LMFDB - Embedded newform 418.2.e.i.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(45,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("418.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.101617200.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8x^{4} - 4x^{3} + 64x^{2} - 16x + 4 $ x^6 + 8x^4 - 4x^3 + 64x^2 - 16x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			353.2
Root			$0.126000 - 0.218239i$ of defining polynomial
Character	$\chi$	$=$	418.353
Dual form			418.2.e.i.45.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.126000 + 0.218239i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.126000 + 0.218239i) q^{6} +1.74800 q^{7} -1.00000 q^{8} +(1.46825 + 2.54308i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.126000 + 0.218239i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.126000 + 0.218239i) q^{6} +1.74800 q^{7} -1.00000 q^{8} +(1.46825 + 2.54308i) q^{9} +(1.00000 + 1.73205i) q^{10} +1.00000 q^{11} +0.252000 q^{12} +(1.46825 + 2.54308i) q^{13} +(0.874000 - 1.51381i) q^{14} +(-0.252000 - 0.436477i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.842248 - 1.45882i) q^{17} +2.93650 q^{18} +(4.31050 + 0.647787i) q^{19} +2.00000 q^{20} +(-0.220248 + 0.381481i) q^{21} +(0.500000 - 0.866025i) q^{22} +(-2.25200 - 3.90058i) q^{23} +(0.126000 - 0.218239i) q^{24} +(0.500000 + 0.866025i) q^{25} +2.93650 q^{26} -1.49600 q^{27} +(-0.874000 - 1.51381i) q^{28} +(0.500000 + 0.866025i) q^{29} -0.504001 q^{30} +5.43250 q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.126000 + 0.218239i) q^{33} +(-0.842248 - 1.45882i) q^{34} +(-1.74800 + 3.02762i) q^{35} +(1.46825 - 2.54308i) q^{36} -3.18049 q^{37} +(2.71625 - 3.40911i) q^{38} -0.739998 q^{39} +(1.00000 - 1.73205i) q^{40} +(1.09425 - 1.89529i) q^{41} +(0.220248 + 0.381481i) q^{42} +(-3.59425 + 6.22542i) q^{43} +(-0.500000 - 0.866025i) q^{44} -5.87299 q^{45} -4.50400 q^{46} +(-3.31050 - 5.73395i) q^{47} +(-0.126000 - 0.218239i) q^{48} -3.94450 q^{49} +1.00000 q^{50} +(0.212247 + 0.367622i) q^{51} +(1.46825 - 2.54308i) q^{52} +(0.504001 + 0.872955i) q^{53} +(-0.748000 + 1.29557i) q^{54} +(-1.00000 + 1.73205i) q^{55} -1.74800 q^{56} +(-0.684495 + 0.859096i) q^{57} +1.00000 q^{58} +(-0.252000 + 0.436477i) q^{60} +(-4.72025 - 8.17571i) q^{61} +(2.71625 - 4.70468i) q^{62} +(2.56650 + 4.44530i) q^{63} +1.00000 q^{64} -5.87299 q^{65} +(0.126000 + 0.218239i) q^{66} +(0.378001 + 0.654716i) q^{67} -1.68450 q^{68} +1.13501 q^{69} +(1.74800 + 3.02762i) q^{70} +(3.59425 - 6.22542i) q^{71} +(-1.46825 - 2.54308i) q^{72} +(-4.09425 + 7.09145i) q^{73} +(-1.59025 + 2.75439i) q^{74} -0.252000 q^{75} +(-1.59425 - 4.05689i) q^{76} +1.74800 q^{77} +(-0.369999 + 0.640857i) q^{78} +(-1.37800 + 2.38677i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-4.21625 + 7.30275i) q^{81} +(-1.09425 - 1.89529i) q^{82} -3.69250 q^{83} +0.440497 q^{84} +(1.68450 + 2.91763i) q^{85} +(3.59425 + 6.22542i) q^{86} -0.252000 q^{87} -1.00000 q^{88} +(-5.18450 - 8.97981i) q^{89} +(-2.93650 + 5.08616i) q^{90} +(2.56650 + 4.44530i) q^{91} +(-2.25200 + 3.90058i) q^{92} +(-0.684495 + 1.18558i) q^{93} -6.62099 q^{94} +(-5.43250 + 6.81821i) q^{95} -0.252000 q^{96} +(6.18450 - 10.7119i) q^{97} +(-1.97225 + 3.41603i) q^{98} +(1.46825 + 2.54308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 - 7 * q^9	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} - 7 q^{9} + 6 q^{10} + 6 q^{11} - 7 q^{13} + 6 q^{14} - 3 q^{16} - 10 q^{17} - 14 q^{18} - 5 q^{19} + 12 q^{20} + 16 q^{21} + 3 q^{22} - 12 q^{23} + 3 q^{25} - 14 q^{26} - 12 q^{27} - 6 q^{28} + 3 q^{29} + 4 q^{31} + 3 q^{32} + 10 q^{34} - 12 q^{35} - 7 q^{36} + 8 q^{37} + 2 q^{38} - 12 q^{39} + 6 q^{40} - 10 q^{41} - 16 q^{42} - 5 q^{43} - 3 q^{44} + 28 q^{45} - 24 q^{46} + 11 q^{47} + 14 q^{49} + 6 q^{50} - 10 q^{51} - 7 q^{52} - 6 q^{54} - 6 q^{55} - 12 q^{56} + 26 q^{57} + 6 q^{58} - 11 q^{61} + 2 q^{62} - 20 q^{63} + 6 q^{64} + 28 q^{65} + 20 q^{68} + 64 q^{69} + 12 q^{70} + 5 q^{71} + 7 q^{72} - 8 q^{73} + 4 q^{74} + 7 q^{76} + 12 q^{77} - 6 q^{78} - 6 q^{79} - 6 q^{80} - 11 q^{81} + 10 q^{82} + 14 q^{83} - 32 q^{84} - 20 q^{85} + 5 q^{86} - 6 q^{88} - q^{89} + 14 q^{90} - 20 q^{91} - 12 q^{92} + 26 q^{93} + 22 q^{94} - 4 q^{95} + 7 q^{97} + 7 q^{98} - 7 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 - 7 * q^9 + 6 * q^10 + 6 * q^11 - 7 * q^13 + 6 * q^14 - 3 * q^16 - 10 * q^17 - 14 * q^18 - 5 * q^19 + 12 * q^20 + 16 * q^21 + 3 * q^22 - 12 * q^23 + 3 * q^25 - 14 * q^26 - 12 * q^27 - 6 * q^28 + 3 * q^29 + 4 * q^31 + 3 * q^32 + 10 * q^34 - 12 * q^35 - 7 * q^36 + 8 * q^37 + 2 * q^38 - 12 * q^39 + 6 * q^40 - 10 * q^41 - 16 * q^42 - 5 * q^43 - 3 * q^44 + 28 * q^45 - 24 * q^46 + 11 * q^47 + 14 * q^49 + 6 * q^50 - 10 * q^51 - 7 * q^52 - 6 * q^54 - 6 * q^55 - 12 * q^56 + 26 * q^57 + 6 * q^58 - 11 * q^61 + 2 * q^62 - 20 * q^63 + 6 * q^64 + 28 * q^65 + 20 * q^68 + 64 * q^69 + 12 * q^70 + 5 * q^71 + 7 * q^72 - 8 * q^73 + 4 * q^74 + 7 * q^76 + 12 * q^77 - 6 * q^78 - 6 * q^79 - 6 * q^80 - 11 * q^81 + 10 * q^82 + 14 * q^83 - 32 * q^84 - 20 * q^85 + 5 * q^86 - 6 * q^88 - q^89 + 14 * q^90 - 20 * q^91 - 12 * q^92 + 26 * q^93 + 22 * q^94 - 4 * q^95 + 7 * q^97 + 7 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.126000	+	0.218239i	−0.0727462	+	0.126000i	−0.900104	−	0.435675i	$-0.856510\pi$
$3$	−0.126000	+	0.218239i	−0.0727462	+	0.126000i	0.827358	+	0.561675i	$0.189843\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$	0.126000	+	0.218239i	0.0514394	+	0.0890956i
$7$	1.74800			0.660682			0.330341	−	0.943862i	$-0.392836\pi$
$7$	1.74800			0.660682			0.330341	+	0.943862i	$0.392836\pi$
$8$	−1.00000			−0.353553
$9$	1.46825	+	2.54308i	0.489416	+	0.847693i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$	0.252000			0.0727462
$13$	1.46825	+	2.54308i	0.407219	+	0.705323i	0.994577	−	0.104004i	$-0.0331653\pi$
$13$	1.46825	+	2.54308i	0.407219	+	0.705323i	−0.587358	+	0.809327i	$0.699832\pi$
$14$	0.874000	−	1.51381i	0.233586	−	0.404583i
$15$	−0.252000	−	0.436477i	−0.0650662	−	0.112698i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.842248	−	1.45882i	0.204275	−	0.353815i	−0.745626	−	0.666364i	$-0.767850\pi$
$17$	0.842248	−	1.45882i	0.204275	−	0.353815i	0.949902	+	0.312549i	$0.101183\pi$
$18$	2.93650			0.692139
$19$	4.31050	+	0.647787i	0.988896	+	0.148612i
$19$	4.31050	+	0.647787i	0.988896	+	0.148612i
$20$	2.00000			0.447214
$21$	−0.220248	+	0.381481i	−0.0480621	+	0.0832460i
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$	−2.25200	−	3.90058i	−0.469575	−	0.813327i	0.529820	−	0.848110i	$-0.322259\pi$
$23$	−2.25200	−	3.90058i	−0.469575	−	0.813327i	−0.999395	+	0.0347829i	$0.988926\pi$
$24$	0.126000	−	0.218239i	0.0257197	−	0.0445478i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.93650			0.575894
$27$	−1.49600			−0.287905
$28$	−0.874000	−	1.51381i	−0.165170	−	0.286084i
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$	−0.504001			−0.0920175
$31$	5.43250			0.975705			0.487852	−	0.872926i	$-0.337780\pi$
$31$	5.43250			0.975705			0.487852	+	0.872926i	$0.337780\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.126000	+	0.218239i	−0.0219338	+	0.0379905i
$34$	−0.842248	−	1.45882i	−0.144444	−	0.250185i
$35$	−1.74800	+	3.02762i	−0.295466	+	0.511762i
$36$	1.46825	−	2.54308i	0.244708	−	0.423847i
$37$	−3.18049			−0.522870			−0.261435	−	0.965221i	$-0.584196\pi$
$37$	−3.18049			−0.522870			−0.261435	+	0.965221i	$0.584196\pi$
$38$	2.71625	−	3.40911i	0.440634	−	0.553030i
$39$	−0.739998			−0.118495
$40$	1.00000	−	1.73205i	0.158114	−	0.273861i
$41$	1.09425	−	1.89529i	0.170893	−	0.295995i	−0.767839	−	0.640642i	$-0.778668\pi$
$41$	1.09425	−	1.89529i	0.170893	−	0.295995i	0.938732	+	0.344647i	$0.112001\pi$
$42$	0.220248	+	0.381481i	0.0339850	+	0.0588638i
$43$	−3.59425	+	6.22542i	−0.548118	+	0.949368i	0.450286	+	0.892884i	$0.351322\pi$
$43$	−3.59425	+	6.22542i	−0.548118	+	0.949368i	−0.998404	+	0.0564832i	$0.982011\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−5.87299			−0.875494
$46$	−4.50400			−0.664079
$47$	−3.31050	−	5.73395i	−0.482885	−	0.836382i	0.516921	−	0.856033i	$-0.327078\pi$
$47$	−3.31050	−	5.73395i	−0.482885	−	0.836382i	−0.999807	+	0.0196507i	$0.993745\pi$
$48$	−0.126000	−	0.218239i	−0.0181866	−	0.0315000i
$49$	−3.94450			−0.563500
$50$	1.00000			0.141421
$51$	0.212247	+	0.367622i	0.0297205	+	0.0514774i
$52$	1.46825	−	2.54308i	0.203609	−	0.352662i
$53$	0.504001	+	0.872955i	0.0692298	+	0.119910i	0.898562	−	0.438846i	$-0.144612\pi$
$53$	0.504001	+	0.872955i	0.0692298	+	0.119910i	−0.829333	+	0.558755i	$0.811279\pi$
$54$	−0.748000	+	1.29557i	−0.101790	+	0.176305i
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	−1.74800			−0.233586
$57$	−0.684495	+	0.859096i	−0.0906636	+	0.113790i
