LMFDB - Embedded newform 110.2.g.a.91.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,2,Mod(31,110)] 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("110.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.878354422234$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	110.91
Dual form			110.2.g.a.81.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(1.00000 + 3.07768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-2.61803 - 1.90211i) q^{6} +(0.809017 - 2.48990i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-6.04508 + 4.39201i) q^{9} -1.00000 q^{10} +(-2.54508 - 2.12663i) q^{11} +3.23607 q^{12} +(1.30902 - 0.951057i) q^{13} +(0.809017 + 2.48990i) q^{14} +(-1.00000 + 3.07768i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.23607 + 3.07768i) q^{17} +(2.30902 - 7.10642i) q^{18} +(-1.26393 - 3.88998i) q^{19} +(0.809017 - 0.587785i) q^{20} +8.47214 q^{21} +(3.30902 + 0.224514i) q^{22} +0.145898 q^{23} +(-2.61803 + 1.90211i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.500000 + 1.53884i) q^{26} +(-11.7082 - 8.50651i) q^{27} +(-2.11803 - 1.53884i) q^{28} +(-0.381966 + 1.17557i) q^{29} +(-1.00000 - 3.07768i) q^{30} +(5.85410 - 4.25325i) q^{31} +1.00000 q^{32} +(4.00000 - 9.95959i) q^{33} -5.23607 q^{34} +(2.11803 - 1.53884i) q^{35} +(2.30902 + 7.10642i) q^{36} +(-0.263932 + 0.812299i) q^{37} +(3.30902 + 2.40414i) q^{38} +(4.23607 + 3.07768i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-0.572949 - 1.76336i) q^{41} +(-6.85410 + 4.97980i) q^{42} -9.23607 q^{43} +(-2.80902 + 1.76336i) q^{44} -7.47214 q^{45} +(-0.118034 + 0.0857567i) q^{46} +(3.50000 + 10.7719i) q^{47} +(1.00000 - 3.07768i) q^{48} +(0.118034 + 0.0857567i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-5.23607 + 16.1150i) q^{51} +(-0.500000 - 1.53884i) q^{52} +(-0.736068 + 0.534785i) q^{53} +14.4721 q^{54} +(-0.809017 - 3.21644i) q^{55} +2.61803 q^{56} +(10.7082 - 7.77997i) q^{57} +(-0.381966 - 1.17557i) q^{58} +(0.736068 - 2.26538i) q^{59} +(2.61803 + 1.90211i) q^{60} +(-7.23607 - 5.25731i) q^{61} +(-2.23607 + 6.88191i) q^{62} +(6.04508 + 18.6049i) q^{63} +(-0.809017 + 0.587785i) q^{64} +1.61803 q^{65} +(2.61803 + 10.4086i) q^{66} +0.763932 q^{67} +(4.23607 - 3.07768i) q^{68} +(0.145898 + 0.449028i) q^{69} +(-0.809017 + 2.48990i) q^{70} +(-10.7082 - 7.77997i) q^{71} +(-6.04508 - 4.39201i) q^{72} +(-0.527864 + 1.62460i) q^{73} +(-0.263932 - 0.812299i) q^{74} +(-2.61803 + 1.90211i) q^{75} -4.09017 q^{76} +(-7.35410 + 4.61653i) q^{77} -5.23607 q^{78} +(1.23607 - 0.898056i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(7.54508 - 23.2214i) q^{81} +(1.50000 + 1.08981i) q^{82} +(-12.7082 - 9.23305i) q^{83} +(2.61803 - 8.05748i) q^{84} +(1.61803 + 4.97980i) q^{85} +(7.47214 - 5.42882i) q^{86} -4.00000 q^{87} +(1.23607 - 3.07768i) q^{88} -12.0344 q^{89} +(6.04508 - 4.39201i) q^{90} +(-1.30902 - 4.02874i) q^{91} +(0.0450850 - 0.138757i) q^{92} +(18.9443 + 13.7638i) q^{93} +(-9.16312 - 6.65740i) q^{94} +(1.26393 - 3.88998i) q^{95} +(1.00000 + 3.07768i) q^{96} +(9.70820 - 7.05342i) q^{97} -0.145898 q^{98} +(24.7254 + 1.67760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 4 q^{3} - q^{4} + q^{5} - 6 q^{6} + q^{7} - q^{8} - 13 q^{9} - 4 q^{10} + q^{11} + 4 q^{12} + 3 q^{13} + q^{14} - 4 q^{15} - q^{16} + 8 q^{17} + 7 q^{18} - 14 q^{19} + q^{20} + 16 q^{21}+ \cdots + 43 q^{99}+O(q^{100}) $ 4 * q - q^2 + 4 * q^3 - q^4 + q^5 - 6 * q^6 + q^7 - q^8 - 13 * q^9 - 4 * q^10 + q^11 + 4 * q^12 + 3 * q^13 + q^14 - 4 * q^15 - q^16 + 8 * q^17 + 7 * q^18 - 14 * q^19 + q^20 + 16 * q^21 + 11 * q^22 + 14 * q^23 - 6 * q^24 - q^25 - 2 * q^26 - 20 * q^27 - 4 * q^28 - 6 * q^29 - 4 * q^30 + 10 * q^31 + 4 * q^32 + 16 * q^33 - 12 * q^34 + 4 * q^35 + 7 * q^36 - 10 * q^37 + 11 * q^38 + 8 * q^39 + q^40 - 9 * q^41 - 14 * q^42 - 28 * q^43 - 9 * q^44 - 12 * q^45 + 4 * q^46 + 14 * q^47 + 4 * q^48 - 4 * q^49 - q^50 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 40 * q^54 - q^55 + 6 * q^56 + 16 * q^57 - 6 * q^58 - 6 * q^59 + 6 * q^60 - 20 * q^61 + 13 * q^63 - q^64 + 2 * q^65 + 6 * q^66 + 12 * q^67 + 8 * q^68 + 14 * q^69 - q^70 - 16 * q^71 - 13 * q^72 - 20 * q^73 - 10 * q^74 - 6 * q^75 + 6 * q^76 - 16 * q^77 - 12 * q^78 - 4 * q^79 + q^80 + 19 * q^81 + 6 * q^82 - 24 * q^83 + 6 * q^84 + 2 * q^85 + 12 * q^86 - 16 * q^87 - 4 * q^88 + 10 * q^89 + 13 * q^90 - 3 * q^91 - 11 * q^92 + 40 * q^93 - 21 * q^94 + 14 * q^95 + 4 * q^96 + 12 * q^97 - 14 * q^98 + 43 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	1.00000	+	3.07768i	0.577350	+	1.77690i	0.628033	+	0.778187i	$0.283860\pi$
$3$	1.00000	+	3.07768i	0.577350	+	1.77690i	−0.0506828	+	0.998715i	$0.516140\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	−2.61803	−	1.90211i	−1.06881	−	0.776534i
$7$	0.809017	−	2.48990i	0.305780	−	0.941093i	−0.673605	−	0.739091i	$-0.735255\pi$
$7$	0.809017	−	2.48990i	0.305780	−	0.941093i	0.979385	−	0.202002i	$-0.0647447\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−6.04508	+	4.39201i	−2.01503	+	1.46400i
$10$	−1.00000			−0.316228
$11$	−2.54508	−	2.12663i	−0.767372	−	0.641202i
$11$	−2.54508	−	2.12663i	−0.767372	−	0.641202i
$12$	3.23607			0.934172
$13$	1.30902	−	0.951057i	0.363056	−	0.263776i	−0.391270	−	0.920276i	$-0.627964\pi$
$13$	1.30902	−	0.951057i	0.363056	−	0.263776i	0.754326	+	0.656500i	$0.227964\pi$
$14$	0.809017	+	2.48990i	0.216219	+	0.665453i
$15$	−1.00000	+	3.07768i	−0.258199	+	0.794654i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.23607	+	3.07768i	1.02740	+	0.746448i	0.967786	−	0.251774i	$-0.0810139\pi$
$17$	4.23607	+	3.07768i	1.02740	+	0.746448i	0.0596113	+	0.998222i	$0.481014\pi$
$18$	2.30902	−	7.10642i	0.544241	−	1.67500i
$19$	−1.26393	−	3.88998i	−0.289966	−	0.892423i	−0.984866	−	0.173317i	$-0.944551\pi$
$19$	−1.26393	−	3.88998i	−0.289966	−	0.892423i	0.694900	−	0.719106i	$-0.255449\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	8.47214			1.84877
$22$	3.30902	+	0.224514i	0.705485	+	0.0478665i
$23$	0.145898			0.0304218			0.0152109	−	0.999884i	$-0.495158\pi$
$23$	0.145898			0.0304218			0.0152109	+	0.999884i	$0.495158\pi$
$24$	−2.61803	+	1.90211i	−0.534404	+	0.388267i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.500000	+	1.53884i	−0.0980581	+	0.301792i
$27$	−11.7082	−	8.50651i	−2.25324	−	1.63708i
$28$	−2.11803	−	1.53884i	−0.400271	−	0.290814i
$29$	−0.381966	+	1.17557i	−0.0709293	+	0.218298i	−0.980237	−	0.197826i	$-0.936612\pi$
$29$	−0.381966	+	1.17557i	−0.0709293	+	0.218298i	0.909308	+	0.416124i	$0.136612\pi$
$30$	−1.00000	−	3.07768i	−0.182574	−	0.561906i
$31$	5.85410	−	4.25325i	1.05143	−	0.763907i	0.0789443	−	0.996879i	$-0.474845\pi$
$31$	5.85410	−	4.25325i	1.05143	−	0.763907i	0.972483	+	0.232972i	$0.0748451\pi$
$32$	1.00000			0.176777
$33$	4.00000	−	9.95959i	0.696311	−	1.73374i
$34$	−5.23607			−0.897978
$35$	2.11803	−	1.53884i	0.358013	−	0.260112i
$36$	2.30902	+	7.10642i	0.384836	+	1.18440i
$37$	−0.263932	+	0.812299i	−0.0433902	+	0.133541i	−0.970405	−	0.241484i	$-0.922366\pi$
$37$	−0.263932	+	0.812299i	−0.0433902	+	0.133541i	0.927015	+	0.375025i	$0.122366\pi$
$38$	3.30902	+	2.40414i	0.536793	+	0.390003i
$39$	4.23607	+	3.07768i	0.678314	+	0.492824i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	−0.572949	−	1.76336i	−0.0894796	−	0.275390i	0.896296	−	0.443456i	$-0.146248\pi$
$41$	−0.572949	−	1.76336i	−0.0894796	−	0.275390i	−0.985776	+	0.168066i	$0.946248\pi$
$42$	−6.85410	+	4.97980i	−1.05761	+	0.768399i
$43$	−9.23607			−1.40849			−0.704244	−	0.709958i	$-0.748714\pi$
$43$	−9.23607			−1.40849			−0.704244	+	0.709958i	$0.748714\pi$
$44$	−2.80902	+	1.76336i	−0.423475	+	0.265836i
$45$	−7.47214			−1.11388
$46$	−0.118034	+	0.0857567i	−0.0174032	+	0.0126441i
$47$	3.50000	+	10.7719i	0.510527	+	1.57124i	0.791275	+	0.611460i	$0.209418\pi$
$47$	3.50000	+	10.7719i	0.510527	+	1.57124i	−0.280748	+	0.959782i	$0.590582\pi$
$48$	1.00000	−	3.07768i	0.144338	−	0.444225i
$49$	0.118034	+	0.0857567i	0.0168620	+	0.0122510i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−5.23607	+	16.1150i	−0.733196	+	2.25655i
$52$	−0.500000	−	1.53884i	−0.0693375	−	0.213399i
$53$	−0.736068	+	0.534785i	−0.101107	+	0.0734583i	−0.637190	−	0.770707i	$-0.719903\pi$
$53$	−0.736068	+	0.534785i	−0.101107	+	0.0734583i	0.536083	+	0.844165i	$0.319903\pi$
$54$	14.4721			1.96941
$55$	−0.809017	−	3.21644i	−0.109088	−	0.433705i
$56$	2.61803			0.349850
$57$	10.7082	−	7.77997i	1.41834	−	1.03048i
$58$	−0.381966	−	1.17557i	−0.0501546	−	0.154360i
$59$	0.736068	−	2.26538i	0.0958279	−	0.294928i	−0.891641	−	0.452744i	$-0.850445\pi$
$59$	0.736068	−	2.26538i	0.0958279	−	0.294928i	0.987469	+	0.157816i	$0.0504452\pi$
$60$	2.61803	+	1.90211i	0.337987	+	0.245562i
$61$	−7.23607	−	5.25731i	−0.926484	−	0.673130i	0.0186458	−	0.999826i	$-0.494065\pi$
$61$	−7.23607	−	5.25731i	−0.926484	−	0.673130i	−0.945129	+	0.326696i	$0.894065\pi$
$62$	−2.23607	+	6.88191i	−0.283981	+	0.874003i
$63$	6.04508	+	18.6049i	0.761609	+	2.34399i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	1.61803			0.200692
$66$	2.61803	+	10.4086i	0.322258	+	1.28121i
$67$	0.763932			0.0933292			0.0466646	−	0.998911i	$-0.485141\pi$
$67$	0.763932			0.0933292			0.0466646	+	0.998911i	$0.485141\pi$
