LMFDB - Embedded newform 462.2.p.a.241.5

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			241.5
Root			$0.500000 + 3.32851i$ of defining polynomial
Character	$\chi$	$=$	462.241
Dual form			462.2.p.a.439.5

$q$-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 $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

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

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	−0.894233	−	0.447602i	$-0.852278\pi$
$5$	−2.13257	+	1.23124i	−0.953715	+	0.550628i	−0.0594819	+	0.998229i	$0.518945\pi$
$6$	−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	0.456103	+	0.889927i	$0.349245\pi$
$17$	−2.23739	+	3.87528i	−0.542647	+	0.939893i	−0.998751	+	0.0499662i	$0.984089\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−2.21589	−	3.83803i	−0.508359	−	0.880504i	−0.999953	−	0.00967966i	$-0.996919\pi$
$19$	−2.21589	−	3.83803i	−0.508359	−	0.880504i	0.491594	−	0.870825i	$-0.336415\pi$
$20$			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	0.867754	+	0.496995i	$0.165563\pi$
$23$	4.14497	+	7.17931i	0.864287	+	1.49699i	−0.00346670	+	0.999994i	$0.501103\pi$
$24$	−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	$-0.957192\pi$
$29$		−	1.44409i		−	0.268162i	0.990970	−	0.134081i	$-0.0428082\pi$
$30$	2.13257	−	1.23124i	0.389352	−	0.224793i
$31$	2.34801	+	1.35562i	0.421715	+	0.243477i	0.695811	−	0.718225i	$-0.255045\pi$
$31$	2.34801	+	1.35562i	0.421715	+	0.243477i	−0.274096	+	0.961702i	$0.588379\pi$
$32$	−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	0.994362	−	0.106040i	$-0.0338172\pi$
$37$	2.46563	+	4.27060i	0.405347	+	0.702082i	−0.589014	+	0.808122i	$0.700484\pi$
$38$	−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	$-0.737235\pi$
$43$		−	9.63797i		−	1.46978i	0.678188	−	0.734888i	$-0.262765\pi$
$44$	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	−0.547692	−	0.836680i	$-0.684493\pi$
$47$	−0.664664	+	0.383744i	−0.0969512	+	0.0559748i	0.450741	+	0.892655i	$0.351160\pi$
$48$			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	−0.793714	−	0.608292i	$-0.791855\pi$
$53$	0.945971	−	1.63847i	0.129939	−	0.225061i	0.923653	+	0.383230i	$0.125188\pi$
$54$	−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	0.870015	−	0.493025i	$-0.164109\pi$
$59$	6.74444	+	3.89390i	0.878051	+	0.506943i	0.00803571	+	0.999968i	$0.497442\pi$
$60$	1.23124	−	2.13257i	0.158952	−	0.275314i
$61$	−2.23943	−	3.87880i	−0.286729	−	0.496630i	0.686298	−	0.727321i	$-0.259235\pi$
$61$	−2.23943	−	3.87880i	−0.286729	−	0.496630i	−0.973027	+	0.230691i	$0.925901\pi$
$62$	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	−0.808566	−	0.588405i	$-0.799756\pi$
$67$	0.861844	−	1.49276i	0.105291	−	0.182369i	0.913857	+	0.406036i	$0.133089\pi$
$68$	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	0.328371	+	0.944549i	$0.393500\pi$
$73$	−5.58622	+	9.67562i	−0.653818	+	1.13245i	−0.982189	+	0.187897i	$0.939833\pi$
$74$	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	−0.350490	−	0.936567i	$-0.613985\pi$
$79$	2.53630	−	1.46433i	0.285356	−	0.164750i	0.635846	+	0.771816i	$0.280651\pi$
$80$	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	−0.951700	−	0.307029i	$-0.900665\pi$
$89$	−10.9590	+	6.32720i	−1.16165	+	0.670682i	−0.209955	+	0.977711i	$0.567332\pi$
