LMFDB - Embedded newform 1295.2.j.a.186.13

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			186.13
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.458759 + 0.794593i) q^{2} +(1.13848 - 1.97191i) q^{3} +(0.579081 - 1.00300i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.08916 q^{6} +(2.28132 + 1.33999i) q^{7} +2.89767 q^{8} +(-1.09229 - 1.89191i) q^{9} +(0.458759 - 0.794593i) q^{10} +(2.39130 - 4.14186i) q^{11} +(-1.31855 - 2.28380i) q^{12} -3.72989 q^{13} +(-0.0181694 + 2.42745i) q^{14} -2.27697 q^{15} +(0.171167 + 0.296470i) q^{16} +(0.222230 - 0.384914i) q^{17} +(1.00220 - 1.73586i) q^{18} +(2.38732 + 4.13495i) q^{19} -1.15816 q^{20} +(5.23959 - 2.97301i) q^{21} +4.38812 q^{22} +(-0.214992 - 0.372377i) q^{23} +(3.29895 - 5.71395i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.71112 - 2.96374i) q^{26} +1.85667 q^{27} +(2.66508 - 1.51220i) q^{28} +1.38092 q^{29} +(-1.04458 - 1.80926i) q^{30} +(-3.13418 + 5.42856i) q^{31} +(2.74062 - 4.74689i) q^{32} +(-5.44492 - 9.43088i) q^{33} +0.407800 q^{34} +(0.0198028 - 2.64568i) q^{35} -2.53011 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-2.19040 + 3.79389i) q^{38} +(-4.24642 + 7.35501i) q^{39} +(-1.44883 - 2.50945i) q^{40} -0.522569 q^{41} +(4.76604 + 2.79945i) q^{42} -7.86533 q^{43} +(-2.76952 - 4.79694i) q^{44} +(-1.09229 + 1.89191i) q^{45} +(0.197259 - 0.341662i) q^{46} +(-0.276077 - 0.478180i) q^{47} +0.779485 q^{48} +(3.40886 + 6.11389i) q^{49} -0.917517 q^{50} +(-0.506011 - 0.876437i) q^{51} +(-2.15991 + 3.74107i) q^{52} +(-1.59277 + 2.75876i) q^{53} +(0.851762 + 1.47529i) q^{54} -4.78260 q^{55} +(6.61051 + 3.88284i) q^{56} +10.8717 q^{57} +(0.633509 + 1.09727i) q^{58} +(-5.46263 + 9.46156i) q^{59} +(-1.31855 + 2.28380i) q^{60} +(-4.19575 - 7.26725i) q^{61} -5.75133 q^{62} +(0.0432610 - 5.77972i) q^{63} +5.71380 q^{64} +(1.86494 + 3.23018i) q^{65} +(4.99581 - 8.65299i) q^{66} +(0.709398 - 1.22871i) q^{67} +(-0.257379 - 0.445793i) q^{68} -0.979061 q^{69} +(2.11132 - 1.19799i) q^{70} -4.65250 q^{71} +(-3.16511 - 5.48212i) q^{72} +(0.899935 - 1.55873i) q^{73} +(0.458759 - 0.794593i) q^{74} +(1.13848 + 1.97191i) q^{75} +5.52980 q^{76} +(11.0054 - 6.24459i) q^{77} -7.79232 q^{78} +(-3.60672 - 6.24702i) q^{79} +(0.171167 - 0.296470i) q^{80} +(5.39067 - 9.33691i) q^{81} +(-0.239733 - 0.415230i) q^{82} +1.45351 q^{83} +(0.0522220 - 6.97692i) q^{84} -0.444460 q^{85} +(-3.60829 - 6.24974i) q^{86} +(1.57216 - 2.72305i) q^{87} +(6.92920 - 12.0017i) q^{88} +(7.15348 + 12.3902i) q^{89} -2.00440 q^{90} +(-8.50907 - 4.99800i) q^{91} -0.497992 q^{92} +(7.13643 + 12.3607i) q^{93} +(0.253306 - 0.438738i) q^{94} +(2.38732 - 4.13495i) q^{95} +(-6.24030 - 10.8085i) q^{96} -3.70052 q^{97} +(-3.29421 + 5.51346i) q^{98} -10.4480 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 $

$2$	0.458759	+	0.794593i	0.324391	+	0.561862i	0.981389	−	0.192030i	$-0.0615072\pi$
$2$	0.458759	+	0.794593i	0.324391	+	0.561862i	−0.656998	+	0.753893i	$0.728174\pi$
$3$	1.13848	−	1.97191i	0.657304	−	1.13848i	−0.324006	−	0.946055i	$-0.605030\pi$
$3$	1.13848	−	1.97191i	0.657304	−	1.13848i	0.981311	−	0.192430i	$-0.0616367\pi$
$4$	0.579081	−	1.00300i	0.289541	−	0.501499i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.08916			0.852895
$7$	2.28132	+	1.33999i	0.862259	+	0.506468i
$7$	2.28132	+	1.33999i	0.862259	+	0.506468i
$8$	2.89767			1.02448
$9$	−1.09229	−	1.89191i	−0.364098	−	0.630636i
$10$	0.458759	−	0.794593i	0.145072	−	0.251272i
$11$	2.39130	−	4.14186i	0.721005	−	1.24882i	−0.239593	−	0.970873i	$-0.577014\pi$
$11$	2.39130	−	4.14186i	0.721005	−	1.24882i	0.960597	−	0.277943i	$-0.0896527\pi$
$12$	−1.31855	−	2.28380i	−0.380633	−	0.659275i
$13$	−3.72989			−1.03448			−0.517242	−	0.855839i	$-0.673041\pi$
$13$	−3.72989			−1.03448			−0.517242	+	0.855839i	$0.673041\pi$
$14$	−0.0181694	+	2.42745i	−0.00485598	+	0.648764i
$15$	−2.27697			−0.587911
$16$	0.171167	+	0.296470i	0.0427918	+	0.0741176i
$17$	0.222230	−	0.384914i	0.0538987	−	0.0933554i	−0.837817	−	0.545951i	$-0.816169\pi$
$17$	0.222230	−	0.384914i	0.0538987	−	0.0933554i	0.891716	+	0.452596i	$0.149502\pi$
$18$	1.00220	−	1.73586i	0.236220	−	0.409146i
$19$	2.38732	+	4.13495i	0.547688	+	0.948623i	0.998432	+	0.0559703i	$0.0178252\pi$
$19$	2.38732	+	4.13495i	0.547688	+	0.948623i	−0.450745	+	0.892653i	$0.648841\pi$
$20$	−1.15816			−0.258973
$21$	5.23959	−	2.97301i	1.14337	−	0.648765i
$22$	4.38812			0.935550
$23$	−0.214992	−	0.372377i	−0.0448290	−	0.0776460i	0.842740	−	0.538320i	$-0.180941\pi$
$23$	−0.214992	−	0.372377i	−0.0448290	−	0.0776460i	−0.887569	+	0.460674i	$0.847608\pi$
$24$	3.29895	−	5.71395i	0.673395	−	1.16636i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.71112	−	2.96374i	−0.335578	−	0.581237i
$27$	1.85667			0.357316
$28$	2.66508	−	1.51220i	0.503652	−	0.285779i
$29$	1.38092			0.256430			0.128215	−	0.991746i	$-0.459075\pi$
$29$	1.38092			0.256430			0.128215	+	0.991746i	$0.459075\pi$
$30$	−1.04458	−	1.80926i	−0.190713	−	0.330325i
$31$	−3.13418	+	5.42856i	−0.562916	+	0.974998i	0.434325	+	0.900756i	$0.356987\pi$
$31$	−3.13418	+	5.42856i	−0.562916	+	0.974998i	−0.997240	+	0.0742419i	$0.976346\pi$
$32$	2.74062	−	4.74689i	0.484478	−	0.839140i
$33$	−5.44492	−	9.43088i	−0.947839	−	1.64171i
$34$	0.407800			0.0699371
$35$	0.0198028	−	2.64568i	0.00334728	−	0.447201i
$36$	−2.53011			−0.421685
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	−2.19040	+	3.79389i	−0.355330	+	0.615450i
$39$	−4.24642	+	7.35501i	−0.679971	+	1.17774i
$40$	−1.44883	−	2.50945i	−0.229081	−	0.396780i
$41$	−0.522569			−0.0816116			−0.0408058	−	0.999167i	$-0.512992\pi$
$41$	−0.522569			−0.0816116			−0.0408058	+	0.999167i	$0.512992\pi$
$42$	4.76604	+	2.79945i	0.735416	+	0.431964i
$43$	−7.86533			−1.19945			−0.599726	−	0.800206i	$-0.704724\pi$
$43$	−7.86533			−1.19945			−0.599726	+	0.800206i	$0.704724\pi$
$44$	−2.76952	−	4.79694i	−0.417520	−	0.723166i
$45$	−1.09229	+	1.89191i	−0.162830	+	0.282029i
$46$	0.197259	−	0.341662i	0.0290842	−	0.0503754i
$47$	−0.276077	−	0.478180i	−0.0402700	−	0.0697497i	0.845188	−	0.534469i	$-0.179488\pi$
$47$	−0.276077	−	0.478180i	−0.0402700	−	0.0697497i	−0.885458	+	0.464720i	$0.846155\pi$
$48$	0.779485			0.112509
$49$	3.40886	+	6.11389i	0.486980	+	0.873413i
$50$	−0.917517			−0.129757
$51$	−0.506011	−	0.876437i	−0.0708558	−	0.122726i
$52$	−2.15991	+	3.74107i	−0.299525	+	0.518793i
$53$	−1.59277	+	2.75876i	−0.218784	+	0.378945i	−0.954436	−	0.298414i	$-0.903542\pi$
$53$	−1.59277	+	2.75876i	−0.218784	+	0.378945i	0.735653	+	0.677359i	$0.236876\pi$
$54$	0.851762	+	1.47529i	0.115910	+	0.200762i
$55$	−4.78260			−0.644886
$56$	6.61051	+	3.88284i	0.883367	+	0.518866i
$57$	10.8717			1.43999
$58$	0.633509	+	1.09727i	0.0831838	+	0.144079i
$59$	−5.46263	+	9.46156i	−0.711174	+	1.23179i	0.253242	+	0.967403i	$0.418503\pi$
$59$	−5.46263	+	9.46156i	−0.711174	+	1.23179i	−0.964417	+	0.264387i	$0.914830\pi$
$60$	−1.31855	+	2.28380i	−0.170224	+	0.294837i
$61$	−4.19575	−	7.26725i	−0.537211	−	0.930476i	−0.999053	−	0.0435140i	$-0.986145\pi$
$61$	−4.19575	−	7.26725i	−0.537211	−	0.930476i	0.461842	−	0.886962i	$-0.347189\pi$
$62$	−5.75133			−0.730420
$63$	0.0432610	−	5.77972i	0.00545037	−	0.728176i
$64$	5.71380			0.714225
$65$	1.86494	+	3.23018i	0.231318	+	0.400654i
$66$	4.99581	−	8.65299i	0.614941	−	1.06511i
$67$	0.709398	−	1.22871i	0.0866667	−	0.150111i	−0.819433	−	0.573174i	$-0.805712\pi$
$67$	0.709398	−	1.22871i	0.0866667	−	0.150111i	0.906100	+	0.423063i	$0.139045\pi$
$68$	−0.257379	−	0.445793i	−0.0312118	−	0.0540603i
$69$	−0.979061			−0.117865
$70$	2.11132	−	1.19799i	0.252351	−	0.143187i
$71$	−4.65250			−0.552150			−0.276075	−	0.961136i	$-0.589034\pi$
$71$	−4.65250			−0.552150			−0.276075	+	0.961136i	$0.589034\pi$
$72$	−3.16511	−	5.48212i	−0.373011	−	0.646075i
$73$	0.899935	−	1.55873i	0.105329	−	0.182436i	−0.808543	−	0.588437i	$-0.799744\pi$
$73$	0.899935	−	1.55873i	0.105329	−	0.182436i	0.913873	+	0.406001i	$0.133077\pi$
$74$	0.458759	−	0.794593i	0.0533296	−	0.0923696i
$75$	1.13848	+	1.97191i	0.131461	+	0.227697i
$76$	5.52980			0.634312
$77$	11.0054	−	6.24459i	1.25418	−	0.711637i
$78$	−7.79232			−0.882307
$79$	−3.60672	−	6.24702i	−0.405787	−	0.702844i	0.588625	−	0.808406i	$-0.299669\pi$
$79$	−3.60672	−	6.24702i	−0.405787	−	0.702844i	−0.994413	+	0.105562i	$0.966336\pi$
$80$	0.171167	−	0.296470i	0.0191371	−	0.0331464i
$81$	5.39067	−	9.33691i	0.598963	−	1.03743i