$68$	4.23607	−	3.07768i	0.513699	−	0.373224i
$69$	0.145898	+	0.449028i	0.0175641	+	0.0540566i
$70$	−0.809017	+	2.48990i	−0.0966960	+	0.297600i
$71$	−10.7082	−	7.77997i	−1.27083	−	0.923312i	−0.271595	−	0.962412i	$-0.587551\pi$
$71$	−10.7082	−	7.77997i	−1.27083	−	0.923312i	−0.999235	+	0.0390997i	$0.987551\pi$
$72$	−6.04508	−	4.39201i	−0.712420	−	0.517603i
$73$	−0.527864	+	1.62460i	−0.0617818	+	0.190145i	−0.977184	−	0.212397i	$-0.931873\pi$
$73$	−0.527864	+	1.62460i	−0.0617818	+	0.190145i	0.915402	+	0.402542i	$0.131873\pi$
$74$	−0.263932	−	0.812299i	−0.0306815	−	0.0944279i
$75$	−2.61803	+	1.90211i	−0.302305	+	0.219637i
$76$	−4.09017			−0.469175
$77$	−7.35410	+	4.61653i	−0.838078	+	0.526102i
$78$	−5.23607			−0.592868
$79$	1.23607	−	0.898056i	0.139069	−	0.101039i	−0.516076	−	0.856543i	$-0.672608\pi$
$79$	1.23607	−	0.898056i	0.139069	−	0.101039i	0.655144	+	0.755504i	$0.272608\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	7.54508	−	23.2214i	0.838343	−	2.58015i
$82$	1.50000	+	1.08981i	0.165647	+	0.120350i
$83$	−12.7082	−	9.23305i	−1.39491	−	1.01346i	−0.995307	−	0.0967693i	$-0.969149\pi$
$83$	−12.7082	−	9.23305i	−1.39491	−	1.01346i	−0.399600	−	0.916690i	$-0.630851\pi$
$84$	2.61803	−	8.05748i	0.285651	−	0.879143i
$85$	1.61803	+	4.97980i	0.175500	+	0.540135i
$86$	7.47214	−	5.42882i	0.805741	−	0.585405i
$87$	−4.00000			−0.428845
$88$	1.23607	−	3.07768i	0.131765	−	0.328082i
$89$	−12.0344			−1.27565			−0.637824	−	0.770182i	$-0.720165\pi$
$89$	−12.0344			−1.27565			−0.637824	+	0.770182i	$0.720165\pi$
$90$	6.04508	−	4.39201i	0.637208	−	0.462959i
$91$	−1.30902	−	4.02874i	−0.137222	−	0.422327i
$92$	0.0450850	−	0.138757i	0.00470043	−	0.0144664i
$93$	18.9443	+	13.7638i	1.96443	+	1.42724i
$94$	−9.16312	−	6.65740i	−0.945104	−	0.686658i
$95$	1.26393	−	3.88998i	0.129677	−	0.399104i
$96$	1.00000	+	3.07768i	0.102062	+	0.314115i
$97$	9.70820	−	7.05342i	0.985719	−	0.716167i	0.0267394	−	0.999642i	$-0.491488\pi$
$97$	9.70820	−	7.05342i	0.985719	−	0.716167i	0.958979	+	0.283476i	$0.0914876\pi$
$98$	−0.145898			−0.0147379
$99$	24.7254	+	1.67760i	2.48500	+	0.168605i
$100$	1.00000			0.100000
$101$	−3.00000	+	2.17963i	−0.298511	+	0.216881i	−0.726951	−	0.686689i	$-0.759063\pi$
$101$	−3.00000	+	2.17963i	−0.298511	+	0.216881i	0.428440	+	0.903570i	$0.359063\pi$
$102$	−5.23607	−	16.1150i	−0.518448	−	1.59562i
$103$	−3.50000	+	10.7719i	−0.344865	+	1.06139i	0.616791	+	0.787127i	$0.288433\pi$
$103$	−3.50000	+	10.7719i	−0.344865	+	1.06139i	−0.961656	+	0.274259i	$0.911567\pi$
$104$	1.30902	+	0.951057i	0.128360	+	0.0932588i
$105$	6.85410	+	4.97980i	0.668892	+	0.485978i
$106$	0.281153	−	0.865300i	0.0273080	−	0.0840453i
$107$	−2.32624	−	7.15942i	−0.224886	−	0.692128i	−0.998303	−	0.0582304i	$-0.981454\pi$
$107$	−2.32624	−	7.15942i	−0.224886	−	0.692128i	0.773417	−	0.633897i	$-0.218546\pi$
$108$	−11.7082	+	8.50651i	−1.12662	+	0.818539i
$109$	7.52786			0.721039			0.360519	−	0.932752i	$-0.382599\pi$
$109$	7.52786			0.721039			0.360519	+	0.932752i	$0.382599\pi$
$110$	2.54508	+	2.12663i	0.242664	+	0.202766i
$111$	−2.76393			−0.262341
$112$	−2.11803	+	1.53884i	−0.200135	+	0.145407i
$113$	1.94427	+	5.98385i	0.182902	+	0.562914i	0.999906	−	0.0137181i	$-0.00436676\pi$
$113$	1.94427	+	5.98385i	0.182902	+	0.562914i	−0.817004	+	0.576632i	$0.804367\pi$
$114$	−4.09017	+	12.5882i	−0.383080	+	1.17900i
$115$	0.118034	+	0.0857567i	0.0110067	+	0.00799685i
$116$	1.00000	+	0.726543i	0.0928477	+	0.0674578i
$117$	−3.73607	+	11.4984i	−0.345400	+	1.06303i
$118$	0.736068	+	2.26538i	0.0677605	+	0.208546i
$119$	11.0902	−	8.05748i	1.01663	−	0.738628i
$120$	−3.23607			−0.295411
$121$	1.95492	+	10.8249i	0.177720	+	0.984081i
$122$	8.94427			0.809776
$123$	4.85410	−	3.52671i	0.437680	−	0.317993i
$124$	−2.23607	−	6.88191i	−0.200805	−	0.618014i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−15.8262	−	11.4984i	−1.40991	−	1.02436i
$127$	1.92705	+	1.40008i	0.170998	+	0.124237i	0.669993	−	0.742368i	$-0.266297\pi$
$127$	1.92705	+	1.40008i	0.170998	+	0.124237i	−0.498995	+	0.866605i	$0.666297\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−9.23607	−	28.4257i	−0.813190	−	2.50274i
$130$	−1.30902	+	0.951057i	−0.114808	+	0.0834132i
$131$	11.4164			0.997456			0.498728	−	0.866758i	$-0.333801\pi$
$131$	11.4164			0.997456			0.498728	+	0.866758i	$0.333801\pi$
$132$	−8.23607	−	6.88191i	−0.716858	−	0.598993i
$133$	−10.7082			−0.928519
$134$	−0.618034	+	0.449028i	−0.0533900	+	0.0387901i
$135$	−4.47214	−	13.7638i	−0.384900	−	1.18460i
$136$	−1.61803	+	4.97980i	−0.138745	+	0.427014i
$137$	4.23607	+	3.07768i	0.361912	+	0.262944i	0.753849	−	0.657048i	$-0.228195\pi$
$137$	4.23607	+	3.07768i	0.361912	+	0.262944i	−0.391937	+	0.919992i	$0.628195\pi$
$138$	−0.381966	−	0.277515i	−0.0325151	−	0.0236236i
$139$	−2.51722	+	7.74721i	−0.213508	+	0.657110i	0.785748	+	0.618546i	$0.212278\pi$
$139$	−2.51722	+	7.74721i	−0.213508	+	0.657110i	−0.999256	+	0.0385633i	$0.987722\pi$
$140$	−0.809017	−	2.48990i	−0.0683744	−	0.210435i
$141$	−29.6525	+	21.5438i	−2.49719	+	1.81431i
$142$	13.2361			1.11075
$143$	−5.35410	−	0.363271i	−0.447732	−	0.0303783i
$144$	7.47214			0.622678
$145$	−1.00000	+	0.726543i	−0.0830455	+	0.0603361i
$146$	−0.527864	−	1.62460i	−0.0436863	−	0.134453i
$147$	−0.145898	+	0.449028i	−0.0120335	+	0.0370352i
$148$	0.690983	+	0.502029i	0.0567985	+	0.0412665i
$149$	3.23607	+	2.35114i	0.265109	+	0.192613i	0.712396	−	0.701777i	$-0.247610\pi$
$149$	3.23607	+	2.35114i	0.265109	+	0.192613i	−0.447287	+	0.894390i	$0.647610\pi$
$150$	1.00000	−	3.07768i	0.0816497	−	0.251292i
$151$	3.90983	+	12.0332i	0.318177	+	0.979250i	0.974427	+	0.224705i	$0.0721420\pi$
$151$	3.90983	+	12.0332i	0.318177	+	0.979250i	−0.656249	+	0.754544i	$0.727858\pi$
$152$	3.30902	−	2.40414i	0.268397	−	0.195002i
$153$	−39.1246			−3.16304
$154$	3.23607	−	8.05748i	0.260770	−	0.649290i
$155$	7.23607			0.581215
$156$	4.23607	−	3.07768i	0.339157	−	0.246412i
$157$	2.66312	+	8.19624i	0.212540	+	0.654131i	0.999319	+	0.0368962i	$0.0117471\pi$
$157$	2.66312	+	8.19624i	0.212540	+	0.654131i	−0.786779	+	0.617235i	$0.788253\pi$
$158$	−0.472136	+	1.45309i	−0.0375611	+	0.115601i
$159$	−2.38197	−	1.73060i	−0.188902	−	0.137245i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	0.118034	−	0.363271i	0.00930238	−	0.0286298i
$162$	7.54508	+	23.2214i	0.592798	+	1.82444i
$163$	5.85410	−	4.25325i	0.458529	−	0.333141i	−0.334425	−	0.942422i	$-0.608542\pi$
$163$	5.85410	−	4.25325i	0.458529	−	0.333141i	0.792954	+	0.609282i	$0.208542\pi$
$164$	−1.85410			−0.144781
$165$	9.09017	−	5.70634i	0.707669	−	0.444238i
$166$	15.7082			1.21919
$167$	−6.39919	+	4.64928i	−0.495184	+	0.359772i	−0.807174	−	0.590313i	$-0.799004\pi$
$167$	−6.39919	+	4.64928i	−0.495184	+	0.359772i	0.311990	+	0.950085i	$0.399004\pi$
$168$	2.61803	+	8.05748i	0.201986	+	0.621648i
$169$	−3.20820	+	9.87384i	−0.246785	+	0.759526i
$170$	−4.23607	−	3.07768i	−0.324892	−	0.236048i
$171$	24.7254	+	17.9641i	1.89080	+	1.37375i
$172$	−2.85410	+	8.78402i	−0.217623	+	0.669775i
$173$	−3.89919	−	12.0005i	−0.296450	−	0.912378i	−0.982731	−	0.185042i	$-0.940758\pi$
$173$	−3.89919	−	12.0005i	−0.296450	−	0.912378i	0.686281	−	0.727337i	$-0.259242\pi$
$174$	3.23607	−	2.35114i	0.245326	−	0.178240i
$175$	2.61803			0.197905
$176$	0.809017	+	3.21644i	0.0609820	+	0.242448i
$177$	7.70820			0.579384
$178$	9.73607	−	7.07367i	0.729749	−	0.530194i
$179$	−0.899187	−	2.76741i	−0.0672084	−	0.206846i	0.911812	−	0.410607i	$-0.134683\pi$
$179$	−0.899187	−	2.76741i	−0.0672084	−	0.206846i	−0.979021	+	0.203761i	$0.934683\pi$
$180$	−2.30902	+	7.10642i	−0.172104	+	0.529682i
$181$	16.5623	+	12.0332i	1.23107	+	0.894422i	0.996970	−	0.0777911i	$-0.0247867\pi$
$181$	16.5623	+	12.0332i	1.23107	+	0.894422i	0.234097	+	0.972213i	$0.424787\pi$
$182$	3.42705	+	2.48990i	0.254030	+	0.184564i
$183$	8.94427	−	27.5276i	0.661180	−	2.03490i
$184$	0.0450850	+	0.138757i	0.00332371	+	0.0102293i
$185$	−0.690983	+	0.502029i	−0.0508021	+	0.0369099i
$186$	−23.4164			−1.71697
$187$	−4.23607	−	16.8415i	−0.309772	−	1.23157i
$188$	11.3262			0.826051
$189$	−30.6525	+	22.2703i	−2.22964	+	1.61993i
$190$	1.26393	+	3.88998i	0.0916953	+	0.282209i
$191$	7.85410	−	24.1724i	0.568303	−	1.74906i	−0.0896251	−	0.995976i	$-0.528567\pi$
$191$	7.85410	−	24.1724i	0.568303	−	1.74906i	0.657928	−	0.753081i	$-0.271433\pi$
$192$	−2.61803	−	1.90211i	−0.188940	−	0.137273i
$193$	4.38197	+	3.18368i	0.315421	+	0.229167i	0.734219	−	0.678913i	$-0.237549\pi$
$193$	4.38197	+	3.18368i	0.315421	+	0.229167i	−0.418798	+	0.908079i	$0.637549\pi$
$194$	−3.70820	+	11.4127i	−0.266234	+	0.819383i
$195$	1.61803	+	4.97980i	0.115870	+	0.356611i
$196$	0.118034	−	0.0857567i	0.00843100	−	0.00612548i
$197$	−4.90983			−0.349811			−0.174905	−	0.984585i	$-0.555962\pi$
$197$	−4.90983			−0.349811			−0.174905	+	0.984585i	$0.555962\pi$
$198$	−20.9894	+	13.1760i	−1.49165	+	0.936380i
$199$	1.70820			0.121091			0.0605457	−	0.998165i	$-0.480716\pi$
$199$	1.70820			0.121091			0.0605457	+	0.998165i	$0.480716\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	0.763932	+	2.35114i	0.0538836	+	0.165837i
$202$	1.14590	−	3.52671i	0.0806251	−	0.248139i