$58$	1.00000			0.131306
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	−0.252000	+	0.436477i	−0.0325331	+	0.0563490i
$61$	−4.72025	−	8.17571i	−0.604366	−	1.04679i	−0.992151	−	0.125043i	$-0.960093\pi$
$61$	−4.72025	−	8.17571i	−0.604366	−	1.04679i	0.387785	−	0.921750i	$-0.373240\pi$
$62$	2.71625	−	4.70468i	0.344964	−	0.597495i
$63$	2.56650	+	4.44530i	0.323348	+	0.560056i
$64$	1.00000			0.125000
$65$	−5.87299			−0.728455
$66$	0.126000	+	0.218239i	0.0155096	+	0.0268633i
$67$	0.378001	+	0.654716i	0.0461801	+	0.0799863i	0.888192	−	0.459473i	$-0.151962\pi$
$67$	0.378001	+	0.654716i	0.0461801	+	0.0799863i	−0.842011	+	0.539460i	$0.818629\pi$
$68$	−1.68450			−0.204275
$69$	1.13501			0.136639
$70$	1.74800	+	3.02762i	0.208926	+	0.361870i
$71$	3.59425	−	6.22542i	0.426559	−	0.738821i	−0.570006	−	0.821641i	$-0.693059\pi$
$71$	3.59425	−	6.22542i	0.426559	−	0.738821i	0.996565	+	0.0828192i	$0.0263924\pi$
$72$	−1.46825	−	2.54308i	−0.173035	−	0.299705i
$73$	−4.09425	+	7.09145i	−0.479195	+	0.829991i	−0.999715	−	0.0238586i	$-0.992405\pi$
$73$	−4.09425	+	7.09145i	−0.479195	+	0.829991i	0.520520	+	0.853850i	$0.325738\pi$
$74$	−1.59025	+	2.75439i	−0.184862	+	0.320191i
$75$	−0.252000			−0.0290985
$76$	−1.59425	−	4.05689i	−0.182873	−	0.465357i
$77$	1.74800			0.199203
$78$	−0.369999	+	0.640857i	−0.0418941	+	0.0725628i
$79$	−1.37800	+	2.38677i	−0.155037	+	0.268532i	−0.933073	−	0.359688i	$-0.882883\pi$
$79$	−1.37800	+	2.38677i	−0.155037	+	0.268532i	0.778035	+	0.628220i	$0.216216\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	−4.21625	+	7.30275i	−0.468472	+	0.811417i
$82$	−1.09425	−	1.89529i	−0.120839	−	0.209300i
$83$	−3.69250			−0.405304			−0.202652	−	0.979251i	$-0.564956\pi$
$83$	−3.69250			−0.405304			−0.202652	+	0.979251i	$0.564956\pi$
$84$	0.440497			0.0480621
$85$	1.68450	+	2.91763i	0.182709	+	0.316462i
$86$	3.59425	+	6.22542i	0.387578	+	0.671304i
$87$	−0.252000			−0.0270173
$88$	−1.00000			−0.106600
$89$	−5.18450	−	8.97981i	−0.549555	−	0.951858i	−0.998305	−	0.0582003i	$-0.981464\pi$
$89$	−5.18450	−	8.97981i	−0.549555	−	0.951858i	0.448750	−	0.893658i	$-0.351870\pi$
$90$	−2.93650	+	5.08616i	−0.309534	+	0.536128i
$91$	2.56650	+	4.44530i	0.269042	+	0.465994i
$92$	−2.25200	+	3.90058i	−0.234787	+	0.406663i
$93$	−0.684495	+	1.18558i	−0.0709789	+	0.122939i
$94$	−6.62099			−0.682903
$95$	−5.43250	+	6.81821i	−0.557362	+	0.699534i
$96$	−0.252000			−0.0257197
$97$	6.18450	−	10.7119i	0.627940	−	1.08762i	−0.360024	−	0.932943i	$-0.617232\pi$
$97$	6.18450	−	10.7119i	0.627940	−	1.08762i	0.987964	−	0.154682i	$-0.0494352\pi$
$98$	−1.97225	+	3.41603i	−0.199227	+	0.345072i
$99$	1.46825	+	2.54308i	0.147564	+	0.255589i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−3.46825	−	6.00718i	−0.345104	−	0.597737i	0.640269	−	0.768151i	$-0.278823\pi$
$101$	−3.46825	−	6.00718i	−0.345104	−	0.597737i	−0.985373	+	0.170414i	$0.945490\pi$
$102$	0.424493			0.0420311
$103$	6.62099			0.652386			0.326193	−	0.945303i	$-0.394234\pi$
$103$	6.62099			0.652386			0.326193	+	0.945303i	$0.394234\pi$
$104$	−1.46825	−	2.54308i	−0.143974	−	0.249370i
$105$	−0.440497	−	0.762962i	−0.0429881	−	0.0744575i
$106$	1.00800			0.0979058
$107$	17.6130			1.70271			0.851356	−	0.524588i	$-0.175781\pi$
$107$	17.6130			1.70271			0.851356	+	0.524588i	$0.175781\pi$
$108$	0.748000	+	1.29557i	0.0719763	+	0.124667i
$109$	1.97225	−	3.41603i	0.188907	−	0.327197i	−0.755979	−	0.654596i	$-0.772839\pi$
$109$	1.97225	−	3.41603i	0.188907	−	0.327197i	0.944886	+	0.327399i	$0.106172\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$	0.400743	−	0.694107i	0.0380368	−	0.0658817i
$112$	−0.874000	+	1.51381i	−0.0825852	+	0.143042i
$113$	−14.3690			−1.35172			−0.675860	−	0.737030i	$-0.736228\pi$
$113$	−14.3690			−1.35172			−0.675860	+	0.737030i	$0.736228\pi$
$114$	0.401751	+	1.02234i	0.0376274	+	0.0957508i
$115$	9.00800			0.840000
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	−4.31150	+	7.46774i	−0.398599	+	0.690393i
$118$		0			0
$119$	1.47225	−	2.55001i	0.134961	−	0.233759i
$120$	0.252000	+	0.436477i	0.0230044	+	0.0398448i
$121$	1.00000			0.0909091
$122$	−9.44050			−0.854702
$123$	0.275751	+	0.477615i	0.0248636	+	0.0430651i
$124$	−2.71625	−	4.70468i	−0.243926	−	0.422493i
$125$	−12.0000			−1.07331
$126$	5.13299			0.457283
$127$	−5.93650	−	10.2823i	−0.526779	−	0.912408i	−0.999513	−	0.0312026i	$-0.990066\pi$
$127$	−5.93650	−	10.2823i	−0.526779	−	0.912408i	0.472734	−	0.881205i	$-0.343267\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.905752	−	1.56881i	−0.0797470	−	0.138126i
$130$	−2.93650	+	5.08616i	−0.257548	+	0.446086i
$131$	−5.80649	+	10.0571i	−0.507316	+	0.878697i	0.492648	+	0.870228i	$0.336029\pi$
$131$	−5.80649	+	10.0571i	−0.507316	+	0.878697i	−0.999964	+	0.00846827i	$0.997304\pi$
$132$	0.252000			0.0219338
$133$	7.53474	+	1.13233i	0.653345	+	0.0981855i
$134$	0.756001			0.0653086
$135$	1.49600	−	2.59115i	0.128755	−	0.223010i
$136$	−0.842248	+	1.45882i	−0.0722221	+	0.125092i
$137$	−4.96425	−	8.59833i	−0.424124	−	0.734605i	0.572214	−	0.820104i	$-0.306085\pi$
$137$	−4.96425	−	8.59833i	−0.424124	−	0.734605i	−0.996338	+	0.0854996i	$0.972751\pi$
$138$	0.567505	−	0.982947i	0.0483092	−	0.0836740i
$139$	−2.75600	−	4.77353i	−0.233761	−	0.404886i	0.725151	−	0.688590i	$-0.241770\pi$
$139$	−2.75600	−	4.77353i	−0.233761	−	0.404886i	−0.958912	+	0.283704i	$0.908437\pi$
$140$	3.49600			0.295466
$141$	1.66849			0.140512
$142$	−3.59425	−	6.22542i	−0.301623	−	0.522426i
$143$	1.46825	+	2.54308i	0.122781	+	0.212663i
$144$	−2.93650			−0.244708
$145$	−2.00000			−0.166091
$146$	4.09425	+	7.09145i	0.338842	+	0.586892i
$147$	0.497007	−	0.860842i	0.0409925	−	0.0710011i
$148$	1.59025	+	2.75439i	0.130718	+	0.226409i
$149$	−4.21225	+	7.29583i	−0.345081	+	0.597697i	−0.985368	−	0.170438i	$-0.945482\pi$
$149$	−4.21225	+	7.29583i	−0.345081	+	0.597697i	0.640288	+	0.768135i	$0.278815\pi$
$150$	−0.126000	+	0.218239i	−0.0102879	+	0.0178191i
$151$	13.9980			1.13914			0.569570	−	0.821943i	$-0.307110\pi$
$151$	13.9980			1.13914			0.569570	+	0.821943i	$0.307110\pi$
$152$	−4.31050	−	0.647787i	−0.349627	−	0.0525424i
$153$	4.94651			0.399902
$154$	0.874000	−	1.51381i	0.0704289	−	0.121986i
$155$	−5.43250	+	9.40936i	−0.436349	+	0.755778i
$156$	0.369999	+	0.640857i	0.0296236	+	0.0513096i
$157$	−0.504001	+	0.872955i	−0.0402236	+	0.0696694i	−0.885436	−	0.464761i	$-0.846140\pi$
$157$	−0.504001	+	0.872955i	−0.0402236	+	0.0696694i	0.845213	+	0.534430i	$0.179474\pi$
$158$	1.37800	+	2.38677i	0.109628	+	0.189881i
$159$	−0.254017			−0.0201448
$160$	−2.00000			−0.158114
$161$	−3.93650	−	6.81821i	−0.310239	−	0.537350i
$162$	4.21625	+	7.30275i	0.331260	+	0.573759i
$163$	17.2420			1.35050			0.675248	−	0.737591i	$-0.264037\pi$
$163$	17.2420			1.35050			0.675248	+	0.737591i	$0.264037\pi$
$164$	−2.18850			−0.170893
$165$	−0.252000	−	0.436477i	−0.0196182	−	0.0339797i
$166$	−1.84625	+	3.19780i	−0.143297	+	0.248197i
$167$	−11.2430	−	19.4734i	−0.870009	−	1.50690i	−0.861986	−	0.506932i	$-0.830780\pi$
$167$	−11.2430	−	19.4734i	−0.870009	−	1.50690i	−0.00802240	−	0.999968i	$-0.502554\pi$
$168$	0.220248	−	0.381481i	0.0169925	−	0.0294319i
$169$	2.18850	−	3.79059i	0.168346	−	0.291584i
$170$	3.36899			0.258390
$171$	4.68150	+	11.9130i	0.358003	+	0.911013i
$172$	7.18850			0.548118
$173$	4.71625	−	8.16878i	0.358570	−	0.621061i	−0.629152	−	0.777282i	$-0.716598\pi$
$173$	4.71625	−	8.16878i	0.358570	−	0.621061i	0.987722	+	0.156221i	$0.0499312\pi$
$174$	−0.126000	+	0.218239i	−0.00955205	+	0.0165446i
$175$	0.874000	+	1.51381i	0.0660682	+	0.114433i
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$		0			0
$178$	−10.3690			−0.777189
$179$	10.5040			0.785106			0.392553	−	0.919729i	$-0.371592\pi$
$179$	10.5040			0.785106			0.392553	+	0.919729i	$0.371592\pi$
$180$	2.93650	+	5.08616i	0.218873	+	0.379100i
$181$	4.59825	+	7.96440i	0.341785	+	0.591989i	0.984764	−	0.173894i	$-0.0556352\pi$
$181$	4.59825	+	7.96440i	0.341785	+	0.591989i	−0.642979	+	0.765884i	$0.722302\pi$
$182$	5.13299			0.380483
$183$	2.37901			0.175861
$184$	2.25200	+	3.90058i	0.166020	+	0.287555i
$185$	3.18049	−	5.50878i	0.233835	−	0.405013i
$186$	0.684495	+	1.18558i	0.0501896	+	0.0869310i
$187$	0.842248	−	1.45882i	0.0615913	−	0.106679i
$188$	−3.31050	+	5.73395i	−0.241443	+	0.418191i
$189$	−2.61501			−0.190214
$190$	3.18850	+	8.11378i	0.231318	+	0.588636i
$191$	24.6210			1.78151			0.890756	−	0.454481i	$-0.150175\pi$
$191$	24.6210			1.78151			0.890756	+	0.454481i	$0.150175\pi$
$192$	−0.126000	+	0.218239i	−0.00909328	+	0.0157500i
$193$	−6.34625	+	10.9920i	−0.456813	+	0.791223i	−0.998790	−	0.0491698i	$-0.984342\pi$
$193$	−6.34625	+	10.9920i	−0.456813	+	0.791223i	0.541977	+	0.840393i	$0.317676\pi$
$194$	−6.18450	−	10.7119i	−0.444021	−	0.769067i
$195$	0.739998	−	1.28171i	0.0529924	−	0.0917855i
