LMFDB - Embedded newform 961.2.d.g.374.1

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)

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);

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")

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 = [4,2,4,-2] 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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			374.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	961.374
Dual form			961.2.d.g.388.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.363271i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-0.500000 - 1.53884i) q^{4} +1.00000 q^{5} +0.763932 q^{6} +(-1.30902 - 4.02874i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.454915 + 1.40008i) q^{9} +(0.500000 + 0.363271i) q^{10} +(-0.618034 - 1.90211i) q^{11} +(-1.61803 - 1.17557i) q^{12} +(1.00000 - 0.726543i) q^{13} +(0.809017 - 2.48990i) q^{14} +(1.00000 - 0.726543i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(-1.61803 + 4.97980i) q^{17} +(-0.736068 + 0.534785i) q^{18} +(-1.80902 - 1.31433i) q^{19} +(-0.500000 - 1.53884i) q^{20} +(-4.23607 - 3.07768i) q^{21} +(0.381966 - 1.17557i) q^{22} +(2.38197 - 7.33094i) q^{23} +(-0.854102 - 2.62866i) q^{24} -4.00000 q^{25} +0.763932 q^{26} +(1.70820 + 5.25731i) q^{27} +(-5.54508 + 4.02874i) q^{28} +(5.85410 + 4.25325i) q^{29} +0.763932 q^{30} -5.61803 q^{32} +(-2.00000 - 1.45309i) q^{33} +(-2.61803 + 1.90211i) q^{34} +(-1.30902 - 4.02874i) q^{35} +2.38197 q^{36} +2.00000 q^{37} +(-0.427051 - 1.31433i) q^{38} +(0.472136 - 1.45309i) q^{39} +(0.690983 - 2.12663i) q^{40} +(-5.66312 - 4.11450i) q^{41} +(-1.00000 - 3.07768i) q^{42} +(-2.61803 - 1.90211i) q^{43} +(-2.61803 + 1.90211i) q^{44} +(-0.454915 + 1.40008i) q^{45} +(3.85410 - 2.80017i) q^{46} +(5.23607 - 3.80423i) q^{47} +(-0.708204 + 2.17963i) q^{48} +(-8.85410 + 6.43288i) q^{49} +(-2.00000 - 1.45309i) q^{50} +(2.00000 + 6.15537i) q^{51} +(-1.61803 - 1.17557i) q^{52} +(0.472136 - 1.45309i) q^{53} +(-1.05573 + 3.24920i) q^{54} +(-0.618034 - 1.90211i) q^{55} -9.47214 q^{56} -2.76393 q^{57} +(1.38197 + 4.25325i) q^{58} +(1.80902 - 1.31433i) q^{59} +(-1.61803 - 1.17557i) q^{60} +14.1803 q^{61} +6.23607 q^{63} +(0.190983 + 0.138757i) q^{64} +(1.00000 - 0.726543i) q^{65} +(-0.472136 - 1.45309i) q^{66} +8.00000 q^{67} +8.47214 q^{68} +(-2.94427 - 9.06154i) q^{69} +(0.809017 - 2.48990i) q^{70} +(4.07295 - 12.5352i) q^{71} +(2.66312 + 1.93487i) q^{72} +(0.145898 + 0.449028i) q^{73} +(1.00000 + 0.726543i) q^{74} +(-4.00000 + 2.90617i) q^{75} +(-1.11803 + 3.44095i) q^{76} +(-6.85410 + 4.97980i) q^{77} +(0.763932 - 0.555029i) q^{78} +(-0.527864 + 1.62460i) q^{79} +(-1.50000 + 1.08981i) q^{80} +(1.95492 + 1.42033i) q^{81} +(-1.33688 - 4.11450i) q^{82} +(2.38197 + 1.73060i) q^{83} +(-2.61803 + 8.05748i) q^{84} +(-1.61803 + 4.97980i) q^{85} +(-0.618034 - 1.90211i) q^{86} +8.94427 q^{87} -4.47214 q^{88} +(0.527864 + 1.62460i) q^{89} +(-0.736068 + 0.534785i) q^{90} +(-4.23607 - 3.07768i) q^{91} -12.4721 q^{92} +4.00000 q^{94} +(-1.80902 - 1.31433i) q^{95} +(-5.61803 + 4.08174i) q^{96} +(0.600813 + 1.84911i) q^{97} -6.76393 q^{98} +2.94427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 4 q^{5} + 12 q^{6} - 3 q^{7} + 5 q^{8} - 13 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} - 6 q^{16} - 2 q^{17} + 6 q^{18} - 5 q^{19} - 2 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 4 * q^5 + 12 * q^6 - 3 * q^7 + 5 * q^8 - 13 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 + 4 * q^13 + q^14 + 4 * q^15 - 6 * q^16 - 2 * q^17 + 6 * q^18 - 5 * q^19 - 2 * q^20 - 8 * q^21 + 6 * q^22 + 14 * q^23 + 10 * q^24 - 16 * q^25 + 12 * q^26 - 20 * q^27 - 11 * q^28 + 10 * q^29 + 12 * q^30 - 18 * q^32 - 8 * q^33 - 6 * q^34 - 3 * q^35 + 14 * q^36 + 8 * q^37 + 5 * q^38 - 16 * q^39 + 5 * q^40 - 7 * q^41 - 4 * q^42 - 6 * q^43 - 6 * q^44 - 13 * q^45 + 2 * q^46 + 12 * q^47 + 24 * q^48 - 22 * q^49 - 8 * q^50 + 8 * q^51 - 2 * q^52 - 16 * q^53 - 40 * q^54 + 2 * q^55 - 20 * q^56 - 20 * q^57 + 10 * q^58 + 5 * q^59 - 2 * q^60 + 12 * q^61 + 16 * q^63 + 3 * q^64 + 4 * q^65 + 16 * q^66 + 32 * q^67 + 16 * q^68 + 24 * q^69 + q^70 + 23 * q^71 - 5 * q^72 + 14 * q^73 + 4 * q^74 - 16 * q^75 - 14 * q^77 + 12 * q^78 - 20 * q^79 - 6 * q^80 + 19 * q^81 - 21 * q^82 + 14 * q^83 - 6 * q^84 - 2 * q^85 + 2 * q^86 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 32 * q^92 + 16 * q^94 - 5 * q^95 - 18 * q^96 + 27 * q^97 - 36 * q^98 - 24 * 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 $

$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	0.750358	−	0.661031i	$-0.229881\pi$
$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	−0.396805	+	0.917903i	$0.629881\pi$
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	−0.260418	−	0.965496i	$-0.583860\pi$
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	0.837768	+	0.546027i	$0.183860\pi$
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	0.763932			0.311874
$7$	−1.30902	−	4.02874i	−0.494762	−	1.52272i	−0.817327	−	0.576173i	$-0.804545\pi$
$7$	−1.30902	−	4.02874i	−0.494762	−	1.52272i	0.322566	−	0.946547i	$-0.395455\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	−0.454915	+	1.40008i	−0.151638	+	0.466695i
$10$	0.500000	+	0.363271i	0.158114	+	0.114876i
$11$	−0.618034	−	1.90211i	−0.186344	−	0.573509i	0.813625	−	0.581390i	$-0.197491\pi$
$11$	−0.618034	−	1.90211i	−0.186344	−	0.573509i	−0.999969	+	0.00788181i	$0.997491\pi$
$12$	−1.61803	−	1.17557i	−0.467086	−	0.339358i
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	−0.440411	−	0.897796i	$-0.645167\pi$
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	0.717761	+	0.696290i	$0.245167\pi$
$14$	0.809017	−	2.48990i	0.216219	−	0.665453i
$15$	1.00000	−	0.726543i	0.258199	−	0.187592i
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	−1.61803	+	4.97980i	−0.392431	+	1.20778i	0.538513	+	0.842617i	$0.318986\pi$
$17$	−1.61803	+	4.97980i	−0.392431	+	1.20778i	−0.930944	+	0.365161i	$0.881014\pi$
$18$	−0.736068	+	0.534785i	−0.173493	+	0.126050i
$19$	−1.80902	−	1.31433i	−0.415017	−	0.301527i	0.360613	−	0.932716i	$-0.382568\pi$
$19$	−1.80902	−	1.31433i	−0.415017	−	0.301527i	−0.775630	+	0.631188i	$0.782568\pi$
$20$	−0.500000	−	1.53884i	−0.111803	−	0.344095i
$21$	−4.23607	−	3.07768i	−0.924386	−	0.671606i
$22$	0.381966	−	1.17557i	0.0814354	−	0.250632i
$23$	2.38197	−	7.33094i	0.496674	−	1.52861i	−0.317657	−	0.948206i	$-0.602896\pi$
$23$	2.38197	−	7.33094i	0.496674	−	1.52861i	0.814331	−	0.580400i	$-0.197104\pi$
$24$	−0.854102	−	2.62866i	−0.174343	−	0.536572i
$25$	−4.00000			−0.800000
$26$	0.763932			0.149819
$27$	1.70820	+	5.25731i	0.328744	+	1.01177i
$28$	−5.54508	+	4.02874i	−1.04792	+	0.761360i
$29$	5.85410	+	4.25325i	1.08708	+	0.789809i	0.978904	−	0.204322i	$-0.0654991\pi$
$29$	5.85410	+	4.25325i	1.08708	+	0.789809i	0.108176	+	0.994132i	$0.465499\pi$
$30$	0.763932			0.139474
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	−2.00000	−	1.45309i	−0.348155	−	0.252950i
$34$	−2.61803	+	1.90211i	−0.448989	+	0.326210i
$35$	−1.30902	−	4.02874i	−0.221264	−	0.680981i
$36$	2.38197			0.396994
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−0.427051	−	1.31433i	−0.0692768	−	0.213212i
$39$	0.472136	−	1.45309i	0.0756023	−	0.232680i
$40$	0.690983	−	2.12663i	0.109254	−	0.336249i
$41$	−5.66312	−	4.11450i	−0.884431	−	0.642576i	0.0499893	−	0.998750i	$-0.484081\pi$
$41$	−5.66312	−	4.11450i	−0.884431	−	0.642576i	−0.934420	+	0.356173i	$0.884081\pi$
$42$	−1.00000	−	3.07768i	−0.154303	−	0.474897i
$43$	−2.61803	−	1.90211i	−0.399246	−	0.290070i	0.369988	−	0.929037i	$-0.379362\pi$
$43$	−2.61803	−	1.90211i	−0.399246	−	0.290070i	−0.769234	+	0.638967i	$0.779362\pi$
$44$	−2.61803	+	1.90211i	−0.394683	+	0.286754i
$45$	−0.454915	+	1.40008i	−0.0678147	+	0.208712i
$46$	3.85410	−	2.80017i	0.568256	−	0.412862i
$47$	5.23607	−	3.80423i	0.763759	−	0.554903i	−0.136302	−	0.990667i	$-0.543522\pi$
$47$	5.23607	−	3.80423i	0.763759	−	0.554903i	0.900061	+	0.435764i	$0.143522\pi$
$48$	−0.708204	+	2.17963i	−0.102220	+	0.314602i
$49$	−8.85410	+	6.43288i	−1.26487	+	0.918983i
$50$	−2.00000	−	1.45309i	−0.282843	−	0.205497i
$51$	2.00000	+	6.15537i	0.280056	+	0.861924i
$52$	−1.61803	−	1.17557i	−0.224381	−	0.163022i
$53$	0.472136	−	1.45309i	0.0648529	−	0.199597i	−0.913379	−	0.407109i	$-0.866537\pi$
$53$	0.472136	−	1.45309i	0.0648529	−	0.199597i	0.978232	+	0.207513i	$0.0665368\pi$
$54$	−1.05573	+	3.24920i	−0.143666	+	0.442160i
$55$	−0.618034	−	1.90211i	−0.0833357	−	0.256481i
$56$	−9.47214			−1.26577
$57$	−2.76393			−0.366092
$58$	1.38197	+	4.25325i	0.181461	+	0.558480i
$59$	1.80902	−	1.31433i	0.235514	−	0.171111i	−0.463768	−	0.885956i	$-0.653503\pi$
$59$	1.80902	−	1.31433i	0.235514	−	0.171111i	0.699282	+	0.714846i	$0.253503\pi$
$60$	−1.61803	−	1.17557i	−0.208887	−	0.151765i
$61$	14.1803			1.81561			0.907803	−	0.419396i	$-0.137758\pi$
$61$	14.1803			1.81561			0.907803	+	0.419396i	$0.137758\pi$
$62$		0			0
$63$	6.23607			0.785671
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$	1.00000	−	0.726543i	0.124035	−	0.0901165i
$66$	−0.472136	−	1.45309i	−0.0581159	−	0.178862i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	8.47214			1.02740
