LMFDB - Embedded newform 209.2.f.a.115.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [209,2,Mod(20,209)] 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("209.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(209, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			115.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	209.115
Dual form			209.2.f.a.20.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.690983 - 2.12663i) q^{2} +(-2.61803 - 1.90211i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.500000 + 1.53884i) q^{5} +(-2.23607 + 6.88191i) q^{6} +(0.309017 - 0.224514i) q^{7} +(1.80902 + 1.31433i) q^{8} +(2.30902 + 7.10642i) q^{9} +3.61803 q^{10} +(-2.19098 - 2.48990i) q^{11} +9.70820 q^{12} +(-0.763932 - 2.35114i) q^{13} +(-0.690983 - 0.502029i) q^{14} +(4.23607 - 3.07768i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.954915 + 2.93893i) q^{17} +(13.5172 - 9.82084i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-1.50000 - 4.61653i) q^{20} -1.23607 q^{21} +(-3.78115 + 6.37988i) q^{22} -0.618034 q^{23} +(-2.23607 - 6.88191i) q^{24} +(1.92705 + 1.40008i) q^{25} +(-4.47214 + 3.24920i) q^{26} +(4.47214 - 13.7638i) q^{27} +(-0.354102 + 1.08981i) q^{28} +(-6.85410 + 4.97980i) q^{29} +(-9.47214 - 6.88191i) q^{30} +(2.47214 + 7.60845i) q^{31} +6.70820 q^{32} +(1.00000 + 10.6861i) q^{33} +6.90983 q^{34} +(0.190983 + 0.587785i) q^{35} +(-18.1353 - 13.1760i) q^{36} +(1.61803 - 1.17557i) q^{37} +(-0.690983 + 2.12663i) q^{38} +(-2.47214 + 7.60845i) q^{39} +(-2.92705 + 2.12663i) q^{40} +(-9.47214 - 6.88191i) q^{41} +(0.854102 + 2.62866i) q^{42} -3.09017 q^{43} +(9.70820 + 2.17963i) q^{44} -12.0902 q^{45} +(0.427051 + 1.31433i) q^{46} +(-6.97214 - 5.06555i) q^{47} +(2.61803 - 1.90211i) q^{48} +(-2.11803 + 6.51864i) q^{49} +(1.64590 - 5.06555i) q^{50} +(8.09017 - 5.87785i) q^{51} +(6.00000 + 4.35926i) q^{52} +(0.472136 + 1.45309i) q^{53} -32.3607 q^{54} +(4.92705 - 2.12663i) q^{55} +0.854102 q^{56} +(1.00000 + 3.07768i) q^{57} +(15.3262 + 11.1352i) q^{58} +(-10.0902 + 7.33094i) q^{59} +(-4.85410 + 14.9394i) q^{60} +(2.66312 - 8.19624i) q^{61} +(14.4721 - 10.5146i) q^{62} +(2.30902 + 1.67760i) q^{63} +(-4.01722 - 12.3637i) q^{64} +4.00000 q^{65} +(22.0344 - 9.51057i) q^{66} -8.47214 q^{67} +(-2.86475 - 8.81678i) q^{68} +(1.61803 + 1.17557i) q^{69} +(1.11803 - 0.812299i) q^{70} +(3.61803 - 11.1352i) q^{71} +(-5.16312 + 15.8904i) q^{72} +(-2.85410 + 2.07363i) q^{73} +(-3.61803 - 2.62866i) q^{74} +(-2.38197 - 7.33094i) q^{75} +3.00000 q^{76} +(-1.23607 - 0.277515i) q^{77} +17.8885 q^{78} +(0.909830 + 2.80017i) q^{79} +(-1.30902 - 0.951057i) q^{80} +(-19.7533 + 14.3516i) q^{81} +(-8.09017 + 24.8990i) q^{82} +(1.64590 - 5.06555i) q^{83} +(3.00000 - 2.17963i) q^{84} +(-4.04508 - 2.93893i) q^{85} +(2.13525 + 6.57164i) q^{86} +27.4164 q^{87} +(-0.690983 - 7.38394i) q^{88} -3.23607 q^{89} +(8.35410 + 25.7113i) q^{90} +(-0.763932 - 0.555029i) q^{91} +(1.50000 - 1.08981i) q^{92} +(8.00000 - 24.6215i) q^{93} +(-5.95492 + 18.3273i) q^{94} +(1.30902 - 0.951057i) q^{95} +(-17.5623 - 12.7598i) q^{96} +(-3.76393 - 11.5842i) q^{97} +15.3262 q^{98} +(12.6353 - 21.3193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} - 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9} + 10 q^{10} - 11 q^{11} + 12 q^{12} - 12 q^{13} - 5 q^{14} + 8 q^{15} + q^{16} - 15 q^{17} + 25 q^{18} - q^{19} - 6 q^{20} + 4 q^{21}+ \cdots + 17 q^{99}+O(q^{100}) $ 4 * q - 5 * q^2 - 6 * q^3 - 3 * q^4 - 2 * q^5 - q^7 + 5 * q^8 + 7 * q^9 + 10 * q^10 - 11 * q^11 + 12 * q^12 - 12 * q^13 - 5 * q^14 + 8 * q^15 + q^16 - 15 * q^17 + 25 * q^18 - q^19 - 6 * q^20 + 4 * q^21 + 5 * q^22 + 2 * q^23 + q^25 + 12 * q^28 - 14 * q^29 - 20 * q^30 - 8 * q^31 + 4 * q^33 + 50 * q^34 + 3 * q^35 - 39 * q^36 + 2 * q^37 - 5 * q^38 + 8 * q^39 - 5 * q^40 - 20 * q^41 - 10 * q^42 + 10 * q^43 + 12 * q^44 - 26 * q^45 - 5 * q^46 - 10 * q^47 + 6 * q^48 - 4 * q^49 + 20 * q^50 + 10 * q^51 + 24 * q^52 - 16 * q^53 - 40 * q^54 + 13 * q^55 - 10 * q^56 + 4 * q^57 + 30 * q^58 - 18 * q^59 - 6 * q^60 - 5 * q^61 + 40 * q^62 + 7 * q^63 + 13 * q^64 + 16 * q^65 + 30 * q^66 - 16 * q^67 - 45 * q^68 + 2 * q^69 + 10 * q^71 - 5 * q^72 + 2 * q^73 - 10 * q^74 - 14 * q^75 + 12 * q^76 + 4 * q^77 + 26 * q^79 - 3 * q^80 - 41 * q^81 - 10 * q^82 + 20 * q^83 + 12 * q^84 - 5 * q^85 - 25 * q^86 + 56 * q^87 - 5 * q^88 - 4 * q^89 + 20 * q^90 - 12 * q^91 + 6 * q^92 + 32 * q^93 - 35 * q^94 + 3 * q^95 - 30 * q^96 - 24 * q^97 + 30 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.690983	−	2.12663i	−0.488599	−	1.50375i	−0.826700	−	0.562643i	$-0.809785\pi$
$2$	−0.690983	−	2.12663i	−0.488599	−	1.50375i	0.338101	−	0.941110i	$-0.390215\pi$
$3$	−2.61803	−	1.90211i	−1.51152	−	1.09819i	−0.965496	−	0.260418i	$-0.916140\pi$
$3$	−2.61803	−	1.90211i	−1.51152	−	1.09819i	−0.546027	−	0.837768i	$-0.683860\pi$
$4$	−2.42705	+	1.76336i	−1.21353	+	0.881678i
$5$	−0.500000	+	1.53884i	−0.223607	+	0.688191i	0.774823	+	0.632178i	$0.217839\pi$
$5$	−0.500000	+	1.53884i	−0.223607	+	0.688191i	−0.998430	+	0.0560130i	$0.982161\pi$
$6$	−2.23607	+	6.88191i	−0.912871	+	2.80953i
$7$	0.309017	−	0.224514i	0.116797	−	0.0848583i	−0.527853	−	0.849336i	$-0.677003\pi$
$7$	0.309017	−	0.224514i	0.116797	−	0.0848583i	0.644651	+	0.764477i	$0.277003\pi$
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$	2.30902	+	7.10642i	0.769672	+	2.36881i
$10$	3.61803			1.14412
$11$	−2.19098	−	2.48990i	−0.660606	−	0.750733i
$11$	−2.19098	−	2.48990i	−0.660606	−	0.750733i
$12$	9.70820			2.80252
$13$	−0.763932	−	2.35114i	−0.211877	−	0.652089i	−0.999361	−	0.0357541i	$-0.988617\pi$
$13$	−0.763932	−	2.35114i	−0.211877	−	0.652089i	0.787484	−	0.616335i	$-0.211383\pi$
$14$	−0.690983	−	0.502029i	−0.184673	−	0.134173i
$15$	4.23607	−	3.07768i	1.09375	−	0.794654i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.954915	+	2.93893i	−0.231601	+	0.712794i	0.765953	+	0.642896i	$0.222267\pi$
$17$	−0.954915	+	2.93893i	−0.231601	+	0.712794i	−0.997554	+	0.0698980i	$0.977733\pi$
$18$	13.5172	−	9.82084i	3.18604	−	2.31479i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i
$20$	−1.50000	−	4.61653i	−0.335410	−	1.03229i
$21$	−1.23607			−0.269732
$22$	−3.78115	+	6.37988i	−0.806145	+	1.36020i
$23$	−0.618034			−0.128869			−0.0644345	−	0.997922i	$-0.520524\pi$
$23$	−0.618034			−0.128869			−0.0644345	+	0.997922i	$0.520524\pi$
$24$	−2.23607	−	6.88191i	−0.456435	−	1.40476i
$25$	1.92705	+	1.40008i	0.385410	+	0.280017i
$26$	−4.47214	+	3.24920i	−0.877058	+	0.637220i
$27$	4.47214	−	13.7638i	0.860663	−	2.64885i
$28$	−0.354102	+	1.08981i	−0.0669190	+	0.205955i
$29$	−6.85410	+	4.97980i	−1.27277	+	0.924725i	−0.999309	−	0.0371569i	$-0.988170\pi$
$29$	−6.85410	+	4.97980i	−1.27277	+	0.924725i	−0.273465	+	0.961882i	$0.588170\pi$
$30$	−9.47214	−	6.88191i	−1.72937	−	1.25646i
$31$	2.47214	+	7.60845i	0.444009	+	1.36652i	0.883567	+	0.468304i	$0.155135\pi$
$31$	2.47214	+	7.60845i	0.444009	+	1.36652i	−0.439558	+	0.898214i	$0.644865\pi$
$32$	6.70820			1.18585
$33$	1.00000	+	10.6861i	0.174078	+	1.86022i
$34$	6.90983			1.18503
$35$	0.190983	+	0.587785i	0.0322820	+	0.0993538i
$36$	−18.1353	−	13.1760i	−3.02254	−	2.19601i
$37$	1.61803	−	1.17557i	0.266003	−	0.193263i	−0.446786	−	0.894641i	$-0.647432\pi$
$37$	1.61803	−	1.17557i	0.266003	−	0.193263i	0.712789	+	0.701378i	$0.247432\pi$
$38$	−0.690983	+	2.12663i	−0.112092	+	0.344984i
$39$	−2.47214	+	7.60845i	−0.395859	+	1.21833i
$40$	−2.92705	+	2.12663i	−0.462807	+	0.336249i
$41$	−9.47214	−	6.88191i	−1.47930	−	1.07477i	−0.977782	−	0.209626i	$-0.932775\pi$
$41$	−9.47214	−	6.88191i	−1.47930	−	1.07477i	−0.501518	−	0.865147i	$-0.667225\pi$
$42$	0.854102	+	2.62866i	0.131791	+	0.405610i
$43$	−3.09017			−0.471246			−0.235623	−	0.971844i	$-0.575713\pi$
$43$	−3.09017			−0.471246			−0.235623	+	0.971844i	$0.575713\pi$
$44$	9.70820	+	2.17963i	1.46357	+	0.328591i
$45$	−12.0902			−1.80230
$46$	0.427051	+	1.31433i	0.0629652	+	0.193787i
$47$	−6.97214	−	5.06555i	−1.01699	−	0.738887i	−0.0513268	−	0.998682i	$-0.516345\pi$
$47$	−6.97214	−	5.06555i	−1.01699	−	0.738887i	−0.965664	+	0.259795i	$0.916345\pi$
$48$	2.61803	−	1.90211i	0.377881	−	0.274546i
$49$	−2.11803	+	6.51864i	−0.302576	+	0.931234i
$50$	1.64590	−	5.06555i	0.232765	−	0.716377i
$51$	8.09017	−	5.87785i	1.13285	−	0.823064i
$52$	6.00000	+	4.35926i	0.832050	+	0.604520i
$53$	0.472136	+	1.45309i	0.0648529	+	0.199597i	0.978232	−	0.207513i	$-0.0665368\pi$
$53$	0.472136	+	1.45309i	0.0648529	+	0.199597i	−0.913379	+	0.407109i	$0.866537\pi$
$54$	−32.3607			−4.40373
$55$	4.92705	−	2.12663i	0.664363	−	0.286754i
$56$	0.854102			0.114134
$57$	1.00000	+	3.07768i	0.132453	+	0.407649i
$58$	15.3262	+	11.1352i	2.01243	+	1.46212i
$59$	−10.0902	+	7.33094i	−1.31363	+	0.954407i	−0.313640	+	0.949542i	$0.601549\pi$
$59$	−10.0902	+	7.33094i	−1.31363	+	0.954407i	−0.999988	+	0.00486483i	$0.998451\pi$
$60$	−4.85410	+	14.9394i	−0.626662	+	1.92867i
$61$	2.66312	−	8.19624i	0.340977	−	1.04942i	−0.622725	−	0.782441i	$-0.713974\pi$
