LMFDB - Embedded newform 494.2.m.b.153.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [494,2,Mod(153,494)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("494.153"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(494, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] 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:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			153.3
Character	$\chi$	$=$	494.153
Dual form			494.2.m.b.381.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.750797 - 1.30042i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.98870i q^{5} +(1.30042 + 0.750797i) q^{6} +(-3.23154 - 1.86573i) q^{7} +1.00000i q^{8} +(0.372609 - 0.645378i) q^{9} +(1.49435 + 2.58829i) q^{10} +(3.30334 - 1.90718i) q^{11} -1.50159 q^{12} +(-3.05046 + 1.92216i) q^{13} +3.73146 q^{14} +(-3.88656 + 2.24390i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.44565 + 2.50393i) q^{17} +0.745218i q^{18} +(0.866025 + 0.500000i) q^{19} +(-2.58829 - 1.49435i) q^{20} +5.60313i q^{21} +(-1.90718 + 3.30334i) q^{22} +(-0.834742 - 1.44582i) q^{23} +(1.30042 - 0.750797i) q^{24} -3.93232 q^{25} +(1.68070 - 3.18987i) q^{26} -5.62379 q^{27} +(-3.23154 + 1.86573i) q^{28} +(4.25622 + 7.37199i) q^{29} +(2.24390 - 3.88656i) q^{30} -1.71712i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.96027 - 2.86381i) q^{33} -2.89129i q^{34} +(-5.57610 + 9.65809i) q^{35} +(-0.372609 - 0.645378i) q^{36} +(4.52113 - 2.61028i) q^{37} -1.00000 q^{38} +(4.78988 + 2.52372i) q^{39} +2.98870 q^{40} +(-9.21784 + 5.32192i) q^{41} +(-2.80157 - 4.85246i) q^{42} +(2.71360 - 4.70009i) q^{43} -3.81437i q^{44} +(-1.92884 - 1.11362i) q^{45} +(1.44582 + 0.834742i) q^{46} -6.13466i q^{47} +(-0.750797 + 1.30042i) q^{48} +(3.46189 + 5.99618i) q^{49} +(3.40549 - 1.96616i) q^{50} +4.34155 q^{51} +(0.139408 + 3.60286i) q^{52} -13.2870 q^{53} +(4.87035 - 2.81190i) q^{54} +(-5.69999 - 9.87268i) q^{55} +(1.86573 - 3.23154i) q^{56} -1.50159i q^{57} +(-7.37199 - 4.25622i) q^{58} +(-4.78593 - 2.76316i) q^{59} +4.48781i q^{60} +(2.99576 - 5.18882i) q^{61} +(0.858561 + 1.48707i) q^{62} +(-2.40820 + 1.39038i) q^{63} -1.00000 q^{64} +(5.74475 + 9.11691i) q^{65} +5.72763 q^{66} +(6.36580 - 3.67530i) q^{67} +(1.44565 + 2.50393i) q^{68} +(-1.25344 + 2.17103i) q^{69} -11.1522i q^{70} +(-8.45239 - 4.87999i) q^{71} +(0.645378 + 0.372609i) q^{72} -0.118233i q^{73} +(-2.61028 + 4.52113i) q^{74} +(2.95237 + 5.11366i) q^{75} +(0.866025 - 0.500000i) q^{76} -14.2332 q^{77} +(-5.41002 + 0.209334i) q^{78} +3.04474 q^{79} +(-2.58829 + 1.49435i) q^{80} +(3.10450 + 5.37715i) q^{81} +(5.32192 - 9.21784i) q^{82} +1.22342i q^{83} +(4.85246 + 2.80157i) q^{84} +(7.48350 + 4.32060i) q^{85} +5.42719i q^{86} +(6.39111 - 11.0697i) q^{87} +(1.90718 + 3.30334i) q^{88} +(12.8331 - 7.40919i) q^{89} +2.22723 q^{90} +(13.4439 - 0.520194i) q^{91} -1.66948 q^{92} +(-2.23298 + 1.28921i) q^{93} +(3.06733 + 5.31277i) q^{94} +(1.49435 - 2.58829i) q^{95} -1.50159i q^{96} +(12.8856 + 7.43949i) q^{97} +(-5.99618 - 3.46189i) q^{98} -2.84253i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{3} + 14 q^{4} - 18 q^{9} - 2 q^{10} - 6 q^{11} - 8 q^{12} + 8 q^{13} + 4 q^{14} + 42 q^{15} - 14 q^{16} + 2 q^{17} - 10 q^{22} + 12 q^{23} - 88 q^{25} + 2 q^{26} + 20 q^{27} - 4 q^{29} - 4 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) $ 28 * q - 4 * q^3 + 14 * q^4 - 18 * q^9 - 2 * q^10 - 6 * q^11 - 8 * q^12 + 8 * q^13 + 4 * q^14 + 42 * q^15 - 14 * q^16 + 2 * q^17 - 10 * q^22 + 12 * q^23 - 88 * q^25 + 2 * q^26 + 20 * q^27 - 4 * q^29 - 4 * q^30 - 54 * q^33 - 14 * q^35 + 18 * q^36 + 6 * q^37 - 28 * q^38 + 60 * q^39 - 4 * q^40 + 42 * q^41 + 18 * q^42 + 28 * q^43 - 30 * q^45 - 12 * q^46 - 4 * q^48 + 28 * q^49 + 12 * q^50 - 20 * q^51 + 4 * q^52 + 24 * q^53 + 54 * q^54 + 2 * q^55 + 2 * q^56 - 6 * q^58 - 96 * q^59 - 30 * q^61 + 4 * q^62 + 12 * q^63 - 28 * q^64 + 82 * q^65 + 24 * q^66 - 6 * q^67 - 2 * q^68 - 42 * q^69 - 6 * q^71 + 12 * q^72 - 18 * q^74 + 46 * q^75 - 136 * q^77 + 50 * q^78 + 68 * q^79 + 6 * q^81 + 6 * q^82 + 12 * q^84 - 72 * q^85 - 52 * q^87 + 10 * q^88 + 48 * q^89 - 16 * q^90 + 44 * q^91 + 24 * q^92 + 30 * q^93 + 20 * q^94 - 2 * q^95 + 12 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.750797	−	1.30042i	−0.433473	−	0.750797i	0.563697	−	0.825982i	$-0.309379\pi$
$3$	−0.750797	−	1.30042i	−0.433473	−	0.750797i	−0.997170	+	0.0751851i	$0.976045\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	2.98870i		−	1.33659i	−0.743898	−	0.668293i	$-0.767025\pi$
$5$		−	2.98870i		−	1.33659i	0.743898	−	0.668293i	$-0.232975\pi$
$6$	1.30042	+	0.750797i	0.530893	+	0.306511i
$7$	−3.23154	−	1.86573i	−1.22141	−	0.705180i	−0.256189	−	0.966627i	$-0.582467\pi$
$7$	−3.23154	−	1.86573i	−1.22141	−	0.705180i	−0.965218	+	0.261447i	$0.915800\pi$
$8$			1.00000i			0.353553i
$9$	0.372609	−	0.645378i	0.124203	−	0.215126i
$10$	1.49435	+	2.58829i	0.472555	+	0.818489i
$11$	3.30334	−	1.90718i	0.995994	−	0.575037i	0.0889333	−	0.996038i	$-0.471654\pi$
$11$	3.30334	−	1.90718i	0.995994	−	0.575037i	0.907060	+	0.421000i	$0.138321\pi$
$12$	−1.50159			−0.433473
$13$	−3.05046	+	1.92216i	−0.846045	+	0.533111i
$13$	−3.05046	+	1.92216i	−0.846045	+	0.533111i
$14$	3.73146			0.997274
$15$	−3.88656	+	2.24390i	−1.00350	+	0.579374i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.44565	+	2.50393i	−0.350621	+	0.607293i	−0.986358	−	0.164612i	$-0.947363\pi$
$17$	−1.44565	+	2.50393i	−0.350621	+	0.607293i	0.635737	+	0.771905i	$0.280696\pi$
$18$			0.745218i			0.175650i
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i
$20$	−2.58829	−	1.49435i	−0.578759	−	0.334147i
$21$			5.60313i			1.22270i
$22$	−1.90718	+	3.30334i	−0.406613	+	0.704274i
$23$	−0.834742	−	1.44582i	−0.174056	−	0.301473i	0.765778	−	0.643105i	$-0.222354\pi$
$23$	−0.834742	−	1.44582i	−0.174056	−	0.301473i	−0.939834	+	0.341631i	$0.889021\pi$
$24$	1.30042	−	0.750797i	0.265447	−	0.153256i
$25$	−3.93232			−0.786464
$26$	1.68070	−	3.18987i	0.329612	−	0.625585i
$27$	−5.62379			−1.08230
$28$	−3.23154	+	1.86573i	−0.610703	+	0.352590i
$29$	4.25622	+	7.37199i	0.790360	+	1.36894i	0.925744	+	0.378150i	$0.123440\pi$
$29$	4.25622	+	7.37199i	0.790360	+	1.36894i	−0.135384	+	0.990793i	$0.543227\pi$
$30$	2.24390	−	3.88656i	0.409679	−	0.709585i
$31$		−	1.71712i		−	0.308404i	−0.988039	−	0.154202i	$-0.950719\pi$
$31$		−	1.71712i		−	0.308404i	0.988039	−	0.154202i	$-0.0492807\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.96027	−	2.86381i	−0.863472	−	0.498526i
$34$		−	2.89129i		−	0.495853i
$35$	−5.57610	+	9.65809i	−0.942534	+	1.63252i
$36$	−0.372609	−	0.645378i	−0.0621015	−	0.107563i
$37$	4.52113	−	2.61028i	0.743269	−	0.429127i	−0.0799874	−	0.996796i	$-0.525488\pi$
$37$	4.52113	−	2.61028i	0.743269	−	0.429127i	0.823257	+	0.567669i	$0.192155\pi$
$38$	−1.00000			−0.162221
$39$	4.78988	+	2.52372i	0.766995	+	0.404119i
$40$	2.98870			0.472555
$41$	−9.21784	+	5.32192i	−1.43958	+	0.831145i	−0.997821	−	0.0659865i	$-0.978981\pi$
$41$	−9.21784	+	5.32192i	−1.43958	+	0.831145i	−0.441764	+	0.897131i	$0.645647\pi$
$42$	−2.80157	−	4.85246i	−0.432291	−	0.748750i
$43$	2.71360	−	4.70009i	0.413820	−	0.716757i	−0.581484	−	0.813558i	$-0.697528\pi$
$43$	2.71360	−	4.70009i	0.413820	−	0.716757i	0.995304	+	0.0968012i	$0.0308611\pi$
$44$		−	3.81437i		−	0.575037i
$45$	−1.92884	−	1.11362i	−0.287534	−	0.166008i
$46$	1.44582	+	0.834742i	0.213174	+	0.123076i
$47$		−	6.13466i		−	0.894831i	−0.894326	−	0.447416i	$-0.852344\pi$
$47$		−	6.13466i		−	0.894831i	0.894326	−	0.447416i	$-0.147656\pi$
$48$	−0.750797	+	1.30042i	−0.108368	+	0.187699i
$49$	3.46189	+	5.99618i	0.494556	+	0.856597i
$50$	3.40549	−	1.96616i	0.481609	−	0.278057i
$51$	4.34155			0.607938
$52$	0.139408	+	3.60286i	0.0193324	+	0.499626i
$53$	−13.2870			−1.82511			−0.912553	−	0.408959i	$-0.865892\pi$
$53$	−13.2870			−1.82511			−0.912553	+	0.408959i	$0.865892\pi$
$54$	4.87035	−	2.81190i	0.662770	−	0.382651i
$55$	−5.69999	−	9.87268i	−0.768587	−	1.33123i
$56$	1.86573	−	3.23154i	0.249319	−	0.431832i
$57$		−	1.50159i		−	0.198891i
$58$	−7.37199	−	4.25622i	−0.967989	−	0.558869i
$59$	−4.78593	−	2.76316i	−0.623075	−	0.359732i	0.154990	−	0.987916i	$-0.450465\pi$
$59$	−4.78593	−	2.76316i	−0.623075	−	0.359732i	−0.778065	+	0.628184i	$0.783799\pi$
$60$			4.48781i			0.579374i
$61$	2.99576	−	5.18882i	0.383568	−	0.664360i	−0.608001	−	0.793936i	$-0.708028\pi$
$61$	2.99576	−	5.18882i	0.383568	−	0.664360i	0.991569	+	0.129576i	$0.0413617\pi$
$62$	0.858561	+	1.48707i	0.109037	+	0.188858i
$63$	−2.40820	+	1.39038i	−0.303405	+	0.175171i
$64$	−1.00000			−0.125000
$65$	5.74475	+	9.11691i	0.712549	+	1.13081i
$66$	5.72763			0.705022
