LMFDB - Embedded newform 462.2.p.a.439.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(241,462)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("462.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.5
Root			$0.500000 - 3.32851i$ of defining polynomial
Character	$\chi$	$=$	462.439
Dual form			462.2.p.a.241.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13257 - 1.23124i) q^{5} -1.00000 q^{6} +(-0.941950 - 2.47239i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13257 - 1.23124i) q^{5} -1.00000 q^{6} +(-0.941950 - 2.47239i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.23124 - 2.13257i) q^{10} +(-0.881768 - 3.19726i) q^{11} +(-0.866025 - 0.500000i) q^{12} -1.32035 q^{13} +(0.420444 - 2.61213i) q^{14} +2.46248 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.23739 - 3.87528i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.21589 + 3.83803i) q^{19} -2.46248i q^{20} +(2.05195 + 1.67018i) q^{21} +(0.834997 - 3.20979i) q^{22} +(4.14497 - 7.17931i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.531907 + 0.921289i) q^{25} +(-1.14346 - 0.660177i) q^{26} +1.00000i q^{27} +(1.67018 - 2.05195i) q^{28} +1.44409i q^{29} +(2.13257 + 1.23124i) q^{30} +(2.34801 - 1.35562i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.36226 + 2.32803i) q^{33} -4.47479i q^{34} +(-1.03534 + 6.43232i) q^{35} +1.00000 q^{36} +(2.46563 - 4.27060i) q^{37} +(-3.83803 + 2.21589i) q^{38} +(1.14346 - 0.660177i) q^{39} +(1.23124 - 2.13257i) q^{40} -8.18233 q^{41} +(0.941950 + 2.47239i) q^{42} +9.63797i q^{43} +(2.32803 - 2.36226i) q^{44} +(-2.13257 + 1.23124i) q^{45} +(7.17931 - 4.14497i) q^{46} +(-0.664664 - 0.383744i) q^{47} -1.00000i q^{48} +(-5.22546 + 4.65774i) q^{49} +1.06381i q^{50} +(3.87528 + 2.23739i) q^{51} +(-0.660177 - 1.14346i) q^{52} +(0.945971 + 1.63847i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.05616 + 7.90406i) q^{55} +(2.47239 - 0.941950i) q^{56} -4.43177i q^{57} +(-0.722047 + 1.25062i) q^{58} +(6.74444 - 3.89390i) q^{59} +(1.23124 + 2.13257i) q^{60} +(-2.23943 + 3.87880i) q^{61} +2.71125 q^{62} +(-2.61213 - 0.420444i) q^{63} -1.00000 q^{64} +(2.81575 + 1.62567i) q^{65} +(0.881768 + 3.19726i) q^{66} +(0.861844 + 1.49276i) q^{67} +(2.23739 - 3.87528i) q^{68} +8.28995i q^{69} +(-4.11279 + 5.05289i) q^{70} -10.3771 q^{71} +(0.866025 + 0.500000i) q^{72} +(-5.58622 - 9.67562i) q^{73} +(4.27060 - 2.46563i) q^{74} +(-0.921289 - 0.531907i) q^{75} -4.43177 q^{76} +(-7.07431 + 5.19174i) q^{77} +1.32035 q^{78} +(2.53630 + 1.46433i) q^{79} +(2.13257 - 1.23124i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.08611 - 4.09116i) q^{82} +10.1118 q^{83} +(-0.420444 + 2.61213i) q^{84} +11.0191i q^{85} +(-4.81898 + 8.34672i) q^{86} +(-0.722047 - 1.25062i) q^{87} +(3.19726 - 0.881768i) q^{88} +(-10.9590 - 6.32720i) q^{89} -2.46248 q^{90} +(1.24371 + 3.26444i) q^{91} +8.28995 q^{92} +(-1.35562 + 2.34801i) q^{93} +(-0.383744 - 0.664664i) q^{94} +(9.45107 - 5.45658i) q^{95} +(0.500000 - 0.866025i) q^{96} -1.37808i q^{97} +(-6.85425 + 1.42099i) q^{98} +(-3.20979 - 0.834997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 10 * q^19 - 4 * q^21 + 2 * q^22 - 4 * q^23 - 8 * q^24 + 10 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^31 + 2 * q^33 - 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 - 12 * q^39 - 2 * q^40 + 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 + 18 * q^46 - 24 * q^47 - 6 * q^49 + 6 * q^51 - 8 * q^54 - 14 * q^55 + 4 * q^56 - 2 * q^60 + 28 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 72 * q^65 + 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 - 44 * q^73 + 24 * q^74 - 12 * q^75 - 20 * q^76 + 32 * q^77 - 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 + 8 * q^83 - 8 * q^84 - 12 * q^86 + 4 * q^88 - 36 * q^89 + 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 + 72 * q^95 + 8 * q^96 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.13257	−	1.23124i	−0.953715	−	0.550628i	−0.0594819	−	0.998229i	$-0.518945\pi$
$5$	−2.13257	−	1.23124i	−0.953715	−	0.550628i	−0.894233	+	0.447602i	$0.852278\pi$
$6$	−1.00000			−0.408248
$7$	−0.941950	−	2.47239i	−0.356024	−	0.934477i
$7$	−0.941950	−	2.47239i	−0.356024	−	0.934477i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.23124	−	2.13257i	−0.389352	−	0.674378i
$11$	−0.881768	−	3.19726i	−0.265863	−	0.964011i
$11$	−0.881768	−	3.19726i	−0.265863	−	0.964011i
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−1.32035			−0.366201			−0.183100	−	0.983094i	$-0.558613\pi$
$13$	−1.32035			−0.366201			−0.183100	+	0.983094i	$0.558613\pi$
$14$	0.420444	−	2.61213i	0.112369	−	0.698121i
$15$	2.46248			0.635810
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.23739	−	3.87528i	−0.542647	−	0.939893i	−0.998751	−	0.0499662i	$-0.984089\pi$
$17$	−2.23739	−	3.87528i	−0.542647	−	0.939893i	0.456103	−	0.889927i	$-0.349245\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−2.21589	+	3.83803i	−0.508359	+	0.880504i	0.491594	+	0.870825i	$0.336415\pi$
$19$	−2.21589	+	3.83803i	−0.508359	+	0.880504i	−0.999953	+	0.00967966i	$0.996919\pi$
$20$		−	2.46248i		−	0.550628i
$21$	2.05195	+	1.67018i	0.447772	+	0.364463i
$22$	0.834997	−	3.20979i	0.178022	−	0.684330i
$23$	4.14497	−	7.17931i	0.864287	−	1.49699i	−0.00346670	−	0.999994i	$-0.501103\pi$
$23$	4.14497	−	7.17931i	0.864287	−	1.49699i	0.867754	−	0.496995i	$-0.165563\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	0.531907	+	0.921289i	0.106381	+	0.184258i
$26$	−1.14346	−	0.660177i	−0.224251	−	0.129471i
$27$			1.00000i			0.192450i
$28$	1.67018	−	2.05195i	0.315635	−	0.387782i
$29$			1.44409i			0.268162i	0.990970	+	0.134081i	$0.0428082\pi$
$29$			1.44409i			0.268162i	−0.990970	+	0.134081i	$0.957192\pi$
$30$	2.13257	+	1.23124i	0.389352	+	0.224793i
$31$	2.34801	−	1.35562i	0.421715	−	0.243477i	−0.274096	−	0.961702i	$-0.588379\pi$
$31$	2.34801	−	1.35562i	0.421715	−	0.243477i	0.695811	+	0.718225i	$0.255045\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.36226	+	2.32803i	0.411218	+	0.405257i
$34$		−	4.47479i		−	0.767419i
$35$	−1.03534	+	6.43232i	−0.175004	+	1.08726i
$36$	1.00000			0.166667
$37$	2.46563	−	4.27060i	0.405347	−	0.702082i	−0.589014	−	0.808122i	$-0.700484\pi$
$37$	2.46563	−	4.27060i	0.405347	−	0.702082i	0.994362	+	0.106040i	$0.0338172\pi$
$38$	−3.83803	+	2.21589i	−0.622611	+	0.359464i
$39$	1.14346	−	0.660177i	0.183100	−	0.105713i
$40$	1.23124	−	2.13257i	0.194676	−	0.337189i
$41$	−8.18233			−1.27787			−0.638933	−	0.769263i	$-0.720624\pi$
$41$	−8.18233			−1.27787			−0.638933	+	0.769263i	$0.720624\pi$
$42$	0.941950	+	2.47239i	0.145346	+	0.381499i
$43$			9.63797i			1.46978i	0.678188	+	0.734888i	$0.262765\pi$
$43$			9.63797i			1.46978i	−0.678188	+	0.734888i	$0.737235\pi$
$44$	2.32803	−	2.36226i	0.350963	−	0.356125i
$45$	−2.13257	+	1.23124i	−0.317905	+	0.183543i
$46$	7.17931	−	4.14497i	1.05853	−	0.611143i
$47$	−0.664664	−	0.383744i	−0.0969512	−	0.0559748i	0.450741	−	0.892655i	$-0.351160\pi$
$47$	−0.664664	−	0.383744i	−0.0969512	−	0.0559748i	−0.547692	+	0.836680i	$0.684493\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−5.22546	+	4.65774i	−0.746494	+	0.665392i
$50$			1.06381i			0.150446i
$51$	3.87528	+	2.23739i	0.542647	+	0.313298i
$52$	−0.660177	−	1.14346i	−0.0915501	−	0.158569i
$53$	0.945971	+	1.63847i	0.129939	+	0.225061i	0.923653	−	0.383230i	$-0.125188\pi$
$53$	0.945971	+	1.63847i	0.129939	+	0.225061i	−0.793714	+	0.608292i	$0.791855\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−2.05616	+	7.90406i	−0.277253	+	1.06578i
$56$	2.47239	−	0.941950i	0.330388	−	0.125873i
$57$		−	4.43177i		−	0.587003i
$58$	−0.722047	+	1.25062i	−0.0948095	+	0.164215i
$59$	6.74444	−	3.89390i	0.878051	−	0.506943i	0.00803571	−	0.999968i	$-0.497442\pi$
$59$	6.74444	−	3.89390i	0.878051	−	0.506943i	0.870015	+	0.493025i	$0.164109\pi$
$60$	1.23124	+	2.13257i	0.158952	+	0.275314i
$61$	−2.23943	+	3.87880i	−0.286729	+	0.496630i	−0.973027	−	0.230691i	$-0.925901\pi$
$61$	−2.23943	+	3.87880i	−0.286729	+	0.496630i	0.686298	+	0.727321i	$0.259235\pi$
$62$	2.71125			0.344329
$63$	−2.61213	−	0.420444i	−0.329098	−	0.0529710i
$64$	−1.00000			−0.125000
$65$	2.81575	+	1.62567i	0.349251	+	0.201640i
$66$	0.881768	+	3.19726i	0.108538	+	0.393556i
$67$	0.861844	+	1.49276i	0.105291	+	0.182369i	0.913857	−	0.406036i	$-0.133089\pi$
$67$	0.861844	+	1.49276i	0.105291	+	0.182369i	−0.808566	+	0.588405i	$0.799756\pi$
$68$	2.23739	−	3.87528i	0.271324	−	0.469946i
$69$			8.28995i			0.997992i
$70$	−4.11279	+	5.05289i	−0.491572	+	0.603935i
$71$	−10.3771			−1.23153			−0.615766	−	0.787929i	$-0.711153\pi$
$71$	−10.3771			−1.23153			−0.615766	+	0.787929i	$0.711153\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−5.58622	−	9.67562i	−0.653818	−	1.13245i	−0.982189	−	0.187897i	$-0.939833\pi$
