LMFDB - Embedded newform 1295.2.j.a.186.19

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)

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")

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);

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			186.19
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.33719 + 2.31608i) q^{2} +(0.134228 - 0.232489i) q^{3} +(-2.57617 + 4.46205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.717953 q^{6} +(-0.292931 + 2.62948i) q^{7} -8.43054 q^{8} +(1.46397 + 2.53566i) q^{9} +(1.33719 - 2.31608i) q^{10} +(-0.251910 + 0.436320i) q^{11} +(0.691586 + 1.19786i) q^{12} +1.35726 q^{13} +(-6.48182 + 2.83767i) q^{14} -0.268456 q^{15} +(-6.12093 - 10.6018i) q^{16} +(-1.70272 + 2.94921i) q^{17} +(-3.91521 + 6.78134i) q^{18} +(0.177570 + 0.307561i) q^{19} +5.15233 q^{20} +(0.572008 + 0.421053i) q^{21} -1.34741 q^{22} +(-3.56975 - 6.18299i) q^{23} +(-1.13161 + 1.96001i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.81491 + 3.14352i) q^{26} +1.59139 q^{27} +(-10.9783 - 8.08106i) q^{28} +0.607107 q^{29} +(-0.358977 - 0.621766i) q^{30} +(-0.696461 + 1.20631i) q^{31} +(7.93916 - 13.7510i) q^{32} +(0.0676266 + 0.117133i) q^{33} -9.10748 q^{34} +(2.42367 - 1.06106i) q^{35} -15.0857 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-0.474892 + 0.822537i) q^{38} +(0.182182 - 0.315548i) q^{39} +(4.21527 + 7.30107i) q^{40} +0.101491 q^{41} +(-0.210311 + 1.88785i) q^{42} -11.0929 q^{43} +(-1.29792 - 2.24807i) q^{44} +(1.46397 - 2.53566i) q^{45} +(9.54689 - 16.5357i) q^{46} +(5.77940 + 10.0102i) q^{47} -3.28639 q^{48} +(-6.82838 - 1.54052i) q^{49} -2.67438 q^{50} +(0.457106 + 0.791731i) q^{51} +(-3.49652 + 6.05615i) q^{52} +(-0.0816235 + 0.141376i) q^{53} +(2.12799 + 3.68579i) q^{54} +0.503819 q^{55} +(2.46957 - 22.1680i) q^{56} +0.0953396 q^{57} +(0.811819 + 1.40611i) q^{58} +(5.97878 - 10.3555i) q^{59} +(0.691586 - 1.19786i) q^{60} +(2.88750 + 5.00129i) q^{61} -3.72521 q^{62} +(-7.09633 + 3.10670i) q^{63} +17.9810 q^{64} +(-0.678629 - 1.17542i) q^{65} +(-0.180859 + 0.313258i) q^{66} +(7.27675 - 12.6037i) q^{67} +(-8.77300 - 15.1953i) q^{68} -1.91664 q^{69} +(5.69840 + 4.19458i) q^{70} -2.66145 q^{71} +(-12.3420 - 21.3770i) q^{72} +(-5.86820 + 10.1640i) q^{73} +(1.33719 - 2.31608i) q^{74} +(0.134228 + 0.232489i) q^{75} -1.82980 q^{76} +(-1.07351 - 0.790205i) q^{77} +0.974448 q^{78} +(3.42770 + 5.93695i) q^{79} +(-6.12093 + 10.6018i) q^{80} +(-4.17829 + 7.23701i) q^{81} +(0.135713 + 0.235062i) q^{82} +8.24563 q^{83} +(-3.35235 + 1.46762i) q^{84} +3.40545 q^{85} +(-14.8333 - 25.6920i) q^{86} +(0.0814906 - 0.141146i) q^{87} +(2.12374 - 3.67842i) q^{88} +(5.38411 + 9.32556i) q^{89} +7.83041 q^{90} +(-0.397583 + 3.56889i) q^{91} +36.7851 q^{92} +(0.186969 + 0.323839i) q^{93} +(-15.4563 + 26.7712i) q^{94} +(0.177570 - 0.307561i) q^{95} +(-2.13131 - 3.69154i) q^{96} +0.540259 q^{97} +(-5.56289 - 17.8751i) q^{98} -1.47515 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 $

$2$	1.33719	+	2.31608i	0.945538	+	1.63772i	0.754671	+	0.656103i	$0.227796\pi$
$2$	1.33719	+	2.31608i	0.945538	+	1.63772i	0.190866	+	0.981616i	$0.438870\pi$
$3$	0.134228	−	0.232489i	0.0774965	−	0.134228i	−0.824673	−	0.565610i	$-0.808641\pi$
$3$	0.134228	−	0.232489i	0.0774965	−	0.134228i	0.902169	+	0.431382i	$0.141974\pi$
$4$	−2.57617	+	4.46205i	−1.28808	+	2.23102i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.717953			0.293103
$7$	−0.292931	+	2.62948i	−0.110718	+	0.993852i
$7$	−0.292931	+	2.62948i	−0.110718	+	0.993852i
$8$	−8.43054			−2.98065
$9$	1.46397	+	2.53566i	0.487989	+	0.845221i
$10$	1.33719	−	2.31608i	0.422857	−	0.732410i
$11$	−0.251910	+	0.436320i	−0.0759536	+	0.131556i	−0.901501	−	0.432778i	$-0.857533\pi$
$11$	−0.251910	+	0.436320i	−0.0759536	+	0.131556i	0.825547	+	0.564333i	$0.190867\pi$
$12$	0.691586	+	1.19786i	0.199644	+	0.345793i
$13$	1.35726			0.376436			0.188218	−	0.982127i	$-0.439729\pi$
$13$	1.35726			0.376436			0.188218	+	0.982127i	$0.439729\pi$
$14$	−6.48182	+	2.83767i	−1.73234	+	0.758400i
$15$	−0.268456			−0.0693149
$16$	−6.12093	−	10.6018i	−1.53023	−	2.65044i
$17$	−1.70272	+	2.94921i	−0.412971	+	0.715287i	−0.995213	−	0.0977283i	$-0.968842\pi$
$17$	−1.70272	+	2.94921i	−0.412971	+	0.715287i	0.582242	+	0.813016i	$0.302176\pi$
$18$	−3.91521	+	6.78134i	−0.922823	+	1.59838i
$19$	0.177570	+	0.307561i	0.0407375	+	0.0705594i	0.885675	−	0.464305i	$-0.153696\pi$
$19$	0.177570	+	0.307561i	0.0407375	+	0.0705594i	−0.844938	+	0.534865i	$0.820363\pi$
$20$	5.15233			1.15210
$21$	0.572008	+	0.421053i	0.124822	+	0.0918814i
$22$	−1.34741			−0.287268
$23$	−3.56975	−	6.18299i	−0.744345	−	1.28924i	−0.950500	−	0.310724i	$-0.899428\pi$
$23$	−3.56975	−	6.18299i	−0.744345	−	1.28924i	0.206155	−	0.978519i	$-0.433905\pi$
$24$	−1.13161	+	1.96001i	−0.230990	+	0.400086i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.81491	+	3.14352i	0.355934	+	0.616496i
$27$	1.59139			0.306262
$28$	−10.9783	−	8.08106i	−2.07469	−	1.52718i
$29$	0.607107			0.112737			0.0563685	−	0.998410i	$-0.482048\pi$
$29$	0.607107			0.112737			0.0563685	+	0.998410i	$0.482048\pi$
$30$	−0.358977	−	0.621766i	−0.0655399	−	0.113518i
$31$	−0.696461	+	1.20631i	−0.125088	+	0.216659i	−0.921767	−	0.387743i	$-0.873255\pi$
$31$	−0.696461	+	1.20631i	−0.125088	+	0.216659i	0.796679	+	0.604402i	$0.206588\pi$
$32$	7.93916	−	13.7510i	1.40346	−	2.43086i
$33$	0.0676266	+	0.117133i	0.0117723	+	0.0203902i
$34$	−9.10748			−1.56192
$35$	2.42367	−	1.06106i	0.409674	−	0.179351i
$36$	−15.0857			−2.51428
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	−0.474892	+	0.822537i	−0.0770376	+	0.133433i
$39$	0.182182	−	0.315548i	0.0291724	−	0.0505281i
$40$	4.21527	+	7.30107i	0.666493	+	1.15440i
$41$	0.101491			0.0158502			0.00792511	−	0.999969i	$-0.497477\pi$
$41$	0.101491			0.0158502			0.00792511	+	0.999969i	$0.497477\pi$
$42$	−0.210311	+	1.88785i	−0.0324517	+	0.291301i
$43$	−11.0929			−1.69165			−0.845824	−	0.533462i	$-0.820891\pi$
$43$	−11.0929			−1.69165			−0.845824	+	0.533462i	$0.820891\pi$
$44$	−1.29792	−	2.24807i	−0.195669	−	0.338909i
$45$	1.46397	−	2.53566i	0.218235	−	0.377994i
$46$	9.54689	−	16.5357i	1.40761	−	2.43806i
$47$	5.77940	+	10.0102i	0.843012	+	1.46014i	0.887337	+	0.461122i	$0.152553\pi$
$47$	5.77940	+	10.0102i	0.843012	+	1.46014i	−0.0443247	+	0.999017i	$0.514114\pi$
$48$	−3.28639			−0.474350
$49$	−6.82838	−	1.54052i	−0.975483	−	0.220074i
$50$	−2.67438			−0.378215
$51$	0.457106	+	0.791731i	0.0640076	+	0.110864i
$52$	−3.49652	+	6.05615i	−0.484880	+	0.839837i
$53$	−0.0816235	+	0.141376i	−0.0112118	+	0.0194195i	−0.871577	−	0.490259i	$-0.836902\pi$
$53$	−0.0816235	+	0.141376i	−0.0112118	+	0.0194195i	0.860365	+	0.509678i	$0.170236\pi$
$54$	2.12799	+	3.68579i	0.289583	+	0.501572i
$55$	0.503819			0.0679350
$56$	2.46957	−	22.1680i	0.330010	−	2.96232i
$57$	0.0953396			0.0126280
$58$	0.811819	+	1.40611i	0.106597	+	0.184631i
$59$	5.97878	−	10.3555i	0.778370	−	1.34818i	−0.154510	−	0.987991i	$-0.549380\pi$
$59$	5.97878	−	10.3555i	0.778370	−	1.34818i	0.932881	−	0.360186i	$-0.117287\pi$
$60$	0.691586	−	1.19786i	0.0892834	−	0.154643i
$61$	2.88750	+	5.00129i	0.369706	+	0.640350i	0.989519	−	0.144400i	$-0.0461251\pi$
$61$	2.88750	+	5.00129i	0.369706	+	0.640350i	−0.619813	+	0.784749i	$0.712792\pi$
$62$	−3.72521			−0.473102
$63$	−7.09633	+	3.10670i	−0.894053	+	0.391408i
$64$	17.9810			2.24763
$65$	−0.678629	−	1.17542i	−0.0841736	−	0.145793i
$66$	−0.180859	+	0.313258i	−0.0222623	+	0.0385594i
$67$	7.27675	−	12.6037i	0.888997	−	1.53979i	0.0479336	−	0.998851i	$-0.484736\pi$
$67$	7.27675	−	12.6037i	0.888997	−	1.53979i	0.841063	−	0.540937i	$-0.181930\pi$
$68$	−8.77300	−	15.1953i	−1.06388	−	1.84270i
$69$	−1.91664			−0.230736
$70$	5.69840	+	4.19458i	0.681090	+	0.501348i
$71$	−2.66145			−0.315856			−0.157928	−	0.987451i	$-0.550481\pi$
$71$	−2.66145			−0.315856			−0.157928	+	0.987451i	$0.550481\pi$
$72$	−12.3420	−	21.3770i	−1.45452	−	2.51931i
$73$	−5.86820	+	10.1640i	−0.686820	+	1.18961i	0.286041	+	0.958217i	$0.407661\pi$
$73$	−5.86820	+	10.1640i	−0.686820	+	1.18961i	−0.972861	+	0.231390i	$0.925673\pi$
$74$	1.33719	−	2.31608i	0.155445	−	0.269239i
$75$	0.134228	+	0.232489i	0.0154993	+	0.0268456i
$76$	−1.82980			−0.209893
$77$	−1.07351	−	0.790205i	−0.122337	−	0.0900522i
$78$	0.974448			0.110335
$79$	3.42770	+	5.93695i	0.385647	+	0.667959i	0.991859	−	0.127344i	$-0.0406451\pi$
