LMFDB - Embedded newform 731.2.m.b.87.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.11
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.993125 - 0.993125i) q^{2} +(-1.41917 + 0.587838i) q^{3} -0.0274062i q^{4} +(0.967808 + 2.33649i) q^{5} +(1.99321 + 0.825613i) q^{6} +(0.386865 - 0.933975i) q^{7} +(-2.01347 + 2.01347i) q^{8} +(-0.452840 + 0.452840i) q^{9} +O(q^{10})$	\(q+(-0.993125 - 0.993125i) q^{2} +(-1.41917 + 0.587838i) q^{3} -0.0274062i q^{4} +(0.967808 + 2.33649i) q^{5} +(1.99321 + 0.825613i) q^{6} +(0.386865 - 0.933975i) q^{7} +(-2.01347 + 2.01347i) q^{8} +(-0.452840 + 0.452840i) q^{9} +(1.35928 - 3.28158i) q^{10} +(-4.15951 - 1.72293i) q^{11} +(0.0161104 + 0.0388940i) q^{12} -5.14463i q^{13} +(-1.31176 + 0.543349i) q^{14} +(-2.74696 - 2.74696i) q^{15} +3.94444 q^{16} +(1.86404 + 3.67768i) q^{17} +0.899452 q^{18} +(-1.72787 - 1.72787i) q^{19} +(0.0640345 - 0.0265240i) q^{20} +1.55288i q^{21} +(2.41983 + 5.84199i) q^{22} +(6.07795 + 2.51757i) q^{23} +(1.67385 - 4.04104i) q^{24} +(-0.987019 + 0.987019i) q^{25} +(-5.10926 + 5.10926i) q^{26} +(2.13997 - 5.16635i) q^{27} +(-0.0255967 - 0.0106025i) q^{28} +(1.66211 + 4.01269i) q^{29} +5.45615i q^{30} +(6.70561 - 2.77755i) q^{31} +(0.109617 + 0.109617i) q^{32} +6.91584 q^{33} +(1.80117 - 5.50362i) q^{34} +2.55664 q^{35} +(0.0124106 + 0.0124106i) q^{36} +(-0.459357 + 0.190272i) q^{37} +3.43198i q^{38} +(3.02421 + 7.30109i) q^{39} +(-6.65310 - 2.75581i) q^{40} +(1.15749 - 2.79443i) q^{41} +(1.54220 - 1.54220i) q^{42} +(0.707107 - 0.707107i) q^{43} +(-0.0472189 + 0.113997i) q^{44} +(-1.49632 - 0.619795i) q^{45} +(-3.53590 - 8.53642i) q^{46} -9.72841i q^{47} +(-5.59781 + 2.31869i) q^{48} +(4.22710 + 4.22710i) q^{49} +1.96047 q^{50} +(-4.80727 - 4.12349i) q^{51} -0.140995 q^{52} +(-2.58813 - 2.58813i) q^{53} +(-7.25609 + 3.00557i) q^{54} -11.3861i q^{55} +(1.10159 + 2.65947i) q^{56} +(3.46784 + 1.43643i) q^{57} +(2.33442 - 5.63579i) q^{58} +(7.93852 - 7.93852i) q^{59} +(-0.0752838 + 0.0752838i) q^{60} +(2.44413 - 5.90066i) q^{61} +(-9.41797 - 3.90105i) q^{62} +(0.247753 + 0.598129i) q^{63} -8.10660i q^{64} +(12.0204 - 4.97901i) q^{65} +(-6.86829 - 6.86829i) q^{66} -2.45429 q^{67} +(0.100791 - 0.0510864i) q^{68} -10.1055 q^{69} +(-2.53906 - 2.53906i) q^{70} +(-0.194881 + 0.0807225i) q^{71} -1.82356i q^{72} +(1.10700 + 2.67253i) q^{73} +(0.645163 + 0.267235i) q^{74} +(0.820537 - 1.98095i) q^{75} +(-0.0473544 + 0.0473544i) q^{76} +(-3.21834 + 3.21834i) q^{77} +(4.24748 - 10.2543i) q^{78} +(13.9754 + 5.78881i) q^{79} +(3.81746 + 9.21615i) q^{80} +6.66864i q^{81} +(-3.92475 + 1.62569i) q^{82} +(-1.94133 - 1.94133i) q^{83} +0.0425586 q^{84} +(-6.78884 + 7.91462i) q^{85} -1.40449 q^{86} +(-4.71763 - 4.71763i) q^{87} +(11.8441 - 4.90599i) q^{88} +2.37453i q^{89} +(0.870497 + 2.10157i) q^{90} +(-4.80496 - 1.99028i) q^{91} +(0.0689971 - 0.166574i) q^{92} +(-7.88363 + 7.88363i) q^{93} +(-9.66153 + 9.66153i) q^{94} +(2.36491 - 5.70940i) q^{95} +(-0.220002 - 0.0911279i) q^{96} +(-4.78749 - 11.5580i) q^{97} -8.39608i q^{98} +(2.66380 - 1.10338i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.993125	−	0.993125i	−0.702245	−	0.702245i	0.262647	−	0.964892i	$-0.415405\pi$
$2$	−0.993125	−	0.993125i	−0.702245	−	0.702245i	−0.964892	+	0.262647i	$0.915405\pi$
$3$	−1.41917	+	0.587838i	−0.819356	+	0.339389i	−0.752680	−	0.658386i	$-0.771239\pi$
$3$	−1.41917	+	0.587838i	−0.819356	+	0.339389i	−0.0666760	+	0.997775i	$0.521239\pi$
$4$		−	0.0274062i		−	0.0137031i
$5$	0.967808	+	2.33649i	0.432817	+	1.04491i	0.978375	+	0.206839i	$0.0663176\pi$
$5$	0.967808	+	2.33649i	0.432817	+	1.04491i	−0.545558	+	0.838073i	$0.683682\pi$
$6$	1.99321	+	0.825613i	0.813723	+	0.337055i
$7$	0.386865	−	0.933975i	0.146221	−	0.353009i	−0.833752	−	0.552139i	$-0.813812\pi$
$7$	0.386865	−	0.933975i	0.146221	−	0.353009i	0.979973	+	0.199130i	$0.0638116\pi$
$8$	−2.01347	+	2.01347i	−0.711868	+	0.711868i
$9$	−0.452840	+	0.452840i	−0.150947	+	0.150947i
$10$	1.35928	−	3.28158i	0.429841	−	1.03773i
$11$	−4.15951	−	1.72293i	−1.25414	−	0.519482i	−0.346034	−	0.938222i	$-0.612472\pi$
$11$	−4.15951	−	1.72293i	−1.25414	−	0.519482i	−0.908106	+	0.418740i	$0.862472\pi$
$12$	0.0161104	+	0.0388940i	0.00465068	+	0.0112277i
$13$		−	5.14463i		−	1.42686i	−0.700724	−	0.713432i	$-0.747140\pi$
$13$		−	5.14463i		−	1.42686i	0.700724	−	0.713432i	$-0.252860\pi$
$14$	−1.31176	+	0.543349i	−0.350582	+	0.145216i
$15$	−2.74696	−	2.74696i	−0.709262	−	0.709262i
$16$	3.94444			0.986109
$17$	1.86404	+	3.67768i	0.452097	+	0.891969i
$17$	1.86404	+	3.67768i	0.452097	+	0.891969i
$18$	0.899452			0.212003
$19$	−1.72787	−	1.72787i	−0.396400	−	0.396400i	0.480561	−	0.876961i	$-0.340433\pi$
$19$	−1.72787	−	1.72787i	−0.396400	−	0.396400i	−0.876961	+	0.480561i	$0.840433\pi$
$20$	0.0640345	−	0.0265240i	0.0143185	−	0.00593094i
$21$			1.55288i			0.338866i
$22$	2.41983	+	5.84199i	0.515910	+	1.24552i
$23$	6.07795	+	2.51757i	1.26734	+	0.524949i	0.912155	−	0.409846i	$-0.134418\pi$
$23$	6.07795	+	2.51757i	1.26734	+	0.524949i	0.355186	+	0.934796i	$0.384418\pi$
$24$	1.67385	−	4.04104i	0.341674	−	0.824874i
$25$	−0.987019	+	0.987019i	−0.197404	+	0.197404i
$26$	−5.10926	+	5.10926i	−1.00201	+	1.00201i
$27$	2.13997	−	5.16635i	0.411838	−	0.994265i
$28$	−0.0255967	−	0.0106025i	−0.00483733	−	0.00200369i
$29$	1.66211	+	4.01269i	0.308647	+	0.745139i	0.999749	+	0.0223823i	$0.00712510\pi$
$29$	1.66211	+	4.01269i	0.308647	+	0.745139i	−0.691103	+	0.722756i	$0.742875\pi$
$30$			5.45615i			0.996152i
$31$	6.70561	−	2.77755i	1.20436	−	0.498864i	0.311957	−	0.950096i	$-0.399016\pi$
$31$	6.70561	−	2.77755i	1.20436	−	0.498864i	0.892406	+	0.451233i	$0.149016\pi$
$32$	0.109617	+	0.109617i	0.0193778	+	0.0193778i
$33$	6.91584			1.20389
$34$	1.80117	−	5.50362i	0.308898	−	0.943864i
$35$	2.55664			0.432151
$36$	0.0124106	+	0.0124106i	0.00206844	+	0.00206844i
$37$	−0.459357	+	0.190272i	−0.0755178	+	0.0312805i	−0.420123	−	0.907467i	$-0.638013\pi$
$37$	−0.459357	+	0.190272i	−0.0755178	+	0.0312805i	0.344605	+	0.938748i	$0.388013\pi$
$38$			3.43198i			0.556741i
$39$	3.02421	+	7.30109i	0.484261	+	1.16911i
$40$	−6.65310	−	2.75581i	−1.05195	−	0.435731i
$41$	1.15749	−	2.79443i	0.180770	−	0.436417i	−0.807356	−	0.590065i	$-0.799102\pi$
$41$	1.15749	−	2.79443i	0.180770	−	0.436417i	0.988126	+	0.153648i	$0.0491022\pi$
$42$	1.54220	−	1.54220i	0.237967	−	0.237967i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	−0.0472189	+	0.113997i	−0.00711852	+	0.0171856i
$45$	−1.49632	−	0.619795i	−0.223058	−	0.0923937i
$46$	−3.53590	−	8.53642i	−0.521340	−	1.25863i
$47$		−	9.72841i		−	1.41903i	−0.704688	−	0.709517i	$-0.748913\pi$
$47$		−	9.72841i		−	1.41903i	0.704688	−	0.709517i	$-0.251087\pi$
$48$	−5.59781	+	2.31869i	−0.807975	+	0.334674i
$49$	4.22710	+	4.22710i	0.603872	+	0.603872i
$50$	1.96047			0.277252
$51$	−4.80727	−	4.12349i	−0.673153	−	0.577404i
$52$	−0.140995			−0.0195525
$53$	−2.58813	−	2.58813i	−0.355508	−	0.355508i	0.506646	−	0.862154i	$-0.330885\pi$
$53$	−2.58813	−	2.58813i	−0.355508	−	0.355508i	−0.862154	+	0.506646i	$0.830885\pi$
$54$	−7.25609	+	3.00557i	−0.987429	+	0.409007i
$55$		−	11.3861i		−	1.53531i
$56$	1.10159	+	2.65947i	0.147206	+	0.355387i
$57$	3.46784	+	1.43643i	0.459327	+	0.190259i
$58$	2.33442	−	5.63579i	0.306525	−	0.740016i
$59$	7.93852	−	7.93852i	1.03351	−	1.03351i	0.0340879	−	0.999419i	$-0.489147\pi$
$59$	7.93852	−	7.93852i	1.03351	−	1.03351i	0.999419	−	0.0340879i	$-0.0108526\pi$
$60$	−0.0752838	+	0.0752838i	−0.00971910	+	0.00971910i
$61$	2.44413	−	5.90066i	0.312939	−	0.755502i	−0.686654	−	0.726984i	$-0.740921\pi$
$61$	2.44413	−	5.90066i	0.312939	−	0.755502i	0.999593	−	0.0285177i	$-0.00907871\pi$
$62$	−9.41797	−	3.90105i	−1.19608	−	0.495434i
$63$	0.247753	+	0.598129i	0.0312140	+	0.0753572i
$64$		−	8.10660i		−	1.01332i
$65$	12.0204	−	4.97901i	1.49095	−	0.617571i
$66$	−6.86829	−	6.86829i	−0.845429	−	0.845429i
$67$	−2.45429			−0.299839			−0.149919	−	0.988698i	$-0.547901\pi$
$67$	−2.45429			−0.299839			−0.149919	+	0.988698i	$0.547901\pi$
$68$	0.100791	−	0.0510864i	0.0122227	−	0.00619514i
$69$	−10.1055			−1.21656
$70$	−2.53906	−	2.53906i	−0.303476	−	0.303476i
$71$	−0.194881	+	0.0807225i	−0.0231282	+	0.00958000i	−0.394218	−	0.919017i	$-0.628984\pi$
$71$	−0.194881	+	0.0807225i	−0.0231282	+	0.00958000i	0.371089	+	0.928597i	$0.378984\pi$
$72$		−	1.82356i		−	0.214908i
$73$	1.10700	+	2.67253i	0.129564	+	0.312795i	0.975328	−	0.220763i	$-0.0708546\pi$
$73$	1.10700	+	2.67253i	0.129564	+	0.312795i	−0.845763	+	0.533558i	$0.820855\pi$
$74$	0.645163	+	0.267235i	0.0749986	+	0.0310655i
$75$	0.820537	−	1.98095i	0.0947475	−	0.228741i
$76$	−0.0473544	+	0.0473544i	−0.00543192	+	0.00543192i
$77$	−3.21834	+	3.21834i	−0.366764	+	0.366764i
