LMFDB - Embedded newform 637.2.q.h.491.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.3
Root			$1.34408 + 0.439820i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.h.589.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104235 + 0.0601799i) q^{2} +(-0.291146 - 0.504280i) q^{3} +(-0.992757 + 1.71951i) q^{4} -1.68817i q^{5} +(0.0606950 + 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 - 2.30444i) q^{9} +O(q^{10})$	\(q+(-0.104235 + 0.0601799i) q^{2} +(-0.291146 - 0.504280i) q^{3} +(-0.992757 + 1.71951i) q^{4} -1.68817i q^{5} +(0.0606950 + 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 - 2.30444i) q^{9} +(0.101594 + 0.175965i) q^{10} +(-0.315769 + 0.182309i) q^{11} +1.15615 q^{12} +(-1.80124 + 3.12338i) q^{13} +(-0.851308 + 0.491503i) q^{15} +(-1.95665 - 3.38901i) q^{16} +(1.59277 - 2.75877i) q^{17} +0.320270i q^{18} +(-1.25046 - 0.721954i) q^{19} +(2.90281 + 1.67594i) q^{20} +(0.0219427 - 0.0380059i) q^{22} +(-2.54161 - 4.40219i) q^{23} +(-0.241901 + 0.139662i) q^{24} +2.15010 q^{25} +(-0.000212944 - 0.433964i) q^{26} -3.29632 q^{27} +(-4.09831 - 7.09848i) q^{29} +(0.0591572 - 0.102463i) q^{30} -4.69775i q^{31} +(1.23876 + 0.715198i) q^{32} +(0.183870 + 0.106157i) q^{33} +0.383412i q^{34} +(2.64166 + 4.57549i) q^{36} +(5.46967 - 3.15792i) q^{37} +0.173789 q^{38} +(2.09948 - 0.00103020i) q^{39} -0.809806 q^{40} +(5.04661 - 2.91366i) q^{41} +(-0.386561 + 0.669543i) q^{43} -0.723954i q^{44} +(-3.89027 - 2.24605i) q^{45} +(0.529847 + 0.305907i) q^{46} -12.7905i q^{47} +(-1.13934 + 1.97339i) q^{48} +(-0.224115 + 0.129393i) q^{50} -1.85492 q^{51} +(-3.58248 - 6.19801i) q^{52} +1.37110 q^{53} +(0.343591 - 0.198372i) q^{54} +(0.307768 + 0.533070i) q^{55} +0.840776i q^{57} +(0.854372 + 0.493272i) q^{58} +(8.10770 + 4.68098i) q^{59} -1.95177i q^{60} +(-4.51242 + 7.81574i) q^{61} +(0.282711 + 0.489669i) q^{62} +7.65442 q^{64} +(5.27279 + 3.04080i) q^{65} -0.0255541 q^{66} +(-11.6705 + 6.73797i) q^{67} +(3.16247 + 5.47757i) q^{68} +(-1.47996 + 2.56336i) q^{69} +(-6.13246 - 3.54058i) q^{71} +(-1.10543 - 0.638220i) q^{72} +2.16083i q^{73} +(-0.380087 + 0.658329i) q^{74} +(-0.625992 - 1.08425i) q^{75} +(2.48281 - 1.43345i) q^{76} +(-0.218777 + 0.126454i) q^{78} -6.88781 q^{79} +(-5.72121 + 3.30314i) q^{80} +(-3.03169 - 5.25105i) q^{81} +(-0.350688 + 0.607409i) q^{82} +0.567380i q^{83} +(-4.65725 - 2.68887i) q^{85} -0.0930528i q^{86} +(-2.38641 + 4.13339i) q^{87} +(0.0874529 + 0.151473i) q^{88} +(0.986346 - 0.569467i) q^{89} +0.540669 q^{90} +10.0928 q^{92} +(-2.36898 + 1.36773i) q^{93} +(0.769734 + 1.33322i) q^{94} +(-1.21878 + 2.11098i) q^{95} -0.832908i q^{96} +(-6.86572 - 3.96393i) q^{97} +0.970225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.104235	+	0.0601799i	−0.0737051	+	0.0425536i	−0.536400	−	0.843964i	$-0.680216\pi$
$2$	−0.104235	+	0.0601799i	−0.0737051	+	0.0425536i	0.462695	+	0.886518i	$0.346883\pi$
$3$	−0.291146	−	0.504280i	−0.168093	−	0.291146i	0.769656	−	0.638459i	$-0.220428\pi$
$3$	−0.291146	−	0.504280i	−0.168093	−	0.291146i	−0.937749	+	0.347313i	$0.887094\pi$
$4$	−0.992757	+	1.71951i	−0.496378	+	0.859753i
$5$		−	1.68817i		−	0.754971i	−0.926016	−	0.377485i	$-0.876789\pi$
$5$		−	1.68817i		−	0.754971i	0.926016	−	0.377485i	$-0.123211\pi$
$6$	0.0606950	+	0.0350423i	0.0247786	+	0.0143060i
$7$		0			0
$7$		0			0
$8$		−	0.479696i		−	0.169598i
$9$	1.33047	−	2.30444i	0.443489	−	0.768146i
$10$	0.101594	+	0.175965i	0.0321267	+	0.0556452i
$11$	−0.315769	+	0.182309i	−0.0952078	+	0.0549682i	−0.546848	−	0.837232i	$-0.684172\pi$
$11$	−0.315769	+	0.182309i	−0.0952078	+	0.0549682i	0.451640	+	0.892200i	$0.350839\pi$
$12$	1.15615			0.333751
$13$	−1.80124	+	3.12338i	−0.499575	+	0.866271i
$13$	−1.80124	+	3.12338i	−0.499575	+	0.866271i
$14$		0			0
$15$	−0.851308	+	0.491503i	−0.219807	+	0.126905i
$16$	−1.95665	−	3.38901i	−0.489161	−	0.847252i
$17$	1.59277	−	2.75877i	0.386304	−	0.669099i	−0.605645	−	0.795735i	$-0.707085\pi$
$17$	1.59277	−	2.75877i	0.386304	−	0.669099i	0.991949	+	0.126636i	$0.0404181\pi$
$18$			0.320270i			0.0754884i
$19$	−1.25046	−	0.721954i	−0.286875	−	0.165628i	0.349657	−	0.936878i	$-0.386298\pi$
$19$	−1.25046	−	0.721954i	−0.286875	−	0.165628i	−0.636532	+	0.771250i	$0.719632\pi$
$20$	2.90281	+	1.67594i	0.649088	+	0.374751i
$21$		0			0
$22$	0.0219427	−	0.0380059i	0.00467820	−	0.00810288i
$23$	−2.54161	−	4.40219i	−0.529962	−	0.917920i	−0.999389	−	0.0349493i	$-0.988873\pi$
$23$	−2.54161	−	4.40219i	−0.529962	−	0.917920i	0.469428	−	0.882971i	$-0.344460\pi$
$24$	−0.241901	+	0.139662i	−0.0493778	+	0.0285083i
$25$	2.15010			0.430020
$26$	−0.000212944	−	0.433964i	−4.17617e−5	−	0.0851073i
$27$	−3.29632			−0.634377
$28$		0			0
$29$	−4.09831	−	7.09848i	−0.761037	−	1.31815i	−0.942317	−	0.334723i	$-0.891357\pi$
$29$	−4.09831	−	7.09848i	−0.761037	−	1.31815i	0.181280	−	0.983432i	$-0.441976\pi$
$30$	0.0591572	−	0.102463i	0.0108006	−	0.0187071i
$31$		−	4.69775i		−	0.843742i	−0.906656	−	0.421871i	$-0.861374\pi$
$31$		−	4.69775i		−	0.843742i	0.906656	−	0.421871i	$-0.138626\pi$
$32$	1.23876	+	0.715198i	0.218984	+	0.126430i
$33$	0.183870	+	0.106157i	0.0320076	+	0.0184796i
$34$			0.383412i			0.0657546i
$35$		0			0
$36$	2.64166	+	4.57549i	0.440277	+	0.762582i
$37$	5.46967	−	3.15792i	0.899209	−	0.519159i	0.0222655	−	0.999752i	$-0.492912\pi$
$37$	5.46967	−	3.15792i	0.899209	−	0.519159i	0.876943	+	0.480594i	$0.159579\pi$
$38$	0.173789			0.0281922
$39$	2.09948	−	0.00103020i	0.336186	−	0.000164965i
$40$	−0.809806			−0.128042
$41$	5.04661	−	2.91366i	0.788148	−	0.455037i	−0.0511624	−	0.998690i	$-0.516293\pi$
$41$	5.04661	−	2.91366i	0.788148	−	0.455037i	0.839310	+	0.543653i	$0.182959\pi$
$42$		0			0
$43$	−0.386561	+	0.669543i	−0.0589500	+	0.102104i	−0.893994	−	0.448078i	$-0.852109\pi$
$43$	−0.386561	+	0.669543i	−0.0589500	+	0.102104i	0.835044	+	0.550183i	$0.185442\pi$
$44$		−	0.723954i		−	0.109140i
$45$	−3.89027	−	2.24605i	−0.579928	−	0.334821i
$46$	0.529847	+	0.305907i	0.0781217	+	0.0451036i
$47$		−	12.7905i		−	1.86569i	−0.360275	−	0.932846i	$-0.617317\pi$
$47$		−	12.7905i		−	1.86569i	0.360275	−	0.932846i	$-0.382683\pi$
$48$	−1.13934	+	1.97339i	−0.164449	+	0.284835i
$49$		0			0
$50$	−0.224115	+	0.129393i	−0.0316946	+	0.0182989i
$51$	−1.85492			−0.259741
$52$	−3.58248	−	6.19801i	−0.496800	−	0.859509i
$53$	1.37110			0.188334			0.0941672	−	0.995556i	$-0.469981\pi$
$53$	1.37110			0.188334			0.0941672	+	0.995556i	$0.469981\pi$
$54$	0.343591	−	0.198372i	0.0467568	−	0.0269950i
$55$	0.307768	+	0.533070i	0.0414994	+	0.0718791i
$56$		0			0
$57$			0.840776i			0.111363i
$58$	0.854372	+	0.493272i	0.112185	+	0.0647698i
$59$	8.10770	+	4.68098i	1.05553	+	0.609412i	0.924193	−	0.381925i	$-0.124739\pi$
$59$	8.10770	+	4.68098i	1.05553	+	0.609412i	0.131340	+	0.991337i	$0.458072\pi$
$60$		−	1.95177i		−	0.251972i
$61$	−4.51242	+	7.81574i	−0.577756	+	1.00070i	0.417980	+	0.908456i	$0.362738\pi$
$61$	−4.51242	+	7.81574i	−0.577756	+	1.00070i	−0.995736	+	0.0922469i	$0.970595\pi$
$62$	0.282711	+	0.489669i	0.0359043	+	0.0621880i
$63$		0			0
$64$	7.65442			0.956802
$65$	5.27279	+	3.04080i	0.654009	+	0.377164i
$66$	−0.0255541			−0.00314549
$67$	−11.6705	+	6.73797i	−1.42578	+	0.823174i	−0.996784	−	0.0801330i	$-0.974466\pi$
$67$	−11.6705	+	6.73797i	−1.42578	+	0.823174i	−0.428995	+	0.903307i	$0.641132\pi$
$68$	3.16247	+	5.47757i	0.383506	+	0.664252i
$69$	−1.47996	+	2.56336i	−0.178166	+	0.308592i
$70$		0			0
$71$	−6.13246	−	3.54058i	−0.727789	−	0.420189i	0.0898239	−	0.995958i	$-0.471370\pi$
$71$	−6.13246	−	3.54058i	−0.727789	−	0.420189i	−0.817613	+	0.575769i	$0.804703\pi$
$72$	−1.10543	−	0.638220i	−0.130276	−	0.0752150i
$73$			2.16083i			0.252906i	0.991973	+	0.126453i	$0.0403592\pi$
$73$			2.16083i			0.252906i	−0.991973	+	0.126453i	$0.959641\pi$
$74$	−0.380087	+	0.658329i	−0.0441842	+	0.0765292i
$75$	−0.625992	−	1.08425i	−0.0722834	−	0.125198i
$76$	2.48281	−	1.43345i	0.284797	−	0.164428i
$77$		0			0
$78$	−0.218777	+	0.126454i	−0.0247716	+	0.0143181i
$79$	−6.88781			−0.774940			−0.387470	−	0.921882i	$-0.626651\pi$
$79$	−6.88781			−0.774940			−0.387470	+	0.921882i	$0.626651\pi$
