LMFDB - Embedded newform 961.2.d.n.374.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6,-9,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			374.3
Root			$-2.52368i$ of defining polynomial
Character	$\chi$	$=$	961.374
Dual form			961.2.d.n.388.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.284315 - 0.206567i) q^{2} +(-2.34072 + 1.70063i) q^{3} +(-0.579869 - 1.78465i) q^{4} +2.97323 q^{5} +1.01680 q^{6} +(-0.334395 - 1.02916i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(1.65977 - 5.10826i) q^{9} +(-0.845333 - 0.614171i) q^{10} +(0.751335 + 2.31237i) q^{11} +(4.39235 + 3.19123i) q^{12} +(2.32483 - 1.68909i) q^{13} +(-0.117517 + 0.361681i) q^{14} +(-6.95951 + 5.05638i) q^{15} +(-2.64890 + 1.92454i) q^{16} +(0.563883 - 1.73545i) q^{17} +(-1.52709 + 1.10950i) q^{18} +(-1.71372 - 1.24509i) q^{19} +(-1.72408 - 5.30618i) q^{20} +(2.53296 + 1.84030i) q^{21} +(0.264043 - 0.812642i) q^{22} +(0.136652 - 0.420572i) q^{23} +(-1.21802 - 3.74869i) q^{24} +3.84010 q^{25} -1.00989 q^{26} +(2.11998 + 6.52462i) q^{27} +(-1.64279 + 1.19356i) q^{28} +(-2.55579 - 1.85689i) q^{29} +3.02317 q^{30} +3.87532 q^{32} +(-5.69116 - 4.13487i) q^{33} +(-0.518808 + 0.376936i) q^{34} +(-0.994234 - 3.05994i) q^{35} -10.0789 q^{36} -3.14675 q^{37} +(0.230042 + 0.707995i) q^{38} +(-2.56926 + 7.90738i) q^{39} +(-1.25168 + 3.85226i) q^{40} +(5.61962 + 4.08290i) q^{41} +(-0.340012 - 1.04645i) q^{42} +(-6.80576 - 4.94467i) q^{43} +(3.69110 - 2.68174i) q^{44} +(4.93489 - 15.1880i) q^{45} +(-0.125728 + 0.0913471i) q^{46} +(6.44144 - 4.67998i) q^{47} +(2.92741 - 9.00963i) q^{48} +(4.71576 - 3.42620i) q^{49} +(-1.09180 - 0.793236i) q^{50} +(1.63148 + 5.02118i) q^{51} +(-4.36254 - 3.16957i) q^{52} +(1.53798 - 4.73341i) q^{53} +(0.745029 - 2.29296i) q^{54} +(2.23389 + 6.87521i) q^{55} +1.47421 q^{56} +6.12878 q^{57} +(0.343078 + 1.05588i) q^{58} +(9.71948 - 7.06161i) q^{59} +(13.0595 + 9.48827i) q^{60} +14.4351 q^{61} -5.81225 q^{63} +(4.19600 + 3.04857i) q^{64} +(6.91226 - 5.02205i) q^{65} +(0.763955 + 2.35121i) q^{66} -6.43759 q^{67} -3.42416 q^{68} +(0.395375 + 1.21684i) q^{69} +(-0.349406 + 1.07536i) q^{70} +(0.518492 - 1.59575i) q^{71} +(5.91977 + 4.30097i) q^{72} +(-4.43754 - 13.6573i) q^{73} +(0.894668 + 0.650014i) q^{74} +(-8.98860 + 6.53060i) q^{75} +(-1.22832 + 3.78038i) q^{76} +(2.12856 - 1.54649i) q^{77} +(2.36388 - 1.71746i) q^{78} +(1.06538 - 3.27890i) q^{79} +(-7.87580 + 5.72210i) q^{80} +(-3.02226 - 2.19580i) q^{81} +(-0.754352 - 2.32166i) q^{82} +(10.3988 + 7.55516i) q^{83} +(1.81552 - 5.58758i) q^{84} +(1.67655 - 5.15991i) q^{85} +(0.913573 + 2.81169i) q^{86} +9.14030 q^{87} -3.31232 q^{88} +(-0.698188 - 2.14880i) q^{89} +(-4.54040 + 3.29880i) q^{90} +(-2.51576 - 1.82781i) q^{91} -0.829816 q^{92} -2.79812 q^{94} +(-5.09528 - 3.70194i) q^{95} +(-9.07105 + 6.59050i) q^{96} +(1.05463 + 3.24582i) q^{97} -2.04850 q^{98} +13.0592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 9 q^{3} - 14 q^{4} + 6 q^{5} + 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} - 14 q^{11} - 5 q^{12} + q^{13} + 27 q^{14} - 14 q^{15} - 2 q^{16} + 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots + 12 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 - 9 * q^3 - 14 * q^4 + 6 * q^5 + 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 - 14 * q^11 - 5 * q^12 + q^13 + 27 * q^14 - 14 * q^15 - 2 * q^16 + 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 + 3 * q^21 - 12 * q^22 - q^23 - 25 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 - 15 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 - 49 * q^34 - 9 * q^35 - 2 * q^36 - 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 + 18 * q^42 - 14 * q^43 + 33 * q^44 + 5 * q^45 - 34 * q^46 + 14 * q^47 + 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 - 17 * q^52 - 3 * q^53 + 46 * q^54 + q^55 + 60 * q^56 - 34 * q^57 + 15 * q^58 + 7 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 + 6 * q^65 - 30 * q^66 - 26 * q^67 + 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 - 11 * q^73 + 56 * q^74 - 4 * q^75 + 24 * q^76 - 18 * q^77 - 15 * q^78 + 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 + 28 * q^83 + 31 * q^84 - 37 * q^85 - 7 * q^86 - 30 * q^87 - 34 * q^88 - q^89 + 16 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 + 16 * q^96 + 3 * q^97 + 20 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.284315	−	0.206567i	−0.201041	−	0.146065i	0.482710	−	0.875780i	$-0.339653\pi$
$2$	−0.284315	−	0.206567i	−0.201041	−	0.146065i	−0.683751	+	0.729715i	$0.739653\pi$
$3$	−2.34072	+	1.70063i	−1.35142	+	0.981862i	−0.352477	+	0.935820i	$0.614661\pi$
$3$	−2.34072	+	1.70063i	−1.35142	+	0.981862i	−0.998940	+	0.0460413i	$0.985339\pi$
$4$	−0.579869	−	1.78465i	−0.289934	−	0.892327i
$5$	2.97323			1.32967			0.664834	−	0.746991i	$-0.268502\pi$
$5$	2.97323			1.32967			0.664834	+	0.746991i	$0.268502\pi$
$6$	1.01680			0.415106
$7$	−0.334395	−	1.02916i	−0.126390	−	0.388987i	0.867762	−	0.496980i	$-0.165558\pi$
$7$	−0.334395	−	1.02916i	−0.126390	−	0.388987i	−0.994152	+	0.107993i	$0.965558\pi$
$8$	−0.420982	+	1.29565i	−0.148840	+	0.458081i
$9$	1.65977	−	5.10826i	0.553258	−	1.70275i
$10$	−0.845333	−	0.614171i	−0.267318	−	0.194218i
$11$	0.751335	+	2.31237i	0.226536	+	0.697206i	0.998132	+	0.0610932i	$0.0194587\pi$
$11$	0.751335	+	2.31237i	0.226536	+	0.697206i	−0.771596	+	0.636113i	$0.780541\pi$
$12$	4.39235	+	3.19123i	1.26796	+	0.921229i
$13$	2.32483	−	1.68909i	0.644793	−	0.468469i	−0.216701	−	0.976238i	$-0.569530\pi$
$13$	2.32483	−	1.68909i	0.644793	−	0.468469i	0.861493	+	0.507769i	$0.169530\pi$
$14$	−0.117517	+	0.361681i	−0.0314078	+	0.0966634i
$15$	−6.95951	+	5.05638i	−1.79694	+	1.30555i
$16$	−2.64890	+	1.92454i	−0.662226	+	0.481135i
$17$	0.563883	−	1.73545i	0.136762	−	0.420910i	−0.859098	−	0.511811i	$-0.828975\pi$
$17$	0.563883	−	1.73545i	0.136762	−	0.420910i	0.995860	+	0.0909014i	$0.0289748\pi$
$18$	−1.52709	+	1.10950i	−0.359940	+	0.261511i
$19$	−1.71372	−	1.24509i	−0.393154	−	0.285643i	0.373593	−	0.927593i	$-0.378126\pi$
$19$	−1.71372	−	1.24509i	−0.393154	−	0.285643i	−0.766747	+	0.641950i	$0.778126\pi$
$20$	−1.72408	−	5.30618i	−0.385517	−	1.18650i
$21$	2.53296	+	1.84030i	0.552736	+	0.401586i
$22$	0.264043	−	0.812642i	0.0562942	−	0.173256i
$23$	0.136652	−	0.420572i	0.0284939	−	0.0876953i	−0.935798	−	0.352536i	$-0.885319\pi$
$23$	0.136652	−	0.420572i	0.0284939	−	0.0876953i	0.964292	+	0.264841i	$0.0853194\pi$
$24$	−1.21802	−	3.74869i	−0.248628	−	0.765198i
$25$	3.84010			0.768019
$26$	−1.00989			−0.198057
$27$	2.11998	+	6.52462i	0.407990	+	1.25566i
$28$	−1.64279	+	1.19356i	−0.310459	+	0.225561i
$29$	−2.55579	−	1.85689i	−0.474599	−	0.344816i	0.324632	−	0.945840i	$-0.394760\pi$
$29$	−2.55579	−	1.85689i	−0.474599	−	0.344816i	−0.799231	+	0.601024i	$0.794760\pi$
$30$	3.02317			0.551953
$31$		0			0
$31$		0			0
$32$	3.87532			0.685067
$33$	−5.69116	−	4.13487i	−0.990704	−	0.719789i
$34$	−0.518808	+	0.376936i	−0.0889748	+	0.0646440i
$35$	−0.994234	−	3.05994i	−0.168056	−	0.517224i
$36$	−10.0789			−1.67982
$37$	−3.14675			−0.517323			−0.258661	−	0.965968i	$-0.583281\pi$
$37$	−3.14675			−0.517323			−0.258661	+	0.965968i	$0.583281\pi$
$38$	0.230042	+	0.707995i	0.0373177	+	0.114852i
$39$	−2.56926	+	7.90738i	−0.411412	+	1.26619i
$40$	−1.25168	+	3.85226i	−0.197907	+	0.609096i
$41$	5.61962	+	4.08290i	0.877638	+	0.637641i	0.932625	−	0.360846i	$-0.117512\pi$
$41$	5.61962	+	4.08290i	0.877638	+	0.637641i	−0.0549877	+	0.998487i	$0.517512\pi$
$42$	−0.340012	−	1.04645i	−0.0524650	−	0.161471i
$43$	−6.80576	−	4.94467i	−1.03787	−	0.754055i	−0.0680000	−	0.997685i	$-0.521662\pi$
$43$	−6.80576	−	4.94467i	−1.03787	−	0.754055i	−0.969868	+	0.243630i	$0.921662\pi$
$44$	3.69110	−	2.68174i	0.556455	−	0.404288i
$45$	4.93489	−	15.1880i	0.735649	−	2.26410i
$46$	−0.125728	+	0.0913471i	−0.0185377	+	0.0134684i
$47$	6.44144	−	4.67998i	0.939580	−	0.682645i	−0.00873953	−	0.999962i	$-0.502782\pi$
$47$	6.44144	−	4.67998i	0.939580	−	0.682645i	0.948320	+	0.317317i	$0.102782\pi$
$48$	2.92741	−	9.00963i	0.422535	−	1.30043i
$49$	4.71576	−	3.42620i	0.673680	−	0.489457i
$50$	−1.09180	−	0.793236i	−0.154403	−	0.112181i
$51$	1.63148	+	5.02118i	0.228453	+	0.703105i
$52$	−4.36254	−	3.16957i	−0.604975	−	0.439540i
$53$	1.53798	−	4.73341i	0.211257	−	0.650183i	−0.788141	−	0.615495i	$-0.788956\pi$
$53$	1.53798	−	4.73341i	0.211257	−	0.650183i	0.999398	−	0.0346884i	$-0.0110439\pi$
$54$	0.745029	−	2.29296i	0.101386	−	0.312033i
$55$	2.23389	+	6.87521i	0.301218	+	0.927053i
$56$	1.47421			0.196999
$57$	6.12878			0.811777
$58$	0.343078	+	1.05588i	0.0450483	+	0.138644i
$59$	9.71948	−	7.06161i	1.26537	−	0.919344i	0.266360	−	0.963874i	$-0.414179\pi$
$59$	9.71948	−	7.06161i	1.26537	−	0.919344i	0.999008	+	0.0445297i	$0.0141789\pi$
$60$	13.0595	+	9.48827i	1.68597	+	1.22493i
$61$	14.4351			1.84823			0.924115	−	0.382115i	$-0.124804\pi$
$61$	14.4351			1.84823			0.924115	+	0.382115i	$0.124804\pi$
$62$		0			0
$63$	−5.81225			−0.732274
$64$	4.19600	+	3.04857i	0.524499	+	0.381071i
$65$	6.91226	−	5.02205i	0.857361	−	0.622909i
$66$	0.763955	+	2.35121i	0.0940363	+	0.289414i
$67$	−6.43759			−0.786476			−0.393238	−	0.919437i	$-0.628645\pi$
$67$	−6.43759			−0.786476			−0.393238	+	0.919437i	$0.628645\pi$