$79$	3.42770	+	5.93695i	0.385647	+	0.667959i	−0.606212	+	0.795303i	$0.707312\pi$
$80$	−6.12093	+	10.6018i	−0.684340	+	1.18531i
$81$	−4.17829	+	7.23701i	−0.464254	+	0.804112i
$82$	0.135713	+	0.235062i	0.0149870	+	0.0259582i
$83$	8.24563			0.905075			0.452538	−	0.891745i	$-0.350519\pi$
$83$	8.24563			0.905075			0.452538	+	0.891745i	$0.350519\pi$
$84$	−3.35235	+	1.46762i	−0.365771	+	0.160131i
$85$	3.40545			0.369373
$86$	−14.8333	−	25.6920i	−1.59952	−	2.77044i
$87$	0.0814906	−	0.141146i	0.00873671	−	0.0151324i
$88$	2.12374	−	3.67842i	0.226391	−	0.392121i
$89$	5.38411	+	9.32556i	0.570715	+	0.988507i	0.996493	+	0.0836793i	$0.0266671\pi$
$89$	5.38411	+	9.32556i	0.570715	+	0.988507i	−0.425778	+	0.904828i	$0.640000\pi$
$90$	7.83041			0.825398
$91$	−0.397583	+	3.56889i	−0.0416780	+	0.374121i
$92$	36.7851			3.83511
$93$	0.186969	+	0.323839i	0.0193878	+	0.0335806i
$94$	−15.4563	+	26.7712i	−1.59420	+	2.76123i
$95$	0.177570	−	0.307561i	0.0182183	−	0.0315551i
$96$	−2.13131	−	3.69154i	−0.217526	−	0.376767i
$97$	0.540259			0.0548549			0.0274275	−	0.999624i	$-0.491268\pi$
$97$	0.540259			0.0548549			0.0274275	+	0.999624i	$0.491268\pi$
$98$	−5.56289	−	17.8751i	−0.561937	−	1.80566i
$99$	−1.47515			−0.148258
$100$	−2.57617	−	4.46205i	−0.257617	−	0.446205i
$101$	3.33691	−	5.77970i	0.332035	−	0.575102i	−0.650876	−	0.759184i	$-0.725598\pi$
$101$	3.33691	−	5.77970i	0.332035	−	0.575102i	0.982911	+	0.184083i	$0.0589314\pi$
$102$	−1.22248	+	2.11739i	−0.121043	+	0.209653i
$103$	6.11027	+	10.5833i	0.602063	+	1.04280i	0.992508	+	0.122177i	$0.0389876\pi$
$103$	6.11027	+	10.5833i	0.602063	+	1.04280i	−0.390446	+	0.920626i	$0.627679\pi$
$104$	−11.4424			−1.12202
$105$	0.0786390	−	0.705900i	0.00767438	−	0.0688888i
$106$	−0.436585			−0.0424049
$107$	−3.09477	−	5.36030i	−0.299182	−	0.518199i	0.676767	−	0.736198i	$-0.263381\pi$
$107$	−3.09477	−	5.36030i	−0.299182	−	0.518199i	−0.975949	+	0.217998i	$0.930047\pi$
$108$	−4.09968	+	7.10085i	−0.394491	+	0.683279i
$109$	−3.49605	+	6.05534i	−0.334861	+	0.579997i	−0.983458	−	0.181135i	$-0.942023\pi$
$109$	−3.49605	+	6.05534i	−0.334861	+	0.579997i	0.648597	+	0.761132i	$0.275356\pi$
$110$	0.673703	+	1.16689i	0.0642351	+	0.111258i
$111$	−0.268456			−0.0254807
$112$	29.6702	−	12.9893i	2.80357	−	1.22737i
$113$	12.9216			1.21556			0.607780	−	0.794105i	$-0.292060\pi$
$113$	12.9216			1.21556			0.607780	+	0.794105i	$0.292060\pi$
$114$	0.127487	+	0.220815i	0.0119403	+	0.0206812i
$115$	−3.56975	+	6.18299i	−0.332881	+	0.576567i
$116$	−1.56401	+	2.70894i	−0.145214	+	0.251519i
$117$	1.98698	+	3.44155i	0.183696	+	0.318171i
$118$	31.9791			2.94391
$119$	−7.25611	−	5.34120i	−0.665167	−	0.489627i
$120$	2.26323			0.206603
$121$	5.37308	+	9.30645i	0.488462	+	0.846041i
$122$	−7.72227	+	13.3754i	−0.699142	+	1.21095i
$123$	0.0136229	−	0.0235956i	0.00122834	−	0.00212754i
$124$	−3.58840	−	6.21528i	−0.322247	−	0.558149i
$125$	1.00000			0.0894427
$126$	−16.6845	−	12.2814i	−1.48638	−	1.09412i
$127$	0.0823130			0.00730410			0.00365205	−	0.999993i	$-0.498838\pi$
$127$	0.0823130			0.00730410			0.00365205	+	0.999993i	$0.498838\pi$
$128$	8.16579	+	14.1436i	0.721760	+	1.25013i
$129$	−1.48897	+	2.57898i	−0.131097	+	0.227066i
$130$	1.81491	−	3.14352i	0.159179	−	0.275705i
$131$	9.47054	+	16.4035i	0.827445	+	1.43318i	0.900036	+	0.435815i	$0.143540\pi$
$131$	9.47054	+	16.4035i	0.827445	+	1.43318i	−0.0725915	+	0.997362i	$0.523127\pi$
$132$	−0.696869			−0.0606547
$133$	−0.860743	+	0.376825i	−0.0746359	+	0.0326748i
$134$	38.9217			3.36232
$135$	−0.795693	−	1.37818i	−0.0684824	−	0.118615i
$136$	14.3549	−	24.8634i	1.23092	−	2.13202i
$137$	−7.11322	+	12.3205i	−0.607724	+	1.05261i	0.383891	+	0.923378i	$0.374584\pi$
$137$	−7.11322	+	12.3205i	−0.607724	+	1.05261i	−0.991615	+	0.129230i	$0.958749\pi$
$138$	−2.56292	−	4.43910i	−0.218170	−	0.377881i
$139$	6.43564			0.545863			0.272932	−	0.962033i	$-0.412007\pi$
$139$	6.43564			0.545863			0.272932	+	0.962033i	$0.412007\pi$
$140$	−1.50928	+	13.5480i	−0.127557	+	1.14501i
$141$	3.10302			0.261322
$142$	−3.55887	−	6.16414i	−0.298653	−	0.517283i
$143$	−0.341906	+	0.592199i	−0.0285917	+	0.0495222i
$144$	17.9217	−	31.0412i	1.49347	−	2.58677i
$145$	−0.303553	−	0.525770i	−0.0252087	−	0.0436628i
$146$	−31.3876			−2.59766
$147$	−1.27471	+	1.38075i	−0.105137	+	0.113882i
$148$	5.15233			0.423519
$149$	2.16707	+	3.75348i	0.177533	+	0.307497i	0.941035	−	0.338309i	$-0.109855\pi$
$149$	2.16707	+	3.75348i	0.177533	+	0.307497i	−0.763502	+	0.645806i	$0.776522\pi$
$150$	−0.358977	+	0.621766i	−0.0293103	+	0.0507670i
$151$	−5.80908	+	10.0616i	−0.472736	+	0.818803i	−0.999513	−	0.0312003i	$-0.990067\pi$
$151$	−5.80908	+	10.0616i	−0.472736	+	0.818803i	0.526777	+	0.850004i	$0.323400\pi$
$152$	−1.49702	−	2.59291i	−0.121424	−	0.210313i
$153$	−9.97092			−0.806101
$154$	0.394698	−	3.54299i	0.0318056	−	0.285502i
$155$	1.39292			0.111882
$156$	0.938661	+	1.62581i	0.0751530	+	0.130169i
$157$	−1.86334	+	3.22740i	−0.148711	+	0.257574i	−0.930751	−	0.365653i	$-0.880846\pi$
$157$	−1.86334	+	3.22740i	−0.148711	+	0.257574i	0.782041	+	0.623228i	$0.214179\pi$
$158$	−9.16699	+	15.8777i	−0.729287	+	1.26316i
$159$	0.0219123	+	0.0379532i	0.00173776	+	0.00300988i
$160$	−15.8783			−1.25529
$161$	17.3038	−	7.57542i	1.36373	−	0.597027i
$162$	−22.3487			−1.75588
$163$	−1.09128	−	1.89014i	−0.0854753	−	0.148048i	0.820118	−	0.572194i	$-0.193908\pi$
$163$	−1.09128	−	1.89014i	−0.0854753	−	0.148048i	−0.905594	+	0.424146i	$0.860574\pi$
$164$	−0.261457	+	0.452857i	−0.0204164	+	0.0353622i
$165$	0.0676266	−	0.117133i	0.00526472	−	0.00911877i
$166$	11.0260	+	19.0976i	0.855783	+	1.48226i
$167$	11.8566			0.917491			0.458745	−	0.888568i	$-0.348299\pi$
$167$	11.8566			0.917491			0.458745	+	0.888568i	$0.348299\pi$
$168$	−4.82234	−	3.54971i	−0.372051	−	0.273866i
$169$	−11.1579			−0.858296
$170$	4.55374	+	7.88731i	0.349256	+	0.604929i
$171$	−0.519914	+	0.900518i	−0.0397588	+	0.0688643i
$172$	28.5771	−	49.4970i	2.17898	−	3.77411i
$173$	−9.33855	−	16.1748i	−0.709997	−	1.22975i	−0.964858	−	0.262773i	$-0.915363\pi$
$173$	−9.33855	−	16.1748i	−0.709997	−	1.22975i	0.254861	−	0.966978i	$-0.417970\pi$
$174$	0.435875			0.0330436
$175$	−2.13074	−	1.56843i	−0.161068	−	0.118562i
$176$	6.16768			0.464907
$177$	−1.60504	−	2.78000i	−0.120642	−	0.208958i
$178$	−14.3992	+	24.9401i	−1.07926	+	1.86934i
$179$	−5.72475	+	9.91556i	−0.427888	+	0.741124i	−0.996685	−	0.0813538i	$-0.974076\pi$
$179$	−5.72475	+	9.91556i	−0.427888	+	0.741124i	0.568797	+	0.822478i	$0.307409\pi$
$180$	7.54284	+	13.0646i	0.562210	+	0.973776i
$181$	6.60901			0.491244			0.245622	−	0.969366i	$-0.421008\pi$
$181$	6.60901			0.491244			0.245622	+	0.969366i	$0.421008\pi$
$182$	−8.79749	+	3.85145i	−0.652114	+	0.285489i
$183$	1.55033			0.114604
$184$	30.0950	+	52.1260i	2.21863	+	3.84278i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	−0.500026	+	0.866071i	−0.0366637	+	0.0635034i
$187$	−0.857866	−	1.48587i	−0.0627334	−	0.108657i
$188$	−59.5547			−4.34348
$189$	−0.466167	+	4.18453i	−0.0339087	+	0.304380i
$190$	0.949783			0.0689045
$191$	5.53658	+	9.58964i	0.400613	+	0.693882i	0.993800	−	0.111183i	$-0.0354638\pi$
$191$	5.53658	+	9.58964i	0.400613	+	0.693882i	−0.593187	+	0.805065i	$0.702131\pi$
$192$	2.41356	−	4.18040i	0.174183	−	0.301695i
$193$	6.56294	−	11.3673i	0.472411	−	0.818239i	−0.527091	−	0.849809i	$-0.676717\pi$
$193$	6.56294	−	11.3673i	0.472411	−	0.818239i	0.999502	+	0.0315696i	$0.0100506\pi$
$194$	0.722429	+	1.25128i	0.0518674	+	0.0898370i
$195$	−0.364363			−0.0260926
$196$	24.4649	−	26.5000i	1.74749	−	1.89285i
$197$	−7.64052			−0.544364			−0.272182	−	0.962246i	$-0.587745\pi$
$197$	−7.64052			−0.544364			−0.272182	+	0.962246i	$0.587745\pi$
$198$	−1.97256	−	3.41657i	−0.140184	−	0.242805i
$199$	11.6111	−	20.1111i	0.823092	−	1.42564i	−0.0802769	−	0.996773i	$-0.525580\pi$
$199$	11.6111	−	20.1111i	0.823092	−	1.42564i	0.903369	−	0.428864i	$-0.141086\pi$
$200$	4.21527	−	7.30107i	0.298065	−	0.516263i
$201$	−1.95348	−	3.38354i	−0.137788	−	0.238656i
$202$	17.8484			1.25581
$203$	−0.177841	+	1.59638i	−0.0124820	+	0.112044i
$204$	−4.71032			−0.329789
$205$	−0.0507454	−	0.0878937i	−0.00354422	−	0.00613876i
$206$	−16.3412	+	28.3038i	−1.13855	+	1.97202i
$207$	10.4520	−	18.1034i	0.726464	−	1.25827i
$208$	−8.30768	−	14.3893i	−0.576034	−	0.997720i
$209$	−0.178927			−0.0123766
$210$	1.74008	−	0.761789i	0.120077	−	0.0525685i
$211$	0.763483			0.0525603			0.0262802	−	0.999655i	$-0.491634\pi$