$61$	2.66312	−	8.19624i	0.340977	−	1.04942i	0.963702	−	0.266980i	$-0.0860257\pi$
$62$	14.4721	−	10.5146i	1.83796	−	1.33536i
$63$	2.30902	+	1.67760i	0.290909	+	0.211358i
$64$	−4.01722	−	12.3637i	−0.502153	−	1.54547i
$65$	4.00000			0.496139
$66$	22.0344	−	9.51057i	2.71225	−	1.17067i
$67$	−8.47214			−1.03504			−0.517518	−	0.855672i	$-0.673144\pi$
$67$	−8.47214			−1.03504			−0.517518	+	0.855672i	$0.673144\pi$
$68$	−2.86475	−	8.81678i	−0.347401	−	1.06919i
$69$	1.61803	+	1.17557i	0.194788	+	0.141522i
$70$	1.11803	−	0.812299i	0.133631	−	0.0970883i
$71$	3.61803	−	11.1352i	0.429382	−	1.32150i	−0.469354	−	0.883010i	$-0.655513\pi$
$71$	3.61803	−	11.1352i	0.429382	−	1.32150i	0.898736	−	0.438491i	$-0.144487\pi$
$72$	−5.16312	+	15.8904i	−0.608479	+	1.87271i
$73$	−2.85410	+	2.07363i	−0.334047	+	0.242700i	−0.742146	−	0.670238i	$-0.766192\pi$
$73$	−2.85410	+	2.07363i	−0.334047	+	0.242700i	0.408099	+	0.912938i	$0.366192\pi$
$74$	−3.61803	−	2.62866i	−0.420588	−	0.305575i
$75$	−2.38197	−	7.33094i	−0.275046	−	0.846504i
$76$	3.00000			0.344124
$77$	−1.23607	−	0.277515i	−0.140863	−	0.0316257i
$78$	17.8885			2.02548
$79$	0.909830	+	2.80017i	0.102364	+	0.315044i	0.989103	−	0.147227i	$-0.0470348\pi$
$79$	0.909830	+	2.80017i	0.102364	+	0.315044i	−0.886739	+	0.462271i	$0.847035\pi$
$80$	−1.30902	−	0.951057i	−0.146353	−	0.106331i
$81$	−19.7533	+	14.3516i	−2.19481	+	1.59462i
$82$	−8.09017	+	24.8990i	−0.893410	+	2.74963i
$83$	1.64590	−	5.06555i	0.180661	−	0.556017i	−0.819186	−	0.573528i	$-0.805574\pi$
$83$	1.64590	−	5.06555i	0.180661	−	0.556017i	0.999847	+	0.0175114i	$0.00557434\pi$
$84$	3.00000	−	2.17963i	0.327327	−	0.237817i
$85$	−4.04508	−	2.93893i	−0.438751	−	0.318771i
$86$	2.13525	+	6.57164i	0.230250	+	0.708638i
$87$	27.4164			2.93935
$88$	−0.690983	−	7.38394i	−0.0736590	−	0.787130i
$89$	−3.23607			−0.343023			−0.171511	−	0.985182i	$-0.554865\pi$
$89$	−3.23607			−0.343023			−0.171511	+	0.985182i	$0.554865\pi$
$90$	8.35410	+	25.7113i	0.880600	+	2.71021i
$91$	−0.763932	−	0.555029i	−0.0800818	−	0.0581829i
$92$	1.50000	−	1.08981i	0.156386	−	0.113621i
$93$	8.00000	−	24.6215i	0.829561	−	2.55313i
$94$	−5.95492	+	18.3273i	−0.614203	+	1.89032i
$95$	1.30902	−	0.951057i	0.134302	−	0.0975763i
$96$	−17.5623	−	12.7598i	−1.79245	−	1.30229i
$97$	−3.76393	−	11.5842i	−0.382169	−	1.17620i	−0.938513	−	0.345244i	$-0.887796\pi$
$97$	−3.76393	−	11.5842i	−0.382169	−	1.17620i	0.556344	−	0.830952i	$-0.312204\pi$
$98$	15.3262			1.54818
$99$	12.6353	−	21.3193i	1.26989	−	2.14267i
$100$	−7.14590			−0.714590
$101$	−1.97214	−	6.06961i	−0.196235	−	0.603949i	−0.999960	−	0.00894800i	$-0.997152\pi$
$101$	−1.97214	−	6.06961i	−0.196235	−	0.603949i	0.803725	−	0.595001i	$-0.202848\pi$
$102$	−18.0902	−	13.1433i	−1.79119	−	1.30138i
$103$	−12.7082	+	9.23305i	−1.25218	+	0.909760i	−0.998346	−	0.0574892i	$-0.981691\pi$
$103$	−12.7082	+	9.23305i	−1.25218	+	0.909760i	−0.253830	+	0.967249i	$0.581691\pi$
$104$	1.70820	−	5.25731i	0.167503	−	0.515522i
$105$	0.618034	−	1.90211i	0.0603139	−	0.185627i
$106$	2.76393	−	2.00811i	0.268457	−	0.195045i
$107$	4.23607	+	3.07768i	0.409516	+	0.297531i	0.773406	−	0.633911i	$-0.218552\pi$
$107$	4.23607	+	3.07768i	0.409516	+	0.297531i	−0.363890	+	0.931442i	$0.618552\pi$
$108$	13.4164	+	41.2915i	1.29099	+	3.97327i
$109$	10.9443			1.04827			0.524136	−	0.851635i	$-0.324389\pi$
$109$	10.9443			1.04827			0.524136	+	0.851635i	$0.324389\pi$
$110$	−7.92705	−	9.00854i	−0.755815	−	0.858930i
$111$	−6.47214			−0.614308
$112$	0.118034	+	0.363271i	0.0111532	+	0.0343259i
$113$	9.09017	+	6.60440i	0.855131	+	0.621289i	0.926556	−	0.376157i	$-0.122755\pi$
$113$	9.09017	+	6.60440i	0.855131	+	0.621289i	−0.0714248	+	0.997446i	$0.522755\pi$
$114$	5.85410	−	4.25325i	0.548287	−	0.398354i
$115$	0.309017	−	0.951057i	0.0288160	−	0.0886865i
$116$	7.85410	−	24.1724i	0.729235	−	2.24435i
$117$	14.9443	−	10.8576i	1.38160	−	1.00379i
$118$	22.5623	+	16.3925i	2.07703	+	1.50905i
$119$	0.364745	+	1.12257i	0.0334361	+	0.102906i
$120$	11.7082			1.06881
$121$	−1.39919	+	10.9106i	−0.127199	+	0.991877i
$122$	−19.2705			−1.74467
$123$	11.7082	+	36.0341i	1.05569	+	3.24909i
$124$	−19.4164	−	14.1068i	−1.74364	−	1.26683i
$125$	−9.66312	+	7.02067i	−0.864296	+	0.627948i
$126$	1.97214	−	6.06961i	0.175692	−	0.540724i
$127$	0.618034	−	1.90211i	0.0548416	−	0.168785i	−0.919884	−	0.392191i	$-0.871717\pi$
$127$	0.618034	−	1.90211i	0.0548416	−	0.168785i	0.974726	+	0.223405i	$0.0717174\pi$
$128$	−12.6631	+	9.20029i	−1.11927	+	0.813199i
$129$	8.09017	+	5.87785i	0.712300	+	0.517516i
$130$	−2.76393	−	8.50651i	−0.242413	−	0.746070i
$131$	11.0344			0.964084			0.482042	−	0.876148i	$-0.339895\pi$
$131$	11.0344			0.964084			0.482042	+	0.876148i	$0.339895\pi$
$132$	−21.2705	−	24.1724i	−1.85136	−	2.10394i
$133$	−0.381966			−0.0331207
$134$	5.85410	+	18.0171i	0.505717	+	1.55644i
$135$	18.9443	+	13.7638i	1.63046	+	1.18460i
$136$	−5.59017	+	4.06150i	−0.479353	+	0.348270i
$137$	−1.50000	+	4.61653i	−0.128154	+	0.394416i	−0.994462	−	0.105092i	$-0.966486\pi$
$137$	−1.50000	+	4.61653i	−0.128154	+	0.394416i	0.866309	+	0.499509i	$0.166486\pi$
$138$	1.38197	−	4.25325i	0.117641	−	0.362061i
$139$	7.20820	−	5.23707i	0.611392	−	0.444202i	−0.238512	−	0.971139i	$-0.576660\pi$
$139$	7.20820	−	5.23707i	0.611392	−	0.444202i	0.849904	+	0.526937i	$0.176660\pi$
$140$	−1.50000	−	1.08981i	−0.126773	−	0.0921061i
$141$	8.61803	+	26.5236i	0.725769	+	2.23369i
$142$	−26.1803			−2.19701
$143$	−4.18034	+	7.05342i	−0.349578	+	0.589837i
$144$	−7.47214			−0.622678
$145$	−4.23607	−	13.0373i	−0.351786	−	1.08269i
$146$	6.38197	+	4.63677i	0.528175	+	0.383742i
$147$	17.9443	−	13.0373i	1.48002	−	1.07530i
$148$	−1.85410	+	5.70634i	−0.152406	+	0.469058i
$149$	−2.90983	+	8.95554i	−0.238383	+	0.733666i	0.758272	+	0.651938i	$0.226044\pi$
$149$	−2.90983	+	8.95554i	−0.238383	+	0.733666i	−0.996655	+	0.0817279i	$0.973956\pi$
$150$	−13.9443	+	10.1311i	−1.13855	+	0.827201i
$151$	−5.85410	−	4.25325i	−0.476400	−	0.346125i	0.323530	−	0.946218i	$-0.395130\pi$
$151$	−5.85410	−	4.25325i	−0.476400	−	0.346125i	−0.799930	+	0.600093i	$0.795130\pi$
$152$	−0.690983	−	2.12663i	−0.0560461	−	0.172492i
$153$	−23.0902			−1.86673
$154$	0.263932	+	2.82041i	0.0212682	+	0.227275i
$155$	−12.9443			−1.03971
$156$	−7.41641	−	22.8254i	−0.593788	−	1.82749i
$157$	−11.7812	−	8.55951i	−0.940238	−	0.683123i	0.00823967	−	0.999966i	$-0.497377\pi$
$157$	−11.7812	−	8.55951i	−0.940238	−	0.683123i	−0.948478	+	0.316843i	$0.897377\pi$
$158$	5.32624	−	3.86974i	0.423733	−	0.307860i
$159$	1.52786	−	4.70228i	0.121168	−	0.372915i
$160$	−3.35410	+	10.3229i	−0.265165	+	0.816094i
$161$	−0.190983	+	0.138757i	−0.0150516	+	0.0109356i
$162$	44.1697	+	32.0912i	3.47030	+	2.52132i
$163$	−2.88197	−	8.86978i	−0.225733	−	0.694735i	−0.998216	−	0.0596998i	$-0.980986\pi$
$163$	−2.88197	−	8.86978i	−0.225733	−	0.694735i	0.772483	−	0.635035i	$-0.219014\pi$
$164$	35.1246			2.74277
$165$	−16.9443	−	3.80423i	−1.31911	−	0.296159i
$166$	−11.9098			−0.924382
$167$	−7.47214	−	22.9969i	−0.578211	−	1.77955i	−0.624974	−	0.780645i	$-0.714891\pi$
$167$	−7.47214	−	22.9969i	−0.578211	−	1.77955i	0.0467632	−	0.998906i	$-0.485109\pi$
$168$	−2.23607	−	1.62460i	−0.172516	−	0.125340i
$169$	5.57295	−	4.04898i	0.428688	−	0.311460i
$170$	−3.45492	+	10.6331i	−0.264980	+	0.815524i
$171$	2.30902	−	7.10642i	0.176575	−	0.543442i
$172$	7.50000	−	5.44907i	0.571870	−	0.415488i
$173$	−7.70820	−	5.60034i	−0.586044	−	0.425786i	0.254854	−	0.966980i	$-0.417973\pi$
$173$	−7.70820	−	5.60034i	−0.586044	−	0.425786i	−0.840898	+	0.541194i	$0.817973\pi$
$174$	−18.9443	−	58.3045i	−1.43616	−	4.42005i
$175$	0.909830			0.0687767
$176$	3.04508	−	1.31433i	0.229532	−	0.0990712i
$177$	40.3607			3.03369
$178$	2.23607	+	6.88191i	0.167600	+	0.515821i
$179$	5.00000	+	3.63271i	0.373718	+	0.271522i	0.758751	−	0.651381i	$-0.225810\pi$
$179$	5.00000	+	3.63271i	0.373718	+	0.271522i	−0.385033	+	0.922903i	$0.625810\pi$
$180$	29.3435	−	21.3193i	2.18713	−	1.58904i
$181$	−2.00000	+	6.15537i	−0.148659	+	0.457525i	−0.997463	−	0.0711820i	$-0.977323\pi$
$181$	−2.00000	+	6.15537i	−0.148659	+	0.457525i	0.848805	+	0.528707i	$0.177323\pi$
$182$	−0.652476	+	2.00811i	−0.0483647	+	0.148851i
$183$	−22.5623	+	16.3925i	−1.66785	+	1.21177i
$184$	−1.11803	−	0.812299i	−0.0824226	−	0.0598835i
$185$	1.00000	+	3.07768i	0.0735215	+	0.226276i
$186$	−57.8885			−4.24459
$187$	9.40983	−	4.06150i	0.688115	−	0.297006i
$188$	25.8541			1.88560
$189$	−1.70820	−	5.25731i	−0.124254	−	0.382413i
$190$	−2.92705	−	2.12663i	−0.212351	−	0.154282i
$191$	1.54508	−	1.12257i	0.111798	−	0.0812263i	−0.530481	−	0.847697i	$-0.677989\pi$
$191$	1.54508	−	1.12257i	0.111798	−	0.0812263i	0.642280	+	0.766470i	$0.277989\pi$
$192$	−13.0000	+	40.0099i	−0.938194	+	2.88746i
$193$	2.70820	−	8.33499i	0.194941	−	0.599966i	−0.805036	−	0.593225i	$-0.797854\pi$
$193$	2.70820	−	8.33499i	0.194941	−	0.599966i	0.999977	−	0.00674076i	$-0.00214567\pi$
$194$	−22.0344	+	16.0090i	−1.58198	+	1.14938i
$195$	−10.4721	−	7.60845i	−0.749925	−	0.544853i
$196$	−6.35410	−	19.5559i	−0.453864	−	1.39685i
