LMFDB - Embedded newform 272.2.l.c.205.11

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			205.11
Character	$\chi$	$=$	272.205
Dual form			272.2.l.c.69.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.591533 - 1.28456i) q^{2} +(0.915574 + 0.915574i) q^{3} +(-1.30018 - 1.51972i) q^{4} +(2.93727 - 2.93727i) q^{5} +(1.71770 - 0.634516i) q^{6} +1.91420i q^{7} +(-2.72126 + 0.771193i) q^{8} -1.32345i q^{9} +(-2.03560 - 5.51058i) q^{10} +(-2.96543 + 2.96543i) q^{11} +(0.201003 - 2.58182i) q^{12} +(1.16040 + 1.16040i) q^{13} +(2.45890 + 1.13231i) q^{14} +5.37857 q^{15} +(-0.619073 + 3.95180i) q^{16} +1.00000 q^{17} +(-1.70004 - 0.782862i) q^{18} +(-1.64396 - 1.64396i) q^{19} +(-8.28279 - 0.644841i) q^{20} +(-1.75259 + 1.75259i) q^{21} +(2.05512 + 5.56341i) q^{22} +0.425350i q^{23} +(-3.19760 - 1.78543i) q^{24} -12.2551i q^{25} +(2.17701 - 0.804184i) q^{26} +(3.95844 - 3.95844i) q^{27} +(2.90904 - 2.48880i) q^{28} +(4.17622 + 4.17622i) q^{29} +(3.18160 - 6.90909i) q^{30} -4.08327 q^{31} +(4.71012 + 3.13286i) q^{32} -5.43014 q^{33} +(0.591533 - 1.28456i) q^{34} +(5.62252 + 5.62252i) q^{35} +(-2.01126 + 1.72072i) q^{36} +(-7.58603 + 7.58603i) q^{37} +(-3.08421 + 1.13930i) q^{38} +2.12486i q^{39} +(-5.72787 + 10.2583i) q^{40} +11.1907i q^{41} +(1.21459 + 3.28802i) q^{42} +(4.70645 - 4.70645i) q^{43} +(8.36219 + 0.651023i) q^{44} +(-3.88732 - 3.88732i) q^{45} +(0.546387 + 0.251609i) q^{46} -1.47082 q^{47} +(-4.18498 + 3.05136i) q^{48} +3.33584 q^{49} +(-15.7424 - 7.24928i) q^{50} +(0.915574 + 0.915574i) q^{51} +(0.254751 - 3.27220i) q^{52} +(-1.05515 + 1.05515i) q^{53} +(-2.74330 - 7.42639i) q^{54} +17.4205i q^{55} +(-1.47622 - 5.20904i) q^{56} -3.01033i q^{57} +(7.83496 - 2.89422i) q^{58} +(-6.30743 + 6.30743i) q^{59} +(-6.99310 - 8.17390i) q^{60} +(-6.38682 - 6.38682i) q^{61} +(-2.41539 + 5.24519i) q^{62} +2.53334 q^{63} +(6.81052 - 4.19723i) q^{64} +6.81679 q^{65} +(-3.21210 + 6.97532i) q^{66} +(-3.95752 - 3.95752i) q^{67} +(-1.30018 - 1.51972i) q^{68} +(-0.389440 + 0.389440i) q^{69} +(10.5483 - 3.89655i) q^{70} +7.48068i q^{71} +(1.02063 + 3.60145i) q^{72} -0.137605i q^{73} +(5.25731 + 14.2321i) q^{74} +(11.2204 - 11.2204i) q^{75} +(-0.360910 + 4.63578i) q^{76} +(-5.67642 - 5.67642i) q^{77} +(2.72950 + 1.25692i) q^{78} +15.5985 q^{79} +(9.78912 + 13.4259i) q^{80} +3.27814 q^{81} +(14.3751 + 6.61968i) q^{82} +(-9.36325 - 9.36325i) q^{83} +(4.94212 + 0.384760i) q^{84} +(2.93727 - 2.93727i) q^{85} +(-3.26169 - 8.82972i) q^{86} +7.64727i q^{87} +(5.78278 - 10.3566i) q^{88} -3.78735i q^{89} +(-7.29296 + 2.69401i) q^{90} +(-2.22123 + 2.22123i) q^{91} +(0.646412 - 0.553031i) q^{92} +(-3.73853 - 3.73853i) q^{93} +(-0.870040 + 1.88936i) q^{94} -9.65748 q^{95} +(1.44410 + 7.18083i) q^{96} +1.68978 q^{97} +(1.97326 - 4.28508i) q^{98} +(3.92459 + 3.92459i) 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 $

$2$	0.591533	−	1.28456i	0.418277	−	0.908320i
$2$	0.591533	−	1.28456i	0.418277	−	0.908320i
$3$	0.915574	+	0.915574i	0.528607	+	0.528607i	0.920157	−	0.391550i	$-0.128061\pi$
$3$	0.915574	+	0.915574i	0.528607	+	0.528607i	−0.391550	+	0.920157i	$0.628061\pi$
$4$	−1.30018	−	1.51972i	−0.650089	−	0.759858i
$5$	2.93727	−	2.93727i	1.31359	−	1.31359i	0.394834	−	0.918753i	$-0.370802\pi$
$5$	2.93727	−	2.93727i	1.31359	−	1.31359i	0.918753	−	0.394834i	$-0.129198\pi$
$6$	1.71770	−	0.634516i	0.701248	−	0.259040i
$7$			1.91420i			0.723499i	0.932275	+	0.361750i	$0.117820\pi$
$7$			1.91420i			0.723499i	−0.932275	+	0.361750i	$0.882180\pi$
$8$	−2.72126	+	0.771193i	−0.962111	+	0.272658i
$9$		−	1.32345i		−	0.441149i
$10$	−2.03560	−	5.51058i	−0.643714	−	1.74260i
$11$	−2.96543	+	2.96543i	−0.894110	+	0.894110i	−0.994907	−	0.100797i	$-0.967861\pi$
$11$	−2.96543	+	2.96543i	−0.894110	+	0.894110i	0.100797	+	0.994907i	$0.467861\pi$
$12$	0.201003	−	2.58182i	0.0580246	−	0.745308i
$13$	1.16040	+	1.16040i	0.321836	+	0.321836i	0.849471	−	0.527635i	$-0.176921\pi$
$13$	1.16040	+	1.16040i	0.321836	+	0.321836i	−0.527635	+	0.849471i	$0.676921\pi$
$14$	2.45890	+	1.13231i	0.657169	+	0.302623i
$15$	5.37857			1.38874
$16$	−0.619073	+	3.95180i	−0.154768	+	0.987951i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−1.70004	−	0.782862i	−0.400704	−	0.184522i
$19$	−1.64396	−	1.64396i	−0.377149	−	0.377149i	0.492923	−	0.870073i	$-0.335928\pi$
$19$	−1.64396	−	1.64396i	−0.377149	−	0.377149i	−0.870073	+	0.492923i	$0.835928\pi$
$20$	−8.28279	−	0.644841i	−1.85209	−	0.144191i
$21$	−1.75259	+	1.75259i	−0.382447	+	0.382447i
$22$	2.05512	+	5.56341i	0.438152	+	1.18612i
$23$			0.425350i			0.0886917i	0.999016	+	0.0443458i	$0.0141203\pi$
$23$			0.425350i			0.0886917i	−0.999016	+	0.0443458i	$0.985880\pi$
$24$	−3.19760	−	1.78543i	−0.652708	−	0.364450i
$25$		−	12.2551i		−	2.45102i
$26$	2.17701	−	0.804184i	0.426947	−	0.157714i
$27$	3.95844	−	3.95844i	0.761802	−	0.761802i
$28$	2.90904	−	2.48880i	0.549757	−	0.470339i
$29$	4.17622	+	4.17622i	0.775504	+	0.775504i	0.979063	−	0.203559i	$-0.0652508\pi$
$29$	4.17622	+	4.17622i	0.775504	+	0.775504i	−0.203559	+	0.979063i	$0.565251\pi$
$30$	3.18160	−	6.90909i	0.580878	−	1.26142i
$31$	−4.08327			−0.733376			−0.366688	−	0.930344i	$-0.619508\pi$
$31$	−4.08327			−0.733376			−0.366688	+	0.930344i	$0.619508\pi$
$32$	4.71012	+	3.13286i	0.832639	+	0.553816i
$33$	−5.43014			−0.945265
$34$	0.591533	−	1.28456i	0.101447	−	0.220300i
$35$	5.62252	+	5.62252i	0.950379	+	0.950379i
$36$	−2.01126	+	1.72072i	−0.335211	+	0.286786i
$37$	−7.58603	+	7.58603i	−1.24714	+	1.24714i	−0.290157	+	0.956979i	$0.593708\pi$
$37$	−7.58603	+	7.58603i	−1.24714	+	1.24714i	−0.956979	+	0.290157i	$0.906292\pi$
$38$	−3.08421	+	1.13930i	−0.500325	+	0.184819i
$39$			2.12486i			0.340250i
$40$	−5.72787	+	10.2583i	−0.905656	+	1.62198i
$41$			11.1907i			1.74770i	0.486197	+	0.873849i	$0.338384\pi$
$41$			11.1907i			1.74770i	−0.486197	+	0.873849i	$0.661616\pi$
$42$	1.21459	+	3.28802i	0.187415	+	0.507353i
$43$	4.70645	−	4.70645i	0.717727	−	0.717727i	−0.250413	−	0.968139i	$-0.580566\pi$
$43$	4.70645	−	4.70645i	0.717727	−	0.717727i	0.968139	+	0.250413i	$0.0805663\pi$
$44$	8.36219	+	0.651023i	1.26065	+	0.0981454i
$45$	−3.88732	−	3.88732i	−0.579487	−	0.579487i
$46$	0.546387	+	0.251609i	0.0805604	+	0.0370977i
$47$	−1.47082			−0.214542			−0.107271	−	0.994230i	$-0.534211\pi$
$47$	−1.47082			−0.214542			−0.107271	+	0.994230i	$0.534211\pi$
$48$	−4.18498	+	3.05136i	−0.604049	+	0.440426i
$49$	3.33584			0.476549
$50$	−15.7424	−	7.24928i	−2.22631	−	1.02520i
$51$	0.915574	+	0.915574i	0.128206	+	0.128206i
$52$	0.254751	−	3.27220i	0.0353276	−	0.453772i
$53$	−1.05515	+	1.05515i	−0.144936	+	0.144936i	−0.775851	−	0.630916i	$-0.782679\pi$
$53$	−1.05515	+	1.05515i	−0.144936	+	0.144936i	0.630916	+	0.775851i	$0.282679\pi$
$54$	−2.74330	−	7.42639i	−0.373315	−	1.01060i
$55$			17.4205i			2.34898i
$56$	−1.47622	−	5.20904i	−0.197268	−	0.696087i
$57$		−	3.01033i		−	0.398728i
$58$	7.83496	−	2.89422i	1.02878	−	0.380030i
$59$	−6.30743	+	6.30743i	−0.821158	+	0.821158i	−0.986274	−	0.165116i	$-0.947200\pi$
$59$	−6.30743	+	6.30743i	−0.821158	+	0.821158i	0.165116	+	0.986274i	$0.447200\pi$
$60$	−6.99310	−	8.17390i	−0.902806	−	1.05525i
$61$	−6.38682	−	6.38682i	−0.817749	−	0.817749i	0.168032	−	0.985781i	$-0.446259\pi$
$61$	−6.38682	−	6.38682i	−0.817749	−	0.817749i	−0.985781	+	0.168032i	$0.946259\pi$
$62$	−2.41539	+	5.24519i	−0.306754	+	0.666140i
$63$	2.53334			0.319171
$64$	6.81052	−	4.19723i	0.851315	−	0.524654i
$65$	6.81679			0.845519
$66$	−3.21210	+	6.97532i	−0.395383	+	0.858603i
$67$	−3.95752	−	3.95752i	−0.483488	−	0.483488i	0.422756	−	0.906244i	$-0.361063\pi$
$67$	−3.95752	−	3.95752i	−0.483488	−	0.483488i	−0.906244	+	0.422756i	$0.861063\pi$
$68$	−1.30018	−	1.51972i	−0.157670	−	0.184293i
$69$	−0.389440	+	0.389440i	−0.0468830	+	0.0468830i
$70$	10.5483	−	3.89655i	1.26077	−	0.465726i
$71$			7.48068i			0.887794i	0.896078	+	0.443897i	$0.146404\pi$
$71$			7.48068i			0.887794i	−0.896078	+	0.443897i	$0.853596\pi$
$72$	1.02063	+	3.60145i	0.120283	+	0.424435i
$73$		−	0.137605i		−	0.0161055i	−0.999968	−	0.00805274i	$-0.997437\pi$
$73$		−	0.137605i		−	0.0161055i	0.999968	−	0.00805274i	$-0.00256329\pi$
$74$	5.25731	+	14.2321i	0.611150	+	1.65445i
$75$	11.2204	−	11.2204i	1.29563	−	1.29563i
$76$	−0.360910	+	4.63578i	−0.0413993	+	0.531761i
$77$	−5.67642	−	5.67642i	−0.646888	−	0.646888i
$78$	2.72950	+	1.25692i	0.309056	+	0.142319i
$79$	15.5985			1.75497			0.877486	−	0.479602i	$-0.159219\pi$