$211$	0.763483			0.0525603			0.0262802	+	0.999655i	$0.491634\pi$
$212$	−0.420551	−	0.728416i	−0.0288836	−	0.0500278i
$213$	−0.357240	+	0.618758i	−0.0244777	+	0.0423966i
$214$	8.27660	−	14.3355i	0.565777	−	0.979954i
$215$	5.54644	+	9.60671i	0.378264	+	0.655173i
$216$	−13.4163			−0.912860
$217$	−2.96795	−	2.18470i	−0.201477	−	0.148307i
$218$	−18.6996			−1.26650
$219$	1.57535	+	2.72859i	0.106452	+	0.184381i
$220$	−1.29792	+	2.24807i	−0.0875059	+	0.151565i
$221$	−2.31104	+	4.00283i	−0.155457	+	0.269260i
$222$	−0.358977	−	0.621766i	−0.0240929	−	0.0417302i
$223$	3.59249			0.240571			0.120286	−	0.992739i	$-0.461619\pi$
$223$	3.59249			0.240571			0.120286	+	0.992739i	$0.461619\pi$
$224$	33.8325	+	24.9040i	2.26053	+	1.66397i
$225$	−2.92793			−0.195195
$226$	17.2786	+	29.9275i	1.14936	+	1.99075i
$227$	−8.17321	+	14.1564i	−0.542475	+	0.939594i	0.456286	+	0.889833i	$0.349179\pi$
$227$	−8.17321	+	14.1564i	−0.542475	+	0.939594i	−0.998761	+	0.0497610i	$0.984154\pi$
$228$	−0.245611	+	0.425410i	−0.0162660	+	0.0281735i
$229$	8.16811	+	14.1476i	0.539764	+	0.934898i	0.998916	+	0.0465410i	$0.0148198\pi$
$229$	8.16811	+	14.1476i	0.539764	+	0.934898i	−0.459153	+	0.888357i	$0.651847\pi$
$230$	−19.0938			−1.25901
$231$	−0.327809	+	0.143511i	−0.0215682	+	0.00944235i
$232$	−5.11824			−0.336029
$233$	4.57552	+	7.92504i	0.299752	+	0.519186i	0.976079	−	0.217415i	$-0.0697626\pi$
$233$	4.57552	+	7.92504i	0.299752	+	0.519186i	−0.676327	+	0.736602i	$0.736429\pi$
$234$	−5.31395	+	9.20402i	−0.347383	+	0.601686i
$235$	5.77940	−	10.0102i	0.377006	−	0.652994i
$236$	30.8046	+	53.3552i	2.00521	+	3.47313i
$237$	1.84037			0.119545
$238$	2.66787	−	23.9480i	0.172932	−	1.55232i
$239$	28.9577			1.87312			0.936559	−	0.350509i	$-0.113991\pi$
$239$	28.9577			1.87312			0.936559	+	0.350509i	$0.113991\pi$
$240$	1.64320	+	2.84610i	0.106068	+	0.183715i
$241$	1.27914	−	2.21553i	0.0823964	−	0.142715i	−0.821882	−	0.569657i	$-0.807076\pi$
$241$	1.27914	−	2.21553i	0.0823964	−	0.142715i	0.904279	+	0.426942i	$0.140409\pi$
$242$	−14.3697	+	24.8890i	−0.923719	+	1.59993i
$243$	3.50876	+	6.07736i	0.225087	+	0.389863i
$244$	−29.7547			−1.90485
$245$	2.08006	+	6.68381i	0.132890	+	0.427013i
$246$	0.0728657			0.00464575
$247$	0.241009	+	0.417440i	0.0153350	+	0.0265611i
$248$	5.87154	−	10.1698i	0.372843	−	0.645784i
$249$	1.10679	−	1.91702i	0.0701401	−	0.121486i
$250$	1.33719	+	2.31608i	0.0845715	+	0.146482i
$251$	21.3295			1.34631			0.673153	−	0.739503i	$-0.264940\pi$
$251$	21.3295			1.34631			0.673153	+	0.739503i	$0.264940\pi$
$252$	4.41907	−	39.6675i	0.278375	−	2.49882i
$253$	3.59702			0.226143
$254$	0.110068	+	0.190644i	0.00690630	+	0.0119621i
$255$	0.457106	−	0.791731i	0.0286251	−	0.0495801i
$256$	−3.85740	+	6.68122i	−0.241088	+	0.417576i
$257$	−8.81665	−	15.2709i	−0.549967	−	0.952571i	−0.998276	−	0.0586925i	$-0.981307\pi$
$257$	−8.81665	−	15.2709i	−0.549967	−	0.952571i	0.448309	−	0.893879i	$-0.352026\pi$
$258$	−7.96417			−0.495828
$259$	2.42367	−	1.06106i	0.150599	−	0.0659308i
$260$	6.99304			0.433690
$261$	0.888784	+	1.53942i	0.0550143	+	0.0952876i
$262$	−25.3279	+	43.8691i	−1.56476	+	2.71024i
$263$	4.49855	−	7.79172i	0.277393	−	0.480458i	−0.693343	−	0.720607i	$-0.743863\pi$
$263$	4.49855	−	7.79172i	0.277393	−	0.480458i	0.970736	+	0.240149i	$0.0771964\pi$
$264$	−0.570129	−	0.987492i	−0.0350890	−	0.0607759i
$265$	0.163247			0.0100282
$266$	−2.02374	−	1.48967i	−0.124083	−	0.0913374i
$267$	2.89079			0.176913
$268$	37.4922	+	64.9385i	2.29020	+	3.96675i
$269$	0.257790	−	0.446505i	0.0157177	−	0.0272239i	−0.858060	−	0.513550i	$-0.828330\pi$
$269$	0.257790	−	0.446505i	0.0157177	−	0.0272239i	0.873777	+	0.486326i	$0.161663\pi$
$270$	2.12799	−	3.68579i	0.129505	−	0.224310i
$271$	−6.38318	−	11.0560i	−0.387751	−	0.671604i	0.604396	−	0.796684i	$-0.293415\pi$
$271$	−6.38318	−	11.0560i	−0.387751	−	0.671604i	−0.992147	+	0.125080i	$0.960081\pi$
$272$	41.6890			2.52777
$273$	0.776362	+	0.571478i	0.0469876	+	0.0345874i
$274$	−38.0470			−2.29850
$275$	−0.251910	−	0.436320i	−0.0151907	−	0.0263111i
$276$	4.93758	−	8.55215i	0.297208	−	0.514779i
$277$	−2.40819	+	4.17111i	−0.144694	+	0.250618i	−0.929259	−	0.369429i	$-0.879553\pi$
$277$	−2.40819	+	4.17111i	−0.144694	+	0.250618i	0.784565	+	0.620047i	$0.212886\pi$
$278$	8.60568	+	14.9055i	0.516134	+	0.893971i
$279$	−4.07838			−0.244166
$280$	−20.4328	+	8.94528i	−1.22109	+	0.534583i
$281$	−31.0144			−1.85017			−0.925083	−	0.379766i	$-0.876005\pi$
$281$	−31.0144			−1.85017			−0.925083	+	0.379766i	$0.876005\pi$
$282$	4.14934	+	7.18687i	0.247090	+	0.427972i
$283$	11.5717	−	20.0427i	0.687864	−	1.19142i	−0.284664	−	0.958627i	$-0.591882\pi$
$283$	11.5717	−	20.0427i	0.687864	−	1.19142i	0.972528	−	0.232788i	$-0.0747848\pi$
$284$	6.85633	−	11.8755i	0.406848	−	0.704682i
$285$	−0.0476698	−	0.0825665i	−0.00282372	−	0.00489082i
$286$	−1.82878			−0.108138
$287$	−0.0297299	+	0.266869i	−0.00175490	+	0.0157528i
$288$	46.4907			2.73949
$289$	2.70146	+	4.67906i	0.158909	+	0.275239i
$290$	0.811819	−	1.40611i	0.0476716	−	0.0825697i
$291$	0.0725177	−	0.125604i	0.00425106	−	0.00736306i
$292$	−30.2349	−	52.3684i	−1.76936	−	3.06463i
$293$	11.9847			0.700153			0.350076	−	0.936721i	$-0.386156\pi$
$293$	11.9847			0.700153			0.350076	+	0.936721i	$0.386156\pi$
$294$	−4.90246	−	1.10602i	−0.285917	−	0.0645044i
$295$	−11.9576			−0.696196
$296$	4.21527	+	7.30107i	0.245008	+	0.424366i
$297$	−0.400886	+	0.694355i	−0.0232618	+	0.0402905i
$298$	−5.79558	+	10.0382i	−0.335729	+	0.581500i
$299$	−4.84508	−	8.39192i	−0.280198	−	0.485317i
$300$	−1.38317			−0.0798575
$301$	3.24945	−	29.1686i	0.187295	−	1.68125i
$302$	−31.0714			−1.78796
$303$	−0.895813	−	1.55159i	−0.0514631	−	0.0891367i
$304$	2.17379	−	3.76512i	0.124676	−	0.215944i
$305$	2.88750	−	5.00129i	0.165338	−	0.286373i
$306$	−13.3330	−	23.0935i	−0.762199	−	1.32017i
$307$	−29.6202			−1.69051			−0.845257	−	0.534360i	$-0.820553\pi$
$307$	−29.6202			−1.69051			−0.845257	+	0.534360i	$0.820553\pi$
$308$	6.29146	−	2.75434i	0.358489	−	0.156943i
$309$	3.28067			0.186631
$310$	1.86260	+	3.22612i	0.105789	+	0.183232i
$311$	14.1257	−	24.4664i	0.800993	−	1.38736i	−0.117970	−	0.993017i	$-0.537639\pi$
$311$	14.1257	−	24.4664i	0.800993	−	1.38736i	0.918963	−	0.394343i	$-0.129028\pi$
$312$	−1.53589	+	2.66024i	−0.0869527	+	0.150607i
$313$	−12.3972	−	21.4727i	−0.700734	−	1.21371i	−0.968209	−	0.250142i	$-0.919523\pi$
$313$	−12.3972	−	21.4727i	−0.700734	−	1.21371i	0.267475	−	0.963565i	$-0.413811\pi$
$314$	−9.96657			−0.562446
$315$	6.23865	+	4.59225i	0.351508	+	0.258744i
$316$	−35.3213			−1.98698
$317$	−11.2329	−	19.4559i	−0.630901	−	1.09275i	−0.987368	−	0.158444i	$-0.949352\pi$
$317$	−11.2329	−	19.4559i	−0.630901	−	1.09275i	0.356467	−	0.934308i	$-0.383981\pi$
$318$	−0.0586019	+	0.101501i	−0.00328623	+	0.00569192i
$319$	−0.152936	+	0.264893i	−0.00856278	+	0.0148312i
$320$	−8.99052	−	15.5720i	−0.502586	−	0.870504i
$321$	−1.66162			−0.0927423
$322$	40.6838	+	29.9472i	2.26722	+	1.66889i
$323$	−1.20941			−0.0672936
$324$	−21.5279	−	37.2875i	−1.19600	−	2.07153i
$325$	−0.678629	+	1.17542i	−0.0376436	+	0.0652006i
$326$	2.91849	−	5.05497i	0.161640	−	0.279969i
$327$	0.938535	+	1.62559i	0.0519011	+	0.0898954i
$328$	−0.855624			−0.0472439
$329$	−28.0147	+	12.2645i	−1.54450	+	0.676166i
$330$	0.361719			0.0199120
$331$	−7.05425	−	12.2183i	−0.387737	−	0.671580i	0.604408	−	0.796675i	$-0.293410\pi$
$331$	−7.05425	−	12.2183i	−0.387737	−	0.671580i	−0.992145	+	0.125095i	$0.960076\pi$
$332$	−21.2421	+	36.7924i	−1.16581	+	2.01925i
$333$	1.46397	−	2.53566i	0.0802248	−	0.138953i
$334$	15.8545	+	27.4609i	0.867522	+	1.50259i
$335$	−14.5535			−0.795143
$336$	0.962688	−	8.64152i	0.0525189	−	0.471434i
$337$	−21.4756			−1.16985			−0.584924	−	0.811088i	$-0.698876\pi$
$337$	−21.4756			−1.16985			−0.584924	+	0.811088i	$0.698876\pi$
$338$	−14.9202	−	25.8425i	−0.811551	−	1.40565i
$339$	1.73444	−	3.00413i	0.0942017	−	0.163162i
$340$	−8.77300	+	15.1953i	−0.475783	+	0.824080i
$341$	−0.350890	−	0.607760i	−0.0190018	−	0.0329121i
$342$	−2.78090			−0.150374
$343$	6.05101	−	17.5039i	0.326724	−	0.945120i
$344$	93.5190			5.04221
$345$	0.958320	+	1.65986i	0.0515942	+	0.0893638i
$346$	24.9749	−	43.2577i	1.34266	−	2.32555i
$347$	−2.19584	+	3.80330i	−0.117879	+	0.204172i	−0.918927	−	0.394428i	$-0.870943\pi$
$347$	−2.19584	+	3.80330i	−0.117879	+	0.204172i	0.801048	+	0.598600i	$0.204276\pi$