$78$	4.24748	−	10.2543i	0.480932	−	1.16107i
$79$	13.9754	+	5.78881i	1.57236	+	0.651292i	0.987180	−	0.159613i	$-0.0510246\pi$
$79$	13.9754	+	5.78881i	1.57236	+	0.651292i	0.585178	+	0.810905i	$0.301025\pi$
$80$	3.81746	+	9.21615i	0.426804	+	1.03040i
$81$			6.66864i			0.740960i
$82$	−3.92475	+	1.62569i	−0.433416	+	0.179527i
$83$	−1.94133	−	1.94133i	−0.213089	−	0.213089i	0.592489	−	0.805578i	$-0.298145\pi$
$83$	−1.94133	−	1.94133i	−0.213089	−	0.213089i	−0.805578	+	0.592489i	$0.798145\pi$
$84$	0.0425586			0.00464352
$85$	−6.78884	+	7.91462i	−0.736354	+	0.858461i
$86$	−1.40449			−0.151450
$87$	−4.71763	−	4.71763i	−0.505783	−	0.505783i
$88$	11.8441	−	4.90599i	1.26258	−	0.522980i
$89$			2.37453i			0.251700i	0.992049	+	0.125850i	$0.0401658\pi$
$89$			2.37453i			0.251700i	−0.992049	+	0.125850i	$0.959834\pi$
$90$	0.870497	+	2.10157i	0.0917584	+	0.221524i
$91$	−4.80496	−	1.99028i	−0.503697	−	0.208638i
$92$	0.0689971	−	0.166574i	0.00719344	−	0.0173665i
$93$	−7.88363	+	7.88363i	−0.817494	+	0.817494i
$94$	−9.66153	+	9.66153i	−0.996511	+	0.996511i
$95$	2.36491	−	5.70940i	0.242635	−	0.585772i
$96$	−0.220002	−	0.0911279i	−0.0224539	−	0.00930070i
$97$	−4.78749	−	11.5580i	−0.486096	−	1.17354i	−0.956669	−	0.291178i	$-0.905953\pi$
$97$	−4.78749	−	11.5580i	−0.486096	−	1.17354i	0.470573	−	0.882361i	$-0.344047\pi$
$98$		−	8.39608i		−	0.848132i
$99$	2.66380	−	1.10338i	0.267722	−	0.110894i
$100$	0.0270505	+	0.0270505i	0.00270505	+	0.00270505i
$101$	11.5789			1.15215			0.576073	−	0.817399i	$-0.304585\pi$
$101$	11.5789			1.15215			0.576073	+	0.817399i	$0.304585\pi$
$102$	0.679083	+	8.86936i	0.0672392	+	0.878197i
$103$	−4.56510			−0.449813			−0.224907	−	0.974380i	$-0.572208\pi$
$103$	−4.56510			−0.449813			−0.224907	+	0.974380i	$0.572208\pi$
$104$	10.3585	+	10.3585i	1.01574	+	1.01574i
$105$	−3.62830	+	1.50289i	−0.354086	+	0.146667i
$106$			5.14068i			0.499307i
$107$	−3.90470	−	9.42677i	−0.377481	−	0.911320i	−0.992437	−	0.122758i	$-0.960826\pi$
$107$	−3.90470	−	9.42677i	−0.377481	−	0.911320i	0.614955	−	0.788562i	$-0.289174\pi$
$108$	−0.141590	−	0.0586486i	−0.0136245	−	0.00564346i
$109$	−3.90554	+	9.42882i	−0.374083	+	0.903117i	0.618966	+	0.785418i	$0.287552\pi$
$109$	−3.90554	+	9.42882i	−0.374083	+	0.903117i	−0.993049	+	0.117699i	$0.962448\pi$
$110$	−11.3079	+	11.3079i	−1.07816	+	1.07816i
$111$	0.540055	−	0.540055i	0.0512598	−	0.0512598i
$112$	1.52597	−	3.68401i	0.144190	−	0.348106i
$113$	−1.94804	−	0.806907i	−0.183257	−	0.0759074i	0.289168	−	0.957278i	$-0.406621\pi$
$113$	−1.94804	−	0.806907i	−0.183257	−	0.0759074i	−0.472425	+	0.881371i	$0.656621\pi$
$114$	−2.01745	−	4.87055i	−0.188951	−	0.456169i
$115$			16.6376i			1.55147i
$116$	0.109973	−	0.0455522i	0.0102107	−	0.00422942i
$117$	2.32969	+	2.32969i	0.215380	+	0.215380i
$118$	−15.7679			−1.45155
$119$	4.15600	−	0.318204i	0.380980	−	0.0291697i
$120$	11.0618			1.00980
$121$	6.55489	+	6.55489i	0.595899	+	0.595899i
$122$	−8.28742	+	3.43276i	−0.750308	+	0.310788i
$123$			4.64618i			0.418932i
$124$	−0.0761223	−	0.183775i	−0.00683598	−	0.0165035i
$125$	8.42106	+	3.48812i	0.753203	+	0.311987i
$126$	0.347967	−	0.840066i	0.0309994	−	0.0748391i
$127$	7.75018	−	7.75018i	0.687717	−	0.687717i	−0.274010	−	0.961727i	$-0.588350\pi$
$127$	7.75018	−	7.75018i	0.687717	−	0.687717i	0.961727	+	0.274010i	$0.0883501\pi$
$128$	−7.83163	+	7.83163i	−0.692225	+	0.692225i
$129$	−0.587838	+	1.41917i	−0.0517563	+	0.124951i
$130$	−16.8825	−	6.99298i	−1.48070	−	0.613325i
$131$	0.362457	+	0.875049i	0.0316680	+	0.0764533i	0.938922	−	0.344129i	$-0.111826\pi$
$131$	0.362457	+	0.875049i	0.0316680	+	0.0764533i	−0.907254	+	0.420582i	$0.861826\pi$
$132$		−	0.189537i		−	0.0164971i
$133$	−2.28224	+	0.945335i	−0.197895	+	0.0819709i
$134$	2.43741	+	2.43741i	0.210561	+	0.210561i
$135$	14.1422			1.21717
$136$	−11.1581	−	3.65170i	−0.956798	−	0.313131i
$137$	−17.1162			−1.46233			−0.731166	−	0.682200i	$-0.761023\pi$
$137$	−17.1162			−1.46233			−0.731166	+	0.682200i	$0.761023\pi$
$138$	10.0361	+	10.0361i	0.854327	+	0.854327i
$139$	−10.8165	+	4.48033i	−0.917442	+	0.380017i	−0.790901	−	0.611944i	$-0.790388\pi$
$139$	−10.8165	+	4.48033i	−0.917442	+	0.380017i	−0.126541	+	0.991961i	$0.540388\pi$
$140$		−	0.0700678i		−	0.00592181i
$141$	5.71873	+	13.8062i	0.481604	+	1.16270i
$142$	0.273709	+	0.113374i	0.0229692	+	0.00951413i
$143$	−8.86382	+	21.3992i	−0.741230	+	1.78949i
$144$	−1.78620	+	1.78620i	−0.148850	+	0.148850i
$145$	−7.76703	+	7.76703i	−0.645017	+	0.645017i
$146$	1.55477	−	3.75354i	0.128673	−	0.310645i
$147$	−8.48382	−	3.51411i	−0.699733	−	0.289839i
$148$	0.00521464	+	0.0125892i	0.000428640	+	0.00103483i
$149$			2.73883i			0.224374i	0.993687	+	0.112187i	$0.0357855\pi$
$149$			2.73883i			0.224374i	−0.993687	+	0.112187i	$0.964214\pi$
$150$	−2.78223	+	1.15244i	−0.227168	+	0.0940961i
$151$	1.71732	+	1.71732i	0.139754	+	0.139754i	0.773523	−	0.633769i	$-0.218493\pi$
$151$	1.71732	+	1.71732i	0.139754	+	0.139754i	−0.633769	+	0.773523i	$0.718493\pi$
$152$	6.95802			0.564370
$153$	−2.50951	−	0.821287i	−0.202882	−	0.0663971i
$154$	6.39243			0.515117
$155$	12.9795	+	12.9795i	1.04254	+	1.04254i
$156$	0.200095	−	0.0828822i	0.0160204	−	0.00663589i
$157$			10.9661i			0.875188i	0.899173	+	0.437594i	$0.144169\pi$
$157$			10.9661i			0.875188i	−0.899173	+	0.437594i	$0.855831\pi$
$158$	−8.13033	−	19.6283i	−0.646814	−	1.56155i
$159$	5.19440	+	2.15159i	0.411942	+	0.170632i
$160$	−0.150032	+	0.362208i	−0.0118610	+	0.0286351i
$161$	4.70269	−	4.70269i	0.370624	−	0.370624i
$162$	6.62279	−	6.62279i	0.520335	−	0.520335i
$163$	5.35365	−	12.9249i	0.419330	−	1.01235i	−0.563212	−	0.826313i	$-0.690434\pi$
$163$	5.35365	−	12.9249i	0.419330	−	1.01235i	0.982542	−	0.186040i	$-0.0595655\pi$
$164$	−0.0765848	−	0.0317225i	−0.00598027	−	0.00247711i
$165$	6.69320	+	16.1588i	0.521065	+	1.25796i
$166$			3.85597i			0.299281i
$167$	4.20660	−	1.74243i	0.325517	−	0.134833i	−0.213940	−	0.976847i	$-0.568630\pi$
$167$	4.20660	−	1.74243i	0.325517	−	0.134833i	0.539457	+	0.842013i	$0.318630\pi$
$168$	−3.12668	−	3.12668i	−0.241228	−	0.241228i
$169$	−13.4672			−1.03594
$170$	14.6024	−	1.11803i	1.11995	−	0.0857491i
$171$	1.56490			0.119671
$172$	−0.0193791	−	0.0193791i	−0.00147764	−	0.00147764i
$173$	21.0076	−	8.70165i	1.59718	−	0.661574i	0.606168	−	0.795337i	$-0.292706\pi$
$173$	21.0076	−	8.70165i	1.59718	−	0.661574i	0.991013	+	0.133762i	$0.0427058\pi$
$174$			9.37039i			0.710367i
$175$	0.540008	+	1.30370i	0.0408208	+	0.0985501i
$176$	−16.4069	−	6.79597i	−1.23672	−	0.512266i
$177$	−6.59952	+	15.9326i	−0.496050	+	1.19757i
$178$	2.35821	−	2.35821i	0.176755	−	0.176755i
$179$	−3.42749	+	3.42749i	−0.256183	+	0.256183i	−0.823500	−	0.567317i	$-0.807981\pi$
$179$	−3.42749	+	3.42749i	−0.256183	+	0.256183i	0.567317	+	0.823500i	$0.307981\pi$
$180$	−0.0169863	+	0.0410084i	−0.00126608	+	0.00305659i
$181$	10.4123	+	4.31291i	0.773940	+	0.320576i	0.734467	−	0.678644i	$-0.237432\pi$
$181$	10.4123	+	4.31291i	0.773940	+	0.320576i	0.0394726	+	0.999221i	$0.487432\pi$
$182$	2.79533	+	6.74852i	0.207204	+	0.500234i
$183$			9.81077i			0.725233i
$184$	−17.3068	+	7.16871i	−1.27587	+	0.528484i
$185$	−0.889139	−	0.889139i	−0.0653708	−	0.0653708i
$186$	15.6589			1.14816
$187$	−1.41714	−	18.5090i	−0.103632	−	1.35351i
$188$	−0.266619			−0.0194452
$189$	−3.99736	−	3.99736i	−0.290765	−	0.290765i
$190$	−8.01880	+	3.32150i	−0.581745	+	0.240967i
$191$		−	2.58807i		−	0.187266i	−0.995607	−	0.0936331i	$-0.970152\pi$
$191$		−	2.58807i		−	0.187266i	0.995607	−	0.0936331i	$-0.0298481\pi$
$192$	4.76537	+	11.5046i	0.343911	+	0.830274i
$193$	−15.5518	−	6.44178i	−1.11945	−	0.463690i	−0.255265	−	0.966871i	$-0.582163\pi$
$193$	−15.5518	−	6.44178i	−1.11945	−	0.463690i	−0.864181	+	0.503182i	$0.832163\pi$
$194$	−6.72398	+	16.2331i	−0.482754	+	1.16547i
$195$	−14.1321	+	14.1321i	−1.01202	+	1.01202i
$196$	0.115849	−	0.115849i	0.00827492	−	0.00827492i
$197$	9.04008	−	21.8247i	0.644079	−	1.55494i	−0.177050	−	0.984202i	$-0.556655\pi$
$197$	9.04008	−	21.8247i	0.644079	−	1.55494i	0.821129	−	0.570743i	$-0.193345\pi$
$198$	−3.74128	−	1.54969i	−0.265881	−	0.110132i
$199$	10.1988	+	24.6220i	0.722973	+	1.74541i	0.664701	+	0.747110i	$0.268559\pi$
$199$	10.1988	+	24.6220i	0.722973	+	1.74541i	0.0582717	+	0.998301i	$0.481441\pi$
$200$		−	3.97466i		−	0.281051i
$201$	3.48304	−	1.44272i	0.245675	−	0.101762i
$202$	−11.4993	−	11.4993i	−0.809089	−	0.809089i
$203$	4.39077			0.308172
$204$	−0.113009	+	0.131749i	−0.00791223	+	0.00922429i
$205$	7.64940			0.534257
$206$	4.53372	+	4.53372i	0.315879	+	0.315879i
$207$	−3.89239	+	1.61228i	−0.270540	+	0.112061i
$208$		−	20.2927i		−	1.40704i
$209$	4.21010	+	10.1641i	0.291219	+	0.703064i
$210$	5.09591	+	2.11079i	0.351651	+	0.145659i
