LMFDB - Embedded newform 1295.2.j.a.186.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(186,1295)] 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("1295.186"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] 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:	$10.3406270618$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			186.3
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.966124 - 1.67338i) q^{2} +(1.39627 - 2.41841i) q^{3} +(-0.866792 + 1.50133i) q^{4} +(-0.500000 - 0.866025i) q^{5} -5.39588 q^{6} +(-1.04689 - 2.42982i) q^{7} -0.514782 q^{8} +(-2.39913 - 4.15542i) q^{9} +(-0.966124 + 1.67338i) q^{10} +(2.17821 - 3.77276i) q^{11} +(2.42055 + 4.19251i) q^{12} +0.574369 q^{13} +(-3.05458 + 4.09934i) q^{14} -2.79254 q^{15} +(2.23093 + 3.86408i) q^{16} +(-2.85705 + 4.94855i) q^{17} +(-4.63572 + 8.02930i) q^{18} +(-1.51551 - 2.62493i) q^{19} +1.73358 q^{20} +(-7.33803 - 0.860886i) q^{21} -8.41767 q^{22} +(0.282673 + 0.489604i) q^{23} +(-0.718774 + 1.24495i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.554911 - 0.961135i) q^{26} -5.02172 q^{27} +(4.55539 + 0.534431i) q^{28} +0.750761 q^{29} +(2.69794 + 4.67297i) q^{30} +(3.88317 - 6.72584i) q^{31} +(3.79592 - 6.57473i) q^{32} +(-6.08272 - 10.5356i) q^{33} +11.0411 q^{34} +(-1.58084 + 2.12154i) q^{35} +8.31819 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-2.92834 + 5.07203i) q^{38} +(0.801973 - 1.38906i) q^{39} +(0.257391 + 0.445815i) q^{40} +9.36744 q^{41} +(5.64886 + 13.1110i) q^{42} -6.47497 q^{43} +(3.77610 + 6.54040i) q^{44} +(-2.39913 + 4.15542i) q^{45} +(0.546194 - 0.946036i) q^{46} +(2.60943 + 4.51966i) q^{47} +12.4599 q^{48} +(-4.80806 + 5.08749i) q^{49} +1.93225 q^{50} +(7.97841 + 13.8190i) q^{51} +(-0.497858 + 0.862315i) q^{52} +(-1.30332 + 2.25741i) q^{53} +(4.85161 + 8.40323i) q^{54} -4.35641 q^{55} +(0.538918 + 1.25083i) q^{56} -8.46422 q^{57} +(-0.725328 - 1.25631i) q^{58} +(-1.40960 + 2.44150i) q^{59} +(2.42055 - 4.19251i) q^{60} +(-5.28313 - 9.15066i) q^{61} -15.0065 q^{62} +(-7.58531 + 10.1797i) q^{63} -5.74562 q^{64} +(-0.287184 - 0.497418i) q^{65} +(-11.7533 + 20.3574i) q^{66} +(3.07973 - 5.33425i) q^{67} +(-4.95293 - 8.57873i) q^{68} +1.57875 q^{69} +(5.07743 + 0.595675i) q^{70} +7.73849 q^{71} +(1.23503 + 2.13914i) q^{72} +(0.562977 - 0.975104i) q^{73} +(-0.966124 + 1.67338i) q^{74} +(1.39627 + 2.41841i) q^{75} +5.25452 q^{76} +(-11.4475 - 1.34300i) q^{77} -3.09922 q^{78} +(6.64754 + 11.5139i) q^{79} +(2.23093 - 3.86408i) q^{80} +(0.185725 - 0.321686i) q^{81} +(-9.05011 - 15.6752i) q^{82} +7.67133 q^{83} +(7.65302 - 10.2706i) q^{84} +5.71410 q^{85} +(6.25563 + 10.8351i) q^{86} +(1.04826 - 1.81565i) q^{87} +(-1.12130 + 1.94215i) q^{88} +(1.56342 + 2.70793i) q^{89} +9.27144 q^{90} +(-0.601298 - 1.39561i) q^{91} -0.980074 q^{92} +(-10.8439 - 18.7822i) q^{93} +(5.04206 - 8.73310i) q^{94} +(-1.51551 + 2.62493i) q^{95} +(-10.6003 - 18.3602i) q^{96} -10.3503 q^{97} +(13.1585 + 3.13055i) q^{98} -20.9032 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) $ 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1295\mathbb{Z}\right)^\times$.

$n$	$556$	$631$	$1037$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.966124	−	1.67338i	−0.683153	−	1.18326i	−0.974013	−	0.226490i	$-0.927275\pi$
$2$	−0.966124	−	1.67338i	−0.683153	−	1.18326i	0.290860	−	0.956765i	$-0.406058\pi$
$3$	1.39627	−	2.41841i	0.806136	−	1.39627i	−0.109385	−	0.993999i	$-0.534888\pi$
$3$	1.39627	−	2.41841i	0.806136	−	1.39627i	0.915521	−	0.402269i	$-0.131778\pi$
$4$	−0.866792	+	1.50133i	−0.433396	+	0.750664i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−5.39588			−2.20286
$7$	−1.04689	−	2.42982i	−0.395686	−	0.918386i
$7$	−1.04689	−	2.42982i	−0.395686	−	0.918386i
$8$	−0.514782			−0.182003
$9$	−2.39913	−	4.15542i	−0.799711	−	1.38514i
$10$	−0.966124	+	1.67338i	−0.305515	+	0.529168i
$11$	2.17821	−	3.77276i	0.656754	−	1.13753i	−0.324697	−	0.945818i	$-0.605262\pi$
$11$	2.17821	−	3.77276i	0.656754	−	1.13753i	0.981451	−	0.191713i	$-0.0614042\pi$
$12$	2.42055	+	4.19251i	0.698752	+	1.21027i
$13$	0.574369			0.159301			0.0796506	−	0.996823i	$-0.474620\pi$
$13$	0.574369			0.159301			0.0796506	+	0.996823i	$0.474620\pi$
$14$	−3.05458	+	4.09934i	−0.816372	+	1.09560i
$15$	−2.79254			−0.721030
$16$	2.23093	+	3.86408i	0.557732	+	0.966020i
$17$	−2.85705	+	4.94855i	−0.692936	+	1.20020i	0.277935	+	0.960600i	$0.410350\pi$
$17$	−2.85705	+	4.94855i	−0.692936	+	1.20020i	−0.970872	+	0.239601i	$0.922983\pi$
$18$	−4.63572	+	8.02930i	−1.09265	+	1.89252i
$19$	−1.51551	−	2.62493i	−0.347681	−	0.602201i	0.638156	−	0.769907i	$-0.279697\pi$
$19$	−1.51551	−	2.62493i	−0.347681	−	0.602201i	−0.985837	+	0.167706i	$0.946364\pi$
$20$	1.73358			0.387641
$21$	−7.33803	−	0.860886i	−1.60129	−	0.187861i
$22$	−8.41767			−1.79465
$23$	0.282673	+	0.489604i	0.0589413	+	0.102089i	0.893990	−	0.448086i	$-0.147894\pi$
$23$	0.282673	+	0.489604i	0.0589413	+	0.102089i	−0.835049	+	0.550175i	$0.814561\pi$
$24$	−0.718774	+	1.24495i	−0.146719	+	0.254125i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.554911	−	0.961135i	−0.108827	−	0.188494i
$27$	−5.02172			−0.966431
$28$	4.55539	+	0.534431i	0.860888	+	0.100998i
$29$	0.750761			0.139413			0.0697064	−	0.997568i	$-0.477794\pi$
$29$	0.750761			0.139413			0.0697064	+	0.997568i	$0.477794\pi$
$30$	2.69794	+	4.67297i	0.492574	+	0.853163i
$31$	3.88317	−	6.72584i	0.697437	−	1.20800i	−0.271915	−	0.962321i	$-0.587657\pi$
$31$	3.88317	−	6.72584i	0.697437	−	1.20800i	0.969352	−	0.245675i	$-0.0790096\pi$
$32$	3.79592	−	6.57473i	0.671031	−	1.16226i
$33$	−6.08272	−	10.5356i	−1.05887	−	1.83401i
$34$	11.0411			1.89353
$35$	−1.58084	+	2.12154i	−0.267211	+	0.358606i
$36$	8.31819			1.38637
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	−2.92834	+	5.07203i	−0.475039	+	0.822791i
$39$	0.801973	−	1.38906i	0.128418	−	0.222427i
$40$	0.257391	+	0.445815i	0.0406971	+	0.0704895i
$41$	9.36744			1.46295			0.731474	−	0.681869i	$-0.238833\pi$
$41$	9.36744			1.46295			0.731474	+	0.681869i	$0.238833\pi$
$42$	5.64886	+	13.1110i	0.871639	+	2.02307i
$43$	−6.47497			−0.987424			−0.493712	−	0.869626i	$-0.664360\pi$
$43$	−6.47497			−0.987424			−0.493712	+	0.869626i	$0.664360\pi$
$44$	3.77610	+	6.54040i	0.569269	+	0.986003i
$45$	−2.39913	+	4.15542i	−0.357642	+	0.619453i
$46$	0.546194	−	0.946036i	0.0805319	−	0.139485i
$47$	2.60943	+	4.51966i	0.380624	+	0.659260i	0.991152	−	0.132735i	$-0.0423759\pi$
$47$	2.60943	+	4.51966i	0.380624	+	0.659260i	−0.610528	+	0.791995i	$0.709043\pi$
$48$	12.4599			1.79843
$49$	−4.80806	+	5.08749i	−0.686866	+	0.726784i
$50$	1.93225			0.273261
$51$	7.97841	+	13.8190i	1.11720	+	1.93505i
$52$	−0.497858	+	0.862315i	−0.0690405	+	0.119582i
$53$	−1.30332	+	2.25741i	−0.179024	+	0.310079i	−0.941547	−	0.336883i	$-0.890627\pi$
$53$	−1.30332	+	2.25741i	−0.179024	+	0.310079i	0.762522	+	0.646962i	$0.223961\pi$
$54$	4.85161	+	8.40323i	0.660220	+	1.14353i
$55$	−4.35641			−0.587418
$56$	0.538918	+	1.25083i	0.0720160	+	0.167149i
$57$	−8.46422			−1.12111
$58$	−0.725328	−	1.25631i	−0.0952403	−	0.164961i
$59$	−1.40960	+	2.44150i	−0.183515	+	0.317857i	−0.943075	−	0.332580i	$-0.892081\pi$
$59$	−1.40960	+	2.44150i	−0.183515	+	0.317857i	0.759560	+	0.650437i	$0.225414\pi$
$60$	2.42055	−	4.19251i	0.312491	−	0.541251i
$61$	−5.28313	−	9.15066i	−0.676436	−	1.17162i	−0.976047	−	0.217560i	$-0.930190\pi$
$61$	−5.28313	−	9.15066i	−0.676436	−	1.17162i	0.299611	−	0.954061i	$-0.403143\pi$
$62$	−15.0065			−1.90582
$63$	−7.58531	+	10.1797i	−0.955659	+	1.28252i
$64$	−5.74562			−0.718203
$65$	−0.287184	−	0.497418i	−0.0356208	−	0.0616971i
$66$	−11.7533	+	20.3574i	−1.44673	+	2.50582i
$67$	3.07973	−	5.33425i	0.376249	−	0.651682i	−0.614264	−	0.789100i	$-0.710547\pi$
$67$	3.07973	−	5.33425i	0.376249	−	0.651682i	0.990513	+	0.137418i	$0.0438804\pi$
$68$	−4.95293	−	8.57873i	−0.600631	−	1.04032i
$69$	1.57875			0.190059
$70$	5.07743	+	0.595675i	0.606869	+	0.0711968i
$71$	7.73849			0.918390			0.459195	−	0.888336i	$-0.348138\pi$
$71$	7.73849			0.918390			0.459195	+	0.888336i	$0.348138\pi$
$72$	1.23503	+	2.13914i	0.145550	+	0.252100i
$73$	0.562977	−	0.975104i	0.0658915	−	0.114127i	−0.831198	−	0.555977i	$-0.812344\pi$
$73$	0.562977	−	0.975104i	0.0658915	−	0.114127i	0.897089	+	0.441850i	$0.145678\pi$
$74$	−0.966124	+	1.67338i	−0.112310	+	0.194526i
$75$	1.39627	+	2.41841i	0.161227	+	0.279254i
