LMFDB - Embedded newform 605.2.m.d.602.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(112,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.112"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,6,0,-2,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			602.4
Character	$\chi$	$=$	605.602
Dual form			605.2.m.d.403.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.396609 - 2.50409i) q^{2} +(-1.78637 - 0.910200i) q^{3} +(-4.21106 - 1.36825i) q^{4} +(-2.22815 + 0.188039i) q^{5} +(-2.98771 + 4.11224i) q^{6} +(0.820825 + 1.61096i) q^{7} +(-2.79437 + 5.48426i) q^{8} +(0.599293 + 0.824856i) q^{9} +(-0.412838 + 5.65406i) q^{10} +(6.27711 + 6.27711i) q^{12} +(-2.22802 - 0.352884i) q^{13} +(4.35953 - 1.41650i) q^{14} +(4.15145 + 1.69215i) q^{15} +(5.46052 + 3.96730i) q^{16} +(3.32262 - 0.526252i) q^{17} +(2.30320 - 1.17354i) q^{18} +(-0.403535 - 1.24195i) q^{19} +(9.64014 + 2.25683i) q^{20} -3.62488i q^{21} +(-3.16488 + 3.16488i) q^{23} +(9.98354 - 7.25347i) q^{24} +(4.92928 - 0.837955i) q^{25} +(-1.76731 + 5.43922i) q^{26} +(0.621127 + 3.92164i) q^{27} +(-1.25234 - 7.90694i) q^{28} +(-0.907432 + 2.79279i) q^{29} +(5.88381 - 9.72447i) q^{30} +(3.24439 - 2.35719i) q^{31} +(3.39552 - 3.39552i) q^{32} -8.52886i q^{34} +(-2.13184 - 3.43511i) q^{35} +(-1.39504 - 4.29350i) q^{36} +(-2.85918 + 1.45682i) q^{37} +(-3.27001 + 0.517918i) q^{38} +(3.65888 + 2.65833i) q^{39} +(5.19501 - 12.7452i) q^{40} +(-1.23988 + 0.402861i) q^{41} +(-9.07703 - 1.43766i) q^{42} +(-4.55431 - 4.55431i) q^{43} +(-1.49042 - 1.72521i) q^{45} +(6.66992 + 9.18035i) q^{46} +(-3.50645 + 6.88180i) q^{47} +(-6.14347 - 12.0572i) q^{48} +(2.19306 - 3.01849i) q^{49} +(-0.143318 - 12.6757i) q^{50} +(-6.41442 - 2.08417i) q^{51} +(8.89950 + 4.53452i) q^{52} +(-0.996331 + 6.29058i) q^{53} +10.0665 q^{54} -11.1286 q^{56} +(-0.409564 + 2.58588i) q^{57} +(6.63350 + 3.37994i) q^{58} +(11.7815 + 3.82803i) q^{59} +(-15.1667 - 12.8060i) q^{60} +(-5.47229 + 7.53196i) q^{61} +(-4.61586 - 9.05913i) q^{62} +(-0.836895 + 1.64250i) q^{63} +(0.778618 + 1.07168i) q^{64} +(5.03072 + 0.367324i) q^{65} +(-2.46236 - 2.46236i) q^{67} +(-14.7118 - 2.33012i) q^{68} +(8.53431 - 2.77296i) q^{69} +(-9.44733 + 3.97593i) q^{70} +(5.47805 + 3.98004i) q^{71} +(-6.19837 + 0.981725i) q^{72} +(-8.41458 + 4.28744i) q^{73} +(2.51404 + 7.73743i) q^{74} +(-9.56823 - 2.98974i) q^{75} +5.78207i q^{76} +(8.10784 - 8.10784i) q^{78} +(0.926417 - 0.673081i) q^{79} +(-12.9129 - 7.81295i) q^{80} +(3.40512 - 10.4799i) q^{81} +(0.517053 + 3.26455i) q^{82} +(1.63706 + 10.3360i) q^{83} +(-4.95976 + 15.2646i) q^{84} +(-7.30434 + 1.79735i) q^{85} +(-13.2107 + 9.59813i) q^{86} +(4.16301 - 4.16301i) q^{87} +3.85743i q^{89} +(-4.91120 + 3.04791i) q^{90} +(-1.26034 - 3.87891i) q^{91} +(17.6578 - 8.99711i) q^{92} +(-7.94119 + 1.25776i) q^{93} +(15.8420 + 11.5099i) q^{94} +(1.13267 + 2.69137i) q^{95} +(-9.15625 + 2.97505i) q^{96} +(0.768472 + 0.121714i) q^{97} +(-6.68878 - 6.68878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{3} - 2 q^{5} + 20 q^{7} - 20 q^{8} + 12 q^{12} - 20 q^{13} + 4 q^{15} + 12 q^{16} + 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} - 20 q^{28} + 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) $ 32 * q + 6 * q^3 - 2 * q^5 + 20 * q^7 - 20 * q^8 + 12 * q^12 - 20 * q^13 + 4 * q^15 + 12 * q^16 + 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 - 20 * q^28 + 40 * q^30 + 32 * q^31 + 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 - 20 * q^42 - 28 * q^45 + 20 * q^46 + 42 * q^47 + 26 * q^48 + 80 * q^50 - 100 * q^51 - 20 * q^52 - 34 * q^53 - 80 * q^56 - 40 * q^57 + 90 * q^58 - 86 * q^60 + 10 * q^62 - 10 * q^63 - 8 * q^67 - 70 * q^68 + 10 * q^70 - 36 * q^71 - 70 * q^72 + 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 - 60 * q^83 + 60 * q^85 - 80 * q^86 + 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 - 30 * q^95 - 38 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.396609	−	2.50409i	0.280445	−	1.77066i	−0.297636	−	0.954679i	$-0.596198\pi$
$2$	0.396609	−	2.50409i	0.280445	−	1.77066i	0.578081	−	0.815980i	$-0.303802\pi$
$3$	−1.78637	−	0.910200i	−1.03136	−	0.525504i	−0.145452	−	0.989365i	$-0.546464\pi$
$3$	−1.78637	−	0.910200i	−1.03136	−	0.525504i	−0.885908	+	0.463861i	$0.846464\pi$
$4$	−4.21106	−	1.36825i	−2.10553	−	0.684127i
$5$	−2.22815	+	0.188039i	−0.996458	+	0.0840934i
$5$	−2.22815	+	0.188039i	−0.996458	+	0.0840934i
$6$	−2.98771	+	4.11224i	−1.21973	+	1.67881i
$7$	0.820825	+	1.61096i	0.310243	+	0.608885i	0.992502	−	0.122224i	$-0.0390028\pi$
$7$	0.820825	+	1.61096i	0.310243	+	0.608885i	−0.682260	+	0.731110i	$0.739003\pi$
$8$	−2.79437	+	5.48426i	−0.987958	+	1.93898i
$9$	0.599293	+	0.824856i	0.199764	+	0.274952i
$10$	−0.412838	+	5.65406i	−0.130551	+	1.78797i
$11$		0			0
$11$		0			0
$12$	6.27711	+	6.27711i	1.81205	+	1.81205i
$13$	−2.22802	−	0.352884i	−0.617943	−	0.0978725i	−0.160388	−	0.987054i	$-0.551275\pi$
$13$	−2.22802	−	0.352884i	−0.617943	−	0.0978725i	−0.457555	+	0.889181i	$0.651275\pi$
$14$	4.35953	−	1.41650i	1.16513	−	0.378575i
$15$	4.15145	+	1.69215i	1.07190	+	0.436912i
$16$	5.46052	+	3.96730i	1.36513	+	0.991826i
$17$	3.32262	−	0.526252i	0.805854	−	0.127635i	0.260102	−	0.965581i	$-0.416244\pi$
$17$	3.32262	−	0.526252i	0.805854	−	0.127635i	0.545753	+	0.837946i	$0.316244\pi$
$18$	2.30320	−	1.17354i	0.542869	−	0.276606i
$19$	−0.403535	−	1.24195i	−0.0925772	−	0.284923i	0.894037	−	0.447992i	$-0.147861\pi$
$19$	−0.403535	−	1.24195i	−0.0925772	−	0.284923i	−0.986615	+	0.163069i	$0.947861\pi$
$20$	9.64014	+	2.25683i	2.15560	+	0.504643i
$21$		−	3.62488i		−	0.791014i
$22$		0			0
$23$	−3.16488	+	3.16488i	−0.659922	+	0.659922i	−0.955362	−	0.295439i	$-0.904534\pi$
$23$	−3.16488	+	3.16488i	−0.659922	+	0.659922i	0.295439	+	0.955362i	$0.404534\pi$
$24$	9.98354	−	7.25347i	2.03788	−	1.48061i
$25$	4.92928	−	0.837955i	0.985857	−	0.167591i
$26$	−1.76731	+	5.43922i	−0.346598	+	1.06672i
$27$	0.621127	+	3.92164i	0.119536	+	0.754720i
$28$	−1.25234	−	7.90694i	−0.236669	−	1.49427i
$29$	−0.907432	+	2.79279i	−0.168506	+	0.518608i	−0.999278	−	0.0380055i	$-0.987900\pi$
$29$	−0.907432	+	2.79279i	−0.168506	+	0.518608i	0.830772	+	0.556614i	$0.187900\pi$
$30$	5.88381	−	9.72447i	1.07423	−	1.77544i
$31$	3.24439	−	2.35719i	0.582710	−	0.423363i	−0.256990	−	0.966414i	$-0.582731\pi$
$31$	3.24439	−	2.35719i	0.582710	−	0.423363i	0.839700	+	0.543051i	$0.182731\pi$
$32$	3.39552	−	3.39552i	0.600248	−	0.600248i
$33$		0			0
$34$		−	8.52886i		−	1.46269i
$35$	−2.13184	−	3.43511i	−0.360347	−	0.580639i
$36$	−1.39504	−	4.29350i	−0.232507	−	0.715584i
$37$	−2.85918	+	1.45682i	−0.470046	+	0.239500i	−0.672935	−	0.739701i	$-0.734967\pi$
$37$	−2.85918	+	1.45682i	−0.470046	+	0.239500i	0.202889	+	0.979202i	$0.434967\pi$
$38$	−3.27001	+	0.517918i	−0.530465	+	0.0840174i
$39$	3.65888	+	2.65833i	0.585889	+	0.425674i
$40$	5.19501	−	12.7452i	0.821404	−	2.01519i
$41$	−1.23988	+	0.402861i	−0.193637	+	0.0629163i	−0.404230	−	0.914657i	$-0.632460\pi$
$41$	−1.23988	+	0.402861i	−0.193637	+	0.0629163i	0.210593	+	0.977574i	$0.432460\pi$
$42$	−9.07703	−	1.43766i	−1.40062	−	0.221836i
$43$	−4.55431	−	4.55431i	−0.694526	−	0.694526i	0.268698	−	0.963224i	$-0.413407\pi$
$43$	−4.55431	−	4.55431i	−0.694526	−	0.694526i	−0.963224	+	0.268698i	$0.913407\pi$
$44$		0			0
$45$	−1.49042	−	1.72521i	−0.222178	−	0.257179i
$46$	6.66992	+	9.18035i	0.983426	+	1.35357i
$47$	−3.50645	+	6.88180i	−0.511469	+	1.00381i	0.480460	+	0.877017i	$0.340470\pi$
$47$	−3.50645	+	6.88180i	−0.511469	+	1.00381i	−0.991929	+	0.126797i	$0.959530\pi$
$48$	−6.14347	−	12.0572i	−0.886734	−	1.74031i
$49$	2.19306	−	3.01849i	0.313294	−	0.431213i
$50$	−0.143318	−	12.6757i	−0.0202682	−	1.79262i
$51$	−6.41442	−	2.08417i	−0.898199	−	0.291843i
$52$	8.89950	+	4.53452i	1.23414	+	0.628825i
$53$	−0.996331	+	6.29058i	−0.136857	+	0.864078i	0.819756	+	0.572714i	$0.194109\pi$
$53$	−0.996331	+	6.29058i	−0.136857	+	0.864078i	−0.956612	+	0.291365i	$0.905891\pi$
$54$	10.0665			1.36988
$55$		0			0
$56$	−11.1286			−1.48712
$57$	−0.409564	+	2.58588i	−0.0542480	+	0.342509i
$58$	6.63350	+	3.37994i	0.871021	+	0.443808i
$59$	11.7815	+	3.82803i	1.53382	+	0.498368i	0.949663	−	0.313274i	$-0.101426\pi$
$59$	11.7815	+	3.82803i	1.53382	+	0.498368i	0.584155	+	0.811642i	$0.301426\pi$
$60$	−15.1667	−	12.8060i	−1.95801	−	1.65325i
$61$	−5.47229	+	7.53196i	−0.700655	+	0.964369i	0.299293	+	0.954161i	$0.403249\pi$
$61$	−5.47229	+	7.53196i	−0.700655	+	0.964369i	−0.999948	+	0.0102078i	$0.996751\pi$
$62$	−4.61586	−	9.05913i	−0.586214	−	1.15051i
$63$	−0.836895	+	1.64250i	−0.105439	+	0.206935i
$64$	0.778618	+	1.07168i	0.0973272	+	0.133959i
$65$	5.03072	+	0.367324i	0.623984	+	0.0455609i
$66$		0			0
$67$	−2.46236	−	2.46236i	−0.300825	−	0.300825i	0.540512	−	0.841336i	$-0.318231\pi$
$67$	−2.46236	−	2.46236i	−0.300825	−	0.300825i	−0.841336	+	0.540512i	$0.818231\pi$
$68$	−14.7118	−	2.33012i	−1.78407	−	0.282569i
$69$	8.53431	−	2.77296i	1.02741	−	0.333826i
$70$	−9.44733	+	3.97593i	−1.12917	+	0.475214i
$71$	5.47805	+	3.98004i	0.650125	+	0.472344i	0.863314	−	0.504667i	$-0.168385\pi$