$211$	4.81950	−	11.6353i	0.331788	−	0.801007i	−0.666662	−	0.745360i	$-0.732278\pi$
$211$	4.81950	−	11.6353i	0.331788	−	0.801007i	0.998450	−	0.0556476i	$-0.0177223\pi$
$212$	−0.0709310	+	0.0709310i	−0.00487156	+	0.00487156i
$213$	0.229117	−	0.229117i	0.0156989	−	0.0156989i
$214$	−5.48411	+	13.2398i	−0.374886	+	0.905055i
$215$	2.33649	+	0.967808i	0.159348	+	0.0660039i
$216$	6.09352	+	14.7110i	0.414611	+	1.00096i
$217$		−	7.33741i		−	0.498096i
$218$	13.2427	−	5.48530i	0.896908	−	0.371511i
$219$	−3.14203	−	3.14203i	−0.212318	−	0.212318i
$220$	−0.312051			−0.0210385
$221$	18.9203	−	9.58982i	1.27272	−	0.645081i
$222$	−1.07268			−0.0719939
$223$	−2.50094	−	2.50094i	−0.167476	−	0.167476i	0.618393	−	0.785869i	$-0.287784\pi$
$223$	−2.50094	−	2.50094i	−0.167476	−	0.167476i	−0.785869	+	0.618393i	$0.787784\pi$
$224$	0.144787	−	0.0599726i	0.00967397	−	0.00400709i
$225$		−	0.893923i		−	0.0595949i
$226$	1.13329	+	2.73601i	0.0753855	+	0.181997i
$227$	−16.3304	−	6.76427i	−1.08389	−	0.448961i	−0.232016	−	0.972712i	$-0.574532\pi$
$227$	−16.3304	−	6.76427i	−1.08389	−	0.448961i	−0.851871	+	0.523751i	$0.824532\pi$
$228$	0.0393671	−	0.0950405i	0.00260715	−	0.00629421i
$229$	−6.65525	+	6.65525i	−0.439791	+	0.439791i	−0.891942	−	0.452151i	$-0.850657\pi$
$229$	−6.65525	+	6.65525i	−0.439791	+	0.439791i	0.452151	+	0.891942i	$0.350657\pi$
$230$	16.5232	−	16.5232i	1.08951	−	1.08951i
$231$	2.67550	−	6.45923i	0.176035	−	0.424986i
$232$	−11.4260	−	4.73282i	−0.750156	−	0.310725i
$233$	4.12757	+	9.96484i	0.270406	+	0.652819i	0.999501	−	0.0315945i	$-0.0100585\pi$
$233$	4.12757	+	9.96484i	0.270406	+	0.652819i	−0.729094	+	0.684413i	$0.760059\pi$
$234$		−	4.62735i		−	0.302499i
$235$	22.7304	−	9.41523i	1.48277	−	0.614182i
$236$	−0.217565	−	0.217565i	−0.0141623	−	0.0141623i
$237$	−23.2363			−1.50936
$238$	−4.44344	−	3.81141i	−0.288025	−	0.247057i
$239$	−0.384109			−0.0248460			−0.0124230	−	0.999923i	$-0.503954\pi$
$239$	−0.384109			−0.0248460			−0.0124230	+	0.999923i	$0.503954\pi$
$240$	−10.8352	−	10.8352i	−0.699410	−	0.699410i
$241$	26.5107	−	10.9811i	1.70770	−	0.707354i	0.707704	−	0.706509i	$-0.249731\pi$
$241$	26.5107	−	10.9811i	1.70770	−	0.707354i	1.00000		0.000844498i	$-0.000268812\pi$
$242$		−	13.0196i		−	0.836934i
$243$	2.49984	+	6.03515i	0.160365	+	0.387155i
$244$	−0.161715	−	0.0669845i	−0.0103527	−	0.00428824i
$245$	−5.78558	+	13.9676i	−0.369627	+	0.892359i
$246$	4.61424	−	4.61424i	0.294193	−	0.294193i
$247$	−8.88925	+	8.88925i	−0.565609	+	0.565609i
$248$	−7.90901	+	19.0940i	−0.502223	+	1.21247i
$249$	3.89626	+	1.61388i	0.246916	+	0.102276i
$250$	−4.89903	−	11.8273i	−0.309842	−	0.748024i
$251$			19.2225i			1.21332i	0.794963	+	0.606658i	$0.207490\pi$
$251$			19.2225i			1.21332i	−0.794963	+	0.606658i	$0.792510\pi$
$252$	0.0163925	−	0.00678998i	0.00103263	−	0.000427728i
$253$	−20.9437	−	20.9437i	−1.31672	−	1.31672i
$254$	−15.3938			−0.965892
$255$	4.98199	−	15.2229i	0.311984	−	0.953295i
$256$	−0.657625			−0.0411016
$257$	10.1325	+	10.1325i	0.632046	+	0.632046i	0.948581	−	0.316535i	$-0.102519\pi$
$257$	10.1325	+	10.1325i	0.632046	+	0.632046i	−0.316535	+	0.948581i	$0.602519\pi$
$258$	1.99321	−	0.825613i	0.124092	−	0.0514004i
$259$			0.502638i			0.0312324i
$260$	−0.136456	−	0.329434i	−0.00846264	−	0.0204306i
$261$	−2.56978	−	1.06444i	−0.159065	−	0.0658870i
$262$	0.509067	−	1.22900i	0.0314503	−	0.0759277i
$263$	−3.11964	+	3.11964i	−0.192365	+	0.192365i	−0.796717	−	0.604352i	$-0.793432\pi$
$263$	−3.11964	+	3.11964i	−0.192365	+	0.192365i	0.604352	+	0.796717i	$0.293432\pi$
$264$	−13.9248	+	13.9248i	−0.857014	+	0.857014i
$265$	3.54234	−	8.55197i	0.217604	−	0.525344i
$266$	3.20538	+	1.32771i	0.196535	+	0.0814074i
$267$	−1.39584	−	3.36986i	−0.0854241	−	0.206232i
$268$			0.0672628i			0.00410873i
$269$	−11.7058	+	4.84870i	−0.713715	+	0.295630i	−0.709841	−	0.704362i	$-0.751233\pi$
$269$	−11.7058	+	4.84870i	−0.713715	+	0.295630i	−0.00387384	+	0.999992i	$0.501233\pi$
$270$	−14.0450	−	14.0450i	−0.854752	−	0.854752i
$271$	−1.90825			−0.115918			−0.0579589	−	0.998319i	$-0.518459\pi$
$271$	−1.90825			−0.115918			−0.0579589	+	0.998319i	$0.518459\pi$
$272$	7.35260	+	14.5064i	0.445817	+	0.879578i
$273$	7.98900			0.483516
$274$	16.9985	+	16.9985i	1.02692	+	1.02692i
$275$	5.80608	−	2.40496i	0.350120	−	0.145024i
$276$			0.276955i			0.0166707i
$277$	−4.89468	−	11.8168i	−0.294093	−	0.710004i	−0.999999	−	0.00169749i	$-0.999460\pi$
$277$	−4.89468	−	11.8168i	−0.294093	−	0.710004i	0.705905	−	0.708306i	$-0.250540\pi$
$278$	15.1917	+	6.29259i	0.911135	+	0.377404i
$279$	−1.77878	+	4.29435i	−0.106493	+	0.257096i
$280$	−5.14771	+	5.14771i	−0.307634	+	0.307634i
$281$	−16.4758	+	16.4758i	−0.982866	+	0.982866i	−0.999856	−	0.0169896i	$-0.994592\pi$
$281$	−16.4758	+	16.4758i	−0.982866	+	0.982866i	0.0169896	+	0.999856i	$0.494592\pi$
$282$	8.03191	−	19.3907i	0.478293	−	1.15470i
$283$	−26.8769	−	11.1328i	−1.59767	−	0.661775i	−0.606583	−	0.795020i	$-0.707460\pi$
$283$	−26.8769	−	11.1328i	−1.59767	−	0.661775i	−0.991083	+	0.133245i	$0.957460\pi$
$284$	0.00221230	+	0.00534096i	0.000131276	+	0.000316928i
$285$			9.49278i			0.562304i
$286$	30.0549	−	12.4492i	1.77718	−	0.736134i
$287$	−2.16214	−	2.16214i	−0.127627	−	0.127627i
$288$	−0.0992780			−0.00585001
$289$	−10.0507	+	13.7107i	−0.591216	+	0.806513i
$290$	15.4273			0.905920
$291$	13.5885	+	13.5885i	0.796571	+	0.796571i
$292$	0.0732439	−	0.0303386i	0.00428627	−	0.00177543i
$293$			22.4044i			1.30888i	0.756115	+	0.654439i	$0.227095\pi$
$293$			22.4044i			1.30888i	−0.756115	+	0.654439i	$0.772905\pi$
$294$	4.93554	+	11.9154i	0.287846	+	0.694922i
$295$	26.2313	+	10.8653i	1.52724	+	0.632605i
$296$	0.541794	−	1.30801i	0.0314911	−	0.0760264i
$297$	−17.8025	+	17.8025i	−1.03300	+	1.03300i
$298$	2.72000	−	2.72000i	0.157566	−	0.157566i
$299$	12.9520	−	31.2688i	0.749031	−	1.80832i
$300$	−0.0542904	−	0.0224878i	−0.00313446	−	0.00129834i
$301$	−0.386865	−	0.933975i	−0.0222985	−	0.0538334i
$302$		−	3.41103i		−	0.196283i
$303$	−16.4324	+	6.80653i	−0.944018	+	0.391025i
$304$	−6.81547	−	6.81547i	−0.390894	−	0.390894i
$305$	16.1523			0.924878
$306$	1.67662	+	3.30790i	0.0958459	+	0.189100i
$307$	−10.6398			−0.607247			−0.303623	−	0.952792i	$-0.598196\pi$
$307$	−10.6398			−0.607247			−0.303623	+	0.952792i	$0.598196\pi$
$308$	0.0882026	+	0.0882026i	0.00502581	+	0.00502581i
$309$	6.47864	−	2.68354i	0.368557	−	0.152661i
$310$		−	25.7805i		−	1.46423i
$311$	3.31404	+	8.00080i	0.187922	+	0.453683i	0.989559	−	0.144127i	$-0.0460374\pi$
$311$	3.31404	+	8.00080i	0.187922	+	0.453683i	−0.801637	+	0.597811i	$0.796037\pi$
$312$	−20.7897	−	8.61136i	−1.17698	−	0.487522i
$313$	8.34572	−	20.1483i	0.471728	−	1.13885i	−0.491671	−	0.870781i	$-0.663614\pi$
$313$	8.34572	−	20.1483i	0.471728	−	1.13885i	0.963399	−	0.268071i	$-0.0863861\pi$
$314$	10.8907	−	10.8907i	0.614597	−	0.614597i
$315$	−1.15775	+	1.15775i	−0.0652317	+	0.0652317i
$316$	0.158649	−	0.383014i	0.00892473	−	0.0215462i
$317$	−8.21474	−	3.40266i	−0.461386	−	0.191112i	0.139868	−	0.990170i	$-0.455332\pi$
$317$	−8.21474	−	3.40266i	−0.461386	−	0.191112i	−0.601254	+	0.799058i	$0.705332\pi$
$318$	−3.02189	−	7.29548i	−0.169459	−	0.409110i
$319$		−	19.5545i		−	1.09484i
$320$	18.9410	−	7.84563i	1.05884	−	0.438584i
$321$	11.0828	+	11.0828i	0.618583	+	0.618583i
$322$	−9.34073			−0.520538
$323$	3.13373	−	9.57538i	0.174365	−	0.532788i
$324$	0.182762			0.0101535
$325$	5.07785	+	5.07785i	0.281668	+	0.281668i
$326$	−18.1528	+	7.51915i	−1.00539	+	0.416447i
$327$		−	15.6769i		−	0.866934i
$328$	3.29592	+	7.95707i	0.181987	+	0.439355i
$329$	−9.08610	−	3.76359i	−0.500933	−	0.207493i
$330$	9.40054	−	22.6949i	0.517483	−	1.24931i
$331$	21.1508	−	21.1508i	1.16255	−	1.16255i	0.178638	−	0.983915i	$-0.442831\pi$
$331$	21.1508	−	21.1508i	1.16255	−	1.16255i	0.983915	−	0.178638i	$-0.0571691\pi$
$332$	−0.0532046	+	0.0532046i	−0.00291998	+	0.00291998i
$333$	0.121852	−	0.294178i	0.00667747	−	0.0161208i
$334$	−5.90813	−	2.44723i	−0.323279	−	0.133906i
$335$	−2.37528	−	5.73443i	−0.129775	−	0.313305i
$336$			6.12524i			0.334159i
$337$	−1.70807	+	0.707504i	−0.0930442	+	0.0385402i	−0.428720	−	0.903437i	$-0.641035\pi$
$337$	−1.70807	+	0.707504i	−0.0930442	+	0.0385402i	0.335676	+	0.941978i	$0.391035\pi$
$338$	13.3746	+	13.3746i	0.727485	+	0.727485i
$339$	3.23893			0.175915
$340$	0.216910	+	0.186057i	0.0117636	+	0.0100903i
$341$	−32.6776			−1.76959
$342$	−1.55414	−	1.55414i	−0.0840381	−	0.0840381i
$343$	12.1212	−	5.02075i	0.654481	−	0.271095i
$344$			2.84747i			0.153525i
$345$	−9.78022	−	23.6116i	−0.526550	−	1.27120i
$346$	−29.5050	−	12.2214i	−1.58620	−	0.657026i
$347$	−0.203693	+	0.491758i	−0.0109348	+	0.0263989i	−0.929253	−	0.369445i	$-0.879548\pi$
$347$	−0.203693	+	0.491758i	−0.0109348	+	0.0263989i	0.918318	+	0.395844i	$0.129548\pi$
