LMFDB - Embedded newform 588.2.o.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(19,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("588.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (of order $6$, degree $2$, not 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.432972864.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 4x^{5} - 6x^{4} + 8x^{3} + 4x^{2} - 8x + 16 $ x^8 - x^7 + x^6 + 4x^5 - 6x^4 + 8x^3 + 4x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$0.121053 + 1.40902i$ of defining polynomial
Character	$\chi$	$=$	588.19
Dual form			588.2.o.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.121053 - 1.40902i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.97069 - 0.341134i) q^{4} +(2.88831 + 1.66757i) q^{5} +(-1.28078 + 0.599676i) q^{6} +(-0.719224 + 2.73546i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.121053 - 1.40902i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.97069 - 0.341134i) q^{4} +(2.88831 + 1.66757i) q^{5} +(-1.28078 + 0.599676i) q^{6} +(-0.719224 + 2.73546i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.69928 - 3.86783i) q^{10} +(0.810969 - 0.468213i) q^{11} +(0.689916 + 1.87724i) q^{12} -1.87285i q^{13} -3.33513i q^{15} +(3.76726 + 1.34454i) q^{16} +(4.51025 - 2.60399i) q^{17} +(1.15972 + 0.809347i) q^{18} +(3.56155 - 6.16879i) q^{19} +(-5.12311 - 4.27156i) q^{20} +(-0.561553 - 1.19935i) q^{22} +(0.810969 + 0.468213i) q^{23} +(2.72859 - 0.744862i) q^{24} +(3.06155 + 5.30277i) q^{25} +(-2.63889 - 0.226715i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-4.69928 - 0.403728i) q^{30} +(2.35052 - 5.14539i) q^{32} +(-0.810969 - 0.468213i) q^{33} +(-3.12311 - 6.67026i) q^{34} +(1.28078 - 1.53610i) q^{36} +(-0.561553 + 0.972638i) q^{37} +(-8.26083 - 5.76506i) q^{38} +(-1.62194 + 0.936426i) q^{39} +(-6.63889 + 6.70149i) q^{40} +1.46228i q^{41} +9.06897i q^{43} +(-1.75789 + 0.646055i) q^{44} +(-2.88831 + 1.66757i) q^{45} +(0.757894 - 1.08600i) q^{46} +(3.12311 - 5.40938i) q^{47} +(-0.719224 - 3.93481i) q^{48} +(7.84233 - 3.67188i) q^{50} +(-4.51025 - 2.60399i) q^{51} +(-0.638893 + 3.69082i) q^{52} +(-6.12311 - 10.6055i) q^{53} +(0.121053 - 1.40902i) q^{54} +3.12311 q^{55} -7.12311 q^{57} +(-0.242106 + 2.81805i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-1.13773 + 6.57252i) q^{60} +(4.15468 + 2.39871i) q^{61} +(-6.96543 - 3.93481i) q^{64} +(3.12311 - 5.40938i) q^{65} +(-0.757894 + 1.08600i) q^{66} +(-9.47590 + 5.47091i) q^{67} +(-9.77662 + 3.59307i) q^{68} -0.936426i q^{69} -3.86098i q^{71} +(-2.00936 - 1.99059i) q^{72} +(-5.77662 + 3.33513i) q^{73} +(1.30249 + 0.908982i) q^{74} +(3.06155 - 5.30277i) q^{75} +(-9.12311 + 10.9418i) q^{76} +(1.12311 + 2.39871i) q^{78} +(2.07734 + 1.19935i) q^{79} +(8.63889 + 10.1656i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.06039 + 0.177014i) q^{82} +10.2462 q^{83} +17.3693 q^{85} +(12.7784 + 1.09783i) q^{86} +(1.00000 + 1.73205i) q^{87} +(0.697508 + 2.55512i) q^{88} +(1.26637 + 0.731140i) q^{89} +(2.00000 + 4.27156i) q^{90} +(-1.43845 - 1.19935i) q^{92} +(-7.24388 - 5.05535i) q^{94} +(20.5737 - 11.8782i) q^{95} +(-5.63130 + 0.537082i) q^{96} +10.4160i q^{97} +0.936426i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{16} + q^{18} + 12 q^{19} - 8 q^{20} + 12 q^{22} + 7 q^{24} + 8 q^{25} + 12 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 9 q^{32} + 8 q^{34} + 2 q^{36} + 12 q^{37} - 20 q^{38} - 20 q^{40} - 14 q^{44} + 6 q^{46} - 8 q^{47} - 14 q^{48} + 38 q^{50} + 28 q^{52} - 16 q^{53} + q^{54} - 8 q^{55} - 24 q^{57} - 2 q^{58} + 16 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{65} - 6 q^{66} - 32 q^{68} + 7 q^{72} + 14 q^{74} + 8 q^{75} - 40 q^{76} - 24 q^{78} + 36 q^{80} - 4 q^{81} + 20 q^{82} + 16 q^{83} + 40 q^{85} + 30 q^{86} + 8 q^{87} + 2 q^{88} + 16 q^{90} - 28 q^{92} - 32 q^{94} - 9 q^{96}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9 - 8 * q^10 - q^12 + 7 * q^16 + q^18 + 12 * q^19 - 8 * q^20 + 12 * q^22 + 7 * q^24 + 8 * q^25 + 12 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 9 * q^32 + 8 * q^34 + 2 * q^36 + 12 * q^37 - 20 * q^38 - 20 * q^40 - 14 * q^44 + 6 * q^46 - 8 * q^47 - 14 * q^48 + 38 * q^50 + 28 * q^52 - 16 * q^53 + q^54 - 8 * q^55 - 24 * q^57 - 2 * q^58 + 16 * q^59 + 4 * q^60 + 2 * q^64 - 8 * q^65 - 6 * q^66 - 32 * q^68 + 7 * q^72 + 14 * q^74 + 8 * q^75 - 40 * q^76 - 24 * q^78 + 36 * q^80 - 4 * q^81 + 20 * q^82 + 16 * q^83 + 40 * q^85 + 30 * q^86 + 8 * q^87 + 2 * q^88 + 16 * q^90 - 28 * q^92 - 32 * q^94 - 9 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.121053	−	1.40902i	0.0855975	−	0.996330i
$2$	0.121053	−	1.40902i	0.0855975	−	0.996330i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.97069	−	0.341134i	−0.985346	−	0.170567i
$5$	2.88831	+	1.66757i	1.29169	+	0.745758i	0.978954	−	0.204082i	$-0.0654208\pi$
$5$	2.88831	+	1.66757i	1.29169	+	0.745758i	0.312737	+	0.949840i	$0.398754\pi$
$6$	−1.28078	+	0.599676i	−0.522875	+	0.244817i
$7$		0			0
$7$		0			0
$8$	−0.719224	+	2.73546i	−0.254284	+	0.967130i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.69928	−	3.86783i	0.853587	−	1.22312i
$11$	0.810969	−	0.468213i	0.244516	−	0.141172i	−0.372734	−	0.927938i	$-0.621580\pi$
$11$	0.810969	−	0.468213i	0.244516	−	0.141172i	0.617251	+	0.786766i	$0.288246\pi$
$12$	0.689916	+	1.87724i	0.199162	+	0.541911i
$13$		−	1.87285i		−	0.519436i	−0.965685	−	0.259718i	$-0.916370\pi$
$13$		−	1.87285i		−	0.519436i	0.965685	−	0.259718i	$-0.0836296\pi$
$14$		0			0
$15$		−	3.33513i		−	0.861127i
$16$	3.76726	+	1.34454i	0.941814	+	0.336135i
$17$	4.51025	−	2.60399i	1.09390	−	0.631561i	0.159285	−	0.987233i	$-0.449081\pi$
$17$	4.51025	−	2.60399i	1.09390	−	0.631561i	0.934611	+	0.355672i	$0.115748\pi$
$18$	1.15972	+	0.809347i	0.273349	+	0.190765i
$19$	3.56155	−	6.16879i	0.817076	−	1.41522i	−0.0907512	−	0.995874i	$-0.528927\pi$
$19$	3.56155	−	6.16879i	0.817076	−	1.41522i	0.907827	−	0.419344i	$-0.137740\pi$
$20$	−5.12311	−	4.27156i	−1.14556	−	0.955149i
$21$		0			0
$22$	−0.561553	−	1.19935i	−0.119723	−	0.255703i
$23$	0.810969	+	0.468213i	0.169099	+	0.0976292i	0.582161	−	0.813074i	$-0.302207\pi$
$23$	0.810969	+	0.468213i	0.169099	+	0.0976292i	−0.413062	+	0.910703i	$0.635541\pi$
$24$	2.72859	−	0.744862i	0.556970	−	0.152044i
$25$	3.06155	+	5.30277i	0.612311	+	1.06055i
$26$	−2.63889	−	0.226715i	−0.517529	−	0.0444624i
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−4.69928	−	0.403728i	−0.857967	−	0.0737104i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	2.35052	−	5.14539i	0.415518	−	0.909585i
$33$	−0.810969	−	0.468213i	−0.141172	−	0.0815055i
$34$	−3.12311	−	6.67026i	−0.535608	−	1.14394i
$35$		0			0
$36$	1.28078	−	1.53610i	0.213463	−	0.256017i
$37$	−0.561553	+	0.972638i	−0.0923187	+	0.159901i	−0.908486	−	0.417914i	$-0.862761\pi$
$37$	−0.561553	+	0.972638i	−0.0923187	+	0.159901i	0.816168	+	0.577815i	$0.196095\pi$
$38$	−8.26083	−	5.76506i	−1.34008	−	0.935217i
$39$	−1.62194	+	0.936426i	−0.259718	+	0.149948i
$40$	−6.63889	+	6.70149i	−1.04970	+	1.05960i
$41$			1.46228i			0.228370i	0.993460	+	0.114185i	$0.0364256\pi$
$41$			1.46228i			0.228370i	−0.993460	+	0.114185i	$0.963574\pi$
$42$		0			0
$43$			9.06897i			1.38300i	0.722374	+	0.691502i	$0.243051\pi$
$43$			9.06897i			1.38300i	−0.722374	+	0.691502i	$0.756949\pi$
$44$	−1.75789	+	0.646055i	−0.265012	+	0.0973965i
$45$	−2.88831	+	1.66757i	−0.430564	+	0.248586i
$46$	0.757894	−	1.08600i	0.111745	−	0.160121i
$47$	3.12311	−	5.40938i	0.455552	−	0.789039i	−0.543168	−	0.839624i	$-0.682775\pi$
$47$	3.12311	−	5.40938i	0.455552	−	0.789039i	0.998720	+	0.0505852i	$0.0161087\pi$
$48$	−0.719224	−	3.93481i	−0.103811	−	0.567941i
$49$		0			0
$50$	7.84233	−	3.67188i	1.10907	−	0.519283i
$51$	−4.51025	−	2.60399i	−0.631561	−	0.364632i
$52$	−0.638893	+	3.69082i	−0.0885985	+	0.511824i
$53$	−6.12311	−	10.6055i	−0.841073	−	1.45678i	−0.888988	−	0.457930i	$-0.848591\pi$
$53$	−6.12311	−	10.6055i	−0.841073	−	1.45678i	0.0479149	−	0.998851i	$-0.484742\pi$
$54$	0.121053	−	1.40902i	0.0164733	−	0.191744i
$55$	3.12311			0.421119
$56$		0			0
$57$	−7.12311			−0.943478
$58$	−0.242106	+	2.81805i	−0.0317901	+	0.370028i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	−1.13773	+	6.57252i	−0.146880	+	0.848509i
$61$	4.15468	+	2.39871i	0.531952	+	0.307123i	0.741811	−	0.670609i	$-0.233967\pi$
$61$	4.15468	+	2.39871i	0.531952	+	0.307123i	−0.209859	+	0.977732i	$0.567300\pi$
