LMFDB - Embedded newform 1295.2.j.a.926.1

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			926.1
Character	$\chi$	$=$	1295.926
Dual form			1295.2.j.a.186.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20852 + 2.09322i) q^{2} +(-0.326680 - 0.565827i) q^{3} +(-1.92105 - 3.32736i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.57920 q^{6} +(-2.27698 + 1.34736i) q^{7} +4.45245 q^{8} +(1.28656 - 2.22839i) q^{9} +(-1.20852 - 2.09322i) q^{10} +(1.67352 + 2.89862i) q^{11} +(-1.25514 + 2.17397i) q^{12} -1.53040 q^{13} +(-0.0685340 - 6.39453i) q^{14} +0.653361 q^{15} +(-1.53878 + 2.66525i) q^{16} +(3.86152 + 6.68836i) q^{17} +(3.10967 + 5.38611i) q^{18} +(-0.645445 + 1.11794i) q^{19} +3.84211 q^{20} +(1.50621 + 0.848221i) q^{21} -8.08995 q^{22} +(1.40939 - 2.44113i) q^{23} +(-1.45453 - 2.51932i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.84952 - 3.20346i) q^{26} -3.64126 q^{27} +(8.85733 + 4.98799i) q^{28} +1.36237 q^{29} +(-0.789601 + 1.36763i) q^{30} +(0.352415 + 0.610400i) q^{31} +(0.733147 + 1.26985i) q^{32} +(1.09341 - 1.89385i) q^{33} -18.6670 q^{34} +(-0.0283545 - 2.64560i) q^{35} -9.88620 q^{36} +(-0.500000 + 0.866025i) q^{37} +(-1.56007 - 2.70212i) q^{38} +(0.499951 + 0.865940i) q^{39} +(-2.22623 + 3.85594i) q^{40} -1.85215 q^{41} +(-3.59581 + 2.12775i) q^{42} -6.98260 q^{43} +(6.42984 - 11.1368i) q^{44} +(1.28656 + 2.22839i) q^{45} +(3.40655 + 5.90032i) q^{46} +(-3.68502 + 6.38264i) q^{47} +2.01076 q^{48} +(3.36927 - 6.13580i) q^{49} +2.41704 q^{50} +(2.52297 - 4.36991i) q^{51} +(2.93997 + 5.09218i) q^{52} +(1.29420 + 2.24161i) q^{53} +(4.40054 - 7.62196i) q^{54} -3.34704 q^{55} +(-10.1381 + 5.99903i) q^{56} +0.843416 q^{57} +(-1.64645 + 2.85174i) q^{58} +(-3.33206 - 5.77130i) q^{59} +(-1.25514 - 2.17397i) q^{60} +(-3.41274 + 5.91104i) q^{61} -1.70360 q^{62} +(0.0729594 + 6.80744i) q^{63} -9.69923 q^{64} +(0.765199 - 1.32536i) q^{65} +(2.64283 + 4.57751i) q^{66} +(-1.72977 - 2.99605i) q^{67} +(14.8364 - 25.6974i) q^{68} -1.84167 q^{69} +(5.57209 + 3.13791i) q^{70} -16.7482 q^{71} +(5.72835 - 9.92179i) q^{72} +(-2.63278 - 4.56011i) q^{73} +(-1.20852 - 2.09322i) q^{74} +(-0.326680 + 0.565827i) q^{75} +4.95973 q^{76} +(-7.71605 - 4.34528i) q^{77} -2.41681 q^{78} +(2.68642 - 4.65302i) q^{79} +(-1.53878 - 2.66525i) q^{80} +(-2.67015 - 4.62484i) q^{81} +(2.23836 - 3.87696i) q^{82} -4.33201 q^{83} +(-0.0711776 - 6.64120i) q^{84} -7.72305 q^{85} +(8.43863 - 14.6161i) q^{86} +(-0.445058 - 0.770864i) q^{87} +(7.45127 + 12.9060i) q^{88} +(1.19908 - 2.07686i) q^{89} -6.21935 q^{90} +(3.48468 - 2.06199i) q^{91} -10.8300 q^{92} +(0.230254 - 0.398811i) q^{93} +(-8.90686 - 15.4271i) q^{94} +(-0.645445 - 1.11794i) q^{95} +(0.479009 - 0.829669i) q^{96} -15.2590 q^{97} +(8.77176 + 14.4679i) q^{98} +8.61234 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 $\left(\mathbb{Z}/1295\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.20852	+	2.09322i	−0.854554	+	1.48013i	0.0225034	+	0.999747i	$0.492836\pi$
$2$	−1.20852	+	2.09322i	−0.854554	+	1.48013i	−0.877058	+	0.480385i	$0.840497\pi$
$3$	−0.326680	−	0.565827i	−0.188609	−	0.326680i	0.756178	−	0.654366i	$-0.227065\pi$
$3$	−0.326680	−	0.565827i	−0.188609	−	0.326680i	−0.944787	+	0.327686i	$0.893731\pi$
$4$	−1.92105	−	3.32736i	−0.960526	−	1.66368i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.57920			0.644706
$7$	−2.27698	+	1.34736i	−0.860617	+	0.509252i
$7$	−2.27698	+	1.34736i	−0.860617	+	0.509252i
$8$	4.45245			1.57418
$9$	1.28656	−	2.22839i	0.428853	−	0.742796i
$10$	−1.20852	−	2.09322i	−0.382168	−	0.661935i
$11$	1.67352	+	2.89862i	0.504585	+	0.873968i	0.999986	+	0.00530287i	$0.00168796\pi$
$11$	1.67352	+	2.89862i	0.504585	+	0.873968i	−0.495401	+	0.868665i	$0.664979\pi$
$12$	−1.25514	+	2.17397i	−0.362328	+	0.627570i
$13$	−1.53040			−0.424456			−0.212228	−	0.977220i	$-0.568072\pi$
$13$	−1.53040			−0.424456			−0.212228	+	0.977220i	$0.568072\pi$
$14$	−0.0685340	−	6.39453i	−0.0183165	−	1.70901i
$15$	0.653361			0.168697
$16$	−1.53878	+	2.66525i	−0.384695	+	0.666312i
$17$	3.86152	+	6.68836i	0.936557	+	1.62216i	0.771833	+	0.635825i	$0.219340\pi$
$17$	3.86152	+	6.68836i	0.936557	+	1.62216i	0.164724	+	0.986340i	$0.447327\pi$
$18$	3.10967	+	5.38611i	0.732957	+	1.26952i
$19$	−0.645445	+	1.11794i	−0.148075	+	0.256474i	−0.930516	−	0.366251i	$-0.880641\pi$
$19$	−0.645445	+	1.11794i	−0.148075	+	0.256474i	0.782441	+	0.622725i	$0.213974\pi$
$20$	3.84211			0.859121
$21$	1.50621	+	0.848221i	0.328683	+	0.185097i
$22$	−8.08995			−1.72478
$23$	1.40939	−	2.44113i	0.293877	−	0.509011i	−0.680846	−	0.732427i	$-0.738388\pi$
$23$	1.40939	−	2.44113i	0.293877	−	0.509011i	0.974723	+	0.223416i	$0.0717209\pi$
$24$	−1.45453	−	2.51932i	−0.296904	−	0.514253i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.84952	−	3.20346i	0.362721	−	0.628250i
$27$	−3.64126			−0.700760
$28$	8.85733	+	4.98799i	1.67388	+	0.942642i
$29$	1.36237			0.252985			0.126493	−	0.991968i	$-0.459628\pi$
$29$	1.36237			0.252985			0.126493	+	0.991968i	$0.459628\pi$
$30$	−0.789601	+	1.36763i	−0.144161	+	0.249694i
$31$	0.352415	+	0.610400i	0.0632955	+	0.109631i	0.895937	−	0.444182i	$-0.146506\pi$
$31$	0.352415	+	0.610400i	0.0632955	+	0.109631i	−0.832641	+	0.553813i	$0.813172\pi$
$32$	0.733147	+	1.26985i	0.129603	+	0.224480i
$33$	1.09341	−	1.89385i	0.190339	−	0.329676i
$34$	−18.6670			−3.20136
$35$	−0.0283545	−	2.64560i	−0.00479278	−	0.447188i
$36$	−9.88620			−1.64770
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i
$38$	−1.56007	−	2.70212i	−0.253077	−	0.438342i
$39$	0.499951	+	0.865940i	0.0800562	+	0.138661i
$40$	−2.22623	+	3.85594i	−0.351997	+	0.609677i
$41$	−1.85215			−0.289257			−0.144628	−	0.989486i	$-0.546199\pi$
$41$	−1.85215			−0.289257			−0.144628	+	0.989486i	$0.546199\pi$
$42$	−3.59581	+	2.12775i	−0.554845	+	0.328318i
$43$	−6.98260			−1.06484			−0.532418	−	0.846481i	$-0.678717\pi$
$43$	−6.98260			−1.06484			−0.532418	+	0.846481i	$0.678717\pi$
$44$	6.42984	−	11.1368i	0.969335	−	1.67894i
$45$	1.28656	+	2.22839i	0.191789	+	0.332188i
$46$	3.40655	+	5.90032i	0.502268	+	0.869954i
$47$	−3.68502	+	6.38264i	−0.537515	+	0.931004i	0.461522	+	0.887129i	$0.347304\pi$
$47$	−3.68502	+	6.38264i	−0.537515	+	0.931004i	−0.999037	+	0.0438749i	$0.986030\pi$
$48$	2.01076			0.290228
$49$	3.36927	−	6.13580i	0.481324	−	0.876543i
$50$	2.41704			0.341822
$51$	2.52297	−	4.36991i	0.353286	−	0.611909i
$52$	2.93997	+	5.09218i	0.407701	+	0.706159i
$53$	1.29420	+	2.24161i	0.177772	+	0.307909i	0.941117	−	0.338081i	$-0.109778\pi$
$53$	1.29420	+	2.24161i	0.177772	+	0.307909i	−0.763345	+	0.645991i	$0.776445\pi$
$54$	4.40054	−	7.62196i	0.598838	−	1.03722i
$55$	−3.34704			−0.451315
$56$	−10.1381	+	5.99903i	−1.35477	+	0.801655i
$57$	0.843416			0.111713
$58$	−1.64645	+	2.85174i	−0.216190	+	0.374451i
$59$	−3.33206	−	5.77130i	−0.433797	−	0.751359i	0.563399	−	0.826185i	$-0.309493\pi$
$59$	−3.33206	−	5.77130i	−0.433797	−	0.751359i	−0.997197	+	0.0748257i	$0.976160\pi$
$60$	−1.25514	−	2.17397i	−0.162038	−	0.280658i
$61$	−3.41274	+	5.91104i	−0.436956	+	0.756831i	−0.997453	−	0.0713259i	$-0.977277\pi$
$61$	−3.41274	+	5.91104i	−0.436956	+	0.756831i	0.560497	+	0.828157i	$0.310610\pi$
$62$	−1.70360			−0.216358
$63$	0.0729594	+	6.80744i	0.00919202	+	0.857657i
$64$	−9.69923			−1.21240
$65$	0.765199	−	1.32536i	0.0949112	−	0.164391i
$66$	2.64283	+	4.57751i	0.325309	+	0.563452i
$67$	−1.72977	−	2.99605i	−0.211325	−	0.366026i	0.740804	−	0.671721i	$-0.234445\pi$
$67$	−1.72977	−	2.99605i	−0.211325	−	0.366026i	−0.952129	+	0.305695i	$0.901111\pi$
$68$	14.8364	−	25.6974i	1.79918	−	3.11626i
$69$	−1.84167			−0.221712
$70$	5.57209	+	3.13791i	0.665993	+	0.375052i
$71$	−16.7482			−1.98764			−0.993822	−	0.110988i	$-0.964599\pi$
$71$	−16.7482			−1.98764			−0.993822	+	0.110988i	$0.964599\pi$
$72$	5.72835	−	9.92179i	0.675092	−	1.16929i
$73$	−2.63278	−	4.56011i	−0.308144	−	0.533720i	0.669813	−	0.742530i	$-0.266374\pi$
$73$	−2.63278	−	4.56011i	−0.308144	−	0.533720i	−0.977956	+	0.208810i	$0.933041\pi$
$74$	−1.20852	−	2.09322i	−0.140488	−	0.243332i
$75$	−0.326680	+	0.565827i	−0.0377218	+	0.0653361i
$76$	4.95973			0.568920
$77$	−7.71605	−	4.34528i	−0.879325	−	0.495190i
$78$	−2.41681			−0.273649
$79$	2.68642	−	4.65302i	0.302246	−	0.523505i	−0.674398	−	0.738368i	$-0.735597\pi$
$79$	2.68642	−	4.65302i	0.302246	−	0.523505i	0.976644	+	0.214862i	$0.0689303\pi$