$68$	−3.42416			−0.415241
$69$	0.395375	+	1.21684i	0.0475975	+	0.146490i
$70$	−0.349406	+	1.07536i	−0.0417620	+	0.128530i
$71$	0.518492	−	1.59575i	0.0615337	−	0.189381i	−0.915564	−	0.402172i	$-0.868255\pi$
$71$	0.518492	−	1.59575i	0.0615337	−	0.189381i	0.977098	+	0.212791i	$0.0682553\pi$
$72$	5.91977	+	4.30097i	0.697652	+	0.506874i
$73$	−4.43754	−	13.6573i	−0.519374	−	1.59847i	−0.775179	−	0.631741i	$-0.782341\pi$
$73$	−4.43754	−	13.6573i	−0.519374	−	1.59847i	0.255805	−	0.966728i	$-0.417659\pi$
$74$	0.894668	+	0.650014i	0.104003	+	0.0755626i
$75$	−8.98860	+	6.53060i	−1.03791	+	0.754089i
$76$	−1.22832	+	3.78038i	−0.140898	+	0.433640i
$77$	2.12856	−	1.54649i	0.242572	−	0.176239i
$78$	2.36388	−	1.71746i	0.267657	−	0.194464i
$79$	1.06538	−	3.27890i	0.119865	−	0.368906i	−0.873066	−	0.487602i	$-0.837872\pi$
$79$	1.06538	−	3.27890i	0.119865	−	0.368906i	0.992931	+	0.118697i	$0.0378716\pi$
$80$	−7.87580	+	5.72210i	−0.880541	+	0.639751i
$81$	−3.02226	−	2.19580i	−0.335806	−	0.243977i
$82$	−0.754352	−	2.32166i	−0.0833042	−	0.256384i
$83$	10.3988	+	7.55516i	1.14142	+	0.829287i	0.987316	−	0.158768i	$-0.0507523\pi$
$83$	10.3988	+	7.55516i	1.14142	+	0.829287i	0.154100	+	0.988055i	$0.450752\pi$
$84$	1.81552	−	5.58758i	0.198089	−	0.609655i
$85$	1.67655	−	5.15991i	0.181848	−	0.559670i
$86$	0.913573	+	2.81169i	0.0985131	+	0.303192i
$87$	9.14030			0.979943
$88$	−3.31232			−0.353094
$89$	−0.698188	−	2.14880i	−0.0740078	−	0.227773i	0.907209	−	0.420680i	$-0.138208\pi$
$89$	−0.698188	−	2.14880i	−0.0740078	−	0.227773i	−0.981217	+	0.192907i	$0.938208\pi$
$90$	−4.54040	+	3.29880i	−0.478600	+	0.347724i
$91$	−2.51576	−	1.82781i	−0.263724	−	0.191606i
$92$	−0.829816			−0.0865143
$93$		0			0
$94$	−2.79812			−0.288604
$95$	−5.09528	−	3.70194i	−0.522765	−	0.379811i
$96$	−9.07105	+	6.59050i	−0.925810	+	0.672641i
$97$	1.05463	+	3.24582i	0.107082	+	0.329563i	0.990213	−	0.139562i	$-0.0445693\pi$
$97$	1.05463	+	3.24582i	0.107082	+	0.329563i	−0.883132	+	0.469125i	$0.844569\pi$
$98$	−2.04850			−0.206930
$99$	13.0592			1.31250
$100$	−2.22675	−	6.85324i	−0.222675	−	0.685324i
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	−0.176741	−	0.984257i	$-0.556555\pi$
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	0.721518	−	0.692395i	$-0.243445\pi$
$102$	0.573355	−	1.76460i	0.0567706	−	0.174722i
$103$	−6.53188	−	4.74569i	−0.643605	−	0.467607i	0.217482	−	0.976064i	$-0.430216\pi$
$103$	−6.53188	−	4.74569i	−0.643605	−	0.467607i	−0.861087	+	0.508458i	$0.830216\pi$
$104$	1.20976	+	3.72325i	0.118626	+	0.365094i
$105$	7.53106	+	5.47164i	0.734956	+	0.533977i
$106$	−1.41503	+	1.02808i	−0.137440	+	0.0998562i
$107$	−3.75493	+	11.5565i	−0.363002	+	1.11721i	0.588220	+	0.808701i	$0.299829\pi$
$107$	−3.75493	+	11.5565i	−0.363002	+	1.11721i	−0.951223	+	0.308506i	$0.900171\pi$
$108$	10.4149	−	7.56685i	1.00217	−	0.728121i
$109$	0.511381	−	0.371540i	0.0489815	−	0.0355871i	−0.563025	−	0.826440i	$-0.690363\pi$
$109$	0.511381	−	0.371540i	0.0489815	−	0.0355871i	0.612007	+	0.790853i	$0.290363\pi$
$110$	0.785062	−	2.41617i	0.0748527	−	0.230373i
$111$	7.36567	−	5.35147i	0.699119	−	0.507939i
$112$	2.86645	+	2.08260i	0.270854	+	0.196787i
$113$	−3.49200	−	10.7473i	−0.328500	−	1.01102i	−0.969836	−	0.243758i	$-0.921620\pi$
$113$	−3.49200	−	10.7473i	−0.328500	−	1.01102i	0.641337	−	0.767260i	$-0.278380\pi$
$114$	−1.74250	−	1.26600i	−0.163200	−	0.118572i
$115$	0.406298	−	1.25046i	0.0378875	−	0.116606i
$116$	−1.83188	+	5.63796i	−0.170086	+	0.523472i
$117$	−4.76961	−	14.6794i	−0.440951	−	1.35711i
$118$	−4.22209			−0.388675
$119$	−1.97463			−0.181014
$120$	−3.62146	−	11.1457i	−0.330593	−	1.01746i
$121$	4.11663	−	2.99091i	0.374239	−	0.271901i
$122$	−4.10412	−	2.98182i	−0.371570	−	0.269961i
$123$	−20.0975			−1.81213
$124$		0			0
$125$	−3.44866			−0.308458
$126$	1.65251	+	1.20062i	0.147217	+	0.106960i
$127$	0.0953072	−	0.0692447i	0.00845715	−	0.00614448i	−0.583549	−	0.812078i	$-0.698336\pi$
$127$	0.0953072	−	0.0692447i	0.00845715	−	0.00614448i	0.592006	+	0.805934i	$0.298336\pi$
$128$	−2.95833	−	9.10481i	−0.261482	−	0.804759i
$129$	24.3395			2.14297
$130$	−3.00265			−0.263350
$131$	1.78734	+	5.50087i	0.156161	+	0.480613i	0.998277	−	0.0586835i	$-0.0186903\pi$
$131$	1.78734	+	5.50087i	0.156161	+	0.480613i	−0.842116	+	0.539296i	$0.818690\pi$
$132$	−4.07918	+	12.5544i	−0.355047	+	1.09272i
$133$	−0.708341	+	2.18005i	−0.0614209	+	0.189034i
$134$	1.83030	+	1.32979i	0.158114	+	0.114877i
$135$	6.30318	+	19.3992i	0.542492	+	1.66962i
$136$	2.01116	+	1.46119i	0.172455	+	0.125296i
$137$	9.55079	−	6.93905i	0.815979	−	0.592843i	−0.0995790	−	0.995030i	$-0.531750\pi$
$137$	9.55079	−	6.93905i	0.815979	−	0.592843i	0.915558	+	0.402186i	$0.131750\pi$
$138$	0.138947	−	0.427636i	0.0118280	−	0.0364028i
$139$	−12.4767	+	9.06482i	−1.05826	+	0.768868i	−0.973765	−	0.227556i	$-0.926927\pi$
$139$	−12.4767	+	9.06482i	−1.05826	+	0.768868i	−0.0844915	+	0.996424i	$0.526927\pi$
$140$	−4.88440	+	3.54873i	−0.412807	+	0.299922i
$141$	−7.11868	+	21.9091i	−0.599501	+	1.84508i
$142$	−0.477045	+	0.346593i	−0.0400327	+	0.0290855i
$143$	5.65253	+	4.10680i	0.472688	+	0.343428i
$144$	5.43447	+	16.7256i	0.452872	+	1.39380i
$145$	−7.59896	−	5.52097i	−0.631060	−	0.458492i
$146$	−1.55949	+	4.79963i	−0.129065	+	0.397220i
$147$	−5.21157	+	16.0396i	−0.429843	+	1.32292i
$148$	1.82470	+	5.61586i	0.149990	+	0.461621i
$149$	−11.9502			−0.979001			−0.489500	−	0.872003i	$-0.662821\pi$
$149$	−11.9502			−0.979001			−0.489500	+	0.872003i	$0.662821\pi$
$150$	3.90460			0.318809
$151$	1.33561	+	4.11059i	0.108691	+	0.334515i	0.990579	−	0.136943i	$-0.0437278\pi$
$151$	1.33561	+	4.11059i	0.108691	+	0.334515i	−0.881888	+	0.471458i	$0.843728\pi$
$152$	2.33465	−	1.69622i	0.189365	−	0.137582i
$153$	−7.92923	−	5.76092i	−0.641040	−	0.465743i
$154$	−0.924636			−0.0745093
$155$		0			0
$156$	15.6018			1.24914
$157$	7.04204	+	5.11634i	0.562016	+	0.408328i	0.832196	−	0.554481i	$-0.187083\pi$
$157$	7.04204	+	5.11634i	0.562016	+	0.408328i	−0.270180	+	0.962810i	$0.587083\pi$
$158$	−0.980216	+	0.712169i	−0.0779818	+	0.0566571i
$159$	4.44982	+	13.6951i	0.352893	+	1.08609i
$160$	11.5222			0.910912
$161$	−0.478533			−0.0377137
$162$	0.405693	+	1.24860i	0.0318743	+	0.0980989i
$163$	0.966575	−	2.97481i	0.0757080	−	0.233005i	−0.906040	−	0.423192i	$-0.860909\pi$
$163$	0.966575	−	2.97481i	0.0757080	−	0.233005i	0.981748	+	0.190187i	$0.0609095\pi$
$164$	4.02791	−	12.3966i	0.314527	−	0.968014i
$165$	−16.9211	−	12.2939i	−1.31731	−	0.957081i
$166$	−1.39588	−	4.29609i	−0.108342	−	0.333441i
$167$	−10.8044	−	7.84983i	−0.836067	−	0.607438i	0.0852022	−	0.996364i	$-0.472846\pi$
$167$	−10.8044	−	7.84983i	−0.836067	−	0.607438i	−0.921269	+	0.388925i	$0.872846\pi$
$168$	−3.45071	+	2.50709i	−0.266228	+	0.193426i
$169$	−1.46540	+	4.51003i	−0.112723	+	0.346925i
$170$	−1.54253	+	1.12072i	−0.118307	+	0.0859551i
$171$	−9.20462	+	6.68755i	−0.703895	+	0.511410i
$172$	−4.87808	+	15.0132i	−0.371950	+	1.14474i
$173$	−15.4075	+	11.1942i	−1.17141	+	0.851080i	−0.991177	−	0.132543i	$-0.957686\pi$
$173$	−15.4075	+	11.1942i	−1.17141	+	0.851080i	−0.180235	+	0.983624i	$0.557686\pi$
$174$	−2.59872	−	1.88808i	−0.197009	−	0.143135i
$175$	−1.28411	−	3.95208i	−0.0970696	−	0.298749i
$176$	−6.44047	−	4.67927i	−0.485468	−	0.352713i
$177$	−10.7414	+	33.0586i	−0.807371	+	2.48483i
$178$	−0.245366	+	0.755159i	−0.0183910	+	0.0566016i
$179$	0.0245143	+	0.0754473i	0.00183229	+	0.00563919i	0.951968	−	0.306196i	$-0.0990563\pi$
$179$	0.0245143	+	0.0754473i	0.00183229	+	0.00563919i	−0.950136	+	0.311835i	$0.899056\pi$
$180$	−29.9669			−2.23360
$181$	−2.16285			−0.160763			−0.0803817	−	0.996764i	$-0.525614\pi$
$181$	−2.16285			−0.160763			−0.0803817	+	0.996764i	$0.525614\pi$
$182$	0.337704	+	1.03935i	0.0250323	+	0.0770415i
$183$	−33.7886	+	24.5489i	−2.49773	+	1.81471i
$184$	0.487386	+	0.354107i	0.0359306	+	0.0261051i
$185$	−9.35601			−0.687868
$186$		0			0
$187$	4.43668			0.324442
$188$	−12.0873	−	8.78195i	−0.881559	−	0.640490i
$189$	6.00599	−	4.36361i	0.436871	−	0.317406i
$190$	0.683966	+	2.10503i	0.0496201	+	0.152715i
$191$	−5.34169			−0.386511			−0.193256	−	0.981148i	$-0.561905\pi$
$191$	−5.34169			−0.386511			−0.193256	+	0.981148i	$0.561905\pi$
$192$	−15.0062			−1.08298
$193$	−0.659342	−	2.02925i	−0.0474605	−	0.146068i	0.924518	−	0.381139i	$-0.124468\pi$
$193$	−0.659342	−	2.02925i	−0.0474605	−	0.146068i	−0.971978	+	0.235070i	$0.924468\pi$
$194$	0.370632	−	1.14069i	0.0266098	−	0.0818966i
$195$	−7.63901	+	23.5105i	−0.547041	+	1.68362i
$196$	−8.84911	−	6.42925i	−0.632079	−	0.459232i
$197$	1.81570	+	5.58815i	0.129363	+	0.398139i	0.994671	−	0.103102i	$-0.0328769\pi$
$197$	1.81570	+	5.58815i	0.129363	+	0.398139i	−0.865307	+	0.501241i	$0.832877\pi$
$198$	−3.71293	−	2.69760i	−0.263867	−	0.191710i
$199$	5.60484	−	4.07215i	0.397317	−	0.288667i	−0.371131	−	0.928581i	$-0.621030\pi$
$199$	5.60484	−	4.07215i	0.397317	−	0.288667i	0.768447	+	0.639913i	$0.221030\pi$
$200$	−1.61661	+	4.97542i	−0.114312	+	0.351815i
$201$	15.0686	−	10.9480i	1.06286	−	0.772211i
$202$	−5.03729	+	3.65981i	−0.354423	+	0.257503i
$203$	−1.05640	+	3.25126i	−0.0741447	+	0.228194i
$204$	8.01501	−	5.82325i	0.561163	−	0.407709i
$205$	16.7084	+	12.1394i	1.16697	+	0.847852i