$196$	1.97225	+	3.41603i	0.140875	+	0.244002i
$197$	−20.3690			−1.45123			−0.725615	−	0.688101i	$-0.758445\pi$
$197$	−20.3690			−1.45123			−0.725615	+	0.688101i	$0.758445\pi$
$198$	2.93650			0.208688
$199$	−4.40575	−	7.63099i	−0.312315	−	0.540946i	0.666548	−	0.745462i	$-0.267771\pi$
$199$	−4.40575	−	7.63099i	−0.312315	−	0.540946i	−0.978863	+	0.204516i	$0.934438\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−0.190513			−0.0134377
$202$	−6.93650			−0.488050
$203$	0.874000	+	1.51381i	0.0613428	+	0.106249i
$204$	0.212247	−	0.367622i	0.0148602	−	0.0257387i
$205$	2.18850	+	3.79059i	0.152851	+	0.264746i
$206$	3.31050	−	5.73395i	0.230653	−	0.399503i
$207$	6.61299	−	11.4540i	0.459635	−	0.796110i
$208$	−2.93650			−0.203609
$209$	4.31050	+	0.647787i	0.298163	+	0.0448083i
$210$	−0.880993			−0.0607943
$211$	3.24400	−	5.61877i	0.223326	−	0.386812i	−0.732490	−	0.680778i	$-0.761642\pi$
$211$	3.24400	−	5.61877i	0.223326	−	0.386812i	0.955816	+	0.293966i	$0.0949752\pi$
$212$	0.504001	−	0.872955i	0.0346149	−	0.0599548i
$213$	0.905752	+	1.56881i	0.0620611	+	0.107493i
$214$	8.80649	−	15.2533i	0.602000	−	1.04269i
$215$	−7.18850	−	12.4508i	−0.490251	−	0.849140i
$216$	1.49600			0.101790
$217$	9.49600			0.644630
$218$	−1.97225	−	3.41603i	−0.133578	−	0.231363i
$219$	−1.03175	−	1.78705i	−0.0697193	−	0.120757i
$220$	2.00000			0.134840
$221$	4.94651			0.332739
$222$	−0.400743	−	0.694107i	−0.0268961	−	0.0465854i
$223$	9.59425	−	16.6177i	0.642478	−	1.11281i	−0.342399	−	0.939555i	$-0.611240\pi$
$223$	9.59425	−	16.6177i	0.642478	−	1.11281i	0.984878	−	0.173251i	$-0.0554271\pi$
$224$	0.874000	+	1.51381i	0.0583966	+	0.101146i
$225$	−1.46825	+	2.54308i	−0.0978832	+	0.169539i
$226$	−7.18450	+	12.4439i	−0.477906	+	0.827757i
$227$	−0.551502			−0.0366045			−0.0183022	−	0.999833i	$-0.505826\pi$
$227$	−0.551502			−0.0366045			−0.0183022	+	0.999833i	$0.505826\pi$
$228$	1.08625	+	0.163242i	0.0719384	+	0.0108110i
$229$	24.0615			1.59003			0.795014	−	0.606591i	$-0.207463\pi$
$229$	24.0615			1.59003			0.795014	+	0.606591i	$0.207463\pi$
$230$	4.50400	−	7.80116i	0.296985	−	0.514393i
$231$	−0.220248	+	0.381481i	−0.0144913	+	0.0250996i
$232$	−0.500000	−	0.866025i	−0.0328266	−	0.0568574i
$233$	8.71524	−	15.0952i	0.570954	−	0.988922i	−0.425514	−	0.904952i	$-0.639907\pi$
$233$	8.71524	−	15.0952i	0.570954	−	0.988922i	0.996468	−	0.0839700i	$-0.0267600\pi$
$234$	4.31150	+	7.46774i	0.281852	+	0.488182i
$235$	13.2420			0.863812
$236$		0			0
$237$	−0.347257	−	0.601466i	−0.0225567	−	0.0390694i
$238$	−1.47225	−	2.55001i	−0.0954317	−	0.165293i
$239$	−10.9920			−0.711013			−0.355507	−	0.934674i	$-0.615692\pi$
$239$	−10.9920			−0.711013			−0.355507	+	0.934674i	$0.615692\pi$
$240$	0.504001			0.0325331
$241$	−4.44050	−	7.69117i	−0.286038	−	0.495432i	0.686823	−	0.726825i	$-0.259005\pi$
$241$	−4.44050	−	7.69117i	−0.286038	−	0.495432i	−0.972860	+	0.231393i	$0.925672\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	−3.30649	−	5.72702i	−0.212112	−	0.367388i
$244$	−4.72025	+	8.17571i	−0.302183	+	0.523396i
$245$	3.94450	−	6.83207i	0.252005	−	0.436485i
$246$	0.551502			0.0351625
$247$	4.68150	+	11.9130i	0.297877	+	0.758009i
$248$	−5.43250			−0.344964
$249$	0.465255	−	0.805846i	0.0294844	−	0.0510684i
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	3.55850	+	6.16349i	0.224610	+	0.389036i	0.956202	−	0.292706i	$-0.0945558\pi$
$251$	3.55850	+	6.16349i	0.224610	+	0.389036i	−0.731592	+	0.681743i	$0.761222\pi$
$252$	2.56650	−	4.44530i	0.161674	−	0.280028i
$253$	−2.25200	−	3.90058i	−0.141582	−	0.245227i
$254$	−11.8730			−0.744978
$255$	−0.848987			−0.0531656
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.62099	−	14.9320i	−0.537763	−	0.931432i	−0.999024	−	0.0441680i	$-0.985936\pi$
$257$	−8.62099	−	14.9320i	−0.537763	−	0.931432i	0.461261	−	0.887264i	$-0.347397\pi$
$258$	−1.81150			−0.112779
$259$	−5.55950			−0.345451
$260$	2.93650	+	5.08616i	0.182114	+	0.315430i
$261$	−1.46825	+	2.54308i	−0.0908823	+	0.157413i
$262$	5.80649	+	10.0571i	0.358726	+	0.621332i
$263$	−11.6925	+	20.2520i	−0.720990	+	1.24879i	0.239613	+	0.970868i	$0.422979\pi$
$263$	−11.6925	+	20.2520i	−0.720990	+	1.24879i	−0.960603	+	0.277923i	$0.910354\pi$
$264$	0.126000	−	0.218239i	0.00775478	−	0.0134317i
$265$	−2.01600			−0.123842
$266$	4.74800	−	5.95911i	0.291119	−	0.365377i
$267$	2.61299			0.159912
$268$	0.378001	−	0.654716i	0.0230901	−	0.0399932i
$269$	0.157752	−	0.273235i	0.00961833	−	0.0166594i	−0.861176	−	0.508307i	$-0.830272\pi$
$269$	0.157752	−	0.273235i	0.00961833	−	0.0166594i	0.870795	+	0.491647i	$0.163605\pi$
$270$	−1.49600	−	2.59115i	−0.0910436	−	0.157692i
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	−0.624218	−	0.781251i	$-0.714582\pi$
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	0.988692	+	0.149963i	$0.0479155\pi$
$272$	0.842248	+	1.45882i	0.0510688	+	0.0884537i
$273$	−1.29352			−0.0782872
$274$	−9.92849			−0.599802
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−0.567505	−	0.982947i	−0.0341598	−	0.0591665i
$277$	−1.44050			−0.0865511			−0.0432755	−	0.999063i	$-0.513779\pi$
$277$	−1.44050			−0.0865511			−0.0432755	+	0.999063i	$0.513779\pi$
$278$	−5.51200			−0.330588
$279$	7.97625	+	13.8153i	0.477526	+	0.827099i
$280$	1.74800	−	3.02762i	0.104463	−	0.180935i
$281$	7.52674	+	13.0367i	0.449008	+	0.777704i	0.998322	−	0.0579117i	$-0.0184442\pi$
$281$	7.52674	+	13.0367i	0.449008	+	0.777704i	−0.549314	+	0.835616i	$0.685111\pi$
$282$	0.834246	−	1.44496i	0.0496786	−	0.0860459i
$283$	−11.6210	+	20.1281i	−0.690796	+	1.19649i	0.280781	+	0.959772i	$0.409407\pi$
$283$	−11.6210	+	20.1281i	−0.690796	+	1.19649i	−0.971577	+	0.236722i	$0.923927\pi$
$284$	−7.18850			−0.426559
$285$	−0.803502	−	2.04468i	−0.0475954	−	0.121116i
$286$	2.93650			0.173639
$287$	1.91275	−	3.31297i	0.112906	−	0.195559i
$288$	−1.46825	+	2.54308i	−0.0865173	+	0.149852i
$289$	7.08124	+	12.2651i	0.416543	+	0.721474i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$	1.55850	+	2.69939i	0.0913606	+	0.158241i
$292$	8.18850			0.479195
$293$	14.0080			0.818356			0.409178	−	0.912455i	$-0.365815\pi$
$293$	14.0080			0.818356			0.409178	+	0.912455i	$0.365815\pi$
$294$	−0.497007	−	0.860842i	−0.0289861	−	0.0502053i
$295$		0			0
$296$	3.18049			0.184862
$297$	−1.49600			−0.0868067
$298$	4.21225	+	7.29583i	0.244009	+	0.422636i
$299$	6.61299	−	11.4540i	0.382439	−	0.662404i
$300$	0.126000	+	0.218239i	0.00727462	+	0.0126000i
$301$	−6.28274	+	10.8820i	−0.362131	+	0.627230i
$302$	6.99899	−	12.1226i	0.402747	−	0.697578i
$303$	1.74800			0.100420
$304$	−2.71625	+	3.40911i	−0.155787	+	0.195526i
$305$	18.8810			1.08112
$306$	2.47326	−	4.28381i	0.141387	−	0.244889i
$307$	−7.05049	+	12.2118i	−0.402393	+	0.696965i	−0.994014	−	0.109251i	$-0.965155\pi$
$307$	−7.05049	+	12.2118i	−0.402393	+	0.696965i	0.591621	+	0.806216i	$0.298488\pi$
$308$	−0.874000	−	1.51381i	−0.0498008	−	0.0862574i
$309$	−0.834246	+	1.44496i	−0.0474586	+	0.0822007i
$310$	5.43250	+	9.40936i	0.308545	+	0.534416i
$311$	−19.6130			−1.11215			−0.556075	−	0.831132i	$-0.687693\pi$
$311$	−19.6130			−1.11215			−0.556075	+	0.831132i	$0.687693\pi$
$312$	0.739998			0.0418941
$313$	9.15274	+	15.8530i	0.517344	+	0.896065i	0.999797	+	0.0201439i	$0.00641242\pi$
$313$	9.15274	+	15.8530i	0.517344	+	0.896065i	−0.482453	+	0.875922i	$0.660254\pi$
$314$	0.504001	+	0.872955i	0.0284424	+	0.0492637i
$315$	−10.2660			−0.578423
$316$	2.75600			0.155037
$317$	7.71524	+	13.3632i	0.433331	+	0.750551i	0.997158	−	0.0753418i	$-0.0240048\pi$
$317$	7.71524	+	13.3632i	0.433331	+	0.750551i	−0.563827	+	0.825893i	$0.690671\pi$
$318$	−0.127008	+	0.219985i	−0.00712228	+	0.0123361i
$319$	0.500000	+	0.866025i	0.0279946	+	0.0484881i
$320$	−1.00000	+	1.73205i	−0.0559017	+	0.0968246i
$321$	−2.21924	+	3.84384i	−0.123866	+	0.214542i
$322$	−7.87299			−0.438745
$323$	4.57551	−	5.74262i	0.254588	−	0.319528i
$324$	8.43250			0.468472
$325$	−1.46825	+	2.54308i	−0.0814437	+	0.141065i
$326$	8.62099	−	14.9320i	0.477473	−	0.827007i
$327$	0.497007	+	0.860842i	0.0274846	+	0.0476047i
$328$	−1.09425	+	1.89529i	−0.0604197	+	0.104650i
$329$	−5.78675	−	10.0229i	−0.319034	−	0.552582i
$330$	−0.504001			−0.0277443
$331$	14.1250			0.776380			0.388190	−	0.921579i	$-0.373100\pi$
$331$	14.1250			0.776380			0.388190	+	0.921579i	$0.373100\pi$
$332$	1.84625	+	3.19780i	0.101326	+	0.175502i
$333$	−4.66975	−	8.08825i	−0.255901	−	0.443233i
$334$	−22.4860			−1.23038
$335$	−1.51200			−0.0826095
$336$	−0.220248	−	0.381481i	−0.0120155	−	0.0208115i
$337$	−14.3055	+	24.7778i	−0.779270	+	1.34973i	0.153094	+	0.988212i	$0.451076\pi$
$337$	−14.3055	+	24.7778i	−0.779270	+	1.34973i	−0.932363	+	0.361523i	$0.882257\pi$
$338$	−2.18850	−	3.79059i	−0.119038	−	0.206181i
$339$	1.81050	−	3.13587i	0.0983326	−	0.170317i
$340$	1.68450	−	2.91763i	0.0913546	−	0.158231i