$80$	−1.53878	−	2.66525i	−0.172041	−	0.297984i
$81$	−2.67015	−	4.62484i	−0.296684	−	0.513871i
$82$	2.23836	−	3.87696i	0.247186	−	0.428138i
$83$	−4.33201			−0.475500			−0.237750	−	0.971326i	$-0.576410\pi$
$83$	−4.33201			−0.475500			−0.237750	+	0.971326i	$0.576410\pi$
$84$	−0.0711776	−	6.64120i	−0.00776612	−	0.724614i
$85$	−7.72305			−0.837682
$86$	8.43863	−	14.6161i	0.909961	−	1.57610i
$87$	−0.445058	−	0.770864i	−0.0477153	−	0.0826453i
$88$	7.45127	+	12.9060i	0.794308	+	1.37578i
$89$	1.19908	−	2.07686i	0.127102	−	0.220147i	−0.795451	−	0.606018i	$-0.792766\pi$
$89$	1.19908	−	2.07686i	0.127102	−	0.220147i	0.922553	+	0.385871i	$0.126099\pi$
$90$	−6.21935			−0.655577
$91$	3.48468	−	2.06199i	0.365294	−	0.216155i
$92$	−10.8300			−1.12911
$93$	0.230254	−	0.398811i	0.0238762	−	0.0413548i
$94$	−8.90686	−	15.4271i	−0.918672	−	1.59119i
$95$	−0.645445	−	1.11794i	−0.0662212	−	0.114699i
$96$	0.479009	−	0.829669i	0.0488887	−	0.0846777i
$97$	−15.2590			−1.54931			−0.774657	−	0.632381i	$-0.782078\pi$
$97$	−15.2590			−1.54931			−0.774657	+	0.632381i	$0.782078\pi$
$98$	8.77176	+	14.4679i	0.886081	+	1.46148i
$99$	8.61234			0.865573
$100$	−1.92105	+	3.32736i	−0.192105	+	0.332736i
$101$	−4.76686	−	8.25645i	−0.474321	−	0.821547i	0.525247	−	0.850950i	$-0.323973\pi$
$101$	−4.76686	−	8.25645i	−0.474321	−	0.821547i	−0.999568	+	0.0294025i	$0.990640\pi$
$102$	6.09813	+	10.5623i	0.603804	+	1.04582i
$103$	−4.68948	+	8.12242i	−0.462068	+	0.800325i	−0.999064	−	0.0432596i	$-0.986226\pi$
$103$	−4.68948	+	8.12242i	−0.462068	+	0.800325i	0.536996	+	0.843585i	$0.319559\pi$
$104$	−6.81402			−0.668170
$105$	−1.48769	+	0.880309i	−0.145184	+	0.0859093i
$106$	−6.25626			−0.607662
$107$	2.97310	−	5.14956i	0.287420	−	0.497826i	−0.685773	−	0.727816i	$-0.740536\pi$
$107$	2.97310	−	5.14956i	0.287420	−	0.497826i	0.973193	+	0.229989i	$0.0738690\pi$
$108$	6.99505	+	12.1158i	0.673099	+	1.16584i
$109$	8.86047	+	15.3468i	0.848679	+	1.46995i	0.882388	+	0.470523i	$0.155935\pi$
$109$	8.86047	+	15.3468i	0.848679	+	1.46995i	−0.0337089	+	0.999432i	$0.510732\pi$
$110$	4.04497	−	7.00610i	0.385673	−	0.668005i
$111$	0.653361			0.0620142
$112$	−0.0872626	−	8.14200i	−0.00824554	−	0.769347i
$113$	−2.90345			−0.273134			−0.136567	−	0.990631i	$-0.543607\pi$
$113$	−2.90345			−0.273134			−0.136567	+	0.990631i	$0.543607\pi$
$114$	−1.01929	+	1.76546i	−0.0954650	+	0.165350i
$115$	1.40939	+	2.44113i	0.131426	+	0.227636i
$116$	−2.61718	−	4.53309i	−0.242999	−	0.420887i
$117$	−1.96895	+	3.41032i	−0.182029	+	0.315284i
$118$	16.1075			1.48281
$119$	−17.8042	−	10.0264i	−1.63211	−	0.919119i
$120$	2.90906			0.265559
$121$	−0.101341	+	0.175528i	−0.00921282	+	0.0159571i
$122$	−8.24874	−	14.2872i	−0.746806	−	1.29351i
$123$	0.605060	+	1.04799i	0.0545564	+	0.0944945i
$124$	1.35401	−	2.34522i	0.121594	−	0.210607i
$125$	1.00000			0.0894427
$126$	−14.3377	−	8.07423i	−1.27730	−	0.719309i
$127$	−6.45718			−0.572982			−0.286491	−	0.958083i	$-0.592489\pi$
$127$	−6.45718			−0.572982			−0.286491	+	0.958083i	$0.592489\pi$
$128$	10.2554	−	17.7629i	0.906461	−	1.57004i
$129$	2.28108	+	3.95094i	0.200838	+	0.347861i
$130$	1.84952	+	3.20346i	0.162214	+	0.280962i
$131$	0.913379	−	1.58202i	0.0798023	−	0.138222i	−0.823362	−	0.567516i	$-0.807904\pi$
$131$	0.913379	−	1.58202i	0.0798023	−	0.138222i	0.903165	+	0.429295i	$0.141238\pi$
$132$	−8.40201			−0.731301
$133$	−0.0366025	−	3.41518i	−0.00317384	−	0.296133i
$134$	8.36186			0.722355
$135$	1.82063	−	3.15342i	0.156695	−	0.271403i
$136$	17.1932	+	29.7796i	1.47431	+	2.55358i
$137$	−3.96793	−	6.87266i	−0.339003	−	0.587171i	0.645242	−	0.763978i	$-0.276757\pi$
$137$	−3.96793	−	6.87266i	−0.339003	−	0.587171i	−0.984246	+	0.176807i	$0.943423\pi$
$138$	2.22571	−	3.85503i	0.189465	−	0.328162i
$139$	7.09507			0.601796			0.300898	−	0.953656i	$-0.402714\pi$
$139$	7.09507			0.601796			0.300898	+	0.953656i	$0.402714\pi$
$140$	−8.74839	+	5.17668i	−0.739374	+	0.437509i
$141$	4.81529			0.405521
$142$	20.2406	−	35.0577i	1.69855	−	2.94197i
$143$	−2.56115	−	4.43604i	−0.214174	−	0.370961i
$144$	3.95947	+	6.85800i	0.329956	+	0.571500i
$145$	−0.681184	+	1.17984i	−0.0565692	+	0.0979808i
$146$	12.7271			1.05330
$147$	−4.57247	+	0.0980231i	−0.377131	+	0.00808481i
$148$	3.84211			0.315819
$149$	−2.54943	+	4.41574i	−0.208857	+	0.361751i	−0.951355	−	0.308097i	$-0.900308\pi$
$149$	−2.54943	+	4.41574i	−0.208857	+	0.361751i	0.742498	+	0.669849i	$0.233641\pi$
$150$	−0.789601	−	1.36763i	−0.0644706	−	0.111666i
$151$	1.28587	+	2.22719i	0.104643	+	0.181246i	0.913592	−	0.406632i	$-0.133297\pi$
$151$	1.28587	+	2.22719i	0.104643	+	0.181246i	−0.808950	+	0.587878i	$0.799963\pi$
$152$	−2.87381	+	4.97759i	−0.233097	+	0.403736i
$153$	19.8723			1.60658
$154$	18.4206	−	10.9000i	1.48438	−	0.878350i
$155$	−0.704829			−0.0566133
$156$	1.92086	−	3.32703i	0.153792	−	0.266376i
$157$	7.81381	+	13.5339i	0.623610	+	1.08012i	0.988808	+	0.149194i	$0.0476680\pi$
$157$	7.81381	+	13.5339i	0.623610	+	1.08012i	−0.365198	+	0.930930i	$0.618999\pi$
$158$	6.49320	+	11.2466i	0.516571	+	0.894728i
$159$	0.845577	−	1.46458i	0.0670586	−	0.116149i
$160$	−1.46629			−0.115921
$161$	0.0799248	+	7.45734i	0.00629895	+	0.587721i
$162$	12.9078			1.01413
$163$	−6.37385	+	11.0398i	−0.499239	+	0.864707i	−1.00000		0.000878921i	$-0.999720\pi$
$163$	−6.37385	+	11.0398i	−0.499239	+	0.864707i	0.500761	+	0.865586i	$0.333054\pi$
$164$	3.55807	+	6.16276i	0.277839	+	0.481231i
$165$	1.09341	+	1.89385i	0.0851220	+	0.147436i
$166$	5.23534	−	9.06787i	0.406341	−	0.703803i
$167$	22.0225			1.70415			0.852076	−	0.523419i	$-0.175344\pi$
$167$	22.0225			1.70415			0.852076	+	0.523419i	$0.175344\pi$
$168$	6.70634	+	3.77666i	0.517406	+	0.291376i
$169$	−10.6579			−0.819837
$170$	9.33348	−	16.1661i	0.715845	−	1.23988i
$171$	1.66081	+	2.87660i	0.127005	+	0.219979i
$172$	13.4139	+	23.2336i	1.02280	+	1.77155i
$173$	−6.21758	+	10.7692i	−0.472714	+	0.818765i	−0.999512	−	0.0312256i	$-0.990059\pi$
$173$	−6.21758	+	10.7692i	−0.472714	+	0.818765i	0.526798	+	0.849990i	$0.323392\pi$
$174$	2.15145			0.163101
$175$	2.30533	+	1.29824i	0.174267	+	0.0981380i
$176$	−10.3007			−0.776447
$177$	−2.17704	+	3.77074i	−0.163636	+	0.283426i
$178$	2.89822	+	5.01987i	0.217231	+	0.376255i
$179$	−3.08551	−	5.34425i	−0.230622	−	0.399448i	0.727370	−	0.686246i	$-0.240743\pi$
$179$	−3.08551	−	5.34425i	−0.230622	−	0.399448i	−0.957991	+	0.286798i	$0.907409\pi$
$180$	4.94310	−	8.56170i	0.368437	−	0.638151i
$181$	15.1179			1.12370			0.561852	−	0.827238i	$-0.310089\pi$
$181$	15.1179			1.12370			0.561852	+	0.827238i	$0.310089\pi$
$182$	0.104884	+	9.78617i	0.00777454	+	0.725399i
$183$	4.45950			0.329656
$184$	6.27522	−	10.8690i	0.462616	−	0.801274i
$185$	−0.500000	−	0.866025i	−0.0367607	−	0.0636715i
$186$	0.556534	+	0.963945i	0.0408070	+	0.0706799i
$187$	−12.9247	+	22.3862i	−0.945146	+	1.63704i
$188$	28.3165			2.06519
$189$	8.29106	−	4.90607i	0.603086	−	0.356864i
$190$	3.12014			0.226359
$191$	0.920173	−	1.59379i	0.0665814	−	0.115322i	−0.830813	−	0.556552i	$-0.812124\pi$
$191$	0.920173	−	1.59379i	0.0665814	−	0.115322i	0.897394	+	0.441229i	$0.145457\pi$
$192$	3.16855	+	5.48808i	0.228670	+	0.396068i
$193$	−3.27309	−	5.66916i	−0.235602	−	0.408075i	0.723845	−	0.689962i	$-0.242373\pi$
$193$	−3.27309	−	5.66916i	−0.235602	−	0.408075i	−0.959448	+	0.281887i	$0.909040\pi$
$194$	18.4408	−	31.9404i	1.32397	−	2.29319i
$195$	−0.999901			−0.0716044
$196$	−26.8886	+	0.576427i	−1.92061	+	0.0411734i
$197$	5.67229			0.404134			0.202067	−	0.979372i	$-0.435234\pi$
$197$	5.67229			0.404134			0.202067	+	0.979372i	$0.435234\pi$
$198$	−10.4082	+	18.0275i	−0.739679	+	1.28116i
$199$	−6.20232	−	10.7427i	−0.439670	−	0.761532i	0.557993	−	0.829845i	$-0.311571\pi$
$199$	−6.20232	−	10.7427i	−0.439670	−	0.761532i	−0.997664	+	0.0683138i	$0.978238\pi$
$200$	−2.22623	−	3.85594i	−0.157418	−	0.272656i
$201$	−1.13016	+	1.95750i	−0.0797156	+	0.138071i
$202$	23.0434			1.62133
$203$	−3.10208	+	1.83559i	−0.217723	+	0.128833i
$204$	−19.3870			−1.35736
$205$	0.926074	−	1.60401i	0.0646798	−	0.112029i
$206$	−11.3347	−	19.6322i	−0.789725	−	1.36784i
$207$	−3.62652	−	6.28132i	−0.252061	−	0.436582i
$208$	2.35495	−	4.07889i	0.163286	−	0.282820i
$209$	−4.32066			−0.298866
$210$	−0.0447774	−	4.17793i	−0.00308993	−	0.288305i
$211$	−26.8798			−1.85048			−0.925242	−	0.379378i	$-0.876138\pi$