$203$	2.61803	+	1.90211i	0.183750	+	0.133502i
$204$	13.7082	+	9.95959i	0.959766	+	0.697311i
$205$	0.572949	−	1.76336i	0.0400165	−	0.123158i
$206$	−3.50000	−	10.7719i	−0.243857	−	0.750513i
$207$	−0.881966	+	0.640786i	−0.0613009	+	0.0445377i
$208$	−1.61803			−0.112190
$209$	−5.05573	+	12.5882i	−0.349712	+	0.870747i
$210$	−8.47214			−0.584633
$211$	−16.9443	+	12.3107i	−1.16649	+	0.847506i	−0.990585	−	0.136901i	$-0.956286\pi$
$211$	−16.9443	+	12.3107i	−1.16649	+	0.847506i	−0.175907	+	0.984407i	$0.556286\pi$
$212$	0.281153	+	0.865300i	0.0193097	+	0.0594290i
$213$	13.2361	−	40.7364i	0.906920	−	2.79121i
$214$	6.09017	+	4.42477i	0.416315	+	0.302471i
$215$	−7.47214	−	5.42882i	−0.509595	−	0.370243i
$216$	4.47214	−	13.7638i	0.304290	−	0.936509i
$217$	−5.85410	−	18.0171i	−0.397402	−	1.22308i
$218$	−6.09017	+	4.42477i	−0.412478	+	0.299683i
$219$	−5.52786			−0.373538
$220$	−3.30902	−	0.224514i	−0.223094	−	0.0151367i
$221$	8.47214			0.569898
$222$	2.23607	−	1.62460i	0.150075	−	0.109036i
$223$	2.98936	+	9.20029i	0.200182	+	0.616097i	0.999877	+	0.0156905i	$0.00499465\pi$
$223$	2.98936	+	9.20029i	0.200182	+	0.616097i	−0.799695	+	0.600407i	$0.795005\pi$
$224$	0.809017	−	2.48990i	0.0540547	−	0.166363i
$225$	−6.04508	−	4.39201i	−0.403006	−	0.292801i
$226$	−5.09017	−	3.69822i	−0.338593	−	0.246002i
$227$	−5.09017	+	15.6659i	−0.337846	+	1.03978i	0.627456	+	0.778652i	$0.284096\pi$
$227$	−5.09017	+	15.6659i	−0.337846	+	1.03978i	−0.965303	+	0.261133i	$0.915904\pi$
$228$	−4.09017	−	12.5882i	−0.270878	−	0.833677i
$229$	22.7984	−	16.5640i	1.50656	−	1.09458i	0.538884	−	0.842380i	$-0.318846\pi$
$229$	22.7984	−	16.5640i	1.50656	−	1.09458i	0.967675	−	0.252199i	$-0.0811537\pi$
$230$	−0.145898			−0.00962023
$231$	−21.5623	−	18.0171i	−1.41870	−	1.18544i
$232$	−1.23607			−0.0811518
$233$	−12.3262	+	8.95554i	−0.807519	+	0.586697i	−0.913110	−	0.407713i	$-0.866326\pi$
$233$	−12.3262	+	8.95554i	−0.807519	+	0.586697i	0.105591	+	0.994410i	$0.466326\pi$
$234$	−3.73607	−	11.4984i	−0.244234	−	0.751676i
$235$	−3.50000	+	10.7719i	−0.228315	+	0.702681i
$236$	−1.92705	−	1.40008i	−0.125440	−	0.0911377i
$237$	4.00000	+	2.90617i	0.259828	+	0.188776i
$238$	−4.23607	+	13.0373i	−0.274584	+	0.845081i
$239$	2.94427	+	9.06154i	0.190449	+	0.586142i	1.00000		0.000908170i	$-0.000289080\pi$
$239$	2.94427	+	9.06154i	0.190449	+	0.586142i	−0.809550	+	0.587050i	$0.800289\pi$
$240$	2.61803	−	1.90211i	0.168993	−	0.122781i
$241$	−1.85410			−0.119433			−0.0597166	−	0.998215i	$-0.519020\pi$
$241$	−1.85410			−0.119433			−0.0597166	+	0.998215i	$0.519020\pi$
$242$	−7.94427	−	7.60845i	−0.510677	−	0.489090i
$243$	35.5967			2.28353
$244$	−7.23607	+	5.25731i	−0.463242	+	0.336565i
$245$	0.0450850	+	0.138757i	0.00288037	+	0.00886488i
$246$	−1.85410	+	5.70634i	−0.118213	+	0.363823i
$247$	−5.35410	−	3.88998i	−0.340673	−	0.247514i
$248$	5.85410	+	4.25325i	0.371736	+	0.270082i
$249$	15.7082	−	48.3449i	0.995467	−	3.06373i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	8.11803	−	5.89810i	0.512406	−	0.372285i	−0.301330	−	0.953520i	$-0.597430\pi$
$251$	8.11803	−	5.89810i	0.512406	−	0.372285i	0.813735	+	0.581235i	$0.197430\pi$
$252$	19.5623			1.23231
$253$	−0.371323	−	0.310271i	−0.0233449	−	0.0195066i
$254$	−2.38197			−0.149458
$255$	−13.7082	+	9.95959i	−0.858441	+	0.623694i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−3.70820	+	11.4127i	−0.231311	+	0.711903i	0.766278	+	0.642509i	$0.222107\pi$
$257$	−3.70820	+	11.4127i	−0.231311	+	0.711903i	−0.997589	+	0.0693940i	$0.977893\pi$
$258$	24.1803	+	17.5680i	1.50540	+	1.09374i
$259$	1.80902	+	1.31433i	0.112407	+	0.0816684i
$260$	0.500000	−	1.53884i	0.0310087	−	0.0954349i
$261$	−2.85410	−	8.78402i	−0.176664	−	0.543717i
$262$	−9.23607	+	6.71040i	−0.570606	+	0.414570i
$263$	25.7984			1.59080			0.795398	−	0.606088i	$-0.207262\pi$
$263$	25.7984			1.59080			0.795398	+	0.606088i	$0.207262\pi$
$264$	10.7082	+	0.726543i	0.659044	+	0.0447156i
$265$	−0.909830			−0.0558904
$266$	8.66312	−	6.29412i	0.531170	−	0.385918i
$267$	−12.0344	−	37.0382i	−0.736496	−	2.26670i
$268$	0.236068	−	0.726543i	0.0144201	−	0.0443806i
$269$	−14.2361	−	10.3431i	−0.867988	−	0.630630i	0.0620580	−	0.998073i	$-0.480234\pi$
$269$	−14.2361	−	10.3431i	−0.867988	−	0.630630i	−0.930046	+	0.367442i	$0.880234\pi$
$270$	11.7082	+	8.50651i	0.712539	+	0.517690i
$271$	4.14590	−	12.7598i	0.251845	−	0.775100i	−0.742589	−	0.669747i	$-0.766403\pi$
$271$	4.14590	−	12.7598i	0.251845	−	0.775100i	0.994435	−	0.105353i	$-0.0335974\pi$
$272$	−1.61803	−	4.97980i	−0.0981077	−	0.301945i
$273$	11.0902	−	8.05748i	0.671208	−	0.487661i
$274$	−5.23607			−0.316322
$275$	1.23607	−	3.07768i	0.0745377	−	0.185591i
$276$	0.472136			0.0284192
$277$	0.500000	−	0.363271i	0.0300421	−	0.0218269i	−0.572663	−	0.819791i	$-0.694090\pi$
$277$	0.500000	−	0.363271i	0.0300421	−	0.0218269i	0.602705	+	0.797964i	$0.294090\pi$
$278$	−2.51722	−	7.74721i	−0.150973	−	0.464647i
$279$	−16.7082	+	51.4226i	−1.00029	+	3.07859i
$280$	2.11803	+	1.53884i	0.126577	+	0.0919634i
$281$	−14.5623	−	10.5801i	−0.868714	−	0.631158i	0.0615273	−	0.998105i	$-0.480403\pi$
$281$	−14.5623	−	10.5801i	−0.868714	−	0.631158i	−0.930242	+	0.366947i	$0.880403\pi$
$282$	11.3262	−	34.8586i	0.674468	−	2.07580i
$283$	7.67376	+	23.6174i	0.456158	+	1.40391i	0.869771	+	0.493456i	$0.164267\pi$
$283$	7.67376	+	23.6174i	0.456158	+	1.40391i	−0.413613	+	0.910453i	$0.635733\pi$
$284$	−10.7082	+	7.77997i	−0.635415	+	0.461656i
$285$	13.2361			0.784037
$286$	4.54508	−	2.85317i	0.268757	−	0.168711i
$287$	−4.85410			−0.286529
$288$	−6.04508	+	4.39201i	−0.356210	+	0.258802i
$289$	3.21885	+	9.90659i	0.189344	+	0.582741i
$290$	0.381966	−	1.17557i	0.0224298	−	0.0690319i
$291$	31.4164	+	22.8254i	1.84166	+	1.33805i
$292$	1.38197	+	1.00406i	0.0808734	+	0.0587580i
$293$	−7.33688	+	22.5806i	−0.428625	+	1.31917i	0.470855	+	0.882211i	$0.343946\pi$
$293$	−7.33688	+	22.5806i	−0.428625	+	1.31917i	−0.899480	+	0.436962i	$0.856054\pi$
$294$	−0.145898	−	0.449028i	−0.00850895	−	0.0261878i
$295$	1.92705	−	1.40008i	0.112197	−	0.0815161i
$296$	−0.854102			−0.0496437
$297$	11.7082	+	46.5488i	0.679379	+	2.70103i
$298$	−4.00000			−0.231714
$299$	0.190983	−	0.138757i	0.0110448	−	0.00802454i
$300$	1.00000	+	3.07768i	0.0577350	+	0.177690i
$301$	−7.47214	+	22.9969i	−0.430687	+	1.32552i
$302$	−10.2361	−	7.43694i	−0.589020	−	0.427948i
$303$	−9.70820	−	7.05342i	−0.557722	−	0.405209i
$304$	−1.26393	+	3.88998i	−0.0724915	+	0.223106i
$305$	−2.76393	−	8.50651i	−0.158262	−	0.487081i
$306$	31.6525	−	22.9969i	1.80945	−	1.31464i
$307$	−26.9443			−1.53779			−0.768895	−	0.639375i	$-0.779193\pi$
$307$	−26.9443			−1.53779			−0.768895	+	0.639375i	$0.779193\pi$
$308$	2.11803	+	8.42075i	0.120686	+	0.479817i
$309$	−36.6525			−2.08509
$310$	−5.85410	+	4.25325i	−0.332491	+	0.241569i
$311$	−0.763932	−	2.35114i	−0.0433186	−	0.133321i	0.927058	−	0.374917i	$-0.122329\pi$
$311$	−0.763932	−	2.35114i	−0.0433186	−	0.133321i	−0.970377	+	0.241597i	$0.922329\pi$
$312$	−1.61803	+	4.97980i	−0.0916031	+	0.281925i
$313$	−22.1803	−	16.1150i	−1.25371	−	0.910871i	−0.255276	−	0.966868i	$-0.582166\pi$
$313$	−22.1803	−	16.1150i	−1.25371	−	0.910871i	−0.998431	+	0.0559968i	$0.982166\pi$
$314$	−6.97214	−	5.06555i	−0.393460	−	0.285866i
$315$	−6.04508	+	18.6049i	−0.340602	+	1.04827i
$316$	−0.472136	−	1.45309i	−0.0265597	−	0.0817424i
$317$	−5.01722	+	3.64522i	−0.281795	+	0.204736i	−0.719700	−	0.694285i	$-0.755721\pi$
$317$	−5.01722	+	3.64522i	−0.281795	+	0.204736i	0.437905	+	0.899021i	$0.355721\pi$
$318$	2.94427			0.165107
$319$	3.47214	−	2.17963i	0.194402	−	0.122036i
$320$	−1.00000			−0.0559017
$321$	19.7082	−	14.3188i	1.10000	−	0.799200i
$322$	0.118034	+	0.363271i	0.00657778	+	0.0202443i
$323$	6.61803	−	20.3682i	0.368237	−	1.13332i
$324$	−19.7533	−	14.3516i	−1.09740	−	0.797311i
$325$	1.30902	+	0.951057i	0.0726112	+	0.0527551i
$326$	−2.23607	+	6.88191i	−0.123844	+	0.381154i
$327$	7.52786	+	23.1684i	0.416292	+	1.28121i
$328$	1.50000	−	1.08981i	0.0828236	−	0.0601749i
$329$	29.6525			1.63479
$330$	−4.00000	+	9.95959i	−0.220193	+	0.548258i
$331$	−14.3820			−0.790504			−0.395252	−	0.918573i	$-0.629343\pi$
$331$	−14.3820			−0.790504			−0.395252	+	0.918573i	$0.629343\pi$
$332$	−12.7082	+	9.23305i	−0.697453	+	0.506729i
$333$	−1.97214	−	6.06961i	−0.108072	−	0.332613i
$334$	2.44427	−	7.52270i	0.133745	−	0.411624i
$335$	0.618034	+	0.449028i	0.0337668	+	0.0245330i
$336$	−6.85410	−	4.97980i	−0.373922	−	0.271670i
$337$	10.9443	−	33.6830i	0.596172	−	1.83483i	0.0473712	−	0.998877i	$-0.484916\pi$
$337$	10.9443	−	33.6830i	0.596172	−	1.83483i	0.548801	−	0.835953i	$-0.315084\pi$
$338$	−3.20820	−	9.87384i	−0.174503	−	0.537066i
$339$	−16.4721	+	11.9677i	−0.894644	+	0.649997i
$340$	5.23607			0.283966
$341$	−23.9443	−	1.62460i	−1.29666	−	0.0879769i
$342$	−30.5623			−1.65262
$343$	15.1353	−	10.9964i	0.817227	−	0.593750i
$344$	−2.85410	−	8.78402i	−0.153883	−	0.473603i
$345$	−0.145898	+	0.449028i	−0.00785489	+	0.0241749i
$346$	10.2082	+	7.41669i	0.548796	+	0.398724i
$347$	21.9443	+	15.9434i	1.17803	+	0.855889i	0.991948	−	0.126645i	$-0.0404209\pi$
$347$	21.9443	+	15.9434i	1.17803	+	0.855889i	0.186082	+	0.982534i	$0.440421\pi$
$348$	−1.23607	+	3.80423i	−0.0662602	+	0.203928i