$67$	6.36580	−	3.67530i	0.777706	−	0.449009i	−0.0579106	−	0.998322i	$-0.518444\pi$
$67$	6.36580	−	3.67530i	0.777706	−	0.449009i	0.835617	+	0.549313i	$0.185110\pi$
$68$	1.44565	+	2.50393i	0.175310	+	0.303647i
$69$	−1.25344	+	2.17103i	−0.150897	+	0.261361i
$70$		−	11.1522i		−	1.33294i
$71$	−8.45239	−	4.87999i	−1.00311	−	0.579148i	−0.0939458	−	0.995577i	$-0.529948\pi$
$71$	−8.45239	−	4.87999i	−1.00311	−	0.579148i	−0.909168	+	0.416429i	$0.863281\pi$
$72$	0.645378	+	0.372609i	0.0760585	+	0.0439124i
$73$		−	0.118233i		−	0.0138382i	−0.999976	−	0.00691908i	$-0.997798\pi$
$73$		−	0.118233i		−	0.0138382i	0.999976	−	0.00691908i	$-0.00220243\pi$
$74$	−2.61028	+	4.52113i	−0.303438	+	0.525571i
$75$	2.95237	+	5.11366i	0.340911	+	0.590474i
$76$	0.866025	−	0.500000i	0.0993399	−	0.0573539i
$77$	−14.2332			−1.62202
$78$	−5.41002	+	0.209334i	−0.612564	+	0.0237024i
$79$	3.04474			0.342560			0.171280	−	0.985222i	$-0.445210\pi$
$79$	3.04474			0.342560			0.171280	+	0.985222i	$0.445210\pi$
$80$	−2.58829	+	1.49435i	−0.289379	+	0.167073i
$81$	3.10450	+	5.37715i	0.344944	+	0.597461i
$82$	5.32192	−	9.21784i	0.587708	−	1.01794i
$83$			1.22342i			0.134288i	0.997743	+	0.0671439i	$0.0213887\pi$
$83$			1.22342i			0.134288i	−0.997743	+	0.0671439i	$0.978611\pi$
$84$	4.85246	+	2.80157i	0.529446	+	0.305676i
$85$	7.48350	+	4.32060i	0.811700	+	0.468635i
$86$			5.42719i			0.585229i
$87$	6.39111	−	11.0697i	0.685199	−	1.18680i
$88$	1.90718	+	3.30334i	0.203306	+	0.352137i
$89$	12.8331	−	7.40919i	1.36031	−	0.785372i	0.370641	−	0.928776i	$-0.379138\pi$
$89$	12.8331	−	7.40919i	1.36031	−	0.785372i	0.989664	+	0.143404i	$0.0458048\pi$
$90$	2.22723			0.234771
$91$	13.4439	−	0.520194i	1.40930	−	0.0545311i
$92$	−1.66948			−0.174056
$93$	−2.23298	+	1.28921i	−0.231549	+	0.133685i
$94$	3.06733	+	5.31277i	0.316371	+	0.547970i
$95$	1.49435	−	2.58829i	0.153317	−	0.265553i
$96$		−	1.50159i		−	0.153256i
$97$	12.8856	+	7.43949i	1.30833	+	0.755366i	0.981818	−	0.189826i	$-0.0607924\pi$
$97$	12.8856	+	7.43949i	1.30833	+	0.755366i	0.326515	+	0.945192i	$0.394126\pi$
$98$	−5.99618	−	3.46189i	−0.605705	−	0.349704i
$99$		−	2.84253i		−	0.285685i
$100$	−1.96616	+	3.40549i	−0.196616	+	0.340549i
$101$	7.21248	+	12.4924i	0.717669	+	1.24304i	0.961921	+	0.273327i	$0.0881242\pi$
$101$	7.21248	+	12.4924i	0.717669	+	1.24304i	−0.244252	+	0.969712i	$0.578542\pi$
$102$	−3.75989	+	2.17077i	−0.372285	+	0.214939i
$103$	−9.25772			−0.912190			−0.456095	−	0.889931i	$-0.650752\pi$
$103$	−9.25772			−0.912190			−0.456095	+	0.889931i	$0.650752\pi$
$104$	−1.92216	−	3.05046i	−0.188483	−	0.299122i
$105$	16.7461			1.63425
$106$	11.5069	−	6.64348i	1.11764	−	0.645272i
$107$	5.83157	+	10.1006i	0.563759	+	0.976459i	0.997164	+	0.0752600i	$0.0239787\pi$
$107$	5.83157	+	10.1006i	0.563759	+	0.976459i	−0.433405	+	0.901199i	$0.642688\pi$
$108$	−2.81190	+	4.87035i	−0.270575	+	0.468649i
$109$		−	6.07064i		−	0.581462i	−0.956805	−	0.290731i	$-0.906102\pi$
$109$		−	6.07064i		−	0.581462i	0.956805	−	0.290731i	$-0.0938984\pi$
$110$	9.87268	+	5.69999i	0.941323	+	0.543473i
$111$	−6.78890	−	3.91957i	−0.644374	−	0.372029i
$112$			3.73146i			0.352590i
$113$	2.64546	−	4.58207i	0.248864	−	0.431045i	−0.714347	−	0.699792i	$-0.753276\pi$
$113$	2.64546	−	4.58207i	0.248864	−	0.431045i	0.963211	+	0.268747i	$0.0866095\pi$
$114$	0.750797	+	1.30042i	0.0703185	+	0.121795i
$115$	−4.32111	+	2.49479i	−0.402945	+	0.232641i
$116$	8.51244			0.790360
$117$	0.103889	+	2.68491i	0.00960455	+	0.248220i
$118$	5.52632			0.508739
$119$	9.34333	−	5.39437i	0.856502	−	0.494501i
$120$	−2.24390	−	3.88656i	−0.204840	−	0.354792i
$121$	1.77469	−	3.07386i	0.161336	−	0.279442i
$122$			5.99153i			0.542448i
$123$	13.8414	+	7.99136i	1.24804	+	0.720557i
$124$	−1.48707	−	0.858561i	−0.133543	−	0.0771010i
$125$		−	3.19098i		−	0.285410i
$126$	1.39038	−	2.40820i	0.123864	−	0.214540i
$127$	−5.63430	−	9.75890i	−0.499963	−	0.865962i	0.500037	−	0.866004i	$-0.333320\pi$
$127$	−5.63430	−	9.75890i	−0.499963	−	0.865962i	−1.00000		4.21753e-5i	$0.999987\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−8.14944			−0.717518
$130$	−9.53355	−	5.02310i	−0.836148	−	0.440555i
$131$	−12.7617			−1.11499			−0.557495	−	0.830180i	$-0.688238\pi$
$131$	−12.7617			−1.11499			−0.557495	+	0.830180i	$0.688238\pi$
$132$	−4.96027	+	2.86381i	−0.431736	+	0.249263i
$133$	−1.86573	−	3.23154i	−0.161779	−	0.280210i
$134$	−3.67530	+	6.36580i	−0.317497	+	0.549921i
$135$			16.8078i			1.44659i
$136$	−2.50393	−	1.44565i	−0.214711	−	0.123963i
$137$	7.01819	+	4.05195i	0.599604	+	0.346182i	0.768886	−	0.639386i	$-0.220811\pi$
$137$	7.01819	+	4.05195i	0.599604	+	0.346182i	−0.169282	+	0.985568i	$0.554145\pi$
$138$		−	2.50689i		−	0.213400i
$139$	−4.95004	+	8.57373i	−0.419857	+	0.727214i	−0.995925	−	0.0901881i	$-0.971253\pi$
$139$	−4.95004	+	8.57373i	−0.419857	+	0.727214i	0.576068	+	0.817402i	$0.304587\pi$
$140$	5.57610	+	9.65809i	0.471267	+	0.816258i
$141$	−7.97761	+	4.60588i	−0.671836	+	0.387885i
$142$	9.75998			0.819039
$143$	−6.41079	+	12.1673i	−0.536097	+	1.01748i
$144$	−0.745218			−0.0621015
$145$	22.0326	−	12.7206i	1.82971	−	1.05638i
$146$	0.0591166	+	0.102393i	0.00489253	+	0.00847411i
$147$	5.19836	−	9.00382i	0.428753	−	0.742622i
$148$		−	5.22055i		−	0.429127i
$149$	−20.0651	−	11.5846i	−1.64380	−	0.949045i	−0.979467	−	0.201604i	$-0.935385\pi$
$149$	−20.0651	−	11.5846i	−1.64380	−	0.949045i	−0.664328	−	0.747441i	$-0.731282\pi$
$150$	−5.11366	−	2.95237i	−0.417528	−	0.241060i
$151$		−	20.1390i		−	1.63889i	−0.573157	−	0.819446i	$-0.694282\pi$
$151$		−	20.1390i		−	1.63889i	0.573157	−	0.819446i	$-0.305718\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	1.07732	+	1.86598i	0.0870963	+	0.150855i
$154$	12.3263	−	7.11658i	0.993279	−	0.573470i
$155$	−5.13196			−0.412209
$156$	4.58055	−	2.88630i	0.366738	−	0.231089i
$157$	−13.0900			−1.04470			−0.522349	−	0.852732i	$-0.674944\pi$
$157$	−13.0900			−1.04470			−0.522349	+	0.852732i	$0.674944\pi$
$158$	−2.63682	+	1.52237i	−0.209774	+	0.121113i
$159$	9.97581	+	17.2786i	0.791133	+	1.37028i
$160$	1.49435	−	2.58829i	0.118139	−	0.204622i
$161$			6.22961i			0.490962i
$162$	−5.37715	−	3.10450i	−0.422469	−	0.243912i
$163$	−5.11176	−	2.95127i	−0.400384	−	0.231162i	0.286266	−	0.958150i	$-0.407586\pi$
$163$	−5.11176	−	2.95127i	−0.400384	−	0.231162i	−0.686650	+	0.726989i	$0.740919\pi$
$164$			10.6438i			0.831145i
$165$	−8.55907	+	14.8247i	−0.666323	+	1.15411i
$166$	−0.611710	−	1.05951i	−0.0474779	−	0.0822342i
$167$	14.4251	−	8.32836i	1.11625	−	0.644468i	0.175810	−	0.984424i	$-0.443745\pi$
$167$	14.4251	−	8.32836i	1.11625	−	0.644468i	0.940441	+	0.339956i	$0.110412\pi$
$168$	−5.60313			−0.432291
$169$	5.61062	−	11.7269i	0.431586	−	0.902072i
$170$	−8.64121			−0.662750
$171$	0.645378	−	0.372609i	0.0493533	−	0.0284941i
$172$	−2.71360	−	4.70009i	−0.206910	−	0.358378i
$173$	−4.73645	+	8.20377i	−0.360105	+	0.623721i	−0.987978	−	0.154595i	$-0.950593\pi$
$173$	−4.73645	+	8.20377i	−0.360105	+	0.623721i	0.627873	+	0.778316i	$0.283926\pi$
$174$			12.7822i			0.969017i
$175$	12.7074	+	7.33664i	0.960592	+	0.554598i
$176$	−3.30334	−	1.90718i	−0.248998	−	0.143759i
$177$			8.29828i			0.623737i
$178$	−7.40919	+	12.8331i	−0.555342	+	0.961881i
$179$	−2.50220	−	4.33395i	−0.187024	−	0.323934i	0.757233	−	0.653145i	$-0.226551\pi$
$179$	−2.50220	−	4.33395i	−0.187024	−	0.323934i	−0.944257	+	0.329211i	$0.893217\pi$
$180$	−1.92884	+	1.11362i	−0.143767	+	0.0830040i
$181$	1.97399			0.146726			0.0733629	−	0.997305i	$-0.476627\pi$
$181$	1.97399			0.146726			0.0733629	+	0.997305i	$0.476627\pi$
$182$	−11.3827	+	7.17245i	−0.843740	+	0.531658i
$183$	−8.99684			−0.665065
$184$	1.44582	−	0.834742i	0.106587	−	0.0615380i
$185$	−7.80133	−	13.5123i	−0.573565	−	0.993444i
$186$	1.28921	−	2.23298i	0.0945294	−	0.163730i
$187$			11.0285i			0.806480i
$188$	−5.31277	−	3.06733i	−0.387473	−	0.223708i
$189$	18.1735	+	10.4925i	1.32193	+	0.763216i
$190$			2.98870i			0.216823i
$191$	10.4068	−	18.0251i	0.753010	−	1.30425i	−0.193347	−	0.981130i	$-0.561934\pi$
$191$	10.4068	−	18.0251i	0.753010	−	1.30425i	0.946358	−	0.323121i	$-0.104732\pi$
$192$	0.750797	+	1.30042i	0.0541841	+	0.0938496i
$193$	18.4519	−	10.6532i	1.32819	−	0.766833i	0.343174	−	0.939272i	$-0.388498\pi$
$193$	18.4519	−	10.6532i	1.32819	−	0.766833i	0.985020	+	0.172439i	$0.0551647\pi$
$194$	−14.8790			−1.06825
$195$	7.54265	−	14.3155i	0.540140	−	1.02516i
$196$	6.92379			0.494556
$197$	7.46727	−	4.31123i	0.532021	−	0.307162i	−0.209818	−	0.977740i	$-0.567287\pi$
$197$	7.46727	−	4.31123i	0.532021	−	0.307162i	0.741839	+	0.670578i	$0.233954\pi$
$198$	1.42127	+	2.46171i	0.101005	+	0.174946i
$199$	2.00205	−	3.46766i	0.141922	−	0.245816i	−0.786298	−	0.617847i	$-0.788005\pi$
