91498i	−0.120574	−	0.0991697i
$865$	−6.04605			−0.205572
$866$	−19.5671	+	28.0620i	−0.664916	+	0.953584i
$867$	−0.0958959	−	0.0958959i	−0.00325680	−	0.00325680i
$868$	−9.83362	+	3.62300i	−0.333775	+	0.122973i
$869$	9.61249	−	9.61249i	0.326082	−	0.326082i
$870$	−0.323723	+	0.0577377i	−0.0109752	+	0.00195749i
$871$			31.0760i			1.05297i
$872$	12.0076	+	20.5173i	0.406628	+	0.694803i
$873$		−	44.1173i		−	1.49314i
$874$	6.81848	+	38.2298i	0.230639	+	1.29314i
$875$	−2.61589	+	2.61589i	−0.0884332	+	0.0884332i
$876$	3.12680	+	1.44311i	0.105645	+	0.0487581i
$877$	16.0120	+	16.0120i	0.540687	+	0.540687i	0.923730	−	0.383043i	$-0.125124\pi$
$877$	16.0120	+	16.0120i	0.540687	+	0.540687i	−0.383043	+	0.923730i	$0.625124\pi$
$878$	−28.2299	−	19.6842i	−0.952714	−	0.664309i
$879$	3.12876			0.105531
$880$	−7.90888	−	9.27628i	−0.266608	−	0.312703i
$881$	10.9681			0.369525			0.184762	−	0.982783i	$-0.440848\pi$
$881$	10.9681			0.369525			0.184762	+	0.982783i	$0.440848\pi$
$882$	−22.9294	−	15.9883i	−0.772075	−	0.538353i
$883$	−8.54066	−	8.54066i	−0.287416	−	0.287416i	0.548642	−	0.836058i	$-0.315145\pi$
$883$	−8.54066	−	8.54066i	−0.287416	−	0.287416i	−0.836058	+	0.548642i	$0.815145\pi$
$884$	−2.87421	+	6.22758i	−0.0966700	+	0.209456i
$885$	0.311813	−	0.311813i	0.0104815	−	0.0104815i
$886$	5.89644	+	33.0601i	0.198095	+	1.11068i
$887$			50.6985i			1.70229i	0.524933	+	0.851144i	$0.324091\pi$
$887$			50.6985i			1.70229i	−0.524933	+	0.851144i	$0.675909\pi$
$888$	1.25819	+	0.329190i	0.0422222	+	0.0110469i
$889$			6.48936i			0.217646i
$890$	−4.78181	+	0.852860i	−0.160287	+	0.0285879i
$891$	−30.0787	+	30.0787i	−1.00767	+	1.00767i
$892$	−7.66739	−	20.8110i	−0.256723	−	0.696803i
$893$	11.5701	+	11.5701i	0.387179	+	0.387179i
$894$	−0.224009	+	0.321260i	−0.00749197	+	0.0107445i
$895$	15.9810			0.534187
$896$	−2.99685	−	6.20243i	−0.100118	−	0.207209i
$897$	−3.92759			−0.131138
$898$	−29.7659	+	42.6885i	−0.993302	+	1.42454i
$899$	−16.4839	−	16.4839i	−0.549769	−	0.549769i
$900$	−9.48188	−	25.7359i	−0.316063	−	0.857863i
$901$	−8.40199	+	8.40199i	−0.279911	+	0.279911i
$902$	−30.4441	+	5.42987i	−1.01368	+	0.180795i
$903$		−	0.262642i		−	0.00874019i
$904$	18.2240	+	4.76807i	0.606121	+	0.158584i
$905$			7.51470i			0.249797i
$906$	0.0975363	+	0.546866i	0.00324043	+	0.0181684i
$907$	13.3190	−	13.3190i	0.442249	−	0.442249i	−0.450518	−	0.892767i	$-0.648761\pi$
$907$	13.3190	−	13.3190i	0.442249	−	0.442249i	0.892767	+	0.450518i	$0.148761\pi$