$211$	−26.8798			−1.85048			−0.925242	+	0.379378i	$0.876138\pi$
$212$	4.97244	−	8.61252i	0.341509	−	0.591510i
$213$	5.47130	+	9.47657i	0.374887	+	0.649324i
$214$	7.18611	+	12.4467i	0.491232	+	0.850840i
$215$	3.49130	−	6.04711i	0.238105	−	0.412410i
$216$	−16.2125			−1.10312
$217$	−1.62487	−	0.915041i	−0.110303	−	0.0621170i
$218$	−42.8323			−2.90097
$219$	−1.72015	+	2.97940i	−0.116237	+	0.201329i
$220$	6.42984	+	11.1368i	0.433500	+	0.750844i
$221$	−5.90967	−	10.2358i	−0.397527	−	0.688537i
$222$	−0.789601	+	1.36763i	−0.0529945	+	0.0917892i
$223$	8.54586			0.572273			0.286137	−	0.958189i	$-0.407629\pi$
$223$	8.54586			0.572273			0.286137	+	0.958189i	$0.407629\pi$
$224$	−3.38030	−	1.90361i	−0.225856	−	0.127190i
$225$	−2.57312			−0.171541
$226$	3.50889	−	6.07757i	0.233408	−	0.404274i
$227$	6.92482	+	11.9941i	0.459617	+	0.796079i	0.998941	−	0.0460190i	$-0.0146535\pi$
$227$	6.92482	+	11.9941i	0.459617	+	0.796079i	−0.539324	+	0.842098i	$0.681320\pi$
$228$	−1.62025	−	2.80635i	−0.107303	−	0.185855i
$229$	−5.79382	+	10.0352i	−0.382866	+	0.663144i	−0.991471	−	0.130330i	$-0.958396\pi$
$229$	−5.79382	+	10.0352i	−0.382866	+	0.663144i	0.608605	+	0.793474i	$0.291730\pi$
$230$	−6.81310			−0.449243
$231$	0.0620062	+	5.78546i	0.00407971	+	0.380655i
$232$	6.06587			0.398244
$233$	1.01611	−	1.75996i	0.0665677	−	0.115299i	−0.830821	−	0.556540i	$-0.812128\pi$
$233$	1.01611	−	1.75996i	0.0665677	−	0.115299i	0.897388	+	0.441242i	$0.145462\pi$
$234$	−4.75904	−	8.24289i	−0.311108	−	0.538855i
$235$	−3.68502	−	6.38264i	−0.240384	−	0.416358i
$236$	−12.8021	+	22.1739i	−0.833348	+	1.44340i
$237$	−3.51040			−0.228025
$238$	42.5043	−	25.1510i	2.75514	−	1.63030i
$239$	−25.1351			−1.62585			−0.812927	−	0.582366i	$-0.802127\pi$
$239$	−25.1351			−1.62585			−0.812927	+	0.582366i	$0.802127\pi$
$240$	−1.00538	+	1.74137i	−0.0648969	+	0.112405i
$241$	9.62692	+	16.6743i	0.620125	+	1.07409i	0.989462	+	0.144792i	$0.0462513\pi$
$241$	9.62692	+	16.6743i	0.620125	+	1.07409i	−0.369338	+	0.929295i	$0.620415\pi$
$242$	−0.244946	−	0.424259i	−0.0157457	−	0.0272724i
$243$	−7.20646	+	12.4820i	−0.462294	+	0.800718i
$244$	26.2242			1.67883
$245$	3.62913	+	5.98577i	0.231856	+	0.382417i
$246$	−2.92491			−0.186486
$247$	0.987787	−	1.71090i	0.0628514	−	0.108862i
$248$	1.56911	+	2.71778i	0.0996385	+	0.172579i
$249$	1.41518	+	2.45117i	0.0896836	+	0.155337i
$250$	−1.20852	+	2.09322i	−0.0764337	+	0.132387i
$251$	−20.6831			−1.30551			−0.652754	−	0.757570i	$-0.726386\pi$
$251$	−20.6831			−1.30551			−0.652754	+	0.757570i	$0.726386\pi$
$252$	22.5107	−	13.3202i	1.41804	−	0.839095i
$253$	9.43455			0.593145
$254$	7.80364	−	13.5163i	0.489644	−	0.848088i
$255$	2.52297	+	4.36991i	0.157994	+	0.273654i
$256$	15.0886	+	26.1343i	0.943039	+	1.63339i
$257$	5.54611	−	9.60614i	0.345957	−	0.599215i	−0.639570	−	0.768733i	$-0.720888\pi$
$257$	5.54611	−	9.60614i	0.345957	−	0.599215i	0.985527	+	0.169518i	$0.0542210\pi$
$258$	−11.0269			−0.686507
$259$	−0.0283545	−	2.64560i	−0.00176186	−	0.164390i
$260$	−5.87995			−0.364659
$261$	1.75277	−	3.03588i	0.108494	−	0.187916i
$262$	2.20768	+	3.82381i	0.136391	+	0.236236i
$263$	−10.3665	−	17.9552i	−0.639224	−	1.10717i	−0.985603	−	0.169074i	$-0.945922\pi$
$263$	−10.3665	−	17.9552i	−0.639224	−	1.10717i	0.346380	−	0.938094i	$-0.387411\pi$
$264$	4.86836	−	8.43225i	0.299627	−	0.518969i
$265$	−2.58839			−0.159004
$266$	7.19296	+	4.05070i	0.441029	+	0.248364i
$267$	−1.56686			−0.0958902
$268$	−6.64596	+	11.5111i	−0.405966	+	0.703154i
$269$	5.45662	+	9.45114i	0.332696	+	0.576246i	0.983039	−	0.183394i	$-0.0587084\pi$
$269$	5.45662	+	9.45114i	0.332696	+	0.576246i	−0.650344	+	0.759640i	$0.725375\pi$
$270$	4.40054	+	7.62196i	0.267808	+	0.463858i
$271$	−8.36203	+	14.4835i	−0.507957	+	0.879807i	0.492001	+	0.870595i	$0.336266\pi$
$271$	−8.36203	+	14.4835i	−0.507957	+	0.879807i	−0.999958	+	0.00921240i	$0.997068\pi$
$272$	−23.7682			−1.44116
$273$	−2.30511	−	1.29812i	−0.139511	−	0.0785655i
$274$	19.1813			1.15879
$275$	1.67352	−	2.89862i	0.100917	−	0.174794i
$276$	3.53795	+	6.12792i	0.212960	+	0.368857i
$277$	−13.3017	−	23.0392i	−0.799220	−	1.38429i	−0.920125	−	0.391626i	$-0.871913\pi$
$277$	−13.3017	−	23.0392i	−0.799220	−	1.38429i	0.120904	−	0.992664i	$-0.461421\pi$
$278$	−8.57455	+	14.8516i	−0.514267	+	0.890737i
$279$	1.81361			0.108578
$280$	−0.126247	−	11.7794i	−0.00754469	−	0.703954i
$281$	20.3839			1.21600			0.608002	−	0.793936i	$-0.291971\pi$
$281$	20.3839			1.21600			0.608002	+	0.793936i	$0.291971\pi$
$282$	−5.81939	+	10.0795i	−0.346540	+	0.600224i
$283$	11.3065	+	19.5835i	0.672103	+	1.16412i	0.977307	+	0.211829i	$0.0679419\pi$
$283$	11.3065	+	19.5835i	0.672103	+	1.16412i	−0.305204	+	0.952287i	$0.598725\pi$
$284$	32.1741	+	55.7272i	1.90918	+	3.30680i
$285$	−0.421708	+	0.730420i	−0.0249798	+	0.0432663i
$286$	12.3808			0.732094
$287$	4.21730	−	2.49550i	0.248939	−	0.147305i
$288$	3.77295			0.222323
$289$	−21.3227	+	36.9321i	−1.25428	+	2.17247i
$290$	−1.64645	−	2.85174i	−0.0966829	−	0.167460i
$291$	4.98481	+	8.63394i	0.292215	+	0.506130i
$292$	−10.1154	+	17.5204i	−0.591960	+	1.02530i
$293$	−11.9773			−0.699724			−0.349862	−	0.936801i	$-0.613771\pi$
$293$	−11.9773			−0.699724			−0.349862	+	0.936801i	$0.613771\pi$
$294$	5.32075	−	9.68966i	0.310313	−	0.565113i
$295$	6.66412			0.388000
$296$	−2.22623	+	3.85594i	−0.129397	+	0.224122i
$297$	−6.09372	−	10.5546i	−0.353593	−	0.612442i
$298$	−6.16208	−	10.6730i	−0.356960	−	0.618273i
$299$	−2.15692	+	3.73590i	−0.124738	+	0.216052i
$300$	2.51028			0.144931
$301$	15.8992	−	9.40805i	0.916417	−	0.542271i
$302$	−6.21601			−0.357691
$303$	−3.11448	+	5.39444i	−0.178922	+	0.309902i
$304$	−1.98640	−	3.44054i	−0.113928	−	0.197329i
$305$	−3.41274	−	5.91104i	−0.195413	−	0.338465i
$306$	−24.0162	+	41.5972i	−1.37291	+	2.37795i
$307$	−3.39748			−0.193904			−0.0969522	−	0.995289i	$-0.530909\pi$
$307$	−3.39748			−0.193904			−0.0969522	+	0.995289i	$0.530909\pi$
$308$	0.364629	+	34.0216i	0.0207767	+	1.93856i
$309$	6.12784			0.348601
$310$	0.851802	−	1.47536i	0.0483791	−	0.0837951i
$311$	−1.22102	−	2.11486i	−0.0692376	−	0.119923i	0.829328	−	0.558762i	$-0.188723\pi$
$311$	−1.22102	−	2.11486i	−0.0692376	−	0.119923i	−0.898566	+	0.438839i	$0.855390\pi$
$312$	2.22601	+	3.85555i	0.126023	+	0.218278i
$313$	2.74200	−	4.74928i	0.154987	−	0.268445i	−0.778067	−	0.628181i	$-0.783800\pi$
$313$	2.74200	−	4.74928i	0.154987	−	0.268445i	0.933054	+	0.359736i	$0.117133\pi$
$314$	−37.7727			−2.13163
$315$	−5.93190	−	3.34054i	−0.334225	−	0.188218i
$316$	−20.6430			−1.16126
$317$	−15.0678	+	26.0981i	−0.846290	+	1.46582i	0.0382067	+	0.999270i	$0.487835\pi$
$317$	−15.0678	+	26.0981i	−0.846290	+	1.46582i	−0.884496	+	0.466547i	$0.845498\pi$
$318$	2.04380	+	3.53996i	0.114610	+	0.198511i
$319$	2.27995	+	3.94899i	0.127653	+	0.221101i
$320$	4.84961	−	8.39978i	0.271102	−	0.469562i
$321$	−3.88501			−0.216840
$322$	−15.7065	−	8.84507i	−0.875287	−	0.492916i
$323$	−9.96960			−0.554724
$324$	−10.2590	+	17.7691i	−0.569945	+	0.987174i
$325$	0.765199	+	1.32536i	0.0424456	+	0.0735179i
$326$	−15.4059	−	26.6838i	−0.853253	−	1.47788i
$327$	5.78908	−	10.0270i	0.320137	−	0.554493i
$328$	−8.24660			−0.455342
$329$	−0.208973	−	19.4982i	−0.0115211	−	1.07497i
$330$	−5.28565			−0.290966
$331$	7.66283	−	13.2724i	0.421187	−	0.729517i	−0.574869	−	0.818246i	$-0.694947\pi$
$331$	7.66283	−	13.2724i	0.421187	−	0.729517i	0.996056	+	0.0887281i	$0.0282802\pi$
$332$	8.32203	+	14.4142i	0.456731	+	0.791081i
$333$	1.28656	+	2.22839i	0.0705031	+	0.122115i
$334$	−26.6147	+	46.0980i	−1.45629	+	2.52237i
$335$	3.45954			0.189015
$336$	−4.57845	+	2.70921i	−0.249775	+	0.147799i
$337$	−5.85823			−0.319118			−0.159559	−	0.987188i	$-0.551007\pi$
$337$	−5.85823			−0.319118			−0.159559	+	0.987188i	$0.551007\pi$
$338$	12.8803	−	22.3093i	0.700596	−	1.21347i
$339$	0.948500	+	1.64285i	0.0515154	+	0.0892274i
$340$	14.8364	+	25.6974i	0.804616	+	1.39364i
$341$	−1.17955	+	2.04303i	−0.0638760	+	0.110637i
$342$	−8.02849			−0.434131
$343$	0.595352	+	18.5107i	0.0321460	+	0.999483i
$344$	−31.0897			−1.67624
$345$	0.920837	−	1.59494i	0.0495762	−	0.0858685i
$346$	−15.0282	−	26.0296i	−0.807920	−	1.39936i
$347$	−18.3044	−	31.7042i	−0.982632	−	1.70197i	−0.652020	−	0.758202i	$-0.726078\pi$
$347$	−18.3044	−	31.7042i	−0.982632	−	1.70197i	−0.330612	−	0.943767i	$-0.607255\pi$
$348$	−1.70996	+	2.96174i	−0.0916636	+	0.158766i