$90$	−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	$0.0222876\pi$
$97$			1.37808i			0.139923i	−0.997550	+	0.0699613i	$0.977712\pi$
$98$	−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	−0.990548	−	0.137167i	$-0.956200\pi$
$101$	−3.78361	+	6.55341i	−0.376483	+	0.652089i	0.614064	+	0.789256i	$0.289534\pi$
$102$	2.23739	−	3.87528i	0.221535	−	0.383710i
$103$	14.2858	−	8.24790i	1.40762	−	0.812690i	0.412461	−	0.910975i	$-0.364669\pi$
$103$	14.2858	−	8.24790i	1.40762	−	0.812690i	0.995158	+	0.0982855i	$0.0313358\pi$
$104$			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	−0.721650	−	0.692258i	$-0.756616\pi$
$107$	−4.99579	+	2.88432i	−0.482961	+	0.278838i	0.238689	+	0.971096i	$0.423282\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	7.47550	+	4.31598i	0.716023	+	0.413396i	0.813287	−	0.581862i	$-0.197676\pi$
$109$	7.47550	+	4.31598i	0.716023	+	0.413396i	−0.0972641	+	0.995259i	$0.531009\pi$
$110$	−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	$-0.819683\pi$
$127$		−	12.0959i		−	1.07333i	0.843794	−	0.536667i	$-0.180317\pi$
$128$	−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	0.946264	+	0.323394i	$0.104824\pi$
$131$	8.62077	+	14.9316i	0.753200	+	1.30458i	−0.193064	+	0.981186i	$0.561843\pi$
$132$	−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	−0.914636	−	0.404277i	$-0.867523\pi$
$137$	−1.25479	+	2.17335i	−0.107204	+	0.185682i	0.807433	+	0.589960i	$0.200856\pi$
$138$	−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	−0.805067	−	0.593184i	$-0.797871\pi$
$149$	−8.46998	+	4.89014i	−0.693888	+	0.400616i	0.111179	+	0.993800i	$0.464537\pi$
$150$	−0.531907	+	0.921289i	−0.0434300	+	0.0752229i
$151$	2.31521	+	1.33669i	0.188409	+	0.108778i	0.591237	−	0.806498i	$-0.298640\pi$
$151$	2.31521	+	1.33669i	0.188409	+	0.108778i	−0.402829	+	0.915275i	$0.631973\pi$
$152$	−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	0.934750	−	0.355306i	$-0.115623\pi$
$157$	13.7131	+	7.91724i	1.09442	+	0.631865i	0.159671	+	0.987170i	$0.448957\pi$
$158$	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	0.921293	+	0.388870i	$0.127135\pi$
$163$	10.1807	+	17.6336i	0.797418	+	1.38117i	−0.123875	+	0.992298i	$0.539532\pi$
$164$	−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	0.694771	−	0.719231i	$-0.255506\pi$
$173$	−3.62347	−	6.27604i	−0.275487	−	0.477158i	−0.970258	+	0.242073i	$0.922173\pi$
$174$			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	−0.997178	−	0.0750767i	$-0.976080\pi$
$179$	−5.80078	+	10.0472i	−0.433571	+	0.750966i	0.563607	+	0.826043i	$0.309413\pi$
$180$	−2.13257	+	1.23124i	−0.158952	+	0.0917713i
$181$			7.74423i			0.575624i	0.957687	+	0.287812i	$0.0929279\pi$
$181$			7.74423i			0.575624i	−0.957687	+	0.287812i	$0.907072\pi$
$182$	−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	0.938579	+	0.345065i	$0.112143\pi$
$191$	10.6157	+	18.3869i	0.768125	+	1.33043i	−0.170454	+	0.985366i	$0.554523\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−3.04258	−	1.75664i	−0.219010	−	0.126445i	0.386482	−	0.922297i	$-0.373690\pi$
$193$	−3.04258	−	1.75664i	−0.219010	−	0.126445i	−0.605492	+	0.795852i	$0.707024\pi$
$194$	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	$-0.713841\pi$
$197$		−	21.9715i		−	1.56540i	0.622397	−	0.782702i	$-0.286159\pi$