$197$	−3.52786			−0.251350			−0.125675	−	0.992071i	$-0.540110\pi$
$197$	−3.52786			−0.251350			−0.125675	+	0.992071i	$0.540110\pi$
$198$	−54.0689	−	12.1392i	−3.84251	−	0.862697i
$199$	−3.43769			−0.243692			−0.121846	−	0.992549i	$-0.538881\pi$
$199$	−3.43769			−0.243692			−0.121846	+	0.992549i	$0.538881\pi$
$200$	1.64590	+	5.06555i	0.116383	+	0.358189i
$201$	22.1803	+	16.1150i	1.56448	+	1.13666i
$202$	−11.5451	+	8.38800i	−0.812309	+	0.590177i
$203$	−1.00000	+	3.07768i	−0.0701862	+	0.216011i
$204$	−9.27051	+	28.5317i	−0.649066	+	1.99762i
$205$	15.3262	−	11.1352i	1.07043	−	0.777714i
$206$	28.4164	+	20.6457i	1.97986	+	1.43846i
$207$	−1.42705	−	4.39201i	−0.0991869	−	0.305266i
$208$	2.47214			0.171412
$209$	0.309017	+	3.30220i	0.0213752	+	0.228418i
$210$	−4.47214			−0.308607
$211$	−1.47214	−	4.53077i	−0.101346	−	0.311911i	0.887509	−	0.460789i	$-0.152434\pi$
$211$	−1.47214	−	4.53077i	−0.101346	−	0.311911i	−0.988855	+	0.148878i	$0.952434\pi$
$212$	−3.70820	−	2.69417i	−0.254680	−	0.185036i
$213$	−30.6525	+	22.2703i	−2.10027	+	1.52594i
$214$	3.61803	−	11.1352i	0.247324	−	0.761184i
$215$	1.54508	−	4.75528i	0.105374	−	0.324308i
$216$	26.1803	−	19.0211i	1.78135	−	1.29422i
$217$	2.47214	+	1.79611i	0.167820	+	0.121928i
$218$	−7.56231	−	23.2744i	−0.512184	−	1.57634i
$219$	11.4164			0.771449
$220$	−8.20820	+	13.8496i	−0.553397	+	0.933738i
$221$	7.63932			0.513876
$222$	4.47214	+	13.7638i	0.300150	+	0.923767i
$223$	−7.23607	−	5.25731i	−0.484563	−	0.352056i	0.318527	−	0.947914i	$-0.396812\pi$
$223$	−7.23607	−	5.25731i	−0.484563	−	0.352056i	−0.803090	+	0.595858i	$0.796812\pi$
$224$	2.07295	−	1.50609i	0.138505	−	0.100630i
$225$	−5.50000	+	16.9273i	−0.366667	+	1.12848i
$226$	7.76393	−	23.8949i	0.516449	−	1.58947i
$227$	−18.7082	+	13.5923i	−1.24171	+	0.902153i	−0.997711	−	0.0676232i	$-0.978458\pi$
$227$	−18.7082	+	13.5923i	−1.24171	+	0.902153i	−0.243996	+	0.969776i	$0.578458\pi$
$228$	−7.85410	−	5.70634i	−0.520151	−	0.377912i
$229$	−3.42705	−	10.5474i	−0.226466	−	0.696990i	−0.998139	−	0.0609716i	$-0.980580\pi$
$229$	−3.42705	−	10.5474i	−0.226466	−	0.696990i	0.771674	−	0.636019i	$-0.219420\pi$
$230$	−2.23607			−0.147442
$231$	2.70820	+	3.07768i	0.178187	+	0.202497i
$232$	−18.9443			−1.24375
$233$	−1.73607	−	5.34307i	−0.113734	−	0.350036i	0.877947	−	0.478757i	$-0.158913\pi$
$233$	−1.73607	−	5.34307i	−0.113734	−	0.350036i	−0.991681	+	0.128721i	$0.958913\pi$
$234$	−33.4164	−	24.2784i	−2.18450	−	1.58713i
$235$	11.2812	−	8.19624i	0.735901	−	0.534664i
$236$	11.5623	−	35.5851i	0.752642	−	2.31639i
$237$	2.94427	−	9.06154i	0.191251	−	0.588610i
$238$	2.13525	−	1.55135i	0.138408	−	0.100559i
$239$	15.6803	+	11.3924i	1.01428	+	0.736915i	0.965102	−	0.261875i	$-0.0843408\pi$
$239$	15.6803	+	11.3924i	1.01428	+	0.736915i	0.0491750	+	0.998790i	$0.484341\pi$
$240$	1.61803	+	4.97980i	0.104444	+	0.321444i
$241$	24.4721			1.57639			0.788194	−	0.615426i	$-0.211016\pi$
$241$	24.4721			1.57639			0.788194	+	0.615426i	$0.211016\pi$
$242$	24.1697	−	4.56352i	1.55369	−	0.293354i
$243$	35.5967			2.28353
$244$	7.98936	+	24.5887i	0.511466	+	1.57413i
$245$	−8.97214	−	6.51864i	−0.573209	−	0.416461i
$246$	68.5410	−	49.7980i	4.37002	−	3.17500i
$247$	−0.763932	+	2.35114i	−0.0486078	+	0.149600i
$248$	−5.52786	+	17.0130i	−0.351020	+	1.08033i
$249$	−13.9443	+	10.1311i	−0.883682	+	0.642033i
$250$	21.6074	+	15.6987i	1.36657	+	0.992872i
$251$	5.89919	+	18.1558i	0.372353	+	1.14599i	0.945247	+	0.326356i	$0.105821\pi$
$251$	5.89919	+	18.1558i	0.372353	+	1.14599i	−0.572894	+	0.819630i	$0.694179\pi$
$252$	−8.56231			−0.539375
$253$	1.35410	+	1.53884i	0.0851317	+	0.0967462i
$254$	−4.47214			−0.280607
$255$	5.00000	+	15.3884i	0.313112	+	0.963660i
$256$	7.28115	+	5.29007i	0.455072	+	0.330629i
$257$	4.00000	−	2.90617i	0.249513	−	0.181282i	−0.455998	−	0.889981i	$-0.650718\pi$
$257$	4.00000	−	2.90617i	0.249513	−	0.181282i	0.705511	+	0.708699i	$0.250718\pi$
$258$	6.90983	−	21.2663i	0.430187	−	1.32398i
$259$	0.236068	−	0.726543i	0.0146686	−	0.0451452i
$260$	−9.70820	+	7.05342i	−0.602077	+	0.437435i
$261$	−51.2148	−	37.2097i	−3.17012	−	2.30322i
$262$	−7.62461	−	23.4661i	−0.471050	−	1.44974i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−12.2361	+	20.6457i	−0.753078	+	1.27066i
$265$	−2.47214			−0.151862
$266$	0.263932	+	0.812299i	0.0161827	+	0.0498053i
$267$	8.47214	+	6.15537i	0.518486	+	0.376702i
$268$	20.5623	−	14.9394i	1.25604	−	0.912568i
$269$	0.326238	−	1.00406i	0.0198911	−	0.0612184i	−0.940618	−	0.339466i	$-0.889754\pi$
$269$	0.326238	−	1.00406i	0.0198911	−	0.0612184i	0.960509	+	0.278248i	$0.0897536\pi$
$270$	16.1803	−	49.7980i	0.984704	−	3.03061i
$271$	−12.9721	+	9.42481i	−0.788001	+	0.572516i	−0.907370	−	0.420334i	$-0.861913\pi$
$271$	−12.9721	+	9.42481i	−0.788001	+	0.572516i	0.119368	+	0.992850i	$0.461913\pi$
$272$	−2.50000	−	1.81636i	−0.151585	−	0.110133i
$273$	0.944272	+	2.90617i	0.0571499	+	0.175889i
$274$	10.8541			0.655720
$275$	−0.736068	−	7.86572i	−0.0443866	−	0.474321i
$276$	−6.00000			−0.361158
$277$	1.85410	+	5.70634i	0.111402	+	0.342861i	0.991180	−	0.132525i	$-0.0423085\pi$
$277$	1.85410	+	5.70634i	0.111402	+	0.342861i	−0.879777	+	0.475386i	$0.842309\pi$
$278$	−16.1180	−	11.7104i	−0.966695	−	0.702345i
$279$	−48.3607	+	35.1361i	−2.89528	+	2.10354i
$280$	−0.427051	+	1.31433i	−0.0255212	+	0.0785461i
$281$	1.38197	−	4.25325i	0.0824412	−	0.253728i	−0.901337	−	0.433119i	$-0.857413\pi$
$281$	1.38197	−	4.25325i	0.0824412	−	0.253728i	0.983778	+	0.179391i	$0.0574129\pi$
$282$	50.4508	−	36.6547i	3.00430	−	2.18275i
$283$	15.8713	+	11.5312i	0.943452	+	0.685458i	0.949249	−	0.314525i	$-0.101845\pi$
$283$	15.8713	+	11.5312i	0.943452	+	0.685458i	−0.00579696	+	0.999983i	$0.501845\pi$
$284$	10.8541	+	33.4055i	0.644072	+	1.98225i
$285$	−5.23607			−0.310158
$286$	17.8885	+	4.01623i	1.05777	+	0.237485i
$287$	−4.47214			−0.263982
$288$	15.4894	+	47.6713i	0.912719	+	2.80906i
$289$	6.02786	+	4.37950i	0.354580	+	0.257618i
$290$	−24.7984	+	18.0171i	−1.45621	+	1.05800i
$291$	−12.1803	+	37.4872i	−0.714024	+	2.19754i
$292$	3.27051	−	10.0656i	0.191392	−	0.589044i
$293$	13.3262	−	9.68208i	0.778527	−	0.565633i	−0.126009	−	0.992029i	$-0.540217\pi$
$293$	13.3262	−	9.68208i	0.778527	−	0.565633i	0.904537	+	0.426396i	$0.140217\pi$
$294$	−40.1246	−	29.1522i	−2.34011	−	1.70019i
$295$	−6.23607	−	19.1926i	−0.363078	−	1.11744i
$296$	4.47214			0.259938
$297$	−44.0689	+	19.0211i	−2.55714	+	1.10372i
$298$	21.0557			1.21973
$299$	0.472136	+	1.45309i	0.0273043	+	0.0840341i
$300$	18.7082	+	13.5923i	1.08012	+	0.784752i
$301$	−0.954915	+	0.693786i	−0.0550404	+	0.0399892i
$302$	−5.00000	+	15.3884i	−0.287718	+	0.885504i
$303$	−6.38197	+	19.6417i	−0.366634	+	1.12838i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	11.2812	+	8.19624i	0.645957	+	0.469315i
$306$	15.9549	+	49.1042i	0.912082	+	2.80710i
$307$	−25.8885			−1.47754			−0.738769	−	0.673959i	$-0.764592\pi$
$307$	−25.8885			−1.47754			−0.738769	+	0.673959i	$0.764592\pi$
$308$	3.48936	−	1.50609i	0.198825	−	0.0858172i
$309$	50.8328			2.89178
$310$	8.94427	+	27.5276i	0.508001	+	1.56346i
$311$	1.26393	+	0.918300i	0.0716710	+	0.0520720i	0.623044	−	0.782187i	$-0.285896\pi$
$311$	1.26393	+	0.918300i	0.0716710	+	0.0520720i	−0.551373	+	0.834259i	$0.685896\pi$
$312$	−14.4721	+	10.5146i	−0.819323	+	0.595273i
$313$	−2.28115	+	7.02067i	−0.128938	+	0.396832i	−0.994598	−	0.103801i	$-0.966899\pi$
$313$	−2.28115	+	7.02067i	−0.128938	+	0.396832i	0.865660	+	0.500633i	$0.166899\pi$
$314$	−10.0623	+	30.9686i	−0.567849	+	1.74766i
$315$	−3.73607	+	2.71441i	−0.210504	+	0.152940i
$316$	−7.14590	−	5.19180i	−0.401988	−	0.292062i
$317$	9.14590	+	28.1482i	0.513685	+	1.58096i	0.785662	+	0.618656i	$0.212322\pi$
$317$	9.14590	+	28.1482i	0.513685	+	1.58096i	−0.271977	+	0.962304i	$0.587678\pi$
$318$	−11.0557			−0.619974
$319$	27.4164	+	6.15537i	1.53502	+	0.344634i
$320$	21.0344			1.17586
$321$	−5.23607	−	16.1150i	−0.292249	−	0.899449i
$322$	0.427051	+	0.310271i	0.0237986	+	0.0172907i
$323$	2.50000	−	1.81636i	0.139104	−	0.101065i
$324$	22.6353	−	69.6642i	1.25751	−	3.87023i
$325$	1.81966	−	5.60034i	0.100937	−	0.310651i
$326$	−16.8713	+	12.2577i	−0.934416	+	0.678893i
$327$	−28.6525	−	20.8172i	−1.58449	−	1.15120i
$328$	−8.09017	−	24.8990i	−0.446705	−	1.37482i
$329$	−3.29180			−0.181483
$330$	3.61803	+	38.6628i	0.199166	+	2.12832i
$331$	−10.2918			−0.565688			−0.282844	−	0.959166i	$-0.591278\pi$
$331$	−10.2918			−0.565688			−0.282844	+	0.959166i	$0.591278\pi$
$332$	4.93769	+	15.1967i	0.270991	+	0.834025i
$333$	12.0902	+	8.78402i	0.662537	+	0.481361i
$334$	−43.7426	+	31.7809i	−2.39349	+	1.73897i
$335$	4.23607	−	13.0373i	0.231441	−	0.712303i
$336$	0.381966	−	1.17557i	0.0208380	−	0.0641326i
$337$	6.00000	−	4.35926i	0.326841	−	0.237464i	−0.412248	−	0.911072i	$-0.635256\pi$
$337$	6.00000	−	4.35926i	0.326841	−	0.237464i	0.739089	+	0.673608i	$0.235256\pi$
$338$	−12.4615	−	9.05380i	−0.677816	−	0.492462i
$339$	−11.2361	−	34.5811i	−0.610259	−	1.87819i
$340$	15.0000			0.813489
