LMFDB - Embedded newform 63.2.s.b.47.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,2,Mod(47,63)] 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("63.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10] 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.5
Root			$0.827154 - 1.43267i$ of defining polynomial
Character	$\chi$	$=$	63.47
Dual form			63.2.s.b.59.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.81474 - 1.04774i) q^{2} +(-0.769825 + 1.55157i) q^{3} +(1.19552 - 2.07070i) q^{4} -2.08983 q^{5} +(0.228612 + 3.62227i) q^{6} +(-0.879217 - 2.49539i) q^{7} -0.819421i q^{8} +(-1.81474 - 2.38887i) q^{9} +(-3.79250 + 2.18960i) q^{10} +3.22878i q^{11} +(2.29250 + 3.44901i) q^{12} +(2.68740 - 1.55157i) q^{13} +(-4.21007 - 3.60729i) q^{14} +(1.60880 - 3.24252i) q^{15} +(1.53250 + 2.65437i) q^{16} +(-0.816304 - 1.41388i) q^{17} +(-5.79620 - 2.43381i) q^{18} +(4.79094 + 2.76605i) q^{19} +(-2.49844 + 4.32742i) q^{20} +(4.54862 + 0.556847i) q^{21} +(3.38292 + 5.85939i) q^{22} +1.16078i q^{23} +(1.27139 + 0.630810i) q^{24} -0.632608 q^{25} +(3.25129 - 5.63139i) q^{26} +(5.10354 - 0.976682i) q^{27} +(-6.21834 - 1.16270i) q^{28} +(-7.05749 - 4.07464i) q^{29} +(-0.477759 - 7.56994i) q^{30} +(-5.16886 - 2.98424i) q^{31} +(6.98146 + 4.03075i) q^{32} +(-5.00967 - 2.48559i) q^{33} +(-2.96276 - 1.71055i) q^{34} +(1.83741 + 5.21495i) q^{35} +(-7.11621 + 0.901839i) q^{36} +(2.82656 - 4.89575i) q^{37} +11.5924 q^{38} +(0.338544 + 5.36412i) q^{39} +1.71245i q^{40} +(-1.35369 - 2.34465i) q^{41} +(8.83799 - 3.75524i) q^{42} +(-0.974903 + 1.68858i) q^{43} +(6.68583 + 3.86007i) q^{44} +(3.79250 + 4.99234i) q^{45} +(1.21620 + 2.10652i) q^{46} +(4.06759 + 7.04527i) q^{47} +(-5.29820 + 0.334384i) q^{48} +(-5.45395 + 4.38798i) q^{49} +(-1.14802 + 0.662809i) q^{50} +(2.82214 - 0.178113i) q^{51} -7.41974i q^{52} +(5.27766 - 3.04706i) q^{53} +(8.23828 - 7.11961i) q^{54} -6.74759i q^{55} +(-2.04477 + 0.720448i) q^{56} +(-7.97990 + 5.30410i) q^{57} -17.0767 q^{58} +(-1.98103 + 3.43124i) q^{59} +(-4.79094 - 7.20785i) q^{60} +(-4.15016 + 2.39609i) q^{61} -12.5068 q^{62} +(-4.36562 + 6.62882i) q^{63} +10.7627 q^{64} +(-5.61621 + 3.24252i) q^{65} +(-11.6955 + 0.738135i) q^{66} +(0.336981 - 0.583668i) q^{67} -3.90363 q^{68} +(-1.80103 - 0.893598i) q^{69} +(8.79834 + 7.53864i) q^{70} -7.01535i q^{71} +(-1.95749 + 1.48704i) q^{72} +(-2.96276 + 1.71055i) q^{73} -11.8460i q^{74} +(0.486997 - 0.981535i) q^{75} +(11.4553 - 6.61374i) q^{76} +(8.05706 - 2.83879i) q^{77} +(6.23458 + 9.37978i) q^{78} +(7.07973 + 12.2625i) q^{79} +(-3.20267 - 5.54718i) q^{80} +(-2.41344 + 8.67037i) q^{81} +(-4.91318 - 2.83662i) q^{82} +(1.54535 - 2.67662i) q^{83} +(6.59103 - 8.75311i) q^{84} +(1.70594 + 2.95477i) q^{85} +4.08578i q^{86} +(11.7551 - 7.81343i) q^{87} +2.64572 q^{88} +(-2.45766 + 4.25679i) q^{89} +(12.1131 + 5.08625i) q^{90} +(-6.23458 - 5.34194i) q^{91} +(2.40363 + 1.38774i) q^{92} +(8.60938 - 5.72251i) q^{93} +(14.7632 + 8.52356i) q^{94} +(-10.0122 - 5.78057i) q^{95} +(-11.6285 + 7.72926i) q^{96} +(2.07939 + 1.20054i) q^{97} +(-5.30004 + 13.6774i) q^{98} +(7.71314 - 5.85939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7} - 15 q^{10} + 6 q^{13} - 6 q^{14} - 3 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} + 3 q^{19} - 3 q^{20} + 18 q^{21} + 5 q^{22} + 27 q^{24} - 14 q^{25} + 3 q^{26} + 27 q^{27}+ \cdots + 21 q^{99}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7 - 15 * q^10 + 6 * q^13 - 6 * q^14 - 3 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 + 3 * q^19 - 3 * q^20 + 18 * q^21 + 5 * q^22 + 27 * q^24 - 14 * q^25 + 3 * q^26 + 27 * q^27 + 2 * q^28 - 15 * q^29 - 9 * q^31 + 48 * q^32 - 9 * q^33 + 3 * q^34 - 15 * q^35 - 18 * q^36 + 6 * q^37 + 36 * q^38 + 12 * q^39 - 9 * q^41 - 6 * q^42 + 3 * q^43 + 24 * q^44 + 15 * q^45 - 13 * q^46 + 15 * q^47 - 15 * q^48 - 23 * q^49 + 3 * q^50 - 24 * q^51 - 9 * q^53 + 27 * q^54 - 51 * q^56 - 36 * q^57 - 16 * q^58 - 18 * q^59 - 3 * q^60 + 12 * q^61 + 12 * q^62 + 9 * q^63 + 6 * q^64 - 3 * q^65 - 33 * q^66 - 10 * q^67 - 54 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^72 + 3 * q^73 - 21 * q^75 + 9 * q^76 + 45 * q^77 + 24 * q^78 + 20 * q^79 - 30 * q^80 - 48 * q^81 + 9 * q^82 - 15 * q^83 + 60 * q^84 + 18 * q^85 + 30 * q^87 + 16 * q^88 + 24 * q^89 + 24 * q^90 - 24 * q^91 + 39 * q^92 + 6 * q^93 - 3 * q^94 + 3 * q^96 + 6 * q^97 + 45 * q^98 + 21 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.81474	−	1.04774i	1.28321	−	0.740865i	0.305780	−	0.952102i	$-0.401083\pi$
$2$	1.81474	−	1.04774i	1.28321	−	0.740865i	0.977435	+	0.211238i	$0.0677494\pi$
$3$	−0.769825	+	1.55157i	−0.444458	+	0.895799i
$3$	−0.769825	+	1.55157i	−0.444458	+	0.895799i
$4$	1.19552	−	2.07070i	0.597760	−	1.03535i
$5$	−2.08983			−0.934601			−0.467300	−	0.884099i	$-0.654773\pi$
$5$	−2.08983			−0.934601			−0.467300	+	0.884099i	$0.654773\pi$
$6$	0.228612	+	3.62227i	0.0933303	+	1.47879i
$7$	−0.879217	−	2.49539i	−0.332313	−	0.943169i
$7$	−0.879217	−	2.49539i	−0.332313	−	0.943169i
$8$		−	0.819421i		−	0.289709i
$9$	−1.81474	−	2.38887i	−0.604913	−	0.796291i
$10$	−3.79250	+	2.18960i	−1.19929	+	0.692412i
$11$			3.22878i			0.973512i	0.873538	+	0.486756i	$0.161820\pi$
$11$			3.22878i			0.973512i	−0.873538	+	0.486756i	$0.838180\pi$
$12$	2.29250	+	3.44901i	0.661788	+	0.995644i
$13$	2.68740	−	1.55157i	0.745350	−	0.430328i	−0.0786612	−	0.996901i	$-0.525065\pi$
$13$	2.68740	−	1.55157i	0.745350	−	0.430328i	0.824011	+	0.566573i	$0.191731\pi$
$14$	−4.21007	−	3.60729i	−1.12519	−	0.964090i
$15$	1.60880	−	3.24252i	0.415391	−	0.837215i
$16$	1.53250	+	2.65437i	0.383125	+	0.663593i
$17$	−0.816304	−	1.41388i	−0.197983	−	0.342916i	0.749891	−	0.661561i	$-0.230106\pi$
$17$	−0.816304	−	1.41388i	−0.197983	−	0.342916i	−0.947874	+	0.318645i	$0.896772\pi$
$18$	−5.79620	−	2.43381i	−1.36618	−	0.573654i
$19$	4.79094	+	2.76605i	1.09912	+	0.634575i	0.935989	−	0.352030i	$-0.114509\pi$
$19$	4.79094	+	2.76605i	1.09912	+	0.634575i	0.163127	+	0.986605i	$0.447842\pi$
$20$	−2.49844	+	4.32742i	−0.558667	+	0.967640i
$21$	4.54862	+	0.556847i	0.992590	+	0.121514i
$22$	3.38292	+	5.85939i	0.721241	+	1.24923i
$23$			1.16078i			0.242040i	0.992650	+	0.121020i	$0.0386165\pi$
$23$			1.16078i			0.242040i	−0.992650	+	0.121020i	$0.961384\pi$
$24$	1.27139	+	0.630810i	0.259521	+	0.128764i
$25$	−0.632608			−0.126522
$26$	3.25129	−	5.63139i	0.637630	−	1.10441i
$27$	5.10354	−	0.976682i	0.982176	−	0.187963i
$28$	−6.21834	−	1.16270i	−1.17516	−	0.219729i
$29$	−7.05749	−	4.07464i	−1.31054	−	0.756643i	−0.328357	−	0.944554i	$-0.606495\pi$
$29$	−7.05749	−	4.07464i	−1.31054	−	0.756643i	−0.982186	+	0.187911i	$0.939828\pi$
$30$	−0.477759	−	7.56994i	−0.0872265	−	1.38208i
$31$	−5.16886	−	2.98424i	−0.928355	−	0.535986i	−0.0420638	−	0.999115i	$-0.513393\pi$
$31$	−5.16886	−	2.98424i	−0.928355	−	0.535986i	−0.886291	+	0.463129i	$0.846727\pi$
$32$	6.98146	+	4.03075i	1.23416	+	0.712542i
$33$	−5.00967	−	2.48559i	−0.872072	−	0.432686i
$34$	−2.96276	−	1.71055i	−0.508109	−	0.293357i
$35$	1.83741	+	5.21495i	0.310580	+	0.881487i
$36$	−7.11621	+	0.901839i	−1.18603	+	0.150306i
$37$	2.82656	−	4.89575i	0.464684	−	0.804857i	−0.534503	−	0.845167i	$-0.679501\pi$
$37$	2.82656	−	4.89575i	0.464684	−	0.804857i	0.999187	+	0.0403097i	$0.0128345\pi$
$38$	11.5924			1.88054
$39$	0.338544	+	5.36412i	0.0542105	+	0.858947i
$40$			1.71245i			0.270762i
$41$	−1.35369	−	2.34465i	−0.211410	−	0.366173i	0.740746	−	0.671785i	$-0.234472\pi$
$41$	−1.35369	−	2.34465i	−0.211410	−	0.366173i	−0.952156	+	0.305612i	$0.901139\pi$
$42$	8.83799	−	3.75524i	1.36373	−	0.579446i
$43$	−0.974903	+	1.68858i	−0.148671	+	0.257506i	−0.930737	−	0.365690i	$-0.880833\pi$
$43$	−0.974903	+	1.68858i	−0.148671	+	0.257506i	0.782065	+	0.623196i	$0.214166\pi$
$44$	6.68583	+	3.86007i	1.00793	+	0.581927i
$45$	3.79250	+	4.99234i	0.565352	+	0.744214i
$46$	1.21620	+	2.10652i	0.179319	+	0.310589i
$47$	4.06759	+	7.04527i	0.593319	+	1.02766i	0.993782	+	0.111346i	$0.0355161\pi$
$47$	4.06759	+	7.04527i	0.593319	+	1.02766i	−0.400463	+	0.916313i	$0.631151\pi$
$48$	−5.29820	+	0.334384i	−0.764729	+	0.0482641i
$49$	−5.45395	+	4.38798i	−0.779136	+	0.626854i
$50$	−1.14802	+	0.662809i	−0.162354	+	0.0937353i
$51$	2.82214	−	0.178113i	0.395179	−	0.0249408i
$52$		−	7.41974i		−	1.02893i
$53$	5.27766	−	3.04706i	0.724943	−	0.418546i	−0.0916264	−	0.995793i	$-0.529207\pi$
$53$	5.27766	−	3.04706i	0.724943	−	0.418546i	0.816569	+	0.577248i	$0.195873\pi$
$54$	8.23828	−	7.11961i	1.12109	−	0.968856i
$55$		−	6.74759i		−	0.909845i
$56$	−2.04477	+	0.720448i	−0.273245	+	0.0962740i
$57$	−7.97990	+	5.30410i	−1.05696	+	0.702545i
$58$	−17.0767			−2.24228
$59$	−1.98103	+	3.43124i	−0.257908	+	0.446709i	−0.965681	−	0.259730i	$-0.916366\pi$
$59$	−1.98103	+	3.43124i	−0.257908	+	0.446709i	0.707773	+	0.706439i	$0.249700\pi$
$60$	−4.79094	−	7.20785i	−0.618507	−	0.930530i
$61$	−4.15016	+	2.39609i	−0.531373	+	0.306788i	−0.741575	−	0.670869i	$-0.765921\pi$
$61$	−4.15016	+	2.39609i	−0.531373	+	0.306788i	0.210202	+	0.977658i	$0.432588\pi$
$62$	−12.5068			−1.58837
$63$	−4.36562	+	6.62882i	−0.550017	+	0.835153i
$64$	10.7627			1.34534
$65$	−5.61621	+	3.24252i	−0.696605	+	0.402185i
$66$	−11.6955	+	0.738135i	−1.43962	+	0.0908582i