$348$	−0.129292	+	0.129292i	−0.00693080	+	0.00693080i
$349$	12.5849	−	12.5849i	0.673654	−	0.673654i	−0.284902	−	0.958557i	$-0.591961\pi$
$349$	12.5849	−	12.5849i	0.673654	−	0.673654i	0.958557	+	0.284902i	$0.0919611\pi$
$350$	0.758436	−	1.83103i	0.0405401	−	0.0978725i
$351$	−26.5790	−	11.0094i	−1.41868	−	0.587637i
$352$	−0.267092	−	0.644816i	−0.0142360	−	0.0343688i
$353$			33.5932i			1.78799i	0.448079	+	0.893994i	$0.352108\pi$
$353$			33.5932i			1.78799i	−0.448079	+	0.893994i	$0.647892\pi$
$354$	22.3772	−	9.26896i	1.18934	−	0.492640i
$355$	−0.377215	−	0.377215i	−0.0200205	−	0.0200205i
$356$	0.0650770			0.00344907
$357$	−5.71100	+	2.89464i	−0.302258	+	0.153201i
$358$	6.80785			0.359806
$359$	4.49165	+	4.49165i	0.237060	+	0.237060i	0.815632	−	0.578571i	$-0.196390\pi$
$359$	4.49165	+	4.49165i	0.237060	+	0.237060i	−0.578571	+	0.815632i	$0.696390\pi$
$360$	4.26073	−	1.76485i	0.224560	−	0.0930158i
$361$		−	13.0289i		−	0.685733i
$362$	−6.05745	−	14.6240i	−0.318372	−	0.768619i
$363$	−13.1557	−	5.44926i	−0.690495	−	0.286012i
$364$	−0.0545460	+	0.131686i	−0.00285899	+	0.00690221i
$365$	−5.17298	+	5.17298i	−0.270766	+	0.270766i
$366$	9.74332	−	9.74332i	0.509292	−	0.509292i
$367$	5.37831	−	12.9844i	0.280746	−	0.677780i	−0.719108	−	0.694898i	$-0.755449\pi$
$367$	5.37831	−	12.9844i	0.280746	−	0.677780i	0.999853	+	0.0171188i	$0.00544934\pi$
$368$	23.9741	+	9.93039i	1.24974	+	0.517657i
$369$	0.741271	+	1.78959i	0.0385890	+	0.0931622i
$370$			1.76605i			0.0918126i
$371$	−3.41851	+	1.41599i	−0.177480	+	0.0735147i
$372$	0.216060	+	0.216060i	0.0112022	+	0.0112022i
$373$	20.3222			1.05225			0.526123	−	0.850408i	$-0.323645\pi$
$373$	20.3222			1.05225			0.526123	+	0.850408i	$0.323645\pi$
$374$	−16.9743	+	19.7891i	−0.877721	+	1.02327i
$375$	−14.0013			−0.723026
$376$	19.5878	+	19.5878i	1.01017	+	1.01017i
$377$	20.6438	−	8.55096i	1.06321	−	0.440397i
$378$			7.93976i			0.408377i
$379$	−7.36945	−	17.7914i	−0.378543	−	0.913885i	−0.992239	−	0.124342i	$-0.960318\pi$
$379$	−7.36945	−	17.7914i	−0.378543	−	0.913885i	0.613696	−	0.789542i	$-0.289682\pi$
$380$	−0.156473	−	0.0648133i	−0.00802690	−	0.00332485i
$381$	−6.44294	+	15.5546i	−0.330082	+	0.796888i
$382$	−2.57028	+	2.57028i	−0.131507	+	0.131507i
$383$	26.8916	−	26.8916i	1.37410	−	1.37410i	0.519819	−	0.854277i	$-0.326000\pi$
$383$	26.8916	−	26.8916i	1.37410	−	1.37410i	0.854277	−	0.519819i	$-0.174000\pi$
$384$	6.51066	−	15.7181i	0.332246	−	0.802112i
$385$	−10.6344	−	4.40490i	−0.541978	−	0.224494i
$386$	9.04742	+	21.8424i	0.460502	+	1.11175i
$387$			0.640412i			0.0325540i
$388$	−0.316762	+	0.131207i	−0.0160811	+	0.00666102i
$389$	−0.750892	−	0.750892i	−0.0380717	−	0.0380717i	0.687815	−	0.725886i	$-0.258570\pi$
$389$	−0.750892	−	0.750892i	−0.0380717	−	0.0380717i	−0.725886	+	0.687815i	$0.758570\pi$
$390$	28.0699			1.42137
$391$	2.07075	+	27.0456i	0.104722	+	1.36776i
$392$	−17.0223			−0.859754
$393$	−1.02877	−	1.02877i	−0.0518948	−	0.0518948i
$394$	−30.6526	+	12.6967i	−1.54425	+	0.639651i
$395$			38.2559i			1.92487i
$396$	−0.0302395	−	0.0730047i	−0.00151959	−	0.00366863i
$397$	−10.3248	−	4.27668i	−0.518188	−	0.214641i	0.108233	−	0.994126i	$-0.465481\pi$
$397$	−10.3248	−	4.27668i	−0.518188	−	0.214641i	−0.626421	+	0.779485i	$0.715481\pi$
$398$	14.3241	−	34.5814i	0.718002	−	1.73341i
$399$	2.68318	−	2.68318i	0.134327	−	0.134327i
$400$	−3.89323	+	3.89323i	−0.194662	+	0.194662i
$401$	0.496965	−	1.19978i	0.0248173	−	0.0599142i	−0.910985	−	0.412439i	$-0.864677\pi$
$401$	0.496965	−	1.19978i	0.0248173	−	0.0599142i	0.935802	+	0.352525i	$0.114677\pi$
$402$	−4.89190	−	2.02629i	−0.243986	−	0.101062i
$403$	−14.2895	−	34.4979i	−0.711810	−	1.71846i
$404$		−	0.317334i		−	0.0157880i
$405$	−15.5812	+	6.45396i	−0.774238	+	0.320700i
$406$	−4.36058	−	4.36058i	−0.216412	−	0.216412i
$407$	2.23853			0.110960
$408$	17.9818	−	1.37678i	0.890231	−	0.0681606i
$409$	−33.9592			−1.67918			−0.839588	−	0.543224i	$-0.817204\pi$
$409$	−33.9592			−1.67918			−0.839588	+	0.543224i	$0.817204\pi$
$410$	−7.59681	−	7.59681i	−0.375180	−	0.375180i
$411$	24.2907	−	10.0615i	1.19817	−	0.496299i
$412$			0.125112i			0.00616384i
$413$	−4.34324	−	10.4855i	−0.213717	−	0.515958i
$414$	5.46683	+	2.26443i	0.268680	+	0.111291i
$415$	2.65707	−	6.41474i	0.130431	−	0.314887i
$416$	0.563940	−	0.563940i	0.0276494	−	0.0276494i
$417$	12.7167	−	12.7167i	0.622739	−	0.622739i
$418$	5.91305	−	14.2754i	0.289217	−	0.698231i
$419$	−13.1611	−	5.45152i	−0.642964	−	0.266324i	0.0372862	−	0.999305i	$-0.488129\pi$
$419$	−13.1611	−	5.45152i	−0.642964	−	0.266324i	−0.680250	+	0.732980i	$0.738129\pi$
$420$	0.0411885	+	0.0994379i	0.00200980	+	0.00485207i
$421$			17.7788i			0.866485i	0.901277	+	0.433243i	$0.142631\pi$
$421$			17.7788i			0.866485i	−0.901277	+	0.433243i	$0.857369\pi$
$422$	−16.3417	+	6.76894i	−0.795500	+	0.329507i
$423$	4.40541	+	4.40541i	0.214198	+	0.214198i
$424$	10.4222			0.506149
$425$	−5.46979	−	1.79009i	−0.265324	−	0.0868323i
$426$	−0.455084			−0.0220489
$427$	−4.56552	−	4.56552i	−0.220941	−	0.220941i
$428$	−0.258352	+	0.107013i	−0.0124879	+	0.00517267i
$429$		−	35.5795i		−	1.71779i
$430$	−1.35928	−	3.28158i	−0.0655501	−	0.158252i
$431$	−27.5163	−	11.3976i	−1.32541	−	0.549005i	−0.396071	−	0.918220i	$-0.629626\pi$
$431$	−27.5163	−	11.3976i	−1.32541	−	0.549005i	−0.929344	+	0.369216i	$0.879626\pi$
$432$	8.44099	−	20.3783i	0.406117	−	0.980454i
$433$	−21.8518	+	21.8518i	−1.05013	+	1.05013i	−0.0514548	+	0.998675i	$0.516386\pi$
$433$	−21.8518	+	21.8518i	−1.05013	+	1.05013i	−0.998675	+	0.0514548i	$0.983614\pi$
$434$	−7.28697	+	7.28697i	−0.349786	+	0.349786i
$435$	6.45696	−	15.5885i	0.309587	−	0.747410i
$436$	0.258408	+	0.107036i	0.0123755	+	0.00512610i
$437$	−6.15187	−	14.8519i	−0.294284	−	0.710464i
$438$			6.24085i			0.298199i
$439$	17.3146	−	7.17193i	0.826379	−	0.342297i	0.0709109	−	0.997483i	$-0.477409\pi$
$439$	17.3146	−	7.17193i	0.826379	−	0.342297i	0.755468	+	0.655185i	$0.227409\pi$
$440$	22.9256	+	22.9256i	1.09294	+	1.09294i
$441$	−3.82840			−0.182305
$442$	−28.3141	−	9.26635i	−1.34677	−	0.440755i
$443$	24.4958			1.16383			0.581915	−	0.813249i	$-0.302303\pi$
$443$	24.4958			1.16383			0.581915	+	0.813249i	$0.302303\pi$
$444$	−0.0148009	−	0.0148009i	−0.000702419	−	0.000702419i
$445$	−5.54808	+	2.29809i	−0.263004	+	0.108940i
$446$			4.96750i			0.235218i
$447$	−1.60999	−	3.88686i	−0.0761499	−	0.183842i
$448$	−7.57136	−	3.13616i	−0.357713	−	0.148170i
$449$	−0.00628802	+	0.0151806i	−0.000296750	+	0.000716418i	−0.924028	−	0.382325i	$-0.875123\pi$
$449$	−0.00628802	+	0.0151806i	−0.000296750	+	0.000716418i	0.923731	+	0.383042i	$0.125123\pi$
$450$	−0.887777	+	0.887777i	−0.0418502	+	0.0418502i
$451$	−9.62920	+	9.62920i	−0.453421	+	0.453421i
$452$	−0.0221143	+	0.0533886i	−0.00104017	+	0.00251119i
$453$	−3.44668	−	1.42766i	−0.161939	−	0.0670773i
$454$	9.50036	+	22.9359i	0.445874	+	1.07643i
$455$		−	13.1530i		−	0.616620i
$456$	−9.87459	+	4.09019i	−0.462420	+	0.191541i
$457$	−17.4329	−	17.4329i	−0.815474	−	0.815474i	0.169974	−	0.985449i	$-0.445632\pi$
$457$	−17.4329	−	17.4329i	−0.815474	−	0.815474i	−0.985449	+	0.169974i	$0.945632\pi$
$458$	13.2190			0.617682
$459$	22.9892	−	1.76017i	1.07304	−	0.0821577i
$460$	0.455974			0.0212599
$461$	−26.5914	−	26.5914i	−1.23848	−	1.23848i	−0.960620	−	0.277864i	$-0.910373\pi$
$461$	−26.5914	−	26.5914i	−1.23848	−	1.23848i	−0.277864	−	0.960620i	$-0.589627\pi$
$462$	−9.07192	+	3.75771i	−0.422064	+	0.174825i
$463$			25.5870i			1.18913i	0.804047	+	0.594565i	$0.202676\pi$
$463$			25.5870i			1.18913i	−0.804047	+	0.594565i	$0.797324\pi$
$464$	6.55610	+	15.8278i	0.304359	+	0.734788i
$465$	−26.0499	−	10.7902i	−1.20803	−	0.500384i
$466$	5.79714	−	13.9955i	0.268547	−	0.648330i
$467$	7.76530	−	7.76530i	0.359335	−	0.359335i	−0.504233	−	0.863568i	$-0.668225\pi$
$467$	7.76530	−	7.76530i	0.359335	−	0.359335i	0.863568	+	0.504233i	$0.168225\pi$
$468$	0.0638481	−	0.0638481i	0.00295138	−	0.00295138i
$469$	−0.949479	+	2.29224i	−0.0438429	+	0.105846i
$470$	−31.9246	−	13.2236i	−1.47257	−	0.609959i
$471$	−6.44628	−	15.5627i	−0.297029	−	0.717091i
$472$			31.9679i			1.47144i
$473$	−4.15951	+	1.72293i	−0.191255	+	0.0792202i
$474$	23.0766	+	23.0766i	1.05994	+	1.05994i
$475$	3.41088			0.156502
$476$	−0.00872078	−	0.113900i	−0.000399716	−	0.00522061i
$477$	2.34402			0.107325
$478$	0.381468	+	0.381468i	0.0174480	+	0.0174480i
$479$	−5.48853	+	2.27342i	−0.250777	+	0.103875i	−0.504531	−	0.863393i	$-0.668335\pi$
$479$	−5.48853	+	2.27342i	−0.250777	+	0.103875i	0.253754	+	0.967269i	$0.418335\pi$
$480$		−	0.602228i		−	0.0274878i
$481$	0.978879	+	2.36322i	0.0446330	+	0.107754i
$482$	−37.2340	−	15.4228i	−1.69596	−	0.702491i
$483$	−3.90949	+	9.43833i	−0.177888	+	0.429459i