$62$		0			0
$63$		0			0
$64$	−6.96543	−	3.93481i	−0.870679	−	0.491851i
$65$	3.12311	−	5.40938i	0.387374	−	0.670951i
$66$	−0.757894	+	1.08600i	−0.0932903	+	0.133677i
$67$	−9.47590	+	5.47091i	−1.15766	+	0.668378i	−0.950743	−	0.309979i	$-0.899678\pi$
$67$	−9.47590	+	5.47091i	−1.15766	+	0.668378i	−0.206922	+	0.978358i	$0.566345\pi$
$68$	−9.77662	+	3.59307i	−1.18559	+	0.435724i
$69$		−	0.936426i		−	0.112732i
$70$		0			0
$71$		−	3.86098i		−	0.458215i	−0.973401	−	0.229107i	$-0.926419\pi$
$71$		−	3.86098i		−	0.458215i	0.973401	−	0.229107i	$-0.0735807\pi$
$72$	−2.00936	−	1.99059i	−0.236806	−	0.234594i
$73$	−5.77662	+	3.33513i	−0.676102	+	0.390348i	−0.798385	−	0.602148i	$-0.794312\pi$
$73$	−5.77662	+	3.33513i	−0.676102	+	0.390348i	0.122283	+	0.992495i	$0.460979\pi$
$74$	1.30249	+	0.908982i	0.151412	+	0.105667i
$75$	3.06155	−	5.30277i	0.353518	−	0.612311i
$76$	−9.12311	+	10.9418i	−1.04649	+	1.25511i
$77$		0			0
$78$	1.12311	+	2.39871i	0.127167	+	0.271600i
$79$	2.07734	+	1.19935i	0.233719	+	0.134938i	0.612287	−	0.790636i	$-0.290250\pi$
$79$	2.07734	+	1.19935i	0.233719	+	0.134938i	−0.378568	+	0.925574i	$0.623583\pi$
$80$	8.63889	+	10.1656i	0.965858	+	1.13655i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.06039	+	0.177014i	0.227531	+	0.0195479i
$83$	10.2462			1.12467			0.562334	−	0.826910i	$-0.309904\pi$
$83$	10.2462			1.12467			0.562334	+	0.826910i	$0.309904\pi$
$84$		0			0
$85$	17.3693			1.88397
$86$	12.7784	+	1.09783i	1.37793	+	0.118382i
$87$	1.00000	+	1.73205i	0.107211	+	0.185695i
$88$	0.697508	+	2.55512i	0.0743546	+	0.272377i
$89$	1.26637	+	0.731140i	0.134235	+	0.0775006i	0.565614	−	0.824670i	$-0.308639\pi$
$89$	1.26637	+	0.731140i	0.134235	+	0.0775006i	−0.431379	+	0.902171i	$0.641973\pi$
$90$	2.00000	+	4.27156i	0.210819	+	0.450262i
$91$		0			0
$92$	−1.43845	−	1.19935i	−0.149968	−	0.125041i
$93$		0			0
$94$	−7.24388	−	5.05535i	−0.747149	−	0.521420i
$95$	20.5737	−	11.8782i	2.11082	−	1.21868i
$96$	−5.63130	+	0.537082i	−0.574742	+	0.0548157i
$97$			10.4160i			1.05758i	0.848752	+	0.528791i	$0.177354\pi$
$97$			10.4160i			1.05758i	−0.848752	+	0.528791i	$0.822646\pi$
$98$		0			0
$99$			0.936426i			0.0941144i
$100$	−4.22443	−	11.4945i	−0.422443	−	1.14945i
$101$	−11.9088	+	6.87555i	−1.18497	+	0.684143i	−0.957159	−	0.289562i	$-0.906490\pi$
$101$	−11.9088	+	6.87555i	−1.18497	+	0.684143i	−0.227811	+	0.973705i	$0.573157\pi$
$102$	−4.21507	+	6.03982i	−0.417354	+	0.598031i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	5.12311	+	1.34700i	0.502362	+	0.132084i
$105$		0			0
$106$	−15.6847	+	7.34376i	−1.52343	+	0.713289i
$107$	8.20953	+	4.73977i	0.793645	+	0.458211i	0.841244	−	0.540655i	$-0.181824\pi$
$107$	8.20953	+	4.73977i	0.793645	+	0.458211i	−0.0475993	+	0.998867i	$0.515157\pi$
$108$	−1.97069	−	0.341134i	−0.189630	−	0.0328256i
$109$	4.12311	+	7.14143i	0.394922	+	0.684025i	0.993091	−	0.117345i	$-0.0374383\pi$
$109$	4.12311	+	7.14143i	0.394922	+	0.684025i	−0.598169	+	0.801370i	$0.704105\pi$
$110$	0.378062	−	4.40053i	0.0360468	−	0.419574i
$111$	1.12311			0.106600
$112$		0			0
$113$	−4.24621			−0.399450			−0.199725	−	0.979852i	$-0.564005\pi$
$113$	−4.24621			−0.399450			−0.199725	+	0.979852i	$0.564005\pi$
$114$	−0.862275	+	10.0366i	−0.0807594	+	0.940016i
$115$	1.56155	+	2.70469i	0.145616	+	0.252214i
$116$	3.94138	+	0.682267i	0.365948	+	0.0633469i
$117$	1.62194	+	0.936426i	0.149948	+	0.0865726i
$118$	5.12311	−	2.39871i	0.471620	−	0.220819i
$119$		0			0
$120$	9.12311	+	2.39871i	0.832822	+	0.218971i
$121$	−5.06155	+	8.76687i	−0.460141	+	0.796988i
$122$	3.88277	−	5.56367i	0.351529	−	0.503711i
$123$	1.26637	−	0.731140i	0.114185	−	0.0659246i
$124$		0			0
$125$			3.74571i			0.335026i
$126$		0			0
$127$		−	9.89012i		−	0.877606i	−0.898583	−	0.438803i	$-0.855403\pi$
$127$		−	9.89012i		−	0.877606i	0.898583	−	0.438803i	$-0.144597\pi$
$128$	−6.38742	+	9.33814i	−0.564574	+	0.825383i
$129$	7.85396	−	4.53448i	0.691502	−	0.399239i
$130$	−7.24388	−	5.05535i	−0.635330	−	0.443384i
$131$	2.87689	−	4.98293i	0.251355	−	0.435360i	−0.712544	−	0.701628i	$-0.752457\pi$
$131$	2.87689	−	4.98293i	0.251355	−	0.435360i	0.963899	+	0.266267i	$0.0857904\pi$
$132$	1.43845	+	1.19935i	0.125201	+	0.104390i
$133$		0			0
$134$	6.56155	+	14.0140i	0.566832	+	1.21063i
$135$	2.88831	+	1.66757i	0.248586	+	0.143521i
$136$	3.87923	+	14.2104i	0.332641	+	1.21853i
$137$	−0.123106	−	0.213225i	−0.0105176	−	0.0182171i	0.860719	−	0.509081i	$-0.170015\pi$
$137$	−0.123106	−	0.213225i	−0.0105176	−	0.0182171i	−0.871236	+	0.490864i	$0.836681\pi$
$138$	−1.31945	−	0.113357i	−0.112319	−	0.00964962i
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$	−6.24621			−0.526026
$142$	−5.44022	−	0.467385i	−0.456533	−	0.0392220i
$143$	−0.876894	−	1.51883i	−0.0733296	−	0.127011i
$144$	−3.04803	+	2.59027i	−0.254003	+	0.215856i
$145$	−5.77662	−	3.33513i	−0.479722	−	0.276968i
$146$	4.00000	+	8.54312i	0.331042	+	0.707033i
$147$		0			0
$148$	1.43845	−	1.72521i	0.118240	−	0.141811i
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	−7.10111	−	4.95572i	−0.579803	−	0.404632i
$151$	−7.85396	+	4.53448i	−0.639146	+	0.369011i	−0.784286	−	0.620400i	$-0.786970\pi$
$151$	−7.85396	+	4.53448i	−0.639146	+	0.369011i	0.145139	+	0.989411i	$0.453637\pi$
$152$	14.3129	+	14.1792i	1.16093	+	1.15009i
$153$			5.20798i			0.421041i
$154$		0			0
$155$		0			0
$156$	3.51579	−	1.29211i	0.281488	−	0.103452i
$157$	18.9518	−	10.9418i	1.51252	−	0.873252i	0.512625	−	0.858613i	$-0.328673\pi$
$157$	18.9518	−	10.9418i	1.51252	−	0.873252i	0.999893	−	0.0146398i	$-0.00466016\pi$
$158$	1.94138	−	2.78183i	0.154448	−	0.221311i
$159$	−6.12311	+	10.6055i	−0.485594	+	0.841073i
$160$	15.3693	−	10.9418i	1.21505	−	0.865027i
$161$		0			0
$162$	−1.28078	+	0.599676i	−0.100627	+	0.0471150i
$163$	−13.6306	−	7.86962i	−1.06763	−	0.616396i	−0.140096	−	0.990138i	$-0.544741\pi$
$163$	−13.6306	−	7.86962i	−1.06763	−	0.616396i	−0.927533	+	0.373742i	$0.878075\pi$
$164$	0.498832	−	2.88170i	0.0389523	−	0.225023i
$165$	−1.56155	−	2.70469i	−0.121567	−	0.210560i
$166$	1.24034	−	14.4371i	0.0962688	−	1.12054i
$167$	−14.2462			−1.10240			−0.551202	−	0.834372i	$-0.685831\pi$
$167$	−14.2462			−1.10240			−0.551202	+	0.834372i	$0.685831\pi$
$168$		0			0
$169$	9.49242			0.730186
$170$	2.10261	−	24.4738i	0.161263	−	1.87705i
$171$	3.56155	+	6.16879i	0.272359	+	0.471739i
$172$	3.09373	−	17.8721i	0.235895	−	1.36274i
$173$	−14.4415	−	8.33783i	−1.09797	−	0.633913i	−0.162283	−	0.986744i	$-0.551886\pi$
$173$	−14.4415	−	8.33783i	−1.09797	−	0.633913i	−0.935687	+	0.352831i	$0.885219\pi$
$174$	2.56155	−	1.19935i	0.194191	−	0.0909227i
$175$		0			0
$176$	3.68466	−	0.673500i	0.277742	−	0.0507670i
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	1.18349	−	1.69584i	0.0887064	−	0.127109i
$179$	−13.9861	+	8.07490i	−1.04537	+	0.603547i	−0.921351	−	0.388733i	$-0.872913\pi$
$179$	−13.9861	+	8.07490i	−1.04537	+	0.603547i	−0.124023	+	0.992279i	$0.539580\pi$
$180$	6.26083	−	2.30096i	0.466655	−	0.171503i
$181$			1.87285i			0.139208i	0.997575	+	0.0696040i	$0.0221736\pi$
$181$			1.87285i			0.139208i	−0.997575	+	0.0696040i	$0.977826\pi$
$182$		0			0
$183$		−	4.79741i		−	0.354635i
$184$	−1.86404	+	1.88162i	−0.137419	+	0.138715i
$185$	−3.24388	+	1.87285i	−0.238495	+	0.137695i
$186$		0			0
$187$	2.43845	−	4.22351i	0.178317	−	0.308854i
$188$	−8.00000	+	9.59482i	−0.583460	+	0.699774i
$189$		0			0
$190$	−14.2462	−	30.4268i	−1.03353	−	2.20739i
$191$	−2.43291	−	1.40464i	−0.176039	−	0.101636i	0.409391	−	0.912359i	$-0.365741\pi$
$191$	−2.43291	−	1.40464i	−0.176039	−	0.101636i	−0.585430	+	0.810723i	$0.699074\pi$
$192$	0.0750734	+	7.99965i	0.00541795	+	0.577325i
$193$	7.68466	+	13.3102i	0.553154	+	0.958091i	0.998045	+	0.0625057i	$0.0199092\pi$
$193$	7.68466	+	13.3102i	0.553154	+	0.958091i	−0.444891	+	0.895585i	$0.646758\pi$
$194$	14.6763	+	1.26089i	1.05370	+	0.0905264i
$195$	−6.24621			−0.447300
$196$		0			0
$197$	−16.2462			−1.15749			−0.578747	−	0.815507i	$-0.696458\pi$
$197$	−16.2462			−1.15749			−0.578747	+	0.815507i	$0.696458\pi$
$198$	1.31945	+	0.113357i	0.0937690	+	0.00805596i
$199$	−1.56155	−	2.70469i	−0.110696	−	0.191730i	0.805355	−	0.592792i	$-0.201975\pi$
$199$	−1.56155	−	2.70469i	−0.110696	−	0.191730i	−0.916051	+	0.401062i	$0.868641\pi$
$200$	−16.7074	+	4.56087i	−1.18139	+	0.322502i
$201$	9.47590	+	5.47091i	0.668378	+	0.385888i
$202$	8.24621	+	17.6121i	0.580201	+	1.23918i