$206$	0.876809	+	2.69854i	0.0610901	+	0.188016i
$207$	−1.92158	−	1.39611i	−0.133559	−	0.0970363i
$208$	−2.90754	+	8.94847i	−0.201601	+	0.620465i
$209$	1.59153	−	4.89823i	0.110089	−	0.338818i
$210$	−1.01093	−	3.11133i	−0.0697611	−	0.214702i
$211$	16.7087			1.15028			0.575139	−	0.818056i	$-0.304948\pi$
$211$	16.7087			1.15028			0.575139	+	0.818056i	$0.304948\pi$
$212$	−9.33931			−0.641427
$213$	1.50015	+	4.61698i	0.102788	+	0.316350i
$214$	3.45476	−	2.51003i	0.236163	−	0.171582i
$215$	−20.2351	−	14.7016i	−1.38002	−	1.00264i
$216$	−9.34610			−0.635921
$217$		0			0
$218$	−0.222141			−0.0150453
$219$	33.6132	+	24.4214i	2.27137	+	1.65024i
$220$	10.9745	−	7.97344i	0.739901	−	0.537569i
$221$	−1.62040	−	4.98709i	−0.109000	−	0.335468i
$222$	−3.19961			−0.214744
$223$	6.26156			0.419305			0.209653	−	0.977776i	$-0.432767\pi$
$223$	6.26156			0.419305			0.209653	+	0.977776i	$0.432767\pi$
$224$	−1.29589	−	3.98834i	−0.0865852	−	0.266482i
$225$	6.37369	−	19.6162i	0.424912	−	1.30775i
$226$	−1.22720	+	3.77694i	−0.0816322	+	0.251238i
$227$	6.34877	+	4.61265i	0.421383	+	0.306153i	0.778194	−	0.628024i	$-0.216136\pi$
$227$	6.34877	+	4.61265i	0.421383	+	0.306153i	−0.356811	+	0.934177i	$0.616136\pi$
$228$	−3.55389	−	10.9378i	−0.235362	−	0.724370i
$229$	10.3336	+	7.50777i	0.682861	+	0.496128i	0.874306	−	0.485376i	$-0.161317\pi$
$229$	10.3336	+	7.50777i	0.682861	+	0.496128i	−0.191445	+	0.981503i	$0.561317\pi$
$230$	−0.373820	+	0.271596i	−0.0246489	+	0.0179085i
$231$	−2.35236	+	7.23982i	−0.154774	+	0.476345i
$232$	3.48183	−	2.52969i	0.228593	−	0.166083i
$233$	−10.2887	+	7.47514i	−0.674032	+	0.489713i	−0.871373	−	0.490622i	$-0.836770\pi$
$233$	−10.2887	+	7.47514i	−0.674032	+	0.489713i	0.197340	+	0.980335i	$0.436770\pi$
$234$	−1.67620	+	5.15880i	−0.109576	+	0.337241i
$235$	19.1519	−	13.9146i	1.24933	−	0.907692i
$236$	−18.2386	−	13.2511i	−1.18723	−	0.862572i
$237$	3.08246	+	9.48683i	0.200227	+	0.616236i
$238$	0.561415	+	0.407892i	0.0363912	+	0.0264397i
$239$	7.85664	−	24.1802i	0.508204	−	1.56409i	−0.287114	−	0.957897i	$-0.592696\pi$
$239$	7.85664	−	24.1802i	0.508204	−	1.56409i	0.795317	−	0.606193i	$-0.207304\pi$
$240$	8.70385	−	26.7877i	0.561831	−	1.72914i
$241$	−0.729583	−	2.24543i	−0.0469966	−	0.144641i	0.924805	−	0.380443i	$-0.124228\pi$
$241$	−0.729583	−	2.24543i	−0.0469966	−	0.144641i	−0.971801	+	0.235802i	$0.924228\pi$
$242$	−1.78824			−0.114953
$243$	−9.77268			−0.626918
$244$	−8.37048	−	25.7617i	−0.535865	−	1.64922i
$245$	14.0210	−	10.1869i	0.895772	−	0.650816i
$246$	5.71401	+	4.15147i	0.364312	+	0.264688i
$247$	−6.08718			−0.387318
$248$		0			0
$249$	−37.1893			−2.35677
$250$	0.980506	+	0.712379i	0.0620126	+	0.0450548i
$251$	1.90656	−	1.38520i	0.120341	−	0.0874328i	−0.525987	−	0.850493i	$-0.676304\pi$
$251$	1.90656	−	1.38520i	0.120341	−	0.0874328i	0.646328	+	0.763060i	$0.276304\pi$
$252$	3.37034	+	10.3728i	0.212312	+	0.653428i
$253$	1.07519			0.0675966
$254$	−0.0414009			−0.00259772
$255$	4.85076	+	14.9291i	0.303767	+	0.934897i
$256$	2.16580	−	6.66565i	0.135363	−	0.416603i
$257$	−8.03877	+	24.7408i	−0.501445	+	1.54329i	0.305222	+	0.952281i	$0.401269\pi$
$257$	−8.03877	+	24.7408i	−0.501445	+	1.54329i	−0.806666	+	0.591007i	$0.798731\pi$
$258$	−6.92007	−	5.02773i	−0.430825	−	0.313013i
$259$	1.05226	+	3.23852i	0.0653842	+	0.201232i
$260$	−12.9708	−	9.42386i	−0.804417	−	0.584443i
$261$	−13.7275	+	9.97363i	−0.849712	+	0.617352i
$262$	0.628129	−	1.93318i	0.0388059	−	0.119432i
$263$	18.5552	−	13.4812i	1.14417	−	0.831285i	0.156471	−	0.987683i	$-0.449988\pi$
$263$	18.5552	−	13.4812i	1.14417	−	0.831285i	0.987694	+	0.156398i	$0.0499881\pi$
$264$	7.75322	−	5.63304i	0.477178	−	0.346690i
$265$	4.57276	−	14.0735i	0.280902	−	0.864529i
$266$	0.651718	−	0.473500i	0.0399594	−	0.0290322i
$267$	5.28859	+	3.84239i	0.323657	+	0.235150i
$268$	3.73296	+	11.4889i	0.228027	+	0.701794i
$269$	−13.7916	−	10.0202i	−0.840887	−	0.610940i	0.0817310	−	0.996654i	$-0.473955\pi$
$269$	−13.7916	−	10.0202i	−0.840887	−	0.610940i	−0.922618	+	0.385714i	$0.873955\pi$
$270$	2.21514	−	6.81751i	0.134809	−	0.414901i
$271$	−2.23929	+	6.89184i	−0.136027	+	0.418649i	−0.995748	−	0.0921146i	$-0.970637\pi$
$271$	−2.23929	+	6.89184i	−0.136027	+	0.418649i	0.859721	+	0.510764i	$0.170637\pi$
$272$	1.84628	+	5.68227i	0.111947	+	0.344538i
$273$	8.99714			0.544531
$274$	−4.14881			−0.250639
$275$	2.88520	+	8.87972i	0.173984	+	0.535467i
$276$	1.94237	−	1.41121i	0.116917	−	0.0849450i
$277$	12.2188	+	8.87748i	0.734157	+	0.533396i	0.890876	−	0.454247i	$-0.150092\pi$
$277$	12.2188	+	8.87748i	0.734157	+	0.533396i	−0.156719	+	0.987643i	$0.550092\pi$
$278$	5.41979			0.325058
$279$		0			0
$280$	4.38316			0.261944
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	0.646181	−	0.763184i	$-0.276365\pi$
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	−0.526150	+	0.850392i	$0.676365\pi$
$282$	6.54963	−	4.75859i	0.390025	−	0.283370i
$283$	−1.46052	−	4.49503i	−0.0868192	−	0.267202i	0.898216	−	0.439554i	$-0.144863\pi$
$283$	−1.46052	−	4.49503i	−0.0868192	−	0.267202i	−0.985035	+	0.172352i	$0.944863\pi$
$284$	−3.14852			−0.186831
$285$	18.2223			1.07939
$286$	−0.758769	−	2.33525i	−0.0448670	−	0.138086i
$287$	2.32279	−	7.14881i	0.137110	−	0.421981i
$288$	6.43215	−	19.7961i	0.379018	−	1.16650i
$289$	11.0595	+	8.03516i	0.650556	+	0.472657i
$290$	1.02005	+	3.13939i	0.0598993	+	0.184351i
$291$	−7.98856	−	5.80403i	−0.468298	−	0.340238i
$292$	−21.8004	+	15.8389i	−1.27577	+	0.926903i
$293$	−3.25979	+	10.0326i	−0.190439	+	0.586110i	−1.00000		0.000925815i	$-0.999705\pi$
$293$	−3.25979	+	10.0326i	−0.190439	+	0.586110i	0.809561	+	0.587036i	$0.199705\pi$
$294$	4.79497	−	3.48375i	0.279648	−	0.203177i
$295$	28.8982	−	20.9958i	1.68252	−	1.22242i
$296$	1.32473	−	4.07709i	0.0769981	−	0.236976i
$297$	−13.4945	+	9.80435i	−0.783032	+	0.568906i
$298$	3.39763	+	2.46852i	0.196819	+	0.142998i
$299$	−0.392691	−	1.20858i	−0.0227099	−	0.0698939i
$300$	16.8671	+	12.2546i	0.973820	+	0.707522i
$301$	−2.81306	+	8.65771i	−0.162142	+	0.499022i
$302$	0.469377	−	1.44459i	0.0270096	−	0.0831271i
$303$	15.8406	+	48.7524i	0.910020	+	2.80075i
$304$	6.93570			0.397790
$305$	42.9190			2.45753
$306$	1.06438	+	3.27583i	0.0608467	+	0.187267i
$307$	−2.14268	+	1.55675i	−0.122289	+	0.0888485i	−0.647249	−	0.762279i	$-0.724081\pi$
$307$	−2.14268	+	1.55675i	−0.122289	+	0.0888485i	0.524959	+	0.851127i	$0.324081\pi$
$308$	−3.99424	−	2.90198i	−0.227593	−	0.165356i
$309$	23.3600			1.32890
$310$		0			0
$311$	5.51283			0.312604			0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283			0.312604			0.156302	+	0.987709i	$0.450043\pi$
$312$	−9.16358	−	6.65773i	−0.518786	−	0.376920i
$313$	−21.5809	+	15.6794i	−1.21982	+	0.886254i	−0.996086	−	0.0883946i	$-0.971826\pi$
$313$	−21.5809	+	15.6794i	−1.21982	+	0.886254i	−0.223739	+	0.974649i	$0.571826\pi$
$314$	−0.945290	−	2.90930i	−0.0533458	−	0.164181i
$315$	−17.2811			−0.973682
$316$	−6.46949			−0.363937
$317$	3.31891	+	10.2146i	0.186409	+	0.573707i	0.999970	−	0.00777223i	$-0.00247400\pi$
$317$	3.31891	+	10.2146i	0.186409	+	0.573707i	−0.813561	+	0.581480i	$0.802474\pi$
$318$	1.56381	−	4.81291i	0.0876941	−	0.269895i
$319$	2.37357	−	7.30509i	0.132894	−	0.409007i
$320$	12.4757	+	9.06410i	0.697411	+	0.506698i
$321$	−10.8641	−	33.4362i	−0.606375	−	1.86623i
$322$	0.136054	+	0.0988491i	0.00758200	+	0.00550864i
$323$	−3.12714	+	2.27200i	−0.173998	+	0.126417i
$324$	−2.16622	+	6.66695i	−0.120346	+	0.370386i
$325$	8.92758	−	6.48627i	0.495213	−	0.359793i
$326$	−0.889309	+	0.646121i	−0.0492543	+	0.0357853i
$327$	−0.565148	+	1.73935i	−0.0312527	+	0.0961860i
$328$	−7.65576	+	5.56224i	−0.422719	+	0.307123i
$329$	−6.97044	−	5.06432i	−0.384293	−	0.279205i
$330$	2.27141	+	6.99069i	0.125037	+	0.384825i
$331$	15.8953	+	11.5486i	0.873682	+	0.634767i	0.931572	−	0.363556i	$-0.118437\pi$
$331$	15.8953	+	11.5486i	0.873682	+	0.634767i	−0.0578904	+	0.998323i	$0.518437\pi$
$332$	7.45341	−	22.9392i	0.409059	−	1.25895i
$333$	−5.22289	+	16.0744i	−0.286213	+	0.880872i
$334$	1.45033	+	4.46365i	0.0793584	+	0.244240i
$335$	−19.1404			−1.04575
$336$	−10.2513			−0.559254
$337$	−5.92655	−	18.2401i	−0.322840	−	0.993599i	−0.972406	−	0.233294i	$-0.925050\pi$
$337$	−5.92655	−	18.2401i	−0.322840	−	0.993599i	0.649566	−	0.760305i	$-0.274950\pi$
$338$	1.34826	−	0.979565i	0.0733355	−	0.0532813i
$339$	26.4510	+	19.2178i	1.43662	+	1.04376i
$340$	−10.1808			−0.552133
$341$		0			0
$342$	3.99844			0.216211
$343$	−11.2313	−	8.15999i	−0.606431	−	0.440598i
$344$	9.27166	−	6.73626i	0.499895	−	0.363195i
$345$	1.17554	+	3.61794i	0.0632889	+	0.194783i
$346$	6.69294			0.359815
$347$	−10.6600			−0.572257			−0.286128	−	0.958191i	$-0.592368\pi$
$347$	−10.6600			−0.572257			−0.286128	+	0.958191i	$0.592368\pi$
$348$	−5.30018	−	16.3123i	−0.284119	−	0.874429i
$349$	−5.77910	+	17.7862i	−0.309348	+	0.952075i	0.668671	+	0.743559i	$0.266864\pi$
$349$	−5.77910	+	17.7862i	−0.309348	+	0.952075i	−0.978019	+	0.208517i	$0.933136\pi$
$350$	−0.451278	+	1.38889i	−0.0241218	+	0.0742393i
$351$	15.9493	+	11.5878i	0.851309	+	0.618513i
$352$	2.91166	+	8.96118i	0.155192	+	0.477632i
$353$	−10.2440	−	7.44268i	−0.545232	−	0.396134i	0.280793	−	0.959768i	$-0.409403\pi$