$67$	0.336981	−	0.583668i	0.0411687	−	0.0713063i	−0.844707	−	0.535229i	$-0.820225\pi$
$67$	0.336981	−	0.583668i	0.0411687	−	0.0713063i	0.885876	+	0.463923i	$0.153559\pi$
$68$	−3.90363			−0.473385
$69$	−1.80103	−	0.893598i	−0.216819	−	0.107577i
$70$	8.79834	+	7.53864i	1.05160	+	0.901039i
$71$		−	7.01535i		−	0.832568i	−0.909235	−	0.416284i	$-0.863332\pi$
$71$		−	7.01535i		−	0.832568i	0.909235	−	0.416284i	$-0.136668\pi$
$72$	−1.95749	+	1.48704i	−0.230693	+	0.175249i
$73$	−2.96276	+	1.71055i	−0.346765	+	0.200205i	−0.663259	−	0.748390i	$-0.730827\pi$
$73$	−2.96276	+	1.71055i	−0.346765	+	0.200205i	0.316495	+	0.948594i	$0.397494\pi$
$74$		−	11.8460i		−	1.37707i
$75$	0.486997	−	0.981535i	0.0562336	−	0.113338i
$76$	11.4553	−	6.61374i	1.31402	−	0.758648i
$77$	8.05706	−	2.83879i	0.918187	−	0.323511i
$78$	6.23458	+	9.37978i	0.705927	+	1.06205i
$79$	7.07973	+	12.2625i	0.796532	+	1.37963i	0.921862	+	0.387519i	$0.126668\pi$
$79$	7.07973	+	12.2625i	0.796532	+	1.37963i	−0.125330	+	0.992115i	$0.539999\pi$
$80$	−3.20267	−	5.54718i	−0.358069	−	0.620194i
$81$	−2.41344	+	8.67037i	−0.268160	+	0.963374i
$82$	−4.91318	−	2.83662i	−0.542570	−	0.313253i
$83$	1.54535	−	2.67662i	0.169624	−	0.293798i	−0.768664	−	0.639653i	$-0.779078\pi$
$83$	1.54535	−	2.67662i	0.169624	−	0.293798i	0.938288	+	0.345856i	$0.112411\pi$
$84$	6.59103	−	8.75311i	0.719140	−	0.955043i
$85$	1.70594	+	2.95477i	0.185035	+	0.320490i
$86$			4.08578i			0.440581i
$87$	11.7551	−	7.81343i	1.26028	−	0.837688i
$88$	2.64572			0.282035
$89$	−2.45766	+	4.25679i	−0.260511	+	0.451219i	−0.966378	−	0.257126i	$-0.917224\pi$
$89$	−2.45766	+	4.25679i	−0.260511	+	0.451219i	0.705867	+	0.708345i	$0.250558\pi$
$90$	12.1131	+	5.08625i	1.27683	+	0.536138i
$91$	−6.23458	−	5.34194i	−0.653562	−	0.559988i
$92$	2.40363	+	1.38774i	0.250596	+	0.144682i
$93$	8.60938	−	5.72251i	0.892751	−	0.593396i
$94$	14.7632	+	8.52356i	1.52271	+	0.879138i
$95$	−10.0122	−	5.78057i	−1.02723	−	0.593074i
$96$	−11.6285	+	7.72926i	−1.18683	+	0.788864i
$97$	2.07939	+	1.20054i	0.211130	+	0.121896i	0.601837	−	0.798619i	$-0.294436\pi$
$97$	2.07939	+	1.20054i	0.211130	+	0.121896i	−0.390706	+	0.920515i	$0.627769\pi$
$98$	−5.30004	+	13.6774i	−0.535385	+	1.38162i
$99$	7.71314	−	5.85939i	0.775199	−	0.588891i
$100$	−0.756296	+	1.30994i	−0.0756296	+	0.130994i
$101$	−3.52051			−0.350304			−0.175152	−	0.984541i	$-0.556042\pi$
$101$	−3.52051			−0.350304			−0.175152	+	0.984541i	$0.556042\pi$
$102$	4.93484	−	3.28010i	0.488622	−	0.324779i
$103$		−	15.6846i		−	1.54545i	−0.634743	−	0.772723i	$-0.718894\pi$
$103$		−	15.6846i		−	1.54545i	0.634743	−	0.772723i	$-0.281106\pi$
$104$	−1.27139	−	2.20211i	−0.124670	−	0.215935i
$105$	−9.50584	−	1.16372i	−0.927675	−	0.113567i
$106$	6.38506	−	11.0592i	0.620172	−	1.07417i
$107$	−1.41984	−	0.819746i	−0.137261	−	0.0792478i	0.429797	−	0.902926i	$-0.358585\pi$
$107$	−1.41984	−	0.819746i	−0.137261	−	0.0792478i	−0.567058	+	0.823678i	$0.691919\pi$
$108$	4.07897	−	11.7356i	0.392499	−	1.12925i
$109$	2.90672	+	5.03459i	0.278414	+	0.482227i	0.970991	−	0.239117i	$-0.0768581\pi$
$109$	2.90672	+	5.03459i	0.278414	+	0.482227i	−0.692577	+	0.721344i	$0.743525\pi$
$110$	−7.06973	−	12.2451i	−0.674072	−	1.16753i
$111$	5.42015	+	8.15449i	0.514458	+	0.773989i
$112$	5.27629	−	6.15796i	0.498563	−	0.581872i
$113$	13.9931	−	8.07894i	1.31636	−	0.760003i	0.333222	−	0.942848i	$-0.391864\pi$
$113$	13.9931	−	8.07894i	1.31636	−	0.760003i	0.983142	+	0.182845i	$0.0585307\pi$
$114$	−8.92412	+	17.9864i	−0.835820	+	1.68458i
$115$		−	2.42584i		−	0.226210i
$116$	−16.8748	+	9.74265i	−1.56678	+	0.904582i
$117$	−8.58343	−	3.60416i	−0.793539	−	0.333205i
$118$			8.30241i			0.764299i
$119$	−2.81047	+	3.28010i	−0.257636	+	0.300687i
$120$	−2.65699	−	1.31829i	−0.242549	−	0.120343i
$121$	0.575009			0.0522736
$122$	−5.02097	+	8.69658i	−0.454577	+	0.787351i
$123$	4.67999	−	0.295367i	0.421981	−	0.0266324i
$124$	−12.3590	+	7.13545i	−1.10987	+	0.640782i
$125$	11.7712			1.05285
$126$	−0.977185	+	16.6036i	−0.0870545	+	1.47917i
$127$	−9.59240			−0.851188			−0.425594	−	0.904914i	$-0.639935\pi$
$127$	−9.59240			−0.851188			−0.425594	+	0.904914i	$0.639935\pi$
$128$	5.56860	−	3.21503i	0.492199	−	0.284171i
$129$	−1.86945	−	2.81254i	−0.164596	−	0.247631i
$130$	−6.79464	+	11.7687i	−0.595929	+	1.03218i
$131$	2.46122			0.215038			0.107519	−	0.994203i	$-0.465709\pi$
$131$	2.46122			0.215038			0.107519	+	0.994203i	$0.465709\pi$
$132$	−11.1361	+	7.40197i	−0.969272	+	0.644258i
$133$	2.69010	−	14.3872i	0.233261	−	1.24753i
$134$		−	1.41227i		−	0.122002i
$135$	−10.6655	+	2.04110i	−0.917943	+	0.175670i
$136$	−1.15856	+	0.668896i	−0.0993459	+	0.0573574i
$137$		−	17.3864i		−	1.48542i	−0.669611	−	0.742712i	$-0.733539\pi$
$137$		−	17.3864i		−	1.48542i	0.669611	−	0.742712i	$-0.266461\pi$
$138$	−4.20467	+	0.265368i	−0.357925	+	0.0225896i
$139$	−8.61174	+	4.97199i	−0.730438	+	0.421719i	−0.818582	−	0.574389i	$-0.805240\pi$
$139$	−8.61174	+	4.97199i	−0.730438	+	0.421719i	0.0881443	+	0.996108i	$0.471906\pi$
$140$	12.9953	+	2.42984i	1.09830	+	0.205359i
$141$	−14.0626	+	0.887527i	−1.18428	+	0.0747432i
$142$	−7.35026	−	12.7310i	−0.616820	−	1.06836i
$143$	5.00967	+	8.67701i	0.418930	+	0.725608i
$144$	3.55986	−	8.47795i	0.296655	−	0.706495i
$145$	14.7490	+	8.51532i	1.22483	+	0.707159i
$146$	−3.58442	+	6.20840i	−0.296649	+	0.513811i
$147$	−2.60967	−	11.8402i	−0.215242	−	0.976561i
$148$	−6.75843	−	11.7060i	−0.555540	−	0.962223i
$149$		−	9.25717i		−	0.758377i	−0.925319	−	0.379189i	$-0.876203\pi$
$149$		−	9.25717i		−	0.758377i	0.925319	−	0.379189i	$-0.123797\pi$
$150$	−0.144621	−	2.29148i	−0.0118083	−	0.187098i
$151$	−11.9698			−0.974087			−0.487044	−	0.873378i	$-0.661925\pi$
$151$	−11.9698			−0.974087			−0.487044	+	0.873378i	$0.661925\pi$
$152$	2.26656	−	3.92579i	0.183842	−	0.318424i
$153$	−1.89620	+	4.51587i	−0.153299	+	0.365087i
$154$	11.6471	−	13.5934i	0.938554	−	1.09539i
$155$	10.8020	+	6.23656i	0.867641	+	0.500933i
$156$	11.5122	+	5.71190i	0.921717	+	0.457318i
$157$	15.4598	+	8.92569i	1.23382	+	0.712348i	0.967825	−	0.251626i	$-0.0809651\pi$
$157$	15.4598	+	8.92569i	1.23382	+	0.712348i	0.265998	+	0.963974i	$0.414298\pi$
$158$	25.6957	+	14.8354i	2.04424	+	1.18024i
$159$	0.664853	+	10.5344i	0.0527262	+	0.835430i
$160$	−14.5901	−	8.42358i	−1.15345	−	0.665943i
$161$	2.89660	−	1.02058i	0.228284	−	0.0804329i
$162$	4.70454	+	18.2631i	0.369623	+	1.43489i
$163$	−8.91768	+	15.4459i	−0.698486	+	1.20981i	0.270505	+	0.962719i	$0.412809\pi$
$163$	−8.91768	+	15.4459i	−0.698486	+	1.20981i	−0.968991	+	0.247095i	$0.920524\pi$
$164$	−6.47344			−0.505491
$165$	10.4694	+	5.19446i	0.815039	+	0.404388i
$166$		−	6.47650i		−	0.502674i
$167$	−6.16899	−	10.6850i	−0.477371	−	0.826830i	0.522293	−	0.852766i	$-0.325077\pi$
$167$	−6.16899	−	10.6850i	−0.477371	−	0.826830i	−0.999664	+	0.0259359i	$0.991743\pi$
$168$	0.456292	−	3.72723i	0.0352037	−	0.287562i
$169$	−1.68526	+	2.91896i	−0.129635	+	0.224535i
$170$	6.19166	+	3.57476i	0.474879	+	0.274171i
$171$	−2.08656	−	16.4646i	−0.159563	−	1.25908i
$172$	2.33103	+	4.03747i	0.177740	+	0.307854i
$173$	4.53368	+	7.85256i	0.344689	+	0.597019i	0.985297	−	0.170849i	$-0.0546509\pi$
$173$	4.53368	+	7.85256i	0.344689	+	0.597019i	−0.640608	+	0.767868i	$0.721318\pi$
$174$	13.1461	−	26.4957i	0.996600	−	2.00863i
$175$	0.556199	+	1.57860i	0.0420447	+	0.119331i
$176$	−8.57037	+	4.94810i	−0.646016	+	0.372977i
$177$	−3.79877	−	5.71516i	−0.285533	−	0.429577i
$178$			10.2999i			0.772014i
$179$	−13.0086	+	7.51051i	−0.972307	+	0.561362i	−0.899939	−	0.436016i	$-0.856389\pi$
$179$	−13.0086	+	7.51051i	−0.972307	+	0.561362i	−0.0723682	+	0.997378i	$0.523056\pi$
$180$	14.8717	−	1.88469i	1.10847	−	0.140477i
$181$		−	2.34159i		−	0.174049i	−0.996206	−	0.0870246i	$-0.972264\pi$
$181$		−	2.34159i		−	0.174049i	0.996206	−	0.0870246i	$-0.0277359\pi$
$182$	−16.9111	−	3.16201i	−1.25354	−	0.234384i
$183$	−0.522815	−	8.28383i	−0.0386476	−	0.612358i
$184$	0.951168			0.0701210
$185$	−5.90704	+	10.2313i	−0.434294	+	0.752220i
$186$	9.62808	−	19.4053i	0.705965	−	1.42286i
$187$	4.56510	−	2.63566i	0.333833	−	0.192739i
$188$	19.4516			1.41865
$189$	−6.92432	−	11.8766i	−0.503670	−	0.863896i
$190$	−24.2262			−1.75755
$191$	7.82585	−	4.51825i	0.566258	−	0.326929i	−0.189395	−	0.981901i	$-0.560653\pi$
$191$	7.82585	−	4.51825i	0.566258	−	0.326929i	0.755654	+	0.654972i	$0.227319\pi$
$192$	−8.28540	+	16.6991i	−0.597947	+	1.20515i
$193$	2.74134	−	4.74815i	0.197326	−	0.341779i	−0.750334	−	0.661058i	$-0.770108\pi$
$193$	2.74134	−	4.74815i	0.197326	−	0.341779i	0.947661	+	0.319279i	$0.103441\pi$
$194$	5.03141			0.361234
$195$	−0.707501	−	11.2101i	−0.0506652	−	0.802773i
$196$	2.56589	+	16.5394i	0.183278	+	1.18139i
$197$			2.88946i			0.205865i	0.994688	+	0.102933i	$0.0328226\pi$
$197$			2.88946i			0.205865i	−0.994688	+	0.102933i	$0.967177\pi$
$198$	7.85822	−	18.7146i	0.558459	−	1.32999i
$199$	4.45419	−	2.57163i	0.315749	−	0.182298i	−0.333747	−	0.942663i	$-0.608313\pi$
$199$	4.45419	−	2.57163i	0.315749	−	0.182298i	0.649496	+	0.760365i	$0.274980\pi$
$200$			0.518372i			0.0366544i
$201$	0.646185	+	0.972171i	0.0455784	+	0.0685716i
$202$	−6.38881	+	3.68858i	−0.449515	+	0.259528i
$203$	−3.96277	+	21.1937i	−0.278132	+	1.48751i
$204$	3.00511	−	6.05676i	0.210400	−	0.424058i
$205$	2.82897	+	4.89993i	0.197584	+	0.342226i