$484$	0.179645	−	0.179645i	0.00816567	−	0.00816567i
$485$	22.3719	−	22.3719i	1.01585	−	1.01585i
$486$	3.51100	−	8.47631i	0.159262	−	0.384493i
$487$	36.5589	+	15.1432i	1.65664	+	0.686204i	0.997814	−	0.0660887i	$-0.0210520\pi$
$487$	36.5589	+	15.1432i	1.65664	+	0.686204i	0.658829	+	0.752293i	$0.271052\pi$
$488$	6.95960	+	16.8020i	0.315046	+	0.760589i
$489$			21.4896i			0.971794i
$490$	19.6174	−	8.12579i	0.886223	−	0.367086i
$491$	−17.7982	−	17.7982i	−0.803220	−	0.803220i	0.180378	−	0.983597i	$-0.442268\pi$
$491$	−17.7982	−	17.7982i	−0.803220	−	0.803220i	−0.983597	+	0.180378i	$0.942268\pi$
$492$	0.127334			0.00574067
$493$	−11.6592	+	13.5926i	−0.525102	+	0.612178i
$494$	17.6563			0.794393
$495$	5.15609	+	5.15609i	0.231749	+	0.231749i
$496$	26.4499	−	10.9559i	1.18763	−	0.491934i
$497$			0.213243i			0.00956526i
$498$	−2.26669	−	5.47226i	−0.101573	−	0.245218i
$499$	23.8345	+	9.87258i	1.06698	+	0.441957i	0.845924	−	0.533304i	$-0.179050\pi$
$499$	23.8345	+	9.87258i	1.06698	+	0.441957i	0.221056	+	0.975261i	$0.429050\pi$
$500$	0.0955961	−	0.230790i	0.00427519	−	0.0103212i
$501$	−4.94560	+	4.94560i	−0.220953	+	0.220953i
$502$	19.0904	−	19.0904i	0.852045	−	0.852045i
$503$	−4.62488	+	11.1655i	−0.206213	+	0.497843i	−0.992821	−	0.119610i	$-0.961836\pi$
$503$	−4.62488	+	11.1655i	−0.206213	+	0.497843i	0.786608	+	0.617453i	$0.211836\pi$
$504$	−1.70316	−	0.705470i	−0.0758646	−	0.0314241i
$505$	11.2062	+	27.0541i	0.498668	+	1.20389i
$506$			41.5994i			1.84932i
$507$	19.1122	−	7.91655i	0.848805	−	0.351586i
$508$	−0.212403	−	0.212403i	−0.00942386	−	0.00942386i
$509$	27.1386			1.20290			0.601450	−	0.798911i	$-0.294590\pi$
$509$	27.1386			1.20290			0.601450	+	0.798911i	$0.294590\pi$
$510$	−20.0660	+	10.1705i	−0.888536	+	0.450357i
$511$	2.92433			0.129365
$512$	16.3164	+	16.3164i	0.721088	+	0.721088i
$513$	−12.6244	+	5.22919i	−0.557380	+	0.230874i
$514$		−	20.1256i		−	0.887703i
$515$	−4.41814	−	10.6663i	−0.194687	−	0.470015i
$516$	0.0388940	+	0.0161104i	0.00171221	+	0.000709222i
$517$	−16.7613	+	40.4654i	−0.737163	+	1.77967i
$518$	0.499182	−	0.499182i	0.0219328	−	0.0219328i
$519$	−24.6982	+	24.6982i	−1.08413	+	1.08413i
$520$	−14.1776	+	34.2278i	−0.621729	+	1.50099i
$521$	17.8930	+	7.41152i	0.783907	+	0.324705i	0.738491	−	0.674263i	$-0.235539\pi$
$521$	17.8930	+	7.41152i	0.783907	+	0.324705i	0.0454158	+	0.998968i	$0.485539\pi$
$522$	1.49499	+	3.60923i	0.0654340	+	0.157972i
$523$			33.6820i			1.47281i	0.676540	+	0.736406i	$0.263478\pi$
$523$			33.6820i			1.47281i	−0.676540	+	0.736406i	$0.736522\pi$
$524$	0.0239818	−	0.00993358i	0.00104765	−	0.000433950i
$525$	−1.53272	−	1.53272i	−0.0668935	−	0.0668935i
$526$	6.19639			0.270175
$527$	22.7145	+	19.4836i	0.989460	+	0.848719i
$528$	27.2791			1.18717
$529$	14.3399	+	14.3399i	0.623472	+	0.623472i
$530$	−12.0112	+	4.97519i	−0.521732	+	0.216108i
$531$			7.18975i			0.312009i
$532$	0.0259081	+	0.0625476i	0.00112326	+	0.00271178i
$533$	−14.3763	−	5.95487i	−0.622707	−	0.257934i
$534$	−1.96045	+	4.73294i	−0.0848368	+	0.204814i
$535$	18.2466	−	18.2466i	0.788869	−	0.788869i
$536$	4.94163	−	4.94163i	0.213446	−	0.213446i
$537$	2.84937	−	6.87899i	0.122959	−	0.296850i
$538$	16.4407	+	6.80995i	0.708808	+	0.293598i
$539$	−10.2997	−	24.8657i	−0.443639	−	1.07104i
$540$		−	0.387585i		−	0.0166790i
$541$	−6.47763	+	2.68312i	−0.278495	+	0.115356i	−0.517559	−	0.855647i	$-0.673159\pi$
$541$	−6.47763	+	2.68312i	−0.278495	+	0.115356i	0.239064	+	0.971004i	$0.423159\pi$
$542$	1.89513	+	1.89513i	0.0814027	+	0.0814027i
$543$	−17.3121			−0.742932
$544$	−0.198806	+	0.607468i	−0.00852373	+	0.0260450i
$545$	−25.8102			−1.10559
$546$	−7.93407	−	7.93407i	−0.339547	−	0.339547i
$547$	37.4682	−	15.5199i	1.60203	−	0.663581i	0.610326	−	0.792151i	$-0.291039\pi$
$547$	37.4682	−	15.5199i	1.60203	−	0.663581i	0.991700	+	0.128570i	$0.0410386\pi$
$548$			0.469089i			0.0200385i
$549$	1.56525	+	3.77885i	0.0668033	+	0.161277i
$550$	−8.15458	−	3.37774i	−0.347713	−	0.144027i
$551$	4.06150	−	9.80532i	0.173026	−	0.417721i
$552$	20.3472	−	20.3472i	0.866034	−	0.866034i
$553$	10.8132	−	10.8132i	0.459824	−	0.459824i
$554$	−6.87454	+	16.5966i	−0.292071	+	0.705122i
$555$	1.78451	+	0.739166i	0.0757480	+	0.0313759i
$556$	0.122789	+	0.296439i	0.00520742	+	0.0125718i
$557$		−	7.10373i		−	0.300995i	−0.988610	−	0.150497i	$-0.951913\pi$
$557$		−	7.10373i		−	0.300995i	0.988610	−	0.150497i	$-0.0480875\pi$
$558$	6.03138	−	2.49828i	0.255329	−	0.105761i
$559$	−3.63780	−	3.63780i	−0.153863	−	0.153863i
$560$	10.0845			0.426148
$561$	12.8914	+	25.4343i	0.544277	+	1.07384i
$562$	32.7251			1.38043
$563$	−21.7101	−	21.7101i	−0.914970	−	0.914970i	0.0816881	−	0.996658i	$-0.473969\pi$
$563$	−21.7101	−	21.7101i	−0.914970	−	0.914970i	−0.996658	+	0.0816881i	$0.973969\pi$
$564$	0.378377	−	0.156729i	0.0159325	−	0.00659948i
$565$		−	5.33253i		−	0.224341i
$566$	15.6359	+	37.7484i	0.657225	+	1.58668i
$567$	6.22834	+	2.57986i	0.261566	+	0.108344i
$568$	0.229855	−	0.554919i	0.00964451	−	0.0232839i
$569$	21.4046	−	21.4046i	0.897328	−	0.897328i	−0.0978713	−	0.995199i	$-0.531203\pi$
$569$	21.4046	−	21.4046i	0.897328	−	0.897328i	0.995199	+	0.0978713i	$0.0312033\pi$
$570$	9.42751	−	9.42751i	0.394875	−	0.394875i
$571$	9.85333	−	23.7880i	0.412349	−	0.995498i	−0.572156	−	0.820144i	$-0.693893\pi$
$571$	9.85333	−	23.7880i	0.412349	−	0.995498i	0.984505	−	0.175354i	$-0.0561070\pi$
$572$	0.586470	+	0.242924i	0.0245215	+	0.0101572i
$573$	1.52137	+	3.67290i	0.0635560	+	0.153438i
$574$			4.29454i			0.179251i
$575$	−8.48394	+	3.51416i	−0.353805	+	0.146551i
$576$	3.67099	+	3.67099i	0.152958	+	0.152958i
$577$	2.79078			0.116182			0.0580908	−	0.998311i	$-0.481499\pi$
$577$	2.79078			0.116182			0.0580908	+	0.998311i	$0.481499\pi$
$578$	23.5980	−	3.63488i	0.981549	−	0.151191i
$579$	25.8574			1.07460
$580$	0.212865	+	0.212865i	0.00883874	+	0.00883874i
$581$	−2.56419	+	1.06212i	−0.106380	+	0.0440642i
$582$		−	26.9901i		−	1.11878i
$583$	6.30621	+	15.2245i	0.261176	+	0.630536i
$584$	−7.60995	−	3.15214i	−0.314902	−	0.130437i
$585$	−3.18862	+	7.69801i	−0.131833	+	0.318273i
$586$	22.2504	−	22.2504i	0.919154	−	0.919154i
$587$	−25.5745	+	25.5745i	−1.05557	+	1.05557i	−0.0572116	+	0.998362i	$0.518221\pi$
$587$	−25.5745	+	25.5745i	−1.05557	+	1.05557i	−0.998362	+	0.0572116i	$0.981779\pi$
$588$	−0.0963085	+	0.232509i	−0.00397170	+	0.00958852i
$589$	−16.3857	−	6.78717i	−0.675160	−	0.279660i
$590$	−15.2603	−	36.8415i	−0.628255	−	1.51674i
$591$			36.2870i			1.49265i
$592$	−1.81190	+	0.750516i	−0.0744688	+	0.0308460i
$593$	3.45105	+	3.45105i	0.141718	+	0.141718i	0.774406	−	0.632689i	$-0.218049\pi$
$593$	3.45105	+	3.45105i	0.141718	+	0.141718i	−0.632689	+	0.774406i	$0.718049\pi$
$594$	35.3602			1.45085
$595$	4.76569	+	9.40250i	0.195374	+	0.385465i
$596$	0.0750611			0.00307462
$597$	−28.9476	−	28.9476i	−1.18474	−	1.18474i
$598$	−43.9167	+	18.1909i	−1.79589	+	0.743882i
$599$			1.10464i			0.0451346i	0.999745	+	0.0225673i	$0.00718400\pi$
$599$			1.10464i			0.0451346i	−0.999745	+	0.0225673i	$0.992816\pi$
$600$	2.33646	+	5.64071i	0.0953855	+	0.230281i
$601$	−20.8621	−	8.64135i	−0.850981	−	0.352488i	−0.0858073	−	0.996312i	$-0.527347\pi$
$601$	−20.8621	−	8.64135i	−0.850981	−	0.352488i	−0.765174	+	0.643824i	$0.777347\pi$
$602$	−0.543349	+	1.31176i	−0.0221452	+	0.0534633i
$603$	1.11140	−	1.11140i	0.0452597	−	0.0452597i
$604$	0.0470653	−	0.0470653i	0.00191506	−	0.00191506i
$605$	−8.97158	+	21.6593i	−0.364747	+	0.880577i
$606$	23.0792	+	9.55971i	0.937527	+	0.388336i
$607$	−14.6478	−	35.3629i	−0.594535	−	1.43534i	−0.879081	−	0.476673i	$-0.841843\pi$
$607$	−14.6478	−	35.3629i	−0.594535	−	1.43534i	0.284545	−	0.958663i	$-0.408157\pi$
$608$		−	0.378808i		−	0.0153627i
$609$	−6.23124	+	2.58106i	−0.252502	+	0.104590i
$610$	−16.0413	−	16.0413i	−0.649491	−	0.649491i
$611$	−50.0491			−2.02477
$612$	−0.0225084	+	0.0687763i	−0.000909847	+	0.00278012i
$613$	12.7822			0.516267			0.258133	−	0.966109i	$-0.416893\pi$
$613$	12.7822			0.516267			0.258133	+	0.966109i	$0.416893\pi$
$614$	10.5667	+	10.5667i	0.426436	+	0.426436i
$615$	−10.8558	+	4.49661i	−0.437747	+	0.181321i
$616$		−	12.9600i		−	0.522175i
$617$	14.4640	+	34.9192i	0.582299	+	1.40579i	0.890723	+	0.454546i	$0.150198\pi$
$617$	14.4640	+	34.9192i	0.582299	+	1.40579i	−0.308424	+	0.951249i	$0.599802\pi$
$618$	−9.09920	−	3.76901i	−0.366023	−	0.151612i
$619$	9.94196	−	24.0020i	0.399601	−	0.964723i	−0.588159	−	0.808745i	$-0.700147\pi$
$619$	9.94196	−	24.0020i	0.399601	−	0.964723i	0.987761	−	0.155978i	$-0.0498528\pi$
$620$	0.355719	−	0.355719i	0.0142860	−	0.0142860i
$621$	26.0133	−	26.0133i	1.04388	−	1.04388i
$622$	4.65454	−	11.2370i	0.186630	−	0.450564i
$623$	2.21776	+	0.918625i	0.0888525	+	0.0368039i
$624$	11.9288	+	28.7987i	0.477534	+	1.15287i