$73$	−5.58622	−	9.67562i	−0.653818	−	1.13245i	0.328371	−	0.944549i	$-0.393500\pi$
$74$	4.27060	−	2.46563i	0.496447	−	0.286624i
$75$	−0.921289	−	0.531907i	−0.106381	−	0.0614193i
$76$	−4.43177			−0.508359
$77$	−7.07431	+	5.19174i	−0.806192	+	0.591654i
$78$	1.32035			0.149501
$79$	2.53630	+	1.46433i	0.285356	+	0.164750i	0.635846	−	0.771816i	$-0.280651\pi$
$79$	2.53630	+	1.46433i	0.285356	+	0.164750i	−0.350490	+	0.936567i	$0.613985\pi$
$80$	2.13257	−	1.23124i	0.238429	−	0.137657i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.08611	−	4.09116i	−0.782529	−	0.451794i
$83$	10.1118			1.10991			0.554957	−	0.831879i	$-0.312735\pi$
$83$	10.1118			1.10991			0.554957	+	0.831879i	$0.312735\pi$
$84$	−0.420444	+	2.61213i	−0.0458742	+	0.285007i
$85$			11.0191i			1.19519i
$86$	−4.81898	+	8.34672i	−0.519644	+	0.900050i
$87$	−0.722047	−	1.25062i	−0.0774116	−	0.134081i
$88$	3.19726	−	0.881768i	0.340829	−	0.0939968i
$89$	−10.9590	−	6.32720i	−1.16165	−	0.670682i	−0.209955	−	0.977711i	$-0.567332\pi$
$89$	−10.9590	−	6.32720i	−1.16165	−	0.670682i	−0.951700	+	0.307029i	$0.900665\pi$
$90$	−2.46248			−0.259568
$91$	1.24371	+	3.26444i	0.130376	+	0.342206i
$92$	8.28995			0.864287
$93$	−1.35562	+	2.34801i	−0.140572	+	0.243477i
$94$	−0.383744	−	0.664664i	−0.0395801	−	0.0685548i
$95$	9.45107	−	5.45658i	0.969660	−	0.559833i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	1.37808i		−	0.139923i	−0.997550	−	0.0699613i	$-0.977712\pi$
$97$		−	1.37808i		−	0.139923i	0.997550	−	0.0699613i	$-0.0222876\pi$
$98$	−6.85425	+	1.42099i	−0.692384	+	0.143542i
$99$	−3.20979	−	0.834997i	−0.322596	−	0.0839204i
$100$	−0.531907	+	0.921289i	−0.0531907	+	0.0921289i
$101$	−3.78361	−	6.55341i	−0.376483	−	0.652089i	0.614064	−	0.789256i	$-0.289534\pi$
$101$	−3.78361	−	6.55341i	−0.376483	−	0.652089i	−0.990548	+	0.137167i	$0.956200\pi$
$102$	2.23739	+	3.87528i	0.221535	+	0.383710i
$103$	14.2858	+	8.24790i	1.40762	+	0.812690i	0.995158	−	0.0982855i	$-0.0313358\pi$
$103$	14.2858	+	8.24790i	1.40762	+	0.812690i	0.412461	+	0.910975i	$0.364669\pi$
$104$		−	1.32035i		−	0.129471i
$105$	−2.31953	−	6.08822i	−0.226363	−	0.594150i
$106$			1.89194i			0.183762i
$107$	−4.99579	−	2.88432i	−0.482961	−	0.278838i	0.238689	−	0.971096i	$-0.423282\pi$
$107$	−4.99579	−	2.88432i	−0.482961	−	0.278838i	−0.721650	+	0.692258i	$0.756616\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	7.47550	−	4.31598i	0.716023	−	0.413396i	−0.0972641	−	0.995259i	$-0.531009\pi$
$109$	7.47550	−	4.31598i	0.716023	−	0.413396i	0.813287	+	0.581862i	$0.197676\pi$
$110$	−5.73272	+	5.81703i	−0.546593	+	0.554632i
$111$			4.93126i			0.468055i
$112$	2.61213	+	0.420444i	0.246823	+	0.0397283i
$113$	17.4933			1.64563			0.822817	−	0.568306i	$-0.192401\pi$
$113$	17.4933			1.64563			0.822817	+	0.568306i	$0.192401\pi$
$114$	2.21589	−	3.83803i	0.207537	−	0.359464i
$115$	−17.6789	+	10.2069i	−1.64857	+	0.951800i
$116$	−1.25062	+	0.722047i	−0.116117	+	0.0670404i
$117$	−0.660177	+	1.14346i	−0.0610334	+	0.105713i
$118$	7.78781			0.716926
$119$	−7.47370	+	9.18203i	−0.685113	+	0.841716i
$120$			2.46248i			0.224793i
$121$	−9.44497	+	5.63849i	−0.858634	+	0.512590i
$122$	−3.87880	+	2.23943i	−0.351170	+	0.202748i
$123$	7.08611	−	4.09116i	0.638933	−	0.368888i
$124$	2.34801	+	1.35562i	0.210858	+	0.121739i
$125$			9.69279i			0.866949i
$126$	−2.05195	−	1.67018i	−0.182802	−	0.148792i
$127$			12.0959i			1.07333i	0.843794	+	0.536667i	$0.180317\pi$
$127$			12.0959i			1.07333i	−0.843794	+	0.536667i	$0.819683\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−4.81898	−	8.34672i	−0.424288	−	0.734888i
$130$	1.62567	+	2.81575i	0.142581	+	0.246958i
$131$	8.62077	−	14.9316i	0.753200	−	1.30458i	−0.193064	−	0.981186i	$-0.561843\pi$
$131$	8.62077	−	14.9316i	0.753200	−	1.30458i	0.946264	−	0.323394i	$-0.104824\pi$
$132$	−0.834997	+	3.20979i	−0.0726772	+	0.279377i
$133$	11.5764	+	1.86331i	1.00380	+	0.161570i
$134$			1.72369i			0.148904i
$135$	1.23124	−	2.13257i	0.105968	−	0.183543i
$136$	3.87528	−	2.23739i	0.332302	−	0.191855i
$137$	−1.25479	−	2.17335i	−0.107204	−	0.185682i	0.807433	−	0.589960i	$-0.200856\pi$
$137$	−1.25479	−	2.17335i	−0.107204	−	0.185682i	−0.914636	+	0.404277i	$0.867523\pi$
$138$	−4.14497	+	7.17931i	−0.352844	+	0.611143i
$139$	19.9532			1.69241			0.846206	−	0.532856i	$-0.178881\pi$
$139$	19.9532			1.69241			0.846206	+	0.532856i	$0.178881\pi$
$140$	−6.08822	+	2.31953i	−0.514549	+	0.196036i
$141$	0.767488			0.0646341
$142$	−8.98681	−	5.18854i	−0.754156	−	0.435412i
$143$	1.16425	+	4.22152i	0.0973592	+	0.353021i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	1.77803	−	3.07963i	0.147657	−	0.255750i
$146$		−	11.1724i		−	0.924638i
$147$	2.19651	−	6.64645i	0.181165	−	0.548190i
$148$	4.93126			0.405347
$149$	−8.46998	−	4.89014i	−0.693888	−	0.400616i	0.111179	−	0.993800i	$-0.464537\pi$
$149$	−8.46998	−	4.89014i	−0.693888	−	0.400616i	−0.805067	+	0.593184i	$0.797871\pi$
$150$	−0.531907	−	0.921289i	−0.0434300	−	0.0752229i
$151$	2.31521	−	1.33669i	0.188409	−	0.108778i	−0.402829	−	0.915275i	$-0.631973\pi$
$151$	2.31521	−	1.33669i	0.188409	−	0.108778i	0.591237	+	0.806498i	$0.298640\pi$
$152$	−3.83803	−	2.21589i	−0.311305	−	0.179732i
$153$	−4.47479			−0.361765
$154$	−8.72240	+	0.959023i	−0.702871	+	0.0772803i
$155$	−6.67640			−0.536261
$156$	1.14346	+	0.660177i	0.0915501	+	0.0528565i
$157$	13.7131	−	7.91724i	1.09442	−	0.631865i	0.159671	−	0.987170i	$-0.448957\pi$
$157$	13.7131	−	7.91724i	1.09442	−	0.631865i	0.934750	+	0.355306i	$0.115623\pi$
$158$	1.46433	+	2.53630i	0.116496	+	0.201777i
$159$	−1.63847	−	0.945971i	−0.129939	−	0.0750204i
$160$	2.46248			0.194676
$161$	−21.6544	−	3.48546i	−1.70661	−	0.274693i
$162$		−	1.00000i		−	0.0785674i
$163$	10.1807	−	17.6336i	0.797418	−	1.38117i	−0.123875	−	0.992298i	$-0.539532\pi$
$163$	10.1807	−	17.6336i	0.797418	−	1.38117i	0.921293	−	0.388870i	$-0.127135\pi$
$164$	−4.09116	−	7.08611i	−0.319466	−	0.553332i
$165$	−2.17134	−	7.87320i	−0.169038	−	0.612928i
$166$	8.75707	+	5.05590i	0.679680	+	0.392414i
$167$	16.1119			1.24678			0.623389	−	0.781912i	$-0.285755\pi$
$167$	16.1119			1.24678			0.623389	+	0.781912i	$0.285755\pi$
$168$	−1.67018	+	2.05195i	−0.128857	+	0.158311i
$169$	−11.2567			−0.865897
$170$	−5.50954	+	9.54280i	−0.422562	+	0.731899i
$171$	2.21589	+	3.83803i	0.169453	+	0.293501i
$172$	−8.34672	+	4.81898i	−0.636432	+	0.367444i
$173$	−3.62347	+	6.27604i	−0.275487	+	0.477158i	−0.970258	−	0.242073i	$-0.922173\pi$
$173$	−3.62347	+	6.27604i	−0.275487	+	0.477158i	0.694771	+	0.719231i	$0.255506\pi$
$174$		−	1.44409i		−	0.109477i
$175$	1.77676	−	2.18289i	0.134310	−	0.165011i
$176$	3.20979	+	0.834997i	0.241947	+	0.0629403i
$177$	−3.89390	+	6.74444i	−0.292684	+	0.506943i
$178$	−6.32720	−	10.9590i	−0.474244	−	0.821414i
$179$	−5.80078	−	10.0472i	−0.433571	−	0.750966i	0.563607	−	0.826043i	$-0.309413\pi$
$179$	−5.80078	−	10.0472i	−0.433571	−	0.750966i	−0.997178	+	0.0750767i	$0.976080\pi$
$180$	−2.13257	−	1.23124i	−0.158952	−	0.0917713i
$181$		−	7.74423i		−	0.575624i	−0.957687	−	0.287812i	$-0.907072\pi$
$181$		−	7.74423i		−	0.575624i	0.957687	−	0.287812i	$-0.0929279\pi$
$182$	−0.555136	+	3.44894i	−0.0411494	+	0.255652i
$183$		−	4.47886i		−	0.331087i
$184$	7.17931	+	4.14497i	0.529265	+	0.305572i
$185$	−10.5163	+	6.07157i	−0.773172	+	0.446391i
$186$	−2.34801	+	1.35562i	−0.172164	+	0.0993992i
$187$	−10.4174	+	10.5706i	−0.761797	+	0.773001i
$188$		−	0.767488i		−	0.0559748i
$189$	2.47239	−	0.941950i	0.179840	−	0.0685168i
$190$	10.9132			0.791724
$191$	10.6157	−	18.3869i	0.768125	−	1.33043i	−0.170454	−	0.985366i	$-0.554523\pi$
$191$	10.6157	−	18.3869i	0.768125	−	1.33043i	0.938579	−	0.345065i	$-0.112143\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−3.04258	+	1.75664i	−0.219010	+	0.126445i	−0.605492	−	0.795852i	$-0.707024\pi$
$193$	−3.04258	+	1.75664i	−0.219010	+	0.126445i	0.386482	+	0.922297i	$0.373690\pi$
$194$	0.689039	−	1.19345i	0.0494701	−	0.0856847i
$195$	−3.25135			−0.232834
$196$	−6.64645	−	2.19651i	−0.474747	−	0.156894i
$197$			21.9715i			1.56540i	0.622397	+	0.782702i	$0.286159\pi$
$197$			21.9715i			1.56540i	−0.622397	+	0.782702i	$0.713841\pi$
$198$	−2.36226	−	2.32803i	−0.167879	−	0.165446i
$199$	1.24863	−	0.720899i	0.0885133	−	0.0511032i	−0.455090	−	0.890445i	$-0.650393\pi$
$199$	1.24863	−	0.720899i	0.0885133	−	0.0511032i	0.543603	+	0.839342i	$0.317060\pi$
$200$	−0.921289	+	0.531907i	−0.0651450	+	0.0376115i
$201$	−1.49276	−	0.861844i	−0.105291	−	0.0607898i
$202$		−	7.56722i		−	0.532428i
$203$	3.57037	−	1.36026i	0.250591	−	0.0954719i
$204$			4.47479i			0.313298i
$205$	17.4494	+	10.0744i	1.21872	+	0.703628i
$206$	8.24790	+	14.2858i	0.574658	+	0.995337i
$207$	−4.14497	−	7.17931i	−0.288096	−	0.498996i
$208$	0.660177	−	1.14346i	0.0457751	−	0.0792847i
$209$	14.2251	+	3.70052i	0.983970	+	0.255970i