$199$	2.00205	−	3.46766i	0.141922	−	0.245816i	0.928220	+	0.372031i	$0.121339\pi$
$200$		−	3.93232i		−	0.278057i
$201$	−9.55884	−	5.51880i	−0.674229	−	0.389266i
$202$	−12.4924	−	7.21248i	−0.878961	−	0.507469i
$203$		−	31.7638i		−	2.22938i
$204$	2.17077	−	3.75989i	0.151985	−	0.263245i
$205$	15.9056	+	27.5493i	1.11090	+	1.92413i
$206$	8.01742	−	4.62886i	0.558600	−	0.322508i
$207$	−1.24413			−0.0864730
$208$	3.18987	+	1.68070i	0.221178	+	0.116535i
$209$	3.81437			0.263845
$210$	−14.5025	+	8.37304i	−1.00077	+	0.577795i
$211$	−4.14958	−	7.18728i	−0.285669	−	0.494793i	0.687102	−	0.726561i	$-0.258882\pi$
$211$	−4.14958	−	7.18728i	−0.285669	−	0.494793i	−0.972771	+	0.231768i	$0.925549\pi$
$212$	−6.64348	+	11.5069i	−0.456276	+	0.790294i
$213$			14.6555i			1.00418i
$214$	−10.1006	−	5.83157i	−0.690461	−	0.398638i
$215$	−14.0471	−	8.11012i	−0.958007	−	0.553106i
$216$		−	5.62379i		−	0.382651i
$217$	−3.20369	+	5.54895i	−0.217480	+	0.376687i
$218$	3.03532	+	5.25733i	0.205578	+	0.356071i
$219$	−0.153753	+	0.0887692i	−0.0103896	+	0.00599846i
$220$	−11.4000			−0.768587
$221$	−0.403069	−	10.4169i	−0.0271133	−	0.700718i
$222$	7.83915			0.526129
$223$	−7.63487	+	4.40799i	−0.511269	+	0.295181i	−0.733355	−	0.679846i	$-0.762047\pi$
$223$	−7.63487	+	4.40799i	−0.511269	+	0.295181i	0.222086	+	0.975027i	$0.428713\pi$
$224$	−1.86573	−	3.23154i	−0.124659	−	0.215916i
$225$	−1.46522	+	2.53783i	−0.0976812	+	0.169189i
$226$			5.29092i			0.351947i
$227$	−3.62774	−	2.09447i	−0.240781	−	0.139015i	0.374754	−	0.927124i	$-0.377727\pi$
$227$	−3.62774	−	2.09447i	−0.240781	−	0.139015i	−0.615536	+	0.788109i	$0.711060\pi$
$228$	−1.30042	−	0.750797i	−0.0861223	−	0.0497227i
$229$		−	24.2635i		−	1.60338i	−0.597741	−	0.801689i	$-0.703935\pi$
$229$		−	24.2635i		−	1.60338i	0.597741	−	0.801689i	$-0.296065\pi$
$230$	2.49479	−	4.32111i	0.164502	−	0.284925i
$231$	10.6862	+	18.5090i	0.703100	+	1.21781i
$232$	−7.37199	+	4.25622i	−0.483995	+	0.279434i
$233$	−17.9212			−1.17405			−0.587027	−	0.809567i	$-0.699702\pi$
$233$	−17.9212			−1.17405			−0.587027	+	0.809567i	$0.699702\pi$
$234$	−1.43243	−	2.27326i	−0.0936407	−	0.148608i
$235$	−18.3346			−1.19602
$236$	−4.78593	+	2.76316i	−0.311537	+	0.179866i
$237$	−2.28598	−	3.95943i	−0.148490	−	0.257193i
$238$	−5.39437	+	9.34333i	−0.349665	+	0.605638i
$239$			22.3178i			1.44362i	0.692093	+	0.721808i	$0.256689\pi$
$239$			22.3178i			1.44362i	−0.692093	+	0.721808i	$0.743311\pi$
$240$	3.88656	+	2.24390i	0.250876	+	0.144843i
$241$	−19.3957	−	11.1981i	−1.24939	−	0.721334i	−0.278399	−	0.960465i	$-0.589804\pi$
$241$	−19.3957	−	11.1981i	−1.24939	−	0.721334i	−0.970987	+	0.239132i	$0.923137\pi$
$242$			3.54939i			0.228163i
$243$	−3.77400	+	6.53675i	−0.242102	+	0.419333i
$244$	−2.99576	−	5.18882i	−0.191784	−	0.332180i
$245$	17.9208	−	10.3466i	1.14492	−	0.661017i
$246$	−15.9827			−1.01902
$247$	−3.60286	+	0.139408i	−0.229244	+	0.00887030i
$248$	1.71712			0.109037
$249$	1.59096	−	0.918540i	0.100823	−	0.0582101i
$250$	1.59549	+	2.76347i	0.100908	+	0.174777i
$251$	1.84333	−	3.19274i	0.116350	−	0.201524i	−0.801969	−	0.597366i	$-0.796214\pi$
$251$	1.84333	−	3.19274i	0.116350	−	0.201524i	0.918318	+	0.395842i	$0.129547\pi$
$252$			2.78075i			0.175171i
$253$	−5.51487	−	3.18401i	−0.346717	−	0.200177i
$254$	9.75890	+	5.63430i	0.612328	+	0.353528i
$255$		−	12.9756i		−	0.812562i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.35412	+	11.0057i	0.396359	+	0.686514i	0.993274	−	0.115791i	$-0.0369402\pi$
$257$	6.35412	+	11.0057i	0.396359	+	0.686514i	−0.596915	+	0.802305i	$0.703607\pi$
$258$	7.05762	−	4.07472i	0.439388	−	0.253681i
$259$	−19.4803			−1.21045
$260$	10.7678	−	0.416647i	0.667794	−	0.0258394i
$261$	6.34362			0.392660
$262$	11.0519	−	6.38083i	0.682790	−	0.394209i
$263$	−1.62458	−	2.81385i	−0.100176	−	0.173510i	0.811581	−	0.584240i	$-0.198607\pi$
$263$	−1.62458	−	2.81385i	−0.100176	−	0.173510i	−0.911757	+	0.410730i	$0.865274\pi$
$264$	2.86381	−	4.96027i	0.176255	−	0.305283i
$265$			39.7107i			2.43941i
$266$	3.23154	+	1.86573i	0.198138	+	0.114395i
$267$	−19.2701	−	11.1256i	−1.17931	−	0.680875i
$268$		−	7.35059i		−	0.449009i
$269$	−5.47011	+	9.47451i	−0.333519	+	0.577671i	−0.983199	−	0.182536i	$-0.941569\pi$
$269$	−5.47011	+	9.47451i	−0.333519	+	0.577671i	0.649681	+	0.760207i	$0.274903\pi$
$270$	−8.40391	−	14.5560i	−0.511446	−	0.885850i
$271$	−0.838793	+	0.484277i	−0.0509530	+	0.0294178i	−0.525260	−	0.850942i	$-0.676032\pi$
$271$	−0.838793	+	0.484277i	−0.0509530	+	0.0294178i	0.474307	+	0.880359i	$0.342699\pi$
$272$	2.89129			0.175310
$273$	−10.7701	−	17.0921i	−0.651837	−	1.03446i
$274$	−8.10390			−0.489575
$275$	−12.9898	+	7.49965i	−0.783313	+	0.452246i
$276$	1.25344	+	2.17103i	0.0754484	+	0.130680i
$277$	4.01320	−	6.95107i	0.241130	−	0.417649i	−0.719907	−	0.694071i	$-0.755815\pi$
$277$	4.01320	−	6.95107i	0.241130	−	0.417649i	0.961036	+	0.276422i	$0.0891487\pi$
$278$		−	9.90009i		−	0.593768i
$279$	−1.10819	−	0.639815i	−0.0663457	−	0.0383047i
$280$	−9.65809	−	5.57610i	−0.577182	−	0.333236i
$281$		−	4.41792i		−	0.263551i	−0.991280	−	0.131775i	$-0.957932\pi$
$281$		−	4.41792i		−	0.263551i	0.991280	−	0.131775i	$-0.0420678\pi$
$282$	4.60588	−	7.97761i	0.274276	−	0.475060i
$283$	−7.89502	−	13.6746i	−0.469310	−	0.812870i	0.530074	−	0.847951i	$-0.322164\pi$
$283$	−7.89502	−	13.6746i	−0.469310	−	0.812870i	−0.999384	+	0.0350818i	$0.988831\pi$
$284$	−8.45239	+	4.87999i	−0.501557	+	0.289574i
$285$	−4.48781			−0.265835
$286$	−0.531752	−	13.7426i	−0.0314431	−	0.812617i
$287$	39.7171			2.34442
$288$	0.645378	−	0.372609i	0.0380292	−	0.0219562i
$289$	4.32021	+	7.48282i	0.254130	+	0.440166i
$290$	−12.7206	+	22.0326i	−0.746977	+	1.29380i
$291$		−	22.3422i		−	1.30972i
$292$	−0.102393	−	0.0591166i	−0.00599210	−	0.00345954i
$293$	−29.4499	−	17.0029i	−1.72048	−	0.993320i	−0.917935	−	0.396730i	$-0.870145\pi$
$293$	−29.4499	−	17.0029i	−1.72048	−	0.993320i	−0.802546	−	0.596590i	$-0.796522\pi$
$294$			10.3967i			0.606349i
$295$	−8.25825	+	14.3037i	−0.480814	+	0.832794i
$296$	2.61028	+	4.52113i	0.151719	+	0.262785i
$297$	−18.5773	+	10.7256i	−1.07796	+	0.622363i
$298$	23.1692			1.34215
$299$	5.32543	+	2.80590i	0.307978	+	0.162269i
$300$	5.90474			0.340911
$301$	−17.5382	+	10.1257i	−1.01088	+	0.583634i
$302$	10.0695	+	17.4409i	0.579435	+	1.00361i
$303$	10.8302	−	18.7585i	0.622180	−	1.07765i
$304$		−	1.00000i		−	0.0573539i
$305$	−15.5078	−	8.95344i	−0.887975	−	0.512672i
$306$	−1.86598	−	1.07732i	−0.106671	−	0.0615864i
$307$		−	29.2156i		−	1.66743i	−0.552199	−	0.833713i	$-0.686211\pi$
$307$		−	29.2156i		−	1.66743i	0.552199	−	0.833713i	$-0.313789\pi$
$308$	−7.11658	+	12.3263i	−0.405505	+	0.702354i
$309$	6.95066	+	12.0389i	0.395409	+	0.684869i
$310$	4.44441	−	2.56598i	0.252425	−	0.145738i
$311$	13.1516			0.745761			0.372881	−	0.927879i	$-0.378370\pi$
$311$	13.1516			0.745761			0.372881	+	0.927879i	$0.378370\pi$
$312$	−2.52372	+	4.78988i	−0.142878	+	0.271174i
$313$	22.1828			1.25385			0.626924	−	0.779080i	$-0.284314\pi$
$313$	22.1828			1.25385			0.626924	+	0.779080i	$0.284314\pi$
$314$	11.3363	−	6.54501i	0.639744	−	0.369356i
$315$	4.15541	+	7.19739i	0.234131	+	0.405527i
$316$	1.52237	−	2.63682i	0.0856400	−	0.148333i
$317$			25.2932i			1.42061i	0.703896	+	0.710303i	$0.251442\pi$
$317$			25.2932i			1.42061i	−0.703896	+	0.710303i	$0.748558\pi$
$318$	−17.2786	−	9.97581i	−0.968936	−	0.559416i
$319$	28.1195	+	16.2348i	1.57439	+	0.908973i
$320$			2.98870i			0.167073i
$321$	8.75664	−	15.1670i	0.488748	−	0.846537i
$322$	−3.11481	−	5.39500i	−0.173581	−	0.300652i
$323$	−2.50393	+	1.44565i	−0.139323	+	0.0804380i
$324$	6.20900			0.344944
$325$	11.9954	−	7.55854i	0.665384	−	0.419272i
$326$	5.90255			0.326912
$327$	−7.89436	+	4.55781i	−0.436559	+	0.252048i
$328$	−5.32192	−	9.21784i	−0.293854	−	0.508970i
$329$	−11.4456	+	19.8244i	−0.631017	+	1.09295i
$330$		−	17.1181i		−	0.942323i
$331$	23.9226	+	13.8117i	1.31491	+	0.759162i	0.982905	−	0.184116i	$-0.0589422\pi$
$331$	23.9226	+	13.8117i	1.31491	+	0.759162i	0.332003	+	0.943278i	$0.392276\pi$
$332$	1.05951	+	0.611710i	0.0581483	+	0.0335720i
$333$		−	3.89045i		−	0.213195i
$334$	−8.32836	+	14.4251i	−0.455708	+	0.789309i
$335$	−10.9844	−	19.0255i	−0.600139	−	1.03947i
$336$	4.85246	−	2.80157i	0.264723	−	0.152838i
$337$	21.3984			1.16565			0.582824	−	0.812599i	$-0.301948\pi$
$337$	21.3984			1.16565			0.582824	+	0.812599i	$0.301948\pi$
$338$	1.00453	+	12.9611i	0.0546393	+	0.704993i
$339$	−7.94481			−0.431503
$340$	7.48350	−	4.32060i	0.405850	−	0.234318i
$341$	−3.27487	−	5.67223i	−0.177344	−	0.307169i
$342$	−0.372609	+	0.645378i	−0.0201484	+	0.0348980i
$343$			0.284381i			0.0153551i
$344$	4.70009	+	2.71360i	0.253412	+	0.146307i