$353$	−10.2440	−	7.44268i	−0.545232	−	0.396134i	−0.826024	+	0.563635i	$0.809403\pi$
$354$	9.88273	−	7.18023i	0.525261	−	0.381625i
$355$	1.54160	−	4.74454i	0.0818194	−	0.251814i
$356$	−3.43001	+	2.49205i	−0.181790	+	0.132078i
$357$	4.62205	−	3.35812i	0.244625	−	0.177730i
$358$	0.00861512	−	0.0265146i	0.000455323	−	0.00140134i
$359$	18.3470	−	13.3299i	0.968317	−	0.703523i	0.0132495	−	0.999912i	$-0.495782\pi$
$359$	18.3470	−	13.3299i	0.968317	−	0.703523i	0.955067	+	0.296389i	$0.0957824\pi$
$360$	17.6008	+	12.7878i	0.927646	+	0.673974i
$361$	−4.48474	−	13.8026i	−0.236039	−	0.726453i
$362$	0.614931	+	0.446773i	0.0323200	+	0.0234819i
$363$	−4.54945	+	14.0018i	−0.238784	+	0.734903i
$364$	−1.80319	+	5.54965i	−0.0945129	+	0.290881i
$365$	−13.1938	−	40.6064i	−0.690596	−	2.12543i
$366$	14.6776			0.767210
$367$	−8.71968			−0.455164			−0.227582	−	0.973759i	$-0.573082\pi$
$367$	−8.71968			−0.455164			−0.227582	+	0.973759i	$0.573082\pi$
$368$	0.447430	+	1.37705i	0.0233239	+	0.0717836i
$369$	30.1838	−	21.9298i	1.57130	−	1.14162i
$370$	2.66005	+	1.93264i	0.138290	+	0.100473i
$371$	−5.38574			−0.279614
$372$		0			0
$373$	25.4134			1.31586			0.657928	−	0.753081i	$-0.271433\pi$
$373$	25.4134			1.31586			0.657928	+	0.753081i	$0.271433\pi$
$374$	−1.26141	−	0.916471i	−0.0652262	−	0.0473896i
$375$	8.07236	−	5.86491i	0.416855	−	0.302863i
$376$	3.35188	+	10.3160i	0.172860	+	0.532009i
$377$	−9.07826			−0.467554
$378$	−2.60897			−0.134191
$379$	6.82862	+	21.0163i	0.350763	+	1.07954i	0.958426	+	0.285342i	$0.0921071\pi$
$379$	6.82862	+	21.0163i	0.350763	+	1.07954i	−0.607663	+	0.794195i	$0.707893\pi$
$380$	−3.65208	+	11.2399i	−0.187348	+	0.576597i
$381$	−0.105328	+	0.324165i	−0.00539610	+	0.0166075i
$382$	1.51872	+	1.10342i	0.0777046	+	0.0564557i
$383$	8.23303	+	25.3386i	0.420688	+	1.29474i	0.907063	+	0.420994i	$0.138319\pi$
$383$	8.23303	+	25.3386i	0.420688	+	1.29474i	−0.486375	+	0.873750i	$0.661681\pi$
$384$	22.4086	+	16.2808i	1.14353	+	0.830825i
$385$	6.32871	−	4.59807i	0.322541	−	0.234340i
$386$	−0.231714	+	0.713143i	−0.0117939	+	0.0362980i
$387$	−36.5547	+	26.5585i	−1.85818	+	1.35005i
$388$	5.18112	−	3.76430i	0.263032	−	0.191104i
$389$	4.00333	−	12.3210i	0.202977	−	0.624699i	−0.796813	−	0.604225i	$-0.793483\pi$
$389$	4.00333	−	12.3210i	0.202977	−	0.624699i	0.999790	−	0.0204735i	$-0.00651738\pi$
$390$	7.02837	−	5.10641i	0.355895	−	0.258573i
$391$	−0.652828	−	0.474307i	−0.0330149	−	0.0239868i
$392$	2.45391	+	7.55234i	0.123941	+	0.381451i
$393$	−13.5386	−	9.83639i	−0.682933	−	0.496180i
$394$	0.638096	−	1.96386i	0.0321468	−	0.0989377i
$395$	3.16762	−	9.74894i	0.159380	−	0.490522i
$396$	−7.57264	−	23.3062i	−0.380539	−	1.17118i
$397$	−2.92725			−0.146915			−0.0734574	−	0.997298i	$-0.523403\pi$
$397$	−2.92725			−0.146915			−0.0734574	+	0.997298i	$0.523403\pi$
$398$	−2.43471			−0.122041
$399$	−2.04944	−	6.30752i	−0.102600	−	0.315771i
$400$	−10.1720	+	7.39042i	−0.508602	+	0.369521i
$401$	−9.93025	−	7.21475i	−0.495893	−	0.360287i	0.311553	−	0.950229i	$-0.399151\pi$
$401$	−9.93025	−	7.21475i	−0.495893	−	0.360287i	−0.807446	+	0.589942i	$0.799151\pi$
$402$	−6.54572			−0.326471
$403$		0			0
$404$	−33.2464			−1.65407
$405$	−8.98586	−	6.52861i	−0.446511	−	0.324409i
$406$	0.971954	−	0.706166i	0.0482373	−	0.0350464i
$407$	−2.36426	−	7.27645i	−0.117192	−	0.360680i
$408$	−7.19251			−0.356082
$409$	17.1972			0.850348			0.425174	−	0.905112i	$-0.360213\pi$
$409$	17.1972			0.850348			0.425174	+	0.905112i	$0.360213\pi$
$410$	−2.24286	−	6.90282i	−0.110767	−	0.340906i
$411$	−10.5549	+	32.4848i	−0.520637	+	1.60236i
$412$	−4.68177	+	14.4090i	−0.230654	+	0.709881i
$413$	−10.5177	−	7.64156i	−0.517542	−	0.376016i
$414$	0.257944	+	0.793869i	0.0126772	+	0.0390165i
$415$	30.9180	+	22.4632i	1.51770	+	1.10268i
$416$	9.00948	−	6.54577i	0.441726	−	0.320933i
$417$	13.7884	−	42.4365i	0.675223	−	2.07812i
$418$	−1.46431	+	1.06388i	−0.0716217	+	0.0520362i
$419$	−18.7251	+	13.6046i	−0.914782	+	0.664628i	−0.942220	−	0.334996i	$-0.891265\pi$
$419$	−18.7251	+	13.6046i	−0.914782	+	0.664628i	0.0274378	+	0.999624i	$0.491265\pi$
$420$	5.39794	−	16.6132i	0.263393	−	0.810639i
$421$	−23.6089	+	17.1529i	−1.15063	+	0.835981i	−0.988564	−	0.150800i	$-0.951815\pi$
$421$	−23.6089	+	17.1529i	−1.15063	+	0.835981i	−0.162064	+	0.986780i	$0.551815\pi$
$422$	−4.75054	−	3.45147i	−0.231253	−	0.168015i
$423$	−13.2152	−	40.6722i	−0.642545	−	1.97755i
$424$	5.48537	+	3.98536i	0.266393	+	0.193546i
$425$	2.16537	−	6.66431i	0.105036	−	0.323267i
$426$	0.527201	−	1.62256i	0.0255430	−	0.0786132i
$427$	−4.82704	−	14.8561i	−0.233597	−	0.718937i
$428$	22.8017			1.10216
$429$	−20.2152			−0.975998
$430$	2.71626	+	8.35979i	0.130990	+	0.403145i
$431$	−24.5555	+	17.8406i	−1.18279	+	0.859351i	−0.992484	−	0.122373i	$-0.960950\pi$
$431$	−24.5555	+	17.8406i	−1.18279	+	0.859351i	−0.190311	+	0.981724i	$0.560950\pi$
$432$	−18.1725	−	13.2031i	−0.874326	−	0.635235i
$433$	13.8400			0.665107			0.332553	−	0.943084i	$-0.392090\pi$
$433$	13.8400			0.665107			0.332553	+	0.943084i	$0.392090\pi$
$434$		0			0
$435$	27.1762			1.30300
$436$	−0.959605	−	0.697194i	−0.0459567	−	0.0333895i
$437$	−0.757834	+	0.550598i	−0.0362521	+	0.0263387i
$438$	−4.51207	−	13.8867i	−0.215595	−	0.663534i
$439$	12.9201			0.616644			0.308322	−	0.951282i	$-0.400233\pi$
$439$	12.9201			0.616644			0.308322	+	0.951282i	$0.400233\pi$
$440$	−9.84829			−0.469499
$441$	−9.67482	−	29.7760i	−0.460706	−	1.41791i
$442$	−0.569463	+	1.75263i	−0.0270866	+	0.0833639i
$443$	7.34171	−	22.5955i	0.348815	−	1.07354i	−0.610695	−	0.791866i	$-0.709110\pi$
$443$	7.34171	−	22.5955i	0.348815	−	1.07354i	0.959510	−	0.281676i	$-0.0908903\pi$
$444$	−13.8216	−	10.0420i	−0.655946	−	0.476573i
$445$	−2.07587	−	6.38888i	−0.0984059	−	0.302862i
$446$	−1.78026	−	1.29343i	−0.0842975	−	0.0612458i
$447$	27.9722	−	20.3230i	1.32304	−	0.961243i
$448$	1.73435	−	5.33779i	0.0819405	−	0.252187i
$449$	−15.7054	+	11.4106i	−0.741181	+	0.538500i	−0.893081	−	0.449896i	$-0.851461\pi$
$449$	−15.7054	+	11.4106i	−0.741181	+	0.538500i	0.151900	+	0.988396i	$0.451461\pi$
$450$	−5.86419	+	4.26058i	−0.276440	+	0.200846i
$451$	−5.21895	+	16.0623i	−0.245751	+	0.756343i
$452$	−17.1552	+	12.4640i	−0.806914	+	0.586258i
$453$	−10.1169	−	7.35036i	−0.475334	−	0.345350i
$454$	−0.852229	−	2.62289i	−0.0399971	−	0.123098i
$455$	−7.47994	−	5.43449i	−0.350665	−	0.254773i
$456$	−2.58011	+	7.94076i	−0.120825	+	0.371860i
$457$	−7.52208	+	23.1506i	−0.351868	+	1.08294i	0.605935	+	0.795514i	$0.292799\pi$
$457$	−7.52208	+	23.1506i	−0.351868	+	1.08294i	−0.957803	+	0.287424i	$0.907201\pi$
$458$	−1.38713	−	4.26914i	−0.0648162	−	0.199484i
$459$	12.5186			0.584319
$460$	−2.46723			−0.115035
$461$	11.8487	+	36.4665i	0.551848	+	1.69841i	0.704126	+	0.710075i	$0.251339\pi$
$461$	11.8487	+	36.4665i	0.551848	+	1.69841i	−0.152279	+	0.988338i	$0.548661\pi$
$462$	2.16432	−	1.57247i	0.100693	−	0.0731578i
$463$	−5.33489	−	3.87603i	−0.247934	−	0.180134i	0.456877	−	0.889530i	$-0.348968\pi$
$463$	−5.33489	−	3.87603i	−0.247934	−	0.180134i	−0.704810	+	0.709396i	$0.748968\pi$
$464$	10.3437			0.480195
$465$		0			0
$466$	4.46933			0.207038
$467$	−31.0674	−	22.5718i	−1.43763	−	1.04450i	−0.988532	−	0.151014i	$-0.951746\pi$
$467$	−31.0674	−	22.5718i	−1.43763	−	1.04450i	−0.449096	−	0.893484i	$-0.648254\pi$
$468$	−23.4318	+	17.0242i	−1.08314	+	0.786944i
$469$	2.15270	+	6.62532i	0.0994024	+	0.305929i
$470$	−8.31947			−0.383748
$471$	−25.1845			−1.16044
$472$	5.05765	+	15.5658i	0.232797	+	0.716476i
$473$	6.32051	−	19.4525i	0.290617	−	0.894429i
$474$	1.08328	−	3.33398i	0.0497565	−	0.153135i
$475$	−6.58085	−	4.78126i	−0.301950	−	0.219379i
$476$	1.14502	+	3.52402i	0.0524821	+	0.161523i
$477$	−21.6268	−	15.7128i	−0.990221	−	0.719438i
$478$	−7.22859	+	5.25188i	−0.330628	+	0.240215i
$479$	2.32540	−	7.15684i	0.106250	−	0.327005i	−0.883772	−	0.467918i	$-0.845004\pi$
$479$	2.32540	−	7.15684i	0.106250	−	0.327005i	0.990022	+	0.140914i	$0.0450041\pi$
$480$	−26.9703	+	19.5951i	−1.23102	+	0.894389i
$481$	−7.31567	+	5.31515i	−0.333566	+	0.242350i
$482$	−0.256399	+	0.789116i	−0.0116787	+	0.0359432i
$483$	1.12011	−	0.813810i	0.0509669	−	0.0370296i
$484$	−7.72484	−	5.61243i	−0.351129	−	0.255110i
$485$	3.13566	+	9.65058i	0.142383	+	0.438210i
$486$	2.77852	+	2.01871i	0.126036	+	0.0915706i
$487$	−7.73539	+	23.8071i	−0.350524	+	1.07880i	0.608035	+	0.793910i	$0.291958\pi$
$487$	−7.73539	+	23.8071i	−0.350524	+	1.07880i	−0.958560	+	0.284892i	$0.908042\pi$
$488$	−6.07693	+	18.7029i	−0.275090	+	0.846639i
$489$	2.79658	+	8.60700i	0.126466	+	0.389222i
$490$	−6.09066			−0.275148
$491$	39.7100			1.79209			0.896044	−	0.443964i	$-0.146428\pi$
$491$	39.7100			1.79209			0.896044	+	0.443964i	$0.146428\pi$
$492$	11.6539	+	35.8670i	0.525399	+	1.61701i
$493$	−4.66372	+	3.38839i	−0.210044	+	0.152606i
$494$	1.73068	+	1.25741i	0.0778668	+	0.0565735i
$495$	38.8281			1.74519
$496$		0			0
$497$	−1.81567			−0.0814440
$498$	10.5735	+	7.68207i	0.473808	+	0.344242i
$499$	−19.1366	+	13.9035i	−0.856670	+	0.622407i	−0.926977	−	0.375118i	$-0.877602\pi$
$499$	−19.1366	+	13.9035i	−0.856670	+	0.622407i	0.0703072	+	0.997525i	$0.477602\pi$
$500$	1.99977	+	6.15467i	0.0894325	+	0.275245i
$501$	38.6397			1.72630
$502$	−0.828199			−0.0369643