$198$	−2.36226	+	2.32803i	−0.167879	+	0.165446i
$199$	1.24863	+	0.720899i	0.0885133	+	0.0511032i	0.543603	−	0.839342i	$-0.317060\pi$
$199$	1.24863	+	0.720899i	0.0885133	+	0.0511032i	−0.455090	+	0.890445i	$0.650393\pi$
$200$	−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	$0.00179431\pi$
$211$			0.163763i			0.0112739i	−0.999984	+	0.00563697i	$0.998206\pi$
$212$	−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	$0.369323\pi$
$223$			27.3847i			1.83382i	−0.399099	+	0.916908i	$0.630677\pi$
$224$	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	−0.793976	−	0.607949i	$-0.791993\pi$
$227$	1.95128	−	3.37971i	0.129511	−	0.224319i	0.923487	+	0.383629i	$0.125326\pi$
$228$	3.83803	+	2.21589i	0.254180	+	0.146751i
$229$	−4.36524	+	2.52028i	−0.288463	+	0.166544i	−0.637249	−	0.770658i	$-0.719928\pi$
$229$	−4.36524	+	2.52028i	−0.288463	+	0.166544i	0.348785	+	0.937203i	$0.386594\pi$
$230$	−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	−0.961747	−	0.273940i	$-0.911673\pi$
$233$	−18.3993	+	10.6229i	−1.20538	+	0.695927i	−0.243634	+	0.969867i	$0.578340\pi$
$234$	−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	$-0.941598\pi$
$239$		−	5.64110i		−	0.364893i	0.983216	−	0.182446i	$-0.0584016\pi$
$240$	−1.23124	−	2.13257i	−0.0794762	−	0.137657i
$241$	3.88733	−	6.73305i	0.250405	−	0.433714i	−0.713232	−	0.700928i	$-0.752770\pi$
$241$	3.88733	−	6.73305i	0.250405	−	0.433714i	0.963637	+	0.267213i	$0.0861029\pi$
$242$	−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	$-0.748588\pi$
$251$		−	22.5045i		−	1.42047i	0.703963	−	0.710236i	$-0.251412\pi$
$252$	−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	−0.416325	−	0.909216i	$-0.636682\pi$
$257$	2.61175	−	1.50789i	0.162916	−	0.0940597i	0.579241	+	0.815156i	$0.303349\pi$
$258$			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	0.999983	+	0.00575106i	$0.00183063\pi$
$263$	24.4063	+	14.0910i	1.50496	+	0.868887i	0.504972	+	0.863136i	$0.331503\pi$
$264$	−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	0.483954	−	0.875093i	$-0.339200\pi$
$269$	−0.523552	−	0.302273i	−0.0319215	−	0.0184299i	−0.515876	+	0.856663i	$0.672533\pi$
$270$	2.13257	+	1.23124i	0.129784	+	0.0749309i
$271$	−9.89654	−	17.1413i	−0.601172	−	1.04126i	−0.992644	−	0.121071i	$-0.961367\pi$
$271$	−9.89654	−	17.1413i	−0.601172	−	1.04126i	0.391472	−	0.920190i	$-0.371966\pi$
$272$	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	0.555255	−	0.831680i	$-0.312621\pi$
$277$	1.87448	+	1.08223i	0.112626	+	0.0650249i	−0.442629	+	0.896705i	$0.645954\pi$
$278$	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	$0.342231\pi$
$281$			29.4916i			1.75932i	−0.475601	+	0.879661i	$0.657769\pi$
$282$	0.664664	−	0.383744i	0.0395801	−	0.0228516i
$283$	−14.1940	+	24.5847i	−0.843745	+	1.46141i	0.0429613	+	0.999077i	$0.486321\pi$
$283$	−14.1940	+	24.5847i	−0.843745	+	1.46141i	−0.886707	+	0.462333i	$0.847013\pi$
$284$	−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	0.503074	−	0.864243i	$-0.332202\pi$
$311$	0.108539	+	0.0626652i	0.00615470	+	0.00355342i	−0.496919	+	0.867797i	$0.665536\pi$
$312$	0.660177	−	1.14346i	0.0373752	−	0.0647357i
$313$	−6.69427	+	3.86494i	−0.378382	+	0.218459i	−0.677114	−	0.735878i	$-0.736770\pi$