$625$			30.0309i			1.20123i
$626$	−28.2982	+	11.7215i	−1.13102	+	0.468485i
$627$	−11.9497	−	11.9497i	−0.477224	−	0.477224i
$628$	0.300539			0.0119928
$629$	−1.55602	−	1.33469i	−0.0620426	−	0.0532177i
$630$	2.29958			0.0916173
$631$	25.0594	+	25.0594i	0.997599	+	0.997599i	0.999997	−	0.00239824i	$-0.000763385\pi$
$631$	25.0594	+	25.0594i	0.997599	+	0.997599i	−0.00239824	+	0.999997i	$0.500763\pi$
$632$	−39.7946	+	16.4835i	−1.58295	+	0.655678i
$633$			19.3455i			0.768916i
$634$	4.77900	+	11.5375i	0.189798	+	0.458213i
$635$	25.6089	+	10.6076i	1.01626	+	0.420948i
$636$	0.0589670	−	0.142359i	0.00233819	−	0.00564489i
$637$	21.7469	−	21.7469i	0.861643	−	0.861643i
$638$	−19.4201	+	19.4201i	−0.768849	+	0.768849i
$639$	0.0516957	−	0.124804i	0.00204505	−	0.00493718i
$640$	−25.8781	−	10.7190i	−1.02292	−	0.423708i
$641$	4.44742	+	10.7370i	0.175663	+	0.424087i	0.987048	−	0.160424i	$-0.0512863\pi$
$641$	4.44742	+	10.7370i	0.175663	+	0.424087i	−0.811386	+	0.584511i	$0.801286\pi$
$642$		−	22.0133i		−	0.868794i
$643$	−36.3709	+	15.0653i	−1.43433	+	0.594118i	−0.958416	−	0.285374i	$-0.907882\pi$
$643$	−36.3709	+	15.0653i	−1.43433	+	0.594118i	−0.475912	+	0.879493i	$0.657882\pi$
$644$	−0.128883	−	0.128883i	−0.00507871	−	0.00507871i
$645$	−3.88479			−0.152963
$646$	−12.6217	+	6.39736i	−0.496595	+	0.251701i
$647$	−5.55476			−0.218380			−0.109190	−	0.994021i	$-0.534826\pi$
$647$	−5.55476			−0.218380			−0.109190	+	0.994021i	$0.534826\pi$
$648$	−13.4271	−	13.4271i	−0.527466	−	0.527466i
$649$	−46.6978	+	19.3429i	−1.83305	+	0.759274i
$650$		−	10.0859i		−	0.395601i
$651$	4.31321	+	10.4130i	0.169048	+	0.408118i
$652$	−0.354222	−	0.146723i	−0.0138724	−	0.00574613i
$653$	7.98609	−	19.2801i	0.312520	−	0.754490i	−0.687090	−	0.726572i	$-0.741112\pi$
$653$	7.98609	−	19.2801i	0.312520	−	0.754490i	0.999610	−	0.0279178i	$-0.00888767\pi$
$654$	−15.5691	+	15.5691i	−0.608800	+	0.608800i
$655$	−1.69376	+	1.69376i	−0.0661806	+	0.0661806i
$656$	4.56565	−	11.0225i	0.178259	−	0.430355i
$657$	−1.71152	−	0.708934i	−0.0667727	−	0.0276581i
$658$	5.28592	+	12.7613i	0.206067	+	0.497489i
$659$		−	27.4376i		−	1.06882i	−0.845226	−	0.534409i	$-0.820534\pi$
$659$		−	27.4376i		−	1.06882i	0.845226	−	0.534409i	$-0.179466\pi$
$660$	0.442852	−	0.183435i	0.0172380	−	0.00714022i
$661$	7.67353	+	7.67353i	0.298466	+	0.298466i	0.840413	−	0.541947i	$-0.182313\pi$
$661$	7.67353	+	7.67353i	0.298466	+	0.298466i	−0.541947	+	0.840413i	$0.682313\pi$
$662$	−42.0108			−1.63279
$663$	−21.2138	+	24.7316i	−0.823876	+	0.960497i
$664$	7.81761			0.303382
$665$	−4.41754	−	4.41754i	−0.171305	−	0.171305i
$666$	−0.413170	+	0.171141i	−0.0160100	+	0.00663156i
$667$			28.5734i			1.10637i
$668$	−0.0477535	−	0.115287i	−0.00184764	−	0.00446059i
$669$	5.01940	+	2.07911i	0.194061	+	0.0803829i
$670$	−3.33606	+	8.05395i	−0.128883	+	0.311151i
$671$	−20.3328	+	20.3328i	−0.784939	+	0.784939i
$672$	−0.170222	+	0.170222i	−0.00656647	+	0.00656647i
$673$	−5.91840	+	14.2883i	−0.228138	+	0.550773i	−0.995951	−	0.0899009i	$-0.971345\pi$
$673$	−5.91840	+	14.2883i	−0.228138	+	0.550773i	0.767813	+	0.640674i	$0.221345\pi$
$674$	2.39896	+	0.993682i	0.0924045	+	0.0382752i
$675$	2.98709	+	7.21148i	0.114973	+	0.277570i
$676$			0.369086i			0.0141956i
$677$	24.6913	−	10.2275i	0.948963	−	0.393073i	0.146122	−	0.989267i	$-0.453321\pi$
$677$	24.6913	−	10.2275i	0.948963	−	0.393073i	0.802841	+	0.596193i	$0.203321\pi$
$678$	−3.21666	−	3.21666i	−0.123535	−	0.123535i
$679$	−12.6470			−0.485348
$680$	−2.26670	−	29.6049i	−0.0869241	−	1.13530i
$681$	27.1519			1.04046
$682$	32.4529	+	32.4529i	1.24269	+	1.24269i
$683$	−38.9760	+	16.1444i	−1.49137	+	0.617747i	−0.971615	−	0.236566i	$-0.923978\pi$
$683$	−38.9760	+	16.1444i	−1.49137	+	0.617747i	−0.519758	+	0.854313i	$0.673978\pi$
$684$		−	0.0428879i		−	0.00163986i
$685$	−16.5651	−	39.9918i	−0.632922	−	1.52801i
$686$	−17.0240	−	7.05159i	−0.649981	−	0.269231i
$687$	5.53270	−	13.3571i	0.211086	−	0.509606i
$688$	2.78914	−	2.78914i	0.106335	−	0.106335i
$689$	−13.3150	+	13.3150i	−0.507261	+	0.507261i
$690$	−13.7362	+	33.1622i	−0.522929	+	1.26246i
$691$	20.2480	+	8.38699i	0.770270	+	0.319056i	0.732982	−	0.680248i	$-0.238128\pi$
$691$	20.2480	+	8.38699i	0.770270	+	0.319056i	0.0372882	+	0.999305i	$0.488128\pi$
$692$	−0.238479	−	0.575740i	−0.00906563	−	0.0218864i
$693$		−	2.91478i		−	0.110723i
$694$	0.690669	−	0.286084i	0.0262174	−	0.0108596i
$695$	−20.9366	−	20.9366i	−0.794169	−	0.794169i
$696$	18.9976			0.720102
$697$	12.4346	−	0.952059i	0.470996	−	0.0360618i
$698$	−24.9968			−0.946141
$699$	−11.7154	−	11.7154i	−0.443118	−	0.443118i
$700$	0.0357294	−	0.0147996i	0.00135044	−	0.000559372i
$701$			27.1561i			1.02567i	0.858486	+	0.512836i	$0.171405\pi$
$701$			27.1561i			1.02567i	−0.858486	+	0.512836i	$0.828595\pi$
$702$	15.4626	+	37.3299i	0.583597	+	1.40893i
$703$	1.12247	+	0.464944i	0.0423349	+	0.0175357i
$704$	−13.9671	+	33.7195i	−0.526404	+	1.27085i
$705$	−26.7236	+	26.7236i	−1.00647	+	1.00647i
$706$	33.3623	−	33.3623i	1.25561	−	1.25561i
$707$	4.47948	−	10.8144i	0.168468	−	0.406718i
$708$	0.436654	+	0.180868i	0.0164104	+	0.00679743i
$709$	14.0486	+	33.9163i	0.527606	+	1.27375i	0.933087	+	0.359650i	$0.117104\pi$
$709$	14.0486	+	33.9163i	0.527606	+	1.27375i	−0.405481	+	0.914103i	$0.632896\pi$
$710$			0.749244i			0.0281186i
$711$	−8.95003	+	3.70722i	−0.335652	+	0.139032i
$712$	−4.78105	−	4.78105i	−0.179177	−	0.179177i
$713$	47.7490			1.78822
$714$	8.54647	+	2.79700i	0.319844	+	0.104675i
$715$	−58.5775			−2.19067
$716$	0.0939346	+	0.0939346i	0.00351050	+	0.00351050i
$717$	0.545115	−	0.225794i	0.0203577	−	0.00843243i
$718$		−	8.92154i		−	0.332949i
$719$	1.63484	+	3.94686i	0.0609694	+	0.147193i	0.951428	−	0.307871i	$-0.0996164\pi$
$719$	1.63484	+	3.94686i	0.0609694	+	0.147193i	−0.890459	+	0.455064i	$0.849616\pi$
$720$	−5.90213	−	2.44474i	−0.219960	−	0.0911102i
$721$	−1.76608	+	4.26369i	−0.0657723	+	0.158788i
$722$	−12.9394	+	12.9394i	−0.481553	+	0.481553i
$723$	−31.1680	+	31.1680i	−1.15915	+	1.15915i
$724$	0.118201	−	0.285362i	0.00439289	−	0.0106054i
$725$	−5.60114	−	2.32007i	−0.208021	−	0.0861652i
$726$	7.65344	+	18.4770i	0.284046	+	0.685747i
$727$			15.4745i			0.573917i	0.957943	+	0.286958i	$0.0926442\pi$
$727$			15.4745i			0.573917i	−0.957943	+	0.286958i	$0.907356\pi$
$728$	13.6820	−	5.66727i	0.507088	−	0.210043i
$729$	−21.2417	−	21.2417i	−0.786729	−	0.786729i
$730$	10.2748			0.380289
$731$	3.91859	+	1.28244i	0.144934	+	0.0474326i
$732$	0.268876			0.00993795
$733$	28.6153	+	28.6153i	1.05693	+	1.05693i	0.998279	+	0.0586499i	$0.0186796\pi$
$733$	28.6153	+	28.6153i	1.05693	+	1.05693i	0.0586499	+	0.998279i	$0.481320\pi$
$734$	−18.2365	+	7.55379i	−0.673120	+	0.278815i
$735$		−	23.2234i		−	0.856607i
$736$	0.390279	+	0.942216i	0.0143859	+	0.0347306i
$737$	10.2086	+	4.22856i	0.376040	+	0.155761i
$738$	1.04111	−	2.51346i	0.0383237	−	0.0925217i
$739$	9.36584	−	9.36584i	0.344528	−	0.344528i	−0.513539	−	0.858067i	$-0.671666\pi$
$739$	9.36584	−	9.36584i	0.344528	−	0.344528i	0.858067	+	0.513539i	$0.171666\pi$
$740$	−0.0243679	+	0.0243679i	−0.000895783	+	0.000895783i
$741$	7.38989	−	17.8408i	0.271474	−	0.655397i
$742$	4.80127	+	1.98875i	0.176260	+	0.0730093i
$743$	−12.3841	−	29.8980i	−0.454330	−	1.09685i	−0.970659	−	0.240460i	$-0.922702\pi$
$743$	−12.3841	−	29.8980i	−0.454330	−	1.09685i	0.516329	−	0.856390i	$-0.327298\pi$
$744$		−	31.7469i		−	1.16390i
$745$	−6.39927	+	2.65066i	−0.234451	+	0.0971128i
$746$	−20.1825	−	20.1825i	−0.738935	−	0.738935i
$747$	1.75822			0.0643300
$748$	−0.507261	+	0.0388385i	−0.0185473	+	0.00142008i
$749$	−10.3150			−0.376900
$750$	13.9051	+	13.9051i	0.507742	+	0.507742i
$751$	−36.3737	+	15.0665i	−1.32730	+	0.549784i	−0.929883	−	0.367856i	$-0.880092\pi$
$751$	−36.3737	+	15.0665i	−1.32730	+	0.549784i	−0.397413	+	0.917640i	$0.630092\pi$
$752$		−	38.3731i		−	1.39932i
$753$	−11.2997	−	27.2800i	−0.411785	−	0.994138i
$754$	−28.9941	−	12.0097i	−1.05590	−	0.437369i
$755$	−2.35048	+	5.67455i	−0.0855426	+	0.206518i
$756$	−0.109553	+	0.109553i	−0.00398439	+	0.00398439i
$757$	−8.23011	+	8.23011i	−0.299128	+	0.299128i	−0.840672	−	0.541544i	$-0.817840\pi$
$757$	−8.23011	+	8.23011i	−0.299128	+	0.299128i	0.541544	+	0.840672i	$0.317840\pi$
$758$	−10.3503	+	24.9879i	−0.375941	+	0.907602i
$759$	42.0341	+	17.4111i	1.52574	+	0.631983i
$760$	6.73402	+	16.2574i	0.244269	+	0.589717i
$761$		−	38.6374i		−	1.40061i	−0.713846	−	0.700303i	$-0.753048\pi$
$761$		−	38.6374i		−	1.40061i	0.713846	−	0.700303i	$-0.246952\pi$
$762$	21.8463	−	9.04905i	0.791410	−	0.327813i
$763$	7.29536	+	7.29536i	0.264110	+	0.264110i
$764$	−0.0709293			−0.00256613
$765$	−0.509794	−	6.65831i	−0.0184316	−	0.240732i
$766$	−53.4134			−1.92990
$767$	−40.8407	−	40.8407i	−1.47467	−	1.47467i