$503$	−6.23795	−	19.1984i	−0.278136	−	0.856016i	−0.988372	−	0.152052i	$-0.951412\pi$
$503$	−6.23795	−	19.1984i	−0.278136	−	0.856016i	0.710236	−	0.703964i	$-0.248588\pi$
$504$	2.44685	−	7.53063i	0.108991	−	0.335441i
$505$	16.2783	−	50.0994i	0.724374	−	2.22939i
$506$	−0.305693	−	0.222099i	−0.0135897	−	0.00987349i
$507$	−4.23982	−	13.0488i	−0.188297	−	0.579519i
$508$	−0.178843	−	0.129937i	−0.00793490	−	0.00576504i
$509$	9.57796	−	6.95880i	0.424536	−	0.308443i	−0.354925	−	0.934895i	$-0.615493\pi$
$509$	9.57796	−	6.95880i	0.424536	−	0.308443i	0.779460	+	0.626452i	$0.215493\pi$
$510$	1.70472	−	5.24658i	0.0754861	−	0.232322i
$511$	−12.5717	+	9.13389i	−0.556140	+	0.404060i
$512$	−17.4827	+	12.7019i	−0.772633	+	0.561351i
$513$	4.49070	−	13.8209i	0.198269	−	0.610209i
$514$	7.39617	−	5.37363i	0.326231	−	0.237021i
$515$	−19.4208	−	14.1100i	−0.855782	−	0.621762i
$516$	−14.1137	−	43.4375i	−0.621321	−	1.91223i
$517$	15.6615	+	11.3788i	0.688793	+	0.500437i
$518$	0.369798	−	1.13812i	0.0162480	−	0.0500062i
$519$	17.0275	−	52.4051i	0.747422	−	2.30033i
$520$	3.59688	+	11.0701i	0.157734	+	0.485454i
$521$	−32.7484			−1.43474			−0.717368	−	0.696695i	$-0.754653\pi$
$521$	−32.7484			−1.43474			−0.717368	+	0.696695i	$0.754653\pi$
$522$	5.96316			0.261000
$523$	9.11682	+	28.0587i	0.398651	+	1.22692i	0.926082	+	0.377323i	$0.123155\pi$
$523$	9.11682	+	28.0587i	0.398651	+	1.22692i	−0.527431	+	0.849598i	$0.676845\pi$
$524$	8.78071	−	6.37956i	0.383587	−	0.278692i
$525$	9.72679	+	7.06693i	0.424512	+	0.308426i
$526$	−8.06030			−0.351446
$527$		0			0
$528$	23.0331			1.00239
$529$	18.4492	+	13.4041i	0.802138	+	0.582788i
$530$	−4.20722	+	3.05673i	−0.182750	+	0.132776i
$531$	−19.9404	−	61.3703i	−0.865340	−	2.66324i
$532$	4.30138			0.186488
$533$	19.9611			0.864610
$534$	−0.709916	−	2.18490i	−0.0307211	−	0.0945497i
$535$	−11.1643	+	34.3600i	−0.482673	+	1.48551i
$536$	2.71011	−	8.34085i	0.117059	−	0.360270i
$537$	−0.185689	−	0.134911i	−0.00801309	−	0.00582185i
$538$	1.85132	+	5.69777i	0.0798159	+	0.245648i
$539$	11.4658	+	8.33037i	0.493866	+	0.358814i
$540$	30.9658	−	22.4980i	1.33256	−	0.968160i
$541$	4.09937	−	12.6165i	0.176245	−	0.542428i	−0.823443	−	0.567399i	$-0.807950\pi$
$541$	4.09937	−	12.6165i	0.176245	−	0.542428i	0.999688	+	0.0249716i	$0.00794955\pi$
$542$	2.06029	−	1.49689i	0.0884970	−	0.0642968i
$543$	5.06264	−	3.67822i	0.217258	−	0.157848i
$544$	2.18523	−	6.72544i	0.0936909	−	0.288351i
$545$	1.52045	−	1.10467i	0.0651291	−	0.0473191i
$546$	−2.55802	−	1.85851i	−0.109473	−	0.0795369i
$547$	11.6697	+	35.9156i	0.498959	+	1.53564i	0.810695	+	0.585469i	$0.199090\pi$
$547$	11.6697	+	35.9156i	0.498959	+	1.53564i	−0.311735	+	0.950169i	$0.600910\pi$
$548$	−17.9220	−	13.0211i	−0.765590	−	0.556234i
$549$	23.9590	−	73.7384i	1.02255	−	3.14708i
$550$	1.01395	−	3.12062i	0.0432351	−	0.133064i
$551$	2.06792	+	6.36439i	0.0880961	+	0.271132i
$552$	−1.74304			−0.0741887
$553$	−3.73078			−0.158649
$554$	−1.64019	−	5.04800i	−0.0696852	−	0.214469i
$555$	21.8998	−	15.9112i	0.929596	−	0.675391i
$556$	23.4124	+	17.0101i	0.992907	+	0.721389i
$557$	11.3637			0.481496			0.240748	−	0.970588i	$-0.422607\pi$
$557$	11.3637			0.481496			0.240748	+	0.970588i	$0.422607\pi$
$558$		0			0
$559$	−24.1743			−1.02246
$560$	8.52261	+	6.19204i	0.360146	+	0.261661i
$561$	−10.3850	+	7.54517i	−0.438457	+	0.318557i
$562$	−0.270094	−	0.831262i	−0.0113932	−	0.0350647i
$563$	−20.1865			−0.850762			−0.425381	−	0.905014i	$-0.639860\pi$
$563$	−20.1865			−0.850762			−0.425381	+	0.905014i	$0.639860\pi$
$564$	43.2280			1.82023
$565$	−10.3825	−	31.9541i	−0.436796	−	1.34432i
$566$	−0.513276	+	1.57970i	−0.0215746	+	0.0663998i
$567$	−1.24920	+	3.84466i	−0.0524617	+	0.161460i
$568$	1.84926	+	1.34357i	0.0775933	+	0.0563748i
$569$	9.57633	+	29.4729i	0.401461	+	1.23557i	0.923815	+	0.382840i	$0.125054\pi$
$569$	9.57633	+	29.4729i	0.401461	+	1.23557i	−0.522354	+	0.852729i	$0.674946\pi$
$570$	−5.18087	−	3.76412i	−0.217003	−	0.157662i
$571$	−8.41353	+	6.11279i	−0.352095	+	0.255812i	−0.749748	−	0.661724i	$-0.769825\pi$
$571$	−8.41353	+	6.11279i	−0.352095	+	0.255812i	0.397652	+	0.917536i	$0.369825\pi$
$572$	4.05149	−	12.4692i	0.169401	−	0.521364i
$573$	12.5034	−	9.08427i	0.522338	−	0.379501i
$574$	−2.13711	+	1.55270i	−0.0892012	+	0.0648085i
$575$	0.524757	−	1.61504i	0.0218839	−	0.0673517i
$576$	22.5373	−	16.3743i	0.939053	−	0.682262i
$577$	−4.37990	−	3.18219i	−0.182338	−	0.132476i	0.492872	−	0.870102i	$-0.335947\pi$
$577$	−4.37990	−	3.18219i	−0.182338	−	0.132476i	−0.675210	+	0.737626i	$0.735947\pi$
$578$	−1.48457	−	4.56903i	−0.0617499	−	0.190047i
$579$	4.99434	+	3.62860i	0.207558	+	0.150800i
$580$	−5.44661	+	16.7630i	−0.226158	+	0.696044i
$581$	4.29819	−	13.2285i	0.178319	−	0.548809i
$582$	1.07235	+	3.30034i	0.0444502	+	0.136804i
$583$	12.1009			0.501169
$584$	19.5632			0.809532
$585$	−14.1811	−	43.6451i	−0.586318	−	1.80450i
$586$	2.99921	−	2.17905i	0.123896	−	0.0900158i
$587$	−10.1635	−	7.38424i	−0.419494	−	0.304780i	0.357940	−	0.933744i	$-0.383479\pi$
$587$	−10.1635	−	7.38424i	−0.419494	−	0.304780i	−0.777434	+	0.628964i	$0.783479\pi$
$588$	31.6471			1.30510
$589$		0			0
$590$	−12.5532			−0.516809
$591$	−13.7535	−	9.99247i	−0.565741	−	0.411035i
$592$	8.33544	−	6.05605i	0.342584	−	0.248902i
$593$	8.36510	+	25.7451i	0.343513	+	1.05723i	0.962375	+	0.271726i	$0.0875943\pi$
$593$	8.36510	+	25.7451i	0.343513	+	1.05723i	−0.618861	+	0.785500i	$0.712406\pi$
$594$	5.86195			0.240519
$595$	−5.87102			−0.240688
$596$	6.92957	+	21.3270i	0.283846	+	0.873588i
$597$	−6.19413	+	19.0636i	−0.253509	+	0.780220i
$598$	−0.138004	+	0.424734i	−0.00564342	+	0.0173686i
$599$	11.6135	+	8.43770i	0.474515	+	0.344755i	0.799198	−	0.601068i	$-0.205258\pi$
$599$	11.6135	+	8.43770i	0.474515	+	0.344755i	−0.324683	+	0.945823i	$0.605258\pi$
$600$	−4.67733	−	14.3953i	−0.190951	−	0.587687i
$601$	0.517784	+	0.376192i	0.0211209	+	0.0153452i	0.598296	−	0.801275i	$-0.295845\pi$
$601$	0.517784	+	0.376192i	0.0211209	+	0.0153452i	−0.577175	+	0.816621i	$0.695845\pi$
$602$	2.58819	−	1.88043i	0.105487	−	0.0766406i
$603$	−10.6849	+	32.8848i	−0.435124	+	1.33917i
$604$	6.56150	−	4.76721i	0.266984	−	0.193975i
$605$	12.2397	−	8.89266i	0.497614	−	0.361538i
$606$	5.56691	−	17.1332i	0.226140	−	0.695988i
$607$	5.27303	−	3.83108i	0.214026	−	0.155499i	−0.475608	−	0.879658i	$-0.657772\pi$
$607$	5.27303	−	3.83108i	0.214026	−	0.155499i	0.689633	+	0.724159i	$0.257772\pi$
$608$	−6.64121	−	4.82512i	−0.269337	−	0.195685i
$609$	−3.05647	−	9.40686i	−0.123855	−	0.381185i
$610$	−12.2025	−	8.86563i	−0.494065	−	0.358959i
$611$	7.07036	−	21.7603i	0.286036	−	0.880329i
$612$	−5.68333	+	17.4915i	−0.229735	+	0.707052i
$613$	−3.22778	−	9.93409i	−0.130369	−	0.401234i	0.864472	−	0.502681i	$-0.167653\pi$
$613$	−3.22778	−	9.93409i	−0.130369	−	0.401234i	−0.994841	+	0.101447i	$0.967653\pi$
$614$	0.930770			0.0375628
$615$	−59.7545			−2.40953
$616$	1.10762	+	3.40892i	0.0446274	+	0.137349i
$617$	−17.5584	+	12.7569i	−0.706874	+	0.513574i	−0.882164	−	0.470943i	$-0.843914\pi$
$617$	−17.5584	+	12.7569i	−0.706874	+	0.513574i	0.175290	+	0.984517i	$0.443914\pi$
$618$	−6.64159	−	4.82540i	−0.267164	−	0.194106i
$619$	−28.5478			−1.14743			−0.573716	−	0.819054i	$-0.694499\pi$
$619$	−28.5478			−1.14743			−0.573716	+	0.819054i	$0.694499\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$	−1.56738	−	1.13877i	−0.0628462	−	0.0456604i
$623$	−1.97800	+	1.43710i	−0.0792468	+	0.0575762i
$624$	−8.41235	−	25.8906i	−0.336764	−	1.03645i
$625$	−29.4541			−1.17817
$626$	9.37462			0.374685
$627$	4.60477	+	14.1720i	0.183897	+	0.565976i
$628$	5.04743	−	15.5344i	0.201414	−	0.619890i
$629$	−1.77440	+	5.46104i	−0.0707500	+	0.217746i
$630$	4.91329	+	3.56971i	0.195750	+	0.142221i
$631$	−8.41778	−	25.9073i	−0.335107	−	1.03135i	−0.966670	−	0.256027i	$-0.917586\pi$
$631$	−8.41778	−	25.9073i	−0.335107	−	1.03135i	0.631563	−	0.775325i	$-0.282414\pi$
$632$	3.79980	+	2.76072i	0.151148	+	0.109816i
$633$	−39.1105	+	28.4155i	−1.55450	+	1.12941i
$634$	1.16637	−	3.58973i	0.0463226	−	0.142566i
$635$	0.283370	−	0.205880i	0.0112452	−	0.00817012i
$636$	21.8607	−	15.8828i	0.866835	−	0.629792i
$637$	5.17620	−	15.9307i	0.205088	−	0.631197i
$638$	−2.18383	+	1.58665i	−0.0864587	+	0.0628159i
$639$	−7.29094	−	5.29718i	−0.288425	−	0.209553i
$640$	−8.79580	−	27.0707i	−0.347684	−	1.07006i
$641$	33.3380	+	24.2215i	1.31677	+	0.956692i	0.999966	+	0.00820217i	$0.00261086\pi$
$641$	33.3380	+	24.2215i	1.31677	+	0.956692i	0.316807	+	0.948490i	$0.397389\pi$
$642$	−3.81800	+	11.7506i	−0.150684	+	0.463759i
$643$	9.52156	−	29.3044i	0.375494	−	1.15565i	−0.567651	−	0.823269i	$-0.692148\pi$
$643$	9.52156	−	29.3044i	0.375494	−	1.15565i	0.943145	−	0.332382i	$-0.107852\pi$
$644$	0.277486	+	0.854015i	0.0109345	+	0.0336529i
$645$	72.3668			2.84944
$646$	1.35841			0.0534459
$647$	−2.75525	−	8.47978i	−0.108320	−	0.333375i	0.882175	−	0.470921i	$-0.156078\pi$
$647$	−2.75525	−	8.47978i	−0.108320	−	0.333375i	−0.990495	+	0.137547i	$0.956078\pi$
$648$	4.11730	−	2.99139i	0.161743	−	0.117513i
$649$	23.6317	+	17.1694i	0.927623	+	0.673958i
$650$	−3.87809			−0.152111
$651$		0			0
$652$	−5.86949			−0.229867
$653$	−31.7469	−	23.0655i	−1.24235	−	0.902623i	−0.244601	−	0.969624i	$-0.578657\pi$