$69$	−2.94427	−	9.06154i	−0.354449	−	1.09088i
$70$	0.809017	−	2.48990i	0.0966960	−	0.297600i
$71$	4.07295	−	12.5352i	0.483370	−	1.48766i	−0.350958	−	0.936391i	$-0.614144\pi$
$71$	4.07295	−	12.5352i	0.483370	−	1.48766i	0.834328	−	0.551269i	$-0.185856\pi$
$72$	2.66312	+	1.93487i	0.313852	+	0.228027i
$73$	0.145898	+	0.449028i	0.0170761	+	0.0525547i	0.959231	−	0.282622i	$-0.0912041\pi$
$73$	0.145898	+	0.449028i	0.0170761	+	0.0525547i	−0.942155	+	0.335176i	$0.891204\pi$
$74$	1.00000	+	0.726543i	0.116248	+	0.0844589i
$75$	−4.00000	+	2.90617i	−0.461880	+	0.335576i
$76$	−1.11803	+	3.44095i	−0.128247	+	0.394705i
$77$	−6.85410	+	4.97980i	−0.781097	+	0.567500i
$78$	0.763932	−	0.555029i	0.0864983	−	0.0628447i
$79$	−0.527864	+	1.62460i	−0.0593893	+	0.182782i	−0.976350	−	0.216196i	$-0.930635\pi$
$79$	−0.527864	+	1.62460i	−0.0593893	+	0.182782i	0.916961	+	0.398978i	$0.130635\pi$
$80$	−1.50000	+	1.08981i	−0.167705	+	0.121845i
$81$	1.95492	+	1.42033i	0.217213	+	0.157814i
$82$	−1.33688	−	4.11450i	−0.147634	−	0.454370i
$83$	2.38197	+	1.73060i	0.261455	+	0.189958i	0.710788	−	0.703406i	$-0.248338\pi$
$83$	2.38197	+	1.73060i	0.261455	+	0.189958i	−0.449333	+	0.893364i	$0.648338\pi$
$84$	−2.61803	+	8.05748i	−0.285651	+	0.879143i
$85$	−1.61803	+	4.97980i	−0.175500	+	0.540135i
$86$	−0.618034	−	1.90211i	−0.0666443	−	0.205110i
$87$	8.94427			0.958927
$88$	−4.47214			−0.476731
$89$	0.527864	+	1.62460i	0.0559535	+	0.172207i	0.975128	−	0.221644i	$-0.0711424\pi$
$89$	0.527864	+	1.62460i	0.0559535	+	0.172207i	−0.919174	+	0.393852i	$0.871142\pi$
$90$	−0.736068	+	0.534785i	−0.0775884	+	0.0563713i
$91$	−4.23607	−	3.07768i	−0.444061	−	0.322629i
$92$	−12.4721			−1.30031
$93$		0			0
$94$	4.00000			0.412568
$95$	−1.80902	−	1.31433i	−0.185601	−	0.134847i
$96$	−5.61803	+	4.08174i	−0.573388	+	0.416591i
$97$	0.600813	+	1.84911i	0.0610033	+	0.187749i	0.976914	−	0.213634i	$-0.0685298\pi$
$97$	0.600813	+	1.84911i	0.0610033	+	0.187749i	−0.915911	+	0.401382i	$0.868530\pi$
$98$	−6.76393			−0.683260
$99$	2.94427			0.295910
$100$	2.00000	+	6.15537i	0.200000	+	0.615537i
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	−0.986526	−	0.163605i	$-0.947688\pi$
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	0.894281	+	0.447506i	$0.147688\pi$
$102$	−1.23607	+	3.80423i	−0.122389	+	0.376675i
$103$	−1.42705	−	1.03681i	−0.140612	−	0.102160i	0.515256	−	0.857036i	$-0.327697\pi$
$103$	−1.42705	−	1.03681i	−0.140612	−	0.102160i	−0.655867	+	0.754876i	$0.727697\pi$
$104$	−0.854102	−	2.62866i	−0.0837516	−	0.257761i
$105$	−4.23607	−	3.07768i	−0.413398	−	0.300351i
$106$	0.763932	−	0.555029i	0.0741996	−	0.0539092i
$107$	3.16312	−	9.73508i	0.305790	−	0.941126i	−0.673591	−	0.739104i	$-0.735249\pi$
$107$	3.16312	−	9.73508i	0.305790	−	0.941126i	0.979381	−	0.202021i	$-0.0647510\pi$
$108$	7.23607	−	5.25731i	0.696291	−	0.505885i
$109$	−3.19098	+	2.31838i	−0.305641	+	0.222061i	−0.730024	−	0.683422i	$-0.760491\pi$
$109$	−3.19098	+	2.31838i	−0.305641	+	0.222061i	0.424383	+	0.905483i	$0.360491\pi$
$110$	0.381966	−	1.17557i	0.0364190	−	0.112086i
$111$	2.00000	−	1.45309i	0.189832	−	0.137921i
$112$	6.35410	+	4.61653i	0.600406	+	0.436221i
$113$	−1.69098	−	5.20431i	−0.159074	−	0.489580i	0.839477	−	0.543396i	$-0.182862\pi$
$113$	−1.69098	−	5.20431i	−0.159074	−	0.489580i	−0.998551	+	0.0538155i	$0.982862\pi$
$114$	−1.38197	−	1.00406i	−0.129433	−	0.0940386i
$115$	2.38197	−	7.33094i	0.222119	−	0.683613i
$116$	3.61803	−	11.1352i	0.335926	−	1.03387i
$117$	0.562306	+	1.73060i	0.0519852	+	0.159994i
$118$	1.38197			0.127220
$119$	22.1803			2.03327
$120$	−0.854102	−	2.62866i	−0.0779685	−	0.239962i
$121$	5.66312	−	4.11450i	0.514829	−	0.374045i
$122$	7.09017	+	5.15131i	0.641914	+	0.466378i
$123$	−8.65248			−0.780167
$124$		0			0
$125$	−9.00000			−0.804984
$126$	3.11803	+	2.26538i	0.277777	+	0.201816i
$127$	2.85410	−	2.07363i	0.253261	−	0.184005i	−0.453910	−	0.891048i	$-0.649971\pi$
$127$	2.85410	−	2.07363i	0.253261	−	0.184005i	0.707171	+	0.707043i	$0.249971\pi$
$128$	3.51722	+	10.8249i	0.310881	+	0.956794i
$129$	−4.00000			−0.352180
$130$	0.763932			0.0670013
$131$	3.70820	+	11.4127i	0.323987	+	0.997130i	0.971896	+	0.235412i	$0.0756440\pi$
$131$	3.70820	+	11.4127i	0.323987	+	0.997130i	−0.647908	+	0.761718i	$0.724356\pi$
$132$	−1.23607	+	3.80423i	−0.107586	+	0.331115i
$133$	−2.92705	+	9.00854i	−0.253808	+	0.781139i
$134$	4.00000	+	2.90617i	0.345547	+	0.251055i
$135$	1.70820	+	5.25731i	0.147019	+	0.452477i
$136$	9.47214	+	6.88191i	0.812229	+	0.590119i
$137$	15.9443	−	11.5842i	1.36221	−	0.989704i	0.363910	−	0.931434i	$-0.381441\pi$
$137$	15.9443	−	11.5842i	1.36221	−	0.989704i	0.998301	−	0.0582703i	$-0.0185585\pi$
$138$	1.81966	−	5.60034i	0.154900	−	0.476732i
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	−0.943681	−	0.330855i	$-0.892663\pi$
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	0.0230486	+	0.999734i	$0.492663\pi$
$140$	−5.54508	+	4.02874i	−0.468645	+	0.340491i
$141$	2.47214	−	7.60845i	0.208191	−	0.640747i
$142$	6.59017	−	4.78804i	0.553035	−	0.401803i
$143$	−2.00000	−	1.45309i	−0.167248	−	0.121513i
$144$	−0.843459	−	2.59590i	−0.0702882	−	0.216325i
$145$	5.85410	+	4.25325i	0.486157	+	0.353214i
$146$	−0.0901699	+	0.277515i	−0.00746252	+	0.0229673i
$147$	−4.18034	+	12.8658i	−0.344789	+	1.06115i
$148$	−1.00000	−	3.07768i	−0.0821995	−	0.252984i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	−3.05573			−0.249499
$151$	−2.52786	−	7.77997i	−0.205715	−	0.633125i	−0.999683	−	0.0251659i	$-0.991989\pi$
$151$	−2.52786	−	7.77997i	−0.205715	−	0.633125i	0.793969	−	0.607959i	$-0.208011\pi$
$152$	−4.04508	+	2.93893i	−0.328100	+	0.238378i
$153$	−6.23607	−	4.53077i	−0.504156	−	0.366291i
$154$	−5.23607			−0.421934
$155$		0			0
$156$	−2.47214			−0.197929
$157$	12.0451	+	8.75127i	0.961302	+	0.698427i	0.953453	−	0.301542i	$-0.0975014\pi$
$157$	12.0451	+	8.75127i	0.961302	+	0.698427i	0.00784957	+	0.999969i	$0.497501\pi$
$158$	−0.854102	+	0.620541i	−0.0679487	+	0.0493676i
$159$	−0.583592	−	1.79611i	−0.0462819	−	0.142441i
$160$	−5.61803			−0.444145
$161$	−32.6525			−2.57338
$162$	0.461493	+	1.42033i	0.0362583	+	0.111592i
$163$	−0.836881	+	2.57565i	−0.0655496	+	0.201741i	−0.978467	−	0.206404i	$-0.933824\pi$
$163$	−0.836881	+	2.57565i	−0.0655496	+	0.201741i	0.912917	+	0.408144i	$0.133824\pi$
$164$	−3.50000	+	10.7719i	−0.273304	+	0.841143i
$165$	−2.00000	−	1.45309i	−0.155700	−	0.113123i
$166$	0.562306	+	1.73060i	0.0436434	+	0.134321i
$167$	2.00000	+	1.45309i	0.154765	+	0.112443i	0.662473	−	0.749086i	$-0.269507\pi$
$167$	2.00000	+	1.45309i	0.154765	+	0.112443i	−0.507708	+	0.861529i	$0.669507\pi$
$168$	−9.47214	+	6.88191i	−0.730791	+	0.530951i
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$	−2.61803	+	1.90211i	−0.200794	+	0.145885i
$171$	2.66312	−	1.93487i	0.203654	−	0.147963i
$172$	−1.61803	+	4.97980i	−0.123374	+	0.379706i
$173$	12.0902	−	8.78402i	0.919199	−	0.667837i	−0.0241258	−	0.999709i	$-0.507680\pi$
$173$	12.0902	−	8.78402i	0.919199	−	0.667837i	0.943324	+	0.331872i	$0.107680\pi$
$174$	4.47214	+	3.24920i	0.339032	+	0.246321i
$175$	5.23607	+	16.1150i	0.395810	+	1.21818i
$176$	3.00000	+	2.17963i	0.226134	+	0.164296i
$177$	0.854102	−	2.62866i	0.0641982	−	0.197582i
$178$	−0.326238	+	1.00406i	−0.0244526	+	0.0752573i
$179$	3.61803	+	11.1352i	0.270425	+	0.832281i	0.990394	+	0.138275i	$0.0441559\pi$
$179$	3.61803	+	11.1352i	0.270425	+	0.832281i	−0.719969	+	0.694006i	$0.755844\pi$
$180$	2.38197			0.177541
$181$	−18.1803			−1.35133			−0.675667	−	0.737207i	$-0.736144\pi$
$181$	−18.1803			−1.35133			−0.675667	+	0.737207i	$0.736144\pi$
$182$	−1.00000	−	3.07768i	−0.0741249	−	0.228133i
$183$	14.1803	−	10.3026i	1.04824	−	0.761592i
$184$	−13.9443	−	10.1311i	−1.02799	−	0.746875i
$185$	2.00000			0.147043
$186$		0			0
$187$	10.4721			0.765798
$188$	−8.47214	−	6.15537i	−0.617894	−	0.448926i
$189$	18.9443	−	13.7638i	1.37799	−	1.00117i
$190$	−0.427051	−	1.31433i	−0.0309815	−	0.0953514i
$191$	3.18034			0.230121			0.115061	−	0.993358i	$-0.463294\pi$
$191$	3.18034			0.230121			0.115061	+	0.993358i	$0.463294\pi$
$192$	0.291796			0.0210586
$193$	−1.69098	−	5.20431i	−0.121720	−	0.374614i	0.871570	−	0.490272i	$-0.163103\pi$
$193$	−1.69098	−	5.20431i	−0.121720	−	0.374614i	−0.993289	+	0.115657i	$0.963103\pi$
$194$	−0.371323	+	1.14281i	−0.0266594	+	0.0820493i
$195$	0.472136	−	1.45309i	0.0338104	−	0.104058i
$196$	14.3262	+	10.4086i	1.02330	+	0.743473i
$197$	4.76393	+	14.6619i	0.339416	+	1.04462i	0.964506	+	0.264062i	$0.0850625\pi$
$197$	4.76393	+	14.6619i	0.339416	+	1.04462i	−0.625090	+	0.780553i	$0.714938\pi$
$198$	1.47214	+	1.06957i	0.104620	+	0.0760110i
$199$	−0.854102	+	0.620541i	−0.0605457	+	0.0439890i	−0.617646	−	0.786456i	$-0.711914\pi$
$199$	−0.854102	+	0.620541i	−0.0605457	+	0.0439890i	0.557101	+	0.830445i	$0.311914\pi$
$200$	−2.76393	+	8.50651i	−0.195440	+	0.601501i
$201$	8.00000	−	5.81234i	0.564276	−	0.409971i
$202$	−1.50000	+	1.08981i	−0.105540	+	0.0766790i
$203$	9.47214	−	29.1522i	0.664814	−	2.04609i
$204$	8.47214	−	6.15537i	0.593168	−	0.430962i
$205$	−5.66312	−	4.11450i	−0.395529	−	0.287369i