$79$	15.5985			1.75497			0.877486	+	0.479602i	$0.159219\pi$
$80$	9.78912	+	13.4259i	1.09446	+	1.50106i
$81$	3.27814			0.364238
$82$	14.3751	+	6.61968i	1.58747	+	0.731022i
$83$	−9.36325	−	9.36325i	−1.02775	−	1.02775i	−0.999604	−	0.0281462i	$-0.991040\pi$
$83$	−9.36325	−	9.36325i	−1.02775	−	1.02775i	−0.0281462	−	0.999604i	$-0.508960\pi$
$84$	4.94212	+	0.384760i	0.539230	+	0.0419808i
$85$	2.93727	−	2.93727i	0.318591	−	0.318591i
$86$	−3.26169	−	8.82972i	−0.351717	−	0.952133i
$87$			7.64727i			0.819874i
$88$	5.78278	−	10.3566i	0.616447	−	1.10402i
$89$		−	3.78735i		−	0.401458i	−0.979647	−	0.200729i	$-0.935669\pi$
$89$		−	3.78735i		−	0.401458i	0.979647	−	0.200729i	$-0.0643311\pi$
$90$	−7.29296	+	2.69401i	−0.768746	+	0.283974i
$91$	−2.22123	+	2.22123i	−0.232848	+	0.232848i
$92$	0.646412	−	0.553031i	0.0673931	−	0.0576575i
$93$	−3.73853	−	3.73853i	−0.387668	−	0.387668i
$94$	−0.870040	+	1.88936i	−0.0897378	+	0.194872i
$95$	−9.65748			−0.990836
$96$	1.44410	+	7.18083i	0.147388	+	0.732890i
$97$	1.68978			0.171571			0.0857855	−	0.996314i	$-0.472660\pi$
$97$	1.68978			0.171571			0.0857855	+	0.996314i	$0.472660\pi$
$98$	1.97326	−	4.28508i	0.199329	−	0.432859i
$99$	3.92459	+	3.92459i	0.394436	+	0.394436i
$100$	−18.6243	+	15.9338i	−1.86243	+	1.59338i
$101$	2.40086	−	2.40086i	0.238895	−	0.238895i	−0.577498	−	0.816392i	$-0.695971\pi$
$101$	2.40086	−	2.40086i	0.238895	−	0.238895i	0.816392	+	0.577498i	$0.195971\pi$
$102$	1.71770	−	0.634516i	0.170078	−	0.0628265i
$103$			4.93499i			0.486259i	0.969994	+	0.243129i	$0.0781740\pi$
$103$			4.93499i			0.486259i	−0.969994	+	0.243129i	$0.921826\pi$
$104$	−4.05263	−	2.26285i	−0.397393	−	0.221891i
$105$			10.2957i			1.00475i
$106$	0.731244	+	1.97955i	0.0710247	+	0.192271i
$107$	13.9279	−	13.9279i	1.34646	−	1.34646i	0.456993	−	0.889470i	$-0.348927\pi$
$107$	13.9279	−	13.9279i	1.34646	−	1.34646i	0.889470	−	0.456993i	$-0.151073\pi$
$108$	−11.1624	−	0.869026i	−1.07410	−	0.0836221i
$109$	−6.89083	−	6.89083i	−0.660022	−	0.660022i	0.295363	−	0.955385i	$-0.404559\pi$
$109$	−6.89083	−	6.89083i	−0.660022	−	0.660022i	−0.955385	+	0.295363i	$0.904559\pi$
$110$	22.3776	+	10.3048i	2.13363	+	0.982524i
$111$	−13.8912			−1.31849
$112$	−7.56454	−	1.18503i	−0.714782	−	0.111975i
$113$	−5.92173			−0.557069			−0.278535	−	0.960426i	$-0.589849\pi$
$113$	−5.92173			−0.557069			−0.278535	+	0.960426i	$0.589849\pi$
$114$	−3.86694	−	1.78071i	−0.362172	−	0.166779i
$115$	1.24937	+	1.24937i	0.116504	+	0.116504i
$116$	0.916837	−	11.7765i	0.0851262	−	1.09342i
$117$	1.53572	−	1.53572i	0.141978	−	0.141978i
$118$	4.37121	+	11.8333i	0.402403	+	1.08934i
$119$			1.91420i			0.175474i
$120$	−14.6365	+	4.14792i	−1.33612	+	0.378651i
$121$		−	6.58751i		−	0.598864i
$122$	−11.9823	+	4.42623i	−1.08482	+	0.400732i
$123$	−10.2459	+	10.2459i	−0.923846	+	0.923846i
$124$	5.30897	+	6.20540i	0.476760	+	0.557262i
$125$	−21.3101	−	21.3101i	−1.90604	−	1.90604i
$126$	1.49855	−	3.25422i	0.133502	−	0.289909i
$127$	−5.93843			−0.526951			−0.263475	−	0.964666i	$-0.584869\pi$
$127$	−5.93843			−0.526951			−0.263475	+	0.964666i	$0.584869\pi$
$128$	−1.36294	−	11.2313i	−0.120468	−	0.992717i
$129$	8.61820			0.758791
$130$	4.03236	−	8.75657i	0.353661	−	0.768002i
$131$	−10.4950	−	10.4950i	−0.916956	−	0.916956i	0.0798505	−	0.996807i	$-0.474556\pi$
$131$	−10.4950	−	10.4950i	−0.916956	−	0.916956i	−0.996807	+	0.0798505i	$0.974556\pi$
$132$	7.06015	+	8.25227i	0.614507	+	0.718267i
$133$	3.14686	−	3.14686i	0.272867	−	0.272867i
$134$	−7.42466	+	2.74266i	−0.641393	+	0.236930i
$135$		−	23.2540i		−	2.00138i
$136$	−2.72126	+	0.771193i	−0.233346	+	0.0661292i
$137$		−	7.10624i		−	0.607127i	−0.952811	−	0.303563i	$-0.901824\pi$
$137$		−	7.10624i		−	0.607127i	0.952811	−	0.303563i	$-0.0981764\pi$
$138$	0.269892	+	0.730624i	0.0229747	+	0.0621949i
$139$	11.2068	−	11.2068i	0.950546	−	0.950546i	−0.0482875	−	0.998833i	$-0.515376\pi$
$139$	11.2068	−	11.2068i	0.950546	−	0.950546i	0.998833	+	0.0482875i	$0.0153764\pi$
$140$	1.23435	−	15.8549i	0.104322	−	1.33998i
$141$	−1.34665	−	1.34665i	−0.113408	−	0.113408i
$142$	9.60937	+	4.42507i	0.806400	+	0.371343i
$143$	−6.88214			−0.575514
$144$	5.23000	+	0.819311i	0.435834	+	0.0682759i
$145$	24.5333			2.03738
$146$	−0.176762	−	0.0813980i	−0.0146289	−	0.00673655i
$147$	3.05421	+	3.05421i	0.251907	+	0.251907i
$148$	21.3918	+	1.66542i	1.75840	+	0.136897i
$149$	−10.0729	+	10.0729i	−0.825201	+	0.825201i	−0.986849	−	0.161647i	$-0.948319\pi$
$149$	−10.0729	+	10.0729i	−0.825201	+	0.825201i	0.161647	+	0.986849i	$0.448319\pi$
$150$	−7.77605	−	21.0506i	−0.634912	−	1.71877i
$151$			5.78045i			0.470407i	0.971946	+	0.235203i	$0.0755756\pi$
$151$			5.78045i			0.470407i	−0.971946	+	0.235203i	$0.924424\pi$
$152$	5.74144	+	3.20583i	0.465692	+	0.260027i
$153$		−	1.32345i		−	0.106994i
$154$	−10.6495	+	3.93390i	−0.858159	+	0.317003i
$155$	−11.9936	+	11.9936i	−0.963353	+	0.963353i
$156$	3.22918	−	2.76270i	0.258542	−	0.221193i
$157$	6.72462	+	6.72462i	0.536683	+	0.536683i	0.922553	−	0.385870i	$-0.126099\pi$
$157$	6.72462	+	6.72462i	0.536683	+	0.536683i	−0.385870	+	0.922553i	$0.626099\pi$
$158$	9.22704	−	20.0372i	0.734064	−	1.59408i
$159$	−1.93213			−0.153228
$160$	23.0369	−	4.63284i	1.82123	−	0.366258i
$161$	−0.814205			−0.0641684
$162$	1.93913	−	4.21097i	0.152352	−	0.330845i
$163$	−9.93227	−	9.93227i	−0.777955	−	0.777955i	0.201527	−	0.979483i	$-0.435409\pi$
$163$	−9.93227	−	9.93227i	−0.777955	−	0.777955i	−0.979483	+	0.201527i	$0.935409\pi$
$164$	17.0067	−	14.5499i	1.32800	−	1.13616i
$165$	−15.9498	+	15.9498i	−1.24169	+	1.24169i
$166$	−17.5663	+	6.48897i	−1.36341	+	0.503642i
$167$			7.81828i			0.604997i	0.953150	+	0.302498i	$0.0978207\pi$
$167$			7.81828i			0.604997i	−0.953150	+	0.302498i	$0.902179\pi$
$168$	3.41767	−	6.12084i	0.263679	−	0.472233i
$169$		−	10.3070i		−	0.792843i
$170$	−2.03560	−	5.51058i	−0.156123	−	0.422642i
$171$	−2.17569	+	2.17569i	−0.166379	+	0.166379i
$172$	−13.2717	−	1.03324i	−1.01196	−	0.0787840i
$173$	−0.562763	−	0.562763i	−0.0427861	−	0.0427861i	0.685390	−	0.728176i	$-0.259632\pi$
$173$	−0.562763	−	0.562763i	−0.0427861	−	0.0427861i	−0.728176	+	0.685390i	$0.759632\pi$
$174$	9.82337	+	4.52361i	0.744708	+	0.342934i
$175$	23.4587			1.77331
$176$	−9.88297	−	13.5546i	−0.744957	−	1.02172i
$177$	−11.5498			−0.868140
$178$	−4.86507	−	2.24034i	−0.364652	−	0.167921i
$179$	−3.83028	−	3.83028i	−0.286288	−	0.286288i	0.549322	−	0.835611i	$-0.314886\pi$
$179$	−3.83028	−	3.83028i	−0.286288	−	0.286288i	−0.835611	+	0.549322i	$0.814886\pi$
$180$	−0.853413	+	10.9618i	−0.0636097	+	0.817047i
$181$	−0.219366	+	0.219366i	−0.0163054	+	0.0163054i	−0.715212	−	0.698907i	$-0.753670\pi$
$181$	−0.219366	+	0.219366i	−0.0163054	+	0.0163054i	0.698907	+	0.715212i	$0.253670\pi$
$182$	1.53937	+	4.16723i	0.114106	+	0.308896i
$183$		−	11.6952i		−	0.864536i
$184$	−0.328027	−	1.15749i	−0.0241825	−	0.0853312i
$185$			44.5644i			3.27644i
$186$	−7.01383	+	2.59090i	−0.514279	+	0.189974i
$187$	−2.96543	+	2.96543i	−0.216853	+	0.216853i
$188$	1.91233	+	2.23523i	0.139471	+	0.163021i
$189$	7.57724	+	7.57724i	0.551163	+	0.551163i
$190$	−5.71271	+	12.4056i	−0.414444	+	0.899996i
$191$	3.21567			0.232677			0.116339	−	0.993210i	$-0.462884\pi$
$191$	3.21567			0.232677			0.116339	+	0.993210i	$0.462884\pi$
$192$	10.0784	+	2.39266i	0.727347	+	0.172676i
$193$	15.8802			1.14308			0.571542	−	0.820573i	$-0.306346\pi$
$193$	15.8802			1.14308			0.571542	+	0.820573i	$0.306346\pi$
$194$	0.999560	−	2.17062i	0.0717642	−	0.155841i
$195$	6.24128	+	6.24128i	0.446947	+	0.446947i
$196$	−4.33719	−	5.06953i	−0.309799	−	0.362109i
$197$	−0.417650	+	0.417650i	−0.0297563	+	0.0297563i	−0.721828	−	0.692072i	$-0.756698\pi$
$197$	−0.417650	+	0.417650i	−0.0297563	+	0.0297563i	0.692072	+	0.721828i	$0.256698\pi$
$198$	7.36288	−	2.71984i	0.523257	−	0.193290i
$199$		−	20.8176i		−	1.47572i	−0.674954	−	0.737859i	$-0.735837\pi$
$199$		−	20.8176i		−	1.47572i	0.674954	−	0.737859i	$-0.264163\pi$
$200$	9.45103	+	33.3493i	0.668289	+	2.35815i
$201$		−	7.24680i		−	0.511150i
$202$	−1.66386	−	4.50424i	−0.117069	−	0.316917i
$203$	−7.99411	+	7.99411i	−0.561077	+	0.561077i
$204$	0.201003	−	2.58182i	0.0140730	−	0.180764i
$205$	32.8702	+	32.8702i	2.29575	+	2.29575i
$206$	6.33928	+	2.91921i	0.441678	+	0.203391i
$207$	0.562929			0.0391263
$208$	−5.30403	+	3.86729i	−0.367768	+	0.268148i
$209$	9.75006			0.674426
$210$	13.2254	+	6.09022i	0.912637	+	0.420265i
$211$	−11.4639	−	11.4639i	−0.789208	−	0.789208i	0.192156	−	0.981364i	$-0.438452\pi$