$653$	−31.7469	−	23.0655i	−1.24235	−	0.902623i	−0.997753	+	0.0670010i	$0.978657\pi$
$654$	0.519971	−	0.377781i	0.0203325	−	0.0147724i
$655$	5.31417	+	16.3553i	0.207642	+	0.639056i
$656$	−22.7435			−0.887986
$657$	−77.1304			−3.00914
$658$	0.935679	+	2.87973i	0.0364766	+	0.112263i
$659$	10.1832	−	31.3407i	0.396681	−	1.22086i	−0.530963	−	0.847395i	$-0.678170\pi$
$659$	10.1832	−	31.3407i	0.396681	−	1.22086i	0.927644	−	0.373465i	$-0.121830\pi$
$660$	−12.1283	+	37.3272i	−0.472095	+	1.45296i
$661$	0.137270	+	0.0997326i	0.00533919	+	0.00387915i	0.590452	−	0.807073i	$-0.298950\pi$
$661$	0.137270	+	0.0997326i	0.00533919	+	0.00387915i	−0.585112	+	0.810952i	$0.698950\pi$
$662$	−2.13370	−	6.56686i	−0.0829287	−	0.255228i
$663$	12.2741	+	8.91768i	0.476688	+	0.346334i
$664$	−14.1665	+	10.2926i	−0.549769	+	0.399430i
$665$	−2.10606	+	6.48179i	−0.0816695	+	0.251353i
$666$	4.80539	−	3.49132i	0.186205	−	0.135286i
$667$	−1.13021	+	0.821147i	−0.0437620	+	0.0317950i
$668$	−7.74411	+	23.8339i	−0.299629	+	0.922162i
$669$	−14.6566	+	10.6486i	−0.566656	+	0.411700i
$670$	5.44191	+	3.95378i	0.210239	+	0.152748i
$671$	10.8456	+	33.3794i	0.418690	+	1.28860i
$672$	9.81602	+	7.13176i	0.378661	+	0.275113i
$673$	4.50743	−	13.8724i	0.173749	−	0.534743i	−0.825825	−	0.563926i	$-0.809290\pi$
$673$	4.50743	−	13.8724i	0.173749	−	0.534743i	0.999574	+	0.0291825i	$0.00929039\pi$
$674$	−2.08278	+	6.41015i	−0.0802258	+	0.246910i
$675$	8.14092	+	25.0552i	0.313344	+	0.964374i
$676$	8.89857			0.342253
$677$	−15.7668			−0.605968			−0.302984	−	0.952996i	$-0.597983\pi$
$677$	−15.7668			−0.605968			−0.302984	+	0.952996i	$0.597983\pi$
$678$	−3.55065	−	10.9278i	−0.136362	−	0.419679i
$679$	2.98782	−	2.17078i	0.114662	−	0.0833067i
$680$	5.97963	+	4.34445i	0.229308	+	0.166602i
$681$	−22.7051			−0.870063
$682$		0			0
$683$	20.5935			0.787988			0.393994	−	0.919113i	$-0.371093\pi$
$683$	20.5935			0.787988			0.393994	+	0.919113i	$0.371093\pi$
$684$	17.2724	+	12.5492i	0.660428	+	0.479829i
$685$	28.3967	−	20.6314i	1.08498	−	0.788285i
$686$	1.50763	+	4.64001i	0.0575616	+	0.177156i
$687$	−36.9560			−1.40996
$688$	27.5440			1.05011
$689$	−4.41961	−	13.6022i	−0.168374	−	0.518201i
$690$	0.413123	−	1.27146i	0.0157273	−	0.0484037i
$691$	−1.83918	+	5.66041i	−0.0699657	+	0.215332i	−0.979925	−	0.199364i	$-0.936112\pi$
$691$	−1.83918	+	5.66041i	−0.0699657	+	0.215332i	0.909960	+	0.414697i	$0.136112\pi$
$692$	28.9121	+	21.0059i	1.09907	+	0.798524i
$693$	−4.36694	−	13.4401i	−0.165886	−	0.510546i
$694$	3.03078	+	2.20199i	0.115047	+	0.0835866i
$695$	−37.0960	+	26.9518i	−1.40713	+	1.02234i
$696$	−3.84790	+	11.8426i	−0.145854	+	0.448894i
$697$	10.2545	−	7.45032i	0.388417	−	0.282201i
$698$	5.31713	−	3.86312i	0.201256	−	0.146221i
$699$	11.3704	−	34.9945i	0.430068	−	1.32361i
$700$	−6.30848	+	4.58338i	−0.238438	+	0.173236i
$701$	21.5445	+	15.6530i	0.813723	+	0.591204i	0.914908	−	0.403663i	$-0.132263\pi$
$701$	21.5445	+	15.6530i	0.813723	+	0.591204i	−0.101185	+	0.994868i	$0.532263\pi$
$702$	−2.14096	−	6.58918i	−0.0808052	−	0.248693i
$703$	5.39265	+	3.91799i	0.203388	+	0.147770i
$704$	−3.89682	+	11.9932i	−0.146867	+	0.452010i
$705$	−21.1655	+	65.1407i	−0.797138	+	2.45334i
$706$	1.37510	+	4.23213i	0.0517526	+	0.159278i
$707$	−19.1723			−0.721050
$708$	65.2266			2.45137
$709$	0.816662	+	2.51343i	0.0306704	+	0.0943938i	0.965220	−	0.261439i	$-0.0841971\pi$
$709$	0.816662	+	2.51343i	0.0306704	+	0.0943938i	−0.934550	+	0.355833i	$0.884197\pi$
$710$	−1.41836	+	1.03050i	−0.0532302	+	0.0386740i
$711$	−14.9812	−	10.8845i	−0.561839	−	0.408200i
$712$	3.07802			0.115354
$713$		0			0
$714$	−2.00779			−0.0751398
$715$	16.8063	+	12.2105i	0.628519	+	0.456646i
$716$	0.120432	−	0.0874991i	0.00450076	−	0.00326999i
$717$	22.7315	+	69.9605i	0.848925	+	2.61272i
$718$	−7.96983			−0.297431
$719$	−5.19824			−0.193862			−0.0969308	−	0.995291i	$-0.530903\pi$
$719$	−5.19824			−0.193862			−0.0969308	+	0.995291i	$0.530903\pi$
$720$	16.1579	+	49.7290i	0.602170	+	1.85329i
$721$	−2.69986	+	8.30930i	−0.100548	+	0.309455i
$722$	−1.57608	+	4.85068i	−0.0586557	+	0.180524i
$723$	5.52640	+	4.01517i	0.205529	+	0.149326i
$724$	1.25417	+	3.85994i	0.0466109	+	0.143454i
$725$	−9.81449	−	7.13065i	−0.364501	−	0.264826i
$726$	4.18578	−	3.04115i	0.155349	−	0.112868i
$727$	7.48020	−	23.0217i	0.277425	−	0.853827i	−0.711142	−	0.703048i	$-0.751822\pi$
$727$	7.48020	−	23.0217i	0.277425	−	0.853827i	0.988567	−	0.150779i	$-0.0481782\pi$
$728$	3.42729	−	2.49007i	0.127024	−	0.0922882i
$729$	31.9419	−	23.2071i	1.18303	−	0.859524i
$730$	−4.63673	+	14.2704i	−0.171613	+	0.528171i
$731$	−12.4189	+	9.02287i	−0.459330	+	0.333723i
$732$	63.4042	+	46.0659i	2.34349	+	1.70264i
$733$	12.4728	+	38.3873i	0.460693	+	1.41787i	0.864320	+	0.502942i	$0.167749\pi$
$733$	12.4728	+	38.3873i	0.460693	+	1.41787i	−0.403627	+	0.914923i	$0.632251\pi$
$734$	2.47914	+	1.80120i	0.0915066	+	0.0664834i
$735$	−15.4952	+	47.6893i	−0.571549	+	1.75905i
$736$	0.529571	−	1.62985i	0.0195202	−	0.0600771i
$737$	−4.83678	−	14.8861i	−0.178165	−	0.548336i
$738$	−13.1117			−0.482647
$739$	−6.09785			−0.224313			−0.112157	−	0.993691i	$-0.535776\pi$
$739$	−6.09785			−0.224313			−0.112157	+	0.993691i	$0.535776\pi$
$740$	5.42526	+	16.6972i	0.199437	+	0.613803i
$741$	14.2484	−	10.3521i	0.523428	−	0.380293i
$742$	1.53125	+	1.11251i	0.0562138	+	0.0408417i
$743$	−16.2263			−0.595284			−0.297642	−	0.954678i	$-0.596200\pi$
$743$	−16.2263			−0.595284			−0.297642	+	0.954678i	$0.596200\pi$
$744$		0			0
$745$	−35.5308			−1.30175
$746$	−7.22540	−	5.24956i	−0.264541	−	0.192200i
$747$	55.8534	−	40.5798i	2.04357	−	1.48474i
$748$	−2.57269	−	7.91793i	−0.0940670	−	0.289508i
$749$	13.1491			0.480458
$750$	−3.50659			−0.128043
$751$	11.2620	+	34.6607i	0.410955	+	1.26479i	0.915820	+	0.401590i	$0.131542\pi$
$751$	11.2620	+	34.6607i	0.410955	+	1.26479i	−0.504865	+	0.863198i	$0.668458\pi$
$752$	−8.05593	+	24.7936i	−0.293770	+	0.904130i
$753$	−2.10701	+	6.48472i	−0.0767838	+	0.236316i
$754$	2.58108	+	1.87527i	0.0939975	+	0.0682932i
$755$	3.97108	+	12.2217i	0.144522	+	0.444794i
$756$	−11.2702	−	8.18829i	−0.409894	−	0.297805i
$757$	35.2426	−	25.6052i	1.28091	−	0.930637i	0.281332	−	0.959610i	$-0.409224\pi$
$757$	35.2426	−	25.6052i	1.28091	−	0.930637i	0.999580	+	0.0289730i	$0.00922370\pi$
$758$	2.39980	−	7.38582i	0.0871646	−	0.268265i
$759$	−2.51672	+	1.82851i	−0.0913512	+	0.0663705i
$760$	6.94144	−	5.04325i	0.251792	−	0.182938i
$761$	−1.01953	+	3.13780i	−0.0369580	+	0.113745i	−0.967834	−	0.251591i	$-0.919046\pi$
$761$	−1.01953	+	3.13780i	−0.0369580	+	0.113745i	0.930875	+	0.365337i	$0.119046\pi$
$762$	0.0969080	−	0.0704078i	0.00351061	−	0.00255061i
$763$	−0.553379	−	0.402053i	−0.0200337	−	0.0145553i
$764$	3.09748	+	9.53307i	0.112063	+	0.344894i
$765$	−23.5754	−	17.1285i	−0.852371	−	0.619284i
$766$	2.89335	−	8.90482i	0.104541	−	0.321744i
$767$	10.6685	−	32.8342i	0.385216	−	1.18557i
$768$	6.26630	+	19.2857i	0.226116	+	0.695912i
$769$	−45.7136			−1.64847			−0.824237	−	0.566244i	$-0.808396\pi$
$769$	−45.7136			−1.64847			−0.824237	+	0.566244i	$0.808396\pi$
$770$	−2.74916			−0.0990727
$771$	−23.2585	−	71.5823i	−0.837635	−	2.57798i
$772$	−3.23917	+	2.35339i	−0.116580	+	0.0847005i
$773$	24.2710	+	17.6339i	0.872969	+	0.634249i	0.931382	−	0.364044i	$-0.118604\pi$
$773$	24.2710	+	17.6339i	0.872969	+	0.634249i	−0.0584131	+	0.998292i	$0.518604\pi$
$774$	15.8791			0.570764
$775$		0			0
$776$	−4.64943			−0.166905
$777$	−7.97058	−	5.79097i	−0.285943	−	0.207750i
$778$	−3.68331	+	2.67608i	−0.132053	+	0.0959423i
$779$	−4.54689	−	13.9939i	−0.162909	−	0.501383i
$780$	46.3877			1.66094
$781$	4.07953			0.145977
$782$	0.0876325	+	0.269705i	0.00313373	+	0.00964464i
$783$	6.69730	−	20.6122i	0.239342	−	0.736619i
$784$	−5.89773	+	18.1514i	−0.210633	+	0.648263i
$785$	20.9376	+	15.2121i	0.747295	+	0.542941i
$786$	1.81736	+	5.59326i	0.0648231	+	0.199505i
$787$	−34.9754	−	25.4111i	−1.24674	−	0.905809i	−0.248710	−	0.968578i	$-0.580007\pi$
$787$	−34.9754	−	25.4111i	−1.24674	−	0.905809i	−0.998028	+	0.0627693i	$0.980007\pi$
$788$	8.92004	−	6.48079i	0.317763	−	0.230869i
$789$	−20.5061	+	63.1114i	−0.730038	+	2.24682i
$790$	−2.91441	+	2.11744i	−0.103690	+	0.0753352i
$791$	−9.89298	+	7.18767i	−0.351754	+	0.255564i
$792$	−5.49770	+	16.9202i	−0.195352	+	0.601232i
$793$	33.5593	−	24.3822i	1.19172	−	0.865839i
$794$	0.832262	+	0.604674i	0.0295359	+	0.0214591i
$795$	13.2303	+	40.7188i	0.469231	+	1.44415i
$796$	−10.5175	−	7.64138i	−0.372781	−	0.270841i
$797$	−7.05292	+	21.7067i	−0.249827	+	0.768890i	0.744977	+	0.667090i	$0.232460\pi$
$797$	−7.05292	+	21.7067i	−0.249827	+	0.768890i	−0.994805	+	0.101800i	$0.967540\pi$
$798$	−0.720239	+	2.21667i	−0.0254962	+	0.0784691i
$799$	−4.48967	−	13.8178i	−0.158833	−	0.488838i
$800$	14.8816			0.526144
$801$	−12.1355			−0.428786
$802$	1.33299	+	4.10252i	0.0470695	+	0.144865i
$803$	28.2467	−	20.5225i	0.996805	−	0.724222i
$804$	−28.2762	−	20.5438i	−0.997223	−	0.724525i
$805$	−1.42279			−0.0501467
$806$		0			0
$807$	49.3229			1.73625
$808$	19.5270	+	14.1872i	0.686959	+	0.499105i
$809$	−17.1822	+	12.4836i	−0.604095	+	0.438901i	−0.847330	−	0.531066i	$-0.821791\pi$
$809$	−17.1822	+	12.4836i	−0.604095	+	0.438901i	0.243235	+	0.969967i	$0.421791\pi$
$810$	1.20622	+	3.71236i	0.0423822	+	0.130439i