$76$	5.25452			0.602734
$77$	−11.4475	−	1.34300i	−1.30456	−	0.153049i
$78$	−3.09922			−0.350918
$79$	6.64754	+	11.5139i	0.747907	+	1.29541i	0.948824	+	0.315804i	$0.102274\pi$
$79$	6.64754	+	11.5139i	0.747907	+	1.29541i	−0.200918	+	0.979608i	$0.564392\pi$
$80$	2.23093	−	3.86408i	0.249425	−	0.432017i
$81$	0.185725	−	0.321686i	0.0206362	−	0.0357429i
$82$	−9.05011	−	15.6752i	−0.999417	−	1.73104i
$83$	7.67133			0.842038			0.421019	−	0.907052i	$-0.361673\pi$
$83$	7.67133			0.842038			0.421019	+	0.907052i	$0.361673\pi$
$84$	7.65302	−	10.2706i	0.835013	−	1.12061i
$85$	5.71410			0.619781
$86$	6.25563	+	10.8351i	0.674561	+	1.16837i
$87$	1.04826	−	1.81565i	0.112386	−	0.194658i
$88$	−1.12130	+	1.94215i	−0.119531	+	0.207034i
$89$	1.56342	+	2.70793i	0.165723	+	0.287040i	0.936912	−	0.349566i	$-0.113671\pi$
$89$	1.56342	+	2.70793i	0.165723	+	0.287040i	−0.771189	+	0.636606i	$0.780338\pi$
$90$	9.27144			0.977295
$91$	−0.601298	−	1.39561i	−0.0630332	−	0.146300i
$92$	−0.980074			−0.102180
$93$	−10.8439	−	18.7822i	−1.12446	−	1.94762i
$94$	5.04206	−	8.73310i	0.520049	−	0.900751i
$95$	−1.51551	+	2.62493i	−0.155488	+	0.269313i
$96$	−10.6003	−	18.3602i	−1.08188	−	1.87388i
$97$	−10.3503			−1.05091			−0.525455	−	0.850821i	$-0.676105\pi$
$97$	−10.3503			−1.05091			−0.525455	+	0.850821i	$0.676105\pi$
$98$	13.1585	+	3.13055i	1.32921	+	0.316233i
$99$	−20.9032			−2.10085
$100$	−0.866792	−	1.50133i	−0.0866792	−	0.150133i
$101$	4.35282	−	7.53930i	0.433121	−	0.750188i	−0.564019	−	0.825762i	$-0.690745\pi$
$101$	4.35282	−	7.53930i	0.433121	−	0.750188i	0.997140	+	0.0755736i	$0.0240788\pi$
$102$	15.4163	−	26.7018i	1.52644	−	2.64387i
$103$	−5.36077	−	9.28513i	−0.528213	−	0.914891i	−0.999459	−	0.0328894i	$-0.989529\pi$
$103$	−5.36077	−	9.28513i	−0.528213	−	0.914891i	0.471246	−	0.882002i	$-0.343804\pi$
$104$	−0.295675			−0.0289933
$105$	2.92347	+	6.78537i	0.285301	+	0.662184i
$106$	5.03666			0.489204
$107$	0.256690	+	0.444600i	0.0248152	+	0.0429811i	0.878166	−	0.478355i	$-0.158767\pi$
$107$	0.256690	+	0.444600i	0.0248152	+	0.0429811i	−0.853351	+	0.521337i	$0.825434\pi$
$108$	4.35279	−	7.53925i	0.418847	−	0.725465i
$109$	−6.27102	+	10.8617i	−0.600654	+	1.04036i	0.392068	+	0.919936i	$0.371760\pi$
$109$	−6.27102	+	10.8617i	−0.600654	+	1.04036i	−0.992722	+	0.120428i	$0.961573\pi$
$110$	4.20883	+	7.28992i	0.401297	+	0.695066i
$111$	−2.79254			−0.265056
$112$	7.05350	−	9.46600i	0.666493	−	0.894453i
$113$	−5.82254			−0.547739			−0.273869	−	0.961767i	$-0.588304\pi$
$113$	−5.82254			−0.547739			−0.273869	+	0.961767i	$0.588304\pi$
$114$	8.17749	+	14.1638i	0.765892	+	1.32656i
$115$	0.282673	−	0.489604i	0.0263594	−	0.0456558i
$116$	−0.650754	+	1.12714i	−0.0604209	+	0.104652i
$117$	−1.37799	−	2.38674i	−0.127395	−	0.220654i
$118$	5.44740			0.501474
$119$	15.0151	+	1.76155i	1.37643	+	0.161481i
$120$	1.43755			0.131230
$121$	−3.98916	−	6.90943i	−0.362651	−	0.628130i
$122$	−10.2083	+	17.6813i	−0.924219	+	1.60079i
$123$	13.0795	−	22.6543i	1.17934	−	2.04267i
$124$	6.73179	+	11.6598i	0.604533	+	1.04708i
$125$	1.00000			0.0894427
$126$	24.3628	+	2.85821i	2.17041	+	0.254629i
$127$	3.39345			0.301120			0.150560	−	0.988601i	$-0.451892\pi$
$127$	3.39345			0.301120			0.150560	+	0.988601i	$0.451892\pi$
$128$	−2.04086	−	3.53487i	−0.180388	−	0.312442i
$129$	−9.04080	+	15.6591i	−0.795998	+	1.37871i
$130$	−0.554911	+	0.961135i	−0.0486689	+	0.0842971i
$131$	6.86969	+	11.8986i	0.600207	+	1.03959i	0.992789	+	0.119873i	$0.0382486\pi$
$131$	6.86969	+	11.8986i	0.600207	+	1.03959i	−0.392582	+	0.919717i	$0.628418\pi$
$132$	21.0898			1.83563
$133$	−4.79156	+	6.43042i	−0.415481	+	0.557588i
$134$	−11.9016			−1.02814
$135$	2.51086	+	4.34894i	0.216100	+	0.374297i
$136$	1.47076	−	2.54743i	0.126116	−	0.218440i
$137$	5.32705	−	9.22672i	0.455121	−	0.788292i	−0.543574	−	0.839361i	$-0.682929\pi$
$137$	5.32705	−	9.22672i	0.455121	−	0.788292i	0.998695	+	0.0510688i	$0.0162628\pi$
$138$	−1.52527	−	2.64184i	−0.129839	−	0.224888i
$139$	−3.90433			−0.331161			−0.165581	−	0.986196i	$-0.552950\pi$
$139$	−3.90433			−0.331161			−0.165581	+	0.986196i	$0.552950\pi$
$140$	−1.81486	−	4.21230i	−0.153384	−	0.356004i
$141$	14.5738			1.22734
$142$	−7.47634	−	12.9494i	−0.627401	−	1.08669i
$143$	1.25109	−	2.16696i	0.104622	−	0.181210i
$144$	10.7046	−	18.5409i	0.892048	−	1.54507i
$145$	−0.375380	−	0.650178i	−0.0311737	−	0.0539943i
$146$	−2.17562			−0.180056
$147$	5.59028	+	18.7314i	0.461079	+	1.54494i
$148$	1.73358			0.142500
$149$	5.77030	+	9.99445i	0.472721	+	0.818778i	0.999513	−	0.0312171i	$-0.00993833\pi$
$149$	5.77030	+	9.99445i	0.472721	+	0.818778i	−0.526791	+	0.849995i	$0.676605\pi$
$150$	2.69794	−	4.67297i	0.220286	−	0.381546i
$151$	5.69053	−	9.85629i	0.463089	−	0.802093i	−0.536024	−	0.844203i	$-0.680074\pi$
$151$	5.69053	−	9.85629i	0.463089	−	0.802093i	0.999113	+	0.0421094i	$0.0134078\pi$
$152$	0.780156	+	1.35127i	0.0632790	+	0.109602i
$153$	27.4177			2.21659
$154$	8.81234	+	20.4534i	0.710118	+	1.64818i
$155$	−7.76633			−0.623807
$156$	1.39029	+	2.40805i	0.111312	+	0.192798i
$157$	−2.20186	+	3.81373i	−0.175728	+	0.304369i	−0.940413	−	0.340035i	$-0.889561\pi$
$157$	−2.20186	+	3.81373i	−0.175728	+	0.304369i	0.764685	+	0.644404i	$0.222894\pi$
$158$	12.8447	−	22.2477i	1.02187	−	1.76993i
$159$	3.63956	+	6.30391i	0.288636	+	0.499932i
$160$	−7.59185			−0.600188
$161$	0.893723	−	1.19940i	0.0704352	−	0.0945262i
$162$	−0.717735			−0.0563906
$163$	−3.00223	−	5.20001i	−0.235153	−	0.407297i	0.724164	−	0.689627i	$-0.242226\pi$
$163$	−3.00223	−	5.20001i	−0.235153	−	0.407297i	−0.959317	+	0.282331i	$0.908892\pi$
$164$	−8.11962	+	14.0636i	−0.634036	+	1.09818i
$165$	−6.08272	+	10.5356i	−0.473539	+	0.820194i
$166$	−7.41146	−	12.8370i	−0.575241	−	0.996346i
$167$	−24.8848			−1.92564			−0.962821	−	0.270142i	$-0.912929\pi$
$167$	−24.8848			−1.92564			−0.962821	+	0.270142i	$0.912929\pi$
$168$	3.77749	+	0.443169i	0.291440	+	0.0341912i
$169$	−12.6701			−0.974623
$170$	−5.52053	−	9.56183i	−0.423405	−	0.733359i
$171$	−7.27180	+	12.5951i	−0.556089	+	0.963174i
$172$	5.61245	−	9.72105i	0.427945	−	0.741223i
$173$	7.28045	+	12.6101i	0.553523	+	0.958729i	0.998017	+	0.0629475i	$0.0200501\pi$
$173$	7.28045	+	12.6101i	0.553523	+	0.958729i	−0.444494	+	0.895782i	$0.646617\pi$
$174$	−4.05101			−0.307106
$175$	2.62773	+	0.308281i	0.198638	+	0.0233039i
$176$	19.4377			1.46517
$177$	3.93637	+	6.81799i	0.295875	+	0.512471i
$178$	3.02092	−	5.23239i	0.226428	−	0.392184i
$179$	10.8848	−	18.8531i	0.813571	−	1.40915i	−0.0967788	−	0.995306i	$-0.530854\pi$
$179$	10.8848	−	18.8531i	0.813571	−	1.40915i	0.910350	−	0.413840i	$-0.135813\pi$
$180$	−4.15910	−	7.20377i	−0.310001	−	0.536937i
$181$	−2.56463			−0.190627			−0.0953136	−	0.995447i	$-0.530385\pi$
$181$	−2.56463			−0.190627			−0.0953136	+	0.995447i	$0.530385\pi$
$182$	−1.75446	+	2.35453i	−0.130049	+	0.174530i
$183$	−29.5067			−2.18120
$184$	−0.145515	−	0.252039i	−0.0107275	−	0.0185806i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	−20.9531	+	36.2918i	−1.53635	+	2.66104i
$187$	12.4465	+	21.5579i	0.910177	+	1.57647i
$188$	−9.04732			−0.659843
$189$	5.25717	+	12.2019i	0.382403	+	0.887556i
$190$	5.85667			0.424888
$191$	−0.645116	−	1.11737i	−0.0466790	−	0.0808503i	0.841742	−	0.539880i	$-0.181530\pi$
$191$	−0.645116	−	1.11737i	−0.0466790	−	0.0808503i	−0.888421	+	0.459030i	$0.848197\pi$
$192$	−8.02244	+	13.8953i	−0.578969	+	1.00280i
$193$	5.68256	−	9.84248i	0.409039	−	0.708477i	−0.585743	−	0.810497i	$-0.699197\pi$
$193$	5.68256	−	9.84248i	0.409039	−	0.708477i	0.994782	+	0.102020i	$0.0325305\pi$
$194$	9.99964	+	17.3199i	0.717933	+	1.24350i
$195$	−1.60395			−0.114861
$196$	−3.47040	−	11.6283i	−0.247886	−	0.830591i
$197$	−8.16979			−0.582073			−0.291037	−	0.956712i	$-0.594000\pi$
$197$	−8.16979			−0.582073			−0.291037	+	0.956712i	$0.594000\pi$
$198$	20.1951	+	34.9789i	1.43520	+	2.48585i
$199$	10.7850	−	18.6802i	0.764532	−	1.32421i	−0.175962	−	0.984397i	$-0.556304\pi$
$199$	10.7850	−	18.6802i	0.764532	−	1.32421i	0.940494	−	0.339811i	$-0.110363\pi$
$200$	0.257391	−	0.445815i	0.0182003	−	0.0315238i
$201$	−8.60026	−	14.8961i	−0.606616	−	1.05069i
$202$	−16.8214			−1.18355
$203$	−0.785961	−	1.82421i	−0.0551636	−	0.128035i
$204$	−27.6625			−1.93676
$205$	−4.68372	−	8.11244i	−0.327125	−	0.566597i
$206$	−10.3583	+	17.9412i	−0.721700	+	1.25002i
$207$	1.35634	−	2.34925i	0.0942721	−	0.163284i