$206$	−0.336881	−	1.03681i	−0.0234716	−	0.0722382i
$207$	9.18034	+	6.66991i	0.638078	+	0.463591i
$208$	−0.708204	+	2.17963i	−0.0491051	+	0.151130i
$209$	−1.38197	+	4.25325i	−0.0955926	+	0.294204i
$210$	−1.00000	−	3.07768i	−0.0690066	−	0.212380i
$211$	0.819660			0.0564277			0.0282139	−	0.999602i	$-0.491018\pi$
$211$	0.819660			0.0564277			0.0282139	+	0.999602i	$0.491018\pi$
$212$	−2.47214			−0.169787
$213$	−5.03444	−	15.4944i	−0.344954	−	1.06166i
$214$	5.11803	−	3.71847i	0.349862	−	0.254189i
$215$	−2.61803	−	1.90211i	−0.178548	−	0.129723i
$216$	12.3607			0.841038
$217$		0			0
$218$	−2.43769			−0.165101
$219$	0.472136	+	0.343027i	0.0319040	+	0.0231796i
$220$	−2.61803	+	1.90211i	−0.176508	+	0.128240i
$221$	2.00000	+	6.15537i	0.134535	+	0.414055i
$222$	1.52786			0.102544
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$	7.35410	+	22.6336i	0.491367	+	1.51227i
$225$	1.81966	−	5.60034i	0.121311	−	0.373356i
$226$	1.04508	−	3.21644i	0.0695180	−	0.213954i
$227$	−2.00000	−	1.45309i	−0.132745	−	0.0964446i	0.519431	−	0.854512i	$-0.326144\pi$
$227$	−2.00000	−	1.45309i	−0.132745	−	0.0964446i	−0.652176	+	0.758067i	$0.726144\pi$
$228$	1.38197	+	4.25325i	0.0915229	+	0.281679i
$229$	10.8541	+	7.88597i	0.717259	+	0.521119i	0.885507	−	0.464625i	$-0.153811\pi$
$229$	10.8541	+	7.88597i	0.717259	+	0.521119i	−0.168248	+	0.985745i	$0.553811\pi$
$230$	3.85410	−	2.80017i	0.254132	−	0.184638i
$231$	−3.23607	+	9.95959i	−0.212918	+	0.655293i
$232$	13.0902	−	9.51057i	0.859412	−	0.624399i
$233$	−0.0450850	+	0.0327561i	−0.00295361	+	0.00214593i	−0.589261	−	0.807943i	$-0.700581\pi$
$233$	−0.0450850	+	0.0327561i	−0.00295361	+	0.00214593i	0.586307	+	0.810089i	$0.300581\pi$
$234$	−0.347524	+	1.06957i	−0.0227184	+	0.0699199i
$235$	5.23607	−	3.80423i	0.341563	−	0.248160i
$236$	−2.92705	−	2.12663i	−0.190535	−	0.138432i
$237$	0.652476	+	2.00811i	0.0423829	+	0.130441i
$238$	11.0902	+	8.05748i	0.718869	+	0.522289i
$239$	−0.527864	+	1.62460i	−0.0341447	+	0.105087i	−0.966676	−	0.256002i	$-0.917595\pi$
$239$	−0.527864	+	1.62460i	−0.0341447	+	0.105087i	0.932532	+	0.361088i	$0.117595\pi$
$240$	−0.708204	+	2.17963i	−0.0457144	+	0.140694i
$241$	9.38197	+	28.8747i	0.604346	+	1.85998i	0.501228	+	0.865315i	$0.332882\pi$
$241$	9.38197	+	28.8747i	0.604346	+	1.85998i	0.103117	+	0.994669i	$0.467118\pi$
$242$	4.32624			0.278101
$243$	−13.5967			−0.872232
$244$	−7.09017	−	21.8213i	−0.453902	−	1.39697i
$245$	−8.85410	+	6.43288i	−0.565668	+	0.410982i
$246$	−4.32624	−	3.14320i	−0.275831	−	0.200403i
$247$	−2.76393			−0.175865
$248$		0			0
$249$	3.63932			0.230633
$250$	−4.50000	−	3.26944i	−0.284605	−	0.206778i
$251$	−19.5623	+	14.2128i	−1.23476	+	0.897107i	−0.997238	−	0.0742747i	$-0.976336\pi$
$251$	−19.5623	+	14.2128i	−1.23476	+	0.897107i	−0.237524	+	0.971382i	$0.576336\pi$
$252$	−3.11803	−	9.59632i	−0.196418	−	0.604511i
$253$	−15.4164			−0.969221
$254$	2.18034			0.136807
$255$	2.00000	+	6.15537i	0.125245	+	0.385464i
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	−4.92705	+	15.1639i	−0.307341	+	0.945898i	0.671452	+	0.741048i	$0.265671\pi$
$257$	−4.92705	+	15.1639i	−0.307341	+	0.945898i	−0.978793	+	0.204851i	$0.934329\pi$
$258$	−2.00000	−	1.45309i	−0.124515	−	0.0904651i
$259$	−2.61803	−	8.05748i	−0.162677	−	0.500667i
$260$	−1.61803	−	1.17557i	−0.100346	−	0.0729058i
$261$	−8.61803	+	6.26137i	−0.533443	+	0.387569i
$262$	−2.29180	+	7.05342i	−0.141588	+	0.435762i
$263$	−15.1803	+	11.0292i	−0.936060	+	0.680087i	−0.947469	−	0.319848i	$-0.896368\pi$
$263$	−15.1803	+	11.0292i	−0.936060	+	0.680087i	0.0114091	+	0.999935i	$0.496368\pi$
$264$	−4.47214	+	3.24920i	−0.275241	+	0.199974i
$265$	0.472136	−	1.45309i	0.0290031	−	0.0892623i
$266$	−4.73607	+	3.44095i	−0.290387	+	0.210978i
$267$	1.70820	+	1.24108i	0.104540	+	0.0759530i
$268$	−4.00000	−	12.3107i	−0.244339	−	0.751998i
$269$	−23.4164	−	17.0130i	−1.42772	−	1.03730i	−0.990435	−	0.137981i	$-0.955939\pi$
$269$	−23.4164	−	17.0130i	−1.42772	−	1.03730i	−0.437289	−	0.899321i	$-0.644061\pi$
$270$	−1.05573	+	3.24920i	−0.0642496	+	0.197740i
$271$	−2.52786	+	7.77997i	−0.153557	+	0.472599i	−0.998012	−	0.0630273i	$-0.979924\pi$
$271$	−2.52786	+	7.77997i	−0.153557	+	0.472599i	0.844455	+	0.535627i	$0.179924\pi$
$272$	−3.00000	−	9.23305i	−0.181902	−	0.559836i
$273$	−6.47214			−0.391711
$274$	12.1803			0.735841
$275$	2.47214	+	7.60845i	0.149075	+	0.458807i
$276$	−12.4721	+	9.06154i	−0.750734	+	0.545440i
$277$	15.0902	+	10.9637i	0.906680	+	0.658742i	0.940173	−	0.340697i	$-0.110663\pi$
$277$	15.0902	+	10.9637i	0.906680	+	0.658742i	−0.0334927	+	0.999439i	$0.510663\pi$
$278$	−8.29180			−0.497309
$279$		0			0
$280$	−9.47214			−0.566068
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	0.0963896	−	0.995344i	$-0.469271\pi$
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	−0.916842	+	0.399250i	$0.869271\pi$
$282$	4.00000	−	2.90617i	0.238197	−	0.173060i
$283$	6.76393	+	20.8172i	0.402074	+	1.23746i	0.923314	+	0.384046i	$0.125470\pi$
$283$	6.76393	+	20.8172i	0.402074	+	1.23746i	−0.521240	+	0.853410i	$0.674530\pi$
$284$	−21.3262			−1.26548
$285$	−2.76393			−0.163721
$286$	−0.472136	−	1.45309i	−0.0279180	−	0.0859227i
$287$	−9.16312	+	28.2012i	−0.540882	+	1.66466i
$288$	2.55573	−	7.86572i	0.150598	−	0.463492i
$289$	−8.42705	−	6.12261i	−0.495709	−	0.360154i
$290$	1.38197	+	4.25325i	0.0811518	+	0.249760i
$291$	1.94427	+	1.41260i	0.113975	+	0.0828079i
$292$	0.618034	−	0.449028i	0.0361677	−	0.0262774i
$293$	2.61803	−	8.05748i	0.152947	−	0.470723i	−0.845000	−	0.534766i	$-0.820400\pi$
$293$	2.61803	−	8.05748i	0.152947	−	0.470723i	0.997947	+	0.0640434i	$0.0203996\pi$
$294$	−6.76393	+	4.91428i	−0.394481	+	0.286607i
$295$	1.80902	−	1.31433i	0.105325	−	0.0765231i
$296$	1.38197	−	4.25325i	0.0803251	−	0.247215i
$297$	8.94427	−	6.49839i	0.518999	−	0.377075i
$298$	5.00000	+	3.63271i	0.289642	+	0.210437i
$299$	−2.94427	−	9.06154i	−0.170272	−	0.524042i
$300$	6.47214	+	4.70228i	0.373669	+	0.271486i
$301$	−4.23607	+	13.0373i	−0.244163	+	0.751456i
$302$	1.56231	−	4.80828i	0.0899006	−	0.276686i
$303$	1.14590	+	3.52671i	0.0658301	+	0.202604i
$304$	4.14590			0.237784
$305$	14.1803			0.811964
$306$	−1.47214	−	4.53077i	−0.0841564	−	0.259007i
$307$	12.3713	−	8.98829i	0.706069	−	0.512989i	−0.175834	−	0.984420i	$-0.556262\pi$
$307$	12.3713	−	8.98829i	0.706069	−	0.512989i	0.881903	+	0.471431i	$0.156262\pi$
$308$	11.0902	+	8.05748i	0.631921	+	0.459118i
$309$	−2.18034			−0.124035
$310$		0			0
$311$	−6.81966			−0.386707			−0.193354	−	0.981129i	$-0.561936\pi$
$311$	−6.81966			−0.386707			−0.193354	+	0.981129i	$0.561936\pi$
$312$	−2.76393	−	2.00811i	−0.156477	−	0.113687i
$313$	17.1803	−	12.4822i	0.971090	−	0.705538i	0.0153904	−	0.999882i	$-0.495101\pi$
$313$	17.1803	−	12.4822i	0.971090	−	0.705538i	0.955700	+	0.294343i	$0.0951009\pi$
$314$	2.84346	+	8.75127i	0.160466	+	0.493863i
$315$	6.23607			0.351363
$316$	2.76393			0.155483
$317$	6.78115	+	20.8702i	0.380867	+	1.17219i	0.939434	+	0.342730i	$0.111352\pi$
$317$	6.78115	+	20.8702i	0.380867	+	1.17219i	−0.558567	+	0.829460i	$0.688648\pi$
$318$	0.360680	−	1.11006i	0.0202259	−	0.0622490i
$319$	4.47214	−	13.7638i	0.250392	−	0.770626i
$320$	0.190983	+	0.138757i	0.0106763	+	0.00775677i
$321$	−3.90983	−	12.0332i	−0.218225	−	0.671629i
$322$	−16.3262	−	11.8617i	−0.909826	−	0.661027i
$323$	9.47214	−	6.88191i	0.527044	−	0.382920i
$324$	1.20820	−	3.71847i	0.0671224	−	0.206582i
$325$	−4.00000	+	2.90617i	−0.221880	+	0.161205i
$326$	−1.35410	+	0.983813i	−0.0749968	+	0.0544883i
$327$	−1.50658	+	4.63677i	−0.0833139	+	0.256414i
$328$	−12.6631	+	9.20029i	−0.699204	+	0.508001i
$329$	−22.1803	−	16.1150i	−1.22284	−	0.888447i
$330$	−0.472136	−	1.45309i	−0.0259902	−	0.0799897i
$331$	1.61803	+	1.17557i	0.0889352	+	0.0646152i	0.631364	−	0.775486i	$-0.282495\pi$
$331$	1.61803	+	1.17557i	0.0889352	+	0.0646152i	−0.542429	+	0.840102i	$0.682495\pi$
$332$	1.47214	−	4.53077i	0.0807940	−	0.248658i
$333$	−0.909830	+	2.80017i	−0.0498584	+	0.153448i
$334$	0.472136	+	1.45309i	0.0258341	+	0.0795093i
$335$	8.00000			0.437087
$336$	9.70820			0.529626
$337$	5.94427	+	18.2946i	0.323805	+	0.996570i	0.971977	+	0.235076i	$0.0755338\pi$
$337$	5.94427	+	18.2946i	0.323805	+	0.996570i	−0.648172	+	0.761494i	$0.724466\pi$
$338$	−5.73607	+	4.16750i	−0.312001	+	0.226682i
$339$	−5.47214	−	3.97574i	−0.297206	−	0.215933i
$340$	8.47214			0.459466
$341$		0			0
$342$	2.03444			0.110010
$343$	13.5172	+	9.82084i	0.729861	+	0.530275i
$344$	−5.85410	+	4.25325i	−0.315632	+	0.229320i
$345$	−2.94427	−	9.06154i	−0.158514	−	0.487857i
$346$	9.23607			0.496534
$347$	−1.81966			−0.0976845			−0.0488422	−	0.998807i	$-0.515553\pi$
$347$	−1.81966			−0.0976845			−0.0488422	+	0.998807i	$0.515553\pi$
$348$	−4.47214	−	13.7638i	−0.239732	−	0.737818i
$349$	8.61803	−	26.5236i	0.461313	−	1.41977i	−0.402248	−	0.915531i	$-0.631771\pi$
$349$	8.61803	−	26.5236i	0.461313	−	1.41977i	0.863561	−	0.504244i	$-0.168229\pi$
$350$	−3.23607	+	9.95959i	−0.172975	+	0.532363i
$351$	5.52786	+	4.01623i	0.295056	+	0.214370i
$352$	3.47214	+	10.6861i	0.185065	+	0.569573i
$353$	−15.7082	−	11.4127i	−0.836063	−	0.607436i	0.0852049	−	0.996363i	$-0.472846\pi$