$349$	9.56231	+	29.4298i	0.511858	+	1.57534i	0.788926	+	0.614488i	$0.210637\pi$
$349$	9.56231	+	29.4298i	0.511858	+	1.57534i	−0.277068	+	0.960850i	$0.589363\pi$
$350$	−2.11803	+	1.53884i	−0.113214	+	0.0822546i
$351$	−23.4164			−1.24988
$352$	−2.54508	−	2.12663i	−0.135653	−	0.113350i
$353$	11.7082			0.623165			0.311582	−	0.950219i	$-0.399141\pi$
$353$	11.7082			0.623165			0.311582	+	0.950219i	$0.399141\pi$
$354$	−6.23607	+	4.53077i	−0.331443	+	0.240808i
$355$	−4.09017	−	12.5882i	−0.217084	−	0.668115i
$356$	−3.71885	+	11.4454i	−0.197098	+	0.606607i
$357$	35.8885	+	26.0746i	1.89942	+	1.38001i
$358$	2.35410	+	1.71036i	0.124418	+	0.0903951i
$359$	−9.41641	+	28.9807i	−0.496979	+	1.52954i	0.316871	+	0.948469i	$0.397368\pi$
$359$	−9.41641	+	28.9807i	−0.496979	+	1.52954i	−0.813850	+	0.581075i	$0.802632\pi$
$360$	−2.30902	−	7.10642i	−0.121696	−	0.374541i
$361$	1.83688	−	1.33457i	0.0966779	−	0.0702406i
$362$	−20.4721			−1.07599
$363$	−31.3607	+	16.8415i	−1.64601	+	0.883950i
$364$	−4.23607			−0.222030
$365$	−1.38197	+	1.00406i	−0.0723354	+	0.0525547i
$366$	8.94427	+	27.5276i	0.467525	+	1.43889i
$367$	3.23607	−	9.95959i	0.168921	−	0.519887i	−0.830382	−	0.557194i	$-0.811878\pi$
$367$	3.23607	−	9.95959i	0.168921	−	0.519887i	0.999304	+	0.0373073i	$0.0118780\pi$
$368$	−0.118034	−	0.0857567i	−0.00615295	−	0.00447038i
$369$	11.2082	+	8.14324i	0.583476	+	0.423920i
$370$	0.263932	−	0.812299i	0.0137212	−	0.0422294i
$371$	0.736068	+	2.26538i	0.0382147	+	0.117613i
$372$	18.9443	−	13.7638i	0.982215	−	0.713621i
$373$	6.96556			0.360663			0.180331	−	0.983606i	$-0.442283\pi$
$373$	6.96556			0.360663			0.180331	+	0.983606i	$0.442283\pi$
$374$	13.3262	+	11.1352i	0.689083	+	0.575786i
$375$	−3.23607			−0.167110
$376$	−9.16312	+	6.65740i	−0.472552	+	0.343329i
$377$	0.618034	+	1.90211i	0.0318304	+	0.0979638i
$378$	11.7082	−	36.0341i	0.602205	−	1.85340i
$379$	8.35410	+	6.06961i	0.429121	+	0.311775i	0.781297	−	0.624159i	$-0.214558\pi$
$379$	8.35410	+	6.06961i	0.429121	+	0.311775i	−0.352176	+	0.935934i	$0.614558\pi$
$380$	−3.30902	−	2.40414i	−0.169749	−	0.123330i
$381$	−2.38197	+	7.33094i	−0.122032	+	0.375575i
$382$	7.85410	+	24.1724i	0.401851	+	1.23677i
$383$	12.8262	−	9.31881i	0.655390	−	0.476169i	−0.209713	−	0.977763i	$-0.567253\pi$
$383$	12.8262	−	9.31881i	0.655390	−	0.476169i	0.865103	+	0.501594i	$0.167253\pi$
$384$	3.23607			0.165140
$385$	−8.66312	−	0.587785i	−0.441513	−	0.0299563i
$386$	−5.41641			−0.275688
$387$	55.8328	−	40.5649i	2.83814	−	2.06203i
$388$	−3.70820	−	11.4127i	−0.188256	−	0.579391i
$389$	3.76393	−	11.5842i	0.190839	−	0.587342i	−0.809161	−	0.587587i	$-0.800078\pi$
$389$	3.76393	−	11.5842i	0.190839	−	0.587342i	1.00000		0.000245108i	$7.80203e-5\pi$
$390$	−4.23607	−	3.07768i	−0.214502	−	0.155845i
$391$	0.618034	+	0.449028i	0.0312553	+	0.0227083i
$392$	−0.0450850	+	0.138757i	−0.00227713	+	0.00700830i
$393$	11.4164	+	35.1361i	0.575882	+	1.77238i
$394$	3.97214	−	2.88593i	0.200113	−	0.145391i
$395$	1.52786			0.0768752
$396$	9.23607	−	22.9969i	0.464130	−	1.15564i
$397$	6.79837			0.341201			0.170600	−	0.985340i	$-0.445429\pi$
$397$	6.79837			0.341201			0.170600	+	0.985340i	$0.445429\pi$
$398$	−1.38197	+	1.00406i	−0.0692717	+	0.0503288i
$399$	−10.7082	−	32.9565i	−0.536081	−	1.64989i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	8.69098	+	6.31437i	0.434007	+	0.315325i	0.783249	−	0.621708i	$-0.213561\pi$
$401$	8.69098	+	6.31437i	0.434007	+	0.315325i	−0.349242	+	0.937033i	$0.613561\pi$
$402$	−2.00000	−	1.45309i	−0.0997509	−	0.0724733i
$403$	3.61803	−	11.1352i	0.180227	−	0.554682i
$404$	1.14590	+	3.52671i	0.0570106	+	0.175460i
$405$	19.7533	−	14.3516i	0.981549	−	0.713137i
$406$	−3.23607			−0.160603
$407$	2.39919	−	1.50609i	0.118923	−	0.0746539i
$408$	−16.9443			−0.838866
$409$	18.8713	−	13.7108i	0.933127	−	0.677956i	−0.0136296	−	0.999907i	$-0.504339\pi$
$409$	18.8713	−	13.7108i	0.933127	−	0.677956i	0.946756	+	0.321951i	$0.104339\pi$
$410$	0.572949	+	1.76336i	0.0282959	+	0.0870859i
$411$	−5.23607	+	16.1150i	−0.258276	+	0.794892i
$412$	9.16312	+	6.65740i	0.451434	+	0.327986i
$413$	−5.04508	−	3.66547i	−0.248252	−	0.180366i
$414$	0.336881	−	1.03681i	0.0165568	−	0.0509566i
$415$	−4.85410	−	14.9394i	−0.238278	−	0.733346i
$416$	1.30902	−	0.951057i	0.0641798	−	0.0466294i
$417$	−26.3607			−1.29089
$418$	−3.30902	−	13.1558i	−0.161849	−	0.643471i
$419$	−1.61803			−0.0790461			−0.0395231	−	0.999219i	$-0.512584\pi$
$419$	−1.61803			−0.0790461			−0.0395231	+	0.999219i	$0.512584\pi$
$420$	6.85410	−	4.97980i	0.334446	−	0.242989i
$421$	−5.76393	−	17.7396i	−0.280917	−	0.864573i	−0.987593	−	0.157036i	$-0.949806\pi$
$421$	−5.76393	−	17.7396i	−0.280917	−	0.864573i	0.706676	−	0.707537i	$-0.250194\pi$
$422$	6.47214	−	19.9192i	0.315059	−	0.969651i
$423$	−68.4681	−	49.7450i	−3.32903	−	2.41868i
$424$	−0.736068	−	0.534785i	−0.0357466	−	0.0259714i
$425$	−1.61803	+	4.97980i	−0.0784862	+	0.241556i
$426$	13.2361	+	40.7364i	0.641290	+	1.97369i
$427$	−18.9443	+	13.7638i	−0.916778	+	0.666078i
$428$	−7.52786			−0.363873
$429$	−4.23607	−	16.8415i	−0.204519	−	0.813115i
$430$	9.23607			0.445403
$431$	21.1803	−	15.3884i	1.02022	−	0.741234i	0.0538929	−	0.998547i	$-0.482837\pi$
$431$	21.1803	−	15.3884i	1.02022	−	0.741234i	0.966328	+	0.257313i	$0.0828370\pi$
$432$	4.47214	+	13.7638i	0.215166	+	0.662212i
$433$	2.94427	−	9.06154i	0.141493	−	0.435470i	−0.855051	−	0.518545i	$-0.826474\pi$
$433$	2.94427	−	9.06154i	0.141493	−	0.435470i	0.996543	+	0.0830748i	$0.0264741\pi$
$434$	15.3262	+	11.1352i	0.735683	+	0.534505i
$435$	−3.23607	−	2.35114i	−0.155158	−	0.112729i
$436$	2.32624	−	7.15942i	0.111407	−	0.342874i
$437$	−0.184405	−	0.567541i	−0.00882130	−	0.0271492i
$438$	4.47214	−	3.24920i	0.213687	−	0.155253i
$439$	−13.1246			−0.626404			−0.313202	−	0.949687i	$-0.601402\pi$
$439$	−13.1246			−0.626404			−0.313202	+	0.949687i	$0.601402\pi$
$440$	2.80902	−	1.76336i	0.133915	−	0.0840647i
$441$	−1.09017			−0.0519129
$442$	−6.85410	+	4.97980i	−0.326016	+	0.236865i
$443$	0.416408	+	1.28157i	0.0197841	+	0.0608893i	0.960461	−	0.278414i	$-0.0898087\pi$
$443$	0.416408	+	1.28157i	0.0197841	+	0.0608893i	−0.940677	+	0.339303i	$0.889809\pi$
$444$	−0.854102	+	2.62866i	−0.0405339	+	0.124750i
$445$	−9.73607	−	7.07367i	−0.461534	−	0.335324i
$446$	−7.82624	−	5.68609i	−0.370583	−	0.269244i
$447$	−4.00000	+	12.3107i	−0.189194	+	0.582278i
$448$	0.809017	+	2.48990i	0.0382225	+	0.117637i
$449$	−2.54508	+	1.84911i	−0.120110	+	0.0872650i	−0.646219	−	0.763152i	$-0.723651\pi$
$449$	−2.54508	+	1.84911i	−0.120110	+	0.0872650i	0.526109	+	0.850417i	$0.323651\pi$
$450$	7.47214			0.352240
$451$	−2.29180	+	5.70634i	−0.107916	+	0.268701i
$452$	6.29180			0.295941
$453$	−33.1246	+	24.0664i	−1.55633	+	1.13074i
$454$	−5.09017	−	15.6659i	−0.238894	−	0.735239i
$455$	1.30902	−	4.02874i	0.0613677	−	0.188870i
$456$	10.7082	+	7.77997i	0.501458	+	0.364330i
$457$	−26.3262	−	19.1271i	−1.23149	−	0.894729i	−0.234489	−	0.972119i	$-0.575342\pi$
$457$	−26.3262	−	19.1271i	−1.23149	−	0.894729i	−0.997001	+	0.0773894i	$0.975342\pi$
$458$	−8.70820	+	26.8011i	−0.406908	+	1.25233i
$459$	−23.4164	−	72.0683i	−1.09298	−	3.36386i
$460$	0.118034	−	0.0857567i	0.00550336	−	0.00399843i
$461$	28.5410			1.32929			0.664644	−	0.747160i	$-0.268583\pi$
$461$	28.5410			1.32929			0.664644	+	0.747160i	$0.268583\pi$
$462$	28.0344	+	1.90211i	1.30428	+	0.0884943i
$463$	15.5066			0.720652			0.360326	−	0.932826i	$-0.382665\pi$
$463$	15.5066			0.720652			0.360326	+	0.932826i	$0.382665\pi$
$464$	1.00000	−	0.726543i	0.0464238	−	0.0337289i
$465$	7.23607	+	22.2703i	0.335565	+	1.03276i
$466$	4.70820	−	14.4904i	0.218103	−	0.671253i
$467$	−13.9443	−	10.1311i	−0.645264	−	0.468812i	0.216391	−	0.976307i	$-0.430572\pi$
$467$	−13.9443	−	10.1311i	−0.645264	−	0.468812i	−0.861655	+	0.507495i	$0.830572\pi$
$468$	9.78115	+	7.10642i	0.452134	+	0.328495i
$469$	0.618034	−	1.90211i	0.0285382	−	0.0878314i
$470$	−3.50000	−	10.7719i	−0.161443	−	0.496870i
$471$	−22.5623	+	16.3925i	−1.03962	+	0.755325i
$472$	2.38197			0.109639
$473$	23.5066	+	19.6417i	1.08083	+	0.903125i
$474$	−4.94427			−0.227098
$475$	3.30902	−	2.40414i	0.151828	−	0.110310i
$476$	−4.23607	−	13.0373i	−0.194160	−	0.597563i
$477$	2.10081	−	6.46564i	0.0961896	−	0.296041i
$478$	−7.70820	−	5.60034i	−0.352565	−	0.256153i
$479$	23.9443	+	17.3965i	1.09404	+	0.794868i	0.980077	−	0.198617i	$-0.0636450\pi$
$479$	23.9443	+	17.3965i	1.09404	+	0.794868i	0.113965	+	0.993485i	$0.463645\pi$
$480$	−1.00000	+	3.07768i	−0.0456435	+	0.140476i
$481$	0.427051	+	1.31433i	0.0194718	+	0.0599282i
$482$	1.50000	−	1.08981i	0.0683231	−	0.0496397i
$483$	1.23607			0.0562430
$484$	10.8992	+	1.48584i	0.495418	+	0.0675382i
$485$	12.0000			0.544892
$486$	−28.7984	+	20.9232i	−1.30632	+	0.949098i
$487$	11.4164	+	35.1361i	0.517327	+	1.59217i	0.779008	+	0.627014i	$0.215723\pi$
$487$	11.4164	+	35.1361i	0.517327	+	1.59217i	−0.261681	+	0.965154i	$0.584277\pi$
$488$	2.76393	−	8.50651i	0.125117	−	0.385072i
$489$	18.9443	+	13.7638i	0.856690	+	0.622421i
$490$	−0.118034	−	0.0857567i	−0.00533223	−	0.00387409i
$491$	11.2639	−	34.6668i	0.508334	−	1.56449i	−0.286758	−	0.958003i	$-0.592578\pi$