$82$	−0.239733	−	0.415230i	−0.0264741	−	0.0458545i
$83$	1.45351			0.159544			0.0797719	−	0.996813i	$-0.474581\pi$
$83$	1.45351			0.159544			0.0797719	+	0.996813i	$0.474581\pi$
$84$	0.0522220	−	6.97692i	0.00569788	−	0.761244i
$85$	−0.444460			−0.0482085
$86$	−3.60829	−	6.24974i	−0.389092	−	0.673927i
$87$	1.57216	−	2.72305i	0.168553	−	0.291942i
$88$	6.92920	−	12.0017i	0.738655	−	1.27939i
$89$	7.15348	+	12.3902i	0.758268	+	1.31336i	0.943733	+	0.330707i	$0.107287\pi$
$89$	7.15348	+	12.3902i	0.758268	+	1.31336i	−0.185466	+	0.982651i	$0.559379\pi$
$90$	−2.00440			−0.211282
$91$	−8.50907	−	4.99800i	−0.891993	−	0.523933i
$92$	−0.497992			−0.0519192
$93$	7.13643	+	12.3607i	0.740014	+	1.28174i
$94$	0.253306	−	0.438738i	0.0261265	−	0.0452524i
$95$	2.38732	−	4.13495i	0.244933	−	0.424237i
$96$	−6.24030	−	10.8085i	−0.636898	−	1.10314i
$97$	−3.70052			−0.375731			−0.187866	−	0.982195i	$-0.560157\pi$
$97$	−3.70052			−0.375731			−0.187866	+	0.982195i	$0.560157\pi$
$98$	−3.29421	+	5.51346i	−0.332765	+	0.556943i
$99$	−10.4480			−1.05007
$100$	0.579081	+	1.00300i	0.0579081	+	0.100300i
$101$	0.538927	−	0.933448i	0.0536252	−	0.0928816i	−0.837967	−	0.545721i	$-0.816256\pi$
$101$	0.538927	−	0.933448i	0.0536252	−	0.0928816i	0.891592	+	0.452840i	$0.149589\pi$
$102$	0.464274	−	0.804146i	0.0459700	−	0.0796223i
$103$	−1.94058	−	3.36118i	−0.191211	−	0.331187i	0.754441	−	0.656368i	$-0.227908\pi$
$103$	−1.94058	−	3.36118i	−0.191211	−	0.331187i	−0.945652	+	0.325181i	$0.894575\pi$
$104$	−10.8080			−1.05981
$105$	−5.19450	−	3.05111i	−0.506931	−	0.297758i
$106$	−2.92279			−0.283886
$107$	−3.24695	−	5.62389i	−0.313895	−	0.543682i	0.665307	−	0.746570i	$-0.268301\pi$
$107$	−3.24695	−	5.62389i	−0.313895	−	0.543682i	−0.979202	+	0.202888i	$0.934967\pi$
$108$	1.07516	−	1.86223i	0.103457	−	0.179194i
$109$	1.02308	−	1.77203i	0.0979932	−	0.169729i	−0.812861	−	0.582458i	$-0.802091\pi$
$109$	1.02308	−	1.77203i	0.0979932	−	0.169729i	0.910854	+	0.412729i	$0.135424\pi$
$110$	−2.19406	−	3.80022i	−0.209195	−	0.362337i
$111$	−2.27697			−0.216120
$112$	−0.00677918	+	0.905707i	−0.000640572	+	0.0855812i
$113$	13.1060			1.23291			0.616455	−	0.787390i	$-0.288568\pi$
$113$	13.1060			1.23291			0.616455	+	0.787390i	$0.288568\pi$
$114$	4.98748	+	8.63857i	0.467120	+	0.809076i
$115$	−0.214992	+	0.372377i	−0.0200481	+	0.0347244i
$116$	0.799665	−	1.38506i	0.0742470	−	0.128600i
$117$	4.07413	+	7.05660i	0.376654	+	0.652383i
$118$	−10.0241			−0.922795
$119$	1.02276	−	0.580327i	0.0937562	−	0.0531985i
$120$	−6.59790			−0.602303
$121$	−5.93665	−	10.2826i	−0.539695	−	0.934780i
$122$	3.84967	−	6.66783i	0.348533	−	0.603677i
$123$	−0.594937	+	1.03046i	−0.0536437	+	0.0929136i
$124$	3.62989	+	6.28716i	0.325974	+	0.564603i
$125$	1.00000			0.0894427
$126$	4.61237	−	2.61712i	0.410902	−	0.233151i
$127$	−4.09488			−0.363362			−0.181681	−	0.983358i	$-0.558154\pi$
$127$	−4.09488			−0.363362			−0.181681	+	0.983358i	$0.558154\pi$
$128$	−2.85998	−	4.95364i	−0.252789	−	0.437844i
$129$	−8.95456	+	15.5097i	−0.788405	+	1.36556i
$130$	−1.71112	+	2.96374i	−0.150075	+	0.259937i
$131$	8.85714	+	15.3410i	0.773851	+	1.34035i	0.935438	+	0.353492i	$0.115006\pi$
$131$	8.85714	+	15.3410i	0.773851	+	1.34035i	−0.161586	+	0.986859i	$0.551661\pi$
$132$	−12.6122			−1.09775
$133$	−0.0945511	+	12.6321i	−0.00819862	+	1.09535i
$134$	1.30177			0.112456
$135$	−0.928334	−	1.60792i	−0.0798982	−	0.138388i
$136$	0.643949	−	1.11535i	0.0552182	−	0.0956407i
$137$	−7.83912	+	13.5777i	−0.669741	+	1.16003i	0.308235	+	0.951310i	$0.400262\pi$
$137$	−7.83912	+	13.5777i	−0.669741	+	1.16003i	−0.977976	+	0.208715i	$0.933072\pi$
$138$	−0.449152	−	0.777955i	−0.0382344	−	0.0662239i
$139$	18.9153			1.60437			0.802186	−	0.597075i	$-0.203670\pi$
$139$	18.9153			1.60437			0.802186	+	0.597075i	$0.203670\pi$
$140$	−2.64214	−	1.55192i	−0.223302	−	0.131162i
$141$	−1.25724			−0.105879
$142$	−2.13437	−	3.69684i	−0.179113	−	0.310232i
$143$	−8.91928	+	15.4487i	−0.745868	+	1.29188i
$144$	0.373930	−	0.647666i	0.0311608	−	0.0539722i
$145$	−0.690460	−	1.19591i	−0.0573396	−	0.0993151i
$146$	1.65141			0.136672
$147$	15.9370	+	0.238589i	1.31446	+	0.0196785i
$148$	−1.15816			−0.0952004
$149$	−3.79255	−	6.56889i	−0.310698	−	0.538145i	0.667816	−	0.744327i	$-0.267229\pi$
$149$	−3.79255	−	6.56889i	−0.310698	−	0.538145i	−0.978514	+	0.206182i	$0.933896\pi$
$150$	−1.04458	+	1.80926i	−0.0852895	+	0.147726i
$151$	4.10206	−	7.10497i	0.333821	−	0.578194i	−0.649437	−	0.760415i	$-0.724995\pi$
$151$	4.10206	−	7.10497i	0.333821	−	0.578194i	0.983258	+	0.182221i	$0.0583287\pi$
$152$	6.91765	+	11.9817i	0.561095	+	0.971846i
$153$	−0.970963			−0.0784977
$154$	10.0107	+	5.88003i	0.806687	+	0.473826i
$155$	6.26836			0.503487
$156$	4.91804	+	8.51830i	0.393758	+	0.682010i
$157$	−8.60555	+	14.9052i	−0.686798	+	1.18957i	0.286071	+	0.958208i	$0.407651\pi$
$157$	−8.60555	+	14.9052i	−0.686798	+	1.18957i	−0.972868	+	0.231360i	$0.925683\pi$
$158$	3.30922	−	5.73174i	0.263268	−	0.455993i
$159$	3.62669	+	6.28161i	0.287615	+	0.498164i
$160$	−5.48124			−0.433330
$161$	0.00851489	−	1.13760i	0.000671067	−	0.0896554i
$162$	9.89206			0.777194
$163$	−1.02390	−	1.77345i	−0.0801981	−	0.138907i	0.823137	−	0.567843i	$-0.192222\pi$
$163$	−1.02390	−	1.77345i	−0.0801981	−	0.138907i	−0.903335	+	0.428936i	$0.858889\pi$
$164$	−0.302610	+	0.524136i	−0.0236299	+	0.0409281i
$165$	−5.44492	+	9.43088i	−0.423886	+	0.734193i
$166$	0.666812	+	1.15495i	0.0517546	+	0.0896416i
$167$	−4.61721			−0.357291			−0.178645	−	0.983914i	$-0.557171\pi$
$167$	−4.61721			−0.357291			−0.178645	+	0.983914i	$0.557171\pi$
$168$	15.1826	−	8.61480i	1.17136	−	0.664647i
$169$	0.912047			0.0701575
$170$	−0.203900	−	0.353165i	−0.0156384	−	0.0270865i
$171$	5.21530	−	9.03317i	0.398824	−	0.690784i
$172$	−4.55467	+	7.88891i	−0.347290	+	0.601524i
$173$	3.55560	+	6.15847i	0.270327	+	0.468220i	0.968946	−	0.247274i	$-0.0795349\pi$
$173$	3.55560	+	6.15847i	0.270327	+	0.468220i	−0.698619	+	0.715494i	$0.746202\pi$
$174$	2.88496			0.218708
$175$	−2.30113	+	1.30569i	−0.173949	+	0.0987008i
$176$	1.63725			0.123412
$177$	12.4383	+	21.5437i	0.934916	+	1.61932i
$178$	−6.56344	+	11.3682i	−0.491951	+	0.852084i
$179$	4.57904	−	7.93114i	0.342254	−	0.592801i	−0.642597	−	0.766204i	$-0.722143\pi$
$179$	4.57904	−	7.93114i	0.342254	−	0.592801i	0.984851	+	0.173403i	$0.0554764\pi$
$180$	1.26505	+	2.19114i	0.0942916	+	0.163318i
$181$	15.7401			1.16995			0.584977	−	0.811050i	$-0.301104\pi$
$181$	15.7401			1.16995			0.584977	+	0.811050i	$0.301104\pi$
$182$	0.0677698	−	9.05413i	0.00502343	−	0.671136i
$183$	−19.1072			−1.41244
$184$	−0.622976	−	1.07903i	−0.0459264	−	0.0795468i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	−6.54780	+	11.3411i	−0.480108	+	0.831571i
$187$	−1.06284	−	1.84089i	−0.0777225	−	0.134619i
$188$	−0.639485			−0.0466392
$189$	4.23566	+	2.48791i	0.308099	+	0.180969i
$190$	4.38081			0.317817
$191$	10.2065	+	17.6781i	0.738513	+	1.27914i	0.953165	+	0.302451i	$0.0978049\pi$
$191$	10.2065	+	17.6781i	0.738513	+	1.27914i	−0.214652	+	0.976691i	$0.568862\pi$
$192$	6.50507	−	11.2671i	0.469463	−	0.813134i
$193$	10.7039	−	18.5397i	0.770485	−	1.33452i	−0.166812	−	0.985989i	$-0.553347\pi$
$193$	10.7039	−	18.5397i	0.770485	−	1.33452i	0.937297	−	0.348531i	$-0.113319\pi$
$194$	−1.69765	−	2.94041i	−0.121884	−	0.211109i
$195$	8.49283			0.608185
$196$	8.10623	+	0.121356i	0.579016	+	0.00866832i
$197$	18.6733			1.33042			0.665209	−	0.746657i	$-0.268342\pi$
$197$	18.6733			1.33042			0.665209	+	0.746657i	$0.268342\pi$
$198$	−4.79312	−	8.30192i	−0.340632	−	0.589992i
$199$	−9.66772	+	16.7450i	−0.685326	+	1.18702i	0.288008	+	0.957628i	$0.407007\pi$
$199$	−9.66772	+	16.7450i	−0.685326	+	1.18702i	−0.973334	+	0.229392i	$0.926326\pi$
$200$	−1.44883	+	2.50945i	−0.102448	+	0.177445i
$201$	−1.61528	−	2.79774i	−0.113933	−	0.197337i
$202$	0.988949			0.0695822
$203$	3.15032	+	1.85042i	0.221109	+	0.129874i
$204$	−1.17209			−0.0820625
$205$	0.261285	+	0.452558i	0.0182489	+	0.0316080i
$206$	1.78052	−	3.08394i	0.124054	−	0.214869i
$207$	−0.469669	+	0.813491i	−0.0326443	+	0.0565415i
$208$	−0.638434	−	1.10580i	−0.0442675	−	0.0766735i
$209$	22.8352			1.57954
$210$	0.0413712	−	5.52724i	0.00285488	−	0.381416i
$211$	−1.81133			−0.124697			−0.0623486	−	0.998054i	$-0.519859\pi$
$211$	−1.81133			−0.124697			−0.0623486	+	0.998054i	$0.519859\pi$
$212$	1.84469	+	3.19509i	0.126694	+	0.219440i