$206$	−16.4334	−	28.4634i	−1.14497	−	1.98314i
$207$	2.77296	−	2.10652i	0.192734	−	0.146413i
$208$	8.23688	+	4.75557i	0.571125	+	0.329739i
$209$	−8.93095	+	15.4689i	−0.617767	+	1.07000i
$210$	−18.4699	+	7.84781i	−1.27454	+	0.541551i
$211$	7.93224	+	13.7390i	0.546078	+	0.945835i	0.998538	+	0.0540502i	$0.0172131\pi$
$211$	7.93224	+	13.7390i	0.546078	+	0.945835i	−0.452460	+	0.891785i	$0.649454\pi$
$212$		−	14.5713i		−	1.00076i
$213$	10.8848	+	5.40059i	0.745814	+	0.370042i
$214$	−3.43552			−0.234848
$215$	2.03738	−	3.52885i	0.138948	−	0.240666i
$216$	−0.800314	−	4.18194i	−0.0544544	−	0.284545i
$217$	−2.90230	+	15.5221i	−0.197021	+	1.05371i
$218$	10.5499	+	6.09099i	0.714529	+	0.412534i
$219$	−0.373233	−	5.91375i	−0.0252207	−	0.399614i
$220$	−13.9723	−	8.06689i	−0.942010	−	0.543870i
$221$	−4.38747	−	2.53311i	−0.295133	−	0.170395i
$222$	18.3799	+	9.11936i	1.23358	+	0.612052i
$223$	13.5288	+	7.81085i	0.905955	+	0.523053i	0.879127	−	0.476587i	$-0.158126\pi$
$223$	13.5288	+	7.81085i	0.905955	+	0.523053i	0.0268275	+	0.999640i	$0.491460\pi$
$224$	3.92008	−	20.9654i	0.261921	−	1.40081i
$225$	1.14802	+	1.51122i	0.0765346	+	0.100748i
$226$	16.9293	−	29.3224i	1.12612	−	1.95049i
$227$	2.08089			0.138114			0.0690569	−	0.997613i	$-0.478001\pi$
$227$	2.08089			0.138114			0.0690569	+	0.997613i	$0.478001\pi$
$228$	1.44308	+	22.8652i	0.0955705	+	1.51428i
$229$			6.43437i			0.425195i	0.977140	+	0.212598i	$0.0681923\pi$
$229$			6.43437i			0.425195i	−0.977140	+	0.212598i	$0.931808\pi$
$230$	−2.54165	−	4.40226i	−0.167591	−	0.290277i
$231$	−1.79793	+	14.6865i	−0.118295	+	0.966298i
$232$	−3.33885	+	5.78305i	−0.219206	+	0.379676i
$233$	−13.5222	−	7.80704i	−0.885868	−	0.511456i	−0.0132791	−	0.999912i	$-0.504227\pi$
$233$	−13.5222	−	7.80704i	−0.885868	−	0.511456i	−0.872589	+	0.488456i	$0.837560\pi$
$234$	−19.3529	+	2.45260i	−1.26514	+	0.160332i
$235$	−8.50057	−	14.7234i	−0.554516	−	0.960450i
$236$	4.73672	+	8.20424i	0.308334	+	0.534050i
$237$	−24.4762	+	1.54476i	−1.58990	+	0.100343i
$238$	−1.66358	+	8.89719i	−0.107834	+	0.576719i
$239$	−14.8777	+	8.58964i	−0.962358	+	0.555618i	−0.896898	−	0.442238i	$-0.854185\pi$
$239$	−14.8777	+	8.58964i	−0.962358	+	0.555618i	−0.0654600	+	0.997855i	$0.520851\pi$
$240$	11.0723	−	0.698806i	0.714716	−	0.0451077i
$241$		−	11.2184i		−	0.722642i	−0.932441	−	0.361321i	$-0.882326\pi$
$241$		−	11.2184i		−	0.722642i	0.932441	−	0.361321i	$-0.117674\pi$
$242$	1.04349	−	0.602460i	0.0670782	−	0.0387276i
$243$	−11.5948	−	10.4193i	−0.743804	−	0.668397i
$244$			11.4583i			0.733544i
$245$	11.3978	−	9.17014i	0.728181	−	0.585859i
$246$	8.18350	−	5.43943i	0.521761	−	0.346806i
$247$	17.1669			1.09230
$248$	−2.44535	+	4.23547i	−0.155280	+	0.268953i
$249$	2.96332	+	4.45825i	0.187793	+	0.282530i
$250$	21.3617	−	12.3332i	1.35103	−	0.780018i
$251$	11.3837			0.718535			0.359267	−	0.933235i	$-0.383027\pi$
$251$	11.3837			0.718535			0.359267	+	0.933235i	$0.383027\pi$
$252$	8.50713	+	16.9648i	0.535899	+	1.06868i
$253$	−3.74790			−0.235629
$254$	−17.4077	+	10.0504i	−1.09226	+	0.630615i
$255$	−5.89780	+	0.372226i	−0.369335	+	0.0233097i
$256$	−4.02567	+	6.97267i	−0.251604	+	0.435792i
$257$	9.38048			0.585138			0.292569	−	0.956244i	$-0.405490\pi$
$257$	9.38048			0.585138			0.292569	+	0.956244i	$0.405490\pi$
$258$	−6.33938	−	3.14534i	−0.394672	−	0.195820i
$259$	−14.7020	−	2.74895i	−0.913537	−	0.170812i
$260$			15.5060i			0.961641i
$261$	3.07370	+	24.2539i	0.190257	+	1.50128i
$262$	4.46647	−	2.57872i	0.275940	−	0.159314i
$263$		−	8.80306i		−	0.542820i	−0.962464	−	0.271410i	$-0.912510\pi$
$263$		−	8.80306i		−	0.542820i	0.962464	−	0.271410i	$-0.0874899\pi$
$264$	−2.03674	+	4.10503i	−0.125353	+	0.252647i
$265$	−11.0294	+	6.36784i	−0.677532	+	0.391173i
$266$	−10.1922	−	28.9276i	−0.624926	−	1.77366i
$267$	−4.71274	−	7.09021i	−0.288415	−	0.433914i
$268$	−0.805735	−	1.39557i	−0.0492181	−	0.0852482i
$269$	8.16473	+	14.1417i	0.497812	+	0.862236i	0.999997	−	0.00252412i	$-0.000803452\pi$
$269$	8.16473	+	14.1417i	0.497812	+	0.862236i	−0.502184	+	0.864761i	$0.667470\pi$
$270$	−17.2166	+	14.8788i	−1.04777	+	0.905493i
$271$	−12.6186	−	7.28538i	−0.766528	−	0.442555i	0.0651065	−	0.997878i	$-0.479261\pi$
$271$	−12.6186	−	7.28538i	−0.766528	−	0.442555i	−0.831635	+	0.555323i	$0.812595\pi$
$272$	2.50197	−	4.33355i	0.151704	−	0.262760i
$273$	13.0879	−	5.56103i	0.792118	−	0.336569i
$274$	−18.2165	−	31.5519i	−1.10050	−	1.90612i
$275$		−	2.04255i		−	0.123170i
$276$	−4.00355	+	2.66109i	−0.240985	+	0.160179i
$277$	28.7137			1.72524			0.862618	−	0.505855i	$-0.168823\pi$
$277$	28.7137			1.72524			0.862618	+	0.505855i	$0.168823\pi$
$278$	−10.4187	+	18.0457i	−0.624873	+	1.08231i
$279$	2.25116	+	17.7634i	0.134773	+	1.06347i
$280$	4.27323	−	1.50562i	0.255375	−	0.0899777i
$281$	−4.76893	−	2.75334i	−0.284490	−	0.164251i	0.350964	−	0.936389i	$-0.385854\pi$
$281$	−4.76893	−	2.75334i	−0.284490	−	0.164251i	−0.635455	+	0.772138i	$0.719187\pi$
$282$	−24.5900	+	16.3446i	−1.46431	+	0.973304i
$283$	−26.2257	−	15.1414i	−1.55896	−	0.900065i	−0.997357	−	0.0726567i	$-0.976852\pi$
$283$	−26.2257	−	15.1414i	−1.55896	−	0.900065i	−0.561601	−	0.827408i	$-0.689814\pi$
$284$	−14.5267	−	8.38699i	−0.862001	−	0.497676i
$285$	16.6766	−	11.0847i	0.987839	−	0.656599i
$286$	18.1825	+	10.4977i	1.07515	+	0.620740i
$287$	−4.66064	+	5.43943i	−0.275109	+	0.321080i
$288$	−3.04059	−	23.9926i	−0.179168	−	1.41378i
$289$	7.16730	−	12.4141i	0.421606	−	0.730242i
$290$	35.6874			2.09564
$291$	−3.46349	+	2.30212i	−0.203033	+	0.134953i
$292$			8.17999i			0.478698i
$293$	−3.54362	−	6.13773i	−0.207021	−	0.358570i	0.743754	−	0.668453i	$-0.233043\pi$
$293$	−3.54362	−	6.13773i	−0.207021	−	0.358570i	−0.950775	+	0.309883i	$0.899710\pi$
$294$	−17.1413	−	18.7526i	−0.999701	−	1.09367i
$295$	4.14001	−	7.17071i	0.241041	−	0.417495i
$296$	−4.01168	−	2.31615i	−0.233174	−	0.134623i
$297$	3.15349	+	16.4782i	0.182984	+	0.956161i
$298$	−9.69912	−	16.7994i	−0.561855	−	0.973161i
$299$	1.80103	+	3.11948i	0.104156	+	0.180404i
$300$	−1.45025	−	2.18187i	−0.0837304	−	0.125970i
$301$	5.07082	+	0.948135i	0.292277	+	0.0546496i
$302$	−21.7220	+	12.5412i	−1.24996	+	0.721667i
$303$	2.71017	−	5.46232i	0.155695	−	0.313802i
$304$			16.9559i			0.972487i
$305$	8.67313	−	5.00743i	0.496622	−	0.286725i
$306$	1.29035	+	10.1819i	0.0737644	+	0.582058i
$307$			3.11346i			0.177695i	0.996045	+	0.0888473i	$0.0283183\pi$
$307$			3.11346i			0.177695i	−0.996045	+	0.0888473i	$0.971682\pi$
$308$	3.75408	−	20.0776i	0.213909	−	1.14403i
$309$	24.3357	+	12.0744i	1.38441	+	0.686887i
$310$	26.1372			1.48449
$311$	9.72605	−	16.8460i	0.551514	−	0.955249i	−0.446652	−	0.894708i	$-0.647384\pi$
$311$	9.72605	−	16.8460i	0.551514	−	0.955249i	0.998166	−	0.0605417i	$-0.0192828\pi$
$312$	4.39547	−	0.277410i	0.248845	−	0.0157053i
$313$	−22.1224	+	12.7724i	−1.25043	+	0.721937i	−0.971195	−	0.238285i	$-0.923415\pi$
$313$	−22.1224	+	12.7724i	−1.25043	+	0.721937i	−0.279237	+	0.960222i	$0.590081\pi$
$314$	37.4073			2.11101
$315$	9.12342	−	13.8531i	0.514046	−	0.780535i
$316$	33.8559			1.90454
$317$	−14.0534	+	8.11372i	−0.789316	+	0.455712i	−0.839722	−	0.543017i	$-0.817282\pi$
$317$	−14.0534	+	8.11372i	−0.789316	+	0.455712i	0.0504056	+	0.998729i	$0.483949\pi$
$318$	12.2438	+	18.4205i	0.686599	+	1.03297i
$319$	13.1561	−	22.7871i	0.736601	−	1.27583i
$320$	−22.4922			−1.25735
$321$	2.36492	−	1.57192i	0.131997	−	0.0877362i
$322$	4.18728	−	4.88697i	0.233348	−	0.272340i
$323$		−	9.03174i		−	0.502540i
$324$	15.0684	+	15.3631i	0.837136	+	0.853507i
$325$	−1.70007	+	0.981535i	−0.0943029	+	0.0544458i
$326$			37.3736i			2.06993i
$327$	−10.0492	+	0.634232i	−0.555722	+	0.0350731i
$328$	−1.92126	+	1.10924i	−0.106084	+	0.0612474i
$329$	14.0044	−	16.3446i	0.772089	−	0.901104i
$330$	24.4416	−	1.54258i	1.34547	−	0.0849161i
$331$	−11.6558	−	20.1885i	−0.640662	−	1.10966i	−0.985285	−	0.170919i	$-0.945326\pi$
$331$	−11.6558	−	20.1885i	−0.640662	−	1.10966i	0.344623	−	0.938741i	$-0.388007\pi$
$332$	−3.69499	−	6.39992i	−0.202789	−	0.351241i
$333$	−16.8248	+	2.13221i	−0.921994	+	0.116845i
$334$	−22.3902	−	12.9270i	−1.22514	−	0.707334i
$335$	−0.704232	+	1.21977i	−0.0384763	+	0.0666430i
$336$	5.49269	+	12.9271i	0.299651	+	0.705230i
$337$	5.93515	+	10.2800i	0.323308	+	0.559986i	0.981168	−	0.193154i	$-0.0618717\pi$
$337$	5.93515	+	10.2800i	0.323308	+	0.559986i	−0.657860	+	0.753140i	$0.728538\pi$
$338$			7.06286i			0.384169i
$339$	1.76278	+	27.9307i	0.0957413	+	1.51699i
$340$	8.15793			0.442426
$341$	9.63545	−	16.6891i	0.521789	−	0.903765i
$342$	−21.0372	−	27.6928i	−1.13756	−	1.49745i
$343$	15.7449	+	9.75176i	0.850147	+	0.526546i
$344$	1.38366	+	0.798855i	0.0746019	+	0.0430714i
$345$	3.76386	+	1.86747i	0.202639	+	0.100541i
$346$	16.4549	+	9.50024i	0.884621	+	0.510736i
$347$	18.7979	+	10.8530i	1.00913	+	0.582619i	0.910936	−	0.412549i	$-0.135361\pi$
$347$	18.7979	+	10.8530i	1.00913	+	0.582619i	0.0981903	+	0.995168i	$0.468695\pi$
$348$	−2.12579	−	33.6825i	−0.113955	−	1.80557i
$349$	2.20868	+	1.27518i	0.118228	+	0.0682588i	0.557948	−	0.829876i	$-0.311589\pi$
$349$	2.20868	+	1.27518i	0.118228	+	0.0682588i	−0.439720	+	0.898135i	$0.644922\pi$
$350$	2.66332	+	2.28200i	0.142361	+	0.121978i
$351$	12.1998	−	10.5432i	0.651180	−	0.562756i
$352$	−13.0144	+	22.5416i	−0.693669	+	1.20147i