$210$	1.03534	−	6.43232i	0.0714450	−	0.443872i
$211$		−	0.163763i		−	0.0112739i	−0.999984	−	0.00563697i	$-0.998206\pi$
$211$		−	0.163763i		−	0.0112739i	0.999984	−	0.00563697i	$-0.00179431\pi$
$212$	−0.945971	+	1.63847i	−0.0649695	+	0.112531i
$213$	8.98681	−	5.18854i	0.615766	−	0.355513i
$214$	−2.88432	−	4.99579i	−0.197168	−	0.341505i
$215$	11.8667	−	20.5537i	0.809299	−	1.40175i
$216$	−1.00000			−0.0680414
$217$	−5.56334	−	4.52828i	−0.377664	−	0.307399i
$218$	8.63196			0.584630
$219$	9.67562	+	5.58622i	0.653818	+	0.377482i
$220$	−7.87320	+	2.17134i	−0.530811	+	0.146392i
$221$	2.95415	+	5.11674i	0.198718	+	0.344189i
$222$	−2.46563	+	4.27060i	−0.165482	+	0.286624i
$223$		−	27.3847i		−	1.83382i	−0.399099	−	0.916908i	$-0.630677\pi$
$223$		−	27.3847i		−	1.83382i	0.399099	−	0.916908i	$-0.369323\pi$
$224$	2.05195	+	1.67018i	0.137102	+	0.111594i
$225$	1.06381			0.0709209
$226$	15.1497	+	8.74667i	1.00774	+	0.581820i
$227$	1.95128	+	3.37971i	0.129511	+	0.224319i	0.923487	−	0.383629i	$-0.125326\pi$
$227$	1.95128	+	3.37971i	0.129511	+	0.224319i	−0.793976	+	0.607949i	$0.791993\pi$
$228$	3.83803	−	2.21589i	0.254180	−	0.146751i
$229$	−4.36524	−	2.52028i	−0.288463	−	0.166544i	0.348785	−	0.937203i	$-0.386594\pi$
$229$	−4.36524	−	2.52028i	−0.288463	−	0.166544i	−0.637249	+	0.770658i	$0.719928\pi$
$230$	−20.4138			−1.34605
$231$	3.53066	−	8.03333i	0.232300	−	0.528554i
$232$	−1.44409			−0.0948095
$233$	−18.3993	−	10.6229i	−1.20538	−	0.695927i	−0.243634	−	0.969867i	$-0.578340\pi$
$233$	−18.3993	−	10.6229i	−1.20538	−	0.695927i	−0.961747	+	0.273940i	$0.911673\pi$
$234$	−1.14346	+	0.660177i	−0.0747504	+	0.0431572i
$235$	0.944962	+	1.63672i	0.0616425	+	0.106768i
$236$	6.74444	+	3.89390i	0.439026	+	0.253471i
$237$	−2.92867			−0.190237
$238$	−11.0634	+	4.21502i	−0.717136	+	0.273219i
$239$			5.64110i			0.364893i	0.983216	+	0.182446i	$0.0584016\pi$
$239$			5.64110i			0.364893i	−0.983216	+	0.182446i	$0.941598\pi$
$240$	−1.23124	+	2.13257i	−0.0794762	+	0.137657i
$241$	3.88733	+	6.73305i	0.250405	+	0.433714i	0.963637	−	0.267213i	$-0.0861029\pi$
$241$	3.88733	+	6.73305i	0.250405	+	0.433714i	−0.713232	+	0.700928i	$0.752770\pi$
$242$	−10.9988	+	0.160590i	−0.707031	+	0.0103231i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−4.47886			−0.286729
$245$	16.8785	−	3.49917i	1.07833	−	0.223553i
$246$	8.18233			0.521686
$247$	2.92576	−	5.06756i	0.186162	−	0.322441i
$248$	1.35562	+	2.34801i	0.0860822	+	0.149099i
$249$	−8.75707	+	5.05590i	−0.554957	+	0.320404i
$250$	−4.84639	+	8.39420i	−0.306513	+	0.530896i
$251$			22.5045i			1.42047i	0.703963	+	0.710236i	$0.251412\pi$
$251$			22.5045i			1.42047i	−0.703963	+	0.710236i	$0.748588\pi$
$252$	−0.941950	−	2.47239i	−0.0593373	−	0.155746i
$253$	−26.6090	−	6.92208i	−1.67290	−	0.435188i
$254$	−6.04793	+	10.4753i	−0.379481	+	0.657281i
$255$	−5.50954	−	9.54280i	−0.345021	−	0.597593i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.61175	+	1.50789i	0.162916	+	0.0940597i	0.579241	−	0.815156i	$-0.303349\pi$
$257$	2.61175	+	1.50789i	0.162916	+	0.0940597i	−0.416325	+	0.909216i	$0.636682\pi$
$258$		−	9.63797i		−	0.600034i
$259$	−12.8811	−	2.07332i	−0.800393	−	0.128830i
$260$			3.25135i			0.201640i
$261$	1.25062	+	0.722047i	0.0774116	+	0.0446936i
$262$	14.9316	−	8.62077i	0.922478	−	0.532593i
$263$	24.4063	−	14.0910i	1.50496	−	0.868887i	0.504972	−	0.863136i	$-0.331503\pi$
$263$	24.4063	−	14.0910i	1.50496	−	0.868887i	0.999983	−	0.00575106i	$-0.00183063\pi$
$264$	−2.32803	+	2.36226i	−0.143280	+	0.145387i
$265$		−	4.65887i		−	0.286192i
$266$	9.09378	+	7.40187i	0.557575	+	0.453837i
$267$	12.6544			0.774437
$268$	−0.861844	+	1.49276i	−0.0526455	+	0.0911847i
$269$	−0.523552	+	0.302273i	−0.0319215	+	0.0184299i	−0.515876	−	0.856663i	$-0.672533\pi$
$269$	−0.523552	+	0.302273i	−0.0319215	+	0.0184299i	0.483954	+	0.875093i	$0.339200\pi$
$270$	2.13257	−	1.23124i	0.129784	−	0.0749309i
$271$	−9.89654	+	17.1413i	−0.601172	+	1.04126i	0.391472	+	0.920190i	$0.371966\pi$
$271$	−9.89654	+	17.1413i	−0.601172	+	1.04126i	−0.992644	+	0.121071i	$0.961367\pi$
$272$	4.47479			0.271324
$273$	−2.70930	−	2.20523i	−0.163974	−	0.133467i
$274$		−	2.50957i		−	0.151609i
$275$	2.47658	−	2.51301i	0.149344	−	0.151540i
$276$	−7.17931	+	4.14497i	−0.432143	+	0.249498i
$277$	1.87448	−	1.08223i	0.112626	−	0.0650249i	−0.442629	−	0.896705i	$-0.645954\pi$
$277$	1.87448	−	1.08223i	0.112626	−	0.0650249i	0.555255	+	0.831680i	$0.312621\pi$
$278$	17.2800	+	9.97662i	1.03639	+	0.598358i
$279$		−	2.71125i		−	0.162318i
$280$	−6.43232	−	1.03534i	−0.384405	−	0.0618732i
$281$		−	29.4916i		−	1.75932i	−0.475601	−	0.879661i	$-0.657769\pi$
$281$		−	29.4916i		−	1.75932i	0.475601	−	0.879661i	$-0.342231\pi$
$282$	0.664664	+	0.383744i	0.0395801	+	0.0228516i
$283$	−14.1940	−	24.5847i	−0.843745	−	1.46141i	−0.886707	−	0.462333i	$-0.847013\pi$
$283$	−14.1940	−	24.5847i	−0.843745	−	1.46141i	0.0429613	−	0.999077i	$-0.486321\pi$
$284$	−5.18854	−	8.98681i	−0.307883	−	0.533269i
$285$	−5.45658	+	9.45107i	−0.323220	+	0.559833i
$286$	−1.10249	+	4.23807i	−0.0651918	+	0.250602i
$287$	7.70734	+	20.2299i	0.454950	+	1.19414i
$288$			1.00000i			0.0589256i
$289$	−1.51185	+	2.61860i	−0.0889324	+	0.154036i
$290$	3.07963	−	1.77803i	0.180842	−	0.104409i
$291$	0.689039	+	1.19345i	0.0403922	+	0.0699613i
$292$	5.58622	−	9.67562i	0.326909	−	0.566223i
$293$	9.39403			0.548805			0.274403	−	0.961615i	$-0.411520\pi$
$293$	9.39403			0.548805			0.274403	+	0.961615i	$0.411520\pi$
$294$	5.22546	−	4.65774i	0.304755	−	0.271645i
$295$	−19.1773			−1.11655
$296$	4.27060	+	2.46563i	0.248224	+	0.143312i
$297$	3.19726	−	0.881768i	0.185524	−	0.0511654i
$298$	−4.89014	−	8.46998i	−0.283278	−	0.490653i
$299$	−5.47284	+	9.47923i	−0.316502	+	0.548198i
$300$		−	1.06381i		−	0.0614193i
$301$	23.8288	−	9.07848i	1.37347	−	0.523275i
$302$	2.67337			0.153835
$303$	6.55341	+	3.78361i	0.376483	+	0.217363i
$304$	−2.21589	−	3.83803i	−0.127090	−	0.220126i
$305$	9.55148	−	5.51455i	0.546916	−	0.315762i
$306$	−3.87528	−	2.23739i	−0.221535	−	0.127903i
$307$	−26.9732			−1.53944			−0.769722	−	0.638380i	$-0.779605\pi$
$307$	−26.9732			−1.53944			−0.769722	+	0.638380i	$0.779605\pi$
$308$	−8.03333	−	3.53066i	−0.457742	−	0.201178i
$309$	−16.4958			−0.938413
$310$	−5.78193	−	3.33820i	−0.328392	−	0.189597i
$311$	0.108539	−	0.0626652i	0.00615470	−	0.00355342i	−0.496919	−	0.867797i	$-0.665536\pi$
$311$	0.108539	−	0.0626652i	0.00615470	−	0.00355342i	0.503074	+	0.864243i	$0.332202\pi$
$312$	0.660177	+	1.14346i	0.0373752	+	0.0647357i
$313$	−6.69427	−	3.86494i	−0.378382	−	0.218459i	0.298732	−	0.954337i	$-0.403436\pi$
$313$	−6.69427	−	3.86494i	−0.378382	−	0.218459i	−0.677114	+	0.735878i	$0.736770\pi$
$314$	15.8345			0.893591
$315$	5.05289	+	4.11279i	0.284698	+	0.231729i
$316$			2.92867i			0.164750i
$317$	−12.1901	+	21.1139i	−0.684665	+	1.18587i	0.288877	+	0.957366i	$0.406718\pi$
$317$	−12.1901	+	21.1139i	−0.684665	+	1.18587i	−0.973542	+	0.228508i	$0.926615\pi$
$318$	−0.945971	−	1.63847i	−0.0530474	−	0.0918808i
$319$	4.61715	−	1.27336i	0.258511	−	0.0712943i
$320$	2.13257	+	1.23124i	0.119214	+	0.0688284i
$321$	5.76864			0.321974
$322$	−17.0106	−	13.8457i	−0.947961	−	0.771591i
$323$	19.8312			1.10344
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−0.702305	−	1.21643i	−0.0389569	−	0.0674753i
$326$	17.6336	−	10.1807i	0.976633	−	0.563859i
$327$	−4.31598	+	7.47550i	−0.238674	+	0.413396i
$328$		−	8.18233i		−	0.451794i
$329$	−0.322686	+	2.00478i	−0.0177902	+	0.110527i
$330$	2.05616	−	7.90406i	0.113188	−	0.435104i
$331$	10.7266	−	18.5790i	0.589588	−	1.02120i	−0.404698	−	0.914450i	$-0.632623\pi$
$331$	10.7266	−	18.5790i	0.589588	−	1.02120i	0.994286	−	0.106746i	$-0.0340432\pi$
$332$	5.05590	+	8.75707i	0.277478	+	0.480607i
$333$	−2.46563	−	4.27060i	−0.135116	−	0.234027i
$334$	13.9533	+	8.05596i	0.763493	+	0.440803i
$335$		−	4.24455i		−	0.231905i
$336$	−2.47239	+	0.941950i	−0.134880	+	0.0513876i
$337$		−	30.0086i		−	1.63467i	−0.576163	−	0.817335i	$-0.695451\pi$
$337$		−	30.0086i		−	1.63467i	0.576163	−	0.817335i	$-0.304549\pi$
$338$	−9.74856	−	5.62833i	−0.530252	−	0.306141i
$339$	−15.1497	+	8.74667i	−0.822817	+	0.475054i
$340$	−9.54280	+	5.50954i	−0.517531	+	0.298797i
$341$	−6.40469	−	6.31186i	−0.346833	−	0.341806i
$342$			4.43177i			0.239643i
$343$	16.4379	+	8.53204i	0.887563	+	0.460687i
$344$	−9.63797			−0.519644
$345$	10.2069	−	17.6789i	0.549522	−	0.951800i
$346$	−6.27604	+	3.62347i	−0.337402	+	0.194799i
$347$	−29.9073	+	17.2670i	−1.60551	+	0.926942i	−0.615152	+	0.788408i	$0.710906\pi$
$347$	−29.9073	+	17.2670i	−1.60551	+	0.926942i	−0.990358	+	0.138533i	$0.955761\pi$
$348$	0.722047	−	1.25062i	0.0387058	−	0.0670404i
$349$	−4.77961			−0.255847			−0.127923	−	0.991784i	$-0.540831\pi$
$349$	−4.77961			−0.255847			−0.127923	+	0.991784i	$0.540831\pi$