$208$	1.28137	+	2.21941i	0.0888473	+	0.153888i
$209$	−13.2043			−0.913364
$210$	8.53004	−	11.4476i	0.588629	−	0.789957i
$211$	3.53744			0.243528			0.121764	−	0.992559i	$-0.461145\pi$
$211$	3.53744			0.243528			0.121764	+	0.992559i	$0.461145\pi$
$212$	−2.25941	−	3.91341i	−0.155177	−	0.268774i
$213$	10.8050	−	18.7148i	0.740347	−	1.28232i
$214$	0.495989	−	0.859078i	0.0339051	−	0.0587254i
$215$	3.23748	+	5.60749i	0.220795	+	0.382428i
$216$	2.58509			0.175893
$217$	−20.4078	−	2.39421i	−1.38537	−	0.162530i
$218$	24.2343			1.64136
$219$	−1.57213	−	2.72302i	−0.106235	−	0.184004i
$220$	3.77610	−	6.54040i	0.254585	−	0.440954i
$221$	−1.64100	+	2.84229i	−0.110386	+	0.191193i
$222$	2.69794	+	4.67297i	0.181074	+	0.313629i
$223$	24.2011			1.62062			0.810312	−	0.585998i	$-0.199298\pi$
$223$	24.2011			1.62062			0.810312	+	0.585998i	$0.199298\pi$
$224$	−19.9493	−	2.34042i	−1.33292	−	0.156376i
$225$	4.79826			0.319884
$226$	5.62530	+	9.74330i	0.374189	+	0.648115i
$227$	−12.0354	+	20.8460i	−0.798819	+	1.38359i	0.121567	+	0.992583i	$0.461208\pi$
$227$	−12.0354	+	20.8460i	−0.798819	+	1.38359i	−0.920386	+	0.391011i	$0.872125\pi$
$228$	7.33672	−	12.7076i	0.485886	−	0.841579i
$229$	−13.8176	−	23.9328i	−0.913092	−	1.58152i	−0.809671	−	0.586884i	$-0.800354\pi$
$229$	−13.8176	−	23.9328i	−0.913092	−	1.58152i	−0.103421	−	0.994638i	$-0.532979\pi$
$230$	−1.09239			−0.0720299
$231$	−19.2317	+	25.8095i	−1.26535	+	1.69814i
$232$	−0.386478			−0.0253736
$233$	−4.69008	−	8.12345i	−0.307257	−	0.532185i	0.670504	−	0.741906i	$-0.266078\pi$
$233$	−4.69008	−	8.12345i	−0.307257	−	0.532185i	−0.977761	+	0.209721i	$0.932745\pi$
$234$	−2.66261	+	4.61178i	−0.174060	+	0.301481i
$235$	2.60943	−	4.51966i	0.170220	−	0.294830i
$236$	−2.44366	−	4.23255i	−0.159069	−	0.275516i
$237$	37.1270			2.41166
$238$	−11.5587	−	26.8278i	−0.749241	−	1.73899i
$239$	22.7846			1.47382			0.736908	−	0.675993i	$-0.236285\pi$
$239$	22.7846			1.47382			0.736908	+	0.675993i	$0.236285\pi$
$240$	−6.22995	−	10.7906i	−0.402141	−	0.696529i
$241$	−12.1682	+	21.0759i	−0.783820	+	1.35762i	0.145882	+	0.989302i	$0.453398\pi$
$241$	−12.1682	+	21.0759i	−0.783820	+	1.35762i	−0.929702	+	0.368313i	$0.879935\pi$
$242$	−7.70805	+	13.3507i	−0.495492	+	0.858218i
$243$	−8.05123	−	13.9451i	−0.516486	−	0.894581i
$244$	18.3175			1.17266
$245$	6.80993	+	1.62016i	0.435070	+	0.103508i
$246$	−50.5455			−3.22267
$247$	−0.870459	−	1.50768i	−0.0553860	−	0.0959314i
$248$	−1.99898	+	3.46234i	−0.126936	+	0.219859i
$249$	10.7112	−	18.5524i	0.678797	−	1.17571i
$250$	−0.966124	−	1.67338i	−0.0611031	−	0.105834i
$251$	−25.8151			−1.62943			−0.814716	−	0.579860i	$-0.803107\pi$
$251$	−25.8151			−1.62943			−0.814716	+	0.579860i	$0.803107\pi$
$252$	−8.70820	−	20.2117i	−0.548565	−	1.27322i
$253$	2.46288			0.154840
$254$	−3.27850	−	5.67852i	−0.205711	−	0.356302i
$255$	7.97841	−	13.8190i	0.499628	−	0.865381i
$256$	−9.68907	+	16.7820i	−0.605567	+	1.04887i
$257$	12.7433	+	22.0721i	0.794906	+	1.37682i	0.922899	+	0.385043i	$0.125813\pi$
$257$	12.7433	+	22.0721i	0.794906	+	1.37682i	−0.127993	+	0.991775i	$0.540853\pi$
$258$	34.9381			2.17515
$259$	−1.58084	+	2.12154i	−0.0982289	+	0.131826i
$260$	0.995716			0.0617517
$261$	−1.80117	−	3.11973i	−0.111490	−	0.193106i
$262$	13.2739	−	22.9911i	0.820067	−	1.42040i
$263$	−4.64797	+	8.05052i	−0.286606	+	0.496416i	−0.972997	−	0.230816i	$-0.925860\pi$
$263$	−4.64797	+	8.05052i	−0.286606	+	0.496416i	0.686391	+	0.727232i	$0.259194\pi$
$264$	3.13128	+	5.42353i	0.192717	+	0.333795i
$265$	2.60663			0.160124
$266$	15.3897	+	1.80550i	0.943606	+	0.110702i
$267$	8.73184			0.534380
$268$	5.33897	+	9.24737i	0.326130	+	0.564873i
$269$	3.28626	−	5.69196i	0.200367	−	0.347045i	−0.748280	−	0.663383i	$-0.769120\pi$
$269$	3.28626	−	5.69196i	0.200367	−	0.347045i	0.948647	+	0.316338i	$0.102453\pi$
$270$	4.85161	−	8.40323i	0.295259	−	0.511404i
$271$	0.0434468	+	0.0752521i	0.00263921	+	0.00457124i	0.867342	−	0.497713i	$-0.165827\pi$
$271$	0.0434468	+	0.0752521i	0.00263921	+	0.00457124i	−0.864703	+	0.502284i	$0.832493\pi$
$272$	−25.4955			−1.54589
$273$	−4.21474	−	0.494466i	−0.255087	−	0.0299264i
$274$	−20.5864			−1.24367
$275$	2.17821	+	3.77276i	0.131351	+	0.227506i
$276$	−1.36845	+	2.37022i	−0.0823708	+	0.142670i
$277$	6.78442	−	11.7510i	0.407636	−	0.706046i	−0.586988	−	0.809595i	$-0.699687\pi$
$277$	6.78442	−	11.7510i	0.407636	−	0.706046i	0.994624	+	0.103549i	$0.0330199\pi$
$278$	3.77207	+	6.53342i	0.226234	+	0.391848i
$279$	−37.2649			−2.23099
$280$	0.813790	−	1.09213i	0.0486333	−	0.0652673i
$281$	−25.6191			−1.52831			−0.764155	−	0.645033i	$-0.776844\pi$
$281$	−25.6191			−1.52831			−0.764155	+	0.645033i	$0.776844\pi$
$282$	−14.0801	−	24.3875i	−0.838460	−	1.45226i
$283$	5.14255	−	8.90716i	0.305693	−	0.529475i	−0.671723	−	0.740803i	$-0.734445\pi$
$283$	5.14255	−	8.90716i	0.305693	−	0.529475i	0.977415	+	0.211327i	$0.0677786\pi$
$284$	−6.70766	+	11.6180i	−0.398026	+	0.689402i
$285$	4.23211	+	7.33023i	0.250689	+	0.434205i
$286$	−4.83484			−0.285890
$287$	−9.80664	−	22.7612i	−0.578867	−	1.34355i
$288$	−36.4277			−2.14652
$289$	−7.82545	−	13.5541i	−0.460321	−	0.797299i
$290$	−0.725328	+	1.25631i	−0.0425927	+	0.0737728i
$291$	−14.4518	+	25.0312i	−0.847177	+	1.46735i
$292$	0.975967	+	1.69043i	0.0571142	+	0.0989247i
$293$	−13.3664			−0.780876			−0.390438	−	0.920629i	$-0.627676\pi$
$293$	−13.3664			−0.780876			−0.390438	+	0.920629i	$0.627676\pi$
$294$	25.9437	−	27.4515i	1.51307	−	1.60100i
$295$	2.81920			0.164140
$296$	0.257391	+	0.445815i	0.0149606	+	0.0259124i
$297$	−10.9383	+	18.9458i	−0.634707	+	1.09934i
$298$	11.1497	−	19.3118i	0.645882	−	1.11870i
$299$	0.162358	+	0.281213i	0.00938942	+	0.0162630i
$300$	−4.84110			−0.279501
$301$	6.77855	+	15.7330i	0.390709	+	0.906836i
$302$	−21.9910			−1.26544
$303$	−12.1554	−	21.0538i	−0.698310	−	1.20951i
$304$	6.76197	−	11.7121i	0.387826	−	0.671734i
$305$	−5.28313	+	9.15066i	−0.302511	+	0.523965i
$306$	−26.4890	−	45.8802i	−1.51427	−	2.62280i
$307$	−23.6376			−1.34907			−0.674536	−	0.738242i	$-0.735656\pi$
$307$	−23.6376			−1.34907			−0.674536	+	0.738242i	$0.735656\pi$
$308$	11.9389	−	16.0223i	0.680280	−	0.912956i
$309$	−29.9403			−1.70324
$310$	7.50324	+	12.9960i	0.426155	+	0.738123i
$311$	12.5983	−	21.8208i	0.714382	−	1.23735i	−0.248815	−	0.968551i	$-0.580041\pi$
$311$	12.5983	−	21.8208i	0.714382	−	1.23735i	0.963197	−	0.268795i	$-0.0866255\pi$
$312$	−0.412841	+	0.715062i	−0.0233725	+	0.0404824i
$313$	0.113744	+	0.197011i	0.00642921	+	0.0111357i	0.869222	−	0.494422i	$-0.164620\pi$
$313$	0.113744	+	0.197011i	0.00642921	+	0.0111357i	−0.862793	+	0.505558i	$0.831287\pi$
$314$	8.50908			0.480195
$315$	12.6085	+	1.47921i	0.710411	+	0.0833442i
$316$	−23.0481			−1.29656
$317$	3.44990	+	5.97540i	0.193766	+	0.335612i	0.946495	−	0.322718i	$-0.104597\pi$
$317$	3.44990	+	5.97540i	0.193766	+	0.335612i	−0.752730	+	0.658330i	$0.771263\pi$
$318$	7.03254	−	12.1807i	0.394365	−	0.683060i
$319$	1.63531	−	2.83244i	0.0915599	−	0.158586i
$320$	2.87281	+	4.97586i	0.160595	+	0.278159i
$321$	1.43363			0.0800176
$322$	−2.87050	−	0.336762i	−0.159967	−	0.0187670i
$323$	17.3195			0.963683
$324$	0.321970	+	0.557669i	0.0178872	+	0.0309816i
$325$	−0.287184	+	0.497418i	−0.0159301	+	0.0275918i
$326$	−5.80105	+	10.0477i	−0.321291	+	0.556492i
$327$	17.5120	+	30.3318i	0.968418	+	1.67735i
$328$	−4.82219			−0.266261
$329$	8.25019	−	11.0720i	0.454848	−	0.610419i
$330$	23.5067			1.29400
$331$	3.03323	+	5.25371i	0.166721	+	0.288770i	0.937265	−	0.348617i	$-0.113349\pi$
$331$	3.03323	+	5.25371i	0.166721	+	0.288770i	−0.770544	+	0.637387i	$0.780015\pi$
$332$	−6.64945	+	11.5172i	−0.364936	+	0.632087i
$333$	−2.39913	+	4.15542i	−0.131472	+	0.227716i
$334$	24.0418	+	41.6416i	1.31551	+	2.27853i
$335$	−6.15946			−0.336527
$336$	−13.0441	−	30.2753i	−0.711613	−	1.65165i
$337$	4.00130			0.217965			0.108982	−	0.994044i	$-0.465241\pi$
$337$	4.00130			0.217965			0.108982	+	0.994044i	$0.465241\pi$
$338$	12.2409	+	21.2018i	0.665817	+	1.15323i
$339$	−8.12983	+	14.0813i	−0.441552	+	0.764790i
$340$	−4.95293	+	8.57873i	−0.268611	+	0.465247i
$341$	−16.9167	−	29.3005i	−0.916089	−	1.58671i
$342$	28.1019			1.51957
$343$	17.3952	+	6.35671i	0.939251	+	0.343230i
$344$	3.33320			0.179714
$345$	−0.789374	−	1.36724i	−0.0424985	−	0.0736095i
$346$	14.0676	−	24.3659i	0.756281	−	1.30992i
