LMFDB - Embedded newform 399.2.j.c.58.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(58,399)] 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("399.58"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			58.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	399.58
Dual form			399.2.j.c.172.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20711 - 2.09077i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(1.91421 - 3.31552i) q^{5} -2.41421 q^{6} +(-2.50000 + 0.866025i) q^{7} -4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.62132 - 8.00436i) q^{10} +(1.91421 + 3.31552i) q^{11} +(-1.91421 + 3.31552i) q^{12} +2.82843 q^{13} +(-1.20711 + 6.27231i) q^{14} -3.82843 q^{15} +(-1.50000 + 2.59808i) q^{16} +(1.82843 + 3.16693i) q^{17} +(1.20711 + 2.09077i) q^{18} +(0.500000 - 0.866025i) q^{19} -14.6569 q^{20} +(2.00000 + 1.73205i) q^{21} +9.24264 q^{22} +(0.914214 - 1.58346i) q^{23} +(2.20711 + 3.82282i) q^{24} +(-4.82843 - 8.36308i) q^{25} +(3.41421 - 5.91359i) q^{26} +1.00000 q^{27} +(7.65685 + 6.63103i) q^{28} -4.82843 q^{29} +(-4.62132 + 8.00436i) q^{30} +(1.58579 + 2.74666i) q^{31} +(-0.792893 - 1.37333i) q^{32} +(1.91421 - 3.31552i) q^{33} +8.82843 q^{34} +(-1.91421 + 9.94655i) q^{35} +3.82843 q^{36} +(-0.585786 + 1.01461i) q^{37} +(-1.20711 - 2.09077i) q^{38} +(-1.41421 - 2.44949i) q^{39} +(-8.44975 + 14.6354i) q^{40} +7.65685 q^{41} +(6.03553 - 2.09077i) q^{42} -12.6569 q^{43} +(7.32843 - 12.6932i) q^{44} +(1.91421 + 3.31552i) q^{45} +(-2.20711 - 3.82282i) q^{46} +(-3.08579 + 5.34474i) q^{47} +3.00000 q^{48} +(5.50000 - 4.33013i) q^{49} -23.3137 q^{50} +(1.82843 - 3.16693i) q^{51} +(-5.41421 - 9.37769i) q^{52} +(1.00000 + 1.73205i) q^{53} +(1.20711 - 2.09077i) q^{54} +14.6569 q^{55} +(11.0355 - 3.82282i) q^{56} -1.00000 q^{57} +(-5.82843 + 10.0951i) q^{58} +(-5.41421 - 9.37769i) q^{59} +(7.32843 + 12.6932i) q^{60} +(7.32843 - 12.6932i) q^{61} +7.65685 q^{62} +(0.500000 - 2.59808i) q^{63} -9.82843 q^{64} +(5.41421 - 9.37769i) q^{65} +(-4.62132 - 8.00436i) q^{66} +(6.00000 + 10.3923i) q^{67} +(7.00000 - 12.1244i) q^{68} -1.82843 q^{69} +(18.4853 + 16.0087i) q^{70} +4.34315 q^{71} +(2.20711 - 3.82282i) q^{72} +(5.15685 + 8.93193i) q^{73} +(1.41421 + 2.44949i) q^{74} +(-4.82843 + 8.36308i) q^{75} -3.82843 q^{76} +(-7.65685 - 6.63103i) q^{77} -6.82843 q^{78} +(-1.17157 + 2.02922i) q^{79} +(5.74264 + 9.94655i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.24264 - 16.0087i) q^{82} +4.17157 q^{83} +(1.91421 - 9.94655i) q^{84} +14.0000 q^{85} +(-15.2782 + 26.4626i) q^{86} +(2.41421 + 4.18154i) q^{87} +(-8.44975 - 14.6354i) q^{88} +(-5.41421 + 9.37769i) q^{89} +9.24264 q^{90} +(-7.07107 + 2.44949i) q^{91} -7.00000 q^{92} +(1.58579 - 2.74666i) q^{93} +(7.44975 + 12.9033i) q^{94} +(-1.91421 - 3.31552i) q^{95} +(-0.792893 + 1.37333i) q^{96} +16.8284 q^{97} +(-2.41421 - 16.7262i) q^{98} -3.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 10 q^{7} - 12 q^{8} - 2 q^{9} - 10 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} - 4 q^{15} - 6 q^{16} - 4 q^{17} + 2 q^{18} + 2 q^{19} - 36 q^{20} + 8 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 10 * q^7 - 12 * q^8 - 2 * q^9 - 10 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^14 - 4 * q^15 - 6 * q^16 - 4 * q^17 + 2 * q^18 + 2 * q^19 - 36 * q^20 + 8 * q^21 + 20 * q^22 - 2 * q^23 + 6 * q^24 - 8 * q^25 + 8 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 - 10 * q^30 + 12 * q^31 - 6 * q^32 + 2 * q^33 + 24 * q^34 - 2 * q^35 + 4 * q^36 - 8 * q^37 - 2 * q^38 - 14 * q^40 + 8 * q^41 + 10 * q^42 - 28 * q^43 + 18 * q^44 + 2 * q^45 - 6 * q^46 - 18 * q^47 + 12 * q^48 + 22 * q^49 - 48 * q^50 - 4 * q^51 - 16 * q^52 + 4 * q^53 + 2 * q^54 + 36 * q^55 + 30 * q^56 - 4 * q^57 - 12 * q^58 - 16 * q^59 + 18 * q^60 + 18 * q^61 + 8 * q^62 + 2 * q^63 - 28 * q^64 + 16 * q^65 - 10 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 40 * q^70 + 40 * q^71 + 6 * q^72 - 2 * q^73 - 8 * q^75 - 4 * q^76 - 8 * q^77 - 16 * q^78 - 16 * q^79 + 6 * q^80 - 2 * q^81 + 20 * q^82 + 28 * q^83 + 2 * q^84 + 56 * q^85 - 30 * q^86 + 4 * q^87 - 14 * q^88 - 16 * q^89 + 20 * q^90 - 28 * q^92 + 12 * q^93 + 10 * q^94 - 2 * q^95 - 6 * q^96 + 56 * q^97 - 4 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	1.20711	−	2.09077i	0.853553	−	1.47840i	−0.0244272	−	0.999702i	$-0.507776\pi$
$2$	1.20711	−	2.09077i	0.853553	−	1.47840i	0.877981	−	0.478696i	$-0.158890\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.91421	−	3.31552i	−0.957107	−	1.65776i
$5$	1.91421	−	3.31552i	0.856062	−	1.48274i	−0.0195936	−	0.999808i	$-0.506237\pi$
$5$	1.91421	−	3.31552i	0.856062	−	1.48274i	0.875656	−	0.482935i	$-0.160429\pi$
$6$	−2.41421			−0.985599
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−4.41421			−1.56066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−4.62132	−	8.00436i	−1.46139	−	2.53120i
$11$	1.91421	+	3.31552i	0.577157	+	0.999665i	0.995804	+	0.0915161i	$0.0291713\pi$
$11$	1.91421	+	3.31552i	0.577157	+	0.999665i	−0.418646	+	0.908149i	$0.637495\pi$
$12$	−1.91421	+	3.31552i	−0.552586	+	0.957107i
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$	−1.20711	+	6.27231i	−0.322613	+	1.67635i
$15$	−3.82843			−0.988496
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	1.82843	+	3.16693i	0.443459	+	0.768093i	0.997943	−	0.0641009i	$-0.0204179\pi$
$17$	1.82843	+	3.16693i	0.443459	+	0.768093i	−0.554485	+	0.832194i	$0.687085\pi$
$18$	1.20711	+	2.09077i	0.284518	+	0.492799i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	−14.6569			−3.27737
$21$	2.00000	+	1.73205i	0.436436	+	0.377964i
$22$	9.24264			1.97054
$23$	0.914214	−	1.58346i	0.190627	−	0.330175i	−0.754831	−	0.655919i	$-0.772281\pi$
$23$	0.914214	−	1.58346i	0.190627	−	0.330175i	0.945458	+	0.325744i	$0.105615\pi$
$24$	2.20711	+	3.82282i	0.450524	+	0.780330i
$25$	−4.82843	−	8.36308i	−0.965685	−	1.67262i
$26$	3.41421	−	5.91359i	0.669582	−	1.15975i
$27$	1.00000			0.192450
$28$	7.65685	+	6.63103i	1.44701	+	1.25315i
$29$	−4.82843			−0.896616			−0.448308	−	0.893879i	$-0.647973\pi$
$29$	−4.82843			−0.896616			−0.448308	+	0.893879i	$0.647973\pi$
$30$	−4.62132	+	8.00436i	−0.843734	+	1.46139i
$31$	1.58579	+	2.74666i	0.284816	+	0.493315i	0.972564	−	0.232634i	$-0.0747343\pi$
$31$	1.58579	+	2.74666i	0.284816	+	0.493315i	−0.687749	+	0.725949i	$0.741401\pi$
$32$	−0.792893	−	1.37333i	−0.140165	−	0.242773i
$33$	1.91421	−	3.31552i	0.333222	−	0.577157i
$34$	8.82843			1.51406
$35$	−1.91421	+	9.94655i	−0.323561	+	1.68127i
$36$	3.82843			0.638071
$37$	−0.585786	+	1.01461i	−0.0963027	+	0.166801i	−0.910152	−	0.414275i	$-0.864035\pi$
$37$	−0.585786	+	1.01461i	−0.0963027	+	0.166801i	0.813849	+	0.581077i	$0.197368\pi$
$38$	−1.20711	−	2.09077i	−0.195819	−	0.339168i
$39$	−1.41421	−	2.44949i	−0.226455	−	0.392232i
$40$	−8.44975	+	14.6354i	−1.33602	+	2.31406i
$41$	7.65685			1.19580			0.597900	−	0.801571i	$-0.296002\pi$
$41$	7.65685			1.19580			0.597900	+	0.801571i	$0.296002\pi$
$42$	6.03553	−	2.09077i	0.931303	−	0.322613i
$43$	−12.6569			−1.93015			−0.965076	−	0.261970i	$-0.915628\pi$
$43$	−12.6569			−1.93015			−0.965076	+	0.261970i	$0.915628\pi$
$44$	7.32843	−	12.6932i	1.10480	−	1.91357i
$45$	1.91421	+	3.31552i	0.285354	+	0.494248i
$46$	−2.20711	−	3.82282i	−0.325420	−	0.563644i
$47$	−3.08579	+	5.34474i	−0.450108	+	0.779610i	−0.998392	−	0.0566819i	$-0.981948\pi$
$47$	−3.08579	+	5.34474i	−0.450108	+	0.779610i	0.548284	+	0.836292i	$0.315281\pi$
$48$	3.00000			0.433013
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−23.3137			−3.29706
$51$	1.82843	−	3.16693i	0.256031	−	0.443459i
$52$	−5.41421	−	9.37769i	−0.750816	−	1.30045i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	1.20711	−	2.09077i	0.164266	−	0.284518i
$55$	14.6569			1.97633
$56$	11.0355	−	3.82282i	1.47469	−	0.510846i
$57$	−1.00000			−0.132453
$58$	−5.82843	+	10.0951i	−0.765310	+	1.32556i
$59$	−5.41421	−	9.37769i	−0.704871	−	1.22087i	−0.966738	−	0.255768i	$-0.917672\pi$
$59$	−5.41421	−	9.37769i	−0.704871	−	1.22087i	0.261868	−	0.965104i	$-0.415662\pi$
$60$	7.32843	+	12.6932i	0.946096	+	1.63869i
$61$	7.32843	−	12.6932i	0.938309	−	1.62520i	0.169685	−	0.985498i	$-0.445725\pi$
$61$	7.32843	−	12.6932i	0.938309	−	1.62520i	0.768624	−	0.639700i	$-0.220942\pi$
$62$	7.65685			0.972421
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$	−9.82843			−1.22855
$65$	5.41421	−	9.37769i	0.671551	−	1.16316i
$66$	−4.62132	−	8.00436i	−0.568845	−	0.985269i
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$	7.00000	−	12.1244i	0.848875	−	1.47029i