$341$	5.43250			0.294186
$342$	12.6578	+	1.90222i	0.684453	+	0.102860i
$343$	−19.1310			−1.03298
$344$	3.59425	−	6.22542i	0.193789	−	0.335652i
$345$	−1.13501	+	1.96589i	−0.0611069	+	0.105840i
$346$	−4.71625	−	8.16878i	−0.253547	−	0.439156i
$347$	−3.81450	+	6.60690i	−0.204773	+	0.354677i	−0.950060	−	0.312066i	$-0.898979\pi$
$347$	−3.81450	+	6.60690i	−0.204773	+	0.354677i	0.745287	+	0.666743i	$0.232312\pi$
$348$	0.126000	+	0.218239i	0.00675432	+	0.0116988i
$349$	−25.1230			−1.34480			−0.672401	−	0.740187i	$-0.734737\pi$
$349$	−25.1230			−1.34480			−0.672401	+	0.740187i	$0.734737\pi$
$350$	1.74800			0.0934345
$351$	−2.19650	−	3.80445i	−0.117240	−	0.203066i
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−26.7620			−1.42440			−0.712198	−	0.701978i	$-0.752300\pi$
$353$	−26.7620			−1.42440			−0.712198	+	0.701978i	$0.752300\pi$
$354$		0			0
$355$	7.18850	+	12.4508i	0.381526	+	0.660822i
$356$	−5.18450	+	8.97981i	−0.274778	+	0.475929i
$357$	0.371007	+	0.642603i	0.0196358	+	0.0340102i
$358$	5.25200	−	9.09673i	0.277577	−	0.480777i
$359$	−3.81951	+	6.61558i	−0.201586	+	0.349157i	−0.949040	−	0.315157i	$-0.897943\pi$
$359$	−3.81951	+	6.61558i	−0.201586	+	0.349157i	0.747454	+	0.664314i	$0.231276\pi$
$360$	5.87299			0.309534
$361$	18.1607	+	5.58456i	0.955829	+	0.293924i
$362$	9.19650			0.483357
$363$	−0.126000	+	0.218239i	−0.00661330	+	0.0114546i
$364$	2.56650	−	4.44530i	0.134521	−	0.232997i
$365$	−8.18850	−	14.1829i	−0.428605	−	0.742366i
$366$	1.18950	−	2.06028i	0.0621764	−	0.107693i
$367$	−13.7747	−	23.8586i	−0.719036	−	1.24541i	−0.961382	−	0.275217i	$-0.911250\pi$
$367$	−13.7747	−	23.8586i	−0.719036	−	1.24541i	0.242347	−	0.970190i	$-0.422083\pi$
$368$	4.50400			0.234787
$369$	6.42651			0.334551
$370$	−3.18049	−	5.50878i	−0.165346	−	0.286388i
$371$	0.880993	+	1.52592i	0.0457389	+	0.0792221i
$372$	1.36899			0.0709789
$373$	−32.9285			−1.70497			−0.852486	−	0.522749i	$-0.824906\pi$
$373$	−32.9285			−1.70497			−0.852486	+	0.522749i	$0.824906\pi$
$374$	−0.842248	−	1.45882i	−0.0435516	−	0.0754336i
$375$	1.51200	−	2.61886i	0.0780795	−	0.135238i
$376$	3.31050	+	5.73395i	0.170726	+	0.295706i
$377$	−1.46825	+	2.54308i	−0.0756186	+	0.130975i
$378$	−1.30750	+	2.26466i	−0.0672507	+	0.116482i
$379$	−30.5020			−1.56678			−0.783391	−	0.621529i	$-0.786512\pi$
$379$	−30.5020			−1.56678			−0.783391	+	0.621529i	$0.786512\pi$
$380$	8.62099	+	1.29557i	0.442248	+	0.0664615i
$381$	2.99200			0.153285
$382$	12.3105	−	21.3224i	0.629860	−	1.09095i
$383$	4.75600	−	8.23764i	0.243020	−	0.420924i	−0.718553	−	0.695472i	$-0.755195\pi$
$383$	4.75600	−	8.23764i	0.243020	−	0.420924i	0.961573	+	0.274549i	$0.0885285\pi$
$384$	0.126000	+	0.218239i	0.00642992	+	0.0111369i
$385$	−1.74800	+	3.02762i	−0.0890863	+	0.154302i
$386$	6.34625	+	10.9920i	0.323016	+	0.559479i
$387$	−21.1090			−1.07303
$388$	−12.3690			−0.627940
$389$	−14.5267	−	25.1611i	−0.736535	−	1.27572i	−0.954047	−	0.299658i	$-0.903127\pi$
$389$	−14.5267	−	25.1611i	−0.736535	−	1.27572i	0.217511	−	0.976058i	$-0.430206\pi$
$390$	−0.739998	−	1.28171i	−0.0374713	−	0.0649021i
$391$	−7.58697			−0.383689
$392$	3.94450			0.199227
$393$	−1.46324	−	2.53440i	−0.0738106	−	0.127844i
$394$	−10.1845	+	17.6401i	−0.513087	+	0.888694i
$395$	−2.75600	−	4.77353i	−0.138669	−	0.240183i
$396$	1.46825	−	2.54308i	0.0737822	−	0.127795i
$397$	8.59025	−	14.8787i	0.431132	−	0.746743i	−0.565839	−	0.824516i	$-0.691448\pi$
$397$	8.59025	−	14.8787i	0.431132	−	0.746743i	0.996971	+	0.0777730i	$0.0247809\pi$
$398$	−8.81150			−0.441681
$399$	−1.19650	+	1.50170i	−0.0598998	+	0.0751790i
$400$	−1.00000			−0.0500000
$401$	−15.4087	+	26.6887i	−0.769476	+	1.33277i	0.168371	+	0.985724i	$0.446149\pi$
$401$	−15.4087	+	26.6887i	−0.769476	+	1.33277i	−0.937847	+	0.347048i	$0.887184\pi$
$402$	−0.0952563	+	0.164989i	−0.00475095	+	0.00822889i
$403$	7.97625	+	13.8153i	0.397325	+	0.688188i
$404$	−3.46825	+	6.00718i	−0.172552	+	0.298868i
$405$	−8.43250	−	14.6055i	−0.419014	−	0.725754i
$406$	1.74800			0.0867518
$407$	−3.18049			−0.157651
$408$	−0.212247	−	0.367622i	−0.0105078	−	0.0182000i
$409$	14.4552	+	25.0372i	0.714765	+	1.23801i	0.963050	+	0.269323i	$0.0867999\pi$
$409$	14.4552	+	25.0372i	0.714765	+	1.23801i	−0.248284	+	0.968687i	$0.579867\pi$
$410$	4.37699			0.216164
$411$	2.50198			0.123414
$412$	−3.31050	−	5.73395i	−0.163096	−	0.282491i
$413$		0			0
$414$	−6.61299	−	11.4540i	−0.325011	−	0.562935i
$415$	3.69250	−	6.39559i	0.181258	−	0.313947i
$416$	−1.46825	+	2.54308i	−0.0719868	+	0.124685i
$417$	1.38903			0.0680209
$418$	2.71625	−	3.40911i	0.132856	−	0.166745i
$419$	−14.2520			−0.696256			−0.348128	−	0.937447i	$-0.613183\pi$
$419$	−14.2520			−0.696256			−0.348128	+	0.937447i	$0.613183\pi$
$420$	−0.440497	+	0.762962i	−0.0214940	+	0.0372288i
$421$	−11.3462	+	19.6523i	−0.552982	+	0.957793i	0.445075	+	0.895493i	$0.353177\pi$
$421$	−11.3462	+	19.6523i	−0.552982	+	0.957793i	−0.998057	+	0.0623002i	$0.980156\pi$
$422$	−3.24400	−	5.61877i	−0.157915	−	0.273517i
$423$	9.72126	−	16.8377i	0.472664	−	0.818677i
$424$	−0.504001	−	0.872955i	−0.0244764	−	0.0423944i
$425$	1.68450			0.0817100
$426$	1.81150			0.0877676
$427$	−8.25099	−	14.2911i	−0.399293	−	0.691597i
$428$	−8.80649	−	15.2533i	−0.425678	−	0.737296i
$429$	−0.739998			−0.0357274
$430$	−14.3770			−0.693320
$431$	12.3145	+	21.3293i	0.593168	+	1.02740i	0.993803	+	0.111160i	$0.0354565\pi$
$431$	12.3145	+	21.3293i	0.593168	+	1.02740i	−0.400634	+	0.916238i	$0.631210\pi$
$432$	0.748000	−	1.29557i	0.0359881	−	0.0623333i
$433$	−11.0257	−	19.0971i	−0.529863	−	0.917750i	−0.999393	−	0.0348332i	$-0.988910\pi$
$433$	−11.0257	−	19.0971i	−0.529863	−	0.917750i	0.469530	−	0.882916i	$-0.344423\pi$
$434$	4.74800	−	8.22378i	0.227911	−	0.394754i
$435$	0.252000	−	0.436477i	0.0120825	−	0.0209275i
$436$	−3.94450			−0.188907
$437$	−7.18049	−	18.2722i	−0.343490	−	0.874080i
$438$	−2.06350			−0.0985980
$439$	13.9365	−	24.1387i	0.665153	−	1.15208i	−0.314091	−	0.949393i	$-0.601700\pi$
$439$	13.9365	−	24.1387i	0.665153	−	1.15208i	0.979244	−	0.202685i	$-0.0649669\pi$
$440$	1.00000	−	1.73205i	0.0476731	−	0.0825723i
$441$	−5.79150	−	10.0312i	−0.275786	−	0.477675i
$442$	2.47326	−	4.28381i	0.117641	−	0.203760i
$443$	9.50299	+	16.4597i	0.451501	+	0.782022i	0.998480	−	0.0551242i	$-0.0175555\pi$
$443$	9.50299	+	16.4597i	0.451501	+	0.782022i	−0.546979	+	0.837147i	$0.684222\pi$
$444$	−0.801486			−0.0380368
$445$	20.7380			0.983075
$446$	−9.59425	−	16.6177i	−0.454301	−	0.786872i
$447$	−1.06149	−	1.83855i	−0.0502067	−	0.0869605i
$448$	1.74800			0.0825852
$449$	33.3055			1.57178			0.785892	−	0.618364i	$-0.212204\pi$
$449$	33.3055			1.57178			0.785892	+	0.618364i	$0.212204\pi$
$450$	1.46825	+	2.54308i	0.0692139	+	0.119882i
$451$	1.09425	−	1.89529i	0.0515261	−	0.0892459i
$452$	7.18450	+	12.4439i	0.337930	+	0.585312i
$453$	−1.76375	+	3.05490i	−0.0828681	+	0.143532i
$454$	−0.275751	+	0.477615i	−0.0129416	+	0.0224156i
$455$	−10.2660			−0.481277
$456$	0.684495	−	0.859096i	0.0320544	−	0.0402308i
$457$	−10.3155			−0.482539			−0.241269	−	0.970458i	$-0.577564\pi$
$457$	−10.3155			−0.482539			−0.241269	+	0.970458i	$0.577564\pi$
$458$	12.0307	−	20.8379i	0.562160	−	0.973689i
$459$	−1.26000	+	2.18239i	−0.0588119	+	0.101865i
$460$	−4.50400	−	7.80116i	−0.210000	−	0.363731i
$461$	−12.1607	+	21.0630i	−0.566382	+	0.981003i	0.430537	+	0.902573i	$0.358324\pi$
$461$	−12.1607	+	21.0630i	−0.566382	+	0.981003i	−0.996920	+	0.0784302i	$0.975009\pi$
$462$	0.220248	+	0.381481i	0.0102469	+	0.0177481i
$463$	−15.6130			−0.725597			−0.362799	−	0.931868i	$-0.618179\pi$
$463$	−15.6130			−0.725597			−0.362799	+	0.931868i	$0.618179\pi$
$464$	−1.00000			−0.0464238
$465$	−1.36899	−	2.37116i	−0.0634854	−	0.109960i
$466$	−8.71524	−	15.0952i	−0.403726	−	0.699273i
$467$	10.1250			0.468529			0.234264	−	0.972173i	$-0.424732\pi$
$467$	10.1250			0.468529			0.234264	+	0.972173i	$0.424732\pi$
$468$	8.62301			0.398599
$469$	0.660745	+	1.14444i	0.0305104	+	0.0528455i
$470$	6.62099	−	11.4679i	0.305404	−	0.528974i
$471$	−0.127008	−	0.219985i	−0.00585224	−	0.0101364i
$472$		0			0
$473$	−3.59425	+	6.22542i	−0.165264	+	0.286245i
$474$	−0.694513			−0.0319001
$475$	1.59425	+	4.05689i	0.0731491	+	0.186143i
$476$	−2.94450			−0.134961
$477$	−1.48000	+	2.56343i	−0.0677644	+	0.117371i
$478$	−5.49600	+	9.51935i	−0.251381	+	0.435405i
$479$	−10.8105	−	18.7243i	−0.493944	−	0.855536i	0.506031	−	0.862515i	$-0.331112\pi$
$479$	−10.8105	−	18.7243i	−0.493944	−	0.855536i	−0.999976	+	0.00697863i	$0.997779\pi$
$480$	0.252000	−	0.436477i	0.0115022	−	0.0199224i
$481$	−4.66975	−	8.08825i	−0.212922	−	0.368793i
$482$	−8.88099			−0.404518
$483$	1.98400			0.0902750
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	12.3690	+	21.4237i	0.561647	+	0.972801i
$486$	−6.61299			−0.299971