$353$	−15.7082	−	11.4127i	−0.836063	−	0.607436i	−0.921268	+	0.388928i	$0.872846\pi$
$354$	1.38197	−	1.00406i	0.0734507	−	0.0533650i
$355$	4.07295	−	12.5352i	0.216170	−	0.665302i
$356$	2.23607	−	1.62460i	0.118511	−	0.0861035i
$357$	22.1803	−	16.1150i	1.17391	−	0.852894i
$358$	−2.23607	+	6.88191i	−0.118180	+	0.363720i
$359$	−14.3713	+	10.4414i	−0.758489	+	0.551075i	−0.898447	−	0.439083i	$-0.855303\pi$
$359$	−14.3713	+	10.4414i	−0.758489	+	0.551075i	0.139957	+	0.990158i	$0.455303\pi$
$360$	2.66312	+	1.93487i	0.140359	+	0.101977i
$361$	−4.32624	−	13.3148i	−0.227697	−	0.700778i
$362$	−9.09017	−	6.60440i	−0.477769	−	0.347119i
$363$	2.67376	−	8.22899i	0.140336	−	0.431910i
$364$	−2.61803	+	8.05748i	−0.137222	+	0.422327i
$365$	0.145898	+	0.449028i	0.00763665	+	0.0235032i
$366$	10.8328			0.566240
$367$	−18.0000			−0.939592			−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$368$	4.41641	+	13.5923i	0.230221	+	0.708548i
$369$	8.33688	−	6.05710i	0.434001	−	0.315320i
$370$	1.00000	+	0.726543i	0.0519875	+	0.0377711i
$371$	−6.47214			−0.336017
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	5.23607	+	3.80423i	0.270751	+	0.196712i
$375$	−9.00000	+	6.53888i	−0.464758	+	0.337666i
$376$	−4.47214	−	13.7638i	−0.230633	−	0.709815i
$377$	8.94427			0.460653
$378$	14.4721			0.744366
$379$	−11.7082	−	36.0341i	−0.601410	−	1.85095i	−0.519805	−	0.854285i	$-0.673995\pi$
$379$	−11.7082	−	36.0341i	−0.601410	−	1.85095i	−0.0816052	−	0.996665i	$-0.526005\pi$
$380$	−1.11803	+	3.44095i	−0.0573539	+	0.176517i
$381$	1.34752	−	4.14725i	0.0690358	−	0.212470i
$382$	1.59017	+	1.15533i	0.0813602	+	0.0591116i
$383$	−3.67376	−	11.3067i	−0.187720	−	0.577744i	0.812264	−	0.583290i	$-0.198235\pi$
$383$	−3.67376	−	11.3067i	−0.187720	−	0.577744i	−0.999985	+	0.00554556i	$0.998235\pi$
$384$	11.3820	+	8.26948i	0.580834	+	0.422000i
$385$	−6.85410	+	4.97980i	−0.349317	+	0.253794i
$386$	1.04508	−	3.21644i	0.0531934	−	0.163713i
$387$	3.85410	−	2.80017i	0.195915	−	0.142341i
$388$	2.54508	−	1.84911i	0.129207	−	0.0938745i
$389$	−5.52786	+	17.0130i	−0.280274	+	0.862594i	0.707502	+	0.706712i	$0.249822\pi$
$389$	−5.52786	+	17.0130i	−0.280274	+	0.862594i	−0.987776	+	0.155883i	$0.950178\pi$
$390$	0.763932	−	0.555029i	0.0386832	−	0.0281050i
$391$	32.6525	+	23.7234i	1.65131	+	1.19974i
$392$	7.56231	+	23.2744i	0.381954	+	1.17553i
$393$	12.0000	+	8.71851i	0.605320	+	0.439791i
$394$	−2.94427	+	9.06154i	−0.148330	+	0.456514i
$395$	−0.527864	+	1.62460i	−0.0265597	+	0.0817424i
$396$	−1.47214	−	4.53077i	−0.0739776	−	0.227680i
$397$	−7.00000			−0.351320			−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000			−0.351320			−0.175660	+	0.984451i	$0.556206\pi$
$398$	−0.652476			−0.0327057
$399$	3.61803	+	11.1352i	0.181128	+	0.557455i
$400$	6.00000	−	4.35926i	0.300000	−	0.217963i
$401$	12.7984	+	9.29856i	0.639120	+	0.464348i	0.859548	−	0.511055i	$-0.170745\pi$
$401$	12.7984	+	9.29856i	0.639120	+	0.464348i	−0.220428	+	0.975403i	$0.570745\pi$
$402$	6.11146			0.304812
$403$		0			0
$404$	4.85410			0.241501
$405$	1.95492	+	1.42033i	0.0971405	+	0.0705767i
$406$	15.3262	−	11.1352i	0.760628	−	0.552629i
$407$	−1.23607	−	3.80423i	−0.0612696	−	0.188568i
$408$	14.4721			0.716477
$409$	26.1803			1.29453			0.647267	−	0.762263i	$-0.275912\pi$
$409$	26.1803			1.29453			0.647267	+	0.762263i	$0.275912\pi$
$410$	−1.33688	−	4.11450i	−0.0660238	−	0.203201i
$411$	7.52786	−	23.1684i	0.371322	−	1.14281i
$412$	−0.881966	+	2.71441i	−0.0434513	+	0.133729i
$413$	−7.66312	−	5.56758i	−0.377077	−	0.273963i
$414$	2.16718	+	6.66991i	0.106511	+	0.327808i
$415$	2.38197	+	1.73060i	0.116926	+	0.0849518i
$416$	−5.61803	+	4.08174i	−0.275447	+	0.200124i
$417$	−5.12461	+	15.7719i	−0.250953	+	0.772355i
$418$	−2.23607	+	1.62460i	−0.109370	+	0.0794617i
$419$	−24.3713	+	17.7068i	−1.19062	+	0.865034i	−0.993329	−	0.115312i	$-0.963213\pi$
$419$	−24.3713	+	17.7068i	−1.19062	+	0.865034i	−0.197288	+	0.980346i	$0.563213\pi$
$420$	−2.61803	+	8.05748i	−0.127747	+	0.393165i
$421$	12.4271	−	9.02878i	0.605657	−	0.440036i	−0.242225	−	0.970220i	$-0.577877\pi$
$421$	12.4271	−	9.02878i	0.605657	−	0.440036i	0.847882	+	0.530184i	$0.177877\pi$
$422$	0.409830	+	0.297759i	0.0199502	+	0.0144947i
$423$	2.94427	+	9.06154i	0.143155	+	0.440587i
$424$	−2.76393	−	2.00811i	−0.134228	−	0.0975226i
$425$	6.47214	−	19.9192i	0.313945	−	0.966222i
$426$	3.11146	−	9.57608i	0.150751	−	0.463962i
$427$	−18.5623	−	57.1289i	−0.898293	−	2.76466i
$428$	−16.5623			−0.800569
$429$	−3.05573			−0.147532
$430$	−0.618034	−	1.90211i	−0.0298042	−	0.0917280i
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	−0.796516	−	0.604617i	$-0.793326\pi$
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	0.328888	+	0.944369i	$0.393326\pi$
$432$	−8.29180	−	6.02434i	−0.398939	−	0.289846i
$433$	12.1803			0.585350			0.292675	−	0.956212i	$-0.405455\pi$
$433$	12.1803			0.585350			0.292675	+	0.956212i	$0.405455\pi$
$434$		0			0
$435$	8.94427			0.428845
$436$	5.16312	+	3.75123i	0.247269	+	0.179651i
$437$	−13.9443	+	10.1311i	−0.667045	+	0.484637i
$438$	0.111456	+	0.343027i	0.00532558	+	0.0163905i
$439$	21.1803			1.01088			0.505441	−	0.862861i	$-0.331330\pi$
$439$	21.1803			1.01088			0.505441	+	0.862861i	$0.331330\pi$
$440$	−4.47214			−0.213201
$441$	−4.97871	−	15.3229i	−0.237082	−	0.729662i
$442$	−1.23607	+	3.80423i	−0.0587938	+	0.180949i
$443$	5.34346	−	16.4455i	0.253875	−	0.781348i	−0.740174	−	0.672416i	$-0.765257\pi$
$443$	5.34346	−	16.4455i	0.253875	−	0.781348i	0.994049	−	0.108932i	$-0.0347432\pi$
$444$	−3.23607	−	2.35114i	−0.153577	−	0.111580i
$445$	0.527864	+	1.62460i	0.0250232	+	0.0770134i
$446$	−2.00000	−	1.45309i	−0.0947027	−	0.0688056i
$447$	10.0000	−	7.26543i	0.472984	−	0.343643i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	25.3262	−	18.4006i	1.19522	−	0.868377i	0.201413	−	0.979506i	$-0.435447\pi$
$449$	25.3262	−	18.4006i	1.19522	−	0.868377i	0.993806	+	0.111129i	$0.0354466\pi$
$450$	2.94427	−	2.13914i	0.138794	−	0.100840i
$451$	−4.32624	+	13.3148i	−0.203715	+	0.626969i
$452$	−7.16312	+	5.20431i	−0.336925	+	0.244790i
$453$	−8.18034	−	5.94336i	−0.384346	−	0.279244i
$454$	−0.472136	−	1.45309i	−0.0221584	−	0.0681967i
$455$	−4.23607	−	3.07768i	−0.198590	−	0.144284i
$456$	−1.90983	+	5.87785i	−0.0894360	+	0.275256i
$457$	6.47214	−	19.9192i	0.302754	−	0.931780i	−0.677752	−	0.735290i	$-0.737046\pi$
$457$	6.47214	−	19.9192i	0.302754	−	0.931780i	0.980506	−	0.196490i	$-0.0629543\pi$
$458$	2.56231	+	7.88597i	0.119729	+	0.368487i
$459$	−28.9443			−1.35100
$460$	−12.4721			−0.581516
$461$	3.20163	+	9.85359i	0.149115	+	0.458928i	0.997517	−	0.0704241i	$-0.0224352\pi$
$461$	3.20163	+	9.85359i	0.149115	+	0.458928i	−0.848403	+	0.529352i	$0.822435\pi$
$462$	−5.23607	+	3.80423i	−0.243604	+	0.176989i
$463$	−23.7984	−	17.2905i	−1.10600	−	0.803559i	−0.123975	−	0.992285i	$-0.539564\pi$
$463$	−23.7984	−	17.2905i	−1.10600	−	0.803559i	−0.982030	+	0.188726i	$0.939564\pi$
$464$	−13.4164			−0.622841
$465$		0			0
$466$	−0.0344419			−0.00159549
$467$	7.04508	+	5.11855i	0.326008	+	0.236858i	0.738735	−	0.673996i	$-0.235424\pi$
$467$	7.04508	+	5.11855i	0.326008	+	0.236858i	−0.412727	+	0.910855i	$0.635424\pi$
$468$	2.38197	−	1.73060i	0.110106	−	0.0799970i
$469$	−10.4721	−	32.2299i	−0.483558	−	1.48824i
$470$	4.00000			0.184506
$471$	18.4033			0.847977
$472$	−1.54508	−	4.75528i	−0.0711183	−	0.218880i
$473$	−2.00000	+	6.15537i	−0.0919601	+	0.283024i
$474$	−0.403252	+	1.24108i	−0.0185220	+	0.0570048i
$475$	7.23607	+	5.25731i	0.332014	+	0.241222i
$476$	−11.0902	−	34.1320i	−0.508317	−	1.56444i
$477$	1.81966	+	1.32206i	0.0833165	+	0.0605330i
$478$	−0.854102	+	0.620541i	−0.0390657	+	0.0283829i
$479$	11.3435	−	34.9116i	0.518296	−	1.59515i	−0.258908	−	0.965902i	$-0.583363\pi$
$479$	11.3435	−	34.9116i	0.518296	−	1.59515i	0.777204	−	0.629249i	$-0.216637\pi$
$480$	−5.61803	+	4.08174i	−0.256427	+	0.186305i
$481$	2.00000	−	1.45309i	0.0911922	−	0.0662550i
$482$	−5.79837	+	17.8456i	−0.264109	+	0.812843i
$483$	−32.6525	+	23.7234i	−1.48574	+	1.07945i
$484$	−9.16312	−	6.65740i	−0.416505	−	0.302609i
$485$	0.600813	+	1.84911i	0.0272815	+	0.0839639i
$486$	−6.79837	−	4.93931i	−0.308381	−	0.224052i
$487$	4.56231	−	14.0413i	0.206738	−	0.636274i	−0.792900	−	0.609352i	$-0.791430\pi$
$487$	4.56231	−	14.0413i	0.206738	−	0.636274i	0.999638	−	0.0269214i	$-0.00857040\pi$
$488$	9.79837	−	30.1563i	0.443552	−	1.36511i
$489$	1.03444	+	3.18368i	0.0467791	+	0.143971i
$490$	−6.76393			−0.305563
$491$	40.3607			1.82145			0.910726	−	0.413011i	$-0.135523\pi$
$491$	40.3607			1.82145			0.910726	+	0.413011i	$0.135523\pi$
$492$	4.32624	+	13.3148i	0.195042	+	0.600277i
$493$	−30.6525	+	22.2703i	−1.38052	+	1.00301i
$494$	−1.38197	−	1.00406i	−0.0621776	−	0.0451747i
$495$	2.94427			0.132335
$496$		0			0
$497$	−55.8328			−2.50444
$498$	1.81966	+	1.32206i	0.0815409	+	0.0592429i
$499$	−27.0344	+	19.6417i	−1.21023	+	0.879282i	−0.995251	−	0.0973373i	$-0.968967\pi$
$499$	−27.0344	+	19.6417i	−1.21023	+	0.879282i	−0.214976	+	0.976619i	$0.568967\pi$
$500$	4.50000	+	13.8496i	0.201246	+	0.619372i
$501$	3.05573			0.136520
$502$	−14.9443			−0.666995
$503$	−0.510643	−	1.57160i	−0.0227685	−	0.0700741i	0.939027	−	0.343844i	$-0.111729\pi$