$69$	−1.82843			−0.220117
$70$	18.4853	+	16.0087i	2.20941	+	1.91341i
$71$	4.34315			0.515437			0.257718	−	0.966220i	$-0.417029\pi$
$71$	4.34315			0.515437			0.257718	+	0.966220i	$0.417029\pi$
$72$	2.20711	−	3.82282i	0.260110	−	0.450524i
$73$	5.15685	+	8.93193i	0.603564	+	1.04540i	0.992277	+	0.124045i	$0.0395866\pi$
$73$	5.15685	+	8.93193i	0.603564	+	1.04540i	−0.388712	+	0.921359i	$0.627080\pi$
$74$	1.41421	+	2.44949i	0.164399	+	0.284747i
$75$	−4.82843	+	8.36308i	−0.557539	+	0.965685i
$76$	−3.82843			−0.439151
$77$	−7.65685	−	6.63103i	−0.872580	−	0.755676i
$78$	−6.82843			−0.773167
$79$	−1.17157	+	2.02922i	−0.131812	+	0.228306i	−0.924375	−	0.381485i	$-0.875413\pi$
$79$	−1.17157	+	2.02922i	−0.131812	+	0.228306i	0.792563	+	0.609790i	$0.208746\pi$
$80$	5.74264	+	9.94655i	0.642047	+	1.11206i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	9.24264	−	16.0087i	1.02068	−	1.76787i
$83$	4.17157			0.457890			0.228945	−	0.973439i	$-0.426472\pi$
$83$	4.17157			0.457890			0.228945	+	0.973439i	$0.426472\pi$
$84$	1.91421	−	9.94655i	0.208858	−	1.08526i
$85$	14.0000			1.51851
$86$	−15.2782	+	26.4626i	−1.64749	+	2.85353i
$87$	2.41421	+	4.18154i	0.258831	+	0.448308i
$88$	−8.44975	−	14.6354i	−0.900746	−	1.56014i
$89$	−5.41421	+	9.37769i	−0.573905	+	0.994033i	0.422254	+	0.906478i	$0.361239\pi$
$89$	−5.41421	+	9.37769i	−0.573905	+	0.994033i	−0.996160	+	0.0875560i	$0.972094\pi$
$90$	9.24264			0.974260
$91$	−7.07107	+	2.44949i	−0.741249	+	0.256776i
$92$	−7.00000			−0.729800
$93$	1.58579	−	2.74666i	0.164438	−	0.284816i
$94$	7.44975	+	12.9033i	0.768383	+	1.33088i
$95$	−1.91421	−	3.31552i	−0.196394	−	0.340165i
$96$	−0.792893	+	1.37333i	−0.0809243	+	0.140165i
$97$	16.8284			1.70867			0.854334	−	0.519724i	$-0.173965\pi$
$97$	16.8284			1.70867			0.854334	+	0.519724i	$0.173965\pi$
$98$	−2.41421	−	16.7262i	−0.243872	−	1.68960i
$99$	−3.82843			−0.384771
$100$	−18.4853	+	32.0174i	−1.84853	+	3.20174i
$101$	1.74264	+	3.01834i	0.173399	+	0.300336i	0.939606	−	0.342258i	$-0.111192\pi$
$101$	1.74264	+	3.01834i	0.173399	+	0.300336i	−0.766207	+	0.642594i	$0.777858\pi$
$102$	−4.41421	−	7.64564i	−0.437072	−	0.757031i
$103$	−1.82843	+	3.16693i	−0.180160	+	0.312047i	−0.941935	−	0.335795i	$-0.890995\pi$
$103$	−1.82843	+	3.16693i	−0.180160	+	0.312047i	0.761775	+	0.647842i	$0.224328\pi$
$104$	−12.4853			−1.22428
$105$	9.57107	−	3.31552i	0.934041	−	0.323561i
$106$	4.82843			0.468978
$107$	1.41421	−	2.44949i	0.136717	−	0.236801i	−0.789535	−	0.613706i	$-0.789678\pi$
$107$	1.41421	−	2.44949i	0.136717	−	0.236801i	0.926252	+	0.376905i	$0.123012\pi$
$108$	−1.91421	−	3.31552i	−0.184195	−	0.319036i
$109$	−9.07107	−	15.7116i	−0.868851	−	1.50489i	−0.863172	−	0.504910i	$-0.831526\pi$
$109$	−9.07107	−	15.7116i	−0.868851	−	1.50489i	−0.00567856	−	0.999984i	$-0.501808\pi$
$110$	17.6924	−	30.6441i	1.68690	−	2.92180i
$111$	1.17157			0.111201
$112$	1.50000	−	7.79423i	0.141737	−	0.736485i
$113$	−12.8284			−1.20680			−0.603398	−	0.797440i	$-0.706187\pi$
$113$	−12.8284			−1.20680			−0.603398	+	0.797440i	$0.706187\pi$
$114$	−1.20711	+	2.09077i	−0.113056	+	0.195819i
$115$	−3.50000	−	6.06218i	−0.326377	−	0.565301i
$116$	9.24264	+	16.0087i	0.858158	+	1.48637i
$117$	−1.41421	+	2.44949i	−0.130744	+	0.226455i
$118$	−26.1421			−2.40658
$119$	−7.31371	−	6.33386i	−0.670447	−	0.580624i
$120$	16.8995			1.54271
$121$	−1.82843	+	3.16693i	−0.166221	+	0.287903i
$122$	−17.6924	−	30.6441i	−1.60179	−	2.77439i
$123$	−3.82843	−	6.63103i	−0.345198	−	0.597900i
$124$	6.07107	−	10.5154i	0.545198	−	0.944311i
$125$	−17.8284			−1.59462
$126$	−4.82843	−	4.18154i	−0.430150	−	0.372521i
$127$	16.9706			1.50589			0.752947	−	0.658081i	$-0.228632\pi$
$127$	16.9706			1.50589			0.752947	+	0.658081i	$0.228632\pi$
$128$	−10.2782	+	17.8023i	−0.908471	+	1.57352i
$129$	6.32843	+	10.9612i	0.557187	+	0.965076i
$130$	−13.0711	−	22.6398i	−1.14641	−	1.98564i
$131$	−5.17157	+	8.95743i	−0.451842	+	0.782614i	−0.998501	−	0.0547419i	$-0.982566\pi$
$131$	−5.17157	+	8.95743i	−0.451842	+	0.782614i	0.546658	+	0.837356i	$0.315900\pi$
$132$	−14.6569			−1.27572
$133$	−0.500000	+	2.59808i	−0.0433555	+	0.225282i
$134$	28.9706			2.50268
$135$	1.91421	−	3.31552i	0.164749	−	0.285354i
$136$	−8.07107	−	13.9795i	−0.692088	−	1.19873i
$137$	6.91421	+	11.9758i	0.590721	+	1.02316i	0.994136	+	0.108142i	$0.0344900\pi$
$137$	6.91421	+	11.9758i	0.590721	+	1.02316i	−0.403414	+	0.915017i	$0.632177\pi$
$138$	−2.20711	+	3.82282i	−0.187881	+	0.325420i
$139$	−6.65685			−0.564627			−0.282314	−	0.959322i	$-0.591102\pi$
$139$	−6.65685			−0.564627			−0.282314	+	0.959322i	$0.591102\pi$
$140$	36.6421	−	12.6932i	3.09683	−	1.07277i
$141$	6.17157			0.519740
$142$	5.24264	−	9.08052i	0.439953	−	0.762020i
$143$	5.41421	+	9.37769i	0.452759	+	0.784202i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	−9.24264	+	16.0087i	−0.767560	+	1.32945i
$146$	24.8995			2.06070
$147$	−6.50000	−	2.59808i	−0.536111	−	0.214286i
$148$	4.48528			0.368688
$149$	−1.91421	+	3.31552i	−0.156818	+	0.271618i	−0.933720	−	0.358005i	$-0.883457\pi$
$149$	−1.91421	+	3.31552i	−0.156818	+	0.271618i	0.776901	+	0.629623i	$0.216790\pi$
$150$	11.6569	+	20.1903i	0.951778	+	1.64853i
$151$	4.65685	+	8.06591i	0.378969	+	0.656394i	0.990913	−	0.134507i	$-0.0429452\pi$
$151$	4.65685	+	8.06591i	0.378969	+	0.656394i	−0.611943	+	0.790902i	$0.709612\pi$
$152$	−2.20711	+	3.82282i	−0.179020	+	0.310072i
$153$	−3.65685			−0.295639
$154$	−23.1066	+	8.00436i	−1.86198	+	0.645010i
$155$	12.1421			0.975280
$156$	−5.41421	+	9.37769i	−0.433484	+	0.750816i
$157$	−5.32843	−	9.22911i	−0.425255	−	0.736563i	0.571189	−	0.820818i	$-0.306482\pi$
$157$	−5.32843	−	9.22911i	−0.425255	−	0.736563i	−0.996444	+	0.0842554i	$0.973149\pi$
$158$	2.82843	+	4.89898i	0.225018	+	0.389742i
$159$	1.00000	−	1.73205i	0.0793052	−	0.137361i
$160$	−6.07107			−0.479960
$161$	−0.914214	+	4.75039i	−0.0720501	+	0.374383i
$162$	−2.41421			−0.189679
$163$	−10.9853	+	19.0271i	−0.860434	+	1.49031i	0.0110773	+	0.999939i	$0.496474\pi$
$163$	−10.9853	+	19.0271i	−0.860434	+	1.49031i	−0.871511	+	0.490376i	$0.836859\pi$
$164$	−14.6569	−	25.3864i	−1.14451	−	1.98235i
$165$	−7.32843	−	12.6932i	−0.570517	−	0.988165i
$166$	5.03553	−	8.72180i	0.390833	−	0.676943i
$167$	8.82843			0.683164			0.341582	−	0.939852i	$-0.389037\pi$
$167$	8.82843			0.683164			0.341582	+	0.939852i	$0.389037\pi$
$168$	−8.82843	−	7.64564i	−0.681128	−	0.589874i
$169$	−5.00000			−0.384615
$170$	16.8995	−	29.2708i	1.29613	−	2.24497i
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	24.2279	+	41.9640i	1.84736	+	3.19972i
$173$	−1.41421	+	2.44949i	−0.107521	+	0.186231i	−0.914765	−	0.403986i	$-0.867625\pi$
$173$	−1.41421	+	2.44949i	−0.107521	+	0.186231i	0.807245	+	0.590217i	$0.200958\pi$
$174$	11.6569			0.883704
$175$	19.3137	+	16.7262i	1.45998	+	1.26438i
$176$	−11.4853			−0.865736
$177$	−5.41421	+	9.37769i	−0.406957	+	0.704871i
$178$	13.0711	+	22.6398i	0.979718	+	1.69692i
$179$	5.24264	+	9.08052i	0.391853	+	0.678710i	0.992694	−	0.120659i	$-0.0385007\pi$
$179$	5.24264	+	9.08052i	0.391853	+	0.678710i	−0.600841	+	0.799369i	$0.705167\pi$
$180$	7.32843	−	12.6932i	0.546229	−	0.946096i
$181$	−11.6569			−0.866447			−0.433224	−	0.901286i	$-0.642624\pi$
$181$	−11.6569			−0.866447			−0.433224	+	0.901286i	$0.642624\pi$
$182$	−3.41421	+	17.7408i	−0.253078	+	1.31503i
$183$	−14.6569			−1.08347
$184$	−4.03553	+	6.98975i	−0.297504	+	0.515291i
$185$	2.24264	+	3.88437i	0.164882	+	0.285584i
$186$	−3.82843	−	6.63103i	−0.280714	−	0.486211i
$187$	−7.00000	+	12.1244i	−0.511891	+	0.886621i
$188$	23.6274			1.72321
$189$	−2.50000	+	0.866025i	−0.181848	+	0.0629941i
$190$	−9.24264			−0.670532
$191$	−5.91421	+	10.2437i	−0.427937	+	0.741209i	−0.996690	−	0.0812994i	$-0.974093\pi$
$191$	−5.91421	+	10.2437i	−0.427937	+	0.741209i	0.568752	+	0.822509i	$0.307426\pi$
$192$	4.91421	+	8.51167i	0.354653	+	0.614277i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	20.3137	−	35.1844i	1.45844	−	2.52609i
$195$	−10.8284			−0.775440
$196$	−24.8848	−	9.94655i	−1.77748	−	0.710468i
$197$	−17.4853			−1.24577			−0.622887	−	0.782312i	$-0.714041\pi$
$197$	−17.4853			−1.24577			−0.622887	+	0.782312i	$0.714041\pi$
$198$	−4.62132	+	8.00436i	−0.328423	+	0.568845i
$199$	−1.67157	−	2.89525i	−0.118495	−	0.205239i	0.800677	−	0.599097i	$-0.204474\pi$
$199$	−1.67157	−	2.89525i	−0.118495	−	0.205239i	−0.919171	+	0.393858i	$0.871140\pi$
$200$	21.3137	+	36.9164i	1.50711	+	2.61039i
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$	8.41421			0.592022
$203$	12.0711	−	4.18154i	0.847223	−	0.293487i