$80$	−5.72121	+	3.30314i	−0.639651	+	0.369302i
$81$	−3.03169	−	5.25105i	−0.336855	−	0.583450i
$82$	−0.350688	+	0.607409i	−0.0387270	+	0.0670771i
$83$			0.567380i			0.0622780i	0.999515	+	0.0311390i	$0.00991345\pi$
$83$			0.567380i			0.0622780i	−0.999515	+	0.0311390i	$0.990087\pi$
$84$		0			0
$85$	−4.65725	−	2.68887i	−0.505150	−	0.291648i
$86$		−	0.0930528i		−	0.0100341i
$87$	−2.38641	+	4.13339i	−0.255850	+	0.443146i
$88$	0.0874529	+	0.151473i	0.00932251	+	0.0161471i
$89$	0.986346	−	0.569467i	0.104553	−	0.0603634i	−0.446812	−	0.894628i	$-0.647441\pi$
$89$	0.986346	−	0.569467i	0.104553	−	0.0603634i	0.551364	+	0.834264i	$0.314107\pi$
$90$	0.540669			0.0569915
$91$		0			0
$92$	10.0928			1.05225
$93$	−2.36898	+	1.36773i	−0.245652	+	0.141827i
$94$	0.769734	+	1.33322i	0.0793920	+	0.137511i
$95$	−1.21878	+	2.11098i	−0.125044	+	0.216582i
$96$		−	0.832908i		−	0.0850083i
$97$	−6.86572	−	3.96393i	−0.697109	−	0.402476i	0.109161	−	0.994024i	$-0.465184\pi$
$97$	−6.86572	−	3.96393i	−0.697109	−	0.402476i	−0.806270	+	0.591548i	$0.798517\pi$
$98$		0			0
$99$			0.970225i			0.0975113i
$100$	−2.13452	+	3.69710i	−0.213452	+	0.369710i
$101$	7.77322	+	13.4636i	0.773465	+	1.33968i	0.935653	+	0.352920i	$0.114811\pi$
$101$	7.77322	+	13.4636i	0.773465	+	1.33968i	−0.162189	+	0.986760i	$0.551855\pi$
$102$	0.193347	−	0.111629i	0.0191442	−	0.0110529i
$103$	10.2982			1.01471			0.507354	−	0.861738i	$-0.330624\pi$
$103$	10.2982			1.01471			0.507354	+	0.861738i	$0.330624\pi$
$104$	1.49827	+	0.864049i	0.146918	+	0.0847270i
$105$		0			0
$106$	−0.142916	+	0.0825124i	−0.0138812	+	0.00801432i
$107$	6.56220	+	11.3661i	0.634391	+	1.09880i	0.986644	+	0.162893i	$0.0520826\pi$
$107$	6.56220	+	11.3661i	0.634391	+	1.09880i	−0.352252	+	0.935905i	$0.614584\pi$
$108$	3.27244	−	5.66804i	0.314891	−	0.545407i
$109$		−	10.4459i		−	1.00054i	−0.865871	−	0.500268i	$-0.833235\pi$
$109$		−	10.4459i		−	1.00054i	0.865871	−	0.500268i	$-0.166765\pi$
$110$	−0.0641602	−	0.0370429i	−0.00611743	−	0.00353190i
$111$	−3.18495	−	1.83883i	−0.302302	−	0.174534i
$112$		0			0
$113$	−2.47631	+	4.28909i	−0.232952	+	0.403484i	−0.958675	−	0.284502i	$-0.908172\pi$
$113$	−2.47631	+	4.28909i	−0.232952	+	0.403484i	0.725724	+	0.687986i	$0.241505\pi$
$114$	−0.0505978	−	0.0876380i	−0.00473892	−	0.00820805i
$115$	−7.43163	+	4.29065i	−0.693003	+	0.400105i
$116$	16.2745			1.51105
$117$	4.80115	+	8.30642i	0.443866	+	0.767928i
$118$	−1.12681			−0.103731
$119$		0			0
$120$	0.235772	+	0.408369i	0.0215229	+	0.0372788i
$121$	−5.43353	+	9.41114i	−0.493957	+	0.855559i
$122$		−	1.08623i		−	0.0983425i
$123$	−2.93860	−	1.69660i	−0.264965	−	0.152977i
$124$	8.07781	+	4.66373i	0.725409	+	0.418815i
$125$		−	12.0705i		−	1.07962i
$126$		0			0
$127$	4.03366	+	6.98650i	0.357929	+	0.619951i	0.987615	−	0.156899i	$-0.0501496\pi$
$127$	4.03366	+	6.98650i	0.357929	+	0.619951i	−0.629686	+	0.776850i	$0.716816\pi$
$128$	−3.27537	+	1.89104i	−0.289505	+	0.167146i
$129$	0.450183			0.0396364
$130$	−0.732603		0.000359484i	−0.0642535		3.15288e-5i
$131$	−18.9039			−1.65164			−0.825820	−	0.563934i	$-0.809287\pi$
$131$	−18.9039			−1.65164			−0.825820	+	0.563934i	$0.809287\pi$
$132$	−0.365075	+	0.210776i	−0.0317757	+	0.0183457i
$133$		0			0
$134$	0.810981	−	1.40466i	0.0700581	−	0.121344i
$135$			5.56473i			0.478936i
$136$	−1.32337	−	0.764047i	−0.113478	−	0.0655165i
$137$	15.7837	+	9.11274i	1.34850	+	0.778554i	0.988036	−	0.154221i	$-0.0492867\pi$
$137$	15.7837	+	9.11274i	1.34850	+	0.778554i	0.360459	+	0.932775i	$0.382620\pi$
$138$		−	0.356255i		−	0.0303264i
$139$	2.62542	−	4.54737i	0.222686	−	0.385703i	−0.732937	−	0.680297i	$-0.761851\pi$
$139$	2.62542	−	4.54737i	0.222686	−	0.385703i	0.955623	+	0.294594i	$0.0951843\pi$
$140$		0			0
$141$	−6.45001	+	3.72392i	−0.543189	+	0.313610i
$142$	0.852287			0.0715223
$143$	−0.000645091	−	1.31465i	−5.39452e−5	−	0.109936i
$144$	−10.4130			−0.867751
$145$	−11.9834	+	6.91862i	−0.995167	+	0.574560i
$146$	−0.130038	−	0.225233i	−0.0107621	−	0.0186404i
$147$		0			0
$148$			12.5402i			1.03080i
$149$	8.03073	+	4.63654i	0.657903	+	0.379841i	0.791478	−	0.611198i	$-0.209312\pi$
$149$	8.03073	+	4.63654i	0.657903	+	0.379841i	−0.133574	+	0.991039i	$0.542646\pi$
$150$	0.130500	+	0.0753444i	0.0106553	+	0.00615184i
$151$		−	14.0132i		−	1.14038i	−0.821513	−	0.570189i	$-0.806870\pi$
$151$		−	14.0132i		−	1.14038i	0.821513	−	0.570189i	$-0.193130\pi$
$152$	−0.346318	+	0.599841i	−0.0280901	+	0.0486535i
$153$	−4.23827	−	7.34090i	−0.342644	−	0.593476i
$154$		0			0
$155$	−7.93059			−0.637000
$156$	−2.08250	+	3.61110i	−0.166734	+	0.289119i
$157$	17.1825			1.37131			0.685656	−	0.727925i	$-0.259515\pi$
$157$	17.1825			1.37131			0.685656	+	0.727925i	$0.259515\pi$
$158$	0.717949	−	0.414508i	0.0571170	−	0.0329765i
$159$	−0.399189	−	0.691415i	−0.0316577	−	0.0548328i
$160$	1.20737	−	2.09123i	0.0954511	−	0.165326i
$161$		0			0
$162$	0.632016	+	0.364894i	0.0496558	+	0.0286688i
$163$	10.2128	+	5.89637i	0.799930	+	0.461840i	0.843447	−	0.537213i	$-0.180523\pi$
$163$	10.2128	+	5.89637i	0.799930	+	0.461840i	−0.0435169	+	0.999053i	$0.513856\pi$
$164$			11.5702i			0.903482i
$165$	0.179211	−	0.310402i	0.0139515	−	0.0241648i
$166$	−0.0341449	−	0.0591407i	−0.00265016	−	0.00459021i
$167$	−3.73852	+	2.15843i	−0.289295	+	0.167025i	−0.637624	−	0.770348i	$-0.720083\pi$
$167$	−3.73852	+	2.15843i	−0.289295	+	0.167025i	0.348329	+	0.937372i	$0.386749\pi$
$168$		0			0
$169$	−6.51105	−	11.2519i	−0.500850	−	0.865534i
$170$	0.647263			0.0496428
$171$	−3.32739	+	1.92107i	−0.254452	+	0.146908i
$172$	−0.767522	−	1.32939i	−0.0585230	−	0.101365i
$173$	−6.25985	+	10.8424i	−0.475928	+	0.824331i	−0.999620	−	0.0275769i	$-0.991221\pi$
$173$	−6.25985	+	10.8424i	−0.475928	+	0.824331i	0.523692	+	0.851908i	$0.324554\pi$
$174$		−	0.574457i		−	0.0435494i
$175$		0			0
$176$	1.23569	+	0.713428i	0.0931440	+	0.0537767i
$177$		−	5.45140i		−	0.409752i
$178$	−0.0685410	+	0.118717i	−0.00513737	+	0.00889818i
$179$	−3.29767	−	5.71173i	−0.246479	−	0.426915i	0.716067	−	0.698031i	$-0.245940\pi$
$179$	−3.29767	−	5.71173i	−0.246479	−	0.426915i	−0.962547	+	0.271117i	$0.912607\pi$
$180$	7.72419	−	4.45956i	0.575727	−	0.332396i
$181$	11.0157			0.818791			0.409395	−	0.912357i	$-0.365740\pi$
$181$	11.0157			0.818791			0.409395	+	0.912357i	$0.365740\pi$
$182$		0			0
$183$	5.25509			0.388468
$184$	−2.11171	+	1.21920i	−0.155678	+	0.0898805i
$185$	−5.33109	−	9.23371i	−0.391949	−	0.678876i
$186$	0.164620	−	0.285130i	0.0120705	−	0.0209068i
$187$			1.16151i			0.0849379i
$188$	21.9934	+	12.6979i	1.60403	+	0.926089i
$189$		0			0
$190$		−	0.293384i		−	0.0212843i
$191$	−2.96606	+	5.13737i	−0.214617	+	0.371727i	−0.953154	−	0.302486i	$-0.902184\pi$
$191$	−2.96606	+	5.13737i	−0.214617	+	0.371727i	0.738537	+	0.674213i	$0.235517\pi$
$192$	−2.22855	−	3.85997i	−0.160832	−	0.278569i
$193$	3.63380	−	2.09798i	0.261567	−	0.151016i	−0.363482	−	0.931601i	$-0.618412\pi$
$193$	3.63380	−	2.09798i	0.261567	−	0.151016i	0.625049	+	0.780586i	$0.285079\pi$
$194$	0.954196			0.0685073
$195$	−0.00173916	−	3.54428i	−0.000124544	−	0.253811i
$196$		0			0
$197$	5.00990	−	2.89247i	0.356941	−	0.206080i	−0.310797	−	0.950476i	$-0.600596\pi$
$197$	5.00990	−	2.89247i	0.356941	−	0.206080i	0.667738	+	0.744396i	$0.267263\pi$
$198$	−0.0583881	−	0.101131i	−0.00414946	−	0.00718708i
$199$	−5.97988	+	10.3575i	−0.423903	+	0.734221i	−0.996317	−	0.0857435i	$-0.972673\pi$
$199$	−5.97988	+	10.3575i	−0.423903	+	0.734221i	0.572415	+	0.819964i	$0.306007\pi$
$200$		−	1.03139i		−	0.0729305i
$201$	6.79564	+	3.92347i	0.479328	+	0.276740i
$202$	−1.62048	−	0.935584i	−0.114017	−	0.0658275i
$203$		0			0
$204$	1.84148	−	3.18954i	0.128930	−	0.223313i
$205$	−4.91874	−	8.51951i	−0.343540	−	0.595028i
$206$	−1.07343	+	0.619743i	−0.0747891	+	0.0431795i
$207$	−13.5261			−0.940129
$208$	14.1096	−	0.00692349i	0.978323	−	0.000480057i
$209$	0.526475			0.0364170
$210$		0			0
$211$	4.11795	+	7.13251i	0.283492	+	0.491022i	0.972242	−	0.233976i	$-0.0751738\pi$
$211$	4.11795	+	7.13251i	0.283492	+	0.491022i	−0.688751	+	0.724998i	$0.741840\pi$
$212$	−1.36116	+	2.35761i	−0.0934851	+	0.161921i