$341$	13.5279	−	22.8254i	0.732575	−	1.23606i
$342$	−16.7082			−0.903476
$343$	1.63525	+	5.03280i	0.0882955	+	0.271746i
$344$	−5.59017	−	4.06150i	−0.301402	−	0.218981i
$345$	−2.61803	+	1.90211i	−0.140950	+	0.102406i
$346$	−6.58359	+	20.2622i	−0.353936	+	1.08930i
$347$	−0.663119	+	2.04087i	−0.0355981	+	0.109560i	−0.967277	−	0.253724i	$-0.918344\pi$
$347$	−0.663119	+	2.04087i	−0.0355981	+	0.109560i	0.931679	+	0.363284i	$0.118344\pi$
$348$	−66.5410	+	48.3449i	−3.56697	+	2.59156i
$349$	7.16312	+	5.20431i	0.383433	+	0.278580i	0.762759	−	0.646683i	$-0.223844\pi$
$349$	7.16312	+	5.20431i	0.383433	+	0.278580i	−0.379326	+	0.925263i	$0.623844\pi$
$350$	−0.628677	−	1.93487i	−0.0336042	−	0.103423i
$351$	−35.7771			−1.90964
$352$	−14.6976	−	16.7027i	−0.783383	−	0.890259i
$353$	12.0902			0.643495			0.321747	−	0.946826i	$-0.395730\pi$
$353$	12.0902			0.643495			0.321747	+	0.946826i	$0.395730\pi$
$354$	−27.8885	−	85.8321i	−1.48226	−	4.56193i
$355$	15.3262	+	11.1352i	0.813432	+	0.590993i
$356$	7.85410	−	5.70634i	0.416267	−	0.302435i
$357$	1.18034	−	3.63271i	0.0624702	−	0.192264i
$358$	4.27051	−	13.1433i	0.225703	−	0.694644i
$359$	−21.6803	+	15.7517i	−1.14424	+	0.831342i	−0.987705	−	0.156329i	$-0.950034\pi$
$359$	−21.6803	+	15.7517i	−1.14424	+	0.831342i	−0.156540	+	0.987672i	$0.550034\pi$
$360$	−21.8713	−	15.8904i	−1.15272	−	0.837500i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	14.4721			0.760639
$363$	24.4164	−	25.9030i	1.28153	−	1.35956i
$364$	2.83282			0.148480
$365$	−1.76393	−	5.42882i	−0.0923284	−	0.284158i
$366$	50.4508	+	36.6547i	2.63711	+	1.91597i
$367$	−2.16312	+	1.57160i	−0.112914	+	0.0820367i	−0.642809	−	0.766026i	$-0.722231\pi$
$367$	−2.16312	+	1.57160i	−0.112914	+	0.0820367i	0.529895	+	0.848063i	$0.322231\pi$
$368$	0.190983	−	0.587785i	0.00995568	−	0.0306404i
$369$	27.0344	−	83.2035i	1.40736	−	4.33140i
$370$	5.85410	−	4.25325i	0.304340	−	0.221116i
$371$	0.472136	+	0.343027i	0.0245121	+	0.0178091i
$372$	24.0000	+	73.8644i	1.24434	+	3.82969i
$373$	−18.7639			−0.971560			−0.485780	−	0.874081i	$-0.661464\pi$
$373$	−18.7639			−0.971560			−0.485780	+	0.874081i	$0.661464\pi$
$374$	−15.1393	−	17.2048i	−0.782836	−	0.889638i
$375$	38.6525			1.99601
$376$	−5.95492	−	18.3273i	−0.307101	−	0.945161i
$377$	16.9443	+	12.3107i	0.872674	+	0.634035i
$378$	−10.0000	+	7.26543i	−0.514344	+	0.373693i
$379$	6.38197	−	19.6417i	0.327820	−	1.00892i	−0.642332	−	0.766426i	$-0.722033\pi$
$379$	6.38197	−	19.6417i	0.327820	−	1.00892i	0.970152	−	0.242499i	$-0.0779670\pi$
$380$	−1.50000	+	4.61653i	−0.0769484	+	0.236823i
$381$	−5.23607	+	3.80423i	−0.268252	+	0.194896i
$382$	−3.45492	−	2.51014i	−0.176769	−	0.128430i
$383$	10.2361	+	31.5034i	0.523039	+	1.60975i	0.768162	+	0.640256i	$0.221172\pi$
$383$	10.2361	+	31.5034i	0.523039	+	1.60975i	−0.245123	+	0.969492i	$0.578828\pi$
$384$	50.6525			2.58485
$385$	1.04508	−	1.76336i	0.0532625	−	0.0898689i
$386$	−19.5967			−0.997448
$387$	−7.13525	−	21.9601i	−0.362705	−	1.11629i
$388$	29.5623	+	21.4783i	1.50080	+	1.09039i
$389$	18.4443	−	13.4005i	0.935162	−	0.679435i	−0.0120895	−	0.999927i	$-0.503848\pi$
$389$	18.4443	−	13.4005i	0.935162	−	0.679435i	0.947251	+	0.320492i	$0.103848\pi$
$390$	−8.94427	+	27.5276i	−0.452911	+	1.39392i
$391$	0.590170	−	1.81636i	0.0298462	−	0.0918571i
$392$	−12.3992	+	9.00854i	−0.626254	+	0.455000i
$393$	−28.8885	−	20.9888i	−1.45723	−	1.05874i
$394$	2.43769	+	7.50245i	0.122809	+	0.377968i
$395$	−4.76393			−0.239699
$396$	6.92705	+	74.0234i	0.348097	+	3.71982i
$397$	−13.5623			−0.680673			−0.340336	−	0.940304i	$-0.610541\pi$
$397$	−13.5623			−0.680673			−0.340336	+	0.940304i	$0.610541\pi$
$398$	2.37539	+	7.31069i	0.119067	+	0.366452i
$399$	1.00000	+	0.726543i	0.0500626	+	0.0363726i
$400$	−1.92705	+	1.40008i	−0.0963525	+	0.0700042i
$401$	−0.527864	+	1.62460i	−0.0263603	+	0.0811286i	−0.963371	−	0.268171i	$-0.913581\pi$
$401$	−0.527864	+	1.62460i	−0.0263603	+	0.0811286i	0.937011	+	0.349300i	$0.113581\pi$
$402$	18.9443	−	58.3045i	0.944854	−	2.90796i
$403$	16.0000	−	11.6247i	0.797017	−	0.579067i
$404$	15.4894	+	11.2537i	0.770624	+	0.559891i
$405$	−12.2082	−	37.5730i	−0.606631	−	1.86702i
$406$	7.23607			0.359120
$407$	−6.47214	−	1.45309i	−0.320812	−	0.0720268i
$408$	22.3607			1.10702
$409$	−7.14590	−	21.9928i	−0.353342	−	1.08747i	−0.956965	−	0.290205i	$-0.906277\pi$
$409$	−7.14590	−	21.9928i	−0.353342	−	1.08747i	0.603623	−	0.797270i	$-0.293723\pi$
$410$	−34.2705	−	24.8990i	−1.69250	−	1.22967i
$411$	12.7082	−	9.23305i	0.626849	−	0.455433i
$412$	14.5623	−	44.8182i	0.717433	−	2.20803i
$413$	−1.47214	+	4.53077i	−0.0724391	+	0.222945i
$414$	−8.35410	+	6.06961i	−0.410582	+	0.298305i
$415$	6.97214	+	5.06555i	0.342249	+	0.248658i
$416$	−5.12461	−	15.7719i	−0.251255	−	0.773283i
$417$	−28.8328			−1.41195
$418$	6.80902	−	2.93893i	0.333040	−	0.143748i
$419$	−13.8541			−0.676817			−0.338409	−	0.940999i	$-0.609889\pi$
$419$	−13.8541			−0.676817			−0.338409	+	0.940999i	$0.609889\pi$
$420$	1.85410	+	5.70634i	0.0904709	+	0.278441i
$421$	−7.09017	−	5.15131i	−0.345554	−	0.251059i	0.401448	−	0.915882i	$-0.368507\pi$
$421$	−7.09017	−	5.15131i	−0.345554	−	0.251059i	−0.747001	+	0.664822i	$0.768507\pi$
$422$	−8.61803	+	6.26137i	−0.419519	+	0.304799i
$423$	19.8992	−	61.2434i	0.967532	−	2.97776i
$424$	−1.05573	+	3.24920i	−0.0512707	+	0.157795i
$425$	−5.95492	+	4.32650i	−0.288856	+	0.209866i
$426$	68.5410	+	49.7980i	3.32082	+	2.41272i
$427$	−1.01722	−	3.13068i	−0.0492268	−	0.151504i
$428$	−15.7082			−0.759285
$429$	24.3607	−	10.5146i	1.17614	−	0.507651i
$430$	−11.1803			−0.539164
$431$	−10.7984	−	33.2340i	−0.520139	−	1.60082i	−0.773732	−	0.633513i	$-0.781612\pi$
$431$	−10.7984	−	33.2340i	−0.520139	−	1.60082i	0.253592	−	0.967311i	$-0.418388\pi$
$432$	11.7082	+	8.50651i	0.563311	+	0.409270i
$433$	10.6180	−	7.71445i	0.510270	−	0.370733i	−0.302656	−	0.953100i	$-0.597873\pi$
$433$	10.6180	−	7.71445i	0.510270	−	0.370733i	0.812926	+	0.582367i	$0.197873\pi$
$434$	2.11146	−	6.49839i	0.101353	−	0.311933i
$435$	−13.7082	+	42.1895i	−0.657258	+	2.02283i
$436$	−26.5623	+	19.2986i	−1.27210	+	0.924237i
$437$	0.500000	+	0.363271i	0.0239182	+	0.0173776i
$438$	−7.88854	−	24.2784i	−0.376929	−	1.16007i
$439$	−13.2361			−0.631723			−0.315862	−	0.948805i	$-0.602294\pi$
$439$	−13.2361			−0.631723			−0.315862	+	0.948805i	$0.602294\pi$
$440$	11.7082	+	2.62866i	0.558167	+	0.125316i
$441$	−51.2148			−2.43880
$442$	−5.27864	−	16.2460i	−0.251079	−	0.772743i
$443$	−22.4894	−	16.3395i	−1.06850	−	0.776312i	−0.0928593	−	0.995679i	$-0.529601\pi$
$443$	−22.4894	−	16.3395i	−1.06850	−	0.776312i	−0.975642	+	0.219367i	$0.929601\pi$
$444$	15.7082	−	11.4127i	0.745478	−	0.541622i
$445$	1.61803	−	4.97980i	0.0767022	−	0.236065i
$446$	−6.18034	+	19.0211i	−0.292648	+	0.900677i
$447$	24.6525	−	17.9111i	1.16602	−	0.847165i
$448$	−4.01722	−	2.91868i	−0.189796	−	0.137895i
$449$	10.0344	+	30.8828i	0.473555	+	1.45745i	0.847897	+	0.530161i	$0.177868\pi$
$449$	10.0344	+	30.8828i	0.473555	+	1.45745i	−0.374343	+	0.927290i	$0.622132\pi$
$450$	39.7984			1.87611
$451$	3.61803	+	38.6628i	0.170367	+	1.82056i
$452$	−33.7082			−1.58550
$453$	7.23607	+	22.2703i	0.339980	+	1.04635i
$454$	41.8328	+	30.3933i	1.96331	+	1.42643i
$455$	1.23607	−	0.898056i	0.0579478	−	0.0421015i
$456$	−2.23607	+	6.88191i	−0.104713	+	0.322275i
$457$	−10.3885	+	31.9727i	−0.485956	+	1.49562i	0.344637	+	0.938736i	$0.388002\pi$
$457$	−10.3885	+	31.9727i	−0.485956	+	1.49562i	−0.830592	+	0.556881i	$0.811998\pi$
$458$	−20.0623	+	14.5761i	−0.937450	+	0.681097i
$459$	36.1803	+	26.2866i	1.68875	+	1.22695i
$460$	0.927051	+	2.85317i	0.0432240	+	0.133030i
$461$	3.50658			0.163318			0.0816588	−	0.996660i	$-0.473978\pi$
$461$	3.50658			0.163318			0.0816588	+	0.996660i	$0.473978\pi$
$462$	4.67376	−	7.88597i	0.217443	−	0.366888i
$463$	7.61803			0.354040			0.177020	−	0.984207i	$-0.443354\pi$
$463$	7.61803			0.354040			0.177020	+	0.984207i	$0.443354\pi$
$464$	−2.61803	−	8.05748i	−0.121539	−	0.374059i
$465$	33.8885	+	24.6215i	1.57154	+	1.14179i
$466$	−10.1631	+	7.38394i	−0.470797	+	0.342054i
$467$	12.0623	−	37.1240i	0.558177	−	1.71789i	−0.129225	−	0.991615i	$-0.541249\pi$
$467$	12.0623	−	37.1240i	0.558177	−	1.71789i	0.687402	−	0.726277i	$-0.258751\pi$
$468$	−17.1246	+	52.7041i	−0.791585	+	2.43625i
$469$	−2.61803	+	1.90211i	−0.120890	+	0.0878314i
$470$	−25.2254	−	18.3273i	−1.16356	−	0.845377i
$471$	14.5623	+	44.8182i	0.670996	+	2.06511i
$472$	−27.8885			−1.28367
$473$	6.77051	+	7.69421i	0.311308	+	0.353780i
$474$	−21.3050			−0.978569
$475$	−0.736068	−	2.26538i	−0.0337731	−	0.103943i
$476$	−2.86475	−	2.08136i	−0.131305	−	0.0953989i
$477$	−9.23607	+	6.71040i	−0.422891	+	0.307248i
$478$	13.3926	−	41.2182i	0.612564	−	1.88528i
$479$	3.04508	−	9.37181i	0.139133	−	0.428209i	−0.857077	−	0.515189i	$-0.827722\pi$
$479$	3.04508	−	9.37181i	0.139133	−	0.428209i	0.996210	+	0.0869802i	$0.0277217\pi$
$480$	28.4164	−	20.6457i	1.29703	−	0.942344i
$481$	−4.00000	−	2.90617i	−0.182384	−	0.132510i
$482$	−16.9098	−	52.0431i	−0.770222	−	2.37050i