$347$	−9.69945	+	16.7999i	−0.520694	+	0.901868i	0.479017	+	0.877806i	$0.340993\pi$
$347$	−9.69945	+	16.7999i	−0.520694	+	0.901868i	−0.999710	+	0.0240624i	$0.992340\pi$
$348$	1.81725	+	3.14758i	0.0974150	+	0.168728i
$349$	−18.9027			−1.01184			−0.505918	−	0.862581i	$-0.668846\pi$
$349$	−18.9027			−1.01184			−0.505918	+	0.862581i	$0.668846\pi$
$350$	−2.02284	−	4.69502i	−0.108126	−	0.250959i
$351$	−2.88432			−0.153954
$352$	−16.5366	−	28.6422i	−0.881404	−	1.52664i
$353$	15.3169	−	26.5297i	0.815237	−	1.41203i	−0.0939212	−	0.995580i	$-0.529940\pi$
$353$	15.3169	−	26.5297i	0.815237	−	1.41203i	0.909158	−	0.416452i	$-0.136726\pi$
$354$	7.60604	−	13.1740i	0.404256	−	0.700193i
$355$	−3.86924	−	6.70173i	−0.205358	−	0.355691i
$356$	−5.42065			−0.287294
$357$	25.2253	−	33.8531i	1.33506	−	1.79169i
$358$	−42.0644			−2.22317
$359$	−4.59758	−	7.96324i	−0.242651	−	0.420284i	0.718818	−	0.695199i	$-0.244684\pi$
$359$	−4.59758	−	7.96324i	−0.242651	−	0.420284i	−0.961469	+	0.274915i	$0.911350\pi$
$360$	1.23503	−	2.13914i	0.0650918	−	0.112742i
$361$	4.90648	−	8.49827i	0.258236	−	0.447277i
$362$	2.47775	+	4.29158i	0.130228	+	0.225561i
$363$	−22.2798			−1.16938
$364$	2.61647	+	0.306960i	0.137140	+	0.0160891i
$365$	−1.12595			−0.0589351
$366$	28.5071	+	49.3758i	1.49009	+	2.58091i
$367$	−5.68864	+	9.85300i	−0.296944	+	0.514323i	−0.975435	−	0.220286i	$-0.929301\pi$
$367$	−5.68864	+	9.85300i	−0.296944	+	0.514323i	0.678491	+	0.734609i	$0.262634\pi$
$368$	−1.26124	+	2.18454i	−0.0657469	+	0.113877i
$369$	−22.4737	−	38.9256i	−1.16994	−	2.02639i
$370$	1.93225			0.100453
$371$	6.84953	+	0.803576i	0.355610	+	0.0417196i
$372$	37.5976			1.94934
$373$	4.92858	+	8.53655i	0.255192	+	0.442006i	0.964948	−	0.262442i	$-0.0845280\pi$
$373$	4.92858	+	8.53655i	0.255192	+	0.442006i	−0.709756	+	0.704448i	$0.751195\pi$
$374$	24.0497	−	41.6553i	1.24358	−	2.15394i
$375$	1.39627	−	2.41841i	0.0721030	−	0.124886i
$376$	−1.34329	−	2.32664i	−0.0692747	−	0.119987i
$377$	0.431213			0.0222086
$378$	15.3393	−	20.5858i	0.788967	−	1.05882i
$379$	−24.2545			−1.24587			−0.622934	−	0.782275i	$-0.714059\pi$
$379$	−24.2545			−1.24587			−0.622934	+	0.782275i	$0.714059\pi$
$380$	−2.62726	−	4.55054i	−0.134775	−	0.233438i
$381$	4.73817	−	8.20675i	0.242744	−	0.420445i
$382$	−1.24652	+	2.15904i	−0.0637777	+	0.110466i
$383$	−8.95443	−	15.5095i	−0.457550	−	0.792500i	0.541281	−	0.840842i	$-0.317940\pi$
$383$	−8.95443	−	15.5095i	−0.457550	−	0.792500i	−0.998831	+	0.0483419i	$0.984606\pi$
$384$	−11.3984			−0.581670
$385$	4.56066	+	10.5853i	0.232433	+	0.539477i
$386$	−21.9602			−1.11775
$387$	15.5343	+	26.9062i	0.789653	+	1.36772i
$388$	8.97153	−	15.5391i	0.455460	−	0.788880i
$389$	−19.1826	+	33.2253i	−0.972599	+	1.68459i	−0.284956	+	0.958541i	$0.591979\pi$
$389$	−19.1826	+	33.2253i	−0.972599	+	1.68459i	−0.687642	+	0.726050i	$0.741354\pi$
$390$	1.54961	+	2.68400i	0.0784676	+	0.135910i
$391$	−3.23044			−0.163370
$392$	2.47510	−	2.61895i	0.125012	−	0.132277i
$393$	38.3677			1.93540
$394$	7.89303	+	13.6711i	0.397645	+	0.688741i
$395$	6.64754	−	11.5139i	0.334474	−	0.579326i
$396$	18.1187	−	31.3826i	0.910501	−	1.57703i
$397$	−13.7583	−	23.8300i	−0.690507	−	1.19599i	−0.971672	−	0.236334i	$-0.924054\pi$
$397$	−13.7583	−	23.8300i	−0.690507	−	1.19599i	0.281165	−	0.959659i	$-0.409279\pi$
$398$	−41.6788			−2.08917
$399$	8.86107	+	20.5665i	0.443608	+	1.02961i
$400$	−4.46185			−0.223093
$401$	8.47760	+	14.6836i	0.423351	+	0.733266i	0.996265	−	0.0863500i	$-0.0275203\pi$
$401$	8.47760	+	14.6836i	0.423351	+	0.733266i	−0.572914	+	0.819616i	$0.694187\pi$
$402$	−16.6178	+	28.7830i	−0.828823	+	1.43556i
$403$	2.23037	−	3.86311i	0.111103	−	0.192435i
$404$	7.54597	+	13.0700i	0.375426	+	0.650257i
$405$	−0.371451			−0.0184575
$406$	−2.29326	+	3.07763i	−0.113813	+	0.152740i
$407$	−4.35641			−0.215939
$408$	−4.10715	−	7.11379i	−0.203334	−	0.352185i
$409$	8.06694	−	13.9723i	0.398884	−	0.690888i	−0.594704	−	0.803945i	$-0.702731\pi$
$409$	8.06694	−	13.9723i	0.398884	−	0.690888i	0.993589	+	0.113057i	$0.0360641\pi$
$410$	−9.05011	+	15.6752i	−0.446953	+	0.774145i
$411$	−14.8760	−	25.7660i	−0.733778	−	1.27094i
$412$	18.5867			0.915701
$413$	7.40811	+	0.869107i	0.364529	+	0.0427660i
$414$	−5.24157			−0.257609
$415$	−3.83566	−	6.64357i	−0.188285	−	0.326120i
$416$	2.18026	−	3.77632i	0.106896	−	0.185149i
$417$	−5.45150	+	9.44227i	−0.266961	+	0.462390i
$418$	12.7570	+	22.0958i	0.623967	+	1.08074i
$419$	−24.0766			−1.17622			−0.588110	−	0.808781i	$-0.700128\pi$
$419$	−24.0766			−1.17622			−0.588110	+	0.808781i	$0.700128\pi$
$420$	−12.7211	−	1.49242i	−0.620726	−	0.0728225i
$421$	38.4325			1.87309			0.936544	−	0.350551i	$-0.114006\pi$
$421$	38.4325			1.87309			0.936544	+	0.350551i	$0.114006\pi$
$422$	−3.41761	−	5.91947i	−0.166367	−	0.288155i
$423$	12.5207	−	21.6865i	0.608778	−	1.05443i
$424$	0.670925	−	1.16208i	0.0325830	−	0.0564354i
$425$	−2.85705	−	4.94855i	−0.138587	−	0.240040i
$426$	−41.7559			−2.02308
$427$	−16.7036	+	22.4168i	−0.808345	+	1.08482i
$428$	−0.889988			−0.0430192
$429$	−3.49372	−	6.05131i	−0.168679	−	0.292160i
$430$	6.25563	−	10.8351i	0.301673	−	0.522513i
$431$	6.01946	−	10.4260i	0.289947	−	0.502203i	−0.683850	−	0.729623i	$-0.739696\pi$
$431$	6.01946	−	10.4260i	0.289947	−	0.502203i	0.973797	+	0.227420i	$0.0730289\pi$
$432$	−11.2031	−	19.4043i	−0.539009	−	0.933591i
$433$	−21.0820			−1.01314			−0.506569	−	0.862200i	$-0.669086\pi$
$433$	−21.0820			−1.01314			−0.506569	+	0.862200i	$0.669086\pi$
$434$	15.7101	+	36.4631i	0.754107	+	1.75028i
$435$	−2.09653			−0.100521
$436$	−10.8713	−	18.8297i	−0.520642	−	0.901779i
$437$	0.856785	−	1.48400i	0.0409856	−	0.0709891i
$438$	−3.03775	+	5.26154i	−0.145149	+	0.251406i
$439$	−12.6768	−	21.9568i	−0.605029	−	1.04794i	−0.992047	−	0.125869i	$-0.959828\pi$
$439$	−12.6768	−	21.9568i	−0.605029	−	1.04794i	0.387018	−	0.922072i	$-0.373505\pi$
$440$	2.24260			0.106912
$441$	32.6758	+	7.77395i	1.55599	+	0.370188i
$442$	6.34163			0.301641
$443$	15.8208	+	27.4024i	0.751667	+	1.30193i	0.947014	+	0.321191i	$0.104083\pi$
$443$	15.8208	+	27.4024i	0.751667	+	1.30193i	−0.195348	+	0.980734i	$0.562583\pi$
$444$	2.42055	−	4.19251i	0.114874	−	0.198968i
$445$	1.56342	−	2.70793i	0.0741134	−	0.128368i
$446$	−23.3813	−	40.4975i	−1.10713	−	1.91761i
$447$	32.2276			1.52431
$448$	6.01501	+	13.9608i	0.284183	+	0.659588i
$449$	10.7005			0.504986			0.252493	−	0.967599i	$-0.418750\pi$
$449$	10.7005			0.504986			0.252493	+	0.967599i	$0.418750\pi$
$450$	−4.63572	−	8.02930i	−0.218530	−	0.378505i
$451$	20.4042	−	35.3411i	0.960797	−	1.66415i
$452$	5.04693	−	8.74154i	0.237388	−	0.411168i
$453$	−15.8910	−	27.5240i	−0.746625	−	1.29319i
$454$	46.5108			2.18286
$455$	−0.907987	+	1.21855i	−0.0425671	+	0.0571263i
$456$	4.35723			0.204046
$457$	9.68219	+	16.7700i	0.452914	+	0.784470i	0.998566	−	0.0535424i	$-0.0170512\pi$
$457$	9.68219	+	16.7700i	0.452914	+	0.784470i	−0.545652	+	0.838012i	$0.683718\pi$
$458$	−26.6990	+	46.2441i	−1.24756	+	2.16084i
$459$	14.3473	−	24.8503i	0.669675	−	1.15991i
$460$	0.490037	+	0.848769i	0.0228481	+	0.0395741i
$461$	−23.3884			−1.08931			−0.544654	−	0.838661i	$-0.683339\pi$
$461$	−23.3884			−1.08931			−0.544654	+	0.838661i	$0.683339\pi$
$462$	61.7691	+	7.24665i	2.87376	+	0.337145i
$463$	16.2360			0.754553			0.377276	−	0.926101i	$-0.376861\pi$
$463$	16.2360			0.754553			0.377276	+	0.926101i	$0.376861\pi$
$464$	1.67489	+	2.90100i	0.0777550	+	0.134676i
$465$	−10.8439	+	18.7822i	−0.502873	+	0.871002i
$466$	−9.06239	+	15.6965i	−0.419807	+	0.727128i
$467$	5.59720	+	9.69464i	0.259008	+	0.448614i	0.965976	−	0.258630i	$-0.0832712\pi$
$467$	5.59720	+	9.69464i	0.259008	+	0.448614i	−0.706969	+	0.707245i	$0.749938\pi$
$468$	4.77771			0.220850
$469$	−16.1854	−	1.89884i	−0.747372	−	0.0876805i
$470$	−10.0841			−0.465146
$471$	6.14878	+	10.6500i	0.283321	+	0.490726i
$472$	0.725638	−	1.25684i	0.0334002	−	0.0578509i
$473$	−14.1038	+	24.4285i	−0.648494	+	1.12322i
$474$	−35.8693	−	62.1274i	−1.64753	−	2.85361i
$475$	3.03101			0.139072
$476$	−15.6596	+	21.0157i	−0.717758	+	0.963253i
$477$	12.5073			0.572671
$478$	−22.0128	−	38.1273i	−1.00684	−	1.74390i
$479$	3.31820	−	5.74729i	0.151612	−	0.262600i	−0.780208	−	0.625520i	$-0.784887\pi$
$479$	3.31820	−	5.74729i	0.151612	−	0.262600i	0.931820	+	0.362920i	$0.118220\pi$
$480$	−10.6003	+	18.3602i	−0.483833	+	0.838024i
$481$	−0.287184	−	0.497418i	−0.0130945	−	0.0226803i
$482$	47.0238			2.14187