$811$	2.12314			0.0745534			0.0372767	−	0.999305i	$-0.488132\pi$
$811$	2.12314			0.0745534			0.0372767	+	0.999305i	$0.488132\pi$
$812$	6.41495			0.225121
$813$	−6.47893	−	19.9401i	−0.227226	−	0.699330i
$814$	−0.830879	+	2.55718i	−0.0291223	+	0.0896292i
$815$	2.87385	−	8.84480i	0.100667	−	0.309820i
$816$	−13.9851	−	10.1608i	−0.489576	−	0.355698i
$817$	5.50660	+	16.9476i	0.192651	+	0.592920i
$818$	−4.88943	−	3.55238i	−0.170955	−	0.124206i
$819$	−13.5125	+	9.81741i	−0.472165	+	0.343048i
$820$	11.9759	−	36.8580i	0.418216	−	1.28714i
$821$	33.8104	−	24.5647i	1.17999	−	0.857313i	0.187819	−	0.982204i	$-0.439858\pi$
$821$	33.8104	−	24.5647i	1.17999	−	0.857313i	0.992171	+	0.124891i	$0.0398580\pi$
$822$	9.71121	−	7.05561i	0.338717	−	0.246093i
$823$	−5.03651	+	15.5008i	−0.175562	+	0.540324i	−0.999659	−	0.0261251i	$-0.991683\pi$
$823$	−5.03651	+	15.5008i	−0.175562	+	0.540324i	0.824097	+	0.566449i	$0.191683\pi$
$824$	8.89855	−	6.46518i	0.309996	−	0.225225i
$825$	−21.8546	−	15.8783i	−0.760880	−	0.552812i
$826$	1.41185	+	4.34522i	0.0491244	+	0.151189i
$827$	−25.1519	−	18.2740i	−0.874619	−	0.635448i	0.0572034	−	0.998363i	$-0.481782\pi$
$827$	−25.1519	−	18.2740i	−0.874619	−	0.635448i	−0.931822	+	0.362915i	$0.881782\pi$
$828$	−1.37731	+	4.23891i	−0.0478647	+	0.147312i
$829$	8.66756	−	26.6760i	0.301037	−	0.926496i	−0.680090	−	0.733129i	$-0.738059\pi$
$829$	8.66756	−	26.6760i	0.301037	−	0.926496i	0.981126	−	0.193367i	$-0.0619409\pi$
$830$	−4.15029	−	12.7733i	−0.144059	−	0.443367i
$831$	−43.6982			−1.51587
$832$	14.9043			0.516714
$833$	−3.28688	−	10.1160i	−0.113884	−	0.350498i
$834$	−12.6862	+	9.21708i	−0.439288	+	0.319162i
$835$	−32.1239	−	23.3394i	−1.11169	−	0.807692i
$836$	−9.66453			−0.334255
$837$		0			0
$838$	8.13409			0.280987
$839$	18.6621	+	13.5588i	0.644287	+	0.468102i	0.861320	−	0.508062i	$-0.169638\pi$
$839$	18.6621	+	13.5588i	0.644287	+	0.468102i	−0.217034	+	0.976164i	$0.569638\pi$
$840$	−10.2598	+	7.45415i	−0.353995	+	0.257193i
$841$	−5.87746	−	18.0890i	−0.202671	−	0.623757i
$842$	10.2556			0.353431
$843$	−7.19585			−0.247838
$844$	−9.68888	−	29.8193i	−0.333505	−	1.02642i
$845$	−4.35696	+	13.4093i	−0.149884	+	0.461296i
$846$	−4.64425	+	14.2935i	−0.159673	+	0.491422i
$847$	−4.45472	−	3.23654i	−0.153066	−	0.111209i
$848$	5.03568	+	15.4982i	0.172926	+	0.532212i
$849$	11.0631	+	8.03781i	0.379684	+	0.275857i
$850$	−1.99227	+	1.44747i	−0.0683343	+	0.0496478i
$851$	−0.430010	+	1.32344i	−0.0147406	+	0.0453668i
$852$	7.36982	−	5.35449i	0.252486	−	0.183442i
$853$	−24.2874	+	17.6458i	−0.831585	+	0.604182i	−0.920007	−	0.391901i	$-0.871818\pi$
$853$	−24.2874	+	17.6458i	−0.831585	+	0.604182i	0.0884221	+	0.996083i	$0.471818\pi$
$854$	−1.69638	+	5.22092i	−0.0580489	+	0.178656i
$855$	−27.3675	+	19.8836i	−0.935947	+	0.680006i
$856$	−13.3924	−	9.73013i	−0.457742	−	0.332569i
$857$	−16.8684	−	51.9157i	−0.576215	−	1.77341i	−0.632006	−	0.774964i	$-0.717768\pi$
$857$	−16.8684	−	51.9157i	−0.576215	−	1.77341i	0.0557914	−	0.998442i	$-0.482232\pi$
$858$	5.74748	+	4.17579i	0.196216	+	0.142559i
$859$	−2.88511	+	8.87945i	−0.0984386	+	0.302963i	−0.988135	−	0.153591i	$-0.950916\pi$
$859$	−2.88511	+	8.87945i	−0.0984386	+	0.302963i	0.889696	+	0.456554i	$0.150916\pi$
$860$	−14.5036	+	44.6376i	−0.494570	+	1.52213i
$861$	6.72051	+	20.6836i	0.229034	+	0.704895i
$862$	10.6668			0.363311
$863$	−13.3167			−0.453307			−0.226653	−	0.973975i	$-0.572778\pi$
$863$	−13.3167			−0.453307			−0.226653	+	0.973975i	$0.572778\pi$
$864$	8.21560	+	25.2850i	0.279500	+	0.860214i
$865$	−45.8101	+	33.2830i	−1.55759	+	1.13166i
$866$	−3.93491	−	2.85888i	−0.133714	−	0.0971487i
$867$	−39.5520			−1.34326
$868$		0			0
$869$	8.38250			0.284357
$870$	−7.72660	−	5.61370i	−0.261956	−	0.190322i
$871$	−14.9663	+	10.8737i	−0.507114	+	0.368440i
$872$	0.266104	+	0.818983i	0.00901141	+	0.0277343i
$873$	18.3309			0.620409
$874$	0.329199			0.0111353
$875$	1.15322	+	3.54924i	0.0389858	+	0.119986i
$876$	24.0925	−	74.1490i	0.814010	−	2.50526i
$877$	−13.1536	+	40.4827i	−0.444167	+	1.36700i	0.439228	+	0.898375i	$0.355252\pi$
$877$	−13.1536	+	40.4827i	−0.444167	+	1.36700i	−0.883395	+	0.468629i	$0.844748\pi$
$878$	−3.67338	−	2.66887i	−0.123971	−	0.0900700i
$879$	−9.43151	−	29.0272i	−0.318117	−	0.979064i
$880$	−19.1490	−	13.9126i	−0.645512	−	0.468992i
$881$	−4.67056	+	3.39336i	−0.157355	+	0.114325i	−0.663677	−	0.748020i	$-0.731005\pi$
$881$	−4.67056	+	3.39336i	−0.157355	+	0.114325i	0.506321	+	0.862345i	$0.331005\pi$
$882$	−3.40005	+	10.4643i	−0.114486	+	0.352350i
$883$	22.0029	−	15.9860i	0.740457	−	0.537973i	−0.152397	−	0.988319i	$-0.548699\pi$
$883$	22.0029	−	15.9860i	0.740457	−	0.537973i	0.892854	+	0.450346i	$0.148699\pi$
$884$	−7.96061	+	5.78372i	−0.267744	+	0.194528i
$885$	−31.9366	+	98.2907i	−1.07354	+	3.30401i
$886$	−6.75483	+	4.90767i	−0.226933	+	0.164876i
$887$	5.96382	+	4.33297i	0.200246	+	0.145487i	0.683389	−	0.730054i	$-0.260505\pi$
$887$	5.96382	+	4.33297i	0.200246	+	0.145487i	−0.483144	+	0.875541i	$0.660505\pi$
$888$	3.83282	+	11.7962i	0.128621	+	0.395855i
$889$	−0.103134	−	0.0749315i	−0.00345902	−	0.00251312i
$890$	−0.729530	+	2.24526i	−0.0244539	+	0.0752613i
$891$	2.80677	−	8.63835i	0.0940304	−	0.289396i
$892$	−3.63089	−	11.1747i	−0.121571	−	0.374157i
$893$	−16.8658			−0.564393
$894$	−12.1510			−0.406389
$895$	0.0728867	+	0.224322i	0.00243633	+	0.00749826i
$896$	−8.38108	+	6.08921i	−0.279992	+	0.203426i
$897$	2.97453	+	2.16112i	0.0993166	+	0.0721578i
$898$	6.82232			0.227664
$899$		0			0
$900$	−38.7040			−1.29013
$901$	−7.34737	−	5.33818i	−0.244776	−	0.177841i
$902$	4.80176	−	3.48868i	0.159881	−	0.116160i
$903$	−8.13900	−	25.0493i	−0.270849	−	0.833588i
$904$	15.3948			0.512022
$905$	−6.43065			−0.213762
$906$	1.35805	+	4.17963i	0.0451180	+	0.138859i
$907$	5.09354	−	15.6763i	0.169128	−	0.520523i	−0.830189	−	0.557482i	$-0.811767\pi$
$907$	5.09354	−	15.6763i	0.169128	−	0.520523i	0.999317	+	0.0369599i	$0.0117674\pi$
$908$	4.55053	−	14.0051i	0.151015	−	0.464775i
$909$	−76.9877	−	55.9349i	−2.55352	−	1.85524i
$910$	1.00407	+	3.09021i	0.0332847	+	0.102440i
$911$	36.2496	+	26.3369i	1.20100	+	0.872581i	0.994383	−	0.105840i	$-0.0337532\pi$
$911$	36.2496	+	26.3369i	1.20100	+	0.872581i	0.206621	+	0.978421i	$0.433753\pi$
$912$	−16.2346	+	11.7951i	−0.537580	+	0.390575i
$913$	−9.65737	+	29.7223i	−0.319612	+	0.983665i
$914$	6.92078	−	5.02824i	0.228919	−	0.166319i
$915$	−100.461	+	72.9895i	−3.32115	+	2.41296i
$916$	7.40666	−	22.7953i	0.244723	−	0.753179i
$917$	5.06361	−	3.67893i	0.167215	−	0.121489i
$918$	−3.55923	−	2.58593i	−0.117472	−	0.0853484i
$919$	−3.20043	−	9.84992i	−0.105573	−	0.324919i	0.884292	−	0.466935i	$-0.154642\pi$
$919$	−3.20043	−	9.84992i	−0.105573	−	0.324919i	−0.989864	+	0.142016i	$0.954642\pi$
$920$	1.44911	+	1.05284i	0.0477757	+	0.0347111i
$921$	2.36796	−	7.28784i	0.0780270	−	0.240143i
$922$	4.16401	−	12.8155i	0.137134	−	0.422056i
$923$	−1.48997	−	4.58564i	−0.0490428	−	0.150938i
$924$	14.2846			0.469929
$925$	−12.0838			−0.397314
$926$	0.716131	+	2.20402i	0.0235335	+	0.0724287i
$927$	−35.0836	+	25.4897i	−1.15230	+	0.837193i
$928$	−9.90452	−	7.19606i	−0.325132	−	0.236222i
$929$	−44.0624			−1.44564			−0.722820	−	0.691037i	$-0.757154\pi$
$929$	−44.0624			−1.44564			−0.722820	+	0.691037i	$0.757154\pi$
$930$		0			0
$931$	−12.3474			−0.404671
$932$	19.3066	+	14.0271i	0.632409	+	0.459472i
$933$	−12.9040	+	9.37531i	−0.422458	+	0.306934i
$934$	4.17034	+	12.8350i	0.136458	+	0.419974i
$935$	13.1913			0.431401
$936$	21.0272			0.687296
$937$	−10.6818	−	32.8751i	−0.348958	−	1.07398i	−0.959430	−	0.281945i	$-0.909020\pi$
$937$	−10.6818	−	32.8751i	−0.348958	−	1.07398i	0.610472	−	0.792038i	$-0.290980\pi$
$938$	0.756528	−	2.32835i	0.0247015	−	0.0760235i
$939$	23.8499	−	73.4024i	0.778312	−	2.39540i
$940$	−35.9384	−	26.1108i	−1.17218	−	0.851639i
$941$	6.84444	+	21.0650i	0.223122	+	0.686700i	0.998477	+	0.0551736i	$0.0175712\pi$
$941$	6.84444	+	21.0650i	0.223122	+	0.686700i	−0.775354	+	0.631526i	$0.782429\pi$
$942$	7.16032	+	5.20228i	0.233296	+	0.169499i
$943$	2.48509	−	1.80552i	0.0809255	−	0.0587958i
$944$	−12.1556	+	37.4111i	−0.395631	+	1.21763i
$945$	17.8572	−	12.9740i	0.580894	−	0.422044i
$946$	−5.81526	+	4.22504i	−0.189071	+	0.137368i
$947$	8.67799	−	26.7081i	0.281997	−	0.867897i	−0.705286	−	0.708923i	$-0.749181\pi$
$947$	8.67799	−	26.7081i	0.281997	−	0.867897i	0.987283	−	0.158974i	$-0.0508185\pi$
$948$	15.1433	−	11.0022i	0.491831	−	0.357336i
$949$	−33.3850	−	24.2556i	−1.08372	−	0.787371i
$950$	0.883382	+	2.71877i	0.0286607	+	0.0882085i
$951$	−25.1399	−	18.2652i	−0.815217	−	0.592290i
$952$	0.831282	−	2.55842i	0.0269420	−	0.0829189i
$953$	−2.36916	+	7.29152i	−0.0767446	+	0.236196i	−0.982068	−	0.188527i	$-0.939629\pi$
$953$	−2.36916	+	7.29152i	−0.0767446	+	0.236196i	0.905323	+	0.424723i	$0.139629\pi$
$954$	2.90307	+	8.93474i	0.0939905	+	0.289273i
$955$	−15.8821			−0.513932
$956$	−47.7092			−1.54302
$957$	6.86743	+	21.1358i	0.221992	+	0.683222i
$958$	−2.13951	+	1.55445i	−0.0691245	+	0.0502219i
$959$	−10.3352	−	7.50893i	−0.333740	−	0.242476i
$960$	−44.6168			−1.44000
$961$		0			0
$962$	3.17789			0.102459
$963$	52.8011	+	38.3622i	1.70149	+	1.23621i
$964$	−3.58424	+	2.60411i	−0.115441	+	0.0838726i