$487$	3.04548			0.138004			0.0690020	−	0.997617i	$-0.478019\pi$
$487$	3.04548			0.138004			0.0690020	+	0.997617i	$0.478019\pi$
$488$	4.72025	+	8.17571i	0.213676	+	0.370097i
$489$	−2.17249	+	3.76287i	−0.0982435	+	0.170163i
$490$	−3.94450	−	6.83207i	−0.178194	−	0.308641i
$491$	−13.6210	+	23.5922i	−0.614707	+	1.06470i	0.375729	+	0.926730i	$0.377392\pi$
$491$	−13.6210	+	23.5922i	−0.614707	+	1.06470i	−0.990436	+	0.137974i	$0.955941\pi$
$492$	0.275751	−	0.477615i	0.0124318	−	0.0215325i
$493$	1.68450			0.0758659
$494$	12.6578	+	1.90222i	0.569499	+	0.0855851i
$495$	−5.87299			−0.263971
$496$	−2.71625	+	4.70468i	−0.121963	+	0.211246i
$497$	6.28274	−	10.8820i	0.281820	−	0.488126i
$498$	−0.465255	−	0.805846i	−0.0208486	−	0.0361108i
$499$	5.93650	−	10.2823i	0.265754	−	0.460300i	−0.702007	−	0.712170i	$-0.747712\pi$
$499$	5.93650	−	10.2823i	0.265754	−	0.460300i	0.967761	+	0.251871i	$0.0810458\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$	5.66648			0.253159
$502$	7.11699			0.317647
$503$	−0.567505	−	0.982947i	−0.0253038	−	0.0438275i	0.853096	−	0.521754i	$-0.174722\pi$
$503$	−0.567505	−	0.982947i	−0.0253038	−	0.0438275i	−0.878400	+	0.477926i	$0.841389\pi$
$504$	−2.56650	−	4.44530i	−0.114321	−	0.198010i
$505$	13.8730			0.617340
$506$	−4.50400			−0.200227
$507$	0.551502	+	0.955229i	0.0244931	+	0.0424232i
$508$	−5.93650	+	10.2823i	−0.263389	+	0.456204i
$509$	11.4325	+	19.8017i	0.506736	+	0.877693i	0.999970	+	0.00779611i	$0.00248160\pi$
$509$	11.4325	+	19.8017i	0.506736	+	0.877693i	−0.493233	+	0.869897i	$0.664185\pi$
$510$	−0.424493	+	0.735244i	−0.0187969	+	0.0325572i
$511$	−7.15674	+	12.3958i	−0.316596	+	0.548360i
$512$	−1.00000			−0.0441942
$513$	−6.44850	−	0.969088i	−0.284708	−	0.0427863i
$514$	−17.2420			−0.760511
$515$	−6.62099	+	11.4679i	−0.291756	+	0.505336i
$516$	−0.905752	+	1.56881i	−0.0398735	+	0.0690629i
$517$	−3.31050	−	5.73395i	−0.145595	−	0.252179i
$518$	−2.77975	+	4.81467i	−0.122135	+	0.211545i
$519$	1.18850	+	2.05854i	0.0521692	+	0.0903597i
$520$	5.87299			0.257548
$521$	24.9525			1.09319			0.546594	−	0.837397i	$-0.315924\pi$
$521$	24.9525			1.09319			0.546594	+	0.837397i	$0.315924\pi$
$522$	1.46825	+	2.54308i	0.0642635	+	0.111308i
$523$	2.68950	+	4.65836i	0.117604	+	0.203696i	0.918818	−	0.394682i	$-0.129145\pi$
$523$	2.68950	+	4.65836i	0.117604	+	0.203696i	−0.801214	+	0.598378i	$0.795812\pi$
$524$	11.6130			0.507316
$525$	−0.440497			−0.0192248
$526$	11.6925	+	20.2520i	0.509817	+	0.883029i
$527$	4.57551	−	7.92501i	0.199312	−	0.345219i
$528$	−0.126000	−	0.218239i	−0.00548345	−	0.00949762i
$529$	1.35699	−	2.35037i	0.0589995	−	0.102190i
$530$	−1.00800	+	1.74591i	−0.0437848	+	0.0758375i
$531$		0			0
$532$	−2.78675	−	7.09145i	−0.120821	−	0.307453i
$533$	6.42651			0.278363
$534$	1.30649	−	2.26292i	0.0565376	−	0.0979259i
$535$	−17.6130	+	30.5066i	−0.761476	+	1.31892i
$536$	−0.378001	−	0.654716i	−0.0163271	−	0.0282794i
$537$	−1.32351	+	2.29238i	−0.0571135	+	0.0989235i
$538$	−0.157752	−	0.273235i	−0.00680118	−	0.0117800i
$539$	−3.94450			−0.169902
$540$	−2.99200			−0.128755
$541$	15.9127	+	27.5617i	0.684142	+	1.18497i	0.973706	+	0.227810i	$0.0731566\pi$
$541$	15.9127	+	27.5617i	0.684142	+	1.18497i	−0.289563	+	0.957159i	$0.593510\pi$
$542$	−6.00000	−	10.3923i	−0.257722	−	0.446388i
$543$	−2.31752			−0.0994543
$544$	1.68450			0.0722221
$545$	3.94450	+	6.83207i	0.168964	+	0.292654i
$546$	−0.646758	+	1.12022i	−0.0276787	+	0.0479409i
$547$	−3.59425	−	6.22542i	−0.153679	−	0.266180i	0.778898	−	0.627150i	$-0.215779\pi$
$547$	−3.59425	−	6.22542i	−0.153679	−	0.266180i	−0.932577	+	0.360971i	$0.882445\pi$
$548$	−4.96425	+	8.59833i	−0.212062	+	0.367302i
$549$	13.8610	−	24.0079i	0.591573	−	1.02463i
$550$	1.00000			0.0426401
$551$	1.59425	+	4.05689i	0.0679173	+	0.172829i
$552$	−1.13501			−0.0483092
$553$	−2.40874	+	4.17207i	−0.102430	+	0.177414i
$554$	−0.720248	+	1.24751i	−0.0306004	+	0.0530015i
$555$	0.801486	+	1.38821i	0.0340212	+	0.0589264i
$556$	−2.75600	+	4.77353i	−0.116880	+	0.202443i
$557$	−15.4682	−	26.7918i	−0.655411	−	1.13520i	−0.981791	−	0.189966i	$-0.939162\pi$
$557$	−15.4682	−	26.7918i	−0.655411	−	1.13520i	0.326380	−	0.945239i	$-0.394171\pi$
$558$	15.9525			0.675323
$559$	−21.1090			−0.892815
$560$	−1.74800	−	3.02762i	−0.0738665	−	0.127940i
$561$	0.212247	+	0.367622i	0.00896106	+	0.0155210i
$562$	15.0535			0.634993
$563$	10.4880			0.442016			0.221008	−	0.975272i	$-0.429065\pi$
$563$	10.4880			0.442016			0.221008	+	0.975272i	$0.429065\pi$
$564$	−0.834246	−	1.44496i	−0.0351281	−	0.0608437i
$565$	14.3690	−	24.8878i	0.604508	−	1.04704i
$566$	11.6210	+	20.1281i	0.488467	+	0.846049i
$567$	−7.37000	+	12.7652i	−0.309511	+	0.536089i
$568$	−3.59425	+	6.22542i	−0.150811	+	0.261213i
$569$	17.6190			0.738626			0.369313	−	0.929305i	$-0.379593\pi$
$569$	17.6190			0.738626			0.369313	+	0.929305i	$0.379593\pi$
$570$	−2.17249	−	0.326485i	−0.0909957	−	0.0136750i
$571$	17.6130			0.737081			0.368540	−	0.929612i	$-0.379858\pi$
$571$	17.6130			0.737081			0.368540	+	0.929612i	$0.379858\pi$
$572$	1.46825	−	2.54308i	0.0613905	−	0.106332i
$573$	−3.10225	+	5.37325i	−0.129598	+	0.224471i
$574$	−1.91275	−	3.31297i	−0.0798364	−	0.138281i
$575$	2.25200	−	3.90058i	0.0939149	−	0.162665i
$576$	1.46825	+	2.54308i	0.0611770	+	0.105962i
$577$	−26.1865			−1.09016			−0.545079	−	0.838385i	$-0.683500\pi$
$577$	−26.1865			−1.09016			−0.545079	+	0.838385i	$0.683500\pi$
$578$	14.1625			0.589081
$579$	−1.59926	−	2.76999i	−0.0664629	−	0.115117i
$580$	1.00000	+	1.73205i	0.0415227	+	0.0719195i
$581$	−6.45448			−0.267777
$582$	3.11699			0.129203
$583$	0.504001	+	0.872955i	0.0208736	+	0.0361541i
$584$	4.09425	−	7.09145i	0.169421	−	0.293446i
$585$	−8.62301	−	14.9355i	−0.356517	−	0.617506i
$586$	7.00400	−	12.1313i	0.289333	−	0.501139i
$587$	−11.1260	+	19.2708i	−0.459219	+	0.795391i	−0.998920	−	0.0464660i	$-0.985204\pi$
$587$	−11.1260	+	19.2708i	−0.459219	+	0.795391i	0.539701	+	0.841857i	$0.318537\pi$
$588$	−0.994015			−0.0409925
$589$	23.4167	+	3.51910i	0.964870	+	0.145002i
$590$		0			0
$591$	2.56650	−	4.44530i	0.105572	−	0.182855i
$592$	1.59025	−	2.75439i	0.0653588	−	0.113205i
$593$	1.43250	+	2.48115i	0.0588255	+	0.101889i	0.893938	−	0.448190i	$-0.147931\pi$
$593$	1.43250	+	2.48115i	0.0588255	+	0.101889i	−0.835113	+	0.550079i	$0.814598\pi$
$594$	−0.748000	+	1.29557i	−0.0306908	+	0.0531580i
$595$	2.94450	+	5.10002i	0.120713	+	0.209080i
$596$	8.42449			0.345081
$597$	2.22050			0.0908791
$598$	−6.61299	−	11.4540i	−0.270425	−	0.468390i
$599$	8.65775	+	14.9957i	0.353746	+	0.612706i	0.986903	−	0.161318i	$-0.0515743\pi$
$599$	8.65775	+	14.9957i	0.353746	+	0.612706i	−0.633156	+	0.774024i	$0.718241\pi$
$600$	0.252000			0.0102879
$601$	19.7300			0.804803			0.402401	−	0.915463i	$-0.368176\pi$
$601$	19.7300			0.804803			0.402401	+	0.915463i	$0.368176\pi$
$602$	6.28274	+	10.8820i	0.256066	+	0.443519i
$603$	−1.11000	+	1.92257i	−0.0452026	+	0.0782932i
$604$	−6.99899	−	12.1226i	−0.284785	−	0.493262i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	0.874000	−	1.51381i	0.0355038	−	0.0614944i
$607$	8.12499			0.329783			0.164892	−	0.986312i	$-0.447273\pi$
$607$	8.12499			0.329783			0.164892	+	0.986312i	$0.447273\pi$
$608$	1.59425	+	4.05689i	0.0646553	+	0.164529i
$609$	−0.440497			−0.0178498
$610$	9.44050	−	16.3514i	0.382235	−	0.662050i
$611$	9.72126	−	16.8377i	0.393280	−	0.681181i
$612$	−2.47326	−	4.28381i	−0.0999755	−	0.173163i
$613$	0.980250	−	1.69784i	0.0395919	−	0.0685752i	−0.845550	−	0.533896i	$-0.820728\pi$
$613$	0.980250	−	1.69784i	0.0395919	−	0.0685752i	0.885142	+	0.465320i	$0.154061\pi$
$614$	7.05049	+	12.2118i	0.284535	+	0.492829i
$615$	−1.10300			−0.0444774
$616$	−1.74800			−0.0704289
$617$	−0.0277513	−	0.0480667i	−0.00111723	−	0.00193509i	0.865466	−	0.500967i	$-0.167022\pi$
$617$	−0.0277513	−	0.0480667i	−0.00111723	−	0.00193509i	−0.866583	+	0.499032i	$0.833689\pi$
$618$	0.834246	+	1.44496i	0.0335583	+	0.0581247i
$619$	43.3850			1.74379			0.871895	−	0.489693i	$-0.162891\pi$
$619$	43.3850			1.74379			0.871895	+	0.489693i	$0.162891\pi$
$620$	10.8650			0.436349
$621$	3.36899	+	5.83526i	0.135193	+	0.234161i
$622$	−9.80649	+	16.9853i	−0.393205	+	0.681050i
$623$	−9.06250	−	15.6967i	−0.363081	−	0.628875i
$624$	0.369999	−	0.640857i	0.0148118	−	0.0256548i
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	18.3055			0.731634
$627$	−0.684495	+	0.859096i	−0.0273361	+	0.0343090i
$628$	1.00800			0.0402236
$629$	−2.67876	+	4.63976i	−0.106809	+	0.184999i
$630$	−5.13299	+	8.89061i	−0.204503	+	0.354210i
$631$	7.90175	+	13.6862i	0.314564	+	0.544840i	0.979345	−	0.202198i	$-0.0648084\pi$
$631$	7.90175	+	13.6862i	0.314564	+	0.544840i	−0.664781	+	0.747038i	$0.731475\pi$
$632$	1.37800	−	2.38677i	0.0548139	−	0.0949405i
$633$	0.817489	+	1.41593i	0.0324923	+	0.0562783i
$634$	15.4305			0.612823