$350$	2.63016	−	1.00206i	0.140588	−	0.0535623i
$351$		−	1.32035i		−	0.0704753i
$352$	2.36226	+	2.32803i	0.125909	+	0.124084i
$353$	11.7581	−	6.78853i	0.625819	−	0.361317i	−0.153312	−	0.988178i	$-0.548994\pi$
$353$	11.7581	−	6.78853i	0.625819	−	0.361317i	0.779131	+	0.626861i	$0.215661\pi$
$354$	−6.74444	+	3.89390i	−0.358463	+	0.206959i
$355$	22.1298	+	12.7767i	1.17453	+	0.678115i
$356$		−	12.6544i		−	0.670682i
$357$	1.88140	−	11.6887i	0.0995742	−	0.618633i
$358$		−	11.6016i		−	0.613161i
$359$	−1.49631	−	0.863893i	−0.0789720	−	0.0455945i	0.459994	−	0.887922i	$-0.347852\pi$
$359$	−1.49631	−	0.863893i	−0.0789720	−	0.0455945i	−0.538966	+	0.842328i	$0.681185\pi$
$360$	−1.23124	−	2.13257i	−0.0648921	−	0.112396i
$361$	−0.320313	−	0.554798i	−0.0168586	−	0.0291999i
$362$	3.87212	−	6.70670i	0.203514	−	0.352496i
$363$	5.36034	−	9.60556i	0.281345	−	0.504161i
$364$	−2.20523	+	2.70930i	−0.115586	+	0.142006i
$365$			27.5119i			1.44004i
$366$	2.23943	−	3.87880i	0.117057	−	0.202748i
$367$	−22.0716	+	12.7430i	−1.15213	+	0.665182i	−0.949405	−	0.314054i	$-0.898313\pi$
$367$	−22.0716	+	12.7430i	−1.15213	+	0.665182i	−0.202724	+	0.979236i	$0.564979\pi$
$368$	4.14497	+	7.17931i	0.216072	+	0.374247i
$369$	−4.09116	+	7.08611i	−0.212978	+	0.368888i
$370$	−12.1431			−0.631292
$371$	3.15988	−	3.88217i	0.164053	−	0.201552i
$372$	−2.71125			−0.140572
$373$	28.8675	+	16.6667i	1.49470	+	0.862968i	0.999982	−	0.00608223i	$-0.00193605\pi$
$373$	28.8675	+	16.6667i	1.49470	+	0.862968i	0.494723	+	0.869051i	$0.335269\pi$
$374$	−14.3071	+	3.94572i	−0.739801	+	0.204029i
$375$	−4.84639	−	8.39420i	−0.250267	−	0.433475i
$376$	0.383744	−	0.664664i	0.0197901	−	0.0342774i
$377$		−	1.90672i		−	0.0982010i
$378$	2.61213	+	0.420444i	0.134354	+	0.0216253i
$379$	−19.2656			−0.989610			−0.494805	−	0.869004i	$-0.664760\pi$
$379$	−19.2656			−0.989610			−0.494805	+	0.869004i	$0.664760\pi$
$380$	9.45107	+	5.45658i	0.484830	+	0.279917i
$381$	−6.04793	−	10.4753i	−0.309845	−	0.536667i
$382$	18.3869	−	10.6157i	0.940757	−	0.543146i
$383$	4.46444	+	2.57755i	0.228122	+	0.131706i	0.609705	−	0.792628i	$-0.291288\pi$
$383$	4.46444	+	2.57755i	0.228122	+	0.131706i	−0.381583	+	0.924334i	$0.624621\pi$
$384$	1.00000			0.0510310
$385$	21.4787	−	2.36158i	1.09466	−	0.120357i
$386$	−3.51327			−0.178821
$387$	8.34672	+	4.81898i	0.424288	+	0.244963i
$388$	1.19345	−	0.689039i	0.0605882	−	0.0349806i
$389$	2.58228	+	4.47264i	0.130927	+	0.226772i	0.924034	−	0.382310i	$-0.124871\pi$
$389$	2.58228	+	4.47264i	0.130927	+	0.226772i	−0.793107	+	0.609082i	$0.791538\pi$
$390$	−2.81575	−	1.62567i	−0.142581	−	0.0823192i
$391$	−37.0957			−1.87601
$392$	−4.65774	−	5.22546i	−0.235251	−	0.263926i
$393$			17.2415i			0.869720i
$394$	−10.9857	+	19.0279i	−0.553454	+	0.958610i
$395$	−3.60589	−	6.24559i	−0.181432	−	0.314250i
$396$	−0.881768	−	3.19726i	−0.0443105	−	0.160668i
$397$	5.49312	+	3.17146i	0.275692	+	0.159171i	0.631472	−	0.775399i	$-0.282451\pi$
$397$	5.49312	+	3.17146i	0.275692	+	0.159171i	−0.355780	+	0.934570i	$0.615785\pi$
$398$	1.44180			0.0722708
$399$	−10.9571	+	4.17451i	−0.548541	+	0.208987i
$400$	−1.06381			−0.0531907
$401$	−11.0008	+	19.0539i	−0.549351	+	0.951504i	0.448968	+	0.893548i	$0.351792\pi$
$401$	−11.0008	+	19.0539i	−0.549351	+	0.951504i	−0.998319	+	0.0579565i	$0.981542\pi$
$402$	−0.861844	−	1.49276i	−0.0429849	−	0.0744520i
$403$	−3.10021	+	1.78991i	−0.154432	+	0.0891615i
$404$	3.78361	−	6.55341i	0.188242	−	0.326044i
$405$			2.46248i			0.122362i
$406$	3.77216	+	0.607162i	0.187209	+	0.0301329i
$407$	−15.8283	−	4.11759i	−0.784582	−	0.204101i
$408$	−2.23739	+	3.87528i	−0.110767	+	0.191855i
$409$	−7.05947	−	12.2274i	−0.349068	−	0.604604i	0.637016	−	0.770851i	$-0.280169\pi$
$409$	−7.05947	−	12.2274i	−0.349068	−	0.604604i	−0.986084	+	0.166247i	$0.946835\pi$
$410$	10.0744	+	17.4494i	0.497540	+	0.861764i
$411$	2.17335	+	1.25479i	0.107204	+	0.0618940i
$412$			16.4958i			0.812690i
$413$	−15.9802	−	13.0070i	−0.786333	−	0.640035i
$414$		−	8.28995i		−	0.407429i
$415$	−21.5641	−	12.4500i	−1.05854	−	0.611149i
$416$	1.14346	−	0.660177i	0.0560628	−	0.0323679i
$417$	−17.2800	+	9.97662i	−0.846206	+	0.488557i
$418$	10.4690	+	10.3173i	0.512057	+	0.504635i
$419$			22.7760i			1.11268i	0.830955	+	0.556340i	$0.187795\pi$
$419$			22.7760i			1.11268i	−0.830955	+	0.556340i	$0.812205\pi$
$420$	4.11279	−	5.05289i	0.200684	−	0.246556i
$421$	−6.80960			−0.331880			−0.165940	−	0.986136i	$-0.553066\pi$
$421$	−6.80960			−0.331880			−0.165940	+	0.986136i	$0.553066\pi$
$422$	0.0818817	−	0.141823i	0.00398594	−	0.00690385i
$423$	−0.664664	+	0.383744i	−0.0323171	+	0.0186583i
$424$	−1.63847	+	0.945971i	−0.0795711	+	0.0459404i
$425$	2.38017	−	4.12257i	0.115455	−	0.199974i
$426$	10.3771			0.502771
$427$	11.6994	+	1.88311i	0.566172	+	0.0911301i
$428$		−	5.76864i		−	0.278838i
$429$	−3.11903	−	3.07382i	−0.150588	−	0.148405i
$430$	20.5537	−	11.8667i	0.991185	−	0.572261i
$431$	−26.7290	+	15.4320i	−1.28749	+	0.743334i	−0.978206	−	0.207635i	$-0.933423\pi$
$431$	−26.7290	+	15.4320i	−1.28749	+	0.743334i	−0.309286	+	0.950969i	$0.600090\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			32.2967i			1.55208i	0.630683	+	0.776040i	$0.282775\pi$
$433$			32.2967i			1.55208i	−0.630683	+	0.776040i	$0.717225\pi$
$434$	−2.55386	−	6.70327i	−0.122589	−	0.321767i
$435$			3.55606i			0.170500i
$436$	7.47550	+	4.31598i	0.358012	+	0.206698i
$437$	18.3696	+	31.8171i	0.878737	+	1.52202i
$438$	5.58622	+	9.67562i	0.266920	+	0.462319i
$439$	14.3357	−	24.8302i	0.684208	−	1.18508i	−0.289478	−	0.957185i	$-0.593482\pi$
$439$	14.3357	−	24.8302i	0.684208	−	1.18508i	0.973685	−	0.227898i	$-0.0731851\pi$
$440$	−7.90406	−	2.05616i	−0.376811	−	0.0980238i
$441$	1.42099	+	6.85425i	0.0676663	+	0.326393i
$442$			5.90830i			0.281029i
$443$	−17.4908	+	30.2949i	−0.831013	+	1.43936i	0.0662231	+	0.997805i	$0.478905\pi$
$443$	−17.4908	+	30.2949i	−0.831013	+	1.43936i	−0.897236	+	0.441552i	$0.854428\pi$
$444$	−4.27060	+	2.46563i	−0.202674	+	0.117014i
$445$	15.5806	+	26.9864i	0.738592	+	1.27928i
$446$	13.6924	−	23.7159i	0.648352	−	1.12298i
$447$	9.78029			0.462592
$448$	0.941950	+	2.47239i	0.0445029	+	0.116810i
$449$	−3.57926			−0.168916			−0.0844579	−	0.996427i	$-0.526916\pi$
$449$	−3.57926			−0.168916			−0.0844579	+	0.996427i	$0.526916\pi$
$450$	0.921289	+	0.531907i	0.0434300	+	0.0250743i
$451$	7.21492	+	26.1611i	0.339737	+	1.23188i
$452$	8.74667	+	15.1497i	0.411409	+	0.712581i
$453$	−1.33669	+	2.31521i	−0.0628030	+	0.108778i
$454$			3.90255i			0.183156i
$455$	1.36701	−	8.49295i	0.0640865	−	0.398156i
$456$	4.43177			0.207537
$457$	17.6664	+	10.1997i	0.826398	+	0.477121i	0.852618	−	0.522535i	$-0.175014\pi$
$457$	17.6664	+	10.1997i	0.826398	+	0.477121i	−0.0262200	+	0.999656i	$0.508347\pi$
$458$	−2.52028	−	4.36524i	−0.117765	−	0.203974i
$459$	3.87528	−	2.23739i	0.180882	−	0.104433i
$460$	−17.6789	−	10.2069i	−0.824283	−	0.475900i
$461$	13.9967			0.651892			0.325946	−	0.945388i	$-0.394317\pi$
$461$	13.9967			0.651892			0.325946	+	0.945388i	$0.394317\pi$
$462$	7.07431	−	5.19174i	0.329127	−	0.241542i
$463$	33.6499			1.56384			0.781922	−	0.623376i	$-0.214239\pi$
$463$	33.6499			1.56384			0.781922	+	0.623376i	$0.214239\pi$
$464$	−1.25062	−	0.722047i	−0.0580587	−	0.0335202i
$465$	5.78193	−	3.33820i	0.268131	−	0.154805i
$466$	−10.6229	−	18.3993i	−0.492095	−	0.852333i
$467$	7.87190	+	4.54484i	0.364268	+	0.210310i	0.670951	−	0.741501i	$-0.265886\pi$
$467$	7.87190	+	4.54484i	0.364268	+	0.210310i	−0.306683	+	0.951812i	$0.599219\pi$
$468$	−1.32035			−0.0610334
$469$	2.87887	−	3.53692i	0.132934	−	0.163320i
$470$			1.88992i			0.0871757i
$471$	−7.91724	+	13.7131i	−0.364807	+	0.631865i
$472$	3.89390	+	6.74444i	0.179231	+	0.310438i
$473$	30.8151	−	8.49845i	1.41688	−	0.390759i
$474$	−2.53630	−	1.46433i	−0.116496	−	0.0672591i
$475$	−4.71458			−0.216320
$476$	−11.6887	−	1.88140i	−0.535752	−	0.0862338i
$477$	1.89194			0.0866260
$478$	−2.82055	+	4.88534i	−0.129009	+	0.223450i
$479$	19.7827	+	34.2647i	0.903897	+	1.56560i	0.822391	+	0.568922i	$0.192639\pi$
$479$	19.7827	+	34.2647i	0.903897	+	1.56560i	0.0815054	+	0.996673i	$0.474027\pi$
$480$	−2.13257	+	1.23124i	−0.0973381	+	0.0561982i
$481$	−3.25551	+	5.63871i	−0.148438	+	0.257103i
$482$			7.77466i			0.354126i
$483$	20.4960	−	7.80871i	0.932601	−	0.355309i
$484$	−9.60556	−	5.36034i	−0.436616	−	0.243652i
$485$	−1.69674	+	2.93885i	−0.0770452	+	0.133446i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	1.60461	+	2.77927i	0.0727120	+	0.125941i	0.900089	−	0.435706i	$-0.143501\pi$
$487$	1.60461	+	2.77927i	0.0727120	+	0.125941i	−0.827377	+	0.561647i	$0.810168\pi$
$488$	−3.87880	−	2.23943i	−0.175585	−	0.101374i
$489$			20.3615i			0.920779i
$490$	16.3668	+	5.40887i	0.739375	+	0.244348i
$491$			19.0209i			0.858401i	0.903209	+	0.429200i	$0.141205\pi$