$211$	−11.4639	−	11.4639i	−0.789208	−	0.789208i	−0.981364	+	0.192156i	$0.938452\pi$
$212$	2.97541	+	0.231645i	0.204352	+	0.0159094i
$213$	−6.84912	+	6.84912i	−0.469294	+	0.469294i
$214$	−9.65240	−	26.1300i	−0.659825	−	1.78621i
$215$		−	27.6482i		−	1.88559i
$216$	−7.71922	+	13.8247i	−0.525227	+	0.940649i
$217$		−	7.81618i		−	0.530597i
$218$	−12.9278	+	4.77552i	−0.875583	+	0.323439i
$219$	0.125988	−	0.125988i	0.00851347	−	0.00851347i
$220$	26.4742	−	22.6498i	1.78489	−	1.52705i
$221$	1.16040	+	1.16040i	0.0780567	+	0.0780567i
$222$	−8.21707	+	17.8440i	−0.551494	+	1.19761i
$223$	−11.0552			−0.740313			−0.370157	−	0.928969i	$-0.620696\pi$
$223$	−11.0552			−0.740313			−0.370157	+	0.928969i	$0.620696\pi$
$224$	−5.99691	+	9.01610i	−0.400685	+	0.602414i
$225$	−16.2190			−1.08126
$226$	−3.50289	+	7.60680i	−0.233009	+	0.505997i
$227$	4.84456	+	4.84456i	0.321545	+	0.321545i	0.849360	−	0.527815i	$-0.176988\pi$
$227$	4.84456	+	4.84456i	0.321545	+	0.321545i	−0.527815	+	0.849360i	$0.676988\pi$
$228$	−4.57484	+	3.91396i	−0.302976	+	0.259209i
$229$	6.60647	−	6.60647i	0.436568	−	0.436568i	−0.454287	−	0.890855i	$-0.650106\pi$
$229$	6.60647	−	6.60647i	0.436568	−	0.436568i	0.890855	+	0.454287i	$0.150106\pi$
$230$	2.34393	−	0.865843i	0.154554	−	0.0570920i
$231$		−	10.3944i		−	0.683899i
$232$	−14.5852	−	8.14391i	−0.957568	−	0.534674i
$233$			22.5206i			1.47537i	0.675143	+	0.737687i	$0.264082\pi$
$233$			22.5206i			1.47537i	−0.675143	+	0.737687i	$0.735918\pi$
$234$	−1.06430	−	2.88116i	−0.0695752	−	0.188347i
$235$	−4.32020	+	4.32020i	−0.281819	+	0.281819i
$236$	17.7863	+	1.38472i	1.15779	+	0.0901376i
$237$	14.2816	+	14.2816i	0.927691	+	0.927691i
$238$	2.45890	+	1.13231i	0.159387	+	0.0733968i
$239$	7.24955			0.468934			0.234467	−	0.972124i	$-0.424665\pi$
$239$	7.24955			0.468934			0.234467	+	0.972124i	$0.424665\pi$
$240$	−3.32973	+	21.2551i	−0.214933	+	1.37201i
$241$	17.5538			1.13074			0.565369	−	0.824838i	$-0.308734\pi$
$241$	17.5538			1.13074			0.565369	+	0.824838i	$0.308734\pi$
$242$	−8.46204	−	3.89673i	−0.543960	−	0.250491i
$243$	−8.87393	−	8.87393i	−0.569263	−	0.569263i
$244$	−1.40215	+	18.0102i	−0.0897634	+	1.15298i
$245$	9.79826	−	9.79826i	0.625988	−	0.625988i
$246$	7.10070	+	19.2223i	0.452724	+	1.22557i
$247$		−	3.81528i		−	0.242761i
$248$	11.1116	−	3.14898i	0.705589	−	0.199961i
$249$		−	17.1455i		−	1.08655i
$250$	−39.9797	+	14.7685i	−2.52854	+	0.934040i
$251$	9.65571	−	9.65571i	0.609463	−	0.609463i	−0.333343	−	0.942806i	$-0.608177\pi$
$251$	9.65571	−	9.65571i	0.609463	−	0.609463i	0.942806	+	0.333343i	$0.108177\pi$
$252$	−3.29380	−	3.84996i	−0.207490	−	0.242525i
$253$	−1.26135	−	1.26135i	−0.0793001	−	0.0793001i
$254$	−3.51278	+	7.62826i	−0.220411	+	0.478640i
$255$	5.37857			0.336819
$256$	−15.2335	−	4.89291i	−0.952094	−	0.305807i
$257$	−27.0496			−1.68731			−0.843655	−	0.536885i	$-0.819601\pi$
$257$	−27.0496			−1.68731			−0.843655	+	0.536885i	$0.819601\pi$
$258$	5.09795	−	11.0706i	0.317384	−	0.689224i
$259$	−14.5212	−	14.5212i	−0.902302	−	0.902302i
$260$	−8.86305	−	10.3596i	−0.549663	−	0.642475i
$261$	5.52700	−	5.52700i	0.342113	−	0.342113i
$262$	−19.6897	+	7.27333i	−1.21643	+	0.449348i
$263$			10.2744i			0.633548i	0.948501	+	0.316774i	$0.102600\pi$
$263$			10.2744i			0.633548i	−0.948501	+	0.316774i	$0.897400\pi$
$264$	14.7768	−	4.18768i	0.909450	−	0.257734i
$265$			6.19850i			0.380771i
$266$	−2.18085	−	5.90379i	−0.133717	−	0.361985i
$267$	3.46760	−	3.46760i	0.212214	−	0.212214i
$268$	−0.868824	+	11.1598i	−0.0530719	+	0.681692i
$269$	1.48239	+	1.48239i	0.0903828	+	0.0903828i	0.750853	−	0.660470i	$-0.229643\pi$
$269$	1.48239	+	1.48239i	0.0903828	+	0.0903828i	−0.660470	+	0.750853i	$0.729643\pi$
$270$	−29.8711	−	13.7555i	−1.81790	−	0.837132i
$271$	31.1942			1.89491			0.947457	−	0.319882i	$-0.103643\pi$
$271$	31.1942			1.89491			0.947457	+	0.319882i	$0.103643\pi$
$272$	−0.619073	+	3.95180i	−0.0375368	+	0.239613i
$273$	−4.06740			−0.246170
$274$	−9.12837	−	4.20357i	−0.551465	−	0.253947i
$275$	36.3416	+	36.3416i	2.19148	+	2.19148i
$276$	1.09818	+	0.0854967i	0.0661026	+	0.00514630i
$277$	−3.64733	+	3.64733i	−0.219147	+	0.219147i	−0.808139	−	0.588992i	$-0.799525\pi$
$277$	−3.64733	+	3.64733i	−0.219147	+	0.219147i	0.588992	+	0.808139i	$0.299525\pi$
$278$	−7.76658	−	21.0249i	−0.465808	−	1.26099i
$279$			5.40399i			0.323528i
$280$	−19.6364	−	10.9643i	−1.17350	−	0.655242i
$281$		−	1.14571i		−	0.0683473i	−0.999416	−	0.0341737i	$-0.989120\pi$
$281$		−	1.14571i		−	0.0683473i	0.999416	−	0.0341737i	$-0.0108799\pi$
$282$	−2.52643	+	0.933261i	−0.150447	+	0.0555749i
$283$	−10.7612	+	10.7612i	−0.639686	+	0.639686i	−0.950478	−	0.310792i	$-0.899406\pi$
$283$	−10.7612	+	10.7612i	−0.639686	+	0.639686i	0.310792	+	0.950478i	$0.399406\pi$
$284$	11.3685	−	9.72622i	0.674597	−	0.577145i
$285$	−8.84214	−	8.84214i	−0.523763	−	0.523763i
$286$	−4.07101	+	8.84051i	−0.240724	+	0.522750i
$287$	−21.4213			−1.26446
$288$	4.14617	−	6.23359i	0.244315	−	0.367318i
$289$	1.00000			0.0588235
$290$	14.5123	−	31.5145i	0.852190	−	1.85059i
$291$	1.54712	+	1.54712i	0.0906937	+	0.0906937i
$292$	−0.209121	+	0.178911i	−0.0122379	+	0.0104700i
$293$	3.56707	−	3.56707i	0.208390	−	0.208390i	−0.595193	−	0.803583i	$-0.702924\pi$
$293$	3.56707	−	3.56707i	0.208390	−	0.208390i	0.803583	+	0.595193i	$0.202924\pi$
$294$	5.72998	−	2.11665i	0.334179	−	0.123445i
$295$			37.0532i			2.15732i
$296$	14.7933	−	26.4939i	0.859842	−	1.53993i
$297$			23.4769i			1.36227i
$298$	6.98075	+	18.8976i	0.404384	+	1.09471i
$299$	−0.493575	+	0.493575i	−0.0285442	+	0.0285442i
$300$	−31.6405	−	2.46331i	−1.82676	−	0.142219i
$301$	9.00908	+	9.00908i	0.519275	+	0.519275i
$302$	7.42533	+	3.41933i	0.427280	+	0.196760i
$303$	4.39634			0.252563
$304$	7.51432	−	5.47886i	0.430976	−	0.314234i
$305$	−37.5196			−2.14837
$306$	−1.70004	−	0.782862i	−0.0971851	−	0.0447533i
$307$	1.56785	+	1.56785i	0.0894822	+	0.0894822i	0.750431	−	0.660949i	$-0.229846\pi$
$307$	1.56785	+	1.56785i	0.0894822	+	0.0894822i	−0.660949	+	0.750431i	$0.729846\pi$
$308$	−1.24619	+	16.0069i	−0.0710081	+	0.912077i
$309$	−4.51835	+	4.51835i	−0.257040	+	0.257040i
$310$	8.31190	+	22.5012i	0.472084	+	1.27798i
$311$			24.5729i			1.39340i	0.717361	+	0.696702i	$0.245350\pi$
$311$			24.5729i			1.39340i	−0.717361	+	0.696702i	$0.754650\pi$
$312$	−1.63868	−	5.78230i	−0.0927717	−	0.327358i
$313$		−	13.7255i		−	0.775814i	−0.921699	−	0.387907i	$-0.873198\pi$
$313$		−	13.7255i		−	0.775814i	0.921699	−	0.387907i	$-0.126802\pi$
$314$	12.6160	−	4.66033i	0.711962	−	0.262998i
$315$	7.44110	−	7.44110i	0.419259	−	0.419259i
$316$	−20.2809	−	23.7053i	−1.14089	−	1.33353i
$317$	20.9868	+	20.9868i	1.17874	+	1.17874i	0.980066	+	0.198671i	$0.0636624\pi$
$317$	20.9868	+	20.9868i	1.17874	+	1.17874i	0.198671	+	0.980066i	$0.436338\pi$
$318$	−1.14292	+	2.48194i	−0.0640917	+	0.139180i
$319$	−24.7685			−1.38677
$320$	7.67594	−	32.3327i	0.429098	−	1.80745i
$321$	25.5041			1.42350
$322$	−0.481629	+	1.04589i	−0.0268401	+	0.0582854i
$323$	−1.64396	−	1.64396i	−0.0914722	−	0.0914722i
$324$	−4.26217	−	4.98185i	−0.236787	−	0.276769i
$325$	14.2208	−	14.2208i	0.788826	−	0.788826i
$326$	−18.6338	+	6.88331i	−1.03203	+	0.381232i
$327$		−	12.6181i		−	0.697785i
$328$	−8.63021	−	30.4529i	−0.476524	−	1.68148i
$329$		−	2.81545i		−	0.155221i
$330$	11.0536	+	29.9232i	0.608480	+	1.64722i
$331$	−23.5100	+	23.5100i	−1.29223	+	1.29223i	−0.358818	+	0.933407i	$0.616820\pi$
$331$	−23.5100	+	23.5100i	−1.29223	+	1.29223i	−0.933407	+	0.358818i	$0.883180\pi$
$332$	−2.05559	+	26.4034i	−0.112815	+	1.44907i
$333$	10.0397	+	10.0397i	0.550173	+	0.550173i
$334$	10.0430	+	4.62477i	0.549531	+	0.253056i
$335$	−23.2486			−1.27021
$336$	−5.84091	−	8.01088i	−0.318648	−	0.437029i
$337$	2.96026			0.161255			0.0806277	−	0.996744i	$-0.474308\pi$
$337$	2.96026			0.161255			0.0806277	+	0.996744i	$0.474308\pi$
$338$	−13.2399	−	6.09690i	−0.720155	−	0.331628i
$339$	−5.42178	−	5.42178i	−0.294471	−	0.294471i
$340$	−8.28279	−	0.644841i	−0.449197	−	0.0349714i
$341$	12.1086	−	12.1086i	0.655719	−	0.655719i
$342$	1.50781	+	4.08179i	0.0815329	+	0.220718i
$343$			19.7849i			1.06828i
$344$	−9.17790	+	16.4371i	−0.494839	+	0.886226i
$345$			2.28778i			0.123170i
$346$	−1.05579	+	0.390009i	−0.0567598	+	0.0209670i
$347$	19.2917	−	19.2917i	1.03563	−	1.03563i	0.0362923	−	0.999341i	$-0.488445\pi$
$347$	19.2917	−	19.2917i	1.03563	−	1.03563i	0.999341	−	0.0362923i	$-0.0115547\pi$
$348$	11.6217	−	9.94282i	0.622988	−	0.532991i