$353$	−25.3747			−1.35056			−0.675279	−	0.737563i	$-0.735977\pi$
$353$	−25.3747			−1.35056			−0.675279	+	0.737563i	$0.735977\pi$
$354$	−12.8818	−	6.39140i	−0.684659	−	0.339699i
$355$			14.6609i			0.778119i
$356$	5.87636	+	10.1782i	0.311446	+	0.539441i
$357$	−2.92574	−	6.88575i	−0.154847	−	0.364433i
$358$	−15.7381	+	27.2592i	−0.831786	+	1.44070i
$359$	−9.73735	−	5.62186i	−0.513918	−	0.296711i	0.220525	−	0.975381i	$-0.429223\pi$
$359$	−9.73735	−	5.62186i	−0.513918	−	0.296711i	−0.734443	+	0.678671i	$0.762556\pi$
$360$	4.09083	−	3.10765i	0.215606	−	0.163788i
$361$	5.80204	+	10.0494i	0.305371	+	0.528917i
$362$	−2.45338	−	4.24938i	−0.128947	−	0.223342i
$363$	−0.442656	+	0.892167i	−0.0232334	+	0.0468266i
$364$	−18.5151	+	6.52356i	−0.970458	+	0.341927i
$365$	6.19166	−	3.57476i	0.324086	−	0.187111i
$366$	−9.62808	−	14.4852i	−0.503268	−	0.757155i
$367$		−	3.31180i		−	0.172874i	−0.996257	−	0.0864372i	$-0.972452\pi$
$367$		−	3.31180i		−	0.172874i	0.996257	−	0.0864372i	$-0.0275482\pi$
$368$	−3.08114	+	1.77890i	−0.160616	+	0.0927315i
$369$	−3.14449	+	7.48872i	−0.163696	+	0.389847i
$370$			24.7562i			1.28701i
$371$	−12.2438	−	10.4908i	−0.635667	−	0.544656i
$372$	−1.55692	−	24.6688i	−0.0807224	−	1.27902i
$373$	−6.64541			−0.344087			−0.172043	−	0.985089i	$-0.555037\pi$
$373$	−6.64541			−0.344087			−0.172043	+	0.985089i	$0.555037\pi$
$374$	5.52298	−	9.56608i	0.285586	−	0.494650i
$375$	−9.06176	+	18.2638i	−0.467947	+	0.943140i
$376$	5.77304	−	3.33307i	0.297722	−	0.171890i
$377$	−25.2884			−1.30242
$378$	−25.0094	−	14.2981i	−1.28635	−	0.735413i
$379$	−3.84940			−0.197730			−0.0988652	−	0.995101i	$-0.531521\pi$
$379$	−3.84940			−0.197730			−0.0988652	+	0.995101i	$0.531521\pi$
$380$	−23.9397	+	13.8216i	−1.22808	+	0.709033i
$381$	7.38447	−	14.8833i	0.378318	−	0.762494i
$382$	9.46792	−	16.3989i	0.484421	−	0.839041i
$383$	−34.2223			−1.74868			−0.874339	−	0.485316i	$-0.838705\pi$
$383$	−34.2223			−1.74868			−0.874339	+	0.485316i	$0.838705\pi$
$384$	0.701503	+	11.1151i	0.0357984	+	0.567214i
$385$	−16.8379	+	5.93260i	−0.858138	+	0.302353i
$386$		−	11.4889i		−	0.584768i
$387$	5.80300	−	0.735416i	0.294983	−	0.0373833i
$388$	4.97191	−	2.87054i	0.252411	−	0.145729i
$389$			13.4796i			0.683445i	0.939801	+	0.341723i	$0.111010\pi$
$389$			13.4796i			0.683445i	−0.939801	+	0.341723i	$0.888990\pi$
$390$	−13.0292	−	19.6022i	−0.659760	−	0.992594i
$391$	1.64121	−	0.947550i	0.0829993	−	0.0479197i
$392$	3.59560	+	4.46908i	0.181605	+	0.225723i
$393$	−1.89471	+	3.81875i	−0.0955753	+	0.192631i
$394$	3.02740	+	5.24361i	0.152518	+	0.264169i
$395$	−14.7954	−	25.6265i	−0.744440	−	1.28941i
$396$	−2.91183	−	22.9766i	−0.146325	−	1.15462i
$397$	−25.5501	−	14.7513i	−1.28232	−	0.740349i	−0.305049	−	0.952337i	$-0.598673\pi$
$397$	−25.5501	−	14.7513i	−1.28232	−	0.740349i	−0.977272	+	0.211988i	$0.932006\pi$
$398$	5.38880	−	9.33367i	0.270116	−	0.467855i
$399$	20.2519	+	15.2495i	1.01386	+	0.763430i
$400$	−0.969472	−	1.67918i	−0.0484736	−	0.0839588i
$401$			29.0446i			1.45042i	0.688528	+	0.725209i	$0.258257\pi$
$401$			29.0446i			1.45042i	−0.688528	+	0.725209i	$0.741743\pi$
$402$	2.19124	+	1.08720i	0.109289	+	0.0542247i
$403$	−18.5210			−0.922599
$404$	−4.20884	+	7.28993i	−0.209398	+	0.362687i
$405$	5.04368	−	18.1196i	0.250622	−	0.900370i
$406$	15.0141	+	42.6130i	0.745138	+	2.11485i
$407$	15.8073	+	9.12634i	0.783538	+	0.452376i
$408$	−0.145950	−	2.31252i	−0.00722558	−	0.114487i
$409$	−26.2193	−	15.1377i	−1.29646	−	0.748513i	−0.316671	−	0.948536i	$-0.602565\pi$
$409$	−26.2193	−	15.1377i	−1.29646	−	0.748513i	−0.979791	+	0.200023i	$0.935898\pi$
$410$	10.2677	+	5.92806i	0.507086	+	0.292766i
$411$	26.9763	+	13.3845i	1.33064	+	0.660209i
$412$	−32.4781	−	18.7512i	−1.60008	−	0.923806i
$413$	10.3040	+	1.92663i	0.507029	+	0.0948035i
$414$	2.82512	−	6.72812i	0.138847	−	0.330669i
$415$	−3.22952	+	5.59369i	−0.158531	+	0.274583i
$416$	25.0160			1.22651
$417$	−1.08486	−	17.1893i	−0.0531259	−	0.841763i
$418$			37.4293i			1.83073i
$419$	18.2902	+	31.6795i	0.893534	+	1.54765i	0.835609	+	0.549325i	$0.185115\pi$
$419$	18.2902	+	31.6795i	0.893534	+	1.54765i	0.0579246	+	0.998321i	$0.481552\pi$
$420$	−13.7741	+	18.2925i	−0.672109	+	0.892584i
$421$	3.85999	−	6.68570i	0.188124	−	0.325841i	−0.756501	−	0.653993i	$-0.773093\pi$
$421$	3.85999	−	6.68570i	0.188124	−	0.325841i	0.944625	+	0.328152i	$0.106426\pi$
$422$	28.7899	+	16.6219i	1.40147	+	0.809140i
$423$	9.44865	−	22.5023i	0.459409	−	1.09410i
$424$	−2.49682	−	4.32463i	−0.121256	−	0.210022i
$425$	0.516400	+	0.894431i	0.0250491	+	0.0433863i
$426$	25.4115	−	1.60379i	1.23119	−	0.0777038i
$427$	9.62808	+	8.24958i	0.465935	+	0.399225i
$428$	−3.39490	+	1.96005i	−0.164099	+	0.0947424i
$429$	−17.3196	+	1.09308i	−0.836196	+	0.0527746i
$430$		−	8.53859i		−	0.411767i
$431$	−20.0311	+	11.5650i	−0.964865	+	0.557065i	−0.897667	−	0.440674i	$-0.854739\pi$
$431$	−20.0311	+	11.5650i	−0.964865	+	0.557065i	−0.0671983	+	0.997740i	$0.521406\pi$
$432$	10.4137	+	12.0499i	0.501027	+	0.579752i
$433$		−	34.9265i		−	1.67846i	−0.543776	−	0.839230i	$-0.683006\pi$
$433$		−	34.9265i		−	1.67846i	0.543776	−	0.839230i	$-0.316994\pi$
$434$	10.9962	+	31.2095i	0.527836	+	1.49810i
$435$	−24.5662	+	16.3288i	−1.17786	+	0.782904i
$436$	13.9002			0.665699
$437$	−3.21078	+	5.56123i	−0.153592	+	0.266030i
$438$	−6.87340	−	10.3409i	−0.328424	−	0.494106i
$439$	33.6842	−	19.4476i	1.60766	−	0.928184i	0.617770	−	0.786359i	$-0.288036\pi$
$439$	33.6842	−	19.4476i	1.60766	−	0.928184i	0.989892	−	0.141824i	$-0.0452969\pi$
$440$	−5.52912			−0.263590
$441$	20.3798	+	5.06577i	0.970469	+	0.241227i
$442$	−10.6161			−0.504959
$443$	32.3277	−	18.6644i	1.53594	−	0.886774i	0.536867	−	0.843667i	$-0.319608\pi$
$443$	32.3277	−	18.6644i	1.53594	−	0.886774i	0.999070	−	0.0431065i	$-0.0137255\pi$
$444$	23.3654	−	1.47465i	1.10887	−	0.0699840i
$445$	5.13609	−	8.89596i	0.243474	−	0.421709i
$446$	32.7350			1.55005
$447$	14.3632	+	7.12640i	0.679354	+	0.337067i
$448$	−9.46276	−	26.8572i	−0.447073	−	1.26888i
$449$			23.9224i			1.12897i	0.825445	+	0.564483i	$0.190924\pi$
$449$			23.9224i			1.12897i	−0.825445	+	0.564483i	$0.809076\pi$
$450$	3.66672	+	1.53965i	0.172851	+	0.0725796i
$451$	7.57036	−	4.37075i	0.356474	−	0.205810i
$452$		−	38.6342i		−	1.81720i
$453$	9.21464	−	18.5720i	0.432941	−	0.872587i
$454$	3.77628	−	2.18024i	0.177230	−	0.102324i
$455$	13.0292	+	11.1638i	0.610819	+	0.523365i
$456$	4.34629	+	6.53889i	0.203534	+	0.306212i
$457$	−4.99031	−	8.64348i	−0.233437	−	0.404325i	0.725380	−	0.688348i	$-0.241664\pi$
$457$	−4.99031	−	8.64348i	−0.233437	−	0.404325i	−0.958817	+	0.284024i	$0.908331\pi$
$458$	6.74155	+	11.6767i	0.315012	+	0.545617i
$459$	−5.54695	−	6.41852i	−0.258909	−	0.299591i
$460$	−5.02319	−	2.90014i	−0.234207	−	0.135220i
$461$	16.7279	−	28.9735i	0.779094	−	1.34943i	−0.153371	−	0.988169i	$-0.549013\pi$
$461$	16.7279	−	28.9735i	0.779094	−	1.34943i	0.932465	−	0.361261i	$-0.117654\pi$
$462$	12.1248	+	28.5359i	0.564098	+	1.32761i
$463$	11.5353	+	19.9798i	0.536092	+	0.928538i	0.999110	+	0.0421893i	$0.0134333\pi$
$463$	11.5353	+	19.9798i	0.536092	+	0.928538i	−0.463018	+	0.886349i	$0.653233\pi$
$464$		−	24.9776i		−	1.15956i
$465$	−17.9921	+	11.9591i	−0.834366	+	0.554588i
$466$	−32.7190			−1.51568
$467$	20.1395	−	34.8827i	0.931946	−	1.61418i	0.151955	−	0.988387i	$-0.451443\pi$
$467$	20.1395	−	34.8827i	0.931946	−	1.61418i	0.779991	−	0.625791i	$-0.215224\pi$
$468$	−17.7248	+	13.4649i	−0.819330	+	0.622415i
$469$	−1.75276	−	0.327728i	−0.0809349	−	0.0151331i
$470$	−30.8527	−	17.8128i	−1.42313	−	0.821643i
$471$	−25.7501	+	17.1157i	−1.18650	+	0.788649i
$472$	2.81163	+	1.62329i	0.129416	+	0.0747182i
$473$	−5.45205	−	3.14774i	−0.250686	−	0.144733i
$474$	−42.7995	+	28.4481i	−1.96584	+	1.30666i
$475$	−3.03078	−	1.74982i	−0.139062	−	0.0802874i
$476$	3.43214	+	9.74109i	0.157312	+	0.446482i
$477$	−16.8566	−	7.07805i	−0.771812	−	0.324082i
$478$	−17.9994	+	31.1759i	−0.823275	+	1.42595i
$479$	−0.155503			−0.00710509			−0.00355255	−	0.999994i	$-0.501131\pi$
$479$	−0.155503			−0.00710509			−0.00355255	+	0.999994i	$0.501131\pi$
$480$	24.3016	−	16.1528i	1.10921	−	0.737273i
$481$		−	17.5425i		−	0.799867i
$482$	−11.7540	−	20.3585i	−0.535380	−	0.927305i
$483$	−0.646377	+	5.27995i	−0.0294112	+	0.240246i
$484$	0.687435	−	1.19067i	0.0312471	−	0.0541215i
$485$	−4.34558	−	2.50892i	−0.197323	−	0.113924i
$486$	−31.9582	−	6.75998i	−1.44965	−	0.306639i
$487$	8.25111	+	14.2913i	0.373893	+	0.647602i	0.990161	−	0.139935i	$-0.0446892\pi$
$487$	8.25111	+	14.2913i	0.373893	+	0.647602i	−0.616267	+	0.787537i	$0.711356\pi$
$488$	1.96341	+	3.40072i	0.0888793	+	0.153944i
$489$	−17.1003	−	25.7270i	−0.773302	−	1.16342i
$490$	11.0762	−	28.5834i	0.500371	−	1.29127i
$491$	8.10003	−	4.67655i	0.365549	−	0.211050i	−0.305963	−	0.952043i	$-0.598978\pi$
$491$	8.10003	−	4.67655i	0.365549	−	0.211050i	0.671512	+	0.740993i	$0.265645\pi$
$492$	4.98341	−	10.0440i	0.224670	−	0.452818i
$493$			13.3046i			0.599209i
$494$	31.1534	−	17.9864i	1.40166	−	0.809248i
$495$	−16.1192	+	12.2451i	−0.724502	+	0.550378i
$496$		−	18.2934i		−	0.821399i
$497$	−17.5060	+	6.16801i	−0.785253	+	0.276673i
$498$	10.0487	+	4.98577i	0.450295	+	0.223418i
$499$	1.99623			0.0893637			0.0446818	−	0.999001i	$-0.485773\pi$
$499$	1.99623			0.0893637			0.0446818	+	0.999001i	$0.485773\pi$