$203$		0			0
$204$	8.00000	+	6.67026i	0.560112	+	0.467012i
$205$	−2.43845	+	4.22351i	−0.170309	+	0.294983i
$206$	9.27779	+	6.47477i	0.646414	+	0.451119i
$207$	−0.810969	+	0.468213i	−0.0563662	+	0.0325431i
$208$	2.51812	−	7.05552i	0.174600	−	0.489212i
$209$		−	6.67026i		−	0.461392i
$210$		0			0
$211$			12.8147i			0.882199i	0.897458	+	0.441099i	$0.145411\pi$
$211$			12.8147i			0.882199i	−0.897458	+	0.441099i	$0.854589\pi$
$212$	8.44886	+	22.9890i	0.580270	+	1.57889i
$213$	−3.34371	+	1.93049i	−0.229107	+	0.132275i
$214$	7.67224	−	10.9936i	0.524463	−	0.751510i
$215$	−15.1231	+	26.1940i	−1.03139	+	1.78642i
$216$	−0.719224	+	2.73546i	−0.0489370	+	0.186124i
$217$		0			0
$218$	10.5616	−	4.94506i	0.715319	−	0.334922i
$219$	5.77662	+	3.33513i	0.390348	+	0.225367i
$220$	−6.15468	−	1.06540i	−0.414948	−	0.0718290i
$221$	−4.87689	−	8.44703i	−0.328055	−	0.568209i
$222$	0.135956	−	1.58248i	0.00912474	−	0.106209i
$223$	−27.1231			−1.81630			−0.908149	−	0.418648i	$-0.862504\pi$
$223$	−27.1231			−1.81630			−0.908149	+	0.418648i	$0.862504\pi$
$224$		0			0
$225$	−6.12311			−0.408207
$226$	−0.514017	+	5.98301i	−0.0341919	+	0.397984i
$227$	−8.24621	−	14.2829i	−0.547320	−	0.947987i	−0.998457	−	0.0555316i	$-0.982315\pi$
$227$	−8.24621	−	14.2829i	−0.547320	−	0.947987i	0.451137	−	0.892455i	$-0.351019\pi$
$228$	14.0374	+	2.42993i	0.929653	+	0.160926i
$229$	4.86581	+	2.80928i	0.321542	+	0.185642i	0.652080	−	0.758150i	$-0.273897\pi$
$229$	4.86581	+	2.80928i	0.321542	+	0.185642i	−0.330538	+	0.943793i	$0.607230\pi$
$230$	4.00000	−	1.87285i	0.263752	−	0.123492i
$231$		0			0
$232$	1.43845	−	5.47091i	0.0944387	−	0.359183i
$233$	−11.2462	+	19.4790i	−0.736764	+	1.27611i	0.217181	+	0.976131i	$0.430314\pi$
$233$	−11.2462	+	19.4790i	−0.736764	+	1.27611i	−0.953945	+	0.299981i	$0.903020\pi$
$234$	1.51579	−	2.17199i	0.0990901	−	0.141987i
$235$	18.0410	−	10.4160i	1.17686	−	0.679463i
$236$	−2.75966	−	7.50895i	−0.179639	−	0.488791i
$237$		−	2.39871i		−	0.155813i
$238$		0			0
$239$			16.1498i			1.04464i	0.852748	+	0.522322i	$0.174934\pi$
$239$			16.1498i			1.04464i	−0.852748	+	0.522322i	$0.825066\pi$
$240$	4.48421	−	12.5643i	0.289455	−	0.811022i
$241$	−20.5737	+	11.8782i	−1.32527	+	0.765145i	−0.984564	−	0.175024i	$-0.944000\pi$
$241$	−20.5737	+	11.8782i	−1.32527	+	0.765145i	−0.340706	+	0.940170i	$0.610666\pi$
$242$	11.7400	+	8.19310i	0.754676	+	0.526673i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−7.36932	−	6.14441i	−0.471772	−	0.393356i
$245$		0			0
$246$	−0.876894	−	1.87285i	−0.0559087	−	0.119409i
$247$	−11.5532	−	6.67026i	−0.735115	−	0.424419i
$248$		0			0
$249$	−5.12311	−	8.87348i	−0.324664	−	0.562334i
$250$	5.27779	+	0.453430i	0.333796	+	0.0286774i
$251$	5.75379			0.363176			0.181588	−	0.983375i	$-0.441876\pi$
$251$	5.75379			0.363176			0.181588	+	0.983375i	$0.441876\pi$
$252$		0			0
$253$	0.876894			0.0551299
$254$	−13.9354	−	1.19723i	−0.874385	−	0.0751209i
$255$	−8.68466	−	15.0423i	−0.543854	−	0.941983i
$256$	12.3844	+	10.1304i	0.774027	+	0.633152i
$257$	1.97751	+	1.14171i	0.123353	+	0.0712181i	0.560407	−	0.828217i	$-0.310645\pi$
$257$	1.97751	+	1.14171i	0.123353	+	0.0712181i	−0.437054	+	0.899435i	$0.643978\pi$
$258$	−5.43845	−	11.6153i	−0.338583	−	0.723138i
$259$		0			0
$260$	−8.00000	+	9.59482i	−0.496139	+	0.595046i
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$	−6.67280	−	4.65681i	−0.412247	−	0.287699i
$263$	−21.3847	+	12.3465i	−1.31864	+	0.761315i	−0.983509	−	0.180857i	$-0.942113\pi$
$263$	−21.3847	+	12.3465i	−1.31864	+	0.761315i	−0.335128	+	0.942173i	$0.608779\pi$
$264$	1.86404	−	1.88162i	0.114724	−	0.115806i
$265$		−	40.8427i		−	2.50895i
$266$		0			0
$267$		−	1.46228i		−	0.0894900i
$268$	20.5404	−	7.54894i	1.25470	−	0.461125i
$269$	9.37606	−	5.41327i	0.571669	−	0.330053i	−0.186147	−	0.982522i	$-0.559600\pi$
$269$	9.37606	−	5.41327i	0.571669	−	0.330053i	0.757815	+	0.652469i	$0.226267\pi$
$270$	2.69928	−	3.86783i	0.164273	−	0.235389i
$271$	−14.2462	+	24.6752i	−0.865396	+	1.49891i	0.00125803	+	0.999999i	$0.499600\pi$
$271$	−14.2462	+	24.6752i	−0.865396	+	1.49891i	−0.866654	+	0.498910i	$0.833734\pi$
$272$	20.4924	−	3.74571i	1.24254	−	0.227117i
$273$		0			0
$274$	−0.315342	+	0.147647i	−0.0190505	+	0.00891969i
$275$	4.96565	+	2.86692i	0.299440	+	0.172882i
$276$	−0.319446	+	1.84541i	−0.0192284	+	0.111081i
$277$	2.56155	+	4.43674i	0.153909	+	0.266578i	0.932661	−	0.360754i	$-0.117480\pi$
$277$	2.56155	+	4.43674i	0.153909	+	0.266578i	−0.778752	+	0.627331i	$0.784147\pi$
$278$	1.45264	−	16.9083i	0.0871235	−	1.01409i
$279$		0			0
$280$		0			0
$281$	16.2462			0.969168			0.484584	−	0.874745i	$-0.338971\pi$
$281$	16.2462			0.969168			0.484584	+	0.874745i	$0.338971\pi$
$282$	−0.756124	+	8.80106i	−0.0450265	+	0.524095i
$283$	4.43845	+	7.68762i	0.263838	+	0.456981i	0.967259	−	0.253793i	$-0.0816781\pi$
$283$	4.43845	+	7.68762i	0.263838	+	0.456981i	−0.703420	+	0.710774i	$0.748345\pi$
$284$	−1.31711	+	7.60881i	−0.0781562	+	0.451500i
$285$	−20.5737	−	11.8782i	−1.21868	−	0.703607i
$286$	−2.24621	+	1.05171i	−0.132821	+	0.0621887i
$287$		0			0
$288$	3.28078	+	4.60831i	0.193322	+	0.271547i
$289$	5.06155	−	8.76687i	0.297738	−	0.515698i
$290$	−5.39856	+	7.73566i	−0.317014	+	0.454254i
$291$	9.02049	−	5.20798i	0.528791	−	0.305297i
$292$	12.5217	−	4.60192i	0.732775	−	0.269307i
$293$		−	13.7511i		−	0.803348i	−0.915783	−	0.401674i	$-0.868429\pi$
$293$		−	13.7511i		−	0.803348i	0.915783	−	0.401674i	$-0.131571\pi$
$294$		0			0
$295$			13.3405i			0.776716i
$296$	−2.25673	−	2.23565i	−0.131170	−	0.129944i
$297$	0.810969	−	0.468213i	0.0470572	−	0.0271685i
$298$	−11.5972	−	8.09347i	−0.671810	−	0.468842i
$299$	0.876894	−	1.51883i	0.0507121	−	0.0878360i
$300$	−7.84233	+	9.40572i	−0.452777	+	0.543039i
$301$		0			0
$302$	5.43845	+	11.6153i	0.312947	+	0.668387i
$303$	11.9088	+	6.87555i	0.684143	+	0.394990i
$304$	21.7115	−	18.4508i	1.24524	−	1.05822i
$305$	8.00000	+	13.8564i	0.458079	+	0.793416i
$306$	7.33817	+	0.630443i	0.419495	+	0.0360400i
$307$	−19.6155			−1.11952			−0.559759	−	0.828656i	$-0.689106\pi$
$307$	−19.6155			−1.11952			−0.559759	+	0.828656i	$0.689106\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	0.956864	−	0.290537i	$-0.0938340\pi$
$311$	4.00000	+	6.92820i	0.226819	+	0.392862i	−0.730044	+	0.683400i	$0.760501\pi$
$312$	−1.39502	−	5.11024i	−0.0789773	−	0.289310i
$313$	−19.8626	−	11.4677i	−1.12270	−	0.648191i	−0.180611	−	0.983555i	$-0.557808\pi$
$313$	−19.8626	−	11.4677i	−1.12270	−	0.648191i	−0.942089	+	0.335363i	$0.891141\pi$
$314$	−13.1231	−	28.0281i	−0.740580	−	1.58171i
$315$		0			0
$316$	−3.68466	−	3.07221i	−0.207278	−	0.172825i
$317$	7.24621	−	12.5508i	0.406988	−	0.704923i	−0.587563	−	0.809179i	$-0.699912\pi$
$317$	7.24621	−	12.5508i	0.406988	−	0.704923i	0.994551	+	0.104255i	$0.0332458\pi$
$318$	14.2022	+	9.91143i	0.796421	+	0.555805i
$319$	−1.62194	+	0.936426i	−0.0908111	+	0.0524298i
$320$	−13.5568	−	22.9803i	−0.757847	−	1.28464i
$321$		−	9.47954i		−	0.529097i
$322$		0			0
$323$		−	37.0970i		−	2.06413i
$324$	0.689916	+	1.87724i	0.0383287	+	0.104291i
$325$	9.93130	−	5.73384i	0.550889	−	0.318056i
$326$	−12.7385	+	18.2532i	−0.705520	+	1.01095i
$327$	4.12311	−	7.14143i	0.228008	−	0.394922i
$328$	−4.00000	−	1.05171i	−0.220863	−	0.0580707i
$329$		0			0
$330$	−4.00000	+	1.87285i	−0.220193	+	0.103097i
$331$	15.2525	+	8.80604i	0.838354	+	0.484024i	0.856704	−	0.515808i	$-0.172508\pi$
$331$	15.2525	+	8.80604i	0.838354	+	0.484024i	−0.0183504	+	0.999832i	$0.505841\pi$
$332$	−20.1921	−	3.49533i	−1.10819	−	0.191831i
$333$	−0.561553	−	0.972638i	−0.0307729	−	0.0533002i
$334$	−1.72455	+	20.0732i	−0.0943631	+	1.09836i
$335$	−36.4924			−1.99379
$336$		0			0
$337$	8.24621			0.449200			0.224600	−	0.974451i	$-0.427892\pi$
$337$	8.24621			0.449200			0.224600	+	0.974451i	$0.427892\pi$
$338$	1.14909	−	13.3750i	0.0625022	−	0.727506i
$339$	2.12311	+	3.67733i	0.115311	+	0.199725i
$340$	−34.2296	−	5.92526i	−1.85636	−	0.321342i
$341$		0			0
$342$	9.12311	−	4.27156i	0.493321	−	0.230979i
$343$		0			0
$344$	−24.8078	−	6.52262i	−1.33754	−	0.351676i
$345$	1.56155	−	2.70469i	0.0840712	−	0.145616i
$346$	−13.4964	+	19.3392i	−0.725570	+	1.03968i
$347$	17.4297	−	10.0630i	0.935675	−	0.540212i	0.0470729	−	0.998891i	$-0.485011\pi$
$347$	17.4297	−	10.0630i	0.935675	−	0.540212i	0.888602	+	0.458679i	$0.151677\pi$
$348$	−1.37983	−	3.75447i	−0.0739667	−	0.201261i