$348$	0.419867	+	0.727230i	0.0225072	+	0.0389836i
$349$	−23.8988			−1.27927			−0.639637	−	0.768677i	$-0.720915\pi$
$349$	−23.8988			−1.27927			−0.639637	+	0.768677i	$0.720915\pi$
$350$	0.783411	−	7.03225i	0.0418751	−	0.375890i
$351$	2.15992			0.115288
$352$	3.99991	+	6.92804i	0.213196	+	0.369266i
$353$	−10.9603	+	18.9838i	−0.583357	+	1.01040i	0.411721	+	0.911310i	$0.364928\pi$
$353$	−10.9603	+	18.9838i	−0.583357	+	1.01040i	−0.995078	+	0.0990938i	$0.968406\pi$
$354$	4.29248	−	7.43480i	0.228143	−	0.395155i
$355$	1.33072	+	2.30488i	0.0706275	+	0.122330i
$356$	−55.4815			−2.94051
$357$	−2.21574	+	0.970031i	−0.117270	+	0.0513395i
$358$	−30.6204			−1.61834
$359$	9.05261	+	15.6796i	0.477778	+	0.827536i	0.999676	−	0.0254721i	$-0.00810891\pi$
$359$	9.05261	+	15.6796i	0.477778	+	0.827536i	−0.521897	+	0.853008i	$0.674776\pi$
$360$	−12.3420	+	21.3770i	−0.650482	+	1.12667i
$361$	9.43694	−	16.3453i	0.496681	−	0.860277i
$362$	8.83752	+	15.3070i	0.464490	+	0.804520i
$363$	2.88487			0.151416
$364$	−14.9003	−	10.9681i	−0.780989	−	0.574884i
$365$	11.7364			0.614311
$366$	2.07309	+	3.59069i	0.108362	+	0.187689i
$367$	−5.76353	+	9.98272i	−0.300854	+	0.521094i	−0.976330	−	0.216288i	$-0.930605\pi$
$367$	−5.76353	+	9.98272i	−0.300854	+	0.521094i	0.675476	+	0.737382i	$0.263938\pi$
$368$	−43.7004	+	75.6913i	−2.27804	+	3.94568i
$369$	0.148579	+	0.257347i	0.00773472	+	0.0133969i
$370$	−2.67438			−0.139035
$371$	−0.347836	−	0.256041i	−0.0180588	−	0.0132930i
$372$	−1.92665			−0.0998921
$373$	9.77398	+	16.9290i	0.506077	+	0.876552i	0.999975	+	0.00703180i	$0.00223831\pi$
$373$	9.77398	+	16.9290i	0.506077	+	0.876552i	−0.493898	+	0.869520i	$0.664428\pi$
$374$	2.29426	−	3.97378i	0.118634	−	0.205479i
$375$	0.134228	−	0.232489i	0.00693149	−	0.0120057i
$376$	−48.7235	−	84.3915i	−2.51272	−	4.35216i
$377$	0.824001			0.0424382
$378$	−10.3151	+	4.51583i	−0.530550	+	0.232269i
$379$	−14.0880			−0.723650			−0.361825	−	0.932246i	$-0.617846\pi$
$379$	−14.0880			−0.723650			−0.361825	+	0.932246i	$0.617846\pi$
$380$	0.914902	+	1.58466i	0.0469335	+	0.0812912i
$381$	0.0110487	−	0.0191369i	0.000566042	−	0.000980413i
$382$	−14.8069	+	25.6464i	−0.757589	+	1.31218i
$383$	−9.43271	−	16.3379i	−0.481989	−	0.834829i	0.517797	−	0.855503i	$-0.326752\pi$
$383$	−9.43271	−	16.3379i	−0.481989	−	0.834829i	−0.999786	+	0.0206740i	$0.993419\pi$
$384$	4.38430			0.223735
$385$	−0.147584	+	1.32479i	−0.00752160	+	0.0675173i
$386$	35.1036			1.78673
$387$	−16.2396	−	28.1278i	−0.825505	−	1.42982i
$388$	−1.39180	+	2.41066i	−0.0706577	+	0.122383i
$389$	16.4616	−	28.5124i	0.834637	−	1.44563i	−0.0596882	−	0.998217i	$-0.519011\pi$
$389$	16.4616	−	28.5124i	0.834637	−	1.44563i	0.894325	−	0.447417i	$-0.147656\pi$
$390$	−0.487224	−	0.843897i	−0.0246715	−	0.0427324i
$391$	24.3132			1.22957
$392$	57.5670	+	12.9874i	2.90757	+	0.655962i
$393$	5.08484			0.256496
$394$	−10.2168	−	17.6961i	−0.514717	−	0.891516i
$395$	3.42770	−	5.93695i	0.172466	−	0.298721i
$396$	3.80023	−	6.58219i	0.190969	−	0.330767i
$397$	1.44547	+	2.50362i	0.0725459	+	0.125653i	0.900016	−	0.435856i	$-0.143554\pi$
$397$	1.44547	+	2.50362i	0.0725459	+	0.125653i	−0.827471	+	0.561509i	$0.810221\pi$
$398$	62.1053			3.11306
$399$	−0.0279279	+	0.250694i	−0.00139815	+	0.0125504i
$400$	12.2419			0.612093
$401$	8.81670	+	15.2710i	0.440285	+	0.762596i	0.997710	−	0.0676311i	$-0.0215441\pi$
$401$	8.81670	+	15.2710i	0.440285	+	0.762596i	−0.557425	+	0.830227i	$0.688211\pi$
$402$	5.22437	−	9.04887i	0.260568	−	0.451317i
$403$	−0.945277	+	1.63727i	−0.0470876	+	0.0815581i
$404$	17.1929	+	29.7789i	0.855378	+	1.48156i
$405$	8.35658			0.415242
$406$	−3.93516	+	1.72277i	−0.195298	+	0.0854997i
$407$	0.503819			0.0249734
$408$	−3.85365	−	6.67472i	−0.190784	−	0.330448i
$409$	4.64571	−	8.04660i	0.229715	−	0.397879i	−0.728008	−	0.685568i	$-0.759554\pi$
$409$	4.64571	−	8.04660i	0.229715	−	0.397879i	0.957724	+	0.287690i	$0.0928871\pi$
$410$	0.135713	−	0.235062i	0.00670238	−	0.0116089i
$411$	1.90958	+	3.30750i	0.0941929	+	0.163147i
$412$	−62.9642			−3.10203
$413$	25.4784	+	18.7546i	1.25371	+	0.922852i
$414$	55.9053			2.74760
$415$	−4.12281	−	7.14092i	−0.202381	−	0.350534i
$416$	10.7755	−	18.6637i	0.528312	−	0.915063i
$417$	0.863841	−	1.49622i	0.0423025	−	0.0732701i
$418$	−0.239260	−	0.414410i	−0.0117026	−	0.0202695i
$419$	3.99338			0.195089			0.0975446	−	0.995231i	$-0.468901\pi$
$419$	3.99338			0.195089			0.0975446	+	0.995231i	$0.468901\pi$
$420$	2.94717	+	2.16941i	0.143807	+	0.105856i
$421$	19.5403			0.952335			0.476167	−	0.879355i	$-0.342026\pi$
$421$	19.5403			0.952335			0.476167	+	0.879355i	$0.342026\pi$
$422$	1.02092	+	1.76829i	0.0496978	+	0.0860791i
$423$	−16.9217	+	29.3092i	−0.822760	+	1.42506i
$424$	0.688131	−	1.19188i	0.0334186	−	0.0578827i
$425$	−1.70272	−	2.94921i	−0.0825943	−	0.143057i
$426$	−1.91080			−0.0925784
$427$	−13.9967	+	6.12759i	−0.677346	+	0.296535i
$428$	31.8905			1.54149
$429$	0.0917867	+	0.158979i	0.00443150	+	0.00767559i
$430$	−14.8333	+	25.6920i	−0.715326	+	1.23898i
$431$	−0.416577	+	0.721533i	−0.0200658	+	0.0347550i	−0.875884	−	0.482522i	$-0.839721\pi$
$431$	−0.416577	+	0.721533i	−0.0200658	+	0.0347550i	0.855818	+	0.517277i	$0.173054\pi$
$432$	−9.74076	−	16.8715i	−0.468653	−	0.811730i
$433$	2.54002			0.122066			0.0610328	−	0.998136i	$-0.480561\pi$
$433$	2.54002			0.122066			0.0610328	+	0.998136i	$0.480561\pi$
$434$	1.09123	−	9.79538i	0.0523807	−	0.470193i
$435$	−0.162981			−0.00781435
$436$	−18.0128	−	31.1991i	−0.862658	−	1.49417i
$437$	1.26777	−	2.19583i	0.0606455	−	0.105041i
$438$	−4.21309	+	7.29729i	−0.201309	+	0.348678i
$439$	5.74097	+	9.94364i	0.274001	+	0.474584i	0.969883	−	0.243573i	$-0.0783194\pi$
$439$	5.74097	+	9.94364i	0.274001	+	0.474584i	−0.695881	+	0.718157i	$0.744986\pi$
$440$	−4.24747			−0.202490
$441$	−6.09029	−	19.5697i	−0.290014	−	0.931892i
$442$	−12.3612			−0.587962
$443$	−0.460287	−	0.797241i	−0.0218689	−	0.0378780i	0.854884	−	0.518819i	$-0.173628\pi$
$443$	−0.460287	−	0.797241i	−0.0218689	−	0.0378780i	−0.876753	+	0.480941i	$0.840295\pi$
$444$	0.691586	−	1.19786i	0.0328212	−	0.0568480i
$445$	5.38411	−	9.32556i	0.255231	−	0.442074i
$446$	4.80385	+	8.32052i	0.227469	+	0.393988i
$447$	1.16353			0.0550329
$448$	−5.26721	+	47.2809i	−0.248852	+	2.23381i
$449$	13.0323			0.615034			0.307517	−	0.951543i	$-0.400502\pi$
$449$	13.0323			0.615034			0.307517	+	0.951543i	$0.400502\pi$
$450$	−3.91521	−	6.78134i	−0.184565	−	0.319675i
$451$	−0.0255665	+	0.0442826i	−0.00120388	+	0.00208518i
$452$	−33.2881	+	57.6568i	−1.56574	+	2.71195i
$453$	1.55948	+	2.70110i	0.0732708	+	0.126909i
$454$	−43.7166			−2.05172
$455$	3.28954	−	1.44013i	0.154216	−	0.0675142i
$456$	−0.803765			−0.0376397
$457$	19.3472	+	33.5104i	0.905025	+	1.56755i	0.820883	+	0.571096i	$0.193482\pi$
$457$	19.3472	+	33.5104i	0.905025	+	1.56755i	0.0841420	+	0.996454i	$0.473185\pi$
$458$	−21.8447	+	37.8361i	−1.02073	+	1.76796i
$459$	−2.70969	+	4.69333i	−0.126478	+	0.219066i
$460$	−18.3926	−	31.8568i	−0.857557	−	1.48533i
$461$	8.30974			0.387023			0.193512	−	0.981098i	$-0.438012\pi$
$461$	8.30974			0.387023			0.193512	+	0.981098i	$0.438012\pi$
$462$	−0.770727	−	0.567330i	−0.0358575	−	0.0263946i
$463$	−1.28979			−0.0599415			−0.0299707	−	0.999551i	$-0.509541\pi$
$463$	−1.28979			−0.0599415			−0.0299707	+	0.999551i	$0.509541\pi$
$464$	−3.71606	−	6.43640i	−0.172514	−	0.298802i
$465$	0.186969	−	0.323839i	0.00867047	−	0.0150177i
$466$	−12.2367	+	21.1946i	−0.566854	+	0.981820i
$467$	−10.1906	−	17.6507i	−0.471566	−	0.816776i	0.527905	−	0.849304i	$-0.322978\pi$
$467$	−10.1906	−	17.6507i	−0.471566	−	0.816776i	−0.999471	+	0.0325272i	$0.989644\pi$
$468$	−20.4751			−0.946464
$469$	31.0097	+	22.8261i	1.43189	+	1.05401i
$470$	30.9127			1.42589
$471$	0.500224	+	0.866413i	0.0230491	+	0.0399222i
$472$	−50.4043	+	87.3029i	−2.32005	+	4.01844i
$473$	2.79440	−	4.84005i	0.128487	−	0.222546i
$474$	2.46093	+	4.26246i	0.113034	+	0.195781i
$475$	−0.355141			−0.0162950
$476$	42.5257	−	18.6173i	1.94916	−	0.853323i
$477$	−0.477976			−0.0218850
$478$	38.7220	+	67.0685i	1.77110	+	3.06764i
$479$	4.17229	−	7.22662i	0.190637	−	0.330193i	−0.754825	−	0.655927i	$-0.772278\pi$
$479$	4.17229	−	7.22662i	0.190637	−	0.330193i	0.945461	+	0.325734i	$0.105611\pi$
$480$	−2.13131	+	3.69154i	−0.0972807	+	0.168495i
$481$	−0.678629	−	1.17542i	−0.0309428	−	0.0535945i
$482$	6.84181			0.311636
$483$	0.561444	−	5.03978i	0.0255466	−	0.229318i
$484$	−55.3678			−2.51672