$483$	0.763932			0.0347601
$484$	−15.8435	−	28.9480i	−0.720157	−	1.31582i
$485$	19.7082			0.894903
$486$	−24.5967	−	75.7010i	−1.11573	−	3.43387i
$487$	−31.7984	−	23.1029i	−1.44092	−	1.04689i	−0.987849	−	0.155418i	$-0.950328\pi$
$487$	−31.7984	−	23.1029i	−1.44092	−	1.04689i	−0.453073	−	0.891473i	$-0.649672\pi$
$488$	15.5902	−	11.3269i	0.705734	−	0.512746i
$489$	−9.32624	+	28.7032i	−0.421747	+	1.29800i
$490$	−7.66312	+	23.5847i	−0.346184	+	1.06545i
$491$	7.39919	−	5.37582i	0.333921	−	0.242608i	−0.408172	−	0.912905i	$-0.633834\pi$
$491$	7.39919	−	5.37582i	0.333921	−	0.242608i	0.742092	+	0.670298i	$0.233834\pi$
$492$	−91.9574	−	66.8110i	−4.14576	−	3.01207i
$493$	−8.09017	−	24.8990i	−0.364363	−	1.12139i
$494$	5.52786			0.248710
$495$	26.4894	+	30.1033i	1.19061	+	1.35304i
$496$	−8.00000			−0.359211
$497$	−1.38197	−	4.25325i	−0.0619896	−	0.190785i
$498$	31.1803	+	22.6538i	1.39722	+	1.01514i
$499$	−13.3992	+	9.73508i	−0.599830	+	0.435802i	−0.845819	−	0.533471i	$-0.820887\pi$
$499$	−13.3992	+	9.73508i	−0.599830	+	0.435802i	0.245989	+	0.969273i	$0.420887\pi$
$500$	11.0729	−	34.0790i	0.495197	−	1.52406i
$501$	−24.1803	+	74.4194i	−1.08030	+	3.32482i
$502$	34.5344	−	25.0907i	1.54135	−	1.11985i
$503$	−22.6525	−	16.4580i	−1.01002	−	0.733825i	−0.0458099	−	0.998950i	$-0.514587\pi$
$503$	−22.6525	−	16.4580i	−1.01002	−	0.733825i	−0.964214	+	0.265125i	$0.914587\pi$
$504$	1.97214	+	6.06961i	0.0878459	+	0.270362i
$505$	10.3262			0.459512
$506$	2.33688	−	3.94298i	0.103887	−	0.175287i
$507$	−22.2918			−0.990013
$508$	1.85410	+	5.70634i	0.0822625	+	0.253178i
$509$	−15.7082	−	11.4127i	−0.696254	−	0.505858i	0.182456	−	0.983214i	$-0.441595\pi$
$509$	−15.7082	−	11.4127i	−0.696254	−	0.505858i	−0.878710	+	0.477356i	$0.841595\pi$
$510$	29.2705	−	21.2663i	1.29612	−	0.941686i
$511$	−0.416408	+	1.28157i	−0.0184208	+	0.0566934i
$512$	−3.45492	+	10.6331i	−0.152687	+	0.469923i
$513$	−11.7082	+	8.50651i	−0.516930	+	0.375572i
$514$	−8.94427	−	6.49839i	−0.394515	−	0.286632i
$515$	−7.85410	−	24.1724i	−0.346093	−	1.06516i
$516$	−30.0000			−1.32068
$517$	2.66312	+	28.4585i	0.117124	+	1.25160i
$518$	−1.70820			−0.0750542
$519$	9.52786	+	29.3238i	0.418227	+	1.28717i
$520$	7.23607	+	5.25731i	0.317323	+	0.230548i
$521$	−9.61803	+	6.98791i	−0.421374	+	0.306146i	−0.778190	−	0.628029i	$-0.783862\pi$
$521$	−9.61803	+	6.98791i	−0.421374	+	0.306146i	0.356817	+	0.934174i	$0.383862\pi$
$522$	−43.7426	+	134.626i	−1.91456	+	5.89242i
$523$	4.65248	−	14.3188i	0.203439	−	0.626120i	−0.796335	−	0.604855i	$-0.793231\pi$
$523$	4.65248	−	14.3188i	0.203439	−	0.626120i	0.999774	−	0.0212641i	$-0.00676909\pi$
$524$	−26.7812	+	19.4576i	−1.16994	+	0.850011i
$525$	−2.38197	−	1.73060i	−0.103958	−	0.0755296i
$526$		0			0
$527$	−24.7214			−1.07688
$528$	−10.4721	−	2.35114i	−0.455741	−	0.102320i
$529$	−22.6180			−0.983393
$530$	1.70820	+	5.25731i	0.0741996	+	0.228363i
$531$	−75.3951	−	54.7778i	−3.27187	−	2.37715i
$532$	0.927051	−	0.673542i	0.0401928	−	0.0292017i
$533$	−8.94427	+	27.5276i	−0.387419	+	1.19235i
$534$	7.23607	−	22.2703i	0.313135	−	0.963731i
$535$	−6.85410	+	4.97980i	−0.296329	+	0.215295i
$536$	−15.3262	−	11.1352i	−0.661993	−	0.480966i
$537$	−6.18034	−	19.0211i	−0.266701	−	0.820822i
$538$	−2.36068			−0.101776
$539$	20.8713	−	9.00854i	0.898992	−	0.388025i
$540$	−70.2492			−3.02305
$541$	−0.753289	−	2.31838i	−0.0323864	−	0.0996752i	0.933557	−	0.358430i	$-0.116688\pi$
$541$	−0.753289	−	2.31838i	−0.0323864	−	0.0996752i	−0.965943	+	0.258755i	$0.916688\pi$
$542$	29.0066	+	21.0745i	1.24594	+	0.905228i
$543$	16.9443	−	12.3107i	0.727148	−	0.528304i
$544$	−6.40576	+	19.7149i	−0.274645	+	0.845270i
$545$	−5.47214	+	16.8415i	−0.234401	+	0.721411i
$546$	5.52786	−	4.01623i	0.236571	−	0.171879i
$547$	6.94427	+	5.04531i	0.296916	+	0.215722i	0.726262	−	0.687418i	$-0.241256\pi$
$547$	6.94427	+	5.04531i	0.296916	+	0.215722i	−0.429346	+	0.903140i	$0.641256\pi$
$548$	−4.50000	−	13.8496i	−0.192230	−	0.591625i
$549$	64.3951			2.74832
$550$	−16.2188	+	7.00042i	−0.691574	+	0.298499i
$551$	8.47214			0.360925
$552$	1.38197	+	4.25325i	0.0588204	+	0.181031i
$553$	0.909830	+	0.661030i	0.0386899	+	0.0281099i
$554$	10.8541	−	7.88597i	0.461147	−	0.335043i
$555$	3.23607	−	9.95959i	0.137363	−	0.422761i
$556$	−8.25987	+	25.4213i	−0.350296	+	1.07810i
$557$	28.5795	−	20.7642i	1.21095	−	0.879809i	0.215636	−	0.976474i	$-0.430817\pi$
$557$	28.5795	−	20.7642i	1.21095	−	0.879809i	0.995317	+	0.0966646i	$0.0308174\pi$
$558$	108.138	+	78.5667i	4.57784	+	3.32599i
$559$	2.36068	+	7.26543i	0.0998461	+	0.307295i
$560$	−0.618034			−0.0261167
$561$	−32.3607	−	7.26543i	−1.36627	−	0.306746i
$562$	−10.0000			−0.421825
$563$	2.41641	+	7.43694i	0.101839	+	0.313430i	0.988976	−	0.148078i	$-0.0473087\pi$
$563$	2.41641	+	7.43694i	0.101839	+	0.313430i	−0.887136	+	0.461508i	$0.847309\pi$
$564$	−67.6869	−	49.1774i	−2.85013	−	2.07074i
$565$	−14.7082	+	10.6861i	−0.618779	+	0.449569i
$566$	13.5557	−	41.7202i	0.569790	−	1.75363i
$567$	−2.88197	+	8.86978i	−0.121031	+	0.372496i
$568$	21.1803	−	15.3884i	0.888707	−	0.645684i
$569$	36.9787	+	26.8666i	1.55023	+	1.12631i	0.943488	+	0.331407i	$0.107523\pi$
$569$	36.9787	+	26.8666i	1.55023	+	1.12631i	0.606740	+	0.794900i	$0.292477\pi$
$570$	3.61803	+	11.1352i	0.151543	+	0.466401i
$571$	−21.3262			−0.892475			−0.446238	−	0.894915i	$-0.647236\pi$
$571$	−21.3262			−0.892475			−0.446238	+	0.894915i	$0.647236\pi$
$572$	−2.29180	−	24.4904i	−0.0958248	−	1.02400i
$573$	−6.18034			−0.258187
$574$	3.09017	+	9.51057i	0.128981	+	0.396963i
$575$	−1.19098	−	0.865300i	−0.0496674	−	0.0360855i
$576$	78.5861	−	57.0961i	3.27442	−	2.37901i
$577$	3.20163	−	9.85359i	0.133285	−	0.410210i	−0.862034	−	0.506851i	$-0.830810\pi$
$577$	3.20163	−	9.85359i	0.133285	−	0.410210i	0.995319	+	0.0966401i	$0.0308096\pi$
$578$	5.14841	−	15.8452i	0.214146	−	0.659073i
$579$	−22.9443	+	16.6700i	−0.953531	+	0.692781i
$580$	33.2705	+	24.1724i	1.38148	+	1.00371i
$581$	−0.628677	−	1.93487i	−0.0260819	−	0.0802719i
$582$	88.1378			3.65343
$583$	2.58359	−	4.35926i	0.107001	−	0.180542i
$584$	−7.88854			−0.326430
$585$	9.23607	+	28.4257i	0.381864	+	1.17526i
$586$	−29.7984	−	21.6498i	−1.23096	−	0.894344i
$587$	−6.00000	+	4.35926i	−0.247647	+	0.179926i	−0.704683	−	0.709522i	$-0.748911\pi$
$587$	−6.00000	+	4.35926i	−0.247647	+	0.179926i	0.457037	+	0.889448i	$0.348911\pi$
$588$	−20.5623	+	63.2843i	−0.847975	+	2.60980i
$589$	2.47214	−	7.60845i	0.101863	−	0.313501i
$590$	−36.5066	+	26.5236i	−1.50295	+	1.09196i
$591$	9.23607	+	6.71040i	0.379921	+	0.276029i
$592$	0.618034	+	1.90211i	0.0254010	+	0.0781764i
$593$	−9.27051			−0.380694			−0.190347	−	0.981717i	$-0.560961\pi$
$593$	−9.27051			−0.380694			−0.190347	+	0.981717i	$0.560961\pi$
$594$	70.9017	+	80.5748i	2.90913	+	3.30602i
$595$	−1.90983			−0.0782954
$596$	−8.72949	−	26.8666i	−0.357574	−	1.10050i
$597$	9.00000	+	6.53888i	0.368345	+	0.267619i
$598$	2.76393	−	2.00811i	0.113026	−	0.0821179i
$599$	−11.2361	+	34.5811i	−0.459093	+	1.41294i	0.407168	+	0.913353i	$0.366516\pi$
$599$	−11.2361	+	34.5811i	−0.459093	+	1.41294i	−0.866262	+	0.499591i	$0.833484\pi$
$600$	5.32624	−	16.3925i	0.217443	−	0.669220i
$601$	17.0344	−	12.3762i	0.694849	−	0.504838i	−0.183401	−	0.983038i	$-0.558711\pi$
$601$	17.0344	−	12.3762i	0.694849	−	0.504838i	0.878251	+	0.478201i	$0.158711\pi$
$602$	2.13525	+	1.55135i	0.0870265	+	0.0632284i
$603$	−19.5623	−	60.2066i	−0.796639	−	2.45180i
$604$	21.7082			0.883294
$605$	−16.0902	−	7.60845i	−0.654158	−	0.309328i
$606$	46.1803			1.87595
$607$	8.85410	+	27.2501i	0.359377	+	1.10605i	0.953428	+	0.301621i	$0.0975277\pi$
$607$	8.85410	+	27.2501i	0.359377	+	1.10605i	−0.594051	+	0.804427i	$0.702472\pi$
$608$	−5.42705	−	3.94298i	−0.220096	−	0.159909i
$609$	8.47214	−	6.15537i	0.343308	−	0.249428i
$610$	9.63525	−	29.6543i	0.390120	−	1.20067i
$611$	−6.58359	+	20.2622i	−0.266344	+	0.819721i
$612$	56.0410	−	40.7162i	2.26532	−	1.64585i
$613$	7.26393	+	5.27756i	0.293387	+	0.213158i	0.724736	−	0.689027i	$-0.241962\pi$
$613$	7.26393	+	5.27756i	0.293387	+	0.213158i	−0.431348	+	0.902186i	$0.641962\pi$
$614$	17.8885	+	55.0553i	0.721923	+	2.22185i
$615$	−61.3050			−2.47205
$616$	−1.87132	−	2.12663i	−0.0753977	−	0.0856842i
$617$	−6.58359			−0.265045			−0.132523	−	0.991180i	$-0.542308\pi$
$617$	−6.58359			−0.265045			−0.132523	+	0.991180i	$0.542308\pi$
$618$	−35.1246	−	108.102i	−1.41292	−	4.34852i
$619$	20.6803	+	15.0251i	0.831213	+	0.603912i	0.919902	−	0.392148i	$-0.128268\pi$
$619$	20.6803	+	15.0251i	0.831213	+	0.603912i	−0.0886892	+	0.996059i	$0.528268\pi$
$620$	31.4164	−	22.8254i	1.26171	−	0.916688i
$621$	−2.76393	+	8.50651i	−0.110913	+	0.341354i
$622$	1.07953	−	3.32244i	0.0432851	−	0.133218i
$623$	−1.00000	+	0.726543i	−0.0400642	+	0.0291083i
$624$	−6.47214	−	4.70228i	−0.259093	−	0.188242i
$625$	−2.29180	−	7.05342i	−0.0916718	−	0.282137i
$626$	16.5066			0.659736
$627$	5.47214	−	9.23305i	0.218536	−	0.368733i
$628$	43.6869			1.74330
$629$	1.90983	+	5.87785i	0.0761499	+	0.234365i
$630$	8.35410	+	6.06961i	0.332835	+	0.241819i