$204$	−14.0000			−0.980196
$205$	14.6569	−	25.3864i	1.02368	−	1.77306i
$206$	4.41421	+	7.64564i	0.307553	+	0.532697i
$207$	0.914214	+	1.58346i	0.0635422	+	0.110058i
$208$	−4.24264	+	7.34847i	−0.294174	+	0.509525i
$209$	3.82843			0.264818
$210$	4.62132	−	24.0131i	0.318901	−	1.65706i
$211$	16.4853			1.13489			0.567447	−	0.823410i	$-0.307931\pi$
$211$	16.4853			1.13489			0.567447	+	0.823410i	$0.307931\pi$
$212$	3.82843	−	6.63103i	0.262937	−	0.455421i
$213$	−2.17157	−	3.76127i	−0.148794	−	0.257718i
$214$	−3.41421	−	5.91359i	−0.233391	−	0.404245i
$215$	−24.2279	+	41.9640i	−1.65233	+	2.86192i
$216$	−4.41421			−0.300349
$217$	−6.34315	−	5.49333i	−0.430601	−	0.372911i
$218$	−43.7990			−2.96644
$219$	5.15685	−	8.93193i	0.348468	−	0.603564i
$220$	−28.0563	−	48.5950i	−1.89156	−	3.27628i
$221$	5.17157	+	8.95743i	0.347878	+	0.602542i
$222$	1.41421	−	2.44949i	0.0949158	−	0.164399i
$223$	21.7990			1.45977			0.729884	−	0.683571i	$-0.239574\pi$
$223$	21.7990			1.45977			0.729884	+	0.683571i	$0.239574\pi$
$224$	3.17157	+	2.74666i	0.211910	+	0.183519i
$225$	9.65685			0.643790
$226$	−15.4853	+	26.8213i	−1.03007	+	1.78413i
$227$	3.17157	+	5.49333i	0.210505	+	0.364605i	0.951873	−	0.306494i	$-0.0991559\pi$
$227$	3.17157	+	5.49333i	0.210505	+	0.364605i	−0.741368	+	0.671099i	$0.765823\pi$
$228$	1.91421	+	3.31552i	0.126772	+	0.219575i
$229$	7.82843	−	13.5592i	0.517317	−	0.896019i	−0.482481	−	0.875907i	$-0.660264\pi$
$229$	7.82843	−	13.5592i	0.517317	−	0.896019i	0.999798	−	0.0201128i	$-0.00640252\pi$
$230$	−16.8995			−1.11432
$231$	−1.91421	+	9.94655i	−0.125946	+	0.654435i
$232$	21.3137			1.39931
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	3.41421	+	5.91359i	0.223194	+	0.386584i
$235$	11.8137	+	20.4619i	0.770641	+	1.33479i
$236$	−20.7279	+	35.9018i	−1.34927	+	2.33701i
$237$	2.34315			0.152204
$238$	−22.0711	+	7.64564i	−1.43065	+	0.495593i
$239$	2.34315			0.151565			0.0757827	−	0.997124i	$-0.475854\pi$
$239$	2.34315			0.151565			0.0757827	+	0.997124i	$0.475854\pi$
$240$	5.74264	−	9.94655i	0.370686	−	0.642047i
$241$	−9.89949	−	17.1464i	−0.637683	−	1.10450i	−0.985940	−	0.167100i	$-0.946560\pi$
$241$	−9.89949	−	17.1464i	−0.637683	−	1.10450i	0.348257	−	0.937399i	$-0.386773\pi$
$242$	4.41421	+	7.64564i	0.283756	+	0.491480i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−56.1127			−3.59225
$245$	−3.82843	−	26.5241i	−0.244589	−	1.69456i
$246$	−18.4853			−1.17858
$247$	1.41421	−	2.44949i	0.0899843	−	0.155857i
$248$	−7.00000	−	12.1244i	−0.444500	−	0.769897i
$249$	−2.08579	−	3.61269i	−0.132181	−	0.228945i
$250$	−21.5208	+	37.2751i	−1.36110	+	2.35749i
$251$	−13.4853			−0.851183			−0.425592	−	0.904915i	$-0.639934\pi$
$251$	−13.4853			−0.851183			−0.425592	+	0.904915i	$0.639934\pi$
$252$	−9.57107	+	3.31552i	−0.602921	+	0.208858i
$253$	7.00000			0.440086
$254$	20.4853	−	35.4815i	1.28536	−	2.22631i
$255$	−7.00000	−	12.1244i	−0.438357	−	0.759257i
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	0.101305	+	0.994855i	$0.467698\pi$
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	−0.912222	+	0.409695i	$0.865635\pi$
$258$	30.5563			1.90236
$259$	0.585786	−	3.04384i	0.0363990	−	0.189135i
$260$	−41.4558			−2.57098
$261$	2.41421	−	4.18154i	0.149436	−	0.258831i
$262$	12.4853	+	21.6251i	0.771343	+	1.33601i
$263$	−5.65685	−	9.79796i	−0.348817	−	0.604168i	0.637223	−	0.770680i	$-0.280083\pi$
$263$	−5.65685	−	9.79796i	−0.348817	−	0.604168i	−0.986040	+	0.166511i	$0.946750\pi$
$264$	−8.44975	+	14.6354i	−0.520046	+	0.900746i
$265$	7.65685			0.470357
$266$	4.82843	+	4.18154i	0.296050	+	0.256387i
$267$	10.8284			0.662689
$268$	22.9706	−	39.7862i	1.40315	−	2.43033i
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	0.961817	−	0.273692i	$-0.0882449\pi$
$269$	4.00000	+	6.92820i	0.243884	+	0.422420i	−0.717933	+	0.696112i	$0.754912\pi$
$270$	−4.62132	−	8.00436i	−0.281245	−	0.487130i
$271$	9.81371	−	16.9978i	0.596140	−	1.03255i	−0.397245	−	0.917713i	$-0.630034\pi$
$271$	9.81371	−	16.9978i	0.596140	−	1.03255i	0.993385	−	0.114833i	$-0.0366331\pi$
$272$	−10.9706			−0.665188
$273$	5.65685	+	4.89898i	0.342368	+	0.296500i
$274$	33.3848			2.01685
$275$	18.4853	−	32.0174i	1.11470	−	1.93072i
$276$	3.50000	+	6.06218i	0.210675	+	0.364900i
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	0.601975	−	0.798515i	$-0.294381\pi$
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	−0.992522	+	0.122068i	$0.961047\pi$
$278$	−8.03553	+	13.9180i	−0.481939	+	0.834743i
$279$	−3.17157			−0.189877
$280$	8.44975	−	43.9062i	0.504969	−	2.62390i
$281$	6.97056			0.415829			0.207914	−	0.978147i	$-0.433332\pi$
$281$	6.97056			0.415829			0.207914	+	0.978147i	$0.433332\pi$
$282$	7.44975	−	12.9033i	0.443626	−	0.768383i
$283$	−15.8137	−	27.3901i	−0.940027	−	1.62818i	−0.765414	−	0.643538i	$-0.777466\pi$
$283$	−15.8137	−	27.3901i	−0.940027	−	1.62818i	−0.174613	−	0.984637i	$-0.555868\pi$
$284$	−8.31371	−	14.3998i	−0.493328	−	0.854469i
$285$	−1.91421	+	3.31552i	−0.113388	+	0.196394i
$286$	26.1421			1.54582
$287$	−19.1421	+	6.63103i	−1.12992	+	0.391417i
$288$	1.58579			0.0934434
$289$	1.81371	−	3.14144i	0.106689	−	0.184790i
$290$	22.3137	+	38.6485i	1.31031	+	2.26952i
$291$	−8.41421	−	14.5738i	−0.493250	−	0.854334i
$292$	19.7426	−	34.1953i	1.15535	−	2.00113i
$293$	−0.828427			−0.0483972			−0.0241986	−	0.999707i	$-0.507703\pi$
$293$	−0.828427			−0.0483972			−0.0241986	+	0.999707i	$0.507703\pi$
$294$	−13.2782	+	10.4539i	−0.774399	+	0.609681i
$295$	−41.4558			−2.41365
$296$	2.58579	−	4.47871i	0.150296	−	0.260320i
$297$	1.91421	+	3.31552i	0.111074	+	0.192386i
$298$	4.62132	+	8.00436i	0.267706	+	0.463680i
$299$	2.58579	−	4.47871i	0.149540	−	0.259011i
$300$	36.9706			2.13450
$301$	31.6421	−	10.9612i	1.82382	−	0.631791i
$302$	22.4853			1.29388
$303$	1.74264	−	3.01834i	0.100112	−	0.173399i
$304$	1.50000	+	2.59808i	0.0860309	+	0.149010i
$305$	−28.0563	−	48.5950i	−1.60650	−	2.78254i
$306$	−4.41421	+	7.64564i	−0.252344	+	0.437072i
$307$	2.48528			0.141843			0.0709213	−	0.997482i	$-0.477406\pi$
$307$	2.48528			0.141843			0.0709213	+	0.997482i	$0.477406\pi$
$308$	−7.32843	+	38.0796i	−0.417576	+	2.16979i
$309$	3.65685			0.208031
$310$	14.6569	−	25.3864i	0.832453	−	1.44185i
$311$	−11.3137	−	19.5959i	−0.641542	−	1.11118i	−0.985089	−	0.172047i	$-0.944962\pi$
$311$	−11.3137	−	19.5959i	−0.641542	−	1.11118i	0.343547	−	0.939135i	$-0.388371\pi$
$312$	6.24264	+	10.8126i	0.353420	+	0.612141i
$313$	−15.6421	+	27.0930i	−0.884146	+	1.53139i	−0.0374562	+	0.999298i	$0.511925\pi$
$313$	−15.6421	+	27.0930i	−0.884146	+	1.53139i	−0.846690	+	0.532087i	$0.821408\pi$
$314$	−25.7279			−1.45191
$315$	−7.65685	−	6.63103i	−0.431415	−	0.373616i
$316$	8.97056			0.504634
$317$	−14.8995	+	25.8067i	−0.836839	+	1.44945i	0.0556853	+	0.998448i	$0.482266\pi$
$317$	−14.8995	+	25.8067i	−0.836839	+	1.44945i	−0.892524	+	0.450999i	$0.851068\pi$
$318$	−2.41421	−	4.18154i	−0.135382	−	0.234489i
$319$	−9.24264	−	16.0087i	−0.517489	−	0.896316i
$320$	−18.8137	+	32.5863i	−1.05172	+	1.82163i
$321$	−2.82843			−0.157867
$322$	8.82843	+	7.64564i	0.491989	+	0.426075i
$323$	3.65685			0.203473
$324$	−1.91421	+	3.31552i	−0.106345	+	0.184195i
$325$	−13.6569	−	23.6544i	−0.757546	−	1.31211i
$326$	26.5208	+	45.9354i	1.46885	+	2.54413i
$327$	−9.07107	+	15.7116i	−0.501631	+	0.868851i
$328$	−33.7990			−1.86624
$329$	3.08579	−	16.0342i	0.170125	−	0.883995i
$330$	−35.3848			−1.94787
$331$	2.75736	−	4.77589i	0.151558	−	0.262506i	−0.780242	−	0.625477i	$-0.784904\pi$
$331$	2.75736	−	4.77589i	0.151558	−	0.262506i	0.931800	+	0.362971i	$0.118238\pi$
$332$	−7.98528	−	13.8309i	−0.438249	−	0.759070i
$333$	−0.585786	−	1.01461i	−0.0321009	−	0.0556004i
$334$	10.6569	−	18.4582i	0.583117	−	1.00999i
$335$	45.9411			2.51003
$336$	−7.50000	+	2.59808i	−0.409159	+	0.141737i
$337$	−6.48528			−0.353276			−0.176638	−	0.984276i	$-0.556522\pi$
$337$	−6.48528			−0.353276			−0.176638	+	0.984276i	$0.556522\pi$
$338$	−6.03553	+	10.4539i	−0.328290	+	0.568615i
$339$	6.41421	+	11.1097i	0.348372	+	0.603398i
$340$	−26.7990	−	46.4172i	−1.45338	−	2.51733i
$341$	−6.07107	+	10.5154i	−0.328767	+	0.569441i
$342$	2.41421			0.130546
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	55.8701			3.01231
$345$	−3.50000	+	6.06218i	−0.188434	+	0.326377i
$346$	3.41421	+	5.91359i	0.183549	+	0.317917i
$347$	−10.2279	−	17.7153i	−0.549064	−	0.951006i	−0.998339	−	0.0576128i	$-0.981651\pi$
$347$	−10.2279	−	17.7153i	−0.549064	−	0.951006i	0.449275	−	0.893393i	$-0.351682\pi$
$348$	9.24264	−	16.0087i	0.495458	−	0.858158i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	58.2843	−	20.1903i	3.11543	−	1.07921i