$485$	−0.270129	−	0.467878i	−0.0122659	−	0.0212452i
$486$	−9.38379	+	16.2532i	−0.425657	+	0.737260i
$487$	−13.3472	+	23.1180i	−0.604817	+	1.04757i	0.387263	+	0.921969i	$0.373421\pi$
$487$	−13.3472	+	23.1180i	−0.604817	+	1.04757i	−0.992080	+	0.125605i	$0.959913\pi$
$488$	−24.3432	−	42.1636i	−1.10196	−	1.90866i
$489$	−0.585918			−0.0264961
$490$	−12.6988	+	13.7551i	−0.573675	+	0.621394i
$491$	39.0928			1.76423			0.882116	−	0.471031i	$-0.156118\pi$
$491$	39.0928			1.76423			0.882116	+	0.471031i	$0.156118\pi$
$492$	0.0701897	+	0.121572i	0.00316440	+	0.00548089i
$493$	−1.03374	+	1.79048i	−0.0465571	+	0.0806393i
$494$	−0.644551	+	1.11639i	−0.0289997	+	0.0502290i
$495$	0.737574	+	1.27752i	0.0331515	+	0.0574201i
$496$	17.0519			0.765655
$497$	0.779621	−	6.99824i	0.0349708	−	0.313914i
$498$	5.91998			0.265280
$499$	−19.1260	−	33.1272i	−0.856196	−	1.48298i	−0.875531	−	0.483163i	$-0.839488\pi$
$499$	−19.1260	−	33.1272i	−0.856196	−	1.48298i	0.0193342	−	0.999813i	$-0.493845\pi$
$500$	−2.57617	+	4.46205i	−0.115210	+	0.199549i
$501$	1.59148	−	2.75653i	0.0711023	−	0.123153i
$502$	28.5216	+	49.4009i	1.27298	+	2.20487i
$503$	6.06642			0.270488			0.135244	−	0.990812i	$-0.456818\pi$
$503$	6.06642			0.270488			0.135244	+	0.990812i	$0.456818\pi$
$504$	59.8259	−	26.1912i	2.66486	−	1.16665i
$505$	−6.67382			−0.296981
$506$	4.80991	+	8.33101i	0.213827	+	0.370359i
$507$	−1.49769	+	2.59408i	−0.0665149	+	0.115207i
$508$	−0.212052	+	0.367285i	−0.00940828	+	0.0162956i
$509$	3.64370	+	6.31107i	0.161504	+	0.279733i	0.935408	−	0.353569i	$-0.115032\pi$
$509$	3.64370	+	6.31107i	0.161504	+	0.279733i	−0.773904	+	0.633303i	$0.781699\pi$
$510$	2.44495			0.108264
$511$	−25.0071	−	18.4077i	−1.10625	−	0.814308i
$512$	12.0308			0.531691
$513$	0.282583	+	0.489449i	0.0124764	+	0.0216097i
$514$	23.5791	−	40.8402i	1.04003	−	1.80138i
$515$	6.11027	−	10.5833i	0.269251	−	0.466356i
$516$	−7.67168	−	13.2877i	−0.337727	−	0.584960i
$517$	−5.82355			−0.256119
$518$	5.69840	+	4.19458i	0.250374	+	0.184299i
$519$	−5.01397			−0.220089
$520$	5.72121	+	9.90943i	0.250892	+	0.434557i
$521$	−7.61014	+	13.1811i	−0.333406	+	0.577476i	−0.983177	−	0.182653i	$-0.941531\pi$
$521$	−7.61014	+	13.1811i	−0.333406	+	0.577476i	0.649771	+	0.760130i	$0.274865\pi$
$522$	−2.37695	+	4.11700i	−0.104036	+	0.180196i
$523$	1.98645	+	3.44064i	0.0868616	+	0.150449i	0.906183	−	0.422886i	$-0.138983\pi$
$523$	1.98645	+	3.44064i	0.0868616	+	0.150449i	−0.819321	+	0.573335i	$0.805650\pi$
$524$	−97.5907			−4.26327
$525$	−0.650647	+	0.284847i	−0.0283966	+	0.0124317i
$526$	24.0617			1.04914
$527$	−2.37176	−	4.10801i	−0.103316	−	0.178948i
$528$	0.827875	−	1.43392i	0.0360286	−	0.0624034i
$529$	−13.9863	+	24.2250i	−0.608099	+	1.05326i
$530$	0.218293	+	0.378094i	0.00948202	+	0.0164233i
$531$	35.0109			1.51934
$532$	0.536007	−	4.81144i	0.0232388	−	0.208602i
$533$	0.137749			0.00596659
$534$	3.86554	+	6.69532i	0.167278	+	0.289735i
$535$	−3.09477	+	5.36030i	−0.133798	+	0.231746i
$536$	−61.3470	+	106.256i	−2.64979	+	4.58956i
$537$	1.53684	+	2.66189i	0.0663196	+	0.114869i
$538$	1.37886			0.0594468
$539$	2.39230	−	2.59129i	0.103043	−	0.111615i
$540$	8.19935			0.352844
$541$	11.1449	+	19.3035i	0.479155	+	0.829921i	0.999714	−	0.0239049i	$-0.00760991\pi$
$541$	11.1449	+	19.3035i	0.479155	+	0.829921i	−0.520559	+	0.853825i	$0.674277\pi$
$542$	17.0711	−	29.5680i	0.733266	−	1.27005i
$543$	0.887113	−	1.53653i	0.0380697	−	0.0659386i
$544$	27.0364	+	46.8285i	1.15918	+	2.00775i
$545$	6.99211			0.299509
$546$	−0.285446	+	2.56230i	−0.0122160	+	0.109656i
$547$	−40.2534			−1.72111			−0.860556	−	0.509356i	$-0.829884\pi$
$547$	−40.2534			−1.72111			−0.860556	+	0.509356i	$0.829884\pi$
$548$	−36.6497	−	63.4791i	−1.56560	−	2.71169i
$549$	−8.45439	+	14.6434i	−0.360825	+	0.624967i
$550$	0.673703	−	1.16689i	0.0287268	−	0.0497563i
$551$	0.107804	+	0.186722i	0.00459262	+	0.00795465i
$552$	16.1583			0.687744
$553$	−16.6152	+	7.27397i	−0.706551	+	0.309321i
$554$	−12.8809			−0.547255
$555$	0.134228	+	0.232489i	0.00569765	+	0.00986862i
$556$	−16.5793	+	28.7161i	−0.703117	+	1.21783i
$557$	11.6081	−	20.1058i	0.491852	−	0.851912i	−0.508104	−	0.861296i	$-0.669654\pi$
$557$	11.6081	−	20.1058i	0.491852	−	0.851912i	0.999956	+	0.00938350i	$0.00298690\pi$
$558$	−5.45358	−	9.44587i	−0.230868	−	0.399876i
$559$	−15.0559			−0.636797
$560$	−26.0841	−	19.2005i	−1.10226	−	0.811368i
$561$	−0.460598			−0.0194465
$562$	−41.4722	−	71.8320i	−1.74940	−	3.03005i
$563$	6.50185	−	11.2615i	0.274020	−	0.474617i	−0.695867	−	0.718171i	$-0.744980\pi$
$563$	6.50185	−	11.2615i	0.274020	−	0.474617i	0.969888	+	0.243553i	$0.0783131\pi$
$564$	−7.99390	+	13.8458i	−0.336604	+	0.583015i
$565$	−6.46079	−	11.1904i	−0.271808	−	0.470785i
$566$	61.8941			2.60160
$567$	−17.8057	−	13.1067i	−0.747767	−	0.550429i
$568$	22.4375			0.941455
$569$	9.31604	+	16.1359i	0.390549	+	0.676450i	0.992522	−	0.122066i	$-0.0389520\pi$
$569$	9.31604	+	16.1359i	0.390549	+	0.676450i	−0.601973	+	0.798516i	$0.705619\pi$
$570$	0.127487	−	0.220815i	0.00533986	−	0.00924890i
$571$	20.7505	−	35.9409i	0.868381	−	1.50408i	0.00473039	−	0.999989i	$-0.498494\pi$
$571$	20.7505	−	35.9409i	0.868381	−	1.50408i	0.863651	−	0.504091i	$-0.168172\pi$
$572$	−1.76162	−	3.05121i	−0.0736568	−	0.127577i
$573$	2.97265			0.124184
$574$	−0.657845	+	0.287998i	−0.0274579	+	0.0120208i
$575$	7.13951			0.297738
$576$	26.3236	+	45.5939i	1.09682	+	1.89974i
$577$	20.6185	−	35.7124i	0.858361	−	1.48673i	−0.0151298	−	0.999886i	$-0.504816\pi$
$577$	20.6185	−	35.7124i	0.858361	−	1.48673i	0.873491	−	0.486840i	$-0.161851\pi$
$578$	−7.22474	+	12.5136i	−0.300509	+	0.520498i
$579$	−1.76186	−	3.05163i	−0.0732203	−	0.126821i
$580$	3.12802			0.129884
$581$	−2.41540	+	21.6818i	−0.100208	+	0.899511i
$582$	0.387880			0.0160782
$583$	−0.0411235	−	0.0712280i	−0.00170316	−	0.00294996i
$584$	49.4721	−	85.6882i	2.04717	−	3.54580i
$585$	1.98698	−	3.44155i	0.0821515	−	0.142291i
$586$	16.0258	+	27.7575i	0.662021	+	1.14665i
$587$	−2.42823			−0.100224			−0.0501118	−	0.998744i	$-0.515958\pi$
$587$	−2.42823			−0.100224			−0.0501118	+	0.998744i	$0.515958\pi$
$588$	−2.87709	−	9.24486i	−0.118649	−	0.381252i
$589$	−0.494683			−0.0203831
$590$	−15.9895	−	27.6947i	−0.658279	−	1.14017i
$591$	−1.02557	+	1.77634i	−0.0421863	+	0.0730688i
$592$	−6.12093	+	10.6018i	−0.251569	+	0.435729i
$593$	−8.80313	−	15.2475i	−0.361501	−	0.626138i	0.626707	−	0.779255i	$-0.284402\pi$
$593$	−8.80313	−	15.2475i	−0.361501	−	0.626138i	−0.988208	+	0.153117i	$0.951069\pi$
$594$	−2.14425			−0.0879794
$595$	−0.997563	+	8.95458i	−0.0408961	+	0.367102i
$596$	−22.3309			−0.914711
$597$	−3.11708	−	5.39893i	−0.127573	−	0.220964i
$598$	12.9576	−	22.4432i	0.529875	−	0.917771i
$599$	2.44622	−	4.23698i	0.0999499	−	0.173118i	−0.811714	−	0.584055i	$-0.801465\pi$
$599$	2.44622	−	4.23698i	0.0999499	−	0.173118i	0.911664	+	0.410937i	$0.134798\pi$
$600$	−1.13161	−	1.96001i	−0.0461979	−	0.0800172i
$601$	3.92552			0.160125			0.0800627	−	0.996790i	$-0.474488\pi$
$601$	3.92552			0.160125			0.0800627	+	0.996790i	$0.474488\pi$
$602$	71.9020	−	31.4780i	2.93051	−	1.28295i
$603$	42.6117			1.73528
$604$	−29.9303	−	51.8408i	−1.21785	−	2.10937i
$605$	5.37308	−	9.30645i	0.218447	−	0.378361i
$606$	2.39575	−	4.14956i	0.0973206	−	0.168564i
$607$	17.8875	+	30.9821i	0.726032	+	1.25752i	0.958548	+	0.284932i	$0.0919710\pi$
$607$	17.8875	+	30.9821i	0.726032	+	1.25752i	−0.232516	+	0.972593i	$0.574696\pi$
$608$	5.63905			0.228693
$609$	0.347270	+	0.255624i	0.0140721	+	0.0103584i
$610$	15.4445			0.625331
$611$	7.84413	+	13.5864i	0.317340	+	0.549648i
$612$	25.6867	−	44.4907i	1.03833	−	1.79843i
$613$	−13.6005	+	23.5567i	−0.549318	+	0.951447i	0.449003	+	0.893530i	$0.351779\pi$
$613$	−13.6005	+	23.5567i	−0.549318	+	0.951447i	−0.998321	+	0.0579169i	$0.981554\pi$
$614$	−39.6079	−	68.6029i	−1.59844	−	2.76859i
$615$	−0.0272458			−0.00109866
$616$	9.05024	+	6.66186i	0.364645	+	0.268414i
$617$	−13.4525			−0.541579			−0.270790	−	0.962639i	$-0.587285\pi$
$617$	−13.4525			−0.541579			−0.270790	+	0.962639i	$0.587285\pi$
$618$	4.38689	+	7.59831i	0.176467	+	0.305649i
$619$	4.03392	−	6.98695i	0.162137	−	0.280829i	−0.773498	−	0.633799i	$-0.781495\pi$
$619$	4.03392	−	6.98695i	0.162137	−	0.280829i	0.935635	+	0.352970i	$0.114828\pi$
$620$	−3.58840	+	6.21528i	−0.144113	+	0.249612i
$621$	−5.68086	−	9.83953i	−0.227965	−	0.394847i
$622$	75.5549			3.02948
$623$	−26.0986	+	11.4257i	−1.04562	+	0.457761i