$349$	−2.15002	−	2.15002i	−0.115088	−	0.115088i	0.647217	−	0.762305i	$-0.275933\pi$
$349$	−2.15002	−	2.15002i	−0.115088	−	0.115088i	−0.762305	+	0.647217i	$0.775933\pi$
$350$	13.8766	−	30.1340i	0.741734	−	1.61073i
$351$	9.18672			0.490351
$352$	−23.2578	+	4.67725i	−1.23964	+	0.249299i
$353$	−19.5532			−1.04071			−0.520355	−	0.853950i	$-0.674200\pi$
$353$	−19.5532			−1.04071			−0.520355	+	0.853950i	$0.674200\pi$
$354$	−6.83211	+	14.8364i	−0.363123	+	0.788548i
$355$	21.9728	+	21.9728i	1.16619	+	1.16619i
$356$	−5.75570	+	4.92423i	−0.305051	+	0.260984i
$357$	−1.75259	+	1.75259i	−0.0927570	+	0.0927570i
$358$	−7.18595	+	2.65448i	−0.379789	+	0.140294i
$359$			2.99664i			0.158157i	0.996868	+	0.0790783i	$0.0251977\pi$
$359$			2.99664i			0.158157i	−0.996868	+	0.0790783i	$0.974802\pi$
$360$	13.5763	+	7.58054i	0.715533	+	0.399530i
$361$		−	13.5948i		−	0.715517i
$362$	0.152026	+	0.411551i	0.00799032	+	0.0216306i
$363$	6.03135	−	6.03135i	0.316564	−	0.316564i
$364$	6.26364	+	0.487644i	0.328304	+	0.0255595i
$365$	−0.404184	−	0.404184i	−0.0211559	−	0.0211559i
$366$	−15.0232	−	6.91811i	−0.785275	−	0.361615i
$367$	31.7706			1.65841			0.829205	−	0.558944i	$-0.188793\pi$
$367$	31.7706			1.65841			0.829205	+	0.558944i	$0.188793\pi$
$368$	−1.68090	−	0.263323i	−0.0876230	−	0.0137267i
$369$	14.8103			0.770996
$370$	57.2456	+	26.3613i	2.97606	+	1.37046i
$371$	−2.01976	−	2.01976i	−0.104861	−	0.104861i
$372$	−0.820749	+	10.5423i	−0.0425539	+	0.546591i
$373$	−19.1741	+	19.1741i	−0.992799	+	0.992799i	−0.999974	−	0.00717519i	$-0.997716\pi$
$373$	−19.1741	+	19.1741i	−0.992799	+	0.992799i	0.00717519	+	0.999974i	$0.497716\pi$
$374$	2.05512	+	5.56341i	0.106267	+	0.287677i
$375$		−	39.0220i		−	2.01509i
$376$	4.00250	−	1.13429i	0.206413	−	0.0584965i
$377$			9.69214i			0.499171i
$378$	14.2156	−	5.25122i	0.731171	−	0.270093i
$379$	−18.5793	+	18.5793i	−0.954355	+	0.954355i	−0.999003	−	0.0446480i	$-0.985783\pi$
$379$	−18.5793	+	18.5793i	−0.954355	+	0.954355i	0.0446480	+	0.999003i	$0.485783\pi$
$380$	12.5564	+	14.6766i	0.644132	+	0.752895i
$381$	−5.43707	−	5.43707i	−0.278550	−	0.278550i
$382$	1.90217	−	4.13071i	0.0973236	−	0.211345i
$383$	9.41797			0.481236			0.240618	−	0.970620i	$-0.422650\pi$
$383$	9.41797			0.481236			0.240618	+	0.970620i	$0.422650\pi$
$384$	9.03523	−	11.5310i	0.461077	−	0.588438i
$385$	−33.3463			−1.69949
$386$	9.39367	−	20.3991i	0.478125	−	1.03829i
$387$	−6.22874	−	6.22874i	−0.316624	−	0.316624i
$388$	−2.19701	−	2.56798i	−0.111536	−	0.130370i
$389$	−4.00504	+	4.00504i	−0.203064	+	0.203064i	−0.801311	−	0.598248i	$-0.795864\pi$
$389$	−4.00504	+	4.00504i	−0.203064	+	0.203064i	0.598248	+	0.801311i	$0.295864\pi$
$390$	11.7092	−	4.32537i	0.592919	−	0.219023i
$391$			0.425350i			0.0215109i
$392$	−9.07770	+	2.57258i	−0.458493	+	0.129935i
$393$		−	19.2180i		−	0.969419i
$394$	0.289442	+	0.783548i	0.0145819	+	0.0394746i
$395$	45.8171	−	45.8171i	2.30531	−	2.30531i
$396$	0.861595	−	11.0669i	0.0432968	−	0.556134i
$397$	−27.2892	−	27.2892i	−1.36961	−	1.36961i	−0.860996	−	0.508611i	$-0.830159\pi$
$397$	−27.2892	−	27.2892i	−1.36961	−	1.36961i	−0.508611	−	0.860996i	$-0.669841\pi$
$398$	−26.7414	−	12.3143i	−1.34042	−	0.617259i
$399$	5.76237			0.288479
$400$	48.4297	+	7.58680i	2.42148	+	0.379340i
$401$	18.9964			0.948637			0.474319	−	0.880353i	$-0.342694\pi$
$401$	18.9964			0.948637			0.474319	+	0.880353i	$0.342694\pi$
$402$	−9.30894	−	4.28672i	−0.464288	−	0.213802i
$403$	−4.73821	−	4.73821i	−0.236027	−	0.236027i
$404$	−6.77018	−	0.527080i	−0.336829	−	0.0262232i
$405$	9.62879	−	9.62879i	0.478458	−	0.478458i
$406$	5.54012	+	14.9977i	0.274952	+	0.744322i
$407$		−	44.9917i		−	2.23015i
$408$	−3.19760	−	1.78543i	−0.158305	−	0.0883921i
$409$			11.7972i			0.583335i	0.956520	+	0.291668i	$0.0942101\pi$
$409$			11.7972i			0.583335i	−0.956520	+	0.291668i	$0.905790\pi$
$410$	61.6674	−	22.7799i	3.04554	−	1.12502i
$411$	6.50629	−	6.50629i	0.320932	−	0.320932i
$412$	7.49978	−	6.41636i	0.369488	−	0.316111i
$413$	−12.0737	−	12.0737i	−0.594107	−	0.594107i
$414$	0.332991	−	0.723115i	0.0163656	−	0.0355391i
$415$	−55.0047			−2.70008
$416$	1.83025	+	9.10096i	0.0897354	+	0.446211i
$417$	20.5213			1.00493
$418$	5.76748	−	12.5245i	0.282097	−	0.612594i
$419$	23.2461	+	23.2461i	1.13565	+	1.13565i	0.989222	+	0.146424i	$0.0467763\pi$
$419$	23.2461	+	23.2461i	1.13565	+	1.13565i	0.146424	+	0.989222i	$0.453224\pi$
$420$	15.6465	−	13.3862i	0.763470	−	0.653179i
$421$	24.0868	−	24.0868i	1.17392	−	1.17392i	0.192649	−	0.981268i	$-0.438292\pi$
$421$	24.0868	−	24.0868i	1.17392	−	1.17392i	0.981268	−	0.192649i	$-0.0617078\pi$
$422$	−21.5073	+	7.94478i	−1.04696	+	0.386746i
$423$			1.94656i			0.0946449i
$424$	2.05761	−	3.68506i	0.0999264	−	0.178962i
$425$		−	12.2551i		−	0.594459i
$426$	4.74661	+	12.8496i	0.229974	+	0.622564i
$427$	12.2257	−	12.2257i	0.591641	−	0.591641i
$428$	−39.2753	−	3.05770i	−1.89844	−	0.147800i
$429$	−6.30111	−	6.30111i	−0.304221	−	0.304221i
$430$	−35.5157	−	16.3548i	−1.71272	−	0.788699i
$431$	−6.77278			−0.326233			−0.163117	−	0.986607i	$-0.552155\pi$
$431$	−6.77278			−0.326233			−0.163117	+	0.986607i	$0.552155\pi$
$432$	13.1924	+	18.0935i	0.634720	+	0.870525i
$433$	−16.2468			−0.780772			−0.390386	−	0.920651i	$-0.627658\pi$
$433$	−16.2468			−0.780772			−0.390386	+	0.920651i	$0.627658\pi$
$434$	−10.0403	−	4.62353i	−0.481952	−	0.221936i
$435$	22.4621	+	22.4621i	1.07698	+	1.07698i
$436$	−1.51280	+	19.4314i	−0.0724499	+	0.930596i
$437$	0.699257	−	0.699257i	0.0334500	−	0.0334500i
$438$	−0.0873128	−	0.236365i	−0.00417197	−	0.0112939i
$439$		−	18.2586i		−	0.871437i	−0.900083	−	0.435718i	$-0.856494\pi$
$439$		−	18.2586i		−	0.871437i	0.900083	−	0.435718i	$-0.143506\pi$
$440$	−13.4346	−	47.4057i	−0.640468	−	2.25998i
$441$		−	4.41481i		−	0.210229i
$442$	2.17701	−	0.804184i	0.103550	−	0.0382512i
$443$	−15.4561	+	15.4561i	−0.734342	+	0.734342i	−0.971477	−	0.237135i	$-0.923792\pi$
$443$	−15.4561	+	15.4561i	−0.734342	+	0.734342i	0.237135	+	0.971477i	$0.423792\pi$
$444$	18.0610	+	21.1106i	0.857136	+	1.00187i
$445$	−11.1245	−	11.1245i	−0.527350	−	0.527350i
$446$	−6.53953	+	14.2011i	−0.309656	+	0.672441i
$447$	−18.4449			−0.872414
$448$	8.03434	+	13.0367i	0.379587	+	0.615926i
$449$	3.76619			0.177737			0.0888687	−	0.996043i	$-0.471675\pi$
$449$	3.76619			0.177737			0.0888687	+	0.996043i	$0.471675\pi$
$450$	−9.59405	+	20.8342i	−0.452268	+	0.982134i
$451$	−33.1853	−	33.1853i	−1.56263	−	1.56263i
$452$	7.69930	+	8.99934i	0.362145	+	0.423293i
$453$	−5.29243	+	5.29243i	−0.248660	+	0.248660i
$454$	9.08884	−	3.35740i	0.426560	−	0.157571i
$455$			13.0487i			0.611733i
$456$	2.32154	+	8.19189i	0.108716	+	0.383620i
$457$			3.58004i			0.167467i	0.996488	+	0.0837337i	$0.0266845\pi$
$457$			3.58004i			0.167467i	−0.996488	+	0.0837337i	$0.973315\pi$
$458$	−4.57845	−	12.3943i	−0.213937	−	0.579150i
$459$	3.95844	−	3.95844i	0.184764	−	0.184764i
$460$	0.274283	−	3.52309i	0.0127885	−	0.164265i
$461$	−7.08206	−	7.08206i	−0.329844	−	0.329844i	0.522683	−	0.852527i	$-0.324931\pi$
$461$	−7.08206	−	7.08206i	−0.329844	−	0.329844i	−0.852527	+	0.522683i	$0.824931\pi$
$462$	−13.3522	−	6.14860i	−0.621199	−	0.286059i
$463$	−24.4270			−1.13522			−0.567608	−	0.823299i	$-0.692131\pi$
$463$	−24.4270			−1.13522			−0.567608	+	0.823299i	$0.692131\pi$
$464$	−19.0890	+	13.9182i	−0.886183	+	0.646136i
$465$	−21.9621			−1.01847
$466$	28.9290	+	13.3217i	1.34011	+	0.617114i
$467$	−6.87038	−	6.87038i	−0.317923	−	0.317923i	0.530046	−	0.847969i	$-0.322175\pi$
$467$	−6.87038	−	6.87038i	−0.317923	−	0.317923i	−0.847969	+	0.530046i	$0.822175\pi$
$468$	−4.33058	−	0.337149i	−0.200181	−	0.0155847i
$469$	7.57548	−	7.57548i	0.349803	−	0.349803i
$470$	2.99401	+	8.10509i	0.138103	+	0.373860i
$471$			12.3138i			0.567389i
$472$	12.2999	−	22.0284i	0.566150	−	1.01394i
$473$			27.9132i			1.28345i
$474$	26.7936	−	9.89752i	1.23067	−	0.454608i
$475$	−20.1468	+	20.1468i	−0.924400	+	0.924400i
$476$	2.90904	−	2.48880i	0.133336	−	0.114074i
$477$	1.39643	+	1.39643i	0.0639383	+	0.0639383i
$478$	4.28835	−	9.31247i	0.196144	−	0.425942i
$479$	21.5863			0.986303			0.493152	−	0.869943i	$-0.335845\pi$
$479$	21.5863			0.986303			0.493152	+	0.869943i	$0.335845\pi$
$480$	25.3337	+	16.8503i	1.15632	+	0.769107i
$481$	−17.6056			−0.802747
$482$	10.3836	−	22.5488i	0.472962	−	1.02707i
$483$	−0.745465	−	0.745465i	−0.0339198	−	0.0339198i
$484$	−10.0111	+	8.56494i	−0.455052	+	0.389315i
$485$	4.96333	−	4.96333i	0.225373	−	0.225373i