$213$	−5.29680	+	9.17432i	−0.362930	+	0.628614i
$214$	2.97913	−	5.16001i	0.203649	−	0.352731i
$215$	3.93267	+	6.81158i	0.268206	+	0.464546i
$216$	5.38000			0.366063
$217$	−14.4243	+	8.18453i	−0.979184	+	0.555602i
$218$	1.87739			0.127153
$219$	−2.04913	−	3.54919i	−0.138467	−	0.239832i
$220$	−2.76952	+	4.79694i	−0.186721	+	0.323410i
$221$	−0.828893	+	1.43569i	−0.0557574	+	0.0965746i
$222$	−1.04458	−	1.80926i	−0.0701075	−	0.121430i
$223$	−23.0694			−1.54484			−0.772422	−	0.635110i	$-0.780955\pi$
$223$	−23.0694			−1.54484			−0.772422	+	0.635110i	$0.780955\pi$
$224$	12.6130	−	7.15679i	0.842742	−	0.478183i
$225$	2.18459			0.145639
$226$	6.01250	+	10.4140i	0.399945	+	0.692726i
$227$	−13.9097	+	24.0922i	−0.923216	+	1.59906i	−0.128811	+	0.991669i	$0.541116\pi$
$227$	−13.9097	+	24.0922i	−0.923216	+	1.59906i	−0.794405	+	0.607388i	$0.792217\pi$
$228$	6.29559	−	10.9043i	0.416936	−	0.722154i
$229$	−8.23980	−	14.2717i	−0.544501	−	0.943103i	−0.998638	−	0.0521716i	$-0.983386\pi$
$229$	−8.23980	−	14.2717i	−0.544501	−	0.943103i	0.454137	−	0.890932i	$-0.349948\pi$
$230$	−0.394518			−0.0260137
$231$	0.215649	−	28.8110i	0.0141887	−	1.89562i
$232$	4.00145			0.262708
$233$	3.26108	+	5.64835i	0.213640	+	0.370036i	0.952851	−	0.303438i	$-0.0981346\pi$
$233$	3.26108	+	5.64835i	0.213640	+	0.370036i	−0.739211	+	0.673474i	$0.764801\pi$
$234$	−3.73809	+	6.47455i	−0.244366	+	0.423255i
$235$	−0.276077	+	0.478180i	−0.0180093	+	0.0311930i
$236$	6.32662	+	10.9580i	0.411828	+	0.713307i
$237$	−16.4248			−1.06690
$238$	0.930323	+	0.546447i	0.0603039	+	0.0354209i
$239$	−23.2932			−1.50671			−0.753355	−	0.657614i	$-0.771566\pi$
$239$	−23.2932			−1.50671			−0.753355	+	0.657614i	$0.771566\pi$
$240$	−0.389743	−	0.675054i	−0.0251578	−	0.0435746i
$241$	−10.6538	+	18.4529i	−0.686271	+	1.18866i	0.286765	+	0.958001i	$0.407420\pi$
$241$	−10.6538	+	18.4529i	−0.686271	+	1.18866i	−0.973036	+	0.230655i	$0.925913\pi$
$242$	5.44698	−	9.43444i	0.350145	−	0.606469i
$243$	−9.48939	−	16.4361i	−0.608744	−	1.05438i
$244$	−9.71872			−0.622177
$245$	3.59035	−	6.00911i	0.229379	−	0.383908i
$246$	−1.09173			−0.0696061
$247$	−8.90442	−	15.4229i	−0.566574	−	0.981336i
$248$	−9.08182	+	15.7302i	−0.576696	+	0.998867i
$249$	1.65480	−	2.86620i	0.104869	−	0.181638i
$250$	0.458759	+	0.794593i	0.0290144	+	0.0502545i
$251$	26.7802			1.69035			0.845177	−	0.534487i	$-0.179495\pi$
$251$	26.7802			1.69035			0.845177	+	0.534487i	$0.179495\pi$
$252$	−5.77199	−	3.39032i	−0.363601	−	0.213570i
$253$	−2.05644			−0.129288
$254$	−1.87856	−	3.25377i	−0.117871	−	0.204159i
$255$	−0.506011	+	0.876437i	−0.0316877	+	0.0548846i
$256$	8.33788	−	14.4416i	0.521118	−	0.902602i
$257$	−1.76793	−	3.06214i	−0.110280	−	0.191011i	0.805603	−	0.592456i	$-0.201842\pi$
$257$	−1.76793	−	3.06214i	−0.110280	−	0.191011i	−0.915883	+	0.401445i	$0.868508\pi$
$258$	−16.4319			−1.02301
$259$	0.0198028	−	2.64568i	0.00123049	−	0.164394i
$260$	4.31981			0.267903
$261$	−1.50837	−	2.61257i	−0.0933658	−	0.161714i
$262$	−8.12657	+	14.0756i	−0.502061	+	0.869596i
$263$	−8.77582	+	15.2002i	−0.541140	+	0.937282i	0.457699	+	0.889107i	$0.348674\pi$
$263$	−8.77582	+	15.2002i	−0.541140	+	0.937282i	−0.998839	+	0.0481748i	$0.984660\pi$
$264$	−15.7776	−	27.3276i	−0.971042	−	1.68189i
$265$	3.18554			0.195686
$266$	−10.0808	+	5.71997i	−0.618093	+	0.350714i
$267$	32.5765			1.99365
$268$	−0.821598	−	1.42305i	−0.0501871	−	0.0869266i
$269$	4.81480	−	8.33947i	0.293563	−	0.508467i	−0.681086	−	0.732203i	$-0.738492\pi$
$269$	4.81480	−	8.33947i	0.293563	−	0.508467i	0.974650	+	0.223736i	$0.0718255\pi$
$270$	0.851762	−	1.47529i	0.0518366	−	0.0897836i
$271$	1.09781	+	1.90146i	0.0666870	+	0.115505i	0.897441	−	0.441134i	$-0.145424\pi$
$271$	1.09781	+	1.90146i	0.0666870	+	0.115505i	−0.830754	+	0.556640i	$0.812090\pi$
$272$	0.152154			0.00922570
$273$	−19.5431	+	11.0890i	−1.18280	+	0.671137i
$274$	−14.3850			−0.869032
$275$	2.39130	+	4.14186i	0.144201	+	0.249763i
$276$	−0.566956	+	0.981996i	−0.0341267	+	0.0591092i
$277$	−11.1863	+	19.3753i	−0.672120	+	1.16415i	0.305181	+	0.952294i	$0.401283\pi$
$277$	−11.1863	+	19.3753i	−0.672120	+	1.16415i	−0.977302	+	0.211852i	$0.932050\pi$
$278$	8.67753	+	15.0299i	0.520444	+	0.901435i
$279$	13.6938			0.819826
$280$	0.0573819	−	7.66629i	0.00342923	−	0.458149i
$281$	23.6888			1.41315			0.706577	−	0.707636i	$-0.250238\pi$
$281$	23.6888			1.41315			0.706577	+	0.707636i	$0.250238\pi$
$282$	−0.576769	−	0.998993i	−0.0343461	−	0.0594892i
$283$	4.92568	−	8.53152i	0.292801	−	0.507146i	−0.681670	−	0.731660i	$-0.738746\pi$
$283$	4.92568	−	8.53152i	0.292801	−	0.507146i	0.974471	+	0.224514i	$0.0720793\pi$
$284$	−2.69417	+	4.66645i	−0.159870	+	0.276903i
$285$	−5.43585	−	9.41516i	−0.321992	−	0.557706i
$286$	−16.3672			−0.967812
$287$	−1.19215	−	0.700237i	−0.0703703	−	0.0413337i
$288$	−11.9742			−0.705589
$289$	8.40123	+	14.5514i	0.494190	+	0.855962i
$290$	0.633509	−	1.09727i	0.0372009	−	0.0644339i
$291$	−4.21299	+	7.29711i	−0.246970	+	0.427764i
$292$	−1.04227	−	1.80527i	−0.0609943	−	0.105645i
$293$	10.2905			0.601179			0.300589	−	0.953754i	$-0.402817\pi$
$293$	10.2905			0.601179			0.300589	+	0.953754i	$0.402817\pi$
$294$	7.12165	+	12.7729i	0.415343	+	0.744930i
$295$	10.9253			0.636094
$296$	−1.44883	−	2.50945i	−0.0842118	−	0.145859i
$297$	4.43985	−	7.69005i	0.257626	−	0.446222i
$298$	3.47973	−	6.02707i	0.201575	−	0.349139i
$299$	0.801896	+	1.38892i	0.0463748	+	0.0803236i
$300$	2.63710			0.152253
$301$	−17.9434	−	10.5395i	−1.03424	−	0.607484i
$302$	7.52741			0.433154
$303$	−1.22712	−	2.12543i	−0.0704962	−	0.122103i
$304$	−0.817261	+	1.41554i	−0.0468731	+	0.0811866i
$305$	−4.19575	+	7.26725i	−0.240248	+	0.416122i
$306$	−0.445438	−	0.771521i	−0.0254640	−	0.0441049i
$307$	11.5781			0.660797			0.330398	−	0.943842i	$-0.392817\pi$
$307$	11.5781			0.660797			0.330398	+	0.943842i	$0.392817\pi$
$308$	0.109688	−	14.6545i	0.00625007	−	0.835017i
$309$	−8.83728			−0.502736
$310$	2.87566	+	4.98080i	0.163327	+	0.282890i
$311$	−0.530049	+	0.918072i	−0.0300563	+	0.0520591i	−0.880662	−	0.473745i	$-0.842902\pi$
$311$	−0.530049	+	0.918072i	−0.0300563	+	0.0520591i	0.850606	+	0.525804i	$0.176235\pi$
$312$	−12.3047	+	21.3124i	−0.696617	+	1.20658i
$313$	−14.2028	−	24.5999i	−0.802788	−	1.39047i	−0.917774	−	0.397103i	$-0.870015\pi$
$313$	−14.2028	−	24.5999i	−0.802788	−	1.39047i	0.114985	−	0.993367i	$-0.463318\pi$
$314$	−15.7915			−0.891164
$315$	−5.02701	+	2.85239i	−0.283240	+	0.160714i
$316$	−8.35433			−0.469968
$317$	−9.85336	−	17.0665i	−0.553420	−	0.958551i	−0.998025	−	0.0628241i	$-0.979989\pi$
$317$	−9.85336	−	17.0665i	−0.553420	−	0.958551i	0.444605	−	0.895727i	$-0.353344\pi$
$318$	−3.32755	+	5.76348i	−0.186600	+	0.323200i
$319$	3.30220	−	5.71957i	0.184888	−	0.320235i
$320$	−2.85690	−	4.94829i	−0.159706	−	0.276618i
$321$	−14.7864			−0.825298
$322$	0.907835	−	0.515118i	0.0505917	−	0.0287064i
$323$	2.12214			0.118079
$324$	−6.24327	−	10.8137i	−0.346848	−	0.600759i
$325$	1.86494	−	3.23018i	0.103448	−	0.179178i
$326$	0.939447	−	1.62717i	0.0520311	−	0.0901206i
$327$	−2.32952	−	4.03485i	−0.128823	−	0.223128i
$328$	−1.51423			−0.0836095
$329$	0.0109342	−	1.46082i	0.000602822	−	0.0805378i
$330$	−9.99161			−0.550020
$331$	12.4681	+	21.5954i	0.685308	+	1.18699i	0.973340	+	0.229367i	$0.0736656\pi$
$331$	12.4681	+	21.5954i	0.685308	+	1.18699i	−0.288032	+	0.957621i	$0.593001\pi$
$332$	0.841702	−	1.45787i	0.0461944	−	0.0800111i
$333$	−1.09229	+	1.89191i	−0.0598574	+	0.103676i
$334$	−2.11819	−	3.66881i	−0.115902	−	0.200748i
$335$	−1.41880			−0.0775171
$336$	1.77826	+	1.04450i	0.0970119	+	0.0569822i
$337$	−13.4057			−0.730258			−0.365129	−	0.930957i	$-0.618975\pi$
$337$	−13.4057			−0.730258			−0.365129	+	0.930957i	$0.618975\pi$
$338$	0.418409	+	0.724706i	0.0227585	+	0.0394188i
$339$	14.9210	−	25.8439i	0.810398	−	1.40365i
$340$	−0.257379	+	0.445793i	−0.0139583	+	0.0241765i
$341$	14.9895	+	25.9627i	0.811729	+	1.40596i
$342$	9.57026			0.517500
$343$	−0.415828	+	18.5156i	−0.0224526	+	0.999748i
$344$	−22.7911			−1.22881
$345$	0.489530	+	0.847891i	0.0263554	+	0.0456489i
$346$	−3.26232	+	5.65050i	−0.175383	+	0.303773i
$347$	11.3222	−	19.6107i	0.607810	−	1.05276i	−0.383791	−	0.923420i	$-0.625382\pi$
$347$	11.3222	−	19.6107i	0.607810	−	1.05276i	0.991601	−	0.129338i	$-0.0412851\pi$
$348$	−1.82081	−	3.15374i	−0.0976058	−	0.169058i
$349$	15.4314			0.826025			0.413013	−	0.910725i	$-0.364477\pi$