$351$	2.82843			0.150970
$352$	3.03553	−	5.25770i	0.161795	−	0.280236i
$353$	0.656854	+	1.13770i	0.0349608	+	0.0605539i	0.882976	−	0.469417i	$-0.155536\pi$
$353$	0.656854	+	1.13770i	0.0349608	+	0.0605539i	−0.848016	+	0.529971i	$0.822203\pi$
$354$	13.0711	+	22.6398i	0.694719	+	1.20329i
$355$	8.31371	−	14.3998i	0.441246	−	0.764260i
$356$	41.4558			2.19716
$357$	−1.82843	+	9.50079i	−0.0967706	+	0.502835i
$358$	25.3137			1.33787
$359$	3.08579	−	5.34474i	0.162862	−	0.282085i	−0.773032	−	0.634367i	$-0.781261\pi$
$359$	3.08579	−	5.34474i	0.162862	−	0.282085i	0.935894	+	0.352282i	$0.114594\pi$
$360$	−8.44975	−	14.6354i	−0.445341	−	0.771353i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−14.0711	+	24.3718i	−0.739559	+	1.28095i
$363$	3.65685			0.191935
$364$	21.6569	+	18.7554i	1.13513	+	0.983049i
$365$	39.4853			2.06675
$366$	−17.6924	+	30.6441i	−0.924796	+	1.60179i
$367$	−14.8284	−	25.6836i	−0.774038	−	1.34067i	−0.935334	−	0.353766i	$-0.884901\pi$
$367$	−14.8284	−	25.6836i	−0.774038	−	1.34067i	0.161296	−	0.986906i	$-0.448433\pi$
$368$	2.74264	+	4.75039i	0.142970	+	0.247631i
$369$	−3.82843	+	6.63103i	−0.199300	+	0.345198i
$370$	10.8284			0.562943
$371$	−4.00000	−	3.46410i	−0.207670	−	0.179847i
$372$	−12.1421			−0.629540
$373$	−10.1421	+	17.5667i	−0.525140	+	0.909569i	0.474431	+	0.880292i	$0.342654\pi$
$373$	−10.1421	+	17.5667i	−0.525140	+	0.909569i	−0.999571	+	0.0292765i	$0.990680\pi$
$374$	16.8995	+	29.2708i	0.873852	+	1.51356i
$375$	8.91421	+	15.4399i	0.460328	+	0.797311i
$376$	13.6213	−	23.5928i	0.702466	−	1.21671i
$377$	−13.6569			−0.703364
$378$	−1.20711	+	6.27231i	−0.0620869	+	0.322613i
$379$	−16.4853			−0.846792			−0.423396	−	0.905945i	$-0.639162\pi$
$379$	−16.4853			−0.846792			−0.423396	+	0.905945i	$0.639162\pi$
$380$	−7.32843	+	12.6932i	−0.375940	+	0.651148i
$381$	−8.48528	−	14.6969i	−0.434714	−	0.752947i
$382$	14.2782	+	24.7305i	0.730535	+	1.26532i
$383$	−8.00000	+	13.8564i	−0.408781	+	0.708029i	−0.994753	−	0.102302i	$-0.967379\pi$
$383$	−8.00000	+	13.8564i	−0.408781	+	0.708029i	0.585973	+	0.810331i	$0.300713\pi$
$384$	20.5563			1.04901
$385$	−36.6421	+	12.6932i	−1.86746	+	0.646906i
$386$	−9.65685			−0.491521
$387$	6.32843	−	10.9612i	0.321692	−	0.557187i
$388$	−32.2132	−	55.7949i	−1.63538	−	2.83256i
$389$	−2.17157	−	3.76127i	−0.110103	−	0.190704i	0.805709	−	0.592312i	$-0.201785\pi$
$389$	−2.17157	−	3.76127i	−0.110103	−	0.190704i	−0.915812	+	0.401608i	$0.868451\pi$
$390$	−13.0711	+	22.6398i	−0.661879	+	1.14641i
$391$	6.68629			0.338140
$392$	−24.2782	+	19.1141i	−1.22623	+	0.965408i
$393$	10.3431			0.521743
$394$	−21.1066	+	36.5577i	−1.06334	+	1.84175i
$395$	4.48528	+	7.76874i	0.225679	+	0.390887i
$396$	7.32843	+	12.6932i	0.368267	+	0.637858i
$397$	−2.65685	+	4.60181i	−0.133344	+	0.230958i	−0.924964	−	0.380056i	$-0.875905\pi$
$397$	−2.65685	+	4.60181i	−0.133344	+	0.230958i	0.791620	+	0.611014i	$0.209238\pi$
$398$	−8.07107			−0.404566
$399$	2.50000	−	0.866025i	0.125157	−	0.0433555i
$400$	28.9706			1.44853
$401$	0.343146	−	0.594346i	0.0171359	−	0.0296802i	−0.857330	−	0.514767i	$-0.827879\pi$
$401$	0.343146	−	0.594346i	0.0171359	−	0.0296802i	0.874466	+	0.485086i	$0.161212\pi$
$402$	−14.4853	−	25.0892i	−0.722460	−	1.25134i
$403$	4.48528	+	7.76874i	0.223428	+	0.386988i
$404$	6.67157	−	11.5555i	0.331923	−	0.574908i
$405$	−3.82843			−0.190236
$406$	5.82843	−	30.2854i	0.289260	−	1.50304i
$407$	−4.48528			−0.222327
$408$	−8.07107	+	13.9795i	−0.399577	+	0.692088i
$409$	−2.65685	−	4.60181i	−0.131373	−	0.227545i	0.792833	−	0.609439i	$-0.208605\pi$
$409$	−2.65685	−	4.60181i	−0.131373	−	0.227545i	−0.924206	+	0.381894i	$0.875272\pi$
$410$	−35.3848	−	61.2882i	−1.74753	−	3.02681i
$411$	6.91421	−	11.9758i	0.341053	−	0.590721i
$412$	14.0000			0.689730
$413$	21.6569	+	18.7554i	1.06566	+	0.922892i
$414$	4.41421			0.216947
$415$	7.98528	−	13.8309i	0.391982	−	0.678933i
$416$	−2.24264	−	3.88437i	−0.109955	−	0.190447i
$417$	3.32843	+	5.76500i	0.162994	+	0.282314i
$418$	4.62132	−	8.00436i	0.226036	−	0.391506i
$419$	−10.1716			−0.496914			−0.248457	−	0.968643i	$-0.579923\pi$
$419$	−10.1716			−0.496914			−0.248457	+	0.968643i	$0.579923\pi$
$420$	−29.3137	−	25.3864i	−1.43036	−	1.23873i
$421$	19.1716			0.934365			0.467183	−	0.884161i	$-0.345269\pi$
$421$	19.1716			0.934365			0.467183	+	0.884161i	$0.345269\pi$
$422$	19.8995	−	34.4669i	0.968692	−	1.67782i
$423$	−3.08579	−	5.34474i	−0.150036	−	0.259870i
$424$	−4.41421	−	7.64564i	−0.214373	−	0.371305i
$425$	17.6569	−	30.5826i	0.856483	−	1.48347i
$426$	−10.4853			−0.508014
$427$	−7.32843	+	38.0796i	−0.354647	+	1.84280i
$428$	−10.8284			−0.523412
$429$	5.41421	−	9.37769i	0.261401	−	0.452759i
$430$	58.4914	+	101.310i	2.82070	+	4.88560i
$431$	11.5858	+	20.0672i	0.558068	+	0.966602i	0.997658	+	0.0684031i	$0.0217904\pi$
$431$	11.5858	+	20.0672i	0.558068	+	0.966602i	−0.439590	+	0.898199i	$0.644876\pi$
$432$	−1.50000	+	2.59808i	−0.0721688	+	0.125000i
$433$	8.48528			0.407777			0.203888	−	0.978994i	$-0.434642\pi$
$433$	8.48528			0.407777			0.203888	+	0.978994i	$0.434642\pi$
$434$	−19.1421	+	6.63103i	−0.918852	+	0.318300i
$435$	18.4853			0.886301
$436$	−34.7279	+	60.1505i	−1.66317	+	2.88069i
$437$	−0.914214	−	1.58346i	−0.0437328	−	0.0757474i
$438$	−12.4497	−	21.5636i	−0.594872	−	1.03035i
$439$	9.89949	−	17.1464i	0.472477	−	0.818354i	−0.527027	−	0.849849i	$-0.676693\pi$
$439$	9.89949	−	17.1464i	0.472477	−	0.818354i	0.999504	+	0.0314943i	$0.0100266\pi$
$440$	−64.6985			−3.08438
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$	24.9706			1.18773
$443$	16.8284	−	29.1477i	0.799543	−	1.38485i	−0.120372	−	0.992729i	$-0.538409\pi$
$443$	16.8284	−	29.1477i	0.799543	−	1.38485i	0.919914	−	0.392120i	$-0.128258\pi$
$444$	−2.24264	−	3.88437i	−0.106431	−	0.184344i
$445$	20.7279	+	35.9018i	0.982598	+	1.70191i
$446$	26.3137	−	45.5767i	1.24599	−	2.15812i
$447$	3.82843			0.181078
$448$	24.5711	−	8.51167i	1.16087	−	0.402138i
$449$	26.1421			1.23372			0.616862	−	0.787071i	$-0.288404\pi$
$449$	26.1421			1.23372			0.616862	+	0.787071i	$0.288404\pi$
$450$	11.6569	−	20.1903i	0.549509	−	0.951778i
$451$	14.6569	+	25.3864i	0.690164	+	1.19540i
$452$	24.5563	+	42.5328i	1.15503	+	2.00058i
$453$	4.65685	−	8.06591i	0.218798	−	0.378969i
$454$	15.3137			0.718708
$455$	−5.41421	+	28.1331i	−0.253822	+	1.31890i
$456$	4.41421			0.206714
$457$	7.32843	−	12.6932i	0.342809	−	0.593763i	−0.642144	−	0.766584i	$-0.721955\pi$
$457$	7.32843	−	12.6932i	0.342809	−	0.593763i	0.984953	+	0.172821i	$0.0552882\pi$
$458$	−18.8995	−	32.7349i	−0.883115	−	1.52960i
$459$	1.82843	+	3.16693i	0.0853437	+	0.147820i
$460$	−13.3995	+	23.2086i	−0.624755	+	1.08211i
$461$	22.4558			1.04587			0.522936	−	0.852372i	$-0.324836\pi$
$461$	22.4558			1.04587			0.522936	+	0.852372i	$0.324836\pi$
$462$	18.4853	+	16.0087i	0.860013	+	0.744793i
$463$	−20.6569			−0.960005			−0.480003	−	0.877267i	$-0.659364\pi$
$463$	−20.6569			−0.960005			−0.480003	+	0.877267i	$0.659364\pi$
$464$	7.24264	−	12.5446i	0.336231	−	0.582369i
$465$	−6.07107	−	10.5154i	−0.281539	−	0.487640i
$466$	7.24264	+	12.5446i	0.335509	+	0.581118i
$467$	−12.7426	+	22.0709i	−0.589659	+	1.02132i	0.404618	+	0.914486i	$0.367405\pi$
$467$	−12.7426	+	22.0709i	−0.589659	+	1.02132i	−0.994277	+	0.106834i	$0.965929\pi$
$468$	10.8284			0.500544
$469$	−24.0000	−	20.7846i	−1.10822	−	0.959744i
$470$	57.0416			2.63113
$471$	−5.32843	+	9.22911i	−0.245521	+	0.425255i
$472$	23.8995	+	41.3951i	1.10006	+	1.90537i
$473$	−24.2279	−	41.9640i	−1.11400	−	1.92951i
$474$	2.82843	−	4.89898i	0.129914	−	0.225018i
$475$	−9.65685			−0.443087
$476$	−7.00000	+	36.3731i	−0.320844	+	1.66716i
$477$	−2.00000			−0.0915737
$478$	2.82843	−	4.89898i	0.129369	−	0.224074i
$479$	−6.08579	−	10.5409i	−0.278067	−	0.481626i	0.692838	−	0.721094i	$-0.256360\pi$
$479$	−6.08579	−	10.5409i	−0.278067	−	0.481626i	−0.970904	+	0.239468i	$0.923027\pi$
$480$	3.03553	+	5.25770i	0.138553	+	0.239980i
$481$	−1.65685	+	2.86976i	−0.0755461	+	0.130850i
$482$	−47.7990			−2.17718
$483$	4.57107	−	1.58346i	0.207991	−	0.0720501i
$484$	14.0000			0.636364
$485$	32.2132	−	55.7949i	1.46273	−	2.53352i
$486$	1.20711	+	2.09077i	0.0547555	+	0.0948393i
$487$	0.171573	+	0.297173i	0.00777471	+	0.0134662i	0.869887	−	0.493252i	$-0.164192\pi$
$487$	0.171573	+	0.297173i	0.00777471	+	0.0134662i	−0.862112	+	0.506718i	$0.830859\pi$
$488$	−32.3492	+	56.0305i	−1.46438	+	2.53638i
$489$	21.9706			0.993543
$490$	−60.0772	−	24.0131i	−2.71401	−	1.08480i
$491$	−8.51472			−0.384264			−0.192132	−	0.981369i	$-0.561540\pi$