$313$	−6.69427	+	3.86494i	−0.378382	+	0.218459i	0.298732	+	0.954337i	$0.403436\pi$
$314$	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	−0.973542	−	0.228508i	$-0.926615\pi$
$317$	−12.1901	−	21.1139i	−0.684665	−	1.18587i	0.288877	−	0.957366i	$-0.406718\pi$
$318$	−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	0.994286	+	0.106746i	$0.0340432\pi$
$331$	10.7266	+	18.5790i	0.589588	+	1.02120i	−0.404698	+	0.914450i	$0.632623\pi$
$332$	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	$0.304549\pi$
$337$			30.0086i			1.63467i	−0.576163	+	0.817335i	$0.695451\pi$
$338$	−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	−0.990358	−	0.138533i	$-0.955761\pi$
$347$	−29.9073	−	17.2670i	−1.60551	−	0.926942i	−0.615152	−	0.788408i	$-0.710906\pi$
$348$	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	0.779131	−	0.626861i	$-0.215661\pi$
$353$	11.7581	+	6.78853i	0.625819	+	0.361317i	−0.153312	+	0.988178i	$0.548994\pi$
$354$	−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	−0.538966	−	0.842328i	$-0.681185\pi$
$359$	−1.49631	+	0.863893i	−0.0789720	+	0.0455945i	0.459994	+	0.887922i	$0.347852\pi$
$360$	−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	−0.202724	−	0.979236i	$-0.564979\pi$
$367$	−22.0716	−	12.7430i	−1.15213	−	0.665182i	−0.949405	+	0.314054i	$0.898313\pi$
$368$	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	0.494723	−	0.869051i	$-0.335269\pi$
$373$	28.8675	−	16.6667i	1.49470	−	0.862968i	0.999982	+	0.00608223i	$0.00193605\pi$
$374$	−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	−0.381583	−	0.924334i	$-0.624621\pi$
$383$	4.46444	−	2.57755i	0.228122	−	0.131706i	0.609705	+	0.792628i	$0.291288\pi$
$384$	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	−0.793107	−	0.609082i	$-0.791538\pi$
$389$	2.58228	−	4.47264i	0.130927	−	0.226772i	0.924034	+	0.382310i	$0.124871\pi$
$390$	−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	−0.355780	−	0.934570i	$-0.615785\pi$
$397$	5.49312	−	3.17146i	0.275692	−	0.159171i	0.631472	+	0.775399i	$0.282451\pi$
$398$	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	−0.998319	−	0.0579565i	$-0.981542\pi$
$401$	−11.0008	−	19.0539i	−0.549351	−	0.951504i	0.448968	−	0.893548i	$-0.351792\pi$
$402$	−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	−0.986084	−	0.166247i	$-0.946835\pi$
$409$	−7.05947	+	12.2274i	−0.349068	+	0.604604i	0.637016	+	0.770851i	$0.280169\pi$
$410$	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	$-0.812205\pi$
$419$		−	22.7760i		−	1.11268i	0.830955	−	0.556340i	$-0.187795\pi$
$420$	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	−0.309286	−	0.950969i	$-0.600090\pi$
$431$	−26.7290	−	15.4320i	−1.28749	−	0.743334i	−0.978206	+	0.207635i	$0.933423\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$		−	32.2967i		−	1.55208i	−0.630683	−	0.776040i	$-0.717225\pi$
$433$		−	32.2967i		−	1.55208i	0.630683	−	0.776040i	$-0.282775\pi$
$434$	−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	0.973685	+	0.227898i	$0.0731851\pi$
$439$	14.3357	+	24.8302i	0.684208	+	1.18508i	−0.289478	+	0.957185i	$0.593482\pi$
$440$	−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	−0.897236	−	0.441552i	$-0.854428\pi$
$443$	−17.4908	−	30.2949i	−0.831013	−	1.43936i	0.0662231	−	0.997805i	$-0.478905\pi$