$213$			4.12330i			0.282524i
$214$	−1.36802	−	0.789825i	−0.0935157	−	0.0539913i
$215$	1.13030	+	0.652579i	0.0770858	+	0.0445055i
$216$			1.58123i			0.107589i
$217$		0			0
$218$	0.628633	+	1.08882i	0.0425764	+	0.0737445i
$219$	1.08966	−	0.629116i	0.0736325	−	0.0425117i
$220$	−1.22215			−0.0823976
$221$	5.74771	+	9.94405i	0.386633	+	0.668909i
$222$	0.442643			0.0297082
$223$	−13.2515	+	7.65073i	−0.887383	+	0.512331i	−0.873086	−	0.487567i	$-0.837885\pi$
$223$	−13.2515	+	7.65073i	−0.887383	+	0.512331i	−0.0142977	+	0.999898i	$0.504551\pi$
$224$		0			0
$225$	2.86064	−	4.95477i	0.190709	−	0.330318i
$226$		−	0.596097i		−	0.0396518i
$227$	6.02292	+	3.47733i	0.399755	+	0.230799i	0.686378	−	0.727245i	$-0.259199\pi$
$227$	6.02292	+	3.47733i	0.399755	+	0.230799i	−0.286623	+	0.958043i	$0.592533\pi$
$228$	−1.44572	−	0.834686i	−0.0957450	−	0.0552784i
$229$		−	27.4219i		−	1.81209i	−0.423180	−	0.906045i	$-0.639086\pi$
$229$		−	27.4219i		−	1.81209i	0.423180	−	0.906045i	$-0.360914\pi$
$230$	0.516422	−	0.894470i	0.0340519	−	0.0589796i
$231$		0			0
$232$	−3.40511	+	1.96594i	−0.223556	+	0.129070i
$233$	6.85333			0.448976			0.224488	−	0.974477i	$-0.427929\pi$
$233$	6.85333			0.448976			0.224488	+	0.974477i	$0.427929\pi$
$234$	−1.00033	−	0.576884i	−0.0653933	−	0.0377121i
$235$	−21.5926			−1.40854
$236$	−16.0980	+	9.29416i	−1.04789	+	0.604998i
$237$	2.00536	+	3.47338i	0.130262	+	0.225621i
$238$		0			0
$239$		−	22.0754i		−	1.42794i	−0.700177	−	0.713970i	$-0.746895\pi$
$239$		−	22.0754i		−	1.42794i	0.700177	−	0.713970i	$-0.253105\pi$
$240$	3.33141	+	1.92339i	0.215042	+	0.124154i
$241$	−13.6807	−	7.89855i	−0.881251	−	0.508790i	−0.0101802	−	0.999948i	$-0.503241\pi$
$241$	−13.6807	−	7.89855i	−0.881251	−	0.508790i	−0.871071	+	0.491158i	$0.836574\pi$
$242$		−	1.30796i		−	0.0840787i
$243$	−6.70981	+	11.6217i	−0.430434	+	0.745534i
$244$	−8.95947	−	15.5183i	−0.573571	−	0.993455i
$245$		0			0
$246$	0.408405			0.0260390
$247$	4.50732	−	2.60525i	0.286794	−	0.165768i
$248$	−2.25349			−0.143097
$249$	0.286118	−	0.165190i	0.0181320	−	0.0104685i
$250$	0.726405	+	1.25817i	0.0459419	+	0.0795737i
$251$	−11.2783	+	19.5346i	−0.711882	+	1.23302i	0.252268	+	0.967658i	$0.418824\pi$
$251$	−11.2783	+	19.5346i	−0.711882	+	1.23302i	−0.964150	+	0.265359i	$0.914510\pi$
$252$		0			0
$253$	1.60512	+	0.926716i	0.100913	+	0.0582621i
$254$	−0.840894	−	0.485490i	−0.0527624	−	0.0304624i
$255$			3.13141i			0.196097i
$256$	−7.42681	+	12.8636i	−0.464176	+	0.803976i
$257$	−10.2064	−	17.6781i	−0.636660	−	1.10273i	−0.986161	−	0.165791i	$-0.946982\pi$
$257$	−10.2064	−	17.6781i	−0.636660	−	1.10273i	0.349501	−	0.936936i	$-0.386351\pi$
$258$	−0.0469247	+	0.0270920i	−0.00292140	+	0.00168667i
$259$		0			0
$260$	−10.4633	+	6.04781i	−0.648904	+	0.375069i
$261$	−21.8107			−1.35005
$262$	1.97044	−	1.13763i	0.121734	−	0.0702833i
$263$	14.7701	+	25.5826i	0.910764	+	1.57749i	0.812987	+	0.582281i	$0.197840\pi$
$263$	14.7701	+	25.5826i	0.910764	+	1.57749i	0.0977768	+	0.995208i	$0.468827\pi$
$264$	0.0509231	−	0.0882015i	0.00313410	−	0.00542842i
$265$		−	2.31464i		−	0.142187i
$266$		0			0
$267$	−0.574342	−	0.331596i	−0.0351491	−	0.0202934i
$268$		−	26.7567i		−	1.63442i
$269$	13.9581	−	24.1762i	0.851043	−	1.47405i	−0.0292252	−	0.999573i	$-0.509304\pi$
$269$	13.9581	−	24.1762i	0.851043	−	1.47405i	0.880268	−	0.474477i	$-0.157363\pi$
$270$	−0.334885	−	0.580038i	−0.0203805	−	0.0353000i
$271$	25.5036	−	14.7245i	1.54924	−	0.894451i	0.551035	−	0.834482i	$-0.314233\pi$
$271$	25.5036	−	14.7245i	1.54924	−	0.894451i	0.998200	−	0.0599690i	$-0.0191002\pi$
$272$	−12.4660			−0.755861
$273$		0			0
$274$	−2.19362			−0.132521
$275$	−0.678933	+	0.391982i	−0.0409412	+	0.0236374i
$276$	−2.93847	−	5.08959i	−0.176875	−	0.306357i
$277$	3.42927	−	5.93967i	0.206045	−	0.356880i	−0.744420	−	0.667711i	$-0.767274\pi$
$277$	3.42927	−	5.93967i	0.206045	−	0.356880i	0.950465	+	0.310831i	$0.100607\pi$
$278$			0.631992i			0.0379043i
$279$	−10.8257	−	6.25021i	−0.648117	−	0.374190i
$280$		0			0
$281$			29.0940i			1.73561i	0.496909	+	0.867803i	$0.334468\pi$
$281$			29.0940i			1.73561i	−0.496909	+	0.867803i	$0.665532\pi$
$282$	0.448210	−	0.776323i	0.0266905	−	0.0462293i
$283$	−5.80511	−	10.0547i	−0.345078	−	0.597692i	0.640290	−	0.768133i	$-0.278814\pi$
$283$	−5.80511	−	10.0547i	−0.345078	−	0.597692i	−0.985368	+	0.170441i	$0.945481\pi$
$284$	12.1761	−	7.02986i	0.722517	−	0.417146i
$285$	1.41937			0.0840761
$286$	0.0791828	+	0.136993i	0.00468217	+	0.00810058i
$287$		0			0
$288$	3.29626	−	1.90310i	0.194234	−	0.112141i
$289$	3.42614	+	5.93425i	0.201538	+	0.349074i
$290$	0.832724	−	1.44232i	0.0488993	−	0.0846960i
$291$			4.61633i			0.270614i
$292$	−3.71555	−	2.14517i	−0.217436	−	0.125537i
$293$	15.4054	+	8.89430i	0.899992	+	0.519610i	0.877197	−	0.480130i	$-0.159410\pi$
$293$	15.4054	+	8.89430i	0.899992	+	0.519610i	0.0227942	+	0.999740i	$0.492744\pi$
$294$		0			0
$295$	7.90228	−	13.6871i	0.460088	−	0.796896i
$296$	−1.51484	−	2.62378i	−0.0880483	−	0.152504i
$297$	1.04087	−	0.600949i	0.0603976	−	0.0348706i
$298$	−1.11611			−0.0646544
$299$	18.3278	−	0.00899334i	1.05992	−	0.000520098i
$300$	2.48583			0.143520
$301$		0			0
$302$	0.843314	+	1.46066i	0.0485273	+	0.0840517i
$303$	4.52629	−	7.83976i	0.260028	−	0.450382i
$304$			5.65043i			0.324074i
$305$	13.1943	+	7.61771i	0.755501	+	0.436189i
$306$	0.883550	+	0.510118i	0.0505092	+	0.0291615i
$307$			9.07966i			0.518204i	0.965850	+	0.259102i	$0.0834265\pi$
$307$			9.07966i			0.518204i	−0.965850	+	0.259102i	$0.916573\pi$
$308$		0			0
$309$	−2.99827	−	5.19315i	−0.170566	−	0.295428i
$310$	0.826643	−	0.477262i	0.0469501	−	0.0271067i
$311$	1.57073			0.0890677			0.0445338	−	0.999008i	$-0.485820\pi$
$311$	1.57073			0.0890677			0.0445338	+	0.999008i	$0.485820\pi$
$312$	−0.000494185	−	1.00711i	−2.79777e−5	−	0.0570166i
$313$	−20.6232			−1.16569			−0.582846	−	0.812582i	$-0.698061\pi$
$313$	−20.6232			−1.16569			−0.582846	+	0.812582i	$0.698061\pi$
$314$	−1.79101	+	1.03404i	−0.101073	+	0.0583544i
$315$		0			0
$316$	6.83792	−	11.8436i	0.384663	−	0.666256i
$317$		−	30.5435i		−	1.71549i	−0.514072	−	0.857747i	$-0.671863\pi$
$317$		−	30.5435i		−	1.71549i	0.514072	−	0.857747i	$-0.328137\pi$
$318$	0.0832187	+	0.0480463i	0.00466667	+	0.00269430i
$319$	2.58823	+	1.49432i	0.144913	+	0.0836657i
$320$		−	12.9219i		−	0.722358i
$321$	3.82111	−	6.61836i	0.213274	−	0.369401i
$322$		0			0
$323$	−3.98340	+	2.29982i	−0.221642	+	0.127965i
$324$	12.0389			0.668830
$325$	−3.87285	+	6.71558i	−0.214827	+	0.372513i
$326$	−1.41937			−0.0786118
$327$	−5.26765	+	3.04128i	−0.291302	+	0.168183i
$328$	−1.39767	−	2.42084i	−0.0771735	−	0.133668i
$329$		0			0
$330$			0.0431396i			0.00237476i
$331$	−22.3894	−	12.9265i	−1.23063	−	0.710507i	−0.263472	−	0.964667i	$-0.584868\pi$
$331$	−22.3894	−	12.9265i	−1.23063	−	0.710507i	−0.967162	+	0.254161i	$0.918201\pi$
$332$	−0.975612	−	0.563270i	−0.0535437	−	0.0309135i
$333$		−	16.8060i		−	0.920965i
$334$	0.259789	−	0.449967i	0.0142150	−	0.0246211i
$335$	11.3748	+	19.7017i	0.621472	+	1.07642i
$336$		0			0
$337$	−21.3954			−1.16548			−0.582742	−	0.812657i	$-0.698020\pi$
$337$	−21.3954			−1.16548			−0.582742	+	0.812657i	$0.698020\pi$
$338$	1.35582	+	0.781009i	0.0737468	+	0.0424813i
$339$	2.88387			0.156630
$340$	9.24704	−	5.33878i	0.501491	−	0.289536i
$341$	0.856443	+	1.48340i	0.0463790	+	0.0803308i
$342$	0.231220	−	0.400485i	0.0125029	−	0.0216557i
$343$		0			0
$344$	0.321177	+	0.185432i	0.0173167	+	0.00999781i
$345$	4.32738	+	2.49841i	0.232978	+	0.134510i
$346$		−	1.50687i		−	0.0810098i
$347$	−1.10442	+	1.91291i	−0.0592882	+	0.102690i	−0.894146	−	0.447775i	$-0.852216\pi$
$347$	−1.10442	+	1.91291i	−0.0592882	+	0.102690i	0.834858	+	0.550466i	$0.185550\pi$
$348$	−4.73825	−	8.20689i	−0.253997	−	0.439936i
$349$	9.77843	−	5.64558i	0.523427	−	0.302201i	−0.214908	−	0.976634i	$-0.568945\pi$
$349$	9.77843	−	5.64558i	0.523427	−	0.302201i	0.738336	+	0.674433i	$0.235612\pi$
$350$		0			0
$351$	5.93747	−	10.2957i	0.316919	−	0.549542i
$352$	−0.521548			−0.0277986
$353$	30.8680	−	17.8217i	1.64294	−	0.948552i	0.663158	−	0.748479i	$-0.269216\pi$