$631$	30.1803	−	21.9273i	1.20146	−	0.872912i	0.207033	−	0.978334i	$-0.433619\pi$
$631$	30.1803	−	21.9273i	1.20146	−	0.872912i	0.994428	+	0.105422i	$0.0336193\pi$
$632$	−2.03444	+	6.26137i	−0.0809258	+	0.249064i
$633$	−4.76393	+	14.6619i	−0.189349	+	0.582757i
$634$	53.5410	−	38.8998i	2.12639	−	1.54491i
$635$	2.61803	+	1.90211i	0.103894	+	0.0754831i
$636$	4.58359	+	14.1068i	0.181751	+	0.559373i
$637$	16.9443			0.671356
$638$	−5.85410	−	62.5577i	−0.231766	−	2.47668i
$639$	87.4853			3.46086
$640$	−7.82624	−	24.0867i	−0.309359	−	0.952110i
$641$	30.6525	+	22.2703i	1.21070	+	0.879625i	0.995294	−	0.0968996i	$-0.0308926\pi$
$641$	30.6525	+	22.2703i	1.21070	+	0.879625i	0.215406	+	0.976525i	$0.430893\pi$
$642$	−30.6525	+	22.2703i	−1.20976	+	0.878940i
$643$	4.93363	−	15.1841i	0.194563	−	0.598804i	−0.805418	−	0.592707i	$-0.798059\pi$
$643$	4.93363	−	15.1841i	0.194563	−	0.598804i	0.999981	−	0.00609725i	$-0.00194083\pi$
$644$	0.218847	−	0.673542i	0.00862378	−	0.0265413i
$645$	−13.0902	+	9.51057i	−0.515425	+	0.374478i
$646$	−5.59017	−	4.06150i	−0.219942	−	0.159797i
$647$	4.29180	+	13.2088i	0.168728	+	0.519291i	0.999292	−	0.0376325i	$-0.0119816\pi$
$647$	4.29180	+	13.2088i	0.168728	+	0.519291i	−0.830564	+	0.556924i	$0.811982\pi$
$648$	−54.5967			−2.14476
$649$	40.3607	+	9.06154i	1.58430	+	0.355696i
$650$	−13.1672			−0.516459
$651$	−3.05573	−	9.40456i	−0.119763	−	0.368594i
$652$	22.6353	+	16.4455i	0.886465	+	0.644055i
$653$	4.50000	−	3.26944i	0.176099	−	0.127943i	−0.496244	−	0.868183i	$-0.665288\pi$
$653$	4.50000	−	3.26944i	0.176099	−	0.127943i	0.672343	+	0.740240i	$0.265288\pi$
$654$	−24.4721	+	75.3175i	−0.956936	+	2.94515i
$655$	−5.51722	+	16.9803i	−0.215576	+	0.663474i
$656$	9.47214	−	6.88191i	0.369825	−	0.268693i
$657$	−21.3262	−	15.4944i	−0.832016	−	0.604495i
$658$	2.27458	+	7.00042i	0.0886722	+	0.272905i
$659$	−19.7082			−0.767723			−0.383861	−	0.923391i	$-0.625406\pi$
$659$	−19.7082			−0.767723			−0.383861	+	0.923391i	$0.625406\pi$
$660$	47.8328	−	20.6457i	1.86189	−	0.803634i
$661$	−33.1246			−1.28840			−0.644199	−	0.764858i	$-0.722809\pi$
$661$	−33.1246			−1.28840			−0.644199	+	0.764858i	$0.722809\pi$
$662$	7.11146	+	21.8868i	0.276395	+	0.850655i
$663$	−20.0000	−	14.5309i	−0.776736	−	0.564331i
$664$	9.63525	−	7.00042i	0.373920	−	0.271669i
$665$	0.190983	−	0.587785i	0.00740600	−	0.0227933i
$666$	10.3262	−	31.7809i	0.400134	−	1.23148i
$667$	4.23607	−	3.07768i	0.164021	−	0.119168i
$668$	58.6869	+	42.6385i	2.27067	+	1.64973i
$669$	8.94427	+	27.5276i	0.345806	+	1.06428i
$670$	−30.6525			−1.18421
$671$	−26.2426	+	11.3269i	−1.01309	+	0.437271i
$672$	−8.29180			−0.319863
$673$	−4.41641	−	13.5923i	−0.170240	−	0.523945i	0.829144	−	0.559035i	$-0.188828\pi$
$673$	−4.41641	−	13.5923i	−0.170240	−	0.523945i	−0.999384	+	0.0350900i	$0.988828\pi$
$674$	−13.4164	−	9.74759i	−0.516781	−	0.375463i
$675$	27.8885	−	20.2622i	1.07343	−	0.779893i
$676$	−6.38603	+	19.6542i	−0.245617	+	0.755930i
$677$	−8.47214	+	26.0746i	−0.325611	+	1.00213i	0.645554	+	0.763715i	$0.276627\pi$
$677$	−8.47214	+	26.0746i	−0.325611	+	1.00213i	−0.971164	+	0.238412i	$0.923373\pi$
$678$	−65.7771	+	47.7899i	−2.52615	+	1.83536i
$679$	−3.76393	−	2.73466i	−0.144446	−	0.104946i
$680$	−3.45492	−	10.6331i	−0.132490	−	0.407762i
$681$	74.8328			2.86760
$682$	−57.8885	−	12.9968i	−2.21667	−	0.497673i
$683$	−14.8328			−0.567562			−0.283781	−	0.958889i	$-0.591589\pi$
$683$	−14.8328			−0.567562			−0.283781	+	0.958889i	$0.591589\pi$
$684$	6.92705	+	21.3193i	0.264862	+	0.815163i
$685$	−6.35410	−	4.61653i	−0.242778	−	0.176388i
$686$	9.57295	−	6.95515i	0.365497	−	0.265549i
$687$	−11.0902	+	34.1320i	−0.423116	+	1.30222i
$688$	0.954915	−	2.93893i	0.0364058	−	0.112046i
$689$	3.05573	−	2.22012i	0.116414	−	0.0845797i
$690$	5.85410	+	4.25325i	0.222862	+	0.161919i
$691$	5.88197	+	18.1028i	0.223761	+	0.688664i	0.998415	+	0.0562794i	$0.0179238\pi$
$691$	5.88197	+	18.1028i	0.223761	+	0.688664i	−0.774655	+	0.632385i	$0.782076\pi$
$692$	28.5836			1.08659
$693$	−0.881966	−	9.42481i	−0.0335031	−	0.358019i
$694$	4.79837			0.182144
$695$	4.45492	+	13.7108i	0.168985	+	0.520081i
$696$	49.5967	+	36.0341i	1.87996	+	1.36587i
$697$	29.2705	−	21.2663i	1.10870	−	0.805517i
$698$	6.11803	−	18.8294i	0.231571	−	0.712702i
$699$	−5.61803	+	17.2905i	−0.212494	+	0.653988i
$700$	−2.20820	+	1.60435i	−0.0834623	+	0.0606389i
$701$	−10.9164	−	7.93123i	−0.412307	−	0.299559i	0.362228	−	0.932089i	$-0.382016\pi$
$701$	−10.9164	−	7.93123i	−0.412307	−	0.299559i	−0.774535	+	0.632531i	$0.782016\pi$
$702$	24.7214	+	76.0845i	0.933048	+	2.87163i
$703$	−2.00000			−0.0754314
$704$	−21.9828	+	37.0912i	−0.828507	+	1.39793i
$705$	−45.1246			−1.69949
$706$	−8.35410	−	25.7113i	−0.314411	−	0.967657i
$707$	−1.97214	−	1.43284i	−0.0741698	−	0.0538875i
$708$	−97.9574	+	71.1702i	−3.68147	+	2.67474i
$709$	2.50000	−	7.69421i	0.0938895	−	0.288962i	−0.893073	−	0.449911i	$-0.851456\pi$
$709$	2.50000	−	7.69421i	0.0938895	−	0.288962i	0.986963	+	0.160949i	$0.0514556\pi$
$710$	13.0902	−	40.2874i	0.491265	−	1.51196i
$711$	−17.7984	+	12.9313i	−0.667491	+	0.484961i
$712$	−5.85410	−	4.25325i	−0.219392	−	0.159397i
$713$	−1.52786	−	4.70228i	−0.0572190	−	0.176102i
$714$	−8.54102			−0.319640
$715$	−8.76393	−	9.95959i	−0.327752	−	0.372468i
$716$	−18.5410			−0.692910
$717$	−19.3820	−	59.6516i	−0.723833	−	2.22773i
$718$	48.4787	+	35.2218i	1.80921	+	1.31447i
$719$	16.1631	−	11.7432i	0.602783	−	0.437947i	−0.244083	−	0.969754i	$-0.578487\pi$
$719$	16.1631	−	11.7432i	0.602783	−	0.437947i	0.846865	+	0.531807i	$0.178487\pi$
$720$	3.73607	−	11.4984i	0.139235	−	0.428521i
$721$	−1.85410	+	5.70634i	−0.0690504	+	0.212515i
$722$	1.80902	−	1.31433i	0.0673246	−	0.0489142i
$723$	−64.0689	−	46.5488i	−2.38275	−	1.73117i
$724$	−6.00000	−	18.4661i	−0.222988	−	0.686287i
$725$	−20.1803			−0.749479
$726$	−71.9574	−	34.0260i	−2.67059	−	1.26282i
$727$	−14.1459			−0.524642			−0.262321	−	0.964981i	$-0.584488\pi$
$727$	−14.1459			−0.524642			−0.262321	+	0.964981i	$0.584488\pi$
$728$	−0.652476	−	2.00811i	−0.0241824	−	0.0744257i
$729$	−33.9336	−	24.6542i	−1.25680	−	0.913119i
$730$	−10.3262	+	7.50245i	−0.382191	+	0.277678i
$731$	2.95085	−	9.08178i	0.109141	−	0.335902i
$732$	25.8541	−	79.5707i	0.955595	−	2.94102i
$733$	−39.5238	+	28.7157i	−1.45984	+	1.06064i	−0.476442	+	0.879206i	$0.658074\pi$
$733$	−39.5238	+	28.7157i	−1.45984	+	1.06064i	−0.983403	+	0.181433i	$0.941926\pi$
$734$	4.83688	+	3.51420i	0.178533	+	0.129711i
$735$	11.0902	+	34.1320i	0.409067	+	1.25898i
$736$	−4.14590			−0.152820
$737$	18.5623	+	21.0948i	0.683751	+	0.777035i
$738$	−195.623			−7.20098
$739$	−0.534442	−	1.64484i	−0.0196598	−	0.0605065i	0.940745	−	0.339114i	$-0.110127\pi$
$739$	−0.534442	−	1.64484i	−0.0196598	−	0.0605065i	−0.960405	+	0.278607i	$0.910127\pi$
$740$	−7.85410	−	5.70634i	−0.288723	−	0.209769i
$741$	6.47214	−	4.70228i	0.237760	−	0.172743i
$742$	0.403252	−	1.24108i	0.0148039	−	0.0455616i
$743$	2.43769	−	7.50245i	0.0894303	−	0.275238i	−0.896332	−	0.443384i	$-0.853778\pi$
$743$	2.43769	−	7.50245i	0.0894303	−	0.275238i	0.985762	+	0.168146i	$0.0537779\pi$
$744$	46.8328	−	34.0260i	1.71697	−	1.24745i
$745$	−12.3262	−	8.95554i	−0.451598	−	0.328105i
$746$	12.9656	+	39.9039i	0.474703	+	1.46099i
$747$	39.7984			1.45615
$748$	−15.6763	+	26.4503i	−0.573181	+	0.967120i
$749$	2.00000			0.0730784
$750$	−26.7082	−	82.1994i	−0.975246	−	3.00150i
$751$	−5.47214	−	3.97574i	−0.199681	−	0.145077i	0.483452	−	0.875371i	$-0.339383\pi$
$751$	−5.47214	−	3.97574i	−0.199681	−	0.145077i	−0.683133	+	0.730294i	$0.739383\pi$
$752$	6.97214	−	5.06555i	0.254248	−	0.184722i
$753$	19.0902	−	58.7535i	0.695684	−	2.14110i
$754$	14.4721	−	44.5407i	0.527044	−	1.62207i
$755$	9.47214	−	6.88191i	0.344726	−	0.250458i
$756$	13.4164	+	9.74759i	0.487950	+	0.354516i
$757$	−11.8541	−	36.4832i	−0.430845	−	1.32600i	−0.897285	−	0.441451i	$-0.854464\pi$
$757$	−11.8541	−	36.4832i	−0.430845	−	1.32600i	0.466441	−	0.884552i	$-0.345536\pi$
$758$	−46.1803			−1.67735
$759$	−0.618034	−	6.60440i	−0.0224332	−	0.239724i
$760$	3.61803			0.131240
$761$	−3.49342	−	10.7516i	−0.126636	−	0.389747i	0.867559	−	0.497334i	$-0.165688\pi$
$761$	−3.49342	−	10.7516i	−0.126636	−	0.389747i	−0.994196	+	0.107587i	$0.965688\pi$
$762$	11.7082	+	8.50651i	0.424143	+	0.308158i
$763$	3.38197	−	2.45714i	0.122435	−	0.0889545i
$764$	−1.77051	+	5.44907i	−0.0640548	+	0.197140i
$765$	11.5451	−	35.5321i	0.417413	−	1.28467i
$766$	59.9230	−	43.5366i	2.16511	−	1.57304i
$767$	24.9443	+	18.1231i	0.900685	+	0.654386i
$768$	−9.00000	−	27.6992i	−0.324760	−	0.999507i
$769$	30.7426			1.10861			0.554304	−	0.832314i	$-0.312984\pi$
$769$	30.7426			1.10861			0.554304	+	0.832314i	$0.312984\pi$
$770$	−4.47214	−	1.00406i	−0.161165	−	0.0361837i
$771$	−16.0000			−0.576226
$772$	8.12461	+	25.0050i	0.292411	+	0.899949i
$773$	43.0689	+	31.2914i	1.54908	+	1.12547i	0.944303	+	0.329078i	$0.106738\pi$
$773$	43.0689	+	31.2914i	1.54908	+	1.12547i	0.604777	+	0.796395i	$0.293262\pi$
$774$	−41.7705	+	30.3481i	−1.50141	+	1.09084i