$345$	6.48855	+	3.74616i	0.349332	+	0.201687i
$346$		−	9.47289i		−	0.509266i
$347$	4.24949	−	7.36033i	0.228124	−	0.395123i	−0.729128	−	0.684378i	$-0.760074\pi$
$347$	4.24949	−	7.36033i	0.228124	−	0.395123i	0.957252	+	0.289254i	$0.0934074\pi$
$348$	−6.39111	−	11.0697i	−0.342599	−	0.593400i
$349$	−18.7334	+	10.8157i	−1.00278	+	0.578953i	−0.909068	−	0.416647i	$-0.863205\pi$
$349$	−18.7334	+	10.8157i	−1.00278	+	0.578953i	−0.0937073	+	0.995600i	$0.529872\pi$
$350$	−14.6733			−0.784320
$351$	17.1552	−	10.8098i	0.915675	−	0.576986i
$352$	3.81437			0.203306
$353$	−25.0876	+	14.4843i	−1.33528	+	0.770922i	−0.986103	−	0.166137i	$-0.946871\pi$
$353$	−25.0876	+	14.4843i	−1.33528	+	0.770922i	−0.349173	+	0.937058i	$0.613537\pi$
$354$	−4.14914	−	7.18652i	−0.220524	−	0.381959i
$355$	−14.5848	+	25.2616i	−0.774082	+	1.34075i
$356$		−	14.8184i		−	0.785372i
$357$	−14.0299	−	8.10015i	−0.742540	−	0.428706i
$358$	4.33395	+	2.50220i	0.229056	+	0.132246i
$359$			7.42119i			0.391675i	0.980636	+	0.195838i	$0.0627425\pi$
$359$			7.42119i			0.391675i	−0.980636	+	0.195838i	$0.937257\pi$
$360$	1.11362	−	1.92884i	0.0586927	−	0.101659i
$361$	0.500000	+	0.866025i	0.0263158	+	0.0455803i
$362$	−1.70953	+	0.986997i	−0.0898509	+	0.0518754i
$363$	−5.32973			−0.279738
$364$	6.27145	−	11.9029i	0.328713	−	0.623880i
$365$	−0.353364			−0.0184959
$366$	7.79149	−	4.49842i	0.407268	−	0.235136i
$367$	−6.80675	−	11.7896i	−0.355310	−	0.615414i	0.631861	−	0.775082i	$-0.282291\pi$
$367$	−6.80675	−	11.7896i	−0.355310	−	0.615414i	−0.987171	+	0.159667i	$0.948958\pi$
$368$	−0.834742	+	1.44582i	−0.0435139	+	0.0753684i
$369$			7.93198i			0.412923i
$370$	13.5123	+	7.80133i	0.702471	+	0.405572i
$371$	42.9374	+	24.7899i	2.22920	+	1.28703i
$372$			2.57842i			0.133685i
$373$	1.36842	−	2.37018i	0.0708544	−	0.122723i	−0.828422	−	0.560105i	$-0.810761\pi$
$373$	1.36842	−	2.37018i	0.0708544	−	0.122723i	0.899276	+	0.437382i	$0.144094\pi$
$374$	−5.51423	−	9.55092i	−0.285134	−	0.493866i
$375$	−4.14960	+	2.39577i	−0.214285	+	0.123717i
$376$	6.13466			0.316371
$377$	−27.1535	−	14.3068i	−1.39848	−	0.736839i
$378$	−20.9850			−1.07935
$379$	1.40477	−	0.811042i	0.0721579	−	0.0416604i	−0.463487	−	0.886104i	$-0.653402\pi$
$379$	1.40477	−	0.811042i	0.0721579	−	0.0416604i	0.535645	+	0.844443i	$0.320069\pi$
$380$	−1.49435	−	2.58829i	−0.0766585	−	0.132776i
$381$	−8.46043	+	14.6539i	−0.433441	+	0.750742i
$382$			20.8136i			1.06492i
$383$	27.6931	+	15.9886i	1.41505	+	0.816981i	0.995859	−	0.0909151i	$-0.0289792\pi$
$383$	27.6931	+	15.9886i	1.41505	+	0.816981i	0.419195	+	0.907896i	$0.362313\pi$
$384$	−1.30042	−	0.750797i	−0.0663617	−	0.0383139i
$385$			42.5386i			2.16797i
$386$	−10.6532	+	18.4519i	−0.542233	+	0.939175i
$387$	−2.02222	−	3.50259i	−0.102795	−	0.178047i
$388$	12.8856	−	7.43949i	0.654166	−	0.377683i
$389$	4.42183			0.224195			0.112098	−	0.993697i	$-0.464243\pi$
$389$	4.42183			0.224195			0.112098	+	0.993697i	$0.464243\pi$
$390$	0.625635	+	16.1689i	0.0316803	+	0.818745i
$391$	4.82697			0.244110
$392$	−5.99618	+	3.46189i	−0.302853	+	0.174852i
$393$	9.58141	+	16.5955i	0.483318	+	0.837131i
$394$	−4.31123	+	7.46727i	−0.217197	+	0.376195i
$395$		−	9.09981i		−	0.457861i
$396$	−2.46171	−	1.42127i	−0.123705	−	0.0714213i
$397$	−0.197215	−	0.113862i	−0.00989796	−	0.00571459i	0.495043	−	0.868869i	$-0.335152\pi$
$397$	−0.197215	−	0.113862i	−0.00989796	−	0.00571459i	−0.504941	+	0.863154i	$0.668486\pi$
$398$			4.00411i			0.200708i
$399$	−2.80157	+	4.85246i	−0.140254	+	0.242927i
$400$	1.96616	+	3.40549i	0.0983080	+	0.170274i
$401$	5.89027	−	3.40075i	0.294146	−	0.169825i	−0.345664	−	0.938358i	$-0.612346\pi$
$401$	5.89027	−	3.40075i	0.294146	−	0.169825i	0.639810	+	0.768533i	$0.279013\pi$
$402$	11.0376			0.550505
$403$	3.30058	+	5.23801i	0.164414	+	0.260924i
$404$	14.4250			0.717669
$405$	16.0707	−	9.27841i	0.798558	−	0.461048i
$406$	15.8819	+	27.5083i	0.788206	+	1.36521i
$407$	9.95655	−	17.2452i	0.493528	−	0.854815i
$408$			4.34155i			0.214939i
$409$	13.9269	+	8.04071i	0.688642	+	0.397588i	0.803103	−	0.595840i	$-0.203181\pi$
$409$	13.9269	+	8.04071i	0.688642	+	0.397588i	−0.114461	+	0.993428i	$0.536514\pi$
$410$	−27.5493	−	15.9056i	−1.36057	−	0.785523i
$411$		−	12.1688i		−	0.600241i
$412$	−4.62886	+	8.01742i	−0.228047	+	0.394990i
$413$	10.3106	+	17.8585i	0.507352	+	0.878759i
$414$	1.07745	−	0.622065i	0.0529537	−	0.0305728i
$415$	3.65644			0.179487
$416$	−3.60286	+	0.139408i	−0.176645	+	0.00683502i
$417$	14.8659			0.727986
$418$	−3.30334	+	1.90718i	−0.161572	+	0.0932834i
$419$	10.6998	+	18.5325i	0.522718	+	0.905373i	0.999651	+	0.0264337i	$0.00841510\pi$
$419$	10.6998	+	18.5325i	0.522718	+	0.905373i	−0.476933	+	0.878940i	$0.658252\pi$
$420$	8.37304	−	14.5025i	0.408562	−	0.707651i
$421$		−	26.3895i		−	1.28615i	−0.765804	−	0.643074i	$-0.777659\pi$
$421$		−	26.3895i		−	1.28615i	0.765804	−	0.643074i	$-0.222341\pi$
$422$	7.18728	+	4.14958i	0.349871	+	0.201998i
$423$	−3.95917	−	2.28583i	−0.192501	−	0.111141i
$424$		−	13.2870i		−	0.645272i
$425$	5.68475	−	9.84627i	0.275751	−	0.477614i
$426$	−7.32776	−	12.6920i	−0.355031	−	0.614932i
$427$	−19.3619	+	11.1786i	−0.936986	+	0.540969i
$428$	11.6631			0.563759
$429$	20.6358	−	0.798475i	0.996306	−	0.0385507i
$430$	16.2202			0.782210
$431$	−19.5270	+	11.2739i	−0.940585	+	0.543047i	−0.890144	−	0.455680i	$-0.849396\pi$
$431$	−19.5270	+	11.2739i	−0.940585	+	0.543047i	−0.0504412	+	0.998727i	$0.516063\pi$
$432$	2.81190	+	4.87035i	0.135287	+	0.234325i
$433$	5.75643	−	9.97043i	0.276636	−	0.479148i	−0.693910	−	0.720061i	$-0.744114\pi$
$433$	5.75643	−	9.97043i	0.276636	−	0.479148i	0.970547	+	0.240913i	$0.0774469\pi$
$434$		−	6.40737i		−	0.307564i
$435$	−33.0841	−	19.1011i	−1.58626	−	0.915827i
$436$	−5.25733	−	3.03532i	−0.251780	−	0.145365i
$437$		−	1.66948i		−	0.0798623i
$438$	0.0887692	−	0.153753i	0.00424155	−	0.00734659i
$439$	−5.82242	−	10.0847i	−0.277889	−	0.481318i	0.692971	−	0.720966i	$-0.256301\pi$
$439$	−5.82242	−	10.0847i	−0.277889	−	0.481318i	−0.970860	+	0.239648i	$0.922968\pi$
$440$	9.87268	−	5.69999i	0.470662	−	0.271737i
$441$	5.15973			0.245701
$442$	5.55752	+	8.81978i	0.264345	+	0.419514i
$443$	26.0168			1.23609			0.618047	−	0.786141i	$-0.287924\pi$
$443$	26.0168			1.23609			0.618047	+	0.786141i	$0.287924\pi$
$444$	−6.78890	+	3.91957i	−0.322187	+	0.186015i
$445$	−22.1438	−	38.3542i	−1.04972	−	1.81817i
$446$	4.40799	−	7.63487i	0.208725	−	0.361522i
$447$			34.7906i			1.64554i
$448$	3.23154	+	1.86573i	0.152676	+	0.0881474i
$449$	−10.1597	−	5.86571i	−0.479466	−	0.276820i	0.240728	−	0.970593i	$-0.422614\pi$
$449$	−10.1597	−	5.86571i	−0.479466	−	0.276820i	−0.720194	+	0.693773i	$0.755947\pi$
$450$		−	2.93043i		−	0.138142i
$451$	−20.2998	+	35.1602i	−0.955878	+	1.65563i
$452$	−2.64546	−	4.58207i	−0.124432	−	0.215523i
$453$	−26.1892	+	15.1203i	−1.23047	+	0.710414i
$454$	4.18895			0.196597
$455$	−1.55470	−	40.1798i	−0.0728856	−	1.88366i
$456$	1.50159			0.0703185
$457$	31.8419	−	18.3839i	1.48950	−	0.859963i	0.489572	−	0.871963i	$-0.337153\pi$
$457$	31.8419	−	18.3839i	1.48950	−	0.859963i	0.999928	+	0.0119994i	$0.00381960\pi$
$458$	12.1318	+	21.0128i	0.566880	+	0.981865i
$459$	8.13002	−	14.0816i	0.379477	−	0.657273i
$460$			4.98959i			0.232641i
$461$	−10.3942	−	6.00108i	−0.484105	−	0.279498i	0.238021	−	0.971260i	$-0.423501\pi$
$461$	−10.3942	−	6.00108i	−0.484105	−	0.279498i	−0.722126	+	0.691762i	$0.756835\pi$
$462$	−18.5090	−	10.6862i	−0.861119	−	0.497167i
$463$			15.5101i			0.720815i	0.932795	+	0.360407i	$0.117362\pi$
$463$			15.5101i			0.720815i	−0.932795	+	0.360407i	$0.882638\pi$
$464$	4.25622	−	7.37199i	0.197590	−	0.342236i
$465$	3.85306	+	6.67369i	0.178681	+	0.309485i
$466$	15.5202	−	8.96058i	0.718959	−	0.415091i
$467$	25.8302			1.19528			0.597639	−	0.801765i	$-0.296106\pi$
$467$	25.8302			1.19528			0.597639	+	0.801765i	$0.296106\pi$
$468$	2.37715	+	1.25249i	0.109884	+	0.0578962i
$469$	−27.4284			−1.26653
$470$	15.8783	−	9.16732i	0.732409	−	0.422857i
$471$	9.82794	+	17.0225i	0.452848	+	0.784355i
$472$	2.76316	−	4.78593i	0.127185	−	0.220290i
$473$		−	20.7013i		−	0.951847i
$474$	3.95943	+	2.28598i	0.181863	+	0.104999i
$475$	−3.40549	−	1.96616i	−0.156255	−	0.0902136i
$476$		−	10.7887i		−	0.494501i
$477$	−4.95084	+	8.57511i	−0.226684	+	0.392627i
$478$	−11.1589	−	19.3278i	−0.510396	−	0.884031i
$479$	8.71411	−	5.03109i	0.398158	−	0.229876i	−0.287531	−	0.957771i	$-0.592834\pi$
$479$	8.71411	−	5.03109i	0.398158	−	0.229876i	0.685689	+	0.727895i	$0.259501\pi$
$480$	−4.48781			−0.204840
$481$	−8.77417	+	16.6529i	−0.400068	+	0.759306i
$482$	22.3962			1.02012
$483$	8.10110	−	4.67717i	0.368613	−	0.212819i
$484$	−1.77469	−	3.07386i	−0.0806679	−	0.139721i