$635$	23.7460			0.942331
$636$	0.127008	+	0.219985i	0.00503621	+	0.00872297i
$637$	−5.79150	−	10.0312i	−0.229468	−	0.397450i
$638$	1.00000			0.0395904
$639$	21.1090			0.835059
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	6.99600	−	12.1174i	0.276325	−	0.478610i	−0.694143	−	0.719837i	$-0.744217\pi$
$641$	6.99600	−	12.1174i	0.276325	−	0.478610i	0.970469	+	0.241227i	$0.0775499\pi$
$642$	2.21924	+	3.84384i	0.0875864	+	0.151704i
$643$	−0.945506	+	1.63766i	−0.0372871	+	0.0645831i	−0.884067	−	0.467361i	$-0.845205\pi$
$643$	−0.945506	+	1.63766i	−0.0372871	+	0.0645831i	0.846780	+	0.531944i	$0.178538\pi$
$644$	−3.93650	+	6.81821i	−0.155120	+	0.268675i
$645$	3.62301			0.142656
$646$	−2.68550	−	6.83382i	−0.105660	−	0.268873i
$647$	−37.4225			−1.47123			−0.735615	−	0.677400i	$-0.763107\pi$
$647$	−37.4225			−1.47123			−0.735615	+	0.677400i	$0.763107\pi$
$648$	4.21625	−	7.30275i	0.165630	−	0.286879i
$649$		0			0
$650$	1.46825	+	2.54308i	0.0575894	+	0.0997478i
$651$	−1.19650	+	2.07239i	−0.0468944	+	0.0812236i
$652$	−8.62099	−	14.9320i	−0.337624	−	0.584782i
$653$	20.0455			0.784440			0.392220	−	0.919871i	$-0.371707\pi$
$653$	20.0455			0.784440			0.392220	+	0.919871i	$0.371707\pi$
$654$	0.994015			0.0388691
$655$	−11.6130	−	20.1143i	−0.453757	−	0.785930i
$656$	1.09425	+	1.89529i	0.0427232	+	0.0739988i
$657$	−24.0455			−0.938104
$658$	−11.5735			−0.451182
$659$	9.68950	+	16.7827i	0.377450	+	0.653762i	0.990690	−	0.136134i	$-0.0434678\pi$
$659$	9.68950	+	16.7827i	0.377450	+	0.653762i	−0.613241	+	0.789896i	$0.710135\pi$
$660$	−0.252000	+	0.436477i	−0.00980910	+	0.0169899i
$661$	7.84225	+	13.5832i	0.305028	+	0.528324i	0.977268	−	0.212010i	$-0.0680008\pi$
$661$	7.84225	+	13.5832i	0.305028	+	0.528324i	−0.672239	+	0.740334i	$0.734667\pi$
$662$	7.06250	−	12.2326i	0.274492	−	0.475434i
$663$	−0.623262	+	1.07952i	−0.0242055	+	0.0419251i
$664$	3.69250			0.143297
$665$	−9.49600	+	11.9182i	−0.368239	+	0.462169i
$666$	−9.33951			−0.361899
$667$	2.25200	−	3.90058i	0.0871978	−	0.151031i
$668$	−11.2430	+	19.4734i	−0.435004	+	0.753450i
$669$	2.41775	+	4.18767i	0.0934758	+	0.161905i
$670$	−0.756001	+	1.30943i	−0.0292069	+	0.0505878i
$671$	−4.72025	−	8.17571i	−0.182223	−	0.315620i
$672$	−0.440497			−0.0169925
$673$	14.6605			0.565120			0.282560	−	0.959250i	$-0.408816\pi$
$673$	14.6605			0.565120			0.282560	+	0.959250i	$0.408816\pi$
$674$	14.3055	+	24.7778i	0.551027	+	0.954406i
$675$	−0.748000	−	1.29557i	−0.0287905	−	0.0498666i
$676$	−4.37699			−0.168346
$677$	34.4485			1.32396			0.661982	−	0.749520i	$-0.269716\pi$
$677$	34.4485			1.32396			0.661982	+	0.749520i	$0.269716\pi$
$678$	−1.81050	−	3.13587i	−0.0695317	−	0.120432i
$679$	10.8105	−	18.7243i	0.414869	−	0.718574i
$680$	−1.68450	−	2.91763i	−0.0645975	−	0.111886i
$681$	0.0694893	−	0.120359i	0.00266284	−	0.00461217i
$682$	2.71625	−	4.70468i	0.104010	−	0.180151i
$683$	27.4780			1.05142			0.525708	−	0.850665i	$-0.323801\pi$
$683$	27.4780			1.05142			0.525708	+	0.850665i	$0.323801\pi$
$684$	7.97625	−	10.0108i	0.304980	−	0.382773i
$685$	19.8570			0.758697
$686$	−9.56549	+	16.5679i	−0.365212	+	0.632566i
$687$	−3.03175	+	5.25115i	−0.115669	+	0.200344i
$688$	−3.59425	−	6.22542i	−0.137029	−	0.237342i
$689$	−1.48000	+	2.56343i	−0.0563834	+	0.0976588i
$690$	1.13501	+	1.96589i	0.0432091	+	0.0748403i
$691$	−29.2600			−1.11310			−0.556551	−	0.830813i	$-0.687876\pi$
$691$	−29.2600			−1.11310			−0.556551	+	0.830813i	$0.687876\pi$
$692$	−9.43250			−0.358570
$693$	2.56650	+	4.44530i	0.0974932	+	0.168863i
$694$	3.81450	+	6.60690i	0.144796	+	0.250795i
$695$	11.0240			0.418164
$696$	0.252000			0.00955205
$697$	−1.84326	−	3.19261i	−0.0698183	−	0.120929i
$698$	−12.5615	+	21.7571i	−0.475459	+	0.823520i
$699$	2.19624	+	3.80401i	0.0830696	+	0.143881i
$700$	0.874000	−	1.51381i	0.0330341	−	0.0572167i
$701$	−7.31951	+	12.6778i	−0.276454	+	0.478832i	−0.970501	−	0.241097i	$-0.922493\pi$
$701$	−7.31951	+	12.6778i	−0.276454	+	0.478832i	0.694047	+	0.719930i	$0.255826\pi$
$702$	−4.39300			−0.165803
$703$	−13.7095	−	2.06028i	−0.517064	−	0.0777050i
$704$	1.00000			0.0376889
$705$	−1.66849	+	2.88991i	−0.0628391	+	0.108840i
$706$	−13.3810	+	23.1766i	−0.503600	+	0.872261i
$707$	−6.06250	−	10.5006i	−0.228004	−	0.394914i
$708$		0			0
$709$	−5.99200	−	10.3784i	−0.225034	−	0.389771i	0.731295	−	0.682061i	$-0.238916\pi$
$709$	−5.99200	−	10.3784i	−0.225034	−	0.389771i	−0.956330	+	0.292290i	$0.905583\pi$
$710$	14.3770			0.539559
$711$	−8.09299			−0.303511
$712$	5.18450	+	8.97981i	0.194297	+	0.336533i
$713$	−12.2340	−	21.1899i	−0.458166	−	0.793567i
$714$	0.742014			0.0277692
$715$	−5.87299			−0.219637
$716$	−5.25200	−	9.09673i	−0.196276	−	0.339961i
$717$	1.38499	−	2.39888i	0.0517235	−	0.0895878i
$718$	3.81951	+	6.61558i	0.142543	+	0.246891i
$719$	−5.41375	+	9.37690i	−0.201899	+	0.349699i	−0.949140	−	0.314854i	$-0.898045\pi$
$719$	−5.41375	+	9.37690i	−0.201899	+	0.349699i	0.747241	+	0.664553i	$0.231378\pi$
$720$	2.93650	−	5.08616i	0.109437	−	0.189550i
$721$	11.5735			0.431019
$722$	13.9167	−	12.9354i	0.517928	−	0.481405i
$723$	2.23801			0.0832326
$724$	4.59825	−	7.96440i	0.170893	−	0.295995i
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$	0.126000	+	0.218239i	0.00467631	+	0.00809960i
$727$	13.5387	−	23.4498i	0.502124	−	0.869705i	−0.497873	−	0.867250i	$-0.665885\pi$
$727$	13.5387	−	23.4498i	0.502124	−	0.869705i	0.999997	−	0.00245464i	$-0.000781337\pi$
$728$	−2.56650	−	4.44530i	−0.0951207	−	0.164754i
$729$	−23.6310			−0.875223
$730$	−16.3770			−0.606140
$731$	6.05449	+	10.4867i	0.223934	+	0.387864i
$732$	−1.18950	−	2.06028i	−0.0439653	−	0.0761502i
$733$	44.2975			1.63616			0.818082	−	0.575101i	$-0.195037\pi$
$733$	44.2975			1.63616			0.818082	+	0.575101i	$0.195037\pi$
$734$	−27.5495			−1.01687
$735$	0.994015	+	1.72168i	0.0366648	+	0.0635053i
$736$	2.25200	−	3.90058i	0.0830098	−	0.143777i
$737$	0.378001	+	0.654716i	0.0139238	+	0.0241168i
$738$	3.21325	−	5.56552i	0.118282	−	0.204870i
$739$	10.8145	−	18.7313i	0.397818	−	0.689040i	−0.595639	−	0.803252i	$-0.703101\pi$
$739$	10.8145	−	18.7313i	0.397818	−	0.689040i	0.993456	+	0.114212i	$0.0364343\pi$
$740$	−6.36099			−0.233835
$741$	−3.18976	−	0.479361i	−0.117179	−	0.0176098i
$742$	1.76199			0.0646846
$743$	−18.8185	+	32.5946i	−0.690384	+	1.19578i	0.281329	+	0.959612i	$0.409225\pi$
$743$	−18.8185	+	32.5946i	−0.690384	+	1.19578i	−0.971712	+	0.236168i	$0.924108\pi$
$744$	0.684495	−	1.18558i	0.0250948	−	0.0434655i
$745$	−8.42449	−	14.5917i	−0.308650	−	0.534597i
$746$	−16.4642	+	28.5169i	−0.602799	+	1.04408i
$747$	−5.42150	−	9.39032i	−0.198362	−	0.343574i
$748$	−1.68450			−0.0615913
$749$	30.7875			1.12495
$750$	−1.51200	−	2.61886i	−0.0552105	−	0.0956274i
$751$	−21.4672	−	37.1823i	−0.783351	−	1.35680i	−0.929979	−	0.367612i	$-0.880176\pi$
$751$	−21.4672	−	37.1823i	−0.783351	−	1.35680i	0.146629	−	0.989192i	$-0.453158\pi$
$752$	6.62099			0.241443
$753$	−1.79348			−0.0653582
$754$	1.46825	+	2.54308i	0.0534704	+	0.0926135i
$755$	−13.9980	+	24.2452i	−0.509439	+	0.882374i
$756$	1.30750	+	2.26466i	0.0475534	+	0.0823649i
$757$	−6.44850	+	11.1691i	−0.234375	+	0.405949i	−0.959091	−	0.283099i	$-0.908638\pi$
$757$	−6.44850	+	11.1691i	−0.234375	+	0.405949i	0.724716	+	0.689048i	$0.241971\pi$
$758$	−15.2510	+	26.4155i	−0.553941	+	0.959454i
$759$	1.13501			0.0411983
$760$	5.43250	−	6.81821i	0.197057	−	0.247322i
$761$	15.6030			0.565607			0.282804	−	0.959178i	$-0.408736\pi$
$761$	15.6030			0.565607			0.282804	+	0.959178i	$0.408736\pi$
$762$	1.49600	−	2.59115i	0.0541943	−	0.0938673i
$763$	3.44749	−	5.97123i	0.124808	−	0.216173i
$764$	−12.3105	−	21.3224i	−0.445378	−	0.771417i
$765$	−4.94651	+	8.56761i	−0.178842	+	0.309763i
$766$	−4.75600	−	8.23764i	−0.171841	−	0.297638i
$767$		0			0
$768$	0.252000			0.00909328
$769$	22.9445	+	39.7410i	0.827400	+	1.43310i	0.900071	+	0.435742i	$0.143514\pi$
$769$	22.9445	+	39.7410i	0.827400	+	1.43310i	−0.0726717	+	0.997356i	$0.523153\pi$
$770$	1.74800	+	3.02762i	0.0629935	+	0.109108i
$771$	4.34499			0.156481
$772$	12.6925			0.456813
$773$	−19.4632	−	33.7113i	−0.700044	−	1.21251i	−0.968450	−	0.249206i	$-0.919830\pi$
$773$	−19.4632	−	33.7113i	−0.700044	−	1.21251i	0.268406	−	0.963306i	$-0.413503\pi$
$774$	−10.5545	+	18.2809i	−0.379373	+	0.657094i
$775$	2.71625	+	4.70468i	0.0975705	+	0.168997i
$776$	−6.18450	+	10.7119i	−0.222010	+	0.384533i
$777$	0.700499	−	1.21330i	0.0251302	−	0.0435269i
$778$	−29.0535			−1.04162
$779$	5.94450	−	7.46081i	0.212984	−	0.267311i
$780$	−1.48000			−0.0529924
$781$	3.59425	−	6.22542i	0.128612	−	0.222763i
$782$	−3.79348	+	6.57051i	−0.135655	+	0.234961i
$783$	−0.748000	−	1.29557i	−0.0267313	−	0.0463000i
$784$	1.97225	−	3.41603i	0.0704375	−	0.122001i
$785$	−1.00800	−	1.74591i	−0.0359771	−	0.0623142i
$786$	−2.92648			−0.104384