$491$	−8.51472			−0.384264			−0.192132	+	0.981369i	$0.561540\pi$
$492$	−14.6569	+	25.3864i	−0.660782	+	1.14451i
$493$	−8.82843	−	15.2913i	−0.397612	−	0.688685i
$494$	−3.41421	−	5.91359i	−0.153613	−	0.266065i
$495$	−7.32843	+	12.6932i	−0.329388	+	0.570517i
$496$	−9.51472			−0.427223
$497$	−10.8579	+	3.76127i	−0.487042	+	0.168716i
$498$	−10.0711			−0.451295
$499$	−9.98528	+	17.2950i	−0.447003	+	0.774231i	−0.998189	−	0.0601507i	$-0.980842\pi$
$499$	−9.98528	+	17.2950i	−0.447003	+	0.774231i	0.551187	+	0.834382i	$0.314175\pi$
$500$	34.1274	+	59.1104i	1.52622	+	2.64350i
$501$	−4.41421	−	7.64564i	−0.197213	−	0.341582i
$502$	−16.2782	+	28.1946i	−0.726530	+	1.25839i
$503$	20.1127			0.896781			0.448390	−	0.893838i	$-0.351997\pi$
$503$	20.1127			0.896781			0.448390	+	0.893838i	$0.351997\pi$
$504$	−2.20711	+	11.4685i	−0.0983123	+	0.510846i
$505$	13.3431			0.593762
$506$	8.44975	−	14.6354i	0.375637	−	0.650623i
$507$	2.50000	+	4.33013i	0.111029	+	0.192308i
$508$	−32.4853	−	56.2662i	−1.44130	−	2.49641i
$509$	5.24264	−	9.08052i	0.232376	−	0.402487i	−0.726131	−	0.687557i	$-0.758683\pi$
$509$	5.24264	−	9.08052i	0.232376	−	0.402487i	0.958507	+	0.285070i	$0.0920167\pi$
$510$	−33.7990			−1.49664
$511$	−20.6274	−	17.8639i	−0.912503	−	0.790251i
$512$	31.2426			1.38074
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$	31.3848	+	54.3600i	1.38432	+	2.39772i
$515$	7.00000	+	12.1244i	0.308457	+	0.534263i
$516$	24.2279	−	41.9640i	1.06657	−	1.84736i
$517$	−23.6274			−1.03913
$518$	−5.65685	−	4.89898i	−0.248548	−	0.215249i
$519$	2.82843			0.124154
$520$	−23.8995	+	41.3951i	−1.04806	+	1.81530i
$521$	20.4853	+	35.4815i	0.897476	+	1.55447i	0.830709	+	0.556706i	$0.187935\pi$
$521$	20.4853	+	35.4815i	0.897476	+	1.55447i	0.0667670	+	0.997769i	$0.478732\pi$
$522$	−5.82843	−	10.0951i	−0.255103	−	0.441852i
$523$	18.8995	−	32.7349i	0.826417	−	1.43140i	−0.0744141	−	0.997227i	$-0.523709\pi$
$523$	18.8995	−	32.7349i	0.826417	−	1.43140i	0.900831	−	0.434169i	$-0.142958\pi$
$524$	39.5980			1.72985
$525$	4.82843	−	25.0892i	0.210730	−	1.09498i
$526$	−27.3137			−1.19093
$527$	−5.79899	+	10.0441i	−0.252608	+	0.437530i
$528$	5.74264	+	9.94655i	0.249916	+	0.432868i
$529$	9.82843	+	17.0233i	0.427323	+	0.740145i
$530$	9.24264	−	16.0087i	0.401475	−	0.695375i
$531$	10.8284			0.469914
$532$	9.57107	−	3.31552i	0.414958	−	0.143746i
$533$	21.6569			0.938062
$534$	13.0711	−	22.6398i	0.565640	−	0.979718i
$535$	−5.41421	−	9.37769i	−0.234077	−	0.405433i
$536$	−26.4853	−	45.8739i	−1.14399	−	1.98145i
$537$	5.24264	−	9.08052i	0.226237	−	0.391853i
$538$	19.3137			0.832673
$539$	24.8848	+	9.94655i	1.07186	+	0.428428i
$540$	−14.6569			−0.630731
$541$	−11.5000	+	19.9186i	−0.494424	+	0.856367i	−0.999979	−	0.00642713i	$-0.997954\pi$
$541$	−11.5000	+	19.9186i	−0.494424	+	0.856367i	0.505556	+	0.862794i	$0.331288\pi$
$542$	−23.6924	−	41.0364i	−1.01768	−	1.76267i
$543$	5.82843	+	10.0951i	0.250122	+	0.433224i
$544$	2.89949	−	5.02207i	0.124315	−	0.215320i
$545$	−69.4558			−2.97516
$546$	17.0711	−	5.91359i	0.730574	−	0.253078i
$547$	−5.79899			−0.247947			−0.123973	−	0.992286i	$-0.539564\pi$
$547$	−5.79899			−0.247947			−0.123973	+	0.992286i	$0.539564\pi$
$548$	26.4706	−	45.8484i	1.13077	−	1.95854i
$549$	7.32843	+	12.6932i	0.312770	+	0.541733i
$550$	−44.6274	−	77.2970i	−1.90292	−	3.29595i
$551$	−2.41421	+	4.18154i	−0.102849	+	0.178140i
$552$	8.07107			0.343527
$553$	1.17157	−	6.08767i	0.0498203	−	0.258874i
$554$	−31.3848			−1.33341
$555$	2.24264	−	3.88437i	0.0951948	−	0.164882i
$556$	12.7426	+	22.0709i	0.540408	+	0.936015i
$557$	−7.22792	−	12.5191i	−0.306257	−	0.530452i	0.671283	−	0.741201i	$-0.265743\pi$
$557$	−7.22792	−	12.5191i	−0.306257	−	0.530452i	−0.977540	+	0.210748i	$0.932410\pi$
$558$	−3.82843	+	6.63103i	−0.162070	+	0.280714i
$559$	−35.7990			−1.51414
$560$	−22.9706	−	19.8931i	−0.970683	−	0.840637i
$561$	14.0000			0.591080
$562$	8.41421	−	14.5738i	0.354932	−	0.614761i
$563$	−0.242641	−	0.420266i	−0.0102261	−	0.0177121i	0.860867	−	0.508830i	$-0.169922\pi$
$563$	−0.242641	−	0.420266i	−0.0102261	−	0.0177121i	−0.871093	+	0.491118i	$0.836588\pi$
$564$	−11.8137	−	20.4619i	−0.497447	−	0.861603i
$565$	−24.5563	+	42.5328i	−1.03309	+	1.78937i
$566$	−76.3553			−3.20945
$567$	2.00000	+	1.73205i	0.0839921	+	0.0727393i
$568$	−19.1716			−0.804421
$569$	22.8995	−	39.6631i	0.959997	−	1.66276i	0.237502	−	0.971387i	$-0.423671\pi$
$569$	22.8995	−	39.6631i	0.959997	−	1.66276i	0.722495	−	0.691376i	$-0.242995\pi$
$570$	4.62132	+	8.00436i	0.193566	+	0.335266i
$571$	−13.6421	−	23.6289i	−0.570906	−	0.988838i	−0.996473	−	0.0839109i	$-0.973259\pi$
$571$	−13.6421	−	23.6289i	−0.570906	−	0.988838i	0.425568	−	0.904927i	$-0.360074\pi$
$572$	20.7279	−	35.9018i	0.866678	−	1.50113i
$573$	11.8284			0.494140
$574$	−9.24264	+	48.0262i	−0.385780	+	2.00457i
$575$	−17.6569			−0.736342
$576$	4.91421	−	8.51167i	0.204759	−	0.354653i
$577$	−9.15685	−	15.8601i	−0.381205	−	0.660266i	0.610030	−	0.792378i	$-0.291157\pi$
$577$	−9.15685	−	15.8601i	−0.381205	−	0.660266i	−0.991235	+	0.132112i	$0.957824\pi$
$578$	−4.37868	−	7.58410i	−0.182129	−	0.315457i
$579$	−2.00000	+	3.46410i	−0.0831172	+	0.143963i
$580$	70.7696			2.93855
$581$	−10.4289	+	3.61269i	−0.432665	+	0.149880i
$582$	−40.6274			−1.68406
$583$	−3.82843	+	6.63103i	−0.158557	+	0.274629i
$584$	−22.7635	−	39.4275i	−0.941959	−	1.63152i
$585$	5.41421	+	9.37769i	0.223850	+	0.387720i
$586$	−1.00000	+	1.73205i	−0.0413096	+	0.0715504i
$587$	−26.6274			−1.09903			−0.549516	−	0.835483i	$-0.685188\pi$
$587$	−26.6274			−1.09903			−0.549516	+	0.835483i	$0.685188\pi$
$588$	3.82843	+	26.5241i	0.157882	+	1.09384i
$589$	3.17157			0.130682
$590$	−50.0416	+	86.6746i	−2.06018	+	3.56834i
$591$	8.74264	+	15.1427i	0.359624	+	0.622887i
$592$	−1.75736	−	3.04384i	−0.0722270	−	0.125101i
$593$	−13.7426	+	23.8030i	−0.564343	+	0.977470i	0.432768	+	0.901505i	$0.357537\pi$
$593$	−13.7426	+	23.8030i	−0.564343	+	0.977470i	−0.997111	+	0.0759647i	$0.975796\pi$
$594$	9.24264			0.379230
$595$	−35.0000	+	12.1244i	−1.43486	+	0.497050i
$596$	14.6569			0.600368
$597$	−1.67157	+	2.89525i	−0.0684129	+	0.118495i
$598$	−6.24264	−	10.8126i	−0.255281	−	0.442159i
$599$	14.5563	+	25.2123i	0.594756	+	1.03015i	0.993581	+	0.113121i	$0.0360848\pi$
$599$	14.5563	+	25.2123i	0.594756	+	1.03015i	−0.398825	+	0.917027i	$0.630582\pi$
$600$	21.3137	−	36.9164i	0.870129	−	1.50711i
$601$	−8.68629			−0.354321			−0.177161	−	0.984182i	$-0.556691\pi$
$601$	−8.68629			−0.354321			−0.177161	+	0.984182i	$0.556691\pi$
$602$	15.2782	−	79.3877i	0.622692	−	3.23560i
$603$	−12.0000			−0.488678
$604$	17.8284	−	30.8797i	0.725428	−	1.25648i
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$	−4.20711	−	7.28692i	−0.170902	−	0.296011i
$607$	−6.92893	+	12.0013i	−0.281237	+	0.487116i	−0.971690	−	0.236261i	$-0.924078\pi$
$607$	−6.92893	+	12.0013i	−0.281237	+	0.487116i	0.690453	+	0.723377i	$0.257411\pi$
$608$	−1.58579			−0.0643121
$609$	−9.65685	−	8.36308i	−0.391315	−	0.338889i
$610$	−135.468			−5.48494
$611$	−8.72792	+	15.1172i	−0.353094	+	0.611577i
$612$	7.00000	+	12.1244i	0.282958	+	0.490098i
$613$	18.3137	+	31.7203i	0.739684	+	1.28117i	0.952638	+	0.304108i	$0.0983582\pi$
$613$	18.3137	+	31.7203i	0.739684	+	1.28117i	−0.212954	+	0.977062i	$0.568308\pi$
$614$	3.00000	−	5.19615i	0.121070	−	0.209700i
$615$	−29.3137			−1.18204
$616$	33.7990	+	29.2708i	1.36180	+	1.17935i
$617$	−32.1716			−1.29518			−0.647589	−	0.761989i	$-0.724223\pi$
$617$	−32.1716			−1.29518			−0.647589	+	0.761989i	$0.724223\pi$
$618$	4.41421	−	7.64564i	0.177566	−	0.307553i
$619$	−4.67157	−	8.09140i	−0.187766	−	0.325221i	0.756739	−	0.653717i	$-0.226791\pi$
$619$	−4.67157	−	8.09140i	−0.187766	−	0.325221i	−0.944505	+	0.328496i	$0.893458\pi$
$620$	−23.2426	−	40.2574i	−0.933447	−	1.61678i
$621$	0.914214	−	1.58346i	0.0366861	−	0.0635422i
$622$	−54.6274			−2.19036
$623$	5.41421	−	28.1331i	0.216916	−	1.12713i
$624$	8.48528			0.339683
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$	37.7635	+	65.4082i	1.50933	+	2.61424i
$627$	−1.91421	−	3.31552i	−0.0764463	−	0.132409i
$628$	−20.3995	+	35.3330i	−0.814028	+	1.40994i
$629$	−4.28427			−0.170825
$630$	−23.1066	+	8.00436i	−0.920589	+	0.318901i
$631$	−16.6569			−0.663099			−0.331549	−	0.943438i	$-0.607571\pi$
$631$	−16.6569			−0.663099			−0.331549	+	0.943438i	$0.607571\pi$
$632$	5.17157	−	8.95743i	0.205714	−	0.356307i
$633$	−8.24264	−	14.2767i	−0.327616	−	0.567447i
$634$	35.9706	+	62.3028i	1.42857	+	2.47436i
$635$	32.4853	−	56.2662i	1.28914	−	2.23285i