$444$	−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	−0.0262200	−	0.999656i	$-0.508347\pi$
$457$	17.6664	−	10.1997i	0.826398	−	0.477121i	0.852618	+	0.522535i	$0.175014\pi$
$458$	−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	−0.306683	−	0.951812i	$-0.599219\pi$
$467$	7.87190	−	4.54484i	0.364268	−	0.210310i	0.670951	+	0.741501i	$0.265886\pi$
$468$	−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	0.0815054	−	0.996673i	$-0.474027\pi$
$479$	19.7827	−	34.2647i	0.903897	−	1.56560i	0.822391	−	0.568922i	$-0.192639\pi$
$480$	−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	−0.827377	−	0.561647i	$-0.810168\pi$
$487$	1.60461	−	2.77927i	0.0727120	−	0.125941i	0.900089	+	0.435706i	$0.143501\pi$
$488$	−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	$-0.858795\pi$
$491$		−	19.0209i		−	0.858401i	0.903209	−	0.429200i	$-0.141205\pi$
$492$	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	−0.996236	−	0.0866862i	$-0.972372\pi$
$499$	−12.8041	−	22.1774i	−0.573190	−	0.992795i	0.423045	−	0.906108i	$-0.360961\pi$
$500$	−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	−0.786632	−	0.617422i	$-0.788177\pi$
$509$	−14.5574	+	8.40471i	−0.645245	+	0.372532i	0.141387	+	0.989954i	$0.454844\pi$
$510$			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	0.988163	−	0.153407i	$-0.0490245\pi$
$521$	30.8004	+	17.7826i	1.34939	+	0.779071i	0.361227	+	0.932478i	$0.382358\pi$
$522$	0.722047	−	1.25062i	0.0316032	−	0.0547383i
$523$	1.90926	+	3.30694i	0.0834863	+	0.144603i	0.904745	−	0.425953i	$-0.140061\pi$
$523$	1.90926	+	3.30694i	0.0834863	+	0.144603i	−0.821259	+	0.570556i	$0.806728\pi$
$524$	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	−0.885230	−	0.465153i	$-0.845999\pi$
$541$	−21.5152	+	12.4218i	−0.925011	+	0.534055i	−0.0397805	+	0.999208i	$0.512666\pi$
$542$	−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	$0.398251\pi$
$547$			44.4066i			1.89869i	−0.314237	+	0.949345i	$0.601749\pi$
$548$	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	−0.102911	−	0.994691i	$-0.532816\pi$
$557$	−23.9736	−	13.8412i	−1.01579	−	0.586469i	−0.912883	+	0.408222i	$0.866149\pi$
$558$	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	−0.726014	−	0.687680i	$-0.758629\pi$
$563$	5.51765	−	9.55686i	0.232541	−	0.402773i	0.958555	+	0.284907i	$0.0919626\pi$
$564$	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	−0.999624	−	0.0274209i	$-0.991271\pi$
$569$	−35.2007	+	20.3231i	−1.47569	+	0.851989i	−0.476065	+	0.879410i	$0.657937\pi$
$570$	−9.45107	−	5.45658i	−0.395862	−	0.228551i
$571$	−15.3762	−	8.87748i	−0.643476	−	0.371511i	0.142476	−	0.989798i	$-0.454494\pi$
$571$	−15.3762	−	8.87748i	−0.643476	−	0.371511i	−0.785952	+	0.618287i	$0.787827\pi$
$572$	−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	0.468388	−	0.883523i	$-0.344835\pi$
$577$	−1.50303	−	0.867773i	−0.0625718	−	0.0361259i	−0.530960	+	0.847397i	$0.678168\pi$
$578$	−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	$0.00550363\pi$
$587$			0.837774i			0.0345786i	−0.999851	+	0.0172893i	$0.994496\pi$
$588$	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	0.999199	+	0.0400166i	$0.0127411\pi$
$593$	13.0100	+	22.5339i	0.534255	+	0.925357i	−0.464944	+	0.885340i	$0.653926\pi$