$965$	−1.96038	−	6.03342i	−0.0631067	−	0.194223i
$966$	−0.486571			−0.0156552
$967$	1.85036			0.0595037			0.0297518	−	0.999557i	$-0.490528\pi$
$967$	1.85036			0.0595037			0.0297518	+	0.999557i	$0.490528\pi$
$968$	2.14214	+	6.59283i	0.0688510	+	0.211902i
$969$	3.45592	−	10.6362i	0.111020	−	0.341685i
$970$	1.10197	−	3.39153i	0.0353822	−	0.108895i
$971$	−39.9423	−	29.0198i	−1.28181	−	0.931290i	−0.282205	−	0.959354i	$-0.591066\pi$
$971$	−39.9423	−	29.0198i	−1.28181	−	0.931290i	−0.999606	+	0.0280640i	$0.991066\pi$
$972$	5.66687	+	17.4408i	0.181765	+	0.559415i
$973$	13.5013	+	9.80928i	0.432832	+	0.314471i
$974$	7.11704	−	5.17083i	0.228045	−	0.165684i
$975$	−9.86622	+	30.3651i	−0.315972	+	0.972462i
$976$	−38.2373	+	27.7810i	−1.22395	+	0.889248i
$977$	28.8192	−	20.9383i	0.922007	−	0.669877i	−0.0220160	−	0.999758i	$-0.507008\pi$
$977$	28.8192	−	20.9383i	0.922007	−	0.669877i	0.944023	+	0.329881i	$0.107008\pi$
$978$	0.982810	−	3.02478i	0.0314268	−	0.0967218i
$979$	4.44426	−	3.22894i	0.142039	−	0.103197i
$980$	−26.3104	−	19.1156i	−0.840456	−	0.610627i
$981$	−1.04915	−	3.22894i	−0.0334967	−	0.103092i
$982$	−11.2902	−	8.20278i	−0.360283	−	0.261761i
$983$	1.97264	−	6.07116i	0.0629174	−	0.193640i	−0.914657	−	0.404231i	$-0.867539\pi$
$983$	1.97264	−	6.07116i	0.0629174	−	0.193640i	0.977574	+	0.210592i	$0.0675390\pi$
$984$	8.46068	−	26.0393i	0.269717	−	0.830103i
$985$	5.39849	+	16.6149i	0.172010	+	0.529393i
$986$	2.02590			0.0645177
$987$	24.9284			0.793481
$988$	3.52977	+	10.8635i	0.112297	+	0.345614i
$989$	−3.00961	+	2.18661i	−0.0957001	+	0.0695302i
$990$	−11.0394	−	8.02059i	−0.350855	−	0.254911i
$991$	44.2919			1.40698			0.703489	−	0.710706i	$-0.251624\pi$
$991$	44.2919			1.40698			0.703489	+	0.710706i	$0.251624\pi$
$992$		0			0
$993$	−56.8463			−1.80396
$994$	0.516222	+	0.375058i	0.0163736	+	0.0118961i
$995$	16.6645	−	12.1075i	0.528299	−	0.383832i
$996$	21.5649	+	66.3699i	0.683310	+	2.10301i
$997$	5.32316			0.168586			0.0842931	−	0.996441i	$-0.473137\pi$
$997$	5.32316			0.168586			0.0842931	+	0.996441i	$0.473137\pi$
$998$	8.31281			0.263137
$999$	−6.67105	−	20.5314i	−0.211063	−	0.649584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.n.374.3		16
31.2	even	5		961.2.d.q.628.2		16
31.3	odd	30		961.2.g.k.235.2		16
31.4	even	5		961.2.a.j.1.4		8
31.5	even	3		961.2.g.j.732.2		16
31.6	odd	6		31.2.g.a.10.2	✓	16
31.7	even	15		961.2.c.i.439.4		16
31.8	even	5		961.2.d.q.531.2		16
31.9	even	15		961.2.g.n.844.1		16
31.10	even	15		961.2.g.m.448.1		16
31.11	odd	30		961.2.c.j.521.4		16
31.12	odd	30		961.2.g.t.846.1		16
31.13	odd	30		31.2.g.a.28.2	yes	16
31.14	even	15		961.2.g.m.547.1		16
31.15	odd	10		961.2.d.o.388.3		16
31.16	even	5	inner	961.2.d.n.388.3		16
31.17	odd	30		961.2.g.s.547.1		16
31.18	even	15		961.2.g.l.338.2		16
31.19	even	15		961.2.g.n.846.1		16
31.20	even	15		961.2.c.i.521.4		16
31.21	odd	30		961.2.g.s.448.1		16
31.22	odd	30		961.2.g.t.844.1		16
31.23	odd	10		961.2.d.p.531.2		16
31.24	odd	30		961.2.c.j.439.4		16
31.25	even	3		961.2.g.l.816.2		16
31.26	odd	6		961.2.g.k.732.2		16
31.27	odd	10		961.2.a.i.1.4		8
31.28	even	15		961.2.g.j.235.2		16
31.29	odd	10		961.2.d.p.628.2		16
31.30	odd	2		961.2.d.o.374.3		16
93.35	odd	10		8649.2.a.be.1.5		8
93.44	even	30		279.2.y.c.28.1		16
93.68	even	6		279.2.y.c.10.1		16
93.89	even	10		8649.2.a.bf.1.5		8
124.75	even	30		496.2.bg.c.369.1		16
124.99	even	6		496.2.bg.c.289.1		16
155.13	even	60		775.2.ck.a.524.3		32
155.37	even	12		775.2.ck.a.599.3		32
155.44	odd	30		775.2.bl.a.276.1		16
155.68	even	12		775.2.ck.a.599.2		32
155.99	odd	6		775.2.bl.a.351.1		16
155.137	even	60		775.2.ck.a.524.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	31.6	odd	6
31.2.g.a.28.2	yes	16	31.13	odd	30
279.2.y.c.10.1		16	93.68	even	6
279.2.y.c.28.1		16	93.44	even	30
496.2.bg.c.289.1		16	124.99	even	6
496.2.bg.c.369.1		16	124.75	even	30
775.2.bl.a.276.1		16	155.44	odd	30
775.2.bl.a.351.1		16	155.99	odd	6
775.2.ck.a.524.2		32	155.137	even	60
775.2.ck.a.524.3		32	155.13	even	60
775.2.ck.a.599.2		32	155.68	even	12
775.2.ck.a.599.3		32	155.37	even	12
961.2.a.i.1.4		8	31.27	odd	10
961.2.a.j.1.4		8	31.4	even	5
961.2.c.i.439.4		16	31.7	even	15
961.2.c.i.521.4		16	31.20	even	15
961.2.c.j.439.4		16	31.24	odd	30
961.2.c.j.521.4		16	31.11	odd	30
961.2.d.n.374.3		16	1.1	even	1	trivial
961.2.d.n.388.3		16	31.16	even	5	inner
961.2.d.o.374.3		16	31.30	odd	2
961.2.d.o.388.3		16	31.15	odd	10
961.2.d.p.531.2		16	31.23	odd	10
961.2.d.p.628.2		16	31.29	odd	10
961.2.d.q.531.2		16	31.8	even	5
961.2.d.q.628.2		16	31.2	even	5
961.2.g.j.235.2		16	31.28	even	15
961.2.g.j.732.2		16	31.5	even	3
961.2.g.k.235.2		16	31.3	odd	30
961.2.g.k.732.2		16	31.26	odd	6
961.2.g.l.338.2		16	31.18	even	15
961.2.g.l.816.2		16	31.25	even	3
961.2.g.m.448.1		16	31.10	even	15
961.2.g.m.547.1		16	31.14	even	15
961.2.g.n.844.1		16	31.9	even	15
961.2.g.n.846.1		16	31.19	even	15
961.2.g.s.448.1		16	31.21	odd	30
961.2.g.s.547.1		16	31.17	odd	30
961.2.g.t.844.1		16	31.22	odd	30
961.2.g.t.846.1		16	31.12	odd	30
8649.2.a.be.1.5		8	93.35	odd	10
8649.2.a.bf.1.5		8	93.89	even	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.284315 - 0.206567i) q^{2} +(-2.34072 + 1.70063i) q^{3} +(-0.579869 - 1.78465i) q^{4} +2.97323 q^{5} +1.01680 q^{6} +(-0.334395 - 1.02916i) q^{7} +(-0.420982 + 1.29565i) q^{8} +(1.65977 - 5.10826i) q^{9} +(-0.845333 - 0.614171i) q^{10} +(0.751335 + 2.31237i) q^{11} +(4.39235 + 3.19123i) q^{12} +(2.32483 - 1.68909i) q^{13} +(-0.117517 + 0.361681i) q^{14} +(-6.95951 + 5.05638i) q^{15} +(-2.64890 + 1.92454i) q^{16} +(0.563883 - 1.73545i) q^{17} +(-1.52709 + 1.10950i) q^{18} +(-1.71372 - 1.24509i) q^{19} +(-1.72408 - 5.30618i) q^{20} +(2.53296 + 1.84030i) q^{21} +(0.264043 - 0.812642i) q^{22} +(0.136652 - 0.420572i) q^{23} +(-1.21802 - 3.74869i) q^{24} +3.84010 q^{25} -1.00989 q^{26} +(2.11998 + 6.52462i) q^{27} +(-1.64279 + 1.19356i) q^{28} +(-2.55579 - 1.85689i) q^{29} +3.02317 q^{30} +3.87532 q^{32} +(-5.69116 - 4.13487i) q^{33} +(-0.518808 + 0.376936i) q^{34} +(-0.994234 - 3.05994i) q^{35} -10.0789 q^{36} -3.14675 q^{37} +(0.230042 + 0.707995i) q^{38} +(-2.56926 + 7.90738i) q^{39} +(-1.25168 + 3.85226i) q^{40} +(5.61962 + 4.08290i) q^{41} +(-0.340012 - 1.04645i) q^{42} +(-6.80576 - 4.94467i) q^{43} +(3.69110 - 2.68174i) q^{44} +(4.93489 - 15.1880i) q^{45} +(-0.125728 + 0.0913471i) q^{46} +(6.44144 - 4.67998i) q^{47} +(2.92741 - 9.00963i) q^{48} +(4.71576 - 3.42620i) q^{49} +(-1.09180 - 0.793236i) q^{50} +(1.63148 + 5.02118i) q^{51} +(-4.36254 - 3.16957i) q^{52} +(1.53798 - 4.73341i) q^{53} +(0.745029 - 2.29296i) q^{54} +(2.23389 + 6.87521i) q^{55} +1.47421 q^{56} +6.12878 q^{57} +(0.343078 + 1.05588i) q^{58} +(9.71948 - 7.06161i) q^{59} +(13.0595 + 9.48827i) q^{60} +14.4351 q^{61} -5.81225 q^{63} +(4.19600 + 3.04857i) q^{64} +(6.91226 - 5.02205i) q^{65} +(0.763955 + 2.35121i) q^{66} -6.43759 q^{67} -3.42416 q^{68} +(0.395375 + 1.21684i) q^{69} +(-0.349406 + 1.07536i) q^{70} +(0.518492 - 1.59575i) q^{71} +(5.91977 + 4.30097i) q^{72} +(-4.43754 - 13.6573i) q^{73} +(0.894668 + 0.650014i) q^{74} +(-8.98860 + 6.53060i) q^{75} +(-1.22832 + 3.78038i) q^{76} +(2.12856 - 1.54649i) q^{77} +(2.36388 - 1.71746i) q^{78} +(1.06538 - 3.27890i) q^{79} +(-7.87580 + 5.72210i) q^{80} +(-3.02226 - 2.19580i) q^{81} +(-0.754352 - 2.32166i) q^{82} +(10.3988 + 7.55516i) q^{83} +(1.81552 - 5.58758i) q^{84} +(1.67655 - 5.15991i) q^{85} +(0.913573 + 2.81169i) q^{86} +9.14030 q^{87} -3.31232 q^{88} +(-0.698188 - 2.14880i) q^{89} +(-4.54040 + 3.29880i) q^{90} +(-2.51576 - 1.82781i) q^{91} -0.829816 q^{92} -2.79812 q^{94} +(-5.09528 - 3.70194i) q^{95} +(-9.07105 + 6.59050i) q^{96} +(1.05463 + 3.24582i) q^{97} -2.04850 q^{98} +13.0592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 9 q^{3} - 14 q^{4} + 6 q^{5} + 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} - 14 q^{11} - 5 q^{12} + q^{13} + 27 q^{14} - 14 q^{15} - 2 q^{16} + 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots + 12 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 9 * q^3 - 14 * q^4 + 6 * q^5 + 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 - 14 * q^11 - 5 * q^12 + q^13 + 27 * q^14 - 14 * q^15 - 2 * q^16 + 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 + 3 * q^21 - 12 * q^22 - q^23 - 25 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 - 15 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 - 49 * q^34 - 9 * q^35 - 2 * q^36 - 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 + 18 * q^42 - 14 * q^43 + 33 * q^44 + 5 * q^45 - 34 * q^46 + 14 * q^47 + 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 - 17 * q^52 - 3 * q^53 + 46 * q^54 + q^55 + 60 * q^56 - 34 * q^57 + 15 * q^58 + 7 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 + 6 * q^65 - 30 * q^66 - 26 * q^67 + 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 - 11 * q^73 + 56 * q^74 - 4 * q^75 + 24 * q^76 - 18 * q^77 - 15 * q^78 + 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 + 28 * q^83 + 31 * q^84 - 37 * q^85 - 7 * q^86 - 30 * q^87 - 34 * q^88 - q^89 + 16 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 + 16 * q^96 + 3 * q^97 + 20 * q^98 + 12 * q^99

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