$71$	5.47805	+	3.98004i	0.650125	+	0.472344i	−0.213188	+	0.977011i	$0.568385\pi$
$72$	−6.19837	+	0.981725i	−0.730485	+	0.115697i
$73$	−8.41458	+	4.28744i	−0.984852	+	0.501807i	−0.870784	−	0.491666i	$-0.836388\pi$
$73$	−8.41458	+	4.28744i	−0.984852	+	0.501807i	−0.114068	+	0.993473i	$0.536388\pi$
$74$	2.51404	+	7.73743i	0.292252	+	0.899458i
$75$	−9.56823	−	2.98974i	−1.10484	−	0.345225i
$76$			5.78207i			0.663249i
$77$		0			0
$78$	8.10784	−	8.10784i	0.918032	−	0.918032i
$79$	0.926417	−	0.673081i	0.104230	−	0.0757276i	−0.534449	−	0.845200i	$-0.679481\pi$
$79$	0.926417	−	0.673081i	0.104230	−	0.0757276i	0.638679	+	0.769473i	$0.279481\pi$
$80$	−12.9129	−	7.81295i	−1.44370	−	0.873514i
$81$	3.40512	−	10.4799i	0.378347	−	1.16443i
$82$	0.517053	+	3.26455i	0.0570990	+	0.360509i
$83$	1.63706	+	10.3360i	0.179690	+	1.13452i	0.898390	+	0.439199i	$0.144738\pi$
$83$	1.63706	+	10.3360i	0.179690	+	1.13452i	−0.718699	+	0.695321i	$0.755262\pi$
$84$	−4.95976	+	15.2646i	−0.541155	+	1.66550i
$85$	−7.30434	+	1.79735i	−0.792267	+	0.194950i
$86$	−13.2107	+	9.59813i	−1.42454	+	1.03499i
$87$	4.16301	−	4.16301i	0.446321	−	0.446321i
$88$		0			0
$89$			3.85743i			0.408887i	0.978878	+	0.204443i	$0.0655384\pi$
$89$			3.85743i			0.408887i	−0.978878	+	0.204443i	$0.934462\pi$
$90$	−4.91120	+	3.04791i	−0.517686	+	0.321278i
$91$	−1.26034	−	3.87891i	−0.132119	−	0.406621i
$92$	17.6578	−	8.99711i	1.84096	−	0.938014i
$93$	−7.94119	+	1.25776i	−0.823463	+	0.130424i
$94$	15.8420	+	11.5099i	1.63397	+	1.18715i
$95$	1.13267	+	2.69137i	0.116209	+	0.276129i
$96$	−9.15625	+	2.97505i	−0.934506	+	0.303639i
$97$	0.768472	+	0.121714i	0.0780266	+	0.0123582i	0.195326	−	0.980738i	$-0.437424\pi$
$97$	0.768472	+	0.121714i	0.0780266	+	0.0123582i	−0.117299	+	0.993097i	$0.537424\pi$
$98$	−6.68878	−	6.68878i	−0.675669	−	0.675669i
$99$		0			0
$100$	−21.9040	−	3.21584i	−2.19040	−	0.321584i
$101$	5.74129	+	7.90221i	0.571280	+	0.786299i	0.992706	−	0.120564i	$-0.0384703\pi$
$101$	5.74129	+	7.90221i	0.571280	+	0.786299i	−0.421426	+	0.906863i	$0.638470\pi$
$102$	−7.76297	+	15.2357i	−0.768649	+	1.50856i
$103$	2.12098	+	4.16266i	0.208987	+	0.410159i	0.971577	−	0.236722i	$-0.0760730\pi$
$103$	2.12098	+	4.16266i	0.208987	+	0.410159i	−0.762591	+	0.646881i	$0.776073\pi$
$104$	8.16123	−	11.2330i	0.800274	−	1.10148i
$105$	0.681618	+	8.07677i	0.0665191	+	0.788212i
$106$	15.3570	+	4.98980i	1.49161	+	0.484653i
$107$	−13.6339	−	6.94684i	−1.31804	−	0.671577i	−0.353484	−	0.935441i	$-0.615003\pi$
$107$	−13.6339	−	6.94684i	−1.31804	−	0.671577i	−0.964560	+	0.263864i	$0.915003\pi$
$108$	2.75020	−	17.3641i	0.264639	−	1.67086i
$109$	−17.8837			−1.71295			−0.856476	−	0.516187i	$-0.827351\pi$
$109$	−17.8837			−1.71295			−0.856476	+	0.516187i	$0.827351\pi$
$110$		0			0
$111$	6.43355			0.610646
$112$	−1.90903	+	12.0531i	−0.180386	+	1.13891i
$113$	−6.65542	−	3.39111i	−0.626089	−	0.319009i	0.112003	−	0.993708i	$-0.464273\pi$
$113$	−6.65542	−	3.39111i	−0.626089	−	0.319009i	−0.738093	+	0.674699i	$0.764273\pi$
$114$	6.31285	+	2.05117i	0.591252	+	0.192110i
$115$	6.45669	−	7.64693i	0.602090	−	0.713080i
$116$	7.64250	−	10.5190i	0.709588	−	0.976664i
$117$	−1.04416	−	2.04928i	−0.0965327	−	0.189456i
$118$	14.2584	−	27.9837i	1.31259	−	2.57610i
$119$	3.57506	+	4.92065i	0.327725	+	0.451075i
$120$	−20.8809	+	18.0391i	−1.90615	+	1.64674i
$121$		0			0
$122$	16.6904	+	16.6904i	1.51107	+	1.51107i
$123$	2.58157	+	0.408880i	0.232772	+	0.0368674i
$124$	−16.8875	+	5.48709i	−1.51655	+	0.492756i
$125$	−10.8256	+	2.79398i	−0.968271	+	0.249901i
$126$	3.78105	+	2.74709i	0.336842	+	0.244730i
$127$	−0.203651	+	0.0322551i	−0.0180711	+	0.00286217i	−0.165463	−	0.986216i	$-0.552912\pi$
$127$	−0.203651	+	0.0322551i	−0.0180711	+	0.00286217i	0.147392	+	0.989078i	$0.452912\pi$
$128$	11.5496	−	5.88481i	1.02085	−	0.520148i
$129$	3.99034	+	12.2810i	0.351330	+	1.08128i
$130$	2.91504	−	12.4517i	0.255666	−	1.09209i
$131$		−	0.551708i		−	0.0482029i	−0.999710	−	0.0241015i	$-0.992328\pi$
$131$		−	0.551708i		−	0.0482029i	0.999710	−	0.0241015i	$-0.00767248\pi$
$132$		0			0
$133$	1.66950	−	1.66950i	0.144764	−	0.144764i
$134$	−7.14256	+	5.18937i	−0.617023	+	0.448293i
$135$	−2.12138	−	8.62120i	−0.182579	−	0.741995i
$136$	−6.39853	+	19.6927i	−0.548670	+	1.68863i
$137$	2.42105	+	15.2859i	0.206844	+	1.30596i	0.844465	+	0.535611i	$0.179919\pi$
$137$	2.42105	+	15.2859i	0.206844	+	1.30596i	−0.637621	+	0.770350i	$0.720081\pi$
$138$	−3.55897	−	22.4705i	−0.302960	−	1.91281i
$139$	0.439646	−	1.35309i	0.0372903	−	0.114768i	−0.930679	−	0.365838i	$-0.880782\pi$
$139$	0.439646	−	1.35309i	0.0372903	−	0.114768i	0.967969	+	0.251070i	$0.0807825\pi$
$140$	4.27720	+	17.3823i	0.361489	+	1.46908i
$141$	12.5276	−	9.10186i	1.05502	−	0.766515i
$142$	12.1390	−	12.1390i	1.01868	−	1.01868i
$143$		0			0
$144$			6.88173i			0.573477i
$145$	1.49674	−	6.39338i	0.124298	−	0.530941i
$146$	7.39884	+	22.7713i	0.612333	+	1.88457i
$147$	−6.66505	+	3.39601i	−0.549724	+	0.280098i
$148$	14.0335	−	2.22268i	1.15354	−	0.182703i
$149$	−19.2587	−	13.9922i	−1.57773	−	1.14629i	−0.919239	−	0.393700i	$-0.871195\pi$
$149$	−19.2587	−	13.9922i	−1.57773	−	1.14629i	−0.658491	−	0.752588i	$-0.728805\pi$
$150$	−11.2814	+	22.7739i	−0.921124	+	1.85948i
$151$	13.6820	−	4.44554i	1.11342	−	0.361773i	0.306169	−	0.951977i	$-0.400953\pi$
$151$	13.6820	−	4.44554i	1.11342	−	0.361773i	0.807254	+	0.590204i	$0.200953\pi$
$152$	7.93881	+	1.25738i	0.643923	+	0.101987i
$153$	2.42531	+	2.42531i	0.196075	+	0.196075i
$154$		0			0
$155$	−6.78574	+	5.86223i	−0.545044	+	0.470866i
$156$	−11.7705	−	16.2007i	−0.942391	−	1.29709i
$157$	6.12609	−	12.0231i	0.488915	−	0.959550i	−0.506348	−	0.862330i	$-0.669005\pi$
$157$	6.12609	−	12.0231i	0.488915	−	0.959550i	0.995263	−	0.0972208i	$-0.0309953\pi$
$158$	−1.31803	−	2.58678i	−0.104857	−	0.205793i
$159$	7.50551	−	10.3304i	0.595225	−	0.819257i
$160$	−6.92723	+	8.20420i	−0.547645	+	0.648599i
$161$	−7.69629	−	2.50068i	−0.606553	−	0.197081i
$162$	−24.8921	−	12.6831i	−1.95570	−	0.996481i
$163$	−0.167887	+	1.06000i	−0.0131500	+	0.0830255i	−0.993391	−	0.114783i	$-0.963383\pi$
$163$	−0.167887	+	1.06000i	−0.0131500	+	0.0830255i	0.980241	+	0.197809i	$0.0633826\pi$
$164$	5.77242			0.450750
$165$		0			0
$166$	26.5315			2.05924
$167$	0.295948	−	1.86854i	0.0229011	−	0.144592i	−0.973588	−	0.228311i	$-0.926680\pi$
$167$	0.295948	−	1.86854i	0.0229011	−	0.144592i	0.996489	+	0.0837188i	$0.0266798\pi$
$168$	19.8798	+	10.1293i	1.53376	+	0.781489i
$169$	−7.52417	−	2.44475i	−0.578782	−	0.188058i
$170$	1.60375	+	19.0036i	0.123002	+	1.45751i
$171$	0.782597	−	1.07715i	0.0598467	−	0.0823719i
$172$	12.9470	+	25.4099i	0.987199	+	1.93749i
$173$	−8.60190	+	16.8822i	−0.653990	+	1.28353i	0.291092	+	0.956695i	$0.405981\pi$
$173$	−8.60190	+	16.8822i	−0.653990	+	1.28353i	−0.945082	+	0.326833i	$0.894019\pi$
$174$	−8.77346	−	12.0756i	−0.665114	−	0.915451i
$175$	5.39599	+	7.25306i	0.407898	+	0.548280i
$176$		0			0
$177$	−17.5618	−	17.5618i	−1.32002	−	1.32002i
$178$	9.65935	+	1.52989i	0.723999	+	0.114670i
$179$	−15.5810	+	5.06258i	−1.16458	+	0.378395i	−0.826618	−	0.562764i	$-0.809738\pi$
$179$	−15.5810	+	5.06258i	−1.16458	+	0.378395i	−0.337963	+	0.941159i	$0.609738\pi$
$180$	3.91571	+	9.30423i	0.291860	+	0.693497i
$181$	−12.0248	−	8.73652i	−0.893796	−	0.649380i	0.0430693	−	0.999072i	$-0.486286\pi$
$181$	−12.0248	−	8.73652i	−0.893796	−	0.649380i	−0.936865	+	0.349692i	$0.886286\pi$
$182$	−10.2130	+	1.61758i	−0.757038	+	0.119903i
$183$	16.6311	−	8.47398i	1.22941	−	0.626415i
$184$	−8.51316	−	26.2008i	−0.627599	−	1.93155i
$185$	6.09673	−	3.78366i	0.448241	−	0.278180i
$186$			20.3843i			1.49465i
$187$		0			0
$188$	24.1819	−	24.1819i	1.76365	−	1.76365i
$189$	−5.80777	+	4.21959i	−0.422453	+	0.306930i
$190$	7.18867	−	1.76889i	0.521521	−	0.128328i
$191$	−0.590092	+	1.81612i	−0.0426976	+	0.131410i	−0.970133	−	0.242574i	$-0.922008\pi$
$191$	−0.590092	+	1.81612i	−0.0426976	+	0.131410i	0.927435	+	0.373983i	$0.122008\pi$
$192$	−0.415459	−	2.62311i	−0.0299832	−	0.189306i
$193$	−1.78068	−	11.2428i	−0.128176	−	0.809273i	−0.965086	−	0.261933i	$-0.915640\pi$
$193$	−1.78068	−	11.2428i	−0.128176	−	0.809273i	0.836910	−	0.547341i	$-0.184360\pi$
$194$	0.609566	−	1.87605i	0.0437643	−	0.134693i
$195$	−8.65239	−	5.23514i	−0.619610	−	0.374896i
$196$	−13.3652	+	9.71036i	−0.954654	+	0.693597i
$197$	−13.8092	+	13.8092i	−0.983863	+	0.983863i	−0.999872	−	0.0160086i	$-0.994904\pi$
$197$	−13.8092	+	13.8092i	−0.983863	+	0.983863i	0.0160086	+	0.999872i	$0.494904\pi$
$198$		0			0
$199$			22.3508i			1.58441i	0.610258	+	0.792203i	$0.291066\pi$
$199$			22.3508i			1.58441i	−0.610258	+	0.792203i	$0.708934\pi$
$200$	−9.17867	+	29.3750i	−0.649030	+	2.07713i
$201$	2.15744	+	6.63992i	0.152174	+	0.468344i
$202$	22.0649	−	11.2426i	1.55248	−	0.791028i
$203$	−5.24391	+	0.830554i	−0.368051	+	0.0582935i
$204$	24.1598	+	17.5531i	1.69153	+	1.22897i
$205$	2.68688	−	1.13078i	0.187660	−	0.0789770i
$206$	11.2649	−	3.66018i	0.784862	−	0.255017i
$207$	−4.50726	−	0.713879i	−0.313276	−	0.0496181i
$208$	−10.7662	−	10.7662i	−0.746501	−	0.746501i
$209$		0			0
$210$	20.4953	+	1.49649i	1.41431	+	0.103267i