$491$			19.0209i			0.858401i	−0.903209	+	0.429200i	$0.858795\pi$
$492$	7.08611	+	4.09116i	0.319466	+	0.184444i
$493$	5.59627	−	3.23101i	0.252043	−	0.145517i
$494$	5.06756	−	2.92576i	0.228000	−	0.131636i
$495$	5.81703	+	5.73272i	0.261456	+	0.257667i
$496$			2.71125i			0.121739i
$497$	9.77468	+	25.6562i	0.438454	+	1.15084i
$498$	−10.1118			−0.453120
$499$	−12.8041	+	22.1774i	−0.573190	+	0.992795i	0.423045	+	0.906108i	$0.360961\pi$
$499$	−12.8041	+	22.1774i	−0.573190	+	0.992795i	−0.996236	+	0.0866862i	$0.972372\pi$
$500$	−8.39420	+	4.84639i	−0.375400	+	0.216737i
$501$	−13.9533	+	8.05596i	−0.623389	+	0.359914i
$502$	−11.2523	+	19.4895i	−0.502213	+	0.869858i
$503$	−2.73335			−0.121874			−0.0609370	−	0.998142i	$-0.519409\pi$
$503$	−2.73335			−0.121874			−0.0609370	+	0.998142i	$0.519409\pi$
$504$	0.420444	−	2.61213i	0.0187281	−	0.116354i
$505$			18.6341i			0.829209i
$506$	−19.5831	−	19.2992i	−0.870573	−	0.857955i
$507$	9.74856	−	5.62833i	0.432949	−	0.249963i
$508$	−10.4753	+	6.04793i	−0.464768	+	0.268334i
$509$	−14.5574	−	8.40471i	−0.645245	−	0.372532i	0.141387	−	0.989954i	$-0.454844\pi$
$509$	−14.5574	−	8.40471i	−0.645245	−	0.372532i	−0.786632	+	0.617422i	$0.788177\pi$
$510$		−	11.0191i		−	0.487933i
$511$	−18.6600	+	22.9253i	−0.825470	+	1.01415i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.83803	−	2.21589i	−0.169453	−	0.0978338i
$514$	1.50789	+	2.61175i	0.0665103	+	0.115199i
$515$	−20.3103	−	35.1785i	−0.894979	−	1.55015i
$516$	4.81898	−	8.34672i	0.212144	−	0.367444i
$517$	−0.640850	+	2.46348i	−0.0281845	+	0.108344i
$518$	−10.1187	−	8.23610i	−0.444590	−	0.361874i
$519$		−	7.24694i		−	0.318105i
$520$	−1.62567	+	2.81575i	−0.0712905	+	0.123479i
$521$	30.8004	−	17.7826i	1.34939	−	0.779071i	0.361227	−	0.932478i	$-0.382358\pi$
$521$	30.8004	−	17.7826i	1.34939	−	0.779071i	0.988163	+	0.153407i	$0.0490245\pi$
$522$	0.722047	+	1.25062i	0.0316032	+	0.0547383i
$523$	1.90926	−	3.30694i	0.0834863	−	0.144603i	−0.821259	−	0.570556i	$-0.806728\pi$
$523$	1.90926	−	3.30694i	0.0834863	−	0.144603i	0.904745	+	0.425953i	$0.140061\pi$
$524$	17.2415			0.753200
$525$	−0.447274	+	2.77882i	−0.0195206	+	0.121278i
$526$	28.1819			1.22879
$527$	−10.5068	−	6.06613i	−0.457685	−	0.264245i
$528$	−3.19726	+	0.881768i	−0.139143	+	0.0383740i
$529$	−22.8616	−	39.5975i	−0.993984	−	1.72163i
$530$	2.32943	−	4.03470i	0.101184	−	0.175256i
$531$		−	7.78781i		−	0.337962i
$532$	4.17451	+	10.9571i	0.180988	+	0.475050i
$533$	10.8036			0.467955
$534$	10.9590	+	6.32720i	0.474244	+	0.273805i
$535$	7.10258	+	12.3020i	0.307071	+	0.531863i
$536$	−1.49276	+	0.861844i	−0.0644773	+	0.0372260i
$537$	10.0472	+	5.80078i	0.433571	+	0.250322i
$538$	−0.604546			−0.0260638
$539$	19.4997	+	12.6001i	0.839910	+	0.542726i
$540$	2.46248			0.105968
$541$	−21.5152	−	12.4218i	−0.925011	−	0.534055i	−0.0397805	−	0.999208i	$-0.512666\pi$
$541$	−21.5152	−	12.4218i	−0.925011	−	0.534055i	−0.885230	+	0.465153i	$0.845999\pi$
$542$	−17.1413	+	9.89654i	−0.736283	+	0.425093i
$543$	3.87212	+	6.70670i	0.166168	+	0.287812i
$544$	3.87528	+	2.23739i	0.166151	+	0.0959274i
$545$	−21.2560			−0.910509
$546$	−1.24371	−	3.26444i	−0.0532258	−	0.139705i
$547$		−	44.4066i		−	1.89869i	−0.314237	−	0.949345i	$-0.601749\pi$
$547$		−	44.4066i		−	1.89869i	0.314237	−	0.949345i	$-0.398251\pi$
$548$	1.25479	−	2.17335i	0.0536018	−	0.0928411i
$549$	2.23943	+	3.87880i	0.0955765	+	0.165543i
$550$	3.40129	−	0.938037i	0.145031	−	0.0399980i
$551$	−5.54248	−	3.19995i	−0.236118	−	0.136323i
$552$	−8.28995			−0.352844
$553$	1.23134	−	7.65006i	0.0523620	−	0.325314i
$554$	2.16446			0.0919590
$555$	6.07157	−	10.5163i	0.257724	−	0.446391i
$556$	9.97662	+	17.2800i	0.423103	+	0.732836i
$557$	−23.9736	+	13.8412i	−1.01579	+	0.586469i	−0.912883	−	0.408222i	$-0.866149\pi$
$557$	−23.9736	+	13.8412i	−1.01579	+	0.586469i	−0.102911	+	0.994691i	$0.532816\pi$
$558$	1.35562	−	2.34801i	0.0573881	−	0.0993992i
$559$		−	12.7255i		−	0.538233i
$560$	−5.05289	−	4.11279i	−0.213523	−	0.173797i
$561$	3.73643	−	14.3631i	0.157752	−	0.606412i
$562$	14.7458	−	25.5405i	0.622014	−	1.07736i
$563$	5.51765	+	9.55686i	0.232541	+	0.402773i	0.958555	−	0.284907i	$-0.0919626\pi$
$563$	5.51765	+	9.55686i	0.232541	+	0.402773i	−0.726014	+	0.687680i	$0.758629\pi$
$564$	0.383744	+	0.664664i	0.0161585	+	0.0279874i
$565$	−37.3058	−	21.5385i	−1.56947	−	0.906132i
$566$		−	28.3880i		−	1.19324i
$567$	−1.67018	+	2.05195i	−0.0701410	+	0.0861738i
$568$		−	10.3771i		−	0.435412i
$569$	−35.2007	−	20.3231i	−1.47569	−	0.851989i	−0.476065	−	0.879410i	$-0.657937\pi$
$569$	−35.2007	−	20.3231i	−1.47569	−	0.851989i	−0.999624	+	0.0274209i	$0.991271\pi$
$570$	−9.45107	+	5.45658i	−0.395862	+	0.228551i
$571$	−15.3762	+	8.87748i	−0.643476	+	0.371511i	−0.785952	−	0.618287i	$-0.787827\pi$
$571$	−15.3762	+	8.87748i	−0.643476	+	0.371511i	0.142476	+	0.989798i	$0.454494\pi$
$572$	−3.07382	+	3.11903i	−0.128523	+	0.130413i
$573$			21.2314i			0.886954i
$574$	−3.44022	+	21.3733i	−0.143592	+	0.892105i
$575$	8.81895			0.367776
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−1.50303	+	0.867773i	−0.0625718	+	0.0361259i	−0.530960	−	0.847397i	$-0.678168\pi$
$577$	−1.50303	+	0.867773i	−0.0625718	+	0.0361259i	0.468388	+	0.883523i	$0.344835\pi$
$578$	−2.61860	+	1.51185i	−0.108920	+	0.0628847i
$579$	1.75664	−	3.04258i	0.0730033	−	0.126445i
$580$	3.55606			0.147657
$581$	−9.52480	−	25.0003i	−0.395155	−	1.03719i
$582$			1.37808i			0.0571231i
$583$	4.40449	−	4.46927i	0.182415	−	0.185098i
$584$	9.67562	−	5.58622i	0.400380	−	0.231159i
$585$	2.81575	−	1.62567i	0.116417	−	0.0672134i
$586$	8.13547	+	4.69702i	0.336073	+	0.194032i
$587$		−	0.837774i		−	0.0345786i	−0.999851	−	0.0172893i	$-0.994496\pi$
$587$		−	0.837774i		−	0.0345786i	0.999851	−	0.0172893i	$-0.00550363\pi$
$588$	6.85425	−	1.42099i	0.282665	−	0.0586007i
$589$			12.0156i			0.495096i
$590$	−16.6081	−	9.58866i	−0.683743	−	0.394759i
$591$	−10.9857	−	19.0279i	−0.451893	−	0.782702i
$592$	2.46563	+	4.27060i	0.101337	+	0.175521i
$593$	13.0100	−	22.5339i	0.534255	−	0.925357i	−0.464944	−	0.885340i	$-0.653926\pi$
$593$	13.0100	−	22.5339i	0.534255	−	0.925357i	0.999199	−	0.0400166i	$-0.0127411\pi$
$594$	3.20979	+	0.834997i	0.131699	+	0.0342603i
$595$	27.2435	−	10.3794i	1.11687	−	0.425514i
$596$		−	9.78029i		−	0.400616i
$597$	−0.720899	+	1.24863i	−0.0295044	+	0.0511032i
$598$	−9.47923	+	5.47284i	−0.387635	+	0.223801i
$599$	−5.62081	−	9.73552i	−0.229660	−	0.397783i	0.728047	−	0.685527i	$-0.240428\pi$
$599$	−5.62081	−	9.73552i	−0.229660	−	0.397783i	−0.957707	+	0.287744i	$0.907095\pi$
$600$	0.531907	−	0.921289i	0.0217150	−	0.0376115i
$601$	11.4274			0.466134			0.233067	−	0.972461i	$-0.425124\pi$
$601$	11.4274			0.466134			0.233067	+	0.972461i	$0.425124\pi$
$602$	25.1756	+	4.05223i	1.02608	+	0.165157i
$603$	1.72369			0.0701940
$604$	2.31521	+	1.33669i	0.0942045	+	0.0543890i
$605$	27.0844	−	0.395451i	1.10114	−	0.0160774i
$606$	3.78361	+	6.55341i	0.153699	+	0.266214i
$607$	5.09027	−	8.81661i	0.206608	−	0.357855i	−0.744036	−	0.668139i	$-0.767091\pi$
$607$	5.09027	−	8.81661i	0.206608	−	0.357855i	0.950644	+	0.310284i	$0.100424\pi$
$608$		−	4.43177i		−	0.179732i
$609$	−2.41190	+	2.96321i	−0.0977351	+	0.120075i
$610$	11.0291			0.446555
$611$	0.877592	+	0.506678i	0.0355036	+	0.0204980i
$612$	−2.23739	−	3.87528i	−0.0904412	−	0.156649i
$613$	21.6335	−	12.4901i	0.873770	−	0.504471i	0.00517055	−	0.999987i	$-0.498354\pi$
$613$	21.6335	−	12.4901i	0.873770	−	0.504471i	0.868599	+	0.495515i	$0.165021\pi$
$614$	−23.3595	−	13.4866i	−0.942713	−	0.544275i
$615$	−20.1488			−0.812479
$616$	−5.19174	−	7.07431i	−0.209181	−	0.285032i
$617$	−28.5114			−1.14783			−0.573914	−	0.818916i	$-0.694576\pi$
$617$	−28.5114			−1.14783			−0.573914	+	0.818916i	$0.694576\pi$
$618$	−14.2858	−	8.24790i	−0.574658	−	0.331779i
$619$	−21.1014	+	12.1829i	−0.848137	+	0.489672i	−0.860022	−	0.510258i	$-0.829550\pi$
$619$	−21.1014	+	12.1829i	−0.848137	+	0.489672i	0.0118852	+	0.999929i	$0.496217\pi$
$620$	−3.33820	−	5.78193i	−0.134065	−	0.232208i
$621$	7.17931	+	4.14497i	0.288096	+	0.166332i
$622$	0.125330			0.00502529
$623$	−5.32047	+	33.0549i	−0.213160	+	1.32432i
$624$			1.32035i			0.0528565i
$625$	14.5937	−	25.2770i	0.583747	−	1.01108i
$626$	−3.86494	−	6.69427i	−0.154474	−	0.267557i
$627$	−14.1695	+	3.90780i	−0.565877	+	0.156062i
$628$	13.7131	+	7.91724i	0.547211	+	0.315932i
$629$	−22.0663			−0.879843
$630$	2.31953	+	6.08822i	0.0924124	+	0.242561i
$631$	−18.2463			−0.726374			−0.363187	−	0.931716i	$-0.618311\pi$
$631$	−18.2463			−0.726374			−0.363187	+	0.931716i	$0.618311\pi$
$632$	−1.46433	+	2.53630i	−0.0582481	+	0.100889i
$633$	0.0818817	+	0.141823i	0.00325451	+	0.00563697i
$634$	−21.1139	+	12.1901i	−0.838540	+	0.484131i
$635$	14.8929	−	25.7953i	0.591008	−	1.02366i
$636$		−	1.89194i		−	0.0750204i