$500$	14.0727	−	24.3746i	0.629351	−	1.09007i
$501$	21.3276	−	1.34604i	0.952846	−	0.0601367i
$502$	20.6585	−	11.9272i	0.922035	−	0.532337i
$503$	−15.7008			−0.700063			−0.350032	−	0.936738i	$-0.613829\pi$
$503$	−15.7008			−0.700063			−0.350032	+	0.936738i	$0.613829\pi$
$504$	5.43180	+	3.57728i	0.241951	+	0.159345i
$505$	7.35727			0.327394
$506$	−6.80147	+	3.92683i	−0.302362	+	0.174569i
$507$	−3.23161	−	4.86188i	−0.143521	−	0.215924i
$508$	−11.4679	+	19.8630i	−0.508807	+	0.881279i
$509$	−15.1979			−0.673633			−0.336817	−	0.941570i	$-0.609350\pi$
$509$	−15.1979			−0.673633			−0.336817	+	0.941570i	$0.609350\pi$
$510$	−10.3130	+	6.85486i	−0.456667	+	0.303538i
$511$	6.87340	+	5.88930i	0.304061	+	0.260527i
$512$			29.7316i			1.31396i
$513$	27.1523	+	9.43741i	1.19880	+	0.416672i
$514$	17.0231	−	9.82831i	0.750858	−	0.433508i
$515$			32.7781i			1.44437i
$516$	−8.05890	+	0.508619i	−0.354773	+	0.0223907i
$517$	−22.7476	+	13.1333i	−1.00044	+	0.577603i
$518$	−29.5605	+	10.4152i	−1.29881	+	0.457619i
$519$	−15.6739	+	0.989225i	−0.688010	+	0.0434222i
$520$	2.65699	+	4.60204i	0.116517	+	0.201813i
$521$	20.6160	+	35.7080i	0.903204	+	1.56440i	0.823310	+	0.567592i	$0.192125\pi$
$521$	20.6160	+	35.7080i	0.903204	+	1.56440i	0.0798940	+	0.996803i	$0.474542\pi$
$522$	30.9897	+	40.7940i	1.35638	+	1.78551i
$523$	37.0311	+	21.3799i	1.61926	+	0.934878i	0.987113	+	0.160026i	$0.0511577\pi$
$523$	37.0311	+	21.3799i	1.61926	+	0.934878i	0.632143	+	0.774852i	$0.282176\pi$
$524$	2.94244	−	5.09645i	0.128541	−	0.222640i
$525$	−2.87749	−	0.352266i	−0.125584	−	0.0153741i
$526$	−9.22332	−	15.9753i	−0.402156	−	0.696554i
$527$			9.74419i			0.424464i
$528$	−1.07965	−	17.1067i	−0.0469857	−	0.744473i
$529$	21.6526			0.941417
$530$	−13.3437	+	23.1119i	−0.579613	+	1.00392i
$531$	11.7919	−	1.49438i	0.511723	−	0.0648507i
$532$	−26.5756	−	22.7706i	−1.15220	−	0.987231i
$533$	−7.27579	−	4.20068i	−0.315149	−	0.181952i
$534$	−15.9811	−	7.92915i	−0.691570	−	0.343128i
$535$	2.96723	+	1.71313i	0.128284	+	0.0740650i
$536$	−0.478269	−	0.276129i	−0.0206581	−	0.0119270i
$537$	−1.63875	−	25.9655i	−0.0707174	−	1.12049i
$538$	29.6337	+	17.1090i	1.27760	+	0.737623i
$539$	−14.1678	−	17.6096i	−0.610251	−	0.758499i
$540$	−8.52435	+	24.5253i	−0.366830	+	1.05540i
$541$	8.04309	−	13.9310i	0.345800	−	0.598942i	−0.639699	−	0.768625i	$-0.720941\pi$
$541$	8.04309	−	13.9310i	0.345800	−	0.598942i	0.985499	+	0.169683i	$0.0542744\pi$
$542$	−30.5328			−1.31149
$543$	3.63314	+	1.80261i	0.155913	+	0.0773576i
$544$		−	13.1613i		−	0.564284i
$545$	−6.07456	−	10.5214i	−0.260206	−	0.450689i
$546$	17.9247	−	23.8046i	0.767106	−	1.01874i
$547$	−5.94015	+	10.2886i	−0.253982	+	0.439910i	−0.964619	−	0.263649i	$-0.915074\pi$
$547$	−5.94015	+	10.2886i	−0.253982	+	0.439910i	0.710636	+	0.703560i	$0.248407\pi$
$548$	−36.0021	−	20.7858i	−1.53794	−	0.887927i
$549$	13.2554	+	5.56591i	0.565728	+	0.237547i
$550$	−2.14006	−	3.70669i	−0.0912525	−	0.158054i
$551$	−22.5413	−	39.0427i	−0.960293	−	1.66328i
$552$	−0.732233	+	1.47580i	−0.0311659	+	0.0628144i
$553$	24.3750	−	28.4481i	1.03653	−	1.20973i
$554$	52.1078	−	30.0845i	2.21385	−	1.27817i
$555$	−11.3272	−	17.0415i	−0.480812	−	0.723371i
$556$			23.7765i			1.00835i
$557$	−26.4006	+	15.2424i	−1.11863	+	0.645841i	−0.941051	−	0.338265i	$-0.890160\pi$
$557$	−26.4006	+	15.2424i	−1.11863	+	0.645841i	−0.177579	+	0.984107i	$0.556827\pi$
$558$	22.6967	+	29.8773i	0.960827	+	1.26481i
$559$			6.05052i			0.255910i
$560$	−11.0266	+	12.8691i	−0.465957	+	0.543818i
$561$	0.575088	+	9.11207i	0.0242802	+	0.384712i
$562$	−11.5392			−0.486750
$563$	−11.2686	+	19.5177i	−0.474914	+	0.822575i	−0.999587	−	0.0287288i	$-0.990854\pi$
$563$	−11.2686	+	19.5177i	−0.474914	+	0.822575i	0.524673	+	0.851304i	$0.324187\pi$
$564$	−14.9743	+	30.1805i	−0.630531	+	1.27083i
$565$	−29.2433	+	16.8836i	−1.23027	+	0.710300i
$566$	−63.4572			−2.66730
$567$	23.7579	−	1.60067i	0.997738	−	0.0672217i
$568$	−5.74852			−0.241202
$569$	38.5935	−	22.2819i	1.61792	−	0.934108i	0.630465	−	0.776218i	$-0.282864\pi$
$569$	38.5935	−	22.2819i	1.61792	−	0.934108i	0.987457	−	0.157890i	$-0.0504691\pi$
$570$	18.6499	−	37.5886i	0.781158	−	1.57441i
$571$	−17.6415	+	30.5560i	−0.738274	+	1.27873i	0.214998	+	0.976614i	$0.431025\pi$
$571$	−17.6415	+	30.5560i	−0.738274	+	1.27873i	−0.953272	+	0.302113i	$0.902308\pi$
$572$	23.9567			1.00168
$573$	0.985859	+	15.6206i	0.0411849	+	0.652561i
$574$	−2.75874	+	14.7543i	−0.115147	+	0.615833i
$575$		−	0.734319i		−	0.0306232i
$576$	−19.5315	−	25.7108i	−0.813813	−	1.07128i
$577$	3.25158	−	1.87730i	0.135365	−	0.0781531i	−0.430788	−	0.902453i	$-0.641764\pi$
$577$	3.25158	−	1.87730i	0.135365	−	0.0781531i	0.566153	+	0.824300i	$0.308431\pi$
$578$		−	30.0379i		−	1.24941i
$579$	5.25673	+	7.90863i	0.218462	+	0.328671i
$580$	35.2654	−	20.3605i	1.46432	−	0.845423i
$581$	−8.03792	−	1.50292i	−0.333469	−	0.0623516i
$582$	−3.87330	+	7.80658i	−0.160554	+	0.323593i
$583$	9.83827	+	17.0404i	0.407460	+	0.705741i
$584$	1.40166	+	2.42775i	0.0580011	+	0.100461i
$585$	17.9379	+	7.53208i	0.741642	+	0.311413i
$586$	−12.8615	−	7.42559i	−0.531304	−	0.306748i
$587$	−15.8021	+	27.3700i	−0.652222	+	1.12968i	0.330361	+	0.943855i	$0.392829\pi$
$587$	−15.8021	+	27.3700i	−0.652222	+	1.12968i	−0.982583	+	0.185826i	$0.940504\pi$
$588$	−27.6374	−	8.75132i	−1.13975	−	0.360898i
$589$	−16.5091	−	28.5946i	−0.680246	−	1.17822i
$590$		−	17.3506i		−	0.714314i
$591$	−4.48319	−	2.22437i	−0.184414	−	0.0914985i
$592$	17.3269			0.712129
$593$	−18.5588	+	32.1448i	−0.762120	+	1.32003i	0.179636	+	0.983733i	$0.442508\pi$
$593$	−18.5588	+	32.1448i	−0.762120	+	1.32003i	−0.941756	+	0.336297i	$0.890825\pi$
$594$	22.9876	+	26.5996i	0.943193	+	1.09139i
$595$	5.87342	−	6.85486i	0.240787	−	0.281022i
$596$	−19.1689	−	11.0671i	−0.785187	−	0.453328i
$597$	0.561116	+	8.89069i	0.0229649	+	0.363872i
$598$	6.53682	+	3.77403i	0.267310	+	0.154332i
$599$	−24.5188	−	14.1559i	−1.00181	−	0.578396i	−0.0930277	−	0.995664i	$-0.529655\pi$
$599$	−24.5188	−	14.1559i	−1.00181	−	0.578396i	−0.908784	+	0.417267i	$0.862988\pi$
$600$	−0.804290	−	0.399055i	−0.0328350	−	0.0162914i
$601$	20.8341	+	12.0286i	0.849840	+	0.490655i	0.860597	−	0.509287i	$-0.170091\pi$
$601$	20.8341	+	12.0286i	0.849840	+	0.490655i	−0.0107568	+	0.999942i	$0.503424\pi$
$602$	10.1956	−	3.59229i	0.415543	−	0.146411i
$603$	−2.00584	+	0.254201i	−0.0816841	+	0.0103519i
$604$	−14.3101	+	24.7859i	−0.582271	+	1.00852i
$605$	−1.20167			−0.0488549
$606$	−0.804829	−	12.7522i	−0.0326939	−	0.518025i
$607$			9.52047i			0.386424i	0.981157	+	0.193212i	$0.0618905\pi$
$607$			9.52047i			0.386424i	−0.981157	+	0.193212i	$0.938110\pi$
$608$	22.2985	+	38.6221i	0.904323	+	1.56633i
$609$	−29.8329	−	22.4639i	−1.20889	−	0.910285i
$610$	10.4930	−	18.1744i	0.424848	−	0.735859i
$611$	21.8625	+	12.6223i	0.884461	+	0.510644i
$612$	7.08408	+	9.32529i	0.286357	+	0.376952i
$613$	1.23108	+	2.13230i	0.0497230	+	0.0861227i	0.889816	−	0.456320i	$-0.150833\pi$
$613$	1.23108	+	2.13230i	0.0497230	+	0.0861227i	−0.840093	+	0.542443i	$0.817499\pi$
$614$	3.26210	+	5.65012i	0.131648	+	0.228020i
$615$	−9.78040	+	0.617267i	−0.394384	+	0.0248906i
$616$	−2.32617	−	6.60212i	−0.0937239	−	0.266007i
$617$	18.7738	−	10.8390i	0.755804	−	0.436364i	−0.0719831	−	0.997406i	$-0.522933\pi$
$617$	18.7738	−	10.8390i	0.755804	−	0.436364i	0.827787	+	0.561042i	$0.189599\pi$
$618$	56.8138	−	3.58567i	2.28539	−	0.144237i
$619$			24.1063i			0.968915i	0.874815	+	0.484457i	$0.160983\pi$
$619$			24.1063i			0.968915i	−0.874815	+	0.484457i	$0.839017\pi$
$620$	25.8281	−	14.9119i	1.03728	−	0.598875i
$621$	1.13371	+	5.92409i	0.0454944	+	0.237726i
$622$		−	40.7615i		−	1.63439i
$623$	12.7832	+	2.39018i	0.512147	+	0.0957604i
$624$	−13.7196	+	9.11915i	−0.549222	+	0.365058i
$625$	−21.4368			−0.857471
$626$	−26.7643	+	46.3571i	−1.06972	+	1.85280i
$627$	−17.1258	−	25.7653i	−0.683937	−	1.02897i
$628$	36.9649	−	21.3417i	1.47506	−	0.851627i
$629$	−9.22934			−0.367998
$630$	2.04215	−	34.6988i	0.0813612	−	1.38243i
$631$	3.37520			0.134365			0.0671824	−	0.997741i	$-0.478599\pi$
$631$	3.37520			0.134365			0.0671824	+	0.997741i	$0.478599\pi$
$632$	10.0481	−	5.80128i	0.399692	−	0.230762i
$633$	−27.4235	+	1.73077i	−1.08999	+	0.0687921i
$634$	−17.0021	+	29.4486i	−0.675242	+	1.16955i
$635$	20.0465			0.795521
$636$	22.6084	+	11.2173i	0.896481	+	0.444797i
$637$	−7.84869	+	20.2544i	−0.310976	+	0.802510i
$638$		−	55.1368i		−	2.18289i
$639$	−16.7588	+	12.7310i	−0.662967	+	0.503632i
$640$	−11.6374	+	6.71887i	−0.460010	+	0.265587i
$641$		−	35.6978i		−	1.40998i	−0.709218	−	0.704989i	$-0.750952\pi$
$641$		−	35.6978i		−	1.40998i	0.709218	−	0.704989i	$-0.249048\pi$
$642$	2.64475	−	5.33045i	0.104380	−	0.210376i
$643$	3.03956	−	1.75489i	0.119868	−	0.0692060i	−0.438867	−	0.898552i	$-0.644620\pi$
$643$	3.03956	−	1.75489i	0.119868	−	0.0692060i	0.558735	+	0.829346i	$0.311287\pi$
$644$	1.34963	−	7.21813i	0.0531831	−	0.284434i
$645$	3.90683	+	5.87774i	0.153831	+	0.231436i
$646$	−9.46292	−	16.3903i	−0.372314	−	0.644866i
$647$	−7.02996	−	12.1762i	−0.276376	−	0.478698i	0.694105	−	0.719874i	$-0.255800\pi$
$647$	−7.02996	−	12.1762i	−0.276376	−	0.478698i	−0.970481	+	0.241176i	$0.922467\pi$
$648$	7.10468	+	1.97762i	0.279098	+	0.0776883i
$649$	−11.0787	−	6.39629i	−0.434877	−	0.251076i