$624$	−4.46048			−0.178562
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	33.1550	−	57.4261i	1.32514	−	2.29521i
$627$	−0.0240170	+	0.0415986i	−0.000959145	+	0.00166129i
$628$	−9.60054	−	16.6286i	−0.383103	−	0.663554i
$629$	3.40545			0.135784
$630$	−2.29377	+	20.5900i	−0.0913861	+	0.820323i
$631$	−7.43331			−0.295916			−0.147958	−	0.988994i	$-0.547270\pi$
$631$	−7.43331			−0.295916			−0.147958	+	0.988994i	$0.547270\pi$
$632$	−28.8974	−	50.0517i	−1.14948	−	1.99095i
$633$	0.102481	−	0.177502i	0.00407324	−	0.00705506i
$634$	30.0410	−	52.0325i	1.19308	−	2.06648i
$635$	−0.0411565	−	0.0712852i	−0.00163325	−	0.00282887i
$636$	−0.225799			−0.00895350
$637$	−9.26788	−	2.09088i	−0.367207	−	0.0828436i
$638$	−0.818020			−0.0323857
$639$	−3.89627	−	6.74853i	−0.154134	−	0.266968i
$640$	8.16579	−	14.1436i	0.322781	−	0.559073i
$641$	15.7068	−	27.2050i	0.620381	−	1.07453i	−0.369033	−	0.929416i	$-0.620311\pi$
$641$	15.7068	−	27.2050i	0.620381	−	1.07453i	0.989415	−	0.145116i	$-0.0463555\pi$
$642$	−2.22190	−	3.84844i	−0.0876914	−	0.151886i
$643$	45.7974			1.80607			0.903036	−	0.429564i	$-0.141333\pi$
$643$	45.7974			1.80607			0.903036	+	0.429564i	$0.141333\pi$
$644$	−10.7755	+	96.7259i	−0.424614	+	3.81153i
$645$	2.97795			0.117256
$646$	−1.61722	−	2.80111i	−0.0636287	−	0.110208i
$647$	23.8153	−	41.2493i	0.936275	−	1.62168i	0.163932	−	0.986472i	$-0.447582\pi$
$647$	23.8153	−	41.2493i	0.936275	−	1.62168i	0.772344	−	0.635205i	$-0.219084\pi$
$648$	35.2253	−	61.0119i	1.38378	−	2.39677i
$649$	3.01222	+	5.21732i	0.118240	+	0.204798i
$650$	−3.62983			−0.142374
$651$	−0.906300	+	0.396769i	−0.0355207	+	0.0155506i
$652$	11.2452			0.440397
$653$	−0.917614	−	1.58935i	−0.0359090	−	0.0621962i	0.847512	−	0.530776i	$-0.178099\pi$
$653$	−0.917614	−	1.58935i	−0.0359090	−	0.0621962i	−0.883421	+	0.468579i	$0.844766\pi$
$654$	−2.51000	+	4.34746i	−0.0981489	+	0.169999i
$655$	9.47054	−	16.4035i	0.370045	−	0.640936i
$656$	−0.621218	−	1.07598i	−0.0242545	−	0.0420100i
$657$	−34.3634			−1.34064
$658$	−65.8667	−	48.4843i	−2.56775	−	1.89011i
$659$	−9.57745			−0.373085			−0.186542	−	0.982447i	$-0.559728\pi$
$659$	−9.57745			−0.373085			−0.186542	+	0.982447i	$0.559728\pi$
$660$	0.348435	+	0.603506i	0.0135628	+	0.0234915i
$661$	−12.5837	+	21.7957i	−0.489451	+	0.847754i	−0.999926	−	0.0121386i	$-0.996136\pi$
$661$	−12.5837	+	21.7957i	−0.489451	+	0.847754i	0.510476	+	0.859892i	$0.329469\pi$
$662$	18.8658	−	32.6765i	0.733239	−	1.27001i
$663$	0.620411	+	1.07458i	0.0240948	+	0.0417333i
$664$	−69.5151			−2.69771
$665$	0.756711	+	0.557013i	0.0293440	+	0.0216000i
$666$	7.83041			0.303422
$667$	−2.16722	−	3.75374i	−0.0839152	−	0.145345i
$668$	−30.5445	+	52.9047i	−1.18180	+	2.04694i
$669$	0.482213	−	0.835217i	0.0186434	−	0.0322913i
$670$	−19.4608	−	33.7071i	−0.751837	−	1.30222i
$671$	−2.90955			−0.112322
$672$	10.3312	−	4.52289i	0.398534	−	0.174474i
$673$	−7.91373			−0.305052			−0.152526	−	0.988299i	$-0.548741\pi$
$673$	−7.91373			−0.305052			−0.152526	+	0.988299i	$0.548741\pi$
$674$	−28.7170	−	49.7392i	−1.10614	−	1.91588i
$675$	−0.795693	+	1.37818i	−0.0306262	+	0.0530462i
$676$	28.7445	−	49.7869i	1.10556	−	1.91488i
$677$	14.9167	+	25.8365i	0.573296	+	0.992978i	0.996224	+	0.0868152i	$0.0276690\pi$
$677$	14.9167	+	25.8365i	0.573296	+	0.992978i	−0.422928	+	0.906163i	$0.638998\pi$
$678$	9.27710			0.356285
$679$	−0.158259	+	1.42060i	−0.00607341	+	0.0545177i
$680$	−28.7098			−1.10097
$681$	2.19414	+	3.80037i	0.0840798	+	0.145630i
$682$	0.938416	−	1.62538i	0.0359338	−	0.0622392i
$683$	−11.1594	+	19.3287i	−0.427003	+	0.739591i	−0.996605	−	0.0823299i	$-0.973764\pi$
$683$	−11.1594	+	19.3287i	−0.427003	+	0.739591i	0.569602	+	0.821920i	$0.307097\pi$
$684$	−2.67877	−	4.63977i	−0.102425	−	0.177406i
$685$	14.2264			0.543565
$686$	48.6318	−	9.39137i	1.85677	−	0.358564i
$687$	4.38555			0.167319
$688$	67.8987	+	117.604i	2.58861	+	4.48361i
$689$	−0.110784	+	0.191884i	−0.00422054	+	0.00731019i
$690$	−2.56292	+	4.43910i	−0.0975686	+	0.168994i
$691$	−8.70016	−	15.0691i	−0.330970	−	0.573256i	0.651732	−	0.758449i	$-0.274042\pi$
$691$	−8.70016	−	15.0691i	−0.330970	−	0.573256i	−0.982702	+	0.185192i	$0.940709\pi$
$692$	96.2306			3.65814
$693$	0.432117	−	3.87888i	0.0164148	−	0.147347i
$694$	−11.7450			−0.445835
$695$	−3.21782	−	5.57342i	−0.122059	−	0.211412i
$696$	−0.687010	+	1.18994i	−0.0260411	+	0.0451044i
$697$	−0.172811	+	0.299318i	−0.00654569	+	0.0113375i
$698$	−31.9573	−	55.3516i	−1.20960	−	2.09509i
$699$	2.45665			0.0929190
$700$	12.4875	−	5.46691i	0.471984	−	0.206630i
$701$	−0.731357			−0.0276230			−0.0138115	−	0.999905i	$-0.504396\pi$
$701$	−0.731357			−0.0276230			−0.0138115	+	0.999905i	$0.504396\pi$
$702$	2.88823	+	5.00256i	0.109009	+	0.188810i
$703$	0.177570	−	0.307561i	0.00669720	−	0.0115999i
$704$	−4.52960	+	7.84550i	−0.170716	+	0.295688i
$705$	−1.55151	−	2.68730i	−0.0584333	−	0.101209i
$706$	−58.6240			−2.20634
$707$	14.2202	+	10.4674i	0.534804	+	0.393668i
$708$	16.5394			0.621587
$709$	−16.9775	−	29.4059i	−0.637604	−	1.10436i	−0.985957	−	0.166999i	$-0.946592\pi$
$709$	−16.9775	−	29.4059i	−0.637604	−	1.10436i	0.348354	−	0.937363i	$-0.386741\pi$
$710$	−3.55887	+	6.16414i	−0.133562	+	0.231336i
$711$	−10.0361	+	17.3830i	−0.376382	+	0.651913i
$712$	−45.3910	−	78.6195i	−1.70110	−	2.94639i
$713$	9.94477			0.372435
$714$	−5.20955	−	3.83474i	−0.194962	−	0.143511i
$715$	0.683813			0.0255732
$716$	−29.4958	−	51.0883i	−1.10231	−	1.90926i
$717$	3.88693	−	6.73236i	0.145160	−	0.251425i
$718$	−24.2101	+	41.9332i	−0.903515	+	1.56493i
$719$	16.6880	+	28.9045i	0.622358	+	1.07796i	0.989045	+	0.147612i	$0.0471587\pi$
$719$	16.6880	+	28.9045i	0.622358	+	1.07796i	−0.366687	+	0.930344i	$0.619508\pi$
$720$	−35.8433			−1.33580
$721$	−29.6185	+	12.9667i	−1.10305	+	0.482904i
$722$	50.4760			1.87852
$723$	−0.343391	−	0.594771i	−0.0127709	−	0.0221198i
$724$	−17.0259	+	29.4897i	−0.632763	+	1.09598i
$725$	−0.303553	+	0.525770i	−0.0112737	+	0.0195266i
$726$	3.85762	+	6.68160i	0.143170	+	0.247977i
$727$	−39.1209			−1.45091			−0.725457	−	0.688267i	$-0.758372\pi$
$727$	−39.1209			−1.45091			−0.725457	+	0.688267i	$0.758372\pi$
$728$	3.35184	−	30.0877i	0.124228	−	1.11512i
$729$	−23.1858			−0.858735
$730$	15.6938	+	27.1825i	0.580854	+	1.00607i
$731$	18.8881	−	32.7152i	0.698602	−	1.21001i
$732$	−3.99390	+	6.91764i	−0.147619	+	0.255684i
$733$	19.1073	+	33.0948i	0.705743	+	1.22238i	0.966423	+	0.256958i	$0.0827201\pi$
$733$	19.1073	+	33.0948i	0.705743	+	1.22238i	−0.260680	+	0.965425i	$0.583947\pi$
$734$	−30.8278			−1.13787
$735$	1.83312	+	0.413560i	0.0676156	+	0.0152544i
$736$	−113.363			−4.17863
$737$	3.66617	+	6.34999i	0.135045	+	0.233905i
$738$	−0.397358	+	0.688244i	−0.0146269	+	0.0253346i
$739$	25.3310	−	43.8747i	0.931818	−	1.61396i	0.151605	−	0.988441i	$-0.451556\pi$
$739$	25.3310	−	43.8747i	0.931818	−	1.61396i	0.780213	−	0.625514i	$-0.215111\pi$
$740$	−2.57617	−	4.46205i	−0.0947017	−	0.164028i
$741$	0.129400			0.00475364
$742$	0.127889	−	1.14799i	0.00469497	−	0.0421442i
$743$	−45.6469			−1.67462			−0.837311	−	0.546727i	$-0.815873\pi$
$743$	−45.6469			−1.67462			−0.837311	+	0.546727i	$0.815873\pi$
$744$	−1.57625	−	2.73014i	−0.0577881	−	0.100092i
$745$	2.16707	−	3.75348i	0.0793954	−	0.137517i
$746$	−26.1394	+	45.2747i	−0.957030	+	1.65763i
$747$	12.0713	+	20.9081i	0.441666	+	0.764989i
$748$	8.84002			0.323223
$749$	15.0014	−	6.56745i	0.548138	−	0.239969i
$750$	0.717953			0.0262160
$751$	0.341431	+	0.591375i	0.0124590	+	0.0215796i	0.872188	−	0.489171i	$-0.162701\pi$
$751$	0.341431	+	0.591375i	0.0124590	+	0.0215796i	−0.859729	+	0.510751i	$0.829367\pi$
$752$	70.7505	−	122.544i	2.58001	−	4.46870i
$753$	2.86301	−	4.95888i	0.104334	−	0.180712i
$754$	1.10185	+	1.90846i	0.0401269	+	0.0695018i
$755$	11.6182			0.422828
$756$	−17.4706	−	12.8601i	−0.635401	−	0.467717i
$757$	−14.9800			−0.544459			−0.272229	−	0.962232i	$-0.587761\pi$
$757$	−14.9800			−0.544459			−0.272229	+	0.962232i	$0.587761\pi$
$758$	−18.8383	−	32.6289i	−0.684238	−	1.18514i
$759$	0.482820	−	0.836270i	0.0175253	−	0.0303547i
$760$	−1.49702	+	2.59291i	−0.0543025	+	0.0940546i
$761$	8.06887	+	13.9757i	0.292496	+	0.506619i	0.974399	−	0.224824i	$-0.0721807\pi$
$761$	8.06887	+	13.9757i	0.292496	+	0.506619i	−0.681903	+	0.731443i	$0.738847\pi$
$762$	0.0590969			0.00214086
$763$	−14.8983	−	10.9666i	−0.539356	−	0.397018i
$764$	−57.0526			−2.06409
$765$	4.98546	+	8.63507i	0.180250	+	0.312202i