$483$	−1.65277	−	3.83608i	−0.0752036	−	0.174548i
$484$	13.8311			0.628686
$485$	5.17513	+	8.96359i	0.234991	+	0.407016i
$486$	−15.5570	+	26.9455i	−0.705678	+	1.22227i
$487$	19.0731	−	33.0356i	0.864284	−	1.49698i	−0.00347149	−	0.999994i	$-0.501105\pi$
$487$	19.0731	−	33.0356i	0.864284	−	1.49698i	0.867756	−	0.496991i	$-0.165562\pi$
$488$	2.71966	+	4.71060i	0.123113	+	0.213239i
$489$	−16.7677			−0.758260
$490$	−3.86810	−	12.9608i	−0.174743	−	0.585511i
$491$	−19.7649			−0.891979			−0.445990	−	0.895038i	$-0.647148\pi$
$491$	−19.7649			−0.891979			−0.445990	+	0.895038i	$0.647148\pi$
$492$	22.6743	+	39.2731i	1.02224	+	1.77057i
$493$	−2.14496	+	3.71518i	−0.0966042	+	0.167323i
$494$	−1.68194	+	2.91321i	−0.0756742	+	0.131072i
$495$	10.4516	+	18.1027i	0.469765	+	0.813657i
$496$	34.6522			1.55593
$497$	−8.10131	−	18.8031i	−0.363394	−	0.843436i
$498$	−41.3935			−1.85489
$499$	16.7689	+	29.0447i	0.750681	+	1.30022i	0.947493	+	0.319777i	$0.103608\pi$
$499$	16.7689	+	29.0447i	0.750681	+	1.30022i	−0.196812	+	0.980441i	$0.563059\pi$
$500$	−0.866792	+	1.50133i	−0.0387641	+	0.0671414i
$501$	−34.7458	+	60.1815i	−1.55233	+	2.68871i
$502$	24.9406	+	43.1983i	1.11315	+	1.92804i
$503$	14.1183			0.629502			0.314751	−	0.949174i	$-0.398079\pi$
$503$	14.1183			0.629502			0.314751	+	0.949174i	$0.398079\pi$
$504$	3.90478	−	5.24033i	0.173933	−	0.233423i
$505$	−8.70563			−0.387396
$506$	−2.37945	−	4.12132i	−0.105779	−	0.183215i
$507$	−17.6909	+	30.6415i	−0.785679	+	1.36084i
$508$	−2.94142	+	5.09468i	−0.130504	+	0.226040i
$509$	21.2156	+	36.7464i	0.940363	+	1.62876i	0.764779	+	0.644293i	$0.222848\pi$
$509$	21.2156	+	36.7464i	0.940363	+	1.62876i	0.175585	+	0.984464i	$0.443818\pi$
$510$	−30.8326			−1.36529
$511$	−2.95870	−	0.347110i	−0.130885	−	0.0153552i
$512$	29.2800			1.29400
$513$	7.61045	+	13.1817i	0.336010	+	0.581986i
$514$	24.6233	−	42.6487i	1.08609	−	1.88115i
$515$	−5.36077	+	9.28513i	−0.236224	+	0.409152i
$516$	−15.6730	−	27.1464i	−0.689964	−	1.19505i
$517$	22.7355			0.999905
$518$	5.07743	+	0.595675i	0.223089	+	0.0261725i
$519$	40.6619			1.78486
$520$	0.147837	+	0.256062i	0.00648310	+	0.0112291i
$521$	1.06393	−	1.84279i	0.0466118	−	0.0807340i	−0.841778	−	0.539824i	$-0.818491\pi$
$521$	1.06393	−	1.84279i	0.0466118	−	0.0807340i	0.888390	+	0.459090i	$0.151824\pi$
$522$	−3.48032	+	6.02809i	−0.152329	+	0.263842i
$523$	9.41291	+	16.3036i	0.411598	+	0.712909i	0.995065	−	0.0992285i	$-0.0316375\pi$
$523$	9.41291	+	16.3036i	0.411598	+	0.712909i	−0.583467	+	0.812137i	$0.698304\pi$
$524$	−23.8184			−1.04051
$525$	4.41457	−	5.92448i	0.192667	−	0.258566i
$526$	17.9621			0.783183
$527$	22.1888	+	38.4321i	0.966559	+	1.67413i
$528$	27.1402	−	47.0082i	1.18113	−	2.04577i
$529$	11.3402	−	19.6418i	0.493052	−	0.853991i
$530$	−2.51833	−	4.36188i	−0.109389	−	0.189468i
$531$	13.5273			0.587034
$532$	−5.50088	−	12.7675i	−0.238493	−	0.553543i
$533$	5.38036			0.233049
$534$	−8.43604	−	14.6117i	−0.365063	−	0.632308i
$535$	0.256690	−	0.444600i	0.0110977	−	0.0192217i
$536$	−1.58539	+	2.74598i	−0.0684785	+	0.118608i
$537$	−30.3963	−	52.6480i	−1.31170	−	2.27193i
$538$	−12.6997			−0.547524
$539$	8.72095	+	29.2213i	0.375638	+	1.25865i
$540$	−8.70557			−0.374628
$541$	−12.8749	−	22.2999i	−0.553533	−	0.958748i	−0.998016	−	0.0629603i	$-0.979946\pi$
$541$	−12.8749	−	22.2999i	−0.553533	−	0.958748i	0.444483	−	0.895787i	$-0.353387\pi$
$542$	0.0839500	−	0.145406i	0.00360596	−	0.00624571i
$543$	−3.58091	+	6.20231i	−0.153671	+	0.266167i
$544$	21.6903	+	37.5687i	0.929963	+	1.61074i
$545$	12.5420			0.537242
$546$	3.24453	+	7.53055i	0.138853	+	0.322278i
$547$	−13.8316			−0.591397			−0.295698	−	0.955281i	$-0.595552\pi$
$547$	−13.8316			−0.591397			−0.295698	+	0.955281i	$0.595552\pi$
$548$	9.23489	+	15.9953i	0.394495	+	0.683285i
$549$	−25.3499	+	43.9073i	−1.08191	+	1.87392i
$550$	4.20883	−	7.28992i	0.179465	−	0.310843i
$551$	−1.13778	−	1.97070i	−0.0484712	−	0.0839546i
$552$	−0.812712			−0.0345913
$553$	21.0174	−	28.2060i	0.893753	−	1.19944i
$554$	−26.2184			−1.11391
$555$	1.39627	+	2.41841i	0.0592683	+	0.102656i
$556$	3.38424	−	5.86168i	0.143524	−	0.248591i
$557$	8.80961	−	15.2587i	0.373275	−	0.646531i	−0.616792	−	0.787126i	$-0.711568\pi$
$557$	8.80961	−	15.2587i	0.373275	−	0.646531i	0.990067	+	0.140595i	$0.0449015\pi$
$558$	36.0025	+	62.3582i	1.52411	+	2.63983i
$559$	−3.71902			−0.157298
$560$	−11.7245	−	1.37550i	−0.495453	−	0.0581257i
$561$	69.5145			2.93491
$562$	24.7513	+	42.8705i	1.04407	+	1.80838i
$563$	−16.8848	+	29.2453i	−0.711608	+	1.23254i	0.252645	+	0.967559i	$0.418699\pi$
$563$	−16.8848	+	29.2453i	−0.711608	+	1.23254i	−0.964253	+	0.264982i	$0.914634\pi$
$564$	−12.6325	+	21.8801i	−0.531924	+	0.921319i
$565$	2.91127	+	5.04247i	0.122478	+	0.212138i
$566$	−19.8734			−0.835340
$567$	−0.976072	−	0.114511i	−0.0409912	−	0.00480902i
$568$	−3.98364			−0.167150
$569$	19.6678	+	34.0656i	0.824517	+	1.42811i	0.902287	+	0.431135i	$0.141887\pi$
$569$	19.6678	+	34.0656i	0.824517	+	1.42811i	−0.0777700	+	0.996971i	$0.524780\pi$
$570$	8.17749	−	14.1638i	0.342517	−	0.593257i
$571$	−3.06175	+	5.30311i	−0.128130	+	0.221928i	−0.922952	−	0.384915i	$-0.874231\pi$
$571$	−3.06175	+	5.30311i	−0.128130	+	0.221928i	0.794822	+	0.606843i	$0.207564\pi$
$572$	2.16887	+	3.75660i	0.0906852	+	0.157071i
$573$	−3.60302			−0.150518
$574$	−28.6136	+	38.4003i	−1.19431	+	1.60280i
$575$	−0.565346			−0.0235765
$576$	13.7845	+	23.8755i	0.574355	+	0.994812i
$577$	17.6420	−	30.5569i	0.734447	−	1.27210i	−0.220518	−	0.975383i	$-0.570775\pi$
$577$	17.6420	−	30.5569i	0.734447	−	1.27210i	0.954965	−	0.296717i	$-0.0958918\pi$
$578$	−15.1207	+	26.1899i	−0.628939	+	1.08935i
$579$	−15.8688	−	27.4855i	−0.659483	−	1.14226i
$580$	1.30151			0.0540421
$581$	−8.03100	−	18.6400i	−0.333182	−	0.773316i
$582$	55.8488			2.31501
$583$	5.67779	+	9.83421i	0.235150	+	0.407291i
$584$	−0.289810	+	0.501967i	−0.0119924	+	0.0207715i
$585$	−1.37799	+	2.38674i	−0.0569727	+	0.0986796i
$586$	12.9136	+	22.3671i	0.533458	+	0.923976i
$587$	29.8115			1.23045			0.615226	−	0.788351i	$-0.289065\pi$
$587$	29.8115			1.23045			0.615226	+	0.788351i	$0.289065\pi$
$588$	−32.9675	−	7.84334i	−1.35956	−	0.323454i
$589$	−23.5399			−0.969943
$590$	−2.72370	−	4.71759i	−0.112133	−	0.194220i
$591$	−11.4072	+	19.7579i	−0.469230	+	0.812730i
$592$	2.23093	−	3.86408i	0.0916906	−	0.158813i
$593$	−13.6878	−	23.7080i	−0.562091	−	0.973570i	−0.997314	−	0.0732474i	$-0.976664\pi$
$593$	−13.6878	−	23.7080i	−0.562091	−	0.973570i	0.435223	−	0.900323i	$-0.356670\pi$
$594$	42.2712			1.73441
$595$	−5.98201	−	13.8842i	−0.245238	−	0.569198i
$596$	−20.0066			−0.819502
$597$	−30.1176	−	52.1653i	−1.23263	−	2.13498i
$598$	0.313717	−	0.543373i	0.0128288	−	0.0222202i
$599$	15.6684	−	27.1385i	0.640194	−	1.10885i	−0.345195	−	0.938531i	$-0.612187\pi$
$599$	15.6684	−	27.1385i	0.640194	−	1.10885i	0.985389	−	0.170318i	$-0.0544794\pi$
$600$	−0.718774	−	1.24495i	−0.0293438	−	0.0508250i
$601$	8.15855			0.332794			0.166397	−	0.986059i	$-0.446787\pi$
$601$	8.15855			0.332794			0.166397	+	0.986059i	$0.446787\pi$
$602$	19.7783	−	26.5431i	0.806105	−	1.08182i
$603$	−29.5547			−1.20356
$604$	9.86501	+	17.0867i	0.401402	+	0.695248i
$605$	−3.98916	+	6.90943i	−0.162182	+	0.280908i
$606$	−23.4873	+	40.6811i	−0.954105	+	1.65256i
$607$	−13.2916	−	23.0217i	−0.539489	−	0.934422i	−0.998932	−	0.0462146i	$-0.985284\pi$
$607$	−13.2916	−	23.0217i	−0.539489	−	0.934422i	0.459443	−	0.888207i	$-0.348049\pi$
$608$	−23.0110			−0.933219
$609$	−5.50911	−	0.646320i	−0.223240	−	0.0261902i
$610$	20.4167			0.826646
$611$	1.49877	+	2.59595i	0.0606338	+	0.105021i
$612$	−23.7655	+	41.1630i	−0.960663	+	1.66392i
$613$	−2.04531	+	3.54258i	−0.0826094	+	0.143084i	−0.904370	−	0.426749i	$-0.859659\pi$
$613$	−2.04531	+	3.54258i	−0.0826094	+	0.143084i	0.821761	+	0.569833i	$0.192992\pi$
$614$	22.8369	+	39.5547i	0.921622	+	1.59630i
$615$	−26.1589			−1.05483
$616$	5.89296	+	0.691352i	0.237434	+	0.0278554i
$617$	−19.7115			−0.793554			−0.396777	−	0.917915i	$-0.629871\pi$
$617$	−19.7115			−0.793554			−0.396777	+	0.917915i	$0.629871\pi$
$618$	28.9261	+	50.1014i	1.16358	+	2.01537i
$619$	−12.2991	+	21.3027i	−0.494342	+	0.856226i	−0.999979	−	0.00652074i	$-0.997924\pi$
$619$	−12.2991	+	21.3027i	−0.494342	+	0.856226i	0.505636	+	0.862747i	$0.331258\pi$
$620$	6.73179	−	11.6598i	0.270355	−	0.468269i
$621$	−1.41950	−	2.45865i	−0.0569627	−	0.0986623i