$349$	15.4314			0.826025			0.413013	+	0.910725i	$0.364477\pi$
$350$	−2.09315	−	1.22946i	−0.111884	−	0.0657175i
$351$	−6.92516			−0.369637
$352$	−13.1073	−	22.7025i	−0.698621	−	1.21005i
$353$	−10.6753	+	18.4902i	−0.568189	+	0.984133i	0.428556	+	0.903515i	$0.359022\pi$
$353$	−10.6753	+	18.4902i	−0.568189	+	0.984133i	−0.996745	+	0.0806173i	$0.974311\pi$
$354$	−11.4123	+	19.7667i	−0.606557	+	1.05059i
$355$	2.32625	+	4.02918i	0.123464	+	0.213847i
$356$	16.5698			0.878197
$357$	0.0200409	−	2.67749i	0.00106068	−	0.141708i
$358$	8.40270			0.444097
$359$	15.2379	+	26.3929i	0.804228	+	1.39296i	0.916811	+	0.399322i	$0.130754\pi$
$359$	15.2379	+	26.3929i	0.804228	+	1.39296i	−0.112583	+	0.993642i	$0.535912\pi$
$360$	−3.16511	+	5.48212i	−0.166816	+	0.288933i
$361$	−1.89856	+	3.28840i	−0.0999241	+	0.173074i
$362$	7.22091	+	12.5070i	0.379523	+	0.657352i
$363$	−27.0351			−1.41898
$364$	−9.94043	+	5.64033i	−0.521020	+	0.295634i
$365$	−1.79987			−0.0942095
$366$	−8.76558	−	15.1824i	−0.458184	−	0.793599i
$367$	11.2558	−	19.4957i	0.587550	−	1.01767i	−0.407003	−	0.913427i	$-0.633426\pi$
$367$	11.2558	−	19.4957i	0.587550	−	1.01767i	0.994552	−	0.104239i	$-0.0332406\pi$
$368$	0.0735992	−	0.127478i	0.00383663	−	0.00664523i
$369$	0.570799	+	0.988654i	0.0297146	+	0.0514672i
$370$	−0.917517			−0.0476994
$371$	−7.33033	+	4.15933i	−0.380572	+	0.215941i
$372$	16.5303			0.857056
$373$	0.492766	+	0.853496i	0.0255145	+	0.0441924i	0.878501	−	0.477741i	$-0.158544\pi$
$373$	0.492766	+	0.853496i	0.0255145	+	0.0441924i	−0.852986	+	0.521933i	$0.825211\pi$
$374$	0.975173	−	1.68905i	0.0504250	−	0.0873386i
$375$	1.13848	−	1.97191i	0.0587911	−	0.101829i
$376$	−0.799980	−	1.38561i	−0.0412558	−	0.0714572i
$377$	−5.15067			−0.265273
$378$	−0.0337345	+	4.50697i	−0.00173512	+	0.231814i
$379$	−6.77672			−0.348097			−0.174048	−	0.984737i	$-0.555685\pi$
$379$	−6.77672			−0.348097			−0.174048	+	0.984737i	$0.555685\pi$
$380$	−2.76490	−	4.78895i	−0.141836	−	0.245668i
$381$	−4.66196	+	8.07475i	−0.238839	+	0.413682i
$382$	−9.36459	+	16.2199i	−0.479134	+	0.829885i
$383$	−16.6369	−	28.8159i	−0.850104	−	1.47242i	−0.881114	−	0.472904i	$-0.843206\pi$
$383$	−16.6369	−	28.8159i	−0.850104	−	1.47242i	0.0310099	−	0.999519i	$-0.490128\pi$
$384$	−13.0242			−0.664638
$385$	−10.9107	−	6.40863i	−0.556059	−	0.326614i
$386$	19.6421			0.999755
$387$	8.59126	+	14.8805i	0.436718	+	0.756418i
$388$	−2.14290	+	3.71162i	−0.108789	+	0.188429i
$389$	4.35094	−	7.53605i	0.220601	−	0.382093i	−0.734389	−	0.678728i	$-0.762531\pi$
$389$	4.35094	−	7.53605i	0.220601	−	0.382093i	0.954991	+	0.296636i	$0.0958647\pi$
$390$	3.89616	+	6.74835i	0.197290	+	0.341716i
$391$	−0.191111			−0.00966490
$392$	9.87775	+	17.7160i	0.498902	+	0.894794i
$393$	40.3348			2.03462
$394$	8.56654	+	14.8377i	0.431576	+	0.747511i
$395$	−3.60672	+	6.24702i	−0.181474	+	0.314321i
$396$	−6.05025	+	10.4793i	−0.304037	+	0.526607i
$397$	−10.8182	−	18.7377i	−0.542950	−	0.940417i	−0.998733	−	0.0503263i	$-0.983974\pi$
$397$	−10.8182	−	18.7377i	−0.542950	−	0.940417i	0.455783	−	0.890091i	$-0.349359\pi$
$398$	−17.7406			−0.889256
$399$	24.8018	+	14.5679i	1.24164	+	0.729309i
$400$	−0.342335			−0.0171167
$401$	10.4835	+	18.1580i	0.523522	+	0.906767i	0.999625	+	0.0273772i	$0.00871553\pi$
$401$	10.4835	+	18.1580i	0.523522	+	0.906767i	−0.476103	+	0.879389i	$0.657951\pi$
$402$	1.48204	−	2.56698i	0.0739176	−	0.128029i
$403$	11.6901	−	20.2479i	0.582327	−	1.00862i
$404$	−0.624165	−	1.08108i	−0.0310533	−	0.0537860i
$405$	−10.7813			−0.535729
$406$	−0.0250905	+	3.35212i	−0.00124522	+	0.166363i
$407$	−4.78260			−0.237065
$408$	−1.46625	−	2.53962i	−0.0725903	−	0.125730i
$409$	−3.97744	+	6.88912i	−0.196672	+	0.340645i	−0.947447	−	0.319912i	$-0.896347\pi$
$409$	−3.97744	+	6.88912i	−0.196672	+	0.340645i	0.750776	+	0.660557i	$0.229680\pi$
$410$	−0.239733	+	0.415230i	−0.0118396	+	0.0205067i
$411$	17.8494	+	30.9161i	0.880447	+	1.52498i
$412$	−4.49502			−0.221454
$413$	−25.1404	+	14.2650i	−1.23708	+	0.701935i
$414$	−0.861859			−0.0423581
$415$	−0.726757	−	1.25878i	−0.0356751	−	0.0617911i
$416$	−10.2222	+	17.7054i	−0.501184	+	0.868077i
$417$	21.5347	−	37.2992i	1.05456	−	1.82655i
$418$	10.4758	+	18.1447i	0.512390	+	0.887485i
$419$	−18.4585			−0.901756			−0.450878	−	0.892585i	$-0.648889\pi$
$419$	−18.4585			−0.901756			−0.450878	+	0.892585i	$0.648889\pi$
$420$	−6.06830	+	3.44323i	−0.296103	+	0.168013i
$421$	23.5805			1.14924			0.574622	−	0.818419i	$-0.305149\pi$
$421$	23.5805			1.14924			0.574622	+	0.818419i	$0.305149\pi$
$422$	−0.830963	−	1.43927i	−0.0404507	−	0.0700626i
$423$	−0.603115	+	1.04463i	−0.0293245	+	0.0507915i
$424$	−4.61532	+	7.99397i	−0.224140	+	0.388221i
$425$	0.222230	+	0.384914i	0.0107797	+	0.0186711i
$426$	−9.71980			−0.470926
$427$	0.166175	−	22.2012i	0.00804178	−	1.07439i
$428$	−7.52100			−0.363541
$429$	20.3089	+	35.1761i	0.980524	+	1.69832i
$430$	−3.60829	+	6.24974i	−0.174007	+	0.301389i
$431$	5.43462	−	9.41303i	0.261776	−	0.453410i	−0.704938	−	0.709269i	$-0.749025\pi$
$431$	5.43462	−	9.41303i	0.261776	−	0.453410i	0.966714	+	0.255859i	$0.0823584\pi$
$432$	0.317801	+	0.550447i	0.0152902	+	0.0264834i
$433$	−23.6994			−1.13892			−0.569461	−	0.822018i	$-0.692848\pi$
$433$	−23.6994			−1.13892			−0.569461	+	0.822018i	$0.692848\pi$
$434$	−13.1206	−	7.70671i	−0.629811	−	0.369934i
$435$	−3.14431			−0.150758
$436$	−1.18489	−	2.05229i	−0.0567460	−	0.0982870i
$437$	1.02651	−	1.77796i	0.0491046	−	0.0850516i
$438$	1.88011	−	3.25644i	0.0898350	−	0.155599i
$439$	−8.01491	−	13.8822i	−0.382531	−	0.662563i	0.608892	−	0.793253i	$-0.291614\pi$
$439$	−8.01491	−	13.8822i	−0.382531	−	0.662563i	−0.991423	+	0.130690i	$0.958281\pi$
$440$	−13.8584			−0.660673
$441$	7.84344	−	13.1274i	0.373497	−	0.625115i
$442$	−1.52105			−0.0723488
$443$	2.81842	+	4.88165i	0.133907	+	0.231934i	0.925180	−	0.379530i	$-0.123914\pi$
$443$	2.81842	+	4.88165i	0.133907	+	0.231934i	−0.791272	+	0.611464i	$0.790581\pi$
$444$	−1.31855	+	2.28380i	−0.0625756	+	0.108384i
$445$	7.15348	−	12.3902i	0.339108	−	0.587351i
$446$	−10.5833	−	18.3308i	−0.501134	−	0.867989i
$447$	−17.2711			−0.816893
$448$	13.0350	+	7.65642i	0.615847	+	0.361732i
$449$	−25.3650			−1.19705			−0.598523	−	0.801105i	$-0.704246\pi$
$449$	−25.3650			−1.19705			−0.598523	+	0.801105i	$0.704246\pi$
$450$	1.00220	+	1.73586i	0.0472441	+	0.0818292i
$451$	−1.24962	+	2.16441i	−0.0588424	+	0.101918i
$452$	7.58945	−	13.1453i	0.356978	−	0.618304i
$453$	−9.34026	−	16.1778i	−0.438844	−	0.760099i
$454$	−25.5247			−1.19793
$455$	−0.0738622	+	9.86807i	−0.00346271	+	0.462622i
$456$	31.5026			1.47524
$457$	−6.44686	−	11.1663i	−0.301571	−	0.522337i	0.674921	−	0.737890i	$-0.264178\pi$
$457$	−6.44686	−	11.1663i	−0.301571	−	0.522337i	−0.976492	+	0.215553i	$0.930845\pi$
$458$	7.56015	−	13.0946i	0.353263	−	0.611869i
$459$	0.412608	−	0.714657i	0.0192589	−	0.0333573i
$460$	0.248996	+	0.431273i	0.0116095	+	0.0201082i
$461$	−36.4136			−1.69595			−0.847976	−	0.530035i	$-0.822179\pi$
$461$	−36.4136			−1.69595			−0.847976	+	0.530035i	$0.822179\pi$
$462$	22.9920	−	13.0459i	1.06968	−	0.606952i
$463$	−22.1257			−1.02827			−0.514133	−	0.857710i	$-0.671886\pi$
$463$	−22.1257			−1.02827			−0.514133	+	0.857710i	$0.671886\pi$
$464$	0.236368	+	0.409402i	0.0109731	+	0.0190060i
$465$	7.13643	−	12.3607i	0.330944	−	0.573212i
$466$	−2.99209	+	5.18246i	−0.138606	+	0.240073i
$467$	9.58223	+	16.5969i	0.443413	+	0.768013i	0.997940	−	0.0641520i	$-0.0204343\pi$
$467$	9.58223	+	16.5969i	0.443413	+	0.768013i	−0.554527	+	0.832165i	$0.687101\pi$
$468$	9.43702			0.436226
$469$	3.26483	−	1.85251i	0.150756	−	0.0855408i
$470$	−0.506611			−0.0233682
$471$	19.5946	+	33.9388i	0.902870	+	1.56382i
$472$	−15.8289	+	27.4165i	−0.728584	+	1.26194i
$473$	−18.8084	+	32.5771i	−0.864810	+	1.49790i
$474$	−7.53500	−	13.0510i	−0.346094	−	0.599452i
$475$	−4.77463			−0.219075
$476$	0.0101936	−	1.36188i	0.000467225	−	0.0624218i
$477$	6.95910			0.318635
$478$	−10.6859	−	18.5086i	−0.488764	−	0.846564i
$479$	11.1757	−	19.3569i	0.510631	−	0.884439i	−0.489293	−	0.872120i	$-0.662745\pi$
$479$	11.1757	−	19.3569i	0.510631	−	0.884439i	0.999924	−	0.0123198i	$-0.00392162\pi$
$480$	−6.24030	+	10.8085i	−0.284830	+	0.493339i
$481$	1.86494	+	3.23018i	0.0850341	+	0.147283i
$482$	−19.5501			−0.890481
$483$	−2.23355	−	1.31193i	−0.101630	−	0.0596949i
$484$	−13.7512			−0.625055
$485$	1.85026	+	3.20475i	0.0840161	+	0.145520i