$349$	−33.7342			−1.80575			−0.902875	−	0.429903i	$-0.858548\pi$
$349$	−33.7342			−1.80575			−0.902875	+	0.429903i	$0.858548\pi$
$350$	−5.50356	+	3.25662i	−0.294178	+	0.174074i
$351$	5.57257			0.297442
$352$	−2.45387	+	4.25023i	−0.130792	+	0.226538i
$353$	−9.80861	−	16.9890i	−0.522060	−	0.904234i	−0.999671	−	0.0256624i	$-0.991831\pi$
$353$	−9.80861	−	16.9890i	−0.522060	−	0.904234i	0.477611	−	0.878571i	$-0.341503\pi$
$354$	−5.26200	−	9.11404i	−0.279672	−	0.484406i
$355$	8.37409	−	14.5044i	0.444451	−	0.769811i
$356$	−9.21396			−0.488339
$357$	0.143075	+	13.3495i	0.00757232	+	0.706532i
$358$	14.9156			0.788315
$359$	−9.79154	+	16.9594i	−0.516778	+	0.895085i	0.483033	+	0.875602i	$0.339535\pi$
$359$	−9.79154	+	16.9594i	−0.516778	+	0.895085i	−0.999810	+	0.0194827i	$0.993798\pi$
$360$	5.72835	+	9.92179i	0.301910	+	0.522924i
$361$	8.66680	+	15.0113i	0.456147	+	0.790071i
$362$	−18.2703	+	31.6451i	−0.960266	+	1.66323i
$363$	0.132424			0.00695048
$364$	−13.5552	−	7.63361i	−0.710488	−	0.400110i
$365$	5.26556			0.275612
$366$	−5.38940	+	9.33472i	−0.281709	+	0.487934i
$367$	10.9421	+	18.9522i	0.571171	+	0.989297i	0.996446	+	0.0842331i	$0.0268441\pi$
$367$	10.9421	+	18.9522i	0.571171	+	0.989297i	−0.425275	+	0.905064i	$0.639823\pi$
$368$	4.33748	+	7.51273i	0.226107	+	0.391628i
$369$	−2.38290	+	4.12730i	−0.124049	+	0.214859i
$370$	2.41704			0.125656
$371$	−5.96711	−	3.36037i	−0.309797	−	0.174462i
$372$	−1.76932			−0.0917349
$373$	16.4740	−	28.5338i	0.852990	−	1.47742i	−0.0255065	−	0.999675i	$-0.508120\pi$
$373$	16.4740	−	28.5338i	0.852990	−	1.47742i	0.878497	−	0.477748i	$-0.158547\pi$
$374$	−31.2395	−	54.1084i	−1.61536	−	2.79788i
$375$	−0.326680	−	0.565827i	−0.0168697	−	0.0292192i
$376$	−16.4074	+	28.4184i	−0.846145	+	1.46557i
$377$	−2.08496			−0.107381
$378$	0.249550	+	23.2841i	0.0128355	+	1.19761i
$379$	−4.99129			−0.256385			−0.128193	−	0.991749i	$-0.540918\pi$
$379$	−4.99129			−0.256385			−0.128193	+	0.991749i	$0.540918\pi$
$380$	−2.47987	+	4.29526i	−0.127214	+	0.220342i
$381$	2.10943	+	3.65364i	0.108069	+	0.187182i
$382$	2.22410	+	3.85225i	0.113795	+	0.197098i
$383$	−8.63595	+	14.9579i	−0.441277	+	0.764313i	−0.997785	−	0.0665288i	$-0.978808\pi$
$383$	−8.63595	+	14.9579i	−0.441277	+	0.764313i	0.556508	+	0.830842i	$0.312141\pi$
$384$	−13.4010			−0.683867
$385$	7.62114	−	4.50965i	0.388409	−	0.229833i
$386$	15.8224			0.805340
$387$	−8.98354	+	15.5599i	−0.456659	+	0.790956i
$388$	29.3133	+	50.7721i	1.48816	+	2.57756i
$389$	13.3097	+	23.0531i	0.674830	+	1.16884i	0.976518	+	0.215434i	$0.0691165\pi$
$389$	13.3097	+	23.0531i	0.674830	+	1.16884i	−0.301688	+	0.953407i	$0.597550\pi$
$390$	1.20840	−	2.09302i	0.0611899	−	0.105984i
$391$	21.7695			1.10093
$392$	15.0015	−	27.3193i	0.757690	−	1.37984i
$393$	−1.19353			−0.0602057
$394$	−6.85509	+	11.8734i	−0.345355	+	0.598172i
$395$	2.68642	+	4.65302i	0.135168	+	0.234119i
$396$	−16.5448	−	28.6564i	−0.831405	−	1.44004i
$397$	3.83486	−	6.64218i	0.192466	−	0.333361i	−0.753601	−	0.657332i	$-0.771685\pi$
$397$	3.83486	−	6.64218i	0.192466	−	0.333361i	0.946067	+	0.323971i	$0.105018\pi$
$398$	29.9825			1.50289
$399$	−1.92044	+	1.13638i	−0.0961423	+	0.0568902i
$400$	3.07756			0.153878
$401$	3.04480	−	5.27374i	0.152050	−	0.263358i	−0.779931	−	0.625865i	$-0.784746\pi$
$401$	3.04480	−	5.27374i	0.152050	−	0.263358i	0.931981	+	0.362507i	$0.118079\pi$
$402$	−2.73165	−	4.73136i	−0.136243	−	0.235979i
$403$	−0.539334	−	0.934155i	−0.0268662	−	0.0465336i
$404$	−18.3148	+	31.7221i	−0.911195	+	1.57824i
$405$	5.34031			0.265362
$406$	−0.0933685	−	8.71170i	−0.00463380	−	0.432354i
$407$	−3.34704			−0.165907
$408$	11.2334	−	19.4568i	0.556136	−	0.963255i
$409$	3.57736	+	6.19617i	0.176889	+	0.306381i	0.940813	−	0.338925i	$-0.110063\pi$
$409$	3.57736	+	6.19617i	0.176889	+	0.306381i	−0.763924	+	0.645306i	$0.776730\pi$
$410$	2.23836	+	3.87696i	0.110545	+	0.191469i
$411$	−2.59249	+	4.49033i	−0.127878	+	0.221491i
$412$	36.0349			1.77531
$413$	15.3630	+	8.65166i	0.755965	+	0.425720i
$414$	17.5309			0.861598
$415$	2.16601	−	3.75163i	0.106325	−	0.184161i
$416$	−1.12201	−	1.94337i	−0.0550109	−	0.0952817i
$417$	−2.31782	−	4.01458i	−0.113504	−	0.196595i
$418$	5.22161	−	9.04410i	0.255398	−	0.442361i
$419$	3.45817			0.168943			0.0844713	−	0.996426i	$-0.473080\pi$
$419$	3.45817			0.168943			0.0844713	+	0.996426i	$0.473080\pi$
$420$	5.78703	+	3.25896i	0.282378	+	0.159021i
$421$	17.7896			0.867011			0.433506	−	0.901151i	$-0.357276\pi$
$421$	17.7896			0.867011			0.433506	+	0.901151i	$0.357276\pi$
$422$	32.4849	−	56.2655i	1.58134	−	2.73896i
$423$	9.48200	+	16.4233i	0.461030	+	0.798528i
$424$	5.76235	+	9.98068i	0.279844	+	0.484705i
$425$	3.86152	−	6.68836i	0.187311	−	0.324433i
$426$	−26.4488			−1.28145
$427$	−0.193533	−	18.0575i	−0.00936571	−	0.873863i
$428$	−22.8459			−1.10430
$429$	−1.67335	+	2.89834i	−0.0807903	+	0.139933i
$430$	8.43863	+	14.6161i	0.406947	+	0.704853i
$431$	12.7574	+	22.0964i	0.614501	+	1.06435i	0.990472	+	0.137716i	$0.0439760\pi$
$431$	12.7574	+	22.0964i	0.614501	+	1.06435i	−0.375971	+	0.926632i	$0.622691\pi$
$432$	5.60310	−	9.70485i	0.269579	−	0.466925i
$433$	−22.6318			−1.08762			−0.543808	−	0.839210i	$-0.683018\pi$
$433$	−22.6318			−1.08762			−0.543808	+	0.839210i	$0.683018\pi$
$434$	3.87907	−	2.29536i	0.186201	−	0.110181i
$435$	0.890117			0.0426778
$436$	34.0428	−	58.9639i	1.63036	−	2.82386i
$437$	1.81936	+	3.15123i	0.0870319	+	0.150744i
$438$	−4.15769	−	7.20133i	−0.198662	−	0.344093i
$439$	−15.2715	+	26.4511i	−0.728871	+	1.26244i	0.228489	+	0.973546i	$0.426621\pi$
$439$	−15.2715	+	26.4511i	−0.728871	+	1.26244i	−0.957361	+	0.288896i	$0.906712\pi$
$440$	−14.9025			−0.710451
$441$	−9.33817	−	15.4021i	−0.444675	−	0.733434i
$442$	28.5679			1.35883
$443$	3.21942	−	5.57619i	0.152959	−	0.264933i	−0.779355	−	0.626583i	$-0.784453\pi$
$443$	3.21942	−	5.57619i	0.152959	−	0.264933i	0.932314	+	0.361650i	$0.117786\pi$
$444$	−1.25514	−	2.17397i	−0.0595663	−	0.103172i
$445$	1.19908	+	2.07686i	0.0568417	+	0.0984527i
$446$	−10.3279	+	17.8884i	−0.489038	+	0.847039i
$447$	3.33139			0.157569
$448$	22.0849	−	13.0683i	1.04342	−	0.617419i
$449$	35.6874			1.68419			0.842097	−	0.539326i	$-0.181321\pi$
$449$	35.6874			1.68419			0.842097	+	0.539326i	$0.181321\pi$
$450$	3.10967	−	5.38611i	0.146591	−	0.253904i
$451$	−3.09961	−	5.36868i	−0.145955	−	0.252801i
$452$	5.57768	+	9.66083i	0.262352	+	0.454407i
$453$	0.840136	−	1.45516i	0.0394730	−	0.0683693i
$454$	−33.4752			−1.57107
$455$	0.0433936	+	4.04882i	0.00203432	+	0.189812i
$456$	3.75527			0.175857
$457$	8.67297	−	15.0220i	0.405705	−	0.702701i	−0.588699	−	0.808353i	$-0.700360\pi$
$457$	8.67297	−	15.0220i	0.405705	−	0.702701i	0.994403	+	0.105652i	$0.0336929\pi$
$458$	−14.0039	−	24.2555i	−0.654360	−	1.13338i
$459$	−14.0608	−	24.3540i	−0.656302	−	1.13675i
$460$	5.41501	−	9.37907i	0.252476	−	0.437302i
$461$	41.6702			1.94078			0.970388	−	0.241553i	$-0.0776567\pi$
$461$	41.6702			1.94078			0.970388	+	0.241553i	$0.0776567\pi$
$462$	−12.1852	−	6.86207i	−0.566906	−	0.319252i
$463$	15.2890			0.710542			0.355271	−	0.934763i	$-0.384389\pi$
$463$	15.2890			0.710542			0.355271	+	0.934763i	$0.384389\pi$
$464$	−2.09639	+	3.63105i	−0.0973222	+	0.168567i
$465$	0.230254	+	0.398811i	0.0106778	+	0.0184944i
$466$	2.45599	+	4.25390i	0.113771	+	0.197058i
$467$	−20.2529	+	35.0791i	−0.937193	+	1.62327i	−0.166516	+	0.986039i	$0.553252\pi$
$467$	−20.2529	+	35.0791i	−0.937193	+	1.62327i	−0.770676	+	0.637227i	$0.780081\pi$
$468$	15.1298			0.699376
$469$	7.97539	+	4.49133i	0.368269	+	0.207390i
$470$	17.8137			0.821685
$471$	5.10524	−	8.84253i	0.235237	−	0.407442i
$472$	−14.8358	−	25.6964i	−0.682875	−	1.18277i
$473$	−11.6855	−	20.2399i	−0.537301	−	0.930633i
$474$	4.24240	−	7.34805i	0.194860	−	0.337507i
$475$	1.29089			0.0592301
$476$	0.841355	+	78.5023i	0.0385634	+	3.59814i
$477$	6.66025			0.304952
$478$	30.3763	−	52.6133i	1.38938	−	2.40648i
$479$	−4.42006	−	7.65577i	−0.201958	−	0.349801i	0.747201	−	0.664598i	$-0.231397\pi$
$479$	−4.42006	−	7.65577i	−0.201958	−	0.349801i	−0.949159	+	0.314797i	$0.898064\pi$
$480$	0.479009	+	0.829669i	0.0218637	+	0.0378690i
$481$	0.765199	−	1.32536i	0.0348901	−	0.0604313i
$482$	−46.5374			−2.11972
$483$	4.19346	−	2.48139i	0.190809	−	0.112907i
$484$	0.778726			0.0353966
$485$	7.62949	−	13.2147i	0.346437	−	0.600047i