$503$	−0.510643	−	1.57160i	−0.0227685	−	0.0700741i	−0.961795	+	0.273770i	$0.911729\pi$
$504$	4.30902	−	13.2618i	0.191939	−	0.590727i
$505$	−0.927051	+	2.85317i	−0.0412532	+	0.126964i
$506$	−7.70820	−	5.60034i	−0.342671	−	0.248965i
$507$	4.38197	+	13.4863i	0.194610	+	0.598948i
$508$	−4.61803	−	3.35520i	−0.204892	−	0.148863i
$509$	−15.8541	+	11.5187i	−0.702721	+	0.510556i	−0.880817	−	0.473457i	$-0.843006\pi$
$509$	−15.8541	+	11.5187i	−0.702721	+	0.510556i	0.178096	+	0.984013i	$0.443006\pi$
$510$	−1.23607	+	3.80423i	−0.0547340	+	0.168454i
$511$	1.61803	−	1.17557i	0.0715776	−	0.0520042i
$512$	15.1353	−	10.9964i	0.668890	−	0.485977i
$513$	3.81966	−	11.7557i	0.168642	−	0.519027i
$514$	−7.97214	+	5.79210i	−0.351636	+	0.255478i
$515$	−1.42705	−	1.03681i	−0.0628834	−	0.0456874i
$516$	2.00000	+	6.15537i	0.0880451	+	0.270975i
$517$	−10.4721	−	7.60845i	−0.460564	−	0.334619i
$518$	1.61803	−	4.97980i	0.0710923	−	0.218800i
$519$	5.70820	−	17.5680i	0.250562	−	0.771152i
$520$	−0.854102	−	2.62866i	−0.0374548	−	0.115274i
$521$	2.00000			0.0876216			0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000			0.0876216			0.0438108	+	0.999040i	$0.486050\pi$
$522$	−6.58359			−0.288156
$523$	1.32624	+	4.08174i	0.0579923	+	0.178482i	0.975857	−	0.218413i	$-0.0700878\pi$
$523$	1.32624	+	4.08174i	0.0579923	+	0.178482i	−0.917864	+	0.396895i	$0.870088\pi$
$524$	15.7082	−	11.4127i	0.686216	−	0.498565i
$525$	16.9443	+	12.3107i	0.739509	+	0.537284i
$526$	−11.5967			−0.505642
$527$		0			0
$528$	4.58359			0.199475
$529$	−29.4615	−	21.4050i	−1.28093	−	0.930653i
$530$	0.763932	−	0.555029i	0.0331831	−	0.0241089i
$531$	1.01722	+	3.13068i	0.0441436	+	0.135860i
$532$	15.3262			0.664477
$533$	−8.65248			−0.374780
$534$	0.403252	+	1.24108i	0.0174504	+	0.0537069i
$535$	3.16312	−	9.73508i	0.136754	−	0.420884i
$536$	5.52786	−	17.0130i	0.238767	−	0.734850i
$537$	11.7082	+	8.50651i	0.505246	+	0.367083i
$538$	−5.52786	−	17.0130i	−0.238323	−	0.733483i
$539$	17.7082	+	12.8658i	0.762746	+	0.554168i
$540$	7.23607	−	5.25731i	0.311391	−	0.226239i
$541$	5.98278	−	18.4131i	0.257220	−	0.791641i	−0.736164	−	0.676803i	$-0.763365\pi$
$541$	5.98278	−	18.4131i	0.257220	−	0.791641i	0.993384	−	0.114838i	$-0.0366350\pi$
$542$	−4.09017	+	2.97168i	−0.175688	+	0.127645i
$543$	−18.1803	+	13.2088i	−0.780193	+	0.566843i
$544$	9.09017	−	27.9767i	0.389738	−	1.19949i
$545$	−3.19098	+	2.31838i	−0.136687	+	0.0993087i
$546$	−3.23607	−	2.35114i	−0.138491	−	0.100620i
$547$	8.69098	+	26.7481i	0.371600	+	1.14367i	0.945744	+	0.324912i	$0.105335\pi$
$547$	8.69098	+	26.7481i	0.371600	+	1.14367i	−0.574145	+	0.818754i	$0.694665\pi$
$548$	−25.7984	−	18.7436i	−1.10205	−	0.800688i
$549$	−6.45085	+	19.8537i	−0.275316	+	0.847334i
$550$	−1.52786	+	4.70228i	−0.0651483	+	0.200506i
$551$	−5.00000	−	15.3884i	−0.213007	−	0.655569i
$552$	−21.3050			−0.906799
$553$	7.23607			0.307709
$554$	3.56231	+	10.9637i	0.151348	+	0.465801i
$555$	2.00000	−	1.45309i	0.0848953	−	0.0616800i
$556$	17.5623	+	12.7598i	0.744808	+	0.541134i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	6.35410	+	4.61653i	0.268510	+	0.195084i
$561$	10.4721	−	7.60845i	0.442134	−	0.321229i
$562$	−3.24671	−	9.99235i	−0.136954	−	0.421502i
$563$	−39.5410			−1.66646			−0.833228	−	0.552930i	$-0.813510\pi$
$563$	−39.5410			−1.66646			−0.833228	+	0.552930i	$0.813510\pi$
$564$	−12.9443			−0.545052
$565$	−1.69098	−	5.20431i	−0.0711402	−	0.218947i
$566$	−4.18034	+	12.8658i	−0.175713	+	0.540788i
$567$	3.16312	−	9.73508i	0.132839	−	0.408835i
$568$	−23.8435	−	17.3233i	−1.00045	−	0.726869i
$569$	−4.47214	−	13.7638i	−0.187482	−	0.577009i	0.812501	−	0.582960i	$-0.198106\pi$
$569$	−4.47214	−	13.7638i	−0.187482	−	0.577009i	−0.999982	+	0.00595104i	$0.998106\pi$
$570$	−1.38197	−	1.00406i	−0.0578842	−	0.0420553i
$571$	4.70820	−	3.42071i	0.197032	−	0.143152i	−0.484895	−	0.874572i	$-0.661142\pi$
$571$	4.70820	−	3.42071i	0.197032	−	0.143152i	0.681927	+	0.731420i	$0.261142\pi$
$572$	−1.23607	+	3.80423i	−0.0516826	+	0.159063i
$573$	3.18034	−	2.31065i	0.132861	−	0.0965289i
$574$	−14.8262	+	10.7719i	−0.618835	+	0.449610i
$575$	−9.52786	+	29.3238i	−0.397339	+	1.22288i
$576$	−0.281153	+	0.204270i	−0.0117147	+	0.00851123i
$577$	−20.0902	−	14.5964i	−0.836365	−	0.607655i	0.0849881	−	0.996382i	$-0.472915\pi$
$577$	−20.0902	−	14.5964i	−0.836365	−	0.607655i	−0.921353	+	0.388727i	$0.872915\pi$
$578$	−1.98936	−	6.12261i	−0.0827463	−	0.254667i
$579$	−5.47214	−	3.97574i	−0.227414	−	0.165226i
$580$	3.61803	−	11.1352i	0.150231	−	0.462363i
$581$	3.85410	−	11.8617i	0.159895	−	0.492106i
$582$	0.458980	+	1.41260i	0.0190253	+	0.0585540i
$583$	−3.05573			−0.126555
$584$	1.05573			0.0436863
$585$	0.562306	+	1.73060i	0.0232485	+	0.0715515i
$586$	4.23607	−	3.07768i	0.174990	−	0.127138i
$587$	2.00000	+	1.45309i	0.0825488	+	0.0599752i	0.628294	−	0.777976i	$-0.283753\pi$
$587$	2.00000	+	1.45309i	0.0825488	+	0.0599752i	−0.545745	+	0.837951i	$0.683753\pi$
$588$	21.8885			0.902668
$589$		0			0
$590$	1.38197			0.0568946
$591$	15.4164	+	11.2007i	0.634146	+	0.460734i
$592$	−3.00000	+	2.17963i	−0.123299	+	0.0895821i
$593$	−4.78115	−	14.7149i	−0.196338	−	0.604268i	−0.999958	−	0.00912470i	$-0.997095\pi$
$593$	−4.78115	−	14.7149i	−0.196338	−	0.604268i	0.803620	−	0.595143i	$-0.202905\pi$
$594$	6.83282			0.280354
$595$	22.1803			0.909305
$596$	−5.00000	−	15.3884i	−0.204808	−	0.630334i
$597$	−0.403252	+	1.24108i	−0.0165040	+	0.0507941i
$598$	1.81966	−	5.60034i	0.0744114	−	0.229015i
$599$	−27.9894	−	20.3355i	−1.14361	−	0.830884i	−0.155995	−	0.987758i	$-0.549859\pi$
$599$	−27.9894	−	20.3355i	−1.14361	−	0.830884i	−0.987619	+	0.156873i	$0.949859\pi$
$600$	3.41641	+	10.5146i	0.139474	+	0.429258i
$601$	−29.5623	−	21.4783i	−1.20587	−	0.876117i	−0.211022	−	0.977481i	$-0.567679\pi$
$601$	−29.5623	−	21.4783i	−1.20587	−	0.876117i	−0.994849	+	0.101364i	$0.967679\pi$
$602$	−6.85410	+	4.97980i	−0.279352	+	0.202961i
$603$	−3.63932	+	11.2007i	−0.148205	+	0.456127i
$604$	−10.7082	+	7.77997i	−0.435711	+	0.316562i
$605$	5.66312	−	4.11450i	0.230239	−	0.167278i
$606$	−0.708204	+	2.17963i	−0.0287688	+	0.0885413i
$607$	−10.9443	+	7.95148i	−0.444214	+	0.322741i	−0.787307	−	0.616561i	$-0.788525\pi$
$607$	−10.9443	+	7.95148i	−0.444214	+	0.322741i	0.343093	+	0.939301i	$0.388525\pi$
$608$	10.1631	+	7.38394i	0.412169	+	0.299458i
$609$	−11.7082	−	36.0341i	−0.474440	−	1.46018i
$610$	7.09017	+	5.15131i	0.287073	+	0.208570i
$611$	2.47214	−	7.60845i	0.100012	−	0.307805i
$612$	−3.85410	+	11.8617i	−0.155793	+	0.479481i
$613$	2.50658	+	7.71445i	0.101240	+	0.311584i	0.988830	−	0.149051i	$-0.0476218\pi$
$613$	2.50658	+	7.71445i	0.101240	+	0.311584i	−0.887590	+	0.460635i	$0.847622\pi$
$614$	9.45085			0.381405
$615$	−8.65248			−0.348902
$616$	5.85410	+	18.0171i	0.235868	+	0.725929i
$617$	−19.0344	+	13.8293i	−0.766298	+	0.556748i	−0.900836	−	0.434161i	$-0.857045\pi$
$617$	−19.0344	+	13.8293i	−0.766298	+	0.556748i	0.134538	+	0.990908i	$0.457045\pi$
$618$	−1.09017	−	0.792055i	−0.0438531	−	0.0318611i
$619$	16.1803			0.650343			0.325171	−	0.945655i	$-0.394578\pi$
$619$	16.1803			0.650343			0.325171	+	0.945655i	$0.394578\pi$
$620$		0			0
$621$	42.6099			1.70988
$622$	−3.40983	−	2.47739i	−0.136722	−	0.0993342i
$623$	5.85410	−	4.25325i	0.234540	−	0.170403i
$624$	0.875388	+	2.69417i	0.0350436	+	0.107853i
$625$	11.0000			0.440000
$626$	13.1246			0.524565
$627$	1.70820	+	5.25731i	0.0682191	+	0.209957i
$628$	7.44427	−	22.9111i	0.297059	−	0.914253i
$629$	−3.23607	+	9.95959i	−0.129030	+	0.397115i
$630$	3.11803	+	2.26538i	0.124225	+	0.0902551i
$631$	3.20163	+	9.85359i	0.127455	+	0.392265i	0.994340	−	0.106242i	$-0.0338818\pi$
$631$	3.20163	+	9.85359i	0.127455	+	0.392265i	−0.866886	+	0.498507i	$0.833882\pi$
$632$	3.09017	+	2.24514i	0.122920	+	0.0893069i
$633$	0.819660	−	0.595518i	0.0325786	−	0.0236697i
$634$	−4.19098	+	12.8985i	−0.166445	+	0.512266i
$635$	2.85410	−	2.07363i	0.113262	−	0.0822894i
$636$	−2.47214	+	1.79611i	−0.0980266	+	0.0712205i
$637$	−4.18034	+	12.8658i	−0.165631	+	0.509760i
$638$	7.23607	−	5.25731i	0.286479	−	0.208139i
$639$	15.6976	+	11.4049i	0.620986	+	0.451173i
$640$	3.51722	+	10.8249i	0.139030	+	0.427891i
$641$	9.70820	+	7.05342i	0.383451	+	0.278593i	0.762767	−	0.646674i	$-0.223841\pi$
$641$	9.70820	+	7.05342i	0.383451	+	0.278593i	−0.379316	+	0.925267i	$0.623841\pi$
$642$	2.41641	−	7.43694i	0.0953680	−	0.293513i
$643$	−8.79837	+	27.0786i	−0.346974	+	1.06788i	0.613545	+	0.789660i	$0.289743\pi$
$643$	−8.79837	+	27.0786i	−0.346974	+	1.06788i	−0.960519	+	0.278216i	$0.910257\pi$
$644$	16.3262	+	50.2470i	0.643344	+	1.98001i
$645$	−4.00000			−0.157500
$646$	7.23607			0.284699
$647$	−5.23607	−	16.1150i	−0.205851	−	0.633544i	−0.999677	−	0.0253999i	$-0.991914\pi$
$647$	−5.23607	−	16.1150i	−0.205851	−	0.633544i	0.793826	−	0.608145i	$-0.208086\pi$
$648$	4.37132	−	3.17595i	0.171722	−	0.124763i
$649$	−3.61803	−	2.62866i	−0.142020	−	0.103184i
$650$	−3.05573			−0.119856
$651$		0			0
$652$	4.38197			0.171611
$653$	−12.3820	−	8.99602i	−0.484544	−	0.352042i	0.318538	−	0.947910i	$-0.396808\pi$
$653$	−12.3820	−	8.99602i	−0.484544	−	0.352042i	−0.803082	+	0.595868i	$0.796808\pi$
$654$	−2.43769	+	1.77109i	−0.0953214	+	0.0692550i