$636$	−7.65685			−0.303614
$637$	15.5563	−	12.2474i	0.616365	−	0.485262i
$638$	−44.6274			−1.76682
$639$	−2.17157	+	3.76127i	−0.0859061	+	0.148794i
$640$	39.3492	+	68.1549i	1.55542	+	2.69406i
$641$	2.58579	+	4.47871i	0.102132	+	0.176899i	0.912563	−	0.408936i	$-0.134100\pi$
$641$	2.58579	+	4.47871i	0.102132	+	0.176899i	−0.810431	+	0.585835i	$0.800767\pi$
$642$	−3.41421	+	5.91359i	−0.134748	+	0.233391i
$643$	1.37258			0.0541294			0.0270647	−	0.999634i	$-0.491384\pi$
$643$	1.37258			0.0541294			0.0270647	+	0.999634i	$0.491384\pi$
$644$	17.5000	−	6.06218i	0.689597	−	0.238883i
$645$	48.4558			1.90795
$646$	4.41421	−	7.64564i	0.173675	−	0.300814i
$647$	−3.42893	−	5.93908i	−0.134805	−	0.233490i	0.790718	−	0.612181i	$-0.209708\pi$
$647$	−3.42893	−	5.93908i	−0.134805	−	0.233490i	−0.925523	+	0.378691i	$0.876374\pi$
$648$	2.20711	+	3.82282i	0.0867033	+	0.150175i
$649$	20.7279	−	35.9018i	0.813642	−	1.40927i
$650$	−65.9411			−2.58642
$651$	−1.58579	+	8.23999i	−0.0621519	+	0.322951i
$652$	84.1127			3.29411
$653$	−19.9706	+	34.5900i	−0.781509	+	1.35361i	0.149554	+	0.988754i	$0.452216\pi$
$653$	−19.9706	+	34.5900i	−0.781509	+	1.35361i	−0.931063	+	0.364859i	$0.881117\pi$
$654$	21.8995	+	37.9310i	0.856338	+	1.48322i
$655$	19.7990	+	34.2929i	0.773611	+	1.33993i
$656$	−11.4853	+	19.8931i	−0.448425	+	0.776695i
$657$	−10.3137			−0.402376
$658$	−29.7990	−	25.8067i	−1.16169	−	1.00605i
$659$	−21.5147			−0.838094			−0.419047	−	0.907964i	$-0.637636\pi$
$659$	−21.5147			−0.838094			−0.419047	+	0.907964i	$0.637636\pi$
$660$	−28.0563	+	48.5950i	−1.09209	+	1.89156i
$661$	−6.14214	−	10.6385i	−0.238901	−	0.413789i	0.721498	−	0.692417i	$-0.243454\pi$
$661$	−6.14214	−	10.6385i	−0.238901	−	0.413789i	−0.960399	+	0.278627i	$0.910121\pi$
$662$	−6.65685	−	11.5300i	−0.258726	−	0.448127i
$663$	5.17157	−	8.95743i	0.200847	−	0.347878i
$664$	−18.4142			−0.714610
$665$	7.65685	+	6.63103i	0.296920	+	0.257140i
$666$	−2.82843			−0.109599
$667$	−4.41421	+	7.64564i	−0.170919	+	0.296040i
$668$	−16.8995	−	29.2708i	−0.653861	−	1.13252i
$669$	−10.8995	−	18.8785i	−0.421399	−	0.729884i
$670$	55.4558	−	96.0523i	2.14245	−	3.71083i
$671$	56.1127			2.16621
$672$	0.792893	−	4.11999i	0.0305865	−	0.158932i
$673$	2.82843			0.109028			0.0545139	−	0.998513i	$-0.482639\pi$
$673$	2.82843			0.109028			0.0545139	+	0.998513i	$0.482639\pi$
$674$	−7.82843	+	13.5592i	−0.301540	+	0.522282i
$675$	−4.82843	−	8.36308i	−0.185846	−	0.321895i
$676$	9.57107	+	16.5776i	0.368118	+	0.637599i
$677$	8.00000	−	13.8564i	0.307465	−	0.532545i	−0.670342	−	0.742052i	$-0.733853\pi$
$677$	8.00000	−	13.8564i	0.307465	−	0.532545i	0.977807	+	0.209507i	$0.0671860\pi$
$678$	30.9706			1.18942
$679$	−42.0711	+	14.5738i	−1.61454	+	0.559293i
$680$	−61.7990			−2.36988
$681$	3.17157	−	5.49333i	0.121535	−	0.210505i
$682$	14.6569	+	25.3864i	0.561240	+	0.972096i
$683$	−2.51472	−	4.35562i	−0.0962230	−	0.166663i	0.813895	−	0.581011i	$-0.197343\pi$
$683$	−2.51472	−	4.35562i	−0.0962230	−	0.166663i	−0.910118	+	0.414348i	$0.864010\pi$
$684$	1.91421	−	3.31552i	0.0731918	−	0.126772i
$685$	52.9411			2.02278
$686$	20.5208	+	39.7246i	0.783488	+	1.51669i
$687$	−15.6569			−0.597346
$688$	18.9853	−	32.8835i	0.723807	−	1.25367i
$689$	2.82843	+	4.89898i	0.107754	+	0.186636i
$690$	8.44975	+	14.6354i	0.321676	+	0.557160i
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	−0.957290	−	0.289130i	$-0.906634\pi$
$691$	−6.00000	+	10.3923i	−0.228251	+	0.395342i	0.729039	+	0.684472i	$0.239967\pi$
$692$	10.8284			0.411635
$693$	9.57107	−	3.31552i	0.363575	−	0.125946i
$694$	−49.3848			−1.87462
$695$	−12.7426	+	22.0709i	−0.483356	+	0.837197i
$696$	−10.6569	−	18.4582i	−0.403947	−	0.699657i
$697$	14.0000	+	24.2487i	0.530288	+	0.918485i
$698$	16.8995	−	29.2708i	0.639655	−	1.10792i
$699$	6.00000			0.226941
$700$	18.4853	−	96.0523i	0.698678	−	3.63044i
$701$	2.45584			0.0927560			0.0463780	−	0.998924i	$-0.485232\pi$
$701$	2.45584			0.0927560			0.0463780	+	0.998924i	$0.485232\pi$
$702$	3.41421	−	5.91359i	0.128861	−	0.223194i
$703$	0.585786	+	1.01461i	0.0220934	+	0.0382668i
$704$	−18.8137	−	32.5863i	−0.709068	−	1.22814i
$705$	11.8137	−	20.4619i	0.444930	−	0.770641i
$706$	3.17157			0.119364
$707$	−6.97056	−	6.03668i	−0.262155	−	0.227033i
$708$	41.4558			1.55801
$709$	7.98528	−	13.8309i	0.299894	−	0.519431i	−0.676218	−	0.736702i	$-0.736382\pi$
$709$	7.98528	−	13.8309i	0.299894	−	0.519431i	0.976111	+	0.217271i	$0.0697155\pi$
$710$	−20.0711	−	34.7641i	−0.753254	−	1.30467i
$711$	−1.17157	−	2.02922i	−0.0439374	−	0.0761018i
$712$	23.8995	−	41.3951i	0.895671	−	1.55135i
$713$	5.79899			0.217174
$714$	17.6569	+	15.2913i	0.660791	+	0.572262i
$715$	41.4558			1.55036
$716$	20.0711	−	34.7641i	0.750091	−	1.29920i
$717$	−1.17157	−	2.02922i	−0.0437532	−	0.0757827i
$718$	−7.44975	−	12.9033i	−0.278022	−	0.481548i
$719$	0.485281	−	0.840532i	0.0180979	−	0.0313466i	−0.856835	−	0.515591i	$-0.827572\pi$
$719$	0.485281	−	0.840532i	0.0180979	−	0.0313466i	0.874933	+	0.484245i	$0.160906\pi$
$720$	−11.4853			−0.428031
$721$	1.82843	−	9.50079i	0.0680942	−	0.353828i
$722$	−2.41421			−0.0898477
$723$	−9.89949	+	17.1464i	−0.368166	+	0.637683i
$724$	22.3137	+	38.6485i	0.829282	+	1.43636i
$725$	23.3137	+	40.3805i	0.865849	+	1.49970i
$726$	4.41421	−	7.64564i	0.163827	−	0.283756i
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$	31.2132	−	10.8126i	1.15684	−	0.400741i
$729$	1.00000			0.0370370
$730$	47.6630	−	82.5547i	1.76408	−	3.05548i
$731$	−23.1421	−	40.0834i	−0.855943	−	1.48254i
$732$	28.0563	+	48.5950i	1.03699	+	1.79612i
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	−71.5980			−2.64273
$735$	−21.0563	+	16.5776i	−0.776675	+	0.611473i
$736$	−2.89949			−0.106877
$737$	−22.9706	+	39.7862i	−0.846132	+	1.46554i
$738$	9.24264	+	16.0087i	0.340226	+	0.589289i
$739$	4.00000	+	6.92820i	0.147142	+	0.254858i	0.930170	−	0.367129i	$-0.119659\pi$
$739$	4.00000	+	6.92820i	0.147142	+	0.254858i	−0.783028	+	0.621987i	$0.786326\pi$
$740$	8.58579	−	14.8710i	0.315620	−	0.546670i
$741$	−2.82843			−0.103905
$742$	−12.0711	+	4.18154i	−0.443143	+	0.153509i
$743$	33.1716			1.21695			0.608473	−	0.793574i	$-0.291782\pi$
$743$	33.1716			1.21695			0.608473	+	0.793574i	$0.291782\pi$
$744$	−7.00000	+	12.1244i	−0.256632	+	0.444500i
$745$	7.32843	+	12.6932i	0.268493	+	0.465043i
$746$	24.4853	+	42.4098i	0.896470	+	1.55273i
$747$	−2.08579	+	3.61269i	−0.0763149	+	0.132181i
$748$	53.5980			1.95974
$749$	−1.41421	+	7.34847i	−0.0516742	+	0.268507i
$750$	43.0416			1.57166
$751$	−17.3137	+	29.9882i	−0.631786	+	1.09429i	0.355400	+	0.934714i	$0.384345\pi$
$751$	−17.3137	+	29.9882i	−0.631786	+	1.09429i	−0.987186	+	0.159572i	$0.948989\pi$
$752$	−9.25736	−	16.0342i	−0.337581	−	0.584708i
$753$	6.74264	+	11.6786i	0.245715	+	0.425592i
$754$	−16.4853	+	28.5533i	−0.600359	+	1.03985i
$755$	35.6569			1.29769
$756$	7.65685	+	6.63103i	0.278477	+	0.241168i
$757$	9.34315			0.339582			0.169791	−	0.985480i	$-0.445691\pi$
$757$	9.34315			0.339582			0.169791	+	0.985480i	$0.445691\pi$
$758$	−19.8995	+	34.4669i	−0.722782	+	1.25190i
$759$	−3.50000	−	6.06218i	−0.127042	−	0.220043i
$760$	8.44975	+	14.6354i	0.306505	+	0.530881i
$761$	9.39949	−	16.2804i	0.340731	−	0.590164i	−0.643837	−	0.765162i	$-0.722659\pi$
$761$	9.39949	−	16.2804i	0.340731	−	0.590164i	0.984569	+	0.174998i	$0.0559920\pi$
$762$	−40.9706			−1.48421
$763$	36.2843	+	31.4231i	1.31358	+	1.13759i
$764$	45.2843			1.63833
$765$	−7.00000	+	12.1244i	−0.253086	+	0.438357i
$766$	19.3137	+	33.4523i	0.697833	+	1.20868i
$767$	−15.3137	−	26.5241i	−0.552946	−	0.957731i
$768$	14.9853	−	25.9553i	0.540735	−	0.936580i
$769$	14.3137			0.516166			0.258083	−	0.966123i	$-0.416909\pi$
$769$	14.3137			0.516166			0.258083	+	0.966123i	$0.416909\pi$
$770$	−17.6924	+	91.9323i	−0.637589	+	3.31301i
$771$	26.0000			0.936367
$772$	−7.65685	+	13.2621i	−0.275576	+	0.477312i
$773$	−1.41421	−	2.44949i	−0.0508657	−	0.0881020i	0.839471	−	0.543404i	$-0.182865\pi$
$773$	−1.41421	−	2.44949i	−0.0508657	−	0.0881020i	−0.890337	+	0.455302i	$0.849531\pi$
$774$	−15.2782	−	26.4626i	−0.549163	−	0.951178i
$775$	15.3137	−	26.5241i	0.550085	−	0.952775i
$776$	−74.2843			−2.66665
$777$	−2.92893	+	1.01461i	−0.105075	+	0.0363990i
$778$	−10.4853			−0.375916
$779$	3.82843	−	6.63103i	0.137168	−	0.237581i
$780$	20.7279	+	35.9018i	0.742179	+	1.28549i
$781$	8.31371	+	14.3998i	0.297488	+	0.515264i
$782$	8.07107	−	13.9795i	0.288621	−	0.499906i
$783$	−4.82843			−0.172554
$784$	3.00000	+	20.7846i	0.107143	+	0.742307i
$785$	−40.7990			−1.45618
$786$	12.4853	−	21.6251i	0.445335	−	0.771343i