$908$	−3.19551	+	6.92376i	−0.106047	+	0.229773i
$909$	29.6331	+	29.6331i	0.982868	+	0.982868i
$910$	−1.53317	−	1.06905i	−0.0508240	−	0.0354386i
$911$	−10.6793			−0.353821			−0.176911	−	0.984227i	$-0.556610\pi$
$911$	−10.6793			−0.353821			−0.176911	+	0.984227i	$0.556610\pi$
$912$	1.14440	+	1.34226i	0.0378949	+	0.0444468i
$913$	68.5858			2.26986
$914$	10.0955	+	7.03938i	0.333928	+	0.232842i
$915$	−0.352107	−	0.352107i	−0.0116403	−	0.0116403i
$916$	6.81616	+	3.14585i	0.225212	+	0.103942i
$917$	−3.34040	+	3.34040i	−0.110310	+	0.110310i
$918$	0.201434	+	1.12940i	0.00664833	+	0.0372758i
$919$		−	58.3115i		−	1.92352i	−0.273893	−	0.961760i	$-0.588312\pi$
$919$		−	58.3115i		−	1.92352i	0.273893	−	0.961760i	$-0.411688\pi$
$920$	7.63632	+	13.0481i	0.251762	+	0.430184i
$921$		−	3.52553i		−	0.116170i
$922$	−19.3490	+	3.45100i	−0.637226	+	0.113652i
$923$	33.5304	−	33.5304i	1.10367	−	1.10367i
$924$	0.746107	−	0.274888i	0.0245451	−	0.00904317i
$925$	11.0268	+	11.0268i	0.362558	+	0.362558i
$926$	19.2672	−	27.6319i	0.633160	−	0.908040i
$927$	−9.15371			−0.300647
$928$	9.73361	−	11.8344i	0.319521	−	0.388484i
$929$	1.28973			0.0423145			0.0211573	−	0.999776i	$-0.493265\pi$
$929$	1.28973			0.0423145			0.0211573	+	0.999776i	$0.493265\pi$
$930$	0.597553	−	0.856975i	0.0195945	−	0.0281013i
$931$	15.2423	+	15.2423i	0.499545	+	0.499545i
$932$	29.8549	−	10.9994i	0.977928	−	0.360298i
$933$	−1.46464	+	1.46464i	−0.0479501	+	0.0479501i
$934$	14.9562	−	2.66752i	0.489383	−	0.0872839i
$935$			3.04754i			0.0996652i
$936$	24.9608	−	14.6081i	0.815869	−	0.477481i
$937$			5.07491i			0.165790i	0.996558	+	0.0828951i	$0.0264166\pi$
$937$			5.07491i			0.165790i	−0.996558	+	0.0828951i	$0.973583\pi$
$938$	1.37001	+	7.68136i	0.0447324	+	0.250805i
$939$	1.59507	−	1.59507i	0.0520532	−	0.0520532i
$940$	5.78396	+	2.66947i	0.188652	+	0.0870684i
$941$	−34.5527	−	34.5527i	−1.12639	−	1.12639i	−0.990760	−	0.135628i	$-0.956695\pi$
$941$	−34.5527	−	34.5527i	−1.12639	−	1.12639i	−0.135628	−	0.990760i	$-0.543305\pi$
$942$	0.144455	+	0.100726i	0.00470661	+	0.00328183i
$943$	38.3532			1.24895
$944$	−1.62987	+	20.4838i	−0.0530478	+	0.666692i
$945$	−0.312626			−0.0101697
$946$	17.7657	+	12.3877i	0.577614	+	0.402759i
$947$	−32.7025	−	32.7025i	−1.06269	−	1.06269i	−0.997899	−	0.0647907i	$-0.979362\pi$
$947$	−32.7025	−	32.7025i	−1.06269	−	1.06269i	−0.0647907	−	0.997899i	$-0.520638\pi$
$948$	−0.320912	+	0.695325i	−0.0104227	+	0.0225831i