$485$	22.2344	−	38.5111i	1.00961	−	1.74870i
$486$		−	7.54799i		−	0.342384i
$487$	−4.99457	−	2.88362i	−0.226326	−	0.130669i	0.382550	−	0.923935i	$-0.375046\pi$
$487$	−4.99457	−	2.88362i	−0.226326	−	0.130669i	−0.608876	+	0.793266i	$0.708379\pi$
$488$	5.18882	+	2.99576i	0.234887	+	0.135612i
$489$			8.86323i			0.400809i
$490$	−10.3466	+	17.9208i	−0.467410	+	0.809578i
$491$	9.73364	+	16.8592i	0.439273	+	0.760843i	0.997634	−	0.0687552i	$-0.0219027\pi$
$491$	9.73364	+	16.8592i	0.439273	+	0.760843i	−0.558361	+	0.829598i	$0.688569\pi$
$492$	13.8414	−	7.99136i	0.624021	−	0.360278i
$493$	−24.6120			−1.10847
$494$	3.05046	−	1.92216i	0.137247	−	0.0864820i
$495$	−8.49548			−0.381843
$496$	−1.48707	+	0.858561i	−0.0667715	+	0.0385505i
$497$	18.2095	+	31.5397i	0.816807	+	1.41475i
$498$	−0.918540	+	1.59096i	−0.0411608	+	0.0712925i
$499$		−	4.74563i		−	0.212444i	−0.994342	−	0.106222i	$-0.966125\pi$
$499$		−	4.74563i		−	0.212444i	0.994342	−	0.106222i	$-0.0338754\pi$
$500$	−2.76347	−	1.59549i	−0.123586	−	0.0713524i
$501$	−21.6607	−	12.5058i	−0.967729	−	0.558719i
$502$			3.68665i			0.164543i
$503$	15.2234	−	26.3678i	0.678779	−	1.17568i	−0.296569	−	0.955011i	$-0.595843\pi$
$503$	15.2234	−	26.3678i	0.678779	−	1.17568i	0.975349	−	0.220669i	$-0.0708240\pi$
$504$	−1.39038	−	2.40820i	−0.0619322	−	0.107270i
$505$	37.3360	−	21.5559i	1.66143	−	0.959227i
$506$	6.36802			0.283093
$507$	−19.4623	+	1.50840i	−0.864353	+	0.0669903i
$508$	−11.2686			−0.499963
$509$	5.50741	−	3.17971i	0.244112	−	0.140938i	−0.372953	−	0.927850i	$-0.621655\pi$
$509$	5.50741	−	3.17971i	0.244112	−	0.140938i	0.617065	+	0.786912i	$0.288322\pi$
$510$	6.48779	+	11.2372i	0.287284	+	0.497591i
$511$	−0.220591	+	0.382075i	−0.00975839	+	0.0169020i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.87035	−	2.81190i	−0.215031	−	0.124148i
$514$	−11.0057	−	6.35412i	−0.485439	−	0.280268i
$515$			27.6685i			1.21922i
$516$	−4.07472	+	7.05762i	−0.179379	+	0.310694i
$517$	−11.6999	−	20.2648i	−0.514561	−	0.891246i
$518$	16.8704	−	9.74014i	0.741244	−	0.427957i
$519$	14.2244			0.624383
$520$	−9.11691	+	5.74475i	−0.399803	+	0.251924i
$521$	8.30076			0.363663			0.181832	−	0.983330i	$-0.441797\pi$
$521$	8.30076			0.363663			0.181832	+	0.983330i	$0.441797\pi$
$522$	−5.49374	+	3.17181i	−0.240454	+	0.138826i
$523$	−0.0559583	−	0.0969226i	−0.00244688	−	0.00423813i	0.864799	−	0.502118i	$-0.167446\pi$
$523$	−0.0559583	−	0.0969226i	−0.00244688	−	0.00423813i	−0.867246	+	0.497879i	$0.834112\pi$
$524$	−6.38083	+	11.0519i	−0.278748	+	0.482805i
$525$		−	22.0333i		−	0.961613i
$526$	2.81385	+	1.62458i	0.122690	+	0.0708350i
$527$	4.29956	+	2.48235i	0.187292	+	0.108133i
$528$			5.72763i			0.249263i
$529$	10.1064	−	17.5048i	0.439409	−	0.761079i
$530$	−19.8554	−	34.3905i	−0.862462	−	1.49383i
$531$	−3.56656	+	2.05915i	−0.154776	+	0.0893597i
$532$	−3.73146			−0.161779
$533$	17.8891	−	33.9525i	0.774862	−	1.47064i
$534$	22.2512			0.962903
$535$	30.1876	−	17.4288i	1.30512	−	0.753513i
$536$	3.67530	+	6.36580i	0.158749	+	0.274961i
$537$	−3.75729	+	6.50782i	−0.162139	+	0.280833i
$538$		−	10.9402i		−	0.471667i
$539$	22.8716	+	13.2049i	0.985150	+	0.568777i
$540$	14.5560	+	8.40391i	0.626391	+	0.361647i
$541$			36.1474i			1.55410i	0.629440	+	0.777049i	$0.283284\pi$
$541$			36.1474i			1.55410i	−0.629440	+	0.777049i	$0.716716\pi$
$542$	0.484277	−	0.838793i	0.0208015	−	0.0360292i
$543$	−1.48207	−	2.56702i	−0.0636016	−	0.110161i
$544$	−2.50393	+	1.44565i	−0.107355	+	0.0619816i
$545$	−18.1433			−0.777174
$546$	17.8733	+	9.41717i	0.764905	+	0.403018i
$547$	−5.56274			−0.237846			−0.118923	−	0.992904i	$-0.537944\pi$
$547$	−5.56274			−0.237846			−0.118923	+	0.992904i	$0.537944\pi$
$548$	7.01819	−	4.05195i	0.299802	−	0.173091i
$549$	−2.23250	−	3.86680i	−0.0952807	−	0.165031i
$550$	7.49965	−	12.9898i	0.319786	−	0.553886i
$551$			8.51244i			0.362642i
$552$	−2.17103	−	1.25344i	−0.0924051	−	0.0533501i
$553$	−9.83919	−	5.68066i	−0.418405	−	0.241566i
$554$			8.02640i			0.341009i
$555$	−11.7144	+	20.2900i	−0.497250	+	0.861262i
$556$	4.95004	+	8.57373i	0.209929	+	0.363607i
$557$	11.0129	−	6.35830i	0.466631	−	0.269410i	−0.248197	−	0.968710i	$-0.579838\pi$
$557$	11.0129	−	6.35830i	0.466631	−	0.269410i	0.714829	+	0.699300i	$0.246505\pi$
$558$	1.27963			0.0541711
$559$	0.756592	+	19.5534i	0.0320004	+	0.827020i
$560$	11.1522			0.471267
$561$	14.3416	−	8.28013i	0.605503	−	0.349587i
$562$	2.20896	+	3.82603i	0.0931793	+	0.161391i
$563$	−16.1136	+	27.9095i	−0.679106	+	1.17625i	0.296144	+	0.955143i	$0.404299\pi$
$563$	−16.1136	+	27.9095i	−0.679106	+	1.17625i	−0.975250	+	0.221104i	$0.929034\pi$
$564$			9.21176i			0.387885i
$565$	−13.6944	−	7.90648i	−0.576129	−	0.332628i
$566$	13.6746	+	7.89502i	0.574786	+	0.331853i
$567$		−	23.1686i		−	0.972990i
$568$	4.87999	−	8.45239i	0.204760	−	0.354654i
$569$	−1.84552	−	3.19653i	−0.0773680	−	0.134005i	0.824746	−	0.565504i	$-0.191318\pi$
$569$	−1.84552	−	3.19653i	−0.0773680	−	0.134005i	−0.902114	+	0.431499i	$0.857985\pi$
$570$	3.88656	−	2.24390i	0.162790	−	0.0939868i
$571$	21.2298			0.888440			0.444220	−	0.895918i	$-0.353481\pi$
$571$	21.2298			0.888440			0.444220	+	0.895918i	$0.353481\pi$
$572$	7.33181	+	11.6356i	0.306559	+	0.486508i
$573$	−31.2536			−1.30564
$574$	−34.3960	+	19.8585i	−1.43566	+	0.828879i
$575$	3.28247	+	5.68541i	0.136889	+	0.237098i
$576$	−0.372609	+	0.645378i	−0.0155254	+	0.0268907i
$577$		−	16.7181i		−	0.695983i	−0.937498	−	0.347992i	$-0.886864\pi$
$577$		−	16.7181i		−	0.695983i	0.937498	−	0.347992i	$-0.113136\pi$
$578$	−7.48282	−	4.32021i	−0.311244	−	0.179697i
$579$	−27.7072	−	15.9968i	−1.15147	−	0.664802i
$580$		−	25.4411i		−	1.05638i
$581$	2.28257	−	3.95353i	0.0946970	−	0.164020i
$582$	11.1711	+	19.3489i	0.463057	+	0.802038i
$583$	−43.8913	+	25.3407i	−1.81779	+	1.04950i
$584$	0.118233			0.00489253
$585$	8.02439	−	0.310493i	0.331768	−	0.0128373i
$586$	34.0058			1.40477
$587$	−22.3148	+	12.8835i	−0.921031	+	0.531757i	−0.883964	−	0.467555i	$-0.845135\pi$
$587$	−22.3148	+	12.8835i	−0.921031	+	0.531757i	−0.0370670	+	0.999313i	$0.511801\pi$
$588$	−5.19836	−	9.00382i	−0.214377	−	0.371311i
$589$	0.858561	−	1.48707i	0.0353764	−	0.0612737i
$590$		−	16.5165i		−	0.679973i
$591$	−11.2128	−	6.47371i	−0.461233	−	0.266293i
$592$	−4.52113	−	2.61028i	−0.185817	−	0.107282i
$593$		−	22.0804i		−	0.906734i	−0.891324	−	0.453367i	$-0.850223\pi$
$593$		−	22.0804i		−	0.906734i	0.891324	−	0.453367i	$-0.149777\pi$
$594$	10.7256	−	18.5773i	0.440077	−	0.762235i
$595$	−16.1222	−	27.9244i	−0.660944	−	1.14479i
$596$	−20.0651	+	11.5846i	−0.821898	+	0.474523i
$597$	−6.01254			−0.246077
$598$	−6.01491	+	0.232739i	−0.245968	+	0.00951740i
$599$	−24.2400			−0.990421			−0.495211	−	0.868773i	$-0.664909\pi$
$599$	−24.2400			−0.990421			−0.495211	+	0.868773i	$0.664909\pi$
$600$	−5.11366	+	2.95237i	−0.208764	+	0.120530i
$601$	12.5488	+	21.7351i	0.511875	+	0.886594i	0.999905	+	0.0137668i	$0.00438225\pi$
$601$	12.5488	+	21.7351i	0.511875	+	0.886594i	−0.488030	+	0.872827i	$0.662284\pi$
$602$	10.1257	−	17.5382i	0.412692	−	0.714803i
$603$		−	5.47779i		−	0.223073i
$604$	−17.4409	−	10.0695i	−0.709661	−	0.409723i
$605$	−9.18684	−	5.30402i	−0.373498	−	0.215639i
$606$			21.6604i			0.879895i
$607$	−19.5991	+	33.9466i	−0.795503	+	1.37785i	0.127017	+	0.991901i	$0.459460\pi$
$607$	−19.5991	+	33.9466i	−0.795503	+	1.37785i	−0.922520	+	0.385950i	$0.873874\pi$
$608$	0.500000	+	0.866025i	0.0202777	+	0.0351220i
$609$	−41.3062	+	23.8482i	−1.67381	+	0.966376i
$610$	17.9069			0.725028
$611$	11.7918	+	18.7135i	0.477044	+	0.757068i
$612$	2.15464			0.0870963
$613$	27.6129	−	15.9423i	1.11527	−	0.643904i	0.175084	−	0.984553i	$-0.443980\pi$
$613$	27.6129	−	15.9423i	1.11527	−	0.643904i	0.940190	+	0.340649i	$0.110647\pi$
$614$	14.6078	+	25.3015i	0.589524	+	1.02109i
$615$	23.8838	−	41.3679i	0.963087	−	1.66812i
$616$		−	14.2332i		−	0.573470i
$617$	25.2952	+	14.6042i	1.01835	+	0.587944i	0.913625	−	0.406558i	$-0.133271\pi$
$617$	25.2952	+	14.6042i	1.01835	+	0.587944i	0.104723	+	0.994501i	$0.466604\pi$
$618$	−12.0389	−	6.95066i	−0.484276	−	0.279597i
$619$			34.6290i			1.39186i	0.718111	+	0.695929i	$0.245007\pi$
$619$			34.6290i			1.39186i	−0.718111	+	0.695929i	$0.754993\pi$
$620$	−2.56598	+	4.44441i	−0.103052	+	0.178492i
$621$	4.69442	+	8.13097i	0.188380	+	0.326285i
$622$	−11.3897	+	6.57582i	−0.456684	+	0.263666i
$623$	−55.2942			−2.21531
$624$	−0.209334	−	5.41002i	−0.00838005	−	0.216574i
$625$	−29.1985			−1.16794
$626$	−19.2109	+	11.0914i	−0.767822	+	0.443302i
$627$	−2.86381	−	4.96027i	−0.114370	−	0.198094i
$628$	−6.54501	+	11.3363i	−0.261174	+	0.452367i
$629$			15.0942i			0.601843i
$630$	−7.19739	−	4.15541i	−0.286751	−	0.165556i