$775$	−5.88854	+	18.1231i	−0.211523	+	0.651000i
$776$	8.41641	−	25.9030i	0.302131	−	0.929865i
$777$	−2.00000	+	1.45309i	−0.0717496	+	0.0521291i
$778$	−41.2426	−	29.9645i	−1.47862	−	1.07428i
$779$	3.61803	+	11.1352i	0.129630	+	0.398959i
$780$	38.8328			1.39044
$781$	−35.6525	+	15.3884i	−1.27575	+	0.550641i
$782$	−4.27051			−0.152713
$783$	37.8885	+	116.609i	1.35403	+	4.16726i
$784$	−5.54508	−	4.02874i	−0.198039	−	0.143884i
$785$	19.0623	−	13.8496i	0.680363	−	0.494313i
$786$	−24.6738	+	75.9380i	−0.880084	+	2.70862i
$787$	7.56231	−	23.2744i	0.269567	−	0.829642i	−0.721039	−	0.692895i	$-0.756335\pi$
$787$	7.56231	−	23.2744i	0.269567	−	0.829642i	0.990606	−	0.136748i	$-0.0436649\pi$
$788$	8.56231	−	6.22088i	0.305020	−	0.221610i
$789$		0			0
$790$	3.29180	+	10.1311i	0.117117	+	0.360449i
$791$	4.29180			0.152599
$792$	50.8779	−	21.9601i	1.80787	−	0.780317i
$793$	−21.3050			−0.756561
$794$	9.37132	+	28.8420i	0.332576	+	1.02356i
$795$	6.47214	+	4.70228i	0.229543	+	0.166773i
$796$	8.34346	−	6.06188i	0.295726	−	0.214858i
$797$	−0.909830	+	2.80017i	−0.0322278	+	0.0991871i	−0.965877	−	0.259003i	$-0.916606\pi$
$797$	−0.909830	+	2.80017i	−0.0322278	+	0.0991871i	0.933649	+	0.358190i	$0.116606\pi$
$798$	0.854102	−	2.62866i	0.0302349	−	0.0930534i
$799$	21.5451	−	15.6534i	0.762210	−	0.553778i
$800$	12.9271	+	9.39205i	0.457040	+	0.332059i
$801$	−7.47214	−	22.9969i	−0.264015	−	0.812554i
$802$	3.81966			0.134877
$803$	11.4164	+	2.56314i	0.402876	+	0.0904514i
$804$	−82.2492			−2.90071
$805$	−0.118034	−	0.363271i	−0.00416015	−	0.0128036i
$806$	−35.7771	−	25.9936i	−1.26019	−	0.915585i
$807$	−2.76393	+	2.00811i	−0.0972950	+	0.0706890i
$808$	4.40983	−	13.5721i	0.155137	−	0.477463i
$809$	13.5000	−	41.5487i	0.474635	−	1.46078i	−0.371815	−	0.928307i	$-0.621264\pi$
$809$	13.5000	−	41.5487i	0.474635	−	1.46078i	0.846450	−	0.532469i	$-0.178736\pi$
$810$	−71.4681	+	51.9246i	−2.51113	+	1.82444i
$811$	−7.56231	−	5.49434i	−0.265548	−	0.192932i	0.447041	−	0.894513i	$-0.352478\pi$
$811$	−7.56231	−	5.49434i	−0.265548	−	0.192932i	−0.712590	+	0.701581i	$0.752478\pi$
$812$	−3.00000	−	9.23305i	−0.105279	−	0.324017i
$813$	51.8885			1.81981
$814$	1.38197	+	14.7679i	0.0484379	+	0.517614i
$815$	15.0902			0.528586
$816$	3.09017	+	9.51057i	0.108178	+	0.332936i
$817$	2.50000	+	1.81636i	0.0874639	+	0.0635463i
$818$	−41.8328	+	30.3933i	−1.46265	+	1.06268i
$819$	2.18034	−	6.71040i	0.0761872	−	0.234480i
$820$	−17.5623	+	54.0512i	−0.613302	+	1.88755i
$821$	19.1525	−	13.9151i	0.668426	−	0.485640i	−0.201072	−	0.979576i	$-0.564442\pi$
$821$	19.1525	−	13.9151i	0.668426	−	0.485640i	0.869498	+	0.493937i	$0.164442\pi$
$822$	−28.4164	−	20.6457i	−0.991136	−	0.720102i
$823$	5.88197	+	18.1028i	0.205032	+	0.631025i	0.999712	+	0.0239959i	$0.00763886\pi$
$823$	5.88197	+	18.1028i	0.205032	+	0.631025i	−0.794680	+	0.607029i	$0.792361\pi$
$824$	−35.1246			−1.22362
$825$	−13.0344	+	21.9928i	−0.453801	+	0.765691i
$826$	10.6525			0.370647
$827$	16.2918	+	50.1410i	0.566521	+	1.74357i	0.663388	+	0.748276i	$0.269118\pi$
$827$	16.2918	+	50.1410i	0.566521	+	1.74357i	−0.0968665	+	0.995297i	$0.530882\pi$
$828$	11.2082	+	8.14324i	0.389512	+	0.282997i
$829$	−37.7426	+	27.4216i	−1.31086	+	0.952393i	−0.310858	+	0.950456i	$0.600616\pi$
$829$	−37.7426	+	27.4216i	−1.31086	+	0.952393i	−0.999998	+	0.00193651i	$0.999384\pi$
$830$	5.95492	−	18.3273i	0.206698	−	0.636151i
$831$	6.00000	−	18.4661i	0.208138	−	0.640582i
$832$	−26.0000	+	18.8901i	−0.901388	+	0.654897i
$833$	−17.1353	−	12.4495i	−0.593701	−	0.431349i
$834$	19.9230	+	61.3166i	0.689877	+	2.12322i
$835$	39.1246			1.35396
$836$	−6.57295	−	7.46969i	−0.227330	−	0.258345i
$837$	115.777			4.00184
$838$	9.57295	+	29.4625i	0.330692	+	1.01777i
$839$	3.00000	+	2.17963i	0.103572	+	0.0752491i	0.638366	−	0.769733i	$-0.279611\pi$
$839$	3.00000	+	2.17963i	0.103572	+	0.0752491i	−0.534794	+	0.844982i	$0.679611\pi$
$840$	3.61803	−	2.62866i	0.124834	−	0.0906972i
$841$	13.2188	−	40.6834i	0.455822	−	1.40288i
$842$	−6.05573	+	18.6376i	−0.208694	+	0.642295i
$843$	−11.7082	+	8.50651i	−0.403252	+	0.292980i
$844$	11.5623	+	8.40051i	0.397991	+	0.289157i
$845$	3.44427	+	10.6004i	0.118487	+	0.364664i
$846$	−143.992			−4.95054
$847$	2.01722	+	3.68571i	0.0693125	+	0.126643i
$848$	−1.52786			−0.0524671
$849$	−19.6180	−	60.3781i	−0.673289	−	2.07217i
$850$	13.3156	+	9.67435i	0.456721	+	0.331827i
$851$	−1.00000	+	0.726543i	−0.0342796	+	0.0249056i
$852$	35.1246	−	108.102i	1.20335	−	3.70353i
$853$	−8.28115	+	25.4868i	−0.283541	+	0.872650i	0.703291	+	0.710902i	$0.251713\pi$
$853$	−8.28115	+	25.4868i	−0.283541	+	0.872650i	−0.986832	+	0.161748i	$0.948287\pi$
$854$	−5.95492	+	4.32650i	−0.203773	+	0.148050i
$855$	9.78115	+	7.10642i	0.334508	+	0.243035i
$856$	3.61803	+	11.1352i	0.123662	+	0.380592i
$857$	12.7639			0.436008			0.218004	−	0.975948i	$-0.430045\pi$
$857$	12.7639			0.436008			0.218004	+	0.975948i	$0.430045\pi$
$858$	−39.1935	−	44.5407i	−1.33804	−	1.52059i
$859$	−23.7426			−0.810089			−0.405044	−	0.914297i	$-0.632744\pi$
$859$	−23.7426			−0.810089			−0.405044	+	0.914297i	$0.632744\pi$
$860$	4.63525	+	14.2658i	0.158061	+	0.486461i
$861$	11.7082	+	8.50651i	0.399015	+	0.289901i
$862$	−63.2148	+	45.9282i	−2.15310	+	1.56432i
$863$	−12.6180	+	38.8343i	−0.429523	+	1.32194i	0.469073	+	0.883159i	$0.344588\pi$
$863$	−12.6180	+	38.8343i	−0.429523	+	1.32194i	−0.898596	+	0.438776i	$0.855412\pi$
$864$	30.0000	−	92.3305i	1.02062	−	3.14115i
$865$	12.4721	−	9.06154i	0.424065	−	0.308102i
$866$	−23.7426	−	17.2500i	−0.806808	−	0.586180i
$867$	−7.45085	−	22.9314i	−0.253044	−	0.778790i
$868$	−9.16718			−0.311155
$869$	4.97871	−	8.40051i	0.168891	−	0.284968i
$870$	99.1935			3.36297
$871$	6.47214	+	19.9192i	0.219300	+	0.674936i
$872$	19.7984	+	14.3844i	0.670458	+	0.487116i
$873$	73.6312	−	53.4962i	2.49204	−	1.81057i
$874$	0.427051	−	1.31433i	0.0144452	−	0.0444578i
$875$	−1.40983	+	4.33901i	−0.0476610	+	0.146685i
$876$	−27.7082	+	20.1312i	−0.936173	+	0.680170i
$877$	4.94427	+	3.59222i	0.166956	+	0.121301i	0.668126	−	0.744048i	$-0.267097\pi$
$877$	4.94427	+	3.59222i	0.166956	+	0.121301i	−0.501170	+	0.865349i	$0.667097\pi$
$878$	9.14590	+	28.1482i	0.308659	+	0.949955i
$879$	−53.3050			−1.79793
$880$	0.500000	+	5.34307i	0.0168550	+	0.180115i
$881$	−21.7771			−0.733689			−0.366844	−	0.930282i	$-0.619562\pi$
$881$	−21.7771			−0.733689			−0.366844	+	0.930282i	$0.619562\pi$
$882$	35.3885	+	108.915i	1.19159	+	3.66735i
$883$	4.45492	+	3.23669i	0.149920	+	0.108923i	0.660217	−	0.751075i	$-0.270464\pi$
$883$	4.45492	+	3.23669i	0.149920	+	0.108923i	−0.510297	+	0.859998i	$0.670464\pi$
$884$	−18.5410	+	13.4708i	−0.623602	+	0.453073i
$885$	−20.1803	+	62.1087i	−0.678355	+	2.08776i
$886$	−19.2082	+	59.1168i	−0.645312	+	1.98607i
$887$	22.0902	−	16.0494i	0.741715	−	0.538888i	−0.151533	−	0.988452i	$-0.548421\pi$
$887$	22.0902	−	16.0494i	0.741715	−	0.538888i	0.893248	+	0.449565i	$0.148421\pi$
$888$	−11.7082	−	8.50651i	−0.392902	−	0.285460i
$889$	−0.236068	−	0.726543i	−0.00791747	−	0.0243675i
$890$	−11.7082			−0.392460
$891$	79.0132	+	17.7396i	2.64704	+	0.594298i
$892$	26.8328			0.898429
$893$	2.66312	+	8.19624i	0.0891179	+	0.274277i
$894$	−55.1246	−	40.0504i	−1.84364	−	1.33948i
$895$	−8.09017	+	5.87785i	−0.270425	+	0.196475i
$896$	−1.84752	+	5.68609i	−0.0617215	+	0.189959i
$897$	1.52786	−	4.70228i	0.0510139	−	0.157005i
$898$	58.7426	−	42.6790i	1.96027	−	1.42422i
$899$	−54.8328	−	39.8384i	−1.82878	−	1.32868i
$900$	−16.5000	−	50.7818i	−0.550000	−	1.69273i
$901$	−4.72136			−0.157291
$902$	79.7214	−	34.4095i	2.65443	−	1.14571i
$903$	3.81966			0.127110
$904$	7.76393	+	23.8949i	0.258225	+	0.794733i
$905$	−8.47214	−	6.15537i	−0.281623	−	0.204611i
$906$	42.3607	−	30.7768i	1.40734	−	1.02249i
$907$	−13.3820	+	41.1855i	−0.444341	+	1.36754i	0.438864	+	0.898553i	$0.355381\pi$
$907$	−13.3820	+	41.1855i	−0.444341	+	1.36754i	−0.883205	+	0.468987i	$0.844619\pi$
$908$	21.4377	−	65.9784i	0.711435	−	2.18957i
$909$	38.5795	−	28.0297i	1.27960	−	0.929685i
$910$	−2.76393	−	2.00811i	−0.0916235	−	0.0665683i
$911$	1.18034	+	3.63271i	0.0391064	+	0.120357i	0.968704	−	0.248219i	$-0.0798453\pi$
$911$	1.18034	+	3.63271i	0.0391064	+	0.120357i	−0.929597	+	0.368576i	$0.879845\pi$
$912$	−3.23607			−0.107157
$913$	−16.2188	+	7.00042i	−0.536765	+	0.231680i
$914$	75.1722			2.48648
$915$	−13.9443	−	42.9161i	−0.460983	−	1.41876i
$916$	26.9164	+	19.5559i	0.889343	+	0.646146i
$917$	3.40983	−	2.47739i	0.112603	−	0.0818105i
$918$	30.9017	−	95.1057i	1.01991	−	3.13895i
$919$	4.47871	−	13.7841i	0.147739	−	0.454694i	−0.849614	−	0.527405i	$-0.823165\pi$
$919$	4.47871	−	13.7841i	0.147739	−	0.454694i	0.997353	+	0.0727108i	$0.0231650\pi$
$920$	1.80902	−	1.31433i	0.0596415	−	0.0433321i
$921$	67.7771	+	49.2429i	2.23333	+	1.62261i
$922$	−2.42299	−	7.45718i	−0.0797968	−	0.245589i
$923$	−28.9443			−0.952712
$924$	−12.0000	−	2.69417i	−0.394771	−	0.0886316i
$925$	4.76393			0.156637
$926$	−5.26393	−	16.2007i	−0.172984	−	0.532389i
$927$	−94.9574	−	68.9906i	−3.11881	−	2.26595i