$637$	6.89946	−	6.14987i	0.273367	−	0.243667i
$638$	4.63525	+	1.20582i	0.183511	+	0.0477387i
$639$	−5.18854	+	8.98681i	−0.205255	+	0.355513i
$640$	1.23124	+	2.13257i	0.0486691	+	0.0842973i
$641$	9.69935	+	16.7998i	0.383101	+	0.663551i	0.991504	−	0.130078i	$-0.0415228\pi$
$641$	9.69935	+	16.7998i	0.383101	+	0.663551i	−0.608403	+	0.793628i	$0.708189\pi$
$642$	4.99579	+	2.88432i	0.197168	+	0.113835i
$643$		−	11.3901i		−	0.449182i	−0.974453	−	0.224591i	$-0.927895\pi$
$643$		−	11.3901i		−	0.449182i	0.974453	−	0.224591i	$-0.0721047\pi$
$644$	−7.80871	−	20.4960i	−0.307706	−	0.807656i
$645$			23.7333i			0.934498i
$646$	17.1744	+	9.91562i	0.675716	+	0.390125i
$647$	14.8745	−	8.58781i	0.584778	−	0.337621i	−0.178252	−	0.983985i	$-0.557044\pi$
$647$	14.8745	−	8.58781i	0.584778	−	0.337621i	0.763030	+	0.646363i	$0.223711\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−18.3969	−	18.1302i	−0.722140	−	0.711673i
$650$		−	1.40461i		−	0.0550934i
$651$	7.08214	+	1.13993i	0.277571	+	0.0446774i
$652$	20.3615			0.797418
$653$	16.1982	−	28.0561i	0.633884	−	1.09792i	−0.352866	−	0.935674i	$-0.614793\pi$
$653$	16.1982	−	28.0561i	0.633884	−	1.09792i	0.986750	−	0.162246i	$-0.0518737\pi$
$654$	−7.47550	+	4.31598i	−0.292315	+	0.168768i
$655$	−36.7688	+	21.2285i	−1.43668	+	0.829465i
$656$	4.09116	−	7.08611i	0.159733	−	0.276666i
$657$	−11.1724			−0.435878
$658$	−1.28184	+	1.57485i	−0.0499714	+	0.0613939i
$659$			8.52103i			0.331932i	0.986131	+	0.165966i	$0.0530742\pi$
$659$			8.52103i			0.331932i	−0.986131	+	0.165966i	$0.946926\pi$
$660$	5.73272	−	5.81703i	0.223146	−	0.226428i
$661$	34.1086	−	19.6926i	1.32667	−	0.765953i	0.341886	−	0.939741i	$-0.388934\pi$
$661$	34.1086	−	19.6926i	1.32667	−	0.765953i	0.984783	+	0.173788i	$0.0556009\pi$
$662$	18.5790	−	10.7266i	0.722095	−	0.416902i
$663$	−5.11674	−	2.95415i	−0.198718	−	0.114730i
$664$			10.1118i			0.392414i
$665$	−22.3933	−	18.2270i	−0.868373	−	0.706811i
$666$		−	4.93126i		−	0.191083i
$667$	10.3676	+	5.98574i	0.401435	+	0.231769i
$668$	8.05596	+	13.9533i	0.311695	+	0.539871i
$669$	13.6924	+	23.7159i	0.529377	+	0.916908i
$670$	2.12228	−	3.67589i	0.0819906	−	0.142012i
$671$	14.3762	+	3.73983i	0.554987	+	0.144375i
$672$	−2.61213	−	0.420444i	−0.100765	−	0.0162190i
$673$		−	23.4185i		−	0.902716i	−0.892343	−	0.451358i	$-0.850940\pi$
$673$		−	23.4185i		−	0.902716i	0.892343	−	0.451358i	$-0.149060\pi$
$674$	15.0043	−	25.9882i	0.577943	−	1.00103i
$675$	−0.921289	+	0.531907i	−0.0354604	+	0.0204731i
$676$	−5.62833	−	9.74856i	−0.216474	−	0.374944i
$677$	14.8410	−	25.7054i	0.570388	−	0.987940i	−0.426138	−	0.904658i	$-0.640126\pi$
$677$	14.8410	−	25.7054i	0.570388	−	0.987940i	0.996526	−	0.0832822i	$-0.0265403\pi$
$678$	−17.4933			−0.671828
$679$	−3.40715	+	1.29808i	−0.130754	+	0.0498157i
$680$	−11.0191			−0.422562
$681$	−3.37971	−	1.95128i	−0.129511	−	0.0747731i
$682$	−2.39069	−	8.66857i	−0.0915444	−	0.331937i
$683$	−14.4728	−	25.0677i	−0.553787	−	0.959188i	−0.997997	−	0.0632649i	$-0.979849\pi$
$683$	−14.4728	−	25.0677i	−0.553787	−	0.959188i	0.444209	−	0.895923i	$-0.353485\pi$
$684$	−2.21589	+	3.83803i	−0.0847266	+	0.146751i
$685$			6.17977i			0.236117i
$686$	9.96961	+	15.6079i	0.380642	+	0.595913i
$687$	5.04055			0.192309
$688$	−8.34672	−	4.81898i	−0.318216	−	0.183722i
$689$	−1.24902	−	2.16336i	−0.0475838	−	0.0824175i
$690$	17.6789	−	10.2069i	0.673024	−	0.388571i
$691$	24.2055	+	13.9750i	0.920820	+	0.531636i	0.883897	−	0.467682i	$-0.154911\pi$
$691$	24.2055	+	13.9750i	0.920820	+	0.531636i	0.0369236	+	0.999318i	$0.488244\pi$
$692$	−7.24694			−0.275487
$693$	0.959023	+	8.72240i	0.0364303	+	0.331337i
$694$	−34.5340			−1.31089
$695$	−42.5517	−	24.5672i	−1.61408	−	0.931888i
$696$	1.25062	−	0.722047i	0.0474047	−	0.0273691i
$697$	18.3071	+	31.7088i	0.693430	+	1.20106i
$698$	−4.13927	−	2.38981i	−0.156674	−	0.0904555i
$699$	21.2457			0.803587
$700$	2.77882	+	0.447274i	0.105029	+	0.0169054i
$701$		−	13.2062i		−	0.498793i	−0.968401	−	0.249397i	$-0.919768\pi$
$701$		−	13.2062i		−	0.498793i	0.968401	−	0.249397i	$-0.0802323\pi$
$702$	0.660177	−	1.14346i	0.0249168	−	0.0431572i
$703$	10.9271	+	18.9263i	0.412124	+	0.713820i
$704$	0.881768	+	3.19726i	0.0332329	+	0.120501i
$705$	−1.63672	−	0.944962i	−0.0616425	−	0.0355893i
$706$	13.5771			0.510979
$707$	−12.6386	+	15.5276i	−0.475325	+	0.583974i
$708$	−7.78781			−0.292684
$709$	−7.39039	+	12.8005i	−0.277552	+	0.480734i	−0.970776	−	0.239988i	$-0.922856\pi$
$709$	−7.39039	+	12.8005i	−0.277552	+	0.480734i	0.693224	+	0.720722i	$0.256190\pi$
$710$	12.7767	+	22.1298i	0.479500	+	0.830518i
$711$	2.53630	−	1.46433i	0.0951187	−	0.0549168i
$712$	6.32720	−	10.9590i	0.237122	−	0.410707i
$713$		−	22.4761i		−	0.841737i
$714$	7.47370	−	9.18203i	0.279696	−	0.343629i
$715$	2.71487	−	10.4362i	0.101530	−	0.390290i
$716$	5.80078	−	10.0472i	0.216785	−	0.375483i
$717$	−2.82055	−	4.88534i	−0.105335	−	0.182446i
$718$	−0.863893	−	1.49631i	−0.0322402	−	0.0558416i
$719$	3.21343	+	1.85527i	0.119841	+	0.0691900i	0.558722	−	0.829355i	$-0.311292\pi$
$719$	3.21343	+	1.85527i	0.119841	+	0.0691900i	−0.438881	+	0.898545i	$0.644625\pi$
$720$		−	2.46248i		−	0.0917713i
$721$	6.93557	−	43.0892i	0.258294	−	1.60472i
$722$		−	0.640626i		−	0.0238416i
$723$	−6.73305	−	3.88733i	−0.250405	−	0.144571i
$724$	6.70670	−	3.87212i	0.249253	−	0.143906i
$725$	−1.33043	+	0.768123i	−0.0494109	+	0.0285274i
$726$	9.44497	−	5.63849i	0.350536	−	0.209264i
$727$		−	16.9392i		−	0.628241i	−0.949383	−	0.314120i	$-0.898290\pi$
$727$		−	16.9392i		−	0.628241i	0.949383	−	0.314120i	$-0.101710\pi$
$728$	−3.26444	+	1.24371i	−0.120988	+	0.0460949i
$729$	−1.00000			−0.0370370
$730$	−13.7560	+	23.8260i	−0.509131	+	0.881841i
$731$	37.3498	−	21.5639i	1.38143	−	0.797570i
$732$	3.87880	−	2.23943i	0.143365	−	0.0827716i
$733$	−5.69951	+	9.87183i	−0.210516	+	0.364624i	−0.951876	−	0.306483i	$-0.900848\pi$
$733$	−5.69951	+	9.87183i	−0.210516	+	0.364624i	0.741360	+	0.671107i	$0.234181\pi$
$734$	−25.4861			−0.940709
$735$	−12.8676	+	11.4696i	−0.474629	+	0.423063i
$736$			8.28995i			0.305572i
$737$	4.01279	−	4.07181i	0.147813	−	0.149987i
$738$	−7.08611	+	4.09116i	−0.260843	+	0.150598i
$739$	4.89454	−	2.82586i	0.180049	−	0.103951i	−0.407267	−	0.913309i	$-0.633518\pi$
$739$	4.89454	−	2.82586i	0.180049	−	0.103951i	0.587315	+	0.809358i	$0.300185\pi$
$740$	−10.5163	−	6.07157i	−0.386586	−	0.223195i
$741$			5.85152i			0.214961i
$742$	4.67762	−	1.78211i	0.171721	−	0.0654235i
$743$			2.21080i			0.0811065i	0.999177	+	0.0405533i	$0.0129120\pi$
$743$			2.21080i			0.0811065i	−0.999177	+	0.0405533i	$0.987088\pi$
$744$	−2.34801	−	1.35562i	−0.0860822	−	0.0496996i
$745$	12.0419	+	20.8572i	0.441181	+	0.764147i
$746$	16.6667	+	28.8675i	0.610211	+	1.05692i
$747$	5.05590	−	8.75707i	0.184986	−	0.320404i
$748$	−14.3631	−	3.73643i	−0.525168	−	0.136618i
$749$	−2.42539	+	15.0684i	−0.0886219	+	0.550589i
$750$		−	9.69279i		−	0.353930i
$751$	−2.93707	+	5.08715i	−0.107175	+	0.185633i	−0.914625	−	0.404304i	$-0.867514\pi$
$751$	−2.93707	+	5.08715i	−0.107175	+	0.185633i	0.807450	+	0.589936i	$0.200847\pi$
$752$	0.664664	−	0.383744i	0.0242378	−	0.0139937i
$753$	−11.2523	−	19.4895i	−0.410055	−	0.710236i
$754$	0.953359	−	1.65127i	0.0347193	−	0.0601356i
$755$	−6.58313			−0.239585
$756$	2.05195	+	1.67018i	0.0746287	+	0.0607439i
$757$	15.3568			0.558152			0.279076	−	0.960269i	$-0.409972\pi$
$757$	15.3568			0.558152			0.279076	+	0.960269i	$0.409972\pi$
$758$	−16.6845	−	9.63282i	−0.606010	−	0.349880i
$759$	26.5051	−	7.30981i	0.962076	−	0.265329i
$760$	5.45658	+	9.45107i	0.197931	+	0.342827i
$761$	−11.2463	+	19.4792i	−0.407680	+	0.706122i	−0.994629	−	0.103501i	$-0.966995\pi$
$761$	−11.2463	+	19.4792i	−0.407680	+	0.706122i	0.586950	+	0.809623i	$0.300329\pi$
$762$		−	12.0959i		−	0.438187i
$763$	−17.7124	−	14.4169i	−0.641230	−	0.521928i
$764$	21.2314			0.768125
$765$	9.54280	+	5.50954i	0.345021	+	0.199198i
$766$	2.57755	+	4.46444i	0.0931305	+	0.161307i
$767$	−8.90505	+	5.14133i	−0.321543	+	0.185643i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	39.6302			1.42910			0.714551	−	0.699583i	$-0.246631\pi$
$769$	39.6302			1.42910			0.714551	+	0.699583i	$0.246631\pi$
$770$	19.7819	+	8.69419i	0.712891	+	0.313317i
$771$	−3.01578			−0.108611
$772$	−3.04258	−	1.75664i	−0.109505	−	0.0632227i
$773$	−13.6011	+	7.85260i	−0.489198	+	0.282438i	−0.724242	−	0.689546i	$-0.757810\pi$
$773$	−13.6011	+	7.85260i	−0.489198	+	0.282438i	0.235044	+	0.971985i	$0.424477\pi$
$774$	4.81898	+	8.34672i	0.173215	+	0.300017i
$775$	2.49784	+	1.44213i	0.0897252	+	0.0518029i
$776$	1.37808			0.0494701
$777$	12.1920	−	4.64500i	0.437386	−	0.166639i
$778$			5.16455i			0.185158i
$779$	18.1311	−	31.4040i	0.649615	−	1.12517i
$780$	−1.62567	−	2.81575i	−0.0582085	−	0.100820i
$781$	9.15017	+	33.1782i	0.327419	+	1.18721i