$349$			21.8836i			1.17140i	0.810526	+	0.585702i	$0.199181\pi$
$349$			21.8836i			1.17140i	−0.810526	+	0.585702i	$0.800819\pi$
$350$		0			0
$351$		−	1.87285i		−	0.0999655i
$352$	−0.502937	−	5.27330i	−0.0268066	−	0.281068i
$353$	25.0840	−	14.4822i	1.33509	−	0.770812i	0.349011	−	0.937119i	$-0.386517\pi$
$353$	25.0840	−	14.4822i	1.33509	−	0.770812i	0.986074	+	0.166307i	$0.0531841\pi$
$354$	−4.63889	−	3.23739i	−0.246554	−	0.172065i
$355$	6.43845	−	11.1517i	0.341717	−	0.591872i
$356$	−2.24621	−	1.87285i	−0.119049	−	0.0992610i
$357$		0			0
$358$	9.68466	+	20.6843i	0.511850	+	1.09320i
$359$	−19.7628	−	11.4100i	−1.04304	−	0.602199i	−0.122346	−	0.992487i	$-0.539042\pi$
$359$	−19.7628	−	11.4100i	−1.04304	−	0.602199i	−0.920692	+	0.390289i	$0.872375\pi$
$360$	−2.48421	−	9.10019i	−0.130930	−	0.479622i
$361$	−15.8693	−	27.4865i	−0.835227	−	1.44666i
$362$	2.63889	+	0.226715i	0.138697	+	0.0119159i
$363$	10.1231			0.531325
$364$		0			0
$365$	−22.2462			−1.16442
$366$	−6.75966	−	0.580742i	−0.353333	−	0.0303559i
$367$	−16.6847	−	28.8987i	−0.870932	−	1.50850i	−0.861034	−	0.508548i	$-0.830183\pi$
$367$	−16.6847	−	28.8987i	−0.870932	−	1.50850i	−0.00989821	−	0.999951i	$-0.503151\pi$
$368$	2.42560	+	2.85426i	0.126443	+	0.148788i
$369$	−1.26637	−	0.731140i	−0.0659246	−	0.0380616i
$370$	2.24621	+	4.79741i	0.116775	+	0.249406i
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−5.65585	−	3.94710i	−0.292457	−	0.204100i
$375$	3.24388	−	1.87285i	0.167513	−	0.0967137i
$376$	12.5509	+	12.4337i	0.647263	+	0.641218i
$377$			3.74571i			0.192914i
$378$		0			0
$379$		−	25.1035i		−	1.28948i	−0.764402	−	0.644740i	$-0.776966\pi$
$379$		−	25.1035i		−	1.28948i	0.764402	−	0.644740i	$-0.223034\pi$
$380$	−44.5966	+	16.3900i	−2.28776	+	0.840788i
$381$	−8.56509	+	4.94506i	−0.438803	+	0.253343i
$382$	−2.27368	+	3.25799i	−0.116332	+	0.166693i
$383$	−4.87689	+	8.44703i	−0.249198	+	0.431623i	−0.963303	−	0.268415i	$-0.913500\pi$
$383$	−4.87689	+	8.44703i	−0.249198	+	0.431623i	0.714106	+	0.700038i	$0.246834\pi$
$384$	11.2808	+	0.862603i	0.575670	+	0.0440195i
$385$		0			0
$386$	19.6847	−	9.21662i	1.00192	−	0.469113i
$387$	−7.85396	−	4.53448i	−0.399239	−	0.230501i
$388$	3.55324	−	20.5267i	0.180388	−	1.04208i
$389$	8.12311	+	14.0696i	0.411858	+	0.713359i	0.995093	−	0.0989447i	$-0.0315467\pi$
$389$	8.12311	+	14.0696i	0.411858	+	0.713359i	−0.583235	+	0.812303i	$0.698213\pi$
$390$	−0.756124	+	8.80106i	−0.0382878	+	0.445659i
$391$	4.87689			0.246635
$392$		0			0
$393$	−5.75379			−0.290240
$394$	−1.96666	+	22.8913i	−0.0990787	+	1.15325i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	0.319446	−	1.84541i	0.0160528	−	0.0927353i
$397$	15.7079	+	9.06897i	0.788358	+	0.455159i	0.839384	−	0.543539i	$-0.182916\pi$
$397$	15.7079	+	9.06897i	0.788358	+	0.455159i	−0.0510263	+	0.998697i	$0.516249\pi$
$398$	−4.00000	+	1.87285i	−0.200502	+	0.0938776i
$399$		0			0
$400$	4.40388	+	24.0932i	0.220194	+	1.20466i
$401$	−4.12311	+	7.14143i	−0.205898	+	0.356626i	−0.950418	−	0.310974i	$-0.899345\pi$
$401$	−4.12311	+	7.14143i	−0.205898	+	0.356626i	0.744520	+	0.667600i	$0.232678\pi$
$402$	8.85573	−	12.6895i	0.441684	−	0.632894i
$403$		0			0
$404$	25.8141	−	9.48710i	1.28430	−	0.472001i
$405$		−	3.33513i		−	0.165724i
$406$		0			0
$407$			1.05171i			0.0521311i
$408$	10.3670	−	10.4647i	0.513242	−	0.518081i
$409$	0.711134	−	0.410574i	0.0351633	−	0.0203016i	−0.482315	−	0.875998i	$-0.660204\pi$
$409$	0.711134	−	0.410574i	0.0351633	−	0.0203016i	0.517479	+	0.855696i	$0.326871\pi$
$410$	5.65585	+	3.94710i	0.279322	+	0.194933i
$411$	−0.123106	+	0.213225i	−0.00607235	+	0.0105176i
$412$	10.2462	−	12.2888i	0.504795	−	0.605427i
$413$		0			0
$414$	0.561553	+	1.19935i	0.0275988	+	0.0589450i
$415$	29.5942	+	17.0862i	1.45272	+	0.838730i
$416$	−9.63656	−	4.40219i	−0.472471	−	0.215835i
$417$	−6.00000	−	10.3923i	−0.293821	−	0.508913i
$418$	−9.39856	−	0.807457i	−0.459698	−	0.0394940i
$419$	16.4924			0.805708			0.402854	−	0.915264i	$-0.368018\pi$
$419$	16.4924			0.805708			0.402854	+	0.915264i	$0.368018\pi$
$420$		0			0
$421$	10.8769			0.530107			0.265054	−	0.964234i	$-0.414610\pi$
$421$	10.8769			0.530107			0.265054	+	0.964234i	$0.414610\pi$
$422$	18.0562	+	1.55126i	0.878961	+	0.0755140i
$423$	3.12311	+	5.40938i	0.151851	+	0.263013i
$424$	33.4148	−	9.12174i	1.62277	−	0.442991i
$425$	27.6167	+	15.9445i	1.33961	+	0.773423i
$426$	2.31534	+	4.94506i	0.112179	+	0.239589i
$427$		0			0
$428$	−14.5616	−	12.1412i	−0.703859	−	0.586866i
$429$	−0.876894	+	1.51883i	−0.0423369	+	0.0733296i
$430$	35.0772	+	24.4797i	1.69157	+	1.18051i
$431$	−4.05485	+	2.34107i	−0.195315	+	0.112765i	−0.594468	−	0.804119i	$-0.702637\pi$
$431$	−4.05485	+	2.34107i	−0.195315	+	0.112765i	0.399153	+	0.916884i	$0.369304\pi$
$432$	3.76726	+	1.34454i	0.181252	+	0.0646891i
$433$			13.3405i			0.641105i	0.947231	+	0.320552i	$0.103869\pi$
$433$			13.3405i			0.641105i	−0.947231	+	0.320552i	$0.896131\pi$
$434$		0			0
$435$			6.67026i			0.319815i
$436$	−5.68919	−	15.4801i	−0.272463	−	0.741362i
$437$	5.77662	−	3.33513i	0.276333	−	0.159541i
$438$	5.39856	−	7.73566i	0.257953	−	0.369624i
$439$	−3.31534	+	5.74234i	−0.158233	+	0.274067i	−0.934231	−	0.356667i	$-0.883913\pi$
$439$	−3.31534	+	5.74234i	−0.158233	+	0.274067i	0.775999	+	0.630734i	$0.217246\pi$
$440$	−2.24621	+	8.54312i	−0.107084	+	0.407277i
$441$		0			0
$442$	−12.4924	+	5.84912i	−0.594204	+	0.278214i
$443$	−16.3192	−	9.42190i	−0.775349	−	0.447648i	0.0594302	−	0.998232i	$-0.481072\pi$
$443$	−16.3192	−	9.42190i	−0.775349	−	0.447648i	−0.834780	+	0.550584i	$0.814405\pi$
$444$	−2.21330	−	0.383129i	−0.105038	−	0.0181825i
$445$	2.43845	+	4.22351i	0.115593	+	0.200214i
$446$	−3.28334	+	38.2171i	−0.155471	+	1.80963i
$447$	−10.0000			−0.472984
$448$		0			0
$449$	11.7538			0.554696			0.277348	−	0.960770i	$-0.410545\pi$
$449$	11.7538			0.554696			0.277348	+	0.960770i	$0.410545\pi$
$450$	−0.741222	+	8.62760i	−0.0349415	+	0.406709i
$451$	0.684658	+	1.18586i	0.0322393	+	0.0558401i
$452$	8.36798	+	1.44852i	0.393596	+	0.0681329i
$453$	7.85396	+	4.53448i	0.369011	+	0.213049i
$454$	−21.1231	+	9.89012i	−0.991356	+	0.464166i
$455$		0			0
$456$	5.12311	−	19.4849i	0.239911	−	0.912466i
$457$	−0.123106	+	0.213225i	−0.00575864	+	0.00997425i	−0.868890	−	0.495005i	$-0.835166\pi$
$457$	−0.123106	+	0.213225i	−0.00575864	+	0.00997425i	0.863132	+	0.504979i	$0.168500\pi$
$458$	4.54736	−	6.51597i	0.212484	−	0.304471i
$459$	4.51025	−	2.60399i	0.210520	−	0.121544i
$460$	−2.15468	−	5.86281i	−0.100462	−	0.273355i
$461$			6.25969i			0.291543i	0.989318	+	0.145771i	$0.0465664\pi$
$461$			6.25969i			0.291543i	−0.989318	+	0.145771i	$0.953434\pi$
$462$		0			0
$463$			39.2652i			1.82481i	0.409292	+	0.912404i	$0.365776\pi$
$463$			39.2652i			1.82481i	−0.409292	+	0.912404i	$0.634224\pi$
$464$	−7.53451	−	2.68908i	−0.349781	−	0.124837i
$465$		0			0
$466$	26.0850	+	18.2042i	1.20836	+	0.843292i
$467$	17.1231	−	29.6581i	0.792363	−	1.37241i	−0.132137	−	0.991231i	$-0.542184\pi$
$467$	17.1231	−	29.6581i	0.792363	−	1.37241i	0.924500	−	0.381181i	$-0.124483\pi$
$468$	−2.87689	−	2.39871i	−0.132984	−	0.110880i
$469$		0			0
$470$	−12.4924	−	26.6811i	−0.576232	−	1.23071i
$471$	−18.9518	−	10.9418i	−0.873252	−	0.504173i
$472$	−10.9143	+	2.97945i	−0.502373	+	0.137140i
$473$	4.24621	+	7.35465i	0.195241	+	0.338167i
$474$	−3.37983	−	0.290371i	−0.155241	−	0.0133372i
$475$	43.6155			2.00122
$476$		0			0
$477$	12.2462			0.560715
$478$	22.7555	+	1.95499i	1.04081	+	0.0894190i
$479$	6.24621	+	10.8188i	0.285397	+	0.494322i	0.972705	−	0.232044i	$-0.0745413\pi$
$479$	6.24621	+	10.8188i	0.285397	+	0.494322i	−0.687309	+	0.726366i	$0.741208\pi$
$480$	−17.1606	−	7.83931i	−0.783269	−	0.357814i
$481$	1.82161	+	1.05171i	0.0830582	+	0.0479537i
$482$	14.2462	+	30.4268i	0.648897	+	1.38590i
$483$		0			0
$484$	12.9654	−	15.5501i	0.589338	−	0.706824i
$485$	−17.3693	+	30.0845i	−0.788700	+	1.36607i
$486$	1.15972	+	0.809347i	0.0526061	+	0.0367127i
$487$	−1.36621	+	0.788779i	−0.0619087	+	0.0357430i	−0.530635	−	0.847601i	$-0.678046\pi$
$487$	−1.36621	+	0.788779i	−0.0619087	+	0.0357430i	0.468726	+	0.883344i	$0.344713\pi$
$488$	−9.54970	+	9.63974i	−0.432294	+	0.436370i
$489$			15.7392i			0.711753i
$490$		0			0
$491$			11.3524i			0.512326i	0.966634	+	0.256163i	$0.0824585\pi$
$491$			11.3524i			0.512326i	−0.966634	+	0.256163i	$0.917542\pi$
$492$	−2.74504	+	1.00885i	−0.123756	+	0.0454825i