$928$	−45.9787	+	33.4055i	−1.50933	+	1.09659i
$929$	10.5517	−	32.4747i	0.346189	−	1.06546i	−0.614755	−	0.788718i	$-0.710745\pi$
$929$	10.5517	−	32.4747i	0.346189	−	1.06546i	0.960944	−	0.276742i	$-0.0892547\pi$
$930$	28.9443	−	89.0813i	0.949120	−	2.92109i
$931$	5.54508	−	4.02874i	0.181733	−	0.132037i
$932$	13.6353	+	9.90659i	0.446638	+	0.324501i
$933$	−1.56231	−	4.80828i	−0.0511476	−	0.157416i
$934$	−87.2837			−2.85601
$935$	1.54508	+	16.5110i	0.0505297	+	0.539967i
$936$	41.3050			1.35009
$937$	−9.13525	−	28.1154i	−0.298436	−	0.918491i	−0.982046	−	0.188643i	$-0.939591\pi$
$937$	−9.13525	−	28.1154i	−0.298436	−	0.918491i	0.683610	−	0.729848i	$-0.260409\pi$
$938$	5.85410	+	4.25325i	0.191143	+	0.138874i
$939$	19.3262	−	14.0413i	0.630688	−	0.458222i
$940$	−12.9271	+	39.7854i	−0.421634	+	1.29766i
$941$	−11.5623	+	35.5851i	−0.376920	+	1.16004i	0.565253	+	0.824917i	$0.308778\pi$
$941$	−11.5623	+	35.5851i	−0.376920	+	1.16004i	−0.942174	+	0.335124i	$0.891222\pi$
$942$	85.2492	−	61.9372i	2.77757	−	2.01802i
$943$	5.85410	+	4.25325i	0.190636	+	0.138505i
$944$	−3.85410	−	11.8617i	−0.125440	−	0.386066i
$945$	8.94427			0.290957
$946$	11.6844	−	19.7149i	0.379893	−	0.640987i
$947$	49.6869			1.61461			0.807304	−	0.590136i	$-0.200926\pi$
$947$	49.6869			1.61461			0.807304	+	0.590136i	$0.200926\pi$
$948$	8.83282	+	27.1846i	0.286877	+	0.882915i
$949$	7.05573	+	5.12629i	0.229039	+	0.166406i
$950$	−4.30902	+	3.13068i	−0.139803	+	0.101573i
$951$	29.5967	−	91.0894i	0.959740	−	2.95378i
$952$	−0.815595	+	2.51014i	−0.0264336	+	0.0813542i
$953$	11.5623	−	8.40051i	0.374540	−	0.272119i	−0.384551	−	0.923104i	$-0.625644\pi$
$953$	11.5623	−	8.40051i	0.374540	−	0.272119i	0.759091	+	0.650985i	$0.225644\pi$
$954$	20.6525	+	15.0049i	0.668649	+	0.485802i
$955$	0.954915	+	2.93893i	0.0309003	+	0.0951014i
$956$	−58.1459			−1.88057
$957$	−60.0689	−	68.2641i	−1.94175	−	2.20666i
$958$	−22.0344			−0.711901
$959$	0.572949	+	1.76336i	0.0185015	+	0.0569417i
$960$	−55.0689	−	40.0099i	−1.77734	−	1.29131i
$961$	−26.6976	+	19.3969i	−0.861212	+	0.625707i
$962$	−3.41641	+	10.5146i	−0.110149	+	0.339005i
$963$	−12.0902	+	37.2097i	−0.389600	+	1.19907i
$964$	−59.3951	+	43.1531i	−1.91299	+	1.38987i
$965$	11.4721	+	8.33499i	0.369301	+	0.268313i
$966$	−0.527864	−	1.62460i	−0.0169837	−	0.0522706i
$967$	−37.8541			−1.21731			−0.608653	−	0.793437i	$-0.708290\pi$
$967$	−37.8541			−1.21731			−0.608653	+	0.793437i	$0.708290\pi$
$968$	−16.8713	+	17.8986i	−0.542265	+	0.575282i
$969$	−10.0000			−0.321246
$970$	−13.6180	−	41.9120i	−0.437249	−	1.34571i
$971$	5.00000	+	3.63271i	0.160458	+	0.116579i	0.665117	−	0.746739i	$-0.268382\pi$
$971$	5.00000	+	3.63271i	0.160458	+	0.116579i	−0.504659	+	0.863319i	$0.668382\pi$
$972$	−86.3951	+	62.7697i	−2.77112	+	2.01334i
$973$	1.05166	−	3.23669i	0.0337148	−	0.103763i
$974$	−27.1591	+	83.5870i	−0.870232	+	2.67830i
$975$	−15.4164	+	11.2007i	−0.493720	+	0.358709i
$976$	6.97214	+	5.06555i	0.223173	+	0.162144i
$977$	−12.0902	−	37.2097i	−0.386799	−	1.19044i	−0.935167	−	0.354207i	$-0.884751\pi$
$977$	−12.0902	−	37.2097i	−0.386799	−	1.19044i	0.548368	−	0.836237i	$-0.315249\pi$
$978$	67.4853			2.15794
$979$	7.09017	+	8.05748i	0.226603	+	0.257518i
$980$	33.2705			1.06279
$981$	25.2705	+	77.7746i	0.806825	+	2.48315i
$982$	−16.5451	−	12.0207i	−0.527975	−	0.383596i
$983$	37.3607	−	27.1441i	1.19162	−	0.865763i	0.198186	−	0.980164i	$-0.436495\pi$
$983$	37.3607	−	27.1441i	1.19162	−	0.865763i	0.993435	+	0.114401i	$0.0364950\pi$
$984$	−26.1803	+	80.5748i	−0.834599	+	2.56863i
$985$	1.76393	−	5.42882i	0.0562035	−	0.172977i
$986$	−47.3607	+	34.4095i	−1.50827	+	1.09582i
$987$	8.61803	+	6.26137i	0.274315	+	0.199302i
$988$	−2.29180	−	7.05342i	−0.0729117	−	0.224399i
$989$	1.90983			0.0607291
$990$	45.7148	−	77.1338i	1.45291	−	2.45147i
$991$	8.65248			0.274855			0.137427	−	0.990512i	$-0.456117\pi$
$991$	8.65248			0.274855			0.137427	+	0.990512i	$0.456117\pi$
$992$	16.5836	+	51.0390i	0.526530	+	1.62049i
$993$	26.9443	+	19.5762i	0.855051	+	0.621231i
$994$	−8.09017	+	5.87785i	−0.256605	+	0.186434i
$995$	1.71885	−	5.29007i	0.0544911	−	0.167706i
$996$	15.9787	−	49.1774i	0.506305	−	1.55825i
$997$	10.6910	−	7.76745i	0.338587	−	0.245998i	−0.405479	−	0.914105i	$-0.632895\pi$
$997$	10.6910	−	7.76745i	0.338587	−	0.245998i	0.744065	+	0.668107i	$0.232895\pi$
$998$	29.9615	+	21.7683i	0.948414	+	0.689063i
$999$	−8.94427	−	27.5276i	−0.282984	−	0.870936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.a.115.1	yes	4
11.3	even	5		2299.2.a.g.1.1		2
11.8	odd	10		2299.2.a.h.1.2		2
11.9	even	5	inner	209.2.f.a.20.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.a.20.1	✓	4	11.9	even	5	inner
209.2.f.a.115.1	yes	4	1.1	even	1	trivial
2299.2.a.g.1.1		2	11.3	even	5
2299.2.a.h.1.2		2	11.8	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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.690983 - 2.12663i) q^{2} +(-2.61803 - 1.90211i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-0.500000 + 1.53884i) q^{5} +(-2.23607 + 6.88191i) q^{6} +(0.309017 - 0.224514i) q^{7} +(1.80902 + 1.31433i) q^{8} +(2.30902 + 7.10642i) q^{9} +3.61803 q^{10} +(-2.19098 - 2.48990i) q^{11} +9.70820 q^{12} +(-0.763932 - 2.35114i) q^{13} +(-0.690983 - 0.502029i) q^{14} +(4.23607 - 3.07768i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.954915 + 2.93893i) q^{17} +(13.5172 - 9.82084i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-1.50000 - 4.61653i) q^{20} -1.23607 q^{21} +(-3.78115 + 6.37988i) q^{22} -0.618034 q^{23} +(-2.23607 - 6.88191i) q^{24} +(1.92705 + 1.40008i) q^{25} +(-4.47214 + 3.24920i) q^{26} +(4.47214 - 13.7638i) q^{27} +(-0.354102 + 1.08981i) q^{28} +(-6.85410 + 4.97980i) q^{29} +(-9.47214 - 6.88191i) q^{30} +(2.47214 + 7.60845i) q^{31} +6.70820 q^{32} +(1.00000 + 10.6861i) q^{33} +6.90983 q^{34} +(0.190983 + 0.587785i) q^{35} +(-18.1353 - 13.1760i) q^{36} +(1.61803 - 1.17557i) q^{37} +(-0.690983 + 2.12663i) q^{38} +(-2.47214 + 7.60845i) q^{39} +(-2.92705 + 2.12663i) q^{40} +(-9.47214 - 6.88191i) q^{41} +(0.854102 + 2.62866i) q^{42} -3.09017 q^{43} +(9.70820 + 2.17963i) q^{44} -12.0902 q^{45} +(0.427051 + 1.31433i) q^{46} +(-6.97214 - 5.06555i) q^{47} +(2.61803 - 1.90211i) q^{48} +(-2.11803 + 6.51864i) q^{49} +(1.64590 - 5.06555i) q^{50} +(8.09017 - 5.87785i) q^{51} +(6.00000 + 4.35926i) q^{52} +(0.472136 + 1.45309i) q^{53} -32.3607 q^{54} +(4.92705 - 2.12663i) q^{55} +0.854102 q^{56} +(1.00000 + 3.07768i) q^{57} +(15.3262 + 11.1352i) q^{58} +(-10.0902 + 7.33094i) q^{59} +(-4.85410 + 14.9394i) q^{60} +(2.66312 - 8.19624i) q^{61} +(14.4721 - 10.5146i) q^{62} +(2.30902 + 1.67760i) q^{63} +(-4.01722 - 12.3637i) q^{64} +4.00000 q^{65} +(22.0344 - 9.51057i) q^{66} -8.47214 q^{67} +(-2.86475 - 8.81678i) q^{68} +(1.61803 + 1.17557i) q^{69} +(1.11803 - 0.812299i) q^{70} +(3.61803 - 11.1352i) q^{71} +(-5.16312 + 15.8904i) q^{72} +(-2.85410 + 2.07363i) q^{73} +(-3.61803 - 2.62866i) q^{74} +(-2.38197 - 7.33094i) q^{75} +3.00000 q^{76} +(-1.23607 - 0.277515i) q^{77} +17.8885 q^{78} +(0.909830 + 2.80017i) q^{79} +(-1.30902 - 0.951057i) q^{80} +(-19.7533 + 14.3516i) q^{81} +(-8.09017 + 24.8990i) q^{82} +(1.64590 - 5.06555i) q^{83} +(3.00000 - 2.17963i) q^{84} +(-4.04508 - 2.93893i) q^{85} +(2.13525 + 6.57164i) q^{86} +27.4164 q^{87} +(-0.690983 - 7.38394i) q^{88} -3.23607 q^{89} +(8.35410 + 25.7113i) q^{90} +(-0.763932 - 0.555029i) q^{91} +(1.50000 - 1.08981i) q^{92} +(8.00000 - 24.6215i) q^{93} +(-5.95492 + 18.3273i) q^{94} +(1.30902 - 0.951057i) q^{95} +(-17.5623 - 12.7598i) q^{96} +(-3.76393 - 11.5842i) q^{97} +15.3262 q^{98} +(12.6353 - 21.3193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} - 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9} + 10 q^{10} - 11 q^{11} + 12 q^{12} - 12 q^{13} - 5 q^{14} + 8 q^{15} + q^{16} - 15 q^{17} + 25 q^{18} - q^{19} - 6 q^{20} + 4 q^{21}+ \cdots + 17 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 6 * q^3 - 3 * q^4 - 2 * q^5 - q^7 + 5 * q^8 + 7 * q^9 + 10 * q^10 - 11 * q^11 + 12 * q^12 - 12 * q^13 - 5 * q^14 + 8 * q^15 + q^16 - 15 * q^17 + 25 * q^18 - q^19 - 6 * q^20 + 4 * q^21 + 5 * q^22 + 2 * q^23 + q^25 + 12 * q^28 - 14 * q^29 - 20 * q^30 - 8 * q^31 + 4 * q^33 + 50 * q^34 + 3 * q^35 - 39 * q^36 + 2 * q^37 - 5 * q^38 + 8 * q^39 - 5 * q^40 - 20 * q^41 - 10 * q^42 + 10 * q^43 + 12 * q^44 - 26 * q^45 - 5 * q^46 - 10 * q^47 + 6 * q^48 - 4 * q^49 + 20 * q^50 + 10 * q^51 + 24 * q^52 - 16 * q^53 - 40 * q^54 + 13 * q^55 - 10 * q^56 + 4 * q^57 + 30 * q^58 - 18 * q^59 - 6 * q^60 - 5 * q^61 + 40 * q^62 + 7 * q^63 + 13 * q^64 + 16 * q^65 + 30 * q^66 - 16 * q^67 - 45 * q^68 + 2 * q^69 + 10 * q^71 - 5 * q^72 + 2 * q^73 - 10 * q^74 - 14 * q^75 + 12 * q^76 + 4 * q^77 + 26 * q^79 - 3 * q^80 - 41 * q^81 - 10 * q^82 + 20 * q^83 + 12 * q^84 - 5 * q^85 - 25 * q^86 + 56 * q^87 - 5 * q^88 - 4 * q^89 + 20 * q^90 - 12 * q^91 + 6 * q^92 + 32 * q^93 - 35 * q^94 + 3 * q^95 - 30 * q^96 - 24 * q^97 + 30 * q^98 + 17 * q^99

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