LMFDB - Embedded newform 510.2.l.f.137.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (of order $4$, 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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	510.137
Dual form			510.2.l.f.443.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.10721 + 1.33195i) q^{3} -1.00000i q^{4} +(1.73205 + 1.41421i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.548188 + 2.94949i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.10721 + 1.33195i) q^{3} -1.00000i q^{4} +(1.73205 + 1.41421i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.548188 + 2.94949i) q^{9} +(-2.22474 + 0.224745i) q^{10} +1.41421i q^{11} +(1.33195 - 1.10721i) q^{12} +(-1.77526 + 1.77526i) q^{13} +1.41421 q^{14} +(0.0340742 + 3.87283i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(-1.69798 - 2.47323i) q^{18} +2.55051i q^{19} +(1.41421 - 1.73205i) q^{20} +(0.224745 - 2.43916i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(1.73205 + 1.73205i) q^{23} +(-0.158919 + 1.72474i) q^{24} +(1.00000 + 4.89898i) q^{25} -2.51059i q^{26} +(-4.53553 + 2.53553i) q^{27} +(-1.00000 + 1.00000i) q^{28} +6.61037 q^{29} +(-2.76260 - 2.71441i) q^{30} +3.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.88366 + 1.56583i) q^{33} +1.00000i q^{34} +(-0.317837 - 3.14626i) q^{35} +(2.94949 + 0.548188i) q^{36} +(-6.89898 - 6.89898i) q^{37} +(-1.80348 - 1.80348i) q^{38} +(-4.33013 - 0.398979i) q^{39} +(0.224745 + 2.22474i) q^{40} -5.51399i q^{41} +(1.56583 + 1.88366i) q^{42} +(-2.55051 + 2.55051i) q^{43} +1.41421 q^{44} +(-5.12070 + 4.33341i) q^{45} -2.44949 q^{46} +(-3.53553 + 3.53553i) q^{47} +(-1.10721 - 1.33195i) q^{48} -5.00000i q^{49} +(-4.17121 - 2.75699i) q^{50} +(1.72474 + 0.158919i) q^{51} +(1.77526 + 1.77526i) q^{52} +(7.95315 + 7.95315i) q^{53} +(1.41421 - 5.00000i) q^{54} +(-2.00000 + 2.44949i) q^{55} -1.41421i q^{56} +(-3.39716 + 2.82394i) q^{57} +(-4.67423 + 4.67423i) q^{58} -0.317837 q^{59} +(3.87283 - 0.0340742i) q^{60} +8.34847 q^{61} +(-2.12132 + 2.12132i) q^{62} +(3.49768 - 2.40130i) q^{63} +1.00000i q^{64} +(-5.58542 + 0.564242i) q^{65} +(0.224745 - 2.43916i) q^{66} +(-10.4495 - 10.4495i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(-0.389270 + 4.22474i) q^{69} +(2.44949 + 2.00000i) q^{70} +4.56048i q^{71} +(-2.47323 + 1.69798i) q^{72} +(0.325765 - 0.325765i) q^{73} +9.75663 q^{74} +(-5.41800 + 6.75613i) q^{75} +2.55051 q^{76} +(1.41421 - 1.41421i) q^{77} +(3.34398 - 2.77974i) q^{78} -6.89898i q^{79} +(-1.73205 - 1.41421i) q^{80} +(-8.39898 - 3.23375i) q^{81} +(3.89898 + 3.89898i) q^{82} +(-5.65685 - 5.65685i) q^{83} +(-2.43916 - 0.224745i) q^{84} +(2.22474 - 0.224745i) q^{85} -3.60697i q^{86} +(7.31904 + 8.80469i) q^{87} +(-1.00000 + 1.00000i) q^{88} +15.8742 q^{89} +(0.556696 - 6.68506i) q^{90} +3.55051 q^{91} +(1.73205 - 1.73205i) q^{92} +(3.32162 + 3.99585i) q^{93} -5.00000i q^{94} +(-3.60697 + 4.41761i) q^{95} +(1.72474 + 0.158919i) q^{96} +(4.12372 + 4.12372i) q^{97} +(3.53553 + 3.53553i) q^{98} +(-4.17121 - 0.775255i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	$ 8 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 24 q^{13} + 8 q^{15} - 8 q^{16} + 8 q^{18} - 8 q^{21} - 8 q^{22} + 8 q^{25} - 8 q^{27} - 8 q^{28} - 8 q^{30} + 24 q^{31} - 4 q^{33} + 4 q^{36} - 16 q^{37} - 8 q^{40} + 4 q^{42} - 40 q^{43} + 12 q^{45} - 4 q^{48} + 4 q^{51} + 24 q^{52} - 16 q^{55} + 32 q^{57} - 8 q^{58} + 16 q^{60} + 8 q^{61} + 4 q^{63} - 8 q^{66} - 64 q^{67} - 8 q^{72} + 32 q^{73} - 20 q^{75} + 40 q^{76} - 28 q^{81} - 8 q^{82} + 8 q^{85} + 40 q^{87} - 8 q^{88} - 20 q^{90} + 48 q^{91} + 12 q^{93} + 4 q^{96} - 16 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 24 * q^13 + 8 * q^15 - 8 * q^16 + 8 * q^18 - 8 * q^21 - 8 * q^22 + 8 * q^25 - 8 * q^27 - 8 * q^28 - 8 * q^30 + 24 * q^31 - 4 * q^33 + 4 * q^36 - 16 * q^37 - 8 * q^40 + 4 * q^42 - 40 * q^43 + 12 * q^45 - 4 * q^48 + 4 * q^51 + 24 * q^52 - 16 * q^55 + 32 * q^57 - 8 * q^58 + 16 * q^60 + 8 * q^61 + 4 * q^63 - 8 * q^66 - 64 * q^67 - 8 * q^72 + 32 * q^73 - 20 * q^75 + 40 * q^76 - 28 * q^81 - 8 * q^82 + 8 * q^85 + 40 * q^87 - 8 * q^88 - 20 * q^90 + 48 * q^91 + 12 * q^93 + 4 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.10721	+	1.33195i	0.639246	+	0.769002i
$3$	1.10721	+	1.33195i	0.639246	+	0.769002i
$4$		−	1.00000i		−	0.500000i
$5$	1.73205	+	1.41421i	0.774597	+	0.632456i
$5$	1.73205	+	1.41421i	0.774597	+	0.632456i
$6$	−1.72474	−	0.158919i	−0.704124	−	0.0648783i
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.548188	+	2.94949i	−0.182729	+	0.983163i
$10$	−2.22474	+	0.224745i	−0.703526	+	0.0710706i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$	1.33195	−	1.10721i	0.384501	−	0.319623i
$13$	−1.77526	+	1.77526i	−0.492367	+	0.492367i	−0.909051	−	0.416684i	$-0.863192\pi$
$13$	−1.77526	+	1.77526i	−0.492367	+	0.492367i	0.416684	+	0.909051i	$0.363192\pi$
$14$	1.41421			0.377964
$15$	0.0340742	+	3.87283i	0.00879791	+	0.999961i
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$	−1.69798	−	2.47323i	−0.400217	−	0.582946i
$19$			2.55051i			0.585127i	0.956246	+	0.292564i	$0.0945083\pi$
$19$			2.55051i			0.585127i	−0.956246	+	0.292564i	$0.905492\pi$
$20$	1.41421	−	1.73205i	0.316228	−	0.387298i
$21$	0.224745	−	2.43916i	0.0490434	−	0.532268i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	1.73205	+	1.73205i	0.361158	+	0.361158i	0.864239	−	0.503081i	$-0.167800\pi$
$23$	1.73205	+	1.73205i	0.361158	+	0.361158i	−0.503081	+	0.864239i	$0.667800\pi$
$24$	−0.158919	+	1.72474i	−0.0324391	+	0.352062i
$25$	1.00000	+	4.89898i	0.200000	+	0.979796i
$26$		−	2.51059i		−	0.492367i
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$	6.61037			1.22751			0.613757	−	0.789495i	$-0.289657\pi$
$29$	6.61037			1.22751			0.613757	+	0.789495i	$0.289657\pi$
$30$	−2.76260	−	2.71441i	−0.504380	−	0.495582i
$31$	3.00000			0.538816			0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000			0.538816			0.269408	+	0.963026i	$0.413172\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.88366	+	1.56583i	−0.327904	+	0.272575i
$34$			1.00000i			0.171499i
$35$	−0.317837	−	3.14626i	−0.0537243	−	0.531816i
$36$	2.94949	+	0.548188i	0.491582	+	0.0913647i
$37$	−6.89898	−	6.89898i	−1.13419	−	1.13419i	−0.989474	−	0.144711i	$-0.953775\pi$
$37$	−6.89898	−	6.89898i	−1.13419	−	1.13419i	−0.144711	−	0.989474i	$-0.546225\pi$
$38$	−1.80348	−	1.80348i	−0.292564	−	0.292564i
$39$	−4.33013	−	0.398979i	−0.693375	−	0.0638878i
$40$	0.224745	+	2.22474i	0.0355353	+	0.351763i
$41$		−	5.51399i		−	0.861141i	−0.902557	−	0.430570i	$-0.858312\pi$
$41$		−	5.51399i		−	0.861141i	0.902557	−	0.430570i	$-0.141688\pi$
$42$	1.56583	+	1.88366i	0.241612	+	0.290656i
$43$	−2.55051	+	2.55051i	−0.388949	+	0.388949i	−0.874313	−	0.485363i	$-0.838687\pi$
$43$	−2.55051	+	2.55051i	−0.388949	+	0.388949i	0.485363	+	0.874313i	$0.338687\pi$
$44$	1.41421			0.213201
$45$	−5.12070	+	4.33341i	−0.763349	+	0.645987i
$46$	−2.44949			−0.361158
$47$	−3.53553	+	3.53553i	−0.515711	+	0.515711i	−0.916271	−	0.400560i	$-0.868816\pi$
$47$	−3.53553	+	3.53553i	−0.515711	+	0.515711i	0.400560	+	0.916271i	$0.368816\pi$
$48$	−1.10721	−	1.33195i	−0.159811	−	0.192251i
$49$		−	5.00000i		−	0.714286i
$50$	−4.17121	−	2.75699i	−0.589898	−	0.389898i
$51$	1.72474	+	0.158919i	0.241513	+	0.0222531i
$52$	1.77526	+	1.77526i	0.246184	+	0.246184i
$53$	7.95315	+	7.95315i	1.09245	+	1.09245i	0.995267	+	0.0971822i	$0.0309829\pi$
$53$	7.95315	+	7.95315i	1.09245	+	1.09245i	0.0971822	+	0.995267i	$0.469017\pi$
$54$	1.41421	−	5.00000i	0.192450	−	0.680414i
$55$	−2.00000	+	2.44949i	−0.269680	+	0.330289i
$56$		−	1.41421i		−	0.188982i
$57$	−3.39716	+	2.82394i	−0.449964	+	0.374040i
$58$	−4.67423	+	4.67423i	−0.613757	+	0.613757i
$59$	−0.317837			−0.0413789			−0.0206894	−	0.999786i	$-0.506586\pi$
$59$	−0.317837			−0.0413789			−0.0206894	+	0.999786i	$0.506586\pi$
$60$	3.87283	−	0.0340742i	0.499981	−	0.00439896i
$61$	8.34847			1.06891			0.534456	−	0.845196i	$-0.320517\pi$
$61$	8.34847			1.06891			0.534456	+	0.845196i	$0.320517\pi$
$62$	−2.12132	+	2.12132i	−0.269408	+	0.269408i
$63$	3.49768	−	2.40130i	0.440666	−	0.302536i
$64$			1.00000i			0.125000i
$65$	−5.58542	+	0.564242i	−0.692786	+	0.0699856i
$66$	0.224745	−	2.43916i	0.0276642	−	0.300240i
$67$	−10.4495	−	10.4495i	−1.27661	−	1.27661i	−0.942554	−	0.334055i	$-0.891583\pi$
$67$	−10.4495	−	10.4495i	−1.27661	−	1.27661i	−0.334055	−	0.942554i	$-0.608417\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$	−0.389270	+	4.22474i	−0.0468625	+	0.508600i
$70$	2.44949	+	2.00000i	0.292770	+	0.239046i
$71$			4.56048i			0.541229i	0.962688	+	0.270615i	$0.0872269\pi$
$71$			4.56048i			0.541229i	−0.962688	+	0.270615i	$0.912773\pi$