$493$	−9.02049	+	5.20798i	−0.406263	+	0.234556i
$494$	−10.7971	+	15.4713i	−0.485785	+	0.696088i
$495$	−1.56155	+	2.70469i	−0.0701866	+	0.121567i
$496$		0			0
$497$		0			0
$498$	−13.1231	+	6.14441i	−0.588060	+	0.275338i
$499$	12.0086	+	6.93319i	0.537580	+	0.310372i	0.744098	−	0.668071i	$-0.232880\pi$
$499$	12.0086	+	6.93319i	0.537580	+	0.310372i	−0.206517	+	0.978443i	$0.566213\pi$
$500$	1.27779	−	7.38163i	0.0571443	−	0.330117i
$501$	7.12311	+	12.3376i	0.318237	+	0.551202i
$502$	0.696515	−	8.10722i	0.0310870	−	0.361843i
$503$	26.7386			1.19222			0.596108	−	0.802904i	$-0.296713\pi$
$503$	26.7386			1.19222			0.596108	+	0.802904i	$0.296713\pi$
$504$		0			0
$505$	−45.8617			−2.04082
$506$	0.106151	−	1.23556i	0.00471898	−	0.0549275i
$507$	−4.74621	−	8.22068i	−0.210787	−	0.365093i
$508$	−3.37385	+	19.4904i	−0.149690	+	0.864746i
$509$	−2.88831	−	1.66757i	−0.128022	−	0.0739136i	0.434621	−	0.900613i	$-0.356882\pi$
$509$	−2.88831	−	1.66757i	−0.128022	−	0.0739136i	−0.562643	+	0.826700i	$0.690216\pi$
$510$	−22.2462	+	10.4160i	−0.985079	+	0.461227i
$511$		0			0
$512$	15.7732	−	16.2236i	0.697083	−	0.716990i
$513$	3.56155	−	6.16879i	0.157246	−	0.272359i
$514$	1.84808	−	2.64814i	0.0815155	−	0.116805i
$515$	−23.1065	+	13.3405i	−1.01819	+	0.587854i
$516$	−17.0246	+	6.25683i	−0.749466	+	0.275441i
$517$		−	5.84912i		−	0.257244i
$518$		0			0
$519$			16.6757i			0.731980i
$520$	12.5509	+	12.4337i	0.550393	+	0.545252i
$521$	−25.7951	+	14.8928i	−1.13010	+	0.652466i	−0.943961	−	0.330057i	$-0.892932\pi$
$521$	−25.7951	+	14.8928i	−1.13010	+	0.652466i	−0.186143	+	0.982523i	$0.559599\pi$
$522$	−2.31945	−	1.61869i	−0.101519	−	0.0708483i
$523$	16.2462	−	28.1393i	0.710397	−	1.23044i	−0.254311	−	0.967123i	$-0.581849\pi$
$523$	16.2462	−	28.1393i	0.710397	−	1.23044i	0.964708	−	0.263322i	$-0.0848180\pi$
$524$	−7.36932	+	8.83841i	−0.321930	+	0.386108i
$525$		0			0
$526$	14.8078	+	31.6261i	0.645649	+	1.37896i
$527$		0			0
$528$	−2.42560	−	2.85426i	−0.105561	−	0.124216i
$529$	−11.0616	−	19.1592i	−0.480937	−	0.833007i
$530$	−57.5484	−	4.94414i	−2.49974	−	0.214760i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	2.73863			0.118623
$534$	−2.06039	−	0.177014i	−0.0891616	−	0.00766013i
$535$	15.8078	+	27.3799i	0.683429	+	1.18373i
$536$	−8.15015	−	29.8557i	−0.352033	−	1.28957i
$537$	13.9861	+	8.07490i	0.603547	+	0.348458i
$538$	−6.49242	−	13.8664i	−0.279908	−	0.597822i
$539$		0			0
$540$	−5.12311	−	4.27156i	−0.220463	−	0.183819i
$541$	−1.43845	+	2.49146i	−0.0618437	+	0.107116i	−0.895290	−	0.445485i	$-0.853031\pi$
$541$	−1.43845	+	2.49146i	−0.0618437	+	0.107116i	0.833446	+	0.552601i	$0.186365\pi$
$542$	33.0433	+	23.0602i	1.41933	+	0.990522i
$543$	1.62194	−	0.936426i	0.0696040	−	0.0401859i
$544$	−2.79711	−	29.3277i	−0.119925	−	1.25742i
$545$			27.5022i			1.17806i
$546$		0			0
$547$		−	16.7909i		−	0.717929i	−0.933351	−	0.358964i	$-0.883130\pi$
$547$		−	16.7909i		−	0.717929i	0.933351	−	0.358964i	$-0.116870\pi$
$548$	0.169865	+	0.462197i	0.00725627	+	0.0197441i
$549$	−4.15468	+	2.39871i	−0.177317	+	0.102374i
$550$	4.64066	−	6.64966i	0.197879	−	0.283543i
$551$	−7.12311	+	12.3376i	−0.303455	+	0.525599i
$552$	2.56155	+	0.673500i	0.109027	+	0.0286661i
$553$		0			0
$554$	6.56155	−	3.07221i	0.278774	−	0.130526i
$555$	3.24388	+	1.87285i	0.137695	+	0.0794982i
$556$	−23.6483	−	4.09360i	−1.00291	−	0.173607i
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	0.678756	−	0.734364i	$-0.262519\pi$
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	−0.975356	+	0.220638i	$0.929186\pi$
$558$		0			0
$559$	16.9848			0.718382
$560$		0			0
$561$	−4.87689			−0.205903
$562$	1.96666	−	22.8913i	0.0829584	−	0.965611i
$563$	1.12311	+	1.94528i	0.0473333	+	0.0819836i	0.888721	−	0.458448i	$-0.151594\pi$
$563$	1.12311	+	1.94528i	0.0473333	+	0.0819836i	−0.841388	+	0.540431i	$0.818261\pi$
$564$	12.3094	+	2.13079i	0.518318	+	0.0897225i
$565$	−12.2644	−	7.08084i	−0.515966	−	0.297893i
$566$	11.3693	−	5.32326i	0.477888	−	0.223753i
$567$		0			0
$568$	10.5616	+	2.77691i	0.443153	+	0.116517i
$569$	15.4924	−	26.8337i	0.649476	−	1.12493i	−0.333772	−	0.942654i	$-0.608322\pi$
$569$	15.4924	−	26.8337i	0.649476	−	1.12493i	0.983248	−	0.182272i	$-0.0583451\pi$
$570$	−19.2272	+	27.5510i	−0.805341	+	1.15398i
$571$	−7.65429	+	4.41921i	−0.320322	+	0.184938i	−0.651536	−	0.758618i	$-0.725875\pi$
$571$	−7.65429	+	4.41921i	−0.320322	+	0.184938i	0.331214	+	0.943556i	$0.392542\pi$
$572$	1.20997	+	3.29228i	0.0505912	+	0.137657i
$573$			2.80928i			0.117359i
$574$		0			0
$575$			5.73384i			0.239118i
$576$	6.89036	−	4.06484i	0.287098	−	0.169368i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−11.7400	−	8.19310i	−0.488320	−	0.340788i
$579$	7.68466	−	13.3102i	0.319364	−	0.553154i
$580$	10.2462	+	8.54312i	0.425451	+	0.354734i
$581$		0			0
$582$	−6.24621	−	13.3405i	−0.258914	−	0.552983i
$583$	−9.93130	−	5.73384i	−0.411312	−	0.237471i
$584$	−4.96843	−	18.2004i	−0.205595	−	0.753137i
$585$	3.12311	+	5.40938i	0.129125	+	0.223650i
$586$	−19.3756	−	1.66461i	−0.800399	−	0.0687646i
$587$	21.7538			0.897875			0.448937	−	0.893563i	$-0.351803\pi$
$587$	21.7538			0.897875			0.448937	+	0.893563i	$0.351803\pi$
$588$		0			0
$589$		0			0
$590$	18.7971	+	1.61491i	0.773865	+	0.0664849i
$591$	8.12311	+	14.0696i	0.334140	+	0.578747i
$592$	−3.42326	+	2.90915i	−0.140695	+	0.119565i
$593$	−22.5512	−	13.0200i	−0.926068	−	0.534666i	−0.0405023	−	0.999179i	$-0.512896\pi$
$593$	−22.5512	−	13.0200i	−0.926068	−	0.534666i	−0.885566	+	0.464514i	$0.846229\pi$
$594$	−0.561553	−	1.19935i	−0.0230408	−	0.0492100i
$595$		0			0
$596$	−12.8078	+	15.3610i	−0.524626	+	0.629212i
$597$	−1.56155	+	2.70469i	−0.0639101	+	0.110696i
$598$	−2.03391	−	1.41942i	−0.0831727	−	0.0580445i
$599$	−14.8969	+	8.60076i	−0.608673	+	0.351417i	−0.772446	−	0.635081i	$-0.780967\pi$
$599$	−14.8969	+	8.60076i	−0.608673	+	0.351417i	0.163773	+	0.986498i	$0.447634\pi$
$600$	12.3035	+	12.1886i	0.502290	+	0.497598i
$601$			17.0862i			0.696962i	0.937316	+	0.348481i	$0.113302\pi$
$601$			17.0862i			0.696962i	−0.937316	+	0.348481i	$0.886698\pi$
$602$		0			0
$603$		−	10.9418i		−	0.445585i
$604$	17.0246	−	6.25683i	0.692721	−	0.254587i
$605$	−29.2387	+	16.8809i	−1.18872	+	0.686308i
$606$	11.1294	−	15.9475i	0.452101	−	0.647822i
$607$	3.80776	−	6.59524i	0.154552	−	0.267693i	−0.778344	−	0.627839i	$-0.783940\pi$
$607$	3.80776	−	6.59524i	0.154552	−	0.267693i	0.932896	+	0.360146i	$0.117273\pi$
$608$	−23.3693	−	32.8255i	−0.947751	−	1.33125i
$609$		0			0
$610$	20.4924	−	9.59482i	0.829714	−	0.388483i
$611$	−10.1310	−	5.84912i	−0.409855	−	0.236630i
$612$	1.77662	−	10.2633i	0.0718155	−	0.414871i
$613$	−4.36932	−	7.56788i	−0.176475	−	0.305664i	0.764196	−	0.644984i	$-0.223136\pi$
$613$	−4.36932	−	7.56788i	−0.176475	−	0.305664i	−0.940671	+	0.339321i	$0.889803\pi$
$614$	−2.37452	+	27.6387i	−0.0958279	+	1.11541i
$615$	4.87689			0.196655
$616$		0			0
$617$	32.2462			1.29818			0.649092	−	0.760710i	$-0.275149\pi$
$617$	32.2462			1.29818			0.649092	+	0.760710i	$0.275149\pi$
$618$	0.968426	−	11.2722i	0.0389558	−	0.453434i
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$		0			0
$621$	0.810969	+	0.468213i	0.0325431	+	0.0187887i
$622$	10.2462	−	4.79741i	0.410836	−	0.192359i
$623$		0			0
$624$	−7.36932	+	1.34700i	−0.295009	+	0.0539232i
$625$	9.06155	−	15.6951i	0.362462	−	0.627803i
$626$	−18.5627	+	26.5987i	−0.741913	+	1.06310i
$627$	−5.77662	+	3.33513i	−0.230696	+	0.133192i
$628$	−41.0808	+	15.0979i	−1.63930	+	0.602471i
$629$			5.84912i			0.233220i
$630$		0			0
$631$		−	40.3169i		−	1.60499i	−0.596659	−	0.802495i	$-0.703506\pi$
$631$		−	40.3169i		−	1.60499i	0.596659	−	0.802495i	$-0.296494\pi$
$632$	−4.77485	+	4.81987i	−0.189933	+	0.191724i
$633$	11.0978	−	6.40734i	0.441099	−	0.254669i
$634$	−16.8072	−	11.7294i	−0.667499	−	0.465834i
$635$	16.4924	−	28.5657i	0.654482	−	1.13360i
$636$	15.6847	−	18.8114i	0.621937	−	0.745922i
$637$		0			0
$638$	1.12311	+	2.39871i	0.0444642	+	0.0949657i
$639$	3.34371	+	1.93049i	0.132275	+	0.0763691i
$640$	−34.0208	+	16.3200i	−1.34479	+	0.645104i
$641$	21.2462	+	36.7995i	0.839175	+	1.45349i	0.890585	+	0.454816i	$0.150295\pi$
$641$	21.2462	+	36.7995i	0.839175	+	1.45349i	−0.0514106	+	0.998678i	$0.516372\pi$
$642$	−13.3569	−	1.14753i	−0.527155	−	0.0452894i
$643$	11.6155			0.458072			0.229036	−	0.973418i	$-0.426443\pi$
$643$	11.6155			0.458072			0.229036	+	0.973418i	$0.426443\pi$
$644$		0			0