$768$	0.933280	−	0.386577i	0.0336768	−	0.0139494i
$769$		−	43.0490i		−	1.55239i	−0.630495	−	0.776193i	$-0.717148\pi$
$769$		−	43.0490i		−	1.55239i	0.630495	−	0.776193i	$-0.282852\pi$
$770$	6.18664	+	14.9359i	0.222951	+	0.538251i
$771$	−20.3359	−	8.42341i	−0.732380	−	0.303362i
$772$	−0.176545	+	0.426217i	−0.00635399	+	0.0153399i
$773$	20.0683	−	20.0683i	0.721808	−	0.721808i	−0.247165	−	0.968973i	$-0.579499\pi$
$773$	20.0683	−	20.0683i	0.721808	−	0.721808i	0.968973	+	0.247165i	$0.0794990\pi$
$774$	0.636009	−	0.636009i	0.0228609	−	0.0228609i
$775$	−3.87707	+	9.36007i	−0.139268	+	0.336224i
$776$	32.9111	+	13.6322i	1.18144	+	0.489369i
$777$	−0.295470	−	0.713327i	−0.0105999	−	0.0255905i
$778$			1.49146i			0.0534714i
$779$	−6.82840	+	2.82842i	−0.244653	+	0.101339i
$780$	0.387308	+	0.387308i	0.0138678	+	0.0138678i
$781$	0.949690			0.0339826
$782$	24.8032	−	28.9162i	0.886959	−	1.03404i
$783$	24.2879			0.867977
$784$	16.6735	+	16.6735i	0.595483	+	0.595483i
$785$	−25.6222	+	10.6131i	−0.914495	+	0.378796i
$786$			2.04340i			0.0728857i
$787$	2.58256	+	6.23486i	0.0920585	+	0.222249i	0.963201	−	0.268781i	$-0.0866207\pi$
$787$	2.58256	+	6.23486i	0.0920585	+	0.222249i	−0.871143	+	0.491030i	$0.836621\pi$
$788$	−0.598132	−	0.247754i	−0.0213076	−	0.00882589i
$789$	2.59345	−	6.26114i	0.0923292	−	0.222902i
$790$	37.9929	−	37.9929i	1.35173	−	1.35173i
$791$	−1.50726	+	1.50726i	−0.0535921	+	0.0535921i
$792$	−3.14185	+	7.58510i	−0.111641	+	0.269525i
$793$	−30.3567	−	12.5742i	−1.07800	−	0.446522i
$794$	6.00656	+	14.5011i	0.213165	+	0.514626i
$795$			14.2190i			0.504296i
$796$	0.674797	−	0.279510i	0.0239176	−	0.00990698i
$797$	−1.91408	−	1.91408i	−0.0678003	−	0.0678003i	0.672394	−	0.740194i	$-0.265266\pi$
$797$	−1.91408	−	1.91408i	−0.0678003	−	0.0678003i	−0.740194	+	0.672394i	$0.765266\pi$
$798$	−5.32946			−0.188661
$799$	35.7780	−	18.1342i	1.26573	−	0.641542i
$800$	−0.216388			−0.00765049
$801$	−1.07528	−	1.07528i	−0.0379933	−	0.0379933i
$802$	−1.68508	+	0.697983i	−0.0595022	+	0.0246466i
$803$		−	13.0237i		−	0.459595i
$804$	−0.0395396	−	0.0954571i	−0.00139445	−	0.00336651i
$805$	15.5391	+	6.43652i	0.547682	+	0.226857i
$806$	−20.0695	+	48.4520i	−0.706917	+	1.70665i
$807$	13.7622	−	13.7622i	0.484453	−	0.484453i
$808$	−23.3138	+	23.3138i	−0.820176	+	0.820176i
$809$	−8.01766	+	19.3563i	−0.281886	+	0.680533i	−0.999880	−	0.0155168i	$-0.995061\pi$
$809$	−8.01766	+	19.3563i	−0.281886	+	0.680533i	0.717994	+	0.696050i	$0.245061\pi$
$810$	21.8837	+	9.06452i	0.768915	+	0.318495i
$811$	20.9308	+	50.5313i	0.734978	+	1.77439i	0.625238	+	0.780434i	$0.285002\pi$
$811$	20.9308	+	50.5313i	0.734978	+	1.77439i	0.109740	+	0.993960i	$0.464998\pi$
$812$		−	0.120334i		−	0.00422291i
$813$	2.70812	−	1.12174i	0.0949779	−	0.0393411i
$814$	−2.22314	−	2.22314i	−0.0779209	−	0.0779209i
$815$	35.3802			1.23931
$816$	−18.9620	−	16.2648i	−0.663802	−	0.569383i
$817$	−2.44358			−0.0854899
$818$	33.7258	+	33.7258i	1.17919	+	1.17919i
$819$	3.07715	−	1.27460i	0.107524	−	0.0445381i
$820$		−	0.209641i		−	0.00732099i
$821$	−14.4251	−	34.8253i	−0.503440	−	1.21541i	−0.947599	−	0.319464i	$-0.896497\pi$
$821$	−14.4251	−	34.8253i	−0.503440	−	1.21541i	0.444158	−	0.895948i	$-0.353503\pi$
$822$	−34.1160	−	14.1313i	−1.18993	−	0.492886i
$823$	10.1657	−	24.5422i	0.354355	−	0.855489i	−0.641717	−	0.766942i	$-0.721778\pi$
$823$	10.1657	−	24.5422i	0.354355	−	0.855489i	0.996072	−	0.0885472i	$-0.0282224\pi$
$824$	9.19169	−	9.19169i	0.320208	−	0.320208i
$825$	−6.82607	+	6.82607i	−0.237653	+	0.237653i
$826$	−6.10004	+	14.7268i	−0.212248	+	0.512411i
$827$	−17.9513	−	7.43568i	−0.624229	−	0.258564i	0.0480699	−	0.998844i	$-0.484693\pi$
$827$	−17.9513	−	7.43568i	−0.624229	−	0.258564i	−0.672299	+	0.740280i	$0.734693\pi$
$828$	0.0441865	+	0.106676i	0.00153559	+	0.00370724i
$829$		−	20.3577i		−	0.707052i	−0.935425	−	0.353526i	$-0.884983\pi$
$829$		−	20.3577i		−	0.707052i	0.935425	−	0.353526i	$-0.115017\pi$
$830$	−9.00945	+	3.73184i	−0.312723	+	0.129534i
$831$	13.8927	+	13.8927i	0.481934	+	0.481934i
$832$	−41.7055			−1.44588
$833$	−7.66643	+	23.4254i	−0.265626	+	0.811643i
$834$	−25.2585			−0.874631
$835$	8.14236	+	8.14236i	0.281778	+	0.281778i
$836$	0.278559	−	0.115383i	0.00963417	−	0.00399060i
$837$		−	40.5874i		−	1.40291i
$838$	7.65661	+	18.4847i	0.264493	+	0.638543i
$839$	51.2145	+	21.2137i	1.76812	+	0.732380i	0.995198	+	0.0978790i	$0.0312058\pi$
$839$	51.2145	+	21.2137i	1.76812	+	0.732380i	0.772922	+	0.634501i	$0.218794\pi$
$840$	4.27944	−	10.3315i	0.147655	−	0.356470i
$841$	7.16700	−	7.16700i	0.247138	−	0.247138i
$842$	17.6566	−	17.6566i	0.608485	−	0.608485i
$843$	13.6968	−	33.0671i	0.471744	−	1.13889i
$844$	−0.318880	−	0.132084i	−0.0109763	−	0.00454653i
$845$	−13.0337	−	31.4661i	−0.448372	−	1.08247i
$846$		−	8.75025i		−	0.300840i
$847$	8.65796	−	3.58624i	0.297491	−	0.123225i
$848$	−10.2087	−	10.2087i	−0.350569	−	0.350569i
$849$	44.6871			1.53366
$850$	3.65440	+	7.20997i	0.125345	+	0.247300i
$851$	−3.27097			−0.112127
$852$	−0.00627924	−	0.00627924i	−0.000215123	−	0.000215123i
$853$	43.5861	−	18.0540i	1.49236	−	0.618156i	0.520532	−	0.853842i	$-0.325734\pi$
$853$	43.5861	−	18.0540i	1.49236	−	0.618156i	0.971829	+	0.235686i	$0.0757337\pi$
$854$			9.06826i			0.310310i
$855$	1.51452	+	3.65637i	0.0517954	+	0.125045i
$856$	26.8425	+	11.1185i	0.917457	+	0.380023i
$857$	4.66340	−	11.2585i	0.159299	−	0.384581i	−0.823997	−	0.566594i	$-0.808261\pi$
$857$	4.66340	−	11.2585i	0.159299	−	0.384581i	0.983296	+	0.182012i	$0.0582610\pi$
$858$	−35.3348	+	35.3348i	−1.20631	+	1.20631i
$859$	11.9883	−	11.9883i	0.409034	−	0.409034i	−0.472368	−	0.881402i	$-0.656600\pi$
$859$	11.9883	−	11.9883i	0.409034	−	0.409034i	0.881402	+	0.472368i	$0.156600\pi$
$860$	0.0265240	−	0.0640345i	0.000904459	−	0.00218356i
$861$	4.33942	+	1.79745i	0.147887	+	0.0612568i
$862$	16.0079	+	38.6464i	0.545230	+	1.31630i
$863$		−	27.3348i		−	0.930488i	−0.885182	−	0.465244i	$-0.845967\pi$
$863$		−	27.3348i		−	0.930488i	0.885182	−	0.465244i	$-0.154033\pi$
$864$	0.800899	−	0.331743i	0.0272471	−	0.0112861i
$865$	40.6627	+	40.6627i	1.38257	+	1.38257i
$866$	43.4031			1.47490
$867$	6.20390	−	25.3660i	0.210696	−	0.861474i
$868$	−0.201091			−0.00682547
$869$	−48.1572	−	48.1572i	−1.63362	−	1.63362i
$870$	−21.8939	+	9.06873i	−0.742271	+	0.307459i
$871$			12.6264i			0.427829i
$872$	−11.1209	−	26.8483i	−0.376602	−	0.909198i
$873$	7.40189	+	3.06596i	0.250516	+	0.103767i
$874$	−8.64025	+	20.8594i	−0.292261	+	0.705580i
$875$	6.51563	−	6.51563i	0.220269	−	0.220269i
$876$	−0.0861111	+	0.0861111i	−0.00290942	+	0.00290942i
$877$	11.0935	−	26.7822i	0.374602	−	0.904369i	−0.618356	−	0.785898i	$-0.712201\pi$
$877$	11.0935	−	26.7822i	0.374602	−	0.904369i	0.992958	−	0.118471i	$-0.0377992\pi$
$878$	−24.3181	−	10.0729i	−0.820698	−	0.339944i
$879$	−13.1702	−	31.7956i	−0.444218	−	1.07244i
$880$		−	44.9119i		−	1.51398i
$881$	−1.14127	+	0.472728i	−0.0384503	+	0.0159266i	−0.401826	−	0.915716i	$-0.631624\pi$
$881$	−1.14127	+	0.472728i	−0.0384503	+	0.0159266i	0.363375	+	0.931643i	$0.381624\pi$
$882$	3.80208	+	3.80208i	0.128023	+	0.128023i
$883$	−33.3551			−1.12249			−0.561244	−	0.827651i	$-0.689677\pi$
$883$	−33.3551			−1.12249			−0.561244	+	0.827651i	$0.689677\pi$
$884$	−0.262821	−	0.518534i	−0.00883962	−	0.0174402i
$885$	−43.6136			−1.46605
$886$	−24.3274	−	24.3274i	−0.817295	−	0.817295i
$887$	−33.2813	+	13.7856i	−1.11748	+	0.462874i	−0.863507	−	0.504337i	$-0.831737\pi$
$887$	−33.2813	+	13.7856i	−1.11748	+	0.462874i	−0.253971	+	0.967212i	$0.581737\pi$
$888$			2.17477i			0.0729804i
$889$	−4.24020	−	10.2367i	−0.142212	−	0.343329i
$890$	7.79223	+	3.22765i	0.261196	+	0.108191i
$891$	11.4896	−	27.7383i	0.384915	−	0.929267i
$892$	−0.0685414	+	0.0685414i	−0.00229494	+	0.00229494i
$893$	−16.8094	+	16.8094i	−0.562506	+	0.562506i
$894$	−2.26122	+	5.45906i	−0.0756264	+	0.182578i
$895$	−11.3255	−	4.69116i	−0.378568	−	0.156808i
$896$	4.28476	+	10.3443i	0.143144	+	0.345580i
$897$			51.9893i			1.73587i
$898$	0.0213210	−	0.00883147i	0.000711492	−	0.000294710i
$899$	22.2910	+	22.2910i	0.743445	+	0.743445i
$900$	−0.0244991			−0.000816635
$901$	4.69394	−	14.3427i	0.156378	−	0.477825i
$902$	19.1260			0.636826
$903$	1.09805	+	1.09805i	0.0365409	+	0.0365409i
$904$	5.54701	−	2.29764i	0.184491	−	0.0764185i
$905$			28.5023i			0.947450i
$906$	2.00513	+	4.84082i	0.0666161	+	0.160826i
$907$	−13.6415	−	5.65051i	−0.452960	−	0.187622i	0.144527	−	0.989501i	$-0.453834\pi$
$907$	−13.6415	−	5.65051i	−0.452960	−	0.187622i	−0.597487	+	0.801879i	$0.703834\pi$
$908$	−0.185383	+	0.447555i	−0.00615216	+	0.0148526i
$909$	−5.24339	+	5.24339i	−0.173912	+	0.173912i
$910$	−13.0625	+	13.0625i	−0.433019	+	0.433019i