$486$	−17.4183	−	30.1694i	−0.790112	−	1.36851i
$487$	−3.04712	−	5.27777i	−0.138078	−	0.239158i	0.788691	−	0.614790i	$-0.210759\pi$
$487$	−3.04712	−	5.27777i	−0.138078	−	0.239158i	−0.926769	+	0.375631i	$0.877426\pi$
$488$	−15.1951	+	26.3186i	−0.687848	+	1.19139i
$489$	8.32885			0.376643
$490$	−16.9154	+	0.362627i	−0.764161	+	0.0163818i
$491$	8.30034			0.374589			0.187294	−	0.982304i	$-0.440028\pi$
$491$	8.30034			0.374589			0.187294	+	0.982304i	$0.440028\pi$
$492$	2.32470	−	4.02651i	0.104806	−	0.181529i
$493$	5.26081	+	9.11200i	0.236935	+	0.410384i
$494$	2.38753	+	4.13531i	0.107420	+	0.186057i
$495$	−4.30617	+	7.45850i	−0.193548	+	0.335235i
$496$	−2.16916			−0.0973980
$497$	38.1353	−	22.5658i	1.71060	−	1.01221i
$498$	−6.84112			−0.306558
$499$	−5.31144	+	9.19968i	−0.237773	+	0.411834i	−0.960075	−	0.279743i	$-0.909751\pi$
$499$	−5.31144	+	9.19968i	−0.237773	+	0.411834i	0.722302	+	0.691578i	$0.243084\pi$
$500$	−1.92105	−	3.32736i	−0.0859121	−	0.148804i
$501$	−7.19431	−	12.4609i	−0.321418	−	0.556713i
$502$	24.9960	−	43.2944i	1.11563	−	1.93232i
$503$	−1.43771			−0.0641045			−0.0320522	−	0.999486i	$-0.510204\pi$
$503$	−1.43771			−0.0641045			−0.0320522	+	0.999486i	$0.510204\pi$
$504$	0.324848	+	30.3098i	0.0144699	+	1.35011i
$505$	9.53372			0.424245
$506$	−11.4019	+	19.7486i	−0.506875	+	0.877933i
$507$	3.48172	+	6.03052i	0.154629	+	0.267825i
$508$	12.4046	+	21.4854i	0.550364	+	0.953259i
$509$	15.0021	−	25.9843i	0.664955	−	1.15174i	−0.314343	−	0.949310i	$-0.601784\pi$
$509$	15.0021	−	25.9843i	0.664955	−	1.15174i	0.979298	−	0.202426i	$-0.0648825\pi$
$510$	−12.1963			−0.540059
$511$	12.1389	+	6.83598i	0.536992	+	0.302406i
$512$	−31.9180			−1.41059
$513$	2.35023	−	4.07072i	0.103765	−	0.179727i
$514$	13.4052	+	23.2185i	0.591278	+	1.02412i
$515$	−4.68948	−	8.12242i	−0.206643	−	0.357916i
$516$	8.76414	−	15.1799i	0.385820	−	0.668260i
$517$	−24.6678			−1.08489
$518$	5.57209	+	3.13791i	0.244824	+	0.137872i
$519$	8.12465			0.356632
$520$	3.40701	−	5.90111i	0.149407	−	0.258781i
$521$	−10.6630	−	18.4689i	−0.467157	−	0.809139i	0.532139	−	0.846657i	$-0.321388\pi$
$521$	−10.6630	−	18.4689i	−0.467157	−	0.809139i	−0.999296	+	0.0375178i	$0.988055\pi$
$522$	4.23652	+	7.33786i	0.185427	+	0.321169i
$523$	14.4010	−	24.9433i	0.629713	−	1.09069i	−0.357896	−	0.933761i	$-0.616506\pi$
$523$	14.4010	−	24.9433i	0.629713	−	1.09069i	0.987609	−	0.156933i	$-0.0501608\pi$
$524$	−7.01859			−0.306609
$525$	−0.0185257	−	1.72853i	−0.000808527	−	0.0754392i
$526$	50.1124			2.18501
$527$	−2.72172	+	4.71415i	−0.118560	+	0.205352i
$528$	3.36504	+	5.82843i	0.146445	+	0.253650i
$529$	7.52726	+	13.0376i	0.327272	+	0.566852i
$530$	3.12813	−	5.41808i	0.135877	−	0.235346i
$531$	−17.1476			−0.744142
$532$	−11.2932	+	6.68252i	−0.489623	+	0.289724i
$533$	2.83452			0.122777
$534$	1.89358	−	3.27978i	0.0819434	−	0.141930i
$535$	2.97310	+	5.14956i	0.128538	+	0.222635i
$536$	−7.70171	−	13.3398i	−0.332663	−	0.576190i
$537$	−2.01595	+	3.49172i	−0.0869946	+	0.150679i
$538$	−26.3778			−1.13723
$539$	23.4239	−	0.502153i	1.00894	−	0.0216293i
$540$	−13.9901			−0.602038
$541$	17.7102	−	30.6749i	0.761419	−	1.31882i	−0.180700	−	0.983538i	$-0.557836\pi$
$541$	17.7102	−	30.6749i	0.761419	−	1.31882i	0.942119	−	0.335278i	$-0.108830\pi$
$542$	−20.2114	−	35.0072i	−0.868154	−	1.50369i
$543$	−4.93871	−	8.55410i	−0.211941	−	0.367092i
$544$	−5.66213	+	9.80710i	−0.242762	+	0.420476i
$545$	−17.7209			−0.759081
$546$	5.50302	−	3.25630i	0.235507	−	0.139357i
$547$	−4.94434			−0.211405			−0.105702	−	0.994398i	$-0.533709\pi$
$547$	−4.94434			−0.211405			−0.105702	+	0.994398i	$0.533709\pi$
$548$	−15.2452	+	26.4055i	−0.651244	+	1.12799i
$549$	8.78139	+	15.2098i	0.374781	+	0.649139i
$550$	4.04497	+	7.00610i	0.172478	+	0.298741i
$551$	−0.879333	+	1.52305i	−0.0374608	+	0.0648841i
$552$	−8.19997			−0.349014
$553$	0.152344	+	14.2144i	0.00647833	+	0.604457i
$554$	64.3015			2.73191
$555$	−0.326680	+	0.565827i	−0.0138668	+	0.0240180i
$556$	−13.6300	−	23.6079i	−0.578041	−	1.00120i
$557$	14.7701	+	25.5826i	0.625831	+	1.08397i	0.988380	+	0.152006i	$0.0485733\pi$
$557$	14.7701	+	25.5826i	0.625831	+	1.08397i	−0.362549	+	0.931965i	$0.618093\pi$
$558$	−2.19179	+	3.79629i	−0.0927858	+	0.160710i
$559$	10.6862			0.451976
$560$	7.09481	+	3.99543i	0.299810	+	0.168838i
$561$	16.8889			0.713052
$562$	−24.6344	+	42.6681i	−1.03914	+	1.79985i
$563$	17.6675	+	30.6010i	0.744595	+	1.28968i	0.950384	+	0.311080i	$0.100691\pi$
$563$	17.6675	+	30.6010i	0.744595	+	1.28968i	−0.205789	+	0.978596i	$0.565976\pi$
$564$	−9.25043	−	16.0222i	−0.389513	−	0.674657i
$565$	1.45173	−	2.51446i	0.0610745	−	0.105784i
$566$	−54.6567			−2.29739
$567$	12.3112	+	6.93302i	0.517021	+	0.291160i
$568$	−74.5705			−3.12891
$569$	12.6811	−	21.9644i	0.531621	−	0.920795i	−0.467698	−	0.883889i	$-0.654916\pi$
$569$	12.6811	−	21.9644i	0.531621	−	0.920795i	0.999319	−	0.0369062i	$-0.0117503\pi$
$570$	−1.01929	−	1.76546i	−0.0426933	−	0.0739469i
$571$	−16.8531	−	29.1905i	−0.705282	−	1.22158i	−0.966590	−	0.256329i	$-0.917487\pi$
$571$	−16.8531	−	29.1905i	−0.705282	−	1.22158i	0.261308	−	0.965256i	$-0.415846\pi$
$572$	−9.84021	+	17.0437i	−0.411440	+	0.712635i
$573$	−1.20241			−0.0502314
$574$	0.126935	+	11.8436i	0.00529817	+	0.494343i
$575$	−2.81877			−0.117551
$576$	−12.4786	+	21.6136i	−0.519943	+	0.900568i
$577$	−1.65151	−	2.86050i	−0.0687532	−	0.119084i	0.829600	−	0.558359i	$-0.188569\pi$
$577$	−1.65151	−	2.86050i	−0.0687532	−	0.119084i	−0.898353	+	0.439275i	$0.855235\pi$
$578$	−51.5380	−	89.2665i	−2.14370	−	3.71300i
$579$	−2.13851	+	3.70401i	−0.0888734	+	0.153933i
$580$	5.23436			0.217345
$581$	9.86391	−	5.83676i	0.409224	−	0.242150i
$582$	−24.0970			−0.998853
$583$	−4.33173	+	7.50277i	−0.179402	+	0.310733i
$584$	−11.7223	−	20.3037i	−0.485073	−	0.840172i
$585$	−1.96895	−	3.41032i	−0.0814060	−	0.140999i
$586$	14.4749	−	25.0712i	0.597952	−	1.03568i
$587$	−12.2225			−0.504478			−0.252239	−	0.967665i	$-0.581167\pi$
$587$	−12.2225			−0.504478			−0.252239	+	0.967665i	$0.581167\pi$
$588$	9.11012	+	15.0260i	0.375695	+	0.619660i
$589$	−0.909857			−0.0374900
$590$	−8.05374	+	13.9495i	−0.331567	+	0.574291i
$591$	−1.85303	−	3.20954i	−0.0762233	−	0.132023i
$592$	−1.53878	−	2.66525i	−0.0632435	−	0.109541i
$593$	19.9645	−	34.5795i	0.819844	−	1.42001i	−0.0859534	−	0.996299i	$-0.527394\pi$
$593$	19.9645	−	34.5795i	0.819844	−	1.42001i	0.905797	−	0.423712i	$-0.139273\pi$
$594$	29.4576			1.20866
$595$	17.5852	−	10.4057i	0.720924	−	0.426592i
$596$	19.5903			0.802452
$597$	−4.05235	+	7.01887i	−0.165852	+	0.287263i
$598$	−5.21337	−	9.02983i	−0.213191	−	0.369257i
$599$	13.0921	+	22.6761i	0.534928	+	0.926522i	0.999167	+	0.0408119i	$0.0129945\pi$
$599$	13.0921	+	22.6761i	0.534928	+	0.926522i	−0.464239	+	0.885710i	$0.653672\pi$
$600$	−1.45453	+	2.51932i	−0.0593809	+	0.102851i
$601$	19.4746			0.794385			0.397192	−	0.917735i	$-0.369985\pi$
$601$	19.4746			0.794385			0.397192	+	0.917735i	$0.369985\pi$
$602$	0.478546	+	44.6505i	0.0195041	+	1.81982i
$603$	−8.90181			−0.362510
$604$	4.94045	−	8.55710i	0.201024	−	0.348184i
$605$	−0.101341	−	0.175528i	−0.00412010	−	0.00713622i
$606$	−7.52784	−	13.0386i	−0.305797	−	0.529657i
$607$	10.1855	−	17.6418i	0.413417	−	0.716060i	−0.581844	−	0.813301i	$-0.697668\pi$
$607$	10.1855	−	17.6418i	0.413417	−	0.716060i	0.995261	+	0.0972410i	$0.0310017\pi$
$608$	−1.89282			−0.0767642
$609$	2.05202	+	1.15559i	0.0831519	+	0.0468268i
$610$	16.4975			0.667964
$611$	5.63954	−	9.76797i	0.228151	−	0.395170i
$612$	−38.1758	−	66.1224i	−1.54317	−	2.67284i
$613$	5.47022	+	9.47470i	0.220940	+	0.382679i	0.955094	−	0.296304i	$-0.0957542\pi$
$613$	5.47022	+	9.47470i	0.220940	+	0.382679i	−0.734154	+	0.678983i	$0.762421\pi$
$614$	4.10593	−	7.11168i	0.165702	−	0.287004i
$615$	−1.21012			−0.0487968
$616$	−34.3553	−	19.3471i	−1.38422	−	0.779518i
$617$	26.8262			1.07998			0.539991	−	0.841671i	$-0.318428\pi$
$617$	26.8262			1.07998			0.539991	+	0.841671i	$0.318428\pi$
$618$	−7.40563	+	12.8269i	−0.297898	+	0.515975i
$619$	23.6896	+	41.0317i	0.952167	+	1.64920i	0.740721	+	0.671813i	$0.234484\pi$
$619$	23.6896	+	41.0317i	0.952167	+	1.64920i	0.211446	+	0.977390i	$0.432183\pi$
$620$	1.35401	+	2.34522i	0.0543785	+	0.0941864i
$621$	−5.13194	+	8.88878i	−0.205938	+	0.356694i
$622$	5.90251			0.236669
$623$	0.0679983	+	6.34455i	0.00272430	+	0.254189i
$624$	−3.07726			−0.123189