$486$	8.70667	−	15.0804i	0.394943	−	0.684061i
$487$	17.8944	−	30.9939i	0.810871	−	1.40447i	−0.101385	−	0.994847i	$-0.532327\pi$
$487$	17.8944	−	30.9939i	0.810871	−	1.40447i	0.912255	−	0.409622i	$-0.134339\pi$
$488$	−12.1579	−	21.0581i	−0.550362	−	0.953255i
$489$	−4.66278			−0.210858
$490$	6.42190	+	0.0961407i	0.290112	+	0.00434320i
$491$	−17.3309			−0.782135			−0.391067	−	0.920362i	$-0.627894\pi$
$491$	−17.3309			−0.782135			−0.391067	+	0.920362i	$0.627894\pi$
$492$	0.689034	+	1.19344i	0.0310640	+	0.0538045i
$493$	0.306882	−	0.531535i	0.0138213	−	0.0239392i
$494$	8.16995	−	14.1508i	0.367584	−	0.636674i
$495$	5.22401	+	9.04825i	0.234802	+	0.406689i
$496$	−2.14588			−0.0963527
$497$	−10.6138	−	6.23429i	−0.476096	−	0.279646i
$498$	3.03662			0.136074
$499$	7.25353	+	12.5635i	0.324713	+	0.562419i	0.981454	−	0.191697i	$-0.0613991\pi$
$499$	7.25353	+	12.5635i	0.324713	+	0.562419i	−0.656742	+	0.754116i	$0.728066\pi$
$500$	0.579081	−	1.00300i	0.0258973	−	0.0448554i
$501$	−5.25663	+	9.10475i	−0.234849	+	0.406770i
$502$	12.2857	+	21.2794i	0.548336	+	0.949746i
$503$	−0.623871			−0.0278170			−0.0139085	−	0.999903i	$-0.504427\pi$
$503$	−0.623871			−0.0278170			−0.0139085	+	0.999903i	$0.504427\pi$
$504$	0.125356	−	16.7477i	0.00558379	−	0.746002i
$505$	−1.07785			−0.0479638
$506$	−0.943411	−	1.63404i	−0.0419397	−	0.0726418i
$507$	1.03835	−	1.79848i	0.0461148	−	0.0798732i
$508$	−2.37127	+	4.10716i	−0.105208	+	0.182226i
$509$	−13.4168	−	23.2385i	−0.594687	−	1.03003i	−0.993591	−	0.113036i	$-0.963943\pi$
$509$	−13.4168	−	23.2385i	−0.594687	−	1.03003i	0.398904	−	0.916993i	$-0.369391\pi$
$510$	−0.928548			−0.0411168
$511$	4.14173	−	2.35007i	0.183219	−	0.103961i
$512$	3.86036			0.170605
$513$	4.43245	+	7.67723i	0.195698	+	0.338958i
$514$	1.62211	−	2.80957i	0.0715480	−	0.123925i
$515$	−1.94058	+	3.36118i	−0.0855122	+	0.148111i
$516$	10.3708	+	17.9628i	0.456550	+	0.790769i
$517$	−2.64074			−0.116139
$518$	2.11132	−	1.19799i	0.0927661	−	0.0526367i
$519$	16.1920			0.710748
$520$	5.40398	+	9.35998i	0.236980	+	0.410462i
$521$	20.1567	−	34.9124i	0.883079	−	1.52954i	0.0351802	−	0.999381i	$-0.488799\pi$
$521$	20.1567	−	34.9124i	0.883079	−	1.52954i	0.847899	−	0.530157i	$-0.177867\pi$
$522$	1.38396	−	2.39708i	0.0605741	−	0.104917i
$523$	−5.38986	−	9.33551i	−0.235682	−	0.408213i	0.723789	−	0.690022i	$-0.242399\pi$
$523$	−5.38986	−	9.33551i	−0.235682	−	0.408213i	−0.959471	+	0.281809i	$0.909066\pi$
$524$	20.5160			0.896246
$525$	−0.0450904	+	6.02413i	−0.00196790	+	0.262914i
$526$	−16.1039			−0.702164
$527$	1.39302	+	2.41278i	0.0606809	+	0.105102i
$528$	1.86398	−	3.22852i	0.0811195	−	0.140503i
$529$	11.4076	−	19.7585i	0.495981	−	0.859064i
$530$	1.46139	+	2.53121i	0.0634789	+	0.109949i
$531$	23.8672			1.03575
$532$	12.6153	+	7.40987i	0.546941	+	0.321259i
$533$	1.94912			0.0844259
$534$	14.9448	+	25.8851i	0.646723	+	1.12016i
$535$	−3.24695	+	5.62389i	−0.140378	+	0.243142i
$536$	2.05560	−	3.56040i	0.0887884	−	0.153786i
$537$	−10.4263	−	18.0590i	−0.449930	−	0.779301i
$538$	8.83532			0.380918
$539$	33.4745	+	0.501138i	1.44185	+	0.0215856i
$540$	−2.15032			−0.0925351
$541$	9.59461	+	16.6184i	0.412505	+	0.714479i	0.995163	−	0.0982384i	$-0.0313208\pi$
$541$	9.59461	+	16.6184i	0.412505	+	0.714479i	−0.582658	+	0.812717i	$0.697987\pi$
$542$	−1.00726	+	1.74462i	−0.0432653	+	0.0749378i
$543$	17.9199	−	31.0381i	0.769015	−	1.33197i
$544$	−1.21810	−	2.10981i	−0.0522255	−	0.0904572i
$545$	−2.04616			−0.0876478
$546$	−17.7768	−	10.4416i	−0.760777	−	0.446860i
$547$	30.8450			1.31884			0.659419	−	0.751776i	$-0.270803\pi$
$547$	30.8450			1.31884			0.659419	+	0.751776i	$0.270803\pi$
$548$	9.07897	+	15.7252i	0.387834	+	0.671749i
$549$	−9.16599	+	15.8760i	−0.391195	+	0.677569i
$550$	−2.19406	+	3.80022i	−0.0935550	+	0.162042i
$551$	3.29669	+	5.71004i	0.140444	+	0.243256i
$552$	−2.83699			−0.120750
$553$	0.142846	−	19.0844i	0.00607443	−	0.811552i
$554$	−20.5273			−0.872120
$555$	1.13848	+	1.97191i	0.0483260	+	0.0837030i
$556$	10.9535	−	18.9720i	0.464531	−	0.804591i
$557$	−17.8384	+	30.8970i	−0.755836	+	1.30915i	0.189122	+	0.981954i	$0.439436\pi$
$557$	−17.8384	+	30.8970i	−0.755836	+	1.30915i	−0.944958	+	0.327192i	$0.893897\pi$
$558$	6.28214	+	10.8810i	0.265944	+	0.460629i
$559$	29.3368			1.24081
$560$	0.787755	−	0.446982i	0.0332887	−	0.0188885i
$561$	−4.84010			−0.204349
$562$	10.8674	+	18.8229i	0.458415	+	0.793998i
$563$	−2.54089	+	4.40094i	−0.107086	+	0.185478i	−0.914588	−	0.404386i	$-0.867485\pi$
$563$	−2.54089	+	4.40094i	−0.107086	+	0.185478i	0.807503	+	0.589864i	$0.200819\pi$
$564$	−0.728043	+	1.26101i	−0.0306562	+	0.0530980i
$565$	−6.55301	−	11.3501i	−0.275687	−	0.477504i
$566$	9.03878			0.379928
$567$	24.8092	−	14.0771i	1.04189	−	0.591182i
$568$	−13.4814			−0.565667
$569$	−17.1913	−	29.7762i	−0.720696	−	1.24828i	−0.960721	−	0.277516i	$-0.910489\pi$
$569$	−17.1913	−	29.7762i	−0.720696	−	1.24828i	0.240025	−	0.970767i	$-0.422844\pi$
$570$	4.98748	−	8.63857i	0.208903	−	0.361830i
$571$	16.7372	−	28.9897i	0.700431	−	1.21318i	−0.267885	−	0.963451i	$-0.586325\pi$
$571$	16.7372	−	28.9897i	0.700431	−	1.21318i	0.968315	−	0.249731i	$-0.0803421\pi$
$572$	10.3300	+	17.8920i	0.431918	+	0.748104i
$573$	46.4795			1.94171
$574$	0.00949477	−	1.26851i	0.000396304	−	0.0529467i
$575$	0.429984			0.0179316
$576$	−6.24115	−	10.8100i	−0.260048	−	0.450416i
$577$	−7.72875	+	13.3866i	−0.321752	+	0.557291i	−0.980850	−	0.194767i	$-0.937605\pi$
$577$	−7.72875	+	13.3866i	−0.321752	+	0.557291i	0.659098	+	0.752057i	$0.270938\pi$
$578$	−7.70827	+	13.3511i	−0.320622	+	0.555333i
$579$	−24.3725	−	42.2144i	−1.01289	−	1.75437i
$580$	−1.59933			−0.0664086
$581$	3.31593	+	1.94769i	0.137568	+	0.0808038i
$582$	−7.73098			−0.320459
$583$	7.61759	+	13.1941i	0.315488	+	0.546442i
$584$	2.60771	−	4.51669i	0.107908	−	0.186902i
$585$	4.07413	−	7.05660i	0.168445	−	0.291755i
$586$	4.72087	+	8.17678i	0.195017	+	0.337780i
$587$	−8.32431			−0.343581			−0.171791	−	0.985133i	$-0.554955\pi$
$587$	−8.32431			−0.343581			−0.171791	+	0.985133i	$0.554955\pi$
$588$	9.46812	−	15.8466i	0.390459	−	0.653503i
$589$	−29.9291			−1.23321
$590$	5.01206	+	8.68114i	0.206343	+	0.357397i
$591$	21.2593	−	36.8221i	0.874489	−	1.51466i
$592$	0.171167	−	0.296470i	0.00703493	−	0.0121849i
$593$	2.95840	+	5.12410i	0.121487	+	0.210421i	0.920354	−	0.391086i	$-0.127900\pi$
$593$	2.95840	+	5.12410i	0.121487	+	0.210421i	−0.798867	+	0.601507i	$0.794567\pi$
$594$	8.14728			0.334287
$595$	−1.01396	−	0.595572i	−0.0415682	−	0.0244161i
$596$	−8.78479			−0.359839
$597$	22.0131	+	38.1278i	0.900936	+	1.56047i
$598$	−0.735753	+	1.27436i	−0.0300872	+	0.0521125i
$599$	18.3976	−	31.8656i	0.751706	−	1.30199i	−0.195289	−	0.980746i	$-0.562564\pi$
$599$	18.3976	−	31.8656i	0.751706	−	1.30199i	0.946995	−	0.321248i	$-0.104102\pi$
$600$	3.29895	+	5.71395i	0.134679	+	0.233271i
$601$	−7.15767			−0.291967			−0.145984	−	0.989287i	$-0.546635\pi$
$601$	−7.15767			−0.291967			−0.145984	+	0.989287i	$0.546635\pi$
$602$	0.142908	−	19.0927i	0.00582451	−	0.778162i
$603$	−3.09948			−0.126221
$604$	−4.75085	−	8.22871i	−0.193309	−	0.334822i
$605$	−5.93665	+	10.2826i	−0.241359	+	0.418046i
$606$	1.12590	−	1.95012i	0.0457367	−	0.0792182i
$607$	−19.7842	−	34.2672i	−0.803014	−	1.39086i	−0.917623	−	0.397451i	$-0.869895\pi$
$607$	−19.7842	−	34.2672i	−0.803014	−	1.39086i	0.114609	−	0.993411i	$-0.463439\pi$
$608$	26.1709			1.06137
$609$	7.23546	−	4.10549i	0.293195	−	0.166363i
$610$	−7.69934			−0.311737
$611$	1.02974	+	1.78356i	0.0416587	+	0.0721550i
$612$	−0.562267	+	0.973874i	−0.0227283	+	0.0393665i
$613$	−23.6017	+	40.8793i	−0.953263	+	1.65110i	−0.214970	+	0.976621i	$0.568965\pi$
$613$	−23.6017	+	40.8793i	−0.953263	+	1.65110i	−0.738293	+	0.674480i	$0.764368\pi$
$614$	5.31155	+	9.19987i	0.214357	+	0.371277i
$615$	1.18987			0.0479804
$616$	31.8899	−	18.0948i	1.28488	−	0.729058i
$617$	−15.4297			−0.621176			−0.310588	−	0.950545i	$-0.600526\pi$
$617$	−15.4297			−0.621176			−0.310588	+	0.950545i	$0.600526\pi$
$618$	−4.05418	−	7.02204i	−0.163083	−	0.282468i
$619$	17.5035	−	30.3170i	0.703527	−	1.21854i	−0.263694	−	0.964606i	$-0.584941\pi$
$619$	17.5035	−	30.3170i	0.703527	−	1.21854i	0.967221	−	0.253938i	$-0.0817258\pi$
$620$	3.62989	−	6.28716i	0.145780	−	0.252498i
$621$	−0.399169	−	0.691381i	−0.0160181	−	0.0277441i
$622$	−0.972659			−0.0390001
$623$	−0.283318	+	37.8516i	−0.0113509	+	1.51649i
$624$	−2.90739			−0.116389