$211$	−0.221326	−	0.304629i	−0.0152367	−	0.0209715i	0.801331	−	0.598222i	$-0.204126\pi$
$211$	−0.221326	−	0.304629i	−0.0152367	−	0.0209715i	−0.816567	+	0.577250i	$0.804126\pi$
$212$	12.8027	−	25.1268i	0.879295	−	1.72571i
$213$	−6.16319	−	12.0959i	−0.422295	−	0.828801i
$214$	−22.8029	+	31.3855i	−1.55877	+	2.14547i
$215$	11.0041	+	9.29129i	0.750471	+	0.633661i
$216$	−23.2429	−	7.55209i	−1.58148	−	0.513855i
$217$	6.46041	+	3.29174i	0.438561	+	0.223458i
$218$	−7.09285	+	44.7825i	−0.480388	+	3.03305i
$219$	18.9340			1.27944
$220$		0			0
$221$	−7.58859			−0.510464
$222$	2.55160	−	16.1102i	0.171252	−	1.08125i
$223$	−6.78001	−	3.45459i	−0.454023	−	0.231336i	0.211997	−	0.977270i	$-0.432003\pi$
$223$	−6.78001	−	3.45459i	−0.454023	−	0.231336i	−0.666020	+	0.745934i	$0.732003\pi$
$224$	8.25716	+	2.68292i	0.551705	+	0.179260i
$225$	3.64528	+	3.56377i	0.243019	+	0.237585i
$226$	−11.1312	+	15.3208i	−0.740439	+	1.01913i
$227$	3.72393	+	7.30862i	0.247166	+	0.485090i	0.980942	−	0.194301i	$-0.0622439\pi$
$227$	3.72393	+	7.30862i	0.247166	+	0.485090i	−0.733776	+	0.679391i	$0.762244\pi$
$228$	5.26284	−	10.3289i	0.348540	−	0.684049i
$229$	−4.46080	−	6.13976i	−0.294778	−	0.405727i	0.635781	−	0.771869i	$-0.280678\pi$
$229$	−4.46080	−	6.13976i	−0.294778	−	0.405727i	−0.930559	+	0.366143i	$0.880678\pi$
$230$	−16.5878	−	19.2010i	−1.09377	−	1.26608i
$231$		0			0
$232$	−12.7807	−	12.7807i	−0.839092	−	0.839092i
$233$	−25.8944	−	4.10127i	−1.69640	−	0.268683i	−0.768049	−	0.640391i	$-0.778772\pi$
$233$	−25.8944	−	4.10127i	−1.69640	−	0.268683i	−0.928350	+	0.371708i	$0.878772\pi$
$234$	−5.54571	+	1.80191i	−0.362534	+	0.117795i
$235$	6.51885	−	15.9930i	0.425243	−	1.04327i
$236$	−44.3747	−	32.2401i	−2.88855	−	2.09865i
$237$	−2.26756	+	0.359146i	−0.147294	+	0.0233291i
$238$	13.7396	−	7.00070i	0.890609	−	0.453788i
$239$	−0.703327	−	2.16462i	−0.0454944	−	0.140017i	0.925729	−	0.378187i	$-0.123452\pi$
$239$	−0.703327	−	2.16462i	−0.0454944	−	0.140017i	−0.971224	+	0.238170i	$0.923452\pi$
$240$	15.9558	+	25.7101i	1.02994	+	1.65958i
$241$			6.29531i			0.405517i	0.979229	+	0.202758i	$0.0649906\pi$
$241$			6.29531i			0.405517i	−0.979229	+	0.202758i	$0.935009\pi$
$242$		0			0
$243$	−7.19883	+	7.19883i	−0.461805	+	0.461805i
$244$	33.3498	−	24.2300i	2.13500	−	1.55117i
$245$	−4.31887	+	7.13802i	−0.275923	+	0.456031i
$246$	2.04774	−	6.30231i	0.130559	−	0.401820i
$247$	0.460820	+	2.90950i	0.0293213	+	0.185127i
$248$	3.86140	+	24.3799i	0.245199	+	1.54813i
$249$	6.48342	−	19.9539i	0.410870	−	1.26453i
$250$	2.70286	+	28.2164i	0.170944	+	1.78456i
$251$	21.5157	−	15.6321i	1.35806	−	0.986687i	0.359492	−	0.933148i	$-0.382950\pi$
$251$	21.5157	−	15.6321i	1.35806	−	0.986687i	0.998566	−	0.0535389i	$-0.0170501\pi$
$252$	5.77157	−	5.77157i	0.363575	−	0.363575i
$253$		0			0
$254$			0.522752i			0.0328004i
$255$	14.6842	+	3.43769i	0.919560	+	0.215276i
$256$	−9.33673	−	28.7355i	−0.583546	−	1.79597i
$257$	−17.6189	+	8.97730i	−1.09904	+	0.559988i	−0.906886	−	0.421377i	$-0.861547\pi$
$257$	−17.6189	+	8.97730i	−1.09904	+	0.559988i	−0.192153	+	0.981365i	$0.561547\pi$
$258$	32.3354	−	5.12142i	2.01311	−	0.318846i
$259$	−4.69377	−	3.41022i	−0.291657	−	0.211901i
$260$	−20.6821	−	8.43013i	−1.28265	−	0.522815i
$261$	−2.84747	+	0.925199i	−0.176254	+	0.0572684i
$262$	−1.38153	−	0.218812i	−0.0853510	−	0.0135183i
$263$	5.91748	+	5.91748i	0.364888	+	0.364888i	0.865609	−	0.500721i	$-0.166932\pi$
$263$	5.91748	+	5.91748i	0.364888	+	0.364888i	−0.500721	+	0.865609i	$0.666932\pi$
$264$		0			0
$265$	1.03710	−	14.2037i	0.0637085	−	0.872526i
$266$	−3.51845	−	4.84273i	−0.215730	−	0.296927i
$267$	3.51104	−	6.89079i	0.214872	−	0.421710i
$268$	6.99999	+	13.7383i	0.427592	+	0.839198i
$269$	5.70779	−	7.85609i	0.348010	−	0.478994i	−0.598750	−	0.800936i	$-0.704336\pi$
$269$	5.70779	−	7.85609i	0.348010	−	0.478994i	0.946759	+	0.321942i	$0.104336\pi$
$270$	−22.4296	+	1.89289i	−1.36502	+	0.115197i
$271$	−2.90211	−	0.942954i	−0.176291	−	0.0572804i	0.219542	−	0.975603i	$-0.429544\pi$
$271$	−2.90211	−	0.942954i	−0.176291	−	0.0572804i	−0.395832	+	0.918323i	$0.629544\pi$
$272$	20.2311	+	10.3082i	1.22669	+	0.625029i
$273$	−1.27916	+	8.07633i	−0.0774186	+	0.488802i
$274$	39.2374			2.37042
$275$		0			0
$276$	−39.7326			−2.39162
$277$	0.372337	−	2.35085i	0.0223716	−	0.141249i	−0.973974	−	0.226658i	$-0.927220\pi$
$277$	0.372337	−	2.35085i	0.0223716	−	0.141249i	0.996346	+	0.0854097i	$0.0272199\pi$
$278$	−3.21389	−	1.63756i	−0.192757	−	0.0982144i
$279$	3.88868	+	1.26351i	0.232809	+	0.0756443i
$280$	24.7962	−	2.09261i	1.48185	−	0.125057i
$281$	16.5944	−	22.8402i	0.989939	−	1.36253i	0.0586395	−	0.998279i	$-0.481324\pi$
$281$	16.5944	−	22.8402i	0.989939	−	1.36253i	0.931299	−	0.364255i	$-0.118676\pi$
$282$	−17.8233	−	34.9802i	−1.06136	−	2.08304i
$283$	−7.72394	+	15.1591i	−0.459141	+	0.901114i	0.539124	+	0.842226i	$0.318755\pi$
$283$	−7.72394	+	15.1591i	−0.459141	+	0.901114i	−0.998265	+	0.0588878i	$0.981245\pi$
$284$	−17.6227	−	24.2555i	−1.04571	−	1.43930i
$285$	0.426322	−	5.83874i	0.0252532	−	0.345857i
$286$		0			0
$287$	−1.66672	−	1.66672i	−0.0983831	−	0.0983831i
$288$	4.83573	+	0.765904i	0.284948	+	0.0451313i
$289$	−5.40508	+	1.75622i	−0.317946	+	0.103307i
$290$	−15.4160	−	6.28365i	−0.905257	−	0.368988i
$291$	−1.26199	−	0.916890i	−0.0739792	−	0.0537491i
$292$	41.3006	−	6.54137i	2.41693	−	0.382805i
$293$	−9.52030	+	4.85084i	−0.556182	+	0.283389i	−0.709403	−	0.704803i	$-0.751035\pi$
$293$	−9.52030	+	4.85084i	−0.556182	+	0.283389i	0.153221	+	0.988192i	$0.451035\pi$
$294$	5.86050	+	18.0368i	0.341791	+	1.05193i
$295$	−26.9707	−	6.31405i	−1.57029	−	0.367618i
$296$		−	19.7514i		−	1.14803i
$297$		0			0
$298$	−42.6760	+	42.6760i	−2.47215	+	2.47215i
$299$	8.16826	−	5.93459i	0.472383	−	0.343206i
$300$	36.2016	+	25.6817i	2.09010	+	1.48274i
$301$	3.59852	−	11.0751i	0.207415	−	0.638358i
$302$	−5.70565	−	36.0240i	−0.328323	−	2.07295i
$303$	−3.06347	−	19.3420i	−0.175992	−	1.11117i
$304$	2.72369	−	8.38266i	0.156214	−	0.480778i
$305$	10.7768	−	17.8113i	0.617076	−	1.01987i
$306$	7.03509	−	5.11129i	0.402169	−	0.292193i
$307$	22.9923	−	22.9923i	1.31224	−	1.31224i	0.392474	−	0.919763i	$-0.371619\pi$
$307$	22.9923	−	22.9923i	1.31224	−	1.31224i	0.919763	−	0.392474i	$-0.128381\pi$
$308$		0			0
$309$		−	9.36657i		−	0.532846i
$310$	11.9883	+	19.3171i	0.680888	+	1.09714i
$311$	4.29183	+	13.2089i	0.243367	+	0.749007i	0.995901	+	0.0904531i	$0.0288315\pi$
$311$	4.29183	+	13.2089i	0.243367	+	0.749007i	−0.752534	+	0.658554i	$0.771168\pi$
$312$	−24.8032	+	12.6379i	−1.40421	+	0.715479i
$313$	17.1739	−	2.72008i	0.970728	−	0.153748i	0.349121	−	0.937078i	$-0.386480\pi$
$313$	17.1739	−	2.72008i	0.970728	−	0.153748i	0.621607	+	0.783329i	$0.286480\pi$
$314$	−27.6773	−	20.1088i	−1.56192	−	1.13480i
$315$	1.55587	−	3.81710i	0.0876635	−	0.215069i
$316$	−4.82214	+	1.56681i	−0.271267	+	0.0881399i
$317$	−15.9581	−	2.52751i	−0.896296	−	0.141959i	−0.308743	−	0.951145i	$-0.599908\pi$
$317$	−15.9581	−	2.52751i	−0.896296	−	0.141959i	−0.587552	+	0.809186i	$0.699908\pi$
$318$	−22.8916	−	22.8916i	−1.28370	−	1.28370i
$319$		0			0
$320$	−1.93639	−	2.24144i	−0.108248	−	0.125300i
$321$	18.0322	+	24.8193i	1.00646	+	1.38528i
$322$	−9.31434	+	18.2804i	−0.519068	+	1.01873i
$323$	−1.99437	−	3.91418i	−0.110970	−	0.217791i
$324$	−28.6783	+	39.4723i	−1.59324	+	2.19290i
$325$	−11.2783	+	0.127518i	−0.625606	+	0.00707341i
$326$	2.58775	+	0.840810i	0.143322	+	0.0465682i
$327$	31.9470	+	16.2778i	1.76667	+	0.900164i
$328$	1.25528	−	7.92556i	0.0693115	−	0.437616i
$329$	−13.9645			−0.769887
$330$		0			0
$331$	14.6837			0.807090			0.403545	−	0.914960i	$-0.367778\pi$
$331$	14.6837			0.807090			0.403545	+	0.914960i	$0.367778\pi$
$332$	7.24851	−	45.7653i	0.397813	−	2.51170i
$333$	−2.91516	−	1.48535i	−0.159750	−	0.0813965i
$334$	−4.56162	−	1.48216i	−0.249601	−	0.0811002i
$335$	5.94951	+	5.02348i	0.325057	+	0.274462i
$336$	14.3810	−	19.7938i	0.784548	−	1.07984i
$337$	6.12483	+	12.0207i	0.333641	+	0.654807i	0.995494	−	0.0948269i	$-0.0302297\pi$
$337$	6.12483	+	12.0207i	0.333641	+	0.654807i	−0.661853	+	0.749634i	$0.730230\pi$
$338$	−9.10603	+	17.8716i	−0.495303	+	0.972086i
$339$	8.80245	+	12.1155i	0.478084	+	0.658026i
$340$	33.2182	+	2.42547i	1.80151	+	0.131539i
$341$		0			0
$342$	−2.38690	−	2.38690i	−0.129069	−	0.129069i
$343$	19.1631	+	3.03514i	1.03471	+	0.163882i
$344$	37.7034	−	12.2506i	2.03283	−	0.660507i
$345$	−18.4943	+	7.78335i	−0.995698	+	0.419042i
$346$	38.8629	+	28.2355i	2.08928	+	1.51795i
$347$	12.0852	−	1.91410i	0.648766	−	0.102755i	0.176626	−	0.984278i	$-0.443482\pi$
$347$	12.0852	−	1.91410i	0.648766	−	0.102755i	0.472140	+	0.881523i	$0.343482\pi$
$348$	−23.2267	+	11.8346i	−1.24508	+	0.634401i
$349$	−6.29508	−	19.3743i	−0.336968	−	1.03708i	−0.965745	−	0.259494i	$-0.916444\pi$
$349$	−6.29508	−	19.3743i	−0.336968	−	1.03708i	0.628777	−	0.777586i	$-0.283556\pi$
$350$	20.3024	−	10.6354i	1.08521	−	0.568487i
$351$		−	8.95670i		−	0.478073i
$352$		0			0
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	−0.237495	−	0.971389i	$-0.576326\pi$