$631$	14.6981	+	8.48594i	0.585121	+	0.337820i	0.763166	−	0.646203i	$-0.223644\pi$
$631$	14.6981	+	8.48594i	0.585121	+	0.337820i	−0.178045	+	0.984022i	$0.556977\pi$
$632$			3.04474i			0.121113i
$633$	−6.23098	+	10.7924i	−0.247659	+	0.428958i
$634$	−12.6466	−	21.9045i	−0.502260	−	0.869940i
$635$	−29.1664	+	16.8392i	−1.15743	+	0.668245i
$636$	19.9516			0.791133
$637$	−22.0860	−	11.6368i	−0.875078	−	0.461066i
$638$	−32.4695			−1.28548
$639$	−6.29887	+	3.63665i	−0.249179	+	0.143864i
$640$	−1.49435	−	2.58829i	−0.0590693	−	0.102311i
$641$	−11.1397	+	19.2945i	−0.439991	+	0.762087i	−0.997688	−	0.0679575i	$-0.978352\pi$
$641$	−11.1397	+	19.2945i	−0.439991	+	0.762087i	0.557697	+	0.830045i	$0.311685\pi$
$642$			17.5133i			0.691194i
$643$	−36.8527	−	21.2769i	−1.45333	−	0.839080i	−0.454661	−	0.890664i	$-0.650240\pi$
$643$	−36.8527	−	21.2769i	−1.45333	−	0.839080i	−0.998669	+	0.0515840i	$0.983573\pi$
$644$	5.39500	+	3.11481i	0.212593	+	0.122741i
$645$			24.3562i			0.959025i
$646$	1.44565	−	2.50393i	0.0568782	−	0.0985160i
$647$	18.5821	+	32.1852i	0.730539	+	1.26533i	0.956653	+	0.291230i	$0.0940646\pi$
$647$	18.5821	+	32.1852i	0.730539	+	1.26533i	−0.226114	+	0.974101i	$0.572602\pi$
$648$	−5.37715	+	3.10450i	−0.211234	+	0.121956i
$649$	−21.0794			−0.827438
$650$	−6.60904	+	12.5436i	−0.259228	+	0.492000i
$651$	9.62126			0.377087
$652$	−5.11176	+	2.95127i	−0.200192	+	0.115581i
$653$	21.2206	+	36.7552i	0.830427	+	1.43834i	0.897700	+	0.440607i	$0.145237\pi$
$653$	21.2206	+	36.7552i	0.830427	+	1.43834i	−0.0672728	+	0.997735i	$0.521430\pi$
$654$	4.55781	−	7.89436i	0.178225	−	0.308694i
$655$			38.1407i			1.49028i
$656$	9.21784	+	5.32192i	0.359896	+	0.207786i
$657$	−0.0763051	−	0.0440548i	−0.00297695	−	0.00171874i
$658$		−	22.8912i		−	0.892392i
$659$	16.4373	−	28.4703i	0.640308	−	1.10905i	−0.345056	−	0.938582i	$-0.612140\pi$
$659$	16.4373	−	28.4703i	0.640308	−	1.10905i	0.985364	−	0.170464i	$-0.0545267\pi$
$660$	8.55907	+	14.8247i	0.333161	+	0.577053i
$661$	13.2299	−	7.63827i	0.514583	−	0.297094i	−0.220133	−	0.975470i	$-0.570649\pi$
$661$	13.2299	−	7.63827i	0.514583	−	0.297094i	0.734715	+	0.678376i	$0.237316\pi$
$662$	−27.6235			−1.07362
$663$	−13.2437	+	8.34514i	−0.514343	+	0.324098i
$664$	−1.22342			−0.0474779
$665$	−9.65809	+	5.57610i	−0.374525	+	0.216232i
$666$	1.94522	+	3.36923i	0.0753759	+	0.130555i
$667$	7.10569	−	12.3074i	0.275133	−	0.476545i
$668$		−	16.6567i		−	0.644468i
$669$	11.4645	+	6.61901i	0.443242	+	0.255906i
$670$	19.0255	+	10.9844i	0.735017	+	0.424363i
$671$		−	22.8539i		−	0.882264i
$672$	−2.80157	+	4.85246i	−0.108073	+	0.187188i
$673$	3.40953	+	5.90547i	0.131428	+	0.227639i	0.924227	−	0.381843i	$-0.124711\pi$
$673$	3.40953	+	5.90547i	0.131428	+	0.227639i	−0.792800	+	0.609482i	$0.791377\pi$
$674$	−18.5316	+	10.6992i	−0.713811	+	0.412119i
$675$	22.1146			0.851190
$676$	−7.35051	−	10.7224i	−0.282712	−	0.412400i
$677$	21.0962			0.810793			0.405396	−	0.914141i	$-0.367134\pi$
$677$	21.0962			0.810793			0.405396	+	0.914141i	$0.367134\pi$
$678$	6.88041	−	3.97240i	0.264240	−	0.152559i
$679$	−27.7602	−	48.0820i	−1.06534	−	1.84522i
$680$	−4.32060	+	7.48350i	−0.165688	+	0.286979i
$681$			6.29010i			0.241037i
$682$	5.67223	+	3.27487i	0.217201	+	0.125401i
$683$	−37.8584	−	21.8575i	−1.44861	−	0.836355i	−0.450211	−	0.892922i	$-0.648651\pi$
$683$	−37.8584	−	21.8575i	−1.44861	−	0.836355i	−0.998399	+	0.0565672i	$0.981984\pi$
$684$		−	0.745218i		−	0.0284941i
$685$	12.1101	−	20.9752i	0.462702	−	0.801423i
$686$	−0.142191	−	0.246281i	−0.00542886	−	0.00940306i
$687$	−31.5527	+	18.2170i	−1.20381	+	0.695021i
$688$	−5.42719			−0.206910
$689$	40.5314	−	25.5397i	1.54412	−	0.972983i
$690$	−7.49233			−0.285228
$691$	−37.8291	+	21.8407i	−1.43909	+	0.830858i	−0.997786	−	0.0665011i	$-0.978816\pi$
$691$	−37.8291	+	21.8407i	−1.43909	+	0.830858i	−0.441302	+	0.897359i	$0.645483\pi$
$692$	4.73645	+	8.20377i	0.180053	+	0.311860i
$693$	−5.30340	+	9.18576i	−0.201459	+	0.348938i
$694$			8.49897i			0.322617i
$695$	25.6243	+	14.7942i	0.971985	+	0.561176i
$696$	11.0697	+	6.39111i	0.419597	+	0.242254i
$697$		−	30.7745i		−	1.16567i
$698$	10.8157	−	18.7334i	0.409381	−	0.709069i
$699$	13.4552	+	23.3050i	0.508921	+	0.881476i
$700$	12.7074	−	7.33664i	0.480296	−	0.277299i
$701$	−12.9613			−0.489540			−0.244770	−	0.969581i	$-0.578712\pi$
$701$	−12.9613			−0.489540			−0.244770	+	0.969581i	$0.578712\pi$
$702$	−9.45189	+	17.9392i	−0.356739	+	0.677070i
$703$	5.22055			0.196897
$704$	−3.30334	+	1.90718i	−0.124499	+	0.0718797i
$705$	13.7656	+	23.8427i	0.518442	+	0.897968i
$706$	14.4843	−	25.0876i	0.545124	−	0.944182i
$707$		−	53.8262i		−	2.02434i
$708$	7.18652	+	4.14914i	0.270086	+	0.155934i
$709$	2.76382	+	1.59569i	0.103797	+	0.0599275i	0.551000	−	0.834505i	$-0.314246\pi$
$709$	2.76382	+	1.59569i	0.103797	+	0.0599275i	−0.447203	+	0.894433i	$0.647580\pi$
$710$		−	29.1696i		−	1.09472i
$711$	1.13450	−	1.96501i	0.0425470	−	0.0736935i
$712$	7.40919	+	12.8331i	0.277671	+	0.480940i
$713$	−2.48264	+	1.43335i	−0.0929757	+	0.0536795i
$714$	16.2003			0.606281
$715$	36.3645	+	19.1599i	1.35995	+	0.716541i
$716$	−5.00441			−0.187024
$717$	29.0224	−	16.7561i	1.08386	−	0.625768i
$718$	−3.71059	−	6.42694i	−0.138478	−	0.239851i
$719$	26.1018	−	45.2096i	0.973431	−	1.68603i	0.288413	−	0.957506i	$-0.406872\pi$
$719$	26.1018	−	45.2096i	0.973431	−	1.68603i	0.685018	−	0.728526i	$-0.259794\pi$
$720$			2.22723i			0.0830040i
$721$	29.9167	+	17.2724i	1.11415	+	0.643258i
$722$	−0.866025	−	0.500000i	−0.0322301	−	0.0186081i
$723$			33.6300i			1.25071i
$724$	0.986997	−	1.70953i	0.0366815	−	0.0635341i
$725$	−16.7368	−	28.9890i	−0.621589	−	1.07662i
$726$	4.61568	−	2.66487i	0.171304	−	0.0989025i
$727$	44.7559			1.65990			0.829952	−	0.557835i	$-0.188368\pi$
$727$	44.7559			1.65990			0.829952	+	0.557835i	$0.188368\pi$
$728$	0.520194	+	13.4439i	0.0192797	+	0.498264i
$729$	29.9610			1.10967
$730$	0.306022	−	0.176682i	0.0113264	−	0.00653929i
$731$	7.84581	+	13.5893i	0.290188	+	0.502620i
$732$	−4.49842	+	7.79149i	−0.166266	+	0.287982i
$733$			12.8805i			0.475753i	0.971295	+	0.237877i	$0.0764514\pi$
$733$			12.8805i			0.475753i	−0.971295	+	0.237877i	$0.923549\pi$
$734$	11.7896	+	6.80675i	0.435164	+	0.251242i
$735$	−26.9097	−	15.5363i	−0.992579	−	0.573066i
$736$		−	1.66948i		−	0.0615380i
$737$	14.0189	−	24.2815i	0.516394	−	0.894420i
$738$	−3.96599	−	6.86930i	−0.145990	−	0.252862i
$739$	26.9127	−	15.5381i	0.990000	−	0.571577i	0.0847255	−	0.996404i	$-0.472999\pi$
$739$	26.9127	−	15.5381i	0.990000	−	0.571577i	0.905274	+	0.424828i	$0.139665\pi$
$740$	−15.6027			−0.573565
$741$	2.88630	+	4.58055i	0.106031	+	0.168271i
$742$	−49.5798			−1.82013
$743$	−29.1802	+	16.8472i	−1.07052	+	0.618064i	−0.928323	−	0.371774i	$-0.878750\pi$
$743$	−29.1802	+	16.8472i	−1.07052	+	0.618064i	−0.142196	+	0.989839i	$0.545416\pi$
$744$	−1.28921	−	2.23298i	−0.0472647	−	0.0818649i
$745$	−34.6228	+	59.9685i	−1.26848	+	2.19707i
$746$			2.73685i			0.100203i
$747$	0.789568	+	0.455857i	0.0288888	+	0.0166790i
$748$	9.55092	+	5.51423i	0.349216	+	0.201620i
$749$		−	43.5205i		−	1.59021i
$750$	2.39577	−	4.14960i	0.0874813	−	0.151522i
$751$	0.851713	+	1.47521i	0.0310794	+	0.0538312i	0.881147	−	0.472843i	$-0.156772\pi$
$751$	0.851713	+	1.47521i	0.0310794	+	0.0538312i	−0.850067	+	0.526674i	$0.823439\pi$
$752$	−5.31277	+	3.06733i	−0.193737	+	0.111854i
$753$	−5.53585			−0.201738
$754$	30.6691	−	1.18670i	1.11690	−	0.0432170i
$755$	−60.1895			−2.19052
$756$	18.1735	−	10.4925i	0.660964	−	0.381608i
$757$	−17.6356	−	30.5457i	−0.640976	−	1.11020i	−0.985215	−	0.171321i	$-0.945196\pi$
$757$	−17.6356	−	30.5457i	−0.640976	−	1.11020i	0.344239	−	0.938882i	$-0.388137\pi$
$758$	−0.811042	+	1.40477i	−0.0294584	+	0.0510234i
$759$			9.56218i			0.347085i
$760$	2.58829	+	1.49435i	0.0938871	+	0.0542057i
$761$	−5.74275	−	3.31558i	−0.208175	−	0.120190i	0.392288	−	0.919842i	$-0.371684\pi$
$761$	−5.74275	−	3.31558i	−0.208175	−	0.120190i	−0.600463	+	0.799653i	$0.705017\pi$
$762$		−	16.9209i		−	0.612978i
$763$	−11.3262	+	19.6175i	−0.410035	+	0.710201i
$764$	−10.4068	−	18.0251i	−0.376505	−	0.652126i
$765$	5.57684	−	3.21979i	0.201631	−	0.116412i
$766$	−31.9773			−1.15539
$767$	19.9105	−	0.770411i	0.718927	−	0.0278179i
$768$	1.50159			0.0541841
$769$	17.0713	−	9.85610i	0.615606	−	0.355420i	−0.159550	−	0.987190i	$-0.551004\pi$
$769$	17.0713	−	9.85610i	0.615606	−	0.355420i	0.775156	+	0.631770i	$0.217671\pi$
$770$	−21.2693	−	36.8395i	−0.766492	−	1.32760i
$771$	9.54130	−	16.5260i	0.343622	−	0.595170i
$772$		−	21.3064i		−	0.766833i
$773$	9.37077	+	5.41022i	0.337043	+	0.194592i	0.658964	−	0.752175i	$-0.270995\pi$