$353$	30.8680	−	17.8217i	1.64294	−	0.948552i	0.979781	−	0.200072i	$-0.0641177\pi$
$354$	0.328065	+	0.568225i	0.0174365	+	0.0302008i
$355$	−5.97708	+	10.3526i	−0.317230	+	0.549459i
$356$			2.26137i			0.119852i
$357$		0			0
$358$	0.687464	+	0.396907i	0.0363336	+	0.0209772i
$359$		−	19.3218i		−	1.01976i	−0.860244	−	0.509882i	$-0.829689\pi$
$359$		−	19.3218i		−	1.01976i	0.860244	−	0.509882i	$-0.170311\pi$
$360$	−1.07742	+	1.86615i	−0.0567851	+	0.0983546i
$361$	−8.45757	−	14.6489i	−0.445135	−	0.770997i
$362$	−1.14822	+	0.662924i	−0.0603490	+	0.0348425i
$363$	6.32780			0.332123
$364$		0			0
$365$	3.64783			0.190936
$366$	−0.547763	+	0.316251i	−0.0286320	+	0.0165307i
$367$	−1.86032	−	3.22218i	−0.0971082	−	0.168196i	0.813378	−	0.581735i	$-0.197626\pi$
$367$	−1.86032	−	3.22218i	−0.0971082	−	0.168196i	−0.910487	+	0.413539i	$0.864293\pi$
$368$	−9.94604	+	17.2271i	−0.518473	+	0.898022i
$369$		−	15.5061i		−	0.807217i
$370$	1.11137	+	0.641649i	0.0577773	+	0.0333578i
$371$		0			0
$372$		−	5.43130i		−	0.281600i
$373$	1.75638	−	3.04214i	0.0909420	−	0.157516i	−0.816966	−	0.576686i	$-0.804346\pi$
$373$	1.75638	−	3.04214i	0.0909420	−	0.157516i	0.907908	+	0.419170i	$0.137679\pi$
$374$	−0.0698995	−	0.121070i	−0.00361442	−	0.00626035i
$375$	−6.08693	+	3.51429i	−0.314328	+	0.181477i
$376$	−6.13557			−0.316418
$377$	29.5533	−	0.0145016i	1.52207	−	0.000746873i
$378$		0			0
$379$	21.6647	−	12.5081i	1.11284	−	0.642500i	0.173279	−	0.984873i	$-0.444564\pi$
$379$	21.6647	−	12.5081i	1.11284	−	0.642500i	0.939564	+	0.342373i	$0.111230\pi$
$380$	−2.41990	−	4.19139i	−0.124138	−	0.215014i
$381$	2.34877	−	4.06818i	0.120331	−	0.208419i
$382$		−	0.713990i		−	0.0365309i
$383$	19.4556	+	11.2327i	0.994134	+	0.573964i	0.906507	−	0.422190i	$-0.138738\pi$
$383$	19.4556	+	11.2327i	0.994134	+	0.573964i	0.0876266	+	0.996153i	$0.472072\pi$
$384$	1.90722	+	1.10114i	0.0973276	+	0.0561921i
$385$		0			0
$386$	−0.252512	+	0.437364i	−0.0128525	+	0.0222612i
$387$	1.02861	+	1.78161i	0.0522874	+	0.0905644i
$388$	13.6320	−	7.87043i	0.692059	−	0.399561i
$389$	13.3364			0.676184			0.338092	−	0.941113i	$-0.390219\pi$
$389$	13.3364			0.676184			0.338092	+	0.941113i	$0.390219\pi$
$390$	0.213476	+	0.369332i	0.0108098	+	0.0187018i
$391$	−16.1928			−0.818906
$392$		0			0
$393$	5.50379	+	9.53284i	0.277629	+	0.480868i
$394$	−0.348137	+	0.602991i	−0.0175389	+	0.0303783i
$395$			11.6278i			0.585057i
$396$	−1.66831	−	0.963198i	−0.0838356	−	0.0484025i
$397$	22.3723	+	12.9166i	1.12283	+	0.648268i	0.942123	−	0.335268i	$-0.108827\pi$
$397$	22.3723	+	12.9166i	1.12283	+	0.648268i	0.180710	+	0.983536i	$0.442160\pi$
$398$		−	1.43948i		−	0.0721544i
$399$		0			0
$400$	−4.20698	−	7.28670i	−0.210349	−	0.364335i
$401$	15.2078	−	8.78025i	0.759443	−	0.438465i	−0.0696524	−	0.997571i	$-0.522189\pi$
$401$	15.2078	−	8.78025i	0.759443	−	0.438465i	0.829096	+	0.559106i	$0.188856\pi$
$402$	−0.944456			−0.0471052
$403$	14.6729	+	8.46180i	0.730909	+	0.421512i
$404$	−30.8677			−1.53572
$405$	−8.86464	+	5.11800i	−0.440487	+	0.254316i
$406$		0			0
$407$	−1.15143	+	1.99434i	−0.0570745	+	0.0988559i
$408$			0.889797i			0.0440515i
$409$	−12.5818	−	7.26410i	−0.622129	−	0.359186i	0.155568	−	0.987825i	$-0.450279\pi$
$409$	−12.5818	−	7.26410i	−0.622129	−	0.359186i	−0.777698	+	0.628639i	$0.783612\pi$
$410$	1.02541	+	0.592019i	0.0506412	+	0.0292377i
$411$		−	10.6126i		−	0.523479i
$412$	−10.2236	+	17.7077i	−0.503679	+	0.872398i
$413$		0			0
$414$	1.40989	−	0.814000i	0.0692923	−	0.0400059i
$415$	0.957831			0.0470181
$416$	−4.46514	+	2.58087i	−0.218922	+	0.126538i
$417$	−3.05753			−0.149728
$418$	−0.0548769	+	0.0316832i	−0.00268412	+	0.00154968i
$419$	−2.30096	−	3.98538i	−0.112409	−	0.194699i	0.804332	−	0.594180i	$-0.202523\pi$
$419$	−2.30096	−	3.98538i	−0.112409	−	0.194699i	−0.916741	+	0.399482i	$0.869190\pi$
$420$		0			0
$421$			19.2645i			0.938895i	0.882960	+	0.469447i	$0.155547\pi$
$421$			19.2645i			0.938895i	−0.882960	+	0.469447i	$0.844453\pi$
$422$	−0.858468	−	0.495637i	−0.0417896	−	0.0241272i
$423$	−29.4750	−	17.0174i	−1.43312	−	0.827415i
$424$		−	0.657709i		−	0.0319412i
$425$	3.42462	−	5.93161i	0.166118	−	0.287726i
$426$	−0.248140	−	0.429791i	−0.0120224	−	0.0208234i
$427$		0			0
$428$	−26.0587			−1.25959
$429$	−0.662763	+	0.383080i	−0.0319985	+	0.0184953i
$430$	−0.157089			−0.00757548
$431$	−24.5649	+	14.1825i	−1.18325	+	0.683149i	−0.956764	−	0.290865i	$-0.906057\pi$
$431$	−24.5649	+	14.1825i	−1.18325	+	0.683149i	−0.226485	+	0.974015i	$0.572723\pi$
$432$	6.44973	+	11.1713i	0.310313	+	0.537477i
$433$	6.26014	−	10.8429i	0.300843	−	0.521076i	−0.675484	−	0.737375i	$-0.736065\pi$
$433$	6.26014	−	10.8429i	0.300843	−	0.521076i	0.976327	+	0.216299i	$0.0693986\pi$
$434$		0			0
$435$	6.97784	+	4.02866i	0.334562	+	0.193159i
$436$	17.9618	+	10.3702i	0.860213	+	0.496644i
$437$			7.33969i			0.351105i
$438$	−0.0757203	+	0.131151i	−0.00361806	+	0.00626666i
$439$	−15.8637	−	27.4767i	−0.757132	−	1.31139i	−0.944307	−	0.329064i	$-0.893267\pi$
$439$	−15.8637	−	27.4767i	−0.757132	−	1.31139i	0.187176	−	0.982326i	$-0.440067\pi$
$440$	0.255711	−	0.147635i	0.0121906	−	0.00703822i
$441$		0			0
$442$	−1.19754	−	0.690619i	−0.0569613	−	0.0328494i
$443$	1.73048			0.0822177			0.0411088	−	0.999155i	$-0.486911\pi$
$443$	1.73048			0.0822177			0.0411088	+	0.999155i	$0.486911\pi$
$444$	6.32376	−	3.65102i	0.300112	−	0.173270i
$445$	−0.961355	−	1.66512i	−0.0455726	−	0.0789341i
$446$	0.920842	−	1.59494i	0.0436031	−	0.0755228i
$447$		−	5.39965i		−	0.255394i
$448$		0			0
$449$	−9.14208	−	5.27818i	−0.431442	−	0.249093i	0.268519	−	0.963274i	$-0.413466\pi$
$449$	−9.14208	−	5.27818i	−0.431442	−	0.249093i	−0.699961	+	0.714181i	$0.746799\pi$
$450$			0.688612i			0.0324615i
$451$	−1.06237	+	1.84008i	−0.0500252	+	0.0866462i
$452$	−4.91675	−	8.51605i	−0.231264	−	0.400561i
$453$	−7.06658	+	4.07989i	−0.332017	+	0.191690i
$454$	−0.837063			−0.0392853
$455$		0			0
$456$	0.403317			0.0188870
$457$	−6.88399	+	3.97447i	−0.322019	+	0.185918i	−0.652292	−	0.757968i	$-0.726193\pi$
$457$	−6.88399	+	3.97447i	−0.322019	+	0.185918i	0.330273	+	0.943885i	$0.392859\pi$
$458$	1.65025	+	2.85832i	0.0771111	+	0.133560i
$459$	−5.25029	+	9.09377i	−0.245062	+	0.424461i
$460$		−	17.0383i		−	0.794415i
$461$	−9.43262	−	5.44592i	−0.439321	−	0.253642i	0.263989	−	0.964526i	$-0.414962\pi$
$461$	−9.43262	−	5.44592i	−0.439321	−	0.253642i	−0.703309	+	0.710884i	$0.748295\pi$
$462$		0			0
$463$			35.8227i			1.66482i	0.554158	+	0.832411i	$0.313040\pi$
$463$			35.8227i			1.66482i	−0.554158	+	0.832411i	$0.686960\pi$
$464$	−16.0379	+	27.7784i	−0.744539	+	1.28958i
$465$	2.30896	+	3.99923i	0.107075	+	0.185460i
$466$	−0.714355	+	0.412433i	−0.0330918	+	0.0191056i
$467$	19.8983			0.920785			0.460393	−	0.887715i	$-0.347709\pi$
$467$	19.8983			0.920785			0.460393	+	0.887715i	$0.347709\pi$
$468$	−19.0493	+	0.00934738i	−0.880554	+	0.000432083i
$469$		0			0
$470$	2.25069	−	1.29944i	0.103817	−	0.0599386i
$471$	−5.00262	−	8.66479i	−0.230508	−	0.399252i
$472$	2.24545	−	3.88923i	0.103355	−	0.179016i
$473$		−	0.281894i		−	0.0129615i
$474$	−0.418056	−	0.241365i	−0.0192020	−	0.0110863i
$475$	−2.68861	−	1.55227i	−0.123362	−	0.0712231i
$476$		0			0
$477$	1.82420	−	3.15960i	0.0835243	−	0.144668i
$478$	1.32850	+	2.30102i	0.0607640	+	0.105246i
$479$	−22.7680	+	13.1451i	−1.04030	+	0.600615i	−0.919917	−	0.392113i	$-0.871744\pi$
$479$	−22.7680	+	13.1451i	−1.04030	+	0.600615i	−0.120379	+	0.992728i	$0.538411\pi$
$480$	−1.40609			−0.0641788
$481$	0.0111741	+	22.7721i	0.000509496	+	1.03832i
$482$	1.90134			0.0866035
$483$		0			0
$484$	−10.7883	−	18.6860i	−0.490379	−	0.849362i
$485$	−6.69177	+	11.5905i	−0.303857	+	0.526296i
$486$		−	1.61518i		−	0.0732662i
$487$	5.52491	+	3.18981i	0.250358	+	0.144544i	0.619928	−	0.784659i	$-0.287162\pi$
$487$	5.52491	+	3.18981i	0.250358	+	0.144544i	−0.369570	+	0.929203i	$0.620495\pi$
$488$	3.74918	+	2.16459i	0.169717	+	0.0979864i
$489$		−	6.86682i		−	0.310528i
$490$		0			0
$491$	−1.48384	−	2.57008i	−0.0669647	−	0.115986i	0.830599	−	0.556871i	$-0.187998\pi$
$491$	−1.48384	−	2.57008i	−0.0669647	−	0.115986i	−0.897564	+	0.440885i	$0.854665\pi$