$787$	−8.14214	−	14.1026i	−0.290236	−	0.502703i	0.683630	−	0.729829i	$-0.260400\pi$
$787$	−8.14214	−	14.1026i	−0.290236	−	0.502703i	−0.973865	+	0.227126i	$0.927067\pi$
$788$	33.4706	+	57.9727i	1.19234	+	2.06519i
$789$	−5.65685	+	9.79796i	−0.201389	+	0.348817i
$790$	21.6569			0.770516
$791$	32.0711	−	11.1097i	1.14032	−	0.395017i
$792$	16.8995			0.600497
$793$	20.7279	−	35.9018i	0.736070	−	1.27491i
$794$	6.41421	+	11.1097i	0.227632	+	0.394270i
$795$	−3.82843	−	6.63103i	−0.135780	−	0.235178i
$796$	−6.39949	+	11.0843i	−0.226824	+	0.392871i
$797$	7.51472			0.266185			0.133092	−	0.991104i	$-0.457509\pi$
$797$	7.51472			0.266185			0.133092	+	0.991104i	$0.457509\pi$
$798$	1.20711	−	6.27231i	0.0427311	−	0.222037i
$799$	−22.5685			−0.798418
$800$	−7.65685	+	13.2621i	−0.270711	+	0.468885i
$801$	−5.41421	−	9.37769i	−0.191302	−	0.331344i
$802$	−0.828427	−	1.43488i	−0.0292528	−	0.0506673i
$803$	−19.7426	+	34.1953i	−0.696703	+	1.20672i
$804$	−45.9411			−1.62022
$805$	14.0000	+	12.1244i	0.493435	+	0.427327i
$806$	21.6569			0.762830
$807$	4.00000	−	6.92820i	0.140807	−	0.243884i
$808$	−7.69239	−	13.3236i	−0.270617	−	0.468723i
$809$	12.3995	+	21.4766i	0.435943	+	0.755075i	0.997372	−	0.0724494i	$-0.0230816\pi$
$809$	12.3995	+	21.4766i	0.435943	+	0.755075i	−0.561429	+	0.827525i	$0.689748\pi$
$810$	−4.62132	+	8.00436i	−0.162377	+	0.281245i
$811$	−12.1421			−0.426368			−0.213184	−	0.977012i	$-0.568383\pi$
$811$	−12.1421			−0.426368			−0.213184	+	0.977012i	$0.568383\pi$
$812$	−36.9706	−	32.0174i	−1.29741	−	1.12359i
$813$	−19.6274			−0.688364
$814$	−5.41421	+	9.37769i	−0.189768	+	0.328688i
$815$	42.0563	+	72.8437i	1.47317	+	2.55160i
$816$	5.48528	+	9.50079i	0.192023	+	0.332594i
$817$	−6.32843	+	10.9612i	−0.221404	+	0.383482i
$818$	−12.8284			−0.448535
$819$	1.41421	−	7.34847i	0.0494166	−	0.256776i
$820$	−112.225			−3.91908
$821$	−3.42893	+	5.93908i	−0.119671	+	0.207275i	−0.919637	−	0.392769i	$-0.871517\pi$
$821$	−3.42893	+	5.93908i	−0.119671	+	0.207275i	0.799967	+	0.600045i	$0.204850\pi$
$822$	−16.6924	−	28.9121i	−0.582214	−	1.00842i
$823$	−15.9853	−	27.6873i	−0.557212	−	0.965119i	−0.997728	−	0.0673745i	$-0.978538\pi$
$823$	−15.9853	−	27.6873i	−0.557212	−	0.965119i	0.440516	−	0.897745i	$-0.354796\pi$
$824$	8.07107	−	13.9795i	0.281169	−	0.486999i
$825$	−36.9706			−1.28715
$826$	65.3553	−	22.6398i	2.27400	−	0.787738i
$827$	−15.1127			−0.525520			−0.262760	−	0.964861i	$-0.584633\pi$
$827$	−15.1127			−0.525520			−0.262760	+	0.964861i	$0.584633\pi$
$828$	3.50000	−	6.06218i	0.121633	−	0.210675i
$829$	19.0711	+	33.0321i	0.662366	+	1.14725i	0.979992	+	0.199035i	$0.0637807\pi$
$829$	19.0711	+	33.0321i	0.662366	+	1.14725i	−0.317627	+	0.948216i	$0.602886\pi$
$830$	−19.2782	−	33.3908i	−0.669155	−	1.15901i
$831$	−6.50000	+	11.2583i	−0.225483	+	0.390547i
$832$	−27.7990			−0.963757
$833$	23.7696	+	9.50079i	0.823566	+	0.329183i
$834$	16.0711			0.556496
$835$	16.8995	−	29.2708i	0.584831	−	1.01296i
$836$	−7.32843	−	12.6932i	−0.253459	−	0.439004i
$837$	1.58579	+	2.74666i	0.0548128	+	0.0949386i
$838$	−12.2782	+	21.2664i	−0.424143	+	0.734636i
$839$	−45.2548			−1.56237			−0.781185	−	0.624299i	$-0.785385\pi$
$839$	−45.2548			−1.56237			−0.781185	+	0.624299i	$0.785385\pi$
$840$	−42.2487	+	14.6354i	−1.45772	+	0.504969i
$841$	−5.68629			−0.196079
$842$	23.1421	−	40.0834i	0.797531	−	1.38136i
$843$	−3.48528	−	6.03668i	−0.120039	−	0.207914i
$844$	−31.5563	−	54.6572i	−1.08621	−	1.88138i
$845$	−9.57107	+	16.5776i	−0.329255	+	0.570286i
$846$	−14.8995			−0.512255
$847$	1.82843	−	9.50079i	0.0628255	−	0.326451i
$848$	−6.00000			−0.206041
$849$	−15.8137	+	27.3901i	−0.542725	+	0.940027i
$850$	−42.6274	−	73.8329i	−1.46211	−	2.53245i
$851$	1.07107	+	1.85514i	0.0367157	+	0.0635935i
$852$	−8.31371	+	14.3998i	−0.284823	+	0.493328i
$853$	−6.37258			−0.218193			−0.109097	−	0.994031i	$-0.534796\pi$
$853$	−6.37258			−0.218193			−0.109097	+	0.994031i	$0.534796\pi$
$854$	70.7696	+	61.2882i	2.42168	+	2.09724i
$855$	3.82843			0.130929
$856$	−6.24264	+	10.8126i	−0.213369	+	0.369566i
$857$	13.4142	+	23.2341i	0.458221	+	0.793662i	0.998867	−	0.0475883i	$-0.0151536\pi$
$857$	13.4142	+	23.2341i	0.458221	+	0.793662i	−0.540646	+	0.841250i	$0.681820\pi$
$858$	−13.0711	−	22.6398i	−0.446239	−	0.772908i
$859$	−15.4706	+	26.7958i	−0.527849	+	0.914261i	0.471624	+	0.881800i	$0.343668\pi$
$859$	−15.4706	+	26.7958i	−0.527849	+	0.914261i	−0.999473	+	0.0324613i	$0.989665\pi$
$860$	185.510			6.32583
$861$	15.3137	+	13.2621i	0.521890	+	0.451970i
$862$	55.9411			1.90536
$863$	−3.58579	+	6.21076i	−0.122062	+	0.211417i	−0.920581	−	0.390553i	$-0.872284\pi$
$863$	−3.58579	+	6.21076i	−0.122062	+	0.211417i	0.798519	+	0.601970i	$0.205617\pi$
$864$	−0.792893	−	1.37333i	−0.0269748	−	0.0467217i
$865$	5.41421	+	9.37769i	0.184089	+	0.318851i
$866$	10.2426	−	17.7408i	0.348059	−	0.602856i
$867$	−3.62742			−0.123194
$868$	−6.07107	+	31.5462i	−0.206065	+	1.07075i
$869$	−8.97056			−0.304305
$870$	22.3137	−	38.6485i	0.756506	−	1.31031i
$871$	16.9706	+	29.3939i	0.575026	+	0.995974i
$872$	40.0416	+	69.3541i	1.35598	+	2.34863i
$873$	−8.41421	+	14.5738i	−0.284778	+	0.493250i
$874$	−4.41421			−0.149313
$875$	44.5711	−	15.4399i	1.50678	−	0.521963i
$876$	−39.4853			−1.33408
$877$	−10.8284	+	18.7554i	−0.365650	+	0.633324i	−0.988880	−	0.148714i	$-0.952487\pi$
$877$	−10.8284	+	18.7554i	−0.365650	+	0.633324i	0.623230	+	0.782038i	$0.285820\pi$
$878$	−23.8995	−	41.3951i	−0.806569	−	1.39702i
$879$	0.414214	+	0.717439i	0.0139711	+	0.0241986i
$880$	−21.9853	+	38.0796i	−0.741124	+	1.28366i
$881$	−4.62742			−0.155902			−0.0779508	−	0.996957i	$-0.524838\pi$
$881$	−4.62742			−0.155902			−0.0779508	+	0.996957i	$0.524838\pi$
$882$	15.6924	+	6.27231i	0.528390	+	0.211200i
$883$	−44.9706			−1.51338			−0.756690	−	0.653774i	$-0.773185\pi$
$883$	−44.9706			−1.51338			−0.756690	+	0.653774i	$0.773185\pi$
$884$	19.7990	−	34.2929i	0.665912	−	1.15339i
$885$	20.7279	+	35.9018i	0.696761	+	1.20683i
$886$	−40.6274	−	70.3688i	−1.36490	−	2.36408i
$887$	7.72792	−	13.3852i	0.259478	−	0.449429i	−0.706624	−	0.707589i	$-0.749783\pi$
$887$	7.72792	−	13.3852i	0.259478	−	0.449429i	0.966102	+	0.258160i	$0.0831161\pi$
$888$	−5.17157			−0.173547
$889$	−42.4264	+	14.6969i	−1.42294	+	0.492919i
$890$	100.083			3.35480
$891$	1.91421	−	3.31552i	0.0641286	−	0.111074i
$892$	−41.7279	−	72.2749i	−1.39715	−	2.41994i
$893$	3.08579	+	5.34474i	0.103262	+	0.178855i
$894$	4.62132	−	8.00436i	0.154560	−	0.267706i
$895$	40.1421			1.34180
$896$	10.2782	−	53.4070i	0.343370	−	1.78420i
$897$	−5.17157			−0.172674
$898$	31.5563	−	54.6572i	1.05305	−	1.82393i
$899$	−7.65685	−	13.2621i	−0.255370	−	0.442314i
$900$	−18.4853	−	32.0174i	−0.616176	−	1.06725i
$901$	−3.65685	+	6.33386i	−0.121827	+	0.211011i
$902$	70.7696			2.35637
$903$	−25.3137	−	21.9223i	−0.842387	−	0.729529i
$904$	56.6274			1.88340
$905$	−22.3137	+	38.6485i	−0.741733	+	1.28472i
$906$	−11.2426	−	19.4728i	−0.373512	−	0.646941i
$907$	9.82843	+	17.0233i	0.326348	+	0.565251i	0.981784	−	0.190000i	$-0.0608487\pi$
$907$	9.82843	+	17.0233i	0.326348	+	0.565251i	−0.655437	+	0.755250i	$0.727515\pi$
$908$	12.1421	−	21.0308i	0.402951	−	0.697931i
$909$	−3.48528			−0.115599
$910$	52.2843	+	45.2795i	1.73321	+	1.50100i
$911$	18.0000			0.596367			0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000			0.596367			0.298183	+	0.954509i	$0.403619\pi$
$912$	1.50000	−	2.59808i	0.0496700	−	0.0860309i
$913$	7.98528	+	13.8309i	0.264274	+	0.457736i
$914$	−17.6924	−	30.6441i	−0.585212	−	1.01362i
$915$	−28.0563	+	48.5950i	−0.927514	+	1.60650i
$916$	−59.9411			−1.98051
$917$	5.17157	−	26.8723i	0.170780	−	0.887401i
$918$	8.82843			0.291382
$919$	21.6716	−	37.5363i	0.714879	−	1.23821i	−0.248127	−	0.968728i	$-0.579815\pi$
$919$	21.6716	−	37.5363i	0.714879	−	1.23821i	0.963006	−	0.269480i	$-0.0868517\pi$
$920$	15.4497	+	26.7597i	0.509363	+	0.882243i
$921$	−1.24264	−	2.15232i	−0.0409464	−	0.0709213i
$922$	27.1066	−	46.9500i	0.892708	−	1.54622i
$923$	12.2843			0.404342
$924$	36.6421	−	12.6932i	1.20544	−	0.417576i
$925$	11.3137			0.371992
$926$	−24.9350	+	43.1887i	−0.819416	+	1.41927i
$927$	−1.82843	−	3.16693i	−0.0600534	−	0.104016i
$928$	3.82843	+	6.63103i	0.125674	+	0.217674i
$929$	−8.22792	+	14.2512i	−0.269949	+	0.467566i	−0.968848	−	0.247654i	$-0.920340\pi$
$929$	−8.22792	+	14.2512i	−0.269949	+	0.467566i	0.698899	+	0.715220i	$0.253674\pi$
$930$	−29.3137			−0.961234
$931$	−1.00000	−	6.92820i	−0.0327737	−	0.227063i
$932$	22.9706			0.752426
$933$	−11.3137	+	19.5959i	−0.370394	+	0.641542i
$934$	30.7635	+	53.2839i	1.00661	+	1.74350i