$655$	3.70820	+	11.4127i	0.144892	+	0.445930i
$656$	12.9787			0.506734
$657$	−0.695048			−0.0271164
$658$	−5.23607	−	16.1150i	−0.204123	−	0.628227i
$659$	−1.74671	+	5.37582i	−0.0680422	+	0.209412i	−0.979296	−	0.202432i	$-0.935115\pi$
$659$	−1.74671	+	5.37582i	−0.0680422	+	0.209412i	0.911254	+	0.411845i	$0.135115\pi$
$660$	−1.23607	+	3.80423i	−0.0481139	+	0.148079i
$661$	36.6976	+	26.6623i	1.42737	+	1.03704i	0.990499	+	0.137520i	$0.0439133\pi$
$661$	36.6976	+	26.6623i	1.42737	+	1.03704i	0.436871	+	0.899524i	$0.356087\pi$
$662$	0.381966	+	1.17557i	0.0148455	+	0.0456898i
$663$	6.47214	+	4.70228i	0.251357	+	0.182622i
$664$	5.32624	−	3.86974i	0.206698	−	0.150175i
$665$	−2.92705	+	9.00854i	−0.113506	+	0.349336i
$666$	−1.47214	+	1.06957i	−0.0570441	+	0.0414450i
$667$	45.1246	−	32.7849i	1.74723	−	1.26944i
$668$	1.23607	−	3.80423i	0.0478249	−	0.147190i
$669$	−4.00000	+	2.90617i	−0.154649	+	0.112359i
$670$	4.00000	+	2.90617i	0.154533	+	0.112275i
$671$	−8.76393	−	26.9726i	−0.338328	−	1.04127i
$672$	23.7984	+	17.2905i	0.918042	+	0.666997i
$673$	−14.5279	+	44.7122i	−0.560008	+	1.72353i	0.122329	+	0.992490i	$0.460964\pi$
$673$	−14.5279	+	44.7122i	−0.560008	+	1.72353i	−0.682337	+	0.731038i	$0.739036\pi$
$674$	−3.67376	+	11.3067i	−0.141508	+	0.435517i
$675$	−6.83282	−	21.0292i	−0.262995	−	0.809416i
$676$	18.5623			0.713935
$677$	−42.7214			−1.64192			−0.820958	−	0.570989i	$-0.806560\pi$
$677$	−42.7214			−1.64192			−0.820958	+	0.570989i	$0.806560\pi$
$678$	−1.29180	−	3.97574i	−0.0496111	−	0.152687i
$679$	6.66312	−	4.84104i	0.255707	−	0.185782i
$680$	9.47214	+	6.88191i	0.363240	+	0.263909i
$681$	−3.05573			−0.117096
$682$		0			0
$683$	−17.1803			−0.657387			−0.328694	−	0.944437i	$-0.606608\pi$
$683$	−17.1803			−0.657387			−0.328694	+	0.944437i	$0.606608\pi$
$684$	−4.30902	−	3.13068i	−0.164759	−	0.119705i
$685$	15.9443	−	11.5842i	0.609199	−	0.442609i
$686$	3.19098	+	9.82084i	0.121832	+	0.374961i
$687$	16.5836			0.632704
$688$	6.00000			0.228748
$689$	−0.583592	−	1.79611i	−0.0222331	−	0.0684264i
$690$	1.81966	−	5.60034i	0.0692733	−	0.213201i
$691$	−5.92705	+	18.2416i	−0.225476	+	0.693943i	0.772767	+	0.634689i	$0.218872\pi$
$691$	−5.92705	+	18.2416i	−0.225476	+	0.693943i	−0.998243	+	0.0592533i	$0.981128\pi$
$692$	−19.5623	−	14.2128i	−0.743647	−	0.540291i
$693$	−3.85410	−	11.8617i	−0.146405	−	0.450589i
$694$	−0.909830	−	0.661030i	−0.0345367	−	0.0250924i
$695$	−10.8541	+	7.88597i	−0.411720	+	0.299132i
$696$	6.18034	−	19.0211i	0.234265	−	0.720994i
$697$	29.6525	−	21.5438i	1.12317	−	0.816029i
$698$	13.9443	−	10.1311i	0.527798	−	0.383468i
$699$	−0.0212862	+	0.0655123i	−0.000805119	+	0.00247790i
$700$	22.1803	−	16.1150i	0.838338	−	0.609088i
$701$	−5.66312	−	4.11450i	−0.213893	−	0.155402i	0.475680	−	0.879618i	$-0.342202\pi$
$701$	−5.66312	−	4.11450i	−0.213893	−	0.155402i	−0.689573	+	0.724216i	$0.742202\pi$
$702$	1.30495	+	4.01623i	0.0492522	+	0.151583i
$703$	−3.61803	−	2.62866i	−0.136457	−	0.0991416i
$704$	0.145898	−	0.449028i	0.00549874	−	0.0169234i
$705$	2.47214	−	7.60845i	0.0931060	−	0.286551i
$706$	−3.70820	−	11.4127i	−0.139560	−	0.429522i
$707$	12.7082			0.477941
$708$	−4.47214			−0.168073
$709$	−10.6525	−	32.7849i	−0.400062	−	1.23126i	−0.924949	−	0.380092i	$-0.875892\pi$
$709$	−10.6525	−	32.7849i	−0.400062	−	1.23126i	0.524886	−	0.851172i	$-0.324108\pi$
$710$	6.59017	−	4.78804i	0.247325	−	0.179692i
$711$	−2.03444	−	1.47811i	−0.0762975	−	0.0554334i
$712$	3.81966			0.143148
$713$		0			0
$714$	16.9443			0.634123
$715$	−2.00000	−	1.45309i	−0.0747958	−	0.0543423i
$716$	15.3262	−	11.1352i	0.572768	−	0.416141i
$717$	0.652476	+	2.00811i	0.0243672	+	0.0749944i
$718$	−10.9787			−0.409722
$719$	36.1803			1.34930			0.674649	−	0.738138i	$-0.264295\pi$
$719$	36.1803			1.34930			0.674649	+	0.738138i	$0.264295\pi$
$720$	−0.843459	−	2.59590i	−0.0314339	−	0.0967435i
$721$	−2.30902	+	7.10642i	−0.0859923	+	0.264657i
$722$	2.67376	−	8.22899i	0.0995071	−	0.306251i
$723$	30.3607	+	22.0583i	1.12913	+	0.820358i
$724$	9.09017	+	27.9767i	0.337834	+	1.03974i
$725$	−23.4164	−	17.0130i	−0.869664	−	0.631848i
$726$	4.32624	−	3.14320i	0.160562	−	0.116655i
$727$	−12.2877	+	37.8177i	−0.455727	+	1.40258i	0.414553	+	0.910025i	$0.363938\pi$
$727$	−12.2877	+	37.8177i	−0.455727	+	1.40258i	−0.870280	+	0.492558i	$0.836062\pi$
$728$	−9.47214	+	6.88191i	−0.351061	+	0.255061i
$729$	−19.4615	+	14.1396i	−0.720796	+	0.523689i
$730$	−0.0901699	+	0.277515i	−0.00333734	+	0.0102713i
$731$	13.7082	−	9.95959i	0.507016	−	0.368369i
$732$	−22.9443	−	16.6700i	−0.848045	−	0.616141i
$733$	−1.69098	−	5.20431i	−0.0624579	−	0.192226i	0.914959	−	0.403548i	$-0.132223\pi$
$733$	−1.69098	−	5.20431i	−0.0624579	−	0.192226i	−0.977416	+	0.211322i	$0.932223\pi$
$734$	−9.00000	−	6.53888i	−0.332196	−	0.241355i
$735$	−4.18034	+	12.8658i	−0.154194	+	0.474561i
$736$	−13.3820	+	41.1855i	−0.493266	+	1.51812i
$737$	−4.94427	−	15.2169i	−0.182125	−	0.560522i
$738$	6.36881			0.234439
$739$	16.1803			0.595203			0.297602	−	0.954690i	$-0.403813\pi$
$739$	16.1803			0.595203			0.297602	+	0.954690i	$0.403813\pi$
$740$	−1.00000	−	3.07768i	−0.0367607	−	0.113138i
$741$	−2.76393	+	2.00811i	−0.101536	+	0.0737699i
$742$	−3.23607	−	2.35114i	−0.118800	−	0.0863131i
$743$	−27.8197			−1.02060			−0.510302	−	0.859995i	$-0.670466\pi$
$743$	−27.8197			−1.02060			−0.510302	+	0.859995i	$0.670466\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	9.50000	+	6.90215i	0.347820	+	0.252706i
$747$	−3.50658	+	2.54768i	−0.128299	+	0.0932147i
$748$	−5.23607	−	16.1150i	−0.191450	−	0.589221i
$749$	−43.3607			−1.58436
$750$	−6.87539			−0.251054
$751$	14.0729	+	43.3121i	0.513529	+	1.58048i	0.785942	+	0.618300i	$0.212178\pi$
$751$	14.0729	+	43.3121i	0.513529	+	1.58048i	−0.272413	+	0.962180i	$0.587822\pi$
$752$	−3.70820	+	11.4127i	−0.135224	+	0.416178i
$753$	−9.23607	+	28.4257i	−0.336581	+	1.03589i
$754$	4.47214	+	3.24920i	0.162866	+	0.118329i
$755$	−2.52786	−	7.77997i	−0.0919984	−	0.283142i
$756$	−30.6525	−	22.2703i	−1.11482	−	0.809964i
$757$	−18.3262	+	13.3148i	−0.666078	+	0.483934i	−0.868710	−	0.495321i	$-0.835051\pi$
$757$	−18.3262	+	13.3148i	−0.666078	+	0.483934i	0.202632	+	0.979255i	$0.435051\pi$
$758$	7.23607	−	22.2703i	0.262826	−	0.808895i
$759$	−15.4164	+	11.2007i	−0.559580	+	0.406559i
$760$	−4.04508	+	2.93893i	−0.146731	+	0.106606i
$761$	−0.618034	+	1.90211i	−0.0224037	+	0.0689515i	−0.961633	−	0.274338i	$-0.911541\pi$
$761$	−0.618034	+	1.90211i	−0.0224037	+	0.0689515i	0.939230	+	0.343290i	$0.111541\pi$
$762$	2.18034	−	1.58411i	0.0789854	−	0.0573862i
$763$	13.5172	+	9.82084i	0.489356	+	0.355538i
$764$	−1.59017	−	4.89404i	−0.0575303	−	0.177060i
$765$	−6.23607	−	4.53077i	−0.225466	−	0.163810i
$766$	2.27051	−	6.98791i	0.0820369	−	0.252483i
$767$	0.854102	−	2.62866i	0.0308398	−	0.0949153i
$768$	2.50658	+	7.71445i	0.0904483	+	0.278371i
$769$	−2.63932			−0.0951763			−0.0475882	−	0.998867i	$-0.515154\pi$
$769$	−2.63932			−0.0951763			−0.0475882	+	0.998867i	$0.515154\pi$
$770$	−5.23607			−0.188695
$771$	6.09017	+	18.7436i	0.219332	+	0.675035i
$772$	−7.16312	+	5.20431i	−0.257806	+	0.187307i
$773$	23.5623	+	17.1190i	0.847477	+	0.615728i	0.924449	−	0.381305i	$-0.124525\pi$
$773$	23.5623	+	17.1190i	0.847477	+	0.615728i	−0.0769721	+	0.997033i	$0.524525\pi$
$774$	2.94427			0.105830
$775$		0			0
$776$	4.34752			0.156067
$777$	−8.47214	−	6.15537i	−0.303936	−	0.220823i
$778$	−8.94427	+	6.49839i	−0.320668	+	0.232979i
$779$	4.83688	+	14.8864i	0.173299	+	0.533360i
$780$	−2.47214			−0.0885167
$781$	−26.3607			−0.943259
$782$	7.70820	+	23.7234i	0.275645	+	0.848347i
$783$	−12.3607	+	38.0423i	−0.441735	+	1.35952i
$784$	6.27051	−	19.2986i	0.223947	−	0.689237i
$785$	12.0451	+	8.75127i	0.429908	+	0.312346i
$786$	2.83282	+	8.71851i	0.101043	+	0.310979i
$787$	31.2705	+	22.7194i	1.11467	+	0.809858i	0.983393	−	0.181488i	$-0.0580913\pi$
$787$	31.2705	+	22.7194i	1.11467	+	0.809858i	0.131280	+	0.991345i	$0.458091\pi$
$788$	20.1803	−	14.6619i	0.718895	−	0.522308i
$789$	−7.16718	+	22.0583i	−0.255159	+	0.785297i
$790$	−0.854102	+	0.620541i	−0.0303876	+	0.0220779i
$791$	−18.7533	+	13.6251i	−0.666790	+	0.484451i
$792$	2.03444	−	6.26137i	0.0722907	−	0.222488i
$793$	14.1803	−	10.3026i	0.503559	−	0.365857i
$794$	−3.50000	−	2.54290i	−0.124210	−	0.0902441i
$795$	−0.583592	−	1.79611i	−0.0206979	−	0.0637015i
$796$	1.38197	+	1.00406i	0.0489825	+	0.0355879i
$797$	8.83282	−	27.1846i	0.312874	−	0.962928i	−0.663746	−	0.747958i	$-0.731034\pi$
$797$	8.83282	−	27.1846i	0.312874	−	0.962928i	0.976621	−	0.214970i	$-0.0689655\pi$
$798$	−2.23607	+	6.88191i	−0.0791559	+	0.243617i
$799$	10.4721	+	32.2299i	0.370478	+	1.14021i
$800$	22.4721			0.794510
$801$	−2.51471			−0.0888529
$802$	3.02129	+	9.29856i	0.106685	+	0.328344i
$803$	0.763932	−	0.555029i	0.0269586	−	0.0195866i
$804$	−12.9443	−	9.40456i	−0.456509	−	0.331673i
$805$	−32.6525			−1.15085
$806$		0			0
$807$	−35.7771			−1.25941
$808$	5.42705	+	3.94298i	0.190923	+	0.138714i
$809$	−2.76393	+	2.00811i	−0.0971747	+	0.0706015i	−0.635312	−	0.772256i	$-0.719128\pi$
$809$	−2.76393	+	2.00811i	−0.0971747	+	0.0706015i	0.538137	+	0.842857i	$0.319128\pi$