$594$	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	−0.957707	−	0.287744i	$-0.907095\pi$
$599$	−5.62081	+	9.73552i	−0.229660	+	0.397783i	0.728047	+	0.685527i	$0.240428\pi$
$600$	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	0.950644	−	0.310284i	$-0.100424\pi$
$607$	5.09027	+	8.81661i	0.206608	+	0.357855i	−0.744036	+	0.668139i	$0.767091\pi$
$608$			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	0.868599	−	0.495515i	$-0.165021\pi$
$613$	21.6335	+	12.4901i	0.873770	+	0.504471i	0.00517055	+	0.999987i	$0.498354\pi$
$614$	−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	0.0118852	−	0.999929i	$-0.496217\pi$
$619$	−21.1014	−	12.1829i	−0.848137	−	0.489672i	−0.860022	+	0.510258i	$0.829550\pi$
$620$	−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	−0.608403	−	0.793628i	$-0.708189\pi$
$641$	9.69935	−	16.7998i	0.383101	−	0.663551i	0.991504	+	0.130078i	$0.0415228\pi$
$642$	4.99579	−	2.88432i	0.197168	−	0.113835i
$643$			11.3901i			0.449182i	0.974453	+	0.224591i	$0.0721047\pi$
$643$			11.3901i			0.449182i	−0.974453	+	0.224591i	$0.927895\pi$
$644$	−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	0.763030	−	0.646363i	$-0.223711\pi$
$647$	14.8745	+	8.58781i	0.584778	+	0.337621i	−0.178252	+	0.983985i	$0.557044\pi$
$648$	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	0.986750	+	0.162246i	$0.0518737\pi$
$653$	16.1982	+	28.0561i	0.633884	+	1.09792i	−0.352866	+	0.935674i	$0.614793\pi$
$654$	−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	$-0.946926\pi$
$659$		−	8.52103i		−	0.331932i	0.986131	−	0.165966i	$-0.0530742\pi$
$660$	5.73272	+	5.81703i	0.223146	+	0.226428i
$661$	34.1086	+	19.6926i	1.32667	+	0.765953i	0.984783	−	0.173788i	$-0.0556009\pi$
$661$	34.1086	+	19.6926i	1.32667	+	0.765953i	0.341886	+	0.939741i	$0.388934\pi$
$662$	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	$0.149060\pi$
$673$			23.4185i			0.902716i	−0.892343	+	0.451358i	$0.850940\pi$
$674$	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	0.996526	+	0.0832822i	$0.0265403\pi$
$677$	14.8410	+	25.7054i	0.570388	+	0.987940i	−0.426138	+	0.904658i	$0.640126\pi$
$678$	−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	0.444209	+	0.895923i	$0.353485\pi$
$683$	−14.4728	+	25.0677i	−0.553787	+	0.959188i	−0.997997	+	0.0632649i	$0.979849\pi$
$684$	−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	0.0369236	−	0.999318i	$-0.488244\pi$
$691$	24.2055	−	13.9750i	0.920820	−	0.531636i	0.883897	+	0.467682i	$0.154911\pi$
$692$	−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	$0.0802323\pi$
$701$			13.2062i			0.498793i	−0.968401	+	0.249397i	$0.919768\pi$
$702$	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	0.693224	−	0.720722i	$-0.256190\pi$
$709$	−7.39039	−	12.8005i	−0.277552	−	0.480734i	−0.970776	+	0.239988i	$0.922856\pi$
$710$	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	−0.438881	−	0.898545i	$-0.644625\pi$
$719$	3.21343	−	1.85527i	0.119841	−	0.0691900i	0.558722	+	0.829355i	$0.311292\pi$
$720$			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	$0.101710\pi$
$727$			16.9392i			0.628241i	−0.949383	+	0.314120i	$0.898290\pi$
$728$	−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	0.741360	−	0.671107i	$-0.234181\pi$
$733$	−5.69951	−	9.87183i	−0.210516	−	0.364624i	−0.951876	+	0.306483i	$0.900848\pi$