$935$	26.7990	+	46.4172i	0.876421	+	1.51801i
$936$	6.24264	−	10.8126i	0.204047	−	0.353420i
$937$	−27.0000			−0.882052			−0.441026	−	0.897494i	$-0.645385\pi$
$937$	−27.0000			−0.882052			−0.441026	+	0.897494i	$0.645385\pi$
$938$	−72.4264	+	25.0892i	−2.36481	+	0.819193i
$939$	31.2843			1.02092
$940$	45.2279	−	78.3371i	1.47517	−	2.55507i
$941$	−29.9706	−	51.9105i	−0.977012	−	1.69224i	−0.673128	−	0.739526i	$-0.735050\pi$
$941$	−29.9706	−	51.9105i	−0.977012	−	1.69224i	−0.303885	−	0.952709i	$-0.598284\pi$
$942$	12.8640	+	22.2810i	0.419130	+	0.725955i
$943$	7.00000	−	12.1244i	0.227951	−	0.394823i
$944$	32.4853			1.05731
$945$	−1.91421	+	9.94655i	−0.0622694	+	0.323561i
$946$	−116.983			−3.80344
$947$	8.34315	−	14.4508i	0.271116	−	0.469586i	−0.698032	−	0.716067i	$-0.745941\pi$
$947$	8.34315	−	14.4508i	0.271116	−	0.469586i	0.969148	+	0.246480i	$0.0792740\pi$
$948$	−4.48528	−	7.76874i	−0.145675	−	0.252317i
$949$	14.5858	+	25.2633i	0.473475	+	0.820082i
$950$	−11.6569	+	20.1903i	−0.378198	+	0.655059i
$951$	29.7990			0.966298
$952$	32.2843	+	27.9590i	1.04634	+	0.906156i
$953$	−26.6274			−0.862547			−0.431273	−	0.902221i	$-0.641936\pi$
$953$	−26.6274			−0.862547			−0.431273	+	0.902221i	$0.641936\pi$
$954$	−2.41421	+	4.18154i	−0.0781631	+	0.135382i
$955$	22.6421	+	39.2173i	0.732682	+	1.26904i
$956$	−4.48528	−	7.76874i	−0.145064	−	0.251259i
$957$	−9.24264	+	16.0087i	−0.298772	+	0.517489i
$958$	−29.3848			−0.949379
$959$	−27.6569	−	23.9515i	−0.893086	−	0.773436i
$960$	37.6274			1.21442
$961$	10.4706	−	18.1355i	0.337760	−	0.585018i
$962$	4.00000	+	6.92820i	0.128965	+	0.223374i
$963$	1.41421	+	2.44949i	0.0455724	+	0.0789337i
$964$	−37.8995	+	65.6439i	−1.22066	+	2.11425i
$965$	−15.3137			−0.492966
$966$	2.20711	−	11.4685i	0.0710125	−	0.368992i
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	8.07107	−	13.9795i	0.259414	−	0.449318i
$969$	−1.82843	−	3.16693i	−0.0587375	−	0.101736i
$970$	−77.7696	−	134.701i	−2.49703	−	4.32498i
$971$	19.8995	−	34.4669i	0.638605	−	1.10610i	−0.347134	−	0.937816i	$-0.612845\pi$
$971$	19.8995	−	34.4669i	0.638605	−	1.10610i	0.985739	−	0.168281i	$-0.0538216\pi$
$972$	3.82843			0.122797
$973$	16.6421	−	5.76500i	0.533522	−	0.184818i
$974$	0.828427			0.0265445
$975$	−13.6569	+	23.6544i	−0.437369	+	0.757546i
$976$	21.9853	+	38.0796i	0.703732	+	1.21890i
$977$	−11.5563	−	20.0162i	−0.369720	−	0.640374i	0.619801	−	0.784759i	$-0.287213\pi$
$977$	−11.5563	−	20.0162i	−0.369720	−	0.640374i	−0.989522	+	0.144384i	$0.953880\pi$
$978$	26.5208	−	45.9354i	0.848042	−	1.46885i
$979$	−41.4558			−1.32493
$980$	−80.6127	+	63.4660i	−2.57508	+	2.02735i
$981$	18.1421			0.579234
$982$	−10.2782	+	17.8023i	−0.327990	+	0.568095i
$983$	−1.72792	−	2.99285i	−0.0551122	−	0.0954571i	0.837153	−	0.546969i	$-0.184218\pi$
$983$	−1.72792	−	2.99285i	−0.0551122	−	0.0954571i	−0.892265	+	0.451512i	$0.850885\pi$
$984$	16.8995	+	29.2708i	0.538736	+	0.933119i
$985$	−33.4706	+	57.9727i	−1.06646	+	1.84716i
$986$	−42.6274			−1.35753
$987$	−15.4289	+	5.34474i	−0.491108	+	0.170125i
$988$	−10.8284			−0.344498
$989$	−11.5711	+	20.0417i	−0.367939	+	0.637288i
$990$	17.6924	+	30.6441i	0.562301	+	0.973934i
$991$	−26.6274	−	46.1200i	−0.845848	−	1.46505i	−0.884883	−	0.465813i	$-0.845762\pi$
$991$	−26.6274	−	46.1200i	−0.845848	−	1.46505i	0.0390352	−	0.999238i	$-0.487572\pi$
$992$	2.51472	−	4.35562i	0.0798424	−	0.138291i
$993$	−5.51472			−0.175004
$994$	−5.24264	+	27.2416i	−0.166286	+	0.864050i
$995$	−12.7990			−0.405755
$996$	−7.98528	+	13.8309i	−0.253023	+	0.438249i
$997$	15.0000	+	25.9808i	0.475055	+	0.822819i	0.999592	−	0.0285686i	$-0.00909491\pi$
$997$	15.0000	+	25.9808i	0.475055	+	0.822819i	−0.524537	+	0.851388i	$0.675762\pi$
$998$	24.1066	+	41.7539i	0.763081	+	1.32170i
$999$	−0.585786	+	1.01461i	−0.0185335	+	0.0321009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.j.c.58.2	✓	4
3.2	odd	2		1197.2.j.d.856.1		4
7.2	even	3		2793.2.a.o.1.1		2
7.4	even	3	inner	399.2.j.c.172.2	yes	4
7.5	odd	6		2793.2.a.n.1.1		2
21.2	odd	6		8379.2.a.bm.1.2		2
21.5	even	6		8379.2.a.bh.1.2		2
21.11	odd	6		1197.2.j.d.172.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.c.58.2	✓	4	1.1	even	1	trivial
399.2.j.c.172.2	yes	4	7.4	even	3	inner
1197.2.j.d.172.1		4	21.11	odd	6
1197.2.j.d.856.1		4	3.2	odd	2
2793.2.a.n.1.1		2	7.5	odd	6
2793.2.a.o.1.1		2	7.2	even	3
8379.2.a.bh.1.2		2	21.5	even	6
8379.2.a.bm.1.2		2	21.2	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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 - 2.09077i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(1.91421 - 3.31552i) q^{5} -2.41421 q^{6} +(-2.50000 + 0.866025i) q^{7} -4.41421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.62132 - 8.00436i) q^{10} +(1.91421 + 3.31552i) q^{11} +(-1.91421 + 3.31552i) q^{12} +2.82843 q^{13} +(-1.20711 + 6.27231i) q^{14} -3.82843 q^{15} +(-1.50000 + 2.59808i) q^{16} +(1.82843 + 3.16693i) q^{17} +(1.20711 + 2.09077i) q^{18} +(0.500000 - 0.866025i) q^{19} -14.6569 q^{20} +(2.00000 + 1.73205i) q^{21} +9.24264 q^{22} +(0.914214 - 1.58346i) q^{23} +(2.20711 + 3.82282i) q^{24} +(-4.82843 - 8.36308i) q^{25} +(3.41421 - 5.91359i) q^{26} +1.00000 q^{27} +(7.65685 + 6.63103i) q^{28} -4.82843 q^{29} +(-4.62132 + 8.00436i) q^{30} +(1.58579 + 2.74666i) q^{31} +(-0.792893 - 1.37333i) q^{32} +(1.91421 - 3.31552i) q^{33} +8.82843 q^{34} +(-1.91421 + 9.94655i) q^{35} +3.82843 q^{36} +(-0.585786 + 1.01461i) q^{37} +(-1.20711 - 2.09077i) q^{38} +(-1.41421 - 2.44949i) q^{39} +(-8.44975 + 14.6354i) q^{40} +7.65685 q^{41} +(6.03553 - 2.09077i) q^{42} -12.6569 q^{43} +(7.32843 - 12.6932i) q^{44} +(1.91421 + 3.31552i) q^{45} +(-2.20711 - 3.82282i) q^{46} +(-3.08579 + 5.34474i) q^{47} +3.00000 q^{48} +(5.50000 - 4.33013i) q^{49} -23.3137 q^{50} +(1.82843 - 3.16693i) q^{51} +(-5.41421 - 9.37769i) q^{52} +(1.00000 + 1.73205i) q^{53} +(1.20711 - 2.09077i) q^{54} +14.6569 q^{55} +(11.0355 - 3.82282i) q^{56} -1.00000 q^{57} +(-5.82843 + 10.0951i) q^{58} +(-5.41421 - 9.37769i) q^{59} +(7.32843 + 12.6932i) q^{60} +(7.32843 - 12.6932i) q^{61} +7.65685 q^{62} +(0.500000 - 2.59808i) q^{63} -9.82843 q^{64} +(5.41421 - 9.37769i) q^{65} +(-4.62132 - 8.00436i) q^{66} +(6.00000 + 10.3923i) q^{67} +(7.00000 - 12.1244i) q^{68} -1.82843 q^{69} +(18.4853 + 16.0087i) q^{70} +4.34315 q^{71} +(2.20711 - 3.82282i) q^{72} +(5.15685 + 8.93193i) q^{73} +(1.41421 + 2.44949i) q^{74} +(-4.82843 + 8.36308i) q^{75} -3.82843 q^{76} +(-7.65685 - 6.63103i) q^{77} -6.82843 q^{78} +(-1.17157 + 2.02922i) q^{79} +(5.74264 + 9.94655i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(9.24264 - 16.0087i) q^{82} +4.17157 q^{83} +(1.91421 - 9.94655i) q^{84} +14.0000 q^{85} +(-15.2782 + 26.4626i) q^{86} +(2.41421 + 4.18154i) q^{87} +(-8.44975 - 14.6354i) q^{88} +(-5.41421 + 9.37769i) q^{89} +9.24264 q^{90} +(-7.07107 + 2.44949i) q^{91} -7.00000 q^{92} +(1.58579 - 2.74666i) q^{93} +(7.44975 + 12.9033i) q^{94} +(-1.91421 - 3.31552i) q^{95} +(-0.792893 + 1.37333i) q^{96} +16.8284 q^{97} +(-2.41421 - 16.7262i) q^{98} -3.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 10 q^{7} - 12 q^{8} - 2 q^{9} - 10 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} - 4 q^{15} - 6 q^{16} - 4 q^{17} + 2 q^{18} + 2 q^{19} - 36 q^{20} + 8 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 10 * q^7 - 12 * q^8 - 2 * q^9 - 10 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^14 - 4 * q^15 - 6 * q^16 - 4 * q^17 + 2 * q^18 + 2 * q^19 - 36 * q^20 + 8 * q^21 + 20 * q^22 - 2 * q^23 + 6 * q^24 - 8 * q^25 + 8 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 - 10 * q^30 + 12 * q^31 - 6 * q^32 + 2 * q^33 + 24 * q^34 - 2 * q^35 + 4 * q^36 - 8 * q^37 - 2 * q^38 - 14 * q^40 + 8 * q^41 + 10 * q^42 - 28 * q^43 + 18 * q^44 + 2 * q^45 - 6 * q^46 - 18 * q^47 + 12 * q^48 + 22 * q^49 - 48 * q^50 - 4 * q^51 - 16 * q^52 + 4 * q^53 + 2 * q^54 + 36 * q^55 + 30 * q^56 - 4 * q^57 - 12 * q^58 - 16 * q^59 + 18 * q^60 + 18 * q^61 + 8 * q^62 + 2 * q^63 - 28 * q^64 + 16 * q^65 - 10 * q^66 + 24 * q^67 + 28 * q^68 + 4 * q^69 + 40 * q^70 + 40 * q^71 + 6 * q^72 - 2 * q^73 - 8 * q^75 - 4 * q^76 - 8 * q^77 - 16 * q^78 - 16 * q^79 + 6 * q^80 - 2 * q^81 + 20 * q^82 + 28 * q^83 + 2 * q^84 + 56 * q^85 - 30 * q^86 + 4 * q^87 - 14 * q^88 - 16 * q^89 + 20 * q^90 - 28 * q^92 + 12 * q^93 + 10 * q^94 - 2 * q^95 - 6 * q^96 + 56 * q^97 - 4 * q^98 - 4 * q^99

Introduction

L-functions

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Database

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