$72$	−2.47323	+	1.69798i	−0.291473	+	0.200108i
$73$	0.325765	−	0.325765i	0.0381280	−	0.0381280i	−0.687786	−	0.725914i	$-0.741417\pi$
$73$	0.325765	−	0.325765i	0.0381280	−	0.0381280i	0.725914	+	0.687786i	$0.241417\pi$
$74$	9.75663			1.13419
$75$	−5.41800	+	6.75613i	−0.625616	+	0.780131i
$76$	2.55051			0.292564
$77$	1.41421	−	1.41421i	0.161165	−	0.161165i
$78$	3.34398	−	2.77974i	0.378632	−	0.314744i
$79$		−	6.89898i		−	0.776196i	−0.921618	−	0.388098i	$-0.873132\pi$
$79$		−	6.89898i		−	0.776196i	0.921618	−	0.388098i	$-0.126868\pi$
$80$	−1.73205	−	1.41421i	−0.193649	−	0.158114i
$81$	−8.39898	−	3.23375i	−0.933220	−	0.359306i
$82$	3.89898	+	3.89898i	0.430570	+	0.430570i
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	0.324846	−	0.945767i	$-0.394687\pi$
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	−0.945767	+	0.324846i	$0.894687\pi$
$84$	−2.43916	−	0.224745i	−0.266134	−	0.0245217i
$85$	2.22474	−	0.224745i	0.241307	−	0.0243770i
$86$		−	3.60697i		−	0.388949i
$87$	7.31904	+	8.80469i	0.784683	+	0.943961i
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	15.8742			1.68266			0.841330	−	0.540522i	$-0.181773\pi$
$89$	15.8742			1.68266			0.841330	+	0.540522i	$0.181773\pi$
$90$	0.556696	−	6.68506i	0.0586809	−	0.704668i
$91$	3.55051			0.372195
$92$	1.73205	−	1.73205i	0.180579	−	0.180579i
$93$	3.32162	+	3.99585i	0.344436	+	0.414351i
$94$		−	5.00000i		−	0.515711i
$95$	−3.60697	+	4.41761i	−0.370067	+	0.453238i
$96$	1.72474	+	0.158919i	0.176031	+	0.0162196i
$97$	4.12372	+	4.12372i	0.418701	+	0.418701i	0.884756	−	0.466055i	$-0.154325\pi$
$97$	4.12372	+	4.12372i	0.418701	+	0.418701i	−0.466055	+	0.884756i	$0.654325\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$	−4.17121	−	0.775255i	−0.419222	−	0.0779161i
$100$	4.89898	−	1.00000i	0.489898	−	0.100000i
$101$		−	4.87832i		−	0.485411i	−0.970100	−	0.242705i	$-0.921965\pi$
$101$		−	4.87832i		−	0.485411i	0.970100	−	0.242705i	$-0.0780348\pi$
$102$	−1.33195	+	1.10721i	−0.131883	+	0.109630i
$103$	11.7980	−	11.7980i	1.16249	−	1.16249i	0.178558	−	0.983929i	$-0.442857\pi$
$103$	11.7980	−	11.7980i	1.16249	−	1.16249i	0.983929	−	0.178558i	$-0.0571432\pi$
$104$	−2.51059			−0.246184
$105$	3.83876	−	3.90691i	0.374625	−	0.381275i
$106$	−11.2474			−1.09245
$107$	−1.27135	+	1.27135i	−0.122906	+	0.122906i	−0.765884	−	0.642978i	$-0.777698\pi$
$107$	−1.27135	+	1.27135i	−0.122906	+	0.122906i	0.642978	+	0.765884i	$0.277698\pi$
$108$	2.53553	+	4.53553i	0.243982	+	0.436432i
$109$		−	4.34847i		−	0.416508i	−0.978075	−	0.208254i	$-0.933222\pi$
$109$		−	4.34847i		−	0.416508i	0.978075	−	0.208254i	$-0.0667780\pi$
$110$	−0.317837	−	3.14626i	−0.0303046	−	0.299985i
$111$	1.55051	−	16.8277i	0.147168	−	1.59721i
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	11.8780	+	11.8780i	1.11738	+	1.11738i	0.992124	+	0.125260i	$0.0399764\pi$
$113$	11.8780	+	11.8780i	1.11738	+	1.11738i	0.125260	+	0.992124i	$0.460024\pi$
$114$	0.405324	−	4.39898i	0.0379620	−	0.412002i
$115$	0.550510	+	5.44949i	0.0513353	+	0.508168i
$116$		−	6.61037i		−	0.613757i
$117$	−4.26292	−	6.20927i	−0.394107	−	0.574047i
$118$	0.224745	−	0.224745i	0.0206894	−	0.0206894i
$119$	−1.41421			−0.129641
$120$	−2.71441	+	2.76260i	−0.247791	+	0.252190i
$121$	9.00000			0.818182
$122$	−5.90326	+	5.90326i	−0.534456	+	0.534456i
$123$	7.34437	−	6.10512i	0.662219	−	0.550481i
$124$		−	3.00000i		−	0.269408i
$125$	−5.19615	+	9.89949i	−0.464758	+	0.885438i
$126$	−0.775255	+	4.17121i	−0.0690652	+	0.371601i
$127$	1.22474	+	1.22474i	0.108679	+	0.108679i	0.759355	−	0.650677i	$-0.225515\pi$
$127$	1.22474	+	1.22474i	0.108679	+	0.108679i	−0.650677	+	0.759355i	$0.725515\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−6.22110	−	0.573214i	−0.547737	−	0.0504687i
$130$	3.55051	−	4.34847i	0.311400	−	0.381386i
$131$		−	16.0492i		−	1.40222i	−0.713052	−	0.701111i	$-0.752688\pi$
$131$		−	16.0492i		−	1.40222i	0.713052	−	0.701111i	$-0.247312\pi$
$132$	1.56583	+	1.88366i	0.136288	+	0.163952i
$133$	2.55051	−	2.55051i	0.221157	−	0.221157i
$134$	14.7778			1.27661
$135$	−11.4416	−	2.02254i	−0.984733	−	0.174073i
$136$	1.00000			0.0857493
$137$	6.75323	−	6.75323i	0.576967	−	0.576967i	−0.357099	−	0.934067i	$-0.616234\pi$
$137$	6.75323	−	6.75323i	0.576967	−	0.576967i	0.934067	+	0.357099i	$0.116234\pi$
$138$	−2.71209	−	3.26260i	−0.230868	−	0.277731i
$139$		−	17.7980i		−	1.50960i	−0.655953	−	0.754802i	$-0.727733\pi$
$139$		−	17.7980i		−	1.50960i	0.655953	−	0.754802i	$-0.272267\pi$
$140$	−3.14626	+	0.317837i	−0.265908	+	0.0268622i
$141$	−8.62372	−	0.794593i	−0.726249	−	0.0669168i
$142$	−3.22474	−	3.22474i	−0.270615	−	0.270615i
$143$	−2.51059	−	2.51059i	−0.209946	−	0.209946i
$144$	0.548188	−	2.94949i	0.0456823	−	0.245791i
$145$	11.4495	+	9.34847i	0.950828	+	0.776348i
$146$			0.460702i			0.0381280i
$147$	6.65976	−	5.53603i	0.549287	−	0.456604i
$148$	−6.89898	+	6.89898i	−0.567093	+	0.567093i
$149$	9.61377			0.787590			0.393795	−	0.919198i	$-0.371162\pi$
$149$	9.61377			0.787590			0.393795	+	0.919198i	$0.371162\pi$
$150$	−0.946206	−	8.60841i	−0.0772574	−	0.702874i
$151$	15.3485			1.24904			0.624520	−	0.781009i	$-0.285294\pi$
$151$	15.3485			1.24904			0.624520	+	0.781009i	$0.285294\pi$
$152$	−1.80348	+	1.80348i	−0.146282	+	0.146282i
$153$	1.69798	+	2.47323i	0.137273	+	0.199949i
$154$			2.00000i			0.161165i
$155$	5.19615	+	4.24264i	0.417365	+	0.340777i
$156$	−0.398979	+	4.33013i	−0.0319439	+	0.346688i
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	4.87832	+	4.87832i	0.388098	+	0.388098i
$159$	−1.78743	+	19.3990i	−0.141752	+	1.53844i
$160$	2.22474	−	0.224745i	0.175882	−	0.0177676i
$161$		−	3.46410i		−	0.273009i
$162$	8.22558	−	3.65237i	0.646263	−	0.286957i
$163$	2.44949	−	2.44949i	0.191859	−	0.191859i	−0.604640	−	0.796499i	$-0.706683\pi$
$163$	2.44949	−	2.44949i	0.191859	−	0.191859i	0.796499	+	0.604640i	$0.206683\pi$
$164$	−5.51399			−0.430570
$165$	−5.47701	+	0.0481882i	−0.426385	+	0.00375144i
$166$	8.00000			0.620920
$167$	3.60697	−	3.60697i	0.279115	−	0.279115i	−0.553640	−	0.832756i	$-0.686762\pi$
$167$	3.60697	−	3.60697i	0.279115	−	0.279115i	0.832756	+	0.553640i	$0.186762\pi$
$168$	1.88366	−	1.56583i	0.145328	−	0.120806i
$169$			6.69694i			0.515149i
$170$	−1.41421	+	1.73205i	−0.108465	+	0.132842i
$171$	−7.52270	−	1.39816i	−0.575276	−	0.106920i
$172$	2.55051	+	2.55051i	0.194475	+	0.194475i
$173$	1.87492	+	1.87492i	0.142547	+	0.142547i	0.774779	−	0.632232i	$-0.217861\pi$
$173$	1.87492	+	1.87492i	0.142547	+	0.142547i	−0.632232	+	0.774779i	$0.717861\pi$
$174$	−11.4012	−	1.05051i	−0.864322	−	0.0796390i
$175$	3.89898	−	5.89898i	0.294735	−	0.445921i
$176$		−	1.41421i		−	0.106600i
$177$	−0.351911	−	0.423344i	−0.0264513	−	0.0318205i
$178$	−11.2247	+	11.2247i	−0.841330	+	0.841330i
$179$	−20.1489			−1.50600			−0.753001	−	0.658019i	$-0.771395\pi$
$179$	−20.1489			−1.50600			−0.753001	+	0.658019i	$0.771395\pi$
$180$	4.33341	+	5.12070i	0.322993	+	0.381674i
$181$	−20.6969			−1.53839			−0.769196	−	0.639013i	$-0.779343\pi$
$181$	−20.6969			−1.53839			−0.769196	+	0.639013i	$0.779343\pi$
$182$	−2.51059	+	2.51059i	−0.186097	+	0.186097i
$183$	9.24348	+	11.1198i	0.683298	+	0.821996i
$184$			2.44949i			0.180579i
$185$	−2.19275	−	21.7060i	−0.161214	−	1.59586i
$186$	−5.17423	−	0.476756i	−0.379393	−	0.0349574i
$187$	1.00000	+	1.00000i	0.0731272	+	0.0731272i
$188$	3.53553	+	3.53553i	0.257855	+	0.257855i
$189$	7.07107	+	2.00000i	0.514344	+	0.145479i
$190$	−0.573214	−	5.67423i	−0.0415853	−	0.411652i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	−1.33195	+	1.10721i	−0.0961253	+	0.0799057i
$193$	−0.651531	+	0.651531i	−0.0468982	+	0.0468982i	−0.730167	−	0.683269i	$-0.760558\pi$
$193$	−0.651531	+	0.651531i	−0.0468982	+	0.0468982i	0.683269	+	0.730167i	$0.260558\pi$
$194$	−5.83183			−0.418701
$195$	−6.93576	−	6.81478i	−0.496680	−	0.488016i
$196$	−5.00000			−0.357143
$197$	1.73205	−	1.73205i	0.123404	−	0.123404i	−0.642708	−	0.766111i	$-0.722189\pi$
$197$	1.73205	−	1.73205i	0.123404	−	0.123404i	0.766111	+	0.642708i	$0.222189\pi$
$198$	3.49768	−	2.40130i	0.248569	−	0.170653i
$199$			16.7980i			1.19078i	0.803438	+	0.595388i	$0.203002\pi$
$199$			16.7980i			1.19078i	−0.803438	+	0.595388i	$0.796998\pi$
$200$	−2.75699	+	4.17121i	−0.194949	+	0.294949i
$201$	2.34847	−	25.4880i	0.165648	−	1.79778i
$202$	3.44949	+	3.44949i	0.242705	+	0.242705i
$203$	−6.61037	−	6.61037i	−0.463957	−	0.463957i
$204$	0.158919	−	1.72474i	0.0111265	−	0.120756i
$205$	7.79796	−	9.55051i	0.544633	−	0.667037i
$206$			16.6848i			1.16249i
$207$	−6.05816	+	4.15918i	−0.421071	+	0.289083i
$208$	1.77526	−	1.77526i	0.123092	−	0.123092i
$209$	−3.60697			−0.249499
$210$	0.0481882	+	5.47701i	0.00332530	+	0.377950i