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	6.62754	+	11.4792i	0.264890	+	0.458802i
$627$	1.41147	+	2.44475i	0.0563689	+	0.0976337i
$628$	30.0215	−	51.9987i	1.19799	−	2.07498i
$629$	−7.72305			−0.307938
$630$	14.1613	−	8.37967i	0.564201	−	0.333854i
$631$	−25.2745			−1.00616			−0.503082	−	0.864239i	$-0.667801\pi$
$631$	−25.2745			−1.00616			−0.503082	+	0.864239i	$0.667801\pi$
$632$	11.9612	−	20.7173i	0.475789	−	0.824091i
$633$	8.78111	+	15.2093i	0.349018	+	0.604517i
$634$	−36.4195	−	63.0803i	−1.44640	−	2.50524i
$635$	3.22859	−	5.59208i	0.128123	−	0.221915i
$636$	−6.49759			−0.257646
$637$	−5.15632	+	9.39021i	−0.204301	+	0.372054i
$638$	−11.0215			−0.436344
$639$	−21.5475	+	37.3214i	−0.852408	+	1.47641i
$640$	10.2554	+	17.7629i	0.405382	+	0.702142i
$641$	−1.98975	−	3.44635i	−0.0785904	−	0.136122i	0.824052	−	0.566515i	$-0.191709\pi$
$641$	−1.98975	−	3.44635i	−0.0785904	−	0.136122i	−0.902642	+	0.430392i	$0.858375\pi$
$642$	4.69512	−	8.13219i	0.185302	−	0.320952i
$643$	23.4101			0.923202			0.461601	−	0.887088i	$-0.347275\pi$
$643$	23.4101			0.923202			0.461601	+	0.887088i	$0.347275\pi$
$644$	24.6597	−	14.5919i	0.971730	−	0.575001i
$645$	−4.56216			−0.179635
$646$	12.0485	−	20.8686i	0.474041	−	0.821064i
$647$	−10.6616	−	18.4664i	−0.419149	−	0.725987i	0.576705	−	0.816952i	$-0.304338\pi$
$647$	−10.6616	−	18.4664i	−0.419149	−	0.725987i	−0.995854	+	0.0909652i	$0.971005\pi$
$648$	−11.8887	−	20.5919i	−0.467033	−	0.808925i
$649$	11.1525	−	19.3168i	0.437776	−	0.758250i
$650$	−3.69904			−0.145088
$651$	0.0130574	+	1.21832i	0.000511762	+	0.0477497i
$652$	48.9780			1.91813
$653$	1.06315	−	1.84144i	0.0416044	−	0.0720610i	−0.844473	−	0.535598i	$-0.820086\pi$
$653$	1.06315	−	1.84144i	0.0416044	−	0.0720610i	0.886078	+	0.463537i	$0.153420\pi$
$654$	13.9925	+	24.2357i	0.547149	+	0.947689i
$655$	0.913379	+	1.58202i	0.0356887	+	0.0618146i
$656$	2.85005	−	4.93643i	0.111276	−	0.192735i
$657$	−13.5489			−0.528594
$658$	41.0665	+	23.1265i	1.60094	+	0.901567i
$659$	23.7026			0.923322			0.461661	−	0.887056i	$-0.347254\pi$
$659$	23.7026			0.923322			0.461661	+	0.887056i	$0.347254\pi$
$660$	4.20100	−	7.27635i	0.163524	−	0.283232i
$661$	−18.2165	−	31.5519i	−0.708540	−	1.22723i	−0.965399	−	0.260778i	$-0.916021\pi$
$661$	−18.2165	−	31.5519i	−0.708540	−	1.22723i	0.256859	−	0.966449i	$-0.417312\pi$
$662$	18.5214	+	32.0800i	0.719855	+	1.24682i
$663$	−3.86114	+	6.68769i	−0.149954	+	0.259729i
$664$	−19.2881			−0.748523
$665$	2.97593	+	1.67589i	0.115402	+	0.0649882i
$666$	−6.21935			−0.240995
$667$	1.92010	−	3.32571i	0.0743466	−	0.128772i
$668$	−42.3064	−	73.2768i	−1.63688	−	2.83516i
$669$	−2.79176	−	4.83548i	−0.107936	−	0.186950i
$670$	−4.18093	+	7.24158i	−0.161523	+	0.279767i
$671$	−22.8452			−0.881927
$672$	0.0271641	+	2.53453i	0.00104788	+	0.0977718i
$673$	−29.5571			−1.13934			−0.569672	−	0.821872i	$-0.692930\pi$
$673$	−29.5571			−1.13934			−0.569672	+	0.821872i	$0.692930\pi$
$674$	7.07980	−	12.2626i	0.272704	−	0.472337i
$675$	1.82063	+	3.15342i	0.0700760	+	0.121375i
$676$	20.4744	+	35.4626i	0.787475	+	1.36395i
$677$	−10.0001	+	17.3207i	−0.384335	+	0.665688i	−0.991677	−	0.128753i	$-0.958903\pi$
$677$	−10.0001	+	17.3207i	−0.384335	+	0.665688i	0.607342	+	0.794441i	$0.292236\pi$
$678$	−4.58513			−0.176091
$679$	34.7444	−	20.5593i	1.33337	−	0.788992i
$680$	−34.3865			−1.31866
$681$	4.52441	−	7.83650i	0.173376	−	0.300295i
$682$	−2.85102	−	4.93811i	−0.109171	−	0.189090i
$683$	−0.682643	−	1.18237i	−0.0261206	−	0.0452423i	0.852670	−	0.522451i	$-0.174982\pi$
$683$	−0.682643	−	1.18237i	−0.0261206	−	0.0452423i	−0.878790	+	0.477208i	$0.841649\pi$
$684$	6.38100	−	11.0522i	0.243983	−	0.422592i
$685$	7.93587			0.303214
$686$	−39.4665	−	21.1244i	−1.50684	−	0.806532i
$687$	7.57090			0.288848
$688$	10.7447	−	18.6104i	0.409638	−	0.709514i
$689$	−1.98063	−	3.43056i	−0.0754562	−	0.130694i
$690$	2.22571	+	3.85503i	0.0847312	+	0.146759i
$691$	−0.498543	+	0.863502i	−0.0189655	+	0.0328492i	−0.875352	−	0.483485i	$-0.839371\pi$
$691$	−0.498543	+	0.863502i	−0.0189655	+	0.0328492i	0.856387	+	0.516335i	$0.172704\pi$
$692$	47.7772			1.81622
$693$	−19.6101	+	11.6039i	−0.744927	+	0.440795i
$694$	88.4851			3.35885
$695$	−3.54753	+	6.14451i	−0.134566	+	0.233075i
$696$	−1.98160	−	3.43223i	−0.0751124	−	0.130098i
$697$	−7.15211	−	12.3878i	−0.270906	−	0.469222i
$698$	40.7685	−	70.6132i	1.54311	−	2.67275i
$699$	−1.32777			−0.0502210
$700$	−0.108941	−	10.1647i	−0.00411758	−	0.384188i
$701$	27.6866			1.04571			0.522855	−	0.852422i	$-0.324867\pi$
$701$	27.6866			1.04571			0.522855	+	0.852422i	$0.324867\pi$
$702$	−6.73457	+	11.6646i	−0.254180	+	0.440253i
$703$	−0.645445	−	1.11794i	−0.0243434	−	0.0421640i
$704$	−16.2319	−	28.1144i	−0.611761	−	1.05960i
$705$	−2.40765	+	4.17017i	−0.0906772	+	0.157058i
$706$	47.4157			1.78451
$707$	21.9784	+	12.3771i	0.826583	+	0.465489i
$708$	16.7288			0.628707
$709$	−6.62710	+	11.4785i	−0.248886	+	0.431083i	−0.963217	−	0.268725i	$-0.913398\pi$
$709$	−6.62710	+	11.4785i	−0.248886	+	0.431083i	0.714331	+	0.699808i	$0.246731\pi$
$710$	20.2406	+	35.0577i	0.759614	+	1.31569i
$711$	−6.91248	−	11.9728i	−0.259238	−	0.449014i
$712$	5.33883	−	9.24713i	0.200081	−	0.346551i
$713$	1.98675			0.0744045
$714$	−28.1164	−	15.8337i	−1.05223	−	0.592562i
$715$	5.12230			0.191563
$716$	−11.8548	+	20.5332i	−0.443036	+	0.767361i
$717$	8.21114	+	14.2221i	0.306651	+	0.531134i
$718$	−23.6666	−	40.9917i	−0.883229	−	1.52980i
$719$	0.774015	−	1.34063i	0.0288659	−	0.0499972i	−0.851232	−	0.524790i	$-0.824144\pi$
$719$	0.774015	−	1.34063i	0.0288659	−	0.0499972i	0.880097	+	0.474793i	$0.157477\pi$
$720$	−7.91894			−0.295121
$721$	−0.265935	−	24.8130i	−0.00990395	−	0.924083i
$722$	−41.8961			−1.55921
$723$	6.28985	−	10.8943i	0.233922	−	0.405165i
$724$	−29.0423	−	50.3027i	−1.07935	−	1.86948i
$725$	−0.681184	−	1.17984i	−0.0252985	−	0.0438183i
$726$	−0.160038	+	0.277194i	−0.00593957	+	0.0102876i
$727$	−51.3783			−1.90552			−0.952758	−	0.303729i	$-0.901768\pi$
$727$	−51.3783			−1.90552			−0.952758	+	0.303729i	$0.901768\pi$
$728$	15.5154	−	9.18090i	0.575038	−	0.340267i
$729$	−6.60409			−0.244596
$730$	−6.36355	+	11.0220i	−0.235525	+	0.407942i
$731$	−26.9635	−	46.7021i	−0.997281	−	1.72734i
$732$	−8.56693	−	14.8384i	−0.316643	−	0.548442i
$733$	−19.8173	+	34.3246i	−0.731969	+	1.26781i	0.224071	+	0.974573i	$0.428065\pi$
$733$	−19.8173	+	34.3246i	−0.731969	+	1.26781i	−0.956040	+	0.293235i	$0.905268\pi$
$734$	−52.8949			−1.95239
$735$	2.20135	−	4.00889i	0.0811979	−	0.147870i
$736$	4.13315			0.152350
$737$	5.78961	−	10.0279i	0.213263	−	0.369382i
$738$	−5.75957	−	9.97588i	−0.212013	−	0.367217i
$739$	8.36399	+	14.4869i	0.307674	+	0.532908i	0.977853	−	0.209292i	$-0.0671159\pi$
$739$	8.36399	+	14.4869i	0.307674	+	0.532908i	−0.670179	+	0.742200i	$0.733783\pi$
$740$	−1.92105	+	3.32736i	−0.0706193	+	0.122316i
$741$	−1.29076			−0.0474173
$742$	14.2454	−	8.42941i	0.522964	−	0.309453i
$743$	−24.9515			−0.915383			−0.457692	−	0.889111i	$-0.651324\pi$
$743$	−24.9515			−0.915383			−0.457692	+	0.889111i	$0.651324\pi$
$744$	1.02519	−	1.77569i	0.0375854	−	0.0650999i
$745$	−2.54943	−	4.41574i	−0.0934038	−	0.161780i
$746$	39.8183	+	68.9674i	1.45785	+	2.52508i
$747$	−5.57340	+	9.65341i	−0.203920	+	0.353200i
$748$	99.3160			3.63135
$749$	0.168601	+	15.7313i	0.00616055	+	0.574807i
$750$	1.57920			0.0576643
$751$	2.38196	−	4.12567i	0.0869189	−	0.150548i	−0.819288	−	0.573382i	$-0.805631\pi$
$751$	2.38196	−	4.12567i	0.0869189	−	0.150548i	0.906207	+	0.422834i	$0.138965\pi$
$752$	−11.3409	−	19.6430i	−0.413559	−	0.716306i
$753$	6.75677	+	11.7031i	0.246230	+	0.426483i
$754$	2.51972	−	4.36429i	0.0917629	−	0.158938i
$755$	−2.57174			−0.0935952
$756$	−32.2518	−	18.1626i	−1.17299	−	0.660566i
$757$	−32.7570			−1.19058			−0.595288	−	0.803513i	$-0.702962\pi$
$757$	−32.7570			−1.19058			−0.595288	+	0.803513i	$0.702962\pi$
$758$	6.03208	−	10.4479i	0.219095	−	0.379484i
$759$	−3.08208	−	5.33832i	−0.111872	−	0.193769i
$760$	−2.87381	−	4.97759i	−0.104244	−	0.180556i
$761$	−4.02838	+	6.97736i	−0.146029	+	0.252929i	−0.929756	−	0.368176i	$-0.879982\pi$
$761$	−4.02838	+	6.97736i	−0.146029	+	0.252929i	0.783728	+	0.621105i	$0.213316\pi$
$762$	−10.1972			−0.369405
$763$	−40.8527	−	23.0061i	−1.47897	−	0.832877i
$764$	−7.07080			−0.255813
$765$	−9.93617	+	17.2099i	−0.359243	+	0.622227i