$492$	5.83463	−	3.36862i	0.263045	−	0.151869i
$493$	−26.1107			−1.17597
$494$	−0.313035	+	0.542808i	−0.0140841	+	0.0244221i
$495$	1.63790			0.0736182
$496$	−15.9207	+	9.19184i	−0.714862	+	0.412726i
$497$		0			0
$498$	−0.0198823	+	0.0344371i	−0.000890947	+	0.00154316i
$499$			28.1331i			1.25941i	0.776835	+	0.629704i	$0.216824\pi$
$499$			28.1331i			1.25941i	−0.776835	+	0.629704i	$0.783176\pi$
$500$	20.7554	+	11.9831i	0.928208	+	0.535901i
$501$	2.17691	+	1.25684i	0.0972571	+	0.0561514i
$502$		−	2.71492i		−	0.121173i
$503$	−15.7688	+	27.3124i	−0.703097	+	1.21780i	0.264277	+	0.964447i	$0.414867\pi$
$503$	−15.7688	+	27.3124i	−0.703097	+	1.21780i	−0.967374	+	0.253353i	$0.918467\pi$
$504$		0			0
$505$	22.7288	−	13.1225i	1.01142	−	0.583943i
$506$	−0.223079			−0.00991706
$507$	−3.77846	+	6.55935i	−0.167807	+	0.291311i
$508$	−16.0178			−0.710673
$509$	−11.7731	+	6.79719i	−0.521832	+	0.301280i	−0.737684	−	0.675146i	$-0.764081\pi$
$509$	−11.7731	+	6.79719i	−0.521832	+	0.301280i	0.215852	+	0.976426i	$0.430747\pi$
$510$	−0.188448	−	0.326402i	−0.00834462	−	0.0144533i
$511$		0			0
$512$		−	9.35193i		−	0.413301i
$513$	4.12191	+	2.37979i	0.181987	+	0.105070i
$514$	2.12773	+	1.22845i	0.0938502	+	0.0541844i
$515$		−	17.3850i		−	0.766074i
$516$	−0.446922	+	0.774091i	−0.0196746	+	0.0340775i
$517$	2.33183	+	4.03885i	0.102554	+	0.177628i
$518$		0			0
$519$	7.29012			0.320001
$520$	1.45866	−	2.52933i	0.0639664	−	0.110919i
$521$	−8.78344			−0.384810			−0.192405	−	0.981316i	$-0.561629\pi$
$521$	−8.78344			−0.384810			−0.192405	+	0.981316i	$0.561629\pi$
$522$	2.27343	−	1.31256i	0.0995053	−	0.0574494i
$523$	16.2849	+	28.2063i	0.712088	+	1.23337i	0.964072	+	0.265642i	$0.0855839\pi$
$523$	16.2849	+	28.2063i	0.712088	+	1.23337i	−0.251983	+	0.967732i	$0.581083\pi$
$524$	18.7670	−	32.5053i	0.819838	−	1.42000i
$525$		0			0
$526$	−3.07912	−	1.77773i	−0.134256	−	0.0775127i
$527$	−12.9600	−	7.48246i	−0.564547	−	0.325941i
$528$		−	0.830847i		−	0.0361580i
$529$	−1.41953	+	2.45869i	−0.0617185	+	0.106900i
$530$	0.139295	+	0.241265i	0.00605057	+	0.0104799i
$531$	21.5741	−	12.4558i	0.936235	−	0.540536i
$532$		0			0
$533$	0.0103098	+	21.0107i	0.000446568	+	0.910074i
$534$	0.0798218			0.00345423
$535$	19.1878	−	11.0781i	0.829560	−	0.478947i
$536$	3.23218	+	5.59829i	0.139609	+	0.241809i
$537$	−1.92021	+	3.32590i	−0.0828631	+	0.143523i
$538$			3.36000i			0.144860i
$539$		0			0
$540$	−9.56858	−	5.52442i	−0.411766	−	0.237733i
$541$			6.94870i			0.298748i	0.988781	+	0.149374i	$0.0477258\pi$
$541$			6.94870i			0.298748i	−0.988781	+	0.149374i	$0.952274\pi$
$542$	−1.77224	+	3.06961i	−0.0761243	+	0.131851i
$543$	−3.20718	−	5.55500i	−0.137633	−	0.238388i
$544$	3.94612	−	2.27830i	0.169189	−	0.0976811i
$545$	−17.6344			−0.755375
$546$		0			0
$547$	10.9095			0.466457			0.233229	−	0.972422i	$-0.425071\pi$
$547$	10.9095			0.466457			0.233229	+	0.972422i	$0.425071\pi$
$548$	−31.3388	+	18.0935i	−1.33873	+	0.772915i
$549$	12.0073	+	20.7972i	0.512457	+	0.887602i
$550$	0.0471789	−	0.0817163i	0.00201172	−	0.00348440i
$551$			11.8352i			0.504194i
$552$	1.22963	+	0.709929i	0.0523367	+	0.0302166i
$553$		0			0
$554$			0.825493i			0.0350718i
$555$	−3.10425	+	5.37672i	−0.131768	+	0.228229i
$556$	5.21282	+	9.02886i	0.221073	+	0.382909i
$557$	29.9901	−	17.3148i	1.27072	−	0.733650i	0.295596	−	0.955313i	$-0.404482\pi$
$557$	29.9901	−	17.3148i	1.27072	−	0.733650i	0.975123	+	0.221662i	$0.0711483\pi$
$558$	1.50455			0.0636927
$559$	−1.39495	−	2.41339i	−0.0590001	−	0.102075i
$560$		0			0
$561$	0.585725	−	0.338169i	0.0247293	−	0.0142775i
$562$	−1.75088	−	3.03261i	−0.0738563	−	0.127923i
$563$	−4.56839	+	7.91269i	−0.192535	+	0.333480i	−0.946090	−	0.323905i	$-0.895004\pi$
$563$	−4.56839	+	7.91269i	−0.192535	+	0.333480i	0.753555	+	0.657385i	$0.228338\pi$
$564$		−	14.7878i		−	0.622677i
$565$	7.24070	+	4.18042i	0.304618	+	0.175872i
$566$	1.21019	+	0.698702i	0.0508680	+	0.0293686i
$567$		0			0
$568$	−1.69840	+	2.94172i	−0.0712633	+	0.123432i
$569$	9.15000	+	15.8483i	0.383588	+	0.664394i	0.991572	−	0.129555i	$-0.0413549\pi$
$569$	9.15000	+	15.8483i	0.383588	+	0.664394i	−0.607984	+	0.793949i	$0.708022\pi$
$570$	−0.147947	+	0.0854175i	−0.00619684	+	0.00357775i
$571$	−10.1791			−0.425981			−0.212990	−	0.977054i	$-0.568320\pi$
$571$	−10.1791			−0.425981			−0.212990	+	0.977054i	$0.568320\pi$
$572$	2.26119	+	1.30402i	0.0945450	+	0.0545237i
$573$	3.45423			0.144303
$574$		0			0
$575$	−5.46470	−	9.46514i	−0.227894	−	0.394724i
$576$	10.1840	−	17.6391i	0.424332	−	0.734964i
$577$			19.5165i			0.812482i	0.913766	+	0.406241i	$0.133161\pi$
$577$			19.5165i			0.812482i	−0.913766	+	0.406241i	$0.866839\pi$
$578$	−0.714246	−	0.412370i	−0.0297087	−	0.0171523i
$579$	−2.11593	−	1.22163i	−0.0879352	−	0.0507694i
$580$		−	27.4740i		−	1.14080i
$581$		0			0
$582$	−0.277810	−	0.481182i	−0.0115156	−	0.0199456i
$583$	−0.432949	+	0.249963i	−0.0179309	+	0.0103524i
$584$	1.03654			0.0428923
$585$	14.0226	−	8.10513i	0.579763	−	0.335106i
$586$	−2.14103			−0.0884453
$587$	30.6486	−	17.6950i	1.26501	−	0.730351i	0.290967	−	0.956733i	$-0.406023\pi$
$587$	30.6486	−	17.6950i	1.26501	−	0.730351i	0.974039	+	0.226382i	$0.0726898\pi$
$588$		0			0
$589$	−3.39156	+	5.87436i	−0.139747	+	0.242049i
$590$			1.90223i			0.0783137i
$591$	−2.91723	−	1.68426i	−0.119999	−	0.0692812i
$592$	−21.4044	−	12.3579i	−0.879716	−	0.507905i
$593$		−	18.0881i		−	0.742790i	−0.928475	−	0.371395i	$-0.878880\pi$
$593$		−	18.0881i		−	0.742790i	0.928475	−	0.371395i	$-0.121120\pi$
$594$	−0.0723301	+	0.125279i	−0.00296774	+	0.00514028i
$595$		0			0
$596$	−15.9451	+	9.20592i	−0.653138	+	0.377089i
$597$	6.96407			0.285021
$598$	−1.90985	+	1.10390i	−0.0780996	+	0.0451419i
$599$	9.05992			0.370178			0.185089	−	0.982722i	$-0.440743\pi$
$599$	9.05992			0.370178			0.185089	+	0.982722i	$0.440743\pi$
$600$	−0.520111	+	0.300286i	−0.0212334	+	0.0122591i
$601$	14.6440	+	25.3642i	0.597343	+	1.03463i	0.993212	+	0.116321i	$0.0371102\pi$
$601$	14.6440	+	25.3642i	0.597343	+	1.03463i	−0.395869	+	0.918307i	$0.629556\pi$
$602$		0			0
$603$			35.8586i			1.46028i
$604$	24.0958	+	13.9117i	0.980444	+	0.566059i
$605$	15.8876	+	9.17269i	0.645922	+	0.372923i
$606$			1.08957i			0.0442606i
$607$	−19.6825	+	34.0911i	−0.798887	+	1.38371i	0.121454	+	0.992597i	$0.461244\pi$
$607$	−19.6825	+	34.0911i	−0.798887	+	1.38371i	−0.920341	+	0.391116i	$0.872089\pi$
$608$	−1.03268	−	1.78865i	−0.0418807	−	0.0725394i
$609$		0			0
$610$	−1.83373			−0.0742457
$611$	39.9498	+	23.0389i	1.61619	+	0.932053i
$612$	16.8303			0.680324
$613$	4.79186	−	2.76658i	0.193541	−	0.111741i	−0.400098	−	0.916472i	$-0.631024\pi$
$613$	4.79186	−	2.76658i	0.193541	−	0.111741i	0.593639	+	0.804731i	$0.297691\pi$
$614$	−0.546413	−	0.946416i	−0.0220514	−	0.0381942i
$615$	−2.86414	+	4.96084i	−0.115493	+	0.200040i
$616$		0			0
$617$	10.8959	+	6.29077i	0.438654	+	0.253257i	0.703026	−	0.711164i	$-0.251832\pi$
$617$	10.8959	+	6.29077i	0.438654	+	0.253257i	−0.264373	+	0.964421i	$0.585165\pi$
$618$	0.625047	+	0.360871i	0.0251431	+	0.0145164i
$619$			22.3955i			0.900149i	0.892991	+	0.450075i	$0.148603\pi$
$619$			22.3955i			0.900149i	−0.892991	+	0.450075i	$0.851397\pi$
$620$	7.87314	−	13.6367i	0.316193	−	0.547662i
$621$	8.37794	+	14.5110i	0.336195	+	0.582307i
$622$	−0.163724	+	0.0945262i	−0.00656474	+	0.00379015i
$623$		0			0
$624$	−4.11144	−	7.11315i	−0.164589	−	0.284754i
$625$	−9.62659			−0.385064
$626$	2.14965	−	1.24110i	0.0859175	−	0.0496045i
$627$	−0.153281	−	0.265491i	−0.00612145	−	0.0106027i
$628$	−17.0580	+	29.5454i	−0.680690	+	1.17899i
$629$		−	20.1194i		−	0.802213i
$630$		0			0
$631$	1.68778	+	0.974439i	0.0671894	+	0.0387918i	0.533218	−	0.845978i	$-0.320982\pi$
$631$	1.68778	+	0.974439i	0.0671894	+	0.0387918i	−0.466029	+	0.884769i	$0.654316\pi$
$632$			3.30406i			0.131428i
$633$	2.39785	−	4.15320i	0.0953061	−	0.165075i
$634$	1.83811	+	3.18369i	0.0730005	+	0.126441i
$635$	11.7944	−	6.80948i	0.468045	−	0.270226i
$636$	1.58519			0.0628569
$637$		0			0
$638$	−0.359712			−0.0142411
$639$	−16.3181	+	9.42125i	−0.645533	+	0.372699i