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	0.971389	+	0.237495i	$0.0763264\pi$
$354$	−50.9415	+	37.0111i	−2.70751	+	1.96712i
$355$	−12.9543	−	7.83803i	−0.687544	−	0.415999i
$356$	5.27795	−	16.2439i	0.279731	−	0.860923i
$357$	−1.90760	−	12.0441i	−0.100961	−	0.637442i
$358$	6.49759	+	41.0242i	0.343408	+	2.16819i
$359$	5.10491	−	15.7113i	0.269427	−	0.829210i	−0.721214	−	0.692713i	$-0.756415\pi$
$359$	5.10491	−	15.7113i	0.269427	−	0.829210i	0.990640	−	0.136497i	$-0.0435845\pi$
$360$	13.6263	−	3.35296i	0.718168	−	0.176717i
$361$	13.9917	−	10.1656i	0.736406	−	0.535030i
$362$	−26.6462	+	26.6462i	−1.40049	+	1.40049i
$363$		0			0
$364$			18.0588i			0.946537i
$365$	17.9427	−	11.1353i	0.939165	−	0.582849i
$366$	−14.6236	−	45.0067i	−0.764386	−	2.35254i
$367$	5.73930	−	2.92432i	0.299589	−	0.152648i	−0.297734	−	0.954649i	$-0.596231\pi$
$367$	5.73930	−	2.92432i	0.299589	−	0.152648i	0.597323	+	0.802001i	$0.296231\pi$
$368$	−29.8379	+	4.72586i	−1.55541	+	0.246353i
$369$	−1.07535	−	0.781290i	−0.0559807	−	0.0406723i
$370$	−7.05659	−	16.7674i	−0.366855	−	0.871696i
$371$	−10.9517	+	3.55842i	−0.568583	+	0.184744i
$372$	35.1617	+	5.56907i	1.82305	+	0.288743i
$373$	−9.69631	−	9.69631i	−0.502056	−	0.502056i	0.410021	−	0.912076i	$-0.365522\pi$
$373$	−9.69631	−	9.69631i	−0.502056	−	0.502056i	−0.912076	+	0.410021i	$0.865522\pi$
$374$		0			0
$375$	21.8816	+	4.86238i	1.12996	+	0.251092i
$376$	−27.9433	−	38.4606i	−1.44106	−	1.98345i
$377$	3.00731	−	5.90219i	0.154885	−	0.303978i
$378$	8.26282	+	16.2167i	0.424994	+	0.834097i
$379$	−12.6380	+	17.3947i	−0.649171	+	0.893507i	−0.999063	−	0.0432830i	$-0.986218\pi$
$379$	−12.6380	+	17.3947i	−0.649171	+	0.893507i	0.349892	+	0.936790i	$0.386218\pi$
$380$	−1.08725	−	12.8833i	−0.0557748	−	0.660900i
$381$	0.393154	+	0.127743i	0.0201419	+	0.00654449i
$382$	4.31368	+	2.19793i	0.220707	+	0.112456i
$383$	−0.0474676	+	0.299698i	−0.00242548	+	0.0153139i	−0.988871	−	0.148773i	$-0.952468\pi$
$383$	−0.0474676	+	0.299698i	−0.00242548	+	0.0153139i	0.986446	+	0.164087i	$0.0524677\pi$
$384$	−25.9882			−1.32620
$385$		0			0
$386$	−28.8592			−1.46889
$387$	1.02728	−	6.48602i	0.0522198	−	0.329703i
$388$	−3.06954	−	1.56401i	−0.155833	−	0.0794006i
$389$	3.42506	+	1.11287i	0.173657	+	0.0564247i	0.394555	−	0.918872i	$-0.370899\pi$
$389$	3.42506	+	1.11287i	0.173657	+	0.0564247i	−0.220898	+	0.975297i	$0.570899\pi$
$390$	−16.5409	+	19.5901i	−0.837580	+	0.991981i
$391$	−8.85017	+	12.1812i	−0.447572	+	0.616030i
$392$	10.4259	+	20.4621i	0.526590	+	1.03349i
$393$	−0.502165	+	0.985554i	−0.0253309	+	0.0497146i
$394$	29.1026	+	40.0563i	1.46617	+	2.01801i
$395$	−1.93763	+	1.67393i	−0.0974927	+	0.0842244i
$396$		0			0
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.992731	+	0.120357i	$0.0384039\pi$
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.120357	+	0.992731i	$0.461596\pi$
$398$	55.9684	+	8.86452i	2.80544	+	0.444338i
$399$	−4.50193	+	1.46277i	−0.225378	+	0.0732299i
$400$	30.2409	+	14.9803i	1.51204	+	0.749014i
$401$	8.08801	+	5.87628i	0.403896	+	0.293447i	0.771126	−	0.636683i	$-0.219694\pi$
$401$	8.08801	+	5.87628i	0.403896	+	0.293447i	−0.367230	+	0.930130i	$0.619694\pi$
$402$	17.4826	−	2.76897i	0.871953	−	0.138104i
$403$	−8.06040	+	4.10698i	−0.401517	+	0.204583i
$404$	−13.3647	−	41.1322i	−0.664916	−	2.04640i
$405$	−5.61649	+	23.9910i	−0.279085	+	1.19212i
$406$			13.4606i			0.668040i
$407$		0			0
$408$	29.3544	−	29.3544i	1.45326	−	1.45326i
$409$	−24.5870	+	17.8635i	−1.21575	+	0.883293i	−0.995740	−	0.0922049i	$-0.970609\pi$
$409$	−24.5870	+	17.8635i	−1.21575	+	0.883293i	−0.220009	+	0.975498i	$0.570609\pi$
$410$	−1.76593	−	7.17667i	−0.0872132	−	0.354430i
$411$	9.58834	−	29.5099i	0.472958	−	1.45561i
$412$	−3.23599	−	20.4313i	−0.159426	−	1.00658i
$413$	3.50372	+	22.1216i	0.172407	+	1.08853i
$414$	−3.57524	+	11.0034i	−0.175713	+	0.540790i
$415$	−5.59117	−	22.7222i	−0.274460	−	1.11539i
$416$	−8.76352	+	6.36707i	−0.429667	+	0.312171i
$417$	−2.01695	+	2.01695i	−0.0987706	+	0.0987706i
$418$		0			0
$419$		−	7.48185i		−	0.365512i	−0.983158	−	0.182756i	$-0.941498\pi$
$419$		−	7.48185i		−	0.365512i	0.983158	−	0.182756i	$-0.0585019\pi$
$420$	8.18075	−	34.9444i	0.399180	−	1.70511i
$421$	6.31106	+	19.4234i	0.307582	+	0.946640i	0.978701	+	0.205291i	$0.0658140\pi$
$421$	6.31106	+	19.4234i	0.307582	+	0.946640i	−0.671119	+	0.741350i	$0.734186\pi$
$422$	−0.850599	+	0.433402i	−0.0414065	+	0.0210977i
$423$	−7.77789	+	1.23190i	−0.378174	+	0.0598969i
$424$	−31.7151	−	23.0423i	−1.54022	−	1.11903i
$425$	15.9372	−	5.37825i	0.773066	−	0.260884i
$426$	−32.7337	+	10.6358i	−1.58595	+	0.515308i
$427$	−16.6255	−	2.63322i	−0.804563	−	0.127430i
$428$	47.9083	+	47.9083i	2.31573	+	2.31573i
$429$		0			0
$430$	27.6305	−	23.8702i	1.33246	−	1.15112i
$431$	−19.7884	−	27.2363i	−0.953172	−	1.31193i	−0.950104	−	0.311933i	$-0.899024\pi$
$431$	−19.7884	−	27.2363i	−0.953172	−	1.31193i	−0.00306745	−	0.999995i	$-0.500976\pi$
$432$	−12.1667	+	23.8784i	−0.585369	+	1.14885i
$433$	5.26591	+	10.3349i	0.253063	+	0.496665i	0.982232	−	0.187669i	$-0.0600932\pi$
$433$	5.26591	+	10.3349i	0.253063	+	0.496665i	−0.729169	+	0.684334i	$0.760093\pi$
$434$	10.8051	−	14.8719i	0.518660	−	0.713875i
$435$	−8.49299	+	10.0586i	−0.407208	+	0.482273i
$436$	75.3094	+	24.4695i	3.60667	+	1.17188i
$437$	5.20776	+	2.65349i	0.249121	+	0.126934i
$438$	7.50938	−	47.4124i	0.358812	−	2.26545i
$439$	10.7242			0.511837			0.255918	−	0.966698i	$-0.417622\pi$
$439$	10.7242			0.511837			0.255918	+	0.966698i	$0.417622\pi$
$440$		0			0
$441$	3.80411			0.181148
$442$	−3.00970	+	19.0025i	−0.143157	+	0.903858i
$443$	35.9376	+	18.3111i	1.70745	+	0.869987i	0.983677	+	0.179945i	$0.0575921\pi$
$443$	35.9376	+	18.3111i	1.70745	+	0.869987i	0.723769	+	0.690042i	$0.242408\pi$
$444$	−27.0920	−	8.80274i	−1.28573	−	0.417759i
$445$	−0.725346	−	8.59493i	−0.0343847	−	0.407439i
$446$	−11.3396	+	15.6076i	−0.536946	+	0.739043i
$447$	21.6673	+	42.5245i	1.02483	+	2.01134i
$448$	−1.08732	+	2.13398i	−0.0513709	+	0.100821i
$449$	−2.14048	−	2.94612i	−0.101016	−	0.139036i	0.755517	−	0.655129i	$-0.227386\pi$
$449$	−2.14048	−	2.94612i	−0.101016	−	0.139036i	−0.856532	+	0.516093i	$0.827386\pi$
$450$	10.3698	−	7.71468i	0.488835	−	0.363674i
$451$		0			0
$452$	23.3865	+	23.3865i	1.10001	+	1.10001i
$453$	−28.4874	−	4.51196i	−1.33845	−	0.211990i
$454$	19.7784	−	6.42639i	0.928246	−	0.301605i
$455$	3.53760	+	8.40580i	0.165845	+	0.394070i
$456$	−13.0372	−	9.47206i	−0.610522	−	0.443570i
$457$	−17.8699	+	2.83032i	−0.835920	+	0.132397i	−0.559698	−	0.828697i	$-0.689083\pi$
$457$	−17.8699	+	2.83032i	−0.835920	+	0.132397i	−0.276223	+	0.961094i	$0.589083\pi$
$458$	−17.1437	+	8.73515i	−0.801072	+	0.408167i
$459$	4.12754	+	12.7033i	0.192657	+	0.592938i
$460$	−37.6524	+	23.3672i	−1.75555	+	1.08950i
$461$			35.5884i			1.65751i	0.559608	+	0.828757i	$0.310952\pi$
$461$			35.5884i			1.65751i	−0.559608	+	0.828757i	$0.689048\pi$
$462$		0			0
$463$	−4.46802	+	4.46802i	−0.207647	+	0.207647i	−0.803266	−	0.595620i	$-0.796907\pi$
$463$	−4.46802	+	4.46802i	−0.207647	+	0.207647i	0.595620	+	0.803266i	$0.296907\pi$
$464$	−16.0349	+	11.6500i	−0.744402	+	0.540839i
$465$	17.4576	−	4.29573i	0.809579	−	0.199210i
$466$	−20.5399	+	63.2153i	−0.951492	+	2.92839i
$467$	1.35359	+	8.54624i	0.0626367	+	0.395473i	0.999011	+	0.0444689i	$0.0141596\pi$
$467$	1.35359	+	8.54624i	0.0626367	+	0.395473i	−0.936374	+	0.351004i	$0.885840\pi$
$468$	1.59308	+	10.0583i	0.0736402	+	0.464946i
$469$	1.94559	−	5.98792i	0.0898391	−	0.276496i
$470$	−37.4625	−	22.6668i	−1.72802	−	1.04554i
$471$	−21.8869	+	15.9018i	−1.00850	+	0.732715i
$472$	−53.9157	+	53.9157i	−2.48167	+	2.48167i
$473$		0			0
$474$			5.82062i			0.267350i
$475$	−3.02984	−	5.78379i	−0.139018	−	0.265379i
$476$	−8.32208	−	25.6127i	−0.381442	−	1.17396i
$477$	−5.78592	+	2.94807i	−0.264919	+	0.134983i
$478$	−5.69934	+	0.902687i	−0.260682	+	0.0412880i
$479$	12.4456	+	9.04222i	0.568652	+	0.413150i	0.834615	−	0.550833i	$-0.185690\pi$
$479$	12.4456	+	9.04222i	0.568652	+	0.413150i	−0.265963	+	0.963983i	$0.585690\pi$
$480$	19.8420	−	8.35057i	0.905661	−	0.381150i
$481$	6.88441	−	2.23688i	0.313902	−	0.101993i
$482$	15.7640	+	2.49678i	0.718032	+	0.113725i
$483$	11.4723	+	11.4723i	0.522008	+	0.522008i
$484$		0			0
$485$	−1.73516	−	0.126694i	−0.0787894	−	0.00575290i
$486$	15.1714	+	20.8816i	0.688189	+	0.947211i
$487$	−2.69960	+	5.29826i	−0.122330	+	0.240087i	−0.944048	−	0.329808i	$-0.893016\pi$
$487$	−2.69960	+	5.29826i	−0.122330	+	0.240087i	0.821718	+	0.569895i	$0.193016\pi$
$488$	−26.0156	−	51.0585i	−1.17767	−	2.31131i
$489$	1.26472	−	1.74074i	0.0571926	−	0.0787189i
$490$	16.1613	+	13.6458i	0.730095	+	0.616456i
$491$	−38.9464	−	12.6545i	−1.75763	−	0.571088i	−0.760677	−	0.649130i	$-0.775133\pi$
$491$	−38.9464	−	12.6545i	−1.75763	−	0.571088i	−0.996950	+	0.0780428i	$0.975133\pi$
$492$	−10.3117	−	5.25406i	−0.464886	−	0.236871i
$493$	−1.54535	+	9.75693i	−0.0695988	+	0.439430i
$494$	7.46842			0.336020
$495$		0			0
$496$	27.0678			1.21538
$497$	−1.91516	+	12.0918i	−0.0859066	+	0.542393i
$498$	−47.3950	−	24.1490i	−2.12382	−	1.08214i
$499$	22.0520	+	7.16511i	0.987181	+	0.320755i	0.757732	−	0.652566i	$-0.226308\pi$