$810$	0.461493	+	1.42033i	0.0162152	+	0.0499053i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−49.5967			−1.74050
$813$	3.12461	+	9.61657i	0.109585	+	0.337268i
$814$	0.763932	−	2.35114i	0.0267758	−	0.0824074i
$815$	−0.836881	+	2.57565i	−0.0293147	+	0.0902213i
$816$	−9.70820	−	7.05342i	−0.339855	−	0.246919i
$817$	2.23607	+	6.88191i	0.0782301	+	0.240768i
$818$	13.0902	+	9.51057i	0.457687	+	0.332529i
$819$	6.23607	−	4.53077i	0.217906	−	0.158318i
$820$	−3.50000	+	10.7719i	−0.122225	+	0.376171i
$821$	−29.5623	+	21.4783i	−1.03173	+	0.749597i	−0.968655	−	0.248412i	$-0.920091\pi$
$821$	−29.5623	+	21.4783i	−1.03173	+	0.749597i	−0.0630771	+	0.998009i	$0.520091\pi$
$822$	12.1803	−	8.84953i	0.424838	−	0.308663i
$823$	8.56231	−	26.3521i	0.298463	−	0.918575i	−0.683573	−	0.729882i	$-0.739575\pi$
$823$	8.56231	−	26.3521i	0.298463	−	0.918575i	0.982036	−	0.188693i	$-0.0604251\pi$
$824$	−3.19098	+	2.31838i	−0.111163	+	0.0807648i
$825$	8.00000	+	5.81234i	0.278524	+	0.202360i
$826$	−1.80902	−	5.56758i	−0.0629438	−	0.193721i
$827$	39.3607	+	28.5972i	1.36870	+	0.994422i	0.997837	+	0.0657367i	$0.0209398\pi$
$827$	39.3607	+	28.5972i	1.36870	+	0.994422i	0.370868	+	0.928686i	$0.379060\pi$
$828$	5.67376	−	17.4620i	0.197177	−	0.606848i
$829$	11.3820	−	35.0301i	0.395312	−	1.21665i	−0.533406	−	0.845859i	$-0.679088\pi$
$829$	11.3820	−	35.0301i	0.395312	−	1.21665i	0.928718	−	0.370786i	$-0.120912\pi$
$830$	0.562306	+	1.73060i	0.0195179	+	0.0600700i
$831$	23.0557			0.799794
$832$	0.291796			0.0101162
$833$	−17.7082	−	54.5002i	−0.613553	−	1.88832i
$834$	−8.29180	+	6.02434i	−0.287121	+	0.208606i
$835$	2.00000	+	1.45309i	0.0692129	+	0.0502861i
$836$	7.23607			0.250265
$837$		0			0
$838$	−18.6180			−0.643149
$839$	−8.94427	−	6.49839i	−0.308791	−	0.224349i	0.422587	−	0.906322i	$-0.361122\pi$
$839$	−8.94427	−	6.49839i	−0.308791	−	0.224349i	−0.731377	+	0.681973i	$0.761122\pi$
$840$	−9.47214	+	6.88191i	−0.326820	+	0.237448i
$841$	7.21885	+	22.2173i	0.248926	+	0.766115i
$842$	9.49342			0.327165
$843$	−21.0132			−0.723732
$844$	−0.409830	−	1.26133i	−0.0141069	−	0.0434167i
$845$	−3.54508	+	10.9106i	−0.121955	+	0.375338i
$846$	−1.81966	+	5.60034i	−0.0625612	+	0.192544i
$847$	−23.9894	−	17.4293i	−0.824284	−	0.598877i
$848$	0.875388	+	2.69417i	0.0300610	+	0.0925181i
$849$	21.8885	+	15.9030i	0.751213	+	0.545788i
$850$	10.4721	−	7.60845i	0.359191	−	0.260968i
$851$	4.76393	−	14.6619i	0.163305	−	0.502603i
$852$	−21.3262	+	15.4944i	−0.730625	+	0.530830i
$853$	−30.2705	+	21.9928i	−1.03644	+	0.753020i	−0.969588	−	0.244743i	$-0.921296\pi$
$853$	−30.2705	+	21.9928i	−1.03644	+	0.753020i	−0.0668546	+	0.997763i	$0.521296\pi$
$854$	11.4721	−	35.3076i	0.392568	−	1.20820i
$855$	2.66312	−	1.93487i	0.0910767	−	0.0661711i
$856$	−18.5172	−	13.4535i	−0.632906	−	0.459833i
$857$	15.9656	+	49.1369i	0.545373	+	1.67849i	0.720101	+	0.693869i	$0.244095\pi$
$857$	15.9656	+	49.1369i	0.545373	+	1.67849i	−0.174728	+	0.984617i	$0.555905\pi$
$858$	−1.52786	−	1.11006i	−0.0521604	−	0.0378968i
$859$	−11.7082	+	36.0341i	−0.399479	+	1.22947i	0.525940	+	0.850522i	$0.323714\pi$
$859$	−11.7082	+	36.0341i	−0.399479	+	1.22947i	−0.925418	+	0.378947i	$0.876286\pi$
$860$	−1.61803	+	4.97980i	−0.0551745	+	0.169810i
$861$	11.3262	+	34.8586i	0.385997	+	1.18798i
$862$	−7.41641			−0.252604
$863$	32.1803			1.09543			0.547716	−	0.836664i	$-0.315498\pi$
$863$	32.1803			1.09543			0.547716	+	0.836664i	$0.315498\pi$
$864$	−9.59675	−	29.5358i	−0.326488	−	1.00483i
$865$	12.0902	−	8.78402i	0.411078	−	0.298666i
$866$	6.09017	+	4.42477i	0.206952	+	0.150360i
$867$	−12.8754			−0.437271
$868$		0			0
$869$	3.41641			0.115894
$870$	4.47214	+	3.24920i	0.151620	+	0.110158i
$871$	8.00000	−	5.81234i	0.271070	−	0.196944i
$872$	2.72542	+	8.38800i	0.0922945	+	0.284053i
$873$	−2.86223			−0.0968719
$874$	−10.6525			−0.360325
$875$	11.7812	+	36.2587i	0.398276	+	1.22577i
$876$	0.291796	−	0.898056i	0.00985888	−	0.0303425i
$877$	−11.1074	+	34.1850i	−0.375070	+	1.15435i	0.568362	+	0.822779i	$0.307578\pi$
$877$	−11.1074	+	34.1850i	−0.375070	+	1.15435i	−0.943431	+	0.331568i	$0.892422\pi$
$878$	10.5902	+	7.69421i	0.357401	+	0.259667i
$879$	−3.23607	−	9.95959i	−0.109150	−	0.335929i
$880$	3.00000	+	2.17963i	0.101130	+	0.0734752i
$881$	19.7082	−	14.3188i	0.663986	−	0.482414i	−0.204021	−	0.978967i	$-0.565401\pi$
$881$	19.7082	−	14.3188i	0.663986	−	0.482414i	0.868007	+	0.496552i	$0.165401\pi$
$882$	3.07701	−	9.47008i	0.103608	−	0.318874i
$883$	32.1803	−	23.3804i	1.08295	−	0.786813i	0.104759	−	0.994498i	$-0.466593\pi$
$883$	32.1803	−	23.3804i	1.08295	−	0.786813i	0.978196	+	0.207685i	$0.0665929\pi$
$884$	8.47214	−	6.15537i	0.284949	−	0.207027i
$885$	0.854102	−	2.62866i	0.0287103	−	0.0883613i
$886$	8.64590	−	6.28161i	0.290465	−	0.211035i
$887$	25.1353	+	18.2618i	0.843959	+	0.613172i	0.923474	−	0.383661i	$-0.125337\pi$
$887$	25.1353	+	18.2618i	0.843959	+	0.613172i	−0.0795146	+	0.996834i	$0.525337\pi$
$888$	−1.70820	−	5.25731i	−0.0573236	−	0.176424i
$889$	−12.0902	−	8.78402i	−0.405491	−	0.294607i
$890$	−0.326238	+	1.00406i	−0.0109355	+	0.0336561i
$891$	1.49342	−	4.59628i	0.0500315	−	0.153981i
$892$	2.00000	+	6.15537i	0.0669650	+	0.206097i
$893$	−14.4721			−0.484292
$894$	7.63932			0.255497
$895$	3.61803	+	11.1352i	0.120938	+	0.372207i
$896$	39.0066	−	28.3399i	1.30312	−	0.946771i
$897$	−9.52786	−	6.92240i	−0.318126	−	0.231132i
$898$	19.3475			0.645635
$899$		0			0
$900$	−9.52786			−0.317595
$901$	6.47214	+	4.70228i	0.215618	+	0.156656i
$902$	−7.00000	+	5.08580i	−0.233075	+	0.169339i
$903$	5.23607	+	16.1150i	0.174245	+	0.536272i
$904$	−12.2361			−0.406966
$905$	−18.1803			−0.604335
$906$	−1.93112	−	5.94336i	−0.0641570	−	0.197455i
$907$	−6.10739	+	18.7966i	−0.202793	+	0.624131i	0.797004	+	0.603974i	$0.206417\pi$
$907$	−6.10739	+	18.7966i	−0.202793	+	0.624131i	−0.999797	+	0.0201577i	$0.993583\pi$
$908$	−1.23607	+	3.80423i	−0.0410204	+	0.126248i
$909$	−3.57295	−	2.59590i	−0.118507	−	0.0861005i
$910$	−1.00000	−	3.07768i	−0.0331497	−	0.102024i
$911$	−3.38197	−	2.45714i	−0.112050	−	0.0814088i	0.530349	−	0.847779i	$-0.322061\pi$
$911$	−3.38197	−	2.45714i	−0.112050	−	0.0814088i	−0.642399	+	0.766370i	$0.722061\pi$
$912$	4.14590	−	3.01217i	0.137284	−	0.0997430i
$913$	1.81966	−	5.60034i	0.0602220	−	0.185344i
$914$	10.4721	−	7.60845i	0.346387	−	0.251665i
$915$	14.1803	−	10.3026i	0.468788	−	0.340594i
$916$	6.70820	−	20.6457i	0.221645	−	0.682154i
$917$	41.1246	−	29.8788i	1.35805	−	0.986684i
$918$	−14.4721	−	10.5146i	−0.477652	−	0.347034i
$919$	−1.70820	−	5.25731i	−0.0563484	−	0.173423i	0.918921	−	0.394441i	$-0.129062\pi$
$919$	−1.70820	−	5.25731i	−0.0563484	−	0.173423i	−0.975270	+	0.221019i	$0.929062\pi$
$920$	−13.9443	−	10.1311i	−0.459729	−	0.334013i
$921$	5.84095	−	17.9766i	0.192466	−	0.592349i
$922$	−1.97871	+	6.08985i	−0.0651655	+	0.200559i
$923$	−5.03444	−	15.4944i	−0.165711	−	0.510005i
$924$	16.9443			0.557426
$925$	−8.00000			−0.263038
$926$	−5.61803	−	17.2905i	−0.184620	−	0.568202i
$927$	2.10081	−	1.52633i	0.0689998	−	0.0501313i
$928$	−32.8885	−	23.8949i	−1.07962	−	0.784389i
$929$	20.0000			0.656179			0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000			0.656179			0.328089	+	0.944647i	$0.393595\pi$
$930$		0			0
$931$	24.4721			0.802042
$932$	0.0729490	+	0.0530006i	0.00238952	+	0.00173609i
$933$	−6.81966	+	4.95477i	−0.223266	+	0.162212i
$934$	1.66312	+	5.11855i	0.0544189	+	0.167484i
$935$	10.4721			0.342475
$936$	4.06888			0.132996
$937$	8.32624	+	25.6255i	0.272006	+	0.837149i	0.989996	+	0.141096i	$0.0450625\pi$
$937$	8.32624	+	25.6255i	0.272006	+	0.837149i	−0.717990	+	0.696054i	$0.754937\pi$
$938$	6.47214	−	19.9192i	0.211323	−	0.650384i
$939$	8.11146	−	24.9645i	0.264707	−	0.814686i
$940$	−8.47214	−	6.15537i	−0.276331	−	0.200766i
$941$	11.7426	+	36.1401i	0.382799	+	1.17814i	0.938064	+	0.346462i	$0.112617\pi$
$941$	11.7426	+	36.1401i	0.382799	+	1.17814i	−0.555265	+	0.831674i	$0.687383\pi$
$942$	9.20163	+	6.68537i	0.299805	+	0.217821i
$943$	−43.6525	+	31.7154i	−1.42152	+	1.03279i
$944$	−1.28115	+	3.94298i	−0.0416980	+	0.128333i
$945$	18.9443	−	13.7638i	0.616257	−	0.447737i
$946$	−3.23607	+	2.35114i	−0.105214	+	0.0764422i
$947$	9.56231	−	29.4298i	0.310733	−	0.956338i	−0.666742	−	0.745289i	$-0.732312\pi$
$947$	9.56231	−	29.4298i	0.310733	−	0.956338i	0.977475	−	0.211050i	$-0.0676883\pi$
$948$	2.76393	−	2.00811i	0.0897683	−	0.0652205i
$949$	0.472136	+	0.343027i	0.0153262	+	0.0111351i
$950$	1.70820	+	5.25731i	0.0554215	+	0.170570i
$951$	21.9443	+	15.9434i	0.711592	+	0.517002i
$952$	15.3262	−	47.1693i	0.496726	−	1.52877i
$953$	−9.97871	+	30.7113i	−0.323242	+	0.994837i	0.648986	+	0.760801i	$0.275194\pi$
$953$	−9.97871	+	30.7113i	−0.323242	+	0.994837i	−0.972228	+	0.234037i	$0.924806\pi$
$954$	0.429563	+	1.32206i	0.0139076	+	0.0428033i
$955$	3.18034			0.102913
$956$	2.76393			0.0893920
$957$	−5.52786	−	17.0130i	−0.178690	−	0.549953i
$958$	18.3541	−	13.3350i	0.592994	−	0.430835i
$959$	−67.5410	−	49.0714i	−2.18101	−	1.58460i
$960$	0.291796			0.00941768
$961$		0			0
$962$	1.52786			0.0492603
$963$	12.1910	+	8.85727i	0.392849	+	0.285421i
$964$	39.7426	−	28.8747i	1.28002	−	0.929992i
$965$	−1.69098	−	5.20431i	−0.0544347	−	0.167533i