$949$	−30.7888	+	30.7888i	−0.999447	+	0.999447i
$950$	3.71361	+	20.8214i	0.120485	+	0.675537i
$951$			2.91708i			0.0945929i
$952$	−0.435898	+	1.66604i	−0.0141275	+	0.0539968i
$953$		−	0.0997215i		−	0.00323030i	−0.999999	−	0.00161515i	$-0.999486\pi$
$953$		−	0.0997215i		−	0.00323030i	0.999999	−	0.00161515i	$-0.000514118\pi$
$954$	49.3245	−	8.79728i	1.59694	−	0.284822i
$955$	4.91671	−	4.91671i	0.159101	−	0.159101i
$956$	−5.62113	−	15.2570i	−0.181800	−	0.493446i
$957$	1.25069	+	1.25069i	0.0404289	+	0.0404289i
$958$	4.95707	−	7.10915i	0.160156	−	0.229686i
$959$	12.3805			0.399789
$960$	0.598724	+	0.336319i	0.0193237	+	0.0108546i
$961$	43.0642			1.38917
$962$	−9.40526	+	13.4885i	−0.303238	+	0.434886i
$963$	−8.27898	−	8.27898i	−0.266786	−	0.266786i
$964$	−14.3350	−	38.9082i	−0.461698	−	1.25315i
$965$	7.00565	−	7.00565i	0.225520	−	0.225520i
$966$	−0.970820	+	0.173151i	−0.0312356	+	0.00557103i
$967$		−	55.4027i		−	1.78163i	−0.454365	−	0.890816i	$-0.650134\pi$
$967$		−	55.4027i		−	1.78163i	0.454365	−	0.890816i	$-0.349866\pi$
$968$	−8.72145	+	33.3342i	−0.280318	+	1.07140i
$969$		−	0.440974i		−	0.0141661i
$970$	2.32558	+	13.0390i	0.0746699	+	0.418659i
$971$	22.4810	−	22.4810i	0.721451	−	0.721451i	−0.247450	−	0.968901i	$-0.579592\pi$
$971$	22.4810	−	22.4810i	0.721451	−	0.721451i	0.968901	+	0.247450i	$0.0795925\pi$
$972$	3.04380	−	6.59505i	0.0976300	−	0.211536i
$973$	−1.92640	−	1.92640i	−0.0617576	−	0.0617576i
$974$	5.97262	+	4.16459i	0.191375	+	0.133442i
$975$	−2.13912			−0.0685066
$976$	23.1308	+	1.84049i	0.740400	+	0.0589126i
$977$	1.05316			0.0336937			0.0168468	−	0.999858i	$-0.494637\pi$
$977$	1.05316			0.0336937			0.0168468	+	0.999858i	$0.494637\pi$
$978$	−0.234098	−	0.163232i	−0.00748563	−	0.00521959i
$979$	18.4742	+	18.4742i	0.590439	+	0.590439i
$980$	7.61969	+	3.51671i	0.243402	+	0.112337i
$981$	−17.7202	+	17.7202i	−0.565763	+	0.565763i
$982$	−0.0297897	−	0.167025i	−0.000950629	−	0.00532998i
$983$		−	4.74871i		−	0.151460i	−0.997128	−	0.0757302i	$-0.975871\pi$
$983$		−	4.74871i		−	0.151460i	0.997128	−	0.0757302i	$-0.0241288\pi$
$984$	1.50353	−	0.879932i	0.0479309	−	0.0280512i
$985$			6.36166i			0.202699i
$986$	−3.77126	+	0.672623i	−0.120101	+	0.0214207i
$987$	−0.293815	+	0.293815i	−0.00935224	+	0.00935224i
$988$	−20.9271	+	7.71018i	−0.665780	+	0.245293i
$989$	−18.9935	−	18.9935i	−0.603958	−	0.603958i
$990$	7.34994	−	10.5409i	0.233597	−	0.335010i
$991$	−21.2996			−0.676605			−0.338302	−	0.941037i	$-0.609853\pi$