$499$	22.0520	+	7.16511i	0.987181	+	0.320755i	0.229449	+	0.973321i	$0.426308\pi$
$500$	49.4101	+	3.04657i	2.20969	+	0.136247i
$501$	−2.22942	+	3.06853i	−0.0996031	+	0.137092i
$502$	−30.6108	−	60.0770i	−1.36623	−	2.68137i
$503$	1.51788	−	2.97901i	0.0676789	−	0.132827i	−0.854688	−	0.519141i	$-0.826252\pi$
$503$	1.51788	−	2.97901i	0.0676789	−	0.132827i	0.922367	+	0.386314i	$0.126252\pi$
$504$	−6.66929	−	9.17950i	−0.297074	−	0.408887i
$505$	−14.2784	−	16.5277i	−0.635379	−	0.735473i
$506$		0			0
$507$	11.2157	+	11.2157i	0.498108	+	0.498108i
$508$	0.901717	+	0.142818i	0.0400072	+	0.00633652i
$509$	−21.0623	+	6.84355i	−0.933569	+	0.303335i	−0.736021	−	0.676959i	$-0.763298\pi$
$509$	−21.0623	+	6.84355i	−0.933569	+	0.303335i	−0.197547	+	0.980293i	$0.563298\pi$
$510$	14.4322	−	35.4071i	0.639067	−	1.56785i
$511$	−13.8138	−	10.0363i	−0.611086	−	0.443980i
$512$	−50.0537	+	7.92773i	−2.21208	+	0.350359i
$513$	4.61984	−	2.35393i	0.203971	−	0.103928i
$514$	15.4921	+	47.6799i	0.683329	+	2.10307i
$515$	−5.50860	−	8.87620i	−0.242738	−	0.391132i
$516$		−	57.1759i		−	2.51703i
$517$		0			0
$518$	−10.4011	+	10.4011i	−0.456998	+	0.456998i
$519$	30.7323	−	22.3283i	1.34900	−	0.980105i
$520$	−16.0722	+	26.5633i	−0.704812	+	1.16488i
$521$	−3.28368	+	10.1061i	−0.143861	+	0.442758i	−0.996863	−	0.0791498i	$-0.974779\pi$
$521$	−3.28368	+	10.1061i	−0.143861	+	0.442758i	0.853002	+	0.521908i	$0.174779\pi$
$522$	1.18745	+	7.49726i	0.0519733	+	0.328146i
$523$	−6.76212	−	42.6943i	−0.295687	−	1.86689i	−0.470654	−	0.882318i	$-0.655982\pi$
$523$	−6.76212	−	42.6943i	−0.295687	−	1.86689i	0.174967	−	0.984574i	$-0.444018\pi$
$524$	−0.754877	+	2.32327i	−0.0329770	+	0.101493i
$525$	−3.03749	−	17.8681i	−0.132567	−	0.779827i
$526$	17.1648	−	12.4710i	0.748422	−	0.543761i
$527$	9.53941	−	9.53941i	0.415543	−	0.415543i
$528$		0			0
$529$			2.96712i			0.129005i
$530$	−35.1560	−	8.23030i	−1.52708	−	0.357502i
$531$	3.90298	+	12.0121i	0.169375	+	0.521283i
$532$	−9.31468	+	4.74607i	−0.403842	+	0.205768i
$533$	2.90464	−	0.460050i	0.125814	−	0.0199270i
$534$	−15.8627	−	11.5249i	−0.686445	−	0.498731i
$535$	31.6847	+	12.9149i	1.36985	+	0.558359i
$536$	20.3849	−	6.62347i	0.880495	−	0.286090i
$537$	32.4414	+	5.13822i	1.39995	+	0.221731i
$538$	−17.4086	−	17.4086i	−0.750538	−	0.750538i
$539$		0			0
$540$	−2.86274	+	39.2069i	−0.123193	+	1.68720i
$541$	−12.4089	−	17.0793i	−0.533499	−	0.734298i	0.454160	−	0.890920i	$-0.349940\pi$
$541$	−12.4089	−	17.0793i	−0.533499	−	0.734298i	−0.987659	+	0.156622i	$0.949940\pi$
$542$	−3.51224	+	6.89317i	−0.150864	+	0.296087i
$543$	13.5287	+	26.5516i	0.580573	+	1.13944i
$544$	9.49513	−	13.0689i	0.407100	−	0.560325i
$545$	39.8476	−	3.36283i	1.70688	−	0.144048i
$546$	19.7165	+	6.40629i	0.843789	+	0.274164i
$547$	1.24199	+	0.632824i	0.0531036	+	0.0270576i	0.480341	−	0.877082i	$-0.340513\pi$
$547$	1.24199	+	0.632824i	0.0531036	+	0.0270576i	−0.427237	+	0.904140i	$0.640513\pi$
$548$	10.7198	−	67.6823i	0.457928	−	2.89125i
$549$	−9.49230			−0.405121
$550$		0			0
$551$	3.83469			0.163363
$552$	−8.64035	+	54.5530i	−0.367758	+	2.32193i
$553$	1.84473	+	0.939938i	0.0784460	+	0.0399702i
$554$	−5.73906	−	1.86473i	−0.243829	−	0.0792249i
$555$	−14.3349	+	1.20976i	−0.608483	+	0.0513513i
$556$	−3.70275	+	5.09639i	−0.157031	+	0.216135i
$557$	1.73985	+	3.41464i	0.0737197	+	0.144683i	0.924925	−	0.380150i	$-0.124128\pi$
$557$	1.73985	+	3.41464i	0.0737197	+	0.144683i	−0.851205	+	0.524833i	$0.824128\pi$
$558$	4.70623	−	9.23649i	0.199231	−	0.391012i
$559$	8.53997	+	11.7543i	0.361202	+	0.497152i
$560$	1.98715	−	27.2152i	0.0839722	−	1.15005i
$561$		0			0
$562$	−50.6125	−	50.6125i	−2.13496	−	2.13496i
$563$	−2.41207	−	0.382035i	−0.101657	−	0.0161008i	0.105399	−	0.994430i	$-0.466388\pi$
$563$	−2.41207	−	0.382035i	−0.101657	−	0.0161008i	−0.207056	+	0.978329i	$0.566388\pi$
$564$	−65.2083	+	21.1875i	−2.74576	+	0.892153i
$565$	15.4669	+	6.30441i	0.650698	+	0.265229i
$566$	34.8963	+	25.3537i	1.46680	+	1.06569i
$567$	19.6777	−	3.11664i	0.826384	−	0.130886i
$568$	−37.1353	+	18.9214i	−1.55816	+	0.793923i
$569$	−1.99158	−	6.12946i	−0.0834915	−	0.256961i	0.900592	−	0.434665i	$-0.143133\pi$
$569$	−1.99158	−	6.12946i	−0.0834915	−	0.256961i	−0.984084	+	0.177704i	$0.943133\pi$
$570$	−14.4517	−	3.38325i	−0.605313	−	0.141709i
$571$			13.2864i			0.556019i	0.960578	+	0.278009i	$0.0896747\pi$
$571$			13.2864i			0.556019i	−0.960578	+	0.278009i	$0.910325\pi$
$572$		0			0
$573$	2.70715	−	2.70715i	0.113093	−	0.113093i
$574$	−4.83464	+	3.51257i	−0.201794	+	0.146612i
$575$	−12.9485	+	18.2526i	−0.539992	+	0.761186i
$576$	−0.417358	+	1.28450i	−0.0173899	+	0.0535206i
$577$	−2.92981	−	18.4981i	−0.121969	−	0.770085i	−0.970529	−	0.240985i	$-0.922530\pi$
$577$	−2.92981	−	18.4981i	−0.121969	−	0.770085i	0.848559	−	0.529100i	$-0.177470\pi$
$578$	2.25402	+	14.2313i	0.0937550	+	0.591946i
$579$	−7.05223	+	21.7045i	−0.293081	+	0.902010i
$580$	−15.0506	+	24.8750i	−0.624944	+	1.03288i
$581$	−15.3071	+	11.1213i	−0.635045	+	0.461387i
$582$	−2.79649	+	2.79649i	−0.115918	+	0.115918i
$583$		0			0
$584$		−	58.1284i		−	2.40537i
$585$	2.71189	+	4.36976i	0.112123	+	0.180667i
$586$	8.37110	+	25.7636i	0.345807	+	1.06428i
$587$	7.51037	−	3.82673i	0.309986	−	0.157946i	−0.292076	−	0.956395i	$-0.594346\pi$
$587$	7.51037	−	3.82673i	0.309986	−	0.157946i	0.602062	+	0.798449i	$0.294346\pi$
$588$	32.7135	−	5.18131i	1.34908	−	0.213673i
$589$	−4.23674	−	3.07817i	−0.174572	−	0.126834i
$590$	−26.5078	+	65.0328i	−1.09131	+	2.67736i
$591$	37.2374	−	12.0992i	1.53174	−	0.497693i
$592$	−21.3923	−	3.38820i	−0.879217	−	0.139254i
$593$	−4.37233	−	4.37233i	−0.179550	−	0.179550i	0.611610	−	0.791160i	$-0.290522\pi$
$593$	−4.37233	−	4.37233i	−0.179550	−	0.179550i	−0.791160	+	0.611610i	$0.790522\pi$
$594$		0			0
$595$	−8.89103	−	10.2917i	−0.364497	−	0.421918i
$596$	61.9543	+	85.2728i	2.53775	+	3.49291i
$597$	20.3437	−	39.9268i	0.832612	−	1.63409i
$598$	−11.6211	−	22.8078i	−0.475224	−	0.932679i
$599$	−21.5069	+	29.6017i	−0.878748	+	1.20949i	0.0980183	+	0.995185i	$0.468750\pi$
$599$	−21.5069	+	29.6017i	−0.878748	+	1.20949i	−0.976766	+	0.214308i	$0.931250\pi$
$600$	43.1336	−	44.1202i	1.76092	−	1.80120i
$601$	−10.2436	−	3.32834i	−0.417844	−	0.135766i	0.0925467	−	0.995708i	$-0.470499\pi$
$601$	−10.2436	−	3.32834i	−0.417844	−	0.135766i	−0.510391	+	0.859943i	$0.670499\pi$
$602$	−26.3058	−	13.4035i	−1.07215	−	0.546286i
$603$	0.555417	−	3.50677i	0.0226183	−	0.142807i
$604$	−63.6982			−2.59184
$605$		0			0
$606$	−49.6491			−2.01686
$607$	−5.17723	+	32.6877i	−0.210137	+	1.32675i	0.626682	+	0.779275i	$0.284412\pi$
$607$	−5.17723	+	32.6877i	−0.210137	+	1.32675i	−0.836819	+	0.547479i	$0.815588\pi$
$608$	−5.58728	−	2.84686i	−0.226594	−	0.115455i
$609$	10.1235	+	3.28934i	0.410226	+	0.133291i
$610$	−40.3270	−	34.0501i	−1.63279	−	1.37865i
$611$	10.2409	−	14.0955i	0.414304	−	0.570241i
$612$	−6.89467	−	13.5315i	−0.278700	−	0.546980i
$613$	9.82369	−	19.2801i	0.396775	−	0.778715i	−0.603044	−	0.797708i	$-0.706046\pi$
$613$	9.82369	−	19.2801i	0.396775	−	0.778715i	0.999820	+	0.0189923i	$0.00604581\pi$
$614$	−48.4557	−	66.6936i	−1.95551	−	2.69153i
$615$	−5.82899	−	0.425611i	−0.235048	−	0.0171623i
$616$		0			0
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	0.0616431	−	0.998098i	$-0.480366\pi$
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	−0.998098	+	0.0616431i	$0.980366\pi$
$618$	−23.4547	−	3.71487i	−0.943488	−	0.149434i
$619$	39.3965	−	12.8007i	1.58348	−	0.514503i	0.620528	−	0.784184i	$-0.286918\pi$
$619$	39.3965	−	12.8007i	1.58348	−	0.514503i	0.962950	+	0.269681i	$0.0869184\pi$
$620$	36.5961	−	15.4016i	1.46974	−	0.618542i
$621$	−14.3773	−	10.4457i	−0.576941	−	0.419172i
$622$	34.7784	−	5.50836i	1.39449	−	0.220865i
$623$	−6.21416	+	3.16627i	−0.248965	+	0.126854i
$624$	9.43299	+	29.0318i	0.377622	+	1.16220i
$625$	23.5957	−	8.26104i	0.943826	−	0.330441i
$626$		−	44.0839i		−	1.76195i
$627$		0			0
$628$	−42.2480	+	42.2480i	−1.68588	+	1.68588i
$629$	−8.73332	+	6.34513i	−0.348220	+	0.252997i
$630$	−8.94129	−	5.40994i	−0.356229	−	0.215537i
$631$	−9.72155	+	29.9199i	−0.387009	+	1.19109i	0.548004	+	0.836476i	$0.315388\pi$
$631$	−9.72155	+	29.9199i	−0.387009	+	1.19109i	−0.935013	+	0.354615i	$0.884612\pi$
$632$	1.10260	+	6.96154i	0.0438591	+	0.276915i
$633$	0.118096	+	0.745631i	0.00469391	+	0.0296362i
$634$	−12.6582	+	38.9581i	−0.502723	+	1.54722i
$635$	0.447698	−	0.110163i	0.0177664	−	0.00437169i
$636$	−45.7408	+	33.2326i	−1.81374	+	1.31776i
$637$	−5.95137	+	5.95137i	−0.235802	+	0.235802i
$638$		0			0
$639$			6.90382i			0.273111i
$640$	−24.6276	+	15.2840i	−0.973491	+	0.604152i
$641$	6.34149	+	19.5171i	0.250474	+	0.770879i	0.994688	+	0.102938i	$0.0328243\pi$
$641$	6.34149	+	19.5171i	0.250474	+	0.770879i	−0.744214	+	0.667941i	$0.767176\pi$
$642$	69.3014	−	35.3108i	2.73511	−	1.39361i
$643$	−17.4058	+	2.75681i	−0.686419	+	0.108718i	−0.489896	−	0.871781i	$-0.662965\pi$
$643$	−17.4058	+	2.75681i	−0.686419	+	0.108718i	−0.196523	+	0.980499i	$0.562965\pi$
$644$	28.9880	+	21.0610i	1.14229	+	0.829919i
$645$	−11.2004	−	26.6136i	−0.441015	−	1.04791i