$486$	−16.6483	+	6.14986i	−0.755182	+	0.278963i
$487$			9.48194i			0.429668i	0.976651	+	0.214834i	$0.0689210\pi$
$487$			9.48194i			0.429668i	−0.976651	+	0.214834i	$0.931079\pi$
$488$	22.3057	+	12.4547i	1.00973	+	0.563800i
$489$		−	18.1875i		−	0.822465i
$490$	−6.79044	−	18.3824i	−0.306761	−	0.830433i
$491$	−9.57445	+	9.57445i	−0.432089	+	0.432089i	−0.889338	−	0.457250i	$-0.848835\pi$
$491$	−9.57445	+	9.57445i	−0.432089	+	0.432089i	0.457250	+	0.889338i	$0.348835\pi$
$492$	28.8925	+	2.24937i	1.30257	+	0.101409i
$493$	4.17622	+	4.17622i	0.188087	+	0.188087i
$494$	−4.90095	−	2.25686i	−0.220504	−	0.101541i
$495$	23.0551			1.03625
$496$	2.52784	−	16.1363i	0.113503	−	0.724540i
$497$	−14.3195			−0.642318
$498$	−22.0244	−	10.1421i	−0.986936	−	0.454479i
$499$	18.3357	+	18.3357i	0.820818	+	0.820818i	0.986225	−	0.165407i	$-0.0528939\pi$
$499$	18.3357	+	18.3357i	0.820818	+	0.820818i	−0.165407	+	0.986225i	$0.552894\pi$
$500$	−4.67838	+	60.0923i	−0.209223	+	2.68741i
$501$	−7.15822	+	7.15822i	−0.319806	+	0.319806i
$502$	−6.69165	−	18.1150i	−0.298663	−	0.808512i
$503$			17.9457i			0.800159i	0.916481	+	0.400079i	$0.131017\pi$
$503$			17.9457i			0.800159i	−0.916481	+	0.400079i	$0.868983\pi$
$504$	−6.89388	+	1.95369i	−0.307078	+	0.0870245i
$505$		−	14.1040i		−	0.627618i
$506$	−2.36640	+	0.874144i	−0.105199	+	0.0388604i
$507$	9.43679	−	9.43679i	0.419102	−	0.419102i
$508$	7.72102	+	9.02473i	0.342565	+	0.400408i
$509$	15.1095	+	15.1095i	0.669715	+	0.669715i	0.957650	−	0.287935i	$-0.0929687\pi$
$509$	15.1095	+	15.1095i	0.669715	+	0.669715i	−0.287935	+	0.957650i	$0.592969\pi$
$510$	3.18160	−	6.90909i	0.140884	−	0.305940i
$511$	0.263404			0.0116523
$512$	−15.2963	+	16.6740i	−0.676009	+	0.736893i
$513$	−13.0150			−0.574626
$514$	−16.0007	+	34.7468i	−0.705763	+	1.53262i
$515$	14.4954	+	14.4954i	0.638743	+	0.638743i
$516$	−11.2052	−	13.0972i	−0.493282	−	0.576573i
$517$	4.36162	−	4.36162i	0.191824	−	0.191824i
$518$	−27.2430	+	10.0635i	−1.19699	+	0.442167i
$519$		−	1.03050i		−	0.0452340i
$520$	−18.5503	+	5.25706i	−0.813483	+	0.230537i
$521$		−	16.9507i		−	0.742623i	−0.928508	−	0.371311i	$-0.878908\pi$
$521$		−	16.9507i		−	0.742623i	0.928508	−	0.371311i	$-0.121092\pi$
$522$	−3.83035	−	10.3692i	−0.167650	−	0.453846i
$523$	−18.3841	+	18.3841i	−0.803883	+	0.803883i	−0.983700	−	0.179817i	$-0.942449\pi$
$523$	−18.3841	+	18.3841i	−0.803883	+	0.803883i	0.179817	+	0.983700i	$0.442449\pi$
$524$	−2.30406	+	29.5949i	−0.100653	+	1.29286i
$525$	21.4782	+	21.4782i	0.937384	+	0.937384i
$526$	13.1981	+	6.07766i	0.575464	+	0.264998i
$527$	−4.08327			−0.177870
$528$	3.36165	−	21.4588i	0.146297	−	0.933876i
$529$	22.8191			0.992134
$530$	7.96234	+	3.66662i	0.345862	+	0.159268i
$531$	8.34756	+	8.34756i	0.362253	+	0.362253i
$532$	−8.87381	−	0.690854i	−0.384728	−	0.0299523i
$533$	−12.9857	+	12.9857i	−0.562473	+	0.562473i
$534$	−2.40313	−	6.50553i	−0.103994	−	0.281522i
$535$		−	81.8201i		−	3.53739i
$536$	13.8214	+	7.71743i	0.596996	+	0.333342i
$537$		−	7.01381i		−	0.302668i
$538$	2.78110	−	1.02733i	0.119902	−	0.0442915i
$539$	−9.89220	+	9.89220i	−0.426087	+	0.426087i
$540$	−35.3394	+	30.2343i	−1.52077	+	1.30108i
$541$	22.9230	+	22.9230i	0.985537	+	0.985537i	0.999897	−	0.0143595i	$-0.00457093\pi$
$541$	22.9230	+	22.9230i	0.985537	+	0.985537i	−0.0143595	+	0.999897i	$0.504571\pi$
$542$	18.4524	−	40.0708i	0.792599	−	1.72119i
$543$	−0.401692			−0.0172382
$544$	4.71012	+	3.13286i	0.201945	+	0.134320i
$545$	−40.4805			−1.73399
$546$	−2.40600	+	5.22482i	−0.102967	+	0.223601i
$547$	−23.2817	−	23.2817i	−0.995454	−	0.995454i	0.00453534	−	0.999990i	$-0.498556\pi$
$547$	−23.2817	−	23.2817i	−0.995454	−	0.995454i	−0.999990	+	0.00453534i	$0.998556\pi$
$548$	−10.7995	+	9.23938i	−0.461330	+	0.394687i
$549$	−8.45263	+	8.45263i	−0.360749	+	0.360749i
$550$	68.1801	−	25.1856i	2.90721	−	1.07392i
$551$		−	13.7310i		−	0.584962i
$552$	0.759434	−	1.36010i	0.0323237	−	0.0578897i
$553$			29.8587i			1.26972i
$554$	2.52769	+	6.84272i	0.107391	+	0.290719i
$555$	−40.8020	+	40.8020i	−1.73195	+	1.73195i
$556$	−31.6019	−	2.46031i	−1.34022	−	0.104340i
$557$	−20.9779	−	20.9779i	−0.888861	−	0.888861i	0.105553	−	0.994414i	$-0.466339\pi$
$557$	−20.9779	−	20.9779i	−0.888861	−	0.888861i	−0.994414	+	0.105553i	$0.966339\pi$
$558$	6.94174	+	3.19664i	0.293867	+	0.135324i
$559$	10.9227			0.461981
$560$	−25.6998	+	18.7383i	−1.08602	+	0.791839i
$561$	−5.43014			−0.229261
$562$	−1.47173	−	0.677725i	−0.0620812	−	0.0285881i
$563$	3.66561	+	3.66561i	0.154487	+	0.154487i	0.780119	−	0.625632i	$-0.215159\pi$
$563$	3.66561	+	3.66561i	0.154487	+	0.154487i	−0.625632	+	0.780119i	$0.715159\pi$
$564$	−0.295640	+	3.79741i	−0.0124487	+	0.159900i
$565$	−17.3937	+	17.3937i	−0.731758	+	0.731758i
$566$	7.45777	+	20.1889i	0.313473	+	0.848605i
$567$			6.27502i			0.263526i
$568$	−5.76905	−	20.3569i	−0.242064	−	0.854156i
$569$		−	5.33680i		−	0.223730i	−0.993723	−	0.111865i	$-0.964318\pi$
$569$		−	5.33680i		−	0.223730i	0.993723	−	0.111865i	$-0.0356825\pi$
$570$	−16.5887	+	6.12783i	−0.694822	+	0.256666i
$571$	−2.80602	+	2.80602i	−0.117428	+	0.117428i	−0.763379	−	0.645951i	$-0.776461\pi$
$571$	−2.80602	+	2.80602i	−0.117428	+	0.117428i	0.645951	+	0.763379i	$0.276461\pi$
$572$	8.94801	+	10.4589i	0.374135	+	0.437309i
$573$	2.94418	+	2.94418i	0.122995	+	0.122995i
$574$	−12.6714	+	27.5169i	−0.528894	+	1.14853i
$575$	5.21270			0.217385
$576$	−5.55482	−	9.01337i	−0.231451	−	0.375557i
$577$	30.5852			1.27328			0.636640	−	0.771161i	$-0.280324\pi$
$577$	30.5852			1.27328			0.636640	+	0.771161i	$0.280324\pi$
$578$	0.591533	−	1.28456i	0.0246045	−	0.0534306i
$579$	14.5395	+	14.5395i	0.604242	+	0.604242i
$580$	−31.8977	−	37.2837i	−1.32448	−	1.54812i
$581$	17.9231	−	17.9231i	0.743576	−	0.743576i
$582$	2.90253	−	1.07219i	0.120314	−	0.0444438i
$583$		−	6.25793i		−	0.259177i
$584$	0.106120	+	0.374460i	0.00439129	+	0.0154953i
$585$		−	9.02167i		−	0.373000i
$586$	−2.47207	−	6.69214i	−0.102120	−	0.276450i
$587$	13.5707	−	13.5707i	0.560122	−	0.560122i	−0.369220	−	0.929342i	$-0.620375\pi$
$587$	13.5707	−	13.5707i	0.560122	−	0.560122i	0.929342	+	0.369220i	$0.120375\pi$
$588$	0.670515	−	8.61255i	0.0276516	−	0.355176i
$589$	6.71271	+	6.71271i	0.276592	+	0.276592i
$590$	47.5970	+	21.9182i	1.95954	+	0.902358i
$591$	−0.764778			−0.0314588
$592$	−25.2822	−	34.6748i	−1.03909	−	1.42513i
$593$	7.50668			0.308262			0.154131	−	0.988050i	$-0.450742\pi$
$593$	7.50668			0.308262			0.154131	+	0.988050i	$0.450742\pi$
$594$	30.1575	+	13.8874i	1.23738	+	0.569805i
$595$	5.62252	+	5.62252i	0.230501	+	0.230501i
$596$	28.4044	+	2.21137i	1.16349	+	0.0905814i
$597$	19.0600	−	19.0600i	0.780075	−	0.780075i
$598$	0.342060	+	0.925992i	0.0139879	+	0.0378666i
$599$			32.1259i			1.31263i	0.754488	+	0.656314i	$0.227885\pi$
$599$			32.1259i			1.31263i	−0.754488	+	0.656314i	$0.772115\pi$
$600$	−21.8806	+	39.1869i	−0.893273	+	1.59980i
$601$		−	10.6598i		−	0.434822i	−0.976080	−	0.217411i	$-0.930239\pi$
$601$		−	10.6598i		−	0.434822i	0.976080	−	0.217411i	$-0.0697612\pi$
$602$	16.9018	−	6.24352i	0.688868	−	0.254467i
$603$	−5.23757	+	5.23757i	−0.213290	+	0.213290i
$604$	8.78465	−	7.51562i	0.357442	−	0.305806i
$605$	−19.3493	−	19.3493i	−0.786660	−	0.786660i
$606$	2.60058	−	5.64735i	0.105641	−	0.229408i
$607$	28.1457			1.14240			0.571200	−	0.820811i	$-0.306478\pi$
$607$	28.1457			1.14240			0.571200	+	0.820811i	$0.306478\pi$
$608$	−2.59295	−	12.8935i	−0.105158	−	0.522901i
$609$	−14.6384			−0.593178
$610$	−22.1941	+	48.1961i	−0.898612	+	1.95140i
$611$	−1.70674	−	1.70674i	−0.0690473	−	0.0690473i
$612$	−2.01126	+	1.72072i	−0.0813005	+	0.0695559i
$613$	32.0193	−	32.0193i	1.29325	−	1.29325i	0.360483	−	0.932766i	$-0.382612\pi$
$613$	32.0193	−	32.0193i	1.29325	−	1.29325i	0.932766	−	0.360483i	$-0.117388\pi$
$614$	2.94144	−	1.08656i	0.118707	−	0.0438501i
$615$			60.1902i			2.42710i
$616$	19.8246	+	11.0694i	0.798757	+	0.445999i
$617$			17.1962i			0.692291i	0.938181	+	0.346146i	$0.112510\pi$
$617$			17.1962i			0.692291i	−0.938181	+	0.346146i	$0.887490\pi$
$618$	3.13133	+	8.47683i	0.125961	+	0.340988i
$619$	−10.1800	+	10.1800i	−0.409169	+	0.409169i	−0.881449	−	0.472280i	$-0.843431\pi$
$619$	−10.1800	+	10.1800i	−0.409169	+	0.409169i	0.472280	+	0.881449i	$0.343431\pi$
$620$	33.8208	+	2.63306i	1.35828	+	0.105746i
$621$	1.68372	+	1.68372i	0.0675655	+	0.0675655i
$622$	31.5654	+	14.5357i	1.26566	+	0.582828i
$623$	7.24974			0.290455
$624$	−8.39703	−	1.31544i	−0.336150	−	0.0526599i
$625$	−63.9117			−2.55647