$211$	−15.5505			−1.07054			−0.535271	−	0.844681i	$-0.679790\pi$
$211$	−15.5505			−1.07054			−0.535271	+	0.844681i	$0.679790\pi$
$212$	7.95315	−	7.95315i	0.546224	−	0.546224i
$213$	−6.07433	+	5.04939i	−0.416207	+	0.345979i
$214$		−	1.79796i		−	0.122906i
$215$	−8.02458	+	0.810647i	−0.547272	+	0.0552857i
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$	−3.00000	−	3.00000i	−0.203653	−	0.203653i
$218$	3.07483	+	3.07483i	0.208254	+	0.208254i
$219$	0.794593	+	0.0732141i	0.0536936	+	0.00494735i
$220$	2.44949	+	2.00000i	0.165145	+	0.134840i
$221$			2.51059i			0.168881i
$222$	10.8026	+	12.9954i	0.725023	+	0.872191i
$223$	−7.87628	+	7.87628i	−0.527434	+	0.527434i	−0.919807	−	0.392372i	$-0.871655\pi$
$223$	−7.87628	+	7.87628i	−0.527434	+	0.527434i	0.392372	+	0.919807i	$0.371655\pi$
$224$	−1.41421			−0.0944911
$225$	−14.9977	+	0.263927i	−0.999845	+	0.0175951i
$226$	−16.7980			−1.11738
$227$	−16.5813	+	16.5813i	−1.10054	+	1.10054i	−0.106194	+	0.994345i	$0.533866\pi$
$227$	−16.5813	+	16.5813i	−1.10054	+	1.10054i	−0.994345	+	0.106194i	$0.966134\pi$
$228$	2.82394	+	3.39716i	0.187020	+	0.224982i
$229$		−	0.202041i		−	0.0133512i	−0.999978	−	0.00667562i	$-0.997875\pi$
$229$		−	0.202041i		−	0.0133512i	0.999978	−	0.00667562i	$-0.00212493\pi$
$230$	−4.24264	−	3.46410i	−0.279751	−	0.228416i
$231$	3.44949	+	0.317837i	0.226960	+	0.0209122i
$232$	4.67423	+	4.67423i	0.306879	+	0.306879i
$233$	−9.04952	−	9.04952i	−0.592854	−	0.592854i	0.345547	−	0.938401i	$-0.387693\pi$
$233$	−9.04952	−	9.04952i	−0.592854	−	0.592854i	−0.938401	+	0.345547i	$0.887693\pi$
$234$	7.40496	+	1.37628i	0.484077	+	0.0899700i
$235$	−11.1237	+	1.12372i	−0.725632	+	0.0733037i
$236$			0.317837i			0.0206894i
$237$	9.18910	−	7.63859i	0.596896	−	0.496180i
$238$	1.00000	−	1.00000i	0.0648204	−	0.0648204i
$239$	11.6637			0.754459			0.377230	−	0.926120i	$-0.376877\pi$
$239$	11.6637			0.754459			0.377230	+	0.926120i	$0.376877\pi$
$240$	−0.0340742	−	3.87283i	−0.00219948	−	0.249990i
$241$	17.5505			1.13053			0.565264	−	0.824910i	$-0.308774\pi$
$241$	17.5505			1.13053			0.565264	+	0.824910i	$0.308774\pi$
$242$	−6.36396	+	6.36396i	−0.409091	+	0.409091i
$243$	−4.99221	−	14.7675i	−0.320250	−	0.947333i
$244$		−	8.34847i		−	0.534456i
$245$	7.07107	−	8.66025i	0.451754	−	0.553283i
$246$	−0.876276	+	9.51023i	−0.0558693	+	0.606350i
$247$	−4.52781	−	4.52781i	−0.288097	−	0.288097i
$248$	2.12132	+	2.12132i	0.134704	+	0.134704i
$249$	1.27135	−	13.7980i	0.0805685	−	0.874410i
$250$	−3.32577	−	10.6742i	−0.210340	−	0.675098i
$251$			26.7272i			1.68701i	0.537125	+	0.843503i	$0.319510\pi$
$251$			26.7272i			1.68701i	−0.537125	+	0.843503i	$0.680490\pi$
$252$	−2.40130	−	3.49768i	−0.151268	−	0.220333i
$253$	−2.44949	+	2.44949i	−0.153998	+	0.153998i
$254$	−1.73205			−0.108679
$255$	2.76260	+	2.71441i	0.173001	+	0.169983i
$256$	1.00000			0.0625000
$257$	−6.75323	+	6.75323i	−0.421255	+	0.421255i	−0.885636	−	0.464381i	$-0.846277\pi$
$257$	−6.75323	+	6.75323i	−0.421255	+	0.421255i	0.464381	+	0.885636i	$0.346277\pi$
$258$	4.80430	−	3.99366i	0.299103	−	0.248634i
$259$			13.7980i			0.857363i
$260$	0.564242	+	5.58542i	0.0349928	+	0.346393i
$261$	−3.62372	+	19.4972i	−0.224303	+	1.20685i
$262$	11.3485	+	11.3485i	0.701111	+	0.701111i
$263$	−19.4418	−	19.4418i	−1.19883	−	1.19883i	−0.974516	−	0.224319i	$-0.927984\pi$
$263$	−19.4418	−	19.4418i	−1.19883	−	1.19883i	−0.224319	−	0.974516i	$-0.572016\pi$
$264$	−2.43916	−	0.224745i	−0.150120	−	0.0138321i
$265$	2.52781	+	25.0227i	0.155282	+	1.53713i
$266$			3.60697i			0.221157i
$267$	17.5760	+	21.1436i	1.07563	+	1.29397i
$268$	−10.4495	+	10.4495i	−0.638304	+	0.638304i
$269$	5.97469			0.364283			0.182142	−	0.983272i	$-0.441697\pi$
$269$	5.97469			0.364283			0.182142	+	0.983272i	$0.441697\pi$
$270$	9.52056	−	6.66025i	0.579403	−	0.405330i
$271$	2.24745			0.136523			0.0682614	−	0.997667i	$-0.478255\pi$
$271$	2.24745			0.136523			0.0682614	+	0.997667i	$0.478255\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$	3.93115	+	4.72911i	0.237924	+	0.286219i
$274$			9.55051i			0.576967i
$275$	−6.92820	+	1.41421i	−0.417786	+	0.0852803i
$276$	4.22474	+	0.389270i	0.254300	+	0.0234313i
$277$	13.3485	+	13.3485i	0.802032	+	0.802032i	0.983413	−	0.181381i	$-0.0580568\pi$
$277$	13.3485	+	13.3485i	0.802032	+	0.802032i	−0.181381	+	0.983413i	$0.558057\pi$
$278$	12.5851	+	12.5851i	0.754802	+	0.754802i
$279$	−1.64456	+	8.84847i	−0.0984575	+	0.529744i
$280$	2.00000	−	2.44949i	0.119523	−	0.146385i
$281$		−	25.3451i		−	1.51196i	−0.654594	−	0.755981i	$-0.727160\pi$
$281$		−	25.3451i		−	1.51196i	0.654594	−	0.755981i	$-0.272840\pi$
$282$	6.65976	−	5.53603i	0.396583	−	0.329666i
$283$	−1.77526	+	1.77526i	−0.105528	+	0.105528i	−0.757899	−	0.652371i	$-0.773774\pi$
$283$	−1.77526	+	1.77526i	−0.105528	+	0.105528i	0.652371	+	0.757899i	$0.273774\pi$
$284$	4.56048			0.270615
$285$	−9.87770	+	0.0869065i	−0.585105	+	0.00514790i
$286$	3.55051			0.209946
$287$	−5.51399	+	5.51399i	−0.325481	+	0.325481i
$288$	1.69798	+	2.47323i	0.100054	+	0.145737i
$289$		−	1.00000i		−	0.0588235i
$290$	−14.7064	+	1.48565i	−0.863588	+	0.0872401i
$291$	−0.926786	+	10.0584i	−0.0543292	+	0.589635i
$292$	−0.325765	−	0.325765i	−0.0190640	−	0.0190640i
$293$	−5.12472	−	5.12472i	−0.299389	−	0.299389i	0.541385	−	0.840775i	$-0.317900\pi$
$293$	−5.12472	−	5.12472i	−0.299389	−	0.299389i	−0.840775	+	0.541385i	$0.817900\pi$
$294$	−0.794593	+	8.62372i	−0.0463416	+	0.502946i
$295$	−0.550510	−	0.449490i	−0.0320519	−	0.0261703i
$296$		−	9.75663i		−	0.567093i
$297$	−3.58579	−	6.41421i	−0.208068	−	0.372190i
$298$	−6.79796	+	6.79796i	−0.393795	+	0.393795i
$299$	−6.14966			−0.355644
$300$	6.75613	+	5.41800i	0.390065	+	0.312808i
$301$	5.10102			0.294018
$302$	−10.8530	+	10.8530i	−0.624520	+	0.624520i
$303$	6.49768	−	5.40130i	0.373282	−	0.310297i
$304$		−	2.55051i		−	0.146282i
$305$	14.4600	+	11.8065i	0.827976	+	0.676039i
$306$	−2.94949	−	0.548188i	−0.168611	−	0.0313378i
$307$	−12.0000	−	12.0000i	−0.684876	−	0.684876i	0.276219	−	0.961095i	$-0.410919\pi$
$307$	−12.0000	−	12.0000i	−0.684876	−	0.684876i	−0.961095	+	0.276219i	$0.910919\pi$
$308$	−1.41421	−	1.41421i	−0.0805823	−	0.0805823i
$309$	28.7771	+	2.65153i	1.63707	+	0.150840i
$310$	−6.67423	+	0.674235i	−0.379071	+	0.0382940i
$311$			32.0983i			1.82013i	0.414467	+	0.910064i	$0.363968\pi$
$311$			32.0983i			1.82013i	−0.414467	+	0.910064i	$0.636032\pi$
$312$	−2.77974	−	3.34398i	−0.157372	−	0.189316i
$313$	−14.6969	+	14.6969i	−0.830720	+	0.830720i	−0.987615	−	0.156895i	$-0.949852\pi$
$313$	−14.6969	+	14.6969i	−0.830720	+	0.830720i	0.156895	+	0.987615i	$0.449852\pi$
$314$		0			0
$315$	9.45411	+	0.787287i	0.532679	+	0.0443586i
$316$	−6.89898			−0.388098
$317$	−13.5065	+	13.5065i	−0.758598	+	0.758598i	−0.976067	−	0.217469i	$-0.930220\pi$
$317$	−13.5065	+	13.5065i	−0.758598	+	0.758598i	0.217469	+	0.976067i	$0.430220\pi$
$318$	−12.4532	−	14.9811i	−0.698343	−	0.840096i
$319$			9.34847i			0.523414i
$320$	−1.41421	+	1.73205i	−0.0790569	+	0.0968246i
$321$	−3.10102	−	0.285729i	−0.173082	−	0.0159478i
$322$	2.44949	+	2.44949i	0.136505	+	0.136505i
$323$	1.80348	+	1.80348i	0.100348	+	0.100348i
$324$	−3.23375	+	8.39898i	−0.179653	+	0.466610i
$325$	−10.4722	−	6.92168i	−0.580893	−	0.383946i
$326$			3.46410i			0.191859i
$327$	5.79195	−	4.81465i	0.320296	−	0.266251i
$328$	3.89898	−	3.89898i	0.215285	−	0.215285i
$329$	7.07107			0.389841
$330$	3.83876	−	3.90691i	0.211317	−	0.215068i
$331$	−21.0454			−1.15676			−0.578380	−	0.815767i	$-0.696315\pi$
$331$	−21.0454			−1.15676			−0.578380	+	0.815767i	$0.696315\pi$
$332$	−5.65685	+	5.65685i	−0.310460	+	0.310460i
$333$	24.1304	−	16.5665i	1.32234	−	0.907840i
$334$			5.10102i			0.279115i
$335$	−3.32124	−	32.8769i	−0.181459	−	1.79625i
$336$	−0.224745	+	2.43916i	−0.0122608	+	0.133067i
$337$	−19.4722	−	19.4722i	−1.06072	−	1.06072i	−0.998033	−	0.0626846i	$-0.980034\pi$
$337$	−19.4722	−	19.4722i	−1.06072	−	1.06072i	−0.0626846	−	0.998033i	$-0.519966\pi$
$338$	−4.73545	−	4.73545i	−0.257575	−	0.257575i
$339$	−2.66951	+	28.9722i	−0.144988	+	1.57355i
$340$	−0.224745	−	2.22474i	−0.0121885	−	0.120654i
$341$			4.24264i			0.229752i
$342$	6.30800	−	4.33071i	0.341098	−	0.234178i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	−3.60697			−0.194475
$345$	−6.64893	+	6.76696i	−0.357966	+	0.364321i
$346$	−2.65153			−0.142547
$347$	22.5881	−	22.5881i	1.21259	−	1.21259i	0.242421	−	0.970171i	$-0.422058\pi$
$347$	22.5881	−	22.5881i	1.21259	−	1.21259i	0.970171	−	0.242421i	$-0.0779416\pi$
$348$	8.80469	−	7.31904i	0.471981	−	0.392342i
$349$		−	18.4495i		−	0.987579i	−0.869582	−	0.493789i	$-0.835611\pi$
$349$		−	18.4495i		−	0.987579i	0.869582	−	0.493789i	$-0.164389\pi$