$646$	−10.5924	+	3.44169i	−0.416754	+	0.135412i
$647$	−5.69058	−	0.901299i	−0.223720	−	0.0354337i	0.0435681	−	0.999050i	$-0.486127\pi$
$647$	−5.69058	−	0.901299i	−0.223720	−	0.0354337i	−0.267288	+	0.963617i	$0.586127\pi$
$648$	47.9592	+	47.9592i	1.88401	+	1.88401i
$649$		0			0
$650$	−4.15374	+	28.2924i	−0.162923	+	1.10972i
$651$	−8.54453	−	11.7605i	−0.334886	−	0.460932i
$652$	2.15733	−	4.23400i	0.0844876	−	0.165816i
$653$	2.64867	+	5.19830i	0.103650	+	0.203425i	0.937007	−	0.349310i	$-0.113584\pi$
$653$	2.64867	+	5.19830i	0.103650	+	0.203425i	−0.833357	+	0.552735i	$0.813584\pi$
$654$	53.4315	−	73.5421i	2.08934	−	2.87573i
$655$	0.103742	+	1.22929i	0.00405355	+	0.0480322i
$656$	−8.36866	−	2.71914i	−0.326741	−	0.106165i
$657$	−8.57932	−	4.37138i	−0.334711	−	0.170544i
$658$	−5.53844	+	34.9683i	−0.215911	+	1.36321i
$659$	5.21347			0.203088			0.101544	−	0.994831i	$-0.467622\pi$
$659$	5.21347			0.203088			0.101544	+	0.994831i	$0.467622\pi$
$660$		0			0
$661$	4.56016			0.177369			0.0886847	−	0.996060i	$-0.471734\pi$
$661$	4.56016			0.177369			0.0886847	+	0.996060i	$0.471734\pi$
$662$	5.82370	−	36.7694i	0.226344	−	1.42908i
$663$	13.5560	+	6.90714i	0.526472	+	0.268251i
$664$	−61.2597	−	19.9045i	−2.37734	−	0.772443i
$665$	−3.40597	+	4.03383i	−0.132078	+	0.156425i
$666$	−4.87562	+	6.71071i	−0.188926	+	0.260035i
$667$	−5.96692	−	11.7107i	−0.231040	−	0.453442i
$668$	−3.80289	+	7.46360i	−0.147138	+	0.288775i
$669$	8.96724	+	12.3423i	0.346693	+	0.477182i
$670$	14.9389	−	12.9058i	0.577139	−	0.498593i
$671$		0			0
$672$	−12.3084	−	12.3084i	−0.474805	−	0.474805i
$673$	−0.552500	−	0.0875074i	−0.0212973	−	0.00337316i	0.145777	−	0.989318i	$-0.453432\pi$
$673$	−0.552500	−	0.0875074i	−0.0212973	−	0.00337316i	−0.167074	+	0.985944i	$0.553432\pi$
$674$	32.5300	−	10.5696i	1.25301	−	0.407127i
$675$	6.34787	+	18.8104i	0.244330	+	0.724013i
$676$	28.3397	+	20.5900i	1.08999	+	0.791922i
$677$	−28.7536	+	4.55413i	−1.10509	+	0.175029i	−0.682211	−	0.731156i	$-0.738981\pi$
$677$	−28.7536	+	4.55413i	−1.10509	+	0.175029i	−0.422881	+	0.906185i	$0.638981\pi$
$678$	33.8295	−	17.2370i	1.29922	−	0.661983i
$679$	0.434705	+	1.33788i	0.0166824	+	0.0513433i
$680$	10.5539	−	45.0813i	0.404723	−	1.72879i
$681$		−	16.4454i		−	0.630190i
$682$		0			0
$683$	5.43554	−	5.43554i	0.207985	−	0.207985i	−0.595425	−	0.803411i	$-0.703016\pi$
$683$	5.43554	−	5.43554i	0.207985	−	0.207985i	0.803411	+	0.595425i	$0.203016\pi$
$684$	−4.76938	+	3.46516i	−0.182362	+	0.132494i
$685$	−8.26878	−	33.6040i	−0.315934	−	1.28394i
$686$	15.2005	−	46.7824i	0.580359	−	1.78616i
$687$	2.38022	+	15.0281i	0.0908109	+	0.573357i
$688$	−6.80059	−	42.9373i	−0.259270	−	1.63697i
$689$	4.43970	−	13.6640i	0.169139	−	0.520556i
$690$	12.1552	+	49.3983i	0.462742	+	1.88056i
$691$	7.63722	−	5.54876i	0.290533	−	0.211085i	−0.432965	−	0.901411i	$-0.642533\pi$
$691$	7.63722	−	5.54876i	0.290533	−	0.211085i	0.723499	+	0.690326i	$0.242533\pi$
$692$	59.3222	−	59.3222i	2.25509	−	2.25509i
$693$		0			0
$694$		−	31.0215i		−	1.17756i
$695$	−0.725163	+	3.09756i	−0.0275070	+	0.117497i
$696$	11.1980	+	34.4640i	0.424460	+	1.30635i
$697$	−3.90764	+	1.99104i	−0.148013	+	0.0754162i
$698$	−51.0116	+	8.07944i	−1.93082	+	0.305811i
$699$	42.5240	+	30.8955i	1.60840	+	1.16857i
$700$	−12.7988	−	37.9261i	−0.483748	−	1.43347i
$701$	18.7439	−	6.09025i	0.707946	−	0.230026i	0.0671568	−	0.997742i	$-0.478607\pi$
$701$	18.7439	−	6.09025i	0.707946	−	0.230026i	0.640789	+	0.767717i	$0.278607\pi$
$702$	−22.4284	−	3.55231i	−0.846505	−	0.134073i
$703$	2.96308	+	2.96308i	0.111755	+	0.111755i
$704$		0			0
$705$	−26.2019	+	22.6360i	−0.986822	+	0.852520i
$706$	−29.0592	−	39.9966i	−1.09366	−	1.50529i
$707$	−8.01754	+	15.7353i	−0.301531	+	0.591787i
$708$	49.9247	+	97.9827i	1.87628	+	3.68241i
$709$	26.1327	−	35.9685i	0.981433	−	1.35083i	0.0453796	−	0.998970i	$-0.485550\pi$
$709$	26.1327	−	35.9685i	0.981433	−	1.35083i	0.936054	−	0.351857i	$-0.114450\pi$
$710$	−24.7649	+	29.3301i	−0.929411	+	1.10074i
$711$	1.11039	+	0.360788i	0.0416429	+	0.0135306i
$712$	−21.1551	−	10.7791i	−0.792822	−	0.403963i
$713$	−2.80789	+	17.7283i	−0.105156	+	0.663930i
$714$	−30.9161			−1.15701
$715$		0			0
$716$	72.5395			2.71093
$717$	−0.713834	+	4.50697i	−0.0266586	+	0.168316i
$718$	−37.3178	−	19.0144i	−1.39269	−	0.709610i
$719$	−22.8147	−	7.41293i	−0.850843	−	0.276456i	−0.149044	−	0.988831i	$-0.547620\pi$
$719$	−22.8147	−	7.41293i	−0.850843	−	0.276456i	−0.701799	+	0.712375i	$0.747620\pi$
$720$	−1.29403	−	15.3335i	−0.0482256	−	0.571446i
$721$	−4.96493	+	6.83363i	−0.184903	+	0.254498i
$722$	−19.9063	−	39.0683i	−0.740835	−	1.45397i
$723$	5.73000	−	11.2458i	0.213101	−	0.418234i
$724$	38.6833	+	53.2430i	1.43765	+	1.97876i
$725$	−2.13276	+	14.5268i	−0.0792087	+	0.539513i
$726$		0			0
$727$	−17.6187	−	17.6187i	−0.653441	−	0.653441i	0.300379	−	0.953820i	$-0.402887\pi$
$727$	−17.6187	−	17.6187i	−0.653441	−	0.653441i	−0.953820	+	0.300379i	$0.902887\pi$
$728$	24.7948	+	3.92711i	0.918956	+	0.145548i
$729$	−12.0275	+	3.90797i	−0.445462	+	0.144739i
$730$	−20.7676	−	49.3465i	−0.768643	−	1.82640i
$731$	−17.5290	−	12.7355i	−0.648332	−	0.471041i
$732$	−81.6292	+	12.9288i	−3.01710	+	0.477862i
$733$	−0.0482047	+	0.0245615i	−0.00178048	+	0.000907200i	−0.454881	−	0.890552i	$-0.650318\pi$
$733$	−0.0482047	+	0.0245615i	−0.00178048	+	0.000907200i	0.453100	+	0.891460i	$0.350318\pi$
$734$	−5.04650	−	15.5315i	−0.186270	−	0.573280i
$735$	14.2121	−	8.82010i	0.524222	−	0.325334i
$736$			21.4928i			0.792235i
$737$		0			0
$738$	−2.38292	+	2.38292i	−0.0877163	+	0.0877163i
$739$	−15.5776	+	11.3178i	−0.573031	+	0.416331i	−0.836205	−	0.548417i	$-0.815231\pi$
$739$	−15.5776	+	11.3178i	−0.573031	+	0.416331i	0.263174	+	0.964748i	$0.415231\pi$
$740$	−30.8507	+	7.59130i	−1.13409	+	0.279062i
$741$	1.82504	−	5.61688i	0.0670444	−	0.206341i
$742$	4.56706	+	28.8353i	0.167662	+	1.05858i
$743$	1.16520	+	7.35679i	0.0427471	+	0.269895i	0.999800	−	0.0200201i	$-0.00637303\pi$
$743$	1.16520	+	7.35679i	0.0427471	+	0.269895i	−0.957052	+	0.289915i	$0.906373\pi$
$744$	15.2927	−	47.0662i	0.560659	−	1.72553i
$745$	45.5422	+	27.5554i	1.66854	+	1.00955i
$746$	−28.1261	+	20.4348i	−1.02977	+	0.748171i
$747$	−7.54462	+	7.54462i	−0.276043	+	0.276043i
$748$		0			0
$749$		−	27.6659i		−	1.01089i
$750$	20.8543	−	52.8650i	0.761491	−	1.93036i
$751$	−9.31643	−	28.6730i	−0.339962	−	1.04629i	−0.964226	−	0.265081i	$-0.914601\pi$
$751$	−9.31643	−	28.6730i	−0.339962	−	1.04629i	0.624265	−	0.781213i	$-0.285399\pi$
$752$	−46.4493	+	23.6671i	−1.69383	+	0.863050i
$753$	−52.6633	+	8.34104i	−1.91916	+	0.303964i
$754$	−13.5869	−	9.87144i	−0.494805	−	0.359497i
$755$	−29.6495	+	12.4781i	−1.07906	+	0.454123i
$756$	30.2303	−	9.82242i	1.09947	−	0.357238i
$757$	−43.9547	−	6.96174i	−1.59756	−	0.253029i	−0.706770	−	0.707444i	$-0.749848\pi$
$757$	−43.9547	−	6.96174i	−1.59756	−	0.253029i	−0.890790	+	0.454415i	$0.849848\pi$
$758$	38.5456	+	38.5456i	1.40004	+	1.40004i
$759$		0			0
$760$	−17.9253	−	1.30883i	−0.650218	−	0.0474764i
$761$	27.6916	+	38.1143i	1.00382	+	1.38164i	0.922951	+	0.384917i	$0.125770\pi$
$761$	27.6916	+	38.1143i	1.00382	+	1.38164i	0.0808703	+	0.996725i	$0.474230\pi$
$762$	0.475809	−	0.933828i	0.0172367	−	0.0338290i
$763$	−14.6794	−	28.8100i	−0.531430	−	1.04299i
$764$	4.96982	−	6.84037i	0.179802	−	0.247476i
$765$	−5.85999	−	4.94789i	−0.211869	−	0.178891i
$766$	0.731646	+	0.237726i	0.0264354	+	0.00858940i
$767$	−24.8986	−	12.6865i	−0.899035	−	0.458081i
$768$	−9.47622	+	59.8305i	−0.341944	+	2.15895i
$769$	−29.7849			−1.07407			−0.537036	−	0.843559i	$-0.680456\pi$
$769$	−29.7849			−1.07407			−0.537036	+	0.843559i	$0.680456\pi$
$770$		0			0
$771$	39.6451			1.42778
$772$	−7.88444	+	49.7804i	−0.283767	+	1.79164i
$773$	6.34696	+	3.23394i	0.228284	+	0.116317i	0.564392	−	0.825507i	$-0.309111\pi$
$773$	6.34696	+	3.23394i	0.228284	+	0.116317i	−0.336108	+	0.941824i	$0.609111\pi$
$774$	−15.8342	−	5.14483i	−0.569147	−	0.184927i
$775$	14.0173	−	14.3379i	0.503516	−	0.515032i
$776$	−2.81491	+	3.87439i	−0.101049	+	0.139082i
$777$	5.28082	+	10.3642i	0.189448	+	0.371813i
$778$	4.14513	−	8.13528i	0.148610	−	0.291664i
$779$	1.00067	+	1.37730i	0.0358527	+	0.0493470i
$780$	29.2727	+	33.8842i	1.04813	+	1.21325i
$781$		0			0
$782$	26.9928	+	26.9928i	0.965260	+	0.965260i
$783$	−11.5159	−	1.82395i	−0.411546	−	0.0651826i
$784$	23.9505	−	7.78200i	0.855376	−	0.277928i
$785$	−11.3890	+	27.9413i	−0.406492	+	0.997266i
$786$	2.26875	+	1.64835i	0.0809237	+	0.0587945i
$787$	−28.5017	+	4.51422i	−1.01597	+	0.160915i	−0.642145	−	0.766583i	$-0.721955\pi$
$787$	−28.5017	+	4.51422i	−1.01597	+	0.160915i	−0.373829	+	0.927498i	$0.621955\pi$
$788$	77.0457	−	39.2567i	2.74464	−	1.39846i
$789$	−5.18471	−	15.9569i	−0.184581	−	0.568081i
$790$	3.42318	+	5.51589i	0.121791	+	0.196247i
$791$		−	13.5051i		−	0.480187i
$792$		0			0
$793$	14.8503	−	14.8503i	0.527350	−	0.527350i
$794$	64.3320	−	46.7400i	2.28306	−	1.65874i
$795$	−14.7809	+	24.4291i	−0.524223	+	0.866410i
$796$	30.5816	−	94.1204i	1.08394	−	3.33601i
$797$	4.83989	+	30.5579i	0.171438	+	1.08241i	0.911929	+	0.410349i	$0.134593\pi$