$650$	−2.05679	+	3.56246i	−0.0806739	+	0.139731i
$651$	−21.8494	−	16.4524i	−0.856346	−	0.644822i
$652$	21.3225	+	36.9317i	0.835055	+	1.44636i
$653$			11.8558i			0.463955i	0.972721	+	0.231978i	$0.0745196\pi$
$653$			11.8558i			0.463955i	−0.972721	+	0.231978i	$0.925480\pi$
$654$	−17.5722	+	11.6799i	−0.687126	+	0.456721i
$655$	−5.14353			−0.200974
$656$	4.14905	−	7.18637i	0.161993	−	0.280581i
$657$	9.46292	+	3.97345i	0.369184	+	0.155019i
$658$	8.28952	−	44.3341i	0.323159	−	1.72832i
$659$	5.03144	+	2.90491i	0.195997	+	0.113159i	0.594787	−	0.803883i	$-0.297236\pi$
$659$	5.03144	+	2.90491i	0.195997	+	0.113159i	−0.398790	+	0.917042i	$0.630570\pi$
$660$	23.2725	−	15.4689i	0.905882	−	0.602124i
$661$	8.41592	+	4.85893i	0.327341	+	0.188991i	0.654660	−	0.755923i	$-0.272812\pi$
$661$	8.41592	+	4.85893i	0.327341	+	0.188991i	−0.327319	+	0.944914i	$0.606145\pi$
$662$	−42.3046	−	24.4246i	−1.64422	−	0.949288i
$663$	7.30787	−	4.85742i	0.283814	−	0.188646i
$664$	−2.19328	−	1.26629i	−0.0851158	−	0.0491416i
$665$	−5.62185	+	30.0668i	−0.218006	+	1.16594i
$666$	−28.2987	+	21.4975i	−1.09655	+	0.833010i
$667$	4.72977	−	8.19220i	0.183137	−	0.317203i
$668$	−29.5006			−1.14141
$669$	−22.5339	+	14.9779i	−0.871210	+	0.579078i
$670$			2.95141i			0.114023i
$671$	−7.73645	−	13.3999i	−0.298662	−	0.517298i
$672$	29.5115	+	22.2219i	1.13843	+	0.857230i
$673$	13.4646	−	23.3214i	0.519023	−	0.898975i	−0.480732	−	0.876867i	$-0.659629\pi$
$673$	13.4646	−	23.3214i	0.519023	−	0.898975i	0.999756	−	0.0221072i	$-0.00703750\pi$
$674$	21.5415	+	12.4370i	0.829747	+	0.479055i
$675$	−3.22854	+	0.617857i	−0.124266	+	0.0237813i
$676$	4.02953	+	6.97935i	0.154982	+	0.268436i
$677$	22.7056	+	39.3273i	0.872648	+	1.51147i	0.859247	+	0.511560i	$0.170932\pi$
$677$	22.7056	+	39.3273i	0.872648	+	1.51147i	0.0134007	+	0.999910i	$0.495734\pi$
$678$	32.4631	+	48.8400i	1.24674	+	1.87569i
$679$	1.16757	−	6.24443i	0.0448074	−	0.239639i
$680$	2.42120	−	1.39788i	0.0928487	−	0.0536062i
$681$	−1.60192	+	3.22865i	−0.0613858	+	0.123722i
$682$		−	40.3818i		−	1.54630i
$683$	37.6543	−	21.7397i	1.44080	−	0.831848i	0.442900	−	0.896571i	$-0.353950\pi$
$683$	37.6543	−	21.7397i	1.44080	−	0.831848i	0.997903	+	0.0647226i	$0.0206162\pi$
$684$	−36.5878	−	15.3631i	−1.39897	−	0.587424i
$685$			36.3347i			1.38828i
$686$	38.7903	+	1.20030i	1.48102	+	0.0458278i
$687$	−9.98338	−	4.95334i	−0.380890	−	0.188982i
$688$	−5.97616			−0.227839
$689$	9.45546	−	16.3773i	0.360224	−	0.623927i
$690$	8.78704	−	0.554574i	0.334517	−	0.0211123i
$691$	−23.6991	+	13.6827i	−0.901557	+	0.520514i	−0.877705	−	0.479201i	$-0.840926\pi$
$691$	−23.6991	+	13.6827i	−0.901557	+	0.520514i	−0.0238522	+	0.999715i	$0.507593\pi$
$692$	21.6804			0.824166
$693$	−21.4030	−	14.0956i	−0.813032	−	0.535448i
$694$	45.4845			1.72657
$695$	17.9971	−	10.3906i	0.682668	−	0.394139i
$696$	−6.40249	−	9.63239i	−0.242686	−	0.365115i
$697$	−2.21004	+	3.82790i	−0.0837112	+	0.144992i
$698$	5.34423			0.202282
$699$	22.5229	−	14.9706i	0.851893	−	0.566239i
$700$	3.93377	+	0.735530i	0.148682	+	0.0278004i
$701$			8.26437i			0.312141i	0.987746	+	0.156070i	$0.0498827\pi$
$701$			8.26437i			0.312141i	−0.987746	+	0.156070i	$0.950117\pi$
$702$	11.0930	−	31.9155i	0.418677	−	1.20457i
$703$	27.0838	−	15.6368i	1.02148	−	0.589754i
$704$			34.7504i			1.30970i
$705$	29.3884	−	1.85478i	1.10683	−	0.0698551i
$706$	−46.0484	+	26.5861i	−1.73306	+	1.00058i
$707$	3.09529	+	8.78505i	0.116410	+	0.330396i
$708$	−16.3759	+	1.03353i	−0.615444	+	0.0388423i
$709$	−21.4086	−	37.0807i	−0.804015	−	1.39260i	−0.916954	−	0.398994i	$-0.869360\pi$
$709$	−21.4086	−	37.0807i	−0.804015	−	1.39260i	0.112938	−	0.993602i	$-0.463974\pi$
$710$	15.3608	+	26.6057i	0.576481	+	0.998494i
$711$	16.4456	−	39.1658i	0.616758	−	1.46883i
$712$	3.48810	+	2.01385i	0.130722	+	0.0754724i
$713$	3.46405	−	5.99992i	0.129730	−	0.224699i
$714$	−12.5239	−	9.43044i	−0.468697	−	0.352925i
$715$	−10.4694	−	18.1335i	−0.391532	−	0.678153i
$716$			35.9159i			1.34224i
$717$	−1.87421	−	29.6963i	−0.0699938	−	1.10903i
$718$	−23.5610			−0.879289
$719$	11.5725	−	20.0442i	0.431583	−	0.747523i	−0.565427	−	0.824798i	$-0.691289\pi$
$719$	11.5725	−	20.0442i	0.431583	−	0.747523i	0.997010	+	0.0772751i	$0.0246220\pi$
$720$	−7.43951	+	17.7175i	−0.277254	+	0.660291i
$721$	−39.1391	+	13.7901i	−1.45762	+	0.513571i
$722$	21.0584	+	12.1581i	0.783712	+	0.452477i
$723$	17.4062	+	8.63622i	0.647343	+	0.321184i
$724$	−4.84874	−	2.79942i	−0.180202	−	0.104040i
$725$	4.46462	+	2.57765i	0.165812	+	0.0957316i
$726$	0.131454	+	2.08284i	0.00487870	+	0.0773014i
$727$	4.76878	+	2.75326i	0.176864	+	0.102113i	0.585819	−	0.810442i	$-0.300773\pi$
$727$	4.76878	+	2.75326i	0.176864	+	0.102113i	−0.408954	+	0.912555i	$0.634106\pi$
$728$	−4.37730	+	5.10874i	−0.162233	+	0.189343i
$729$	25.0922	−	9.96907i	0.929340	−	0.369225i
$730$	7.49084	−	12.9745i	0.277248	−	0.480208i
$731$	3.18327			0.117737
$732$	−17.7784	−	8.82090i	−0.657108	−	0.326030i
$733$		−	3.98999i		−	0.147373i	−0.997281	−	0.0736867i	$-0.976524\pi$
$733$		−	3.98999i		−	0.147373i	0.997281	−	0.0736867i	$-0.0234765\pi$
$734$	−3.46991	−	6.01005i	−0.128077	−	0.221835i
$735$	5.45377	+	24.7439i	0.201165	+	0.912694i
$736$	−4.67882	+	8.10395i	−0.172463	+	0.298716i
$737$	1.88453	+	1.08803i	0.0694176	+	0.0400783i
$738$	2.13980	+	16.8847i	0.0787672	+	0.621534i
$739$	0.871657	+	1.50976i	0.0320644	+	0.0555372i	0.881612	−	0.471974i	$-0.156458\pi$
$739$	0.871657	+	1.50976i	0.0320644	+	0.0555372i	−0.849548	+	0.527512i	$0.823125\pi$
$740$	14.1240	+	24.4635i	0.519208	+	0.899295i
$741$	−13.2155	+	26.6356i	−0.485483	+	0.978483i
$742$	−33.2110	−	6.20974i	−1.21921	−	0.227967i
$743$	8.70204	−	5.02413i	0.319247	−	0.184317i	−0.331810	−	0.943346i	$-0.607659\pi$
$743$	8.70204	−	5.02413i	0.319247	−	0.184317i	0.651057	+	0.759029i	$0.274326\pi$
$744$	−4.68914	−	7.05470i	−0.171912	−	0.258638i
$745$			19.3459i			0.708780i
$746$	−12.0597	+	6.96267i	−0.441537	+	0.254921i
$747$	−9.19852	+	1.16573i	−0.336556	+	0.0426519i
$748$		−	12.6040i		−	0.460846i
$749$	−0.797238	+	4.26379i	−0.0291304	+	0.155796i
$750$	2.69103	+	42.6385i	0.0982626	+	1.55694i
$751$	−23.3450			−0.851872			−0.425936	−	0.904753i	$-0.640055\pi$
$751$	−23.3450			−0.851872			−0.425936	+	0.904753i	$0.640055\pi$
$752$	−12.4672	+	21.5938i	−0.454631	+	0.787444i
$753$	−8.76348	+	17.6627i	−0.319359	+	0.643663i
$754$	−45.8919	+	26.4957i	−1.67128	+	0.964916i
$755$	25.0148			0.910383
$756$	−32.8711	+	0.139482i	−1.19551	+	0.00507291i
$757$	−14.3334			−0.520957			−0.260479	−	0.965480i	$-0.583880\pi$
$757$	−14.3334			−0.520957			−0.260479	+	0.965480i	$0.583880\pi$
$758$	−6.98566	+	4.03317i	−0.253730	+	0.146491i
$759$	2.88523	−	5.81513i	0.104727	−	0.211076i
$760$	−4.73672	+	8.20424i	−0.171819	+	0.297599i
$761$	22.6355			0.820537			0.410268	−	0.911965i	$-0.365435\pi$
$761$	22.6355			0.820537			0.410268	+	0.911965i	$0.365435\pi$
$762$	−2.19293	−	34.7463i	−0.0794416	−	1.25873i
$763$	10.0076	−	11.6799i	0.362301	−	0.422841i
$764$		−	21.6067i		−	0.781702i
$765$	3.96274	−	9.43741i	0.143273	−	0.341210i
$766$	−62.1046	+	35.8561i	−2.24393	+	1.29553i
$767$			12.2948i			0.443940i
$768$	−7.71952	−	11.6138i	−0.278554	−	0.419078i
$769$	42.6873	−	24.6455i	1.53934	−	0.888741i	0.540468	−	0.841365i	$-0.318247\pi$
$769$	42.6873	−	24.6455i	1.53934	−	0.888741i	0.998877	−	0.0473762i	$-0.0150860\pi$
$770$	−24.3406	+	28.4079i	−0.877173	+	1.02375i
$771$	−7.22133	+	14.5545i	−0.260070	+	0.524167i
$772$	−6.55467	−	11.3530i	−0.235908	−	0.408604i
$773$	−11.0083	−	19.0670i	−0.395943	−	0.685793i	0.597278	−	0.802034i	$-0.296249\pi$
$773$	−11.0083	−	19.0670i	−0.395943	−	0.685793i	−0.993221	+	0.116241i	$0.962915\pi$
$774$	9.76042	−	7.41463i	0.350831	−	0.266513i
$775$	3.26986	+	1.88785i	0.117457	+	0.0678137i
$776$	0.983745	−	1.70390i	0.0353144	−	0.0611663i
$777$	15.5831	−	20.6949i	0.559042	−	0.742427i
$778$	14.1232	+	24.4621i	0.506340	+	0.877007i
$779$		−	14.9774i		−	0.536622i
$780$	−24.0586	−	11.9369i	−0.861438	−	0.427410i
$781$	22.6510			0.810516
$782$	1.98557	−	3.43911i	0.0710040	−	0.122982i
$783$	−39.9978	−	13.9022i	−1.42941	−	0.496823i
$784$	−20.0055	−	7.75223i	−0.714483	−	0.276865i
$785$	−32.3083	−	18.6532i	−1.15313	−	0.665761i
$786$	0.562663	+	8.91521i	0.0200695	+	0.317995i
$787$	9.40107	+	5.42771i	0.335112	+	0.193477i	0.658108	−	0.752923i	$-0.271357\pi$
$787$	9.40107	+	5.42771i	0.335112	+	0.193477i	−0.322996	+	0.946400i	$0.604690\pi$
$788$	5.98320	+	3.45440i	0.213143	+	0.123058i
$789$	13.6586	+	6.77681i	0.486258	+	0.241261i
$790$	−53.6998	−	31.0036i	−1.91055	−	1.10306i
$791$	−32.4631	−	27.8152i	−1.15426	−	0.988995i
$792$	−4.80130	−	6.32030i	−0.170607	−	0.224582i
$793$	−7.43542	+	12.8785i	−0.264039	+	0.457330i
$794$	−61.8223			−2.19399
$795$	−1.38943	−	22.0150i	−0.0492780	−	0.780793i
$796$		−	12.2977i		−	0.435882i
$797$	1.98299	+	3.43465i	0.0702412	+	0.121661i	0.899007	−	0.437934i	$-0.144290\pi$
$797$	1.98299	+	3.43465i	0.0702412	+	0.121661i	−0.828766	+	0.559596i	$0.810956\pi$
$798$	52.7294	+	6.45519i	1.86660	+	0.228511i
$799$	6.64078	−	11.5022i	0.234934	−	0.406917i
$800$	−4.41653	−	2.54988i	−0.156148	−	0.0901520i
$801$	14.6289	−	1.85393i	0.516888	−	0.0655053i
$802$	30.4312	+	52.7084i	1.07456	+	1.86120i
$803$	−5.52298	−	9.56608i	−0.194902	−	0.337580i