$782$	−32.1259	−	18.5479i	−1.14882	−	0.663270i
$783$	−1.44409			−0.0516077
$784$	−1.42099	−	6.85425i	−0.0507497	−	0.244795i
$785$	−38.9921			−1.39169
$786$	−8.62077	+	14.9316i	−0.307493	+	0.532593i
$787$	−20.6611	−	35.7861i	−0.736488	−	1.27563i	−0.954067	−	0.299592i	$-0.903149\pi$
$787$	−20.6611	−	35.7861i	−0.736488	−	1.27563i	0.217579	−	0.976043i	$-0.430184\pi$
$788$	−19.0279	+	10.9857i	−0.677840	+	0.391351i
$789$	−14.0910	+	24.4063i	−0.501652	+	0.868887i
$790$		−	7.21179i		−	0.256584i
$791$	−16.4778	−	43.2504i	−0.585885	−	1.53781i
$792$	0.834997	−	3.20979i	0.0296703	−	0.114055i
$793$	2.95684	−	5.12140i	0.105000	−	0.181866i
$794$	3.17146	+	5.49312i	0.112551	+	0.194944i
$795$	2.32943	+	4.03470i	0.0826165	+	0.143096i
$796$	1.24863	+	0.720899i	0.0442567	+	0.0255516i
$797$		−	20.2076i		−	0.715789i	−0.933762	−	0.357894i	$-0.883495\pi$
$797$		−	20.2076i		−	0.715789i	0.933762	−	0.357894i	$-0.116505\pi$
$798$	−11.5764	−	1.86331i	−0.409799	−	0.0659606i
$799$			3.43434i			0.121498i
$800$	−0.921289	−	0.531907i	−0.0325725	−	0.0188057i
$801$	−10.9590	+	6.32720i	−0.387218	+	0.223561i
$802$	−19.0539	+	11.0008i	−0.672815	+	0.388450i
$803$	−26.0097	+	26.3923i	−0.917864	+	0.931363i
$804$		−	1.72369i		−	0.0607898i
$805$	41.8882	+	34.0948i	1.47636	+	1.20168i
$806$	−3.57981			−0.126093
$807$	0.302273	−	0.523552i	0.0106405	−	0.0184299i
$808$	6.55341	−	3.78361i	0.230548	−	0.133107i
$809$	−29.2043	+	16.8611i	−1.02677	+	0.592805i	−0.916057	−	0.401048i	$-0.868646\pi$
$809$	−29.2043	+	16.8611i	−1.02677	+	0.592805i	−0.110711	+	0.993853i	$0.535313\pi$
$810$	−1.23124	+	2.13257i	−0.0432614	+	0.0749309i
$811$	−9.84154			−0.345583			−0.172792	−	0.984958i	$-0.555279\pi$
$811$	−9.84154			−0.345583			−0.172792	+	0.984958i	$0.555279\pi$
$812$	2.96321	+	2.41190i	0.103988	+	0.0846411i
$813$		−	19.7931i		−	0.694174i
$814$	−11.6490	−	11.4801i	−0.408296	−	0.402378i
$815$	−43.4223	+	25.0699i	−1.52102	+	0.878160i
$816$	−3.87528	+	2.23739i	−0.135662	+	0.0783244i
$817$	−36.9908	−	21.3566i	−1.29414	−	0.747175i
$818$		−	14.1189i		−	0.493657i
$819$	3.44894	+	0.555136i	0.120516	+	0.0193980i
$820$			20.1488i			0.703628i
$821$	−7.61984	−	4.39932i	−0.265934	−	0.153537i	0.361104	−	0.932525i	$-0.382400\pi$
$821$	−7.61984	−	4.39932i	−0.265934	−	0.153537i	−0.627039	+	0.778988i	$0.715733\pi$
$822$	1.25479	+	2.17335i	0.0437657	+	0.0758044i
$823$	16.4438	+	28.4815i	0.573195	+	0.992802i	0.996235	+	0.0866913i	$0.0276294\pi$
$823$	16.4438	+	28.4815i	0.573195	+	0.992802i	−0.423041	+	0.906111i	$0.639037\pi$
$824$	−8.24790	+	14.2858i	−0.287329	+	0.497669i
$825$	−0.888281	+	3.41462i	−0.0309260	+	0.118882i
$826$	−7.33572	−	19.2545i	−0.255242	−	0.669951i
$827$		−	43.5923i		−	1.51585i	−0.652339	−	0.757927i	$-0.726212\pi$
$827$		−	43.5923i		−	1.51585i	0.652339	−	0.757927i	$-0.273788\pi$
$828$	4.14497	−	7.17931i	0.144048	−	0.249498i
$829$	−27.4160	+	15.8286i	−0.952198	+	0.549752i	−0.893763	−	0.448540i	$-0.851944\pi$
$829$	−27.4160	+	15.8286i	−0.952198	+	0.549752i	−0.0584348	+	0.998291i	$0.518611\pi$
$830$	−12.4500	−	21.5641i	−0.432147	−	0.748501i
$831$	−1.08223	+	1.87448i	−0.0375421	+	0.0650249i
$832$	1.32035			0.0457751
$833$	29.7414	+	9.82892i	1.03048	+	0.340552i
$834$	−19.9532			−0.690924
$835$	−34.3598	−	19.8377i	−1.18907	−	0.686511i
$836$	3.90780	+	14.1695i	0.135154	+	0.490064i
$837$	1.35562	+	2.34801i	0.0468572	+	0.0811591i
$838$	−11.3880	+	19.7246i	−0.393392	+	0.681375i
$839$		−	33.1104i		−	1.14310i	−0.820568	−	0.571549i	$-0.806343\pi$
$839$		−	33.1104i		−	1.14310i	0.820568	−	0.571549i	$-0.193657\pi$
$840$	6.08822	−	2.31953i	0.210064	−	0.0800315i
$841$	26.9146			0.928089
$842$	−5.89729	−	3.40480i	−0.203234	−	0.117337i
$843$	14.7458	+	25.5405i	0.507873	+	0.879661i
$844$	0.141823	−	0.0818817i	0.00488176	−	0.00281848i
$845$	24.0056	+	13.8597i	0.825819	+	0.476787i
$846$	−0.767488			−0.0263868
$847$	22.8373	+	18.0405i	0.784697	+	0.619879i
$848$	−1.89194			−0.0649695
$849$	24.5847	+	14.1940i	0.843745	+	0.487136i
$850$	4.12257	−	2.38017i	0.141403	−	0.0816391i
$851$	−20.4400	−	35.4030i	−0.700673	−	1.21360i
$852$	8.98681	+	5.18854i	0.307883	+	0.177756i
$853$	32.8121			1.12347			0.561733	−	0.827318i	$-0.310135\pi$
$853$	32.8121			1.12347			0.561733	+	0.827318i	$0.310135\pi$
$854$	9.19039	+	7.48050i	0.314489	+	0.255977i
$855$		−	10.9132i		−	0.373222i
$856$	2.88432	−	4.99579i	0.0985840	−	0.170753i
$857$	5.83813	+	10.1119i	0.199427	+	0.345417i	0.948343	−	0.317248i	$-0.102759\pi$
$857$	5.83813	+	10.1119i	0.199427	+	0.345417i	−0.748916	+	0.662665i	$0.769425\pi$
$858$	−1.16425	−	4.22152i	−0.0397467	−	0.144120i
$859$	−35.2623	−	20.3587i	−1.20314	−	0.694631i	−0.241885	−	0.970305i	$-0.577766\pi$
$859$	−35.2623	−	20.3587i	−1.20314	−	0.694631i	−0.961251	+	0.275674i	$0.911099\pi$
$860$	23.7333			0.809299
$861$	−16.7897	−	13.6660i	−0.572192	−	0.465735i
$862$	−30.8640			−1.05123
$863$	9.04438	−	15.6653i	0.307874	−	0.533254i	−0.670023	−	0.742341i	$-0.733716\pi$
$863$	9.04438	−	15.6653i	0.307874	−	0.533254i	0.977897	+	0.209087i	$0.0670490\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	15.4546	−	8.92273i	0.525473	−	0.303382i
$866$	−16.1483	+	27.9698i	−0.548743	+	0.950451i
$867$		−	3.02370i		−	0.102690i
$868$	1.13993	−	7.08214i	0.0386917	−	0.240383i
$869$	2.44543	−	9.40042i	0.0829555	−	0.318887i
$870$	−1.77803	+	3.07963i	−0.0602808	+	0.104409i
$871$	−1.13794	−	1.97097i	−0.0385576	−	0.0667838i
$872$	4.31598	+	7.47550i	0.146158	+	0.253152i
$873$	−1.19345	−	0.689039i	−0.0403922	−	0.0233204i
$874$			36.7392i			1.24272i
$875$	23.9644	−	9.13012i	0.810144	−	0.308654i
$876$			11.1724i			0.377482i
$877$	5.73392	+	3.31048i	0.193621	+	0.111787i	0.593676	−	0.804704i	$-0.297676\pi$
$877$	5.73392	+	3.31048i	0.193621	+	0.111787i	−0.400056	+	0.916491i	$0.631009\pi$
$878$	24.8302	−	14.3357i	0.837980	−	0.483808i
$879$	−8.13547	+	4.69702i	−0.274403	+	0.158426i
$880$	−5.81703	−	5.73272i	−0.196092	−	0.193250i
$881$			16.5800i			0.558594i	0.960205	+	0.279297i	$0.0901014\pi$
$881$			16.5800i			0.558594i	−0.960205	+	0.279297i	$0.909899\pi$
$882$	−2.19651	+	6.64645i	−0.0739604	+	0.223798i
$883$	44.3526			1.49258			0.746292	−	0.665619i	$-0.231832\pi$
$883$	44.3526			1.49258			0.746292	+	0.665619i	$0.231832\pi$
$884$	−2.95415	+	5.11674i	−0.0993589	+	0.172095i
$885$	16.6081	−	9.58866i	0.558274	−	0.322319i
$886$	−30.2949	+	17.4908i	−1.01778	+	0.587615i
$887$	16.2919	−	28.2184i	0.547028	−	0.947480i	−0.451448	−	0.892297i	$-0.649092\pi$
$887$	16.2919	−	28.2184i	0.547028	−	0.947480i	0.998476	−	0.0551831i	$-0.0175742\pi$
$888$	−4.93126			−0.165482
$889$	29.9057	−	11.3937i	1.00301	−	0.382132i
$890$			31.1612i			1.04453i
$891$	−2.32803	+	2.36226i	−0.0779918	+	0.0791389i
$892$	23.7159	−	13.6924i	0.794065	−	0.458454i
$893$	2.94564	−	1.70067i	0.0985721	−	0.0569106i
$894$	8.46998	+	4.89014i	0.283278	+	0.163551i
$895$			28.5686i			0.954944i
$896$	−0.420444	+	2.61213i	−0.0140461	+	0.0872652i
$897$		−	10.9457i		−	0.365465i
$898$	−3.09973	−	1.78963i	−0.103439	−	0.0597207i
$899$	1.95765	+	3.39075i	0.0652913	+	0.113088i
$900$	0.531907	+	0.921289i	0.0177302	+	0.0307096i
$901$	4.23302	−	7.33180i	0.141022	−	0.244258i
$902$	−6.83222	+	26.2636i	−0.227488	+	0.874482i
$903$	−16.0971	+	19.7766i	−0.535680	+	0.658125i
$904$			17.4933i			0.581820i
$905$	−9.53501	+	16.5151i	−0.316955	+	0.548981i
$906$	−2.31521	+	1.33669i	−0.0769176	+	0.0444084i
$907$	20.5472	+	35.5887i	0.682257	+	1.18170i	0.974290	+	0.225296i	$0.0723350\pi$
$907$	20.5472	+	35.5887i	0.682257	+	1.18170i	−0.292033	+	0.956408i	$0.594332\pi$
$908$	−1.95128	+	3.37971i	−0.0647554	+	0.112160i
$909$	−7.56722			−0.250989
$910$	5.43034	−	6.67160i	0.180014	−	0.221161i
$911$	28.2471			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$911$	28.2471			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$912$	3.83803	+	2.21589i	0.127090	+	0.0733754i
$913$	−8.91626	−	32.3300i	−0.295085	−	1.06997i
$914$	10.1997	+	17.6664i	0.337375	+	0.584351i
$915$	−5.51455	+	9.55148i	−0.182305	+	0.315762i
$916$		−	5.04055i		−	0.166544i
$917$	−45.0371	−	7.24911i	−1.48726	−	0.239387i
$918$	4.47479			0.147690
$919$	33.8721	+	19.5561i	1.11734	+	0.645095i	0.940720	−	0.339184i	$-0.110151\pi$
$919$	33.8721	+	19.5561i	1.11734	+	0.645095i	0.176618	+	0.984280i	$0.443484\pi$
$920$	−10.2069	−	17.6789i	−0.336512	−	0.582856i
$921$	23.3595	−	13.4866i	0.769722	−	0.444399i
$922$	12.1215	+	6.99836i	0.399201	+	0.230479i
$923$	13.7014			0.450988
$924$	8.72240	−	0.959023i	0.286946	−	0.0315495i
$925$	5.24594			0.172486
$926$	29.1417	+	16.8250i	0.957655	+	0.552903i
$927$	14.2858	−	8.24790i	0.469207	−	0.270897i
$928$	−0.722047	−	1.25062i	−0.0237024	−	0.0410537i
$929$	21.3559	+	12.3298i	0.700665	+	0.404529i	0.807595	−	0.589737i	$-0.200769\pi$
$929$	21.3559	+	12.3298i	0.700665	+	0.404529i	−0.106930	+	0.994267i	$0.534102\pi$