$622$	−48.6860			−1.95213
$623$	4.94306	−	6.63373i	0.198039	−	0.265775i
$624$	7.15657			0.286492
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.219782	−	0.380674i	0.00878427	−	0.0152148i
$627$	−18.4368	+	31.9335i	−0.736295	+	1.27530i
$628$	−3.81711	−	6.61143i	−0.152319	−	0.263825i
$629$	5.71410			0.227836
$630$	−9.70614	−	22.5279i	−0.386702	−	0.897535i
$631$	25.0708			0.998053			0.499026	−	0.866587i	$-0.333691\pi$
$631$	25.0708			0.998053			0.499026	+	0.866587i	$0.333691\pi$
$632$	−3.42204	−	5.92714i	−0.136121	−	0.235769i
$633$	4.93922	−	8.55498i	0.196316	−	0.340030i
$634$	6.66606	−	11.5460i	0.264743	−	0.458548i
$635$	−1.69673	−	2.93882i	−0.0673325	−	0.116623i
$636$	−12.6190			−0.500375
$637$	−2.76160	+	2.92209i	−0.109419	+	0.115778i
$638$	−6.31966			−0.250198
$639$	−18.5657	−	32.1567i	−0.734446	−	1.27210i
$640$	−2.04086	+	3.53487i	−0.0806721	+	0.139728i
$641$	11.3347	−	19.6322i	0.447692	−	0.775425i	−0.550543	−	0.834807i	$-0.685579\pi$
$641$	11.3347	−	19.6322i	0.447692	−	0.775425i	0.998235	+	0.0593813i	$0.0189128\pi$
$642$	−1.38507	−	2.39901i	−0.0546643	−	0.0946813i
$643$	4.37475			0.172523			0.0862617	−	0.996273i	$-0.472508\pi$
$643$	4.37475			0.172523			0.0862617	+	0.996273i	$0.472508\pi$
$644$	1.02603	+	2.38140i	0.0404311	+	0.0938405i
$645$	18.0816			0.711962
$646$	−16.7328	−	28.9820i	−0.658343	−	1.14028i
$647$	2.32724	−	4.03090i	0.0914934	−	0.158471i	−0.816646	−	0.577138i	$-0.804169\pi$
$647$	2.32724	−	4.03090i	0.0914934	−	0.158471i	0.908140	+	0.418667i	$0.137503\pi$
$648$	−0.0956081	+	0.165598i	−0.00375584	+	0.00650531i
$649$	6.14081	+	10.6362i	0.241048	+	0.417507i
$650$	1.10982			0.0435308
$651$	−34.2850	+	46.0115i	−1.34373	+	1.80333i
$652$	10.4092			0.407657
$653$	6.71055	+	11.6230i	0.262604	+	0.454844i	0.966933	−	0.255030i	$-0.0820854\pi$
$653$	6.71055	+	11.6230i	0.262604	+	0.454844i	−0.704329	+	0.709874i	$0.748752\pi$
$654$	33.8376	−	58.6085i	1.32316	−	2.29177i
$655$	6.86969	−	11.8986i	0.268421	−	0.464919i
$656$	20.8981	+	36.1965i	0.815933	+	1.41324i
$657$	−5.40262			−0.210776
$658$	−26.4983	−	3.10874i	−1.03301	−	0.121191i
$659$	46.9584			1.82924			0.914620	−	0.404315i	$-0.132490\pi$
$659$	46.9584			1.82924			0.914620	+	0.404315i	$0.132490\pi$
$660$	−10.5449	−	18.2643i	−0.410460	−	0.710937i
$661$	19.2808	−	33.3953i	0.749936	−	1.29893i	−0.197917	−	0.980219i	$-0.563418\pi$
$661$	19.2808	−	33.3953i	0.749936	−	1.29893i	0.947853	−	0.318708i	$-0.103249\pi$
$662$	5.86096	−	10.1515i	0.227793	−	0.394548i
$663$	4.58255	+	7.93721i	0.177971	+	0.308256i
$664$	−3.94906			−0.153253
$665$	7.96468	+	0.934404i	0.308857	+	0.0362346i
$666$	9.27144			0.359261
$667$	0.212220	+	0.367575i	0.00821718	+	0.0142326i
$668$	21.5699	−	37.3602i	0.834565	−	1.44551i
$669$	33.7912	−	58.5281i	1.30644	−	2.26283i
$670$	5.95080	+	10.3071i	0.229900	+	0.398198i
$671$	−46.0310			−1.77701
$672$	−33.5147	+	44.9777i	−1.29286	+	1.73505i
$673$	−30.7969			−1.18713			−0.593567	−	0.804784i	$-0.702281\pi$
$673$	−30.7969			−1.18713			−0.593567	+	0.804784i	$0.702281\pi$
$674$	−3.86575	−	6.69568i	−0.148903	−	0.257908i
$675$	2.51086	−	4.34894i	0.0966431	−	0.167391i
$676$	10.9823	−	19.0220i	0.422398	−	0.731614i
$677$	−19.8537	−	34.3876i	−0.763040	−	1.32162i	−0.941277	−	0.337637i	$-0.890373\pi$
$677$	−19.8537	−	34.3876i	−0.763040	−	1.32162i	0.178236	−	0.983988i	$-0.442961\pi$
$678$	31.4177			1.20659
$679$	10.8355	+	25.1493i	0.415830	+	0.965142i
$680$	−2.94152			−0.112802
$681$	33.6094	+	58.2131i	1.28791	+	2.23073i
$682$	−32.6872	+	56.6159i	−1.25166	+	2.16793i
$683$	−18.0821	+	31.3192i	−0.691894	+	1.19840i	0.279323	+	0.960197i	$0.409890\pi$
$683$	−18.0821	+	31.3192i	−0.691894	+	1.19840i	−0.971217	+	0.238198i	$0.923443\pi$
$684$	−12.6063	−	21.8347i	−0.482013	−	0.834871i
$685$	−10.6541			−0.407072
$686$	−6.16874	−	35.2500i	−0.235524	−	1.34585i
$687$	−77.1723			−2.94431
$688$	−14.4452	−	25.0198i	−0.550718	−	0.953871i
$689$	−0.748584	+	1.29659i	−0.0285188	+	0.0493960i
$690$	−1.52527	+	2.64184i	−0.0580659	+	0.100573i
$691$	17.7928	+	30.8180i	0.676868	+	1.17237i	0.975919	+	0.218133i	$0.0699967\pi$
$691$	17.7928	+	30.8180i	0.676868	+	1.17237i	−0.299051	+	0.954237i	$0.596670\pi$
$692$	−25.2425			−0.959578
$693$	21.8833	+	50.7911i	0.831277	+	1.92939i
$694$	37.4835			1.42285
$695$	1.95217	+	3.38125i	0.0740499	+	0.128258i
$696$	−0.539628	+	0.934663i	−0.0204545	+	0.0354283i
$697$	−26.7632	+	46.3553i	−1.01373	+	1.75583i
$698$	18.2623	+	31.6313i	0.691239	+	1.19726i
$699$	−26.1944			−0.990764
$700$	−2.74053	+	3.67787i	−0.103582	+	0.139010i
$701$	40.8015			1.54105			0.770526	−	0.637408i	$-0.219994\pi$
$701$	40.8015			1.54105			0.770526	+	0.637408i	$0.219994\pi$
$702$	2.78661	+	4.82655i	0.105174	+	0.182166i
$703$	−1.51551	+	2.62493i	−0.0571584	+	0.0990013i
$704$	−12.5152	+	21.6769i	−0.471683	+	0.816978i
$705$	−7.28692	−	12.6213i	−0.274441	−	0.475346i
$706$	−59.1921			−2.22773
$707$	−22.8761	−	2.68378i	−0.860342	−	0.100934i
$708$	−13.6480			−0.512925
$709$	12.9618	+	22.4506i	0.486792	+	0.843148i	0.999885	−	0.0151848i	$-0.00483365\pi$
$709$	12.9618	+	22.4506i	0.486792	+	0.843148i	−0.513093	+	0.858333i	$0.671500\pi$
$710$	−7.47634	+	12.9494i	−0.280582	+	0.485982i
$711$	31.8967	−	55.2466i	1.19622	−	2.07191i
$712$	−0.804823	−	1.39399i	−0.0301620	−	0.0522421i
$713$	4.39066			0.164432
$714$	−81.0196	−	9.50509i	−3.03208	−	0.355719i
$715$	−2.50219			−0.0935764
$716$	18.8698	+	32.6834i	0.705197	+	1.22144i
$717$	31.8135	−	55.1026i	1.18810	−	2.05784i
$718$	−8.88367	+	15.3870i	−0.331535	+	0.574236i
$719$	−13.5459	−	23.4621i	−0.505175	−	0.874989i	−0.999982	−	0.00598620i	$-0.998095\pi$
$719$	−13.5459	−	23.4621i	−0.505175	−	0.874989i	0.494807	−	0.869003i	$-0.335239\pi$
$720$	−21.4092			−0.797872
$721$	−16.9491	+	22.7462i	−0.631217	+	0.847112i
$722$	−18.9611			−0.705658
$723$	33.9800	+	58.8551i	1.26373	+	2.18885i
$724$	2.22300	−	3.85034i	0.0826170	−	0.143097i
$725$	−0.375380	+	0.650178i	−0.0139413	+	0.0241470i
$726$	21.5250	+	37.2824i	0.798868	+	1.38368i
$727$	31.2736			1.15987			0.579936	−	0.814662i	$-0.303077\pi$
$727$	31.2736			1.15987			0.579936	+	0.814662i	$0.303077\pi$
$728$	0.309538	+	0.718437i	0.0114722	+	0.0266270i
$729$	−43.8523			−1.62416
$730$	1.08781	+	1.88414i	0.0402617	+	0.0697353i
$731$	18.4993	−	32.0417i	0.684221	−	1.18511i
$732$	25.5762	−	44.2992i	0.945322	−	1.63735i
$733$	−9.37859	−	16.2442i	−0.346406	−	0.599993i	0.639202	−	0.769039i	$-0.279265\pi$
$733$	−9.37859	−	16.2442i	−0.346406	−	0.599993i	−0.985608	+	0.169046i	$0.945931\pi$
$734$	21.9837			0.811434
$735$	13.4267	−	14.2070i	0.495251	−	0.524033i
$736$	4.29202			0.158206
$737$	−13.4166	−	23.2382i	−0.494206	−	0.855990i
$738$	−43.4248	+	75.2140i	−1.59849	+	2.76867i
$739$	5.63447	−	9.75919i	0.207267	−	0.358997i	−0.743585	−	0.668641i	$-0.766876\pi$
$739$	5.63447	−	9.75919i	0.207267	−	0.358997i	0.950853	+	0.309643i	$0.100210\pi$
$740$	−0.866792	−	1.50133i	−0.0318639	−	0.0551899i
$741$	−4.86158			−0.178595
$742$	−5.27281	−	12.2382i	−0.193571	−	0.449278i
$743$	32.8940			1.20676			0.603382	−	0.797453i	$-0.293820\pi$
$743$	32.8940			1.20676			0.603382	+	0.797453i	$0.293820\pi$
$744$	5.58224	+	9.66872i	0.204655	+	0.354473i
$745$	5.77030	−	9.99445i	0.211407	−	0.366168i
$746$	9.52324	−	16.4947i	0.348670	−	0.603915i
$747$	−18.4045	−	31.8776i	−0.673387	−	1.16634i
$748$	−43.1540			−1.57787
$749$	0.811574	−	1.08916i	0.0296543	−	0.0397969i
$750$	−5.39588			−0.197030
$751$	17.7709	+	30.7800i	0.648468	+	1.12318i	0.983489	+	0.180969i	$0.0579232\pi$
$751$	17.7709	+	30.7800i	0.648468	+	1.12318i	−0.335021	+	0.942211i	$0.608743\pi$
$752$	−11.6429	+	20.1661i	−0.424572	+	0.735380i
$753$	−36.0448	+	62.4314i	−1.31354	+	2.27513i
$754$	−0.416606	−	0.721582i	−0.0151719	−	0.0262785i
$755$	−11.3811			−0.414199
$756$	−22.8759	−	2.68376i	−0.831988	−	0.0976075i
$757$	39.0205			1.41822			0.709112	−	0.705096i	$-0.249096\pi$
$757$	39.0205			1.41822			0.709112	+	0.705096i	$0.249096\pi$
$758$	23.4328	+	40.5868i	0.851118	+	1.47418i
$759$	3.43884	−	5.95624i	0.124822	−	0.216198i
$760$	0.780156	−	1.35127i	0.0282992	−	0.0490157i
$761$	16.9042	+	29.2789i	0.612776	+	1.06136i	0.990770	+	0.135551i	$0.0432806\pi$
$761$	16.9042	+	29.2789i	0.612776	+	1.06136i	−0.377994	+	0.925808i	$0.623386\pi$
$762$	−18.3107			−0.663325
$763$	32.9571	+	3.86647i	1.19313	+	0.139976i
$764$	2.23673			0.0809219
$765$	−13.7089	−	23.7445i	−0.495645	−	0.858483i