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.0313	−	22.5709i	0.520835	−	0.902113i
$627$	25.9975	−	45.0290i	1.03824	−	1.79828i
$628$	9.96662	+	17.2627i	0.397712	+	0.688857i
$629$	−0.444460			−0.0177218
$630$	−4.57268	−	2.68587i	−0.182180	−	0.107008i
$631$	−7.46268			−0.297085			−0.148542	−	0.988906i	$-0.547458\pi$
$631$	−7.46268			−0.297085			−0.148542	+	0.988906i	$0.547458\pi$
$632$	−10.4511	−	18.1018i	−0.415721	−	0.720050i
$633$	−2.06217	+	3.57179i	−0.0819640	+	0.141966i
$634$	9.04062	−	15.6588i	0.359049	−	0.621891i
$635$	2.04744	+	3.54627i	0.0812502	+	0.140730i
$636$	8.40059			0.333105
$637$	−12.7147	−	22.8041i	−0.503773	−	0.903532i
$638$	6.05964			0.239904
$639$	5.08189	+	8.80210i	0.201037	+	0.348206i
$640$	−2.85998	+	4.95364i	−0.113051	+	0.195810i
$641$	19.2134	−	33.2785i	0.758883	−	1.31442i	−0.184538	−	0.982825i	$-0.559079\pi$
$641$	19.2134	−	33.2785i	0.758883	−	1.31442i	0.943421	−	0.331598i	$-0.107588\pi$
$642$	−6.78340	−	11.7492i	−0.267719	−	0.463704i
$643$	−24.2258			−0.955372			−0.477686	−	0.878531i	$-0.658524\pi$
$643$	−24.2258			−0.955372			−0.477686	+	0.878531i	$0.658524\pi$
$644$	−1.13608	−	0.667303i	−0.0447678	−	0.0262954i
$645$	17.9091			0.705171
$646$	0.973548	+	1.68623i	0.0383037	+	0.0663440i
$647$	8.94935	−	15.5007i	0.351835	−	0.609397i	−0.634736	−	0.772729i	$-0.718891\pi$
$647$	8.94935	−	15.5007i	0.351835	−	0.609397i	0.986571	+	0.163333i	$0.0522244\pi$
$648$	15.6204	−	27.0553i	0.613626	−	1.06283i
$649$	26.1256	+	45.2509i	1.02552	+	1.77625i
$650$	3.42223			0.134231
$651$	−0.282643	+	37.7614i	−0.0110776	+	1.47999i
$652$	−2.37169			−0.0928825
$653$	1.83087	+	3.17116i	0.0716476	+	0.124097i	0.899624	−	0.436666i	$-0.143841\pi$
$653$	1.83087	+	3.17116i	0.0716476	+	0.124097i	−0.827976	+	0.560764i	$0.810508\pi$
$654$	2.13737	−	3.70204i	0.0835779	−	0.144761i
$655$	8.85714	−	15.3410i	0.346077	−	0.599423i
$656$	−0.0894468	−	0.154926i	−0.00349231	−	0.00604886i
$657$	−3.93198			−0.153401
$658$	1.16578	−	0.661477i	0.0454467	−	0.0257870i
$659$	39.0361			1.52063			0.760315	−	0.649555i	$-0.225045\pi$
$659$	39.0361			1.52063			0.760315	+	0.649555i	$0.225045\pi$
$660$	6.30610	+	10.9225i	0.245465	+	0.425157i
$661$	3.72830	−	6.45760i	0.145014	−	0.251172i	−0.784364	−	0.620301i	$-0.787011\pi$
$661$	3.72830	−	6.45760i	0.145014	−	0.251172i	0.929378	+	0.369129i	$0.120344\pi$
$662$	−11.4397	+	19.8141i	−0.444616	+	0.770097i
$663$	1.88736	+	3.26901i	0.0732992	+	0.126958i
$664$	4.21180			0.163450
$665$	10.9870	−	6.23418i	0.426059	−	0.241751i
$666$	−2.00440			−0.0776688
$667$	−0.296887	−	0.514223i	−0.0114955	−	0.0199108i
$668$	−2.67374	+	4.63106i	−0.103450	+	0.179181i
$669$	−26.2642	+	45.4909i	−1.01543	+	1.75878i
$670$	−0.650885	−	1.12737i	−0.0251459	−	0.0435539i
$671$	−40.1332			−1.54933
$672$	0.247151	−	33.0197i	0.00953406	−	1.27376i
$673$	−40.7322			−1.57011			−0.785056	−	0.619424i	$-0.787366\pi$
$673$	−40.7322			−1.57011			−0.785056	+	0.619424i	$0.787366\pi$
$674$	−6.15000	−	10.6521i	−0.236889	−	0.410304i
$675$	−0.928334	+	1.60792i	−0.0357316	+	0.0618889i
$676$	0.528149	−	0.914782i	0.0203134	−	0.0351839i
$677$	5.51982	+	9.56061i	0.212144	+	0.367444i	0.952385	−	0.304897i	$-0.0986221\pi$
$677$	5.51982	+	9.56061i	0.212144	+	0.367444i	−0.740241	+	0.672341i	$0.765289\pi$
$678$	27.3805			1.05154
$679$	−8.44209	−	4.95866i	−0.323978	−	0.190296i
$680$	−1.28790			−0.0493887
$681$	31.6718	+	54.8572i	1.21367	+	2.10213i
$682$	−13.7532	+	23.8212i	−0.526636	+	0.912160i
$683$	−1.85895	+	3.21979i	−0.0711307	+	0.123202i	−0.899397	−	0.437133i	$-0.855994\pi$
$683$	−1.85895	+	3.21979i	−0.0711307	+	0.123202i	0.828266	+	0.560334i	$0.189327\pi$
$684$	−6.04017	−	10.4619i	−0.230952	−	0.400020i
$685$	15.6782			0.599035
$686$	−14.9031	+	8.16377i	−0.569004	+	0.311694i
$687$	−37.5235			−1.43161
$688$	−1.34629	−	2.33184i	−0.0513267	−	0.0889005i
$689$	5.94085	−	10.2899i	0.226328	−	0.392012i
$690$	−0.449152	+	0.777955i	−0.0170989	+	0.0296162i
$691$	21.0173	+	36.4031i	0.799537	+	1.38484i	0.919918	+	0.392111i	$0.128255\pi$
$691$	21.0173	+	36.4031i	0.799537	+	1.38484i	−0.120380	+	0.992728i	$0.538411\pi$
$692$	8.23592			0.313083
$693$	−23.8353	−	14.0002i	−0.905428	−	0.531825i
$694$	20.7767			0.788673
$695$	−9.45763	−	16.3811i	−0.358748	−	0.621370i
$696$	4.55559	−	7.89051i	0.172679	−	0.299089i
$697$	−0.116131	+	0.201144i	−0.00439876	+	0.00761888i
$698$	7.07930	+	12.2617i	0.267955	+	0.464112i
$699$	14.8507			0.561707
$700$	−0.0229349	+	3.06412i	−0.000866856	+	0.115813i
$701$	1.44546			0.0545942			0.0272971	−	0.999627i	$-0.491310\pi$
$701$	1.44546			0.0545942			0.0272971	+	0.999627i	$0.491310\pi$
$702$	−3.17697	−	5.50268i	−0.119907	−	0.207685i
$703$	2.38732	−	4.13495i	0.0900393	−	0.155953i
$704$	13.6634	−	23.6657i	0.514959	−	0.891936i
$705$	0.628619	+	1.08880i	0.0236752	+	0.0410066i
$706$	−19.5895			−0.737262
$707$	2.48027	−	1.40734i	0.0932803	−	0.0529285i
$708$	28.8110			1.08278
$709$	−10.3675	−	17.9570i	−0.389358	−	0.674388i	0.603005	−	0.797737i	$-0.293970\pi$
$709$	−10.3675	−	17.9570i	−0.389358	−	0.674388i	−0.992363	+	0.123350i	$0.960636\pi$
$710$	−2.13437	+	3.69684i	−0.0801016	+	0.138740i
$711$	−7.87919	+	13.6472i	−0.295493	+	0.511808i
$712$	20.7284	+	35.9027i	0.776830	+	1.34551i
$713$	2.69530			0.100940
$714$	2.13671	−	1.21239i	0.0799642	−	0.0453727i
$715$	17.8386			0.667125
$716$	−5.30328	−	9.18555i	−0.198193	−	0.343280i
$717$	−26.5189	+	45.9321i	−0.990368	+	1.71537i
$718$	−13.9811	+	24.2159i	−0.521769	+	0.903731i
$719$	−12.8297	−	22.2217i	−0.478468	−	0.828731i	0.521227	−	0.853418i	$-0.325474\pi$
$719$	−12.8297	−	22.2217i	−0.478468	−	0.828731i	−0.999695	+	0.0246869i	$0.992141\pi$
$720$	−0.747860			−0.0278711
$721$	0.0768578	−	10.2683i	0.00286234	−	0.382411i
$722$	−3.48392			−0.129658
$723$	24.2583	+	42.0167i	0.902178	+	1.56262i
$724$	9.11480	−	15.7873i	0.338749	−	0.586730i
$725$	−0.690460	+	1.19591i	−0.0256430	+	0.0444150i
$726$	−12.4026	−	21.4819i	−0.460304	−	0.797269i
$727$	9.02233			0.334620			0.167310	−	0.985904i	$-0.446492\pi$
$727$	9.02233			0.334620			0.167310	+	0.985904i	$0.446492\pi$
$728$	−24.6565	−	14.4826i	−0.913829	−	0.536759i
$729$	−10.8701			−0.402595
$730$	−0.825706	−	1.43016i	−0.0305608	−	0.0529328i
$731$	−1.74791	+	3.02748i	−0.0646489	+	0.111975i
$732$	−11.0646	+	19.1645i	−0.408960	+	0.708339i
$733$	2.79269	+	4.83708i	0.103150	+	0.178661i	0.912981	−	0.408002i	$-0.133774\pi$
$733$	2.79269	+	4.83708i	0.103150	+	0.178661i	−0.809831	+	0.586664i	$0.800441\pi$
$734$	20.6548			0.762384
$735$	−7.76187	−	13.9211i	−0.286301	−	0.513489i
$736$	−2.35685			−0.0868745
$737$	−3.39277	−	5.87645i	−0.124974	−	0.216462i
$738$	−0.523718	+	0.907106i	−0.0192783	+	0.0333911i
$739$	−14.1657	+	24.5356i	−0.521092	+	0.902558i	0.478607	+	0.878029i	$0.341142\pi$
$739$	−14.1657	+	24.5356i	−0.521092	+	0.902558i	−0.999699	+	0.0245286i	$0.992192\pi$
$740$	0.579081	+	1.00300i	0.0212875	+	0.0368709i
$741$	−40.5502			−1.48965
$742$	−6.66782	−	3.91650i	−0.244783	−	0.143779i
$743$	−32.5314			−1.19346			−0.596730	−	0.802442i	$-0.703534\pi$
$743$	−32.5314			−1.19346			−0.596730	+	0.802442i	$0.703534\pi$
$744$	20.6790	+	35.8171i	0.758129	+	1.31312i
$745$	−3.79255	+	6.56889i	−0.138948	+	0.240666i
$746$	−0.452121	+	0.783097i	−0.0165533	+	0.0286712i
$747$	−1.58766	−	2.74992i	−0.0580896	−	0.100614i
$748$	−2.46188			−0.0900153
$749$	0.128597	−	17.1808i	0.00469885	−	0.627772i
$750$	2.08916			0.0762853
$751$	18.6431	+	32.2908i	0.680297	+	1.17831i	0.974890	+	0.222687i	$0.0714827\pi$
$751$	18.6431	+	32.2908i	0.680297	+	1.17831i	−0.294593	+	0.955623i	$0.595184\pi$
$752$	0.0945108	−	0.163698i	0.00344645	−	0.00596943i
$753$	30.4889	−	52.8083i	1.11108	−	1.92444i
$754$	−2.36292	−	4.09269i	−0.0860523	−	0.149047i
$755$	−8.20411			−0.298578
$756$	4.94816	−	2.80765i	0.179963	−	0.102113i
$757$	−0.286506			−0.0104132			−0.00520661	−	0.999986i	$-0.501657\pi$
$757$	−0.286506			−0.0104132			−0.00520661	+	0.999986i	$0.501657\pi$
$758$	−3.10888	−	5.38473i	−0.112919	−	0.195582i
$759$	−2.34123	+	4.05513i	−0.0849813	+	0.147192i
$760$	6.91765	−	11.9817i	0.250930	−	0.434623i
$761$	0.724780	+	1.25536i	0.0262733	+	0.0455066i	0.878863	−	0.477074i	$-0.158303\pi$
$761$	0.724780	+	1.25536i	0.0262733	+	0.0455066i	−0.852590	+	0.522581i	$0.824969\pi$
$762$	−8.55486			−0.309910
$763$	4.70847	−	2.67165i	0.170458	−	0.0967201i
$764$	23.6415			0.855318
$765$	0.485482	+	0.840879i	0.0175526	+	0.0304020i
$766$	15.2646	−	26.4391i	0.551533	−	0.955282i