$640$	3.19238	+	5.52937i	0.126190	+	0.218568i
$641$	5.21051	−	9.02487i	0.205803	−	0.356461i	−0.744585	−	0.667527i	$-0.767353\pi$
$641$	5.21051	−	9.02487i	0.205803	−	0.356461i	0.950388	+	0.311066i	$0.100686\pi$
$642$			0.919818i			0.0363023i
$643$	−13.2247	−	7.63531i	−0.521533	−	0.301107i	0.216029	−	0.976387i	$-0.430690\pi$
$643$	−13.2247	−	7.63531i	−0.521533	−	0.301107i	−0.737562	+	0.675280i	$0.764023\pi$
$644$		0			0
$645$		−	0.759983i		−	0.0299243i
$646$	0.276806	−	0.479442i	0.0108908	−	0.0188634i
$647$	−8.75328	−	15.1611i	−0.344127	−	0.596045i	0.641068	−	0.767484i	$-0.278492\pi$
$647$	−8.75328	−	15.1611i	−0.344127	−	0.596045i	−0.985195	+	0.171439i	$0.945158\pi$
$648$	−2.51891	+	1.45429i	−0.0989520	+	0.0571300i
$649$	−3.41354			−0.133993
$650$	−0.000457849	−	0.933064i	−1.79583e−5	−	0.0365978i
$651$		0			0
$652$	−20.2777	+	11.7073i	−0.794136	+	0.458494i
$653$	5.09169	+	8.81906i	0.199253	+	0.345117i	0.948287	−	0.317416i	$-0.102815\pi$
$653$	5.09169	+	8.81906i	0.199253	+	0.345117i	−0.749033	+	0.662532i	$0.769482\pi$
$654$	0.366048	−	0.634014i	0.0143136	−	0.0247919i
$655$			31.9129i			1.24694i
$656$	−19.7488	−	11.4020i	−0.771063	−	0.445173i
$657$	4.97949	+	2.87491i	0.194268	+	0.112161i
$658$		0			0
$659$	21.9294	−	37.9828i	0.854247	−	1.47960i	−0.0230945	−	0.999733i	$-0.507352\pi$
$659$	21.9294	−	37.9828i	0.854247	−	1.47960i	0.877342	−	0.479866i	$-0.159315\pi$
$660$	0.355825	+	0.616308i	0.0138505	+	0.0239897i
$661$	28.5156	−	16.4635i	1.10913	−	0.640356i	0.170526	−	0.985353i	$-0.445453\pi$
$661$	28.5156	−	16.4635i	1.10913	−	0.640356i	0.938604	+	0.344997i	$0.112120\pi$
$662$	3.11167			0.120939
$663$	3.34116	−	5.79362i	0.129760	−	0.225006i
$664$	0.272170			0.0105622
$665$		0			0
$666$	1.01139	+	1.75177i	0.0391904	+	0.0678798i
$667$	−20.8326	+	36.0831i	−0.806640	+	1.39714i
$668$		−	8.57120i		−	0.331630i
$669$	7.71622	+	4.45496i	0.298326	+	0.172239i
$670$	−2.37130	−	1.36907i	−0.0916113	−	0.0528918i
$671$		−	3.29062i		−	0.127033i
$672$		0			0
$673$	13.3423	+	23.1095i	0.514307	+	0.890806i	0.999862	+	0.0165997i	$0.00528409\pi$
$673$	13.3423	+	23.1095i	0.514307	+	0.890806i	−0.485555	+	0.874206i	$0.661383\pi$
$674$	2.23015	−	1.28758i	0.0859021	−	0.0495956i
$675$	−7.08740			−0.272794
$676$	25.8117	−	0.0253313i	0.992756	−	0.000974280i
$677$	−29.5328			−1.13504			−0.567519	−	0.823361i	$-0.692096\pi$
$677$	−29.5328			−1.13504			−0.567519	+	0.823361i	$0.692096\pi$
$678$	−0.300599	+	0.173551i	−0.0115444	+	0.00666519i
$679$		0			0
$680$	−1.28984	+	2.23406i	−0.0494630	+	0.0856725i
$681$		−	4.04965i		−	0.155183i
$682$	−0.178542	−	0.103081i	−0.00683674	−	0.00394719i
$683$	−15.8379	−	9.14400i	−0.606019	−	0.349885i	0.165387	−	0.986229i	$-0.447113\pi$
$683$	−15.8379	−	9.14400i	−0.606019	−	0.349885i	−0.771406	+	0.636343i	$0.780446\pi$
$684$		−	7.62863i		−	0.291688i
$685$	15.3838	−	26.6456i	0.587786	−	1.01807i
$686$		0			0
$687$	−13.8283	+	7.98378i	−0.527583	+	0.304600i
$688$	3.02545			0.115344
$689$	−2.46968	+	4.28246i	−0.0940872	+	0.163149i
$690$	−0.601417			−0.0228956
$691$	8.95525	−	5.17031i	0.340674	−	0.196688i	−0.319896	−	0.947453i	$-0.603648\pi$
$691$	8.95525	−	5.17031i	0.340674	−	0.196688i	0.660570	+	0.750765i	$0.270315\pi$
$692$	−12.4290	−	21.5277i	−0.472480	−	0.818360i
$693$		0			0
$694$		−	0.265855i		−	0.0100917i
$695$	−7.67671	−	4.43215i	−0.291194	−	0.168121i
$696$	1.98277	+	1.14475i	0.0751567	+	0.0433917i
$697$		−	18.5632i		−	0.703131i
$698$	−0.679501	+	1.17693i	−0.0257195	+	0.0445475i
$699$	−1.99532	−	3.45599i	−0.0754699	−	0.130718i
$700$		0			0
$701$	41.6959			1.57483			0.787415	−	0.616423i	$-0.211419\pi$
$701$	41.6959			1.57483			0.787415	+	0.616423i	$0.211419\pi$
$702$	0.000701930		1.43048i	2.64926e−5		0.0539901i
$703$	−9.11948			−0.343948
$704$	−2.41702	+	1.39547i	−0.0910951	+	0.0525938i
$705$	6.28659	+	10.8887i	0.236766	+	0.410092i
$706$	−2.14501	+	3.71527i	−0.0807287	+	0.139826i
$707$		0			0
$708$	9.37371	+	5.41191i	0.352286	+	0.203392i
$709$	0.00947974	+	0.00547313i	0.000356019	+	0.000205548i	0.500178	−	0.865923i	$-0.333268\pi$
$709$	0.00947974	+	0.00547313i	0.000356019	+	0.000205548i	−0.499822	+	0.866128i	$0.666601\pi$
$710$		−	1.43880i		−	0.0539972i
$711$	−9.16402	+	15.8725i	−0.343677	+	0.595267i
$712$	−0.273171	−	0.473146i	−0.0102375	−	0.0177319i
$713$	−20.6804	+	11.9398i	−0.774488	+	0.447151i
$714$		0			0
$715$	−2.21935	+	0.00108902i	−0.0829988	+	4.07271e-5i
$716$	13.0951			0.489388
$717$	−11.1322	+	6.42717i	−0.415739	+	0.240027i
$718$	1.16278	+	2.01400i	0.0433947	+	0.0751618i
$719$	12.7330	−	22.0542i	0.474861	−	0.822484i	−0.524724	−	0.851272i	$-0.675832\pi$
$719$	12.7330	−	22.0542i	0.474861	−	0.822484i	0.999586	+	0.0287885i	$0.00916494\pi$
$720$			17.5789i			0.655127i
$721$		0			0
$722$	1.76314	+	1.01795i	0.0656174	+	0.0378842i
$723$			9.19853i			0.342097i
$724$	−10.9359	+	18.9416i	−0.406430	+	0.703957i
$725$	−8.81176	−	15.2624i	−0.327261	−	0.566832i
$726$	−0.659576	+	0.380807i	−0.0244792	+	0.0141331i
$727$	23.5565			0.873663			0.436831	−	0.899543i	$-0.356101\pi$
$727$	23.5565			0.873663			0.436831	+	0.899543i	$0.356101\pi$
$728$		0			0
$729$	−10.3760			−0.384297
$730$	−0.380231	+	0.219526i	−0.0140730	+	0.00812503i
$731$	1.23141	+	2.13286i	0.0455453	+	0.0788867i
$732$	−5.21703	+	9.03616i	−0.192827	+	0.333986i
$733$			6.23249i			0.230202i	0.993354	+	0.115101i	$0.0367192\pi$
$733$			6.23249i			0.230202i	−0.993354	+	0.115101i	$0.963281\pi$
$734$	0.387821	+	0.223909i	0.0143147	+	0.00826461i
$735$		0			0
$736$		−	7.27100i		−	0.268013i
$737$	2.45679	−	4.25528i	0.0904969	−	0.156745i
$738$	0.933158	+	1.61628i	0.0343500	+	0.0594960i
$739$	1.12339	−	0.648588i	0.0413244	−	0.0238587i	−0.479195	−	0.877708i	$-0.659071\pi$
$739$	1.12339	−	0.648588i	0.0413244	−	0.0238587i	0.520520	+	0.853850i	$0.325738\pi$
$740$	21.1699			0.778221
$741$	−2.62606	−	1.51444i	−0.0964709	−	0.0556344i
$742$		0			0
$743$	5.25627	−	3.03471i	0.192834	−	0.111333i	−0.400475	−	0.916308i	$-0.631155\pi$
$743$	5.25627	−	3.03471i	0.192834	−	0.111333i	0.593309	+	0.804975i	$0.297821\pi$
$744$	0.656096	+	1.13639i	0.0240536	+	0.0416621i
$745$	7.82725	−	13.5572i	0.286768	−	0.496697i
$746$			0.422796i			0.0154797i
$747$	1.30749	+	0.754880i	0.0478386	+	0.0276196i
$748$	−1.99722	−	1.15310i	−0.0730256	−	0.0421613i
$749$		0			0
$750$	0.422980	−	0.732622i	0.0154450	−	0.0267516i
$751$	−18.3023	−	31.7005i	−0.667860	−	1.15677i	−0.978501	−	0.206241i	$-0.933877\pi$
$751$	−18.3023	−	31.7005i	−0.667860	−	1.15677i	0.310641	−	0.950527i	$-0.399456\pi$
$752$	−43.3473	+	25.0266i	−1.58071	+	0.912625i
$753$	13.1346			0.478650
$754$	−3.07961	+	1.78003i	−0.112153	+	0.0648248i
$755$	−23.6566			−0.860952
$756$		0			0
$757$	−5.83991	−	10.1150i	−0.212255	−	0.367636i	0.740165	−	0.672425i	$-0.234747\pi$
$757$	−5.83991	−	10.1150i	−0.212255	−	0.367636i	−0.952420	+	0.304789i	$0.901414\pi$
$758$	−1.50548	+	2.60757i	−0.0546815	+	0.0947111i
$759$		−	1.07924i		−	0.0391739i
$760$	1.01263	+	0.584642i	0.0367320	+	0.0212072i
$761$	34.4408	+	19.8844i	1.24848	+	0.720810i	0.970806	−	0.239866i	$-0.0771035\pi$
$761$	34.4408	+	19.8844i	1.24848	+	0.720810i	0.277673	+	0.960676i	$0.410437\pi$
$762$			0.565394i			0.0204821i
$763$		0			0
$764$	−5.88916	−	10.2003i	−0.213062	−	0.369035i
$765$	−12.3926	+	7.15490i	−0.448057	+	0.258686i
$766$	−2.70393			−0.0976970
$767$	−29.2245	+	16.8919i	−1.05523	+	0.609930i
$768$	8.64915			0.312099
$769$	8.62507	−	4.97969i	0.311028	−	0.179572i	−0.336358	−	0.941734i	$-0.609195\pi$
$769$	8.62507	−	4.97969i	0.311028	−	0.179572i	0.647386	+	0.762162i	$0.275862\pi$
$770$		0			0
$771$	−5.94313	+	10.2938i	−0.214036	+	0.370722i
$772$			8.33112i			0.299843i
$773$	−11.0433	−	6.37588i	−0.397201	−	0.229324i	0.288074	−	0.957608i	$-0.406985\pi$
$773$	−11.0433	−	6.37588i	−0.397201	−	0.229324i	−0.685276	+	0.728284i	$0.740318\pi$
$774$	−0.214435	−	0.123804i	−0.00770769	−	0.00445004i
$775$		−	10.1006i		−	0.362825i
$776$	−1.90148	+	3.29346i	−0.0682592	+	0.118228i
$777$		0			0
$778$	−1.39012	+	0.802586i	−0.0498382	+	0.0287741i
$779$	−8.41411			−0.301467
$780$	6.09613	+	3.51561i	0.218276	+	0.125879i
$781$	2.58192			0.0923882