$491$	11.2639	−	34.6668i	0.508334	−	1.56449i	0.795092	−	0.606489i	$-0.207422\pi$
$492$	−1.85410	−	5.70634i	−0.0835894	−	0.257262i
$493$	−5.23607	+	3.80423i	−0.235821	+	0.171334i
$494$	6.61803			0.297759
$495$	19.0172	+	15.8904i	0.854761	+	0.714222i
$496$	−7.23607			−0.324909
$497$	−28.0344	+	20.3682i	−1.25752	+	0.913639i
$498$	15.7082	+	48.3449i	0.703901	+	2.16639i
$499$	−3.95492	+	12.1720i	−0.177046	+	0.544893i	−0.999721	−	0.0236199i	$-0.992481\pi$
$499$	−3.95492	+	12.1720i	−0.177046	+	0.544893i	0.822675	+	0.568512i	$0.192481\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−20.7082	−	15.0454i	−0.925174	−	0.672178i
$502$	−3.10081	+	9.54332i	−0.138396	+	0.425939i
$503$	2.31966	+	7.13918i	0.103429	+	0.318320i	0.989358	−	0.145499i	$-0.0464787\pi$
$503$	2.31966	+	7.13918i	0.103429	+	0.318320i	−0.885930	+	0.463819i	$0.846479\pi$
$504$	−15.8262	+	11.4984i	−0.704957	+	0.512181i
$505$	−3.70820			−0.165013
$506$	0.482779	+	0.0327561i	0.0214621	+	0.00145619i
$507$	−33.5967			−1.49208
$508$	1.92705	−	1.40008i	0.0854991	−	0.0621187i
$509$	−9.61803	−	29.6013i	−0.426312	−	1.31205i	−0.901733	−	0.432294i	$-0.857704\pi$
$509$	−9.61803	−	29.6013i	−0.426312	−	1.31205i	0.475421	−	0.879759i	$-0.342296\pi$
$510$	5.23607	−	16.1150i	0.231857	−	0.713582i
$511$	3.61803	+	2.62866i	0.160052	+	0.116285i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−18.2918	+	56.2964i	−0.807603	+	2.48554i
$514$	−3.70820	−	11.4127i	−0.163562	−	0.503392i
$515$	−9.16312	+	6.65740i	−0.403775	+	0.293360i
$516$	−29.8885			−1.31577
$517$	14.0000	−	34.8586i	0.615719	−	1.53308i
$518$	−2.23607			−0.0982472
$519$	33.0344	−	24.0009i	1.45005	−	1.05352i
$520$	0.500000	+	1.53884i	0.0219265	+	0.0674827i
$521$	−2.66312	+	8.19624i	−0.116673	+	0.359084i	−0.992292	−	0.123919i	$-0.960454\pi$
$521$	−2.66312	+	8.19624i	−0.116673	+	0.359084i	0.875619	+	0.483002i	$0.160454\pi$
$522$	7.47214	+	5.42882i	0.327047	+	0.237613i
$523$	5.94427	+	4.31877i	0.259925	+	0.188846i	0.710114	−	0.704087i	$-0.248643\pi$
$523$	5.94427	+	4.31877i	0.259925	+	0.188846i	−0.450189	+	0.892933i	$0.648643\pi$
$524$	3.52786	−	10.8576i	0.154115	−	0.474319i
$525$	2.61803	+	8.05748i	0.114260	+	0.351657i
$526$	−20.8713	+	15.1639i	−0.910033	+	0.661178i
$527$	37.8885			1.65045
$528$	−9.09017	+	5.70634i	−0.395599	+	0.248337i
$529$	−22.9787			−0.999075
$530$	0.736068	−	0.534785i	0.0319727	−	0.0232296i
$531$	5.50000	+	16.9273i	0.238680	+	0.734580i
$532$	−3.30902	+	10.1841i	−0.143464	+	0.441537i
$533$	−2.42705	−	1.76336i	−0.105127	−	0.0763794i
$534$	31.5066	+	22.8909i	1.36342	+	0.990585i
$535$	2.32624	−	7.15942i	0.100572	−	0.309529i
$536$	0.236068	+	0.726543i	0.0101966	+	0.0313819i
$537$	7.61803	−	5.53483i	0.328742	−	0.238845i
$538$	17.5967			0.758650
$539$	−0.118034	−	0.469272i	−0.00508408	−	0.0202130i
$540$	−14.4721			−0.622782
$541$	6.47214	−	4.70228i	0.278259	−	0.202167i	−0.439899	−	0.898047i	$-0.644986\pi$
$541$	6.47214	−	4.70228i	0.278259	−	0.202167i	0.718158	+	0.695880i	$0.244986\pi$
$542$	4.14590	+	12.7598i	0.178082	+	0.548079i
$543$	−20.4721	+	63.0068i	−0.878543	+	2.70388i
$544$	4.23607	+	3.07768i	0.181620	+	0.131955i
$545$	6.09017	+	4.42477i	0.260874	+	0.189536i
$546$	−4.23607	+	13.0373i	−0.181287	+	0.557944i
$547$	−4.81966	−	14.8334i	−0.206074	−	0.634230i	−0.999668	−	0.0257820i	$-0.991792\pi$
$547$	−4.81966	−	14.8334i	−0.206074	−	0.634230i	0.793594	−	0.608448i	$-0.208208\pi$
$548$	4.23607	−	3.07768i	0.180956	−	0.131472i
$549$	66.8328			2.85236
$550$	0.809017	+	3.21644i	0.0344966	+	0.137149i
$551$	5.05573			0.215381
$552$	−0.381966	+	0.277515i	−0.0162576	+	0.0118118i
$553$	−1.23607	−	3.80423i	−0.0525630	−	0.161772i
$554$	−0.190983	+	0.587785i	−0.00811409	+	0.0249726i
$555$	−2.23607	−	1.62460i	−0.0949158	−	0.0689604i
$556$	6.59017	+	4.78804i	0.279485	+	0.203058i
$557$	10.2639	−	31.5891i	0.434897	−	1.33847i	−0.458296	−	0.888800i	$-0.651540\pi$
$557$	10.2639	−	31.5891i	0.434897	−	1.33847i	0.893192	−	0.449675i	$-0.148460\pi$
$558$	−16.7082	−	51.4226i	−0.707315	−	2.17689i
$559$	−12.0902	+	8.78402i	−0.511360	+	0.371525i
$560$	−2.61803			−0.110632
$561$	47.5967	−	29.8788i	2.00954	−	1.26148i
$562$	18.0000			0.759284
$563$	−19.3262	+	14.0413i	−0.814504	+	0.591772i	−0.915133	−	0.403152i	$-0.867914\pi$
$563$	−19.3262	+	14.0413i	−0.814504	+	0.591772i	0.100629	+	0.994924i	$0.467914\pi$
$564$	11.3262	+	34.8586i	0.476921	+	1.46781i
$565$	−1.94427	+	5.98385i	−0.0817961	+	0.251743i
$566$	−20.0902	−	14.5964i	−0.844453	−	0.613531i
$567$	−51.7148	−	37.5730i	−2.17182	−	1.57792i
$568$	4.09017	−	12.5882i	0.171620	−	0.528191i
$569$	2.57295	+	7.91872i	0.107864	+	0.331970i	0.990392	−	0.138289i	$-0.0441604\pi$
$569$	2.57295	+	7.91872i	0.107864	+	0.331970i	−0.882528	+	0.470259i	$0.844160\pi$
$570$	−10.7082	+	7.77997i	−0.448517	+	0.325867i
$571$	−29.0902			−1.21739			−0.608693	−	0.793406i	$-0.708306\pi$
$571$	−29.0902			−1.21739			−0.608693	+	0.793406i	$0.708306\pi$
$572$	−2.00000	+	4.97980i	−0.0836242	+	0.208216i
$573$	82.2492			3.43601
$574$	3.92705	−	2.85317i	0.163912	−	0.119089i
$575$	0.0450850	+	0.138757i	0.00188017	+	0.00578658i
$576$	2.30902	−	7.10642i	0.0962090	−	0.296101i
$577$	−12.0902	−	8.78402i	−0.503320	−	0.365684i	0.306963	−	0.951721i	$-0.400687\pi$
$577$	−12.0902	−	8.78402i	−0.503320	−	0.365684i	−0.810284	+	0.586038i	$0.800687\pi$
$578$	−8.42705	−	6.12261i	−0.350519	−	0.254667i
$579$	−5.41641	+	16.6700i	−0.225098	+	0.692781i
$580$	0.381966	+	1.17557i	0.0158603	+	0.0488129i
$581$	−33.2705	+	24.1724i	−1.38029	+	1.00284i
$582$	−38.8328			−1.60967
$583$	3.01064	+	0.204270i	0.124688	+	0.00845998i
$584$	−1.70820			−0.0706860
$585$	−9.78115	+	7.10642i	−0.404401	+	0.293814i
$586$	−7.33688	−	22.5806i	−0.303084	−	0.932796i
$587$	−6.41641	+	19.7477i	−0.264833	+	0.815074i	0.726898	+	0.686745i	$0.240961\pi$
$587$	−6.41641	+	19.7477i	−0.264833	+	0.815074i	−0.991732	+	0.128328i	$0.959039\pi$
$588$	0.381966	+	0.277515i	0.0157520	+	0.0114445i
$589$	−23.9443	−	17.3965i	−0.986607	−	0.716812i
$590$	−0.736068	+	2.26538i	−0.0303034	+	0.0932644i
$591$	−4.90983	−	15.1109i	−0.201963	−	0.621579i
$592$	0.690983	−	0.502029i	0.0283992	−	0.0206332i
$593$	−19.7082			−0.809319			−0.404659	−	0.914467i	$-0.632610\pi$
$593$	−19.7082			−0.809319			−0.404659	+	0.914467i	$0.632610\pi$
$594$	−36.8328	−	30.7768i	−1.51127	−	1.26279i
$595$	13.7082			0.561982
$596$	3.23607	−	2.35114i	0.132555	−	0.0963065i
$597$	1.70820	+	5.25731i	0.0699121	+	0.215167i
$598$	−0.0729490	+	0.224514i	−0.00298311	+	0.00918106i
$599$	−13.3262	−	9.68208i	−0.544495	−	0.395599i	0.281257	−	0.959633i	$-0.409249\pi$
$599$	−13.3262	−	9.68208i	−0.544495	−	0.395599i	−0.825752	+	0.564034i	$0.809249\pi$
$600$	−2.61803	−	1.90211i	−0.106881	−	0.0776534i
$601$	6.97214	−	21.4580i	0.284399	−	0.875291i	−0.702179	−	0.712001i	$-0.747789\pi$
$601$	6.97214	−	21.4580i	0.284399	−	0.875291i	0.986578	−	0.163290i	$-0.0522108\pi$
$602$	−7.47214	−	22.9969i	−0.304542	−	0.937282i
$603$	−4.61803	+	3.35520i	−0.188061	+	0.136634i
$604$	12.6525			0.514822
$605$	−4.78115	+	9.90659i	−0.194382	+	0.402760i
$606$	12.0000			0.487467
$607$	−26.1803	+	19.0211i	−1.06263	+	0.772044i	−0.974573	−	0.224072i	$-0.928065\pi$
$607$	−26.1803	+	19.0211i	−1.06263	+	0.772044i	−0.0880546	+	0.996116i	$0.528065\pi$
$608$	−1.26393	−	3.88998i	−0.0512592	−	0.157760i
$609$	−3.23607	+	9.95959i	−0.131132	+	0.403583i
$610$	7.23607	+	5.25731i	0.292980	+	0.212862i
$611$	14.8262	+	10.7719i	0.599805	+	0.435784i
$612$	−12.0902	+	37.2097i	−0.488716	+	1.50411i
$613$	3.56231	+	10.9637i	0.143880	+	0.442818i	0.996865	−	0.0791176i	$-0.0252103\pi$
$613$	3.56231	+	10.9637i	0.143880	+	0.442818i	−0.852985	+	0.521935i	$0.825210\pi$
$614$	21.7984	−	15.8374i	0.879711	−	0.639147i
$615$	6.00000			0.241943
$616$	−6.66312	−	5.56758i	−0.268465	−	0.224324i
$617$	32.9443			1.32629			0.663143	−	0.748493i	$-0.269222\pi$
$617$	32.9443			1.32629			0.663143	+	0.748493i	$0.269222\pi$
$618$	29.6525	−	21.5438i	1.19280	−	0.866618i
$619$	7.02786	+	21.6295i	0.282474	+	0.869365i	0.987145	+	0.159830i	$0.0510947\pi$
$619$	7.02786	+	21.6295i	0.282474	+	0.869365i	−0.704671	+	0.709534i	$0.748905\pi$
$620$	2.23607	−	6.88191i	0.0898027	−	0.276384i
$621$	−1.70820	−	1.24108i	−0.0685479	−	0.0498029i
$622$	2.00000	+	1.45309i	0.0801927	+	0.0582634i
$623$	−9.73607	+	29.9645i	−0.390067	+	1.20050i
$624$	−1.61803	−	4.97980i	−0.0647732	−	0.199351i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	27.4164			1.09578
$627$	−43.7984	−	2.97168i	−1.74914	−	0.118678i
$628$	8.61803			0.343897
$629$	−3.61803	+	2.62866i	−0.144260	+	0.104811i
$630$	−6.04508	−	18.6049i	−0.240842	−	0.741235i
$631$	2.29180	−	7.05342i	0.0912350	−	0.280792i	−0.895019	−	0.446028i	$-0.852838\pi$
$631$	2.29180	−	7.05342i	0.0912350	−	0.280792i	0.986254	+	0.165235i	$0.0528383\pi$
$632$	1.23607	+	0.898056i	0.0491681	+	0.0357227i
$633$	−54.8328	−	39.8384i	−2.17941	−	1.58343i
$634$	1.91641	−	5.89810i	0.0761103	−	0.234243i
$635$	0.736068	+	2.26538i	0.0292100	+	0.0898990i
$636$	−2.38197	+	1.73060i	−0.0944511	+	0.0686227i
$637$	0.236068			0.00935335
$638$	−1.52786	+	3.80423i	−0.0604887	+	0.150611i
$639$	98.9017			3.91249
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	11.7918	+	36.2914i	0.465748	+	1.43342i	0.858039	+	0.513584i	$0.171682\pi$