$626$	−17.6313	−	8.11911i	−0.704687	−	0.324505i
$627$	8.92691	+	8.92691i	0.356506	+	0.356506i
$628$	1.47631	−	18.9627i	0.0589111	−	0.756695i
$629$	−7.58603	+	7.58603i	−0.302475	+	0.302475i
$630$	−5.15687	−	13.9602i	−0.205455	−	0.556187i
$631$		−	9.80769i		−	0.390438i	−0.980760	−	0.195219i	$-0.937458\pi$
$631$		−	9.80769i		−	0.390438i	0.980760	−	0.195219i	$-0.0625418\pi$
$632$	−42.4477	+	12.0295i	−1.68848	+	0.478507i
$633$		−	20.9921i		−	0.834362i
$634$	39.3732	−	14.5444i	1.56371	−	0.577632i
$635$	−17.4428	+	17.4428i	−0.692195	+	0.692195i
$636$	2.51212	+	2.93629i	0.0996119	+	0.116432i
$637$	3.87090	+	3.87090i	0.153371	+	0.153371i
$638$	−14.6514	+	31.8166i	−0.580054	+	1.25963i
$639$	9.90029			0.391649
$640$	−36.9927	−	28.9861i	−1.46226	−	1.14577i
$641$	4.79538			0.189406			0.0947031	−	0.995506i	$-0.469810\pi$
$641$	4.79538			0.189406			0.0947031	+	0.995506i	$0.469810\pi$
$642$	15.0865	−	32.7615i	0.595417	−	1.29299i
$643$	−1.18375	−	1.18375i	−0.0466827	−	0.0466827i	0.683380	−	0.730063i	$-0.260509\pi$
$643$	−1.18375	−	1.18375i	−0.0466827	−	0.0466827i	−0.730063	+	0.683380i	$0.760509\pi$
$644$	1.05861	+	1.23736i	0.0417151	+	0.0487588i
$645$	25.3140	−	25.3140i	0.996737	−	0.996737i
$646$	−3.08421	+	1.13930i	−0.121347	+	0.0448253i
$647$			9.79140i			0.384940i	0.981303	+	0.192470i	$0.0616497\pi$
$647$			9.79140i			0.384940i	−0.981303	+	0.192470i	$0.938350\pi$
$648$	−8.92069	+	2.52808i	−0.350438	+	0.0993124i
$649$		−	37.4085i		−	1.46841i
$650$	−9.85535	−	26.6794i	−0.386559	−	1.04645i
$651$	7.15630	−	7.15630i	0.280477	−	0.280477i
$652$	−2.18051	+	28.0080i	−0.0853953	+	1.09688i
$653$	−10.4277	−	10.4277i	−0.408068	−	0.408068i	0.472996	−	0.881064i	$-0.343172\pi$
$653$	−10.4277	−	10.4277i	−0.408068	−	0.408068i	−0.881064	+	0.472996i	$0.843172\pi$
$654$	−16.2087	−	7.46404i	−0.633812	−	0.291867i
$655$	−61.6535			−2.40900
$656$	−44.2236	−	6.92788i	−1.72664	−	0.270488i
$657$	−0.182113			−0.00710492
$658$	−3.61661	−	1.66543i	−0.140990	−	0.0649252i
$659$	20.2555	+	20.2555i	0.789041	+	0.789041i	0.981337	−	0.192296i	$-0.0615934\pi$
$659$	20.2555	+	20.2555i	0.789041	+	0.789041i	−0.192296	+	0.981337i	$0.561593\pi$
$660$	44.9767	+	3.50158i	1.75071	+	0.136299i
$661$	7.38826	−	7.38826i	0.287370	−	0.287370i	−0.548669	−	0.836039i	$-0.684865\pi$
$661$	7.38826	−	7.38826i	0.287370	−	0.287370i	0.836039	+	0.548669i	$0.184865\pi$
$662$	16.2930	+	44.1069i	0.633246	+	1.71426i
$663$			2.12486i			0.0825227i
$664$	32.7007	+	18.2590i	1.26903	+	0.708586i
$665$		−	18.4863i		−	0.716869i
$666$	18.8354	−	6.95778i	0.729858	−	0.269608i
$667$	−1.77636	+	1.77636i	−0.0687808	+	0.0687808i
$668$	11.8816	−	10.1652i	0.459712	−	0.393302i
$669$	−10.1219	−	10.1219i	−0.391335	−	0.391335i
$670$	−13.7523	+	29.8641i	−0.531297	+	1.15375i
$671$	37.8793			1.46231
$672$	−13.7455	+	2.76430i	−0.530245	+	0.106635i
$673$	−11.3011			−0.435627			−0.217813	−	0.975990i	$-0.569892\pi$
$673$	−11.3011			−0.435627			−0.217813	+	0.975990i	$0.569892\pi$
$674$	1.75109	−	3.80262i	0.0674494	−	0.146471i
$675$	−48.5110	−	48.5110i	−1.86719	−	1.86719i
$676$	−15.6636	+	13.4009i	−0.602448	+	0.515419i
$677$	−31.7314	+	31.7314i	−1.21954	+	1.21954i	−0.251741	+	0.967795i	$0.581003\pi$
$677$	−31.7314	+	31.7314i	−1.21954	+	1.21954i	−0.967795	+	0.251741i	$0.918997\pi$
$678$	−10.1718	+	3.75743i	−0.390644	+	0.144303i
$679$			3.23457i			0.124132i
$680$	−5.72787	+	10.2583i	−0.219654	+	0.393387i
$681$			8.87112i			0.339942i
$682$	−8.39158	−	22.7169i	−0.321330	−	0.869874i
$683$	−1.73147	+	1.73147i	−0.0662530	+	0.0662530i	−0.739457	−	0.673204i	$-0.764918\pi$
$683$	−1.73147	+	1.73147i	−0.0662530	+	0.0662530i	0.673204	+	0.739457i	$0.264918\pi$
$684$	6.13521	+	0.477646i	0.234586	+	0.0182633i
$685$	−20.8729	−	20.8729i	−0.797514	−	0.797514i
$686$	25.4148	+	11.7034i	0.970341	+	0.446838i
$687$	12.0974			0.461546
$688$	15.6853	+	21.5126i	0.597997	+	0.820160i
$689$	−2.44878			−0.0932911
$690$	2.93878	+	1.35330i	0.111878	+	0.0515191i
$691$	31.6831	+	31.6831i	1.20528	+	1.20528i	0.972538	+	0.232744i	$0.0747705\pi$
$691$	31.6831	+	31.6831i	1.20528	+	1.20528i	0.232744	+	0.972538i	$0.425230\pi$
$692$	−0.123548	+	1.58693i	−0.00469658	+	0.0603261i
$693$	−7.51244	+	7.51244i	−0.285374	+	0.285374i
$694$	−13.3696	−	36.1930i	−0.507505	−	1.37387i
$695$		−	65.8346i		−	2.49725i
$696$	−5.89752	−	20.8102i	−0.223545	−	0.788810i
$697$			11.1907i			0.423879i
$698$	−4.03363	+	1.49002i	−0.152675	+	0.0563980i
$699$	−20.6193	+	20.6193i	−0.779893	+	0.779893i
$700$	−30.5005	−	35.6505i	−1.15281	−	1.34746i
$701$	18.7141	+	18.7141i	0.706822	+	0.706822i	0.965866	−	0.259044i	$-0.0834073\pi$
$701$	18.7141	+	18.7141i	0.706822	+	0.706822i	−0.259044	+	0.965866i	$0.583407\pi$
$702$	5.43424	−	11.8009i	0.205102	−	0.445395i
$703$	24.9422			0.940713
$704$	−7.74952	+	32.6427i	−0.292071	+	1.23027i
$705$	−7.91093			−0.297943
$706$	−11.5663	+	25.1172i	−0.435305	+	0.945297i
$707$	4.59573	+	4.59573i	0.172840	+	0.172840i
$708$	15.0169	+	17.5525i	0.564368	+	0.659663i
$709$	0.260136	−	0.260136i	0.00976960	−	0.00976960i	−0.702205	−	0.711975i	$-0.747801\pi$
$709$	0.260136	−	0.260136i	0.00976960	−	0.00976960i	0.711975	+	0.702205i	$0.247801\pi$
$710$	41.2229	−	15.2277i	1.54707	−	0.571485i
$711$		−	20.6438i		−	0.774205i
$712$	2.92078	+	10.3064i	0.109461	+	0.386247i
$713$		−	1.73682i		−	0.0650444i
$714$	1.21459	+	3.28802i	0.0454549	+	0.123051i
$715$	−20.2147	+	20.2147i	−0.755987	+	0.755987i
$716$	−0.840891	+	10.8010i	−0.0314256	+	0.403652i
$717$	6.63750	+	6.63750i	0.247882	+	0.247882i
$718$	3.84936	+	1.77261i	0.143657	+	0.0661532i
$719$	15.8428			0.590836			0.295418	−	0.955368i	$-0.404541\pi$
$719$	15.8428			0.590836			0.295418	+	0.955368i	$0.404541\pi$
$720$	17.7685	−	12.9554i	0.662191	−	0.482819i
$721$	−9.44655			−0.351808
$722$	−17.4633	−	8.04178i	−0.649918	−	0.299284i
$723$	16.0718	+	16.0718i	0.597716	+	0.597716i
$724$	0.618589	+	0.0481591i	0.0229897	+	0.00178982i
$725$	51.1799	−	51.1799i	1.90077	−	1.90077i
$726$	−4.17988	−	11.3154i	−0.155130	−	0.419953i
$727$		−	12.2637i		−	0.454835i	−0.973797	−	0.227418i	$-0.926972\pi$
$727$		−	12.2637i		−	0.454835i	0.973797	−	0.227418i	$-0.0730283\pi$
$728$	4.33155	−	7.75755i	0.160538	−	0.287514i
$729$		−	26.0839i		−	0.966071i
$730$	−0.758285	+	0.280110i	−0.0280654	+	0.0103673i
$731$	4.70645	−	4.70645i	0.174074	−	0.174074i
$732$	−17.7734	+	15.2059i	−0.656925	+	0.562025i
$733$	5.21560	+	5.21560i	0.192642	+	0.192642i	0.796837	−	0.604194i	$-0.206505\pi$
$733$	5.21560	+	5.21560i	0.192642	+	0.192642i	−0.604194	+	0.796837i	$0.706505\pi$
$734$	18.7933	−	40.8111i	0.693675	−	1.50637i
$735$	17.9421			0.661803
$736$	−1.33256	+	2.00345i	−0.0491189	+	0.0738482i
$737$	23.4715			0.864582
$738$	8.76080	−	19.0247i	0.322490	−	0.700310i
$739$	−19.0681	−	19.0681i	−0.701432	−	0.701432i	0.263286	−	0.964718i	$-0.415194\pi$
$739$	−19.0681	−	19.0681i	−0.701432	−	0.701432i	−0.964718	+	0.263286i	$0.915194\pi$
$740$	67.7253	−	57.9417i	2.48963	−	2.12998i
$741$	3.49318	−	3.49318i	0.128325	−	0.128325i
$742$	−3.78926	+	1.39975i	−0.139108	+	0.0513863i
$743$			31.7602i			1.16517i	0.812770	+	0.582585i	$0.197959\pi$
$743$			31.7602i			1.16517i	−0.812770	+	0.582585i	$0.802041\pi$
$744$	13.0567	+	7.29040i	0.478680	+	0.267279i
$745$			59.1734i			2.16795i
$746$	13.2882	+	35.9724i	0.486514	+	1.31704i
$747$	−12.3918	+	12.3918i	−0.453391	+	0.453391i
$748$	8.36219	+	0.651023i	0.305752	+	0.0238038i
$749$	26.6608	+	26.6608i	0.974165	+	0.974165i
$750$	−50.1260	−	23.0828i	−1.83034	−	0.842865i
$751$	4.29550			0.156745			0.0783726	−	0.996924i	$-0.475028\pi$
$751$	4.29550			0.156745			0.0783726	+	0.996924i	$0.475028\pi$
$752$	0.910548	−	5.81241i	0.0332043	−	0.211957i
$753$	17.6810			0.644333
$754$	12.4501	+	5.73322i	0.453406	+	0.208791i
$755$	16.9787	+	16.9787i	0.617920	+	0.617920i
$756$	1.66349	−	21.3670i	0.0605005	−	0.777110i
$757$	−21.0672	+	21.0672i	−0.765700	+	0.765700i	−0.977346	−	0.211647i	$-0.932117\pi$
$757$	−21.0672	+	21.0672i	−0.765700	+	0.765700i	0.211647	+	0.977346i	$0.432117\pi$
$758$	12.8759	+	34.8565i	0.467675	+	1.26604i
$759$		−	2.30971i		−	0.0838372i
$760$	26.2805	−	7.44778i	0.953295	−	0.270159i
$761$		−	10.1716i		−	0.368720i	−0.982859	−	0.184360i	$-0.940979\pi$
$761$		−	10.1716i		−	0.368720i	0.982859	−	0.184360i	$-0.0590212\pi$
$762$	−10.2004	+	3.76803i	−0.369523	+	0.136501i
$763$	13.1904	−	13.1904i	0.477526	−	0.477526i
$764$	−4.18094	−	4.88690i	−0.151261	−	0.176802i
$765$	−3.88732	−	3.88732i	−0.140546	−	0.140546i