$804$	2.78560	−	0.175807i	0.0982407	−	0.00620024i
$805$	−6.05341	+	2.13284i	−0.213355	+	0.0751726i
$806$	−33.6109	+	19.4053i	−1.18389	+	0.683521i
$807$	−28.2273	+	1.78150i	−0.993648	+	0.0627118i
$808$			2.88478i			0.101486i
$809$	36.0199	−	20.7961i	1.26639	−	0.731152i	0.292088	−	0.956391i	$-0.405650\pi$
$809$	36.0199	−	20.7961i	1.26639	−	0.731152i	0.974303	+	0.225240i	$0.0723166\pi$
$810$	−9.83169	−	38.1668i	−0.345450	−	1.34105i
$811$		−	13.3293i		−	0.468056i	−0.972230	−	0.234028i	$-0.924809\pi$
$811$		−	13.3293i		−	0.468056i	0.972230	−	0.234028i	$-0.0751907\pi$
$812$	39.1483	+	33.5432i	1.37384	+	1.17714i
$813$	21.0179	−	13.9703i	0.737131	−	0.489958i
$814$	38.2482			1.34060
$815$	18.6364	−	32.2792i	0.652806	−	1.13069i
$816$	4.79772	+	7.21806i	0.167954	+	0.252683i
$817$	−9.34139	+	5.39326i	−0.326814	+	0.188686i
$818$	−63.4417			−2.21819
$819$	−1.44709	+	24.5879i	−0.0505653	+	0.859170i
$820$	13.5284			0.472432
$821$	−33.4332	+	19.3027i	−1.16683	+	0.673668i	−0.952931	−	0.303188i	$-0.901949\pi$
$821$	−33.4332	+	19.3027i	−1.16683	+	0.673668i	−0.213897	+	0.976856i	$0.568616\pi$
$822$	62.9784	−	3.97474i	2.19662	−	0.138635i
$823$	5.34881	−	9.26442i	0.186448	−	0.322937i	−0.757616	−	0.652701i	$-0.773636\pi$
$823$	5.34881	−	9.26442i	0.186448	−	0.322937i	0.944063	+	0.329764i	$0.106969\pi$
$824$	−12.8523			−0.447729
$825$	3.16916	+	1.57240i	0.110336	+	0.0547441i
$826$	20.7178	−	7.29962i	0.720863	−	0.253986i
$827$		−	11.7079i		−	0.407125i	−0.979062	−	0.203562i	$-0.934748\pi$
$827$		−	11.7079i		−	0.407125i	0.979062	−	0.203562i	$-0.0652520\pi$
$828$	−1.04684	−	8.26036i	−0.0363801	−	0.287067i
$829$	−15.0948	+	8.71498i	−0.524263	+	0.302684i	−0.738677	−	0.674059i	$-0.764549\pi$
$829$	−15.0948	+	8.71498i	−0.524263	+	0.302684i	0.214414	+	0.976743i	$0.431216\pi$
$830$			13.5348i			0.469799i
$831$	−22.1045	+	44.5513i	−0.766796	+	1.54547i
$832$	28.9237	−	16.6991i	1.00275	−	0.578937i
$833$	10.6562	+	4.12931i	0.369214	+	0.143072i
$834$	−19.9786	−	30.0574i	−0.691804	−	1.04080i
$835$	12.8921	+	22.3298i	0.446151	+	0.772756i
$836$	21.3543	+	36.9867i	0.738553	+	1.27921i
$837$	−29.2941	−	10.1819i	−1.01255	−	0.351937i
$838$	66.3838	+	38.3267i	2.29319	+	1.32397i
$839$	0.704502	−	1.22023i	0.0243221	−	0.0421271i	−0.853608	−	0.520916i	$-0.825591\pi$
$839$	0.704502	−	1.22023i	0.0243221	−	0.0421271i	0.877930	+	0.478789i	$0.158924\pi$
$840$	−0.953572	+	7.78928i	−0.0329014	+	0.268756i
$841$	18.7055	+	32.3988i	0.645016	+	1.11720i
$842$		−	16.1771i		−	0.557498i
$843$	7.94324	−	5.27974i	0.273580	−	0.181844i
$844$	37.9326			1.30570
$845$	3.52191	−	6.10012i	0.121157	−	0.209851i
$846$	−6.42973	−	50.7356i	−0.221059	−	1.74432i
$847$	−0.505558	−	1.43487i	−0.0173712	−	0.0493028i
$848$	16.1761	+	9.33925i	0.555488	+	0.320711i
$849$	43.6822	−	29.0348i	1.49917	−	0.996472i
$850$	1.87426	+	1.08211i	0.0642867	+	0.0371160i
$851$	5.68290	+	3.28102i	0.194807	+	0.112472i
$852$	24.1960	−	16.0827i	0.828942	−	0.550983i
$853$	−28.0716	−	16.2071i	−0.961153	−	0.554922i	−0.0646255	−	0.997910i	$-0.520585\pi$
$853$	−28.0716	−	16.2071i	−0.961153	−	0.554922i	−0.896528	+	0.442987i	$0.853919\pi$
$854$	26.1159	+	4.88311i	0.893667	+	0.167097i
$855$	4.36056	+	34.4082i	0.149128	+	1.17674i
$856$	−0.671716	+	1.16345i	−0.0229588	+	0.0397658i
$857$	44.4539			1.51852			0.759258	−	0.650789i	$-0.225562\pi$
$857$	44.4539			1.51852			0.759258	+	0.650789i	$0.225562\pi$
$858$	−30.2852	+	20.1301i	−1.03392	+	0.687229i
$859$			15.6494i			0.533952i	0.963703	+	0.266976i	$0.0860245\pi$
$859$			15.6494i			0.533952i	−0.963703	+	0.266976i	$0.913976\pi$
$860$	−4.87147	−	8.43763i	−0.166116	−	0.287721i
$861$	−4.85179	−	11.4187i	−0.165348	−	0.389149i
$862$	−24.2342	+	41.9748i	−0.825420	+	1.42967i
$863$	−15.6911	−	9.05927i	−0.534132	−	0.308381i	0.208565	−	0.978008i	$-0.433121\pi$
$863$	−15.6911	−	9.05927i	−0.534132	−	0.308381i	−0.742697	+	0.669627i	$0.766454\pi$
$864$	39.5669	+	13.7524i	1.34609	+	0.467866i
$865$	−9.47462	−	16.4105i	−0.322147	−	0.557975i
$866$	−36.5939	−	63.3825i	−1.24351	−	2.15383i
$867$	13.7438	+	20.6773i	0.466765	+	0.702237i
$868$	28.6719	+	24.5668i	0.973189	+	0.833853i
$869$	−39.5927	+	22.8589i	−1.34309	+	0.775434i
$870$	−27.4730	+	55.3715i	−0.931423	+	1.87727i
$871$		−	2.09140i		−	0.0708643i
$872$	4.12545	−	2.38183i	0.139705	−	0.0806589i
$873$	−0.905623	−	7.14607i	−0.0306507	−	0.241858i
$874$			13.4562i			0.455164i
$875$	−10.3494	−	29.3737i	−0.349875	−	0.993014i
$876$	−12.6918	−	6.29716i	−0.428817	−	0.212761i
$877$	−2.77853			−0.0938243			−0.0469121	−	0.998899i	$-0.514938\pi$
$877$	−2.77853			−0.0938243			−0.0469121	+	0.998899i	$0.514938\pi$
$878$	40.7521	−	70.5847i	1.37532	−	2.38212i
$879$	12.2511	−	0.773200i	0.413219	−	0.0260794i
$880$	17.9106	−	10.3407i	0.603767	−	0.348585i
$881$	−1.96106			−0.0660696			−0.0330348	−	0.999454i	$-0.510517\pi$
$881$	−1.96106			−0.0660696			−0.0330348	+	0.999454i	$0.510517\pi$
$882$	42.2917	−	12.1597i	1.42404	−	0.409440i
$883$	−36.9657			−1.24400			−0.621998	−	0.783019i	$-0.713679\pi$
$883$	−36.9657			−1.24400			−0.621998	+	0.783019i	$0.713679\pi$
$884$	−10.4906	+	6.05676i	−0.352838	+	0.203711i
$885$	7.93878	+	11.9437i	0.266859	+	0.401483i
$886$	39.1110	−	67.7422i	1.31396	−	2.27584i
$887$	−22.5168			−0.756040			−0.378020	−	0.925797i	$-0.623395\pi$
$887$	−22.5168			−0.756040			−0.378020	+	0.925797i	$0.623395\pi$
$888$	6.68195	−	4.44138i	0.224232	−	0.149043i
$889$	8.43380	+	23.9368i	0.282861	+	0.802814i
$890$		−	21.5251i		−	0.721525i
$891$	−27.9947	−	7.79245i	−0.937857	−	0.261057i
$892$	32.3479	−	18.6761i	1.08309	−	0.625321i
$893$			45.0046i			1.50602i
$894$	33.5320	−	2.11630i	1.12148	−	0.0707795i
$895$	27.1857	−	15.6957i	0.908719	−	0.524649i
$896$	−12.9188	−	11.0691i	−0.431586	−	0.369793i
$897$	−6.22657	+	0.392976i	−0.207899	+	0.0131211i
$898$	25.0644	+	43.4129i	0.836411	+	1.44871i
$899$	24.3195	+	42.1225i	0.811099	+	1.40487i
$900$	4.50177	−	0.570510i	0.150059	−	0.0190170i
$901$	−8.61635	−	4.97465i	−0.287052	−	0.165730i
$902$	9.15882	−	15.8635i	0.304955	−	0.528198i
$903$	−5.37474	+	7.13784i	−0.178860	+	0.237532i
$904$	−6.62005	−	11.4663i	−0.220180	−	0.381362i
$905$			4.89353i			0.162666i
$906$	−2.73643	−	43.3578i	−0.0909118	−	1.44047i
$907$	−19.1196			−0.634857			−0.317428	−	0.948282i	$-0.602819\pi$
$907$	−19.1196			−0.634857			−0.317428	+	0.948282i	$0.602819\pi$
$908$	2.48775	−	4.30891i	0.0825589	−	0.142996i
$909$	6.38881	+	8.41005i	0.211903	+	0.278944i
$910$	35.3414	+	6.60808i	1.17155	+	0.219056i
$911$	4.92610	+	2.84408i	0.163209	+	0.0942287i	0.579380	−	0.815058i	$-0.303295\pi$
$911$	4.92610	+	2.84408i	0.163209	+	0.0942287i	−0.416171	+	0.909286i	$0.636628\pi$
$912$	−26.3083	−	13.0531i	−0.871153	−	0.432230i
$913$	8.64222	+	4.98959i	0.286016	+	0.165131i
$914$	−18.1122	−	10.4571i	−0.599100	−	0.345890i
$915$	1.09260	+	17.3118i	0.0361201	+	0.572311i
$916$	13.3237	+	7.69242i	0.440226	+	0.254165i
$917$	−2.16395	−	6.14170i	−0.0714598	−	0.202817i
$918$	−16.7912	−	5.83618i	−0.554193	−	0.192623i
$919$	−10.9255	+	18.9235i	−0.360399	+	0.624230i	−0.988027	−	0.154284i	$-0.950693\pi$
$919$	−10.9255	+	18.9235i	−0.360399	+	0.624230i	0.627627	+	0.778514i	$0.284026\pi$
$920$	−1.98778			−0.0655352
$921$	−4.83075	−	2.39682i	−0.159179	−	0.0789779i
$922$		−	70.1058i		−	2.30881i
$923$	−10.8848	−	18.8530i	−0.358278	−	0.620555i
$924$	28.2618	+	21.2810i	0.929746	+	0.700092i
$925$	−1.78811	+	3.09709i	−0.0587926	+	0.101832i
$926$	41.8672	+	24.1720i	1.37584	+	0.794343i
$927$	−37.4684	+	28.4634i	−1.23063	+	0.934861i
$928$	−32.8477	−	56.8940i	−1.07828	−	1.86764i
$929$	8.08806	+	14.0089i	0.265361	+	0.459618i	0.967658	−	0.252266i	$-0.0811756\pi$
$929$	8.08806	+	14.0089i	0.265361	+	0.459618i	−0.702297	+	0.711884i	$0.747842\pi$
$930$	−20.1211	+	40.5537i	−0.659796	+	1.32981i
$931$	−38.2669	+	5.93663i	−1.25415	+	0.194565i
$932$	−32.3321	+	18.6669i	−1.05907	+	0.611456i
$933$	18.6504	+	28.0591i	0.610587	+	0.918614i
$934$		−	84.4040i		−	2.76178i
$935$	−9.54029	+	5.50809i	−0.312001	+	0.180134i
$936$	−2.95332	+	7.03344i	−0.0965324	+	0.229895i
$937$			14.0440i			0.458799i	0.973332	+	0.229400i	$0.0736762\pi$
$937$			14.0440i			0.458799i	−0.973332	+	0.229400i	$0.926324\pi$
$938$	−3.52417	+	1.24169i	−0.115068	+	0.0405428i
$939$	−2.78686	−	44.1569i	−0.0909459	−	1.44101i
$940$	−40.6505			−1.32587
$941$	21.5934	−	37.4009i	0.703924	−	1.21923i	−0.263154	−	0.964754i	$-0.584763\pi$
$941$	21.5934	−	37.4009i	0.703924	−	1.21923i	0.967078	−	0.254479i	$-0.0819040\pi$
$942$	−28.7970	+	58.0400i	−0.938258	+	1.89104i
$943$	2.72163	−	1.57133i	0.0886284	−	0.0511696i
$944$	−12.1437			−0.395244
$945$	14.4707	+	24.8201i	0.470731	+	0.807398i
$946$	−13.1921			−0.428911
$947$	16.6235	−	9.59758i	0.540191	−	0.311879i	−0.204965	−	0.978769i	$-0.565708\pi$
$947$	16.6235	−	9.59758i	0.540191	−	0.311879i	0.745156	+	0.666890i	$0.232375\pi$
$948$	−26.0631	+	52.5298i	−0.846490	+	1.70609i
$949$	−5.30807	+	9.19386i	−0.172307	+	0.298445i
$950$	−7.33344			−0.237928
$951$	−1.77037	−	28.0509i	−0.0574082	−	0.909614i
$952$	2.68779	+	2.30296i	0.0871116	+	0.0746394i
$953$			5.62718i			0.182282i	0.995838	+	0.0911411i	$0.0290514\pi$
$953$			5.62718i			0.182282i	−0.995838	+	0.0911411i	$0.970949\pi$
$954$	−38.0064	+	4.81656i	−1.23050	+	0.155942i
$955$	−16.3547	+	9.44239i	−0.529225	+	0.305548i
$956$			41.0764i			1.32850i