$787$	−24.9185			−0.888248			−0.444124	−	0.895965i	$-0.646485\pi$
$787$	−24.9185			−0.888248			−0.444124	+	0.895965i	$0.646485\pi$
$788$	10.1845	+	17.6401i	0.362808	+	0.628401i
$789$	−2.94651	−	5.10351i	−0.104899	−	0.181690i
$790$	−5.51200			−0.196108
$791$	−25.1170			−0.893057
$792$	−1.46825	−	2.54308i	−0.0521719	−	0.0903644i
$793$	13.8610	−	24.0079i	0.492218	−	0.852547i
$794$	−8.59025	−	14.8787i	−0.304856	−	0.528027i
$795$	0.254017	−	0.439970i	0.00900905	−	0.0156041i
$796$	−4.40575	+	7.63099i	−0.156158	+	0.270473i
$797$	−34.9265			−1.23716			−0.618580	−	0.785722i	$-0.712292\pi$
$797$	−34.9265			−1.23716			−0.618580	+	0.785722i	$0.712292\pi$
$798$	0.702261	+	1.78705i	0.0248598	+	0.0632608i
$799$	−11.1530			−0.394566
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	15.2242	−	26.3692i	0.537922	−	0.931709i
$802$	15.4087	+	26.6887i	0.544102	+	0.942412i
$803$	−4.09425	+	7.09145i	−0.144483	+	0.250252i
$804$	0.0952563	+	0.164989i	0.00335943	+	0.00581870i
$805$	15.7460			0.554973
$806$	15.9525			0.561903
$807$	0.0397536	+	0.0688553i	0.00139939	+	0.00242382i
$808$	3.46825	+	6.00718i	0.122013	+	0.211332i
$809$	50.0415			1.75936			0.879682	−	0.475563i	$-0.157755\pi$
$809$	50.0415			1.75936			0.879682	+	0.475563i	$0.157755\pi$
$810$	−16.8650			−0.592575
$811$	−7.21524	−	12.4972i	−0.253361	−	0.438835i	0.711088	−	0.703103i	$-0.248203\pi$
$811$	−7.21524	−	12.4972i	−0.253361	−	0.438835i	−0.964449	+	0.264269i	$0.914869\pi$
$812$	0.874000	−	1.51381i	0.0306714	−	0.0531244i
$813$	1.51200	+	2.61886i	0.0530282	+	0.0918476i
$814$	−1.59025	+	2.75439i	−0.0557381	+	0.0965413i
$815$	−17.2420	+	29.8640i	−0.603960	+	1.04609i
$816$	−0.424493			−0.0148602
$817$	−19.5257	+	24.5063i	−0.683119	+	0.857368i
$818$	28.9105			1.01083
$819$	−7.53651	+	13.0536i	−0.263347	+	0.456130i
$820$	2.18850	−	3.79059i	0.0764256	−	0.132373i
$821$	−4.58924	−	7.94880i	−0.160166	−	0.277415i	0.774762	−	0.632253i	$-0.217869\pi$
$821$	−4.58924	−	7.94880i	−0.160166	−	0.277415i	−0.934928	+	0.354838i	$0.884536\pi$
$822$	1.25099	−	2.16678i	0.0436334	−	0.0755752i
$823$	−23.4275	−	40.5776i	−0.816631	−	1.41445i	−0.908151	−	0.418643i	$-0.862506\pi$
$823$	−23.4275	−	40.5776i	−0.816631	−	1.41445i	0.0915201	−	0.995803i	$-0.470827\pi$
$824$	−6.62099			−0.230653
$825$	−0.252000			−0.00877353
$826$		0			0
$827$	−9.71924	−	16.8342i	−0.337971	−	0.585383i	0.646080	−	0.763270i	$-0.276407\pi$
$827$	−9.71924	−	16.8342i	−0.337971	−	0.585383i	−0.984051	+	0.177887i	$0.943074\pi$
$828$	−13.2260			−0.459635
$829$	−25.3035			−0.878826			−0.439413	−	0.898285i	$-0.644813\pi$
$829$	−25.3035			−0.878826			−0.439413	+	0.898285i	$0.644813\pi$
$830$	−3.69250	−	6.39559i	−0.128168	−	0.221994i
$831$	0.181503	−	0.314372i	0.00629626	−	0.0109054i
$832$	1.46825	+	2.54308i	0.0509023	+	0.0881654i
$833$	−3.32224	+	5.75430i	−0.115109	+	0.199375i
$834$	0.694513	−	1.20293i	0.0240490	−	0.0416541i
$835$	44.9720			1.55632
$836$	−1.59425	−	4.05689i	−0.0551382	−	0.140311i
$837$	−8.12701			−0.280911
$838$	−7.12600	+	12.3426i	−0.246164	+	0.426368i
$839$	14.7112	−	25.4806i	0.507888	−	0.879688i	−0.492070	−	0.870556i	$-0.663760\pi$
$839$	14.7112	−	25.4806i	0.507888	−	0.879688i	0.999958	−	0.00913277i	$-0.00290709\pi$
$840$	0.440497	+	0.762962i	0.0151986	+	0.0263247i
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	11.3462	+	19.6523i	0.391018	+	0.677262i
$843$	−3.79348			−0.130655
$844$	−6.48800			−0.223326
$845$	4.37699	+	7.58117i	0.150573	+	0.260800i
$846$	−9.72126	−	16.8377i	−0.334224	−	0.578892i
$847$	1.74800			0.0600620
$848$	−1.00800			−0.0346149
$849$	−2.92849	−	5.07230i	−0.100506	−	0.174081i
$850$	0.842248	−	1.45882i	0.0288889	−	0.0500370i
$851$	7.16248	+	12.4058i	0.245526	+	0.425264i
$852$	0.905752	−	1.56881i	0.0310305	−	0.0537465i
$853$	26.2737	−	45.5074i	0.899596	−	1.55815i	0.0715837	−	0.997435i	$-0.477195\pi$
$853$	26.2737	−	45.5074i	0.899596	−	1.55815i	0.828012	−	0.560711i	$-0.189472\pi$
$854$	−16.5020			−0.564686
$855$	−25.3155	−	3.80445i	−0.865772	−	0.130109i
$856$	−17.6130			−0.602000
$857$	10.8502	−	18.7932i	0.370637	−	0.641963i	−0.619026	−	0.785370i	$-0.712473\pi$
$857$	10.8502	−	18.7932i	0.370637	−	0.641963i	0.989664	+	0.143407i	$0.0458059\pi$
$858$	−0.369999	+	0.640857i	−0.0126316	+	0.0218785i
$859$	−14.4940	−	25.1043i	−0.494528	−	0.856548i	0.505452	−	0.862855i	$-0.331326\pi$
$859$	−14.4940	−	25.1043i	−0.494528	−	0.856548i	−0.999980	+	0.00630668i	$0.997993\pi$
$860$	−7.18850	+	12.4508i	−0.245126	+	0.424570i
$861$	0.482013	+	0.834870i	0.0164269	+	0.0284523i
$862$	24.6290			0.838867
$863$	−6.14900			−0.209314			−0.104657	−	0.994508i	$-0.533375\pi$
$863$	−6.14900			−0.209314			−0.104657	+	0.994508i	$0.533375\pi$
$864$	−0.748000	−	1.29557i	−0.0254475	−	0.0440763i
$865$	9.43250	+	16.3376i	0.320714	+	0.555494i
$866$	−22.0515			−0.749339
$867$	−3.56895			−0.121208
$868$	−4.74800	−	8.22378i	−0.161158	−	0.279133i
$869$	−1.37800	+	2.38677i	−0.0467455	+	0.0809655i
$870$	−0.252000	−	0.436477i	−0.00854361	−	0.0147980i
$871$	−1.11000	+	1.92257i	−0.0376108	+	0.0651438i
$872$	−1.97225	+	3.41603i	−0.0667888	+	0.115682i
$873$	36.3215			1.22930
$874$	−19.4145	−	2.91763i	−0.656704	−	0.0986904i
$875$	−20.9760			−0.709118
$876$	−1.03175	+	1.78705i	−0.0348597	+	0.0603787i
$877$	−22.8730	+	39.6172i	−0.772366	+	1.33778i	0.163897	+	0.986477i	$0.447594\pi$
$877$	−22.8730	+	39.6172i	−0.772366	+	1.33778i	−0.936263	+	0.351300i	$0.885740\pi$
$878$	−13.9365	−	24.1387i	−0.470334	−	0.814642i
$879$	−1.76501	+	3.05709i	−0.0595323	+	0.103113i
$880$	−1.00000	−	1.73205i	−0.0337100	−	0.0583874i
$881$	8.67448			0.292251			0.146125	−	0.989266i	$-0.453320\pi$
$881$	8.67448			0.292251			0.146125	+	0.989266i	$0.453320\pi$
$882$	−11.5830			−0.390020
$883$	3.70151	+	6.41120i	0.124566	+	0.215754i	0.921563	−	0.388229i	$-0.126913\pi$
$883$	3.70151	+	6.41120i	0.124566	+	0.215754i	−0.796997	+	0.603983i	$0.793580\pi$
$884$	−2.47326	−	4.28381i	−0.0831846	−	0.144080i
$885$		0			0
$886$	19.0060			0.638519
$887$	−17.9435	−	31.0790i	−0.602483	−	1.04353i	−0.992444	−	0.122700i	$-0.960845\pi$
$887$	−17.9435	−	31.0790i	−0.602483	−	1.04353i	0.389960	−	0.920832i	$-0.372489\pi$
$888$	−0.400743	+	0.694107i	−0.0134481	+	0.0232927i
$889$	−10.3770	−	17.9735i	−0.348033	−	0.602811i
$890$	10.3690	−	17.9596i	0.347569	−	0.602008i
$891$	−4.21625	+	7.30275i	−0.141250	+	0.244651i
$892$	−19.1885			−0.642478
$893$	−10.5555	−	26.8606i	−0.353226	−	0.898857i
$894$	−2.12298			−0.0710029
$895$	−10.5040	+	18.1935i	−0.351110	+	0.608140i
$896$	0.874000	−	1.51381i	0.0291983	−	0.0505729i
$897$	1.66648	+	2.88642i	0.0556420	+	0.0963748i
$898$	16.6527	−	28.8434i	0.555709	−	0.962517i
$899$	2.71625	+	4.70468i	0.0905919	+	0.156910i
$900$	2.93650			0.0978832
$901$	1.69797			0.0565677
$902$	−1.09425	−	1.89529i	−0.0364345	−	0.0631064i
$903$	−1.58325	−	2.74228i	−0.0526874	−	0.0912572i
$904$	14.3690			0.477906
$905$	−18.3930			−0.611404
$906$	1.76375	+	3.05490i	0.0585966	+	0.101492i
$907$	22.4305	−	38.8507i	0.744792	−	1.29002i	−0.205500	−	0.978657i	$-0.565882\pi$
$907$	22.4305	−	38.8507i	0.744792	−	1.29002i	0.950292	−	0.311360i	$-0.100785\pi$
$908$	0.275751	+	0.477615i	0.00915112	+	0.0158502i
$909$	10.1845	−	17.6401i	0.337798	−	0.585084i
$910$	−5.13299	+	8.89061i	−0.170157	+	0.294721i
$911$	−21.4760			−0.711530			−0.355765	−	0.934575i	$-0.615780\pi$
$911$	−21.4760			−0.711530			−0.355765	+	0.934575i	$0.615780\pi$
$912$	−0.401751	−	1.02234i	−0.0133033	−	0.0338530i
$913$	−3.69250			−0.122204
$914$	−5.15775	+	8.93349i	−0.170603	+	0.295494i
$915$	−2.37901	+	4.12056i	−0.0786476	+	0.136222i
$916$	−12.0307	−	20.8379i	−0.397507	−	0.688502i
$917$	−10.1498	+	17.5799i	−0.335174	+	0.580539i
$918$	1.26000	+	2.18239i	0.0415863	+	0.0720295i
$919$	−44.6090			−1.47151			−0.735757	−	0.677246i	$-0.763173\pi$
$919$	−44.6090			−1.47151			−0.735757	+	0.677246i	$0.763173\pi$
$920$	−9.00800			−0.296985
$921$	−1.77673	−	3.07738i	−0.0585451	−	0.101403i
$922$	12.1607	+	21.0630i	0.400493	+	0.693674i
$923$	21.1090			0.694811
$924$	0.440497			0.0144913
$925$	−1.59025	−	2.75439i	−0.0522870	−	0.0905638i
$926$	−7.80649	+	13.5212i	−0.256537	+	0.444336i
$927$	9.72126	+	16.8377i	0.319288	+	0.553023i
$928$	−0.500000	+	0.866025i	−0.0164133	+	0.0284287i
$929$	−20.8690	+	36.1462i	−0.684689	+	1.18592i	0.288845	+	0.957376i	$0.406729\pi$
$929$	−20.8690	+	36.1462i	−0.684689	+	1.18592i	−0.973534	+	0.228541i	$0.926605\pi$
$930$	−2.73798			−0.0897820
$931$	−17.0027	−	2.55519i	−0.557242	−	0.0837431i
$932$	−17.4305			−0.570954
$933$	2.47124	−	4.28031i	0.0809048	−	0.140131i
$934$	5.06250	−	8.76850i	0.165650	−	0.286914i
$935$	1.68450	+	2.91763i	0.0550889	+	0.0954168i
$936$	4.31150	−	7.46774i	0.140926	−	0.244091i
$937$	−3.01600	−	5.22387i	−0.0985285	−	0.170656i	0.812547	−	0.582895i	$-0.198080\pi$
$937$	−3.01600	−	5.22387i	−0.0985285	−	0.170656i	−0.911076	+	0.412239i	$0.864747\pi$