$991$	−21.2996			−0.676605			−0.338302	+	0.941037i	$0.609853\pi$
$992$	4.71961	+	48.4539i	0.149848	+	1.53841i
$993$	0.449745			0.0142722
$994$	6.80982	−	9.76625i	0.215994	−	0.309767i
$995$	−8.76601	−	8.76601i	−0.277901	−	0.277901i
$996$	−3.62546	+	1.33573i	−0.114877	+	0.0423242i
$997$	−2.00610	+	2.00610i	−0.0635337	+	0.0635337i	−0.738160	−	0.674626i	$-0.764305\pi$
$997$	−2.00610	+	2.00610i	−0.0635337	+	0.0635337i	0.674626	+	0.738160i	$0.264305\pi$
$998$	41.6550	−	7.42938i	1.31857	−	0.235173i
$999$			2.75042i			0.0870193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.c.205.13	yes	32
4.3	odd	2		1088.2.l.c.273.9		32
16.5	even	4	inner	272.2.l.c.69.13	✓	32
16.11	odd	4		1088.2.l.c.817.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.c.69.13	✓	32	16.5	even	4	inner
272.2.l.c.205.13	yes	32	1.1	even	1	trivial
1088.2.l.c.273.9		32	4.3	odd	2
1088.2.l.c.817.9		32	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	272.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.808880 - 1.16005i) q^{2} +(-0.0958959 - 0.0958959i) q^{3} +(-0.691426 - 1.87668i) q^{4} +(-0.447567 + 0.447567i) q^{5} +(-0.188812 + 0.0336756i) q^{6} -0.608862i q^{7} +(-2.73632 - 0.715922i) q^{8} -2.98161i q^{9} +(0.157171 + 0.881227i) q^{10} +(3.40456 - 3.40456i) q^{11} +(-0.113661 + 0.246271i) q^{12} +(-2.42497 - 2.42497i) q^{13} +(-0.706310 - 0.492497i) q^{14} +0.0858396 q^{15} +(-3.04386 + 2.59517i) q^{16} +1.00000 q^{17} +(-3.45881 - 2.41176i) q^{18} +(2.29923 + 2.29923i) q^{19} +(1.14940 + 0.530480i) q^{20} +(-0.0583874 + 0.0583874i) q^{21} +(-1.19558 - 6.70335i) q^{22} +8.44480i q^{23} +(0.193748 + 0.331056i) q^{24} +4.59937i q^{25} +(-4.77459 + 0.851573i) q^{26} +(-0.573612 + 0.573612i) q^{27} +(-1.14264 + 0.420983i) q^{28} +(-1.91539 - 1.91539i) q^{29} +(0.0694340 - 0.0995781i) q^{30} +8.60605 q^{31} +(0.548406 + 5.63021i) q^{32} -0.652968 q^{33} +(0.808880 - 1.16005i) q^{34} +(0.272506 + 0.272506i) q^{35} +(-5.59553 + 2.06156i) q^{36} +(2.39745 - 2.39745i) q^{37} +(4.52702 - 0.807417i) q^{38} +0.465089i q^{39} +(1.54511 - 0.904263i) q^{40} -4.54163i q^{41} +(0.0205038 + 0.114961i) q^{42} +(-2.24913 + 2.24913i) q^{43} +(-8.74329 - 4.03528i) q^{44} +(1.33447 + 1.33447i) q^{45} +(9.79638 + 6.83083i) q^{46} +5.03217 q^{47} +(0.540760 + 0.0430275i) q^{48} +6.62929 q^{49} +(5.33549 + 3.72034i) q^{50} +(-0.0958959 - 0.0958959i) q^{51} +(-2.87421 + 6.22758i) q^{52} +(-8.40199 + 8.40199i) q^{53} +(0.201434 + 