$957$	25.2278	+	37.9547i	0.815500	+	1.22690i
$958$	−0.282197	+	0.162926i	−0.00911736	+	0.00526391i
$959$	−43.3860	+	15.2864i	−1.40101	+	0.493625i
$960$	17.3151	−	34.8983i	0.558842	−	1.12634i
$961$	2.31141	+	4.00348i	0.0745616	+	0.129144i
$962$	−18.3799	−	31.8350i	−0.592593	−	1.02640i
$963$	0.618373	+	4.87945i	0.0199268	+	0.157238i
$964$	−23.2300	−	13.4119i	−0.748189	−	0.431967i
$965$	−5.72894	+	9.92282i	−0.184421	+	0.319427i
$966$	4.35901	+	10.2590i	0.140249	+	0.330077i
$967$	−7.62091	−	13.1998i	−0.245072	−	0.424477i	0.717080	−	0.696991i	$-0.245478\pi$
$967$	−7.62091	−	13.1998i	−0.245072	−	0.424477i	−0.962152	+	0.272514i	$0.912145\pi$
$968$		−	0.471174i		−	0.0151441i
$969$	14.0134	+	6.95286i	0.450175	+	0.223358i
$970$	−10.5148			−0.337610
$971$	−20.4479	+	35.4168i	−0.656205	+	1.13658i	0.325386	+	0.945581i	$0.394506\pi$
$971$	−20.4479	+	35.4168i	−0.656205	+	1.13658i	−0.981590	+	0.190998i	$0.938828\pi$
$972$	−35.4370	+	11.5528i	−1.13664	+	0.370558i
$973$	19.9786	+	17.1182i	0.640486	+	0.548784i
$974$	29.9472	+	17.2900i	0.959571	+	0.554009i
$975$	−0.214166	−	3.39339i	−0.00685880	−	0.108675i
$976$	−12.7202	−	7.34404i	−0.407165	−	0.235077i
$977$	8.98296	+	5.18631i	0.287390	+	0.165925i	0.636764	−	0.771058i	$-0.280272\pi$
$977$	8.98296	+	5.18631i	0.287390	+	0.165925i	−0.349374	+	0.936983i	$0.613606\pi$
$978$	−57.9878	−	28.7712i	−1.85425	−	0.920000i
$979$	−13.7442	−	7.93522i	−0.439267	−	0.253611i
$980$	−5.36227	−	34.5646i	−0.171291	−	1.10413i
$981$	6.75206	−	16.0803i	0.215577	−	0.513404i
$982$	9.79963	−	16.9735i	0.312719	−	0.541645i
$983$	2.11700			0.0675219			0.0337609	−	0.999430i	$-0.489252\pi$
$983$	2.11700			0.0675219			0.0337609	+	0.999430i	$0.489252\pi$
$984$	−0.242030	−	3.83488i	−0.00771563	−	0.122252i
$985$		−	6.03847i		−	0.192402i
$986$	13.9398	+	24.1444i	0.443932	+	0.768914i
$987$	14.5788	+	34.3113i	0.464047	+	1.09214i
$988$	20.5234	−	35.5475i	0.652935	−	1.13092i
$989$	−1.96007	−	1.13165i	−0.0623267	−	0.0359843i
$990$	−16.4224	+	39.1104i	−0.521937	+	1.24301i
$991$	−17.0581	−	29.5456i	−0.541870	−	0.938546i	−0.998797	−	0.0490418i	$-0.984383\pi$
$991$	−17.0581	−	29.5456i	−0.541870	−	0.938546i	0.456927	−	0.889504i	$-0.348950\pi$
$992$	−24.0575	−	41.6688i	−0.763825	−	1.32298i
$993$	40.2968	−	2.54324i	1.27878	−	0.0807073i
$994$	−25.3064	+	29.5351i	−0.802671	+	0.936797i
$995$	−9.30850	+	5.37427i	−0.295099	+	0.170376i
$996$	12.7744	−	0.806229i	0.404773	−	0.0255463i
$997$		−	45.8235i		−	1.45125i	−0.688093	−	0.725623i	$-0.741552\pi$
$997$		−	45.8235i		−	1.45125i	0.688093	−	0.725623i	$-0.258448\pi$
$998$	3.62264	−	2.09153i	0.114673	−	0.0662064i
$999$	9.64388	−	27.7463i	0.305119	−	0.877855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.s.b.47.5	yes	10
3.2	odd	2		189.2.s.b.89.1		10
4.3	odd	2		1008.2.df.b.929.3		10
7.2	even	3		441.2.o.c.146.1		10
7.3	odd	6		63.2.i.b.38.5	yes	10
7.4	even	3		441.2.i.b.227.5		10
7.5	odd	6		441.2.o.d.146.1		10
7.6	odd	2		441.2.s.b.362.5		10
9.2	odd	6		567.2.p.d.404.5		10
9.4	even	3		189.2.i.b.152.5		10
9.5	odd	6		63.2.i.b.5.1	✓	10
9.7	even	3		567.2.p.c.404.1		10
12.11	even	2		3024.2.df.b.1601.5		10
21.2	odd	6		1323.2.o.d.440.5		10
21.5	even	6		1323.2.o.c.440.5		10
21.11	odd	6		1323.2.i.b.521.1		10
21.17	even	6		189.2.i.b.143.1		10
21.20	even	2		1323.2.s.b.656.1		10
28.3	even	6		1008.2.ca.b.353.5		10
36.23	even	6		1008.2.ca.b.257.5		10
36.31	odd	6		3024.2.ca.b.2609.5		10
63.4	even	3		1323.2.s.b.962.1		10
63.5	even	6		441.2.o.c.293.1		10
63.13	odd	6		1323.2.i.b.1097.5		10
63.23	odd	6		441.2.o.d.293.1		10
63.31	odd	6		189.2.s.b.17.1		10
63.32	odd	6		441.2.s.b.374.5		10
63.38	even	6		567.2.p.c.80.1		10
63.40	odd	6		1323.2.o.d.881.5		10
63.41	even	6		441.2.i.b.68.1		10
63.52	odd	6		567.2.p.d.80.5		10
63.58	even	3		1323.2.o.c.881.5		10
63.59	even	6	inner	63.2.s.b.59.5	yes	10
84.59	odd	6		3024.2.ca.b.2033.5		10
252.31	even	6		3024.2.df.b.17.5		10
252.59	odd	6		1008.2.df.b.689.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.1	✓	10	9.5	odd	6
63.2.i.b.38.5	yes	10	7.3	odd	6
63.2.s.b.47.5	yes	10	1.1	even	1	trivial
63.2.s.b.59.5	yes	10	63.59	even	6	inner
189.2.i.b.143.1		10	21.17	even	6
189.2.i.b.152.5		10	9.4	even	3
189.2.s.b.17.1		10	63.31	odd	6
189.2.s.b.89.1		10	3.2	odd	2
441.2.i.b.68.1		10	63.41	even	6
441.2.i.b.227.5		10	7.4	even	3
441.2.o.c.146.1		10	7.2	even	3
441.2.o.c.293.1		10	63.5	even	6
441.2.o.d.146.1		10	7.5	odd	6
441.2.o.d.293.1		10	63.23	odd	6
441.2.s.b.362.5		10	7.6	odd	2
441.2.s.b.374.5		10	63.32	odd	6
567.2.p.c.80.1		10	63.38	even	6
567.2.p.c.404.1		10	9.7	even	3
567.2.p.d.80.5		10	63.52	odd	6
567.2.p.d.404.5		10	9.2	odd	6
1008.2.ca.b.257.5		10	36.23	even	6
1008.2.ca.b.353.5		10	28.3	even	6
1008.2.df.b.689.3		10	252.59	odd	6
1008.2.df.b.929.3		10	4.3	odd	2
1323.2.i.b.521.1		10	21.11	odd	6
1323.2.i.b.1097.5		10	63.13	odd	6
1323.2.o.c.440.5		10	21.5	even	6
1323.2.o.c.881.5		10	63.58	even	3
1323.2.o.d.440.5		10	21.2	odd	6
1323.2.o.d.881.5		10	63.40	odd	6
1323.2.s.b.656.1		10	21.20	even	2
1323.2.s.b.962.1		10	63.4	even	3
3024.2.ca.b.2033.5		10	84.59	odd	6
3024.2.ca.b.2609.5		10	36.31	odd	6
3024.2.df.b.17.5		10	252.31	even	6
3024.2.df.b.1601.5		10	12.11	even	2

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81474 - 1.04774i) q^{2} +(-0.769825 + 1.55157i) q^{3} +(1.19552 - 2.07070i) q^{4} -2.08983 q^{5} +(0.228612 + 3.62227i) q^{6} +(-0.879217 - 2.49539i) q^{7} -0.819421i q^{8} +(-1.81474 - 2.38887i) q^{9} +(-3.79250 + 2.18960i) q^{10} +3.22878i q^{11} +(2.29250 + 3.44901i) q^{12} +(2.68740 - 1.55157i) q^{13} +(-4.21007 - 3.60729i) q^{14} +(1.60880 - 3.24252i) q^{15} +(1.53250 + 2.65437i) q^{16} +(-0.816304 - 1.41388i) q^{17} +(-5.79620 - 2.43381i) q^{18} +(4.79094 + 2.76605i) q^{19} +(-2.49844 + 4.32742i) q^{20} +(4.54862 + 0.556847i) q^{21} +(3.38292 + 5.85939i) q^{22} +1.16078i q^{23} +(1.27139 + 0.630810i) q^{24} -0.632608 q^{25} +(3.25129 - 5.63139i) q^{26} +(5.10354 - 0.976682i) q^{27} +(-6.21834 - 1.16270i) q^{28} +(-7.05749 - 4.07464i) q^{29} +(-0.477759 - 7.56994i) q^{30} +(-5.16886 - 2.98424i) q^{31} +(6.98146 + 4.03075i) q^{32} +(-5.00967 - 2.48559i) q^{33} +(-2.96276 - 1.71055i) q^{34} +(1.83741 + 5.21495i) q^{35} +(-7.11621 + 0.901839i) q^{36} +(2.82656 - 4.89575i) q^{37} +11.5924 q^{38} +(0.338544 + 5.36412i) q^{39} +1.71245i q^{40} +(-1.35369 - 2.34465i) q^{41} +(8.83799 - 3.75524i) q^{42} +(-0.974903 + 1.68858i) q^{43} +(6.68583 + 3.86007i) q^{44} +(3.79250 + 4.99234i) q^{45} +(1.21620 + 2.10652i) q^{46} +(4.06759 + 7.04527i) q^{47} +(-5.29820 + 0.334384i) q^{48} +(-5.45395 + 4.38798i) q^{49} +(-1.14802 + 0.662809i) q^{50} +(2.82214 - 0.178113i) q^{51} -7.41974i q^{52} +(5.27766 - 3.04706i) q^{53} +(8.23828 - 7.11961i) q^{54} -6.74759i q^{55} +(-2.04477 + 0.720448i) q^{56} +(-7.97990 + 5.30410i) q^{57} -17.0767 q^{58} +(-1.98103 + 3.43124i) q^{59} +(-4.79094 - 7.20785i) q^{60} +(-4.15016 + 2.39609i) q^{61} -12.5068 q^{62} +(-4.36562 + 6.62882i) q^{63} +10.7627 q^{64} +(-5.61621 + 3.24252i) q^{65} +(-11.6955 + 0.738135i) q^{66} +(0.336981 - 0.583668i) q^{67} -3.90363 q^{68} +(-1.80103 - 0.893598i) q^{69} +(8.79834 + 7.53864i) q^{70} -7.01535i q^{71} +(-1.95749 + 1.48704i) q^{72} +(-2.96276 + 1.71055i) q^{73} -11.8460i q^{74} +(0.486997 - 0.981535i) q^{75} +(11.4553 - 6.61374i) q^{76} +(8.05706 - 2.83879i) q^{77} +(6.23458 + 9.37978i) q^{78} +(7.07973 + 12.2625i) q^{79} +(-3.20267 - 5.54718i) q^{80} +(-2.41344 + 8.67037i) q^{81} +(-4.91318 - 2.83662i) q^{82} +(1.54535 - 2.67662i) q^{83} +(6.59103 - 8.75311i) q^{84} +(1.70594 + 2.95477i) q^{85} +4.08578i q^{86} +(11.7551 - 7.81343i) q^{87} +2.64572 q^{88} +(-2.45766 + 4.25679i) q^{89} +(12.1131 + 5.08625i) q^{90} +(-6.23458 - 5.34194i) q^{91} +(2.40363 + 1.38774i) q^{92} +(8.60938 - 5.72251i) q^{93} +(14.7632 + 8.52356i) q^{94} +(-10.0122 - 5.78057i) q^{95} +(-11.6285 + 7.72926i) q^{96} +(2.07939 + 1.20054i) q^{97} +(-5.30004 + 13.6774i) q^{98} +(7.71314 - 5.85939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7} - 15 q^{10} + 6 q^{13} - 6 q^{14} - 3 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} + 3 q^{19} - 3 q^{20} + 18 q^{21} + 5 q^{22} + 27 q^{24} - 14 q^{25} + 3 q^{26} + 27 q^{27}+ \cdots + 21 q^{99}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7 - 15 * q^10 + 6 * q^13 - 6 * q^14 - 3 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 + 3 * q^19 - 3 * q^20 + 18 * q^21 + 5 * q^22 + 27 * q^24 - 14 * q^25 + 3 * q^26 + 27 * q^27 + 2 * q^28 - 15 * q^29 - 9 * q^31 + 48 * q^32 - 9 * q^33 + 3 * q^34 - 15 * q^35 - 18 * q^36 + 6 * q^37 + 36 * q^38 + 12 * q^39 - 9 * q^41 - 6 * q^42 + 3 * q^43 + 24 * q^44 + 15 * q^45 - 13 * q^46 + 15 * q^47 - 15 * q^48 - 23 * q^49 + 3 * q^50 - 24 * q^51 - 9 * q^53 + 27 * q^54 - 51 * q^56 - 36 * q^57 - 16 * q^58 - 18 * q^59 - 3 * q^60 + 12 * q^61 + 12 * q^62 + 9 * q^63 + 6 * q^64 - 3 * q^65 - 33 * q^66 - 10 * q^67 - 54 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^72 + 3 * q^73 - 21 * q^75 + 9 * q^76 + 45 * q^77 + 24 * q^78 + 20 * q^79 - 30 * q^80 - 48 * q^81 + 9 * q^82 - 15 * q^83 + 60 * q^84 + 18 * q^85 + 30 * q^87 + 16 * q^88 + 24 * q^89 + 24 * q^90 - 24 * q^91 + 39 * q^92 + 6 * q^93 - 3 * q^94 + 3 * q^96 + 6 * q^97 + 45 * q^98 + 21 * q^99

Introduction

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