$641$	11.7918	+	36.2914i	0.465748	+	1.43342i	−0.392291	+	0.919841i	$0.628318\pi$
$642$	−7.52786	+	23.1684i	−0.297101	+	0.914383i
$643$	10.8541	+	7.88597i	0.428044	+	0.310992i	0.780866	−	0.624698i	$-0.214778\pi$
$643$	10.8541	+	7.88597i	0.428044	+	0.310992i	−0.352822	+	0.935690i	$0.614778\pi$
$644$	−0.309017	−	0.224514i	−0.0121770	−	0.00884709i
$645$	9.23607	−	28.4257i	0.363670	−	1.11926i
$646$	6.61803	+	20.3682i	0.260383	+	0.801377i
$647$	5.70820	−	4.14725i	0.224413	−	0.163045i	−0.469898	−	0.882721i	$-0.655709\pi$
$647$	5.70820	−	4.14725i	0.224413	−	0.163045i	0.694311	+	0.719675i	$0.255709\pi$
$648$	24.4164			0.959167
$649$	−6.69098	+	4.20025i	−0.262644	+	0.164874i
$650$	−1.61803			−0.0634645
$651$	49.5967	−	36.0341i	1.94385	−	1.41229i
$652$	−2.23607	−	6.88191i	−0.0875712	−	0.269516i
$653$	7.97214	−	24.5357i	0.311974	−	0.960157i	−0.665008	−	0.746836i	$-0.731572\pi$
$653$	7.97214	−	24.5357i	0.311974	−	0.960157i	0.976982	−	0.213321i	$-0.0684279\pi$
$654$	−19.7082	−	14.3188i	−0.770652	−	0.559911i
$655$	9.23607	+	6.71040i	0.360883	+	0.262197i
$656$	−0.572949	+	1.76336i	−0.0223699	+	0.0688475i
$657$	−3.94427	−	12.1392i	−0.153881	−	0.473596i
$658$	−23.9894	+	17.4293i	−0.935202	+	0.679464i
$659$	−13.3820			−0.521287			−0.260644	−	0.965435i	$-0.583935\pi$
$659$	−13.3820			−0.521287			−0.260644	+	0.965435i	$0.583935\pi$
$660$	−2.61803	−	10.4086i	−0.101907	−	0.405155i
$661$	2.18034			0.0848054			0.0424027	−	0.999101i	$-0.486499\pi$
$661$	2.18034			0.0848054			0.0424027	+	0.999101i	$0.486499\pi$
$662$	11.6353	−	8.45351i	0.452217	−	0.328555i
$663$	8.47214	+	26.0746i	0.329030	+	1.01265i
$664$	4.85410	−	14.9394i	0.188376	−	0.579761i
$665$	−8.66312	−	6.29412i	−0.335941	−	0.244076i
$666$	5.16312	+	3.75123i	0.200067	+	0.145357i
$667$	−0.0557281	+	0.171513i	−0.00215780	+	0.00664103i
$668$	2.44427	+	7.52270i	0.0945717	+	0.291062i
$669$	−25.3262	+	18.4006i	−0.979169	+	0.711408i
$670$	−0.763932			−0.0295133
$671$	7.23607	+	28.7687i	0.279345	+	1.11060i
$672$	8.47214			0.326820
$673$	3.23607	−	2.35114i	0.124741	−	0.0906298i	−0.523665	−	0.851924i	$-0.675436\pi$
$673$	3.23607	−	2.35114i	0.124741	−	0.0906298i	0.648407	+	0.761294i	$0.275436\pi$
$674$	10.9443	+	33.6830i	0.421558	+	1.29742i
$675$	4.47214	−	13.7638i	0.172133	−	0.529770i
$676$	8.39919	+	6.10237i	0.323046	+	0.234706i
$677$	8.09017	+	5.87785i	0.310930	+	0.225904i	0.732296	−	0.680987i	$-0.238449\pi$
$677$	8.09017	+	5.87785i	0.310930	+	0.225904i	−0.421365	+	0.906891i	$0.638449\pi$
$678$	6.29180	−	19.3642i	0.241635	−	0.743676i
$679$	−9.70820	−	29.8788i	−0.372567	−	1.14664i
$680$	−4.23607	+	3.07768i	−0.162446	+	0.118024i
$681$	−53.3050			−2.04265
$682$	20.3262	−	12.7598i	0.778332	−	0.488597i
$683$	−47.0132			−1.79891			−0.899454	−	0.437015i	$-0.856036\pi$
$683$	−47.0132			−1.79891			−0.899454	+	0.437015i	$0.856036\pi$
$684$	24.7254	−	17.9641i	0.945400	−	0.686873i
$685$	1.61803	+	4.97980i	0.0618219	+	0.190268i
$686$	−5.78115	+	17.7926i	−0.220725	+	0.679323i
$687$	73.7771	+	53.6022i	2.81477	+	2.04505i
$688$	7.47214	+	5.42882i	0.284873	+	0.206972i
$689$	−0.454915	+	1.40008i	−0.0173309	+	0.0533390i
$690$	−0.145898	−	0.449028i	−0.00555424	−	0.0170942i
$691$	−11.1180	+	8.07772i	−0.422950	+	0.307291i	−0.778824	−	0.627243i	$-0.784183\pi$
$691$	−11.1180	+	8.07772i	−0.422950	+	0.307291i	0.355874	+	0.934534i	$0.384183\pi$
$692$	−12.6180			−0.479666
$693$	24.1803	−	60.2066i	0.918535	−	2.28706i
$694$	−27.1246			−1.02964
$695$	−6.59017	+	4.78804i	−0.249979	+	0.181621i
$696$	−1.23607	−	3.80423i	−0.0468530	−	0.144199i
$697$	3.00000	−	9.23305i	0.113633	−	0.349727i
$698$	−25.0344	−	18.1886i	−0.947568	−	0.688448i
$699$	−39.8885	−	28.9807i	−1.50872	−	1.09615i
$700$	0.809017	−	2.48990i	0.0305780	−	0.0941093i
$701$	1.79837	+	5.53483i	0.0679236	+	0.209047i	0.979257	−	0.202621i	$-0.0649461\pi$
$701$	1.79837	+	5.53483i	0.0679236	+	0.209047i	−0.911334	+	0.411669i	$0.864946\pi$
$702$	18.9443	−	13.7638i	0.715005	−	0.519482i
$703$	3.49342			0.131757
$704$	3.30902	+	0.224514i	0.124713	+	0.00846169i
$705$	−36.6525			−1.38041
$706$	−9.47214	+	6.88191i	−0.356489	+	0.259004i
$707$	3.00000	+	9.23305i	0.112827	+	0.347245i
$708$	2.38197	−	7.33094i	0.0895198	−	0.275514i
$709$	−8.79837	−	6.39239i	−0.330430	−	0.240071i	0.410183	−	0.912003i	$-0.365465\pi$
$709$	−8.79837	−	6.39239i	−0.330430	−	0.240071i	−0.740613	+	0.671932i	$0.765465\pi$
$710$	10.7082	+	7.77997i	0.401872	+	0.291977i
$711$	−3.52786	+	10.8576i	−0.132305	+	0.407194i
$712$	−3.71885	−	11.4454i	−0.139370	−	0.428936i
$713$	0.854102	−	0.620541i	0.0319864	−	0.0232395i
$714$	−44.3607			−1.66016
$715$	−4.11803	−	3.44095i	−0.154006	−	0.128684i
$716$	−2.90983			−0.108745
$717$	−24.9443	+	18.1231i	−0.931561	+	0.676819i
$718$	−9.41641	−	28.9807i	−0.351417	−	1.08155i
$719$	7.36068	−	22.6538i	0.274507	−	0.844846i	−0.714842	−	0.699286i	$-0.753502\pi$
$719$	7.36068	−	22.6538i	0.274507	−	0.844846i	0.989349	−	0.145560i	$-0.0464984\pi$
$720$	6.04508	+	4.39201i	0.225287	+	0.163681i
$721$	23.9894	+	17.4293i	0.893410	+	0.649101i
$722$	−0.701626	+	2.15938i	−0.0261118	+	0.0803639i
$723$	−1.85410	−	5.70634i	−0.0689548	−	0.212221i
$724$	16.5623	−	12.0332i	0.615533	−	0.447211i
$725$	−1.23607			−0.0459064
$726$	15.4721	−	32.0584i	0.574225	−	1.18980i
$727$	−8.79837			−0.326314			−0.163157	−	0.986600i	$-0.552168\pi$
$727$	−8.79837			−0.326314			−0.163157	+	0.986600i	$0.552168\pi$
$728$	3.42705	−	2.48990i	0.127015	−	0.0922818i
$729$	12.9615	+	39.8914i	0.480055	+	1.47746i
$730$	0.527864	−	1.62460i	0.0195371	−	0.0601291i
$731$	−39.1246	−	28.4257i	−1.44708	−	1.05136i
$732$	−23.4164	−	17.0130i	−0.865495	−	0.628819i
$733$	11.2016	−	34.4751i	0.413742	−	1.27337i	−0.499630	−	0.866239i	$-0.666531\pi$
$733$	11.2016	−	34.4751i	0.413742	−	1.27337i	0.913372	−	0.407127i	$-0.133469\pi$
$734$	3.23607	+	9.95959i	0.119445	+	0.367615i
$735$	−0.381966	+	0.277515i	−0.0140890	+	0.0102363i
$736$	0.145898			0.00537787
$737$	−1.94427	−	1.62460i	−0.0716182	−	0.0598429i
$738$	−13.8541			−0.509977
$739$	25.7705	−	18.7234i	0.947984	−	0.688750i	−0.00234556	−	0.999997i	$-0.500747\pi$
$739$	25.7705	−	18.7234i	0.947984	−	0.688750i	0.950329	+	0.311247i	$0.100747\pi$
$740$	0.263932	+	0.812299i	0.00970233	+	0.0298607i
$741$	6.61803	−	20.3682i	0.243120	−	0.748245i
$742$	−1.92705	−	1.40008i	−0.0707443	−	0.0513987i
$743$	14.3541	+	10.4289i	0.526601	+	0.382598i	0.819085	−	0.573672i	$-0.194482\pi$
$743$	14.3541	+	10.4289i	0.526601	+	0.382598i	−0.292484	+	0.956270i	$0.594482\pi$
$744$	−7.23607	+	22.2703i	−0.265287	+	0.816470i
$745$	1.23607	+	3.80423i	0.0452860	+	0.139376i
$746$	−5.63525	+	4.09425i	−0.206321	+	0.149901i
$747$	117.374			4.29448
$748$	−17.3262	−	1.17557i	−0.633510	−	0.0429831i
$749$	−19.7082			−0.720122
$750$	2.61803	−	1.90211i	0.0955971	−	0.0694553i
$751$	−3.38197	−	10.4086i	−0.123410	−	0.379816i	0.870198	−	0.492702i	$-0.163991\pi$
$751$	−3.38197	−	10.4086i	−0.123410	−	0.379816i	−0.993608	+	0.112886i	$0.963991\pi$
$752$	3.50000	−	10.7719i	0.127632	−	0.392810i
$753$	26.2705	+	19.0866i	0.957351	+	0.695556i
$754$	−1.61803	−	1.17557i	−0.0589253	−	0.0428118i
$755$	−3.90983	+	12.0332i	−0.142293	+	0.437934i
$756$	11.7082	+	36.0341i	0.425823	+	1.31055i
$757$	−17.9615	+	13.0498i	−0.652822	+	0.474303i	−0.864231	−	0.503095i	$-0.832195\pi$
$757$	−17.9615	+	13.0498i	−0.652822	+	0.474303i	0.211410	+	0.977398i	$0.432195\pi$
$758$	−10.3262			−0.375066
$759$	0.583592	−	1.45309i	0.0211831	−	0.0527436i
$760$	4.09017			0.148366
$761$	−5.32624	+	3.86974i	−0.193076	+	0.140278i	−0.680123	−	0.733098i	$-0.738074\pi$
$761$	−5.32624	+	3.86974i	−0.193076	+	0.140278i	0.487048	+	0.873375i	$0.338074\pi$
$762$	−2.38197	−	7.33094i	−0.0862895	−	0.265572i
$763$	6.09017	−	18.7436i	0.220479	−	0.678564i
$764$	−20.5623	−	14.9394i	−0.743918	−	0.540488i
$765$	−31.6525	−	22.9969i	−1.14440	−	0.831454i
$766$	−4.89919	+	15.0781i	−0.177015	+	0.544796i
$767$	−1.19098	−	3.66547i	−0.0430039	−	0.132352i
$768$	−2.61803	+	1.90211i	−0.0944702	+	0.0686366i
$769$	−32.0902			−1.15720			−0.578601	−	0.815611i	$-0.696401\pi$
$769$	−32.0902			−1.15720			−0.578601	+	0.815611i	$0.696401\pi$
$770$	7.35410	−	4.61653i	0.265023	−	0.166368i
$771$	−38.8328			−1.39853
$772$	4.38197	−	3.18368i	0.157710	−	0.114583i
$773$	−11.6074	−	35.7239i	−0.417489	−	1.28490i	−0.910006	−	0.414596i	$-0.863923\pi$
$773$	−11.6074	−	35.7239i	−0.417489	−	1.28490i	0.492517	−	0.870303i	$-0.336077\pi$
$774$	−21.3262	+	65.6354i	−0.766556	+	2.35922i
$775$	5.85410	+	4.25325i	0.210286	+	0.152781i
$776$	9.70820	+	7.05342i	0.348504	+	0.253203i
$777$	−2.23607	+	6.88191i	−0.0802185	+	0.246887i
$778$	3.76393	+	11.5842i	0.134944	+	0.415313i
$779$	−6.13525	+	4.45752i	−0.219818	+	0.159707i
$780$	5.23607			0.187481
$781$	10.7082	+	42.5730i	0.383170	+	1.52338i
$782$	−0.763932			−0.0273182
$783$	14.4721	−	10.5146i	0.517192	−	0.375762i
$784$	−0.0450850	−	0.138757i	−0.00161018	−	0.00495562i
$785$	−2.66312	+	8.19624i	−0.0950508	+	0.292536i
$786$	−29.8885	−	21.7153i	−1.06609	−	0.774559i
$787$	29.1246	+	21.1603i	1.03818	+	0.754282i	0.969929	−	0.243386i	$-0.0782582\pi$
$787$	29.1246	+	21.1603i	1.03818	+	0.754282i	0.0682508	+	0.997668i	$0.478258\pi$