$930$	6.67640			0.218928
$931$	−6.29751	−	30.3765i	−0.206393	−	0.995550i
$932$		−	21.2457i		−	0.695927i
$933$	−0.0626652	+	0.108539i	−0.00205157	+	0.00355342i
$934$	4.54484	+	7.87190i	0.148712	+	0.257576i
$935$	35.2309	−	9.71627i	1.15217	−	0.317756i
$936$	−1.14346	−	0.660177i	−0.0373752	−	0.0215786i
$937$	10.7483			0.351133			0.175566	−	0.984468i	$-0.443824\pi$
$937$	10.7483			0.351133			0.175566	+	0.984468i	$0.443824\pi$
$938$	4.26164	−	1.62363i	0.139147	−	0.0530133i
$939$	7.72987			0.252255
$940$	−0.944962	+	1.63672i	−0.0308213	+	0.0533840i
$941$	16.9368	+	29.3354i	0.552125	+	0.956308i	0.998121	+	0.0612732i	$0.0195161\pi$
$941$	16.9368	+	29.3354i	0.552125	+	0.956308i	−0.445996	+	0.895035i	$0.647151\pi$
$942$	−13.7131	+	7.91724i	−0.446796	+	0.257958i
$943$	−33.9155	+	58.7434i	−1.10444	+	1.91295i
$944$			7.78781i			0.253471i
$945$	−6.43232	−	1.03534i	−0.209243	−	0.0336795i
$946$	30.9359	+	8.04768i	1.00581	+	0.261652i
$947$	−10.3859	+	17.9889i	−0.337497	+	0.584562i	−0.983961	−	0.178382i	$-0.942914\pi$
$947$	−10.3859	+	17.9889i	−0.337497	+	0.584562i	0.646464	+	0.762944i	$0.276247\pi$
$948$	−1.46433	−	2.53630i	−0.0475593	−	0.0823752i
$949$	7.37579	+	12.7753i	0.239428	+	0.414702i
$950$	−4.08295	−	2.35729i	−0.132468	−	0.0764806i
$951$		−	24.3802i		−	0.790583i
$952$	−9.18203	−	7.47370i	−0.297591	−	0.242224i
$953$		−	1.28486i		−	0.0416205i	−0.999783	−	0.0208103i	$-0.993375\pi$
$953$		−	1.28486i		−	0.0416205i	0.999783	−	0.0208103i	$-0.00662459\pi$
$954$	1.63847	+	0.945971i	0.0530474	+	0.0306269i
$955$	−45.2774	+	26.1409i	−1.46514	+	0.845901i
$956$	−4.88534	+	2.82055i	−0.158003	+	0.0912232i
$957$	−3.36189	+	3.41133i	−0.108674	+	0.110273i
$958$			39.5655i			1.27830i
$959$	−4.19144	+	5.14952i	−0.135349	+	0.166287i
$960$	−2.46248			−0.0794762
$961$	−11.8246	+	20.4807i	−0.381438	+	0.660669i
$962$	−5.63871	+	3.25551i	−0.181799	+	0.104962i
$963$	−4.99579	+	2.88432i	−0.160987	+	0.0929459i
$964$	−3.88733	+	6.73305i	−0.125203	+	0.216857i
$965$	8.65137			0.278497
$966$	21.6544	+	3.48546i	0.696720	+	0.112143i
$967$		−	44.2584i		−	1.42325i	−0.702558	−	0.711627i	$-0.747959\pi$
$967$		−	44.2584i		−	1.42325i	0.702558	−	0.711627i	$-0.252041\pi$
$968$	−5.63849	−	9.44497i	−0.181228	−	0.303573i
$969$	−17.1744	+	9.91562i	−0.551720	+	0.318536i
$970$	−2.93885	+	1.69674i	−0.0943607	+	0.0544792i
$971$	−34.5497	−	19.9473i	−1.10875	−	0.640138i	−0.170246	−	0.985402i	$-0.554456\pi$
$971$	−34.5497	−	19.9473i	−1.10875	−	0.640138i	−0.938506	+	0.345263i	$0.887790\pi$
$972$			1.00000i			0.0320750i
$973$	−18.7949	−	49.3323i	−0.602538	−	1.58152i
$974$			3.20923i			0.102830i
$975$	1.21643	+	0.702305i	0.0389569	+	0.0224918i
$976$	−2.23943	−	3.87880i	−0.0716823	−	0.124157i
$977$	0.803424	+	1.39157i	0.0257038	+	0.0445203i	0.878591	−	0.477575i	$-0.158484\pi$
$977$	0.803424	+	1.39157i	0.0257038	+	0.0445203i	−0.852887	+	0.522095i	$0.825151\pi$
$978$	−10.1807	+	17.6336i	−0.325544	+	0.563859i
$979$	−10.5664	+	40.6180i	−0.337703	+	1.29816i
$980$	11.4696	+	12.8676i	0.366383	+	0.411040i
$981$		−	8.63196i		−	0.275597i
$982$	−9.51044	+	16.4726i	−0.303490	+	0.525661i
$983$	0.981757	−	0.566818i	0.0313132	−	0.0180787i	−0.484262	−	0.874923i	$-0.660912\pi$
$983$	0.981757	−	0.566818i	0.0313132	−	0.0180787i	0.515575	+	0.856845i	$0.327578\pi$
$984$	4.09116	+	7.08611i	0.130422	+	0.225897i
$985$	27.0522	−	46.8558i	0.861954	−	1.49295i
$986$	6.46201			0.205792
$987$	−0.722935	−	1.89753i	−0.0230113	−	0.0603991i
$988$	5.85152			0.186162
$989$	69.1939	+	39.9491i	2.20024	+	1.27031i
$990$	2.17134	+	7.87320i	0.0690097	+	0.250227i
$991$	2.64334	+	4.57840i	0.0839684	+	0.145438i	0.904951	−	0.425515i	$-0.139907\pi$
$991$	2.64334	+	4.57840i	0.0839684	+	0.145438i	−0.820983	+	0.570953i	$0.806574\pi$
$992$	−1.35562	+	2.34801i	−0.0430411	+	0.0745494i
$993$			21.4532i			0.680798i
$994$	−4.36298	+	27.1063i	−0.138385	+	0.859759i
$995$	−3.55040			−0.112555
$996$	−8.75707	−	5.05590i	−0.277478	−	0.160202i
$997$	−0.545190	−	0.944297i	−0.0172663	−	0.0299062i	0.857263	−	0.514879i	$-0.172163\pi$
$997$	−0.545190	−	0.944297i	−0.0172663	−	0.0299062i	−0.874529	+	0.484972i	$0.838830\pi$
$998$	−22.1774	+	12.8041i	−0.702012	+	0.405307i
$999$	4.27060	+	2.46563i	0.135116	+	0.0780091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.p.a.439.5	yes	16
3.2	odd	2		1386.2.bk.a.901.4		16
7.2	even	3		3234.2.e.a.2155.7		16
7.3	odd	6		462.2.p.b.241.1	yes	16
7.5	odd	6		3234.2.e.b.2155.2		16
11.10	odd	2		462.2.p.b.439.1	yes	16
21.17	even	6		1386.2.bk.b.703.8		16
33.32	even	2		1386.2.bk.b.901.8		16
77.10	even	6	inner	462.2.p.a.241.5	✓	16
77.54	even	6		3234.2.e.a.2155.10		16
77.65	odd	6		3234.2.e.b.2155.15		16
231.164	odd	6		1386.2.bk.a.703.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.5	✓	16	77.10	even	6	inner
462.2.p.a.439.5	yes	16	1.1	even	1	trivial
462.2.p.b.241.1	yes	16	7.3	odd	6
462.2.p.b.439.1	yes	16	11.10	odd	2
1386.2.bk.a.703.4		16	231.164	odd	6
1386.2.bk.a.901.4		16	3.2	odd	2
1386.2.bk.b.703.8		16	21.17	even	6
1386.2.bk.b.901.8		16	33.32	even	2
3234.2.e.a.2155.7		16	7.2	even	3
3234.2.e.a.2155.10		16	77.54	even	6
3234.2.e.b.2155.2		16	7.5	odd	6
3234.2.e.b.2155.15		16	77.65	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13257 - 1.23124i) q^{5} -1.00000 q^{6} +(-0.941950 - 2.47239i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13257 - 1.23124i) q^{5} -1.00000 q^{6} +(-0.941950 - 2.47239i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.23124 - 2.13257i) q^{10} +(-0.881768 - 3.19726i) q^{11} +(-0.866025 - 0.500000i) q^{12} -1.32035 q^{13} +(0.420444 - 2.61213i) q^{14} +2.46248 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.23739 - 3.87528i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.21589 + 3.83803i) q^{19} -2.46248i q^{20} +(2.05195 + 1.67018i) q^{21} +(0.834997 - 3.20979i) q^{22} +(4.14497 - 7.17931i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.531907 + 0.921289i) q^{25} +(-1.14346 - 0.660177i) q^{26} +1.00000i q^{27} +(1.67018 - 2.05195i) q^{28} +1.44409i q^{29} +(2.13257 + 1.23124i) q^{30} +(2.34801 - 1.35562i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.36226 + 2.32803i) q^{33} -4.47479i q^{34} +(-1.03534 + 6.43232i) q^{35} +1.00000 q^{36} +(2.46563 - 4.27060i) q^{37} +(-3.83803 + 2.21589i) q^{38} +(1.14346 - 0.660177i) q^{39} +(1.23124 - 2.13257i) q^{40} -8.18233 q^{41} +(0.941950 + 2.47239i) q^{42} +9.63797i q^{43} +(2.32803 - 2.36226i) q^{44} +(-2.13257 + 1.23124i) q^{45} +(7.17931 - 4.14497i) q^{46} +(-0.664664 - 0.383744i) q^{47} -1.00000i q^{48} +(-5.22546 + 4.65774i) q^{49} +1.06381i q^{50} +(3.87528 + 2.23739i) q^{51} +(-0.660177 - 1.14346i) q^{52} +(0.945971 + 1.63847i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.05616 + 7.90406i) q^{55} +(2.47239 - 0.941950i) q^{56} -4.43177i q^{57} +(-0.722047 + 1.25062i) q^{58} +(6.74444 - 3.89390i) q^{59} +(1.23124 + 2.13257i) q^{60} +(-2.23943 + 3.87880i) q^{61} +2.71125 q^{62} +(-2.61213 - 0.420444i) q^{63} -1.00000 q^{64} +(2.81575 + 1.62567i) q^{65} +(0.881768 + 3.19726i) q^{66} +(0.861844 + 1.49276i) q^{67} +(2.23739 - 3.87528i) q^{68} +8.28995i q^{69} +(-4.11279 + 5.05289i) q^{70} -10.3771 q^{71} +(0.866025 + 0.500000i) q^{72} +(-5.58622 - 9.67562i) q^{73} +(4.27060 - 2.46563i) q^{74} +(-0.921289 - 0.531907i) q^{75} -4.43177 q^{76} +(-7.07431 + 5.19174i) q^{77} +1.32035 q^{78} +(2.53630 + 1.46433i) q^{79} +(2.13257 - 1.23124i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.08611 - 4.09116i) q^{82} +10.1118 q^{83} +(-0.420444 + 2.61213i) q^{84} +11.0191i q^{85} +(-4.81898 + 8.34672i) q^{86} +(-0.722047 - 1.25062i) q^{87} +(3.19726 - 0.881768i) q^{88} +(-10.9590 - 6.32720i) q^{89} -2.46248 q^{90} +(1.24371 + 3.26444i) q^{91} +8.28995 q^{92} +(-1.35562 + 2.34801i) q^{93} +(-0.383744 - 0.664664i) q^{94} +(9.45107 - 5.45658i) q^{95} +(0.500000 - 0.866025i) q^{96} -1.37808i q^{97} +(-6.85425 + 1.42099i) q^{98} +(-3.20979 - 0.834997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 10 * q^19 - 4 * q^21 + 2 * q^22 - 4 * q^23 - 8 * q^24 + 10 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^31 + 2 * q^33 - 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 - 12 * q^39 - 2 * q^40 + 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 + 18 * q^46 - 24 * q^47 - 6 * q^49 + 6 * q^51 - 8 * q^54 - 14 * q^55 + 4 * q^56 - 2 * q^60 + 28 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 72 * q^65 + 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 - 44 * q^73 + 24 * q^74 - 12 * q^75 - 20 * q^76 + 32 * q^77 - 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 + 8 * q^83 - 8 * q^84 - 12 * q^86 + 4 * q^88 - 36 * q^89 + 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 + 72 * q^95 + 8 * q^96 - 40 * q^98 - 8 * q^99

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