1.12940i) q^{54} +3.04754i q^{55} +(-0.435898 + 1.66604i) q^{56} -0.440974i q^{57} +(-3.77126 + 0.672623i) q^{58} +(3.63251 - 3.63251i) q^{59} +(-0.0593517 - 0.161094i) q^{60} +(-4.10191 - 4.10191i) q^{61} +(6.96127 - 9.98344i) q^{62} -1.81539 q^{63} +(6.97491 + 3.91799i) q^{64} +2.17067 q^{65} +(-0.528173 + 0.757474i) q^{66} +(-6.40751 - 6.40751i) q^{67} +(-0.691426 - 1.87668i) q^{68} +(0.809822 - 0.809822i) q^{69} +(0.536546 - 0.0956957i) q^{70} +13.8271i q^{71} +(-2.13460 + 8.15864i) q^{72} -12.6966i q^{73} +(-0.841910 - 4.72042i) q^{74} +(0.441061 - 0.441061i) q^{75} +(2.72517 - 5.90467i) q^{76} +(-2.07291 - 2.07291i) q^{77} +(0.539526 + 0.376202i) q^{78} +2.82341 q^{79} +(0.200819 - 2.52384i) q^{80} -8.83481 q^{81} +(-5.26851 - 3.67364i) q^{82} +(10.0726 + 10.0726i) q^{83} +(0.149945 + 0.0692040i) q^{84} +(-0.447567 + 0.447567i) q^{85} +(0.789825 + 4.42839i) q^{86} +0.367355i q^{87} +(-11.7534 + 6.87858i) q^{88} +5.42631i q^{89} +(2.62747 - 0.468623i) q^{90} +(-1.47647 + 1.47647i) q^{91} +(15.8482 - 5.83895i) q^{92} +(-0.825286 - 0.825286i) q^{93} +(4.07042 - 5.83756i) q^{94} -2.05812 q^{95} +(0.487324 - 0.592504i) q^{96} +14.7965 q^{97} +(5.36230 - 7.69030i) q^{98} +(-10.1511 - 10.1511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{4} - 16 q^{6} - 18 q^{8} - 6 q^{10} - 4 q^{11} + 2 q^{12} + 14 q^{14} + 24 q^{15} + 26 q^{16} + 32 q^{17} + 10 q^{18} - 14 q^{20} - 8 q^{22} - 50 q^{24} - 6 q^{26} + 12 q^{27} - 8 q^{29} + 36 q^{30}+ \cdots - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^4 - 16 * q^6 - 18 * q^8 - 6 * q^10 - 4 * q^11 + 2 * q^12 + 14 * q^14 + 24 * q^15 + 26 * q^16 + 32 * q^17 + 10 * q^18 - 14 * q^20 - 8 * q^22 - 50 * q^24 - 6 * q^26 + 12 * q^27 - 8 * q^29 + 36 * q^30 - 24 * q^31 + 10 * q^32 + 12 * q^35 + 16 * q^36 - 8 * q^37 - 34 * q^38 - 38 * q^40 - 12 * q^42 - 12 * q^43 + 38 * q^44 - 40 * q^45 + 26 * q^46 + 32 * q^47 + 30 * q^48 - 32 * q^49 - 2 * q^50 - 54 * q^52 + 8 * q^53 - 52 * q^54 - 36 * q^56 - 26 * q^58 - 12 * q^59 + 28 * q^60 + 6 * q^62 - 40 * q^63 + 10 * q^64 + 28 * q^66 + 8 * q^67 - 2 * q^68 - 32 * q^70 - 32 * q^72 - 14 * q^74 + 8 * q^75 + 30 * q^76 + 56 * q^77 + 108 * q^78 + 48 * q^79 + 90 * q^80 - 64 * q^81 + 32 * q^82 + 4 * q^83 - 8 * q^84 - 54 * q^86 - 66 * q^88 - 66 * q^90 - 28 * q^91 + 24 * q^92 - 24 * q^93 + 12 * q^94 - 40 * q^95 + 70 * q^96 + 12 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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