$766$	−17.3022	+	29.9683i	−0.625153	+	1.08280i
$767$	−0.809631	+	1.40232i	−0.0292341	+	0.0506349i
$768$	27.0571	+	46.8643i	0.976339	+	1.69107i
$769$	5.02796			0.181313			0.0906564	−	0.995882i	$-0.471104\pi$
$769$	5.02796			0.181313			0.0906564	+	0.995882i	$0.471104\pi$
$770$	13.3070	−	17.8584i	0.479552	−	0.643573i
$771$	71.1724			2.56321
$772$	9.85119	+	17.0628i	0.354552	+	0.614102i
$773$	21.6775	−	37.5465i	0.779685	−	1.35045i	−0.152438	−	0.988313i	$-0.548712\pi$
$773$	21.6775	−	37.5465i	0.779685	−	1.35045i	0.932123	−	0.362142i	$-0.117954\pi$
$774$	30.0161	−	51.9895i	1.07891	−	1.86872i
$775$	3.88317	+	6.72584i	0.139487	+	0.241599i
$776$	5.32813			0.191269
$777$	2.92347	+	6.78537i	0.104879	+	0.243424i
$778$	74.1313			2.65773
$779$	−14.1964	−	24.5889i	−0.508639	−	0.880989i
$780$	1.39029	−	2.40805i	0.0497803	−	0.0862219i
$781$	16.8560	−	29.1955i	0.603156	−	1.04470i
$782$	3.12101	+	5.40574i	0.111607	+	0.193309i
$783$	−3.77011			−0.134733
$784$	−30.3849	−	7.22891i	−1.08517	−	0.258175i
$785$	4.40372			0.157176
$786$	−37.0680	−	64.2036i	−1.32217	−	2.29007i
$787$	−24.6037	+	42.6149i	−0.877028	+	1.51906i	−0.0224414	+	0.999748i	$0.507144\pi$
$787$	−24.6037	+	42.6149i	−0.877028	+	1.51906i	−0.854587	+	0.519309i	$0.826189\pi$
$788$	7.08150	−	12.2655i	0.252268	−	0.436941i
$789$	12.9796	+	22.4814i	0.462087	+	0.800358i
$790$	−25.6894			−0.913988
$791$	6.09554	+	14.1477i	0.216732	+	0.503036i
$792$	10.7606			0.382361
$793$	−3.03447	−	5.25585i	−0.107757	−	0.186641i
$794$	−26.5844	+	46.0455i	−0.943444	+	1.63409i
$795$	3.63956	−	6.30391i	0.129082	−	0.223576i
$796$	18.6968	+	32.3838i	0.662690	+	1.14781i
$797$	36.2021			1.28235			0.641173	−	0.767397i	$-0.278448\pi$
$797$	36.2021			1.28235			0.641173	+	0.767397i	$0.278448\pi$
$798$	25.8547	−	34.6977i	0.915245	−	1.22829i
$799$	−29.8210			−1.05499
$800$	3.79592	+	6.57473i	0.134206	+	0.232452i
$801$	7.50172	−	12.9934i	0.265060	−	0.459098i
$802$	16.3808	−	28.3724i	0.578427	−	1.00187i
$803$	−2.45256	−	4.24796i	−0.0865489	−	0.149907i
$804$	29.8186			1.05162
$805$	−1.48558	−	0.174285i	−0.0523596	−	0.00614275i
$806$	−8.61925			−0.303600
$807$	−9.17699	−	15.8950i	−0.323045	−	0.559531i
$808$	−2.24075	+	3.88110i	−0.0788294	+	0.136537i
$809$	24.5863	−	42.5847i	0.864407	−	1.49720i	−0.00322702	−	0.999995i	$-0.501027\pi$
$809$	24.5863	−	42.5847i	0.864407	−	1.49720i	0.867634	−	0.497203i	$-0.165639\pi$
$810$	0.358868	+	0.621577i	0.0126093	+	0.0218400i
$811$	28.8925			1.01455			0.507276	−	0.861784i	$-0.330653\pi$
$811$	28.8925			1.01455			0.507276	+	0.861784i	$0.330653\pi$
$812$	3.42001	+	0.401230i	0.120019	+	0.0140804i
$813$	0.242654			0.00851023
$814$	4.20883	+	7.28992i	0.147520	+	0.255511i
$815$	−3.00223	+	5.20001i	−0.105164	+	0.182149i
$816$	−35.5985	+	61.6585i	−1.24620	+	2.15848i
$817$	9.81286	+	16.9964i	0.343309	+	0.594628i
$818$	−31.1747			−1.09000
$819$	−4.35676	+	5.84691i	−0.152238	+	0.204307i
$820$	16.2392			0.567099
$821$	10.3125	+	17.8617i	0.359907	+	0.623378i	0.987945	−	0.154805i	$-0.0494749\pi$
$821$	10.3125	+	17.8617i	0.359907	+	0.623378i	−0.628038	+	0.778183i	$0.716142\pi$
$822$	−28.7441	+	49.7862i	−1.00257	+	1.73649i
$823$	16.2127	−	28.0812i	0.565138	−	0.978848i	−0.431899	−	0.901922i	$-0.642156\pi$
$823$	16.2127	−	28.0812i	0.565138	−	0.978848i	0.997037	−	0.0769260i	$-0.0245105\pi$
$824$	2.75963	+	4.77982i	0.0961363	+	0.166513i
$825$	12.1654			0.423546
$826$	−5.70281	−	13.2362i	−0.198426	−	0.460547i
$827$	51.3850			1.78683			0.893416	−	0.449231i	$-0.148302\pi$
$827$	51.3850			1.78683			0.893416	+	0.449231i	$0.148302\pi$
$828$	2.35133	+	4.07262i	0.0817143	+	0.141533i
$829$	−26.3364	+	45.6160i	−0.914701	+	1.58431i	−0.107363	+	0.994220i	$0.534241\pi$
$829$	−26.3364	+	45.6160i	−0.914701	+	1.58431i	−0.807338	+	0.590089i	$0.799093\pi$
$830$	−7.41146	+	12.8370i	−0.257255	+	0.445579i
$831$	−18.9457	−	32.8150i	−0.657220	−	1.13834i
$832$	−3.30011			−0.114411
$833$	−11.4388	−	38.3281i	−0.396333	−	1.32799i
$834$	21.0673			0.729501
$835$	12.4424	+	21.5508i	0.430586	+	0.745798i
$836$	11.4454	−	19.8240i	0.395848	−	0.685629i
$837$	−19.5002	+	33.7753i	−0.674025	+	1.16744i
$838$	23.2610	+	40.2893i	0.803539	+	1.39177i
$839$	−14.9149			−0.514919			−0.257459	−	0.966289i	$-0.582885\pi$
$839$	−14.9149			−0.514919			−0.257459	+	0.966289i	$0.582885\pi$
$840$	−1.50495	−	3.49299i	−0.0519257	−	0.120519i
$841$	−28.4364			−0.980564
$842$	−37.1306	−	64.3121i	−1.27961	−	2.21634i
$843$	−35.7712	+	61.9575i	−1.23203	+	2.13393i
$844$	−3.06623	+	5.31086i	−0.105544	+	0.182807i
$845$	6.33505	+	10.9726i	0.217932	+	0.377470i
$846$	−48.3863			−1.66355
$847$	−12.6125	+	16.9263i	−0.433370	+	0.581596i
$848$	−11.6304			−0.399390
$849$	−14.3608	−	24.8736i	−0.492860	−	0.853658i
$850$	−5.52053	+	9.56183i	−0.189353	+	0.327968i
$851$	0.282673	−	0.489604i	0.00968990	−	0.0167834i
$852$	18.7314	+	32.4437i	0.641727	+	1.11150i
$853$	31.7770			1.08802			0.544011	−	0.839078i	$-0.316905\pi$
$853$	31.7770			1.08802			0.544011	+	0.839078i	$0.316905\pi$
$854$	53.6495	+	6.29407i	1.83585	+	0.215379i
$855$	14.5436			0.497381
$856$	−0.132140	−	0.228872i	−0.00451644	−	0.00782270i
$857$	13.7830	−	23.8728i	0.470818	−	0.815480i	−0.528625	−	0.848855i	$-0.677292\pi$
$857$	13.7830	−	23.8728i	0.470818	−	0.815480i	0.999443	+	0.0333754i	$0.0106257\pi$
$858$	−6.75074	+	11.6926i	−0.230467	+	0.399180i
$859$	−5.51336	−	9.54943i	−0.188114	−	0.325822i	0.756508	−	0.653985i	$-0.226904\pi$
$859$	−5.51336	−	9.54943i	−0.188114	−	0.325822i	−0.944621	+	0.328163i	$0.893571\pi$
$860$	−11.2249			−0.382766
$861$	−68.7386	−	8.06430i	−2.34260	−	0.274831i
$862$	−23.2622			−0.792313
$863$	−4.59720	−	7.96258i	−0.156491	−	0.271050i	0.777110	−	0.629365i	$-0.216685\pi$
$863$	−4.59720	−	7.96258i	−0.156491	−	0.271050i	−0.933601	+	0.358315i	$0.883351\pi$
$864$	−19.0621	+	33.0165i	−0.648505	+	1.12324i
$865$	7.28045	−	12.6101i	0.247543	−	0.428757i
$866$	20.3678	+	35.2781i	0.692128	+	1.19880i
$867$	−43.7057			−1.48432
$868$	21.2838	−	28.5635i	0.722420	−	0.969509i
$869$	57.9188			1.96476
$870$	2.02551	+	3.50828i	0.0686711	+	0.118942i
$871$	1.76890	−	3.06383i	0.0599369	−	0.103814i
$872$	3.22821	−	5.59142i	0.109321	−	0.189349i
$873$	24.8317	+	43.0097i	0.840424	+	1.45566i
$874$	−3.31104			−0.111998
$875$	−1.04689	−	2.42982i	−0.0353912	−	0.0821429i
$876$	5.45085			0.184167
$877$	17.8552	+	30.9261i	0.602926	+	1.04430i	0.992376	+	0.123251i	$0.0393320\pi$
$877$	17.8552	+	30.9261i	0.602926	+	1.04430i	−0.389449	+	0.921048i	$0.627335\pi$
$878$	−24.4947	+	42.4260i	−0.826655	+	1.43181i
$879$	−18.6631	+	32.3255i	−0.629492	+	1.09031i
$880$	−9.71884	−	16.8335i	−0.327622	−	0.567458i
$881$	44.8393			1.51068			0.755338	−	0.655336i	$-0.227473\pi$
$881$	44.8393			1.51068			0.755338	+	0.655336i	$0.227473\pi$
$882$	−18.5602	−	62.1895i	−0.624953	−	2.09403i
$883$	16.5572			0.557195			0.278598	−	0.960408i	$-0.410130\pi$
$883$	16.5572			0.557195			0.278598	+	0.960408i	$0.410130\pi$
$884$	−2.84481	−	4.92735i	−0.0956813	−	0.165725i
$885$	3.93637	−	6.81799i	0.132320	−	0.229184i
$886$	30.5696	−	52.9482i	1.02701	−	1.77883i
$887$	−28.6347	−	49.5968i	−0.961461	−	1.66530i	−0.718838	−	0.695178i	$-0.755326\pi$
$887$	−28.6347	−	49.5968i	−0.961461	−	1.66530i	−0.242623	−	0.970121i	$-0.578008\pi$
$888$	1.43755			0.0482410
$889$	−3.55256	−	8.24548i	−0.119149	−	0.276545i
$890$	−6.04185			−0.202523
$891$	−0.809096	−	1.40140i	−0.0271057	−	0.0469485i
$892$	−20.9773	+	36.3338i	−0.702372	+	1.21654i
$893$	7.90921	−	13.6991i	0.264671	−	0.458424i
$894$	−31.1358	−	53.9288i	−1.04134	−	1.80365i
$895$	−21.7697			−0.727680
$896$	−6.45256	+	8.65953i	−0.215565	+	0.289295i
$897$	0.906783			0.0302766
$898$	−10.3380	−	17.9059i	−0.344983	−	0.597527i
$899$	2.91533	−	5.04950i	0.0972317	−	0.168410i
$900$	−4.15910	+	7.20377i	−0.138637	+	0.240126i
$901$	−7.44728	−	12.8991i	−0.248105	−	0.429730i
$902$	−78.8520			−2.62548
$903$	47.5135	+	5.57421i	1.58115	+	0.185498i
$904$	2.99734			0.0996901
$905$	1.28231	+	2.22103i	0.0426255	+	0.0738296i
$906$	−30.7054	+	53.1833i	−1.02012	+	1.76690i
$907$	6.21587	−	10.7662i	0.206395	−	0.357486i	−0.744182	−	0.667977i	$-0.767160\pi$
$907$	6.21587	−	10.7662i	0.206395	−	0.357486i	0.950576	+	0.310491i	$0.100494\pi$
$908$	−20.8644	−	36.1382i	−0.692410	−	1.19929i
$909$	−41.7719			−1.38549
$910$	2.91631	+	0.342137i	0.0966749	+	0.0113417i
$911$	1.47427			0.0488446			0.0244223	−	0.999702i	$-0.492225\pi$