$938$	1.32149			0.0431482
$939$	−4.61299			−0.150539
$940$	−6.62099	−	11.4679i	−0.215953	−	0.374041i
$941$	24.9662	+	43.2428i	0.813876	+	1.40967i	0.910132	+	0.414318i	$0.135980\pi$
$941$	24.9662	+	43.2428i	0.813876	+	1.40967i	−0.0962564	+	0.995357i	$0.530687\pi$
$942$	−0.254017			−0.00827631
$943$	−9.85699			−0.320988
$944$		0			0
$945$	2.61501	−	4.52932i	0.0850662	−	0.147339i
$946$	3.59425	+	6.22542i	0.116859	+	0.202406i
$947$	1.80350	−	3.12376i	0.0586059	−	0.101508i	−0.835234	−	0.549895i	$-0.814668\pi$
$947$	1.80350	−	3.12376i	0.0586059	−	0.101508i	0.893840	+	0.448386i	$0.148001\pi$
$948$	−0.347257	+	0.601466i	−0.0112784	+	0.0195347i
$949$	−24.0455			−0.780549
$950$	4.31050	+	0.647787i	0.139851	+	0.0210170i
$951$	−3.88849			−0.126093
$952$	−1.47225	+	2.55001i	−0.0477159	+	0.0826463i
$953$	−10.8730	+	18.8326i	−0.352211	+	0.610047i	−0.986636	−	0.162937i	$-0.947903\pi$
$953$	−10.8730	+	18.8326i	−0.352211	+	0.610047i	0.634426	+	0.772984i	$0.281237\pi$
$954$	1.48000	+	2.56343i	0.0479166	+	0.0829941i
$955$	−24.6210	+	42.6448i	−0.796717	+	1.37995i
$956$	5.49600	+	9.51935i	0.177753	+	0.307878i
$957$	−0.252000			−0.00814602
$958$	−21.6210			−0.698543
$959$	−8.67750	−	15.0299i	−0.280211	−	0.485340i
$960$	−0.252000	−	0.436477i	−0.00813328	−	0.0140872i
$961$	−1.48800			−0.0479999
$962$	−9.33951			−0.301118
$963$	25.8602	+	44.7912i	0.833334	+	1.44338i
$964$	−4.44050	+	7.69117i	−0.143019	+	0.247716i
$965$	−12.6925	−	21.9840i	−0.408586	−	0.707692i
$966$	0.991998	−	1.71819i	0.0319170	−	0.0552819i
$967$	−0.684495	+	1.18558i	−0.0220119	+	0.0381257i	−0.876822	−	0.480816i	$-0.840341\pi$
$967$	−0.684495	+	1.18558i	−0.0220119	+	0.0381257i	0.854810	+	0.518942i	$0.173674\pi$
$968$	−1.00000			−0.0321412
$969$	0.676748	+	1.72212i	0.0217403	+	0.0553226i
$970$	24.7380			0.794289
$971$	−20.2590	+	35.0896i	−0.650142	+	1.12608i	0.332946	+	0.942946i	$0.391957\pi$
$971$	−20.2590	+	35.0896i	−0.650142	+	1.12608i	−0.983088	+	0.183133i	$0.941376\pi$
$972$	−3.30649	+	5.72702i	−0.106056	+	0.183694i
$973$	−4.81749	−	8.34414i	−0.154442	−	0.267501i
$974$	1.52274	−	2.63747i	0.0487918	−	0.0845099i
$975$	−0.369999	−	0.640857i	−0.0118495	−	0.0205239i
$976$	9.44050			0.302183
$977$	−25.3770			−0.811882			−0.405941	−	0.913899i	$-0.633056\pi$
$977$	−25.3770			−0.811882			−0.405941	+	0.913899i	$0.633056\pi$
$978$	2.17249	+	3.76287i	0.0694687	+	0.120323i
$979$	−5.18450	−	8.97981i	−0.165697	−	0.286996i
$980$	−7.88899			−0.252005
$981$	11.5830			0.369817
$982$	13.6210	+	23.5922i	0.434663	+	0.752859i
$983$	15.9552	−	27.6353i	0.508893	−	0.881429i	−0.491054	−	0.871129i	$-0.663388\pi$
$983$	15.9552	−	27.6353i	0.508893	−	0.881429i	0.999947	−	0.0102994i	$-0.00327847\pi$
$984$	−0.275751	−	0.477615i	−0.00879062	−	0.0152258i
$985$	20.3690	−	35.2801i	0.649010	−	1.12412i
$986$	0.842248	−	1.45882i	0.0268226	−	0.0464582i
$987$	2.91652			0.0928340
$988$	7.97625	−	10.0108i	0.253758	−	0.318487i
$989$	32.3770			1.02953
$990$	−2.93650	+	5.08616i	−0.0933280	+	0.161649i
$991$	10.9395	−	18.9477i	0.347504	−	0.601895i	−0.638301	−	0.769787i	$-0.720363\pi$
$991$	10.9395	−	18.9477i	0.347504	−	0.601895i	0.985805	+	0.167892i	$0.0536959\pi$
$992$	2.71625	+	4.70468i	0.0862409	+	0.149374i
$993$	−1.77975	+	3.08262i	−0.0564787	+	0.0978240i
$994$	−6.28274	−	10.8820i	−0.199277	−	0.345157i
$995$	17.6230			0.558687
$996$	−0.930511			−0.0294844
$997$	1.86499	+	3.23026i	0.0590648	+	0.102303i	0.894046	−	0.447975i	$-0.147855\pi$
$997$	1.86499	+	3.23026i	0.0590648	+	0.102303i	−0.834981	+	0.550279i	$0.814521\pi$
$998$	−5.93650	−	10.2823i	−0.187916	−	0.325481i
$999$	4.75802			0.150537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.e.i.353.2	yes	6
19.7	even	3	inner	418.2.e.i.45.2	✓	6
19.8	odd	6		7942.2.a.bj.1.2		3
19.11	even	3		7942.2.a.bd.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.i.45.2	✓	6	19.7	even	3	inner
418.2.e.i.353.2	yes	6	1.1	even	1	trivial
7942.2.a.bd.1.2		3	19.11	even	3
7942.2.a.bj.1.2		3	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.126000 + 0.218239i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.126000 + 0.218239i) q^{6} +1.74800 q^{7} -1.00000 q^{8} +(1.46825 + 2.54308i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.126000 + 0.218239i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.126000 + 0.218239i) q^{6} +1.74800 q^{7} -1.00000 q^{8} +(1.46825 + 2.54308i) q^{9} +(1.00000 + 1.73205i) q^{10} +1.00000 q^{11} +0.252000 q^{12} +(1.46825 + 2.54308i) q^{13} +(0.874000 - 1.51381i) q^{14} +(-0.252000 - 0.436477i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.842248 - 1.45882i) q^{17} +2.93650 q^{18} +(4.31050 + 0.647787i) q^{19} +2.00000 q^{20} +(-0.220248 + 0.381481i) q^{21} +(0.500000 - 0.866025i) q^{22} +(-2.25200 - 3.90058i) q^{23} +(0.126000 - 0.218239i) q^{24} +(0.500000 + 0.866025i) q^{25} +2.93650 q^{26} -1.49600 q^{27} +(-0.874000 - 1.51381i) q^{28} +(0.500000 + 0.866025i) q^{29} -0.504001 q^{30} +5.43250 q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.126000 + 0.218239i) q^{33} +(-0.842248 - 1.45882i) q^{34} +(-1.74800 + 3.02762i) q^{35} +(1.46825 - 2.54308i) q^{36} -3.18049 q^{37} +(2.71625 - 3.40911i) q^{38} -0.739998 q^{39} +(1.00000 - 1.73205i) q^{40} +(1.09425 - 1.89529i) q^{41} +(0.220248 + 0.381481i) q^{42} +(-3.59425 + 6.22542i) q^{43} +(-0.500000 - 0.866025i) q^{44} -5.87299 q^{45} -4.50400 q^{46} +(-3.31050 - 5.73395i) q^{47} +(-0.126000 - 0.218239i) q^{48} -3.94450 q^{49} +1.00000 q^{50} +(0.212247 + 0.367622i) q^{51} +(1.46825 - 2.54308i) q^{52} +(0.504001 + 0.872955i) q^{53} +(-0.748000 + 1.29557i) q^{54} +(-1.00000 + 1.73205i) q^{55} -1.74800 q^{56} +(-0.684495 + 0.859096i) q^{57} +1.00000 q^{58} +(-0.252000 + 0.436477i) q^{60} +(-4.72025 - 8.17571i) q^{61} +(2.71625 - 4.70468i) q^{62} +(2.56650 + 4.44530i) q^{63} +1.00000 q^{64} -5.87299 q^{65} +(0.126000 + 0.218239i) q^{66} +(0.378001 + 0.654716i) q^{67} -1.68450 q^{68} +1.13501 q^{69} +(1.74800 + 3.02762i) q^{70} +(3.59425 - 6.22542i) q^{71} +(-1.46825 - 2.54308i) q^{72} +(-4.09425 + 7.09145i) q^{73} +(-1.59025 + 2.75439i) q^{74} -0.252000 q^{75} +(-1.59425 - 4.05689i) q^{76} +1.74800 q^{77} +(-0.369999 + 0.640857i) q^{78} +(-1.37800 + 2.38677i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-4.21625 + 7.30275i) q^{81} +(-1.09425 - 1.89529i) q^{82} -3.69250 q^{83} +0.440497 q^{84} +(1.68450 + 2.91763i) q^{85} +(3.59425 + 6.22542i) q^{86} -0.252000 q^{87} -1.00000 q^{88} +(-5.18450 - 8.97981i) q^{89} +(-2.93650 + 5.08616i) q^{90} +(2.56650 + 4.44530i) q^{91} +(-2.25200 + 3.90058i) q^{92} +(-0.684495 + 1.18558i) q^{93} -6.62099 q^{94} +(-5.43250 + 6.81821i) q^{95} -0.252000 q^{96} +(6.18450 - 10.7119i) q^{97} +(-1.97225 + 3.41603i) q^{98} +(1.46825 + 2.54308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 - 7 * q^9	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} - 7 q^{9} + 6 q^{10} + 6 q^{11} - 7 q^{13} + 6 q^{14} - 3 q^{16} - 10 q^{17} - 14 q^{18} - 5 q^{19} + 12 q^{20} + 16 q^{21} + 3 q^{22} - 12 q^{23} + 3 q^{25} - 14 q^{26} - 12 q^{27} - 6 q^{28} + 3 q^{29} + 4 q^{31} + 3 q^{32} + 10 q^{34} - 12 q^{35} - 7 q^{36} + 8 q^{37} + 2 q^{38} - 12 q^{39} + 6 q^{40} - 10 q^{41} - 16 q^{42} - 5 q^{43} - 3 q^{44} + 28 q^{45} - 24 q^{46} + 11 q^{47} + 14 q^{49} + 6 q^{50} - 10 q^{51} - 7 q^{52} - 6 q^{54} - 6 q^{55} - 12 q^{56} + 26 q^{57} + 6 q^{58} - 11 q^{61} + 2 q^{62} - 20 q^{63} + 6 q^{64} + 28 q^{65} + 20 q^{68} + 64 q^{69} + 12 q^{70} + 5 q^{71} + 7 q^{72} - 8 q^{73} + 4 q^{74} + 7 q^{76} + 12 q^{77} - 6 q^{78} - 6 q^{79} - 6 q^{80} - 11 q^{81} + 10 q^{82} + 14 q^{83} - 32 q^{84} - 20 q^{85} + 5 q^{86} - 6 q^{88} - q^{89} + 14 q^{90} - 20 q^{91} - 12 q^{92} + 26 q^{93} + 22 q^{94} - 4 q^{95} + 7 q^{97} + 7 q^{98} - 7 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 - 7 * q^9 + 6 * q^10 + 6 * q^11 - 7 * q^13 + 6 * q^14 - 3 * q^16 - 10 * q^17 - 14 * q^18 - 5 * q^19 + 12 * q^20 + 16 * q^21 + 3 * q^22 - 12 * q^23 + 3 * q^25 - 14 * q^26 - 12 * q^27 - 6 * q^28 + 3 * q^29 + 4 * q^31 + 3 * q^32 + 10 * q^34 - 12 * q^35 - 7 * q^36 + 8 * q^37 + 2 * q^38 - 12 * q^39 + 6 * q^40 - 10 * q^41 - 16 * q^42 - 5 * q^43 - 3 * q^44 + 28 * q^45 - 24 * q^46 + 11 * q^47 + 14 * q^49 + 6 * q^50 - 10 * q^51 - 7 * q^52 - 6 * q^54 - 6 * q^55 - 12 * q^56 + 26 * q^57 + 6 * q^58 - 11 * q^61 + 2 * q^62 - 20 * q^63 + 6 * q^64 + 28 * q^65 + 20 * q^68 + 64 * q^69 + 12 * q^70 + 5 * q^71 + 7 * q^72 - 8 * q^73 + 4 * q^74 + 7 * q^76 + 12 * q^77 - 6 * q^78 - 6 * q^79 - 6 * q^80 - 11 * q^81 + 10 * q^82 + 14 * q^83 - 32 * q^84 - 20 * q^85 + 5 * q^86 - 6 * q^88 - q^89 + 14 * q^90 - 20 * q^91 - 12 * q^92 + 26 * q^93 + 22 * q^94 - 4 * q^95 + 7 * q^97 + 7 * q^98 - 7 * q^99

Introduction

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