$773$	9.37077	+	5.41022i	0.337043	+	0.194592i	−0.321920	+	0.946767i	$0.604328\pi$
$774$	3.50259	+	2.02222i	0.125898	+	0.0726872i
$775$			6.75227i			0.242549i
$776$	−7.43949	+	12.8856i	−0.267062	+	0.462565i
$777$	14.6257	+	25.3325i	0.524695	+	0.908799i
$778$	−3.82941	+	2.21091i	−0.137291	+	0.0792651i
$779$	−10.6438			−0.381355
$780$	−8.62628	−	13.6899i	−0.308870	−	0.490176i
$781$	−37.2281			−1.33213
$782$	−4.18028	+	2.41349i	−0.149486	+	0.0863061i
$783$	−23.9361	−	41.4585i	−0.855406	−	1.48161i
$784$	3.46189	−	5.99618i	0.123639	−	0.214149i
$785$			39.1221i			1.39633i
$786$	−16.5955	−	9.58141i	−0.591941	−	0.341757i
$787$	41.5800	+	24.0062i	1.48217	+	0.855729i	0.999795	−	0.0202373i	$-0.00644218\pi$
$787$	41.5800	+	24.0062i	1.48217	+	0.855729i	0.482372	+	0.875967i	$0.339776\pi$
$788$		−	8.62246i		−	0.307162i
$789$	−2.43946	+	4.22526i	−0.0868470	+	0.150423i
$790$	4.54990	+	7.88066i	0.161878	+	0.280381i
$791$	−17.0978	+	9.87143i	−0.607928	+	0.350988i
$792$	2.84253			0.101005
$793$	0.835265	+	21.5866i	0.0296611	+	0.766563i
$794$	0.227725			0.00808165
$795$	51.6406	−	29.8147i	1.83150	−	1.05742i
$796$	−2.00205	−	3.46766i	−0.0709609	−	0.122908i
$797$	11.4302	−	19.7976i	0.404878	−	0.701268i	−0.589430	−	0.807820i	$-0.700647\pi$
$797$	11.4302	−	19.7976i	0.404878	−	0.701268i	0.994307	+	0.106551i	$0.0339808\pi$
$798$		−	5.60313i		−	0.198349i
$799$	15.3608	+	8.86855i	0.543425	+	0.313747i
$800$	−3.40549	−	1.96616i	−0.120402	−	0.0695142i
$801$		−	11.0429i		−	0.390182i
$802$	−3.40075	+	5.89027i	−0.120085	+	0.207993i
$803$	−0.225493	−	0.390564i	−0.00795746	−	0.0137827i
$804$	−9.55884	+	5.51880i	−0.337114	+	0.194633i
$805$	18.6184			0.656214
$806$	−5.47739	−	2.88596i	−0.192933	−	0.101654i
$807$	16.4278			0.578285
$808$	−12.4924	+	7.21248i	−0.439481	+	0.253734i
$809$	−8.15307	−	14.1215i	−0.286647	−	0.496487i	0.686360	−	0.727262i	$-0.259207\pi$
$809$	−8.15307	−	14.1215i	−0.286647	−	0.496487i	−0.973007	+	0.230775i	$0.925874\pi$
$810$	−9.27841	+	16.0707i	−0.326010	+	0.564666i
$811$			0.810412i			0.0284574i	0.999899	+	0.0142287i	$0.00452929\pi$
$811$			0.810412i			0.0284574i	−0.999899	+	0.0142287i	$0.995471\pi$
$812$	−27.5083	−	15.8819i	−0.965351	−	0.557346i
$813$	1.25953	+	0.727187i	0.0441735	+	0.0255036i
$814$			19.9131i			0.697954i
$815$	−8.82047	+	15.2775i	−0.308968	+	0.535148i
$816$	−2.17077	−	3.75989i	−0.0759923	−	0.131623i
$817$	4.70009	−	2.71360i	0.164435	−	0.0949367i
$818$	−16.0814			−0.562274
$819$	4.67360	−	8.87023i	0.163309	−	0.309951i
$820$	31.8112			1.11090
$821$	5.63800	−	3.25510i	0.196768	−	0.113604i	−0.398379	−	0.917221i	$-0.630427\pi$
$821$	5.63800	−	3.25510i	0.196768	−	0.113604i	0.595147	+	0.803617i	$0.297094\pi$
$822$	6.08438	+	10.5385i	0.212217	+	0.367571i
$823$	11.0832	−	19.1966i	0.386335	−	0.669152i	−0.605618	−	0.795755i	$-0.707074\pi$
$823$	11.0832	−	19.1966i	0.386335	−	0.669152i	0.991953	+	0.126603i	$0.0404075\pi$
$824$		−	9.25772i		−	0.322508i
$825$	19.5054	+	11.2614i	0.679090	+	0.392073i
$826$	−17.8585	−	10.3106i	−0.621377	−	0.358752i
$827$			8.74542i			0.304108i	0.988372	+	0.152054i	$0.0485888\pi$
$827$			8.74542i			0.304108i	−0.988372	+	0.152054i	$0.951411\pi$
$828$	−0.622065	+	1.07745i	−0.0216182	+	0.0374439i
$829$	−11.1008	−	19.2271i	−0.385546	−	0.667786i	0.606299	−	0.795237i	$-0.292654\pi$
$829$	−11.1008	−	19.2271i	−0.385546	−	0.667786i	−0.991845	+	0.127451i	$0.959320\pi$
$830$	−3.16657	+	1.82822i	−0.109913	+	0.0634584i
$831$	−12.0524			−0.418093
$832$	3.05046	−	1.92216i	0.105756	−	0.0666388i
$833$	−20.0187			−0.693607
$834$	−12.8743	+	7.43295i	−0.445799	+	0.257382i
$835$	−24.8910	−	43.1124i	−0.861388	−	1.49197i
$836$	1.90718	−	3.30334i	0.0659613	−	0.114248i
$837$			9.65674i			0.333786i
$838$	−18.5325	−	10.6998i	−0.640196	−	0.369617i
$839$	−27.5170	−	15.8870i	−0.949993	−	0.548479i	−0.0569146	−	0.998379i	$-0.518126\pi$
$839$	−27.5170	−	15.8870i	−0.949993	−	0.548479i	−0.893079	+	0.449900i	$0.851460\pi$
$840$			16.7461i			0.577795i
$841$	−21.7308	+	37.6388i	−0.749338	+	1.29789i
$842$	13.1948	+	22.8540i	0.454722	+	0.787601i
$843$	−5.74514	+	3.31696i	−0.197873	+	0.114242i
$844$	−8.29916			−0.285669
$845$	−35.0483	−	16.7684i	−1.20570	−	0.576852i
$846$	4.57165			0.157177
$847$	−11.4700	+	6.62219i	−0.394113	+	0.227541i
$848$	6.64348	+	11.5069i	0.228138	+	0.395147i
$849$	−11.8551	+	20.5337i	−0.406866	+	0.704713i
$850$			11.3695i			0.389970i
$851$	−7.54796	−	4.35782i	−0.258741	−	0.149384i
$852$	12.6920	+	7.32776i	0.434822	+	0.251045i
$853$			56.4010i			1.93113i	0.260154	+	0.965567i	$0.416227\pi$
$853$			56.4010i			1.93113i	−0.260154	+	0.965567i	$0.583773\pi$
$854$	11.1786	−	19.3619i	0.382523	−	0.662549i
$855$	−1.11362	−	1.92884i	−0.0380849	−	0.0659649i
$856$	−10.1006	+	5.83157i	−0.345230	+	0.199319i
$857$	26.8812			0.918244			0.459122	−	0.888373i	$-0.348164\pi$
$857$	26.8812			0.918244			0.459122	+	0.888373i	$0.348164\pi$
$858$	−17.4719	+	11.0094i	−0.596481	+	0.375855i
$859$	21.5548			0.735440			0.367720	−	0.929937i	$-0.380138\pi$
$859$	21.5548			0.735440			0.367720	+	0.929937i	$0.380138\pi$
$860$	−14.0471	+	8.11012i	−0.479004	+	0.276553i
$861$	−29.8194	−	51.6488i	−1.01624	−	1.76019i
$862$	11.2739	−	19.5270i	0.383992	−	0.665094i
$863$			28.9587i			0.985767i	0.870095	+	0.492883i	$0.164057\pi$
$863$			28.9587i			0.985767i	−0.870095	+	0.492883i	$0.835943\pi$
$864$	−4.87035	−	2.81190i	−0.165693	−	0.0956627i
$865$	24.5186	+	14.1558i	0.833657	+	0.481312i
$866$			11.5129i			0.391223i
$867$	6.48720	−	11.2362i	0.220317	−	0.381600i
$868$	3.20369	+	5.54895i	0.108740	+	0.188343i
$869$	10.0578	−	5.80687i	0.341188	−	0.196985i
$870$	38.2022			1.29518
$871$	−12.3541	+	23.4474i	−0.418603	+	0.794485i
$872$	6.07064			0.205578
$873$	9.60256	−	5.54404i	0.324998	−	0.187637i
$874$	0.834742	+	1.44582i	0.0282356	+	0.0489054i
$875$	−5.95350	+	10.3118i	−0.201265	+	0.348601i
$876$			0.177538i			0.00599846i
$877$	8.05080	+	4.64813i	0.271856	+	0.156956i	0.629731	−	0.776813i	$-0.283165\pi$
$877$	8.05080	+	4.64813i	0.271856	+	0.156956i	−0.357875	+	0.933770i	$0.616498\pi$
$878$	10.0847	+	5.82242i	0.340343	+	0.196497i
$879$			51.0629i			1.72231i
$880$	−5.69999	+	9.87268i	−0.192147	+	0.332808i
$881$	−8.34122	−	14.4474i	−0.281023	−	0.486746i	0.690614	−	0.723223i	$-0.257340\pi$
$881$	−8.34122	−	14.4474i	−0.281023	−	0.486746i	−0.971637	+	0.236478i	$0.924007\pi$
$882$	−4.46846	+	2.57987i	−0.150461	+	0.0868686i
$883$	−44.8252			−1.50849			−0.754245	−	0.656594i	$-0.771997\pi$
$883$	−44.8252			−1.50849			−0.754245	+	0.656594i	$0.771997\pi$
$884$	−9.22285	−	4.85939i	−0.310198	−	0.163439i
$885$	24.8011			0.833678
$886$	−22.5312	+	13.0084i	−0.756950	+	0.437025i
$887$	−25.7496	−	44.5995i	−0.864586	−	1.49751i	−0.867458	−	0.497510i	$-0.834248\pi$
$887$	−25.7496	−	44.5995i	−0.864586	−	1.49751i	0.00287234	−	0.999996i	$-0.499086\pi$
$888$	3.91957	−	6.78890i	0.131532	−	0.227821i
$889$			42.0483i			1.41026i
$890$	38.3542	+	22.1438i	1.28564	+	0.742263i
$891$	20.5104	+	11.8417i	0.687125	+	0.396712i
$892$			8.81599i			0.295181i
$893$	3.06733	−	5.31277i	0.102644	−	0.177785i
$894$	−17.3953	−	30.1296i	−0.581787	−	1.00768i
$895$	−12.9529	+	7.47834i	−0.432966	+	0.249973i
$896$	−3.73146			−0.124659
$897$	−0.349479	−	9.03195i	−0.0116688	−	0.301568i
$898$	11.7314			0.391482
$899$	12.6586	−	7.30845i	0.422188	−	0.243750i
$900$	1.46522	+	2.53783i	0.0488406	+	0.0845944i
$901$	19.2083	−	33.2697i	0.639920	−	1.10837i
$902$		−	40.5995i		−	1.35182i
$903$	26.3352	+	15.2046i	0.876381	+	0.505979i
$904$	4.58207	+	2.64546i	0.152397	+	0.0879867i
$905$		−	5.89967i		−	0.196112i
$906$	15.1203	−	26.1892i	0.502339	−	0.870076i
$907$	15.8536	+	27.4593i	0.526411	+	0.911771i	0.999526	+	0.0307707i	$0.00979617\pi$
$907$	15.8536	+	27.4593i	0.526411	+	0.911771i	−0.473115	+	0.881001i	$0.656870\pi$
$908$	−3.62774	+	2.09447i	−0.120391	+	0.0695076i
$909$	10.7497			0.356546
$910$	21.4363	+	34.0194i	0.710607	+	1.12773i
$911$	−46.0327			−1.52513			−0.762566	−	0.646911i	$-0.776061\pi$
$911$	−46.0327			−1.52513			−0.762566	+	0.646911i	$0.776061\pi$
$912$	−1.30042	+	0.750797i	−0.0430611	+	0.0248614i
$913$	2.33329	+	4.04137i	0.0772205	+	0.133750i
$914$	−18.3839	+	31.8419i	−0.608086	+	1.05324i
$915$			26.8888i			0.888918i
$916$	−21.0128	−	12.1318i	−0.694283	−	0.400845i
$917$	41.2398	+	23.8098i	1.36186	+	0.786269i
$918$			16.2600i			0.536661i
$919$	−8.29537	+	14.3680i	−0.273639	+	0.473957i	−0.969791	−	0.243938i	$-0.921561\pi$
$919$	−8.29537	+	14.3680i	−0.273639	+	0.473957i	0.696152	+	0.717895i	$0.254894\pi$
$920$	−2.49479	−	4.32111i	−0.0822509	−	0.142463i
$921$	−37.9925	+	21.9350i	−1.25190	+	0.722783i
$922$	12.0022			0.395270
$923$	35.1638	−	1.36062i	1.15743	−	0.0447852i
$924$	21.3724			0.703100