$767$	20.3750	−	35.2905i	0.735699	−	1.27427i
$768$	−18.9851	−	32.8832i	−0.685066	−	1.18657i
$769$	−44.9607			−1.62132			−0.810662	−	0.585514i	$-0.800893\pi$
$769$	−44.9607			−1.62132			−0.810662	+	0.585514i	$0.800893\pi$
$770$	0.0868970	−	11.6096i	0.00313155	−	0.418379i
$771$	−8.05104			−0.289951
$772$	−12.3969	−	21.4720i	−0.446174	−	0.772795i
$773$	13.4615	−	23.3160i	0.484176	−	0.838617i	−0.515659	−	0.856794i	$-0.672453\pi$
$773$	13.4615	−	23.3160i	0.484176	−	0.838617i	0.999835	+	0.0181770i	$0.00578624\pi$
$774$	−7.88262	+	13.6531i	−0.283335	+	0.490751i
$775$	−3.13418	−	5.42856i	−0.112583	−	0.195000i
$776$	−10.7229			−0.384929
$777$	−5.19450	−	3.05111i	−0.186352	−	0.109458i
$778$	7.98412			0.286245
$779$	−1.24754	−	2.16080i	−0.0446977	−	0.0774187i
$780$	4.91804	−	8.51830i	0.176094	−	0.305004i
$781$	−11.1255	+	19.2700i	−0.398103	+	0.689534i
$782$	−0.0876738	−	0.151855i	−0.00313521	−	0.00543034i
$783$	2.56391			0.0916266
$784$	−1.22910	+	2.05713i	−0.0438965	+	0.0734688i
$785$	17.2111			0.614290
$786$	18.5040	+	32.0498i	0.660014	+	1.14318i
$787$	−3.27219	+	5.66760i	−0.116641	+	0.202028i	−0.918435	−	0.395573i	$-0.870546\pi$
$787$	−3.27219	+	5.66760i	−0.116641	+	0.202028i	0.801793	+	0.597601i	$0.203879\pi$
$788$	10.8134	−	18.7293i	0.385210	−	0.667203i
$789$	19.9823	+	34.6103i	0.711387	+	1.23216i
$790$	−6.61845			−0.235474
$791$	29.8991	+	17.5619i	1.06309	+	0.624430i
$792$	−30.2749			−1.07577
$793$	15.6497	+	27.1060i	0.555736	+	0.962563i
$794$	9.92589	−	17.1921i	0.352257	−	0.610126i
$795$	3.62669	−	6.28161i	0.128625	−	0.222786i
$796$	11.1968	+	19.3934i	0.396860	+	0.687381i
$797$	27.3601			0.969146			0.484573	−	0.874751i	$-0.338975\pi$
$797$	27.3601			0.969146			0.484573	+	0.874751i	$0.338975\pi$
$798$	−0.197532	+	26.3905i	−0.00699256	+	0.934215i
$799$	−0.245411			−0.00868201
$800$	2.74062	+	4.74689i	0.0968955	+	0.167828i
$801$	15.6274	−	27.0675i	0.552167	−	0.956382i
$802$	−9.61881	+	16.6603i	−0.339652	+	0.588294i
$803$	−4.30403	−	7.45481i	−0.151886	−	0.263074i
$804$	−3.74151			−0.131953
$805$	−0.989447	+	0.561426i	−0.0348734	+	0.0197877i
$806$	21.4518			0.755607
$807$	−10.9631	−	18.9887i	−0.385921	−	0.668435i
$808$	1.56163	−	2.70482i	0.0549380	−	0.0951553i
$809$	−14.7001	+	25.4613i	−0.516828	+	0.895172i	0.482981	+	0.875631i	$0.339554\pi$
$809$	−14.7001	+	25.4613i	−0.516828	+	0.895172i	−0.999809	+	0.0195413i	$0.993779\pi$
$810$	−4.94603	−	8.56678i	−0.173786	−	0.301006i
$811$	−1.55800			−0.0547086			−0.0273543	−	0.999626i	$-0.508708\pi$
$811$	−1.55800			−0.0547086			−0.0273543	+	0.999626i	$0.508708\pi$
$812$	3.68026	−	2.08823i	0.129152	−	0.0732824i
$813$	4.99934			0.175335
$814$	−2.19406	−	3.80022i	−0.0769018	−	0.133198i
$815$	−1.02390	+	1.77345i	−0.0358657	+	0.0621212i
$816$	0.173225	−	0.300035i	0.00606409	−	0.0105033i
$817$	−18.7770	−	32.5228i	−0.656925	−	1.13783i
$818$	−7.29873			−0.255194
$819$	−0.161358	+	21.5577i	−0.00563832	+	0.753286i
$820$	0.605220			0.0211352
$821$	23.7680	+	41.1673i	0.829508	+	1.43675i	0.898425	+	0.439127i	$0.144712\pi$
$821$	23.7680	+	41.1673i	0.829508	+	1.43675i	−0.0689169	+	0.997622i	$0.521954\pi$
$822$	−16.3772	+	28.3661i	−0.571219	+	0.989380i
$823$	−17.1890	+	29.7722i	−0.599170	+	1.03779i	0.393774	+	0.919207i	$0.371169\pi$
$823$	−17.1890	+	29.7722i	−0.599170	+	1.03779i	−0.992944	+	0.118585i	$0.962164\pi$
$824$	−5.62316	−	9.73960i	−0.195892	−	0.339295i
$825$	10.8898			0.379136
$826$	−22.8683	−	13.4322i	−0.795688	−	0.467366i
$827$	13.4406			0.467374			0.233687	−	0.972312i	$-0.424921\pi$
$827$	13.4406			0.467374			0.233687	+	0.972312i	$0.424921\pi$
$828$	0.543953	+	0.942155i	0.0189037	+	0.0327421i
$829$	16.1842	−	28.0318i	0.562100	−	0.973585i	−0.435213	−	0.900327i	$-0.643327\pi$
$829$	16.1842	−	28.0318i	0.562100	−	0.973585i	0.997313	−	0.0732579i	$-0.0233396\pi$
$830$	0.666812	−	1.15495i	0.0231454	−	0.0400890i
$831$	25.4709	+	44.1169i	0.883575	+	1.53040i
$832$	−21.3118			−0.738854
$833$	3.11087	+	0.0465722i	0.107785	+	0.00161363i
$834$	39.5170			1.36836
$835$	2.30861	+	3.99863i	0.0798927	+	0.138378i
$836$	13.2234	−	22.9036i	0.457342	−	0.792139i
$837$	−5.81913	+	10.0790i	−0.201139	+	0.348382i
$838$	−8.46799	−	14.6670i	−0.292522	−	0.506663i
$839$	−3.82090			−0.131912			−0.0659561	−	0.997823i	$-0.521010\pi$
$839$	−3.82090			−0.131912			−0.0659561	+	0.997823i	$0.521010\pi$
$840$	−15.0519	−	8.84111i	−0.519341	−	0.305047i
$841$	−27.0931			−0.934243
$842$	10.8178	+	18.7369i	0.372804	+	0.645716i
$843$	26.9693	−	46.7122i	0.928872	−	1.60885i
$844$	−1.04891	+	1.81676i	−0.0361049	+	0.0625355i
$845$	−0.456024	−	0.789856i	−0.0156877	−	0.0271719i
$846$	−1.10674			−0.0380504
$847$	0.235125	−	31.4129i	0.00807897	−	1.07936i
$848$	−1.09052			−0.0374486
$849$	−11.2156	−	19.4260i	−0.384919	−	0.666699i
$850$	−0.203900	+	0.353165i	−0.00699371	+	0.0121135i
$851$	−0.214992	+	0.372377i	−0.00736983	+	0.0127649i
$852$	6.13455	+	10.6254i	0.210166	+	0.364019i
$853$	−48.8089			−1.67119			−0.835593	−	0.549349i	$-0.814876\pi$
$853$	−48.8089			−1.67119			−0.835593	+	0.549349i	$0.814876\pi$
$854$	17.7172	−	10.0529i	0.606268	−	0.344005i
$855$	−10.4306			−0.356719
$856$	−9.40859	−	16.2962i	−0.321579	−	0.556991i
$857$	22.6050	−	39.1530i	0.772171	−	1.33744i	−0.164199	−	0.986427i	$-0.552504\pi$
$857$	22.6050	−	39.1530i	0.772171	−	1.33744i	0.936371	−	0.351013i	$-0.114163\pi$
$858$	−18.6338	+	32.2747i	−0.636147	+	1.10184i
$859$	−11.5742	−	20.0470i	−0.394905	−	0.683995i	0.598184	−	0.801359i	$-0.295889\pi$
$859$	−11.5742	−	20.0470i	−0.394905	−	0.683995i	−0.993089	+	0.117363i	$0.962556\pi$
$860$	9.10933			0.310626
$861$	−2.73805	+	1.55361i	−0.0933125	+	0.0529467i
$862$	9.97271			0.339672
$863$	−7.96668	−	13.7987i	−0.271189	−	0.469713i	0.697978	−	0.716120i	$-0.254083\pi$
$863$	−7.96668	−	13.7987i	−0.271189	−	0.469713i	−0.969167	+	0.246407i	$0.920750\pi$
$864$	5.08842	−	8.81340i	0.173111	−	0.299838i
$865$	3.55560	−	6.15847i	0.120894	−	0.209394i
$866$	−10.8723	−	18.8314i	−0.369457	−	0.639918i
$867$	38.2587			1.29933
$868$	−0.143764	+	19.2070i	−0.00487967	+	0.651929i
$869$	−34.4990			−1.17030
$870$	−1.44248	−	2.49845i	−0.0489047	−	0.0847053i
$871$	−2.64597	+	4.58296i	−0.0896554	+	0.155288i
$872$	2.96454	−	5.13474i	0.100392	−	0.173884i
$873$	4.04206	+	7.00106i	0.136803	+	0.236950i
$874$	1.88368			0.0637163
$875$	2.28132	+	1.33999i	0.0771228	+	0.0452999i
$876$	−4.74644			−0.160367
$877$	−18.5352	−	32.1040i	−0.625891	−	1.08407i	−0.988368	−	0.152082i	$-0.951402\pi$
$877$	−18.5352	−	32.1040i	−0.625891	−	1.08407i	0.362477	−	0.931993i	$-0.381931\pi$
$878$	7.35382	−	12.7372i	0.248179	−	0.429859i
$879$	11.7156	−	20.2920i	0.395157	−	0.684433i
$880$	−0.818625	−	1.41790i	−0.0275959	−	0.0477974i
$881$	6.21756			0.209475			0.104737	−	0.994500i	$-0.466600\pi$
$881$	6.21756			0.209475			0.104737	+	0.994500i	$0.466600\pi$
$882$	14.0292	+	0.210028i	0.472388	+	0.00707201i
$883$	3.51871			0.118414			0.0592070	−	0.998246i	$-0.481143\pi$
$883$	3.51871			0.118414			0.0592070	+	0.998246i	$0.481143\pi$
$884$	0.959993	+	1.66276i	0.0322881	+	0.0559246i
$885$	12.4383	−	21.5437i	0.418107	−	0.724183i
$886$	−2.58595	+	4.47900i	−0.0868767	+	0.150475i
$887$	17.3641	+	30.0755i	0.583029	+	1.00984i	0.995118	+	0.0986923i	$0.0314659\pi$
$887$	17.3641	+	30.0755i	0.583029	+	1.00984i	−0.412089	+	0.911144i	$0.635201\pi$
$888$	−6.59790			−0.221411
$889$	−9.34175	−	5.48710i	−0.313312	−	0.184031i
$890$	13.1269			0.440014
$891$	−25.7814	−	44.6548i	−0.863711	−	1.49599i
$892$	−13.3591	+	23.1386i	−0.447295	+	0.774737i
$893$	1.31817	−	2.28313i	0.0441108	−	0.0764021i
$894$	−7.92324	−	13.7235i	−0.264993	−	0.458981i
$895$	−9.15809			−0.306121
$896$	0.113271	−	15.1332i	0.00378413	−	0.505564i
$897$	3.65178			0.121930
$898$	−11.6364	−	20.1548i	−0.388312	−	0.672575i
$899$	−4.32805	+	7.49641i	−0.144349	+	0.250019i
$900$	1.26505	−	2.19114i	0.0421685	−	0.0730379i
$901$	0.707924	+	1.22616i	0.0235844	+	0.0408493i
$902$	−2.29310			−0.0763518
$903$	−41.2111	+	23.3837i	−1.37142	+	0.778162i
$904$	37.9769			1.26309
$905$	−7.87005	−	13.6313i	−0.261609	−	0.453121i
$906$	8.56985	−	14.8434i	0.284714	−	0.493139i
$907$	3.98527	−	6.90269i	0.132329	−	0.229200i	−0.792245	−	0.610203i	$-0.791088\pi$
$907$	3.98527	−	6.90269i	0.132329	−	0.229200i	0.924574	+	0.381003i	$0.124421\pi$
$908$	16.1096	+	27.9027i	0.534617	+	0.925984i
$909$	−2.35467			−0.0780993
$910$	−7.87499	+	4.46837i	−0.261053	+	0.148125i