$966$	−24.9443			−0.802569
$967$	−15.6393			−0.502927			−0.251463	−	0.967867i	$-0.580912\pi$
$967$	−15.6393			−0.502927			−0.251463	+	0.967867i	$0.580912\pi$
$968$	−4.83688	−	14.8864i	−0.155463	−	0.478467i
$969$	4.47214	−	13.7638i	0.143666	−	0.442158i
$970$	−0.371323	+	1.14281i	−0.0119225	+	0.0366936i
$971$	22.6525	+	16.4580i	0.726953	+	0.528162i	0.888598	−	0.458687i	$-0.151680\pi$
$971$	22.6525	+	16.4580i	0.726953	+	0.528162i	−0.161645	+	0.986849i	$0.551680\pi$
$972$	6.79837	+	20.9232i	0.218058	+	0.671113i
$973$	45.9787	+	33.4055i	1.47401	+	1.07093i
$974$	7.38197	−	5.36331i	0.236533	−	0.171852i
$975$	−1.88854	+	5.81234i	−0.0604818	+	0.186144i
$976$	−21.2705	+	15.4539i	−0.680852	+	0.494668i
$977$	−26.8992	+	19.5434i	−0.860581	+	0.625249i	−0.928043	−	0.372473i	$-0.878510\pi$
$977$	−26.8992	+	19.5434i	−0.860581	+	0.625249i	0.0674618	+	0.997722i	$0.478510\pi$
$978$	−0.639320	+	1.96763i	−0.0204432	+	0.0629177i
$979$	2.76393	−	2.00811i	0.0883357	−	0.0641796i
$980$	14.3262	+	10.4086i	0.457635	+	0.332491i
$981$	−1.79431	−	5.52231i	−0.0572879	−	0.176314i
$982$	20.1803	+	14.6619i	0.643981	+	0.467879i
$983$	−14.9787	+	46.0997i	−0.477747	+	1.47035i	0.364470	+	0.931215i	$0.381250\pi$
$983$	−14.9787	+	46.0997i	−0.477747	+	1.47035i	−0.842217	+	0.539138i	$0.818750\pi$
$984$	−5.97871	+	18.4006i	−0.190594	+	0.586589i
$985$	4.76393	+	14.6619i	0.151791	+	0.467166i
$986$	−23.4164			−0.745730
$987$	−33.8885			−1.07868
$988$	1.38197	+	4.25325i	0.0439662	+	0.135314i
$989$	−20.1803	+	14.6619i	−0.641697	+	0.466221i
$990$	1.47214	+	1.06957i	0.0467876	+	0.0339931i
$991$	−50.5410			−1.60549			−0.802744	−	0.596324i	$-0.796628\pi$
$991$	−50.5410			−1.60549			−0.802744	+	0.596324i	$0.796628\pi$
$992$		0			0
$993$	2.47214			0.0784509
$994$	−27.9164	−	20.2825i	−0.885455	−	0.643320i
$995$	−0.854102	+	0.620541i	−0.0270769	+	0.0196725i
$996$	−1.81966	−	5.60034i	−0.0576581	−	0.177453i
$997$	15.3607			0.486478			0.243239	−	0.969966i	$-0.421790\pi$
$997$	15.3607			0.486478			0.243239	+	0.969966i	$0.421790\pi$
$998$	−20.6525			−0.653743
$999$	3.41641	+	10.5146i	0.108090	+	0.332668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.g.374.1		4
31.2	even	5		961.2.d.a.628.1		4
31.3	odd	30		961.2.g.h.235.1		8
31.4	even	5		961.2.a.f.1.1		2
31.5	even	3		961.2.g.e.732.1		8
31.6	odd	6		961.2.g.h.816.1		8
31.7	even	15		961.2.c.c.439.1		4
31.8	even	5		961.2.d.a.531.1		4
31.9	even	15		961.2.g.d.844.1		8
31.10	even	15		961.2.g.d.448.1		8
31.11	odd	30		961.2.c.e.521.1		4
31.12	odd	30		961.2.g.a.846.1		8
31.13	odd	30		961.2.g.h.338.1		8
31.14	even	15		961.2.g.d.547.1		8
31.15	odd	10		961.2.d.d.388.1		4
31.16	even	5	inner	961.2.d.g.388.1		4
31.17	odd	30		961.2.g.a.547.1		8
31.18	even	15		961.2.g.e.338.1		8
31.19	even	15		961.2.g.d.846.1		8
31.20	even	15		961.2.c.c.521.1		4
31.21	odd	30		961.2.g.a.448.1		8
31.22	odd	30		961.2.g.a.844.1		8
31.23	odd	10		961.2.d.c.531.1		4
31.24	odd	30		961.2.c.e.439.1		4
31.25	even	3		961.2.g.e.816.1		8
31.26	odd	6		961.2.g.h.732.1		8
31.27	odd	10		31.2.a.a.1.1	✓	2
31.28	even	15		961.2.g.e.235.1		8
31.29	odd	10		961.2.d.c.628.1		4
31.30	odd	2		961.2.d.d.374.1		4
93.35	odd	10		8649.2.a.c.1.2		2
93.89	even	10		279.2.a.a.1.2		2
124.27	even	10		496.2.a.i.1.1		2
155.27	even	20		775.2.b.d.249.2		4
155.58	even	20		775.2.b.d.249.3		4
155.89	odd	10		775.2.a.d.1.2		2
217.27	even	10		1519.2.a.a.1.1		2
248.27	even	10		1984.2.a.n.1.2		2
248.213	odd	10		1984.2.a.r.1.1		2
341.120	even	10		3751.2.a.b.1.2		2
372.275	odd	10		4464.2.a.bf.1.2		2
403.337	odd	10		5239.2.a.f.1.2		2
465.89	even	10		6975.2.a.y.1.1		2
527.492	odd	10		8959.2.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.1	✓	2	31.27	odd	10
279.2.a.a.1.2		2	93.89	even	10
496.2.a.i.1.1		2	124.27	even	10
775.2.a.d.1.2		2	155.89	odd	10
775.2.b.d.249.2		4	155.27	even	20
775.2.b.d.249.3		4	155.58	even	20
961.2.a.f.1.1		2	31.4	even	5
961.2.c.c.439.1		4	31.7	even	15
961.2.c.c.521.1		4	31.20	even	15
961.2.c.e.439.1		4	31.24	odd	30
961.2.c.e.521.1		4	31.11	odd	30
961.2.d.a.531.1		4	31.8	even	5
961.2.d.a.628.1		4	31.2	even	5
961.2.d.c.531.1		4	31.23	odd	10
961.2.d.c.628.1		4	31.29	odd	10
961.2.d.d.374.1		4	31.30	odd	2
961.2.d.d.388.1		4	31.15	odd	10
961.2.d.g.374.1		4	1.1	even	1	trivial
961.2.d.g.388.1		4	31.16	even	5	inner
961.2.g.a.448.1		8	31.21	odd	30
961.2.g.a.547.1		8	31.17	odd	30
961.2.g.a.844.1		8	31.22	odd	30
961.2.g.a.846.1		8	31.12	odd	30
961.2.g.d.448.1		8	31.10	even	15
961.2.g.d.547.1		8	31.14	even	15
961.2.g.d.844.1		8	31.9	even	15
961.2.g.d.846.1		8	31.19	even	15
961.2.g.e.235.1		8	31.28	even	15
961.2.g.e.338.1		8	31.18	even	15
961.2.g.e.732.1		8	31.5	even	3
961.2.g.e.816.1		8	31.25	even	3
961.2.g.h.235.1		8	31.3	odd	30
961.2.g.h.338.1		8	31.13	odd	30
961.2.g.h.732.1		8	31.26	odd	6
961.2.g.h.816.1		8	31.6	odd	6
1519.2.a.a.1.1		2	217.27	even	10
1984.2.a.n.1.2		2	248.27	even	10
1984.2.a.r.1.1		2	248.213	odd	10
3751.2.a.b.1.2		2	341.120	even	10
4464.2.a.bf.1.2		2	372.275	odd	10
5239.2.a.f.1.2		2	403.337	odd	10
6975.2.a.y.1.1		2	465.89	even	10
8649.2.a.c.1.2		2	93.35	odd	10
8959.2.a.b.1.1		2	527.492	odd	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+(0.500000 + 0.363271i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-0.500000 - 1.53884i) q^{4} +1.00000 q^{5} +0.763932 q^{6} +(-1.30902 - 4.02874i) q^{7} +(0.690983 - 2.12663i) q^{8} +(-0.454915 + 1.40008i) q^{9} +(0.500000 + 0.363271i) q^{10} +(-0.618034 - 1.90211i) q^{11} +(-1.61803 - 1.17557i) q^{12} +(1.00000 - 0.726543i) q^{13} +(0.809017 - 2.48990i) q^{14} +(1.00000 - 0.726543i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(-1.61803 + 4.97980i) q^{17} +(-0.736068 + 0.534785i) q^{18} +(-1.80902 - 1.31433i) q^{19} +(-0.500000 - 1.53884i) q^{20} +(-4.23607 - 3.07768i) q^{21} +(0.381966 - 1.17557i) q^{22} +(2.38197 - 7.33094i) q^{23} +(-0.854102 - 2.62866i) q^{24} -4.00000 q^{25} +0.763932 q^{26} +(1.70820 + 5.25731i) q^{27} +(-5.54508 + 4.02874i) q^{28} +(5.85410 + 4.25325i) q^{29} +0.763932 q^{30} -5.61803 q^{32} +(-2.00000 - 1.45309i) q^{33} +(-2.61803 + 1.90211i) q^{34} +(-1.30902 - 4.02874i) q^{35} +2.38197 q^{36} +2.00000 q^{37} +(-0.427051 - 1.31433i) q^{38} +(0.472136 - 1.45309i) q^{39} +(0.690983 - 2.12663i) q^{40} +(-5.66312 - 4.11450i) q^{41} +(-1.00000 - 3.07768i) q^{42} +(-2.61803 - 1.90211i) q^{43} +(-2.61803 + 1.90211i) q^{44} +(-0.454915 + 1.40008i) q^{45} +(3.85410 - 2.80017i) q^{46} +(5.23607 - 3.80423i) q^{47} +(-0.708204 + 2.17963i) q^{48} +(-8.85410 + 6.43288i) q^{49} +(-2.00000 - 1.45309i) q^{50} +(2.00000 + 6.15537i) q^{51} +(-1.61803 - 1.17557i) q^{52} +(0.472136 - 1.45309i) q^{53} +(-1.05573 + 3.24920i) q^{54} +(-0.618034 - 1.90211i) q^{55} -9.47214 q^{56} -2.76393 q^{57} +(1.38197 + 4.25325i) q^{58} +(1.80902 - 1.31433i) q^{59} +(-1.61803 - 1.17557i) q^{60} +14.1803 q^{61} +6.23607 q^{63} +(0.190983 + 0.138757i) q^{64} +(1.00000 - 0.726543i) q^{65} +(-0.472136 - 1.45309i) q^{66} +8.00000 q^{67} +8.47214 q^{68} +(-2.94427 - 9.06154i) q^{69} +(0.809017 - 2.48990i) q^{70} +(4.07295 - 12.5352i) q^{71} +(2.66312 + 1.93487i) q^{72} +(0.145898 + 0.449028i) q^{73} +(1.00000 + 0.726543i) q^{74} +(-4.00000 + 2.90617i) q^{75} +(-1.11803 + 3.44095i) q^{76} +(-6.85410 + 4.97980i) q^{77} +(0.763932 - 0.555029i) q^{78} +(-0.527864 + 1.62460i) q^{79} +(-1.50000 + 1.08981i) q^{80} +(1.95492 + 1.42033i) q^{81} +(-1.33688 - 4.11450i) q^{82} +(2.38197 + 1.73060i) q^{83} +(-2.61803 + 8.05748i) q^{84} +(-1.61803 + 4.97980i) q^{85} +(-0.618034 - 1.90211i) q^{86} +8.94427 q^{87} -4.47214 q^{88} +(0.527864 + 1.62460i) q^{89} +(-0.736068 + 0.534785i) q^{90} +(-4.23607 - 3.07768i) q^{91} -12.4721 q^{92} +4.00000 q^{94} +(-1.80902 - 1.31433i) q^{95} +(-5.61803 + 4.08174i) q^{96} +(0.600813 + 1.84911i) q^{97} -6.76393 q^{98} +2.94427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 4 q^{5} + 12 q^{6} - 3 q^{7} + 5 q^{8} - 13 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} - 6 q^{16} - 2 q^{17} + 6 q^{18} - 5 q^{19} - 2 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 + 4 * q^5 + 12 * q^6 - 3 * q^7 + 5 * q^8 - 13 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 + 4 * q^13 + q^14 + 4 * q^15 - 6 * q^16 - 2 * q^17 + 6 * q^18 - 5 * q^19 - 2 * q^20 - 8 * q^21 + 6 * q^22 + 14 * q^23 + 10 * q^24 - 16 * q^25 + 12 * q^26 - 20 * q^27 - 11 * q^28 + 10 * q^29 + 12 * q^30 - 18 * q^32 - 8 * q^33 - 6 * q^34 - 3 * q^35 + 14 * q^36 + 8 * q^37 + 5 * q^38 - 16 * q^39 + 5 * q^40 - 7 * q^41 - 4 * q^42 - 6 * q^43 - 6 * q^44 - 13 * q^45 + 2 * q^46 + 12 * q^47 + 24 * q^48 - 22 * q^49 - 8 * q^50 + 8 * q^51 - 2 * q^52 - 16 * q^53 - 40 * q^54 + 2 * q^55 - 20 * q^56 - 20 * q^57 + 10 * q^58 + 5 * q^59 - 2 * q^60 + 12 * q^61 + 16 * q^63 + 3 * q^64 + 4 * q^65 + 16 * q^66 + 32 * q^67 + 16 * q^68 + 24 * q^69 + q^70 + 23 * q^71 - 5 * q^72 + 14 * q^73 + 4 * q^74 - 16 * q^75 - 14 * q^77 + 12 * q^78 - 20 * q^79 - 6 * q^80 + 19 * q^81 - 21 * q^82 + 14 * q^83 - 6 * q^84 - 2 * q^85 + 2 * q^86 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 32 * q^92 + 16 * q^94 - 5 * q^95 - 18 * q^96 + 27 * q^97 - 36 * q^98 - 24 * q^99

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