$925$	−17.7785	+	10.2644i	−0.584555	+	0.337493i
$926$	−7.75504	−	13.4321i	−0.254846	−	0.441407i
$927$	−3.44951	+	5.97472i	−0.113297	+	0.196236i
$928$			8.51244i			0.279434i
$929$	−42.3450	−	24.4479i	−1.38930	−	0.802110i	−0.396059	−	0.918225i	$-0.629623\pi$
$929$	−42.3450	−	24.4479i	−1.38930	−	0.802110i	−0.993236	+	0.116115i	$0.962956\pi$
$930$	−6.67369	−	3.85306i	−0.218839	−	0.126347i
$931$			6.92379i			0.226918i
$932$	−8.96058	+	15.5202i	−0.293514	+	0.508381i
$933$	−9.87421	−	17.1026i	−0.323267	−	0.559915i
$934$	−22.3696	+	12.9151i	−0.731955	+	0.422595i
$935$	32.9607			1.07793
$936$	−2.68491	+	0.103889i	−0.0877591	+	0.00339572i
$937$	23.3908			0.764144			0.382072	−	0.924133i	$-0.375211\pi$
$937$	23.3908			0.764144			0.382072	+	0.924133i	$0.375211\pi$
$938$	23.7537	−	13.7142i	0.775586	−	0.447785i
$939$	−16.6548	−	28.8470i	−0.543509	−	0.941385i
$940$	−9.16732	+	15.8783i	−0.299005	+	0.517892i
$941$		−	17.0539i		−	0.555940i	−0.960590	−	0.277970i	$-0.910338\pi$
$941$		−	17.0539i		−	0.555940i	0.960590	−	0.277970i	$-0.0896617\pi$
$942$	−17.0225	−	9.82794i	−0.554623	−	0.320212i
$943$	15.3890	+	8.88487i	0.501136	+	0.289331i
$944$			5.52632i			0.179866i
$945$	31.3589	−	54.3151i	1.02010	−	1.76687i
$946$	10.3506	+	17.9279i	0.336529	+	0.582885i
$947$	−15.5112	+	8.95537i	−0.504045	+	0.291010i	−0.730382	−	0.683038i	$-0.760658\pi$
$947$	−15.5112	+	8.95537i	−0.504045	+	0.291010i	0.226337	+	0.974049i	$0.427325\pi$
$948$	−4.57196			−0.148490
$949$	0.227263	+	0.360666i	0.00737727	+	0.0117077i
$950$	3.93232			0.127581
$951$	32.8917	−	18.9900i	1.06659	−	0.615794i
$952$	5.39437	+	9.34333i	0.174833	+	0.302819i
$953$	4.01344	−	6.95149i	0.130008	−	0.225181i	−0.793671	−	0.608347i	$-0.791833\pi$
$953$	4.01344	−	6.95149i	0.130008	−	0.225181i	0.923679	+	0.383166i	$0.125166\pi$
$954$		−	9.90169i		−	0.320579i
$955$	−53.8716	−	31.1028i	−1.74325	−	1.00646i
$956$	19.3278	+	11.1589i	0.625104	+	0.360904i
$957$		−	48.7560i		−	1.57606i
$958$	−5.03109	+	8.71411i	−0.162547	+	0.281540i
$959$	−15.1197	−	26.1881i	−0.488240	−	0.845657i
$960$	3.88656	−	2.24390i	0.125438	−	0.0724217i
$961$	28.0515			0.904887
$962$	−0.727785	−	18.8089i	−0.0234647	−	0.606423i
$963$	8.69158			0.280082
$964$	−19.3957	+	11.1981i	−0.624693	+	0.360667i
$965$	−31.8392	−	55.1470i	−1.02494	−	1.77525i
$966$	−4.67717	+	8.10110i	−0.150486	+	0.260649i
$967$		−	31.4562i		−	1.01156i	−0.862662	−	0.505781i	$-0.831204\pi$
$967$		−	31.4562i		−	1.01156i	0.862662	−	0.505781i	$-0.168796\pi$
$968$	3.07386	+	1.77469i	0.0987975	+	0.0570408i
$969$	3.75989	+	2.17077i	0.120785	+	0.0697353i
$970$			44.4688i			1.42781i
$971$	8.35956	−	14.4792i	0.268271	−	0.464659i	−0.700144	−	0.714001i	$-0.746881\pi$
$971$	8.35956	−	14.4792i	0.268271	−	0.464659i	0.968415	+	0.249342i	$0.0802144\pi$
$972$	3.77400	+	6.53675i	0.121051	+	0.209667i
$973$	31.9925	−	18.4709i	1.02563	−	0.592149i
$974$	5.76723			0.184794
$975$	−18.8354	−	9.92409i	−0.603214	−	0.317825i
$976$	−5.99153			−0.191784
$977$	7.85791	−	4.53677i	0.251397	−	0.145144i	−0.369007	−	0.929427i	$-0.620302\pi$
$977$	7.85791	−	4.53677i	0.251397	−	0.145144i	0.620404	+	0.784283i	$0.286969\pi$
$978$	−4.43161	−	7.67578i	−0.141707	−	0.245444i
$979$	28.2614	−	48.9501i	0.903237	−	1.56445i
$980$		−	20.6931i		−	0.661017i
$981$	−3.91785	−	2.26197i	−0.125087	−	0.0722193i
$982$	−16.8592	−	9.73364i	−0.537997	−	0.310613i
$983$			48.1584i			1.53601i	0.640442	+	0.768007i	$0.278751\pi$
$983$			48.1584i			1.53601i	−0.640442	+	0.768007i	$0.721249\pi$
$984$	−7.99136	+	13.8414i	−0.254755	+	0.441249i
$985$	−12.8850	−	22.3174i	−0.410549	−	0.711092i
$986$	21.3146	−	12.3060i	0.678795	−	0.391902i
$987$	34.3733			1.09411
$988$	−1.68070	+	3.18987i	−0.0534701	+	0.101483i
$989$	−9.06061			−0.288111
$990$	7.35730	−	4.24774i	0.233830	−	0.135002i
$991$	21.6542	+	37.5062i	0.687869	+	1.19142i	0.972526	+	0.232795i	$0.0747870\pi$
$991$	21.6542	+	37.5062i	0.687869	+	1.19142i	−0.284657	+	0.958629i	$0.591880\pi$
$992$	0.858561	−	1.48707i	0.0272593	−	0.0472146i
$993$		−	41.4793i		−	1.31630i
$994$	−31.5397	−	18.2095i	−1.00038	−	0.577570i
$995$	−10.3638	−	5.98353i	−0.328554	−	0.189691i
$996$		−	1.83708i		−	0.0582101i
$997$	28.8365	−	49.9462i	0.913260	−	1.58181i	0.103831	−	0.994595i	$-0.466890\pi$
$997$	28.8365	−	49.9462i	0.913260	−	1.58181i	0.809429	−	0.587218i	$-0.199777\pi$
$998$	2.37282	+	4.10984i	0.0751102	+	0.130095i
$999$	−25.4259	+	14.6797i	−0.804440	+	0.464444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.m.b.153.3	✓	28
13.2	odd	12		6422.2.a.bm.1.9		14
13.4	even	6	inner	494.2.m.b.381.3	yes	28
13.11	odd	12		6422.2.a.bn.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.3	✓	28	1.1	even	1	trivial
494.2.m.b.381.3	yes	28	13.4	even	6	inner
6422.2.a.bm.1.9		14	13.2	odd	12
6422.2.a.bn.1.9		14	13.11	odd	12

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:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.750797 - 1.30042i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.98870i q^{5} +(1.30042 + 0.750797i) q^{6} +(-3.23154 - 1.86573i) q^{7} +1.00000i q^{8} +(0.372609 - 0.645378i) q^{9} +(1.49435 + 2.58829i) q^{10} +(3.30334 - 1.90718i) q^{11} -1.50159 q^{12} +(-3.05046 + 1.92216i) q^{13} +3.73146 q^{14} +(-3.88656 + 2.24390i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.44565 + 2.50393i) q^{17} +0.745218i q^{18} +(0.866025 + 0.500000i) q^{19} +(-2.58829 - 1.49435i) q^{20} +5.60313i q^{21} +(-1.90718 + 3.30334i) q^{22} +(-0.834742 - 1.44582i) q^{23} +(1.30042 - 0.750797i) q^{24} -3.93232 q^{25} +(1.68070 - 3.18987i) q^{26} -5.62379 q^{27} +(-3.23154 + 1.86573i) q^{28} +(4.25622 + 7.37199i) q^{29} +(2.24390 - 3.88656i) q^{30} -1.71712i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.96027 - 2.86381i) q^{33} -2.89129i q^{34} +(-5.57610 + 9.65809i) q^{35} +(-0.372609 - 0.645378i) q^{36} +(4.52113 - 2.61028i) q^{37} -1.00000 q^{38} +(4.78988 + 2.52372i) q^{39} +2.98870 q^{40} +(-9.21784 + 5.32192i) q^{41} +(-2.80157 - 4.85246i) q^{42} +(2.71360 - 4.70009i) q^{43} -3.81437i q^{44} +(-1.92884 - 1.11362i) q^{45} +(1.44582 + 0.834742i) q^{46} -6.13466i q^{47} +(-0.750797 + 1.30042i) q^{48} +(3.46189 + 5.99618i) q^{49} +(3.40549 - 1.96616i) q^{50} +4.34155 q^{51} +(0.139408 + 3.60286i) q^{52} -13.2870 q^{53} +(4.87035 - 2.81190i) q^{54} +(-5.69999 - 9.87268i) q^{55} +(1.86573 - 3.23154i) q^{56} -1.50159i q^{57} +(-7.37199 - 4.25622i) q^{58} +(-4.78593 - 2.76316i) q^{59} +4.48781i q^{60} +(2.99576 - 5.18882i) q^{61} +(0.858561 + 1.48707i) q^{62} +(-2.40820 + 1.39038i) q^{63} -1.00000 q^{64} +(5.74475 + 9.11691i) q^{65} +5.72763 q^{66} +(6.36580 - 3.67530i) q^{67} +(1.44565 + 2.50393i) q^{68} +(-1.25344 + 2.17103i) q^{69} -11.1522i q^{70} +(-8.45239 - 4.87999i) q^{71} +(0.645378 + 0.372609i) q^{72} -0.118233i q^{73} +(-2.61028 + 4.52113i) q^{74} +(2.95237 + 5.11366i) q^{75} +(0.866025 - 0.500000i) q^{76} -14.2332 q^{77} +(-5.41002 + 0.209334i) q^{78} +3.04474 q^{79} +(-2.58829 + 1.49435i) q^{80} +(3.10450 + 5.37715i) q^{81} +(5.32192 - 9.21784i) q^{82} +1.22342i q^{83} +(4.85246 + 2.80157i) q^{84} +(7.48350 + 4.32060i) q^{85} +5.42719i q^{86} +(6.39111 - 11.0697i) q^{87} +(1.90718 + 3.30334i) q^{88} +(12.8331 - 7.40919i) q^{89} +2.22723 q^{90} +(13.4439 - 0.520194i) q^{91} -1.66948 q^{92} +(-2.23298 + 1.28921i) q^{93} +(3.06733 + 5.31277i) q^{94} +(1.49435 - 2.58829i) q^{95} -1.50159i q^{96} +(12.8856 + 7.43949i) q^{97} +(-5.99618 - 3.46189i) q^{98} -2.84253i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{3} + 14 q^{4} - 18 q^{9} - 2 q^{10} - 6 q^{11} - 8 q^{12} + 8 q^{13} + 4 q^{14} + 42 q^{15} - 14 q^{16} + 2 q^{17} - 10 q^{22} + 12 q^{23} - 88 q^{25} + 2 q^{26} + 20 q^{27} - 4 q^{29} - 4 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) \) 28 * q - 4 * q^3 + 14 * q^4 - 18 * q^9 - 2 * q^10 - 6 * q^11 - 8 * q^12 + 8 * q^13 + 4 * q^14 + 42 * q^15 - 14 * q^16 + 2 * q^17 - 10 * q^22 + 12 * q^23 - 88 * q^25 + 2 * q^26 + 20 * q^27 - 4 * q^29 - 4 * q^30 - 54 * q^33 - 14 * q^35 + 18 * q^36 + 6 * q^37 - 28 * q^38 + 60 * q^39 - 4 * q^40 + 42 * q^41 + 18 * q^42 + 28 * q^43 - 30 * q^45 - 12 * q^46 - 4 * q^48 + 28 * q^49 + 12 * q^50 - 20 * q^51 + 4 * q^52 + 24 * q^53 + 54 * q^54 + 2 * q^55 + 2 * q^56 - 6 * q^58 - 96 * q^59 - 30 * q^61 + 4 * q^62 + 12 * q^63 - 28 * q^64 + 82 * q^65 + 24 * q^66 - 6 * q^67 - 2 * q^68 - 42 * q^69 - 6 * q^71 + 12 * q^72 - 18 * q^74 + 46 * q^75 - 136 * q^77 + 50 * q^78 + 68 * q^79 + 6 * q^81 + 6 * q^82 + 12 * q^84 - 72 * q^85 - 52 * q^87 + 10 * q^88 + 48 * q^89 - 16 * q^90 + 44 * q^91 + 24 * q^92 + 30 * q^93 + 20 * q^94 - 2 * q^95 + 12 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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