$645$	30.2462			1.19094
$646$	−52.2706	−	4.49071i	−2.05656	−	0.176685i
$647$	−16.4924	−	28.5657i	−0.648384	−	1.12303i	−0.983509	−	0.180860i	$-0.942112\pi$
$647$	−16.4924	−	28.5657i	−0.648384	−	1.12303i	0.335125	−	0.942174i	$-0.391222\pi$
$648$	2.72859	−	0.744862i	0.107189	−	0.0292609i
$649$	3.24388	+	1.87285i	0.127333	+	0.0735159i
$650$	−6.87689	−	14.6875i	−0.269734	−	0.576092i
$651$		0			0
$652$	24.1771	+	20.1584i	0.946848	+	0.789465i
$653$	−8.36932	+	14.4961i	−0.327517	+	0.567276i	−0.982018	−	0.188785i	$-0.939545\pi$
$653$	−8.36932	+	14.4961i	−0.327517	+	0.567276i	0.654502	+	0.756060i	$0.272878\pi$
$654$	−9.56332	−	6.67404i	−0.373956	−	0.260976i
$655$	16.6187	−	9.59482i	0.649347	−	0.374901i
$656$	−1.96609	+	5.50878i	−0.0767629	+	0.215082i
$657$		−	6.67026i		−	0.260232i
$658$		0			0
$659$			26.7963i			1.04384i	0.852995	+	0.521919i	$0.174783\pi$
$659$			26.7963i			1.04384i	−0.852995	+	0.521919i	$0.825217\pi$
$660$	2.15468	+	5.86281i	0.0838708	+	0.228209i
$661$	−7.39856	+	4.27156i	−0.287770	+	0.166144i	−0.636936	−	0.770917i	$-0.719798\pi$
$661$	−7.39856	+	4.27156i	−0.287770	+	0.166144i	0.349165	+	0.937061i	$0.386465\pi$
$662$	14.2543	−	20.4251i	0.554008	−	0.793846i
$663$	−4.87689	+	8.44703i	−0.189403	+	0.328055i
$664$	−7.36932	+	28.0281i	−0.285985	+	1.08770i
$665$		0			0
$666$	−1.43845	+	0.673500i	−0.0557387	+	0.0260976i
$667$	−1.62194	−	0.936426i	−0.0628017	−	0.0362586i
$668$	28.0749	+	4.85986i	1.08625	+	0.188034i
$669$	13.5616	+	23.4893i	0.524320	+	0.908149i
$670$	−4.41752	+	51.4187i	−0.170664	+	1.98648i
$671$	4.49242			0.173428
$672$		0			0
$673$	−27.8617			−1.07399			−0.536996	−	0.843585i	$-0.680441\pi$
$673$	−27.8617			−1.07399			−0.536996	+	0.843585i	$0.680441\pi$
$674$	0.998230	−	11.6191i	0.0384504	−	0.447551i
$675$	3.06155	+	5.30277i	0.117839	+	0.204104i
$676$	−18.7066	−	3.23818i	−0.719486	−	0.124546i
$677$	7.95379	+	4.59212i	0.305689	+	0.176490i	0.644996	−	0.764186i	$-0.276859\pi$
$677$	7.95379	+	4.59212i	0.305689	+	0.176490i	−0.339307	+	0.940676i	$0.610192\pi$
$678$	5.43845	−	2.54635i	0.208862	−	0.0977921i
$679$		0			0
$680$	−12.4924	+	47.5130i	−0.479063	+	1.82204i
$681$	−8.24621	+	14.2829i	−0.315996	+	0.547320i
$682$		0			0
$683$	27.8725	−	16.0922i	1.06651	−	0.615750i	0.139284	−	0.990252i	$-0.455520\pi$
$683$	27.8725	−	16.0922i	1.06651	−	0.615750i	0.927226	+	0.374503i	$0.122187\pi$
$684$	−4.91434	−	13.3718i	−0.187905	−	0.511282i
$685$		−	0.821147i		−	0.0313744i
$686$		0			0
$687$		−	5.61856i		−	0.214361i
$688$	−12.1936	+	34.1651i	−0.464876	+	1.30253i
$689$	−19.8626	+	11.4677i	−0.756705	+	0.436884i
$690$	−3.62194	−	2.52768i	−0.137885	−	0.0962270i
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$	25.6155	+	21.3578i	0.973756	+	0.811901i
$693$		0			0
$694$	−12.0691	−	25.7770i	−0.458138	−	0.978481i
$695$	34.6597	+	20.0108i	1.31472	+	0.759053i
$696$	−5.45717	+	1.48972i	−0.206854	+	0.0564678i
$697$	3.80776	+	6.59524i	0.144229	+	0.249813i
$698$	30.8346	+	2.64909i	1.16711	+	0.100269i
$699$	22.4924			0.850742
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$	−2.63889	−	0.226715i	−0.0995986	−	0.00855680i
$703$	4.00000	+	6.92820i	0.150863	+	0.261302i
$704$	−7.49108	+	0.0703007i	−0.282331	+	0.00264956i
$705$	−18.0410	−	10.4160i	−0.679463	−	0.392288i
$706$	−17.3693	−	37.0970i	−0.653703	−	1.39616i
$707$		0			0
$708$	−5.12311	+	6.14441i	−0.192538	+	0.230921i
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$	−14.9336	−	10.4219i	−0.560449	−	0.391126i
$711$	−2.07734	+	1.19935i	−0.0779063	+	0.0449792i
$712$	−2.91080	+	2.93825i	−0.109087	+	0.110116i
$713$		0			0
$714$		0			0
$715$		−	5.84912i		−	0.218745i
$716$	30.3170	−	11.1420i	1.13300	−	0.416396i
$717$	13.9861	−	8.07490i	0.522322	−	0.301563i
$718$	−18.4693	+	26.4650i	−0.689270	+	0.987664i
$719$	14.2462	−	24.6752i	0.531294	−	0.920228i	−0.468039	−	0.883708i	$-0.655039\pi$
$719$	14.2462	−	24.6752i	0.531294	−	0.920228i	0.999333	−	0.0365204i	$-0.0116274\pi$
$720$	−13.1231	+	2.39871i	−0.489069	+	0.0893945i
$721$		0			0
$722$	−40.6501	+	19.0329i	−1.51284	+	0.708332i
$723$	20.5737	+	11.8782i	0.765145	+	0.441757i
$724$	0.638893	−	3.69082i	0.0237443	−	0.137168i
$725$	−6.12311	−	10.6055i	−0.227406	−	0.393879i
$726$	1.22543	−	14.2637i	0.0454801	−	0.529375i
$727$	−32.9848			−1.22334			−0.611670	−	0.791113i	$-0.709502\pi$
$727$	−32.9848			−1.22334			−0.611670	+	0.791113i	$0.709502\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−2.69298	+	31.3454i	−0.0996715	+	1.16015i
$731$	23.6155	+	40.9033i	0.873452	+	1.51286i
$732$	−1.63656	+	9.45422i	−0.0604889	+	0.349438i
$733$	31.2162	+	18.0227i	1.15300	+	0.665682i	0.949615	−	0.313418i	$-0.101474\pi$
$733$	31.2162	+	18.0227i	1.15300	+	0.665682i	0.203380	+	0.979100i	$0.434807\pi$
$734$	−42.7386	+	20.0108i	−1.57751	+	0.738612i
$735$		0			0
$736$	4.31534	−	3.07221i	0.159066	−	0.113243i
$737$	−5.12311	+	8.87348i	−0.188712	+	0.326859i
$738$	−1.18349	+	1.69584i	−0.0435649	+	0.0624247i
$739$	31.6716	−	18.2856i	1.16506	−	0.672646i	0.212547	−	0.977151i	$-0.431824\pi$
$739$	31.6716	−	18.2856i	1.16506	−	0.672646i	0.952511	+	0.304505i	$0.0984910\pi$
$740$	7.03157	−	2.58422i	0.258486	−	0.0949979i
$741$			13.3405i			0.490077i
$742$		0			0
$743$		−	35.1089i		−	1.28802i	−0.765017	−	0.644010i	$-0.777269\pi$
$743$		−	35.1089i		−	1.28802i	0.765017	−	0.644010i	$-0.222731\pi$
$744$		0			0
$745$	28.8831	−	16.6757i	1.05819	−	0.610949i
$746$	−11.5972	−	8.09347i	−0.424605	−	0.296323i
$747$	−5.12311	+	8.87348i	−0.187445	+	0.324664i
$748$	−6.24621	+	7.49141i	−0.228384	+	0.273913i
$749$		0			0
$750$	−2.24621	−	4.79741i	−0.0820200	−	0.175177i
$751$	−24.9841	−	14.4246i	−0.911684	−	0.526361i	−0.0307116	−	0.999528i	$-0.509777\pi$
$751$	−24.9841	−	14.4246i	−0.911684	−	0.526361i	−0.880973	+	0.473167i	$0.843111\pi$
$752$	19.0387	−	16.1794i	0.694268	−	0.590001i
$753$	−2.87689	−	4.98293i	−0.104840	−	0.181588i
$754$	5.27779	+	0.453430i	0.192206	+	0.0165129i
$755$	−30.2462			−1.10077
$756$		0			0
$757$	−34.9848			−1.27155			−0.635773	−	0.771876i	$-0.719319\pi$
$757$	−34.9848			−1.27155			−0.635773	+	0.771876i	$0.719319\pi$
$758$	−35.3714	−	3.03886i	−1.28475	−	0.110376i
$759$	−0.438447	−	0.759413i	−0.0159146	−	0.0275649i
$760$	17.6953	+	64.8216i	0.641876	+	2.35133i
$761$	−25.7951	−	14.8928i	−0.935072	−	0.539864i	−0.0466599	−	0.998911i	$-0.514858\pi$
$761$	−25.7951	−	14.8928i	−0.935072	−	0.539864i	−0.888412	+	0.459047i	$0.848191\pi$
$762$	5.93087	+	12.6670i	0.214853	+	0.458878i
$763$		0			0
$764$	4.31534	+	3.59806i	0.156124	+	0.130173i
$765$	−8.68466	+	15.0423i	−0.313994	+	0.543854i
$766$	11.3117	+	7.89420i	0.408708	+	0.285229i
$767$	6.48775	−	3.74571i	0.234259	−	0.135250i
$768$	2.58100	−	15.7905i	0.0931339	−	0.569789i
$769$			32.5302i			1.17307i	0.809925	+	0.586534i	$0.199508\pi$
$769$			32.5302i			1.17307i	−0.809925	+	0.586534i	$0.800492\pi$
$770$		0			0
$771$		−	2.28343i		−	0.0822356i
$772$	−10.6035	−	28.8518i	−0.381630	−	1.03840i
$773$	−2.88831	+	1.66757i	−0.103885	+	0.0599782i	−0.551042	−	0.834477i	$-0.685770\pi$
$773$	−2.88831	+	1.66757i	−0.103885	+	0.0599782i	0.447157	+	0.894455i	$0.352436\pi$
$774$	−7.33994	+	10.5175i	−0.263829	+	0.378044i
$775$		0			0
$776$	−28.4924	−	7.49141i	−1.02282	−	0.268926i
$777$		0			0
$778$	20.8078	−	9.74247i	0.745994	−	0.349284i
$779$	9.02049	+	5.20798i	0.323193	+	0.186595i
$780$	12.3094	+	2.13079i	0.440746	+	0.0762946i
$781$	−1.80776	−	3.13114i	−0.0646869	−	0.112041i
$782$	0.590364	−	6.87166i	0.0211114	−	0.245730i
$783$	−2.00000			−0.0714742
$784$		0			0
$785$	72.9848			2.60494
$786$	−0.696515	+	8.10722i	−0.0248439	+	0.289175i
$787$	−22.4924	−	38.9580i	−0.801768	−	1.38870i	−0.918451	−	0.395534i	$-0.870559\pi$
$787$	−22.4924	−	38.9580i	−0.801768	−	1.38870i	0.116683	−	0.993169i	$-0.462774\pi$
$788$	32.0163	+	5.54213i	1.14053	+	0.197430i
$789$	21.3847	+	12.3465i	0.761315	+	0.439546i
$790$	10.2462	−	4.79741i	0.364544	−	0.170684i
$791$		0			0
$792$	−2.56155	−	0.673500i	−0.0910208	−	0.0239318i
$793$	4.49242	−	7.78110i	0.159531	−	0.276315i
$794$	14.6799	−	21.0350i	0.520969	−	0.746504i
$795$	−35.3708	+	20.4214i	−1.25447	+	0.724271i
$796$	2.15468	+	5.86281i	0.0763706	+	0.207802i
$797$		−	39.6110i		−	1.40309i	−0.712623	−	0.701547i	$-0.752493\pi$
$797$		−	39.6110i		−	1.40309i	0.712623	−	0.701547i	$-0.247507\pi$
$798$		0			0
$799$		−	32.5302i		−	1.15083i
$800$	34.4810	−	3.28861i	1.21909	−	0.116270i
$801$	−1.26637	+	0.731140i	−0.0447450	+	0.0258335i