$766$	25.2267	−	43.6939i	0.911477	−	1.57872i
$767$	8.11474	−	14.0551i	0.293006	−	0.507502i
$768$	1.03554	+	1.79361i	0.0373669	+	0.0647213i
$769$	20.5327			0.740427			0.370214	−	0.928947i	$-0.379284\pi$
$769$	20.5327			0.740427			0.370214	+	0.928947i	$0.379284\pi$
$770$	−3.26566	+	1.42967i	−0.117686	+	0.0515219i
$771$	−4.73376			−0.170482
$772$	33.8144	+	58.5683i	1.21701	+	2.10792i
$773$	13.7027	−	23.7338i	0.492853	−	0.853646i	−0.507113	−	0.861879i	$-0.669287\pi$
$773$	13.7027	−	23.7338i	0.492853	−	0.853646i	0.999966	+	0.00823318i	$0.00262073\pi$
$774$	43.4309	−	75.2246i	1.56109	−	2.70389i
$775$	−0.696461	−	1.20631i	−0.0250176	−	0.0433318i
$776$	−4.55467			−0.163503
$777$	0.0786390	−	0.705900i	0.00282116	−	0.0253240i
$778$	88.0494			3.15672
$779$	0.0180218	+	0.0312147i	0.000645698	+	0.00111838i
$780$	0.938661	−	1.62581i	0.0336094	−	0.0582133i
$781$	0.670445	−	1.16124i	0.0239904	−	0.0415526i
$782$	32.5115	+	56.3115i	1.16261	+	2.01370i
$783$	0.966142			0.0345271
$784$	25.4638	+	81.8222i	0.909423	+	2.92222i
$785$	3.72668			0.133011
$786$	6.79941	+	11.7769i	0.242527	+	0.420069i
$787$	20.1609	−	34.9198i	0.718660	−	1.24476i	−0.242870	−	0.970059i	$-0.578089\pi$
$787$	20.1609	−	34.9198i	0.718660	−	1.24476i	0.961531	−	0.274697i	$-0.0885777\pi$
$788$	19.6832	−	34.0924i	0.701186	−	1.21449i
$789$	−1.20766	−	2.09173i	−0.0429939	−	0.0744676i
$790$	18.3340			0.652294
$791$	−3.78514	+	33.9771i	−0.134584	+	1.20809i
$792$	12.4363			0.441905
$793$	3.91908	+	6.78804i	0.139170	+	0.241050i
$794$	−3.86573	+	6.69565i	−0.137190	+	0.237620i
$795$	0.0219123	−	0.0379532i	0.000777149	−	0.00134606i
$796$	59.8244	+	103.619i	2.12042	+	3.67268i
$797$	0.567617			0.0201060			0.0100530	−	0.999949i	$-0.496800\pi$
$797$	0.567617			0.0201060			0.0100530	+	0.999949i	$0.496800\pi$
$798$	−0.617974	+	0.270543i	−0.0218760	+	0.00957710i
$799$	−39.3629			−1.39256
$800$	7.93916	+	13.7510i	0.280692	+	0.486173i
$801$	−15.7643	+	27.3046i	−0.557005	+	0.964760i
$802$	−23.5792	+	40.8404i	−0.832612	+	1.44213i
$803$	−2.95651	−	5.12083i	−0.104333	−	0.180710i
$804$	20.1300			0.709930
$805$	−15.2124	−	11.1978i	−0.536167	−	0.394671i
$806$	−5.05607			−0.178092
$807$	−0.0692052	−	0.119867i	−0.00243614	−	0.00421951i
$808$	−28.1320	+	48.7260i	−0.989680	+	1.71418i
$809$	2.34102	−	4.05476i	0.0823057	−	0.142558i	−0.821934	−	0.569582i	$-0.807105\pi$
$809$	2.34102	−	4.05476i	0.0823057	−	0.142558i	0.904240	+	0.427025i	$0.140438\pi$
$810$	11.1744	+	19.3545i	0.392627	+	0.680049i
$811$	20.5731			0.722421			0.361210	−	0.932484i	$-0.382364\pi$
$811$	20.5731			0.722421			0.361210	+	0.932484i	$0.382364\pi$
$812$	−6.66497	−	4.90607i	−0.233895	−	0.172169i
$813$	−3.42720			−0.120197
$814$	0.673703	+	1.16689i	0.0236133	+	0.0408994i
$815$	−1.09128	+	1.89014i	−0.0382257	+	0.0662089i
$816$	5.59582	−	9.69225i	0.195893	−	0.339297i
$817$	−1.96977	−	3.41174i	−0.0689135	−	0.119362i
$818$	24.8488			0.868818
$819$	−9.63155	+	4.21659i	−0.336554	+	0.147340i
$820$	0.522915			0.0182610
$821$	3.12324	+	5.40961i	0.109002	+	0.188797i	0.915366	−	0.402622i	$-0.131901\pi$
$821$	3.12324	+	5.40961i	0.109002	+	0.188797i	−0.806364	+	0.591419i	$0.798568\pi$
$822$	−5.10696	+	8.84552i	−0.178126	+	0.308523i
$823$	3.99804	−	6.92480i	0.139363	−	0.241384i	−0.787893	−	0.615812i	$-0.788828\pi$
$823$	3.99804	−	6.92480i	0.139363	−	0.241384i	0.927256	+	0.374429i	$0.122161\pi$
$824$	−51.5129	−	89.2229i	−1.79454	−	3.10823i
$825$	−0.135253			−0.00470891
$826$	−9.36768	+	84.0885i	−0.325943	+	2.92581i
$827$	−2.74166			−0.0953367			−0.0476684	−	0.998863i	$-0.515179\pi$
$827$	−2.74166			−0.0953367			−0.0476684	+	0.998863i	$0.515179\pi$
$828$	53.8521	+	93.2746i	1.87149	+	3.24152i
$829$	−17.6546	+	30.5786i	−0.613169	+	1.06204i	0.377534	+	0.925996i	$0.376772\pi$
$829$	−17.6546	+	30.5786i	−0.613169	+	1.06204i	−0.990703	+	0.136044i	$0.956561\pi$
$830$	11.0260	−	19.0976i	0.382718	−	0.662886i
$831$	0.646492	+	1.11976i	0.0224266	+	0.0388440i
$832$	24.4049			0.846088
$833$	16.1702	−	17.5152i	0.560263	−	0.606867i
$834$	4.62049			0.159994
$835$	−5.92830	−	10.2681i	−0.205157	−	0.355343i
$836$	0.460945	−	0.798381i	0.0159421	−	0.0276126i
$837$	−1.10834	+	1.91970i	−0.0383098	+	0.0663545i
$838$	5.33991	+	9.24900i	0.184464	+	0.319501i
$839$	42.7124			1.47460			0.737298	−	0.675568i	$-0.236101\pi$
$839$	42.7124			1.47460			0.737298	+	0.675568i	$0.236101\pi$
$840$	−0.662970	+	5.95112i	−0.0228746	+	0.205333i
$841$	−28.6314			−0.987290
$842$	26.1291	+	45.2569i	0.900468	+	1.55966i
$843$	−4.16300	+	7.21052i	−0.143381	+	0.248344i
$844$	−1.96686	+	3.40670i	−0.0677021	+	0.117263i
$845$	5.57893	+	9.66298i	0.191921	+	0.332417i
$846$	−90.5102			−3.11180
$847$	−26.0451	+	11.4023i	−0.894921	+	0.391787i
$848$	1.99845			0.0686269
$849$	−3.10648	−	5.38058i	−0.106614	−	0.184661i
$850$	4.55374	−	7.88731i	0.156192	−	0.270532i
$851$	−3.56975	+	6.18299i	−0.122370	+	0.211950i
$852$	−1.84062	−	3.18805i	−0.0630586	−	0.109221i
$853$	29.1241			0.997191			0.498596	−	0.866835i	$-0.333849\pi$
$853$	29.1241			0.997191			0.498596	+	0.866835i	$0.333849\pi$
$854$	−32.9082	−	24.2237i	−1.12610	−	0.828917i
$855$	1.03983			0.0355614
$856$	26.0906	+	45.1902i	0.891758	+	1.54457i
$857$	15.7797	−	27.3312i	0.539024	−	0.933616i	−0.459933	−	0.887953i	$-0.652127\pi$
$857$	15.7797	−	27.3312i	0.539024	−	0.933616i	0.998957	−	0.0456628i	$-0.0145400\pi$
$858$	−0.245473	+	0.425172i	−0.00838031	+	0.0145151i
$859$	−25.2074	−	43.6605i	−0.860066	−	1.48968i	−0.871864	−	0.489748i	$-0.837089\pi$
$859$	−25.2074	−	43.6605i	−0.860066	−	1.48968i	0.0117975	−	0.999930i	$-0.496245\pi$
$860$	−57.1542			−1.94894
$861$	0.0580536	+	0.0427331i	0.00197846	+	0.00145634i
$862$	−2.22818			−0.0758920
$863$	12.3351	+	21.3650i	0.419892	+	0.727273i	0.995928	−	0.0901504i	$-0.0287348\pi$
$863$	12.3351	+	21.3650i	0.419892	+	0.727273i	−0.576037	+	0.817424i	$0.695401\pi$
$864$	12.6343	−	21.8832i	0.429827	−	0.744482i
$865$	−9.33855	+	16.1748i	−0.317520	+	0.549961i
$866$	3.39650	+	5.88290i	0.115418	+	0.199909i
$867$	1.45044			0.0492596
$868$	17.3941	−	7.61498i	0.590396	−	0.258469i
$869$	−3.45389			−0.117165
$870$	−0.217937	−	0.377478i	−0.00738877	−	0.0127977i
$871$	9.87643	−	17.1065i	0.334650	−	0.579631i
$872$	29.4736	−	51.0498i	0.998103	−	1.72877i
$873$	0.790920	+	1.36991i	0.0267686	+	0.0463645i
$874$	6.78099			0.229370
$875$	−0.292931	+	2.62948i	−0.00990288	+	0.0888928i
$876$	−16.2335			−0.548477
$877$	−16.3444	−	28.3094i	−0.551913	−	0.955941i	−0.998137	−	0.0610194i	$-0.980565\pi$
$877$	−16.3444	−	28.3094i	−0.551913	−	0.955941i	0.446224	−	0.894921i	$-0.352768\pi$
$878$	−15.3535	+	26.5931i	−0.518157	+	0.897474i
$879$	1.60868	−	2.78631i	0.0542594	−	0.0939800i
$880$	−3.08384	−	5.34137i	−0.103956	−	0.180058i
$881$	14.5972			0.491792			0.245896	−	0.969296i	$-0.420918\pi$
$881$	14.5972			0.491792			0.245896	+	0.969296i	$0.420918\pi$
$882$	37.1813	−	40.2741i	1.25196	−	1.35610i
$883$	−41.4745			−1.39573			−0.697864	−	0.716230i	$-0.745866\pi$
$883$	−41.4745			−1.39573			−0.697864	+	0.716230i	$0.745866\pi$
$884$	−11.9072	−	20.6239i	−0.400483	−	0.693657i
$885$	−1.60504	+	2.78000i	−0.0539527	+	0.0934488i
$886$	1.23098	−	2.13213i	0.0413557	−	0.0716302i
$887$	−27.5770	−	47.7648i	−0.925946	−	1.60379i	−0.790032	−	0.613066i	$-0.789936\pi$
$887$	−27.5770	−	47.7648i	−0.925946	−	1.60379i	−0.135914	−	0.990721i	$-0.543397\pi$
$888$	2.26323			0.0759489
$889$	−0.0241121	+	0.216441i	−0.000808692	+	0.00725919i
$890$	28.7984			0.965324
$891$	−2.10510	−	3.64615i	−0.0705236	−	0.122150i
$892$	−9.25486	+	16.0299i	−0.309876	+	0.536720i
$893$	−2.05250	+	3.55504i	−0.0686843	+	0.118965i
$894$	1.55586	+	2.69482i	0.0520356	+	0.0901284i
$895$	11.4495			0.382715
$896$	−39.5823	+	17.3287i	−1.32235	+	0.578912i
$897$	−2.60138			−0.0868574
$898$	17.4267	+	30.1840i	0.581537	+	1.00725i
$899$	−0.422826	+	0.732356i	−0.0141020	+	0.0244254i
$900$	7.54284	−	13.0646i	0.251428	−	0.435486i
$901$	−0.277965	−	0.481449i	−0.00926035	−	0.0160394i
$902$	−0.136750			−0.00455326
$903$	−6.34521	−	4.67069i	−0.211155	−	0.155431i
$904$	−108.936			−3.62316
$905$	−3.30451	−	5.72357i	−0.109846	−	0.190258i
$906$	−4.17065	+	7.22378i	−0.138561	+	0.239994i
$907$	28.3630	−	49.1262i	0.941779	−	1.63121i	0.179705	−	0.983721i	$-0.442486\pi$
$907$	28.3630	−	49.1262i	0.941779	−	1.63121i	0.762075	−	0.647489i	$-0.224181\pi$
$908$	−42.1111	−	72.9385i	−1.39750	−	2.42055i
$909$	19.5405			0.648117
$910$	7.73420	+	5.69313i	0.256386	+	0.188725i