$350$	1.41421	+	6.92820i	0.0755929	+	0.370328i
$351$	3.55051	−	12.5529i	0.189512	−	0.670027i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	−1.09638	−	1.09638i	−0.0583542	−	0.0583542i	0.677327	−	0.735682i	$-0.263138\pi$
$353$	−1.09638	−	1.09638i	−0.0583542	−	0.0583542i	−0.735682	+	0.677327i	$0.763138\pi$
$354$	0.548188	+	0.0505103i	0.0291359	+	0.00268459i
$355$	−6.44949	+	7.89898i	−0.342303	+	0.419234i
$356$		−	15.8742i		−	0.841330i
$357$	−1.56583	−	1.88366i	−0.0828723	−	0.0996940i
$358$	14.2474	−	14.2474i	0.753001	−	0.753001i
$359$	−0.142865			−0.00754010			−0.00377005	−	0.999993i	$-0.501200\pi$
$359$	−0.142865			−0.00754010			−0.00377005	+	0.999993i	$0.501200\pi$
$360$	−6.68506	−	0.556696i	−0.352334	−	0.0293405i
$361$	12.4949			0.657626
$362$	14.6349	−	14.6349i	0.769196	−	0.769196i
$363$	9.96486	+	11.9876i	0.523019	+	0.629184i
$364$		−	3.55051i		−	0.186097i
$365$	1.02494	−	0.103540i	0.0536480	−	0.00541955i
$366$	−14.3990	−	1.32673i	−0.752647	−	0.0693491i
$367$	−6.24745	−	6.24745i	−0.326114	−	0.326114i	0.524993	−	0.851107i	$-0.324068\pi$
$367$	−6.24745	−	6.24745i	−0.326114	−	0.326114i	−0.851107	+	0.524993i	$0.824068\pi$
$368$	−1.73205	−	1.73205i	−0.0902894	−	0.0902894i
$369$	16.2635	+	3.02270i	0.846642	+	0.157356i
$370$	16.8990	+	13.7980i	0.878536	+	0.717322i
$371$		−	15.9063i		−	0.825814i
$372$	3.99585	−	3.32162i	0.207175	−	0.172218i
$373$	16.8990	−	16.8990i	0.874996	−	0.874996i	−0.118016	−	0.993012i	$-0.537653\pi$
$373$	16.8990	−	16.8990i	0.874996	−	0.874996i	0.993012	+	0.118016i	$0.0376533\pi$
$374$	−1.41421			−0.0731272
$375$	−18.9389	+	4.03976i	−0.977998	+	0.208612i
$376$	−5.00000			−0.257855
$377$	−11.7351	+	11.7351i	−0.604388	+	0.604388i
$378$	−6.41421	+	3.58579i	−0.329912	+	0.184433i
$379$		−	15.5959i		−	0.801108i	−0.916273	−	0.400554i	$-0.868818\pi$
$379$		−	15.5959i		−	0.801108i	0.916273	−	0.400554i	$-0.131182\pi$
$380$	4.41761	+	3.60697i	0.226619	+	0.185033i
$381$	−0.275255	+	2.98735i	−0.0141017	+	0.153046i
$382$	−2.00000	−	2.00000i	−0.102329	−	0.102329i
$383$	−9.82806	−	9.82806i	−0.502191	−	0.502191i	0.409928	−	0.912118i	$-0.365554\pi$
$383$	−9.82806	−	9.82806i	−0.502191	−	0.502191i	−0.912118	+	0.409928i	$0.865554\pi$
$384$	0.158919	−	1.72474i	0.00810978	−	0.0880155i
$385$	4.44949	−	0.449490i	0.226767	−	0.0229081i
$386$		−	0.921404i		−	0.0468982i
$387$	−6.12454	−	8.92086i	−0.311328	−	0.453473i
$388$	4.12372	−	4.12372i	0.209350	−	0.209350i
$389$	−22.4846			−1.14001			−0.570006	−	0.821641i	$-0.693059\pi$
$389$	−22.4846			−1.14001			−0.570006	+	0.821641i	$0.693059\pi$
$390$	9.72310	−	0.0855463i	0.492348	−	0.00433180i
$391$	2.44949			0.123876
$392$	3.53553	−	3.53553i	0.178571	−	0.178571i
$393$	21.3767	−	17.7697i	1.07831	−	0.896364i
$394$			2.44949i			0.123404i
$395$	9.75663	−	11.9494i	0.490909	−	0.601239i
$396$	−0.775255	+	4.17121i	−0.0389580	+	0.209611i
$397$	−1.69694	−	1.69694i	−0.0851669	−	0.0851669i	0.663240	−	0.748407i	$-0.269181\pi$
$397$	−1.69694	−	1.69694i	−0.0851669	−	0.0851669i	−0.748407	+	0.663240i	$0.769181\pi$
$398$	−11.8780	−	11.8780i	−0.595388	−	0.595388i
$399$	6.22110	+	0.573214i	0.311444	+	0.0286966i
$400$	−1.00000	−	4.89898i	−0.0500000	−	0.244949i
$401$		−	25.9487i		−	1.29581i	−0.761719	−	0.647907i	$-0.775645\pi$
$401$		−	25.9487i		−	1.29581i	0.761719	−	0.647907i	$-0.224355\pi$
$402$	16.3621	+	19.6833i	0.816067	+	0.981715i
$403$	−5.32577	+	5.32577i	−0.265295	+	0.265295i
$404$	−4.87832			−0.242705
$405$	−9.97425	−	17.4790i	−0.495624	−	0.868537i
$406$	9.34847			0.463957
$407$	9.75663	−	9.75663i	0.483618	−	0.483618i
$408$	1.10721	+	1.33195i	0.0548149	+	0.0659414i
$409$		−	25.0000i		−	1.23617i	−0.786111	−	0.618085i	$-0.787909\pi$
$409$		−	25.0000i		−	1.23617i	0.786111	−	0.618085i	$-0.212091\pi$
$410$	1.23924	+	12.2672i	0.0612017	+	0.605835i
$411$	16.4722	+	1.51775i	0.812513	+	0.0748653i
$412$	−11.7980	−	11.7980i	−0.581244	−	0.581244i
$413$	0.317837	+	0.317837i	0.0156397	+	0.0156397i
$414$	1.34278	−	7.22474i	0.0659941	−	0.355077i
$415$	−1.79796	−	17.7980i	−0.0882583	−	0.873667i
$416$			2.51059i			0.123092i
$417$	23.7060	−	19.7060i	1.16089	−	0.965008i
$418$	2.55051	−	2.55051i	0.124750	−	0.124750i
$419$	−6.14966			−0.300431			−0.150215	−	0.988653i	$-0.547997\pi$
$419$	−6.14966			−0.300431			−0.150215	+	0.988653i	$0.547997\pi$
$420$	−3.90691	−	3.83876i	−0.190638	−	0.187312i
$421$	16.8990			0.823606			0.411803	−	0.911273i	$-0.364899\pi$
$421$	16.8990			0.823606			0.411803	+	0.911273i	$0.364899\pi$
$422$	10.9959	−	10.9959i	0.535271	−	0.535271i
$423$	−8.48988	−	12.3662i	−0.412792	−	0.601263i
$424$			11.2474i			0.546224i
$425$	4.17121	+	2.75699i	0.202333	+	0.133734i
$426$	0.724745	−	7.86566i	0.0351140	−	0.381093i
$427$	−8.34847	−	8.34847i	−0.404011	−	0.404011i
$428$	1.27135	+	1.27135i	0.0614530	+	0.0614530i
$429$	0.564242	−	6.12372i	0.0272419	−	0.295656i
$430$	5.10102	−	6.24745i	0.245993	−	0.301279i
$431$			39.3123i			1.89360i	0.321816	+	0.946802i	$0.395707\pi$
$431$			39.3123i			1.89360i	−0.321816	+	0.946802i	$0.604293\pi$
$432$	4.53553	−	2.53553i	0.218216	−	0.121991i
$433$	−13.8990	+	13.8990i	−0.667942	+	0.667942i	−0.957239	−	0.289297i	$-0.906578\pi$
$433$	−13.8990	+	13.8990i	−0.667942	+	0.667942i	0.289297	+	0.957239i	$0.406578\pi$
$434$	4.24264			0.203653
$435$	0.225243	+	25.6008i	0.0107996	+	1.22747i
$436$	−4.34847			−0.208254
$437$	−4.41761	+	4.41761i	−0.211323	+	0.211323i
$438$	−0.613632	+	0.510092i	−0.0293205	+	0.0243731i
$439$			6.89898i			0.329270i	0.986355	+	0.164635i	$0.0526447\pi$
$439$			6.89898i			0.329270i	−0.986355	+	0.164635i	$0.947355\pi$
$440$	−3.14626	+	0.317837i	−0.149992	+	0.0151523i
$441$	14.7474	+	2.74094i	0.702259	+	0.130521i
$442$	−1.77526	−	1.77526i	−0.0844403	−	0.0844403i
$443$	−16.5099	−	16.5099i	−0.784407	−	0.784407i	0.196164	−	0.980571i	$-0.437152\pi$
$443$	−16.5099	−	16.5099i	−0.784407	−	0.784407i	−0.980571	+	0.196164i	$0.937152\pi$
$444$	−16.8277	−	1.55051i	−0.798607	−	0.0735840i
$445$	27.4949	+	22.4495i	1.30338	+	1.06421i
$446$		−	11.1387i		−	0.527434i
$447$	10.6444	+	12.8051i	0.503464	+	0.605659i
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	−10.2494			−0.483701			−0.241850	−	0.970314i	$-0.577754\pi$
$449$	−10.2494			−0.483701			−0.241850	+	0.970314i	$0.577754\pi$
$450$	10.4183	−	10.7916i	0.491125	−	0.508720i
$451$	7.79796			0.367192
$452$	11.8780	−	11.8780i	0.558692	−	0.558692i
$453$	16.9939	+	20.4434i	0.798444	+	0.960515i
$454$		−	23.4495i		−	1.10054i
$455$	6.14966	+	5.02118i	0.288301	+	0.235397i
$456$	−4.39898	−	0.405324i	−0.206001	−	0.0189810i
$457$	−20.7980	−	20.7980i	−0.972887	−	0.972887i	0.0267545	−	0.999642i	$-0.491483\pi$
$457$	−20.7980	−	20.7980i	−0.972887	−	0.972887i	−0.999642	+	0.0267545i	$0.991483\pi$
$458$	0.142865	+	0.142865i	0.00667562	+	0.00667562i
$459$	−1.41421	+	5.00000i	−0.0660098	+	0.233380i
$460$	5.44949	−	0.550510i	0.254084	−	0.0256677i
$461$			28.4914i			1.32697i	0.748188	+	0.663487i	$0.230924\pi$
$461$			28.4914i			1.32697i	−0.748188	+	0.663487i	$0.769076\pi$
$462$	−2.66390	+	2.21441i	−0.123936	+	0.103024i
$463$	21.9217	−	21.9217i	1.01879	−	1.01879i	0.0189669	−	0.999820i	$-0.493962\pi$
$463$	21.9217	−	21.9217i	1.01879	−	1.01879i	0.999820	−	0.0189669i	$-0.00603772\pi$
$464$	−6.61037			−0.306879
$465$	0.102223	+	11.6185i	0.00474046	+	0.538795i
$466$	12.7980			0.592854
$467$	−12.1244	+	12.1244i	−0.561048	+	0.561048i	−0.929605	−	0.368557i	$-0.879852\pi$
$467$	−12.1244	+	12.1244i	−0.561048	+	0.561048i	0.368557	+	0.929605i	$0.379852\pi$
$468$	−6.20927	+	4.26292i	−0.287024	+	0.197054i
$469$			20.8990i			0.965025i
$470$	7.07107	−	8.66025i	0.326164	−	0.399468i
$471$		0			0
$472$	−0.224745	−	0.224745i	−0.0103447	−	0.0103447i
$473$	−3.60697	−	3.60697i	−0.165848	−	0.165848i
$474$	−1.09638	+	11.8990i	−0.0503582	+	0.546538i
$475$	−12.4949	+	2.55051i	−0.573305	+	0.117025i
$476$			1.41421i			0.0648204i
$477$	−27.8175	+	19.0979i	−1.27368	+	0.874433i
$478$	−8.24745	+	8.24745i	−0.377230	+	0.377230i
$479$	−4.21053			−0.192384			−0.0961921	−	0.995363i	$-0.530666\pi$
$479$	−4.21053			−0.192384			−0.0961921	+	0.995363i	$0.530666\pi$
$480$	2.76260	+	2.71441i	0.126095	+	0.123895i
$481$	24.4949			1.11687
$482$	−12.4101	+	12.4101i	−0.565264	+	0.565264i
$483$	4.61401	−	3.83548i	0.209945	−	0.174520i
$484$		−	9.00000i		−	0.409091i
$485$	1.31067	+	12.9743i	0.0595146	+	0.589134i
$486$	13.9722	+	6.91215i	0.633792	+	0.313541i
$487$	14.6515	+	14.6515i	0.663924	+	0.663924i	0.956303	−	0.292378i	$-0.0944467\pi$
$487$	14.6515	+	14.6515i	0.663924	+	0.663924i	−0.292378	+	0.956303i	$0.594447\pi$
$488$	5.90326	+	5.90326i	0.267228	+	0.267228i
$489$	5.97469	+	0.550510i	0.270185	+	0.0248949i
$490$	1.12372	+	11.1237i	0.0507647	+	0.502519i