$797$	4.83989	+	30.5579i	0.171438	+	1.08241i	−0.740491	+	0.672066i	$0.765407\pi$
$798$	1.87739	+	11.8534i	0.0664590	+	0.419605i
$799$	−8.02906	+	24.7109i	−0.284048	+	0.874209i
$800$	13.8922	−	19.5828i	0.491163	−	0.692355i
$801$	−3.18183	+	2.31173i	−0.112424	+	0.0816811i
$802$	17.9225	−	17.9225i	0.632866	−	0.632866i
$803$		0			0
$804$		−	30.9130i		−	1.09022i
$805$	17.6187	+	4.12468i	0.620978	+	0.145376i
$806$	7.08741	+	21.8128i	0.249644	+	0.768324i
$807$	−17.3468	+	8.83865i	−0.610637	+	0.311135i
$808$	−59.3810	+	9.40503i	−2.08902	+	0.330868i
$809$	15.9139	+	11.5621i	0.559503	+	0.406503i	0.831277	−	0.555858i	$-0.187610\pi$
$809$	15.9139	+	11.5621i	0.559503	+	0.406503i	−0.271774	+	0.962361i	$0.587610\pi$
$810$	57.8481	+	23.5792i	2.03257	+	0.828490i
$811$	−40.1916	+	13.0591i	−1.41132	+	0.458565i	−0.912833	−	0.408332i	$-0.866110\pi$
$811$	−40.1916	+	13.0591i	−1.41132	+	0.458565i	−0.498486	+	0.866898i	$0.666110\pi$
$812$	23.2188	+	3.67750i	0.814821	+	0.129055i
$813$	4.32597	+	4.32597i	0.151718	+	0.151718i
$814$		0			0
$815$	0.174757	−	2.39340i	0.00612147	−	0.0838373i
$816$	−26.7576	−	36.8286i	−0.936703	−	1.28926i
$817$	−3.81841	+	7.49406i	−0.133589	+	0.262184i
$818$	34.9804	+	68.6529i	1.22306	+	2.40039i
$819$	2.44424	−	3.36420i	0.0854085	−	0.117555i
$820$	−12.8618	+	1.08544i	−0.449153	+	0.0379051i
$821$	50.5707	+	16.4314i	1.76493	+	0.573461i	0.997692	−	0.0679009i	$-0.0216302\pi$
$821$	50.5707	+	16.4314i	1.76493	+	0.573461i	0.767239	+	0.641362i	$0.221630\pi$
$822$	−70.0925	−	35.7139i	−2.44476	−	1.24567i
$823$	0.219079	−	1.38321i	0.00763662	−	0.0482157i	−0.983576	−	0.180496i	$-0.942230\pi$
$823$	0.219079	−	1.38321i	0.00763662	−	0.0482157i	0.991212	+	0.132280i	$0.0422298\pi$
$824$	−28.7559			−1.00176
$825$		0			0
$826$	56.7841			1.97577
$827$	2.70418	−	17.0735i	0.0940334	−	0.593704i	−0.895006	−	0.446054i	$-0.852829\pi$
$827$	2.70418	−	17.0735i	0.0940334	−	0.593704i	0.989040	−	0.147650i	$-0.0471710\pi$
$828$	18.0035	+	9.17326i	0.625666	+	0.318793i
$829$	34.1356	+	11.0913i	1.18558	+	0.385217i	0.834436	−	0.551105i	$-0.185794\pi$
$829$	34.1356	+	11.0913i	1.18558	+	0.385217i	0.351141	+	0.936322i	$0.385794\pi$
$830$	−59.1160	+	4.98894i	−2.05195	+	0.173169i
$831$	−2.80487	+	3.86058i	−0.0973000	+	0.133922i
$832$	−1.35660	−	2.66248i	−0.0470317	−	0.0923049i
$833$	5.69823	−	11.1834i	0.197432	−	0.387482i
$834$	4.25069	+	5.85057i	0.147189	+	0.202589i
$835$	−0.308058	+	4.21903i	−0.0106608	+	0.146006i
$836$		0			0
$837$	11.2592	+	11.2592i	0.389176	+	0.389176i
$838$	−18.7352	−	2.96737i	−0.647198	−	0.102506i
$839$	4.71797	−	1.53296i	0.162883	−	0.0529238i	−0.226441	−	0.974025i	$-0.572709\pi$
$839$	4.71797	−	1.53296i	0.162883	−	0.0529238i	0.389323	+	0.921101i	$0.372709\pi$
$840$	−46.1998	−	18.8313i	−1.59404	−	0.649742i
$841$	16.4853	+	11.9772i	0.568457	+	0.413008i
$842$	51.1411	−	8.09995i	1.76244	−	0.279143i
$843$	−50.4329	+	25.6968i	−1.73700	+	0.885046i
$844$	0.515206	+	1.58564i	0.0177341	+	0.0545800i
$845$	17.2247	+	4.03243i	0.592547	+	0.138720i
$846$			19.9651i			0.686415i
$847$		0			0
$848$	−30.3971	+	30.3971i	−1.04384	+	1.04384i
$849$	27.5956	−	20.0494i	0.947079	−	0.688093i
$850$	−7.14681	−	42.0412i	−0.245133	−	1.44200i
$851$	4.43828	−	13.6596i	0.152142	−	0.468246i
$852$	9.40321	+	59.3695i	0.322149	+	2.03397i
$853$	4.15759	+	26.2500i	0.142353	+	0.898782i	0.950708	+	0.310087i	$0.100358\pi$
$853$	4.15759	+	26.2500i	0.142353	+	0.898782i	−0.808355	+	0.588695i	$0.799642\pi$
$854$	−13.1876	+	40.5873i	−0.451271	+	1.38887i
$855$	−1.54119	+	2.54721i	−0.0527078	+	0.0871128i
$856$	76.1965	−	55.3600i	2.60434	−	1.89217i
$857$	1.04396	−	1.04396i	0.0356609	−	0.0356609i	−0.689051	−	0.724712i	$-0.741973\pi$
$857$	1.04396	−	1.04396i	0.0356609	−	0.0356609i	0.724712	+	0.689051i	$0.241973\pi$
$858$		0			0
$859$			13.9402i			0.475633i	0.971310	+	0.237816i	$0.0764316\pi$
$859$			13.9402i			0.475633i	−0.971310	+	0.237816i	$0.923568\pi$
$860$	−33.6259	−	54.1825i	−1.14663	−	1.84761i
$861$	1.46032	+	4.49441i	0.0497677	+	0.153169i
$862$	−76.0505	+	38.7497i	−2.59029	+	1.31982i
$863$	50.6772	−	8.02648i	1.72507	−	0.273225i	0.786321	−	0.617819i	$-0.211983\pi$
$863$	50.6772	−	8.02648i	1.72507	−	0.273225i	0.938752	+	0.344594i	$0.111983\pi$
$864$	15.4250	+	11.2070i	0.524771	+	0.381268i
$865$	15.9918	−	39.2335i	0.543737	−	1.33398i
$866$	27.9681	−	9.08738i	0.950394	−	0.308802i
$867$	11.2540	+	1.78245i	0.382205	+	0.0605353i
$868$	−22.7012	−	22.7012i	−0.770529	−	0.770529i
$869$		0			0
$870$	21.8192	+	25.2565i	0.739742	+	0.856277i
$871$	4.61726	+	6.35512i	0.156450	+	0.215335i
$872$	49.9738	−	98.0790i	1.69232	−	3.32137i
$873$	0.360144	+	0.706822i	0.0121890	+	0.0239223i
$874$	8.71002	−	11.9883i	0.294621	−	0.405511i
$875$	−13.3869	−	15.1462i	−0.452560	−	0.512036i
$876$	−79.7320	−	25.9065i	−2.69389	−	0.875300i
$877$	5.94588	+	3.02958i	0.200778	+	0.102301i	0.551489	−	0.834182i	$-0.314060\pi$
$877$	5.94588	+	3.02958i	0.200778	+	0.102301i	−0.350711	+	0.936484i	$0.614060\pi$
$878$	4.25330	−	26.8543i	0.143542	−	0.906288i
$879$	21.4220			0.722546
$880$		0			0
$881$	−14.4573			−0.487080			−0.243540	−	0.969891i	$-0.578309\pi$
$881$	−14.4573			−0.487080			−0.243540	+	0.969891i	$0.578309\pi$
$882$	1.50874	−	9.52583i	0.0508020	−	0.320751i
$883$	9.32102	+	4.74930i	0.313677	+	0.159827i	0.603740	−	0.797181i	$-0.293676\pi$
$883$	9.32102	+	4.74930i	0.313677	+	0.159827i	−0.290063	+	0.957007i	$0.593676\pi$
$884$	31.9560	+	10.3831i	1.07480	+	0.349222i
$885$	42.4325	+	35.8280i	1.42635	+	1.20434i
$886$	60.1058	−	82.7286i	2.01930	−	2.77932i
$887$	−4.48682	−	8.80588i	−0.150653	−	0.295673i	0.803330	−	0.595534i	$-0.203060\pi$
$887$	−4.48682	−	8.80588i	−0.150653	−	0.295673i	−0.953983	+	0.299861i	$0.903060\pi$
$888$	−17.9777	+	35.2832i	−0.603292	+	1.18403i
$889$	−0.219123	−	0.301597i	−0.00734915	−	0.0101152i
$890$	−21.8101	−	1.59249i	−0.731078	−	0.0533805i
$891$		0			0
$892$	23.8243	+	23.8243i	0.797695	+	0.797695i
$893$	9.96185	+	1.57780i	0.333361	+	0.0527991i
$894$	115.079	−	37.3913i	3.84881	−	1.25055i
$895$	33.7649	−	14.2100i	1.12864	−	0.474989i
$896$	18.9604	+	13.7755i	0.633421	+	0.460207i
$897$	−19.9932	+	3.16661i	−0.667553	+	0.105730i
$898$	−8.22628	+	4.19150i	−0.274515	+	0.139872i
$899$	3.63906	+	11.1999i	0.121370	+	0.373537i
$900$	−10.4743	−	19.9949i	−0.349144	−	0.666497i
$901$			21.4256i			0.713789i
$902$		0			0
$903$	−16.5088	+	16.5088i	−0.549380	+	0.549380i
$904$	37.1954	−	27.0240i	1.23710	−	0.898806i
$905$	28.4358	+	17.2051i	0.945238	+	0.571918i
$906$	−22.5967	+	69.5455i	−0.750725	+	2.31049i
$907$	1.81013	+	11.4287i	0.0601042	+	0.379483i	0.999344	+	0.0362209i	$0.0115320\pi$
$907$	1.81013	+	11.4287i	0.0601042	+	0.379483i	−0.939240	+	0.343262i	$0.888468\pi$
$908$	−5.68162	−	35.8723i	−0.188551	−	1.19046i
$909$	−3.07747	+	9.47148i	−0.102073	+	0.314149i
$910$	22.4519	−	5.52465i	0.744274	−	0.183140i
$911$	7.05585	−	5.12638i	0.233771	−	0.169844i	−0.464733	−	0.885451i	$-0.653850\pi$
$911$	7.05585	−	5.12638i	0.233771	−	0.169844i	0.698504	+	0.715607i	$0.253850\pi$
$912$	−12.4954	+	12.4954i	−0.413765	+	0.413765i
$913$		0			0
$914$			45.8704i			1.51726i
$915$	−35.4632	+	22.0086i	−1.17238	+	0.727581i
$916$	10.3839	+	31.9584i	0.343094	+	1.05593i
$917$	0.888779	−	0.452856i	0.0293501	−	0.0149546i
$918$	33.4471	−	5.29751i	1.10392	−	0.174844i
$919$	4.67338	+	3.39541i	0.154160	+	0.112004i	0.662192	−	0.749335i	$-0.269627\pi$
$919$	4.67338	+	3.39541i	0.154160	+	0.112004i	−0.508031	+	0.861339i	$0.669627\pi$
$920$	23.8953	+	56.7785i	0.787806	+	1.87193i
$921$	−62.0002	+	20.1451i	−2.04298	+	0.663803i
$922$	89.1164	+	14.1147i	2.93489	+	0.464842i
$923$	−10.8007	−	10.8007i	−0.355511	−	0.355511i
$924$		0			0
$925$	−12.8729	+	9.57696i	−0.423260	+	0.314889i
$926$	9.41628	+	12.9604i	0.309438	+	0.425905i
$927$	−2.16251	+	4.24416i	−0.0710261	+	0.139397i
$928$	6.40176	+	12.5642i	0.210148	+	0.412439i
$929$	10.6620	−	14.6749i	0.349807	−	0.481468i	−0.597466	−	0.801894i	$-0.703826\pi$
$929$	10.6620	−	14.6749i	0.349807	−	0.481468i	0.947274	+	0.320425i	$0.103826\pi$
$930$	−3.83303	−	45.4192i	−0.125690	−	1.48935i
$931$	−4.63380	−	1.50561i	−0.151867	−	0.0493444i
$932$	103.431	+	52.7008i	3.38800	+	1.72627i
$933$	4.35595	−	27.5024i	0.142607	−	0.900387i
$934$	21.9374			0.717813
$935$		0			0
$936$	14.1566			0.462722
$937$	5.02763	−	31.7432i	0.164245	−	1.03700i	−0.758522	−	0.651648i	$-0.774078\pi$
$937$	5.02763	−	31.7432i	0.164245	−	1.03700i	0.922767	−	0.385357i	$-0.125922\pi$
$938$	−14.2227	−	7.24680i	−0.464386	−	0.236617i
$939$	−33.1548	−	10.7727i	−1.08197	−	0.351552i
$940$	−49.3338	+	58.4281i	−1.60909	+	1.90571i
$941$	−3.06305	+	4.21593i	−0.0998526	+	0.137435i	−0.856020	−	0.516943i	$-0.827070\pi$
$941$	−3.06305	+	4.21593i	−0.0998526	+	0.137435i	0.756167	+	0.654379i	$0.227070\pi$
$942$	31.1389	+	61.1136i	1.01456	+	1.99119i
$943$	2.64906	−	5.19907i	0.0862652	−	0.169305i
$944$	49.1461	+	67.6438i	1.59957	+	2.20162i
$945$	12.1471	−	10.4940i	0.395146	−	0.341368i
$946$		0			0
$947$	−0.545091	−	0.545091i	−0.0177131	−	0.0177131i	0.698195	−	0.715908i	$-0.253987\pi$
$947$	−0.545091	−	0.545091i	−0.0177131	−	0.0177131i	−0.715908	+	0.698195i	$0.753987\pi$