$766$	5.57104	−	12.0979i	0.201290	−	0.437116i
$767$	−14.6383			−0.528557
$768$	−9.46757	−	18.4272i	−0.341632	−	0.664935i
$769$	47.0356			1.69615			0.848073	−	0.529879i	$-0.177763\pi$
$769$	47.0356			1.69615			0.848073	+	0.529879i	$0.177763\pi$
$770$	−19.7254	+	42.8353i	−0.710855	+	1.54368i
$771$	−24.7660	−	24.7660i	−0.891924	−	0.891924i
$772$	−20.6471	−	24.1334i	−0.743106	−	0.868581i
$773$	−28.1162	+	28.1162i	−1.01127	+	1.01127i	−0.0113345	+	0.999936i	$0.503608\pi$
$773$	−28.1162	+	28.1162i	−1.01127	+	1.01127i	−0.999936	+	0.0113345i	$0.996392\pi$
$774$	−11.6857	+	4.31667i	−0.420033	+	0.155160i
$775$			50.0408i			1.79752i
$776$	−4.59833	+	1.30315i	−0.165070	+	0.0467802i
$777$		−	26.5904i		−	0.953927i
$778$	2.77560	+	7.51383i	0.0995100	+	0.269384i
$779$	18.3971	−	18.3971i	0.659143	−	0.659143i
$780$	1.37020	−	17.5998i	0.0490609	−	0.630172i
$781$	−22.1834	−	22.1834i	−0.793785	−	0.793785i
$782$	0.546387	+	0.251609i	0.0195388	+	0.00899750i
$783$	33.0626			1.18156
$784$	−2.06513	+	13.1826i	−0.0737547	+	0.470807i
$785$	39.5040			1.40996
$786$	−24.6866	−	11.3681i	−0.880542	−	0.405485i
$787$	12.9893	+	12.9893i	0.463020	+	0.463020i	0.899644	−	0.436624i	$-0.143826\pi$
$787$	12.9893	+	12.9893i	0.463020	+	0.463020i	−0.436624	+	0.899644i	$0.643826\pi$
$788$	1.17773	+	0.0916899i	0.0419548	+	0.00326632i
$789$	−9.40700	+	9.40700i	−0.334898	+	0.334898i
$790$	−31.7524	−	85.9570i	−1.12970	−	3.05821i
$791$		−	11.3354i		−	0.403039i
$792$	−13.7064	−	7.65321i	−0.487037	−	0.271945i
$793$		−	14.8225i		−	0.526363i
$794$	−51.1971	+	18.9121i	−1.81692	+	0.671166i
$795$	−5.67519	+	5.67519i	−0.201278	+	0.201278i
$796$	−31.6368	+	27.0666i	−1.12134	+	0.959349i
$797$	−2.64339	−	2.64339i	−0.0936338	−	0.0936338i	0.658738	−	0.752372i	$-0.271090\pi$
$797$	−2.64339	−	2.64339i	−0.0936338	−	0.0936338i	−0.752372	+	0.658738i	$0.771090\pi$
$798$	3.40863	−	7.40209i	0.120664	−	0.262031i
$799$	−1.47082			−0.0520340
$800$	38.3934	−	57.7229i	1.35741	−	2.04081i
$801$	−5.01236			−0.177103
$802$	11.2370	−	24.4020i	0.396793	−	0.861666i
$803$	0.408058	+	0.408058i	0.0144001	+	0.0144001i
$804$	−11.0131	+	9.42213i	−0.388401	+	0.332293i
$805$	−2.39154	+	2.39154i	−0.0842907	+	0.0842907i
$806$	−8.88931	+	3.28370i	−0.313113	+	0.115663i
$807$			2.71447i			0.0955540i
$808$	−4.68185	+	8.38490i	−0.164707	+	0.294980i
$809$			27.5076i			0.967117i	0.875312	+	0.483559i	$0.160656\pi$
$809$			27.5076i			0.967117i	−0.875312	+	0.483559i	$0.839344\pi$
$810$	−6.67299	−	18.0645i	−0.234465	−	0.634721i
$811$	4.86403	−	4.86403i	0.170799	−	0.170799i	−0.616531	−	0.787330i	$-0.711463\pi$
$811$	4.86403	−	4.86403i	0.170799	−	0.170799i	0.787330	+	0.616531i	$0.211463\pi$
$812$	22.5425	+	1.75501i	0.791088	+	0.0615887i
$813$	28.5606	+	28.5606i	1.00167	+	1.00167i
$814$	−57.7944	−	26.6140i	−2.02569	−	0.932821i
$815$	−58.3475			−2.04382
$816$	−4.18498	+	3.05136i	−0.146503	+	0.106819i
$817$	−15.4744			−0.541380
$818$	15.1542	+	6.97844i	0.529855	+	0.243996i
$819$	2.93968	+	2.93968i	0.102721	+	0.102721i
$820$	7.21624	−	92.6904i	0.252002	−	3.23689i
$821$	4.96364	−	4.96364i	0.173232	−	0.173232i	−0.615166	−	0.788398i	$-0.710911\pi$
$821$	4.96364	−	4.96364i	0.173232	−	0.173232i	0.788398	+	0.615166i	$0.210911\pi$
$822$	−4.50902	−	12.2064i	−0.157270	−	0.425747i
$823$		−	16.2032i		−	0.564809i	−0.959295	−	0.282404i	$-0.908868\pi$
$823$		−	16.2032i		−	0.564809i	0.959295	−	0.282404i	$-0.0911320\pi$
$824$	−3.80583	−	13.4294i	−0.132582	−	0.467835i
$825$			66.5468i			2.31686i
$826$	−22.6513	+	8.36737i	−0.788140	+	0.291138i
$827$	33.3978	−	33.3978i	1.16136	−	1.16136i	0.177178	−	0.984179i	$-0.443303\pi$
$827$	33.3978	−	33.3978i	1.16136	−	1.16136i	0.984179	−	0.177178i	$-0.0566968\pi$
$828$	−0.731908	−	0.855492i	−0.0254356	−	0.0297304i
$829$	5.19197	+	5.19197i	0.180325	+	0.180325i	0.791497	−	0.611173i	$-0.209302\pi$
$829$	5.19197	+	5.19197i	0.180325	+	0.180325i	−0.611173	+	0.791497i	$0.709302\pi$
$830$	−32.5371	+	70.6568i	−1.12938	+	2.45253i
$831$	−6.67880			−0.231685
$832$	12.7734	+	3.03245i	0.442837	+	0.105131i
$833$	3.33584			0.115580
$834$	12.1390	−	26.3608i	0.420339	−	0.912798i
$835$	22.9644	+	22.9644i	0.794716	+	0.794716i
$836$	−12.6768	−	14.8173i	−0.438437	−	0.512468i
$837$	−16.1634	+	16.1634i	−0.558687	+	0.558687i
$838$	43.6118	−	16.1101i	1.50654	−	0.556515i
$839$		−	16.3603i		−	0.564821i	−0.959294	−	0.282410i	$-0.908866\pi$
$839$		−	16.3603i		−	0.564821i	0.959294	−	0.282410i	$-0.0911340\pi$
$840$	−7.93994	−	28.0172i	−0.273954	−	0.966685i
$841$			5.88159i			0.202813i
$842$	−16.6927	−	45.1889i	−0.575269	−	1.55731i
$843$	1.04898	−	1.04898i	0.0361289	−	0.0361289i
$844$	−2.51676	+	32.3270i	−0.0866305	+	1.11274i
$845$	−30.2743	−	30.2743i	−1.04147	−	1.04147i
$846$	2.50047	+	1.15145i	0.0859678	+	0.0395878i
$847$	12.6098			0.433278
$848$	−3.51652	−	4.82295i	−0.120758	−	0.165621i
$849$	−19.7053			−0.676285
$850$	−15.7424	−	7.24928i	−0.539959	−	0.248648i
$851$	−3.22672	−	3.22672i	−0.110611	−	0.110611i
$852$	19.3138	+	1.50364i	0.661680	+	0.0515139i
$853$	16.5619	−	16.5619i	0.567070	−	0.567070i	−0.364237	−	0.931306i	$-0.618670\pi$
$853$	16.5619	−	16.5619i	0.567070	−	0.567070i	0.931306	+	0.364237i	$0.118670\pi$
$854$	−8.47269	−	22.9364i	−0.289929	−	0.784869i
$855$			12.7812i			0.437107i
$856$	−27.1604	+	48.6426i	−0.928323	+	1.66257i
$857$			30.6293i			1.04628i	0.852247	+	0.523139i	$0.175239\pi$
$857$			30.6293i			1.04628i	−0.852247	+	0.523139i	$0.824761\pi$
$858$	−11.8215	+	4.36683i	−0.403578	+	0.149081i
$859$	30.9534	−	30.9534i	1.05612	−	1.05612i	0.0577876	−	0.998329i	$-0.481595\pi$
$859$	30.9534	−	30.9534i	1.05612	−	1.05612i	0.998329	−	0.0577876i	$-0.0184046\pi$
$860$	−42.0174	+	35.9476i	−1.43278	+	1.22580i
$861$	−19.6128	−	19.6128i	−0.668402	−	0.668402i
$862$	−4.00632	+	8.70003i	−0.136456	+	0.296324i
$863$	6.81263			0.231905			0.115952	−	0.993255i	$-0.463008\pi$
$863$	6.81263			0.231905			0.115952	+	0.993255i	$0.463008\pi$
$864$	31.0459	−	6.24349i	1.05620	−	0.212408i
$865$	−3.30597			−0.112406
$866$	−9.61052	+	20.8700i	−0.326579	+	0.709190i
$867$	0.915574	+	0.915574i	0.0310945	+	0.0310945i
$868$	−11.8784	+	10.1624i	−0.403178	+	0.344935i
$869$	−46.2563	+	46.2563i	−1.56914	+	1.56914i
$870$	42.1409	−	15.5668i	1.42871	−	0.527764i
$871$		−	9.18458i		−	0.311208i
$872$	24.0659	+	13.4376i	0.814975	+	0.455055i
$873$		−	2.23633i		−	0.0756884i
$874$	−0.484603	−	1.31187i	−0.0163919	−	0.0443747i
$875$	40.7918	−	40.7918i	1.37902	−	1.37902i
$876$	−0.355272	−	0.0276591i	−0.0120035	−	0.000934514i
$877$	−26.2073	−	26.2073i	−0.884957	−	0.884957i	0.109076	−	0.994033i	$-0.465211\pi$
$877$	−26.2073	−	26.2073i	−0.884957	−	0.884957i	−0.994033	+	0.109076i	$0.965211\pi$
$878$	−23.4543	−	10.8006i	−0.791543	−	0.364502i
$879$	6.53183			0.220313
$880$	−68.8424	−	10.7846i	−2.32068	−	0.363548i
$881$	42.1590			1.42037			0.710187	−	0.704013i	$-0.248610\pi$
$881$	42.1590			1.42037			0.710187	+	0.704013i	$0.248610\pi$
$882$	−5.67108	−	2.61151i	−0.190955	−	0.0879340i
$883$	11.4035	+	11.4035i	0.383758	+	0.383758i	0.872454	−	0.488696i	$-0.162527\pi$
$883$	11.4035	+	11.4035i	0.383758	+	0.383758i	−0.488696	+	0.872454i	$0.662527\pi$
$884$	0.254751	−	3.27220i	0.00856820	−	0.110056i
$885$	−33.9250	+	33.9250i	−1.14038	+	1.14038i
$886$	10.7115	+	28.9970i	0.359859	+	0.974175i
$887$		−	18.7407i		−	0.629252i	−0.949216	−	0.314626i	$-0.898121\pi$
$887$		−	18.7407i		−	0.629252i	0.949216	−	0.314626i	$-0.101879\pi$
$888$	37.8015	−	10.7128i	1.26853	−	0.359497i
$889$		−	11.3673i		−	0.381248i
$890$	−20.8705	+	7.70953i	−0.699581	+	0.258424i
$891$	−9.72110	+	9.72110i	−0.325669	+	0.325669i
$892$	14.3738	+	16.8008i	0.481270	+	0.562533i
$893$	2.41797	+	2.41797i	0.0809143	+	0.0809143i
$894$	−10.9108	+	23.6936i	−0.364911	+	0.792431i
$895$	−22.5011			−0.752129
$896$	21.4990	−	2.60894i	0.718230	−	0.0871586i
$897$	−0.903810			−0.0301773
$898$	2.22782	−	4.83789i	0.0743434	−	0.161442i
$899$	−17.0526	−	17.0526i	−0.568736	−	0.568736i
$900$	21.0875	+	24.6482i	0.702918	+	0.821607i
$901$	−1.05515	+	1.05515i	−0.0351521	+	0.0351521i
$902$	−62.2586	+	22.9982i	−2.07298	+	0.765758i
$903$			16.4970i			0.548984i
$904$	16.1146	−	4.56679i	0.535962	−	0.151889i
$905$			1.28867i			0.0428370i
$906$	3.66779	+	9.92909i	0.121854	+	0.329872i
$907$	22.6508	−	22.6508i	0.752108	−	0.752108i	−0.222764	−	0.974872i	$-0.571508\pi$
$907$	22.6508	−	22.6508i	0.752108	−	0.752108i	0.974872	+	0.222764i	$0.0715079\pi$
$908$	1.06356	−	13.6612i	0.0352956	−	0.453361i
$909$	−3.17742	−	3.17742i	−0.105388	−	0.105388i