$491$			28.3164i			1.27790i	0.769248	+	0.638950i	$0.220631\pi$
$491$			28.3164i			1.27790i	−0.769248	+	0.638950i	$0.779369\pi$
$492$	−6.10512	−	7.34437i	−0.275240	−	0.331110i
$493$	4.67423	−	4.67423i	0.210517	−	0.210517i
$494$	6.40329			0.288097
$495$	−6.12837	−	7.24176i	−0.275450	−	0.325493i
$496$	−3.00000			−0.134704
$497$	4.56048	−	4.56048i	0.204565	−	0.204565i
$498$	8.85765	+	10.6556i	0.396921	+	0.477489i
$499$		−	15.1464i		−	0.678047i	−0.940778	−	0.339024i	$-0.889903\pi$
$499$		−	15.1464i		−	0.678047i	0.940778	−	0.339024i	$-0.110097\pi$
$500$	9.89949	+	5.19615i	0.442719	+	0.232379i
$501$	8.79796	+	0.810647i	0.393064	+	0.0362170i
$502$	−18.8990	−	18.8990i	−0.843503	−	0.843503i
$503$	26.4094	+	26.4094i	1.17753	+	1.17753i	0.980370	+	0.197165i	$0.0631733\pi$
$503$	26.4094	+	26.4094i	1.17753	+	1.17753i	0.197165	+	0.980370i	$0.436827\pi$
$504$	4.17121	+	0.775255i	0.185800	+	0.0345326i
$505$	6.89898	−	8.44949i	0.307001	−	0.375997i
$506$		−	3.46410i		−	0.153998i
$507$	−8.92000	+	7.41489i	−0.396151	+	0.329307i
$508$	1.22474	−	1.22474i	0.0543393	−	0.0543393i
$509$	−33.6554			−1.49175			−0.745875	−	0.666086i	$-0.767968\pi$
$509$	−33.6554			−1.49175			−0.745875	+	0.666086i	$0.767968\pi$
$510$	−3.87283	+	0.0340742i	−0.171492	+	0.00150883i
$511$	−0.651531			−0.0288220
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−6.46691	−	11.5679i	−0.285521	−	0.510736i
$514$		−	9.55051i		−	0.421255i
$515$	37.1195	−	3.74983i	1.63568	−	0.165237i
$516$	−0.573214	+	6.22110i	−0.0252343	+	0.273869i
$517$	−5.00000	−	5.00000i	−0.219900	−	0.219900i
$518$	−9.75663	−	9.75663i	−0.428682	−	0.428682i
$519$	−0.421378	+	4.57321i	−0.0184964	+	0.200742i
$520$	−4.34847	−	3.55051i	−0.190693	−	0.155700i
$521$			33.6554i			1.47447i	0.675637	+	0.737235i	$0.263869\pi$
$521$			33.6554i			1.47447i	−0.675637	+	0.737235i	$0.736131\pi$
$522$	−11.2242	−	16.3490i	−0.491272	−	0.715575i
$523$	22.2474	−	22.2474i	0.972813	−	0.972813i	−0.0268271	−	0.999640i	$-0.508540\pi$
$523$	22.2474	−	22.2474i	0.972813	−	0.972813i	0.999640	+	0.0268271i	$0.00854035\pi$
$524$	−16.0492			−0.701111
$525$	12.1741	−	1.33814i	0.531322	−	0.0584011i
$526$	27.4949			1.19883
$527$	2.12132	−	2.12132i	0.0924062	−	0.0924062i
$528$	1.88366	−	1.56583i	0.0819759	−	0.0681438i
$529$		−	17.0000i		−	0.739130i
$530$	−19.4812	−	15.9063i	−0.846207	−	0.690925i
$531$	0.174235	−	0.937458i	0.00756114	−	0.0406822i
$532$	−2.55051	−	2.55051i	−0.110579	−	0.110579i
$533$	9.78874	+	9.78874i	0.423997	+	0.423997i
$534$	−27.3789	−	2.52270i	−1.18480	−	0.109168i
$535$	−4.00000	+	0.404082i	−0.172935	+	0.0174700i
$536$		−	14.7778i		−	0.638304i
$537$	−22.3090	−	26.8374i	−0.962706	−	1.15812i
$538$	−4.22474	+	4.22474i	−0.182142	+	0.182142i
$539$	7.07107			0.304572
$540$	−2.02254	+	11.4416i	−0.0870363	+	0.492366i
$541$	0.898979			0.0386501			0.0193251	−	0.999813i	$-0.493848\pi$
$541$	0.898979			0.0386501			0.0193251	+	0.999813i	$0.493848\pi$
$542$	−1.58919	+	1.58919i	−0.0682614	+	0.0682614i
$543$	−22.9158	−	27.5673i	−0.983410	−	1.18303i
$544$		−	1.00000i		−	0.0428746i
$545$	6.14966	−	7.53177i	0.263423	−	0.322626i
$546$	−6.12372	−	0.564242i	−0.262071	−	0.0241473i
$547$	8.42679	+	8.42679i	0.360303	+	0.360303i	0.863925	−	0.503621i	$-0.167999\pi$
$547$	8.42679	+	8.42679i	0.360303	+	0.360303i	−0.503621	+	0.863925i	$0.667999\pi$
$548$	−6.75323	−	6.75323i	−0.288484	−	0.288484i
$549$	−4.57653	+	24.6237i	−0.195322	+	1.05091i
$550$	3.89898	−	5.89898i	0.166253	−	0.251533i
$551$			16.8598i			0.718252i
$552$	−3.26260	+	2.71209i	−0.138866	+	0.115434i
$553$	−6.89898	+	6.89898i	−0.293374	+	0.293374i
$554$	−18.8776			−0.802032
$555$	26.4835	−	26.9537i	1.12416	−	1.14412i
$556$	−17.7980			−0.754802
$557$	−11.2744	+	11.2744i	−0.477711	+	0.477711i	−0.904399	−	0.426688i	$-0.859680\pi$
$557$	−11.2744	+	11.2744i	−0.477711	+	0.477711i	0.426688	+	0.904399i	$0.359680\pi$
$558$	−5.09393	−	7.41970i	−0.215643	−	0.314101i
$559$		−	9.05561i		−	0.383012i
$560$	0.317837	+	3.14626i	0.0134311	+	0.132954i
$561$	−0.224745	+	2.43916i	−0.00948874	+	0.102981i
$562$	17.9217	+	17.9217i	0.755981	+	0.755981i
$563$	2.51059	+	2.51059i	0.105809	+	0.105809i	0.758029	−	0.652221i	$-0.226162\pi$
$563$	2.51059	+	2.51059i	0.105809	+	0.105809i	−0.652221	+	0.758029i	$0.726162\pi$
$564$	−0.794593	+	8.62372i	−0.0334584	+	0.363124i
$565$	3.77526	+	37.3712i	0.158826	+	1.57222i
$566$		−	2.51059i		−	0.105528i
$567$	5.16523	+	11.6327i	0.216919	+	0.488529i
$568$	−3.22474	+	3.22474i	−0.135307	+	0.135307i
$569$	−10.5031			−0.440311			−0.220156	−	0.975465i	$-0.570657\pi$
$569$	−10.5031			−0.440311			−0.220156	+	0.975465i	$0.570657\pi$
$570$	6.92314	−	7.04604i	0.289978	−	0.295126i
$571$	4.20204			0.175850			0.0879250	−	0.996127i	$-0.471976\pi$
$571$	4.20204			0.175850			0.0879250	+	0.996127i	$0.471976\pi$
$572$	−2.51059	+	2.51059i	−0.104973	+	0.104973i
$573$	−3.76733	+	3.13165i	−0.157382	+	0.130827i
$574$		−	7.79796i		−	0.325481i
$575$	−6.75323	+	10.2173i	−0.281629	+	0.426092i
$576$	−2.94949	−	0.548188i	−0.122895	−	0.0228412i
$577$	3.79796	+	3.79796i	0.158111	+	0.158111i	0.781729	−	0.623618i	$-0.214338\pi$
$577$	3.79796	+	3.79796i	0.158111	+	0.158111i	−0.623618	+	0.781729i	$0.714338\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$	−1.58919	−	0.146428i	−0.0660443	−	0.00608535i
$580$	9.34847	−	11.4495i	0.388174	−	0.475414i
$581$			11.3137i			0.469372i
$582$	−6.45704	−	7.76771i	−0.267653	−	0.321982i
$583$	−11.2474	+	11.2474i	−0.465822	+	0.465822i
$584$	0.460702			0.0190640
$585$	1.39764	−	16.7835i	0.0577851	−	0.693910i
$586$	7.24745			0.299389
$587$	30.2234	−	30.2234i	1.24745	−	1.24745i	0.290613	−	0.956841i	$-0.406141\pi$
$587$	30.2234	−	30.2234i	1.24745	−	1.24745i	0.956841	−	0.290613i	$-0.0938591\pi$
$588$	−5.53603	−	6.65976i	−0.228302	−	0.274644i
$589$			7.65153i			0.315276i
$590$	0.707107	−	0.0714323i	0.0291111	−	0.00294082i
$591$	4.22474	+	0.389270i	0.173783	+	0.0160124i
$592$	6.89898	+	6.89898i	0.283546	+	0.283546i
$593$	−31.9555	−	31.9555i	−1.31225	−	1.31225i	−0.919751	−	0.392502i	$-0.871610\pi$
$593$	−31.9555	−	31.9555i	−1.31225	−	1.31225i	−0.392502	−	0.919751i	$-0.628390\pi$
$594$	7.07107	+	2.00000i	0.290129	+	0.0820610i
$595$	−2.44949	−	2.00000i	−0.100419	−	0.0819920i
$596$		−	9.61377i		−	0.393795i
$597$	−22.3741	+	18.5988i	−0.915709	+	0.761198i
$598$	4.34847	−	4.34847i	0.177822	−	0.177822i
$599$	13.9993			0.571995			0.285997	−	0.958230i	$-0.407675\pi$
$599$	13.9993			0.571995			0.285997	+	0.958230i	$0.407675\pi$
$600$	−8.60841	+	0.946206i	−0.351437	+	0.0386287i
$601$	35.1464			1.43365			0.716826	−	0.697252i	$-0.245594\pi$
$601$	35.1464			1.43365			0.716826	+	0.697252i	$0.245594\pi$
$602$	−3.60697	+	3.60697i	−0.147009	+	0.147009i
$603$	36.5489	−	25.0924i	1.48839	−	1.02184i
$604$		−	15.3485i		−	0.624520i
$605$	15.5885	+	12.7279i	0.633761	+	0.517464i
$606$	−0.775255	+	8.41385i	−0.0314926	+	0.341789i
$607$	18.7980	+	18.7980i	0.762986	+	0.762986i	0.976861	−	0.213875i	$-0.0686086\pi$
$607$	18.7980	+	18.7980i	0.762986	+	0.762986i	−0.213875	+	0.976861i	$0.568609\pi$
$608$	1.80348	+	1.80348i	0.0731409	+	0.0731409i
$609$	1.48565	−	16.1237i	0.0602014	−	0.653366i
$610$	−18.5732	+	1.87628i	−0.752007	+	0.0759682i
$611$		−	12.5529i		−	0.507838i
$612$	2.47323	−	1.69798i	0.0999745	−	0.0686366i
$613$	−28.9217	+	28.9217i	−1.16814	+	1.16814i	−0.185490	+	0.982646i	$0.559387\pi$
$613$	−28.9217	+	28.9217i	−1.16814	+	1.16814i	−0.982646	+	0.185490i	$0.940613\pi$
$614$	16.9706			0.684876
$615$	21.3548	−	0.187885i	0.861107	−	0.00757624i
$616$	2.00000			0.0805823
$617$	16.7563	−	16.7563i	0.674582	−	0.674582i	−0.284187	−	0.958769i	$-0.591724\pi$
$617$	16.7563	−	16.7563i	0.674582	−	0.674582i	0.958769	+	0.284187i	$0.0917237\pi$
$618$	−22.2234	+	18.4736i	−0.893956	+	0.743115i
$619$			12.6969i			0.510333i	0.966897	+	0.255167i	$0.0821303\pi$
$619$			12.6969i			0.510333i	−0.966897	+	0.255167i	$0.917870\pi$
$620$	4.24264	−	5.19615i	0.170389	−	0.208683i
$621$	−12.2474	−	3.46410i	−0.491473	−	0.139010i
$622$	−22.6969	−	22.6969i	−0.910064	−	0.910064i
$623$	−15.8742	−	15.8742i	−0.635986	−	0.635986i
$624$	4.33013	+	0.398979i	0.173344	+	0.0159720i
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$		−	20.7846i		−	0.830720i
$627$	−3.99366	−	4.80430i	−0.159491	−	0.191865i
$628$		0			0
$629$	−9.75663			−0.389022
$630$	−7.24176	+	6.12837i	−0.288519	+	0.244160i
$631$	−43.6413			−1.73733			−0.868667	−	0.495397i	$-0.835023\pi$
$631$	−43.6413			−1.73733			−0.868667	+	0.495397i	$0.835023\pi$
$632$	4.87832	−	4.87832i	0.194049	−	0.194049i
$633$	−17.2176	−	20.7125i	−0.684339	−	0.823249i
$634$		−	19.1010i		−	0.758598i
$635$	0.389270	+	3.85337i	0.0154477	+	0.152916i
$636$	19.3990	+	1.78743i	0.769220	+	0.0708762i