$734$	−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	0.587315	−	0.809358i	$-0.300185\pi$
$739$	4.89454	+	2.82586i	0.180049	+	0.103951i	−0.407267	+	0.913309i	$0.633518\pi$
$740$	−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	$-0.987088\pi$
$743$		−	2.21080i		−	0.0811065i	0.999177	−	0.0405533i	$-0.0129120\pi$
$744$	−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	0.807450	−	0.589936i	$-0.200847\pi$
$751$	−2.93707	−	5.08715i	−0.107175	−	0.185633i	−0.914625	+	0.404304i	$0.867514\pi$
$752$	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	0.586950	−	0.809623i	$-0.300329\pi$
$761$	−11.2463	−	19.4792i	−0.407680	−	0.706122i	−0.994629	+	0.103501i	$0.966995\pi$
$762$			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	0.235044	−	0.971985i	$-0.424477\pi$
$773$	−13.6011	−	7.85260i	−0.489198	−	0.282438i	−0.724242	+	0.689546i	$0.757810\pi$
$774$	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	0.217579	+	0.976043i	$0.430184\pi$
$787$	−20.6611	+	35.7861i	−0.736488	+	1.27563i	−0.954067	+	0.299592i	$0.903149\pi$
$788$	−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	$0.116505\pi$
$797$			20.2076i			0.715789i	−0.933762	+	0.357894i	$0.883495\pi$
$798$	−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	−0.110711	−	0.993853i	$-0.535313\pi$
$809$	−29.2043	−	16.8611i	−1.02677	−	0.592805i	−0.916057	+	0.401048i	$0.868646\pi$
$810$	−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	−0.627039	−	0.778988i	$-0.715733\pi$
$821$	−7.61984	+	4.39932i	−0.265934	+	0.153537i	0.361104	+	0.932525i	$0.382400\pi$
$822$	1.25479	−	2.17335i	0.0437657	−	0.0758044i
$823$	16.4438	−	28.4815i	0.573195	−	0.992802i	−0.423041	−	0.906111i	$-0.639037\pi$
$823$	16.4438	−	28.4815i	0.573195	−	0.992802i	0.996235	−	0.0866913i	$-0.0276294\pi$
$824$	−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	$0.273788\pi$
$827$			43.5923i			1.51585i	−0.652339	+	0.757927i	$0.726212\pi$
$828$	4.14497	+	7.17931i	0.144048	+	0.249498i
$829$	−27.4160	−	15.8286i	−0.952198	−	0.549752i	−0.0584348	−	0.998291i	$-0.518611\pi$
$829$	−27.4160	−	15.8286i	−0.952198	−	0.549752i	−0.893763	+	0.448540i	$0.851944\pi$
$830$	−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	$0.193657\pi$
$839$			33.1104i			1.14310i	−0.820568	+	0.571549i	$0.806343\pi$
$840$	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	−0.748916	−	0.662665i	$-0.769425\pi$
$857$	5.83813	−	10.1119i	0.199427	−	0.345417i	0.948343	+	0.317248i	$0.102759\pi$
$858$	−1.16425	+	4.22152i	−0.0397467	+	0.144120i
$859$	−35.2623	+	20.3587i	−1.20314	+	0.694631i	−0.961251	−	0.275674i	$-0.911099\pi$
$859$	−35.2623	+	20.3587i	−1.20314	+	0.694631i	−0.241885	+	0.970305i	$0.577766\pi$
$860$	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	0.977897	−	0.209087i	$-0.0670490\pi$
$863$	9.04438	+	15.6653i	0.307874	+	0.533254i	−0.670023	+	0.742341i	$0.733716\pi$
$864$	−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	−0.400056	−	0.916491i	$-0.631009\pi$
$877$	5.73392	−	3.31048i	0.193621	−	0.111787i	0.593676	+	0.804704i	$0.297676\pi$
$878$	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	$-0.909899\pi$
$881$		−	16.5800i		−	0.558594i	0.960205	−	0.279297i	$-0.0901014\pi$
$882$	−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	0.998476	+	0.0551831i	$0.0175742\pi$