$802$	9.56332	+	6.67404i	0.337693	+	0.235669i
$803$	−3.12311	+	5.40938i	−0.110212	+	0.190893i
$804$	−16.8078	−	14.0140i	−0.592764	−	0.494237i
$805$		0			0
$806$		0			0
$807$	−9.37606	−	5.41327i	−0.330053	−	0.190556i
$808$	−10.2427	−	37.5211i	−0.360336	−	1.31999i
$809$	−11.2462	−	19.4790i	−0.395396	−	0.684845i	0.597756	−	0.801678i	$-0.296059\pi$
$809$	−11.2462	−	19.4790i	−0.395396	−	0.684845i	−0.993152	+	0.116833i	$0.962726\pi$
$810$	−4.69928	−	0.403728i	−0.165116	−	0.0141856i
$811$	−0.492423			−0.0172913			−0.00864565	−	0.999963i	$-0.502752\pi$
$811$	−0.492423			−0.0172913			−0.00864565	+	0.999963i	$0.502752\pi$
$812$		0			0
$813$	28.4924			0.999273
$814$	1.48188	+	0.127312i	0.0519398	+	0.00446230i
$815$	−26.2462	−	45.4598i	−0.919365	−	1.59239i
$816$	−13.4901	−	15.8741i	−0.472248	−	0.555705i
$817$	55.9446	+	32.2996i	1.95725	+	1.13002i
$818$	−0.492423	−	1.05171i	−0.0172171	−	0.0367720i
$819$		0			0
$820$	6.24621	−	7.49141i	0.218127	−	0.261611i
$821$	28.6155	−	49.5635i	0.998689	−	1.72978i	0.455011	−	0.890486i	$-0.349635\pi$
$821$	28.6155	−	49.5635i	0.998689	−	1.72978i	0.543678	−	0.839294i	$-0.317031\pi$
$822$	0.285537	+	0.199270i	0.00995924	+	0.00695035i
$823$	11.2975	−	6.52262i	0.393806	−	0.227364i	−0.290002	−	0.957026i	$-0.593656\pi$
$823$	11.2975	−	6.52262i	0.393806	−	0.227364i	0.683808	+	0.729662i	$0.260323\pi$
$824$	−16.0749	−	15.9247i	−0.559996	−	0.554765i
$825$		−	5.73384i		−	0.199627i
$826$		0			0
$827$			55.9408i			1.94525i	0.232373	+	0.972627i	$0.425351\pi$
$827$			55.9408i			1.94525i	−0.232373	+	0.972627i	$0.574649\pi$
$828$	1.75789	−	0.646055i	0.0610910	−	0.0224520i
$829$	−18.2407	+	10.5312i	−0.633524	+	0.365765i	−0.782116	−	0.623133i	$-0.785859\pi$
$829$	−18.2407	+	10.5312i	−0.633524	+	0.365765i	0.148591	+	0.988899i	$0.452526\pi$
$830$	27.6574	−	39.6306i	0.960001	−	1.37560i
$831$	2.56155	−	4.43674i	0.0888593	−	0.153909i
$832$	−7.36932	+	13.0452i	−0.255485	+	0.452262i
$833$		0			0
$834$	−15.3693	+	7.19612i	−0.532196	+	0.249181i
$835$	−41.1475	−	23.7565i	−1.42397	−	0.822128i
$836$	−2.27545	+	13.1450i	−0.0786981	+	0.454631i
$837$		0			0
$838$	1.99646	−	23.2382i	0.0689666	−	0.802750i
$839$	42.7386			1.47550			0.737751	−	0.675073i	$-0.235888\pi$
$839$	42.7386			1.47550			0.737751	+	0.675073i	$0.235888\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	1.31668	−	15.3258i	0.0453759	−	0.528162i
$843$	−8.12311	−	14.0696i	−0.279775	−	0.484584i
$844$	4.37152	−	25.2538i	0.150474	−	0.869271i
$845$	27.4170	+	15.8292i	0.943175	+	0.544542i
$846$	8.00000	−	3.74571i	0.275046	−	0.128780i
$847$		0			0
$848$	−8.80776	−	48.1865i	−0.302460	−	1.65473i
$849$	4.43845	−	7.68762i	0.152327	−	0.263838i
$850$	25.8093	−	36.9825i	0.885251	−	1.26849i
$851$	−0.910804	+	0.525853i	−0.0312220	+	0.0180260i
$852$	7.24798	−	2.66375i	0.248312	−	0.0912587i
$853$		−	50.2070i		−	1.71905i	−0.511090	−	0.859527i	$-0.670758\pi$
$853$		−	50.2070i		−	1.71905i	0.511090	−	0.859527i	$-0.329242\pi$
$854$		0			0
$855$			23.7565i			0.812455i
$856$	−18.8699	+	19.0478i	−0.644961	+	0.651042i
$857$	48.9016	−	28.2333i	1.67045	−	0.964433i	0.703059	−	0.711132i	$-0.251817\pi$
$857$	48.9016	−	28.2333i	1.67045	−	0.964433i	0.967388	−	0.253301i	$-0.0815163\pi$
$858$	2.03391	+	1.41942i	0.0694365	+	0.0484583i
$859$	−12.9309	+	22.3969i	−0.441196	+	0.764173i	−0.997778	−	0.0666189i	$-0.978779\pi$
$859$	−12.9309	+	22.3969i	−0.441196	+	0.764173i	0.556583	+	0.830792i	$0.312112\pi$
$860$	38.7386	−	46.4613i	1.32098	−	1.58432i
$861$		0			0
$862$	2.80776	+	5.99676i	0.0956328	+	0.204251i
$863$	−7.49839	−	4.32920i	−0.255248	−	0.147368i	0.366917	−	0.930254i	$-0.380413\pi$
$863$	−7.49839	−	4.32920i	−0.255248	−	0.147368i	−0.622165	+	0.782886i	$0.713747\pi$
$864$	2.35052	−	5.14539i	0.0799664	−	0.175050i
$865$	−27.8078	−	48.1645i	−0.945492	−	1.63764i
$866$	18.7971	+	1.61491i	0.638752	+	0.0548770i
$867$	−10.1231			−0.343799
$868$		0			0
$869$	2.24621			0.0761975
$870$	9.39856	+	0.807457i	0.318641	+	0.0273753i
$871$	10.2462	+	17.7470i	0.347180	+	0.601333i
$872$	−22.5005	+	6.14229i	−0.761963	+	0.208004i
$873$	−9.02049	−	5.20798i	−0.305297	−	0.176264i
$874$	−4.00000	−	8.54312i	−0.135302	−	0.288975i
$875$		0			0
$876$	−10.2462	−	8.54312i	−0.346187	−	0.288645i
$877$	−18.1231	+	31.3901i	−0.611974	+	1.05997i	0.378934	+	0.925424i	$0.376291\pi$
$877$	−18.1231	+	31.3901i	−0.611974	+	1.05997i	−0.990907	+	0.134546i	$0.957042\pi$
$878$	7.68976	+	5.36652i	0.259517	+	0.181111i
$879$	−11.9088	+	6.87555i	−0.401674	+	0.231907i
$880$	11.7655	+	4.19914i	0.396616	+	0.141553i
$881$		−	46.8719i		−	1.57915i	−0.613652	−	0.789577i	$-0.710300\pi$
$881$		−	46.8719i		−	1.57915i	0.613652	−	0.789577i	$-0.289700\pi$
$882$		0			0
$883$			18.6638i			0.628087i	0.949409	+	0.314043i	$0.101684\pi$
$883$			18.6638i			0.628087i	−0.949409	+	0.314043i	$0.898316\pi$
$884$	6.72929	+	18.3102i	0.226331	+	0.615838i
$885$	11.5532	−	6.67026i	0.388358	−	0.224218i
$886$	−15.2512	+	21.8536i	−0.512373	+	0.734186i
$887$	−13.3693	+	23.1563i	−0.448898	+	0.777514i	−0.998315	−	0.0580347i	$-0.981517\pi$
$887$	−13.3693	+	23.1563i	−0.448898	+	0.777514i	0.549417	+	0.835548i	$0.314850\pi$
$888$	−0.807764	+	3.07221i	−0.0271068	+	0.103096i
$889$		0			0
$890$	6.24621	−	2.92456i	0.209373	−	0.0980314i
$891$	−0.810969	−	0.468213i	−0.0271685	−	0.0156857i
$892$	53.4513	+	9.25260i	1.78968	+	0.309800i
$893$	−22.2462	−	38.5316i	−0.744441	−	1.28941i
$894$	−1.21053	+	14.0902i	−0.0404862	+	0.471248i
$895$	−53.8617			−1.80040
$896$		0			0
$897$	−1.75379			−0.0585573
$898$	1.42283	−	16.5614i	0.0474806	−	0.552660i
$899$		0			0
$900$	12.0668	+	2.08880i	0.402225	+	0.0696265i
$901$	−55.2334	−	31.8890i	−1.84009	−	1.06238i
$902$	1.75379	−	0.821147i	0.0583948	−	0.0273412i
$903$		0			0
$904$	3.05398	−	11.6153i	0.101574	−	0.386320i
$905$	−3.12311	+	5.40938i	−0.103816	+	0.179814i
$906$	7.33994	−	10.5175i	0.243853	−	0.349420i
$907$	−33.2935	+	19.2220i	−1.10549	+	0.638256i	−0.937658	−	0.347559i	$-0.887011\pi$
$907$	−33.2935	+	19.2220i	−1.10549	+	0.638256i	−0.167834	+	0.985815i	$0.553677\pi$
$908$	11.3784	+	30.9602i	0.377605	+	1.02745i
$909$		−	13.7511i		−	0.456095i
$910$		0			0
$911$			5.73384i			0.189971i	0.995479	+	0.0949853i	$0.0302804\pi$
$911$			5.73384i			0.189971i	−0.995479	+	0.0949853i	$0.969720\pi$
$912$	−26.8346	−	9.57729i	−0.888581	−	0.317136i
$913$	8.30936	−	4.79741i	0.275000	−	0.158771i
$914$	0.285537	+	0.199270i	0.00944472	+	0.00659127i
$915$	8.00000	−	13.8564i	0.264472	−	0.458079i
$916$	−8.63068	−	7.19612i	−0.285166	−	0.237766i
$917$		0			0
$918$	−3.12311	−	6.67026i	−0.103078	−	0.220152i
$919$	7.85396	+	4.53448i	0.259078	+	0.149579i	0.623914	−	0.781493i	$-0.285542\pi$
$919$	7.85396	+	4.53448i	0.259078	+	0.149579i	−0.364836	+	0.931072i	$0.618875\pi$
$920$	−8.52166	+	2.32628i	−0.280951	+	0.0766953i
$921$	9.80776	+	16.9875i	0.323177	+	0.559759i
$922$	8.82005	+	0.757756i	0.290473	+	0.0249554i
$923$	−7.23106			−0.238013
$924$		0			0
$925$	−6.87689			−0.226111
$926$	55.3255	+	4.75317i	1.81811	+	0.156199i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	−4.70105	+	10.2908i	−0.154319	+	0.337811i
$929$	−3.08798	−	1.78285i	−0.101313	−	0.0584933i	0.448487	−	0.893789i	$-0.351963\pi$
$929$	−3.08798	−	1.78285i	−0.101313	−	0.0584933i	−0.549801	+	0.835296i	$0.685296\pi$
$930$		0			0
$931$		0			0
$932$	28.8078	−	34.5507i	0.943630	−	1.13174i
$933$	4.00000	−	6.92820i	0.130954	−	0.226819i
$934$	−39.7161	−	27.7171i	−1.29955	−	0.906930i
$935$	14.0860	−	8.13254i	0.460661	−	0.265963i
$936$	−3.72809	+	3.76324i	−0.121856	+	0.123005i
$937$		−	28.7845i		−	0.940348i	−0.882574	−	0.470174i	$-0.844191\pi$
$937$		−	28.7845i		−	0.940348i	0.882574	−	0.470174i	$-0.155809\pi$
$938$		0			0
$939$			22.9354i			0.748467i
$940$	−39.1065	+	14.3723i	−1.27551	+	0.468772i
$941$	46.5685	−	26.8863i	1.51809	−	0.876470i	0.518317	−	0.855189i	$-0.326559\pi$
$941$	46.5685	−	26.8863i	1.51809	−	0.876470i	0.999774	−	0.0212809i	$-0.00677443\pi$
$942$	−17.7115	+	25.3790i	−0.577070	+	0.826892i
$943$	−0.684658	+	1.18586i	−0.0222955	+	0.0386170i
$944$	2.87689	+	15.7392i	0.0936349	+	0.512268i
$945$		0			0
$946$	10.8769	−	5.09271i	0.353638	−	0.165578i
$947$	42.1581	+	24.3400i	1.36995	+	0.790943i	0.990922	−	0.134440i	$-0.0429235\pi$
$947$	42.1581	+	24.3400i	1.36995	+	0.790943i	0.379032	+	0.925383i	$0.376257\pi$
$948$	−0.818279	+	4.72711i	−0.0265765	+	0.153529i
$949$	6.24621	+	10.8188i	0.202761	+	0.351192i