$637$	8.87628	+	8.87628i	0.351691	+	0.351691i
$638$	−6.61037	−	6.61037i	−0.261707	−	0.261707i
$639$	−13.4511	−	2.50000i	−0.532117	−	0.0988985i
$640$	−0.224745	−	2.22474i	−0.00888382	−	0.0879408i
$641$			3.46410i			0.136824i	0.997657	+	0.0684119i	$0.0217932\pi$
$641$			3.46410i			0.136824i	−0.997657	+	0.0684119i	$0.978207\pi$
$642$	2.39479	−	1.99071i	0.0945150	−	0.0785671i
$643$	−30.4949	+	30.4949i	−1.20260	+	1.20260i	−0.229229	+	0.973373i	$0.573620\pi$
$643$	−30.4949	+	30.4949i	−1.20260	+	1.20260i	−0.973373	+	0.229229i	$0.926380\pi$
$644$	−3.46410			−0.136505
$645$	−9.96461	−	9.79079i	−0.392356	−	0.385512i
$646$	−2.55051			−0.100348
$647$	−0.0714323	+	0.0714323i	−0.00280829	+	0.00280829i	−0.708510	−	0.705701i	$-0.750632\pi$
$647$	−0.0714323	+	0.0714323i	−0.00280829	+	0.00280829i	0.705701	+	0.708510i	$0.250632\pi$
$648$	−3.65237	−	8.22558i	−0.143479	−	0.323131i
$649$		−	0.449490i		−	0.0176440i
$650$	12.2993	−	2.51059i	0.482419	−	0.0984734i
$651$	0.674235	−	7.31747i	0.0264253	−	0.286794i
$652$	−2.44949	−	2.44949i	−0.0959294	−	0.0959294i
$653$	8.05669	+	8.05669i	0.315283	+	0.315283i	0.846952	−	0.531669i	$-0.178435\pi$
$653$	8.05669	+	8.05669i	0.315283	+	0.315283i	−0.531669	+	0.846952i	$0.678435\pi$
$654$	−0.691053	+	7.50000i	−0.0270223	+	0.293273i
$655$	22.6969	−	27.7980i	0.886843	−	1.08616i
$656$			5.51399i			0.215285i
$657$	0.782261	+	1.13942i	0.0305189	+	0.0444531i
$658$	−5.00000	+	5.00000i	−0.194920	+	0.194920i
$659$	−20.7525			−0.808403			−0.404201	−	0.914670i	$-0.632450\pi$
$659$	−20.7525			−0.808403			−0.404201	+	0.914670i	$0.632450\pi$
$660$	0.0481882	+	5.47701i	0.00187572	+	0.213192i
$661$	−7.10102			−0.276198			−0.138099	−	0.990418i	$-0.544099\pi$
$661$	−7.10102			−0.276198			−0.138099	+	0.990418i	$0.544099\pi$
$662$	14.8814	−	14.8814i	0.578380	−	0.578380i
$663$	−3.34398	+	2.77974i	−0.129870	+	0.107956i
$664$		−	8.00000i		−	0.310460i
$665$	8.02458	−	0.810647i	0.311180	−	0.0314355i
$666$	−5.34847	+	28.7771i	−0.207249	+	1.11509i
$667$	11.4495	+	11.4495i	0.443326	+	0.443326i
$668$	−3.60697	−	3.60697i	−0.139558	−	0.139558i
$669$	−19.2115	−	1.77015i	−0.742759	−	0.0684381i
$670$	25.5959	+	20.8990i	0.988857	+	0.807398i
$671$			11.8065i			0.455786i
$672$	−1.56583	−	1.88366i	−0.0604031	−	0.0726639i
$673$	−33.9217	+	33.9217i	−1.30758	+	1.30758i	−0.384431	+	0.923154i	$0.625602\pi$
$673$	−33.9217	+	33.9217i	−1.30758	+	1.30758i	−0.923154	+	0.384431i	$0.874398\pi$
$674$	27.5378			1.06072
$675$	−16.9571	−	19.6840i	−0.652678	−	0.757636i
$676$	6.69694			0.257575
$677$	24.5023	−	24.5023i	0.941701	−	0.941701i	−0.0566907	−	0.998392i	$-0.518055\pi$
$677$	24.5023	−	24.5023i	0.941701	−	0.941701i	0.998392	+	0.0566907i	$0.0180549\pi$
$678$	−18.5988	−	22.3741i	−0.714283	−	0.859271i
$679$		−	8.24745i		−	0.316508i
$680$	1.73205	+	1.41421i	0.0664211	+	0.0542326i
$681$	−40.4444	−	3.72656i	−1.54983	−	0.142802i
$682$	−3.00000	−	3.00000i	−0.114876	−	0.114876i
$683$	24.4309	+	24.4309i	0.934822	+	0.934822i	0.998002	−	0.0631798i	$-0.0201241\pi$
$683$	24.4309	+	24.4309i	0.934822	+	0.934822i	−0.0631798	+	0.998002i	$0.520124\pi$
$684$	−1.39816	+	7.52270i	−0.0534600	+	0.287638i
$685$	21.2474	−	2.14643i	0.811823	−	0.0820108i
$686$		−	16.9706i		−	0.647939i
$687$	0.269109	−	0.223701i	0.0102671	−	0.00853473i
$688$	2.55051	−	2.55051i	0.0972373	−	0.0972373i
$689$	−28.2377			−1.07577
$690$	−0.0834643	−	9.48647i	−0.00317743	−	0.361144i
$691$	−26.6969			−1.01560			−0.507800	−	0.861475i	$-0.669541\pi$
$691$	−26.6969			−1.01560			−0.507800	+	0.861475i	$0.669541\pi$
$692$	1.87492	−	1.87492i	0.0712736	−	0.0712736i
$693$	3.39595	+	4.94646i	0.129002	+	0.187901i
$694$			31.9444i			1.21259i
$695$	25.1701	−	30.8270i	0.954757	−	1.16933i
$696$	−1.05051	+	11.4012i	−0.0398195	+	0.432161i
$697$	−3.89898	−	3.89898i	−0.147684	−	0.147684i
$698$	13.0458	+	13.0458i	0.493789	+	0.493789i
$699$	2.03383	−	22.0732i	0.0769267	−	0.834886i
$700$	−5.89898	−	3.89898i	−0.222960	−	0.147368i
$701$			32.0983i			1.21234i	0.795336	+	0.606168i	$0.207294\pi$
$701$			32.0983i			1.21234i	−0.795336	+	0.606168i	$0.792706\pi$
$702$	6.36569	+	11.3869i	0.240257	+	0.429770i
$703$	17.5959	−	17.5959i	0.663643	−	0.663643i
$704$	−1.41421			−0.0533002
$705$	−13.8130	−	13.5721i	−0.520228	−	0.511153i
$706$	1.55051			0.0583542
$707$	−4.87832	+	4.87832i	−0.183468	+	0.183468i
$708$	−0.423344	+	0.351911i	−0.0159102	+	0.0132256i
$709$		−	17.2474i		−	0.647742i	−0.946101	−	0.323871i	$-0.895016\pi$
$709$		−	17.2474i		−	0.647742i	0.946101	−	0.323871i	$-0.104984\pi$
$710$	−1.02494	−	10.1459i	−0.0384655	−	0.380769i
$711$	20.3485	+	3.78194i	0.763127	+	0.141834i
$712$	11.2247	+	11.2247i	0.420665	+	0.420665i
$713$	5.19615	+	5.19615i	0.194597	+	0.194597i
$714$	2.43916	+	0.224745i	0.0912832	+	0.00841087i
$715$	−0.797959	−	7.89898i	−0.0298420	−	0.295405i
$716$			20.1489i			0.753001i
$717$	12.9141	+	15.5354i	0.482285	+	0.580181i
$718$	0.101021	−	0.101021i	0.00377005	−	0.00377005i
$719$	−3.00340			−0.112008			−0.0560040	−	0.998431i	$-0.517836\pi$
$719$	−3.00340			−0.112008			−0.0560040	+	0.998431i	$0.517836\pi$
$720$	5.12070	−	4.33341i	0.190837	−	0.161497i
$721$	−23.5959			−0.878758
$722$	−8.83523	+	8.83523i	−0.328813	+	0.328813i
$723$	19.4320	+	23.3764i	0.722685	+	0.869379i
$724$			20.6969i			0.769196i
$725$	6.61037	+	32.3840i	0.245503	+	1.20271i
$726$	−15.5227	−	1.43027i	−0.576102	−	0.0530822i
$727$	−36.3712	−	36.3712i	−1.34893	−	1.34893i	−0.886823	−	0.462109i	$-0.847093\pi$
$727$	−36.3712	−	36.3712i	−1.34893	−	1.34893i	−0.462109	−	0.886823i	$-0.652907\pi$
$728$	2.51059	+	2.51059i	0.0930487	+	0.0930487i
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	−0.651531	+	0.797959i	−0.0241142	+	0.0295338i
$731$			3.60697i			0.133408i
$732$	11.1198	−	9.24348i	0.410998	−	0.341649i
$733$	−23.3939	+	23.3939i	−0.864073	+	0.864073i	−0.991808	−	0.127736i	$-0.959229\pi$
$733$	−23.3939	+	23.3939i	−0.864073	+	0.864073i	0.127736	+	0.991808i	$0.459229\pi$
$734$	8.83523			0.326114
$735$	19.3642	−	0.170371i	0.714258	−	0.00628422i
$736$	2.44949			0.0902894
$737$	14.7778	−	14.7778i	0.544348	−	0.544348i
$738$	−13.6374	+	9.36263i	−0.501999	+	0.344643i
$739$			23.0454i			0.847739i	0.905723	+	0.423870i	$0.139328\pi$
$739$			23.0454i			0.847739i	−0.905723	+	0.423870i	$0.860672\pi$
$740$	−21.7060	+	2.19275i	−0.797929	+	0.0806072i
$741$	1.01760	−	11.0440i	0.0373825	−	0.405713i
$742$	11.2474	+	11.2474i	0.412907	+	0.412907i
$743$	−9.29593	−	9.29593i	−0.341035	−	0.341035i	0.515722	−	0.856756i	$-0.327524\pi$
$743$	−9.29593	−	9.29593i	−0.341035	−	0.341035i	−0.856756	+	0.515722i	$0.827524\pi$
$744$	−0.476756	+	5.17423i	−0.0174787	+	0.189697i
$745$	16.6515	+	13.5959i	0.610065	+	0.498116i
$746$			23.8988i			0.874996i
$747$	19.7859	−	13.5838i	0.723927	−	0.497006i
$748$	1.00000	−	1.00000i	0.0365636	−	0.0365636i
$749$	2.54270			0.0929082
$750$	10.5353	−	16.2483i	0.384693	−	0.593305i
$751$	−15.0000			−0.547358			−0.273679	−	0.961821i	$-0.588241\pi$
$751$	−15.0000			−0.547358			−0.273679	+	0.961821i	$0.588241\pi$
$752$	3.53553	−	3.53553i	0.128928	−	0.128928i
$753$	−35.5993	+	29.5925i	−1.29731	+	1.07841i
$754$		−	16.5959i		−	0.604388i
$755$	26.5843	+	21.7060i	0.967503	+	0.789963i
$756$	2.00000	−	7.07107i	0.0727393	−	0.257172i
$757$	33.3712	+	33.3712i	1.21290	+	1.21290i	0.970070	+	0.242826i	$0.0780744\pi$
$757$	33.3712	+	33.3712i	1.21290	+	1.21290i	0.242826	+	0.970070i	$0.421926\pi$
$758$	11.0280	+	11.0280i	0.400554	+	0.400554i
$759$	−5.97469	−	0.550510i	−0.216868	−	0.0199823i
$760$	−5.67423	+	0.573214i	−0.205826	+	0.0207927i
$761$		−	42.2049i		−	1.52993i	−0.644074	−	0.764963i	$-0.722757\pi$
$761$		−	42.2049i		−	1.52993i	0.644074	−	0.764963i	$-0.277243\pi$
$762$	−1.91774	−	2.30701i	−0.0694723	−	0.0835741i
$763$	−4.34847	+	4.34847i	−0.157425	+	0.157425i
$764$	2.82843			0.102329
$765$	−0.556696	+	6.68506i	−0.0201274	+	0.241699i
$766$	13.8990			0.502191
$767$	0.564242	−	0.564242i	0.0203736	−	0.0203736i
$768$	1.10721	+	1.33195i	0.0399529	+	0.0480627i
$769$			50.3939i			1.81725i	0.417613	+	0.908625i	$0.362867\pi$
$769$			50.3939i			1.81725i	−0.417613	+	0.908625i	$0.637133\pi$
$770$	−2.82843	+	3.46410i	−0.101929	+	0.124838i
$771$	−16.4722	−	1.51775i	−0.593232	−	0.0546606i
$772$	0.651531	+	0.651531i	0.0234491	+	0.0234491i
$773$	−2.33562	−	2.33562i	−0.0840063	−	0.0840063i	0.663855	−	0.747861i	$-0.268919\pi$
$773$	−2.33562	−	2.33562i	−0.0840063	−	0.0840063i	−0.747861	+	0.663855i	$0.768919\pi$
$774$	10.6387	+	1.97730i	0.382401	+	0.0710724i
$775$	3.00000	+	14.6969i	0.107763	+	0.527930i
$776$			5.83183i			0.209350i
$777$	−18.3782	+	15.2772i	−0.659315	+	0.548066i
$778$	15.8990	−	15.8990i	0.570006	−	0.570006i
$779$	14.0635			0.503877