$766$	−20.8735	−	36.1539i	−0.754190	−	1.30629i
$767$	5.09938	+	8.83238i	0.184128	+	0.318919i
$768$	9.85831	−	17.0751i	0.355731	−	0.616144i
$769$	0.596333			0.0215043			0.0107522	−	0.999942i	$-0.496577\pi$
$769$	0.596333			0.0215043			0.0107522	+	0.999942i	$0.496577\pi$
$770$	0.229386	+	21.4028i	0.00826650	+	0.771302i
$771$	−7.24722			−0.261002
$772$	−12.5756	+	21.7815i	−0.452604	+	0.783934i
$773$	14.5644	+	25.2262i	0.523844	+	0.907325i	0.999615	+	0.0277556i	$0.00883601\pi$
$773$	14.5644	+	25.2262i	0.523844	+	0.907325i	−0.475770	+	0.879570i	$0.657831\pi$
$774$	−21.7136	−	37.6091i	−0.780480	−	1.35183i
$775$	0.352415	−	0.610400i	0.0126591	−	0.0219262i
$776$	−67.9398			−2.43890
$777$	−1.48769	+	0.880309i	−0.0533705	+	0.0315809i
$778$	−64.3404			−2.30672
$779$	1.19546	−	2.07060i	0.0428318	−	0.0741868i
$780$	1.92086	+	3.32703i	0.0687779	+	0.119127i
$781$	−28.0284	−	48.5467i	−1.00294	−	1.73714i
$782$	−26.3090	+	45.5684i	−0.940806	+	1.62952i
$783$	−4.96073			−0.177282
$784$	11.1689	+	18.4216i	0.398888	+	0.657914i
$785$	−15.6276			−0.557774
$786$	1.44241	−	2.49833i	0.0514490	−	0.0891123i
$787$	11.7667	+	20.3806i	0.419439	+	0.726489i	0.995883	−	0.0906474i	$-0.0288936\pi$
$787$	11.7667	+	20.3806i	0.419439	+	0.726489i	−0.576444	+	0.817136i	$0.695560\pi$
$788$	−10.8968	−	18.8738i	−0.388182	−	0.672350i
$789$	−6.77304	+	11.7312i	−0.241127	+	0.417644i
$790$	−12.9864			−0.462035
$791$	6.61110	−	3.91198i	0.235064	−	0.139094i
$792$	38.3460			1.36257
$793$	5.22285	−	9.04624i	0.185469	−	0.321241i
$794$	9.26904	+	16.0544i	0.328946	+	0.569751i
$795$	0.845577	+	1.46458i	0.0299895	+	0.0519434i
$796$	−23.8300	+	41.2747i	−0.844630	+	1.46294i
$797$	17.7828			0.629898			0.314949	−	0.949109i	$-0.398013\pi$
$797$	17.7828			0.629898			0.314949	+	0.949109i	$0.398013\pi$
$798$	−0.0578027	−	5.39325i	−0.00204619	−	0.190919i
$799$	−56.9192			−2.01366
$800$	0.733147	−	1.26985i	0.0259207	−	0.0448959i
$801$	−3.08537	−	5.34401i	−0.109016	−	0.188821i
$802$	7.35941	+	12.7469i	0.259870	+	0.450108i
$803$	8.81202	−	15.2629i	0.310970	−	0.538615i
$804$	8.68441			0.306276
$805$	−6.49821	−	3.65945i	−0.229032	−	0.128979i
$806$	2.60719			0.0918344
$807$	3.56514	−	6.17500i	0.125499	−	0.217370i
$808$	−21.2242	−	36.7614i	−0.746666	−	1.29326i
$809$	20.7516	+	35.9428i	0.729587	+	1.26368i	0.957058	+	0.289897i	$0.0936212\pi$
$809$	20.7516	+	35.9428i	0.729587	+	1.26368i	−0.227470	+	0.973785i	$0.573045\pi$
$810$	−6.45388	+	11.1784i	−0.226766	+	0.392771i
$811$	−7.48186			−0.262724			−0.131362	−	0.991334i	$-0.541935\pi$
$811$	−7.48186			−0.262724			−0.131362	+	0.991334i	$0.541935\pi$
$812$	12.0669	+	6.79547i	0.423467	+	0.238474i
$813$	10.9268			0.383221
$814$	4.04497	−	7.00610i	0.141776	−	0.245564i
$815$	−6.37385	−	11.0398i	−0.223266	−	0.386709i
$816$	7.76459	+	13.4487i	0.271815	+	0.470798i
$817$	4.50688	−	7.80615i	0.157676	−	0.273103i
$818$	−17.2933			−0.604645
$819$	−0.111657	−	10.4181i	−0.00390161	−	0.364038i
$820$	−7.11615			−0.248507
$821$	−8.15871	+	14.1313i	−0.284741	+	0.493186i	−0.972546	−	0.232709i	$-0.925241\pi$
$821$	−8.15871	+	14.1313i	−0.284741	+	0.493186i	0.687805	+	0.725895i	$0.258574\pi$
$822$	−6.26617	−	10.8533i	−0.218558	−	0.378553i
$823$	−2.07833	−	3.59978i	−0.0724461	−	0.125480i	0.827527	−	0.561426i	$-0.189747\pi$
$823$	−2.07833	−	3.59978i	−0.0724461	−	0.125480i	−0.899973	+	0.435946i	$0.856414\pi$
$824$	−20.8797	+	36.1647i	−0.727378	+	1.25986i
$825$	−2.18682			−0.0761354
$826$	−36.6764	+	21.7025i	−1.27613	+	0.755126i
$827$	5.40282			0.187874			0.0939372	−	0.995578i	$-0.470055\pi$
$827$	5.40282			0.187874			0.0939372	+	0.995578i	$0.470055\pi$
$828$	−13.9335	+	24.1335i	−0.484222	+	0.838697i
$829$	25.1641	+	43.5856i	0.873987	+	1.51379i	0.857838	+	0.513920i	$0.171807\pi$
$829$	25.1641	+	43.5856i	0.873987	+	1.51379i	0.0161484	+	0.999870i	$0.494860\pi$
$830$	5.23534	+	9.06787i	0.181721	+	0.314750i
$831$	−8.69079	+	15.0529i	−0.301480	+	0.522179i
$832$	14.8437			0.514612
$833$	54.0489	−	1.15868i	1.87268	−	0.0401459i
$834$	11.2045			0.387982
$835$	−11.0112	+	19.0720i	−0.381060	+	0.660015i
$836$	8.30022	+	14.3764i	0.287069	+	0.497218i
$837$	−1.28323	−	2.22262i	−0.0443550	−	0.0768251i
$838$	−4.17927	+	7.23871i	−0.144371	+	0.250057i
$839$	17.9416			0.619414			0.309707	−	0.950832i	$-0.399769\pi$
$839$	17.9416			0.619414			0.309707	+	0.950832i	$0.399769\pi$
$840$	−6.62386	+	3.91953i	−0.228545	+	0.135237i
$841$	−27.1440			−0.935998
$842$	−21.4991	+	37.2376i	−0.740908	+	1.28329i
$843$	−6.65903	−	11.5338i	−0.229349	−	0.397244i
$844$	51.6376	+	89.4389i	1.77744	+	3.07861i
$845$	5.32894	−	9.23000i	0.183321	−	0.317522i
$846$	−45.8368			−1.57590
$847$	−0.00574694	−	0.536216i	−0.000197467	−	0.0184246i
$848$	−7.96594			−0.273552
$849$	7.38723	−	12.7951i	0.253529	−	0.439125i
$850$	9.33348	+	16.1661i	0.320136	+	0.554491i
$851$	1.40939	+	2.44113i	0.0483131	+	0.0836808i
$852$	21.0213	−	36.4100i	0.720178	−	1.24739i
$853$	−28.3492			−0.970658			−0.485329	−	0.874332i	$-0.661300\pi$
$853$	−28.3492			−0.970658			−0.485329	+	0.874332i	$0.661300\pi$
$854$	38.0322	+	21.4178i	1.30144	+	0.732901i
$855$	−3.32161			−0.113597
$856$	13.2376	−	22.9282i	0.452451	−	0.783668i
$857$	−12.2737	−	21.2586i	−0.419261	−	0.726181i	0.576605	−	0.817023i	$-0.304377\pi$
$857$	−12.2737	−	21.2586i	−0.419261	−	0.726181i	−0.995865	+	0.0908425i	$0.971044\pi$
$858$	−4.04457	−	7.00541i	−0.138079	−	0.239161i
$859$	16.8245	−	29.1408i	0.574043	−	0.994272i	−0.422101	−	0.906549i	$-0.638707\pi$
$859$	16.8245	−	29.1408i	0.574043	−	0.994272i	0.996145	−	0.0877237i	$-0.0279593\pi$
$860$	−26.8279			−0.914824
$861$	−2.78973	−	1.57103i	−0.0950738	−	0.0535406i
$862$	−61.6703			−2.10050
$863$	−6.37974	+	11.0500i	−0.217169	+	0.376147i	−0.953941	−	0.299993i	$-0.903016\pi$
$863$	−6.37974	+	11.0500i	−0.217169	+	0.376147i	0.736773	+	0.676141i	$0.236349\pi$
$864$	−2.66958	−	4.62384i	−0.0908209	−	0.157306i
$865$	−6.21758	−	10.7692i	−0.211404	−	0.366163i
$866$	27.3510	−	47.3734i	0.929426	−	1.60981i
$867$	27.8629			0.946273
$868$	0.0767847	+	7.16436i	0.00260624	+	0.243174i
$869$	17.9831			0.610036
$870$	−1.07573	+	1.86321i	−0.0364705	+	0.0631688i
$871$	2.64723	+	4.58514i	0.0896981	+	0.155362i
$872$	39.4508	+	68.3308i	1.33597	+	2.31397i
$873$	−19.6316	+	34.0029i	−0.664429	+	1.15082i
$874$	−8.79496			−0.297494
$875$	−2.27698	+	1.34736i	−0.0769759	+	0.0455489i
$876$	13.2180			0.446596
$877$	16.5729	−	28.7051i	0.559627	−	0.969302i	−0.437900	−	0.899024i	$-0.644278\pi$
$877$	16.5729	−	28.7051i	0.559627	−	0.969302i	0.997527	−	0.0702790i	$-0.0223889\pi$
$878$	−36.9120	−	63.9335i	−1.24572	−	2.15765i
$879$	3.91276	+	6.77710i	0.131974	+	0.228586i
$880$	5.15036	−	8.92069i	0.173619	−	0.300717i
$881$	−0.871592			−0.0293647			−0.0146823	−	0.999892i	$-0.504674\pi$
$881$	−0.871592			−0.0293647			−0.0146823	+	0.999892i	$0.504674\pi$
$882$	43.5254	−	0.933083i	1.46558	−	0.0314185i
$883$	−36.4887			−1.22794			−0.613972	−	0.789328i	$-0.710429\pi$
$883$	−36.4887			−1.22794			−0.613972	+	0.789328i	$0.710429\pi$
$884$	−22.7056	+	39.3272i	−0.763671	+	1.32272i
$885$	−2.17704	−	3.77074i	−0.0731803	−	0.126752i
$886$	7.78147	+	13.4779i	0.261424	+	0.452799i
$887$	−20.3752	+	35.2909i	−0.684132	+	1.18495i	0.289576	+	0.957155i	$0.406486\pi$
$887$	−20.3752	+	35.2909i	−0.684132	+	1.18495i	−0.973709	+	0.227797i	$0.926848\pi$
$888$	2.90906			0.0976215
$889$	14.7029	−	8.70011i	0.493118	−	0.291792i
$890$	−5.79644			−0.194297
$891$	8.93711	−	15.4795i	0.299405	−	0.518584i
$892$	−16.4170	−	28.4352i	−0.549683	−	0.952079i
$893$	−4.75695	−	8.23928i	−0.159185	−	0.275717i
$894$	−4.02606	+	6.97334i	−0.134652	+	0.233223i
$895$	6.17101			0.206274
$896$	0.581575	+	54.2636i	0.0194290	+	1.81282i
$897$	2.81849			0.0941068
$898$	−43.1291	+	74.7017i	−1.43924	+	2.49283i
$899$	0.480118	+	0.831589i	0.0160128	+	0.0277350i
$900$	4.94310	+	8.56170i	0.164770	+	0.285390i
$901$	−9.99514	+	17.3121i	−0.332987	+	0.576750i
$902$	14.9838			0.498905
$903$	−10.5173	−	5.92279i	−0.349994	−	0.197098i
$904$	−12.9275			−0.429961
$905$	−7.55894	+	13.0925i	−0.251268	+	0.435208i
$906$	2.03065	+	3.51718i	0.0674637	+	0.116851i
$907$	−25.8052	−	44.6959i	−0.856848	−	1.48410i	−0.874920	−	0.484267i	$-0.839086\pi$
$907$	−25.8052	−	44.6959i	−0.856848	−	1.48410i	0.0180726	−	0.999837i	$-0.494247\pi$
$908$	26.6059	−	46.0828i	0.882948	−	1.52931i
$909$	−24.5314			−0.813656
$910$	−8.52752	−	4.80225i	−0.282684	−	0.159193i