$911$	8.13952			0.269674			0.134837	−	0.990868i	$-0.456949\pi$
$911$	8.13952			0.269674			0.134837	+	0.990868i	$0.456949\pi$
$912$	1.86088	+	3.22314i	0.0616198	+	0.106729i
$913$	3.47579	−	6.02024i	0.115032	−	0.199241i
$914$	5.91510	−	10.2453i	0.195654	−	0.338883i
$915$	9.55359	+	16.5473i	0.315832	+	0.547037i
$916$	−19.0860			−0.630621
$917$	−0.350792	+	46.8662i	−0.0115842	+	1.54766i
$918$	0.757149			0.0249896
$919$	−6.20808	−	10.7527i	−0.204786	−	0.354699i	0.745279	−	0.666753i	$-0.232316\pi$
$919$	−6.20808	−	10.7527i	−0.204786	−	0.354699i	−0.950064	+	0.312054i	$0.898983\pi$
$920$	−0.622976	+	1.07903i	−0.0205389	+	0.0355744i
$921$	13.1815	−	22.8310i	0.434345	−	0.752307i
$922$	−16.7051	−	28.9340i	−0.550152	−	0.952891i
$923$	17.3533			0.571190
$924$	−28.7725	−	16.9002i	−0.946546	−	0.555976i
$925$	1.00000			0.0328798
$926$	−10.1503	−	17.5809i	−0.333561	−	0.577744i
$927$	−4.23937	+	7.34280i	−0.139239	+	0.241169i
$928$	3.78458	−	6.55508i	0.124235	−	0.215181i
$929$	9.55517	+	16.5500i	0.313495	+	0.542989i	0.979116	−	0.203300i	$-0.0651668\pi$
$929$	9.55517	+	16.5500i	0.313495	+	0.542989i	−0.665622	+	0.746289i	$0.731833\pi$
$930$	13.0956			0.429422
$931$	−17.1426	+	28.6913i	−0.561827	+	0.940319i
$932$	7.55372			0.247430
$933$	1.20691	+	2.09042i	0.0395123	+	0.0684374i
$934$	−8.79186	+	15.2279i	−0.287678	+	0.498274i
$935$	−1.06284	+	1.84089i	−0.0347586	+	0.0602036i
$936$	11.8055	+	20.4477i	0.385874	+	0.668354i
$937$	−53.7744			−1.75673			−0.878367	−	0.477987i	$-0.841367\pi$
$937$	−53.7744			−1.75673			−0.878367	+	0.477987i	$0.841367\pi$
$938$	2.96975	+	1.74436i	0.0969659	+	0.0569552i
$939$	−64.6786			−2.11071
$940$	0.319742	+	0.553810i	0.0104288	+	0.0180633i
$941$	−8.20091	+	14.2044i	−0.267342	+	0.463050i	−0.968175	−	0.250276i	$-0.919479\pi$
$941$	−8.20091	+	14.2044i	−0.267342	+	0.463050i	0.700832	+	0.713326i	$0.252812\pi$
$942$	−17.9783	+	31.1394i	−0.585766	+	1.01458i
$943$	0.112348	+	0.194593i	0.00365856	+	0.00633682i
$944$	−3.74010			−0.121730
$945$	0.0367672	−	4.91214i	0.00119604	−	0.159792i
$946$	−34.5140			−1.12215
$947$	0.994322	+	1.72222i	0.0323111	+	0.0559645i	0.881729	−	0.471757i	$-0.156380\pi$
$947$	0.994322	+	1.72222i	0.0323111	+	0.0559645i	−0.849418	+	0.527721i	$0.823047\pi$
$948$	−9.51127	+	16.4740i	−0.308912	+	0.535051i
$949$	−3.35666	+	5.81390i	−0.108962	+	0.188727i
$950$	−2.19040	−	3.79389i	−0.0710661	−	0.123090i
$951$	−44.8716			−1.45506
$952$	2.96362	−	1.68159i	0.0960513	−	0.0545008i
$953$	−46.1261			−1.49417			−0.747085	−	0.664728i	$-0.768547\pi$
$953$	−46.1261			−1.49417			−0.747085	+	0.664728i	$0.768547\pi$
$954$	3.19254	+	5.52965i	0.103362	+	0.179029i
$955$	10.2065	−	17.6781i	0.330273	−	0.572050i
$956$	−13.4886	+	23.3630i	−0.436254	+	0.755614i
$957$	−7.51900	−	13.0233i	−0.243055	−	0.420983i
$958$	20.5078			0.662577
$959$	−36.0776	+	20.4709i	−1.16501	+	0.661040i
$960$	−13.0101			−0.419901
$961$	−4.14618	−	7.18140i	−0.133748	−	0.231658i
$962$	−1.71112	+	2.96374i	−0.0551686	+	0.0955549i
$963$	−7.09326	+	12.2859i	−0.228577	+	0.395907i
$964$	12.3388	+	21.3715i	0.397407	+	0.688328i
$965$	−21.4078			−0.689143
$966$	0.0177889	−	2.37662i	0.000572350	−	0.0764666i
$967$	−34.9457			−1.12378			−0.561889	−	0.827213i	$-0.689925\pi$
$967$	−34.9457			−1.12378			−0.561889	+	0.827213i	$0.689925\pi$
$968$	−17.2024	−	29.7955i	−0.552907	−	0.957664i
$969$	2.41602	−	4.18467i	0.0776137	−	0.134431i
$970$	−1.69765	+	2.94041i	−0.0545082	+	0.0944109i
$971$	−24.8922	−	43.1145i	−0.798828	−	1.38361i	−0.920380	−	0.391026i	$-0.872120\pi$
$971$	−24.8922	−	43.1145i	−0.798828	−	1.38361i	0.121551	−	0.992585i	$-0.461213\pi$
$972$	−21.9805			−0.705025
$973$	43.1518	+	25.3462i	1.38338	+	0.812563i
$974$	32.8367			1.05216
$975$	−4.24642	−	7.35501i	−0.135994	−	0.235549i
$976$	1.43635	−	2.48783i	0.0459764	−	0.0796335i
$977$	1.36248	−	2.35989i	0.0435897	−	0.0754996i	−0.843407	−	0.537275i	$-0.819454\pi$
$977$	1.36248	−	2.35989i	0.0435897	−	0.0754996i	0.886997	+	0.461775i	$0.152787\pi$
$978$	−2.13909	−	3.70501i	−0.0684006	−	0.118473i
$979$	68.4245			2.18686
$980$	−3.94802	−	7.08088i	−0.126115	−	0.226190i
$981$	−4.47001			−0.142717
$982$	−7.95072	−	13.7711i	−0.253718	−	0.439452i
$983$	12.1254	−	21.0019i	0.386741	−	0.669855i	−0.605268	−	0.796022i	$-0.706934\pi$
$983$	12.1254	−	21.0019i	0.386741	−	0.669855i	0.992009	+	0.126167i	$0.0402674\pi$
$984$	−1.72393	+	2.98593i	−0.0549569	+	0.0951881i
$985$	−9.33665	−	16.1716i	−0.297490	−	0.515269i
$986$	0.563139			0.0179340
$987$	−2.86817	−	1.68469i	−0.0912948	−	0.0536241i
$988$	−20.6255			−0.656185
$989$	1.69098	+	2.92887i	0.0537702	+	0.0931327i
$990$	−4.79312	+	8.30192i	−0.152335	+	0.263852i
$991$	4.15664	−	7.19951i	0.132040	−	0.228700i	−0.792423	−	0.609972i	$-0.791181\pi$
$991$	4.15664	−	7.19951i	0.132040	−	0.228700i	0.924463	+	0.381272i	$0.124514\pi$
$992$	17.1792	+	29.7552i	0.545440	+	0.944730i
$993$	56.7789			1.80182
$994$	0.0845331	−	11.2937i	0.00268123	−	0.358215i
$995$	19.3354			0.612975
$996$	−1.91653	−	3.31953i	−0.0607276	−	0.105183i
$997$	−3.39040	+	5.87234i	−0.107375	+	0.185979i	−0.914706	−	0.404120i	$-0.867578\pi$
$997$	−3.39040	+	5.87234i	−0.107375	+	0.185979i	0.807331	+	0.590099i	$0.200911\pi$
$998$	−6.65524	+	11.5272i	−0.210668	+	0.364887i
$999$	−0.928334	−	1.60792i	−0.0293712	−	0.0508724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.13	✓	38
7.2	even	3	inner	1295.2.j.a.926.13	yes	38
7.3	odd	6		9065.2.a.s.1.7		19
7.4	even	3		9065.2.a.r.1.7		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.13	✓	38	1.1	even	1	trivial
1295.2.j.a.926.13	yes	38	7.2	even	3	inner
9065.2.a.r.1.7		19	7.4	even	3
9065.2.a.s.1.7		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+(0.458759 + 0.794593i) q^{2} +(1.13848 - 1.97191i) q^{3} +(0.579081 - 1.00300i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.08916 q^{6} +(2.28132 + 1.33999i) q^{7} +2.89767 q^{8} +(-1.09229 - 1.89191i) q^{9} +(0.458759 - 0.794593i) q^{10} +(2.39130 - 4.14186i) q^{11} +(-1.31855 - 2.28380i) q^{12} -3.72989 q^{13} +(-0.0181694 + 2.42745i) q^{14} -2.27697 q^{15} +(0.171167 + 0.296470i) q^{16} +(0.222230 - 0.384914i) q^{17} +(1.00220 - 1.73586i) q^{18} +(2.38732 + 4.13495i) q^{19} -1.15816 q^{20} +(5.23959 - 2.97301i) q^{21} +4.38812 q^{22} +(-0.214992 - 0.372377i) q^{23} +(3.29895 - 5.71395i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.71112 - 2.96374i) q^{26} +1.85667 q^{27} +(2.66508 - 1.51220i) q^{28} +1.38092 q^{29} +(-1.04458 - 1.80926i) q^{30} +(-3.13418 + 5.42856i) q^{31} +(2.74062 - 4.74689i) q^{32} +(-5.44492 - 9.43088i) q^{33} +0.407800 q^{34} +(0.0198028 - 2.64568i) q^{35} -2.53011 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-2.19040 + 3.79389i) q^{38} +(-4.24642 + 7.35501i) q^{39} +(-1.44883 - 2.50945i) q^{40} -0.522569 q^{41} +(4.76604 + 2.79945i) q^{42} -7.86533 q^{43} +(-2.76952 - 4.79694i) q^{44} +(-1.09229 + 1.89191i) q^{45} +(0.197259 - 0.341662i) q^{46} +(-0.276077 - 0.478180i) q^{47} +0.779485 q^{48} +(3.40886 + 6.11389i) q^{49} -0.917517 q^{50} +(-0.506011 - 0.876437i) q^{51} +(-2.15991 + 3.74107i) q^{52} +(-1.59277 + 2.75876i) q^{53} +(0.851762 + 1.47529i) q^{54} -4.78260 q^{55} +(6.61051 + 3.88284i) q^{56} +10.8717 q^{57} +(0.633509 + 1.09727i) q^{58} +(-5.46263 + 9.46156i) q^{59} +(-1.31855 + 2.28380i) q^{60} +(-4.19575 - 7.26725i) q^{61} -5.75133 q^{62} +(0.0432610 - 5.77972i) q^{63} +5.71380 q^{64} +(1.86494 + 3.23018i) q^{65} +(4.99581 - 8.65299i) q^{66} +(0.709398 - 1.22871i) q^{67} +(-0.257379 - 0.445793i) q^{68} -0.979061 q^{69} +(2.11132 - 1.19799i) q^{70} -4.65250 q^{71} +(-3.16511 - 5.48212i) q^{72} +(0.899935 - 1.55873i) q^{73} +(0.458759 - 0.794593i) q^{74} +(1.13848 + 1.97191i) q^{75} +5.52980 q^{76} +(11.0054 - 6.24459i) q^{77} -7.79232 q^{78} +(-3.60672 - 6.24702i) q^{79} +(0.171167 - 0.296470i) q^{80} +(5.39067 - 9.33691i) q^{81} +(-0.239733 - 0.415230i) q^{82} +1.45351 q^{83} +(0.0522220 - 6.97692i) q^{84} -0.444460 q^{85} +(-3.60829 - 6.24974i) q^{86} +(1.57216 - 2.72305i) q^{87} +(6.92920 - 12.0017i) q^{88} +(7.15348 + 12.3902i) q^{89} -2.00440 q^{90} +(-8.50907 - 4.99800i) q^{91} -0.497992 q^{92} +(7.13643 + 12.3607i) q^{93} +(0.253306 - 0.438738i) q^{94} +(2.38732 - 4.13495i) q^{95} +(-6.24030 - 10.8085i) q^{96} -3.70052 q^{97} +(-3.29421 + 5.51346i) q^{98} -10.4480 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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