$911$	29.2569			0.969325			0.484662	−	0.874701i	$-0.338943\pi$
$911$	29.2569			0.969325			0.484662	+	0.874701i	$0.338943\pi$
$912$	−0.583567	−	1.01077i	−0.0193238	−	0.0334698i
$913$	−2.07715	+	3.59774i	−0.0687438	+	0.119068i
$914$	−51.7419	+	89.6196i	−1.71147	+	2.96435i
$915$	−0.775165	−	1.34262i	−0.0256261	−	0.0443858i
$916$	−84.1696			−2.78104
$917$	−45.9069	+	20.0976i	−1.51598	+	0.663680i
$918$	−14.4935			−0.478357
$919$	−9.44388	−	16.3573i	−0.311525	−	0.539577i	0.667168	−	0.744908i	$-0.267506\pi$
$919$	−9.44388	−	16.3573i	−0.311525	−	0.539577i	−0.978693	+	0.205330i	$0.934173\pi$
$920$	30.0950	−	52.1260i	0.992202	−	1.71854i
$921$	−3.97585	+	6.88638i	−0.131009	+	0.226914i
$922$	11.1117	+	19.2461i	0.365945	+	0.633836i
$923$	−3.61227			−0.118899
$924$	0.204135	−	1.83241i	0.00671554	−	0.0602818i
$925$	1.00000			0.0328798
$926$	−1.72469	−	2.98725i	−0.0566769	−	0.0981673i
$927$	−17.8904	+	30.9872i	−0.587599	+	1.01775i
$928$	4.81992	−	8.34835i	0.158222	−	0.274048i
$929$	7.77839	+	13.4726i	0.255201	+	0.442021i	0.964950	−	0.262434i	$-0.0845251\pi$
$929$	7.77839	+	13.4726i	0.255201	+	0.442021i	−0.709749	+	0.704454i	$0.751192\pi$
$930$	1.00005			0.0327930
$931$	−0.738716	−	2.37370i	−0.0242104	−	0.0777947i
$932$	−47.1492			−1.54442
$933$	−3.79211	−	6.56813i	−0.124148	−	0.215031i
$934$	27.2537	−	47.2047i	0.891767	−	1.54459i
$935$	−0.857866	+	1.48587i	−0.0280552	+	0.0485931i
$936$	−16.7513	−	29.0141i	−0.547534	−	0.948356i
$937$	−37.1698			−1.21428			−0.607142	−	0.794593i	$-0.707684\pi$
$937$	−37.1698			−1.21428			−0.607142	+	0.794593i	$0.707684\pi$
$938$	−11.4014	+	102.344i	−0.372268	+	3.34165i
$939$	−6.65622			−0.217218
$940$	29.7774	+	51.5759i	0.971231	+	1.68222i
$941$	−17.7827	+	30.8006i	−0.579700	+	1.00407i	0.415814	+	0.909450i	$0.363497\pi$
$941$	−17.7827	+	30.8006i	−0.579700	+	1.00407i	−0.995513	+	0.0946199i	$0.969836\pi$
$942$	−1.33779	+	2.31712i	−0.0435876	+	0.0754959i
$943$	−0.362298	−	0.627518i	−0.0117980	−	0.0204348i
$944$	−146.383			−4.76435
$945$	3.85699	−	1.68855i	0.125468	−	0.0549286i
$946$	14.9466			0.485957
$947$	21.2022	+	36.7233i	0.688979	+	1.19335i	0.972168	+	0.234283i	$0.0752742\pi$
$947$	21.2022	+	36.7233i	0.688979	+	1.19335i	−0.283189	+	0.959064i	$0.591392\pi$
$948$	−4.74110	+	8.21183i	−0.153984	+	0.266708i
$949$	−7.96465	+	13.7952i	−0.258544	+	0.447811i
$950$	−0.474892	−	0.822537i	−0.0154075	−	0.0266866i
$951$	−6.03105			−0.195570
$952$	61.1730	+	45.0293i	1.98263	+	1.45941i
$953$	−19.5628			−0.633703			−0.316851	−	0.948475i	$-0.602626\pi$
$953$	−19.5628			−0.633703			−0.316851	+	0.948475i	$0.602626\pi$
$954$	−0.639146	−	1.10703i	−0.0206931	−	0.0358415i
$955$	5.53658	−	9.58964i	0.179160	−	0.310314i
$956$	−74.5999	+	129.211i	−2.41273	+	4.17897i
$957$	0.0410566	+	0.0711121i	0.00132717	+	0.00229873i
$958$	22.3166			0.721017
$959$	−30.3128	−	22.3132i	−0.978851	−	0.720530i
$960$	−4.82711			−0.155794
$961$	14.5299	+	25.1665i	0.468706	+	0.811823i
$962$	1.81491	−	3.14352i	0.0585152	−	0.101351i
$963$	9.06127	−	15.6946i	0.291995	−	0.505751i
$964$	6.59054	+	11.4151i	0.212267	+	0.367657i
$965$	−13.1259			−0.422537
$966$	12.4233	−	5.43880i	0.399714	−	0.174991i
$967$	−45.7186			−1.47021			−0.735105	−	0.677954i	$-0.762867\pi$
$967$	−45.7186			−1.47021			−0.735105	+	0.677954i	$0.762867\pi$
$968$	−45.2980	−	78.4585i	−1.45593	−	2.52175i
$969$	−0.162337	+	0.281176i	−0.00521502	+	0.00903268i
$970$	0.722429	−	1.25128i	0.0231958	−	0.0401763i
$971$	7.84926	+	13.5953i	0.251895	+	0.436294i	0.964047	−	0.265730i	$-0.0856130\pi$
$971$	7.84926	+	13.5953i	0.251895	+	0.436294i	−0.712153	+	0.702025i	$0.752280\pi$
$972$	−36.1566			−1.15972
$973$	−1.88520	+	16.9224i	−0.0604367	+	0.542507i
$974$	−71.3909			−2.28751
$975$	0.182182	+	0.315548i	0.00583449	+	0.0101056i
$976$	35.3483	−	61.2251i	1.13147	−	1.95977i
$977$	6.68484	−	11.5785i	0.213867	−	0.370429i	−0.739054	−	0.673646i	$-0.764727\pi$
$977$	6.68484	−	11.5785i	0.213867	−	0.370429i	0.952922	+	0.303217i	$0.0980607\pi$
$978$	−0.783485	−	1.35704i	−0.0250531	−	0.0433932i
$979$	−5.42524			−0.173391
$980$	−35.1821	−	7.93725i	−1.12385	−	0.253546i
$981$	−20.4724			−0.653634
$982$	52.2746	+	90.5422i	1.66815	+	2.88932i
$983$	−5.18357	+	8.97821i	−0.165330	+	0.286360i	−0.936773	−	0.349939i	$-0.886202\pi$
$983$	−5.18357	+	8.97821i	−0.165330	+	0.286360i	0.771442	+	0.636299i	$0.219536\pi$
$984$	−0.114848	+	0.198923i	−0.00366124	+	0.00634145i
$985$	3.82026	+	6.61688i	0.121724	+	0.210831i
$986$	−5.52921			−0.176086
$987$	−0.908973	+	8.15936i	−0.0289329	+	0.259715i
$988$	−2.48352			−0.0790112
$989$	39.5988	+	68.5872i	1.25917	+	2.18095i
$990$	−1.97256	+	3.41657i	−0.0626920	+	0.108586i
$991$	11.6008	−	20.0933i	0.368513	−	0.638283i	−0.620820	−	0.783953i	$-0.713200\pi$
$991$	11.6008	−	20.0933i	0.368513	−	0.638283i	0.989333	+	0.145670i	$0.0465337\pi$
$992$	11.0586	+	19.1541i	0.351112	+	0.608144i
$993$	−3.78751			−0.120193
$994$	17.2510	−	7.55232i	0.547169	−	0.239545i
$995$	−23.2223			−0.736196
$996$	5.70256	+	9.87713i	0.180693	+	0.312969i
$997$	−27.1685	+	47.0572i	−0.860435	+	1.49032i	0.0110753	+	0.999939i	$0.496475\pi$
$997$	−27.1685	+	47.0572i	−0.860435	+	1.49032i	−0.871510	+	0.490378i	$0.836859\pi$
$998$	51.1502	−	88.5948i	1.61913	−	2.80442i
$999$	−0.795693	−	1.37818i	−0.0251746	−	0.0436037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.19	✓	38
7.2	even	3	inner	1295.2.j.a.926.19	yes	38
7.3	odd	6		9065.2.a.s.1.1		19
7.4	even	3		9065.2.a.r.1.1		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.19	✓	38	1.1	even	1	trivial
1295.2.j.a.926.19	yes	38	7.2	even	3	inner
9065.2.a.r.1.1		19	7.4	even	3
9065.2.a.s.1.1		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+(1.33719 + 2.31608i) q^{2} +(0.134228 - 0.232489i) q^{3} +(-2.57617 + 4.46205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.717953 q^{6} +(-0.292931 + 2.62948i) q^{7} -8.43054 q^{8} +(1.46397 + 2.53566i) q^{9} +(1.33719 - 2.31608i) q^{10} +(-0.251910 + 0.436320i) q^{11} +(0.691586 + 1.19786i) q^{12} +1.35726 q^{13} +(-6.48182 + 2.83767i) q^{14} -0.268456 q^{15} +(-6.12093 - 10.6018i) q^{16} +(-1.70272 + 2.94921i) q^{17} +(-3.91521 + 6.78134i) q^{18} +(0.177570 + 0.307561i) q^{19} +5.15233 q^{20} +(0.572008 + 0.421053i) q^{21} -1.34741 q^{22} +(-3.56975 - 6.18299i) q^{23} +(-1.13161 + 1.96001i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.81491 + 3.14352i) q^{26} +1.59139 q^{27} +(-10.9783 - 8.08106i) q^{28} +0.607107 q^{29} +(-0.358977 - 0.621766i) q^{30} +(-0.696461 + 1.20631i) q^{31} +(7.93916 - 13.7510i) q^{32} +(0.0676266 + 0.117133i) q^{33} -9.10748 q^{34} +(2.42367 - 1.06106i) q^{35} -15.0857 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-0.474892 + 0.822537i) q^{38} +(0.182182 - 0.315548i) q^{39} +(4.21527 + 7.30107i) q^{40} +0.101491 q^{41} +(-0.210311 + 1.88785i) q^{42} -11.0929 q^{43} +(-1.29792 - 2.24807i) q^{44} +(1.46397 - 2.53566i) q^{45} +(9.54689 - 16.5357i) q^{46} +(5.77940 + 10.0102i) q^{47} -3.28639 q^{48} +(-6.82838 - 1.54052i) q^{49} -2.67438 q^{50} +(0.457106 + 0.791731i) q^{51} +(-3.49652 + 6.05615i) q^{52} +(-0.0816235 + 0.141376i) q^{53} +(2.12799 + 3.68579i) q^{54} +0.503819 q^{55} +(2.46957 - 22.1680i) q^{56} +0.0953396 q^{57} +(0.811819 + 1.40611i) q^{58} +(5.97878 - 10.3555i) q^{59} +(0.691586 - 1.19786i) q^{60} +(2.88750 + 5.00129i) q^{61} -3.72521 q^{62} +(-7.09633 + 3.10670i) q^{63} +17.9810 q^{64} +(-0.678629 - 1.17542i) q^{65} +(-0.180859 + 0.313258i) q^{66} +(7.27675 - 12.6037i) q^{67} +(-8.77300 - 15.1953i) q^{68} -1.91664 q^{69} +(5.69840 + 4.19458i) q^{70} -2.66145 q^{71} +(-12.3420 - 21.3770i) q^{72} +(-5.86820 + 10.1640i) q^{73} +(1.33719 - 2.31608i) q^{74} +(0.134228 + 0.232489i) q^{75} -1.82980 q^{76} +(-1.07351 - 0.790205i) q^{77} +0.974448 q^{78} +(3.42770 + 5.93695i) q^{79} +(-6.12093 + 10.6018i) q^{80} +(-4.17829 + 7.23701i) q^{81} +(0.135713 + 0.235062i) q^{82} +8.24563 q^{83} +(-3.35235 + 1.46762i) q^{84} +3.40545 q^{85} +(-14.8333 - 25.6920i) q^{86} +(0.0814906 - 0.141146i) q^{87} +(2.12374 - 3.67842i) q^{88} +(5.38411 + 9.32556i) q^{89} +7.83041 q^{90} +(-0.397583 + 3.56889i) q^{91} +36.7851 q^{92} +(0.186969 + 0.323839i) q^{93} +(-15.4563 + 26.7712i) q^{94} +(0.177570 - 0.307561i) q^{95} +(-2.13131 - 3.69154i) q^{96} +0.540259 q^{97} +(-5.56289 - 17.8751i) q^{98} -1.47515 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

Related objects

Downloads

Learn more