$911$	41.1042			1.36184			0.680921	−	0.732357i	$-0.261580\pi$
$911$	41.1042			1.36184			0.680921	+	0.732357i	$0.261580\pi$
$912$	−1.29783	+	2.24791i	−0.0429756	+	0.0744358i
$913$	−7.24972	−	12.5569i	−0.239931	−	0.415572i
$914$	20.9630	+	36.3089i	0.693393	+	1.20099i
$915$	−2.22975	+	3.86204i	−0.0737132	+	0.127675i
$916$	44.5209			1.47101
$917$	0.0517967	+	4.83287i	0.00171048	+	0.159595i
$918$	67.9712			2.24338
$919$	14.4377	−	25.0067i	0.476254	−	0.824896i	−0.523376	−	0.852102i	$-0.675328\pi$
$919$	14.4377	−	25.0067i	0.476254	−	0.824896i	0.999630	+	0.0272056i	$0.00866089\pi$
$920$	6.27522	+	10.8690i	0.206888	+	0.358341i
$921$	1.10989	+	1.92239i	0.0365721	+	0.0633448i
$922$	−50.3594	+	87.2250i	−1.65850	+	2.87260i
$923$	25.6314			0.843667
$924$	19.1312	−	11.3205i	0.629370	−	0.372417i
$925$	1.00000			0.0328798
$926$	−18.4771	+	32.0033i	−0.607196	+	1.05170i
$927$	12.0666	+	20.8999i	0.396319	+	0.686444i
$928$	0.998816	+	1.73000i	0.0327877	+	0.0567900i
$929$	20.0666	−	34.7563i	0.658363	−	1.14032i	−0.322676	−	0.946510i	$-0.604582\pi$
$929$	20.0666	−	34.7563i	0.658363	−	1.14032i	0.981039	−	0.193809i	$-0.0620843\pi$
$930$	−1.11307			−0.0364989
$931$	4.68480	+	7.72697i	0.153538	+	0.253241i
$932$	−7.80802			−0.255760
$933$	−0.797765	+	1.38177i	−0.0261176	+	0.0452371i
$934$	−48.9522	−	84.7877i	−1.60176	−	2.77434i
$935$	−12.9247	−	22.3862i	−0.422682	−	0.732107i
$936$	−8.76664	+	15.1843i	−0.286547	+	0.496313i
$937$	39.6270			1.29456			0.647279	−	0.762253i	$-0.275907\pi$
$937$	39.6270			1.29456			0.647279	+	0.762253i	$0.275907\pi$
$938$	−19.0398	+	11.2664i	−0.621671	+	0.367861i
$939$	−3.58303			−0.116928
$940$	−14.1582	+	24.5228i	−0.461791	+	0.799845i
$941$	15.1340	+	26.2128i	0.493353	+	0.854513i	0.999971	−	0.00765817i	$-0.00243769\pi$
$941$	15.1340	+	26.2128i	0.493353	+	0.854513i	−0.506618	+	0.862171i	$0.669104\pi$
$942$	12.3396	+	21.3728i	0.402045	+	0.696363i
$943$	−2.61039	+	4.52133i	−0.0850061	+	0.147235i
$944$	20.5093			0.667519
$945$	0.103246	+	9.63331i	0.00335859	+	0.313371i
$946$	56.4889			1.83661
$947$	19.0075	−	32.9220i	0.617661	−	1.06982i	−0.372251	−	0.928132i	$-0.621414\pi$
$947$	19.0075	−	32.9220i	0.617661	−	1.06982i	0.989911	−	0.141688i	$-0.0452529\pi$
$948$	6.74367	+	11.6804i	0.219024	+	0.379361i
$949$	4.02920	+	6.97878i	0.130793	+	0.226541i
$950$	−1.56007	+	2.70212i	−0.0506153	+	0.0876683i
$951$	19.6894			0.638471
$952$	−79.2723	−	44.6421i	−2.56923	−	1.44686i
$953$	40.9410			1.32621			0.663105	−	0.748527i	$-0.269238\pi$
$953$	40.9410			1.32621			0.663105	+	0.748527i	$0.269238\pi$
$954$	−8.04906	+	13.9414i	−0.260598	+	0.451369i
$955$	0.920173	+	1.59379i	0.0297761	+	0.0515737i
$956$	48.2858	+	83.6335i	1.56168	+	2.70490i
$957$	1.48963	−	2.58011i	0.0481529	−	0.0834032i
$958$	21.3670			0.690336
$959$	18.2948	+	10.3027i	0.590771	+	0.332691i
$960$	−6.33709			−0.204529
$961$	15.2516	−	26.4166i	0.491987	−	0.852147i
$962$	1.84952	+	3.20346i	0.0596309	+	0.103284i
$963$	−7.65014	−	13.2504i	−0.246522	−	0.426989i
$964$	36.9876	−	64.0645i	1.19129	−	2.06338i
$965$	6.54618			0.210729
$966$	0.126217	+	11.7766i	0.00406098	+	0.378907i
$967$	−30.4378			−0.978814			−0.489407	−	0.872055i	$-0.662787\pi$
$967$	−30.4378			−0.978814			−0.489407	+	0.872055i	$0.662787\pi$
$968$	−0.451216	+	0.781529i	−0.0145026	+	0.0251193i
$969$	3.25687	+	5.64107i	0.104626	+	0.181217i
$970$	18.4408	+	31.9404i	0.592099	+	1.02555i
$971$	16.2558	−	28.1559i	0.521674	−	0.903566i	−0.478008	−	0.878355i	$-0.658641\pi$
$971$	16.2558	−	28.1559i	0.521674	−	0.903566i	0.999682	−	0.0252103i	$-0.00802555\pi$
$972$	55.3759			1.77618
$973$	−16.1553	+	9.55958i	−0.517916	+	0.306466i
$974$	14.7301			0.471981
$975$	0.499951	−	0.865940i	0.0160112	−	0.0277323i
$976$	−10.5029	−	18.1916i	−0.336190	−	0.582299i
$977$	−14.3142	−	24.7929i	−0.457952	−	0.793195i	0.540901	−	0.841086i	$-0.318083\pi$
$977$	−14.3142	−	24.7929i	−0.457952	−	0.793195i	−0.998853	+	0.0478908i	$0.984750\pi$
$978$	−10.0656	+	17.4341i	−0.321862	+	0.557482i
$979$	8.02672			0.256535
$980$	12.9451	−	23.5744i	0.413515	−	0.753056i
$981$	45.5981			1.45583
$982$	−10.0311	+	17.3744i	−0.320107	+	0.554441i
$983$	8.14253	+	14.1033i	0.259706	+	0.449825i	0.966163	−	0.257931i	$-0.0830409\pi$
$983$	8.14253	+	14.1033i	0.259706	+	0.449825i	−0.706457	+	0.707756i	$0.749708\pi$
$984$	2.69400	+	4.66615i	0.0858816	+	0.148751i
$985$	−2.83615	+	4.91235i	−0.0903672	+	0.156521i
$986$	−25.4312			−0.809896
$987$	−10.9643	+	6.48791i	−0.348998	+	0.206512i
$988$	−7.59036			−0.241482
$989$	−9.84119	+	17.0454i	−0.312931	+	0.542013i
$990$	−10.4082	−	18.0275i	−0.330794	−	0.572953i
$991$	−25.8461	−	44.7668i	−0.821028	−	1.42206i	−0.904917	−	0.425588i	$-0.860067\pi$
$991$	−25.8461	−	44.7668i	−0.821028	−	1.42206i	0.0838887	−	0.996475i	$-0.473266\pi$
$992$	−0.516744	+	0.895026i	−0.0164066	+	0.0284171i
$993$	−10.0132			−0.317759
$994$	1.14782	+	107.097i	0.0364066	+	3.39690i
$995$	12.4046			0.393253
$996$	5.43729	−	9.41765i	0.172287	−	0.298410i
$997$	−7.28543	−	12.6187i	−0.230732	−	0.399640i	0.727292	−	0.686328i	$-0.240779\pi$
$997$	−7.28543	−	12.6187i	−0.230732	−	0.399640i	−0.958024	+	0.286689i	$0.907445\pi$
$998$	−12.8380	−	22.2360i	−0.406379	−	0.703870i
$999$	1.82063	−	3.15342i	0.0576021	−	0.0997698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.926.1	yes	38
7.2	even	3		9065.2.a.r.1.19		19
7.4	even	3	inner	1295.2.j.a.186.1	✓	38
7.5	odd	6		9065.2.a.s.1.19		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.1	✓	38	7.4	even	3	inner
1295.2.j.a.926.1	yes	38	1.1	even	1	trivial
9065.2.a.r.1.19		19	7.2	even	3
9065.2.a.s.1.19		19	7.5	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+(-1.20852 + 2.09322i) q^{2} +(-0.326680 - 0.565827i) q^{3} +(-1.92105 - 3.32736i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.57920 q^{6} +(-2.27698 + 1.34736i) q^{7} +4.45245 q^{8} +(1.28656 - 2.22839i) q^{9} +(-1.20852 - 2.09322i) q^{10} +(1.67352 + 2.89862i) q^{11} +(-1.25514 + 2.17397i) q^{12} -1.53040 q^{13} +(-0.0685340 - 6.39453i) q^{14} +0.653361 q^{15} +(-1.53878 + 2.66525i) q^{16} +(3.86152 + 6.68836i) q^{17} +(3.10967 + 5.38611i) q^{18} +(-0.645445 + 1.11794i) q^{19} +3.84211 q^{20} +(1.50621 + 0.848221i) q^{21} -8.08995 q^{22} +(1.40939 - 2.44113i) q^{23} +(-1.45453 - 2.51932i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.84952 - 3.20346i) q^{26} -3.64126 q^{27} +(8.85733 + 4.98799i) q^{28} +1.36237 q^{29} +(-0.789601 + 1.36763i) q^{30} +(0.352415 + 0.610400i) q^{31} +(0.733147 + 1.26985i) q^{32} +(1.09341 - 1.89385i) q^{33} -18.6670 q^{34} +(-0.0283545 - 2.64560i) q^{35} -9.88620 q^{36} +(-0.500000 + 0.866025i) q^{37} +(-1.56007 - 2.70212i) q^{38} +(0.499951 + 0.865940i) q^{39} +(-2.22623 + 3.85594i) q^{40} -1.85215 q^{41} +(-3.59581 + 2.12775i) q^{42} -6.98260 q^{43} +(6.42984 - 11.1368i) q^{44} +(1.28656 + 2.22839i) q^{45} +(3.40655 + 5.90032i) q^{46} +(-3.68502 + 6.38264i) q^{47} +2.01076 q^{48} +(3.36927 - 6.13580i) q^{49} +2.41704 q^{50} +(2.52297 - 4.36991i) q^{51} +(2.93997 + 5.09218i) q^{52} +(1.29420 + 2.24161i) q^{53} +(4.40054 - 7.62196i) q^{54} -3.34704 q^{55} +(-10.1381 + 5.99903i) q^{56} +0.843416 q^{57} +(-1.64645 + 2.85174i) q^{58} +(-3.33206 - 5.77130i) q^{59} +(-1.25514 - 2.17397i) q^{60} +(-3.41274 + 5.91104i) q^{61} -1.70360 q^{62} +(0.0729594 + 6.80744i) q^{63} -9.69923 q^{64} +(0.765199 - 1.32536i) q^{65} +(2.64283 + 4.57751i) q^{66} +(-1.72977 - 2.99605i) q^{67} +(14.8364 - 25.6974i) q^{68} -1.84167 q^{69} +(5.57209 + 3.13791i) q^{70} -16.7482 q^{71} +(5.72835 - 9.92179i) q^{72} +(-2.63278 - 4.56011i) q^{73} +(-1.20852 - 2.09322i) q^{74} +(-0.326680 + 0.565827i) q^{75} +4.95973 q^{76} +(-7.71605 - 4.34528i) q^{77} -2.41681 q^{78} +(2.68642 - 4.65302i) q^{79} +(-1.53878 - 2.66525i) q^{80} +(-2.67015 - 4.62484i) q^{81} +(2.23836 - 3.87696i) q^{82} -4.33201 q^{83} +(-0.0711776 - 6.64120i) q^{84} -7.72305 q^{85} +(8.43863 - 14.6161i) q^{86} +(-0.445058 - 0.770864i) q^{87} +(7.45127 + 12.9060i) q^{88} +(1.19908 - 2.07686i) q^{89} -6.21935 q^{90} +(3.48468 - 2.06199i) q^{91} -10.8300 q^{92} +(0.230254 - 0.398811i) q^{93} +(-8.90686 - 15.4271i) q^{94} +(-0.645445 - 1.11794i) q^{95} +(0.479009 - 0.829669i) q^{96} -15.2590 q^{97} +(8.77176 + 14.4679i) q^{98} +8.61234 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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