$887$	16.2919	+	28.2184i	0.547028	+	0.947480i	−0.451448	+	0.892297i	$0.649092\pi$
$888$	−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	−0.292033	−	0.956408i	$-0.594332\pi$
$907$	20.5472	−	35.5887i	0.682257	−	1.18170i	0.974290	−	0.225296i	$-0.0723350\pi$
$908$	−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	0.176618	−	0.984280i	$-0.443484\pi$
$919$	33.8721	−	19.5561i	1.11734	−	0.645095i	0.940720	+	0.339184i	$0.110151\pi$
$920$	−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	−0.106930	−	0.994267i	$-0.534102\pi$
$929$	21.3559	−	12.3298i	0.700665	−	0.404529i	0.807595	+	0.589737i	$0.200769\pi$
$930$	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	−0.445996	−	0.895035i	$-0.647151\pi$
$941$	16.9368	−	29.3354i	0.552125	−	0.956308i	0.998121	−	0.0612732i	$-0.0195161\pi$
$942$	−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	0.646464	−	0.762944i	$-0.276247\pi$
$947$	−10.3859	−	17.9889i	−0.337497	−	0.584562i	−0.983961	+	0.178382i	$0.942914\pi$
$948$	−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	$0.00662459\pi$
$953$			1.28486i			0.0416205i	−0.999783	+	0.0208103i	$0.993375\pi$
$954$	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	$0.252041\pi$
$967$			44.2584i			1.42325i	−0.702558	+	0.711627i	$0.747959\pi$
$968$	−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	−0.938506	−	0.345263i	$-0.887790\pi$
$971$	−34.5497	+	19.9473i	−1.10875	+	0.640138i	−0.170246	+	0.985402i	$0.554456\pi$
$972$		−	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	−0.852887	−	0.522095i	$-0.825151\pi$
$977$	0.803424	−	1.39157i	0.0257038	−	0.0445203i	0.878591	+	0.477575i	$0.158484\pi$
$978$	−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	0.515575	−	0.856845i	$-0.327578\pi$
$983$	0.981757	+	0.566818i	0.0313132	+	0.0180787i	−0.484262	+	0.874923i	$0.660912\pi$
$984$	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	−0.820983	−	0.570953i	$-0.806574\pi$
$991$	2.64334	−	4.57840i	0.0839684	−	0.145438i	0.904951	+	0.425515i	$0.139907\pi$
$992$	−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	−0.874529	−	0.484972i	$-0.838830\pi$
$997$	−0.545190	+	0.944297i	−0.0172663	+	0.0299062i	0.857263	+	0.514879i	$0.172163\pi$
$998$	−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.241.5	✓	16
3.2	odd	2		1386.2.bk.a.703.4		16
7.3	odd	6		3234.2.e.b.2155.15		16
7.4	even	3		3234.2.e.a.2155.10		16
7.5	odd	6		462.2.p.b.439.1	yes	16
11.10	odd	2		462.2.p.b.241.1	yes	16
21.5	even	6		1386.2.bk.b.901.8		16
33.32	even	2		1386.2.bk.b.703.8		16
77.10	even	6		3234.2.e.a.2155.7		16
77.32	odd	6		3234.2.e.b.2155.2		16
77.54	even	6	inner	462.2.p.a.439.5	yes	16
231.131	odd	6		1386.2.bk.a.901.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.5	✓	16	1.1	even	1	trivial
462.2.p.a.439.5	yes	16	77.54	even	6	inner
462.2.p.b.241.1	yes	16	11.10	odd	2
462.2.p.b.439.1	yes	16	7.5	odd	6
1386.2.bk.a.703.4		16	3.2	odd	2
1386.2.bk.a.901.4		16	231.131	odd	6
1386.2.bk.b.703.8		16	33.32	even	2
1386.2.bk.b.901.8		16	21.5	even	6
3234.2.e.a.2155.7		16	77.10	even	6
3234.2.e.a.2155.10		16	7.4	even	3
3234.2.e.b.2155.2		16	77.32	odd	6
3234.2.e.b.2155.15		16	7.3	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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