$948$	10.0402	+	1.59022i	0.326092	+	0.0516478i
$949$	20.2609	−	6.58315i	0.657695	−	0.213698i
$950$	−15.6848	+	5.29308i	−0.508882	+	0.171730i
$951$	26.2065	+	19.0401i	0.849804	+	0.617419i
$952$	−36.9761	+	5.85644i	−1.19840	+	0.189808i
$953$	12.1009	−	6.16570i	0.391986	−	0.199727i	−0.246878	−	0.969047i	$-0.579405\pi$
$953$	12.1009	−	6.16570i	0.391986	−	0.199727i	0.638864	+	0.769320i	$0.279405\pi$
$954$	5.08750	+	15.6577i	0.164714	+	0.506937i
$955$	0.973312	−	4.15754i	0.0314957	−	0.134535i
$956$			10.0777i			0.325935i
$957$		0			0
$958$	27.5786	−	27.5786i	0.891023	−	0.891023i
$959$	−22.6377	+	16.4472i	−0.731009	+	0.531109i
$960$	1.41895	+	5.76654i	0.0457964	+	0.186114i
$961$	−4.60979	+	14.1875i	−0.148703	+	0.457661i
$962$	−2.87093	−	18.1264i	−0.0925626	−	0.584417i
$963$	−2.44059	−	15.4092i	−0.0786468	−	0.496556i
$964$	8.61359	−	26.5099i	0.277425	−	0.853827i
$965$	6.08170	+	24.7157i	0.195777	+	0.795628i
$966$	33.2777	−	24.1777i	1.07069	−	0.777904i
$967$	−28.7882	+	28.7882i	−0.925767	+	0.925767i	−0.997429	−	0.0716619i	$-0.977170\pi$
$967$	−28.7882	+	28.7882i	−0.925767	+	0.925767i	0.0716619	+	0.997429i	$0.477170\pi$
$968$		0			0
$969$			8.80745i			0.282936i
$970$	−1.00543	+	4.29474i	−0.0322825	+	0.137896i
$971$	−9.07745	−	27.9375i	−0.291309	−	0.896557i	−0.984436	−	0.175742i	$-0.943768\pi$
$971$	−9.07745	−	27.9375i	−0.291309	−	0.896557i	0.693127	−	0.720815i	$-0.256232\pi$
$972$	40.1645	−	20.4648i	1.28828	−	0.656410i
$973$	2.54065	−	0.402399i	0.0814494	−	0.0129003i
$974$	12.1966	+	8.86137i	0.390805	+	0.283937i
$975$	20.2632	+	10.0377i	0.648942	+	0.321463i
$976$	−59.7632	+	19.4182i	−1.91297	+	0.621562i
$977$	23.1072	+	3.65982i	0.739265	+	0.117088i	0.514699	−	0.857371i	$-0.327904\pi$
$977$	23.1072	+	3.65982i	0.739265	+	0.117088i	0.224566	+	0.974459i	$0.427904\pi$
$978$	−3.85737	−	3.85737i	−0.123345	−	0.123345i
$979$		0			0
$980$	27.9536	−	24.1493i	0.892946	−	0.771420i
$981$	−10.7176	−	14.7515i	−0.342187	−	0.470980i
$982$	−47.1344	+	92.5065i	−1.50412	+	2.95200i
$983$	−9.46916	−	18.5843i	−0.302019	−	0.592746i	0.689262	−	0.724513i	$-0.257935\pi$
$983$	−9.46916	−	18.5843i	−0.302019	−	0.592746i	−0.991281	+	0.131767i	$0.957935\pi$
$984$	−9.45625	+	13.0154i	−0.301454	+	0.414916i
$985$	28.1722	−	33.3655i	0.897642	−	1.06311i
$986$	23.8193	+	7.73937i	0.758562	+	0.246472i
$987$	24.9457	+	12.7105i	0.794031	+	0.404579i
$988$	2.04040	−	12.8826i	0.0649138	−	0.409850i
$989$	28.8277			0.916666
$990$		0			0
$991$	−6.50787			−0.206729			−0.103365	−	0.994644i	$-0.532961\pi$
$991$	−6.50787			−0.206729			−0.103365	+	0.994644i	$0.532961\pi$
$992$	3.01251	−	19.0203i	0.0956474	−	0.603894i
$993$	−26.2305	−	13.3651i	−0.832401	−	0.424130i
$994$	29.5195	+	9.59146i	0.936301	+	0.304223i
$995$	−4.20281	−	49.8009i	−0.133238	−	1.57879i
$996$	−54.6041	+	75.1561i	−1.73020	+	2.38141i
$997$	−11.9879	−	23.5276i	−0.379660	−	0.745126i	0.619546	−	0.784960i	$-0.287317\pi$
$997$	−11.9879	−	23.5276i	−0.379660	−	0.745126i	−0.999206	+	0.0398349i	$0.987317\pi$
$998$	26.6881	−	52.3783i	0.844797	−	1.65801i
$999$	−7.48905	−	10.3078i	−0.236943	−	0.326124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.d.602.4		32
5.3	odd	4	inner	605.2.m.d.118.1		32
11.2	odd	10		605.2.e.b.362.16		32
11.3	even	5		55.2.l.a.17.1	yes	32
11.4	even	5		605.2.m.c.282.4		32
11.5	even	5		605.2.m.e.112.4		32
11.6	odd	10		55.2.l.a.2.1	✓	32
11.7	odd	10	inner	605.2.m.d.282.1		32
11.8	odd	10		605.2.m.e.457.4		32
11.9	even	5		605.2.e.b.362.1		32
11.10	odd	2		605.2.m.c.602.1		32
33.14	odd	10		495.2.bj.a.127.4		32
33.17	even	10		495.2.bj.a.442.4		32
44.3	odd	10		880.2.cm.a.17.1		32
44.39	even	10		880.2.cm.a.497.1		32
55.3	odd	20		55.2.l.a.28.1	yes	32
55.8	even	20		605.2.m.e.578.4		32
55.13	even	20		605.2.e.b.483.1		32
55.14	even	10		275.2.bm.b.182.4		32
55.17	even	20		275.2.bm.b.68.4		32
55.18	even	20	inner	605.2.m.d.403.4		32
55.28	even	20		55.2.l.a.13.1	yes	32
55.38	odd	20		605.2.m.e.233.4		32
55.39	odd	10		275.2.bm.b.57.4		32
55.43	even	4		605.2.m.c.118.4		32
55.47	odd	20		275.2.bm.b.193.4		32
55.48	odd	20		605.2.m.c.403.1		32
55.53	odd	20		605.2.e.b.483.16		32
165.83	odd	20		495.2.bj.a.343.4		32
165.113	even	20		495.2.bj.a.28.4		32
220.3	even	20		880.2.cm.a.193.1		32
220.83	odd	20		880.2.cm.a.673.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.1	✓	32	11.6	odd	10
55.2.l.a.13.1	yes	32	55.28	even	20
55.2.l.a.17.1	yes	32	11.3	even	5
55.2.l.a.28.1	yes	32	55.3	odd	20
275.2.bm.b.57.4		32	55.39	odd	10
275.2.bm.b.68.4		32	55.17	even	20
275.2.bm.b.182.4		32	55.14	even	10
275.2.bm.b.193.4		32	55.47	odd	20
495.2.bj.a.28.4		32	165.113	even	20
495.2.bj.a.127.4		32	33.14	odd	10
495.2.bj.a.343.4		32	165.83	odd	20
495.2.bj.a.442.4		32	33.17	even	10
605.2.e.b.362.1		32	11.9	even	5
605.2.e.b.362.16		32	11.2	odd	10
605.2.e.b.483.1		32	55.13	even	20
605.2.e.b.483.16		32	55.53	odd	20
605.2.m.c.118.4		32	55.43	even	4
605.2.m.c.282.4		32	11.4	even	5
605.2.m.c.403.1		32	55.48	odd	20
605.2.m.c.602.1		32	11.10	odd	2
605.2.m.d.118.1		32	5.3	odd	4	inner
605.2.m.d.282.1		32	11.7	odd	10	inner
605.2.m.d.403.4		32	55.18	even	20	inner
605.2.m.d.602.4		32	1.1	even	1	trivial
605.2.m.e.112.4		32	11.5	even	5
605.2.m.e.233.4		32	55.38	odd	20
605.2.m.e.457.4		32	11.8	odd	10
605.2.m.e.578.4		32	55.8	even	20
880.2.cm.a.17.1		32	44.3	odd	10
880.2.cm.a.193.1		32	220.3	even	20
880.2.cm.a.497.1		32	44.39	even	10
880.2.cm.a.673.1		32	220.83	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.396609 - 2.50409i) q^{2} +(-1.78637 - 0.910200i) q^{3} +(-4.21106 - 1.36825i) q^{4} +(-2.22815 + 0.188039i) q^{5} +(-2.98771 + 4.11224i) q^{6} +(0.820825 + 1.61096i) q^{7} +(-2.79437 + 5.48426i) q^{8} +(0.599293 + 0.824856i) q^{9} +(-0.412838 + 5.65406i) q^{10} +(6.27711 + 6.27711i) q^{12} +(-2.22802 - 0.352884i) q^{13} +(4.35953 - 1.41650i) q^{14} +(4.15145 + 1.69215i) q^{15} +(5.46052 + 3.96730i) q^{16} +(3.32262 - 0.526252i) q^{17} +(2.30320 - 1.17354i) q^{18} +(-0.403535 - 1.24195i) q^{19} +(9.64014 + 2.25683i) q^{20} -3.62488i q^{21} +(-3.16488 + 3.16488i) q^{23} +(9.98354 - 7.25347i) q^{24} +(4.92928 - 0.837955i) q^{25} +(-1.76731 + 5.43922i) q^{26} +(0.621127 + 3.92164i) q^{27} +(-1.25234 - 7.90694i) q^{28} +(-0.907432 + 2.79279i) q^{29} +(5.88381 - 9.72447i) q^{30} +(3.24439 - 2.35719i) q^{31} +(3.39552 - 3.39552i) q^{32} -8.52886i q^{34} +(-2.13184 - 3.43511i) q^{35} +(-1.39504 - 4.29350i) q^{36} +(-2.85918 + 1.45682i) q^{37} +(-3.27001 + 0.517918i) q^{38} +(3.65888 + 2.65833i) q^{39} +(5.19501 - 12.7452i) q^{40} +(-1.23988 + 0.402861i) q^{41} +(-9.07703 - 1.43766i) q^{42} +(-4.55431 - 4.55431i) q^{43} +(-1.49042 - 1.72521i) q^{45} +(6.66992 + 9.18035i) q^{46} +(-3.50645 + 6.88180i) q^{47} +(-6.14347 - 12.0572i) q^{48} +(2.19306 - 3.01849i) q^{49} +(-0.143318 - 12.6757i) q^{50} +(-6.41442 - 2.08417i) q^{51} +(8.89950 + 4.53452i) q^{52} +(-0.996331 + 6.29058i) q^{53} +10.0665 q^{54} -11.1286 q^{56} +(-0.409564 + 2.58588i) q^{57} +(6.63350 + 3.37994i) q^{58} +(11.7815 + 3.82803i) q^{59} +(-15.1667 - 12.8060i) q^{60} +(-5.47229 + 7.53196i) q^{61} +(-4.61586 - 9.05913i) q^{62} +(-0.836895 + 1.64250i) q^{63} +(0.778618 + 1.07168i) q^{64} +(5.03072 + 0.367324i) q^{65} +(-2.46236 - 2.46236i) q^{67} +(-14.7118 - 2.33012i) q^{68} +(8.53431 - 2.77296i) q^{69} +(-9.44733 + 3.97593i) q^{70} +(5.47805 + 3.98004i) q^{71} +(-6.19837 + 0.981725i) q^{72} +(-8.41458 + 4.28744i) q^{73} +(2.51404 + 7.73743i) q^{74} +(-9.56823 - 2.98974i) q^{75} +5.78207i q^{76} +(8.10784 - 8.10784i) q^{78} +(0.926417 - 0.673081i) q^{79} +(-12.9129 - 7.81295i) q^{80} +(3.40512 - 10.4799i) q^{81} +(0.517053 + 3.26455i) q^{82} +(1.63706 + 10.3360i) q^{83} +(-4.95976 + 15.2646i) q^{84} +(-7.30434 + 1.79735i) q^{85} +(-13.2107 + 9.59813i) q^{86} +(4.16301 - 4.16301i) q^{87} +3.85743i q^{89} +(-4.91120 + 3.04791i) q^{90} +(-1.26034 - 3.87891i) q^{91} +(17.6578 - 8.99711i) q^{92} +(-7.94119 + 1.25776i) q^{93} +(15.8420 + 11.5099i) q^{94} +(1.13267 + 2.69137i) q^{95} +(-9.15625 + 2.97505i) q^{96} +(0.768472 + 0.121714i) q^{97} +(-6.68878 - 6.68878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{3} - 2 q^{5} + 20 q^{7} - 20 q^{8} + 12 q^{12} - 20 q^{13} + 4 q^{15} + 12 q^{16} + 30 q^{18} + 16 q^{20} - 24 q^{23} - 24 q^{25} - 20 q^{26} + 24 q^{27} - 20 q^{28} + 40 q^{30} + 32 q^{31}+ \cdots - 38 q^{97}+O(q^{100}) \) 32 * q + 6 * q^3 - 2 * q^5 + 20 * q^7 - 20 * q^8 + 12 * q^12 - 20 * q^13 + 4 * q^15 + 12 * q^16 + 30 * q^18 + 16 * q^20 - 24 * q^23 - 24 * q^25 - 20 * q^26 + 24 * q^27 - 20 * q^28 + 40 * q^30 + 32 * q^31 + 30 * q^35 - 36 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 - 20 * q^42 - 28 * q^45 + 20 * q^46 + 42 * q^47 + 26 * q^48 + 80 * q^50 - 100 * q^51 - 20 * q^52 - 34 * q^53 - 80 * q^56 - 40 * q^57 + 90 * q^58 - 86 * q^60 + 10 * q^62 - 10 * q^63 - 8 * q^67 - 70 * q^68 + 10 * q^70 - 36 * q^71 - 70 * q^72 + 30 * q^73 + 4 * q^75 + 60 * q^78 - 102 * q^80 + 8 * q^81 + 20 * q^82 - 60 * q^83 + 60 * q^85 - 80 * q^86 + 130 * q^90 - 60 * q^91 + 42 * q^92 - 8 * q^93 - 30 * q^95 - 38 * q^97

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