$910$	16.7618	+	7.71873i	0.555649	+	0.255873i
$911$	−25.2568			−0.836796			−0.418398	−	0.908264i	$-0.637408\pi$
$911$	−25.2568			−0.836796			−0.418398	+	0.908264i	$0.637408\pi$
$912$	11.8962	+	1.86361i	0.393923	+	0.0617104i
$913$	55.5321			1.83784
$914$	4.59877	+	2.11771i	0.152114	+	0.0700477i
$915$	−34.3520	−	34.3520i	−1.13564	−	1.13564i
$916$	−18.6296	−	1.45037i	−0.615538	−	0.0479216i
$917$	20.0896	−	20.0896i	0.663417	−	0.663417i
$918$	−2.74330	−	7.42639i	−0.0905423	−	0.245107i
$919$		−	16.7510i		−	0.552564i	−0.961077	−	0.276282i	$-0.910898\pi$
$919$		−	16.7510i		−	0.552564i	0.961077	−	0.276282i	$-0.0891023\pi$
$920$	−4.36336	−	2.43635i	−0.143856	−	0.0803242i
$921$			2.87097i			0.0946018i
$922$	−13.2866	+	4.90804i	−0.437570	+	0.161638i
$923$	−8.68056	+	8.68056i	−0.285724	+	0.285724i
$924$	−15.7965	+	13.5145i	−0.519666	+	0.444595i
$925$	92.9675	+	92.9675i	3.05675	+	3.05675i
$926$	−14.4493	+	31.3778i	−0.474835	+	1.03114i
$927$	6.53120			0.214513
$928$	6.58699	+	32.7540i	0.216229	+	1.07520i
$929$	−12.0439			−0.395147			−0.197573	−	0.980288i	$-0.563306\pi$
$929$	−12.0439			−0.395147			−0.197573	+	0.980288i	$0.563306\pi$
$930$	−12.9913	+	28.2117i	−0.426002	+	0.925097i
$931$	−5.48398	−	5.48398i	−0.179730	−	0.179730i
$932$	34.2249	−	29.2808i	1.12107	−	0.959124i
$933$	−22.4984	+	22.4984i	−0.736563	+	0.736563i
$934$	−12.8894	+	4.76134i	−0.421756	+	0.155796i
$935$			17.4205i			0.569711i
$936$	−2.99477	+	5.36345i	−0.0978871	+	0.175310i
$937$		−	0.394586i		−	0.0128906i	−0.999979	−	0.00644528i	$-0.997948\pi$
$937$		−	0.394586i		−	0.0128906i	0.999979	−	0.00644528i	$-0.00205161\pi$
$938$	−5.25000	−	14.2123i	−0.171418	−	0.464047i
$939$	12.5668	−	12.5668i	0.410101	−	0.410101i
$940$	12.1825	+	0.948448i	0.397350	+	0.0309350i
$941$	−36.2931	−	36.2931i	−1.18312	−	1.18312i	−0.978931	−	0.204192i	$-0.934543\pi$
$941$	−36.2931	−	36.2931i	−1.18312	−	1.18312i	−0.204192	−	0.978931i	$-0.565457\pi$
$942$	15.8178	+	7.28400i	0.515370	+	0.237326i
$943$	−4.75998			−0.155006
$944$	−21.0210	−	28.8305i	−0.684174	−	0.938353i
$945$	44.5127			1.44800
$946$	35.8562	+	16.5116i	1.16579	+	0.536838i
$947$	−7.10426	−	7.10426i	−0.230857	−	0.230857i	0.582193	−	0.813051i	$-0.302195\pi$
$947$	−7.10426	−	7.10426i	−0.230857	−	0.230857i	−0.813051	+	0.582193i	$0.802195\pi$
$948$	3.13535	−	40.2727i	0.101832	−	1.30799i
$949$	0.159677	−	0.159677i	0.00518333	−	0.00518333i
$950$	13.9623	+	37.7973i	0.452996	+	1.22631i
$951$			38.4300i			1.24618i
$952$	−1.47622	−	5.20904i	−0.0478444	−	0.168826i
$953$			23.0412i			0.746377i	0.927756	+	0.373188i	$0.121736\pi$
$953$			23.0412i			0.746377i	−0.927756	+	0.373188i	$0.878264\pi$
$954$	2.61983	−	0.967763i	0.0848203	−	0.0313325i
$955$	9.44527	−	9.44527i	0.305642	−	0.305642i
$956$	−9.42571	−	11.0173i	−0.304849	−	0.356324i
$957$	−22.6774	−	22.6774i	−0.733057	−	0.733057i
$958$	12.7690	−	27.7289i	0.412548	−	0.895879i
$959$	13.6028			0.439256
$960$	36.6309	−	22.5751i	1.18226	−	0.728609i
$961$	−14.3269			−0.462159
$962$	−10.4143	+	22.6154i	−0.335771	+	0.729151i
$963$	−18.4329	−	18.4329i	−0.593991	−	0.593991i
$964$	−22.8230	−	26.6768i	−0.735081	−	0.859201i
$965$	46.6445	−	46.6445i	1.50154	−	1.50154i
$966$	−1.39856	+	0.516626i	−0.0449979	+	0.0166222i
$967$		−	27.7107i		−	0.891115i	−0.895253	−	0.445557i	$-0.853006\pi$
$967$		−	27.7107i		−	0.891115i	0.895253	−	0.445557i	$-0.146994\pi$
$968$	5.08024	+	17.9263i	0.163285	+	0.576174i
$969$		−	3.01033i		−	0.0967057i
$970$	−3.43972	−	9.31167i	−0.110443	−	0.298980i
$971$	15.1296	−	15.1296i	0.485532	−	0.485532i	−0.421361	−	0.906893i	$-0.638447\pi$
$971$	15.1296	−	15.1296i	0.485532	−	0.485532i	0.906893	+	0.421361i	$0.138447\pi$
$972$	−1.94816	+	25.0235i	−0.0624873	+	0.802630i
$973$	21.4520	+	21.4520i	0.687719	+	0.687719i
$974$	12.1801	+	5.60888i	0.390276	+	0.179720i
$975$	26.0403			0.833958
$976$	29.1934	−	21.2856i	0.934458	−	0.681334i
$977$	32.4997			1.03976			0.519878	−	0.854240i	$-0.325977\pi$
$977$	32.4997			1.03976			0.519878	+	0.854240i	$0.325977\pi$
$978$	−23.3628	−	10.7585i	−0.747062	−	0.344018i
$979$	11.2311	+	11.2311i	0.358948	+	0.358948i
$980$	−27.6301	−	2.15109i	−0.882610	−	0.0687140i
$981$	−9.11966	+	9.11966i	−0.291168	+	0.291168i
$982$	6.63533	+	17.9625i	0.211742	+	0.573207i
$983$		−	12.9181i		−	0.412024i	−0.978549	−	0.206012i	$-0.933951\pi$
$983$		−	12.9181i		−	0.412024i	0.978549	−	0.206012i	$-0.0660486\pi$
$984$	19.9803	−	35.7835i	0.636948	−	1.14074i
$985$			2.45350i			0.0781749i
$986$	7.83496	−	2.89422i	0.249516	−	0.0921709i
$987$	2.57775	−	2.57775i	0.0820508	−	0.0820508i
$988$	−5.79815	+	4.96055i	−0.184464	+	0.157816i
$989$	2.00189	+	2.00189i	0.0636564	+	0.0636564i
$990$	13.6379	−	29.6156i	0.433440	−	0.941247i
$991$	−50.4366			−1.60217			−0.801086	−	0.598549i	$-0.795744\pi$
$991$	−50.4366			−1.60217			−0.801086	+	0.598549i	$0.795744\pi$
$992$	−19.2327	−	12.7923i	−0.610638	−	0.406155i
$993$	−43.0503			−1.36616
$994$	−8.47046	+	18.3942i	−0.268667	+	0.583430i
$995$	−61.1468	−	61.1468i	−1.93848	−	1.93848i
$996$	−26.0563	+	22.2922i	−0.825625	+	0.706356i
$997$	0.400248	−	0.400248i	0.0126760	−	0.0126760i	−0.700740	−	0.713416i	$-0.747147\pi$
$997$	0.400248	−	0.400248i	0.0126760	−	0.0126760i	0.713416	+	0.700740i	$0.247147\pi$
$998$	34.3994	−	12.7071i	1.08889	−	0.402236i
$999$			60.0577i			1.90014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.2.l.c.205.11	yes	32
4.3	odd	2		1088.2.l.c.273.5		32
16.5	even	4	inner	272.2.l.c.69.11	✓	32
16.11	odd	4		1088.2.l.c.817.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.2.l.c.69.11	✓	32	16.5	even	4	inner
272.2.l.c.205.11	yes	32	1.1	even	1	trivial
1088.2.l.c.273.5		32	4.3	odd	2
1088.2.l.c.817.5		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+(0.591533 - 1.28456i) q^{2} +(0.915574 + 0.915574i) q^{3} +(-1.30018 - 1.51972i) q^{4} +(2.93727 - 2.93727i) q^{5} +(1.71770 - 0.634516i) q^{6} +1.91420i q^{7} +(-2.72126 + 0.771193i) q^{8} -1.32345i q^{9} +(-2.03560 - 5.51058i) q^{10} +(-2.96543 + 2.96543i) q^{11} +(0.201003 - 2.58182i) q^{12} +(1.16040 + 1.16040i) q^{13} +(2.45890 + 1.13231i) q^{14} +5.37857 q^{15} +(-0.619073 + 3.95180i) q^{16} +1.00000 q^{17} +(-1.70004 - 0.782862i) q^{18} +(-1.64396 - 1.64396i) q^{19} +(-8.28279 - 0.644841i) q^{20} +(-1.75259 + 1.75259i) q^{21} +(2.05512 + 5.56341i) q^{22} +0.425350i q^{23} +(-3.19760 - 1.78543i) q^{24} -12.2551i q^{25} +(2.17701 - 0.804184i) q^{26} +(3.95844 - 3.95844i) q^{27} +(2.90904 - 2.48880i) q^{28} +(4.17622 + 4.17622i) q^{29} +(3.18160 - 6.90909i) q^{30} -4.08327 q^{31} +(4.71012 + 3.13286i) q^{32} -5.43014 q^{33} +(0.591533 - 1.28456i) q^{34} +(5.62252 + 5.62252i) q^{35} +(-2.01126 + 1.72072i) q^{36} +(-7.58603 + 7.58603i) q^{37} +(-3.08421 + 1.13930i) q^{38} +2.12486i q^{39} +(-5.72787 + 10.2583i) q^{40} +11.1907i q^{41} +(1.21459 + 3.28802i) q^{42} +(4.70645 - 4.70645i) q^{43} +(8.36219 + 0.651023i) q^{44} +(-3.88732 - 3.88732i) q^{45} +(0.546387 + 0.251609i) q^{46} -1.47082 q^{47} +(-4.18498 + 3.05136i) q^{48} +3.33584 q^{49} +(-15.7424 - 7.24928i) q^{50} +(0.915574 + 0.915574i) q^{51} +(0.254751 - 3.27220i) q^{52} +(-1.05515 + 1.05515i) q^{53} +(-2.74330 - 7.42639i) q^{54} +17.4205i q^{55} +(-1.47622 - 5.20904i) q^{56} -3.01033i q^{57} +(7.83496 - 2.89422i) q^{58} +(-6.30743 + 6.30743i) q^{59} +(-6.99310 - 8.17390i) q^{60} +(-6.38682 - 6.38682i) q^{61} +(-2.41539 + 5.24519i) q^{62} +2.53334 q^{63} +(6.81052 - 4.19723i) q^{64} +6.81679 q^{65} +(-3.21210 + 6.97532i) q^{66} +(-3.95752 - 3.95752i) q^{67} +(-1.30018 - 1.51972i) q^{68} +(-0.389440 + 0.389440i) q^{69} +(10.5483 - 3.89655i) q^{70} +7.48068i q^{71} +(1.02063 + 3.60145i) q^{72} -0.137605i q^{73} +(5.25731 + 14.2321i) q^{74} +(11.2204 - 11.2204i) q^{75} +(-0.360910 + 4.63578i) q^{76} +(-5.67642 - 5.67642i) q^{77} +(2.72950 + 1.25692i) q^{78} +15.5985 q^{79} +(9.78912 + 13.4259i) q^{80} +3.27814 q^{81} +(14.3751 + 6.61968i) q^{82} +(-9.36325 - 9.36325i) q^{83} +(4.94212 + 0.384760i) q^{84} +(2.93727 - 2.93727i) q^{85} +(-3.26169 - 8.82972i) q^{86} +7.64727i q^{87} +(5.78278 - 10.3566i) q^{88} -3.78735i q^{89} +(-7.29296 + 2.69401i) q^{90} +(-2.22123 + 2.22123i) q^{91} +(0.646412 - 0.553031i) q^{92} +(-3.73853 - 3.73853i) q^{93} +(-0.870040 + 1.88936i) q^{94} -9.65748 q^{95} +(1.44410 + 7.18083i) q^{96} +1.68978 q^{97} +(1.97326 - 4.28508i) q^{98} +(3.92459 + 3.92459i) 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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