$788$	−1.51722	+	4.66953i	−0.0540488	+	0.166345i
$789$	25.7984	+	79.3992i	0.918446	+	2.82669i
$790$	−1.23607	+	0.898056i	−0.0439773	+	0.0319514i
$791$	16.4721			0.585682
$792$	6.04508	+	24.0337i	0.214803	+	0.854000i
$793$	−14.4721			−0.513921
$794$	−5.50000	+	3.99598i	−0.195188	+	0.141812i
$795$	−0.909830	−	2.80017i	−0.0322683	−	0.0993118i
$796$	0.527864	−	1.62460i	0.0187096	−	0.0575824i
$797$	−29.9615	−	21.7683i	−1.06129	−	0.771073i	−0.0869638	−	0.996211i	$-0.527716\pi$
$797$	−29.9615	−	21.7683i	−1.06129	−	0.771073i	−0.974327	+	0.225139i	$0.927716\pi$
$798$	28.0344	+	20.3682i	0.992408	+	0.721027i
$799$	−18.3262	+	56.4024i	−0.648336	+	1.99537i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	72.7492	−	52.8554i	2.57047	−	1.86755i
$802$	−10.7426			−0.379336
$803$	4.79837	−	3.01217i	0.169331	−	0.106297i
$804$	2.47214			0.0871855
$805$	0.309017	−	0.224514i	0.0108914	−	0.00791308i
$806$	3.61803	+	11.1352i	0.127440	+	0.392219i
$807$	17.5967	−	54.1572i	0.619435	−	1.90642i
$808$	−3.00000	−	2.17963i	−0.105540	−	0.0766790i
$809$	7.30902	+	5.31031i	0.256971	+	0.186701i	0.708811	−	0.705399i	$-0.249232\pi$
$809$	7.30902	+	5.31031i	0.256971	+	0.186701i	−0.451839	+	0.892099i	$0.649232\pi$
$810$	−7.54508	+	23.2214i	−0.265107	+	0.815916i
$811$	−14.4058	−	44.3364i	−0.505855	−	1.55686i	−0.799329	−	0.600894i	$-0.794811\pi$
$811$	−14.4058	−	44.3364i	−0.505855	−	1.55686i	0.293474	−	0.955967i	$-0.405189\pi$
$812$	2.61803	−	1.90211i	0.0918750	−	0.0667511i
$813$	43.4164			1.52268
$814$	−1.05573	+	2.62866i	−0.0370033	+	0.0921343i
$815$	7.23607			0.253468
$816$	13.7082	−	9.95959i	0.479883	−	0.348655i
$817$	11.6738	+	35.9281i	0.408413	+	1.25697i
$818$	−7.20820	+	22.1846i	−0.252029	+	0.775665i
$819$	25.6074	+	18.6049i	0.894795	+	0.650106i
$820$	−1.50000	−	1.08981i	−0.0523823	−	0.0380579i
$821$	−7.52786	+	23.1684i	−0.262724	+	0.808582i	0.729485	+	0.683997i	$0.239760\pi$
$821$	−7.52786	+	23.1684i	−0.262724	+	0.808582i	−0.992209	+	0.124585i	$0.960240\pi$
$822$	−5.23607	−	16.1150i	−0.182629	−	0.562074i
$823$	13.7812	−	10.0126i	0.480381	−	0.349017i	−0.321092	−	0.947048i	$-0.604050\pi$
$823$	13.7812	−	10.0126i	0.480381	−	0.349017i	0.801473	+	0.598031i	$0.204050\pi$
$824$	−11.3262			−0.394568
$825$	10.7082	+	0.726543i	0.372812	+	0.0252950i
$826$	6.23607			0.216981
$827$	−17.7984	+	12.9313i	−0.618910	+	0.449665i	−0.852541	−	0.522661i	$-0.824939\pi$
$827$	−17.7984	+	12.9313i	−0.618910	+	0.449665i	0.233631	+	0.972325i	$0.424939\pi$
$828$	0.336881	+	1.03681i	0.0117074	+	0.0360318i
$829$	−4.00000	+	12.3107i	−0.138926	+	0.427569i	−0.996180	−	0.0873239i	$-0.972168\pi$
$829$	−4.00000	+	12.3107i	−0.138926	+	0.427569i	0.857254	+	0.514893i	$0.172168\pi$
$830$	12.7082	+	9.23305i	0.441108	+	0.320484i
$831$	1.61803	+	1.17557i	0.0561290	+	0.0407801i
$832$	−0.500000	+	1.53884i	−0.0173344	+	0.0533497i
$833$	0.236068	+	0.726543i	0.00817927	+	0.0251732i
$834$	21.3262	−	15.4944i	0.738467	−	0.536528i
$835$	−7.90983			−0.273731
$836$	10.4098	+	8.69827i	0.360032	+	0.300836i
$837$	−104.721			−3.61970
$838$	1.30902	−	0.951057i	0.0452192	−	0.0328537i
$839$	−16.2361	−	49.9695i	−0.560531	−	1.72514i	−0.680869	−	0.732405i	$-0.738398\pi$
$839$	−16.2361	−	49.9695i	−0.560531	−	1.72514i	0.120338	−	0.992733i	$-0.461602\pi$
$840$	−2.61803	+	8.05748i	−0.0903308	+	0.278009i
$841$	22.2254	+	16.1477i	0.766394	+	0.556818i
$842$	15.0902	+	10.9637i	0.520042	+	0.377832i
$843$	18.0000	−	55.3983i	0.619953	−	1.90802i
$844$	6.47214	+	19.9192i	0.222780	+	0.685647i
$845$	−8.39919	+	6.10237i	−0.288941	+	0.209928i
$846$	84.6312			2.90968
$847$	28.5344	+	3.88998i	0.980455	+	0.133661i
$848$	0.909830			0.0312437
$849$	−65.0132	+	47.2348i	−2.23125	+	1.62109i
$850$	−1.61803	−	4.97980i	−0.0554981	−	0.170806i
$851$	−0.0385072	+	0.118513i	−0.00132001	+	0.00406257i
$852$	−34.6525	−	25.1765i	−1.18717	−	0.862533i
$853$	−12.9164	−	9.38432i	−0.442249	−	0.321313i	0.344279	−	0.938867i	$-0.388123\pi$
$853$	−12.9164	−	9.38432i	−0.442249	−	0.321313i	−0.786528	+	0.617555i	$0.788123\pi$
$854$	7.23607	−	22.2703i	0.247613	−	0.762075i
$855$	9.44427	+	29.0665i	0.322987	+	0.994053i
$856$	6.09017	−	4.42477i	0.208158	−	0.151235i
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$	13.3262	+	11.1352i	0.454950	+	0.380148i
$859$	−30.9098			−1.05463			−0.527315	−	0.849670i	$-0.676801\pi$
$859$	−30.9098			−1.05463			−0.527315	+	0.849670i	$0.676801\pi$
$860$	−7.47214	+	5.42882i	−0.254798	+	0.185121i
$861$	−4.85410	−	14.9394i	−0.165427	−	0.509133i
$862$	−8.09017	+	24.8990i	−0.275552	+	0.848063i
$863$	5.01722	+	3.64522i	0.170788	+	0.124085i	0.669896	−	0.742455i	$-0.266339\pi$
$863$	5.01722	+	3.64522i	0.170788	+	0.124085i	−0.499108	+	0.866540i	$0.666339\pi$
$864$	−11.7082	−	8.50651i	−0.398321	−	0.289397i
$865$	3.89919	−	12.0005i	0.132576	−	0.408028i
$866$	2.94427	+	9.06154i	0.100050	+	0.307924i
$867$	−27.2705	+	19.8132i	−0.926155	+	0.672891i
$868$	−18.9443			−0.643010
$869$	−5.05573	−	0.343027i	−0.171504	−	0.0116364i
$870$	4.00000			0.135613
$871$	1.00000	−	0.726543i	0.0338837	−	0.0246180i
$872$	2.32624	+	7.15942i	0.0787764	+	0.242449i
$873$	−27.7082	+	85.2771i	−0.937781	+	2.88619i
$874$	0.482779	+	0.350760i	0.0163302	+	0.0118646i
$875$	2.11803	+	1.53884i	0.0716026	+	0.0520223i
$876$	−1.70820	+	5.25731i	−0.0577149	+	0.177628i
$877$	0.736068	+	2.26538i	0.0248552	+	0.0764966i	0.962715	−	0.270519i	$-0.0871952\pi$
$877$	0.736068	+	2.26538i	0.0248552	+	0.0764966i	−0.937859	+	0.347015i	$0.887195\pi$
$878$	10.6180	−	7.71445i	0.358341	−	0.260350i
$879$	−76.8328			−2.59151
$880$	−1.23607	+	3.07768i	−0.0416678	+	0.103749i
$881$	−27.4508			−0.924843			−0.462421	−	0.886660i	$-0.653019\pi$
$881$	−27.4508			−0.924843			−0.462421	+	0.886660i	$0.653019\pi$
$882$	0.881966	−	0.640786i	0.0296973	−	0.0215764i
$883$	9.47214	+	29.1522i	0.318763	+	0.981051i	0.974178	+	0.225782i	$0.0724937\pi$
$883$	9.47214	+	29.1522i	0.318763	+	0.981051i	−0.655415	+	0.755269i	$0.727506\pi$
$884$	2.61803	−	8.05748i	0.0880540	−	0.271002i
$885$	6.23607	+	4.53077i	0.209623	+	0.152300i
$886$	−1.09017	−	0.792055i	−0.0366250	−	0.0266096i
$887$	14.6074	−	44.9569i	0.490468	−	1.50951i	−0.333434	−	0.942774i	$-0.608207\pi$
$887$	14.6074	−	44.9569i	0.490468	−	1.50951i	0.823902	−	0.566732i	$-0.191793\pi$
$888$	−0.854102	−	2.62866i	−0.0286618	−	0.0882119i
$889$	5.04508	−	3.66547i	0.169207	−	0.122936i
$890$	12.0344			0.403395
$891$	−68.5861	+	43.0548i	−2.29772	+	1.44239i
$892$	9.67376			0.323902
$893$	37.4787	−	27.2299i	1.25418	−	0.911213i
$894$	−4.00000	−	12.3107i	−0.133780	−	0.411733i
$895$	0.899187	−	2.76741i	0.0300565	−	0.0925044i
$896$	−2.11803	−	1.53884i	−0.0707585	−	0.0514091i
$897$	0.618034	+	0.449028i	0.0206356	+	0.0149926i
$898$	0.972136	−	2.99193i	0.0324406	−	0.0998419i
$899$	2.76393	+	8.50651i	0.0921823	+	0.283708i
$900$	−6.04508	+	4.39201i	−0.201503	+	0.146400i
$901$	−4.76393			−0.158710
$902$	−1.50000	−	5.96361i	−0.0499445	−	0.198566i
$903$	−78.2492			−2.60397
$904$	−5.09017	+	3.69822i	−0.169297	+	0.123001i
$905$	6.32624	+	19.4702i	0.210291	+	0.647210i
$906$	12.6525	−	38.9403i	0.420350	−	1.29371i
$907$	10.2361	+	7.43694i	0.339883	+	0.246939i	0.744612	−	0.667497i	$-0.232634\pi$
$907$	10.2361	+	7.43694i	0.339883	+	0.246939i	−0.404729	+	0.914436i	$0.632634\pi$
$908$	13.3262	+	9.68208i	0.442247	+	0.321311i
$909$	8.56231	−	26.3521i	0.283994	−	0.874043i
$910$	1.30902	+	4.02874i	0.0433935	+	0.133551i
$911$	16.9443	−	12.3107i	0.561389	−	0.407873i	−0.270578	−	0.962698i	$-0.587215\pi$
$911$	16.9443	−	12.3107i	0.561389	−	0.407873i	0.831967	+	0.554825i	$0.187215\pi$
$912$	−13.2361			−0.438290
$913$	12.7082	+	50.5245i	0.420580	+	1.67212i
$914$	32.5410			1.07636
$915$	23.4164	−	17.0130i	0.774123	−	0.562433i
$916$	−8.70820	−	26.8011i	−0.287727	−	0.885533i
$917$	9.23607	−	28.4257i	0.305002	−	0.938699i
$918$	61.3050	+	44.5407i	2.02336	+	1.47006i
$919$	9.70820	+	7.05342i	0.320244	+	0.232671i	0.736280	−	0.676677i	$-0.236581\pi$
$919$	9.70820	+	7.05342i	0.320244	+	0.232671i	−0.416036	+	0.909348i	$0.636581\pi$
$920$	−0.0450850	+	0.138757i	−0.00148641	+	0.00457469i
$921$	−26.9443	−	82.9259i	−0.887844	−	2.73250i
$922$	−23.0902	+	16.7760i	−0.760434	+	0.552488i
$923$	−21.4164			−0.704930
$924$	−23.7984	+	14.9394i	−0.782909	+	0.491470i
$925$	−0.854102			−0.0280827
$926$	−12.5451	+	9.11454i	−0.412257	+	0.299522i
$927$	−26.1525	−	80.4890i	−0.858960	−	2.64361i
$928$	−0.381966	+	1.17557i	−0.0125386	+	0.0385900i
$929$	−43.0967	−	31.3116i	−1.41396	−	1.02730i	−0.992732	−	0.120345i	$-0.961600\pi$
$929$	−43.0967	−	31.3116i	−1.41396	−	1.02730i	−0.421226	−	0.906956i	$-0.638400\pi$
$930$	−18.9443	−	13.7638i	−0.621207	−	0.451333i
$931$	0.184405	−	0.567541i	0.00604364	−	0.0186004i
$932$	4.70820	+	14.4904i	0.154222	+	0.474648i
$933$	6.47214	−	4.70228i	0.211888	−	0.153946i
$934$	17.2361			0.563981
$935$	6.47214	−	16.1150i	0.211661	−	0.527016i
$936$	−12.0902			−0.395180
$937$	38.9787	−	28.3197i	1.27338	−	0.925164i	0.274047	−	0.961716i	$-0.411638\pi$
$937$	38.9787	−	28.3197i	1.27338	−	0.925164i	0.999332	+	0.0365522i	$0.0116375\pi$
$938$	0.618034	+	1.90211i	0.0201795	+	0.0621062i
$939$	27.4164	−	84.3790i	0.894701	−	2.75361i
$940$	9.16312	+	6.65740i	0.298868	+	0.217140i