$780$	−6.81478	+	6.93576i	−0.244008	+	0.248340i
$781$	−6.44949			−0.230781
$782$	−1.73205	+	1.73205i	−0.0619380	+	0.0619380i
$783$	−29.9815	+	16.7608i	−1.07145	+	0.598982i
$784$			5.00000i			0.178571i
$785$		0			0
$786$	−2.55051	+	27.6807i	−0.0909737	+	0.987338i
$787$	4.92168	+	4.92168i	0.175439	+	0.175439i	0.789364	−	0.613925i	$-0.210410\pi$
$787$	4.92168	+	4.92168i	0.175439	+	0.175439i	−0.613925	+	0.789364i	$0.710410\pi$
$788$	−1.73205	−	1.73205i	−0.0617018	−	0.0617018i
$789$	4.36945	−	47.4217i	0.155557	−	1.68826i
$790$	1.55051	+	15.3485i	0.0551647	+	0.546074i
$791$		−	23.7559i		−	0.844663i
$792$	−2.40130	−	3.49768i	−0.0853265	−	0.124285i
$793$	−14.8207	+	14.8207i	−0.526297	+	0.526297i
$794$	2.39983			0.0851669
$795$	−30.5302	+	31.0722i	−1.08280	+	1.10202i
$796$	16.7980			0.595388
$797$	21.7060	−	21.7060i	0.768866	−	0.768866i	−0.209041	−	0.977907i	$-0.567034\pi$
$797$	21.7060	−	21.7060i	0.768866	−	0.768866i	0.977907	+	0.209041i	$0.0670341\pi$
$798$	−4.80430	+	3.99366i	−0.170070	+	0.141374i
$799$			5.00000i			0.176887i
$800$	4.17121	+	2.75699i	0.147474	+	0.0974745i
$801$	−8.70204	+	46.8208i	−0.307472	+	1.65433i
$802$	18.3485	+	18.3485i	0.647907	+	0.647907i
$803$	0.460702	+	0.460702i	0.0162578	+	0.0162578i
$804$	−25.4880	−	2.34847i	−0.898891	−	0.0828241i
$805$	4.89898	−	6.00000i	0.172666	−	0.211472i
$806$		−	7.53177i		−	0.265295i
$807$	6.61522	+	7.95800i	0.232867	+	0.280135i
$808$	3.44949	−	3.44949i	0.121353	−	0.121353i
$809$	−24.8202			−0.872631			−0.436315	−	0.899794i	$-0.643717\pi$
$809$	−24.8202			−0.872631			−0.436315	+	0.899794i	$0.643717\pi$
$810$	19.4124	+	5.30664i	0.682081	+	0.186456i
$811$	−32.0454			−1.12527			−0.562633	−	0.826707i	$-0.690212\pi$
$811$	−32.0454			−1.12527			−0.562633	+	0.826707i	$0.690212\pi$
$812$	−6.61037	+	6.61037i	−0.231978	+	0.231978i
$813$	2.48839	+	2.99349i	0.0872716	+	0.104986i
$814$			13.7980i			0.483618i
$815$	7.70674	−	0.778539i	0.269955	−	0.0272710i
$816$	−1.72474	−	0.158919i	−0.0603781	−	0.00556326i
$817$	−6.50510	−	6.50510i	−0.227585	−	0.227585i
$818$	17.6777	+	17.6777i	0.618085	+	0.618085i
$819$	−1.94635	+	10.4722i	−0.0680109	+	0.365928i
$820$	−9.55051	−	7.79796i	−0.333518	−	0.272317i
$821$			16.0171i			0.558999i	0.960146	+	0.279499i	$0.0901685\pi$
$821$			16.0171i			0.558999i	−0.960146	+	0.279499i	$0.909831\pi$
$822$	−12.7208	+	10.5744i	−0.443689	+	0.368824i
$823$	3.55051	−	3.55051i	0.123763	−	0.123763i	−0.642512	−	0.766275i	$-0.722108\pi$
$823$	3.55051	−	3.55051i	0.123763	−	0.123763i	0.766275	+	0.642512i	$0.222108\pi$
$824$	16.6848			0.581244
$825$	−9.55461	−	7.66220i	−0.332649	−	0.266764i
$826$	−0.449490			−0.0156397
$827$	31.1769	−	31.1769i	1.08413	−	1.08413i	0.0880078	−	0.996120i	$-0.471950\pi$
$827$	31.1769	−	31.1769i	1.08413	−	1.08413i	0.996120	−	0.0880078i	$-0.0280500\pi$
$828$	4.15918	+	6.05816i	0.144541	+	0.210535i
$829$		−	21.1464i		−	0.734446i	−0.930133	−	0.367223i	$-0.880309\pi$
$829$		−	21.1464i		−	0.734446i	0.930133	−	0.367223i	$-0.119691\pi$
$830$	13.8564	+	11.3137i	0.480963	+	0.392705i
$831$	−3.00000	+	32.5590i	−0.104069	+	1.12946i
$832$	−1.77526	−	1.77526i	−0.0615459	−	0.0615459i
$833$	−3.53553	−	3.53553i	−0.122499	−	0.122499i
$834$	−2.82843	+	30.6969i	−0.0979404	+	1.06295i
$835$	11.3485	−	1.14643i	0.392730	−	0.0396738i
$836$			3.60697i			0.124750i
$837$	−13.6066	+	7.60660i	−0.470313	+	0.262923i
$838$	4.34847	−	4.34847i	0.150215	−	0.150215i
$839$	46.7012			1.61230			0.806151	−	0.591709i	$-0.201547\pi$
$839$	46.7012			1.61230			0.806151	+	0.591709i	$0.201547\pi$
$840$	5.47701	−	0.0481882i	0.188975	−	0.00166265i
$841$	14.6969			0.506791
$842$	−11.9494	+	11.9494i	−0.411803	+	0.411803i
$843$	33.7584	−	28.0622i	1.16270	−	0.966515i
$844$			15.5505i			0.535271i
$845$	−9.47090	+	11.5994i	−0.325809	+	0.399033i
$846$	14.7474	+	2.74094i	0.507028	+	0.0942355i
$847$	−9.00000	−	9.00000i	−0.309244	−	0.309244i
$848$	−7.95315	−	7.95315i	−0.273112	−	0.273112i
$849$	−4.33013	−	0.398979i	−0.148610	−	0.0136929i
$850$	−4.89898	+	1.00000i	−0.168034	+	0.0342997i
$851$		−	23.8988i		−	0.819239i
$852$	5.04939	+	6.07433i	0.172989	+	0.208103i
$853$	−27.1464	+	27.1464i	−0.929476	+	0.929476i	−0.997672	−	0.0681959i	$-0.978276\pi$
$853$	−27.1464	+	27.1464i	−0.929476	+	0.929476i	0.0681959	+	0.997672i	$0.478276\pi$
$854$	11.8065			0.404011
$855$	−11.0524	−	13.0604i	−0.377984	−	0.446656i
$856$	−1.79796			−0.0614530
$857$	−1.83559	+	1.83559i	−0.0627026	+	0.0627026i	−0.737763	−	0.675060i	$-0.764118\pi$
$857$	−1.83559	+	1.83559i	−0.0627026	+	0.0627026i	0.675060	+	0.737763i	$0.264118\pi$
$858$	3.93115	+	4.72911i	0.134207	+	0.161449i
$859$			14.7526i			0.503351i	0.967812	+	0.251675i	$0.0809815\pi$
$859$			14.7526i			0.503351i	−0.967812	+	0.251675i	$0.919019\pi$
$860$	0.810647	+	8.02458i	0.0276428	+	0.273636i
$861$	−13.4495	−	1.23924i	−0.458357	−	0.0422332i
$862$	−27.7980	−	27.7980i	−0.946802	−	0.946802i
$863$	13.8564	+	13.8564i	0.471678	+	0.471678i	0.902457	−	0.430780i	$-0.141761\pi$
$863$	13.8564	+	13.8564i	0.471678	+	0.471678i	−0.430780	+	0.902457i	$0.641761\pi$
$864$	−1.41421	+	5.00000i	−0.0481125	+	0.170103i
$865$	0.595918	+	5.89898i	0.0202618	+	0.200571i
$866$		−	19.6561i		−	0.667942i
$867$	1.33195	−	1.10721i	0.0452354	−	0.0376027i
$868$	−3.00000	+	3.00000i	−0.101827	+	0.101827i
$869$	9.75663			0.330971
$870$	−18.2618	−	17.9433i	−0.619133	−	0.608334i
$871$	37.1010			1.25712
$872$	3.07483	−	3.07483i	0.104127	−	0.104127i
$873$	−14.4235	+	9.90231i	−0.488160	+	0.335142i
$874$		−	6.24745i		−	0.211323i
$875$	15.0956	−	4.70334i	0.510326	−	0.159002i
$876$	0.0732141	−	0.794593i	0.00247368	−	0.0268468i
$877$	−21.0000	−	21.0000i	−0.709120	−	0.709120i	0.257230	−	0.966350i	$-0.417190\pi$
$877$	−21.0000	−	21.0000i	−0.709120	−	0.709120i	−0.966350	+	0.257230i	$0.917190\pi$
$878$	−4.87832	−	4.87832i	−0.164635	−	0.164635i
$879$	1.15175	−	12.5000i	0.0388477	−	0.421615i
$880$	2.00000	−	2.44949i	0.0674200	−	0.0825723i
$881$		−	20.7204i		−	0.698088i	−0.937106	−	0.349044i	$-0.886506\pi$
$881$		−	20.7204i		−	0.698088i	0.937106	−	0.349044i	$-0.113494\pi$
$882$	−12.3662	+	8.48988i	−0.416390	+	0.285869i
$883$	22.0454	−	22.0454i	0.741887	−	0.741887i	−0.231054	−	0.972941i	$-0.574217\pi$
$883$	22.0454	−	22.0454i	0.741887	−	0.741887i	0.972941	+	0.231054i	$0.0742174\pi$
$884$	2.51059			0.0844403
$885$	−0.0108300	−	1.23093i	−0.000364048	−	0.0413773i
$886$	23.3485			0.784407
$887$	−6.43539	+	6.43539i	−0.216079	+	0.216079i	−0.806844	−	0.590765i	$-0.798826\pi$
$887$	−6.43539	+	6.43539i	−0.216079	+	0.216079i	0.590765	+	0.806844i	$0.298826\pi$
$888$	12.9954	−	10.8026i	0.436096	−	0.362512i
$889$		−	2.44949i		−	0.0821532i
$890$	−35.3160	+	3.56764i	−1.18380	+	0.119588i
$891$	4.57321	−	11.8780i	0.153208	−	0.397926i
$892$	7.87628	+	7.87628i	0.263717	+	0.263717i
$893$	−9.01742	−	9.01742i	−0.301756	−	0.301756i
$894$	−16.5813	−	1.52781i	−0.554561	−	0.0510975i
$895$	−34.8990	−	28.4949i	−1.16654	−	0.952479i
$896$			1.41421i			0.0472456i
$897$	−6.80895	−	8.19105i	−0.227344	−	0.273491i
$898$	7.24745	−	7.24745i	0.241850	−	0.241850i
$899$	19.8311			0.661404
$900$	0.263927	+	14.9977i	0.00879757	+	0.499923i
$901$	11.2474			0.374707
$902$	−5.51399	+	5.51399i	−0.183596	+	0.183596i
$903$	5.64788	+	6.79431i	0.187950	+	0.226100i
$904$			16.7980i			0.558692i
$905$	−35.8481	−	29.2699i	−1.19163	−	0.972964i
$906$	−26.4722	−	2.43916i	−0.879480	−	0.0810356i
$907$	36.9671	+	36.9671i	1.22747	+	1.22747i	0.964917	+	0.262555i	$0.0845652\pi$
$907$	36.9671	+	36.9671i	1.22747	+	1.22747i	0.262555	+	0.964917i	$0.415435\pi$
$908$	16.5813	+	16.5813i	0.550270	+	0.550270i
$909$	14.3885	+	2.67423i	0.477238	+	0.0886988i
$910$	−7.89898	+	0.797959i	−0.261849	+	0.0264521i
$911$		−	8.54950i		−	0.283257i	−0.989920	−	0.141629i	$-0.954766\pi$
$911$		−	8.54950i		−	0.283257i	0.989920	−	0.141629i	$-0.0452339\pi$
$912$	3.39716	−	2.82394i	0.112491	−	0.0935100i
$913$	8.00000	−	8.00000i	0.264761	−	0.264761i
$914$	29.4128			0.972887
$915$	0.284467	+	32.3322i	0.00940420	+	1.06887i
$916$	−0.202041			−0.00667562
$917$	−16.0492	+	16.0492i	−0.529990	+	0.529990i
$918$	−2.53553	−	4.53553i	−0.0836851	−	0.149695i
$919$		−	57.1918i		−	1.88658i	−0.331963	−	0.943292i	$-0.607711\pi$
$919$		−	57.1918i		−	1.88658i	0.331963	−	0.943292i	$-0.392289\pi$
$920$	−3.46410	+	4.24264i	−0.114208	+	0.139876i
$921$	2.69694	−	29.2699i	0.0888671	−	0.964476i
$922$	−20.1464	−	20.1464i	−0.663487	−	0.663487i
$923$	−8.09601	−	8.09601i	−0.266483	−	0.266483i
$924$	0.317837	−	3.44949i	0.0104561	−	0.113480i
$925$	26.8990	−	40.6969i	0.884433	−	1.33811i
$926$			31.0019i			1.01879i
$927$	28.3305	+	41.2655i	0.930494	+	1.35534i
$928$	4.67423	−	4.67423i	0.153439	−	0.153439i
$929$	−38.6766			−1.26894			−0.634469	−	0.772949i	$-0.718781\pi$