$911$	1.47427			0.0488446			0.0244223	+	0.999702i	$0.492225\pi$
$912$	−18.8831	−	32.7064i	−0.625281	−	1.08302i
$913$	16.7097	−	28.9421i	0.553011	−	0.957844i
$914$	18.7084	−	32.4039i	0.618819	−	1.07183i
$915$	14.7534	+	25.5536i	0.487731	+	0.844774i
$916$	47.9079			1.58292
$917$	21.7198	−	29.1486i	0.717251	−	0.962573i
$918$	−55.4451			−1.82996
$919$	20.7386	+	35.9202i	0.684102	+	1.18490i	0.973718	+	0.227756i	$0.0731389\pi$
$919$	20.7386	+	35.9202i	0.684102	+	1.18490i	−0.289617	+	0.957143i	$0.593528\pi$
$920$	−0.145515	+	0.252039i	−0.00479749	+	0.00830949i
$921$	−33.0045	+	57.1655i	−1.08754	+	1.88367i
$922$	22.5961	+	39.1376i	0.744164	+	1.28893i
$923$	4.44474			0.146301
$924$	−22.0786	−	51.2445i	−0.726333	−	1.68582i
$925$	1.00000			0.0328798
$926$	−15.6860	−	27.1690i	−0.515475	−	0.892829i
$927$	−25.7224	+	44.5525i	−0.844835	+	1.46330i
$928$	2.84983	−	4.93605i	0.0935503	−	0.162034i
$929$	−26.0067	−	45.0449i	−0.853251	−	1.47787i	−0.878258	−	0.478188i	$-0.841294\pi$
$929$	−26.0067	−	45.0449i	−0.853251	−	1.47787i	0.0250063	−	0.999687i	$-0.492039\pi$
$930$	41.9062			1.37416
$931$	20.6410	+	4.91072i	0.676481	+	0.160942i
$932$	16.2613			0.532656
$933$	−35.1811	−	60.9355i	−1.15178	−	1.99494i
$934$	10.8152	−	18.7324i	0.353884	−	0.612944i
$935$	12.4465	−	21.5579i	0.407043	−	0.705020i
$936$	0.709363	+	1.22865i	0.0231862	+	0.0401598i
$937$	4.28374			0.139944			0.0699718	−	0.997549i	$-0.477709\pi$
$937$	4.28374			0.139944			0.0699718	+	0.997549i	$0.477709\pi$
$938$	12.4596	+	28.9188i	0.406821	+	0.944232i
$939$	0.635271			0.0207313
$940$	4.52366	+	7.83521i	0.147545	+	0.255556i
$941$	−12.4323	+	21.5333i	−0.405281	+	0.701967i	−0.994354	−	0.106113i	$-0.966160\pi$
$941$	−12.4323	+	21.5333i	−0.405281	+	0.701967i	0.589073	+	0.808080i	$0.299493\pi$
$942$	11.8810	−	20.5784i	0.387103	−	0.670482i
$943$	2.64792	+	4.58633i	0.0862281	+	0.149352i
$944$	−12.5789			−0.409408
$945$	7.93856	−	10.6538i	0.258241	−	0.346568i
$946$	54.5042			1.77208
$947$	−26.3989	−	45.7243i	−0.857849	−	1.48584i	−0.873976	−	0.485969i	$-0.838467\pi$
$947$	−26.3989	−	45.7243i	−0.857849	−	1.48584i	0.0161270	−	0.999870i	$-0.494866\pi$
$948$	−32.1814	+	55.7398i	−1.04520	+	1.81034i
$949$	0.323356	−	0.560069i	0.0104966	−	0.0181806i
$950$	−2.92834	−	5.07203i	−0.0950078	−	0.164558i
$951$	19.2679			0.624805
$952$	−7.72951	−	0.906813i	−0.250515	−	0.0293900i
$953$	55.7613			1.80628			0.903142	−	0.429341i	$-0.141254\pi$
$953$	55.7613			1.80628			0.903142	+	0.429341i	$0.141254\pi$
$954$	−12.0836	−	20.9295i	−0.391222	−	0.677616i
$955$	−0.645116	+	1.11737i	−0.0208755	+	0.0361574i
$956$	−19.7495	+	34.2072i	−0.638746	+	1.10634i
$957$	−4.56667	−	7.90970i	−0.147619	−	0.255684i
$958$	−12.8232			−0.414298
$959$	−27.9961	−	3.28446i	−0.904041	−	0.106061i
$960$	16.0449			0.517846
$961$	−14.6579	−	25.3883i	−0.472837	−	0.818977i
$962$	−0.554911	+	0.961135i	−0.0178911	+	0.0309882i
$963$	1.23167	−	2.13331i	0.0396899	−	0.0687450i
$964$	−21.0945	−	36.5368i	−0.679408	−	1.17677i
$965$	−11.3651			−0.365856
$966$	−4.82242	+	6.47183i	−0.155159	+	0.208228i
$967$	1.40998			0.0453419			0.0226710	−	0.999743i	$-0.492783\pi$
$967$	1.40998			0.0453419			0.0226710	+	0.999743i	$0.492783\pi$
$968$	2.05355	+	3.55685i	0.0660036	+	0.114322i
$969$	24.1827	−	41.8856i	0.776860	−	1.34556i
$970$	9.99964	−	17.3199i	0.321069	−	0.556108i
$971$	−21.6292	−	37.4628i	−0.694114	−	1.20224i	−0.970479	−	0.241187i	$-0.922463\pi$
$971$	−21.6292	−	37.4628i	−0.694114	−	1.20224i	0.276365	−	0.961053i	$-0.410870\pi$
$972$	27.9150			0.895372
$973$	4.08739	+	9.48683i	0.131036	+	0.304134i
$974$	−73.7079			−2.36175
$975$	0.801973	+	1.38906i	0.0256837	+	0.0444854i
$976$	23.5726	−	40.8289i	0.754540	−	1.30690i
$977$	−4.39354	+	7.60984i	−0.140562	+	0.243460i	−0.927708	−	0.373306i	$-0.878224\pi$
$977$	−4.39354	+	7.60984i	−0.140562	+	0.243460i	0.787146	+	0.616766i	$0.211558\pi$
$978$	16.1997	+	28.0586i	0.518008	+	0.897216i
$979$	13.6218			0.435356
$980$	−8.33518	+	8.81959i	−0.266257	+	0.281731i
$981$	60.1800			1.92140
$982$	19.0954	+	33.0742i	0.609358	+	1.05544i
$983$	9.55447	−	16.5488i	0.304740	−	0.527826i	−0.672463	−	0.740131i	$-0.734764\pi$
$983$	9.55447	−	16.5488i	0.304740	−	0.527826i	0.977203	+	0.212305i	$0.0680970\pi$
$984$	−6.73307	+	11.6620i	−0.214643	+	0.371772i
$985$	4.08489	+	7.07524i	0.130155	+	0.225436i
$986$	8.28919			0.263982
$987$	−15.2571	−	35.4118i	−0.485640	−	1.12717i
$988$	3.01803			0.0960163
$989$	−1.83030	−	3.17017i	−0.0582001	−	0.100805i
$990$	20.1951	−	34.9789i	0.641842	−	1.11170i
$991$	4.21801	−	7.30581i	0.133990	−	0.232077i	−0.791221	−	0.611530i	$-0.790554\pi$
$991$	4.21801	−	7.30581i	0.133990	−	0.232077i	0.925211	+	0.379453i	$0.123888\pi$
$992$	−29.4804	−	51.0615i	−0.936003	−	1.62121i
$993$	16.9408			0.537601
$994$	−23.6379	+	31.7227i	−0.749747	+	1.00618i
$995$	−21.5701			−0.683818
$996$	18.5688	+	32.1621i	0.588376	+	1.01910i
$997$	19.2547	−	33.3501i	0.609802	−	1.05621i	−0.381470	−	0.924381i	$-0.624582\pi$
$997$	19.2547	−	33.3501i	0.609802	−	1.05621i	0.991273	−	0.131828i	$-0.0420845\pi$
$998$	32.4018	−	56.1215i	1.02566	−	1.77650i
$999$	2.51086	+	4.34894i	0.0794401	+	0.137594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.3	✓	38
7.2	even	3	inner	1295.2.j.a.926.3	yes	38
7.3	odd	6		9065.2.a.s.1.17		19
7.4	even	3		9065.2.a.r.1.17		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.3	✓	38	1.1	even	1	trivial
1295.2.j.a.926.3	yes	38	7.2	even	3	inner
9065.2.a.r.1.17		19	7.4	even	3
9065.2.a.s.1.17		19	7.3	odd	6

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:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.966124 - 1.67338i) q^{2} +(1.39627 - 2.41841i) q^{3} +(-0.866792 + 1.50133i) q^{4} +(-0.500000 - 0.866025i) q^{5} -5.39588 q^{6} +(-1.04689 - 2.42982i) q^{7} -0.514782 q^{8} +(-2.39913 - 4.15542i) q^{9} +(-0.966124 + 1.67338i) q^{10} +(2.17821 - 3.77276i) q^{11} +(2.42055 + 4.19251i) q^{12} +0.574369 q^{13} +(-3.05458 + 4.09934i) q^{14} -2.79254 q^{15} +(2.23093 + 3.86408i) q^{16} +(-2.85705 + 4.94855i) q^{17} +(-4.63572 + 8.02930i) q^{18} +(-1.51551 - 2.62493i) q^{19} +1.73358 q^{20} +(-7.33803 - 0.860886i) q^{21} -8.41767 q^{22} +(0.282673 + 0.489604i) q^{23} +(-0.718774 + 1.24495i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.554911 - 0.961135i) q^{26} -5.02172 q^{27} +(4.55539 + 0.534431i) q^{28} +0.750761 q^{29} +(2.69794 + 4.67297i) q^{30} +(3.88317 - 6.72584i) q^{31} +(3.79592 - 6.57473i) q^{32} +(-6.08272 - 10.5356i) q^{33} +11.0411 q^{34} +(-1.58084 + 2.12154i) q^{35} +8.31819 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-2.92834 + 5.07203i) q^{38} +(0.801973 - 1.38906i) q^{39} +(0.257391 + 0.445815i) q^{40} +9.36744 q^{41} +(5.64886 + 13.1110i) q^{42} -6.47497 q^{43} +(3.77610 + 6.54040i) q^{44} +(-2.39913 + 4.15542i) q^{45} +(0.546194 - 0.946036i) q^{46} +(2.60943 + 4.51966i) q^{47} +12.4599 q^{48} +(-4.80806 + 5.08749i) q^{49} +1.93225 q^{50} +(7.97841 + 13.8190i) q^{51} +(-0.497858 + 0.862315i) q^{52} +(-1.30332 + 2.25741i) q^{53} +(4.85161 + 8.40323i) q^{54} -4.35641 q^{55} +(0.538918 + 1.25083i) q^{56} -8.46422 q^{57} +(-0.725328 - 1.25631i) q^{58} +(-1.40960 + 2.44150i) q^{59} +(2.42055 - 4.19251i) q^{60} +(-5.28313 - 9.15066i) q^{61} -15.0065 q^{62} +(-7.58531 + 10.1797i) q^{63} -5.74562 q^{64} +(-0.287184 - 0.497418i) q^{65} +(-11.7533 + 20.3574i) q^{66} +(3.07973 - 5.33425i) q^{67} +(-4.95293 - 8.57873i) q^{68} +1.57875 q^{69} +(5.07743 + 0.595675i) q^{70} +7.73849 q^{71} +(1.23503 + 2.13914i) q^{72} +(0.562977 - 0.975104i) q^{73} +(-0.966124 + 1.67338i) q^{74} +(1.39627 + 2.41841i) q^{75} +5.25452 q^{76} +(-11.4475 - 1.34300i) q^{77} -3.09922 q^{78} +(6.64754 + 11.5139i) q^{79} +(2.23093 - 3.86408i) q^{80} +(0.185725 - 0.321686i) q^{81} +(-9.05011 - 15.6752i) q^{82} +7.67133 q^{83} +(7.65302 - 10.2706i) q^{84} +5.71410 q^{85} +(6.25563 + 10.8351i) q^{86} +(1.04826 - 1.81565i) q^{87} +(-1.12130 + 1.94215i) q^{88} +(1.56342 + 2.70793i) q^{89} +9.27144 q^{90} +(-0.601298 - 1.39561i) q^{91} -0.980074 q^{92} +(-10.8439 - 18.7822i) q^{93} +(5.04206 - 8.73310i) q^{94} +(-1.51551 + 2.62493i) q^{95} +(-10.6003 - 18.3602i) q^{96} -10.3503 q^{97} +(13.1585 + 3.13055i) q^{98} -20.9032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) \) 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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