$911$	−10.1085	+	24.4042i	−0.334911	+	0.808546i	0.663277	+	0.748374i	$0.269165\pi$
$911$	−10.1085	+	24.4042i	−0.334911	+	0.808546i	−0.998188	+	0.0601722i	$0.980835\pi$
$912$	13.6787	+	5.66590i	0.452946	+	0.187617i
$913$	4.73022	+	11.4198i	0.156547	+	0.377939i
$914$			34.6260i			1.14533i
$915$	−22.9228	+	9.49494i	−0.757805	+	0.313893i
$916$	0.182395	+	0.182395i	0.00602651	+	0.00602651i
$917$	0.957496			0.0316193
$918$	−24.5792	−	21.0831i	−0.811235	−	0.695845i
$919$	−28.0529			−0.925380			−0.462690	−	0.886520i	$-0.653116\pi$
$919$	−28.0529			−0.925380			−0.462690	+	0.886520i	$0.653116\pi$
$920$	−33.4993	−	33.4993i	−1.10444	−	1.10444i
$921$	15.0997	−	6.25450i	0.497552	−	0.206093i
$922$			52.8171i			1.73944i
$923$	0.415288	+	1.00259i	0.0136694	+	0.0330007i
$924$	−0.177023	−	0.0733253i	−0.00582363	−	0.00241223i
$925$	0.265592	−	0.641196i	0.00873262	−	0.0210824i
$926$	25.4111	−	25.4111i	0.835061	−	0.835061i
$927$	2.06726	−	2.06726i	0.0678977	−	0.0678977i
$928$	−0.257664	+	0.622056i	−0.00845824	+	0.0204200i
$929$	−50.1183	−	20.7597i	−1.64433	−	0.681103i	−0.647605	−	0.761977i	$-0.724229\pi$
$929$	−50.1183	−	20.7597i	−1.64433	−	0.681103i	−0.996724	+	0.0808733i	$0.974229\pi$
$930$	15.1548	+	36.5868i	0.496944	+	1.19973i
$931$		−	14.6078i		−	0.478750i
$932$	0.273099	−	0.113121i	0.00894565	−	0.00370541i
$933$	−9.40635	−	9.40635i	−0.307950	−	0.307950i
$934$	−15.4238			−0.504683
$935$	41.8746	−	21.2243i	1.36944	−	0.694107i
$936$	−9.38152			−0.306645
$937$	5.41699	+	5.41699i	0.176965	+	0.176965i	0.790031	−	0.613066i	$-0.210064\pi$
$937$	5.41699	+	5.41699i	0.176965	+	0.176965i	−0.613066	+	0.790031i	$0.710064\pi$
$938$	3.21944	−	1.33353i	0.105118	−	0.0435414i
$939$			33.4998i			1.09322i
$940$	−0.258036	−	0.622954i	−0.00841621	−	0.0203185i
$941$	24.8477	+	10.2923i	0.810012	+	0.335518i	0.748959	−	0.662617i	$-0.230554\pi$
$941$	24.8477	+	10.2923i	0.810012	+	0.335518i	0.0610532	+	0.998135i	$0.480554\pi$
$942$	−9.05374	+	21.8577i	−0.294987	+	0.712161i
$943$	14.0703	−	14.0703i	0.458193	−	0.458193i
$944$	31.3130	−	31.3130i	1.01915	−	1.01915i
$945$	5.47114	−	13.2085i	0.177976	−	0.429672i
$946$	5.84199	+	2.41983i	0.189940	+	0.0786756i
$947$	−3.94940	−	9.53470i	−0.128338	−	0.309836i	0.846629	−	0.532183i	$-0.178628\pi$
$947$	−3.94940	−	9.53470i	−0.128338	−	0.309836i	−0.974968	+	0.222347i	$0.928628\pi$
$948$			0.636820i			0.0206830i
$949$	13.7492	−	5.69509i	0.446317	−	0.184870i
$950$	−3.38743	−	3.38743i	−0.109903	−	0.109903i
$951$	13.6583			0.442900
$952$	−7.72727	+	9.00866i	−0.250442	+	0.291972i
$953$	42.9949			1.39274			0.696371	−	0.717682i	$-0.254797\pi$
$953$	42.9949			1.39274			0.696371	+	0.717682i	$0.254797\pi$
$954$	−2.32790	−	2.32790i	−0.0753686	−	0.0753686i
$955$	6.04701	−	2.50475i	0.195677	−	0.0810519i
$956$			0.0105270i			0.000340467i
$957$	11.4949	+	27.7512i	0.371578	+	0.897068i
$958$	7.70859	+	3.19300i	0.249053	+	0.103161i
$959$	−6.62164	+	15.9861i	−0.213824	+	0.516217i
$960$	−22.2685	+	22.2685i	−0.718713	+	0.718713i
$961$	15.3301	−	15.3301i	0.494519	−	0.494519i
$962$	1.37483	−	3.31912i	0.0443262	−	0.107013i
$963$	6.03702	+	2.50061i	0.194540	+	0.0805811i
$964$	−0.300950	−	0.726558i	−0.00969295	−	0.0234009i
$965$		−	42.5712i		−	1.37041i
$966$	13.2560	−	5.49083i	0.426506	−	0.176665i
$967$	−29.8899	−	29.8899i	−0.961195	−	0.961195i	0.0380799	−	0.999275i	$-0.487876\pi$
$967$	−29.8899	−	29.8899i	−0.961195	−	0.961195i	−0.999275	+	0.0380799i	$0.987876\pi$
$968$	−26.3961			−0.848403
$969$	1.18149	+	15.4312i	0.0379549	+	0.495721i
$970$	−44.4361			−1.42676
$971$	−25.3846	−	25.3846i	−0.814630	−	0.814630i	0.170694	−	0.985324i	$-0.445399\pi$
$971$	−25.3846	−	25.3846i	−0.814630	−	0.814630i	−0.985324	+	0.170694i	$0.945399\pi$
$972$	0.165401	−	0.0685112i	0.00530523	−	0.00219750i
$973$			11.8356i			0.379432i
$974$	−21.2685	−	51.3467i	−0.681486	−	1.64525i
$975$	−10.1913	−	4.22136i	−0.326382	−	0.135192i
$976$	9.64073	−	23.2748i	0.308592	−	0.745007i
$977$	38.9197	−	38.9197i	1.24515	−	1.24515i	0.287315	−	0.957836i	$-0.407237\pi$
$977$	38.9197	−	38.9197i	1.24515	−	1.24515i	0.957836	−	0.287315i	$-0.0927627\pi$
$978$	21.3419	−	21.3419i	0.682438	−	0.682438i
$979$	4.09115	−	9.87690i	0.130754	−	0.315667i
$980$	0.382800	+	0.158561i	0.0122281	+	0.00506504i
$981$	−2.50116	−	6.03833i	−0.0798558	−	0.192789i
$982$			35.3516i			1.12811i
$983$	28.3755	−	11.7535i	0.905037	−	0.374879i	0.118882	−	0.992908i	$-0.462069\pi$
$983$	28.3755	−	11.7535i	0.905037	−	0.374879i	0.786155	+	0.618030i	$0.212069\pi$
$984$	−9.35493	−	9.35493i	−0.298224	−	0.298224i
$985$	59.7423			1.90355
$986$	25.0781	−	1.92011i	0.798650	−	0.0611487i
$987$	15.1071			0.480863
$988$	0.243621	+	0.243621i	0.00775061	+	0.00775061i
$989$	6.07795	−	2.51757i	0.193268	−	0.0800540i
$990$		−	10.2413i		−	0.325489i
$991$	−3.20534	−	7.73838i	−0.101821	−	0.245818i	0.864757	−	0.502191i	$-0.167472\pi$
$991$	−3.20534	−	7.73838i	−0.101821	−	0.245818i	−0.966578	+	0.256373i	$0.917472\pi$
$992$	1.03952	+	0.430582i	0.0330047	+	0.0136710i
$993$	−17.5833	+	42.4497i	−0.557988	+	1.34710i
$994$	0.211777	−	0.211777i	0.00671716	−	0.00671716i
$995$	−47.6588	+	47.6588i	−1.51089	+	1.51089i
$996$	0.0442305	−	0.106782i	0.00140150	−	0.00338351i
$997$	−14.9382	−	6.18759i	−0.473096	−	0.195963i	0.133379	−	0.991065i	$-0.457417\pi$
$997$	−14.9382	−	6.18759i	−0.473096	−	0.195963i	−0.606475	+	0.795102i	$0.707417\pi$
$998$	−13.8659	−	33.4754i	−0.438919	−	1.05964i
$999$			2.78038i			0.0879672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.11	✓	116
17.9	even	8	inner	731.2.m.b.689.11	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.11	✓	116	1.1	even	1	trivial
731.2.m.b.689.11	yes	116	17.9	even	8	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.993125 - 0.993125i) q^{2} +(-1.41917 + 0.587838i) q^{3} -0.0274062i q^{4} +(0.967808 + 2.33649i) q^{5} +(1.99321 + 0.825613i) q^{6} +(0.386865 - 0.933975i) q^{7} +(-2.01347 + 2.01347i) q^{8} +(-0.452840 + 0.452840i) q^{9} +O(q^{10})\)	\(q+(-0.993125 - 0.993125i) q^{2} +(-1.41917 + 0.587838i) q^{3} -0.0274062i q^{4} +(0.967808 + 2.33649i) q^{5} +(1.99321 + 0.825613i) q^{6} +(0.386865 - 0.933975i) q^{7} +(-2.01347 + 2.01347i) q^{8} +(-0.452840 + 0.452840i) q^{9} +(1.35928 - 3.28158i) q^{10} +(-4.15951 - 1.72293i) q^{11} +(0.0161104 + 0.0388940i) q^{12} -5.14463i q^{13} +(-1.31176 + 0.543349i) q^{14} +(-2.74696 - 2.74696i) q^{15} +3.94444 q^{16} +(1.86404 + 3.67768i) q^{17} +0.899452 q^{18} +(-1.72787 - 1.72787i) q^{19} +(0.0640345 - 0.0265240i) q^{20} +1.55288i q^{21} +(2.41983 + 5.84199i) q^{22} +(6.07795 + 2.51757i) q^{23} +(1.67385 - 4.04104i) q^{24} +(-0.987019 + 0.987019i) q^{25} +(-5.10926 + 5.10926i) q^{26} +(2.13997 - 5.16635i) q^{27} +(-0.0255967 - 0.0106025i) q^{28} +(1.66211 + 4.01269i) q^{29} +5.45615i q^{30} +(6.70561 - 2.77755i) q^{31} +(0.109617 + 0.109617i) q^{32} +6.91584 q^{33} +(1.80117 - 5.50362i) q^{34} +2.55664 q^{35} +(0.0124106 + 0.0124106i) q^{36} +(-0.459357 + 0.190272i) q^{37} +3.43198i q^{38} +(3.02421 + 7.30109i) q^{39} +(-6.65310 - 2.75581i) q^{40} +(1.15749 - 2.79443i) q^{41} +(1.54220 - 1.54220i) q^{42} +(0.707107 - 0.707107i) q^{43} +(-0.0472189 + 0.113997i) q^{44} +(-1.49632 - 0.619795i) q^{45} +(-3.53590 - 8.53642i) q^{46} -9.72841i q^{47} +(-5.59781 + 2.31869i) q^{48} +(4.22710 + 4.22710i) q^{49} +1.96047 q^{50} +(-4.80727 - 4.12349i) q^{51} -0.140995 q^{52} +(-2.58813 - 2.58813i) q^{53} +(-7.25609 + 3.00557i) q^{54} -11.3861i q^{55} +(1.10159 + 2.65947i) q^{56} +(3.46784 + 1.43643i) q^{57} +(2.33442 - 5.63579i) q^{58} +(7.93852 - 7.93852i) q^{59} +(-0.0752838 + 0.0752838i) q^{60} +(2.44413 - 5.90066i) q^{61} +(-9.41797 - 3.90105i) q^{62} +(0.247753 + 0.598129i) q^{63} -8.10660i q^{64} +(12.0204 - 4.97901i) q^{65} +(-6.86829 - 6.86829i) q^{66} -2.45429 q^{67} +(0.100791 - 0.0510864i) q^{68} -10.1055 q^{69} +(-2.53906 - 2.53906i) q^{70} +(-0.194881 + 0.0807225i) q^{71} -1.82356i q^{72} +(1.10700 + 2.67253i) q^{73} +(0.645163 + 0.267235i) q^{74} +(0.820537 - 1.98095i) q^{75} +(-0.0473544 + 0.0473544i) q^{76} +(-3.21834 + 3.21834i) q^{77} +(4.24748 - 10.2543i) q^{78} +(13.9754 + 5.78881i) q^{79} +(3.81746 + 9.21615i) q^{80} +6.66864i q^{81} +(-3.92475 + 1.62569i) q^{82} +(-1.94133 - 1.94133i) q^{83} +0.0425586 q^{84} +(-6.78884 + 7.91462i) q^{85} -1.40449 q^{86} +(-4.71763 - 4.71763i) q^{87} +(11.8441 - 4.90599i) q^{88} +2.37453i q^{89} +(0.870497 + 2.10157i) q^{90} +(-4.80496 - 1.99028i) q^{91} +(0.0689971 - 0.166574i) q^{92} +(-7.88363 + 7.88363i) q^{93} +(-9.66153 + 9.66153i) q^{94} +(2.36491 - 5.70940i) q^{95} +(-0.220002 - 0.0911279i) q^{96} +(-4.78749 - 11.5580i) q^{97} -8.39608i q^{98} +(2.66380 - 1.10338i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

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