$929$	−38.6766			−1.26894			−0.634469	+	0.772949i	$0.718781\pi$
$930$	−8.28780	−	8.14324i	−0.271768	−	0.267027i
$931$	12.7526			0.417948
$932$	−9.04952	+	9.04952i	−0.296427	+	0.296427i
$933$	−42.7534	+	35.5395i	−1.39968	+	1.16351i
$934$		−	17.1464i		−	0.561048i
$935$	0.317837	+	3.14626i	0.0103944	+	0.102894i
$936$	1.37628	−	7.40496i	0.0449850	−	0.242039i
$937$	17.1010	+	17.1010i	0.558666	+	0.558666i	0.928928	−	0.370262i	$-0.120732\pi$
$937$	17.1010	+	17.1010i	0.558666	+	0.558666i	−0.370262	+	0.928928i	$0.620732\pi$
$938$	−14.7778	−	14.7778i	−0.482513	−	0.482513i
$939$	−35.8481	−	3.30306i	−1.16986	−	0.107791i
$940$	1.12372	+	11.1237i	0.0366518	+	0.362816i
$941$		−	30.1592i		−	0.983161i	−0.870832	−	0.491581i	$-0.836419\pi$
$941$		−	30.1592i		−	0.983161i	0.870832	−	0.491581i	$-0.163581\pi$
$942$		0			0
$943$	9.55051	−	9.55051i	0.311007	−	0.311007i
$944$	0.317837			0.0103447
$945$	9.41902	+	13.4641i	0.306401	+	0.437987i
$946$	5.10102			0.165848
$947$	21.6667	−	21.6667i	0.704073	−	0.704073i	−0.261209	−	0.965282i	$-0.584121\pi$
$947$	21.6667	−	21.6667i	0.704073	−	0.704073i	0.965282	+	0.261209i	$0.0841213\pi$
$948$	−7.63859	−	9.18910i	−0.248090	−	0.298448i
$949$			1.15663i			0.0375459i
$950$	7.03174	−	10.6387i	0.228140	−	0.345165i
$951$	−32.9444	−	3.03551i	−1.06829	−	0.0984331i
$952$	−1.00000	−	1.00000i	−0.0324102	−	0.0324102i
$953$	27.7128	+	27.7128i	0.897706	+	0.897706i	0.995233	−	0.0975268i	$-0.0310932\pi$
$953$	27.7128	+	27.7128i	0.897706	+	0.897706i	−0.0975268	+	0.995233i	$0.531093\pi$
$954$	6.16572	−	33.1742i	0.199622	−	1.07406i
$955$	−4.00000	+	4.89898i	−0.129437	+	0.158527i
$956$		−	11.6637i		−	0.377230i
$957$	−12.4517	+	10.3507i	−0.402506	+	0.334590i
$958$	2.97730	−	2.97730i	0.0961921	−	0.0961921i
$959$	−13.5065			−0.436146
$960$	−3.87283	+	0.0340742i	−0.124995	+	0.00109974i
$961$	−22.0000			−0.709677
$962$	−17.3205	+	17.3205i	−0.558436	+	0.558436i
$963$	−3.05289	−	4.44677i	−0.0983781	−	0.143295i
$964$		−	17.5505i		−	0.565264i
$965$	−2.04989	+	0.207081i	−0.0659882	+	0.00666617i
$966$	−0.550510	+	5.97469i	−0.0177124	+	0.192233i
$967$	−30.4949	−	30.4949i	−0.980650	−	0.980650i	0.0191665	−	0.999816i	$-0.493899\pi$
$967$	−30.4949	−	30.4949i	−0.980650	−	0.980650i	−0.999816	+	0.0191665i	$0.993899\pi$
$968$	6.36396	+	6.36396i	0.204545	+	0.204545i
$969$	−0.405324	+	4.39898i	−0.0130209	+	0.141316i
$970$	−10.1010	−	8.24745i	−0.324324	−	0.264810i
$971$		−	47.4797i		−	1.52370i	−0.647756	−	0.761848i	$-0.724292\pi$
$971$		−	47.4797i		−	1.52370i	0.647756	−	0.761848i	$-0.275708\pi$
$972$	−14.7675	+	4.99221i	−0.473667	+	0.160125i
$973$	−17.7980	+	17.7980i	−0.570576	+	0.570576i
$974$	−20.7204			−0.663924
$975$	−2.37553	−	21.6122i	−0.0760780	−	0.692144i
$976$	−8.34847			−0.267228
$977$	10.3602	−	10.3602i	0.331452	−	0.331452i	−0.521686	−	0.853138i	$-0.674697\pi$
$977$	10.3602	−	10.3602i	0.331452	−	0.331452i	0.853138	+	0.521686i	$0.174697\pi$
$978$	−4.61401	+	3.83548i	−0.147540	+	0.122645i
$979$			22.4495i			0.717489i
$980$	−8.66025	−	7.07107i	−0.276642	−	0.225877i
$981$	12.8258	+	2.38378i	0.409495	+	0.0761082i
$982$	−20.0227	−	20.0227i	−0.638950	−	0.638950i
$983$	12.0922	+	12.0922i	0.385683	+	0.385683i	0.873144	−	0.487462i	$-0.162077\pi$
$983$	12.0922	+	12.0922i	0.385683	+	0.385683i	−0.487462	+	0.873144i	$0.662077\pi$
$984$	9.51023	+	0.876276i	0.303175	+	0.0279346i
$985$	5.44949	−	0.550510i	0.173635	−	0.0175407i
$986$			6.61037i			0.210517i
$987$	7.82913	+	9.41832i	0.249204	+	0.299788i
$988$	−4.52781	+	4.52781i	−0.144049	+	0.144049i
$989$	−8.83523			−0.280944
$990$	9.45411	+	0.787287i	0.300471	+	0.0250216i
$991$	2.39388			0.0760440			0.0380220	−	0.999277i	$-0.487894\pi$
$991$	2.39388			0.0760440			0.0380220	+	0.999277i	$0.487894\pi$
$992$	2.12132	−	2.12132i	0.0673520	−	0.0673520i
$993$	−23.3016	−	28.0315i	−0.739454	−	0.889551i
$994$			6.44949i			0.204565i
$995$	−23.7559	+	29.0949i	−0.753113	+	0.922371i
$996$	−13.7980	−	1.27135i	−0.437205	−	0.0402842i
$997$	40.8434	+	40.8434i	1.29352	+	1.29352i	0.932593	+	0.360929i	$0.117540\pi$
$997$	40.8434	+	40.8434i	1.29352	+	1.29352i	0.360929	+	0.932593i	$0.382460\pi$
$998$	10.7101	+	10.7101i	0.339024	+	0.339024i
$999$	48.7832	+	13.7980i	1.54343	+	0.436548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.f.137.2	✓	8
3.2	odd	2	inner	510.2.l.f.137.3	yes	8
5.3	odd	4	inner	510.2.l.f.443.3	yes	8
15.8	even	4	inner	510.2.l.f.443.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.f.137.2	✓	8	1.1	even	1	trivial
510.2.l.f.137.3	yes	8	3.2	odd	2	inner
510.2.l.f.443.2	yes	8	15.8	even	4	inner
510.2.l.f.443.3	yes	8	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.10721 + 1.33195i) q^{3} -1.00000i q^{4} +(1.73205 + 1.41421i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.548188 + 2.94949i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.10721 + 1.33195i) q^{3} -1.00000i q^{4} +(1.73205 + 1.41421i) q^{5} +(-1.72474 - 0.158919i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.548188 + 2.94949i) q^{9} +(-2.22474 + 0.224745i) q^{10} +1.41421i q^{11} +(1.33195 - 1.10721i) q^{12} +(-1.77526 + 1.77526i) q^{13} +1.41421 q^{14} +(0.0340742 + 3.87283i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(-1.69798 - 2.47323i) q^{18} +2.55051i q^{19} +(1.41421 - 1.73205i) q^{20} +(0.224745 - 2.43916i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(1.73205 + 1.73205i) q^{23} +(-0.158919 + 1.72474i) q^{24} +(1.00000 + 4.89898i) q^{25} -2.51059i q^{26} +(-4.53553 + 2.53553i) q^{27} +(-1.00000 + 1.00000i) q^{28} +6.61037 q^{29} +(-2.76260 - 2.71441i) q^{30} +3.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.88366 + 1.56583i) q^{33} +1.00000i q^{34} +(-0.317837 - 3.14626i) q^{35} +(2.94949 + 0.548188i) q^{36} +(-6.89898 - 6.89898i) q^{37} +(-1.80348 - 1.80348i) q^{38} +(-4.33013 - 0.398979i) q^{39} +(0.224745 + 2.22474i) q^{40} -5.51399i q^{41} +(1.56583 + 1.88366i) q^{42} +(-2.55051 + 2.55051i) q^{43} +1.41421 q^{44} +(-5.12070 + 4.33341i) q^{45} -2.44949 q^{46} +(-3.53553 + 3.53553i) q^{47} +(-1.10721 - 1.33195i) q^{48} -5.00000i q^{49} +(-4.17121 - 2.75699i) q^{50} +(1.72474 + 0.158919i) q^{51} +(1.77526 + 1.77526i) q^{52} +(7.95315 + 7.95315i) q^{53} +(1.41421 - 5.00000i) q^{54} +(-2.00000 + 2.44949i) q^{55} -1.41421i q^{56} +(-3.39716 + 2.82394i) q^{57} +(-4.67423 + 4.67423i) q^{58} -0.317837 q^{59} +(3.87283 - 0.0340742i) q^{60} +8.34847 q^{61} +(-2.12132 + 2.12132i) q^{62} +(3.49768 - 2.40130i) q^{63} +1.00000i q^{64} +(-5.58542 + 0.564242i) q^{65} +(0.224745 - 2.43916i) q^{66} +(-10.4495 - 10.4495i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(-0.389270 + 4.22474i) q^{69} +(2.44949 + 2.00000i) q^{70} +4.56048i q^{71} +(-2.47323 + 1.69798i) q^{72} +(0.325765 - 0.325765i) q^{73} +9.75663 q^{74} +(-5.41800 + 6.75613i) q^{75} +2.55051 q^{76} +(1.41421 - 1.41421i) q^{77} +(3.34398 - 2.77974i) q^{78} -6.89898i q^{79} +(-1.73205 - 1.41421i) q^{80} +(-8.39898 - 3.23375i) q^{81} +(3.89898 + 3.89898i) q^{82} +(-5.65685 - 5.65685i) q^{83} +(-2.43916 - 0.224745i) q^{84} +(2.22474 - 0.224745i) q^{85} -3.60697i q^{86} +(7.31904 + 8.80469i) q^{87} +(-1.00000 + 1.00000i) q^{88} +15.8742 q^{89} +(0.556696 - 6.68506i) q^{90} +3.55051 q^{91} +(1.73205 - 1.73205i) q^{92} +(3.32162 + 3.99585i) q^{93} -5.00000i q^{94} +(-3.60697 + 4.41761i) q^{95} +(1.72474 + 0.158919i) q^{96} +(4.12372 + 4.12372i) q^{97} +(3.53553 + 3.53553i) q^{98} +(-4.17121 - 0.775255i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	\( 8 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 24 q^{13} + 8 q^{15} - 8 q^{16} + 8 q^{18} - 8 q^{21} - 8 q^{22} + 8 q^{25} - 8 q^{27} - 8 q^{28} - 8 q^{30} + 24 q^{31} - 4 q^{33} + 4 q^{36} - 16 q^{37} - 8 q^{40} + 4 q^{42} - 40 q^{43} + 12 q^{45} - 4 q^{48} + 4 q^{51} + 24 q^{52} - 16 q^{55} + 32 q^{57} - 8 q^{58} + 16 q^{60} + 8 q^{61} + 4 q^{63} - 8 q^{66} - 64 q^{67} - 8 q^{72} + 32 q^{73} - 20 q^{75} + 40 q^{76} - 28 q^{81} - 8 q^{82} + 8 q^{85} + 40 q^{87} - 8 q^{88} - 20 q^{90} + 48 q^{91} + 12 q^{93} + 4 q^{96} - 16 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 24 * q^13 + 8 * q^15 - 8 * q^16 + 8 * q^18 - 8 * q^21 - 8 * q^22 + 8 * q^25 - 8 * q^27 - 8 * q^28 - 8 * q^30 + 24 * q^31 - 4 * q^33 + 4 * q^36 - 16 * q^37 - 8 * q^40 + 4 * q^42 - 40 * q^43 + 12 * q^45 - 4 * q^48 + 4 * q^51 + 24 * q^52 - 16 * q^55 + 32 * q^57 - 8 * q^58 + 16 * q^60 + 8 * q^61 + 4 * q^63 - 8 * q^66 - 64 * q^67 - 8 * q^72 + 32 * q^73 - 20 * q^75 + 40 * q^76 - 28 * q^81 - 8 * q^82 + 8 * q^85 + 40 * q^87 - 8 * q^88 - 20 * q^90 + 48 * q^91 + 12 * q^93 + 4 * q^96 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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