$950$	5.27980	−	61.4553i	0.171299	−	1.99387i
$951$	−14.4924			−0.469949
$952$		0			0
$953$	−21.2311			−0.687741			−0.343871	−	0.939017i	$-0.611738\pi$
$953$	−21.2311			−0.687741			−0.343871	+	0.939017i	$0.611738\pi$
$954$	1.48244	−	17.2552i	0.0479959	−	0.558658i
$955$	−4.68466	−	8.11407i	−0.151592	−	0.262565i
$956$	5.50924	−	31.8263i	0.178182	−	1.02934i
$957$	1.62194	+	0.936426i	0.0524298	+	0.0302704i
$958$	16.0000	−	7.49141i	0.516937	−	0.242037i
$959$		0			0
$960$	−13.1231	+	23.2306i	−0.423546	+	0.749766i
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	1.70239	−	2.43938i	0.0548872	−	0.0786486i
$963$	−8.20953	+	4.73977i	−0.264548	+	0.152737i
$964$	44.5966	−	16.3900i	1.43636	−	0.527886i
$965$			51.2587i			1.65008i
$966$		0			0
$967$			8.83841i			0.284224i	0.989851	+	0.142112i	$0.0453893\pi$
$967$			8.83841i			0.284224i	−0.989851	+	0.142112i	$0.954611\pi$
$968$	−20.3410	−	20.1510i	−0.653784	−	0.647677i
$969$	−32.1270	+	18.5485i	−1.03207	+	0.595864i
$970$	40.2872	+	28.1156i	1.29354	+	0.902737i
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$	1.28078	−	1.53610i	0.0410809	−	0.0492705i
$973$		0			0
$974$	0.946025	+	2.02050i	0.0303126	+	0.0647410i
$975$	−9.93130	−	5.73384i	−0.318056	−	0.183630i
$976$	12.4266	+	14.6227i	0.397765	+	0.468060i
$977$	5.63068	+	9.75263i	0.180142	+	0.312014i	0.941929	−	0.335813i	$-0.109011\pi$
$977$	5.63068	+	9.75263i	0.180142	+	0.312014i	−0.761787	+	0.647827i	$0.775678\pi$
$978$	22.1769	+	1.90528i	0.709140	+	0.0609243i
$979$	1.36932			0.0437636
$980$		0			0
$981$	−8.24621			−0.263281
$982$	15.9958	+	1.37424i	0.510446	+	0.0438539i
$983$	2.63068	+	4.55648i	0.0839058	+	0.145329i	0.904924	−	0.425572i	$-0.139927\pi$
$983$	2.63068	+	4.55648i	0.0839058	+	0.145329i	−0.821019	+	0.570901i	$0.806594\pi$
$984$	1.08920	+	3.98995i	0.0347223	+	0.127195i
$985$	−46.9241	−	27.0916i	−1.49513	−	0.863211i
$986$	6.24621	+	13.3405i	0.198920	+	0.424849i
$987$		0			0
$988$	20.4924	+	17.0862i	0.651951	+	0.543586i
$989$	−4.24621	+	7.35465i	−0.135022	+	0.233864i
$990$	3.62194	+	2.52768i	0.115113	+	0.0803348i
$991$	0.455402	−	0.262926i	0.0144663	−	0.00835213i	−0.492749	−	0.870171i	$-0.664008\pi$
$991$	0.455402	−	0.262926i	0.0144663	−	0.00835213i	0.507216	+	0.861819i	$0.330675\pi$
$992$		0			0
$993$		−	17.6121i		−	0.558903i
$994$		0			0
$995$		−	10.4160i		−	0.330208i
$996$	7.06902	+	19.2346i	0.223991	+	0.609470i
$997$	17.1302	−	9.89012i	0.542518	−	0.313223i	−0.203581	−	0.979058i	$-0.565258\pi$
$997$	17.1302	−	9.89012i	0.542518	−	0.313223i	0.746099	+	0.665835i	$0.231925\pi$
$998$	11.2227	−	16.0812i	0.355249	−	0.509040i
$999$	−0.561553	+	0.972638i	−0.0177667	+	0.0307729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.a.19.2		8
4.3	odd	2		588.2.o.c.19.4		8
7.2	even	3		84.2.b.b.55.2	yes	4
7.3	odd	6		588.2.o.c.31.4		8
7.4	even	3	inner	588.2.o.a.31.4		8
7.5	odd	6		84.2.b.a.55.2	yes	4
7.6	odd	2		588.2.o.c.19.2		8
21.2	odd	6		252.2.b.d.55.3		4
21.5	even	6		252.2.b.e.55.3		4
28.3	even	6	inner	588.2.o.a.31.2		8
28.11	odd	6		588.2.o.c.31.2		8
28.19	even	6		84.2.b.b.55.1	yes	4
28.23	odd	6		84.2.b.a.55.1	✓	4
28.27	even	2	inner	588.2.o.a.19.4		8
56.5	odd	6		1344.2.b.f.895.1		4
56.19	even	6		1344.2.b.e.895.1		4
56.37	even	6		1344.2.b.e.895.4		4
56.51	odd	6		1344.2.b.f.895.4		4
84.23	even	6		252.2.b.e.55.4		4
84.47	odd	6		252.2.b.d.55.4		4
168.5	even	6		4032.2.b.n.3583.4		4
168.107	even	6		4032.2.b.n.3583.1		4
168.131	odd	6		4032.2.b.j.3583.4		4
168.149	odd	6		4032.2.b.j.3583.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.b.a.55.1	✓	4	28.23	odd	6
84.2.b.a.55.2	yes	4	7.5	odd	6
84.2.b.b.55.1	yes	4	28.19	even	6
84.2.b.b.55.2	yes	4	7.2	even	3
252.2.b.d.55.3		4	21.2	odd	6
252.2.b.d.55.4		4	84.47	odd	6
252.2.b.e.55.3		4	21.5	even	6
252.2.b.e.55.4		4	84.23	even	6
588.2.o.a.19.2		8	1.1	even	1	trivial
588.2.o.a.19.4		8	28.27	even	2	inner
588.2.o.a.31.2		8	28.3	even	6	inner
588.2.o.a.31.4		8	7.4	even	3	inner
588.2.o.c.19.2		8	7.6	odd	2
588.2.o.c.19.4		8	4.3	odd	2
588.2.o.c.31.2		8	28.11	odd	6
588.2.o.c.31.4		8	7.3	odd	6
1344.2.b.e.895.1		4	56.19	even	6
1344.2.b.e.895.4		4	56.37	even	6
1344.2.b.f.895.1		4	56.5	odd	6
1344.2.b.f.895.4		4	56.51	odd	6
4032.2.b.j.3583.1		4	168.149	odd	6
4032.2.b.j.3583.4		4	168.131	odd	6
4032.2.b.n.3583.1		4	168.107	even	6
4032.2.b.n.3583.4		4	168.5	even	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.121053 - 1.40902i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.97069 - 0.341134i) q^{4} +(2.88831 + 1.66757i) q^{5} +(-1.28078 + 0.599676i) q^{6} +(-0.719224 + 2.73546i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.121053 - 1.40902i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.97069 - 0.341134i) q^{4} +(2.88831 + 1.66757i) q^{5} +(-1.28078 + 0.599676i) q^{6} +(-0.719224 + 2.73546i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.69928 - 3.86783i) q^{10} +(0.810969 - 0.468213i) q^{11} +(0.689916 + 1.87724i) q^{12} -1.87285i q^{13} -3.33513i q^{15} +(3.76726 + 1.34454i) q^{16} +(4.51025 - 2.60399i) q^{17} +(1.15972 + 0.809347i) q^{18} +(3.56155 - 6.16879i) q^{19} +(-5.12311 - 4.27156i) q^{20} +(-0.561553 - 1.19935i) q^{22} +(0.810969 + 0.468213i) q^{23} +(2.72859 - 0.744862i) q^{24} +(3.06155 + 5.30277i) q^{25} +(-2.63889 - 0.226715i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-4.69928 - 0.403728i) q^{30} +(2.35052 - 5.14539i) q^{32} +(-0.810969 - 0.468213i) q^{33} +(-3.12311 - 6.67026i) q^{34} +(1.28078 - 1.53610i) q^{36} +(-0.561553 + 0.972638i) q^{37} +(-8.26083 - 5.76506i) q^{38} +(-1.62194 + 0.936426i) q^{39} +(-6.63889 + 6.70149i) q^{40} +1.46228i q^{41} +9.06897i q^{43} +(-1.75789 + 0.646055i) q^{44} +(-2.88831 + 1.66757i) q^{45} +(0.757894 - 1.08600i) q^{46} +(3.12311 - 5.40938i) q^{47} +(-0.719224 - 3.93481i) q^{48} +(7.84233 - 3.67188i) q^{50} +(-4.51025 - 2.60399i) q^{51} +(-0.638893 + 3.69082i) q^{52} +(-6.12311 - 10.6055i) q^{53} +(0.121053 - 1.40902i) q^{54} +3.12311 q^{55} -7.12311 q^{57} +(-0.242106 + 2.81805i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-1.13773 + 6.57252i) q^{60} +(4.15468 + 2.39871i) q^{61} +(-6.96543 - 3.93481i) q^{64} +(3.12311 - 5.40938i) q^{65} +(-0.757894 + 1.08600i) q^{66} +(-9.47590 + 5.47091i) q^{67} +(-9.77662 + 3.59307i) q^{68} -0.936426i q^{69} -3.86098i q^{71} +(-2.00936 - 1.99059i) q^{72} +(-5.77662 + 3.33513i) q^{73} +(1.30249 + 0.908982i) q^{74} +(3.06155 - 5.30277i) q^{75} +(-9.12311 + 10.9418i) q^{76} +(1.12311 + 2.39871i) q^{78} +(2.07734 + 1.19935i) q^{79} +(8.63889 + 10.1656i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.06039 + 0.177014i) q^{82} +10.2462 q^{83} +17.3693 q^{85} +(12.7784 + 1.09783i) q^{86} +(1.00000 + 1.73205i) q^{87} +(0.697508 + 2.55512i) q^{88} +(1.26637 + 0.731140i) q^{89} +(2.00000 + 4.27156i) q^{90} +(-1.43845 - 1.19935i) q^{92} +(-7.24388 - 5.05535i) q^{94} +(20.5737 - 11.8782i) q^{95} +(-5.63130 + 0.537082i) q^{96} +10.4160i q^{97} +0.936426i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{16} + q^{18} + 12 q^{19} - 8 q^{20} + 12 q^{22} + 7 q^{24} + 8 q^{25} + 12 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 9 q^{32} + 8 q^{34} + 2 q^{36} + 12 q^{37} - 20 q^{38} - 20 q^{40} - 14 q^{44} + 6 q^{46} - 8 q^{47} - 14 q^{48} + 38 q^{50} + 28 q^{52} - 16 q^{53} + q^{54} - 8 q^{55} - 24 q^{57} - 2 q^{58} + 16 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{65} - 6 q^{66} - 32 q^{68} + 7 q^{72} + 14 q^{74} + 8 q^{75} - 40 q^{76} - 24 q^{78} + 36 q^{80} - 4 q^{81} + 20 q^{82} + 16 q^{83} + 40 q^{85} + 30 q^{86} + 8 q^{87} + 2 q^{88} + 16 q^{90} - 28 q^{92} - 32 q^{94} - 9 q^{96}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9 - 8 * q^10 - q^12 + 7 * q^16 + q^18 + 12 * q^19 - 8 * q^20 + 12 * q^22 + 7 * q^24 + 8 * q^25 + 12 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 9 * q^32 + 8 * q^34 + 2 * q^36 + 12 * q^37 - 20 * q^38 - 20 * q^40 - 14 * q^44 + 6 * q^46 - 8 * q^47 - 14 * q^48 + 38 * q^50 + 28 * q^52 - 16 * q^53 + q^54 - 8 * q^55 - 24 * q^57 - 2 * q^58 + 16 * q^59 + 4 * q^60 + 2 * q^64 - 8 * q^65 - 6 * q^66 - 32 * q^68 + 7 * q^72 + 14 * q^74 + 8 * q^75 - 40 * q^76 - 24 * q^78 + 36 * q^80 - 4 * q^81 + 20 * q^82 + 16 * q^83 + 40 * q^85 + 30 * q^86 + 8 * q^87 + 2 * q^88 + 16 * q^90 - 28 * q^92 - 32 * q^94 - 9 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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