$782$	1.68785	−	0.974483i	0.0603575	−	0.0348474i
$783$	13.5093	+	23.3988i	0.482784	+	0.836206i
$784$		0			0
$785$		−	29.0069i		−	1.03530i
$786$	−1.14737	−	0.662435i	−0.0409254	−	0.0236283i
$787$	−7.52380	−	4.34387i	−0.268194	−	0.154842i	0.359872	−	0.933002i	$-0.382820\pi$
$787$	−7.52380	−	4.34387i	−0.268194	−	0.154842i	−0.628067	+	0.778159i	$0.716154\pi$
$788$			11.4861i			0.409174i
$789$	8.60052	−	14.8965i	0.306187	−	0.530331i
$790$	−0.699759	−	1.21202i	−0.0248963	−	0.0431216i
$791$		0			0
$792$	0.465413			0.0165377
$793$	−16.2836	−	28.1721i	−0.578247	−	1.00042i
$794$	−3.10929			−0.110345
$795$	−1.16722	+	0.673897i	−0.0413972	+	0.0239007i
$796$	−11.8731	−	20.5649i	−0.420832	−	0.728903i
$797$	−19.3719	+	33.5531i	−0.686187	+	1.18851i	0.286875	+	0.957968i	$0.407384\pi$
$797$	−19.3719	+	33.5531i	−0.686187	+	1.18851i	−0.973062	+	0.230543i	$0.925950\pi$
$798$		0			0
$799$	−35.2861	−	20.3724i	−1.24833	−	0.720725i
$800$	2.66345	+	1.53774i	0.0941672	+	0.0543675i
$801$		−	3.03063i		−	0.107082i
$802$	−1.05679	+	1.83041i	−0.0373166	+	0.0646342i
$803$	−0.393938	−	0.682321i	−0.0139018	−	0.0240786i
$804$	−13.4928	+	7.79009i	−0.475856	+	0.274735i
$805$		0			0
$806$	−2.03866	+	0.00100036i	−0.0718086	+	3.52361e-5i
$807$	−16.2554			−0.572218
$808$	6.45844	−	3.72878i	0.227207	−	0.131178i
$809$	−14.4275	−	24.9892i	−0.507244	−	0.878573i	−0.999965	−	0.00838530i	$-0.997331\pi$
$809$	−14.4275	−	24.9892i	−0.507244	−	0.878573i	0.492721	−	0.870188i	$-0.336002\pi$
$810$	0.616002	−	1.06695i	0.0216441	−	0.0374887i
$811$		−	12.3917i		−	0.435131i	−0.976046	−	0.217566i	$-0.930188\pi$
$811$		−	12.3917i		−	0.435131i	0.976046	−	0.217566i	$-0.0698116\pi$
$812$		0			0
$813$	−14.8506	−	8.57397i	−0.520832	−	0.300702i
$814$		−	0.277173i		−	0.00971491i
$815$	9.95405	−	17.2409i	0.348675	−	0.603923i
$816$	3.62942	+	6.28634i	0.127055	+	0.220066i
$817$	0.966758	−	0.558158i	0.0338226	−	0.0195275i
$818$	1.74861			0.0611388
$819$		0			0
$820$	19.5324			0.682103
$821$	35.5277	−	20.5119i	1.23992	−	0.715870i	0.270845	−	0.962623i	$-0.412697\pi$
$821$	35.5277	−	20.5119i	1.23992	−	0.715870i	0.969079	+	0.246753i	$0.0793635\pi$
$822$	0.638663	+	1.10620i	0.0222759	+	0.0385830i
$823$	−1.06806	+	1.84994i	−0.0372304	+	0.0644849i	−0.884040	−	0.467411i	$-0.845187\pi$
$823$	−1.06806	+	1.84994i	−0.0372304	+	0.0644849i	0.846810	+	0.531896i	$0.178520\pi$
$824$		−	4.93999i		−	0.172093i
$825$	0.395337	+	0.228248i	0.0137639	+	0.00794658i
$826$		0			0
$827$		−	8.54938i		−	0.297291i	−0.988891	−	0.148645i	$-0.952509\pi$
$827$		−	8.54938i		−	0.297291i	0.988891	−	0.148645i	$-0.0474913\pi$
$828$	13.4281	−	23.2582i	0.466660	−	0.808278i
$829$	7.37844	+	12.7798i	0.256264	+	0.443862i	0.965238	−	0.261373i	$-0.0841751\pi$
$829$	7.37844	+	12.7798i	0.256264	+	0.443862i	−0.708974	+	0.705234i	$0.750842\pi$
$830$	−0.0998392	+	0.0576422i	−0.00346547	+	0.00200079i
$831$	−3.99367			−0.138539
$832$	−13.7875	+	23.9077i	−0.477995	+	0.828850i
$833$		0			0
$834$	0.318701	−	0.184002i	0.0110357	−	0.00637146i
$835$	3.64379	+	6.31123i	0.126099	+	0.218409i
$836$	−0.522661	+	0.905276i	−0.0180766	+	0.0313096i
$837$			15.4853i			0.535250i
$838$	0.479680	+	0.276943i	0.0165703	+	0.00956685i
$839$	−23.3581	−	13.4858i	−0.806411	−	0.465582i	0.0392968	−	0.999228i	$-0.487488\pi$
$839$	−23.3581	−	13.4858i	−0.806411	−	0.465582i	−0.845708	+	0.533646i	$0.820822\pi$
$840$		0			0
$841$	−19.0923	+	33.0687i	−0.658353	+	1.14030i
$842$	−1.15934	−	2.00803i	−0.0399534	−	0.0692013i
$843$	14.6715	−	8.47062i	0.505315	−	0.291743i
$844$	−16.3525			−0.562877
$845$	−18.9951	+	10.9917i	−0.653453	+	0.378127i
$846$	4.09643			0.140838
$847$		0			0
$848$	−2.68275	−	4.64665i	−0.0921259	−	0.159567i
$849$	−3.38027	+	5.85479i	−0.116010	+	0.200936i
$850$			0.824374i			0.0282758i
$851$	−27.8035	−	16.0524i	−0.953092	−	0.550268i
$852$	−7.09003	−	4.09343i	−0.242901	−	0.140239i
$853$			25.6332i			0.877665i	0.898569	+	0.438832i	$0.144608\pi$
$853$			25.6332i			0.877665i	−0.898569	+	0.438832i	$0.855392\pi$
$854$		0			0
$855$	3.24309	+	5.61719i	0.110911	+	0.192104i
$856$	5.45225	−	3.14786i	0.186354	−	0.107592i
$857$	11.7653			0.401894			0.200947	−	0.979602i	$-0.435598\pi$
$857$	11.7653			0.401894			0.200947	+	0.979602i	$0.435598\pi$
$858$	0.0460292	−	0.0798153i	0.00157141	−	0.00272485i
$859$	21.7761			0.742992			0.371496	−	0.928435i	$-0.378845\pi$
$859$	21.7761			0.742992			0.371496	+	0.928435i	$0.378845\pi$
$860$	−2.24422	+	1.29570i	−0.0765274	+	0.0441831i
$861$		0			0
$862$	1.70701	−	2.95663i	0.0581410	−	0.100703i
$863$		−	41.0575i		−	1.39761i	−0.715310	−	0.698807i	$-0.753715\pi$
$863$		−	41.0575i		−	1.39761i	0.715310	−	0.698807i	$-0.246285\pi$
$864$	−4.08334	−	2.35752i	−0.138918	−	0.0802044i
$865$	18.3037	+	10.5677i	0.622345	+	0.359311i
$866$			1.50694i			0.0512079i
$867$	1.99502	−	3.45547i	0.0677543	−	0.117354i
$868$		0			0
$869$	2.17496	−	1.25571i	0.0737803	−	0.0425971i
$870$	−0.969778			−0.0328785
$871$	−0.0238420	−	48.5882i	−0.000807854	−	1.64635i
$872$	−5.01085			−0.169689
$873$	−18.2693	+	10.5478i	−0.618320	+	0.356987i
$874$	−0.441702	−	0.765050i	−0.0149408	−	0.0258782i
$875$		0			0
$876$			2.49824i			0.0844076i
$877$	5.96788	+	3.44556i	0.201521	+	0.116348i	0.597365	−	0.801970i	$-0.296214\pi$
$877$	5.96788	+	3.44556i	0.201521	+	0.116348i	−0.395844	+	0.918318i	$0.629548\pi$
$878$	3.30709	+	1.90935i	0.111609	+	0.0644374i
$879$		−	10.3582i		−	0.349372i
$880$	1.20439	−	2.08606i	0.0405998	−	0.0703209i
$881$	5.32288	+	9.21950i	0.179332	+	0.310613i	0.941652	−	0.336588i	$-0.109273\pi$
$881$	5.32288	+	9.21950i	0.179332	+	0.310613i	−0.762320	+	0.647201i	$0.775940\pi$
$882$		0			0
$883$	21.3844			0.719641			0.359821	−	0.933022i	$-0.382838\pi$
$883$	21.3844			0.719641			0.359821	+	0.933022i	$0.382838\pi$
$884$	−22.8049	+	0.0111902i	−0.767012	+	0.000376369i
$885$	−9.20286			−0.309351
$886$	−0.180376	+	0.104140i	−0.00605986	+	0.00349866i
$887$	−17.0575	−	29.5445i	−0.572735	−	0.992007i	−0.996284	−	0.0861333i	$-0.972549\pi$
$887$	−17.0575	−	29.5445i	−0.572735	−	0.992007i	0.423548	−	0.905874i	$-0.360784\pi$
$888$	−0.882080	+	1.52781i	−0.0296007	+	0.0512698i
$889$		0			0
$890$	0.200413	+	0.115709i	0.00671786	+	0.00387856i
$891$	1.91463	+	1.10541i	0.0641424	+	0.0370326i
$892$		−	30.3813i		−	1.01724i
$893$	−9.23418	+	15.9941i	−0.309010	+	0.535221i
$894$	0.324950	+	0.562831i	0.0108680	+	0.0188239i
$895$	−9.64235	+	5.56701i	−0.322308	+	0.186085i
$896$		0			0
$897$	−5.34060	−	9.23971i	−0.178317	−	0.308505i
$898$	1.27056			0.0423992
$899$	−33.3469	+	19.2528i	−1.11218	+	0.642118i
$900$	5.67983	+	9.83776i	0.189328	+	0.327925i
$901$	2.18384	−	3.78253i	0.0727544	−	0.126014i
$902$		−	0.255734i		−	0.00851502i
$903$		0			0
$904$	2.05746	+	1.18788i	0.0684301	+	0.0395081i
$905$		−	18.5963i		−	0.618163i
$906$	0.491055	−	0.850532i	0.0163142	−	0.0282570i
$907$	21.0758	+	36.5043i	0.699810	+	1.21211i	0.968532	+	0.248888i	$0.0800652\pi$
$907$	21.0758	+	36.5043i	0.699810	+	1.21211i	−0.268723	+	0.963218i	$0.586601\pi$
$908$	−11.9586	+	6.90429i	−0.396860	+	0.229127i
$909$	41.3681			1.37209
$910$		0			0
$911$	20.9947			0.695584			0.347792	−	0.937572i	$-0.386932\pi$
$911$	20.9947			0.695584			0.347792	+	0.937572i	$0.386932\pi$
$912$	2.84940	−	1.64510i	0.0943529	−	0.0544747i
$913$	−0.103438	−	0.179161i	−0.00342331	−	0.00592935i
$914$	0.478367	−	0.828556i	0.0158230	−	0.0274062i
$915$		−	8.87147i		−	0.293282i
$916$	47.1521	+	27.2233i	1.55795	+	0.899483i
$917$		0			0
$918$		−	1.26385i		−	0.0417132i
$919$	7.14699	−	12.3789i	0.235757	−	0.408344i	−0.723735	−	0.690078i	$-0.757576\pi$
$919$	7.14699	−	12.3789i	0.235757	−	0.408344i	0.959493	+	0.281734i	$0.0909096\pi$
$920$	2.05821	+	3.56492i	0.0678571	+	0.117532i
$921$	4.57869	−	2.64351i	0.150873	−	0.0871065i
$922$	1.31094			0.0431736
$923$	22.1046	−	12.7766i	0.727583	−	0.420546i
$924$		0			0
$925$	11.7603	−	6.78983i	0.386677	−	0.223248i
$926$	−2.15581	−	3.73397i	−0.0708443	−	0.122706i
$927$	13.7014	−	23.7315i	0.450012	−	0.779444i
$928$		−	11.7244i		−	0.384872i
$929$	−5.89524	−	3.40362i	−0.193416	−	0.111669i	0.400164	−	0.916443i	$-0.368953\pi$