$941$	−45.3607	−	32.9565i	−1.47872	−	1.07435i	−0.977968	−	0.208757i	$-0.933058\pi$
$941$	−45.3607	−	32.9565i	−1.47872	−	1.07435i	−0.500748	−	0.865593i	$-0.666942\pi$
$942$	8.61803	−	26.5236i	0.280791	−	0.864185i
$943$	−0.0835921	−	0.257270i	−0.00272213	−	0.00837787i
$944$	−1.92705	+	1.40008i	−0.0627202	+	0.0455689i
$945$	−37.8885			−1.23251
$946$	−30.5623	−	2.07363i	−0.993666	−	0.0674194i
$947$	49.9574			1.62340			0.811699	−	0.584076i	$-0.198543\pi$
$947$	49.9574			1.62340			0.811699	+	0.584076i	$0.198543\pi$
$948$	4.00000	−	2.90617i	0.129914	−	0.0943880i
$949$	0.854102	+	2.62866i	0.0277253	+	0.0853298i
$950$	−1.26393	+	3.88998i	−0.0410074	+	0.126208i
$951$	−16.2361	−	11.7962i	−0.526491	−	0.382518i
$952$	11.0902	+	8.05748i	0.359434	+	0.261144i
$953$	4.85410	−	14.9394i	0.157240	−	0.483934i	−0.841141	−	0.540816i	$-0.818116\pi$
$953$	4.85410	−	14.9394i	0.157240	−	0.483934i	0.998381	+	0.0568813i	$0.0181157\pi$
$954$	2.10081	+	6.46564i	0.0680163	+	0.209333i
$955$	20.5623	−	14.9394i	0.665381	−	0.483427i
$956$	9.52786			0.308153
$957$	10.1803	+	8.50651i	0.329084	+	0.274976i
$958$	−29.5967			−0.956228
$959$	11.0902	−	8.05748i	0.358120	−	0.260190i
$960$	−1.00000	−	3.07768i	−0.0322749	−	0.0993318i
$961$	6.60081	−	20.3152i	0.212929	−	0.655329i
$962$	−1.11803	−	0.812299i	−0.0360469	−	0.0261896i
$963$	45.5066	+	33.0625i	1.46643	+	1.06542i
$964$	−0.572949	+	1.76336i	−0.0184534	+	0.0567939i
$965$	1.67376	+	5.15131i	0.0538803	+	0.165827i
$966$	−1.00000	+	0.726543i	−0.0321745	+	0.0233761i
$967$	3.90983			0.125732			0.0628658	−	0.998022i	$-0.479976\pi$
$967$	3.90983			0.125732			0.0628658	+	0.998022i	$0.479976\pi$
$968$	−9.69098	+	5.20431i	−0.311480	+	0.167273i
$969$	69.3050			2.22640
$970$	−9.70820	+	7.05342i	−0.311712	+	0.226472i
$971$	12.1565	+	37.4140i	0.390122	+	1.20067i	0.932696	+	0.360664i	$0.117450\pi$
$971$	12.1565	+	37.4140i	0.390122	+	1.20067i	−0.542574	+	0.840008i	$0.682550\pi$
$972$	11.0000	−	33.8545i	0.352825	−	1.08588i
$973$	17.2533	+	12.5352i	0.553115	+	0.401862i
$974$	−29.8885	−	21.7153i	−0.957691	−	0.695803i
$975$	−1.61803	+	4.97980i	−0.0518186	+	0.159481i
$976$	2.76393	+	8.50651i	0.0884713	+	0.272287i
$977$	3.38197	−	2.45714i	0.108199	−	0.0786109i	−0.532370	−	0.846512i	$-0.678699\pi$
$977$	3.38197	−	2.45714i	0.108199	−	0.0786109i	0.640569	+	0.767901i	$0.278699\pi$
$978$	−23.4164			−0.748774
$979$	30.6287	+	25.5928i	0.978897	+	0.817948i
$980$	0.145898			0.00466054
$981$	−45.5066	+	33.0625i	−1.45291	+	1.05560i
$982$	11.2639	+	34.6668i	0.359447	+	1.10626i
$983$	3.10081	−	9.54332i	0.0989006	−	0.304385i	−0.889350	−	0.457227i	$-0.848843\pi$
$983$	3.10081	−	9.54332i	0.0989006	−	0.304385i	0.988251	+	0.152842i	$0.0488427\pi$
$984$	4.85410	+	3.52671i	0.154743	+	0.112427i
$985$	−3.97214	−	2.88593i	−0.126563	−	0.0919532i
$986$	2.00000	−	6.15537i	0.0636930	−	0.196027i
$987$	29.6525	+	91.2609i	0.943849	+	2.90487i
$988$	−5.35410	+	3.88998i	−0.170337	+	0.123757i
$989$	−1.34752			−0.0428488
$990$	−24.7254	−	1.67760i	−0.785826	−	0.0533176i
$991$	54.7214			1.73828			0.869141	−	0.494565i	$-0.164673\pi$
$991$	54.7214			1.73828			0.869141	+	0.494565i	$0.164673\pi$
$992$	5.85410	−	4.25325i	0.185868	−	0.135041i
$993$	−14.3820	−	44.2631i	−0.456398	−	1.40465i
$994$	10.7082	−	32.9565i	0.339644	−	1.04532i
$995$	1.38197	+	1.00406i	0.0438113	+	0.0318307i
$996$	−41.1246	−	29.8788i	−1.30308	−	0.946745i
$997$	−16.2148	+	49.9040i	−0.513527	+	1.58047i	0.272418	+	0.962179i	$0.412177\pi$
$997$	−16.2148	+	49.9040i	−0.513527	+	1.58047i	−0.785946	+	0.618296i	$0.787823\pi$
$998$	−3.95492	−	12.1720i	−0.125191	−	0.385297i
$999$	10.0000	−	7.26543i	0.316386	−	0.229868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.g.a.91.1	yes	4
3.2	odd	2		990.2.n.f.91.1		4
4.3	odd	2		880.2.bo.a.641.1		4
5.2	odd	4		550.2.ba.a.399.1		8
5.3	odd	4		550.2.ba.a.399.2		8
5.4	even	2		550.2.h.f.201.1		4
11.2	odd	10		1210.2.a.p.1.2		2
11.4	even	5	inner	110.2.g.a.81.1	✓	4
11.9	even	5		1210.2.a.t.1.2		2
33.26	odd	10		990.2.n.f.631.1		4
44.15	odd	10		880.2.bo.a.81.1		4
44.31	odd	10		9680.2.a.bh.1.1		2
44.35	even	10		9680.2.a.bi.1.1		2
55.4	even	10		550.2.h.f.301.1		4
55.9	even	10		6050.2.a.bu.1.1		2
55.24	odd	10		6050.2.a.cm.1.1		2
55.37	odd	20		550.2.ba.a.499.2		8
55.48	odd	20		550.2.ba.a.499.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.a.81.1	✓	4	11.4	even	5	inner
110.2.g.a.91.1	yes	4	1.1	even	1	trivial
550.2.h.f.201.1		4	5.4	even	2
550.2.h.f.301.1		4	55.4	even	10
550.2.ba.a.399.1		8	5.2	odd	4
550.2.ba.a.399.2		8	5.3	odd	4
550.2.ba.a.499.1		8	55.48	odd	20
550.2.ba.a.499.2		8	55.37	odd	20
880.2.bo.a.81.1		4	44.15	odd	10
880.2.bo.a.641.1		4	4.3	odd	2
990.2.n.f.91.1		4	3.2	odd	2
990.2.n.f.631.1		4	33.26	odd	10
1210.2.a.p.1.2		2	11.2	odd	10
1210.2.a.t.1.2		2	11.9	even	5
6050.2.a.bu.1.1		2	55.9	even	10
6050.2.a.cm.1.1		2	55.24	odd	10
9680.2.a.bh.1.1		2	44.31	odd	10
9680.2.a.bi.1.1		2	44.35	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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(1.00000 + 3.07768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-2.61803 - 1.90211i) q^{6} +(0.809017 - 2.48990i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-6.04508 + 4.39201i) q^{9} -1.00000 q^{10} +(-2.54508 - 2.12663i) q^{11} +3.23607 q^{12} +(1.30902 - 0.951057i) q^{13} +(0.809017 + 2.48990i) q^{14} +(-1.00000 + 3.07768i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.23607 + 3.07768i) q^{17} +(2.30902 - 7.10642i) q^{18} +(-1.26393 - 3.88998i) q^{19} +(0.809017 - 0.587785i) q^{20} +8.47214 q^{21} +(3.30902 + 0.224514i) q^{22} +0.145898 q^{23} +(-2.61803 + 1.90211i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.500000 + 1.53884i) q^{26} +(-11.7082 - 8.50651i) q^{27} +(-2.11803 - 1.53884i) q^{28} +(-0.381966 + 1.17557i) q^{29} +(-1.00000 - 3.07768i) q^{30} +(5.85410 - 4.25325i) q^{31} +1.00000 q^{32} +(4.00000 - 9.95959i) q^{33} -5.23607 q^{34} +(2.11803 - 1.53884i) q^{35} +(2.30902 + 7.10642i) q^{36} +(-0.263932 + 0.812299i) q^{37} +(3.30902 + 2.40414i) q^{38} +(4.23607 + 3.07768i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-0.572949 - 1.76336i) q^{41} +(-6.85410 + 4.97980i) q^{42} -9.23607 q^{43} +(-2.80902 + 1.76336i) q^{44} -7.47214 q^{45} +(-0.118034 + 0.0857567i) q^{46} +(3.50000 + 10.7719i) q^{47} +(1.00000 - 3.07768i) q^{48} +(0.118034 + 0.0857567i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-5.23607 + 16.1150i) q^{51} +(-0.500000 - 1.53884i) q^{52} +(-0.736068 + 0.534785i) q^{53} +14.4721 q^{54} +(-0.809017 - 3.21644i) q^{55} +2.61803 q^{56} +(10.7082 - 7.77997i) q^{57} +(-0.381966 - 1.17557i) q^{58} +(0.736068 - 2.26538i) q^{59} +(2.61803 + 1.90211i) q^{60} +(-7.23607 - 5.25731i) q^{61} +(-2.23607 + 6.88191i) q^{62} +(6.04508 + 18.6049i) q^{63} +(-0.809017 + 0.587785i) q^{64} +1.61803 q^{65} +(2.61803 + 10.4086i) q^{66} +0.763932 q^{67} +(4.23607 - 3.07768i) q^{68} +(0.145898 + 0.449028i) q^{69} +(-0.809017 + 2.48990i) q^{70} +(-10.7082 - 7.77997i) q^{71} +(-6.04508 - 4.39201i) q^{72} +(-0.527864 + 1.62460i) q^{73} +(-0.263932 - 0.812299i) q^{74} +(-2.61803 + 1.90211i) q^{75} -4.09017 q^{76} +(-7.35410 + 4.61653i) q^{77} -5.23607 q^{78} +(1.23607 - 0.898056i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(7.54508 - 23.2214i) q^{81} +(1.50000 + 1.08981i) q^{82} +(-12.7082 - 9.23305i) q^{83} +(2.61803 - 8.05748i) q^{84} +(1.61803 + 4.97980i) q^{85} +(7.47214 - 5.42882i) q^{86} -4.00000 q^{87} +(1.23607 - 3.07768i) q^{88} -12.0344 q^{89} +(6.04508 - 4.39201i) q^{90} +(-1.30902 - 4.02874i) q^{91} +(0.0450850 - 0.138757i) q^{92} +(18.9443 + 13.7638i) q^{93} +(-9.16312 - 6.65740i) q^{94} +(1.26393 - 3.88998i) q^{95} +(1.00000 + 3.07768i) q^{96} +(9.70820 - 7.05342i) q^{97} -0.145898 q^{98} +(24.7254 + 1.67760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 4 q^{3} - q^{4} + q^{5} - 6 q^{6} + q^{7} - q^{8} - 13 q^{9} - 4 q^{10} + q^{11} + 4 q^{12} + 3 q^{13} + q^{14} - 4 q^{15} - q^{16} + 8 q^{17} + 7 q^{18} - 14 q^{19} + q^{20} + 16 q^{21}+ \cdots + 43 q^{99}+O(q^{100}) \) 4 * q - q^2 + 4 * q^3 - q^4 + q^5 - 6 * q^6 + q^7 - q^8 - 13 * q^9 - 4 * q^10 + q^11 + 4 * q^12 + 3 * q^13 + q^14 - 4 * q^15 - q^16 + 8 * q^17 + 7 * q^18 - 14 * q^19 + q^20 + 16 * q^21 + 11 * q^22 + 14 * q^23 - 6 * q^24 - q^25 - 2 * q^26 - 20 * q^27 - 4 * q^28 - 6 * q^29 - 4 * q^30 + 10 * q^31 + 4 * q^32 + 16 * q^33 - 12 * q^34 + 4 * q^35 + 7 * q^36 - 10 * q^37 + 11 * q^38 + 8 * q^39 + q^40 - 9 * q^41 - 14 * q^42 - 28 * q^43 - 9 * q^44 - 12 * q^45 + 4 * q^46 + 14 * q^47 + 4 * q^48 - 4 * q^49 - q^50 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 40 * q^54 - q^55 + 6 * q^56 + 16 * q^57 - 6 * q^58 - 6 * q^59 + 6 * q^60 - 20 * q^61 + 13 * q^63 - q^64 + 2 * q^65 + 6 * q^66 + 12 * q^67 + 8 * q^68 + 14 * q^69 - q^70 - 16 * q^71 - 13 * q^72 - 20 * q^73 - 10 * q^74 - 6 * q^75 + 6 * q^76 - 16 * q^77 - 12 * q^78 - 4 * q^79 + q^80 + 19 * q^81 + 6 * q^82 - 24 * q^83 + 6 * q^84 + 2 * q^85 + 12 * q^86 - 16 * q^87 - 4 * q^88 + 10 * q^89 + 13 * q^90 - 3 * q^91 - 11 * q^92 + 40 * q^93 - 21 * q^94 + 14 * q^95 + 4 * q^96 + 12 * q^97 - 14 * q^98 + 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more