$929$	−5.89524	−	3.40362i	−0.193416	−	0.111669i	−0.593581	+	0.804774i	$0.702286\pi$
$930$	−0.481347	−	0.277906i	−0.0157840	−	0.00911290i
$931$		0			0
$932$	−6.80369	+	11.7843i	−0.222862	+	0.386009i
$933$	−0.457310	−	0.792085i	−0.0149717	−	0.0259317i
$934$	−2.07410	+	1.19748i	−0.0678666	+	0.0391828i
$935$	1.96082			0.0641256
$936$	3.98455	−	2.30309i	0.130239	−	0.0752789i
$937$	5.22890			0.170821			0.0854104	−	0.996346i	$-0.472780\pi$
$937$	5.22890			0.170821			0.0854104	+	0.996346i	$0.472780\pi$
$938$		0			0
$939$	6.00437	+	10.3999i	0.195945	+	0.339387i
$940$	21.4362	−	37.1285i	0.699170	−	1.21100i
$941$		−	56.4403i		−	1.83990i	−0.392033	−	0.919951i	$-0.628228\pi$
$941$		−	56.4403i		−	1.83990i	0.392033	−	0.919951i	$-0.371772\pi$
$942$	1.04289	+	0.602114i	0.0339793	+	0.0196179i
$943$	−25.6530	−	14.8108i	−0.835376	−	0.482304i
$944$		−	36.6361i		−	1.19240i
$945$		0			0
$946$	0.0169644	+	0.0293832i	0.000551559	+	0.000955329i
$947$	−5.06648	+	2.92513i	−0.164639	+	0.0950541i	−0.580055	−	0.814577i	$-0.696969\pi$
$947$	−5.06648	+	2.92513i	−0.164639	+	0.0950541i	0.415417	+	0.909631i	$0.363636\pi$
$948$	−7.96334			−0.258637
$949$	−6.74909	−	3.89217i	−0.219085	−	0.126345i
$950$	0.373662			0.0121232
$951$	−15.4025	+	8.89262i	−0.499459	+	0.288363i
$952$		0			0
$953$	−10.8742	+	18.8346i	−0.352249	+	0.610114i	−0.986643	−	0.162896i	$-0.947916\pi$
$953$	−10.8742	+	18.8346i	−0.352249	+	0.610114i	0.634394	+	0.773010i	$0.281250\pi$
$954$			0.439121i			0.0142171i
$955$	8.67273	+	5.00720i	0.280643	+	0.162029i
$956$	37.9588	+	21.9155i	1.22767	+	0.708798i
$957$		−	1.74026i		−	0.0562546i
$958$	1.58214	−	2.74035i	0.0511167	−	0.0885368i
$959$		0			0
$960$	−6.51626	+	3.76217i	−0.210312	+	0.121423i
$961$	8.93110			0.288100
$962$	−1.37159	−	2.37297i	−0.0442217	−	0.0765075i
$963$	34.9232			1.12538
$964$	27.1632	−	15.6827i	0.874868	−	0.505105i
$965$	−3.54173	−	6.13446i	−0.114012	−	0.197475i
$966$		0			0
$967$		−	13.3251i		−	0.428507i	−0.976778	−	0.214253i	$-0.931268\pi$
$967$		−	13.3251i		−	0.428507i	0.976778	−	0.214253i	$-0.0687318\pi$
$968$	4.51449	+	2.60644i	0.145101	+	0.0837742i
$969$	2.31950	+	1.33917i	0.0745132	+	0.0430202i
$970$		−	1.61084i		−	0.0517210i
$971$	3.73092	−	6.46215i	0.119731	−	0.207380i	−0.799930	−	0.600093i	$-0.795130\pi$
$971$	3.73092	−	6.46215i	0.119731	−	0.207380i	0.919661	+	0.392713i	$0.128463\pi$
$972$	−13.3224	−	23.0751i	−0.427317	−	0.740134i
$973$		0			0
$974$	−0.767850			−0.0246035
$975$	4.51409	−	0.00221504i	0.144567	−	7.09381e-5i
$976$	35.3168			1.13046
$977$	−9.49204	+	5.48023i	−0.303677	+	0.175328i	−0.644094	−	0.764947i	$-0.722765\pi$
$977$	−9.49204	+	5.48023i	−0.303677	+	0.175328i	0.340416	+	0.940275i	$0.389432\pi$
$978$	0.413245	+	0.715761i	0.0132141	+	0.0228875i
$979$	−0.207638	+	0.359640i	−0.00663614	+	0.0114941i
$980$		0			0
$981$	−24.0719	−	13.8979i	−0.768557	−	0.443727i
$982$	0.309335	+	0.178595i	0.00987127	+	0.00569918i
$983$			16.1441i			0.514918i	0.966289	+	0.257459i	$0.0828852\pi$
$983$			16.1441i			0.514918i	−0.966289	+	0.257459i	$0.917115\pi$
$984$	−0.813853	+	1.40963i	−0.0259447	+	0.0449375i
$985$	−4.88296	−	8.45754i	−0.155584	−	0.269480i
$986$	2.72164	−	1.57134i	0.0866747	−	0.0500417i
$987$		0			0
$988$	0.00507218	+	10.3367i	0.000161368	+	0.328856i
$989$	3.92994			0.124965
$990$	−0.170726	+	0.0985688i	−0.00542603	+	0.00313272i
$991$	−3.35748	−	5.81533i	−0.106654	−	0.184730i	0.807759	−	0.589513i	$-0.200680\pi$
$991$	−3.35748	−	5.81533i	−0.106654	−	0.184730i	−0.914413	+	0.404783i	$0.867347\pi$
$992$	3.35982	−	5.81938i	0.106674	−	0.184766i
$993$			15.0540i			0.477725i
$994$		0			0
$995$	17.4851	+	10.0950i	0.554315	+	0.320034i
$996$			0.655975i			0.0207854i
$997$	−9.22057	+	15.9705i	−0.292018	+	0.505791i	−0.974287	−	0.225311i	$-0.927660\pi$
$997$	−9.22057	+	15.9705i	−0.292018	+	0.505791i	0.682269	+	0.731102i	$0.260993\pi$
$998$	−1.69305	−	2.93244i	−0.0535924	−	0.0928248i
$999$	−18.0298	+	10.4095i	−0.570437	+	0.329342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.h.491.3		12
7.2	even	3		637.2.u.i.361.4		12
7.3	odd	6		637.2.k.h.569.3		12
7.4	even	3		637.2.k.g.569.3		12
7.5	odd	6		637.2.u.h.361.4		12
7.6	odd	2		91.2.q.a.36.3	✓	12
13.2	odd	12		8281.2.a.by.1.4		6
13.4	even	6	inner	637.2.q.h.589.3		12
13.11	odd	12		8281.2.a.ch.1.3		6
21.20	even	2		819.2.ct.a.127.4		12
28.27	even	2		1456.2.cc.c.673.3		12
91.4	even	6		637.2.u.i.30.4		12
91.17	odd	6		637.2.u.h.30.4		12
91.30	even	6		637.2.k.g.459.4		12
91.41	even	12		1183.2.a.m.1.4		6
91.55	odd	6		1183.2.c.i.337.6		12
91.62	odd	6		1183.2.c.i.337.7		12
91.69	odd	6		91.2.q.a.43.3	yes	12
91.76	even	12		1183.2.a.p.1.3		6
91.82	odd	6		637.2.k.h.459.4		12
273.251	even	6		819.2.ct.a.316.4		12
364.251	even	6		1456.2.cc.c.225.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.3	✓	12	7.6	odd	2
91.2.q.a.43.3	yes	12	91.69	odd	6
637.2.k.g.459.4		12	91.30	even	6
637.2.k.g.569.3		12	7.4	even	3
637.2.k.h.459.4		12	91.82	odd	6
637.2.k.h.569.3		12	7.3	odd	6
637.2.q.h.491.3		12	1.1	even	1	trivial
637.2.q.h.589.3		12	13.4	even	6	inner
637.2.u.h.30.4		12	91.17	odd	6
637.2.u.h.361.4		12	7.5	odd	6
637.2.u.i.30.4		12	91.4	even	6
637.2.u.i.361.4		12	7.2	even	3
819.2.ct.a.127.4		12	21.20	even	2
819.2.ct.a.316.4		12	273.251	even	6
1183.2.a.m.1.4		6	91.41	even	12
1183.2.a.p.1.3		6	91.76	even	12
1183.2.c.i.337.6		12	91.55	odd	6
1183.2.c.i.337.7		12	91.62	odd	6
1456.2.cc.c.225.3		12	364.251	even	6
1456.2.cc.c.673.3		12	28.27	even	2
8281.2.a.by.1.4		6	13.2	odd	12
8281.2.a.ch.1.3		6	13.11	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104235 + 0.0601799i) q^{2} +(-0.291146 - 0.504280i) q^{3} +(-0.992757 + 1.71951i) q^{4} -1.68817i q^{5} +(0.0606950 + 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 - 2.30444i) q^{9} +O(q^{10})\)	\(q+(-0.104235 + 0.0601799i) q^{2} +(-0.291146 - 0.504280i) q^{3} +(-0.992757 + 1.71951i) q^{4} -1.68817i q^{5} +(0.0606950 + 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 - 2.30444i) q^{9} +(0.101594 + 0.175965i) q^{10} +(-0.315769 + 0.182309i) q^{11} +1.15615 q^{12} +(-1.80124 + 3.12338i) q^{13} +(-0.851308 + 0.491503i) q^{15} +(-1.95665 - 3.38901i) q^{16} +(1.59277 - 2.75877i) q^{17} +0.320270i q^{18} +(-1.25046 - 0.721954i) q^{19} +(2.90281 + 1.67594i) q^{20} +(0.0219427 - 0.0380059i) q^{22} +(-2.54161 - 4.40219i) q^{23} +(-0.241901 + 0.139662i) q^{24} +2.15010 q^{25} +(-0.000212944 - 0.433964i) q^{26} -3.29632 q^{27} +(-4.09831 - 7.09848i) q^{29} +(0.0591572 - 0.102463i) q^{30} -4.69775i q^{31} +(1.23876 + 0.715198i) q^{32} +(0.183870 + 0.106157i) q^{33} +0.383412i q^{34} +(2.64166 + 4.57549i) q^{36} +(5.46967 - 3.15792i) q^{37} +0.173789 q^{38} +(2.09948 - 0.00103020i) q^{39} -0.809806 q^{40} +(5.04661 - 2.91366i) q^{41} +(-0.386561 + 0.669543i) q^{43} -0.723954i q^{44} +(-3.89027 - 2.24605i) q^{45} +(0.529847 + 0.305907i) q^{46} -12.7905i q^{47} +(-1.13934 + 1.97339i) q^{48} +(-0.224115 + 0.129393i) q^{50} -1.85492 q^{51} +(-3.58248 - 6.19801i) q^{52} +1.37110 q^{53} +(0.343591 - 0.198372i) q^{54} +(0.307768 + 0.533070i) q^{55} +0.840776i q^{57} +(0.854372 + 0.493272i) q^{58} +(8.10770 + 4.68098i) q^{59} -1.95177i q^{60} +(-4.51242 + 7.81574i) q^{61} +(0.282711 + 0.489669i) q^{62} +7.65442 q^{64} +(5.27279 + 3.04080i) q^{65} -0.0255541 q^{66} +(-11.6705 + 6.73797i) q^{67} +(3.16247 + 5.47757i) q^{68} +(-1.47996 + 2.56336i) q^{69} +(-6.13246 - 3.54058i) q^{71} +(-1.10543 - 0.638220i) q^{72} +2.16083i q^{73} +(-0.380087 + 0.658329i) q^{74} +(-0.625992 - 1.08425i) q^{75} +(2.48281 - 1.43345i) q^{76} +(-0.218777 + 0.126454i) q^{78} -6.88781 q^{79} +(-5.72121 + 3.30314i) q^{80} +(-3.03169 - 5.25105i) q^{81} +(-0.350688 + 0.607409i) q^{82} +0.567380i q^{83} +(-4.65725 - 2.68887i) q^{85} -0.0930528i q^{86} +(-2.38641 + 4.13339i) q^{87} +(0.0874529 + 0.151473i) q^{88} +(0.986346 - 0.569467i) q^{89} +0.540669 q^{90} +10.0928 q^{92} +(-2.36898 + 1.36773i) q^{93} +(0.769734 + 1.33322i) q^{94} +(-1.21878 + 2.11098i) q^{95} -0.832908i q^{96} +(-6.86572 - 3.96393i) q^{97} +0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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